diff --git "a/continuous_subarrays/haskell_tests/Main.hs" "b/continuous_subarrays/haskell_tests/Main.hs"
new file mode 100644--- /dev/null
+++ "b/continuous_subarrays/haskell_tests/Main.hs"
@@ -0,0 +1,41 @@
+
+module Main where
+import Test.HUnit
+
+--Program start
+continuousSubarrays :: [Int] -> Int
+continuousSubarrays nums = undefined
+
+--Program end
+
+-- Test cases
+
+test1 :: Test
+test1 = TestCase (assertEqual "for (continuousSubarrays [5,4,2,4])," 8 (continuousSubarrays [5,4,2,4]))
+
+test2 :: Test
+test2 = TestCase (assertEqual "for (continuousSubarrays [1,2,3])," 6 (continuousSubarrays [1,2,3]))
+
+test3 :: Test
+test3 = TestCase (assertEqual "for (continuousSubarrays [415902931, 343918193, 266220156, 251496706, 916594909, 183487908, 819573683, 410909122, 643194414, 542676937, 741361623, 663328036, 45885574, 599661110, 732324972, 589920561, 212123225, 426626601, 807144564, 694302537, 772834813, 789341879, 392314988, 552007717, 263515005, 391851564, 564745148, 139830474, 689551940, 165378192, 321798758, 251764230, 991334235, 455498208, 876688063, 215275076, 108543552, 182735520, 746496562, 176279307, 397900236, 980928708, 345715919, 739154585, 997386296, 31023045, 222116835, 696596571, 13334236, 105144317, 892424821, 880810494, 458810796, 731577998, 56097675, 350216705, 158484779, 258345418, 316801452, 954710160, 978449971, 398444692, 594275240, 970744182, 962445729, 223212988, 94925571, 889775911, 294377878, 667486657, 396086192, 901351444, 76539600, 279516041, 867398776, 310138459, 904219404, 548448102, 981365777, 320181554, 372267031, 666373363, 206976135, 946980399, 57950865, 651010321, 404777463, 765177493, 398996379, 486642989, 896382232, 82044705, 634153953, 204420548, 81201212, 782193870, 359964206, 507217952, 698119207, 239188305, 205081346, 558756534, 684411477, 305146010, 35717138, 817373709, 572024012, 817729927, 163305744, 596313192, 470326851, 276051153, 927905239, 747934607, 406480377, 443170362, 306728982, 961927303, 665406848, 849498963, 666404594, 89932725, 110023860, 623536733, 804489569, 337429056, 27941402, 911436544, 820114609, 735724962, 849542104, 970410031, 824695979, 612989017, 228198781, 163671669, 425047327, 733258319, 175676043, 235542330, 635435810, 111609030, 748803563, 216347518, 690435317, 348292694, 192410068, 756518625, 141133842, 895277409, 423412464, 982930597, 951557454, 450477299, 377496863, 517720039, 535768354, 168937136, 698585749, 48994540, 981597766, 449925297, 426565962, 59344853, 372583531, 135430136, 500904538, 365822648, 612100021, 118903581, 372615514, 498626430, 141267371, 586331432, 605465237, 387101865, 773812695, 44337623, 500160290, 926248803, 539819333, 37656570, 949653760, 818851998, 648245026, 374331139, 981894497, 903376118, 380876813, 117255510, 90479634, 461922021, 733796555, 775917412, 663608923, 916628077, 598712843, 926608942, 340312690, 614996364, 485920670, 763269902, 222557106, 720760553, 659147595, 798312082, 653358631, 431722794, 874054726, 540310355, 700299066, 124649589, 479420597, 74118813, 625057465, 450014467, 808583398, 666844052, 669409336, 172823296, 15052321, 589243485, 972321292, 216810258, 145194116, 58657973, 879739883, 516664462, 201639713, 547169435, 409245973, 361577765, 813347465, 469742829, 267107686, 108123445, 707331600, 727328589, 158875624, 387372819, 545756407, 495169015, 916966998, 76851608, 159552681, 620094824, 88424962, 567795392, 584383377, 699887772, 543563486, 636205583, 935426129, 751767135, 977879847, 240199148, 535654032, 82285700, 382886394, 708611150, 252892534, 51695558, 543309343, 887453022, 787203849, 230828377, 877631359, 564224902, 847641766, 259416389, 122910781, 819435044, 367118408, 43350399, 719347191, 543652343, 382337780, 69323814, 166711995, 278657005, 438130251, 242251507, 173125262, 143778166, 748412300, 161845701, 404818465, 631928486, 904417072, 134001332, 971231479, 364485339, 167348442, 776007602, 425715015, 100769149, 304539230, 303357812, 587295883, 358963447, 967471207, 148562585, 388835795, 45826475, 334158277, 876319935, 629143648, 424816940, 659259782, 752361212, 431337393, 445267894, 398390358, 665687065, 205928369, 953084298, 138321091, 771947051, 346275978, 560808132, 288186377, 760170616, 50086999, 436606484, 858979244, 394007143, 612374509, 665890061, 159186635, 244066046, 711577310, 981120278, 787759585, 530186071, 722324102, 680279425, 971230274, 822541505, 123414448, 274564380, 471408428, 601789956, 885465084, 57027470, 570865181, 979046542, 180027116, 460014818, 985024417, 560074008, 381781773, 473390163, 525110423, 475707615, 126679862, 514656123, 95605997, 67775680, 301098014, 264024852, 926381537, 473311241, 108705898, 500084279, 516676800, 778974925, 553024639, 555337372, 485450061, 104179915, 803004275, 184407279, 235526325, 371294052, 223093969, 655591449, 459926030, 530201851, 642145772, 525023518, 468809826, 874923671, 501587638, 677137377, 950827993, 480428390, 363995121, 155292808, 923762237, 757371572, 88947379, 694894144, 243376480, 729389169, 392027665, 653904713, 813539533, 862793901, 654334365, 931369696, 68302198, 559183607, 665541995, 221591357, 762741076, 159857055, 871227047, 499415051, 486039621, 159431606, 11778775, 632909231, 787866621, 990429816, 912217229, 239241297, 503344535, 60105056, 465265818, 551428341, 131087483, 199786217, 63134374, 323486675, 491542166, 758614678, 357311342, 572343650, 218913868, 564501740, 322199933, 438790300, 225531396, 198062739, 384893895, 441912825, 175638373, 277513619, 91317600, 148289971, 597198109, 205305918, 249361347, 662630540, 65558320, 168764773, 549188770, 643419810, 876225308, 606985887, 273898099, 375519918, 653568634, 265557482, 326560752, 309328679, 14302393, 569914931, 135218898, 516235740, 400077968, 721441250, 476512682, 483941521, 404162131, 393365293, 11449542, 879912141, 262942089, 945331120, 854311826, 340673963, 896206661, 963141047, 370096397, 301784532, 593329434, 852363231, 711714698, 787822287, 434337915, 152493368, 132734514, 388228301, 709145968, 726983239, 523139762, 768797466, 741788982, 752029251, 684075679, 958927940, 577639504, 944217021, 599841786, 707840487, 248977856, 594454445, 900709692, 467976351, 399766897, 379150375, 607917522, 408334398, 854129910, 619887569, 807290715, 320707811, 549330623, 437307127, 833667633, 943075445, 145485948, 81449846, 928745062, 781275911, 37515882, 950948526, 925455693, 67662739, 762077401, 126687793, 299297581, 720002928, 427858529, 403527296, 982673616, 806118267, 39181325, 81126914, 701223925, 527054232, 477357094, 594426372, 179751606, 324394627, 597846435, 977707861, 746832057, 217609570, 254370142, 117410536, 618146951, 881763355, 823970630, 268544114, 200897891, 443180476, 393233634, 32912048, 263885175, 26709958, 912919408, 814596187, 596847315, 140510290, 867848251, 814987943, 475312984, 885538269, 853418525, 130739000, 280308826, 602266456, 938792077, 308991245, 869648497, 621946378, 943797994, 179675240, 110117178, 41430879, 385218589, 212131683, 369930198, 38140291, 316668078, 624460174, 940497197, 454608013, 833389785, 342236403, 181055820, 493301053, 80215646, 659127078, 45340872, 210618389, 696552416, 837934125, 342997290, 853071954, 734877215, 917544854, 852499446, 254114464, 973800383, 811815065, 108099828, 990819965, 463543612, 530888483, 96638612, 411579764, 934331239, 520287528, 37805397, 921106884, 640426059, 416280003, 912937942, 223176476, 774291540, 814531692, 791424121, 359216579, 111950214, 366505788, 988563424, 295247481, 110137226, 156294890, 419560002, 408577301, 313586169, 550357513, 876308477, 437205835, 79377204, 325471745, 12588973, 114081620, 383433022, 834937520, 409231311, 825526602, 368046298, 400032468, 393909536, 101946552, 540132651, 379797928, 890731502, 857575093, 791295460, 489939814, 89323658, 402991123, 427021515, 709457270, 41336560, 938137497, 301887951, 165545221, 362383210, 810879792, 636549198, 489341040, 823131648, 915984233, 303781349, 479498612, 385001542, 541693676, 573558863, 510891225, 444028533, 889454313, 540363646, 928270717, 88745581, 35929672, 488807567, 447994293, 155494206, 698751037, 298450577, 548885397, 255135343, 667981461, 989740351, 20515178, 401874407, 987571033, 726500474, 571041455, 84540112, 31360380, 310260296, 776215999, 198961617, 417963939, 144956746, 628473133, 772183586, 956822830, 999096513, 43685273, 188445688, 654342728, 589270791, 19297632, 641302262, 188550051, 977227750, 404037387, 169012380, 708262880, 764890124, 855467928, 585262432, 314138860, 366288161, 776621414, 317399983, 844938538, 843064638, 51350869, 375136826, 368803587, 256849950, 919061180, 637721104, 686429659, 400201974, 594623130, 733324199, 119938777, 893355661, 261240180, 943725233, 85372073, 25991337, 109468766, 972467970, 866350374, 133906251, 447989266, 334794415, 256900901, 905952094, 117812741, 220933019, 522344545, 615336554, 26921928, 737757611, 644777445, 319778814, 195153693, 56688377, 912675542, 607989150, 359941448, 426924141, 198326046, 521793884, 610626797, 899273984, 551956070, 860233591, 514946423, 14750699, 786155699, 973917161, 494080151, 649919430, 26479127, 905060380, 418727474, 297174942, 846276599, 327938165, 541235879, 480941781, 90636134, 212672689, 904218174, 143551685, 548377510, 343960900, 33212668, 863546682, 114065982, 999189930, 85082454, 918982387, 656568206, 45636337, 969080868, 217059411, 250798351, 784408324, 884424341, 783340188, 315343412, 193563098, 659735953, 121066460, 650016257, 998679653, 383191728, 612291913, 536058969, 281559985, 446460923, 420342884, 979485752, 695888234, 485554056, 800927383, 585717697, 599539894, 917876401, 425935333, 802314797, 261121982, 585796198, 734136831, 782391497, 521669383, 691406502, 372666024, 56537220, 489598454, 181815522, 582336535, 837892317, 490755172, 558334744, 773718272, 384994013, 984251427, 984679836, 44396218, 710244085, 205938018, 125441107, 249899049, 980373875, 548349804, 415091238, 981065993, 610621714, 93111988, 653339519, 890019947, 789187318, 318823886, 614224585, 633385937, 925582926, 864844172, 7868899, 742202417, 545800947, 561876572, 875578320, 921195004, 931366309, 931275275, 788099939, 417768958, 299851617, 836067526, 790105584, 39692929, 616382255, 98140074, 687177418, 761967952, 772748537, 275315241, 118206894, 619824781, 252652477, 794173579, 186382068, 10723234, 187088429, 414963981, 57333333, 874954463, 412518961, 156763648, 670778434, 340118276, 593541945, 888702329, 829245261, 768173067, 495261498, 599363134, 442116198, 209548962, 157114328, 191145118, 273520023, 521543459, 460745407, 804019667, 669709185, 919926155, 496766140, 394107609, 513190794, 205409200, 290347936, 785662769, 280470876, 600661780, 714026288, 114555845, 800388235, 227407620, 985616086, 153380624, 431848248, 618835904, 466713604, 524410020, 162629189, 556422154, 123282528, 237265904, 728600549, 453960639, 946996998, 126725530, 258892519, 655632965, 411844729, 625879106, 899717627, 321193051, 284821106, 59134746, 208723990, 406193397, 64899581, 277501112, 349323520, 987418542, 560639320, 141917865, 390260102, 101455033, 138984464, 498012351, 982652185, 611842758, 632314569, 283311835, 949015010, 760547535, 953130687, 550659892, 929877931, 359473421, 672262007, 137651174, 474010919, 867041306, 770508769, 204424287, 990063011, 173170699, 394339916, 743592053, 692012165, 550116076, 777700405, 816860400, 967099490, 53486911, 694106671, 198151680, 312070798, 792301040, 352617740, 359823999, 633304835, 241725097, 169276529, 945998733, 618684063, 198166443, 816803088, 283080272, 617690904, 576492605, 578188824, 209324202, 276420259, 841043145, 832328682, 94544538, 118719179, 472245613, 339503332, 175011231, 489384553, 380019973, 358751815, 529196253, 238794070, 607676745, 814855859, 355917580, 996980214, 500731470, 200577529, 260006012, 26657560, 991919687, 294784898, 736175780, 219525471, 637569872, 138966025, 189965450, 867559998, 724256132, 569587683, 175695635, 684850772, 298291560, 812231200, 899045283, 810970786, 286761376, 383402950, 458407692, 930299966, 398095497, 847480246, 431422509, 566428017, 791425006, 130818957, 684618461, 968607979, 618042115, 295303881, 454510298, 563179362, 28870578, 194820456, 568782832, 682979358, 855258783, 78583497, 120494735, 772468593, 227204808, 526472013, 884349547, 952231280, 931281800, 467267741, 653091425, 142902506, 631515518, 253553048, 338079384, 627550829, 76932888, 943051586, 126635481, 500954344, 801682612, 979997221, 643283433, 13698932, 28660680, 441726112, 246449766, 599087994, 287026219, 689661734, 397333955, 949483901, 151018152, 130670962, 582993010, 467929741, 990458999, 528218405, 24211219, 886495033, 344673256, 192842794, 491298802, 302058888, 502537110, 988015671, 491420042, 680424891, 618826640, 226642954, 927551037, 998683274, 892575330, 100849562, 140635788, 50012733, 341035251, 852459121, 108464795, 353575354, 180152314, 635450499, 89918449, 582578237, 318984094, 628506862, 329546412, 611824016, 868686128, 245684142, 867652842, 476617049, 560305432, 628271533, 940401454, 716513579, 473252054, 792790347, 89034853, 455673819, 448349076, 991271869, 327105550, 602993663, 910781760, 245948404, 181902160, 893509760, 802439559, 972008647, 574300880, 849416383, 479694826, 213468710, 686417796, 12131605, 759141647, 673343680, 929768719, 398677744, 230171887, 536229341, 502697225, 8621351, 444608161, 954505555, 320444496, 763608538, 541152835, 754093180, 348261790, 731870876, 297215714, 513582291, 33685032, 945308068, 214179253, 722307252, 494532577, 342070717, 549271982, 678121432, 174626782, 273911249, 198443744, 176441839, 578572123, 283499836, 948559193, 820007248, 777345593, 146463876, 794239644, 411276076, 198687112, 369380238, 234625304, 614278361, 568577000, 929861978, 279832732, 833998916, 887232649, 163297983, 906687402, 221457235, 8196848, 623931127, 812420368, 606172951, 290113567, 283129979, 597980013, 36242679, 903081199, 26738657, 41378097, 662575437, 741675378, 889829968, 288350116, 705852682, 226311698, 170109999, 660407202, 56075760, 43814766, 827412657, 376765311, 661831955, 281993556, 160051272, 319774360, 151301347, 184069574, 982240264, 784741467, 244750084, 618309713, 564069246, 307846258, 700893594, 106386154, 941471149, 464414105, 778073539, 769283539, 3763418, 580817187, 437744161, 151350776, 309962724, 557210490, 191442566, 553664640, 35241531, 244878978, 581571292, 922390607, 100939814, 232335133, 229638070, 412208733, 146578803, 913949773, 14029973, 730579429, 520278699, 729811993, 545322699, 440166877, 582515703, 565588988, 130618091, 372864829, 232394494, 348115471, 506460365, 599819717, 135669236, 603693565, 786042117, 111167478, 265267581, 42618303, 8284606, 233792584, 866084623, 49927977, 911140656, 449105107, 643123591, 687395818, 532818270, 689787965, 790340589, 755500740, 48818335, 196865366, 413225471, 396125602, 118780422, 942775087, 595993221, 850156181, 542511697, 959505827, 668010806, 446265171, 731612981, 621407556, 351925506, 652542430, 450549982, 899159930, 40275843, 719902455, 916579810, 48003508, 185006249, 545000289, 508807244, 492022468, 215760334, 847561596, 257239832, 307116450, 6635172, 964773198, 529186330, 840943613, 768013422, 619013824, 505897222, 766105844, 841605557, 484130869, 233569649, 916450692, 376755377, 479426177, 700999389, 53907425, 597054039, 215568397, 620654148, 446264637, 22768052, 134699762, 740678283, 700172819, 523754930, 294118369, 628362335, 392483255, 131631585, 85480732, 305983558, 809282938, 513706258, 303391000, 446476712, 776161599, 915611511, 201467652, 143115152, 626091712, 112487937, 952711908, 172869051, 451301594, 362766179, 242973290, 393353834, 42778944, 654637361, 777266430, 632176682, 990433001, 713784885, 263688680, 284520555, 737811258, 224396004, 197808097, 341480987, 881277109, 975537957, 544704402, 78626213, 100125785, 131586059, 979527441, 623791799, 228831939, 974705152, 368335886, 202810047, 869593497, 643604524, 696160398, 891428634, 164292548, 898212469, 111586326, 859013929, 696000410, 318421120, 898674055, 497806398, 814066756, 834522674, 357888468, 816841562, 211728407, 702680887, 874222899, 238700034, 421065613, 54581, 681152962, 876568723, 285497070, 329623789, 75975532, 920867244, 251148866, 681414139, 957853167, 244914221, 752228579, 279339488, 749666579, 388249400, 4801154, 78712371, 354388024, 242310714, 735109332, 935100651, 795591037, 633980401, 329092036, 282510854, 440041810, 705635003, 936183632, 256236473, 578547139, 161836620, 940234184, 398847610, 33611306, 965471222, 381623886, 955201404, 259720576, 939499629, 643399769, 164048277, 304481041, 400817342, 594069941, 95186122, 657805226, 629679545, 836358435, 881607500, 120267799, 171431270, 696611255, 646038085, 424259836, 109764682, 542153748, 93789679, 724228038, 705852733, 217642123, 446402304, 491951158, 980474347, 708377586, 842372511, 976882548, 432496085, 267659998, 822594553, 130916915, 5134118, 356509195, 263898477, 110999291, 297873854, 355324409, 163011428, 559408446, 99435658, 78131107, 231995598, 815207977, 897258097, 839188204, 784000383, 159108332, 696359633, 50932674, 110776450, 466407712, 952209160, 828860074, 47546523, 891243967, 252519533, 164877954, 381444813, 491867704, 791304451, 17331092, 964255464, 668213815, 871275306, 873264764, 593039755, 187112222, 343064180, 542773845, 264582860, 660393043, 647601005, 776194456, 896998029, 989291709, 113474139, 88662129, 769505031, 482152702, 833393927, 355844506, 894417858, 292492921, 87604666, 902012321, 586207225, 501646501, 981754779, 502288558, 877379895, 706413168, 576148970, 410578235, 20945747, 989181350, 17602072, 683196311, 188584409, 131982612, 978220697, 306486586, 759703963, 144768016, 365980024, 65320353, 799275979, 92406049, 998675190, 338575038, 920898466, 53836609, 968526252, 853152894, 789501549, 414800251, 771545069, 23458685, 639828234, 500157268, 856064389, 316425486, 740406692, 200040871, 83306361, 536199447, 262281238, 267492277, 855876600, 372826863, 921586054, 962690980, 332166512, 846311021, 208139679, 968877624, 900835663, 526083887, 936151061, 58566586, 865214042, 189345854, 42569812, 962868930, 905358820, 701685172, 447789891, 902949797, 415618356, 282859584, 650268084, 8580589, 411700698, 666725777, 668158529, 104897449, 896537086, 488498362, 768907014, 807105438, 356068079, 385921172, 60483201, 174599726, 697904490, 626152102, 625759667, 945859656, 933388664, 566902118, 530910643, 535038847, 535951233, 758715057, 672129773, 898138443, 46515879, 180988489, 713885754, 409614037, 904997139, 622838313, 361280318, 139586565, 805605129, 41162927, 841603864, 112220197, 986753209, 960244374, 728915396, 474392390, 426945710, 634225484, 964830741, 429334280, 97755248, 106752260, 852793020, 976235925, 295065926, 825804272, 415663815, 431893425, 636849261, 727164446, 598380132, 345053103, 455043602, 775522277, 321665020, 742300155, 169443938, 488823775, 203696483, 75850661, 392404870, 591138159, 349384546, 387939524, 11825507, 930571331, 426634776, 680474276, 59946238, 201287729, 292570, 894720462, 345091225, 995739924, 746161431, 912848934, 557137626, 196809404, 835035144, 35619532, 974242760, 592392653, 863278427, 19959589, 286505553, 959675261, 715976838, 182025071, 620280942, 450656400, 638674780, 80528605, 530312303, 4128717, 409664605, 796178829, 414779144, 6030155, 761645867, 35248316, 964474520, 910906170, 268552509, 998034551, 884625023, 3009414, 342066015, 340353639, 161064763, 994890192, 166831059, 621435399, 625304861, 518291640, 557128863, 446249797, 57288599, 152426741, 348092660, 787332614, 809693333, 511269214, 351901108, 944629385, 875581607, 592461905, 121901661, 760211342, 639602791, 959313310, 929319598, 487022892, 603282233, 894982964, 770683677, 628888089, 759460265, 135638920, 121279303, 428917572, 930555972, 21832857, 712376596, 721944545, 586357821, 594600467, 774164215, 649113424, 2414758, 232212123, 3944493, 467426076, 521470628, 995071724, 512231976, 684765594, 247706270, 300585372, 191150210, 449348711, 986573883, 861011457, 215489592, 25705599, 354527756, 900779411, 958352047, 602167790, 989148488, 756985814, 220859629, 19092827, 350932159, 281875443, 545206440, 12865966, 259580504, 432160769, 121654297, 264983790, 501681741, 917960333, 848601766, 163753074, 384446515, 630146161, 211261683, 264531719, 964161482, 394331624, 863397641, 754018903, 21223153, 892687164, 541096705, 887768692, 24463639, 586500507, 637641921, 708831194, 656192636, 655836254, 651099107, 307302717, 812817593, 71808166, 961531667, 481937901, 446164337, 752855343, 371967589, 973987233, 354413351, 522229860, 902204682, 767069940, 965870175, 966880049, 407881245, 780805914, 674811574, 91140507, 994188165, 732896392, 891802091, 158572499, 857223349, 287637819, 986750608, 623374724, 376166470, 950447278, 904412069, 840955386, 401040676, 30513266, 968937242, 953271139, 375372042, 550583618, 562196031, 11916909, 321064846, 562063521, 659899177, 855458794, 97125243, 183133820, 625483434, 149876836, 892305894, 698214810, 670574053, 759144613, 860249775, 799085495, 511329745, 683228791, 798773339, 985665847, 486195449, 35760099, 457314137, 432876689, 128661931, 566801794, 8669810, 489015798, 432577431, 967334461, 988562663, 428296866, 253609377, 626285956, 63799772, 91401723, 713874260, 27688639, 532659291, 253804246, 320566373, 481349217, 774296015, 205418279, 668154756, 686663195, 160111065, 702289077, 384849788, 554419790, 10665826, 907933946, 77613660, 572559725, 502014564, 557192130, 141557761, 709364920, 517389599, 814216513, 447442480, 506846217, 870221089, 125197552, 150325807, 262592179, 506511418, 135061498, 477280673, 740807876, 273773181, 642724083, 314114600, 593756644, 90991288, 853624163, 294179489, 448501554, 665893775, 467779444, 718626157, 404790335, 987039675, 708486901, 970122582, 101432605, 509356055, 501575755, 2563587, 236884014, 908163194, 115523961, 19307673, 842130071, 453858342, 947561791, 656503425, 790588642, 706334271, 215151268, 21285842, 416751109, 985340660, 310289405, 653431282, 501585611, 274181187, 899423229, 748337790, 157178486, 500493615, 270986535, 900485172, 653911191, 320367950, 931052248, 201170969, 554894802, 26300819, 777947238, 498368070, 200020178, 536502490, 82201567, 594930838, 997168827, 977877337, 517137844, 833697582, 180074720, 690381186, 745339479, 364247996, 865682377, 514915225, 179906767, 532890384, 304094368, 248612046, 294792219, 833121134, 550428759, 305328370, 701982542, 301052734, 43851237, 307291628, 973874210, 918700840, 346348197, 796604574, 460052835, 893496414, 505179361, 780071430, 402878401, 171469672, 942128267, 377639456, 253858839, 830942035, 964214713, 458806493, 473632631, 981081405, 922642864, 295549351, 678430230, 914102422, 509611926, 673829145, 627984628, 635600513, 709754968, 290786731, 989744342, 950365514, 766903751, 875964010, 247747342, 192108339, 308274524, 182263423, 562107454, 141241451, 156198738, 425937800, 224086285, 914288065, 404610570, 851852936, 512910205, 43222368, 878034169, 138243509, 938038233, 410478860, 270819312, 264971617, 521702342, 508265327, 584474265, 681247831, 984288181, 172974387, 272581074, 1353079, 805427009, 484659550, 266372693, 633505277, 536132958, 304533156, 948486152, 683118565, 764604085, 805185808, 470262646, 468260655, 475248120, 287633800, 468533733, 258984448, 459073886, 706767891, 236223445, 175585499, 764874224, 942725468, 562574909, 605406847, 887007795, 685272206, 423120220, 137422838, 492249852, 854647241, 198869029, 522582948, 659430846, 917506212, 400306500, 221109888, 341616335, 360738075, 194576435, 169001618, 531509871, 250853688, 324980221, 456714738, 588019672, 495029531, 845713805, 168510951, 978648511, 500666992, 935600802, 762702298, 341328805, 891673763, 301395736, 264730296, 18515792, 484386422, 84127533, 945270089, 640392530, 33969145, 66348030, 204224550, 102584800, 941044349, 131168486, 862882976, 626330819, 459187126, 595521113, 639637110, 173520802, 602440711, 464637515, 143350828, 574873994, 220125693, 613920077, 823042421, 961302344, 793300569, 899578075, 476509459, 323880712, 683293263, 202808518, 585403016, 326329579, 506019079, 518710214, 582497911, 31641984, 920877767, 888450444, 18279944, 48845127, 388522338, 156375295, 685914448, 858397861, 655355569, 80582599, 191712976, 164309889, 142186957, 943803451, 663914691, 646457243, 970009725, 354737149, 417271195, 560883913, 849007805, 838228256, 149440714, 300893149, 59920171, 930281672, 772235928, 242922802, 748561393, 505300356, 129374686, 176169178, 314148666, 739272254, 504761119, 916198290, 653125549, 558384527, 519094754, 258306202, 114719999, 659808559, 8954796, 645212490, 790321989, 158432393, 181222855, 582573524, 347402695, 699753381, 442359487, 359750256, 508747627, 398594543, 870387256, 963415522, 724574928, 653436174, 414480107, 721490191, 889185828, 906219250, 568782816, 537589789, 716532175, 546722697, 777643945, 852130035, 468860539, 7136281, 170526545, 885543856, 82783488, 960449022, 836992151, 514040329, 829975974, 318417595, 641513350, 302678673, 59545782, 42738923, 774542038, 905581919, 419940574, 675426138, 989452754, 385822280, 23332060, 503843889, 739527422, 505868863, 699260049, 188052797, 14161944, 196425888, 974356665, 123482602, 108328254, 87491, 209036214, 587899317, 960678588, 409254501, 165524498, 875497777, 419471823, 384892271, 238034757, 563228577, 235429391, 176675284, 241532658, 19271968, 655004281, 667824195, 910879418, 256305800, 161519927, 396332921, 169550176, 552596823, 369756125, 141390563, 30165568, 980367986, 159807501, 788538051, 24076561, 926637406, 961751216, 324039683, 561135398, 656064151, 897044598, 600511976, 454395708, 205200052, 423051082, 395475821, 845123549, 754290907, 648933244, 158288834, 814191034, 130171591, 195892347, 168525314, 703382543, 997089887, 914834348, 40712576, 427385412, 732430090, 356998681, 55673321, 524723219, 663416841, 564219561, 564840225, 79696385, 556073553, 707208933, 904866516, 280555765, 818083286, 991137230, 824498864, 688568314, 170313710, 515672966, 159115569, 368665922, 781463703, 308637530, 851713997, 31192882, 209788821, 784732418, 673355249, 105154249, 288939922, 291972898, 896421883, 592236738, 706378062, 451867015, 217051569, 292049552, 435396117, 490839926, 779589312, 46507405, 365809494, 852138828, 332718164, 264344949, 907713277, 902999529, 340981875, 992573993, 432887883, 763008077, 540261798, 290691367, 577532090, 180110254, 708922303, 301164153, 328183624, 350475206, 132326927, 563926674, 199917935, 876860122, 876944200, 345798994, 941988910, 967920288, 660162865, 705579271, 239829252, 512245670, 504420813, 822998846, 503533036, 735456800, 31553207, 949425823, 925406174, 684600317, 961678582, 315635977, 451562628, 265510105, 914414632, 749077481, 183981963, 876324458, 594709151, 2415680, 292759144, 221872720, 842964836, 21108827, 929370588, 951935151, 491465769, 188984185, 21789713, 35819677, 799353867, 151215135, 731521792, 183685205, 952687401, 128692770, 953799857, 194612277, 941157061, 535039276, 917931754, 628618722, 534010640, 195685479, 678036431, 467654065, 693847026, 623920989, 742239644, 783326200, 155021930, 711597468, 980106776, 946672526, 179347347, 243721669, 729943923, 155539334, 131500514, 790593009, 169118489, 257009110, 941886483, 446374905, 497385096, 946380366, 725922536, 395095751, 347493276, 972709897, 360229347, 509544962, 525716197, 350361286, 801728928, 118222608, 33113604, 331217478, 444729392, 593230458, 30719189, 433945225, 899385744, 970325010, 813441208, 706390394, 289831299, 861526262, 11998444, 397164252, 848342039, 543245963, 795138065, 399173680, 705074570, 720739547, 278453088, 285185252, 978351894, 59235513, 91750329, 526182231, 25717729, 277883658, 570883659, 111504956, 751345022, 311887111, 387426878, 305247972, 697111263, 820019424, 549168345, 727937903, 409448308, 871266275, 824153472, 216373083, 191211148, 448842413, 444892338, 907140569, 135480380, 121359849, 76328556, 157574604, 901204338, 383863570, 274362722, 592825990, 605671360, 821281508, 49809865, 57744112, 204234285, 735643129, 638923501, 440086792, 709316029, 498926061, 309698225, 560778870, 467769445, 787278636, 17572327, 594392990, 893293763, 670029764, 484477221, 214091117, 753398345, 525451993, 853262702, 127000233, 853471665, 847719135, 439661331, 60562497, 446341768, 990186659, 729298241, 821428284, 432415196, 320514917, 787195136, 824530040, 939554800, 572021302, 264844651, 87550257, 143559288, 641214401, 961704, 271292539, 546329987, 759918532, 824700895, 657950775, 376517340, 136815401, 590783699, 299981013, 889112214, 622831227, 647886225, 945713028, 556087155, 201629127, 703991759, 49674453, 950573617, 920036148, 934861798, 559181277, 176690109, 56644415, 723936341, 40711908, 842650839, 437335441, 312761762, 45733749, 702891371, 592721051, 779314059, 755279408, 707351199, 995477445, 35627566, 275777431, 651906209, 707325827, 314246581, 366587832, 436452577, 385943554, 244764218, 196307856, 749134716, 448204136, 672500824, 875285195, 988257381, 501556942, 425235210, 251132430, 212561451, 363780744, 779626108, 474867596, 438935631, 671036210, 642217212, 808293878, 651218474, 595273753, 471795150, 991634381, 623073862, 714222408, 712361641, 104696774, 138284603, 64215301, 584356429, 767079497, 538805848, 756678304, 631660685, 751535754, 277929961, 196101126, 540771616, 921335378, 575394998, 626149682, 29831438, 528530805, 688473265, 65373099, 393867352, 719021064, 933636066, 278215282, 793601014, 207154299, 994201093, 687435040, 714420099, 61542852, 134559643, 336167506, 712632555, 808916300, 84174198, 367113856, 90690961, 906283671, 545347122, 290794013, 81473713, 824921536, 585082274, 762958943, 819865035, 97716948, 882138458, 177039546, 302292373, 876255621, 13656249, 686378188, 776733755, 646303364, 265037697, 418882722, 934621415, 59455839, 770993104, 690374845, 620860486, 306800565, 102638956, 249114117, 1361679, 655571951, 363732675, 771313247, 587541758, 472950018, 352561537, 438972128, 815825057, 659185329, 231460909, 778161189, 338383234, 331073880, 243888299, 845474066, 692722367, 684926257, 107259986, 726046672, 297000078, 525324147, 588737211, 367206117, 930221753, 682655152, 930229397, 404293378, 318364357, 166218879, 668737992, 560275055, 71067837, 259370899, 836904130, 258163394, 977687649, 206948815, 144271242, 125593593, 681725171, 12730137, 618231856, 8053600, 871570189, 98121064, 797963164, 988867746, 875466438, 435963767, 915037950, 240452333, 597690992, 51257336, 201397400, 444915041, 768969298, 984183653, 51104147, 393013678, 902940549, 674031514, 599027441, 750508791, 363746870, 925920449, 247735641, 426063428, 898000847, 829983881, 562285827, 783447218, 64299320, 288735473, 461458924, 883758583, 617924646, 695380609, 426529013, 780856479, 540668202, 304055968, 433442878, 712210496, 560521401, 820321122, 481086660, 201463147, 373752564, 884526811, 626075310, 19089338, 948867750, 426303328, 230835011, 763132673, 692611124, 785798525, 705531397, 529357762, 564879972, 638215764, 151733868, 510779198, 315740785, 924116968, 587219043, 79446640, 213890462, 231617374, 964891684, 889791689, 668640466, 88550267, 47048711, 443436133, 62733678, 684990526, 289513450, 724123189, 433652105, 226738259, 831821741, 647409553, 998982203, 873852795, 242194410, 688438769, 869360118, 484237129, 155625306, 405586887, 207615877, 498835533, 898959378, 578215941, 230344009, 637230669, 746545734, 857648034, 112222274, 272179815, 547745844, 883604447, 621742824, 54555314, 455834807, 186728529, 136949635, 509063068, 58899286, 111694648, 486509872, 280536314, 888338957, 564037031, 194273036, 770959681, 767353351, 580785982, 289136155, 351758724, 319853571, 892756894, 23988993, 867831183, 953150149, 22164904, 264858929, 203518089, 590008073, 335875412, 282954212, 108700567, 211439667, 794484573, 576085612, 144725404, 519497181, 504422927, 591893887, 3425973, 57504124, 358897482, 903470466, 708298948, 143835130, 282858492, 194083521, 959758225, 960257393, 679072579, 631313489, 999537349, 543878193, 101215271, 331641824, 148813252, 504390411, 593966374, 130352330, 752807454, 647101776, 820029754, 596217715, 983282518, 227345236, 371080203, 39045450, 577253641, 867539365, 551223588, 744180110, 887942973, 778989696, 658344192, 671216812, 101931662, 980573371, 864688771, 332148935, 493406879, 912643998, 110067830, 471796640, 841582894, 886229398, 574154832, 197682510, 212953097, 763492600, 766751726, 840345676, 720958612, 643531644, 637509544, 529331794, 899771987, 840641903, 153724109, 78385266, 839140131, 610645360, 164629148, 642749208, 4421027, 69807590, 23360852, 7020035, 877177343, 108416780, 143386496, 758121575, 881384844, 808508244, 275046481, 422103057, 917292140, 567288480, 267152205, 786655659, 186847654, 665848783, 120604507, 704446652, 909240930, 766275756, 923307169, 710809031, 502746171, 977398420, 417918142, 248303999, 371910201, 732799234, 168416168, 875418307, 582348645, 361637032, 545559979, 401642261, 534123380, 263497778, 521433608, 224845182, 340703130, 907360572, 96185174, 559034378, 584161819, 634989208, 977895406, 163334175, 32301740, 166986686, 766896875, 277741173, 561001873, 943679277, 200736151, 264145803, 747836643, 792980288, 546009057, 499732409, 40715069, 50695203, 565799502, 828652882, 506868534, 233381541, 384550692, 993152294, 795961362, 337284145, 666587260, 289816126, 865918503, 184638132, 576476971, 855766564, 588908155, 396128143, 502396401, 827906009, 904161006, 382384696, 861715844, 132742897, 28024347, 514334491, 614845196, 181999113, 212267557, 208005134, 217249677, 962224102, 772558263, 455268895, 579124267, 148065825, 77777428, 765597927, 919213579, 473532652, 703363566, 745429475, 725888791, 130863808, 76317777, 8437889, 686004386, 337404769, 126267359, 358003748, 400393510, 213467185, 256601769, 841775526, 26665688, 398269704, 120445415, 871095602, 313473180, 735577060, 814897881, 575936677, 901658947, 666598941, 855209966, 938541398, 641652983, 558279227, 68416213, 669858067, 774856151, 559025074, 386415435, 238206531, 51581719, 979897606, 970094486, 349945294, 127827951, 682965401, 332498847, 875467006, 485962539, 290592472, 73213353, 30420750, 30994305, 84277410, 245847874, 350635120, 216732562, 425032605, 910795465, 528276986, 23436768, 465001414, 490505886, 237810766, 479041335, 838368902, 102583395, 323441246, 891864073, 683806601, 136608862, 187436937, 382450689, 94924978, 362251654, 969652987, 401558242, 148807841, 381861825, 684119775, 168347410, 862425263, 394537128, 129602549, 197847870, 978137206, 83817114, 453898620, 955855594, 905276256, 913200900, 589482767, 213136797, 126106883, 564645837, 994350457, 512970598, 237933079, 401004099, 682008451, 769178203, 337849359, 921681489, 417898096, 323839044, 623823174, 85723008, 634068222, 153318662, 136744616, 534625271, 923798641, 342620643, 569799860, 135289623, 281933255, 138921049, 984712248, 904251677, 468017258, 104435268, 54467199, 596535401, 855806457, 948255271, 453634040, 767376716, 864304711, 20895929, 249203434, 825573596, 554395363, 42363227, 742590674, 359287752, 301161333, 812112098, 456346329, 267269692, 782975027, 593850297, 774286012, 223156356, 219999678, 636023742, 954353006, 264700885, 74592620, 9306340, 978875130, 607013509, 572794344, 737590354, 840018898, 345948514, 789047865, 590810027, 522150694, 751470921, 514333725, 282410251, 209692242, 145746425, 21696467, 366057517, 616715532, 10417841, 914078277, 895144716, 276778205, 610426832, 211457085, 810541046, 204825452, 268969612, 492814793, 481710984, 486257420, 293018120, 635094922, 850147771, 616242522, 199004439, 606207999, 987778471, 102343084, 288918600, 705064550, 617382795, 645185193, 644183054, 279972916, 319226118, 560948983, 942375225, 147172918, 172981200, 839474244, 893903042, 72761109, 982514472, 416665095, 743892418, 206139727, 804809438, 263497802, 343237104, 179378397, 486746157, 839942908, 275217159, 532092094, 353897692, 848255469, 385506512, 301839227, 640979296, 446511670, 459279365, 868955420, 815026528, 993110298, 667834189, 125797590, 973267361, 591835244, 144406088, 639364945, 494750170, 222999574, 923995566, 286716235, 662902511, 269082009, 69968867, 364116727, 702367426, 669263622, 598757742, 176660374, 115892541, 527588488, 266123971, 691785196, 509634063, 951518663, 170071456, 975194410, 50622651, 411512883, 59670512, 367652545, 460068608, 217584506, 736213512, 548359003, 826829117, 411004938, 614944882, 913024192, 284329730, 595368049, 429886751, 729973594, 32152604, 796303530, 924245042, 126752684, 7576568, 618616671, 427149452, 944720644, 869613289, 993652463, 756624274, 335458295, 917416480, 22087514, 639889384, 191755521, 407910528, 657353823, 913130230, 114044139, 750872955, 330146788, 645420827, 460095164, 867425183, 536744238, 905903550, 53026344, 678730915, 345580173, 752823115, 948346113, 858452647, 768253890, 975913750, 806033642, 517887012, 253572862, 733835084, 479393634, 856753266, 86549889, 145988337, 124512547, 869625834, 625218842, 184703371, 868299878, 12127038, 980280681, 142925750, 198201609, 702181022, 887150684, 900888333, 687973213, 107868854, 423695358, 162376663, 128647083, 893492704, 127624858, 2237705, 534380460, 624884813, 283406942, 256226786, 907060801, 418055396, 399633442, 784165780, 749779977, 418559083, 299348072, 107750855, 265471494, 379201738, 249284609, 637562724, 88886506, 502024313, 943292346, 651542483, 373803631, 932440516, 652257982, 268479754, 958516031, 447813301, 753396471, 821791096, 686529212, 776584730, 30838080, 252875776, 114630461, 993470059, 104045743, 245573819, 621700203, 100000597, 35405656, 463482677, 754876259, 738876608, 99301486, 426620328, 196980577, 298423183, 484982255, 840507404, 390064205, 7516910, 810682321, 279064637, 220520230, 452273319, 76657611, 885431741, 990023977, 645344195, 633702472, 336463253, 441053010, 467175097, 880764478, 778467388, 510579257, 381848780, 651388414, 360255611, 524323964, 420676763, 261321206, 147830082, 464845052, 382651053, 599404904, 528131057, 997545268, 107825578, 946379193, 721486320, 95698601, 545426131, 703343450, 501727882, 948923279, 40889905, 454114101, 423876743, 907342258, 855496298, 131051661, 224213928, 298280693, 271473571, 787717550, 238303505, 771113048, 558740694, 886495008, 876193924, 730651202, 328057486, 2570045, 230239227, 472616878, 903704852, 316239340, 549306609, 825012922, 179050315, 379029791, 226700157, 688619762, 682127999, 435172760, 295337115, 299740176, 33091827, 231368819, 737662927, 176981076, 518578681, 629760355, 383403231, 921001854, 122745255, 350841562, 783406485, 65044239, 229063536, 116669357, 474162451, 993863307, 10591769, 228725271, 252229427, 811243155, 248023718, 43476370, 366293819, 224912789, 496739875, 119836100, 716808823, 86750966, 591768774, 750654567, 827798010, 594618620, 139543045, 285111750, 993944687, 871777310, 529263520, 2491444, 350737731, 410145280, 366086615, 331584697, 255829950, 563047200, 281712479, 99878733, 788877707, 499602114, 394042971, 314369216, 495280652, 611555499, 41598963, 639588275, 683531562, 914633713, 939063768, 883301847, 270171361, 742300925, 828725969, 675676351, 896288257, 599029718, 92310751, 190625661, 741571778, 536075373, 350286997, 438083707, 751720509, 176981295, 838155610, 101136691, 676811360, 557080919, 233661205, 267771228, 66159654, 960114060, 408258012, 344602266, 405975422, 853679131, 505189221, 595828048, 602373072, 865814659, 824318709, 993512594, 198841049, 588764895, 242390758, 917728097, 191728159, 228072236, 818047093, 911125829, 707988218, 855232458, 257103194, 409433506, 737016235, 657751438, 158388726, 565286151, 336872084, 578728743, 363890951, 196555643, 213470895, 129687054, 376524078, 192754732, 309027010, 245996320, 942849248, 663685761, 958781227, 891860935, 230654850, 681472496, 290676036, 183914244, 515324247, 782387978, 133752198, 251748198, 575626797, 4744706, 981225537, 492109551, 472034976, 276080935, 798196651, 184202960, 734028736, 165849428, 668204662, 406669073, 958889704, 447856431, 687151444, 301833304, 22293577, 416462780, 611246981, 484354792, 380016147, 734627360, 912126177, 608825541, 799283595, 202746384, 679174304, 75122989, 727078983, 530207873, 853087953, 733467992, 580437748, 241683407, 24436740, 195380892, 64726197, 959669596, 203532967, 372751273, 190414363, 371421388, 819483556, 949681580, 644798924, 489058664, 195157903, 621337400, 22943410, 623248722, 335274653, 531735764, 843565416, 458375156, 214713216, 660247216, 990050864, 547012690, 495265582, 415733524, 172230384, 381253795, 913916854, 25046539, 564656670, 339507523, 666849790, 932093525, 580500555, 398583249, 507285244, 40213039, 896521978, 679784543, 610415588, 360346220, 963596874, 764341214, 166507994, 583381648, 913451685, 910228806, 70016110, 146181806, 656561171, 877490613, 470785767, 240757135, 351003919, 933492685, 129973319, 612760171, 685945234, 936316955, 157209987, 167322790, 475270432, 661852068, 40760522, 321160632, 490220187, 654616977, 780974074, 990358749, 633694834, 833875007, 821462137, 226792602, 33270772, 975024790, 914839843, 172085404, 505012305, 669314513, 441268005, 269149629, 25437352, 388918471, 725035515, 595547836, 712909482, 327248841, 324084760, 732018024, 779231850, 422202330, 839776314, 313238497, 945856090, 191419340, 714748912, 330975748, 376824936, 943856371, 55301267, 78130381, 742146555, 940377222, 728085421, 241170881, 996278675, 64033377, 126502693, 378094133, 4191570, 785515694, 329574009, 296919026, 368902403, 643790918, 34741782, 919236768, 145945153, 660958952, 469759148, 970699236, 193173827, 481858074, 842124486, 70196283, 928025070, 481406598, 567181290, 539415305, 100992833, 428202222, 541855117, 763076202, 15918991, 605057282, 99973347, 508169594, 91993775, 59313774, 810641134, 93397806, 663675399, 695801249, 501086788, 874329454, 552686942, 392797584, 43819161, 712866330, 64460756, 931774556, 23909248, 246079665, 666648074, 886365491, 287020519, 595845193, 208120248, 746526051, 727757584, 425410708, 128954719, 469320168, 958471650, 201012359, 820967521, 729957117, 142035133, 312001085, 348573255, 780642124, 699136244, 477438, 91016521, 533043217, 861272074, 429765267, 140984885, 846583794, 29263049, 672757588, 677799486, 348995735, 365953335, 992684125, 205460549, 672660935, 869693663, 48706690, 807798182, 713409265, 220670137, 963434275, 165584667, 179727103, 876165411, 631444513, 217173822, 174068266, 812025033, 966664255, 646825441, 502779315, 630642929, 323480221, 163263983, 227741391, 810848055, 995202920, 446789761, 455292839, 554944695, 573330805, 272458145, 278413775, 403991316, 229026251, 578854845, 261859311, 168782187, 367565029, 239488473, 772902537, 946032907, 881297287, 532867217, 979536, 495996350, 170441496, 369662252, 683323261, 605505351, 846048365, 681988554, 201363734, 553837201, 374503957, 497047332, 555162585, 447118438, 93983070, 742345346, 416909861, 13186265, 655924110, 559490987, 847530705, 986558911, 477360381, 877531297, 998011222, 101997728, 674850970, 648571724, 259556387, 662460750, 86215258, 267201454, 659290731, 196065039, 713635003, 576493323, 56255900, 722184793, 539578902, 712457532, 325252535, 727052093, 545660196, 348011169, 684527121, 365305796, 491247205, 504244792, 748991041, 865933157, 928869790, 38824884, 545969702, 238119302, 308651504, 586957397, 27003841, 354121134, 284977856, 690125034, 551936449, 196959648, 856472947, 705930283, 832274196, 516247611, 137851558, 109749826, 564029660, 536657965, 623263170, 132926658, 958615932, 77223619, 790122672, 462791798, 995851766, 809082654, 391876570, 399296975, 73170126, 564239025, 236032980, 31996854, 504862092, 653309606, 402967218, 208314652, 564014667, 381441131, 919722024, 45277253, 406524165, 126547565, 679260126, 183900673, 588836463, 192900873, 465866748, 429975321, 834400891, 2709735, 46576728, 227645947, 420641123, 578687345, 508734750, 890573014, 994353411, 791276017, 841177987, 973663552, 731386841, 678696775, 279550220, 117518211, 65991158, 777610701, 52182721, 908898233, 939443823, 97165342, 836858550, 984967036, 70138757, 154158881, 367194647, 670377646, 742957068, 711806840, 378483531, 138259937, 249400102, 916979392, 284658703, 150219237, 178124802, 308605545, 558079398, 775294834, 471978839, 717383227, 690660851, 328198071, 65588488, 174063478, 617930904, 297507530, 748311724, 340268090, 982678211, 974493045, 670825499, 742975792, 267949660, 728312619, 285184117, 955587905, 613859533, 392613559, 690436128, 206482246, 2620614, 266996771, 439780760, 814225429, 236102582, 563020650, 583993674, 417117914, 539876842, 287465989, 312956006, 191898225, 682347642, 186348032, 738100573, 74250351, 310962675, 278173500, 26277619, 562593629, 98906068, 18524546, 461440557, 808930329, 652659940, 446502945, 977922529, 626190905, 307175651, 410927850, 638141659, 546777600, 568938130, 869950638, 984583110, 862123711, 366962939, 323418150, 891823892, 886174797, 72681806, 754973795, 857640166, 977371435, 666589443, 982351207, 611142023, 430424743, 898117185, 109834790, 505344709, 665584980, 142915231, 437938791, 351735644, 359568051, 423774480, 6993992, 573096669, 119084755, 321679538, 578402076, 859483582, 734392267, 553355427, 729622436, 698468334, 702995230, 249375369, 629324803, 975130992, 700810792, 763506525, 366135890, 283501465, 966224214, 786096919, 706201229, 142799901, 130011144, 785029656, 365861145, 191448398, 114212590, 56662468, 732047856, 879855790, 991391731, 446775589, 728363071, 672806603, 311922830, 116797573, 945798072, 209626938, 5768610, 195712452, 674470566, 287479903, 448418710, 689257371, 286618423, 349748598, 204060902, 800285695, 116176169, 745279582, 429016182, 577449011, 788569180, 350074207, 356785891, 788567881, 785667052, 43542200, 480488796, 249669200, 105136237, 544600816, 868520580, 395588414, 854839876, 756539574, 228655548, 513009979, 213197658, 505255834, 416624999, 139920008, 809601338, 299175112, 79071848, 242175475, 98353076, 559975524, 286423143, 261250023, 732019233, 498978537, 61547648, 907239492, 985299253, 823428249, 888020510, 840354925, 152693989, 731183523, 151394998, 588927556, 396673454, 952504161, 266679048, 716063050, 980866322, 285869290, 898620073, 783572920, 742510239, 979277325, 117279074, 996939203, 14083716, 88780471, 508373183, 86949684, 700714485, 352219233, 676018866, 362905907, 693996701, 352509690, 873693881, 453350373, 662600963, 201915154, 750259490, 980342462, 373432001, 755221048, 494867575, 294395799, 459872352, 110887653, 325028922, 930857073, 359537548, 248488991, 122788110, 897009353, 434597644, 953240577, 58968576, 60702228, 851818058, 539430818, 878625361, 930836394, 907127584, 256582084, 239390735, 713797461, 494598528, 389254308, 512434124, 953770806, 463683548, 727290855, 543846469, 241562910, 919747212, 107438618, 571297294, 608177854, 968187599, 449800925, 665613826, 589680529, 298816103, 941600680, 415710728, 844773557, 959409068, 944495499, 751928206, 662509163, 521705053, 995173179, 681505678, 130104027, 307499614, 378472544, 32294738, 809755369, 663014837, 81569241, 710249283, 366459629, 499871569, 438015740, 470492309, 225828636, 379015622, 632696719, 980342250, 739693138, 708635066, 671824092, 114670939, 622178303, 895705227, 458574527, 330284024, 976947197, 282346755, 576486025, 733893824, 479488271, 750441276, 354967133, 479628779, 634488686, 350267066, 458881962, 871220161, 241438735, 201711325, 553259521, 444702021, 88967059, 998693553, 984089323, 2196082, 543723663, 309150785, 2353438, 629405631, 436342925, 172369131, 880907432, 86310585, 415632227, 602139888, 576047200, 717026936, 410764830, 48591011, 865639470, 996484319, 593871761, 398468117, 50323804, 730540055, 234745603, 366990334, 853383922, 974742216, 973715461, 731593811, 595674323, 841240410, 682458803, 5757778, 810488681, 872549731, 942352187, 830163596, 399478896, 903417258, 514208885, 208262328, 835452910, 609724829, 494419568, 520695658, 523006950, 421557985, 3408411, 997528956, 550194624, 550538727, 535818264, 345670751, 599021791, 776593644, 815173283, 247520310, 259026791, 311633640, 330543047, 661493524, 550886001, 411938486, 766744312, 521584070, 191096199, 38646782, 640211525, 425406649, 475772529, 670564288, 907022792, 586948435, 764530211, 611912551, 550173782, 517979912, 249187556, 832355672, 75616042, 210491707, 813634873, 547394444, 443297623, 171233823, 228661702, 322483718, 700021223, 733981902, 651338624, 809493543, 495330623, 895103305, 792339232, 306252492, 203743619, 223791521, 116693115, 688511101, 253276052, 900489452, 913468638, 556535228, 38654450, 920169815, 21788919, 123487147, 124179193, 222191687, 145123324, 610956837, 667242639, 697111122, 563760344, 434402659, 824722482, 680509999, 264924943, 502913921, 919064881, 709463169, 256884751, 211518584, 989183593, 521385454, 707715061, 670749785, 91872963, 143322797, 927703853, 899507049, 827790030, 83792448, 972104162, 695747902, 198523373, 924219287, 632098427, 40757580, 204757488, 394419839, 455592909, 235333867, 745367605, 313432794, 523351936, 571028926, 851971622, 614496757, 129787308, 745112371, 421223810, 27446543, 21095463, 439276451, 734947102, 764914472, 64747070, 854136989, 690339956, 225951037, 369199024, 448873668, 267879444, 447071520, 821744179, 165275340, 813415062, 772804483, 5227586, 530169227, 854714613, 743463581, 975874812, 422871006, 854502880, 414854057, 182753053, 657563610, 490162999, 238122548, 397811025, 793960043, 122235356, 623073368, 983167676, 528984150, 633538105, 854175143, 454729868, 264868915, 4375797, 993821853, 453058829, 9436851, 389506336, 469846589, 796141975, 542821368, 104647249, 930981232, 414137352, 474144351, 391860917, 503239395, 272997793, 193338040, 990700505, 375891901, 868378629, 714315000, 89377794, 449022140, 39438317, 171932157, 86116760, 57378687, 674872945, 615276647, 88337957, 434060219, 265525110, 203337212, 877188509, 95593111, 852900655, 717776318, 506758561, 96292486, 513925164, 79954572, 17435480, 302790908, 420676157, 727025575, 718572357, 814078464, 193864572, 796589471, 829232287, 949336040, 763191626, 994169608, 269131065, 825452840, 259068533, 125204722, 841639260, 798291037, 214532581, 306755060, 972946714, 103592665, 617498881, 205565624, 726131269, 611716978, 9908003, 671979434, 940255467, 831022437, 491103300, 405668323, 614557748, 535259389, 267088197, 135997389, 294807808, 911556171, 716437957, 723287091, 813763811, 783871301, 985929547, 86431282, 407667013, 309598471, 535655018, 998696279, 677516788, 86412633, 718242642, 648956616, 830734788, 305468674, 785943318, 431737830, 929726756, 370758765, 948519211, 257523447, 897742480, 735698453, 54401372, 230735906, 795043980, 635849568, 885424138, 621817590, 658591835, 730264365, 376335618, 997452980, 235811547, 744482495, 224747405, 935756955, 982542740, 699860373, 416695423, 752691684, 720636791, 17025305, 373866957, 174439826, 746076422, 807181786, 695731204, 896872757, 778938406, 961789521, 69140209, 585670038, 475503463, 380564224, 585295563, 614444859, 492106303, 465035896, 445904533, 835684364, 117700841, 985113074, 97442240, 326847007, 725039148, 514482924, 943910638, 642582534, 364774420, 473476901, 771824487, 993216107, 733743530, 531470278, 571683060, 476051, 707964069, 708029636, 317577679, 468158315, 473957215, 767715952, 444101521, 87537510, 464962888, 416350081, 235671748, 695121555, 625112370, 824347886, 469820091, 497764470, 637031443, 629072540, 992920548, 547909690, 10782108, 794575803, 231287, 256962173, 917544625, 54879488, 701285661, 29350406, 433187397, 763210288, 510149798, 498583653, 141155812, 720012362, 739937423, 773864652, 573681993, 210500820, 995209655, 43412268, 208884427, 917162266, 263232678, 488850566, 427391588, 650055032, 370164676, 380899450, 240592764, 910240925, 709752833, 621792125, 778855536, 234031021, 240508731, 323940816, 414796438, 65843698, 227114791, 583088891, 199075308, 685015930, 686712085, 536039962, 48701637, 361605621, 558437926, 130365224, 121762225, 774769624, 410311880, 721359198, 261792111, 172261091, 887795727, 80687394, 680032297, 869433027, 517003940, 25433039, 963733788, 339403024, 536227301, 132537853, 56084814, 680471027, 163928038, 780987820, 230101565, 265831799, 126938640, 918554597, 375873685, 336811134, 964811460, 302908245, 560589002, 604055045, 898696763, 200036107, 56136011, 470734372, 865668659, 564738820, 504802020, 77751325, 370244401, 185802644, 925137150, 496273174, 334204340, 589534977, 522639216, 948428701, 768640705, 666697517, 287705712, 802736422, 479554858, 845000004, 799824148, 890125962, 56613276, 626874928, 660690575, 769462754, 70099616, 762432946, 304883234, 608418823, 965250305, 447949549, 762309667, 695239023, 33920728, 694568134, 575588407, 776043836, 473272175, 289382335, 744372935, 977407648, 5331039, 288598506, 389860326, 144157730, 502046253, 826924135, 209185612, 409961868, 247668444, 416836405, 143239890, 377223100, 976238221, 512440799, 269317657, 931905727, 881213675, 257822543, 390620826, 37711447, 727061263, 814988182, 752456680, 952513839, 781134859, 679988678, 544801982, 467679725, 10450910, 161368981, 161158948, 997728427, 80250860, 52242250, 707170604, 873451463, 227040098, 165113561, 39650424, 624013375, 505376612, 800939454, 331512414, 415083187, 435892221, 804319571, 140688147, 97851790, 674174857, 204441952, 596721432, 121626708, 845335523, 266043300, 322505140, 797688936, 530171527, 347931309, 701738989, 871396679, 729473107, 818164527, 414670751, 245014425, 975370383, 974501964, 27477043, 500690703, 474535691, 850193906, 496262457, 695075273, 416267934, 827383869, 803876016, 119570852, 861510533, 453154996, 690513402, 953424922, 593636770, 721168964, 750297687, 228794986, 149752265, 43368340, 825023060, 323961513, 432105601, 479123449, 198116309, 218402681, 128520172, 884216952, 621058075, 973740470, 354837723, 683472262, 99151343, 804090810, 457629216, 663545677, 882057950, 969721694, 320843575, 585411388, 786724462, 351629138, 897168731, 493539220, 816396830, 103295747, 651285225, 91089876, 795680752, 459272204, 892204209, 877252659, 826507874, 419362286, 188968017, 118784883, 176516028, 678011040, 276677040, 870539807, 482840040, 990270004, 752816067, 802160979, 135178570, 333802329, 449781736, 290019685, 171126469, 938728077, 124670465, 418932373, 556390092, 541543377, 8204290, 223599774, 749873119, 905516793, 35719400, 158934990, 484930073, 697058658, 772778437, 164968256, 658267690, 729910246, 228304482, 835349781, 400597692, 281351965, 807018919, 738122301, 643477517, 634529477, 763925981, 212157821, 898541806, 781120768, 564006034, 873469006, 858566692, 510375335, 225462503, 647503365, 35402883, 24716157, 680657624, 240330024, 746317037, 914891666, 384424261, 460986408, 500316853, 946878195, 382249517, 705306822, 250920338, 927193777, 209290844, 78825192, 891114726, 742395451, 983933898, 760333521, 978898144, 287615950, 162341312, 724944653, 811962180, 931416852, 663989360, 388392021, 700748987, 923049972, 353508653, 947744661, 865717590, 995726424, 705994787, 509640325, 742014720, 176979020, 702663052, 646953828, 934421844, 858924257, 921542225, 704181499, 860927023, 442211208, 269365935, 762683156, 31810584, 989884308, 11100100, 605472453, 89037218, 571118577, 963277245, 769304150, 686507649, 152749043, 56866519, 223556433, 749093058, 560899966, 11469584, 165586246, 729358103, 262808700, 707720124, 106236621, 648427514, 162073959, 398656321, 259956930, 158002630, 322287211, 236280751, 490439653, 371129259, 101251953, 628228031, 978238871, 555096369, 35837634, 317839285, 856870051, 327334294, 334741849, 720563367, 470025981, 758508281, 593834474, 647484995, 254164452, 62289410, 541131473, 339658139, 162205893, 523684040, 850064213, 132754624, 749875625, 84505460, 260283201, 460532559, 179508996, 442449202, 860219236, 784045965, 803484296, 931247692, 241393057, 228822586, 372812392, 677573934, 468106155, 974760044, 365486435, 786905715, 852874283, 258717844, 117209115, 671115180, 975236371, 201914411, 811892992, 887989427, 560536195, 56039962, 858805963, 392098950, 12820577, 915265706, 856412493, 26965197, 97510532, 718010526, 396295804, 504211786, 538616097, 38105185, 612499276, 520633855, 214077687, 9549865, 654818889, 616420571, 583736805, 322637902, 440773846, 747055814, 146913124, 431700325, 717588773, 412369170, 351808795, 944312579, 141700143, 36206143, 40472152, 716840329, 746189417, 74412932, 721290858, 824415292, 328225784, 91337665, 704698418, 530651811, 292563258, 686798684, 714684157, 774426984, 859920942, 835869662, 688376201, 23730017, 835816460, 247182458, 536582845, 53525241, 553389320, 264286144, 259372043, 443679490, 27099704, 316148883, 981606058, 793607503, 422380384, 257512435, 776076271, 123272474, 392219676, 588043140, 125617753, 172793746, 378931022, 385903737, 821114277, 923575058, 962633010, 571105531, 121802942, 416470703, 971290981, 305133641, 236714664, 483860846, 893548416, 457615483, 647175519, 741826036, 333408490, 280296932, 234693360, 334112301, 24058091, 865089820, 218078694, 904882290, 967803084, 329427895, 650178572, 608130245, 841351828, 782686816, 429529570, 534416567, 229829893, 794699769, 176007767, 152576974, 825809032, 97072637, 961308925, 833564124, 352161839, 851000396, 552850104, 448229614, 479359327, 97869155, 620435476, 518812255, 585018719, 119815360, 627554108, 85544648, 954492534, 815423469, 541362537, 149077733, 974414840, 249697949, 776500294, 592068410, 546467561, 910678923, 753114873, 337384681, 731691615, 755430577, 60690757, 230691542, 772050228, 676972563, 505856260, 785090134, 181942040, 82114443, 663862534, 299001901, 992882665, 54586659, 178140826, 709185631, 988097299, 273811265, 126547952, 645095416, 24668415, 207488075, 817013119, 83955567, 263287218, 569295803, 716058081, 534860222, 69746086, 421657260, 503792168, 89373621, 148016033, 900784371, 614098056, 705630821, 113402784, 385385582, 579876791, 250559528, 161076647, 910223228, 719115213, 3919912, 997424720, 814281943, 62710172, 96991882, 863151307, 497860425, 334262922, 881961586, 693769531, 616336488, 287810865, 780816409, 228687481, 812351011, 992767858, 807838730, 538695310, 793823524, 338554729, 216011338, 652134904, 471871311, 414372940, 622861889, 923345300, 501147749, 940725919, 537779057, 212887114, 412778768, 756632793, 175994347, 649241450, 780043885, 887596139, 863796001, 237716004, 38729736, 462553270, 957174379, 502131657, 326399978, 174833146, 165250163, 896591360, 620847014, 731167140, 429383203, 6787335, 256521558, 493243865, 191780742, 152927102, 793312839, 436331394, 489086667, 515950143, 262555977, 330107659, 814827673, 738767606, 502845065, 671801045, 169122571, 107257269, 652604794, 542689738, 709234350, 31902059, 446858349, 882187644, 758856227, 772819170, 734889598, 352117000, 496855615, 919114168, 635745610, 513982063, 951068494, 624401050, 924124709, 736724565, 116198352, 8332488, 795508857, 110681593, 654328934, 201785065, 695604459, 616048785, 67309293, 492005846, 785029931, 961327600, 880453948, 513586674, 524850340, 772719618, 514304134, 93026085, 200738795, 702622361, 745261855, 671323641, 408651851, 308470334, 43979219, 842235037, 318080224, 451865391, 209312545, 158791096, 289770844, 612463323, 737518604, 963911605, 179105780, 923686476, 32804968, 266835723, 574449172, 578719220, 669052969, 841177702, 536816102, 569140336, 280721870, 828802069, 651948243, 469051267, 501200770, 914200959, 499615814, 500254680, 813066601, 46774434, 85687701, 567740856, 147795746, 178589107, 442805561, 752460453, 598246337, 637988289, 360578064, 873971959, 380680214, 337490911, 914041813, 124690344, 31987748, 912253293, 153978545, 603214873, 883576112, 686155392, 398786498, 866539043, 234140104, 158538745, 984207636, 891362001, 992947920, 459551214, 18315442, 431355083, 697413911, 851371505, 779779258, 144272964, 245183434, 819653620, 758000813, 8921792, 866219584, 952274087, 800409972, 692062245, 428884459, 98506444, 823004327, 230347214, 524100117, 225218983, 131984039, 479320721, 767142610, 321085885, 163599041, 402528796, 57492331, 248095135, 72923335, 682272952, 432444458, 854554241, 74444952, 734974817, 450068284, 379433139, 163123967, 827611110, 367964079, 357201377, 730764798, 61801537, 672644179, 736305406, 456024585, 764904286, 483153184, 234934053, 55818669, 691244224, 636023595, 962617588, 488942208, 577079197, 752689760, 428671735, 627315526, 981128554, 528622383, 939197095, 962129251, 834950167, 538748935, 686574780, 321203321, 428026239, 577921157, 571898441, 889898101, 325204072, 303447551, 807368718, 665985493, 436436035, 234379799, 393222585, 56202395, 479425102, 465236842, 421644358, 130492330, 111741438, 758988826, 21315571, 571856039, 236706686, 248150079, 31110053, 895924324, 15764188, 191577375, 861082101, 683042771, 134340038, 948227566, 20070041, 9751090, 789604707, 509596460, 634263289, 989780649, 922525198, 452878473, 886821449, 849966619, 301619555, 859364283, 81167872, 789332238, 122641525, 547930179, 901693933, 862514663, 457758807, 343780022, 501579629, 656727348, 708259873, 454792264, 123941919, 198761739, 463539732, 61983681, 215649733, 992242081, 491443608, 583710074, 433190426, 819370258, 181269352, 780378772, 121911957, 55707045, 308461175, 373949681, 831542653, 616426080, 119072505, 708550339, 300325927, 772155518, 486710093, 992192024, 172094261, 210685904, 888242342, 912377700, 589493347, 807902220, 291103120, 374943429, 816015718, 738907302, 843651702, 337936480, 966765425, 77449966, 38983873, 752442018, 888825441, 163485539, 761682926, 864920086, 423662739, 973124887, 648445557, 305449171, 423491190, 157489521, 834061284, 497657556, 355434334, 375943218, 627538845, 518334294, 427105961, 921611121, 774863588, 440215404, 198660947, 705472766, 991861230, 495514340, 911370784, 773452479, 30191424, 650422204, 591787583, 932817216, 752841739, 680641748, 997847709, 507743680, 978075543, 583909774, 546363885, 956094664, 743517472, 123244325, 445458828, 690256309, 398168103, 653818830, 625034022, 432688665, 629434910, 696146596, 115074792, 77551548, 679971598, 639625406, 539134630, 940604197, 273690225, 864986192, 34213169, 10457095, 70578358, 566059734, 1371043, 999924459, 5149359, 671211944, 350827757, 526981555, 661164685, 605352555, 776646726, 554713430, 920517117, 4906521, 389271691, 615750421, 366786377, 141618455, 822206001, 661808742, 511941338, 669785835, 367003641, 85958278, 312401096, 79456847, 577784243, 613327322, 571598360, 539245617, 960722455, 375430280, 526408312, 70926663, 460373513, 17925696, 717382555, 477232927, 892271380, 80898260, 7318851, 529647426, 374684283, 124261404, 322409456, 624210295, 265112194, 17146382, 737495398, 781617658, 497099164, 41268960, 916259041, 220143208, 454129722, 583960434, 561385947, 594668603, 577005424, 47836859, 103519616, 977909615, 194013404, 786803489, 51032123, 343266314, 107857444, 628022959, 460303915, 778864053, 220582857, 834620328, 608525431, 702543962, 790895062, 184063911, 779908696, 825508497, 388401298, 340240674, 886364293, 184414538, 584374505, 16562840, 744239604, 59187971, 853465800, 98842444, 546640798, 243645322, 638989413, 100120518, 211196336, 873741776, 510663686, 552600170, 819056339, 143639047, 210606399, 114265437, 367977345, 701933372, 9522319, 286237086, 89504494, 813490538, 127146057, 135468562, 291227955, 495861144, 964522583, 136885682, 205099244, 263602054, 715539655, 69622335, 121823849, 430507719, 69750973, 175474521, 653881505, 118595907, 80160610, 727531010, 173830772, 512515109, 735194785, 201962104, 488610872, 455110659, 46959178, 539070510, 162636644, 67734521, 893342326, 218426520, 700368295, 11423297, 819425929, 338535617, 241642543, 55922363, 799102932, 357174287, 182491442, 121331269, 307710024, 679195960, 316841401, 861991314, 476629763, 490834143, 159201457, 425007053, 531336771, 267235910, 827865007, 42752184, 15841527, 649279735, 235272327, 31014410, 596249541, 117664923, 158797155, 399089854, 333712019, 173814491, 400756514, 800173176, 671319888, 998672800, 350271213, 904957288, 22618984, 850890160, 601224760, 992234271, 637856302, 34617487, 429948363, 49538064, 430639569, 352137963, 158285205, 696943699, 287518211, 332097205, 652647943, 841772354, 145923343, 145886989, 188091813, 275869909, 61966782, 428675836, 161392015, 454150189, 536921162, 257531030, 733915211, 694608416, 583367028, 609359144, 349448495, 307482580, 952694825, 980353597, 857822453, 533018112, 407279129, 325449323, 479536861, 318096862, 892282319, 594688713, 157034880, 575211375, 878864761, 196323952, 529637887, 334025888, 366292751, 572275469, 975971274, 342202851, 992690959, 905946592, 638617638, 408257906, 893433470, 431337672, 121443311, 204691644, 149215049, 892866387, 499657902, 492373627, 727366084, 817413606, 299830101, 179108792, 793021020, 79484774, 990787475, 806778126, 699771690, 932517360, 396801986, 450369033, 705688179, 601764213, 543650000, 6424246, 101576956, 943742352, 469876599, 789602165, 193861204, 867914166, 855513141, 892781606, 508623681, 94734653, 240839222, 291304372, 782860714, 535793730, 316197460, 437266536, 818734523, 513125053, 341667977, 865885326, 459199730, 800469722, 73959588, 663225978, 938116519, 676396111, 771293940, 134110004, 604210211, 814611864, 809471780, 227147526, 919603684, 718877548, 600688498, 323051501, 99437760, 64384379, 2816967, 818797618, 610590379, 994648835, 573954750, 747757867, 489374354, 906949624, 497465284, 110560861, 743002268, 736660912, 864764678, 239030637, 179921161, 597075825, 648263922, 240484009, 403859859, 323376783, 111561393, 880769415, 754737241, 541693235, 729100522, 440848994, 430876097, 397697044, 986305880, 445501633, 745929129, 961822196, 463370806, 372917087, 929787278, 281491080, 260370802, 723087218, 203568982, 809192786, 127668940, 274859962, 256763793, 907418526, 948574569, 41107521, 275421123, 545480185, 115078834, 811728405, 749430864, 145513085, 516184423, 569736173, 616298152, 237442955, 535206569, 84012508, 226442680, 581787161, 223916070, 714119636, 858533616, 271167651, 4042270, 94481030, 420969509, 860656802, 664057935, 659812836, 635967870, 287614655, 518672419, 860701661, 622898608, 182056539, 606693818, 67809863, 476866592, 641506810, 661823557, 359067162, 146840437, 191874073, 827990527, 830271114, 378743967, 31191003, 914176962, 315775261, 104161347, 925789335, 224846085, 16306171, 697520623, 235541913, 755939652, 575119707, 184347245, 477066085, 539678930, 263733613, 214865263, 441131133, 452288280, 370114451, 916699212, 234272754, 500356074, 969628307, 218075558, 98545440, 643801483, 607531433, 884942838, 741633511, 986510265, 130375579, 687291472, 631810103, 897452246, 935825379, 406107678, 693379832, 889192140, 713870969, 47764934, 14203958, 264162905, 113416437, 614265384, 801578131, 689265440, 512136511, 165983016, 867516514, 758347801, 165973614, 851022298, 934841098, 971138766, 748262675, 581017148, 515614911, 964208870, 75596826, 421017618, 877419449, 554331043, 6041091, 154592380, 506155288, 307883153, 356449276, 6535630, 257739329, 907268228, 14466877, 270547852, 536213606, 723009376, 840425344, 488682197, 742223034, 800330551, 174356028, 154378213, 622316126, 979186215, 648850528, 94387444, 686133908, 625519268, 762398627, 102140889, 568059492, 620235278, 491928965, 561673559, 360605999, 671102238, 418722227, 356698361, 103779373, 306452827, 549138165, 744392295, 209157177, 128661454, 871804462, 188569664, 660533177, 892220710, 596810020, 148592411, 3754514, 316034770, 20560543, 947406831, 493843234, 193634135, 909235904, 739551763, 585249718, 570121942, 974319094, 390024808, 440707295, 832643610, 589779072, 351021387, 285065444, 622379634, 348513382, 239138979, 854608786, 610483556, 461886344, 223078013, 667060284, 472047469, 369143238, 552604544, 953227416, 753771196, 906112849, 860856274, 945392706, 33882596, 83862744, 183911492, 223443659, 266067034, 116358593, 854540787, 736104931, 654803954, 962437282, 682620320, 927570489, 974199461, 284615995, 422644873, 264036756, 527010436, 437700425, 591045885, 374999916, 271141299, 985862755, 711574926, 235092695, 473603161, 246073051, 318396464, 109556329, 252181170, 702194073, 167019192, 827598551, 214212779, 310715990, 952925589, 4726638, 777323627, 548721054, 43937952, 77555877, 23197176, 702509849, 935704911, 41291480, 831748971, 782607941, 363771820, 42493086, 625937011, 757646463, 762987903, 760712817, 250714150, 807968145, 115306189, 654191463, 959235605, 835903789, 167983154, 226372221, 776566089, 354926907, 754460873, 861983428, 77609207, 498433013, 707799890, 594776649, 196556894, 987641522, 497048638, 210299664, 93306080, 387825204, 774785188, 13418717, 530053934, 390953369, 803341086, 652325163, 573077275, 858592443, 563662292, 714630726, 358240954, 535799588, 304481571, 8732306, 868825292, 24184804, 412359413, 934807688, 49450658, 607917679, 462915075, 254876942, 250798488, 321722147, 186292808, 541309452, 35174061, 580684064, 137540335, 325902144, 226778756, 16721881, 520790500, 366570474, 165305178, 612482620, 708345890, 616876972, 486274357, 547241994, 908001151, 331138316, 13070885, 834276235, 223425171, 302712516, 453124853, 425023397, 53772428, 687347885, 759698297, 368039765, 490631626, 864069432, 129160314, 435820388, 680426001, 622918434, 990189451, 514735834, 113433424, 776776197, 554903177, 606811700, 867504111, 578030693, 92234641, 876331154, 495618046, 836099579, 315390596, 814136318, 790979410, 367734233, 994349320, 155931726, 903915483, 915789794, 205187950, 408251066, 726357912, 986553652, 515194521, 328982210, 493238257, 966842950, 421201798, 343360246, 260868800, 861467931, 312550200, 566115317, 834519283, 982818460, 109175736, 931484992, 432447058, 787785257, 523430882, 754624921, 784910829, 603112137, 60091164, 24409092, 703374552, 387038681, 308924099, 995827343, 591667389, 624067836, 224403288, 461352397, 780121764, 571664199, 522426972, 718727579, 992251904, 927417935, 966468934, 35630164, 258145432, 687593880, 304267413, 476720395, 153727916, 614385079, 443500497, 195328563, 329908235, 575507858, 87306548, 69191111, 545785910, 719427743, 332659180, 104143172, 574185106, 432521543, 589289201, 346983013, 784975650, 977306953, 443647197, 736488970, 974196347, 621910393, 130505118, 457386687, 687845733, 960403839, 77941373, 539698579, 323557067, 607955778, 249405900, 847661386, 326846794, 675203421, 277577077, 105821950, 940639460, 185238887, 66943731, 468697164, 333982789, 357991571, 279395721, 965577713, 863569882, 668170092, 146540123, 775683723, 261651818, 20611132, 253479262, 792044647, 398394586, 637607110, 410155958, 890945808, 93808620, 669595703, 919245819, 821748594, 869992923, 225316481, 588237284, 302330692, 946466054, 908506773, 961196343, 697288631, 462521674, 609673323, 220027142, 429813288, 840038150, 29758874, 114003843, 294463447, 332158085, 241487655, 399090795, 641749459, 877165514, 322692024, 126384978, 473276434, 502013960, 830279367, 38957221, 477371946, 20295403, 933906472, 334353108, 515106110, 923794122, 804926653, 461569158, 665335539, 420492641, 350938721, 220783853, 188580028, 625009536, 749331299, 993307251, 321867145, 69596272, 609159675, 394950955, 858715040, 504439218, 369839699, 941284073, 726653957, 414147939, 655042450, 917439904, 34384972, 558078996, 902018355, 775816731, 64726439, 500430057, 402929644, 875959932, 449006196, 240688443, 175432462, 509477193, 871742037, 229789411, 382693190, 960082944, 725361449, 319776621, 120980614, 287310194, 5067101, 171372585, 435177443, 489600474, 297969797, 135540691, 14030012, 405565478, 93787511, 99780297, 872278009, 402995159, 152532224, 145155208, 526740197, 167435871, 482467931, 742641150, 721448707, 677934740, 88238242, 73143776, 244303828, 794853395, 96393106, 539154497, 109305054, 634077769, 871305437, 576705921, 506713104, 777787263, 430431946, 493222240, 645192245, 127246042, 926254644, 453695481, 21307457, 887416858, 398429320, 538076177, 635521041, 521331907, 433259290, 831083088, 951922033, 554251550, 48252836, 373431669, 524832557, 428767902, 95774561, 367580032, 372141051, 37625386, 944666805, 32695231, 278479846, 100155777, 916771938, 760775035, 323942667, 588544030, 361959722, 110859781, 868923159, 546364710, 496702882, 294948761, 219547227, 462897700, 175068209, 365621555, 539113378, 468459284, 125453188, 264188696, 875622787, 767019705, 166798383, 373436371, 272752673, 250191721, 630106440, 549612360, 756162688, 514658878, 479573915, 5396491, 89869587, 799385383, 874436356, 785617950, 399329906, 442469116, 166056671, 240417861, 353322898, 111041478, 685219987, 472330412, 691618513, 546732490, 195002352, 33917765, 519800116, 680476339, 934639627, 400741201, 831479667, 761752166, 493658492, 674279058, 483905566, 133217587, 288218124, 623703729, 731708684, 103934799, 122835630, 65492038, 897964432, 642209468, 338021613, 386119729, 366173475, 104816886, 142536619, 266892579, 449323027, 505757993, 743452223, 91876355, 979839634, 600491861, 318009491, 56098054, 82113135, 332451759, 117304766, 861934996, 700827182, 733462169, 690500226, 294953173, 670975862, 943911981, 884071098, 851114369, 693583070, 134849294, 52834516, 502528424, 16360854, 57312144, 492787651, 243163572, 968956246, 263249298, 248855234, 740573479, 705584315, 418701836, 641220684, 60461181, 464652279, 816095862, 647340092, 578741145, 207699998, 177825020, 758106985, 699679517, 62625373, 786768791, 294833528, 537288508, 997789880, 592450873, 912328263, 386647671, 68243136, 113755562, 213360128, 988906007, 476622382, 284100383, 884695656, 107202600, 334329163, 712710789, 5721133, 561593436, 542378301, 449464653, 186715120, 647975842, 542461762, 278922648, 538688717, 848479961, 681036788, 398527666, 591633135, 687239787, 324013411, 447559622, 855331527, 381498049, 383602799, 675833258, 681136174, 739723370, 126453525, 84846501, 555206920, 890066272, 784115846, 758977820, 929370292, 678550210, 585240687, 548826291, 887365968, 850275275, 553474023, 878077692, 496616841, 21238655, 685909557, 836543949, 888665160, 788623913, 468007734, 342733508, 31839138, 954653660, 938327871, 330977903, 649448930, 206160253, 519662079, 44836845, 908116069, 295036984, 560588283, 953074082, 990879843, 804721271, 853215736, 80983060, 971628893, 996197528, 930362863, 326848267, 342691997, 624403777, 806106773, 390445569, 712400125, 962320978, 710081694, 980746037, 837538283, 528510344, 980782284, 907294789, 725597885, 674971011, 345653260, 958234955, 669303985, 838529764, 596782581, 637851742, 579222382, 439099775, 743834949, 390334071, 101077838, 177166227, 541393130, 786904625, 851826866, 429447119, 850713780, 508157162, 320578422, 109901875, 121508860, 354241569, 856305224, 954337533, 284230692, 213023583, 13179175, 311374933, 112559601, 803340142, 314138992, 399646312, 344724011, 932810846, 604835087, 960375293, 229521824, 695971102, 90007805, 47305658, 125455039, 469820649, 991107498, 786327773, 765024873, 475462827, 407792961, 860316947, 892324559, 393411616, 824630196, 31754524, 656395595, 766521622, 416245172, 297815562, 324104412, 281980812, 407213547, 779421052, 14283795, 594967306, 645937215, 800921720, 490273964, 531235250, 79269340, 378372802, 947328257, 428594596, 41132142, 713447636, 775581231, 7928531, 223609212, 104565727, 403197673, 528458650, 511211356, 121526139, 786964662, 890127319, 194819022, 332307486, 623576925, 216995427, 653528663, 794988033, 47796438, 644488788, 490965901, 301907169, 776095606, 305954029, 459495336, 433332325, 699388655, 181828170, 797752440, 208403307, 453495778, 655596114, 164276342, 544366313, 34982778, 177016299, 49738626, 192627426, 273035515, 769296134, 461200357, 496733328, 63810806, 850344536, 467748672, 164181941, 324013949, 369345595, 611258717, 246810704, 628325856, 971178433, 725444070, 372962967, 754029337, 207618736, 80290824, 519918822, 405186236, 850275737, 541787476, 106022865, 288955645, 737855520, 219207265, 816541954, 371287592, 998066125, 324951154, 151192805, 977002220, 805857770, 221614870, 995695397, 400086055, 300066691, 698539252, 779524256, 512988952, 798717810, 762613069, 842891710, 645029919, 826025466, 141027697, 450887581, 348952704, 161520122, 910761108, 384655067, 9420354, 349632911, 349304030, 916601635, 480919587, 582784459, 741909039, 354493410, 175058175, 320390776, 373497865, 546197423, 617142083, 808273815, 180994996, 8607604, 349248080, 738530212, 8155403, 649892079, 696924653, 384673198, 252228719, 119650547, 109827105, 323071468, 640185016, 879407044, 820978459, 604488077, 449179491, 972979430, 627258775, 390395294, 116606663, 261660798, 231383849, 364728628, 410477331, 18694060, 469158758, 946564039, 741511748, 191759771, 592132798, 529871187, 164061384, 595663587, 432501385, 575950847, 16305304, 167027998, 604878417, 120081633, 733708714, 607373174, 800769350, 587895190, 141518143, 409001187, 39620132, 991333991, 215957156, 428457343, 456293819, 896607335, 851784297, 545943881, 812884020, 130780961, 182574199, 170497183, 105536007, 490660773, 712034024, 240427542, 993782686, 243365278, 537210527, 683211691, 368189501, 448592766, 151916025, 996552569, 710817492, 835806004, 625652629, 855011719, 298255246, 306279850, 946292279, 468253373, 452914965, 638427085, 675512764, 834150145, 446340277, 925291426, 595461975, 697639447, 243238220, 623296120, 888819540, 945419667, 233825000, 750388347, 36862168, 18705703, 53627754, 653471025, 970493302, 122915108, 998501534, 934896189, 673893159, 61538250, 841442279, 503277093, 731403634, 914712325, 823297264, 731744789, 121655016, 598579264, 812431245, 595480469, 964929748, 874349349, 788996874, 113169064, 234051904, 494185742, 499583008, 910830193, 169861842, 5580149, 542634567, 73355300, 370109623, 161667857, 68285663, 771278141, 65758020, 614440259, 104233687, 670706155, 674476265, 871217407, 650566005, 955841537, 717239892, 172644282, 692204954, 350890100, 112323735, 702656494, 384378591, 93901271, 527387036, 210734100, 128906566, 778410300, 694938569, 388708274, 553249134, 577042493, 339771264, 854016710, 350210250, 441777881, 108476529, 297734309, 869309541, 970386946, 206359008, 684112537, 179400915, 477168339, 122556433, 576136939, 456937702, 87195148, 777967308, 852461237, 870223392, 377632432, 255062797, 322801523, 306365542, 657382807, 917471015, 738576708, 882572837, 778323380, 392919571, 4388405, 923808061, 688564499, 266372053, 328668167, 495597572, 445151189, 930197370, 398529015, 343353937, 989923413, 182707922, 119648236, 757250487, 555378946, 400097672, 142584392, 306476650, 771964069, 103017667, 697641658, 961296288, 108616446, 931164431, 545453496, 642124737, 446329493, 174333618, 264739823, 574656196, 254748603, 453478944, 551543864, 539915878, 740184805, 836144113, 727003768, 778186195, 408435120, 512557828, 50209942, 150507308, 269058513, 413828428, 443753163, 491666766, 235799441, 470330580, 398251677, 792578237, 504553404, 326517186, 145779368, 138220083, 750001028, 848772409, 584350291, 455949556, 529041581, 888966409, 510123966, 939342165, 300599501, 533907386, 434199938, 77017833, 183335924, 46423154, 579885465, 726604079, 88176808, 726393388, 522092237, 851051056, 633240540, 959157815, 764321349, 816796895, 718123778, 103623410, 923590079, 986726207, 865364515, 176209932, 870874282, 285234349, 786888050, 631011037, 794644959, 127616434, 628753812, 326689512, 391861019, 266476688, 425284194, 310320054, 365276690, 832512778, 272579385, 666318960, 692666811, 417266775, 714949503, 395220865, 582555783, 371326036, 412999889, 12797336, 614400782, 782565981, 837405760, 718983537, 970964658, 688429869, 596863787, 209320805, 648082550, 309217138, 374760852, 229106283, 457991863, 252842399, 806012760, 609119203, 216298470, 117326167, 450993599, 589734678, 822872900, 603827614, 295000840, 267457644, 190590182, 358248677, 85704281, 550388924, 313708868, 706699969, 891771042, 297010434, 211756128, 602778525, 649917558, 100318827, 997444254, 73885570, 109560645, 72349071, 391291230, 954877646, 812101063, 988284561, 816904768, 239095414, 687170473, 161790494, 153751771, 95112830, 989789643, 55152966, 267610723, 664053343, 77620996, 447750226, 623593943, 580211656, 219793525, 937588256, 937376737, 80401895, 123836140, 458259436, 889825956, 323007010, 39593098, 558903168, 218190453, 544930652, 909269793, 990848500, 999266367, 444632886, 978049396, 633306405, 888852887, 609236272, 73797137, 243081456, 139790594, 825610108, 357078403, 937525163, 110544625, 1963515, 344980894, 801485139, 265605803, 633753879, 967238789, 930542141, 665477404, 668398232, 150068730, 63377946, 757423735, 92057005, 640235696, 978633583, 16695681, 633302134, 377622426, 56607636, 215789155, 631052861, 619564315, 571896996, 569130252, 519673776, 708899967, 730019005, 518960074, 680742433, 787322058, 210913412, 701705279, 188049229, 520697688, 526314212, 345205093, 478655146, 890806169, 570460223, 73732670, 763763848, 425104806, 132198947, 394860222, 897050431, 123922343, 644358393, 282836464, 6787337, 149469662, 288157611, 118742586, 895523326, 34977774, 701292443, 567767556, 60809304, 449231530, 966132706, 622079453, 671633668, 790568837, 608639355, 505790516, 328831094, 515708723, 501809651, 777746043, 573140283, 832706707, 64315717, 410263714, 231849239, 667012714, 366190683, 532685052, 217306240, 451093032, 938794055, 834915243, 629130721, 192229270, 19929555, 611932761, 706702796, 581182902, 416846235, 298848664, 314667347, 704365626, 375887438, 257613225, 700747963, 12907591, 271556007, 456061951, 188071763, 662467260, 853761008, 21843681, 570050616, 785116776, 418234884, 813457569, 704434802, 942938963, 404210160, 266064799, 552484806, 310604547, 959314780, 887747792, 597129453, 608542879, 457621515, 301503355, 851191628, 646714519, 199778537, 49232998, 821109930, 547093999, 130731574, 496002124, 867301642, 170140023, 36894773, 935433871, 131823793, 800415731, 394271547, 119337137, 169287775, 638659211, 344233677, 621556947, 373101626, 697029387, 706272561, 214209751, 553211241, 816283082, 838430850, 323618701, 378294627, 878204186, 136213631, 756437975, 10030867, 662809938, 486446805, 258163671, 145660030, 334079405, 164350938, 351198672, 578580203, 911586789, 819815658, 802811963, 780417361, 688954473, 254419384, 945543358, 466432832, 476059592, 401117953, 952034549, 438454987, 206448094, 536771538, 391289044, 421928588, 97386295, 269183665, 276872938, 57017053, 122346162, 499536838, 108035871, 850691505, 459594115, 190659327, 934867266, 895605262, 747882028, 976134913, 489432750, 19979672, 186178046, 864128916, 479308713, 997551816, 490314502, 394117105, 521735837, 80001909, 158055864, 715184076, 445594579, 255252085, 617574862, 266367410, 540237680, 365395191, 868096395, 725755899, 786798450, 607218427, 727313888, 795270437, 43666355, 738817640, 843193789, 3855641, 875892560, 906031468, 423852505, 561444116, 885366144, 637375313, 784022131, 431465216, 840470185, 757507789, 505946801, 603180842, 797577035, 75736629, 600863269, 263655567, 748263372, 372964916, 363942807, 67237114, 157615862, 940315123, 886165032, 945844114, 969227530, 435471593, 565365316, 415981165, 816953806, 482194506, 237729488, 103621657, 273332309, 991352818, 369088776, 507982743, 517232309, 169547753, 109605442, 607311939, 662451241, 981624868, 351881175, 570450143, 879322885, 191434429, 41541665, 621571000, 444948997, 303444187, 881385623, 224451741, 556549635, 834025802, 620406248, 805263951, 889882299, 200091216, 386306780, 596403745, 673086586, 248921133, 760478472, 941717602, 969905424, 615057398, 291244774, 376249779, 587751007, 228696885, 136867342, 1585020, 462165029, 372238702, 48379001, 140350376, 902763860, 415357215, 609850353, 623699740, 804637234, 955043288, 168325549, 157152206, 934241452, 424143497, 604222635, 685584701, 97652302, 213740193, 997385625, 931562678, 464315734, 234546914, 31193975, 459725342, 834772464, 768639306, 325470264, 287033120, 767025591, 466040188, 621371773, 734334004, 259378947, 249288583, 496074217, 118646336, 241353019, 759094260, 871391512, 68302390, 329651204, 715048383, 801169861, 759932159, 987372295, 753305789, 515375778, 860241269, 292411788, 843895448, 678979362, 767055237, 639906860, 500935637, 799703001, 793513813, 827504534, 487843353, 140388097, 665734430, 489336705, 247569322, 45538993, 61877557, 31209665, 746507266, 648919838, 270820409, 709657910, 78021551, 600462872, 996765182, 213074643, 78316925, 509669621, 285845025, 305080935, 21105642, 282327959, 126164052, 146090653, 418032050, 404825977, 924641878, 462149007, 952896477, 196483221, 856816748, 283929902, 1516215, 674465379, 311447677, 545918238, 34773313, 421180306, 568513514, 259678749, 882055911, 351143747, 154342584, 521080914, 52670044, 389106466, 104110431, 501093110, 749856674, 176447224, 369773443, 168451090, 633178350, 657069199, 213086681, 305442444, 828951056, 552444071, 379643992, 543306794, 871251049, 934945290, 401425740, 791802643, 543247214, 907518613, 881824060, 66811262, 834977315, 102783753, 293844698, 48882882, 878870515, 886834372, 16477939, 741586698, 731546034, 31053940, 583923068, 173528319, 900111517, 44833533, 650103216, 690231897, 659561851, 675456659, 637629373, 58601887, 866058599, 941643688, 531285078, 628962717, 665869410, 271637258, 77262218, 447477542, 296754121, 31550603, 93052729, 968483213, 354851620, 98289420, 929821755, 723659852, 952833474, 682126513, 176779339, 264779266, 109090700, 68604748, 995713649, 750063767, 6248766, 630549776, 976832508, 771049713, 59370986, 684290810, 263777676, 847595307, 218493119, 884584336, 876355911, 487038164, 10519257, 272114834, 859300593, 729451159, 148990950, 340308953, 878343722, 362321660, 15059284, 979363865, 904662327, 544974960, 447745154, 920693160, 541210131, 400601320, 947399495, 303521471, 867283266, 537761309, 886498098, 66792780, 817536556, 357545509, 569380644, 697237890, 6430988, 726195602, 948731695, 578383086, 448964404, 98252737, 883691946, 515916223, 764895435, 397406468, 315395718, 792610327, 53032961, 890807851, 248489597, 582619860, 149957178, 504937111, 533316750, 709508456, 517327713, 311307769, 806344616, 511001473, 33253134, 213444512, 443025517, 886349916, 3950242, 275960024, 542527597, 296354828, 881225963, 196368562, 994278887, 505745253, 668371597, 32740815, 910120240, 186290884, 27191639, 398305913, 306124041, 712985909, 251568607, 943345462, 188481326, 737560598, 427206500, 558073562, 656899218, 968967012, 507732437, 806275434, 907450519, 963054362, 421579730, 216167780, 984693485, 227136138, 846411434, 464971132, 909847238, 349908631, 418368278, 985353437, 835430961, 235573632, 972461489, 61586685, 830050754, 356602647, 185628894, 528850919, 801088969, 898692300, 840238087, 872767767, 358849837, 10312725, 87705803, 16089524, 405446320, 237098642, 240918170, 962640655, 838462734, 298490697, 960252475, 74576729, 30621779, 318731416, 215157369, 73601511, 818063216, 609369428, 79521655, 89005372, 992739253, 549315747, 16691200, 673049680, 463881099, 784352655, 374398365, 982973189, 881992318, 537144841, 521739144, 788863986, 887661285, 866066490, 719232945, 636585032, 906706451, 700091507, 21311601, 686995241, 346593395, 229245196, 978839166, 911116260, 403404294, 15539342, 370228000, 434493547, 415425628, 65937773, 667662900, 128306652, 279558422, 843440107, 875833241, 105488455, 933282610, 987976883, 530271319, 896763797, 577942472, 512128389, 964029019, 547308606, 157098941, 829497681, 142226110, 841368434, 654418970, 169406108, 869105036, 23985130, 445108720, 366027253, 587320508, 206040925, 951616554, 770610544, 244753842, 172909125, 278071193, 568208468, 720977332, 317730835, 269146394, 831352372, 322918854, 387151563, 828918342, 759689322, 361458956, 717057024, 675876134, 726301876, 818813598, 842922121, 331708599, 934834555, 973154188, 688558813, 961336196, 793607995, 690294627, 774947818, 190782745, 966661827, 676495895, 668374574, 508463246, 741743470, 37772701, 854095076, 278101234, 35339627, 67723500, 838619827, 65644075, 209177043, 603335759, 601935848, 317279949, 318176380, 978809745, 643181058, 806484683, 688005310, 957155977, 682916128, 247569630, 33528840, 247562713, 133155632, 680747333, 81800994, 993224915, 866792557, 732424531, 879834088, 418701096, 366030885, 154012993, 791290422, 888853771, 680110921, 671259756, 488559650, 995799391, 583285225, 178632521, 725781975, 923195949, 77191037, 483317466, 64710983, 671280045, 526390859, 801651965, 861253148, 447437216, 112453288, 970539449, 11091560, 125487665, 78865477, 382693410, 414317539, 544070053, 835539742, 745717664, 367254463, 217542497, 450494614, 423151351, 260999018, 738688913, 468744239, 506103664, 303296248, 248242068, 286516065, 792933694, 343408791, 758275986, 593709124, 441881083, 652686041, 527791535, 86577944, 932952190, 35033072, 266290707, 926946893, 911117165, 386588861, 758259811, 768318056, 352048865, 5968275, 389723645, 857594267, 309132558, 316446, 683406492, 277510544, 63254156, 922629133, 473259245, 351091031, 607419144, 197091998, 924010963, 903178968, 964246812, 193542768, 603736379, 865010601, 525899181, 217875276, 352694545, 732324655, 811195720, 111172386, 320368487, 44388975, 991572212, 807778237, 931124202, 172193611, 786015789, 612905103, 472889868, 855712339, 611821882, 299348009, 142031957, 448301128, 243836373, 59460965, 98667555, 628307562, 860322747, 437546796, 696162389, 549448007, 246607830, 666004172, 26184241, 388719153, 360658423, 556154820, 164584801, 334182397, 882561509, 802404595, 463072014, 253600193, 743281117, 179126558, 907932425, 167076885, 582863150, 706432721, 955652140, 158838067, 624284327, 230599416, 89120126, 976403968, 183357487, 840879443, 398669101, 969060745, 629586293, 712723158, 773835631, 200745077, 610618332, 126167937, 313096223, 311371036, 132363216, 395947215, 976039364, 517093952, 747561825, 335329539, 187195875, 719486860, 420967446, 523437130, 448794709, 144463656, 111356572, 343933756, 162543889, 896792388, 517355829, 551500655, 251865942, 26412644, 326631039, 861402787, 243627309, 96273480, 950959909, 200462120, 452893312, 727004645, 634833706, 957701325, 114825293, 527842570, 444165155, 678268906, 195646584, 280726673, 827205443, 438062974, 546572739, 706737172, 191322400, 529210675, 528466554, 951537572, 170064423, 161349103, 525321844, 529986008, 7652947, 200443478, 339948306, 310513595, 287611458, 736335629, 839687432, 210543828, 134541888, 249728509, 111573170, 501776232, 256295319, 5714647, 325361898, 148670655, 740372069, 639072250, 742036839, 565794056, 55932014, 237340597, 732238349, 162578468, 144190322, 232753935, 867280104, 480679794, 667361070, 869063628, 384058524, 141364108, 738825342, 167002148, 689089794, 206430067, 526807957, 771132923, 595034022, 487731342, 72226691, 845526251, 906857460, 932708275, 59366528, 861626174, 346949363, 730878568, 415923499, 135894551, 900083102, 994877044, 326528618, 258121761, 445363367, 640968303, 582160297, 113201285, 375124488, 635276384, 925402630, 476072753, 389270226, 26572881, 991240928, 190935539, 557853273, 609853699, 200278434, 99042867, 943180380, 975629659, 847302938, 128625707, 979002987, 814040054, 267518871, 696724065, 460852257, 126768962, 888949413, 571979255, 173147819, 611649473, 31798288, 59899882, 789193870, 635849130, 945537888, 908060638, 757367326, 227655956, 767195963, 119151661, 238486235, 770062028, 401344807, 309416079, 600186665, 743244035, 519946942, 574727929, 624048098, 710449799, 822957149, 486091796, 196741095, 353506780, 907549862, 723350151, 966583892, 120740588, 743932030, 241336581, 50342824, 389205014, 994730479, 847349104, 428932544, 154858655, 716769821, 573248971, 708494606, 906947076, 953507585, 221099730, 954658142, 443042710, 164050165, 659286725, 691040679, 325082194, 943211903, 385369826, 952858699, 551740289, 724210108, 27061624, 414749766, 587778036, 100009214, 185771943, 206035920, 372861546, 725238447, 204229587, 361259606, 103494136, 23806133, 453866068, 193534313, 786382458, 530642257, 292047524, 946890387, 546425778, 682588873, 571704548, 139435506, 895885106, 225611324, 127179545, 410991195, 135399215, 814343991, 597717970, 276063606, 821677542, 133210900, 214494528, 596024143, 928344559, 179684060, 70886497, 94572256, 831417213, 649683065, 399445753, 985552692, 88587374, 448501028, 223819895, 121696432, 23009327, 658919305, 6607158, 142402894, 235884672, 154286675, 754349524, 302291928, 969551435, 23560113, 947175952, 283029741, 777078214, 635343846, 483485267, 276738191, 177516224, 640880122, 121343294, 770515926, 461861317, 282148396, 403719083, 996808690, 437152661, 88317957, 22719655, 547329889, 744999561, 511727992, 806264073, 552305635, 192357908, 77072147, 16811109, 734673401, 712355975, 691145232, 822284735, 407191543, 1614887, 237366654, 614130200, 798763753, 792557016, 979025990, 684224371, 194779995, 870454018, 329587682, 582479787, 714258452, 813778860, 230595316, 875271994, 42063687, 236280793, 239780357, 604242007, 466683549, 246935943, 435686306, 200777038, 239647977, 107782825, 286050988, 144015799, 895780408, 855700180, 138108923, 277526364, 906802374, 550813685, 609731705, 341880839, 303070081, 942816550, 543643317, 833616433, 328629205, 940382561, 71327138, 964663201, 838771009, 757052437, 116313449, 657762439, 909072087, 908597543, 923846504, 172087493, 606962879, 548583532, 347203674, 626159904, 927911118, 704428002, 56019661, 530823845, 162734156, 264054496, 61338104, 354510280, 967795820, 326896904, 928297193, 444239521, 871522327, 250963888, 56190194, 773773770, 236616722, 859631687, 658603907, 714352154, 640729474, 711405419, 169005491, 230838885, 400583000, 627694817, 487834623, 678094106, 440394278, 847453522, 101405343, 424418635, 749073271, 942643312, 728120382, 865147324, 148260194, 347709795, 324769842, 427547775, 148489024, 225526710, 456808423, 755070835, 571646501, 736747299, 346446018, 136330148, 494808691, 703321835, 363344933, 819064608, 348952600, 521189260, 198548808, 761440327, 54382935, 480021444, 959487218, 710555407, 740223112, 499890133, 724460651, 213279865, 993310494, 702929217, 596357138, 162754343, 984629393, 121447832, 36631443, 80823078, 666279692, 799159504, 511751136, 467053976, 260643449, 257361400, 114194615, 300304658, 922682177, 234002608, 536859246, 827846495, 786023110, 377652523, 263781853, 179942014, 307767573, 312204919, 940092730, 913135921, 159666212, 335423659, 800531266, 611551333, 218194946, 294329759, 10280475, 996715858, 394306742, 369057206, 441041395, 435317494, 545297782, 380858217, 299854297, 47840683, 925396647, 760964535, 259036072, 435628122, 9318359, 457648051, 874689320, 617191308, 539098945, 888393297, 349135585, 421125754, 467217872, 987869568, 290979109, 282392721, 631544683, 529191460, 128290110, 694485407, 526491198, 507342555, 449386791, 998604853, 305087180, 252156890, 936380785, 747374308, 16286458, 655606511, 312348998, 410254269, 563145592, 144527816, 776666853, 273489555, 111909669, 979643862, 102538113, 595323710, 481874376, 105184111, 327389075, 723910250, 69401519, 25900893, 420522198, 349507597, 609844755, 638991118, 257026421, 413116143, 484053020, 774726046, 807290132, 313621325, 226184044, 409077828, 334564716, 162450951, 469124519, 974618176, 533446805, 877951999, 813329676, 944678778, 717188644, 936079494, 97394031, 293980044, 705953199, 846297003, 469999655, 76329064, 669218608, 881809867, 775284846, 414924683, 812086975, 141592855, 362340612, 566175027, 497679073, 452324785, 572924373, 273612755, 883931904, 608209549, 168639237, 123799553, 242666274, 568393394, 234362870, 717103554, 835796977, 537931616, 178278294, 529671837, 742629097, 710083942, 327704428, 789762468, 890344619, 819217235, 30722847, 949429838, 796072579, 843608836, 677718923, 303906499, 953025991, 757153128, 853490416, 417538854, 629647652, 271226916, 936800415, 908895746, 766819711, 632731541, 1892620, 287380753, 433978167, 202536764, 566783211, 380751231, 39175573, 257654298, 833790375, 388123765, 964370966, 400146820, 279273369, 799640862, 602464399, 292182576, 888669439, 375852742, 521695857, 468235429, 207358058, 112171963, 768970206, 827700564, 979396619, 968594233, 663447214, 968133272, 402397608, 984691863, 313968004, 443139898, 747407456, 510428994, 301282446, 854323064, 134586183, 290446180, 140194651, 692061244, 347745650, 403070835, 566038621, 263190911, 824914155, 420021323, 575097465, 163325818, 198736710, 951014786, 725526977, 822819846, 243984494, 219056257, 274757169, 318942226, 143446995, 644497608, 796330834, 756916743, 798445574, 595842731, 556945124, 733231325, 598841267, 564086656, 658268190, 747422276, 465975796, 995991824, 196465974, 859199777, 528013341, 240003311, 694061827, 871005392, 916864394, 191112993, 439543955, 304633878, 403503700, 604525481, 21360106, 668904968, 27274988, 675011627, 139091523, 921595939, 442971159, 771967693, 684139434, 157668910, 386057295, 232920242, 671774393, 943080816, 991510625, 837052663, 548171570, 292007619, 358152472, 499845915, 620359834, 509046409, 438658700, 395086605, 220513161, 543779273, 337422880, 968257579, 678307449, 740734863, 173994243, 954979636, 154554925, 995664028, 182424907, 506451559, 596206282, 76926290, 495093028, 968105799, 820597058, 283032771, 85225655, 108930197, 922041280, 621220546, 151108127, 144234332, 534236490, 854509687, 70123582, 453644994, 979444090, 262562680, 495185864, 229519022, 76597089, 791134248, 834087650, 445913080, 465613009, 915047715, 213903210, 895786509, 975262075, 81020612, 434289057, 928186179, 102454553, 596477775, 426176342, 115923022, 850964463, 674884101, 969565704, 490979214, 572552029, 828424226, 331031216, 684216921, 367151547, 34395541, 486376772, 868705685, 316920679, 511797680, 759512501, 702132200, 21782046, 496743429, 766536116, 507816075, 793954695, 31716303, 531195812, 399956284, 307779266, 814904431, 325904664, 930288013, 464023681, 592803438, 136661761, 251777647, 763987122, 116967067, 32195446, 568004645, 291964493, 128785421, 216075226, 859981678, 959787065, 362866162, 634052227, 21185688, 372128741, 84691095, 996614217, 960363211, 413230263, 324834293, 137476891, 182517397, 253938684, 744058636, 839206499, 587170376, 890388033, 612115615, 779647051, 144920552, 661183386, 46105477, 199398523, 126655110, 963170718, 656893858, 441353425, 684930139, 547876360, 158905, 698626522, 346609563, 27981364, 574102811, 441500490, 552396699, 252501058, 953741451, 221121610, 866281343, 203097669, 865656256, 599532286, 679841315, 952103958, 275622919, 599816702, 297049582, 621952449, 229316019, 839945945, 972354149, 914390668, 564655975, 236113520, 187208675, 978737794, 225222530, 513569133, 838365928, 881729719, 970785509, 368858763, 819087815, 929749153, 483322352, 517932450, 233559928, 263312815, 22978158, 355690553, 778877836, 936799384, 890816849, 140010172, 888203235, 736020544, 870235857, 351225948, 728532062, 283482452, 964361230, 372584606, 538187448, 752032542, 687869736, 802893516, 812838457, 13417346, 316760566, 109610894, 72128527, 4840279, 396369825, 667379957, 207053282, 697967514, 457587081, 907485850, 499273681, 445567852, 129533655, 27466177, 280656420, 588952668, 374115844, 161828227, 268276269, 105260569, 737868670, 644577184, 858909494, 31911312, 668701642, 841091762, 17708331, 433928564, 665611896, 174634219, 23106475, 465415797, 229296313, 292514542, 85373874, 810125266, 845249199, 246244523, 817951932, 586951386, 397648508, 77486040, 572745055, 446041441, 902493319, 419644633, 870268944, 198066945, 706043622, 74588927, 587889495, 147972707, 229169712, 581673978, 432135355, 850441787, 191348783, 449492821, 180150647, 924881852, 144698017, 661742270, 841705818, 396981347, 689381797, 776566663, 954998811, 582761194, 701735129, 99219420, 496918939, 508288088, 386318431, 195127096, 90198647, 314105750, 113208370, 131509327, 373340658, 817423393, 133919868, 755180193, 569166670, 775539429, 851096824, 482915984, 666385163, 495105089, 226794771, 490563589, 76115625, 8883989, 434067525, 66558067, 307870331, 210404050, 920795979, 420418583, 632321568, 530362138, 372506574, 679457705, 552832499, 45226917, 995998298, 659023983, 243381718, 736833674, 562842487, 197584414, 429209136, 460665018, 215576745, 505993136, 163993880, 835770675, 839717017, 669378308, 146792915, 264557834, 732912335, 588422828, 888804579, 297286304, 29972326, 583248230, 269470868, 220909591, 590376413, 940815575, 909670409, 799105473, 666533026, 50157067, 151375690, 906684910, 305483782, 917830948, 243964080, 892754951, 434909498, 143306197, 479719451, 90832822, 194781413, 623043754, 336307744, 174312238, 336253789, 759629886, 638454792, 325565507, 261814314, 693500730, 54716070, 241258921, 131187466, 538725789, 336550264, 580058271, 209457723, 801895638, 526126932, 550017166, 273325591, 855316270, 482366052, 665665863, 276647701, 946674979, 435372385, 364750682, 228822623, 396439515, 100427476, 424316370, 787070883, 73904359, 971799036, 564626782, 915696841, 790203540, 696918800, 394326616, 815732458, 730091287, 222334009, 166259364, 352223157, 941698622, 269888631, 472717014, 621284272, 157871192, 938053698, 427200904, 904959489, 297487945, 723780210, 983417012, 699236586, 550327808, 556872920, 472213753, 977612602, 694359569, 154536031, 957427732, 490662015, 261089974, 487238161, 393864277, 787119381, 184561525, 84367990, 878332739, 879785846, 470979374, 968739962, 613854669, 220356263, 195682041, 534834529, 231746624, 309349494, 23894170, 727827597, 579496458, 442219632, 187740, 732354195, 616830866, 264528847, 187023267, 972864336, 495888442, 497125668, 47794109, 208897096, 100392629, 635092670, 383419324, 463845485, 278562302, 991372028, 332957423, 96651796, 656420552, 964223818, 35771433, 123149498, 228282047, 759116291, 858929586, 639725777, 820052716, 825320131, 502349163, 133923764, 813748228, 315444108, 661731900, 643756456, 690065629, 910043017, 265838913, 63758003, 803808118, 864914163, 114631325, 133086894, 356454000, 69988307, 241714886, 522491068, 386434381, 55763119, 103727757, 917893310, 81524838, 526712879, 193740022, 123975318, 559281462, 75590425, 333126172, 481019243, 186426676, 593994035, 225758446, 439588671, 32112872, 378728443, 91365226, 282487305, 229917835, 826498746, 881685297, 307741458, 173884910, 640624687, 219477721, 600917425, 866440523, 291841179, 634373983, 27442405, 71249426, 553708258, 613900025, 316145012, 651004939, 131358481, 937155100, 322969785, 58384292, 263158339, 531431384, 345035443, 202112992, 832914571, 807358126, 177165069, 832957194, 986910306, 59456900, 244740590, 667123224, 424887886, 113482451, 179765110, 860178639, 372250754, 229611095, 605882494, 656317386, 151303116, 756995494, 870859613, 763876147, 269938522, 307621164, 471117632, 360650934, 214611668, 226482732, 567897285, 63345534, 844229523, 202776159, 649545566, 676482544, 377851299, 748777169, 821246865, 393644394, 933265659, 485037844, 173722412, 616767109, 139497429, 450065701, 338086945, 934199080, 913760661, 14433035, 701077263, 455898488, 957604961, 140522244, 811022995, 856996116, 865099790, 709592100, 393629128, 364693270, 905149788, 196797857, 405669273, 969138926, 245218054, 835136883, 724743101, 265125478, 675449462, 61872795, 556918069, 974590342, 830304978, 698487046, 312526867, 388205891, 734520323, 839139611, 718976431, 834170337, 920920336, 967075233, 702345758, 77436243, 643775069, 885253056, 536353221, 711617081, 427772504, 781604665, 292657831, 964242738, 845465770, 623340138, 70760128, 734528810, 64166766, 943954866, 690755152, 365421437, 891556585, 940747755, 589367343, 295745545, 369693098, 703232606, 872997542, 821558493, 858123354, 211020882, 990604794, 688914515, 733896893, 515351596, 592869613, 2405117, 323023512, 167506287, 868109190, 195666393, 635510488, 421369318, 737859370, 892507909, 527321298, 64972594, 609891649, 988156614, 137909716, 119064581, 419951721, 740381161, 998602896, 281530563, 847607595, 368909551, 320583220, 726512051, 225255808, 73481240, 490846455, 797144294, 529105263, 89305411, 792199098, 111843154, 581574634, 749577565, 304747342, 408277115, 357145124, 114004884, 76730812, 796982054, 745437600, 528624509, 518234903, 165426190, 330010985, 260705031, 185379829, 142583846, 837090307, 605035018, 540196944, 524292146, 247913690, 234360293, 505485598, 983515861, 228188232, 790676679, 335219939, 644241988, 297163, 448698850, 499525201, 976191209, 321484534, 527181161, 232992268, 231978073, 291222666, 222688810, 22920577, 140971131, 438719909, 645897115, 531981304, 385421689, 224957647, 517324423, 824291620, 949784319, 368693066, 438311042, 663362255, 99685848, 446024943, 512678467, 30174645, 421466294, 411030046, 43009129, 854868509, 180948899, 223438951, 107683810, 86189238, 892639228, 531078427, 373779856, 4365716, 686420388, 96784711, 528409452, 82338264, 540568341, 697759606, 513975022, 946601475, 879325869, 523710898, 476588997, 503682654, 937480602, 890484331, 679089787, 202046090, 79923457, 586276921, 357815656, 661614388, 582434081, 225744934, 619807780, 394620102, 66295075, 374834604, 703984967, 608625890, 427360429, 866395769, 954812242, 552276694, 830477440, 729779280, 634132253, 288705843, 966474648, 222530951, 443078722, 498810527, 208527717, 327938791, 890831427, 46479945, 665484128, 477969504, 49496094, 148630265, 521987361, 114877623, 222534003, 805487264, 273227317, 377952290, 284087131, 996068885, 361980484, 460128667, 500639034, 638990910, 685465212, 916496762, 921973425, 694160138, 653694304, 530414123, 119327506, 918491677, 258699091, 498185140, 395157347, 38568977, 105593445, 181121520, 471624249, 514528223, 318748966, 824282766, 85598954, 94697813, 875277489, 833868061, 932387625, 841921180, 773690515, 358585786, 707724060, 916378145, 515550294, 1493696, 286811871, 120578641, 183159325, 526744706, 571356459, 160209938, 665424538, 223623057, 819543072, 257904770, 13605566, 66759590, 852968545, 726808529, 432423776, 739327348, 559757686, 572802230, 18392611, 83012372, 247237893, 804346267, 582028920, 512440966, 950239955, 11475306, 743259819, 166734700, 807958330, 636885074, 122580116, 534645013, 129653693, 34273531, 174685566, 562968875, 587763020, 122353778, 145513399, 925555309, 119966936, 235383508, 745997554, 423478118, 311851226, 440131586, 820599844, 576649988, 363158948, 206274914, 729775905, 103476304, 907557544, 145668634, 565606238, 746219111, 563744522, 810511458, 979190213, 919014956, 124646898, 492932213, 12714067, 972206215, 223710159, 40860685, 380550405, 609306582, 127233435, 546294339, 634445113, 25163382, 755855587, 779771099, 168181090, 562635567, 252139729, 488057304, 989636666, 345793711, 230362952, 802246609, 700541390, 964708886, 401731712, 351777784, 383465265, 102739027, 87229067, 911838970, 763513963, 247635501, 948592242, 607325378, 792300641, 446199191, 144808541, 695932770, 487459216, 787430326, 623340757, 894659726, 708731128, 483719880, 956502573, 144395223, 929576716, 885850002, 975852729, 448707865, 509013330, 292983280, 183928524, 332042492, 215118825, 753889820, 15938710, 100879573, 360365510, 288016894, 857058842, 864890412, 36910606, 366920479, 417426487, 634456834, 188594508, 916222579, 768497989, 606831283, 828017078, 737007121, 845993646, 210782426, 961621524, 844049867, 278605578, 84637449, 124674351, 410971463, 471602149, 423612620, 600110852, 262920511, 668688259, 447418369, 804855662, 564354877, 10006608, 797819480, 57818685, 690343187, 231487841, 588018007, 253610211, 257687443, 869570927, 631311750, 468878203, 940874166, 322029549, 464377636, 530525377, 746508009, 896304649, 870386910, 677065446, 574192820, 26970849, 679997766, 603205886, 979793712, 785099226, 302101111, 200132016, 474361124, 558018176, 126289156, 458322436, 844895821, 302568684, 492895008, 40502578, 627080322, 328861704, 341905260, 409734884, 292918154, 876837899, 624684540, 306127152, 718162784, 557563237, 598119321, 503305861, 277545400, 96032143, 974289501, 527954176, 114955644, 638752306, 964131272, 48697585, 545032203, 143810022, 955311816, 159627015, 478827688, 834098364, 617720381, 927391939, 420854661, 896272032, 303159914, 166759114, 811137308, 513714543, 211507638, 15602527, 645031308, 516613436, 774926894, 706268097, 539618869, 954495062, 986920021, 31974736, 436153026, 888880994, 887762759, 273818288, 972451583, 983871252, 629319627, 503403980, 289067510, 463510357, 455674122, 370930213, 29155154, 436053915, 265326917, 745988590, 683733830, 944196735, 33484006, 298112330, 911548598, 596165061, 917392933, 712337484, 294266421, 222226715, 69744853, 617789792, 81221151, 769849920, 441646449, 179473804, 936374814, 251292175, 93801420, 225848534, 927568546, 142159828, 529884385, 529179741, 539618448, 925287096, 681473740, 178411906, 140054018, 248021256, 398152659, 101533723, 998117023, 779306684, 141956429, 127697751, 356946781, 213507618, 647700876, 913727706, 169623124, 406381813, 439840287, 856721779, 298631271, 177448575, 305274997, 48268875, 805899650, 55146656, 440533876, 953156711, 369350015, 402127551, 613649269, 545760174, 897363918, 615507763, 729320973, 326593812, 167879111, 940491290, 488487081, 341691670, 564373404, 631215795, 615936159, 513819211, 368530540, 870154303, 250393521, 170094493, 926730587, 173457401, 997803945, 512995295, 668969830, 98850599, 465253565, 534495169, 192483836, 363556051, 984547567, 287523008, 292742716, 468975140, 266383431, 36322612, 630200435, 909536749, 992607725, 208184700, 129912514, 273999629, 626480797, 740817506, 710250524, 502556683, 85550985, 725957355, 41766650, 502765964, 947085642, 766255416, 212286591, 77383102, 906629428, 569346133, 48985758, 903429420, 741500816, 159589441, 667921477, 85086534, 128938078, 436355843, 458013114, 807222625, 682439589, 706247330, 23420410, 833500745, 690816690, 623309818, 532842962, 214699212, 841121682, 863429514, 405997568, 560990076, 727955830, 726021315, 882665249, 799354436, 671104439, 80751002, 77889158, 335157287, 932715297, 262589848, 62785560, 825059102, 251189497, 829625494, 560016461, 994484021, 642293924, 642427621, 891909450, 607505778, 243904409, 642401111, 278807871, 208381814, 364686162, 648789449, 236651718, 245087252, 989224924, 799300482, 845396540, 479279042, 521768532, 156223619, 821922953, 314912167, 724496411, 656764655, 978739518, 430245392, 191930989, 88279139, 431659080, 693176839, 165658044, 597541809, 185678887, 842447640, 684061226, 453691428, 824033619, 869138065, 693806589, 946639360, 210090813, 250036573, 663579605, 146811117, 61613102, 246315775, 286001732, 191703160, 404547853, 845553762, 638274496, 762190810, 722708248, 536377244, 547999792, 381555413, 7330998, 980228165, 674554121, 794866520, 399013501, 367689060, 276860064, 820934024, 978129733, 976353264, 862315573, 252967131, 290946748, 304748981, 488900870, 315547114, 261198586, 777432195, 148404770, 245107947, 574400061, 7801143, 100797862, 795408241, 920534859, 747004254, 820721499, 562573381, 263067150, 197074699, 586515261, 401181505, 399822174, 500148247, 655202362, 896155427, 307913351, 328288976, 403767602, 532113945, 297794492, 520533705, 403013653, 991377415, 605776450, 435682552, 785872773, 424925238, 593358660, 156868191, 843238506, 669960590, 862998626, 105592743, 968269002, 948672389, 236630743, 202926037, 991308302, 593882563, 44783667, 583771370, 494403229, 12484289, 506508268, 752553528, 778255333, 195839029, 781632226, 498814968, 740375594, 160723059, 415840716, 127330765, 607158045, 717462603, 348796624, 611856883, 453063437, 212846098, 571968143, 787592691, 404721908, 801934459, 896645450, 569029103, 505694180, 61649005, 761921637, 762921885, 714274692, 621566468, 591148043, 718851043, 449726040, 208105375, 452873649, 301690725, 905497636, 117991340, 132125417, 430242172, 797093770, 772380779, 827672263, 961808334, 885905649, 432777405, 343568380, 585444424, 506770058, 847408438, 320170860, 433313717, 563028385, 759897878, 412942311, 585325073, 806109515, 390929922, 142711836, 208123998, 458165898, 839159768, 863567265, 522554965, 645053303, 161273990, 469712087, 238001365, 580933609, 615832362, 419716408, 683927892, 210842416, 293323805, 401894778, 479868075, 68241399, 135646984, 779799704, 44858655, 906955183, 6126059, 545173540, 272456366, 973459548, 972256160, 74692390, 680213242, 790967699, 859441228, 546881699, 25538635, 453941965, 969673149, 741180146, 233060818, 144012766, 487352293, 452670880, 182176284, 476166110, 774878363, 179793739, 597555669, 630897630, 236980679, 573150714, 99558176, 95920357, 463675353, 187689781, 717926280, 111505322, 374498481, 211294030, 320110452, 32319372, 204677937, 209511675, 637696352, 900209461, 894539628, 784169955, 856595274, 239222799, 89719179, 879339512, 524299201, 512709342, 514493443, 612491531, 402655353, 879332403, 950935309, 668423258, 753070127, 94342579, 877890364, 407986993, 646356293, 781571047, 515059722, 541698726, 851765279, 236977012, 264292341, 772879614, 844095385, 215222391, 226947318, 905680213, 376155211, 496460819, 835446672, 497127940, 987645823, 805196719, 795655731, 127015767, 64013676, 764551266, 204181797, 364351537, 904567417, 495461954, 567918887, 40065282, 658812114, 333456744, 101746199, 617995221, 819632107, 926525411, 393031579, 737044377, 12096313, 587288120, 900681161, 360424369, 191557396, 595106397, 360498429, 840270187, 825811619, 387844476, 479214030, 577845388, 19522144, 271617544, 897496618, 100240031, 421388168, 511078774, 697401462, 2847414, 960206885, 567695114, 8942094, 327761295, 773797430, 329124689, 1070775, 42813933, 375350724, 366395721, 318649751, 532842263, 258408806, 811026169, 549266343, 969543240, 413071714, 91895855, 243855707, 518305154, 966580873, 413559808, 41782270, 900957062, 122728790, 641979999, 202622652, 438450654, 103518179, 767457030, 94407829, 447084778, 987038261, 368090346, 402539184, 508035741, 45307599, 764903510, 148215974, 103739806, 792337999, 793596856, 554294093, 303272971, 10937667, 815500801, 1201387, 814246355, 113264062, 884670643, 228969912, 486067439, 50040031, 856229740, 5245211, 197786008, 452549367, 485361263, 172479938, 541628237, 58193476, 588920462, 591795564, 663707863, 590583262, 759970077, 372631191, 767265183, 25338929, 905179513, 884312359, 472498201, 75921202, 972014241, 919117178, 314855462, 449380244, 494681080, 796316857, 265250945, 178075294, 174378720, 179240340, 884264700, 125729848, 686924861, 999334820, 534197820, 148251941, 574969655, 507698758, 138232853, 828913257, 333423604, 865617453, 338314161, 337209535, 989264682, 321511669, 58610142, 117155956, 294105343, 139570196, 248698784, 75516385, 782773129, 967934515, 591824927, 968996640, 57772953, 814466757, 879520218, 74945156, 732237660, 295580119, 507806324, 114977248, 282676644, 15916365, 106928443, 401120202, 143750421, 100940810, 291017475, 102736053, 874917751, 101734205, 729314311, 699301584, 610055373, 178310327, 757716330, 448258561, 435999441, 175280119, 967008821, 79307392, 484530902, 633482023, 917335568, 160779059, 593738408, 579677310, 624623764, 338755128, 572470551, 146781439, 630326264, 944027306, 399645863, 988498934, 709574880, 605416044, 210251506, 423392745, 242295210, 749281875, 708035836, 615613219, 541286540, 786122102, 753924422, 927343726, 99129873, 847846921, 218105320, 760846005, 880488145, 389636939, 622162134, 778513479, 133368303, 993159180, 755700502, 335555481, 887759899, 886872791, 450170417, 879407282, 881496310, 47204625, 847273497, 656344634, 4900219, 594055922, 140666469, 394162002, 187693001, 183244442, 213561494, 734237212, 727160440, 123023142, 438769780, 478027807, 219243778, 484167673, 581337837, 586420040, 270518628, 87895561, 937255932, 106498779, 396238147, 425171843, 929313058, 247494450, 813192283, 115507370, 183453336, 792630667, 800019636, 87681126, 317675284, 40307889, 292321037, 905426226, 39338957, 836155024, 294880652, 468129158, 36661880, 998609368, 347636150, 208154210, 408973718, 44230871, 989707503, 597750522, 432386330, 787763238, 248259424, 731109681, 457159011, 566956, 586594866, 41512029, 100662668, 296633217, 633905950, 783673212, 886910894, 422931356, 944348616, 756298884, 386626157, 440832423, 175575617, 960475414, 5438370, 525057067, 39809783, 337092226, 163035914, 54220008, 271692113, 277233777, 426518185, 980713812, 598978017, 149753661, 398795574, 630339370, 26650818, 152257671, 500971410, 186956039, 816141362, 881137133, 814871390, 916350182, 339716193, 435164759, 706090084, 239747506, 365756435, 786026881, 510185356, 751588910, 879715442, 28894495, 800767426, 82298510, 902885733, 141790022, 637007667, 243761178, 329216089, 16430943, 479258332, 864611125, 372415641, 801812503, 327091565, 729666532, 319662824, 732109941, 178762291, 584571472, 853581389, 921981559, 91966392, 364795567, 587938450, 729425764, 507957612, 864806715, 836287492, 659418179, 242175737, 831515044, 948389290, 550236985, 940254988, 206055765, 198468569, 261429289, 20580006, 176892430, 170317827, 378544467, 800038116, 976850022, 902716292, 25107985, 298586132, 897999707, 70993381, 427338297, 700779604, 744321334, 467362183, 490479302, 38817962, 857067980, 994233227, 843679462, 420854966, 128160402, 846998369, 658238282, 573446184, 106573074, 621722187, 621683453, 635878714, 843867577, 2458050, 694052209, 762211724, 286197456, 617234570, 418233425, 736438006, 308816928, 130099301, 307573998, 287293470, 161678480, 677355310, 506198042, 562771228, 753875167, 706671927, 443233900, 356679775, 352234249, 223116351, 444540979, 782016431, 794798924, 242624989, 545286392, 253913076, 870317015, 716258246, 717218777, 219471967, 446484779, 505849694, 666886378, 768140744, 467501185, 650280527, 602503397, 24197233, 826009768, 103134868, 901463765, 229498243, 70147768, 154086278, 990270278, 729842895, 531368972, 390859070, 651416991, 470598977, 89178469, 726912823, 64313058, 761996386, 181412766, 786556527, 796470930, 996519655, 904481226, 543906603, 433075512, 604921289, 828152469, 378677460, 923068541, 584288134, 409553741, 200650734, 623706219, 81604982, 607160574, 455412205, 274638356, 545137918, 700002295, 555874695, 456173103, 433181944, 216692670, 342290167, 709336141, 152860447, 462445929, 101805040, 133573590, 369775206, 93231740, 805290244, 119581420, 884575645, 744399260, 98542532, 284685821, 127123212, 280987464, 646053252, 35446495, 555698040, 944483176, 867281788, 829874262, 493998003, 260726958, 789740101, 429885728, 176660251, 644914512, 389757195, 237952679, 739939873, 951283729, 946083910, 996284428, 446008237, 641750011, 494398137, 661327626, 370051432, 541849794, 500665153, 70862501, 313997436, 413323395, 690317619, 180420116, 643335433, 445604115, 614783501, 20053634, 792024778, 554982531, 535065450, 149803219, 55255381, 345877856, 839963634, 845807311, 721236169, 949127391, 134055492, 815071981, 360471905, 838237090, 162163015, 913239096, 370743054, 565579818, 877067411, 245337220, 281722992, 305557441, 266004831, 711336873, 68917587, 403608861, 416484770, 380012192, 89383184, 313542370, 925620107, 469839679, 411167210, 320015481, 768201388, 693273383, 942540000, 831724930, 769835299, 450637806, 934278292, 913799858, 434029191, 523849057, 375525546, 928307655, 369269869, 899318047, 200869984, 474580545, 510674728, 622044542, 166689276, 597363363, 109551750, 89000848, 891482864, 980196173, 770911175, 760492085, 991705162, 799978892, 675481054, 155385392, 459865052, 564370206, 33415674, 46262211, 37120505, 390692885, 814396790, 873245155, 6951939, 953421514, 557633724, 277141142, 267396714, 960859056, 330906971, 427236138, 650915703, 61131436, 786788665, 404345325, 363094919, 568469436, 772166468, 46164131, 691201555, 857836090, 207666322, 180711311, 398887866, 271909009, 510545900, 185545300, 433536852, 18024763, 347155411, 365384020, 9664755, 429919961, 339305228, 754057342, 411344789, 24595413, 179785873, 780665585, 706510128, 369321433, 585830569, 237099967, 498210176, 742391246, 445330217, 283777675, 410404925, 593162758, 930275599, 197179683, 283330221, 894466080, 342885605, 339550870, 462608738, 421670310, 564597115, 177296099, 675016329, 36246039, 41647346, 245706124, 894593821, 473701600, 169638591, 483657613, 962292707, 892470222, 90442360, 437947172, 45643531, 460591297, 825142735, 536283557, 809346011, 885327188, 326963645, 196288550, 416527113, 823075813, 728715845, 411506406, 741460331, 592275125, 965486472, 575309234, 113331285, 860018784, 284683860, 313509834, 30890028, 933122081, 36503694, 270760667, 383359138, 999650774, 630340380, 601413470, 316397928, 25242741, 607604380, 461614534, 62416655, 457205832, 142293289, 157996740, 252068133, 12361039, 639304505, 151435001, 494600090, 191174352, 556053620, 903763415, 754789303, 854844340, 675799274, 385151889, 229054896, 30040062, 648965248, 566835689, 564591660, 714995500, 695746970, 730408564, 658546016, 19277563, 364957967, 735253372, 956443084, 586269636, 539152790, 178364331, 179915395, 717286111, 695148372, 637240014, 731417684, 310370073, 873498238, 745556497, 388475335, 371060097, 904510995, 802221515, 582145589, 625102821, 425092851, 656539517, 900383370, 383864704, 175550286, 46357285, 365780139, 947927570, 584941720, 210754429, 29426985, 466030280, 351901808, 197222593, 504001913, 870465847, 460792615, 779189742, 968677244, 506244323, 207240550, 70362070, 603369610, 315236423, 226479171, 141495637, 453946751, 347591141, 839682512, 483929931, 706230521, 355395849, 984593801, 69013680, 517998396, 711323066, 395713163, 255201229, 120047201, 153606515, 510797931, 930045207, 509646452, 78073144, 603989550, 741863241, 599176515, 539995343, 240427074, 916236828, 684223632, 494784052, 226672558, 591057042, 752883359, 452837395, 538715086, 206897188, 911919012, 606596285, 855681718, 614153241, 306646044, 624530378, 732934476, 719898570, 868942993, 348240379, 852506563, 140557326, 586694771, 712650640, 828831717, 880988884, 5498789, 600821719, 451731948, 746542169, 434129765, 195405235, 758893117, 107694449, 605882104, 380168326, 581356102, 720878792, 248783449, 44231247, 998401501, 92000472, 624957738, 440594835, 435037854, 453670036, 571538270, 784321066, 311425280, 391378239, 975152816, 859443221, 789410516, 779713166, 415841295, 181947099, 868012409, 412433218, 271348525, 198631872, 432263383, 467662827, 715095613, 892789682, 401971931, 951256758, 881550421, 842851524, 284497079, 242477807, 512456242, 653686947, 141570634, 729245036, 476002290, 910890245, 903874956, 727540677, 907372907, 297838735, 670810652, 94179839, 245107839, 427489487, 645687331, 140639787, 280563281, 460933293, 44612582, 577503889, 829890116, 167431388, 267778917, 310006195, 796582779, 902439146, 339166634, 996462393, 763069193, 370487647, 302263122, 301904214, 496166514, 464810672, 423109277, 910603425, 177694851, 228739421, 662595315, 989979179, 256188946, 362500744, 144830387, 529822663, 131354618, 829469465, 384978464, 519646321, 360765927, 840399030, 288873492, 446028344, 40687637, 644335939, 993345168, 119159155, 253213484, 681473681, 229926640, 87803877, 887655713, 402623318, 678616439, 28588427, 588040772, 1126262, 622874903, 504403918, 611689475, 186116336, 337064678, 985773136, 895603696, 774221178, 310253483, 75406587, 571225996, 823025790, 724456095, 768952292, 784435229, 616700188, 194191708, 90061991, 201214065, 154907076, 938161996, 742732463, 523160148, 279620580, 612972292, 351776938, 440851041, 663445813, 922634276, 111284399, 965131187, 869859529, 643422950, 764967452, 825277119, 710188538, 509539517, 180172729, 766987479, 663711015, 126544133, 108680358, 595961046, 999775804, 249380015, 827703966, 478374087, 622721622, 364489938, 950473773, 910787523, 980094388, 329286102, 943229671, 318537191, 290902820, 728356243, 221729727, 581624765, 226766181, 782257923, 215585376, 74320695, 871230117, 539734037, 228838357, 759889731, 528869749, 775885785, 296250743, 9346279, 78827873, 796513676, 695583143, 767182416, 366524558, 293568485, 665153374, 445572066, 114152003, 873549914, 458682416, 794551203, 749443547, 519589885, 6717085, 351196003, 802468570, 436909262, 9016203, 333209166, 427217039, 213998683, 322872434, 250753477, 925149573, 386203047, 91146005, 645259372, 454915302, 576904613, 436528236, 598896207, 550994846, 167257459, 20113732, 657213989, 428934136, 54738093, 270808126, 809839467, 460822254, 777662662, 382365179, 598626599, 743989505, 781309165, 342003887, 250453212, 519378262, 563928287, 825654111, 528074435, 901349786, 586479157, 551933569, 633652871, 1925256, 183376311, 541201676, 246691447, 319224753, 451926304, 46870193, 758347806, 535732377, 237379273, 140121072, 298314762, 707425468, 563747919, 225263386, 697842762, 941663778, 931436019, 131299228, 813715216, 747984919, 133286180, 124867404, 716487955, 616984589, 486258351, 196668619, 586132507, 87893277, 26353883, 349934334, 715401399, 144620325, 990169710, 826263668, 324704951, 953718622, 142882235, 74793282, 463745756, 908443117, 742822647, 292311244, 799763681, 260934217, 805935776, 942916291, 549509676, 592644695, 144244401, 258966334, 400861428, 771154920, 749358434, 322992851, 824982284, 224045660, 543977788, 398523199, 967518397, 344023881, 571882367, 935612894, 136508809, 641262575, 112645172, 603747006, 126903285, 720214465, 828360152, 765586279, 43091678, 642197057, 771087866, 328583958, 263515116, 760306588, 923856538, 743673141, 160845541, 459810350, 170963770, 958226409, 393152319, 745855038, 336605154, 690028495, 568625004, 830859796, 195411530, 886298911, 590198582, 1810033, 360572911, 487348733, 801706654, 942877947, 215449692, 302195283, 496480013, 512094360, 101429037, 908206650, 888632835, 898030257, 616963151, 88889014, 697963325, 224386269, 291808262, 202079063, 122111336, 362764228, 699350115, 160714742, 608212397, 148058347, 176090810, 50866787, 320739844, 959369540, 683888288, 902105812, 314944523, 95599030, 512594441, 257689902, 352115741, 126727376, 902037367, 594878314, 48866027, 753137477, 240998202, 392992685, 925497984, 401388054, 552579219, 224769900, 98481953, 953760539, 897759967, 56974472, 203212872, 502929704, 243273378, 557279890, 200900415, 642673455, 352866346, 167514593, 939635421, 600989914, 35540479, 416292901, 232847294, 706800702, 631175926, 269126558, 677437298, 700232448, 492129246, 125070034, 331903331, 693638784, 916658549, 758389966, 94409759, 417911937, 557679900, 687574830, 808870036, 147494664, 841584610, 690464822, 269744702, 115200388, 350346083, 692191734, 853484276, 730577749, 513492365, 500432518, 32888194, 677654303, 137455513, 323671968, 310495737, 640877454, 123242345, 767443947, 949628817, 842824345, 14905313, 171093503, 335330887, 350151325, 354564774, 588921924, 823182690, 610534862, 537716577, 806776991, 476588836, 376009833, 55604779, 132012358, 266298940, 73180704, 588089674, 246475230, 886598267, 874066789, 994592177, 611922566, 672327342, 732460080, 339843865, 588977632, 361200044, 729019950, 787956935, 745019770, 887330529, 489341485, 674967036, 758832319, 352308254, 27543823, 217269087, 734334680, 837958496, 866163044, 710967130, 168131772, 846390208, 214431654, 367987628, 761004517, 975408612, 732519431, 908312249, 640015554, 267804854, 561661209, 209787062, 512836598, 462660178, 191283014, 510824749, 592308920, 979537183, 905234127, 842560353, 421134090, 291502139, 213739898, 244599138, 446363711, 788555725, 733339086, 382013489, 190255789, 513977479, 373312151, 271365380, 949822238, 230837540, 347984411, 13569898, 112174637, 478555026, 660871897, 720667999, 777474168, 115779698, 463199701, 430216693, 934097317, 471921045, 91850628, 130219282, 739771101, 102087573, 798115097, 516626877, 993767031, 852198703, 588393118, 580574673, 524319647, 340658345, 48575616, 607049264, 102591903, 164426346, 28075347, 829198862, 722898117, 821563365, 830000206, 731995900, 50681376, 9468556, 367631452, 124485313, 508842155, 549453360, 942452409, 670564670, 615230772, 356952925, 384439628, 877200020, 491129205, 296757572, 858705582, 740859256, 228429900, 975871560, 173143188, 315971800, 914061119, 484665060, 747778799, 626222307, 627568451, 310628248, 779864569, 653098516, 938255542, 292202603, 37629150, 289896693, 314482712, 601220573, 387162759, 958501044, 788653029, 750898166, 881487199, 203172838, 78729167, 334263041, 854053566, 433572670, 593614272, 447087120, 631717127, 533140948, 17077726, 886131709, 636141808, 101514555, 954417551, 296352494, 803672725, 914371600, 822037161, 299923350, 812455679, 459761967, 42464997, 254645728, 602872918, 277842263, 106882194, 533159450, 861486763, 996743275, 72956312, 442505270, 600981444, 980965715, 313261605, 99249770, 342878598, 199198133, 791152933, 857910455, 325543347, 721434677, 56624333, 497859518, 837043063, 930267370, 4720500, 343062817, 649610092, 970591431, 417094847, 978359733, 597413067, 256922018, 633024948, 196155088, 869462175, 862597170, 744845170, 306450881, 120381566, 626066816, 700452371, 153661639, 925811473, 419151459, 825038855, 696281672, 281118236, 536943847, 572952903, 985363798, 929512712, 155332403, 344233777, 171650713, 966751823, 669206667, 684238328, 919507229, 278927231, 133171972, 89800805, 335753219, 422154814, 825218948, 743453718, 400922233, 375251099, 420125923, 728338690, 256668343, 561743615, 450817483, 270280069, 598969336, 488490183, 171947900, 482515899, 443990499, 491695214, 179465706, 584366783, 323337054, 610319883, 607030747, 754664683, 623442218, 544529872, 209406916, 184070187, 218465518, 94376472, 130112401, 269250530, 20142092, 956492836, 116380963, 97095841, 104706941, 798010735, 11509645, 340929803, 158803704, 43832140, 385257866, 313154222, 22000593, 506100462, 849370047, 787491645, 213582768, 763405144, 548349600, 392874432, 854000543, 781432744, 428308161, 157756852, 59194494, 330777032, 599256205, 42794255, 96613379, 373692648, 197625993, 461513716, 443213425, 983865993, 233259736, 272213433, 796585752, 144224798, 479046504, 600019389, 924247870, 621816693, 349622903, 175689659, 145617825, 870844653, 72482253, 580256784, 862626822, 79423232, 816691361, 544565188, 62286176, 427192235, 770614070, 559419284, 195468410, 313622853, 998013074, 269630637, 10319621, 515673207, 406361672, 880458184, 653311203, 207772272, 869090753, 20219974, 131177342, 150264742, 64449057, 733395939, 469787880, 718290784, 245744452, 610355944, 631425972, 834789793, 961061669, 504886730, 302892829, 287222236, 359043765, 783139435, 213518070, 739929537, 284186460, 860393588, 6602091, 117519805, 177078433, 400889537, 235280967, 76341180, 69261279, 241111739, 700939571, 434351453, 629233940, 167761412, 49390756, 252855945, 14119319, 464936505, 227818142, 642885945, 68674486, 715000309, 267122957, 696413231, 146467127, 793006100, 597593264, 65848633, 911379436, 819254455, 772182057, 624138651, 593165899, 439455290, 855817464, 102795386, 880009062, 174202208, 944081658, 270437267, 489343578, 923191772, 17490706, 656114667, 645670076, 415342915, 322015236, 742109455, 406933230, 181467538, 912192047, 129787521, 315284754, 195865596, 375740064, 429103738, 284288747, 905673226, 233269225, 994334651, 147244910, 827694642, 960452773, 957338670, 387300459, 951269519, 952043937, 802048372, 583503389, 595363954, 598677385, 677812530, 617704702, 801528963, 207138846, 13569224, 23281554, 602148900, 301687163, 209297871, 32444801, 618420957, 767965156, 889180711, 6709594, 491087800, 568029561, 187214396, 813434197, 138193353, 171152548, 111422859, 820784686, 220970556, 324937004, 222318269, 379305784, 359101948, 176929510, 241263930, 100868839, 343104869, 490874792, 902144593, 319030684, 844940842, 896948492, 985426562, 666195722, 447159813, 963824352, 921527068, 270465466, 232360248, 726214419, 223059729, 431399179, 409530927, 867029404, 988742849, 325962591, 606271263, 976650484, 430166170, 823646155, 965605853, 215933008, 655036168, 256162343, 151375092, 41398651, 433659928, 370322143, 614421357, 101155850, 551521000, 579116291, 897938369, 169010241, 971733618, 300972287, 699678920, 834151311, 757445766, 750724311, 939819221, 280222369, 998015327, 646898493, 602439793, 75757562, 520673231, 601396688, 503851428, 921593141, 289318689, 645243001, 15241732, 966146930, 176740784, 198053177, 972400634, 310571346, 873112589, 315093123, 555625194, 620605568, 295959749, 381075016, 558839323, 915630999, 383621769, 93801851, 930284333, 384363643, 949383904, 720174342, 505132615, 468761268, 968734124, 565323933, 913418683, 135762185, 343953763, 518992338, 340581600, 586553447, 168695518, 742347997, 264982490, 936328602, 940006669, 29110776, 771415544, 997760074, 375909238, 389001959, 557341801, 433438983, 841527058, 685425776, 542428344, 591611368, 448179246, 824023513, 651654517, 279974934, 292037044, 212481217, 961044728, 945278806, 479870144, 455208327, 818412345, 649924454, 917427469, 626407198, 247093633, 878256019, 943980281, 79600848, 307241997, 769992554, 259601344, 198877320, 182170076, 476334376, 580069867, 437460587, 446978551, 702583520, 292793273, 430833191, 473183850, 98421621, 985132218, 266514141, 448591185, 364988325, 925127307, 158368887, 519945413, 428833889, 900865042, 349748611, 846180951, 191550901, 904091929, 381363734, 286433212, 481302731, 4195519, 552892267, 98651957, 165271444, 143282317, 395862308, 557981135, 932240323, 511211359, 735545563, 996873242, 29478707, 87521820, 763189459, 667072482, 162578508, 854706103, 184646012, 891147707, 783790910, 528874106, 877535216, 527410088, 62485780, 875857166, 738122550, 160596556, 279844205, 290571470, 726791738, 179549095, 531408556, 996411131, 593195282, 27106194, 985279911, 918059058, 144463801, 147127737, 748535275, 886005506, 125500959, 591254245, 496754619, 575973760, 802260278, 200406460, 103433268, 230298400, 744948332, 803233456, 991680098, 400272203, 249695530, 832879214, 775918575, 760074250, 932411634, 591020691, 853969878, 761948056, 53629884, 487582934, 619335556, 444900737, 781252828, 332746508, 678107679, 750290247, 934029440, 490041258, 627899093, 820220512, 206413881, 786586577, 153641521, 598125327, 390394228, 299276859, 328992552, 124559755, 242189970, 641080965, 543094805, 324069343, 715465709, 719914738, 183712743, 75561158, 416218598, 5858903, 99646881, 578940937, 587018792, 275792673, 406952079, 136488714, 32389325, 562389175, 829554862, 88304306, 271536071, 276805940, 225148607, 311979651, 513163828, 938762483, 701971456, 718025051, 524163441, 201373878, 566762226, 493697577, 249702262, 167106337, 513340431, 271307670, 262813390, 471509161, 427814468, 75458777, 518536572, 575415913, 127654975, 972077645, 370764862, 531421890, 636300597, 10601968, 426306835, 591595304, 751980509, 335911543, 448536844, 19717366, 785296340, 117635603, 114992183, 223500417, 404160681, 749086733, 335599558, 689329048, 644731982, 330160272, 502144191, 832412682, 239378069, 258460129, 40473753, 362685657, 415773639, 683970980, 158336038, 714636048, 102404828, 485837534, 612009054, 640122922, 575595328, 106683393, 10956757, 335758513, 962629426, 47327849, 914666161, 671021581, 850154856, 8548262, 380743038, 301608244, 430243850, 806627096, 587342818, 407522376, 245294309, 945482463, 612881114, 18187243, 281975708, 257303067, 794306753, 155970207, 340345844, 400946170, 806353892, 544434500, 703897933, 442355185, 316581294, 684189408, 621938175, 208690508, 222799275, 554002812, 31883387, 532508137, 154575732, 424080798, 249136547, 467039511, 236867270, 681401980, 847246268, 851069138, 284281864, 981088812, 809649355, 308627605, 614907789, 861389527, 327657526, 736204679, 562074367, 97154324, 144242884, 677620782, 253993252, 6025289, 353517496, 559744377, 640464975, 660609842, 20854831, 548420541, 51549722, 525675310, 41115447, 120963189, 563180152, 492050967, 664735473, 534918277, 345073315, 187448148, 746965645, 553517931, 839936618, 264860851, 569074008, 6870573, 328639464, 989028437, 639571797, 548173522, 135303194, 980905590, 456443591, 535198172, 530395197, 446504348, 837047899, 686727657, 381449129, 519765706, 424540040, 645769820, 641105100, 290912226, 858791554, 461161802, 419304377, 295939139, 745756683, 33926579, 243059119, 159744542, 602487848, 665325109, 254126239, 416881944, 417750577, 320608170, 228128630, 634630498, 461835599, 342200366, 932479963, 229059220, 833856776, 305728100, 758270896, 967280027, 888729570, 727232250, 765122305, 613894713, 262476780, 449468217, 912232999, 329801062, 296478814, 677789495, 980224308, 363452725, 758379818, 127967386, 864865459, 346395180, 787707428, 227514078, 642885905, 396854655, 729704206, 817558011, 527100601, 740306444, 996170947, 233601668, 705242394, 283654216, 454724353, 811110123, 462434858, 720795391, 776023374, 457833189, 63924965, 608662744, 715858273, 77114085, 930955627, 491674796, 16553004, 398436237, 433617414, 349156562, 403964439, 169020562, 31156080, 11631660, 578166479, 223178570, 990322858, 580442947, 643283999, 536913077, 364292700, 989113098, 126195088, 921244843, 103170949, 68746741, 560853667, 224154570, 998754411, 220905780, 921576270, 233809208, 381853558, 525598085, 743925177, 189810516, 779291553, 218799119, 860777342, 329215468, 346253545, 430616151, 107475751, 215604253, 249689510, 269598529, 25447598, 265070263, 359921829, 967506062, 113258957, 974381912, 806381126, 153637704, 277696792, 741509397, 558247440, 232217984, 564885598, 512518870, 215980162, 657417215, 95778656, 769142300, 197522535, 886114993, 494023256, 785022369, 536841842, 278677087, 491608737, 970541356, 47348690, 370603830, 699763172, 540747851, 423995332, 734113964, 14396512, 52667651, 690773035, 337625602, 625781726, 292786570, 217408386, 800338199, 458857235, 669147255, 26939763, 909496679, 491305129, 503130192, 832770322, 643472559, 22342940, 666896579, 719438996, 290725257, 257387599, 987838991, 432704318, 173648766, 923441872, 545552338, 613708844, 361287576, 136583252, 347127690, 528320472, 39309720, 431411777, 953840021, 121353639, 523181065, 274440138, 92878385, 252479512, 571606185, 928965325, 206819983, 744141114, 49160443, 193051149, 195295084, 559538996, 558900427, 784578185, 708794649, 22566930, 1658474, 857655099, 161142916, 458743720, 567948807, 736328382, 843917922, 321065274, 286110666, 676491589, 83476410, 7561759, 394436957, 667132054, 699669436, 83498581, 535629695, 1003396, 783593553, 428403359, 739239164, 393360118, 336634708, 958260873, 350011959, 257723406, 636540669, 897895729, 471801083, 807832401, 464544422, 33917752, 722449611, 374291163, 979693551, 373438067, 166023636, 953426981, 758195381, 894822198, 748055246, 69502299, 848394258, 90693667, 92400176, 347452350, 919210414, 410731773, 370409206, 589525307, 667407201, 955113407, 379536235, 493618597, 476670661, 376240007, 302941060, 949041618, 590587344, 669354002, 161277984, 746257800, 502635238, 891755315, 566694337, 859529485, 133860971, 493616229, 65533227, 253706283, 236807158, 47821472, 820307622, 995642069, 600065452, 480836143, 545232435, 554366697, 800531889, 794730835, 357093859, 141173133, 859541168, 353520695, 923259519, 486303678, 487739786, 886695909, 208143405, 181845743, 482433343, 753503132, 55525497, 515161332, 494402842, 453162891, 484192428, 332967339, 418814566, 559922655, 245847877, 319457487, 534691871, 441725154, 707249620, 458593156, 594740326, 29842158, 503268762, 982678941, 470236719, 646586313, 520371112, 135948988, 131901277, 799315019, 532422495, 162177424, 450223498, 219021158, 633338566, 409995671, 251042217, 374116598, 305870230, 41289606, 918988421, 789451839, 200411390, 89134397, 688118932, 267757214, 494924471, 646928837, 339580765, 799589742, 596303909, 281061356, 365082586, 49125431, 174728824, 620270686, 931378709, 378420686, 938453360, 976270394, 856832556, 934048475, 40698145, 731613828, 572685620, 555286120, 818890520, 727879563, 60264097, 472907217, 953937854, 580565845, 28685611, 487084993, 215733288, 669972882, 268293848, 290797193, 585412677, 136392297, 831670960, 716304993, 670478175, 568082175, 778986465, 935574287, 374845911, 501285610, 122711572, 314328480, 513910248, 108254074, 760171417, 839298152, 880121563, 510230606, 951380107, 765966769, 699890560, 772966560, 81787297, 869136326, 842794636, 209985653, 117452552, 334817041, 147087135, 905750490, 827675286, 885212900, 667164858, 651763037, 594434906, 737413004, 22509993, 867788023, 782059099, 970204603, 617730144, 471105389, 919456919, 815585044, 317794022, 565666097, 593992655, 601519812, 822392030, 588028143, 919476851, 171845167, 17880208, 624792193, 430570554, 789452833, 554275354, 469704483, 474220676, 984689125, 966619797, 51817810, 36414847, 208026505, 600341889, 82762863, 783518376, 213506720, 201227710, 43316894, 463896783, 22362706, 508175351, 790139712, 845755385, 371513652, 943539140, 978812478, 641554998, 376700902, 955767574, 315505392, 330105210, 844028992, 10175356, 238337176, 59221089, 306415200, 58616633, 291297052, 30664793, 415172814, 910002497, 902615725, 756895577, 686904422, 519265120, 231588460, 466066535, 452661226, 7272133, 528926886, 751394918, 349636619, 867721053, 744812540, 612017067, 740043615, 985750229, 462722200, 628194217, 26728494, 595217683, 926347470, 395225331, 148719610, 18814504, 199525845, 972130268, 210862222, 798880081, 864862198, 502029878, 402310035, 117693298, 328714756, 910806271, 848830764, 410526852, 190819816, 889635554, 449399280, 629036783, 532892571, 290794443, 109691618, 52609812, 515022467, 322501662, 251299700, 112661557, 594534836, 397228264, 545458080, 989540775, 502878995, 869119763, 476973708, 378176745, 548668030, 155740986, 842677881, 450377676, 230898774, 21790045, 735071619, 550916841, 368587772, 56611091, 476044527, 409381692, 778821214, 267430067, 384887660, 260906913, 213804738, 731882011, 497487605, 196537277, 965668240, 996465171, 140168951, 598428497, 61822931, 928469206, 926326264, 583987943, 304871504, 327990, 785709283, 566225656, 232156099, 600241339, 217546863, 636532643, 254643112, 139217081, 814735335, 375095819, 573921663, 749487824, 384241906, 951825004, 580254433, 546244928, 159469428, 942621178, 594964873, 672573417, 97855911, 133807389, 667719641, 29728984, 689053488, 294601878, 190104108, 366615142, 217069600, 990121672, 186467773, 350118129, 649448637, 941380524, 100312232, 967825245, 498752143, 601943538, 310803571, 945092618, 763731090, 406605517, 644565329, 83685935, 926151759, 915578023, 111424391, 479248586, 905447680, 230477733, 222134779, 509024027, 784187129, 699047737, 941384679, 966925157, 17833904, 249007169, 583539467, 33724655, 439801859, 153519275, 116012107, 739941666, 253764574, 666938851, 973986636, 23748639, 962411779, 360033462, 552621249, 18595812, 784399321, 273617586, 809247218, 64204873, 324622318, 845163469, 161494491, 609321880, 930434159, 76759594, 993926631, 970464960, 277299552, 643489078, 172615413, 48775688, 250118529, 132987074, 300940795, 844978537, 210856472, 763068152, 582996834, 869758704, 376568278, 479688411, 547496618, 665518802, 356726800, 327727907, 659765929, 2029785, 758283244, 706510360, 758379690, 616154705, 149235997, 513114784, 889966778, 379639680, 926238919, 484645628, 670675406, 529704705, 774782951, 964744380, 188849972, 60575375, 490126840, 537279510, 663148738, 149735413, 724831019, 331535126, 672990817, 950781634, 759222357, 525764563, 169769276, 509285114, 765449167, 314211041, 718838904, 913969050, 494116362, 691130555, 321550074, 945938054, 748582182, 443682829, 623689884, 755313340, 21360135, 41429208, 385731778, 338420922, 580810768, 264377939, 229467291, 211232914, 189100853, 247092129, 713007500, 585025406, 860002389, 930615396, 923734627, 649783886, 910443228, 558553237, 617411944, 116267811, 311866208, 24546636, 436670695, 65636298, 795143474, 658584852, 491885659, 293394219, 727727581, 870285845, 278915864, 268605831, 37571457, 462083964, 852296455, 887197094, 193495693, 469518771, 933340458, 430706535, 477110114, 721549524, 663014381, 504150067, 537127631, 140222264, 509899521, 419634345, 192941772, 219457847, 284302207, 343699027, 448769754, 614027384, 173163652, 767220256, 831544556, 157970756, 364286611, 142146433, 840047777, 14427812, 646002346, 285834822, 184094831, 766736701, 272791729, 810705803, 378452386, 222649938, 710718341, 986112926, 140321004, 537238975, 504336669, 72847476, 109427532, 846334207, 224810003, 957171669, 804443442, 805229114, 891596815, 696977696, 661493364, 13384778, 570025428, 854567683, 731473367, 55928216, 851151867, 424536364, 602075818, 306584352, 963960675, 808040872, 12490266, 279230478, 453947682, 694674583, 11063580, 680823863, 908976343, 320518728, 923916749, 510011909, 902201008, 749404354, 221573102, 382719190, 83851702, 597874906, 247560720, 658936094, 929569620, 654357797, 418009583, 35680164, 112415477, 523126018, 757982355, 889125076, 970591172, 617168466, 270086742, 816911764, 236912382, 286675919, 945961509, 427224024, 637046, 103576112, 474757585, 509841607, 208946773, 106296307, 945650717, 660477017, 408374865, 347742958, 395510259, 718541505, 889880386, 357725889, 559788706, 367677895, 281732207, 913245579, 861918319, 874819081, 411115758, 423755800, 393544376, 389675648, 532920437, 135631617, 241422292, 998049972, 133844875, 61417756, 409438423, 495655286, 303660893, 752018986, 474923059, 527048704, 8971310, 151306942, 383156107, 361989352, 647656738, 670283352, 611275336, 284965676, 422318172, 321078729, 379045395, 718506565, 906703071, 231441169, 944658162, 394898853, 162092555, 141648609, 725442738, 95147900, 14752664, 745054936, 479121754, 144728882, 767842091, 659533039, 592325330, 635489370, 203016479, 848652963, 517692353, 998398584, 180313171, 893167716, 795723006, 377234247, 437714679, 374742002, 749130904, 665317784, 231864254, 548103274, 786989651, 669334145, 435511449, 361544391, 138729962, 831001299, 713358479, 458845172, 336730110, 560956719, 4368137, 944888759, 879312629, 754979861, 560683455, 107737458, 38786378, 413544315, 362926480, 901049425, 230574760, 664479294, 45744646, 237468601, 441054150, 972248305, 91543086, 11927, 552522826, 578742482, 92400332, 890317396, 79139378, 833181305, 848684788, 818702263, 925299194, 542232153, 993497169, 536860117, 164347090, 895539723, 215431099, 485733081, 159321500, 134036926, 98710710, 597903204, 665605068, 306277888, 353742050, 207944063, 695589741, 973741448, 533154305, 151258960, 900628860, 519847076, 896791159, 269134433, 838952902, 98276589, 530614856, 304664973, 142611287, 329634222, 281685474, 334723767, 567570130, 17559916, 796604144, 387613465, 637653640, 134530189, 279975254, 39569695, 195597991, 192090521, 56790537, 238930389, 968029461, 488129092, 721973771, 29851019, 337401033, 701116115, 880185188, 227479655, 188598375, 117416485, 708333230, 642618056, 591262259, 43558589, 767834111, 890553272, 272987324, 626641231, 399423798, 826794141, 612766293, 743317575, 479652327, 800353248, 873638524, 169744882, 58397258, 272493710, 138601237, 386222516, 646534027, 377734159, 423388558, 656827639, 145186265, 522464209, 188313164, 373205213, 46148603, 896566323, 812558171, 744546532, 839844492, 611463497, 477211938, 518459775, 741860713, 979168240, 975551666, 770570007, 830085493, 261135974, 632441934, 891740875, 939468974, 477488721, 372977196, 361733315, 720997488, 966537899, 381437790, 568443198, 236180626, 677093096, 132176825, 823893213, 818629392, 266410941, 272962160, 806068499, 401563012, 415651999, 115405728, 560008132, 227045755, 876128066, 14738356, 835495550, 297824662, 487310989, 765296184, 518440698, 179222182, 990697711, 21410854, 480755417, 865375019, 983256748, 365575950, 946130114, 479012649, 582265172, 463727373, 563726294, 650900170, 99186949, 268162793, 496167357, 830133919, 749724257, 882643362, 21283316, 689045735, 510948863, 137551922, 549156927, 980421183, 427016897, 276179971, 195704352, 979919690, 962218664, 742920496, 26743542, 922518693, 574189925, 873946758, 526132876, 497233054, 217613592, 935662050, 428452335, 270179849, 903320767, 759343266, 524727516, 288840428, 631419482, 283649508, 85522081, 770253355, 89057574, 174975710, 957861275, 850704683, 679973727, 258227489, 999315495, 105533171, 525425290, 879511583, 922069239, 843736750, 398838206, 828429713, 98775569, 452716714, 35842050, 118029577, 973168766, 141005198, 737720969, 939599661, 622831654, 78291869, 236606447, 990301563, 220906085, 273731621, 725960930, 241498981, 537978299, 619887838, 105230345, 937665486, 596251955, 381137824, 374890135, 891959301, 118844865, 273793483, 172840757, 111855393, 79270840, 542217030, 21733198, 433628153, 293645949, 858496617, 976721846, 361560207, 934837590, 756481231, 631038316, 803358065, 677914072, 457374031, 920900106, 176628335, 805423954, 432223663, 610579950, 459363790, 605550436, 784606393, 153097890, 725010502, 118745250, 909204593, 892850587, 80909589, 788748960, 415640914, 281166572, 382928017, 306153084, 413867579, 433358556, 593781530, 106523606, 489749905, 62200336, 501634061, 32364715, 96305290, 407363922, 461844301, 142271701, 870231731, 365516500, 24106864, 479674890, 905757297, 568489860, 755565484, 922835009, 266127445, 631288273, 570580524, 238913433, 575872979, 639576047, 54026938, 477460212, 129356508, 355469111, 919597606, 56660258, 258099899, 355705461, 702234024, 809831991, 797922542, 641834118, 709930230, 679749666, 563187909, 274357853, 855256434, 546511463, 797547933, 94924700, 490769508, 468297469, 899795600, 810395809, 784737022, 175256197, 247777336, 752408599, 302749753, 105549169, 140309362, 471785137, 320527529, 715787741, 943261856, 716798875, 779523081, 624476641, 942756131, 864634391, 905830966, 910047443, 881134643, 902175733, 744276511, 974942756, 826825703, 283586679, 41294761, 689916880, 767271409, 411808650, 484714520, 702280061, 630482722, 787267134, 735140545, 994705068, 636697958, 777711061, 821860466, 221440957, 46675500, 378607586, 740831369, 219616098, 695696308, 275718862, 251860664, 787403788, 926337216, 529240834, 361006608, 161256348, 947255357, 210156916, 531048685, 280602120, 85631293, 164332609, 491671827, 32584425, 457400557, 273801837, 54832978, 228444713, 490702953, 884897604, 481442817, 790589987, 986151172, 595941468, 141185314, 681897187, 584701437, 296381142, 200167402, 369732872, 447500322, 831136961, 924203439, 402286836, 744426551, 191990823, 238029315, 587597082, 166424913, 502165943, 738094722, 84361831, 431658411, 843290875, 109739232, 339509208, 755908494, 736758789, 939177160, 746811418, 184439385, 677729302, 735249405, 983287925, 455589581, 28721371, 934716939, 809160027, 178684201, 591569359, 72227774, 414086582, 672950844, 590618498, 915333485, 143785652, 281872314, 508744919, 930789719, 551429932, 992785643, 57182443, 382013811, 826542080, 153570096, 101322950, 463491442, 718728628, 976692064, 453849533, 806815613, 965177438, 322593593, 575155798, 245006630, 988361576, 459273387, 913109262, 599389137, 773333106, 984935937, 284959568, 257682124, 720778014, 38212218, 455404066, 77517455, 744545743, 217961975, 947759546, 744460523, 957255302, 35695703, 826125774, 88671210, 533635593, 718950876, 895066446, 365630843, 905086148, 628935763, 4631107, 647133016, 140279867, 31952915, 264411825, 769066519, 298317953, 886131983, 946090751, 568643297, 500057392, 554107893, 502484857, 799154132, 475590910, 82339673, 147599839, 447078165, 276319535, 801569245, 771273750, 825089630, 164387885, 284232865, 339873039, 815802189, 925203957, 107839803, 842972266, 626848857, 293384103, 170658954, 593560565, 353484347, 135454013, 734844015, 556675567, 384590032, 221920401, 245837901, 606001590, 32304982, 234876638, 739567046, 28796140, 834155212, 531177594, 872913733, 437744482, 279928302, 165450163, 639408910, 35608146, 997548215, 822992300, 906783002, 558471464, 289885174, 986492372, 993999323, 790148532, 335371663, 683112017, 375342730, 802987386, 954969560, 350781591, 158455790, 624939618, 550533706, 239558631, 120479582, 153120967, 928841128, 31954369, 997946090, 64557780, 940553446, 147395378, 273092044, 110108893, 887274585, 419526106, 674550421, 988907203, 976738315, 15031637, 533422278, 225339961, 606734768, 838292, 8660567, 822371356, 85011495, 263607445, 931264064, 730494340, 582107241, 926294136, 283950553, 88636685, 149844030, 550563657, 588521614, 413953351, 632069071, 702492888, 734806333, 107605117, 904969311, 568794282, 4342232, 627356903, 960697756, 504958458, 972786116, 953489566, 97994974, 371140059, 908011844, 446535636, 580419653, 208162617, 58426075, 799776526, 275862432, 405959509, 204158122, 24193359, 735541836, 361255965, 772309028, 251125455, 645555606, 806725182, 440357926, 462242447, 620204381, 696114010, 771134103, 439416988, 449259325, 996392481, 426875698, 989529152, 984609019, 225039737, 450070620, 541349373, 146660517, 560948528, 202193006, 605504965, 433570311, 981219733, 463067182, 414406799, 402496840, 197525727, 845470448, 960215043, 976013632, 347749221, 7832615, 888514034, 401355236, 71454391, 379242118, 58575076, 494293981, 163490396, 420166645, 28840099, 584303209, 908413879, 930804402, 813237151, 709635930, 518085426, 341272518, 727011117, 620086647, 926981555, 548132283, 997495448, 430167469, 529746461, 194841680, 553921192, 148491427, 304485892, 403853084, 751994342, 789432055, 539433698, 774391191, 526910052, 499936311, 589724811, 562451765, 716055892, 400121793, 876909716, 638612597, 738496090, 658232748, 709044964, 584394734, 73445006, 62695237, 481908379, 67915421, 966326092, 518678795, 197502391, 972317565, 769930308, 479686415, 131961243, 634577713, 74944669, 661121529, 564742788, 628032639, 8904632, 950950116, 924355063, 135148278, 29517632, 742368081, 733238486, 949205280, 839777220, 361603062, 332499204, 890597028, 644942321, 186511327, 654239807, 301589696, 509894179, 600119589, 357887841, 789663226, 375779707, 940336648, 22717935, 525564071, 612772175, 923468565, 453823195, 61052342, 315597986, 299283037, 9588177, 967004897, 100724143, 583510676, 104058218, 645094791, 752058765, 818969302, 870568131, 87979016, 37320146, 247706437, 264964380, 123931146, 499878442, 856473128, 211628087, 762335758, 804609066, 688599383, 566343777, 285094767, 903412305, 163629874, 874357948, 612730832, 713006780, 194899794, 686172279, 809603289, 396042314, 940149556, 929146400, 728282788, 197685596, 806180509, 503921665, 156132379, 737718307, 686309526, 856083804, 311859508, 203224394, 614838037, 112704401, 212395402, 291670413, 762519510, 609064416, 232025685, 28982905, 593623368, 433774842, 673624994, 998207184, 360364804, 133100159, 458200314, 126175741, 836562602, 822676436, 476191260, 839373264, 538697934, 32271369, 663932491, 988882973, 934882796, 55707082, 29885845, 982593833, 476307175, 282664770, 342968039, 908898870, 646072495, 321673798, 859096147, 864121111, 444009687, 709924967, 380140635, 220035711, 251547890, 103058070, 612221614, 899254297, 216218105, 918045501, 232398178, 216318640, 259257735, 724184883, 126872081, 755438899, 364078417, 986454146, 169649200, 11241696, 530207972, 39419559, 550851254, 49610127, 765830459, 17365399, 966894136, 161264924, 208892264, 535734633, 930463030, 752474668, 476102423, 150578552, 870797888, 892963753, 494536397, 129337377, 650153735, 435281475, 716848874, 242533770, 616472135, 340768870, 777185537, 485621659, 450798339, 642773810, 586556003, 435187390, 448133307, 202057119, 627338570, 788464786, 660911126, 241179721, 297345032, 938059564, 133678444, 837850730, 164118144, 155616792, 635837539, 659202165, 201039770, 74183794, 814678137, 678338020, 488925612, 792253184, 509054358, 650280058, 636269820, 699204243, 358442280, 92663399, 174277328, 55964400, 568069744, 54532530, 526215913, 527507133, 361907885, 25560523, 800853600, 616386763, 51802162, 600533093, 185689471, 660796145, 263177782, 989485795, 943753929, 174884373, 853070846, 396050245, 269056211, 182411750, 320438005, 652592676, 232076869, 226803802, 892368227, 655156263, 921823635, 887406869, 106221200, 822866770, 745946743, 586568401, 400702181, 70664067, 306327330, 973490363, 454727195, 116661139, 319602627, 107133411, 223420591, 260074421, 335187437, 410657122, 590807435, 151356429, 335564854, 690971465, 977455332, 73443699, 395063604, 797822868, 823850535, 926897372, 454045327, 367602742, 842691637, 6094501, 496135319, 109827638, 127216858, 611273753, 128077707, 239136647, 198369220, 94049803, 63956317, 625949814, 313960696, 172624382, 946037105, 445386803, 39185309, 286074028, 601948763, 306252981, 936712260, 280413824, 359082366, 148415062, 287722630, 386436693, 185305015, 384084794, 537579327, 781891466, 228850146, 353907264, 444627385, 776259435, 571949879, 318934377, 548926459, 292248020, 354321504, 15025208, 350770579, 243669233, 137468510, 169496390, 475876027, 278263915, 179809805, 159326409, 262224615, 484326558, 310899452, 516789285, 512446664, 341216767, 768210809, 295798785, 816363071, 283596364, 407013625, 282918575, 411874786, 695389639, 727522877, 622653103, 418049736, 366073728, 105309032, 282585850, 857220055, 678747716, 664803151, 175238497, 798076282, 443252581, 706613184, 178336988, 355955994, 912819946, 330893901, 186695774, 879662438, 937969145, 528581474, 598025984, 63056396, 559880910, 243889138, 808496698, 665968599, 23602464, 118351448, 641554690, 927351532, 427990498, 740834412, 135653792, 359321807, 432450187, 302988759, 820572299, 731572669, 854985956, 813038127, 355932578, 644922842, 377170534, 334636176, 435934834, 391163344, 763582739, 100108695, 167272603, 941428058, 549382591, 565480692, 954997232, 290493739, 854313133, 589888192, 577092180, 701713645, 551622774, 266556521, 424320387, 737856411, 183937786, 540994566, 677102985, 696045708, 274992004, 688481558, 292403564, 20817796, 77686097, 552486375, 358370582, 548139279, 26891279, 102735319, 817974352, 208343405, 467546689, 812313038, 409678333, 514209002, 481617201, 99484323, 818351839, 657703414, 285990300, 536802194, 814125697, 25429512, 862838178, 577219675, 975611117, 472465628, 152949436, 752580535, 908756264, 189675796, 423913093, 174480635, 949538032, 894073807, 656476663, 876561512, 767969539, 799999878, 619316141, 849936921, 276401452, 74564172, 97968155, 702759854, 901552618, 752103650, 78997552, 923052854, 61550013, 194937251, 514569591, 906164829, 880767846, 919269943, 989507659, 931462348, 689403757, 975302133, 421596376, 622306600, 644570566, 600326262, 954062444, 844995687, 380935345, 763663687, 463236632, 91950038, 270485434, 355159312, 694510925, 173513212, 383038458, 308038774, 71857651, 746093738, 271123068, 125039933, 727919384, 857405992, 676624943, 729715367, 298923256, 503245401, 521464834, 400282037, 192989248, 767425172, 449371642, 828493532, 738721465, 646086209, 583945617, 470541828, 597215719, 320013899, 285351193, 126369676, 426225922, 45893792, 881946063, 858284074, 890016645, 22425984, 341468163, 179545350, 908039901, 670198643, 559861036, 870893816, 824453936, 906192115, 157837427, 498863265, 104357862, 825126819, 426123638, 829706128, 515743643, 617959154, 166335254, 558903599, 238655931, 471321087, 103281598, 758059999, 327260517, 556525134, 326304615, 744759426, 462497538, 896184216, 42065996, 80214749, 680579904, 298538394, 266837708, 418368483, 264243682, 872532335, 735272507, 824496959, 627504783, 996853368, 895787704, 232548927, 548977925, 98373025, 928220986, 271290140, 978614153, 381355383, 909760910, 635209421, 787171490, 782129049, 431260181, 479925113, 520099036, 465668665, 613794658, 534031413, 952029124, 893528156, 330614951, 682217401, 954870478, 945262577, 17914692, 328027219, 505523406, 312145825, 956090326, 213403197, 472284357, 833029612, 820966572, 609327461, 860401113, 652578122, 569016493, 242277877, 134957207, 798014697, 628606534, 588275361, 929598381, 406707886, 536645119, 502871531, 886687973, 571238957, 396553443, 410551303, 373585812, 40467733, 660503036, 373469199, 883156138, 24444696, 14343521, 32731802, 194379054, 629748943, 631234281, 350407986, 124573214, 746158369, 95855683, 164761226, 872106048, 927695689, 450565314, 750192619, 838536312, 16399434, 926064518, 533133472, 784139213, 328037426, 355030143, 835047383, 822033296, 249863789, 697521467, 785210219, 16782726, 443575687, 65725778, 748115742, 958261896, 314628946, 119843165, 449055586, 206738301, 961719088, 124823040, 465864915, 140080928, 354608092, 338490898, 902427822, 588435035, 629579245, 204450611, 357738700, 312280529, 598709147, 821763540, 516254241, 989428455, 641067861, 532055610, 957692474, 746907724, 960800271, 149025734, 79619970, 924938494, 6730276, 723325275, 419967768, 962827997, 435367316, 376458383, 686777476, 595319800, 528613235, 942932089, 417025485, 61866611, 339876359, 768344221, 199957588, 832797919, 719885484, 832678617, 859615839, 609494910, 689404800, 918581932, 148958446, 696048031, 433420478, 954899226, 470488776, 79101227, 541655506, 356188394, 752671826, 655082094, 65769158, 15549514, 381577046, 507178852, 18901887, 830397375, 923111106, 706380208, 762098988, 205027270, 795223516, 623590896, 415965904, 203413196, 258338311, 936215215, 549121621, 602700223, 160685991, 448119073, 933255086, 836436681, 196594539, 124916436, 551720534, 893830769, 486315031, 367203418, 929807419, 928153592, 451056222, 957929040, 574162765, 236804866, 261826425, 644798192, 929970819, 151919666, 611792348, 851130159, 868810581, 499177939, 301241173, 812959570, 595201383, 62592181, 763677515, 209496944, 548633307, 869421463, 741097334, 525546018, 101297920, 235267808, 524839331, 421506225, 549119334, 470272642, 489472945, 697697418, 939552693, 328638934, 225102798, 645710536, 387539296, 243847021, 471519735, 374543436, 35943049, 11194791, 374325968, 118587236, 435320895, 171940171, 644643891, 572561370, 461259663, 643449093, 783573435, 209880031, 278289854, 188972882, 458965611, 686699526, 606712019, 789626625, 909735396, 132999253, 995779846, 483356458, 321006989, 274954582, 147578193, 489817116, 128493388, 958994414, 865281307, 40236474, 771436149, 684767681, 39067491, 883756780, 743393616, 849346971, 928692182, 249200140, 396319169, 70168429, 60445216, 109712197, 554147430, 988267550, 414923331, 939376894, 36157983, 483782246, 338022201, 546066413, 313167505, 622555624, 261062178, 973213072, 327312500, 56201777, 838640798, 27256065, 116789882, 922135658, 167116290, 585525370, 409834532, 180671629, 941929440, 194029881, 981348536, 470168818, 169049639, 949248555, 803182918, 554312037, 550067259, 962226158, 881521878, 514454254, 15255960, 492611715, 208026466, 504479369, 553681771, 981391614, 70850243, 253962440, 413036223, 227234892, 318405782, 294871312, 5094009, 377157778, 339098422, 32377339, 555624420, 192285486, 777354708, 276864234, 8651590, 209653074, 498673805, 497156124, 429144614, 802648006, 326138982, 531922725, 323562457, 906741401, 302269423, 921077832, 788858278, 492613703, 829187309, 968449474, 193186826, 748608301, 612511521, 760387975, 999159174, 450460171, 143902818, 507301652, 199306022, 857867198, 26043779, 168930178, 181048493, 992346597, 281012009, 771569052, 655431543, 106670504, 267060691, 169523044, 360461580, 666550409, 424722584, 819169889, 541012736, 709466377, 192409521, 230354518, 392104663, 519401720, 140113606, 409225640, 577178657, 740928336, 501387159, 376373984, 948366015, 366078451, 784466729, 423931329, 111234821, 219217298, 442017735, 133691805, 675673342, 252318313, 179745972, 647717759, 408068442, 358781164, 648649975, 355981891, 172126140, 713004331, 175330501, 933828881, 22735789, 820420542, 314322736, 752289981, 641534257, 546088561, 424456971, 120781032, 947976700, 558906522, 999428364, 371937091, 357629777, 377122899, 868448179, 61434205, 374286420, 478270702, 512729462, 31705283, 963013678, 168588829, 285363403, 13053810, 71927829, 121180713, 121620039, 68730610, 988623163, 237510432, 19688737, 454995240, 457403883, 469207434, 935985351, 187013479, 351740068, 461254745, 221929577, 735786757, 714822057, 968471472, 663575475, 845627953, 934031625, 756944584, 816043547, 804913447, 528122377, 385951944, 690741363, 34184887, 633960331, 839778496, 319951885, 526192181, 34034976, 141202508, 832197737, 156088688, 951810415, 94751249, 968730466, 920352279, 451360918, 662936542, 263804611, 977554912, 736693519, 64820343, 789725966, 7527990, 160139329, 701796456, 857205580, 93692880, 152023705, 391784388, 82448441, 679325593, 598715486, 302540995, 295324435, 781210339, 913820301, 596312402, 797617039, 773831676, 181761495, 215346836, 39585869, 331582982, 670453167, 206330460, 455123197, 670199697, 850530762, 85663600, 299042447, 898195524, 334340242, 493585836, 400608547, 345300840, 656556222, 156928545, 84999832, 320527436, 906368981, 591944920, 763613707, 853434713, 979567972, 428763138, 813144647, 607316218, 655480494, 137983575, 51458205, 890057688, 342175191, 123265745, 703257766, 907612371, 816522445, 296210123, 591445418, 561204915, 90754866, 582337724, 520087789, 578100215, 251247209, 329640413, 86480908, 792609633, 304709024, 47505186, 960228053, 554192028, 987559207, 692564399, 757361052, 199885868, 321794513, 978067179, 521803938, 741156864, 606172754, 620743038, 553046788, 18997327, 389548889, 44906582, 282797353, 517524849, 546995292, 485445179, 242554365, 401011110, 704796703, 761146593, 735868278, 157914180, 289676715, 945517992, 173377977, 855993964, 662793810, 699407766, 412292421, 128437859, 985297569, 531886083, 236280385, 559064456, 835172486, 233110169, 3708506, 765033976, 967125697, 353730643, 857201067, 792339690, 595433695, 818580559, 96128863, 119532653, 190202692, 550829687, 360468632, 627595048, 796613824, 62161591, 895655258, 778500701, 935187448, 945284864, 917181945, 377995330, 452237408, 534523926, 612310511, 425367337, 102875129, 51875025, 813890505, 556517589, 840068639, 544480794, 893190121, 416775537, 175848771, 31188513, 573104595, 61460804, 75470072, 465562719, 709677039, 48424949, 521719482, 365482480, 671310905, 388040490, 601766641, 602873061, 853429919, 213056060, 526450032, 963774318, 583723779, 896845796, 2269049, 252468999, 144076620, 678410678, 429667684, 469972896, 314235413, 117357464, 964406724, 254263986, 724167753, 965154224, 259232339, 335530799, 240500950, 392807355, 862896669, 549600586, 206682987, 339563802, 86719201, 347106601, 265058247, 770750247, 668404506, 1302834, 710146653, 463091504, 338785345, 552942903, 531649421, 947205023, 837917477, 935524784, 51369298, 175900171, 243320090, 53906707, 103064926, 585917522, 405534173, 537747202, 351131740, 736135647, 523314813, 448684839, 661002186, 606738893, 289777473, 363638512, 727942886, 291995589, 339441712, 939169892, 14766695, 11538415, 893724060, 746605776, 560248052, 292420216, 341935251, 273958093, 347480008, 988157651, 456946966, 772191256, 938037438, 107434455, 59264509, 1412577, 366958711, 119048317, 543093730, 455692189, 942297579, 378571216, 578364541, 539712166, 130481846, 589516871, 73946440, 433026240, 378896190, 487776439, 300665697, 937953080, 342333569, 594760321, 745349413, 492076070, 445053551, 167296825, 407201005, 852217234, 910928006, 824523780, 503987484, 928901826, 443999300, 600687159, 603592115, 872093260, 97716006, 623758232, 857600726, 782047047, 299033898, 397439298, 76523667, 700666028, 698102902, 306239488, 365035878, 998365535, 829140590, 776072265, 165997176, 815797309, 373169059, 203006103, 546637349, 326515286, 201641629, 883563390, 101255312, 785615572, 62157233, 425914784, 201084312, 338754009, 423605622, 737469188, 49096139, 508873041, 89550379, 64057218, 287633385, 608782147, 908354699, 900226239, 283012632, 818002079, 577695851, 738819514, 380768743, 889426305, 113312602, 183462870, 990091472, 318736220, 336120134, 700419549, 973448103, 665925106, 331763740, 809133672, 241614740, 788458132, 324680122, 678919336, 145094424, 141976011, 279869582, 935195597, 552329571, 798464396, 816386821, 638770925, 446865613, 655054562, 478009436, 479889820, 319574280, 780900242, 623210025, 935309130, 495489452, 787431851, 951965550, 655754496, 477580840, 580269070, 707325191, 725858698, 465427862, 702275427, 792697225, 108327737, 289220038, 178107251, 54092192, 798802845, 300811173, 206002245, 529673902, 766676481, 168911559, 90566062, 175342467, 498003489, 401350015, 133560733, 834512606, 158521994, 21521843, 542315922, 64013406, 620233383, 90866410, 118143683, 494305119, 838416744, 69657109, 145682026, 968769286, 659532096, 472082115, 587277305, 886494973, 846144339, 794033486, 606209853, 749218231, 513147722, 346672921, 245394218, 145207274, 334956082, 703282032, 35958445, 939978533, 475240302, 244118342, 355189224, 173712017, 814732270, 272392005, 182199750, 345850727, 573307790, 561584501, 748824517, 727964513, 97351620, 728162551, 668184771, 618383624, 794601287, 988925042, 830211680, 67538047, 505691619, 769572284, 739993950, 5454470, 323443370, 724080686, 78919114, 230105437, 542527526, 687977992, 234206836, 406194093, 231072487, 684190202, 549368485, 903346305, 470882842, 592303633, 33814667, 924268184, 337904102, 237070675, 485621425, 415923114, 324166410, 94979200, 949318106, 825580051, 142871654, 312215101, 10304307, 196535439, 787207220, 33970901, 849007875, 719730762, 601372916, 335705646, 873579088, 96474664, 216434804, 91297251, 338386842, 723880361, 673075959, 999421373, 576754794, 21029531, 566644208, 556352230, 547441190, 273298476, 647156109, 822198117, 236022289, 262383570, 69381420, 925418353, 290039063, 934824645, 149203821, 861917893, 435766839, 461484261, 298969804, 118964298, 609262461, 445988105, 841111434, 944061356, 136761534, 758254115, 874830416, 259520996, 572434377, 80237153, 137613057, 508661901, 596906063, 288625518, 852455550, 585185988, 318639366, 38618940, 495758611, 771051908, 986565100, 494743622, 402641661, 529729126, 980119887, 175297976, 681283390, 992055996, 694320940, 682603420, 468332395, 572895670, 130755835, 385177459, 980326328, 545491748, 697432787, 389391314, 853617496, 591687230, 730559996, 515352452, 339358372, 181876507, 873639601, 685458095, 60378683, 151716532, 804031254, 929296874, 805861511, 634521568, 376184587, 441480147, 233189354, 330937499, 238075567, 582375507, 63634045, 435396649, 642305663, 746292732, 812880526, 81243520, 859121868, 281838235, 561978072, 574985577, 39521568, 319019055, 79721561, 714788452, 602736952, 916737450, 288560714, 74913038, 383163458, 20619999, 494337542, 907710667, 225903719, 784253078, 204503260, 776853189, 893678739, 809504488, 826087543, 266742820, 320940660, 472065965, 632641423, 379172935, 925472029, 621307016, 642479569, 631672797, 105009695, 342843046, 3657261, 674843539, 778115923, 768009317, 710430408, 476297389, 709148378, 670953081, 392487760, 456112714, 984914467, 410041816, 773307486, 184207706, 508308726, 81872751, 953170244, 252569377, 906779193, 261654788, 537703084, 480666618, 945807470, 836237623, 437006516, 15052906, 369133355, 926442180, 838220221, 592067183, 832239613, 412803475, 120355233, 825762129, 917783535, 607410638, 474638640, 88617320, 976052548, 490649132, 141110987, 572712600, 215653652, 57617493, 172646307, 128766755, 787593049, 39609334, 451789129, 967692130, 762643792, 641657192, 821596331, 564980981, 999217600, 771165193, 849349519, 813308134, 171516977, 765259346, 659792232, 63375530, 800599387, 142169528, 638264627, 418387494, 243674477, 42334750, 505013259, 504772946, 286817315, 40223755, 983991858, 533512389, 829843367, 334141387, 307096248, 603687225, 685119941, 413792952, 728140537, 679749184, 862367694, 159816315, 778060195, 519535952, 901534093, 598724129, 522379160, 743454577, 446691266, 871478715, 629243115, 105753523, 974983961, 174407029, 941724876, 335202142, 797333148, 935132209, 390999439, 45867411, 888839692, 167250547, 496418167, 775531055, 950093449, 39277141, 340009971, 783579683, 654302854, 906986237, 995807077, 623788955, 144014188, 201834783, 596453959, 806412645, 765730179, 261084986, 861304315, 848950676, 324892812, 224099933, 215095843, 304551796, 159744427, 552955473, 910694406, 891591884, 132749487, 496607857, 593163343, 960716923, 969355375, 893994172, 219044883, 99039714, 433568248, 585378588, 672398866, 638912695, 343812858, 293722892, 649047214, 897496735, 416848980, 942222214, 452385489, 960896243, 346160497, 932327570, 99531099, 578733304, 452940817, 225013567, 269941509, 583783852, 317824248, 314955605, 676232120, 605363914, 167500525, 957236163, 656952502, 717337601, 905618038, 644335463, 198336793, 403716423, 767194663, 683630389, 710002945, 393330327, 113356052, 634682377, 221141422, 105733829, 333223050, 644208839, 316758182, 942132587, 666393027, 477754373, 680030421, 918273517, 213745713, 585920670, 576406784, 414217584, 770544890, 411402260, 697882424, 923080893, 214070769, 329659785, 8600408, 34841030, 5227776, 750130888, 211024655, 22839326, 287987524, 67294957, 70697461, 872715679, 495961757, 946239955, 951110700, 635692265, 638733275, 523034547, 270170060, 176176685, 464868997, 207747432, 384114607, 213360192, 981343103, 989411978, 233422641, 52743857, 266265581, 882385364, 373901795, 442754959, 712637475, 942717089, 436979741, 119973885, 518232031, 361787235, 865114612, 669324901, 722184178, 449407700, 926770376, 239135421, 646863344, 647424430, 199929780, 630678664, 730753813, 669606316, 941728093, 289220509, 961730804, 221118303, 191606279, 540519488, 911549861, 651201851, 248220506, 592002144, 700251091, 676149078, 765059241, 447163597, 698128332, 441675287, 524887240, 362660747, 818686551, 311135748, 572118866, 50348120, 375027109, 129060903, 188204331, 401495535, 548402737, 597909772, 154738593, 501978247, 75497922, 531125509, 522424763, 387120410, 80991319, 145992817, 414911864, 908415508, 604818991, 671971133, 257887476, 580614800, 256081929, 465767796, 336666592, 619264450, 978377566, 331410846, 776757454, 112378559, 353723463, 537086039, 340475233, 426551119, 870871743, 792042357, 446693688, 699308152, 397090404, 917368509, 123244638, 709271821, 31317846, 778768114, 193436130, 319754581, 688152158, 42907572, 276374555, 684901691, 599749199, 198999352, 643635748, 905971109, 497426910, 541316160, 423172950, 382308075, 472653752, 401270869, 263917611, 108112938, 116119988, 92030357, 448961697, 475933273, 635576191, 706529205, 913815188, 97026737, 298105391, 200630330, 563974127, 665894228, 771789930, 335189091, 932675460, 245109190, 954144590, 111764029, 87259038, 927270956, 577332967, 961293261, 877446777, 221786662, 995889637, 103046914, 13374837, 9951030, 78193920, 222070476, 788706335, 998681924, 991560456, 236265923, 87801365, 988850730, 931459995, 355482124, 718476829, 266259213, 756577433, 465105046, 359645455, 7659797, 535226398, 334631435, 108721311, 177128296, 144683452, 5605871, 897872379, 309475626, 886083578, 614884048, 574891095, 930870716, 497803592, 665001558, 598008696, 871707146, 404867185, 719113143, 394559664, 855735751, 476335461, 443167010, 808904222, 771331144, 336600897, 354682543, 139017524, 526638542, 388088256, 931166137, 671239029, 314680981, 789009685, 882633555, 443120402, 418636548, 575602291, 376119951, 147359313, 524979928, 585843505, 979484570, 173995122, 411490488, 381434216, 996802045, 324286182, 56114924, 156392706, 236585398, 387106833, 627964805, 89776524, 222703108, 576013674, 427946340, 571834139, 640990276, 20479070, 287393434, 263630620, 443073543, 267257563, 930163418, 207263299, 88584343, 933860925, 164594583, 655490408, 779857460, 35422972, 545424208, 411077519, 730079621, 602406179, 633752343, 100392185, 790381015, 781077979, 388130139, 899292607, 246679037, 463359007, 168183311, 343019612, 251038146, 401698784, 954485658, 468434864, 937246231, 368753760, 622357520, 123194228, 306226315, 204593728, 920651185, 511561748, 429885517, 621160493, 160451437, 550463504, 418186155, 372071083, 260248888, 5494280, 95451107, 665254658, 569771685, 169082994, 627733508, 703560845, 558644009, 124999435, 685806424, 944595738, 300114459, 439703411, 383200646, 30560137, 188832866, 477974859, 248477500, 611107312, 163782526, 71611869, 411667841, 138824377, 513343085, 342433968, 439895397, 449459063, 595597073, 780612645, 138528734, 647465383, 500714889, 283807455, 593745869, 652790020, 503244154, 935605403, 105152606, 355177408, 684886492, 58578783, 309323166, 261004854, 642381128, 229195082, 717289808, 120409039, 349882190, 507555872, 319327843, 150760517, 331732418, 421111333, 895742259, 207763607, 824576537, 915937807, 739597646, 44938763, 696800601, 508095499, 901773323, 329665174, 867025050, 270870520, 943381448, 568187532, 571639427, 537051746, 187223660, 333340328, 203234869, 401437601, 626020633, 436436405, 854808964, 743153565, 50050625, 344250320, 285765006, 732300026, 516768804, 328406692, 219729883, 495247959, 487924416, 199697640, 691513803, 52206199, 979364501, 769619673, 792627237, 54991797, 934017793, 235944992, 799577557, 164686674, 656185153, 340812523, 897026370, 494043493, 835247913, 937875022, 764137132, 212867171, 593392606, 742822058, 405075918, 330018085, 19012513, 39175933, 922188877, 529876284, 119529634, 132791624, 856769245, 340540352, 551070169, 135096531, 980635837, 92227989, 318592562, 369270415, 176412454, 278590522, 765762163, 225696387, 16098896, 960324187, 800546140, 568803513, 859636975, 633283170, 999868021, 108527470, 321137211, 426868186, 190256050, 763322258, 106246438, 417004030, 766654439, 579528639, 676646021, 44573347, 106571229, 143307583, 843397445, 646972455, 192040006, 956718742, 463540838, 525393499, 314800375, 172227552, 812446416, 934099741, 92992272, 135991901, 697439443, 147634296, 364639915, 336411246, 307510484, 992195291, 208456570, 961672896, 497537435, 727019600, 466568334, 190511341, 242866514, 423102815, 244846636, 686405830, 577200419, 327152894, 716698405, 257164338, 305854396, 532982082, 102169837, 847479456, 1463516, 724595824, 690033865, 155241340, 605278974, 573963099, 185419309, 376672571, 998217133, 864962329, 937607000, 938926840, 342892469, 283953964, 596158941, 621339421, 324625489, 192521687, 50251134, 347195544, 637574060, 858677971, 965471889, 679541469, 867137991, 12231743, 422732257, 563594320, 862820743, 923305171, 336037442, 52363561, 896767714, 981194847, 395607533, 65393263, 910211722, 631015918, 544353662, 477361151, 70094985, 663451520, 359938172, 351997405, 393990740, 540024070, 823558602, 916455075, 208738565, 187613650, 983026112, 406056892, 732907413, 753980017, 398634150, 132919179, 348686279, 853577402, 982612353, 695452351, 601463683, 956914494, 306054210, 946405828, 509141333, 85800210, 707814336, 277990868, 40573923, 851667830, 490123087, 353284481, 300291260, 194215100, 437309786, 434676994, 551322104, 45317912, 8566484, 525501348, 188640616, 944419377, 518031303, 349197502, 375413130, 234859288, 106168944, 561919233, 57050827, 212362707, 903347756, 568335685, 221457297, 893850586, 476598572, 754617776, 747260956, 377009558, 32444232, 510207118, 51232386, 825790409, 986773371, 342103945, 872684265, 341516595, 104055475, 781256631, 510067989, 893538312, 680874835, 330051498, 414194225, 9537288, 625358849, 778782154, 758451953, 818074709, 596366998, 115730375, 928546471, 637163471, 645085995, 502483758, 857842705, 871454449, 549495247, 468390062, 380595794, 56061279, 867729794, 478318160, 907739766, 519953633, 383446543, 349879651, 478309078, 155862074, 50481308, 684306874, 836516087, 244582643, 511488353, 828729109, 174130139, 116051796, 334730746, 468547629, 940740626, 406339184, 264075255, 498566052, 816978621, 931375284, 165321962, 376850347, 202349298, 273374401, 747095341, 317197240, 390756102, 481754064, 679740924, 763207086, 455957681, 96541121, 30895441, 936508598, 613884776, 395756905, 858807495, 825847630, 233792634, 907858246, 648391728, 287537715, 287299385, 256675259, 764798013, 253587483, 64555099, 705438811, 514681865, 287891596, 207584478, 992546403, 828930743, 164338242, 173704530, 922728997, 62696677, 169393577, 67794467, 791400223, 340249134, 992939015, 409132802, 235200548, 696618389, 998390251, 21478345, 268060698, 614248441, 518952245, 76836983, 107110025, 945139664, 867374185, 518434943, 328071955, 317661597, 119817732, 482630315, 830767917, 552557989, 430017755, 176401823, 281607352, 168148672, 164002698, 383747428, 734344972, 11831573, 685005062, 590339725, 381808394, 835804854, 754757989, 572932384, 37348917, 438145139, 29885359, 130512541, 784571007, 603230196, 825323092, 380853543, 774526196, 367188519, 487886529, 316449540, 464412600, 228305629, 542076333, 388725457, 758292653, 906438411, 166142311, 342510148, 573303577, 483226232, 939378657, 371297594, 955270910, 629204003, 445102069, 729959664, 251459111, 11390805, 849389094, 577203722, 200356904, 49847588, 4660955, 316379197, 940365548, 207241759, 956242498, 118746087, 967756565, 599567019, 35737964, 488504269, 680551297, 88226899, 422932269, 149264479, 638866420, 926451147, 84190583, 472774837, 794746507, 996187962, 301578632, 12322883, 176853066, 397802237, 637477921, 853846808, 909801890, 495589689, 106404951, 594550643, 516377894, 104601394, 383484810, 239261252, 908652911, 388296339, 130575885, 150016599, 968577081, 784335442, 511700456, 140807577, 756983509, 106869192, 727830224, 522178760, 383845795, 705641930, 782330882, 585255942, 711360056, 452757102, 70007627, 103237576, 133521689, 877409364, 260384557, 220663215, 404991986, 401292750, 704775188, 565690084, 453222842, 838699590, 919739834, 388838909, 412854860, 682260286, 912216964, 671401135, 249114555, 75308912, 823548990, 64464154, 622606058, 424297936, 652961301, 816966743, 49671577, 375040470, 728236001, 348776007, 300192796, 403150955, 934496527, 719715101, 240285357, 840516745, 987019640, 8993223, 227616323, 793455557, 874570293, 448034759, 586233370, 969071200, 690872480, 697307806, 194851897, 117083801, 234123297, 697694032, 751766756, 654990531, 236255227, 587449596, 482946765, 539420237, 532777052, 727465759, 921233759, 635783396, 531148478, 506626906, 306002554, 115400598, 60727943, 568268633, 201926561, 130100084, 104679676, 970339027, 74873134, 735321803, 775417333, 754714327, 621700221, 859878566, 916348489, 222840659, 866610098, 154017673, 478454727, 982396664, 283730058, 852281777, 70375151, 537748221, 514611239, 817953204, 197199106, 845650, 270137412, 398145215, 506796983, 307644596, 200682561, 516649832, 390866867, 549198437, 216719139, 625995184, 490630786, 743600438, 598934362, 952461000, 873278670, 381797277, 306225462, 91875109, 669545961, 806527540, 668206158, 25693322, 825769718, 40770674, 991238149, 879532120, 529581580, 246610803, 863193314, 509394447, 874127999, 471637386, 187110897, 530462652, 512995187, 47390857, 821560434, 544409795, 755025474, 17995561, 60503482, 29397594, 160185457, 915040400, 645162521, 740373606, 43563618, 422310037, 941301130, 379766982, 788994120, 54584797, 183751691, 198341560, 847328407, 560369208, 491618087, 368208691, 328109816, 896398885, 779647341, 42068480, 569486358, 256856182, 188983388, 318035855, 35163314, 510484132, 923179367, 254914740, 673284963, 997031485, 218089033, 292517541, 331156816, 26700019, 619499006, 591593308, 750513843, 33192773, 401887017, 208404341, 201792872, 793423977, 259603376, 64805980, 958079717, 860136264, 609659466, 199539657, 566874885, 216741099, 333733522, 43701398, 170809043, 8406500, 542001473, 989186301, 249060621, 901167915, 219330955, 855724670, 290792705, 658288815, 875898561, 522679861, 263923689, 40406907, 498353176, 499525708, 773841100, 322312641, 229793585, 575989643, 795981136, 879459912, 897923518, 61658420, 600625790, 842937304, 288551817, 118946563, 585198898, 743233730, 488348911, 514513485, 802877807, 505579032, 682963670, 867909104, 575720932, 30027139, 38685395, 423374943, 299912739, 193860743, 246494144, 415917187, 692561471, 545405312, 690071802, 775700364, 332103230, 178961871, 751044790, 505942250, 90088473, 90295823, 101190101, 537346178, 42958098, 420978435, 821707012, 41512310, 595261991, 192851643, 316833754, 9164808, 829537081, 796587527, 139144497, 627498379, 121760483, 808985396, 630864295, 46890266, 526023161, 268808958, 765420344, 651238717, 352332360, 807082412, 524737331, 366945072, 752843678, 694040815, 973287908, 611421769, 877627600, 161254104, 303825985, 152189123, 149333640, 892108082, 559602034, 897996229, 110191757, 831132346, 156608796, 367013069, 23548953, 252920325, 304913606, 79033785, 645497065, 741727287, 816798529, 455679219, 527290470, 620234123, 734344153, 825781427, 754830175, 493307676, 595147282, 557360365, 693049081, 386695992, 842764724, 234442491, 663771397, 212066399, 814462964, 642291926, 974634090, 450930570, 955748811, 295937688, 109766009, 602138409, 365088093, 241763017, 604171561, 58461573, 422682138, 790576133, 27799324, 129099389, 107694995, 101900569, 135537987, 20498999, 20712856, 836280102, 91742329, 788712295, 520582297, 152983320, 194028455, 503101157, 300262150, 382417713, 541482929, 176191185, 717977402, 962125626, 651908612, 937833893, 746482496, 378452468, 793921833, 907428216, 68217207, 483927679, 299226269, 914669896, 352393813, 400119856, 59583791, 973196041, 351309612, 256683234, 87376762, 951340438, 233272729, 909061106, 25623133, 800077487, 842764539, 317785732, 880512653, 922446014, 545651681, 848503470, 324949980, 531944588, 133349987, 859675250, 666406836, 935180429, 65727043, 51392136, 161537274, 937703440, 777227880, 699922236, 557108229, 298808654, 511722185, 803608600, 520680441, 531591169, 707010573, 451762535, 696474535, 733396932, 102689447, 770001564, 202891432, 146375615, 661847260, 738189058, 499204821, 585682460, 475211524, 352282041, 120904561, 141039482, 859843258, 918964438, 321171654, 672005068, 527262040, 590005098, 372245837, 49827646, 185477892, 656368221, 113242497, 252986841, 260310604, 800722117, 408083827, 770783592, 960207916, 223992292, 691900446, 686861703, 734044485, 529888819, 245476135, 380171123, 413005194, 614341337, 697068440, 69111229, 384176175, 62236706, 848847479, 743067995, 582192179, 946397335, 339929927, 107157466, 202621527, 995486504, 25659031, 153324480, 323391425, 88804685, 626513679, 846793120, 3268397, 279179087, 51350447, 177601071, 942545265, 748923131, 997298647, 39963159, 217108968, 834279534, 599694537, 527119547, 896623442, 522904506, 995747008, 711740861, 250607089, 277067488, 605560465, 872466106, 859222633, 490493753, 584402430, 808600743, 203366278, 235976247, 831499416, 683157226, 574917111, 389527069, 392822265, 116036641, 887845854, 575282759, 938874963, 249210075, 386594226, 427459603, 888397737, 770189818, 896661769, 961039484, 512683449, 182181458, 133305052, 420971339, 975949962, 963822753, 465882191, 888351755, 980820202, 434567016, 83159802, 951003403, 593818782, 795548028, 249144711, 436476958, 887244216, 220594204, 285362175, 555798596, 551185624, 817086740, 168428707, 565669042, 109309326, 764158541, 147599081, 757169353, 368415519, 187948778, 662668636, 962331746, 31411209, 903866562, 764367662, 32266332, 998680142, 905993366, 881377287, 447489279, 929667176, 605808333, 313308148, 931202524, 755706584, 468572381, 661154578, 422885901, 985066119, 259392055, 715605981, 691930195, 578525092, 193951978, 564986310, 546843356, 982823358, 302947773, 934740238, 772427320, 376518106, 487052449, 834896345, 522182021, 512137815, 203290456, 988262238, 243321610, 65395719, 937967426, 251820179, 878862448, 313647597, 710188941, 744430980, 262873983, 382581354, 483793652, 966167134, 454672540, 603560964, 496567002, 57418472, 155775015, 298144749, 70530864, 627121724, 978021432, 259084339, 771667254, 410197351, 851058314, 508394068, 395686592, 884167093, 228734216, 813862959, 492406519, 733345739, 890134012, 430625402, 771989841, 219063473, 861199642, 290812323, 362743253, 968210658, 665812989, 860182076, 897581612, 892806546, 368217542, 50585846, 489330075, 475140295, 292425777, 815684349, 524714945, 403843171, 661546694, 808321047, 380143415, 808513913, 608896910, 68288018, 671152877, 813281019, 161980917, 985375716, 683363408, 33528621, 121953146, 710551179, 109512912, 30453370, 204181811, 487495666, 807713103, 16812347, 223445027, 418206430, 239979147, 180710487, 881046851, 854749419, 970827678, 875165836, 711885551, 39935301, 329377761, 623519755, 391210881, 778625669, 408985570, 230948175, 876475828, 561731448, 114720131, 775479818, 409174963, 544193243, 791763111, 825837796, 587853306, 376459581, 928242149, 931557965, 454987596, 271897160, 432073460, 713711246, 662380940, 854541634, 260219666, 204445964, 226967495, 377760066, 127781480, 317396543, 859329970, 860322569, 312793692, 288862621, 566534384, 495605340, 253416494, 22485406, 916218669, 36148853, 987666353, 722443503, 491969169, 511181617, 301163356, 240123050, 291497002, 470860625, 196586958, 724871839, 269902921, 509695338, 994580936, 195878185, 252698762, 383498623, 526484220, 860888449, 483488101, 367976718, 358641458, 991454752, 896010816, 610256749, 445540683, 829712360, 623657508, 43214394, 203869932, 655619939, 390970332, 761100917, 551532571, 638609046, 817072285, 478400132, 905733616, 390204651, 221286127, 706408102, 592828284, 109404140, 504611593, 786066588, 822444205, 214567436, 626713788, 766218811, 503924314, 144468557, 410057676, 78432340, 463652904, 919436762, 7267547, 827696233, 501169246, 770410963, 418240975, 925065541, 498270350, 852097302, 92144512, 47163368, 476431603, 782697020, 56130633, 702241384, 511388604, 44202274, 102441626, 655121174, 373856936, 863958642, 306114029, 214373056, 930961082, 459126646, 532693217, 939024679, 295847335, 857303302, 546847724, 996656312, 964035068, 61155429, 874163837, 967738396, 462870825, 749609417, 976936072, 293001686, 922925001, 933320893, 120586264, 969569606, 370196895, 550987575, 700558445, 737509686, 913120696, 980661687, 351857235, 657524423, 879095665, 712044116, 421189749, 961376020, 197674601, 332444503, 29268879, 548769473, 841416900, 365897362, 304006658, 994424024, 681744639, 852423799, 692725492, 650071634, 353598672, 582734445, 59112425, 167662921, 556817956, 951552368, 149448561, 285223431, 336031973, 735958317, 187328065, 694696467, 550556455, 539451632, 818019469, 322852472, 539982498, 441909878, 249743032, 649083201, 239320146, 822368152, 256066142, 810415292, 600706487, 356783213, 137975220, 823759932, 237654746, 819316343, 523287383, 683761280, 518493081, 458671312, 935424461, 303712075, 813055887, 796547080, 424753129, 433938372, 413497422, 706650821, 384266408, 382194283, 244454367, 779684575, 519278024, 696073833, 800308633, 145205148, 242069381, 962596183, 799265584, 157646502, 133955185, 34225419, 904303175, 413030071, 556497231, 211919791, 669420893, 291968135, 847619445, 213634913, 172223040, 518789313, 271617852, 688275349, 774809343, 266405182, 384591280, 932600535, 76918990, 294536932, 102204115, 805782558, 472153789, 773089799, 796691033, 238203420, 984770197, 381463597, 294395489, 236231500, 884748462, 999181679, 551274047, 29066335, 679596976, 426214477, 710576411, 473669405, 710823549, 933716672, 481888016, 215651816, 922656198, 813551400, 861580839, 679976137, 896932601, 525367858, 251554773, 740223814, 417000211, 977382053, 856353099, 826231075, 206181023, 712235123, 752101838, 415073546, 764329435, 919677405, 199724673, 10266011, 184051679, 533291145, 306317256, 15832081, 19002639, 340242785, 934737897, 728945572, 737830033, 544671398, 511706922, 363857603, 394512149, 294677095, 845622480, 875275261, 197131912, 219904494, 517737234, 561588125, 878429394, 573126199, 300426930, 223176198, 488304644, 985860245, 811079253, 775061071, 95537550, 11461466, 329019433, 35548906, 707846081, 339468059, 899312108, 670291070, 564042697, 631733792, 85895521, 350174517, 602868888, 483445557, 329421764, 791188720, 628580633, 84513481, 776585214, 410105813, 894426827, 166923388, 563432259, 258635461, 583766384, 352431406, 114625381, 253379166, 789903333, 773335597, 530638740, 754959445, 287419732, 245298125, 406323121, 329318066, 152865065, 790757089, 774611428, 262519327, 226307566, 751792949, 573534881, 318011362, 268081259, 79602833, 397690184, 559537131, 251267124, 790626568, 343718614, 747530913, 281917551, 714994147, 704179829, 256859237, 994808626, 559804099, 587082266, 719203955, 542321112, 564055583, 125244477, 778785985, 26863704, 817747752, 481096483, 515528217, 284514308, 681917482, 462236281, 372210690, 893631536, 528653705, 828005134, 439970808, 366886743, 790853343, 857438457, 39898329, 889485297, 299017624, 968749646, 219996524, 488772580, 247897050, 664474829, 744579916, 551212016, 273711854, 164391024, 480973094, 295503984, 749297848, 521190829, 215699547, 740122570, 862406838, 580459008, 516780202, 157946400, 547922722, 771719944, 66350978, 368882925, 153998828, 208985844, 833489372, 809821021, 767027687, 846278204, 939448353, 878823205, 5353537, 92853765, 93543950, 755099266, 24607469, 456326230, 135381382, 581079985, 421883520, 268672369, 415778603, 776936203, 933568578, 620078526, 498973700, 402542391, 408132709, 208397700, 864141877, 662819293, 447004243, 287624088, 185247212, 909228233, 451971606, 366480460, 827115342, 796611427, 437630325, 752279854, 773006887, 513489028, 903549507, 718670909, 666242890, 769190443, 79358299, 346866669, 420138557, 643385097, 256708654, 326869611, 984292668, 994609407, 91761327, 917864072, 719861185, 937640167, 362576759, 379394941, 792557224, 730437679, 554015363, 699935169, 43380670, 126421303, 446890186, 420050502, 147567534, 152443587, 526024500, 448306614, 781029867, 71334941, 531653875, 930150246, 276504212, 391699558, 102753666, 272924101, 211971299, 472376751, 365339686, 796184871, 396912492, 521507250, 980033572, 341261891, 492433306, 994072857, 196988021, 154933582, 132454670, 153156669, 516666071, 188259256, 318537751, 832983449, 183180283, 348724839, 123939559, 240269660, 671374486, 670329580, 109005998, 638784625, 168146428, 593962710, 797316704, 972163843, 123698364, 332329826, 319797197, 551582880, 480910230, 219603972, 58630968, 669058279, 879345297, 926679278, 748969192, 331839551, 942225758, 820532041, 81975577, 896183107, 320076347, 535755276, 166574183, 646395998, 267453749, 627210047, 491938561, 179327004, 901105616, 332346054, 265224077, 417623325, 948516376, 130227618, 62626809, 853257867, 449278164, 470878471, 101896365, 181047309, 620674919, 923145329, 523616717, 681166080, 925437187, 411317826, 310190975, 45054023, 458322376, 242937382, 341746628, 541523510, 159242023, 536955164, 345091432, 707944153, 428880969, 61820856, 907614502, 610998302, 969622216, 708436587, 284362469, 399773050, 120345577, 163885348, 63810671, 643978311, 933493090, 623411637, 269405142, 522485355, 581135279, 477248287, 837641582, 432587184, 210967815, 193787924, 980477485, 999340608, 559822950, 568570895, 679690966, 817412484, 739194430, 837943024, 996090892, 689181481, 752396295, 616741775, 799163500, 213113822, 885530390, 556286291, 972012262, 690437318, 276517027, 648166940, 454266724, 546599173, 70806194, 260179687, 797380664, 91815707, 275575120, 493206352, 271592680, 138993624, 800066480, 172560588, 682598259, 52549243, 248816778, 219497863, 486188312, 616014162, 595066904, 774917782, 193164329, 466245873, 773489672, 49677799, 393598007, 130941553, 294017382, 599837450, 600174737, 419473709, 800093447, 146398794, 221862802, 115477655, 874630146, 945090957, 984729159, 737371630, 407764031, 107395658, 770456863, 165488265, 125237298, 729001975, 733689657, 895392660, 873182777, 457470011, 54519899, 81174309, 877917475, 580680533, 114700810, 232451205, 893903274, 140671826, 944809029, 211349171, 209602159, 30899679, 195346577, 558482715, 705102692, 205482411, 988031701, 492234574, 278736646, 489121534, 380802867, 968077799, 591605627, 695678589, 257451706, 166097982, 709852710, 534426192, 735396168, 565822587, 668130671, 667183151, 302838634, 771092163, 977912341, 922106281, 711075598, 490569517, 324611600, 864172701, 973971862, 264537924, 494449240, 914053625, 359936709, 997679405, 96848986, 357084425, 946675465, 477374592, 80245409, 486634846, 16766509, 178172184, 764963973, 226597971, 515711325, 514907545, 853630161, 153520727, 492410530, 20739920, 890789966, 501098408, 749287354, 669032557, 316218600, 227778411, 352452378, 388363135, 203335386, 570118496, 233793898, 340745049, 593750139, 215010279, 629545653, 587836558, 773418104, 291906682, 833810625, 896710719, 738310296, 964405146, 567370034, 75089973, 580549066, 223017896, 125113636, 225348481, 152529636, 796502886, 559716296, 2222269, 132566944, 865913789, 134394174, 269348648, 400426130, 617319114, 882800692, 889849041, 211853210, 80486080, 263819895, 574165112, 270184220, 839342925, 563051107, 332244023, 798887623, 305958482, 457869145, 895283237, 458289441, 975812363, 917028200, 410538450, 282707901, 12030940, 636379190, 770184073, 381047912, 744124991, 322632216, 70936069, 819271669, 897812537, 297466135, 505381010, 509359685, 185892060, 578666497, 583701353, 399095640, 268958728, 86670985, 112770388, 294777865, 175820256, 767881892, 223753451, 725303232, 126169511, 231929192, 289982983, 695571312, 551103075, 139489389, 134246638, 16460073, 155237454, 998532506, 404183891, 782990240, 185699880, 638841387, 122230407, 644400303, 104282199, 192822721, 448445164, 878640635, 388075775, 386278677, 626875132, 222866530, 413333070, 964303501, 128160185, 516322720, 324502458, 696198787, 635755290, 73198684, 20970567, 806278601, 642646214, 422818264, 703358271, 226329391, 645426755, 706569030, 533556446, 36127794, 688158289, 717717696, 720353671, 285298676, 660840993, 486699597, 249452758, 253894938, 99922323, 443052312, 329931885, 128552456, 346543509, 383161337, 679345517, 718354571, 104035849, 318442168, 605144710, 632992537, 992462693, 911055492, 437340596, 251988060, 513245953, 116722268, 94278331, 4296564, 655783790, 585753148, 202374858, 867532748, 745197883, 638989246, 675127021, 845956304, 752971272, 471136199, 388743258, 928961709, 432160143, 852004265, 738573704, 687584393, 917478399, 581609550, 862201927, 230218639, 125022592, 53432964, 171085346, 359182694, 593781794, 442701106, 675832293, 328065314, 850598875, 788276208, 28235250, 498195705, 165715245, 436019611, 468183632, 156476707, 992442842, 346119894, 543163167, 963343597, 875767689, 486243289, 394379451, 451299435, 561964427, 822460608, 943054869, 809187016, 643075819, 530964793, 522275597, 165030019, 268042364, 35130547, 911383724, 56668181, 991982055, 355910513, 433034299, 84186695, 816810798, 193081739, 999531861, 7667839, 553669564, 235040730, 167679886, 246668294, 983449860, 628699349, 300947189, 413383936, 61752514, 450673969, 656650164, 259065573, 747506276, 932364798, 395040892, 709370188, 893361798, 423817546, 427680144, 386563780, 662631997, 357427275, 721000558, 954658615, 41010602, 141500226, 111598960, 978754862, 122886065, 54908717, 626615728, 748350909, 449067253, 675511338, 667172974, 120479113, 281284923, 996845583, 744953143, 351568982, 854245614, 183948898, 946321469, 715649457, 862649430, 944557543, 180462372, 317159030, 64383304, 689339549, 778930311, 961728511, 367683508, 280071935, 223167784, 774352192, 980417749, 765868351, 220458526, 329073876, 933916996, 478636996, 29270526, 641989580, 339608168, 478486647, 518125030, 310409803, 519822096, 702799253, 209765417, 216468950, 529181985, 363176620, 825155402, 597897583, 294755383, 992038850, 456530831, 352301019, 92974336, 750291000, 773724598, 249276123, 663284095, 426964751, 623227601, 851401743, 965523968, 833507438, 644373089, 201559426, 503726864, 218978319, 45044194, 624622217, 846744854, 448288429, 439326916, 289919036, 106214901, 877973184, 398013301, 105412462, 592433358, 495720875, 416934512, 142918608, 112513779, 205053927, 962237786, 143588995, 900496223, 771700798, 920239004, 188322652, 360933493, 951501412, 442901666, 247589695, 907861601, 441692331, 223801429, 617060424, 977440136, 353803807, 498025320, 584186765, 35682688, 411230757, 918913281, 909671649, 814677533, 381065813, 785486562, 570347964, 837659306, 158808211, 837321122, 749014283, 694580733, 998475286, 189906478, 351568128, 524922822, 524166563, 972438552, 613498827, 749570717, 131756808, 687499688, 633895985, 69976946, 963890141, 894000711, 118909168, 173422419, 983500190, 761403340, 183362071, 328241286, 942405600, 303267976, 925272324, 900241925, 670757519, 656540170, 276561463, 326712656, 336837618, 477459249, 914293526, 535947995, 349338377, 843745600, 687363750, 447408319, 984372132, 586919004, 182066373, 462723750, 22872947, 577227527, 348151056, 977264946, 166931403, 652541759, 178514674, 72487560, 39901528, 362915499, 957589049, 378586079, 159331652, 564994925, 227812999, 777232632, 838140481, 543184493, 52076992, 895701, 981490615, 646924103, 61657228, 719040791, 655105741, 843883901, 589584547, 287291299, 994674140, 441878332, 787553934, 222176606, 241842962, 63200767, 671898328, 284159658, 141605787, 496699656, 723789705, 327045112, 540660107, 741815534, 170510038, 348119969, 53328802, 645702221, 734664904, 264977334, 576307572, 313726919, 35196688, 95551387, 854125934, 636699947, 210356234, 867269240, 901870048, 855396188, 338956692, 401997432, 25967920, 69316581, 113645370, 820689430, 973553693, 711752511, 795562426, 288654896, 239474062, 492311617, 108695744, 456434274, 700386211, 866693390, 677160770, 727066391, 328415347, 225395586, 560205534, 58180139, 479459501, 221041539, 810635555, 381809670, 204752422, 67110934, 146743552, 195211028, 276119066, 935121482, 665931915, 328594844, 36491200, 640268046, 185755509, 776279469, 783898079, 724547407, 660982540, 115162069, 529071803, 244953709, 117032672, 219257407, 566451240, 660863408, 499935440, 468344459, 82620887, 944609109, 218244955, 32283990, 3207286, 947764773, 909240766, 937055611, 734149398, 271877098, 490404546, 211734652, 20024230, 372545904, 519031231, 767166124, 966550809, 227315980, 155700295, 311904303, 184894297, 259739853, 688342636, 701535987, 112047754, 456278218, 114132524, 215171595, 45989576, 335534291, 363443926, 494129232, 335409663, 101247308, 167261650, 42762182, 55352506, 11764276, 556445915, 679920194, 866499751, 6991811, 184654273, 542653730, 841948541, 177315823, 918694704, 27249612, 269849091, 489052604, 196855267, 867127973, 761425860, 942094338, 620558416, 152237381, 529605906, 328031377, 9218698, 891162852, 305803192, 305087356, 61901359, 496422745, 382710807, 19143006, 812579371, 801617161, 906854680, 214305178, 986399988, 349988483, 470172702, 905817944, 131710881, 167648804, 841778880, 192159101, 827547703, 634913802, 967383307, 274745823, 589322372, 363260351, 747943926, 675275635, 834583262, 718312420, 182474047, 143104522, 757926346, 313333695, 322883359, 705422516, 167305014, 666567468, 404011475, 724539797, 688904814, 310898074, 814934513, 449855024, 806543590, 673497337, 774739108, 589278564, 692617398, 323523308, 472949518, 643629624, 667358645, 525307255, 737074954, 771960162, 986184023, 422094352, 468520228, 576571461, 311231604, 404982617, 69880918, 629568850, 865200689, 337373929, 295412461, 588033030, 703252432, 435417875, 295581366, 507723282, 942775208, 645611423, 267860760, 15337383, 943760025, 736493088, 30780639, 936817749, 789295913, 47224596, 88597360, 499846292, 639439694, 71247674, 9992788, 660660445, 631160257, 620239, 555834644, 485398529, 103539004, 369882946, 624334025, 924095222, 921020984, 176466465, 100747493, 247487155, 715895679, 62535495, 552321402, 822375464, 203651681, 442988171, 345938539, 754602971, 927572096, 772219944, 404169830, 101102230, 446258164, 625477800, 669049923, 830459510, 112061175, 577656212, 804010017, 440257220, 289858339, 786790378, 663236701, 604311798, 275413207, 708999955, 189262728, 283164009, 275115922, 334377355, 997591831, 385629393, 656681007, 847042014, 641416831, 932119109, 360300013, 993611935, 556818239, 952590781, 510242946, 583792067, 490562526, 275366315, 697994737, 215278485, 172157343, 460293635, 886102411, 53594931, 2489252, 500899515, 214183283, 958559677, 157260586, 470112862, 587280712, 865876352, 856925326, 397371046, 562547650, 231169480, 40433049, 626853753, 625118291, 378078233, 430376597, 639294788, 992776848, 52368936, 804346912, 861757127, 716344018, 820196419, 8057324, 456688345, 850770653, 529308949, 24207663, 453596898, 813133511, 757022390, 74050225, 292005482, 204194272, 883760801, 311561543, 958553838, 80214820, 527810997, 832427278, 562603227, 765505956, 375892105, 986725482, 811819208, 158003462, 240557182, 733880901, 512200588, 355374891, 819124938, 27697807, 774056067, 698118340, 904095150, 511156198, 209818731, 621748190, 118002313, 804792089, 127477, 739895643, 302361061, 735419365, 654879508, 153380045, 661473308, 588658090, 442817478, 173223184, 476070823, 710347085, 932386818, 874021515, 654240874, 124352018, 791842805, 216754846, 801807082, 29830412, 158108668, 164197588, 581350769, 678767497, 190971568, 224094116, 271378264, 428583404, 518816805, 870195492, 810751924, 286694744, 778479655, 407059249, 360759585, 98757688, 305698230, 545415962, 735518958, 727176495, 437903066, 786063860, 530028914, 559418000, 28947898, 508567703, 191578528, 10474009, 220819554, 557278379, 594971083, 904017047, 828921725, 706430420, 874891376, 27526912, 542553184, 527113732, 241406420, 616254952, 577109508, 262741913, 223137581, 656866375, 249564534, 112613371, 787605116, 126614585, 955827486, 370447122, 278639425, 484329, 426287230, 622559892, 646025601, 460921293, 690776279, 491330254, 124045605, 681548016, 819001323, 20057659, 638674020, 497917072, 235768359, 467115818, 206149435, 156892351, 766546038, 996541093, 129463523, 884284834, 935306796, 431565773, 500681550, 261792861, 753291082, 948301176, 268035519, 163106294, 916948628, 354898974, 219933438, 236592294, 693006256, 188285530, 206355267, 178978202, 884206349, 69687580, 985795894, 331610062, 111664829, 416817188, 377402297, 299442172, 344890482, 696229612, 263360782, 996625339, 221474509, 297995066, 595769889, 208042473, 410470680, 500515397, 499989380, 706669129, 814985458, 759077123, 263493292, 699170037, 631339993, 253633610, 673192124, 675153141, 874958993, 37008724, 711343196, 613401322, 852648143, 600678990, 192394648, 51380980, 829820044, 894915171, 847149398, 860985105, 605447682, 142829439, 20193112, 398855510, 410702835, 806976249, 502955234, 489964236, 998431646, 920991916, 139015393, 636790415, 978489841, 749580590, 243184338, 112588051, 425231137, 510066260, 731698381, 889502629, 242625057, 657241337, 526938482, 176143480, 312508964, 478147944, 392967815, 61867452, 738099801, 806995199, 28148513, 334041363, 526994652, 549523512, 997330143, 647203687, 590394654, 318388976, 762861552, 664472564, 219924447, 332483135, 478404589, 454506275, 555239576, 611009977, 664994653, 565399650, 550644317, 651817697, 990580966, 872172148, 778173761, 127493417, 946517596, 971821630, 991518081, 484533600, 873710238, 768278376, 610970377, 444471745, 802122109, 289559545, 53692899, 84198386, 88979806, 967806712, 206892122, 75939707, 755808621, 248474676, 436137086, 891079738, 811733611, 744072298, 32439052, 548305781, 283647264, 55200538, 724422252, 800358284, 531016959, 501470485, 935251647, 830909481, 892557521, 273232579, 575399940, 913241549, 992301788, 771887932, 969566616, 300056777, 33027736, 975420829, 841222812, 572343830, 346788874, 721287826, 294625586, 604646283, 780128537, 392076861, 139362064, 250657742, 870803342, 309935086, 376093361, 245163505, 170388143, 816448783, 340979164, 554358651, 371377783, 465152588, 908135407, 494658147, 121791944, 645611620, 582822942, 818214185, 134241336, 353206920, 343114124, 326255233, 649106459, 489165018, 233153938, 685605118, 211485005, 447450089, 285024179, 195241537, 565056018, 246324474, 132907079, 731327708, 176019591, 219547312, 632887307, 775792115, 95889334, 617462687, 118422240, 881714259, 359904982, 534443588, 361941965, 601011066, 19152667, 953768602, 385249628, 339896257, 939834422, 601880479, 40700547, 323048022, 957326118, 805975658, 727097429, 912537037, 79310161, 888873514, 236679939, 144834296, 555877519, 258273497, 117582904, 983278122, 595211525, 945227383, 907062005, 395049156, 820361411, 493387429, 588956513, 39714758, 601891195, 450393111, 813911734, 661918883, 139466027, 359814867, 263450008, 213494868, 395076209, 223693248, 994099272, 308686372, 362186690, 187179680, 484417252, 441646315, 502952031, 288255039, 337438545, 38857252, 11799186, 712908756, 50904556, 69639046, 155995327, 96157440, 635963592, 371780164, 37520382, 443480608, 710939489, 759085732, 906222952, 140007168, 838758451, 493094423, 853477895, 793640028, 253765299, 129229440, 607351012, 535035005, 923353901, 355140445, 955579327, 496811034, 301502339, 840610700, 219380006, 100220383, 646030967, 301643694, 504969823, 366188601, 949179021, 312511339, 468984024, 478105334, 278045498, 395881531, 694835154, 101712731, 737040035, 99905163, 267056637, 601786518, 136249352, 228647165, 76088369, 308669737, 274645567, 76231167, 650842107, 177273533, 390541831, 315853188, 458698482, 862432231, 651299469, 772351625, 496172954, 434273998, 623443386, 407681939, 460978329, 472032575, 578294801, 951734031, 814997775, 121899461, 531317607, 987058322, 232519090, 982546151, 920045591, 140511203, 755837030, 701754928, 802310336, 672168874, 99741713, 261312495, 264869930, 336371467, 753080039, 937520766, 138934044, 332960014, 743445692, 139055284, 494595886, 335395673, 519169752, 603537709, 914846993, 754532808, 384628026, 204867798, 356837423, 362795446, 933100334, 468106281, 562887088, 832500809, 984723757, 309292029, 302777636, 762940997, 859182498, 463467917, 105321213, 54985471, 839279794, 263374397, 107429858, 972148947, 922410684, 660763770, 844363642, 456461716, 439363063, 770433373, 1417753, 96317378, 720084812, 662508277, 824171486, 107475608, 701768363, 249390976, 669283116, 586425300, 702342692, 243790459, 245960695, 656946889, 744763795, 661193474, 803720756, 649770505, 213887785, 41089897, 797862045, 273588905, 217114848, 357889603, 127756619, 188937683, 917491244, 464365607, 976448096, 701516983, 302462356, 57602382, 645130507, 675469545, 858621811, 819486668, 750634579, 196530735, 570863568, 261871813, 286548526, 441157270, 371153461, 443277117, 563537775, 363696273, 494551943, 939506113, 692882022, 320427364, 204599404, 655916406, 879950460, 108348520, 871580316, 633618504, 896359204, 679702914, 448350085, 207275270, 919654100, 982626997, 52329222, 636235147, 221223082, 326059345, 404316320, 757495426, 134140786, 863715451, 25201970, 631359077, 161453992, 427546327, 103466596, 785678344, 711293690, 31536692, 270984375, 212341308, 883885024, 299622932, 438504416, 238473964, 32935297, 359080417, 254612763, 182411867, 314556471, 288722054, 400619833, 405171111, 557603721, 801636532, 328343224, 141141921, 271952298, 988934438, 577375719, 624587101, 769860801, 819329174, 632820525, 637881046, 242326192, 598341118, 699040149, 685705025, 581449529, 18602552, 171407868, 691266286, 722576152, 562897587, 679172454, 383661719, 176029747, 299774287, 720594048, 189866900, 3984142, 512905887, 791918569, 509950363, 508852782, 339852949, 973192598, 834715119, 403450280, 25584717, 686904464, 767084432, 24396485, 42434761, 90138536, 286760949, 912593686, 59814451, 138347163, 19201776, 420863997, 714522176, 241866978, 456230245, 4528682, 517250456, 854467403, 765724934, 556372603, 709702275, 443864959, 410318209, 550877613, 253107307, 680346108, 248150350, 640762850, 135451228, 907722613, 399661689, 748150228, 117177457, 440750283, 673876283, 188648874, 172568866, 230438631, 746940000, 118842486, 224081645, 741016444, 968345642, 963670447, 415519105, 89169867, 887685073, 744356177, 920055415, 246619445, 891571441, 348138997, 315720491, 341695393, 582932781, 230597498, 810390489, 714609552, 825865668, 896556045, 767326619, 437688846, 135498886, 168422509, 235823186, 956796056, 160416668, 533704085, 59903191, 916076026, 585551355, 204320993, 189501701, 164473007, 854246696, 564102667, 202538389, 553226576, 155902965, 231103295, 290075301, 797898168, 553018877, 406020713, 109054901, 104504049, 816557830, 831468947, 708315999, 802406183, 418204134, 891692840, 786748545, 771824375, 238944438, 818080487, 402621486, 496172317, 542110697, 143321570, 337569097, 463361946, 999107757, 461559300, 506390479, 562547167, 861648039, 386466507, 166634189, 969173429, 209377606, 50763384, 532913236, 88577727, 33809533, 657342657, 777676882, 6401302, 41984805, 451605115, 525041225, 698687170, 887666480, 841538404, 443886390, 421539125, 932434209, 255025236, 57063758, 212549696, 220241061, 558250560, 756442511, 956202486, 705850527, 502128718, 722600006, 26665731, 301194501, 893771741, 17536631, 194166516, 265265083, 173725555, 648339216, 346697943, 603537529, 844452241, 265232685, 328970815, 933677449, 19404256, 956411069, 527982430, 22041086, 142709929, 693468734, 351748984, 552648273, 588417636, 382972484, 765775291, 52497928, 453675760, 631800592, 256564591, 300127942, 972099832, 309874812, 223682015, 690792026, 342795520, 556531897, 836635526, 439368379, 21649523, 467709699, 806958719, 241996791, 515663175, 39325315, 830342504, 726913695, 690841957, 457918223, 880904737, 549589852, 612413421, 475321702, 322765138, 147471558, 886896445, 798388500, 298413844, 546376948, 210589724, 389892434, 620127692, 28363001, 742750505, 614452928, 74742464, 999315754, 570207098, 114397329, 774393905, 136187306, 275515992, 776296003, 2864113, 711334087, 262286133, 306959544, 18516733, 437230890, 640221503, 486969561, 433991256, 516741707, 980973944, 146334787, 44797735, 994651776, 50221544, 91798450, 304522266, 157948551, 353186649, 98892189, 64362155, 132907984, 461130008, 17075932, 878446764, 570523433, 457457680, 895598755, 374559411, 903312440, 429577018, 525323712, 152819652, 432330364, 193109046, 109800758, 848466094, 909911386, 962875284, 619017693, 890625699, 565335848, 126844206, 916804286, 379769066, 136778820, 17857559, 624946121, 260161453, 464055999, 113734199, 148861681, 239178161, 539977570, 468346890, 779485957, 217827913, 738904037, 109009094, 193259237, 209371104, 104284876, 994714651, 69807734, 237140423, 795626915, 470350423, 621758541, 8003794, 911530840, 176935074, 913807547, 582411415, 751265917, 989451829, 197998463, 8317038, 599474465, 279199919, 487323218, 21386752, 936271012, 23042345, 376027103, 421118601, 768640274, 184239161, 157866672, 628673029, 659279293, 591145005, 58312144, 420843028, 763862992, 571713235, 911460944, 694001543, 594082542, 383030232, 792502732, 572771185, 403347361, 252904736, 706213094, 92262739, 645273186, 323358538, 614295601, 967331890, 214391285, 499410179, 889866767, 15502582, 587425995, 163077395, 740023846, 33168729, 204529541, 410459690, 39360683, 205902288, 261178856, 573498091, 677668637, 833560110, 272759826, 781930829, 882654392, 319579828, 203413948, 725664625, 526328245, 180604572, 886568902, 852119305, 348417880, 768560433, 581082098, 746185909, 145021289, 844105775, 582296634, 212463008, 80871768, 828284303, 524540516, 337809383, 273883655, 13090504, 211394396, 944261926, 78498162, 47024161, 109673128, 42598639, 29547248, 311918130, 400464295, 445507337, 22727708, 666047420, 452000946, 185098222, 434951807, 372389615, 434857591, 992786030, 634432553, 60308056, 906952631, 277194079, 659043672, 763175007, 477211565, 362902436, 756246484, 369104895, 723673851, 157404699, 738120182, 999387121, 329654278, 963098152, 406351880, 544915269, 879079838, 932976359, 478384699, 752794669, 951450797, 267733394, 935553427, 397002660, 557606834, 444705668, 650315692, 74763654, 810107730, 11810701, 131683672, 479213397, 633700557, 783052714, 237451712, 998578604, 23714871, 586686638, 260773767, 402721708, 397571405, 872559166, 333605832, 976721352, 887262991, 26786076, 565267798, 517120720, 842483579, 175200806, 685113315, 186883802, 27939032, 129089384, 418926634, 876846466, 438868506, 62843661, 606423792, 569434867, 725475205, 256412494, 1339948, 718399109, 577414596, 967657410, 164704622, 246769505, 563788533, 338213641, 887013994, 595802577, 605322210, 16422056, 380118947, 451100359, 648441431, 705243318, 819715230, 625282049, 555234838, 566455098, 175648281, 493591835, 739003271, 602610139, 506208292, 907265212, 415666079, 213661953, 59107965, 761951793, 255184265, 473043218, 852885030, 145489181, 502576969, 796183292, 22207498, 115736872, 704584424, 319370084, 154849744, 174166910, 273547898, 638232869, 192004621, 611892830, 872176572, 602220690, 300759799, 821896943, 349249622, 856194353, 424656517, 228176179, 511850408, 311455871, 250131351, 897075604, 869609614, 649018761, 595984422, 887175282, 588084682, 8811775, 578977043, 762894983, 202618649, 488865500, 447747209, 509010545, 825193593, 273744241, 499146846, 147255257, 45725285, 86545108, 572755715, 297431453, 94722824, 378944715, 779477956, 977181830, 435713357, 577050463, 142378245, 679207691, 362576227, 877529158, 487468658, 801732091, 14128923, 398076287, 117690076, 658395878, 196556255, 599437958, 942091884, 435917417, 177244239, 763635195, 47209859, 548917447, 221810682, 644590859, 842781373, 304754915, 875857566, 168782272, 809599609, 855536254, 687706729, 929073658, 228058790, 118953571, 663284928, 935480625, 273278755, 92069202, 218633529, 923215189, 134018078, 168877088, 812529636, 434819979, 430082965, 860505636, 820381237, 409303894, 434323284, 665013721, 647861575, 746981751, 429484365, 890581277, 479444956, 497844347, 90267805, 419228046, 514766174, 346480837, 408025143, 587179290, 524423163, 214190250, 97583272, 992493680, 559539842, 171375888, 378820084, 47206471, 579527851, 356068260, 162699553, 441525836, 438658777, 153650270, 618447193, 242078095, 101081467, 139084962, 554790883, 30625269, 746796880, 929976901, 590111786, 726979268, 600286405, 154538076, 334112403, 696532337, 1077015, 618521238, 695196842, 869541730, 378717921, 748062712, 126253823, 782811046, 291873211, 277453099, 778938695, 846283566, 935221786, 209042564, 730033820, 755437777, 218112551, 409481901, 368484037, 896162187, 536195631, 932579581, 558011253, 110910120, 381251541, 699269212, 798456558, 887406129, 842215228, 643152261, 767109372, 26762558, 497813620, 998342961, 382414263, 606090593, 157268542, 879097191, 212746217, 977819610, 125573414, 178718049, 177997110, 584705337, 477159193, 669001614, 25041540, 174643978, 760107346, 992674848, 779220743, 827550477, 978249947, 390220975, 329848185, 918869414, 592560505, 860747249, 107762257, 898690241, 807914501, 514767281, 507008176, 329101999, 779334267, 400044936, 762993047, 369514973, 295382622, 892268415, 481738056, 517877701, 825338825, 970696129, 668864083, 593155499, 382218773, 812127623, 838783189, 51322216, 385900355, 762510790, 349934365, 208324328, 699119185, 780516503, 643235373, 219751442, 687312596, 441587503, 396550978, 401276436, 381831681, 406209023, 589705358, 288906247, 74987055, 414927852, 934748697, 909116694, 706654917, 212542034, 716505783, 147041000, 371844038, 38896367, 443169252, 234812857, 716954362, 945941011, 537070895, 498004912, 729989546, 462645041, 811747484, 850933087, 218968896, 376537858, 289037058, 657083837, 874004972, 17678804, 439065922, 637197974, 3430469, 424829115, 385124487, 431650963, 750032551, 445471856, 414463000, 657277426, 356836194, 693648341, 500245352, 995509877, 763517870, 642651086, 325030865, 85166635, 884532587, 921232590, 816674057, 37582465, 782690727, 608399503, 602167210, 378834005, 888391837, 367475510, 113495717, 70990586, 348112483, 125840684, 226707321, 264584017, 827046332, 709982105, 453627211, 307123827, 959009945, 593170069, 96725357, 460833174, 876021010, 577282566, 881534381, 322033030, 699104063, 571250404, 308070503, 870012640, 687311003, 280032042, 432999299, 85326454, 242481354, 222377979, 902143893, 947209039, 226025946, 740943849, 413226785, 799931928, 66938196, 726785487, 507093729, 50330490, 129662188, 376451399, 995681940, 225737484, 393751056, 721231554, 803229382, 53194261, 359775605, 187634186, 946745313, 573527133, 234167251, 149972314, 488966889, 833931935, 178881112, 361362022, 910509140, 604868478, 555268623, 593821293, 706641164, 126389386, 194151412, 316328656, 141709613, 886665858, 252139757, 208463176, 159376730, 172124186, 940854926, 783926630, 692332734, 379943196, 830330795, 304555320, 185795500, 365223336, 245155436, 262885216, 293102674, 130281234, 203447665, 562322487, 227468982, 393666365, 925215790, 569163533, 811120920, 794309094, 933802469, 255339696, 984129773, 92450081, 178348046, 206563091, 639447306, 698080218, 232540253, 862062096, 297483934, 68184301, 295146476, 717600998, 187765279, 697970541, 240889913, 904184012, 54504519, 373807650, 860523204, 974813891, 561852923, 247270914, 630327673, 416836525, 80840158, 121609071, 726835292, 617984446, 663909321, 940017907, 926253781, 957969212, 288669252, 599379374, 590585063, 500792025, 466011950, 333883191, 140540858, 336674347, 190345724, 495947866, 100176728, 725467764, 428906362, 535729055, 690857381, 648858391, 277548172, 489841941, 608757268, 87794427, 289734714, 830969769, 114107720, 684968894, 632499617, 702206203, 691109888, 320889185, 105253442, 892882482, 474291687, 430830526, 76971150, 229508241, 102343427, 244140534, 423376506, 801613087, 52775791, 754726978, 790072357, 323651834, 53314129, 438667195, 127866193, 277422155, 615801550, 856384450, 776902459, 690077440, 825054819, 316188158, 902852027, 458792737, 281490613, 785462375, 139675566, 475083866, 189682146, 875289467, 358185787, 472984899, 168152706, 788004676, 820428316, 30549218, 742463350, 64428483, 535316292, 844229717, 793912811, 265412523, 325971711, 193405244, 731144498, 618429665, 431879052, 670584997, 85261190, 49373171, 322266377, 198465669, 516826100, 976106893, 42217512, 613929403, 858774041, 894803222, 724168447, 657443080, 8549236, 978124950, 120661605, 807395005, 672062728, 709755617, 261193647, 296548783, 203123004, 504684198, 334158949, 864028422, 553033197, 521966681, 755842938, 40405558, 249566408, 956040895, 301564371, 711247279, 973468664, 195023617, 826941170, 626914912, 150502118, 734858361, 848662108, 971330240, 640882190, 112871512, 648790913, 615987317, 50702464, 530775375, 477931469, 707875726, 893731086, 178075012, 165545679, 642285660, 388651697, 438300870, 236067937, 56816092, 785397543, 443965139, 989269367, 616277246, 75278980, 126532845, 926765690, 626462706, 598311855, 869233220, 853131085, 804389425, 656688688, 109817009, 600432081, 599560689, 434330119, 779358934, 295525051, 920579721, 30995226, 16916323, 474383938, 800516684, 357607748, 224956907, 539294734, 269766333, 924926124, 289684125, 721706655, 592687393, 262491814, 620485728, 986498372, 811342203, 942261199, 521214733, 810647242, 674064415, 818029961, 595677740, 311547868, 923030159, 351456885, 688740836, 774014713, 797582285, 478247387, 591340244, 755418935, 897657197, 506693486, 582265111, 559838698, 654491284, 434276207, 798263097, 321536352, 902745552, 81909663, 936937521, 259355636, 448503640, 457740945, 357035933, 692526813, 987694171, 534600756, 960623936, 115888894, 142863996, 449635102, 627842560, 435103563, 474934184, 760437029, 230260823, 806614654, 807708581, 110411393, 745384073, 933731448, 369646761, 48531489, 931146132, 775640600, 267345028, 748291616, 154764042, 375562743, 241470447, 383894039, 400338625, 29903072, 812454682, 148278695, 364175193, 798776791, 287827740, 334542537, 593396647, 905932382, 457747836, 962155740, 164515226, 499299774, 10015436, 245931565, 574006352, 467196920, 768901285, 37760066, 97072574, 521029010, 373748848, 821454127, 875240346, 245342105, 63575657, 474122588, 121214152, 868235779, 657183686, 636770791, 769344889, 250421193, 141349788, 765707389, 128158924, 612234819, 818397609, 24511623, 822562094, 440456789, 895510955, 9852750, 272556396, 134687882, 291163696, 699958793, 403743063, 582033450, 778734654, 855697418, 822636123, 559309785, 613673088, 530519247, 361042535, 654444923, 385904039, 813297910, 327235979, 663838153, 862197552, 76449585, 746779492, 595223212, 915070646, 292723065, 290775395, 136050207, 460140376, 573988458, 187493232, 902871375, 376997800, 499235627, 385152915, 103668745, 430454858, 657863577, 871647105, 820996673, 152039939, 195987833, 850759059, 103425373, 28922318, 782340232, 86388842, 394632127, 639789004, 445875127, 317388769, 901144152, 382517655, 232949995, 601269323, 15122119, 602635409, 78252711, 928822088, 202016537, 633082032, 759458272, 594645445, 356842775, 448984395, 632264083, 506098044, 799766645, 609019447, 436875542, 11462047, 450733516, 388540604, 829753356, 656089699, 31084687, 144536964, 443874235, 340787093, 935330707, 603735350, 910810757, 168344420, 726527562, 171976590, 59046835, 406506808, 525606008, 506691831, 716383001, 538170404, 413143454, 213388101, 98247690, 992759579, 490271333, 918411787, 526374372, 940147736, 766306993, 713206084, 743670964, 750412230, 277621893, 344601845, 366514256, 997462810, 256359791, 734856725, 888005153, 719730498, 120070092, 688612218, 84080888, 424060456, 898273861, 489469483, 752240169, 186313744, 68568845, 262165198, 53938886, 720316277, 409102370, 565431354, 394532930, 148940016, 655242533, 929726820, 41376044, 147170680, 528204629, 154595305, 382545790, 372671388, 857192753, 157354419, 805913869, 356679461, 137117749, 954324332, 633788176, 890445467, 966729177, 310954147, 833773720, 385693265, 352529007, 618213465, 555662053, 955972217, 883118486, 110340268, 38034790, 505708672, 492246932, 506276202, 919693487, 466178246, 189215483, 524639535, 463247069, 337810951, 537479891, 966961776, 40780969, 37336322, 584694795, 72893337, 496182853, 869752069, 788278183, 970657378, 702029676, 629773316, 363278252, 433079866, 897744332, 558940849, 922387927, 279017001, 431411072, 308011163, 497512105, 837328666, 931283917, 518541395, 945170885, 707387622, 944479722, 17919600, 676711445, 808533238, 917457309, 207936015, 386391548, 937017153, 167137303, 165274266, 354649645, 380128564, 84517066, 61768415, 590658030, 591665903, 142058042, 846153906, 396890871, 598712122, 421092537, 263014535, 983425634, 236845330, 440640793, 234615804, 439856261, 665496335, 950727179, 692405443, 380543272, 537250421, 31996142, 275088422, 537353452, 656240893, 969985886, 906230904, 245803351, 306937369, 521679754, 44300624, 35528998, 685932336, 179382193, 14347865, 593127450, 697491830, 99425465, 611447134, 425919262, 899351158, 608115415, 236959650, 768071992, 956428306, 334818441, 751663353, 158841298, 734432078, 819525906, 888504659, 900381749, 777540623, 217224703, 104447426, 116054724, 227342584, 46276759, 913151203, 497687583, 677403, 160302570, 768080248, 127776183, 28797918, 116240180, 301356089, 460336715, 78527329, 524578260, 692812458, 121250876, 568173438, 738156583, 233522775, 599987478, 820907947, 799060974, 838910971, 30140179, 918448559, 849500990, 113528562, 374797795, 695655578, 746918688, 385732829, 910338706, 249915200, 30394365, 626664496, 11659149, 457890061, 740736119, 407306161, 265813560, 598145488, 562342082, 816786296, 851418824, 154915299, 228344323, 808184250, 56838203, 705213790, 326212626, 422325556, 22950164, 677703694, 3019282, 451457497, 974158612, 408762295, 784694852, 712255448, 299676204, 924756691, 728134740, 642135287, 210597931, 883124389, 924965957, 783258697, 71595694, 727250118, 467148416, 125740707, 479113347, 316869714, 30717866, 982118842, 489343847, 977044589, 119090510, 307708818, 625696004, 23530062, 443996739, 162687358, 659550591, 710837783, 878025368, 188719872, 637595529, 528842839, 192714305, 937200855, 540728922, 673050154, 734087360, 325145565, 784736664, 579582576, 763008528, 373032337, 578043323, 599812887, 325340862, 274066433, 31308094, 129362893, 858883932, 344683035, 587516760, 53228499, 383013525, 120737840, 487736954, 695690415, 119606250, 588458258, 408950274, 749944463, 622718322, 461477205, 713612938, 174632056, 70299054, 591029812, 200768712, 805928948, 632231372, 564620915, 573507717, 226554701, 184473955, 399735244, 7223393, 949361599, 112776749, 410374285, 893618674, 908472643, 375269081, 134059671, 16600084, 861601781, 245690502, 464729641, 962046502, 445583539, 744829353, 506453651, 863520462, 56855334, 881706238, 950703026, 916537396, 261443106, 104913796, 290677616, 685782818, 874577268, 94710204, 299599267, 674519200, 346186234, 909969009, 235984718, 484795850, 578015525, 717635958, 232887365, 323462094, 521291367, 285207051, 278346037, 953498883, 883504890, 616006254, 203669814, 531358179, 855634523, 235025580, 705131314, 246123860, 240663489, 350951470, 38681221, 770100540, 133258713, 802526501, 387935237, 615222342, 875499077, 845947402, 485291492, 43618225, 401321593, 853793018, 208479109, 790935798, 511665169, 56664604, 363864836, 267890696, 274599221, 582653669, 585416240, 126508837, 367025832, 274113841, 673064395, 714186880, 688936050, 89279536, 267119390, 542822265, 106001723, 30662879, 769586747, 886480502, 440506889, 911833553, 300723781, 78486651, 831809276, 128510119, 431851907, 289528963, 138644244, 757891627, 648566083, 295045003, 293589568, 88629454, 304933013, 521221527, 446040659, 97129190, 329619277, 372011983, 486349528, 928180901, 259454053, 371389147, 495444298, 474558742, 420543219, 767700737, 280369292, 331061750, 460939722, 106672120, 43620907, 548248447, 102628085, 497380929, 865733651, 114849146, 572758714, 13577351, 975629584, 29523472, 883077939, 158868632, 300722618, 685460150, 986158379, 47564819, 139705909, 939469952, 362391155, 464598163, 79363692, 983580727, 351350179, 307674682, 386970754, 245108838, 50234617, 235068712, 509594566, 258167014, 596064130, 828050299, 491944781, 460041950, 839141334, 856806323, 665188007, 623432512, 869189487, 97842526, 943622895, 324381850, 640036930, 835397391, 209892214, 758033562, 470769723, 726013237, 900063986, 106894372, 906893238, 120825864, 836945311, 981549454, 428904988, 929308913, 291702381, 756338381, 309548644, 812450990, 504109998, 810125681, 653369839, 272557886, 246887379, 713046433, 301325067, 639354785, 158503068, 459516842, 856074168, 878204054, 36557164, 360834290, 746496195, 222289435, 916750059, 929237605, 260534918, 454325284, 487492004, 367828863, 842001647, 913021341, 329741659, 789779145, 189750510, 977519230, 208409728, 767607703, 167659925, 855883328, 546580728, 58874333, 95628512, 81751841, 43801027, 244823849, 421706868, 689197966, 843929874, 812199386, 287995818, 875217883, 827259568, 24790200, 991884476, 541682905, 952531414, 96677249, 117916622, 883011830, 860020903, 847643064, 158521955, 205587302, 838529161, 162888620, 681789504, 664261695, 522810810, 998448385, 220613870, 308088518, 560054332, 178877802, 725840018, 456215807, 847476751, 238085923, 182248870, 985172964, 783711673, 361328101, 716461129, 477774976, 417413864, 373145342, 17150855, 43509979, 274627562, 554792502, 893356104, 559075715, 135343297, 873183618, 445273288, 569469879, 245873584, 363363981, 834943680, 347605172, 872968365, 527869044, 694815665, 153125420, 637355791, 896939249, 915728807, 27444900, 922033563, 921855882, 277301690, 575481005, 162153756, 163853329, 481201045, 296155141, 756457708, 901060185, 195675794, 217936692, 364493024, 61434761, 131126362, 870470561, 189890544, 641774036, 46517980, 119321179, 596736714, 228459721, 485118487, 242049107, 126196134, 32531433, 103725996, 301048872, 349849034, 564862110, 620500446, 324710666, 795335813, 335956172, 267308978, 828861281, 142996589, 498222481, 547238399, 635896867, 677138856, 470748401, 733404382, 351376008, 72515190, 207772873, 11343098, 808023433, 29443396, 58826960, 796825727, 717225597, 439769447, 995125173, 356683897, 194635318, 373718443, 605798583, 727624925, 783191294, 489409286, 201492433, 57641990, 359569956, 819104147, 795664636, 740950742, 168674752, 589488128, 324083733, 300024243, 40737812, 324882906, 856273590, 303522106, 279567373, 945909377, 459488216, 930067298, 179099437, 519374885, 454963991, 42420956, 4116859, 150911745, 227226597, 109139706, 7815158, 196679091, 415587897, 38659132, 760895434, 492302112, 704190548, 281591460, 209294963, 227692270, 821198676, 57634937, 903870702, 659928947, 835732760, 914797490, 346688632, 377931500, 611022676, 985773875, 556835727, 339897172, 337649660, 595569966, 512647760, 135836986, 11332383, 613223796, 527161435, 45621716, 614596364, 49358072, 28683833, 666541122, 536325044, 584664389, 788706559, 862532560, 953836857, 105542615, 373555542, 546021439, 320088626, 357621387, 721822377, 509490610, 4655898, 350200894, 619829527, 347366158, 363249662, 325973020, 237572053, 692304724, 392515816, 378416444, 290118225, 331539116, 19414523, 860198111, 213598105, 382821394, 166131399, 802371177, 889486248, 77770993, 757710861, 604427207, 217662356, 563923889, 250179316, 463331004, 862648688, 992102944, 401720281, 886658212, 837987806, 389899420, 979199859, 912228151, 439592991, 976916863, 290338806, 20799983, 748502383, 516549738, 392822307, 959251502, 563914876, 27804247, 601967916, 191681303, 656937990, 572403566, 609540232, 460549032, 922052607, 742389113, 21936845, 349384935, 369088395, 723455024, 624095854, 1548430, 445489511, 167368520, 171770706, 470689207, 565227397, 876667933, 400411412, 261403578, 910898248, 286515389, 529835068, 203212658, 614341299, 702872967, 430053176, 466525560, 777878215, 702374103, 3552794, 450204238, 409424013, 318329091, 585753290, 624938707, 164615625, 892558739, 191440483, 230013644, 238478488, 887700280, 196584505, 305769421, 871828410, 452397650, 807127006, 922629372, 358374057, 406265301, 605644411, 75912524, 764739132, 85265969, 649468760, 196462725, 346689357, 510109176, 528901219, 286585575, 293637695, 811302582, 59101614, 151261439, 519095850, 517050524, 631334846, 321108636, 811812759, 971527098, 253910835, 879838626, 549502188, 332946901, 79450967, 631296297, 215362527, 133913156, 586116961, 35623089, 6024214, 860829666, 788776454, 653907395, 319791400, 67022274, 552505054, 770741595, 126233765, 631889696, 480950716, 83249555, 694782335, 140907420, 470477761, 765136424, 448442267, 785993506, 200578581, 541679080, 198635730, 858305701, 891628985, 9659826, 504988026, 237424774, 915796033, 968038032, 524380001, 178565496, 901052740, 822719558, 231809940, 41917432, 519930668, 356960129, 300100539, 847010947, 990655534, 728983782, 172274615, 78468174, 677328424, 544689510, 19005926, 337289194, 667148295, 951884869, 155948433, 497160816, 944560082, 401625931, 325055665, 137315653, 542071790, 209109143, 751042561, 415391277, 113640574, 887348413, 610991822, 252299863, 93116609, 330764788, 803510923, 655510523, 608614358, 818062223, 273329600, 527643819, 635117535, 633598212, 438163038, 242332743, 831973842, 780109612, 737231886, 315322639, 97508906, 881221045, 553387464, 713951774, 461824405, 480876614, 874963066, 878550508, 443920934, 695111174, 127376756, 914853982, 907424498, 184545145, 341996974, 245426177, 58183828, 515296442, 327538092, 217933694, 971113739, 407186971, 580291849, 377440843, 235769980, 295621144, 357611654, 554704196, 128406826, 829541491, 30466616, 257997904, 370532473, 618606756, 936771549, 204291158, 803781839, 897501949, 171434622, 673373600, 670559816, 694877963, 590720507, 902874117, 301883512, 518793197, 671124926, 881112596, 770848481, 315222975, 663104905, 494946600, 564388150, 97267561, 372154749, 518924991, 303964551, 900799306, 740035372, 142141013, 107527541, 848929095, 182848487, 655933176, 125702344, 675988092, 111165940, 495740814, 30373490, 815851093, 449922636, 64656239, 29149277, 26089487, 581809328, 226607355, 848085177, 705675331, 613417979, 16570140, 506886428, 123067839, 719629827, 795787423, 598606497, 967568991, 899243260, 271756892, 700371092, 25931308, 26198816, 403639769, 767167335, 602386321, 931084191, 88224520, 38415275, 926286667, 392131471, 910154934, 11075179, 420481914, 442483240, 72836359, 698547310, 246659535, 864027147, 791493809, 684809394, 76509389, 366254389, 34617774, 978992564, 626153707, 546072469, 591354578, 598519903, 761884761, 457777677, 212728064, 15849212, 4611980, 964254701, 82651506, 73732866, 392234076, 802150653, 487613192, 944103032, 816939389, 604559892, 759237854, 260730274, 35192643, 89055870, 386354938, 848264754, 946936969, 843111068, 323973969, 806719816, 980100423, 98463770, 758711925, 886799243, 164798552, 41698868, 436092096, 619210580, 667520407, 36451125, 909125133, 821657718, 238778562, 377235211, 721775411, 456509216, 462914427, 518197024, 88293058, 932114554, 313882095, 312733745, 872355533, 263949758, 388415784, 305435606, 28412617, 319533350, 94639747, 762587981, 666710679, 83859407, 542871024, 271967250, 148545220, 353831150, 791551191, 125862223, 362590246, 323977890, 115484677, 6019688, 512936262, 717014809, 82100506, 227961676, 557417753, 745246928, 68257842, 323017522, 773016783, 736077339, 12961891, 602649399, 731548317, 372838068, 846933162, 626671355, 210406311, 925337561, 665586888, 968626701, 892005616, 540728317, 413006333, 355656633, 966292243, 96435156, 973262840, 100999979, 600510043, 97821795, 170374302, 647660956, 539807106, 986717507, 293868082, 349696651, 819508671, 878619309, 944288454, 936523004, 309312441, 875997557, 749946495, 280640834, 87768712, 956114985, 166830175, 105132211, 95548008, 380955894, 387943747, 811540045, 336313080, 698082597, 498864752, 758019087, 832010724, 950082791, 629932730, 808475336, 860309916, 351071325, 238366065, 935296592, 3668412, 938311508, 126957413, 355047600, 865710883, 323900481, 288564082, 565191639, 935367477, 788689910, 870412611, 537639195, 698917985, 386072577, 7313761, 290860953, 515772543, 959855068, 954524664, 8862308, 798400357, 842800663, 917070356, 383651130, 577331904, 148484329, 17306149, 342813917, 614770534, 659286665, 874813984, 152177045, 554106801, 839284810, 962679130, 575789993, 8131636, 783866774, 841292657, 645148612, 91068980, 88645169, 558652560, 226906559, 527308124, 17465991, 430136063, 383516320, 869818047, 802266189, 76916045, 564826273, 532061275, 892516066, 89803371, 883444819, 929065932, 8616812, 359827101, 232999039, 693727481, 735243923, 435022588, 295275264, 728668698, 898155963, 963202554, 403847556, 230791474, 877819350, 905102345, 169769499, 213247503, 340177494, 90992303, 245947109, 109174818, 958638393, 121299546, 504449620, 234662785, 553987266, 341945512, 714565280, 175678558, 773193395, 1623139, 574660747, 103582682, 276429086, 346651444, 157839180, 617795120, 148651093, 593181423, 740330698, 209079550, 923937856, 12797567, 126162468, 886995713, 968604512, 740841017, 243020815, 700443436, 807296832, 194677922, 117711649, 732063259, 710693098, 832409885, 873537819, 297527157, 181688902, 152642064, 862941280, 292622165, 351047372, 64754880, 569426378, 190922132, 294760274, 470233271, 438504247, 993548254, 471454325, 901519269, 734319218, 349263348, 478176604, 866378393, 745053775, 744953362, 844854784, 615555932, 387129023, 294130679, 969627478, 805654692, 731743662, 124238449, 461513883, 868520111, 14919334, 94511310, 29032185, 731897651, 817953686, 256890004, 971008401, 514799272, 448367624, 650827652, 985024345, 52719299, 843465238, 658303241, 636499056, 996739013, 756494292, 680835804, 697655371, 718397989, 17550748, 355927579, 956916810, 890700805, 433984990, 473044896, 275985041, 445102639, 419200798, 524492877, 891046142, 907647773, 242056973, 483590826, 665978327, 121765916, 557719973, 533354486, 925365446, 226007661, 5332999, 423016141, 420580133, 102845040, 163149943, 873510515, 862420849, 97975506, 215978997, 220043430, 983523729, 753191373, 593980938, 839919307, 296370250, 375744665, 705022664, 775580516, 196876485, 76138266, 128175397, 945919836, 125457932, 426710260, 506214449, 727157848, 978595295, 545500007, 34203901, 797893775, 541670420, 737025198, 298445709, 871107063, 532855197, 224150596, 75475204, 272399715, 168726488, 207600990, 708753406, 561245500, 86712315, 727500531, 398510647, 524484692, 465521780, 953826676, 175745332, 401610474, 14579580, 529133310, 288533963, 833672219, 955018458, 81989640, 271138425, 674572195, 671535383, 235269731, 862448664, 504036447, 51621376, 945800535, 6476043, 573152709, 865440492, 719620781, 114688104, 809545526, 751817545, 742229461, 489481270, 33792834, 632890735, 505618866, 360285116, 386805994, 892462501, 104767598, 269078066, 514657557, 514708623, 996557048, 260494303, 814901967, 616156134, 118440104, 765734358, 428810034, 209563708, 447230756, 235021263, 14216783, 553730314, 288914882, 491057744, 339368314, 864577974, 528632241, 34812240, 243993642, 338103428, 312376520, 899321460, 590466953, 297501317, 688043276, 540565541, 124608341, 839758824, 356843605, 614184891, 317991766, 596635352, 286017058, 609109896, 480042853, 574436014, 58248051, 106942818, 996905257, 121309945, 225020857, 555435680, 30747136, 928718344, 708858781, 993885791, 170740655, 960711902, 291478121, 643450211, 829084170, 215798592, 857932810, 575576701, 113119216, 560521496, 409189838, 319393816, 585412307, 425194133, 27003322, 362523744, 729733417, 646102152, 423154308, 936374439, 146326580, 385979185, 103809860, 387008936, 464588824, 213104709, 684103624, 217825204, 797301245, 405360474, 802858892, 293486672, 873656470, 133576916, 120602821, 739294818, 528498865, 415758517, 326902787, 483636190, 119510556, 141534409, 665738013, 212909891, 517042878, 203094947, 983302662, 78187401, 31258488, 63921641, 56412730, 794006325, 52219410, 634469709, 425550343, 52666923, 4534842, 299751529, 678607400, 390982702, 935633177, 355940152, 678024050, 841649185, 218284022, 22301541, 226896557, 421813960, 420616579, 865697516, 56065528, 19821122, 508167721, 756024829, 546901121, 991034233, 176294376, 872175804, 482536733, 498987920, 59917598, 863370901, 511223228, 583465000, 613393262, 198814777, 487832434, 961546742, 547451709, 795944975, 829045542, 941328067, 248849396, 505256106, 138175580, 522429434, 449269580, 793883394, 113187057, 976117237, 783508721, 909115204, 470794726, 181649534, 573976775, 253646660, 781575941, 425942890, 109197689, 746517302, 789279569, 142003625, 424948020, 223550689, 645645272, 193586664, 27159457, 148296075, 275607365, 927524129, 412552829, 548980957, 935128069, 419780876, 852001130, 956430665, 48172800, 673549923, 941872796, 886985021, 609672461, 794695207, 671872035, 305772305, 234868324, 726864652, 931028418, 539788876, 867812158, 183927169, 75412063, 634636264, 924156982, 708803038, 496750268, 877334720, 477417514, 99420418, 857346448, 765923280, 804701617, 339488092, 61909880, 679469359, 126367090, 654494806, 751169726, 737175897, 166378801, 155035088, 17299194, 709331313, 308071141, 180738283, 793775583, 19684127, 19209381, 243515653, 930538119, 842710230, 17942610, 264680471, 506344209, 56980873, 210374721, 304759042, 746666873, 838257766, 839160696, 64688604, 95393123, 927580673, 550257677, 352497594, 790510488, 734295464, 854342993, 999610464, 620761083, 767742344, 235174184, 874773291, 624201581, 815080398, 188342840, 371842308, 939194113, 852928767, 652657499, 817369621, 614854964, 453203774, 551407712, 699096411, 705055547, 780781647, 321656814, 385862264, 85928873, 300692331, 678684351, 120011662, 735584336, 527690193, 790515950, 868669623, 603883528, 217466522, 855616916, 660196817, 845540867, 273499993, 254192723, 694358771, 666706615, 645763054, 286168359, 727300873, 532457391, 43003832, 170204350, 422518343, 947654308, 574167677, 645626117, 945607201, 542735900, 685320487, 366221387, 230529006, 409773422, 472875821, 709577376, 801032056, 740830868, 51538542, 469369696, 77406672, 813350152, 552968528, 673791239, 225229775, 205663862, 786688701, 176306956, 422243110, 527658493, 510568415, 682245454, 592406766, 847743954, 820578667, 830034912, 373970368, 806327924, 566529993, 516526444, 285312740, 886104424, 809905263, 623686604, 426659654, 645681381, 232945425, 68128278, 909176104, 161713788, 644253273, 588404918, 828240957, 150260697, 328749007, 476060571, 114600678, 135001089, 673140275, 365439013, 416424678, 644060071, 864787817, 613194722, 393923865, 866870978, 889793885, 861865710, 102915296, 256337588, 614063701, 767674342, 716229356, 150124209, 968811881, 564065141, 375653299, 527637992, 48686693, 150335930, 378745956, 212028729, 732050540, 862181103, 340083089, 414762063, 959842447, 833911605, 983332929, 353604631, 44366063, 687822279, 888168686, 238190510, 808831972, 563099313, 967871510, 845853609, 66208014, 36617996, 938833023, 222902138, 488301174, 692166263, 139693364, 205176816, 921771151, 930159289, 481391862, 557038577, 465332151, 482606905, 996701952, 66247429, 727031819, 311807070, 73660129, 111020327, 145266747, 240923858, 131613367, 302799568, 548838018, 876298265, 645908321, 964300742, 276266534, 621312810, 721784815, 500260074, 619281019, 683238664, 868776652, 707233888, 832531814, 280823841, 674502504, 90865619, 913683729, 842972115, 945967240, 926890243, 760838143, 655240474, 286670486, 514483584, 816190499, 666858598, 435379960, 313264412, 336667109, 373246507, 282413623, 442281779, 276295425, 267898608, 189406036, 599761947, 99047858, 804313191, 814305045, 967582946, 92553991, 965052562, 223541662, 133044252, 895188983, 43923505, 820256936, 8594043, 740168068, 492939924, 711099256, 218566894, 944813295, 424283290, 61327394, 626058633, 741515909, 712179036, 653967523, 715107228, 751981527, 3137913, 918542318, 725007031, 520858238, 69450244, 839892895, 155869144, 937976567, 39643643, 644910253, 868051409, 885568722, 393526762, 229483146, 70003895, 64860386, 887739113, 128700963, 758553273, 271566278, 816646492, 418291717, 944548856, 399782106, 831628998, 376708256, 812214926, 470034651, 31789836, 28807170, 374287928, 776560793, 764269717, 799733444, 748907506, 380034697, 895917184, 404831593, 183687816, 745952, 944191970, 509268923, 600980427, 5085298, 714547544, 382406660, 729990061, 155344396, 356028284, 149528194, 831015131, 674678123, 490489722, 430065616, 53570901, 482246653, 410184220, 334612217, 810601908, 828203049, 572410539, 527657403, 228224705, 214139651, 950886686, 314580937, 129067424, 589263987, 91603442, 775722452, 457016009, 534903576, 637161065, 719531877, 209424915, 208069716, 752095594, 903274913, 618476907, 243974664, 277212057, 76885468, 796375448, 974645489, 24556775, 285338503, 123154396, 551747290, 111568229, 46999531, 230863837, 587333606, 691557862, 481543386, 625537143, 790306826, 997033083, 954250167, 197159879, 406987481, 511246551, 794438953, 82295816, 106753047, 734799017, 664600551, 168249693, 167157596, 758413417, 519373845, 62559757, 703076654, 726147534, 654504152, 750182552, 5264990, 15922142, 917974257, 316831820, 443996663, 284087452, 844875327, 279146242, 417926613, 483629159, 383181748, 116237977, 408538347, 602146203, 961904220, 142700688, 562814588, 920263661, 718640522, 998173338, 809140976, 932469993, 572186583, 894547704, 156069635, 514345330, 772451942, 718237761, 801885816, 175146371, 61598703, 863247014, 605820245, 206981152, 68404201, 604116784, 641547639, 568741525, 536934066, 935590773, 23653388, 149106803, 548946924, 426149657, 326692408, 594743368, 695108009, 866838431, 301511561, 628519622, 805310959, 544911922, 57886393, 495120213, 812554999, 483002266, 463016315, 998417223, 666747464, 26515421, 301017550, 472342633, 333022634, 897247115, 978458544, 625752749, 950263734, 92310953, 754996106, 480528958, 27722696, 75653458, 159238529, 722627505, 609465531, 90252449, 322310944, 31642264, 131515499, 444705042, 649074604, 379237923, 132195596, 119998172, 828962578, 898593598, 273412104, 476024050, 4691744, 442569029, 849636847, 904622886, 955571047, 222935633, 168794944, 573115349, 741911696, 304202440, 936926723, 760321100, 575543903, 682718866, 400328710, 525289560, 822239178, 815183269, 817713730, 926901807, 32127581, 272993221, 298745498, 111813516, 360645676, 401403586, 644223332, 998249508, 31600255, 829507382, 816246621, 579917048, 130089293, 652837932, 920066782, 821334313, 90514469, 350411779, 400131314, 216197299, 863952707, 456280890, 560188289, 773206930, 148650077, 672029565, 585208908, 116431784, 685210989, 971178315, 240010842, 448516288, 16254123, 565203423, 110907214, 982732622, 902708667, 819433430, 230416152, 48752405, 465763617, 231065968, 500581465, 487572986, 718193419, 990965742, 953416798, 776457902, 143368707, 158913776, 466462100, 866263181, 515896352, 972975201, 684560309, 894291144, 338949867, 326373275, 123112646, 789189837, 581926181, 17732616, 851344473, 184711382, 461032758, 273594742, 571678423, 860215006, 724749278, 427702468, 82506316, 670945348, 827789646, 559117106, 401369614, 697218993, 667648338, 988268806, 947038199, 463646942, 546115687, 97510810, 99569623, 829736657, 103305674, 29229871, 550005752, 154579876, 744489439, 886664995, 386125615, 908051924, 19736711, 401271857, 604399556, 306617997, 364652507, 586968340, 781873588, 503104593, 488002539, 586410121, 768846050, 1568432, 818992504, 7660625, 224557192, 255343396, 767900074, 585557136, 306599221, 773730806, 73353819, 891720632, 50908631, 904627298, 855529184, 43126526, 968407908, 881762608, 559155108, 134192569, 280792979, 753461065, 900957975, 263234229, 44208724, 87645819, 655477151, 233967427, 407749621, 212623287, 478618156, 566917681, 792173789, 966169951, 840914823, 237786858, 926234103, 375473205, 910693978, 944084181, 45421831, 149547911, 38207073, 51686632, 614707792, 104856427, 425021309, 401633962, 94751769, 244941043, 750126923, 448097611, 623233884, 204095126, 507432378, 166202606, 122524828, 605197623, 776785850, 685650400, 331841512, 545711454, 714010478, 216636264, 984384218, 404488873, 54131301, 56062909, 306998960, 633046080, 276267690, 194603695, 472147326, 15185984, 628611355, 277440106, 590285907, 875651847, 974237284, 719676543, 174143026, 518017108, 726801932, 944456157, 989133564, 798939736, 769985371, 82041569, 441256904, 210350810, 521474088, 734098578, 435775015, 689526258, 736890258, 565145607, 49857634, 267134755, 717545579, 739822624, 281879211, 530606124, 730607789, 168727429, 97834024, 337856638, 363074111, 861213638, 904341948, 261635739, 932107255, 30452938, 48409254, 297354743, 162103906, 454598914, 34186374, 408835788, 705307603, 337552519, 321641288, 241277747, 369379670, 567396904, 134986305, 695314153, 404110092, 754917643, 790827746, 535059301, 889740079, 589446825, 90604502, 556159162, 668176069, 896513407, 391987402, 238172319, 435834827, 43391744, 973969804, 48416097, 358944138, 509782945, 139625456, 559444596, 883900479, 834792492, 682790324, 802552884, 829648362, 352517731, 788207221, 899858942, 134819556, 621650791, 412441163, 915063643, 887548612, 411437797, 120317155, 796662395, 425994519, 936900104, 227353806, 720744740, 17266916, 169285698, 752787598, 848679353, 112364338, 401141318, 733764168, 55858987, 103004765, 39944461, 54906123, 205273841, 973602612, 942819055, 61825655, 93301826, 485952105, 164406926, 845223727, 679506763, 391680125, 554553421, 571657240, 73595615, 122757790, 354157299, 150688560, 276376243, 523638912, 810520648, 476866392, 904314344, 38053179, 210873598, 603618974, 438570548, 142469442, 290568677, 893005246, 49567424, 617727696, 521610602, 618011574, 638420441, 341063479, 96294263, 796185533, 709721583, 798283654, 312405541, 138995958, 709272470, 798006148, 987699783, 325398884, 511675272, 590142503, 774432085, 10148820, 406562717, 183971506, 874279690, 19464947, 948277442, 568139416, 943667805, 574992148, 991268467, 236753669, 637636823, 43640085, 583717194, 972092724, 295279743, 61260554, 763512092, 581909167, 163217939, 148941335, 126166204, 150916561, 381711653, 538618169, 546746730, 952017771, 513459929, 431201762, 89528089, 8548438, 559853679, 94887378, 927744167, 71653291, 740173671, 32063491, 312321850, 57973410, 991679818, 839392567, 898612627, 834553983, 436369257, 644991453, 832386995, 938693234, 699894228, 14206193, 658850009, 432583042, 325336156, 2017106, 366384796, 260300826, 60919533, 993052492, 794683065, 918075298, 205580301, 951019619, 975593477, 265482399, 969456666, 57956716, 792598880, 563455480, 436192097, 690520685, 582618554, 260757957, 134367008, 955407464, 812663967, 783729153, 580231398, 81835895, 430821380, 943755880, 741126943, 374756490, 398723405, 453215474, 248946356, 45483650, 43835542, 870458881, 713282757, 235785518, 531230255, 661933192, 252727748, 70146922, 118156690, 987210600, 141993235, 601468995, 889008403, 636986991, 298595624, 419355583, 178200335, 674820236, 160936623, 884847754, 935220425, 501174492, 659575282, 756210355, 149812858, 595788790, 874684823, 47211140, 320735117, 793610159, 675011797, 394652841, 44857752, 722438102, 986969957, 103850695, 301225586, 654151211, 234011728, 259958319, 295080655, 136706538, 452785692, 481021383, 115520790, 365727621, 997088003, 45071623, 841714903, 787060319, 364843656, 195461527, 827127026, 459147883, 651183239, 118368451, 246920127, 317715813, 874385144, 544755707, 305642648, 505495417, 840161332, 698450842, 361262978, 121252920, 338092984, 633814892, 901076050, 74831546, 335399023, 74856230, 12453937, 904123315, 644357029, 186796279, 456160770, 243611970, 657494820, 400279817, 482387450, 975726499, 429259375, 832238962, 612281269, 598269967, 296854634, 644151908, 763334758, 569677954, 592901958, 608758975, 51813314, 873120703, 907643013, 603557405, 731284175, 314622742, 609236123, 608679428, 319463638, 175281955, 596859643, 644970081, 444844174, 316948019, 820327300, 843869552, 567108503, 776242629, 450280760, 949250668, 670853958, 582014473, 831968209, 190593455, 974535914, 647543843, 671463718, 532563503, 431820998, 146460320, 206291638, 515928881, 862361568, 896724018, 982747716, 938051336, 403604782, 256805610, 104749047, 538276656, 911456011, 975368893, 401643676, 569543605, 967727735, 545979119, 455271450, 85200834, 33816116, 290436955, 213806573, 821784743, 437644754, 394187563, 108117940, 63496517, 512403146, 80411999, 505262537, 622606409, 217765854, 766050030, 285790230, 959204863, 187333399, 753169501, 141271239, 389520933, 462335941, 980801386, 180291396, 655802756, 947183562, 94889144, 274831586, 131095571, 109003229, 813827549, 721217896, 161108571, 314621071, 492343666, 876114107, 73636738, 589095043, 924972392, 197631930, 899162227, 282358044, 929309417, 254890528, 245900069, 656489844, 665046564, 217247169, 359675751, 177277125, 450598091, 983506699, 330382298, 913886350, 493957722, 45481941, 384019839, 882682410, 502017352, 462995930, 957857740, 852788741, 418426246, 608130514, 273922584, 356220908, 813611614, 214487950, 741091149, 869773729, 893380408, 46781772, 559460274, 395363551, 197874410, 101478046, 389423897, 343649548, 944120608, 315190705, 786339034, 439198290, 589460741, 789166110, 313079000, 673711264, 747451599, 914912580, 541357844, 991159504, 615465879, 275506511, 448689159, 978279083, 835259544, 543999257, 24687318, 908666056, 279332005, 729723883, 516302641, 605964459, 705159115, 663261779, 384831929, 434184409, 531735619, 785367151, 557881968, 357603987, 891126518, 598032362, 31055738, 97820923, 924133545, 815336238, 561488901, 56097497, 122139263, 749523833, 59884775, 341755541, 866095435, 315464137, 77598137, 174502776, 189203630, 602987773, 205920893, 17429446, 179025913, 502496808, 153120931, 752291006, 447186540, 487138560, 948921569, 291680212, 253600639, 90395214, 289067518, 451101410, 547791463, 421063291, 969595279, 306175125, 406763569, 864735434, 982483727, 599590376, 217680334, 901167557, 585216014, 786244347, 160480052, 422615502, 99387364, 762112403, 374864743, 848003242, 77602407, 178270711, 396222631, 971761615, 177748879, 348161389, 802983027, 11913253, 493651836, 868344718, 90877235, 129660921, 627492804, 73371451, 983441681, 298122262, 8152844, 979818347, 307882985, 895089115, 771679146, 808414486, 407457050, 503285195, 614840972, 342929459, 549965672, 344996240, 87238266, 35458675, 714809930, 605169889, 682626401, 776540511, 551156960, 691351312, 962295238, 626221321, 863972724, 29278597, 468457304, 749753627, 147711730, 509893903, 94810845, 211621586, 721567103, 901058636, 654172457, 401715456, 545843713, 317460982, 192680383, 791897081, 564178132, 790014838, 100757419, 680995064, 812719090, 961552685, 613357458, 64763884, 576092755, 358580603, 470939552, 675202461, 451306154, 999876339, 119171633, 533613119, 987008322, 449507825, 740047442, 181868530, 869945832, 369019657, 920946484, 635280211, 804018697, 500679846, 745537736, 425306021, 152897328, 202841691, 366797627, 825436644, 687363010, 734577782, 444621678, 776494496, 16083514, 745337355, 188924033, 348598556, 827908871, 115309849, 710269220, 297687841, 924756512, 823131383, 249303202, 734208123, 444912918, 59554789, 84223398, 688585079, 62200453, 842083359, 980049132, 290993973, 245471651, 753578616, 172063049, 987348048, 489423523, 368975402, 159457570, 687922523, 675862684, 288947500, 358855219, 71303348, 810512326, 197915930, 953536947, 36401469, 199196430, 967892885, 963818708, 405115570, 407802255, 399521244, 921808441, 728531559, 394930638, 721154429, 93797015, 39687564, 136828780, 316138329, 663225070, 391522423, 319873735, 692864702, 997173652, 232296279, 259435829, 98585663, 646637451, 139095057, 868684859, 964603089, 608595472, 459641968, 130988088, 246045199, 644587559, 456320423, 924917484, 881886535, 43361075, 150343412, 686888672, 232192739, 265414421, 250488334, 783410977, 978691742, 288922073, 503694916, 229737611, 479789616, 70285402, 936475020, 774343921, 17274824, 226108933, 788431057, 397799784, 192540886, 105930664, 731417747, 254553082, 720291425, 596464526, 511360628, 553006632, 297268702, 886853745, 941920279, 380472650, 504978217, 58298503, 355176448, 923418073, 387687218, 676698940, 157599566, 365999746, 437213782, 496873955, 401710291, 233551650, 16975153, 523933492, 749021060, 784273253, 519291477, 343687585, 93830913, 776999815, 659438029, 947046894, 578309902, 111728011, 667415000, 357582665, 558883773, 830776375, 333849278, 721722182, 703540756, 898570374, 617124387, 310787083, 774334607, 772413005, 794459560, 595783345, 895633763, 34416355, 409114322, 915035757, 316654196, 772560011, 949583102, 974102427, 395781286, 990743938, 147323388, 400043070, 349311507, 921454242, 474764869, 437229296, 304901550, 693151514, 326086363, 253675125, 244932862, 842929624, 13282319, 475239205, 90848049, 373719392, 560711086, 183781342, 271831595, 409396200, 389511672, 462623986, 726496289, 709349406, 958355389, 74189009, 845300554, 58675752, 352831574, 864587334, 115366442, 609513971, 934845243, 35643750, 885915528, 911273591, 816954089, 437247942, 930241408, 170933878, 20604308, 650123995, 709383080, 482773516, 283646983, 373432115, 904676107, 444534127, 531094891, 43995747, 157281359, 169239209, 604056518, 278049886, 132660973, 439015261, 287551777, 54818071, 415686787, 218330469, 377529158, 839957254, 862102121, 151043944, 674950136, 483167665, 849126797, 241481054, 922737226, 784746057, 614746993, 396043846, 834335070, 604554326, 730756514, 385495111, 674377389, 956379977, 618305763, 337785935, 715440644, 476972793, 802308420, 428149247, 887740980, 368144840, 85353542, 249523063, 276382215, 976332091, 98153276, 494916727, 946366131, 344065388, 72009121, 929805104, 80873833, 320602429, 919267454, 470275413, 140854826, 822495941, 817491610, 666985383, 284740209, 18716842, 209938324, 696184993, 236965932, 578667392, 506509357, 785204807, 846699167, 767665314, 394963136, 334413827, 368171370, 482615567, 737658627, 117552309, 76450895, 445157856, 340498158, 65574130, 448058823, 315729914, 979556668, 14630130, 904904952, 44172352, 458335033, 504051238, 854000915, 662700933, 281384055, 506081984, 503903839, 145261992, 151445689, 927469417, 528118494, 88281267, 894116944, 115807196, 124927351, 729722350, 277392278, 98191301, 327349936, 142566864, 254881259, 874156992, 403161705, 989767753, 552612175, 40427362, 527620265, 89550006, 538429069, 247953851, 183931256, 510305736, 958715645, 27694868, 869051946, 312870119, 856399506, 400740567, 890945059, 733473860, 603796796, 808286810, 969246206, 868976883, 912387714, 519024913, 539864705, 412882258, 889747215, 272563010, 198088245, 308093706, 680768634, 772158495, 978812588, 280637011, 282555321, 869870544, 318271157, 856221828, 216451469, 595255797, 376782223, 684968008, 759816298, 144167171, 574205142, 929047629, 355330925, 302416213, 469724939, 947829143, 276146311, 763306375, 460726273, 737494178, 638825071, 785539555, 710083490, 882370261, 346455611, 471854852, 335361979, 136826708, 435103126, 844328474, 868180702, 220022580, 257223934, 677936320, 14671391, 813270396, 15710393, 919057131, 752304937, 822014627, 407790228, 760568240, 185970632, 760380959, 949184336, 268453583, 642531661, 968139014, 169211546, 611416364, 354863554, 210214008, 701285014, 617848206, 287025237, 5318640, 124590067, 766913767, 331985859, 780854872, 627796985, 898425314, 186695148, 865405493, 751346933, 762588586, 904982268, 51115700, 192568706, 29132853, 715023727, 28570065, 81358613, 343701056, 898252970, 576704912, 741378426, 203033417, 671063232, 785526687, 888065902, 321377600, 627763203, 981446803, 96120970, 479938043, 987141460, 943224019, 512366250, 852714074, 379899980, 107071413, 530507645, 55300908, 597823255, 892858167, 297502490, 550517556, 984755957, 981917255, 138022217, 337271484, 949808621, 24650377, 387718345, 469310635, 305953421, 188264951, 968642843, 132467493, 418745577, 889150904, 84258153, 95161213, 443494753, 595902024, 891001573, 517428278, 831384917, 91626797, 253675083, 963101964, 780726771, 800360336, 178014068, 709308416, 949425695, 640714251, 207550165, 707897245, 974917586, 594823928, 905138312, 837108710, 683557234, 652273201, 367851126, 316971601, 303069439, 432162576, 199290590, 619667187, 726805345, 679128959, 912269828, 96268891, 746215224, 516526659, 175743768, 875196862, 690086086, 252201484, 566388019, 782882236, 137075038, 321711624, 512419296, 650204411, 307762804, 965121313, 438651448, 336839422, 185351177, 960778884, 340651733, 835682389, 928222948, 429260244, 78806605, 537362978, 554855102, 781171816, 419601749, 491924074, 297878948, 914319951, 76966368, 461638852, 442909041, 234435927, 415528462, 893342427, 453624218, 105704223, 762344355, 845418225, 270554669, 232123815, 51115109, 718049547, 67851399, 616049285, 784732421, 927185976, 9577156, 474627485, 326528843, 231403147, 774274924, 382524038, 308271310, 33445745, 139727837, 248085934, 77457391, 322849257, 976383339, 813849395, 899322820, 874679746, 110835574, 344643414, 358754932, 371434302, 821388655, 260605552, 442620237, 951610963, 450332860, 176779883, 111867346, 892903248, 498764257, 694953669, 792857581, 628229355, 562994707, 66497461, 106298323, 278122870, 572593785, 436870733, 572721622, 668881828, 180107548, 766075694, 385441364, 112918300, 423982389, 447523912, 96187471, 616701601, 514933772, 9400477, 924143705, 295995027, 469623814, 121473651, 76135021, 176985357, 723696159, 315783421, 337462972, 699565982, 96321467, 230026055, 608942560, 454013562, 37328281, 6226158, 543175927, 547927152, 669055477, 732078064, 327975341, 242118642, 379383347, 115307271, 62547668, 386037581, 847848534, 368133106, 301811262, 815159943, 650874510, 6610665, 932848416, 410932843, 207289493, 793566364, 886005647, 811797370, 989840316, 440796671, 382278245, 660790301, 149691151, 262630483, 983936200, 10160859, 818574610, 636152082, 599839463, 253176246, 473472964, 658581596, 330045502, 392216654, 722130960, 220274359, 371833359, 132544099, 984208176, 798416404, 198180975, 965268905, 661821990, 295530165, 673940949, 577071104, 591967766, 928931597, 367242190, 637987145, 772524160, 251621324, 934126591, 403672712, 25954882, 76598895, 875234480, 10365108, 709232600, 327839019, 656747799, 688629858, 740532162, 584034555, 985067624, 268909441, 301879935, 140291245, 480677240, 196547519, 436136950, 644334751, 556210480, 905776854, 812831078, 262066944, 143805656, 670802242, 694411898, 923983490, 51135633, 750844230, 216591495, 183212770, 603734896, 535985853, 48308319, 440033330, 809099784, 857589810, 981197910, 207525349, 829985644, 146687324, 626187141, 577517817, 972689526, 640729464, 130861076, 999302083, 514062771, 190821441, 212862011, 246813141, 369451481, 914550944, 47567079, 821062161, 166021817, 970546084, 812627705, 279084238, 676490359, 947722702, 351408433, 361154436, 937109077, 91923324, 166334042, 889787831, 253730049, 989911782, 928913374, 940956891, 685223932, 61699272, 797638545, 333640474, 432637638, 787687668, 553225501, 880890464, 885696854, 397606740, 829426099, 819792404, 531716641, 483221066, 865402521, 911765533, 449904398, 847733500, 138465491, 85569405, 28288348, 285394937, 170342054, 895089897, 939936556, 120732502, 440061965, 421660926, 456095193, 15897264, 470313662, 185697389, 574287421, 461787190, 860090592, 686290821, 303183329, 891117920, 944586299, 438954930, 503368482, 82563807, 130517307, 846457859, 880407011, 822314222, 302055157, 159486794, 695093537, 145461483, 481075175, 801479217, 834691539, 20538128, 193200153, 678420992, 295503949, 138039823, 196614693, 555531364, 250330811, 811372081, 760591746, 303014091, 500619917, 311709537, 278891613, 601935342, 963263444, 900190846, 771612218, 822436847, 647037262, 587952537, 696933423, 968346167, 259615459, 983735163, 936253262, 545826338, 697939069, 831467829, 244571288, 714137746, 568661112, 940668198, 944679119, 923366414, 468992775, 603841188, 23988697, 358820016, 395550064, 69504218, 87171965, 721760467, 751764017, 648693369, 432636867, 943043743, 600405146, 706927965, 67381461, 487260800, 381405647, 760188543, 293613717, 846662087, 85055359, 159800756, 997510607, 910355503, 185908729, 775202980, 992227391, 609527152, 496299628, 584513719, 507829193, 338835407, 888227410, 654941591, 808315709, 944770255, 861394266, 979652018, 816533438, 781289530, 644939830, 681921615, 249490102, 78477911, 679545200, 559417025, 840463968, 488779434, 923382244, 619971862, 555872294, 54032763, 196126575, 700415450, 694612797, 21377429, 389852150, 581927608, 366910142, 995476030, 220549731, 603850177, 555291635, 828132043, 434126545, 259773337, 336451282, 75973494, 829458445, 725794027, 871439186, 905841179, 975078434, 547054908, 944789768, 705411467, 986497922, 802074382, 876881151, 335581922, 348663554, 861956468, 152419514, 143997610, 745448980, 104532376, 157461435, 834253089, 611899538, 794195452, 464804029, 443749517, 34193413, 489623521, 230260220, 159092739, 291906959, 430301064, 957817843, 960741374, 767218762, 512759558, 539041532, 383892026, 542183075, 96505862, 614081703, 142566740, 562194765, 113784384, 12529021, 607132482, 15151804, 964577886, 886198175, 389771128, 586455776, 989436403, 352964607, 177131479, 521161974, 874807813, 139466017, 83627168, 819880164, 869055942, 282924254, 204313095, 945273561, 359126467, 597693132, 925975971, 686693026, 538571049, 46412789, 864626821, 548864691, 667003151, 293927924, 148604970, 772885730, 563538268, 550496729, 415766291, 987145060, 897006840, 323346684, 395995531, 517987997, 303300453, 790154721, 909626644, 540196536, 100810964, 925326678, 506377382, 610316070, 985987989, 607131854, 931495812, 570215717, 458244077, 994460092, 271883382, 730940026, 944244720, 482331242, 371730676, 887369551, 927279438, 249736161, 584237821, 448804101, 993074467, 150406190, 932722509, 969701251, 657216141, 188361118, 75540944, 932319092, 461985603, 953238763, 299938175, 747565366, 781736600, 326127811, 493624139, 992531689, 742789451, 382192287, 966395750, 389082114, 750089157, 156525144, 299222615, 42879007, 290637483, 231691017, 586334906, 897987801, 681812492, 720030171, 891086281, 183470388, 264226255, 85234670, 639142651, 989692943, 511944157, 534325709, 125728565, 638052388, 234604890, 810104329, 786068194, 678424485, 207548671, 317508662, 112290165, 640278950, 382789498, 316893425, 861480667, 579393553, 423945170, 573192301, 232019063, 134873293, 577950646, 559426174, 712291603, 805205627, 968348071, 196249838, 11273598, 900890342, 852607553, 2092480, 511080642, 177240960, 41991025, 282019292, 702635969, 156040542, 479734814, 828870412, 278764113, 327364761, 206616556, 656772247, 548974322, 315074308, 540039087, 35209794, 33385118, 377659826, 324094692, 936911919, 562528769, 699014555, 310802219, 909291484, 692358284, 29976384, 445452689, 509044045, 620488420, 891110788, 815666156, 475347377, 893716856, 404254587, 204196159, 281162520, 236110427, 261210854, 166025111, 665028857, 858260367, 890803065, 541040632, 450196625, 318551951, 118420016, 295310347, 177489350, 327999170, 989086722, 406245948, 782584111, 187896846, 235470538, 478932399, 858380152, 65838457, 761915555, 454489758, 741023771, 401844800, 444908818, 748349166, 591227847, 954570155, 618853600, 724592979, 799570103, 841809436, 255002747, 222938470, 429579245, 655928815, 262239002, 597595484, 239416391, 228709147, 736776686, 892520131, 145269129, 889161014, 679683110, 934710844, 479917953, 389543161, 629265212, 28883113, 191025099, 543313312, 185575710, 444350106, 55229428, 267468801, 768868101, 980227238, 873235713, 723785255, 778035336, 78274878, 65447628, 347440985, 70670310, 245695741, 421176432, 649648427, 452988508, 987329629, 181368479, 649612571, 864339977, 8286834, 697277444, 27550235, 884508029, 626700206, 132808698, 668176243, 787300225, 54307772, 130167509, 298539950, 57011203, 445804423, 836948877, 699275234, 985715863, 879774960, 484377972, 687853990, 554657569, 643786802, 551904098, 785717044, 912231894, 640923634, 617072265, 277974177, 470978826, 585705441, 980293258, 111951931, 637579820, 668727514, 262455814, 580261118, 387068369, 128241831, 184198682, 78218521, 931004966, 420962546, 843515939, 317665992, 613204656, 307289048, 840385811, 193262438, 61324030, 372605339, 298049913, 198586775, 73066831, 86584475, 770145539, 109594817, 768928559, 647747021, 731904339, 382809585, 552383279, 674200106, 254398644, 200568701, 717108682, 210484212, 17324687, 255153733, 245606011, 817820092, 647664186, 443138215, 358615268, 280346724, 978355719, 41966747, 307605659, 809043273, 892483853, 47957799, 642788996, 95780706, 350936185, 968613140, 246099476, 61121081, 23470314, 597565214, 134959753, 445583888, 973575203, 259914712, 415871824, 190481887, 660058837, 611189687, 430885489, 137973310, 209146025, 895140823, 748549999, 133294602, 78988699, 925188432, 497345012, 72718333, 692861073, 73109324, 136435164, 272642619, 384798509, 627649165, 542287902, 794898764, 801226296, 667248942, 988745423, 830405924, 963908103, 67103009, 866546522, 464302623, 509069996, 976843215, 230452633, 718696203, 785857939, 259028654, 579477709, 732080055, 136335386, 709251730, 548389016, 209676699, 738496698, 767542447, 963827992, 356509277, 704159518, 910092100, 150657723, 50741583, 354343274, 238880448, 567698747, 716515387, 571372127, 231365434, 525971805, 91906832, 3594602, 33615066, 911385668, 972698466, 343225181, 553396326, 960406354, 359951737, 512229221, 592189505, 651087507, 799071390, 795479601, 351663978, 148635677, 926003189, 460364463, 182635544, 717103329, 839250927, 803427691, 947428484, 891134371, 595004107, 913962930, 612001139, 205250125, 629994181, 853432742, 833022171, 164511390, 699876546, 83274973, 95604156, 279146206, 48659543, 304966079, 273488873, 797654205, 392699493, 662206963, 74708350, 529544416, 730013989, 762022558, 853654917, 27245213, 320656874, 989611388, 552683453, 659599435, 950395368, 229697563, 570133185, 77415048, 135365194, 200063614, 184318016, 550197555, 124487641, 716938895, 831195577, 801034811, 775738536, 138254562, 468684293, 389788379, 317159797, 383507328, 559410039, 669310546, 692847564, 779721311, 826646435, 723374252, 836718883, 172633754, 685273946, 267577752, 824804561, 206438216, 956915911, 679017582, 626167694, 234280253, 845846980, 150377798, 946256952, 808167382, 95612590, 245633876, 627871141, 282591039, 300677254, 989254351, 403796095, 956479534, 620304679, 962294757, 976716696, 382037163, 383446885, 995527043, 658189853, 174337925, 586664182, 286938684, 238077493, 1128307, 301633106, 594866783, 243288409, 954873759, 83821218, 693162893, 753185799, 110027549, 452326758, 522028900, 233693856, 201564575, 241882300, 30710011, 987888151, 162039324, 292757802, 522041856, 886829877, 709704384, 735727774, 715413099, 87066061, 157583319, 697044486, 876387139, 709426017, 362203080, 522771670, 449039494, 599193577, 889418432, 122319170, 634091149, 487625888, 527577829, 533203620, 426243366, 419135114, 783066495, 428601772, 335418352, 90149537, 11031146, 128225836, 117073344, 786496485, 627070974, 953891074, 37510795, 619903423, 73631200, 240318414, 482330508, 482165088, 290185580, 146095876, 18670628, 286150061, 538055448, 377362910, 738774635, 491972670, 185313693, 146399327, 463044504, 863117849, 329026786, 664867878, 685832689, 228738536, 291584996, 58373247, 174984021, 646644752, 170069709, 363896840, 906220289, 549471596, 47913704, 223405988, 303274584, 478316723, 159823190, 69410919, 240396522, 847932345, 852222255, 842326651, 474709214, 525539321, 603590103, 916341304, 601671201, 731087050, 115636628, 345631330, 328408428, 221367692, 364468949, 207696819, 334508108, 626958220, 167873023, 965848071, 937686607, 158728445, 840229221, 998742019, 775463311, 765322689, 844323707, 743642336, 334193743, 523263675, 60795740, 659698335, 206519976, 868983671, 994982622, 389994576, 331596265, 261328850, 491014006, 720531436, 688811440, 931672213, 455093993, 231715702, 289113247, 471270993, 178480600, 976884947, 232690582, 626720319, 991015645, 987596899, 209741862, 717897922, 599522881, 241410652, 813053529, 638842442, 483065153, 785688159, 217469483, 660592843, 253538978, 247799960, 397484047, 118955338, 89509069, 679792859, 993161196, 705612378, 333786067, 646931039, 337155301, 721224774, 490087558, 651501, 961233097, 924088050, 315885639, 42108183, 970314385, 114021175, 944274724, 107834385, 977833912, 930307576, 513141792, 458452002, 84545576, 603023254, 790567496, 535495113, 482673637, 952124154, 225268086, 760853587, 90731450, 332582604, 942559062, 930137847, 458625060, 301921063, 441543456, 259150286, 512220117, 11845456, 626039040, 732192741, 830868730, 678264807, 209181403, 962606415, 154830778, 283382922, 885993852, 798773008, 120151715, 217783974, 232610471, 937006066, 702743193, 444441761, 130310874, 810675237, 431852514, 366908409, 409177174, 639236574, 304650325, 246817502, 46327543, 14644535, 945926370, 750376370, 865330364, 190954518, 179507800, 934427703, 331454190, 981072265, 181460726, 977366428, 352419527, 138510014, 161772273, 589657898, 553010396, 324167031, 970301578, 717977855, 684076619, 876116007, 727796822, 833456814, 65312880, 242977977, 532634994, 9477022, 489298688, 192060412, 555687952, 462420809, 232521611, 798590253, 508650954, 331458908, 466554699, 543131577, 318712368, 726732658, 131051438, 91759003, 214048666, 554974843, 368742350, 45970065, 131018213, 496957436, 37747138, 30221812, 282842211, 100950340, 61773625, 911393116, 11107252, 471398835, 407818318, 187285431, 561714709, 458538337, 28323369, 560514097, 448493139, 448569341, 124989671, 617164589, 309237291, 17962098, 513936494, 271430107, 226219306, 382900537, 114124839, 356573247, 461879186, 788607678, 594345, 996006626, 389403417, 216053564, 861370623, 26130081, 733436704, 86032314, 80826352, 765188105, 917070145, 421878481, 660854217, 377021137, 529869069, 562793779, 796514386, 732698378, 183626306, 619438472, 957669601, 975280602, 229478131, 576037035, 457838935, 202246603, 457853510, 287831885, 66524419, 418873459, 484263300, 487092045, 883332572, 280013565, 539412224, 682459499, 630520705, 116604355, 292772434, 101682370, 642434787, 440454927, 384772311, 488273760, 979486450, 728072219, 168640950, 264485091, 591909416, 511576048, 33458089, 580588724, 183715259, 322658420, 952715429, 548677654, 51025091, 766141356, 860743050, 337149838, 305550020, 121017817, 793435641, 786430604, 907616539, 899200508, 522136004, 851666335, 441098977, 574992432, 357038122, 207887139, 750881487, 223274962, 43194540, 881059582, 981473596, 500973007, 302561920, 620768474, 425314151, 227568780, 625251324, 905976266, 800119508, 351217418, 985378387, 652749762, 431268606, 200408952, 801112549, 213048144, 709643566, 733420072, 94473137, 876066258, 825663372, 558484231, 725152204, 301715101, 290260179, 10142952, 295476243, 725972353, 344252157, 413840560, 586945060, 943768233, 404480097, 271531321, 299743521, 747669487, 623483125, 937288591, 296292587, 151639943, 40178234, 310402849, 732928233, 644639446, 678980357, 264201457, 357452761, 56591632, 223130917, 909512235, 519155852, 184875884, 187011448, 758478613, 831025656, 799225721, 657072571, 56207609, 501306361, 54415289, 838860323, 660017997, 794543846, 139731383, 440415215, 931596203, 728052447, 377807727, 174183005, 295915771, 488893916, 843282439, 528385792, 353712634, 707382768, 88750845, 751247076, 204240686, 805779579, 900164724, 225283834, 233925202, 298032640, 443227858, 578035899, 690408302, 522430129, 109281438, 203029005, 83458298, 732660580, 881905479, 660910260, 995939664, 1533222, 347827400, 77679339, 95459853, 344470314, 549103187, 863403428, 596994802, 585046838, 795057146, 527324586, 592355627, 300672287, 250565546, 165933665, 827483406, 27867909, 100042483, 790330979, 368616054, 515920351, 569178545, 430373230, 489689537, 308367723, 260724209, 898368077, 848505717, 72300348, 194929321, 12459285, 11366716, 586233983, 755049469, 510016615, 589409520, 809161962, 177624440, 477810503, 689680582, 30896378, 881313617, 367978309, 697815512, 92499016, 705196058, 457773955, 235327608, 639977947, 771066287, 293900663, 489235567, 819782450, 185919305, 9946597, 235738961, 947137340, 314629171, 434668878, 732149352, 642012655, 805225147, 954387127, 922306309, 208114506, 557966881, 152843300, 986866282, 653321515, 161919311, 954682917, 708102132, 576288081, 570165759, 368660853, 794932687, 440768033, 148970103, 766945059, 567138732, 521902510, 435505053, 79703989, 281358882, 144834454, 24352959, 795951346, 905611558, 324267718, 190653265, 529300049, 166411526, 337024187, 329374670, 8120402, 242414094, 687147658, 626063976, 881987027, 288948573, 871535172, 245903786, 517075076, 155676150, 662740234, 139969102, 837424460, 304227836, 474502811, 87441389, 665883954, 98524551, 504474714, 456237690, 928246409, 796820784, 17073783, 167229234, 556603187, 64165224, 697560588, 98506856, 932753721, 278792156, 530487587, 372889949, 646815170, 116200624, 527597065, 618896251, 574178641, 712613491, 485475459, 66652020, 52274175, 595353864, 840433623, 937214941, 395407587, 979984651, 42416671, 894764438, 253590402, 140935146, 197131948, 688381316, 401549320, 517796652, 512189684, 25330689, 821466819, 242834083, 729982696, 761434392, 193534767, 172154121, 721973207, 324913058, 510423583, 660869409, 428975321, 750372185, 405393955, 376408884, 975740054, 127578414, 433855257, 598791180, 218602954, 139794380, 734796373, 251035835, 412585951, 788985407, 833901641, 782802766, 665936799, 619951324, 71516015, 873386855, 756183225, 238099075, 745234696, 185756180, 983407354, 714057624, 967317916, 312756143, 163424660, 913703168, 127552451, 451347486, 731983812, 356658019, 876649290, 885122672, 887709022, 961003625, 114957649, 710185673, 979820182, 768086067, 325526595, 895703770, 368878374, 214045945, 771838741, 617164218, 672098605, 736155093, 400591986, 765963466, 394736496, 214666494, 713493381, 232808884, 269359, 419190045, 492516852, 749602246, 901508342, 74472179, 376835101, 427674435, 420811947, 689776040, 863915821, 343324989, 469052665, 339251354, 523108184, 420760852, 566547066, 415610175, 163981049, 950901097, 855420234, 365562586, 182333846, 630963161, 149042767, 800531937, 154618439, 403533256, 631242047, 76082585, 743308886, 895507065, 652818324, 361525400, 998002156, 815273059, 887577843, 468416455, 762067028, 102652597, 653633785, 36591287, 573505953, 587180279, 449403522, 300518673, 31680347, 232891659, 682733813, 425569702, 854216171, 294497656, 521712515, 739293465, 530371586, 959733486, 707143793, 114238386, 186782298, 162852958, 215075198, 401321026, 70024512, 304608613, 419987956, 113264464, 393890821, 62508115, 592013828, 300361752, 368238586, 728095340, 805305157, 973028023, 959685159, 874254685, 542918352, 283377047, 397887482, 838676120, 81971065, 149629881, 256796346, 722551451, 127835090, 182297476, 950325049, 908514172, 872679431, 701382825, 370789044, 303101219, 348482562, 737675681, 756250742, 486636947, 407477501, 428116765, 538371512, 859554047, 341020706, 307486962, 886466826, 225968129, 135163463, 743725480, 891826936, 91141026, 265724544, 713262379, 711803228, 573388257, 665389254, 175485300, 852577495, 934405415, 283619255, 817495299, 178036095, 238225972, 66666436, 861397174, 714233904, 466841354, 233457883, 607839050, 589692161, 475558151, 994727038, 288615172, 838678206, 2831112, 97323642, 754841129, 85718371, 377552143, 221918048, 803305384, 156411239, 331693421, 505521423, 699011167, 164530005, 147189091, 335672103, 780150994, 636738281, 447551765, 362447663, 375908633, 723559917, 388178658, 886695479, 892743615, 784220110, 272495575, 211331903, 944288766, 919430762, 472502744, 690527923, 53909304, 212359889, 576731443, 454097321, 825034430, 332125957, 767566892, 447711386, 405668828, 317356509, 784045609, 178694991, 250813837, 645921950, 468392157, 259890654, 245763242, 669936962, 600900129, 412079808, 163085066, 889643036, 544925442, 236630065, 440977918, 331589878, 16616683, 554612145, 808047558, 589092301, 662230331, 70944396, 608232740, 715560647, 180867917, 642251075, 280419429, 841921341, 911287337, 978523113, 740751457, 521310548, 227674582, 473836769, 765806401, 681386382, 55831038, 724926991, 317945807, 511292475, 924878636, 968502091, 148934437, 620927372, 191383510, 349854444, 961501149, 447561396, 998206428, 64109690, 748032450, 221271770, 114865752, 113979975, 488911462, 673075479, 847384481, 353009995, 617253041, 313306595, 240146490, 448271606, 619811389, 608225236, 592203972, 915600649, 953106659, 527239049, 665548430, 296688189, 619513299, 260495933, 124323684, 506677759, 607182004, 245835222, 625965628, 528512673, 38739393, 394699974, 459521718, 312703614, 646780319, 794978036, 853757565, 576301953, 301413681, 762449383, 139426151, 233248356, 54962488, 274315751, 755694998, 601548780, 764822650, 452918991, 918882713, 268116256, 374283648, 981531487, 268265014, 492293563, 675866166, 119285859, 364129782, 485956201, 199400621, 920292413, 249556812, 749280524, 250117203, 955125834, 917759287, 805405387, 127842476, 813387152, 397784426, 859188483, 607409822, 894798880, 519176406, 810568589, 586737144, 48597192, 777116399, 915418575, 507336709, 554132494, 579559638, 642135143, 938384991, 492222125, 992841295, 875373168, 212383256, 86263690, 630459993, 686234698, 588498309, 887144640, 231152392, 518900017, 781727302, 697963245, 717506677, 980545022, 642302034, 348415033, 204435241, 739851812, 175473772, 426501930, 665633200, 19784536, 86799306, 519220252, 235653978, 103152350, 834215198, 598871549, 810043661, 79608387, 168577748, 44016491, 274184306, 270793362, 528976808, 897561480, 487036523, 322939413, 800704947, 740076994, 920535348, 707261814, 319133545, 969302798, 269825968, 912972139, 833488316, 818192584, 945946284, 943869149, 355525287, 671854541, 73438707, 516876101, 231851029, 396905039, 797442885, 936921577, 666301425, 356956241, 963999346, 223895655, 832374555, 165001915, 615228349, 999355943, 465170500, 660769615, 960861693, 953133003, 705625562, 914910808, 337724409, 999193699, 389535419, 330047855, 72942719, 699524753, 8238083, 630032566, 455800723, 173165159, 233182346, 494797847, 950741898, 24015500, 965058985, 352506967, 765323711, 649885412, 438941541, 628810055, 378837995, 160563904, 857865723, 446048701, 312021314, 453331054, 546552229, 108808652, 115333911, 405898713, 77581923, 564063607, 892129998, 713993922, 926427568, 692255724, 359693085, 493203680, 39192962, 539767605, 20642628, 456027431, 974451248, 3394009, 411515322, 983954584, 562392125, 672968219, 796569846, 722856513, 277902841, 100392650, 671951295, 30165245, 147105775, 508541799, 173595995, 654725233, 240202319, 523642459, 264504770, 269276039, 819822956, 585393037, 888389746, 841828863, 36962482, 659629110, 254077377, 120449830, 924539795, 732925721, 311815185, 123264733, 825440440, 53138620, 929112731, 88867294, 736089833, 722685725, 887659796, 213639842, 365190438, 52039113, 887645291, 60768736, 90013755, 293575068, 363385186, 389021038, 807681941, 629646833, 389279047, 153651663, 92492013, 867108869, 524356228, 397792030, 176870650, 813336141, 500701508, 544390223, 410727770, 481441492, 511200746, 980394948, 725305544, 523062292, 285884472, 224063541, 383530452, 841501627, 499268614, 19517295, 788188313, 74239864, 185815303, 25225607, 60583072, 961819436, 476316719, 529407477, 179360901, 174337199, 453811707, 746921698, 472828443, 248366099, 215182457, 917679912, 260398888, 484196198, 178286779, 392165264, 982674832, 646597883, 274726024, 695654657, 988573667, 61872163, 558642312, 817679408, 806988918, 655247870, 59196105, 411706242, 541875474, 996785005, 730646616, 604813597, 734298726, 905139724, 166944353, 777969408, 241692506, 114119498, 612476506, 681276230, 428332327, 984075453, 408037393, 267746677, 64531503, 990995779, 927125731, 459696851, 666212845, 447451952, 313746951, 376322177, 770271986, 603633059, 526574301, 401477203, 987376504, 920974509, 20087913, 742535216, 872645307, 175790442, 865065765, 756048637, 605221504, 310362095, 514086804, 581835095, 975148676, 500854353, 715412305, 708614247, 99654722, 266940, 482904621, 182166742, 861658082, 196628958, 824391791, 681878787, 571409969, 811983496, 273620051, 19915793, 296475080, 620847097, 457440699, 957802564, 327930746, 635852543, 168038063, 894925419, 452818433, 472228964, 184271887, 771840129, 941197106, 777321156, 941760533, 764565475, 865561748, 39617509, 51000983, 919618824, 981062326, 294005214, 816174001, 439289243, 461380181, 30016694, 525882593, 523243198, 945412251, 918757844, 646185212, 578234660, 904795300, 453655635, 390120024, 82635185, 340135591, 363107839, 837257739, 111966891, 430023492, 166446045, 187744594, 506217115, 389922205, 47706800, 921970035, 698497101, 277374644, 136795691, 810857112, 641057220, 162132998, 28524017, 403827858, 915387837, 415614807, 550557651, 844250532, 269818830, 15873343, 765430602, 436989592, 41270237, 763240957, 568727147, 385409316, 910719212, 716623259, 86726827, 369589996, 902481571, 213792647, 100681792, 933789824, 402330310, 835808749, 903859533, 409096316, 746452742, 785441759, 552158217, 589703086, 206385267, 911467551, 45043854, 998457074, 901489575, 696507471, 651425093, 169014798, 689111503, 164891841, 506291510, 138494360, 534754613, 22188041, 452390466, 166173145, 635903458, 480324945, 979655946, 802036078, 217364315, 626593430, 793763432, 815075599, 364695268, 473453515, 179191687, 427241778, 445872068, 59532848, 509128725, 399038243, 958301361, 287735274, 41382930, 453812930, 838057908, 387232891, 50713270, 393010187, 180413290, 43113414, 102149420, 861562674, 866949839, 319187780, 161379108, 876591323, 645055646, 244162553, 752379071, 222564340, 645553425, 769535566, 324097413, 789169284, 670627154, 447159346, 483649146, 227395903, 747623665, 539667022, 290592768, 258014876, 726336517, 646027059, 950849758, 520384256, 649575008, 70447522, 172672894, 289772670, 4585933, 873607768, 957453205, 731748920, 283693437, 161708153, 952340604, 654367446, 454721446, 986654506, 359104130, 701010370, 262720584, 850129295, 43272741, 386784834, 970343338, 855713120, 26482074, 427102425, 52660236, 356346107, 567416494, 845411189, 24874973, 498801892, 149451198, 928393241, 219776720, 855160793, 796756888, 938502537, 297772219, 344714023, 290038904, 591622274, 275904303, 775219238, 318668135, 723287742, 545801568, 328292310, 153340680, 800150687, 302174147, 22088036, 880804228, 14044218, 284559113, 499802170, 118915368, 599866244, 489046944, 66882094, 588790749, 899821139, 989772004, 82019433, 209059029, 450586584, 720651777, 238328097, 613411562, 145073868, 866032325, 848706923, 934204705, 623064641, 550589565, 814470275, 830308755, 22276261, 944728670, 872929336, 922996945, 836489157, 648523709, 34799265, 511285985, 109091915, 825022993, 375942777, 723028060, 736923045, 869159556, 583497354, 520647326, 947691488, 218944721, 974225458, 218111035, 290640182, 702107428, 308651330, 676077713, 266807701, 864047647, 413863130, 837730510, 643402136, 962926627, 304107140, 482084197, 424730363, 207174370, 106197371, 583450981, 909011791, 589737969, 441411451, 287177722, 47910024, 818524057, 285781511, 456846096, 32194747, 120949932, 791221771, 240958837, 118424129, 31631068, 597958117, 723655166, 934175422, 856065122, 295343388, 864015962, 376344370, 899630890, 906286798, 481503403, 378257274, 394389573, 189843087, 632098511, 619847051, 31471639, 455757177, 616764918, 686847996, 245554810, 90044307, 578898509, 878275386, 40469328, 756481548, 121849742, 627959000, 366876278, 992078090, 15997464, 721783309, 961962528, 538394850, 337592752, 825483331, 99979962, 179805254, 918203255, 590464278, 270001547, 824381350, 543886234, 489319078, 470115186, 104364152, 436807837, 155258611, 13503010, 227677752, 960853361, 579048892, 147176315, 330681488, 415481880, 358404239, 770933342, 803270394, 269180750, 185362632, 260743592, 970701062, 297274974, 747068165, 386613260, 913583765, 683224602, 604885824, 715127528, 884155284, 476826845, 777025350, 454308463, 315492237, 574966866, 810246610, 505932291, 793396848, 948251803, 318348637, 840923423, 69897854, 947018036, 559005044, 295990103, 948674468, 665807899, 381073507, 1554218, 584869824, 462266226, 858400184, 50226691, 92198801, 716134725, 375334421, 795704843, 403353055, 896742717, 588287551, 965137270, 717201164, 984327485, 498422077, 690528915, 745211201, 791448934, 152279904, 357655654, 865299716, 938255140, 650033559, 664835059, 201504501, 635225874, 189997056, 733157209, 789701848, 245798506, 103437124, 966774604, 954228284, 937325339, 691899751, 717282920, 950971053, 407073405, 248085598, 650302263, 236680728, 404331160, 668371320, 321839571, 235047939, 481949015, 170122206, 657150372, 490241441, 682019495, 158438370, 890279448, 720796624, 27259780, 193481696, 214917708, 264420375, 727031833, 657095520, 754554124, 48697326, 76863449, 192850644, 540902259, 668690448, 660607279, 141593022, 473529427, 209392791, 249097962, 3019310, 572535739, 414926579, 604155824, 128737921, 567982047, 878965982, 422108339, 987654964, 759027218, 912469002, 986486574, 577127573, 523188205, 691593952, 220175812, 738098292, 703886905, 974462252, 833141944, 32381676, 614235418, 60094797, 387863322, 965876996, 358241824, 880204293, 214735964, 574352956, 703432283, 382024624, 998291849, 65524781, 720060477, 239942004, 781470459, 902983496, 206784949, 318896066, 964499805, 238755088, 167059976, 348754321, 100274242, 240690837, 544411492, 830501230, 71639328, 785503796, 531415799, 435541113, 363357966, 808056479, 577622722, 925391982, 442847184, 565862472, 156546062, 636098198, 595739302, 31616990, 670754246, 796642305, 13397404, 96980893, 764195026, 928080639, 604856410, 414764058, 522298316, 527610955, 54113323, 973517079, 387045075, 135125237, 207164046, 21956345, 824542203, 572123185, 729982733, 594310293, 728565639, 935102057, 893126966, 843040787, 787649882, 636259842, 769706526, 500965438, 438350185, 417933775, 728701446, 648122573, 76129266, 988577165, 533885242, 631855720, 653231325, 819382011, 165887530, 287039309, 802211628, 232446386, 599254511, 660990439, 85323859, 123142199, 766466696, 707242774, 508104420, 166826430, 111252673, 978632991, 106277912, 17692303, 513834522, 271489947, 84367308, 815136282, 387637864, 411920647, 203355783, 896578754, 52571039, 140507971, 156124287, 891916845, 166000077, 829070326, 892387940, 542711984, 206671449, 71915814, 436929605, 878606705, 396365251, 342708598, 639522066, 21341416, 441023227, 783938909, 980669413, 184484809, 185669044, 746475214, 688359282, 138856747, 710214725, 332254700, 30157970, 536586961, 761808438, 941330020, 805106123, 474534012, 676058116, 286559943, 76095522, 549086192, 61510584, 737998489, 828066357, 787364358, 575262434, 122800790, 101978149, 567279140, 386733948, 727820138, 701358576, 143934296, 646263019, 12454431, 337030256, 763600131, 65954601, 202140646, 409881908, 284051251, 626842636, 122613105, 798378926, 608082102, 273390570, 640817478, 133308092, 745871495, 953840110, 985477135, 557649851, 67257281, 603400982, 791936496, 552502386, 612503686, 555523612, 837849652, 753903592, 568449827, 586453627, 776875154, 423770213, 864143151, 837492427, 722744268, 581932755, 65062830, 129654599, 759513836, 488776070, 615628724, 488313079, 607667504, 154316434, 829241801, 3392231, 902291708, 860604915, 491349908, 844759954, 351715143, 569998588, 518492493, 881515812, 357349302, 253769856, 579024766, 504857405, 515694012, 796531349, 967029191, 797653003, 335406576, 891223186, 873172428, 554099246, 310162333, 392271043, 262971767, 280281608, 318734789, 749904024, 804433356, 273913278, 80927476, 765956240, 626377985, 971823614, 170190573, 436589484, 281444764, 158172847, 887982508, 876848120, 147004822, 779220207, 124254787, 805214024, 201090656, 822327914, 860872350, 720428376, 764099609, 897956935, 281416671, 617722014, 660627958, 815178436, 318997454, 630504514, 476787069, 187028754, 343970539, 336502135, 396321139, 981530985, 159229667, 44440419, 99053645, 909080543, 280920142, 55466735, 854563808, 440297295, 510878852, 720795601, 615565530, 403869557, 468407321, 70317533, 893865008, 537352221, 758683061, 438455137, 329302708, 877842560, 428356756, 927406997, 827082479, 467358486, 166836411, 548237337, 285002563, 283175489, 195447277, 638618552, 274147200, 449016510, 581025446, 723247697, 809041728, 824542615, 412225186, 814994694, 829791417, 317033926, 87856880, 479001947, 886360676, 229344921, 855153788, 79113547, 802104377, 968716801, 151626258, 129744566, 408201318, 785984467, 503943260, 785704929, 648848701, 394201354, 681604023, 822559947, 989662760, 747316713, 229106985, 608654997, 566782575, 971261407, 676287192, 630013757, 969292856, 836643180, 735651708, 497502129, 601551188, 737667987, 520703202, 578234151, 936555076, 388668193, 582102680, 718038156, 352429557, 770648241, 783313988, 61360085, 736447983, 386493070, 403041837, 978974961, 528399966, 123213273, 586235516, 398884156, 621581027, 494093996, 166167009, 674743574, 254314824, 106190143, 515383803, 938300164, 4209049, 208334692, 524883220, 592981818, 502087991, 617231149, 684109734, 806466830, 477143107, 44371606, 700182243, 852748847, 551087239, 204465206, 897037567, 983948593, 901022360, 556178284, 740470654, 286837151, 261509877, 580736514, 385015357, 403875469, 929530461, 238669238, 984515965, 79108220, 573724580, 836931529, 352366534, 513407711, 900698142, 765120333, 93390432, 684578245, 663103540, 582006377, 469892053, 601537778, 141424392, 962795, 986151333, 504333977, 715399314, 722165357, 407045245, 970883831, 8324569, 251292570, 573937574, 297369479, 597815965, 909138350, 557885413, 373570706, 114990739, 685285343, 423174574, 972783452, 54499526, 67403682, 965595031, 972766352, 123976012, 889548238, 280645750, 428400091, 782225492, 407289007, 877161084, 800282893, 971875779, 159511246, 654890786, 300496791, 143920864, 160334441, 404107032, 228721096, 327861599, 824678303, 416794854, 468793247, 299089270, 58948106, 718321457, 439535496, 575362235, 658956772, 214779393, 321356764, 128277595, 517014739, 478649867, 164028593, 283130633, 264668999, 495499403, 265406333, 185244617, 640109586, 541964080, 102107737, 208632254, 622769333, 494824630, 361490329, 377983550, 508273231, 54518568, 882484350, 530206132, 854014421, 755849296, 67115340, 487154481, 408161320, 935323257, 614337247, 666581733, 48467536, 187657531, 760725350, 398566643, 7146981, 862334201, 247318858, 905977933, 926505063, 251734645, 781733046, 180417150, 812532530, 249892605, 264572052, 670975080, 350914986, 48110274, 781125092, 875364558, 811342413, 422431626, 278719547, 554239262, 151216417, 203411972, 501117115, 588148429, 271937720, 417721374, 642515507, 593731267, 66317909, 167637304, 392653590, 438937617, 934449956, 218410264, 560497207, 187328077, 957927334, 814297997, 210897623, 1736621, 65784617, 389020276, 80739363, 190749363, 213618867, 74507180, 838983167, 286006763, 701420066, 788042374, 233564653, 626303688, 767659783, 102157104, 575175238, 783039212, 826771243, 528025973, 796183707, 536690508, 870526778, 290775053, 72711500, 534832913, 811426858, 614973193, 153212346, 806849296, 569066799, 481470404, 973453723, 769594014, 494863706, 103797606, 546764144, 320714185, 343519312, 751131670, 673793282, 792203483, 461312105, 428652545, 906905069, 419045137, 942952407, 723905365, 732436216, 514671916, 607962476, 905707742, 385506023, 616954609, 511797227, 395393436, 845246109, 137281336, 582527239, 327383115, 144698449, 734454466, 302640917, 555853804, 928950338, 30571845, 792887811, 813082976, 464359094, 444088916, 42382745, 716467208, 822465668, 473360169, 677599386, 406104537, 406157769, 942403393, 395890256, 883398976, 329214518, 811093956, 484346013, 112427689, 253025662, 827388074, 104744403, 793966794, 86386380, 724718446, 372172864, 234153571, 208559265, 63894885, 954768878, 58844523, 864673059, 389090435, 678138465, 602904272, 268200102, 707794195, 595335640, 529858382, 72068605, 377076331, 259593171, 783348123, 308077516, 927019126, 824260369, 716173499, 767684277, 837690464, 310702594, 217029763, 443995112, 574670376, 482718544, 423892576, 718278443, 778858710, 754658302, 519088685, 640410966, 167427289, 24640306, 25396055, 441568582, 694929726, 541769953, 636961112, 785822928, 975346943, 829567802, 34575367, 352245586, 186339924, 175653493, 14771015, 618591565, 635537406, 724117020, 44130500, 284622246, 693222051, 734735526, 10707727, 831624274, 913622003, 287127629, 447394049, 538957140, 225015351, 403210480, 687725188, 227988701, 931691055, 528054326, 877312542, 343338675, 167221927, 329056752, 80671282, 589218802, 212692264, 565152158, 869591138, 429376342, 427741423, 486946529, 587436813, 441879845, 965931196, 374936548, 292200415, 521946388, 563599580, 85086446, 824607339, 733133206, 207769554, 121068678, 220982273, 819716431, 904338701, 166961063, 611032376, 705352073, 622934913, 791340340, 260483995, 787693585, 1141885, 382826863, 594729293, 597077503, 391246996, 966016791, 527623542, 815845976, 745160503, 677676842, 979957941, 482458670, 250427855, 26066562, 311853539, 142913193, 1437168, 327924165, 141804407, 901560767, 96295118, 97201883, 355215344, 241170962, 705473909, 688417915, 181768632, 734058242, 346993362, 423378831, 359295436, 62746253, 970169904, 839611581, 888687981, 524381672, 444789438, 312355128, 71386364, 445292750, 936224837, 225298350, 417946729, 382556084, 231430958, 507699243, 20177194, 86983407, 189408402, 181576173, 923900999, 390819236, 228006998, 719498010, 14854264, 374790777, 818428871, 730863724, 550633298, 535662714, 948502360, 475801421, 68412321, 942830066, 932783346, 480016279, 422515395, 47079310, 756255607, 159091155, 681799741, 332332050, 937143978, 967389007, 367629092, 648049359, 162700922, 321055878, 431934915, 634655793, 156104156, 121365093, 611057091, 700302677, 7970501, 887164879, 558922168, 715763865, 883700236, 656013012, 816655114, 770519940, 39703092, 653455782, 223307600, 346309726, 367314466, 890825165, 420817712, 372623970, 335842284, 566954185, 485756128, 552618784, 442011521, 62159854, 401894087, 261397022, 97059186, 503564230, 73918081, 959162967, 518136418, 367163691, 5151872, 293041074, 316308309, 108403751, 242536931, 904879232, 829805556, 552320838, 248257532, 473124737, 158575116, 107000174, 30777235, 193406974, 452496193, 196258454, 265589132, 410933835, 737880189, 975688243, 416716389, 987572830, 423018127, 196037969, 80484779, 651989071, 212384199, 115089402, 117437275, 46842255, 31476731, 361197388, 57072281, 693718105, 535234437, 725466115, 613456351, 588014580, 94056054, 487495648, 714499364, 550023989, 348905769, 974193035, 857748987, 793488284, 759950436, 196492441, 168751315, 29124177, 184825221, 667834565, 856368161, 607855159, 246660047, 277461574, 521003894, 891376467, 595113166, 301941845, 111112085, 61405965, 281597724, 974558977, 408019621, 468088668, 502197439, 279310647, 993253055, 665756784, 788847572, 879992124, 950425600, 345539690, 966023400, 316942471, 715070914, 591088560, 617503772, 556830379, 773995748, 787558050, 279577058, 131826995, 382821256, 601427851, 971944853, 633452488, 701461651, 438142824, 740416759, 70319907, 643663437, 149802151, 923642170, 975800469, 848854011, 977778823, 947359900, 969666151, 931222119, 82232344, 167086195, 191365846, 601927763, 82166781, 766998849, 182717297, 536148644, 264266409, 604190474, 936534431, 673671095, 728572654, 666279050, 618196195, 36390107, 400601600, 175978420, 387397013, 814283125, 239259002, 188023759, 200639368, 837038613, 904635935, 475083521, 762929324, 223257130, 146917543, 816709699, 288857328, 377527898, 918811345, 722647861, 539028034, 855355615, 279931911, 540135654, 946488765, 531906198, 466332306, 838934537, 988469880, 335297279, 449464400, 278921077, 675351171, 811151232, 528885414, 710379774, 986918920, 713459063, 98123610, 807198007, 236117898, 159753681, 605036646, 259804088, 172174940, 665595227, 104936544, 284150804, 619867428, 606215411, 5319512, 781096240, 587856773, 623108420, 79564826, 228366713, 525910061, 827203853, 653552189, 9768312, 756794031, 218171069, 167853888, 133462236, 295297030, 105201825, 5130149, 710012840, 543872285, 567746776, 234321210, 873445553, 867252354, 800359832, 129641068, 140072106, 695689235, 605588829, 243752918, 604799203, 318258411, 960675943, 232609091, 430555610, 595056434, 969985172, 963008384, 185716810, 885261382, 998828995, 841347603, 618839775, 389267491, 84957415, 645521653, 983107324, 994778722, 283239140, 392853065, 570455082, 525265864, 760049489, 741772905, 264601961, 726686951, 613524876, 145408112, 40625885, 997814464, 180337939, 728791621, 695830015, 141109775, 931308825, 385772875, 368714641, 937563632, 123544261, 446760123, 824198134, 588324798, 90060186, 828382319, 974133799, 340177401, 105123539, 26622071, 407820287, 40771786, 756632395, 911235955, 990491678, 53345035, 97502339, 67092938, 665080702, 921172153, 626201914, 195577084, 390512020, 992043794, 169386155, 149899531, 166684397, 16796170, 164466954, 119590137, 481617365, 609288569, 184388031, 628854697, 92860676, 983844939, 99680427, 686568426, 571075120, 990032557, 442417389, 251450581, 164254410, 381164129, 944068115, 145002272, 101983817, 243608349, 697568159, 412596375, 992308126, 494904352, 428526819, 845656805, 268870021, 541225861, 519160783, 5099334, 950882778, 678757245, 884626617, 708448589, 664696998, 615677040, 217265113, 872804716, 567443681, 513882041, 123323350, 578067717, 57065278, 574759808, 775492680, 187557473, 607175842, 29180218, 2455119, 18319952, 132596647, 103398867, 637481407, 605336769, 520564366, 920851443, 58903899, 880531705, 165458715, 588677045, 764846640, 297423995, 838381573, 224583871, 899659010, 268323702, 132967197, 822224955, 155696800, 565510980, 834486992, 18256804, 252649333, 43819866, 430367059, 500977729, 797867259, 940973627, 282513313, 491961969, 598882054, 13602513, 679674211, 481554363, 586945915, 496495700, 752232056, 954166397, 954298366, 55025888, 565313035, 918603932, 412570266, 22153414, 803620999, 798817269, 571500583, 38196439, 156666960, 811340418, 138134232, 370769305, 119794266, 630864467, 238318747, 558279114, 599064212, 553610059, 792871213, 747154688, 621483479, 291142516, 101862075, 415000410, 490998600, 615681028, 469291876, 241282157, 479336353, 627312947, 598677488, 618819578, 640186835, 816484044, 760066970, 491271083, 88260878, 636406709, 531369929, 496853294, 470267415, 143282696, 747704526, 180207084, 765816832, 661865365, 876685690, 446608755, 660681025, 307535566, 359219886, 831583227, 815032603, 672575391, 783653862, 655277325, 944355197, 390941478, 484381181, 946609427, 620170407, 782579233, 751725101, 983199507, 818953684, 128673169, 219526396, 549951169, 717495947, 593452942, 419247680, 726357612, 18382476, 734815070, 572905901, 139546327, 320139298, 54138237, 150915940, 395035118, 672869950, 514868732, 199267821, 615974640, 114057388, 739864921, 389417176, 644860667, 740342322, 186751832, 201880925, 287548787, 21329501, 486365551, 765273525, 669219675, 453795955, 250296480, 719679999, 952992405, 731270144, 870695960, 750098028, 186352894, 383961924, 799664893, 465944661, 411987498, 470245369, 23594191, 547566212, 743774299, 891557239, 942147372, 597576533, 357372628, 728050360, 510288758, 951440146, 410551828, 607457169, 635126707, 415989863, 790798273, 965524170, 893455338, 811907037, 316922844, 809393335, 556536212, 66661633, 643135678, 410903180, 397258366, 95945435, 408402347, 496201055, 690634400, 332769895, 686150258, 946988254, 997524376, 328236901, 691213884, 433588440, 894221098, 618683502, 549797117, 820493944, 21849067, 233983857, 971203012, 735347595, 864928653, 756487259, 144521247, 528392463, 770921151, 63286842, 649572421, 342109802, 677790049, 839286235, 411762911, 732728370, 874725433, 404540450, 334657812, 982352847, 597947922, 336347042, 244517921, 401108928, 604070846, 246533487, 576752480, 122791025, 159407012, 98018885, 149300758, 907576475, 582989493, 656486610, 729186244, 593416575, 66645207, 939899866, 694461893, 711375394, 764363426, 348523616, 423268482, 830658001, 39295969, 120548978, 374234511, 794449039, 351001313, 555062424, 28520307, 281935654, 488020862, 138889010, 193876725, 62662983, 379490308, 10947060, 663964153, 12199270, 272938260, 896325792, 918042111, 989752174, 308315644, 193830720, 611436517, 447015411, 217607258, 351124805, 289496740, 259742886, 991696562, 878104069, 911155562, 945159481, 101906088, 630001906, 84560183, 566159088, 470042817, 251625904, 362325543, 310900152, 14987631, 437814157, 15030670, 569630791, 327434574, 327550948, 26186724, 205152207, 777284131, 205007434, 294932224, 913112300, 878054253, 374228747, 253043513, 592849847, 49237040, 29306282, 433331498, 245280766, 183603567, 167252171, 567699306, 644539731, 357712723, 682672537, 798432371, 297886765, 623731830, 260225308, 431352164, 493101145, 718654901, 933886506, 191764377, 288517215, 843296759, 801745597, 790147029, 959206572, 642836159, 468362956, 372053143, 706561128, 655631550, 297371956, 354061014, 416854565, 309982049, 521087665, 345653392, 749903572, 407200424, 568669943, 849567112, 15192838, 725869046, 899758914, 793152637, 290837835, 892644475, 857762152, 453070873, 266558755, 696416538, 517386318, 50036308, 581667743, 704226191, 955470580, 374426073, 237211940, 420828485, 45175313, 125090090, 692258263, 592263696, 15200387, 27595697, 741910346, 603200540, 743988815, 729359887, 732489696, 615065305, 76817202, 651434099, 512910478, 600690492, 456588455, 627352611, 63581066, 704665403, 178897911, 144808632, 182585581, 827401883, 265170395, 347102582, 225262649, 711566667, 64342827, 172297813, 680689415, 653157974, 455027868, 225951198, 926260588, 488613261, 723122790, 413538635, 526292865, 605058272, 122444762, 499063910, 239576106, 855545608, 366999014, 52576115, 654862668, 516321679, 515768005, 946404237, 824035465, 996537835, 452167144, 316440751, 104837732, 180697653, 34266449, 918274089, 203712902, 764898797, 107257420, 427693199, 822768566, 94451989, 586892301, 433896931, 929634829, 422140343, 362538623, 465251389, 977241649, 757073661, 232342709, 302511918, 680290054, 181027720, 961740537, 557527184, 822812203, 41813544, 638055631, 870810303, 735037865, 418981743, 463511022, 320911808, 63706573, 257138435, 475416110, 809623404, 594260350, 857652934, 454694824, 858602992, 969595721, 326968804, 14988992, 432334801, 322679960, 314188775, 493701495, 1584241, 891621337, 872379884, 986673900, 429590064, 449708667, 884353210, 484647236, 767717927, 292287281, 937636319, 703385172, 333613842, 12038761, 72765034, 4629036, 212319376, 786654340, 671726618, 51605123, 13556407, 398401616, 775360784, 785762811, 133158091, 690696513, 674415586, 673707909, 497796836, 701725222, 94192824, 410125685, 786989383, 805904451, 412862013, 379374435, 63670185, 318658974, 347353204, 943204109, 913718582, 951528951, 838054244, 231290062, 952677930, 694177863, 618921755, 184658152, 25263442, 385997495, 142754720, 142552457, 274776214, 809241935, 282743041, 766959763, 481050180, 251570295, 705475545, 386722760, 230383380, 538197624, 919653811, 707976563, 231838108, 537326870, 458669111, 908015465, 263853802, 685861186, 202563917, 366309202, 586940679, 955502075, 179812569, 432980022, 79930227, 547834923, 538476664, 693116219, 643881604, 775827007, 120993376, 638437849, 42601814, 96508068, 517387810, 95291891, 941984470, 964569443, 25494283, 815959562, 787711518, 518893947, 479078916, 909037807, 323130480, 706037475, 573730142, 851003861, 660361587, 613700741, 566428083, 637235230, 479175999, 682993859, 684835656, 603223172, 316921672, 178842642, 242839228, 487153888, 685567124, 299490793, 145839658, 625221913, 204315802, 290304084, 307043469, 466356150, 215147396, 78745548, 618602723, 953110101, 562069561, 694890071, 340410824, 33636060, 854874903, 662873406, 823310730, 831822412, 321719658, 930704739, 282035251, 417560903, 569331577, 423011538, 709600013, 332351873, 391464047, 167737715, 629624495, 856206434, 826234210, 697305010, 152885062, 892427253, 29637942, 270421413, 34673425, 882372067, 804532432, 871781568, 742390034, 402880953, 289632223, 939524086, 617785294, 962688520, 960021553, 368271433, 283745154, 476425574, 462479116, 998042622, 398163969, 940256407, 82549069, 838396746, 371892746, 705420883, 268679931, 859521948, 388041221, 612300846, 595583727, 474357807, 863823299, 446828441, 183897515, 818364938, 315364050, 389213110, 434982132, 6343493, 340098552, 937729566, 675867049, 6824016, 496951707, 203628591, 839810773, 722757306, 264053774, 775718649, 555443808, 415528797, 434809260, 642234792, 692186694, 405341627, 873715142, 792290732, 495417002, 415539990, 286166750, 331191828, 608110787, 719200625, 918985067, 192485553, 965301213, 592154672, 36807349, 294124513, 552399006, 541290759, 105068730, 307884250, 589854908, 685494170, 805964384, 31875127, 169103033, 285111080, 201032005, 625515179, 48026210, 397029570, 817454832, 497217729, 752862461, 372519251, 26306954, 73147961, 316888808, 596915705, 483516859, 730906767, 861222836, 967216340, 868868788, 233422130, 833254589, 109244862, 127023207, 27757930, 303200182, 248407370, 655152703, 393733906, 691343563, 385494745, 819688892, 131913159, 142553484, 525075633, 994192992, 295379830, 124323748, 850685329, 353405161, 227421839, 191971420, 343431203, 617771573, 324501375, 981275176, 567797423, 143371399, 500238099, 846272276, 466980313, 817426716, 294469226, 103033984, 812725381, 506989377, 60851078, 55315776, 963023795, 990941898, 664863468, 441446069, 509293157, 10289983, 875757321, 750312219, 367943466, 29054920, 327609316, 633987446, 420126758, 781003698, 183600821, 227136872, 171356450, 780622788, 744747104, 946449902, 107669309, 832192553, 629929208, 458490493, 547108399, 302766754, 22066636, 146395869, 968152701, 621437442, 678991292, 715353943, 856000396, 676641361, 404219440, 303715791, 360141438, 383432141, 744456336, 881961773, 788571532, 782398489, 776643166, 472810939, 132010569, 726342873, 421677461, 84965271, 389408152, 304101699, 737683122, 634075591, 242558542, 969695879, 73878962, 447693755, 333134928, 208553345, 700106979, 101005444, 502839233, 968588110, 301214674, 86078302, 565025101, 946587577, 5004926, 242908143, 105430837, 607089096, 819096348, 438763921, 156791832, 843483562, 513102877, 736794236, 635164566, 545868062, 343711869, 962801428, 297202258, 505419493, 637859373, 206843930, 946452462, 595585659, 653011644, 37763284, 670080065, 969997130, 219168554, 204609473, 745717117, 566476591, 77148512, 473725466, 798642833, 136079116, 869909785, 230771057, 748288891, 364001209, 927460218, 996075513, 680430909, 42441610, 674549448, 397174874, 878110845, 884561876, 219080884, 75077426, 27011483, 24185976, 396510846, 879278485, 267557403, 280322417, 410844278, 870455215, 326409524, 849196762, 365413106, 732548957, 258006568, 846700589, 401415954, 51563804, 978610807, 218837934, 237197069, 879996354, 620870954, 927681663, 744796094, 236238048, 39893115, 461657565, 976900460, 881764632, 510309740, 813134240, 468295085, 958722941, 276304042, 377689911, 956863880, 802574705, 350264517, 576683798, 386489803, 276943744, 544178554, 535528091, 735387198, 47239867, 511748969, 613569565, 577026289, 440241817, 894369028, 442294696, 595541233, 759430860, 230658750, 33194482, 9018475, 772487398, 823225496, 739246458, 642639746, 72435085, 784029723, 486064082, 640736528, 446789989, 258899834, 443225817, 596626310, 498286619, 773364594, 947480794, 835197406, 760762719, 41907061, 883648337, 2542583, 37352935, 358409243, 560526881, 467454380, 349422184, 515182609, 934320882, 365701333, 965364535, 469163560, 245169175, 748857412, 560654164, 203960829, 265071699, 22830403, 58590920, 781669190, 630576597, 107482783, 328192249, 721949577, 379734539, 909579292, 813616762, 221416409, 410935964, 763116134, 985177126, 509703536, 712930735, 233085423, 32440014, 415317994, 149826509, 766898405, 862759587, 393820917, 704227059, 161637746, 718214728, 481726854, 392868702, 855117242, 881619325, 223740547, 746058325, 575605063, 961096072, 501003615, 80398909, 877348041, 695475912, 947140648, 884024653, 480080065, 194783250, 456051991, 717923226, 854891835, 766897337, 887829018, 91690281, 901618733, 772610970, 670226974, 273476133, 990547810, 32989547, 897210953, 816375976, 740141462, 590994377, 258446298, 372417164, 344795065, 95619953, 397449674, 862693153, 371263306, 101075464, 446398609, 609922743, 828611072, 903739689, 522297594, 664117649, 419154370, 869152036, 298633688, 423454105, 187810731, 489360810, 720057777, 985418768, 473673771, 328792264, 468341710, 704041164, 330948557, 843503911, 626829699, 490934662, 387876112, 276679881, 366734048, 219251492, 647061435, 374949591, 943556929, 334267900, 963936199, 687170980, 261784422, 233661289, 666768851, 176585140, 761365346, 458524679, 1365341, 734297995, 777269140, 651733478, 478798108, 661958776, 235362170, 544666175, 545582226, 493427706, 402572203, 432145273, 903239952, 368599370, 994970544, 292780901, 273694082, 535738376, 629672643, 16354924, 442927878, 660586277, 306333132, 278083948, 644878960, 12671259, 598479702, 128286889, 683015784, 799323341, 859419201, 824537103, 674267069, 142426544, 826355759, 538828025, 511996982, 449870741, 317944831, 701491269, 676518779, 611286957, 28936815, 693252686, 803537626, 496609635, 670755406, 796384361, 852646656, 232242238, 937349396, 922863817, 467340556, 788522757, 687101594, 250724379, 662754127, 235058585, 822939651, 104616424, 107510309, 411422977, 565136230, 99256726, 199188691, 30052947, 796830131, 83566260, 328079881, 926101276, 559702885, 220710684, 84758958, 309674098, 355334299, 419392991, 634666122, 298351196, 909715122, 914819256, 427994049, 216485586, 175580335, 655354939, 18832455, 197035464, 730239175, 590225844, 145510470, 91101044, 39686928, 750206318, 997530665, 460218503, 540388440, 170551234, 983737939, 166768684, 25217455, 865036914, 119299096, 358587936, 29316322, 530732155, 868810687, 636190044, 123130648, 617542815, 141428413, 202689068, 846457769, 727993996, 331508262, 931541016, 413185813, 97655363, 336663536, 983479606, 839805749, 707771189, 121230316, 311908997, 305864708, 938222845, 229752577, 135305188, 464492704, 15073015, 292879587, 939694803, 834590630, 304738012, 590950426, 385863837, 536614333, 27956055, 106317597, 971650056, 889159030, 529931743, 787429329, 738588281, 164048348, 7573131, 436568335, 148601717, 186435698, 493481895, 313944444, 244766093, 173139073, 367910876, 703458416, 940648505, 49913651, 126209058, 938895686, 667679312, 12244943, 76845108, 123681146, 619255043, 841233041, 149512881, 376379572, 572251037, 826790995, 31001256, 123592080, 664489978, 561385136, 511490921, 747179159, 421024757, 936529513, 302661071, 713855076, 505817587, 516775487, 306762097, 487810794, 957547345, 254874401, 540169914, 620181221, 468719021, 342685031, 710842591, 924082934, 247024472, 674739047, 565850079, 224034255, 240926021, 448742819, 754037457, 917595012, 324997604, 229117837, 890941048, 4350978, 756373034, 536419305, 742475145, 953564491, 29497969, 421245401, 883936821, 383205213, 255934756, 149198382, 639578068, 53664636, 224362434, 205459513, 486306838, 690199980, 816540211, 527601089, 257074627, 437685854, 422294399, 883824417, 32138806, 273758513, 240900622, 482952612, 153987760, 194758425, 888007203, 616723345, 23823002, 673662071, 848365761, 364849877, 886949380, 392374958, 267855989, 943547863, 980132320, 141884465, 644499295, 108367149, 769565987, 38386744, 212492274, 780629310, 363660892, 246365928, 327437464, 733902662, 721604832, 257077501, 53492345, 795277369, 195112337, 609235799, 585430106, 265034886, 857887409, 278229402, 839860985, 528911194, 685935169, 524581336, 399400347, 125056922, 301188130, 206486595, 558612778, 416797215, 907709853, 368632198, 246634392, 732529103, 764151385, 255550230, 1327742, 652571009, 785238148, 14062355, 503964208, 861458116, 205538384, 848011074, 65586906, 160377035, 668878835, 300986452, 767676277, 430524754, 993697215, 160207020, 625197433, 446712213, 666913992, 852688651, 930342836, 255680911, 171298495, 217001178, 207019747, 590485953, 405323270, 551520189, 67263403, 452344587, 567587838, 504739749, 414052004, 200274843, 862322109, 16387939, 416581666, 648845286, 954271441, 398642850, 597813831, 164584985, 399048495, 481442014, 976928302, 530777389, 112058457, 861629000, 377847883, 684686922, 710588957, 168014918, 547129386, 420498235, 895952178, 769617672, 45145289, 821303043, 905514307, 984459587, 680519531, 117797884, 915933931, 803663551, 695255132, 987791451, 915682437, 287984977, 477123814, 559834830, 610324883, 649740481, 404142999, 701690798, 230367935, 329901574, 707870110, 453667203, 361204604, 681205892, 979373283, 329013081, 412494647, 918411198, 620006712, 165119554, 135905365, 649996880, 434298598, 445293996, 129894730, 673283816, 11033069, 399438711, 240376587, 920059050, 670559398, 829320614, 475384761, 689497510, 757038308, 301415194, 159197404, 982401358, 955727018, 997545641, 922047100, 319154075, 975479615, 35083202, 845181396, 340982785, 938695471, 597524931, 944165141, 753539070, 345361932, 529808647, 135115662, 823371188, 321965178, 638261988, 909023726, 261360328, 372692914, 989690426, 738338716, 428603689, 52946489, 167024884, 883819276, 749101057, 865879762, 681036676, 590525400, 286081224, 643529930, 841154652, 576582473, 612880803, 984889221, 61281553, 847306991, 597648641, 496267532, 837438247, 592993499, 508398977, 637007695, 464810390, 805656527, 765722137, 498580299, 129392761, 103926056, 334696358, 800924047, 456366900, 185229520, 29074159, 36850698, 975078288, 903175906, 932774519, 755802543, 136900796, 463467897, 355103728, 507918752, 548729291, 199561754, 296024627, 154456203, 375868491, 725506318, 297169837, 381323083, 487310233, 54331073, 297611765, 373829094, 491966532, 741655139, 13338732, 248199871, 132146352, 447386148, 762036071, 557439512, 58980653, 721304850, 967131217, 897728621, 115577377, 260508187, 677557613, 647378340, 865060498, 579142413, 186915351, 467776712, 31547286, 501341172, 925122975, 250060417, 798741671, 614163312, 526451405, 777675638, 510679093, 461511331, 262360306, 73085046, 605239644, 513921574, 329245096, 937630979, 819064596, 783856835, 470069798, 764849993, 860546206, 263142865, 61428739, 6415401, 972775086, 580164460, 624296144, 705505999, 191565343, 184182062, 271339198, 784753373, 719863860, 210534795, 424038326, 764688390, 560023913, 88272533, 448736632, 123513730, 590925424, 80148205, 447412456, 70724481, 952981183, 631525384, 452064578, 677612798, 645170735, 547509443, 539758381, 187395827, 332891505, 275033815, 130320546, 958732610, 559227667, 850477899, 406932198, 469643375, 973347536, 483973136, 300878848, 642475117, 348037229, 42711220, 695864161, 652645462, 626473666, 447468890, 875241919, 759096086, 114821358, 271174409, 241566409, 453364579, 935056484, 476670049, 460459902, 639682433, 473452218, 661801978, 566581105, 626496125, 232322929, 615541556, 484644357, 535009066, 573856450, 907995003, 114265481, 221868820, 533693696, 164916559, 195713052, 572331702, 783958724, 126163428, 64963075, 91162342, 909240399, 473783717, 992499679, 423634830, 605310627, 70262991, 916599077, 573950512, 640517077, 29644207, 153245705, 981072101, 900472042, 844130686, 562028106, 639952337, 533486527, 805373863, 201372110, 174465573, 605942097, 184262291, 697915325, 419002204, 149236003, 898915383, 847176023, 395199352, 656869813, 707842680, 800671491, 537949516, 926062478, 232078956, 139060572, 924787823, 253109262, 20375925, 89815406, 100258326, 966716240, 943541002, 717744009, 787679220, 687647881, 493817776, 817448728, 257970540, 810866105, 141604906, 358306054, 776977509, 363130503, 513825762, 998760571, 998356719, 324368334, 580253382, 519580797, 570844020, 715684889, 315473019, 49072851, 508711666, 995876752, 408269070, 628748246, 59555216, 506776737, 461443393, 283353345, 608189248, 797503564, 836162910, 377928741, 457550295, 324968660, 410800720, 200313302, 901292750, 833250159, 436144304, 707758788, 267749459, 804483462, 52918975, 397335519, 796360897, 612225389, 767012807, 113321643, 620696030, 113820266, 178450313, 697155928, 613507776, 551871482, 737386087, 882441629, 958565563, 952863862, 140073618, 958231393, 589424726, 185135144, 417710062, 797313955, 186078950, 570707058, 514513684, 37352809, 282544221, 382384210, 798410320, 140720687, 405660084, 493941546, 601085531, 198018405, 62340345, 94101442, 45399524, 870494516, 865955322, 723554973, 171498166, 883964931, 764539842, 608222461, 71640960, 446493794, 133211198, 108411161, 293645761, 429474864, 939516301, 791817781, 308459625, 447485394, 950758601, 999531631, 940578496, 219411620, 341116937, 641962079, 750827771, 775299748, 303180650, 906868409, 204207846, 97042683, 65661802, 388535964, 412591276, 416859497, 216786621, 479909856, 861633571, 728974077, 869461065, 773789902, 566293437, 614149181, 343123668, 35163812, 72826970, 552486119, 665433736, 564795395, 640465676, 586777476, 694156637, 594202116, 259555719, 90627804, 593802781, 270625542, 99366167, 203058221, 52590351, 391564726, 603563747, 447412760, 945863113, 376856144, 653854652, 346141118, 502895080, 224688055, 134942855, 169144956, 232271940, 592365279, 405505080, 86909757, 945925330, 218377727, 590708721, 490058061, 28189435, 701505430, 581394443, 908073195, 406705884, 725264687, 621885455, 512485571, 912057647, 288940309, 169796418, 716211630, 398938393, 915802552, 371715301, 843655439, 852821406, 7379719, 132189037, 998829660, 188939417, 356778987, 92198633, 670558547, 667680433, 270284608, 904862789, 78357598, 906618243, 511349689, 780176215, 18125042, 162405450, 817056828, 591116868, 346633153, 380552864, 614032186, 332863159, 833252284, 465921229, 251682389, 843091265, 9169544, 109048041, 172282158, 161379540, 721234131, 66794052, 732461106, 506306742, 256553515, 340285247, 935824576, 75659822, 380330783, 793039476, 237625382, 803170181, 35274381, 830596382, 464853621, 487545536, 821744498, 652607434, 496588420, 687384982, 699399627, 70594307, 251442115, 298057422, 477394417, 164837461, 250611419, 998189708, 706811300, 955065647, 890764476, 731020470, 963233464, 445448825, 459309330, 980369460, 492199603, 889138818, 246981363, 333995270, 458999039, 983410294, 482757429, 717539177, 616332726, 46553293, 674745752, 48600257, 367098880, 806247562, 625295688, 699601276, 50885775, 911509850, 538844814, 827766470, 142558354, 5120653, 619099823, 779262941, 950287566, 492216660, 487259474, 389102550, 788575361, 595643031, 223979653, 946678423, 462033493, 986592525, 593352550, 662079648, 615254985, 381075875, 285781416, 920774892, 123990354, 7642886, 880728427, 250121837, 147806435, 667728587, 48494157, 466875106, 589384633, 438678092, 749761802, 805692707, 863896663, 64304501, 438729963, 742751265, 872610969, 606778014, 932351231, 432870767, 589587147, 77846731, 160503820, 314904606, 219392231, 403738644, 189509473, 76493455, 640786605, 935435032, 78069564, 332678494, 472895927, 54436614, 984385838, 788047696, 982969656, 924631685, 729030317, 608148300, 931771973, 553909071, 614387377, 936876741, 795653029, 973982396, 736223525, 693683324, 534640149, 35253693, 222806424, 216770662, 884041549, 302578549, 689384229, 134050994, 100464724, 537050312, 765114859, 345414955, 631022153, 854630404, 408594653, 294442033, 406716511, 844625072, 44315075, 459833534, 390923804, 125730126, 101195539, 597508169, 717533794, 915994667, 52077401, 21090568, 672883128, 409153209, 196002440, 80658097, 961074704, 736183168, 808520994, 826200405, 47057328, 92774242, 95886216, 623442280, 739367536, 191026639, 692278691, 537637247, 537247363, 981697533, 371311332, 248448171, 561838845, 516644909, 881082062, 440694382, 81000096, 943933394, 687880704, 676037296, 375911857, 817552907, 258373260, 881226399, 464643851, 978774698, 49444695, 350268855, 563448863, 362438092, 970626506, 554353997, 734565833, 542032398, 175582544, 298270202, 287609736, 660670233, 683791071, 396109163, 876888663, 991111263, 631367508, 364094331, 876097191, 369437440, 228842873, 488450074, 911360650, 992454449, 967717535, 951932712, 662479410, 96641967, 143659822, 507125269, 977777499, 708992967, 972482057, 566844102, 336043380, 813060644, 349385059, 917443587, 223220003, 566932995, 169319676, 172216017, 571450955, 865740288, 185167813, 306818048, 898252501, 153978412, 158786163, 938485904, 272370562, 903836928, 313041514, 587712317, 478452473, 506728329, 607674144, 647405864, 167393292, 476475855, 165745887, 589742891, 824693663, 863753186, 79914725, 334083057, 63341280, 767751288, 51460653, 925134194, 224301059, 319231096, 347423331, 320389221, 483633482, 136883141, 100752258, 73926087, 842199766, 646217872, 747107281, 571791896, 28444942, 251855323, 352105490, 982552975, 111452523, 151178798, 436225946, 801416953, 684891089, 805172230, 917849135, 607329545, 966992665, 97948961, 344191586, 921651440, 447042916, 503036538, 832947322, 132347388, 226763543, 904685120, 748923658, 239475811, 592388209, 792215450, 879598668, 956609297, 871618627, 184872916, 131475466, 797240238, 426871754, 238242657, 184352166, 434067197, 76810734, 664414810, 602888680, 119839802, 526524765, 833539607, 432473712, 79331156, 751993769, 527845274, 908787850, 691768898, 890998586, 105334182, 957542713, 434382156, 569518909, 948563423, 894355818, 523866029, 115221272, 6744199, 352434384, 617774096, 64083445, 466018876, 678396955, 938004562, 777455809, 54355508, 500347762, 802014403, 120821223, 509460888, 722171649, 435134284, 683525175, 459229050, 868414680, 974772475, 799829253, 995976281, 716897108, 492744407, 486069460, 541357860, 195679307, 370205034, 77676430, 549400064, 151022726, 286233203, 68063311, 909107695, 901384974, 679478588, 219545058, 884622513, 396038513, 393446745, 368426319, 471250956, 905938934, 639822755, 851206842, 680813257, 548987471, 132314410, 72587405, 541149292, 705589059, 697154968, 869086704, 550143162, 520311187, 665526413, 570679823, 923509313, 4912212, 832046583, 947611115, 214702149, 98522999, 162175966, 96868044, 566904955, 895067889, 988383296, 957742934, 961954191, 727237571, 538969495, 976771514, 246432704, 989756732, 361994716, 30679845, 670285846, 483122395, 549244483, 121121426, 547805193, 12545488, 396479234, 814713828, 639008946, 210712956, 269924870, 89316836, 165144976, 330994680, 446115671, 148685934, 635241726, 370279875, 579214642, 782524018, 420115210, 396977481, 37863909, 438672305, 591486826, 586415211, 920169895, 674715168, 965518556, 865850491, 728515089, 983732207, 381162951, 912712524, 17643208, 109540704, 910225970, 97847418, 587051007, 676220237, 18904025, 959038019, 913811522, 148011983, 89793829, 686367744, 373329377, 203461540, 861869669, 496104214, 875124123, 313770236, 863982276, 687209589, 142226371, 883075725, 665245862, 214495766, 568541616, 945487020, 365530074, 570640409, 362257350, 651184978, 531458757, 761605439, 160455445, 635550563, 693820374, 43361353, 398132337, 971047098, 713392220, 606761403, 209891738, 39743260, 702507466, 20043366, 838735703, 55762404, 769294647, 812132291, 975560770, 242842641, 900416151, 71018767, 782696746, 99691068, 185258526, 222673914, 868562818, 169319514, 536478360, 287421184, 341941677, 169286393, 409051003, 839842461, 869218082, 633764226, 114540651, 949228402, 530142310, 281447409, 740027257, 517096274, 898318011, 63685075, 378744503, 610545107, 304231458, 644847196, 511516533, 682959351, 149315847, 266814040, 319263452, 267776019, 848238787, 750926765, 840045327, 862325117, 348733864, 298138703, 284103598, 598492580, 156001880, 70279098, 474460193, 55455136, 869473966, 756409230, 758012695, 298015263, 525530124, 386557302, 211952772, 335553538, 957935662, 244349152, 354739297, 720795168, 485356310, 123375568, 127688490, 524548650, 233259706, 673615856, 905091702, 872192099, 565369869, 678722703, 998707985, 214658472, 14750930, 551578757, 954889053, 51954916, 193284787, 168201586, 728476660, 929438341, 351726612, 315727004, 861429475, 536919812, 343507402, 340090007, 957939125, 896896141, 108832853, 969619126, 854127712, 908048109, 226093267, 481683719, 862001740, 83009830, 719129431, 947949324, 682702677, 765969829, 920320169, 430992852, 944702337, 21696046, 595218194, 71718902, 456900254, 401937727, 940533337, 494203404, 420795947, 936000370, 793390778, 898448496, 886943470, 723450332, 167326337, 671009820, 905745253, 79751207, 44135507, 471347988, 76469739, 852248037, 23228115, 855406855, 77040443, 490388316, 718114335, 158903506, 46272561, 696770576, 233752836, 236411556, 840163347, 655377204, 430704745, 690839716, 457192987, 311567722, 643311361, 710309085, 719450806, 692934508, 675093608, 602377699, 560004843, 887192737, 22411572, 700243769, 778601769, 475398829, 416714946, 333179498, 377534651, 722464325, 572207172, 774386588, 605749620, 126491177, 722624992, 792360758, 80682917, 702867878, 690550568, 690575300, 727975933, 517876721, 673831410, 103814711, 280342868, 430219673, 870955233, 922615792, 495412461, 273205147, 303205068, 217276601, 155926139, 650525550, 607250188, 153066784, 754460842, 123776351, 324631794, 201912444, 902626410, 200004682, 196197395, 991865543, 851427095, 853377876, 76141036, 745644546, 141393876, 705712792, 842861082, 625257810, 772385545, 894792161, 252360651, 219017589, 277016199, 302023929, 623389210, 253319888, 608772325, 244520059, 331285887, 24354541, 709469850, 69520653, 114155173, 145349975, 651754933, 414033701, 760143896, 357131644, 885091615, 692610222, 754394433, 602591700, 120210569, 480536385, 872061791, 693478065, 347202054, 507368878, 850778921, 811337843, 260106746, 371979786, 8929237, 905410654, 938041333, 960282568, 487617716, 997254909, 865594720, 73572436, 696694378, 193410759, 852642201, 613898265, 142698161, 407904688, 432888090, 418918189, 614915278, 49054610, 571490650, 790831059, 23777042, 828384584, 336056479, 261645030, 378464012, 219823651, 558456330, 139998861, 261295658, 242664484, 996227168, 29251656, 141410053, 250377572, 803100611, 92012, 430968598, 442929607, 105511481, 292521351, 156235931, 747991148, 810091891, 477555189, 500494900, 237715401, 106614576, 52224509, 240033921, 316130890, 166783020, 530933598, 504461133, 627444297, 341890771, 493617553, 164265460, 892682518, 285126970, 874065798, 74491465, 216537320, 46381117, 190774584, 730597372, 81085129, 824801693, 4264951, 314183570, 493730080, 609463874, 262977862, 552598301, 169742682, 2717924, 523912583, 489606623, 48086801, 97752479, 205989894, 777970808, 883350775, 589463072, 356072888, 237721004, 620799002, 910633983, 438918286, 616077332, 432510106, 755711076, 840235599, 131107530, 175183969, 913891278, 606759694, 296531310, 799391173, 439648937, 469221439, 375101853, 729058273, 835224804, 703889654, 985151777, 961183997, 967729004, 25460789, 769207088, 773819302, 334545345, 34959312, 644985576, 466276560, 36864997, 805694317, 478388474, 634923222, 127178231, 551939651, 592766391, 967506463, 201609935, 475015688, 56367885, 537253900, 707778631, 300635082, 71339940, 751600620, 325887850, 475631430, 306752845, 732378524, 277186924, 676604047, 306397938, 882411484, 7467471, 762004370, 934014113, 342600712, 398796987, 467505420, 562673092, 322440937, 115173532, 397510632, 880904923, 260859141, 798193717, 506262731, 203215006, 302682278, 513286514, 702090227, 960404344, 689154089, 549080107, 123121095, 66886473, 531905326, 118024980, 2530105, 847815736, 958177182, 194873862, 803381291, 75976161, 53148937, 359540342, 51816049, 823380223, 680926877, 450335756, 486075014, 505281008, 22328596, 268572783, 763937705, 31285725, 1490149, 193186070, 548215060, 904011013, 226966158, 15883576, 20449347, 380003454, 124948509, 851676191, 202152941, 230750250, 325540143, 876610807, 793297544, 210910282, 113591317, 675455634, 973910660, 343457815, 123802311, 208383568, 659759003, 957791868, 81115208, 83357213, 872503697, 458340231, 247136352, 264154363, 702945225, 612682958, 636787450, 571342288, 71868090, 511751863, 749668031, 189480048, 896177882, 69178461, 687856429, 688005027, 300743505, 146813275, 477909257, 902093771, 119359819, 177535230, 938285764, 334990553, 482431990, 333785572, 366405620, 308207640, 181625642, 188278251, 1120001, 764630472, 561960298, 495954878, 802895099, 778447631, 948605242, 672191870, 249794636, 459235334, 608424875, 18856435, 816614426, 754836096, 321580704, 762034905, 220697054, 499501758, 689796596, 856012205, 84585822, 31154571, 858449527, 335102074, 287243405, 972515664, 160496370, 487348865, 862413755, 565012391, 379906906, 681231134, 486597044, 225038285, 992991410, 251512361, 557519713, 802457639, 999649295, 303729162, 228166252, 252031495, 934957882, 370582676, 575190019, 922739612, 480672950, 90177929, 502430701, 754680920, 176478999, 107303491, 695587054, 754050276, 441217963, 656906828, 703268637, 176417343, 446376324, 840483470, 528163210, 560713899, 12872649, 583295124, 310247923, 385193287, 723396763, 364211143, 236379543, 476926827, 479110903, 390236327, 354347068, 680329802, 131435850, 899084927, 49142712, 235375070, 414619974, 814202848, 262038252, 182497609, 621656340, 107838354, 207989677, 611184534, 136332834, 357256751, 678214351, 243755527, 694268024, 445207774, 641331052, 19400354, 301687116, 405520482, 854370923, 490079338, 199438685, 698924799, 361927749, 551884346, 542364845, 430584064, 73885538, 931301869, 796893733, 277083243, 299548105, 539576943, 756739912, 589122630, 153394732, 850874263, 49440874, 139295255, 895911239, 848993590, 253215267, 352119307, 458565631, 500622962, 665816443, 40493780, 924774054, 173275480, 576341301, 640972481, 619584790, 217837207, 203572536, 462705768, 817710546, 11222125, 833703791, 224118611, 894602733, 844246186, 242786851, 1626716, 337444821, 572449080, 907079174, 717099848, 12872406, 700155314, 853790999, 865319040, 14991083, 534951518, 226785982, 170023525, 733952829, 216248691, 295065498, 318834367, 982069084, 487305924, 665621841, 563012424, 843918839, 290569547, 412725567, 566748231, 885420703, 194237836, 607262707, 825779317, 495416864, 753284858, 899707563, 673363538, 947333975, 796603952, 277322975, 890561749, 316514452, 367215622, 76275368, 967089384, 677323852, 409177393, 566428052, 355326702, 737727008, 495855625, 766195686, 591975746, 166650278, 964624876, 479743051, 292691259, 199085408, 459115576, 431247567, 835225942, 398057778, 57764488, 780606895, 676680772, 651343600, 498065609, 415766402, 676568606, 473429865, 949108920, 346661088, 797251586, 724409481, 921633268, 150607069, 786038434, 921325784, 866019834, 555591873, 82722367, 175508451, 162063692, 235955513, 966586059, 552570288, 566268647, 133973616, 39296087, 632149152, 743910111, 491034962, 625168313, 522775644, 634468589, 698563565, 598973149, 329683564, 766841271, 703372805, 584353424, 311709842, 622816196, 435562461, 472587272, 208596878, 545711741, 189553679, 348667437, 37848836, 80982679, 157771245, 683995160, 515474203, 20395949, 160026638, 201831632, 12092947, 338727075, 621943181, 818835146, 634923552, 579349428, 769202923, 291288997, 649375760, 344238786, 518246554, 549849341, 196134627, 703996673, 128749066, 576438999, 923373021, 131735927, 423690859, 404778736, 488340349, 563419568, 360665187, 143544584, 821226407, 857155784, 688130769, 356670908, 583430317, 933083858, 253716341, 878497189, 341439357, 275767077, 453487174, 264945563, 656200217, 448335079, 719359259, 295787903, 602088793, 186588769, 967403504, 689102406, 37857585, 96818128, 446289709, 869604933, 121273503, 234559218, 263247276, 159402397, 765407457, 533557146, 879799386, 731990380, 89076708, 261975271, 704433446, 72675785, 990723421, 531485340, 968672883, 161386409, 518837508, 96900738, 822563796, 719697634, 831892115, 685193391, 762088336, 314795525, 588570591, 54547269, 326898331, 209515675, 537361501, 768542759, 2704924, 353474983, 178067655, 659994441, 645943601, 75493661, 19757886, 54004552, 771076364, 747034842, 32152706, 994687684, 860790309, 989995866, 643003328, 38917322, 500591536, 159139808, 835673109, 583146859, 82830911, 969237702, 346722052, 795972089, 405762595, 64555013, 147232281, 186284975, 340087277, 258461662, 28340001, 145133800, 931973547, 977195422, 23307560, 748831944, 835828643, 105465266, 537316570, 894541240, 488472448, 737468322, 93677690, 531509403, 992979434, 955206809, 251848145, 535520842, 374726935, 839328306, 308362059, 755571984, 525891006, 45186530, 691137656, 239260643, 826143281, 3924534, 339948134, 2393386, 376999174, 755164266, 17805246, 370503312, 738576104, 828399565, 37747151, 331118012, 383960632, 890037686, 234334122, 150743545, 541574422, 922476348, 980138490, 349402957, 263458211, 279693650, 755435040, 190558603, 418132508, 537504248, 144729177, 257038397, 63633228, 209961314, 698221260, 430404905, 285123583, 283247740, 584047566, 106525573, 80268842, 809426095, 27285556, 641904454, 33092207, 221902235, 489767643, 652219124, 812581543, 468805520, 260634403, 702302943, 323164098, 637775531, 329869128, 974539466, 378310722, 38038584, 148147175, 74163375, 53138113, 976409102, 256793272, 372451042, 185849953, 87886840, 462708284, 454349840, 755634114, 211069115, 759714956, 607269525, 790889615, 121622359, 142729995, 321696264, 365404344, 718019825, 380391820, 858827796, 394484442, 613536961, 20963351, 666425786, 642419765, 360168124, 935507649, 852978796, 810032696, 495820120, 865268181, 144148395, 718055139, 316905052, 295707808, 720513159, 451974842, 640986466, 116606312, 455772103, 175216647, 746986152, 220381381, 807199723, 249624091, 55425477, 33961874, 801665859, 319755998, 839492201, 596883187, 152551908, 713807824, 650475079, 545379673, 688469607, 257173467, 731427071, 770996635, 977306881, 400362045, 45091872, 467742437, 549099436, 424165873, 688796598, 816722397, 245737575, 497824853, 209985835, 291790575, 110785224, 855942913, 682613937, 925806986, 154585802, 874890541, 513869099, 115113927, 191049290, 331046489, 436709962, 520586521, 262599836, 812398202, 326919529, 646884061, 70056291, 105526753, 142972695, 41266850, 436870496, 449334247, 351602553, 157767359, 646967564, 5847910, 91022098, 291702335, 864884740, 147364380, 306041485, 430528514, 397392421, 787305883, 785457961, 400018428, 142318447, 27267128, 424049315, 286687863, 186559212, 251405344, 191162445, 694171325, 897305968, 157468355, 891272261, 109117703, 497034604, 407375759, 55211198, 257306500, 161683695, 591017300, 111973328, 482039376, 440449701, 380248121, 24366404, 757836088, 30910964, 905847343, 62988958, 565659007, 607931516, 435533247, 253777236, 249524255, 155785714, 944839240, 788972092, 525256327, 390837119, 324737593, 420003876, 483708665, 198201857, 216384065, 582581688, 758866424, 95912084, 28521379, 134313930, 414898912, 50766360, 600958917, 632338924, 958645060, 501049669, 977034596, 43690804, 923354576, 162291433, 918883344, 540157210, 81303463, 860572571, 524780466, 457263485, 862777508, 264412304, 601474420, 786417436, 218546496, 707340844, 955649750, 158423727, 780757978, 138787304, 904514775, 319847020, 879599473, 26349047, 253296952, 941332016, 267616305, 945582051, 921822422, 579802344, 158619125, 403561693, 629403755, 490875031, 677722343, 885531344, 303664799, 173147892, 438699578, 463391765, 924448359, 706404864, 890551474, 630939371, 344450522, 843976557, 396579427, 805243468, 54922797, 666903987, 776786585, 649592321, 94063542, 567100627, 428669819, 820724270, 976078849, 333598183, 740272345, 9472894, 519708345, 432143133, 798309401, 986123297, 600581039, 300753822, 656331863, 897025561, 505910358, 916136263, 593551690, 635551729, 27142402, 34915468, 590600740, 402802610, 807837063, 715601358, 193469435, 212214600, 941352562, 384664210, 681320750, 713121618, 530388947, 365940642, 997589877, 156056812, 336487584, 736332050, 813947456, 874367389, 110458863, 365194718, 45806893, 650006198, 468944422, 466913215, 749314184, 671356418, 799895305, 225592363, 440294891, 33335743, 851193943, 963633821, 757399992, 845109834, 545099422, 946902805, 406294836, 650242597, 14637192, 196251920, 550757873, 96495476, 237624208, 775455047, 622591480, 906271747, 214718068, 185591323, 94952195, 581819315, 694980611, 745120141, 915499347, 748278701, 633511920, 144488003, 666609223, 600749702, 31098737, 508741918, 972145225, 157753564, 237626202, 635239306, 231600519, 242112745, 372375813, 761969309, 16958408, 300319490, 276776283, 47139665, 378025765, 846801746, 819358591, 718742601, 478949542, 903948506, 575802445, 832652970, 16477097, 193795462, 589414169, 675268046, 811370312, 937576852, 917417449, 185074641, 826683548, 655956446, 324087399, 333761806, 37884453, 159569628, 413902223, 263011329, 613749098, 640516753, 811502529, 997014111, 558709667, 593312586, 652999579, 713042049, 640530678, 795907205, 58296997, 5779918, 531357883, 632621011, 438418554, 247007671, 706823417, 546197661, 585925234, 830034271, 142834711, 354014519, 308803712, 948147678, 101032523, 511626172, 724880770, 122823219, 869204075, 205698691, 859277975, 649904171, 651812879, 781676952, 291704388, 48256992, 980883852, 44580292, 647485547, 830005400, 993446947, 294489882, 986809708, 599365087, 643842297, 657333976, 357253791, 398267546, 452289351, 380254489, 419375400, 526999252, 905238136, 133785845, 155646545, 997917643, 155644299, 158874631, 159099258, 549501240, 75501958, 258487471, 635259232, 808783947, 112544057, 955583089, 331371423, 852408065, 68909064, 922943663, 304547540, 491141468, 451777060, 792556049, 117199630, 874123773, 284201004, 156234167, 246149039, 904614522, 151025834, 998093899, 150984435, 990082075, 788356074, 754459656, 656211190, 793536570, 760570746, 246782063, 366982251, 996956613, 468781991, 823529875, 68012383, 220705378, 551937214, 853094121, 700836205, 460071446, 814823631, 816356231, 496760944, 42682993, 241948488, 960710145, 992404263, 655042903, 188388506, 308781463, 476925542, 673692857, 265918320, 540517399, 845233919, 968740565, 171372741, 12955042, 221012981, 328593338, 978274785, 108618597, 983679546, 356543336, 499924856, 454713166, 131231082, 619896204, 979837961, 584371580, 838251137, 150514397, 880464395, 289618124, 122707954, 970783817, 337376341, 308586439, 464986650, 841448967, 270034850, 776211940, 84998276, 487118423, 362891082, 962214481, 19374523, 587980757, 34907071, 588406678, 831272940, 797310771, 861445469, 762867708, 434276559, 736236304, 239846299, 303009375, 238925540, 358961644, 252956070, 228485456, 706342921, 783596295, 159369318, 105387654, 895811481, 912338592, 689524399, 541158479, 68148043, 632375786, 63202909, 359524886, 64687992, 853407528, 337592393, 528907896, 844131799, 95937968, 412398462, 37527326, 22269183, 619083463, 542327708, 831127949, 809320379, 538117152, 988994249, 737471173, 771226652, 443448517, 841960765, 24661685, 931066885, 97778247, 938398770, 156336162, 696298116, 929058088, 576528718, 277072177, 574614962, 112969307, 326512342, 767985658, 116845106, 561684704, 639430226, 283979809, 379398947, 450599552, 448309973, 172865646, 180293354, 148408857, 647193833, 857925443, 66574543, 624269443, 191155214, 157487477, 750640198, 641023377, 156785898, 572435761, 837555642, 417789155, 627286204, 690197031, 614013242, 207228906, 5081552, 309356296, 86025595, 66571346, 801415372, 439452798, 708416621, 484172828, 57543287, 253731464, 40421986, 23729660, 643862447, 427506060, 735589600, 578611003, 554435762, 453020574, 866465878, 315170626, 677340828, 338024326, 715899750, 58091038, 642640449, 904065578, 624719806, 210041724, 370649884, 6176694, 800034973, 856528159, 123271985, 671525573, 559350615, 246934346, 719086201, 795715840, 930590041, 265065060, 398571241, 717083029, 548786614, 351257173, 302901296, 998962598, 233355336, 191758626, 500372507, 610924613, 389657505, 790115508, 678043751, 608356033, 367549996, 578616980, 212651769, 802783955, 352423374, 60999796, 22265752, 176833355, 272523510, 344381619, 78433501, 476145830, 489656547, 970156113, 999750092, 40976203, 776772833, 538031929, 549610938, 196520051, 96094493, 345605987, 546187814, 216833120, 876771838, 824816573, 649995435, 286489382, 321151153, 542908898, 720660057, 658521399, 447726412, 160680599, 334522954, 948237605, 813270377, 761775470, 595151090, 405710481, 93567640, 212305786, 724107659, 61415952, 651631718, 545751084, 630468928, 590234002, 286583157, 439917074, 708266855, 924515083, 502337206, 72182768, 29098221, 995416609, 286225671, 200169268, 470071249, 635196129, 884577351, 950165666, 726454174, 452554720, 657613276, 873497506, 355499768, 398466391, 447472229, 919579030, 330067693, 156724060, 186011527, 247096979, 416628426, 276948638, 727949776, 482901337, 523719507, 937403003, 188743803, 31102352, 39673364, 936647089, 592221138, 437295761, 352380082, 145500255, 598835630, 102232431, 428690733, 133201008, 706917251, 955064605, 445683542, 847821811, 13235533, 585252510, 712418892, 271086424, 844189815, 314497363, 337696241, 386646620, 977617902, 149102659, 746620491, 350033754, 751906858, 859696001, 614031666, 591916642, 766155826, 603708469, 878475170, 12615255, 767415468, 546397593, 444423393, 196565011, 952199677, 218653466, 261017912, 487837282, 586853024, 72955245, 191710681, 945993210, 458847286, 871144849, 63914246, 552249496, 614876070, 739826919, 995810018, 841067875, 203427763, 700977803, 785910286, 130114550, 904765032, 319649434, 191209334, 141868339, 265335796, 908678341, 44895986, 594201139, 618834845, 57243166, 447023205, 874633019, 666359197, 407908348, 319405581, 640356619, 973905641, 601993077, 604020905, 506466170, 850956425, 15638830, 166955425, 561791267, 686346554, 115903823, 113519442, 131959057, 998330503, 288942613, 540488479, 995492474, 24933017, 819238368, 542926850, 278070078, 18012023, 734826254, 305179231, 636667406, 549617006, 465736366, 211009901, 760574807, 496184509, 267791089, 724280725, 955002545, 279342650, 204909994, 924593450, 242610646, 398865073, 104097922, 152429363, 591936579, 70159688, 696882281, 565161438, 668213993, 262052060, 65162662, 824074537, 371807585, 205439089, 454405832, 652119639, 742893994, 568191062, 783780366, 651636053, 972684608, 130785150, 518796688, 864996374, 810546823, 251459691, 281815316, 556752589, 452680129, 329805361, 560188041, 948729184, 814768698, 335519719, 54320054, 906876265, 997068773, 300667398, 282124805, 466014012, 262003898, 105531224, 578451497, 161444026, 818552487, 569446272, 344381419, 963256698, 505947870, 263694571, 959422082, 413241059, 207216939, 892025765, 929735911, 882205191, 780114641, 128697851, 559131550, 619636493, 368263992, 510119515, 934041601, 12537274, 259309639, 458844880, 575782848, 809648547, 5659203, 362113060, 185316928, 326190738, 760588816, 592625557, 348453953, 710827666, 6364237, 564715624, 373729768, 135923549, 288370763, 194726191, 924679955, 389628147, 690749079, 107248236, 381277988, 13501494, 803167399, 283864282, 128391205, 678096064, 628778993, 401147445, 853061843, 938733155, 376047194, 427554187, 562769918, 531692029, 671773361, 537788959, 410369089, 700516512, 817876876, 886293788, 254659725, 715459908, 279371174, 156237833, 903523154, 61280409, 545770024, 702572026, 167674327, 497876364, 598193429, 411293663, 403393801, 856029844, 997983171, 720398842, 280107103, 948014520, 376669076, 817032944, 223137201, 164733036, 850968841, 124552965, 116162950, 615170706, 908498760, 640711656, 96590479, 753255084, 169950830, 236235204, 501972611, 814946220, 158735517, 497504936, 183151501, 327233513, 132305429, 917442090, 136542475, 399703145, 736350544, 116325304, 585469091, 416333078, 948692662, 545222976, 884947002, 762925102, 968375974, 593349218, 343230522, 72541035, 25622333, 984265093, 711829917, 590802186, 696573831, 377950466, 441429880, 190181372, 300642809, 401174542, 13682513, 864753240, 41730274, 654970054, 646606233, 612359979, 408885030, 529793546, 817149085, 327861534, 70436246, 882770297, 546795207, 902217238, 280235664, 333829531, 979363251, 120926588, 627926261, 690886778, 777141234, 231247195, 868822225, 67241343, 278372592, 607858675, 160797347, 898024399, 245467183, 746763899, 41483768, 780629919, 925213233, 432760142, 998787104, 927980079, 353325402, 170844807, 127315951, 718660702, 898962647, 454313126, 891690896, 693832531, 103644824, 135015818, 69968330, 637613636, 269185139, 981652041, 594787261, 550268543, 853595549, 25608167, 410869870, 206988831, 702393255, 141481409, 819718926, 696216512, 398047961, 29128563, 216680397, 859924445, 833767440, 980582758, 793198904, 454345072, 185322622, 264945057, 943702960, 3428281, 75771316, 324518343, 824673998, 820124127, 874666249, 786552001, 798106541, 456904586, 52241516, 164280712, 834502254, 397598486, 522035539, 476976795, 874257195, 92674321, 705030142, 5139879, 324765015, 528848726, 697520162, 401171623, 975321740, 274174906, 486145853, 439917751, 281054235, 300416623, 959862287, 898484516, 572947358, 102947879, 105184660, 557067564, 173018541, 516361737, 171972566, 793853857, 281377037, 927836500, 735073784, 755543807, 500945139, 575391144, 360300261, 157837226, 680880279, 630384423, 580773216, 281793424, 755954266, 740575201, 924125544, 947495390, 582396865, 119919317, 597984681, 989564249, 244955979, 33834478, 829483558, 566475435, 173006646, 465682659, 526883062, 33230870, 911861585, 886787122, 359362855, 810163567, 219292679, 910460268, 922477065, 200061409, 324318509, 292677602, 40409568, 964410137, 412792573, 869907446, 160425500, 114062228, 406156927, 173489601, 604756042, 241603759, 687689863, 135015530, 626402002, 59814971, 664173393, 891037799, 611483413, 216661426, 9593361, 177856247, 211903819, 861936957, 143419204, 594108706, 548742799, 247156831, 347718747, 324323347, 631674453, 646384067, 834891733, 87051233, 339815246, 100443300, 850390664, 5675643, 128147563, 719976785, 350269465, 74410097, 206575141, 32786053, 651338274, 545730925, 653381868, 165453830, 304948106, 485957523, 588335650, 294677046, 318017537, 517677248, 707967166, 404657146, 872719093, 541052357, 563936387, 438251297, 776841137, 204978386, 802107491, 408335242, 832314806, 237755133, 353557070, 751816315, 829958599, 612444995, 37406965, 636922026, 532548682, 543669396, 633929606, 741219339, 678299600, 156436834, 231755252, 432766802, 763956104, 21405365, 727878454, 884328990, 168187109, 609172858, 306431718, 88392317, 265741404, 334870911, 678318728, 362741200, 56519518, 863252453, 983860376, 465239187, 261646502, 65602235, 484583502, 400178629, 946479624, 954123456, 617921721, 909335952, 729747162, 179827756, 601219364, 149668612, 244390766, 920004411, 93998213, 115349062, 568523639, 589643334, 160298099, 412365247, 687940535, 511075809, 454831845, 15833111, 553619073, 567386919, 986268015, 494237450, 615339071, 403808253, 564784445, 968845658, 581694536, 41934964, 608075212, 932539464, 825011275, 426904252, 550655011, 628663520, 587448286, 13155263, 694299757, 998139450, 402770935, 601017253, 473859303, 450810423, 692061422, 371354415, 707700007, 696067335, 988596117, 994896374, 156686987, 90175576, 710936140, 277339305, 587933534, 778303533, 811643741, 675086127, 478838290, 40176237, 794915475, 95817686, 348146223, 701066500, 130241518, 567456621, 3883997, 653440175, 239691094, 162399616, 34388533, 285476333, 568548574, 356100042, 900107167, 647098215, 398997170, 815002863, 749035479, 395803339, 118003746, 526313541, 498523326, 888731431, 739347198, 776781589, 249679789, 245660446, 760496796, 132697318, 951836075, 177833157, 183510763, 141813975, 416613228, 176609149, 446365456, 959197643, 117140485, 204243776, 964118750, 421038929, 727604614, 753462634, 992512051, 338767147, 874918365, 94241566, 322400444, 34049754, 750633923, 525104654, 330956926, 153643449, 701916774, 1974943, 828804104, 477902811, 260347886, 138230605, 212662097, 524106908, 716296005, 828932965, 564117401, 311623521, 570111357, 48325583, 565309957, 151119535, 242009148, 832076721, 93700992, 65448813, 714226256, 881904500, 397913555, 986394889, 384786719, 202087600, 639755912, 265723526, 207546783, 177620320, 47266697, 695005001, 355447187, 671502360, 946481749, 317711771, 33565289, 373501580, 443937709, 924661503, 54600948, 321606620, 794677852, 305184408, 273347339, 596625910, 348837334, 343935274, 687453049, 663418681, 356056884, 263412467, 220673159, 277361060, 889447355, 948711518, 901454950, 470004238, 413819728, 382283961, 138417452, 605740722, 996157939, 711745139, 249284275, 327075291, 402809192, 744453636, 19698837, 944445663, 148852387, 361207738, 350373342, 548797283, 179279770, 886151107, 401742530, 189683524, 854983356, 836591923, 377665710, 95275059, 88351156, 83111314, 517393609, 125360516, 266907728, 971155337, 201948823, 153189381, 71926127, 134493358, 636584340, 18229555, 162091798, 670572871, 774949121, 540472520, 238339364, 824761330, 496437599, 741436943, 515144480, 654880175, 951370196, 222601195, 131655834, 91108166, 38392678, 295705870, 333196877, 872305877, 318667201, 412556089, 797259633, 434088012, 590256236, 781427900, 391680790, 438575783, 876507659, 112118339, 32407553, 414778348, 688324718, 565394764, 503358945, 379803959, 445737035, 158699961, 553418088, 36381714, 136811247, 114807249, 384307988, 730617848, 660183085, 945754243, 742211791, 290023577, 53871094, 456702202, 860380860, 32881012, 742963328, 970191790, 936259215, 739568493, 69753001, 516902012, 523555636, 466801417, 572381845, 909746156, 607276076, 717724532, 611638845, 9390037, 739247198, 275717399, 121299067, 675833988, 187556489, 589005597, 300672851, 821977798, 960984225, 528519287, 74308208, 960733978, 889900956, 76291635, 217703701, 697749479, 531697204, 549463802, 526821484, 879429576, 407783006, 406480901, 856982442, 909410128, 853820393, 717337144, 1975436, 113457691, 286755306, 869984206, 524137002, 778843365, 763002458, 491295412, 415697839, 967851844, 810245591, 908841959, 949246367, 470853482, 912044787, 866944363, 489180706, 579379547, 174655621, 820175163, 310102326, 633354561, 58535443, 896725473, 50128430, 648758461, 682018062, 197970484, 719322875, 393300193, 454457397, 524745418, 857135998, 666126741, 797513895, 419159096, 305893465, 322591995, 876045697, 9157370, 372496841, 840280011, 210469909, 182676048, 441542949, 16531079, 792132339, 660790788, 809033568, 747316805, 596788498, 938943601, 11710585, 172666543, 371104417, 401405815, 848493977, 11219632, 113419791, 137335564, 795189733, 532933347, 237049279, 665890178, 656538553, 564743625, 880515346, 697863932, 501855683, 713821112, 174165014, 127767814, 94262816, 171292462, 684303226, 125756047, 187861073, 184747021, 248728788, 526809937, 618190795, 553105204, 999145087, 314744628, 809276264, 98401548, 699677790, 930731812, 469997495, 94529444, 367087368, 730046634, 954098315, 493464050, 155362161, 14909055, 348899367, 576815533, 610108398, 972585860, 963624864, 525984599, 575282552, 685295240, 746114132, 654218415, 348106966, 4922381, 116323393, 251019558, 640453876, 852015457, 212361977, 839103717, 370915580, 489415512, 701815307, 434533422, 124623127, 327372175, 164241126, 279531892, 374272019, 446672266, 558730870, 596182269, 665917688, 11935636, 823967734, 946872136, 159858919, 485172664, 94774043, 367557802, 978952370, 274205577, 800219796, 154418162, 676578333, 543991831, 635814096, 131449564, 487887037, 484501584, 816020938, 498104948, 41366076, 957076391, 228688971, 393366193, 200226641, 670917542, 396614674, 927959330, 906368036, 354270123, 211450321, 56074952, 473595456, 761747982, 120675608, 644359441, 658367149, 123846268, 28826016, 830081658, 222631555, 812113607, 938445554, 68859909, 896170052, 917660270, 315804298, 960116850, 148108490, 70481713, 372766467, 368455291, 16536038, 906137549, 171733539, 470393834, 19380955, 308469556, 206743893, 66281853, 46223697, 231563193, 390508776, 939182438, 343540245, 875425665, 630664511, 977161203, 24697313, 611331583, 217776154, 752122464, 822409432, 474763640, 406470958, 346832724, 941556521, 251576689, 873718098, 914613524, 922112992, 816721440, 207867327, 682027630, 853923079, 977663951, 234947733, 989961493, 705406231, 819229097, 765647120, 512250713, 484346048, 97138372, 836043942, 797492064, 816103552, 835151401, 53709254, 878472235, 15162040, 822513747, 342990225, 283196973, 368704780, 982599155, 691861406, 44160637, 689123636, 488392953, 739442394, 639203625, 602709379, 601083967, 487668109, 553726289, 228982457, 12781622, 406576517, 136726494, 141610011, 490568773, 678025066, 88789511, 102227886, 606490376, 443784095, 909558772, 467115066, 919793954, 325475519, 170825769, 971543620, 780724273, 730507476, 113617255, 488197897, 631921848, 108011115, 262972314, 195483433, 352433001, 471304983, 16571476, 855604506, 431915080, 857002700, 175380791, 470227214, 954289188, 450472303, 90869012, 53990760, 295339327, 59147350, 920808889, 198219676, 14297271, 181548151, 950448394, 501369842, 688326819, 232845525, 445072087, 252347719, 400838974, 728590523, 200686890, 879921342, 181487716, 757427486, 553698442, 943079564, 907620090, 581796675, 472313640, 882407703, 863863697, 178572111, 712405697, 297564581, 52682896, 860386830, 905416558, 540807989, 337680093, 790898552, 587935348, 544113991, 645261624, 299802296, 149259485, 343034328, 526390823, 408233617, 935906523, 339076508, 755259492, 858861828, 84220229, 890587134, 627352873, 319020556, 116469421, 205789025, 638918908, 515891307, 24363605, 804097411, 630837010, 849865622, 107347396, 902466808, 784128893, 539829700, 451191372, 110862961, 780004212, 459012455, 658269243, 94851582, 496255242, 586555906, 405021132, 252949971, 545820600, 245475968, 875007666, 583706597, 110471429, 72858669, 639464041, 891598252, 656211062, 597519738, 82939104, 300265506, 570124159, 418659655, 449753161, 669346409, 808467153, 880398206, 895019627, 4535942, 265385224, 540624660, 368179372, 519900385, 304265685, 745516468, 149256512, 102284469, 845111962, 873099079, 977390397, 424782363, 154073540, 796310579, 702924834, 136524919, 125172694, 921654476, 49949140, 974865494, 344226052, 294433065, 774046627, 557015847, 867124487, 724849990, 825995453, 798046670, 961070590, 206686022, 569115195, 758154495, 813490932, 87616902, 29040804, 466845567, 715751821, 875011792, 363470491, 903555178, 276215813, 645969929, 30772478, 29865478, 113005018, 874722211, 372614267, 5065640, 958586751, 735277886, 934901137, 420429962, 398790160, 443639130, 875030893, 292523292, 203344541, 296382730, 837142232, 976042022, 79433328, 860629216, 927951820, 137115312, 643448139, 656789271, 137481374, 378362513, 553350394, 444940745, 507714924, 619788588, 743623026, 376223692, 433544897, 769073422, 976764559, 330029808, 441059935, 518760277, 848284148, 327931489, 513552103, 804656234, 801989572, 390421771, 424990758, 479696693, 304837576, 321037983, 920630561, 330470728, 312331798, 877067197, 504523988, 181448149, 305997738, 53381337, 171407377, 185577184, 879406923, 658029648, 193591395, 805301094, 62312627, 659162161, 101624231, 160374514, 534307724, 343502762, 453910470, 14612774, 462071456, 512307534, 853237945, 388663488, 245089204, 537933346, 853255086, 635821329, 893113602, 220085641, 51355022, 735745259, 758882227, 428620855, 685249444, 685220575, 407057570, 568522373, 723566989, 920368268, 645686275, 239782027, 19498212, 66344682, 892944127, 253161072, 173426367, 33017317, 461906955, 461219089, 330463026, 936197757, 559227139, 470602932, 932901662, 838157912, 588909880, 853556782, 219911334, 332886581, 286111018, 995140527, 801111731, 453427221, 114223422, 324331254, 301907602, 939901216, 937704185, 656495405, 477411365, 800542263, 270893168, 109184237, 499120113, 222812294, 740550287, 327587982, 98000374, 231066078, 195511574, 132997763, 419190522, 83958786, 91442593, 391019121, 798120878, 518907373, 814177300, 859541104, 139053105, 256690191, 62692280, 767490785, 767729973, 742825311, 102446961, 347056980, 148347628, 923652001, 136299829, 528897960, 142976183, 263783076, 587763766, 248538485, 489190825, 377939806, 855296556, 957931262, 774533869, 384115004, 827540469, 52884203, 843568095, 877547904, 329275374, 375160261, 426113676, 252282536, 227502799, 436000554, 469912863, 655616109, 506511100, 801207450, 130526307, 725788431, 303893506, 233618122, 480305794, 435037908, 775078976, 234431700, 219064637, 511749224, 962819397, 666455759, 624554934, 987121869, 414687821, 636746845, 747003712, 905392876, 557395787, 158643051, 498868497, 498667802, 833921766, 762418526, 474082018, 443670536, 426368275, 348835650, 494440466, 144679434, 347281357, 745996954, 727317461, 134285580, 372389153, 356087757, 766402239, 870585719, 827922125, 724805724, 340709069, 652278587, 870377283, 848550822, 177383874, 403768702, 269976239, 407226770, 986018437, 407218600, 952942860, 539213778, 667224976, 854504011, 455793167, 550134301, 123397924, 99251561, 142404435, 945732386, 385926344, 498916961, 989825945, 331679357, 155403397, 92127007, 150816802, 718474919, 376352974, 172640866, 349898392, 628597904, 39240242, 179241144, 451211, 932735585, 900332492, 398715614, 370913100, 730681584, 850244695, 469331111, 322172475, 140876990, 395807367, 122030826, 243312225, 332199769, 615092971, 462782050, 881489876, 21278135, 834670763, 640002338, 46625230, 610265494, 706209066, 877090739, 813020842, 512394066, 13779744, 848482323, 521065771, 357050785, 967207883, 143121881, 815604351, 482846556, 391854734, 912290195, 263365135, 369804285, 21131434, 682702216, 214079116, 458851353, 31494661, 49824317, 234137005, 798760213, 204519292, 835034556, 743340726, 925892407, 67436266, 972776810, 466495159, 616943010, 425721915, 7480729, 469834736, 50021837, 206313136, 685059226, 839902880, 327327971, 736641430, 318831489, 219338187, 144583121, 367915659, 945328207, 17301198, 811839862, 674241887, 480136844, 276482132, 432468391, 953201600, 83319820, 65302120, 602959337, 715150627, 81114757, 679203142, 521803047, 107171022, 515290384, 394494585, 933407334, 4338500, 918467718, 571570852, 537434473, 646279758, 40108342, 434957819, 837380009, 49373132, 319319556, 374354261, 545165181, 566141987, 224823559, 273770520, 598989020, 947397532, 417556675, 575825188, 567091465, 728716420, 271720260, 456372962, 444706180, 620806277, 973214828, 95540180, 737934579, 925359380, 102296916, 948916142, 101795493, 556601825, 190300710, 176358334, 785363801, 163177025, 709311667, 782268691, 263388230, 435336765, 870625999, 360855424, 829014816, 548546195, 679107844, 78608279, 262946493, 871856692, 172147795, 149509090, 361331995, 956254705, 148079966, 535704158, 257152287, 231590347, 603880265, 145248038, 995823373, 300655693, 667641156, 975804655, 10806900, 272251333, 962434678, 614807851, 71690717, 793993428, 355082050, 775891158, 414798527, 883894124, 177261331, 541005425, 62945603, 768663941, 44910625, 511843111, 510176737, 689235239, 58674162, 947753274, 768780233, 581057148, 50285626, 111622936, 430410249, 537754492, 361712594, 534803906, 809253345, 155163340, 509697880, 132243138, 997810155, 777305407, 990240764, 405897242, 297608532, 113670143, 476786787, 342887321, 794388103, 182543020, 551469882, 3548620, 109134387, 737779820, 547932506, 680707029, 780359550, 11581821, 275643522, 807295012, 96777814, 204271831, 663546049, 983061819, 274812281, 688307722, 271350054, 472266874, 124699619, 7205993, 309273601, 517597961, 801030326, 893367494, 651634909, 81794384, 775132071, 717723205, 846315318, 689211164, 659095797, 503606401, 934910662, 506407308, 602530302, 316400767, 122567062, 541607689, 192765891, 303636816, 116605176, 876376296, 69965607, 613780723, 279585437, 344498298, 931090463, 797715053, 255271425, 949386622, 703077982, 843209012, 798959607, 897935229, 340392418, 253858089, 230621608, 596355344, 889882022, 475877105, 984413704, 748565788, 475640969, 184150158, 514816680, 194713545, 785267805, 690008396, 162222069, 455487641, 334317282, 49900903, 420992363, 679984037, 190515905, 853167236, 125002452, 786631977, 952780648, 293727641, 493560532, 158792621, 360435144, 231213207, 874231447, 60101927, 374752999, 445286526, 524776305, 454067045, 943589537, 379176159, 504839988, 260562726, 371250385, 280124372, 353739310, 587178908, 827832360, 193425616, 78704579, 765061900, 756955188, 981601564, 759886321, 809691012, 745884990, 591540617, 812761256, 884141116, 885396263, 212149091, 474507725, 418885788, 477545909, 636950437, 51906259, 375827194, 923522353, 114317143, 842679762, 737111465, 369328416, 532716530, 58474709, 521789503, 39654893, 285470103, 327229601, 369214566, 518370716, 263597005, 425379343, 392666773, 883010927, 68943156, 354494557, 72378026, 118355287, 967021693, 487574027, 899675031, 892131423, 847654904, 235797667, 722197906, 386848777, 585543033, 845127096, 462097809, 639581639, 107662184, 307089773, 234482314, 9329745, 91377726, 702007484, 207941280, 193570873, 73339391, 701444318, 350548637, 140285825, 656777964, 14643464, 89317093, 711444855, 60716584, 617880520, 667794581, 13363364, 924657032, 793248652, 432737219, 733798703, 484737389, 99467329, 957036639, 618554275, 395893039, 940858273, 857365386, 145910780, 543474084, 182850117, 206196212, 591106097, 174377014, 196747671, 127542930, 461202959, 619103469, 905604838, 234958075, 314864374, 284302144, 517694999, 561544048, 531156533, 722250229, 16120011, 79197785, 210579133, 369644761, 976034523, 780616536, 781062277, 444558122, 94057753, 123691578, 749385244, 243981627, 705161881, 555836889, 786976080, 860892797, 725147663, 691348887, 655986735, 645887587, 204974993, 719407719, 807595868, 401965981, 59649690, 857089481, 58494494, 592052291, 490115144, 928788912, 135871630, 535912562, 981314265, 657191819, 99858241, 673439947, 174013975, 774807148, 180679407, 644528453, 645796491, 648409826, 378277379, 756190956, 134530974, 319349562, 797378367, 960005709, 807902563, 885626960, 653487719, 366382163, 972697623, 102116335, 365594961, 621723183, 794044455, 820227375, 871577362, 3559901, 333557218, 528902406, 499692321, 807271995, 832392046, 756382701, 454012926, 420467896, 191676943, 149151515, 249139104, 606769484, 837856977, 571285073, 960861027, 142271750, 122913827, 652881911, 661163673, 352207153, 713256838, 975593439, 827635059, 977536924, 652281416, 634987015, 417008757, 588178719, 761218098, 350051161, 975760630, 221700062, 126945178, 445313770, 447461115, 398116718, 806264798, 230043349, 504725817, 15211187, 272886334, 468101167, 978643869, 172927015, 565140902, 313149986, 203449927, 159079521, 186390886, 504518823, 672120318, 259525396, 524223072, 473286234, 609662997, 833403390, 21612987, 760785591, 619830605, 142117573, 659285704, 292258276, 784837229, 166313325, 476089772, 963854405, 639074050, 179644850, 159333373, 119315931, 780165353, 809213579, 630135703, 565164120, 59477542, 575070981, 657950090, 552556012, 140615702, 427131123, 112045950, 579247773, 926332532, 244755224, 172368135, 315379620, 623470225, 578946247, 52285027, 310700394, 98966614, 636306390, 816721440, 755748482, 777048565, 291294415, 597128729, 930182300, 42243943, 610956997, 721938279, 896904420, 520702471, 483534409, 978139698, 802548202, 178691995, 936246653, 298968760, 920764134, 728659339, 733683551, 253243462, 407350299, 546345010, 466616236, 461460709, 391247425, 578847145, 183322456, 857097560, 16790494, 74424992, 245271437, 17228398, 238244540, 129328559, 294192722, 828254175, 790441160, 818338566, 84377515, 778481652, 448400817, 297499064, 646772071, 361533333, 250293295, 691791103, 768470752, 493330653, 303107211, 255989004, 272404891, 95622575, 49656525, 830696774, 879724362, 185607104, 391485723, 782379069, 699845145, 510340619, 871341779, 829014568, 806963775, 161928601, 816654738, 991746858, 781439835, 320345211, 823196713, 991854773, 154883436, 772875805, 718058988, 163074870, 939449467, 466933612, 767266719, 243438984, 584698453, 716592639, 487445640, 482144492, 413704731, 188616791, 716783556, 597372903, 86988156, 994506966, 632716727, 446408764, 356004926, 793239253, 341211116, 559528328, 233274545, 241271422, 709965251, 311289106, 543974177, 859986060, 529504205, 623275046, 295442717, 248695125, 458709201, 773759727, 979922086, 300408428, 666239331, 114250572, 91048221, 751835006, 346550038, 977803293, 177860187, 287052667, 110242590, 96296950, 144768456, 130248636, 772995595, 905675121, 563185628, 593257355, 97405138, 139024057, 862644281, 739425317, 979695352, 617513637, 973535948, 56704895, 386039033, 679862871, 485721730, 123488352, 200172106, 456692555, 878192907, 819914199, 96318837, 898101788, 723605645, 397810098, 812079778, 373564212, 462859085, 633323969, 724293132, 23096476, 221760597, 246350152, 352693268, 522791905, 27010914, 869790678, 635839058, 460263522, 111161151, 446182861, 211242736, 131559873, 384684918, 465218882, 965501218, 290077119, 930770630, 755631630, 802989865, 547231716, 744422618, 648647485, 752100793, 17236646, 336471118, 426091108, 783043392, 381808572, 988024813, 864582294, 720024258, 809892144, 212291155, 400138532, 496765396, 882414945, 32344693, 36282059, 21602677, 453441860, 251084989, 422550438, 771864102, 91267360, 519008492, 948577208, 179031069, 536701982, 698806432, 143774923, 172080681, 334976568, 55417855, 310499046, 367885494, 413630644, 40399684, 733185151, 535236857, 86654415, 553922197, 674798438, 74866915, 248221207, 243600898, 75485330, 99707461, 244252519, 536633278, 708784404, 600577020, 521869998, 391540738, 324282349, 389475826, 364004043, 654962871, 971182203, 894112922, 195518606, 504240016, 768623576, 574031903, 408524585, 911561827, 391633817, 979534592, 266416819, 615988989, 737075049, 390373755, 767122710, 472173302, 150800597, 269701255, 858872148, 697788463, 103968425, 168159251, 844427719, 139932703, 835736917, 187289979, 839965455, 441808158, 889508185, 254789357, 400698017, 71891421, 227749918, 600605955, 748717370, 460672147, 546085187, 532236368, 26252743, 399863286, 289732604, 833763874, 605971882, 808549224, 662321257, 184863408, 648893239, 833078660, 82975107, 35196610, 59860297, 333364288, 872303547, 329586321, 569314984, 227663505, 309303305, 957779058, 795344867, 12925900, 666144228, 922155834, 148177370, 201342735, 476288139, 7031854, 408888148, 907013036, 652498214, 602358953, 540940904, 191477172, 25280335, 668991083, 553333298, 189607418, 995032888, 378994158, 139401343, 631052634, 277823985, 625059721, 146827481, 73021186, 827391694, 872075679, 710675073, 234219925, 457763252, 732344772, 795326225, 247629600, 718086688, 899925356, 891716350, 395918676, 797810623, 852490946, 526682265, 347990402, 129869764, 657513930, 263703597, 160558122, 849834121, 919107216, 342436598, 491692640, 478832393, 386550885, 955230740, 203796205, 424871147, 620993611, 375356715, 509807272, 223555963, 765910020, 983152828, 522238657, 13089880, 923761523, 338995163, 479410912, 752252235, 2930605, 532867784, 233539401, 779392618, 614329619, 244444766, 758098805, 178142614, 748504712, 310236735, 621416437, 161196180, 295424600, 78465427, 278026061, 912628510, 503877017, 954623680, 219268711, 762092222, 851800548, 928961464, 373195061, 51800354, 754523626, 843721335, 933436205, 627751114, 794200578, 903441212, 174664328, 664682447, 289497349, 823386714, 783281589, 113057708, 864423065, 412763543, 207521098, 484938454, 86243355, 268449499, 493053270, 685227052, 352968900, 19584989, 916488253, 130925059, 676848330, 845211025, 909734937, 520997904, 56958998, 536927939, 795004033, 759868152, 188507000, 104917147, 212967737, 833416061, 880062585, 711087419, 607208890, 74940437, 251662724, 128979193, 183250502, 916383159, 673113597, 183681696, 6707130, 421365481, 515266009, 227378217, 902891850, 826572750, 797880091, 798274195, 665276706, 573291964, 285180877, 869445765, 616443699, 438962527, 491072675, 661819443, 585285094, 840706869, 166830189, 27568566, 258653724, 937228914, 796369443, 626966409, 380689209, 876145900, 774750489, 855045348, 394298561, 219231181, 740692470, 714036701, 128692742, 943136202, 521469032, 900632222, 565640828, 490702226, 916209283, 681875496, 576509402, 763051945, 541639496, 690221840, 826847045, 213033656, 433712557, 511408844, 835757091, 830862634, 616715901, 647894450, 253018460, 785009994, 138203799, 478567377, 132954800, 679479087, 812108165, 556259215, 905677377, 70514536, 520818726, 42124574, 344249017, 655227407, 426727621, 687703183, 546854242, 949248839, 76679400, 137127147, 613249789, 32090325, 842555922, 854938371, 456742974, 472711461, 910301352, 17494039, 971099607, 781903596, 939703899, 13668295, 418420814, 915111936, 890427564, 608903686, 274922917, 395916600, 266518982, 193160800, 686134516, 4934087, 873871325, 364835375, 942255870, 103810196, 127047932, 914647193, 225514996, 125409687, 961176530, 732660677, 182790892, 508305747, 891765514, 755132054, 646516886, 56852602, 476686531, 715521789, 801895200, 780995555, 8319291, 773800979, 138905745, 330878154, 529834156, 160341615, 783942148, 501180881, 530287862, 164478505, 936239943, 797284947, 425796239, 439738279, 332851498, 385554511, 791649525, 414023004, 389736969, 667034583, 735867796, 360322653, 773908129, 798960740, 101162576, 867061248, 603514447, 563399637, 861603706, 245621086, 962040668, 862464047, 782130731, 522625452, 233101608, 523437262, 762387393, 637985766, 855688620, 555105530, 206637915, 201629869, 262632872, 639142766, 789073834, 885177783, 807287729, 267682914, 475873735, 571560349, 64562066, 623932509, 725941902, 609294532, 764705297, 545819751, 600273801, 92381224, 404564477, 650729402, 825677453, 976003780, 790750673, 875489760, 275011842, 182173834, 334896168, 711715132, 616444198, 879734695, 755596474, 902362491, 815387761, 356424511, 358882207, 898891966, 856008133, 331745021, 534421919, 212325327, 99372088, 121890446, 56591192, 235744693, 472108438, 271278804, 830807230, 257864147, 520453506, 912453546, 451621316, 420320293, 471580864, 721027712, 277756895, 912424312, 807142615, 162503753, 478020543, 856694318, 657956176, 696275091, 168637067, 754363776, 734843750, 956120814, 745553865, 618305597, 199823583, 784953172, 818522829, 159609422, 625497808, 316207645, 341396133, 173898901, 940977132, 901820382, 672445379, 602260707, 758918771, 561234725, 675001158, 103465814, 661044316, 356610318, 986543195, 815247646, 899940374, 131514168, 207480561, 810495386, 137938233, 984859569, 181719562, 166594144, 999101763, 536356054, 17463023, 392454691, 445401423, 444675125, 509891020, 665655001, 628650677, 129357271, 536835537, 457209883, 35146862, 60110620, 284437669, 195305959, 648433538, 252266066, 892050875, 573916558, 330824328, 892166959, 881112458, 406796489, 945697077, 902266273, 460693762, 884045070, 662159402, 328478335, 1248177, 594477268, 847287420, 571041459, 771798770, 833063738, 419801132, 741769498, 308621134, 262451009, 308911151, 660352203, 226518788, 594914337, 528012489, 948327505, 291570076, 861258017, 882344773, 39051160, 424300126, 151193848, 860398723, 939100507, 382611029, 832840503, 137282800, 232653831, 659596285, 208741380, 575534826, 33718269, 339957113, 842994085, 830688244, 562123042, 813882837, 484217598, 996503768, 987398728, 588304860, 862471291, 997393228, 381257947, 252863559, 692447830, 736464287, 816631428, 306378266, 580754870, 176253070, 137152836, 652188809, 99617498, 491361607, 223481550, 289473908, 100347574, 424294633, 742649437, 765422456, 54167058, 323151546, 37987725, 73136697, 81217285, 855773918, 797476373, 749844484, 379866671, 926815162, 373068195, 109790807, 515141876, 277202614, 445285634, 127171204, 423087774, 822863084, 328939149, 369213663, 166530578, 286408536, 122001861, 368640710, 242962713, 895486392, 436776933, 804825566, 188042806, 96254910, 986479664, 651033524, 650207125, 376130291, 514867560, 506048454, 668762922, 557645339, 710805403, 1103699, 181449518, 301921380, 343188055, 819588591, 212902070, 314560317, 9424462, 511325265, 446086472, 276743915, 225015506, 759077320, 350889884, 649340534, 511460540, 655981613, 663609380, 237436360, 881831209, 533831109, 15135320, 773361623, 354971015, 171082187, 688159225, 288751017, 618313486, 828399581, 985325606, 968135037, 797084929, 504235677, 608971199, 487810617, 610136133, 474308744, 561043892, 973564531, 981405977, 837439081, 418032850, 433382119, 701076151, 509491667, 771028976, 881893754, 822381283, 612664698, 730879069, 647810376, 356971286, 160053814, 596320941, 915994744, 932185887, 49587493, 155598257, 588561585, 63889893, 880179721, 433838762, 118366972, 851398535, 637150246, 421024674, 589546543, 566389937, 6633140, 453472938, 539074437, 368841425, 61818664, 884788174, 908159330, 185921272, 190732469, 62636819, 971682128, 124374294, 481202196, 532447590, 617672755, 699283026, 264461370, 163161795, 536418728, 628418839, 639258714, 118480522, 92393487, 723326704, 6786929, 499814287, 471468729, 540025398, 191713673, 237745402, 7991692, 46970927, 905027296, 905371604, 148745463, 43815164, 248537076, 332647971, 951178858, 995341494, 37921885, 143108352, 829733581, 421828191, 163971748, 125282777, 347257600, 322445671, 93219878, 268928691, 137877126, 688491495, 211205015, 946306250, 485584653, 391613037, 156612330, 105795440, 646890414, 130950670, 50543037, 204771351, 423915439, 797608962, 134894474, 496343966, 852625485, 23268936, 927432177, 755482955, 324184451, 333428372, 926591810, 807662764, 887403107, 545517452, 206003931, 316697958, 187706045, 939425354, 671760577, 847383851, 59137286, 765944096, 497521245, 367516537, 182365669, 905508875, 788443869, 96755286, 91525342, 80501025, 242993415, 93908430, 739969214, 674996260, 617578067, 809821829, 650663596, 484439953, 347348739, 768638889, 762090309, 719589097, 278180042, 743462557, 141647820, 501434997, 985967491, 580765927, 981872683, 204381930, 811918865, 628051570, 42179359, 137102114, 189986771, 794204313, 700471405, 316568221, 715331730, 899045531, 88015147, 609625938, 800099667, 713220323, 683633379, 375989977, 363448300, 852819871, 42419935, 141372385, 727777359, 234542857, 186757723, 168731013, 854307705, 931509374, 379142996, 323726928, 989790132, 308290010, 849169924, 481571466, 892874614, 245273713, 318020179, 674304257, 538118293, 558466547, 480923321, 626649346, 75839825, 978205247, 534201063, 619764962, 802183118, 368001961, 359154917, 938450882, 153932572, 969140709, 445882300, 336787966, 26458254, 953062561, 774838684, 625192122, 391025461, 978246587, 110078681, 804769134, 28718756, 133113959, 367393718, 782742916, 851398438, 29073407, 849924062, 917887145, 785786360, 318559820, 506989195, 224356348, 649408952, 424972615, 525723330, 513667636, 735137676, 998083528, 659217859, 408333123, 323715719, 69180730, 705443423, 653416224, 789994820, 565674993, 821686206, 429878819, 70349811, 460469361, 553789945, 489512984, 806145540, 386250386, 169880439, 747244464, 97839102, 893579038, 786762100, 990421845, 56014953, 844874722, 493382460, 37454683, 78670257, 441608721, 783765385, 986706102, 76454055, 820905164, 995695108, 332304737, 661094984, 355826979, 807888301, 585956062, 396735721, 792927421, 510675130, 51275248, 293387043, 32674467, 568317053, 997100827, 97620321, 63233533, 315382832, 671364718, 867976285, 234380574, 196830605, 230412063, 262097759, 271702042, 953723548, 367517739, 531799284, 373113809, 27894279, 15801513, 405091962, 611678010, 165862228, 821776595, 328990122, 52660598, 775270368, 409813699, 534859533, 708706750, 934563972, 82603808, 15133790, 597778323, 861694670, 709156291, 764412958, 671352217, 801822213, 469672824, 780227467, 926492848, 96664752, 629060807, 989701283, 183103103, 921657810, 998316310, 126741504, 149175403, 556405661, 576135998, 791521836, 996962060, 278406980, 306893620, 495661410, 572350485, 978170624, 766824932, 977001120, 91145224, 637378199, 356912348, 678421392, 280730531, 518573469, 812006476, 746786660, 223077681, 226039457, 449954960, 860876488, 857523748, 211948271, 638281598, 996774605, 768016347, 364888746, 89778755, 93459379, 147803200, 59498766, 90103100, 895785640, 835546595, 596507885, 469789432, 436333088, 13515465, 23149870, 257849151, 334159039, 162801240, 293369863, 579020470, 562488036, 932348118, 247750629, 89321391, 602347555, 512407001, 547459831, 117020079, 508355445, 777911474, 117837629, 244528978, 324682794, 373268979, 49854769, 489530303, 914723331, 953494865, 458840495, 300861627, 829288652, 695132910, 649633463, 111575188, 263752670, 315166736, 209458725, 278684041, 601706487, 956025358, 10727204, 467097086, 644017055, 763488785, 515266080, 246025191, 899091594, 3738487, 974739917, 118347406, 5800269, 386137711, 637717304, 908236878, 976446296, 971077351, 801337355, 753414777, 434108784, 59720306, 919054084, 582472901, 261255031, 55931310, 156987335, 745308173, 118444641, 789235761, 135061872, 581599069, 887289800, 128752306, 220194953, 759227246, 180345504, 208415813, 894274447, 294791668, 188802528, 216173502, 459494631, 54830372, 777524638, 902372978, 522621561, 249563693, 263596190, 292143581, 759920934, 860708814, 918074885, 735196943, 357682324, 301449004, 631801535, 161529368, 947829401, 500885443, 34482715, 591961159, 424459373, 607519439, 551221579, 636635697, 564963295, 345817413, 184999660, 361207779, 628336713, 879600209, 526763986, 621373276, 783516735, 951075997, 599654573, 227254972, 736746047, 44147050, 494064713, 262711274, 145013306, 577811410, 557802000, 183112717, 257719732, 892764035, 945179367, 370248083, 792824279, 47346647, 40280827, 90904695, 849453399, 771790415, 792332684, 491510568, 195136096, 943776074, 308127539, 472497984, 859630624, 737281499, 629433717, 881378836, 368874568, 903179528, 299943158, 332132978, 174373201, 520871122, 742803018, 842334851, 115737855, 617494609, 96374133, 285855153, 147402444, 822940626, 565408179, 437190215, 714670396, 196099160, 643731571, 786330918, 540788410, 530690290, 609393236, 401895709, 218575767, 555734150, 725986740, 817723691, 395012371, 761638521, 340997989, 958744273, 257870508, 993334909, 93723055, 270867521, 714445982, 270053618, 970320863, 195625385, 8762629, 724423602, 581137281, 353744754, 609347862, 192314514, 911345588, 761318548, 944955624, 483009507, 702505002, 590910864, 85491915, 184169878, 425952042, 605348992, 913175082, 12952999, 643536107, 131438677, 284040713, 953505566, 364522135, 842705601, 780121833, 756930541, 86801448, 633514902, 520770822, 465707657, 726974508, 122745830, 246267790, 910311665, 222589619, 207792722, 382383720, 761203130, 824610515, 714059231, 182877716, 899090314, 140222348, 414710949, 906099114, 532952399, 704381893, 950060422, 932170433, 437843112, 286819311, 233681117, 104144656, 240475947, 480419368, 954422521, 926642689, 912221275, 580593354, 331814545, 766617163, 993769254, 865502380, 180604774, 489933539, 424783024, 318073629, 815704791, 166909235, 190115599, 719148202, 692511164, 91922100, 248376364, 314472117, 558044155, 327072850, 201419685, 721496173, 740620316, 492247143, 408886561, 620725595, 985727458, 26311209, 757817502, 825601017, 111461838, 374533912, 992348710, 363077426, 945249365, 32836275, 566419117, 460803059, 735600974, 90478259, 560790458, 191882737, 350407949, 11804719, 135619204, 942757582, 815892470, 4537934, 66725409, 974873117, 710156323, 30015365, 542824226, 905911808, 317123249, 482563414, 60350217, 94672854, 728945030, 15412376, 373037033, 557502714, 831607417, 600707723, 874460316, 195929260, 294435024, 385980942, 900229392, 971112358, 937159887, 536216921, 757082019, 430723652, 969312622, 143423698, 6081719, 275341105, 92120724, 96795000, 935427257, 674972764, 798065588, 510562755, 83319993, 432388979, 53424438, 810311927, 675079661, 370580978, 365243105, 87732583, 2882255, 17771025, 742973988, 336610435, 127748894, 744594067, 140101965, 717267447, 414710433, 656219456, 201041005, 366131947, 824828229, 395382018, 573557049, 512768501, 945970728, 183879823, 527766009, 524070383, 467319246, 979173261, 23885322, 525320798, 395508976, 729034913, 533754066, 527912820, 374303513, 870552722, 408544893, 150994149, 348130103, 825040851, 687586118, 174072632, 313990236, 195506512, 818399079, 589998819, 836793423, 748759435, 384107578, 41136448, 346176412, 337396409, 276159194, 389110244, 584728006, 805391126, 170446223, 34294827, 369682096, 729509318, 592566414, 208080800, 361228440, 815015717, 47873658, 715633554, 529311783, 864597513, 87860861, 903871407, 312167924, 591519727, 235043341, 302380072, 391789708, 168494676, 1125174, 815827735, 650137046, 204107518, 551473510, 632027968, 353466026, 868788858, 713144948, 67511840, 823725057, 168146451, 77268905, 867156366, 415530936, 939534991, 936154520, 948180741, 88895648, 177809060, 491928369, 396964091, 546372196, 24582472, 561250221, 694596976, 447580062, 789100619, 707258400, 929826276, 606470092, 608215378, 6308158, 68569088, 888053888, 156055316, 888733310, 475399663, 171045534, 300667620, 994529895, 138018895, 890463666, 773386457, 816633221, 696370375, 143285925, 157021355, 930704158, 619143769, 436889949, 722619719, 356928571, 877005245, 431523799, 324621358, 778427551, 835352926, 449918360, 243657341, 342203357, 492959422, 927252971, 381402047, 639839692, 626847995, 284409679, 440971926, 351819459, 111091505, 778249399, 416933197, 732480196, 400298058, 649842485, 257485809, 544242353, 190674034, 397225084, 897776740, 531640999, 552442542, 481982051, 488199327, 723564743, 903706625, 554514669, 440746721, 840770824, 579550990, 372251541, 546363460, 182759234, 292920219, 168658082, 11635852, 677847836, 875591147, 946046711, 757928682, 262633201, 723803348, 957109494, 601843109, 446028009, 689313484, 53065876, 474245439, 742292792, 501705683, 640672328, 961960200, 776363489, 25868408, 247369817, 438106492, 148110044, 25406683, 434421740, 474567156, 517417407, 227836, 216571535, 696060875, 819932690, 438409551, 746612633, 714960360, 258043373, 919725359, 244736164, 144004721, 633854018, 699910831, 119285341, 180305344, 182637091, 537144892, 732604112, 824261122, 136882175, 53047690, 626957740, 512340722, 669531673, 98616653, 210022699, 211040046, 407852366, 724787426, 581357436, 279503755, 7213190, 819991786, 95057338, 771874576, 917473337, 379639651, 431340517, 306459586, 215332780, 631614278, 139797082, 960076907, 754370246, 939794091, 702083533, 404923056, 240200652, 923833375, 592841415, 819948805, 769888636, 378152077, 185106724, 989314092, 625828513, 675863223, 823031507, 268353287, 73884878, 953170080, 105633529, 741159998, 557591044, 23929579, 710033153, 613426099, 191282792, 533152297, 772016202, 625634691, 352459930, 900988511, 844431327, 575958148, 289419900, 125159341, 585345210, 781212033, 283721180, 709662586, 592516046, 259839910, 978333831, 121022906, 286340168, 550891493, 591590552, 101237116, 24268324, 10045797, 144525647, 658333731, 437278351, 27314616, 802462076, 136969380, 45885227, 862572373, 230832822, 960812929, 639468122, 903590456, 570465451, 683686441, 839882516, 595832832, 710235814, 384168315, 956496436, 141133164, 783082777, 35211483, 200633374, 366713864, 215441694, 48580313, 403181808, 386598503, 42310998, 56810066, 227683136, 234402523, 179292812, 479170291, 736932756, 110998376, 330726133, 906871892, 397970878, 204322857, 305970720, 41379210, 294628506, 565289032, 858840491, 668993350, 104598740, 794296366, 700715468, 39854651, 169178891, 503368036, 253508405, 723804855, 53877247, 618359392, 679618434, 959000129, 796676250, 616441601, 380456098, 82737501, 800931696, 774965111, 848386829, 49951585, 356232259, 636739347, 164318676, 843507507, 355422071, 840127160, 737760200, 984928607, 147000171, 383722448, 416221705, 93833318, 655644823, 728355826, 214411038, 123529275, 846141340, 522229601, 393672550, 228622325, 731490197, 320845602, 704405900, 310560228, 998252763, 407741942, 65234895, 543383712, 514928762, 330954029, 90681486, 812138819, 327564962, 517940684, 606094386, 937740654, 455703340, 117706005, 151586059, 432987679, 420695420, 457633301, 711436949, 170142163, 989614554, 206091841, 127358526, 494671184, 709167715, 518821783, 713895580, 517932413, 751629723, 14926485, 869126154, 451883048, 100194099, 595693740, 871918228, 515739778, 731979985, 659152008, 525733438, 449980730, 50814764, 298216209, 226245251, 855290571, 674061694, 552292212, 82903996, 912274521, 811961074, 385351695, 753196216, 352466203, 901336790, 432012590, 221556139, 921033563, 755684400, 970328114, 519947152, 594898594, 784739163, 916113861, 196890368, 874585276, 617083802, 136557470, 649643861, 506964787, 46494554, 584934542, 77488200, 691453480, 239519828, 567097581, 808809062, 143195141, 832596247, 158253340, 996669953, 690183733, 164033892, 865042060, 173848081, 798445170, 832175568, 575126593, 371187161, 363348582, 972273077, 720235957, 392749507, 844564348, 769089509, 54158992, 138218950, 165070803, 693164461, 669468457, 616041694, 365307097, 452360166, 638255383, 435915982, 328306648, 618910800, 438320222, 566293061, 754991206, 199151950, 797707559, 356180326, 673687925, 834897342, 582677295, 532159549, 119448085, 68534757, 29114738, 528989674, 154092751, 981364903, 692892188, 557927055, 448564024, 784320594, 325572738, 530733979, 893751785, 786660502, 887240991, 844465255, 830618084, 4133678, 336514461, 628770578, 121278207, 566279062, 707093197, 256544382, 765169177, 871635194, 134013847, 898968454, 720336127, 503288047, 649328999, 275274301, 2777535, 433077531, 683015843, 659795675, 365215316, 96818206, 563947964, 414776342, 950440447, 406354468, 43603539, 910312622, 956299967, 934984104, 14717383, 746109779, 871782930, 525852313, 7229394, 541006536, 51853530, 113144863, 568738518, 690780040, 540953882, 244161804, 855634032, 486703147, 51814560, 82044715, 207986727, 124733813, 742357651, 959696328, 370914044, 406776525, 717694801, 450656530, 888410334, 805122350, 697014077, 329782798, 684066919, 744218380, 814546367, 326148986, 195420251, 268634400, 364312180, 418921466, 684810830, 882274919, 781018305, 628920467, 505292968, 54629407, 876854453, 675111157, 469693007, 940610723, 739938313, 285394510, 242535789, 689780335, 264834821, 59743076, 212892685, 494928477, 865121847, 114047745, 254717231, 736146020, 661752033, 538350061, 372502980, 28632108, 966959836, 469731158, 433485816, 676208333, 975349879, 853529361, 316746099, 917989091, 307934617, 913047788, 362531365, 9828214, 290132343, 28582016, 224186148, 692153206, 306229690, 886303777, 955012482, 768677985, 895677810, 524921679, 380192594, 787723361, 298067355, 679081312, 469110918, 754854639, 81924332, 718435084, 767078915, 896919813, 450236868, 921995588, 390246105, 107594349, 840250913, 430040452, 245551671, 790237672, 972188732, 905410192, 283588289, 76319427, 1953829, 984690188, 819048049, 234285583, 898805323, 166827536, 332757137, 372170547, 600196656, 884261314, 757000396, 816198634, 643293044, 368797728, 633368306, 676992131, 725442443, 278664049, 307451753, 60450184, 973273397, 586303062, 530243954, 826090480, 164023723, 292089605, 313173090, 759788145, 366966130, 351128173, 993446006, 867727350, 310504024, 821484748, 958661318, 982167731, 174182212, 895826212, 367206230, 51714324, 172497868, 88526265, 107560657, 499971790, 835569259, 75379328, 680953683, 248855453, 663252792, 334756094, 471370845, 919919507, 203137975, 837591398, 605821711, 295761375, 870390476, 454047899, 86875071, 501959246, 595614486, 871257144, 805244777, 686602375, 97402119, 213617708, 17962089, 397271141, 801498154, 10088796, 864452088, 941186551, 220987649, 751093228, 180103596, 15259901, 394860076, 492181443, 779818980, 551816743, 792097912, 371675781, 118800304, 971046353, 578787355, 745283687, 898838230, 929609563, 628563182, 244525589, 612009433, 531126330, 735432436, 634427210, 30904382, 47012917, 415143815, 892900063, 727841477, 97507326, 603893349, 344392185, 765021468, 325826386, 755141794, 775295804, 524954649, 814806360, 54875433, 413900528, 242145815, 588076475, 949067839, 165105209, 382965679, 614790819, 167258856, 509033375, 144033288, 257385547, 907383813, 202420016, 828423000, 823520598, 876569297, 605380333, 79087835, 357294120, 334628033, 807523102, 565769518, 671090412, 71000886, 772062012, 535036235, 26492858, 694418796, 847204233, 761383800, 658251286, 884397048, 570100108, 752880756, 51160484, 127662325, 649289147, 191834925, 135718296, 474759814, 875561012, 138729188, 484268089, 766030120, 839443707, 589601561, 923864260, 657757261, 736170722, 23929549, 104837711, 736243232, 599807247, 279468157, 51308054, 923129622, 958712770, 504817706, 119846292, 89664579, 277358290, 362354448, 121931789, 443824432, 917282732, 744924466, 643658702, 814190511, 328840532, 666485050, 264996913, 176466371, 559255632, 233449185, 26643086, 701586001, 422484058, 949446166, 205146853, 344927748, 856310311, 741603644, 63541304, 285784266, 185708516, 151763083, 533092041, 960411189, 164387900, 142035599, 370939951, 736225597, 313181333, 18441862, 11638378, 892655906, 930712841, 836360315, 980769074, 64374548, 731066359, 31228323, 559893625, 230809421, 308917897, 604645639, 124448451, 949392808, 141783310, 351591175, 733660387, 980693741, 256134743, 918910640, 585764265, 477282286, 834303212, 632914647, 561443753, 629849802, 70104236, 635707874, 328049098, 437909819, 471459916, 761010643, 494592543, 388747507, 138615446, 558960602, 198100558, 886585961, 706134888, 200849171, 607349207, 719832002, 331626448, 829291681, 781569256, 953458818, 491000641, 842469982, 518990874, 162684443, 257859904, 623916918, 324098278, 536872015, 84024176, 720646416, 279532184, 420780377, 566142365, 515336408, 248690810, 843833991, 730656414, 61347566, 736819667, 743262351, 706607147, 645240870, 293782234, 713981832, 350674321, 43867152, 91788976, 60521529, 978587899, 408565530, 409814186, 958029339, 703428576, 501501339, 983605731, 849950009, 135022010, 742191812, 161869299, 574559176, 539217270, 916707070, 614912838, 966594606, 532483655, 990205272, 92525681, 451063482, 851857001, 89026378, 256829322, 152545709, 355442299, 423122508, 155275014, 7791950, 809646393, 601402222, 399442556, 443912113, 360839500, 425879213, 334758001, 778866261, 493430435, 557843589, 217592053, 112139442, 993512353, 560733302, 467387059, 400760436, 810582945, 637234760, 793921464, 957269548, 43643240, 370281577, 116203127, 636985677, 123688593, 946653773, 118631620, 911671814, 822988245, 160779321, 206506209, 933787411, 987354859, 441180683, 197235128, 630115926, 954937313, 142541167, 74316008, 645592813, 613118778, 80097437, 489049881, 526865403, 178436918, 279998435, 193369089, 43713251, 130108845, 573699291, 660881097, 903952780, 386140115, 943780511, 832435772, 736077324, 589294049, 348866736, 229378043, 662842259, 208250449, 249592652, 524166960, 517935951, 181437462, 266321615, 647114967, 145665211, 700199349, 128102439, 272020345, 188660775, 578868813, 475635983, 415227190, 433636699, 446890070, 822714733, 360183442, 993794886, 286369680, 757584438, 337765081, 587652394, 793501906, 799225912, 646786255, 803090175, 969713399, 390345449, 482133, 238008343, 444033664, 818287798, 188978431, 745776578, 553807645, 258760999, 118370225, 454886459, 998702080, 826135020, 634591522, 776445064, 898460379, 550066816, 716682940, 58562328, 536554566, 973304634, 744914493, 527091284, 893806021, 176029763, 244340391, 931318909, 318996332, 438145314, 890309255, 781108666, 135078703, 830021614, 593111200, 119230352, 994499987, 988228680, 430298614, 30775265, 653131574, 902368065, 202051908, 951682357, 666790868, 414004266, 820575465, 387630233, 733445403, 941329274, 990255179, 930129593, 902782929, 888496984, 732366859, 334497578, 280315454, 224705134, 518870039, 462684997, 701195466, 431276433, 354954237, 332528989, 526701758, 222039935, 212732021, 541677431, 893390045, 953929262, 924633831, 752552177, 619748582, 523090904, 592575439, 306502796, 56021950, 433915458, 660976403, 867521482, 694443500, 604988036, 81875217, 321296141, 275087944, 854011115, 700168114, 984834563, 356409692, 362492789, 634664659, 521115103, 942600023, 584087876, 834181628, 430578483, 575738974, 637671077, 469827815, 689813572, 90265612, 481492625, 85732439, 65939351, 311646556, 106689191, 827244654, 682942666, 234034547, 496114354, 315421004, 537725124, 81658901, 361132316, 73259857, 34373783, 36962648, 18311780, 48928871, 99460691, 243332212, 433216654, 635715607, 338782311, 148090685, 829871319, 616434423, 691615996, 728415765, 164752684, 109533794, 54034445, 878822487, 281563669, 102322265, 173504882, 805957446, 253081691, 154028298, 908251098, 151048198, 770558055, 394323931, 711870788, 400767929, 273529888, 364710894, 186720063, 203903383, 764083177, 951489458, 830766614, 481194371, 14621108, 526954309, 774921399, 72318616, 413726201, 842830643, 375469294, 13298591, 454712912, 764834303, 788508992, 252635712, 40810356, 602998310, 212062367, 719478248, 202406736, 84058777, 419072272, 919686461, 719472718, 942226558, 848998623, 471110957, 726226044, 585560562, 248926452, 287946280, 781111867, 439378031, 435327629, 458393081, 345388581, 764055753, 635346153, 995493057, 999318935, 166202898, 146460462, 547866916, 314008766, 575125012, 526199502, 100729003, 802542174, 227292368, 163373902, 789181259, 784936329, 582074407, 916913627, 388305321, 964550089, 879746359, 296360677, 48880930, 475063773, 806723686, 367761152, 734352311, 547827477, 93985803, 407018146, 350793919, 800042370, 875703632, 439618456, 906493131, 865901709, 181822384, 658364560, 572982154, 113833042, 917276090, 11693876, 214673957, 311293959, 619493371, 743840433, 178396345, 892215163, 65350740, 198446589, 839043754, 947404763, 705184818, 322265786, 611095208, 678771279, 762685184, 290268075, 858188852, 417274545, 666896508, 651035059, 431098723, 267975097, 700798166, 125297468, 679727043, 697366672, 671617066, 457340217, 801557146, 422118165, 586395874, 446228698, 806908570, 750017207, 693706900, 361580499, 485516320, 44724990, 533049460, 805446622, 16109379, 294797176, 450488698, 258496215, 742998251, 357327876, 488470035, 53932170, 733579744, 375616907, 494933166, 253705259, 316142911, 816123300, 863435092, 946349868, 207739213, 235122677, 345149888, 446498795, 64894442, 406750353, 204166487, 121632622, 610367127, 468610515, 938747853, 624565440, 737699201, 39908753, 342937293, 388778217, 891700802, 912726805, 338990470, 300781589, 535591469, 60283705, 400840888, 40615297, 676360606, 110419657, 283476080, 470854247, 930549360, 545573195, 676024003, 834939919, 496803786, 744460140, 334970456, 725902053, 205588448, 692409843, 715708029, 145765591, 640164725, 209049938, 892547168, 372374694, 782087313, 459908562, 927800101, 519926632, 449367535, 475777040, 814154568, 159565715, 93717517, 398196853, 648027168, 230889678, 555019749, 614878567, 24179258, 530307841, 401940222, 40096179, 58544007, 175241394, 508696777, 733975223, 739506865, 63101122, 660868076, 815425855, 553439443, 741662991, 49367310, 973353871, 736294270, 573625999, 143745089, 167239276, 299383102, 691299085, 308585450, 113098141, 342485849, 610543863, 386861278, 768309757, 367149525, 431876488, 155199268, 453006603, 839647272, 637890308, 916920232, 524915412, 893376600, 625749130, 987669124, 877942382, 708176307, 163331506, 844411659, 636495281, 381084681, 836225143, 729974134, 268402178, 622649171, 395847654, 801204711, 613592121, 38963756, 711407077, 635772023, 112423862, 608481177, 227299789, 264324762, 499526228, 593920388, 552608969, 250193284, 189675826, 851581719, 305132085, 364595305, 385995094, 541906033, 720286621, 846265824, 660604601, 563943647, 142319697, 489304840, 336206377, 875571355, 166225042, 863450759, 321918575, 739441737, 385359384, 438148633, 540649135, 949890102, 505526412, 220230922, 563877759, 592002549, 806625451, 181168378, 459373761, 217738991, 65103285, 934432451, 657638050, 438468108, 582302514, 567301915, 234851119, 377904102, 303827571, 4439966, 665885741, 393264566, 760126680, 993792681, 202067685, 220013635, 260253126, 17126522, 599289121, 286522304, 459392316, 392303278, 466967180, 168397669, 861944715, 586002736, 963080404, 165018139, 77427952, 399668067, 51565447, 831601194, 19374143, 221980898, 365447168, 953070310, 943440277, 39255069, 700518809, 565266721, 588521731, 392928183, 545733900, 37067529, 278300397, 365947218, 6414400, 17322264, 710992824, 938712028, 672659040, 390046505, 630681429, 855799997, 492270589, 710250378, 358252438, 902747750, 963508836, 184212592, 208187661, 622493648, 876961865, 190279506, 444931092, 3569175, 426657486, 521857654, 553241548, 912453445, 986283270, 411663500, 308519804, 714484290, 291860157, 902550831, 180218607, 936211190, 172163521, 125194202, 691828937, 825638546, 187602245, 885840895, 683826283, 928031406, 409512059, 779798711, 887948398, 317401364, 900813319, 100453837, 692534248, 220363263, 503959144, 650049882, 467929218, 17090900, 687598231, 282930285, 327684814, 718787869, 283522129, 508547076, 666664349, 483427660, 675148315, 559771911, 950674160, 305304092, 248285395, 20846614, 277863253, 80540330, 113553152, 479105288, 164243247, 711528688, 149515993, 61327079, 851292848, 613958905, 11822622, 279781806, 4678630, 542162722, 203409494, 439859533, 152669029, 536542770, 497359022, 340902631, 933938399, 931731480, 484999951, 177895770, 358157400, 952745828, 503469208, 299227383, 641598932, 698755356, 312496985, 926820703, 24415843, 522048737, 185409199, 754573385, 801093688, 311039048, 275638742, 734159497, 447299729, 467890320, 924539263, 585246723, 364037368, 587482678, 145386396, 578291396, 647802789, 718212635, 491798369, 699884659, 223265082, 114290775, 808657812, 914366379, 285083303, 633830080, 391323301, 317844762, 137910128, 7429141, 157169514, 553396773, 926951609, 407660907, 229914916, 424037404, 474239163, 135894910, 378560755, 431621856, 244496301, 408886082, 945790534, 143994822, 773243772, 784665997, 362944750, 98682425, 478578304, 136772375, 505509732, 361937893, 427394957, 563260755, 785897782, 394268122, 978402286, 872602058, 418918655, 620525200, 521745199, 273641193, 458654650, 153242581, 175385535, 737491509, 962774637, 64578567, 21809593, 280397988, 413964542, 251878004, 615720468, 358993063, 284589062, 270427074, 834280022, 1667835, 188729218, 606363219, 939840313, 151686391, 581105088, 807374800, 697366784, 834634790, 359724875, 20786639, 678237904, 650350580, 573539131, 757913914, 365119059, 165928424, 874006212, 798655700, 541045081, 337959908, 488762174, 591086912, 617240359, 899783908, 491605222, 772119427, 359591326, 350002738, 257632258, 966417521, 206887571, 696443034, 111278204, 166917297, 73854553, 172680019, 665494600, 632976158, 522167320, 793650033, 742275607, 870886325, 397284944, 723803107, 469315497, 872750341, 582366362, 241910306, 353221975, 463260500, 881109507, 12700500, 913640, 628635474, 305054978, 934325647, 562135430, 650292256, 682118248, 252113498, 929083330, 426136197, 729623682, 459776616, 642927591, 551617976, 213600611, 458374999, 366640695, 320649836, 836431204, 356274160, 439016711, 271513484, 57669468, 761676005, 46953832, 264371353, 517646572, 831585319, 282734509, 345134425, 847115765, 429363979, 927528575, 441424050, 162982009, 582053405, 337212788, 705211157, 603568638, 97459067, 953378280, 25312497, 734596284, 688505591, 851324149, 476896744, 990513270, 914231009, 356709206, 9278054, 408302009, 116508763, 371947152, 327254934, 82241609, 815473704, 143596533, 902266859, 839183299, 686883965, 977878133, 63228038, 95837940, 542544385, 202025370, 854343637, 825793945, 937278935, 208290561, 26974805, 677822455, 463277909, 116781879, 989468501, 632889397, 739206824, 664915879, 149955813, 164494161, 747275848, 936841443, 603515041, 536066120, 10421781, 167083599, 35412506, 33242408, 929066787, 35660746, 825964745, 607902800, 395003602, 8139386, 935735775, 28152108, 202403018, 769008167, 341234395, 577562075, 431018016, 99671317, 595015312, 251888544, 582933340, 79424393, 8788042, 745787096, 280692533, 473429334, 175912819, 513350572, 137878443, 798448076, 594792063, 846429834, 697773027, 818778652, 239656537, 795844325, 69307893, 212637005, 75173913, 196026865, 154086791, 426260476, 380781993, 367348334, 386244551, 979019491, 121723269, 289179090, 981481979, 838403266, 317804760, 978431305, 950888140, 997845673, 331729542, 971601254, 926816436, 782626720, 361075449, 237442275, 879591311, 13356060, 869446643, 334157967, 883555050, 851515175, 15079629, 736782271, 548480422, 249371393, 208874941, 599798492, 901145587, 52973619, 492114761, 385774916, 217316340, 696740397, 276889089, 152616198, 877758806, 549934384, 188455903, 642080798, 219991040, 715777999, 324484559, 807892431, 781860050, 272566717, 813749847, 117540227, 837760263, 646903740, 857892920, 829504824, 589670208, 368781825, 615757027, 949588867, 360461699, 72031325, 175071235, 393354655, 349895705, 267374205, 242204920, 711657173, 167596278, 534048617, 527841972, 539278104, 815988177, 881077964, 183174397, 314990768, 203521435, 75687153, 137483867, 539371622, 689403412, 341515902, 225654106, 395790815, 716285311, 388020625, 136865294, 794529970, 913532407, 432384515, 323235970, 117410198, 607063512, 111306202, 948501775, 253343278, 105270065, 329977329, 946314966, 377140068, 176906451, 454563089, 152453444, 525209700, 979993293, 697795660, 619981965, 72063258, 85691948, 267533130, 741186707, 622860633, 722619944, 293332405, 848161794, 828693988, 106851003, 915102470, 149375872, 449510186, 555687046, 906783505, 267980869, 14205151, 207369613, 225547270, 270254217, 974492995, 877655412, 523758970, 118926846, 383875423, 496333812, 902617734, 754108699, 512053625, 2035823, 358904331, 178407189, 129415016, 342355721, 738169600, 777916963, 395036161, 274616174, 839485442, 407126529, 906159071, 882883299, 828611228, 645665906, 458216734, 195112314, 175015070, 116139245, 183303699, 480343661, 804870296, 520428672, 559753721, 416246747, 359414214, 260247578, 717121252, 226905555, 980112034, 864360083, 584812408, 123589901, 893186020, 281301078, 299846521, 193467716, 33177185, 408979455, 922251965, 559373432, 113287777, 80633071, 504990024, 847140235, 607989342, 181157719, 26048543, 164041767, 380902168, 138201298, 557549945, 223731087, 269258919, 816638917, 885401511, 754565368, 436659607, 291066919, 145741757, 961277049, 380354473, 308183656, 342541957, 910061103, 418486209, 980576415, 35525516, 800014245, 161965776, 86078841, 893298894, 994979910, 157609178, 151394215, 548461989, 978690411, 38012077, 238930263, 511194983, 197747026, 232042700, 178802259, 916058108, 41556938, 721360653, 839961508, 252084545, 760390706, 758003621, 886766524, 828985735, 830062769, 656040165, 868860344, 51010246, 437516428, 517487845, 388208155, 595427375, 867967596, 204162909, 102896991, 525765314, 50219312, 420449105, 693356091, 473523505, 601239628, 353170848, 388864723, 999649892, 768389739, 533299773, 917155856, 174288340, 584527240, 747917015, 73150528, 627543555, 203775628, 209746035, 244612781, 876234706, 601531873, 999348736, 904760577, 895774028, 93357328, 609600389, 624753981, 478492283, 898338575, 114527986, 358948905, 893734356, 332479109, 461385452, 716952785, 395179355, 496664423, 794767583, 237628512, 640585324, 563471572, 437190996, 405506052, 895330092, 356389936, 583977718, 810304098, 746667083, 122459232, 243236230, 553774828, 959601913, 388345857, 929498248, 500463763, 378487467, 793079972, 942187788, 62933738, 958026540, 887678434, 636779266, 260494035, 804844177, 423036465, 662784359, 730793990, 38091930, 10535793, 615670302, 705970924, 783756237, 162614373, 94517383, 96023814, 214187766, 558384162, 733949455, 650184246, 459975260, 590075774, 884394385, 445727756, 148469720, 858559774, 98360516, 215252418, 573310952, 117066296, 969111462, 689609529, 161852448, 684784608, 906920449, 833658598, 536096596, 522244270, 459035476, 321299872, 205064247, 574647572, 119849120, 855899529, 669794822, 500864876, 612614967, 564615427, 619029242, 537581145, 450183856, 576549130, 952084169, 761362544, 174971814, 653749380, 355312683, 629732380, 118581486, 934854342, 669451054, 636154079, 946354387, 677968894, 577377799, 977654735, 926139226, 458957062, 462480882, 508306527, 301656194, 938212680, 596922786, 319475923, 168680404, 116673983, 833563711, 91963659, 432878428, 55308345, 729964953, 2605984, 36813072, 184224502, 368815443, 953443104, 146224318, 633089317, 929984544, 435541419, 191571073, 965089204, 964785890, 786750942, 788423018, 812012263, 446900207, 257591240, 147318376, 331457961, 129142666, 86903879, 542965331, 809006415, 750561917, 937919122, 700857591, 112244447, 140620668, 965212633, 66525560, 93023960, 538819316, 759995479, 143789329, 619055855, 809659547, 780591279, 440557650, 392792125, 936962496, 251662839, 765371250, 106631101, 733159304, 577683461, 814150046, 803319139, 223616288, 722765945, 986910645, 578947037, 567622869, 573934147, 298987415, 101799664, 202990837, 917549458, 254108356, 531312368, 824046762, 63994605, 222811644, 224641046, 653302890, 406824973, 445409041, 44036677, 798184805, 933786077, 669345801, 64449623, 93090855, 374164052, 986058386, 801223459, 895945248, 557702942, 918899187, 716273874, 503933920, 423160618, 464210086, 626190792, 538518171, 372870728, 146287741, 559899866, 251265478, 501736103, 428683569, 595248634, 531511572, 256041942, 750833885, 630519969, 475362729, 436898595, 796196298, 310802643, 703742491, 409926550, 2939558, 739065256, 277898786, 995480221, 655240668, 239856798, 659132153, 921705584, 463024316, 666058234, 462608969, 154775044, 785339768, 397038090, 22370043, 754575246, 933322081, 844110615, 913225990, 641707583, 34172023, 641666441, 41836341, 203552616, 277678799, 340912851, 279448145, 120808465, 919367532, 421807628, 459859159, 625083149, 359155808, 611385575, 458460908, 290078479, 527629716, 453086809, 915763266, 182926633, 289844778, 947386328, 807841971, 420093857, 646641937, 574831540, 570964383, 726152207, 690277460, 933465661, 626541763, 163765759, 438001581, 776569882, 909213947, 366143732, 669010183, 482753996, 879426765, 833536115, 890731412, 554900746, 204194929, 576795434, 440185543, 35744270, 760436040, 61562440, 547865427, 856423185, 215871414, 143543295, 631406986, 971194924, 687732015, 311390818, 947322125, 302837983, 364371797, 142280683, 650806693, 908934057, 121100915, 459352816, 382665644, 345388990, 786277373, 79776065, 217745070, 679864474, 473833777, 280683396, 426421582, 875587930, 952668025, 403809387, 188666232, 741381130, 585908261, 784460117, 150658051, 67525293, 797558573, 713845071, 5783057, 582058160, 281381108, 375770262, 381605541, 718805733, 959058704, 529710781, 758556495, 623147910, 265466475, 457372028, 815087375, 873375635, 389490230, 784527077, 351132088, 208493765, 603226446, 994485567, 187715850, 909635247, 481381078, 957321954, 651767830, 857500599, 191566654, 698065404, 83996915, 507463213, 386863835, 530807300, 428361531, 45557014, 851959510, 53911109, 947791015, 694574986, 589439344, 614333407, 496288070, 175482342, 523348990, 415301653, 266407009, 933363089, 579759363, 918364522, 557410228, 78567411, 38538050, 154327643, 469533142, 753589414, 777426760, 638826193, 825649620, 89907962, 728404907, 181665517, 641384427, 61170406, 755530815, 879667761, 441834414, 387070740, 443710331, 274651599, 628218557, 240929846, 195153231, 226397848, 326249576, 23008334, 983828753, 176143110, 682200570, 322975464, 563615797, 413647125, 347199757, 90527143, 609160732, 30202076, 729926884, 19018197, 443847009, 2056226, 732386855, 96255813, 465133430, 289170979, 903974771, 292253001, 192679053, 243360013, 134537096, 99766602, 807397287, 643739721, 981318126, 59186993, 693108285, 755467678, 261344437, 66051387, 20307871, 280451882, 587806027, 678313826, 821138298, 358931056, 341664076, 903050105, 369021547, 241913813, 4118166, 721260297, 91205646, 288345344, 660570684, 235891322, 543579682, 4574591, 968484657, 195947551, 429876265, 534859023, 929201296, 769585755, 294844596, 736368465, 769200996, 360024085, 932716010, 925847482, 25642136, 13680764, 65468278, 746767261, 433989579, 93961373, 252184113, 874095468, 86022185, 94250938, 929508844, 95203134, 174494517, 742674704, 884210820, 655534128, 739127169, 355958031, 765742297, 64566443, 131905826, 468070283, 297766841, 11954134, 247010347, 425273250, 595699621, 591653440, 634060401, 284193151, 192354634, 103895310, 660768230, 294360765, 217806469, 357771498, 801051808, 506714138, 319280032, 733166419, 909887961, 520667370, 766649218, 719950933, 280315603, 541141095, 579706092, 243414616, 748929330, 986590903, 409008601, 777891076, 331831488, 81154545, 707570872, 418533992, 534758843, 632807502, 306224007, 414611410, 905622216, 464951972, 186778778, 970150597, 909608250, 132105028, 907088217, 41639710, 192516857, 774051423, 747410011, 323761630, 748450652, 394721393, 760897688, 468511836, 507122275, 918754848, 703865949, 800175763, 435172395, 341290431, 101342456, 748245768, 357628033, 523720346, 987544969, 492241194, 41414152, 273741371, 483252554, 430016103, 365671135, 301722763, 559474692, 533429488, 875663781, 479611562, 450974072, 759225551, 468403998, 6521812, 372092875, 74709664, 868526845, 810076909, 121856922, 970252187, 282771224, 837836228, 439056374, 3880811, 641929188, 946505221, 507524099, 953597122, 993130855, 783045821, 761171969, 997613430, 867878176, 715554635, 573007551, 314869855, 467822883, 100323211, 775324382, 680008566, 189121313, 278776511, 853043797, 39462859, 136787748, 848028963, 306033020, 483415803, 170959775, 162738640, 956117496, 418002450, 59954806, 608633065, 347196192, 461226706, 344003735, 361189796, 876234813, 206212144, 117233385, 669359564, 372417294, 527054354, 650990463, 723960024, 116596886, 113452214, 286200780, 387886767, 59880710, 485440317, 322912340, 47325852, 247355627, 486828455, 84361535, 559240310, 967058751, 673618465, 679078576, 415418839, 966536252, 53992511, 697958506, 198880723, 899704260, 357616346, 626958112, 990420973, 876701418, 461981116, 571630774, 973765404, 299842216, 104127362, 730475716, 273642205, 817068488, 899314826, 594981751, 485684898, 417695333, 910543612, 747881162, 470167621, 392260127, 747283493, 403320921, 134481423, 969928513, 899264987, 94038928, 417442012, 408031966, 465112251, 160386835, 831376807, 293276751, 988700242, 466725027, 873489729, 579072801, 149946516, 163724037, 456322672, 329780659, 474589450, 574239082, 451558337, 439666456, 449107179, 391268438, 15378107, 59142136, 624500440, 88912597, 57590, 2340880, 830039812, 213489929, 883776600, 990317341, 657585505, 130820688, 42389883, 984618569, 739889356, 444884441, 180741677, 272794426, 870903008, 141024456, 403927404, 889440593, 657504583, 315968923, 480626847, 244230629, 723253906, 67824344, 903492054, 412952539, 976734405, 851039826, 294468295, 524175470, 874228948, 570856082, 5821163, 532220796, 334279357, 418823228, 638453078, 818115823, 843558384, 509738033, 276231089, 873240306, 476754165, 717542958, 29039022, 804651164, 189919496, 399697451, 449195615, 707243334, 297108551, 464799847, 584793814, 189382022, 282144925, 375447073, 913848802, 276292013, 365907168, 59249348, 709490243, 319464495, 568655550, 866950408, 394762430, 384605490, 440322028, 310100292, 129256031, 681280869, 374519038, 176416773, 394252460, 104418032, 183110314, 705457547, 46279071, 403432343, 945172208, 153183017, 471076577, 113468032, 998384383, 199300068, 346138841, 501744520, 579170544, 183170513, 741636466, 570974030, 646846037, 965563672, 390475218, 603332696, 959642349, 388640972, 673501404, 252424987, 774886317, 436508230, 547198581, 630663558, 539390002, 276548662, 764678873, 330297075, 810869722, 667036876, 196016345, 673604701, 289892817, 822443132, 462926107, 563690342, 924927781, 858917043, 315705387, 297277044, 140826617, 958633323, 873065496, 479163047, 309372141, 174329270, 179556506, 231837172, 818251832, 489211123, 164483826, 957362079, 209021248, 824885370, 309830268, 930574471, 774930879, 816051074, 619730884, 756895414, 429154887, 168819168, 930154263, 329288330, 451634211, 670730925, 244266726, 39960795, 93410513, 270744714, 116418141, 911836100, 318968261, 773421685, 885685703, 822754732, 942088470, 15316835, 641847187, 947355448, 583831963, 917387773, 199224403, 708010195, 269890790, 257980063, 489849725, 781834370, 959402111, 64261592, 539156716, 329591700, 765948862, 454387921, 49790256, 929793378, 821378100, 275429269, 260458794, 415215944, 518300587, 812501519, 983886064, 415519639, 618553012, 985300973, 433575857, 846449539, 504279677, 71999581, 79497984, 520384089, 810983637, 661982946, 788828540, 922632176, 955510998, 202530703, 842129136, 95439172, 553355634, 678548001, 353074885, 606288037, 154522689, 960733149, 617499942, 220251619, 978914035, 452971147, 609829831, 460420845, 440256941, 153268048, 995006238, 147067928, 296685253, 20740237, 819522869, 896118665, 499135106, 580422680, 124250240, 882392918, 819093948, 639835435, 967130626, 809686511, 278510763, 307959549, 404042970, 926480407, 115070218, 965952901, 167261692, 631299240, 316834325, 754861831, 390785645, 650450786, 817132080, 839056643, 508793754, 630449502, 648130500, 985481079, 510872585, 429283011, 559644204, 59325590, 961959683, 927882081, 167630174, 513882143, 405903801, 179986241, 67578135, 520523988, 854815020, 868238308, 273380198, 456034186, 132824281, 321421291, 926821681, 315892962, 471235178, 130910484, 512058539, 706739395, 303322589, 572964301, 346429827, 31972094, 227825472, 747130221, 944334549, 213920275, 119195210, 401493048, 976893884, 354325145, 528111544, 113457236, 344380490, 586885117, 620426662, 825752344, 621733659, 465147091, 682127714, 996073062, 992509729, 700111099, 329837670, 665409931, 261877882, 103229924, 157525505, 321142571, 1743443, 533346538, 58554077, 841224345, 942660261, 669434041, 154228126, 719920908, 117811143, 160842164, 770717782, 193741542, 298331200, 5579052, 712675451, 498066554, 238732947, 57659856, 793517913, 440983281, 576751893, 88785877, 361876236, 960919284, 990460245, 570087442, 478313038, 690935170, 257858751, 730031327, 789298602, 939264204, 491415498, 732031332, 210132738, 943206713, 815422970, 363716170, 804017683, 276182729, 351670559, 36852020, 137040869, 780781135, 66942945, 623255666, 444400708, 624336273, 645483063, 268396691, 733790611, 332296076, 698721063, 519437232, 5578138, 923786280, 988683897, 528623377, 392667737, 480580819, 561051567, 591522730, 594350572, 683609751, 858585056, 309802206, 972675842, 804401192, 912702297, 92323968, 735921798, 287314381, 413991125, 271148010, 214065982, 295801342, 907634509, 161677694, 469629957, 988573788, 251733456, 515938883, 46158897, 613013026, 19991775, 471480999, 959516357, 12111, 225772357, 851809410, 97348052, 372358337, 638481331, 574812523, 528603435, 674848173, 550366392, 549002209, 713998133, 860248604, 53068171, 367279525, 36243698, 370353233, 251879896, 313053532, 116759955, 336555716, 451806096, 92976171, 814334672, 459194315, 418480317, 2131079, 538208400, 148045934, 165419803, 478321886, 157715472, 475938005, 734396643, 383099243, 803794476, 127039413, 244968686, 287375482, 372431733, 350638209, 223404498, 454382832, 225923070, 545458048, 259007639, 581097461, 920681557, 839089373, 637715700, 56887642, 151919898, 160297258, 140717005, 624736957, 107991796, 526462803, 90298517, 503585128, 690091124, 754231770, 523231832, 206649172, 564941056, 506277661, 768850522, 185978425, 291758351, 664210693, 866287836, 577045096, 359074327, 834468489, 654184910, 254021444, 368287059, 536585521, 79392151, 560980748, 591127714, 747232714, 899506883, 295810572, 136476996, 710190841, 759314643, 506371530, 105674655, 89895451, 88596497, 605963921, 141763295, 777127387, 347771362, 604495391, 17465870, 509723834, 5693519, 478914628, 443486006, 184035843, 371645964, 938734477, 892828644, 55083847, 340526933, 260141635, 869052712, 544560343, 794270526, 505045524, 349638085, 742551321, 777940600, 309261621, 143974323, 14373902, 903453412, 277738457, 320310127, 756238714, 92238385, 239595309, 688389827, 910692012, 437548203, 91223882, 602676471, 68896122, 935451613, 605097871, 709906823, 8321578, 974107231, 23652705, 716558614, 410268443, 461311885, 562384223, 800629240, 492177551, 602798632, 187588399, 834334345, 256200822, 917948006, 992183959, 527989425, 886907299, 966342503, 294987702, 240581881, 443949525, 467191684, 608294252, 768283158, 831068397, 685613679, 933531715, 720271755, 553897054, 284835506, 785178967, 289254792, 678025564, 632334391, 611788889, 255248179, 455737774, 619829544, 920853809, 397226154, 935781592, 500897629, 499761898, 184712953, 772820539, 507777632, 272886358, 852826592, 347229688, 527092521, 537101187, 409475529, 77106305, 855371923, 803888788, 841044884, 970533417, 586044321, 60412976, 688624205, 440254046, 36432561, 212192315, 940279027, 980885613, 630545483, 243159977, 203296086, 450301836, 788716721, 202307591, 144920305, 928926012, 174437871, 843063202, 771880424, 659551233, 392639384, 446261477, 20493139, 610999415, 603521091, 957367991, 323107397, 286689544, 106277618, 900029434, 775305681, 201593255, 860773326, 987600182, 925787219, 240420351, 751609327, 184324660, 542874372, 2107969, 916967980, 997958522, 789983692, 393446902, 904608295, 213211698, 173356742, 253391332, 352280739, 426436037, 53540533, 442547789, 525703474, 756125819, 63194928, 698391269, 108559310, 435652345, 355001426, 41273816, 791101485, 838694713, 712825376, 465718444, 360808499, 397671621, 654762415, 788066955, 658928058, 346736486, 2779510, 254767325, 803382844, 831000873, 57266968, 646661502, 592554263, 990947115, 642653270, 861382669, 216559223, 171671015, 385957835, 930412047, 560391417, 615409768, 991659808, 447841529, 896091106, 935477310, 730129776, 798194374, 162804566, 143395916, 64296990, 830544464, 407197530, 231886328, 937275299, 131934288, 484787003, 140151847, 166614690, 848671508, 492655558, 789288758, 627650265, 746819352, 355256944, 930536531, 745097520, 767435875, 364373877, 492538616, 809805408, 45183561, 549169700, 269466721, 986947203, 489970123, 197356464, 499051016, 24674670, 860055084, 457118438, 170347301, 775013168, 14978819, 635327186, 633191418, 514415140, 858457149, 192913692, 221618459, 197021616, 348116174, 712468926, 532760326, 729504768, 470712881, 645775366, 443508461, 37749468, 240602966, 286736908, 313051775, 165655704, 896265919, 541013708, 740026149, 671740069, 92033089, 51157398, 278508852, 911370483, 986017875, 812473377, 533151638, 558717881, 256547534, 889324730, 888860110, 823691387, 209782655, 795425077, 15201544, 234403079, 928612033, 150462803, 949788183, 213020807, 251043106, 812056186, 408225739, 199228907, 814285001, 165572729, 423825323, 795118983, 60775129, 144536382, 496201265, 785460398, 159429688, 253236979, 810771709, 692859021, 620169388, 136780808, 992975721, 357401124, 135523945, 161523422, 943363557, 164411852, 609858429, 322590766, 322572606, 575557640, 758153868, 950650399, 778946887, 519024304, 804098556, 105308645, 66326842, 865634145, 276478087, 332178038, 839043654, 776815127, 531803683, 30197552, 4733341, 206084039, 84349421, 671419341, 627632440, 40596399, 205402973, 64220425, 605460451, 773111367, 665062111, 803313606, 675761434, 462476666, 668677128, 838817280, 310064952, 692322475, 832823055, 524446833, 829964803, 439665594, 253335656, 91258666, 637443303, 838241953, 581252926, 312230397, 342685364, 599886241, 818299269, 958476892, 839092154, 967377194, 54481904, 59749337, 259102742, 202374100, 291749931, 493971424, 421998158, 542946128, 894317831, 627886609, 976457997, 561978598, 126358261, 977602371, 773512722, 113935890, 584931163, 603598373, 874831102, 433222750, 565724217, 805526294, 798654991, 546067626, 50198304, 294890454, 99739515, 23864734, 496641198, 805630955, 634110784, 542440456, 101633115, 215339812, 930870018, 151579248, 756148646, 473072316, 930999322, 660107471, 140048095, 173013841, 976270308, 573676436, 727042818, 502377578, 680396608, 290918301, 715683520, 777117845, 680044050, 382672006, 934731983, 787692165, 514305736, 590666812, 811938833, 673814370, 212531288, 855947946, 400892863, 860982269, 560539452, 610558083, 689706994, 11065968, 34850853, 189524688, 608466157, 705005313, 846985145, 21085611, 167857162, 401535941, 169656148, 932474146, 247339048, 282978868, 888953932, 997117021, 435573028, 722729797, 138340050, 45101487, 305876689, 530544258, 901030171, 155760493, 140813652, 105610367, 441283158, 631309110, 100762530, 83922353, 519516970, 666137615, 663935246, 814974216, 89493439, 880894528, 703716872, 899271297, 166055648, 427353845, 182967947, 933418977, 384028543, 899907006, 929161346, 301784906, 156398670, 922564900, 693022448, 331928188, 538764568, 184561541, 125676952, 371646546, 291848249, 600512202, 626232135, 691494899, 819640652, 76609009, 639541196, 315638309, 242411879, 297262863, 165369718, 946861913, 448305936, 844971381, 863290159, 691059603, 523892430, 879593614, 635390790, 761196792, 189399583, 804448137, 884004874, 781272706, 734518978, 697195676, 287363955, 786258053, 891378710, 104561761, 840960650, 629962440, 915382511, 571421284, 298263132, 132930682, 843677520, 881117954, 736290223, 862516117, 710804977, 392314680, 906929975, 539068678, 174499499, 266073516, 181317361, 365255597, 560037828, 409207301, 477606739, 993796749, 241611882, 856364640, 735199239, 745448574, 184870696, 983137623, 98172885, 361261195, 961632263, 828261049, 866948636, 744670093, 279800186, 546742524, 884576854, 877934671, 441343549, 927120446, 256470090, 51630490, 538010666, 550799515, 534733562, 442359443, 33046028, 706948022, 160351982, 235110166, 507006328, 857823330, 909637018, 688584158, 156506694, 720108500, 2905273, 821709794, 802591565, 412109676, 618512619, 221268775, 861656990, 487850392, 600476115, 394798851, 57829760, 220126539, 841403840, 751733045, 518761692, 255705758, 959187512, 518555005, 500739274, 621912591, 576481533, 882931145, 121981446, 184691600, 314801935, 56239966, 278843237, 686721031, 596754421, 392276229, 659442104, 342488874, 751629021, 912809296, 362853029, 765139193, 29093597, 694445085, 45292008, 741541926, 923335886, 470128010, 920324460, 833652387, 355929619, 513549651, 454639317, 105897314, 307625082, 607778694, 403398953, 278140806, 91477460, 92940549, 385760883, 991995248, 673195982, 302151275, 281942777, 325512511, 175461141, 798047189, 360012603, 418516211, 827046756, 202043946, 884742615, 442268665, 722841600, 806825177, 451001580, 88852632, 997132917, 429814447, 521546930, 107093219, 695654874, 916167262, 943333559, 454839021, 6389231, 533042776, 890420340, 136518384, 223863073, 58481928, 813749198, 572714968, 852432903, 598435021, 800723803, 483873769, 531096436, 926324258, 285885525, 424399341, 99874681, 322043683, 703254314, 800226998, 197364278, 980638105, 308796195, 871476504, 284680599, 162499377, 109118677, 345823379, 184353920, 38657888, 960419656, 734667033, 155477357, 394077271, 236519199, 191710181, 504133000, 604757055, 275052993, 188303908, 79219365, 716579612, 902195544, 127857085, 717361919, 857431657, 793250847, 445515618, 83823565, 170954940, 60856912, 633483727, 829942123, 620544538, 965720544, 459481009, 428601061, 897424519, 382330885, 715790086, 23145506, 547911734, 111408861, 262036290, 663785936, 58886610, 975642913, 853974938, 585106612, 787812198, 224964435, 633164705, 510665298, 542577494, 681562487, 426310018, 230668096, 359911234, 912593284, 371598482, 709019792, 710630445, 695762257, 322052536, 791747461, 904864119, 606421313, 969191161, 504092236, 603055605, 165504188, 936565503, 418483584, 276025732, 409801302, 323511606, 508012180, 384873201, 214413291, 905446837, 499987674, 185347954, 550556085, 953996339, 495259823, 805265214, 787505333, 411989403, 710915668, 683889040, 772431338, 59121259, 107304994, 776090448, 201635028, 783952968, 750389114, 107498129, 101490356, 221011666, 262831289, 564997379, 579225251, 719146020, 242960704, 693703497, 547512679, 431435745, 393720258, 634429038, 221213062, 722791940, 684503525, 309996299, 572794510, 795689484, 39292580, 77954271, 439495135, 287996790, 430422067, 598188778, 483931014, 960567333, 24807147, 560626188, 471944087, 534052865, 350315260, 961905863, 284431129, 390315874, 30834808, 587307193, 158852650, 568970797, 251657107, 298557619, 311064204, 675732302, 904735663, 271436425, 872951302, 136218271, 22297482, 452724522, 91627036, 149020233, 459412537, 131007150, 352914759, 611713639, 681902323, 961290185, 464160783, 838090961, 62746879, 751129301, 865788812, 211285349, 403723623, 598943083, 552657833, 263730609, 556429072, 397025352, 676852120, 517492550, 82575906, 384977981, 696654919, 218817398, 580505358, 812138866, 348241788, 841773185, 99132567, 506745272, 86957992, 425357199, 900541830, 406492737, 459354069, 849519310, 656058151, 900646995, 494234216, 538486840, 997748649, 268469623, 983002776, 350341267, 839125001, 89411448, 729149366, 366815759, 78552347, 62455975, 922162137, 253841883, 615886150, 243006011, 559644279, 442882766, 276302744, 90880780, 257532147, 357322419, 776104634, 978632357, 728524339, 532817734, 807928501, 468080200, 442262852, 362507575, 610040090, 344684470, 278300201, 170005533, 565100686, 706546763, 560926000, 882779424, 817519543, 417311799, 569154893, 343393094, 939548781, 380310475, 878640521, 146336975, 477938234, 605705346, 28859660, 212352118, 855630884, 716040422, 732579072, 998314636, 848697746, 479344444, 838622719, 891754795, 740572601, 348655665, 498757165, 341505748, 224267940, 356479947, 623798082, 865480073, 212178921, 175503891, 789042513, 381537538, 363067679, 716949794, 68005454, 194862590, 461449233, 664778179, 449453637, 56476486, 85808649, 815776673, 247062801, 528829087, 848436456, 67384527, 611583161, 624724926, 277545490, 953039539, 492506686, 494492145, 8860328, 290502236, 435238358, 534685687, 945850741, 371318539, 937878947, 950272166, 10609133, 777636288, 79729177, 122837595, 899798452, 332423954, 126384097, 597920660, 574506916, 335509470, 555002315, 114318138, 983244624, 247722753, 466409213, 223319027, 867881428, 670256192, 85421518, 227014684, 25685829, 377193211, 852205601, 964004090, 113382815, 974754018, 723017683, 60062848, 119102364, 145331372, 59447064, 964351485, 999277401, 52540125, 91880450, 759767624, 220506016, 815045299, 444998604, 710907196, 393033423, 555093270, 152216668, 714807924, 826179451, 319226063, 368728976, 622377682, 556607721, 676820315, 531176188, 720077552, 416457459, 279803298, 84548877, 985898378, 497163114, 431885598, 410048981, 826661877, 671235678, 452211005, 356557567, 398256876, 452358517, 529454370, 376259113, 876513783, 399406680, 947028339, 560585614, 231675864, 787996051, 814859008, 112770908, 978115001, 692864949, 701312069, 337815152, 18000932, 798558286, 392578603, 906499101, 217852164, 909301913, 726200507, 907707161, 868281328, 842596474, 222409242, 343394322, 900346546, 313594322, 386667313, 830978190, 287409938, 3098673, 548312055, 886586086, 710457184, 518829989, 340902933, 99571812, 353475286, 756230038, 143407665, 842188681, 472722426, 735167436, 105900646, 225473947, 184836273, 231567463, 143549106, 528843879, 220779456, 561082079, 14486797, 195496757, 787955775, 349857789, 497769649, 221109097, 153033889, 765900640, 800795899, 720334380, 593086441, 299123651, 264264733, 30028798, 25932878, 56542218, 327188354, 988533890, 268347021, 353301456, 140687090, 70802945, 600895709, 612660996, 934373948, 563192265, 973135364, 903836959, 841752471, 424411686, 514152049, 555560763, 923200844, 717654440, 889239643, 597268391, 941570369, 884908498, 493516525, 651696155, 931881847, 88825327, 924534843, 954712480, 782383869, 776418079, 635970376, 416424385, 456801944, 171332983, 335852171, 1974843, 57207539, 597540013, 987043640, 104358915, 879646156, 936324813, 369884474, 503370247, 492664431, 902801686, 638582850, 964463518, 669538521, 254102655, 61675092, 713236791, 287406961, 437380131, 741675477, 803834099, 594069915, 379914801, 493642810, 948365835, 512801290, 613024695, 637654124, 746263584, 21636373, 750548999, 677258087, 95160309, 47937107, 948732884, 810907561, 652293929, 115181490, 278104058, 622035764, 952340815, 725223263, 158180700, 143047073, 619492773, 892435783, 134454712, 508681246, 297283344, 950567342, 773216843, 62198193, 285510042, 665302949, 187377084, 77586670, 946276215, 489964974, 765306453, 282153951, 81831097, 128753776, 890498538, 239092567, 348340235, 392159239, 190690351, 896030777, 352961817, 705451192, 251551241, 822998241, 218140885, 993322242, 802944428, 409236111, 531913867, 332217458, 654545309, 192376351, 204238431, 247389792, 400564233, 195573138, 506741256, 184503187, 671541156, 259947397, 469221529, 744537640, 864210356, 681697799, 375079249, 890032230, 843750071, 287024743, 621361961, 325920039, 820435832, 658424432, 696027407, 477242973, 527491520, 355773000, 882092445, 190076220, 30195682, 583167954, 424690510, 451732221, 130512938, 449791071, 796273129, 875934888, 198865960, 591716659, 517918480, 294201687, 949821777, 520926274, 47110037, 892145568, 434634513, 95331204, 591542299, 9528892, 322213439, 37233537, 724517351, 577600805, 641241332, 298249715, 920599699, 397525373, 741315328, 438305861, 348181438, 167847360, 821388347, 808403715, 236902433, 301024448, 707896863, 95685570, 859319259, 795929248, 502091326, 31925446, 587062673, 678744209, 431220823, 800390380, 68782010, 171623313, 753876846, 218540126, 9086118, 173725297, 88735181, 531225302, 87977229, 85125724, 242017975, 547722436, 989145460, 176154815, 891998570, 684628122, 402554555, 575925888, 972333455, 889711947, 449297481, 798409841, 749103825, 439594240, 729056591, 489426544, 352390670, 537625628, 715378614, 577932414, 830642439, 304145900, 338039319, 338771478, 254610620, 602884903, 756176215, 358548426, 906538330, 925944434, 371021446, 259535810, 759191334, 669194756, 561203862, 692018279, 654322158, 217601691, 676892159, 157454889, 875414255, 887135634, 520957846, 288500295, 731568314, 802351122, 20533988, 825447292, 670111270, 139472969, 976846130, 307111806, 143694009, 996397715, 681262136, 867271616, 369536480, 509725225, 387320638, 897135434, 882831777, 119653512, 949658995, 586433554, 843766815, 456848318, 250124905, 583295748, 920479916, 371789412, 545943408, 401317241, 408923376, 596313025, 475237872, 71314579, 972760027, 678038903, 974523166, 369335229, 22622088, 982525373, 893607550, 517561485, 359806128, 274617587, 826160213, 368101759, 927956351, 712200781, 512059093, 109490437, 654420860, 404973788, 776877332, 28508143, 957692374, 63542965, 208534222, 196813776, 554917760, 101631102, 278606039, 161090202, 558420375, 744877441, 822278838, 342179515, 289070978, 147303154, 689214364, 717783717, 787148685, 418946061, 948006239, 107439739, 915478828, 665988350, 917375491, 980085347, 710719311, 670244414, 959034140, 651516882, 524873546, 398721413, 232014060, 985418833, 614939714, 686971707, 952706599, 839597714, 231971992, 989245900, 872303269, 682678605, 910729604, 967110033, 447174638, 584545084, 447057023, 803654431, 675155385, 241590513, 939576363, 557370860, 912305120, 335940907, 677201468, 386526883, 599113016, 248184520, 571993757, 613233952, 576341049, 194098652, 92071209, 359679997, 493274959, 361099977, 184174270, 898090252, 291500633, 445857769, 117237528, 509040878, 900783542, 25535441, 347317710, 471658678, 540347377, 858579886, 797711223, 16426315, 455132645, 200288070, 423889031, 71045107, 49766711, 762632846, 285773505, 369459003, 693911129, 311764732, 123372707, 295844016, 530721977, 738050559, 79855917, 435544503, 602936002, 778556811, 994327894, 892404743, 648336543, 999443140, 123377249, 931418432, 804920793, 844051013, 849639015, 493614654, 182005993, 32013189, 530737123, 627060430, 286754841, 936157868, 588560152, 221591223, 917172707, 613742466, 417256379, 742830135, 420055838, 685672141, 231519692, 584682837, 27050586, 260642711, 986202629, 267228142, 465239277, 615239487, 488194545, 926520755, 28524111, 869962700, 666981317, 373440980, 429591093, 228822577, 761097195, 199223478, 842176488, 279773666, 588854934, 741614636, 753200198, 254639383, 974911470, 411043464, 3989295, 171369686, 458735648, 773608976, 175763474, 92988845, 688866385, 283213556, 157243148, 48727232, 844406224, 857675016, 219866766, 66783607, 276573639, 275552115, 948573835, 797588179, 434412287, 385559080, 784254528, 460491681, 649498200, 20790755, 773830274, 877796450, 766622290, 593626130, 912140605, 231801639, 986829704, 550132518, 38824634, 512449243, 75845938, 787473021, 91483460, 143376550, 224931378, 423280636, 64474622, 222918233, 467536615, 868315479, 975006321, 207048759, 403218441, 803968307, 132106951, 102750885, 763629600, 777055455, 99597750, 704398913, 389687242, 198780432, 562146070, 763913022, 119583361, 790735437, 588679701, 733666446, 700369089, 393513705, 629375352, 960764372, 402346215, 963992942, 707953246, 350438637, 340276563, 640779810, 887784297, 367312321, 787857573, 547244472, 818786835, 693617295, 881894928, 220067242, 861029356, 37251622, 326849886, 702522883, 184533999, 191080389, 178189482, 92785744, 923091969, 316136000, 801913292, 972131797, 978697135, 614945217, 409368891, 908282032, 42602728, 284024984, 847132034, 976363091, 594320831, 677263278, 966621809, 726841903, 367325902, 442536052, 758417275, 706326928, 589160355, 421479060, 30113673, 647417181, 923031611, 720301477, 92646699, 849283914, 938903264, 984680650, 134452439, 735638748, 142341777, 430634029, 745601656, 5770607, 128395023, 417738645, 812401695, 511802566, 459298765, 424001100, 581529534, 678217823, 198681441, 592534220, 981914093, 405069272, 145506677, 3632092, 985965279, 271872576, 689035001, 26711338, 459796105, 834249537, 690475701, 247329244, 335270412, 751586225, 706056882, 943796646, 847265442, 161386259, 509461595, 681721668, 946924169, 576821184, 929667269, 88990986, 927747019, 614490507, 106856748, 740918225, 861018704, 271139599, 437209127, 82555355, 570963597, 993928641, 530906595, 397749751, 792848367, 766568589, 450629727, 224767004, 76083764, 227429419, 511768720, 126920059, 208724388, 60174118, 55371973, 114436328, 553400181, 957066613, 160861498, 627381248, 458689657, 296831691, 158622247, 993476588, 924395567, 389101850, 811714307, 307972195, 329010962, 928842462, 976929314, 84340481, 140126627, 13244278, 908147370, 282001816, 228606203, 175010083, 249010413, 392603460, 500346211, 334943800, 743742189, 515419973, 376739163, 330777288, 511316408, 449759706, 736020166, 364379672, 63190296, 981967388, 587330850, 589165762, 76614795, 298341043, 746495085, 744579079, 677565551, 37186257, 588996503, 805938133, 406097182, 88340783, 383747110, 471339172, 472073334, 870671253, 417151971, 965653399, 142538103, 321045537, 84179974, 111235617, 559536202, 541771568, 825908451, 18634353, 298382969, 586842017, 561030401, 435683332, 529124432, 424372972, 683325454, 62747717, 368411521, 847908872, 734677066, 138625601, 968111824, 362604888, 330156339, 377021987, 114831902, 435293889, 960313635, 370879461, 214691350, 773599890, 850434833, 104105978, 341710088, 768074339, 294885324, 865172903, 862208833, 581243647, 960447478, 738865305, 908357803, 318367244, 660279634, 2993817, 484258211, 503943585, 975184869, 728853213, 921202606, 896064616, 703932666, 788173429, 456077595, 499694074, 699301854, 722427053, 149269748, 683315945, 563775364, 52061621, 50953404, 802104722, 727425560, 56878662, 346385367, 708346539, 816856421, 999259886, 830184067, 819841159, 695577498, 392227217, 185624042, 176920305, 28405167, 173066508, 442482096, 104810077, 110892211, 354910883, 103948045, 110481945, 713721430, 686914903, 714892646, 495112408, 56579543, 714674240, 579662160, 640615529, 441490254, 732420994, 364893145, 821301831, 353570820, 253567246, 942568204, 499065116, 386937101, 955608816, 748327452, 839543635, 290590228, 747469238, 675252591, 680934682, 24601096, 986454927, 265085084, 879065144, 76186231, 309187308, 495285503, 200495578, 155015484, 135465105, 128262928, 335079402, 87479359, 118565457, 890119315, 55510978, 211128513, 41615251, 648025428, 19633676, 983429138, 257954699, 818660108, 468555063, 684911651, 645868377, 844930085, 425903804, 119663636, 419808931, 495072422, 863563609, 248439566, 923980141, 65153816, 68309945, 658123263, 554701962, 460990616, 241777215, 88191341, 766974437, 704880522, 197577893, 10291639, 695761939, 847943642, 842573361, 525906757, 442633984, 185359857, 264754118, 489248420, 268367859, 700400622, 617109535, 171439003, 532485397, 408781778, 189954090, 483292688, 561606367, 896439414, 645275306, 204247367, 584736526, 394925280, 736406924, 851092538, 845453271, 740663636, 578545993, 182035762, 974533153, 213812248, 294663037, 83485536, 948897848, 39607378, 890689909, 830270433, 795691355, 83103023, 609131839, 103124315, 180923626, 641505107, 400009525, 489808373, 251154317, 833322874, 111577321, 580796587, 771889288, 684477107, 252556254, 704655042, 544990410, 852776408, 459111616, 274543270, 99149936, 998020472, 646957493, 388954144, 700918862, 515965322, 57765445, 985412021, 17852875, 485819126, 500038181, 690122270, 183315034, 15638536, 757160869, 600578379, 740603447, 930148206, 245243807, 780464089, 379204189, 373490993, 610478664, 122985287, 959493758, 27116996, 751203948, 732345762, 480723478, 422239648, 310270377, 948200469, 102698335, 588865977, 107658807, 325101836, 763648876, 679976475, 643664496, 622974389, 861448889, 973546317, 691315135, 884059821, 131859027, 668774289, 172535088, 202508296, 321053099, 166919027, 171552941, 150221486, 826147217, 890779117, 693036460, 103452310, 103080717, 786869236, 774378715, 924117051, 431160, 236829489, 537193790, 836657883, 471832082, 244981839, 922866236, 359515422, 178379727, 453666351, 388210150, 251733914, 739477389, 480701591, 690611422, 845749432, 974237208, 830649539, 892826033, 318719211, 255794087, 8542743, 304614138, 726518994, 373788931, 974824405, 743835976, 680280834, 154046180, 138266699, 2765959, 395571037, 239833282, 108312102, 93448015, 961245990, 688306215, 871434609, 318548234, 460304278, 168799542, 713206254, 990549476, 370373683, 198335810, 181111418, 229746112, 770994459, 283851034, 923677787, 662870722, 688068159, 350424386, 483834274, 343976709, 417280890, 980803329, 559085965, 893287737, 870250221, 870391406, 927987867, 611340522, 997605464, 315567728, 695101057, 159357043, 791049654, 276628156, 712739920, 407774645, 524486978, 469796296, 541830952, 294488421, 431846353, 691649513, 843040161, 700978250, 432213907, 124091995, 363754447, 833271800, 979460710, 43312655, 360034718, 443626213, 576738632, 181105035, 188668998, 335419443, 301035680, 266354637, 281649518, 884141275, 163397097, 467237254, 916886000, 534173730, 238946663, 568308448, 639110220, 621127034, 313199134, 759242429, 850235777, 421964863, 951921684, 887699516, 358173638, 53026916, 813430739, 665366197, 781590862, 724768560, 870080364, 592362969, 518929296, 257704366, 895545943, 245317372, 25917255, 634365770, 128739159, 491453742, 769440334, 641188742, 473521782, 845336148, 728636767, 431279475, 246753639, 797687979, 127652757, 566224930, 519573444, 646300306, 374690240, 545902332, 792688589, 322914405, 759415631, 311057936, 763854175, 164011704, 778552779, 105359898, 977059881, 807804455, 436064259, 163963140, 216171844, 892779331, 539869707, 777510542, 725215569, 312581809, 528525533, 446104950, 235190480, 776285262, 996274378, 906075685, 986986711, 571411616, 623502187, 283646376, 996236571, 834206081, 413465777, 241956671, 670839837, 304725782, 592519188, 55315318, 24530518, 926930864, 7817094, 284053758, 865309298, 877687861, 417767746, 981930508, 204271123, 804750146, 481199057, 775516580, 948047092, 952497411, 463351483, 38498878, 903688633, 116378456, 799491525, 330082150, 716563263, 311406019, 868889238, 3814948, 144103887, 977154497, 71859078, 962328933, 442543027, 656967095, 115139059, 400197973, 97861210, 869684411, 532229739, 837291831, 537772329, 445847543, 64725927, 893703203, 942515151, 438958014, 992117674, 667215270, 114410249, 895581920, 608084901, 865493082, 387249720, 788522708, 462149785, 609615992, 334580020, 492319262, 287657206, 578619285, 381041586, 409270561, 775107983, 246359774, 137425118, 987338996, 865768196, 940230590, 684433830, 344834828, 689095835, 319150084, 246431488, 38273747, 696390047, 453718561, 59773631, 670743134, 225257774, 455122638, 437853356, 387947963, 8017627, 844160252, 484013424, 807289888, 215654807, 331626673, 81520405, 919840531, 564787131, 627597459, 925943440, 84989038, 73405511, 657027342, 690496305, 956537332, 548681002, 57563937, 684642341, 268638738, 78175307, 427854870, 837830957, 887530319, 10681834, 368859999, 173033785, 478681249, 620866211, 605657654, 576092168, 884281300, 50931232, 93496263, 534703950, 796995342, 329394314, 162168479, 533515516, 461761060, 821440211, 786750125, 47699711, 740033985, 266906687, 264892306, 935244076, 398908407, 277363227, 673778389, 919133696, 317649311, 905245075, 88137821, 457967537, 666232772, 329478978, 160989661, 127137708, 3451334, 934956479, 1590074, 531898485, 986550273, 704542401, 611580482, 152832392, 106119052, 367600326, 617872796, 956568320, 503750870, 783056630, 633626459, 280591451, 506169979, 645362998, 75076032, 602949416, 26578011, 45873942, 15784880, 489516989, 990472392, 826100325, 241492975, 699128284, 82705347, 220086251, 43471696, 567070432, 42814933, 492460693, 725200706, 825416646, 888472237, 539118715, 315970344, 825268857, 762712770, 975642946, 367419772, 270700330, 246174809, 5571193, 457276187, 173712989, 624695810, 572948814, 859982821, 251291314, 597394351, 264014738, 679132832, 165787755, 859177005, 326689375, 10542783, 974535283, 888557381, 957367625, 671459857, 792726345, 409985431, 31535924, 4353523, 487995171, 407528357, 738561336, 844473757, 293959920, 596362642, 564206453, 994931890, 448662958, 495160983, 747174370, 335724957, 393881317, 591647815, 399382707, 330189207, 256686347, 239380416, 13970503, 83086391, 770517577, 735157685, 28602417, 820242159, 964991393, 394542477, 62404280, 736263531, 124502058, 654433456, 827511368, 340549921, 591000029, 996249458, 647651148, 361597668, 645220133, 873372929, 165207457, 60014328, 308788027, 80119268, 343630727, 451879617, 949704403, 343818468, 557780468, 105147136, 629419695, 241380493, 417187963, 679236208, 381717709, 357960194, 189811448, 966606384, 47091449, 453465896, 278075572, 712874926, 946381891, 804470503, 418528314, 406702360, 710928730, 327556200, 731313558, 996011998, 805833426, 394134232, 330103921, 956532385, 272248857, 302620491, 543166879, 726903398, 472655624, 285125000, 738113274, 272060784, 784299198, 888077186, 495399490, 710657203, 228851086, 660355682, 937717705, 928431946, 722377014, 9408660, 129158217, 299965190, 627720096, 908664091, 746337305, 639884827, 212645327, 560098950, 895984255, 381617133, 593890621, 686172115, 77064307, 741991395, 327351945, 488157588, 165494398, 273895902, 618771917, 362369752, 536502578, 451194580, 264082498, 860328751, 896556487, 729604272, 690703756, 957623012, 939957364, 209925585, 936465014, 322622472, 419477545, 173083264, 999727234, 872261183, 138737982, 40459851, 888084253, 404932251, 500902887, 583717975, 701620137, 529669042, 722646297, 419175991, 525016685, 298114673, 78585840, 311215578, 252718349, 362503213, 901385805, 92871938, 81617874, 810437219, 361012710, 184064772, 142508982, 937435203, 396742132, 692448455, 112845425, 470048273, 678578137, 176852820, 856568468, 739854978, 985879123, 930516678, 349569253, 992991393, 407318683, 857011551, 275682730, 580294377, 265599994, 136097010, 732709729, 447961274, 554984269, 204300311, 827813633, 157201662, 687803737, 185862104, 612030138, 945332087, 971160130, 66347099, 46177788, 210261251, 821159117, 507735523, 200087181, 228950604, 286589671, 428017589, 902297697, 77552342, 950835447, 766032703, 369925651, 835272069, 66779310, 345013199, 922675246, 274881724, 623185826, 441200027, 186943173, 300136411, 660989502, 551181188, 554477684, 659419644, 383891171, 401453909, 127959006, 657360438, 901066413, 806286109, 890578811, 149882952, 539207385, 908269480, 963705621, 437102244, 128811072, 620752763, 249012911, 23043335, 277087199, 307904911, 639723461, 566740738, 828524330, 828372065, 113222217, 813892922, 350456740, 619530546, 171859377, 42411313, 375205672, 4110306, 617678890, 875829920, 196719446, 84971941, 960129029, 354330557, 238901325, 944168954, 239246187, 853515971, 307462677, 803582328, 375385313, 411495089, 340149193, 363489558, 574656572, 417422585, 17688397, 169311267, 572012175, 815803568, 166640811, 406268282, 316509117, 743939456, 926261890, 354292053, 972550670, 75688254, 235654347, 131076596, 1722057, 923808899, 58324126, 810239443, 448219447, 487470492, 134225100, 32328803, 980763108, 16747641, 542710575, 741646145, 345807176, 861869411, 668650866, 862649021, 321296771, 741645345, 346436867, 33749007, 781473203, 158576983, 271579904, 807461796, 310357159, 766465443, 84867087, 186246773, 808268159, 954066206, 576566800, 960766384, 171476242, 4160503, 605583973, 885830574, 379165410, 322121190, 411765585, 476131255, 87471509, 670550077, 801423630, 819885013, 578286536, 254690419, 140702226, 47258773, 272369144, 348573101, 509072355, 901219116, 42470959, 609775270, 592576420, 437239044, 787005799, 703075064, 960426684, 130226823, 525126157, 352416950, 867374293, 293230178, 970163957, 407354881, 695284689, 92520986, 952477771, 940273135, 786111107, 841162800, 115852810, 334649406, 975679710, 468090655, 928036684, 275692423, 693899778, 140369408, 381244432, 920501795, 831270957, 914891729, 290651276, 996230516, 581646389, 409263522, 818892081, 605315078, 436330910, 889114906, 514849994, 855419611, 686219237, 838020354, 213922789, 929679750, 334236539, 422848030, 57405189, 11958360, 105627569, 703804363, 432210059, 731677422, 950454270, 381019873, 400450902, 319777813, 331368306, 664494948, 740315392, 788958345, 94547932, 642884032, 703834332, 927304115, 499244924, 230283614, 193686362, 638523287, 949452556, 547220373, 226200699, 586665866, 105781000, 523676359, 149220524, 160026727, 123512306, 241740661, 386256774, 791476741, 621639705, 488993409, 690106586, 769290035, 513659464, 454416088, 12619573, 589305523, 643659412, 668923826, 576295091, 572803708, 465582616, 495743339, 800825067, 566762319, 351726582, 597370357, 941433733, 417007761, 145811350, 209394050, 167898421, 666776325, 593596124, 930562783, 5040044, 20269235, 946204694, 628661571, 741760822, 902902850, 577004917, 699313457, 21238997, 731555480, 914189067, 612964513, 446423306, 396049515, 579250130, 185607255, 376344721, 425601162, 524719191, 536048067, 258640710, 844356045, 527540008, 651801826, 305867907, 400024693, 61218613, 195229055, 366760632, 966523561, 324066263, 837176368, 620267096, 761817928, 530653973, 350403912, 622087723, 312865768, 501384753, 501217595, 907392238, 460602908, 459438703, 831976081, 803546026, 517854844, 891388162, 781830479, 861171380, 276096502, 452131292, 160737786, 784492883, 663854888, 574376064, 999995278, 670535550, 497592542, 59022778, 619461689, 877509905, 378287681, 219757365, 781684031, 742755443, 598201212, 146675201, 626408245, 383725859, 286042777, 73412725, 728858824, 775968078, 941833314, 108406233, 550553033, 700457984, 448763253, 654806878, 665419639, 959871461, 609501189, 554058004, 791505976, 338394240, 49415942, 344902729, 180860979, 145517285, 215093429, 841554, 422017541, 894654790, 320037778, 489378636, 588343062, 592238318, 70077287, 40062575, 210648465, 887734776, 519738204, 205129138, 520077520, 516222786, 572321541, 514392433, 365546224, 375584600, 1416723, 201194330, 347571084, 772108691, 673980382, 40785111, 668389268, 568594289, 555399638, 309041455, 874006237, 590215893, 184657229, 132194749, 255056308, 388955112, 71041211, 528236276, 612194315, 890894706, 876461388, 740683970, 72388444, 779620939, 854055114, 354259369, 435455670, 863145461, 992866183, 314151502, 868235323, 559355984, 958579771, 328860150, 906747815, 736087233, 916408762, 614295204, 835902022, 145385787, 806444084, 130811967, 876484074, 14700914, 881979990, 682509003, 988407047, 536843463, 122397371, 898638446, 365718299, 731222328, 249203083, 342369123, 747815162, 627298437, 788513784, 770873655, 690130084, 113530671, 997047436, 265962980, 737278137, 537553397, 859734120, 238733023, 644188666, 139370354, 499936826, 858975930, 346785446, 67324201, 751968684, 661005387, 388313764, 707989807, 774822704, 215245238, 205721723, 193234735, 969414176, 152604116, 345304285, 701824669, 242856443, 515843026, 15347417, 153204622, 392345798, 165078993, 806536832, 94750412, 774316875, 75740532, 315262191, 701952801, 229036352, 617633616, 911112982, 744814292, 280124205, 960876277, 623068266, 733831048, 23192797, 700415710, 579493479, 369081556, 162736612, 105107262, 207433121, 606138765, 753213545, 121846793, 932038297, 150414129, 349749851, 651217281, 936465381, 28161316, 840909642, 174041171, 335822833, 664767186, 118885132, 377643944, 616658794, 706884143, 590657598, 27201744, 643745056, 51684075, 316779565, 297886445, 560408816, 35752087, 907960562, 523770419, 984830858, 707649602, 818245715, 575595603, 457070890, 47519946, 778189285, 116544979, 310867876, 649456528, 184872825, 860937140, 106661867, 709258301, 971484025, 996602858, 258195807, 78808769, 785879478, 226646500, 173243874, 266143811, 203298819, 950881971, 735193349, 267379043, 390199692, 250835803, 6313583, 833222964, 22653782, 796486382, 445704720, 26179210, 944460049, 607076257, 180458111, 256314495, 438961229, 82982062, 147212015, 20292666, 630976936, 659189946, 891373880, 860672940, 937367362, 833312333, 192821121, 266879405, 141832388, 402983357, 405049497, 729577383, 154182185, 128360984, 891092465, 21494095, 8819285, 111923315, 906217553, 609893685, 998602779, 457805575, 141447149, 847562769, 477909830, 873294053, 373779555, 391571767, 950472913, 932461589, 23722903, 708525876, 732990610, 362289751, 327010812, 905881484, 228816135, 67484265, 640066887, 655007688, 564053763, 712646890, 880160418, 197586097, 394213322, 849046908, 548031787, 810386089, 407298339, 429961173, 479285997, 953018966, 837922030, 966647657, 121413212, 961868952, 800048134, 45102811, 87599343, 70205632, 234826179, 350065848, 358257915, 488407299, 473126916, 935797154, 49043966, 327096364, 732953438, 476832342, 77183298, 291900112, 281571929, 932925152, 905313653, 825791590, 718278588, 92896415, 129411629, 717291605, 874375885, 638539430, 982531893, 812396331, 230520934, 23357769, 367074177, 161026612, 248032617, 150611699, 916539150, 757113466, 309103997, 79099618, 541653722, 881982362, 577647010, 468578773, 95298530, 79613451, 835234786, 376219779, 422146485, 560276314, 104356205, 1342389, 15353834, 980645456, 777941654, 180650754, 922145045, 924728508, 302265733, 217954886, 410221054, 816724727, 872067914, 113828339, 663323008, 795907452, 991191713, 760150362, 752915519, 850422105, 610766297, 825123341, 108860098, 370112183, 132004583, 896553704, 576054134, 13541692, 708339878, 545418615, 721872296, 256665109, 1607348, 409366172, 730443497, 458665520, 349721291, 356904805, 250223431, 49819993, 130740352, 461517173, 477592459, 603296291, 291745893, 263899305, 685200666, 418899353, 642112488, 100255463, 25701237, 674111261, 12025155, 702821920, 380627308, 997250220, 899956851, 774423224, 858229392, 922064343, 862487497, 746274828, 632114242, 261835932, 884207416, 288727330, 556576561, 205784699, 103017253, 358432135, 574742070, 608681256, 682380082, 379896762, 290683954, 823587634, 639179822, 618252869, 375290467, 673945207, 183919405, 721871079, 887844371, 98292588, 492194901, 781351951, 823252188, 627284067, 119252763, 967844988, 829609134, 195344150, 641668484, 39457297, 668196730, 561250404, 293411311, 910790202, 83270589, 755182386, 248586398, 758418022, 900406478, 67489470, 675425665, 778050545, 28450192, 377755269, 864075268, 572700161, 159671682, 189516084, 769692085, 982684692, 232171500, 955846837, 936498911, 60604561, 24817107, 290863396, 320998329, 975949546, 568038318, 981190313, 839934801, 731076705, 308765076, 49096444, 819186033, 121848308, 70048167, 433291522, 267715821, 205039677, 592805204, 319299929, 885698777, 511372058, 929917426, 125995414, 149593146, 378173517, 302916978, 392260726, 751594922, 402696501, 895475947, 442135723, 328589509, 513754209, 286390704, 709180855, 492694123, 166449611, 464697345, 526361930, 488788749, 928531443, 158484487, 837956847, 428447401, 864250592, 398249607, 869305947, 701822825, 743938133, 262454938, 639477906, 823531685, 624565409, 547453600, 716607163, 806726068, 481458249, 239251348, 870986740, 805274234, 294326136, 127686964, 597119402, 549132515, 605297229, 770281527, 148357605, 205384978, 651242353, 965017706, 402552297, 486551664, 112902824, 994657928, 833204318, 100259244, 953265919, 917913257, 169572574, 130576841, 377044599, 492524142, 697767640, 913104551, 10323877, 854551002, 184070460, 141705341, 37213362, 971900688, 638515304, 642255796, 534598067, 280654043, 886918634, 198479778, 801969393, 738096985, 725846998, 789502966, 353429063, 81959903, 503451428, 502892741, 639583507, 266210379, 257818524, 961709196, 756459501, 174365787, 959290232, 625277241, 187319629, 622669583, 778823768, 219913430, 766405926, 481760814, 579456342, 458888610, 585156669, 410860238, 306914197, 753019689, 794847260, 820699408, 698750276, 119911626, 96469984, 400732723, 972435836, 520100117, 993044448, 514252505, 28815651, 534081884, 250501681, 568185731, 899370670, 418614384, 218916756, 355712045, 800709750, 268575475, 301944096, 561825157, 184448060, 634721854, 533861926, 378212406, 772078093, 269433184, 126996252, 698777501, 721810714, 28087101, 687535443, 618074056, 664651926, 990624850, 65429409, 206178162, 379516774, 737428978, 993696277, 907080269, 890636506, 365954149, 372075589, 895539291, 200688630, 155093737, 217407844, 313369250, 281664062, 487411721, 782448068, 606642099, 408623587, 932294305, 431402982, 330435073, 81843943, 979806998, 199052785, 248061742, 694000650, 206143634, 497270481, 460595782, 592159296, 721565842, 949741474, 159068462, 317224176, 754896533, 315677303, 523947264, 390911335, 498970408, 926554262, 206207584, 29159701, 345630764, 900017854, 862775304, 285288725, 286757121, 921923860, 237932922, 550426579, 912594793, 939091280, 682666570, 432894167, 108345360, 346974721, 626010936, 727440122, 893700162, 24427209, 780211311, 215237705, 926933860, 514718056, 558913948, 546502064, 680001471, 331080809, 829837662, 940260271, 920065237, 329586397, 240802001, 66061750, 644707066, 454416644, 639583822, 189923386, 861059742, 918108818, 952514870, 313067234, 762961370, 617122400, 716367107, 416111129, 793769920, 994579454, 174294660, 248181693, 865607163, 999612287, 886616722, 812267661, 896452488, 268929903, 935083768, 625326191, 321815584, 758910465, 94325909, 424456375, 366318098, 576671933, 752702039, 607984122, 954793058, 528538097, 631521441, 785409695, 711247709, 129886807, 723174714, 579019024, 427531135, 792577934, 781814716, 301976476, 276836254, 423758968, 138461301, 217095310, 559241948, 251074859, 121758120, 672695387, 62634887, 678739134, 60803625, 264413498, 872794947, 542608089, 155102053, 891599423, 593557492, 156314271, 391257589, 438763959, 397186178, 334079305, 801519993, 572384721, 345572421, 422482995, 437290636, 756070197, 758153784, 299011331, 228449661, 905562385, 434695259, 442618304, 903574091, 816464082, 399504768, 43393125, 567699662, 131345620, 764297345, 726119381, 488990960, 386878970, 439910989, 375851945, 890203966, 645881115, 735114187, 413663934, 25616477, 587727201, 130229047, 567982580, 970916394, 426600189, 709198830, 503618645, 314738216, 875784367, 820105548, 786487762, 747375788, 100935413, 380531094, 870586371, 184424237, 180925452, 249080301, 300873502, 707095615, 991649326, 604409542, 746179093, 448056978, 222712467, 10652066, 295170028, 379912045, 356226814, 756706027, 756702184, 602355017, 507271882, 59477287, 567562787, 506417145, 746326779, 491088687, 900164466, 690226362, 174394369, 201451106, 905837076, 57510648, 520338877, 531968668, 897624432, 292988956, 106847123, 728612905, 782846108, 723426789, 178445313, 228282496, 531425874, 922829591, 618799612, 773976976, 651204481, 950326242, 203982938, 143930337, 105098311, 502859877, 332207266, 579771900, 940568866, 71774420, 349028765, 733676706, 986929313, 226123177, 620869389, 319563133, 446485371, 539266235, 722918988, 814852538, 539538060, 39938660, 438355010, 951593634, 663448841, 593198973, 79814677, 660590436, 677357699, 440613670, 593202513, 503089629, 760195487, 250838500, 919950306, 646537243, 927152562, 592441407, 538104302, 536409150, 63571155, 195702296, 918404527, 162808808, 693940238, 560230958, 737510986, 992392320, 844265228, 695521770, 300308712, 786523306, 487218310, 192343466, 661469699, 108679465, 430226867, 941561661, 461895340, 112417918, 736377990, 696227950, 240271069, 206256338, 935980941, 859978405, 353098420, 111547317, 152239363, 296988839, 477144360, 128393417, 77685469, 763115205, 546450049, 859618098, 567035474, 829775445, 372053443, 677584951, 854608609, 586334765, 303868057, 945647995, 450081540, 245322512, 50888693, 646961712, 809340243, 163667088, 967984985, 37105772, 230666976, 471431092, 865794920, 557360524, 196712220, 339655058, 984593717, 71799367, 836631493, 767861911, 195845936, 847825229, 513338989, 802246030, 100630025, 146623935, 496400989, 932211814, 234071598, 224569877, 212150251, 989658302, 773018140, 976829309, 210704071, 976454018, 227206920, 82585603, 20943243, 941517943, 980858113, 716249194, 468918057, 297765611, 189316142, 704333714, 98158910, 660412419, 774432518, 256872964, 178332466, 149690971, 905953659, 191707343, 673508706, 328690641, 152589756, 642170662, 375870459, 82332887, 99686233, 361876656, 531997253, 587656815, 636795244, 376732436, 281463785, 333131270, 647351778, 413343918, 530826653, 121568113, 646639273, 918388676, 180500470, 141528682, 795381584, 243632557, 949920568, 770960434, 23477918, 367109645, 280753972, 931871308, 777106938, 807302416, 119782236, 838050188, 517701944, 521018678, 279999069, 95294174, 913737779, 636716456, 213917257, 313642548, 724258807, 447114817, 435888466, 688936509, 47173272, 757534023, 459798670, 218477703, 224684154, 883265694, 862519344, 103648905, 389801582, 376781257, 649196382, 193076183, 176342182, 370017815, 415275631, 159459129, 577741346, 183493187, 934288505, 247335347, 680384923, 640793051, 446100812, 472090670, 104942002, 443836486, 490041392, 177861385, 182011718, 801415588, 809341777, 72587813, 979246912, 373413730, 543484643, 164487103, 622207939, 593024874, 889723386, 281975696, 224739623, 847452859, 27688987, 249712284, 49278176, 778315245, 61413908, 393049784, 885481747, 700978812, 723208366, 480023487, 158133910, 744919697, 806460295, 823887288, 210260880, 457677739, 661354635, 237870652, 806351141, 832699714, 595028474, 205208168, 971927854, 620022468, 261394736, 608445279, 70608879, 316478064, 600923836, 184037461, 511106281, 211892154, 577399998, 591623370, 330101496, 12593437, 354113973, 838697794, 583284694, 481393874, 687939971, 407908306, 836809663, 455605995, 788731391, 825055676, 787999762, 919830905, 695143520, 985655555, 914583133, 822069478, 827882170, 259953787, 36258899, 44924245, 482745229, 160721907, 441951657, 13756175, 788419518, 239467471, 374394446, 567140355, 179443822, 367630466, 626006099, 32115082, 770233251, 492727231, 478887944, 49498660, 732566538, 359927810, 694733241, 61383462, 691640937, 793612756, 136625897, 217858549, 226697256, 224263712, 425925466, 968665597, 674867775, 823074177, 57135845, 585582062, 715076040, 16222845, 866849959, 420382573, 576433211, 881826771, 682534407, 630957686, 559897318, 915979386, 542457716, 183018756, 533483784, 303313739, 836061103, 52095550, 703490829, 804568453, 727605640, 17741610, 750354895, 658319560, 602467989, 152247655, 640059348, 147546790, 802741668, 491599574, 359205192, 128978041, 335392585, 920059071, 724881286, 164761861, 74506138, 251655400, 376606047, 187632675, 954085460, 491543906, 314263706, 541062769, 386121910, 460000369, 239530270, 667753828, 766688938, 293938179, 184910094, 670113885, 893199925, 771504370, 948104827, 701269977, 641880425, 220216127, 731833509, 586288679, 196876265, 842847229, 258464438, 770351034, 651737610, 601857225, 845208530, 595359819, 882383666, 56413156, 804256367, 506536033, 677124433, 252185609, 964068805, 537509060, 671176618, 165315873, 41014665, 472336214, 898902122, 683936452, 198500860, 170436612, 706490309, 38423920, 112712878, 495319565, 892397346, 423861052, 906994181, 144585515, 277837207, 176663919, 182309856, 272310725, 147517632, 92438574, 215878046, 639965865, 740778766, 600302269, 172452913, 88162526, 868882029, 863756969, 920355219, 319549022, 290145457, 968719172, 223606840, 992979019, 286752499, 444628732, 234516285, 456064198, 222598220, 62019544, 246705815, 477455618, 311305598, 972631214, 58570703, 699338302, 856781226, 515276101, 717064938, 281106287, 963140726, 742666030, 542940631, 617610884, 718051984, 9458187, 281266719, 974025170, 71010849, 945000308, 957312201, 12661887, 952210413, 37586241, 244367147, 693355069, 768621069, 570128064, 286258546, 14209477, 656843801, 428674664, 208228544, 245281137, 773344534, 162726310, 829385596, 79419488, 29622322, 26364387, 236412837, 564124049, 578043092, 181981427, 378318581, 951698671, 646657929, 654453223, 97630280, 337799602, 466920219, 654768773, 40999192, 104101280, 596167394, 541048870, 961765887, 95775979, 611844052, 679343016, 49706730, 214281688, 336615021, 429098028, 187109385, 522822226, 999131590, 348409261, 928001355, 800795138, 115249263, 817916391, 598378394, 901810915, 15426892, 929183101, 836639467, 449226988, 803376748, 516864930, 595759449, 876179767, 302810570, 911105003, 754877076, 627357498, 277243518, 852714689, 845500606, 747059088, 826752809, 494131778, 90643925, 218330975, 473714548, 278485257, 325158152, 313443972, 864013402, 620460524, 171319262, 826599922, 302716081, 507641478, 644252176, 279360256, 811783829, 418522458, 563650588, 818568140, 828179919, 397989588, 398312466, 679213376, 901671329, 723516429, 901751708, 724950819, 972463050, 129760569, 548945517, 256587032, 683859186, 527168802, 870762572, 471671274, 228150215, 976998768, 397350704, 277022553, 352371755, 634518561, 944496870, 970417615, 565093552, 323075343, 695646928, 923049675, 127509861, 426939471, 80647168, 278587870, 986101073, 541892219, 153184724, 281448877, 915817759, 675929611, 660563444, 803466012, 619169162, 376148284, 598717220, 471163578, 660758257, 338496830, 840989232, 187014176, 197286497, 551485906, 501175098, 54454374, 30365751, 271075152, 424823263, 593152331, 969861594, 527487488, 559978081, 535208831, 439400614, 427620258, 884716390, 805154667, 442355131, 292627100, 556411349, 179758470, 129390911, 764136577, 671854115, 205764046, 202448424, 238833900, 773462265, 253384939, 812617559, 354045667, 688097513, 429441745, 732315839, 516989520, 703830955, 919763229, 75294885, 617500955, 172388021, 743020974, 470001001, 613497749, 646195932, 367451432, 882315779, 43497988, 487948579, 557252860, 232058132, 524476577, 839345455, 993776674, 420250222, 1913133, 454045963, 914470548, 774070945, 342734955, 173226677, 620101764, 304759028, 984123820, 81225448, 307537157, 424216080, 122575324, 500081254, 695099937, 811189310, 482832521, 752463613, 857278114, 809118614, 823548858, 195669101, 261692553, 42773179, 586548671, 240450526, 559459840, 798835970, 868765894, 999872234, 342758104, 17764630, 472872145, 196338709, 934444670, 888178235, 84660711, 839878120, 578087845, 698797046, 575891142, 316849797, 424624362, 780510560, 644352590, 626612877, 110517612, 237891092, 569186058, 386881298, 923874884, 173795807, 806669314, 341186257, 228287547, 246554493, 545970967, 410859780, 998136726, 993522176, 902292008, 863049491, 223587499, 19496433, 773060595, 405926224, 924269855, 231393751, 328588237, 765748592, 682696120, 757190467, 18792577, 386803083, 497830525, 395988661, 408935545, 69474536, 380255480, 766835024, 22681387, 762002283, 877392476, 532258465, 790444418, 472439415, 85883557, 44878408, 975894962, 748379242, 484876275, 445800852, 636377636, 990959012, 937235068, 330612604, 12467297, 282339212, 184661749, 193339062, 451228795, 538940041, 707576411, 867118255, 414696298, 703008715, 563315975, 308224864, 391356790, 923133549, 657896048, 433280274, 654098768, 218504177, 277676776, 248400497, 279072849, 168938385, 914725779, 199607979, 951772405, 38589679, 156599831, 478975954, 53681060, 461656714, 223350405, 469194693, 935552940, 496383908, 448465991, 185253607, 719878247, 820689070, 681472723, 47407593, 488612871, 537766625, 540819211, 728713922, 252352715, 746308276, 132742427, 637614102, 818555327, 113697671, 637530328, 418332040, 446157688, 387243488, 334661624, 409410725, 56015245, 882722365, 367295491, 901027463, 794551603, 420177205, 633556901, 214533284, 206157335, 464651555, 808338321, 990973969, 368172382, 888326931, 276141218, 951786507, 351330032, 254253330, 162972076, 433198264, 957833273, 552434934, 937716921, 299277434, 334046503, 947587349, 997835410, 147226679, 612135318, 650868657, 48608212, 638841584, 116562312, 67051100, 257074132, 552480989, 493649344, 128397634, 971327381, 740553511, 421439501, 284611909, 753006851, 908168862, 56138391, 662379622, 37639964, 231723248, 180986054, 114003435, 817174841, 709687984, 786055222, 636694325, 900653619, 98235204, 4711197, 516854899, 528389917, 587599108, 538460343, 2764429, 134983680, 221978572, 242313151, 199344927, 935549253, 380020379, 606425865, 951847987, 809348110, 880041450, 203170148, 971360092, 738718955, 619946809, 843667553, 770468189, 468756390, 339835011, 18736880, 556973580, 800215569, 463187887, 342354259, 313727781, 278073554, 704692555, 724449516, 911499786, 157842319, 119603932, 415291609, 430810296, 132546435, 181079145, 211586023, 626196615, 767649903, 395487822, 70511601, 696503364, 238839678, 283255737, 307431735, 130129005, 139211810, 785569410, 255589422, 187332572, 157519975, 281610763, 775352768, 373144456, 972532112, 419823028, 285053345, 464928355, 363682110, 469854815, 90401612, 413984341, 784175133, 553769787, 900472192, 358398467, 439896514, 649956686, 927503116, 477154221, 301288347, 668649156, 330976866, 261704175, 538154137, 392100474, 359441208, 183656866, 741697161, 544007107, 610320916, 908430466, 506991457, 683407968, 374300015, 548729042, 49450102, 627618692, 780220556, 822591767, 583816920, 654521963, 694013265, 401987244, 244292376, 326082751, 251283375, 93248080, 992759449, 56937713, 24465600, 108247816, 961829522, 789457735, 352685433, 337913227, 67902597, 750133939, 486610936, 338123792, 179907632, 535494034, 226127448, 875119800, 590247702, 580361870, 143520698, 810481745, 686505013, 762344956, 352984990, 92135135, 322748082, 283763199, 467105271, 117105077, 155498379, 238507790, 326895033, 669816161, 552889777, 396771481, 992458264, 785996055, 809239797, 817017877, 57094253, 965558634, 207470353, 855196839, 186851546, 127469170, 620433282, 243352928, 410521534, 190212699, 830120638, 571548048, 357836282, 660186128, 378058742, 350246209, 575398937, 46431318, 47752769, 602409341, 321279087, 401376194, 854196437, 659422639, 473520463, 862296335, 721525654, 858965248, 226733709, 85194717, 102555190, 260250087, 289514521, 235179832, 698968630, 647471236, 202503307, 580385309, 649909599, 742070822, 484246120, 365075406, 784896651, 144737114, 313886682, 733049240, 933702850, 310640161, 122097778, 675681822, 519495675, 910382534, 247269379, 658103888, 798878957, 775107953, 671672820, 672451421, 349972413, 124806330, 528396773, 372005098, 612279007, 787864930, 664002059, 562251608, 60958261, 560928871, 660934128, 53976395, 21576670, 820913125, 172248379, 658537841, 278384946, 27117462, 761099682, 226440057, 365933137, 728517659, 165109077, 418207544, 460599736, 49712905, 637453334, 944289156, 160156879, 727501276, 102937410, 843375939, 547936181, 672807900, 186620365, 316375162, 39238831, 251245059, 96480966, 631355815, 901320348, 979823934, 630892660, 323439069, 910291436, 201145450, 251559498, 520531822, 719773012, 639607695, 740067248, 771437766, 988203645, 605267457, 626403557, 219166347, 501467351, 625905676, 812950168, 464569225, 665449793, 715839673, 101220427, 324586669, 821202461, 586933322, 865305405, 308800566, 164707277, 173763732, 125958629, 842726979, 173504002, 468054664, 972425841, 811900999, 580363392, 147617601, 835509798, 586268817, 255766342, 710683549, 81054839, 853371585, 779155196, 211419676, 215702924, 841940332, 523658258, 106011703, 808359275, 368833996, 611079143, 644325712, 148509006, 276750666, 974094231, 910761251, 166254048, 189980545, 747661621, 649393683, 140168362, 112606454, 417041566, 532425453, 702189896, 818229909, 36582856, 376097954, 736240669, 959936089, 35098257, 353251615, 729146668, 52502076, 496370666, 156534192, 948596251, 593148087, 130375235, 771601255, 27723479, 814112238, 197353412, 838159472, 491869831, 553427608, 738204568, 367305902, 253851119, 641950056, 606707191, 101126064, 942332598, 914747161, 976250764, 747862552, 802137931, 593659481, 455638638, 711652350, 159254369, 820734447, 609361237, 317743622, 690056596, 120541526, 318554890, 866047389, 990423498, 26552026, 459608194, 509169633, 150646280, 800851394, 221294909, 940195473, 199772394, 708237922, 580215162, 201358189, 972625651, 562590992, 898786720, 848625244, 130211626, 998588457, 276062186, 770813342, 629020424, 296020606, 765637682, 494837709, 549351307, 51202478, 746257728, 132826123, 745360694, 164045193, 753502947, 951762166, 763745617, 147003822, 566873293, 689310305, 608389808, 891266120, 61881636, 794146598, 703680901, 345562574, 94844606, 527617208, 378625152, 837775172, 459255739, 952773263, 3910784, 620019536, 728902861, 29737133, 69000193, 471047579, 683560250, 883734875, 735542594, 433980112, 862184157, 806494463, 643927846, 1260790, 957737070, 438925264, 152068574, 440734046, 366965622, 326004607, 792741555, 480258936, 187758095, 78102796, 607499604, 942737999, 150345910, 489338894, 31431213, 96526654, 913927086, 660213893, 567300418, 128020074, 487168112, 155038325, 263963376, 677042663, 26344860, 235159292, 587885849, 366422141, 544144665, 198998295, 687944977, 272309646, 1558838, 140370765, 292674599, 886424664, 440903662, 434935529, 171364745, 475351052, 950326251, 846483214, 631050117, 186579712, 873312028, 463333178, 339375413, 565769586, 117268184, 352587014, 256978061, 192857391, 872802971, 457990054, 44488193, 573256176, 83728087, 103056749, 785579001, 315428427, 868168979, 153181406, 698657314, 448655731, 867942952, 10348205, 374511484, 124739575, 752195756, 144637140, 281096310, 548446730, 841716408, 230920634, 134975068, 673712028, 87905828, 588381542, 691269327, 185416091, 398606705, 154204, 781000575, 607260521, 490345209, 591993472, 96296926, 256705569, 622251118, 990525939, 345635967, 870712667, 342817748, 966923265, 779675456, 63012805, 941504268, 154067712, 30259265, 518675449, 970905121, 933425347, 539160890, 654218086, 777678030, 27135596, 536515440, 641940479, 505428068, 137495111, 184096727, 921463563, 77530425, 87171947, 610944741, 401130695, 829957065, 712011461, 254156195, 592106433, 3178536, 909861919, 683676992, 671911192, 836376054, 291600465, 564561664, 86267478, 595213415, 739154762, 828644225, 947838610, 389031844, 697740158, 923753059, 110317989, 981756799, 425617564, 395377178, 583408252, 947426712, 425724830, 168728654, 953580474, 422961103, 755438460, 591307945, 332981709, 91903585, 605172595, 300895246, 939613098, 903238262, 639761308, 788521612, 619795476, 834117676, 268016778, 63083761, 317729661, 537958082, 917249569, 426133166, 258333276, 665295092, 492789168, 481059807, 865583773, 136579696, 576010529, 95311269, 662109983, 30159655, 415833906, 527410808, 127784161, 907309728, 20492066, 370484898, 904276, 430833131, 58156061, 440884857, 13512197, 596764219, 216277803, 915251680, 70112810, 287633300, 989541579, 861315207, 874906441, 151973011, 479738366, 593707531, 591293349, 181434296, 495686347, 590457701, 130226981, 511155165, 105362323, 115619176, 448545746, 610364315, 80535625, 605479066, 856468648, 555572550, 484893856, 125171029, 828282631, 24773241, 52260854, 270645178, 627339677, 221435210, 72539087, 537869611, 246661668, 647484866, 699982624, 365206092, 550220071, 373889871, 306383593, 947251694, 949752938, 947418133, 264335760, 579410851, 582406686, 472265691, 962600000, 371579081, 313490243, 138513687, 165377208, 205834408, 402623809, 798206125, 88959978, 56982090, 86692718, 973703419, 232437734, 342255950, 315941605, 804762126, 971189258, 874321994, 715677407, 284049032, 937082522, 807553455, 650281605, 674384241, 620330757, 982560761, 770613120, 998549460, 561243961, 206978316, 743960018, 636674591, 244374138, 354913062, 849750121, 5560236, 775851908, 951891170, 552525312, 731325023, 259997041, 649341103, 960377011, 862863567, 844587856, 499081282, 553632003, 111528312, 664470570, 433329449, 950270396, 156582835, 467344570, 821551208, 973350710, 808207976, 546381753, 304533747, 741355803, 401661311, 910541552, 301145392, 647120912, 45789386, 776339013, 367147003, 221556320, 872217147, 475358444, 179411142, 512822315, 503491767, 417096999, 358070270, 642118631, 927791154, 716250120, 218403963, 299720485, 158491193, 723273760, 409675150, 140829728, 536626499, 634305565, 906301950, 446195249, 896743248, 152971623, 253715324, 857011953, 535614701, 61738417, 231705097, 66900874, 91541353, 651221428, 850483773, 551974400, 751365263, 967786418, 952350687, 773850385, 832276273, 175710382, 479105915, 272421331, 614885263, 83890396, 642469862, 123833323, 402036882, 525178302, 359682748, 370481361, 417789550, 755528834, 427846241, 968624206, 445237634, 830368376, 724369380, 143458206, 726162354, 293792799, 371629214, 616436096, 556734964, 227344632, 403173585, 467748545, 550212781, 393533866, 451115325, 55262707, 802055255, 859575865, 816585000, 354218330, 204512506, 705463578, 612215509, 93132747, 890371178, 325539314, 505076009, 615630441, 660480699, 122975311, 889130968, 414285555, 324148357, 748688082, 590959740, 284735164, 23254324, 683581633, 253034571, 398837349, 118548164, 318088348, 803123585, 228070291, 95192170, 177746189, 612859566, 492260627, 78566336, 315961823, 557397067, 872223060, 749431839, 73620436, 141041980, 371349471, 557368137, 30577247, 120960927, 436466255, 973792644, 904100640, 863498923, 885874753, 795770248, 550714389, 82033884, 792653857, 211453518, 521111429, 380788987, 394726702, 599357063, 449599058, 843913661, 923894328, 840770108, 676040156, 337761751, 556117949, 62278243, 582806182, 53930493, 623148086, 909837281, 799999355, 874297196, 683601041, 182070728, 695985152, 926250732, 814673942, 500590932, 888021422, 984303811, 719737476, 36715831, 196811810, 575035046, 403494161, 346201556, 938769320, 804897909, 301390119, 1263384, 420122719, 429792765, 916404256, 111581760, 873140541, 950038906, 226356606, 737234919, 913603791, 348374433, 45774736, 43605369, 337694975, 663735286, 396273012, 523029091, 645052881, 9901980, 827909503, 363424956, 862248704, 763352587, 668719364, 487656899, 705948471, 36816049, 446095347, 945534157, 738815911, 604696874, 55298873, 399546161, 399965498, 550088877, 229565403, 657388262, 372691227, 509794106, 859565767, 426254757, 461473581, 143448595, 991993666, 449698783, 36297451, 307551354, 746037862, 56760110, 457741093, 467275158, 278275219, 411190092, 237528705, 913524326, 418922309, 838858325, 971669630, 864218897, 655550124, 553795312, 554222208, 667260113, 599528533, 50423070, 268646598, 594248142, 920513190, 6237994, 452349752, 991412768, 412199671, 60643934, 572047614, 66233451, 40166888, 448667264, 15419032, 702602243, 210456209, 570727861, 168207178, 262340890, 285605665, 635957969, 711011944, 692038068, 865686695, 181942335, 3121641, 604353418, 627436721, 682297836, 154939108, 81128403, 817245092, 347257060, 585119056, 607020795, 790584184, 589877500, 762381128, 27228748, 550811872, 885132123, 54374852, 88413412, 261238660, 972185056, 696056202, 378902383, 312024803, 334722898, 525460340, 572363610, 458633758, 962397979, 572762989, 342709514, 630809155, 285855471, 568232519, 909037856, 794616394, 983536228, 43496949, 557905365, 306484841, 832560073, 775740442, 881813056, 451487157, 25535871, 864757162, 842332613, 18481143, 529536438, 326361243, 589197096, 792521603, 532033640, 47389378, 873650406, 708989137, 768562210, 103823319, 65945204, 784496483, 445089304, 672162276, 404169225, 286651231, 878875149, 650505516, 253746733, 865322303, 52690969, 694002328, 427759579, 415746536, 781742531, 335424638, 430013924, 490079771, 9943360, 399062439, 886330522, 687814063, 976213110, 371372842, 214373639, 527264517, 12173787, 163384275, 546868303, 540323733, 946453458, 226237810, 300221862, 412840051, 669294402, 641936613, 292645443, 315519911, 728352526, 458226052, 546785163, 263462741, 403752629, 230281430, 687889384, 624818007, 806072861, 361930601, 408387900, 328418229, 769393599, 949767289, 754950199, 406209966, 710392146, 593523789, 728357475, 549387164, 688603670, 483819332, 417376673, 207546210, 744024663, 772600826, 483049585, 886248443, 271342650, 216252862, 991394591, 656530294, 165288336, 229045636, 256062228, 106408122, 445451532, 632815157, 34376587, 198212080, 65683699, 714932516, 562296394, 350467107, 681119163, 500661421, 942201613, 33436726, 318498939, 67704704, 772430469, 975816378, 608781556, 366532602, 140232144, 966361080, 660191024, 83634447, 640500020, 690918435, 331708301, 372438838, 565835115, 808066971, 450832573, 218217728, 164129506, 521411904, 376980265, 256192596, 507584828, 258870903, 944570800, 676599072, 258832998, 913984417, 767030274, 552320992, 647625077, 916283361, 671776634, 685255274, 843840238, 25948010, 527558374, 593422299, 747487487, 122825539, 890070207, 700248798, 95460173, 193876453, 970660701, 105032705, 509446895, 163352843, 413157125, 168637737, 478314906, 830921297, 207021512, 677862497, 740715531, 6624579, 307788152, 699906878, 559109733, 972270512, 441367423, 832030151, 660952890, 513246692, 872818602, 689747068, 56455147, 954041746, 914778521, 724112037, 255475106, 250541777, 273675771, 745664323, 109313078, 562029126, 114022457, 273834881, 23240835, 38183968, 723848753, 630001789, 4101864, 771778324, 789401154, 245822201, 482972685, 638405196, 929109489, 522489938, 256962182, 858123508, 738377667, 755198136, 453669910, 175600977, 215419491, 975388309, 1341551, 732049942, 228388576, 193950768, 779212415, 209200986, 197396478, 398819315, 570642256, 675313605, 512923638, 455802113, 751368409, 792319384, 717305022, 983090558, 81196302, 419595775, 369590119, 392057145, 225551885, 117591869, 10987196, 383340271, 432964419, 425989569, 187089116, 943909683, 14997552, 995605691, 278566694, 82083968, 555887035, 816305135, 890641557, 245274445, 807293387, 231259532, 198652027, 794125132, 975194455, 278487549, 707715256, 214745101, 690168077, 774917214, 152991753, 534900948, 810958074, 703728244, 123525040, 738863204, 66685481, 246327294, 87236325, 430163101, 318493496, 607515299, 809485072, 18415703, 145332253, 799981218, 988309539, 920810524, 580764883, 871679443, 459915359, 686331534, 165321728, 219913782, 83533550, 185509961, 926348141, 666759786, 636715482, 52262111, 660751248, 626666374, 18728321, 915280576, 32705376, 521892735, 883712957, 449411792, 617647110, 952209142, 963086177, 44147852, 168661743, 359588306, 469136284, 384452900, 887052822, 165877397, 972801305, 583042150, 817623663, 630806586, 913071020, 436023233, 773577742, 269239176, 506825173, 797471073, 425565824, 868596770, 61810602, 472328253, 207343987, 706613889, 808120019, 308556276, 462301920, 249197357, 594191044, 590255708, 275078443, 132267816, 975439899, 498830245, 815524146, 853737533, 799020191, 268883223, 616159941, 902046336, 710727747, 543802411, 296705630, 652437341, 852892329, 673803490, 247686, 56673706, 747240110, 312584270, 848628545, 772143589, 920017422, 966072022, 809240159, 61846261, 885207646, 554080908, 394269600, 235763422, 169984595, 370038207, 669818483, 154972286, 874095156, 529461364, 843883814, 326233207, 930683155, 248470639, 988953775, 64747049, 998167888, 503078230, 775109019, 170863346, 106911199, 992411058, 293989174, 816498418, 782357901, 122944638, 726658681, 322203367, 766625116, 290987939, 409187408, 361289236, 265700234, 84954305, 987115437, 875509660, 695407535, 545983262, 734854605, 26260232, 651892459, 373531196, 393156367, 385793910, 926144629, 940089174, 614626622, 422246667, 889034293, 10157176, 965305133, 581883975, 788785988, 284548600, 272184811, 58066463, 243875477, 259312663, 564849730, 920478608, 638830717, 187048267, 158272394, 670180068, 906875759, 579708997, 915136613, 506026541, 606981038, 713710218, 252223951, 937559665, 758734935, 748553001, 442900274, 701974261, 418254280, 858603366, 604774668, 145289820, 654766922, 437555790, 356495277, 79914321, 68588378, 457051902, 70511012, 736044940, 558895232, 46404403, 319273954, 315143273, 543934163, 349335410, 76277153, 978287821, 419814361, 633883644, 185978006, 226229967, 358351668, 226348145, 884917733, 461247990, 291757446, 303906649, 272725723, 361263479, 824464670, 642200502, 657355565, 48958996, 329164789, 151923716, 678265507, 475803121, 113527682, 906508381, 174862924, 200463375, 540042909, 685235858, 486276306, 539136750, 771690258, 36620006, 226525121, 100522554, 295468063, 61026113, 380704974, 62227708, 463393930, 424036891, 67605917, 916975624, 129336240, 932152680, 680110289, 628555235, 198525727, 206174520, 27346133, 424054251, 374591262, 305602197, 283387367, 449425755, 155646449, 244254216, 64199014, 798096446, 943440238, 530995282, 92045871, 381418275, 989047448, 27372176, 355370600, 279520839, 181715184, 863623389, 858314765, 48389427, 15393510, 432341180, 121917398, 620207161, 916690744, 248390926, 444214925, 548706444, 337216591, 220463718, 418488644, 730701174, 441820320, 704203526, 834603621, 460985406, 738874912, 908327294, 44640929, 212671255, 565167684, 393814042, 735288712, 721206895, 518482816, 381140941, 417664478, 807165260, 189755908, 400186575, 303259190, 69185018, 469908871, 881632243, 896067877, 549724019, 236553338, 929142368, 115036899, 324746567, 471249309, 99237378, 386588466, 737799053, 898789757, 536034271, 850726624, 696340173, 679982626, 700495545, 254139539, 506626701, 742061832, 36646263, 813532022, 267953463, 991772917, 631499621, 261717487, 948874681, 112702910, 358090968, 775308156, 790469068, 373774125, 689435158, 113845537, 944309723, 103086222, 587437792, 442505825, 955659299, 822479969, 75929908, 414705383, 881874393, 796882167, 121016121, 480429108, 683439022, 165153694, 477300320, 168437019, 928454754, 228697590, 625987462, 792553058, 543375217, 575761543, 493078687, 275735428, 934847132, 151158514, 310989741, 485921552, 835219177, 819143563, 202177779, 214149743, 93873331, 249551044, 304588686, 728550248, 419058857, 492166808, 104093084, 464246976, 67803533, 369570385, 719503273, 663796880, 435975223, 598361030, 609847853, 128919527, 761942030, 981399429, 117242577, 923181498, 55149415, 874572728, 303048462, 287943100, 998991697, 19115703, 173800483, 211059632, 189241183, 996595127, 792473146, 582352480, 911040372, 366724361, 639367351, 915483368, 95471672, 426834906, 963060060, 464101347, 68273671, 2341270, 853552608, 799688823, 871374119, 256375927, 68388439, 127954007, 959344388, 348976726, 959258807, 733111030, 265717621, 65985958, 709037003, 684260638, 300291856, 654566806, 134579059, 885238268, 780253265, 877448542, 561997523, 500194154, 684820017, 519513159, 914706809, 83437914, 170929289, 393202383, 324027501, 227735062, 850375694, 30205220, 681358596, 30410756, 237304965, 323070818, 797537448, 25616963, 632003531, 619469237, 184976183, 58537164, 112382186, 569446008, 809389126, 509179169, 267814615, 226133980, 331442730, 188321025, 111020104, 728640900, 542188253, 139839698, 450509319, 127261619, 839171984, 647038920, 484874454, 199750942, 357061765, 645847161, 7560695, 63367623, 386152488, 25348094, 697882748, 226412164, 557756335, 320851051, 426094125, 586781322, 480684615, 157268079, 51987820, 671715772, 187320255, 814937799, 730244475, 530772095, 649736669, 407348304, 805891326, 772586122, 306255918, 294921104, 696569664, 330613594, 818468268, 703868881, 574950598, 117436502, 513572463, 688949047, 186581234, 242668426, 968908492, 58691872, 416168282, 297907324, 120623060, 509176547, 507482716, 519724103, 85972711, 925203982, 158659710, 865364490, 507145484, 393922874, 733006847, 45269021, 830801459, 150396250, 616289141, 578899217, 734134024, 328702650, 901486738, 3984002, 5705505, 335620742, 855000392, 770307290, 417196881, 750493321, 971381486, 207659583, 608270963, 875266615, 102981449, 870837391, 952780965, 60328358, 966216793, 444654308, 340461478, 650901286, 617201589, 606312959, 53990111, 233465169, 772964106, 777510565, 289021480, 372706848, 4468243, 628444786, 863310035, 88591576, 591644749, 463273284, 367312598, 791848167, 741414560, 265217350, 635358523, 123654254, 317294768, 649501454, 275916638, 631786015, 946840823, 310399512, 932911978, 6134969, 678245271, 279317599, 168338749, 94673018, 732029643, 708384871, 345169628, 270469369, 529782520, 449719415, 917199830, 184020461, 697235376, 554485284, 967122452, 102779432, 106014520, 384104117, 269946290, 538913778, 307803560, 464639564, 395498010, 437344058, 986703022, 667762188, 203379052, 308661339, 658763522, 164882446, 579143770, 639969073, 875867704, 146243780, 294343177, 894153118, 123164026, 616824629, 585243236, 787645256, 406014529, 831892166, 764639558, 49795792, 709210788, 143288280, 944589913, 670451458, 636604746, 199913816, 44711982, 702901136, 154201716, 93412218, 184123785, 451533852, 799368906, 602098033, 625313942, 468300853, 907696079, 49015703, 498364241, 622175095, 883151545, 223907478, 637868163, 942719089, 615128681, 632838897, 403604492, 565165379, 716239468, 342928942, 444059621, 634646320, 818731926, 397470242, 560074853, 57669244, 657353947, 680634498, 203222375, 597496360, 712920749, 102248430, 741380638, 795476400, 554103189, 891518000, 175817158, 9768620, 166220575, 350207135, 563014487, 697126335, 468549836, 366168742, 956876988, 77989735, 16803890, 492091314, 983588322, 702807493, 798242058, 81318862, 631065966, 54338346, 326600787, 893063098, 889086426, 337999978, 402779191, 2458783, 742951499, 554344512, 271482619, 262694572, 838149233, 956610653, 86591257, 692057217, 17525753, 943735255, 395062524, 314626230, 582099639, 146244666, 646809172, 440147634, 252038220, 992018464, 901246598, 762522401, 109482209, 212162395, 811523850, 414871731, 303284289, 83065352, 749400549, 803430711, 719348245, 52087598, 657730714, 644512696, 250892956, 390838192, 99479848, 571583078, 973246908, 4221601, 463549077, 118180061, 894384427, 150331299, 42029388, 193556976, 650164029, 716808554, 291519439, 206855953, 818172063, 953712438, 600825783, 87612831, 62580812, 573101481, 194210151, 733237450, 511978659, 338943466, 455926923, 370071606, 434808346, 499904136, 1578530, 399562183, 168389909, 270328016, 519542640, 440260315, 683575708, 636335887, 999596771, 646564854, 932417922, 697126744, 78790771, 152306815, 206824842, 92857537, 284078311, 839099450, 872089334, 344332718, 957990125, 345750444, 68907, 997994529, 328067693, 197231849, 199645918, 882493255, 744858955, 199109643, 290856376, 111335178, 202902698, 874557369, 385046566, 405424801, 764338524, 47703822, 377321496, 819327790, 462801230, 657478523, 939564217, 454610966, 408545189, 564934958, 89637812, 120912072, 1397468, 28896250, 143746241, 560952254, 550611439, 424971782, 37651571, 860608225, 780839734, 514584512, 839747604, 858538136, 744362034, 342836008, 267373989, 164083168, 136206635, 54542621, 712295402, 840871325, 851807982, 210618207, 472060599, 656410677, 161504117, 172020829, 83201788, 207585381, 206603015, 455156945, 206722047, 69974517, 862025303, 317225410, 577237162, 530800748, 301477573, 974890295, 241493267, 320458531, 918989201, 27562256, 662807951, 994848492, 841821070, 847341743, 97426581, 15783323, 690064837, 235663537, 845169862, 212780495, 241237562, 749375576, 267117956, 396067730, 986884027, 94677294, 758314287, 612343787, 334176097, 978649497, 344532713, 289535441, 863771748, 780292134, 905735440, 984331374, 767835467, 484577913, 415025655, 233562732, 577436977, 631498094, 411937822, 243720234, 718281124, 348234622, 357780913, 806032090, 155982709, 797821997, 662597701, 867748821, 441022999, 627093466, 379189743, 427316988, 31447649, 928195731, 871290142, 854549495, 940310473, 777041674, 881830767, 387691683, 166935569, 815690515, 824694783, 589713099, 92969066, 504630088, 304821076, 223324520, 974525671, 218688287, 510634710, 745910286, 955522673, 632044048, 322930166, 880097970, 34515278, 711504283, 71601451, 244264714, 704987399, 188764431, 124126857, 115459332, 778999183, 239412483, 296992451, 400939645, 820803394, 510838401, 894170600, 638538004, 329849232, 993805125, 398988409, 373435678, 981191906, 123738426, 176982384, 871581404, 588446734, 233584279, 507733047, 130363082, 824197818, 896479518, 831463631, 502601821, 720694724, 874320792, 200164110, 680470011, 867493222, 435811669, 972594802, 78084604, 918420610, 981271955, 615459740, 977985162, 586062411, 592450158, 635372564, 860177535, 920199220, 23089846, 742623858, 329261313, 720541688, 662367095, 635773995, 63766187, 37625105, 345867822, 368097248, 216646791, 234222315, 173126067, 2071620, 528587467, 220441984, 327565990, 767413440, 527745509, 81060519, 153414233, 178751194, 781332765, 993186497, 950873601, 205252280, 790284397, 398784543, 642239700, 457778342, 221203745, 28567299, 104255973, 239366319, 87157699, 372515433, 356957866, 800941371, 496931239, 776772148, 218811710, 449516592, 644389522, 973904951, 682340873, 898454458, 369376634, 856666725, 117680915, 155395253, 197325335, 443504520, 297642696, 653241672, 419805916, 571509748, 251807577, 860343707, 78309712, 497395866, 3107153, 748825575, 731413961, 465235985, 255669190, 119253188, 286309266, 514654832, 403118878, 153962305, 734465926, 897969513, 876218337, 424556148, 865559186, 858128903, 816470609, 623725530, 28671387, 811622071, 340023043, 67653398, 259560838, 528559547, 302614226, 843356540, 528213414, 787376593, 624363934, 861175746, 732385330, 691425954, 452274065, 868411829, 828348924, 699045547, 239737143, 964540669, 92293279, 159939784, 379890015, 135661886, 334895896, 94000218, 609174573, 230248439, 330328849, 94842560, 339637926, 67873318, 988944887, 878506567, 19794548, 995470246, 666084354, 25579417, 551239335, 105019642, 318202489, 56476001, 259533942, 869954844, 598344990, 280861458, 478895992, 291294099, 639964119, 499907884, 953428619, 452867496, 616216540, 964507910, 360486256, 149818312, 978921988, 63549404, 880177684, 59325767, 105141560, 85447942, 45105319, 40611515, 671745231, 521846637, 445650881, 896525484, 645681992, 120681477, 845589659, 693705759, 751179002, 414504541, 404635932, 650645753, 60233135, 150991810, 153508977, 935103259, 612537078, 744874571, 315336833, 596066484, 946366709, 691265672, 249006225, 151100770, 973627096, 679801847, 779792602, 609946083, 47012720, 468385780, 878252609, 358464170, 119610670, 94491688, 297033986, 272684836, 699605465, 78903846, 45448882, 580452385, 468023517, 156289568, 300256527, 482437761, 210553345, 732433437, 475611942, 222760217, 660519680, 960968145, 743088201, 934102399, 822950111, 467904702, 955851820, 629357975, 741229226, 898602388, 349341477, 323877098, 3370871, 981589194, 362809749, 418254680, 146071819, 761196847, 530555833, 94218756, 39687439, 74610854, 700708611, 235963412, 720409100, 739320716, 139380333, 20883922, 598956445, 673946598, 577984877, 719561268, 318332982, 264908801, 830120205, 414786847, 359981680, 712490848, 782559216, 342884817, 788483469, 150667055, 515161439, 830993671, 131180703, 653233033, 199932422, 998782256, 550851713, 56702765, 889107210, 105835060, 365878083, 994724248, 701578689, 998097250, 696739399, 977726160, 589951820, 649439579, 53841862, 593943647, 641539068, 64337365, 422643129, 152695446, 770144832, 799898377, 24948396, 138520954, 852892894, 97623505, 408991769, 611441866, 528759384, 513815251, 766410895, 822196014, 472129302, 480211517, 601538422, 826405944, 5965991, 89425933, 611367626, 42250955, 304156653, 191240172, 732400231, 327439064, 900906822, 71728537, 426469625, 589779995, 192509071, 302283674, 157617849, 516696474, 678485157, 281091661, 329454561, 95268910, 644153521, 94801079, 855841794, 222102572, 334804812, 827990203, 31726390, 866361833, 58866571, 916363208, 769650200, 951277649, 299075917, 995494051, 417447917, 884690628, 46450626, 361101810, 159444281, 434850816, 713763804, 257559431, 265050242, 192719451, 871707400, 625850660, 331333056, 609134780, 803065440, 294130503, 792732845, 560797148, 905037609, 801867836, 913745298, 517538610, 11306582, 11666448, 429951744, 35232843, 313001341, 524616045, 960683793, 276379506, 321856629, 534291179, 822493383, 488501677, 580355544, 989899512, 574860184, 719093185, 879851375, 731772308, 516089241, 772815674, 185736545, 208002740, 837692494, 796014127, 932552741, 729162581, 109205588, 518288738, 400827588, 893633517, 320080539, 582645896, 371475886, 422654542, 482153896, 331995211, 103757570, 424415355, 301025149, 750063904, 166319671, 667304843, 816573121, 58614808, 294025297, 829954656, 551841013, 113440689, 98135134, 128442058, 71580984, 168569526, 115651252, 134326576, 381249905, 123220264, 140430226, 303237503, 824129782, 341293914, 152899672, 76031228, 448212723, 665643043, 264824205, 741073356, 895049321, 871199102, 998934237, 995097557, 129637324, 984643534, 775932383, 152039893, 825483102, 860267048, 490333641, 21540183, 343160933, 936014042, 201599371, 950713498, 488990359, 332827180, 866462513, 897289942, 568656003, 737351142, 800828306, 96500538, 61945808, 594716179, 782642897, 627804663, 710504208, 584172822, 256010072, 27171885, 725391444, 728620645, 675682741, 922224046, 555625819, 786157190, 178274876, 591567902, 834799983, 797605070, 912854415, 468355615, 587849032, 141148822, 949111403, 64487515, 330851688, 703273305, 795845490, 949830945, 636592816, 576956323, 913065648, 53300688, 828014535, 628294855, 776258188, 471283132, 175228700, 427002246, 357022566, 86826134, 750971578, 752503690, 747879904, 729587557, 57194809, 148114144, 705564294, 780724888, 44658409, 376553807, 351010051, 827314634, 223014764, 972283383, 444532966, 824418069, 88457936, 872443682, 114913775, 83977637, 764653092, 231165011, 20608681, 177179856, 267600585, 267258902, 626287775, 708405250, 817412727, 382852014, 420678103, 339265904, 943198643, 611435473, 530885073, 868538150, 15034382, 729507749, 951349260, 317900535, 51617915, 907449103, 928113628, 528236094, 283684244, 756989197, 677110172, 842528857, 889744181, 594318087, 726488815, 862874197, 489493965, 489405934, 67316597, 98866000, 285109940, 361527616, 400488779, 806982986, 356298196, 376818697, 843921425, 921633233, 836106511, 934971888, 752868871, 264423151, 693592679, 138937614, 502928325, 963975450, 33086503, 182449377, 774308940, 883844529, 589414649, 487075898, 548397798, 252721690, 450578829, 670608699, 173629403, 191237173, 669250687, 532737872, 516603373, 753751091, 677944924, 221484645, 112892554, 547682133, 966889915, 92134416, 322828514, 188733628, 988471745, 584157224, 248507846, 760369427, 726614340, 168240441, 123065783, 300883366, 139284667, 14223461, 698713370, 835325969, 82504760, 830603341, 273654735, 164417465, 769240417, 577140326, 202966501, 753934918, 140700605, 429454516, 741922316, 432134883, 320797171, 175764515, 506445799, 402213870, 896134005, 656069329, 549232042, 45606345, 71531685, 226150096, 960447635, 349492954, 946423836, 170700562, 553412817, 697965710, 275628366, 333726328, 614147994, 497438148, 410207591, 142940450, 603738661, 13058948, 817686875, 407495698, 346128302, 264338939, 888092064, 932054891, 603764741, 528540693, 356277685, 251656572, 618356585, 967637438, 247402217, 849212558, 349216835, 554656824, 541840395, 195022282, 672612999, 623597166, 336349675, 285410162, 942418666, 915617831, 70493441, 982780213, 655809856, 493168926, 43931639, 537368858, 685667438, 351755460, 211006045, 539548235, 691901067, 55877949, 673336879, 780073805, 433563414, 624941405, 769235186, 141023366, 446281745, 857415853, 574153216, 949938974, 742026155, 975112426, 196065775, 261011361, 755281867, 928212881, 388180840, 678268799, 502221460, 412393671, 95127732, 31814485, 182618077, 347339558, 761042505, 573728198, 593378980, 434016377, 556261263, 694166949, 190858242, 727246081, 172554208, 372745953, 90342500, 940558536, 918136389, 229006550, 692583747, 142118027, 904519239, 619156448, 592324657, 832848281, 210934199, 128334353, 63168295, 298310796, 761136679, 91230637, 53501624, 946698290, 217902075, 306020741, 565770264, 577575477, 897944639, 456642087, 338732458, 947033887, 449146166, 126142435, 22221990, 921990494, 258822261, 622657386, 643422912, 807370080, 522211941, 303364678, 417068326, 423294127, 629851895, 95038696, 794001714, 219637, 31008864, 134397553, 318956349, 268122997, 544785274, 312883401, 805836641, 514963266, 136136417, 322746437, 441113787, 823098437, 568681696, 804967323, 812299290, 143847954, 531427634, 553142495, 9459599, 241792518, 40585455, 496989631, 926704891, 9822542, 64754155, 822874185, 595045929, 319539296, 709488235, 884197732, 738723580, 475067370, 287698433, 808544423, 87884813, 596286810, 642756151, 554722445, 2779158, 218717735, 47228779, 972389851, 285158769, 476159527, 397943531, 523867996, 470831300, 283735772, 15848437, 667473104, 410508651, 69400047, 126264693, 809778158, 303060091, 631120722, 733608557, 798846594, 655257041, 773116415, 124383577, 344293351, 904901004, 56600756, 299740642, 615358537, 856973810, 75235638, 352503810, 115082218, 146339258, 254524457, 470189527, 268326922, 293783467, 718481027, 564772932, 63126580, 468300839, 6633465, 490367776, 415715401, 69765036, 150012818, 454308105, 575839271, 467482441, 211098170, 893693939, 119992600, 198534530, 711993977, 902632498, 129365800, 620292065, 581547336, 371526047, 85976173, 73713517, 78560297, 346978601, 894652122, 281440884, 630950779, 755801081, 668858972, 865477231, 587203476, 303366998, 811551394, 61659372, 287162279, 877457710, 722568882, 948636325, 53564515, 467661123, 828566169, 411419545, 486433131, 951208570, 43124601, 794505997, 489742510, 804884823, 496114816, 311906294, 9576813, 194314961, 517559527, 701904527, 883613989, 112829514, 717714656, 318652662, 278820780, 191625563, 783270433, 736548973, 562367511, 569749347, 227848464, 395119015, 420756645, 412714517, 644467195, 576469676, 184266146, 95941775, 567418534, 652941148, 14065729, 873606470, 61674248, 654846992, 320056500, 68495554, 150754609, 547746910, 492669687, 40560917, 582063822, 998873529, 910233424, 920299036, 956180933, 747324718, 513983214, 948699255, 415911326, 887714907, 399666852, 262209895, 137511767, 21208737, 4210592, 630028752, 955730276, 388998258, 635081035, 762499544, 582570370, 849637818, 354632333, 842977837, 848076687, 316064094, 686820993, 33759547, 228876521, 778579829, 997985999, 196216182, 198146581, 984510375, 852295143, 350541383, 387254037, 588995288, 86947537, 394365331, 37874217, 725843917, 237799100, 267591845, 617533426, 931253701, 506931874, 394113497, 920463756, 829137669, 543907280, 374341917, 965190496, 182471688, 716243882, 944548529, 400093572, 656860457, 159490958, 414433658, 1133657, 771175763, 954898280, 648763463, 108282510, 870034242, 194642228, 591411907, 360162705, 795994594, 721490235, 260268071, 725641022, 80553166, 25847589, 574976269, 17136731, 954794822, 8465676, 475056644, 302649761, 366454725, 591774324, 114862902, 263279541, 244898666, 361204725, 944713531, 100888005, 214329173, 612593548, 521593601, 956642071, 533104985, 283999536, 343045808, 503727083, 814164924, 524022532, 161235165, 11798242, 44426795, 701663488, 370962338, 638459874, 492856060, 838674304, 812038642, 55502718, 240080629, 652013645, 451130556, 665005986, 547826364, 69724787, 603978111, 150045688, 473450658, 950041346, 962759669, 192453746, 534437591, 545862325, 54804488, 757185229, 485566262, 642607902, 464674466, 147738764, 42068905, 300824919, 151519516, 996504159, 694330035, 897147263, 488329747, 805576373, 482721717, 606210396, 428908346, 355132124, 257022813, 662623421, 875381851, 244292817, 917456975, 718227056, 529976905, 761286582, 384366749, 581305999, 748677229, 100648155, 735620290, 553535127, 23160075, 454131603, 456290676, 374210151, 534624394, 809741368, 503636351, 864984530, 857384664, 110950737, 217686264, 241262217, 455933334, 439397140, 695086678, 900585424, 419653073, 496746247, 764354511, 617824397, 115785168, 447042137, 738205803, 530945607, 400830511, 875289412, 478543662, 373509604, 7672992, 246206958, 100028727, 209074313, 101382148, 78419105, 703193780, 968533612, 111944858, 448566225, 776521228, 38827038, 354604231, 310912124, 826430618, 484923211, 570647226, 745846639, 633507417, 983540307, 52117726, 165372006, 5775868, 134944571, 642328868, 941041311, 134960166, 940278931, 749347680, 152168028, 110984637, 598991297, 905839151, 779311459, 896963765, 4282197, 191336787, 269129671, 592492463, 954936531, 635168074, 612409117, 358324670, 33578788, 854618250, 747053158, 265920331, 280301242, 289853830, 413724106, 188826467, 880353526, 373097002, 614778318, 778827379, 659981504, 182396473, 717899527, 842626294, 369947426, 140034790, 283128122, 344448421, 688616258, 152415190, 368847622, 652677586, 281153275, 837251103, 659045755, 569329682, 429278987, 1937114, 184548951, 382714166, 699350214, 833387479, 453922239, 472901197, 706434259, 10495759, 474278570, 52246564, 795643674, 804915740, 361127791, 115215691, 3659034, 828203175, 885067979, 503459643, 603548659, 731404805, 302215672, 629501643, 547490664, 681029574, 223672637, 198429442, 987594348, 780921858, 33238126, 70882342, 28960598, 648602541, 286610183, 840856646, 237257814, 29741226, 519370401, 142946131, 715272061, 438169917, 68560476, 293986268, 911004525, 402964136, 659897726, 569516052, 596755939, 437859971, 239105066, 458501178, 743391695, 76354951, 672207912, 974431681, 464181423, 147066931, 848452465, 470922437, 659651420, 204842960, 518133525, 935672977, 15065899, 816346509, 789754234, 450282096, 20470941, 740578332, 298747023, 712798324, 382640065, 415431159, 324319080, 529754781, 95394586, 190017515, 912035468, 936131239, 680381125, 706296747, 697084209, 836346002, 971856503, 123851213, 175528082, 60801199, 457623982, 365232791, 610893375, 23826318, 705936275, 297049962, 909850050, 452714550, 916202701, 251705112, 790817448, 401410453, 529136746, 599232551, 704276247, 714104136, 422648499, 309706145, 608901045, 367096940, 892327671, 764897778, 228697170, 360421136, 486239854, 808690388, 731491589, 137614323, 533589587, 357539280, 394853151, 759705304, 32986699, 873239439, 126853231, 991454255, 95857925, 792929905, 862692323, 155476384, 985639271, 68435055, 969455727, 487342747, 230453217, 422524699, 607980322, 143061150, 718791669, 201023791, 569043225, 756178920, 88431838, 964198974, 321569686, 968812864, 941890734, 163057106, 454965134, 641361341, 227345038, 354460082, 709819714, 222731518, 832815951, 619780665, 699169121, 219023076, 361645020, 643363697, 766594352, 689353822, 25366558, 441616564, 906392129, 183330636, 479784953, 130806224, 437021985, 964564269, 120580864, 167622785, 761534006, 226720790, 442433093, 661978919, 337614030, 399867004, 205678868, 391467624, 675966443, 658882310, 589196965, 905733, 396088188, 919768945, 211762684, 867984958, 772392522, 242953552, 503705591, 616618325, 887244535, 264527228, 627215691, 268067873, 394370004, 714709657, 860538255, 470087594, 29122963, 733404065, 855207245, 588718411, 926776356, 382731419, 803974120, 830021928, 493718260, 932561944, 954116526, 370174112, 550630790, 925257379, 398457061, 26234442, 123648414, 731936633, 329938704, 432349310, 112057391, 489851845, 91275071, 60051596, 247216770, 297912447, 135652529, 869555488, 163554468, 682523289, 626339069, 620024533, 638860030, 525539335, 104397441, 44907547, 560383259, 538643650, 770193228, 421007130, 102030749, 51062469, 456874056, 40340720, 566975712, 592700677, 20994768, 971951699, 801224666, 892946094, 701127980, 970526791, 130981692, 406238794, 125611834, 520466253, 757168217, 839970955, 112422811, 937290285, 465541821, 155842166, 349222602, 3220927, 10054001, 140232670, 152722708, 838448122, 751930641, 49564261, 127942543, 853753919, 504541501, 23599843, 450562268, 458043077, 234790446, 287564331, 175840019, 531268895, 469574412, 809411734, 223960322, 267875077, 748105675, 327666555, 418161294, 966247641, 256488127, 576054959, 772787653, 783983961, 378629609, 960047300, 392476366, 932461177, 796796230, 453472823, 102688653, 370008857, 807312098, 543768454, 490931575, 772721807, 317837000, 652611084, 829044480, 740554289, 57236664, 438478706, 442963180, 839103640, 423026026, 975697732, 709150590, 138371458, 132007616, 654274111, 702687230, 987729992, 290086818, 496073391, 350577862, 986085278, 412829401, 891902960, 728976629, 93786959, 480675727, 961010631, 524213546, 105786276, 309969094, 675935740, 672996396, 88508491, 62667275, 232848785, 342476201, 445190547, 596047024, 219420736, 297190484, 386066145, 645430525, 851345879, 730792331, 603379070, 529387594, 86684583, 715110599, 937648075, 565471845, 864475769, 347386294, 703453078, 704594433, 404707610, 697299398, 838907644, 265789536, 191673419, 218721085, 562130375, 642817703, 793708851, 314465899, 392693108, 289083822, 247862464, 901650367, 254481091, 164175357, 616082678, 204875023, 548526858, 824321192, 667884015, 570298097, 119079989, 426905998, 176878247, 359361120, 189325478, 6878874, 624000141, 118733127, 727540637, 492024715, 278843100, 678556790, 365137696, 615515746, 693916281, 116252489, 692473908, 436913683, 575652790, 941932312, 207692389, 53285816, 688945837, 982714410, 271796105, 830735764, 648412282, 250903187, 831908222, 357191174, 49310981, 954310834, 52108506, 872961349, 33324033, 789036529, 526561389, 29670325, 632436692, 878700696, 147059711, 535970737, 266589239, 831254457, 602574447, 806757038, 639700664, 69907060, 468382280, 453122403, 132288748, 29105443, 338314891, 628393012, 901686238, 784377188, 100570552, 610189182, 430972347, 861731829, 658126804, 980400247, 546581738, 908287644, 658940109, 386357455, 411150701, 231618444, 661489681, 970601893, 667085880, 524724372, 810913997, 563686675, 203601584, 120633776, 805026761, 558720445, 864665729, 427431188, 922187669, 661693117, 201429177, 889821157, 931000381, 632507316, 69329096, 997956290, 466029771, 63699567, 35034940, 423349924, 99624454, 139071617, 416895479, 185402925, 894324790, 136194422, 338685815, 857809596, 659240085, 95335519, 433286985, 347115737, 999106925, 855941696, 367215628, 293295819, 298963181, 778810963, 573089352, 970619900, 816635811, 281601799, 394834303, 555777164, 109927505, 97724979, 866206780, 907187972, 389337332, 474535122, 277084950, 959474109, 721761588, 164702149, 800445289, 290702744, 695973477, 449931174, 95643240, 772415936, 813820160, 957781385, 242240273, 112522169, 884455510, 993321311, 39795590, 149671289, 294133110, 947000117, 676117910, 657735818, 331402061, 36948144, 887703781, 608279358, 966428039, 20701351, 52542442, 842539891, 593601247, 636541334, 723032402, 947120076, 474925260, 301020493, 274564763, 541685835, 823641499, 497184504, 219768064, 85515020, 559231929, 518269849, 509268664, 567646171, 781124565, 757331478, 800909006, 387308409, 318239624, 785295799, 129574641, 484317987, 530026576, 669413867, 285812755, 842786585, 105008725, 388856408, 354423872, 933367852, 568619890, 432008061, 107277729, 62540403, 717610896, 200272092, 367271670, 530939253, 875652406, 120878733, 171414619, 672178448, 312564906, 781909090, 330132873, 960441181, 208956082, 138966619, 695759545, 491780377, 175834485, 922150690, 674387961, 759811736, 613385073, 38338809, 625477122, 686819443, 300896012, 966998277, 782173044, 804873256, 237465721, 460661085, 686025481, 907903644, 371320905, 325462464, 649781438, 112005930, 303600462, 795469145, 66217737, 561108682, 870192785, 819196033, 266068207, 794062450, 555083808, 545661654, 682637105, 979593736, 379620528, 196755378, 253724380, 819565264, 326976332, 355735355, 471721333, 402298661, 675198106, 243027719, 622363488, 326616790, 574204079, 140618438, 640066821, 403362363, 350068111, 376703477, 610718222, 527006658, 982042598, 150158756, 108375069, 620829874, 956632682, 234044081, 972564362, 448918582, 401740556, 347301825, 962301343, 621662735, 433703259, 540042530, 168082820, 572623933, 303334385, 785167053, 42924731, 174666671, 995706698, 417450989, 950130297, 642052011, 406872128, 424214957, 366556661, 69574083, 25129815, 848261659, 118751441, 286325278, 315799630, 336618553, 313018489, 284212089, 132612650, 855062558, 180634887, 628077339, 848213984, 653218421, 75910787, 110468337, 696378126, 367146327, 99432321, 205334279, 778383678, 780275519, 865482323, 961420622, 465121525, 841010558, 359935239, 574182188, 934169253, 16010236, 423399674, 225236538, 196592483, 287534722, 112239001, 842869156, 160108472, 222383377, 727296912, 205079554, 94492128, 371827163, 268386225, 268180249, 761197952, 906237738, 635121138, 10269875, 97885476, 451404423, 450642449, 383977952, 187141740, 837252430, 24575693, 896151168, 262739269, 206000686, 317293327, 273856737, 993033791, 159801720, 33657334, 630165423, 731909319, 224567786, 392270465, 47647798, 239892797, 709632602, 205625974, 490068683, 859456672, 880770659, 420305433, 673332038, 96917693, 793673224, 743588899, 280262453, 281982897, 850715526, 12004626, 259523749, 427375317, 796845692, 595169865, 395898449, 469756066, 577620256, 485891404, 605200077, 733177340, 555808747, 330965340, 548131477, 590938568, 544604312, 660166928, 140285880, 60953882, 751856114, 996918242, 445216051, 298328478, 144501400, 441944593, 718209605, 908966979, 839703924, 528194701, 709884883, 610284515, 115247912, 257248906, 462729124, 627231771, 633321558, 229348978, 771555959, 456619655, 77549645, 582044302, 439124494, 167071770, 679736238, 882106808, 64734308, 533294118, 722092405, 541160376, 703632646, 48701150, 372328693, 993184002, 680391953, 489764894, 165009951, 969111854, 856849763, 204636472, 228411938, 118342664, 813410269, 998104264, 354246516, 963104919, 496518901, 653532428, 105712215, 335385511, 285794185, 954592489, 793551527, 798988335, 217626587, 602888702, 295637374, 396148892, 474750642, 826485485, 196684406, 332184133, 930592752, 250384371, 714610663, 361268909, 370678984, 142676247, 538220894, 46107117, 142432983, 971531768, 548439584, 214668513, 326016672, 5027246, 58431796, 547222747, 658868972, 605393445, 724158548, 940403317, 474635136, 149312970, 334507321, 627143110, 257335009, 634717859, 649569138, 69244685, 804003568, 675931402, 934806865, 368721781, 186518658, 462505082, 35294739, 227398121, 691888775, 762626198, 734504209, 874609055, 311254525, 114223945, 873304858, 341075070, 79497601, 331643330, 178552676, 298246201, 866419667, 188008153, 942825192, 933414426, 455674908, 182017047, 627627334, 597549539, 28355614, 222898578, 73833485, 964952915, 901689015, 373754801, 825118661, 391637783, 472585219, 780253683, 367924946, 376270106, 474644709, 302369796, 271004407, 28172173, 966664699, 203252657, 946919434, 727971588, 2245589, 760546598, 887777704, 737009565, 916625350, 414087101, 529949093, 543596565, 543299444, 145769779, 480783324, 449184693, 291742723, 658366796, 889398709, 363094617, 288562274, 821630406, 259855167, 512752487, 562945598, 338102200, 644232214, 256946394, 633996642, 525370661, 33172455, 908526909, 174608876, 554068394, 985509835, 940619444, 555187999, 908173027, 974159985, 114976058, 26443441, 403979630, 633352508, 466910688, 931542954, 401222492, 453466288, 214049533, 508247630, 278634399, 349822103, 781029547, 645177876, 414023679, 512839350, 169484490, 412149050, 33824288, 957852286, 529646199, 741507457, 503232578, 772065963, 892264370, 8947406, 82697908, 137668095, 2852904, 849592349, 497435310, 98461172, 771829780, 25960744, 886156581, 473566121, 86689860, 129748377, 510853179, 333874183, 523567712, 10314556, 249795431, 411596729, 598480288, 565206805, 569361279, 159499535, 953174609, 230051657, 919333609, 980647090, 996174497, 30394299, 874666227, 409061092, 442528317, 222590525, 583155077, 519457494, 414201369, 144943668, 124539816, 693051880, 776940082, 90303098, 721757588, 758471085, 953407680, 655544558, 591510798, 495513662, 965452220, 15022080, 995166582, 386301220, 137638326, 848855324, 297344879, 913451145, 73784982, 622117731, 844353260, 802726226, 724889948, 994568335, 21152400, 17472044, 563147320, 713374492, 56167206, 278488908, 846876624, 200274917, 209304271, 157474056, 407756049, 138225539, 606388947, 765525192, 471240380, 735749073, 49073890, 814041990, 134778986, 29976989, 307696311, 174417053, 4839077, 186591490, 734185409, 331483083, 618665147, 463022931, 38212157, 815941539, 559552845, 901697239, 959625709, 856423847, 573792099, 65699896, 773085021, 559819778, 389558730, 694547450, 563694396, 911950213, 723437554, 455617952, 556237108, 677131646, 470655810, 624128788, 362291335, 696337115, 4319286, 789831112, 102360593, 223649622, 409803996, 558711791, 56313319, 410440565, 93939562, 102416715, 91513326, 645374271, 22180918, 689868287, 995958262, 6453145, 225764248, 214270274, 35276945, 609303617, 77888362, 333135070, 747762253, 647703331, 632389298, 170587820, 692361252, 897138775, 756090830, 331208404, 186919925, 556365840, 849857942, 255200726, 518401486, 301867575, 246097724, 751026341, 536360098, 682935868, 798560937, 975189162, 514378573, 948399580, 400230170, 413560152, 79488268, 972784242, 769498350, 532179632, 602424392, 418426470, 3539060, 796967963, 934763581, 275346060, 723301022, 400699809, 71084551, 200205405, 137861415, 814698844, 476044897, 809347015, 957956574, 198823302, 656999627, 74644300, 802791591, 308037515, 7838495, 440891184, 693637365, 336530274, 842141879, 992338849, 186723046, 305209539, 945697929, 829742248, 716065220, 942983692, 873737553, 523012920, 757172731, 483806324, 556125032, 156508460, 275882759, 92293762, 83140028, 512570852, 544312639, 366360895, 381259836, 326975252, 765643759, 160095817, 825065592, 411661040, 249357137, 13081433, 958857723, 278251918, 513657861, 355571752, 670087476, 767003174, 944772127, 650837151, 427049776, 6619270, 367353703, 203376636, 306317891, 1574219, 194480963, 391327587, 379779312, 357023064, 619151102, 480493038, 453933779, 872691126, 258914608, 510306916, 278337386, 23404686, 121827592, 135583285, 980893634, 157769699, 418583658, 584220539, 384049183, 780467381, 23088271, 142547309, 625239537, 400576925, 421391225, 832463617, 738255232, 338180208, 96750050, 505806364, 138045954, 724381888, 759023841, 391598403, 949450267, 925061045, 198710580, 35870525, 972157244, 549759582, 476126217, 236440135, 306202374, 408247920, 20939764, 891880006, 85821610, 167697328, 90917284, 16647091, 499023241, 959309921, 874561970, 586743098, 23183194, 69851155, 467452296, 920179680, 204184571, 227619017, 534506631, 920786040, 408800887, 960641257, 202759317, 3129482, 663625693, 105683528, 356559967, 503308842, 592084717, 384391931, 834658799, 686625514, 993911238, 4233577, 727602095, 79724211, 297573747, 750082793, 353127545, 785414509, 704275364, 453402488, 764475194, 314395510, 132506997, 679707030, 2950757, 54287386, 390671123, 803092079, 744228693, 54910483, 610261248, 654656278, 946609052, 948600754, 303497517, 440393258, 414574996, 872516198, 295756031, 556242573, 371977098, 409970020, 831284447, 624923900, 985975119, 657000350, 796809078, 405275155, 465150582, 925259853, 776413105, 132161166, 945356898, 487769231, 319719393, 845229347, 278275799, 21878817, 465584490, 501143136, 152082008, 342771820, 692209063, 550910239, 500222992, 784666242, 374432757, 509711513, 442923378, 918791562, 88026796, 479999925, 478565631, 85945059, 607229273, 128544788, 873542187, 679833668, 459319239, 4378744, 279392415, 775426119, 177595002, 692491534, 806815161, 241097352, 971362104, 730695694, 533299300, 231383625, 794615852, 719016719, 629581107, 544245684, 358444154, 884382902, 466027572, 232896593, 164010543, 13089982, 599077283, 136229046, 879380041, 978578789, 170503282, 30526736, 311532317, 248611557, 996066247, 578720273, 665493614, 359299262, 667127102, 320009341, 740395305, 323713355, 372467819, 726534637, 148788761, 571880045, 470002833, 991285981, 162672294, 972359392, 53631243, 203525839, 834129429, 852402115, 813756719, 565099541, 223767809, 283135344, 783266576, 467115260, 92156013, 774134729, 90286569, 91752391, 325434656, 484201252, 502661200, 17963587, 587933611, 888943045, 202774448, 824163467, 661529510, 549969382, 388459458, 345468161, 164820672, 638102815, 654074007, 802434037, 838786049, 364745838, 183574684, 518836746, 776583100, 228810515, 563149365, 798231663, 288791524, 642483371, 104014997, 381243014, 705741351, 584985482, 25108804, 624863431, 825762092, 137499178, 468554989, 414395460, 515457067, 122206856, 784448513, 728539177, 295306060, 363859037, 236602550, 916139484, 135773389, 650975135, 786595446, 124381352, 907260046, 689215354, 858907925, 891476390, 898027518, 983683609, 606353435, 174243341, 102706622, 33331912, 295971422, 555725421, 257668599, 436994948, 491531244, 122398437, 127854539, 598291067, 152537069, 980037062, 610593887, 713551254, 992369022, 261403728, 768756430, 910664220, 716041643, 13661757, 466234970, 308704361, 286923188, 284633760, 818062871, 99180722, 37386448, 195620096, 567629247, 819093708, 668981645, 801552231, 284397150, 797421926, 941901552, 419296890, 197966811, 600660709, 67181366, 648253750, 670205920, 250078349, 80915482, 233085261, 384719762, 651049756, 614290614, 224673359, 82979171, 29575154, 141321246, 993798013, 24148588, 684954283, 579900668, 130733510, 321554542, 618220794, 92615640, 618773241, 88538172, 457328573, 291268588, 917444124, 48660565, 988973394, 370910908, 926283363, 253763461, 111479641, 338282730, 895663909, 312971088, 26802, 625826831, 251084935, 134430103, 450886215, 732464229, 944456318, 214377588, 792241372, 10195169, 434024977, 889394168, 959038815, 493498430, 159745882, 187006341, 832341418, 295586460, 447514348, 663361772, 684314717, 544418033, 268355279, 465353559, 310855020, 787686898, 717205173, 265020649, 265354895, 455483542, 223868546, 54040567, 759652627, 210444407, 201354157, 100774243, 950337243, 333931640, 62284682, 792180099, 975101318, 339204695, 369560710, 601305149, 138113119, 600665541, 420811890, 666523098, 102407005, 902331856, 833403447, 807673980, 531414141, 97647738, 686497289, 337605276, 3300163, 631877637, 139439707, 393694606, 99315224, 758208580, 250984328, 803269462, 595276078, 451522512, 514540661, 579881401, 337902242, 556887527, 453280464, 472095347, 106214487, 276030758, 806314708, 922010400, 481683855, 730166131, 404054580, 892682360, 370564146, 809637049, 345209813, 858425314, 657326976, 116948054, 176797671, 251918468, 342004658, 231406095, 331364575, 816159566, 290262053, 956496110, 127412590, 471176664, 822506870, 43834425, 310456497, 504823090, 546240870, 351208080, 947681731, 754246139, 119057926, 668268388, 584597641, 988090613, 662140513, 359528532, 227476437, 133257393, 495041862, 266905265, 301026194, 947678438, 257662721, 982073974, 295894169, 868148526, 472823335, 869859722, 625124031, 801839136, 106286369, 149793645, 143872614, 108376176, 867941587, 394752399, 296892083, 138559861, 122262037, 593001734, 168734801, 403268192, 758112454, 561077742, 390606545, 986669232, 73370146, 573465117, 768191714, 888590742, 328220577, 168111959, 765989875, 339660218, 904441032, 122691831, 949037364, 227891367, 783567634, 13892948, 327691837, 784244859, 12815698, 863503987, 466393187, 346145548, 189597770, 495948258, 303367441, 233534124, 966071524, 810083228, 754757336, 54611188, 244848272, 521553738, 827454909, 242223845, 297953298, 621936864, 221192911, 318038105, 872029634, 359305896, 404101629, 634749021, 688597408, 70412030, 712712142, 774793097, 268511917, 550139353, 372592064, 635103994, 865727217, 349983406, 808193263, 772684515, 58944972, 865841330, 471911518, 361147468, 868763358, 388469449, 615269031, 885875666, 213289918, 117169359, 277096870, 545184653, 182775700, 107907808, 443568105, 272949977, 270747017, 355312362, 471897144, 666390772, 273942938, 800690995, 466265555, 348609147, 322974393, 747861409, 103344933, 660685071, 904261827, 918037482, 596757481, 79950356, 362780382, 992067425, 717369502, 900405206, 663468374, 278080927, 517587678, 468955754, 447455789, 885275224, 593299556, 638006671, 51050550, 36377101, 495761980, 372314190, 724540660, 141606417, 922875376, 955449348, 76270425, 321658324, 967025527, 584385402, 253571850, 608759072, 897395378, 725180150, 184505949, 775218817, 305677702, 4249027, 119941715, 356379691, 353495162, 425620857, 999006031, 942800208, 896273841, 148828740, 946058667, 548405301, 384402566, 140651797, 339696053, 946172680, 314794629, 220722210, 402506901, 283906492, 780616666, 869936848, 772997994, 629147349, 296655722, 243536409, 819533180, 266234875, 226489337, 839776144, 693017088, 609817284, 315111464, 884664545, 155353037, 310877300, 54680380, 196773358, 556774326, 984740972, 758431238, 560064538, 772181737, 754645810, 859373576, 233027191, 959695229, 981614352, 263009133, 779963901, 256483823, 158677668, 821822801, 719531110, 947140072, 320394444, 944087041, 819255565, 112474578, 405704144, 78412140, 938909254, 516732926, 171326552, 974408022, 527904500, 696379985, 522391966, 424719125, 289937346, 730673738, 319431875, 586858522, 382900841, 989907670, 56152252, 545913740, 325102629, 224137763, 715427767, 410920728, 144374780, 265078724, 154050584, 722178525, 165020842, 345503463, 467229867, 254185388, 988900710, 255605861, 469533240, 956735214, 403077779, 456081089, 455794876, 260481917, 577925696, 332012544, 838022769, 500049551, 774286573, 475862096, 276106977, 358111800, 676246962, 654203067, 437049944, 12343988, 222032039, 870712925, 407377266, 445994122, 5642683, 838407745, 90643359, 280419648, 478947794, 88880796, 829822973, 353748394, 550935646, 928319945, 503834001, 33974940, 505590641, 554543757, 828240673, 696791165, 730512859, 950348201, 658043834, 359181896, 931219992, 275312372, 151770524, 103768511, 448183007, 216760426, 984856591, 352680696, 371634069, 752356780, 334591065, 295883632, 241791724, 925049392, 917605542, 683416392, 850228974, 703119618, 371370292, 417555927, 976414893, 6472918, 195166222, 330715471, 699646676, 817281196, 252278408, 477550153, 461256178, 852412563, 902199106, 935934061, 575260093, 35434871, 953915916, 253138290, 472056404, 313837256, 72522519, 796715584, 58964419, 111494638, 485520295, 105894144, 54586550, 434508842, 502390445, 620593083, 975672477, 559517397, 609179108, 381114569, 973594239, 725484197, 363313997, 79883418, 611684850, 357585828, 447136560, 264400872, 954723997, 790610302, 439964188, 965284268, 938234570, 914516363, 394196949, 215962244, 844699301, 131243425, 91110073, 350129940, 277181735, 590367044, 888674790, 485662094, 703094325, 796067001, 998124898, 772924450, 630491161, 156117716, 75823054, 439437286, 887856852, 605806396, 479044049, 302009688, 555824465, 40572426, 489316764, 755690364, 539470819, 80812225, 852597923, 852018563, 207989195, 183121247, 574248282, 400263922, 435233398, 824490208, 936536038, 747692871, 747906712, 271034753, 879750480, 669375186, 119591854, 601984589, 496812852, 326789969, 949256616, 687254448, 795797134, 474455365, 767467938, 233133495, 619067151, 887235075, 141798306, 750546489, 142636726, 774935494, 979394862, 79437563, 804039136, 408399476, 888838413, 887271389, 906435468, 410549220, 367148067, 413976139, 58221986, 232380209, 452369661, 526912077, 519022527, 882351753, 376551583, 721360600, 747371498, 584547196, 961394834, 771346663, 362818828, 339986708, 495936294, 385771104, 879230702, 12020449, 945487270, 464708101, 595951949, 656603673, 287565064, 326525678, 482604859, 250785428, 636034396, 404194865, 990190974, 986600513, 419457408, 199323530, 748779030, 126144563, 241888055, 773980032, 114079140, 929741969, 89693477, 569469818, 415866137, 740816017, 944457991, 874613185, 849528284, 512865830, 294796116, 23133401, 884947423, 362148252, 735407733, 612559768, 744346524, 372511214, 181228619, 810877410, 245586023, 488665387, 237835358, 432038671, 539149179, 497815533, 268915788, 971576576, 579362576, 301064230, 290176860, 917033266, 29462485, 388234197, 72191565, 440941601, 515626844, 936297964, 103111143, 51079081, 364754912, 525723310, 88979747, 552616985, 917621957, 266733375, 305434047, 136070240, 489539969, 642850763, 872367951, 686086960, 828421532, 365331063, 102483794, 396206422, 33486691, 332187138, 83007141, 682193845, 552803748, 705754424, 507223092, 720940783, 477006305, 809845547, 777064072, 577252368, 54622512, 224781675, 267060696, 99281235, 498912793, 18627661, 262626234, 456567614, 927211208, 378717932, 848699014, 582444389, 628876469, 707145107, 248622053, 388768778, 406682354, 642143062, 999840032, 576634783, 12264605, 639221186, 355541179, 282648908, 116899253, 753101205, 996055470, 162668930, 385589386, 712253667, 546639391, 641644389, 777408898, 380435078, 353768552, 775343338, 222060269, 940450664, 737215033, 969157217, 84916151, 283949064, 60154463, 417277305, 273246735, 734961966, 621382468, 618688373, 170397794, 712492837, 122209589, 766832737, 886727592, 611655309, 215534548, 905816354, 28142860, 672737754, 246052577, 954463651, 355829875, 774761167, 761926427, 939909337, 246542781, 256053330, 157790335, 756201140, 518328367, 824000285, 743869178, 403400113, 456646391, 437482792, 137225002, 373226478, 463566988, 535256814, 942209421, 633521950, 597698796, 702827799, 97708850, 228532632, 230312030, 613435474, 110817923, 9051069, 540365492, 33395274, 640995313, 361029618, 97705170, 242656234, 899616792, 482315733, 345853852, 746524465, 374749697, 285583271, 184674830, 255561785, 123551091, 959184429, 652683264, 78588361, 993687904, 288467216, 987243548, 250211234, 131780353, 267802457, 280014442, 8902426, 285272582, 651812631, 263808163, 725386367, 494493666, 741324437, 659460411, 635310573, 745155474, 865232066, 302327704, 457031120, 154039206, 168735173, 790575420, 175935653, 641015204, 677474422, 990437134, 883872194, 18774841, 611100552, 684269242, 90256907, 74131584, 682350314, 61377044, 865904420, 584691493, 301854886, 612421939, 505966137, 987933869, 245234953, 501866788, 389690949, 334967736, 219629919, 236499064, 341115527, 341144733, 589361133, 511432447, 292685391, 974072231, 895851884, 557175747, 711025124, 264533749, 624322953, 759069767, 977520541, 520090982, 888396703, 6245393, 189275154, 334474360, 480444220, 532317403, 33211212, 698013021, 171735719, 312157803, 876727998, 216483209, 17451359, 799232989, 579409125, 443384143, 887255794, 706234073, 823263626, 799504315, 850514787, 402853812, 347745557, 995957981, 841250752, 272957529, 45311730, 997069946, 570891917, 977145130, 392165641, 843439777, 515669568, 464380439, 813071744, 992604562, 89368902, 271186450, 187073392, 497462707, 429368051, 21731223, 50240910, 144115814, 762113915, 529077481, 739274429, 851913828, 880888027, 157454228, 930701862, 358648204, 329879429, 188977223, 373956015, 21698327, 765757272, 95667819, 338764715, 23309432, 528903370, 935243996, 175096977, 715414158, 374380692, 63702550, 831795961, 91692633, 622109365, 617243374, 746788571, 969943102, 126833849, 45573965, 528386121, 754734607, 971338666, 936756085, 638635845, 31574292, 461321534, 276479450, 988540069, 531170958, 352706105, 912681245, 593814319, 142078713, 111087291, 15396193, 422725927, 649168568, 85662094, 955858783, 152584268, 175087220, 183931163, 826324652, 261596992, 732178503, 997879745, 677623103, 541900014, 686020508, 929782017, 973612123, 387037782, 740729196, 526150585, 612281677, 222073771, 844240512, 130422991, 940634436, 289658463, 105884846, 625711263, 347649742, 126549078, 722576240, 347658075, 114871361, 277070928, 612895070, 408312527, 377951537, 206420059, 690978425, 721903482, 428101022, 548181980, 275480418, 779202234, 534324759, 286311008, 508360732, 741631344, 588049850, 544032123, 389117746, 95243124, 610002492, 898247079, 141061030, 888733741, 395938588, 602679523, 271260017, 345195142, 189361893, 273346375, 905208204, 383013050, 454392107, 562107414, 262103703, 135085405, 798719942, 217489654, 753014647, 958121147, 484746811, 805069935, 683413808, 507922103, 272659666, 356539812, 633580247, 645699643, 981036173, 409989797, 357814538, 27810139, 409146286, 512188533, 520417895, 782111415, 529957762, 375278513, 724690139, 223244129, 800591985, 575098413, 11995842, 478320009, 558097363, 810176309, 686846206, 753496835, 800384843, 271675480, 70251975, 832904145, 197103225, 334782156, 807233636, 960297725, 586462577, 585808716, 872719373, 487362136, 1017490, 355461951, 367457050, 948943451, 726381566, 331213830, 487227235, 3719645, 811601496, 28294986, 342240154, 852898188, 275045834, 883506493, 325783281, 592456777, 916893875, 706652303, 834321339, 746112266, 539478489, 405426029, 625799013, 122772121, 273451351, 485440160, 711648756, 426909156, 80196773, 826538411, 750189718, 672809440, 613760596, 419535879, 896941078, 192651899, 363673321, 555667238, 392663504, 260628361, 442144216, 188179660, 839792202, 475360007, 754322630, 535555564, 590023503, 855646560, 963158170, 24082058, 666604866, 139972759, 970981346, 77499806, 398931992, 249971158, 882667035, 217759178, 478478326, 722602719, 909612951, 978367056, 59189261, 848559009, 33300824, 185619513, 518710312, 311309639, 778802410, 95142895, 330412381, 420064744, 646367587, 101465742, 844891740, 319400717, 760804297, 811519489, 93753233, 516520445, 599498486, 290463574, 308026445, 528204269, 370450294, 902943040, 681158445, 447950165, 412420394, 291391395, 740924885, 464486411, 979866689, 605334952, 128791245, 512257566, 729551149, 810091736, 678873524, 495480801, 453094540, 840370131, 810945797, 428747481, 430926493, 943728365, 434604435, 5678555, 723077592, 41326157, 464134268, 39538118, 75900227, 640558876, 83699757, 111989307, 225664731, 695160296, 830128476, 927414066, 664294281, 240686910, 979395990, 256772269, 766952673, 683074893, 943286786, 460338228, 9605788, 329752940, 121128456, 104864118, 400361386, 200431815, 215542147, 669143557, 79053341, 197273425, 145666636, 200446296, 410944924, 703639764, 945739290, 497352188, 292254199, 552894023, 141902862, 404225156, 399825012, 836515502, 198552142, 120657045, 427408410, 126475413, 321960697, 310331765, 332676647, 204392361, 838163250, 229516936, 562921931, 784632755, 630354394, 99983668, 359890490, 678749010, 376655840, 828186317, 987195113, 6085681, 560361912, 233859127, 168468932, 692661358, 86180958, 260445855, 668259657, 200378712, 280222556, 710993367, 851239120, 918992344, 254612132, 646615345, 501622314, 525479978, 341623729, 201289413, 472841468, 512139528, 442060648, 195183264, 177838863, 904176620, 420774032, 938206812, 457443476, 47613629, 395725411, 219614742, 537347603, 652098378, 742719464, 288022048, 183776710, 506422625, 11657154, 60751611, 110432051, 377773769, 883583743, 791926227, 413690648, 91869299, 683624796, 743098704, 316373281, 877188373, 785262535, 396768051, 726397211, 756764176, 406539205, 359541203, 944306046, 128074105, 352971060, 401019968, 734743147, 714148339, 326892091, 519582726, 16013321, 79702894, 936171845, 311927871, 47010850, 925705623, 442745003, 952989985, 103323338, 277819893, 973733943, 258937597, 854299623, 820404937, 755922904, 69475546, 254915288, 187679999, 657014252, 630238743, 918303380, 398385056, 42584814, 254692494, 714157638, 336919220, 264001602, 792986970, 970560392, 144091544, 826216360, 840759195, 839790315, 393356376, 678671395, 117329270, 43315325, 15918321, 801713729, 108238831, 171865285, 781483779, 164116876, 846441544, 672724662, 155481376, 63922284, 336696061, 264874968, 159013403, 509361777, 900982756, 795157696, 402901793, 211037769, 625894639, 696929807, 157134370, 678640377, 112971376, 240332188, 450127994, 768783384, 126868315, 802417919, 743101114, 2713717, 510111391, 577884350, 106892874, 213931641, 771736755, 634745557, 536312208, 68190812, 821623877, 754680438, 953018554, 35774793, 67722678, 15036665, 106955357, 802129602, 48317984, 485541604, 558467499, 858951745, 191447810, 468837311, 708052857, 187957426, 543236947, 894189810, 917286029, 217928493, 893893469, 513733716, 784279412, 77468135, 479216527, 990982216, 130255712, 393138570, 394437113, 929742630, 769263055, 153798280, 924849345, 699144200, 464366856, 79219083, 794980169, 971795028, 974221082, 868378468, 988463018, 417226811, 890445188, 442846243, 690463043, 481216461, 711710284, 819654041, 723691412, 44929371, 141680941, 342728581, 108764085, 967624907, 497879764, 636376359, 609441132, 441159142, 823344044, 617770666, 433081045, 960054358, 268553828, 302466316, 694487016, 461574760, 39888791, 365762306, 331868916, 784791928, 915148069, 133202339, 291896876, 457584558, 652491502, 636574402, 401390072, 548770598, 726406405, 956584701, 4587938, 535288852, 670223822, 775389761, 95321184, 45666113, 273290591, 516781243, 186029701, 304314767, 339680577, 644849331, 529607435, 675420877, 721734907, 898478585, 924913501, 590477345, 737887027, 336933564, 681243872, 50047850, 302079952, 275906485, 968678182, 299927506, 727212133, 167450393, 342259603, 509935956, 838885059, 753968585, 273259069, 448827091, 176163644, 875587836, 567445475, 60166618, 829940142, 619000647, 379817563, 322670752, 404046573, 163417773, 83240400, 419452707, 178395479, 736822092, 646067341, 946086910, 955555578, 242260081, 861446984, 527608239, 363140684, 31708986, 648339024, 260082691, 968839562, 126373007, 164577916, 653431754, 132046215, 941994021, 702593737, 448856551, 362581690, 713145821, 929012986, 551702166, 263437201, 817851613, 233124971, 625941827, 314985820, 364363080, 986125842, 957966219, 488000348, 610311944, 962724305, 856114899, 640134825, 678965186, 105177491, 961234823, 519362578, 575175437, 17005455, 729539819, 381156882, 728458331, 89433920, 92427682, 965117299, 307375788, 827657249, 989961358, 813693656, 950615781, 184028439, 888844964, 910021049, 106953268, 176801172, 399026806, 286058083, 939555037, 931388613, 922370352, 213004839, 931617624, 772089882, 170192073, 857593210, 439223651, 652025933, 66481435, 876405731, 4151809, 773915370, 285572597, 631551603, 127000907, 724510495, 885586533, 803800306, 839624643, 708544496, 366602313, 659595704, 301383874, 530943457, 699047760, 215705712, 416135145, 758829186, 921278196, 82625709, 795489764, 738744414, 68377609, 544077841, 316972553, 425456303, 471982164, 471671679, 240094710, 825838861, 107667078, 100555506, 950513526, 15445381, 401219764, 639924783, 564044679, 176950632, 239825490, 822585836, 584629026, 910262626, 425314965, 928043059, 30554177, 368839451, 883917379, 308619568, 577623229, 22057351, 305992653, 830114833, 350250997, 948975351, 23059666, 731031102, 772422744, 289463241, 946855570, 287621226, 972487952, 870263909, 476536675, 606066330, 815261863, 713695365, 161340506, 519661090, 51464691, 611176860, 193219867, 724458632, 928006593, 685920743, 357730337, 687801920, 466983418, 433482581, 440866050, 199474823, 145119222, 703618700, 549221351, 365038362, 736138080, 610621897, 184556643, 109544286, 407808218, 700640221, 932534929, 598127245, 50506281, 284963042, 553054801, 349809154, 146911966, 397441806, 808457099, 804175425, 901530442, 977662625, 195639614, 326350474, 80782081, 429398938, 60042889, 882379786, 978309420, 409500006, 805151207, 498408053, 974776742, 224066811, 261353655, 681802012, 355747270, 157975526, 907499773, 827537261, 27351677, 81886443, 168509412, 591098663, 91143832, 339087277, 704302850, 762875918, 477454323, 439373427, 739064552, 345479929, 601736726, 440591130, 696966640, 518003836, 887735214, 567653050, 380620730, 598903407, 982963302, 784472768, 226152073, 808300929, 105347778, 227919922, 607368944, 865155800, 447089239, 272100648, 163609195, 33893511, 938239039, 105641708, 241190311, 530555194, 954540847, 20531209, 798688349, 172465357, 389953147, 134750204, 975246142, 468539556, 718668074, 877052911, 771823438, 297665804, 607399622, 395223881, 513505749, 535319277, 311528659, 910711820, 518906657, 806604258, 214601345, 750620695, 103671337, 70885243, 671083061, 458443279, 426597097, 606135019, 734861977, 322937501, 965094288, 295096051, 989242053, 436279985, 173137805, 752981335, 161132238, 895455750, 67893908, 727174769, 502297125, 27674351, 926670067, 815913274, 105350952, 82264927, 258901901, 241839301, 204098860, 933903085, 760841352, 212988080, 55994035, 862291191, 902689151, 847242195, 5734324, 407486278, 377169027, 694128111, 455605243, 47158401, 85321277, 867939997, 520124139, 357430354, 949211241, 979103029, 434038145, 290087031, 640850303, 874538746, 288939607, 162442570, 941626621, 936271723, 694249081, 588338570, 925339357, 578987077, 860252554, 372673889, 923941383, 644178638, 559583277, 828818933, 798887626, 19630434, 618180336, 358493660, 580450664, 129688430, 447359203, 963410375, 244357058, 139031669, 453141732, 864249762, 807588272, 417610410, 431009129, 186134864, 953320204, 467843198, 410159498, 431349590, 940868430, 147443459, 465142619, 258479198, 439810188, 883095478, 899255705, 860423864, 392578417, 860201054, 64872247, 42486601, 546168376, 885495093, 781238354, 197176140, 817146792, 343887223, 270293279, 834476232, 715914486, 351611498, 380546119, 336003286, 296624241, 2566714, 60124712, 404407247, 117907604, 798042205, 137855485, 17170262, 576611637, 231525651, 341080939, 150621665, 466088230, 224943824, 207226820, 743651954, 427122092, 815529447, 939485333, 46120500, 975120323, 719880192, 337465508, 986398338, 581305405, 541628405, 124001352, 398636064, 473002458, 84292607, 564251894, 367094425, 314707343, 448347810, 58354442, 634084042, 497938861, 25957733, 900590575, 259869371, 905027868, 499087127, 175908206, 897741518, 885585653, 185807524, 95669485, 145262771, 122124966, 936703596, 185879020, 296209606, 247157464, 338548461, 619394431, 311689380, 561498505, 639473230, 473351282, 259889704, 241274937, 250127947, 350293005, 540763304, 425785303, 981576255, 793350754, 928277866, 196477698, 911075979, 620918047, 932500108, 623033257, 516939501, 890922568, 566292553, 455878680, 318452481, 180566550, 32089212, 553619129, 955406811, 232375246, 52420501, 241702942, 396245062, 904420966, 671891103, 361457942, 615250532, 210356100, 627168518, 510082334, 150926564, 276599771, 147321446, 558181697, 35744343, 546931577, 693637827, 965973088, 898227234, 943476883, 559395677, 53569784, 314882472, 114682964, 633713602, 310501361, 193811544, 594823059, 223523780, 764782993, 884906133, 671678011, 106305238, 113036083, 266266529, 671138281, 496677079, 38353992, 817834925, 897560719, 553884975, 742670441, 262302764, 168411890, 245762926, 540495844, 93921331, 773011071, 61217213, 351432781, 114896038, 530269675, 143751758, 257819862, 431983459, 191755684, 644648568, 350257172, 121974000, 462520981, 649619966, 997557930, 255367387, 299235356, 659354670, 642055273, 51221043, 307052989, 81969782, 332702630, 427815197, 912370363, 987291946, 965145934, 75902371, 635941275, 131548611, 811688714, 781209336, 524058816, 272195831, 375213155, 376026192, 393272550, 873998263, 574638417, 91431605, 792268784, 210141176, 174921821, 964949184, 151230475, 344775484, 84309935, 60872491, 844427712, 31868679, 833086874, 167658221, 834886812, 628415840, 317054670, 860804132, 671143580, 106836748, 807129533, 678409579, 412135036, 756907980, 203426460, 411033710, 473050847, 285012916, 20264500, 752605311, 154461777, 556217686, 892561970, 33617493, 11090123, 839336238, 631513075, 633699889, 73590133, 218545835, 982961791, 812081633, 961688897, 811453225, 402400859, 973046473, 56132813, 54232922, 833254626, 333270102, 997027807, 460547367, 128125547, 143584932, 952598888, 445902039, 428037064, 622257895, 607371635, 973626683, 414039374, 568293498, 23387120, 59157078, 950966319, 154532539, 967990688, 256771200, 117494629, 426877926, 877058767, 686809356, 108905567, 705432698, 972517599, 5270996, 510926180, 504870938, 273427679, 921014108, 396985051, 571667646, 699368016, 33532848, 174548745, 825443607, 735464066, 809914687, 14934135, 777449575, 100408495, 749220908, 315002411, 768485795, 342472390, 641864151, 431465217, 661082676, 637230044, 289397696, 925200487, 428062887, 974463570, 361844463, 829096432, 119530045, 226527049, 478685877, 27335131, 101875924, 260780163, 204862891, 767819459, 58834123, 658800178, 961007694, 94917624, 676020709, 418883298, 852474348, 321350403, 657842892, 471801265, 831664406, 247742270, 955489928, 927010753, 307289728, 711969523, 221819789, 591082624, 66489478, 596877802, 304738088, 995400532, 278405993, 827974811, 33808812, 608530945, 501484895, 643574467, 49784961, 898705604, 776474727, 291371685, 319946487, 191980198, 620102450, 894552860, 330951854, 673125016, 856024353, 620028956, 228181178, 222999326, 86365185, 795566916, 380893136, 200172436, 527725564, 999446906, 671786401, 617240022, 522914936, 595618515, 2377179, 713860557, 162067420, 984999357, 332253225, 734887117, 140211286, 766094569, 141023619, 238852034, 870028298, 863868983, 873845290, 297117645, 135734091, 564713047, 611880535, 781291438, 721776804, 748910083, 944221918, 582281310, 525144137, 191665411, 826438441, 579824856, 853357976, 296668117, 777506569, 185868247, 160068047, 968203631, 55979660, 645378386, 82841701, 473322009, 415076516, 658832565, 416927762, 340465534, 545574470, 760628918, 372717547, 767678386, 954133897, 112689346, 516969288, 96201420, 893026650, 722808085, 710209825, 503913114, 919695537, 473711096, 585149629, 599438231, 607203514, 168259364, 162164976, 768975780, 468352159, 928725004, 821600907, 49430914, 180043516, 13244561, 100312512, 561416450, 61169736, 631722015, 52911406, 419735938, 514517672, 752211044, 428906788, 224630057, 993207600, 530433988, 284359055, 634052239, 257703792, 934804092, 898862698, 246747418, 787135740, 264510677, 426273432, 825477179, 65542105, 633669483, 519849379, 456066156, 160301149, 919596716, 108467428, 232295738, 394049816, 528086680, 772974283, 929497438, 401888349, 627455832, 289312524, 391102849, 331784605, 786911952, 619199061, 575234327, 598284810, 126190201, 826287156, 136632457, 46941682, 165917915, 79451986, 803843792, 933414053, 821004427, 968494227, 734138028, 910091527, 996834305, 714753434, 353890784, 943868192, 963277463, 291019294, 604484329, 787641555, 377194622, 108268318, 47145894, 492205845, 984106979, 166611222, 470385816, 269535614, 674921721, 605456485, 275780304, 992293404, 546713982, 598396077, 937508704, 286448591, 838625149, 699573137, 862811947, 526922443, 27251769, 847873229, 918729407, 371360577, 911928866, 929056823, 849921002, 978168154, 818366717, 999760855, 383259510, 705163819, 180448100, 416834211, 18053606, 916064290, 348905453, 674629846, 651340100, 127020457, 761569283, 723557015, 156274627, 516286006, 645216793, 973096054, 861195377, 846105633, 695956460, 429978134, 916719962, 989849218, 788417847, 83373252, 289743496, 883747108, 625327506, 242864545, 338443287, 301125552, 795464189, 999538822, 795727733, 802035225, 391477993, 478870872, 797478215, 546475995, 812673634, 650347821, 688715824, 395767161, 820128156, 555287848, 849065976, 831436407, 143822602, 641984840, 772334219, 753378747, 115329086, 490594183, 3866816, 756927618, 117975398, 208563173, 376965664, 931454961, 193548117, 962376940, 85716545, 441038848, 91715964, 155742797, 252507746, 150504672, 958655793, 764582482, 594192924, 954954301, 985670071, 179690263, 912457272, 463933579, 847563860, 311032728, 104480524, 521868833, 427736807, 363711800, 49504140, 818744784, 850162462, 178601271, 780623515, 287294986, 318120543, 632837717, 319404926, 256346757, 632683442, 636136244, 660969965, 189287537, 877709551, 23971903, 457527663, 871915703, 673682885, 623840303, 223267949, 351980883, 262029334, 357551163, 768529339, 39897554, 348977903, 936044114, 856952592, 219653342, 684924316, 968245783, 65971285, 689287881, 37379013, 397592224, 609315024, 156738086, 819139924, 740556143, 716722658, 647724882, 737505979, 634965601, 818594448, 141098648, 621848521, 549361261, 808602626, 700170772, 45494994, 922051691, 214588198, 1207175, 183412268, 832821107, 15566627, 603576055, 981587660, 237974863, 781032253, 632565224, 358257294, 872671467, 4732699, 720366406, 680249833, 234304289, 909116448, 926986870, 43508566, 960475039, 6618370, 649969199, 252236357, 705628018, 237578733, 713941475, 649333345, 591465120, 557009814, 117269814, 361095779, 389976269, 433640934, 72825156, 330572845, 140550806, 127388890, 383365084, 541377031, 53267365, 246988991, 843668754, 37437213, 673931943, 719174911, 923227152, 104984216, 627764762, 26174087, 237354551, 381361256, 253114536, 836790412, 427221140, 579137846, 105553114, 393439039, 11755838, 824630644, 713833443, 273525816, 213092609, 394439667, 962406346, 50538109, 738576505, 451702680, 402573509, 859584149, 482402133, 78797992, 90161172, 559118707, 997569871, 536933061, 221608795, 274719736, 195748563, 564351063, 667905973, 676270441, 719278038, 660836010, 769541730, 904019596, 626947657, 904272398, 535259471, 359011044, 260084721, 623924729, 944691448, 439824276, 465486292, 26732858, 952341656, 421061862, 955672787, 879168080, 689990437, 446155536, 552881746, 224936523, 968887261, 102593717, 799120241, 648277599, 752102014, 464757969, 969672124, 244196761, 477349655, 625520240, 660611936, 597056538, 770529278, 435998007, 513832673, 560674823, 847558353, 4947584, 693235921, 961433609, 428307930, 669869315, 208005139, 616726726, 783856851, 139813198, 406594855, 954066242, 683851476, 962394236, 338950972, 905772428, 628187660, 406960327, 53388860, 689899276, 812258970, 848990670, 63724121, 399172680, 353616029, 70940854, 332032359, 489135827, 666273900, 634025338, 41146902, 966613581, 723565441, 682872329, 633734213, 575795925, 148545626, 413978292, 922701902, 239008672, 837835118, 205738248, 807689160, 407699210, 172866539, 903194796, 54198271, 411780110, 461488247, 183827147, 878487376, 807955327, 934019949, 894051063, 153471799, 591593097, 514109595, 834471408, 759385361, 504418916, 824068196, 478248500, 373407148, 610747160, 388788564, 972510933, 823684226, 589811930, 651030498, 181963391, 965997384, 746225049, 895796268, 617112155, 44253979, 324470018, 514227500, 7864302, 731129196, 939372599, 897043553, 975603680, 596898481, 729775332, 917373017, 397615785, 26815235, 179233900, 57262037, 700157820, 610918501, 861454632, 525986250, 731723212, 651079262, 952188682, 787813549, 370030449, 422907912, 195761391, 38879888, 824143558, 56218488, 68251711, 801659670, 801784480, 999512938, 751373792, 360081055, 181771617, 25277191, 648470738, 631419401, 95041700, 302890426, 224550341, 120155085, 30840434, 395743488, 497890881, 101658019, 394572579, 259826404, 932692290, 717933302, 605016484, 601426732, 658736116, 88829625, 726696493, 691807535, 371722208, 433202495, 624396456, 771188146, 284701456, 700357232, 916259370, 942866865, 806629428, 954972266, 752408308, 235337489, 194242534, 136252709, 814256159, 423192980, 638645885, 558194367, 255952258, 356365221, 436313473, 382360334, 622449974, 91676908, 945212732, 247300108, 392682534, 80627533, 616996492, 913326655, 107938295, 743155156, 515130761, 77809785, 871572922, 400271063, 599999742, 968426173, 487364405, 882703450, 226958451, 336087451, 436595239, 468558662, 956127568, 565850546, 825522717, 436170145, 787454301, 36874946, 998697886, 925219546, 74653148, 583166093, 513744330, 898561962, 487741958, 427579201, 934264679, 640896501, 670546506, 212924157, 547463019, 246355623, 835353791, 568045093, 304387102, 200052484, 148853302, 980820609, 934953215, 771101087, 35167987, 855075742, 365284255, 983076031, 868807985, 369551005, 501907142, 749571777, 40521132, 189169655, 922785908, 617190509, 884284209, 588402879, 209669491, 198524640, 121559662, 864373136, 636638421, 30512733, 778609583, 924585868, 318253317, 724598657, 446906269, 493149285, 965363342, 664606174, 164673459, 80424511, 942218416, 395425620, 682230879, 65251546, 835311400, 212429444, 310172839, 35445077, 174852697, 246707530, 164945124, 892668468, 377423052, 209777489, 205322668, 756750927, 594688432, 587208595, 139605493, 748448721, 485348038, 920372412, 191123866, 75256149, 165598545, 881107473, 487998043, 230401296, 75630688, 301125815, 360817863, 9661318, 969745295, 407456989, 257376691, 690660950, 681970426, 149443876, 597632031, 634315784, 427034449, 526008026, 830854027, 541717768, 647972257, 557005501, 904711865, 65143136, 587646957, 788742182, 854461208, 333956035, 315967676, 437567091, 499439812, 643840428, 297174481, 440272714, 636510124, 190250022, 574458290, 493479689, 104637812, 461512625, 37129397, 6028156, 368816976, 631071910, 936626669, 835738849, 662364278, 854695704, 696176195, 977985188, 340456947, 433355029, 778826416, 638063389, 482771125, 998752777, 972997935, 151802131, 663306804, 218552494, 921328485, 820674399, 445813203, 771617768, 414413743, 478847723, 776242984, 985767408, 540705318, 191843532, 952773790, 509500937, 241143118, 38102342, 129254953, 201491848, 182249585, 754939230, 935774395, 656132100, 515474560, 90364004, 309658457, 578269361, 605431674, 898300472, 950256266, 287668356, 121069584, 176924909, 812118035, 513137738, 16303976, 940919245, 873201899, 92217061, 687532355, 463661264, 886187509, 896897466, 64844394, 565733764, 28513649, 898964771, 74059362, 512267072, 245469087, 694138693, 826373591, 684096351, 532038809, 725245025, 74301497, 280905977, 834827628, 388227964, 100666200, 388673315, 528473001, 801966808, 68433018, 555782035, 965348929, 469078078, 24443634, 397606845, 674128782, 498327486, 444916199, 441343076, 895468497, 300080802, 960240867, 373610880, 560241538, 848236161, 673961121, 185853276, 588874153, 657038493, 844343630, 2480167, 585431126, 944690393, 145157699, 160544834, 607702334, 144139106, 700401754, 868340912, 55392083, 180060199, 308981141, 618354553, 247612775, 341227084, 21889755, 476925288, 140807619, 444855041, 848210083, 320168872, 743204087, 866752897, 558004290, 912523124, 307491192, 273868373, 900985301, 945761991, 84084164, 647084043, 944609991, 402563404, 7409146, 272625476, 939566637, 351968239, 587101764, 74943514, 660717862, 475498949, 415106664, 864708774, 66410847, 754941575, 693235817, 239551758, 244585705, 342377475, 765517029, 244757598, 354281720, 981049074, 231184444, 524880786, 97932670, 503958229, 116314684, 684947776, 244086664, 611485091, 33746522, 363578446, 190341075, 323231507, 39230888, 701446566, 446487677, 947677430, 154793986, 768090685, 481684294, 256554968, 620622603, 5781572, 849322375, 483771366, 604529220, 653935096, 947645938, 3056223, 650624451, 689870538, 225082076, 297924363, 220812199, 909884911, 372967915, 972517259, 238740473, 850946169, 852002780, 734494956, 624785756, 933426680, 865901368, 928267683, 829489658, 661403662, 729099795, 820743106, 308359490, 880276370, 442416115, 930067183, 670390954, 14121003, 183286612, 901154192, 565654333, 77615201, 953432653, 376912547, 469506294, 32333582, 628868171, 504787918, 873819778, 756208401, 444313594, 457127113, 356654268, 46100635, 760381055, 107430121, 824007657, 437985269, 321820914, 720064804, 87269430, 942705591, 109702648, 116916096, 832338244, 511255923, 575628916, 456610254, 248238183, 837864258, 482017241, 857457182, 479079094, 128930238, 801216297, 619505644, 701100877, 219773017, 988396634, 156336043, 190594824, 579143048, 786822109, 450307525, 682880378, 102791559, 935283776, 528482280, 322661924, 343941727, 910207393, 739009469, 682424545, 838947490, 784726716, 122783124, 524244237, 312771085, 185621426, 694971037, 240863863, 437099971, 487335599, 568734049, 280154858, 74136308, 209218288, 182527611, 609175881, 70898926, 398786729, 923015696, 432225148, 925743726, 522512902, 624120921, 894885556, 30083964, 745798546, 4914983, 140750008, 643647839, 710176892, 78046433, 528831729, 9827353, 374852506, 98765219, 177400801, 604595751, 902856139, 519313344, 252154770, 721827647, 588308984, 863889284, 37418918, 723655282, 515992254, 487587902, 832395319, 69480212, 986723240, 25446161, 982218425, 397621113, 363413344, 726793462, 574569503, 750747195, 520894994, 259526135, 721863832, 839121116, 323677176, 456307422, 127185657, 288380958, 445660533, 327255313, 598457088, 386187277, 149000515, 847005477, 959874260, 536040611, 542095317, 765482806, 200643926, 299614478, 898144547, 838371801, 941417611, 805333261, 804891675, 895613438, 397295052, 834620167, 451145525, 617548117, 268313777, 91646986, 618543566, 278416236, 539879857, 201773403, 817062584, 43979556, 107182814, 460502347, 205293786, 570472346, 741054920, 942238881, 56682444, 311100478, 578991951, 928694460, 643874122, 640143286, 845584762, 613658672, 758148656, 706680141, 476062881, 127436242, 925548909, 315049030, 875256450, 408667041, 318813553, 586242290, 902403805, 868374884, 164174600, 226485674, 850711313, 464317274, 219502684, 490318272, 881915564, 241747867, 63701721, 406680366, 129215011, 468895363, 287494294, 946636984, 21050146, 60969747, 550733458, 842849691, 324242499, 596912193, 781749454, 424434579, 178692299, 41004495, 674634595, 522286251, 57284252, 568503594, 370045035, 123406048, 762060536, 280010007, 202381549, 74496337, 67868807, 300433998, 441124267, 603178976, 117411491, 346371312, 135865042, 773735568, 962196071, 698786137, 324178251, 982893120, 859072225, 889464000, 561487562, 57249630, 118416359, 517442560, 574244156, 535003954, 681828617, 499088152, 829089612, 847601707, 731578008, 649948469, 173447065, 709119971, 796908421, 343090023, 80736940, 717322927, 938418371, 240652168, 820221135, 114977330, 440943823, 266861999, 183565408, 291254884, 964942477, 873150888, 84993111, 685088032, 393777548, 550900502, 814429509, 416094659, 148066771, 940291909, 155502901, 694307839, 199423322, 816664625, 412356991, 937117171, 275822685, 349227227, 488496724, 907609660, 251857119, 252432108, 85834635, 299716405, 751263379, 129032533, 977858696, 164143272, 944530985, 367704191, 950471232, 561885976, 590034771, 957665940, 276341469, 984743161, 883569545, 922257260, 436537005, 88453223, 267487071, 813864675, 486514815, 984378401, 650318652, 879919622, 350888252, 362667384, 672753035, 619706288, 587470884, 777920127, 35489176, 114275354, 934279301, 590479505, 446899825, 287350783, 741461454, 781631723, 167893318, 743221274, 19905201, 900560752, 891458656, 902815500, 220052673, 559740574, 943200464, 73496681, 881438704, 532888905, 157853392, 181372819, 62712023, 888291996, 46142742, 838887694, 453094925, 987731732, 901442193, 942551074, 14708937, 693715975, 599148692, 902463761, 954645400, 488605043, 840740407, 906431585, 57035546, 944142827, 658390331, 973000137, 484657738, 602318045, 174683528, 821470866, 666060025, 213223373, 702553254, 374763623, 70925328, 462735975, 4963777, 393271322, 33126199, 175304468, 784112547, 653297880, 101946138, 604505608, 763134235, 121476732, 291760134, 99933519, 470390410, 385678615, 414740250, 582566278, 908953411, 809175105, 993170623, 716432181, 529445977, 474074487, 951128290, 669483238, 660975828, 934764, 521790961, 799582352, 319706284, 603501529, 20971879, 587852367, 4647391, 91558411, 400145715, 209310146, 590326708, 239301226, 984567849, 988646156, 749131566, 786090598, 716647975, 883415758, 437647506, 289455108, 869099655, 999389673, 826147277, 706399713, 915240234, 75100787, 971326337, 952019079, 416150118, 688510843, 927119757, 586260822, 259266884, 717962809, 380194, 109645369, 886433956, 641107360, 839421904, 516365416, 113583376, 985757471, 340558356, 486099838, 942243326, 543138066, 9681700, 452752238, 216763802, 394438469, 594669426, 671698464, 777471299, 956246584, 822217430, 748674864, 420655829, 647762634, 948848938, 439557848, 409758667, 551719063, 393401735, 497154005, 971413360, 10557683, 695318102, 614349571, 891404031, 44685567, 627303470, 886016060, 366234776, 173158491, 451880355, 522587020, 153416109, 366230689, 42670862, 609151337, 468760139, 9713798, 95285851, 870835162, 437214056, 615722391, 370675022, 682115251, 18874212, 505322959, 624290943, 469611322, 528990801, 804916708, 671689075, 306923636, 363348618, 652921476, 842603530, 941782105, 835773798, 941256054, 857560835, 975022510, 313734699, 514068700, 607447705, 863621152, 845502734, 900274358, 55533445, 522348910, 921047808, 603994503, 536247285, 674708907, 572513695, 353944596, 865348045, 673528916, 155351017, 189817410, 977733505, 559027268, 869436500, 563152336, 102797034, 538876163, 116771134, 607973650, 104284662, 520102360, 734840276, 581836419, 926307392, 797564685, 596498449, 410502027, 106543286, 734839042, 38286107, 126433475, 885677202, 528165406, 909458851, 745930957, 801474807, 869048610, 401583996, 411784681, 413089678, 90135217, 462376035, 554361729, 545653740, 976497606, 125768206, 260077051, 631436559, 4255713, 114013991, 71790325, 64693169, 917321588, 782241657, 465142061, 713925770, 143951767, 78606601, 572799935, 478986421, 296773156, 455941631, 746018558, 36184207, 400143913, 584834541, 250644101, 331064754, 963541663, 777664141, 674516108, 593926417, 579953178, 270193848, 837637437, 816704663, 179325218, 963418067, 37390240, 282376946, 673492893, 456319100, 819078306, 160604707, 799794633, 782675304, 188898596, 505237529, 514339591, 362343983, 570986924, 769635288, 253783184, 384809138, 509249171, 353275101, 843335284, 753499370, 239022196, 96789623, 102658832, 762291499, 729366620, 852725217, 186026388, 905257127, 516468109, 531795733, 637865091, 548205127, 124917846, 392697266, 266808452, 298922740, 140994807, 26289693, 896246548, 386701882, 154511906, 824477495, 403024478, 697119392, 610453794, 320892936, 342943112, 240640213, 843645975, 933079921, 316376429, 383330094, 972591519, 575846044, 860006247, 489374186, 229435402, 299138462, 697543234, 176585257, 564024825, 134148676, 649977751, 99237092, 963514428, 366660178, 308918349, 429367231, 413131748, 351623239, 412145604, 62901370, 60629614, 296801846, 892187863, 231511621, 331919374, 797818955, 817466610, 973242761, 313016255, 15083681, 208522392, 902869917, 674390433, 318046321, 378094528, 269509893, 661458627, 851518644, 996914007, 333077758, 416802588, 84963490, 286514519, 31519047, 417853246, 824049685, 266523000, 917602453, 577186800, 258636910, 777716422, 906591023, 688262327, 641151842, 610471466, 136195464, 739350512, 756156376, 793904676, 962858006, 157907228, 13846592, 452036667, 751835294, 191689501, 840349703, 596773783, 672022149, 121454966, 519345548, 226209036, 932405741, 828865447, 134222604, 924442604, 213348592, 201120066, 196916968, 462877264, 903933621, 927688394, 634840956, 934925974, 274062903, 883273363, 499224725, 929511940, 232882108, 892671121, 987073827, 383805138, 957811226, 460942576, 177874871, 448191102, 843537103, 839776824, 548238253, 381297159, 813141667, 682459961, 107956482, 305809004, 878190334, 957466759, 771702292, 892324788, 83761116, 979989717, 858558342, 12324619, 584713961, 632603432, 793103119, 818382417, 911518576, 573204907, 518308168, 585232060, 629786127, 167729863, 35663000, 783543597, 373841326, 612253794, 271258180, 959649529, 918076882, 76761830, 100087304, 869145763, 940923630, 383083983, 554079323, 308897912, 162766157, 468630272, 477367283, 681394469, 647612580, 734275699, 328886945, 558843319, 235877977, 955091666, 569665948, 159391056, 174211264, 229782060, 27248555, 794629141, 949167498, 917712653, 285051763, 227365684, 169919545, 67424834, 199765942, 991531232, 767072611, 931804676, 146580901, 829650770, 423005406, 128087048, 323460565, 29972556, 843882118, 887100917, 117373248, 401938920, 270583421, 294264399, 392411707, 139707496, 728395103, 264369435, 323131495, 260398833, 993857929, 297649320, 469426442, 651775118, 343251262, 853899095, 355949795, 278161625, 422610536, 772702500, 54860979, 240881252, 38302286, 331563411, 961005333, 633361220, 805832562, 453392808, 564601339, 983108230, 806809648, 166134666, 842703047, 626500683, 494130618, 909672854, 172894387, 223968095, 315976111, 219639208, 104802260, 638272872, 97307735, 614818366, 388482436, 427882619, 316331429, 279162665, 68974461, 814868406, 735844964, 502646216, 402971636, 352033806, 713758100, 817558798, 399537930, 256053203, 550443126, 215434418, 873880435, 149774910, 646716515, 516582746, 118423161, 928013081, 655259572, 192166919, 761899800, 625584209, 790269049, 898107678, 355261320, 151017956, 927183660, 901046989, 978125493, 699665128, 506121159, 940067840, 329307444, 484709189, 179078036, 367539878, 196912629, 598191365, 650968175, 507455546, 140662363, 317944938, 860691378, 667804426, 118983643, 694871405, 756790655, 339504637, 191411358, 684972275, 805076591, 72954868, 954324318, 444926076, 612635024, 80472025, 165838897, 110288979, 607855292, 765549807, 705723348, 293708374, 601713690, 752720479, 722780511, 451171514, 760135362, 506773487, 511147268, 904944281, 50265339, 109021529, 4267929, 578041343, 666060082, 834698382, 951796527, 794400567, 211340585, 473879013, 578093871, 426855378, 655888390, 765773157, 423335472, 536784717, 785431551, 590665872, 689589066, 826454684, 903398157, 575670300, 662842376, 340449422, 464776110, 777864185, 536762891, 893089860, 467974665, 802030318, 952092388, 52364860, 673661390, 186820208, 785864861, 729537468, 817344929, 897462045, 300583856, 256301628, 654014091, 364647211, 107568830, 264616052, 836594567, 377392976, 69716454, 735663285, 628502636, 245416092, 987627180, 75877844, 836608087, 148890969, 466402640, 184824552, 161896476, 380077987, 738116693, 925632885, 989602071, 257997609, 939828880, 253287524, 959838798, 110731292, 34345880, 185899651, 954248550, 863393011, 282286369, 207447318, 837122152, 586802655, 340496603, 102479075, 826635185, 825281817, 650698092, 33438612, 12950803, 562501837, 95872077, 447346827, 384222998, 914984976, 629634895, 737509610, 623434359, 521877612, 544115447, 409638843, 571303277, 908284728, 625212919, 777663797, 261398798, 132267048, 134186971, 651437285, 501901760, 805973067, 233503060, 98848505, 486180288, 836815994, 479038499, 332036327, 854056013, 409256242, 602157300, 335614059, 52619776, 848193246, 604645290, 520063535, 351728791, 76632589, 211890222, 906157746, 924511775, 107446708, 159973930, 820489916, 231817059, 601301516, 440560157, 12933268, 669132670, 808373610, 824890609, 236442215, 20632954, 443156108, 44295285, 203761471, 468886899, 972075431, 301578469, 856113551, 879360048, 459737209, 750956022, 552423090, 449821356, 601667332, 460643414, 240050034, 940790192, 377402125, 450829162, 716880651, 124856574, 828419438, 417615779, 895166265, 348247944, 593636929, 101763891, 280498599, 242198648, 426199413, 368740667, 317882355, 976732846, 591651874, 286155702, 281600154, 55163115, 393734114, 268209051, 934561909, 623396324, 16024633, 225243403, 371860202, 284531835, 380023600, 403365318, 68510897, 297670185, 308351529, 476249297, 895546457, 556620130, 791123657, 159873121, 200766959, 511763872, 522614366, 17855435, 769557196, 272261992, 854397103, 244616186, 935456379, 42497208, 899213379, 313032796, 552184006, 866951889, 902324592, 230805713, 592420377, 120134695, 759794998, 342567821, 741666931, 732115005, 164041702, 220861529, 519368132, 633132168, 827106602, 270850742, 61171375, 988732049, 179100796, 4116131, 737206092, 806677693, 547901929, 446283571, 705743409, 126827665, 941666643, 270061621, 758050818, 338636704, 584054820, 173499400, 679959085, 794822335, 504839491, 101993911, 712997236, 54022831, 356154960, 639216695, 827723394, 906862441, 448645233, 248173559, 830456851, 43732023, 527020999, 99396276, 568932629, 931437159, 435045081, 200448241, 170900820, 31550315, 347148923, 586320307, 759055177, 663458515, 238620462, 634476728, 561748719, 743604791, 761189356, 494322720, 777109720, 306584257, 595176244, 909819988, 961858955, 447951857, 472902925, 373303117, 62459921, 801078357, 534818861, 566041820, 836457142, 115282334, 200597818, 102503136, 64190551, 840102170, 507313202, 391873976, 550278521, 106582782, 835356033, 27094824, 971043462, 511336849, 502736477, 603985111, 563172451, 574779458, 455220906, 488767983, 587019108, 968645153, 635835414, 881790154, 671198453, 797906853, 215629244, 918612364, 727968806, 438823214, 42142929, 780152617, 639350136, 101995894, 398590460, 475663585, 824791263, 657178983, 135528029, 279498641, 660433376, 870857251, 774853172, 977739928, 310386265, 148840556, 349581905, 849222426, 173199358, 626470090, 246250023, 853882092, 523811058, 616608936, 495959373, 798981276, 90332676, 883235787, 403264837, 581738883, 769665944, 727371298, 537907107, 768491552, 752515650, 233036088, 911944660, 99981895, 41450036, 177399482, 301801618, 854393684, 934005902, 957474632, 508397381, 612284548, 348583540, 651475609, 55024198, 253751100, 545903471, 131147411, 471544796, 720661855, 178624167, 774345914, 424752084, 791510751, 634461842, 39584525, 245819012, 97869673, 171969118, 300823256, 804693513, 89783357, 173472196, 738343478, 493500133, 357318864, 971319427, 988457794, 565314232, 948141068, 329518695, 44448860, 481853254, 924040126, 925020206, 505088956, 221730999, 328120468, 767091432, 806460938, 69577281, 45516403, 14373613, 8646318, 656633629, 642741126, 129039404, 514163459, 480839984, 835886102, 523609674, 714052681, 364704966, 799203845, 17978030, 25935293, 777726980, 207218216, 336260304, 253346013, 323353766, 218349471, 718104495, 593713853, 88495678, 549103385, 474582696, 424785846, 792395498, 279166132, 946156444, 505834506, 800482914, 396683495, 841978742, 119680208, 428740148, 292973238, 55281897, 271197487, 318292491, 583571859, 633693597, 816216556, 302547419, 430050107, 945571352, 751637669, 466472072, 503772768, 964583777, 932580679, 191315269, 256700926, 316742748, 885467729, 604433566, 473810862, 327115194, 394125865, 789943308, 978761074, 978630944, 404934949, 681849049, 410066015, 292161928, 335403467, 720125188, 304386924, 443506291, 938601180, 662002257, 879055663, 907479831, 183027987, 363467528, 860809152, 911079402, 771687594, 685286992, 638222487, 790109622, 4853430, 69124975, 408048088, 371813737, 107931039, 461700838, 674334374, 406202640, 913571569, 280851934, 257820760, 674020524, 533667161, 257210687, 891722501, 176277590, 565719126, 955447338, 505239267, 835627754, 3906038, 906504647, 959214439, 905993577, 117496797, 356705577, 413128754, 567644214, 396003573, 28244, 218271991, 142710070, 33012061, 702230754, 304521700, 529303569, 267336793, 268385732, 805257061, 535257034, 527007280, 241196995, 68766400, 854532469, 68470673, 985697767, 19685662, 995204332, 920535616, 589783340, 93075080, 488358133, 81080741, 69871556, 124586277, 564908852, 651407181, 779670132, 359191792, 562398944, 173737333, 328658137, 456742637, 60692810, 966077745, 593592970, 521157046, 196414849, 665860347, 315517934, 898675595, 348074581, 149698369, 195790409, 2782647, 774829277, 391730618, 307588143, 827863219, 558016826, 137369112, 828384337, 615086152, 748536570, 693716847, 311401976, 768308743, 370689494, 486979285, 349271534, 476551299, 552911081, 487882570, 550691372, 828234176, 116663976, 247611953, 142638662, 321303569, 497615768, 135282842, 475910355, 758003902, 522009435, 248539714, 803610662, 454617137, 497696447, 152133005, 123245609, 920403696, 554492744, 799622979, 348653403, 22324013, 866606414, 568598040, 280229000, 346339736, 228609493, 972242399, 531356648, 433706771, 342108644, 746974285, 700105442, 625504496, 853752434, 52844995, 183991145, 495669693, 434889799, 987509580, 363660962, 454550091, 287331365, 140594500, 441003799, 354613915, 767687746, 109051469, 93625101, 649090790, 395707268, 514486382, 420958355, 208905031, 788948443, 793401454, 848280977, 188656495, 832146816, 946141126, 771205804, 992244567, 330197294, 842103289, 489089040, 684322339, 223646171, 140864782, 515566405, 208626336, 10244747, 542045352, 575748788, 136828945, 969214219, 365758634, 507883341, 35393056, 112057917, 540202328, 557945483, 961684434, 14957837, 422388736, 383256063, 330583070, 993815066, 482867614, 692583121, 21201994, 938511471, 747730065, 746426309, 156314028, 574649662, 971474352, 773835223, 820596839, 131539172, 70534909, 386305608, 246383468, 469524275, 967507870, 445523506, 529431823, 225653792, 502677538, 187046411, 907807775, 22868511, 118241441, 355448411, 987684315, 803241387, 4722750, 136524734, 58027273, 139563084, 161923827, 602923401, 2079035, 20327479, 407720917, 709010916, 598660990, 911869444, 823752003, 301181110, 88351652, 883439663, 469907099, 386066389, 548625868, 252585316, 334093271, 30844916, 793996095, 983045835, 585724984, 287730, 163279379, 223557408, 518227493, 308831002, 800744514, 266959816, 557610561, 219319622, 520496859, 804234974, 905325615, 797787841, 660477827, 544798023, 978585350, 514661096, 746711587, 991402267, 6100414, 935321909, 614074675, 679640880, 575175107, 640805405, 1440207, 869422700, 606398154, 844716013, 320098844, 985435831, 193409833, 122812626, 858675525, 183811430, 608468523, 326981665, 535100691, 752314225, 459522734, 755751256, 665899668, 240678510, 868233002, 121326822, 449978351, 514103113, 685632689, 173564918, 424912831, 433576276, 505400018, 442373795, 837046061, 922391663, 306700500, 605122326, 839145405, 462015266, 928774884, 328937725, 383304671, 904168335, 276936045, 908575504, 128144999, 235005557, 594551408, 922731277, 508412759, 578029486, 331482028, 190471622, 292648527, 978599240, 823068601, 47178580, 479820547, 461357545, 829092408, 392967123, 710219841, 928368712, 549275288, 658721641, 139106428, 770300849, 916191638, 875379877, 777192028, 646421179, 528131343, 409790783, 506866585, 234527887, 340719189, 165268317, 237926987, 401677737, 117403894, 131078477, 563125250, 486471620, 772281869, 973153919, 393217439, 613514866, 57213597, 180438995, 866558332, 463059033, 284124597, 436251671, 445174744, 994760777, 317058483, 625832068, 393377353, 371950179, 721551834, 320393347, 366486621, 993750454, 360966567, 891922189, 795824010, 85074362, 250574113, 611935889, 937814118, 549050659, 361835285, 847353414, 164115521, 819573783, 48784824, 992570847, 508803973, 526796332, 567485451, 672287748, 650909253, 533376651, 142728223, 349238301, 480320100, 444903303, 190742081, 913313485, 354391188, 145175425, 786923183, 326337595, 382447673, 19636381, 247966063, 324880100, 283860698, 81734442, 854860153, 888521264, 484438076, 302127338, 437006473, 683896936, 429664571, 210394428, 755239313, 329042276, 601043750, 537987397, 517374778, 331649578, 997282503, 635250115, 840098893, 754126514, 470254024, 50277060, 623968149, 362622883, 622338494, 696362928, 751120852, 841797941, 318586874, 211424892, 260689410, 964080219, 727049021, 146013990, 123515515, 519527441, 797989813, 450012590, 57946585, 614840084, 327281862, 353525679, 268674394, 867212291, 252555578, 956043514, 713118107, 670318186, 522179156, 289415195, 831067703, 146587072, 567234676, 613162147, 788690466, 440769750, 58951686, 785426981, 750990277, 869802778, 219982102, 962492189, 358235725, 30260262, 126507282, 697264269, 114411850, 216273950, 916127622, 811211183, 118555323, 915653673, 785686415, 737932809, 39377865, 89806192, 842560895, 448637960, 552231367, 355611835, 530547700, 613920949, 580601350, 448537480, 864934990, 924624121, 251283098, 147729722, 151359298, 196536761, 122121659, 463678322, 349281863, 18479376, 450980010, 363808521, 704567963, 351088017, 367700701, 491177640, 202432217, 726329593, 394508207, 339924880, 33558962, 162084888, 52328072, 711595278, 514100643, 190580410, 863398261, 809765267, 54681000, 315630705, 400448324, 673793450, 144678162, 250216550, 816021880, 450403846, 8558980, 713812696, 77959169, 745347446, 895885472, 127986015, 959593465, 843461576, 58439061, 676448489, 717351426, 555127174, 412755048, 284811141, 129401350, 840565739, 682902224, 948412964, 374567192, 122749865, 472582897, 866456554, 761381388, 273014484, 837520851, 587283890, 515381668, 793398401, 496734824, 217382148, 420790990, 894438793, 631224260, 248162243, 999883202, 513474091, 608652265, 192671988, 969819837, 100800834, 187821261, 912825859, 158233805, 754947483, 997371305, 768936496, 986980757, 404663899, 173463995, 116210435, 856523778, 432996029, 385250055, 643364997, 942368085, 713830890, 23652549, 908358637, 912921536, 191906754, 975367496, 389955866, 435879617, 630290560, 323048229, 7779687, 321267335, 340284972, 574280143, 723783013, 265077614, 131308542, 776928377, 174390374, 555874413, 660716368, 313296796, 52266827, 11533117, 384307356, 519672559, 808124832, 915889716, 902234797, 405088763, 120245661, 429615586, 702736212, 281812473, 807732777, 561007175, 670614991, 332303930, 792711329, 848928529, 506503142, 757023287, 647946087, 327581343, 904798386, 454573600, 481789308, 729740694, 292617488, 530421398, 561675056, 652715752, 787453268, 673909034, 632072954, 50250737, 13626792, 77869609, 537528870, 435585195, 876276468, 426036206, 340707008, 443212348, 356927578, 305429367, 195679919, 248876033, 118155183, 3113845, 853245268, 599248801, 621707337, 481463969, 713740078, 744798626, 897538990, 110695246, 788009648, 643951371, 298047455, 48423719, 789674857, 545785806, 165025115, 632462636, 624477185, 465841467, 577857953, 684617055, 454273994, 22184752, 375963911, 406192965, 570669846, 742227781, 889445596, 137106323, 91934029, 914511895, 316256580, 952728290, 726208569, 703859842, 289057929, 250954584, 966749852, 982067284, 284476736, 877453769, 594973069, 769534647, 580968175, 472121323, 88559169, 685864350, 894084740, 372521778, 188794362, 119142774, 240965582, 101421851, 762855831, 732555575, 957728970, 87347321, 486133591, 159142458, 269899297, 600175608, 445557249, 248025402, 526270961, 455991738, 584859308, 352535638, 700236161, 719159801, 539439026, 670286911, 582353995, 392518643, 717371262, 164436710, 49434987, 418824103, 548998260, 803319833, 110883865, 511369278, 950434445, 100263830, 806853177, 414946763, 556358212, 734247131, 740748283, 156564542, 515110770, 747218318, 1498061, 832323021, 165357278, 658103568, 528013715, 904487704, 531236999, 558819306, 924144275, 633535182, 886580669, 806626475, 536733832, 749423036, 13535337, 161633875, 159540176, 712661279, 678570346, 819309982, 68606159, 573578914, 755386514, 35465819, 95187969, 416617081, 896674972, 552598607, 665036588, 800713433, 287180480, 805138033, 677570945, 75594626, 639314355, 264575503, 371197958, 71409054, 651003750, 467982745, 438520534, 905252806, 422058740, 282297771, 256013323, 22454071, 320578501, 75399992, 23606343, 653283846, 789868548, 272154554, 352528964, 92016600, 701710321, 410079702, 329245332, 134959636, 551492296, 780747424, 414999245, 689838118, 866203472, 359856794, 162380489, 745917491, 842322032, 740988448, 211613619, 732508142, 796854200, 593722846, 341121003, 398363281, 686505113, 465301558, 202995017, 431163600, 403009791, 415627199, 905334843, 923179341, 232502610, 863507052, 371507292, 179828881, 701895675, 324581463, 170635190, 525567420, 175769921, 617973037, 468789557, 445223705, 56046503, 216621542, 679212607, 402705893, 721632394, 544271024, 346286019, 54589283, 391551333, 691509458, 64040800, 640533053, 599980940, 77650814, 769057939, 994864110, 11888892, 113710300, 270036226, 633898476, 603399897, 605417984, 251008482, 420406922, 131115864, 372774432, 874151751, 943203773, 705766076, 167231839, 866606174, 197951730, 408121373, 838437913, 51490614, 690686263, 735117657, 784206944, 819391929, 557416004, 983348479, 893227330, 885857478, 386937417, 803774889, 834631994, 702799210, 565252625, 309888900, 871358877, 203832688, 583462528, 48840810, 311339361, 187758242, 451995885, 4069907, 528188759, 350912339, 488189119, 103449878, 377318914, 288177913, 605711655, 875572048, 975352038, 984780334, 532409084, 284263443, 59004274, 853584436, 847466105, 587068144, 864856108, 424388507, 162880645, 820349109, 409579507, 1064265, 728122388, 664803758, 54171052, 597457446, 84892094, 307657964, 288911258, 456607, 71603433, 195484615, 150291408, 368930716, 369411451, 96285010, 959203857, 919534004, 498183021, 175223597, 700400368, 328362745, 140659531, 367871584, 8384960, 207264759, 808707870, 794657371, 245204439, 180151216, 606798864, 947082059, 647779055, 279761945, 19803485, 758153088, 407228056, 336112906, 827522211, 359190975, 994229204, 421283047, 60237334, 171970781, 925119727, 390545327, 341955282, 52574165, 312475124, 28548625, 650090241, 891343280, 989917154, 927551777, 779552423, 694511410, 572049570, 718544788, 148494843, 952415068, 258521340, 582460802, 363671916, 167412683, 583977797, 257904646, 162074482, 877823925, 943964975, 195820489, 618710341, 512335027, 272101125, 170468441, 49540449, 867441937, 211064554, 276589498, 827160070, 677412628, 159334357, 517167128, 762136836, 92631185, 929099293, 189611537, 10162985, 143048978, 324992017, 454611188, 975733143, 929419951, 314829751, 796312403, 203993435, 159325914, 56414393, 304814637, 305629290, 842600827, 844599813, 385435511, 551711111, 863900333, 744811161, 794895609, 858786768, 687033257, 446788794, 487235428, 826923608, 797164884, 811407760, 292255284, 691835989, 70879386, 335455465, 490915608, 282110383, 191297065, 318348330, 426658464, 348328032, 597350555, 413199934, 364581660, 464496364, 130584928, 73118628, 525825510, 103978258, 904314279, 981335897, 264697239, 957858109, 259215085, 582466771, 808976922, 553297692, 424561962, 83429879, 752857452, 238766841, 978943229, 828774229, 315690388, 5236022, 551643281, 816549539, 512594675, 425046241, 53734276, 60643739, 425132015, 136112188, 499601432, 749145606, 711034290, 474117764, 422654300, 237212879, 666325677, 197086238, 846541544, 955729386, 177142607, 902229762, 975424918, 766369249, 600735765, 68794718, 185587301, 213601629, 738363310, 267876906, 360306930, 706311362, 262572166, 290791118, 638795199, 923537830, 428878817, 380349249, 517184281, 120375917, 806992876, 85416194, 255247038, 315775360, 758011125, 615052859, 183686325, 45286046, 646542626, 506309248, 596333782, 93907682, 621617795, 975600598, 869977003, 990613788, 665118478, 996096644, 619269591, 36703269, 454033770, 183041358, 875586924, 217306106, 278000341, 874634320, 846739375, 549272169, 39076595, 587630029, 738256490, 913152035, 550116894, 803621473, 234756781, 885579622, 253033264, 730718933, 890503243, 51664053, 189938564, 164453357, 430349758, 341082149, 905123851, 80427495, 330473925, 746672134, 581346028, 977738204, 635895339, 341523009, 18672678, 158888267, 106705666, 63649010, 13177489, 54972767, 584223297, 285110575, 583389274, 66481704, 383356705, 161459987, 496600305, 46694042, 839794126, 238573723, 705282668, 988622700, 77126480, 515265757, 607007270, 694136485, 980020793, 150831022, 770288211, 491285241, 798498327, 631091303, 584910655, 571335942, 731767094, 223213805, 56088022, 25770126, 324137874, 63295411, 741746038, 419266821, 67460150, 28229419, 939439337, 714601278, 40139978, 423823391, 901059680, 328475141, 36156642, 250355469, 961392592, 462781539, 637526341, 344090057, 916185844, 183651464, 205203185, 971455377, 856497326, 336744985, 532478434, 264367611, 58501554, 627539219, 804777444, 533167441, 31060232, 923285366, 434848228, 630289945, 177904990, 128450120, 841430839, 532471787, 411500973, 721534577, 208813346, 536558046, 721336477, 603161192, 637504309, 816564701, 725041135, 806251230, 705205476, 906549518, 784519288, 532090027, 451176481, 460674371, 618563174, 721609986, 141878270, 673052789, 515791, 968578291, 402526783, 851400985, 252408899, 661119348, 935715814, 925652386, 794929695, 300847380, 637148471, 251422959, 917749400, 669390697, 84360616, 881319400, 137634208, 430927155, 544735213, 796152862, 988669447, 587919995, 19039231, 397243616, 619500214, 374368041, 212496618, 785751657, 504363999, 783675468, 58109062, 456527245, 176600067, 464746788, 539525636, 974120502, 2196361, 37168794, 211222428, 29633955, 972343608, 750300475, 647501541, 489705113, 144348236, 120376446, 909730108, 983576844, 42149344, 680026507, 95892552, 449201742, 867278203, 500257547, 4089930, 795996936, 465739826, 364873000, 21022783, 938338517, 98339645, 548134514, 862304392, 556986970, 667856343, 699275815, 559843375, 562202156, 826098030, 345037321, 412182719, 889780449, 767474432, 352124925, 615745022, 51162617, 887799392, 783990394, 286711663, 585978631, 585806699, 208142555, 558655100, 88758698, 116150230, 924604672, 528556035, 682108618, 725708053, 883638524, 645647220, 593510485, 263622806, 686572808, 279048222, 447250688, 87314483, 189461519, 332790448, 772047053, 406313632, 620176865, 228119742, 981298268, 797440753, 881387846, 614584531, 802612738, 267991741, 37712361, 395571909, 339497244, 694984929, 696289863, 126160646, 749156066, 22976806, 663820969, 950134578, 636192158, 959262446, 197675564, 738169283, 378566175, 948862079, 569140734, 758688332, 742834992, 481158719, 547150064, 134431771, 856609477, 402163950, 126008897, 107547931, 818983519, 333237909, 32924730, 606269395, 311085079, 19561707, 6883491, 125983504, 643263502, 202246112, 929631867, 990181199, 198920103, 67935200, 456461929, 661342053, 255853086, 648081906, 167509990, 345775625, 293184169, 444209811, 604512507, 262203682, 452373123, 942789896, 708072607, 626346892, 885653408, 801530006, 139089867, 121543754, 420357235, 73537338, 375902339, 57275413, 674386702, 46025213, 889221796, 857658248, 586092052, 564734638, 668525806, 364495279, 852395155, 305755518, 304351531, 832735978, 877789895, 202893935, 144206341, 696251467, 319143973, 102853250, 708663464, 860450204, 921030329, 493909114, 755003043, 108078960, 948496441, 672012318, 226070809, 353427011, 121340810, 374127294, 384605081, 298548862, 580062999, 810945908, 113262655, 663363470, 225878331, 921367243, 14382517, 819831429, 294536905, 588635511, 168375448, 9525521, 753271367, 610032231, 560123896, 763148844, 684025792, 77962271, 918931505, 355744878, 831892855, 648985177, 803778091, 210407200, 929023297, 547533179, 412466417, 768291780, 606181811, 402599451, 412799900, 997131631, 251863070, 429375386, 554118372, 833715861, 188293390, 941973115, 896282530, 57496181, 121553842, 375686988, 999926415, 17215707, 315717889, 216355359, 920118252, 407556569, 131675287, 426896629, 64710279, 652921475, 900833498, 13606274, 471408115, 50721889, 843130099, 141137647, 615287599, 40932991, 897865276, 376112091, 687312966, 245423264, 749281933, 843685580, 97935135, 639527844, 430279392, 708455214, 591047669, 302520341, 709213837, 694038547, 224060837, 655264550, 301607836, 212904604, 3884052, 861814789, 4784592, 231299353, 440622191, 407351114, 10503698, 86396702, 23538578, 889180678, 918583294, 95470673, 19484927, 417909621, 355941292, 24232175, 631574633, 479758383, 557590902, 793445162, 37787728, 922688287, 549670192, 633631310, 48213020, 71067311, 702788498, 330026801, 413489396, 683133832, 827862696, 98007386, 903349596, 322926898, 933443395, 769737275, 400159902, 595739964, 499066962, 567231962, 150068115, 784789477, 370617650, 693252060, 183333408, 939095699, 972844611, 167342180, 714206655, 886544898, 1455556, 589254699, 58537120, 438570954, 11209084, 475847982, 142498685, 73557718, 627398589, 206553537, 687716355, 847301650, 473744101, 843120033, 19379489, 280771805, 448674169, 95241233, 513535958, 454036505, 327947380, 880210638, 460007530, 546988618, 123829201, 18270041, 452220294, 541885669, 944880199, 428588781, 120315669, 471190856, 786786593, 856194551, 348126778, 380342816, 164608961, 730795284, 930965006, 845245064, 904852214, 893527134, 906986326, 523785804, 222840149, 783892429, 888511422, 486947195, 585948881, 390977015, 912782937, 882657496, 641458511, 2182664, 994608713, 226984087, 481617826, 452427783, 464618708, 549839623, 485178568, 251351929, 344142183, 155442059, 488414439, 231558947, 618101703, 689963756, 521385637, 864597551, 617858218, 631982323, 159356308, 274403415, 86088631, 454170895, 362081195, 450331481, 595207497, 981181397, 705070274, 224053613, 286775240, 315074568, 648006741, 6520361, 158787631, 290029351, 366531835, 77916290, 470868415, 95637030, 786297872, 563219913, 32615573, 884919680, 654306789, 893564745, 318701647, 314343125, 566458328, 482701992, 472185696, 705690178, 908205419, 11530383, 977620946, 819975038, 557804403, 725996256, 904800633, 548172214, 422550610, 887775374, 395512, 868684197, 913220175, 610441530, 127583213, 674563137, 823678458, 720028863, 561596866, 702101955, 121394322, 474314509, 243588271, 327927253, 416242016, 555175302, 544113817, 196775085, 887742060, 570082888, 118598072, 675768506, 697768796, 852765525, 669424629, 870156655, 750529409, 862262764, 708976068, 612876277, 401992190, 491308412, 317277754, 340993668, 684649909, 737992191, 258029929, 819323016, 265402524, 414693564, 993744023, 421324169, 733086219, 458622145, 531021768, 101345015, 442225410, 918298910, 282042538, 875955513, 546239252, 665661704, 693790070, 406507812, 578512137, 879105740, 812103902, 948277124, 507889546, 87264987, 34800054, 394635796, 443115580, 476044649, 733390552, 285800826, 561371571, 314194487, 300048184, 208464315, 216763853, 364794431, 298030456, 95218669, 231207071, 516112462, 78804304, 865634744, 367957084, 234827920, 474867620, 671238214, 197911, 412789466, 696299030, 25156169, 5447143, 338731591, 375390139, 572545564, 531580307, 565093887, 13761282, 435334146, 740078367, 389715368, 48541695, 215571355, 232322593, 912349142, 738517144, 20543258, 350230235, 940844497, 590219154, 643439487, 283346058, 134440434, 187530867, 304132303, 83662444, 524145582, 46268430, 159062440, 612951754, 141582956, 679559249, 73689098, 591757601, 301987971, 902239766, 140096873, 252017356, 238842671, 591800410, 666839758, 685467358, 819632954, 601592692, 771167431, 801001765, 81897725, 605424387, 329617460, 889143001, 881111552, 30064110, 456793820, 975392461, 353001409, 943116148, 701230963, 616407467, 766380498, 587154729, 247113623, 974584233, 687190427, 153600806, 781655452, 130971586, 619225130, 652031049, 661761192, 948795414, 845199039, 138911245, 210930409, 738604077, 717543997, 413226667, 945613147, 350837174, 934072425, 529397044, 647500284, 795419666, 274203168, 62495707, 312906335, 658415691, 77768248, 492147859, 250716728, 120160654, 621979850, 360882249, 93476096, 840623839, 811641377, 708480933, 666252336, 102283979, 87812208, 114231555, 540257313, 744171945, 490065820, 625620072, 506716954, 737994685, 357937987, 99869724, 147026068, 336962923, 236456743, 311607542, 560489322, 991508028, 605716349, 140990420, 407378104, 213312586, 82656624, 189463739, 5731979, 140102324, 431902365, 56614957, 294599981, 541502951, 861632250, 311081915, 645273935, 171886367, 690181795, 784649683, 375851590, 252304302, 380304859, 52447602, 73667891, 527609408, 210950139, 791384022, 39393756, 230190173, 769165344, 782191266, 642448806, 833549710, 782531703, 374289096, 83343495, 93592022, 916492590, 42710083, 816936587, 786913724, 197468671, 963577124, 106089943, 769446930, 348920124, 689418796, 364687425, 891842141, 670056239, 255704990, 465712365, 510954833, 317912881, 588164607, 241239926, 256228942, 363091051, 117349979, 106589229, 959879510, 607175617, 750871820, 681895565, 351550441, 987146293, 887609297, 282501485, 898892874, 185450283, 99697056, 30294797, 136598652, 537047867, 550878310, 339901619, 477460868, 10729790, 394685146, 726108357, 943532504, 929009556, 502679933, 869592965, 637974769, 548674695, 719924496, 613167090, 818916069, 245273461, 283623624, 248072197, 656662180, 745586841, 584706763, 731716309, 313320833, 913739400, 487475296, 227995422, 79156108, 652069794, 3172073, 965758713, 919633694, 751077945, 580449469, 241945912, 637564013, 760725186, 563302955, 109183201, 298445679, 713480683, 950042190, 361688964, 297481825, 250583620, 937041551, 624869484, 758598598, 697399595, 1385588, 805460725, 306196234, 419954557, 36557777, 329026922, 40467033, 176964037, 802663755, 15296884, 957896499, 400714248, 216206125, 249878971, 131677032, 72987513, 347455256, 213311662, 30308431, 680771237, 916173334, 53781588, 547932843, 22262943, 263644108, 96670307, 704320194, 163942363, 858654998, 334621594, 918062814, 84251369, 9369413, 19273284, 871556009, 459587124, 263391412, 767864360, 631134034, 73069113, 325136605, 346837401, 762601072, 660648328, 352643281, 750457680, 292033786, 881931661, 753504161, 214175086, 91052730, 886076345, 577362205, 842149426, 637563289, 325997338, 671741851, 170342510, 544542286, 501442092, 152441070, 79428150, 688922994, 716888822, 420040656, 88715784, 842525203, 871990951, 444240926, 682670752, 846093540, 545950739, 412683135, 439541776, 4851908, 950600058, 530207868, 419036588, 36653749, 463591779, 973671187, 921624113, 932912577, 682160478, 851171297, 201861393, 129660461, 38339418, 243967220, 691480732, 890461712, 977903067, 827782698, 357429804, 805718637, 797892456, 332052539, 497155475, 234195235, 340986004, 897086314, 452570302, 215617717, 112285923, 387152042, 668376141, 538434571, 87634957, 171973752, 338488519, 370531032, 429781396, 618623738, 535377288, 244843111, 521919083, 7447394, 334514969, 108824143, 783054035, 245777708, 667372913, 638285106, 252530952, 654646527, 663984502, 857205351, 859467863, 23886735, 165600923, 83920770, 406716563, 711878910, 827448676, 444580221, 324111205, 880239244, 450807840, 277737905, 20893920, 151189533, 531804197, 577840878, 256734677, 342342598, 401725842, 856615115, 654923124, 360324440, 282541394, 664205132, 144335924, 671953863, 316879067, 200159232, 762154536, 519388119, 682213778, 205002054, 97677542, 16796509, 698215181, 77195979, 470190262, 815499275, 313843106, 205668302, 845658570, 723443721, 945832678, 727296173, 371513148, 461334404, 717004840, 100029103, 624152712, 455890673, 897060547, 442157290, 803068423, 109227984, 689108929, 477705957, 400582127, 889817038, 999680862, 874201937, 516920021, 358554849, 575406928, 661804907, 992723925, 392211939, 155268499, 531363776, 331863300, 643297813, 260233764, 232070007, 255729173, 622813264, 352834344, 370242479, 643642, 643660040, 814818480, 996425396, 403995234, 857454812, 46666344, 19524452, 805948940, 952132022, 311048956, 526071714, 770815862, 695587213, 449125589, 787475708, 734082522, 455641403, 625139490, 735204605, 220539184, 130074045, 805806644, 429483844, 499516371, 842408312, 499637766, 856063092, 323933094, 40487406, 773610069, 860899059, 230175531, 549526691, 257940658, 756051940, 621160632, 217437664, 13775178, 862088391, 160700990, 928036891, 501778234, 173606308, 112484109, 584967916, 575138216, 776935528, 425751986, 143279317, 427359312, 577342251, 324032283, 35482446, 848424975, 522258889, 525009391, 741428874, 552132499, 437335882, 253389060, 237601148, 97590597, 500823408, 151714685, 487768801, 408489080, 331860861, 995435458, 249887106, 492665635, 609098539, 388666959, 493833014, 406459155, 403207474, 735913372, 217891377, 137371754, 529956695, 23004729, 902311705, 89196574, 60599627, 373542083, 427288343, 148549200, 210212732, 472007085, 712452021, 972060779, 627571000, 591984325, 551780067, 34464828, 991232620, 366971725, 622709300, 668622028, 500625283, 384917104, 394013513, 920899262, 440731629, 217838160, 871869566, 185156805, 541026408, 867420795, 6620250, 711649462, 742522548, 646115660, 539204740, 573538416, 924798055, 994665597, 414773757, 572111570, 154909645, 413314785, 329315869, 591865914, 254116729, 56676250, 628665844, 107387630, 778249699, 542685621, 516878647, 484105992, 998041013, 192711184, 99460992, 557352849, 494861291, 336966251, 584300089, 946080491, 359877482, 972906416, 768483523, 74293108, 709894029, 660015618, 514256810, 134588350, 674146954, 298526818, 122889682, 851486380, 436397841, 41537415, 721956612, 685157069, 971467668, 923922426, 857365148, 159527789, 735423586, 309475237, 283276752, 361449606, 923872419, 804072893, 12703812, 917624553, 258859398, 417007768, 515926605, 426611673, 293191967, 116757510, 372424866, 356599821, 87802494, 723876547, 853946071, 698048166, 407514682, 381346139, 370148448, 208860644, 661972270, 7631392, 255375050, 627543215, 639909695, 953910083, 723914217, 671932709, 137095411, 258020750, 117282674, 956834540, 458802237, 256413569, 34218426, 887315476, 84579637, 443096283, 133835676, 407074992, 294381781, 978005474, 683160004, 956086699, 388277870, 670806584, 725666613, 510941979, 123288378, 106437580, 187898241, 535899836, 63837225, 238681181, 488358639, 837266185, 473745047, 566331135, 227938069, 159446756, 624867784, 778505295, 271745746, 843044456, 434901823, 779570320, 861385738, 484933786, 426269642, 342902819, 362223435, 578998592, 409247285, 737617979, 97927684, 859137900, 712375937, 509775710, 935219591, 270807157, 223523183, 128541079, 145995033, 128679164, 343098737, 810411899, 226760522, 272469946, 670666023, 337984609, 171962628, 443043876, 596234885, 167380992, 791325717, 357548777, 245978250, 432603290, 645531952, 893757789, 206829590, 785225367, 848089920, 666000362, 548118134, 735182591, 691479391, 756163493, 214493644, 281639567, 799388086, 742784703, 861699740, 923527420, 370382526, 626243493, 499012837, 842969844, 945654928, 803306724, 970146945, 180473430, 525461115, 867098302, 814334512, 17950786, 531283545, 586952674, 457828710, 6303463, 179573409, 119180585, 133545076, 882779623, 876922109, 939992692, 76367727, 46392593, 136748952, 437952891, 803326925, 724603842, 408884911, 629181773, 735422731, 775936934, 511686925, 339432922, 71980793, 92337480, 936459234, 172596610, 331125628, 846052132, 971661733, 222513475, 874646556, 733211487, 493533347, 916661983, 6234298, 426953771, 930437366, 310069624, 572772580, 468658316, 831326858, 17807353, 268832964, 800766245, 797680061, 451947165, 629552296, 484098778, 682233184, 783032231, 522497756, 333201045, 430030824, 869674954, 934405129, 353695631, 408523480, 42120626, 850286753, 635120488, 173418809, 55090537, 221966138, 53640771, 594729034, 690454273, 720902570, 613905479, 911155794, 499125460, 830506043, 717559942, 857982224, 177852420, 752002100, 672092476, 111452721, 750504363, 625813062, 134135546, 486770612, 487178704, 172857836, 228962956, 510382936, 28869933, 135047273, 123603613, 618821730, 836614346, 562284171, 669390851, 258429715, 111618682, 907647146, 55868476, 692294543, 266144336, 805531912, 823281732, 178395080, 947546472, 719310330, 882464072, 423253260, 489904736, 747775470, 308013537, 18067916, 804613582, 657161369, 476710557, 972721949, 166791831, 77788604, 910287421, 73806271, 904825609, 65726586, 833275190, 314070097, 776612819, 673105969, 128028511, 141038747, 502908002, 216261632, 437761987, 281613477, 240661756, 629547358, 310382054, 813395932, 25106105, 459484006, 772017673, 819185806, 799343864, 290217771, 530642280, 446170254, 86880299, 494090809, 5529173, 59037265, 722181576, 474054662, 890388297, 187603474, 708631987, 296634762, 323732703, 441510474, 531925395, 413667481, 8130239, 82949621, 122254017, 505703677, 173826147, 652211269, 224882654, 744691815, 111489527, 393158505, 312587464, 308556464, 730094442, 204851902, 436127127, 645218235, 808751948, 873664179, 57399696, 339589318, 74862241, 517766174, 717226417, 518470300, 418418262, 184289171, 947307320, 291737747, 319095893, 759875535, 765951477, 908772535, 501345951, 90518298, 451696862, 434509180, 109570056, 342134865, 578469742, 636132282, 24917896, 950996074, 222104618, 186442741, 602743056, 619172466, 389518718, 134794099, 519401811, 569068839, 504226539, 827578595, 122380983, 906308778, 187114948, 668064372, 683272235, 31323124, 19054753, 973413119, 140659418, 371591845, 85452784, 635741625, 820566074, 522855192, 373678247, 299441975, 760643921, 292545509, 421738045, 634784980, 967750348, 526220142, 785495639, 483508149, 912652588, 67214985, 310952145, 248780061, 161554277, 311733629, 733489223, 307554410, 227423316, 416116587, 410475564, 288850260, 733833234, 451493567, 990627054, 500407468, 678537361, 255554749, 715888460, 252194861, 909408253, 860631398, 64874418, 878022956, 724825210, 954738995, 439348997, 831597143, 454922377, 212654997, 759570, 723311351, 131197009, 664606273, 895365655, 157510762, 775378642, 114524747, 370252969, 569455678, 517036829, 885017461, 866212222, 717798387, 479731361, 92276538, 741333894, 995355301, 451379494, 882088419, 705279707, 217021834, 116753174, 469282918, 294399813, 48194704, 15307114, 555296817, 149986660, 988378941, 326012774, 987107498, 154821470, 897937775, 360215862, 523867796, 515805536, 992915995, 504190684, 278883547, 267133893, 611220371, 626162839, 289214463, 207263544, 21921778, 920850022, 454415038, 109756135, 699877872, 697116451, 401911980, 777032384, 985452430, 382089998, 138462226, 989307716, 286610409, 701863534, 272441664, 474857990, 903139143, 667779314, 71136163, 816509900, 775846007, 677444449, 325479799, 338661137, 781499098, 872121463, 892227029, 130849340, 903290512, 551229024, 835050421, 925955070, 162960301, 705799242, 758872074, 489660366, 480135656, 538751334, 521528696, 396996424, 839910942, 963233502, 324738329, 559067898, 655057954, 812265702, 53950299, 599022071, 726775209, 739666441, 385263780, 875426269, 349448739, 292939654, 740813083, 763017916, 966610396, 235396534, 345953253, 21122814, 152347089, 281145934, 451233673, 915769204, 222249966, 663202679, 767985340, 171098894, 883058722, 880418520, 733343915, 288507051, 853643356, 125523625, 525155198, 597991, 303719826, 740239895, 284708958, 992343595, 91881470, 298016169, 350384620, 359213832, 697549611, 944174670, 552275067, 810661269, 882244626, 614146217, 464310826, 261819603, 411901237, 381011098, 700256932, 39975463, 725630177, 771044779, 472725591, 48442435, 739904486, 434255617, 26881058, 727070626, 989782361, 959544863, 841092477, 783693910, 846552889, 4971498, 649132079, 912347877, 421656595, 865071251, 302100273, 379708133, 602958695, 915263198, 930383775, 216864065, 93430322, 69430195, 356915364, 850018899, 240905838, 314408532, 131906928, 702117465, 88415019, 701965936, 336837718, 210940720, 701964121, 695379034, 991094537, 562792449, 27322845, 962950752, 272287919, 897985566, 432304440, 576567349, 905712256, 431716057, 387607587, 691748730, 707612389, 508209647, 38044283, 233804943, 7626539, 336354874, 753389637, 806882826, 115198018, 898017994, 405643696, 680486528, 618520395, 277887238, 626974844, 312116083, 853862213, 818073820, 774711033, 464849194, 964438463, 40501391, 537224568, 6022963, 900721565, 216681209, 745418864, 522296151, 785134800, 983221473, 944163245, 838108835, 217688309, 731234913, 96702736, 119771112, 95717056, 295197810, 344753144, 259736236, 560061377, 774148425, 989732269, 195570326, 321622502, 693526359, 321102851, 54817321, 754864168, 538599992, 320395341, 632494815, 383976558, 455957246, 621703228, 209621412, 452001247, 410792984, 771858854, 825721751, 7906944, 197009266, 777964645, 542078297, 663280456, 577087983, 642068517, 559654110, 486229459, 788516331, 497690196, 254306652, 645524793, 645894391, 662575747, 656472683, 21752048, 661880902, 861346874, 442194253, 906291022, 244766293, 712383311, 939911139, 938221742, 522341582, 340443487, 884121741, 222124929, 594794702, 699422441, 620599897, 946520662, 403085482, 919405131, 990824065, 967217835, 950773349, 127642454, 622330563, 89626190, 729536034, 694830010, 353261694, 956002349, 195367552, 572798073, 741149140, 726082262, 729994675, 313532900, 246802923, 737618489, 746522255, 493381615, 812640286, 815385220, 422902891, 44470188, 140303431, 517009008, 830664058, 87393405, 121940457, 80538188, 239846785, 39284265, 359250248, 359317437, 533759100, 667837736, 820122622, 333959643, 997504658, 901740026, 571006131, 145853815, 176517262, 420160662, 29299797, 729392233, 161524156, 597633823, 239435335, 597868529, 460542119, 361117790, 319155827, 121360617, 536868982, 462210240, 429589411, 78449619, 113035797, 99602065, 19138309, 209802369, 195102206, 268023867, 201721637, 777522735, 407015514, 164074996, 724955725, 618351933, 914455767, 538314180, 691917778, 258874392, 399758611, 241304507, 187200022, 310795325, 190987541, 81126699, 572935573, 131085516, 319180750, 56379446, 873339119, 172205536, 219619010, 104801832, 632696598, 818793892, 521927635, 610924859, 563932571, 106914467, 47369864, 51392109, 286628834, 415527984, 474546165, 404538676, 719722748, 680183541, 107451518, 910764238, 356293529, 211900596, 683936545, 436701331, 700305542, 721765147, 956127743, 962090723, 400095954, 473305511, 730976536, 579156990, 548245596, 319729880, 22006638, 631146282, 534409814, 518966614, 707692314, 162463571, 461586460, 638667896, 534769546, 483942380, 391779352, 542697086, 670333620, 54276904, 684068150, 982538689, 832691929, 938043726, 986811857, 76932318, 404429816, 243678551, 834215626, 154186605, 854971665, 672247517, 793173783, 873179570, 490534907, 494871306, 490491941, 824664384, 68612686, 856603846, 663752611, 603851212, 142143587, 647084914, 820937700, 393535803, 563712680, 751352907, 866554800, 746512419, 818642943, 746130168, 147131514, 720611436, 895140563, 701608295, 761698125, 419364201, 38622472, 635250190, 812079944, 528170346, 796742183, 629000690, 840930530, 990755987, 225717945, 6096473, 107166464, 587159469, 940452748, 683502454, 284718220, 638888120, 986823629, 424621738, 286002502, 923886755, 837601440, 436479720, 883321931, 212400077, 84343811, 594433398, 232602972, 411706845, 58239013, 960124222, 715270869, 337439664, 851855818, 146467174, 733838816, 86933039, 857499178, 94926064, 421682230, 633202201, 586448668, 270788634, 885799901, 267143807, 284771917, 623054728, 819852752, 322668552, 472630841, 126023343, 733512885, 57006572, 472185220, 848916436, 586372736, 140586999, 100798050, 727668954, 304781355, 18286096, 83688457, 855581148, 276643748, 555591199, 75193990, 220356710, 484516442, 487322364, 232321239, 314409304, 424888664, 444855104, 718014097, 295878006, 507162235, 145459265, 108303652, 492402948, 831914635, 110040502, 325976105, 285040187, 861443256, 186388050, 794170164, 735769834, 853375164, 899352049, 184897007, 51207762, 389041049, 668719878, 491722806, 672050722, 225539449, 48370819, 778965215, 761196731, 564448201, 287102539, 991518446, 555709102, 238514273, 126468640, 346637080, 640342, 876255496, 227778411, 887086122, 951642312, 658383965, 387567857, 701017358, 96133025, 526442193, 39363286, 654843532, 932019066, 52791620, 289899806, 132492939, 378474892, 853108611, 10536789, 887354348, 100392780, 29172133, 964463816, 941380131, 372593929, 328685842, 514932337, 239580185, 582771077, 188679585, 244314258, 883214, 882029049, 136229142, 440181293, 659684598, 345207451, 209837013, 165831311, 367539369, 510946714, 97264874, 84792435, 489421617, 947876694, 345981841, 814750774, 498751363, 509812584, 176056844, 199384022, 377438809, 71734298, 458550537, 162216822, 846234563, 32083519, 561540687, 271450347, 573760913, 23054491, 486551866, 708176113, 545054940, 730303868, 946752911, 898097592, 801980503, 193803535, 738062025, 132249392, 845013165, 89245132, 836561109, 836684708, 87722634, 823059794, 376055479, 436437778, 950371137, 479754188, 440570680, 368434694, 355851500, 417129157, 333004439, 875606246, 128827282, 905861252, 749464542, 976692161, 856737283, 224337812, 321595139, 971014074, 388952801, 537116131, 650509354, 282507516, 775063621, 211766803, 677911548, 924028240, 205277205, 889867325, 857192005, 96214936, 639575729, 177223155, 860484440, 645789872, 588959811, 465008050, 649468058, 12783376, 49565888, 377503550, 704130162, 752625437, 36333350, 134600366, 647579316, 827565862, 788096689, 495749788, 790383012, 66298270, 80186741, 701730185, 476827737, 344290233, 423828995, 734071423, 747509500, 968434707, 229471079, 866633212, 755426237, 396775694, 762479393, 924205838, 893388905, 374315730, 937381609, 946789913, 22422793, 598209905, 441381147, 100508387, 420209568, 493380103, 538598814, 410706676, 857254058, 823212159, 281271258, 124595404, 794941896, 225709888, 133894881, 202094706, 779551548, 36687403, 343002359, 202938297, 47845821, 439497238, 113534549, 993836179, 381605869, 38287682, 638144034, 384961915, 625952374, 895803110, 939552350, 931989380, 594756238, 86896043, 4476371, 200620444, 273381922, 515198858, 967516245, 344172438, 669670402, 593484157, 938208898, 660610991, 183374408, 999869451, 838880333, 114368650, 438722497, 169685040, 398284527, 296928632, 266426420, 712039823, 570349110, 805392418, 953868370, 834566154, 93927377, 18654787, 931358769, 608415607, 893858812, 875978175, 987823105, 622060480, 387840395, 444764206, 840340618, 821888958, 948029829, 764348226, 856915849, 660607827, 711365348, 249888296, 459931212, 631587405, 887995022, 262605203, 126390792, 378891836, 718555690, 11387043, 524791519, 912584618, 986664869, 855133424, 986137719, 814660128, 712348464, 773543533, 199784558, 453624286, 823724949, 654197057, 575805209, 22465468, 560351200, 934205288, 902646505, 598710569, 102963922, 108726978, 133179127, 731774159, 30999031, 14608324, 217960601, 567814349, 86840009, 410544741, 556072815, 726372795, 740142077, 768395414, 485795606, 662145899, 566973373, 324023470, 984424679, 571551177, 754189879, 509539432, 370381635, 12221226, 342618407, 588241548, 128470319, 787298456, 142142554, 771519326, 531906079, 606219804, 699919029, 790896276, 163628536, 131916199, 131582796, 551725110, 162756141, 323012598, 710406341, 831649752, 824110803, 200001609, 473065974, 118626445, 715344412, 395919787, 554460369, 556583161, 236370746, 173144909, 643915931, 24822291, 558466471, 129206596, 859204679, 886078021, 904196308, 848492402, 765262631, 399193745, 779369707, 899540028, 107366087, 896288149, 989716692, 458470929, 591824917, 171639004, 816235581, 410501137, 10328734, 258508522, 258928093, 987835603, 82622933, 37251170, 710768498, 327060689, 604132067, 744821382, 182543560, 701211587, 784440865, 872099873, 728661974, 756055088, 895123637, 583502856, 154135621, 375846676, 929700577, 195312775, 836243218, 893402969, 499316964, 384331403, 91739242, 230511450, 234908546, 951194191, 685463719, 672369015, 8591732, 421606504, 994164273, 231642760, 739183363, 291333220, 649452581, 325278615, 299816826, 298496222, 331240338, 716064635, 800157801, 924900761, 100002861, 850824126, 251274881, 810573405, 772944834, 387314549, 197129060, 291398181, 437283361, 426709266, 126872501, 256070220, 413878008, 794100285, 541979393, 562577971, 804554804, 858904420, 263995678, 440219778, 840227854, 857836140, 801441747, 330010659, 267679411, 196602178, 914064380, 648797638, 83691150, 973221213, 525930113, 710788644, 588904712, 454568806, 367880697, 734278103, 235244665, 881516791, 63308297, 328311799, 712099517, 640484167, 407757637, 423576467, 198213428, 657369589, 157008730, 694462989, 38016203, 664283743, 566265230, 957552147, 585469781, 878729925, 123283897, 371401540, 353589668, 783681170, 663104433, 380214533, 685206697, 273440283, 594320771, 85957129, 96311794, 875836702, 204154993, 666386391, 715472589, 913017246, 973484183, 574241592, 528617626, 463226868, 588065289, 600858743, 342557678, 396484004, 639677541, 915983874, 396242834, 802236180, 662100045, 994717362, 829359929, 82624681, 359278287, 980231182, 603373215, 782935958, 239455058, 687375205, 345703364, 35271873, 326827742, 542691403, 303286372, 923124583, 232711794, 861915624, 782685470, 443231754, 616253683, 40615286, 382408637, 775481427, 279593697, 334618563, 853367860, 950103033, 863858747, 670946915, 734062146, 990444469, 421594302, 529840467, 401180143, 695600764, 544860842, 614790974, 765564258, 483726591, 842737082, 577368052, 392709369, 204395246, 549502105, 305667103, 158963730, 893378081, 58789146, 310625959, 499555778, 93587, 574765447, 671214934, 510997651, 267576315, 16363114, 353452381, 318290623, 935422310, 990033076, 367697743, 206472232, 765782274, 174010513, 403849897, 85032655, 631339718, 315373280, 710924405, 640007919, 813317471, 669341530, 135270586, 27307807, 409610407, 886372765, 244880853, 635611423, 332734445, 121579684, 398985077, 814386065, 850271684, 983882324, 3113426, 748030310, 324921381, 122959497, 280005488, 425363359, 29459623, 111319179, 10207115, 558634318, 683913364, 841138938, 632234357, 249857093, 923951877, 362530454, 13774722, 699741895, 272465161, 973591919, 759784245, 75535176, 477486088, 582484229, 817467152, 564487475, 622520423, 603779404, 771109959, 27467153, 636290716, 823043340, 875427909, 418298615, 723236483, 72724371, 81905821, 793670717, 80101737, 503839691, 620046967, 508915286, 930557011, 723991493, 748542756, 393109702, 167755067, 428292515, 969108653, 464656327, 162961498, 303433350, 75208470, 407453106, 853502034, 875066993, 296100677, 777780093, 437372145, 924434051, 496902231, 102145325, 745480032, 553119587, 409946069, 348286530, 945847267, 541433023, 555134290, 249295696, 354599092, 148276785, 427132965, 747835349, 169595789, 961791109, 849728251, 668601919, 297300702, 506122006, 377228176, 901899043, 736088603, 687100763, 797502091, 63248853, 95293009, 248019177, 56897017, 32918564, 658306706, 321266059, 982220756, 332594198, 232946594, 464214519, 850548580, 642831215, 488088741, 973109032, 333728429, 86837813, 204155692, 99035314, 289403700, 617798760, 867292180, 401633552, 10632021, 395255280, 706904397, 445627590, 221611275, 732963760, 692262107, 685086818, 534556438, 415244651, 911783420, 990334226, 322811485, 781278460, 847438890, 500173071, 958723401, 819251475, 560830353, 112270609, 252806452, 186938096, 584463321, 276773482, 134538236, 17648178, 439351309, 147192221, 216621940, 936112052, 278339961, 32947708, 39039732, 278324860, 271558070, 754528190, 517773187, 792034230, 957275304, 24327563, 804601988, 983883678, 851433097, 536650674, 170055632, 389731590, 890049220, 744001240, 211412551, 948400959, 705431614, 564351180, 283841338, 775637162, 316498145, 140443180, 626558016, 700063619, 528065930, 765119219, 34570267, 36300001, 804044889, 418247823, 800837613, 632648533, 881901307, 102088175, 439124161, 216603347, 213459302, 22418429, 293020113, 772818769, 632749761, 12919466, 613498789, 962722463, 34761328, 261989538, 914102928, 963111010, 976672026, 968699190, 412451737, 342100374, 774461202, 405722125, 820147651, 923945413, 878990251, 840979183, 101722750, 401255939, 264072912, 94987716, 289778809, 668898693, 116779991, 907669464, 428226916, 244306465, 135796586, 322135415, 771292865, 475976687, 474146964, 178565543, 915054248, 88479425, 196138115, 645579002, 426508394, 311937265, 1633321, 548012166, 938555654, 143060254, 558332504, 65239750, 106784502, 360948834, 759828407, 816675686, 243295912, 885847243, 384693362, 879762178, 918540178, 98439086, 493871618, 723796105, 567832412, 141891609, 712901035, 579161618, 378623324, 677622264, 458535377, 367843870, 613453594, 364666621, 508929549, 190109504, 103126716, 406873840, 710221469, 569007468, 632388642, 415583820, 512922108, 337560010, 238585124, 481503504, 197800144, 949547444, 438926075, 181903280, 352515548, 987197422, 741903900, 723255722, 2877815, 528549205, 253181555, 957453774, 976059202, 676526638, 99427773, 730067617, 826489985, 419985441, 993960862, 889003320, 143687818, 130326880, 860958948, 9531557, 72293840, 689443177, 650946846, 361514173, 329036014, 917344491, 985959228, 352715460, 796313073, 821889896, 308955665, 464672140, 209084846, 241899601, 998539171, 98412887, 251424471, 468111615, 320010255, 609068161, 494015543, 137704139, 193417614, 875643299, 439235546, 321759095, 651253897, 29895155, 33827110, 202891541, 175584663, 843457348, 823919403, 621105621, 708796051, 73063292, 647111168, 752337850, 764854109, 232573403, 956840575, 197859504, 687414367, 262838322, 255739363, 543681389, 848006483, 716450898, 267196919, 921445195, 849639244, 908285621, 670001007, 380988952, 231364478, 293366893, 213770150, 126724603, 333464015, 945020444, 3096392, 765322298, 437165816, 982022454, 398670322, 260441940, 62744703, 13844313, 302556302, 902227738, 597992339, 692820955, 828503622, 24136669, 437260131, 165061996, 27821333, 611061557, 115770802, 807628609, 147138930, 966818012, 363401728, 989362491, 141653290, 756624585, 405880717, 787045487, 130113089, 247018620, 816505780, 737978909, 138336556, 19717666, 851511778, 160656185, 743001292, 673580770, 832978922, 11679580, 841551469, 73567220, 264905736, 410986849, 46768355, 642265346, 513821785, 303874330, 900319389, 956699296, 413136022, 366058272, 346302727, 600987145, 50896235, 82482047, 612744378, 823383903, 535600152, 714443084, 616206374, 82818359, 538416320, 61124843, 41823917, 208399872, 356909220, 129307256, 620653895, 923422236, 944595885, 341513983, 311645837, 815635289, 870990779, 700688754, 647033435, 570441673, 663758090, 665375270, 360631941, 645749245, 915737500, 470170472, 644878331, 132805531, 38635541, 964505155, 637535879, 871247824, 766945008, 643863409, 808325863, 227118845, 932255828, 943329173, 567995345, 481130098, 559543763, 363635008, 290771177, 385652410, 756996880, 25810468, 179334639, 74200409, 910058875, 588965933, 199050458, 670859976, 106777387, 258540389, 849411233, 902123762, 322943576, 954663564, 678372921, 387818349, 24530465, 134111767, 827319103, 401353590, 121266292, 858090697, 235170497, 843634116, 372269721, 141622814, 142626893, 553812724, 711642722, 676524264, 982213974, 652356647, 429837371, 952839867, 898578837, 773589495, 485405977, 307833730, 830424506, 416437242, 324420751, 648010923, 97165472, 727812363, 635612863, 223724830, 928122200, 437044460, 19049119, 624502997, 220946006, 679294013, 759692275, 189451026, 829035054, 188725819, 389567777, 61574997, 456002731, 773435353, 240449927, 972808418, 440971660, 767437680, 112245054, 864677117, 760122107, 656037047, 203076124, 550222476, 8715494, 712745129, 126585446, 361142130, 781688257, 729539971, 868681643, 86902866, 886040633, 91528540, 493082944, 691102501, 524577136, 204392477, 433056474, 74459052, 794147767, 613278827, 69520917, 935990524, 956540907, 956950731, 961084876, 142346982, 868203937, 39915912, 866668509, 302501964, 550108044, 417345932, 835547681, 10574508, 286723556, 118226749, 213298184, 459442082, 493577317, 183184897, 13183631, 749965073, 16082113, 704078635, 297181893, 379138617, 207359536, 826645876, 160821168, 206549932, 213413447, 762206029, 794330097, 805900423, 791875535, 851788657, 473369390, 5019590, 766933340, 592408319, 503886946, 273695337, 130022626, 234453069, 581380037, 785596724, 461851245, 941518314, 146726985, 764940696, 721439023, 596489130, 825889273, 305366197, 241803410, 416147553, 953247016, 711594447, 449543843, 798036064, 192023192, 161693853, 431053120, 144989949, 232887852, 93338230, 928517143, 227351087, 871685720, 875674283, 957396949, 768920881, 873353714, 260103103, 589874921, 413934249, 175884174, 148648425, 249357998, 883112264, 402875393, 199454803, 894615630, 729249012, 926116502, 309860028, 532011155, 583013444, 586875001, 204813871, 301522698, 732717169, 993064903, 759209899, 479643634, 631481496, 234715512, 180084174, 608959402, 124290661, 730828788, 971644280, 868303749, 494584497, 899957718, 832301033, 224459849, 599465199, 474852188, 772018238, 708442134, 311090502, 249904010, 915425304, 702722924, 703392253, 766122909, 671059791, 733426629, 603952706, 536633193, 234839651, 572606725, 265366205, 89410873, 891504482, 177470507, 420368832, 830226339, 43701758, 10436046, 741302837, 660793760, 711123687, 866107266, 466192773, 696571436, 383649299, 253162522, 846658159, 61824447, 678542978, 774230302, 369452187, 106245723, 235179563, 899912525, 657775133, 494999314, 250197993, 8780966, 473470138, 832921224, 664701193, 256885685, 597427809, 434829006, 952107675, 619632964, 614730157, 21508788, 222286935, 669595047, 22492463, 33480479, 140641744, 162815769, 418484294, 540957252, 113067229, 771625998, 247335022, 618158390, 565959167, 566093190, 962413993, 438517582, 88101480, 94805432, 177350721, 789018538, 869721448, 636065980, 76491972, 526307758, 100116781, 564268252, 925456733, 206926031, 40117869, 567721441, 284129189, 595575218, 443113646, 331726952, 718368293, 626802014, 124245225, 438574704, 719213003, 186849335, 539673806, 843446924, 735758066, 682278629, 137731194, 377169539, 609136298, 793100953, 981360811, 666133274, 30994236, 28842307, 207178577, 596341800, 819841326, 9488778, 245407971, 657787493, 227895910, 945607323, 532889052, 294940995, 774757815, 552725875, 281147851, 8220609, 714020570, 827675104, 200957306, 70800236, 615154244, 214123452, 413607831, 435556643, 918856749, 590391206, 884421150, 935271868, 805484798, 759989465, 351776455, 396635311, 315833226, 75761736, 233800131, 882040674, 595215391, 340483382, 94784085, 119781751, 982980471, 342494288, 471055246, 659487834, 159911711, 997905463, 118342457, 566877198, 813572085, 972898879, 101564965, 855611308, 811558467, 191082073, 698938287, 469590044, 237550595, 425138348, 857880945, 328845580, 709700434, 885793286, 776214353, 884264611, 581974400, 845060807, 648611268, 228545752, 384310795, 51851221, 601950025, 233179272, 13972242, 380141707, 6161991, 729817051, 468968682, 262923971, 344768907, 808731440, 312272615, 791053049, 928026969, 270430627, 613410777, 297116191, 934872535, 614359616, 351748332, 34841598, 204096049, 248818011, 483627223, 686981747, 64851789, 30355940, 107340628, 713492991, 475945043, 943762379, 51470488, 274617816, 918434326, 967539906, 9960391, 647096709, 870671695, 284036824, 195256249, 802360310, 758747265, 84409471, 472091497, 845021082, 746556848, 494710543, 3183234, 337465251, 145568610, 130817388, 386011207, 502690292, 323753213, 317727037, 759213248, 221248475, 495444814, 973506433, 617391151, 53292746, 381593192, 385035739, 138361640, 939912136, 362747712, 319290219, 51632964, 351333241, 99398118, 64384543, 636796185, 825476017, 611703624, 329523055, 888972273, 142454668, 873213030, 564501373, 238274389, 886622760, 991038296, 471327572, 288673186, 164481026, 294313334, 174631922, 958015244, 727784516, 355093404, 222039741, 676260336, 361087302, 560050763, 902797717, 306106009, 699868183, 169561723, 800517245, 152145578, 284015561, 532140528, 972681274, 369044568, 486320429, 820085736, 868329339, 708301963, 340712138, 853232939, 154792383, 355141670, 205267283, 98767705, 166824770, 794836594, 784388300, 317787271, 449795530, 606270852, 676811270, 355100151, 675298964, 319932367, 3979637, 5703240, 52575838, 915175672, 514124531, 996131467, 760613483, 721904279, 344509203, 437366028, 750455012, 281392524, 122965627, 626806845, 660931454, 566092012, 160922470, 749171113, 584572733, 706287283, 317791907, 938848431, 19507816, 970678483, 229685118, 338407941, 345991741, 575385466, 321273206, 316449194, 967226837, 977508451, 518490768, 182401862, 414633146, 103831885, 286116213, 773170122, 979220704, 11668335, 116695346, 86406546, 876782082, 199170765, 310740665, 278652891, 76505865, 293591316, 97037405, 549369903, 416482327, 261746564, 751983301, 756217620, 691186984, 481440632, 359117273, 529813237, 212074815, 691873855, 196125323, 620577542, 594993428, 85274947, 709315039, 104293799, 52975829, 510720081, 394840919, 676048279, 644848292, 554980997, 580477762, 551079875, 229456353, 201801700, 37075847, 220811838, 572215069, 328594004, 691211279, 405920547, 668397732, 418068789, 660843325, 493885415, 435894513, 969861602, 587040858, 562180335, 883320047, 692110642, 836093524, 118919332, 532099825, 123002159, 748456994, 729855077, 485600793, 85739305, 106760944, 91573169, 182478393, 853471073, 96057820, 501608503, 100481816, 343452486, 987012275, 238280583, 796046819, 6799607, 351452566, 588850020, 840476369, 759970958, 113986758, 495724605, 762562777, 425528197, 376366658, 484617777, 337729756, 191588987, 68687597, 331526091, 83320812, 532064120, 125128897, 3043667, 543082567, 79777788, 130927166, 739478821, 138865336, 806975536, 138621330, 251565828, 439436118, 414009063, 166433384, 817531892, 187550248, 176381894, 59816427, 357001767, 690897445, 822325898, 635222664, 905173951, 449696052, 649724479, 498201941, 935856279, 829801070, 852444469, 566146561, 738151313, 581790790, 942701190, 745594872, 277123073, 688072662, 157919513, 86501526, 596012613, 188910883, 981607915, 396530858, 439997751, 960403243, 933862785, 992635975, 761896074, 778733943, 733474824, 382298750, 779547377, 379295984, 45222728, 793316156, 292535745, 321434795, 488320652, 355626767, 474355426, 622093108, 311376144, 775566901, 178865806, 103696549, 175422751, 399490598, 445605495, 34196418, 625157259, 415083907, 28837441, 839136302, 409548241, 816889953, 78357668, 866365289, 177313005, 840005311, 669068786, 131498735, 889248577, 631128643, 161254128, 666088113, 430687171, 44348150, 209139038, 606488053, 821079442, 348540942, 601287885, 825768861, 954622027, 749958021, 810599834, 998722234, 273289056, 721569461, 238785754, 48413915, 107475657, 739072347, 724892904, 873510742, 329425141, 240430917, 109467417, 847802570, 892853386, 547102090, 710270224, 182221766, 146426304, 368294472, 716696792, 556514132, 668723337, 653381559, 199082178, 926413589, 319010140, 805878740, 210869267, 463671604, 408297125, 934721348, 445715380, 99894889, 737223699, 428463935, 817580614, 875224484, 787391965, 969059647, 718229330, 109746605, 660257825, 878037691, 389395330, 45796366, 358199037, 98054020, 928727027, 168280246, 485224229, 578390674, 142367908, 501718703, 9401630, 116796145, 988017857, 506112986, 306097244, 898470902, 166183458, 768999962, 780785138, 667013109, 814864737, 835818540, 290800018, 106037850, 264023459, 897463435, 628791911, 529694880, 899900375, 663695687, 865946883, 878915422, 485792710, 351826191, 134112359, 878348318, 114712065, 818018079, 968145016, 496178166, 80716071, 938720158, 566898123, 669847307, 230180053, 142757050, 137513344, 53226811, 20442883, 829789748, 449692049, 750068432, 794437590, 324386234, 549335550, 973990640, 783478128, 694706156, 116633977, 668337867, 688446952, 372835633, 226789162, 456869793, 97554850, 893773806, 108074825, 564164181, 178508470, 712227058, 125289244, 994867594, 233853414, 440232357, 84974815, 561533947, 607789403, 120987194, 417569521, 503285453, 10880317, 281345536, 597115486, 192385710, 772715416, 239442142, 164333731, 884807963, 231798682, 672967463, 484726372, 581769052, 586564323, 631756829, 731181998, 764950027, 402703700, 127354818, 470204690, 994846084, 373795026, 92264081, 415204840, 881411154, 977904798, 481984660, 207443873, 88290977, 950900051, 37947971, 69024573, 636782454, 447190373, 178239953, 888687147, 625570485, 585137573, 142329450, 492085560, 298271257, 673314500, 532097678, 260884868, 943687504, 972571729, 748274253, 955841533, 752010386, 544429464, 951772021, 830591353, 498656168, 23263853, 749516158, 12045170, 331089984, 741735061, 428948340, 551381557, 236630221, 793436138, 550313991, 390865276, 340011346, 527426032, 520400887, 468673327, 237000480, 589350680, 214860372, 643224437, 962536790, 488786949, 788388956, 892681727, 506745922, 295887576, 537555350, 132800561, 985322876, 103300972, 71648553, 128547205, 539866012, 70099799, 711579141, 967926941, 339440667, 132252943, 277252463, 148025442, 548108280, 527597617, 42535793, 31258977, 74174931, 109792965, 107037503, 716766791, 485517670, 181700269, 806438393, 746799478, 520764254, 709714724, 211850824, 177713895, 482991363, 694296077, 787738655, 123700616, 311729819, 411112065, 15942643, 201675635, 970738039, 711337880, 159155692, 469675751, 617766105, 147550165, 488578782, 791050391, 432330780, 653785286, 793329611, 531132643, 450496914, 184262969, 332792930, 614932472, 927624316, 124633374, 79527425, 366307659, 299062641, 171374488, 168867464, 379674944, 125155061, 871337818, 240632290, 411568611, 772350020, 750592963, 749319616, 565069890, 596873409, 709234155, 536815400, 558985742, 260377938, 905917260, 193420815, 481324761, 671076974, 517455601, 479289658, 679832852, 963631567, 273197068, 55830928, 632432352, 605895131, 491860438, 485900635, 71047027, 94863671, 264082297, 437028972, 690023867, 916013230, 821676173, 329464422, 559503790, 528307949, 652297852, 758649300, 892475988, 250633016, 285504607, 882110628, 233004761, 214534060, 452952689, 79111233, 381950439, 588641544, 106192636, 892693489, 187673437, 443086879, 758881662, 952773454, 143116686, 846111356, 107535103, 81951122, 223889091, 758998983, 107524525, 497835783, 665148257, 586925035, 878975863, 25850366, 542238778, 952968198, 158374301, 441648776, 337785661, 587089523, 715722050, 796055367, 673200157, 577523035, 611832712, 828975481, 544370092, 545311972, 312832843, 99207442, 602282474, 319879729, 185105916, 177803722, 67049533, 667025608, 809408656, 939976331, 518455271, 904809040, 909163777, 754612459, 160373983, 539181344, 533041126, 832019095, 66527236, 270873372, 683622179, 935625122, 163194853, 289804769, 853451379, 443493417, 542638589, 651252362, 357591241, 159474172, 268992840, 932903171, 705794561, 688001549, 872560209, 290064271, 759346987, 395715810, 321303829, 408703412, 375491319, 600004402, 438041658, 930961556, 828926676, 307982855, 31389777, 337768288, 430021507, 306973005, 693366376, 992207899, 378621963, 836187606, 475799336, 493993922, 433232920, 22991301, 300533101, 465858331, 201933340, 967501590, 936659398, 470005291, 208807234, 663018523, 57414643, 337586488, 431917752, 968501753, 338848254, 230060941, 633477826, 731050864, 132387064, 899959768, 40698516, 776948639, 946753446, 481936211, 728144770, 787422130, 761355720, 259879643, 216203065, 297467818, 661216357, 9655133, 576511025, 563770208, 73597746, 72061578, 315630154, 526733930, 51626417, 496126778, 308193238, 375929374, 760447962, 618653219, 291625441, 329460712, 416581795, 283158260, 870097790, 514614428, 224932116, 962915407, 520351052, 802241052, 966446930, 506214030, 568740636, 716772968, 609103386, 315944256, 164697534, 510395834, 559790206, 79989442, 273490094, 823052610, 534883143, 299458513, 671590556, 968846677, 114676221, 18224900, 409913146, 498825903, 458790035, 230632046, 444947940, 448589158, 992042937, 385322313, 514458127, 97460724, 826972663, 493855246, 578538532, 928061498, 470878808, 440010370, 449345759, 86259978, 964464308, 147277355, 265393078, 40406366, 305638218, 591248296, 997227358, 286771748, 947054646, 443565614, 235324071, 173721889, 729551250, 204423269, 66669347, 977033711, 622285499, 837919406, 88086789, 352159772, 568300910, 661170440, 36651071, 655134502, 623327034, 888665391, 784626895, 651357368, 968678727, 407214940, 157022181, 165376421, 913025949, 797301149, 96788561, 391087087, 396735878, 41689546, 869159650, 453496001, 994736828, 683524301, 849381502, 887063964, 204473051, 977315162, 88961882, 140919961, 256590503, 447965640, 877618327, 30416040, 229674134, 655303579, 85856250, 95005140, 797259698, 249004397, 996526674, 981191427, 731009986, 226998032, 781474124, 898544461, 866610105, 509269067, 124085398, 952045983, 228723176, 588460743, 439147458, 362229570, 709013580, 809855695, 472408892, 185470235, 281079096, 286488182, 295529166, 978547497, 791749480, 704593938, 674028004, 981580788, 303235994, 748995582, 711074575, 86345645, 965270414, 27547641, 25772171, 373472897, 805840741, 277527583, 11831327, 42422636, 701398740, 233588261, 978410427, 164554369, 47865131, 133721005, 510708059, 641925024, 983286568, 539046058, 116898544, 476540228, 559944945, 623606611, 772571542, 78061068, 15366223, 310867771, 347371920, 259695860, 733123941, 32837418, 718390603, 687709109, 841281211, 455890362, 611861241, 841107927, 453578772, 659766434, 388669125, 185685897, 64626587, 882921891, 773756403, 99666528, 145152957, 272017312, 135892933, 601794234, 585770717, 503642500, 960223625, 587203750, 990923919, 681436120, 260005417, 958800543, 754720914, 110348614, 134377837, 376655269, 565988530, 863806482, 78558818, 993357517, 831107832, 280071336, 185298647, 235394731, 204011378, 998289498, 576774641, 946994567, 150068109, 37367480, 282285753, 384493376, 854819010, 944788498, 32302095, 750254343, 791286211, 418755359, 931015041, 342352971, 742201610, 905783633, 420363469, 4991115, 193141038, 27068657, 702536853, 532720851, 142789709, 370713794, 376726309, 926545806, 817657569, 650447622, 684022549, 539800236, 58065255, 345477728, 776882193, 632758844, 715000683, 960942372, 55123402, 505846347, 699373791, 600721036, 463104561, 589187038, 234160992, 451992678, 119803436, 974478951, 204206283, 895776722, 563186693, 681980096, 69732416, 439164784, 688001799, 463271921, 346487707, 377423740, 866886242, 678851010, 862007248, 776044374, 461391060, 125142551, 140973022, 805430945, 525730892, 859475023, 897886216, 651472028, 825375084, 598665292, 853097580, 901562313, 410399347, 642075096, 543093635, 77245170, 192869528, 598924599, 415503235, 720661265, 412693013, 821335728, 839128974, 781163627, 789580782, 974985727, 354875135, 819232642, 893118187, 346619374, 461412383, 344289404, 586236567, 702821076, 473078953, 429846849, 762805954, 49893455, 224680395, 396513429, 510192132, 233235323, 501392058, 989858071, 435783512, 479448738, 62985713, 122126468, 620789000, 136833235, 903248636, 840195464, 32524504, 183103970, 275418129, 647205347, 602763646, 278900140, 761330644, 804103328, 992506708, 297551323, 793957928, 572349507, 410444914, 190728172, 937537627, 420999765, 225144539, 705163560, 465495258, 127354674, 237286619, 671360023, 627810056, 546532556, 58905212, 990738353, 242727664, 638373447, 606581181, 761591539, 294185303, 270869625, 90481830, 383262384, 655866576, 9335057, 380811675, 322038908, 393713075, 164293174, 789988898, 461405725, 497354242, 349621170, 549920952, 849341126, 162402404, 437873678, 389432107, 892786956, 231914373, 639250063, 121730177, 300770611, 434285145, 886959937, 547271706, 102333456, 150322067, 231377278, 964770493, 766583725, 647997915, 700469153, 452995630, 745711142, 173756320, 161550184, 665559220, 856021818, 173304921, 476952055, 172774212, 635850173, 400363240, 192698739, 884855387, 308703269, 365295568, 196650328, 609556517, 560998578, 361631971, 951646424, 345872638, 642529015, 607938633, 838199494, 904845185, 36482177, 298944863, 363880718, 46999042, 426470692, 826430894, 819889370, 862434390, 62734672, 423131112, 216151182, 821484269, 16632260, 269385126, 856329672, 800927349, 862332615, 104697816, 930842509, 601961159, 47274575, 170314276, 515311784, 206878824, 343550671, 135816285, 816335157, 137764313, 628840142, 522811955, 261005298, 461308734, 910308833, 63525632, 554608972, 339567732, 442546316, 298721657, 992204930, 379195182, 359963983, 493486391, 985328959, 919838702, 253039560, 462745421, 569513722, 404011851, 100322754, 920075754, 426436875, 498122370, 97223513, 415008412, 724797092, 193478271, 86062243, 301768862, 587533123, 51115534, 861499068, 983703049, 784053792, 107965203, 544769337, 722285034, 187372124, 43156774, 547312812, 960542199, 963421988, 425074510, 463100934, 148314464, 337252785, 921599176, 478673057, 899831797, 151876917, 326512411, 787934574, 537191618, 260956691, 356818389, 597231775, 213892882, 77089563, 718061716, 331410468, 29554601, 9105137, 910372412, 709082263, 266844064, 900678635, 841506996, 326521650, 882351399, 770668404, 714984351, 436444539, 171759254, 252575292, 949319654, 909871601, 605880418, 178351218, 296041799, 106357159, 11334689, 360388530, 170979566, 786256087, 655949664, 360445653, 825163202, 566144218, 287211844, 294695434, 800707655, 428516566, 82349278, 1513730, 869645462, 195436281, 943863714, 752281156, 890919313, 866217822, 212349232, 427253630, 208713803, 336359734, 650886044, 920727930, 858417103, 683961623, 561330179, 349656121, 996882057, 300383352, 117317432, 454640362, 790691206, 297313562, 338944291, 767195547, 9654694, 190015823, 882228869, 891416296, 711376963, 976563841, 250738925, 436759261, 832081939, 543181505, 12652324, 719578992, 655941169, 659436660, 395170313, 351442570, 790202583, 731529435, 238172120, 594338932, 617660043, 460408671, 793665921, 994692138, 761247825, 424116001, 361105849, 700321100, 389633646, 289292452, 374645850, 842502580, 48777746, 394023122, 283443215, 135640637, 422409135, 536735081, 209084632, 146904954, 258657239, 246344290, 737439395, 79259863, 647897930, 542800681, 293528484, 381851659, 877692189, 571009670, 843000755, 989758612, 599143928, 36277369, 620072705, 259404573, 686741635, 349963357, 200275310, 114853685, 681226069, 109803830, 261868438, 454002732, 646839715, 682927492, 455306351, 493202348, 481496718, 153003614, 257596610, 996475951, 358975743, 725075683, 367695390, 883608302, 473338961, 793006975, 576793504, 479730315, 671868995, 85174998, 669373197, 745066312, 301774371, 226903028, 440161265, 318348463, 289318170, 825613355, 981822670, 940935570, 420254866, 808798797, 374734765, 135526773, 185955919, 543077507, 36330248, 769778638, 761991095, 700328672, 907597735, 783075756, 814955543, 746117199, 995856594, 570633959, 611839280, 202882714, 679503710, 640668580, 780963218, 659747276, 346554419, 729907514, 503526684, 247620542, 502072449, 843447899, 251076614, 397535719, 707760528, 634713947, 348309511, 447838947, 714146092, 251135610, 729102283, 18067815, 845286182, 359024970, 444782805, 422288216, 550496408, 803372316, 308246837, 355539913, 425527065, 947069928, 591455399, 853912383, 697373399, 166260254, 575797622, 217030224, 713066950, 793828310, 313509278, 646781504, 921316841, 8288238, 78063613, 831021910, 257911749, 550734454, 862089265, 862702103, 509941772, 226365566, 81075519, 908500265, 193143978, 100934664, 60850665, 429104473, 14036086, 548732957, 276309549, 713750240, 692527920, 452458673, 97675723, 673013692, 6146452, 905913219, 699594741, 974475712, 743018215, 730449488, 961310274, 755357870, 582246469, 486064033, 873883950, 884958852, 712636477, 883527129, 793279214, 530233455, 212457632, 903681041, 989593713, 724201519, 709139499, 14766469, 188964355, 849178637, 902053305, 701293319, 169337026, 121551527, 866421801, 634296725, 563293153, 454195523, 608490619, 754649756, 960211167, 522917556, 455008773, 446212943, 704632127, 554818515, 732672658, 818154443, 647812258, 588453321, 872764781, 727394109, 282827928, 907152596, 381581635, 32836953, 291831822, 681416378, 296565197, 650236529, 978506961, 237628279, 442049718, 859018214, 252358072, 19876323, 655059675, 701937045, 775517730, 964790471, 640241971, 472900153, 249388588, 812469604, 541292630, 415977102, 399392757, 904835592, 800958124, 60534654, 257488042, 997491158, 915399565, 285839767, 437477008, 827916407, 418262054, 673397142, 640265141, 781465715, 139353327, 106911151, 989059545, 561937884, 879036536, 926432405, 479330104, 919880512, 650683500, 478610431, 560986366, 347376401, 637737146, 110953912, 857457337, 391764005, 976494687, 632660308, 921024647, 985147545, 636701795, 4489000, 65188949, 921673201, 697821131, 193526773, 917321933, 374797665, 962592992, 314887041, 433299954, 72500135, 887845758, 773526180, 936863473, 514968656, 212986168, 730847123, 376314381, 131542803, 713358820, 522011894, 422673631, 468838859, 530578164, 810746699, 643115407, 372210472, 624411881, 117286810, 771604716, 924416241, 220238837, 349856478, 440785215, 985488396, 796737453, 937270615, 57490506, 992743045, 431529498, 25676287, 846286374, 258031104, 539332299, 762350153, 203636094, 475776338, 704518567, 785979519, 840692764, 701922991, 575640950, 816079493, 658558077, 824664782, 414969191, 626327027, 882497385, 744751338, 811309754, 835032097, 804306609, 346484802, 819908136, 51360072, 87936829, 588813229, 571237463, 756279621, 131197148, 196761212, 586682185, 777570896, 186068422, 319696880, 426982428, 323161637, 817768454, 803601574, 814114087, 760613951, 233464055, 575289907, 124373489, 612136104, 100253413, 916600497, 532456812, 733030908, 832138447, 472130089, 724950915, 809230764, 229336617, 274063025, 346103744, 243170533, 388581795, 392737952, 984034038, 357635065, 9644038, 114883469, 187976818, 479635105, 192000579, 816608600, 309759489, 516049677, 667867321, 162740867, 586000593, 713242969, 490288711, 113558043, 970027878, 546386683, 425104968, 830682868, 76348024, 423881816, 415558711, 586549647, 145607826, 446738210, 984555781, 418336243, 439803557, 953391141, 488068154, 442422728, 150678321, 936208413, 224578758, 744301545, 140495320, 602881523, 334067954, 641562607, 938611891, 513144912, 41309900, 351562871, 317234065, 405119269, 902669073, 682756809, 461441405, 694558494, 627628275, 83560412, 517927837, 544366983, 112638806, 147355817, 732916880, 674361358, 326588048, 8922707, 957299214, 907198454, 309397959, 654217650, 704702046, 593023276, 919753245, 404575443, 838703436, 522698415, 106366518, 815029104, 380621314, 166070346, 848089860, 463299859, 686272355, 980518510, 462476509, 98838868, 771595022, 453174862, 317787366, 764404114, 619312369, 19457529, 191377603, 891874126, 82769594, 180226081, 800036338, 906534633, 583793729, 363317607, 394382778, 447663748, 425004675, 364430327, 890696254, 79757751, 725704926, 736719711, 757565609, 186115226, 89098457, 815289899, 936360444, 654495069, 974495081, 361733252, 878963864, 872293285, 871684325, 614025500, 966245100, 119971411, 561973374, 11795220, 160799619, 990752739, 306781904, 388342988, 700247036, 374388718, 80284970, 775341312, 48675002, 656912707, 42215521, 35763230, 694491618, 660880833, 291809634, 95554624, 264812750, 880006076, 869295036, 975623734, 642447063, 280372307, 508095761, 10302984, 155723628, 99458798, 654875014, 955316325, 275374975, 261430872, 808243975, 549345266, 607460048, 684560573, 636205339, 118910603, 222455587, 106590478, 126315663, 54763351, 653437449, 745268422, 688171473, 861926298, 677638171, 512642654, 666219366, 633893230, 942983131, 680324129, 318696854, 996835557, 985208111, 675908767, 245787446, 372585731, 831356740, 885218192, 536926778, 843440502, 707433562, 562101548, 760792649, 111288202, 141245921, 694139806, 221762693, 555819791, 956123647, 417804974, 361920528, 79767938, 101585075, 852088068, 57311784, 265459962, 821922662, 452684471, 5631530, 673330321, 532858314, 575087618, 448898265, 373361990, 357965046, 53421597, 880014188, 717245206, 189084474, 408825936, 872453532, 873946220, 738536084, 891896460, 141185246, 111864066, 423992440, 853431428, 425128439, 974314342, 135451562, 66887258, 859537966, 17615308, 593831358, 817822793, 797424316, 318331928, 106232649, 33687172, 262962413, 81134803, 803328284, 388507815, 464418993, 925362009, 470353106, 237171847, 470437132, 55103872, 163201473, 870774679, 109967396, 221489978, 32533184, 178290380, 425622630, 778211346, 927302433, 610350628, 150285049, 369770664, 374978638, 191357068, 728830894, 710315554, 300266585, 105340817, 609032739, 246391892, 942889798, 443049254, 599136805, 74560515, 302748595, 834486334, 753451703, 822873308, 775136722, 516595944, 485130549, 706068855, 822477359, 136532978, 157314574, 341501867, 232572229, 175578417, 50707498, 530936275, 891077181, 626793556, 983627825, 359214713, 398088894, 693328073, 94847666, 661003042, 951821784, 846527720, 582960296, 550590927, 155690391, 216722217, 705550155, 562210045, 487053389, 419911484, 390933857, 184641905, 837030444, 994573000, 764904683, 830344169, 629927318, 130434266, 578093297, 451998851, 21073731, 515579517, 78034590, 350199876, 450573128, 367313683, 707982635, 884290957, 231198902, 60923075, 885914953, 78662388, 324134437, 914907864, 415304450, 539348808, 841284960, 584773440, 920163586, 928491721, 129078001, 584008260, 39511485, 876413509, 603368407, 636989327, 353512833, 571325592, 466785802, 74676420, 590837382, 435550097, 706753689, 219633781, 688407641, 186197062, 310930369, 326836890, 622240534, 427405814, 211446665, 9754488, 46982737, 519150188, 662121788, 915931465, 878199306, 737921676, 571339034, 823863345, 561073464, 423722571, 187179115, 650931837, 449021848, 717738126, 569087817, 896996119, 319640176, 818190235, 798625797, 629332636, 379627020, 921051767, 194367868, 127828495, 378642580, 142411921, 194152511, 989503405, 391158276, 872787872, 653545716, 469238075, 364839320, 602164401, 963153173, 67714248, 886047915, 138881322, 199675923, 423694185, 734785849, 663852887, 876040855, 954133193, 749495021, 968473792, 354434032, 511973602, 203974420, 517473401, 799760629, 925625978, 251507223, 688792997, 852976400, 921769467, 169241715, 631002899, 408092794, 599129394, 78151745, 734920141, 527795782, 360046688, 828832090, 2199838, 858544576, 485760523, 923574112, 119654945, 43520402, 678517720, 963374614, 357215099, 305048045, 890059729, 220597366, 938492329, 202112051, 221863000, 244199936, 857393017, 29428243, 65935739, 301978803, 120095041, 256236628, 294141261, 112483282, 432074194, 833454064, 427217237, 130617017, 147489765, 325686392, 518469521, 968711335, 947363702, 774142586, 906384329, 532942851, 399249907, 777480366, 166238399, 93290290, 189085229, 463077183, 170569166, 404994943, 532652600, 801672045, 144418563, 461207717, 483975503, 87919998, 413722885, 556075015, 192029059, 825476816, 163615426, 803842720, 703599151, 923978527, 390851286, 271672382, 472552476, 884948050, 320143080, 344361890, 544615214, 662675730, 735339983, 462753312, 603577743, 770098743, 418674149, 590121723, 472033907, 260813265, 495449169, 510863586, 572169413, 303926215, 334475959, 894459870, 189295393, 94597570, 501762649, 792071064, 380237433, 456966372, 654517180, 563584078, 186002595, 645474672, 811018149, 322083614, 773690113, 396465706, 836018056, 492466742, 596889182, 914604256, 287242596, 524874720, 499343688, 728970952, 730224462, 753740617, 306544844, 673778214, 828565091, 690413118, 707782776, 65132317, 227278267, 233876939, 674951472, 799757717, 456565004, 788994289, 390233455, 797368452, 512454677, 212250790, 506801446, 298147805, 958565692, 925042572, 944085763, 500112976, 441334045, 803967836, 147238932, 886475283, 878321295, 28187919, 29789021, 909212425, 793808024, 77686052, 186524862, 149782761, 232751943, 730336935, 339014696, 541613942, 461041180, 815145463, 677251377, 688841614, 519834559, 815861578, 210234072, 482431035, 649492631, 295242936, 643429900, 146074440, 791072589, 14833420, 945018623, 191739418, 700956084, 347477176, 368521557, 45329050, 510290900, 409798458, 946015702, 732259375, 472214798, 308221349, 14024251, 617451592, 729592859, 129580787, 251132976, 763382685, 762960870, 368847370, 791465389, 34644645, 893122317, 809205638, 171071124, 95933531, 906335758, 179400391, 578920503, 268775092, 175524410, 545816300, 982608293, 615320162, 337138429, 160024463, 950760017, 188330695, 383210605, 274363988, 785766875, 513018603, 278330821, 767610138, 463967108, 48132923, 959307282, 173178812, 106273227, 751317760, 777775084, 823542485, 510816522, 171586076, 345913003, 461399495, 551139699, 296818054, 832141339, 714757833, 668841857, 6239059, 66375880, 539860191, 597857154, 98665655, 628501588, 535086477, 630994518, 507930018, 531580878, 865226366, 731738256, 935365869, 24352679, 193176389, 584115369, 222271366, 245160116, 658974155, 84672262, 978704989, 690373093, 863497439, 484828143, 877255404, 266352060, 762398352, 257690505, 939810511, 72875426, 253412351, 484223564, 223757294, 537911915, 145499986, 98344884, 350505255, 156514831, 328729540, 374451968, 756305373, 251015971, 652856223, 509882997, 550475531, 239576173, 929322420, 383871465, 100487323, 687817622, 838571719, 388345923, 436445106, 7885532, 974026499, 423169044, 356168374, 397323438, 462377064, 881897635, 114150420, 877823436, 667980386, 142675619, 842947371, 495753039, 30440570, 102485868, 856132228, 181344002, 947589104, 341501910, 651881894, 5865341, 674831911, 949352176, 400012594, 64732798, 106471599, 302279031, 802518204, 560774411, 689726674, 989560548, 422113715, 351180728, 825537537, 367011591, 170894491, 213915783, 500481032, 753467956, 956920694, 393646153, 202447988, 205375358, 341011555, 42702686, 573726800, 130118003, 230990849, 119288449, 798814985, 675320261, 632821417, 150701836, 725867308, 745930922, 782485640, 845406581, 282904555, 946201656, 510056627, 754865319, 133505161, 111776133, 964542694, 571267972, 427138231, 583335682, 235039620, 759689510, 509200186, 426257072, 643636168, 885775563, 957574886, 590676670, 379718424, 604446480, 232145973, 393019459, 430126488, 526870843, 807921792, 275274346, 742615616, 471173663, 433904255, 512472394, 161071692, 47150940, 644623638, 901577738, 219663947, 514032150, 914383714, 809060921, 660279998, 775566232, 696621472, 698118064, 127304149, 351581712, 5087985, 485175792, 482286817, 557676836, 646381666, 597043448, 943714531, 122745483, 162479035, 891628909, 922637342, 432652036, 212955457, 287132663, 183497530, 704578140, 283488569, 415000556, 248051612, 29198434, 317317699, 682850229, 658568098, 662264518, 819646552, 566369096, 798734251, 992903367, 360545857, 770117481, 191616289, 153114037, 258937109, 975439078, 896697306, 244884946, 251696193, 904491547, 88600270, 365063654, 368998843, 794183339, 930745090, 829376618, 268862790, 391472863, 686175191, 470766229, 236890649, 874501788, 647563389, 987435722, 984253514, 480673058, 928933408, 902923500, 420450563, 734594180, 101147111, 829453503, 257906018, 435030209, 392775392, 546886840, 55807219, 265589592, 20633644, 740545455, 687598057, 412887336, 28022988, 715183448, 327937018, 748833678, 463287049, 465251617, 969255483, 407182690, 293519242, 745241318, 628782531, 847711730, 620129620, 941729679, 924383382, 626568779, 255140266, 843762659, 305137455, 476539642, 801314593, 160371289, 376465919, 750008071, 254836121, 637666913, 4623445, 677339302, 192894294, 589422681, 82856760, 55620383, 54802667, 436163404, 545201919, 276977929, 126791454, 352360216, 478848834, 296194726, 846060791, 770279965, 356110416, 436469995, 696141908, 560241639, 206039978, 361639052, 963751447, 446597069, 569961949, 236117376, 162204406, 46791261, 442258682, 62889473, 373368274, 703456332, 765516730, 90163624, 942094242, 825285954, 934024972, 493497264, 298432370, 321088785, 749912996, 972081568, 395297053, 390043499, 908868394, 11904280, 172998691, 883758689, 920326576, 562020693, 610269420, 529939902, 672529315, 652934747, 360005869, 295243535, 587652232, 754893820, 249320260, 118366504, 552360960, 148287526, 926158729, 728179947, 240499881, 874092906, 215778848, 731526216, 895058098, 952603108, 706803245, 191913258, 687555788, 420083571, 254558296, 646905909, 204014386, 333572309, 493363471, 730632026, 389032755, 158304670, 329728434, 535486608, 315881556, 976221900, 482762471, 333783040, 452225678, 384669587, 750734493, 581634541, 640538435, 739993837, 682013924, 276294106, 12704395, 179494377, 871332924, 770671314, 262084448, 470312427, 654656994, 113538074, 390960552, 825151172, 464065271, 784477590, 516093706, 662668648, 720169380, 275718470, 796180415, 725243099, 747997405, 473583852, 534248180, 544869491, 280019157, 898528932, 839933722, 517327546, 324115693, 33512418, 589129627, 645663375, 339786439, 445205700, 321878697, 835666517, 188430161, 554115850, 83809604, 289480407, 652014086, 458092083, 881354002, 802841903, 371763024, 313018031, 888160089, 874565843, 204910655, 32709993, 748058090, 507759397, 669341356, 69056719, 25140097, 889564169, 81310379, 153765790, 519527849, 263071738, 846655343, 988246859, 23547256, 64274358, 309621772, 108091722, 44823037, 306018774, 375458271, 824348293, 637291909, 849569403, 488901391, 499324847, 90698282, 237153472, 740956963, 485385145, 895416057, 115231049, 583237280, 103559863, 96141361, 802459728, 683768088, 383459676, 402027244, 193973670, 655502744, 830079928, 359944782, 942091219, 621166010, 629102536, 158282962, 682825849, 584527540, 335657192, 768812641, 769354957, 810151248, 14428302, 918014017, 318111384, 892500980, 868058526, 107894078, 279538251, 574862512, 711465816, 391561161, 353558186, 558581617, 712599124, 199415579, 142705903, 423482618, 707665306, 94835936, 518070631, 771844394, 42331016, 241478274, 457825668, 701526314, 811461054, 298256107, 532835505, 705893376, 163035128, 932769786, 877915393, 148729522, 233736901, 797247115, 193514292, 79715625, 567316232, 949070633, 223404013, 146450084, 743159987, 984944857, 470724542, 351022513, 580337720, 861156281, 960783877, 988163582, 56205032, 657861261, 119928040, 933146084, 511151411, 214054184, 720952062, 74889359, 316345372, 189197953, 696073840, 540695748, 75698490, 165104884, 679725866, 420650185, 718699715, 963945751, 646317172, 26625004, 252346631, 6326784, 551259616, 745239928, 354265268, 379868289, 711567671, 713558376, 731286970, 579105455, 867918966, 687727352, 625444777, 92666031, 961817505, 610218336, 75135649, 631865402, 134775726, 934137480, 917689390, 412146838, 39621797, 709240423, 144341612, 823020667, 984062397, 427099887, 924357087, 975390144, 107653330, 848520369, 823978717, 553302030, 120258497, 808217116, 125872550, 206532672, 510791812, 128998629, 428661430, 86478712, 862702907, 89193944, 110447024, 541833339, 518927928, 661817757, 359826441, 990029790, 454439069, 188363543, 735287629, 339799374, 241024295, 895141187, 696354583, 372031987, 835014018, 652522659, 806270463, 184934619, 362439592, 718494745, 60904349, 107390773, 397483390, 761857634, 986271058, 558024332, 190278615, 308412513, 602878425, 679134443, 334113403, 119939461, 429633423, 941842105, 801183091, 257278011, 780044944, 262986606, 572757570, 873642366, 555369914, 858514273, 122621821, 410470942, 174216592, 328239892, 760252284, 269055786, 561779992, 742623797, 783352015, 258521569, 36706354, 355302536, 50312117, 867585367, 379317911, 35169262, 391865832, 192563536, 644252925, 985314360, 945851484, 864218193, 840102992, 710948752, 731908037, 183294757, 709886093, 34870060, 569724765, 502334582, 772889827, 286765004, 599366636, 34806415, 308206755, 244150557, 328643969, 84285611, 370617433, 441908180, 357813132, 989587954, 397089111, 216099352, 825526942, 329735761, 76821680, 108299908, 803154173, 644492201, 872730523, 414289756, 481989548, 894829821, 454256298, 448013175, 596336652, 636112830, 557663050, 88586296, 657226686, 366257035, 991818586, 45977711, 278334772, 428542779, 830536130, 872401720, 225216559, 427011929, 440832032, 232423610, 202980786, 786417221, 436903232, 317677208, 382237213, 796306773, 832205863, 953185660, 441222594, 244645732, 798657208, 377363307, 14648115, 887982420, 179918376, 61753173, 275830075, 136766512, 359187691, 951145550, 17058802, 842466289, 313273400, 138197374, 732098826, 820502450, 184766102, 887714849, 942220145, 93783981, 480391122, 564897458, 737492992, 820546126, 857762254, 310572772, 888431620, 577687433, 751804303, 703713661, 97423096, 869564822, 203930671, 662573479, 559014282, 694656174, 109619805, 177692062, 430570041, 293208523, 166824624, 225763182, 165748608, 115251272, 793991584, 127874452, 936139284, 270426309, 70939617, 143448150, 79595633, 654637863, 660059659, 525890005, 94271328, 589659189, 885568008, 440396376, 228310495, 592596625, 256569122, 590117724, 46236972, 435860259, 902392322, 888915267, 415165988, 355383313, 250024706, 782666244, 236068076, 599478943, 182305088, 110289236, 674190562, 528420000, 318216519, 775961110, 558385619, 84857305, 689239298, 768313078, 9858758, 429919545, 404618535, 162434848, 888409509, 845971391, 623749095, 934341361, 205464012, 322099004, 529196818, 361437204, 762920255, 559217615, 712657435, 982461612, 147733352, 96695180, 44747943, 749451861, 91407470, 741542438, 487661475, 898822858, 2712547, 351303445, 903833876, 577926809, 386540403, 440550637, 599036842, 593118009, 573548010, 953981606, 438367585, 556036186, 160631931, 144476531, 497636818, 537829269, 938647419, 648711480, 962911105, 122419856, 509265594, 93458552, 616286509, 320699713, 830129952, 790884095, 707354421, 297131210, 710159504, 897642251, 343087014, 622601107, 619718908, 940757977, 426712591, 722864827, 801971157, 425943160, 368461632, 335884685, 212562535, 100143164, 684557999, 216513708, 253484433, 785179545, 383423948, 157884726, 104412831, 172990370, 825879244, 933344630, 89193930, 759423480, 668970639, 443474682, 360666936, 113681364, 135526993, 962782833, 283216173, 930212195, 520825462, 621012610, 424586012, 402946653, 557803224, 508398581, 719820073, 273738884, 245693430, 974544575, 909608002, 802497009, 767073392, 232719969, 194635034, 53883987, 612393575, 862803394, 702146867, 614158348, 674023804, 22688994, 393922556, 336389831, 341045857, 170437245, 864200317, 467377735, 698406805, 216301208, 726314826, 816904475, 338606210, 145151939, 721805354, 305801697, 536757511, 856934447, 232981634, 998950298, 825299130, 117074878, 714673801, 602669359, 569313464, 915493288, 333444096, 925010480, 288281766, 326354132, 710666449, 670224741, 249329045, 537133684, 128380112, 296076186, 822181080, 170217508, 719034559, 241827561, 491543970, 841737540, 533062554, 590272935, 617777279, 8321195, 368226686, 125612212, 393481059, 867942649, 374990875, 644696211, 980375781, 257325825, 102485220, 218024700, 708844177, 520984295, 965164253, 128497323, 174435209, 225416749, 475449817, 86157745, 903573205, 62676266, 999651097, 187827466, 480978420, 438558990, 731800709, 147895340, 709410777, 207621195, 404243635, 511155198, 822295457, 972965181, 926864872, 725800386, 899105742, 740573865, 561840627, 618780807, 375092062, 739387054, 81056399, 192290041, 779750705, 571569199, 799033182, 907923189, 798261756, 381197804, 61258231, 416760798, 649657701, 427057664, 199574252, 731268725, 48741658, 199582188, 862216154, 121275805, 370814637, 428033053, 274307961, 209403150, 417428374, 581430597, 874214864, 362436318, 724701754, 770659112, 427342588, 7169680, 586736635, 216412437, 495290730, 247035007, 620744249, 617300848, 515575914, 184139770, 780053042, 147199860, 77711105, 596036543, 130778919, 789598639, 689083616, 437482557, 145420222, 674912486, 382929764, 202313664, 426282257, 734015296, 476721768, 268099782, 459151872, 425140250, 425382351, 253413718, 792228278, 243300472, 644533861, 154959103, 165976815, 845493762, 501516175, 298629022, 380014337, 237439781, 518202548, 361097802, 540543496, 958259792, 546853606, 113957800, 734121282, 109787225, 137862680, 746715286, 688279283, 788509967, 541102594, 196717648, 780812829, 949633099, 18753885, 471673117, 46063738, 4310394, 525686377, 460579465, 610198143, 74993847, 858783171, 799624099, 518501402, 101777365, 452051845, 627233389, 371924176, 981619161, 809095987, 454250912, 49253889, 531183506, 49094053, 767832575, 749718729, 234904330, 240057536, 912993648, 733138712, 67454908, 102412256, 534511509, 714014623, 750591692, 358242948, 698914308, 329170993, 638577338, 214199965, 401708544, 203714827, 15761679, 631965686, 24563524, 473822732, 446197987, 514987551, 716547059, 756062648, 894381928, 547132416, 297437330, 535313839, 115216942, 386569736, 139075661, 82129828, 684469533, 546723292, 817577296, 614510839, 877561441, 961201094, 968568753, 669329857, 917830423, 995141867, 156048176, 396256863, 576752276, 712865897, 480222744, 290088454, 338355137, 784924422, 558735332, 408872312, 405135255, 860923206, 649360449, 916173792, 856129031, 70771648, 495458871, 555660932, 359743672, 839855388, 78325628, 199918602, 366170004, 755987065, 310939322, 837898837, 362594955, 282145138, 994637217, 363474257, 35872067, 890731126, 328921366, 951598952, 879826282, 815376534, 111293821, 849807640, 508558397, 859527179, 669364924, 361374896, 555593563, 831733076, 918621025, 453450459, 364118525, 960731253, 606186967, 526127088, 434692658, 750941216, 254251628, 760138928, 338116656, 995653643, 669573976, 975571508, 867283968, 82266565, 821027547, 912993841, 216282737, 562785394, 824820749, 699761082, 405850222, 165257969, 43982116, 337487989, 85288207, 903870134, 477889168, 398294131, 877260236, 208946319, 623270141, 587142952, 968497694, 537473676, 389042821, 351444527, 78333607, 958659411, 956062376, 13970319, 121156751, 986809579, 372085348, 193647658, 852796549, 5964690, 965133144, 80815201, 636409274, 256780084, 993305992, 907516328, 221495058, 771967911, 625871828, 388212111, 404988229, 413856951, 62947790, 131873222, 938051463, 653498950, 221240136, 934502620, 416723984, 573421923, 454133935, 598788114, 588650938, 105529281, 206721864, 229823751, 113743272, 703380383, 408033873, 503385364, 154688569, 216002477, 320260507, 731798905, 649339934, 95722290, 604977220, 49777938, 415188908, 881562163, 503888374, 897437256, 690279279, 215447411, 224799896, 361769122, 230157215, 846508574, 162568319, 685006248, 314445334, 812662000, 590370376, 279370358, 603018559, 421181682, 610872879, 464473861, 622641185, 12007884, 963603635, 452981157, 428011682, 332378626, 38126152, 179858011, 536169851, 924034203, 475573729, 303378807, 288997523, 419480330, 383859487, 324170952, 688945504, 924192985, 961547806, 883893850, 533683426, 799320404, 314744693, 303631977, 739540811, 335768920, 89184592, 133378072, 437037933, 33453680, 112939092, 149019071, 579357913, 133648002, 808902351, 155640548, 421061742, 457086435, 386977664, 103425366, 732468855, 851981616, 867413392, 968527753, 718240507, 859675910, 392543612, 113812939, 428674482, 986252101, 793516901, 342898373, 938958208, 817170018, 968525020, 819517424, 498446647, 137360744, 18866470, 935356961, 626448561, 677196242, 322219784, 125805443, 596104821, 915709891, 533404350, 315459774, 138434297, 621797342, 109257705, 883791781, 4219220, 124831669, 892767167, 315242656, 636697622, 958510219, 823812249, 112828112, 959476400, 46220013, 37156486, 354793200, 619599485, 954001330, 189654506, 771685104, 778222573, 875227656, 982771887, 615455996, 32288707, 378077771, 236982339, 681624124, 13918967, 680352843, 696147487, 261419734, 73005788, 707534759, 382769920, 907277954, 976724625, 42307132, 407426291, 911084189, 430819448, 581342824, 345246534, 794477026, 346328848, 666383969, 419002151, 516766041, 599110332, 316831841, 655353816, 119485564, 93882866, 108611193, 411854227, 7066937, 954559435, 648487543, 604329275, 280218694, 554177373, 71215188, 155441048, 198727658, 154314698, 197254125, 582756073, 152552004, 708573406, 463953334, 138022478, 859415403, 700964464, 90143636, 959795111, 308796574, 539359961, 695132229, 52018842, 7869156, 754150615, 581600512, 431819488, 75869719, 550802762, 876506787, 352888672, 735649044, 71028723, 477502403, 674659526, 137000191, 867466954, 626159001, 86151185, 652163675, 875459737, 931747826, 827899151, 822847113, 444691524, 917283716, 538008540, 567887668, 942238825, 582789494, 900696339, 312179893, 519118629, 156722027, 588166313, 394695248, 623608245, 748454192, 624977311, 82077857, 914408336, 679286071, 463058966, 964466499, 439887762, 630055531, 414411936, 435955145, 486530787, 985345523, 131845973, 838171801, 15580441, 407579483, 250881447, 569935283, 195676201, 471682619, 136748040, 652985196, 845798274, 977277345, 969281985, 562769658, 954677164, 336645103, 846700035, 285227830, 453397000, 66246726, 372786750, 154514671, 225363784, 140519100, 24687124, 196750559, 463099077, 559003600, 336489278, 268740551, 9114222, 357265515, 347831369, 583238201, 63132763, 818981390, 80707007, 394908963, 496756482, 352926999, 913097545, 946064198, 685666693, 374182832, 565275100, 992963212, 98678926, 394042864, 907703474, 892097647, 39244483, 742158582, 648579740, 97567708, 845472327, 371509011, 692168526, 442052983, 358555355, 858690395, 507062175, 825495951, 846539122, 700772512, 484807297, 34618534, 173075709, 431307067, 287930543, 859133969, 849920311, 660956206, 951891196, 979111212, 154702810, 830059573, 691029743, 98030433, 629225990, 287454421, 541525369, 295665213, 579711639, 181707303, 270863340, 826206533, 129918529, 226949125, 393813251, 27632199, 219599102, 42533580, 906427937, 142523298, 210032413, 903611912, 45898977, 632282466, 170311728, 998318657, 782251127, 607252314, 334207179, 142840357, 575826507, 70011166, 151340577, 725782952, 597523408, 586920757, 592529654, 420145717, 483133709, 919399536, 854847708, 288529766, 504429740, 62778793, 223526246, 789307417, 554769911, 650793356, 632505518, 507388716, 819452503, 398978522, 292778334, 129662033, 242587223, 337804326, 317350863, 892107172, 591864272, 286095755, 578227659, 80740532, 352456221, 686798859, 505287351, 381946953, 275356746, 883240768, 72372131, 347498435, 327609495, 145020051, 710851393, 436270804, 803553855, 230958290, 381343268, 987714180, 993609078, 91828268, 40496139, 176926963, 175088491, 291588840, 399477269, 303732580, 579229267, 820426465, 41257135, 833532519, 40823139, 628465699, 49688976, 31578203, 364657981, 585081753, 803666943, 668280831, 234571486, 641600563, 762733126, 610818138, 197341048, 272608622, 509464408, 619127444, 736348753, 286157365, 644361130, 979817532, 200295736, 179934071, 881989235, 964815216, 838066074, 76045281, 613124107, 845896278, 485789107, 288835272, 230484028, 447081096, 474265689, 107641084, 923818902, 516317009, 500887889, 890078653, 60052627, 52863095, 270362545, 323929289, 239412132, 251183825, 429910781, 257122297, 109386714, 85383694, 617455578, 73516378, 320482474, 823752827, 569065284, 372311029, 652924147, 726189763, 643757153, 273322210, 949372126, 224707978, 292681603, 961759899, 811399092, 737071839, 677746745, 999342689, 969732344, 189852076, 13000244, 613414535, 177928398, 879316091, 366974990, 902089072, 939516654, 464478760, 911456267, 857057644, 258394710, 290913027, 715221496, 572782269, 156459868, 252295374, 527185866, 699351588, 417794960, 676032008, 99830089, 97719614, 851428761, 61255178, 909852889, 78552145, 42902976, 587698628, 292615921, 856360750, 766970949, 649594043, 599763752, 112763470, 281984507, 456968251, 635504646, 669124255, 968089339, 398857258, 651559390, 49429897, 693840498, 970522429, 182354286, 785991061, 312236519, 336775518, 572052240, 2720985, 940483566, 3266264, 787718820, 332615506, 179111803, 814014864, 440471327, 686274294, 337675153, 433224530, 923814779, 558496291, 793915653, 371064283, 121507131, 636362529, 451808565, 958066853, 917857359, 941231408, 73930420, 560517322, 549388134, 242196721, 826146804, 594868434, 641762579, 246884442, 629721184, 993370539, 37298935, 713440132, 364526921, 405369256, 853279684, 980857350, 444732569, 847199647, 646416097, 262182494, 850405072, 375830473, 375801357, 19516269, 849173279, 604942155, 581611017, 611277835, 766795375, 542232261, 965135419, 755936453, 365112338, 709286015, 31541771, 140050167, 583844122, 686950180, 558018088, 537932891, 391784405, 946178397, 711647927, 303783712, 904192393, 883597464, 73031737, 858269565, 949689554, 753172809, 286558384, 716472317, 857250539, 610118646, 529052243, 971724148, 686821008, 117350953, 204574936, 255552073, 420405835, 544507676, 582079831, 3434612, 184932051, 483686687, 516366757, 800927022, 968082037, 568157180, 234085412, 233468877, 562636549, 338817096, 62512519, 634099038, 125968689, 865328053, 171805415, 214879095, 9226319, 967119800, 155753314, 627317415, 724184613, 456754141, 383088794, 388048149, 348733286, 72487263, 545653332, 595163686, 238179454, 696852179, 136775774, 543089084, 575336218, 493389321, 57905433, 780393841, 28373297, 875649011, 60597705, 10501533, 769981057, 175473036, 454059480, 214447932, 766981010, 833771553, 699994713, 336114201, 228358652, 167219923, 626507358, 829513101, 545724343, 764125036, 819964160, 811145258, 733546061, 137516951, 836572101, 443913679, 423128644, 477039982, 44086094, 914979747, 425015143, 545945206, 350856623, 422882999, 542728376, 281472705, 146323965, 387539114, 887101322, 203928796, 557015044, 539385958, 160505770, 530050888, 920938189, 290251262, 19526307, 397188919, 333664364, 995279125, 189200254, 403498451, 859591333, 362474496, 994557218, 701788292, 949051372, 547760826, 533028076, 394415801, 719105695, 340535042, 176211141, 992722424, 26045749, 42702260, 736307368, 263277284, 590740589, 827123683, 871983320, 711390299, 818760622, 788269519, 346305754, 66908693, 410365062, 441253237, 406640661, 963914443, 587194277, 768278450, 827750999, 989044531, 59946125, 792592002, 602369575, 410248708, 177749731, 630491484, 661911639, 255971937, 593895713, 738453984, 932290444, 797665165, 921091967, 406733209, 713173564, 651484988, 982401752, 642896846, 712275321, 831209815, 852699150, 472753354, 287344590, 936240944, 831206703, 319293337, 34399520, 359515854, 626594229, 781038498, 465806003, 838190655, 680150058, 705506639, 605270192, 601821583, 438886076, 550841005, 947497369, 597570830, 699474285, 241873586, 701525400, 320134357, 183541137, 370326644, 948967689, 860305139, 407671131, 326040882, 669595634, 592411655, 895709392, 217757214, 555473407, 216641971, 23528645, 714948306, 813649979, 83885115, 274112601, 490636448, 864490134, 127818590, 544376055, 928393661, 771093415, 136568556, 100766791, 420283630, 889095275, 101687816, 834322627, 486530399, 520558689, 845589648, 393921403, 463135491, 856810967, 845238662, 978864674, 964502754, 373317924, 358265835, 636567811, 241636499, 783293004, 60275530, 246390175, 137046182, 394732566, 515710543, 841243459, 946727883, 767690507, 903781621, 547324798, 555499585, 292112372, 764800653, 383971334, 725118709, 758358350, 74343053, 290321764, 709753831, 961727254, 168944974, 164483605, 377520402, 63184171, 139884319, 234827181, 358034748, 712875470, 509365064, 203387578, 952587845, 965701034, 383217975, 445305780, 218396267, 562259632, 824145321, 370470991, 341762551, 710766547, 990520754, 514526360, 434163576, 77872344, 686492264, 21064751, 127405510, 75445008, 380604912, 595265163, 54308005, 895004898, 664540229, 552210857, 773156450, 598763949, 888554498, 223250727, 487776946, 1004849, 774886071, 482601251, 442683578, 688520956, 742214158, 790763854, 920969505, 993129003, 271269749, 637075292, 818445372, 721605926, 905003698, 219244526, 416379451, 916731989, 726588022, 567383859, 620600218, 44375163, 713741125, 233594139, 901958256, 73737415, 914528879, 177557364, 124271772, 201694637, 468664391, 644614497, 939541007, 278275413, 343909517, 586466301, 694693596, 94277030, 709783283, 254974856, 342910617, 629704015, 189273187, 897327588, 607620004, 142939548, 175585887, 652384065, 709864026, 877268801, 797778039, 818198196, 965787908, 324349236, 230071142, 176549925, 142310954, 567371671, 999043630, 425926098, 201620705, 365221887, 901539758, 987192568, 35857210, 636154234, 39524948, 513969655, 760250257, 861149844, 796804091, 100793722, 317526463, 855921597, 829715530, 797308981, 195353875, 814430976, 519201226, 483995969, 335820001, 730403515, 956295411, 271039610, 438852302, 339142415, 3098589, 689362615, 411893289, 327273672, 126646191, 697698265, 65817979, 927387394, 726493719, 271378715, 417906457, 679376495, 303165334, 796289975, 954520765, 498748873, 862324350, 332408280, 860568570, 207316986, 929451339, 230212808, 372598683, 216771952, 200821338, 393613509, 493269646, 636905778, 934124638, 510587586, 220477781, 444587291, 871051525, 395096920, 979256175, 206725288, 770510089, 369085609, 714498509, 2650289, 862009189, 762057157, 757153233, 495104670, 914680447, 487882646, 800309270, 88291968, 35916177, 932844104, 484462763, 358311909, 571260433, 991906925, 970995100, 961948568, 703600202, 765079278, 871048366, 486448876, 218799603, 485594672, 489727328, 990482433, 450153566, 62336841, 548334986, 535390219, 953448374, 880084929, 342380600, 215108339, 922924027, 690432480, 785397233, 58400038, 799799262, 766129224, 411271650, 691985514, 381715138, 421535494, 690656902, 43556730, 72397941, 422101676, 308818772, 593765517, 225437881, 408677824, 634379960, 71267728, 710752715, 679182931, 859542561, 473579746, 122628141, 205257820, 871893168, 341356720, 265659050, 330762252, 135663849, 775303884, 234886289, 934709789, 360323689, 463500635, 911847219, 361601045, 703758281, 790377891, 907188577, 476260980, 662712616, 932983767, 206862301, 581400931, 1530848, 354117037, 142951889, 526760368, 688566135, 402495204, 524756342, 229753913, 20526514, 453345809, 927377229, 748980693, 551710740, 818360440, 123224710, 384209785, 405535651, 293336655, 851339202, 123770648, 176437030, 730557898, 765251582, 852596847, 509487100, 850278726, 561834648, 925358556, 921898392, 149315038, 152388192, 91051579, 200492799, 145051700, 540282940, 178567734, 18660538, 15081249, 264282102, 369480355, 988236843, 841418606, 680196565, 799832616, 716415137, 274774922, 609715968, 760813266, 296717810, 632608492, 748345617, 188215522, 449647077, 290531101, 440034753, 561488800, 765664028, 290706087, 548573700, 889786316, 729277620, 98160245, 662349459, 942761055, 349747141, 169882815, 408654261, 979120637, 629296501, 622388221, 206122533, 253261021, 234351731, 441783122, 300292782, 366568555, 177913477, 886275902, 453991962, 121236578, 918700279, 276782381, 332428745, 628325053, 36312585, 297996158, 658832188, 723564913, 94252361, 332785893, 97541263, 613285026, 459417240, 180312047, 437640160, 422184487, 277447196, 477815263, 677858641, 851621339, 22047706, 277068487, 111859841, 604580126, 199090146, 867183836, 827363000, 84839888, 69898493, 641417979, 74680499, 348566259, 563998473, 409997274, 878459211, 900467847, 745843328, 473458089, 780692735, 102787690, 758196351, 470988426, 609714186, 974450846, 877155461, 536988221, 493069451, 1453580, 725803442, 922316235, 497450853, 138675997, 228190108, 99727895, 540356270, 375125959, 300017294, 976538266, 442929743, 556082892, 253282766, 387931054, 643946660, 415818108, 848412050, 107254365, 567225790, 846774202, 732925650, 300507432, 952371218, 499201049, 94339492, 49848278, 603185444, 313437640, 30559294, 453110321, 742921878, 31489104, 950201985, 137893033, 240451850, 756081087, 384724585, 673202438, 350500625, 304681919, 805937342, 783496485, 132714877, 466293006, 514324490, 144168475, 125290896, 89688038, 230390897, 336705247, 882376959, 587224376, 182704799, 25600937, 411947224, 485103606, 209713885, 632155908, 713547836, 650768792, 768255514, 562032464, 827474202, 98610936, 980224527, 929502240, 735751804, 856184223, 729924400, 462604268, 540151663, 758716552, 30909858, 985367816, 2987637, 395069485, 960287989, 34553694, 207189124, 441352475, 352094595, 968808598, 604341095, 423605230, 416501038, 858724793, 277541499, 813185970, 310349687, 910464479, 756149781, 254759034, 810590379, 949199574, 579423805, 34439604, 158310592, 475594217, 756856051, 27068424, 857286840, 351494439, 837494901, 658123850, 247665784, 74747809, 12120699, 618357918, 120873751, 904081756, 762310140, 460148798, 873761784, 40239606, 915233925, 571568951, 287868859, 649923592, 642239833, 233488362, 987542477, 276798158, 327208642, 256876300, 589241301, 958321030, 422696199, 374530894, 499502144, 782656580, 787340392, 619502197, 547692574, 427486486, 576224208, 429555873, 763934982, 585400520, 678924670, 479413996, 879049613, 454771049, 140790072, 737705552, 584148829, 967177466, 601472796, 558031960, 738168052, 261767222, 179577027, 490535465, 343665522, 66784508, 322863888, 113870301, 261945046, 190332957, 397238167, 852904102, 864710597, 457979672, 246688793, 515286074, 113946652, 464819157, 853989284, 76543177, 854487075, 404117048, 9456958, 97489937, 674065828, 685605622, 863825650, 352193762, 112423389, 736341751, 512750552, 776362773, 226406391, 710452630, 148110918, 334290521, 155556186, 582077371, 797824765, 860144610, 29837664, 402664700, 273036857, 295384986, 869468647, 512169570, 662284334, 348321704, 449654337, 615117886, 204240368, 737639325, 596491747, 1778297, 992742473, 797486845, 812883625, 691275240, 682141035, 632459859, 515103343, 840336448, 388801056, 892168071, 375748831, 832195705, 103613062, 88858393, 178792449, 607131057, 493792001, 566061698, 380511692, 292057129, 740094751, 560042352, 600729404, 107361027, 162039487, 884954959, 937322002, 557776239, 195228465, 499935567, 904078535, 685638759, 451284205, 38748604, 439895534, 507543511, 547482878, 150048083, 466027281, 498317433, 922799669, 245384579, 566291956, 37524328, 394963685, 188508654, 329924214, 783539204, 157453523, 544458923, 789204005, 723898481, 907875341, 343386510, 488856696, 380990891, 40967873, 108288561, 487360658, 487416954, 468762448, 368887450, 662678627, 250780491, 201872907, 786225119, 497709873, 889214914, 26471067, 792380984, 276474160, 215765593, 854211157, 571138447, 948692049, 506930195, 487843274, 170162978, 992498549, 438094991, 774805651, 360452057, 264850711, 858726636, 184755653, 601227390, 316543592, 270517491, 844840088, 644682121, 325920183, 63510358, 40924721, 201362442, 31459972, 666759663, 223210660, 483033461, 261505021, 670416609, 830324356, 69423645, 228346258, 144130957, 200104378, 416255458, 646363604, 748423128, 17669405, 728389107, 849439564, 393658932, 480516522, 377409374, 657639274, 702087086, 963578502, 208999513, 285846993, 499188836, 52387832, 208494369, 297854244, 361550784, 417205855, 298959188, 564889591, 171678957, 110802026, 792798175, 196408775, 182731561, 50118507, 503717502, 409283158, 347159088, 157888270, 982234182, 599070611, 980643417, 621936584, 223208489, 120900403, 565917355, 824907606, 310317795, 129042116, 195587952, 843766468, 756033729, 53502021, 525774634, 308332485, 696973954, 43387247, 743203554, 929938531, 931865379, 894621642, 893770610, 209064646, 146165254, 220620903, 955471756, 525508420, 230197674, 757023859, 140903645, 17960882, 134063743, 527186633, 520177450, 633371752, 394826332, 541179346, 168209535, 835536448, 864549299, 786288235, 404359034, 547750144, 570726841, 561658198, 515267032, 283576921, 672079993, 270310838, 904935060, 174064572, 522453297, 917662814, 695756459, 890068744, 632736145, 28818790, 746411531, 643225342, 19868075, 922393993, 197499284, 907093854, 329021792, 568072148, 432064132, 803855327, 768778359, 744146217, 285337675, 233027064, 235738280, 475069789, 343478427, 974924421, 534925483, 915324187, 404342408, 341314805, 500200359, 664796294, 905539260, 569742784, 650660889, 90036679, 505088271, 767517951, 837870211, 755814771, 691459591, 992893690, 465614303, 584540661, 292306160, 753332558, 758362959, 544812045, 187788867, 129314254, 613506261, 645565046, 748914596, 201265364, 661891426, 713295144, 775925245, 649660227, 270391344, 244390627, 26976186, 439343844, 606581913, 402469269, 194838366, 919249683, 556605026, 275027970, 521387327, 154113796, 7518592, 799154260, 695010464, 833953489, 987125409, 516309641, 77816421, 402969097, 147648365, 564384998, 916198004, 39007486, 381773405, 771344213, 791517741, 48325217, 726881247, 326935544, 87490294, 767356783, 51267217, 888400644, 59440086, 537316087, 992701890, 419747229, 292433093, 785041135, 868286229, 721946957, 665780205, 612395877, 982017549, 533891983, 849314125, 660216005, 205093549, 886638823, 924572913, 460896448, 695965718, 235459061, 328941207, 498658085, 478555930, 987710596, 177888993, 274251616, 759341908, 249071773, 583373250, 232773697, 967908345, 732341387, 497682800, 196756014, 885713951, 990562171, 721624828, 663126666, 122206826, 680872716, 678360006, 656043287, 388658986, 80228346, 802900682, 460344226, 962554285, 251877979, 931072675, 13251703, 229684721, 74512179, 408805872, 846127565, 746019186, 209165243, 196798342, 717835359, 680641736, 325302443, 926427294, 917624519, 240975095, 283842769, 285320633, 923637933, 962848481, 659560206, 274073990, 109517719, 766749744, 159233601, 463262705, 582798612, 332420045, 604803617, 99815403, 309263379, 801913377, 921169745, 507390195, 49351412, 891225042, 186378212, 745450315, 480140981, 604118933, 128803565, 173284915, 623154511, 174667270, 979847380, 360891841, 596192209, 541294967, 984565838, 243153998, 167359901, 472940817, 380902959, 115184265, 7496250, 251733383, 475422600, 493781920, 677275565, 775165701, 429018484, 706707561, 19671681, 24290291, 154894358, 393574615, 862311012, 258913498, 213097972, 412383745, 109564119, 791048503, 967319935, 472246493, 92591341, 498032641, 291626644, 369703820, 23191010, 427282293, 878901713, 188197462, 534720785, 775084629, 408808555, 585389623, 424058376, 729256668, 939747888, 261893656, 166175916, 336340250, 33677084, 882089024, 916749486, 620274169, 571025477, 760787486, 134463346, 260256750, 83835954, 353865745, 17637081, 150483063, 788400380, 288719002, 642624149, 243211747, 438484909, 911248810, 839159093, 387978842, 468363311, 798904821, 331356215, 408720815, 279641762, 396443139, 857431043, 524394243, 728180439, 695092217, 6728802, 729487612, 426166941, 818825619, 412888165, 205173498, 585898257, 158019819, 360563875, 401948224, 397710340, 100424040, 372567835, 337850659, 873232988, 211659814, 492305617, 527630034, 965808631, 336755757, 347408089, 170894892, 852799138, 475314713, 981967321, 848441035, 285282213, 898104402, 372843879, 866080483, 457590082, 722541367, 758059609, 663955067, 913945600, 751915428, 611167691, 117334755, 572447225, 933799485, 354615711, 182142631, 787008926, 142999279, 146579397, 614888274, 609204299, 322921411, 967063211, 534347223, 735928840, 854807349, 860154263, 593424647, 683695312, 305100128, 118864210, 339919170, 225250473, 520580709, 264673700, 402524164, 495370576, 119625939, 202485996, 280585741, 503762094, 875142290, 527859735, 311624963, 105696547, 747399731, 408280049, 431730291, 721763019, 171228557, 842902514, 642404769, 776160920, 893777101, 156627530, 243291, 349373974, 765087966, 774094700, 84837670, 726730378, 355829599, 169415420, 374154930, 805871024, 117318386, 465491036, 893448035, 342798795, 414142348, 252316068, 807265194, 815746496, 559406342, 478331686, 355944935, 166109699, 94744777, 903169835, 309464204, 367036110, 297449012, 113693814, 356161515, 150977603, 919299167, 139731632, 877255824, 497394566, 894601891, 180987131, 981886527, 605378692, 726995629, 737452495, 741994473, 219093102, 937316920, 616216209, 637575205, 222375085, 71921485, 802821842, 6935555, 621553245, 723256757, 191100975, 69800952, 31074772, 599198173, 141417353, 659474974, 263631939, 95607180, 10142881, 262761912, 765704743, 654631066, 122104034, 19724920, 437243160, 969207631, 7146199, 792984391, 37047653, 976980701, 550668751, 720156838, 745601903, 696348992, 313593250, 620244008, 320677745, 231391621, 590232360, 242874008, 678391481, 984601259, 361273373, 896060180, 946110504, 933750206, 908039357, 85014791, 241404147, 300985406, 158562082, 750397585, 195300358, 786077332, 368575103, 235079973, 643280990, 874330097, 838104001, 254104695, 472813792, 442046958, 901817507, 99987886, 691661010, 34846040, 634192313, 633256910, 341435033, 958121013, 808232179, 193807605, 702974730, 276330736, 496523737, 584451646, 361652597, 619197334, 167768962, 927063635, 784901840, 769906717, 363793795, 106302296, 276573604, 566494384, 134990942, 66753992, 41954520, 111369038, 997305486, 27448214, 254759449, 563931816, 575471912, 554623427, 753459153, 887582767, 719438466, 440940345, 186941394, 773592840, 905741581, 631594963, 664173991, 270503686, 340091128, 406701708, 564604679, 450490144, 114379061, 692289455, 520417602, 764783344, 655864683, 458747326, 991475650, 81985194, 964947830, 79535981, 52222489, 431547248, 575108764, 494455715, 580839031, 836846223, 247111433, 839639098, 155280010, 987577551, 357763881, 803316135, 677175043, 534061741, 110555568, 402225595, 101245545, 584903374, 359481630, 436801208, 841677764, 774625396, 353949202, 622432092, 862244028, 516533709, 956641035, 262156521, 993641842, 894887591, 494988406, 435308180, 502212487, 126184386, 680207901, 950664804, 365343632, 179217307, 120170478, 468602970, 119806436, 893119739, 937981712, 410669539, 503890205, 556513152, 772495378, 861904860, 312039747, 147818511, 348518600, 350928667, 821803495, 331540952, 322036758, 921683957, 252572236, 928944123, 842500201, 390453284, 793668457, 500184602, 9159102, 753614702, 155303542, 397739146, 663061359, 630250507, 154844524, 665978369, 415364063, 361103696, 686308792, 992169347, 641021828, 200573798, 128881871, 904151778, 110308868, 365017733, 507713337, 204336521, 288721272, 228366890, 485287135, 573434176, 633447792, 396553272, 366954688, 869603753, 569891912, 891119050, 356937369, 582049329, 955289468, 350500745, 963548576, 408978740, 147135909, 185386174, 567433724, 47076786, 285927185, 335279470, 637760856, 49152532, 145826676, 376582132, 21623559, 689378117, 476563805, 892123458, 996305259, 330418329, 11110467, 568605523, 979703399, 352663274, 911370165, 250801747, 637964410, 117867343, 673985295, 929958206, 376792683, 878192255, 928022992, 850372418, 526394119, 197011774, 786804199, 963649209, 261397347, 482492826, 752331645, 220340807, 165346486, 337104740, 919836091, 957840940, 321730959, 427914886, 933788775, 568069431, 716498802, 247213543, 640914069, 938107795, 305818259, 42659700, 46834563, 103810680, 238358164, 151068718, 486963496, 76651562, 771294677, 312071605, 562221750, 227882320, 796145732, 323786331, 263145416, 506017227, 962610919, 601824209, 323570436, 822643480, 931127127, 211184262, 420117361, 954449931, 619369427, 624727355, 790801172, 125399136, 479488557, 695648444, 206954400, 120238918, 186105244, 674965280, 598226841, 62839372, 366321901, 809403099, 151788028, 29828382, 824258489, 523918561, 565076286, 830930592, 233248570, 565495665, 306171271, 996475249, 256039483, 70600319, 420934999, 981670081, 8561225, 940251235, 204130644, 712809900, 888411709, 904047918, 183383453, 713465431, 133428936, 576879755, 562042927, 356821453, 22903182, 656948581, 45649600, 450958842, 913354713, 737623591, 456356020, 245530062, 29704831, 143505532, 998807255, 408151007, 669389686, 804285410, 415832335, 623157164, 880688919, 776754266, 521076192, 188776510, 611939070, 959487935, 608760182, 712441131, 560490454, 915766307, 830377031, 296963387, 2036989, 661213946, 339983886, 52400994, 74768106, 413028868, 271803580, 828320361, 757694521, 708182170, 158705170, 881909040, 427996893, 195763849, 179602305, 573240358, 349230970, 903789826, 588479259, 933799892, 484457149, 526356564, 897505385, 896568592, 829017898, 986228821, 994145242, 729753512, 207567606, 795150900, 697401979, 310205794, 518157387, 716640940, 702054192, 671516236, 835593866, 132381371, 922394143, 854321138, 26641278, 288345548, 569562661, 893374739, 922607743, 560760422, 68922219, 593491543, 154656349, 107813530, 523257106, 489856049, 171030973, 502054854, 306364414, 990117867, 756757248, 530862397, 686477562, 124588275, 471703247, 901747005, 59761733, 529362380, 587252688, 433785550, 739420563, 980421667, 317777187, 188995250, 296011612, 48010352, 794090563, 148248120, 850233010, 411810006, 463622610, 872368977, 403167054, 897446352, 167143701, 56116635, 894842726, 178700708, 789743111, 740621723, 31207345, 771566845, 159251234, 496034505, 831346329, 413623623, 114963052, 465233827, 148321755, 889416968, 358079469, 351954485, 827373390, 780336948, 552298162, 655108231, 974548979, 945778847, 563473607, 700847989, 507783183, 96528717, 535239795, 284031564, 702200285, 528635268, 59587954, 414261700, 881936920, 500511905, 125619221, 14452663, 122964142, 114968247, 270172815, 310370963, 229891866, 262071725, 637728823, 467250928, 382605208, 737557033, 684354820, 792326008, 654361563, 111090385, 439900336, 136006355, 800655151, 588884485, 243071811, 615019534, 208566806, 248717088, 118429648, 930859354, 321678701, 760322841, 907060451, 967500506, 319624540, 363529680, 91235816, 970634202, 430960463, 609416487, 643871339, 318696298, 888867896, 867763669, 148144905, 470112059, 712856948, 201064634, 438946802, 103123157, 469150263, 906209462, 946344563, 535191639, 443106913, 56152086, 346903884, 644151673, 875445357, 661009490, 989092979, 619169424, 949334297, 810873048, 170858833, 59653529, 359650450, 640326280, 428946327, 770837982, 634442379, 293655548, 551950508, 551648803, 834062451, 151173558, 333200299, 348647914, 984703426, 333596333, 858211804, 561851164, 806237886, 167165427, 837403292, 749805515, 628572576, 494655843, 366959825, 839488381, 840260167, 494138259, 297808612, 893194248, 124286964, 363891002, 809064066, 517963391, 885664494, 59160324, 754118117, 416839325, 195756071, 821439470, 548554567, 939357145, 552504900, 82440261, 258395798, 935624023, 71190970, 280790479, 555978146, 470172162, 34520064, 204587056, 778064587, 952790414, 561047196, 630210732, 619668130, 125507602, 80397813, 395822791, 383864227, 23378705, 51794298, 67750768, 850126393, 201855331, 697559359, 172025993, 905580798, 473186795, 183465560, 505883149, 684169657, 118418271, 230156695, 894857395, 163837297, 531074578, 559061344, 304165242, 490747400, 66485587, 596752912, 133742425, 965548111, 578236796, 903165249, 752435594, 130083264, 499875124, 123909349, 344388744, 599605843, 696168228, 614382534, 901908089, 633817464, 211154931, 147000631, 553776424, 324790148, 279178657, 839830495, 879237830, 304257069, 186748741, 210730427, 190599768, 748808881, 871865927, 717969038, 535978059, 358949544, 960218507, 855646915, 491743483, 487507393, 652488398, 832856949, 313311144, 587496292, 446265885, 688011135, 397385061, 106292696, 257239453, 579551372, 192128097, 220333209, 551825050, 130065547, 910741650, 129708968, 930890062, 757505171, 570922336, 172646426, 90858516, 990871622, 896098402, 805956707, 561337442, 339258466, 296588263, 682806413, 92324789, 774074227, 771763939, 625686167, 71789638, 798437213, 661455702, 603251630, 396815831, 452001521, 238577919, 453985900, 796153636, 906783031, 416360878, 942672055, 560502, 542954707, 482438181, 773470733, 741300610, 111450385, 812338903, 5487072, 779763712, 521666564, 12280389, 346882826, 703890662, 892551954, 485841806, 276850210, 338192111, 488328367, 168421843, 822948536, 729613428, 829563924, 459246234, 852975497, 566627607, 683708010, 181914040, 648963640, 373569200, 907619696, 959603391, 419968966, 532729869, 160865597, 498869816, 782302473, 587594814, 621310086, 297648197, 754826319, 345640377, 310014593, 627062299, 392186480, 943095832, 730178786, 895061623, 176584029, 325739235, 961636966, 987156653, 627432169, 106241720, 824381779, 322826000, 663212520, 191382508, 143179546, 354511491, 369913190, 498519639, 30149272, 65581840, 106236163, 546362796, 603742125, 202643957, 619040047, 771967871, 586954909, 947750245, 496980132, 447018734, 888802386, 177719059, 131630658, 339479359, 683315818, 593020947, 941283312, 194650087, 450157803, 154708017, 906223515, 633820410, 192202036, 158587839, 154610461, 726123810, 996168889, 483547130, 816615442, 355898710, 739000257, 393403002, 846198142, 654849791, 569102334, 937744526, 134765335, 18424328, 304817560, 251288947, 782041247, 429850178, 167653120, 373258807, 394422831, 736336049, 152983309, 571350204, 657407158, 992098086, 12961438, 908351643, 585811993, 679309305, 97255213, 204583774, 745869995, 506245299, 836960154, 555487591, 525265569, 486488756, 874064076, 460638694, 921352767, 806276623, 542884078, 189257429, 435177937, 225378817, 159190793, 539668114, 350660349, 48184874, 520591561, 613816561, 212351651, 509826047, 39636903, 884562169, 928474127, 441262243, 120548227, 862948313, 65028574, 169000667, 908836391, 507003960, 471285150, 143645322, 609493250, 135653081, 428437601, 684333942, 665367285, 921383746, 590323843, 776251016, 785630492, 815870714, 11467123, 352592544, 312263732, 285234175, 343326782, 348324488, 513995807, 508040357, 777113542, 951091777, 517402870, 637644471, 944922382, 413779289, 247968200, 458193942, 760291416, 354911155, 19070025, 245822249, 513088595, 649922224, 878634675, 209305763, 966250415, 840414919, 707248297, 399076743, 564099686, 854333093, 919756608, 634353213, 824078852, 849535750, 401876186, 673102838, 816261620, 959518090, 432870981, 455332540, 184490139, 629449375, 852594520, 316752706, 738688699, 553092442, 349366188, 631637879, 94590781, 830208458, 558025688, 455505955, 528470567, 430963901, 229802822, 244182196, 439885777, 737779146, 671349703, 107983419, 652183127, 737391546, 416694914, 46428632, 744839277, 788310232, 595752023, 158233343, 108187196, 552511378, 186119698, 659260408, 501758311, 499199030, 393224126, 670518502, 397048807, 234387995, 398680132, 611846997, 78383793, 659182628, 21093709, 300367961, 722045384, 791814408, 488517144, 890917224, 68187061, 438907607, 89337043, 352103997, 549214371, 884269453, 901155286, 927539970, 690032329, 253374797, 832515741, 515976604, 163779925, 201216582, 389580342, 541121509, 410349594, 531048127, 334350789, 720258708, 792356343, 739896567, 618357999, 352294268, 503518160, 821392572, 287431166, 639545430, 823168314, 307026971, 966037919, 985764237, 663108584, 553757560, 4341109, 654407770, 954935272, 779844989, 415830439, 768315642, 897167108, 643785475, 701552621, 452427360, 136436555, 673997088, 5673621, 507147925, 887886829, 263805579, 908867825, 117907310, 912217052, 153272806, 533464688, 418640017, 47692837, 673952602, 828197198, 512166334, 917227558, 438662946, 922889933, 630006721, 351249583, 25620101, 530276902, 917186543, 315126802, 126514347, 113814093, 953302838, 702023834, 276009714, 999850003, 84936663, 980757889, 118496758, 96832531, 35006274, 98031213, 645877692, 274448458, 249276093, 901360431, 999811172, 416265247, 324407250, 642950723, 779514959, 109209382, 956064847, 890077781, 835471026, 552521145, 608006448, 708261921, 620556702, 799844316, 358486079, 156421274, 30417672, 607035688, 265397862, 102458493, 269667822, 557036394, 541557777, 244576739, 475796991, 569363308, 889695654, 867259509, 84250926, 93710115, 869415849, 894241356, 655955794, 472635026, 997531599, 122565270, 18211049, 520911932, 905844007, 751629009, 940338956, 394678858, 191786217, 891650592, 561719551, 246766857, 400880546, 19054753, 657343654, 223812333, 5327902, 980713553, 780899248, 416005863, 767432963, 195441645, 156857569, 110345834, 254638977, 299710109, 718578167, 462314951, 90950307, 705040222, 718547439, 675497988, 793203853, 58165013, 135082490, 860633973, 675021861, 740961612, 244504750, 692729671, 468810569, 10109869, 842043443, 208593884, 545852697, 989034248, 315788225, 773137277, 214306982, 43924390, 270620929, 676584667, 886907645, 753864983, 522166492, 506755685, 784738470, 741146812, 509200737, 328194388, 88330115, 292803896, 794412343, 422253090, 497676400, 609502806, 506957503, 307162290, 338393498, 238955057, 464897857, 9694983, 965916061, 196739682, 89313150, 3004774, 239826176, 737832581, 467400795, 899358846, 175774063, 357574465, 308026850, 735716002, 903304201, 756325246, 712610092, 753421336, 572457816, 407334489, 513276442, 591742398, 65595398, 775233155, 277614544, 915039191, 423511113, 332840832, 246296063, 447620496, 94940561, 995227741, 496127760, 436546702, 261708418, 796785121, 776619704, 385831504, 237024445, 379006253, 615113148, 928527371, 137709036, 507646028, 866111104, 809146548, 287901617, 215293975, 778568726, 509014195, 670853524, 112504188, 408585370, 671621569, 333434837, 477713799, 454529581, 5370662, 116442963, 721220380, 591491209, 924975630, 133659786, 510852096, 166115606, 648294180, 554479298, 466658177, 769317744, 641486082, 135091669, 496606687, 253936845, 209103798, 368281422, 299719982, 492184935, 694811018, 765015080, 971255649, 166119812, 466964229, 961273385, 20871786, 411511297, 552979442, 142939488, 905178983, 848617703, 452660138, 431610392, 877581622, 400937345, 239131087, 761645203, 206895154, 567547753, 967073586, 388435628, 354141383, 216956207, 762850121, 986681408, 230323688, 796452571, 634270763, 688156504, 96756363, 729054437, 190678546, 632022567, 105108485, 473617091, 68715423, 991648071, 631205371, 737509449, 641874860, 568267702, 916151757, 578700538, 848478409, 38787185, 724873244, 511872723, 863872680, 945395930, 83787482, 526760120, 247728070, 632193527, 822121371, 375492926, 940763459, 306466361, 768653638, 422711968, 45470795, 578942469, 354096470, 258505563, 27777715, 197001921, 533814782, 398435349, 183938499, 879391393, 940201110, 557143784, 883292710, 973351512, 985184330, 975263815, 166613410, 801898611, 301157163, 646554907, 820764831, 268915697, 204757494, 999404135, 38573352, 376841334, 634703713, 407423456, 450646831, 315309115, 802168357, 155103734, 280227435, 916413715, 308180292, 54497083, 550978914, 940932120, 579322972, 412803393, 774269326, 618765908, 185336042, 595824003, 52256028, 61811449, 488024852, 460020474, 159743991, 319988881, 191001741, 124442620, 180311571, 341723764, 342368399, 84083583, 960114977, 483375440, 528859630, 713035442, 247954439, 889409403, 798369251, 874593304, 969607915, 873620638, 435904635, 96887427, 307035768, 876756406, 264823780, 820821967, 316659616, 268152011, 264436824, 828499712, 689920431, 648245366, 432276367, 384883299, 95891726, 123185057, 134964946, 479664032, 837568046, 156487816, 140505009, 489429671, 358604094, 322048270, 633341553, 890748396, 490526790, 207662437, 542484635, 236881541, 791098454, 440470978, 809597047, 119227929, 438040740, 918264969, 478505930, 153444458, 846128046, 570264549, 12757834, 93213380, 239466018, 901428185, 478247049, 767773274, 779997665, 663161874, 771471076, 131889902, 224700295, 69119347, 778928446, 290242546, 220900143, 482641315, 392016875, 763616911, 307446367, 445792133, 513363104, 617136989, 317775920, 94108073, 459462138, 424824665, 671587024, 885870674, 5592035, 73326943, 477918191, 376921053, 825545330, 938804136, 169523479, 729047496, 401138333, 653464787, 613254213, 171141043, 119499439, 763029052, 128953891, 378321681, 353089455, 926769273, 892390362, 384029967, 588075542, 291319894, 450482607, 507045341, 416652315, 14235798, 927248119, 964387930, 341778092, 4904033, 477206654, 109448714, 835864949, 666848687, 396743099, 701337638, 686843627, 584688755, 349479095, 714769792, 177900476, 485779600, 631953196, 171923259, 958361803, 512631027, 150462729, 892102100, 28933801, 863566214, 951235275, 965690567, 895773752, 783028928, 340202823, 913990755, 409521785, 172941467, 385400663, 110651598, 280524662, 122608601, 786544557, 962861710, 28718474, 671267307, 582408860, 777627451, 815655, 410762244, 936167693, 21293175, 57274010, 824173919, 764743855, 107178466, 876948704, 700565135, 781505695, 160910171, 630174148, 947622828, 507614358, 705702577, 127249627, 166417060, 608983170, 338602556, 315245071, 539682467, 59545020, 423306346, 970391448, 188865159, 850461178, 497493975, 713392801, 455568205, 442393343, 964623111, 420466744, 270684487, 229662437, 627542146, 449569012, 700616169, 784079762, 784476723, 549122327, 875263267, 632893451, 717304143, 823918420, 897147431, 869837697, 598343087, 719174759, 261978601, 586407675, 687071631, 409504491, 440626393, 168886132, 698812644, 887132519, 635195208, 634119601, 835153244, 652729070, 593048275, 436878393, 889655075, 833193455, 634255664, 983289239, 556158646, 653060944, 511327498, 198467895, 791712181, 662274973, 160275673, 784671161, 145517634, 857802443, 532841373, 695973673, 860631939, 320610875, 913535410, 594354554, 453333644, 745933056, 940736039, 109686413, 678024881, 889495964, 366855229, 705219429, 595221998, 641103846, 223543494, 526865776, 533506606, 454031750, 54499518, 677290520, 824430367, 221693726, 465248439, 172739941, 469658795, 68130181, 313005342, 442091731, 359210851, 299621555, 356307830, 22295235, 666305576, 622266923, 344337827, 165658509, 652037495, 501550314, 934592887, 798490895, 872132761, 747609964, 238639496, 840817221, 783231998, 877167674, 544220997, 243625454, 729401512, 478359033, 756615423, 391641029, 856482511, 227861057, 748565064, 852915328, 506612224, 834752900, 763838429, 338202842, 814912124, 591892372, 128661681, 934094994, 756575064, 453721288, 88422906, 635602321, 338334357, 239223545, 337092972, 476671606, 341428223, 137413326, 139131672, 892905220, 629364019, 849091202, 236790266, 329505574, 444460767, 20568624, 882248642, 2571008, 508417123, 531777958, 98515365, 899558091, 366851045, 375500438, 823336369, 185072236, 716367241, 879425602, 843030322, 829922287, 570456585, 549910778, 936616715, 339764094, 802778611, 479994705, 258167503, 211609914, 354193638, 361373432, 208127450, 669147958, 826210833, 705612307, 736094989, 832675084, 251454220, 141879804, 317138609, 107638312, 478012147, 272168494, 767578279, 221529469, 781754373, 105813015, 130798478, 410968860, 80185502, 625617539, 601848511, 355838495, 832857246, 911703546, 133411427, 469568635, 560925770, 900330414, 351548369, 3521477, 566349368, 648214794, 105609513, 138052287, 527544571, 458921545, 899347973, 669011974, 213036557, 337997768, 651554644, 582237327, 369908357, 288392361, 931443119, 395666848, 634908216, 297400652, 53749325, 985362747, 849770548, 943471335, 577124761, 741133499, 411393452, 439144223, 411107905, 675931188, 319514963, 979596665, 133022527, 828349289, 730068827, 440525399, 199516636, 286611426, 95976589, 571025998, 756915492, 197932383, 875148110, 222987792, 831159435, 348355885, 460891660, 206218143, 402871479, 83813266, 752561462, 709600121, 591353859, 935833269, 571499364, 344470817, 161531517, 157660765, 574147021, 722194645, 474544377, 586479999, 436254832, 963581782, 83386059, 364675001, 924879790, 892140219, 734061755, 63714833, 640144659, 561489995, 538224973, 98611417, 980310766, 83939986, 600038470, 637359607, 847434528, 797840770, 435045202, 352724430, 461737152, 225529477, 658663412, 525174222, 232830628, 239013097, 389208690, 862778801, 699304414, 974103199, 850857442, 102390193, 350817921, 19769815, 831552803, 300288574, 173333411, 329164610, 900841820, 799731376, 72906687, 281409880, 210822534, 773384747, 568208095, 98368083, 311027377, 772054171, 111607737, 998775245, 877965950, 290733275, 232324037, 511912666, 251004446, 944057988, 451918023, 823202324, 299577984, 614092414, 260429315, 182788002, 504076169, 487777101, 139161669, 28978957, 275264637, 225898355, 872101988, 716323700, 373421581, 253965309, 492186536, 266040325, 520337995, 770388705, 568140945, 647065312, 476512940, 700480455, 801498179, 802126142, 373571515, 309139971, 202957657, 793611974, 668845100, 524851603, 525580314, 795396431, 331495802, 947593319, 278941415, 46460631, 399495589, 869969661, 663459661, 660089309, 220427491, 76170475, 710923557, 883978192, 39378973, 791513838, 501692383, 665566328, 314670657, 873162949, 787055985, 989856616, 461642927, 756218097, 673134320, 550646990, 167978831, 50225130, 297968503, 261024236, 901966420, 735535302, 480005979, 454662903, 12284259, 332989719, 416696146, 515271406, 563878313, 632374245, 161487509, 839853148, 463756670, 640148867, 966165957, 983734178, 110418001, 929665664, 979457566, 756656205, 890679259, 166761221, 284327074, 548143379, 376951296, 423301823, 377083143, 394729917, 800172293, 150773581, 682562039, 426895370, 112219566, 762148519, 373765500, 620985558, 932118422, 803436498, 668130678, 532541389, 212465492, 435215084, 158206717, 41537335, 503965950, 458891305, 469296292, 991983343, 495971328, 233501683, 350615076, 505237700, 324847168, 326165811, 366364368, 240129627, 432376761, 388043699, 152534796, 643603723, 350136296, 967140723, 841749929, 768184502, 616739699, 570309872, 644191368, 404157378, 659097853, 776551810, 761009548, 881778884, 182658010, 699473127, 287736986, 529659709, 150145514, 987664547, 574303751, 742069178, 374237709, 500672267, 124880668, 3895767, 906774767, 866389653, 138466184, 205044671, 405986188, 381495968, 839167681, 79512218, 774735974, 852403513, 288563692, 132985625, 610694726, 142589782, 719163698, 647984266, 245202702, 394953902, 685589902, 370855310, 868642456, 365302141, 763344079, 995595732, 427368759, 55261273, 107112901, 288958615, 793074691, 324769595, 605602454, 518650577, 283481077, 425786462, 163353996, 889668473, 680023596, 820601010, 902353307, 234537997, 527015514, 374605913, 909696535, 784238847, 731923122, 248043141, 677813857, 535241674, 89867068, 470820513, 660983971, 402715209, 29077263, 507950105, 726730471, 214534764, 319835341, 477215941, 141035693, 271594671, 914200369, 48468211, 906995098, 801984257, 213884299, 976741911, 46407092, 644929628, 549347332, 410239912, 257511055, 417214772, 276780936, 567133738, 528754063, 834563967, 782074958, 910072082, 990358342, 830481457, 179270087, 359905609, 367251770, 56166012, 606347880, 559912710, 813222551, 44867473, 501168792, 766627230, 831638985, 166917183, 422896387, 235070050, 896975975, 869158698, 815216959, 438560061, 130190749, 215614604, 4124245, 210343113, 366385810, 500362783, 546193836, 43215051, 354975937, 726436418, 464437300, 659492013, 629558502, 173981846, 293171207, 638219006, 758724823, 23707600, 92011142, 542868481, 785832991, 45514816, 993115166, 284210122, 749322879, 386815938, 173410293, 264051670, 613763945, 696895445, 15086443, 64848866, 379968600, 197006680, 575664811, 328013895, 629264989, 538227647, 335517499, 361906969, 39427217, 283825337, 280275181, 952971143, 933337508, 706756096, 324166706, 271803859, 12504750, 19974332, 515570230, 250913556, 815366834, 901619452, 733106703, 568882338, 899483463, 390877069, 459953931, 85464906, 40505771, 624637120, 600674771, 626360229, 703887121, 419568224, 887163591, 601770453, 362619547, 826548447, 902137712, 132411985, 392301499, 22693515, 900769122, 904717469, 258760463, 693419132, 813690628, 393283760, 980872786, 769697529, 7937261, 343331663, 922598235, 959059855, 1919403, 905020291, 19537029, 447824694, 83576387, 210872580, 663973659, 97492767, 725318255, 761211030, 633397170, 673517225, 722515686, 396391501, 884040212, 483029354, 698317665, 681204005, 595415319, 698137425, 177041382, 385436595, 280657591, 786395036, 2316314, 555354425, 792487712, 522138828, 916373268, 978168103, 387366474, 606067889, 346962517, 288455207, 434297148, 186368362, 197930681, 978842432, 667898252, 425053863, 998275141, 935434408, 679017407, 526532744, 730682128, 588310224, 943028887, 726943702, 252340066, 950311849, 278960048, 182604689, 294114584, 149733440, 817520121, 646833490, 892135119, 69643032, 56898201, 40576712, 669412734, 397277190, 369002984, 250542402, 790687183, 264087273, 763015285, 619169001, 102928930, 996378917, 597315401, 775457810, 754194205, 692156911, 47229571, 584486795, 773461985, 473015636, 936723381, 770321978, 540594278, 855737579, 273731821, 19532456, 892209266, 930374199, 909484189, 226589693, 383606382, 437484438, 843353235, 180493494, 31074068, 987150103, 109152981, 239057981, 598176220, 578931775, 234123307, 694403138, 306927010, 86457531, 378027192, 678583736, 5740535, 462964852, 348471064, 863947755, 848364515, 781597259, 831935021, 970199383, 635344115, 407028321, 353130830, 90394691, 396530676, 816815406, 225421591, 495857643, 425141262, 844777245, 883132238, 165644105, 721002174, 523519010, 613006877, 791405040, 435038744, 430961716, 122223148, 773057392, 256979920, 562282275, 584839368, 222147190, 462961335, 445282659, 889525558, 708163082, 469537945, 891079184, 676983051, 256831379, 789475076, 152130578, 390325827, 798509711, 913740661, 811225104, 796351248, 477115385, 492105962, 684710404, 863057899, 489858720, 261062014, 16651325, 650920130, 394698582, 583075511, 131654334, 258869183, 465821411, 23269182, 763520875, 609521671, 939510917, 289960770, 45407208, 404623837, 971876729, 462397213, 619086302, 137987189, 902988465, 525576516, 170111880, 341656179, 905167467, 296019775, 430806458, 124363613, 978768218, 296389170, 627958005, 655964770, 625535984, 57425965, 93792867, 338947882, 114878362, 5171519, 242232656, 961163740, 260187243, 719149499, 221099926, 18403705, 269041831, 656151748, 229891540, 732777824, 964511683, 637028398, 878686546, 944145878, 402865511, 228019652, 169845547, 902352984, 958848549, 136748122, 959990382, 858140713, 294707128, 808418969, 334308342, 619928447, 328306850, 206451800, 435844773, 199025214, 541064359, 608019246, 925333268, 935604288, 500138604, 178924976, 368030885, 10904453, 367798779, 833833859, 372789296, 578207504, 112243667, 957684036, 513861505, 490140794, 762123701, 580727665, 983475088, 203846221, 226295203, 857727811, 820680867, 937536681, 433470260, 133424480, 563296038, 883486664, 431336871, 698542386, 685988732, 315469180, 957608564, 785674739, 445441879, 493439907, 635363348, 185686736, 720903134, 858079057, 96434374, 152021295, 126247417, 32651113, 93927807, 628227467, 175462847, 243278476, 387388337, 648499160, 141984621, 111421223, 588802843, 390372525, 871820060, 346368767, 318827524, 655329735, 2195018, 587284148, 846630632, 153270631, 588787264, 985076680, 795219954, 142664243, 414751783, 248276241, 756905909, 928698281, 72399084, 194373370, 264953813, 416751469, 61085048, 890921461, 57132686, 711153362, 796513629, 677622795, 883069101, 672622034, 954107116, 99760828, 300793912, 289468788, 552532652, 562657521, 974619910, 774845487, 157253812, 647097364, 969379611, 311838174, 313707515, 120493140, 78926016, 635465380, 696466420, 90732205, 8698593, 630052446, 298132652, 866913630, 366665770, 253077527, 594963777, 33381794, 635610504, 912902194, 187790098, 13181142, 541206956, 271446571, 255186211, 377768255, 167632508, 960823115, 566820915, 947274340, 533524180, 400013185, 828498796, 844880261, 503856382, 811938466, 40471060, 441452474, 280082831, 289343636, 400023726, 347292226, 500152893, 72150792, 615694946, 942066479, 211687170, 377510665, 289756261, 767304154, 553143144, 100544804, 908776349, 470657665, 127555862, 969747043, 10811584, 558683526, 391023227, 475245702, 334884370, 325001973, 577926949, 140909008, 827958606, 380865224, 517730849, 709616434, 177758485, 503019056, 124227149, 478856898, 227518239, 705353873, 525439791, 411567454, 151569478, 795451578, 519095346, 904421715, 953643655, 308959187, 965124903, 688599845, 731157625, 464700355, 932882395, 51431780, 67243725, 976739293, 552289707, 483784608, 423638223, 997563486, 696477750, 286648187, 854978098, 426837814, 827615551, 765239623, 842543176, 796591735, 838475420, 663292186, 610359737, 92664276, 31702427, 805248607, 155698316, 510229788, 549029033, 331713383, 306752838, 383545415, 302191626, 657284313, 280973126, 798862721, 308014264, 546031856, 517670544, 835865675, 701829425, 322029157, 81065154, 316495571, 54696325, 571191728, 5335867, 774691108, 40169435, 422519406, 60176515, 137394853, 789526718, 178305649, 56978192, 276222714, 427710483, 785407383, 418437007, 349364699, 835961586, 758701695, 771421772, 171920640, 399299845, 732219075, 42585112, 533779177, 783914356, 683015857, 316681019, 586329111, 715464328, 427082179, 11190868, 95455382, 612905135, 874129629, 526335048, 320810998, 351780057, 635206482, 146182981, 429273595, 895552847, 945921268, 677471298, 850503457, 88447012, 929712058, 302782058, 123955111, 732722521, 544950426, 226810990, 580817476, 684829679, 749592241, 542967851, 276411972, 898650506, 793161611, 807966269, 768820571, 284075625, 695522401, 956821185, 800125006, 75055031, 962932811, 26257358, 80251680, 769088021, 382052572, 678934760, 67420375, 874657805, 624688366, 605732326, 262265134, 925645698, 236270829, 110507421, 157839926, 59592681, 155890635, 188670235, 905843758, 754823048, 495026555, 176336234, 406142975, 645092306, 508933605, 242592364, 461092820, 825810846, 303658056, 960080476, 617869252, 482335596, 773025193, 466273659, 320307531, 95279953, 189056370, 501860144, 342617327, 306819175, 910836658, 169119665, 89516117, 895225223, 12007320, 358430892, 586190485, 34417219, 638866076, 591577651, 689244006, 26783403, 289046137, 825841765, 629605311, 887561206, 801058514, 764608296, 29599168, 22793186, 76735196, 79630950, 916635170, 263769362, 414568114, 464321917, 555397290, 820506634, 599208628, 96125595, 837792557, 707460949, 145540672, 352971819, 301603880, 522763502, 630935117, 927920989, 358939256, 464416006, 12854451, 838932152, 508239258, 148550208, 787821103, 493639467, 637763841, 398216541, 38732460, 494347236, 693723097, 77670697, 829696252, 226394751, 398827822, 620096317, 702277404, 377061960, 998901179, 311781290, 926688238, 761938581, 168791757, 766104021, 853691588, 773220657, 80636913, 997136156, 131316170, 837945065, 777454145, 955250471, 206075619, 979603247, 602643111, 500562628, 8136657, 362669890, 221957051, 492119150, 306144364, 30209899, 372451582, 856509579, 981398285, 11873727, 129049984, 974545956, 767929296, 475089603, 971886003, 511926360, 666866138, 855353642, 329926176, 219767328, 828070180, 422730265, 538056525, 711541834, 755512747, 979061006, 181046924, 322900187, 631351012, 600859123, 922706132, 798202824, 995404606, 310006911, 113307031, 974826372, 399919881, 20313367, 33632615, 741326540, 59387850, 432455066, 288671896, 97294062, 952708180, 206269297, 154657796, 231798498, 983950362, 416289491, 902831039, 615891540, 736329339, 276311493, 582300027, 724483915, 481157662, 158852983, 865733829, 28735187, 401607252, 940300393, 787883183, 835677038, 228773236, 634745171, 269668947, 780369317, 870560943, 419074246, 71220731, 768525566, 891335333, 214352838, 276461321, 691279459, 616134541, 504765210, 465319606, 381452371, 820450842, 643125613, 440816707, 373300518, 564389399, 218661447, 837758997, 222185815, 148685957, 335676136, 418487888, 709396918, 673791031, 469040997, 393649286, 832903243, 258130257, 973015684, 13234322, 811236120, 938049459, 945373125, 979729847, 762266503, 996917742, 964824262, 903329751, 529617363, 747599218, 990823627, 798390823, 353805927, 606445627, 584897498, 387001101, 902911576, 851679362, 948614433, 698723252, 242731621, 378798416, 182066888, 371213400, 999429233, 810646541, 687345911, 358541628, 787914706, 727608893, 475076882, 522033594, 13058470, 699360716, 865049020, 561198955, 648696344, 693576436, 799233467, 912461047, 709722394, 639739299, 856911528, 923166831, 615281606, 845987592, 740301524, 447244682, 309807842, 260895942, 777323689, 411645852, 105481718, 492880528, 56828371, 984487423, 939469865, 109854138, 462641880, 302569297, 753631886, 357492955, 791134853, 974253624, 919872955, 390245348, 833402767, 607915465, 419993766, 869859578, 255888493, 645972826, 614822923, 861496743, 453939774, 652327063, 636692058, 26961949, 393348929, 577208754, 570384349, 915464008, 555603908, 688080143, 739867290, 278667745, 852496861, 340240289, 274799760, 834123553, 676872267, 873358572, 747351498, 542857304, 877843704, 646459977, 316765278, 13930173, 634453191, 776784081, 515900594, 513100554, 391542313, 277921695, 830225473, 785380638, 271857327, 70542421, 842102462, 532670509, 818649580, 751543355, 121119619, 161668041, 67271312, 11587448, 746697016, 5815704, 921711072, 455808595, 611623731, 75143801, 747708738, 359458004, 289588999, 300164818, 7218314, 576126946, 355454873, 134085123, 568227460, 266095195, 895382647, 759100076, 186887897, 503804915, 698444275, 1303338, 452137144, 946822488, 956402565, 888320654, 971272546, 463405661, 985436841, 316483605, 483563761, 999417010, 409158569, 298782710, 270977266, 942134475, 934408220, 517190036, 468709465, 333404333, 403664744, 47084799, 36330309, 106144999, 266455191, 626970100, 853603880, 720670490, 111144959, 892912098, 233179826, 951407546, 484684930, 816685322, 14403859, 120167585, 100472012, 901721526, 905717422, 497610121, 245786690, 971912593, 595550001, 619178743, 651303552, 414328581, 532041263, 94258691, 652679665, 86609560, 271816928, 768918537, 506849117, 883072504, 159342653, 738381828, 807797342, 65167708, 579130706, 92369748, 194340084, 446759947, 154870070, 588974633, 198917824, 884453032, 911739598, 905587893, 27199943, 83269458, 209921886, 526370086, 195582269, 576265621, 579569864, 813758183, 688907048, 883112835, 679864341, 818278955, 58846261, 614856158, 847048235, 619491944, 466675950, 78789834, 133330722, 85048607, 412694965, 308957872, 916326502, 249420990, 27464433, 96548839, 52867228, 482257041, 25450655, 221395468, 331777688, 691107656, 256088944, 713890515, 651776348, 101440838, 566785316, 777461547, 228634008, 695324295, 970362837, 272266352, 776084922, 368279583, 306674439, 393434752, 315185721, 714747355, 449158848, 997891749, 575699223, 182930309, 313694453, 797437133, 292740822, 95560805, 489825763, 259806195, 529647674, 747149176, 957072515, 930826218, 679585112, 674318242, 761725325, 398470022, 108923066, 45358222, 257001088, 488737298, 241332224, 593950965, 438075066, 535411989, 518770077, 337421363, 690976482, 317299601, 229968987, 531544099, 477972526, 342858643, 90204496, 319804246, 161933161, 363480956, 631723618, 735494831, 500730910, 725016895, 237396589, 52731275, 613024988, 394139220, 69800914, 333125088, 74275999, 776228724, 933703839, 895745222, 666202886, 333351230, 515288710, 260228570, 613235948, 784408227, 920314402, 198983555, 883739329, 118119155, 1314806, 655870883, 170317759, 71965625, 29859368, 980426024, 25680078, 17978464, 107632410, 750798799, 434375292, 979585387, 167394995, 219295896, 441210394, 598073505, 629489128, 503029683, 872587973, 10702330, 798126599, 921818727, 979236600, 941612281, 710758608, 924291445, 976743214, 89713257, 265059590, 981230401, 843310683, 520938987, 291592371, 904386679, 319001396, 113607103, 725847323, 589987618, 794694413, 734197838, 167538740, 64441325, 613554745, 177713860, 926939769, 21763073, 557309378, 199008331, 254922143, 225195101, 421981080, 498384076, 774473617, 331234859, 865283235, 934930609, 905353017, 963705139, 651484089, 210724854, 423578566, 695541503, 17919456, 545249524, 65238734, 765457386, 327660920, 792104583, 646752630, 357839751, 12591903, 226954702, 768422548, 58765345, 956916646, 726903987, 211954004, 906500141, 106154614, 54748039, 414414390, 75149149, 972476262, 989209927, 330668258, 843836362, 320977684, 748846096, 44580453, 190809275, 978596989, 308659624, 275412907, 147180938, 547647937, 14690205, 806866898, 359958094, 56971225, 241209220, 112855212, 937691826, 538654852, 525096766, 620049389, 782660260, 720924466, 44559752, 714797745, 165733089, 546450930, 549937395, 986113491, 544164994, 839487137, 627292386, 367194578, 746782920, 348056578, 588657227, 786724684, 303346008, 226967049, 134363643, 524851289, 465256257, 391600851, 271816188, 415848525, 211445857, 346962517, 21379632, 347435685, 486524888, 751882964, 937956734, 368700789, 131983127, 287061992, 603820209, 645783901, 644259818, 670100040, 99107159, 872760311, 660081346, 667370232, 790345479, 306882574, 641444723, 82647803, 302909309, 79945067, 84803397, 968793904, 607659918, 492556144, 14697269, 964087087, 479901140, 921061463, 506497985, 466313742, 939127174, 814641983, 644859558, 657951941, 302252831, 236052260, 75297976, 579992712, 216630676, 479175455, 227724935, 734508726, 269402372, 132804373, 843732932, 672970359, 740183346, 819894740, 792788794, 272605491, 172489088, 978904410, 124025700, 764626958, 771078826, 930171120, 791434755, 905572640, 784788972, 944670367, 857769900, 839261637, 9594810, 21603400, 505674287, 880593418, 154019928, 521074491, 882577849, 456519813, 564021901, 393284413, 897061608, 830248440, 848871373, 583033859, 910679957, 791147321, 661202118, 339367669, 936626914, 59929433, 341109252, 157560603, 435863277, 577447333, 362128643, 864945983, 62389073, 756117584, 116578963, 181681040, 283250950, 693510016, 467333107, 575079923, 456568635, 16637679, 868389577, 463060698, 774341709, 890428627, 639933602, 208317379, 927303711, 183954074, 363686409, 722445291, 990613859, 623663050, 842011954, 218863088, 835816007, 715297021, 415331564, 789388359, 157484509, 485540153, 242294939, 849829400, 650545651, 710009614, 915979997, 151580704, 550927066, 298886974, 268424250, 369925581, 613571583, 499664023, 177851543, 52654554, 533753285, 959813892, 979201252, 777086219, 551576833, 208673905, 503915585, 353936619, 889404925, 272324092, 389528009, 999839191, 130872116, 709319892, 720091222, 353658467, 778246500, 402441242, 774166153, 736775515, 743919106, 982160236, 491154165, 506895893, 303042686, 943607163, 373677820, 587497446, 988628839, 227282748, 397954754, 15411863, 294599943, 480961678, 910117201, 904592286, 562812227, 552283067, 399829815, 574944305, 968694116, 965843832, 438930486, 5022343, 622134929, 76748049, 289234571, 836609726, 490012629, 329161652, 402442218, 419370560, 633737295, 521670862, 169724533, 433529267, 438529052, 106417334, 985734045, 114258302, 481620854, 166219356, 371301632, 615858922, 933295830, 880654542, 253209112, 881361464, 625265286, 39978427, 50074429, 455650705, 702022074, 984694110, 417789802, 289604331, 932424707, 241747896, 141277632, 70220177, 220028656, 545508748, 596462002, 744441721, 134043637, 195322384, 25789241, 122717981, 940299381, 68797754, 152668259, 537168582, 728233051, 582947482, 430997905, 876347615, 783872679, 900688430, 686403473, 561489812, 261083602, 627666963, 360067110, 571831207, 855971387, 188388797, 483195833, 755508928, 828663106, 471012789, 630524989, 427181794, 721394201, 209847638, 427365252, 503702343, 409903443, 298212081, 855741865, 655035223, 25376517, 528058808, 238829521, 795865551, 181357024, 400686450, 459670441, 923810071, 485069576, 751147503, 306231269, 708371113, 395848307, 415192636, 155378765, 920821998, 727464757, 147474184, 316956777, 170866426, 475750867, 446648156, 492020672, 800674799, 808868103, 364409530, 3958306, 40209234, 701370673, 243272041, 796117332, 270193136, 357124494, 235125490, 719232973, 965881857, 539054508, 236818300, 347858877, 895479324, 184256136, 988041309, 708220281, 810150827, 74556832, 6939617, 534133939, 124645090, 694728504, 65087308, 465808815, 632306117, 679374238, 856748840, 129155688, 684330629, 989716346, 291947844, 358112382, 698410832, 477052622, 292854700, 909225836, 760668181, 74781137, 116818899, 490232069, 941228501, 632429247, 744394, 875448560, 566145810, 498758025, 819964886, 225393135, 735342219, 400555715, 113323001, 293237924, 316772064, 447563558, 558932810, 3564697, 533368513, 171790746, 802073295, 289427371, 465765628, 674261253, 392922510, 813842718, 463625375, 634729950, 353043279, 34962369, 169243900, 442727126, 20373050, 571677244, 480462287, 200599331, 109675100, 303623931, 721862548, 853784309, 4944577, 908560390, 93320675, 613369062, 473647091, 643671963, 726017620, 835622224, 398190425, 829661237, 323183349, 195625860, 904370381, 789057007, 616104033, 236716704, 920610352, 721841561, 712525522, 275092143, 106962413, 748490581, 899509374, 958972274, 406645489, 25052616, 473566949, 987155700, 931655820, 523649957, 513212466, 515950560, 156447269, 28039913, 384141311, 123829138, 600887828, 560782307, 22521761, 510980104, 259179528, 399167589, 614648425, 696929265, 552834908, 273838022, 211669431, 815817727, 866551573, 384124621, 200703310, 489704623, 25068370, 668235513, 66961863, 991085611, 887680569, 167144758, 697311896, 394610774, 437419404, 957994445, 358944698, 373042858, 57888877, 701340018, 438154038, 371149142, 932365775, 536060517, 459232046, 762597796, 706952657, 155243101, 522378222, 273245356, 209992084, 880048493, 264330762, 177849144, 689318427, 934012886, 993864239, 499807429, 740397780, 450750511, 632216772, 927771836, 202940221, 591817134, 722388479, 410196766, 732073080, 390225839, 728967104, 438403863, 928231128, 105480813, 720316220, 236562869, 544055785, 855818479, 149351822, 984887029, 150670612, 906133314, 488738530, 390296853, 119336246, 514623874, 131943329, 43690192, 203360404, 639113947, 842272451, 534965890, 295759081, 616480439, 77866178, 836786394, 915754563, 981802762, 675768704, 451534341, 739295199, 530905473, 597794122, 717950814, 258732470, 997231761, 469133892, 166328026, 944491503, 188762526, 609447847, 352132729, 229717568, 50933973, 52107404, 958895022, 218752711, 816758689, 670653464, 644181198, 913228391, 254703025, 434939456, 228100669, 439175110, 708116522, 261391731, 171136552, 234530911, 366467989, 781924305, 435647087, 244213643, 63267264, 31182890, 880897696, 385314181, 719670585, 81492066, 908462286, 487802053, 927103466, 54505309, 177085070, 834823745, 129352465, 989013711, 445956925, 67370824, 218440862, 480616191, 769162777, 118639220, 890916187, 935750445, 481737372, 920077038, 294698869, 340130919, 757580753, 363912144, 44550535, 710447917, 752911899, 308464902, 15700549, 638002560, 495935540, 550044614, 519258823, 521152382, 20324966, 984783720, 135293298, 602170815, 61420738, 438325217, 121474002, 651356725, 24127248, 620011059, 25312717, 493272641, 983592838, 74557504, 166134329, 674693831, 538423007, 434482138, 552562935, 206016947, 138071284, 371965062, 549566018, 451140067, 900989560, 282719257, 147398415, 126729487, 120236564, 616682248, 957243273, 948759948, 444256596, 404902592, 897860326, 111318623, 537865175, 32750649, 634111448, 337406107, 751299649, 819691915, 946985872, 265367831, 335041076, 955732322, 838399646, 496113106, 952002986, 285740039, 790711204, 230585089, 241288847, 355448527, 633000175, 802541649, 640093780, 24167048, 500482046, 234458890, 549515174, 993937566, 934446227, 89188743, 437857081, 960518490, 389456969, 442718180, 961459893, 627386383, 971024398, 713327312, 204100312, 244239283, 234190138, 900377183, 841120815, 414853647, 886947927, 327915415, 520874931, 537768064, 378724138, 975452513, 761247015, 504875074, 377911946, 965421218, 3597172, 565263980, 537549910, 407354428, 190388071, 712269503, 246353043, 502172526, 421925677, 512747273, 772314420, 682103455, 468097468, 283060185, 648346784, 950168035, 78384702, 841127759, 407692749, 942767286, 497855207, 448835105, 785583580, 141266566, 557765110, 855224841, 407384142, 823116158, 341599514, 446405822, 692074716, 502405962, 488605958, 989163663, 39428288, 770272167, 710153203, 949272438, 188756395, 655724788, 665025175, 499976718, 647830479, 287492925, 824948783, 322837858, 691005959, 738456283, 76231328, 507486328, 878875245, 353934955, 611748891, 438955820, 20344676, 971958933, 556348114, 340725381, 496845277, 294559687, 549563057, 43942722, 468526640, 858217904, 786885232, 145848591, 261269689, 313228810, 989409821, 430075305, 905869119, 297832781, 359364525, 379445959, 595696756, 2726833, 452026848, 592914836, 720360237, 194308220, 466199533, 600076193, 766694664, 910366909, 738121379, 640195747, 245597010, 837280424, 587520798, 888942319, 173502759, 294746105, 849782813, 660192612, 48578573, 904827291, 55085557, 830144991, 958920936, 556497803, 586509666, 946149452, 383633545, 634031279, 477406574, 516734070, 321834935, 407565383, 873020056, 587992987, 391621719, 53320374, 998811058, 311345890, 661240675, 867110328, 427974875, 597132106, 127394151, 765815004, 265110505, 577192060, 285153351, 278071262, 720568443, 539431692, 169076822, 238215648, 5740443, 691837132, 224527249, 235569528, 41001320, 77377328, 598688529, 87713375, 594345093, 558394736, 481718931, 846880657, 378559572, 228887106, 747695952, 501187310, 543035060, 529143103, 62397247, 564697662, 20730445, 872787813, 424627998, 501072945, 978349855, 12833325, 173158458, 601579657, 650316173, 114784390, 977536467, 329119273, 601258183, 886617583, 579320262, 609499062, 147310476, 645023080, 506180405, 96760350, 985688818, 532916359, 851826637, 62274855, 910759494, 160748668, 134048105, 977738565, 695727079, 30548563, 390162674, 606788849, 406069849, 598940243, 730228903, 481297338, 241549237, 915985251, 577612905, 270360815, 195567679, 67170188, 914533713, 5456131, 977573581, 321639873, 427348242, 191596216, 563982191, 837524761, 558081798, 953252855, 29027491, 928173257, 42992490, 883817996, 250513479, 344333921, 355774576, 952424121, 911423891, 142221050, 466870660, 363927635, 986778225, 898883247, 631158224, 60082126, 811347403, 152529631, 994786011, 937691531, 75861085, 750357533, 608901857, 460771829, 565057119, 432570642, 262872518, 10452929, 999752473, 177869033, 886100984, 30663522, 985468000, 733295601, 759210545, 527001400, 194079878, 730859753, 580583154, 225247840, 766801410, 720221581, 4072751, 468256583, 747025047, 298565272, 935422603, 268669804, 647612038, 410838873, 13516392, 216386972, 631567485, 196120957, 604042428, 996116555, 112813558, 118151990, 336710, 759272980, 961881335, 124730586, 681845778, 167967264, 611994261, 912366543, 212775663, 607317630, 186387888, 10923832, 874144781, 468210691, 375625472, 188499871, 581576249, 769920666, 84612058, 925243996, 675472295, 117876212, 895713389, 330159047, 308133840, 579766125, 85831607, 501641346, 896813213, 160657167, 139590170, 678350882, 133291121, 733853112, 414451096, 995059960, 893382609, 189394922, 256267826, 526169776, 446597846, 438782695, 253451589, 574791815, 718712556, 511814195, 168428443, 323179978, 666832649, 214626074, 354490576, 130268154, 589399796, 715357110, 682753662, 75626490, 856351079, 229911278, 796356384, 261247558, 367818390, 731885525, 751291694, 691868831, 319572739, 735316807, 877434840, 138812504, 35533768, 515384542, 887235991, 502970914, 360528188, 160272198, 461446063, 347001621, 624112443, 35083895, 433108775, 692834177, 816245874, 216341000, 28382785, 737984920, 620737656, 394148746, 718863078, 576723877, 862866106, 731528691, 400097419, 220553715, 827239768, 781669201, 323554380, 861587256, 354778100, 137537716, 228720444, 249634478, 840308266, 45476595, 619844297, 599321858, 642279310, 646378008, 687735047, 992088191, 181697420, 330987892, 222753197, 125301344, 399802088, 345945142, 131018401, 222824179, 418638153, 147577682, 47905080, 992285378, 564246134, 108985672, 284056804, 417116769, 850586089, 770060146, 433406648, 438705091, 860229778, 669974017, 85742378, 857751676, 18523296, 664766901, 297943566, 849637043, 962807000, 979472127, 703468989, 851080753, 476113249, 243971369, 690688322, 777808421, 301960214, 115572116, 747408907, 722406108, 850208604, 606039383, 330053923, 703967495, 428020135, 985752246, 774887180, 717392934, 278656334, 229470446, 791163106, 612732073, 138011880, 315413086, 846002968, 455208289, 541326271, 417040254, 362013400, 577536744, 253706480, 966873188, 379702951, 996205416, 627385760, 542794793, 667584290, 754538437, 854436351, 975254079, 142283019, 100574540, 624264867, 31738104, 457070578, 667475270, 494582229, 356437103, 325067913, 760791434, 244106293, 919564974, 194404691, 50046265, 96489370, 829089796, 373998751, 12969404, 606707597, 853275659, 870239786, 826955395, 443896757, 585546180, 378475198, 733977225, 518540753, 917889187, 9370279, 514452136, 326007834, 187250430, 348125898, 718608089, 571722957, 821378585, 361861733, 475149544, 331236168, 787964266, 927563304, 688448074, 53759865, 129088187, 904220414, 309868897, 482833389, 437055898, 834821434, 354956736, 679458694, 527256301, 966173999, 423565759, 501328355, 674483039, 855559115, 549969944, 643148227, 118819534, 916601744, 426253736, 938020567, 216591235, 884291550, 65619928, 365862701, 977157042, 839112138, 756016511, 343617485, 859319468, 574183795, 553885439, 231195067, 13204058, 477411580, 170034361, 95612755, 76173611, 987347040, 543194069, 911394337, 408910208, 44793880, 911251151, 566327505, 964427343, 224743517, 382048904, 986245046, 991957518, 482079118, 730654567, 573922023, 934115451, 544953326, 360586088, 1126811, 974058558, 539004387, 525215261, 845329572, 18023599, 300210461, 750003980, 853251337, 909517530, 111958144, 334859959, 234117275, 614797019, 234551185, 551320300, 85466095, 203989952, 918911369, 137976140, 481529708, 696311130, 966232044, 72790881, 280150123, 261671612, 51298762, 465301380, 576661383, 749303328, 559108747, 708562549, 47672985, 916950319, 355835182, 450965966, 185021208, 260585624, 434103250, 964475799, 931117746, 555120091, 470042740, 347417589, 933741507, 593300864, 125701168, 470746022, 753373722, 944836698, 215701784, 938439610, 459744818, 826349595, 622490439, 554447595, 485751300, 131790475, 390825819, 849410640, 577334156, 395120842, 70197602, 631249282, 766952728, 997654164, 192804214, 401774451, 363842000, 744276951, 94171074, 438366636, 272749477, 38846124, 446574883, 356324719, 461486787, 233940657, 222390934, 143803705, 10980942, 549726942, 909479785, 182474114, 974347838, 633730901, 587654762, 988003282, 480456598, 55622329, 143382007, 265478654, 821587026, 256541060, 675882970, 27372001, 26715510, 600125717, 703250994, 953370352, 46656027, 463111214, 608516332, 652766552, 11835667, 310243567, 218474343, 659018138, 598996186, 323479685, 284520226, 878710928, 423488620, 74937952, 790155916, 597145410, 442963428, 984537001, 127701340, 52368130, 852694434, 903467135, 165689694, 992104607, 594385012, 119171394, 216873805, 617115132, 842390781, 149958427, 138274235, 681587061, 665546174, 836564362, 609120171, 986612050, 626694609, 619327540, 828110418, 396487217, 227594842, 181739026, 843823945, 599046142, 681491704, 743860347, 57138292, 919477927, 949144669, 319009342, 551194247, 225464746, 578667131, 523837154, 477192631, 418437386, 69637003, 916196834, 443353777, 298189381, 698175615, 36175982, 536024231, 145432579, 429346451, 760980955, 450085805, 984941589, 156752776, 591124425, 799610279, 340478180, 994623944, 647005900, 191728321, 843359670, 161306004, 690565492, 971005720, 116364887, 744650636, 412424248, 903854628, 671915958, 418385906, 299381003, 314376368, 605857635, 770386362, 343725942, 896323759, 971695231, 60197474, 678155694, 82705310, 29898208, 280278100, 22677175, 531015239, 145943025, 160901236, 75923088, 270323053, 258108882, 748267356, 446508534, 171820302, 891169654, 880491220, 921461385, 791771127, 493432684, 487743458, 83722855, 405479700, 570771185, 11530161, 397897055, 177026757, 518535556, 298689693, 800236368, 89101988, 395769527, 638409810, 992911378, 706320109, 785900169, 651551191, 370725312, 923992644, 447586697, 270184793, 805668140, 944535092, 53787002, 575290574, 805870483, 340453164, 474263504, 680560784, 117332378, 741972373, 234984965, 367483386, 303530368, 581672093, 585508815, 318531106, 14537308, 157523565, 547637378, 765747416, 430658802, 23341923, 323781067, 863630319, 451830580, 146017369, 374315606, 92943701, 736153614, 395015407, 556934150, 945271940, 293870471, 755646217, 391595272, 206279495, 922168060, 111445859, 817624539, 409636053, 494433798, 302464360, 327818083, 215138055, 472878864, 806017704, 450269044, 983791480, 624244433, 314906243, 798618751, 624497407, 704632096, 192246452, 367377206, 716198936, 271529747, 663989441, 92439241, 672933319, 608933959, 374299069, 991678693, 926317900, 965533587, 207598680, 418253901, 538236740, 668235038, 504378091, 736171529, 653017103, 63379366, 154006885, 609050190, 468560458, 891252233, 371729888, 428083002, 698755701, 487114773, 142230275, 752513267, 363884915, 180151625, 859202502, 969688535, 686566351, 684018812, 24483476, 28646075, 952556254, 881593840, 710200122, 954543371, 787015339, 27454053, 206617704, 880976708, 900996968, 97663371, 447842664, 904058052, 710909966, 175922232, 316174703, 633645595, 589930024, 863143554, 344386226, 47901130, 943900175, 343624862, 896034301, 762183646, 38494376, 445160143, 32325533, 74386520, 40749150, 845739031, 426696252, 675932537, 322632569, 255037707, 52639097, 497996902, 396144155, 44155123, 64636113, 180461689, 283381780, 925963686, 154418343, 818307263, 600314640, 718610567, 60094177, 260310866, 837581056, 25310401, 332785862, 29009643, 695496907, 827538757, 857177979, 258373837, 123289899, 35442979, 197604701, 989184015, 109023337, 507139572, 685580374, 297659784, 679350766, 124503585, 340586112, 710606342, 532952316, 626278108, 639450768, 937342098, 561907859, 216884717, 85377019, 91314093, 772771211, 320208447, 848211720, 474744040, 321068667, 360306752, 795473429, 905689757, 48499098, 440603852, 257393865, 207363949, 417693413, 186066481, 294619043, 949909882, 760607143, 894853675, 309565188, 757276800, 352746162, 317691185, 424790180, 356815555, 418968877, 801808837, 584776380, 458375331, 884922990, 424640202, 955661579, 221605235, 385246648, 259124235, 370734110, 809581661, 733837774, 850415773, 542071171, 762888903, 808491492, 804153283, 638528500, 583694002, 156202758, 321605925, 366974652, 484084075, 142506762, 484078523, 984225954, 440289727, 468411889, 381351054, 730787514, 507343788, 944617893, 497131475, 214969549, 944375119, 286962000, 648890985, 567584679, 264257611, 799265938, 346974698, 355714931, 332783871, 150129267, 931064848, 28746249, 710880098, 786298409, 505453097, 297621349, 996826022, 576410881, 384912784, 626017127, 365108843, 115983757, 478380973, 170932813, 102702704, 624594366, 590748261, 196501028, 625748603, 122706292, 248009455, 976624572, 105844655, 157033705, 791997912, 242986345, 908036429, 143385746, 669025552, 811662888, 38689137, 448845805, 848984038, 790755775, 716540089, 156225983, 495250665, 656896957, 150071397, 212796205, 134618234, 670984747, 461414326, 188127693, 281947246, 79474859, 854442434, 923683154, 479200562, 752561322, 318312295, 546145500, 445250614, 884822009, 535310568, 196636960, 483994347, 216856527, 404662388, 250514201, 461507594, 688427256, 864600290, 150826721, 317812586, 612073850, 307534248, 800188057, 910852100, 25166200, 375623581, 54963900, 181621151, 894507683, 877503424, 89078210, 738870182, 659871227, 744090903, 816405507, 306504776, 262983664, 220862229, 432824486, 338653627, 996940193, 600822915, 78653676, 966471475, 357273878, 533539110, 450125235, 564252309, 326782933, 833960591, 396711730, 979790595, 673714765, 955787736, 893599453, 882144702, 381913228, 62494403, 701060504, 774985287, 108067428, 340562457, 483570047, 470426731, 544930870, 469766347, 264300198, 926178936, 592743103, 53767873, 475693550, 844731794, 96186106, 418364147, 561244863, 221114620, 700029857, 850572359, 507132091, 216001369, 326949206, 741590143, 737395859, 346306084, 743404158, 709661022, 124449377, 240072742, 181900604, 170158954, 142382314, 815466814, 99764061, 230767720, 981939635, 849999291, 764405609, 272892170, 934120779, 617100485, 864988761, 815236854, 383935340, 815465816, 649809881, 526859761, 38941741, 11162526, 213680804, 685250266, 831439228, 879011090, 571551965, 785137090, 784933207, 347529863, 683705176, 420369270, 563854103, 450967064, 638801778, 821673117, 283759424, 26924407, 77905568, 848905132, 112553358, 22518699, 460615564, 428219937, 649473223, 136723827, 855270355, 482508303, 16207639, 568533375, 39866568, 985579852, 33770912, 814732097, 62754593, 653547925, 937482700, 259706381, 167079987, 215150094, 56518700, 178868040, 668946046, 985034588, 333834605, 36055608, 32556886, 398130822, 313873187, 252279703, 416824326, 215684622, 402223565, 58311376, 371412509, 555745970, 212606872, 847842000, 137746428, 304532289, 776827343, 911408130, 137708874, 743143024, 198296870, 224721880, 911877954, 569974391, 723570980, 929641011, 292353949, 397026671, 170838961, 913855480, 670290062, 381099506, 869497753, 846911003, 390139807, 142104158, 614859931, 173248001, 241207734, 435360388, 556666383, 118667880, 255117145, 81092036, 781655388, 813099897, 431076125, 76716286, 676884499, 656228120, 393270378, 321975561, 270713407, 662818150, 480272941, 169253688, 934098038, 488503951, 1258627, 128480479, 606522008, 831867100, 134152583, 978177819, 87172043, 627282697, 786650093, 375982630, 288295884, 155109851, 762352950, 445870914, 697002011, 738212640, 499269483, 826486081, 23867964, 666661404, 138017928, 404455132, 405549151, 798798167, 721231319, 59032946, 285933821, 922679632, 329837171, 304503386, 481755327, 774779262, 669046792, 117015298, 541262643, 596409418, 246786975, 275466183, 702236833, 369300903, 945482010, 429144841, 846322698, 243978312, 792312407, 401292408, 971084162, 271424910, 961206693, 483013145, 505673149, 243530000, 789795071, 636513810, 804283748, 640991869, 923917263, 434973231, 393197576, 539569220, 442190812, 306055655, 154119330, 40852481, 484851141, 679303558, 713137641, 598685517, 255073719, 195035006, 706444901, 670743411, 12588112, 187906693, 261264634, 595146731, 868078413, 815176688, 76513761, 574838786, 930437341, 243256460, 376653500, 932878848, 450624164, 667176137, 952570439, 861825040, 841432007, 870737199, 273713888, 689463567, 911461424, 577671470, 344939184, 312028484, 130950357, 861091348, 897311486, 491334435, 483999686, 71873433, 308329059, 491936390, 805735404, 606991518, 304757977, 968143805, 9418007, 693718288, 388659747, 365290662, 74778825, 476559804, 341918501, 192770602, 492924500, 984982690, 256134487, 999237046, 536444074, 110505706, 390985346, 632676378, 314403287, 546469361, 55029514, 220966899, 763610009, 119275949, 94597302, 624815903, 569098357, 464388828, 211550335, 967684527, 333255860, 596218321, 829746733, 893935774, 135733069, 444224814, 125040302, 950388202, 906736360, 495242671, 596018588, 786121052, 773388734, 83658976, 499895329, 395862373, 248886819, 461414772, 168685266, 328908162, 488521550, 572377703, 381463565, 768685446, 810312101, 629418425, 179921848, 80723656, 77129408, 619966785, 62645920, 924451815, 795378085, 863319385, 411272486, 526591426, 357379185, 162535868, 691072356, 316903018, 758440888, 897804876, 946248935, 135856097, 332100918, 567987462, 494216775, 876182539, 228327938, 973468236, 14657211, 595181696, 316908557, 809942827, 188055567, 241062387, 689085018, 568884400, 129459038, 459663139, 518322002, 454581595, 568246653, 583585915, 402368319, 984248032, 67201333, 491701349, 984257581, 349280248, 305259956, 143949216, 770118898, 969228546, 724337308, 240912492, 209895783, 344314680, 40938072, 615673292, 133171812, 546045234, 750163875, 598145662, 73706511, 694188674, 143101156, 826829041, 466409016, 189595204, 970269120, 567037830, 83897120, 268298223, 366201015, 823655146, 760980960, 201393427, 169291890, 754004906, 128881971, 816624344, 940900864, 870402153, 185272258, 160552854, 454673468, 590524618, 413661754, 849999731, 348926886, 363950480, 898309673, 989368836, 78936563, 925624810, 934819235, 813904691, 896645443, 996823509, 772667734, 221835841, 587860356, 887701003, 384272483, 571187617, 314085435, 369900501, 243336322, 217223240, 355450268, 900064041, 116935503, 297019746, 228259081, 110179657, 309460819, 340004089, 978122501, 602362029, 645948193, 116474987, 98523430, 583937701, 158642314, 786571882, 100821232, 848776645, 105080643, 918028466, 823961920, 264530355, 686600098, 400943775, 938248615, 447431535, 547694840, 27211026, 960615761, 681380917, 181601095, 154803678, 894019126, 655665065, 943618893, 962321621, 564777430, 255935481, 585160591, 49446091, 429986631, 7106256, 379032718, 815370129, 442223223, 810599818, 829518073, 500846988, 904950161, 908378067, 609972622, 815483780, 496063040, 900496505, 27992381, 306965622, 553043406, 724079957, 199739566, 920495465, 528864076, 167714032, 659610856, 482707531, 779869875, 973999201, 106218166, 187880277, 61556202, 13349351, 136133915, 473402042, 924039206, 848181009, 832525174, 497839158, 962341577, 406750703, 578609610, 549024155, 679999082, 791433315, 663560670, 470454086, 480471081, 527765202, 484163529, 621698988, 975124162, 150379744, 822867511, 498365207, 55932698, 179850069, 651178289, 300465853, 506084658, 586394336, 370894762, 808127850, 851193142, 763351272, 127505893, 12517271, 558794633, 773822516, 654129253, 745196755, 902128261, 98627727, 513811269, 651131516, 289004500, 648497004, 539140849, 340811579, 554316021, 490623072, 753528271, 540352790, 693212732, 863715412, 539231801, 12956480, 949628409, 991024402, 407890132, 883145154, 973348979, 52895610, 59641920, 672042215, 451899623, 169334973, 593601810, 820064742, 881623129, 998777953, 569012647, 298991358, 183764972, 290605336, 23678256, 414911685, 947221827, 22307553, 135925152, 974459464, 795578744, 45429430, 962135099, 822576021, 386358894, 735168031, 302606911, 113122226, 208912544, 691085970, 767085831, 982196631, 115786866, 463331198, 866345267, 802601220, 624534227, 985048007, 637132404, 50829904, 253964941, 381380167, 508802121, 358921261, 667956862, 236594876, 662684379, 111566795, 539629398, 84657973, 370005337, 239401006, 667891187, 865003018, 990533400, 501438887, 405091991, 625616534, 612545710, 773105562, 679072139, 793214063, 438834397, 882244800, 122719009, 186291502, 731177761, 440776721, 614840267, 510005329, 640231152, 499239661, 971596585, 200089786, 874711218, 780167101, 230847521, 453048368, 234876263, 566183479, 905281860, 50535289, 779760842, 756622801, 11861897, 24203685, 761064321, 152182601, 295573477, 311871089, 19388530, 95246339, 897595566, 966973066, 860498267, 940333730, 959980821, 245810455, 663585717, 741392096, 631256873, 591444899, 674791824, 701615484, 654137077, 820508309, 474187501, 94601642, 175367460, 352475832, 70813243, 763614412, 62632914, 407861042, 625689595, 176711261, 144744079, 18501107, 430436800, 191539830, 493289027, 908953662, 893856498, 611951445, 211754734, 954252396, 957365849, 830384003, 259233512, 455682250, 183812518, 284004972, 975130500, 234353378, 168653457, 247093864, 770175284, 630384846, 767353520, 21117691, 796379953, 713810572, 631816127, 822028086, 568857258, 313877017, 875687817, 627083679, 516159962, 717935151, 52563741, 266095254, 330524193, 670799145, 394171092, 402572073, 734864751, 798942254, 294060388, 748816178, 214274513, 220858698, 205850837, 513718631, 519214960, 936553373, 811314221, 440553089, 82405590, 601318004, 634130851, 960377456, 624362166, 619068451, 405927380, 194587343, 783466395, 734161941, 531730089, 289237911, 889477943, 342845015, 594622957, 400185460, 255725874, 149524192, 191887966, 83806972, 949853376, 552348603, 982047103, 940996450, 385600935, 730478848, 864525586, 775605489, 202137592, 812944592, 866887016, 458832007, 571813626, 295856471, 453930200, 406651878, 308997113, 468386750, 437982160, 54945833, 524890516, 944532781, 808507055, 15963636, 578405473, 481883215, 179392871, 464135894, 596319762, 249661645, 350139982, 63487953, 778200526, 619642320, 2226483, 60725891, 312686723, 872340599, 781997706, 243203695, 852552321, 410471908, 703292247, 672850009, 372731254, 466201161, 265545508, 44247586, 170814873, 11631951, 123009807, 318889397, 195627144, 292547811, 671775203, 277727479, 179326987, 440493628, 129426096, 121634017, 3306539, 27011000, 900450520, 473033743, 582470505, 276836809, 778685284, 797572125, 378541893, 131068581, 819123665, 76788598, 981821629, 888831752, 952466774, 22380426, 449999927, 477067092, 709999035, 220976801, 515661141, 36535452, 390257907, 618639687, 437561512, 388014836, 211990799, 100798049, 601586903, 487756422, 700506398, 773065432, 308475164, 820054734, 857273013, 351968330, 162690949, 638817732, 702704880, 776543614, 978295334, 861746072, 305884329, 564529890, 624471795, 872044194, 909097819, 229201953, 607909023, 700267844, 430263257, 558203554, 784386595, 537667863, 414725684, 355204731, 536941919, 254521514, 579064247, 636917144, 892376568, 812932701, 144684894, 227883929, 99209098, 840626330, 63958400, 183154609, 638236184, 342703948, 604969705, 825924498, 799999691, 176042291, 123374437, 649149920, 719658364, 11596502, 820356928, 762960489, 863293368, 216001657, 993638104, 930527485, 881911904, 176446374, 414157785, 540550308, 364058844, 303358518, 383239444, 359502408, 348858095, 439638486, 924375827, 745210188, 875663067, 377683061, 5294414, 511253455, 771714698, 601038041, 237730914, 910597773, 96901821, 944616135, 441421419, 459800523, 156854785, 520373741, 409541936, 341799565, 194494165, 580900994, 426608837, 442749257, 245054494, 65912420, 529913774, 689073379, 71140048, 434702682, 617412843, 801515353, 18503872, 996406112, 138294580, 646572925, 309478279, 756359080, 848909592, 6242677, 6058112, 354052116, 283260626, 675928939, 482326094, 751887326, 291522809, 336569630, 588763530, 16318540, 349263379, 140248930, 769899886, 222705128, 392571115, 6613716, 487997739, 510080009, 523802447, 434449601, 433308260, 748413197, 165451039, 614037753, 22044296, 13124429, 44424024, 225934121, 241502933, 34969730, 628988593, 648027131, 406329057, 129819061, 776404991, 839595412, 774340477, 827131663, 203321846, 623519542, 718354708, 425719083, 675000981, 470049478, 420098832, 716498519, 974120492, 950086442, 344086548, 105283892, 596115563, 186685678, 220801903, 215467372, 804636910, 675053405, 734412990, 285787711, 676625417, 624270543, 784592333, 563049720, 359301868, 294696990, 788864324, 376299094, 249470861, 752486027, 857567021, 819813894, 855061790, 273802879, 21337309, 35956915, 319937763, 340702214, 847824000, 984408446, 681388086, 325626564, 980865196, 30688604, 13933104, 695838757, 748951804, 274271761, 434969835, 195142749, 328352453, 903810981, 905734835, 408689688, 452332745, 616869391, 278932662, 19746523, 245626623, 916191578, 610725432, 407647225, 327870548, 292258240, 800787539, 426389162, 508878136, 855759122, 882465458, 522788873, 911067857, 382404903, 146921439, 931745648, 548527625, 335056583, 343592265, 593068068, 185162012, 905294370, 720959487, 373574171, 391759693, 135438128, 478758116, 736205643, 427319510, 624601551, 408053646, 473856335, 636417576, 568015134, 573533821, 704614390, 535608265, 687493801, 722433562, 444785132, 212977319, 469686101, 899821418, 591655951, 908272982, 895328534, 521157364, 271802614, 413128292, 696426607, 314209058, 916358914, 459183286, 3763841, 401565765, 817722715, 527893262, 766990589, 287562157, 63471639, 469727490, 223595688, 221397526, 723893863, 182667092, 833994030, 251737602, 538352327, 72007591, 389258013, 458832958, 917081935, 192299626, 985793532, 595224812, 497994539, 716620840, 119465678, 770434688, 468684571, 971619081, 921267602, 866345905, 622052953, 796275893, 556975492, 948730090, 994704270, 5451, 21388367, 819743463, 49886540, 880287725, 445486866, 420457915, 358686860, 335962831, 32016978, 126124913, 616868112, 430397271, 85457687, 458697312, 909466961, 901025110, 403368718, 42309129, 20935675, 520489137, 749392194, 265208254, 943491259, 460347429, 111349522, 435525859, 835698795, 838678305, 662253362, 851635812, 313446573, 385408848, 285450857, 794964187, 123606917, 888489122, 266722620, 227980392, 900639352, 867157889, 460355312, 779236460, 116034433, 226862175, 453827948, 751845844, 863787112, 759674565, 133500353, 701806781, 95732238, 395221784, 472395140, 942810533, 359308128, 681916606, 489835133, 572574738, 639437466, 308219514, 636468236, 637432850, 212774190, 14225556, 554559786, 101203409, 285584537, 587719332, 580791024, 437549755, 18560448, 246309499, 852648045, 415826751, 190292077, 456201517, 849768139, 317265747, 40698751, 110438327, 778170729, 887345958, 392263227, 871926122, 148645276, 247758792, 418201112, 530529080, 284421082, 338256742, 233523990, 760608831, 393752530, 66577273, 635502856, 209013504, 628290915, 841460280, 650198253, 708658128, 57548810, 663422283, 421158175, 787825730, 544092553, 566496723, 972658499, 719126557, 678462458, 488913294, 423559686, 659887179, 63758187, 696944024, 191789154, 966417183, 88900791, 242819335, 856397152, 37671727, 636957520, 586003864, 17711885, 355588648, 837928707, 492214325, 649786124, 235696476, 419852001, 105901323, 441618874, 607401639, 871729664, 322824259, 760191644, 369981363, 20308240, 132260411, 584535042, 997631648, 537758384, 643154628, 671324108, 714633250, 96881698, 311836526, 529741248, 271078229, 726177571, 516092424, 913131674, 145767047, 931704124, 506268524, 934884211, 308999088, 451175704, 177837244, 376714224, 692667537, 877505787, 536048799, 674311877, 670255696, 78863716, 973053581, 351397648, 618415064, 769978106, 578808313, 410047568, 826973812, 741140107, 945544631, 967144167, 705512422, 412539541, 631816344, 13844949, 551987707, 31649700, 266623046, 589591912, 67312836, 522679599, 994037853, 891093250, 801875595, 408874898, 249908869, 199855115, 182326585, 65447873, 43304958, 688696896, 852918975, 29457803, 620460629, 524543090, 902871048, 894723295, 48946669, 894453545, 672648358, 493755809, 26925784, 337860831, 651550049, 864358503, 239953127, 378674989, 938426050, 964218306, 786636101, 387950075, 348591827, 195780946, 309513983, 162505385, 299479918, 743170838, 616089840, 4629427, 663860635, 206530808, 493301743, 520795695, 715743635, 60275444, 133771952, 435257607, 577350815, 31878755, 626235565, 531821073, 621369130, 14918810, 877955897, 52285829, 482111654, 758264312, 71774503, 328929479, 240495491, 991443151, 364344769, 661029631, 965175067, 733134538, 509429937, 547442825, 55316833, 180594550, 174236013, 946248485, 688141629, 262165411, 361681900, 867576061, 344494307, 486925798, 197960815, 763734584, 233457619, 756845246, 536507183, 134767853, 520023243, 5249600, 695609618, 587586955, 641856055, 262461253, 998747739, 63796461, 579061142, 448693490, 470335259, 975376281, 62348590, 502327478, 887934180, 277671390, 55700527, 517978804, 476086966, 810025466, 416579848, 996310124, 878340297, 806890814, 474999700, 163720512, 921776889, 569389806, 266993258, 426378326, 468843207, 167423822, 13192155, 945921477, 561759084, 959360940, 803494373, 641873434, 789361714, 292208344, 150778150, 211846432, 386398977, 527431167, 342981484, 637994856, 232734734, 828909293, 396563953, 929843649, 873878600, 686619520, 633354005, 860508589, 530776987, 842826107, 159359460, 413364371, 318455385, 148746792, 55872321, 942871817, 680846182, 777277300, 109211618, 203995057, 328386045, 442612418, 583611321, 968024278, 202711464, 884741285, 262729553, 299935539, 257873823, 315011121, 773295512, 390118152, 835569614, 444735955, 474385653, 171559653, 540740507, 680815301, 799554360, 714406280, 851106452, 150861644, 525158085, 588040640, 24934673, 836673444, 146869215, 751813480, 718111045, 819176737, 82429331, 899305849, 783473191, 607914842, 828653209, 753161537, 320453453, 806249442, 412425784, 126419306, 793479317, 111229187, 446941232, 654230069, 806519288, 579689509, 136060595, 537716062, 894991678, 816359418, 236327769, 829332165, 988513605, 188038387, 722736465, 760310456, 646522094, 503869805, 417828525, 647778053, 718271697, 645559641, 250347753, 377952061, 956691227, 110529428, 932442436, 588214112, 803759511, 378802832, 313095237, 634600506, 315411254, 368456851, 99191823, 915323601, 535083664, 471984372, 107854429, 59545779, 98822874, 347855344, 618595812, 39633383, 65364126, 920820997, 665434078, 583471067, 266939431, 754755880, 930486360, 179891126, 866722375, 393036292, 697797824, 451835480, 132745311, 219180184, 774697413, 604738078, 913243668, 134444546, 306432694, 299695949, 76455921, 840022333, 800823782, 322911385, 897145029, 409389269, 412013884, 699818132, 416905145, 55432185, 530201486, 729868853, 758735932, 977766150, 449167461, 644725534, 880707652, 83816225, 962742923, 810384611, 461730774, 308536951, 137737846, 916370973, 508346837, 7947347, 712687865, 431943768, 48253826, 188760312, 354208703, 442260764, 115340459, 685291907, 894383482, 449664371, 563563259, 434625241, 129924932, 807202670, 830631477, 239302116, 704785707, 926382657, 286985399, 172583754, 56278402, 245125556, 434053777, 214543439, 850737750, 180354992, 691660390, 948983610, 842695555, 943462401, 188610217, 101727230, 751135106, 419645905, 974514677, 704650815, 871648690, 596391672, 713646182, 866949509, 18032943, 647539255, 196784932, 967529101, 575237605, 379973862, 962537720, 91408338, 867608392, 285229690, 433222992, 34035841, 166206918, 121673190, 618585856, 738325109, 204590783, 84995179, 956118351, 601706981, 736492663, 246987772, 204477313, 684410600, 534391142, 23992846, 828851467, 761908263, 609245082, 332174365, 58205600, 243738682, 844148981, 70931597, 836772188, 568617181, 289758840, 852248999, 919324245, 294594769, 235158028, 458114155, 857537513, 634314292, 949379362, 711380407, 134667184, 231049763, 626738661, 536813610, 766046157, 139044278, 693210396, 140747965, 791823960, 649761013, 138316888, 962481002, 330906265, 588730838, 895544205, 972585975, 460578729, 628058488, 875361941, 446333527, 523074082, 479446775, 919540190, 197278994, 797664533, 251523082, 794799353, 995751194, 563747359, 462607106, 758141902, 459995607, 105759109, 729814263, 218393614, 587337002, 18753197, 453329204, 523402909, 562866933, 800281797, 28235147, 582705938, 273586723, 33214029, 779254855, 609881579, 822359657, 48110023, 924890799, 454319290, 578927783, 912660594, 432111684, 393361063, 536825639, 236088344, 402639872, 656757773, 701905597, 700411738, 778891135, 223704817, 953997944, 957796838, 167681283, 52184291, 551303620, 466139233, 886171651, 739445628, 846610333, 119131626, 418385351, 974084249, 597064585, 973171232, 671977545, 594481980, 530970173, 114822117, 23953329, 416533850, 485670485, 629683595, 637494942, 628839211, 62995842, 202862925, 923695254, 752412479, 228218578, 74656354, 485207305, 962067457, 592178223, 440832620, 231393669, 788268414, 331093441, 473747184, 838980904, 680197394, 454493715, 717945255, 811312090, 714618831, 12441799, 776405525, 367132019, 85616229, 701327735, 206445471, 460120832, 336410113, 624136494, 276137526, 254338617, 318189595, 638984924, 589763919, 448746083, 403027243, 205007848, 300311654, 528512358, 182918960, 331923866, 52811545, 370823591, 180797898, 235374396, 296899525, 405023233, 720309995, 369420783, 338076867, 649483558, 434452240, 93797246, 407833263, 141601401, 695069683, 672481258, 868836875, 825191114, 473571925, 169601259, 307304096, 484065982, 555529522, 773366895, 261952094, 646005111, 218299921, 654732982, 283110652, 392977452, 873544141, 915467830, 398960008, 57595329, 153544604, 128229562, 977159567, 901514162, 928101, 596555770, 136685921, 785731998, 610623121, 876643524, 450230891, 691265603, 298603026, 560095829, 610754534, 258504340, 529262820, 981436596, 403302860, 220312179, 115493058, 925724461, 666597995, 958308977, 941870864, 491431304, 739811549, 814287061, 366209055, 916689745, 984169801, 758183710, 969846268, 102518935, 340415256, 644204350, 120734877, 854036415, 864386148, 122548795, 284757531, 744098878, 339087330, 746681854, 27144416, 136575169, 353567340, 78910736, 386113338, 191281693, 672060236, 51108535, 206713464, 806080566, 904623365, 253557284, 838667880, 264379242, 53491285, 136322583, 604542930, 554489095, 341506024, 241850919, 513214370, 117242843, 220133445, 101932629, 275827536, 786668882, 648815061, 138918912, 563634251, 231435046, 429235034, 88612452, 33710291, 636786940, 917541222, 780636653, 20600889, 949098017, 102517723, 818409257, 780195268, 788024980, 415139947, 352553828, 690841871, 846814366, 974641934, 691129629, 63590820, 291237246, 61071557, 736323427, 357549972, 868138781, 537499102, 326364590, 587220639, 418513751, 896669810, 698382245, 72594382, 725153444, 220038085, 871606542, 163921693, 120025253, 241770845, 47357217, 136507412, 676031655, 643155249, 208289238, 904527050, 475515817, 177817740, 583293815, 987224699, 520356245, 769806899, 783404363, 574325262, 98642872, 838488858, 375511738, 13957472, 169985029, 422478407, 178250965, 378753979, 460229118, 866572918, 791949771, 159510714, 376445279, 700931457, 42832532, 469227797, 126151691, 457350070, 593685429, 381224837, 12898428, 554870190, 23179211, 537171548, 738146582, 1769928, 700659726, 594764418, 188805195, 11976673, 182783567, 685407291, 751116966, 403060292, 977346470, 312485781, 532577219, 687526466, 424133918, 743812488, 73352732, 454226264, 717281815, 615884334, 541736179, 873239533, 945203317, 864028279, 692337077, 391962638, 305424767, 18257787, 850334498, 459066488, 126306004, 536436807, 347469579, 950384567, 758719393, 968891962, 39934437, 35499119, 674268127, 962230114, 3236798, 319653175, 572995629, 151082434, 304159341, 432473771, 971275277, 461816601, 957962599, 545119336, 284680151, 144333874, 618095902, 932917507, 278599805, 608910641, 205847165, 564775384, 623859354, 991150106, 286827510, 110812482, 445761050, 402493117, 9102165, 80809154, 503908438, 769295535, 417165630, 535392282, 116452195, 303464368, 145164424, 626490918, 156138666, 790252511, 812334394, 78023254, 973026316, 684464817, 672888129, 387748246, 670379810, 933804415, 203287496, 398958059, 868058097, 158918750, 697471963, 471171626, 938936777, 418574849, 684272680, 536664353, 195243872, 726497297, 53471695, 771544680, 504081930, 895964376, 754771551, 995118945, 616539886, 963061523, 97047003, 374176971, 474961123, 448338768, 710030859, 331562778, 254858465, 237599498, 960847172, 809898805, 636293623, 911832656, 199761742, 895961497, 509687837, 138529600, 323829549, 808277547, 438588633, 162431607, 870806826, 437483311, 389985504, 514672074, 933258571, 548897179, 43497189, 979097145, 12234182, 866275687, 769868182, 502224188, 193225240, 848361226, 255061959, 372499563, 551495041, 805719567, 949048178, 140195801, 971703109, 738299904, 525771832, 425092684, 655684237, 348458464, 951887441, 371720060, 398051868, 664503700, 760440369, 446784024, 761995375, 953062642, 597811767, 527247973, 4976502, 225333114, 468496402, 826238709, 63301609, 329428625, 317607049, 783503238, 712036410, 972362106, 454108165, 424886003, 686830782, 5577339, 936250257, 973965801, 2140444, 36448087, 468860114, 544621066, 426178303, 241562367, 206216472, 276307666, 700408058, 625863208, 79266763, 412093905, 399690643, 381839420, 467850144, 891184649, 501956241, 24373048, 262139692, 559109240, 804459599, 685326711, 404703091, 599124058, 705638160, 66010830, 572382694, 142393392, 755617027, 211256597, 157972323, 426272782, 170355761, 847696831, 686432641, 383382240, 282582534, 593709538, 320752146, 133156989, 886648903, 855759513, 85513480, 491658679, 725486533, 676320995, 114846874, 210181058, 267633091, 41505797, 802469150, 368384837, 332907465, 459876656, 350386959, 139301990, 476515542, 284084715, 608952961, 912412161, 497156205, 204280075, 930784971, 779122436, 639912989, 126609283, 254803045, 835189517, 130235340, 316733032, 108977237, 592160052, 37559923, 194568423, 914335770, 685720404, 107547937, 637317444, 953315988, 871460781, 22332913, 592472818, 476939353, 297916785, 439299040, 992445713, 152212871, 344276681, 822954572, 414689233, 644588139, 922214511, 181235967, 809186715, 534838706, 927285069, 376960469, 120421171, 944612098, 340608828, 141185974, 654039010, 301901081, 296186418, 137070738, 599074841, 97389257, 797992442, 433678538, 559504188, 996494166, 739448830, 475427719, 869762822, 394867932, 948262789, 452271808, 834513047, 199150185, 49650093, 828712800, 627921535, 363158976, 76454190, 146135990, 427597937, 669425666, 934284804, 522926621, 637831676, 483300813, 114082465, 545888377, 453056547, 949172295, 419258192, 514041620, 231384501, 107162413, 73173992, 844227465, 791239420, 837866605, 216244547, 826610670, 19449906, 468624328, 729637119, 836224906, 281505863, 705697748, 279335372, 582478498, 417570183, 690295152, 936613103, 941382488, 199769479, 29332370, 323861994, 429166102, 112235116, 272958779, 45111599, 422460962, 248191757, 935338823, 304617377, 568451880, 442521459, 432216121, 233999610, 635146751, 881002163, 131782129, 566256909, 411335999, 96899947, 981800344, 279218293, 646961444, 814063665, 667514231, 135908328, 634464926, 479559167, 13326366, 8053499, 901327496, 453296333, 737690369, 632593901, 16736277, 768217155, 398071355, 455319406, 20732209, 642669175, 702322195, 321919264, 943641048, 163523569, 604140947, 837388404, 746504612, 981439957, 669071566, 501080562, 735676194, 993993615, 660724997, 658015335, 679238625, 982401811, 505908363, 673436266, 709620947, 46276131, 148724631, 484351392, 891626508, 135667940, 588451983, 920108566, 210473120, 164587258, 257897584, 78366094, 132963361, 715418987, 482733481, 371780191, 413850129, 15539465, 536690171, 118445333, 325068590, 351406067, 292084841, 99114858, 294398919, 164521563, 274689230, 615947561, 392233866, 985684016, 334590391, 369483441, 434626832, 555283060, 499384303, 791918638, 454703383, 488556164, 876860330, 924345537, 28765313, 655633708, 889124475, 444366319, 426514394, 210665198, 438034637, 770416812, 573475298, 904958203, 879680280, 666883397, 412068834, 661612041, 943371819, 601381717, 209406950, 840725928, 151935684, 915005139, 363569388, 850895284, 806207458, 110967716, 41915685, 646848310, 377072799, 359707201, 613943867, 803593949, 710470490, 104448854, 971452585, 800074634, 741153947, 178462544, 368493638, 764001095, 298633485, 875307858, 840634400, 667643094, 662433945, 444892132, 728864651, 532977551, 889069664, 807924, 742002064, 866017576, 654011940, 360116974, 283588474, 926554740, 153631244, 492723950, 813957638, 106061139, 684115387, 317117289, 559313868, 300954149, 172098112, 745117159, 912973270, 352957873, 326936914, 51617341, 190367403, 855154936, 103124606, 409507018, 606395673, 786767335, 129979253, 613448143, 419384239, 212267072, 171258435, 303796924, 344583355, 908336288, 485870464, 639764421, 74829793, 264784508, 726395338, 372680437, 202248279, 333743230, 731416931, 188997414, 688025043, 5850816, 895405449, 274592023, 365763467, 47461045, 622161502, 55726973, 611743179, 373698512, 382501536, 854432535, 654911538, 936565555, 358261394, 338745461, 523140080, 180902944, 742266099, 515122874, 906478704, 18472792, 643495385, 212687378, 50306737, 162854659, 116210285, 215397323, 435304947, 858970704, 945142858, 293827102, 699132952, 239733461, 318999582, 89424477, 962962328, 670970111, 700199825, 594821401, 287849514, 651805837, 996426373, 603739389, 995484455, 80670999, 283902621, 905025733, 641494535, 440253166, 239773961, 963709201, 87595318, 842810197, 721349503, 378316046, 512241754, 716445867, 428229630, 156658108, 263208207, 404506438, 356637324, 331203229, 785352427, 231184022, 603592734, 173657167, 488530074, 520535989, 936765610, 856553595, 319830812, 187803920, 500330895, 446062724, 550827838, 662333613, 437902361, 867236970, 416574785, 201726601, 573567927, 868043551, 243801239, 745033756, 246537645, 471806556, 867238304, 958583866, 482867740, 576361648, 660624690, 535078703, 594913976, 903258780, 359908762, 900226174, 585340443, 916495363, 216485045, 265371628, 496435409, 726898377, 41144029, 302746813, 380489301, 605332707, 513513567, 677333326, 855863940, 673708101, 326537382, 372873872, 648703632, 307927537, 754280336, 62756143, 756163237, 639572402, 872453641, 445049794, 933385441, 998929831, 196088114, 896181348, 518154537, 163512885, 403332405, 207273960, 960858415, 11355527, 362597447, 655464361, 347233276, 878817314, 891229215, 501385125, 97030473, 839996025, 122006554, 152724566, 349729655, 761924896, 209630356, 617976090, 705655657, 670722120, 172272479, 693499243, 990491492, 262398490, 863904363, 923210683, 28682529, 759389037, 174370056, 988004597, 755673964, 834991350, 144921258, 420593340, 506311894, 973161848, 157079244, 135413222, 58304016, 496958845, 588566346, 535500549, 119836563, 343436158, 799624665, 597392933, 406080332, 328261411, 948115679, 600446251, 941059120, 607635504, 368194071, 584872438, 262462331, 426732312, 491416496, 195379450, 969148608, 339353658, 446461402, 466041038, 105972947, 79417410, 58560540, 300060929, 732410237, 151918892, 854732464, 994757575, 895358910, 153713943, 55951387, 8598408, 802408915, 107524404, 715749762, 211784814, 956756809, 946813397, 610348846, 36306237, 946624774, 841662139, 969945009, 759310763, 474127191, 88758597, 694652524, 141456515, 141156584, 161934615, 328601789, 151239441, 433913175, 124753, 939319358, 792831625, 104331331, 965759500, 144222653, 265703692, 622649950, 793680491, 641485277, 639262901, 935068163, 493022054, 506865658, 766466007, 128909819, 292847498, 548470070, 620197397, 189770322, 969859786, 137679954, 101547459, 745346962, 434736562, 881034880, 896325302, 373049874, 809467514, 530164831, 633387571, 197476040, 314216624, 329011377, 574011244, 119582829, 207882371, 796041543, 923655974, 34393238, 584968327, 927853862, 149250315, 742545690, 583840842, 583311892, 489656802, 448754094, 2834435, 857339246, 951899538, 736705098, 572840769, 328095335, 532707073, 792022036, 718214733, 713143237, 371481719, 268499181, 604110640, 524647235, 879705605, 924568170, 7835774, 958515330, 408752313, 626595107, 26987701, 725553471, 474571867, 483130638, 406157551, 708720495, 680646016, 383006931, 490687371, 535979899, 879403030, 420058062, 536275830, 516180757, 449225759, 227880059, 629632803, 459688318, 37597535, 647290604, 661729984, 379879, 673210808, 655786710, 114463277, 49543061, 898587159, 11730702, 186895213, 490977758, 968165117, 450026073, 358566779, 728050844, 471317450, 559436176, 650792609, 148400895, 751401074, 818289392, 585569299, 519520571, 220538992, 630081749, 733916306, 948852718, 592787813, 66817993, 826751458, 192995057, 414891696, 411627534, 636749010, 713172241, 380794287, 430100767, 271009912, 631231085, 15712776, 955533373, 263032839, 59274823, 145561183, 778962443, 409595079, 241368227, 305497116, 612047125, 170448961, 73980308, 475045977, 891218969, 414708731, 693222833, 459026369, 764089741, 344269105, 972445416, 142450416, 313522221, 587975819, 21963285, 243302684, 963521039, 951741230, 148124676, 522694615, 842622031, 132343563, 667177117, 901624028, 936088725, 516969275, 578853217, 195748012, 138548437, 308962539, 335439469, 571603870, 421392907, 872515199, 358251102, 400914164, 255811698, 328756209, 987857882, 947821767, 978124379, 143520806, 228549738, 277319837, 404772139, 740917155, 189823463, 364610517, 312257877, 506552745, 497851023, 402855307, 276279337, 274210177, 804559867, 471318350, 308464080, 309640295, 261565277, 775570410, 300809580, 217037388, 118942880, 290261894, 589251896, 972564721, 225120993, 276710948, 606196787, 493459965, 746678313, 143335555, 333199341, 356291417, 512846878, 715631057, 97601150, 244565172, 241035453, 804701305, 563072490, 653759253, 830304968, 763369009, 403908899, 37819216, 953811137, 493966603, 287797355, 233844590, 678028934, 284861956, 787513354, 425134604, 132488942, 641345361, 819423998, 575077797, 200592483, 2678552, 773880057, 633459454, 418563614, 392330851, 53212443, 112684611, 649380531, 328469427, 983813704, 615259884, 814402505, 935668118, 581255443, 729541466, 655588752, 547940385, 296523214, 198690732, 246785975, 37038678, 977056316, 190079920, 76964565, 730323231, 453821513, 457798402, 623681788, 805291730, 685126162, 321816683, 649250576, 302155794, 142455974, 505599982, 354378562, 929596157, 273283199, 463125059, 886143505, 420115678, 366762201, 154930404, 861281071, 170433470, 395481742, 422967595, 587784502, 656545184, 467303459, 318795281, 28748024, 817771840, 360241290, 575114910, 564917197, 946197544, 618544260, 562695341, 431249937, 234341302, 783954580, 7024662, 257034295, 457366561, 732256592, 616184899, 706997628, 156243262, 741336635, 546908373, 798077900, 694840547, 382900399, 6011952, 74351086, 482868741, 20890979, 844166201, 5406679, 695182597, 460949325, 948918620, 331990010, 250830343, 330993093, 413773690, 518079844, 671649230, 893777350, 433234593, 113262501, 447877602, 171748848, 786528553, 508517418, 206849124, 179607539, 873787404, 693804552, 133527269, 338498122, 648352384, 221852846, 53147155, 5039473, 518172082, 635210705, 450156488, 352542533, 58309066, 889341414, 339804847, 182104577, 986048056, 629396229, 88241540, 718131849, 680926054, 693248975, 960145606, 798684739, 689611077, 965278245, 606817738, 117064123, 135766461, 739869133, 26272425, 969218639, 51685576, 354166142, 21620455, 708455293, 579972830, 639037404, 545179844, 462306787, 41017015, 406597850, 957222892, 253527972, 646198619, 41776694, 931089216, 723025614, 126360990, 990637099, 423774546, 806233157, 804855073, 646341675, 504251829, 95978726, 92082401, 496686842, 402813376, 605453412, 562835197, 445997342, 675575871, 930738057, 659512908, 335853945, 264393594, 756491177, 623396826, 75463716, 804288438, 671546524, 515932979, 608570615, 175913080, 699535464, 873197485, 1235886, 754748928, 845619208, 7775689, 445300472, 950025231, 587977959, 121783002, 613480763, 563448530, 189533576, 774780941, 299658518, 415321340, 112042900, 405626181, 770359242, 230060980, 923793704, 511067252, 13926320, 753401249, 377714922, 106315129, 864640114, 32467658, 67145493, 942321434, 361682231, 471271200, 569440122, 481037197, 360152106, 962520811, 608334954, 254612331, 494273414, 494904107, 143927285, 294939700, 946235820, 473960484, 596130772, 675431275, 944655743, 108281304, 824777687, 199959754, 242834399, 688765874, 35889707, 678971377, 930501862, 645887731, 306404364, 120102038, 570107199, 221754217, 392551873, 837739481, 195447329, 669499174, 498493729, 127058810, 171270982, 693350777, 24750477, 621501128, 779020574, 137961706, 596481080, 505225841, 649416601, 330705626, 819330571, 100316246, 648884869, 367732051, 528042454, 615861941, 940936065, 654855678, 953366975, 187481608, 13072638, 811563545, 176862973, 522491762, 495515206, 549662553, 231145375, 36782719, 413277187, 444180605, 756986446, 203515708, 356450660, 222154044, 853252026, 529607447, 867300249, 732549380, 219730350, 718870401, 112120688, 770606473, 102332607, 962369809, 882034564, 651617852, 561265444, 268446713, 939250007, 969624108, 64451741, 952377938, 883373895, 132371322, 139707884, 641203269, 32987856, 984267863, 695377651, 57723811, 737422362, 430204648, 720248917, 964235271, 999265669, 565793202, 161475336, 872470203, 385556983, 640201530, 104663033, 718964960, 786588872, 940797799, 529448619, 163018069, 524103470, 376880209, 640251054, 97835934, 228739014, 548098012, 899736858, 339149079, 614779366, 947639599, 470642489, 417249951, 316961151, 414333711, 258341310, 360088804, 675046147, 470679507, 285802352, 57614758, 452835053, 525322379, 970191599, 89808854, 571026504, 456714222, 419922046, 592018774, 615747648, 695435219, 230282942, 282777475, 736393158, 19027186, 500857806, 328180103, 410335868, 421517559, 188003876, 848931266, 833227144, 329088548, 213052606, 373398306, 69897169, 517252605, 87024929, 719786334, 246381133, 564818808, 443340473, 952030767, 677881411, 28073688, 313720006, 258070858, 419197606, 678884472, 517474104, 441104056, 25877018, 998969973, 429423301, 58293248, 893615921, 831187574, 396327903, 69762474, 275664475, 331044192, 586204871, 106698065, 247457562, 661032380, 101932883, 447005962, 830147110, 269798384, 140963714, 577736926, 678331403, 12262090, 7718308, 382537070, 861072232, 433366443, 918335824, 598268800, 194624175, 815428099, 466058727, 931830544, 618703552, 810220066, 347643021, 478508217, 72972744, 538683457, 998761021, 657416269, 940321975, 469048308, 633557531, 858683477, 985474306, 510053092, 794978431, 836488913, 896719885, 23804625, 30806693, 157532818, 624146655, 476398805, 387193175, 244376833, 87650656, 888101216, 172038950, 852567177, 756587007, 905863962, 555013874, 328667493, 961773176, 321150165, 788629383, 700998117, 651260224, 965802674, 734859467, 79853966, 113427845, 608384883, 810082674, 219112661, 212980418, 124213121, 537871681, 888487471, 367407161, 330543173, 180677716, 495153276, 974566420, 961653137, 656949846, 251304735, 576177486, 749967326, 941263585, 28263370, 548196683, 189813118, 710001157, 164411129, 393696462, 834633907, 666732441, 260179634, 539904565, 189832686, 383401181, 487000708, 672805381, 207548254, 404084050, 604070349, 338899226, 833731952, 920558768, 436405367, 560084907, 879184661, 93690221, 599280644, 345063158, 611733895, 353608516, 792441748, 444101403, 537979629, 658345857, 838773947, 779864149, 834201101, 479653095, 691457214, 718337264, 491274972, 402520551, 104392337, 926884884, 395517545, 254933075, 727980238, 882106090, 347186957, 20608694, 280345993, 599682670, 287347521, 39854710, 684024577, 532733710, 940891925, 988151524, 63414860, 969363141, 732575580, 417204027, 381302365, 700029604, 703415918, 268410373, 224500928, 615496156, 200194768, 681646882, 755638019, 266681525, 802501579, 656022656, 415591448, 507732230, 943287867, 411045609, 286299838, 388388295, 501861736, 794699105, 450466659, 436375043, 425439174, 290704808, 429067527, 427946670, 664867137, 352539309, 458320186, 78714192, 447366161, 212681025, 588285688, 566049567, 245592497, 587298081, 662326130, 666706699, 702381884, 7592924, 138896928, 155057636, 776656461, 422402262, 57603399, 329846427, 818530855, 871148075, 877979407, 736669122, 170979261, 170583394, 933231858, 468321787, 22126824, 620955654, 462989135, 331827527, 781195440, 843241523, 553955086, 54608876, 595706087, 718793510, 73604859, 260899739, 821072403, 570358702, 683195371, 593278089, 12886136, 895685746, 369237408, 874556913, 597268509, 565632490, 373084816, 972892219, 284084779, 994471530, 951892323, 436655083, 184869456, 39590983, 950471416, 797947180, 792950891, 212173316, 972900026, 737709144, 20777465, 997520116, 627332892, 932808769, 678303614, 435019578, 726829720, 511500938, 514525836, 876805157, 914501926, 607581263, 127851827, 96501445, 610427742, 419727390, 750061395, 90478656, 494842949, 54431076, 858662555, 497395645, 493028117, 971284183, 716106554, 670509587, 289901395, 415463207, 126539911, 957463568, 353605623, 315642204, 374457039, 564502927, 518000656, 988345288, 931138660, 615697628, 749355521, 279016208, 121491804, 163872656, 350425773, 559543267, 839261249, 647395242, 954222185, 234723840, 650277200, 93871672, 187940418, 967206552, 449319428, 939717694, 538549072, 154602092, 672585063, 101605166, 556530089, 588194428, 560428735, 600059376, 505614677, 168977539, 725249056, 714022029, 619514652, 644722743, 385679800, 941790760, 811608986, 30901675, 677095131, 804262519, 424357828, 935482699, 499716783, 980412699, 519211457, 368290666, 950202144, 414258732, 620167270, 139456889, 594305651, 68112144, 900793613, 399183537, 375581465, 139077972, 706786733, 848676550, 568605333, 408921619, 833324418, 205158209, 958888669, 408778556, 674522081, 61404557, 66659955, 517119318, 220798575, 342410124, 942997198, 759359747, 453888785, 320436683, 747554144, 382103145, 868163749, 973141939, 456013886, 729708382, 554392993, 457645263, 668634903, 919073463, 461790106, 650462250, 189437569, 399436263, 502082567, 312593647, 225035721, 445911753, 135961367, 964992135, 839364616, 247428634, 776675884, 513764682, 294642958, 487608878, 59504588, 67829667, 268968665, 45154894, 875783464, 256848320, 197476740, 541799467, 578759351, 976674707, 965996471, 445125700, 314892022, 744787113, 410607235, 431423448, 122290488, 174230020, 490760509, 637890779, 38927948, 695445304, 659280339, 530814257, 520837155, 907755971, 188952565, 519565801, 568939429, 191522571, 729691675, 568079039, 18309712, 390048160, 33812139, 402634569, 167523322, 567199770, 830809055, 387882589, 743010101, 321667970, 223747632, 679685016, 740856529, 59848359, 7257301, 542869034, 536679854, 426876851, 974413622, 22802000, 76123639, 34253152, 357708838, 349233243, 130171244, 760365664, 715677036, 390826466, 485464569, 525268882, 692813758, 360974898, 441696132, 312207247, 486391436, 142114675, 658280508, 255704059, 423616460, 378383307, 295668321, 869418639, 4211304, 606455055, 396895987, 652902194, 248201178, 846175223, 307592875, 68689032, 109471583, 41585253, 618173530, 546610551, 650690402, 150713403, 62711242, 93682846, 919898919, 344382756, 548160845, 110202710, 302120498, 283762195, 607701279, 865483098, 429102743, 568890983, 158120607, 600070360, 996796751, 159666361, 919967250, 561799388, 652453184, 612136378, 577092472, 459147191, 460170206, 659757661, 681030567, 462976811, 597146215, 577999915, 149602264, 296550530, 595153335, 97753311, 762648008, 64087671, 436222693, 721013187, 632404607, 208527341, 276913648, 360289251, 510781128, 573748346, 209506769, 930171893, 103390511, 188577258, 993927050, 216961923, 456135489, 632370952, 163221303, 503172850, 93975624, 765584731, 761562242, 395870350, 556408824, 55181124, 499209900, 125463160, 54483587, 89983194, 432647433, 767068348, 670638831, 705597153, 299888368, 386170405, 833224111, 480277528, 730782444, 314599378, 664059384, 527695050, 596832188, 523719703, 540159396, 1827734, 343512877, 254059191, 790714859, 942919423, 241081502, 454132448, 435159111, 260902280, 81595491, 505694945, 67928147, 161318028, 341233204, 296806228, 449654063, 142664840, 110315501, 589804701, 244296235, 622667903, 970962840, 260284849, 486218971, 944837002, 813999962, 201469049, 217350655, 721812625, 349634930, 111528599, 904476691, 816155149, 89509770, 145160943, 816696022, 442672587, 518645662, 203758762, 683434830, 956774160, 251508525, 830837216, 313419712, 461464370, 606169250, 494435991, 147924710, 376345341, 655256284, 713194796, 103538203, 80962776, 592023070, 99817335, 302987006, 616607483, 381302266, 934511029, 972636400, 272903324, 720910635, 520213821, 458861488, 580680884, 693688209, 545322626, 754172978, 276489538, 107591087, 715137357, 470049812, 412495976, 429126691, 206087088, 760835382, 574016449, 25154295, 703303469, 420760337, 711166091, 78551339, 211201451, 919221365, 683716679, 495720350, 1489083, 127919248, 952559782, 574913105, 273767648, 452974357, 696803150, 735544443, 923605964, 230624645, 813323993, 432565911, 842651514, 328096372, 523034825, 824755677, 785888138, 992427019, 892400498, 185449677, 573940349, 80317066, 952652231, 372062501, 88712961, 925226644, 824178547, 806069142, 414696501, 972060445, 976047469, 1943241, 593948567, 85854949, 462510807, 733794811, 607882411, 199497035, 901089382, 103566478, 73423526, 353359450, 886510312, 29515623, 361454114, 335907138, 396664089, 604304169, 54193487, 843279880, 645213498, 709910955, 960077256, 237269686, 308053328, 85251357, 740726676, 130252148, 757630859, 62008964, 55622821, 840787843, 488855194, 323934134, 178437086, 755596706, 237579770, 781989734, 638405408, 28492153, 472071443, 768863297, 449197703, 829056366, 863630980, 685269673, 259472907, 578217443, 374532904, 54812020, 853338604, 257338514, 536893066, 561111444, 398153109, 188686358, 908746998, 19858409, 468950810, 337260851, 658829005, 47955174, 363073945, 942761098, 337828130, 830877831, 341319081, 645052767, 558254104, 475432900, 92897661, 736869237, 507115861, 453705290, 8103596, 621297911, 334949886, 89549364, 650068336, 166926536, 396620762, 944055544, 106128975, 328200689, 921640660, 187842384, 278523528, 667931202, 63316543, 798805414, 389246196, 759456462, 781862651, 203427557, 885312024, 507420363, 32435899, 650902630, 543212033, 284326977, 549382037, 401649743, 635488515, 240279670, 20532210, 745401998, 279452968, 604112438, 192010168, 410976398, 943355094, 606705879, 954451853, 309924074, 118242178, 823057346, 450193989, 142904542, 460650256, 560564885, 442891012, 376969095, 20287140, 648722379, 278707732, 117209374, 217559502, 34597079, 180732673, 75341315, 547706254, 432291901, 949467342, 594796136, 413284488, 189241423, 188041627, 804874822, 461851486, 494088151, 994394766, 23577820, 424181067, 624368325, 280815689, 923757504, 954440881, 437115018, 368355517, 438623365, 945607041, 664015520, 268251864, 10039328, 926018893, 949941948, 636774300, 882698447, 29903935, 11749110, 482921479, 5994153, 92419280, 675433980, 187967030, 522871804, 6560600, 485538232, 717934999, 47512681, 600134529, 364154985, 929961983, 210039990, 992389496, 886652754, 585469472, 708340350, 147692530, 728252743, 780881376, 778996304, 344614999, 862656006, 290273929, 61527365, 240402157, 697029112, 874941917, 69732831, 509932152, 122032276, 453943424, 753323179, 357816985, 237566569, 806822296, 176346524, 889628870, 451920125, 436797016, 47009747, 827783438, 164301943, 378855140, 773982429, 403317048, 978777250, 856975997, 102381675, 263681982, 105431600, 392945628, 191147829, 410959457, 352639845, 693127258, 604552840, 290493741, 12938023, 782099757, 526194415, 843390096, 476798929, 645265394, 925964622, 34878746, 591501842, 71703717, 976619772, 204761005, 103732350, 751236564, 926802506, 37288273, 869522497, 766248350, 774142686, 676229664, 857674426, 76521517, 208235942, 507355293, 586553827, 685828354, 108575516, 299057852, 155157682, 768522426, 134774150, 346709638, 516474602, 632160355, 343374737, 891607539, 750737100, 792015439, 765772907, 265010066, 67069619, 105548256, 411777512, 322754819, 288439374, 287714508, 366796672, 101070776, 157038394, 9844160, 844144089, 378993199, 949904936, 898475096, 59730013, 454628782, 813987969, 218487630, 123332815, 548131200, 313119730, 678002330, 528647702, 42190126, 921956980, 484396219, 105696027, 312080216, 364652758, 126930845, 70688533, 429593213, 942127361, 28026149, 988803528, 149540358, 72352263, 198331891, 966030806, 318514174, 653683902, 408013344, 319763927, 272980332, 436859647, 660404189, 454092514, 576029198, 23454836, 333841160, 410890535, 108841435, 106097731, 560779128, 744997752, 49190282, 21862704, 12296944, 315295697, 318529598, 862140561, 19730801, 871831935, 97818175, 280342881, 826474825, 631737687, 188181695, 916889024, 323960931, 116278491, 411763512, 945593964, 75620691, 253743109, 356901230, 74491, 461054191, 676224826, 899985858, 845906432, 416058238, 515440476, 395773905, 798359484, 250794975, 642980335, 211944980, 595445056, 84146634, 65105911, 476238921, 661894951, 398878288, 196789467, 471907544, 304816424, 95596574, 634376441, 182169178, 703562960, 511957000, 687358401, 629465076, 515072607, 308883369, 388190008, 62450068, 67879479, 739189054, 281683990, 381182432, 224503331, 87094570, 338271053, 166002021, 575824828, 710383364, 363830087, 317693526, 763695560, 444389091, 579977050, 621292506, 292171269, 292036142, 576908307, 583158825, 355141763, 26569236, 900368538, 424912772, 297803740, 401465098, 692951565, 675614906, 487572644, 628278290, 245504108, 777142957, 132725311, 108269053, 217465599, 269412591, 468720599, 599053337, 54776237, 483125667, 450537345, 983301403, 214983269, 480505186, 365836245, 539034751, 246994365, 178130738, 880124086, 71621815, 176828227, 106982176, 414203362, 780390979, 521956409, 920724803, 596177494, 490056152, 958227187, 261272311, 285649190, 300332085, 441304985, 240464391, 533649392, 164238207, 502114127, 331594292, 298934149, 947669621, 36751468, 232522956, 741957135, 238678731, 835647820, 512663447, 622029974, 991843804, 536217485, 352734832, 838182897, 215689599, 486477496, 287584769, 714126903, 370223203, 619271833, 590834869, 462693107, 955149778, 910383191, 239414719, 372593387, 554289349, 407608616, 831634986, 597245795, 201235601, 827562794, 622103496, 322527681, 835031358, 131615771, 512222838, 604527335, 705351655, 813184053, 82116070, 663014810, 364896329, 550609700, 687126791, 238474644, 287184742, 323887654, 634876308, 467773750, 562857153, 198099198, 167047672, 491333821, 460577234, 770241682, 704386002, 587002638, 452318744, 326462931, 444057587, 975586497, 385201391, 481913313, 132476205, 569399784, 347397156, 119448826, 496990273, 944347738, 932211089, 331708225, 713392877, 759466099, 258212480, 301576651, 915298979, 257119860, 763561276, 809372108, 665090309, 149701804, 594211649, 325639206, 298523674, 520986936, 814054495, 97740115, 856838477, 255841214, 897575341, 850972062, 121307254, 48812244, 701609591, 621161859, 872845322, 135688387, 175200093, 630484481, 120429717, 405822240, 818492399, 333561585, 620603847, 770001654, 247363681, 839816985, 853031016, 630698442, 218699840, 948490508, 890784741, 340850183, 811334721, 370837256, 875285081, 346867064, 759138882, 44896094, 860240021, 996786680, 203095330, 663479406, 55627309, 679023496, 813841007, 801648280, 853477103, 109264626, 45529671, 831357322, 674888319, 688589802, 278490369, 90713271, 521838323, 563946099, 638454800, 274324920, 471110778, 720349522, 891361376, 58837066, 126968899, 132779449, 372878697, 550212995, 768271789, 388388921, 490611293, 520729888, 714010503, 425367677, 980499590, 53682826, 495814758, 420209720, 425398878, 637592680, 802478359, 74146929, 59204571, 687020073, 600045690, 915772320, 104776854, 767876472, 261305102, 173080802, 889442235, 700394821, 913551944, 163358995, 356012385, 20836437, 889116796, 675684916, 669545631, 873234091, 43643591, 510913886, 896915606, 670586605, 613337861, 274447604, 810969909, 839071190, 842027954, 348907324, 88169643, 95965620, 389162190, 365294233, 353038016, 937646503, 256765092, 629695370, 63027373, 781300611, 359253006, 933728524, 582093218, 863710005, 466720740, 913645571, 73393635, 768988105, 382849926, 422095214, 657963948, 97538044, 692109490, 220102113, 835937404, 797274440, 329842730, 133698736, 400147858, 26257416, 259742917, 62181145, 904229089, 388469144, 519008913, 215499732, 866810355, 121597512, 369821025, 941069709, 218655641, 160226328, 409153117, 336544517, 101259216, 489175794, 300287376, 992784245, 749164341, 2445580, 89046366, 388248785, 66474015, 346576524, 227382280, 63271439, 727220011, 744583940, 108069042, 31350640, 790439316, 823055234, 929789968, 387337050, 751556105, 145534419, 519287566, 352444842, 330076346, 840679099, 593565633, 736330035, 24958015, 976674700, 893633365, 317059470, 533037162, 894170894, 927997023, 754581161, 991362642, 364472771, 208485181, 322378908, 361671838, 173979241, 81552606, 209426265, 834925895, 556019333, 198221426, 170669184, 384994908, 80428378, 704881807, 3593661, 6573334, 144754552, 114947552, 461728654, 451694388, 964977072, 238226403, 585543415, 472709928, 195004430, 107335633, 1506421, 189522516, 192666685, 297647017, 530803825, 936143496, 796374115, 33331044, 877735110, 373495429, 256780854, 666405337, 266424732, 642194561, 218778538, 933301884, 560458711, 862667019, 641270826, 597489802, 825055454, 310991037, 886716246, 801331300, 819686132, 377716810, 538967083, 721233431, 540443917, 736405181, 108878961, 614085225, 609650688, 793930364, 750643081, 964600424, 58043472, 475618636, 216180544, 561389226, 899874894, 890924761, 390586212, 115841647, 444324272, 968327932, 897277973, 306121267, 757235260, 981547317, 984408976, 933568848, 782478810, 503705698, 227520156, 366931172, 802643943, 586174083, 268766476, 278658148, 37789721, 855010202, 864026513, 780859044, 890812990, 368123493, 771935899, 623584376, 625916325, 624700824, 386228782, 114220512, 507684639, 340450878, 297399858, 45731979, 786502574, 346322754, 345148341, 977686173, 381465141, 960637916, 452569653, 404815054, 971199706, 231132982, 319193096, 341019585, 435491198, 52940167, 890561479, 134154826, 729804631, 174736103, 155227399, 143146097, 388636857, 323059754, 367354052, 329389346, 222308289, 366840704, 775083788, 881243409, 718043524, 602841187, 282168672, 996385689, 646079310, 227344377, 71242692, 46212885, 838422408, 428386912, 664362693, 100226579, 544958506, 824252857, 19555337, 197705844, 3370325, 20915689, 620549380, 955517319, 369067648, 158922429, 787727323, 693109087, 906417445, 442401453, 118666206, 212861101, 699529174, 693802742, 775385644, 153536184, 309748861, 205434461, 572291399, 358580593, 255183429, 345737914, 615682211, 860712112, 165165201, 674424704, 878020737, 32346616, 33146329, 389321732, 547301754, 614722937, 636962093, 296216623, 936539595, 487557205, 148332466, 113187609, 192088392, 701326689, 668156251, 473199433, 110849130, 493153163, 651492432, 486136285, 584213745, 983857765, 102083034, 179594138, 639270791, 533560064, 52237668, 617203425, 942172480, 948509668, 207264349, 980993235, 882855042, 331402061, 325265725, 943263833, 138095142, 790230557, 460522616, 332759364, 215231904, 696654532, 895661065, 485737571, 768338443, 143834007, 78369031, 715480182, 693304751, 352750107, 497185408, 2523751, 942447795, 300229745, 366247638, 979614797, 457280837, 963792885, 691321472, 743819903, 543788388, 582935739, 491631260, 722900042, 560189706, 364130304, 434732407, 60869560, 240234989, 327131400, 431354404, 584870517, 426661355, 341572312, 496353025, 256219850, 179538208, 903373229, 262869646, 243539230, 45745999, 215034504, 219065284, 325162518, 145914071, 756078132, 15082699, 249267847, 724457743, 131756655, 709646699, 719684624, 448066462, 174534914, 237294283, 748572127, 732240040, 760127555, 152306910, 590786293, 354965083, 704223824, 656864509, 200374705, 2383527, 452395401, 611883578, 702291743, 28505247, 660251665, 581619957, 492688829, 714298256, 689841673, 260247621, 905630266, 654225147, 543682463, 420906249, 216940023, 295195823, 972740617, 56721378, 824712797, 819681621, 978746224, 770375314, 951445894, 883044334, 740303190, 123859735, 658396848, 306381452, 793349926, 242463072, 942836885, 801427657, 148508709, 554498083, 553057726, 397332994, 125026222, 392847144, 175666647, 654252491, 342320257, 577296451, 885432146, 107299371, 551511668, 984317166, 530511670, 462401524, 428062502, 883017289, 882702968, 254456105, 205997673, 842550803, 883475577, 51583597, 257508423, 169601296, 400333457, 551645008, 192117576, 84841898, 99631549, 33596512, 224702761, 811524188, 667180317, 146653430, 508120889, 206559501, 69242418, 627241156, 487344554, 330354300, 742646173, 229226978, 966146983, 341149966, 579037588, 968431926, 924871227, 969773792, 655567459, 833370721, 481360755, 187527263, 938923514, 859136319, 341243051, 323888544, 328098446, 485872718, 143493190, 127354097, 558364639, 940054105, 245522026, 312419188, 535690438, 604357574, 603202724, 238375522, 451369855, 551622989, 777113536, 353551108, 148824621, 897163892, 787118567, 835224753, 868124404, 978863311, 318984169, 516507005, 786243998, 756725958, 519329520, 382069550, 726336105, 673036944, 314855287, 809979333, 857615322, 497763965, 632086525, 506845477, 429090790, 939618221, 340583166, 530479476, 422177190, 51846929, 133174439, 999396899, 280030502, 832076716, 123684871, 930810433, 401218833, 216824866, 161760394, 322801574, 413989659, 399632867, 405322007, 274936556, 415787731, 178403620, 589775356, 290509818, 1601168, 144754912, 143545673, 373928266, 368590723, 878872932, 97010082, 600303422, 705718608, 902996225, 790289993, 87617603, 624692735, 825189477, 715272771, 556408060, 401207721, 337386383, 916549505, 563513543, 79951149, 552089828, 815068660, 130738413, 11673128, 386126425, 933528386, 58175310, 964007685, 892528561, 564738022, 674705551, 438209291, 178102526, 615044425, 556943805, 812673853, 807368096, 284142562, 886263918, 130311560, 15890729, 944567519, 222452928, 216414152, 466215237, 142021951, 16708020, 563449197, 651349363, 247087142, 664239003, 154194589, 364609849, 371122379, 170254603, 634904674, 749839009, 182497156, 126840791, 888781594, 364322195, 970994422, 801257174, 633513663, 809688600, 241600422, 164467942, 305190218, 470914282, 34861712, 217859685, 911379349, 669307726, 654280506, 687427573, 86894855, 827724312, 505143355, 876224905, 184027147, 472225952, 942661575, 759292581, 211679644, 262274951, 779460004, 509335415, 222788471, 890122298, 2485663, 457665923, 943755770, 302538453, 840242731, 816058606, 761123380, 999309343, 883258988, 126298867, 732641819, 263165112, 963564214, 68520911, 345626042, 896294063, 700530502, 24099753, 994019818, 181983119, 202853918, 341250889, 538910168, 931148305, 511343367, 292780224, 918370088, 114772976, 901218520, 427136681, 447266585, 141521387, 934492809, 164704934, 113228195, 864807970, 575177924, 55857009, 237638244, 352920568, 272892643, 448511894, 947639874, 473477295, 980573371, 832876567, 334488506, 180502246, 2667579, 926665041, 493853260, 908430489, 767168278, 496559748, 232989943, 266544120, 749282697, 690366929, 937139268, 233068594, 831929174, 736739566, 727045468, 965773062, 371713766, 661706358, 979640337, 607841724, 612573592, 337131509, 122530384, 346218166, 252738386, 402912045, 650099766, 589424664, 81672649, 342581915, 368197438, 583738839, 50024709, 824583477, 915916573, 279240560, 790247458, 148060909, 919816496, 216976280, 177696024, 673713296, 623364768, 252499773, 308706932, 734633216, 683751755, 329116579, 576084207, 307699920, 718036261, 207495697, 718824263, 467510407, 604823437, 560787959, 237520535, 200288283, 972596876, 76041606, 404206687, 388291571, 758236157, 475568166, 475269504, 703208960, 213125488, 304925875, 502024460, 233120100, 930681011, 260235569, 534784773, 459685507, 351343802, 552396959, 753404014, 217165295, 929798959, 320628615, 795057070, 707534466, 138166761, 899116919, 418097506, 330595338, 839062347, 298487868, 175306744, 165776804, 57775889, 629015561, 838168884, 764475714, 860993265, 305178868, 75508475, 872411436, 819931085, 266973893, 793306073, 401603803, 777150241, 536363636, 139947850, 922371896, 752902245, 102256873, 907289116, 290881460, 113101821, 400500599, 894313620, 911494699, 239336965, 944458417, 512154529, 886405457, 160329315, 730082805, 85485640, 99262117, 611245911, 704135901, 434894127, 849356200, 831961923, 375123350, 259481359, 523297796, 669473132, 142420477, 776309401, 523684234, 706139880, 472202510, 689611632, 959583568, 976517997, 904880718, 68276919, 964232683, 652509757, 86329083, 439739195, 253834810, 539377712, 221754327, 619743674, 805569353, 622923257, 332163490, 207568608, 501753456, 54831042, 168242744, 253588700, 356703694, 706830327, 60964459, 256051364, 444735418, 443350605, 778741678, 480965483, 448239926, 825414080, 361418670, 778509057, 766004579, 949666109, 180237364, 720493277, 889353474, 609610535, 643973157, 299202854, 841892295, 923691777, 256096429, 174952113, 37460992, 579635160, 930008193, 674772619, 223516959, 229232679, 877028463, 934688075, 36673116, 695967154, 701633702, 642075008, 930139426, 566911508, 789317256, 846376915, 516290108, 306063274, 169921887, 28663614, 94398885, 66035640, 455852177, 959317061, 575941490, 715419348, 913017952, 297555982, 318473550, 459066456, 570968712, 681546928, 112548413, 838295220, 847734635, 964279083, 553568080, 387997512, 373410940, 562825422, 132025854, 537333869, 903874802, 529750167, 821765812, 135162531, 810993747, 629049966, 932315768, 759525251, 276365297, 206587206, 421837164, 923536030, 364735029, 383830653, 706426910, 597353050, 912534172, 408520016, 241381474, 241959948, 536939940, 58809499, 819547366, 57143611, 768468372, 815771249, 624232541, 227518437, 241975940, 588806495, 140319253, 513104836, 800619733, 184823257, 592576364, 323451691, 595372536, 45330000, 299675436, 405134548, 579137606, 475131579, 416297046, 766734725, 287540872, 636347073, 930603949, 822285694, 920249163, 254442680, 958829309, 601831420, 870720724, 87291397, 742381866, 2228039, 353775504, 419403740, 614699305, 575177325, 858031502, 390153394, 667231167, 567415415, 229643799, 456195978, 728795127, 108203092, 820895212, 224531809, 382719967, 713011118, 821354012, 506570790, 334414589, 578416645, 251787310, 38547919, 370034031, 288451980, 191857427, 272695304, 703941354, 790194270, 221349815, 105621231, 820066783, 243458598, 244395440, 310989609, 909875910, 815092113, 898862982, 241159448, 1296261, 452049123, 149478599, 343661398, 248083261, 633418014, 553161072, 664630466, 97610452, 965474329, 946391479, 203230743, 205961880, 232915649, 734262918, 423821462, 133643776, 747079142, 303219204, 806389553, 246554436, 44527246, 247570725, 383841522, 851527552, 340236384, 292862879, 769897558, 103663194, 763486975, 739692368, 401500295, 795508782, 109523558, 61633284, 434619539, 438516970, 992915766, 388568812, 267489593, 130757655, 186140258, 286667871, 952323471, 752237878, 935848017, 878307741, 109018889, 601394567, 563482529, 571999777, 322626077, 390909376, 846096402, 600190399, 735143653, 196835312, 233498935, 437596815, 178633224, 484556384, 144762194, 590861648, 46661593, 361771628, 602207099, 203561652, 150419743, 130284977, 564834683, 810698675, 476041763, 13636022, 355284560, 710289813, 536185256, 899216126, 609060768, 68988526, 497756395, 562852365, 947561840, 434860180, 748728941, 256552555, 476843760, 576388339, 79097457, 286291504, 943030870, 185050331, 225573288, 74761609, 934719307, 897073749, 496878800, 367622760, 884236366, 328496395, 919260032, 584022119, 469228965, 318167713, 181561505, 662284707, 429180824, 300203570, 771659821, 724977173, 787883979, 301894567, 585785234, 881804964, 274799149, 331230395, 307487166, 302843983, 846587780, 44447204, 202469318, 36206237, 511684632, 277516549, 307472079, 939080385, 225766701, 849930939, 311384788, 472394583, 527915803, 832195220, 200077877, 796096062, 516491784, 708719819, 342934450, 812498928, 526206335, 389347399, 148204903, 15454129, 984873711, 428957646, 512757933, 269747731, 606281997, 313802008, 855946928, 513112949, 683315728, 539858367, 91354308, 879165180, 340090554, 43228532, 708742219, 911530212, 149971695, 988428945, 131583109, 735401458, 365829087, 211828031, 421143619, 601238749, 476819781, 335582459, 671069547, 768184350, 989155159, 805870337, 388145753, 807171417, 642895230, 419971784, 167123588, 819677966, 111163060, 352757236, 858616860, 786441520, 563078389, 835716764, 876846931, 177740995, 328312724, 258150732, 999457331, 381137206, 773002559, 930941119, 33331064, 571808822, 860224325, 5169680, 44572311, 428506129, 715544445, 95366896, 760678428, 914902051, 822799281, 51839294, 270529588, 606751816, 358002938, 994201837, 661340921, 29504257, 82806294, 786556737, 687179247, 71880628, 860013534, 590758571, 478196158, 889139433, 607486470, 673083735, 792292981, 210148629, 871020208, 296988135, 233098230, 463974030, 202080817, 643689123, 681727633, 141195606, 249765139, 711030920, 417679139, 745849483, 492218423, 220908611, 613301584, 368211950, 314933825, 871266213, 968142539, 332040435, 334231192, 921237534, 378894771, 664142716, 229317303, 697854093, 774119586, 148802767, 382102830, 366670070, 789535873, 534122571, 309711560, 94011939, 589926549, 188834194, 115535191, 711162082, 555925720, 7002979, 204269970, 393755795, 83598919, 889087085, 231054541, 616367603, 332172663, 846354361, 762904132, 483978370, 388053245, 349375464, 120420667, 965019387, 992698407, 608212998, 123029673, 646705046, 700986443, 140089200, 608882686, 828866257, 839379649, 157327266, 652885627, 195294517, 720232077, 708097578, 835011664, 714642895, 774567496, 789382768, 691386834, 118687277, 875135935, 71172363, 894427614, 567968557, 652801945, 779084789, 757904635, 650130426, 923491064, 685599842, 569616529, 892586384, 941009696, 597647632, 224218049, 771556670, 840143713, 568434477, 427421857, 834610506, 109965859, 488724535, 527432403, 991424658, 466773105, 328668150, 243222109, 719929839, 304734422, 173288498, 984566971, 522176431, 466762075, 395098292, 593833827, 98854392, 276443183, 507344064, 675117556, 149691642, 37771841, 474639929, 220141075, 602080023, 457835165, 546781840, 674934648, 661852974, 75086349, 468540557, 965844612, 775126601, 771689260, 429699114, 371626800, 370841970, 525603562, 322408121, 690021656, 926277651, 792721379, 16272622, 35485842, 210387990, 898597928, 108645744, 2122338, 411426190, 82592546, 245267840, 315012850, 229946792, 35764774, 273148739, 814845359, 711749648, 175399244, 696448135, 341232351, 576764631, 473822515, 970752050, 335225912, 737781582, 382496644, 7594891, 705643247, 650504436, 253528048, 614337705, 143988244, 375320933, 776355647, 34118973, 409615468, 290052317, 747616370, 991319298, 77343623, 492351330, 889219555, 571052103, 264197346, 247410103, 653749837, 517908997, 644968678, 259191940, 779786323, 116813849, 645593174, 747223943, 669162150, 743898321, 373779841, 5589128, 485343360, 955151562, 19124982, 913191265, 959180333, 941395844, 57177975, 247733200, 348242644, 932809486, 220801027, 314342817, 849078913, 689837274, 828320817, 812512107, 935871982, 491117533, 705969573, 883338164, 191921328, 431054839, 955886323, 610036057, 733194257, 165461689, 636722801, 332074028, 465750804, 468435845, 281400399, 282961663, 746820271, 630074460, 917511048, 764910893, 421072816, 300235348, 552676462, 309288173, 699634446, 590918152, 684936405, 967946280, 967174568, 512619680, 99143832, 509732001, 183734492, 495372619, 691135819, 648986742, 531741064, 464867561, 714753942, 197139021, 535870931, 614757446, 869709312, 870406399, 67617404, 9532461, 665321242, 727950511, 416493618, 987460764, 267632368, 911455087, 676717286, 321418732, 11414781, 326943209, 721435123, 635384222, 349346928, 963909163, 60519145, 916205082, 370407446, 466782439, 574824633, 926709069, 740768506, 113442229, 7099927, 84276494, 840923872, 172624922, 191484246, 933722128, 592540553, 628852234, 354826023, 23853996, 489562495, 870293185, 57272384, 216692016, 496486622, 151222573, 56892477, 69034191, 541218678, 772923674, 887714933, 996255454, 489434690, 753229808, 153655952, 359026852, 372931952, 995642003, 462555795, 573333976, 97599821, 833230391, 155796415, 880422019, 498213570, 623747778, 10257600, 393879633, 133079599, 236923018, 16209432, 967195347, 884797525, 265378276, 873268277, 663377583, 491378097, 300579224, 550160857, 469099337, 83868101, 748082505, 49856278, 565885323, 290601848, 756941219, 576053152, 38689647, 753409730, 845067880, 737596433, 737716690, 326247243, 30917059, 663643978, 800967165, 655075700, 379185499, 396183545, 17045327, 443155730, 290198922, 174686966, 558767936, 100406785, 147259422, 778019993, 277061718, 226951249, 26011274, 15131696, 535899174, 195883282, 975962472, 784007110, 92945434, 523330577, 966222974, 611528047, 16453396, 162138411, 124157487, 304154289, 909044262, 856171425, 337183716, 98122241, 863543840, 531080568, 541100194, 246561842, 277479130, 135229144, 878675223, 189501363, 292224679, 54657174, 242082221, 922715502, 681909321, 409630571, 392113409, 402072938, 599517801, 943374964, 501999289, 272167844, 417319790, 165328261, 300527810, 844672458, 216509946, 141248846, 151663122, 150795969, 400378226, 204280555, 987794009, 56750015, 521960578, 664746724, 506197840, 613830596, 393932286, 440269670, 70201417, 160493840, 996595899, 275357254, 351930528, 486991418, 945286016, 549429112, 412112715, 555782806, 162316099, 296837100, 206012207, 25357440, 481480845, 151977343, 357652412, 248345190, 533804092, 722314689, 176960096, 982616939, 275331478, 797803913, 13590981, 104029170, 436774925, 589004145, 316468010, 461980739, 170244783, 981474134, 716620545, 277327619, 603363148, 355457043, 663178978, 981669626, 477396845, 241670793, 532933152, 574585592, 131785969, 311376382, 603434083, 481091976, 192072288, 99957937, 169751692, 712626952, 129418392, 307211730, 910058086, 845955868, 385565675, 46699667, 864248098, 551437871, 197447398, 966503550, 217043248, 413667088, 895134918, 656726631, 957185869, 951787169, 143911377, 905649549, 978293390, 238054220, 924931296, 594201964, 716282060, 77895784, 725070524, 159931695, 628579595, 469318889, 455314685, 12780779, 652005745, 831500225, 716871523, 568703431, 341115995, 612982744, 317635473, 480886618, 881743556, 987465115, 299557621, 166997973, 497051603, 517146577, 337993194, 263795916, 220726857, 954944514, 727356457, 160869937, 742894002, 484894289, 873105749, 264300683, 470101030, 828410616, 649834954, 131310764, 708815372, 340464412, 284525032, 948060390, 718750297, 608238287, 819121332, 690457673, 442092316, 311572830, 889430496, 605093391, 150639231, 458908945, 77062919, 160065624, 538556792, 425544731, 883991837, 497783498, 255807027, 311584357, 501770813, 269053359, 970462178, 726903766, 775357828, 36082331, 325059679, 182992512, 255348018, 696651389, 617717502, 346072263, 720856940, 562149168, 197332779, 402881934, 114039203, 678561105, 955531152, 846893828, 111671648, 833589533, 275772851, 561794370, 302337714, 75522716, 652442405, 759656840, 670438152, 875738200, 717154166, 88492204, 360820963, 731214487, 826149847, 60136248, 492581032, 48401069, 582886153, 746082421, 628459051, 301513073, 964931427, 943822349, 881602448, 471077261, 899039051, 537271100, 125285514, 364863463, 304738885, 810734949, 217525536, 622262443, 298060722, 255484731, 77270943, 903089531, 369231310, 76156529, 740081942, 414904814, 780670037, 347410204, 590085941, 111809332, 163678961, 762224814, 456650521, 512545263, 248460257, 924684394, 135093636, 305759105, 792431560, 297965023, 73160054, 60953215, 356429391, 838476535, 769244685, 819076971, 355140181, 989750865, 60697465, 238913001, 171875699, 715041701, 129116169, 914905188, 444205677, 538507012, 894534372, 726501558, 746750356, 463645596, 447093311, 955572002, 303904900, 820498411, 614198317, 299601807, 672475985, 178329893, 386898082, 507951567, 90565613, 408052189, 206031063, 735769477, 512330187, 658469434, 988204162, 360136538, 857806660, 8455218, 725382235, 423369085, 174745676, 391247427, 659798470, 481576274, 721609002, 696155145, 134764146, 543546156, 981562542, 112395501, 949402400, 675883947, 309908241, 212495333, 347638318, 441209541, 429208245, 810701423, 905161622, 338946563, 285410195, 177610725, 349822007, 384801457, 71583996, 679740398, 992348606, 624275578, 970495818, 202958244, 549899989, 355193618, 891539908, 380565576, 485567079, 786777132, 175571018, 350228502, 186642900, 670911587, 623604626, 35961283, 197941849, 444438724, 651175756, 365739718, 853779461, 15479468, 343423745, 408758931, 270847298, 115704228, 441298396, 856469504, 711561693, 754271585, 23230733, 603922514, 790928213, 172902891, 790489409, 288302827, 496632360, 127693902, 139212275, 856095775, 578240697, 830556423, 211371312, 216137333, 574601624, 643039625, 47447139, 451853615, 526473527, 324910681, 833191106, 940216557, 256952189, 438936023, 118832893, 866666735, 692895981, 202717367, 838461080, 793432999, 333566924, 142056040, 500648794, 394128810, 683669364, 625600654, 116238339, 250517781, 182900485, 427175538, 684114567, 54652850, 517991841, 208053068, 321004655, 869524981, 503126253, 15557551, 986350531, 172638625, 462310546, 692730350, 830874415, 538007466, 467568665, 688214734, 35635582, 910572150, 551848542, 737790899, 314129203, 848213256, 795562662, 890237924, 144281277, 959918406, 326788360, 516676508, 127183260, 129295268, 14861176, 849229381, 278317776, 588361935, 739228600, 458668599, 921049505, 89684662, 305769415, 952522839, 174783528, 108113333, 200231713, 752854707, 875611991, 562106566, 884732125, 84445640, 773011082, 311306365, 285960302, 243351270, 444429032, 612119425, 605613360, 148132650, 727859972, 775426506, 218757739, 965869805, 186283139, 265651912, 552284647, 531621238, 308091299, 285858091, 496561622, 356903067, 105598590, 834172098, 337784026, 184429501, 103680041, 260411022, 866912870, 268222471, 882691939, 885800129, 216761758, 720517285, 471827117, 503656485, 379784579, 193611947, 230617499, 393598069, 147872704, 47832212, 795154177, 334416484, 812608691, 880233927, 318271661, 389366914, 825446723, 846128679, 786364948, 146390401, 359052760, 658841513, 188786748, 193229739, 317841406, 397940755, 779133883, 433548372, 63169169, 68198992, 347732960, 895531743, 340262530, 883829645, 577687667, 809082901, 974856984, 147195649, 211503847, 964963305, 326018069, 666639000, 731789399, 402456596, 136500214, 866543620, 509551470, 382859698, 420308931, 65053306, 860155374, 587342532, 141352738, 85276281, 364810473, 943359649, 903331516, 664664903, 72762453, 233735741, 621234292, 889690254, 761570973, 351172749, 983178971, 687758375, 761151584, 197501459, 809638294, 326961600, 920557209, 292709367, 89133171, 857600178, 57601131, 846460825, 51023366, 655520080, 922782738, 399704722, 617942162, 960947717, 429122176, 97534186, 186054681, 343987988, 705646722, 309696483, 235932081, 493382332, 726182976, 318921176, 354494666, 738291736, 888761660, 697356338, 584807198, 266813260, 975682510, 866908729, 240093246, 859579902, 419350290, 723804590, 248681241, 815836032, 510995374, 531738829, 7294828, 708931767, 471288353, 275554581, 618558978, 816952183, 187278273, 749390099, 703631527, 604621831, 429506151, 154142891, 302263749, 611545796, 846996636, 43594794, 801839565, 921413438, 525828007, 122589475, 176277933, 903890452, 799404702, 308100551, 150631897, 305282410, 810160102, 19465048, 395391701, 311613343, 648529542, 629343567, 718329806, 559516352, 357111461, 274287963, 8396295, 725989407, 327415991, 190099864, 105927111, 377603136, 450288513, 133656877, 500766126, 851238139, 884020449, 325151013, 743169062, 902497773, 652079030, 668378518, 368995896, 386607899, 691214199, 346704290, 647945835, 161377006, 924157048, 474027284, 96591334, 459468867, 319762330, 829990219, 582794329, 720027533, 542448290, 712524913, 317718028, 409626144, 566929994, 154869526, 762725987, 114903451, 34519031, 230779239, 273692280, 500305727, 245412385, 946397573, 52926862, 178810396, 626767046, 179518163, 23796736, 111524030, 400570064, 179070689, 543990876, 844081156, 274898140, 973996279, 701255714, 277361320, 287179620, 782401892, 646999208, 110750671, 495036513, 537220560, 508259917, 70677560, 256037934, 159185267, 568087093, 885847818, 696253671, 304208261, 822676334, 317873669, 940468425, 994816474, 684051003, 67601297, 401219950, 261683736, 245892788, 782852866, 171908151, 951625960, 45067575, 174071999, 553856152, 524671144, 579325786, 76781989, 198115961, 754188767, 516706797, 433475716, 757620603, 121182807, 214891664, 783574129, 848486995, 776850156, 552864948, 702330954, 559557619, 349584080, 232934983, 604905862, 908307233, 357069126, 439021576, 785155835, 464802891, 947499991, 935236956, 921709856, 557576206, 459424110, 874578471, 538500711, 404985096, 961299571, 662645529, 187108129, 707013682, 564861756, 139054917, 254934715, 108146740, 332654662, 618218064, 326797180, 446502064, 635943360, 242264112, 624446528, 419804928, 657372576, 496590563, 487422112, 520487459, 65002759, 954926411, 420739264, 4629750, 307770915, 76050249, 178083942, 613797993, 905776840, 595481503, 403495519, 537391643, 196618850, 555136813, 623974333, 788305609, 156975859, 496600549, 696842923, 212423308, 186174568, 455889854, 824159707, 877694475, 87778188, 592755245, 325440794, 700036990, 34435983, 100302179, 445082027, 763969412, 647203902, 900999318, 780639300, 605114802, 679171390, 735548210, 732261499, 161093461, 686410673, 413103646, 728683711, 536976503, 381454765, 565448107, 718075155, 778796721, 637835073, 800609433, 452390068, 761330317, 312139148, 888760704, 678280849, 308320574, 49932207, 483223159, 588307426, 893664014, 517592341, 530807511, 285954986, 468545089, 689707523, 800292117, 772152244, 7990946, 891084183, 129210434, 951134505, 819426818, 500608988, 955321609, 514431922, 463864482, 629546791, 181577976, 271996530, 535077051, 229462337, 478501101, 345534216, 465204493, 583777110, 717878463, 292950875, 244663870, 768202612, 39017386, 321258634, 318946714, 180481276, 895538835, 397071999, 667920254, 411635159, 875946097, 747823292, 261573979, 323812523, 301870962, 556806316, 261836318, 208149186, 370451018, 319893586, 869934944, 481834746, 584462390, 425569080, 222748252, 198928317, 285395565, 229135683, 507914373, 351151814, 855402136, 691906968, 426792279, 384295637, 815344288, 299476620, 621787210, 72688715, 573638719, 118159492, 813317062, 994846028, 4518752, 798829121, 765741657, 16192504, 602114207, 216799126, 958166645, 31378869, 959813391, 38799008, 555998006, 497116372, 27872651, 800158934, 667857678, 982254864, 635789645, 168248783, 417541716, 121571114, 124069427, 436448702, 714468125, 695824381, 238411132, 362919883, 845521108, 642908282, 369896308, 795794078, 600607153, 170322601, 37316977, 499898838, 926569982, 990917842, 469875189, 104152639, 99860091, 279168211, 935503027, 368338079, 330131944, 475639669, 948780662, 847346418, 579235732, 124880009, 530392900, 795897982, 768824022, 954123240, 462406279, 924424797, 271196728, 503132798, 112346724, 118022598, 203211167, 307096610, 570181950, 614159128, 867605898, 410742420, 314167217, 361318670, 899673072, 398413446, 822289399, 225042271, 111860077, 898337153, 39966731, 945479122, 660408043, 845059975, 143399043, 806008074, 413451096, 414416193, 882411200, 16467106, 790011171, 226695776, 725643439, 40797494, 150773881, 983952594, 604341536, 730296585, 462680154, 251211854, 290187860, 799818218, 906571088, 254653050, 675372550, 22801816, 126530220, 14992927, 112264564, 197089011, 172244655, 614451555, 768365014, 910822113, 992760204, 129105921, 430226591, 897497459, 931249745, 396653738, 422624723, 984091384, 987436359, 341613038, 580252753, 783511148, 757908942, 978700651, 927146214, 584752419, 673605257, 657736746, 324743661, 976406808, 359282989, 427280636, 179512188, 909630560, 754288656, 188828236, 606197728, 758084015, 663095475, 934501590, 927520701, 900522789, 330291429, 503860088, 399510835, 307728662, 173252641, 190927166, 533564841, 701766501, 844110625, 148396215, 861656275, 661961990, 64951157, 991494201, 233129004, 193781672, 968119667, 875042747, 617016784, 480017654, 478798824, 141272492, 745543379, 69825142, 415018371, 381816417, 368776100, 159288793, 888985412, 25290786, 209986561, 574212323, 959608734, 995090267, 818328775, 673706716, 658366558, 758679706, 458933821, 461397169, 972451593, 761393454, 916773126, 220517251, 225025006, 283461914, 555531728, 809655698, 508845674, 429550590, 427426595, 945744151, 593790337, 188549867, 476709000, 51051831, 798837119, 572177077, 925240360, 335418319, 131390798, 99192267, 758080151, 207985688, 563466124, 131095658, 342935963, 978176437, 470369552, 299131973, 801073091, 776822740, 456306989, 628620799, 820493540, 787041232, 6243147, 234409988, 950735830, 628679782, 469878802, 72828184, 641006927, 145431804, 602398804, 998999125, 458603689, 337191743, 208454223, 425335525, 486375173, 989392470, 528634601, 194727811, 448152245, 946919045, 757048922, 521692152, 338281894, 892459725, 424895829, 333941973, 473741293, 247440605, 40670577, 692498579, 18670188, 653396756, 423016873, 801403100, 956227446, 636510628, 768939005, 278377353, 716953529, 191407110, 91905230, 172073469, 347664546, 272555482, 753808787, 451551423, 832087710, 443615580, 520424033, 776052281, 607462583, 724575925, 317633901, 812609719, 2123362, 27338353, 536282733, 556556246, 793860415, 71892544, 408921483, 490926112, 290977205, 139922581, 942851221, 485979213, 425565270, 498526273, 477252590, 735288530, 320511031, 643534400, 948761843, 6062060, 338082334, 253569001, 69953406, 746691762, 155047173, 633969955, 867499129, 75974374, 664091355, 343328002, 829788132, 127356930, 945528225, 930054458, 189130372, 69641007, 633813815, 372877113, 422463142, 159493494, 662290207, 582961340, 259523895, 265534659, 947062497, 39193004, 169607885, 798633839, 572503040, 59268612, 83391474, 879046339, 214542828, 501727947, 59607806, 840194374, 793431503, 507318085, 536940569, 615228298, 813658951, 711058619, 678188919, 996405125, 537014986, 864962841, 865219172, 926127086, 351716147, 5532763, 599119923, 104044892, 863462685, 59128067, 650009465, 469558120, 730585965, 826619064, 125531271, 508194600, 629206389, 93682068, 929897225, 503854469, 694922612, 723810797, 504102898, 457409913, 875128004, 886435398, 994570782, 547788137, 544245401, 792116850, 934845653, 224117300, 409765727, 232696031, 970537147, 885716035, 257918310, 21766258, 440238376, 585103, 175180772, 961001575, 217336654, 750104600, 663067202, 593124946, 702360918, 205878464, 675604149, 624848659, 37621198, 353523419, 44604915, 414411983, 822466911, 284229964, 693200442, 201085636, 66652553, 678600220, 857513784, 265681564, 2634919, 830262353, 419942391, 518243928, 973816995, 508762293, 915895590, 955592045, 647055065, 397133921, 18404091, 318704917, 234618765, 414279541, 338562826, 172562464, 751637284, 404663270, 411900230, 697542074, 500432460, 446304358, 843049679, 127682874, 688213872, 718669293, 573669660, 139164543, 940154519, 711262562, 359787702, 281862412, 171028332, 513025326, 680936782, 5840703, 540144934, 205943106, 875660770, 966797941, 140616484, 363784210, 692978019, 746911363, 973865916, 21801190, 437893652, 171042937, 304330193, 120141866, 312031003, 604213879, 186753555, 443861318, 260166074, 878561332, 378505876, 545709446, 526078568, 542512918, 764011468, 740588089, 127430507, 748464746, 128475758, 628497294, 567766730, 763651187, 520372201, 918350055, 122606408, 996516682, 343718057, 243224024, 530779607, 816268678, 155627972, 469029077, 590312590, 955278863, 464546808, 750730596, 981183498, 372919482, 178917821, 983361403, 669249557, 530656676, 542347487, 300382153, 640703376, 862693477, 915807583, 754319238, 667931297, 277695713, 567509215, 304775440, 156804645, 748620999, 96842103, 395624317, 877820303, 352429059, 963328853, 596971381, 334477253, 542714249, 149069517, 18922218, 725596522, 195552591, 77586151, 574212434, 487673267, 400189355, 602993115, 42068555, 333323319, 724609620, 92001005, 849146586, 912888814, 117718205, 418477790, 916351977, 860568965, 989748234, 588527144, 762189401, 662701463, 395672053, 301918579, 566820522, 148782127, 72278525, 330759668, 846810129, 842230373, 97869517, 593999050, 761648581, 94611834, 747092268, 369346441, 367912108, 329416244, 247606616, 616608785, 325832252, 349374731, 991740801, 842111329, 662880403, 623283953, 92052232, 27096275, 727899619, 173471258, 42210095, 393821421, 437672781, 975131583, 170427152, 126579046, 974766557, 846276687, 776250462, 577975466, 86805397, 147274409, 661951435, 920700474, 185920969, 881524519, 232349359, 32094884, 629279004, 724170033, 321859424, 561341086, 832264344, 941690320, 884457614, 215014820, 48778200, 38317258, 430264388, 247498361, 660811849, 731699823, 468608115, 122680988, 996623292, 448138703, 921259446, 170588224, 426518798, 740754664, 146092905, 774532843, 999598186, 228862194, 728701430, 709041649, 451448124, 12673110, 398077222, 10145558, 574000842, 307962802, 164633735, 674594144, 737643842, 483477931, 89231851, 419530854, 945206210, 810942446, 227845366, 279357143, 85522573, 672232296, 273864431, 582784037, 458572422, 230471286, 842313932, 492004802, 84349535, 688251683, 75533206, 221111379, 392875447, 960730521, 904367201, 31061810, 163296581, 950873878, 725153848, 34762116, 671222165, 421995968, 849169075, 618703, 186087838, 20310161, 922578010, 566849685, 706955468, 502341830, 423849812, 117956418, 812811910, 977188191, 490623796, 896035879, 953758371, 20300728, 492115445, 143626011, 523202449, 501639598, 780326204, 657805533, 136989631, 68057135, 709013701, 497984592, 291850040, 874372123, 758688953, 421531785, 932379707, 139446219, 734803972, 968566756, 556417757, 5463962, 46411771, 341517340, 989855559, 399889963, 12508339, 455826521, 95298546, 345834111, 595281212, 334367367, 863876879, 991293576, 879939102, 976284344, 327078879, 641312125, 302125856, 634283529, 687025996, 577241716, 686084243, 408475343, 883194009, 457590867, 712527060, 776312645, 371182687, 655550945, 904302794, 848856568, 177566205, 452421150, 792891423, 502564371, 12889411, 672824632, 536746953, 948121097, 456829368, 63791442, 288392371, 965655874, 289551684, 807489352, 638193304, 833786542, 88939464, 499826737, 382636595, 267970667, 728557945, 387542058, 251870225, 366082874, 364439185, 609281689, 995299790, 879469353, 750492966, 851180596, 800537934, 438221990, 702619853, 769710889, 543253597, 481424686, 904952991, 397822114, 654196327, 609656351, 618809948, 92345007, 996960062, 430542233, 274110731, 443261276, 78953965, 521766202, 449397073, 908735073, 150108952, 884455242, 678736953, 47316804, 372658521, 431370285, 362278592, 426954851, 216869521, 404442097, 467814045, 591484208, 758169339, 745515792, 545531735, 409355490, 547694681, 363879947, 857024914, 839823687, 577714911, 602666929, 789701545, 662097372, 590304211, 488943070, 782049498, 930522465, 528568704, 591409651, 374185178, 854180997, 896823216, 262625983, 468893523, 303729596, 559170176, 490341118, 163740787, 372403262, 793491979, 139993592, 918225282, 756453821, 815732063, 909032269, 25113064, 891333392, 159127127, 1166393, 840245859, 414020533, 872426908, 141314563, 599041324, 180593413, 550974040, 136434290, 347624591, 865955613, 576917179, 694539698, 767459286, 630089274, 840961655, 467525953, 311803922, 641187733, 894988761, 981966925, 692981462, 528350338, 511788360, 686673388, 496634318, 772298426, 956085350, 235110236, 927824853, 313660530, 545523335, 369114990, 747756670, 189413897, 449317398, 573911904, 279377462, 473420217, 643309154, 414783725, 164413347, 766472341, 375564352, 3070629, 783875228, 409896611, 620724521, 717720069, 105232794, 152674724, 497805196, 524588767, 464225067, 970217473, 27051937, 829336033, 530677974, 77942200, 200871418, 918048605, 116441112, 842100203, 682209119, 796679807, 551970413, 292813998, 496884177, 228168826, 9002, 383761188, 513332114, 913591088, 356842389, 455309386, 887256484, 148048177, 184943520, 141366146, 761916048, 721320700, 461241056, 243950689, 627919217, 496343154, 444789023, 445794174, 311082572, 730964663, 577240561, 557284531, 347120217, 572751935, 4921833, 550731064, 221923920, 496648484, 87553845, 385255773, 356147595, 272202509, 780854366, 618502161, 39069566, 448268177, 829110970, 812097036, 753466775, 109630295, 798328618, 303059905, 239205094, 284656879, 249367507, 608231062, 195847211, 781017573, 253165658, 364562267, 623126018, 895615591, 487970847, 697707141, 170265960, 885068400, 893254717, 559726357, 1625722, 191849768, 86403235, 944948865, 711287377, 509372874, 185075115, 263250385, 754380540, 744979383, 48338350, 477748441, 74163673, 554244567, 744001177, 491204009, 499167714, 275080218, 42811197, 127401543, 291964823, 435802911, 185924818, 851621651, 731399711, 90274020, 51651798, 942737439, 681779844, 500067834, 997289118, 808878014, 720550440, 407688098, 90088994, 239063903, 872579987, 349566142, 658303479, 966234619, 597640461, 543582196, 465551875, 339429028, 976633173, 939276382, 803128839, 363687141, 302126418, 215903652, 523858361, 456141849, 462360439, 270365611, 902323608, 445521165, 149947423, 487001555, 685945721, 806614383, 145709319, 736237874, 23114099, 271897495, 190128443, 727457086, 555390860, 121482675, 533558919, 952750520, 469122751, 934969770, 491308568, 705394374, 892220170, 108141040, 294173749, 901700058, 871271319, 824412339, 337978955, 24394837, 753634970, 152819050, 845039934, 807180174, 323303595, 504170844, 543650945, 270297895, 193028536, 372658885, 195277657, 205676421, 458111431, 771677452, 577712004, 49159036, 460373024, 719279543, 798868864, 146605061, 822525096, 14472305, 822619403, 563945019, 346501367, 601868326, 553246801, 639400837, 640347548, 442234200, 466561620, 150968772, 955125415, 622490706, 676473055, 303332390, 293535747, 933557448, 599965471, 211034719, 75069761, 699038114, 832590975, 452150111, 853147935, 992377657, 700993901, 307082110, 544751495, 716508988, 419366757, 682063811, 371970282, 175535122, 874395662, 17655787, 832206554, 78031515, 964041370, 142723098, 699620165, 544828487, 486760567, 893112412, 225584953, 284461527, 522313086, 615269937, 20352993, 998736261, 856470927, 64219025, 732735432, 642080958, 640073139, 317465248, 221688300, 469219361, 957972089, 85933514, 309735718, 911102816, 919907858, 115070615, 31178058, 809167645, 361874744, 716383781, 480809679, 386923615, 702025629, 167320151, 310824358, 996494116, 383543104, 546923513, 266944815, 290868920, 517845663, 479200236, 401992149, 110210030, 552607676, 416810290, 722059195, 787209513, 454211899, 319759993, 674575966, 25092225, 87974530, 655701461, 593224292, 258675015, 209081994, 894771806, 87051924, 290039463, 507171741, 352715725, 159428593, 186398754, 495212279, 779470533, 300707805, 234460664, 727204214, 130037421, 882959932, 758321565, 630000930, 826034847, 100529471, 629418312, 572432275, 440918324, 539272300, 331939506, 501178961, 745971046, 942123480, 747654398, 252648179, 902643569, 308451146, 961635599, 117343205, 337324300, 259762997, 772600192, 153682409, 880015690, 893690754, 95232546, 266759478, 176918940, 246275248, 658271850, 186293453, 705672649, 263683978, 626051807, 467188187, 755849838, 902633748, 284720267, 119406929, 589176202, 565836626, 169210125, 914694063, 27087277, 904342663, 896243485, 392325398, 869953005, 540760968, 783881365, 862921147, 683359121, 962570141, 993364908, 536976461, 218326330, 557688875, 748497088, 743017227, 49996398, 990968603, 182370275, 594366378, 331019805, 428954271, 981533720, 998669756, 324620898, 422336972, 257057593, 205141622, 823122865, 956147916, 560168918, 473936456, 904993326, 488784121, 301860067, 625218397, 962960254, 72667017, 494867512, 643134705, 908909256, 843385977, 376213047, 820918674, 155902114, 340807960, 113102222, 523850777, 920655438, 574264621, 721748374, 716844176, 457106805, 549174571, 586595665, 260751247, 99869410, 64967688, 170386860, 945605958, 2915646, 738266814, 496235126, 660365807, 797254075, 247375808, 83189665, 515785932, 742330380, 854999632, 931217773, 106218651, 51171932, 79122323, 34616279, 778602816, 38340453, 848723342, 907765499, 426598038, 818669292, 437852841, 641524398, 618285238, 382443397, 509513851, 447373631, 85109722, 213516420, 287187410, 771249058, 656683894, 552769153, 411178129, 170283963, 236503713, 811999692, 293138810, 848704297, 571967652, 225851700, 789302443, 278377369, 55089922, 524984109, 427848608, 490227808, 128866594, 769035968, 930770487, 257675443, 298729820, 350534085, 295903782, 117467621, 873468370, 900277207, 357735603, 672529134, 918404338, 67333850, 911697447, 837324141, 32987125, 477107079, 872857954, 728787683, 602294721, 241923443, 852271160, 279305574, 61326840, 811129267, 246988302, 92847434, 407860813, 283304568, 113096657, 359089795, 896667524, 50395879, 120164435, 785671334, 720469839, 29754442, 750142462, 118461623, 221555599, 51579543, 553279296, 864881889, 857743765, 811495702, 115036409, 721050568, 632058297, 248472613, 248313994, 556099364, 675399271, 733738264, 650146153, 823912111, 544669965, 78239247, 94364951, 888401524, 123996681, 558421372, 604797640, 795804512, 454745770, 87281718, 713762860, 128151714, 307660553, 761349882, 686412703, 25200201, 57527945, 66281162, 127406537, 164259536, 407793240, 805317675, 874195984, 599920498, 230744498, 150849751, 46962750, 785895519, 223072980, 502484905, 871896324, 25570927, 90644733, 550595474, 331869624, 362997251, 626292815, 796979405, 253724420, 175250430, 236373374, 939118812, 783385614, 617935164, 345998203, 675008799, 879167502, 207307221, 341267643, 474317959, 484214276, 677276874, 214765600, 162189579, 666508096, 288176750, 951645052, 248768513, 290891530, 912639250, 117183593, 964139787, 330721584, 107568697, 79586558, 177305256, 492490449, 82667534, 879083243, 235588250, 348038932, 109488160, 676706706, 377998612, 564634646, 567730182, 239885339, 642627798, 866781427, 452001806, 416563953, 123510513, 212551691, 382351088, 842106733, 551745212, 177421195, 555406372, 798234763, 663878793, 620921762, 795864421, 880032894, 44381369, 19975347, 121616413, 758251504, 172223215, 389952527, 409879132, 887986114, 505659008, 721058070, 42418411, 736869077, 755403688, 970632666, 906530692, 398649991, 39768877, 21591863, 314430225, 950596894, 584739521, 293754949, 566589556, 863419433, 98086370, 410910778, 674511838, 557950069, 153171618, 451214835, 946172638, 483605291, 941441799, 830668948, 381506259, 550538814, 934551268, 95435329, 344808081, 14397811, 631152940, 281594650, 761716086, 617646974, 474524945, 131168378, 418869157, 804522082, 548804490, 59483564, 696576852, 288068411, 827821, 340371111, 103482864, 652972291, 211771275, 828376763, 284256111, 270964189, 173489491, 956489270, 481662032, 579351483, 26499681, 749038880, 734188304, 551072551, 923958103, 487405309, 598958747, 313354043, 442854807, 348805306, 408244560, 940915858, 557713163, 735365586, 802402329, 693450653, 435181457, 192256430, 243158623, 923696962, 539951334, 751580904, 879217608, 148859772, 928162926, 348487723, 453346500, 265954316, 153692291, 586855476, 873795937, 315595392, 683110827, 150406926, 68609308, 859989796, 36062431, 118016838, 516267916, 751436649, 531973380, 708293748, 862623012, 687119256, 299060494, 665064111, 449743174, 384920207, 210687345, 279685575, 632824075, 981323839, 736849445, 929213759, 931124089, 627625020, 504334589, 663535492, 332513200, 90241144, 348938537, 936694387, 469595529, 589409476, 611533102, 177047815, 259418737, 206915403, 788703518, 237631503, 328527492, 332886237, 208258966, 475568666, 367149003, 47280511, 745508534, 395204189, 301858471, 74941891, 609374951, 640516019, 804974838, 944011773, 977949257, 867863831, 662435172, 25002908, 984433969, 651171458, 680042261, 308491114, 792304972, 877840026, 212163272, 624573832, 225444674, 736834575, 297592630, 163249895, 866801280, 673600643, 668149643, 730097564, 870604351, 23028511, 326701115, 801693710, 620185204, 598629248, 510299550, 773077218, 292294698, 825415848, 42952968, 464518246, 221993879, 845045871, 864108824, 917410073, 890221131, 376969467, 587603135, 548146119, 492748216, 227484187, 925724008, 264203574, 119367923, 409642187, 920034397, 224044508, 75103657, 528504116, 263007961, 244760518, 31060442, 602872839, 101544490, 220737007, 534642351, 507584900, 545711974, 951619010, 450732023, 736293985, 497186547, 693795481, 388597647, 541993474, 593172412, 424481725, 986986960, 813723136, 317811654, 390089347, 424312192, 18389420, 414751865, 247872031, 472378444, 30106405, 819092800, 877672426, 271152285, 244873466, 193675075, 39504709, 93020264, 784813255, 184003574, 99171110, 871377247, 97535070, 197769064, 182091377, 255486331, 911247066, 604820161, 794209216, 566617041, 267105416, 632208258, 742913615, 500593146, 923435524, 344462488, 231510265, 927884456, 318340821, 929581859, 911201998, 101374620, 816488781, 665631462, 807052637, 514143740, 252741212, 305621260, 123191259, 593027293, 256806244, 978128865, 450506218, 217473858, 148133862, 857385816, 80227371, 333614925, 237986514, 66555395, 718029246, 929257101, 960731843, 195024002, 78777010, 27156837, 263930958, 795576591, 152669485, 889684631, 244638891, 882639335, 735806932, 11033883, 965668168, 664779084, 663144957, 939821228, 774831927, 195862315, 134770606, 386001729, 520388848, 432356118, 845307934, 45372364, 951010539, 883740350, 372678819, 664683921, 521944839, 391306128, 495706584, 122410736, 644112771, 352965300, 530056459, 895717333, 30398820, 873301074, 38023842, 142393430, 343086050, 616339272, 571334809, 289408906, 715675417, 448462735, 835320769, 600065195, 575101960, 42833064, 686249313, 779688248, 538476535, 904065507, 392193762, 147147345, 432617469, 166349766, 182705766, 250858257, 299181802, 959034232, 829440998, 758451243, 871743259, 10849845, 452580721, 61893308, 314831240, 187476990, 846325599, 455236546, 900354678, 269408184, 205083881, 430817783, 897442298, 453784565, 518856868, 992136493, 101334000, 873190966, 842794440, 400867773, 5870275, 588661789, 647339774, 198368833, 349757968, 218523480, 317276918, 747191122, 80812693, 448932261, 624440051, 555441369, 871777857, 275975199, 486710100, 184894478, 384705526, 674821004, 280145306, 380622836, 159627859, 627988039, 993095061, 291873488, 603066658, 19536019, 513529811, 366756216, 675738536, 275170660, 411885395, 783072420, 869117975, 345758753, 78848921, 391406991, 743639241, 806275253, 315789899, 555545216, 50029190, 648113469, 990213328, 824624122, 205898194, 729176262, 364827422, 125990223, 66120001, 493114454, 492924446, 976085250, 307121221, 286131962, 150916213, 857668228, 161612510, 559565295, 627754256, 523021692, 816618358, 30675506, 848101652, 892865662, 266124541, 415019035, 678471210, 382967344, 561809370, 635014401, 495741783, 395643318, 431852287, 342919530, 868841626, 78921080, 710226696, 736474807, 803945855, 498045042, 264103921, 249753894, 495180175, 818507572, 239823810, 716317451, 985980127, 823226831, 275432655, 234899543, 870663309, 291961274, 657162898, 597432744, 939756506, 172567516, 165107711, 914749612, 318224819, 821136643, 70992016, 125809735, 390877847, 827364090, 209216292, 941318369, 639694675, 104425881, 968045102, 31689536, 646918343, 326568365, 176738539, 192650295, 890113478, 89256854, 125684452, 443303487, 368970322, 245477783, 205143903, 74634896, 646143854, 2313269, 852169294, 999624965, 194020037, 258517926, 539669781, 611579159, 923623707, 326491279, 381823261, 244952588, 787701204, 756990093, 440642180, 26146631, 580141655, 746429499, 273932111, 309739984, 135288941, 921548395, 696019574, 923068893, 565289436, 5920449, 388136116, 171002567, 609108149, 241582811, 654088587, 716767179, 698877526, 114555046, 511440154, 345824280, 195657750, 80400500, 552373333, 585575265, 743185539, 966720440, 351599822, 563929045, 781918842, 83976513, 286092446, 410334549, 452153750, 687366019, 388848442, 623507801, 852834266, 949531581, 389347394, 783691325, 170384420, 783851466, 422966893, 742529629, 537249372, 616935711, 49807692, 713369949, 974385793, 834813126, 908231872, 350741531, 897258593, 136111780, 853347563, 185165477, 246499107, 950203405, 743912083, 455451075, 97756295, 306848189, 912915684, 708212232, 772775890, 240863921, 910278623, 444241, 405928325, 459886060, 702490861, 982653969, 935919093, 135561545, 19196304, 127255552, 435110386, 387326281, 506738300, 847324585, 628323197, 967475008, 82057568, 267379329, 563167247, 287977126, 11613202, 993563246, 228170723, 3711614, 319651328, 311041799, 461831748, 827941228, 951926315, 148951144, 59499195, 935991822, 998558186, 611420172, 142660744, 858160176, 410204174, 912614255, 244974856, 263087375, 791283669, 290751547, 290256008, 612636638, 14574967, 465706520, 35371889, 768776531, 114109610, 27023131, 198720726, 382283197, 681405322, 495233533, 504317482, 704287780, 265180206, 580582765, 138240277, 166318033, 653198184, 53161715, 523108395, 838164081, 205309029, 661017815, 186327553, 300528245, 474952187, 557111666, 412869369, 166301947, 20805975, 405056961, 984326663, 516814594, 416390658, 729392748, 830105295, 862393823, 621788606, 816913911, 105497473, 746538819, 285026806, 797661511, 385559853, 467829901, 870646227, 966371443, 767744801, 604633064, 176233498, 154321858, 618618471, 700729818, 969847607, 559688108, 6069540, 115779919, 109662183, 685458938, 215932132, 545641585, 750887340, 214319895, 388611284, 208218483, 999982131, 449627664, 232593753, 397664975, 832447820, 990271980, 959119301, 199131798, 860953254, 956574771, 25773477, 340952798, 290281031, 553615917, 544178837, 734243137, 907080184, 183151985, 484230941, 409862441, 808129224, 266806365, 126943207, 106532225, 909321473, 115804095, 144284677, 461509902, 822557857, 182311579, 601501455, 305693427, 546667162, 682103742, 985944518, 202447347, 250501979, 972550162, 595316537, 35104362, 102217869, 57015151, 782382350, 384962670, 166246264, 360333362, 360632586, 642827928, 347503719, 707600067, 428209044, 128313657, 829500081, 884739430, 165902203, 926591539, 128760563, 916743667, 682508992, 935821757, 447237097, 77623459, 718018189, 401286300, 50749631, 769777622, 819247412, 902311276, 822365049, 694569300, 143008467, 753957160, 669854591, 990520841, 358732310, 82830351, 76306150, 478470292, 614483473, 874270888, 614797745, 312998575, 986278631, 344102598, 284509359, 154158302, 686234744, 703432404, 987715323, 137777378, 31225042, 471454937, 861124055, 317804670, 301241975, 114382669, 275869364, 438941008, 345893624, 650238664, 497107673, 790491995, 103824822, 329367215, 528080265, 626811197, 622346995, 410841461, 242413217, 907946963, 533779989, 709946650, 993907011, 293454115, 708188369, 38302016, 857462812, 382189423, 422745415, 527266187, 560751020, 310123056, 266605567, 381652587, 871364642, 488871430, 389085493, 36291785, 525559348, 388277587, 31889009, 220485010, 721327090, 327012956, 651808614, 927451193, 392183692, 58607752, 23613589, 235424435, 340377563, 962293871, 931624124, 933914858, 571934780, 391841281, 995700919, 344630468, 149978509, 127372469, 276832381, 595843366, 131659518, 995121456, 471238989, 221462727, 706356188, 485105361, 645433543, 462250243, 339317158, 908569807, 663474848, 957897853, 237389024, 371842692, 704416310, 416578563, 832709593, 930066582, 51288805, 924215645, 422345248, 3068943, 106239383, 661595305, 16475489, 12921008, 408969709, 843240842, 691359896, 44046765, 187721156, 262012672, 246085476, 656443535, 588202743, 79503016, 150921774, 733834081, 265900360, 64601423, 133592104, 170405818, 985270691, 590777625, 684593968, 426813443, 575367758, 220901308, 772561085, 397897571, 384822983, 687763354, 282623928, 407409243, 15173252, 927797836, 72629927, 790025466, 637023786, 219575020, 628969976, 271645179, 682266456, 900699959, 69378091, 41681673, 339585563, 261099743, 724910607, 203374654, 64827993, 201085634, 833977908, 208990193, 351985728, 368863205, 217621627, 369282667, 540015136, 148027243, 234635117, 175968244, 701711659, 52917361, 268173190, 562401159, 47631761, 543877061, 110339088, 248356027, 979588027, 270475586, 664897175, 947840869, 641175256, 88020873, 15813981, 602014817, 490617635, 263512432, 51079302, 968580420, 155274822, 147684866, 277304896, 620888505, 304877134, 715973390, 764233623, 759539863, 366174595, 534907434, 851886977, 491226509, 286490658, 685119428, 917273914, 968581542, 778598134, 578403709, 815114056, 352762447, 824384865, 700384250, 111756178, 437965590, 117972775, 264516547, 389747933, 180598028, 443228745, 30354006, 802016089, 436494137, 825568300, 659106260, 408233127, 976477357, 456329418, 510968540, 248019834, 501351006, 162397500, 963292711, 61945607, 402886570, 214503111, 916931425, 378354174, 785008377, 568250709, 973455278, 277150506, 778158299, 999145362, 817793615, 686503534, 655364057, 375948474, 348623360, 61417618, 529282367, 235162711, 899204330, 449696083, 303446738, 925205970, 490479981, 838580420, 719897783, 17591268, 234719133, 178861737, 445342137, 904421055, 536104414, 656484906, 681037550, 227970722, 526412622, 449277937, 36085994, 439244001, 109821134, 994150499, 509872584, 119823672, 326963936, 52732917, 431748140, 321905514, 137809379, 645878746, 519534654, 897586530, 707315307, 23776677, 412800467, 475513538, 861054591, 942787348, 597970241, 134146543, 298454400, 886112739, 518850354, 152536848, 356487057, 392083231, 58215072, 408898878, 346874228, 500795789, 716379264, 79741940, 978178023, 243965288, 900635733, 382506510, 844085181, 268124695, 666886043, 548495813, 360254306, 47998703, 382850456, 554610249, 384569646, 27794740, 577279012, 550944737, 266734548, 801850761, 673172805, 326343749, 45856294, 786988732, 272126137, 349845080, 399011056, 747487824, 317072123, 405467994, 232942155, 483908011, 610576462, 258722770, 162344529, 708808867, 357302648, 823480786, 599123050, 179478503, 695854423, 647959013, 474585868, 568267149, 15797705, 851308527, 643738530, 169189291, 112365917, 825403954, 169657891, 816145596, 94223817, 998921609, 186490579, 689834965, 533798040, 736980973, 417861317, 65814282, 767603947, 129900067, 778296804, 917936420, 594094937, 400020488, 472540212, 431642718, 733861173, 587926658, 983615765, 625790395, 6405753, 852823918, 195734144, 925620283, 86933551, 916292888, 412415225, 838870777, 894847173, 781993892, 543869157, 172585867, 847897073, 194801793, 582377752, 1609793, 376446338, 802963627, 985009524, 866191905, 114843858, 568126239, 863709467, 378393874, 64604884, 519480530, 649266676, 964448947, 218955192, 3129725, 993762963, 370576823, 872937030, 627463598, 884820605, 911788997, 44147335, 965346069, 262207674, 919390586, 272444205, 367627476, 322344725, 512978915, 749085510, 881623431, 410050626, 720326991, 319039700, 672911448, 493339595, 138142653, 87582784, 931069442, 591296875, 351329834, 483860229, 308912961, 65038711, 182518278, 284098738, 362543550, 87699277, 37426830, 424173221, 122593672, 249305782, 53003257, 586454737, 745527100, 335483646, 396998387, 330533795, 176428988, 118896331, 710582452, 671489129, 57846998, 443640433, 923675813, 298171528, 831373905, 226399210, 591702844, 528903128, 757837089, 473443828, 816231013, 398391536, 316283100, 26385697, 518706341, 261783009, 159545207, 102441409, 420844610, 315642074, 123608202, 675484341, 963234415, 456268539, 495792823, 979018725, 731237640, 506657551, 566942489, 157008177, 259284106, 808091446, 168196143, 218060779, 346755943, 273790584, 864232653, 121874096, 204963873, 721436257, 541829714, 355999115, 839041842, 69002561, 871330038, 703316259, 899460867, 746880000, 443930531, 196428636, 943431923, 759496263, 969009680, 19940848, 853952590, 29075341, 853115720, 316810362, 273633078, 711380037, 842934275, 746814529, 726074735, 847695905, 123424555, 907086748, 340653784, 729397221, 887657472, 150518156, 762192886, 946263030, 468666973, 405780857, 300701116, 939723287, 683643266, 793762994, 496025935, 296850116, 821888180, 357667239, 519174949, 835465593, 535532581, 589542288, 157026342, 357063226, 799061860, 667083480, 863663799, 538760595, 153632530, 509838929, 835599105, 412745801, 828907032, 27545674, 932074494, 275087641, 439576775, 894662930, 658943279, 523329967, 209554010, 80558055, 402361577, 224600465, 710064427, 356502077, 630117178, 371652380, 861881399, 442633776, 61120851, 536485084, 158072531, 704828727, 649541888, 703986629, 802663209, 909471264, 160265643, 122035306, 260657388, 427004404, 569383247, 980222219, 345387609, 817561999, 224425902, 326373409, 520580041, 626185341, 252298501, 30205640, 112114095, 96744032, 522983605, 694971737, 58426113, 276967103, 808167946, 808975816, 583173934, 277497371, 561054644, 314912706, 520128355, 995192265, 776829028, 942182012, 709700489, 113328378, 594587973, 101463065, 61939557, 987707728, 868342533, 269225513, 974314092, 577343361, 433281548, 340354381, 906429776, 141160947, 752625782, 656674117, 153678124, 480068883, 482815544, 984388946, 487125484, 781614926, 81117549, 816622588, 101545424, 789973057, 507287449, 76983201, 149538976, 51809920, 729733734, 197213790, 637229128, 305041585, 883775641, 824513531, 289992210, 593015712, 197137827, 979680691, 892964752, 177206371, 117958025, 878750624, 21193918, 608595484, 828901742, 33210012, 434216237, 628480786, 802680611, 691861473, 777564316, 975260603, 806834058, 725357479, 993287975, 627974974, 528040199, 729207799, 572045275, 302450099, 574307121, 495256212, 792491683, 387195438, 396443654, 295858218, 777331467, 143294264, 264556938, 639097429, 445789422, 501192593, 153159498, 444967170, 548441918, 777624732, 821313259, 88891623, 987712510, 890816313, 422516989, 150105376, 444858090, 273700106, 11747370, 94212506, 594771269, 594707124, 593449384, 572518008, 353985124, 955414452, 209203546, 465723106, 977811415, 494478407, 887746154, 474175724, 563100928, 942512059, 305257230, 313027567, 461757553, 352811419, 64077880, 139593834, 847364679, 176525770, 353474902, 149647468, 870478878, 382862288, 728969408, 613611041, 779588692, 773141396, 283044674, 306179080, 484024241, 813700969, 471705700, 497562701, 342138707, 937403561, 311123652, 66724132, 800743653, 859116764, 843676270, 875944567, 194070815, 538764726, 16134459, 68528235, 633404970, 862972980, 581654685, 955440042, 552841500, 939025069, 805831243, 713654603, 347737651, 481188946, 873908689, 348351206, 301702917, 267986686, 638032508, 737345704, 534865941, 326161710, 747719877, 737018073, 310974831, 822380845, 336515966, 151026183, 780337178, 548748119, 73627987, 414028475, 224153933, 441721357, 717873814, 276147797, 258915886, 97729527, 978552536, 509893314, 31661604, 835184571, 320527343, 530483121, 14282598, 118022686, 991143762, 890671420, 502962225, 733794719, 461641918, 797547775, 568471497, 461902678, 182026684, 83896393, 603608244, 464431713, 612235636, 367330362, 405466187, 275723792, 387588722, 578833426, 612443884, 711609830, 751879212, 682083682, 718200942, 338269365, 215294920, 103703303, 923483392, 687221694, 57101337, 239673640, 466288023, 545061098, 557907021, 60651104, 617972156, 449078939, 618142282, 664355728, 730000640, 535089007, 928461272, 300591610, 580153917, 825521176, 767370846, 995345528, 435434380, 853267792, 356438840, 217498573, 207342346, 401350251, 208274496, 981597479, 445193278, 670514568, 714559726, 785763111, 428232625, 394283990, 472764255, 168878482, 195695330, 545627511, 14937665, 900556562, 382571818, 292370146, 158432772, 245833194, 708377545, 4428207, 158233769, 114327770, 453720450, 783010611, 440621064, 499086630, 944550675, 391888760, 965725635, 24650058, 527244752, 193259265, 901534771, 735623551, 536595756, 180000103, 965267056, 355270923, 877562169, 797085745, 554773855, 959752016, 373372613, 250328407, 988466485, 367775232, 603616214, 41295181, 20078679, 336621416, 77643804, 634047072, 351956613, 923168160, 73435134, 187619423, 729915251, 398368183, 562461257, 927345361, 536039882, 502664912, 178386305, 166987892, 252408222, 885986485, 5059778, 686810112, 327199735, 320242676, 824044145, 948701618, 364506608, 997665934, 155740110, 83873719, 318873339, 212811905, 236807453, 542356179, 491877932, 982822368, 278709608, 942974960, 356574063, 408965232, 457621974, 52554688, 585403049, 931366986, 669672410, 47864438, 395626722, 280342025, 459652589, 298145453, 374429329, 878160719, 489958641, 500355584, 124045034, 677048076, 215636566, 178833959, 599759748, 57626498, 592396355, 338420989, 761036761, 544914058, 290663841, 344430383, 773783267, 819738212, 348960205, 135247064, 524775977, 820092487, 432039675, 569608134, 393537843, 497366089, 64476465, 323134564, 130031605, 18462870, 676295051, 324020603, 360705468, 56791678, 413816196, 35028734, 820247737, 70753032, 512279751, 405821237, 426432029, 117987054, 882396610, 792061945, 738431152, 384529642, 471537789, 250500779, 730696194, 672789467, 786566712, 804421022, 297834570, 286541483, 609383454, 377366512, 641095078, 25602869, 678648724, 999160317, 624952790, 218895294, 832998484, 213597675, 981109014, 89664694, 422007755, 990935483, 978273942, 387380626, 252245742, 70293588, 827268635, 828408041, 876817035, 579279130, 92226746, 857311438, 132043424, 808186922, 409020236, 60170179, 156121724, 95112452, 695679443, 590592738, 864069279, 531408081, 257167651, 643892992, 340556485, 678811397, 951607611, 811538058, 23732209, 74223644, 332418840, 479067586, 898886617, 485966866, 609418612, 942861682, 811899138, 935630154, 869102143, 649608730, 308429633, 797830483, 604871566, 227469251, 266591981, 682948507, 731647422, 156485296, 910838158, 974392654, 192930099, 320837702, 136978344, 155520202, 161054255, 817091988, 368147310, 768045830, 652539036, 253927335, 100738957, 56953418, 362575098, 37700042, 658350809, 257647244, 443122291, 378365594, 566458467, 539911913, 838267214, 221787561, 490117007, 704147468, 388864643, 722072017, 395232103, 27118076, 137049222, 402631763, 88776301, 692660182, 89902633, 935865892, 444139243, 55438404, 185643914, 111614362, 295232961, 467915126, 719866986, 907053448, 394472097, 552523438, 952449051, 983340722, 643457566, 889232252, 246407159, 469955525, 49772188, 480219879, 742304669, 776488764, 538985411, 956316982, 877794038, 446132342, 713903930, 33664499, 968608997, 571494274, 363642119, 598279810, 974497150, 936227417, 528828052, 625705029, 13570105, 764478132, 451628070, 368993938, 206341221, 640848858, 869384070, 8417876, 830838851, 210555593, 413974866, 391811094, 709204222, 588628993, 861227918, 313127737, 569198441, 323785964, 301065880, 701929844, 290232744, 182205042, 28974837, 219616934, 242733682, 688121141, 751149453, 949334341, 755823040, 308710298, 128361709, 458677189, 461459692, 212761364, 35467879, 72944143, 207556157, 968622277, 669509521, 239502366, 962590003, 334207434, 784642451, 4109455, 317741316, 998141182, 661359310, 498675645, 19755168, 651130992, 225800952, 452753633, 154725218, 64920166, 338033430, 931559326, 779427466, 268795033, 410706552, 938663646, 525382061, 742541224, 303214108, 761258156, 639272546, 636105991, 732584240, 902497796, 885537942, 417833537, 5851744, 653968976, 967650457, 461498684, 174409034, 399796865, 739326519, 665329727, 493587186, 681811587, 17224243, 21223856, 708523865, 762951960, 317051640, 126552626, 174630180, 638543773, 786640932, 372267071, 953442629, 125472930, 312985014, 536765866, 934276619, 464980113, 90161528, 267167609, 186123959, 325986714, 473280829, 405384688, 2442789, 582632637, 387963461, 128287828, 32639181, 917922938, 543153830, 922558363, 67018370, 837225839, 195229937, 56238945, 255869909, 773598180, 805818231, 734585654, 472123716, 622236759, 739480571, 377296096, 293090566, 392463909, 644517261, 849931749, 924326660, 959550464, 651228013, 776663308, 664605959, 142367692, 818801260, 395824616, 139593472, 536780660, 531400903, 628984907, 539279725, 21385419, 379107316, 536894148, 604272774, 92524053, 729999567, 800819072, 881707523, 51642502, 307695359, 999260576, 798000683, 181226543, 140860022, 487392510, 72218192, 646817894, 710619467, 902150735, 103270906, 796534161, 976500066, 789009779, 230469178, 779657914, 260781576, 60398603, 856247980, 99630394, 12108748, 583079228, 764575806, 653141463, 636451587, 759367608, 322675751, 338289022, 795341712, 664784742, 401170379, 988285352, 270316285, 683673543, 729543107, 883518685, 320516478, 635851664, 395496384, 840915559, 94011541, 935137028, 830156603, 686937946, 621497798, 507318485, 925061797, 239819169, 429912602, 124842310, 802735720, 1729697, 173868093, 639056145, 689719650, 599069285, 173122950, 745560123, 449182731, 171126656, 56583022, 20365731, 523161310, 206190353, 898119337, 17475565, 439055109, 130011694, 238788848, 804209188, 920317243, 333702747, 699267056, 755972765, 402311988, 88577603, 627565459, 782366459, 267824975, 907995242, 865371324, 3129538, 335619750, 720251401, 170588951, 886033227, 699197565, 930265594, 705540429, 235994815, 243521613, 498361171, 341674566, 71211896, 191847674, 234587428, 592084407, 380137030, 448586252, 293720670, 369902633, 560196654, 913923242, 635064285, 813163793, 286705699, 141222943, 802551766, 592541466, 850138134, 23949938, 447509616, 963669331, 19860305, 965005323, 255454121, 714418737, 666048457, 691630944, 470426733, 328361249, 152909713, 278654647, 531403957, 42242495, 662451098, 285188447, 485499333, 195797838, 230814982, 901614650, 981959542, 235323892, 292632990, 963902839, 631210721, 939578841, 740805914, 714326562, 526256009, 633668377, 546748886, 929513111, 194500454, 157765335, 316138015, 532606572, 141365351, 659709709, 390784716, 430914383, 447981479, 544587698, 880511917, 17630480, 192515646, 952208638, 55129882, 254497613, 98473120, 326969117, 410371952, 573265637, 892814804, 889307814, 379916124, 166996816, 500790050, 694619558, 180865399, 327573452, 469093104, 291718830, 683801648, 764982473, 285162760, 238965693, 730012811, 136504334, 78170351, 738645973, 35721794, 531768227, 546306579, 268126822, 539063128, 368181146, 552350303, 356767658, 862822558, 236825035, 245901062, 950005620, 14272786, 200207543, 745789251, 590823229, 438748045, 899250165, 328806623, 859796185, 942471112, 176076458, 674765215, 19539085, 76532989, 521279274, 99198139, 143062465, 66948799, 839478317, 333850025, 778398179, 361047842, 372121859, 721311553, 888749003, 986162915, 510455078, 613948132, 362966672, 786569819, 729674678, 479113208, 719500671, 843560278, 842029480, 752593896, 57119722, 50734047, 784841271, 83112053, 346682949, 935680565, 41562189, 115571888, 59491888, 168662982, 654072449, 511994066, 116660306, 850692134, 679470741, 992210947, 657378163, 742672450, 278336229, 677121144, 908414218, 630648354, 968696043, 113110274, 835065915, 969456603, 28072703, 713010007, 660059669, 372795845, 251497008, 897055738, 758305605, 718445758, 543340135, 185972592, 982501156, 802656158, 700424345, 46908401, 227393848, 375444774, 310992686, 996382757, 669044641, 573386550, 896005558, 238874829, 556826250, 503158441, 730369368, 888722919, 239165838, 414191492, 803754171, 443964965, 115113672, 949019574, 236823349, 819541128, 928147781, 246055766, 741493104, 747100188, 170821001, 454988125, 757065924, 820810995, 953309630, 289371300, 984475870, 885086103, 702663197, 414942882, 589460940, 205973394, 662525664, 30437093, 394071667, 779120928, 846053967, 540181623, 469937197, 746094437, 774799598, 951774328, 440493853, 733152648, 513855226, 542253873, 494028959, 787970505, 598676294, 548897609, 78903400, 829208183, 244412972, 171023288, 420952831, 765095522, 634272689, 548952917, 646270899, 133901598, 793626108, 51793302, 29779102, 252161636, 228356130, 865244004, 826238101, 153431864, 518325333, 918119949, 888195203, 941074053, 924212342, 254961087, 796019736, 970305177, 115678514, 464344689, 487691067, 207255571, 165272427, 617465197, 415124320, 424431245, 697698512, 899733962, 3979885, 734265526, 381512308, 194822081, 296395107, 746761812, 376461751, 767196768, 900682671, 954010667, 309664387, 536650624, 109884722, 212340879, 188792233, 615078929, 141934992, 708794412, 804374719, 123947989, 701689831, 527403824, 405711996, 195292771, 121802953, 593658881, 417430339, 473481859, 760742509, 175371718, 988287313, 886190826, 900766972, 321987960, 420719472, 657248979, 554338386, 914524338, 556644170, 687575951, 762458092, 445566847, 646254269, 257840641, 179264137, 995142802, 802086362, 576229512, 482541705, 205745820, 902985362, 349822933, 27464766, 545731439, 659547241, 811574564, 632142380, 318169391, 97024412, 207961425, 603093340, 308011588, 687673887, 881287051, 733881551, 580304198, 177428038, 417609178, 741000905, 996273996, 475629284, 584732100, 98819287, 306839484, 570984312, 598579955, 660955940, 381914220, 819199284, 626093526, 534361636, 784838936, 636905183, 585492871, 131433179, 428312739, 651982950, 560710293, 783992636, 991802116, 901325956, 305805360, 251205002, 515496459, 862190542, 171474791, 304248990, 700485000, 200606709, 784869043, 541992052, 582551198, 157123878, 781731331, 388293750, 412782038, 385549998, 376228983, 551846128, 231482179, 530153971, 344277548, 793490234, 520755418, 330533344, 356678361, 215307584, 306605571, 459400413, 383441568, 964644560, 689204216, 979534710, 694883277, 965821147, 882275955, 615628262, 107916253, 391497593, 9029457, 660483627, 679689666, 32354205, 94349732, 758622883, 749286009, 325103582, 319022032, 549019161, 906720308, 575212719, 11280971, 974294009, 62535786, 270142806, 179058980, 960322226, 182612352, 261406643, 982717996, 598346227, 961288636, 920230032, 464778886, 867104876, 715286265, 364934480, 487042644, 496387487, 273612604, 203436576, 43098925, 394138281, 740504995, 608945865, 679904145, 153892287, 522703485, 482968943, 44809067, 127926427, 417952047, 899153797, 751472330, 486643482, 296376856, 941520378, 985439073, 703980778, 449600305, 603014422, 845585679, 265916130, 331490323, 270119943, 75121069, 569820853, 861745936, 663432421, 190819602, 942622055, 736977845, 499820068, 611036901, 711984913, 786180879, 350744649, 889572168, 144795605, 390878343, 277311681, 103720044, 402629173, 266116318, 447735225, 537889768, 780078962, 507263575, 194091628, 285234818, 946340962, 113301419, 637414582, 858892215, 605660492, 680113019, 621432269, 411072448, 743652931, 240039860, 981928607, 239586485, 322251677, 598177901, 325964389, 398078498, 411878298, 816377536, 879026140, 649252204, 412540602, 247076479, 894214702, 196325404, 370576798, 700774592, 489638773, 807960496, 773216246, 380095825, 918679592, 492368130, 188468508, 555527322, 458864951, 218175635, 743714974, 862842146, 429017336, 279679773, 501343645, 441986467, 903321921, 55179465, 741122043, 321524860, 39469002, 752583443, 255270804, 931082886, 167514543, 469501974, 831368157, 997857475, 691564117, 642213397, 629622913, 220837497, 610358152, 958159760, 850511113, 677662577, 879942913, 255658527, 139532984, 798420669, 924401063, 668918235, 723217074, 252383548, 6673831, 712236308, 503426254, 229867529, 545756299, 203804140, 149791956, 558286977, 798782293, 97567502, 978564211, 326091304, 363288125, 43482112, 957510168, 95679015, 564065146, 328794173, 472338718, 560282895, 618874742, 800340987, 437908685, 366652048, 563917046, 688973070, 676115523, 452810144, 321677750, 579155289, 670483367, 227916689, 637820078, 829978986, 246344704, 345223314, 914555104, 634747171, 831697677, 650456685, 891846250, 530995014, 499124977, 245264558, 307826710, 643091678, 998086563, 680964793, 547153061, 805882457, 665143592, 143530140, 632524070, 152514254, 398304176, 72650651, 273581399, 615205844, 491504052, 301936896, 301985817, 381780544, 271614315, 798823072, 482666467, 270289148, 774696900, 640068783, 373151502, 964093129, 764029570, 600791217, 327105083, 586721014, 736565627, 977060998, 646607249, 196457366, 218616532, 34967473, 412135164, 340695486, 563101252, 185073377, 976019444, 548274596, 311687507, 305768053, 540472840, 501891911, 614999659, 785907891, 483195987, 103069815, 371862288, 607342500, 289857346, 97731085, 633826744, 430635605, 669934483, 870011241, 697766946, 804605383, 834595582, 86282460, 835202211, 115832469, 222698650, 86847157, 351911942, 594236547, 875293882, 38673256, 383363764, 953522812, 124664193, 162866332, 225590596, 620962003, 928174993, 681513907, 970111983, 582061051, 979686355, 384865854, 454809486, 871481082, 193162923, 666837951, 871116344, 630373326, 897295235, 42620851, 831202886, 962032380, 192626465, 538247075, 128819974, 931570693, 88909646, 904935165, 640647603, 230229059, 614639897, 430247420, 923375597, 840057971, 333292990, 162345315, 951870967, 305684979, 896380867, 358124531, 420176211, 169581374, 865209279, 310613339, 946958266, 728397752, 533810552, 744757210, 532936875, 848678862, 578784974, 487552485, 412044578, 691678155, 415881600, 797270150, 622375844, 219902901, 504251965, 154390411, 208077071, 542408049, 429731458, 921766567, 235783823, 909923268, 353817604, 643492915, 950474199, 320153945, 472230699, 192422216, 921471720, 523841352, 504773272, 839209353, 983935429, 470137805, 137055291, 526452230, 931956992, 862505089, 140873535, 231754514, 398093753, 655554302, 738967249, 894677799, 777043008, 808513542, 436115965, 899445577, 812636492, 514049413, 449311849, 470700296, 177276212, 306649411, 714806793, 652921286, 383553817, 145324776, 480388301, 899982764, 114880376, 985398376, 393184494, 94602249, 764166191, 992088079, 937928657, 994831160, 911214364, 814915382, 149323257, 59276107, 367983490, 942730567, 225958578, 181072723, 902091773, 791276341, 43001654, 529116146, 501812291, 486072657, 655869411, 211437458, 566784889, 571082261, 691681829, 674921493, 336615848, 999615778, 985970902, 733512902, 770431106, 394183496, 782241879, 838971841, 469332774, 463673626, 576105107, 253333626, 836074580, 336213675, 23806137, 704665430, 255236481, 647811926, 705183733, 542096975, 122149066, 443680675, 821867819, 267147373, 871464469, 910586399, 263621266, 447322422, 492780857, 345296599, 738051177, 489460014, 949235438, 567741578, 748469729, 99034078, 613594474, 435295578, 613516580, 644271997, 732548457, 20548156, 817605713, 625347009, 294639829, 938691721, 420854372, 200494490, 431716587, 186354312, 402860548, 420360958, 957332725, 222795859, 317442170, 302901822, 39296985, 729493432, 831320067, 488236640, 967185818, 975529763, 601312450, 994907778, 909208557, 659924122, 522286840, 346888176, 585613906, 800544180, 81783355, 807739560, 272075584, 996924212, 999562263, 56549727, 281460756, 766076671, 320752584, 991050311, 461767360, 262124853, 447469490, 906951946, 211700529, 387753327, 720025191, 546584665, 410833694, 354503912, 486358245, 121170792, 962422074, 611749844, 249004017, 617238107, 671470407, 357809670, 818587256, 789091930, 89042670, 42348708, 901713486, 229683267, 847697958, 905677129, 823204548, 414566596, 770208465, 434680123, 689745649, 980559951, 989194916, 44482386, 10072216, 1876236, 12926208, 315972978, 896673949, 419659177, 509594898, 756756022, 481360692, 278529682, 297688650, 897251121, 877118880, 535715338, 985297603, 309943621, 450682681, 813210698, 18667641, 69407381, 531174463, 670827214, 604060516, 985797527, 678452097, 601710151, 716889037, 643429900, 244411962, 137431665, 730228911, 510592494, 673110625, 941164368, 565960456, 12041488, 945929971, 286010059, 540117814, 786727687, 279367435, 484235407, 310080102, 880947352, 108524130, 301389874, 88018721, 814233558, 793015391, 152355414, 207178444, 437907115, 535993381, 909309652, 816244140, 705983374, 146526548, 749329537, 258128717, 137471209, 32195544, 817073072, 441292564, 531219489, 921784089, 563324200, 637153828, 53554588, 956591090, 750916313, 143249087, 653996009, 781300326, 580953060, 166612221, 988245441, 333201871, 903238346, 183120945, 444264076, 355344220, 803992898, 494346377, 84031416, 414196592, 449279932, 652235740, 211450786, 111850320, 564382767, 521583718, 339558136, 4216530, 409469668, 577752902, 954672617, 569509660, 17285165, 10903163, 830077833, 638121187, 745488910, 928050827, 244078465, 877418291, 803126650, 718623475, 112744617, 500850820, 794052108, 446362045, 623542259, 150886374, 729763252, 877974434, 183060596, 940694168, 906525190, 80722024, 646611494, 856707670, 669793843, 297105856, 911539436, 968527777, 683491913, 316019825, 286471034, 455683029, 193897826, 932827636, 252854050, 435552121, 84226789, 533741047, 192481530, 50399850, 11624682, 963401273, 807187590, 552929750, 790869438, 671199226, 731477809, 159084017, 710823486, 540036907, 105336736, 800023279, 625265725, 511711973, 1102488, 649745982, 43720471, 560481743, 268798099, 23166152, 589901811, 15473993, 673286759, 989931288, 789553782, 855262265, 332277602, 875090158, 296434727, 850410259, 782959957, 996933907, 531574885, 896307326, 135233308, 220956133, 997739626, 616557782, 472127963, 624165502, 491716442, 797531014, 359705318, 567002848, 501919197, 641823953, 363921033, 426117102, 113485203, 52204937, 583042669, 175872172, 254013967, 411983187, 311366764, 38377174, 641446278, 565141599, 135119152, 896514940, 798613178, 859006414, 282578710, 600808458, 76489896, 188836570, 479043421, 162534015, 337370355, 714861939, 322142079, 455989086, 326344376, 139792322, 948960491, 485502046, 211060251, 313817110, 726571596, 691406393, 349705923, 965909385, 116583862, 902734263, 579194323, 80448990, 703994858, 675219185, 762861603, 844117929, 919573445, 733552650, 268991866, 313102387, 227471219, 908503247, 933671759, 440163456, 526625190, 474188372, 125305430, 903909878, 6649952, 713757799, 345266165, 61647477, 582907349, 831055320, 581806417, 338032190, 168333603, 738985555, 780711105, 902946188, 283667672, 157092601, 385128392, 991684410, 216086222, 251394536, 700537247, 312894834, 788263053, 676376542, 716435853, 633646839, 520748471, 931546857, 6141580, 402980246, 481961422, 525248735, 912743020, 430811796, 347561404, 614296042, 646204201, 582988885, 743517091, 134501340, 903123432, 226577528, 658702364, 163047848, 93304710, 468046644, 94627669, 854525972, 241744676, 679150782, 250859640, 12067377, 448586520, 813630714, 608134046, 795613742, 240621719, 476907678, 842226628, 812551963, 233025317, 206424133, 750112557, 939037553, 498447110, 794567927, 208445971, 152620600, 4191693, 313682925, 603313259, 139815883, 883074304, 504582331, 684912556, 568110614, 800999791, 146361373, 168838824, 712956285, 194203785, 39720313, 26582715, 430908956, 388488644, 366721780, 486258045, 415040526, 658546352, 221651997, 199572939, 601075301, 992280017, 916618535, 973436190, 99067514, 526023013, 754697881, 365902454, 129768790, 575996782, 617719632, 780571723, 868856595, 536146785, 371217388, 307163006, 793405940, 755180542, 944141438, 494840545, 589341553, 616047103, 67467537, 655609308, 712592568, 558725398, 358761422, 918260011, 840619383, 547199598, 784276270, 864059457, 645723629, 369324790, 451912972, 85497856, 205128002, 100476368, 809534303, 529790089, 680074835, 154193031, 203570645, 902722736, 185646008, 152318865, 995907602, 835014239, 348826482, 289773143, 601338395, 529258960, 184423589, 869921518, 328747025, 74772488, 713545013, 486924060, 780210602, 383887955, 113153072, 973437945, 646782502, 410843039, 264585006, 530679810, 815868544, 192608559, 838327322, 149364836, 299275137, 118009157, 166823843, 452925384, 606184611, 623542727, 801434546, 141119934, 701730570, 985329385, 727595924, 44363648, 621538446, 474672651, 318610341, 150236847, 973646155, 431586086, 299043116, 246354524, 185742668, 770040294, 367782160, 320564786, 814543874, 796019999, 918605829, 363844322, 843668554, 224597959, 662046040, 7470391, 792346682, 728393240, 210640179, 963471392, 690674632, 871392618, 681859702, 504456696, 548057026, 897243490, 943009073, 541107552, 436897666, 451776479, 648539580, 420802727, 607132608, 457352297, 892291421, 679521994, 506666830, 981051652, 854886942, 219925035, 73088205, 912609785, 449996427, 236959748, 925877036, 753578714, 445128538, 460518651, 397081320, 933250661, 818512958, 223136239, 530836886, 137699630, 253701693, 774870726, 468942556, 881940685, 760364767, 887162358, 906946134, 121909913, 862071112, 868349776, 800093873, 796346939, 428485305, 406085237, 939547589, 360189478, 710106558, 708859361, 381915696, 830199936, 912263133, 314729984, 176310145, 383096287, 620797326, 180753340, 408657889, 822689497, 244127059, 421836576, 684207483, 481023763, 715354240, 356657331, 636325439, 108038870, 528861049, 766633322, 134621708, 586474522, 920916478, 64467511, 655971433, 675434749, 606583417, 594902966, 694887943, 544871557, 205559012, 10644127, 614733962, 823084081, 872496030, 430841590, 984997365, 764956340, 126162875, 986465626, 666535361, 816326930, 201482769, 650859439, 978684192, 371135591, 751554934, 299779581, 809700107, 796266075, 801689412, 652092380, 650535037, 483674233, 207261648, 423336008, 985025487, 706052647, 911692752, 78429952, 338366830, 860549513, 32744794, 878901920, 556381842, 527338078, 333955603, 206142212, 581605796, 743453178, 30038344, 272114661, 106570188, 328128734, 517848446, 755064292, 428223415, 4765392, 896951277, 98858983, 117765450, 329010168, 522590660, 337704245, 780904560, 303607458, 646553137, 649637174, 23055776, 390501556, 116753412, 382540458, 520762439, 265114649, 12316716, 887011575, 273054026, 920031300, 525647637, 922113464, 742547673, 230181150, 309005449, 295108096, 422642957, 658429068, 430551297, 355590285, 994920080, 519134832, 997238983, 653153425, 830979648, 744821097, 254305502, 66327595, 771606400, 632361926, 948170520, 882642156, 213363997, 533889186, 47624813, 883757861, 519796513, 127438503, 930080988, 96578747, 842973683, 155326116, 238611455, 289324931, 650270235, 275685084, 904590931, 882683993, 636175886, 571509842, 466444673, 427855773, 847211993, 366276380, 897172936, 175649775, 166640004, 698487903, 904519633, 712952916, 157033825, 736981864, 388328772, 119618470, 791072676, 642879340, 98134756, 457054610, 934074677, 619357350, 781155571, 756267639, 700178439, 470591204, 133803060, 869900319, 943370486, 400299595, 515645301, 848632632, 105542902, 687131701, 67445378, 52983265, 699459632, 657577783, 609098046, 999895748, 443735751, 666781907, 687906333, 61903826, 375415805, 772027376, 17320594, 117944693, 780236860, 576044577, 482384512, 208701323, 756782480, 672052283, 646234285, 336429985, 868803575, 216904612, 338761092, 347670003, 646170566, 499855316, 168922745, 163364880, 289506466, 261185918, 892080408, 912375692, 937436969, 180531187, 469589512, 323140719, 345189286, 797800309, 534057537, 639672598, 109643603, 577810266, 71547236, 130007223, 982304417, 234441019, 651790644, 34717666, 174491682, 490399777, 29515787, 387044068, 968277679, 327731141, 544132199, 172724471, 482444842, 995260581, 846017654, 484816769, 494657117, 742165162, 955391639, 993701892, 747245356, 981398460, 316853419, 282477237, 271245385, 564497599, 306152648, 428630198, 357829377, 864851903, 830891378, 518108542, 916688665, 446319060, 979631890, 897549993, 343781351, 584415696, 570626055, 410465747, 862405264, 637070170, 697750135, 988243966, 879755885, 117936898, 730715676, 585343999, 615737641, 651505725, 64812626, 342617416, 625390245, 786665076, 76599369, 137591643, 640527855, 151276807, 82877723, 402537373, 849465552, 190364861, 71248406, 156074777, 272116623, 233229000, 654858485, 915360762, 867390005, 83821230, 240345358, 97328507, 551565175, 799640544, 518258040, 174293115, 774229775, 795003215, 668450821, 738453621, 337895098, 982134160, 421154505, 970220939, 77830142, 126119314, 760065544, 451130247, 180251354, 828429471, 505277421, 695952325, 247813824, 55952036, 107011039, 390136916, 132025427, 50638886, 601982997, 311499825, 606221296, 767186474, 499754051, 266866177, 174914203, 197129670, 806230840, 361717617, 887205626, 991422349, 624597401, 488927321, 224992417, 551222570, 810974434, 146860590, 608399760, 162962958, 769278087, 301032470, 190065526, 532344524, 187996919, 437179967, 489449000, 765363278, 808426610, 388508289, 407458730, 157310379, 275229388, 943603696, 961757735, 500155350, 362823283, 80509141, 745358538, 334048707, 986674667, 481653514, 720088066, 794767352, 570164911, 670388047, 293523859, 811905565, 167607800, 662589301, 275029508, 724623591, 130518543, 597926138, 356135704, 256538779, 157993304, 482281190, 250016918, 37252878, 855741536, 621085920, 529320168, 548929905, 515069835, 81568554, 286845984, 795203796, 442156456, 294853036, 116011853, 881676509, 510644087, 257196626, 678452186, 824063243, 506178954, 319619580, 342136843, 815378008, 582173040, 191895289, 181483612, 494444333, 647702176, 239765168, 737953276, 705202469, 802685435, 699502734, 105696703, 395977294, 303255753, 307151628, 989172048, 457689886, 956565142, 890839300, 648178330, 297906636, 665050899, 422189880, 510140791, 25169979, 22086542, 597555734, 690488585, 723328802, 127160205, 739788036, 54062713, 501879612, 33377388, 851948736, 138458204, 706748313, 518390351, 179326422, 640005648, 391285626, 835424489, 893454682, 316875620, 448521294, 48487466, 936172792, 258348270, 257200825, 897799140, 331421345, 681180025, 36233726, 595782953, 190154382, 873903714, 579805099, 803591905, 988526337, 200603205, 207985480, 213076704, 450061271, 516833659, 245938435, 318244649, 830152852, 337878206, 770247061, 591499562, 741869341, 998031507, 29757644, 69481142, 853193126, 152486965, 31385676, 57102545, 726713246, 400023977, 366741112, 465624259, 554628581, 346586740, 725216711, 40823318, 407014742, 365693399, 92065192, 456929731, 495368501, 719165837, 754941306, 555183089, 370718721, 477057718, 555638946, 870661501, 222295668, 621130725, 349007763, 908887530, 298861753, 274642104, 135296703, 525698820, 664045039, 798839003, 488481387, 718556807, 102515726, 820907145, 98239695, 252814421, 807509093, 484890912, 385028023, 498242295, 680728154, 673358634, 575190108, 69900760, 248299124, 867819168, 768624893, 272926716, 774025317, 741731942, 498638567, 899609622, 543383746, 39398391, 991746406, 266943739, 6249874, 525742344, 432816904, 437586062, 177430192, 353951612, 793415326, 485966776, 451262695, 822900058, 974473111, 985770767, 35256174, 608175228, 111012505, 626963382, 859255086, 667074611, 476081105, 25005585, 656677104, 943447938, 310999786, 662302678, 307871379, 496092397, 703687193, 261853127, 920945583, 583453699, 353315955, 93449561, 400856294, 497448462, 419527384, 503165916, 570402054, 770442242, 888394804, 24018167, 384989422, 526396764, 267828414, 892667165, 852979539, 921126340, 388109862, 302632821, 67218402, 520183305, 631865, 42473583, 875811567, 587678118, 995824694, 307403913, 477413003, 43637045, 643086566, 934508781, 194434863, 278519238, 65697684, 734699017, 74345095, 647440944, 487324053, 471288259, 404305515, 725484860, 501593144, 473402617, 875357233, 927703205, 378525897, 460643399, 995457954, 983732107, 110351933, 382207218, 776842911, 436892789, 776478026, 317492757, 709901514, 293404794, 408349571, 698847777, 554047371, 171083783, 492991451, 996610847, 762323685, 113510329, 30397663, 838880002, 431091943, 762375964, 172607798, 457232270, 677099064, 45278460, 343643509, 282625258, 536386012, 623572129, 343557864, 207070604, 861780848, 330391583, 511833104, 965356500, 587941588, 337025890, 993047653, 893757507, 672069728, 775613381, 598565832, 326239915, 105977085, 730819118, 578500584, 398057537, 694244654, 196234371, 683922872, 102803749, 975923839, 494999817, 796753065, 863892375, 178765463, 595478050, 245851555, 144123548, 486316682, 72750528, 971034115, 791098315, 625161960, 981414822, 547863718, 809825678, 619238372, 518295366, 771946608, 781731531, 421288664, 810681132, 327301511, 68400981, 961865539, 303987364, 812935869, 629615935, 992087106, 384044584, 764838825, 422725808, 753265590, 631445652, 462290739, 506992702, 472954955, 166943075, 455996332, 330052972, 183166519, 767450388, 151919399, 777694151, 115624868, 693126730, 412742918, 276339699, 909723994, 394123835, 985644098, 231096412, 455939495, 740444731, 48714941, 77890466, 829855699, 418294928, 664555361, 206530268, 828001660, 874766053, 173358247, 87577803, 592437381, 710160379, 960044147, 913323848, 701377318, 46124061, 54918782, 420168371, 332471514, 985092099, 823399348, 148399866, 307383818, 16213463, 504372371, 873625182, 491035599, 355905572, 604229139, 223841323, 832213544, 809051856, 576426116, 246562658, 303648726, 475713113, 608345795, 713411653, 888314094, 791340526, 957322683, 26686115, 51274608, 739073967, 467320292, 212273973, 27844327, 312936692, 250128509, 958172002, 939444925, 24829943, 789897700, 507218351, 990421421, 345219169, 458579551, 999240212, 62418172, 302875064, 602065114, 489975482, 878639391, 300376549, 934341092, 398829507, 555651244, 569867008, 67830210, 116511934, 976691791, 211950031, 749615015, 206366932, 439818204, 489308365, 676442434, 212643114, 415783683, 246774938, 670542717, 18229470, 770718221, 575125493, 927650943, 945829304, 705015784, 518411848, 830943364, 456938958, 159519816, 884411123, 994404654, 880211885, 965379788, 268527564, 801818286, 463878275, 346570963, 296150583, 533421253, 519799584, 261107120, 783578107, 75750668, 323045039, 842065704, 553132250, 934115055, 172493117, 538664758, 512418833, 762587782, 911160168, 923967341, 248955833, 470174105, 647715169, 414552925, 995787501, 176515683, 322124607, 494349245, 404491574, 17216156, 889146321, 719918986, 244003005, 69526277, 695234226, 891023596, 585643813, 100434614, 608979324, 139781049, 917796181, 551474055, 874197933, 516895152, 816721310, 358740415, 492566391, 902326068, 249923216, 467968550, 653410255, 70654445, 380836438, 233868101, 466952143, 38058659, 143801568, 445048836, 350920626, 484240715, 952709258, 762473188, 218610389, 261956298, 21050248, 418963634, 415553761, 496409839, 527711721, 674519839, 843545729, 409402862, 77673808, 979049110, 918664627, 560700313, 629109723, 233956118, 901021113, 159067317, 89409801, 32571748, 129959394, 361073304, 417040468, 950492025, 207292303, 790947402, 572854057, 465102550, 355581225, 947651879, 890480655, 658086407, 568202192, 633151036, 904720416, 160157293, 648138244, 382366937, 16670061, 590902725, 628488936, 615628483, 710398817, 316899145, 820020039, 878797957, 579239004, 68407657, 257158384, 687972923, 368350212, 183696140, 65715779, 243837687, 417290533, 839661178, 808931610, 711708609, 960681546, 927390508, 322942423, 111333242, 482124557, 241502646, 353908716, 46258546, 179195093, 802890799, 485078041, 182647679, 519492079, 489804609, 595355196, 677020555, 976007475, 136361609, 123681008, 386329250, 996829780, 718018578, 827574023, 766047874, 552808213, 151079121, 671571059, 701964781, 611817126, 782061936, 418257922, 65065911, 203739513, 498954865, 514866542, 240946480, 700023022, 72041340, 612723580, 585572021, 398615193, 645978474, 533267271, 957736093, 303625272, 16044192, 334142717, 593750782, 725026017, 709596173, 445444613, 39014455, 551926971, 438923583, 252232395, 652149870, 171242181, 662343698, 829821118, 620437081, 863574996, 553581994, 655462169, 793786933, 966681584, 279613643, 436537708, 758154659, 233406500, 172493877, 174761113, 652961074, 720739691, 698553783, 747641610, 88165354, 929433707, 63511742, 173769838, 849646351, 837219068, 838766033, 115908575, 821430693, 719797024, 86977358, 883285888, 381497789, 281148014, 466806421, 346048288, 487431479, 754295499, 343779927, 883719395, 136352912, 374892514, 577691385, 443382753, 513771230, 201295366, 129400269, 589116209, 365044718, 875909379, 867537118, 230125326, 224437041, 594977356, 544791242, 9309556, 2403225, 67329345, 113974143, 642521759, 531456406, 547053106, 916954886, 762993534, 25827077, 501109909, 378502384, 209059283, 523060594, 666768822, 237304759, 702984439, 731413650, 799665299, 853614503, 393660400, 180808946, 731750044, 836567176, 136492363, 397960194, 825719167, 531226240, 65845448, 911491861, 521893743, 465942080, 104309263, 921015595, 466323383, 680318523, 145693972, 660226238, 2002506, 389946126, 621208232, 541499088, 29130143, 957437004, 91616250, 995991480, 292507020, 518811718, 645439120, 642088395, 56278298, 45014158, 732864960, 243021652, 785767518, 595740221, 447430378, 442037466, 252310817, 126463849, 166078043, 920439658, 692501619, 967062902, 109703786, 159358652, 292888350, 286946163, 794465073, 953896184, 488696367, 694447833, 514077884, 623698384, 889122540, 988330414, 719823643, 43099113, 783347634, 671180022, 227811921, 34734668, 831445387, 172104314, 718903769, 726053943, 430235276, 612957612, 536751428, 420009525, 140318079, 599216181, 510389499, 798001035, 176714560, 983429806, 4677472, 817201122, 887199114, 229220400, 109743706, 807522285, 796087868, 669220175, 601686973, 81102324, 602514165, 73663214, 752319520, 662264236, 659862950, 637704911, 754783782, 92575578, 987404276, 949971578, 835385227, 931470303, 880576948, 618263818, 296196519, 113105588, 767714964, 2278594, 353673830, 305173248, 711802783, 277857267, 336268075, 580185159, 904664696, 229692712, 398114547, 945075489, 800710525, 170378046, 785456337, 564328581, 994896889, 667945259, 81001836, 349635475, 700002131, 546577256, 523288510, 178830909, 240298462, 84919439, 223369076, 224624250, 177534472, 717814797, 377129908, 181061434, 450944266, 932216735, 148782910, 584803947, 354754710, 737323285, 354999978, 158087133, 403063225, 962796625, 194293808, 918848289, 402965168, 667782082, 112424708, 670411841, 294868685, 801715899, 932495574, 408765928, 591638641, 822866402, 68263756, 220210485, 638843804, 597246151, 366206532, 253487013, 321148092, 629169193, 802954307, 840715490, 170104554, 177789020, 203018664, 758495139, 838387061, 681785218, 651264158, 358689434, 250791885, 810478601, 721794311, 344711552, 372846269, 423598305, 150952440, 84748862, 646502257, 863921611, 644845902, 277811761, 521487702, 364861491, 95604818, 455611392, 724318205, 650255808, 153628075, 327581629, 477706750, 750700531, 351309982, 244853671, 600837550, 404174399, 549152188, 574079186, 709846238, 623164232, 259257009, 162263739, 810210546, 918124580, 144571337, 56788400, 147905858, 545729866, 201411566, 599456185, 471622779, 919007752, 241080123, 682835498, 983937044, 446435730, 945906122, 589737193, 745709079, 512476683, 963627819, 221027097, 350768254, 375727501, 647316329, 18683035, 349547850, 286667764, 16293965, 446083949, 981094735, 870927667, 868739110, 976661508, 65175929, 472726220, 578139078, 815300038, 394781459, 333888493, 471377795, 58901649, 735836776, 408504573, 148214577, 881363648, 464661601, 534174692, 380691076, 895416727, 602877364, 866918970, 566691272, 576641452, 482543394, 460418436, 386704507, 816884897, 983259294, 117135735, 677645174, 234213350, 816419238, 943285126, 438214421, 423243125, 27865639, 757982447, 991362237, 592722701, 805752136, 935959959, 342668517, 317421329, 128037771, 840852495, 889166971, 748591259, 760492811, 496882038, 878296790, 849442641, 850883852, 65236171, 309272990, 583222921, 465397108, 285670366, 304452688, 557657084, 880389805, 38641105, 154228269, 856397665, 316154076, 687898914, 979320295, 638298592, 459222319, 752088173, 922102754, 114176958, 307032142, 676622702, 523860672, 658004157, 721684275, 17195963, 798482930, 244434269, 352554861, 687326174, 366473399, 543754571, 736830796, 519908879, 831000168, 51643123, 997008977, 230670829, 580627594, 279305748, 315248836, 669440377, 169524490, 39199662, 296718757, 771893518, 918588919, 827816302, 196339611, 502277162, 990006215, 983852595, 882289341, 308527219, 537569531, 915782909, 702111537, 550704520, 557828253, 943698148, 248418936, 342955751, 933197852, 340708015, 496074483, 196531117, 337796894, 81549277, 51086747, 753467781, 627767204, 689486741, 175123045, 610898300, 31905517, 440962231, 181523729, 823983124, 231811186, 33296080, 847182087, 699255409, 958890142, 303676846, 462048041, 558807079, 216810094, 819465833, 248355457, 186660198, 759307899, 711783195, 228017511, 805108908, 835032343, 505821695, 312222322, 646057774, 268275680, 427320464, 828525775, 684616028, 512062368, 732444731, 590402042, 937541389, 827410738, 263859008, 264133543, 48811408, 274824270, 317370719, 903210025, 965159828, 286933033, 20439728, 547380658, 487372701, 753492677, 78901656, 585010131, 289998581, 968890289, 76190630, 842697153, 948092837, 90707981, 105540581, 521186842, 596708234, 202486108, 318456535, 51046344, 47323987, 630682720, 388059705, 906762321, 772664000, 271319623, 14953562, 305819364, 638503283, 326860453, 263627347, 181910737, 289239205, 578571383, 901793231, 18876324, 770705189, 142064615, 916913729, 395193970, 250020153, 18744907, 736832061, 151920930, 341648633, 177045183, 186598794, 549474461, 486699745, 602504200, 667460303, 652473499, 505572411, 692860583, 593697343, 621654860, 394110136, 796158926, 313985101, 136154999, 281335981, 438855673, 201569225, 162349639, 755011712, 655934239, 825405401, 723024708, 654813557, 991335689, 130106891, 133673409, 461861464, 980669085, 162133069, 803292025, 808452056, 230956484, 727279753, 375662963, 182329649, 78642792, 174795892, 145421651, 583974269, 412805246, 70489617, 162412821, 759849388, 326291212, 47796241, 910063256, 784650205, 347364078, 372181798, 584482250, 152824871, 206494068, 24226320, 726132935, 420496386, 862292314, 227082843, 559714901, 557205438, 426979968, 494489599, 502235324, 1711233, 294512699, 289442098, 755596690, 823002055, 146867568, 939604013, 776068590, 337101256, 726027215, 927277631, 101217214, 2515924, 401913403, 160036808, 577545223, 610757467, 674452980, 514749692, 199524, 222878231, 462852188, 630981576, 511133957, 953247907, 716652086, 665797138, 995982466, 197985782, 109395425, 362333439, 203926749, 841505612, 453667724, 930855094, 138607912, 284857710, 891402800, 808647926, 372376871, 451961478, 30335963, 212408542, 931647748, 880732298, 909292898, 715618793, 340196968, 627092366, 991879998, 487061701, 959082597, 803594579, 132378013, 404322236, 534025560, 863166986, 874609411, 971361212, 435274099, 808426375, 758540072, 618314760, 542863883, 369970344, 924780878, 251028711, 855973225, 968439363, 688679248, 761133170, 773706712, 160145093, 154955355, 85535639, 113676056, 779428221, 890892940, 236765627, 936041824, 422337656, 733034539, 97889174, 789154270, 988986140, 283635521, 686870549, 566448216, 926944547, 130856677, 477818075, 999051991, 142908712, 780469103, 955418446, 12671596, 203508303, 396308488, 15958049, 80942206, 998856618, 286366185, 773185030, 337242896, 247068161, 572397404, 959747069, 780375337, 920473359, 762358669, 96348666, 191628956, 359912500, 894377997, 383531122, 992513374, 863114411, 123223475, 331117281, 111454815, 146068159, 17998919, 792081960, 324095230, 740738385, 4538105, 23760733, 361416907, 112179756, 640495097, 711389633, 393175299, 904470866, 849687846, 166196956, 854521106, 769661475, 431616954, 47225919, 357753241, 100502841, 435870170, 522505406, 787143188, 777281050, 544006450, 115850087, 776187856, 756841900, 728363744, 487879185, 480237569, 626136148, 680884811, 198794370, 600833948, 312835782, 86755558, 226055073, 84841663, 799070048, 110725383, 507796270, 121213442, 914122816, 236639969, 91225487, 509205021, 241955340, 554195290, 102788987, 532764824, 235979035, 998199025, 519521535, 708147275, 370965510, 717195102, 287307171, 901568896, 196770293, 789106566, 788021202, 320815433, 829344743, 510897421, 226210105, 889983693, 748420295, 269793495, 605485694, 998344298, 417777609, 315159805, 595333107, 266213833, 817869714, 84565829, 26254617, 978680066, 642599485, 901946470, 883737561, 490388772, 620297946, 769128005, 471259975, 878969186, 915349389, 489046350, 942542467, 658807378, 585809855, 28095267, 32487163, 124850969, 475871183, 847426710, 540954617, 845394691, 253340775, 14449069, 221867263, 215042554, 88127131, 396013609, 207768642, 828687069, 323677791, 172338493, 390096979, 435490697, 720454955, 597604713, 655675881, 103210493, 66790975, 385988438, 721779116, 23253398, 114728284, 742143852, 227586237, 130918121, 715557492, 7489087, 15348326, 686882858, 985097392, 477011273, 471349465, 948082076, 56048970, 95307897, 879641798, 236062681, 418679563, 595683699, 833377412, 241666732, 500347542, 179639676, 748742510, 358838083, 700083763, 491514724, 363817309, 796484073, 352543013, 692281114, 853957450, 848210620, 160490076, 646460693, 676518066, 532161387, 568097782, 955767818, 573567415, 224496004, 6956404, 711161963, 720761647, 862038307, 283740191, 463515502, 500709594, 250943765, 26005570, 966322209, 231094183, 553690511, 533821231, 938893141, 959012379, 36426698, 759199812, 674926136, 997232536, 215452537, 712321224, 522709672, 851734082, 183284157, 685126017, 316258728, 351785484, 26090119, 847797045, 261812345, 475486673, 556190962, 105807444, 464714838, 827565151, 502851926, 179000117, 38179848, 831576208, 955753969, 575065051, 903029051, 286214098, 530212463, 158068856, 559040597, 442502743, 162096310, 14441422, 549209899, 687095400, 187906450, 589159800, 874658086, 744488200, 683596034, 13475911, 600132368, 619066920, 764773595, 381069003, 348340709, 675278253, 371895550, 581459614, 614028431, 639445191, 794266771, 256171548, 745242270, 123406029, 608590605, 827544780, 720304329, 468994185, 556249330, 627413, 483246293, 54452325, 104175791, 555424203, 166577823, 488132449, 453713239, 130091690, 780607593, 880774575, 13466214, 625531798, 732519845, 86631301, 510777233, 33188062, 399558906, 355647493])," 81317 (continuousSubarrays [415902931, 343918193, 266220156, 251496706, 916594909, 183487908, 819573683, 410909122, 643194414, 542676937, 741361623, 663328036, 45885574, 599661110, 732324972, 589920561, 212123225, 426626601, 807144564, 694302537, 772834813, 789341879, 392314988, 552007717, 263515005, 391851564, 564745148, 139830474, 689551940, 165378192, 321798758, 251764230, 991334235, 455498208, 876688063, 215275076, 108543552, 182735520, 746496562, 176279307, 397900236, 980928708, 345715919, 739154585, 997386296, 31023045, 222116835, 696596571, 13334236, 105144317, 892424821, 880810494, 458810796, 731577998, 56097675, 350216705, 158484779, 258345418, 316801452, 954710160, 978449971, 398444692, 594275240, 970744182, 962445729, 223212988, 94925571, 889775911, 294377878, 667486657, 396086192, 901351444, 76539600, 279516041, 867398776, 310138459, 904219404, 548448102, 981365777, 320181554, 372267031, 666373363, 206976135, 946980399, 57950865, 651010321, 404777463, 765177493, 398996379, 486642989, 896382232, 82044705, 634153953, 204420548, 81201212, 782193870, 359964206, 507217952, 698119207, 239188305, 205081346, 558756534, 684411477, 305146010, 35717138, 817373709, 572024012, 817729927, 163305744, 596313192, 470326851, 276051153, 927905239, 747934607, 406480377, 443170362, 306728982, 961927303, 665406848, 849498963, 666404594, 89932725, 110023860, 623536733, 804489569, 337429056, 27941402, 911436544, 820114609, 735724962, 849542104, 970410031, 824695979, 612989017, 228198781, 163671669, 425047327, 733258319, 175676043, 235542330, 635435810, 111609030, 748803563, 216347518, 690435317, 348292694, 192410068, 756518625, 141133842, 895277409, 423412464, 982930597, 951557454, 450477299, 377496863, 517720039, 535768354, 168937136, 698585749, 48994540, 981597766, 449925297, 426565962, 59344853, 372583531, 135430136, 500904538, 365822648, 612100021, 118903581, 372615514, 498626430, 141267371, 586331432, 605465237, 387101865, 773812695, 44337623, 500160290, 926248803, 539819333, 37656570, 949653760, 818851998, 648245026, 374331139, 981894497, 903376118, 380876813, 117255510, 90479634, 461922021, 733796555, 775917412, 663608923, 916628077, 598712843, 926608942, 340312690, 614996364, 485920670, 763269902, 222557106, 720760553, 659147595, 798312082, 653358631, 431722794, 874054726, 540310355, 700299066, 124649589, 479420597, 74118813, 625057465, 450014467, 808583398, 666844052, 669409336, 172823296, 15052321, 589243485, 972321292, 216810258, 145194116, 58657973, 879739883, 516664462, 201639713, 547169435, 409245973, 361577765, 813347465, 469742829, 267107686, 108123445, 707331600, 727328589, 158875624, 387372819, 545756407, 495169015, 916966998, 76851608, 159552681, 620094824, 88424962, 567795392, 584383377, 699887772, 543563486, 636205583, 935426129, 751767135, 977879847, 240199148, 535654032, 82285700, 382886394, 708611150, 252892534, 51695558, 543309343, 887453022, 787203849, 230828377, 877631359, 564224902, 847641766, 259416389, 122910781, 819435044, 367118408, 43350399, 719347191, 543652343, 382337780, 69323814, 166711995, 278657005, 438130251, 242251507, 173125262, 143778166, 748412300, 161845701, 404818465, 631928486, 904417072, 134001332, 971231479, 364485339, 167348442, 776007602, 425715015, 100769149, 304539230, 303357812, 587295883, 358963447, 967471207, 148562585, 388835795, 45826475, 334158277, 876319935, 629143648, 424816940, 659259782, 752361212, 431337393, 445267894, 398390358, 665687065, 205928369, 953084298, 138321091, 771947051, 346275978, 560808132, 288186377, 760170616, 50086999, 436606484, 858979244, 394007143, 612374509, 665890061, 159186635, 244066046, 711577310, 981120278, 787759585, 530186071, 722324102, 680279425, 971230274, 822541505, 123414448, 274564380, 471408428, 601789956, 885465084, 57027470, 570865181, 979046542, 180027116, 460014818, 985024417, 560074008, 381781773, 473390163, 525110423, 475707615, 126679862, 514656123, 95605997, 67775680, 301098014, 264024852, 926381537, 473311241, 108705898, 500084279, 516676800, 778974925, 553024639, 555337372, 485450061, 104179915, 803004275, 184407279, 235526325, 371294052, 223093969, 655591449, 459926030, 530201851, 642145772, 525023518, 468809826, 874923671, 501587638, 677137377, 950827993, 480428390, 363995121, 155292808, 923762237, 757371572, 88947379, 694894144, 243376480, 729389169, 392027665, 653904713, 813539533, 862793901, 654334365, 931369696, 68302198, 559183607, 665541995, 221591357, 762741076, 159857055, 871227047, 499415051, 486039621, 159431606, 11778775, 632909231, 787866621, 990429816, 912217229, 239241297, 503344535, 60105056, 465265818, 551428341, 131087483, 199786217, 63134374, 323486675, 491542166, 758614678, 357311342, 572343650, 218913868, 564501740, 322199933, 438790300, 225531396, 198062739, 384893895, 441912825, 175638373, 277513619, 91317600, 148289971, 597198109, 205305918, 249361347, 662630540, 65558320, 168764773, 549188770, 643419810, 876225308, 606985887, 273898099, 375519918, 653568634, 265557482, 326560752, 309328679, 14302393, 569914931, 135218898, 516235740, 400077968, 721441250, 476512682, 483941521, 404162131, 393365293, 11449542, 879912141, 262942089, 945331120, 854311826, 340673963, 896206661, 963141047, 370096397, 301784532, 593329434, 852363231, 711714698, 787822287, 434337915, 152493368, 132734514, 388228301, 709145968, 726983239, 523139762, 768797466, 741788982, 752029251, 684075679, 958927940, 577639504, 944217021, 599841786, 707840487, 248977856, 594454445, 900709692, 467976351, 399766897, 379150375, 607917522, 408334398, 854129910, 619887569, 807290715, 320707811, 549330623, 437307127, 833667633, 943075445, 145485948, 81449846, 928745062, 781275911, 37515882, 950948526, 925455693, 67662739, 762077401, 126687793, 299297581, 720002928, 427858529, 403527296, 982673616, 806118267, 39181325, 81126914, 701223925, 527054232, 477357094, 594426372, 179751606, 324394627, 597846435, 977707861, 746832057, 217609570, 254370142, 117410536, 618146951, 881763355, 823970630, 268544114, 200897891, 443180476, 393233634, 32912048, 263885175, 26709958, 912919408, 814596187, 596847315, 140510290, 867848251, 814987943, 475312984, 885538269, 853418525, 130739000, 280308826, 602266456, 938792077, 308991245, 869648497, 621946378, 943797994, 179675240, 110117178, 41430879, 385218589, 212131683, 369930198, 38140291, 316668078, 624460174, 940497197, 454608013, 833389785, 342236403, 181055820, 493301053, 80215646, 659127078, 45340872, 210618389, 696552416, 837934125, 342997290, 853071954, 734877215, 917544854, 852499446, 254114464, 973800383, 811815065, 108099828, 990819965, 463543612, 530888483, 96638612, 411579764, 934331239, 520287528, 37805397, 921106884, 640426059, 416280003, 912937942, 223176476, 774291540, 814531692, 791424121, 359216579, 111950214, 366505788, 988563424, 295247481, 110137226, 156294890, 419560002, 408577301, 313586169, 550357513, 876308477, 437205835, 79377204, 325471745, 12588973, 114081620, 383433022, 834937520, 409231311, 825526602, 368046298, 400032468, 393909536, 101946552, 540132651, 379797928, 890731502, 857575093, 791295460, 489939814, 89323658, 402991123, 427021515, 709457270, 41336560, 938137497, 301887951, 165545221, 362383210, 810879792, 636549198, 489341040, 823131648, 915984233, 303781349, 479498612, 385001542, 541693676, 573558863, 510891225, 444028533, 889454313, 540363646, 928270717, 88745581, 35929672, 488807567, 447994293, 155494206, 698751037, 298450577, 548885397, 255135343, 667981461, 989740351, 20515178, 401874407, 987571033, 726500474, 571041455, 84540112, 31360380, 310260296, 776215999, 198961617, 417963939, 144956746, 628473133, 772183586, 956822830, 999096513, 43685273, 188445688, 654342728, 589270791, 19297632, 641302262, 188550051, 977227750, 404037387, 169012380, 708262880, 764890124, 855467928, 585262432, 314138860, 366288161, 776621414, 317399983, 844938538, 843064638, 51350869, 375136826, 368803587, 256849950, 919061180, 637721104, 686429659, 400201974, 594623130, 733324199, 119938777, 893355661, 261240180, 943725233, 85372073, 25991337, 109468766, 972467970, 866350374, 133906251, 447989266, 334794415, 256900901, 905952094, 117812741, 220933019, 522344545, 615336554, 26921928, 737757611, 644777445, 319778814, 195153693, 56688377, 912675542, 607989150, 359941448, 426924141, 198326046, 521793884, 610626797, 899273984, 551956070, 860233591, 514946423, 14750699, 786155699, 973917161, 494080151, 649919430, 26479127, 905060380, 418727474, 297174942, 846276599, 327938165, 541235879, 480941781, 90636134, 212672689, 904218174, 143551685, 548377510, 343960900, 33212668, 863546682, 114065982, 999189930, 85082454, 918982387, 656568206, 45636337, 969080868, 217059411, 250798351, 784408324, 884424341, 783340188, 315343412, 193563098, 659735953, 121066460, 650016257, 998679653, 383191728, 612291913, 536058969, 281559985, 446460923, 420342884, 979485752, 695888234, 485554056, 800927383, 585717697, 599539894, 917876401, 425935333, 802314797, 261121982, 585796198, 734136831, 782391497, 521669383, 691406502, 372666024, 56537220, 489598454, 181815522, 582336535, 837892317, 490755172, 558334744, 773718272, 384994013, 984251427, 984679836, 44396218, 710244085, 205938018, 125441107, 249899049, 980373875, 548349804, 415091238, 981065993, 610621714, 93111988, 653339519, 890019947, 789187318, 318823886, 614224585, 633385937, 925582926, 864844172, 7868899, 742202417, 545800947, 561876572, 875578320, 921195004, 931366309, 931275275, 788099939, 417768958, 299851617, 836067526, 790105584, 39692929, 616382255, 98140074, 687177418, 761967952, 772748537, 275315241, 118206894, 619824781, 252652477, 794173579, 186382068, 10723234, 187088429, 414963981, 57333333, 874954463, 412518961, 156763648, 670778434, 340118276, 593541945, 888702329, 829245261, 768173067, 495261498, 599363134, 442116198, 209548962, 157114328, 191145118, 273520023, 521543459, 460745407, 804019667, 669709185, 919926155, 496766140, 394107609, 513190794, 205409200, 290347936, 785662769, 280470876, 600661780, 714026288, 114555845, 800388235, 227407620, 985616086, 153380624, 431848248, 618835904, 466713604, 524410020, 162629189, 556422154, 123282528, 237265904, 728600549, 453960639, 946996998, 126725530, 258892519, 655632965, 411844729, 625879106, 899717627, 321193051, 284821106, 59134746, 208723990, 406193397, 64899581, 277501112, 349323520, 987418542, 560639320, 141917865, 390260102, 101455033, 138984464, 498012351, 982652185, 611842758, 632314569, 283311835, 949015010, 760547535, 953130687, 550659892, 929877931, 359473421, 672262007, 137651174, 474010919, 867041306, 770508769, 204424287, 990063011, 173170699, 394339916, 743592053, 692012165, 550116076, 777700405, 816860400, 967099490, 53486911, 694106671, 198151680, 312070798, 792301040, 352617740, 359823999, 633304835, 241725097, 169276529, 945998733, 618684063, 198166443, 816803088, 283080272, 617690904, 576492605, 578188824, 209324202, 276420259, 841043145, 832328682, 94544538, 118719179, 472245613, 339503332, 175011231, 489384553, 380019973, 358751815, 529196253, 238794070, 607676745, 814855859, 355917580, 996980214, 500731470, 200577529, 260006012, 26657560, 991919687, 294784898, 736175780, 219525471, 637569872, 138966025, 189965450, 867559998, 724256132, 569587683, 175695635, 684850772, 298291560, 812231200, 899045283, 810970786, 286761376, 383402950, 458407692, 930299966, 398095497, 847480246, 431422509, 566428017, 791425006, 130818957, 684618461, 968607979, 618042115, 295303881, 454510298, 563179362, 28870578, 194820456, 568782832, 682979358, 855258783, 78583497, 120494735, 772468593, 227204808, 526472013, 884349547, 952231280, 931281800, 467267741, 653091425, 142902506, 631515518, 253553048, 338079384, 627550829, 76932888, 943051586, 126635481, 500954344, 801682612, 979997221, 643283433, 13698932, 28660680, 441726112, 246449766, 599087994, 287026219, 689661734, 397333955, 949483901, 151018152, 130670962, 582993010, 467929741, 990458999, 528218405, 24211219, 886495033, 344673256, 192842794, 491298802, 302058888, 502537110, 988015671, 491420042, 680424891, 618826640, 226642954, 927551037, 998683274, 892575330, 100849562, 140635788, 50012733, 341035251, 852459121, 108464795, 353575354, 180152314, 635450499, 89918449, 582578237, 318984094, 628506862, 329546412, 611824016, 868686128, 245684142, 867652842, 476617049, 560305432, 628271533, 940401454, 716513579, 473252054, 792790347, 89034853, 455673819, 448349076, 991271869, 327105550, 602993663, 910781760, 245948404, 181902160, 893509760, 802439559, 972008647, 574300880, 849416383, 479694826, 213468710, 686417796, 12131605, 759141647, 673343680, 929768719, 398677744, 230171887, 536229341, 502697225, 8621351, 444608161, 954505555, 320444496, 763608538, 541152835, 754093180, 348261790, 731870876, 297215714, 513582291, 33685032, 945308068, 214179253, 722307252, 494532577, 342070717, 549271982, 678121432, 174626782, 273911249, 198443744, 176441839, 578572123, 283499836, 948559193, 820007248, 777345593, 146463876, 794239644, 411276076, 198687112, 369380238, 234625304, 614278361, 568577000, 929861978, 279832732, 833998916, 887232649, 163297983, 906687402, 221457235, 8196848, 623931127, 812420368, 606172951, 290113567, 283129979, 597980013, 36242679, 903081199, 26738657, 41378097, 662575437, 741675378, 889829968, 288350116, 705852682, 226311698, 170109999, 660407202, 56075760, 43814766, 827412657, 376765311, 661831955, 281993556, 160051272, 319774360, 151301347, 184069574, 982240264, 784741467, 244750084, 618309713, 564069246, 307846258, 700893594, 106386154, 941471149, 464414105, 778073539, 769283539, 3763418, 580817187, 437744161, 151350776, 309962724, 557210490, 191442566, 553664640, 35241531, 244878978, 581571292, 922390607, 100939814, 232335133, 229638070, 412208733, 146578803, 913949773, 14029973, 730579429, 520278699, 729811993, 545322699, 440166877, 582515703, 565588988, 130618091, 372864829, 232394494, 348115471, 506460365, 599819717, 135669236, 603693565, 786042117, 111167478, 265267581, 42618303, 8284606, 233792584, 866084623, 49927977, 911140656, 449105107, 643123591, 687395818, 532818270, 689787965, 790340589, 755500740, 48818335, 196865366, 413225471, 396125602, 118780422, 942775087, 595993221, 850156181, 542511697, 959505827, 668010806, 446265171, 731612981, 621407556, 351925506, 652542430, 450549982, 899159930, 40275843, 719902455, 916579810, 48003508, 185006249, 545000289, 508807244, 492022468, 215760334, 847561596, 257239832, 307116450, 6635172, 964773198, 529186330, 840943613, 768013422, 619013824, 505897222, 766105844, 841605557, 484130869, 233569649, 916450692, 376755377, 479426177, 700999389, 53907425, 597054039, 215568397, 620654148, 446264637, 22768052, 134699762, 740678283, 700172819, 523754930, 294118369, 628362335, 392483255, 131631585, 85480732, 305983558, 809282938, 513706258, 303391000, 446476712, 776161599, 915611511, 201467652, 143115152, 626091712, 112487937, 952711908, 172869051, 451301594, 362766179, 242973290, 393353834, 42778944, 654637361, 777266430, 632176682, 990433001, 713784885, 263688680, 284520555, 737811258, 224396004, 197808097, 341480987, 881277109, 975537957, 544704402, 78626213, 100125785, 131586059, 979527441, 623791799, 228831939, 974705152, 368335886, 202810047, 869593497, 643604524, 696160398, 891428634, 164292548, 898212469, 111586326, 859013929, 696000410, 318421120, 898674055, 497806398, 814066756, 834522674, 357888468, 816841562, 211728407, 702680887, 874222899, 238700034, 421065613, 54581, 681152962, 876568723, 285497070, 329623789, 75975532, 920867244, 251148866, 681414139, 957853167, 244914221, 752228579, 279339488, 749666579, 388249400, 4801154, 78712371, 354388024, 242310714, 735109332, 935100651, 795591037, 633980401, 329092036, 282510854, 440041810, 705635003, 936183632, 256236473, 578547139, 161836620, 940234184, 398847610, 33611306, 965471222, 381623886, 955201404, 259720576, 939499629, 643399769, 164048277, 304481041, 400817342, 594069941, 95186122, 657805226, 629679545, 836358435, 881607500, 120267799, 171431270, 696611255, 646038085, 424259836, 109764682, 542153748, 93789679, 724228038, 705852733, 217642123, 446402304, 491951158, 980474347, 708377586, 842372511, 976882548, 432496085, 267659998, 822594553, 130916915, 5134118, 356509195, 263898477, 110999291, 297873854, 355324409, 163011428, 559408446, 99435658, 78131107, 231995598, 815207977, 897258097, 839188204, 784000383, 159108332, 696359633, 50932674, 110776450, 466407712, 952209160, 828860074, 47546523, 891243967, 252519533, 164877954, 381444813, 491867704, 791304451, 17331092, 964255464, 668213815, 871275306, 873264764, 593039755, 187112222, 343064180, 542773845, 264582860, 660393043, 647601005, 776194456, 896998029, 989291709, 113474139, 88662129, 769505031, 482152702, 833393927, 355844506, 894417858, 292492921, 87604666, 902012321, 586207225, 501646501, 981754779, 502288558, 877379895, 706413168, 576148970, 410578235, 20945747, 989181350, 17602072, 683196311, 188584409, 131982612, 978220697, 306486586, 759703963, 144768016, 365980024, 65320353, 799275979, 92406049, 998675190, 338575038, 920898466, 53836609, 968526252, 853152894, 789501549, 414800251, 771545069, 23458685, 639828234, 500157268, 856064389, 316425486, 740406692, 200040871, 83306361, 536199447, 262281238, 267492277, 855876600, 372826863, 921586054, 962690980, 332166512, 846311021, 208139679, 968877624, 900835663, 526083887, 936151061, 58566586, 865214042, 189345854, 42569812, 962868930, 905358820, 701685172, 447789891, 902949797, 415618356, 282859584, 650268084, 8580589, 411700698, 666725777, 668158529, 104897449, 896537086, 488498362, 768907014, 807105438, 356068079, 385921172, 60483201, 174599726, 697904490, 626152102, 625759667, 945859656, 933388664, 566902118, 530910643, 535038847, 535951233, 758715057, 672129773, 898138443, 46515879, 180988489, 713885754, 409614037, 904997139, 622838313, 361280318, 139586565, 805605129, 41162927, 841603864, 112220197, 986753209, 960244374, 728915396, 474392390, 426945710, 634225484, 964830741, 429334280, 97755248, 106752260, 852793020, 976235925, 295065926, 825804272, 415663815, 431893425, 636849261, 727164446, 598380132, 345053103, 455043602, 775522277, 321665020, 742300155, 169443938, 488823775, 203696483, 75850661, 392404870, 591138159, 349384546, 387939524, 11825507, 930571331, 426634776, 680474276, 59946238, 201287729, 292570, 894720462, 345091225, 995739924, 746161431, 912848934, 557137626, 196809404, 835035144, 35619532, 974242760, 592392653, 863278427, 19959589, 286505553, 959675261, 715976838, 182025071, 620280942, 450656400, 638674780, 80528605, 530312303, 4128717, 409664605, 796178829, 414779144, 6030155, 761645867, 35248316, 964474520, 910906170, 268552509, 998034551, 884625023, 3009414, 342066015, 340353639, 161064763, 994890192, 166831059, 621435399, 625304861, 518291640, 557128863, 446249797, 57288599, 152426741, 348092660, 787332614, 809693333, 511269214, 351901108, 944629385, 875581607, 592461905, 121901661, 760211342, 639602791, 959313310, 929319598, 487022892, 603282233, 894982964, 770683677, 628888089, 759460265, 135638920, 121279303, 428917572, 930555972, 21832857, 712376596, 721944545, 586357821, 594600467, 774164215, 649113424, 2414758, 232212123, 3944493, 467426076, 521470628, 995071724, 512231976, 684765594, 247706270, 300585372, 191150210, 449348711, 986573883, 861011457, 215489592, 25705599, 354527756, 900779411, 958352047, 602167790, 989148488, 756985814, 220859629, 19092827, 350932159, 281875443, 545206440, 12865966, 259580504, 432160769, 121654297, 264983790, 501681741, 917960333, 848601766, 163753074, 384446515, 630146161, 211261683, 264531719, 964161482, 394331624, 863397641, 754018903, 21223153, 892687164, 541096705, 887768692, 24463639, 586500507, 637641921, 708831194, 656192636, 655836254, 651099107, 307302717, 812817593, 71808166, 961531667, 481937901, 446164337, 752855343, 371967589, 973987233, 354413351, 522229860, 902204682, 767069940, 965870175, 966880049, 407881245, 780805914, 674811574, 91140507, 994188165, 732896392, 891802091, 158572499, 857223349, 287637819, 986750608, 623374724, 376166470, 950447278, 904412069, 840955386, 401040676, 30513266, 968937242, 953271139, 375372042, 550583618, 562196031, 11916909, 321064846, 562063521, 659899177, 855458794, 97125243, 183133820, 625483434, 149876836, 892305894, 698214810, 670574053, 759144613, 860249775, 799085495, 511329745, 683228791, 798773339, 985665847, 486195449, 35760099, 457314137, 432876689, 128661931, 566801794, 8669810, 489015798, 432577431, 967334461, 988562663, 428296866, 253609377, 626285956, 63799772, 91401723, 713874260, 27688639, 532659291, 253804246, 320566373, 481349217, 774296015, 205418279, 668154756, 686663195, 160111065, 702289077, 384849788, 554419790, 10665826, 907933946, 77613660, 572559725, 502014564, 557192130, 141557761, 709364920, 517389599, 814216513, 447442480, 506846217, 870221089, 125197552, 150325807, 262592179, 506511418, 135061498, 477280673, 740807876, 273773181, 642724083, 314114600, 593756644, 90991288, 853624163, 294179489, 448501554, 665893775, 467779444, 718626157, 404790335, 987039675, 708486901, 970122582, 101432605, 509356055, 501575755, 2563587, 236884014, 908163194, 115523961, 19307673, 842130071, 453858342, 947561791, 656503425, 790588642, 706334271, 215151268, 21285842, 416751109, 985340660, 310289405, 653431282, 501585611, 274181187, 899423229, 748337790, 157178486, 500493615, 270986535, 900485172, 653911191, 320367950, 931052248, 201170969, 554894802, 26300819, 777947238, 498368070, 200020178, 536502490, 82201567, 594930838, 997168827, 977877337, 517137844, 833697582, 180074720, 690381186, 745339479, 364247996, 865682377, 514915225, 179906767, 532890384, 304094368, 248612046, 294792219, 833121134, 550428759, 305328370, 701982542, 301052734, 43851237, 307291628, 973874210, 918700840, 346348197, 796604574, 460052835, 893496414, 505179361, 780071430, 402878401, 171469672, 942128267, 377639456, 253858839, 830942035, 964214713, 458806493, 473632631, 981081405, 922642864, 295549351, 678430230, 914102422, 509611926, 673829145, 627984628, 635600513, 709754968, 290786731, 989744342, 950365514, 766903751, 875964010, 247747342, 192108339, 308274524, 182263423, 562107454, 141241451, 156198738, 425937800, 224086285, 914288065, 404610570, 851852936, 512910205, 43222368, 878034169, 138243509, 938038233, 410478860, 270819312, 264971617, 521702342, 508265327, 584474265, 681247831, 984288181, 172974387, 272581074, 1353079, 805427009, 484659550, 266372693, 633505277, 536132958, 304533156, 948486152, 683118565, 764604085, 805185808, 470262646, 468260655, 475248120, 287633800, 468533733, 258984448, 459073886, 706767891, 236223445, 175585499, 764874224, 942725468, 562574909, 605406847, 887007795, 685272206, 423120220, 137422838, 492249852, 854647241, 198869029, 522582948, 659430846, 917506212, 400306500, 221109888, 341616335, 360738075, 194576435, 169001618, 531509871, 250853688, 324980221, 456714738, 588019672, 495029531, 845713805, 168510951, 978648511, 500666992, 935600802, 762702298, 341328805, 891673763, 301395736, 264730296, 18515792, 484386422, 84127533, 945270089, 640392530, 33969145, 66348030, 204224550, 102584800, 941044349, 131168486, 862882976, 626330819, 459187126, 595521113, 639637110, 173520802, 602440711, 464637515, 143350828, 574873994, 220125693, 613920077, 823042421, 961302344, 793300569, 899578075, 476509459, 323880712, 683293263, 202808518, 585403016, 326329579, 506019079, 518710214, 582497911, 31641984, 920877767, 888450444, 18279944, 48845127, 388522338, 156375295, 685914448, 858397861, 655355569, 80582599, 191712976, 164309889, 142186957, 943803451, 663914691, 646457243, 970009725, 354737149, 417271195, 560883913, 849007805, 838228256, 149440714, 300893149, 59920171, 930281672, 772235928, 242922802, 748561393, 505300356, 129374686, 176169178, 314148666, 739272254, 504761119, 916198290, 653125549, 558384527, 519094754, 258306202, 114719999, 659808559, 8954796, 645212490, 790321989, 158432393, 181222855, 582573524, 347402695, 699753381, 442359487, 359750256, 508747627, 398594543, 870387256, 963415522, 724574928, 653436174, 414480107, 721490191, 889185828, 906219250, 568782816, 537589789, 716532175, 546722697, 777643945, 852130035, 468860539, 7136281, 170526545, 885543856, 82783488, 960449022, 836992151, 514040329, 829975974, 318417595, 641513350, 302678673, 59545782, 42738923, 774542038, 905581919, 419940574, 675426138, 989452754, 385822280, 23332060, 503843889, 739527422, 505868863, 699260049, 188052797, 14161944, 196425888, 974356665, 123482602, 108328254, 87491, 209036214, 587899317, 960678588, 409254501, 165524498, 875497777, 419471823, 384892271, 238034757, 563228577, 235429391, 176675284, 241532658, 19271968, 655004281, 667824195, 910879418, 256305800, 161519927, 396332921, 169550176, 552596823, 369756125, 141390563, 30165568, 980367986, 159807501, 788538051, 24076561, 926637406, 961751216, 324039683, 561135398, 656064151, 897044598, 600511976, 454395708, 205200052, 423051082, 395475821, 845123549, 754290907, 648933244, 158288834, 814191034, 130171591, 195892347, 168525314, 703382543, 997089887, 914834348, 40712576, 427385412, 732430090, 356998681, 55673321, 524723219, 663416841, 564219561, 564840225, 79696385, 556073553, 707208933, 904866516, 280555765, 818083286, 991137230, 824498864, 688568314, 170313710, 515672966, 159115569, 368665922, 781463703, 308637530, 851713997, 31192882, 209788821, 784732418, 673355249, 105154249, 288939922, 291972898, 896421883, 592236738, 706378062, 451867015, 217051569, 292049552, 435396117, 490839926, 779589312, 46507405, 365809494, 852138828, 332718164, 264344949, 907713277, 902999529, 340981875, 992573993, 432887883, 763008077, 540261798, 290691367, 577532090, 180110254, 708922303, 301164153, 328183624, 350475206, 132326927, 563926674, 199917935, 876860122, 876944200, 345798994, 941988910, 967920288, 660162865, 705579271, 239829252, 512245670, 504420813, 822998846, 503533036, 735456800, 31553207, 949425823, 925406174, 684600317, 961678582, 315635977, 451562628, 265510105, 914414632, 749077481, 183981963, 876324458, 594709151, 2415680, 292759144, 221872720, 842964836, 21108827, 929370588, 951935151, 491465769, 188984185, 21789713, 35819677, 799353867, 151215135, 731521792, 183685205, 952687401, 128692770, 953799857, 194612277, 941157061, 535039276, 917931754, 628618722, 534010640, 195685479, 678036431, 467654065, 693847026, 623920989, 742239644, 783326200, 155021930, 711597468, 980106776, 946672526, 179347347, 243721669, 729943923, 155539334, 131500514, 790593009, 169118489, 257009110, 941886483, 446374905, 497385096, 946380366, 725922536, 395095751, 347493276, 972709897, 360229347, 509544962, 525716197, 350361286, 801728928, 118222608, 33113604, 331217478, 444729392, 593230458, 30719189, 433945225, 899385744, 970325010, 813441208, 706390394, 289831299, 861526262, 11998444, 397164252, 848342039, 543245963, 795138065, 399173680, 705074570, 720739547, 278453088, 285185252, 978351894, 59235513, 91750329, 526182231, 25717729, 277883658, 570883659, 111504956, 751345022, 311887111, 387426878, 305247972, 697111263, 820019424, 549168345, 727937903, 409448308, 871266275, 824153472, 216373083, 191211148, 448842413, 444892338, 907140569, 135480380, 121359849, 76328556, 157574604, 901204338, 383863570, 274362722, 592825990, 605671360, 821281508, 49809865, 57744112, 204234285, 735643129, 638923501, 440086792, 709316029, 498926061, 309698225, 560778870, 467769445, 787278636, 17572327, 594392990, 893293763, 670029764, 484477221, 214091117, 753398345, 525451993, 853262702, 127000233, 853471665, 847719135, 439661331, 60562497, 446341768, 990186659, 729298241, 821428284, 432415196, 320514917, 787195136, 824530040, 939554800, 572021302, 264844651, 87550257, 143559288, 641214401, 961704, 271292539, 546329987, 759918532, 824700895, 657950775, 376517340, 136815401, 590783699, 299981013, 889112214, 622831227, 647886225, 945713028, 556087155, 201629127, 703991759, 49674453, 950573617, 920036148, 934861798, 559181277, 176690109, 56644415, 723936341, 40711908, 842650839, 437335441, 312761762, 45733749, 702891371, 592721051, 779314059, 755279408, 707351199, 995477445, 35627566, 275777431, 651906209, 707325827, 314246581, 366587832, 436452577, 385943554, 244764218, 196307856, 749134716, 448204136, 672500824, 875285195, 988257381, 501556942, 425235210, 251132430, 212561451, 363780744, 779626108, 474867596, 438935631, 671036210, 642217212, 808293878, 651218474, 595273753, 471795150, 991634381, 623073862, 714222408, 712361641, 104696774, 138284603, 64215301, 584356429, 767079497, 538805848, 756678304, 631660685, 751535754, 277929961, 196101126, 540771616, 921335378, 575394998, 626149682, 29831438, 528530805, 688473265, 65373099, 393867352, 719021064, 933636066, 278215282, 793601014, 207154299, 994201093, 687435040, 714420099, 61542852, 134559643, 336167506, 712632555, 808916300, 84174198, 367113856, 90690961, 906283671, 545347122, 290794013, 81473713, 824921536, 585082274, 762958943, 819865035, 97716948, 882138458, 177039546, 302292373, 876255621, 13656249, 686378188, 776733755, 646303364, 265037697, 418882722, 934621415, 59455839, 770993104, 690374845, 620860486, 306800565, 102638956, 249114117, 1361679, 655571951, 363732675, 771313247, 587541758, 472950018, 352561537, 438972128, 815825057, 659185329, 231460909, 778161189, 338383234, 331073880, 243888299, 845474066, 692722367, 684926257, 107259986, 726046672, 297000078, 525324147, 588737211, 367206117, 930221753, 682655152, 930229397, 404293378, 318364357, 166218879, 668737992, 560275055, 71067837, 259370899, 836904130, 258163394, 977687649, 206948815, 144271242, 125593593, 681725171, 12730137, 618231856, 8053600, 871570189, 98121064, 797963164, 988867746, 875466438, 435963767, 915037950, 240452333, 597690992, 51257336, 201397400, 444915041, 768969298, 984183653, 51104147, 393013678, 902940549, 674031514, 599027441, 750508791, 363746870, 925920449, 247735641, 426063428, 898000847, 829983881, 562285827, 783447218, 64299320, 288735473, 461458924, 883758583, 617924646, 695380609, 426529013, 780856479, 540668202, 304055968, 433442878, 712210496, 560521401, 820321122, 481086660, 201463147, 373752564, 884526811, 626075310, 19089338, 948867750, 426303328, 230835011, 763132673, 692611124, 785798525, 705531397, 529357762, 564879972, 638215764, 151733868, 510779198, 315740785, 924116968, 587219043, 79446640, 213890462, 231617374, 964891684, 889791689, 668640466, 88550267, 47048711, 443436133, 62733678, 684990526, 289513450, 724123189, 433652105, 226738259, 831821741, 647409553, 998982203, 873852795, 242194410, 688438769, 869360118, 484237129, 155625306, 405586887, 207615877, 498835533, 898959378, 578215941, 230344009, 637230669, 746545734, 857648034, 112222274, 272179815, 547745844, 883604447, 621742824, 54555314, 455834807, 186728529, 136949635, 509063068, 58899286, 111694648, 486509872, 280536314, 888338957, 564037031, 194273036, 770959681, 767353351, 580785982, 289136155, 351758724, 319853571, 892756894, 23988993, 867831183, 953150149, 22164904, 264858929, 203518089, 590008073, 335875412, 282954212, 108700567, 211439667, 794484573, 576085612, 144725404, 519497181, 504422927, 591893887, 3425973, 57504124, 358897482, 903470466, 708298948, 143835130, 282858492, 194083521, 959758225, 960257393, 679072579, 631313489, 999537349, 543878193, 101215271, 331641824, 148813252, 504390411, 593966374, 130352330, 752807454, 647101776, 820029754, 596217715, 983282518, 227345236, 371080203, 39045450, 577253641, 867539365, 551223588, 744180110, 887942973, 778989696, 658344192, 671216812, 101931662, 980573371, 864688771, 332148935, 493406879, 912643998, 110067830, 471796640, 841582894, 886229398, 574154832, 197682510, 212953097, 763492600, 766751726, 840345676, 720958612, 643531644, 637509544, 529331794, 899771987, 840641903, 153724109, 78385266, 839140131, 610645360, 164629148, 642749208, 4421027, 69807590, 23360852, 7020035, 877177343, 108416780, 143386496, 758121575, 881384844, 808508244, 275046481, 422103057, 917292140, 567288480, 267152205, 786655659, 186847654, 665848783, 120604507, 704446652, 909240930, 766275756, 923307169, 710809031, 502746171, 977398420, 417918142, 248303999, 371910201, 732799234, 168416168, 875418307, 582348645, 361637032, 545559979, 401642261, 534123380, 263497778, 521433608, 224845182, 340703130, 907360572, 96185174, 559034378, 584161819, 634989208, 977895406, 163334175, 32301740, 166986686, 766896875, 277741173, 561001873, 943679277, 200736151, 264145803, 747836643, 792980288, 546009057, 499732409, 40715069, 50695203, 565799502, 828652882, 506868534, 233381541, 384550692, 993152294, 795961362, 337284145, 666587260, 289816126, 865918503, 184638132, 576476971, 855766564, 588908155, 396128143, 502396401, 827906009, 904161006, 382384696, 861715844, 132742897, 28024347, 514334491, 614845196, 181999113, 212267557, 208005134, 217249677, 962224102, 772558263, 455268895, 579124267, 148065825, 77777428, 765597927, 919213579, 473532652, 703363566, 745429475, 725888791, 130863808, 76317777, 8437889, 686004386, 337404769, 126267359, 358003748, 400393510, 213467185, 256601769, 841775526, 26665688, 398269704, 120445415, 871095602, 313473180, 735577060, 814897881, 575936677, 901658947, 666598941, 855209966, 938541398, 641652983, 558279227, 68416213, 669858067, 774856151, 559025074, 386415435, 238206531, 51581719, 979897606, 970094486, 349945294, 127827951, 682965401, 332498847, 875467006, 485962539, 290592472, 73213353, 30420750, 30994305, 84277410, 245847874, 350635120, 216732562, 425032605, 910795465, 528276986, 23436768, 465001414, 490505886, 237810766, 479041335, 838368902, 102583395, 323441246, 891864073, 683806601, 136608862, 187436937, 382450689, 94924978, 362251654, 969652987, 401558242, 148807841, 381861825, 684119775, 168347410, 862425263, 394537128, 129602549, 197847870, 978137206, 83817114, 453898620, 955855594, 905276256, 913200900, 589482767, 213136797, 126106883, 564645837, 994350457, 512970598, 237933079, 401004099, 682008451, 769178203, 337849359, 921681489, 417898096, 323839044, 623823174, 85723008, 634068222, 153318662, 136744616, 534625271, 923798641, 342620643, 569799860, 135289623, 281933255, 138921049, 984712248, 904251677, 468017258, 104435268, 54467199, 596535401, 855806457, 948255271, 453634040, 767376716, 864304711, 20895929, 249203434, 825573596, 554395363, 42363227, 742590674, 359287752, 301161333, 812112098, 456346329, 267269692, 782975027, 593850297, 774286012, 223156356, 219999678, 636023742, 954353006, 264700885, 74592620, 9306340, 978875130, 607013509, 572794344, 737590354, 840018898, 345948514, 789047865, 590810027, 522150694, 751470921, 514333725, 282410251, 209692242, 145746425, 21696467, 366057517, 616715532, 10417841, 914078277, 895144716, 276778205, 610426832, 211457085, 810541046, 204825452, 268969612, 492814793, 481710984, 486257420, 293018120, 635094922, 850147771, 616242522, 199004439, 606207999, 987778471, 102343084, 288918600, 705064550, 617382795, 645185193, 644183054, 279972916, 319226118, 560948983, 942375225, 147172918, 172981200, 839474244, 893903042, 72761109, 982514472, 416665095, 743892418, 206139727, 804809438, 263497802, 343237104, 179378397, 486746157, 839942908, 275217159, 532092094, 353897692, 848255469, 385506512, 301839227, 640979296, 446511670, 459279365, 868955420, 815026528, 993110298, 667834189, 125797590, 973267361, 591835244, 144406088, 639364945, 494750170, 222999574, 923995566, 286716235, 662902511, 269082009, 69968867, 364116727, 702367426, 669263622, 598757742, 176660374, 115892541, 527588488, 266123971, 691785196, 509634063, 951518663, 170071456, 975194410, 50622651, 411512883, 59670512, 367652545, 460068608, 217584506, 736213512, 548359003, 826829117, 411004938, 614944882, 913024192, 284329730, 595368049, 429886751, 729973594, 32152604, 796303530, 924245042, 126752684, 7576568, 618616671, 427149452, 944720644, 869613289, 993652463, 756624274, 335458295, 917416480, 22087514, 639889384, 191755521, 407910528, 657353823, 913130230, 114044139, 750872955, 330146788, 645420827, 460095164, 867425183, 536744238, 905903550, 53026344, 678730915, 345580173, 752823115, 948346113, 858452647, 768253890, 975913750, 806033642, 517887012, 253572862, 733835084, 479393634, 856753266, 86549889, 145988337, 124512547, 869625834, 625218842, 184703371, 868299878, 12127038, 980280681, 142925750, 198201609, 702181022, 887150684, 900888333, 687973213, 107868854, 423695358, 162376663, 128647083, 893492704, 127624858, 2237705, 534380460, 624884813, 283406942, 256226786, 907060801, 418055396, 399633442, 784165780, 749779977, 418559083, 299348072, 107750855, 265471494, 379201738, 249284609, 637562724, 88886506, 502024313, 943292346, 651542483, 373803631, 932440516, 652257982, 268479754, 958516031, 447813301, 753396471, 821791096, 686529212, 776584730, 30838080, 252875776, 114630461, 993470059, 104045743, 245573819, 621700203, 100000597, 35405656, 463482677, 754876259, 738876608, 99301486, 426620328, 196980577, 298423183, 484982255, 840507404, 390064205, 7516910, 810682321, 279064637, 220520230, 452273319, 76657611, 885431741, 990023977, 645344195, 633702472, 336463253, 441053010, 467175097, 880764478, 778467388, 510579257, 381848780, 651388414, 360255611, 524323964, 420676763, 261321206, 147830082, 464845052, 382651053, 599404904, 528131057, 997545268, 107825578, 946379193, 721486320, 95698601, 545426131, 703343450, 501727882, 948923279, 40889905, 454114101, 423876743, 907342258, 855496298, 131051661, 224213928, 298280693, 271473571, 787717550, 238303505, 771113048, 558740694, 886495008, 876193924, 730651202, 328057486, 2570045, 230239227, 472616878, 903704852, 316239340, 549306609, 825012922, 179050315, 379029791, 226700157, 688619762, 682127999, 435172760, 295337115, 299740176, 33091827, 231368819, 737662927, 176981076, 518578681, 629760355, 383403231, 921001854, 122745255, 350841562, 783406485, 65044239, 229063536, 116669357, 474162451, 993863307, 10591769, 228725271, 252229427, 811243155, 248023718, 43476370, 366293819, 224912789, 496739875, 119836100, 716808823, 86750966, 591768774, 750654567, 827798010, 594618620, 139543045, 285111750, 993944687, 871777310, 529263520, 2491444, 350737731, 410145280, 366086615, 331584697, 255829950, 563047200, 281712479, 99878733, 788877707, 499602114, 394042971, 314369216, 495280652, 611555499, 41598963, 639588275, 683531562, 914633713, 939063768, 883301847, 270171361, 742300925, 828725969, 675676351, 896288257, 599029718, 92310751, 190625661, 741571778, 536075373, 350286997, 438083707, 751720509, 176981295, 838155610, 101136691, 676811360, 557080919, 233661205, 267771228, 66159654, 960114060, 408258012, 344602266, 405975422, 853679131, 505189221, 595828048, 602373072, 865814659, 824318709, 993512594, 198841049, 588764895, 242390758, 917728097, 191728159, 228072236, 818047093, 911125829, 707988218, 855232458, 257103194, 409433506, 737016235, 657751438, 158388726, 565286151, 336872084, 578728743, 363890951, 196555643, 213470895, 129687054, 376524078, 192754732, 309027010, 245996320, 942849248, 663685761, 958781227, 891860935, 230654850, 681472496, 290676036, 183914244, 515324247, 782387978, 133752198, 251748198, 575626797, 4744706, 981225537, 492109551, 472034976, 276080935, 798196651, 184202960, 734028736, 165849428, 668204662, 406669073, 958889704, 447856431, 687151444, 301833304, 22293577, 416462780, 611246981, 484354792, 380016147, 734627360, 912126177, 608825541, 799283595, 202746384, 679174304, 75122989, 727078983, 530207873, 853087953, 733467992, 580437748, 241683407, 24436740, 195380892, 64726197, 959669596, 203532967, 372751273, 190414363, 371421388, 819483556, 949681580, 644798924, 489058664, 195157903, 621337400, 22943410, 623248722, 335274653, 531735764, 843565416, 458375156, 214713216, 660247216, 990050864, 547012690, 495265582, 415733524, 172230384, 381253795, 913916854, 25046539, 564656670, 339507523, 666849790, 932093525, 580500555, 398583249, 507285244, 40213039, 896521978, 679784543, 610415588, 360346220, 963596874, 764341214, 166507994, 583381648, 913451685, 910228806, 70016110, 146181806, 656561171, 877490613, 470785767, 240757135, 351003919, 933492685, 129973319, 612760171, 685945234, 936316955, 157209987, 167322790, 475270432, 661852068, 40760522, 321160632, 490220187, 654616977, 780974074, 990358749, 633694834, 833875007, 821462137, 226792602, 33270772, 975024790, 914839843, 172085404, 505012305, 669314513, 441268005, 269149629, 25437352, 388918471, 725035515, 595547836, 712909482, 327248841, 324084760, 732018024, 779231850, 422202330, 839776314, 313238497, 945856090, 191419340, 714748912, 330975748, 376824936, 943856371, 55301267, 78130381, 742146555, 940377222, 728085421, 241170881, 996278675, 64033377, 126502693, 378094133, 4191570, 785515694, 329574009, 296919026, 368902403, 643790918, 34741782, 919236768, 145945153, 660958952, 469759148, 970699236, 193173827, 481858074, 842124486, 70196283, 928025070, 481406598, 567181290, 539415305, 100992833, 428202222, 541855117, 763076202, 15918991, 605057282, 99973347, 508169594, 91993775, 59313774, 810641134, 93397806, 663675399, 695801249, 501086788, 874329454, 552686942, 392797584, 43819161, 712866330, 64460756, 931774556, 23909248, 246079665, 666648074, 886365491, 287020519, 595845193, 208120248, 746526051, 727757584, 425410708, 128954719, 469320168, 958471650, 201012359, 820967521, 729957117, 142035133, 312001085, 348573255, 780642124, 699136244, 477438, 91016521, 533043217, 861272074, 429765267, 140984885, 846583794, 29263049, 672757588, 677799486, 348995735, 365953335, 992684125, 205460549, 672660935, 869693663, 48706690, 807798182, 713409265, 220670137, 963434275, 165584667, 179727103, 876165411, 631444513, 217173822, 174068266, 812025033, 966664255, 646825441, 502779315, 630642929, 323480221, 163263983, 227741391, 810848055, 995202920, 446789761, 455292839, 554944695, 573330805, 272458145, 278413775, 403991316, 229026251, 578854845, 261859311, 168782187, 367565029, 239488473, 772902537, 946032907, 881297287, 532867217, 979536, 495996350, 170441496, 369662252, 683323261, 605505351, 846048365, 681988554, 201363734, 553837201, 374503957, 497047332, 555162585, 447118438, 93983070, 742345346, 416909861, 13186265, 655924110, 559490987, 847530705, 986558911, 477360381, 877531297, 998011222, 101997728, 674850970, 648571724, 259556387, 662460750, 86215258, 267201454, 659290731, 196065039, 713635003, 576493323, 56255900, 722184793, 539578902, 712457532, 325252535, 727052093, 545660196, 348011169, 684527121, 365305796, 491247205, 504244792, 748991041, 865933157, 928869790, 38824884, 545969702, 238119302, 308651504, 586957397, 27003841, 354121134, 284977856, 690125034, 551936449, 196959648, 856472947, 705930283, 832274196, 516247611, 137851558, 109749826, 564029660, 536657965, 623263170, 132926658, 958615932, 77223619, 790122672, 462791798, 995851766, 809082654, 391876570, 399296975, 73170126, 564239025, 236032980, 31996854, 504862092, 653309606, 402967218, 208314652, 564014667, 381441131, 919722024, 45277253, 406524165, 126547565, 679260126, 183900673, 588836463, 192900873, 465866748, 429975321, 834400891, 2709735, 46576728, 227645947, 420641123, 578687345, 508734750, 890573014, 994353411, 791276017, 841177987, 973663552, 731386841, 678696775, 279550220, 117518211, 65991158, 777610701, 52182721, 908898233, 939443823, 97165342, 836858550, 984967036, 70138757, 154158881, 367194647, 670377646, 742957068, 711806840, 378483531, 138259937, 249400102, 916979392, 284658703, 150219237, 178124802, 308605545, 558079398, 775294834, 471978839, 717383227, 690660851, 328198071, 65588488, 174063478, 617930904, 297507530, 748311724, 340268090, 982678211, 974493045, 670825499, 742975792, 267949660, 728312619, 285184117, 955587905, 613859533, 392613559, 690436128, 206482246, 2620614, 266996771, 439780760, 814225429, 236102582, 563020650, 583993674, 417117914, 539876842, 287465989, 312956006, 191898225, 682347642, 186348032, 738100573, 74250351, 310962675, 278173500, 26277619, 562593629, 98906068, 18524546, 461440557, 808930329, 652659940, 446502945, 977922529, 626190905, 307175651, 410927850, 638141659, 546777600, 568938130, 869950638, 984583110, 862123711, 366962939, 323418150, 891823892, 886174797, 72681806, 754973795, 857640166, 977371435, 666589443, 982351207, 611142023, 430424743, 898117185, 109834790, 505344709, 665584980, 142915231, 437938791, 351735644, 359568051, 423774480, 6993992, 573096669, 119084755, 321679538, 578402076, 859483582, 734392267, 553355427, 729622436, 698468334, 702995230, 249375369, 629324803, 975130992, 700810792, 763506525, 366135890, 283501465, 966224214, 786096919, 706201229, 142799901, 130011144, 785029656, 365861145, 191448398, 114212590, 56662468, 732047856, 879855790, 991391731, 446775589, 728363071, 672806603, 311922830, 116797573, 945798072, 209626938, 5768610, 195712452, 674470566, 287479903, 448418710, 689257371, 286618423, 349748598, 204060902, 800285695, 116176169, 745279582, 429016182, 577449011, 788569180, 350074207, 356785891, 788567881, 785667052, 43542200, 480488796, 249669200, 105136237, 544600816, 868520580, 395588414, 854839876, 756539574, 228655548, 513009979, 213197658, 505255834, 416624999, 139920008, 809601338, 299175112, 79071848, 242175475, 98353076, 559975524, 286423143, 261250023, 732019233, 498978537, 61547648, 907239492, 985299253, 823428249, 888020510, 840354925, 152693989, 731183523, 151394998, 588927556, 396673454, 952504161, 266679048, 716063050, 980866322, 285869290, 898620073, 783572920, 742510239, 979277325, 117279074, 996939203, 14083716, 88780471, 508373183, 86949684, 700714485, 352219233, 676018866, 362905907, 693996701, 352509690, 873693881, 453350373, 662600963, 201915154, 750259490, 980342462, 373432001, 755221048, 494867575, 294395799, 459872352, 110887653, 325028922, 930857073, 359537548, 248488991, 122788110, 897009353, 434597644, 953240577, 58968576, 60702228, 851818058, 539430818, 878625361, 930836394, 907127584, 256582084, 239390735, 713797461, 494598528, 389254308, 512434124, 953770806, 463683548, 727290855, 543846469, 241562910, 919747212, 107438618, 571297294, 608177854, 968187599, 449800925, 665613826, 589680529, 298816103, 941600680, 415710728, 844773557, 959409068, 944495499, 751928206, 662509163, 521705053, 995173179, 681505678, 130104027, 307499614, 378472544, 32294738, 809755369, 663014837, 81569241, 710249283, 366459629, 499871569, 438015740, 470492309, 225828636, 379015622, 632696719, 980342250, 739693138, 708635066, 671824092, 114670939, 622178303, 895705227, 458574527, 330284024, 976947197, 282346755, 576486025, 733893824, 479488271, 750441276, 354967133, 479628779, 634488686, 350267066, 458881962, 871220161, 241438735, 201711325, 553259521, 444702021, 88967059, 998693553, 984089323, 2196082, 543723663, 309150785, 2353438, 629405631, 436342925, 172369131, 880907432, 86310585, 415632227, 602139888, 576047200, 717026936, 410764830, 48591011, 865639470, 996484319, 593871761, 398468117, 50323804, 730540055, 234745603, 366990334, 853383922, 974742216, 973715461, 731593811, 595674323, 841240410, 682458803, 5757778, 810488681, 872549731, 942352187, 830163596, 399478896, 903417258, 514208885, 208262328, 835452910, 609724829, 494419568, 520695658, 523006950, 421557985, 3408411, 997528956, 550194624, 550538727, 535818264, 345670751, 599021791, 776593644, 815173283, 247520310, 259026791, 311633640, 330543047, 661493524, 550886001, 411938486, 766744312, 521584070, 191096199, 38646782, 640211525, 425406649, 475772529, 670564288, 907022792, 586948435, 764530211, 611912551, 550173782, 517979912, 249187556, 832355672, 75616042, 210491707, 813634873, 547394444, 443297623, 171233823, 228661702, 322483718, 700021223, 733981902, 651338624, 809493543, 495330623, 895103305, 792339232, 306252492, 203743619, 223791521, 116693115, 688511101, 253276052, 900489452, 913468638, 556535228, 38654450, 920169815, 21788919, 123487147, 124179193, 222191687, 145123324, 610956837, 667242639, 697111122, 563760344, 434402659, 824722482, 680509999, 264924943, 502913921, 919064881, 709463169, 256884751, 211518584, 989183593, 521385454, 707715061, 670749785, 91872963, 143322797, 927703853, 899507049, 827790030, 83792448, 972104162, 695747902, 198523373, 924219287, 632098427, 40757580, 204757488, 394419839, 455592909, 235333867, 745367605, 313432794, 523351936, 571028926, 851971622, 614496757, 129787308, 745112371, 421223810, 27446543, 21095463, 439276451, 734947102, 764914472, 64747070, 854136989, 690339956, 225951037, 369199024, 448873668, 267879444, 447071520, 821744179, 165275340, 813415062, 772804483, 5227586, 530169227, 854714613, 743463581, 975874812, 422871006, 854502880, 414854057, 182753053, 657563610, 490162999, 238122548, 397811025, 793960043, 122235356, 623073368, 983167676, 528984150, 633538105, 854175143, 454729868, 264868915, 4375797, 993821853, 453058829, 9436851, 389506336, 469846589, 796141975, 542821368, 104647249, 930981232, 414137352, 474144351, 391860917, 503239395, 272997793, 193338040, 990700505, 375891901, 868378629, 714315000, 89377794, 449022140, 39438317, 171932157, 86116760, 57378687, 674872945, 615276647, 88337957, 434060219, 265525110, 203337212, 877188509, 95593111, 852900655, 717776318, 506758561, 96292486, 513925164, 79954572, 17435480, 302790908, 420676157, 727025575, 718572357, 814078464, 193864572, 796589471, 829232287, 949336040, 763191626, 994169608, 269131065, 825452840, 259068533, 125204722, 841639260, 798291037, 214532581, 306755060, 972946714, 103592665, 617498881, 205565624, 726131269, 611716978, 9908003, 671979434, 940255467, 831022437, 491103300, 405668323, 614557748, 535259389, 267088197, 135997389, 294807808, 911556171, 716437957, 723287091, 813763811, 783871301, 985929547, 86431282, 407667013, 309598471, 535655018, 998696279, 677516788, 86412633, 718242642, 648956616, 830734788, 305468674, 785943318, 431737830, 929726756, 370758765, 948519211, 257523447, 897742480, 735698453, 54401372, 230735906, 795043980, 635849568, 885424138, 621817590, 658591835, 730264365, 376335618, 997452980, 235811547, 744482495, 224747405, 935756955, 982542740, 699860373, 416695423, 752691684, 720636791, 17025305, 373866957, 174439826, 746076422, 807181786, 695731204, 896872757, 778938406, 961789521, 69140209, 585670038, 475503463, 380564224, 585295563, 614444859, 492106303, 465035896, 445904533, 835684364, 117700841, 985113074, 97442240, 326847007, 725039148, 514482924, 943910638, 642582534, 364774420, 473476901, 771824487, 993216107, 733743530, 531470278, 571683060, 476051, 707964069, 708029636, 317577679, 468158315, 473957215, 767715952, 444101521, 87537510, 464962888, 416350081, 235671748, 695121555, 625112370, 824347886, 469820091, 497764470, 637031443, 629072540, 992920548, 547909690, 10782108, 794575803, 231287, 256962173, 917544625, 54879488, 701285661, 29350406, 433187397, 763210288, 510149798, 498583653, 141155812, 720012362, 739937423, 773864652, 573681993, 210500820, 995209655, 43412268, 208884427, 917162266, 263232678, 488850566, 427391588, 650055032, 370164676, 380899450, 240592764, 910240925, 709752833, 621792125, 778855536, 234031021, 240508731, 323940816, 414796438, 65843698, 227114791, 583088891, 199075308, 685015930, 686712085, 536039962, 48701637, 361605621, 558437926, 130365224, 121762225, 774769624, 410311880, 721359198, 261792111, 172261091, 887795727, 80687394, 680032297, 869433027, 517003940, 25433039, 963733788, 339403024, 536227301, 132537853, 56084814, 680471027, 163928038, 780987820, 230101565, 265831799, 126938640, 918554597, 375873685, 336811134, 964811460, 302908245, 560589002, 604055045, 898696763, 200036107, 56136011, 470734372, 865668659, 564738820, 504802020, 77751325, 370244401, 185802644, 925137150, 496273174, 334204340, 589534977, 522639216, 948428701, 768640705, 666697517, 287705712, 802736422, 479554858, 845000004, 799824148, 890125962, 56613276, 626874928, 660690575, 769462754, 70099616, 762432946, 304883234, 608418823, 965250305, 447949549, 762309667, 695239023, 33920728, 694568134, 575588407, 776043836, 473272175, 289382335, 744372935, 977407648, 5331039, 288598506, 389860326, 144157730, 502046253, 826924135, 209185612, 409961868, 247668444, 416836405, 143239890, 377223100, 976238221, 512440799, 269317657, 931905727, 881213675, 257822543, 390620826, 37711447, 727061263, 814988182, 752456680, 952513839, 781134859, 679988678, 544801982, 467679725, 10450910, 161368981, 161158948, 997728427, 80250860, 52242250, 707170604, 873451463, 227040098, 165113561, 39650424, 624013375, 505376612, 800939454, 331512414, 415083187, 435892221, 804319571, 140688147, 97851790, 674174857, 204441952, 596721432, 121626708, 845335523, 266043300, 322505140, 797688936, 530171527, 347931309, 701738989, 871396679, 729473107, 818164527, 414670751, 245014425, 975370383, 974501964, 27477043, 500690703, 474535691, 850193906, 496262457, 695075273, 416267934, 827383869, 803876016, 119570852, 861510533, 453154996, 690513402, 953424922, 593636770, 721168964, 750297687, 228794986, 149752265, 43368340, 825023060, 323961513, 432105601, 479123449, 198116309, 218402681, 128520172, 884216952, 621058075, 973740470, 354837723, 683472262, 99151343, 804090810, 457629216, 663545677, 882057950, 969721694, 320843575, 585411388, 786724462, 351629138, 897168731, 493539220, 816396830, 103295747, 651285225, 91089876, 795680752, 459272204, 892204209, 877252659, 826507874, 419362286, 188968017, 118784883, 176516028, 678011040, 276677040, 870539807, 482840040, 990270004, 752816067, 802160979, 135178570, 333802329, 449781736, 290019685, 171126469, 938728077, 124670465, 418932373, 556390092, 541543377, 8204290, 223599774, 749873119, 905516793, 35719400, 158934990, 484930073, 697058658, 772778437, 164968256, 658267690, 729910246, 228304482, 835349781, 400597692, 281351965, 807018919, 738122301, 643477517, 634529477, 763925981, 212157821, 898541806, 781120768, 564006034, 873469006, 858566692, 510375335, 225462503, 647503365, 35402883, 24716157, 680657624, 240330024, 746317037, 914891666, 384424261, 460986408, 500316853, 946878195, 382249517, 705306822, 250920338, 927193777, 209290844, 78825192, 891114726, 742395451, 983933898, 760333521, 978898144, 287615950, 162341312, 724944653, 811962180, 931416852, 663989360, 388392021, 700748987, 923049972, 353508653, 947744661, 865717590, 995726424, 705994787, 509640325, 742014720, 176979020, 702663052, 646953828, 934421844, 858924257, 921542225, 704181499, 860927023, 442211208, 269365935, 762683156, 31810584, 989884308, 11100100, 605472453, 89037218, 571118577, 963277245, 769304150, 686507649, 152749043, 56866519, 223556433, 749093058, 560899966, 11469584, 165586246, 729358103, 262808700, 707720124, 106236621, 648427514, 162073959, 398656321, 259956930, 158002630, 322287211, 236280751, 490439653, 371129259, 101251953, 628228031, 978238871, 555096369, 35837634, 317839285, 856870051, 327334294, 334741849, 720563367, 470025981, 758508281, 593834474, 647484995, 254164452, 62289410, 541131473, 339658139, 162205893, 523684040, 850064213, 132754624, 749875625, 84505460, 260283201, 460532559, 179508996, 442449202, 860219236, 784045965, 803484296, 931247692, 241393057, 228822586, 372812392, 677573934, 468106155, 974760044, 365486435, 786905715, 852874283, 258717844, 117209115, 671115180, 975236371, 201914411, 811892992, 887989427, 560536195, 56039962, 858805963, 392098950, 12820577, 915265706, 856412493, 26965197, 97510532, 718010526, 396295804, 504211786, 538616097, 38105185, 612499276, 520633855, 214077687, 9549865, 654818889, 616420571, 583736805, 322637902, 440773846, 747055814, 146913124, 431700325, 717588773, 412369170, 351808795, 944312579, 141700143, 36206143, 40472152, 716840329, 746189417, 74412932, 721290858, 824415292, 328225784, 91337665, 704698418, 530651811, 292563258, 686798684, 714684157, 774426984, 859920942, 835869662, 688376201, 23730017, 835816460, 247182458, 536582845, 53525241, 553389320, 264286144, 259372043, 443679490, 27099704, 316148883, 981606058, 793607503, 422380384, 257512435, 776076271, 123272474, 392219676, 588043140, 125617753, 172793746, 378931022, 385903737, 821114277, 923575058, 962633010, 571105531, 121802942, 416470703, 971290981, 305133641, 236714664, 483860846, 893548416, 457615483, 647175519, 741826036, 333408490, 280296932, 234693360, 334112301, 24058091, 865089820, 218078694, 904882290, 967803084, 329427895, 650178572, 608130245, 841351828, 782686816, 429529570, 534416567, 229829893, 794699769, 176007767, 152576974, 825809032, 97072637, 961308925, 833564124, 352161839, 851000396, 552850104, 448229614, 479359327, 97869155, 620435476, 518812255, 585018719, 119815360, 627554108, 85544648, 954492534, 815423469, 541362537, 149077733, 974414840, 249697949, 776500294, 592068410, 546467561, 910678923, 753114873, 337384681, 731691615, 755430577, 60690757, 230691542, 772050228, 676972563, 505856260, 785090134, 181942040, 82114443, 663862534, 299001901, 992882665, 54586659, 178140826, 709185631, 988097299, 273811265, 126547952, 645095416, 24668415, 207488075, 817013119, 83955567, 263287218, 569295803, 716058081, 534860222, 69746086, 421657260, 503792168, 89373621, 148016033, 900784371, 614098056, 705630821, 113402784, 385385582, 579876791, 250559528, 161076647, 910223228, 719115213, 3919912, 997424720, 814281943, 62710172, 96991882, 863151307, 497860425, 334262922, 881961586, 693769531, 616336488, 287810865, 780816409, 228687481, 812351011, 992767858, 807838730, 538695310, 793823524, 338554729, 216011338, 652134904, 471871311, 414372940, 622861889, 923345300, 501147749, 940725919, 537779057, 212887114, 412778768, 756632793, 175994347, 649241450, 780043885, 887596139, 863796001, 237716004, 38729736, 462553270, 957174379, 502131657, 326399978, 174833146, 165250163, 896591360, 620847014, 731167140, 429383203, 6787335, 256521558, 493243865, 191780742, 152927102, 793312839, 436331394, 489086667, 515950143, 262555977, 330107659, 814827673, 738767606, 502845065, 671801045, 169122571, 107257269, 652604794, 542689738, 709234350, 31902059, 446858349, 882187644, 758856227, 772819170, 734889598, 352117000, 496855615, 919114168, 635745610, 513982063, 951068494, 624401050, 924124709, 736724565, 116198352, 8332488, 795508857, 110681593, 654328934, 201785065, 695604459, 616048785, 67309293, 492005846, 785029931, 961327600, 880453948, 513586674, 524850340, 772719618, 514304134, 93026085, 200738795, 702622361, 745261855, 671323641, 408651851, 308470334, 43979219, 842235037, 318080224, 451865391, 209312545, 158791096, 289770844, 612463323, 737518604, 963911605, 179105780, 923686476, 32804968, 266835723, 574449172, 578719220, 669052969, 841177702, 536816102, 569140336, 280721870, 828802069, 651948243, 469051267, 501200770, 914200959, 499615814, 500254680, 813066601, 46774434, 85687701, 567740856, 147795746, 178589107, 442805561, 752460453, 598246337, 637988289, 360578064, 873971959, 380680214, 337490911, 914041813, 124690344, 31987748, 912253293, 153978545, 603214873, 883576112, 686155392, 398786498, 866539043, 234140104, 158538745, 984207636, 891362001, 992947920, 459551214, 18315442, 431355083, 697413911, 851371505, 779779258, 144272964, 245183434, 819653620, 758000813, 8921792, 866219584, 952274087, 800409972, 692062245, 428884459, 98506444, 823004327, 230347214, 524100117, 225218983, 131984039, 479320721, 767142610, 321085885, 163599041, 402528796, 57492331, 248095135, 72923335, 682272952, 432444458, 854554241, 74444952, 734974817, 450068284, 379433139, 163123967, 827611110, 367964079, 357201377, 730764798, 61801537, 672644179, 736305406, 456024585, 764904286, 483153184, 234934053, 55818669, 691244224, 636023595, 962617588, 488942208, 577079197, 752689760, 428671735, 627315526, 981128554, 528622383, 939197095, 962129251, 834950167, 538748935, 686574780, 321203321, 428026239, 577921157, 571898441, 889898101, 325204072, 303447551, 807368718, 665985493, 436436035, 234379799, 393222585, 56202395, 479425102, 465236842, 421644358, 130492330, 111741438, 758988826, 21315571, 571856039, 236706686, 248150079, 31110053, 895924324, 15764188, 191577375, 861082101, 683042771, 134340038, 948227566, 20070041, 9751090, 789604707, 509596460, 634263289, 989780649, 922525198, 452878473, 886821449, 849966619, 301619555, 859364283, 81167872, 789332238, 122641525, 547930179, 901693933, 862514663, 457758807, 343780022, 501579629, 656727348, 708259873, 454792264, 123941919, 198761739, 463539732, 61983681, 215649733, 992242081, 491443608, 583710074, 433190426, 819370258, 181269352, 780378772, 121911957, 55707045, 308461175, 373949681, 831542653, 616426080, 119072505, 708550339, 300325927, 772155518, 486710093, 992192024, 172094261, 210685904, 888242342, 912377700, 589493347, 807902220, 291103120, 374943429, 816015718, 738907302, 843651702, 337936480, 966765425, 77449966, 38983873, 752442018, 888825441, 163485539, 761682926, 864920086, 423662739, 973124887, 648445557, 305449171, 423491190, 157489521, 834061284, 497657556, 355434334, 375943218, 627538845, 518334294, 427105961, 921611121, 774863588, 440215404, 198660947, 705472766, 991861230, 495514340, 911370784, 773452479, 30191424, 650422204, 591787583, 932817216, 752841739, 680641748, 997847709, 507743680, 978075543, 583909774, 546363885, 956094664, 743517472, 123244325, 445458828, 690256309, 398168103, 653818830, 625034022, 432688665, 629434910, 696146596, 115074792, 77551548, 679971598, 639625406, 539134630, 940604197, 273690225, 864986192, 34213169, 10457095, 70578358, 566059734, 1371043, 999924459, 5149359, 671211944, 350827757, 526981555, 661164685, 605352555, 776646726, 554713430, 920517117, 4906521, 389271691, 615750421, 366786377, 141618455, 822206001, 661808742, 511941338, 669785835, 367003641, 85958278, 312401096, 79456847, 577784243, 613327322, 571598360, 539245617, 960722455, 375430280, 526408312, 70926663, 460373513, 17925696, 717382555, 477232927, 892271380, 80898260, 7318851, 529647426, 374684283, 124261404, 322409456, 624210295, 265112194, 17146382, 737495398, 781617658, 497099164, 41268960, 916259041, 220143208, 454129722, 583960434, 561385947, 594668603, 577005424, 47836859, 103519616, 977909615, 194013404, 786803489, 51032123, 343266314, 107857444, 628022959, 460303915, 778864053, 220582857, 834620328, 608525431, 702543962, 790895062, 184063911, 779908696, 825508497, 388401298, 340240674, 886364293, 184414538, 584374505, 16562840, 744239604, 59187971, 853465800, 98842444, 546640798, 243645322, 638989413, 100120518, 211196336, 873741776, 510663686, 552600170, 819056339, 143639047, 210606399, 114265437, 367977345, 701933372, 9522319, 286237086, 89504494, 813490538, 127146057, 135468562, 291227955, 495861144, 964522583, 136885682, 205099244, 263602054, 715539655, 69622335, 121823849, 430507719, 69750973, 175474521, 653881505, 118595907, 80160610, 727531010, 173830772, 512515109, 735194785, 201962104, 488610872, 455110659, 46959178, 539070510, 162636644, 67734521, 893342326, 218426520, 700368295, 11423297, 819425929, 338535617, 241642543, 55922363, 799102932, 357174287, 182491442, 121331269, 307710024, 679195960, 316841401, 861991314, 476629763, 490834143, 159201457, 425007053, 531336771, 267235910, 827865007, 42752184, 15841527, 649279735, 235272327, 31014410, 596249541, 117664923, 158797155, 399089854, 333712019, 173814491, 400756514, 800173176, 671319888, 998672800, 350271213, 904957288, 22618984, 850890160, 601224760, 992234271, 637856302, 34617487, 429948363, 49538064, 430639569, 352137963, 158285205, 696943699, 287518211, 332097205, 652647943, 841772354, 145923343, 145886989, 188091813, 275869909, 61966782, 428675836, 161392015, 454150189, 536921162, 257531030, 733915211, 694608416, 583367028, 609359144, 349448495, 307482580, 952694825, 980353597, 857822453, 533018112, 407279129, 325449323, 479536861, 318096862, 892282319, 594688713, 157034880, 575211375, 878864761, 196323952, 529637887, 334025888, 366292751, 572275469, 975971274, 342202851, 992690959, 905946592, 638617638, 408257906, 893433470, 431337672, 121443311, 204691644, 149215049, 892866387, 499657902, 492373627, 727366084, 817413606, 299830101, 179108792, 793021020, 79484774, 990787475, 806778126, 699771690, 932517360, 396801986, 450369033, 705688179, 601764213, 543650000, 6424246, 101576956, 943742352, 469876599, 789602165, 193861204, 867914166, 855513141, 892781606, 508623681, 94734653, 240839222, 291304372, 782860714, 535793730, 316197460, 437266536, 818734523, 513125053, 341667977, 865885326, 459199730, 800469722, 73959588, 663225978, 938116519, 676396111, 771293940, 134110004, 604210211, 814611864, 809471780, 227147526, 919603684, 718877548, 600688498, 323051501, 99437760, 64384379, 2816967, 818797618, 610590379, 994648835, 573954750, 747757867, 489374354, 906949624, 497465284, 110560861, 743002268, 736660912, 864764678, 239030637, 179921161, 597075825, 648263922, 240484009, 403859859, 323376783, 111561393, 880769415, 754737241, 541693235, 729100522, 440848994, 430876097, 397697044, 986305880, 445501633, 745929129, 961822196, 463370806, 372917087, 929787278, 281491080, 260370802, 723087218, 203568982, 809192786, 127668940, 274859962, 256763793, 907418526, 948574569, 41107521, 275421123, 545480185, 115078834, 811728405, 749430864, 145513085, 516184423, 569736173, 616298152, 237442955, 535206569, 84012508, 226442680, 581787161, 223916070, 714119636, 858533616, 271167651, 4042270, 94481030, 420969509, 860656802, 664057935, 659812836, 635967870, 287614655, 518672419, 860701661, 622898608, 182056539, 606693818, 67809863, 476866592, 641506810, 661823557, 359067162, 146840437, 191874073, 827990527, 830271114, 378743967, 31191003, 914176962, 315775261, 104161347, 925789335, 224846085, 16306171, 697520623, 235541913, 755939652, 575119707, 184347245, 477066085, 539678930, 263733613, 214865263, 441131133, 452288280, 370114451, 916699212, 234272754, 500356074, 969628307, 218075558, 98545440, 643801483, 607531433, 884942838, 741633511, 986510265, 130375579, 687291472, 631810103, 897452246, 935825379, 406107678, 693379832, 889192140, 713870969, 47764934, 14203958, 264162905, 113416437, 614265384, 801578131, 689265440, 512136511, 165983016, 867516514, 758347801, 165973614, 851022298, 934841098, 971138766, 748262675, 581017148, 515614911, 964208870, 75596826, 421017618, 877419449, 554331043, 6041091, 154592380, 506155288, 307883153, 356449276, 6535630, 257739329, 907268228, 14466877, 270547852, 536213606, 723009376, 840425344, 488682197, 742223034, 800330551, 174356028, 154378213, 622316126, 979186215, 648850528, 94387444, 686133908, 625519268, 762398627, 102140889, 568059492, 620235278, 491928965, 561673559, 360605999, 671102238, 418722227, 356698361, 103779373, 306452827, 549138165, 744392295, 209157177, 128661454, 871804462, 188569664, 660533177, 892220710, 596810020, 148592411, 3754514, 316034770, 20560543, 947406831, 493843234, 193634135, 909235904, 739551763, 585249718, 570121942, 974319094, 390024808, 440707295, 832643610, 589779072, 351021387, 285065444, 622379634, 348513382, 239138979, 854608786, 610483556, 461886344, 223078013, 667060284, 472047469, 369143238, 552604544, 953227416, 753771196, 906112849, 860856274, 945392706, 33882596, 83862744, 183911492, 223443659, 266067034, 116358593, 854540787, 736104931, 654803954, 962437282, 682620320, 927570489, 974199461, 284615995, 422644873, 264036756, 527010436, 437700425, 591045885, 374999916, 271141299, 985862755, 711574926, 235092695, 473603161, 246073051, 318396464, 109556329, 252181170, 702194073, 167019192, 827598551, 214212779, 310715990, 952925589, 4726638, 777323627, 548721054, 43937952, 77555877, 23197176, 702509849, 935704911, 41291480, 831748971, 782607941, 363771820, 42493086, 625937011, 757646463, 762987903, 760712817, 250714150, 807968145, 115306189, 654191463, 959235605, 835903789, 167983154, 226372221, 776566089, 354926907, 754460873, 861983428, 77609207, 498433013, 707799890, 594776649, 196556894, 987641522, 497048638, 210299664, 93306080, 387825204, 774785188, 13418717, 530053934, 390953369, 803341086, 652325163, 573077275, 858592443, 563662292, 714630726, 358240954, 535799588, 304481571, 8732306, 868825292, 24184804, 412359413, 934807688, 49450658, 607917679, 462915075, 254876942, 250798488, 321722147, 186292808, 541309452, 35174061, 580684064, 137540335, 325902144, 226778756, 16721881, 520790500, 366570474, 165305178, 612482620, 708345890, 616876972, 486274357, 547241994, 908001151, 331138316, 13070885, 834276235, 223425171, 302712516, 453124853, 425023397, 53772428, 687347885, 759698297, 368039765, 490631626, 864069432, 129160314, 435820388, 680426001, 622918434, 990189451, 514735834, 113433424, 776776197, 554903177, 606811700, 867504111, 578030693, 92234641, 876331154, 495618046, 836099579, 315390596, 814136318, 790979410, 367734233, 994349320, 155931726, 903915483, 915789794, 205187950, 408251066, 726357912, 986553652, 515194521, 328982210, 493238257, 966842950, 421201798, 343360246, 260868800, 861467931, 312550200, 566115317, 834519283, 982818460, 109175736, 931484992, 432447058, 787785257, 523430882, 754624921, 784910829, 603112137, 60091164, 24409092, 703374552, 387038681, 308924099, 995827343, 591667389, 624067836, 224403288, 461352397, 780121764, 571664199, 522426972, 718727579, 992251904, 927417935, 966468934, 35630164, 258145432, 687593880, 304267413, 476720395, 153727916, 614385079, 443500497, 195328563, 329908235, 575507858, 87306548, 69191111, 545785910, 719427743, 332659180, 104143172, 574185106, 432521543, 589289201, 346983013, 784975650, 977306953, 443647197, 736488970, 974196347, 621910393, 130505118, 457386687, 687845733, 960403839, 77941373, 539698579, 323557067, 607955778, 249405900, 847661386, 326846794, 675203421, 277577077, 105821950, 940639460, 185238887, 66943731, 468697164, 333982789, 357991571, 279395721, 965577713, 863569882, 668170092, 146540123, 775683723, 261651818, 20611132, 253479262, 792044647, 398394586, 637607110, 410155958, 890945808, 93808620, 669595703, 919245819, 821748594, 869992923, 225316481, 588237284, 302330692, 946466054, 908506773, 961196343, 697288631, 462521674, 609673323, 220027142, 429813288, 840038150, 29758874, 114003843, 294463447, 332158085, 241487655, 399090795, 641749459, 877165514, 322692024, 126384978, 473276434, 502013960, 830279367, 38957221, 477371946, 20295403, 933906472, 334353108, 515106110, 923794122, 804926653, 461569158, 665335539, 420492641, 350938721, 220783853, 188580028, 625009536, 749331299, 993307251, 321867145, 69596272, 609159675, 394950955, 858715040, 504439218, 369839699, 941284073, 726653957, 414147939, 655042450, 917439904, 34384972, 558078996, 902018355, 775816731, 64726439, 500430057, 402929644, 875959932, 449006196, 240688443, 175432462, 509477193, 871742037, 229789411, 382693190, 960082944, 725361449, 319776621, 120980614, 287310194, 5067101, 171372585, 435177443, 489600474, 297969797, 135540691, 14030012, 405565478, 93787511, 99780297, 872278009, 402995159, 152532224, 145155208, 526740197, 167435871, 482467931, 742641150, 721448707, 677934740, 88238242, 73143776, 244303828, 794853395, 96393106, 539154497, 109305054, 634077769, 871305437, 576705921, 506713104, 777787263, 430431946, 493222240, 645192245, 127246042, 926254644, 453695481, 21307457, 887416858, 398429320, 538076177, 635521041, 521331907, 433259290, 831083088, 951922033, 554251550, 48252836, 373431669, 524832557, 428767902, 95774561, 367580032, 372141051, 37625386, 944666805, 32695231, 278479846, 100155777, 916771938, 760775035, 323942667, 588544030, 361959722, 110859781, 868923159, 546364710, 496702882, 294948761, 219547227, 462897700, 175068209, 365621555, 539113378, 468459284, 125453188, 264188696, 875622787, 767019705, 166798383, 373436371, 272752673, 250191721, 630106440, 549612360, 756162688, 514658878, 479573915, 5396491, 89869587, 799385383, 874436356, 785617950, 399329906, 442469116, 166056671, 240417861, 353322898, 111041478, 685219987, 472330412, 691618513, 546732490, 195002352, 33917765, 519800116, 680476339, 934639627, 400741201, 831479667, 761752166, 493658492, 674279058, 483905566, 133217587, 288218124, 623703729, 731708684, 103934799, 122835630, 65492038, 897964432, 642209468, 338021613, 386119729, 366173475, 104816886, 142536619, 266892579, 449323027, 505757993, 743452223, 91876355, 979839634, 600491861, 318009491, 56098054, 82113135, 332451759, 117304766, 861934996, 700827182, 733462169, 690500226, 294953173, 670975862, 943911981, 884071098, 851114369, 693583070, 134849294, 52834516, 502528424, 16360854, 57312144, 492787651, 243163572, 968956246, 263249298, 248855234, 740573479, 705584315, 418701836, 641220684, 60461181, 464652279, 816095862, 647340092, 578741145, 207699998, 177825020, 758106985, 699679517, 62625373, 786768791, 294833528, 537288508, 997789880, 592450873, 912328263, 386647671, 68243136, 113755562, 213360128, 988906007, 476622382, 284100383, 884695656, 107202600, 334329163, 712710789, 5721133, 561593436, 542378301, 449464653, 186715120, 647975842, 542461762, 278922648, 538688717, 848479961, 681036788, 398527666, 591633135, 687239787, 324013411, 447559622, 855331527, 381498049, 383602799, 675833258, 681136174, 739723370, 126453525, 84846501, 555206920, 890066272, 784115846, 758977820, 929370292, 678550210, 585240687, 548826291, 887365968, 850275275, 553474023, 878077692, 496616841, 21238655, 685909557, 836543949, 888665160, 788623913, 468007734, 342733508, 31839138, 954653660, 938327871, 330977903, 649448930, 206160253, 519662079, 44836845, 908116069, 295036984, 560588283, 953074082, 990879843, 804721271, 853215736, 80983060, 971628893, 996197528, 930362863, 326848267, 342691997, 624403777, 806106773, 390445569, 712400125, 962320978, 710081694, 980746037, 837538283, 528510344, 980782284, 907294789, 725597885, 674971011, 345653260, 958234955, 669303985, 838529764, 596782581, 637851742, 579222382, 439099775, 743834949, 390334071, 101077838, 177166227, 541393130, 786904625, 851826866, 429447119, 850713780, 508157162, 320578422, 109901875, 121508860, 354241569, 856305224, 954337533, 284230692, 213023583, 13179175, 311374933, 112559601, 803340142, 314138992, 399646312, 344724011, 932810846, 604835087, 960375293, 229521824, 695971102, 90007805, 47305658, 125455039, 469820649, 991107498, 786327773, 765024873, 475462827, 407792961, 860316947, 892324559, 393411616, 824630196, 31754524, 656395595, 766521622, 416245172, 297815562, 324104412, 281980812, 407213547, 779421052, 14283795, 594967306, 645937215, 800921720, 490273964, 531235250, 79269340, 378372802, 947328257, 428594596, 41132142, 713447636, 775581231, 7928531, 223609212, 104565727, 403197673, 528458650, 511211356, 121526139, 786964662, 890127319, 194819022, 332307486, 623576925, 216995427, 653528663, 794988033, 47796438, 644488788, 490965901, 301907169, 776095606, 305954029, 459495336, 433332325, 699388655, 181828170, 797752440, 208403307, 453495778, 655596114, 164276342, 544366313, 34982778, 177016299, 49738626, 192627426, 273035515, 769296134, 461200357, 496733328, 63810806, 850344536, 467748672, 164181941, 324013949, 369345595, 611258717, 246810704, 628325856, 971178433, 725444070, 372962967, 754029337, 207618736, 80290824, 519918822, 405186236, 850275737, 541787476, 106022865, 288955645, 737855520, 219207265, 816541954, 371287592, 998066125, 324951154, 151192805, 977002220, 805857770, 221614870, 995695397, 400086055, 300066691, 698539252, 779524256, 512988952, 798717810, 762613069, 842891710, 645029919, 826025466, 141027697, 450887581, 348952704, 161520122, 910761108, 384655067, 9420354, 349632911, 349304030, 916601635, 480919587, 582784459, 741909039, 354493410, 175058175, 320390776, 373497865, 546197423, 617142083, 808273815, 180994996, 8607604, 349248080, 738530212, 8155403, 649892079, 696924653, 384673198, 252228719, 119650547, 109827105, 323071468, 640185016, 879407044, 820978459, 604488077, 449179491, 972979430, 627258775, 390395294, 116606663, 261660798, 231383849, 364728628, 410477331, 18694060, 469158758, 946564039, 741511748, 191759771, 592132798, 529871187, 164061384, 595663587, 432501385, 575950847, 16305304, 167027998, 604878417, 120081633, 733708714, 607373174, 800769350, 587895190, 141518143, 409001187, 39620132, 991333991, 215957156, 428457343, 456293819, 896607335, 851784297, 545943881, 812884020, 130780961, 182574199, 170497183, 105536007, 490660773, 712034024, 240427542, 993782686, 243365278, 537210527, 683211691, 368189501, 448592766, 151916025, 996552569, 710817492, 835806004, 625652629, 855011719, 298255246, 306279850, 946292279, 468253373, 452914965, 638427085, 675512764, 834150145, 446340277, 925291426, 595461975, 697639447, 243238220, 623296120, 888819540, 945419667, 233825000, 750388347, 36862168, 18705703, 53627754, 653471025, 970493302, 122915108, 998501534, 934896189, 673893159, 61538250, 841442279, 503277093, 731403634, 914712325, 823297264, 731744789, 121655016, 598579264, 812431245, 595480469, 964929748, 874349349, 788996874, 113169064, 234051904, 494185742, 499583008, 910830193, 169861842, 5580149, 542634567, 73355300, 370109623, 161667857, 68285663, 771278141, 65758020, 614440259, 104233687, 670706155, 674476265, 871217407, 650566005, 955841537, 717239892, 172644282, 692204954, 350890100, 112323735, 702656494, 384378591, 93901271, 527387036, 210734100, 128906566, 778410300, 694938569, 388708274, 553249134, 577042493, 339771264, 854016710, 350210250, 441777881, 108476529, 297734309, 869309541, 970386946, 206359008, 684112537, 179400915, 477168339, 122556433, 576136939, 456937702, 87195148, 777967308, 852461237, 870223392, 377632432, 255062797, 322801523, 306365542, 657382807, 917471015, 738576708, 882572837, 778323380, 392919571, 4388405, 923808061, 688564499, 266372053, 328668167, 495597572, 445151189, 930197370, 398529015, 343353937, 989923413, 182707922, 119648236, 757250487, 555378946, 400097672, 142584392, 306476650, 771964069, 103017667, 697641658, 961296288, 108616446, 931164431, 545453496, 642124737, 446329493, 174333618, 264739823, 574656196, 254748603, 453478944, 551543864, 539915878, 740184805, 836144113, 727003768, 778186195, 408435120, 512557828, 50209942, 150507308, 269058513, 413828428, 443753163, 491666766, 235799441, 470330580, 398251677, 792578237, 504553404, 326517186, 145779368, 138220083, 750001028, 848772409, 584350291, 455949556, 529041581, 888966409, 510123966, 939342165, 300599501, 533907386, 434199938, 77017833, 183335924, 46423154, 579885465, 726604079, 88176808, 726393388, 522092237, 851051056, 633240540, 959157815, 764321349, 816796895, 718123778, 103623410, 923590079, 986726207, 865364515, 176209932, 870874282, 285234349, 786888050, 631011037, 794644959, 127616434, 628753812, 326689512, 391861019, 266476688, 425284194, 310320054, 365276690, 832512778, 272579385, 666318960, 692666811, 417266775, 714949503, 395220865, 582555783, 371326036, 412999889, 12797336, 614400782, 782565981, 837405760, 718983537, 970964658, 688429869, 596863787, 209320805, 648082550, 309217138, 374760852, 229106283, 457991863, 252842399, 806012760, 609119203, 216298470, 117326167, 450993599, 589734678, 822872900, 603827614, 295000840, 267457644, 190590182, 358248677, 85704281, 550388924, 313708868, 706699969, 891771042, 297010434, 211756128, 602778525, 649917558, 100318827, 997444254, 73885570, 109560645, 72349071, 391291230, 954877646, 812101063, 988284561, 816904768, 239095414, 687170473, 161790494, 153751771, 95112830, 989789643, 55152966, 267610723, 664053343, 77620996, 447750226, 623593943, 580211656, 219793525, 937588256, 937376737, 80401895, 123836140, 458259436, 889825956, 323007010, 39593098, 558903168, 218190453, 544930652, 909269793, 990848500, 999266367, 444632886, 978049396, 633306405, 888852887, 609236272, 73797137, 243081456, 139790594, 825610108, 357078403, 937525163, 110544625, 1963515, 344980894, 801485139, 265605803, 633753879, 967238789, 930542141, 665477404, 668398232, 150068730, 63377946, 757423735, 92057005, 640235696, 978633583, 16695681, 633302134, 377622426, 56607636, 215789155, 631052861, 619564315, 571896996, 569130252, 519673776, 708899967, 730019005, 518960074, 680742433, 787322058, 210913412, 701705279, 188049229, 520697688, 526314212, 345205093, 478655146, 890806169, 570460223, 73732670, 763763848, 425104806, 132198947, 394860222, 897050431, 123922343, 644358393, 282836464, 6787337, 149469662, 288157611, 118742586, 895523326, 34977774, 701292443, 567767556, 60809304, 449231530, 966132706, 622079453, 671633668, 790568837, 608639355, 505790516, 328831094, 515708723, 501809651, 777746043, 573140283, 832706707, 64315717, 410263714, 231849239, 667012714, 366190683, 532685052, 217306240, 451093032, 938794055, 834915243, 629130721, 192229270, 19929555, 611932761, 706702796, 581182902, 416846235, 298848664, 314667347, 704365626, 375887438, 257613225, 700747963, 12907591, 271556007, 456061951, 188071763, 662467260, 853761008, 21843681, 570050616, 785116776, 418234884, 813457569, 704434802, 942938963, 404210160, 266064799, 552484806, 310604547, 959314780, 887747792, 597129453, 608542879, 457621515, 301503355, 851191628, 646714519, 199778537, 49232998, 821109930, 547093999, 130731574, 496002124, 867301642, 170140023, 36894773, 935433871, 131823793, 800415731, 394271547, 119337137, 169287775, 638659211, 344233677, 621556947, 373101626, 697029387, 706272561, 214209751, 553211241, 816283082, 838430850, 323618701, 378294627, 878204186, 136213631, 756437975, 10030867, 662809938, 486446805, 258163671, 145660030, 334079405, 164350938, 351198672, 578580203, 911586789, 819815658, 802811963, 780417361, 688954473, 254419384, 945543358, 466432832, 476059592, 401117953, 952034549, 438454987, 206448094, 536771538, 391289044, 421928588, 97386295, 269183665, 276872938, 57017053, 122346162, 499536838, 108035871, 850691505, 459594115, 190659327, 934867266, 895605262, 747882028, 976134913, 489432750, 19979672, 186178046, 864128916, 479308713, 997551816, 490314502, 394117105, 521735837, 80001909, 158055864, 715184076, 445594579, 255252085, 617574862, 266367410, 540237680, 365395191, 868096395, 725755899, 786798450, 607218427, 727313888, 795270437, 43666355, 738817640, 843193789, 3855641, 875892560, 906031468, 423852505, 561444116, 885366144, 637375313, 784022131, 431465216, 840470185, 757507789, 505946801, 603180842, 797577035, 75736629, 600863269, 263655567, 748263372, 372964916, 363942807, 67237114, 157615862, 940315123, 886165032, 945844114, 969227530, 435471593, 565365316, 415981165, 816953806, 482194506, 237729488, 103621657, 273332309, 991352818, 369088776, 507982743, 517232309, 169547753, 109605442, 607311939, 662451241, 981624868, 351881175, 570450143, 879322885, 191434429, 41541665, 621571000, 444948997, 303444187, 881385623, 224451741, 556549635, 834025802, 620406248, 805263951, 889882299, 200091216, 386306780, 596403745, 673086586, 248921133, 760478472, 941717602, 969905424, 615057398, 291244774, 376249779, 587751007, 228696885, 136867342, 1585020, 462165029, 372238702, 48379001, 140350376, 902763860, 415357215, 609850353, 623699740, 804637234, 955043288, 168325549, 157152206, 934241452, 424143497, 604222635, 685584701, 97652302, 213740193, 997385625, 931562678, 464315734, 234546914, 31193975, 459725342, 834772464, 768639306, 325470264, 287033120, 767025591, 466040188, 621371773, 734334004, 259378947, 249288583, 496074217, 118646336, 241353019, 759094260, 871391512, 68302390, 329651204, 715048383, 801169861, 759932159, 987372295, 753305789, 515375778, 860241269, 292411788, 843895448, 678979362, 767055237, 639906860, 500935637, 799703001, 793513813, 827504534, 487843353, 140388097, 665734430, 489336705, 247569322, 45538993, 61877557, 31209665, 746507266, 648919838, 270820409, 709657910, 78021551, 600462872, 996765182, 213074643, 78316925, 509669621, 285845025, 305080935, 21105642, 282327959, 126164052, 146090653, 418032050, 404825977, 924641878, 462149007, 952896477, 196483221, 856816748, 283929902, 1516215, 674465379, 311447677, 545918238, 34773313, 421180306, 568513514, 259678749, 882055911, 351143747, 154342584, 521080914, 52670044, 389106466, 104110431, 501093110, 749856674, 176447224, 369773443, 168451090, 633178350, 657069199, 213086681, 305442444, 828951056, 552444071, 379643992, 543306794, 871251049, 934945290, 401425740, 791802643, 543247214, 907518613, 881824060, 66811262, 834977315, 102783753, 293844698, 48882882, 878870515, 886834372, 16477939, 741586698, 731546034, 31053940, 583923068, 173528319, 900111517, 44833533, 650103216, 690231897, 659561851, 675456659, 637629373, 58601887, 866058599, 941643688, 531285078, 628962717, 665869410, 271637258, 77262218, 447477542, 296754121, 31550603, 93052729, 968483213, 354851620, 98289420, 929821755, 723659852, 952833474, 682126513, 176779339, 264779266, 109090700, 68604748, 995713649, 750063767, 6248766, 630549776, 976832508, 771049713, 59370986, 684290810, 263777676, 847595307, 218493119, 884584336, 876355911, 487038164, 10519257, 272114834, 859300593, 729451159, 148990950, 340308953, 878343722, 362321660, 15059284, 979363865, 904662327, 544974960, 447745154, 920693160, 541210131, 400601320, 947399495, 303521471, 867283266, 537761309, 886498098, 66792780, 817536556, 357545509, 569380644, 697237890, 6430988, 726195602, 948731695, 578383086, 448964404, 98252737, 883691946, 515916223, 764895435, 397406468, 315395718, 792610327, 53032961, 890807851, 248489597, 582619860, 149957178, 504937111, 533316750, 709508456, 517327713, 311307769, 806344616, 511001473, 33253134, 213444512, 443025517, 886349916, 3950242, 275960024, 542527597, 296354828, 881225963, 196368562, 994278887, 505745253, 668371597, 32740815, 910120240, 186290884, 27191639, 398305913, 306124041, 712985909, 251568607, 943345462, 188481326, 737560598, 427206500, 558073562, 656899218, 968967012, 507732437, 806275434, 907450519, 963054362, 421579730, 216167780, 984693485, 227136138, 846411434, 464971132, 909847238, 349908631, 418368278, 985353437, 835430961, 235573632, 972461489, 61586685, 830050754, 356602647, 185628894, 528850919, 801088969, 898692300, 840238087, 872767767, 358849837, 10312725, 87705803, 16089524, 405446320, 237098642, 240918170, 962640655, 838462734, 298490697, 960252475, 74576729, 30621779, 318731416, 215157369, 73601511, 818063216, 609369428, 79521655, 89005372, 992739253, 549315747, 16691200, 673049680, 463881099, 784352655, 374398365, 982973189, 881992318, 537144841, 521739144, 788863986, 887661285, 866066490, 719232945, 636585032, 906706451, 700091507, 21311601, 686995241, 346593395, 229245196, 978839166, 911116260, 403404294, 15539342, 370228000, 434493547, 415425628, 65937773, 667662900, 128306652, 279558422, 843440107, 875833241, 105488455, 933282610, 987976883, 530271319, 896763797, 577942472, 512128389, 964029019, 547308606, 157098941, 829497681, 142226110, 841368434, 654418970, 169406108, 869105036, 23985130, 445108720, 366027253, 587320508, 206040925, 951616554, 770610544, 244753842, 172909125, 278071193, 568208468, 720977332, 317730835, 269146394, 831352372, 322918854, 387151563, 828918342, 759689322, 361458956, 717057024, 675876134, 726301876, 818813598, 842922121, 331708599, 934834555, 973154188, 688558813, 961336196, 793607995, 690294627, 774947818, 190782745, 966661827, 676495895, 668374574, 508463246, 741743470, 37772701, 854095076, 278101234, 35339627, 67723500, 838619827, 65644075, 209177043, 603335759, 601935848, 317279949, 318176380, 978809745, 643181058, 806484683, 688005310, 957155977, 682916128, 247569630, 33528840, 247562713, 133155632, 680747333, 81800994, 993224915, 866792557, 732424531, 879834088, 418701096, 366030885, 154012993, 791290422, 888853771, 680110921, 671259756, 488559650, 995799391, 583285225, 178632521, 725781975, 923195949, 77191037, 483317466, 64710983, 671280045, 526390859, 801651965, 861253148, 447437216, 112453288, 970539449, 11091560, 125487665, 78865477, 382693410, 414317539, 544070053, 835539742, 745717664, 367254463, 217542497, 450494614, 423151351, 260999018, 738688913, 468744239, 506103664, 303296248, 248242068, 286516065, 792933694, 343408791, 758275986, 593709124, 441881083, 652686041, 527791535, 86577944, 932952190, 35033072, 266290707, 926946893, 911117165, 386588861, 758259811, 768318056, 352048865, 5968275, 389723645, 857594267, 309132558, 316446, 683406492, 277510544, 63254156, 922629133, 473259245, 351091031, 607419144, 197091998, 924010963, 903178968, 964246812, 193542768, 603736379, 865010601, 525899181, 217875276, 352694545, 732324655, 811195720, 111172386, 320368487, 44388975, 991572212, 807778237, 931124202, 172193611, 786015789, 612905103, 472889868, 855712339, 611821882, 299348009, 142031957, 448301128, 243836373, 59460965, 98667555, 628307562, 860322747, 437546796, 696162389, 549448007, 246607830, 666004172, 26184241, 388719153, 360658423, 556154820, 164584801, 334182397, 882561509, 802404595, 463072014, 253600193, 743281117, 179126558, 907932425, 167076885, 582863150, 706432721, 955652140, 158838067, 624284327, 230599416, 89120126, 976403968, 183357487, 840879443, 398669101, 969060745, 629586293, 712723158, 773835631, 200745077, 610618332, 126167937, 313096223, 311371036, 132363216, 395947215, 976039364, 517093952, 747561825, 335329539, 187195875, 719486860, 420967446, 523437130, 448794709, 144463656, 111356572, 343933756, 162543889, 896792388, 517355829, 551500655, 251865942, 26412644, 326631039, 861402787, 243627309, 96273480, 950959909, 200462120, 452893312, 727004645, 634833706, 957701325, 114825293, 527842570, 444165155, 678268906, 195646584, 280726673, 827205443, 438062974, 546572739, 706737172, 191322400, 529210675, 528466554, 951537572, 170064423, 161349103, 525321844, 529986008, 7652947, 200443478, 339948306, 310513595, 287611458, 736335629, 839687432, 210543828, 134541888, 249728509, 111573170, 501776232, 256295319, 5714647, 325361898, 148670655, 740372069, 639072250, 742036839, 565794056, 55932014, 237340597, 732238349, 162578468, 144190322, 232753935, 867280104, 480679794, 667361070, 869063628, 384058524, 141364108, 738825342, 167002148, 689089794, 206430067, 526807957, 771132923, 595034022, 487731342, 72226691, 845526251, 906857460, 932708275, 59366528, 861626174, 346949363, 730878568, 415923499, 135894551, 900083102, 994877044, 326528618, 258121761, 445363367, 640968303, 582160297, 113201285, 375124488, 635276384, 925402630, 476072753, 389270226, 26572881, 991240928, 190935539, 557853273, 609853699, 200278434, 99042867, 943180380, 975629659, 847302938, 128625707, 979002987, 814040054, 267518871, 696724065, 460852257, 126768962, 888949413, 571979255, 173147819, 611649473, 31798288, 59899882, 789193870, 635849130, 945537888, 908060638, 757367326, 227655956, 767195963, 119151661, 238486235, 770062028, 401344807, 309416079, 600186665, 743244035, 519946942, 574727929, 624048098, 710449799, 822957149, 486091796, 196741095, 353506780, 907549862, 723350151, 966583892, 120740588, 743932030, 241336581, 50342824, 389205014, 994730479, 847349104, 428932544, 154858655, 716769821, 573248971, 708494606, 906947076, 953507585, 221099730, 954658142, 443042710, 164050165, 659286725, 691040679, 325082194, 943211903, 385369826, 952858699, 551740289, 724210108, 27061624, 414749766, 587778036, 100009214, 185771943, 206035920, 372861546, 725238447, 204229587, 361259606, 103494136, 23806133, 453866068, 193534313, 786382458, 530642257, 292047524, 946890387, 546425778, 682588873, 571704548, 139435506, 895885106, 225611324, 127179545, 410991195, 135399215, 814343991, 597717970, 276063606, 821677542, 133210900, 214494528, 596024143, 928344559, 179684060, 70886497, 94572256, 831417213, 649683065, 399445753, 985552692, 88587374, 448501028, 223819895, 121696432, 23009327, 658919305, 6607158, 142402894, 235884672, 154286675, 754349524, 302291928, 969551435, 23560113, 947175952, 283029741, 777078214, 635343846, 483485267, 276738191, 177516224, 640880122, 121343294, 770515926, 461861317, 282148396, 403719083, 996808690, 437152661, 88317957, 22719655, 547329889, 744999561, 511727992, 806264073, 552305635, 192357908, 77072147, 16811109, 734673401, 712355975, 691145232, 822284735, 407191543, 1614887, 237366654, 614130200, 798763753, 792557016, 979025990, 684224371, 194779995, 870454018, 329587682, 582479787, 714258452, 813778860, 230595316, 875271994, 42063687, 236280793, 239780357, 604242007, 466683549, 246935943, 435686306, 200777038, 239647977, 107782825, 286050988, 144015799, 895780408, 855700180, 138108923, 277526364, 906802374, 550813685, 609731705, 341880839, 303070081, 942816550, 543643317, 833616433, 328629205, 940382561, 71327138, 964663201, 838771009, 757052437, 116313449, 657762439, 909072087, 908597543, 923846504, 172087493, 606962879, 548583532, 347203674, 626159904, 927911118, 704428002, 56019661, 530823845, 162734156, 264054496, 61338104, 354510280, 967795820, 326896904, 928297193, 444239521, 871522327, 250963888, 56190194, 773773770, 236616722, 859631687, 658603907, 714352154, 640729474, 711405419, 169005491, 230838885, 400583000, 627694817, 487834623, 678094106, 440394278, 847453522, 101405343, 424418635, 749073271, 942643312, 728120382, 865147324, 148260194, 347709795, 324769842, 427547775, 148489024, 225526710, 456808423, 755070835, 571646501, 736747299, 346446018, 136330148, 494808691, 703321835, 363344933, 819064608, 348952600, 521189260, 198548808, 761440327, 54382935, 480021444, 959487218, 710555407, 740223112, 499890133, 724460651, 213279865, 993310494, 702929217, 596357138, 162754343, 984629393, 121447832, 36631443, 80823078, 666279692, 799159504, 511751136, 467053976, 260643449, 257361400, 114194615, 300304658, 922682177, 234002608, 536859246, 827846495, 786023110, 377652523, 263781853, 179942014, 307767573, 312204919, 940092730, 913135921, 159666212, 335423659, 800531266, 611551333, 218194946, 294329759, 10280475, 996715858, 394306742, 369057206, 441041395, 435317494, 545297782, 380858217, 299854297, 47840683, 925396647, 760964535, 259036072, 435628122, 9318359, 457648051, 874689320, 617191308, 539098945, 888393297, 349135585, 421125754, 467217872, 987869568, 290979109, 282392721, 631544683, 529191460, 128290110, 694485407, 526491198, 507342555, 449386791, 998604853, 305087180, 252156890, 936380785, 747374308, 16286458, 655606511, 312348998, 410254269, 563145592, 144527816, 776666853, 273489555, 111909669, 979643862, 102538113, 595323710, 481874376, 105184111, 327389075, 723910250, 69401519, 25900893, 420522198, 349507597, 609844755, 638991118, 257026421, 413116143, 484053020, 774726046, 807290132, 313621325, 226184044, 409077828, 334564716, 162450951, 469124519, 974618176, 533446805, 877951999, 813329676, 944678778, 717188644, 936079494, 97394031, 293980044, 705953199, 846297003, 469999655, 76329064, 669218608, 881809867, 775284846, 414924683, 812086975, 141592855, 362340612, 566175027, 497679073, 452324785, 572924373, 273612755, 883931904, 608209549, 168639237, 123799553, 242666274, 568393394, 234362870, 717103554, 835796977, 537931616, 178278294, 529671837, 742629097, 710083942, 327704428, 789762468, 890344619, 819217235, 30722847, 949429838, 796072579, 843608836, 677718923, 303906499, 953025991, 757153128, 853490416, 417538854, 629647652, 271226916, 936800415, 908895746, 766819711, 632731541, 1892620, 287380753, 433978167, 202536764, 566783211, 380751231, 39175573, 257654298, 833790375, 388123765, 964370966, 400146820, 279273369, 799640862, 602464399, 292182576, 888669439, 375852742, 521695857, 468235429, 207358058, 112171963, 768970206, 827700564, 979396619, 968594233, 663447214, 968133272, 402397608, 984691863, 313968004, 443139898, 747407456, 510428994, 301282446, 854323064, 134586183, 290446180, 140194651, 692061244, 347745650, 403070835, 566038621, 263190911, 824914155, 420021323, 575097465, 163325818, 198736710, 951014786, 725526977, 822819846, 243984494, 219056257, 274757169, 318942226, 143446995, 644497608, 796330834, 756916743, 798445574, 595842731, 556945124, 733231325, 598841267, 564086656, 658268190, 747422276, 465975796, 995991824, 196465974, 859199777, 528013341, 240003311, 694061827, 871005392, 916864394, 191112993, 439543955, 304633878, 403503700, 604525481, 21360106, 668904968, 27274988, 675011627, 139091523, 921595939, 442971159, 771967693, 684139434, 157668910, 386057295, 232920242, 671774393, 943080816, 991510625, 837052663, 548171570, 292007619, 358152472, 499845915, 620359834, 509046409, 438658700, 395086605, 220513161, 543779273, 337422880, 968257579, 678307449, 740734863, 173994243, 954979636, 154554925, 995664028, 182424907, 506451559, 596206282, 76926290, 495093028, 968105799, 820597058, 283032771, 85225655, 108930197, 922041280, 621220546, 151108127, 144234332, 534236490, 854509687, 70123582, 453644994, 979444090, 262562680, 495185864, 229519022, 76597089, 791134248, 834087650, 445913080, 465613009, 915047715, 213903210, 895786509, 975262075, 81020612, 434289057, 928186179, 102454553, 596477775, 426176342, 115923022, 850964463, 674884101, 969565704, 490979214, 572552029, 828424226, 331031216, 684216921, 367151547, 34395541, 486376772, 868705685, 316920679, 511797680, 759512501, 702132200, 21782046, 496743429, 766536116, 507816075, 793954695, 31716303, 531195812, 399956284, 307779266, 814904431, 325904664, 930288013, 464023681, 592803438, 136661761, 251777647, 763987122, 116967067, 32195446, 568004645, 291964493, 128785421, 216075226, 859981678, 959787065, 362866162, 634052227, 21185688, 372128741, 84691095, 996614217, 960363211, 413230263, 324834293, 137476891, 182517397, 253938684, 744058636, 839206499, 587170376, 890388033, 612115615, 779647051, 144920552, 661183386, 46105477, 199398523, 126655110, 963170718, 656893858, 441353425, 684930139, 547876360, 158905, 698626522, 346609563, 27981364, 574102811, 441500490, 552396699, 252501058, 953741451, 221121610, 866281343, 203097669, 865656256, 599532286, 679841315, 952103958, 275622919, 599816702, 297049582, 621952449, 229316019, 839945945, 972354149, 914390668, 564655975, 236113520, 187208675, 978737794, 225222530, 513569133, 838365928, 881729719, 970785509, 368858763, 819087815, 929749153, 483322352, 517932450, 233559928, 263312815, 22978158, 355690553, 778877836, 936799384, 890816849, 140010172, 888203235, 736020544, 870235857, 351225948, 728532062, 283482452, 964361230, 372584606, 538187448, 752032542, 687869736, 802893516, 812838457, 13417346, 316760566, 109610894, 72128527, 4840279, 396369825, 667379957, 207053282, 697967514, 457587081, 907485850, 499273681, 445567852, 129533655, 27466177, 280656420, 588952668, 374115844, 161828227, 268276269, 105260569, 737868670, 644577184, 858909494, 31911312, 668701642, 841091762, 17708331, 433928564, 665611896, 174634219, 23106475, 465415797, 229296313, 292514542, 85373874, 810125266, 845249199, 246244523, 817951932, 586951386, 397648508, 77486040, 572745055, 446041441, 902493319, 419644633, 870268944, 198066945, 706043622, 74588927, 587889495, 147972707, 229169712, 581673978, 432135355, 850441787, 191348783, 449492821, 180150647, 924881852, 144698017, 661742270, 841705818, 396981347, 689381797, 776566663, 954998811, 582761194, 701735129, 99219420, 496918939, 508288088, 386318431, 195127096, 90198647, 314105750, 113208370, 131509327, 373340658, 817423393, 133919868, 755180193, 569166670, 775539429, 851096824, 482915984, 666385163, 495105089, 226794771, 490563589, 76115625, 8883989, 434067525, 66558067, 307870331, 210404050, 920795979, 420418583, 632321568, 530362138, 372506574, 679457705, 552832499, 45226917, 995998298, 659023983, 243381718, 736833674, 562842487, 197584414, 429209136, 460665018, 215576745, 505993136, 163993880, 835770675, 839717017, 669378308, 146792915, 264557834, 732912335, 588422828, 888804579, 297286304, 29972326, 583248230, 269470868, 220909591, 590376413, 940815575, 909670409, 799105473, 666533026, 50157067, 151375690, 906684910, 305483782, 917830948, 243964080, 892754951, 434909498, 143306197, 479719451, 90832822, 194781413, 623043754, 336307744, 174312238, 336253789, 759629886, 638454792, 325565507, 261814314, 693500730, 54716070, 241258921, 131187466, 538725789, 336550264, 580058271, 209457723, 801895638, 526126932, 550017166, 273325591, 855316270, 482366052, 665665863, 276647701, 946674979, 435372385, 364750682, 228822623, 396439515, 100427476, 424316370, 787070883, 73904359, 971799036, 564626782, 915696841, 790203540, 696918800, 394326616, 815732458, 730091287, 222334009, 166259364, 352223157, 941698622, 269888631, 472717014, 621284272, 157871192, 938053698, 427200904, 904959489, 297487945, 723780210, 983417012, 699236586, 550327808, 556872920, 472213753, 977612602, 694359569, 154536031, 957427732, 490662015, 261089974, 487238161, 393864277, 787119381, 184561525, 84367990, 878332739, 879785846, 470979374, 968739962, 613854669, 220356263, 195682041, 534834529, 231746624, 309349494, 23894170, 727827597, 579496458, 442219632, 187740, 732354195, 616830866, 264528847, 187023267, 972864336, 495888442, 497125668, 47794109, 208897096, 100392629, 635092670, 383419324, 463845485, 278562302, 991372028, 332957423, 96651796, 656420552, 964223818, 35771433, 123149498, 228282047, 759116291, 858929586, 639725777, 820052716, 825320131, 502349163, 133923764, 813748228, 315444108, 661731900, 643756456, 690065629, 910043017, 265838913, 63758003, 803808118, 864914163, 114631325, 133086894, 356454000, 69988307, 241714886, 522491068, 386434381, 55763119, 103727757, 917893310, 81524838, 526712879, 193740022, 123975318, 559281462, 75590425, 333126172, 481019243, 186426676, 593994035, 225758446, 439588671, 32112872, 378728443, 91365226, 282487305, 229917835, 826498746, 881685297, 307741458, 173884910, 640624687, 219477721, 600917425, 866440523, 291841179, 634373983, 27442405, 71249426, 553708258, 613900025, 316145012, 651004939, 131358481, 937155100, 322969785, 58384292, 263158339, 531431384, 345035443, 202112992, 832914571, 807358126, 177165069, 832957194, 986910306, 59456900, 244740590, 667123224, 424887886, 113482451, 179765110, 860178639, 372250754, 229611095, 605882494, 656317386, 151303116, 756995494, 870859613, 763876147, 269938522, 307621164, 471117632, 360650934, 214611668, 226482732, 567897285, 63345534, 844229523, 202776159, 649545566, 676482544, 377851299, 748777169, 821246865, 393644394, 933265659, 485037844, 173722412, 616767109, 139497429, 450065701, 338086945, 934199080, 913760661, 14433035, 701077263, 455898488, 957604961, 140522244, 811022995, 856996116, 865099790, 709592100, 393629128, 364693270, 905149788, 196797857, 405669273, 969138926, 245218054, 835136883, 724743101, 265125478, 675449462, 61872795, 556918069, 974590342, 830304978, 698487046, 312526867, 388205891, 734520323, 839139611, 718976431, 834170337, 920920336, 967075233, 702345758, 77436243, 643775069, 885253056, 536353221, 711617081, 427772504, 781604665, 292657831, 964242738, 845465770, 623340138, 70760128, 734528810, 64166766, 943954866, 690755152, 365421437, 891556585, 940747755, 589367343, 295745545, 369693098, 703232606, 872997542, 821558493, 858123354, 211020882, 990604794, 688914515, 733896893, 515351596, 592869613, 2405117, 323023512, 167506287, 868109190, 195666393, 635510488, 421369318, 737859370, 892507909, 527321298, 64972594, 609891649, 988156614, 137909716, 119064581, 419951721, 740381161, 998602896, 281530563, 847607595, 368909551, 320583220, 726512051, 225255808, 73481240, 490846455, 797144294, 529105263, 89305411, 792199098, 111843154, 581574634, 749577565, 304747342, 408277115, 357145124, 114004884, 76730812, 796982054, 745437600, 528624509, 518234903, 165426190, 330010985, 260705031, 185379829, 142583846, 837090307, 605035018, 540196944, 524292146, 247913690, 234360293, 505485598, 983515861, 228188232, 790676679, 335219939, 644241988, 297163, 448698850, 499525201, 976191209, 321484534, 527181161, 232992268, 231978073, 291222666, 222688810, 22920577, 140971131, 438719909, 645897115, 531981304, 385421689, 224957647, 517324423, 824291620, 949784319, 368693066, 438311042, 663362255, 99685848, 446024943, 512678467, 30174645, 421466294, 411030046, 43009129, 854868509, 180948899, 223438951, 107683810, 86189238, 892639228, 531078427, 373779856, 4365716, 686420388, 96784711, 528409452, 82338264, 540568341, 697759606, 513975022, 946601475, 879325869, 523710898, 476588997, 503682654, 937480602, 890484331, 679089787, 202046090, 79923457, 586276921, 357815656, 661614388, 582434081, 225744934, 619807780, 394620102, 66295075, 374834604, 703984967, 608625890, 427360429, 866395769, 954812242, 552276694, 830477440, 729779280, 634132253, 288705843, 966474648, 222530951, 443078722, 498810527, 208527717, 327938791, 890831427, 46479945, 665484128, 477969504, 49496094, 148630265, 521987361, 114877623, 222534003, 805487264, 273227317, 377952290, 284087131, 996068885, 361980484, 460128667, 500639034, 638990910, 685465212, 916496762, 921973425, 694160138, 653694304, 530414123, 119327506, 918491677, 258699091, 498185140, 395157347, 38568977, 105593445, 181121520, 471624249, 514528223, 318748966, 824282766, 85598954, 94697813, 875277489, 833868061, 932387625, 841921180, 773690515, 358585786, 707724060, 916378145, 515550294, 1493696, 286811871, 120578641, 183159325, 526744706, 571356459, 160209938, 665424538, 223623057, 819543072, 257904770, 13605566, 66759590, 852968545, 726808529, 432423776, 739327348, 559757686, 572802230, 18392611, 83012372, 247237893, 804346267, 582028920, 512440966, 950239955, 11475306, 743259819, 166734700, 807958330, 636885074, 122580116, 534645013, 129653693, 34273531, 174685566, 562968875, 587763020, 122353778, 145513399, 925555309, 119966936, 235383508, 745997554, 423478118, 311851226, 440131586, 820599844, 576649988, 363158948, 206274914, 729775905, 103476304, 907557544, 145668634, 565606238, 746219111, 563744522, 810511458, 979190213, 919014956, 124646898, 492932213, 12714067, 972206215, 223710159, 40860685, 380550405, 609306582, 127233435, 546294339, 634445113, 25163382, 755855587, 779771099, 168181090, 562635567, 252139729, 488057304, 989636666, 345793711, 230362952, 802246609, 700541390, 964708886, 401731712, 351777784, 383465265, 102739027, 87229067, 911838970, 763513963, 247635501, 948592242, 607325378, 792300641, 446199191, 144808541, 695932770, 487459216, 787430326, 623340757, 894659726, 708731128, 483719880, 956502573, 144395223, 929576716, 885850002, 975852729, 448707865, 509013330, 292983280, 183928524, 332042492, 215118825, 753889820, 15938710, 100879573, 360365510, 288016894, 857058842, 864890412, 36910606, 366920479, 417426487, 634456834, 188594508, 916222579, 768497989, 606831283, 828017078, 737007121, 845993646, 210782426, 961621524, 844049867, 278605578, 84637449, 124674351, 410971463, 471602149, 423612620, 600110852, 262920511, 668688259, 447418369, 804855662, 564354877, 10006608, 797819480, 57818685, 690343187, 231487841, 588018007, 253610211, 257687443, 869570927, 631311750, 468878203, 940874166, 322029549, 464377636, 530525377, 746508009, 896304649, 870386910, 677065446, 574192820, 26970849, 679997766, 603205886, 979793712, 785099226, 302101111, 200132016, 474361124, 558018176, 126289156, 458322436, 844895821, 302568684, 492895008, 40502578, 627080322, 328861704, 341905260, 409734884, 292918154, 876837899, 624684540, 306127152, 718162784, 557563237, 598119321, 503305861, 277545400, 96032143, 974289501, 527954176, 114955644, 638752306, 964131272, 48697585, 545032203, 143810022, 955311816, 159627015, 478827688, 834098364, 617720381, 927391939, 420854661, 896272032, 303159914, 166759114, 811137308, 513714543, 211507638, 15602527, 645031308, 516613436, 774926894, 706268097, 539618869, 954495062, 986920021, 31974736, 436153026, 888880994, 887762759, 273818288, 972451583, 983871252, 629319627, 503403980, 289067510, 463510357, 455674122, 370930213, 29155154, 436053915, 265326917, 745988590, 683733830, 944196735, 33484006, 298112330, 911548598, 596165061, 917392933, 712337484, 294266421, 222226715, 69744853, 617789792, 81221151, 769849920, 441646449, 179473804, 936374814, 251292175, 93801420, 225848534, 927568546, 142159828, 529884385, 529179741, 539618448, 925287096, 681473740, 178411906, 140054018, 248021256, 398152659, 101533723, 998117023, 779306684, 141956429, 127697751, 356946781, 213507618, 647700876, 913727706, 169623124, 406381813, 439840287, 856721779, 298631271, 177448575, 305274997, 48268875, 805899650, 55146656, 440533876, 953156711, 369350015, 402127551, 613649269, 545760174, 897363918, 615507763, 729320973, 326593812, 167879111, 940491290, 488487081, 341691670, 564373404, 631215795, 615936159, 513819211, 368530540, 870154303, 250393521, 170094493, 926730587, 173457401, 997803945, 512995295, 668969830, 98850599, 465253565, 534495169, 192483836, 363556051, 984547567, 287523008, 292742716, 468975140, 266383431, 36322612, 630200435, 909536749, 992607725, 208184700, 129912514, 273999629, 626480797, 740817506, 710250524, 502556683, 85550985, 725957355, 41766650, 502765964, 947085642, 766255416, 212286591, 77383102, 906629428, 569346133, 48985758, 903429420, 741500816, 159589441, 667921477, 85086534, 128938078, 436355843, 458013114, 807222625, 682439589, 706247330, 23420410, 833500745, 690816690, 623309818, 532842962, 214699212, 841121682, 863429514, 405997568, 560990076, 727955830, 726021315, 882665249, 799354436, 671104439, 80751002, 77889158, 335157287, 932715297, 262589848, 62785560, 825059102, 251189497, 829625494, 560016461, 994484021, 642293924, 642427621, 891909450, 607505778, 243904409, 642401111, 278807871, 208381814, 364686162, 648789449, 236651718, 245087252, 989224924, 799300482, 845396540, 479279042, 521768532, 156223619, 821922953, 314912167, 724496411, 656764655, 978739518, 430245392, 191930989, 88279139, 431659080, 693176839, 165658044, 597541809, 185678887, 842447640, 684061226, 453691428, 824033619, 869138065, 693806589, 946639360, 210090813, 250036573, 663579605, 146811117, 61613102, 246315775, 286001732, 191703160, 404547853, 845553762, 638274496, 762190810, 722708248, 536377244, 547999792, 381555413, 7330998, 980228165, 674554121, 794866520, 399013501, 367689060, 276860064, 820934024, 978129733, 976353264, 862315573, 252967131, 290946748, 304748981, 488900870, 315547114, 261198586, 777432195, 148404770, 245107947, 574400061, 7801143, 100797862, 795408241, 920534859, 747004254, 820721499, 562573381, 263067150, 197074699, 586515261, 401181505, 399822174, 500148247, 655202362, 896155427, 307913351, 328288976, 403767602, 532113945, 297794492, 520533705, 403013653, 991377415, 605776450, 435682552, 785872773, 424925238, 593358660, 156868191, 843238506, 669960590, 862998626, 105592743, 968269002, 948672389, 236630743, 202926037, 991308302, 593882563, 44783667, 583771370, 494403229, 12484289, 506508268, 752553528, 778255333, 195839029, 781632226, 498814968, 740375594, 160723059, 415840716, 127330765, 607158045, 717462603, 348796624, 611856883, 453063437, 212846098, 571968143, 787592691, 404721908, 801934459, 896645450, 569029103, 505694180, 61649005, 761921637, 762921885, 714274692, 621566468, 591148043, 718851043, 449726040, 208105375, 452873649, 301690725, 905497636, 117991340, 132125417, 430242172, 797093770, 772380779, 827672263, 961808334, 885905649, 432777405, 343568380, 585444424, 506770058, 847408438, 320170860, 433313717, 563028385, 759897878, 412942311, 585325073, 806109515, 390929922, 142711836, 208123998, 458165898, 839159768, 863567265, 522554965, 645053303, 161273990, 469712087, 238001365, 580933609, 615832362, 419716408, 683927892, 210842416, 293323805, 401894778, 479868075, 68241399, 135646984, 779799704, 44858655, 906955183, 6126059, 545173540, 272456366, 973459548, 972256160, 74692390, 680213242, 790967699, 859441228, 546881699, 25538635, 453941965, 969673149, 741180146, 233060818, 144012766, 487352293, 452670880, 182176284, 476166110, 774878363, 179793739, 597555669, 630897630, 236980679, 573150714, 99558176, 95920357, 463675353, 187689781, 717926280, 111505322, 374498481, 211294030, 320110452, 32319372, 204677937, 209511675, 637696352, 900209461, 894539628, 784169955, 856595274, 239222799, 89719179, 879339512, 524299201, 512709342, 514493443, 612491531, 402655353, 879332403, 950935309, 668423258, 753070127, 94342579, 877890364, 407986993, 646356293, 781571047, 515059722, 541698726, 851765279, 236977012, 264292341, 772879614, 844095385, 215222391, 226947318, 905680213, 376155211, 496460819, 835446672, 497127940, 987645823, 805196719, 795655731, 127015767, 64013676, 764551266, 204181797, 364351537, 904567417, 495461954, 567918887, 40065282, 658812114, 333456744, 101746199, 617995221, 819632107, 926525411, 393031579, 737044377, 12096313, 587288120, 900681161, 360424369, 191557396, 595106397, 360498429, 840270187, 825811619, 387844476, 479214030, 577845388, 19522144, 271617544, 897496618, 100240031, 421388168, 511078774, 697401462, 2847414, 960206885, 567695114, 8942094, 327761295, 773797430, 329124689, 1070775, 42813933, 375350724, 366395721, 318649751, 532842263, 258408806, 811026169, 549266343, 969543240, 413071714, 91895855, 243855707, 518305154, 966580873, 413559808, 41782270, 900957062, 122728790, 641979999, 202622652, 438450654, 103518179, 767457030, 94407829, 447084778, 987038261, 368090346, 402539184, 508035741, 45307599, 764903510, 148215974, 103739806, 792337999, 793596856, 554294093, 303272971, 10937667, 815500801, 1201387, 814246355, 113264062, 884670643, 228969912, 486067439, 50040031, 856229740, 5245211, 197786008, 452549367, 485361263, 172479938, 541628237, 58193476, 588920462, 591795564, 663707863, 590583262, 759970077, 372631191, 767265183, 25338929, 905179513, 884312359, 472498201, 75921202, 972014241, 919117178, 314855462, 449380244, 494681080, 796316857, 265250945, 178075294, 174378720, 179240340, 884264700, 125729848, 686924861, 999334820, 534197820, 148251941, 574969655, 507698758, 138232853, 828913257, 333423604, 865617453, 338314161, 337209535, 989264682, 321511669, 58610142, 117155956, 294105343, 139570196, 248698784, 75516385, 782773129, 967934515, 591824927, 968996640, 57772953, 814466757, 879520218, 74945156, 732237660, 295580119, 507806324, 114977248, 282676644, 15916365, 106928443, 401120202, 143750421, 100940810, 291017475, 102736053, 874917751, 101734205, 729314311, 699301584, 610055373, 178310327, 757716330, 448258561, 435999441, 175280119, 967008821, 79307392, 484530902, 633482023, 917335568, 160779059, 593738408, 579677310, 624623764, 338755128, 572470551, 146781439, 630326264, 944027306, 399645863, 988498934, 709574880, 605416044, 210251506, 423392745, 242295210, 749281875, 708035836, 615613219, 541286540, 786122102, 753924422, 927343726, 99129873, 847846921, 218105320, 760846005, 880488145, 389636939, 622162134, 778513479, 133368303, 993159180, 755700502, 335555481, 887759899, 886872791, 450170417, 879407282, 881496310, 47204625, 847273497, 656344634, 4900219, 594055922, 140666469, 394162002, 187693001, 183244442, 213561494, 734237212, 727160440, 123023142, 438769780, 478027807, 219243778, 484167673, 581337837, 586420040, 270518628, 87895561, 937255932, 106498779, 396238147, 425171843, 929313058, 247494450, 813192283, 115507370, 183453336, 792630667, 800019636, 87681126, 317675284, 40307889, 292321037, 905426226, 39338957, 836155024, 294880652, 468129158, 36661880, 998609368, 347636150, 208154210, 408973718, 44230871, 989707503, 597750522, 432386330, 787763238, 248259424, 731109681, 457159011, 566956, 586594866, 41512029, 100662668, 296633217, 633905950, 783673212, 886910894, 422931356, 944348616, 756298884, 386626157, 440832423, 175575617, 960475414, 5438370, 525057067, 39809783, 337092226, 163035914, 54220008, 271692113, 277233777, 426518185, 980713812, 598978017, 149753661, 398795574, 630339370, 26650818, 152257671, 500971410, 186956039, 816141362, 881137133, 814871390, 916350182, 339716193, 435164759, 706090084, 239747506, 365756435, 786026881, 510185356, 751588910, 879715442, 28894495, 800767426, 82298510, 902885733, 141790022, 637007667, 243761178, 329216089, 16430943, 479258332, 864611125, 372415641, 801812503, 327091565, 729666532, 319662824, 732109941, 178762291, 584571472, 853581389, 921981559, 91966392, 364795567, 587938450, 729425764, 507957612, 864806715, 836287492, 659418179, 242175737, 831515044, 948389290, 550236985, 940254988, 206055765, 198468569, 261429289, 20580006, 176892430, 170317827, 378544467, 800038116, 976850022, 902716292, 25107985, 298586132, 897999707, 70993381, 427338297, 700779604, 744321334, 467362183, 490479302, 38817962, 857067980, 994233227, 843679462, 420854966, 128160402, 846998369, 658238282, 573446184, 106573074, 621722187, 621683453, 635878714, 843867577, 2458050, 694052209, 762211724, 286197456, 617234570, 418233425, 736438006, 308816928, 130099301, 307573998, 287293470, 161678480, 677355310, 506198042, 562771228, 753875167, 706671927, 443233900, 356679775, 352234249, 223116351, 444540979, 782016431, 794798924, 242624989, 545286392, 253913076, 870317015, 716258246, 717218777, 219471967, 446484779, 505849694, 666886378, 768140744, 467501185, 650280527, 602503397, 24197233, 826009768, 103134868, 901463765, 229498243, 70147768, 154086278, 990270278, 729842895, 531368972, 390859070, 651416991, 470598977, 89178469, 726912823, 64313058, 761996386, 181412766, 786556527, 796470930, 996519655, 904481226, 543906603, 433075512, 604921289, 828152469, 378677460, 923068541, 584288134, 409553741, 200650734, 623706219, 81604982, 607160574, 455412205, 274638356, 545137918, 700002295, 555874695, 456173103, 433181944, 216692670, 342290167, 709336141, 152860447, 462445929, 101805040, 133573590, 369775206, 93231740, 805290244, 119581420, 884575645, 744399260, 98542532, 284685821, 127123212, 280987464, 646053252, 35446495, 555698040, 944483176, 867281788, 829874262, 493998003, 260726958, 789740101, 429885728, 176660251, 644914512, 389757195, 237952679, 739939873, 951283729, 946083910, 996284428, 446008237, 641750011, 494398137, 661327626, 370051432, 541849794, 500665153, 70862501, 313997436, 413323395, 690317619, 180420116, 643335433, 445604115, 614783501, 20053634, 792024778, 554982531, 535065450, 149803219, 55255381, 345877856, 839963634, 845807311, 721236169, 949127391, 134055492, 815071981, 360471905, 838237090, 162163015, 913239096, 370743054, 565579818, 877067411, 245337220, 281722992, 305557441, 266004831, 711336873, 68917587, 403608861, 416484770, 380012192, 89383184, 313542370, 925620107, 469839679, 411167210, 320015481, 768201388, 693273383, 942540000, 831724930, 769835299, 450637806, 934278292, 913799858, 434029191, 523849057, 375525546, 928307655, 369269869, 899318047, 200869984, 474580545, 510674728, 622044542, 166689276, 597363363, 109551750, 89000848, 891482864, 980196173, 770911175, 760492085, 991705162, 799978892, 675481054, 155385392, 459865052, 564370206, 33415674, 46262211, 37120505, 390692885, 814396790, 873245155, 6951939, 953421514, 557633724, 277141142, 267396714, 960859056, 330906971, 427236138, 650915703, 61131436, 786788665, 404345325, 363094919, 568469436, 772166468, 46164131, 691201555, 857836090, 207666322, 180711311, 398887866, 271909009, 510545900, 185545300, 433536852, 18024763, 347155411, 365384020, 9664755, 429919961, 339305228, 754057342, 411344789, 24595413, 179785873, 780665585, 706510128, 369321433, 585830569, 237099967, 498210176, 742391246, 445330217, 283777675, 410404925, 593162758, 930275599, 197179683, 283330221, 894466080, 342885605, 339550870, 462608738, 421670310, 564597115, 177296099, 675016329, 36246039, 41647346, 245706124, 894593821, 473701600, 169638591, 483657613, 962292707, 892470222, 90442360, 437947172, 45643531, 460591297, 825142735, 536283557, 809346011, 885327188, 326963645, 196288550, 416527113, 823075813, 728715845, 411506406, 741460331, 592275125, 965486472, 575309234, 113331285, 860018784, 284683860, 313509834, 30890028, 933122081, 36503694, 270760667, 383359138, 999650774, 630340380, 601413470, 316397928, 25242741, 607604380, 461614534, 62416655, 457205832, 142293289, 157996740, 252068133, 12361039, 639304505, 151435001, 494600090, 191174352, 556053620, 903763415, 754789303, 854844340, 675799274, 385151889, 229054896, 30040062, 648965248, 566835689, 564591660, 714995500, 695746970, 730408564, 658546016, 19277563, 364957967, 735253372, 956443084, 586269636, 539152790, 178364331, 179915395, 717286111, 695148372, 637240014, 731417684, 310370073, 873498238, 745556497, 388475335, 371060097, 904510995, 802221515, 582145589, 625102821, 425092851, 656539517, 900383370, 383864704, 175550286, 46357285, 365780139, 947927570, 584941720, 210754429, 29426985, 466030280, 351901808, 197222593, 504001913, 870465847, 460792615, 779189742, 968677244, 506244323, 207240550, 70362070, 603369610, 315236423, 226479171, 141495637, 453946751, 347591141, 839682512, 483929931, 706230521, 355395849, 984593801, 69013680, 517998396, 711323066, 395713163, 255201229, 120047201, 153606515, 510797931, 930045207, 509646452, 78073144, 603989550, 741863241, 599176515, 539995343, 240427074, 916236828, 684223632, 494784052, 226672558, 591057042, 752883359, 452837395, 538715086, 206897188, 911919012, 606596285, 855681718, 614153241, 306646044, 624530378, 732934476, 719898570, 868942993, 348240379, 852506563, 140557326, 586694771, 712650640, 828831717, 880988884, 5498789, 600821719, 451731948, 746542169, 434129765, 195405235, 758893117, 107694449, 605882104, 380168326, 581356102, 720878792, 248783449, 44231247, 998401501, 92000472, 624957738, 440594835, 435037854, 453670036, 571538270, 784321066, 311425280, 391378239, 975152816, 859443221, 789410516, 779713166, 415841295, 181947099, 868012409, 412433218, 271348525, 198631872, 432263383, 467662827, 715095613, 892789682, 401971931, 951256758, 881550421, 842851524, 284497079, 242477807, 512456242, 653686947, 141570634, 729245036, 476002290, 910890245, 903874956, 727540677, 907372907, 297838735, 670810652, 94179839, 245107839, 427489487, 645687331, 140639787, 280563281, 460933293, 44612582, 577503889, 829890116, 167431388, 267778917, 310006195, 796582779, 902439146, 339166634, 996462393, 763069193, 370487647, 302263122, 301904214, 496166514, 464810672, 423109277, 910603425, 177694851, 228739421, 662595315, 989979179, 256188946, 362500744, 144830387, 529822663, 131354618, 829469465, 384978464, 519646321, 360765927, 840399030, 288873492, 446028344, 40687637, 644335939, 993345168, 119159155, 253213484, 681473681, 229926640, 87803877, 887655713, 402623318, 678616439, 28588427, 588040772, 1126262, 622874903, 504403918, 611689475, 186116336, 337064678, 985773136, 895603696, 774221178, 310253483, 75406587, 571225996, 823025790, 724456095, 768952292, 784435229, 616700188, 194191708, 90061991, 201214065, 154907076, 938161996, 742732463, 523160148, 279620580, 612972292, 351776938, 440851041, 663445813, 922634276, 111284399, 965131187, 869859529, 643422950, 764967452, 825277119, 710188538, 509539517, 180172729, 766987479, 663711015, 126544133, 108680358, 595961046, 999775804, 249380015, 827703966, 478374087, 622721622, 364489938, 950473773, 910787523, 980094388, 329286102, 943229671, 318537191, 290902820, 728356243, 221729727, 581624765, 226766181, 782257923, 215585376, 74320695, 871230117, 539734037, 228838357, 759889731, 528869749, 775885785, 296250743, 9346279, 78827873, 796513676, 695583143, 767182416, 366524558, 293568485, 665153374, 445572066, 114152003, 873549914, 458682416, 794551203, 749443547, 519589885, 6717085, 351196003, 802468570, 436909262, 9016203, 333209166, 427217039, 213998683, 322872434, 250753477, 925149573, 386203047, 91146005, 645259372, 454915302, 576904613, 436528236, 598896207, 550994846, 167257459, 20113732, 657213989, 428934136, 54738093, 270808126, 809839467, 460822254, 777662662, 382365179, 598626599, 743989505, 781309165, 342003887, 250453212, 519378262, 563928287, 825654111, 528074435, 901349786, 586479157, 551933569, 633652871, 1925256, 183376311, 541201676, 246691447, 319224753, 451926304, 46870193, 758347806, 535732377, 237379273, 140121072, 298314762, 707425468, 563747919, 225263386, 697842762, 941663778, 931436019, 131299228, 813715216, 747984919, 133286180, 124867404, 716487955, 616984589, 486258351, 196668619, 586132507, 87893277, 26353883, 349934334, 715401399, 144620325, 990169710, 826263668, 324704951, 953718622, 142882235, 74793282, 463745756, 908443117, 742822647, 292311244, 799763681, 260934217, 805935776, 942916291, 549509676, 592644695, 144244401, 258966334, 400861428, 771154920, 749358434, 322992851, 824982284, 224045660, 543977788, 398523199, 967518397, 344023881, 571882367, 935612894, 136508809, 641262575, 112645172, 603747006, 126903285, 720214465, 828360152, 765586279, 43091678, 642197057, 771087866, 328583958, 263515116, 760306588, 923856538, 743673141, 160845541, 459810350, 170963770, 958226409, 393152319, 745855038, 336605154, 690028495, 568625004, 830859796, 195411530, 886298911, 590198582, 1810033, 360572911, 487348733, 801706654, 942877947, 215449692, 302195283, 496480013, 512094360, 101429037, 908206650, 888632835, 898030257, 616963151, 88889014, 697963325, 224386269, 291808262, 202079063, 122111336, 362764228, 699350115, 160714742, 608212397, 148058347, 176090810, 50866787, 320739844, 959369540, 683888288, 902105812, 314944523, 95599030, 512594441, 257689902, 352115741, 126727376, 902037367, 594878314, 48866027, 753137477, 240998202, 392992685, 925497984, 401388054, 552579219, 224769900, 98481953, 953760539, 897759967, 56974472, 203212872, 502929704, 243273378, 557279890, 200900415, 642673455, 352866346, 167514593, 939635421, 600989914, 35540479, 416292901, 232847294, 706800702, 631175926, 269126558, 677437298, 700232448, 492129246, 125070034, 331903331, 693638784, 916658549, 758389966, 94409759, 417911937, 557679900, 687574830, 808870036, 147494664, 841584610, 690464822, 269744702, 115200388, 350346083, 692191734, 853484276, 730577749, 513492365, 500432518, 32888194, 677654303, 137455513, 323671968, 310495737, 640877454, 123242345, 767443947, 949628817, 842824345, 14905313, 171093503, 335330887, 350151325, 354564774, 588921924, 823182690, 610534862, 537716577, 806776991, 476588836, 376009833, 55604779, 132012358, 266298940, 73180704, 588089674, 246475230, 886598267, 874066789, 994592177, 611922566, 672327342, 732460080, 339843865, 588977632, 361200044, 729019950, 787956935, 745019770, 887330529, 489341485, 674967036, 758832319, 352308254, 27543823, 217269087, 734334680, 837958496, 866163044, 710967130, 168131772, 846390208, 214431654, 367987628, 761004517, 975408612, 732519431, 908312249, 640015554, 267804854, 561661209, 209787062, 512836598, 462660178, 191283014, 510824749, 592308920, 979537183, 905234127, 842560353, 421134090, 291502139, 213739898, 244599138, 446363711, 788555725, 733339086, 382013489, 190255789, 513977479, 373312151, 271365380, 949822238, 230837540, 347984411, 13569898, 112174637, 478555026, 660871897, 720667999, 777474168, 115779698, 463199701, 430216693, 934097317, 471921045, 91850628, 130219282, 739771101, 102087573, 798115097, 516626877, 993767031, 852198703, 588393118, 580574673, 524319647, 340658345, 48575616, 607049264, 102591903, 164426346, 28075347, 829198862, 722898117, 821563365, 830000206, 731995900, 50681376, 9468556, 367631452, 124485313, 508842155, 549453360, 942452409, 670564670, 615230772, 356952925, 384439628, 877200020, 491129205, 296757572, 858705582, 740859256, 228429900, 975871560, 173143188, 315971800, 914061119, 484665060, 747778799, 626222307, 627568451, 310628248, 779864569, 653098516, 938255542, 292202603, 37629150, 289896693, 314482712, 601220573, 387162759, 958501044, 788653029, 750898166, 881487199, 203172838, 78729167, 334263041, 854053566, 433572670, 593614272, 447087120, 631717127, 533140948, 17077726, 886131709, 636141808, 101514555, 954417551, 296352494, 803672725, 914371600, 822037161, 299923350, 812455679, 459761967, 42464997, 254645728, 602872918, 277842263, 106882194, 533159450, 861486763, 996743275, 72956312, 442505270, 600981444, 980965715, 313261605, 99249770, 342878598, 199198133, 791152933, 857910455, 325543347, 721434677, 56624333, 497859518, 837043063, 930267370, 4720500, 343062817, 649610092, 970591431, 417094847, 978359733, 597413067, 256922018, 633024948, 196155088, 869462175, 862597170, 744845170, 306450881, 120381566, 626066816, 700452371, 153661639, 925811473, 419151459, 825038855, 696281672, 281118236, 536943847, 572952903, 985363798, 929512712, 155332403, 344233777, 171650713, 966751823, 669206667, 684238328, 919507229, 278927231, 133171972, 89800805, 335753219, 422154814, 825218948, 743453718, 400922233, 375251099, 420125923, 728338690, 256668343, 561743615, 450817483, 270280069, 598969336, 488490183, 171947900, 482515899, 443990499, 491695214, 179465706, 584366783, 323337054, 610319883, 607030747, 754664683, 623442218, 544529872, 209406916, 184070187, 218465518, 94376472, 130112401, 269250530, 20142092, 956492836, 116380963, 97095841, 104706941, 798010735, 11509645, 340929803, 158803704, 43832140, 385257866, 313154222, 22000593, 506100462, 849370047, 787491645, 213582768, 763405144, 548349600, 392874432, 854000543, 781432744, 428308161, 157756852, 59194494, 330777032, 599256205, 42794255, 96613379, 373692648, 197625993, 461513716, 443213425, 983865993, 233259736, 272213433, 796585752, 144224798, 479046504, 600019389, 924247870, 621816693, 349622903, 175689659, 145617825, 870844653, 72482253, 580256784, 862626822, 79423232, 816691361, 544565188, 62286176, 427192235, 770614070, 559419284, 195468410, 313622853, 998013074, 269630637, 10319621, 515673207, 406361672, 880458184, 653311203, 207772272, 869090753, 20219974, 131177342, 150264742, 64449057, 733395939, 469787880, 718290784, 245744452, 610355944, 631425972, 834789793, 961061669, 504886730, 302892829, 287222236, 359043765, 783139435, 213518070, 739929537, 284186460, 860393588, 6602091, 117519805, 177078433, 400889537, 235280967, 76341180, 69261279, 241111739, 700939571, 434351453, 629233940, 167761412, 49390756, 252855945, 14119319, 464936505, 227818142, 642885945, 68674486, 715000309, 267122957, 696413231, 146467127, 793006100, 597593264, 65848633, 911379436, 819254455, 772182057, 624138651, 593165899, 439455290, 855817464, 102795386, 880009062, 174202208, 944081658, 270437267, 489343578, 923191772, 17490706, 656114667, 645670076, 415342915, 322015236, 742109455, 406933230, 181467538, 912192047, 129787521, 315284754, 195865596, 375740064, 429103738, 284288747, 905673226, 233269225, 994334651, 147244910, 827694642, 960452773, 957338670, 387300459, 951269519, 952043937, 802048372, 583503389, 595363954, 598677385, 677812530, 617704702, 801528963, 207138846, 13569224, 23281554, 602148900, 301687163, 209297871, 32444801, 618420957, 767965156, 889180711, 6709594, 491087800, 568029561, 187214396, 813434197, 138193353, 171152548, 111422859, 820784686, 220970556, 324937004, 222318269, 379305784, 359101948, 176929510, 241263930, 100868839, 343104869, 490874792, 902144593, 319030684, 844940842, 896948492, 985426562, 666195722, 447159813, 963824352, 921527068, 270465466, 232360248, 726214419, 223059729, 431399179, 409530927, 867029404, 988742849, 325962591, 606271263, 976650484, 430166170, 823646155, 965605853, 215933008, 655036168, 256162343, 151375092, 41398651, 433659928, 370322143, 614421357, 101155850, 551521000, 579116291, 897938369, 169010241, 971733618, 300972287, 699678920, 834151311, 757445766, 750724311, 939819221, 280222369, 998015327, 646898493, 602439793, 75757562, 520673231, 601396688, 503851428, 921593141, 289318689, 645243001, 15241732, 966146930, 176740784, 198053177, 972400634, 310571346, 873112589, 315093123, 555625194, 620605568, 295959749, 381075016, 558839323, 915630999, 383621769, 93801851, 930284333, 384363643, 949383904, 720174342, 505132615, 468761268, 968734124, 565323933, 913418683, 135762185, 343953763, 518992338, 340581600, 586553447, 168695518, 742347997, 264982490, 936328602, 940006669, 29110776, 771415544, 997760074, 375909238, 389001959, 557341801, 433438983, 841527058, 685425776, 542428344, 591611368, 448179246, 824023513, 651654517, 279974934, 292037044, 212481217, 961044728, 945278806, 479870144, 455208327, 818412345, 649924454, 917427469, 626407198, 247093633, 878256019, 943980281, 79600848, 307241997, 769992554, 259601344, 198877320, 182170076, 476334376, 580069867, 437460587, 446978551, 702583520, 292793273, 430833191, 473183850, 98421621, 985132218, 266514141, 448591185, 364988325, 925127307, 158368887, 519945413, 428833889, 900865042, 349748611, 846180951, 191550901, 904091929, 381363734, 286433212, 481302731, 4195519, 552892267, 98651957, 165271444, 143282317, 395862308, 557981135, 932240323, 511211359, 735545563, 996873242, 29478707, 87521820, 763189459, 667072482, 162578508, 854706103, 184646012, 891147707, 783790910, 528874106, 877535216, 527410088, 62485780, 875857166, 738122550, 160596556, 279844205, 290571470, 726791738, 179549095, 531408556, 996411131, 593195282, 27106194, 985279911, 918059058, 144463801, 147127737, 748535275, 886005506, 125500959, 591254245, 496754619, 575973760, 802260278, 200406460, 103433268, 230298400, 744948332, 803233456, 991680098, 400272203, 249695530, 832879214, 775918575, 760074250, 932411634, 591020691, 853969878, 761948056, 53629884, 487582934, 619335556, 444900737, 781252828, 332746508, 678107679, 750290247, 934029440, 490041258, 627899093, 820220512, 206413881, 786586577, 153641521, 598125327, 390394228, 299276859, 328992552, 124559755, 242189970, 641080965, 543094805, 324069343, 715465709, 719914738, 183712743, 75561158, 416218598, 5858903, 99646881, 578940937, 587018792, 275792673, 406952079, 136488714, 32389325, 562389175, 829554862, 88304306, 271536071, 276805940, 225148607, 311979651, 513163828, 938762483, 701971456, 718025051, 524163441, 201373878, 566762226, 493697577, 249702262, 167106337, 513340431, 271307670, 262813390, 471509161, 427814468, 75458777, 518536572, 575415913, 127654975, 972077645, 370764862, 531421890, 636300597, 10601968, 426306835, 591595304, 751980509, 335911543, 448536844, 19717366, 785296340, 117635603, 114992183, 223500417, 404160681, 749086733, 335599558, 689329048, 644731982, 330160272, 502144191, 832412682, 239378069, 258460129, 40473753, 362685657, 415773639, 683970980, 158336038, 714636048, 102404828, 485837534, 612009054, 640122922, 575595328, 106683393, 10956757, 335758513, 962629426, 47327849, 914666161, 671021581, 850154856, 8548262, 380743038, 301608244, 430243850, 806627096, 587342818, 407522376, 245294309, 945482463, 612881114, 18187243, 281975708, 257303067, 794306753, 155970207, 340345844, 400946170, 806353892, 544434500, 703897933, 442355185, 316581294, 684189408, 621938175, 208690508, 222799275, 554002812, 31883387, 532508137, 154575732, 424080798, 249136547, 467039511, 236867270, 681401980, 847246268, 851069138, 284281864, 981088812, 809649355, 308627605, 614907789, 861389527, 327657526, 736204679, 562074367, 97154324, 144242884, 677620782, 253993252, 6025289, 353517496, 559744377, 640464975, 660609842, 20854831, 548420541, 51549722, 525675310, 41115447, 120963189, 563180152, 492050967, 664735473, 534918277, 345073315, 187448148, 746965645, 553517931, 839936618, 264860851, 569074008, 6870573, 328639464, 989028437, 639571797, 548173522, 135303194, 980905590, 456443591, 535198172, 530395197, 446504348, 837047899, 686727657, 381449129, 519765706, 424540040, 645769820, 641105100, 290912226, 858791554, 461161802, 419304377, 295939139, 745756683, 33926579, 243059119, 159744542, 602487848, 665325109, 254126239, 416881944, 417750577, 320608170, 228128630, 634630498, 461835599, 342200366, 932479963, 229059220, 833856776, 305728100, 758270896, 967280027, 888729570, 727232250, 765122305, 613894713, 262476780, 449468217, 912232999, 329801062, 296478814, 677789495, 980224308, 363452725, 758379818, 127967386, 864865459, 346395180, 787707428, 227514078, 642885905, 396854655, 729704206, 817558011, 527100601, 740306444, 996170947, 233601668, 705242394, 283654216, 454724353, 811110123, 462434858, 720795391, 776023374, 457833189, 63924965, 608662744, 715858273, 77114085, 930955627, 491674796, 16553004, 398436237, 433617414, 349156562, 403964439, 169020562, 31156080, 11631660, 578166479, 223178570, 990322858, 580442947, 643283999, 536913077, 364292700, 989113098, 126195088, 921244843, 103170949, 68746741, 560853667, 224154570, 998754411, 220905780, 921576270, 233809208, 381853558, 525598085, 743925177, 189810516, 779291553, 218799119, 860777342, 329215468, 346253545, 430616151, 107475751, 215604253, 249689510, 269598529, 25447598, 265070263, 359921829, 967506062, 113258957, 974381912, 806381126, 153637704, 277696792, 741509397, 558247440, 232217984, 564885598, 512518870, 215980162, 657417215, 95778656, 769142300, 197522535, 886114993, 494023256, 785022369, 536841842, 278677087, 491608737, 970541356, 47348690, 370603830, 699763172, 540747851, 423995332, 734113964, 14396512, 52667651, 690773035, 337625602, 625781726, 292786570, 217408386, 800338199, 458857235, 669147255, 26939763, 909496679, 491305129, 503130192, 832770322, 643472559, 22342940, 666896579, 719438996, 290725257, 257387599, 987838991, 432704318, 173648766, 923441872, 545552338, 613708844, 361287576, 136583252, 347127690, 528320472, 39309720, 431411777, 953840021, 121353639, 523181065, 274440138, 92878385, 252479512, 571606185, 928965325, 206819983, 744141114, 49160443, 193051149, 195295084, 559538996, 558900427, 784578185, 708794649, 22566930, 1658474, 857655099, 161142916, 458743720, 567948807, 736328382, 843917922, 321065274, 286110666, 676491589, 83476410, 7561759, 394436957, 667132054, 699669436, 83498581, 535629695, 1003396, 783593553, 428403359, 739239164, 393360118, 336634708, 958260873, 350011959, 257723406, 636540669, 897895729, 471801083, 807832401, 464544422, 33917752, 722449611, 374291163, 979693551, 373438067, 166023636, 953426981, 758195381, 894822198, 748055246, 69502299, 848394258, 90693667, 92400176, 347452350, 919210414, 410731773, 370409206, 589525307, 667407201, 955113407, 379536235, 493618597, 476670661, 376240007, 302941060, 949041618, 590587344, 669354002, 161277984, 746257800, 502635238, 891755315, 566694337, 859529485, 133860971, 493616229, 65533227, 253706283, 236807158, 47821472, 820307622, 995642069, 600065452, 480836143, 545232435, 554366697, 800531889, 794730835, 357093859, 141173133, 859541168, 353520695, 923259519, 486303678, 487739786, 886695909, 208143405, 181845743, 482433343, 753503132, 55525497, 515161332, 494402842, 453162891, 484192428, 332967339, 418814566, 559922655, 245847877, 319457487, 534691871, 441725154, 707249620, 458593156, 594740326, 29842158, 503268762, 982678941, 470236719, 646586313, 520371112, 135948988, 131901277, 799315019, 532422495, 162177424, 450223498, 219021158, 633338566, 409995671, 251042217, 374116598, 305870230, 41289606, 918988421, 789451839, 200411390, 89134397, 688118932, 267757214, 494924471, 646928837, 339580765, 799589742, 596303909, 281061356, 365082586, 49125431, 174728824, 620270686, 931378709, 378420686, 938453360, 976270394, 856832556, 934048475, 40698145, 731613828, 572685620, 555286120, 818890520, 727879563, 60264097, 472907217, 953937854, 580565845, 28685611, 487084993, 215733288, 669972882, 268293848, 290797193, 585412677, 136392297, 831670960, 716304993, 670478175, 568082175, 778986465, 935574287, 374845911, 501285610, 122711572, 314328480, 513910248, 108254074, 760171417, 839298152, 880121563, 510230606, 951380107, 765966769, 699890560, 772966560, 81787297, 869136326, 842794636, 209985653, 117452552, 334817041, 147087135, 905750490, 827675286, 885212900, 667164858, 651763037, 594434906, 737413004, 22509993, 867788023, 782059099, 970204603, 617730144, 471105389, 919456919, 815585044, 317794022, 565666097, 593992655, 601519812, 822392030, 588028143, 919476851, 171845167, 17880208, 624792193, 430570554, 789452833, 554275354, 469704483, 474220676, 984689125, 966619797, 51817810, 36414847, 208026505, 600341889, 82762863, 783518376, 213506720, 201227710, 43316894, 463896783, 22362706, 508175351, 790139712, 845755385, 371513652, 943539140, 978812478, 641554998, 376700902, 955767574, 315505392, 330105210, 844028992, 10175356, 238337176, 59221089, 306415200, 58616633, 291297052, 30664793, 415172814, 910002497, 902615725, 756895577, 686904422, 519265120, 231588460, 466066535, 452661226, 7272133, 528926886, 751394918, 349636619, 867721053, 744812540, 612017067, 740043615, 985750229, 462722200, 628194217, 26728494, 595217683, 926347470, 395225331, 148719610, 18814504, 199525845, 972130268, 210862222, 798880081, 864862198, 502029878, 402310035, 117693298, 328714756, 910806271, 848830764, 410526852, 190819816, 889635554, 449399280, 629036783, 532892571, 290794443, 109691618, 52609812, 515022467, 322501662, 251299700, 112661557, 594534836, 397228264, 545458080, 989540775, 502878995, 869119763, 476973708, 378176745, 548668030, 155740986, 842677881, 450377676, 230898774, 21790045, 735071619, 550916841, 368587772, 56611091, 476044527, 409381692, 778821214, 267430067, 384887660, 260906913, 213804738, 731882011, 497487605, 196537277, 965668240, 996465171, 140168951, 598428497, 61822931, 928469206, 926326264, 583987943, 304871504, 327990, 785709283, 566225656, 232156099, 600241339, 217546863, 636532643, 254643112, 139217081, 814735335, 375095819, 573921663, 749487824, 384241906, 951825004, 580254433, 546244928, 159469428, 942621178, 594964873, 672573417, 97855911, 133807389, 667719641, 29728984, 689053488, 294601878, 190104108, 366615142, 217069600, 990121672, 186467773, 350118129, 649448637, 941380524, 100312232, 967825245, 498752143, 601943538, 310803571, 945092618, 763731090, 406605517, 644565329, 83685935, 926151759, 915578023, 111424391, 479248586, 905447680, 230477733, 222134779, 509024027, 784187129, 699047737, 941384679, 966925157, 17833904, 249007169, 583539467, 33724655, 439801859, 153519275, 116012107, 739941666, 253764574, 666938851, 973986636, 23748639, 962411779, 360033462, 552621249, 18595812, 784399321, 273617586, 809247218, 64204873, 324622318, 845163469, 161494491, 609321880, 930434159, 76759594, 993926631, 970464960, 277299552, 643489078, 172615413, 48775688, 250118529, 132987074, 300940795, 844978537, 210856472, 763068152, 582996834, 869758704, 376568278, 479688411, 547496618, 665518802, 356726800, 327727907, 659765929, 2029785, 758283244, 706510360, 758379690, 616154705, 149235997, 513114784, 889966778, 379639680, 926238919, 484645628, 670675406, 529704705, 774782951, 964744380, 188849972, 60575375, 490126840, 537279510, 663148738, 149735413, 724831019, 331535126, 672990817, 950781634, 759222357, 525764563, 169769276, 509285114, 765449167, 314211041, 718838904, 913969050, 494116362, 691130555, 321550074, 945938054, 748582182, 443682829, 623689884, 755313340, 21360135, 41429208, 385731778, 338420922, 580810768, 264377939, 229467291, 211232914, 189100853, 247092129, 713007500, 585025406, 860002389, 930615396, 923734627, 649783886, 910443228, 558553237, 617411944, 116267811, 311866208, 24546636, 436670695, 65636298, 795143474, 658584852, 491885659, 293394219, 727727581, 870285845, 278915864, 268605831, 37571457, 462083964, 852296455, 887197094, 193495693, 469518771, 933340458, 430706535, 477110114, 721549524, 663014381, 504150067, 537127631, 140222264, 509899521, 419634345, 192941772, 219457847, 284302207, 343699027, 448769754, 614027384, 173163652, 767220256, 831544556, 157970756, 364286611, 142146433, 840047777, 14427812, 646002346, 285834822, 184094831, 766736701, 272791729, 810705803, 378452386, 222649938, 710718341, 986112926, 140321004, 537238975, 504336669, 72847476, 109427532, 846334207, 224810003, 957171669, 804443442, 805229114, 891596815, 696977696, 661493364, 13384778, 570025428, 854567683, 731473367, 55928216, 851151867, 424536364, 602075818, 306584352, 963960675, 808040872, 12490266, 279230478, 453947682, 694674583, 11063580, 680823863, 908976343, 320518728, 923916749, 510011909, 902201008, 749404354, 221573102, 382719190, 83851702, 597874906, 247560720, 658936094, 929569620, 654357797, 418009583, 35680164, 112415477, 523126018, 757982355, 889125076, 970591172, 617168466, 270086742, 816911764, 236912382, 286675919, 945961509, 427224024, 637046, 103576112, 474757585, 509841607, 208946773, 106296307, 945650717, 660477017, 408374865, 347742958, 395510259, 718541505, 889880386, 357725889, 559788706, 367677895, 281732207, 913245579, 861918319, 874819081, 411115758, 423755800, 393544376, 389675648, 532920437, 135631617, 241422292, 998049972, 133844875, 61417756, 409438423, 495655286, 303660893, 752018986, 474923059, 527048704, 8971310, 151306942, 383156107, 361989352, 647656738, 670283352, 611275336, 284965676, 422318172, 321078729, 379045395, 718506565, 906703071, 231441169, 944658162, 394898853, 162092555, 141648609, 725442738, 95147900, 14752664, 745054936, 479121754, 144728882, 767842091, 659533039, 592325330, 635489370, 203016479, 848652963, 517692353, 998398584, 180313171, 893167716, 795723006, 377234247, 437714679, 374742002, 749130904, 665317784, 231864254, 548103274, 786989651, 669334145, 435511449, 361544391, 138729962, 831001299, 713358479, 458845172, 336730110, 560956719, 4368137, 944888759, 879312629, 754979861, 560683455, 107737458, 38786378, 413544315, 362926480, 901049425, 230574760, 664479294, 45744646, 237468601, 441054150, 972248305, 91543086, 11927, 552522826, 578742482, 92400332, 890317396, 79139378, 833181305, 848684788, 818702263, 925299194, 542232153, 993497169, 536860117, 164347090, 895539723, 215431099, 485733081, 159321500, 134036926, 98710710, 597903204, 665605068, 306277888, 353742050, 207944063, 695589741, 973741448, 533154305, 151258960, 900628860, 519847076, 896791159, 269134433, 838952902, 98276589, 530614856, 304664973, 142611287, 329634222, 281685474, 334723767, 567570130, 17559916, 796604144, 387613465, 637653640, 134530189, 279975254, 39569695, 195597991, 192090521, 56790537, 238930389, 968029461, 488129092, 721973771, 29851019, 337401033, 701116115, 880185188, 227479655, 188598375, 117416485, 708333230, 642618056, 591262259, 43558589, 767834111, 890553272, 272987324, 626641231, 399423798, 826794141, 612766293, 743317575, 479652327, 800353248, 873638524, 169744882, 58397258, 272493710, 138601237, 386222516, 646534027, 377734159, 423388558, 656827639, 145186265, 522464209, 188313164, 373205213, 46148603, 896566323, 812558171, 744546532, 839844492, 611463497, 477211938, 518459775, 741860713, 979168240, 975551666, 770570007, 830085493, 261135974, 632441934, 891740875, 939468974, 477488721, 372977196, 361733315, 720997488, 966537899, 381437790, 568443198, 236180626, 677093096, 132176825, 823893213, 818629392, 266410941, 272962160, 806068499, 401563012, 415651999, 115405728, 560008132, 227045755, 876128066, 14738356, 835495550, 297824662, 487310989, 765296184, 518440698, 179222182, 990697711, 21410854, 480755417, 865375019, 983256748, 365575950, 946130114, 479012649, 582265172, 463727373, 563726294, 650900170, 99186949, 268162793, 496167357, 830133919, 749724257, 882643362, 21283316, 689045735, 510948863, 137551922, 549156927, 980421183, 427016897, 276179971, 195704352, 979919690, 962218664, 742920496, 26743542, 922518693, 574189925, 873946758, 526132876, 497233054, 217613592, 935662050, 428452335, 270179849, 903320767, 759343266, 524727516, 288840428, 631419482, 283649508, 85522081, 770253355, 89057574, 174975710, 957861275, 850704683, 679973727, 258227489, 999315495, 105533171, 525425290, 879511583, 922069239, 843736750, 398838206, 828429713, 98775569, 452716714, 35842050, 118029577, 973168766, 141005198, 737720969, 939599661, 622831654, 78291869, 236606447, 990301563, 220906085, 273731621, 725960930, 241498981, 537978299, 619887838, 105230345, 937665486, 596251955, 381137824, 374890135, 891959301, 118844865, 273793483, 172840757, 111855393, 79270840, 542217030, 21733198, 433628153, 293645949, 858496617, 976721846, 361560207, 934837590, 756481231, 631038316, 803358065, 677914072, 457374031, 920900106, 176628335, 805423954, 432223663, 610579950, 459363790, 605550436, 784606393, 153097890, 725010502, 118745250, 909204593, 892850587, 80909589, 788748960, 415640914, 281166572, 382928017, 306153084, 413867579, 433358556, 593781530, 106523606, 489749905, 62200336, 501634061, 32364715, 96305290, 407363922, 461844301, 142271701, 870231731, 365516500, 24106864, 479674890, 905757297, 568489860, 755565484, 922835009, 266127445, 631288273, 570580524, 238913433, 575872979, 639576047, 54026938, 477460212, 129356508, 355469111, 919597606, 56660258, 258099899, 355705461, 702234024, 809831991, 797922542, 641834118, 709930230, 679749666, 563187909, 274357853, 855256434, 546511463, 797547933, 94924700, 490769508, 468297469, 899795600, 810395809, 784737022, 175256197, 247777336, 752408599, 302749753, 105549169, 140309362, 471785137, 320527529, 715787741, 943261856, 716798875, 779523081, 624476641, 942756131, 864634391, 905830966, 910047443, 881134643, 902175733, 744276511, 974942756, 826825703, 283586679, 41294761, 689916880, 767271409, 411808650, 484714520, 702280061, 630482722, 787267134, 735140545, 994705068, 636697958, 777711061, 821860466, 221440957, 46675500, 378607586, 740831369, 219616098, 695696308, 275718862, 251860664, 787403788, 926337216, 529240834, 361006608, 161256348, 947255357, 210156916, 531048685, 280602120, 85631293, 164332609, 491671827, 32584425, 457400557, 273801837, 54832978, 228444713, 490702953, 884897604, 481442817, 790589987, 986151172, 595941468, 141185314, 681897187, 584701437, 296381142, 200167402, 369732872, 447500322, 831136961, 924203439, 402286836, 744426551, 191990823, 238029315, 587597082, 166424913, 502165943, 738094722, 84361831, 431658411, 843290875, 109739232, 339509208, 755908494, 736758789, 939177160, 746811418, 184439385, 677729302, 735249405, 983287925, 455589581, 28721371, 934716939, 809160027, 178684201, 591569359, 72227774, 414086582, 672950844, 590618498, 915333485, 143785652, 281872314, 508744919, 930789719, 551429932, 992785643, 57182443, 382013811, 826542080, 153570096, 101322950, 463491442, 718728628, 976692064, 453849533, 806815613, 965177438, 322593593, 575155798, 245006630, 988361576, 459273387, 913109262, 599389137, 773333106, 984935937, 284959568, 257682124, 720778014, 38212218, 455404066, 77517455, 744545743, 217961975, 947759546, 744460523, 957255302, 35695703, 826125774, 88671210, 533635593, 718950876, 895066446, 365630843, 905086148, 628935763, 4631107, 647133016, 140279867, 31952915, 264411825, 769066519, 298317953, 886131983, 946090751, 568643297, 500057392, 554107893, 502484857, 799154132, 475590910, 82339673, 147599839, 447078165, 276319535, 801569245, 771273750, 825089630, 164387885, 284232865, 339873039, 815802189, 925203957, 107839803, 842972266, 626848857, 293384103, 170658954, 593560565, 353484347, 135454013, 734844015, 556675567, 384590032, 221920401, 245837901, 606001590, 32304982, 234876638, 739567046, 28796140, 834155212, 531177594, 872913733, 437744482, 279928302, 165450163, 639408910, 35608146, 997548215, 822992300, 906783002, 558471464, 289885174, 986492372, 993999323, 790148532, 335371663, 683112017, 375342730, 802987386, 954969560, 350781591, 158455790, 624939618, 550533706, 239558631, 120479582, 153120967, 928841128, 31954369, 997946090, 64557780, 940553446, 147395378, 273092044, 110108893, 887274585, 419526106, 674550421, 988907203, 976738315, 15031637, 533422278, 225339961, 606734768, 838292, 8660567, 822371356, 85011495, 263607445, 931264064, 730494340, 582107241, 926294136, 283950553, 88636685, 149844030, 550563657, 588521614, 413953351, 632069071, 702492888, 734806333, 107605117, 904969311, 568794282, 4342232, 627356903, 960697756, 504958458, 972786116, 953489566, 97994974, 371140059, 908011844, 446535636, 580419653, 208162617, 58426075, 799776526, 275862432, 405959509, 204158122, 24193359, 735541836, 361255965, 772309028, 251125455, 645555606, 806725182, 440357926, 462242447, 620204381, 696114010, 771134103, 439416988, 449259325, 996392481, 426875698, 989529152, 984609019, 225039737, 450070620, 541349373, 146660517, 560948528, 202193006, 605504965, 433570311, 981219733, 463067182, 414406799, 402496840, 197525727, 845470448, 960215043, 976013632, 347749221, 7832615, 888514034, 401355236, 71454391, 379242118, 58575076, 494293981, 163490396, 420166645, 28840099, 584303209, 908413879, 930804402, 813237151, 709635930, 518085426, 341272518, 727011117, 620086647, 926981555, 548132283, 997495448, 430167469, 529746461, 194841680, 553921192, 148491427, 304485892, 403853084, 751994342, 789432055, 539433698, 774391191, 526910052, 499936311, 589724811, 562451765, 716055892, 400121793, 876909716, 638612597, 738496090, 658232748, 709044964, 584394734, 73445006, 62695237, 481908379, 67915421, 966326092, 518678795, 197502391, 972317565, 769930308, 479686415, 131961243, 634577713, 74944669, 661121529, 564742788, 628032639, 8904632, 950950116, 924355063, 135148278, 29517632, 742368081, 733238486, 949205280, 839777220, 361603062, 332499204, 890597028, 644942321, 186511327, 654239807, 301589696, 509894179, 600119589, 357887841, 789663226, 375779707, 940336648, 22717935, 525564071, 612772175, 923468565, 453823195, 61052342, 315597986, 299283037, 9588177, 967004897, 100724143, 583510676, 104058218, 645094791, 752058765, 818969302, 870568131, 87979016, 37320146, 247706437, 264964380, 123931146, 499878442, 856473128, 211628087, 762335758, 804609066, 688599383, 566343777, 285094767, 903412305, 163629874, 874357948, 612730832, 713006780, 194899794, 686172279, 809603289, 396042314, 940149556, 929146400, 728282788, 197685596, 806180509, 503921665, 156132379, 737718307, 686309526, 856083804, 311859508, 203224394, 614838037, 112704401, 212395402, 291670413, 762519510, 609064416, 232025685, 28982905, 593623368, 433774842, 673624994, 998207184, 360364804, 133100159, 458200314, 126175741, 836562602, 822676436, 476191260, 839373264, 538697934, 32271369, 663932491, 988882973, 934882796, 55707082, 29885845, 982593833, 476307175, 282664770, 342968039, 908898870, 646072495, 321673798, 859096147, 864121111, 444009687, 709924967, 380140635, 220035711, 251547890, 103058070, 612221614, 899254297, 216218105, 918045501, 232398178, 216318640, 259257735, 724184883, 126872081, 755438899, 364078417, 986454146, 169649200, 11241696, 530207972, 39419559, 550851254, 49610127, 765830459, 17365399, 966894136, 161264924, 208892264, 535734633, 930463030, 752474668, 476102423, 150578552, 870797888, 892963753, 494536397, 129337377, 650153735, 435281475, 716848874, 242533770, 616472135, 340768870, 777185537, 485621659, 450798339, 642773810, 586556003, 435187390, 448133307, 202057119, 627338570, 788464786, 660911126, 241179721, 297345032, 938059564, 133678444, 837850730, 164118144, 155616792, 635837539, 659202165, 201039770, 74183794, 814678137, 678338020, 488925612, 792253184, 509054358, 650280058, 636269820, 699204243, 358442280, 92663399, 174277328, 55964400, 568069744, 54532530, 526215913, 527507133, 361907885, 25560523, 800853600, 616386763, 51802162, 600533093, 185689471, 660796145, 263177782, 989485795, 943753929, 174884373, 853070846, 396050245, 269056211, 182411750, 320438005, 652592676, 232076869, 226803802, 892368227, 655156263, 921823635, 887406869, 106221200, 822866770, 745946743, 586568401, 400702181, 70664067, 306327330, 973490363, 454727195, 116661139, 319602627, 107133411, 223420591, 260074421, 335187437, 410657122, 590807435, 151356429, 335564854, 690971465, 977455332, 73443699, 395063604, 797822868, 823850535, 926897372, 454045327, 367602742, 842691637, 6094501, 496135319, 109827638, 127216858, 611273753, 128077707, 239136647, 198369220, 94049803, 63956317, 625949814, 313960696, 172624382, 946037105, 445386803, 39185309, 286074028, 601948763, 306252981, 936712260, 280413824, 359082366, 148415062, 287722630, 386436693, 185305015, 384084794, 537579327, 781891466, 228850146, 353907264, 444627385, 776259435, 571949879, 318934377, 548926459, 292248020, 354321504, 15025208, 350770579, 243669233, 137468510, 169496390, 475876027, 278263915, 179809805, 159326409, 262224615, 484326558, 310899452, 516789285, 512446664, 341216767, 768210809, 295798785, 816363071, 283596364, 407013625, 282918575, 411874786, 695389639, 727522877, 622653103, 418049736, 366073728, 105309032, 282585850, 857220055, 678747716, 664803151, 175238497, 798076282, 443252581, 706613184, 178336988, 355955994, 912819946, 330893901, 186695774, 879662438, 937969145, 528581474, 598025984, 63056396, 559880910, 243889138, 808496698, 665968599, 23602464, 118351448, 641554690, 927351532, 427990498, 740834412, 135653792, 359321807, 432450187, 302988759, 820572299, 731572669, 854985956, 813038127, 355932578, 644922842, 377170534, 334636176, 435934834, 391163344, 763582739, 100108695, 167272603, 941428058, 549382591, 565480692, 954997232, 290493739, 854313133, 589888192, 577092180, 701713645, 551622774, 266556521, 424320387, 737856411, 183937786, 540994566, 677102985, 696045708, 274992004, 688481558, 292403564, 20817796, 77686097, 552486375, 358370582, 548139279, 26891279, 102735319, 817974352, 208343405, 467546689, 812313038, 409678333, 514209002, 481617201, 99484323, 818351839, 657703414, 285990300, 536802194, 814125697, 25429512, 862838178, 577219675, 975611117, 472465628, 152949436, 752580535, 908756264, 189675796, 423913093, 174480635, 949538032, 894073807, 656476663, 876561512, 767969539, 799999878, 619316141, 849936921, 276401452, 74564172, 97968155, 702759854, 901552618, 752103650, 78997552, 923052854, 61550013, 194937251, 514569591, 906164829, 880767846, 919269943, 989507659, 931462348, 689403757, 975302133, 421596376, 622306600, 644570566, 600326262, 954062444, 844995687, 380935345, 763663687, 463236632, 91950038, 270485434, 355159312, 694510925, 173513212, 383038458, 308038774, 71857651, 746093738, 271123068, 125039933, 727919384, 857405992, 676624943, 729715367, 298923256, 503245401, 521464834, 400282037, 192989248, 767425172, 449371642, 828493532, 738721465, 646086209, 583945617, 470541828, 597215719, 320013899, 285351193, 126369676, 426225922, 45893792, 881946063, 858284074, 890016645, 22425984, 341468163, 179545350, 908039901, 670198643, 559861036, 870893816, 824453936, 906192115, 157837427, 498863265, 104357862, 825126819, 426123638, 829706128, 515743643, 617959154, 166335254, 558903599, 238655931, 471321087, 103281598, 758059999, 327260517, 556525134, 326304615, 744759426, 462497538, 896184216, 42065996, 80214749, 680579904, 298538394, 266837708, 418368483, 264243682, 872532335, 735272507, 824496959, 627504783, 996853368, 895787704, 232548927, 548977925, 98373025, 928220986, 271290140, 978614153, 381355383, 909760910, 635209421, 787171490, 782129049, 431260181, 479925113, 520099036, 465668665, 613794658, 534031413, 952029124, 893528156, 330614951, 682217401, 954870478, 945262577, 17914692, 328027219, 505523406, 312145825, 956090326, 213403197, 472284357, 833029612, 820966572, 609327461, 860401113, 652578122, 569016493, 242277877, 134957207, 798014697, 628606534, 588275361, 929598381, 406707886, 536645119, 502871531, 886687973, 571238957, 396553443, 410551303, 373585812, 40467733, 660503036, 373469199, 883156138, 24444696, 14343521, 32731802, 194379054, 629748943, 631234281, 350407986, 124573214, 746158369, 95855683, 164761226, 872106048, 927695689, 450565314, 750192619, 838536312, 16399434, 926064518, 533133472, 784139213, 328037426, 355030143, 835047383, 822033296, 249863789, 697521467, 785210219, 16782726, 443575687, 65725778, 748115742, 958261896, 314628946, 119843165, 449055586, 206738301, 961719088, 124823040, 465864915, 140080928, 354608092, 338490898, 902427822, 588435035, 629579245, 204450611, 357738700, 312280529, 598709147, 821763540, 516254241, 989428455, 641067861, 532055610, 957692474, 746907724, 960800271, 149025734, 79619970, 924938494, 6730276, 723325275, 419967768, 962827997, 435367316, 376458383, 686777476, 595319800, 528613235, 942932089, 417025485, 61866611, 339876359, 768344221, 199957588, 832797919, 719885484, 832678617, 859615839, 609494910, 689404800, 918581932, 148958446, 696048031, 433420478, 954899226, 470488776, 79101227, 541655506, 356188394, 752671826, 655082094, 65769158, 15549514, 381577046, 507178852, 18901887, 830397375, 923111106, 706380208, 762098988, 205027270, 795223516, 623590896, 415965904, 203413196, 258338311, 936215215, 549121621, 602700223, 160685991, 448119073, 933255086, 836436681, 196594539, 124916436, 551720534, 893830769, 486315031, 367203418, 929807419, 928153592, 451056222, 957929040, 574162765, 236804866, 261826425, 644798192, 929970819, 151919666, 611792348, 851130159, 868810581, 499177939, 301241173, 812959570, 595201383, 62592181, 763677515, 209496944, 548633307, 869421463, 741097334, 525546018, 101297920, 235267808, 524839331, 421506225, 549119334, 470272642, 489472945, 697697418, 939552693, 328638934, 225102798, 645710536, 387539296, 243847021, 471519735, 374543436, 35943049, 11194791, 374325968, 118587236, 435320895, 171940171, 644643891, 572561370, 461259663, 643449093, 783573435, 209880031, 278289854, 188972882, 458965611, 686699526, 606712019, 789626625, 909735396, 132999253, 995779846, 483356458, 321006989, 274954582, 147578193, 489817116, 128493388, 958994414, 865281307, 40236474, 771436149, 684767681, 39067491, 883756780, 743393616, 849346971, 928692182, 249200140, 396319169, 70168429, 60445216, 109712197, 554147430, 988267550, 414923331, 939376894, 36157983, 483782246, 338022201, 546066413, 313167505, 622555624, 261062178, 973213072, 327312500, 56201777, 838640798, 27256065, 116789882, 922135658, 167116290, 585525370, 409834532, 180671629, 941929440, 194029881, 981348536, 470168818, 169049639, 949248555, 803182918, 554312037, 550067259, 962226158, 881521878, 514454254, 15255960, 492611715, 208026466, 504479369, 553681771, 981391614, 70850243, 253962440, 413036223, 227234892, 318405782, 294871312, 5094009, 377157778, 339098422, 32377339, 555624420, 192285486, 777354708, 276864234, 8651590, 209653074, 498673805, 497156124, 429144614, 802648006, 326138982, 531922725, 323562457, 906741401, 302269423, 921077832, 788858278, 492613703, 829187309, 968449474, 193186826, 748608301, 612511521, 760387975, 999159174, 450460171, 143902818, 507301652, 199306022, 857867198, 26043779, 168930178, 181048493, 992346597, 281012009, 771569052, 655431543, 106670504, 267060691, 169523044, 360461580, 666550409, 424722584, 819169889, 541012736, 709466377, 192409521, 230354518, 392104663, 519401720, 140113606, 409225640, 577178657, 740928336, 501387159, 376373984, 948366015, 366078451, 784466729, 423931329, 111234821, 219217298, 442017735, 133691805, 675673342, 252318313, 179745972, 647717759, 408068442, 358781164, 648649975, 355981891, 172126140, 713004331, 175330501, 933828881, 22735789, 820420542, 314322736, 752289981, 641534257, 546088561, 424456971, 120781032, 947976700, 558906522, 999428364, 371937091, 357629777, 377122899, 868448179, 61434205, 374286420, 478270702, 512729462, 31705283, 963013678, 168588829, 285363403, 13053810, 71927829, 121180713, 121620039, 68730610, 988623163, 237510432, 19688737, 454995240, 457403883, 469207434, 935985351, 187013479, 351740068, 461254745, 221929577, 735786757, 714822057, 968471472, 663575475, 845627953, 934031625, 756944584, 816043547, 804913447, 528122377, 385951944, 690741363, 34184887, 633960331, 839778496, 319951885, 526192181, 34034976, 141202508, 832197737, 156088688, 951810415, 94751249, 968730466, 920352279, 451360918, 662936542, 263804611, 977554912, 736693519, 64820343, 789725966, 7527990, 160139329, 701796456, 857205580, 93692880, 152023705, 391784388, 82448441, 679325593, 598715486, 302540995, 295324435, 781210339, 913820301, 596312402, 797617039, 773831676, 181761495, 215346836, 39585869, 331582982, 670453167, 206330460, 455123197, 670199697, 850530762, 85663600, 299042447, 898195524, 334340242, 493585836, 400608547, 345300840, 656556222, 156928545, 84999832, 320527436, 906368981, 591944920, 763613707, 853434713, 979567972, 428763138, 813144647, 607316218, 655480494, 137983575, 51458205, 890057688, 342175191, 123265745, 703257766, 907612371, 816522445, 296210123, 591445418, 561204915, 90754866, 582337724, 520087789, 578100215, 251247209, 329640413, 86480908, 792609633, 304709024, 47505186, 960228053, 554192028, 987559207, 692564399, 757361052, 199885868, 321794513, 978067179, 521803938, 741156864, 606172754, 620743038, 553046788, 18997327, 389548889, 44906582, 282797353, 517524849, 546995292, 485445179, 242554365, 401011110, 704796703, 761146593, 735868278, 157914180, 289676715, 945517992, 173377977, 855993964, 662793810, 699407766, 412292421, 128437859, 985297569, 531886083, 236280385, 559064456, 835172486, 233110169, 3708506, 765033976, 967125697, 353730643, 857201067, 792339690, 595433695, 818580559, 96128863, 119532653, 190202692, 550829687, 360468632, 627595048, 796613824, 62161591, 895655258, 778500701, 935187448, 945284864, 917181945, 377995330, 452237408, 534523926, 612310511, 425367337, 102875129, 51875025, 813890505, 556517589, 840068639, 544480794, 893190121, 416775537, 175848771, 31188513, 573104595, 61460804, 75470072, 465562719, 709677039, 48424949, 521719482, 365482480, 671310905, 388040490, 601766641, 602873061, 853429919, 213056060, 526450032, 963774318, 583723779, 896845796, 2269049, 252468999, 144076620, 678410678, 429667684, 469972896, 314235413, 117357464, 964406724, 254263986, 724167753, 965154224, 259232339, 335530799, 240500950, 392807355, 862896669, 549600586, 206682987, 339563802, 86719201, 347106601, 265058247, 770750247, 668404506, 1302834, 710146653, 463091504, 338785345, 552942903, 531649421, 947205023, 837917477, 935524784, 51369298, 175900171, 243320090, 53906707, 103064926, 585917522, 405534173, 537747202, 351131740, 736135647, 523314813, 448684839, 661002186, 606738893, 289777473, 363638512, 727942886, 291995589, 339441712, 939169892, 14766695, 11538415, 893724060, 746605776, 560248052, 292420216, 341935251, 273958093, 347480008, 988157651, 456946966, 772191256, 938037438, 107434455, 59264509, 1412577, 366958711, 119048317, 543093730, 455692189, 942297579, 378571216, 578364541, 539712166, 130481846, 589516871, 73946440, 433026240, 378896190, 487776439, 300665697, 937953080, 342333569, 594760321, 745349413, 492076070, 445053551, 167296825, 407201005, 852217234, 910928006, 824523780, 503987484, 928901826, 443999300, 600687159, 603592115, 872093260, 97716006, 623758232, 857600726, 782047047, 299033898, 397439298, 76523667, 700666028, 698102902, 306239488, 365035878, 998365535, 829140590, 776072265, 165997176, 815797309, 373169059, 203006103, 546637349, 326515286, 201641629, 883563390, 101255312, 785615572, 62157233, 425914784, 201084312, 338754009, 423605622, 737469188, 49096139, 508873041, 89550379, 64057218, 287633385, 608782147, 908354699, 900226239, 283012632, 818002079, 577695851, 738819514, 380768743, 889426305, 113312602, 183462870, 990091472, 318736220, 336120134, 700419549, 973448103, 665925106, 331763740, 809133672, 241614740, 788458132, 324680122, 678919336, 145094424, 141976011, 279869582, 935195597, 552329571, 798464396, 816386821, 638770925, 446865613, 655054562, 478009436, 479889820, 319574280, 780900242, 623210025, 935309130, 495489452, 787431851, 951965550, 655754496, 477580840, 580269070, 707325191, 725858698, 465427862, 702275427, 792697225, 108327737, 289220038, 178107251, 54092192, 798802845, 300811173, 206002245, 529673902, 766676481, 168911559, 90566062, 175342467, 498003489, 401350015, 133560733, 834512606, 158521994, 21521843, 542315922, 64013406, 620233383, 90866410, 118143683, 494305119, 838416744, 69657109, 145682026, 968769286, 659532096, 472082115, 587277305, 886494973, 846144339, 794033486, 606209853, 749218231, 513147722, 346672921, 245394218, 145207274, 334956082, 703282032, 35958445, 939978533, 475240302, 244118342, 355189224, 173712017, 814732270, 272392005, 182199750, 345850727, 573307790, 561584501, 748824517, 727964513, 97351620, 728162551, 668184771, 618383624, 794601287, 988925042, 830211680, 67538047, 505691619, 769572284, 739993950, 5454470, 323443370, 724080686, 78919114, 230105437, 542527526, 687977992, 234206836, 406194093, 231072487, 684190202, 549368485, 903346305, 470882842, 592303633, 33814667, 924268184, 337904102, 237070675, 485621425, 415923114, 324166410, 94979200, 949318106, 825580051, 142871654, 312215101, 10304307, 196535439, 787207220, 33970901, 849007875, 719730762, 601372916, 335705646, 873579088, 96474664, 216434804, 91297251, 338386842, 723880361, 673075959, 999421373, 576754794, 21029531, 566644208, 556352230, 547441190, 273298476, 647156109, 822198117, 236022289, 262383570, 69381420, 925418353, 290039063, 934824645, 149203821, 861917893, 435766839, 461484261, 298969804, 118964298, 609262461, 445988105, 841111434, 944061356, 136761534, 758254115, 874830416, 259520996, 572434377, 80237153, 137613057, 508661901, 596906063, 288625518, 852455550, 585185988, 318639366, 38618940, 495758611, 771051908, 986565100, 494743622, 402641661, 529729126, 980119887, 175297976, 681283390, 992055996, 694320940, 682603420, 468332395, 572895670, 130755835, 385177459, 980326328, 545491748, 697432787, 389391314, 853617496, 591687230, 730559996, 515352452, 339358372, 181876507, 873639601, 685458095, 60378683, 151716532, 804031254, 929296874, 805861511, 634521568, 376184587, 441480147, 233189354, 330937499, 238075567, 582375507, 63634045, 435396649, 642305663, 746292732, 812880526, 81243520, 859121868, 281838235, 561978072, 574985577, 39521568, 319019055, 79721561, 714788452, 602736952, 916737450, 288560714, 74913038, 383163458, 20619999, 494337542, 907710667, 225903719, 784253078, 204503260, 776853189, 893678739, 809504488, 826087543, 266742820, 320940660, 472065965, 632641423, 379172935, 925472029, 621307016, 642479569, 631672797, 105009695, 342843046, 3657261, 674843539, 778115923, 768009317, 710430408, 476297389, 709148378, 670953081, 392487760, 456112714, 984914467, 410041816, 773307486, 184207706, 508308726, 81872751, 953170244, 252569377, 906779193, 261654788, 537703084, 480666618, 945807470, 836237623, 437006516, 15052906, 369133355, 926442180, 838220221, 592067183, 832239613, 412803475, 120355233, 825762129, 917783535, 607410638, 474638640, 88617320, 976052548, 490649132, 141110987, 572712600, 215653652, 57617493, 172646307, 128766755, 787593049, 39609334, 451789129, 967692130, 762643792, 641657192, 821596331, 564980981, 999217600, 771165193, 849349519, 813308134, 171516977, 765259346, 659792232, 63375530, 800599387, 142169528, 638264627, 418387494, 243674477, 42334750, 505013259, 504772946, 286817315, 40223755, 983991858, 533512389, 829843367, 334141387, 307096248, 603687225, 685119941, 413792952, 728140537, 679749184, 862367694, 159816315, 778060195, 519535952, 901534093, 598724129, 522379160, 743454577, 446691266, 871478715, 629243115, 105753523, 974983961, 174407029, 941724876, 335202142, 797333148, 935132209, 390999439, 45867411, 888839692, 167250547, 496418167, 775531055, 950093449, 39277141, 340009971, 783579683, 654302854, 906986237, 995807077, 623788955, 144014188, 201834783, 596453959, 806412645, 765730179, 261084986, 861304315, 848950676, 324892812, 224099933, 215095843, 304551796, 159744427, 552955473, 910694406, 891591884, 132749487, 496607857, 593163343, 960716923, 969355375, 893994172, 219044883, 99039714, 433568248, 585378588, 672398866, 638912695, 343812858, 293722892, 649047214, 897496735, 416848980, 942222214, 452385489, 960896243, 346160497, 932327570, 99531099, 578733304, 452940817, 225013567, 269941509, 583783852, 317824248, 314955605, 676232120, 605363914, 167500525, 957236163, 656952502, 717337601, 905618038, 644335463, 198336793, 403716423, 767194663, 683630389, 710002945, 393330327, 113356052, 634682377, 221141422, 105733829, 333223050, 644208839, 316758182, 942132587, 666393027, 477754373, 680030421, 918273517, 213745713, 585920670, 576406784, 414217584, 770544890, 411402260, 697882424, 923080893, 214070769, 329659785, 8600408, 34841030, 5227776, 750130888, 211024655, 22839326, 287987524, 67294957, 70697461, 872715679, 495961757, 946239955, 951110700, 635692265, 638733275, 523034547, 270170060, 176176685, 464868997, 207747432, 384114607, 213360192, 981343103, 989411978, 233422641, 52743857, 266265581, 882385364, 373901795, 442754959, 712637475, 942717089, 436979741, 119973885, 518232031, 361787235, 865114612, 669324901, 722184178, 449407700, 926770376, 239135421, 646863344, 647424430, 199929780, 630678664, 730753813, 669606316, 941728093, 289220509, 961730804, 221118303, 191606279, 540519488, 911549861, 651201851, 248220506, 592002144, 700251091, 676149078, 765059241, 447163597, 698128332, 441675287, 524887240, 362660747, 818686551, 311135748, 572118866, 50348120, 375027109, 129060903, 188204331, 401495535, 548402737, 597909772, 154738593, 501978247, 75497922, 531125509, 522424763, 387120410, 80991319, 145992817, 414911864, 908415508, 604818991, 671971133, 257887476, 580614800, 256081929, 465767796, 336666592, 619264450, 978377566, 331410846, 776757454, 112378559, 353723463, 537086039, 340475233, 426551119, 870871743, 792042357, 446693688, 699308152, 397090404, 917368509, 123244638, 709271821, 31317846, 778768114, 193436130, 319754581, 688152158, 42907572, 276374555, 684901691, 599749199, 198999352, 643635748, 905971109, 497426910, 541316160, 423172950, 382308075, 472653752, 401270869, 263917611, 108112938, 116119988, 92030357, 448961697, 475933273, 635576191, 706529205, 913815188, 97026737, 298105391, 200630330, 563974127, 665894228, 771789930, 335189091, 932675460, 245109190, 954144590, 111764029, 87259038, 927270956, 577332967, 961293261, 877446777, 221786662, 995889637, 103046914, 13374837, 9951030, 78193920, 222070476, 788706335, 998681924, 991560456, 236265923, 87801365, 988850730, 931459995, 355482124, 718476829, 266259213, 756577433, 465105046, 359645455, 7659797, 535226398, 334631435, 108721311, 177128296, 144683452, 5605871, 897872379, 309475626, 886083578, 614884048, 574891095, 930870716, 497803592, 665001558, 598008696, 871707146, 404867185, 719113143, 394559664, 855735751, 476335461, 443167010, 808904222, 771331144, 336600897, 354682543, 139017524, 526638542, 388088256, 931166137, 671239029, 314680981, 789009685, 882633555, 443120402, 418636548, 575602291, 376119951, 147359313, 524979928, 585843505, 979484570, 173995122, 411490488, 381434216, 996802045, 324286182, 56114924, 156392706, 236585398, 387106833, 627964805, 89776524, 222703108, 576013674, 427946340, 571834139, 640990276, 20479070, 287393434, 263630620, 443073543, 267257563, 930163418, 207263299, 88584343, 933860925, 164594583, 655490408, 779857460, 35422972, 545424208, 411077519, 730079621, 602406179, 633752343, 100392185, 790381015, 781077979, 388130139, 899292607, 246679037, 463359007, 168183311, 343019612, 251038146, 401698784, 954485658, 468434864, 937246231, 368753760, 622357520, 123194228, 306226315, 204593728, 920651185, 511561748, 429885517, 621160493, 160451437, 550463504, 418186155, 372071083, 260248888, 5494280, 95451107, 665254658, 569771685, 169082994, 627733508, 703560845, 558644009, 124999435, 685806424, 944595738, 300114459, 439703411, 383200646, 30560137, 188832866, 477974859, 248477500, 611107312, 163782526, 71611869, 411667841, 138824377, 513343085, 342433968, 439895397, 449459063, 595597073, 780612645, 138528734, 647465383, 500714889, 283807455, 593745869, 652790020, 503244154, 935605403, 105152606, 355177408, 684886492, 58578783, 309323166, 261004854, 642381128, 229195082, 717289808, 120409039, 349882190, 507555872, 319327843, 150760517, 331732418, 421111333, 895742259, 207763607, 824576537, 915937807, 739597646, 44938763, 696800601, 508095499, 901773323, 329665174, 867025050, 270870520, 943381448, 568187532, 571639427, 537051746, 187223660, 333340328, 203234869, 401437601, 626020633, 436436405, 854808964, 743153565, 50050625, 344250320, 285765006, 732300026, 516768804, 328406692, 219729883, 495247959, 487924416, 199697640, 691513803, 52206199, 979364501, 769619673, 792627237, 54991797, 934017793, 235944992, 799577557, 164686674, 656185153, 340812523, 897026370, 494043493, 835247913, 937875022, 764137132, 212867171, 593392606, 742822058, 405075918, 330018085, 19012513, 39175933, 922188877, 529876284, 119529634, 132791624, 856769245, 340540352, 551070169, 135096531, 980635837, 92227989, 318592562, 369270415, 176412454, 278590522, 765762163, 225696387, 16098896, 960324187, 800546140, 568803513, 859636975, 633283170, 999868021, 108527470, 321137211, 426868186, 190256050, 763322258, 106246438, 417004030, 766654439, 579528639, 676646021, 44573347, 106571229, 143307583, 843397445, 646972455, 192040006, 956718742, 463540838, 525393499, 314800375, 172227552, 812446416, 934099741, 92992272, 135991901, 697439443, 147634296, 364639915, 336411246, 307510484, 992195291, 208456570, 961672896, 497537435, 727019600, 466568334, 190511341, 242866514, 423102815, 244846636, 686405830, 577200419, 327152894, 716698405, 257164338, 305854396, 532982082, 102169837, 847479456, 1463516, 724595824, 690033865, 155241340, 605278974, 573963099, 185419309, 376672571, 998217133, 864962329, 937607000, 938926840, 342892469, 283953964, 596158941, 621339421, 324625489, 192521687, 50251134, 347195544, 637574060, 858677971, 965471889, 679541469, 867137991, 12231743, 422732257, 563594320, 862820743, 923305171, 336037442, 52363561, 896767714, 981194847, 395607533, 65393263, 910211722, 631015918, 544353662, 477361151, 70094985, 663451520, 359938172, 351997405, 393990740, 540024070, 823558602, 916455075, 208738565, 187613650, 983026112, 406056892, 732907413, 753980017, 398634150, 132919179, 348686279, 853577402, 982612353, 695452351, 601463683, 956914494, 306054210, 946405828, 509141333, 85800210, 707814336, 277990868, 40573923, 851667830, 490123087, 353284481, 300291260, 194215100, 437309786, 434676994, 551322104, 45317912, 8566484, 525501348, 188640616, 944419377, 518031303, 349197502, 375413130, 234859288, 106168944, 561919233, 57050827, 212362707, 903347756, 568335685, 221457297, 893850586, 476598572, 754617776, 747260956, 377009558, 32444232, 510207118, 51232386, 825790409, 986773371, 342103945, 872684265, 341516595, 104055475, 781256631, 510067989, 893538312, 680874835, 330051498, 414194225, 9537288, 625358849, 778782154, 758451953, 818074709, 596366998, 115730375, 928546471, 637163471, 645085995, 502483758, 857842705, 871454449, 549495247, 468390062, 380595794, 56061279, 867729794, 478318160, 907739766, 519953633, 383446543, 349879651, 478309078, 155862074, 50481308, 684306874, 836516087, 244582643, 511488353, 828729109, 174130139, 116051796, 334730746, 468547629, 940740626, 406339184, 264075255, 498566052, 816978621, 931375284, 165321962, 376850347, 202349298, 273374401, 747095341, 317197240, 390756102, 481754064, 679740924, 763207086, 455957681, 96541121, 30895441, 936508598, 613884776, 395756905, 858807495, 825847630, 233792634, 907858246, 648391728, 287537715, 287299385, 256675259, 764798013, 253587483, 64555099, 705438811, 514681865, 287891596, 207584478, 992546403, 828930743, 164338242, 173704530, 922728997, 62696677, 169393577, 67794467, 791400223, 340249134, 992939015, 409132802, 235200548, 696618389, 998390251, 21478345, 268060698, 614248441, 518952245, 76836983, 107110025, 945139664, 867374185, 518434943, 328071955, 317661597, 119817732, 482630315, 830767917, 552557989, 430017755, 176401823, 281607352, 168148672, 164002698, 383747428, 734344972, 11831573, 685005062, 590339725, 381808394, 835804854, 754757989, 572932384, 37348917, 438145139, 29885359, 130512541, 784571007, 603230196, 825323092, 380853543, 774526196, 367188519, 487886529, 316449540, 464412600, 228305629, 542076333, 388725457, 758292653, 906438411, 166142311, 342510148, 573303577, 483226232, 939378657, 371297594, 955270910, 629204003, 445102069, 729959664, 251459111, 11390805, 849389094, 577203722, 200356904, 49847588, 4660955, 316379197, 940365548, 207241759, 956242498, 118746087, 967756565, 599567019, 35737964, 488504269, 680551297, 88226899, 422932269, 149264479, 638866420, 926451147, 84190583, 472774837, 794746507, 996187962, 301578632, 12322883, 176853066, 397802237, 637477921, 853846808, 909801890, 495589689, 106404951, 594550643, 516377894, 104601394, 383484810, 239261252, 908652911, 388296339, 130575885, 150016599, 968577081, 784335442, 511700456, 140807577, 756983509, 106869192, 727830224, 522178760, 383845795, 705641930, 782330882, 585255942, 711360056, 452757102, 70007627, 103237576, 133521689, 877409364, 260384557, 220663215, 404991986, 401292750, 704775188, 565690084, 453222842, 838699590, 919739834, 388838909, 412854860, 682260286, 912216964, 671401135, 249114555, 75308912, 823548990, 64464154, 622606058, 424297936, 652961301, 816966743, 49671577, 375040470, 728236001, 348776007, 300192796, 403150955, 934496527, 719715101, 240285357, 840516745, 987019640, 8993223, 227616323, 793455557, 874570293, 448034759, 586233370, 969071200, 690872480, 697307806, 194851897, 117083801, 234123297, 697694032, 751766756, 654990531, 236255227, 587449596, 482946765, 539420237, 532777052, 727465759, 921233759, 635783396, 531148478, 506626906, 306002554, 115400598, 60727943, 568268633, 201926561, 130100084, 104679676, 970339027, 74873134, 735321803, 775417333, 754714327, 621700221, 859878566, 916348489, 222840659, 866610098, 154017673, 478454727, 982396664, 283730058, 852281777, 70375151, 537748221, 514611239, 817953204, 197199106, 845650, 270137412, 398145215, 506796983, 307644596, 200682561, 516649832, 390866867, 549198437, 216719139, 625995184, 490630786, 743600438, 598934362, 952461000, 873278670, 381797277, 306225462, 91875109, 669545961, 806527540, 668206158, 25693322, 825769718, 40770674, 991238149, 879532120, 529581580, 246610803, 863193314, 509394447, 874127999, 471637386, 187110897, 530462652, 512995187, 47390857, 821560434, 544409795, 755025474, 17995561, 60503482, 29397594, 160185457, 915040400, 645162521, 740373606, 43563618, 422310037, 941301130, 379766982, 788994120, 54584797, 183751691, 198341560, 847328407, 560369208, 491618087, 368208691, 328109816, 896398885, 779647341, 42068480, 569486358, 256856182, 188983388, 318035855, 35163314, 510484132, 923179367, 254914740, 673284963, 997031485, 218089033, 292517541, 331156816, 26700019, 619499006, 591593308, 750513843, 33192773, 401887017, 208404341, 201792872, 793423977, 259603376, 64805980, 958079717, 860136264, 609659466, 199539657, 566874885, 216741099, 333733522, 43701398, 170809043, 8406500, 542001473, 989186301, 249060621, 901167915, 219330955, 855724670, 290792705, 658288815, 875898561, 522679861, 263923689, 40406907, 498353176, 499525708, 773841100, 322312641, 229793585, 575989643, 795981136, 879459912, 897923518, 61658420, 600625790, 842937304, 288551817, 118946563, 585198898, 743233730, 488348911, 514513485, 802877807, 505579032, 682963670, 867909104, 575720932, 30027139, 38685395, 423374943, 299912739, 193860743, 246494144, 415917187, 692561471, 545405312, 690071802, 775700364, 332103230, 178961871, 751044790, 505942250, 90088473, 90295823, 101190101, 537346178, 42958098, 420978435, 821707012, 41512310, 595261991, 192851643, 316833754, 9164808, 829537081, 796587527, 139144497, 627498379, 121760483, 808985396, 630864295, 46890266, 526023161, 268808958, 765420344, 651238717, 352332360, 807082412, 524737331, 366945072, 752843678, 694040815, 973287908, 611421769, 877627600, 161254104, 303825985, 152189123, 149333640, 892108082, 559602034, 897996229, 110191757, 831132346, 156608796, 367013069, 23548953, 252920325, 304913606, 79033785, 645497065, 741727287, 816798529, 455679219, 527290470, 620234123, 734344153, 825781427, 754830175, 493307676, 595147282, 557360365, 693049081, 386695992, 842764724, 234442491, 663771397, 212066399, 814462964, 642291926, 974634090, 450930570, 955748811, 295937688, 109766009, 602138409, 365088093, 241763017, 604171561, 58461573, 422682138, 790576133, 27799324, 129099389, 107694995, 101900569, 135537987, 20498999, 20712856, 836280102, 91742329, 788712295, 520582297, 152983320, 194028455, 503101157, 300262150, 382417713, 541482929, 176191185, 717977402, 962125626, 651908612, 937833893, 746482496, 378452468, 793921833, 907428216, 68217207, 483927679, 299226269, 914669896, 352393813, 400119856, 59583791, 973196041, 351309612, 256683234, 87376762, 951340438, 233272729, 909061106, 25623133, 800077487, 842764539, 317785732, 880512653, 922446014, 545651681, 848503470, 324949980, 531944588, 133349987, 859675250, 666406836, 935180429, 65727043, 51392136, 161537274, 937703440, 777227880, 699922236, 557108229, 298808654, 511722185, 803608600, 520680441, 531591169, 707010573, 451762535, 696474535, 733396932, 102689447, 770001564, 202891432, 146375615, 661847260, 738189058, 499204821, 585682460, 475211524, 352282041, 120904561, 141039482, 859843258, 918964438, 321171654, 672005068, 527262040, 590005098, 372245837, 49827646, 185477892, 656368221, 113242497, 252986841, 260310604, 800722117, 408083827, 770783592, 960207916, 223992292, 691900446, 686861703, 734044485, 529888819, 245476135, 380171123, 413005194, 614341337, 697068440, 69111229, 384176175, 62236706, 848847479, 743067995, 582192179, 946397335, 339929927, 107157466, 202621527, 995486504, 25659031, 153324480, 323391425, 88804685, 626513679, 846793120, 3268397, 279179087, 51350447, 177601071, 942545265, 748923131, 997298647, 39963159, 217108968, 834279534, 599694537, 527119547, 896623442, 522904506, 995747008, 711740861, 250607089, 277067488, 605560465, 872466106, 859222633, 490493753, 584402430, 808600743, 203366278, 235976247, 831499416, 683157226, 574917111, 389527069, 392822265, 116036641, 887845854, 575282759, 938874963, 249210075, 386594226, 427459603, 888397737, 770189818, 896661769, 961039484, 512683449, 182181458, 133305052, 420971339, 975949962, 963822753, 465882191, 888351755, 980820202, 434567016, 83159802, 951003403, 593818782, 795548028, 249144711, 436476958, 887244216, 220594204, 285362175, 555798596, 551185624, 817086740, 168428707, 565669042, 109309326, 764158541, 147599081, 757169353, 368415519, 187948778, 662668636, 962331746, 31411209, 903866562, 764367662, 32266332, 998680142, 905993366, 881377287, 447489279, 929667176, 605808333, 313308148, 931202524, 755706584, 468572381, 661154578, 422885901, 985066119, 259392055, 715605981, 691930195, 578525092, 193951978, 564986310, 546843356, 982823358, 302947773, 934740238, 772427320, 376518106, 487052449, 834896345, 522182021, 512137815, 203290456, 988262238, 243321610, 65395719, 937967426, 251820179, 878862448, 313647597, 710188941, 744430980, 262873983, 382581354, 483793652, 966167134, 454672540, 603560964, 496567002, 57418472, 155775015, 298144749, 70530864, 627121724, 978021432, 259084339, 771667254, 410197351, 851058314, 508394068, 395686592, 884167093, 228734216, 813862959, 492406519, 733345739, 890134012, 430625402, 771989841, 219063473, 861199642, 290812323, 362743253, 968210658, 665812989, 860182076, 897581612, 892806546, 368217542, 50585846, 489330075, 475140295, 292425777, 815684349, 524714945, 403843171, 661546694, 808321047, 380143415, 808513913, 608896910, 68288018, 671152877, 813281019, 161980917, 985375716, 683363408, 33528621, 121953146, 710551179, 109512912, 30453370, 204181811, 487495666, 807713103, 16812347, 223445027, 418206430, 239979147, 180710487, 881046851, 854749419, 970827678, 875165836, 711885551, 39935301, 329377761, 623519755, 391210881, 778625669, 408985570, 230948175, 876475828, 561731448, 114720131, 775479818, 409174963, 544193243, 791763111, 825837796, 587853306, 376459581, 928242149, 931557965, 454987596, 271897160, 432073460, 713711246, 662380940, 854541634, 260219666, 204445964, 226967495, 377760066, 127781480, 317396543, 859329970, 860322569, 312793692, 288862621, 566534384, 495605340, 253416494, 22485406, 916218669, 36148853, 987666353, 722443503, 491969169, 511181617, 301163356, 240123050, 291497002, 470860625, 196586958, 724871839, 269902921, 509695338, 994580936, 195878185, 252698762, 383498623, 526484220, 860888449, 483488101, 367976718, 358641458, 991454752, 896010816, 610256749, 445540683, 829712360, 623657508, 43214394, 203869932, 655619939, 390970332, 761100917, 551532571, 638609046, 817072285, 478400132, 905733616, 390204651, 221286127, 706408102, 592828284, 109404140, 504611593, 786066588, 822444205, 214567436, 626713788, 766218811, 503924314, 144468557, 410057676, 78432340, 463652904, 919436762, 7267547, 827696233, 501169246, 770410963, 418240975, 925065541, 498270350, 852097302, 92144512, 47163368, 476431603, 782697020, 56130633, 702241384, 511388604, 44202274, 102441626, 655121174, 373856936, 863958642, 306114029, 214373056, 930961082, 459126646, 532693217, 939024679, 295847335, 857303302, 546847724, 996656312, 964035068, 61155429, 874163837, 967738396, 462870825, 749609417, 976936072, 293001686, 922925001, 933320893, 120586264, 969569606, 370196895, 550987575, 700558445, 737509686, 913120696, 980661687, 351857235, 657524423, 879095665, 712044116, 421189749, 961376020, 197674601, 332444503, 29268879, 548769473, 841416900, 365897362, 304006658, 994424024, 681744639, 852423799, 692725492, 650071634, 353598672, 582734445, 59112425, 167662921, 556817956, 951552368, 149448561, 285223431, 336031973, 735958317, 187328065, 694696467, 550556455, 539451632, 818019469, 322852472, 539982498, 441909878, 249743032, 649083201, 239320146, 822368152, 256066142, 810415292, 600706487, 356783213, 137975220, 823759932, 237654746, 819316343, 523287383, 683761280, 518493081, 458671312, 935424461, 303712075, 813055887, 796547080, 424753129, 433938372, 413497422, 706650821, 384266408, 382194283, 244454367, 779684575, 519278024, 696073833, 800308633, 145205148, 242069381, 962596183, 799265584, 157646502, 133955185, 34225419, 904303175, 413030071, 556497231, 211919791, 669420893, 291968135, 847619445, 213634913, 172223040, 518789313, 271617852, 688275349, 774809343, 266405182, 384591280, 932600535, 76918990, 294536932, 102204115, 805782558, 472153789, 773089799, 796691033, 238203420, 984770197, 381463597, 294395489, 236231500, 884748462, 999181679, 551274047, 29066335, 679596976, 426214477, 710576411, 473669405, 710823549, 933716672, 481888016, 215651816, 922656198, 813551400, 861580839, 679976137, 896932601, 525367858, 251554773, 740223814, 417000211, 977382053, 856353099, 826231075, 206181023, 712235123, 752101838, 415073546, 764329435, 919677405, 199724673, 10266011, 184051679, 533291145, 306317256, 15832081, 19002639, 340242785, 934737897, 728945572, 737830033, 544671398, 511706922, 363857603, 394512149, 294677095, 845622480, 875275261, 197131912, 219904494, 517737234, 561588125, 878429394, 573126199, 300426930, 223176198, 488304644, 985860245, 811079253, 775061071, 95537550, 11461466, 329019433, 35548906, 707846081, 339468059, 899312108, 670291070, 564042697, 631733792, 85895521, 350174517, 602868888, 483445557, 329421764, 791188720, 628580633, 84513481, 776585214, 410105813, 894426827, 166923388, 563432259, 258635461, 583766384, 352431406, 114625381, 253379166, 789903333, 773335597, 530638740, 754959445, 287419732, 245298125, 406323121, 329318066, 152865065, 790757089, 774611428, 262519327, 226307566, 751792949, 573534881, 318011362, 268081259, 79602833, 397690184, 559537131, 251267124, 790626568, 343718614, 747530913, 281917551, 714994147, 704179829, 256859237, 994808626, 559804099, 587082266, 719203955, 542321112, 564055583, 125244477, 778785985, 26863704, 817747752, 481096483, 515528217, 284514308, 681917482, 462236281, 372210690, 893631536, 528653705, 828005134, 439970808, 366886743, 790853343, 857438457, 39898329, 889485297, 299017624, 968749646, 219996524, 488772580, 247897050, 664474829, 744579916, 551212016, 273711854, 164391024, 480973094, 295503984, 749297848, 521190829, 215699547, 740122570, 862406838, 580459008, 516780202, 157946400, 547922722, 771719944, 66350978, 368882925, 153998828, 208985844, 833489372, 809821021, 767027687, 846278204, 939448353, 878823205, 5353537, 92853765, 93543950, 755099266, 24607469, 456326230, 135381382, 581079985, 421883520, 268672369, 415778603, 776936203, 933568578, 620078526, 498973700, 402542391, 408132709, 208397700, 864141877, 662819293, 447004243, 287624088, 185247212, 909228233, 451971606, 366480460, 827115342, 796611427, 437630325, 752279854, 773006887, 513489028, 903549507, 718670909, 666242890, 769190443, 79358299, 346866669, 420138557, 643385097, 256708654, 326869611, 984292668, 994609407, 91761327, 917864072, 719861185, 937640167, 362576759, 379394941, 792557224, 730437679, 554015363, 699935169, 43380670, 126421303, 446890186, 420050502, 147567534, 152443587, 526024500, 448306614, 781029867, 71334941, 531653875, 930150246, 276504212, 391699558, 102753666, 272924101, 211971299, 472376751, 365339686, 796184871, 396912492, 521507250, 980033572, 341261891, 492433306, 994072857, 196988021, 154933582, 132454670, 153156669, 516666071, 188259256, 318537751, 832983449, 183180283, 348724839, 123939559, 240269660, 671374486, 670329580, 109005998, 638784625, 168146428, 593962710, 797316704, 972163843, 123698364, 332329826, 319797197, 551582880, 480910230, 219603972, 58630968, 669058279, 879345297, 926679278, 748969192, 331839551, 942225758, 820532041, 81975577, 896183107, 320076347, 535755276, 166574183, 646395998, 267453749, 627210047, 491938561, 179327004, 901105616, 332346054, 265224077, 417623325, 948516376, 130227618, 62626809, 853257867, 449278164, 470878471, 101896365, 181047309, 620674919, 923145329, 523616717, 681166080, 925437187, 411317826, 310190975, 45054023, 458322376, 242937382, 341746628, 541523510, 159242023, 536955164, 345091432, 707944153, 428880969, 61820856, 907614502, 610998302, 969622216, 708436587, 284362469, 399773050, 120345577, 163885348, 63810671, 643978311, 933493090, 623411637, 269405142, 522485355, 581135279, 477248287, 837641582, 432587184, 210967815, 193787924, 980477485, 999340608, 559822950, 568570895, 679690966, 817412484, 739194430, 837943024, 996090892, 689181481, 752396295, 616741775, 799163500, 213113822, 885530390, 556286291, 972012262, 690437318, 276517027, 648166940, 454266724, 546599173, 70806194, 260179687, 797380664, 91815707, 275575120, 493206352, 271592680, 138993624, 800066480, 172560588, 682598259, 52549243, 248816778, 219497863, 486188312, 616014162, 595066904, 774917782, 193164329, 466245873, 773489672, 49677799, 393598007, 130941553, 294017382, 599837450, 600174737, 419473709, 800093447, 146398794, 221862802, 115477655, 874630146, 945090957, 984729159, 737371630, 407764031, 107395658, 770456863, 165488265, 125237298, 729001975, 733689657, 895392660, 873182777, 457470011, 54519899, 81174309, 877917475, 580680533, 114700810, 232451205, 893903274, 140671826, 944809029, 211349171, 209602159, 30899679, 195346577, 558482715, 705102692, 205482411, 988031701, 492234574, 278736646, 489121534, 380802867, 968077799, 591605627, 695678589, 257451706, 166097982, 709852710, 534426192, 735396168, 565822587, 668130671, 667183151, 302838634, 771092163, 977912341, 922106281, 711075598, 490569517, 324611600, 864172701, 973971862, 264537924, 494449240, 914053625, 359936709, 997679405, 96848986, 357084425, 946675465, 477374592, 80245409, 486634846, 16766509, 178172184, 764963973, 226597971, 515711325, 514907545, 853630161, 153520727, 492410530, 20739920, 890789966, 501098408, 749287354, 669032557, 316218600, 227778411, 352452378, 388363135, 203335386, 570118496, 233793898, 340745049, 593750139, 215010279, 629545653, 587836558, 773418104, 291906682, 833810625, 896710719, 738310296, 964405146, 567370034, 75089973, 580549066, 223017896, 125113636, 225348481, 152529636, 796502886, 559716296, 2222269, 132566944, 865913789, 134394174, 269348648, 400426130, 617319114, 882800692, 889849041, 211853210, 80486080, 263819895, 574165112, 270184220, 839342925, 563051107, 332244023, 798887623, 305958482, 457869145, 895283237, 458289441, 975812363, 917028200, 410538450, 282707901, 12030940, 636379190, 770184073, 381047912, 744124991, 322632216, 70936069, 819271669, 897812537, 297466135, 505381010, 509359685, 185892060, 578666497, 583701353, 399095640, 268958728, 86670985, 112770388, 294777865, 175820256, 767881892, 223753451, 725303232, 126169511, 231929192, 289982983, 695571312, 551103075, 139489389, 134246638, 16460073, 155237454, 998532506, 404183891, 782990240, 185699880, 638841387, 122230407, 644400303, 104282199, 192822721, 448445164, 878640635, 388075775, 386278677, 626875132, 222866530, 413333070, 964303501, 128160185, 516322720, 324502458, 696198787, 635755290, 73198684, 20970567, 806278601, 642646214, 422818264, 703358271, 226329391, 645426755, 706569030, 533556446, 36127794, 688158289, 717717696, 720353671, 285298676, 660840993, 486699597, 249452758, 253894938, 99922323, 443052312, 329931885, 128552456, 346543509, 383161337, 679345517, 718354571, 104035849, 318442168, 605144710, 632992537, 992462693, 911055492, 437340596, 251988060, 513245953, 116722268, 94278331, 4296564, 655783790, 585753148, 202374858, 867532748, 745197883, 638989246, 675127021, 845956304, 752971272, 471136199, 388743258, 928961709, 432160143, 852004265, 738573704, 687584393, 917478399, 581609550, 862201927, 230218639, 125022592, 53432964, 171085346, 359182694, 593781794, 442701106, 675832293, 328065314, 850598875, 788276208, 28235250, 498195705, 165715245, 436019611, 468183632, 156476707, 992442842, 346119894, 543163167, 963343597, 875767689, 486243289, 394379451, 451299435, 561964427, 822460608, 943054869, 809187016, 643075819, 530964793, 522275597, 165030019, 268042364, 35130547, 911383724, 56668181, 991982055, 355910513, 433034299, 84186695, 816810798, 193081739, 999531861, 7667839, 553669564, 235040730, 167679886, 246668294, 983449860, 628699349, 300947189, 413383936, 61752514, 450673969, 656650164, 259065573, 747506276, 932364798, 395040892, 709370188, 893361798, 423817546, 427680144, 386563780, 662631997, 357427275, 721000558, 954658615, 41010602, 141500226, 111598960, 978754862, 122886065, 54908717, 626615728, 748350909, 449067253, 675511338, 667172974, 120479113, 281284923, 996845583, 744953143, 351568982, 854245614, 183948898, 946321469, 715649457, 862649430, 944557543, 180462372, 317159030, 64383304, 689339549, 778930311, 961728511, 367683508, 280071935, 223167784, 774352192, 980417749, 765868351, 220458526, 329073876, 933916996, 478636996, 29270526, 641989580, 339608168, 478486647, 518125030, 310409803, 519822096, 702799253, 209765417, 216468950, 529181985, 363176620, 825155402, 597897583, 294755383, 992038850, 456530831, 352301019, 92974336, 750291000, 773724598, 249276123, 663284095, 426964751, 623227601, 851401743, 965523968, 833507438, 644373089, 201559426, 503726864, 218978319, 45044194, 624622217, 846744854, 448288429, 439326916, 289919036, 106214901, 877973184, 398013301, 105412462, 592433358, 495720875, 416934512, 142918608, 112513779, 205053927, 962237786, 143588995, 900496223, 771700798, 920239004, 188322652, 360933493, 951501412, 442901666, 247589695, 907861601, 441692331, 223801429, 617060424, 977440136, 353803807, 498025320, 584186765, 35682688, 411230757, 918913281, 909671649, 814677533, 381065813, 785486562, 570347964, 837659306, 158808211, 837321122, 749014283, 694580733, 998475286, 189906478, 351568128, 524922822, 524166563, 972438552, 613498827, 749570717, 131756808, 687499688, 633895985, 69976946, 963890141, 894000711, 118909168, 173422419, 983500190, 761403340, 183362071, 328241286, 942405600, 303267976, 925272324, 900241925, 670757519, 656540170, 276561463, 326712656, 336837618, 477459249, 914293526, 535947995, 349338377, 843745600, 687363750, 447408319, 984372132, 586919004, 182066373, 462723750, 22872947, 577227527, 348151056, 977264946, 166931403, 652541759, 178514674, 72487560, 39901528, 362915499, 957589049, 378586079, 159331652, 564994925, 227812999, 777232632, 838140481, 543184493, 52076992, 895701, 981490615, 646924103, 61657228, 719040791, 655105741, 843883901, 589584547, 287291299, 994674140, 441878332, 787553934, 222176606, 241842962, 63200767, 671898328, 284159658, 141605787, 496699656, 723789705, 327045112, 540660107, 741815534, 170510038, 348119969, 53328802, 645702221, 734664904, 264977334, 576307572, 313726919, 35196688, 95551387, 854125934, 636699947, 210356234, 867269240, 901870048, 855396188, 338956692, 401997432, 25967920, 69316581, 113645370, 820689430, 973553693, 711752511, 795562426, 288654896, 239474062, 492311617, 108695744, 456434274, 700386211, 866693390, 677160770, 727066391, 328415347, 225395586, 560205534, 58180139, 479459501, 221041539, 810635555, 381809670, 204752422, 67110934, 146743552, 195211028, 276119066, 935121482, 665931915, 328594844, 36491200, 640268046, 185755509, 776279469, 783898079, 724547407, 660982540, 115162069, 529071803, 244953709, 117032672, 219257407, 566451240, 660863408, 499935440, 468344459, 82620887, 944609109, 218244955, 32283990, 3207286, 947764773, 909240766, 937055611, 734149398, 271877098, 490404546, 211734652, 20024230, 372545904, 519031231, 767166124, 966550809, 227315980, 155700295, 311904303, 184894297, 259739853, 688342636, 701535987, 112047754, 456278218, 114132524, 215171595, 45989576, 335534291, 363443926, 494129232, 335409663, 101247308, 167261650, 42762182, 55352506, 11764276, 556445915, 679920194, 866499751, 6991811, 184654273, 542653730, 841948541, 177315823, 918694704, 27249612, 269849091, 489052604, 196855267, 867127973, 761425860, 942094338, 620558416, 152237381, 529605906, 328031377, 9218698, 891162852, 305803192, 305087356, 61901359, 496422745, 382710807, 19143006, 812579371, 801617161, 906854680, 214305178, 986399988, 349988483, 470172702, 905817944, 131710881, 167648804, 841778880, 192159101, 827547703, 634913802, 967383307, 274745823, 589322372, 363260351, 747943926, 675275635, 834583262, 718312420, 182474047, 143104522, 757926346, 313333695, 322883359, 705422516, 167305014, 666567468, 404011475, 724539797, 688904814, 310898074, 814934513, 449855024, 806543590, 673497337, 774739108, 589278564, 692617398, 323523308, 472949518, 643629624, 667358645, 525307255, 737074954, 771960162, 986184023, 422094352, 468520228, 576571461, 311231604, 404982617, 69880918, 629568850, 865200689, 337373929, 295412461, 588033030, 703252432, 435417875, 295581366, 507723282, 942775208, 645611423, 267860760, 15337383, 943760025, 736493088, 30780639, 936817749, 789295913, 47224596, 88597360, 499846292, 639439694, 71247674, 9992788, 660660445, 631160257, 620239, 555834644, 485398529, 103539004, 369882946, 624334025, 924095222, 921020984, 176466465, 100747493, 247487155, 715895679, 62535495, 552321402, 822375464, 203651681, 442988171, 345938539, 754602971, 927572096, 772219944, 404169830, 101102230, 446258164, 625477800, 669049923, 830459510, 112061175, 577656212, 804010017, 440257220, 289858339, 786790378, 663236701, 604311798, 275413207, 708999955, 189262728, 283164009, 275115922, 334377355, 997591831, 385629393, 656681007, 847042014, 641416831, 932119109, 360300013, 993611935, 556818239, 952590781, 510242946, 583792067, 490562526, 275366315, 697994737, 215278485, 172157343, 460293635, 886102411, 53594931, 2489252, 500899515, 214183283, 958559677, 157260586, 470112862, 587280712, 865876352, 856925326, 397371046, 562547650, 231169480, 40433049, 626853753, 625118291, 378078233, 430376597, 639294788, 992776848, 52368936, 804346912, 861757127, 716344018, 820196419, 8057324, 456688345, 850770653, 529308949, 24207663, 453596898, 813133511, 757022390, 74050225, 292005482, 204194272, 883760801, 311561543, 958553838, 80214820, 527810997, 832427278, 562603227, 765505956, 375892105, 986725482, 811819208, 158003462, 240557182, 733880901, 512200588, 355374891, 819124938, 27697807, 774056067, 698118340, 904095150, 511156198, 209818731, 621748190, 118002313, 804792089, 127477, 739895643, 302361061, 735419365, 654879508, 153380045, 661473308, 588658090, 442817478, 173223184, 476070823, 710347085, 932386818, 874021515, 654240874, 124352018, 791842805, 216754846, 801807082, 29830412, 158108668, 164197588, 581350769, 678767497, 190971568, 224094116, 271378264, 428583404, 518816805, 870195492, 810751924, 286694744, 778479655, 407059249, 360759585, 98757688, 305698230, 545415962, 735518958, 727176495, 437903066, 786063860, 530028914, 559418000, 28947898, 508567703, 191578528, 10474009, 220819554, 557278379, 594971083, 904017047, 828921725, 706430420, 874891376, 27526912, 542553184, 527113732, 241406420, 616254952, 577109508, 262741913, 223137581, 656866375, 249564534, 112613371, 787605116, 126614585, 955827486, 370447122, 278639425, 484329, 426287230, 622559892, 646025601, 460921293, 690776279, 491330254, 124045605, 681548016, 819001323, 20057659, 638674020, 497917072, 235768359, 467115818, 206149435, 156892351, 766546038, 996541093, 129463523, 884284834, 935306796, 431565773, 500681550, 261792861, 753291082, 948301176, 268035519, 163106294, 916948628, 354898974, 219933438, 236592294, 693006256, 188285530, 206355267, 178978202, 884206349, 69687580, 985795894, 331610062, 111664829, 416817188, 377402297, 299442172, 344890482, 696229612, 263360782, 996625339, 221474509, 297995066, 595769889, 208042473, 410470680, 500515397, 499989380, 706669129, 814985458, 759077123, 263493292, 699170037, 631339993, 253633610, 673192124, 675153141, 874958993, 37008724, 711343196, 613401322, 852648143, 600678990, 192394648, 51380980, 829820044, 894915171, 847149398, 860985105, 605447682, 142829439, 20193112, 398855510, 410702835, 806976249, 502955234, 489964236, 998431646, 920991916, 139015393, 636790415, 978489841, 749580590, 243184338, 112588051, 425231137, 510066260, 731698381, 889502629, 242625057, 657241337, 526938482, 176143480, 312508964, 478147944, 392967815, 61867452, 738099801, 806995199, 28148513, 334041363, 526994652, 549523512, 997330143, 647203687, 590394654, 318388976, 762861552, 664472564, 219924447, 332483135, 478404589, 454506275, 555239576, 611009977, 664994653, 565399650, 550644317, 651817697, 990580966, 872172148, 778173761, 127493417, 946517596, 971821630, 991518081, 484533600, 873710238, 768278376, 610970377, 444471745, 802122109, 289559545, 53692899, 84198386, 88979806, 967806712, 206892122, 75939707, 755808621, 248474676, 436137086, 891079738, 811733611, 744072298, 32439052, 548305781, 283647264, 55200538, 724422252, 800358284, 531016959, 501470485, 935251647, 830909481, 892557521, 273232579, 575399940, 913241549, 992301788, 771887932, 969566616, 300056777, 33027736, 975420829, 841222812, 572343830, 346788874, 721287826, 294625586, 604646283, 780128537, 392076861, 139362064, 250657742, 870803342, 309935086, 376093361, 245163505, 170388143, 816448783, 340979164, 554358651, 371377783, 465152588, 908135407, 494658147, 121791944, 645611620, 582822942, 818214185, 134241336, 353206920, 343114124, 326255233, 649106459, 489165018, 233153938, 685605118, 211485005, 447450089, 285024179, 195241537, 565056018, 246324474, 132907079, 731327708, 176019591, 219547312, 632887307, 775792115, 95889334, 617462687, 118422240, 881714259, 359904982, 534443588, 361941965, 601011066, 19152667, 953768602, 385249628, 339896257, 939834422, 601880479, 40700547, 323048022, 957326118, 805975658, 727097429, 912537037, 79310161, 888873514, 236679939, 144834296, 555877519, 258273497, 117582904, 983278122, 595211525, 945227383, 907062005, 395049156, 820361411, 493387429, 588956513, 39714758, 601891195, 450393111, 813911734, 661918883, 139466027, 359814867, 263450008, 213494868, 395076209, 223693248, 994099272, 308686372, 362186690, 187179680, 484417252, 441646315, 502952031, 288255039, 337438545, 38857252, 11799186, 712908756, 50904556, 69639046, 155995327, 96157440, 635963592, 371780164, 37520382, 443480608, 710939489, 759085732, 906222952, 140007168, 838758451, 493094423, 853477895, 793640028, 253765299, 129229440, 607351012, 535035005, 923353901, 355140445, 955579327, 496811034, 301502339, 840610700, 219380006, 100220383, 646030967, 301643694, 504969823, 366188601, 949179021, 312511339, 468984024, 478105334, 278045498, 395881531, 694835154, 101712731, 737040035, 99905163, 267056637, 601786518, 136249352, 228647165, 76088369, 308669737, 274645567, 76231167, 650842107, 177273533, 390541831, 315853188, 458698482, 862432231, 651299469, 772351625, 496172954, 434273998, 623443386, 407681939, 460978329, 472032575, 578294801, 951734031, 814997775, 121899461, 531317607, 987058322, 232519090, 982546151, 920045591, 140511203, 755837030, 701754928, 802310336, 672168874, 99741713, 261312495, 264869930, 336371467, 753080039, 937520766, 138934044, 332960014, 743445692, 139055284, 494595886, 335395673, 519169752, 603537709, 914846993, 754532808, 384628026, 204867798, 356837423, 362795446, 933100334, 468106281, 562887088, 832500809, 984723757, 309292029, 302777636, 762940997, 859182498, 463467917, 105321213, 54985471, 839279794, 263374397, 107429858, 972148947, 922410684, 660763770, 844363642, 456461716, 439363063, 770433373, 1417753, 96317378, 720084812, 662508277, 824171486, 107475608, 701768363, 249390976, 669283116, 586425300, 702342692, 243790459, 245960695, 656946889, 744763795, 661193474, 803720756, 649770505, 213887785, 41089897, 797862045, 273588905, 217114848, 357889603, 127756619, 188937683, 917491244, 464365607, 976448096, 701516983, 302462356, 57602382, 645130507, 675469545, 858621811, 819486668, 750634579, 196530735, 570863568, 261871813, 286548526, 441157270, 371153461, 443277117, 563537775, 363696273, 494551943, 939506113, 692882022, 320427364, 204599404, 655916406, 879950460, 108348520, 871580316, 633618504, 896359204, 679702914, 448350085, 207275270, 919654100, 982626997, 52329222, 636235147, 221223082, 326059345, 404316320, 757495426, 134140786, 863715451, 25201970, 631359077, 161453992, 427546327, 103466596, 785678344, 711293690, 31536692, 270984375, 212341308, 883885024, 299622932, 438504416, 238473964, 32935297, 359080417, 254612763, 182411867, 314556471, 288722054, 400619833, 405171111, 557603721, 801636532, 328343224, 141141921, 271952298, 988934438, 577375719, 624587101, 769860801, 819329174, 632820525, 637881046, 242326192, 598341118, 699040149, 685705025, 581449529, 18602552, 171407868, 691266286, 722576152, 562897587, 679172454, 383661719, 176029747, 299774287, 720594048, 189866900, 3984142, 512905887, 791918569, 509950363, 508852782, 339852949, 973192598, 834715119, 403450280, 25584717, 686904464, 767084432, 24396485, 42434761, 90138536, 286760949, 912593686, 59814451, 138347163, 19201776, 420863997, 714522176, 241866978, 456230245, 4528682, 517250456, 854467403, 765724934, 556372603, 709702275, 443864959, 410318209, 550877613, 253107307, 680346108, 248150350, 640762850, 135451228, 907722613, 399661689, 748150228, 117177457, 440750283, 673876283, 188648874, 172568866, 230438631, 746940000, 118842486, 224081645, 741016444, 968345642, 963670447, 415519105, 89169867, 887685073, 744356177, 920055415, 246619445, 891571441, 348138997, 315720491, 341695393, 582932781, 230597498, 810390489, 714609552, 825865668, 896556045, 767326619, 437688846, 135498886, 168422509, 235823186, 956796056, 160416668, 533704085, 59903191, 916076026, 585551355, 204320993, 189501701, 164473007, 854246696, 564102667, 202538389, 553226576, 155902965, 231103295, 290075301, 797898168, 553018877, 406020713, 109054901, 104504049, 816557830, 831468947, 708315999, 802406183, 418204134, 891692840, 786748545, 771824375, 238944438, 818080487, 402621486, 496172317, 542110697, 143321570, 337569097, 463361946, 999107757, 461559300, 506390479, 562547167, 861648039, 386466507, 166634189, 969173429, 209377606, 50763384, 532913236, 88577727, 33809533, 657342657, 777676882, 6401302, 41984805, 451605115, 525041225, 698687170, 887666480, 841538404, 443886390, 421539125, 932434209, 255025236, 57063758, 212549696, 220241061, 558250560, 756442511, 956202486, 705850527, 502128718, 722600006, 26665731, 301194501, 893771741, 17536631, 194166516, 265265083, 173725555, 648339216, 346697943, 603537529, 844452241, 265232685, 328970815, 933677449, 19404256, 956411069, 527982430, 22041086, 142709929, 693468734, 351748984, 552648273, 588417636, 382972484, 765775291, 52497928, 453675760, 631800592, 256564591, 300127942, 972099832, 309874812, 223682015, 690792026, 342795520, 556531897, 836635526, 439368379, 21649523, 467709699, 806958719, 241996791, 515663175, 39325315, 830342504, 726913695, 690841957, 457918223, 880904737, 549589852, 612413421, 475321702, 322765138, 147471558, 886896445, 798388500, 298413844, 546376948, 210589724, 389892434, 620127692, 28363001, 742750505, 614452928, 74742464, 999315754, 570207098, 114397329, 774393905, 136187306, 275515992, 776296003, 2864113, 711334087, 262286133, 306959544, 18516733, 437230890, 640221503, 486969561, 433991256, 516741707, 980973944, 146334787, 44797735, 994651776, 50221544, 91798450, 304522266, 157948551, 353186649, 98892189, 64362155, 132907984, 461130008, 17075932, 878446764, 570523433, 457457680, 895598755, 374559411, 903312440, 429577018, 525323712, 152819652, 432330364, 193109046, 109800758, 848466094, 909911386, 962875284, 619017693, 890625699, 565335848, 126844206, 916804286, 379769066, 136778820, 17857559, 624946121, 260161453, 464055999, 113734199, 148861681, 239178161, 539977570, 468346890, 779485957, 217827913, 738904037, 109009094, 193259237, 209371104, 104284876, 994714651, 69807734, 237140423, 795626915, 470350423, 621758541, 8003794, 911530840, 176935074, 913807547, 582411415, 751265917, 989451829, 197998463, 8317038, 599474465, 279199919, 487323218, 21386752, 936271012, 23042345, 376027103, 421118601, 768640274, 184239161, 157866672, 628673029, 659279293, 591145005, 58312144, 420843028, 763862992, 571713235, 911460944, 694001543, 594082542, 383030232, 792502732, 572771185, 403347361, 252904736, 706213094, 92262739, 645273186, 323358538, 614295601, 967331890, 214391285, 499410179, 889866767, 15502582, 587425995, 163077395, 740023846, 33168729, 204529541, 410459690, 39360683, 205902288, 261178856, 573498091, 677668637, 833560110, 272759826, 781930829, 882654392, 319579828, 203413948, 725664625, 526328245, 180604572, 886568902, 852119305, 348417880, 768560433, 581082098, 746185909, 145021289, 844105775, 582296634, 212463008, 80871768, 828284303, 524540516, 337809383, 273883655, 13090504, 211394396, 944261926, 78498162, 47024161, 109673128, 42598639, 29547248, 311918130, 400464295, 445507337, 22727708, 666047420, 452000946, 185098222, 434951807, 372389615, 434857591, 992786030, 634432553, 60308056, 906952631, 277194079, 659043672, 763175007, 477211565, 362902436, 756246484, 369104895, 723673851, 157404699, 738120182, 999387121, 329654278, 963098152, 406351880, 544915269, 879079838, 932976359, 478384699, 752794669, 951450797, 267733394, 935553427, 397002660, 557606834, 444705668, 650315692, 74763654, 810107730, 11810701, 131683672, 479213397, 633700557, 783052714, 237451712, 998578604, 23714871, 586686638, 260773767, 402721708, 397571405, 872559166, 333605832, 976721352, 887262991, 26786076, 565267798, 517120720, 842483579, 175200806, 685113315, 186883802, 27939032, 129089384, 418926634, 876846466, 438868506, 62843661, 606423792, 569434867, 725475205, 256412494, 1339948, 718399109, 577414596, 967657410, 164704622, 246769505, 563788533, 338213641, 887013994, 595802577, 605322210, 16422056, 380118947, 451100359, 648441431, 705243318, 819715230, 625282049, 555234838, 566455098, 175648281, 493591835, 739003271, 602610139, 506208292, 907265212, 415666079, 213661953, 59107965, 761951793, 255184265, 473043218, 852885030, 145489181, 502576969, 796183292, 22207498, 115736872, 704584424, 319370084, 154849744, 174166910, 273547898, 638232869, 192004621, 611892830, 872176572, 602220690, 300759799, 821896943, 349249622, 856194353, 424656517, 228176179, 511850408, 311455871, 250131351, 897075604, 869609614, 649018761, 595984422, 887175282, 588084682, 8811775, 578977043, 762894983, 202618649, 488865500, 447747209, 509010545, 825193593, 273744241, 499146846, 147255257, 45725285, 86545108, 572755715, 297431453, 94722824, 378944715, 779477956, 977181830, 435713357, 577050463, 142378245, 679207691, 362576227, 877529158, 487468658, 801732091, 14128923, 398076287, 117690076, 658395878, 196556255, 599437958, 942091884, 435917417, 177244239, 763635195, 47209859, 548917447, 221810682, 644590859, 842781373, 304754915, 875857566, 168782272, 809599609, 855536254, 687706729, 929073658, 228058790, 118953571, 663284928, 935480625, 273278755, 92069202, 218633529, 923215189, 134018078, 168877088, 812529636, 434819979, 430082965, 860505636, 820381237, 409303894, 434323284, 665013721, 647861575, 746981751, 429484365, 890581277, 479444956, 497844347, 90267805, 419228046, 514766174, 346480837, 408025143, 587179290, 524423163, 214190250, 97583272, 992493680, 559539842, 171375888, 378820084, 47206471, 579527851, 356068260, 162699553, 441525836, 438658777, 153650270, 618447193, 242078095, 101081467, 139084962, 554790883, 30625269, 746796880, 929976901, 590111786, 726979268, 600286405, 154538076, 334112403, 696532337, 1077015, 618521238, 695196842, 869541730, 378717921, 748062712, 126253823, 782811046, 291873211, 277453099, 778938695, 846283566, 935221786, 209042564, 730033820, 755437777, 218112551, 409481901, 368484037, 896162187, 536195631, 932579581, 558011253, 110910120, 381251541, 699269212, 798456558, 887406129, 842215228, 643152261, 767109372, 26762558, 497813620, 998342961, 382414263, 606090593, 157268542, 879097191, 212746217, 977819610, 125573414, 178718049, 177997110, 584705337, 477159193, 669001614, 25041540, 174643978, 760107346, 992674848, 779220743, 827550477, 978249947, 390220975, 329848185, 918869414, 592560505, 860747249, 107762257, 898690241, 807914501, 514767281, 507008176, 329101999, 779334267, 400044936, 762993047, 369514973, 295382622, 892268415, 481738056, 517877701, 825338825, 970696129, 668864083, 593155499, 382218773, 812127623, 838783189, 51322216, 385900355, 762510790, 349934365, 208324328, 699119185, 780516503, 643235373, 219751442, 687312596, 441587503, 396550978, 401276436, 381831681, 406209023, 589705358, 288906247, 74987055, 414927852, 934748697, 909116694, 706654917, 212542034, 716505783, 147041000, 371844038, 38896367, 443169252, 234812857, 716954362, 945941011, 537070895, 498004912, 729989546, 462645041, 811747484, 850933087, 218968896, 376537858, 289037058, 657083837, 874004972, 17678804, 439065922, 637197974, 3430469, 424829115, 385124487, 431650963, 750032551, 445471856, 414463000, 657277426, 356836194, 693648341, 500245352, 995509877, 763517870, 642651086, 325030865, 85166635, 884532587, 921232590, 816674057, 37582465, 782690727, 608399503, 602167210, 378834005, 888391837, 367475510, 113495717, 70990586, 348112483, 125840684, 226707321, 264584017, 827046332, 709982105, 453627211, 307123827, 959009945, 593170069, 96725357, 460833174, 876021010, 577282566, 881534381, 322033030, 699104063, 571250404, 308070503, 870012640, 687311003, 280032042, 432999299, 85326454, 242481354, 222377979, 902143893, 947209039, 226025946, 740943849, 413226785, 799931928, 66938196, 726785487, 507093729, 50330490, 129662188, 376451399, 995681940, 225737484, 393751056, 721231554, 803229382, 53194261, 359775605, 187634186, 946745313, 573527133, 234167251, 149972314, 488966889, 833931935, 178881112, 361362022, 910509140, 604868478, 555268623, 593821293, 706641164, 126389386, 194151412, 316328656, 141709613, 886665858, 252139757, 208463176, 159376730, 172124186, 940854926, 783926630, 692332734, 379943196, 830330795, 304555320, 185795500, 365223336, 245155436, 262885216, 293102674, 130281234, 203447665, 562322487, 227468982, 393666365, 925215790, 569163533, 811120920, 794309094, 933802469, 255339696, 984129773, 92450081, 178348046, 206563091, 639447306, 698080218, 232540253, 862062096, 297483934, 68184301, 295146476, 717600998, 187765279, 697970541, 240889913, 904184012, 54504519, 373807650, 860523204, 974813891, 561852923, 247270914, 630327673, 416836525, 80840158, 121609071, 726835292, 617984446, 663909321, 940017907, 926253781, 957969212, 288669252, 599379374, 590585063, 500792025, 466011950, 333883191, 140540858, 336674347, 190345724, 495947866, 100176728, 725467764, 428906362, 535729055, 690857381, 648858391, 277548172, 489841941, 608757268, 87794427, 289734714, 830969769, 114107720, 684968894, 632499617, 702206203, 691109888, 320889185, 105253442, 892882482, 474291687, 430830526, 76971150, 229508241, 102343427, 244140534, 423376506, 801613087, 52775791, 754726978, 790072357, 323651834, 53314129, 438667195, 127866193, 277422155, 615801550, 856384450, 776902459, 690077440, 825054819, 316188158, 902852027, 458792737, 281490613, 785462375, 139675566, 475083866, 189682146, 875289467, 358185787, 472984899, 168152706, 788004676, 820428316, 30549218, 742463350, 64428483, 535316292, 844229717, 793912811, 265412523, 325971711, 193405244, 731144498, 618429665, 431879052, 670584997, 85261190, 49373171, 322266377, 198465669, 516826100, 976106893, 42217512, 613929403, 858774041, 894803222, 724168447, 657443080, 8549236, 978124950, 120661605, 807395005, 672062728, 709755617, 261193647, 296548783, 203123004, 504684198, 334158949, 864028422, 553033197, 521966681, 755842938, 40405558, 249566408, 956040895, 301564371, 711247279, 973468664, 195023617, 826941170, 626914912, 150502118, 734858361, 848662108, 971330240, 640882190, 112871512, 648790913, 615987317, 50702464, 530775375, 477931469, 707875726, 893731086, 178075012, 165545679, 642285660, 388651697, 438300870, 236067937, 56816092, 785397543, 443965139, 989269367, 616277246, 75278980, 126532845, 926765690, 626462706, 598311855, 869233220, 853131085, 804389425, 656688688, 109817009, 600432081, 599560689, 434330119, 779358934, 295525051, 920579721, 30995226, 16916323, 474383938, 800516684, 357607748, 224956907, 539294734, 269766333, 924926124, 289684125, 721706655, 592687393, 262491814, 620485728, 986498372, 811342203, 942261199, 521214733, 810647242, 674064415, 818029961, 595677740, 311547868, 923030159, 351456885, 688740836, 774014713, 797582285, 478247387, 591340244, 755418935, 897657197, 506693486, 582265111, 559838698, 654491284, 434276207, 798263097, 321536352, 902745552, 81909663, 936937521, 259355636, 448503640, 457740945, 357035933, 692526813, 987694171, 534600756, 960623936, 115888894, 142863996, 449635102, 627842560, 435103563, 474934184, 760437029, 230260823, 806614654, 807708581, 110411393, 745384073, 933731448, 369646761, 48531489, 931146132, 775640600, 267345028, 748291616, 154764042, 375562743, 241470447, 383894039, 400338625, 29903072, 812454682, 148278695, 364175193, 798776791, 287827740, 334542537, 593396647, 905932382, 457747836, 962155740, 164515226, 499299774, 10015436, 245931565, 574006352, 467196920, 768901285, 37760066, 97072574, 521029010, 373748848, 821454127, 875240346, 245342105, 63575657, 474122588, 121214152, 868235779, 657183686, 636770791, 769344889, 250421193, 141349788, 765707389, 128158924, 612234819, 818397609, 24511623, 822562094, 440456789, 895510955, 9852750, 272556396, 134687882, 291163696, 699958793, 403743063, 582033450, 778734654, 855697418, 822636123, 559309785, 613673088, 530519247, 361042535, 654444923, 385904039, 813297910, 327235979, 663838153, 862197552, 76449585, 746779492, 595223212, 915070646, 292723065, 290775395, 136050207, 460140376, 573988458, 187493232, 902871375, 376997800, 499235627, 385152915, 103668745, 430454858, 657863577, 871647105, 820996673, 152039939, 195987833, 850759059, 103425373, 28922318, 782340232, 86388842, 394632127, 639789004, 445875127, 317388769, 901144152, 382517655, 232949995, 601269323, 15122119, 602635409, 78252711, 928822088, 202016537, 633082032, 759458272, 594645445, 356842775, 448984395, 632264083, 506098044, 799766645, 609019447, 436875542, 11462047, 450733516, 388540604, 829753356, 656089699, 31084687, 144536964, 443874235, 340787093, 935330707, 603735350, 910810757, 168344420, 726527562, 171976590, 59046835, 406506808, 525606008, 506691831, 716383001, 538170404, 413143454, 213388101, 98247690, 992759579, 490271333, 918411787, 526374372, 940147736, 766306993, 713206084, 743670964, 750412230, 277621893, 344601845, 366514256, 997462810, 256359791, 734856725, 888005153, 719730498, 120070092, 688612218, 84080888, 424060456, 898273861, 489469483, 752240169, 186313744, 68568845, 262165198, 53938886, 720316277, 409102370, 565431354, 394532930, 148940016, 655242533, 929726820, 41376044, 147170680, 528204629, 154595305, 382545790, 372671388, 857192753, 157354419, 805913869, 356679461, 137117749, 954324332, 633788176, 890445467, 966729177, 310954147, 833773720, 385693265, 352529007, 618213465, 555662053, 955972217, 883118486, 110340268, 38034790, 505708672, 492246932, 506276202, 919693487, 466178246, 189215483, 524639535, 463247069, 337810951, 537479891, 966961776, 40780969, 37336322, 584694795, 72893337, 496182853, 869752069, 788278183, 970657378, 702029676, 629773316, 363278252, 433079866, 897744332, 558940849, 922387927, 279017001, 431411072, 308011163, 497512105, 837328666, 931283917, 518541395, 945170885, 707387622, 944479722, 17919600, 676711445, 808533238, 917457309, 207936015, 386391548, 937017153, 167137303, 165274266, 354649645, 380128564, 84517066, 61768415, 590658030, 591665903, 142058042, 846153906, 396890871, 598712122, 421092537, 263014535, 983425634, 236845330, 440640793, 234615804, 439856261, 665496335, 950727179, 692405443, 380543272, 537250421, 31996142, 275088422, 537353452, 656240893, 969985886, 906230904, 245803351, 306937369, 521679754, 44300624, 35528998, 685932336, 179382193, 14347865, 593127450, 697491830, 99425465, 611447134, 425919262, 899351158, 608115415, 236959650, 768071992, 956428306, 334818441, 751663353, 158841298, 734432078, 819525906, 888504659, 900381749, 777540623, 217224703, 104447426, 116054724, 227342584, 46276759, 913151203, 497687583, 677403, 160302570, 768080248, 127776183, 28797918, 116240180, 301356089, 460336715, 78527329, 524578260, 692812458, 121250876, 568173438, 738156583, 233522775, 599987478, 820907947, 799060974, 838910971, 30140179, 918448559, 849500990, 113528562, 374797795, 695655578, 746918688, 385732829, 910338706, 249915200, 30394365, 626664496, 11659149, 457890061, 740736119, 407306161, 265813560, 598145488, 562342082, 816786296, 851418824, 154915299, 228344323, 808184250, 56838203, 705213790, 326212626, 422325556, 22950164, 677703694, 3019282, 451457497, 974158612, 408762295, 784694852, 712255448, 299676204, 924756691, 728134740, 642135287, 210597931, 883124389, 924965957, 783258697, 71595694, 727250118, 467148416, 125740707, 479113347, 316869714, 30717866, 982118842, 489343847, 977044589, 119090510, 307708818, 625696004, 23530062, 443996739, 162687358, 659550591, 710837783, 878025368, 188719872, 637595529, 528842839, 192714305, 937200855, 540728922, 673050154, 734087360, 325145565, 784736664, 579582576, 763008528, 373032337, 578043323, 599812887, 325340862, 274066433, 31308094, 129362893, 858883932, 344683035, 587516760, 53228499, 383013525, 120737840, 487736954, 695690415, 119606250, 588458258, 408950274, 749944463, 622718322, 461477205, 713612938, 174632056, 70299054, 591029812, 200768712, 805928948, 632231372, 564620915, 573507717, 226554701, 184473955, 399735244, 7223393, 949361599, 112776749, 410374285, 893618674, 908472643, 375269081, 134059671, 16600084, 861601781, 245690502, 464729641, 962046502, 445583539, 744829353, 506453651, 863520462, 56855334, 881706238, 950703026, 916537396, 261443106, 104913796, 290677616, 685782818, 874577268, 94710204, 299599267, 674519200, 346186234, 909969009, 235984718, 484795850, 578015525, 717635958, 232887365, 323462094, 521291367, 285207051, 278346037, 953498883, 883504890, 616006254, 203669814, 531358179, 855634523, 235025580, 705131314, 246123860, 240663489, 350951470, 38681221, 770100540, 133258713, 802526501, 387935237, 615222342, 875499077, 845947402, 485291492, 43618225, 401321593, 853793018, 208479109, 790935798, 511665169, 56664604, 363864836, 267890696, 274599221, 582653669, 585416240, 126508837, 367025832, 274113841, 673064395, 714186880, 688936050, 89279536, 267119390, 542822265, 106001723, 30662879, 769586747, 886480502, 440506889, 911833553, 300723781, 78486651, 831809276, 128510119, 431851907, 289528963, 138644244, 757891627, 648566083, 295045003, 293589568, 88629454, 304933013, 521221527, 446040659, 97129190, 329619277, 372011983, 486349528, 928180901, 259454053, 371389147, 495444298, 474558742, 420543219, 767700737, 280369292, 331061750, 460939722, 106672120, 43620907, 548248447, 102628085, 497380929, 865733651, 114849146, 572758714, 13577351, 975629584, 29523472, 883077939, 158868632, 300722618, 685460150, 986158379, 47564819, 139705909, 939469952, 362391155, 464598163, 79363692, 983580727, 351350179, 307674682, 386970754, 245108838, 50234617, 235068712, 509594566, 258167014, 596064130, 828050299, 491944781, 460041950, 839141334, 856806323, 665188007, 623432512, 869189487, 97842526, 943622895, 324381850, 640036930, 835397391, 209892214, 758033562, 470769723, 726013237, 900063986, 106894372, 906893238, 120825864, 836945311, 981549454, 428904988, 929308913, 291702381, 756338381, 309548644, 812450990, 504109998, 810125681, 653369839, 272557886, 246887379, 713046433, 301325067, 639354785, 158503068, 459516842, 856074168, 878204054, 36557164, 360834290, 746496195, 222289435, 916750059, 929237605, 260534918, 454325284, 487492004, 367828863, 842001647, 913021341, 329741659, 789779145, 189750510, 977519230, 208409728, 767607703, 167659925, 855883328, 546580728, 58874333, 95628512, 81751841, 43801027, 244823849, 421706868, 689197966, 843929874, 812199386, 287995818, 875217883, 827259568, 24790200, 991884476, 541682905, 952531414, 96677249, 117916622, 883011830, 860020903, 847643064, 158521955, 205587302, 838529161, 162888620, 681789504, 664261695, 522810810, 998448385, 220613870, 308088518, 560054332, 178877802, 725840018, 456215807, 847476751, 238085923, 182248870, 985172964, 783711673, 361328101, 716461129, 477774976, 417413864, 373145342, 17150855, 43509979, 274627562, 554792502, 893356104, 559075715, 135343297, 873183618, 445273288, 569469879, 245873584, 363363981, 834943680, 347605172, 872968365, 527869044, 694815665, 153125420, 637355791, 896939249, 915728807, 27444900, 922033563, 921855882, 277301690, 575481005, 162153756, 163853329, 481201045, 296155141, 756457708, 901060185, 195675794, 217936692, 364493024, 61434761, 131126362, 870470561, 189890544, 641774036, 46517980, 119321179, 596736714, 228459721, 485118487, 242049107, 126196134, 32531433, 103725996, 301048872, 349849034, 564862110, 620500446, 324710666, 795335813, 335956172, 267308978, 828861281, 142996589, 498222481, 547238399, 635896867, 677138856, 470748401, 733404382, 351376008, 72515190, 207772873, 11343098, 808023433, 29443396, 58826960, 796825727, 717225597, 439769447, 995125173, 356683897, 194635318, 373718443, 605798583, 727624925, 783191294, 489409286, 201492433, 57641990, 359569956, 819104147, 795664636, 740950742, 168674752, 589488128, 324083733, 300024243, 40737812, 324882906, 856273590, 303522106, 279567373, 945909377, 459488216, 930067298, 179099437, 519374885, 454963991, 42420956, 4116859, 150911745, 227226597, 109139706, 7815158, 196679091, 415587897, 38659132, 760895434, 492302112, 704190548, 281591460, 209294963, 227692270, 821198676, 57634937, 903870702, 659928947, 835732760, 914797490, 346688632, 377931500, 611022676, 985773875, 556835727, 339897172, 337649660, 595569966, 512647760, 135836986, 11332383, 613223796, 527161435, 45621716, 614596364, 49358072, 28683833, 666541122, 536325044, 584664389, 788706559, 862532560, 953836857, 105542615, 373555542, 546021439, 320088626, 357621387, 721822377, 509490610, 4655898, 350200894, 619829527, 347366158, 363249662, 325973020, 237572053, 692304724, 392515816, 378416444, 290118225, 331539116, 19414523, 860198111, 213598105, 382821394, 166131399, 802371177, 889486248, 77770993, 757710861, 604427207, 217662356, 563923889, 250179316, 463331004, 862648688, 992102944, 401720281, 886658212, 837987806, 389899420, 979199859, 912228151, 439592991, 976916863, 290338806, 20799983, 748502383, 516549738, 392822307, 959251502, 563914876, 27804247, 601967916, 191681303, 656937990, 572403566, 609540232, 460549032, 922052607, 742389113, 21936845, 349384935, 369088395, 723455024, 624095854, 1548430, 445489511, 167368520, 171770706, 470689207, 565227397, 876667933, 400411412, 261403578, 910898248, 286515389, 529835068, 203212658, 614341299, 702872967, 430053176, 466525560, 777878215, 702374103, 3552794, 450204238, 409424013, 318329091, 585753290, 624938707, 164615625, 892558739, 191440483, 230013644, 238478488, 887700280, 196584505, 305769421, 871828410, 452397650, 807127006, 922629372, 358374057, 406265301, 605644411, 75912524, 764739132, 85265969, 649468760, 196462725, 346689357, 510109176, 528901219, 286585575, 293637695, 811302582, 59101614, 151261439, 519095850, 517050524, 631334846, 321108636, 811812759, 971527098, 253910835, 879838626, 549502188, 332946901, 79450967, 631296297, 215362527, 133913156, 586116961, 35623089, 6024214, 860829666, 788776454, 653907395, 319791400, 67022274, 552505054, 770741595, 126233765, 631889696, 480950716, 83249555, 694782335, 140907420, 470477761, 765136424, 448442267, 785993506, 200578581, 541679080, 198635730, 858305701, 891628985, 9659826, 504988026, 237424774, 915796033, 968038032, 524380001, 178565496, 901052740, 822719558, 231809940, 41917432, 519930668, 356960129, 300100539, 847010947, 990655534, 728983782, 172274615, 78468174, 677328424, 544689510, 19005926, 337289194, 667148295, 951884869, 155948433, 497160816, 944560082, 401625931, 325055665, 137315653, 542071790, 209109143, 751042561, 415391277, 113640574, 887348413, 610991822, 252299863, 93116609, 330764788, 803510923, 655510523, 608614358, 818062223, 273329600, 527643819, 635117535, 633598212, 438163038, 242332743, 831973842, 780109612, 737231886, 315322639, 97508906, 881221045, 553387464, 713951774, 461824405, 480876614, 874963066, 878550508, 443920934, 695111174, 127376756, 914853982, 907424498, 184545145, 341996974, 245426177, 58183828, 515296442, 327538092, 217933694, 971113739, 407186971, 580291849, 377440843, 235769980, 295621144, 357611654, 554704196, 128406826, 829541491, 30466616, 257997904, 370532473, 618606756, 936771549, 204291158, 803781839, 897501949, 171434622, 673373600, 670559816, 694877963, 590720507, 902874117, 301883512, 518793197, 671124926, 881112596, 770848481, 315222975, 663104905, 494946600, 564388150, 97267561, 372154749, 518924991, 303964551, 900799306, 740035372, 142141013, 107527541, 848929095, 182848487, 655933176, 125702344, 675988092, 111165940, 495740814, 30373490, 815851093, 449922636, 64656239, 29149277, 26089487, 581809328, 226607355, 848085177, 705675331, 613417979, 16570140, 506886428, 123067839, 719629827, 795787423, 598606497, 967568991, 899243260, 271756892, 700371092, 25931308, 26198816, 403639769, 767167335, 602386321, 931084191, 88224520, 38415275, 926286667, 392131471, 910154934, 11075179, 420481914, 442483240, 72836359, 698547310, 246659535, 864027147, 791493809, 684809394, 76509389, 366254389, 34617774, 978992564, 626153707, 546072469, 591354578, 598519903, 761884761, 457777677, 212728064, 15849212, 4611980, 964254701, 82651506, 73732866, 392234076, 802150653, 487613192, 944103032, 816939389, 604559892, 759237854, 260730274, 35192643, 89055870, 386354938, 848264754, 946936969, 843111068, 323973969, 806719816, 980100423, 98463770, 758711925, 886799243, 164798552, 41698868, 436092096, 619210580, 667520407, 36451125, 909125133, 821657718, 238778562, 377235211, 721775411, 456509216, 462914427, 518197024, 88293058, 932114554, 313882095, 312733745, 872355533, 263949758, 388415784, 305435606, 28412617, 319533350, 94639747, 762587981, 666710679, 83859407, 542871024, 271967250, 148545220, 353831150, 791551191, 125862223, 362590246, 323977890, 115484677, 6019688, 512936262, 717014809, 82100506, 227961676, 557417753, 745246928, 68257842, 323017522, 773016783, 736077339, 12961891, 602649399, 731548317, 372838068, 846933162, 626671355, 210406311, 925337561, 665586888, 968626701, 892005616, 540728317, 413006333, 355656633, 966292243, 96435156, 973262840, 100999979, 600510043, 97821795, 170374302, 647660956, 539807106, 986717507, 293868082, 349696651, 819508671, 878619309, 944288454, 936523004, 309312441, 875997557, 749946495, 280640834, 87768712, 956114985, 166830175, 105132211, 95548008, 380955894, 387943747, 811540045, 336313080, 698082597, 498864752, 758019087, 832010724, 950082791, 629932730, 808475336, 860309916, 351071325, 238366065, 935296592, 3668412, 938311508, 126957413, 355047600, 865710883, 323900481, 288564082, 565191639, 935367477, 788689910, 870412611, 537639195, 698917985, 386072577, 7313761, 290860953, 515772543, 959855068, 954524664, 8862308, 798400357, 842800663, 917070356, 383651130, 577331904, 148484329, 17306149, 342813917, 614770534, 659286665, 874813984, 152177045, 554106801, 839284810, 962679130, 575789993, 8131636, 783866774, 841292657, 645148612, 91068980, 88645169, 558652560, 226906559, 527308124, 17465991, 430136063, 383516320, 869818047, 802266189, 76916045, 564826273, 532061275, 892516066, 89803371, 883444819, 929065932, 8616812, 359827101, 232999039, 693727481, 735243923, 435022588, 295275264, 728668698, 898155963, 963202554, 403847556, 230791474, 877819350, 905102345, 169769499, 213247503, 340177494, 90992303, 245947109, 109174818, 958638393, 121299546, 504449620, 234662785, 553987266, 341945512, 714565280, 175678558, 773193395, 1623139, 574660747, 103582682, 276429086, 346651444, 157839180, 617795120, 148651093, 593181423, 740330698, 209079550, 923937856, 12797567, 126162468, 886995713, 968604512, 740841017, 243020815, 700443436, 807296832, 194677922, 117711649, 732063259, 710693098, 832409885, 873537819, 297527157, 181688902, 152642064, 862941280, 292622165, 351047372, 64754880, 569426378, 190922132, 294760274, 470233271, 438504247, 993548254, 471454325, 901519269, 734319218, 349263348, 478176604, 866378393, 745053775, 744953362, 844854784, 615555932, 387129023, 294130679, 969627478, 805654692, 731743662, 124238449, 461513883, 868520111, 14919334, 94511310, 29032185, 731897651, 817953686, 256890004, 971008401, 514799272, 448367624, 650827652, 985024345, 52719299, 843465238, 658303241, 636499056, 996739013, 756494292, 680835804, 697655371, 718397989, 17550748, 355927579, 956916810, 890700805, 433984990, 473044896, 275985041, 445102639, 419200798, 524492877, 891046142, 907647773, 242056973, 483590826, 665978327, 121765916, 557719973, 533354486, 925365446, 226007661, 5332999, 423016141, 420580133, 102845040, 163149943, 873510515, 862420849, 97975506, 215978997, 220043430, 983523729, 753191373, 593980938, 839919307, 296370250, 375744665, 705022664, 775580516, 196876485, 76138266, 128175397, 945919836, 125457932, 426710260, 506214449, 727157848, 978595295, 545500007, 34203901, 797893775, 541670420, 737025198, 298445709, 871107063, 532855197, 224150596, 75475204, 272399715, 168726488, 207600990, 708753406, 561245500, 86712315, 727500531, 398510647, 524484692, 465521780, 953826676, 175745332, 401610474, 14579580, 529133310, 288533963, 833672219, 955018458, 81989640, 271138425, 674572195, 671535383, 235269731, 862448664, 504036447, 51621376, 945800535, 6476043, 573152709, 865440492, 719620781, 114688104, 809545526, 751817545, 742229461, 489481270, 33792834, 632890735, 505618866, 360285116, 386805994, 892462501, 104767598, 269078066, 514657557, 514708623, 996557048, 260494303, 814901967, 616156134, 118440104, 765734358, 428810034, 209563708, 447230756, 235021263, 14216783, 553730314, 288914882, 491057744, 339368314, 864577974, 528632241, 34812240, 243993642, 338103428, 312376520, 899321460, 590466953, 297501317, 688043276, 540565541, 124608341, 839758824, 356843605, 614184891, 317991766, 596635352, 286017058, 609109896, 480042853, 574436014, 58248051, 106942818, 996905257, 121309945, 225020857, 555435680, 30747136, 928718344, 708858781, 993885791, 170740655, 960711902, 291478121, 643450211, 829084170, 215798592, 857932810, 575576701, 113119216, 560521496, 409189838, 319393816, 585412307, 425194133, 27003322, 362523744, 729733417, 646102152, 423154308, 936374439, 146326580, 385979185, 103809860, 387008936, 464588824, 213104709, 684103624, 217825204, 797301245, 405360474, 802858892, 293486672, 873656470, 133576916, 120602821, 739294818, 528498865, 415758517, 326902787, 483636190, 119510556, 141534409, 665738013, 212909891, 517042878, 203094947, 983302662, 78187401, 31258488, 63921641, 56412730, 794006325, 52219410, 634469709, 425550343, 52666923, 4534842, 299751529, 678607400, 390982702, 935633177, 355940152, 678024050, 841649185, 218284022, 22301541, 226896557, 421813960, 420616579, 865697516, 56065528, 19821122, 508167721, 756024829, 546901121, 991034233, 176294376, 872175804, 482536733, 498987920, 59917598, 863370901, 511223228, 583465000, 613393262, 198814777, 487832434, 961546742, 547451709, 795944975, 829045542, 941328067, 248849396, 505256106, 138175580, 522429434, 449269580, 793883394, 113187057, 976117237, 783508721, 909115204, 470794726, 181649534, 573976775, 253646660, 781575941, 425942890, 109197689, 746517302, 789279569, 142003625, 424948020, 223550689, 645645272, 193586664, 27159457, 148296075, 275607365, 927524129, 412552829, 548980957, 935128069, 419780876, 852001130, 956430665, 48172800, 673549923, 941872796, 886985021, 609672461, 794695207, 671872035, 305772305, 234868324, 726864652, 931028418, 539788876, 867812158, 183927169, 75412063, 634636264, 924156982, 708803038, 496750268, 877334720, 477417514, 99420418, 857346448, 765923280, 804701617, 339488092, 61909880, 679469359, 126367090, 654494806, 751169726, 737175897, 166378801, 155035088, 17299194, 709331313, 308071141, 180738283, 793775583, 19684127, 19209381, 243515653, 930538119, 842710230, 17942610, 264680471, 506344209, 56980873, 210374721, 304759042, 746666873, 838257766, 839160696, 64688604, 95393123, 927580673, 550257677, 352497594, 790510488, 734295464, 854342993, 999610464, 620761083, 767742344, 235174184, 874773291, 624201581, 815080398, 188342840, 371842308, 939194113, 852928767, 652657499, 817369621, 614854964, 453203774, 551407712, 699096411, 705055547, 780781647, 321656814, 385862264, 85928873, 300692331, 678684351, 120011662, 735584336, 527690193, 790515950, 868669623, 603883528, 217466522, 855616916, 660196817, 845540867, 273499993, 254192723, 694358771, 666706615, 645763054, 286168359, 727300873, 532457391, 43003832, 170204350, 422518343, 947654308, 574167677, 645626117, 945607201, 542735900, 685320487, 366221387, 230529006, 409773422, 472875821, 709577376, 801032056, 740830868, 51538542, 469369696, 77406672, 813350152, 552968528, 673791239, 225229775, 205663862, 786688701, 176306956, 422243110, 527658493, 510568415, 682245454, 592406766, 847743954, 820578667, 830034912, 373970368, 806327924, 566529993, 516526444, 285312740, 886104424, 809905263, 623686604, 426659654, 645681381, 232945425, 68128278, 909176104, 161713788, 644253273, 588404918, 828240957, 150260697, 328749007, 476060571, 114600678, 135001089, 673140275, 365439013, 416424678, 644060071, 864787817, 613194722, 393923865, 866870978, 889793885, 861865710, 102915296, 256337588, 614063701, 767674342, 716229356, 150124209, 968811881, 564065141, 375653299, 527637992, 48686693, 150335930, 378745956, 212028729, 732050540, 862181103, 340083089, 414762063, 959842447, 833911605, 983332929, 353604631, 44366063, 687822279, 888168686, 238190510, 808831972, 563099313, 967871510, 845853609, 66208014, 36617996, 938833023, 222902138, 488301174, 692166263, 139693364, 205176816, 921771151, 930159289, 481391862, 557038577, 465332151, 482606905, 996701952, 66247429, 727031819, 311807070, 73660129, 111020327, 145266747, 240923858, 131613367, 302799568, 548838018, 876298265, 645908321, 964300742, 276266534, 621312810, 721784815, 500260074, 619281019, 683238664, 868776652, 707233888, 832531814, 280823841, 674502504, 90865619, 913683729, 842972115, 945967240, 926890243, 760838143, 655240474, 286670486, 514483584, 816190499, 666858598, 435379960, 313264412, 336667109, 373246507, 282413623, 442281779, 276295425, 267898608, 189406036, 599761947, 99047858, 804313191, 814305045, 967582946, 92553991, 965052562, 223541662, 133044252, 895188983, 43923505, 820256936, 8594043, 740168068, 492939924, 711099256, 218566894, 944813295, 424283290, 61327394, 626058633, 741515909, 712179036, 653967523, 715107228, 751981527, 3137913, 918542318, 725007031, 520858238, 69450244, 839892895, 155869144, 937976567, 39643643, 644910253, 868051409, 885568722, 393526762, 229483146, 70003895, 64860386, 887739113, 128700963, 758553273, 271566278, 816646492, 418291717, 944548856, 399782106, 831628998, 376708256, 812214926, 470034651, 31789836, 28807170, 374287928, 776560793, 764269717, 799733444, 748907506, 380034697, 895917184, 404831593, 183687816, 745952, 944191970, 509268923, 600980427, 5085298, 714547544, 382406660, 729990061, 155344396, 356028284, 149528194, 831015131, 674678123, 490489722, 430065616, 53570901, 482246653, 410184220, 334612217, 810601908, 828203049, 572410539, 527657403, 228224705, 214139651, 950886686, 314580937, 129067424, 589263987, 91603442, 775722452, 457016009, 534903576, 637161065, 719531877, 209424915, 208069716, 752095594, 903274913, 618476907, 243974664, 277212057, 76885468, 796375448, 974645489, 24556775, 285338503, 123154396, 551747290, 111568229, 46999531, 230863837, 587333606, 691557862, 481543386, 625537143, 790306826, 997033083, 954250167, 197159879, 406987481, 511246551, 794438953, 82295816, 106753047, 734799017, 664600551, 168249693, 167157596, 758413417, 519373845, 62559757, 703076654, 726147534, 654504152, 750182552, 5264990, 15922142, 917974257, 316831820, 443996663, 284087452, 844875327, 279146242, 417926613, 483629159, 383181748, 116237977, 408538347, 602146203, 961904220, 142700688, 562814588, 920263661, 718640522, 998173338, 809140976, 932469993, 572186583, 894547704, 156069635, 514345330, 772451942, 718237761, 801885816, 175146371, 61598703, 863247014, 605820245, 206981152, 68404201, 604116784, 641547639, 568741525, 536934066, 935590773, 23653388, 149106803, 548946924, 426149657, 326692408, 594743368, 695108009, 866838431, 301511561, 628519622, 805310959, 544911922, 57886393, 495120213, 812554999, 483002266, 463016315, 998417223, 666747464, 26515421, 301017550, 472342633, 333022634, 897247115, 978458544, 625752749, 950263734, 92310953, 754996106, 480528958, 27722696, 75653458, 159238529, 722627505, 609465531, 90252449, 322310944, 31642264, 131515499, 444705042, 649074604, 379237923, 132195596, 119998172, 828962578, 898593598, 273412104, 476024050, 4691744, 442569029, 849636847, 904622886, 955571047, 222935633, 168794944, 573115349, 741911696, 304202440, 936926723, 760321100, 575543903, 682718866, 400328710, 525289560, 822239178, 815183269, 817713730, 926901807, 32127581, 272993221, 298745498, 111813516, 360645676, 401403586, 644223332, 998249508, 31600255, 829507382, 816246621, 579917048, 130089293, 652837932, 920066782, 821334313, 90514469, 350411779, 400131314, 216197299, 863952707, 456280890, 560188289, 773206930, 148650077, 672029565, 585208908, 116431784, 685210989, 971178315, 240010842, 448516288, 16254123, 565203423, 110907214, 982732622, 902708667, 819433430, 230416152, 48752405, 465763617, 231065968, 500581465, 487572986, 718193419, 990965742, 953416798, 776457902, 143368707, 158913776, 466462100, 866263181, 515896352, 972975201, 684560309, 894291144, 338949867, 326373275, 123112646, 789189837, 581926181, 17732616, 851344473, 184711382, 461032758, 273594742, 571678423, 860215006, 724749278, 427702468, 82506316, 670945348, 827789646, 559117106, 401369614, 697218993, 667648338, 988268806, 947038199, 463646942, 546115687, 97510810, 99569623, 829736657, 103305674, 29229871, 550005752, 154579876, 744489439, 886664995, 386125615, 908051924, 19736711, 401271857, 604399556, 306617997, 364652507, 586968340, 781873588, 503104593, 488002539, 586410121, 768846050, 1568432, 818992504, 7660625, 224557192, 255343396, 767900074, 585557136, 306599221, 773730806, 73353819, 891720632, 50908631, 904627298, 855529184, 43126526, 968407908, 881762608, 559155108, 134192569, 280792979, 753461065, 900957975, 263234229, 44208724, 87645819, 655477151, 233967427, 407749621, 212623287, 478618156, 566917681, 792173789, 966169951, 840914823, 237786858, 926234103, 375473205, 910693978, 944084181, 45421831, 149547911, 38207073, 51686632, 614707792, 104856427, 425021309, 401633962, 94751769, 244941043, 750126923, 448097611, 623233884, 204095126, 507432378, 166202606, 122524828, 605197623, 776785850, 685650400, 331841512, 545711454, 714010478, 216636264, 984384218, 404488873, 54131301, 56062909, 306998960, 633046080, 276267690, 194603695, 472147326, 15185984, 628611355, 277440106, 590285907, 875651847, 974237284, 719676543, 174143026, 518017108, 726801932, 944456157, 989133564, 798939736, 769985371, 82041569, 441256904, 210350810, 521474088, 734098578, 435775015, 689526258, 736890258, 565145607, 49857634, 267134755, 717545579, 739822624, 281879211, 530606124, 730607789, 168727429, 97834024, 337856638, 363074111, 861213638, 904341948, 261635739, 932107255, 30452938, 48409254, 297354743, 162103906, 454598914, 34186374, 408835788, 705307603, 337552519, 321641288, 241277747, 369379670, 567396904, 134986305, 695314153, 404110092, 754917643, 790827746, 535059301, 889740079, 589446825, 90604502, 556159162, 668176069, 896513407, 391987402, 238172319, 435834827, 43391744, 973969804, 48416097, 358944138, 509782945, 139625456, 559444596, 883900479, 834792492, 682790324, 802552884, 829648362, 352517731, 788207221, 899858942, 134819556, 621650791, 412441163, 915063643, 887548612, 411437797, 120317155, 796662395, 425994519, 936900104, 227353806, 720744740, 17266916, 169285698, 752787598, 848679353, 112364338, 401141318, 733764168, 55858987, 103004765, 39944461, 54906123, 205273841, 973602612, 942819055, 61825655, 93301826, 485952105, 164406926, 845223727, 679506763, 391680125, 554553421, 571657240, 73595615, 122757790, 354157299, 150688560, 276376243, 523638912, 810520648, 476866392, 904314344, 38053179, 210873598, 603618974, 438570548, 142469442, 290568677, 893005246, 49567424, 617727696, 521610602, 618011574, 638420441, 341063479, 96294263, 796185533, 709721583, 798283654, 312405541, 138995958, 709272470, 798006148, 987699783, 325398884, 511675272, 590142503, 774432085, 10148820, 406562717, 183971506, 874279690, 19464947, 948277442, 568139416, 943667805, 574992148, 991268467, 236753669, 637636823, 43640085, 583717194, 972092724, 295279743, 61260554, 763512092, 581909167, 163217939, 148941335, 126166204, 150916561, 381711653, 538618169, 546746730, 952017771, 513459929, 431201762, 89528089, 8548438, 559853679, 94887378, 927744167, 71653291, 740173671, 32063491, 312321850, 57973410, 991679818, 839392567, 898612627, 834553983, 436369257, 644991453, 832386995, 938693234, 699894228, 14206193, 658850009, 432583042, 325336156, 2017106, 366384796, 260300826, 60919533, 993052492, 794683065, 918075298, 205580301, 951019619, 975593477, 265482399, 969456666, 57956716, 792598880, 563455480, 436192097, 690520685, 582618554, 260757957, 134367008, 955407464, 812663967, 783729153, 580231398, 81835895, 430821380, 943755880, 741126943, 374756490, 398723405, 453215474, 248946356, 45483650, 43835542, 870458881, 713282757, 235785518, 531230255, 661933192, 252727748, 70146922, 118156690, 987210600, 141993235, 601468995, 889008403, 636986991, 298595624, 419355583, 178200335, 674820236, 160936623, 884847754, 935220425, 501174492, 659575282, 756210355, 149812858, 595788790, 874684823, 47211140, 320735117, 793610159, 675011797, 394652841, 44857752, 722438102, 986969957, 103850695, 301225586, 654151211, 234011728, 259958319, 295080655, 136706538, 452785692, 481021383, 115520790, 365727621, 997088003, 45071623, 841714903, 787060319, 364843656, 195461527, 827127026, 459147883, 651183239, 118368451, 246920127, 317715813, 874385144, 544755707, 305642648, 505495417, 840161332, 698450842, 361262978, 121252920, 338092984, 633814892, 901076050, 74831546, 335399023, 74856230, 12453937, 904123315, 644357029, 186796279, 456160770, 243611970, 657494820, 400279817, 482387450, 975726499, 429259375, 832238962, 612281269, 598269967, 296854634, 644151908, 763334758, 569677954, 592901958, 608758975, 51813314, 873120703, 907643013, 603557405, 731284175, 314622742, 609236123, 608679428, 319463638, 175281955, 596859643, 644970081, 444844174, 316948019, 820327300, 843869552, 567108503, 776242629, 450280760, 949250668, 670853958, 582014473, 831968209, 190593455, 974535914, 647543843, 671463718, 532563503, 431820998, 146460320, 206291638, 515928881, 862361568, 896724018, 982747716, 938051336, 403604782, 256805610, 104749047, 538276656, 911456011, 975368893, 401643676, 569543605, 967727735, 545979119, 455271450, 85200834, 33816116, 290436955, 213806573, 821784743, 437644754, 394187563, 108117940, 63496517, 512403146, 80411999, 505262537, 622606409, 217765854, 766050030, 285790230, 959204863, 187333399, 753169501, 141271239, 389520933, 462335941, 980801386, 180291396, 655802756, 947183562, 94889144, 274831586, 131095571, 109003229, 813827549, 721217896, 161108571, 314621071, 492343666, 876114107, 73636738, 589095043, 924972392, 197631930, 899162227, 282358044, 929309417, 254890528, 245900069, 656489844, 665046564, 217247169, 359675751, 177277125, 450598091, 983506699, 330382298, 913886350, 493957722, 45481941, 384019839, 882682410, 502017352, 462995930, 957857740, 852788741, 418426246, 608130514, 273922584, 356220908, 813611614, 214487950, 741091149, 869773729, 893380408, 46781772, 559460274, 395363551, 197874410, 101478046, 389423897, 343649548, 944120608, 315190705, 786339034, 439198290, 589460741, 789166110, 313079000, 673711264, 747451599, 914912580, 541357844, 991159504, 615465879, 275506511, 448689159, 978279083, 835259544, 543999257, 24687318, 908666056, 279332005, 729723883, 516302641, 605964459, 705159115, 663261779, 384831929, 434184409, 531735619, 785367151, 557881968, 357603987, 891126518, 598032362, 31055738, 97820923, 924133545, 815336238, 561488901, 56097497, 122139263, 749523833, 59884775, 341755541, 866095435, 315464137, 77598137, 174502776, 189203630, 602987773, 205920893, 17429446, 179025913, 502496808, 153120931, 752291006, 447186540, 487138560, 948921569, 291680212, 253600639, 90395214, 289067518, 451101410, 547791463, 421063291, 969595279, 306175125, 406763569, 864735434, 982483727, 599590376, 217680334, 901167557, 585216014, 786244347, 160480052, 422615502, 99387364, 762112403, 374864743, 848003242, 77602407, 178270711, 396222631, 971761615, 177748879, 348161389, 802983027, 11913253, 493651836, 868344718, 90877235, 129660921, 627492804, 73371451, 983441681, 298122262, 8152844, 979818347, 307882985, 895089115, 771679146, 808414486, 407457050, 503285195, 614840972, 342929459, 549965672, 344996240, 87238266, 35458675, 714809930, 605169889, 682626401, 776540511, 551156960, 691351312, 962295238, 626221321, 863972724, 29278597, 468457304, 749753627, 147711730, 509893903, 94810845, 211621586, 721567103, 901058636, 654172457, 401715456, 545843713, 317460982, 192680383, 791897081, 564178132, 790014838, 100757419, 680995064, 812719090, 961552685, 613357458, 64763884, 576092755, 358580603, 470939552, 675202461, 451306154, 999876339, 119171633, 533613119, 987008322, 449507825, 740047442, 181868530, 869945832, 369019657, 920946484, 635280211, 804018697, 500679846, 745537736, 425306021, 152897328, 202841691, 366797627, 825436644, 687363010, 734577782, 444621678, 776494496, 16083514, 745337355, 188924033, 348598556, 827908871, 115309849, 710269220, 297687841, 924756512, 823131383, 249303202, 734208123, 444912918, 59554789, 84223398, 688585079, 62200453, 842083359, 980049132, 290993973, 245471651, 753578616, 172063049, 987348048, 489423523, 368975402, 159457570, 687922523, 675862684, 288947500, 358855219, 71303348, 810512326, 197915930, 953536947, 36401469, 199196430, 967892885, 963818708, 405115570, 407802255, 399521244, 921808441, 728531559, 394930638, 721154429, 93797015, 39687564, 136828780, 316138329, 663225070, 391522423, 319873735, 692864702, 997173652, 232296279, 259435829, 98585663, 646637451, 139095057, 868684859, 964603089, 608595472, 459641968, 130988088, 246045199, 644587559, 456320423, 924917484, 881886535, 43361075, 150343412, 686888672, 232192739, 265414421, 250488334, 783410977, 978691742, 288922073, 503694916, 229737611, 479789616, 70285402, 936475020, 774343921, 17274824, 226108933, 788431057, 397799784, 192540886, 105930664, 731417747, 254553082, 720291425, 596464526, 511360628, 553006632, 297268702, 886853745, 941920279, 380472650, 504978217, 58298503, 355176448, 923418073, 387687218, 676698940, 157599566, 365999746, 437213782, 496873955, 401710291, 233551650, 16975153, 523933492, 749021060, 784273253, 519291477, 343687585, 93830913, 776999815, 659438029, 947046894, 578309902, 111728011, 667415000, 357582665, 558883773, 830776375, 333849278, 721722182, 703540756, 898570374, 617124387, 310787083, 774334607, 772413005, 794459560, 595783345, 895633763, 34416355, 409114322, 915035757, 316654196, 772560011, 949583102, 974102427, 395781286, 990743938, 147323388, 400043070, 349311507, 921454242, 474764869, 437229296, 304901550, 693151514, 326086363, 253675125, 244932862, 842929624, 13282319, 475239205, 90848049, 373719392, 560711086, 183781342, 271831595, 409396200, 389511672, 462623986, 726496289, 709349406, 958355389, 74189009, 845300554, 58675752, 352831574, 864587334, 115366442, 609513971, 934845243, 35643750, 885915528, 911273591, 816954089, 437247942, 930241408, 170933878, 20604308, 650123995, 709383080, 482773516, 283646983, 373432115, 904676107, 444534127, 531094891, 43995747, 157281359, 169239209, 604056518, 278049886, 132660973, 439015261, 287551777, 54818071, 415686787, 218330469, 377529158, 839957254, 862102121, 151043944, 674950136, 483167665, 849126797, 241481054, 922737226, 784746057, 614746993, 396043846, 834335070, 604554326, 730756514, 385495111, 674377389, 956379977, 618305763, 337785935, 715440644, 476972793, 802308420, 428149247, 887740980, 368144840, 85353542, 249523063, 276382215, 976332091, 98153276, 494916727, 946366131, 344065388, 72009121, 929805104, 80873833, 320602429, 919267454, 470275413, 140854826, 822495941, 817491610, 666985383, 284740209, 18716842, 209938324, 696184993, 236965932, 578667392, 506509357, 785204807, 846699167, 767665314, 394963136, 334413827, 368171370, 482615567, 737658627, 117552309, 76450895, 445157856, 340498158, 65574130, 448058823, 315729914, 979556668, 14630130, 904904952, 44172352, 458335033, 504051238, 854000915, 662700933, 281384055, 506081984, 503903839, 145261992, 151445689, 927469417, 528118494, 88281267, 894116944, 115807196, 124927351, 729722350, 277392278, 98191301, 327349936, 142566864, 254881259, 874156992, 403161705, 989767753, 552612175, 40427362, 527620265, 89550006, 538429069, 247953851, 183931256, 510305736, 958715645, 27694868, 869051946, 312870119, 856399506, 400740567, 890945059, 733473860, 603796796, 808286810, 969246206, 868976883, 912387714, 519024913, 539864705, 412882258, 889747215, 272563010, 198088245, 308093706, 680768634, 772158495, 978812588, 280637011, 282555321, 869870544, 318271157, 856221828, 216451469, 595255797, 376782223, 684968008, 759816298, 144167171, 574205142, 929047629, 355330925, 302416213, 469724939, 947829143, 276146311, 763306375, 460726273, 737494178, 638825071, 785539555, 710083490, 882370261, 346455611, 471854852, 335361979, 136826708, 435103126, 844328474, 868180702, 220022580, 257223934, 677936320, 14671391, 813270396, 15710393, 919057131, 752304937, 822014627, 407790228, 760568240, 185970632, 760380959, 949184336, 268453583, 642531661, 968139014, 169211546, 611416364, 354863554, 210214008, 701285014, 617848206, 287025237, 5318640, 124590067, 766913767, 331985859, 780854872, 627796985, 898425314, 186695148, 865405493, 751346933, 762588586, 904982268, 51115700, 192568706, 29132853, 715023727, 28570065, 81358613, 343701056, 898252970, 576704912, 741378426, 203033417, 671063232, 785526687, 888065902, 321377600, 627763203, 981446803, 96120970, 479938043, 987141460, 943224019, 512366250, 852714074, 379899980, 107071413, 530507645, 55300908, 597823255, 892858167, 297502490, 550517556, 984755957, 981917255, 138022217, 337271484, 949808621, 24650377, 387718345, 469310635, 305953421, 188264951, 968642843, 132467493, 418745577, 889150904, 84258153, 95161213, 443494753, 595902024, 891001573, 517428278, 831384917, 91626797, 253675083, 963101964, 780726771, 800360336, 178014068, 709308416, 949425695, 640714251, 207550165, 707897245, 974917586, 594823928, 905138312, 837108710, 683557234, 652273201, 367851126, 316971601, 303069439, 432162576, 199290590, 619667187, 726805345, 679128959, 912269828, 96268891, 746215224, 516526659, 175743768, 875196862, 690086086, 252201484, 566388019, 782882236, 137075038, 321711624, 512419296, 650204411, 307762804, 965121313, 438651448, 336839422, 185351177, 960778884, 340651733, 835682389, 928222948, 429260244, 78806605, 537362978, 554855102, 781171816, 419601749, 491924074, 297878948, 914319951, 76966368, 461638852, 442909041, 234435927, 415528462, 893342427, 453624218, 105704223, 762344355, 845418225, 270554669, 232123815, 51115109, 718049547, 67851399, 616049285, 784732421, 927185976, 9577156, 474627485, 326528843, 231403147, 774274924, 382524038, 308271310, 33445745, 139727837, 248085934, 77457391, 322849257, 976383339, 813849395, 899322820, 874679746, 110835574, 344643414, 358754932, 371434302, 821388655, 260605552, 442620237, 951610963, 450332860, 176779883, 111867346, 892903248, 498764257, 694953669, 792857581, 628229355, 562994707, 66497461, 106298323, 278122870, 572593785, 436870733, 572721622, 668881828, 180107548, 766075694, 385441364, 112918300, 423982389, 447523912, 96187471, 616701601, 514933772, 9400477, 924143705, 295995027, 469623814, 121473651, 76135021, 176985357, 723696159, 315783421, 337462972, 699565982, 96321467, 230026055, 608942560, 454013562, 37328281, 6226158, 543175927, 547927152, 669055477, 732078064, 327975341, 242118642, 379383347, 115307271, 62547668, 386037581, 847848534, 368133106, 301811262, 815159943, 650874510, 6610665, 932848416, 410932843, 207289493, 793566364, 886005647, 811797370, 989840316, 440796671, 382278245, 660790301, 149691151, 262630483, 983936200, 10160859, 818574610, 636152082, 599839463, 253176246, 473472964, 658581596, 330045502, 392216654, 722130960, 220274359, 371833359, 132544099, 984208176, 798416404, 198180975, 965268905, 661821990, 295530165, 673940949, 577071104, 591967766, 928931597, 367242190, 637987145, 772524160, 251621324, 934126591, 403672712, 25954882, 76598895, 875234480, 10365108, 709232600, 327839019, 656747799, 688629858, 740532162, 584034555, 985067624, 268909441, 301879935, 140291245, 480677240, 196547519, 436136950, 644334751, 556210480, 905776854, 812831078, 262066944, 143805656, 670802242, 694411898, 923983490, 51135633, 750844230, 216591495, 183212770, 603734896, 535985853, 48308319, 440033330, 809099784, 857589810, 981197910, 207525349, 829985644, 146687324, 626187141, 577517817, 972689526, 640729464, 130861076, 999302083, 514062771, 190821441, 212862011, 246813141, 369451481, 914550944, 47567079, 821062161, 166021817, 970546084, 812627705, 279084238, 676490359, 947722702, 351408433, 361154436, 937109077, 91923324, 166334042, 889787831, 253730049, 989911782, 928913374, 940956891, 685223932, 61699272, 797638545, 333640474, 432637638, 787687668, 553225501, 880890464, 885696854, 397606740, 829426099, 819792404, 531716641, 483221066, 865402521, 911765533, 449904398, 847733500, 138465491, 85569405, 28288348, 285394937, 170342054, 895089897, 939936556, 120732502, 440061965, 421660926, 456095193, 15897264, 470313662, 185697389, 574287421, 461787190, 860090592, 686290821, 303183329, 891117920, 944586299, 438954930, 503368482, 82563807, 130517307, 846457859, 880407011, 822314222, 302055157, 159486794, 695093537, 145461483, 481075175, 801479217, 834691539, 20538128, 193200153, 678420992, 295503949, 138039823, 196614693, 555531364, 250330811, 811372081, 760591746, 303014091, 500619917, 311709537, 278891613, 601935342, 963263444, 900190846, 771612218, 822436847, 647037262, 587952537, 696933423, 968346167, 259615459, 983735163, 936253262, 545826338, 697939069, 831467829, 244571288, 714137746, 568661112, 940668198, 944679119, 923366414, 468992775, 603841188, 23988697, 358820016, 395550064, 69504218, 87171965, 721760467, 751764017, 648693369, 432636867, 943043743, 600405146, 706927965, 67381461, 487260800, 381405647, 760188543, 293613717, 846662087, 85055359, 159800756, 997510607, 910355503, 185908729, 775202980, 992227391, 609527152, 496299628, 584513719, 507829193, 338835407, 888227410, 654941591, 808315709, 944770255, 861394266, 979652018, 816533438, 781289530, 644939830, 681921615, 249490102, 78477911, 679545200, 559417025, 840463968, 488779434, 923382244, 619971862, 555872294, 54032763, 196126575, 700415450, 694612797, 21377429, 389852150, 581927608, 366910142, 995476030, 220549731, 603850177, 555291635, 828132043, 434126545, 259773337, 336451282, 75973494, 829458445, 725794027, 871439186, 905841179, 975078434, 547054908, 944789768, 705411467, 986497922, 802074382, 876881151, 335581922, 348663554, 861956468, 152419514, 143997610, 745448980, 104532376, 157461435, 834253089, 611899538, 794195452, 464804029, 443749517, 34193413, 489623521, 230260220, 159092739, 291906959, 430301064, 957817843, 960741374, 767218762, 512759558, 539041532, 383892026, 542183075, 96505862, 614081703, 142566740, 562194765, 113784384, 12529021, 607132482, 15151804, 964577886, 886198175, 389771128, 586455776, 989436403, 352964607, 177131479, 521161974, 874807813, 139466017, 83627168, 819880164, 869055942, 282924254, 204313095, 945273561, 359126467, 597693132, 925975971, 686693026, 538571049, 46412789, 864626821, 548864691, 667003151, 293927924, 148604970, 772885730, 563538268, 550496729, 415766291, 987145060, 897006840, 323346684, 395995531, 517987997, 303300453, 790154721, 909626644, 540196536, 100810964, 925326678, 506377382, 610316070, 985987989, 607131854, 931495812, 570215717, 458244077, 994460092, 271883382, 730940026, 944244720, 482331242, 371730676, 887369551, 927279438, 249736161, 584237821, 448804101, 993074467, 150406190, 932722509, 969701251, 657216141, 188361118, 75540944, 932319092, 461985603, 953238763, 299938175, 747565366, 781736600, 326127811, 493624139, 992531689, 742789451, 382192287, 966395750, 389082114, 750089157, 156525144, 299222615, 42879007, 290637483, 231691017, 586334906, 897987801, 681812492, 720030171, 891086281, 183470388, 264226255, 85234670, 639142651, 989692943, 511944157, 534325709, 125728565, 638052388, 234604890, 810104329, 786068194, 678424485, 207548671, 317508662, 112290165, 640278950, 382789498, 316893425, 861480667, 579393553, 423945170, 573192301, 232019063, 134873293, 577950646, 559426174, 712291603, 805205627, 968348071, 196249838, 11273598, 900890342, 852607553, 2092480, 511080642, 177240960, 41991025, 282019292, 702635969, 156040542, 479734814, 828870412, 278764113, 327364761, 206616556, 656772247, 548974322, 315074308, 540039087, 35209794, 33385118, 377659826, 324094692, 936911919, 562528769, 699014555, 310802219, 909291484, 692358284, 29976384, 445452689, 509044045, 620488420, 891110788, 815666156, 475347377, 893716856, 404254587, 204196159, 281162520, 236110427, 261210854, 166025111, 665028857, 858260367, 890803065, 541040632, 450196625, 318551951, 118420016, 295310347, 177489350, 327999170, 989086722, 406245948, 782584111, 187896846, 235470538, 478932399, 858380152, 65838457, 761915555, 454489758, 741023771, 401844800, 444908818, 748349166, 591227847, 954570155, 618853600, 724592979, 799570103, 841809436, 255002747, 222938470, 429579245, 655928815, 262239002, 597595484, 239416391, 228709147, 736776686, 892520131, 145269129, 889161014, 679683110, 934710844, 479917953, 389543161, 629265212, 28883113, 191025099, 543313312, 185575710, 444350106, 55229428, 267468801, 768868101, 980227238, 873235713, 723785255, 778035336, 78274878, 65447628, 347440985, 70670310, 245695741, 421176432, 649648427, 452988508, 987329629, 181368479, 649612571, 864339977, 8286834, 697277444, 27550235, 884508029, 626700206, 132808698, 668176243, 787300225, 54307772, 130167509, 298539950, 57011203, 445804423, 836948877, 699275234, 985715863, 879774960, 484377972, 687853990, 554657569, 643786802, 551904098, 785717044, 912231894, 640923634, 617072265, 277974177, 470978826, 585705441, 980293258, 111951931, 637579820, 668727514, 262455814, 580261118, 387068369, 128241831, 184198682, 78218521, 931004966, 420962546, 843515939, 317665992, 613204656, 307289048, 840385811, 193262438, 61324030, 372605339, 298049913, 198586775, 73066831, 86584475, 770145539, 109594817, 768928559, 647747021, 731904339, 382809585, 552383279, 674200106, 254398644, 200568701, 717108682, 210484212, 17324687, 255153733, 245606011, 817820092, 647664186, 443138215, 358615268, 280346724, 978355719, 41966747, 307605659, 809043273, 892483853, 47957799, 642788996, 95780706, 350936185, 968613140, 246099476, 61121081, 23470314, 597565214, 134959753, 445583888, 973575203, 259914712, 415871824, 190481887, 660058837, 611189687, 430885489, 137973310, 209146025, 895140823, 748549999, 133294602, 78988699, 925188432, 497345012, 72718333, 692861073, 73109324, 136435164, 272642619, 384798509, 627649165, 542287902, 794898764, 801226296, 667248942, 988745423, 830405924, 963908103, 67103009, 866546522, 464302623, 509069996, 976843215, 230452633, 718696203, 785857939, 259028654, 579477709, 732080055, 136335386, 709251730, 548389016, 209676699, 738496698, 767542447, 963827992, 356509277, 704159518, 910092100, 150657723, 50741583, 354343274, 238880448, 567698747, 716515387, 571372127, 231365434, 525971805, 91906832, 3594602, 33615066, 911385668, 972698466, 343225181, 553396326, 960406354, 359951737, 512229221, 592189505, 651087507, 799071390, 795479601, 351663978, 148635677, 926003189, 460364463, 182635544, 717103329, 839250927, 803427691, 947428484, 891134371, 595004107, 913962930, 612001139, 205250125, 629994181, 853432742, 833022171, 164511390, 699876546, 83274973, 95604156, 279146206, 48659543, 304966079, 273488873, 797654205, 392699493, 662206963, 74708350, 529544416, 730013989, 762022558, 853654917, 27245213, 320656874, 989611388, 552683453, 659599435, 950395368, 229697563, 570133185, 77415048, 135365194, 200063614, 184318016, 550197555, 124487641, 716938895, 831195577, 801034811, 775738536, 138254562, 468684293, 389788379, 317159797, 383507328, 559410039, 669310546, 692847564, 779721311, 826646435, 723374252, 836718883, 172633754, 685273946, 267577752, 824804561, 206438216, 956915911, 679017582, 626167694, 234280253, 845846980, 150377798, 946256952, 808167382, 95612590, 245633876, 627871141, 282591039, 300677254, 989254351, 403796095, 956479534, 620304679, 962294757, 976716696, 382037163, 383446885, 995527043, 658189853, 174337925, 586664182, 286938684, 238077493, 1128307, 301633106, 594866783, 243288409, 954873759, 83821218, 693162893, 753185799, 110027549, 452326758, 522028900, 233693856, 201564575, 241882300, 30710011, 987888151, 162039324, 292757802, 522041856, 886829877, 709704384, 735727774, 715413099, 87066061, 157583319, 697044486, 876387139, 709426017, 362203080, 522771670, 449039494, 599193577, 889418432, 122319170, 634091149, 487625888, 527577829, 533203620, 426243366, 419135114, 783066495, 428601772, 335418352, 90149537, 11031146, 128225836, 117073344, 786496485, 627070974, 953891074, 37510795, 619903423, 73631200, 240318414, 482330508, 482165088, 290185580, 146095876, 18670628, 286150061, 538055448, 377362910, 738774635, 491972670, 185313693, 146399327, 463044504, 863117849, 329026786, 664867878, 685832689, 228738536, 291584996, 58373247, 174984021, 646644752, 170069709, 363896840, 906220289, 549471596, 47913704, 223405988, 303274584, 478316723, 159823190, 69410919, 240396522, 847932345, 852222255, 842326651, 474709214, 525539321, 603590103, 916341304, 601671201, 731087050, 115636628, 345631330, 328408428, 221367692, 364468949, 207696819, 334508108, 626958220, 167873023, 965848071, 937686607, 158728445, 840229221, 998742019, 775463311, 765322689, 844323707, 743642336, 334193743, 523263675, 60795740, 659698335, 206519976, 868983671, 994982622, 389994576, 331596265, 261328850, 491014006, 720531436, 688811440, 931672213, 455093993, 231715702, 289113247, 471270993, 178480600, 976884947, 232690582, 626720319, 991015645, 987596899, 209741862, 717897922, 599522881, 241410652, 813053529, 638842442, 483065153, 785688159, 217469483, 660592843, 253538978, 247799960, 397484047, 118955338, 89509069, 679792859, 993161196, 705612378, 333786067, 646931039, 337155301, 721224774, 490087558, 651501, 961233097, 924088050, 315885639, 42108183, 970314385, 114021175, 944274724, 107834385, 977833912, 930307576, 513141792, 458452002, 84545576, 603023254, 790567496, 535495113, 482673637, 952124154, 225268086, 760853587, 90731450, 332582604, 942559062, 930137847, 458625060, 301921063, 441543456, 259150286, 512220117, 11845456, 626039040, 732192741, 830868730, 678264807, 209181403, 962606415, 154830778, 283382922, 885993852, 798773008, 120151715, 217783974, 232610471, 937006066, 702743193, 444441761, 130310874, 810675237, 431852514, 366908409, 409177174, 639236574, 304650325, 246817502, 46327543, 14644535, 945926370, 750376370, 865330364, 190954518, 179507800, 934427703, 331454190, 981072265, 181460726, 977366428, 352419527, 138510014, 161772273, 589657898, 553010396, 324167031, 970301578, 717977855, 684076619, 876116007, 727796822, 833456814, 65312880, 242977977, 532634994, 9477022, 489298688, 192060412, 555687952, 462420809, 232521611, 798590253, 508650954, 331458908, 466554699, 543131577, 318712368, 726732658, 131051438, 91759003, 214048666, 554974843, 368742350, 45970065, 131018213, 496957436, 37747138, 30221812, 282842211, 100950340, 61773625, 911393116, 11107252, 471398835, 407818318, 187285431, 561714709, 458538337, 28323369, 560514097, 448493139, 448569341, 124989671, 617164589, 309237291, 17962098, 513936494, 271430107, 226219306, 382900537, 114124839, 356573247, 461879186, 788607678, 594345, 996006626, 389403417, 216053564, 861370623, 26130081, 733436704, 86032314, 80826352, 765188105, 917070145, 421878481, 660854217, 377021137, 529869069, 562793779, 796514386, 732698378, 183626306, 619438472, 957669601, 975280602, 229478131, 576037035, 457838935, 202246603, 457853510, 287831885, 66524419, 418873459, 484263300, 487092045, 883332572, 280013565, 539412224, 682459499, 630520705, 116604355, 292772434, 101682370, 642434787, 440454927, 384772311, 488273760, 979486450, 728072219, 168640950, 264485091, 591909416, 511576048, 33458089, 580588724, 183715259, 322658420, 952715429, 548677654, 51025091, 766141356, 860743050, 337149838, 305550020, 121017817, 793435641, 786430604, 907616539, 899200508, 522136004, 851666335, 441098977, 574992432, 357038122, 207887139, 750881487, 223274962, 43194540, 881059582, 981473596, 500973007, 302561920, 620768474, 425314151, 227568780, 625251324, 905976266, 800119508, 351217418, 985378387, 652749762, 431268606, 200408952, 801112549, 213048144, 709643566, 733420072, 94473137, 876066258, 825663372, 558484231, 725152204, 301715101, 290260179, 10142952, 295476243, 725972353, 344252157, 413840560, 586945060, 943768233, 404480097, 271531321, 299743521, 747669487, 623483125, 937288591, 296292587, 151639943, 40178234, 310402849, 732928233, 644639446, 678980357, 264201457, 357452761, 56591632, 223130917, 909512235, 519155852, 184875884, 187011448, 758478613, 831025656, 799225721, 657072571, 56207609, 501306361, 54415289, 838860323, 660017997, 794543846, 139731383, 440415215, 931596203, 728052447, 377807727, 174183005, 295915771, 488893916, 843282439, 528385792, 353712634, 707382768, 88750845, 751247076, 204240686, 805779579, 900164724, 225283834, 233925202, 298032640, 443227858, 578035899, 690408302, 522430129, 109281438, 203029005, 83458298, 732660580, 881905479, 660910260, 995939664, 1533222, 347827400, 77679339, 95459853, 344470314, 549103187, 863403428, 596994802, 585046838, 795057146, 527324586, 592355627, 300672287, 250565546, 165933665, 827483406, 27867909, 100042483, 790330979, 368616054, 515920351, 569178545, 430373230, 489689537, 308367723, 260724209, 898368077, 848505717, 72300348, 194929321, 12459285, 11366716, 586233983, 755049469, 510016615, 589409520, 809161962, 177624440, 477810503, 689680582, 30896378, 881313617, 367978309, 697815512, 92499016, 705196058, 457773955, 235327608, 639977947, 771066287, 293900663, 489235567, 819782450, 185919305, 9946597, 235738961, 947137340, 314629171, 434668878, 732149352, 642012655, 805225147, 954387127, 922306309, 208114506, 557966881, 152843300, 986866282, 653321515, 161919311, 954682917, 708102132, 576288081, 570165759, 368660853, 794932687, 440768033, 148970103, 766945059, 567138732, 521902510, 435505053, 79703989, 281358882, 144834454, 24352959, 795951346, 905611558, 324267718, 190653265, 529300049, 166411526, 337024187, 329374670, 8120402, 242414094, 687147658, 626063976, 881987027, 288948573, 871535172, 245903786, 517075076, 155676150, 662740234, 139969102, 837424460, 304227836, 474502811, 87441389, 665883954, 98524551, 504474714, 456237690, 928246409, 796820784, 17073783, 167229234, 556603187, 64165224, 697560588, 98506856, 932753721, 278792156, 530487587, 372889949, 646815170, 116200624, 527597065, 618896251, 574178641, 712613491, 485475459, 66652020, 52274175, 595353864, 840433623, 937214941, 395407587, 979984651, 42416671, 894764438, 253590402, 140935146, 197131948, 688381316, 401549320, 517796652, 512189684, 25330689, 821466819, 242834083, 729982696, 761434392, 193534767, 172154121, 721973207, 324913058, 510423583, 660869409, 428975321, 750372185, 405393955, 376408884, 975740054, 127578414, 433855257, 598791180, 218602954, 139794380, 734796373, 251035835, 412585951, 788985407, 833901641, 782802766, 665936799, 619951324, 71516015, 873386855, 756183225, 238099075, 745234696, 185756180, 983407354, 714057624, 967317916, 312756143, 163424660, 913703168, 127552451, 451347486, 731983812, 356658019, 876649290, 885122672, 887709022, 961003625, 114957649, 710185673, 979820182, 768086067, 325526595, 895703770, 368878374, 214045945, 771838741, 617164218, 672098605, 736155093, 400591986, 765963466, 394736496, 214666494, 713493381, 232808884, 269359, 419190045, 492516852, 749602246, 901508342, 74472179, 376835101, 427674435, 420811947, 689776040, 863915821, 343324989, 469052665, 339251354, 523108184, 420760852, 566547066, 415610175, 163981049, 950901097, 855420234, 365562586, 182333846, 630963161, 149042767, 800531937, 154618439, 403533256, 631242047, 76082585, 743308886, 895507065, 652818324, 361525400, 998002156, 815273059, 887577843, 468416455, 762067028, 102652597, 653633785, 36591287, 573505953, 587180279, 449403522, 300518673, 31680347, 232891659, 682733813, 425569702, 854216171, 294497656, 521712515, 739293465, 530371586, 959733486, 707143793, 114238386, 186782298, 162852958, 215075198, 401321026, 70024512, 304608613, 419987956, 113264464, 393890821, 62508115, 592013828, 300361752, 368238586, 728095340, 805305157, 973028023, 959685159, 874254685, 542918352, 283377047, 397887482, 838676120, 81971065, 149629881, 256796346, 722551451, 127835090, 182297476, 950325049, 908514172, 872679431, 701382825, 370789044, 303101219, 348482562, 737675681, 756250742, 486636947, 407477501, 428116765, 538371512, 859554047, 341020706, 307486962, 886466826, 225968129, 135163463, 743725480, 891826936, 91141026, 265724544, 713262379, 711803228, 573388257, 665389254, 175485300, 852577495, 934405415, 283619255, 817495299, 178036095, 238225972, 66666436, 861397174, 714233904, 466841354, 233457883, 607839050, 589692161, 475558151, 994727038, 288615172, 838678206, 2831112, 97323642, 754841129, 85718371, 377552143, 221918048, 803305384, 156411239, 331693421, 505521423, 699011167, 164530005, 147189091, 335672103, 780150994, 636738281, 447551765, 362447663, 375908633, 723559917, 388178658, 886695479, 892743615, 784220110, 272495575, 211331903, 944288766, 919430762, 472502744, 690527923, 53909304, 212359889, 576731443, 454097321, 825034430, 332125957, 767566892, 447711386, 405668828, 317356509, 784045609, 178694991, 250813837, 645921950, 468392157, 259890654, 245763242, 669936962, 600900129, 412079808, 163085066, 889643036, 544925442, 236630065, 440977918, 331589878, 16616683, 554612145, 808047558, 589092301, 662230331, 70944396, 608232740, 715560647, 180867917, 642251075, 280419429, 841921341, 911287337, 978523113, 740751457, 521310548, 227674582, 473836769, 765806401, 681386382, 55831038, 724926991, 317945807, 511292475, 924878636, 968502091, 148934437, 620927372, 191383510, 349854444, 961501149, 447561396, 998206428, 64109690, 748032450, 221271770, 114865752, 113979975, 488911462, 673075479, 847384481, 353009995, 617253041, 313306595, 240146490, 448271606, 619811389, 608225236, 592203972, 915600649, 953106659, 527239049, 665548430, 296688189, 619513299, 260495933, 124323684, 506677759, 607182004, 245835222, 625965628, 528512673, 38739393, 394699974, 459521718, 312703614, 646780319, 794978036, 853757565, 576301953, 301413681, 762449383, 139426151, 233248356, 54962488, 274315751, 755694998, 601548780, 764822650, 452918991, 918882713, 268116256, 374283648, 981531487, 268265014, 492293563, 675866166, 119285859, 364129782, 485956201, 199400621, 920292413, 249556812, 749280524, 250117203, 955125834, 917759287, 805405387, 127842476, 813387152, 397784426, 859188483, 607409822, 894798880, 519176406, 810568589, 586737144, 48597192, 777116399, 915418575, 507336709, 554132494, 579559638, 642135143, 938384991, 492222125, 992841295, 875373168, 212383256, 86263690, 630459993, 686234698, 588498309, 887144640, 231152392, 518900017, 781727302, 697963245, 717506677, 980545022, 642302034, 348415033, 204435241, 739851812, 175473772, 426501930, 665633200, 19784536, 86799306, 519220252, 235653978, 103152350, 834215198, 598871549, 810043661, 79608387, 168577748, 44016491, 274184306, 270793362, 528976808, 897561480, 487036523, 322939413, 800704947, 740076994, 920535348, 707261814, 319133545, 969302798, 269825968, 912972139, 833488316, 818192584, 945946284, 943869149, 355525287, 671854541, 73438707, 516876101, 231851029, 396905039, 797442885, 936921577, 666301425, 356956241, 963999346, 223895655, 832374555, 165001915, 615228349, 999355943, 465170500, 660769615, 960861693, 953133003, 705625562, 914910808, 337724409, 999193699, 389535419, 330047855, 72942719, 699524753, 8238083, 630032566, 455800723, 173165159, 233182346, 494797847, 950741898, 24015500, 965058985, 352506967, 765323711, 649885412, 438941541, 628810055, 378837995, 160563904, 857865723, 446048701, 312021314, 453331054, 546552229, 108808652, 115333911, 405898713, 77581923, 564063607, 892129998, 713993922, 926427568, 692255724, 359693085, 493203680, 39192962, 539767605, 20642628, 456027431, 974451248, 3394009, 411515322, 983954584, 562392125, 672968219, 796569846, 722856513, 277902841, 100392650, 671951295, 30165245, 147105775, 508541799, 173595995, 654725233, 240202319, 523642459, 264504770, 269276039, 819822956, 585393037, 888389746, 841828863, 36962482, 659629110, 254077377, 120449830, 924539795, 732925721, 311815185, 123264733, 825440440, 53138620, 929112731, 88867294, 736089833, 722685725, 887659796, 213639842, 365190438, 52039113, 887645291, 60768736, 90013755, 293575068, 363385186, 389021038, 807681941, 629646833, 389279047, 153651663, 92492013, 867108869, 524356228, 397792030, 176870650, 813336141, 500701508, 544390223, 410727770, 481441492, 511200746, 980394948, 725305544, 523062292, 285884472, 224063541, 383530452, 841501627, 499268614, 19517295, 788188313, 74239864, 185815303, 25225607, 60583072, 961819436, 476316719, 529407477, 179360901, 174337199, 453811707, 746921698, 472828443, 248366099, 215182457, 917679912, 260398888, 484196198, 178286779, 392165264, 982674832, 646597883, 274726024, 695654657, 988573667, 61872163, 558642312, 817679408, 806988918, 655247870, 59196105, 411706242, 541875474, 996785005, 730646616, 604813597, 734298726, 905139724, 166944353, 777969408, 241692506, 114119498, 612476506, 681276230, 428332327, 984075453, 408037393, 267746677, 64531503, 990995779, 927125731, 459696851, 666212845, 447451952, 313746951, 376322177, 770271986, 603633059, 526574301, 401477203, 987376504, 920974509, 20087913, 742535216, 872645307, 175790442, 865065765, 756048637, 605221504, 310362095, 514086804, 581835095, 975148676, 500854353, 715412305, 708614247, 99654722, 266940, 482904621, 182166742, 861658082, 196628958, 824391791, 681878787, 571409969, 811983496, 273620051, 19915793, 296475080, 620847097, 457440699, 957802564, 327930746, 635852543, 168038063, 894925419, 452818433, 472228964, 184271887, 771840129, 941197106, 777321156, 941760533, 764565475, 865561748, 39617509, 51000983, 919618824, 981062326, 294005214, 816174001, 439289243, 461380181, 30016694, 525882593, 523243198, 945412251, 918757844, 646185212, 578234660, 904795300, 453655635, 390120024, 82635185, 340135591, 363107839, 837257739, 111966891, 430023492, 166446045, 187744594, 506217115, 389922205, 47706800, 921970035, 698497101, 277374644, 136795691, 810857112, 641057220, 162132998, 28524017, 403827858, 915387837, 415614807, 550557651, 844250532, 269818830, 15873343, 765430602, 436989592, 41270237, 763240957, 568727147, 385409316, 910719212, 716623259, 86726827, 369589996, 902481571, 213792647, 100681792, 933789824, 402330310, 835808749, 903859533, 409096316, 746452742, 785441759, 552158217, 589703086, 206385267, 911467551, 45043854, 998457074, 901489575, 696507471, 651425093, 169014798, 689111503, 164891841, 506291510, 138494360, 534754613, 22188041, 452390466, 166173145, 635903458, 480324945, 979655946, 802036078, 217364315, 626593430, 793763432, 815075599, 364695268, 473453515, 179191687, 427241778, 445872068, 59532848, 509128725, 399038243, 958301361, 287735274, 41382930, 453812930, 838057908, 387232891, 50713270, 393010187, 180413290, 43113414, 102149420, 861562674, 866949839, 319187780, 161379108, 876591323, 645055646, 244162553, 752379071, 222564340, 645553425, 769535566, 324097413, 789169284, 670627154, 447159346, 483649146, 227395903, 747623665, 539667022, 290592768, 258014876, 726336517, 646027059, 950849758, 520384256, 649575008, 70447522, 172672894, 289772670, 4585933, 873607768, 957453205, 731748920, 283693437, 161708153, 952340604, 654367446, 454721446, 986654506, 359104130, 701010370, 262720584, 850129295, 43272741, 386784834, 970343338, 855713120, 26482074, 427102425, 52660236, 356346107, 567416494, 845411189, 24874973, 498801892, 149451198, 928393241, 219776720, 855160793, 796756888, 938502537, 297772219, 344714023, 290038904, 591622274, 275904303, 775219238, 318668135, 723287742, 545801568, 328292310, 153340680, 800150687, 302174147, 22088036, 880804228, 14044218, 284559113, 499802170, 118915368, 599866244, 489046944, 66882094, 588790749, 899821139, 989772004, 82019433, 209059029, 450586584, 720651777, 238328097, 613411562, 145073868, 866032325, 848706923, 934204705, 623064641, 550589565, 814470275, 830308755, 22276261, 944728670, 872929336, 922996945, 836489157, 648523709, 34799265, 511285985, 109091915, 825022993, 375942777, 723028060, 736923045, 869159556, 583497354, 520647326, 947691488, 218944721, 974225458, 218111035, 290640182, 702107428, 308651330, 676077713, 266807701, 864047647, 413863130, 837730510, 643402136, 962926627, 304107140, 482084197, 424730363, 207174370, 106197371, 583450981, 909011791, 589737969, 441411451, 287177722, 47910024, 818524057, 285781511, 456846096, 32194747, 120949932, 791221771, 240958837, 118424129, 31631068, 597958117, 723655166, 934175422, 856065122, 295343388, 864015962, 376344370, 899630890, 906286798, 481503403, 378257274, 394389573, 189843087, 632098511, 619847051, 31471639, 455757177, 616764918, 686847996, 245554810, 90044307, 578898509, 878275386, 40469328, 756481548, 121849742, 627959000, 366876278, 992078090, 15997464, 721783309, 961962528, 538394850, 337592752, 825483331, 99979962, 179805254, 918203255, 590464278, 270001547, 824381350, 543886234, 489319078, 470115186, 104364152, 436807837, 155258611, 13503010, 227677752, 960853361, 579048892, 147176315, 330681488, 415481880, 358404239, 770933342, 803270394, 269180750, 185362632, 260743592, 970701062, 297274974, 747068165, 386613260, 913583765, 683224602, 604885824, 715127528, 884155284, 476826845, 777025350, 454308463, 315492237, 574966866, 810246610, 505932291, 793396848, 948251803, 318348637, 840923423, 69897854, 947018036, 559005044, 295990103, 948674468, 665807899, 381073507, 1554218, 584869824, 462266226, 858400184, 50226691, 92198801, 716134725, 375334421, 795704843, 403353055, 896742717, 588287551, 965137270, 717201164, 984327485, 498422077, 690528915, 745211201, 791448934, 152279904, 357655654, 865299716, 938255140, 650033559, 664835059, 201504501, 635225874, 189997056, 733157209, 789701848, 245798506, 103437124, 966774604, 954228284, 937325339, 691899751, 717282920, 950971053, 407073405, 248085598, 650302263, 236680728, 404331160, 668371320, 321839571, 235047939, 481949015, 170122206, 657150372, 490241441, 682019495, 158438370, 890279448, 720796624, 27259780, 193481696, 214917708, 264420375, 727031833, 657095520, 754554124, 48697326, 76863449, 192850644, 540902259, 668690448, 660607279, 141593022, 473529427, 209392791, 249097962, 3019310, 572535739, 414926579, 604155824, 128737921, 567982047, 878965982, 422108339, 987654964, 759027218, 912469002, 986486574, 577127573, 523188205, 691593952, 220175812, 738098292, 703886905, 974462252, 833141944, 32381676, 614235418, 60094797, 387863322, 965876996, 358241824, 880204293, 214735964, 574352956, 703432283, 382024624, 998291849, 65524781, 720060477, 239942004, 781470459, 902983496, 206784949, 318896066, 964499805, 238755088, 167059976, 348754321, 100274242, 240690837, 544411492, 830501230, 71639328, 785503796, 531415799, 435541113, 363357966, 808056479, 577622722, 925391982, 442847184, 565862472, 156546062, 636098198, 595739302, 31616990, 670754246, 796642305, 13397404, 96980893, 764195026, 928080639, 604856410, 414764058, 522298316, 527610955, 54113323, 973517079, 387045075, 135125237, 207164046, 21956345, 824542203, 572123185, 729982733, 594310293, 728565639, 935102057, 893126966, 843040787, 787649882, 636259842, 769706526, 500965438, 438350185, 417933775, 728701446, 648122573, 76129266, 988577165, 533885242, 631855720, 653231325, 819382011, 165887530, 287039309, 802211628, 232446386, 599254511, 660990439, 85323859, 123142199, 766466696, 707242774, 508104420, 166826430, 111252673, 978632991, 106277912, 17692303, 513834522, 271489947, 84367308, 815136282, 387637864, 411920647, 203355783, 896578754, 52571039, 140507971, 156124287, 891916845, 166000077, 829070326, 892387940, 542711984, 206671449, 71915814, 436929605, 878606705, 396365251, 342708598, 639522066, 21341416, 441023227, 783938909, 980669413, 184484809, 185669044, 746475214, 688359282, 138856747, 710214725, 332254700, 30157970, 536586961, 761808438, 941330020, 805106123, 474534012, 676058116, 286559943, 76095522, 549086192, 61510584, 737998489, 828066357, 787364358, 575262434, 122800790, 101978149, 567279140, 386733948, 727820138, 701358576, 143934296, 646263019, 12454431, 337030256, 763600131, 65954601, 202140646, 409881908, 284051251, 626842636, 122613105, 798378926, 608082102, 273390570, 640817478, 133308092, 745871495, 953840110, 985477135, 557649851, 67257281, 603400982, 791936496, 552502386, 612503686, 555523612, 837849652, 753903592, 568449827, 586453627, 776875154, 423770213, 864143151, 837492427, 722744268, 581932755, 65062830, 129654599, 759513836, 488776070, 615628724, 488313079, 607667504, 154316434, 829241801, 3392231, 902291708, 860604915, 491349908, 844759954, 351715143, 569998588, 518492493, 881515812, 357349302, 253769856, 579024766, 504857405, 515694012, 796531349, 967029191, 797653003, 335406576, 891223186, 873172428, 554099246, 310162333, 392271043, 262971767, 280281608, 318734789, 749904024, 804433356, 273913278, 80927476, 765956240, 626377985, 971823614, 170190573, 436589484, 281444764, 158172847, 887982508, 876848120, 147004822, 779220207, 124254787, 805214024, 201090656, 822327914, 860872350, 720428376, 764099609, 897956935, 281416671, 617722014, 660627958, 815178436, 318997454, 630504514, 476787069, 187028754, 343970539, 336502135, 396321139, 981530985, 159229667, 44440419, 99053645, 909080543, 280920142, 55466735, 854563808, 440297295, 510878852, 720795601, 615565530, 403869557, 468407321, 70317533, 893865008, 537352221, 758683061, 438455137, 329302708, 877842560, 428356756, 927406997, 827082479, 467358486, 166836411, 548237337, 285002563, 283175489, 195447277, 638618552, 274147200, 449016510, 581025446, 723247697, 809041728, 824542615, 412225186, 814994694, 829791417, 317033926, 87856880, 479001947, 886360676, 229344921, 855153788, 79113547, 802104377, 968716801, 151626258, 129744566, 408201318, 785984467, 503943260, 785704929, 648848701, 394201354, 681604023, 822559947, 989662760, 747316713, 229106985, 608654997, 566782575, 971261407, 676287192, 630013757, 969292856, 836643180, 735651708, 497502129, 601551188, 737667987, 520703202, 578234151, 936555076, 388668193, 582102680, 718038156, 352429557, 770648241, 783313988, 61360085, 736447983, 386493070, 403041837, 978974961, 528399966, 123213273, 586235516, 398884156, 621581027, 494093996, 166167009, 674743574, 254314824, 106190143, 515383803, 938300164, 4209049, 208334692, 524883220, 592981818, 502087991, 617231149, 684109734, 806466830, 477143107, 44371606, 700182243, 852748847, 551087239, 204465206, 897037567, 983948593, 901022360, 556178284, 740470654, 286837151, 261509877, 580736514, 385015357, 403875469, 929530461, 238669238, 984515965, 79108220, 573724580, 836931529, 352366534, 513407711, 900698142, 765120333, 93390432, 684578245, 663103540, 582006377, 469892053, 601537778, 141424392, 962795, 986151333, 504333977, 715399314, 722165357, 407045245, 970883831, 8324569, 251292570, 573937574, 297369479, 597815965, 909138350, 557885413, 373570706, 114990739, 685285343, 423174574, 972783452, 54499526, 67403682, 965595031, 972766352, 123976012, 889548238, 280645750, 428400091, 782225492, 407289007, 877161084, 800282893, 971875779, 159511246, 654890786, 300496791, 143920864, 160334441, 404107032, 228721096, 327861599, 824678303, 416794854, 468793247, 299089270, 58948106, 718321457, 439535496, 575362235, 658956772, 214779393, 321356764, 128277595, 517014739, 478649867, 164028593, 283130633, 264668999, 495499403, 265406333, 185244617, 640109586, 541964080, 102107737, 208632254, 622769333, 494824630, 361490329, 377983550, 508273231, 54518568, 882484350, 530206132, 854014421, 755849296, 67115340, 487154481, 408161320, 935323257, 614337247, 666581733, 48467536, 187657531, 760725350, 398566643, 7146981, 862334201, 247318858, 905977933, 926505063, 251734645, 781733046, 180417150, 812532530, 249892605, 264572052, 670975080, 350914986, 48110274, 781125092, 875364558, 811342413, 422431626, 278719547, 554239262, 151216417, 203411972, 501117115, 588148429, 271937720, 417721374, 642515507, 593731267, 66317909, 167637304, 392653590, 438937617, 934449956, 218410264, 560497207, 187328077, 957927334, 814297997, 210897623, 1736621, 65784617, 389020276, 80739363, 190749363, 213618867, 74507180, 838983167, 286006763, 701420066, 788042374, 233564653, 626303688, 767659783, 102157104, 575175238, 783039212, 826771243, 528025973, 796183707, 536690508, 870526778, 290775053, 72711500, 534832913, 811426858, 614973193, 153212346, 806849296, 569066799, 481470404, 973453723, 769594014, 494863706, 103797606, 546764144, 320714185, 343519312, 751131670, 673793282, 792203483, 461312105, 428652545, 906905069, 419045137, 942952407, 723905365, 732436216, 514671916, 607962476, 905707742, 385506023, 616954609, 511797227, 395393436, 845246109, 137281336, 582527239, 327383115, 144698449, 734454466, 302640917, 555853804, 928950338, 30571845, 792887811, 813082976, 464359094, 444088916, 42382745, 716467208, 822465668, 473360169, 677599386, 406104537, 406157769, 942403393, 395890256, 883398976, 329214518, 811093956, 484346013, 112427689, 253025662, 827388074, 104744403, 793966794, 86386380, 724718446, 372172864, 234153571, 208559265, 63894885, 954768878, 58844523, 864673059, 389090435, 678138465, 602904272, 268200102, 707794195, 595335640, 529858382, 72068605, 377076331, 259593171, 783348123, 308077516, 927019126, 824260369, 716173499, 767684277, 837690464, 310702594, 217029763, 443995112, 574670376, 482718544, 423892576, 718278443, 778858710, 754658302, 519088685, 640410966, 167427289, 24640306, 25396055, 441568582, 694929726, 541769953, 636961112, 785822928, 975346943, 829567802, 34575367, 352245586, 186339924, 175653493, 14771015, 618591565, 635537406, 724117020, 44130500, 284622246, 693222051, 734735526, 10707727, 831624274, 913622003, 287127629, 447394049, 538957140, 225015351, 403210480, 687725188, 227988701, 931691055, 528054326, 877312542, 343338675, 167221927, 329056752, 80671282, 589218802, 212692264, 565152158, 869591138, 429376342, 427741423, 486946529, 587436813, 441879845, 965931196, 374936548, 292200415, 521946388, 563599580, 85086446, 824607339, 733133206, 207769554, 121068678, 220982273, 819716431, 904338701, 166961063, 611032376, 705352073, 622934913, 791340340, 260483995, 787693585, 1141885, 382826863, 594729293, 597077503, 391246996, 966016791, 527623542, 815845976, 745160503, 677676842, 979957941, 482458670, 250427855, 26066562, 311853539, 142913193, 1437168, 327924165, 141804407, 901560767, 96295118, 97201883, 355215344, 241170962, 705473909, 688417915, 181768632, 734058242, 346993362, 423378831, 359295436, 62746253, 970169904, 839611581, 888687981, 524381672, 444789438, 312355128, 71386364, 445292750, 936224837, 225298350, 417946729, 382556084, 231430958, 507699243, 20177194, 86983407, 189408402, 181576173, 923900999, 390819236, 228006998, 719498010, 14854264, 374790777, 818428871, 730863724, 550633298, 535662714, 948502360, 475801421, 68412321, 942830066, 932783346, 480016279, 422515395, 47079310, 756255607, 159091155, 681799741, 332332050, 937143978, 967389007, 367629092, 648049359, 162700922, 321055878, 431934915, 634655793, 156104156, 121365093, 611057091, 700302677, 7970501, 887164879, 558922168, 715763865, 883700236, 656013012, 816655114, 770519940, 39703092, 653455782, 223307600, 346309726, 367314466, 890825165, 420817712, 372623970, 335842284, 566954185, 485756128, 552618784, 442011521, 62159854, 401894087, 261397022, 97059186, 503564230, 73918081, 959162967, 518136418, 367163691, 5151872, 293041074, 316308309, 108403751, 242536931, 904879232, 829805556, 552320838, 248257532, 473124737, 158575116, 107000174, 30777235, 193406974, 452496193, 196258454, 265589132, 410933835, 737880189, 975688243, 416716389, 987572830, 423018127, 196037969, 80484779, 651989071, 212384199, 115089402, 117437275, 46842255, 31476731, 361197388, 57072281, 693718105, 535234437, 725466115, 613456351, 588014580, 94056054, 487495648, 714499364, 550023989, 348905769, 974193035, 857748987, 793488284, 759950436, 196492441, 168751315, 29124177, 184825221, 667834565, 856368161, 607855159, 246660047, 277461574, 521003894, 891376467, 595113166, 301941845, 111112085, 61405965, 281597724, 974558977, 408019621, 468088668, 502197439, 279310647, 993253055, 665756784, 788847572, 879992124, 950425600, 345539690, 966023400, 316942471, 715070914, 591088560, 617503772, 556830379, 773995748, 787558050, 279577058, 131826995, 382821256, 601427851, 971944853, 633452488, 701461651, 438142824, 740416759, 70319907, 643663437, 149802151, 923642170, 975800469, 848854011, 977778823, 947359900, 969666151, 931222119, 82232344, 167086195, 191365846, 601927763, 82166781, 766998849, 182717297, 536148644, 264266409, 604190474, 936534431, 673671095, 728572654, 666279050, 618196195, 36390107, 400601600, 175978420, 387397013, 814283125, 239259002, 188023759, 200639368, 837038613, 904635935, 475083521, 762929324, 223257130, 146917543, 816709699, 288857328, 377527898, 918811345, 722647861, 539028034, 855355615, 279931911, 540135654, 946488765, 531906198, 466332306, 838934537, 988469880, 335297279, 449464400, 278921077, 675351171, 811151232, 528885414, 710379774, 986918920, 713459063, 98123610, 807198007, 236117898, 159753681, 605036646, 259804088, 172174940, 665595227, 104936544, 284150804, 619867428, 606215411, 5319512, 781096240, 587856773, 623108420, 79564826, 228366713, 525910061, 827203853, 653552189, 9768312, 756794031, 218171069, 167853888, 133462236, 295297030, 105201825, 5130149, 710012840, 543872285, 567746776, 234321210, 873445553, 867252354, 800359832, 129641068, 140072106, 695689235, 605588829, 243752918, 604799203, 318258411, 960675943, 232609091, 430555610, 595056434, 969985172, 963008384, 185716810, 885261382, 998828995, 841347603, 618839775, 389267491, 84957415, 645521653, 983107324, 994778722, 283239140, 392853065, 570455082, 525265864, 760049489, 741772905, 264601961, 726686951, 613524876, 145408112, 40625885, 997814464, 180337939, 728791621, 695830015, 141109775, 931308825, 385772875, 368714641, 937563632, 123544261, 446760123, 824198134, 588324798, 90060186, 828382319, 974133799, 340177401, 105123539, 26622071, 407820287, 40771786, 756632395, 911235955, 990491678, 53345035, 97502339, 67092938, 665080702, 921172153, 626201914, 195577084, 390512020, 992043794, 169386155, 149899531, 166684397, 16796170, 164466954, 119590137, 481617365, 609288569, 184388031, 628854697, 92860676, 983844939, 99680427, 686568426, 571075120, 990032557, 442417389, 251450581, 164254410, 381164129, 944068115, 145002272, 101983817, 243608349, 697568159, 412596375, 992308126, 494904352, 428526819, 845656805, 268870021, 541225861, 519160783, 5099334, 950882778, 678757245, 884626617, 708448589, 664696998, 615677040, 217265113, 872804716, 567443681, 513882041, 123323350, 578067717, 57065278, 574759808, 775492680, 187557473, 607175842, 29180218, 2455119, 18319952, 132596647, 103398867, 637481407, 605336769, 520564366, 920851443, 58903899, 880531705, 165458715, 588677045, 764846640, 297423995, 838381573, 224583871, 899659010, 268323702, 132967197, 822224955, 155696800, 565510980, 834486992, 18256804, 252649333, 43819866, 430367059, 500977729, 797867259, 940973627, 282513313, 491961969, 598882054, 13602513, 679674211, 481554363, 586945915, 496495700, 752232056, 954166397, 954298366, 55025888, 565313035, 918603932, 412570266, 22153414, 803620999, 798817269, 571500583, 38196439, 156666960, 811340418, 138134232, 370769305, 119794266, 630864467, 238318747, 558279114, 599064212, 553610059, 792871213, 747154688, 621483479, 291142516, 101862075, 415000410, 490998600, 615681028, 469291876, 241282157, 479336353, 627312947, 598677488, 618819578, 640186835, 816484044, 760066970, 491271083, 88260878, 636406709, 531369929, 496853294, 470267415, 143282696, 747704526, 180207084, 765816832, 661865365, 876685690, 446608755, 660681025, 307535566, 359219886, 831583227, 815032603, 672575391, 783653862, 655277325, 944355197, 390941478, 484381181, 946609427, 620170407, 782579233, 751725101, 983199507, 818953684, 128673169, 219526396, 549951169, 717495947, 593452942, 419247680, 726357612, 18382476, 734815070, 572905901, 139546327, 320139298, 54138237, 150915940, 395035118, 672869950, 514868732, 199267821, 615974640, 114057388, 739864921, 389417176, 644860667, 740342322, 186751832, 201880925, 287548787, 21329501, 486365551, 765273525, 669219675, 453795955, 250296480, 719679999, 952992405, 731270144, 870695960, 750098028, 186352894, 383961924, 799664893, 465944661, 411987498, 470245369, 23594191, 547566212, 743774299, 891557239, 942147372, 597576533, 357372628, 728050360, 510288758, 951440146, 410551828, 607457169, 635126707, 415989863, 790798273, 965524170, 893455338, 811907037, 316922844, 809393335, 556536212, 66661633, 643135678, 410903180, 397258366, 95945435, 408402347, 496201055, 690634400, 332769895, 686150258, 946988254, 997524376, 328236901, 691213884, 433588440, 894221098, 618683502, 549797117, 820493944, 21849067, 233983857, 971203012, 735347595, 864928653, 756487259, 144521247, 528392463, 770921151, 63286842, 649572421, 342109802, 677790049, 839286235, 411762911, 732728370, 874725433, 404540450, 334657812, 982352847, 597947922, 336347042, 244517921, 401108928, 604070846, 246533487, 576752480, 122791025, 159407012, 98018885, 149300758, 907576475, 582989493, 656486610, 729186244, 593416575, 66645207, 939899866, 694461893, 711375394, 764363426, 348523616, 423268482, 830658001, 39295969, 120548978, 374234511, 794449039, 351001313, 555062424, 28520307, 281935654, 488020862, 138889010, 193876725, 62662983, 379490308, 10947060, 663964153, 12199270, 272938260, 896325792, 918042111, 989752174, 308315644, 193830720, 611436517, 447015411, 217607258, 351124805, 289496740, 259742886, 991696562, 878104069, 911155562, 945159481, 101906088, 630001906, 84560183, 566159088, 470042817, 251625904, 362325543, 310900152, 14987631, 437814157, 15030670, 569630791, 327434574, 327550948, 26186724, 205152207, 777284131, 205007434, 294932224, 913112300, 878054253, 374228747, 253043513, 592849847, 49237040, 29306282, 433331498, 245280766, 183603567, 167252171, 567699306, 644539731, 357712723, 682672537, 798432371, 297886765, 623731830, 260225308, 431352164, 493101145, 718654901, 933886506, 191764377, 288517215, 843296759, 801745597, 790147029, 959206572, 642836159, 468362956, 372053143, 706561128, 655631550, 297371956, 354061014, 416854565, 309982049, 521087665, 345653392, 749903572, 407200424, 568669943, 849567112, 15192838, 725869046, 899758914, 793152637, 290837835, 892644475, 857762152, 453070873, 266558755, 696416538, 517386318, 50036308, 581667743, 704226191, 955470580, 374426073, 237211940, 420828485, 45175313, 125090090, 692258263, 592263696, 15200387, 27595697, 741910346, 603200540, 743988815, 729359887, 732489696, 615065305, 76817202, 651434099, 512910478, 600690492, 456588455, 627352611, 63581066, 704665403, 178897911, 144808632, 182585581, 827401883, 265170395, 347102582, 225262649, 711566667, 64342827, 172297813, 680689415, 653157974, 455027868, 225951198, 926260588, 488613261, 723122790, 413538635, 526292865, 605058272, 122444762, 499063910, 239576106, 855545608, 366999014, 52576115, 654862668, 516321679, 515768005, 946404237, 824035465, 996537835, 452167144, 316440751, 104837732, 180697653, 34266449, 918274089, 203712902, 764898797, 107257420, 427693199, 822768566, 94451989, 586892301, 433896931, 929634829, 422140343, 362538623, 465251389, 977241649, 757073661, 232342709, 302511918, 680290054, 181027720, 961740537, 557527184, 822812203, 41813544, 638055631, 870810303, 735037865, 418981743, 463511022, 320911808, 63706573, 257138435, 475416110, 809623404, 594260350, 857652934, 454694824, 858602992, 969595721, 326968804, 14988992, 432334801, 322679960, 314188775, 493701495, 1584241, 891621337, 872379884, 986673900, 429590064, 449708667, 884353210, 484647236, 767717927, 292287281, 937636319, 703385172, 333613842, 12038761, 72765034, 4629036, 212319376, 786654340, 671726618, 51605123, 13556407, 398401616, 775360784, 785762811, 133158091, 690696513, 674415586, 673707909, 497796836, 701725222, 94192824, 410125685, 786989383, 805904451, 412862013, 379374435, 63670185, 318658974, 347353204, 943204109, 913718582, 951528951, 838054244, 231290062, 952677930, 694177863, 618921755, 184658152, 25263442, 385997495, 142754720, 142552457, 274776214, 809241935, 282743041, 766959763, 481050180, 251570295, 705475545, 386722760, 230383380, 538197624, 919653811, 707976563, 231838108, 537326870, 458669111, 908015465, 263853802, 685861186, 202563917, 366309202, 586940679, 955502075, 179812569, 432980022, 79930227, 547834923, 538476664, 693116219, 643881604, 775827007, 120993376, 638437849, 42601814, 96508068, 517387810, 95291891, 941984470, 964569443, 25494283, 815959562, 787711518, 518893947, 479078916, 909037807, 323130480, 706037475, 573730142, 851003861, 660361587, 613700741, 566428083, 637235230, 479175999, 682993859, 684835656, 603223172, 316921672, 178842642, 242839228, 487153888, 685567124, 299490793, 145839658, 625221913, 204315802, 290304084, 307043469, 466356150, 215147396, 78745548, 618602723, 953110101, 562069561, 694890071, 340410824, 33636060, 854874903, 662873406, 823310730, 831822412, 321719658, 930704739, 282035251, 417560903, 569331577, 423011538, 709600013, 332351873, 391464047, 167737715, 629624495, 856206434, 826234210, 697305010, 152885062, 892427253, 29637942, 270421413, 34673425, 882372067, 804532432, 871781568, 742390034, 402880953, 289632223, 939524086, 617785294, 962688520, 960021553, 368271433, 283745154, 476425574, 462479116, 998042622, 398163969, 940256407, 82549069, 838396746, 371892746, 705420883, 268679931, 859521948, 388041221, 612300846, 595583727, 474357807, 863823299, 446828441, 183897515, 818364938, 315364050, 389213110, 434982132, 6343493, 340098552, 937729566, 675867049, 6824016, 496951707, 203628591, 839810773, 722757306, 264053774, 775718649, 555443808, 415528797, 434809260, 642234792, 692186694, 405341627, 873715142, 792290732, 495417002, 415539990, 286166750, 331191828, 608110787, 719200625, 918985067, 192485553, 965301213, 592154672, 36807349, 294124513, 552399006, 541290759, 105068730, 307884250, 589854908, 685494170, 805964384, 31875127, 169103033, 285111080, 201032005, 625515179, 48026210, 397029570, 817454832, 497217729, 752862461, 372519251, 26306954, 73147961, 316888808, 596915705, 483516859, 730906767, 861222836, 967216340, 868868788, 233422130, 833254589, 109244862, 127023207, 27757930, 303200182, 248407370, 655152703, 393733906, 691343563, 385494745, 819688892, 131913159, 142553484, 525075633, 994192992, 295379830, 124323748, 850685329, 353405161, 227421839, 191971420, 343431203, 617771573, 324501375, 981275176, 567797423, 143371399, 500238099, 846272276, 466980313, 817426716, 294469226, 103033984, 812725381, 506989377, 60851078, 55315776, 963023795, 990941898, 664863468, 441446069, 509293157, 10289983, 875757321, 750312219, 367943466, 29054920, 327609316, 633987446, 420126758, 781003698, 183600821, 227136872, 171356450, 780622788, 744747104, 946449902, 107669309, 832192553, 629929208, 458490493, 547108399, 302766754, 22066636, 146395869, 968152701, 621437442, 678991292, 715353943, 856000396, 676641361, 404219440, 303715791, 360141438, 383432141, 744456336, 881961773, 788571532, 782398489, 776643166, 472810939, 132010569, 726342873, 421677461, 84965271, 389408152, 304101699, 737683122, 634075591, 242558542, 969695879, 73878962, 447693755, 333134928, 208553345, 700106979, 101005444, 502839233, 968588110, 301214674, 86078302, 565025101, 946587577, 5004926, 242908143, 105430837, 607089096, 819096348, 438763921, 156791832, 843483562, 513102877, 736794236, 635164566, 545868062, 343711869, 962801428, 297202258, 505419493, 637859373, 206843930, 946452462, 595585659, 653011644, 37763284, 670080065, 969997130, 219168554, 204609473, 745717117, 566476591, 77148512, 473725466, 798642833, 136079116, 869909785, 230771057, 748288891, 364001209, 927460218, 996075513, 680430909, 42441610, 674549448, 397174874, 878110845, 884561876, 219080884, 75077426, 27011483, 24185976, 396510846, 879278485, 267557403, 280322417, 410844278, 870455215, 326409524, 849196762, 365413106, 732548957, 258006568, 846700589, 401415954, 51563804, 978610807, 218837934, 237197069, 879996354, 620870954, 927681663, 744796094, 236238048, 39893115, 461657565, 976900460, 881764632, 510309740, 813134240, 468295085, 958722941, 276304042, 377689911, 956863880, 802574705, 350264517, 576683798, 386489803, 276943744, 544178554, 535528091, 735387198, 47239867, 511748969, 613569565, 577026289, 440241817, 894369028, 442294696, 595541233, 759430860, 230658750, 33194482, 9018475, 772487398, 823225496, 739246458, 642639746, 72435085, 784029723, 486064082, 640736528, 446789989, 258899834, 443225817, 596626310, 498286619, 773364594, 947480794, 835197406, 760762719, 41907061, 883648337, 2542583, 37352935, 358409243, 560526881, 467454380, 349422184, 515182609, 934320882, 365701333, 965364535, 469163560, 245169175, 748857412, 560654164, 203960829, 265071699, 22830403, 58590920, 781669190, 630576597, 107482783, 328192249, 721949577, 379734539, 909579292, 813616762, 221416409, 410935964, 763116134, 985177126, 509703536, 712930735, 233085423, 32440014, 415317994, 149826509, 766898405, 862759587, 393820917, 704227059, 161637746, 718214728, 481726854, 392868702, 855117242, 881619325, 223740547, 746058325, 575605063, 961096072, 501003615, 80398909, 877348041, 695475912, 947140648, 884024653, 480080065, 194783250, 456051991, 717923226, 854891835, 766897337, 887829018, 91690281, 901618733, 772610970, 670226974, 273476133, 990547810, 32989547, 897210953, 816375976, 740141462, 590994377, 258446298, 372417164, 344795065, 95619953, 397449674, 862693153, 371263306, 101075464, 446398609, 609922743, 828611072, 903739689, 522297594, 664117649, 419154370, 869152036, 298633688, 423454105, 187810731, 489360810, 720057777, 985418768, 473673771, 328792264, 468341710, 704041164, 330948557, 843503911, 626829699, 490934662, 387876112, 276679881, 366734048, 219251492, 647061435, 374949591, 943556929, 334267900, 963936199, 687170980, 261784422, 233661289, 666768851, 176585140, 761365346, 458524679, 1365341, 734297995, 777269140, 651733478, 478798108, 661958776, 235362170, 544666175, 545582226, 493427706, 402572203, 432145273, 903239952, 368599370, 994970544, 292780901, 273694082, 535738376, 629672643, 16354924, 442927878, 660586277, 306333132, 278083948, 644878960, 12671259, 598479702, 128286889, 683015784, 799323341, 859419201, 824537103, 674267069, 142426544, 826355759, 538828025, 511996982, 449870741, 317944831, 701491269, 676518779, 611286957, 28936815, 693252686, 803537626, 496609635, 670755406, 796384361, 852646656, 232242238, 937349396, 922863817, 467340556, 788522757, 687101594, 250724379, 662754127, 235058585, 822939651, 104616424, 107510309, 411422977, 565136230, 99256726, 199188691, 30052947, 796830131, 83566260, 328079881, 926101276, 559702885, 220710684, 84758958, 309674098, 355334299, 419392991, 634666122, 298351196, 909715122, 914819256, 427994049, 216485586, 175580335, 655354939, 18832455, 197035464, 730239175, 590225844, 145510470, 91101044, 39686928, 750206318, 997530665, 460218503, 540388440, 170551234, 983737939, 166768684, 25217455, 865036914, 119299096, 358587936, 29316322, 530732155, 868810687, 636190044, 123130648, 617542815, 141428413, 202689068, 846457769, 727993996, 331508262, 931541016, 413185813, 97655363, 336663536, 983479606, 839805749, 707771189, 121230316, 311908997, 305864708, 938222845, 229752577, 135305188, 464492704, 15073015, 292879587, 939694803, 834590630, 304738012, 590950426, 385863837, 536614333, 27956055, 106317597, 971650056, 889159030, 529931743, 787429329, 738588281, 164048348, 7573131, 436568335, 148601717, 186435698, 493481895, 313944444, 244766093, 173139073, 367910876, 703458416, 940648505, 49913651, 126209058, 938895686, 667679312, 12244943, 76845108, 123681146, 619255043, 841233041, 149512881, 376379572, 572251037, 826790995, 31001256, 123592080, 664489978, 561385136, 511490921, 747179159, 421024757, 936529513, 302661071, 713855076, 505817587, 516775487, 306762097, 487810794, 957547345, 254874401, 540169914, 620181221, 468719021, 342685031, 710842591, 924082934, 247024472, 674739047, 565850079, 224034255, 240926021, 448742819, 754037457, 917595012, 324997604, 229117837, 890941048, 4350978, 756373034, 536419305, 742475145, 953564491, 29497969, 421245401, 883936821, 383205213, 255934756, 149198382, 639578068, 53664636, 224362434, 205459513, 486306838, 690199980, 816540211, 527601089, 257074627, 437685854, 422294399, 883824417, 32138806, 273758513, 240900622, 482952612, 153987760, 194758425, 888007203, 616723345, 23823002, 673662071, 848365761, 364849877, 886949380, 392374958, 267855989, 943547863, 980132320, 141884465, 644499295, 108367149, 769565987, 38386744, 212492274, 780629310, 363660892, 246365928, 327437464, 733902662, 721604832, 257077501, 53492345, 795277369, 195112337, 609235799, 585430106, 265034886, 857887409, 278229402, 839860985, 528911194, 685935169, 524581336, 399400347, 125056922, 301188130, 206486595, 558612778, 416797215, 907709853, 368632198, 246634392, 732529103, 764151385, 255550230, 1327742, 652571009, 785238148, 14062355, 503964208, 861458116, 205538384, 848011074, 65586906, 160377035, 668878835, 300986452, 767676277, 430524754, 993697215, 160207020, 625197433, 446712213, 666913992, 852688651, 930342836, 255680911, 171298495, 217001178, 207019747, 590485953, 405323270, 551520189, 67263403, 452344587, 567587838, 504739749, 414052004, 200274843, 862322109, 16387939, 416581666, 648845286, 954271441, 398642850, 597813831, 164584985, 399048495, 481442014, 976928302, 530777389, 112058457, 861629000, 377847883, 684686922, 710588957, 168014918, 547129386, 420498235, 895952178, 769617672, 45145289, 821303043, 905514307, 984459587, 680519531, 117797884, 915933931, 803663551, 695255132, 987791451, 915682437, 287984977, 477123814, 559834830, 610324883, 649740481, 404142999, 701690798, 230367935, 329901574, 707870110, 453667203, 361204604, 681205892, 979373283, 329013081, 412494647, 918411198, 620006712, 165119554, 135905365, 649996880, 434298598, 445293996, 129894730, 673283816, 11033069, 399438711, 240376587, 920059050, 670559398, 829320614, 475384761, 689497510, 757038308, 301415194, 159197404, 982401358, 955727018, 997545641, 922047100, 319154075, 975479615, 35083202, 845181396, 340982785, 938695471, 597524931, 944165141, 753539070, 345361932, 529808647, 135115662, 823371188, 321965178, 638261988, 909023726, 261360328, 372692914, 989690426, 738338716, 428603689, 52946489, 167024884, 883819276, 749101057, 865879762, 681036676, 590525400, 286081224, 643529930, 841154652, 576582473, 612880803, 984889221, 61281553, 847306991, 597648641, 496267532, 837438247, 592993499, 508398977, 637007695, 464810390, 805656527, 765722137, 498580299, 129392761, 103926056, 334696358, 800924047, 456366900, 185229520, 29074159, 36850698, 975078288, 903175906, 932774519, 755802543, 136900796, 463467897, 355103728, 507918752, 548729291, 199561754, 296024627, 154456203, 375868491, 725506318, 297169837, 381323083, 487310233, 54331073, 297611765, 373829094, 491966532, 741655139, 13338732, 248199871, 132146352, 447386148, 762036071, 557439512, 58980653, 721304850, 967131217, 897728621, 115577377, 260508187, 677557613, 647378340, 865060498, 579142413, 186915351, 467776712, 31547286, 501341172, 925122975, 250060417, 798741671, 614163312, 526451405, 777675638, 510679093, 461511331, 262360306, 73085046, 605239644, 513921574, 329245096, 937630979, 819064596, 783856835, 470069798, 764849993, 860546206, 263142865, 61428739, 6415401, 972775086, 580164460, 624296144, 705505999, 191565343, 184182062, 271339198, 784753373, 719863860, 210534795, 424038326, 764688390, 560023913, 88272533, 448736632, 123513730, 590925424, 80148205, 447412456, 70724481, 952981183, 631525384, 452064578, 677612798, 645170735, 547509443, 539758381, 187395827, 332891505, 275033815, 130320546, 958732610, 559227667, 850477899, 406932198, 469643375, 973347536, 483973136, 300878848, 642475117, 348037229, 42711220, 695864161, 652645462, 626473666, 447468890, 875241919, 759096086, 114821358, 271174409, 241566409, 453364579, 935056484, 476670049, 460459902, 639682433, 473452218, 661801978, 566581105, 626496125, 232322929, 615541556, 484644357, 535009066, 573856450, 907995003, 114265481, 221868820, 533693696, 164916559, 195713052, 572331702, 783958724, 126163428, 64963075, 91162342, 909240399, 473783717, 992499679, 423634830, 605310627, 70262991, 916599077, 573950512, 640517077, 29644207, 153245705, 981072101, 900472042, 844130686, 562028106, 639952337, 533486527, 805373863, 201372110, 174465573, 605942097, 184262291, 697915325, 419002204, 149236003, 898915383, 847176023, 395199352, 656869813, 707842680, 800671491, 537949516, 926062478, 232078956, 139060572, 924787823, 253109262, 20375925, 89815406, 100258326, 966716240, 943541002, 717744009, 787679220, 687647881, 493817776, 817448728, 257970540, 810866105, 141604906, 358306054, 776977509, 363130503, 513825762, 998760571, 998356719, 324368334, 580253382, 519580797, 570844020, 715684889, 315473019, 49072851, 508711666, 995876752, 408269070, 628748246, 59555216, 506776737, 461443393, 283353345, 608189248, 797503564, 836162910, 377928741, 457550295, 324968660, 410800720, 200313302, 901292750, 833250159, 436144304, 707758788, 267749459, 804483462, 52918975, 397335519, 796360897, 612225389, 767012807, 113321643, 620696030, 113820266, 178450313, 697155928, 613507776, 551871482, 737386087, 882441629, 958565563, 952863862, 140073618, 958231393, 589424726, 185135144, 417710062, 797313955, 186078950, 570707058, 514513684, 37352809, 282544221, 382384210, 798410320, 140720687, 405660084, 493941546, 601085531, 198018405, 62340345, 94101442, 45399524, 870494516, 865955322, 723554973, 171498166, 883964931, 764539842, 608222461, 71640960, 446493794, 133211198, 108411161, 293645761, 429474864, 939516301, 791817781, 308459625, 447485394, 950758601, 999531631, 940578496, 219411620, 341116937, 641962079, 750827771, 775299748, 303180650, 906868409, 204207846, 97042683, 65661802, 388535964, 412591276, 416859497, 216786621, 479909856, 861633571, 728974077, 869461065, 773789902, 566293437, 614149181, 343123668, 35163812, 72826970, 552486119, 665433736, 564795395, 640465676, 586777476, 694156637, 594202116, 259555719, 90627804, 593802781, 270625542, 99366167, 203058221, 52590351, 391564726, 603563747, 447412760, 945863113, 376856144, 653854652, 346141118, 502895080, 224688055, 134942855, 169144956, 232271940, 592365279, 405505080, 86909757, 945925330, 218377727, 590708721, 490058061, 28189435, 701505430, 581394443, 908073195, 406705884, 725264687, 621885455, 512485571, 912057647, 288940309, 169796418, 716211630, 398938393, 915802552, 371715301, 843655439, 852821406, 7379719, 132189037, 998829660, 188939417, 356778987, 92198633, 670558547, 667680433, 270284608, 904862789, 78357598, 906618243, 511349689, 780176215, 18125042, 162405450, 817056828, 591116868, 346633153, 380552864, 614032186, 332863159, 833252284, 465921229, 251682389, 843091265, 9169544, 109048041, 172282158, 161379540, 721234131, 66794052, 732461106, 506306742, 256553515, 340285247, 935824576, 75659822, 380330783, 793039476, 237625382, 803170181, 35274381, 830596382, 464853621, 487545536, 821744498, 652607434, 496588420, 687384982, 699399627, 70594307, 251442115, 298057422, 477394417, 164837461, 250611419, 998189708, 706811300, 955065647, 890764476, 731020470, 963233464, 445448825, 459309330, 980369460, 492199603, 889138818, 246981363, 333995270, 458999039, 983410294, 482757429, 717539177, 616332726, 46553293, 674745752, 48600257, 367098880, 806247562, 625295688, 699601276, 50885775, 911509850, 538844814, 827766470, 142558354, 5120653, 619099823, 779262941, 950287566, 492216660, 487259474, 389102550, 788575361, 595643031, 223979653, 946678423, 462033493, 986592525, 593352550, 662079648, 615254985, 381075875, 285781416, 920774892, 123990354, 7642886, 880728427, 250121837, 147806435, 667728587, 48494157, 466875106, 589384633, 438678092, 749761802, 805692707, 863896663, 64304501, 438729963, 742751265, 872610969, 606778014, 932351231, 432870767, 589587147, 77846731, 160503820, 314904606, 219392231, 403738644, 189509473, 76493455, 640786605, 935435032, 78069564, 332678494, 472895927, 54436614, 984385838, 788047696, 982969656, 924631685, 729030317, 608148300, 931771973, 553909071, 614387377, 936876741, 795653029, 973982396, 736223525, 693683324, 534640149, 35253693, 222806424, 216770662, 884041549, 302578549, 689384229, 134050994, 100464724, 537050312, 765114859, 345414955, 631022153, 854630404, 408594653, 294442033, 406716511, 844625072, 44315075, 459833534, 390923804, 125730126, 101195539, 597508169, 717533794, 915994667, 52077401, 21090568, 672883128, 409153209, 196002440, 80658097, 961074704, 736183168, 808520994, 826200405, 47057328, 92774242, 95886216, 623442280, 739367536, 191026639, 692278691, 537637247, 537247363, 981697533, 371311332, 248448171, 561838845, 516644909, 881082062, 440694382, 81000096, 943933394, 687880704, 676037296, 375911857, 817552907, 258373260, 881226399, 464643851, 978774698, 49444695, 350268855, 563448863, 362438092, 970626506, 554353997, 734565833, 542032398, 175582544, 298270202, 287609736, 660670233, 683791071, 396109163, 876888663, 991111263, 631367508, 364094331, 876097191, 369437440, 228842873, 488450074, 911360650, 992454449, 967717535, 951932712, 662479410, 96641967, 143659822, 507125269, 977777499, 708992967, 972482057, 566844102, 336043380, 813060644, 349385059, 917443587, 223220003, 566932995, 169319676, 172216017, 571450955, 865740288, 185167813, 306818048, 898252501, 153978412, 158786163, 938485904, 272370562, 903836928, 313041514, 587712317, 478452473, 506728329, 607674144, 647405864, 167393292, 476475855, 165745887, 589742891, 824693663, 863753186, 79914725, 334083057, 63341280, 767751288, 51460653, 925134194, 224301059, 319231096, 347423331, 320389221, 483633482, 136883141, 100752258, 73926087, 842199766, 646217872, 747107281, 571791896, 28444942, 251855323, 352105490, 982552975, 111452523, 151178798, 436225946, 801416953, 684891089, 805172230, 917849135, 607329545, 966992665, 97948961, 344191586, 921651440, 447042916, 503036538, 832947322, 132347388, 226763543, 904685120, 748923658, 239475811, 592388209, 792215450, 879598668, 956609297, 871618627, 184872916, 131475466, 797240238, 426871754, 238242657, 184352166, 434067197, 76810734, 664414810, 602888680, 119839802, 526524765, 833539607, 432473712, 79331156, 751993769, 527845274, 908787850, 691768898, 890998586, 105334182, 957542713, 434382156, 569518909, 948563423, 894355818, 523866029, 115221272, 6744199, 352434384, 617774096, 64083445, 466018876, 678396955, 938004562, 777455809, 54355508, 500347762, 802014403, 120821223, 509460888, 722171649, 435134284, 683525175, 459229050, 868414680, 974772475, 799829253, 995976281, 716897108, 492744407, 486069460, 541357860, 195679307, 370205034, 77676430, 549400064, 151022726, 286233203, 68063311, 909107695, 901384974, 679478588, 219545058, 884622513, 396038513, 393446745, 368426319, 471250956, 905938934, 639822755, 851206842, 680813257, 548987471, 132314410, 72587405, 541149292, 705589059, 697154968, 869086704, 550143162, 520311187, 665526413, 570679823, 923509313, 4912212, 832046583, 947611115, 214702149, 98522999, 162175966, 96868044, 566904955, 895067889, 988383296, 957742934, 961954191, 727237571, 538969495, 976771514, 246432704, 989756732, 361994716, 30679845, 670285846, 483122395, 549244483, 121121426, 547805193, 12545488, 396479234, 814713828, 639008946, 210712956, 269924870, 89316836, 165144976, 330994680, 446115671, 148685934, 635241726, 370279875, 579214642, 782524018, 420115210, 396977481, 37863909, 438672305, 591486826, 586415211, 920169895, 674715168, 965518556, 865850491, 728515089, 983732207, 381162951, 912712524, 17643208, 109540704, 910225970, 97847418, 587051007, 676220237, 18904025, 959038019, 913811522, 148011983, 89793829, 686367744, 373329377, 203461540, 861869669, 496104214, 875124123, 313770236, 863982276, 687209589, 142226371, 883075725, 665245862, 214495766, 568541616, 945487020, 365530074, 570640409, 362257350, 651184978, 531458757, 761605439, 160455445, 635550563, 693820374, 43361353, 398132337, 971047098, 713392220, 606761403, 209891738, 39743260, 702507466, 20043366, 838735703, 55762404, 769294647, 812132291, 975560770, 242842641, 900416151, 71018767, 782696746, 99691068, 185258526, 222673914, 868562818, 169319514, 536478360, 287421184, 341941677, 169286393, 409051003, 839842461, 869218082, 633764226, 114540651, 949228402, 530142310, 281447409, 740027257, 517096274, 898318011, 63685075, 378744503, 610545107, 304231458, 644847196, 511516533, 682959351, 149315847, 266814040, 319263452, 267776019, 848238787, 750926765, 840045327, 862325117, 348733864, 298138703, 284103598, 598492580, 156001880, 70279098, 474460193, 55455136, 869473966, 756409230, 758012695, 298015263, 525530124, 386557302, 211952772, 335553538, 957935662, 244349152, 354739297, 720795168, 485356310, 123375568, 127688490, 524548650, 233259706, 673615856, 905091702, 872192099, 565369869, 678722703, 998707985, 214658472, 14750930, 551578757, 954889053, 51954916, 193284787, 168201586, 728476660, 929438341, 351726612, 315727004, 861429475, 536919812, 343507402, 340090007, 957939125, 896896141, 108832853, 969619126, 854127712, 908048109, 226093267, 481683719, 862001740, 83009830, 719129431, 947949324, 682702677, 765969829, 920320169, 430992852, 944702337, 21696046, 595218194, 71718902, 456900254, 401937727, 940533337, 494203404, 420795947, 936000370, 793390778, 898448496, 886943470, 723450332, 167326337, 671009820, 905745253, 79751207, 44135507, 471347988, 76469739, 852248037, 23228115, 855406855, 77040443, 490388316, 718114335, 158903506, 46272561, 696770576, 233752836, 236411556, 840163347, 655377204, 430704745, 690839716, 457192987, 311567722, 643311361, 710309085, 719450806, 692934508, 675093608, 602377699, 560004843, 887192737, 22411572, 700243769, 778601769, 475398829, 416714946, 333179498, 377534651, 722464325, 572207172, 774386588, 605749620, 126491177, 722624992, 792360758, 80682917, 702867878, 690550568, 690575300, 727975933, 517876721, 673831410, 103814711, 280342868, 430219673, 870955233, 922615792, 495412461, 273205147, 303205068, 217276601, 155926139, 650525550, 607250188, 153066784, 754460842, 123776351, 324631794, 201912444, 902626410, 200004682, 196197395, 991865543, 851427095, 853377876, 76141036, 745644546, 141393876, 705712792, 842861082, 625257810, 772385545, 894792161, 252360651, 219017589, 277016199, 302023929, 623389210, 253319888, 608772325, 244520059, 331285887, 24354541, 709469850, 69520653, 114155173, 145349975, 651754933, 414033701, 760143896, 357131644, 885091615, 692610222, 754394433, 602591700, 120210569, 480536385, 872061791, 693478065, 347202054, 507368878, 850778921, 811337843, 260106746, 371979786, 8929237, 905410654, 938041333, 960282568, 487617716, 997254909, 865594720, 73572436, 696694378, 193410759, 852642201, 613898265, 142698161, 407904688, 432888090, 418918189, 614915278, 49054610, 571490650, 790831059, 23777042, 828384584, 336056479, 261645030, 378464012, 219823651, 558456330, 139998861, 261295658, 242664484, 996227168, 29251656, 141410053, 250377572, 803100611, 92012, 430968598, 442929607, 105511481, 292521351, 156235931, 747991148, 810091891, 477555189, 500494900, 237715401, 106614576, 52224509, 240033921, 316130890, 166783020, 530933598, 504461133, 627444297, 341890771, 493617553, 164265460, 892682518, 285126970, 874065798, 74491465, 216537320, 46381117, 190774584, 730597372, 81085129, 824801693, 4264951, 314183570, 493730080, 609463874, 262977862, 552598301, 169742682, 2717924, 523912583, 489606623, 48086801, 97752479, 205989894, 777970808, 883350775, 589463072, 356072888, 237721004, 620799002, 910633983, 438918286, 616077332, 432510106, 755711076, 840235599, 131107530, 175183969, 913891278, 606759694, 296531310, 799391173, 439648937, 469221439, 375101853, 729058273, 835224804, 703889654, 985151777, 961183997, 967729004, 25460789, 769207088, 773819302, 334545345, 34959312, 644985576, 466276560, 36864997, 805694317, 478388474, 634923222, 127178231, 551939651, 592766391, 967506463, 201609935, 475015688, 56367885, 537253900, 707778631, 300635082, 71339940, 751600620, 325887850, 475631430, 306752845, 732378524, 277186924, 676604047, 306397938, 882411484, 7467471, 762004370, 934014113, 342600712, 398796987, 467505420, 562673092, 322440937, 115173532, 397510632, 880904923, 260859141, 798193717, 506262731, 203215006, 302682278, 513286514, 702090227, 960404344, 689154089, 549080107, 123121095, 66886473, 531905326, 118024980, 2530105, 847815736, 958177182, 194873862, 803381291, 75976161, 53148937, 359540342, 51816049, 823380223, 680926877, 450335756, 486075014, 505281008, 22328596, 268572783, 763937705, 31285725, 1490149, 193186070, 548215060, 904011013, 226966158, 15883576, 20449347, 380003454, 124948509, 851676191, 202152941, 230750250, 325540143, 876610807, 793297544, 210910282, 113591317, 675455634, 973910660, 343457815, 123802311, 208383568, 659759003, 957791868, 81115208, 83357213, 872503697, 458340231, 247136352, 264154363, 702945225, 612682958, 636787450, 571342288, 71868090, 511751863, 749668031, 189480048, 896177882, 69178461, 687856429, 688005027, 300743505, 146813275, 477909257, 902093771, 119359819, 177535230, 938285764, 334990553, 482431990, 333785572, 366405620, 308207640, 181625642, 188278251, 1120001, 764630472, 561960298, 495954878, 802895099, 778447631, 948605242, 672191870, 249794636, 459235334, 608424875, 18856435, 816614426, 754836096, 321580704, 762034905, 220697054, 499501758, 689796596, 856012205, 84585822, 31154571, 858449527, 335102074, 287243405, 972515664, 160496370, 487348865, 862413755, 565012391, 379906906, 681231134, 486597044, 225038285, 992991410, 251512361, 557519713, 802457639, 999649295, 303729162, 228166252, 252031495, 934957882, 370582676, 575190019, 922739612, 480672950, 90177929, 502430701, 754680920, 176478999, 107303491, 695587054, 754050276, 441217963, 656906828, 703268637, 176417343, 446376324, 840483470, 528163210, 560713899, 12872649, 583295124, 310247923, 385193287, 723396763, 364211143, 236379543, 476926827, 479110903, 390236327, 354347068, 680329802, 131435850, 899084927, 49142712, 235375070, 414619974, 814202848, 262038252, 182497609, 621656340, 107838354, 207989677, 611184534, 136332834, 357256751, 678214351, 243755527, 694268024, 445207774, 641331052, 19400354, 301687116, 405520482, 854370923, 490079338, 199438685, 698924799, 361927749, 551884346, 542364845, 430584064, 73885538, 931301869, 796893733, 277083243, 299548105, 539576943, 756739912, 589122630, 153394732, 850874263, 49440874, 139295255, 895911239, 848993590, 253215267, 352119307, 458565631, 500622962, 665816443, 40493780, 924774054, 173275480, 576341301, 640972481, 619584790, 217837207, 203572536, 462705768, 817710546, 11222125, 833703791, 224118611, 894602733, 844246186, 242786851, 1626716, 337444821, 572449080, 907079174, 717099848, 12872406, 700155314, 853790999, 865319040, 14991083, 534951518, 226785982, 170023525, 733952829, 216248691, 295065498, 318834367, 982069084, 487305924, 665621841, 563012424, 843918839, 290569547, 412725567, 566748231, 885420703, 194237836, 607262707, 825779317, 495416864, 753284858, 899707563, 673363538, 947333975, 796603952, 277322975, 890561749, 316514452, 367215622, 76275368, 967089384, 677323852, 409177393, 566428052, 355326702, 737727008, 495855625, 766195686, 591975746, 166650278, 964624876, 479743051, 292691259, 199085408, 459115576, 431247567, 835225942, 398057778, 57764488, 780606895, 676680772, 651343600, 498065609, 415766402, 676568606, 473429865, 949108920, 346661088, 797251586, 724409481, 921633268, 150607069, 786038434, 921325784, 866019834, 555591873, 82722367, 175508451, 162063692, 235955513, 966586059, 552570288, 566268647, 133973616, 39296087, 632149152, 743910111, 491034962, 625168313, 522775644, 634468589, 698563565, 598973149, 329683564, 766841271, 703372805, 584353424, 311709842, 622816196, 435562461, 472587272, 208596878, 545711741, 189553679, 348667437, 37848836, 80982679, 157771245, 683995160, 515474203, 20395949, 160026638, 201831632, 12092947, 338727075, 621943181, 818835146, 634923552, 579349428, 769202923, 291288997, 649375760, 344238786, 518246554, 549849341, 196134627, 703996673, 128749066, 576438999, 923373021, 131735927, 423690859, 404778736, 488340349, 563419568, 360665187, 143544584, 821226407, 857155784, 688130769, 356670908, 583430317, 933083858, 253716341, 878497189, 341439357, 275767077, 453487174, 264945563, 656200217, 448335079, 719359259, 295787903, 602088793, 186588769, 967403504, 689102406, 37857585, 96818128, 446289709, 869604933, 121273503, 234559218, 263247276, 159402397, 765407457, 533557146, 879799386, 731990380, 89076708, 261975271, 704433446, 72675785, 990723421, 531485340, 968672883, 161386409, 518837508, 96900738, 822563796, 719697634, 831892115, 685193391, 762088336, 314795525, 588570591, 54547269, 326898331, 209515675, 537361501, 768542759, 2704924, 353474983, 178067655, 659994441, 645943601, 75493661, 19757886, 54004552, 771076364, 747034842, 32152706, 994687684, 860790309, 989995866, 643003328, 38917322, 500591536, 159139808, 835673109, 583146859, 82830911, 969237702, 346722052, 795972089, 405762595, 64555013, 147232281, 186284975, 340087277, 258461662, 28340001, 145133800, 931973547, 977195422, 23307560, 748831944, 835828643, 105465266, 537316570, 894541240, 488472448, 737468322, 93677690, 531509403, 992979434, 955206809, 251848145, 535520842, 374726935, 839328306, 308362059, 755571984, 525891006, 45186530, 691137656, 239260643, 826143281, 3924534, 339948134, 2393386, 376999174, 755164266, 17805246, 370503312, 738576104, 828399565, 37747151, 331118012, 383960632, 890037686, 234334122, 150743545, 541574422, 922476348, 980138490, 349402957, 263458211, 279693650, 755435040, 190558603, 418132508, 537504248, 144729177, 257038397, 63633228, 209961314, 698221260, 430404905, 285123583, 283247740, 584047566, 106525573, 80268842, 809426095, 27285556, 641904454, 33092207, 221902235, 489767643, 652219124, 812581543, 468805520, 260634403, 702302943, 323164098, 637775531, 329869128, 974539466, 378310722, 38038584, 148147175, 74163375, 53138113, 976409102, 256793272, 372451042, 185849953, 87886840, 462708284, 454349840, 755634114, 211069115, 759714956, 607269525, 790889615, 121622359, 142729995, 321696264, 365404344, 718019825, 380391820, 858827796, 394484442, 613536961, 20963351, 666425786, 642419765, 360168124, 935507649, 852978796, 810032696, 495820120, 865268181, 144148395, 718055139, 316905052, 295707808, 720513159, 451974842, 640986466, 116606312, 455772103, 175216647, 746986152, 220381381, 807199723, 249624091, 55425477, 33961874, 801665859, 319755998, 839492201, 596883187, 152551908, 713807824, 650475079, 545379673, 688469607, 257173467, 731427071, 770996635, 977306881, 400362045, 45091872, 467742437, 549099436, 424165873, 688796598, 816722397, 245737575, 497824853, 209985835, 291790575, 110785224, 855942913, 682613937, 925806986, 154585802, 874890541, 513869099, 115113927, 191049290, 331046489, 436709962, 520586521, 262599836, 812398202, 326919529, 646884061, 70056291, 105526753, 142972695, 41266850, 436870496, 449334247, 351602553, 157767359, 646967564, 5847910, 91022098, 291702335, 864884740, 147364380, 306041485, 430528514, 397392421, 787305883, 785457961, 400018428, 142318447, 27267128, 424049315, 286687863, 186559212, 251405344, 191162445, 694171325, 897305968, 157468355, 891272261, 109117703, 497034604, 407375759, 55211198, 257306500, 161683695, 591017300, 111973328, 482039376, 440449701, 380248121, 24366404, 757836088, 30910964, 905847343, 62988958, 565659007, 607931516, 435533247, 253777236, 249524255, 155785714, 944839240, 788972092, 525256327, 390837119, 324737593, 420003876, 483708665, 198201857, 216384065, 582581688, 758866424, 95912084, 28521379, 134313930, 414898912, 50766360, 600958917, 632338924, 958645060, 501049669, 977034596, 43690804, 923354576, 162291433, 918883344, 540157210, 81303463, 860572571, 524780466, 457263485, 862777508, 264412304, 601474420, 786417436, 218546496, 707340844, 955649750, 158423727, 780757978, 138787304, 904514775, 319847020, 879599473, 26349047, 253296952, 941332016, 267616305, 945582051, 921822422, 579802344, 158619125, 403561693, 629403755, 490875031, 677722343, 885531344, 303664799, 173147892, 438699578, 463391765, 924448359, 706404864, 890551474, 630939371, 344450522, 843976557, 396579427, 805243468, 54922797, 666903987, 776786585, 649592321, 94063542, 567100627, 428669819, 820724270, 976078849, 333598183, 740272345, 9472894, 519708345, 432143133, 798309401, 986123297, 600581039, 300753822, 656331863, 897025561, 505910358, 916136263, 593551690, 635551729, 27142402, 34915468, 590600740, 402802610, 807837063, 715601358, 193469435, 212214600, 941352562, 384664210, 681320750, 713121618, 530388947, 365940642, 997589877, 156056812, 336487584, 736332050, 813947456, 874367389, 110458863, 365194718, 45806893, 650006198, 468944422, 466913215, 749314184, 671356418, 799895305, 225592363, 440294891, 33335743, 851193943, 963633821, 757399992, 845109834, 545099422, 946902805, 406294836, 650242597, 14637192, 196251920, 550757873, 96495476, 237624208, 775455047, 622591480, 906271747, 214718068, 185591323, 94952195, 581819315, 694980611, 745120141, 915499347, 748278701, 633511920, 144488003, 666609223, 600749702, 31098737, 508741918, 972145225, 157753564, 237626202, 635239306, 231600519, 242112745, 372375813, 761969309, 16958408, 300319490, 276776283, 47139665, 378025765, 846801746, 819358591, 718742601, 478949542, 903948506, 575802445, 832652970, 16477097, 193795462, 589414169, 675268046, 811370312, 937576852, 917417449, 185074641, 826683548, 655956446, 324087399, 333761806, 37884453, 159569628, 413902223, 263011329, 613749098, 640516753, 811502529, 997014111, 558709667, 593312586, 652999579, 713042049, 640530678, 795907205, 58296997, 5779918, 531357883, 632621011, 438418554, 247007671, 706823417, 546197661, 585925234, 830034271, 142834711, 354014519, 308803712, 948147678, 101032523, 511626172, 724880770, 122823219, 869204075, 205698691, 859277975, 649904171, 651812879, 781676952, 291704388, 48256992, 980883852, 44580292, 647485547, 830005400, 993446947, 294489882, 986809708, 599365087, 643842297, 657333976, 357253791, 398267546, 452289351, 380254489, 419375400, 526999252, 905238136, 133785845, 155646545, 997917643, 155644299, 158874631, 159099258, 549501240, 75501958, 258487471, 635259232, 808783947, 112544057, 955583089, 331371423, 852408065, 68909064, 922943663, 304547540, 491141468, 451777060, 792556049, 117199630, 874123773, 284201004, 156234167, 246149039, 904614522, 151025834, 998093899, 150984435, 990082075, 788356074, 754459656, 656211190, 793536570, 760570746, 246782063, 366982251, 996956613, 468781991, 823529875, 68012383, 220705378, 551937214, 853094121, 700836205, 460071446, 814823631, 816356231, 496760944, 42682993, 241948488, 960710145, 992404263, 655042903, 188388506, 308781463, 476925542, 673692857, 265918320, 540517399, 845233919, 968740565, 171372741, 12955042, 221012981, 328593338, 978274785, 108618597, 983679546, 356543336, 499924856, 454713166, 131231082, 619896204, 979837961, 584371580, 838251137, 150514397, 880464395, 289618124, 122707954, 970783817, 337376341, 308586439, 464986650, 841448967, 270034850, 776211940, 84998276, 487118423, 362891082, 962214481, 19374523, 587980757, 34907071, 588406678, 831272940, 797310771, 861445469, 762867708, 434276559, 736236304, 239846299, 303009375, 238925540, 358961644, 252956070, 228485456, 706342921, 783596295, 159369318, 105387654, 895811481, 912338592, 689524399, 541158479, 68148043, 632375786, 63202909, 359524886, 64687992, 853407528, 337592393, 528907896, 844131799, 95937968, 412398462, 37527326, 22269183, 619083463, 542327708, 831127949, 809320379, 538117152, 988994249, 737471173, 771226652, 443448517, 841960765, 24661685, 931066885, 97778247, 938398770, 156336162, 696298116, 929058088, 576528718, 277072177, 574614962, 112969307, 326512342, 767985658, 116845106, 561684704, 639430226, 283979809, 379398947, 450599552, 448309973, 172865646, 180293354, 148408857, 647193833, 857925443, 66574543, 624269443, 191155214, 157487477, 750640198, 641023377, 156785898, 572435761, 837555642, 417789155, 627286204, 690197031, 614013242, 207228906, 5081552, 309356296, 86025595, 66571346, 801415372, 439452798, 708416621, 484172828, 57543287, 253731464, 40421986, 23729660, 643862447, 427506060, 735589600, 578611003, 554435762, 453020574, 866465878, 315170626, 677340828, 338024326, 715899750, 58091038, 642640449, 904065578, 624719806, 210041724, 370649884, 6176694, 800034973, 856528159, 123271985, 671525573, 559350615, 246934346, 719086201, 795715840, 930590041, 265065060, 398571241, 717083029, 548786614, 351257173, 302901296, 998962598, 233355336, 191758626, 500372507, 610924613, 389657505, 790115508, 678043751, 608356033, 367549996, 578616980, 212651769, 802783955, 352423374, 60999796, 22265752, 176833355, 272523510, 344381619, 78433501, 476145830, 489656547, 970156113, 999750092, 40976203, 776772833, 538031929, 549610938, 196520051, 96094493, 345605987, 546187814, 216833120, 876771838, 824816573, 649995435, 286489382, 321151153, 542908898, 720660057, 658521399, 447726412, 160680599, 334522954, 948237605, 813270377, 761775470, 595151090, 405710481, 93567640, 212305786, 724107659, 61415952, 651631718, 545751084, 630468928, 590234002, 286583157, 439917074, 708266855, 924515083, 502337206, 72182768, 29098221, 995416609, 286225671, 200169268, 470071249, 635196129, 884577351, 950165666, 726454174, 452554720, 657613276, 873497506, 355499768, 398466391, 447472229, 919579030, 330067693, 156724060, 186011527, 247096979, 416628426, 276948638, 727949776, 482901337, 523719507, 937403003, 188743803, 31102352, 39673364, 936647089, 592221138, 437295761, 352380082, 145500255, 598835630, 102232431, 428690733, 133201008, 706917251, 955064605, 445683542, 847821811, 13235533, 585252510, 712418892, 271086424, 844189815, 314497363, 337696241, 386646620, 977617902, 149102659, 746620491, 350033754, 751906858, 859696001, 614031666, 591916642, 766155826, 603708469, 878475170, 12615255, 767415468, 546397593, 444423393, 196565011, 952199677, 218653466, 261017912, 487837282, 586853024, 72955245, 191710681, 945993210, 458847286, 871144849, 63914246, 552249496, 614876070, 739826919, 995810018, 841067875, 203427763, 700977803, 785910286, 130114550, 904765032, 319649434, 191209334, 141868339, 265335796, 908678341, 44895986, 594201139, 618834845, 57243166, 447023205, 874633019, 666359197, 407908348, 319405581, 640356619, 973905641, 601993077, 604020905, 506466170, 850956425, 15638830, 166955425, 561791267, 686346554, 115903823, 113519442, 131959057, 998330503, 288942613, 540488479, 995492474, 24933017, 819238368, 542926850, 278070078, 18012023, 734826254, 305179231, 636667406, 549617006, 465736366, 211009901, 760574807, 496184509, 267791089, 724280725, 955002545, 279342650, 204909994, 924593450, 242610646, 398865073, 104097922, 152429363, 591936579, 70159688, 696882281, 565161438, 668213993, 262052060, 65162662, 824074537, 371807585, 205439089, 454405832, 652119639, 742893994, 568191062, 783780366, 651636053, 972684608, 130785150, 518796688, 864996374, 810546823, 251459691, 281815316, 556752589, 452680129, 329805361, 560188041, 948729184, 814768698, 335519719, 54320054, 906876265, 997068773, 300667398, 282124805, 466014012, 262003898, 105531224, 578451497, 161444026, 818552487, 569446272, 344381419, 963256698, 505947870, 263694571, 959422082, 413241059, 207216939, 892025765, 929735911, 882205191, 780114641, 128697851, 559131550, 619636493, 368263992, 510119515, 934041601, 12537274, 259309639, 458844880, 575782848, 809648547, 5659203, 362113060, 185316928, 326190738, 760588816, 592625557, 348453953, 710827666, 6364237, 564715624, 373729768, 135923549, 288370763, 194726191, 924679955, 389628147, 690749079, 107248236, 381277988, 13501494, 803167399, 283864282, 128391205, 678096064, 628778993, 401147445, 853061843, 938733155, 376047194, 427554187, 562769918, 531692029, 671773361, 537788959, 410369089, 700516512, 817876876, 886293788, 254659725, 715459908, 279371174, 156237833, 903523154, 61280409, 545770024, 702572026, 167674327, 497876364, 598193429, 411293663, 403393801, 856029844, 997983171, 720398842, 280107103, 948014520, 376669076, 817032944, 223137201, 164733036, 850968841, 124552965, 116162950, 615170706, 908498760, 640711656, 96590479, 753255084, 169950830, 236235204, 501972611, 814946220, 158735517, 497504936, 183151501, 327233513, 132305429, 917442090, 136542475, 399703145, 736350544, 116325304, 585469091, 416333078, 948692662, 545222976, 884947002, 762925102, 968375974, 593349218, 343230522, 72541035, 25622333, 984265093, 711829917, 590802186, 696573831, 377950466, 441429880, 190181372, 300642809, 401174542, 13682513, 864753240, 41730274, 654970054, 646606233, 612359979, 408885030, 529793546, 817149085, 327861534, 70436246, 882770297, 546795207, 902217238, 280235664, 333829531, 979363251, 120926588, 627926261, 690886778, 777141234, 231247195, 868822225, 67241343, 278372592, 607858675, 160797347, 898024399, 245467183, 746763899, 41483768, 780629919, 925213233, 432760142, 998787104, 927980079, 353325402, 170844807, 127315951, 718660702, 898962647, 454313126, 891690896, 693832531, 103644824, 135015818, 69968330, 637613636, 269185139, 981652041, 594787261, 550268543, 853595549, 25608167, 410869870, 206988831, 702393255, 141481409, 819718926, 696216512, 398047961, 29128563, 216680397, 859924445, 833767440, 980582758, 793198904, 454345072, 185322622, 264945057, 943702960, 3428281, 75771316, 324518343, 824673998, 820124127, 874666249, 786552001, 798106541, 456904586, 52241516, 164280712, 834502254, 397598486, 522035539, 476976795, 874257195, 92674321, 705030142, 5139879, 324765015, 528848726, 697520162, 401171623, 975321740, 274174906, 486145853, 439917751, 281054235, 300416623, 959862287, 898484516, 572947358, 102947879, 105184660, 557067564, 173018541, 516361737, 171972566, 793853857, 281377037, 927836500, 735073784, 755543807, 500945139, 575391144, 360300261, 157837226, 680880279, 630384423, 580773216, 281793424, 755954266, 740575201, 924125544, 947495390, 582396865, 119919317, 597984681, 989564249, 244955979, 33834478, 829483558, 566475435, 173006646, 465682659, 526883062, 33230870, 911861585, 886787122, 359362855, 810163567, 219292679, 910460268, 922477065, 200061409, 324318509, 292677602, 40409568, 964410137, 412792573, 869907446, 160425500, 114062228, 406156927, 173489601, 604756042, 241603759, 687689863, 135015530, 626402002, 59814971, 664173393, 891037799, 611483413, 216661426, 9593361, 177856247, 211903819, 861936957, 143419204, 594108706, 548742799, 247156831, 347718747, 324323347, 631674453, 646384067, 834891733, 87051233, 339815246, 100443300, 850390664, 5675643, 128147563, 719976785, 350269465, 74410097, 206575141, 32786053, 651338274, 545730925, 653381868, 165453830, 304948106, 485957523, 588335650, 294677046, 318017537, 517677248, 707967166, 404657146, 872719093, 541052357, 563936387, 438251297, 776841137, 204978386, 802107491, 408335242, 832314806, 237755133, 353557070, 751816315, 829958599, 612444995, 37406965, 636922026, 532548682, 543669396, 633929606, 741219339, 678299600, 156436834, 231755252, 432766802, 763956104, 21405365, 727878454, 884328990, 168187109, 609172858, 306431718, 88392317, 265741404, 334870911, 678318728, 362741200, 56519518, 863252453, 983860376, 465239187, 261646502, 65602235, 484583502, 400178629, 946479624, 954123456, 617921721, 909335952, 729747162, 179827756, 601219364, 149668612, 244390766, 920004411, 93998213, 115349062, 568523639, 589643334, 160298099, 412365247, 687940535, 511075809, 454831845, 15833111, 553619073, 567386919, 986268015, 494237450, 615339071, 403808253, 564784445, 968845658, 581694536, 41934964, 608075212, 932539464, 825011275, 426904252, 550655011, 628663520, 587448286, 13155263, 694299757, 998139450, 402770935, 601017253, 473859303, 450810423, 692061422, 371354415, 707700007, 696067335, 988596117, 994896374, 156686987, 90175576, 710936140, 277339305, 587933534, 778303533, 811643741, 675086127, 478838290, 40176237, 794915475, 95817686, 348146223, 701066500, 130241518, 567456621, 3883997, 653440175, 239691094, 162399616, 34388533, 285476333, 568548574, 356100042, 900107167, 647098215, 398997170, 815002863, 749035479, 395803339, 118003746, 526313541, 498523326, 888731431, 739347198, 776781589, 249679789, 245660446, 760496796, 132697318, 951836075, 177833157, 183510763, 141813975, 416613228, 176609149, 446365456, 959197643, 117140485, 204243776, 964118750, 421038929, 727604614, 753462634, 992512051, 338767147, 874918365, 94241566, 322400444, 34049754, 750633923, 525104654, 330956926, 153643449, 701916774, 1974943, 828804104, 477902811, 260347886, 138230605, 212662097, 524106908, 716296005, 828932965, 564117401, 311623521, 570111357, 48325583, 565309957, 151119535, 242009148, 832076721, 93700992, 65448813, 714226256, 881904500, 397913555, 986394889, 384786719, 202087600, 639755912, 265723526, 207546783, 177620320, 47266697, 695005001, 355447187, 671502360, 946481749, 317711771, 33565289, 373501580, 443937709, 924661503, 54600948, 321606620, 794677852, 305184408, 273347339, 596625910, 348837334, 343935274, 687453049, 663418681, 356056884, 263412467, 220673159, 277361060, 889447355, 948711518, 901454950, 470004238, 413819728, 382283961, 138417452, 605740722, 996157939, 711745139, 249284275, 327075291, 402809192, 744453636, 19698837, 944445663, 148852387, 361207738, 350373342, 548797283, 179279770, 886151107, 401742530, 189683524, 854983356, 836591923, 377665710, 95275059, 88351156, 83111314, 517393609, 125360516, 266907728, 971155337, 201948823, 153189381, 71926127, 134493358, 636584340, 18229555, 162091798, 670572871, 774949121, 540472520, 238339364, 824761330, 496437599, 741436943, 515144480, 654880175, 951370196, 222601195, 131655834, 91108166, 38392678, 295705870, 333196877, 872305877, 318667201, 412556089, 797259633, 434088012, 590256236, 781427900, 391680790, 438575783, 876507659, 112118339, 32407553, 414778348, 688324718, 565394764, 503358945, 379803959, 445737035, 158699961, 553418088, 36381714, 136811247, 114807249, 384307988, 730617848, 660183085, 945754243, 742211791, 290023577, 53871094, 456702202, 860380860, 32881012, 742963328, 970191790, 936259215, 739568493, 69753001, 516902012, 523555636, 466801417, 572381845, 909746156, 607276076, 717724532, 611638845, 9390037, 739247198, 275717399, 121299067, 675833988, 187556489, 589005597, 300672851, 821977798, 960984225, 528519287, 74308208, 960733978, 889900956, 76291635, 217703701, 697749479, 531697204, 549463802, 526821484, 879429576, 407783006, 406480901, 856982442, 909410128, 853820393, 717337144, 1975436, 113457691, 286755306, 869984206, 524137002, 778843365, 763002458, 491295412, 415697839, 967851844, 810245591, 908841959, 949246367, 470853482, 912044787, 866944363, 489180706, 579379547, 174655621, 820175163, 310102326, 633354561, 58535443, 896725473, 50128430, 648758461, 682018062, 197970484, 719322875, 393300193, 454457397, 524745418, 857135998, 666126741, 797513895, 419159096, 305893465, 322591995, 876045697, 9157370, 372496841, 840280011, 210469909, 182676048, 441542949, 16531079, 792132339, 660790788, 809033568, 747316805, 596788498, 938943601, 11710585, 172666543, 371104417, 401405815, 848493977, 11219632, 113419791, 137335564, 795189733, 532933347, 237049279, 665890178, 656538553, 564743625, 880515346, 697863932, 501855683, 713821112, 174165014, 127767814, 94262816, 171292462, 684303226, 125756047, 187861073, 184747021, 248728788, 526809937, 618190795, 553105204, 999145087, 314744628, 809276264, 98401548, 699677790, 930731812, 469997495, 94529444, 367087368, 730046634, 954098315, 493464050, 155362161, 14909055, 348899367, 576815533, 610108398, 972585860, 963624864, 525984599, 575282552, 685295240, 746114132, 654218415, 348106966, 4922381, 116323393, 251019558, 640453876, 852015457, 212361977, 839103717, 370915580, 489415512, 701815307, 434533422, 124623127, 327372175, 164241126, 279531892, 374272019, 446672266, 558730870, 596182269, 665917688, 11935636, 823967734, 946872136, 159858919, 485172664, 94774043, 367557802, 978952370, 274205577, 800219796, 154418162, 676578333, 543991831, 635814096, 131449564, 487887037, 484501584, 816020938, 498104948, 41366076, 957076391, 228688971, 393366193, 200226641, 670917542, 396614674, 927959330, 906368036, 354270123, 211450321, 56074952, 473595456, 761747982, 120675608, 644359441, 658367149, 123846268, 28826016, 830081658, 222631555, 812113607, 938445554, 68859909, 896170052, 917660270, 315804298, 960116850, 148108490, 70481713, 372766467, 368455291, 16536038, 906137549, 171733539, 470393834, 19380955, 308469556, 206743893, 66281853, 46223697, 231563193, 390508776, 939182438, 343540245, 875425665, 630664511, 977161203, 24697313, 611331583, 217776154, 752122464, 822409432, 474763640, 406470958, 346832724, 941556521, 251576689, 873718098, 914613524, 922112992, 816721440, 207867327, 682027630, 853923079, 977663951, 234947733, 989961493, 705406231, 819229097, 765647120, 512250713, 484346048, 97138372, 836043942, 797492064, 816103552, 835151401, 53709254, 878472235, 15162040, 822513747, 342990225, 283196973, 368704780, 982599155, 691861406, 44160637, 689123636, 488392953, 739442394, 639203625, 602709379, 601083967, 487668109, 553726289, 228982457, 12781622, 406576517, 136726494, 141610011, 490568773, 678025066, 88789511, 102227886, 606490376, 443784095, 909558772, 467115066, 919793954, 325475519, 170825769, 971543620, 780724273, 730507476, 113617255, 488197897, 631921848, 108011115, 262972314, 195483433, 352433001, 471304983, 16571476, 855604506, 431915080, 857002700, 175380791, 470227214, 954289188, 450472303, 90869012, 53990760, 295339327, 59147350, 920808889, 198219676, 14297271, 181548151, 950448394, 501369842, 688326819, 232845525, 445072087, 252347719, 400838974, 728590523, 200686890, 879921342, 181487716, 757427486, 553698442, 943079564, 907620090, 581796675, 472313640, 882407703, 863863697, 178572111, 712405697, 297564581, 52682896, 860386830, 905416558, 540807989, 337680093, 790898552, 587935348, 544113991, 645261624, 299802296, 149259485, 343034328, 526390823, 408233617, 935906523, 339076508, 755259492, 858861828, 84220229, 890587134, 627352873, 319020556, 116469421, 205789025, 638918908, 515891307, 24363605, 804097411, 630837010, 849865622, 107347396, 902466808, 784128893, 539829700, 451191372, 110862961, 780004212, 459012455, 658269243, 94851582, 496255242, 586555906, 405021132, 252949971, 545820600, 245475968, 875007666, 583706597, 110471429, 72858669, 639464041, 891598252, 656211062, 597519738, 82939104, 300265506, 570124159, 418659655, 449753161, 669346409, 808467153, 880398206, 895019627, 4535942, 265385224, 540624660, 368179372, 519900385, 304265685, 745516468, 149256512, 102284469, 845111962, 873099079, 977390397, 424782363, 154073540, 796310579, 702924834, 136524919, 125172694, 921654476, 49949140, 974865494, 344226052, 294433065, 774046627, 557015847, 867124487, 724849990, 825995453, 798046670, 961070590, 206686022, 569115195, 758154495, 813490932, 87616902, 29040804, 466845567, 715751821, 875011792, 363470491, 903555178, 276215813, 645969929, 30772478, 29865478, 113005018, 874722211, 372614267, 5065640, 958586751, 735277886, 934901137, 420429962, 398790160, 443639130, 875030893, 292523292, 203344541, 296382730, 837142232, 976042022, 79433328, 860629216, 927951820, 137115312, 643448139, 656789271, 137481374, 378362513, 553350394, 444940745, 507714924, 619788588, 743623026, 376223692, 433544897, 769073422, 976764559, 330029808, 441059935, 518760277, 848284148, 327931489, 513552103, 804656234, 801989572, 390421771, 424990758, 479696693, 304837576, 321037983, 920630561, 330470728, 312331798, 877067197, 504523988, 181448149, 305997738, 53381337, 171407377, 185577184, 879406923, 658029648, 193591395, 805301094, 62312627, 659162161, 101624231, 160374514, 534307724, 343502762, 453910470, 14612774, 462071456, 512307534, 853237945, 388663488, 245089204, 537933346, 853255086, 635821329, 893113602, 220085641, 51355022, 735745259, 758882227, 428620855, 685249444, 685220575, 407057570, 568522373, 723566989, 920368268, 645686275, 239782027, 19498212, 66344682, 892944127, 253161072, 173426367, 33017317, 461906955, 461219089, 330463026, 936197757, 559227139, 470602932, 932901662, 838157912, 588909880, 853556782, 219911334, 332886581, 286111018, 995140527, 801111731, 453427221, 114223422, 324331254, 301907602, 939901216, 937704185, 656495405, 477411365, 800542263, 270893168, 109184237, 499120113, 222812294, 740550287, 327587982, 98000374, 231066078, 195511574, 132997763, 419190522, 83958786, 91442593, 391019121, 798120878, 518907373, 814177300, 859541104, 139053105, 256690191, 62692280, 767490785, 767729973, 742825311, 102446961, 347056980, 148347628, 923652001, 136299829, 528897960, 142976183, 263783076, 587763766, 248538485, 489190825, 377939806, 855296556, 957931262, 774533869, 384115004, 827540469, 52884203, 843568095, 877547904, 329275374, 375160261, 426113676, 252282536, 227502799, 436000554, 469912863, 655616109, 506511100, 801207450, 130526307, 725788431, 303893506, 233618122, 480305794, 435037908, 775078976, 234431700, 219064637, 511749224, 962819397, 666455759, 624554934, 987121869, 414687821, 636746845, 747003712, 905392876, 557395787, 158643051, 498868497, 498667802, 833921766, 762418526, 474082018, 443670536, 426368275, 348835650, 494440466, 144679434, 347281357, 745996954, 727317461, 134285580, 372389153, 356087757, 766402239, 870585719, 827922125, 724805724, 340709069, 652278587, 870377283, 848550822, 177383874, 403768702, 269976239, 407226770, 986018437, 407218600, 952942860, 539213778, 667224976, 854504011, 455793167, 550134301, 123397924, 99251561, 142404435, 945732386, 385926344, 498916961, 989825945, 331679357, 155403397, 92127007, 150816802, 718474919, 376352974, 172640866, 349898392, 628597904, 39240242, 179241144, 451211, 932735585, 900332492, 398715614, 370913100, 730681584, 850244695, 469331111, 322172475, 140876990, 395807367, 122030826, 243312225, 332199769, 615092971, 462782050, 881489876, 21278135, 834670763, 640002338, 46625230, 610265494, 706209066, 877090739, 813020842, 512394066, 13779744, 848482323, 521065771, 357050785, 967207883, 143121881, 815604351, 482846556, 391854734, 912290195, 263365135, 369804285, 21131434, 682702216, 214079116, 458851353, 31494661, 49824317, 234137005, 798760213, 204519292, 835034556, 743340726, 925892407, 67436266, 972776810, 466495159, 616943010, 425721915, 7480729, 469834736, 50021837, 206313136, 685059226, 839902880, 327327971, 736641430, 318831489, 219338187, 144583121, 367915659, 945328207, 17301198, 811839862, 674241887, 480136844, 276482132, 432468391, 953201600, 83319820, 65302120, 602959337, 715150627, 81114757, 679203142, 521803047, 107171022, 515290384, 394494585, 933407334, 4338500, 918467718, 571570852, 537434473, 646279758, 40108342, 434957819, 837380009, 49373132, 319319556, 374354261, 545165181, 566141987, 224823559, 273770520, 598989020, 947397532, 417556675, 575825188, 567091465, 728716420, 271720260, 456372962, 444706180, 620806277, 973214828, 95540180, 737934579, 925359380, 102296916, 948916142, 101795493, 556601825, 190300710, 176358334, 785363801, 163177025, 709311667, 782268691, 263388230, 435336765, 870625999, 360855424, 829014816, 548546195, 679107844, 78608279, 262946493, 871856692, 172147795, 149509090, 361331995, 956254705, 148079966, 535704158, 257152287, 231590347, 603880265, 145248038, 995823373, 300655693, 667641156, 975804655, 10806900, 272251333, 962434678, 614807851, 71690717, 793993428, 355082050, 775891158, 414798527, 883894124, 177261331, 541005425, 62945603, 768663941, 44910625, 511843111, 510176737, 689235239, 58674162, 947753274, 768780233, 581057148, 50285626, 111622936, 430410249, 537754492, 361712594, 534803906, 809253345, 155163340, 509697880, 132243138, 997810155, 777305407, 990240764, 405897242, 297608532, 113670143, 476786787, 342887321, 794388103, 182543020, 551469882, 3548620, 109134387, 737779820, 547932506, 680707029, 780359550, 11581821, 275643522, 807295012, 96777814, 204271831, 663546049, 983061819, 274812281, 688307722, 271350054, 472266874, 124699619, 7205993, 309273601, 517597961, 801030326, 893367494, 651634909, 81794384, 775132071, 717723205, 846315318, 689211164, 659095797, 503606401, 934910662, 506407308, 602530302, 316400767, 122567062, 541607689, 192765891, 303636816, 116605176, 876376296, 69965607, 613780723, 279585437, 344498298, 931090463, 797715053, 255271425, 949386622, 703077982, 843209012, 798959607, 897935229, 340392418, 253858089, 230621608, 596355344, 889882022, 475877105, 984413704, 748565788, 475640969, 184150158, 514816680, 194713545, 785267805, 690008396, 162222069, 455487641, 334317282, 49900903, 420992363, 679984037, 190515905, 853167236, 125002452, 786631977, 952780648, 293727641, 493560532, 158792621, 360435144, 231213207, 874231447, 60101927, 374752999, 445286526, 524776305, 454067045, 943589537, 379176159, 504839988, 260562726, 371250385, 280124372, 353739310, 587178908, 827832360, 193425616, 78704579, 765061900, 756955188, 981601564, 759886321, 809691012, 745884990, 591540617, 812761256, 884141116, 885396263, 212149091, 474507725, 418885788, 477545909, 636950437, 51906259, 375827194, 923522353, 114317143, 842679762, 737111465, 369328416, 532716530, 58474709, 521789503, 39654893, 285470103, 327229601, 369214566, 518370716, 263597005, 425379343, 392666773, 883010927, 68943156, 354494557, 72378026, 118355287, 967021693, 487574027, 899675031, 892131423, 847654904, 235797667, 722197906, 386848777, 585543033, 845127096, 462097809, 639581639, 107662184, 307089773, 234482314, 9329745, 91377726, 702007484, 207941280, 193570873, 73339391, 701444318, 350548637, 140285825, 656777964, 14643464, 89317093, 711444855, 60716584, 617880520, 667794581, 13363364, 924657032, 793248652, 432737219, 733798703, 484737389, 99467329, 957036639, 618554275, 395893039, 940858273, 857365386, 145910780, 543474084, 182850117, 206196212, 591106097, 174377014, 196747671, 127542930, 461202959, 619103469, 905604838, 234958075, 314864374, 284302144, 517694999, 561544048, 531156533, 722250229, 16120011, 79197785, 210579133, 369644761, 976034523, 780616536, 781062277, 444558122, 94057753, 123691578, 749385244, 243981627, 705161881, 555836889, 786976080, 860892797, 725147663, 691348887, 655986735, 645887587, 204974993, 719407719, 807595868, 401965981, 59649690, 857089481, 58494494, 592052291, 490115144, 928788912, 135871630, 535912562, 981314265, 657191819, 99858241, 673439947, 174013975, 774807148, 180679407, 644528453, 645796491, 648409826, 378277379, 756190956, 134530974, 319349562, 797378367, 960005709, 807902563, 885626960, 653487719, 366382163, 972697623, 102116335, 365594961, 621723183, 794044455, 820227375, 871577362, 3559901, 333557218, 528902406, 499692321, 807271995, 832392046, 756382701, 454012926, 420467896, 191676943, 149151515, 249139104, 606769484, 837856977, 571285073, 960861027, 142271750, 122913827, 652881911, 661163673, 352207153, 713256838, 975593439, 827635059, 977536924, 652281416, 634987015, 417008757, 588178719, 761218098, 350051161, 975760630, 221700062, 126945178, 445313770, 447461115, 398116718, 806264798, 230043349, 504725817, 15211187, 272886334, 468101167, 978643869, 172927015, 565140902, 313149986, 203449927, 159079521, 186390886, 504518823, 672120318, 259525396, 524223072, 473286234, 609662997, 833403390, 21612987, 760785591, 619830605, 142117573, 659285704, 292258276, 784837229, 166313325, 476089772, 963854405, 639074050, 179644850, 159333373, 119315931, 780165353, 809213579, 630135703, 565164120, 59477542, 575070981, 657950090, 552556012, 140615702, 427131123, 112045950, 579247773, 926332532, 244755224, 172368135, 315379620, 623470225, 578946247, 52285027, 310700394, 98966614, 636306390, 816721440, 755748482, 777048565, 291294415, 597128729, 930182300, 42243943, 610956997, 721938279, 896904420, 520702471, 483534409, 978139698, 802548202, 178691995, 936246653, 298968760, 920764134, 728659339, 733683551, 253243462, 407350299, 546345010, 466616236, 461460709, 391247425, 578847145, 183322456, 857097560, 16790494, 74424992, 245271437, 17228398, 238244540, 129328559, 294192722, 828254175, 790441160, 818338566, 84377515, 778481652, 448400817, 297499064, 646772071, 361533333, 250293295, 691791103, 768470752, 493330653, 303107211, 255989004, 272404891, 95622575, 49656525, 830696774, 879724362, 185607104, 391485723, 782379069, 699845145, 510340619, 871341779, 829014568, 806963775, 161928601, 816654738, 991746858, 781439835, 320345211, 823196713, 991854773, 154883436, 772875805, 718058988, 163074870, 939449467, 466933612, 767266719, 243438984, 584698453, 716592639, 487445640, 482144492, 413704731, 188616791, 716783556, 597372903, 86988156, 994506966, 632716727, 446408764, 356004926, 793239253, 341211116, 559528328, 233274545, 241271422, 709965251, 311289106, 543974177, 859986060, 529504205, 623275046, 295442717, 248695125, 458709201, 773759727, 979922086, 300408428, 666239331, 114250572, 91048221, 751835006, 346550038, 977803293, 177860187, 287052667, 110242590, 96296950, 144768456, 130248636, 772995595, 905675121, 563185628, 593257355, 97405138, 139024057, 862644281, 739425317, 979695352, 617513637, 973535948, 56704895, 386039033, 679862871, 485721730, 123488352, 200172106, 456692555, 878192907, 819914199, 96318837, 898101788, 723605645, 397810098, 812079778, 373564212, 462859085, 633323969, 724293132, 23096476, 221760597, 246350152, 352693268, 522791905, 27010914, 869790678, 635839058, 460263522, 111161151, 446182861, 211242736, 131559873, 384684918, 465218882, 965501218, 290077119, 930770630, 755631630, 802989865, 547231716, 744422618, 648647485, 752100793, 17236646, 336471118, 426091108, 783043392, 381808572, 988024813, 864582294, 720024258, 809892144, 212291155, 400138532, 496765396, 882414945, 32344693, 36282059, 21602677, 453441860, 251084989, 422550438, 771864102, 91267360, 519008492, 948577208, 179031069, 536701982, 698806432, 143774923, 172080681, 334976568, 55417855, 310499046, 367885494, 413630644, 40399684, 733185151, 535236857, 86654415, 553922197, 674798438, 74866915, 248221207, 243600898, 75485330, 99707461, 244252519, 536633278, 708784404, 600577020, 521869998, 391540738, 324282349, 389475826, 364004043, 654962871, 971182203, 894112922, 195518606, 504240016, 768623576, 574031903, 408524585, 911561827, 391633817, 979534592, 266416819, 615988989, 737075049, 390373755, 767122710, 472173302, 150800597, 269701255, 858872148, 697788463, 103968425, 168159251, 844427719, 139932703, 835736917, 187289979, 839965455, 441808158, 889508185, 254789357, 400698017, 71891421, 227749918, 600605955, 748717370, 460672147, 546085187, 532236368, 26252743, 399863286, 289732604, 833763874, 605971882, 808549224, 662321257, 184863408, 648893239, 833078660, 82975107, 35196610, 59860297, 333364288, 872303547, 329586321, 569314984, 227663505, 309303305, 957779058, 795344867, 12925900, 666144228, 922155834, 148177370, 201342735, 476288139, 7031854, 408888148, 907013036, 652498214, 602358953, 540940904, 191477172, 25280335, 668991083, 553333298, 189607418, 995032888, 378994158, 139401343, 631052634, 277823985, 625059721, 146827481, 73021186, 827391694, 872075679, 710675073, 234219925, 457763252, 732344772, 795326225, 247629600, 718086688, 899925356, 891716350, 395918676, 797810623, 852490946, 526682265, 347990402, 129869764, 657513930, 263703597, 160558122, 849834121, 919107216, 342436598, 491692640, 478832393, 386550885, 955230740, 203796205, 424871147, 620993611, 375356715, 509807272, 223555963, 765910020, 983152828, 522238657, 13089880, 923761523, 338995163, 479410912, 752252235, 2930605, 532867784, 233539401, 779392618, 614329619, 244444766, 758098805, 178142614, 748504712, 310236735, 621416437, 161196180, 295424600, 78465427, 278026061, 912628510, 503877017, 954623680, 219268711, 762092222, 851800548, 928961464, 373195061, 51800354, 754523626, 843721335, 933436205, 627751114, 794200578, 903441212, 174664328, 664682447, 289497349, 823386714, 783281589, 113057708, 864423065, 412763543, 207521098, 484938454, 86243355, 268449499, 493053270, 685227052, 352968900, 19584989, 916488253, 130925059, 676848330, 845211025, 909734937, 520997904, 56958998, 536927939, 795004033, 759868152, 188507000, 104917147, 212967737, 833416061, 880062585, 711087419, 607208890, 74940437, 251662724, 128979193, 183250502, 916383159, 673113597, 183681696, 6707130, 421365481, 515266009, 227378217, 902891850, 826572750, 797880091, 798274195, 665276706, 573291964, 285180877, 869445765, 616443699, 438962527, 491072675, 661819443, 585285094, 840706869, 166830189, 27568566, 258653724, 937228914, 796369443, 626966409, 380689209, 876145900, 774750489, 855045348, 394298561, 219231181, 740692470, 714036701, 128692742, 943136202, 521469032, 900632222, 565640828, 490702226, 916209283, 681875496, 576509402, 763051945, 541639496, 690221840, 826847045, 213033656, 433712557, 511408844, 835757091, 830862634, 616715901, 647894450, 253018460, 785009994, 138203799, 478567377, 132954800, 679479087, 812108165, 556259215, 905677377, 70514536, 520818726, 42124574, 344249017, 655227407, 426727621, 687703183, 546854242, 949248839, 76679400, 137127147, 613249789, 32090325, 842555922, 854938371, 456742974, 472711461, 910301352, 17494039, 971099607, 781903596, 939703899, 13668295, 418420814, 915111936, 890427564, 608903686, 274922917, 395916600, 266518982, 193160800, 686134516, 4934087, 873871325, 364835375, 942255870, 103810196, 127047932, 914647193, 225514996, 125409687, 961176530, 732660677, 182790892, 508305747, 891765514, 755132054, 646516886, 56852602, 476686531, 715521789, 801895200, 780995555, 8319291, 773800979, 138905745, 330878154, 529834156, 160341615, 783942148, 501180881, 530287862, 164478505, 936239943, 797284947, 425796239, 439738279, 332851498, 385554511, 791649525, 414023004, 389736969, 667034583, 735867796, 360322653, 773908129, 798960740, 101162576, 867061248, 603514447, 563399637, 861603706, 245621086, 962040668, 862464047, 782130731, 522625452, 233101608, 523437262, 762387393, 637985766, 855688620, 555105530, 206637915, 201629869, 262632872, 639142766, 789073834, 885177783, 807287729, 267682914, 475873735, 571560349, 64562066, 623932509, 725941902, 609294532, 764705297, 545819751, 600273801, 92381224, 404564477, 650729402, 825677453, 976003780, 790750673, 875489760, 275011842, 182173834, 334896168, 711715132, 616444198, 879734695, 755596474, 902362491, 815387761, 356424511, 358882207, 898891966, 856008133, 331745021, 534421919, 212325327, 99372088, 121890446, 56591192, 235744693, 472108438, 271278804, 830807230, 257864147, 520453506, 912453546, 451621316, 420320293, 471580864, 721027712, 277756895, 912424312, 807142615, 162503753, 478020543, 856694318, 657956176, 696275091, 168637067, 754363776, 734843750, 956120814, 745553865, 618305597, 199823583, 784953172, 818522829, 159609422, 625497808, 316207645, 341396133, 173898901, 940977132, 901820382, 672445379, 602260707, 758918771, 561234725, 675001158, 103465814, 661044316, 356610318, 986543195, 815247646, 899940374, 131514168, 207480561, 810495386, 137938233, 984859569, 181719562, 166594144, 999101763, 536356054, 17463023, 392454691, 445401423, 444675125, 509891020, 665655001, 628650677, 129357271, 536835537, 457209883, 35146862, 60110620, 284437669, 195305959, 648433538, 252266066, 892050875, 573916558, 330824328, 892166959, 881112458, 406796489, 945697077, 902266273, 460693762, 884045070, 662159402, 328478335, 1248177, 594477268, 847287420, 571041459, 771798770, 833063738, 419801132, 741769498, 308621134, 262451009, 308911151, 660352203, 226518788, 594914337, 528012489, 948327505, 291570076, 861258017, 882344773, 39051160, 424300126, 151193848, 860398723, 939100507, 382611029, 832840503, 137282800, 232653831, 659596285, 208741380, 575534826, 33718269, 339957113, 842994085, 830688244, 562123042, 813882837, 484217598, 996503768, 987398728, 588304860, 862471291, 997393228, 381257947, 252863559, 692447830, 736464287, 816631428, 306378266, 580754870, 176253070, 137152836, 652188809, 99617498, 491361607, 223481550, 289473908, 100347574, 424294633, 742649437, 765422456, 54167058, 323151546, 37987725, 73136697, 81217285, 855773918, 797476373, 749844484, 379866671, 926815162, 373068195, 109790807, 515141876, 277202614, 445285634, 127171204, 423087774, 822863084, 328939149, 369213663, 166530578, 286408536, 122001861, 368640710, 242962713, 895486392, 436776933, 804825566, 188042806, 96254910, 986479664, 651033524, 650207125, 376130291, 514867560, 506048454, 668762922, 557645339, 710805403, 1103699, 181449518, 301921380, 343188055, 819588591, 212902070, 314560317, 9424462, 511325265, 446086472, 276743915, 225015506, 759077320, 350889884, 649340534, 511460540, 655981613, 663609380, 237436360, 881831209, 533831109, 15135320, 773361623, 354971015, 171082187, 688159225, 288751017, 618313486, 828399581, 985325606, 968135037, 797084929, 504235677, 608971199, 487810617, 610136133, 474308744, 561043892, 973564531, 981405977, 837439081, 418032850, 433382119, 701076151, 509491667, 771028976, 881893754, 822381283, 612664698, 730879069, 647810376, 356971286, 160053814, 596320941, 915994744, 932185887, 49587493, 155598257, 588561585, 63889893, 880179721, 433838762, 118366972, 851398535, 637150246, 421024674, 589546543, 566389937, 6633140, 453472938, 539074437, 368841425, 61818664, 884788174, 908159330, 185921272, 190732469, 62636819, 971682128, 124374294, 481202196, 532447590, 617672755, 699283026, 264461370, 163161795, 536418728, 628418839, 639258714, 118480522, 92393487, 723326704, 6786929, 499814287, 471468729, 540025398, 191713673, 237745402, 7991692, 46970927, 905027296, 905371604, 148745463, 43815164, 248537076, 332647971, 951178858, 995341494, 37921885, 143108352, 829733581, 421828191, 163971748, 125282777, 347257600, 322445671, 93219878, 268928691, 137877126, 688491495, 211205015, 946306250, 485584653, 391613037, 156612330, 105795440, 646890414, 130950670, 50543037, 204771351, 423915439, 797608962, 134894474, 496343966, 852625485, 23268936, 927432177, 755482955, 324184451, 333428372, 926591810, 807662764, 887403107, 545517452, 206003931, 316697958, 187706045, 939425354, 671760577, 847383851, 59137286, 765944096, 497521245, 367516537, 182365669, 905508875, 788443869, 96755286, 91525342, 80501025, 242993415, 93908430, 739969214, 674996260, 617578067, 809821829, 650663596, 484439953, 347348739, 768638889, 762090309, 719589097, 278180042, 743462557, 141647820, 501434997, 985967491, 580765927, 981872683, 204381930, 811918865, 628051570, 42179359, 137102114, 189986771, 794204313, 700471405, 316568221, 715331730, 899045531, 88015147, 609625938, 800099667, 713220323, 683633379, 375989977, 363448300, 852819871, 42419935, 141372385, 727777359, 234542857, 186757723, 168731013, 854307705, 931509374, 379142996, 323726928, 989790132, 308290010, 849169924, 481571466, 892874614, 245273713, 318020179, 674304257, 538118293, 558466547, 480923321, 626649346, 75839825, 978205247, 534201063, 619764962, 802183118, 368001961, 359154917, 938450882, 153932572, 969140709, 445882300, 336787966, 26458254, 953062561, 774838684, 625192122, 391025461, 978246587, 110078681, 804769134, 28718756, 133113959, 367393718, 782742916, 851398438, 29073407, 849924062, 917887145, 785786360, 318559820, 506989195, 224356348, 649408952, 424972615, 525723330, 513667636, 735137676, 998083528, 659217859, 408333123, 323715719, 69180730, 705443423, 653416224, 789994820, 565674993, 821686206, 429878819, 70349811, 460469361, 553789945, 489512984, 806145540, 386250386, 169880439, 747244464, 97839102, 893579038, 786762100, 990421845, 56014953, 844874722, 493382460, 37454683, 78670257, 441608721, 783765385, 986706102, 76454055, 820905164, 995695108, 332304737, 661094984, 355826979, 807888301, 585956062, 396735721, 792927421, 510675130, 51275248, 293387043, 32674467, 568317053, 997100827, 97620321, 63233533, 315382832, 671364718, 867976285, 234380574, 196830605, 230412063, 262097759, 271702042, 953723548, 367517739, 531799284, 373113809, 27894279, 15801513, 405091962, 611678010, 165862228, 821776595, 328990122, 52660598, 775270368, 409813699, 534859533, 708706750, 934563972, 82603808, 15133790, 597778323, 861694670, 709156291, 764412958, 671352217, 801822213, 469672824, 780227467, 926492848, 96664752, 629060807, 989701283, 183103103, 921657810, 998316310, 126741504, 149175403, 556405661, 576135998, 791521836, 996962060, 278406980, 306893620, 495661410, 572350485, 978170624, 766824932, 977001120, 91145224, 637378199, 356912348, 678421392, 280730531, 518573469, 812006476, 746786660, 223077681, 226039457, 449954960, 860876488, 857523748, 211948271, 638281598, 996774605, 768016347, 364888746, 89778755, 93459379, 147803200, 59498766, 90103100, 895785640, 835546595, 596507885, 469789432, 436333088, 13515465, 23149870, 257849151, 334159039, 162801240, 293369863, 579020470, 562488036, 932348118, 247750629, 89321391, 602347555, 512407001, 547459831, 117020079, 508355445, 777911474, 117837629, 244528978, 324682794, 373268979, 49854769, 489530303, 914723331, 953494865, 458840495, 300861627, 829288652, 695132910, 649633463, 111575188, 263752670, 315166736, 209458725, 278684041, 601706487, 956025358, 10727204, 467097086, 644017055, 763488785, 515266080, 246025191, 899091594, 3738487, 974739917, 118347406, 5800269, 386137711, 637717304, 908236878, 976446296, 971077351, 801337355, 753414777, 434108784, 59720306, 919054084, 582472901, 261255031, 55931310, 156987335, 745308173, 118444641, 789235761, 135061872, 581599069, 887289800, 128752306, 220194953, 759227246, 180345504, 208415813, 894274447, 294791668, 188802528, 216173502, 459494631, 54830372, 777524638, 902372978, 522621561, 249563693, 263596190, 292143581, 759920934, 860708814, 918074885, 735196943, 357682324, 301449004, 631801535, 161529368, 947829401, 500885443, 34482715, 591961159, 424459373, 607519439, 551221579, 636635697, 564963295, 345817413, 184999660, 361207779, 628336713, 879600209, 526763986, 621373276, 783516735, 951075997, 599654573, 227254972, 736746047, 44147050, 494064713, 262711274, 145013306, 577811410, 557802000, 183112717, 257719732, 892764035, 945179367, 370248083, 792824279, 47346647, 40280827, 90904695, 849453399, 771790415, 792332684, 491510568, 195136096, 943776074, 308127539, 472497984, 859630624, 737281499, 629433717, 881378836, 368874568, 903179528, 299943158, 332132978, 174373201, 520871122, 742803018, 842334851, 115737855, 617494609, 96374133, 285855153, 147402444, 822940626, 565408179, 437190215, 714670396, 196099160, 643731571, 786330918, 540788410, 530690290, 609393236, 401895709, 218575767, 555734150, 725986740, 817723691, 395012371, 761638521, 340997989, 958744273, 257870508, 993334909, 93723055, 270867521, 714445982, 270053618, 970320863, 195625385, 8762629, 724423602, 581137281, 353744754, 609347862, 192314514, 911345588, 761318548, 944955624, 483009507, 702505002, 590910864, 85491915, 184169878, 425952042, 605348992, 913175082, 12952999, 643536107, 131438677, 284040713, 953505566, 364522135, 842705601, 780121833, 756930541, 86801448, 633514902, 520770822, 465707657, 726974508, 122745830, 246267790, 910311665, 222589619, 207792722, 382383720, 761203130, 824610515, 714059231, 182877716, 899090314, 140222348, 414710949, 906099114, 532952399, 704381893, 950060422, 932170433, 437843112, 286819311, 233681117, 104144656, 240475947, 480419368, 954422521, 926642689, 912221275, 580593354, 331814545, 766617163, 993769254, 865502380, 180604774, 489933539, 424783024, 318073629, 815704791, 166909235, 190115599, 719148202, 692511164, 91922100, 248376364, 314472117, 558044155, 327072850, 201419685, 721496173, 740620316, 492247143, 408886561, 620725595, 985727458, 26311209, 757817502, 825601017, 111461838, 374533912, 992348710, 363077426, 945249365, 32836275, 566419117, 460803059, 735600974, 90478259, 560790458, 191882737, 350407949, 11804719, 135619204, 942757582, 815892470, 4537934, 66725409, 974873117, 710156323, 30015365, 542824226, 905911808, 317123249, 482563414, 60350217, 94672854, 728945030, 15412376, 373037033, 557502714, 831607417, 600707723, 874460316, 195929260, 294435024, 385980942, 900229392, 971112358, 937159887, 536216921, 757082019, 430723652, 969312622, 143423698, 6081719, 275341105, 92120724, 96795000, 935427257, 674972764, 798065588, 510562755, 83319993, 432388979, 53424438, 810311927, 675079661, 370580978, 365243105, 87732583, 2882255, 17771025, 742973988, 336610435, 127748894, 744594067, 140101965, 717267447, 414710433, 656219456, 201041005, 366131947, 824828229, 395382018, 573557049, 512768501, 945970728, 183879823, 527766009, 524070383, 467319246, 979173261, 23885322, 525320798, 395508976, 729034913, 533754066, 527912820, 374303513, 870552722, 408544893, 150994149, 348130103, 825040851, 687586118, 174072632, 313990236, 195506512, 818399079, 589998819, 836793423, 748759435, 384107578, 41136448, 346176412, 337396409, 276159194, 389110244, 584728006, 805391126, 170446223, 34294827, 369682096, 729509318, 592566414, 208080800, 361228440, 815015717, 47873658, 715633554, 529311783, 864597513, 87860861, 903871407, 312167924, 591519727, 235043341, 302380072, 391789708, 168494676, 1125174, 815827735, 650137046, 204107518, 551473510, 632027968, 353466026, 868788858, 713144948, 67511840, 823725057, 168146451, 77268905, 867156366, 415530936, 939534991, 936154520, 948180741, 88895648, 177809060, 491928369, 396964091, 546372196, 24582472, 561250221, 694596976, 447580062, 789100619, 707258400, 929826276, 606470092, 608215378, 6308158, 68569088, 888053888, 156055316, 888733310, 475399663, 171045534, 300667620, 994529895, 138018895, 890463666, 773386457, 816633221, 696370375, 143285925, 157021355, 930704158, 619143769, 436889949, 722619719, 356928571, 877005245, 431523799, 324621358, 778427551, 835352926, 449918360, 243657341, 342203357, 492959422, 927252971, 381402047, 639839692, 626847995, 284409679, 440971926, 351819459, 111091505, 778249399, 416933197, 732480196, 400298058, 649842485, 257485809, 544242353, 190674034, 397225084, 897776740, 531640999, 552442542, 481982051, 488199327, 723564743, 903706625, 554514669, 440746721, 840770824, 579550990, 372251541, 546363460, 182759234, 292920219, 168658082, 11635852, 677847836, 875591147, 946046711, 757928682, 262633201, 723803348, 957109494, 601843109, 446028009, 689313484, 53065876, 474245439, 742292792, 501705683, 640672328, 961960200, 776363489, 25868408, 247369817, 438106492, 148110044, 25406683, 434421740, 474567156, 517417407, 227836, 216571535, 696060875, 819932690, 438409551, 746612633, 714960360, 258043373, 919725359, 244736164, 144004721, 633854018, 699910831, 119285341, 180305344, 182637091, 537144892, 732604112, 824261122, 136882175, 53047690, 626957740, 512340722, 669531673, 98616653, 210022699, 211040046, 407852366, 724787426, 581357436, 279503755, 7213190, 819991786, 95057338, 771874576, 917473337, 379639651, 431340517, 306459586, 215332780, 631614278, 139797082, 960076907, 754370246, 939794091, 702083533, 404923056, 240200652, 923833375, 592841415, 819948805, 769888636, 378152077, 185106724, 989314092, 625828513, 675863223, 823031507, 268353287, 73884878, 953170080, 105633529, 741159998, 557591044, 23929579, 710033153, 613426099, 191282792, 533152297, 772016202, 625634691, 352459930, 900988511, 844431327, 575958148, 289419900, 125159341, 585345210, 781212033, 283721180, 709662586, 592516046, 259839910, 978333831, 121022906, 286340168, 550891493, 591590552, 101237116, 24268324, 10045797, 144525647, 658333731, 437278351, 27314616, 802462076, 136969380, 45885227, 862572373, 230832822, 960812929, 639468122, 903590456, 570465451, 683686441, 839882516, 595832832, 710235814, 384168315, 956496436, 141133164, 783082777, 35211483, 200633374, 366713864, 215441694, 48580313, 403181808, 386598503, 42310998, 56810066, 227683136, 234402523, 179292812, 479170291, 736932756, 110998376, 330726133, 906871892, 397970878, 204322857, 305970720, 41379210, 294628506, 565289032, 858840491, 668993350, 104598740, 794296366, 700715468, 39854651, 169178891, 503368036, 253508405, 723804855, 53877247, 618359392, 679618434, 959000129, 796676250, 616441601, 380456098, 82737501, 800931696, 774965111, 848386829, 49951585, 356232259, 636739347, 164318676, 843507507, 355422071, 840127160, 737760200, 984928607, 147000171, 383722448, 416221705, 93833318, 655644823, 728355826, 214411038, 123529275, 846141340, 522229601, 393672550, 228622325, 731490197, 320845602, 704405900, 310560228, 998252763, 407741942, 65234895, 543383712, 514928762, 330954029, 90681486, 812138819, 327564962, 517940684, 606094386, 937740654, 455703340, 117706005, 151586059, 432987679, 420695420, 457633301, 711436949, 170142163, 989614554, 206091841, 127358526, 494671184, 709167715, 518821783, 713895580, 517932413, 751629723, 14926485, 869126154, 451883048, 100194099, 595693740, 871918228, 515739778, 731979985, 659152008, 525733438, 449980730, 50814764, 298216209, 226245251, 855290571, 674061694, 552292212, 82903996, 912274521, 811961074, 385351695, 753196216, 352466203, 901336790, 432012590, 221556139, 921033563, 755684400, 970328114, 519947152, 594898594, 784739163, 916113861, 196890368, 874585276, 617083802, 136557470, 649643861, 506964787, 46494554, 584934542, 77488200, 691453480, 239519828, 567097581, 808809062, 143195141, 832596247, 158253340, 996669953, 690183733, 164033892, 865042060, 173848081, 798445170, 832175568, 575126593, 371187161, 363348582, 972273077, 720235957, 392749507, 844564348, 769089509, 54158992, 138218950, 165070803, 693164461, 669468457, 616041694, 365307097, 452360166, 638255383, 435915982, 328306648, 618910800, 438320222, 566293061, 754991206, 199151950, 797707559, 356180326, 673687925, 834897342, 582677295, 532159549, 119448085, 68534757, 29114738, 528989674, 154092751, 981364903, 692892188, 557927055, 448564024, 784320594, 325572738, 530733979, 893751785, 786660502, 887240991, 844465255, 830618084, 4133678, 336514461, 628770578, 121278207, 566279062, 707093197, 256544382, 765169177, 871635194, 134013847, 898968454, 720336127, 503288047, 649328999, 275274301, 2777535, 433077531, 683015843, 659795675, 365215316, 96818206, 563947964, 414776342, 950440447, 406354468, 43603539, 910312622, 956299967, 934984104, 14717383, 746109779, 871782930, 525852313, 7229394, 541006536, 51853530, 113144863, 568738518, 690780040, 540953882, 244161804, 855634032, 486703147, 51814560, 82044715, 207986727, 124733813, 742357651, 959696328, 370914044, 406776525, 717694801, 450656530, 888410334, 805122350, 697014077, 329782798, 684066919, 744218380, 814546367, 326148986, 195420251, 268634400, 364312180, 418921466, 684810830, 882274919, 781018305, 628920467, 505292968, 54629407, 876854453, 675111157, 469693007, 940610723, 739938313, 285394510, 242535789, 689780335, 264834821, 59743076, 212892685, 494928477, 865121847, 114047745, 254717231, 736146020, 661752033, 538350061, 372502980, 28632108, 966959836, 469731158, 433485816, 676208333, 975349879, 853529361, 316746099, 917989091, 307934617, 913047788, 362531365, 9828214, 290132343, 28582016, 224186148, 692153206, 306229690, 886303777, 955012482, 768677985, 895677810, 524921679, 380192594, 787723361, 298067355, 679081312, 469110918, 754854639, 81924332, 718435084, 767078915, 896919813, 450236868, 921995588, 390246105, 107594349, 840250913, 430040452, 245551671, 790237672, 972188732, 905410192, 283588289, 76319427, 1953829, 984690188, 819048049, 234285583, 898805323, 166827536, 332757137, 372170547, 600196656, 884261314, 757000396, 816198634, 643293044, 368797728, 633368306, 676992131, 725442443, 278664049, 307451753, 60450184, 973273397, 586303062, 530243954, 826090480, 164023723, 292089605, 313173090, 759788145, 366966130, 351128173, 993446006, 867727350, 310504024, 821484748, 958661318, 982167731, 174182212, 895826212, 367206230, 51714324, 172497868, 88526265, 107560657, 499971790, 835569259, 75379328, 680953683, 248855453, 663252792, 334756094, 471370845, 919919507, 203137975, 837591398, 605821711, 295761375, 870390476, 454047899, 86875071, 501959246, 595614486, 871257144, 805244777, 686602375, 97402119, 213617708, 17962089, 397271141, 801498154, 10088796, 864452088, 941186551, 220987649, 751093228, 180103596, 15259901, 394860076, 492181443, 779818980, 551816743, 792097912, 371675781, 118800304, 971046353, 578787355, 745283687, 898838230, 929609563, 628563182, 244525589, 612009433, 531126330, 735432436, 634427210, 30904382, 47012917, 415143815, 892900063, 727841477, 97507326, 603893349, 344392185, 765021468, 325826386, 755141794, 775295804, 524954649, 814806360, 54875433, 413900528, 242145815, 588076475, 949067839, 165105209, 382965679, 614790819, 167258856, 509033375, 144033288, 257385547, 907383813, 202420016, 828423000, 823520598, 876569297, 605380333, 79087835, 357294120, 334628033, 807523102, 565769518, 671090412, 71000886, 772062012, 535036235, 26492858, 694418796, 847204233, 761383800, 658251286, 884397048, 570100108, 752880756, 51160484, 127662325, 649289147, 191834925, 135718296, 474759814, 875561012, 138729188, 484268089, 766030120, 839443707, 589601561, 923864260, 657757261, 736170722, 23929549, 104837711, 736243232, 599807247, 279468157, 51308054, 923129622, 958712770, 504817706, 119846292, 89664579, 277358290, 362354448, 121931789, 443824432, 917282732, 744924466, 643658702, 814190511, 328840532, 666485050, 264996913, 176466371, 559255632, 233449185, 26643086, 701586001, 422484058, 949446166, 205146853, 344927748, 856310311, 741603644, 63541304, 285784266, 185708516, 151763083, 533092041, 960411189, 164387900, 142035599, 370939951, 736225597, 313181333, 18441862, 11638378, 892655906, 930712841, 836360315, 980769074, 64374548, 731066359, 31228323, 559893625, 230809421, 308917897, 604645639, 124448451, 949392808, 141783310, 351591175, 733660387, 980693741, 256134743, 918910640, 585764265, 477282286, 834303212, 632914647, 561443753, 629849802, 70104236, 635707874, 328049098, 437909819, 471459916, 761010643, 494592543, 388747507, 138615446, 558960602, 198100558, 886585961, 706134888, 200849171, 607349207, 719832002, 331626448, 829291681, 781569256, 953458818, 491000641, 842469982, 518990874, 162684443, 257859904, 623916918, 324098278, 536872015, 84024176, 720646416, 279532184, 420780377, 566142365, 515336408, 248690810, 843833991, 730656414, 61347566, 736819667, 743262351, 706607147, 645240870, 293782234, 713981832, 350674321, 43867152, 91788976, 60521529, 978587899, 408565530, 409814186, 958029339, 703428576, 501501339, 983605731, 849950009, 135022010, 742191812, 161869299, 574559176, 539217270, 916707070, 614912838, 966594606, 532483655, 990205272, 92525681, 451063482, 851857001, 89026378, 256829322, 152545709, 355442299, 423122508, 155275014, 7791950, 809646393, 601402222, 399442556, 443912113, 360839500, 425879213, 334758001, 778866261, 493430435, 557843589, 217592053, 112139442, 993512353, 560733302, 467387059, 400760436, 810582945, 637234760, 793921464, 957269548, 43643240, 370281577, 116203127, 636985677, 123688593, 946653773, 118631620, 911671814, 822988245, 160779321, 206506209, 933787411, 987354859, 441180683, 197235128, 630115926, 954937313, 142541167, 74316008, 645592813, 613118778, 80097437, 489049881, 526865403, 178436918, 279998435, 193369089, 43713251, 130108845, 573699291, 660881097, 903952780, 386140115, 943780511, 832435772, 736077324, 589294049, 348866736, 229378043, 662842259, 208250449, 249592652, 524166960, 517935951, 181437462, 266321615, 647114967, 145665211, 700199349, 128102439, 272020345, 188660775, 578868813, 475635983, 415227190, 433636699, 446890070, 822714733, 360183442, 993794886, 286369680, 757584438, 337765081, 587652394, 793501906, 799225912, 646786255, 803090175, 969713399, 390345449, 482133, 238008343, 444033664, 818287798, 188978431, 745776578, 553807645, 258760999, 118370225, 454886459, 998702080, 826135020, 634591522, 776445064, 898460379, 550066816, 716682940, 58562328, 536554566, 973304634, 744914493, 527091284, 893806021, 176029763, 244340391, 931318909, 318996332, 438145314, 890309255, 781108666, 135078703, 830021614, 593111200, 119230352, 994499987, 988228680, 430298614, 30775265, 653131574, 902368065, 202051908, 951682357, 666790868, 414004266, 820575465, 387630233, 733445403, 941329274, 990255179, 930129593, 902782929, 888496984, 732366859, 334497578, 280315454, 224705134, 518870039, 462684997, 701195466, 431276433, 354954237, 332528989, 526701758, 222039935, 212732021, 541677431, 893390045, 953929262, 924633831, 752552177, 619748582, 523090904, 592575439, 306502796, 56021950, 433915458, 660976403, 867521482, 694443500, 604988036, 81875217, 321296141, 275087944, 854011115, 700168114, 984834563, 356409692, 362492789, 634664659, 521115103, 942600023, 584087876, 834181628, 430578483, 575738974, 637671077, 469827815, 689813572, 90265612, 481492625, 85732439, 65939351, 311646556, 106689191, 827244654, 682942666, 234034547, 496114354, 315421004, 537725124, 81658901, 361132316, 73259857, 34373783, 36962648, 18311780, 48928871, 99460691, 243332212, 433216654, 635715607, 338782311, 148090685, 829871319, 616434423, 691615996, 728415765, 164752684, 109533794, 54034445, 878822487, 281563669, 102322265, 173504882, 805957446, 253081691, 154028298, 908251098, 151048198, 770558055, 394323931, 711870788, 400767929, 273529888, 364710894, 186720063, 203903383, 764083177, 951489458, 830766614, 481194371, 14621108, 526954309, 774921399, 72318616, 413726201, 842830643, 375469294, 13298591, 454712912, 764834303, 788508992, 252635712, 40810356, 602998310, 212062367, 719478248, 202406736, 84058777, 419072272, 919686461, 719472718, 942226558, 848998623, 471110957, 726226044, 585560562, 248926452, 287946280, 781111867, 439378031, 435327629, 458393081, 345388581, 764055753, 635346153, 995493057, 999318935, 166202898, 146460462, 547866916, 314008766, 575125012, 526199502, 100729003, 802542174, 227292368, 163373902, 789181259, 784936329, 582074407, 916913627, 388305321, 964550089, 879746359, 296360677, 48880930, 475063773, 806723686, 367761152, 734352311, 547827477, 93985803, 407018146, 350793919, 800042370, 875703632, 439618456, 906493131, 865901709, 181822384, 658364560, 572982154, 113833042, 917276090, 11693876, 214673957, 311293959, 619493371, 743840433, 178396345, 892215163, 65350740, 198446589, 839043754, 947404763, 705184818, 322265786, 611095208, 678771279, 762685184, 290268075, 858188852, 417274545, 666896508, 651035059, 431098723, 267975097, 700798166, 125297468, 679727043, 697366672, 671617066, 457340217, 801557146, 422118165, 586395874, 446228698, 806908570, 750017207, 693706900, 361580499, 485516320, 44724990, 533049460, 805446622, 16109379, 294797176, 450488698, 258496215, 742998251, 357327876, 488470035, 53932170, 733579744, 375616907, 494933166, 253705259, 316142911, 816123300, 863435092, 946349868, 207739213, 235122677, 345149888, 446498795, 64894442, 406750353, 204166487, 121632622, 610367127, 468610515, 938747853, 624565440, 737699201, 39908753, 342937293, 388778217, 891700802, 912726805, 338990470, 300781589, 535591469, 60283705, 400840888, 40615297, 676360606, 110419657, 283476080, 470854247, 930549360, 545573195, 676024003, 834939919, 496803786, 744460140, 334970456, 725902053, 205588448, 692409843, 715708029, 145765591, 640164725, 209049938, 892547168, 372374694, 782087313, 459908562, 927800101, 519926632, 449367535, 475777040, 814154568, 159565715, 93717517, 398196853, 648027168, 230889678, 555019749, 614878567, 24179258, 530307841, 401940222, 40096179, 58544007, 175241394, 508696777, 733975223, 739506865, 63101122, 660868076, 815425855, 553439443, 741662991, 49367310, 973353871, 736294270, 573625999, 143745089, 167239276, 299383102, 691299085, 308585450, 113098141, 342485849, 610543863, 386861278, 768309757, 367149525, 431876488, 155199268, 453006603, 839647272, 637890308, 916920232, 524915412, 893376600, 625749130, 987669124, 877942382, 708176307, 163331506, 844411659, 636495281, 381084681, 836225143, 729974134, 268402178, 622649171, 395847654, 801204711, 613592121, 38963756, 711407077, 635772023, 112423862, 608481177, 227299789, 264324762, 499526228, 593920388, 552608969, 250193284, 189675826, 851581719, 305132085, 364595305, 385995094, 541906033, 720286621, 846265824, 660604601, 563943647, 142319697, 489304840, 336206377, 875571355, 166225042, 863450759, 321918575, 739441737, 385359384, 438148633, 540649135, 949890102, 505526412, 220230922, 563877759, 592002549, 806625451, 181168378, 459373761, 217738991, 65103285, 934432451, 657638050, 438468108, 582302514, 567301915, 234851119, 377904102, 303827571, 4439966, 665885741, 393264566, 760126680, 993792681, 202067685, 220013635, 260253126, 17126522, 599289121, 286522304, 459392316, 392303278, 466967180, 168397669, 861944715, 586002736, 963080404, 165018139, 77427952, 399668067, 51565447, 831601194, 19374143, 221980898, 365447168, 953070310, 943440277, 39255069, 700518809, 565266721, 588521731, 392928183, 545733900, 37067529, 278300397, 365947218, 6414400, 17322264, 710992824, 938712028, 672659040, 390046505, 630681429, 855799997, 492270589, 710250378, 358252438, 902747750, 963508836, 184212592, 208187661, 622493648, 876961865, 190279506, 444931092, 3569175, 426657486, 521857654, 553241548, 912453445, 986283270, 411663500, 308519804, 714484290, 291860157, 902550831, 180218607, 936211190, 172163521, 125194202, 691828937, 825638546, 187602245, 885840895, 683826283, 928031406, 409512059, 779798711, 887948398, 317401364, 900813319, 100453837, 692534248, 220363263, 503959144, 650049882, 467929218, 17090900, 687598231, 282930285, 327684814, 718787869, 283522129, 508547076, 666664349, 483427660, 675148315, 559771911, 950674160, 305304092, 248285395, 20846614, 277863253, 80540330, 113553152, 479105288, 164243247, 711528688, 149515993, 61327079, 851292848, 613958905, 11822622, 279781806, 4678630, 542162722, 203409494, 439859533, 152669029, 536542770, 497359022, 340902631, 933938399, 931731480, 484999951, 177895770, 358157400, 952745828, 503469208, 299227383, 641598932, 698755356, 312496985, 926820703, 24415843, 522048737, 185409199, 754573385, 801093688, 311039048, 275638742, 734159497, 447299729, 467890320, 924539263, 585246723, 364037368, 587482678, 145386396, 578291396, 647802789, 718212635, 491798369, 699884659, 223265082, 114290775, 808657812, 914366379, 285083303, 633830080, 391323301, 317844762, 137910128, 7429141, 157169514, 553396773, 926951609, 407660907, 229914916, 424037404, 474239163, 135894910, 378560755, 431621856, 244496301, 408886082, 945790534, 143994822, 773243772, 784665997, 362944750, 98682425, 478578304, 136772375, 505509732, 361937893, 427394957, 563260755, 785897782, 394268122, 978402286, 872602058, 418918655, 620525200, 521745199, 273641193, 458654650, 153242581, 175385535, 737491509, 962774637, 64578567, 21809593, 280397988, 413964542, 251878004, 615720468, 358993063, 284589062, 270427074, 834280022, 1667835, 188729218, 606363219, 939840313, 151686391, 581105088, 807374800, 697366784, 834634790, 359724875, 20786639, 678237904, 650350580, 573539131, 757913914, 365119059, 165928424, 874006212, 798655700, 541045081, 337959908, 488762174, 591086912, 617240359, 899783908, 491605222, 772119427, 359591326, 350002738, 257632258, 966417521, 206887571, 696443034, 111278204, 166917297, 73854553, 172680019, 665494600, 632976158, 522167320, 793650033, 742275607, 870886325, 397284944, 723803107, 469315497, 872750341, 582366362, 241910306, 353221975, 463260500, 881109507, 12700500, 913640, 628635474, 305054978, 934325647, 562135430, 650292256, 682118248, 252113498, 929083330, 426136197, 729623682, 459776616, 642927591, 551617976, 213600611, 458374999, 366640695, 320649836, 836431204, 356274160, 439016711, 271513484, 57669468, 761676005, 46953832, 264371353, 517646572, 831585319, 282734509, 345134425, 847115765, 429363979, 927528575, 441424050, 162982009, 582053405, 337212788, 705211157, 603568638, 97459067, 953378280, 25312497, 734596284, 688505591, 851324149, 476896744, 990513270, 914231009, 356709206, 9278054, 408302009, 116508763, 371947152, 327254934, 82241609, 815473704, 143596533, 902266859, 839183299, 686883965, 977878133, 63228038, 95837940, 542544385, 202025370, 854343637, 825793945, 937278935, 208290561, 26974805, 677822455, 463277909, 116781879, 989468501, 632889397, 739206824, 664915879, 149955813, 164494161, 747275848, 936841443, 603515041, 536066120, 10421781, 167083599, 35412506, 33242408, 929066787, 35660746, 825964745, 607902800, 395003602, 8139386, 935735775, 28152108, 202403018, 769008167, 341234395, 577562075, 431018016, 99671317, 595015312, 251888544, 582933340, 79424393, 8788042, 745787096, 280692533, 473429334, 175912819, 513350572, 137878443, 798448076, 594792063, 846429834, 697773027, 818778652, 239656537, 795844325, 69307893, 212637005, 75173913, 196026865, 154086791, 426260476, 380781993, 367348334, 386244551, 979019491, 121723269, 289179090, 981481979, 838403266, 317804760, 978431305, 950888140, 997845673, 331729542, 971601254, 926816436, 782626720, 361075449, 237442275, 879591311, 13356060, 869446643, 334157967, 883555050, 851515175, 15079629, 736782271, 548480422, 249371393, 208874941, 599798492, 901145587, 52973619, 492114761, 385774916, 217316340, 696740397, 276889089, 152616198, 877758806, 549934384, 188455903, 642080798, 219991040, 715777999, 324484559, 807892431, 781860050, 272566717, 813749847, 117540227, 837760263, 646903740, 857892920, 829504824, 589670208, 368781825, 615757027, 949588867, 360461699, 72031325, 175071235, 393354655, 349895705, 267374205, 242204920, 711657173, 167596278, 534048617, 527841972, 539278104, 815988177, 881077964, 183174397, 314990768, 203521435, 75687153, 137483867, 539371622, 689403412, 341515902, 225654106, 395790815, 716285311, 388020625, 136865294, 794529970, 913532407, 432384515, 323235970, 117410198, 607063512, 111306202, 948501775, 253343278, 105270065, 329977329, 946314966, 377140068, 176906451, 454563089, 152453444, 525209700, 979993293, 697795660, 619981965, 72063258, 85691948, 267533130, 741186707, 622860633, 722619944, 293332405, 848161794, 828693988, 106851003, 915102470, 149375872, 449510186, 555687046, 906783505, 267980869, 14205151, 207369613, 225547270, 270254217, 974492995, 877655412, 523758970, 118926846, 383875423, 496333812, 902617734, 754108699, 512053625, 2035823, 358904331, 178407189, 129415016, 342355721, 738169600, 777916963, 395036161, 274616174, 839485442, 407126529, 906159071, 882883299, 828611228, 645665906, 458216734, 195112314, 175015070, 116139245, 183303699, 480343661, 804870296, 520428672, 559753721, 416246747, 359414214, 260247578, 717121252, 226905555, 980112034, 864360083, 584812408, 123589901, 893186020, 281301078, 299846521, 193467716, 33177185, 408979455, 922251965, 559373432, 113287777, 80633071, 504990024, 847140235, 607989342, 181157719, 26048543, 164041767, 380902168, 138201298, 557549945, 223731087, 269258919, 816638917, 885401511, 754565368, 436659607, 291066919, 145741757, 961277049, 380354473, 308183656, 342541957, 910061103, 418486209, 980576415, 35525516, 800014245, 161965776, 86078841, 893298894, 994979910, 157609178, 151394215, 548461989, 978690411, 38012077, 238930263, 511194983, 197747026, 232042700, 178802259, 916058108, 41556938, 721360653, 839961508, 252084545, 760390706, 758003621, 886766524, 828985735, 830062769, 656040165, 868860344, 51010246, 437516428, 517487845, 388208155, 595427375, 867967596, 204162909, 102896991, 525765314, 50219312, 420449105, 693356091, 473523505, 601239628, 353170848, 388864723, 999649892, 768389739, 533299773, 917155856, 174288340, 584527240, 747917015, 73150528, 627543555, 203775628, 209746035, 244612781, 876234706, 601531873, 999348736, 904760577, 895774028, 93357328, 609600389, 624753981, 478492283, 898338575, 114527986, 358948905, 893734356, 332479109, 461385452, 716952785, 395179355, 496664423, 794767583, 237628512, 640585324, 563471572, 437190996, 405506052, 895330092, 356389936, 583977718, 810304098, 746667083, 122459232, 243236230, 553774828, 959601913, 388345857, 929498248, 500463763, 378487467, 793079972, 942187788, 62933738, 958026540, 887678434, 636779266, 260494035, 804844177, 423036465, 662784359, 730793990, 38091930, 10535793, 615670302, 705970924, 783756237, 162614373, 94517383, 96023814, 214187766, 558384162, 733949455, 650184246, 459975260, 590075774, 884394385, 445727756, 148469720, 858559774, 98360516, 215252418, 573310952, 117066296, 969111462, 689609529, 161852448, 684784608, 906920449, 833658598, 536096596, 522244270, 459035476, 321299872, 205064247, 574647572, 119849120, 855899529, 669794822, 500864876, 612614967, 564615427, 619029242, 537581145, 450183856, 576549130, 952084169, 761362544, 174971814, 653749380, 355312683, 629732380, 118581486, 934854342, 669451054, 636154079, 946354387, 677968894, 577377799, 977654735, 926139226, 458957062, 462480882, 508306527, 301656194, 938212680, 596922786, 319475923, 168680404, 116673983, 833563711, 91963659, 432878428, 55308345, 729964953, 2605984, 36813072, 184224502, 368815443, 953443104, 146224318, 633089317, 929984544, 435541419, 191571073, 965089204, 964785890, 786750942, 788423018, 812012263, 446900207, 257591240, 147318376, 331457961, 129142666, 86903879, 542965331, 809006415, 750561917, 937919122, 700857591, 112244447, 140620668, 965212633, 66525560, 93023960, 538819316, 759995479, 143789329, 619055855, 809659547, 780591279, 440557650, 392792125, 936962496, 251662839, 765371250, 106631101, 733159304, 577683461, 814150046, 803319139, 223616288, 722765945, 986910645, 578947037, 567622869, 573934147, 298987415, 101799664, 202990837, 917549458, 254108356, 531312368, 824046762, 63994605, 222811644, 224641046, 653302890, 406824973, 445409041, 44036677, 798184805, 933786077, 669345801, 64449623, 93090855, 374164052, 986058386, 801223459, 895945248, 557702942, 918899187, 716273874, 503933920, 423160618, 464210086, 626190792, 538518171, 372870728, 146287741, 559899866, 251265478, 501736103, 428683569, 595248634, 531511572, 256041942, 750833885, 630519969, 475362729, 436898595, 796196298, 310802643, 703742491, 409926550, 2939558, 739065256, 277898786, 995480221, 655240668, 239856798, 659132153, 921705584, 463024316, 666058234, 462608969, 154775044, 785339768, 397038090, 22370043, 754575246, 933322081, 844110615, 913225990, 641707583, 34172023, 641666441, 41836341, 203552616, 277678799, 340912851, 279448145, 120808465, 919367532, 421807628, 459859159, 625083149, 359155808, 611385575, 458460908, 290078479, 527629716, 453086809, 915763266, 182926633, 289844778, 947386328, 807841971, 420093857, 646641937, 574831540, 570964383, 726152207, 690277460, 933465661, 626541763, 163765759, 438001581, 776569882, 909213947, 366143732, 669010183, 482753996, 879426765, 833536115, 890731412, 554900746, 204194929, 576795434, 440185543, 35744270, 760436040, 61562440, 547865427, 856423185, 215871414, 143543295, 631406986, 971194924, 687732015, 311390818, 947322125, 302837983, 364371797, 142280683, 650806693, 908934057, 121100915, 459352816, 382665644, 345388990, 786277373, 79776065, 217745070, 679864474, 473833777, 280683396, 426421582, 875587930, 952668025, 403809387, 188666232, 741381130, 585908261, 784460117, 150658051, 67525293, 797558573, 713845071, 5783057, 582058160, 281381108, 375770262, 381605541, 718805733, 959058704, 529710781, 758556495, 623147910, 265466475, 457372028, 815087375, 873375635, 389490230, 784527077, 351132088, 208493765, 603226446, 994485567, 187715850, 909635247, 481381078, 957321954, 651767830, 857500599, 191566654, 698065404, 83996915, 507463213, 386863835, 530807300, 428361531, 45557014, 851959510, 53911109, 947791015, 694574986, 589439344, 614333407, 496288070, 175482342, 523348990, 415301653, 266407009, 933363089, 579759363, 918364522, 557410228, 78567411, 38538050, 154327643, 469533142, 753589414, 777426760, 638826193, 825649620, 89907962, 728404907, 181665517, 641384427, 61170406, 755530815, 879667761, 441834414, 387070740, 443710331, 274651599, 628218557, 240929846, 195153231, 226397848, 326249576, 23008334, 983828753, 176143110, 682200570, 322975464, 563615797, 413647125, 347199757, 90527143, 609160732, 30202076, 729926884, 19018197, 443847009, 2056226, 732386855, 96255813, 465133430, 289170979, 903974771, 292253001, 192679053, 243360013, 134537096, 99766602, 807397287, 643739721, 981318126, 59186993, 693108285, 755467678, 261344437, 66051387, 20307871, 280451882, 587806027, 678313826, 821138298, 358931056, 341664076, 903050105, 369021547, 241913813, 4118166, 721260297, 91205646, 288345344, 660570684, 235891322, 543579682, 4574591, 968484657, 195947551, 429876265, 534859023, 929201296, 769585755, 294844596, 736368465, 769200996, 360024085, 932716010, 925847482, 25642136, 13680764, 65468278, 746767261, 433989579, 93961373, 252184113, 874095468, 86022185, 94250938, 929508844, 95203134, 174494517, 742674704, 884210820, 655534128, 739127169, 355958031, 765742297, 64566443, 131905826, 468070283, 297766841, 11954134, 247010347, 425273250, 595699621, 591653440, 634060401, 284193151, 192354634, 103895310, 660768230, 294360765, 217806469, 357771498, 801051808, 506714138, 319280032, 733166419, 909887961, 520667370, 766649218, 719950933, 280315603, 541141095, 579706092, 243414616, 748929330, 986590903, 409008601, 777891076, 331831488, 81154545, 707570872, 418533992, 534758843, 632807502, 306224007, 414611410, 905622216, 464951972, 186778778, 970150597, 909608250, 132105028, 907088217, 41639710, 192516857, 774051423, 747410011, 323761630, 748450652, 394721393, 760897688, 468511836, 507122275, 918754848, 703865949, 800175763, 435172395, 341290431, 101342456, 748245768, 357628033, 523720346, 987544969, 492241194, 41414152, 273741371, 483252554, 430016103, 365671135, 301722763, 559474692, 533429488, 875663781, 479611562, 450974072, 759225551, 468403998, 6521812, 372092875, 74709664, 868526845, 810076909, 121856922, 970252187, 282771224, 837836228, 439056374, 3880811, 641929188, 946505221, 507524099, 953597122, 993130855, 783045821, 761171969, 997613430, 867878176, 715554635, 573007551, 314869855, 467822883, 100323211, 775324382, 680008566, 189121313, 278776511, 853043797, 39462859, 136787748, 848028963, 306033020, 483415803, 170959775, 162738640, 956117496, 418002450, 59954806, 608633065, 347196192, 461226706, 344003735, 361189796, 876234813, 206212144, 117233385, 669359564, 372417294, 527054354, 650990463, 723960024, 116596886, 113452214, 286200780, 387886767, 59880710, 485440317, 322912340, 47325852, 247355627, 486828455, 84361535, 559240310, 967058751, 673618465, 679078576, 415418839, 966536252, 53992511, 697958506, 198880723, 899704260, 357616346, 626958112, 990420973, 876701418, 461981116, 571630774, 973765404, 299842216, 104127362, 730475716, 273642205, 817068488, 899314826, 594981751, 485684898, 417695333, 910543612, 747881162, 470167621, 392260127, 747283493, 403320921, 134481423, 969928513, 899264987, 94038928, 417442012, 408031966, 465112251, 160386835, 831376807, 293276751, 988700242, 466725027, 873489729, 579072801, 149946516, 163724037, 456322672, 329780659, 474589450, 574239082, 451558337, 439666456, 449107179, 391268438, 15378107, 59142136, 624500440, 88912597, 57590, 2340880, 830039812, 213489929, 883776600, 990317341, 657585505, 130820688, 42389883, 984618569, 739889356, 444884441, 180741677, 272794426, 870903008, 141024456, 403927404, 889440593, 657504583, 315968923, 480626847, 244230629, 723253906, 67824344, 903492054, 412952539, 976734405, 851039826, 294468295, 524175470, 874228948, 570856082, 5821163, 532220796, 334279357, 418823228, 638453078, 818115823, 843558384, 509738033, 276231089, 873240306, 476754165, 717542958, 29039022, 804651164, 189919496, 399697451, 449195615, 707243334, 297108551, 464799847, 584793814, 189382022, 282144925, 375447073, 913848802, 276292013, 365907168, 59249348, 709490243, 319464495, 568655550, 866950408, 394762430, 384605490, 440322028, 310100292, 129256031, 681280869, 374519038, 176416773, 394252460, 104418032, 183110314, 705457547, 46279071, 403432343, 945172208, 153183017, 471076577, 113468032, 998384383, 199300068, 346138841, 501744520, 579170544, 183170513, 741636466, 570974030, 646846037, 965563672, 390475218, 603332696, 959642349, 388640972, 673501404, 252424987, 774886317, 436508230, 547198581, 630663558, 539390002, 276548662, 764678873, 330297075, 810869722, 667036876, 196016345, 673604701, 289892817, 822443132, 462926107, 563690342, 924927781, 858917043, 315705387, 297277044, 140826617, 958633323, 873065496, 479163047, 309372141, 174329270, 179556506, 231837172, 818251832, 489211123, 164483826, 957362079, 209021248, 824885370, 309830268, 930574471, 774930879, 816051074, 619730884, 756895414, 429154887, 168819168, 930154263, 329288330, 451634211, 670730925, 244266726, 39960795, 93410513, 270744714, 116418141, 911836100, 318968261, 773421685, 885685703, 822754732, 942088470, 15316835, 641847187, 947355448, 583831963, 917387773, 199224403, 708010195, 269890790, 257980063, 489849725, 781834370, 959402111, 64261592, 539156716, 329591700, 765948862, 454387921, 49790256, 929793378, 821378100, 275429269, 260458794, 415215944, 518300587, 812501519, 983886064, 415519639, 618553012, 985300973, 433575857, 846449539, 504279677, 71999581, 79497984, 520384089, 810983637, 661982946, 788828540, 922632176, 955510998, 202530703, 842129136, 95439172, 553355634, 678548001, 353074885, 606288037, 154522689, 960733149, 617499942, 220251619, 978914035, 452971147, 609829831, 460420845, 440256941, 153268048, 995006238, 147067928, 296685253, 20740237, 819522869, 896118665, 499135106, 580422680, 124250240, 882392918, 819093948, 639835435, 967130626, 809686511, 278510763, 307959549, 404042970, 926480407, 115070218, 965952901, 167261692, 631299240, 316834325, 754861831, 390785645, 650450786, 817132080, 839056643, 508793754, 630449502, 648130500, 985481079, 510872585, 429283011, 559644204, 59325590, 961959683, 927882081, 167630174, 513882143, 405903801, 179986241, 67578135, 520523988, 854815020, 868238308, 273380198, 456034186, 132824281, 321421291, 926821681, 315892962, 471235178, 130910484, 512058539, 706739395, 303322589, 572964301, 346429827, 31972094, 227825472, 747130221, 944334549, 213920275, 119195210, 401493048, 976893884, 354325145, 528111544, 113457236, 344380490, 586885117, 620426662, 825752344, 621733659, 465147091, 682127714, 996073062, 992509729, 700111099, 329837670, 665409931, 261877882, 103229924, 157525505, 321142571, 1743443, 533346538, 58554077, 841224345, 942660261, 669434041, 154228126, 719920908, 117811143, 160842164, 770717782, 193741542, 298331200, 5579052, 712675451, 498066554, 238732947, 57659856, 793517913, 440983281, 576751893, 88785877, 361876236, 960919284, 990460245, 570087442, 478313038, 690935170, 257858751, 730031327, 789298602, 939264204, 491415498, 732031332, 210132738, 943206713, 815422970, 363716170, 804017683, 276182729, 351670559, 36852020, 137040869, 780781135, 66942945, 623255666, 444400708, 624336273, 645483063, 268396691, 733790611, 332296076, 698721063, 519437232, 5578138, 923786280, 988683897, 528623377, 392667737, 480580819, 561051567, 591522730, 594350572, 683609751, 858585056, 309802206, 972675842, 804401192, 912702297, 92323968, 735921798, 287314381, 413991125, 271148010, 214065982, 295801342, 907634509, 161677694, 469629957, 988573788, 251733456, 515938883, 46158897, 613013026, 19991775, 471480999, 959516357, 12111, 225772357, 851809410, 97348052, 372358337, 638481331, 574812523, 528603435, 674848173, 550366392, 549002209, 713998133, 860248604, 53068171, 367279525, 36243698, 370353233, 251879896, 313053532, 116759955, 336555716, 451806096, 92976171, 814334672, 459194315, 418480317, 2131079, 538208400, 148045934, 165419803, 478321886, 157715472, 475938005, 734396643, 383099243, 803794476, 127039413, 244968686, 287375482, 372431733, 350638209, 223404498, 454382832, 225923070, 545458048, 259007639, 581097461, 920681557, 839089373, 637715700, 56887642, 151919898, 160297258, 140717005, 624736957, 107991796, 526462803, 90298517, 503585128, 690091124, 754231770, 523231832, 206649172, 564941056, 506277661, 768850522, 185978425, 291758351, 664210693, 866287836, 577045096, 359074327, 834468489, 654184910, 254021444, 368287059, 536585521, 79392151, 560980748, 591127714, 747232714, 899506883, 295810572, 136476996, 710190841, 759314643, 506371530, 105674655, 89895451, 88596497, 605963921, 141763295, 777127387, 347771362, 604495391, 17465870, 509723834, 5693519, 478914628, 443486006, 184035843, 371645964, 938734477, 892828644, 55083847, 340526933, 260141635, 869052712, 544560343, 794270526, 505045524, 349638085, 742551321, 777940600, 309261621, 143974323, 14373902, 903453412, 277738457, 320310127, 756238714, 92238385, 239595309, 688389827, 910692012, 437548203, 91223882, 602676471, 68896122, 935451613, 605097871, 709906823, 8321578, 974107231, 23652705, 716558614, 410268443, 461311885, 562384223, 800629240, 492177551, 602798632, 187588399, 834334345, 256200822, 917948006, 992183959, 527989425, 886907299, 966342503, 294987702, 240581881, 443949525, 467191684, 608294252, 768283158, 831068397, 685613679, 933531715, 720271755, 553897054, 284835506, 785178967, 289254792, 678025564, 632334391, 611788889, 255248179, 455737774, 619829544, 920853809, 397226154, 935781592, 500897629, 499761898, 184712953, 772820539, 507777632, 272886358, 852826592, 347229688, 527092521, 537101187, 409475529, 77106305, 855371923, 803888788, 841044884, 970533417, 586044321, 60412976, 688624205, 440254046, 36432561, 212192315, 940279027, 980885613, 630545483, 243159977, 203296086, 450301836, 788716721, 202307591, 144920305, 928926012, 174437871, 843063202, 771880424, 659551233, 392639384, 446261477, 20493139, 610999415, 603521091, 957367991, 323107397, 286689544, 106277618, 900029434, 775305681, 201593255, 860773326, 987600182, 925787219, 240420351, 751609327, 184324660, 542874372, 2107969, 916967980, 997958522, 789983692, 393446902, 904608295, 213211698, 173356742, 253391332, 352280739, 426436037, 53540533, 442547789, 525703474, 756125819, 63194928, 698391269, 108559310, 435652345, 355001426, 41273816, 791101485, 838694713, 712825376, 465718444, 360808499, 397671621, 654762415, 788066955, 658928058, 346736486, 2779510, 254767325, 803382844, 831000873, 57266968, 646661502, 592554263, 990947115, 642653270, 861382669, 216559223, 171671015, 385957835, 930412047, 560391417, 615409768, 991659808, 447841529, 896091106, 935477310, 730129776, 798194374, 162804566, 143395916, 64296990, 830544464, 407197530, 231886328, 937275299, 131934288, 484787003, 140151847, 166614690, 848671508, 492655558, 789288758, 627650265, 746819352, 355256944, 930536531, 745097520, 767435875, 364373877, 492538616, 809805408, 45183561, 549169700, 269466721, 986947203, 489970123, 197356464, 499051016, 24674670, 860055084, 457118438, 170347301, 775013168, 14978819, 635327186, 633191418, 514415140, 858457149, 192913692, 221618459, 197021616, 348116174, 712468926, 532760326, 729504768, 470712881, 645775366, 443508461, 37749468, 240602966, 286736908, 313051775, 165655704, 896265919, 541013708, 740026149, 671740069, 92033089, 51157398, 278508852, 911370483, 986017875, 812473377, 533151638, 558717881, 256547534, 889324730, 888860110, 823691387, 209782655, 795425077, 15201544, 234403079, 928612033, 150462803, 949788183, 213020807, 251043106, 812056186, 408225739, 199228907, 814285001, 165572729, 423825323, 795118983, 60775129, 144536382, 496201265, 785460398, 159429688, 253236979, 810771709, 692859021, 620169388, 136780808, 992975721, 357401124, 135523945, 161523422, 943363557, 164411852, 609858429, 322590766, 322572606, 575557640, 758153868, 950650399, 778946887, 519024304, 804098556, 105308645, 66326842, 865634145, 276478087, 332178038, 839043654, 776815127, 531803683, 30197552, 4733341, 206084039, 84349421, 671419341, 627632440, 40596399, 205402973, 64220425, 605460451, 773111367, 665062111, 803313606, 675761434, 462476666, 668677128, 838817280, 310064952, 692322475, 832823055, 524446833, 829964803, 439665594, 253335656, 91258666, 637443303, 838241953, 581252926, 312230397, 342685364, 599886241, 818299269, 958476892, 839092154, 967377194, 54481904, 59749337, 259102742, 202374100, 291749931, 493971424, 421998158, 542946128, 894317831, 627886609, 976457997, 561978598, 126358261, 977602371, 773512722, 113935890, 584931163, 603598373, 874831102, 433222750, 565724217, 805526294, 798654991, 546067626, 50198304, 294890454, 99739515, 23864734, 496641198, 805630955, 634110784, 542440456, 101633115, 215339812, 930870018, 151579248, 756148646, 473072316, 930999322, 660107471, 140048095, 173013841, 976270308, 573676436, 727042818, 502377578, 680396608, 290918301, 715683520, 777117845, 680044050, 382672006, 934731983, 787692165, 514305736, 590666812, 811938833, 673814370, 212531288, 855947946, 400892863, 860982269, 560539452, 610558083, 689706994, 11065968, 34850853, 189524688, 608466157, 705005313, 846985145, 21085611, 167857162, 401535941, 169656148, 932474146, 247339048, 282978868, 888953932, 997117021, 435573028, 722729797, 138340050, 45101487, 305876689, 530544258, 901030171, 155760493, 140813652, 105610367, 441283158, 631309110, 100762530, 83922353, 519516970, 666137615, 663935246, 814974216, 89493439, 880894528, 703716872, 899271297, 166055648, 427353845, 182967947, 933418977, 384028543, 899907006, 929161346, 301784906, 156398670, 922564900, 693022448, 331928188, 538764568, 184561541, 125676952, 371646546, 291848249, 600512202, 626232135, 691494899, 819640652, 76609009, 639541196, 315638309, 242411879, 297262863, 165369718, 946861913, 448305936, 844971381, 863290159, 691059603, 523892430, 879593614, 635390790, 761196792, 189399583, 804448137, 884004874, 781272706, 734518978, 697195676, 287363955, 786258053, 891378710, 104561761, 840960650, 629962440, 915382511, 571421284, 298263132, 132930682, 843677520, 881117954, 736290223, 862516117, 710804977, 392314680, 906929975, 539068678, 174499499, 266073516, 181317361, 365255597, 560037828, 409207301, 477606739, 993796749, 241611882, 856364640, 735199239, 745448574, 184870696, 983137623, 98172885, 361261195, 961632263, 828261049, 866948636, 744670093, 279800186, 546742524, 884576854, 877934671, 441343549, 927120446, 256470090, 51630490, 538010666, 550799515, 534733562, 442359443, 33046028, 706948022, 160351982, 235110166, 507006328, 857823330, 909637018, 688584158, 156506694, 720108500, 2905273, 821709794, 802591565, 412109676, 618512619, 221268775, 861656990, 487850392, 600476115, 394798851, 57829760, 220126539, 841403840, 751733045, 518761692, 255705758, 959187512, 518555005, 500739274, 621912591, 576481533, 882931145, 121981446, 184691600, 314801935, 56239966, 278843237, 686721031, 596754421, 392276229, 659442104, 342488874, 751629021, 912809296, 362853029, 765139193, 29093597, 694445085, 45292008, 741541926, 923335886, 470128010, 920324460, 833652387, 355929619, 513549651, 454639317, 105897314, 307625082, 607778694, 403398953, 278140806, 91477460, 92940549, 385760883, 991995248, 673195982, 302151275, 281942777, 325512511, 175461141, 798047189, 360012603, 418516211, 827046756, 202043946, 884742615, 442268665, 722841600, 806825177, 451001580, 88852632, 997132917, 429814447, 521546930, 107093219, 695654874, 916167262, 943333559, 454839021, 6389231, 533042776, 890420340, 136518384, 223863073, 58481928, 813749198, 572714968, 852432903, 598435021, 800723803, 483873769, 531096436, 926324258, 285885525, 424399341, 99874681, 322043683, 703254314, 800226998, 197364278, 980638105, 308796195, 871476504, 284680599, 162499377, 109118677, 345823379, 184353920, 38657888, 960419656, 734667033, 155477357, 394077271, 236519199, 191710181, 504133000, 604757055, 275052993, 188303908, 79219365, 716579612, 902195544, 127857085, 717361919, 857431657, 793250847, 445515618, 83823565, 170954940, 60856912, 633483727, 829942123, 620544538, 965720544, 459481009, 428601061, 897424519, 382330885, 715790086, 23145506, 547911734, 111408861, 262036290, 663785936, 58886610, 975642913, 853974938, 585106612, 787812198, 224964435, 633164705, 510665298, 542577494, 681562487, 426310018, 230668096, 359911234, 912593284, 371598482, 709019792, 710630445, 695762257, 322052536, 791747461, 904864119, 606421313, 969191161, 504092236, 603055605, 165504188, 936565503, 418483584, 276025732, 409801302, 323511606, 508012180, 384873201, 214413291, 905446837, 499987674, 185347954, 550556085, 953996339, 495259823, 805265214, 787505333, 411989403, 710915668, 683889040, 772431338, 59121259, 107304994, 776090448, 201635028, 783952968, 750389114, 107498129, 101490356, 221011666, 262831289, 564997379, 579225251, 719146020, 242960704, 693703497, 547512679, 431435745, 393720258, 634429038, 221213062, 722791940, 684503525, 309996299, 572794510, 795689484, 39292580, 77954271, 439495135, 287996790, 430422067, 598188778, 483931014, 960567333, 24807147, 560626188, 471944087, 534052865, 350315260, 961905863, 284431129, 390315874, 30834808, 587307193, 158852650, 568970797, 251657107, 298557619, 311064204, 675732302, 904735663, 271436425, 872951302, 136218271, 22297482, 452724522, 91627036, 149020233, 459412537, 131007150, 352914759, 611713639, 681902323, 961290185, 464160783, 838090961, 62746879, 751129301, 865788812, 211285349, 403723623, 598943083, 552657833, 263730609, 556429072, 397025352, 676852120, 517492550, 82575906, 384977981, 696654919, 218817398, 580505358, 812138866, 348241788, 841773185, 99132567, 506745272, 86957992, 425357199, 900541830, 406492737, 459354069, 849519310, 656058151, 900646995, 494234216, 538486840, 997748649, 268469623, 983002776, 350341267, 839125001, 89411448, 729149366, 366815759, 78552347, 62455975, 922162137, 253841883, 615886150, 243006011, 559644279, 442882766, 276302744, 90880780, 257532147, 357322419, 776104634, 978632357, 728524339, 532817734, 807928501, 468080200, 442262852, 362507575, 610040090, 344684470, 278300201, 170005533, 565100686, 706546763, 560926000, 882779424, 817519543, 417311799, 569154893, 343393094, 939548781, 380310475, 878640521, 146336975, 477938234, 605705346, 28859660, 212352118, 855630884, 716040422, 732579072, 998314636, 848697746, 479344444, 838622719, 891754795, 740572601, 348655665, 498757165, 341505748, 224267940, 356479947, 623798082, 865480073, 212178921, 175503891, 789042513, 381537538, 363067679, 716949794, 68005454, 194862590, 461449233, 664778179, 449453637, 56476486, 85808649, 815776673, 247062801, 528829087, 848436456, 67384527, 611583161, 624724926, 277545490, 953039539, 492506686, 494492145, 8860328, 290502236, 435238358, 534685687, 945850741, 371318539, 937878947, 950272166, 10609133, 777636288, 79729177, 122837595, 899798452, 332423954, 126384097, 597920660, 574506916, 335509470, 555002315, 114318138, 983244624, 247722753, 466409213, 223319027, 867881428, 670256192, 85421518, 227014684, 25685829, 377193211, 852205601, 964004090, 113382815, 974754018, 723017683, 60062848, 119102364, 145331372, 59447064, 964351485, 999277401, 52540125, 91880450, 759767624, 220506016, 815045299, 444998604, 710907196, 393033423, 555093270, 152216668, 714807924, 826179451, 319226063, 368728976, 622377682, 556607721, 676820315, 531176188, 720077552, 416457459, 279803298, 84548877, 985898378, 497163114, 431885598, 410048981, 826661877, 671235678, 452211005, 356557567, 398256876, 452358517, 529454370, 376259113, 876513783, 399406680, 947028339, 560585614, 231675864, 787996051, 814859008, 112770908, 978115001, 692864949, 701312069, 337815152, 18000932, 798558286, 392578603, 906499101, 217852164, 909301913, 726200507, 907707161, 868281328, 842596474, 222409242, 343394322, 900346546, 313594322, 386667313, 830978190, 287409938, 3098673, 548312055, 886586086, 710457184, 518829989, 340902933, 99571812, 353475286, 756230038, 143407665, 842188681, 472722426, 735167436, 105900646, 225473947, 184836273, 231567463, 143549106, 528843879, 220779456, 561082079, 14486797, 195496757, 787955775, 349857789, 497769649, 221109097, 153033889, 765900640, 800795899, 720334380, 593086441, 299123651, 264264733, 30028798, 25932878, 56542218, 327188354, 988533890, 268347021, 353301456, 140687090, 70802945, 600895709, 612660996, 934373948, 563192265, 973135364, 903836959, 841752471, 424411686, 514152049, 555560763, 923200844, 717654440, 889239643, 597268391, 941570369, 884908498, 493516525, 651696155, 931881847, 88825327, 924534843, 954712480, 782383869, 776418079, 635970376, 416424385, 456801944, 171332983, 335852171, 1974843, 57207539, 597540013, 987043640, 104358915, 879646156, 936324813, 369884474, 503370247, 492664431, 902801686, 638582850, 964463518, 669538521, 254102655, 61675092, 713236791, 287406961, 437380131, 741675477, 803834099, 594069915, 379914801, 493642810, 948365835, 512801290, 613024695, 637654124, 746263584, 21636373, 750548999, 677258087, 95160309, 47937107, 948732884, 810907561, 652293929, 115181490, 278104058, 622035764, 952340815, 725223263, 158180700, 143047073, 619492773, 892435783, 134454712, 508681246, 297283344, 950567342, 773216843, 62198193, 285510042, 665302949, 187377084, 77586670, 946276215, 489964974, 765306453, 282153951, 81831097, 128753776, 890498538, 239092567, 348340235, 392159239, 190690351, 896030777, 352961817, 705451192, 251551241, 822998241, 218140885, 993322242, 802944428, 409236111, 531913867, 332217458, 654545309, 192376351, 204238431, 247389792, 400564233, 195573138, 506741256, 184503187, 671541156, 259947397, 469221529, 744537640, 864210356, 681697799, 375079249, 890032230, 843750071, 287024743, 621361961, 325920039, 820435832, 658424432, 696027407, 477242973, 527491520, 355773000, 882092445, 190076220, 30195682, 583167954, 424690510, 451732221, 130512938, 449791071, 796273129, 875934888, 198865960, 591716659, 517918480, 294201687, 949821777, 520926274, 47110037, 892145568, 434634513, 95331204, 591542299, 9528892, 322213439, 37233537, 724517351, 577600805, 641241332, 298249715, 920599699, 397525373, 741315328, 438305861, 348181438, 167847360, 821388347, 808403715, 236902433, 301024448, 707896863, 95685570, 859319259, 795929248, 502091326, 31925446, 587062673, 678744209, 431220823, 800390380, 68782010, 171623313, 753876846, 218540126, 9086118, 173725297, 88735181, 531225302, 87977229, 85125724, 242017975, 547722436, 989145460, 176154815, 891998570, 684628122, 402554555, 575925888, 972333455, 889711947, 449297481, 798409841, 749103825, 439594240, 729056591, 489426544, 352390670, 537625628, 715378614, 577932414, 830642439, 304145900, 338039319, 338771478, 254610620, 602884903, 756176215, 358548426, 906538330, 925944434, 371021446, 259535810, 759191334, 669194756, 561203862, 692018279, 654322158, 217601691, 676892159, 157454889, 875414255, 887135634, 520957846, 288500295, 731568314, 802351122, 20533988, 825447292, 670111270, 139472969, 976846130, 307111806, 143694009, 996397715, 681262136, 867271616, 369536480, 509725225, 387320638, 897135434, 882831777, 119653512, 949658995, 586433554, 843766815, 456848318, 250124905, 583295748, 920479916, 371789412, 545943408, 401317241, 408923376, 596313025, 475237872, 71314579, 972760027, 678038903, 974523166, 369335229, 22622088, 982525373, 893607550, 517561485, 359806128, 274617587, 826160213, 368101759, 927956351, 712200781, 512059093, 109490437, 654420860, 404973788, 776877332, 28508143, 957692374, 63542965, 208534222, 196813776, 554917760, 101631102, 278606039, 161090202, 558420375, 744877441, 822278838, 342179515, 289070978, 147303154, 689214364, 717783717, 787148685, 418946061, 948006239, 107439739, 915478828, 665988350, 917375491, 980085347, 710719311, 670244414, 959034140, 651516882, 524873546, 398721413, 232014060, 985418833, 614939714, 686971707, 952706599, 839597714, 231971992, 989245900, 872303269, 682678605, 910729604, 967110033, 447174638, 584545084, 447057023, 803654431, 675155385, 241590513, 939576363, 557370860, 912305120, 335940907, 677201468, 386526883, 599113016, 248184520, 571993757, 613233952, 576341049, 194098652, 92071209, 359679997, 493274959, 361099977, 184174270, 898090252, 291500633, 445857769, 117237528, 509040878, 900783542, 25535441, 347317710, 471658678, 540347377, 858579886, 797711223, 16426315, 455132645, 200288070, 423889031, 71045107, 49766711, 762632846, 285773505, 369459003, 693911129, 311764732, 123372707, 295844016, 530721977, 738050559, 79855917, 435544503, 602936002, 778556811, 994327894, 892404743, 648336543, 999443140, 123377249, 931418432, 804920793, 844051013, 849639015, 493614654, 182005993, 32013189, 530737123, 627060430, 286754841, 936157868, 588560152, 221591223, 917172707, 613742466, 417256379, 742830135, 420055838, 685672141, 231519692, 584682837, 27050586, 260642711, 986202629, 267228142, 465239277, 615239487, 488194545, 926520755, 28524111, 869962700, 666981317, 373440980, 429591093, 228822577, 761097195, 199223478, 842176488, 279773666, 588854934, 741614636, 753200198, 254639383, 974911470, 411043464, 3989295, 171369686, 458735648, 773608976, 175763474, 92988845, 688866385, 283213556, 157243148, 48727232, 844406224, 857675016, 219866766, 66783607, 276573639, 275552115, 948573835, 797588179, 434412287, 385559080, 784254528, 460491681, 649498200, 20790755, 773830274, 877796450, 766622290, 593626130, 912140605, 231801639, 986829704, 550132518, 38824634, 512449243, 75845938, 787473021, 91483460, 143376550, 224931378, 423280636, 64474622, 222918233, 467536615, 868315479, 975006321, 207048759, 403218441, 803968307, 132106951, 102750885, 763629600, 777055455, 99597750, 704398913, 389687242, 198780432, 562146070, 763913022, 119583361, 790735437, 588679701, 733666446, 700369089, 393513705, 629375352, 960764372, 402346215, 963992942, 707953246, 350438637, 340276563, 640779810, 887784297, 367312321, 787857573, 547244472, 818786835, 693617295, 881894928, 220067242, 861029356, 37251622, 326849886, 702522883, 184533999, 191080389, 178189482, 92785744, 923091969, 316136000, 801913292, 972131797, 978697135, 614945217, 409368891, 908282032, 42602728, 284024984, 847132034, 976363091, 594320831, 677263278, 966621809, 726841903, 367325902, 442536052, 758417275, 706326928, 589160355, 421479060, 30113673, 647417181, 923031611, 720301477, 92646699, 849283914, 938903264, 984680650, 134452439, 735638748, 142341777, 430634029, 745601656, 5770607, 128395023, 417738645, 812401695, 511802566, 459298765, 424001100, 581529534, 678217823, 198681441, 592534220, 981914093, 405069272, 145506677, 3632092, 985965279, 271872576, 689035001, 26711338, 459796105, 834249537, 690475701, 247329244, 335270412, 751586225, 706056882, 943796646, 847265442, 161386259, 509461595, 681721668, 946924169, 576821184, 929667269, 88990986, 927747019, 614490507, 106856748, 740918225, 861018704, 271139599, 437209127, 82555355, 570963597, 993928641, 530906595, 397749751, 792848367, 766568589, 450629727, 224767004, 76083764, 227429419, 511768720, 126920059, 208724388, 60174118, 55371973, 114436328, 553400181, 957066613, 160861498, 627381248, 458689657, 296831691, 158622247, 993476588, 924395567, 389101850, 811714307, 307972195, 329010962, 928842462, 976929314, 84340481, 140126627, 13244278, 908147370, 282001816, 228606203, 175010083, 249010413, 392603460, 500346211, 334943800, 743742189, 515419973, 376739163, 330777288, 511316408, 449759706, 736020166, 364379672, 63190296, 981967388, 587330850, 589165762, 76614795, 298341043, 746495085, 744579079, 677565551, 37186257, 588996503, 805938133, 406097182, 88340783, 383747110, 471339172, 472073334, 870671253, 417151971, 965653399, 142538103, 321045537, 84179974, 111235617, 559536202, 541771568, 825908451, 18634353, 298382969, 586842017, 561030401, 435683332, 529124432, 424372972, 683325454, 62747717, 368411521, 847908872, 734677066, 138625601, 968111824, 362604888, 330156339, 377021987, 114831902, 435293889, 960313635, 370879461, 214691350, 773599890, 850434833, 104105978, 341710088, 768074339, 294885324, 865172903, 862208833, 581243647, 960447478, 738865305, 908357803, 318367244, 660279634, 2993817, 484258211, 503943585, 975184869, 728853213, 921202606, 896064616, 703932666, 788173429, 456077595, 499694074, 699301854, 722427053, 149269748, 683315945, 563775364, 52061621, 50953404, 802104722, 727425560, 56878662, 346385367, 708346539, 816856421, 999259886, 830184067, 819841159, 695577498, 392227217, 185624042, 176920305, 28405167, 173066508, 442482096, 104810077, 110892211, 354910883, 103948045, 110481945, 713721430, 686914903, 714892646, 495112408, 56579543, 714674240, 579662160, 640615529, 441490254, 732420994, 364893145, 821301831, 353570820, 253567246, 942568204, 499065116, 386937101, 955608816, 748327452, 839543635, 290590228, 747469238, 675252591, 680934682, 24601096, 986454927, 265085084, 879065144, 76186231, 309187308, 495285503, 200495578, 155015484, 135465105, 128262928, 335079402, 87479359, 118565457, 890119315, 55510978, 211128513, 41615251, 648025428, 19633676, 983429138, 257954699, 818660108, 468555063, 684911651, 645868377, 844930085, 425903804, 119663636, 419808931, 495072422, 863563609, 248439566, 923980141, 65153816, 68309945, 658123263, 554701962, 460990616, 241777215, 88191341, 766974437, 704880522, 197577893, 10291639, 695761939, 847943642, 842573361, 525906757, 442633984, 185359857, 264754118, 489248420, 268367859, 700400622, 617109535, 171439003, 532485397, 408781778, 189954090, 483292688, 561606367, 896439414, 645275306, 204247367, 584736526, 394925280, 736406924, 851092538, 845453271, 740663636, 578545993, 182035762, 974533153, 213812248, 294663037, 83485536, 948897848, 39607378, 890689909, 830270433, 795691355, 83103023, 609131839, 103124315, 180923626, 641505107, 400009525, 489808373, 251154317, 833322874, 111577321, 580796587, 771889288, 684477107, 252556254, 704655042, 544990410, 852776408, 459111616, 274543270, 99149936, 998020472, 646957493, 388954144, 700918862, 515965322, 57765445, 985412021, 17852875, 485819126, 500038181, 690122270, 183315034, 15638536, 757160869, 600578379, 740603447, 930148206, 245243807, 780464089, 379204189, 373490993, 610478664, 122985287, 959493758, 27116996, 751203948, 732345762, 480723478, 422239648, 310270377, 948200469, 102698335, 588865977, 107658807, 325101836, 763648876, 679976475, 643664496, 622974389, 861448889, 973546317, 691315135, 884059821, 131859027, 668774289, 172535088, 202508296, 321053099, 166919027, 171552941, 150221486, 826147217, 890779117, 693036460, 103452310, 103080717, 786869236, 774378715, 924117051, 431160, 236829489, 537193790, 836657883, 471832082, 244981839, 922866236, 359515422, 178379727, 453666351, 388210150, 251733914, 739477389, 480701591, 690611422, 845749432, 974237208, 830649539, 892826033, 318719211, 255794087, 8542743, 304614138, 726518994, 373788931, 974824405, 743835976, 680280834, 154046180, 138266699, 2765959, 395571037, 239833282, 108312102, 93448015, 961245990, 688306215, 871434609, 318548234, 460304278, 168799542, 713206254, 990549476, 370373683, 198335810, 181111418, 229746112, 770994459, 283851034, 923677787, 662870722, 688068159, 350424386, 483834274, 343976709, 417280890, 980803329, 559085965, 893287737, 870250221, 870391406, 927987867, 611340522, 997605464, 315567728, 695101057, 159357043, 791049654, 276628156, 712739920, 407774645, 524486978, 469796296, 541830952, 294488421, 431846353, 691649513, 843040161, 700978250, 432213907, 124091995, 363754447, 833271800, 979460710, 43312655, 360034718, 443626213, 576738632, 181105035, 188668998, 335419443, 301035680, 266354637, 281649518, 884141275, 163397097, 467237254, 916886000, 534173730, 238946663, 568308448, 639110220, 621127034, 313199134, 759242429, 850235777, 421964863, 951921684, 887699516, 358173638, 53026916, 813430739, 665366197, 781590862, 724768560, 870080364, 592362969, 518929296, 257704366, 895545943, 245317372, 25917255, 634365770, 128739159, 491453742, 769440334, 641188742, 473521782, 845336148, 728636767, 431279475, 246753639, 797687979, 127652757, 566224930, 519573444, 646300306, 374690240, 545902332, 792688589, 322914405, 759415631, 311057936, 763854175, 164011704, 778552779, 105359898, 977059881, 807804455, 436064259, 163963140, 216171844, 892779331, 539869707, 777510542, 725215569, 312581809, 528525533, 446104950, 235190480, 776285262, 996274378, 906075685, 986986711, 571411616, 623502187, 283646376, 996236571, 834206081, 413465777, 241956671, 670839837, 304725782, 592519188, 55315318, 24530518, 926930864, 7817094, 284053758, 865309298, 877687861, 417767746, 981930508, 204271123, 804750146, 481199057, 775516580, 948047092, 952497411, 463351483, 38498878, 903688633, 116378456, 799491525, 330082150, 716563263, 311406019, 868889238, 3814948, 144103887, 977154497, 71859078, 962328933, 442543027, 656967095, 115139059, 400197973, 97861210, 869684411, 532229739, 837291831, 537772329, 445847543, 64725927, 893703203, 942515151, 438958014, 992117674, 667215270, 114410249, 895581920, 608084901, 865493082, 387249720, 788522708, 462149785, 609615992, 334580020, 492319262, 287657206, 578619285, 381041586, 409270561, 775107983, 246359774, 137425118, 987338996, 865768196, 940230590, 684433830, 344834828, 689095835, 319150084, 246431488, 38273747, 696390047, 453718561, 59773631, 670743134, 225257774, 455122638, 437853356, 387947963, 8017627, 844160252, 484013424, 807289888, 215654807, 331626673, 81520405, 919840531, 564787131, 627597459, 925943440, 84989038, 73405511, 657027342, 690496305, 956537332, 548681002, 57563937, 684642341, 268638738, 78175307, 427854870, 837830957, 887530319, 10681834, 368859999, 173033785, 478681249, 620866211, 605657654, 576092168, 884281300, 50931232, 93496263, 534703950, 796995342, 329394314, 162168479, 533515516, 461761060, 821440211, 786750125, 47699711, 740033985, 266906687, 264892306, 935244076, 398908407, 277363227, 673778389, 919133696, 317649311, 905245075, 88137821, 457967537, 666232772, 329478978, 160989661, 127137708, 3451334, 934956479, 1590074, 531898485, 986550273, 704542401, 611580482, 152832392, 106119052, 367600326, 617872796, 956568320, 503750870, 783056630, 633626459, 280591451, 506169979, 645362998, 75076032, 602949416, 26578011, 45873942, 15784880, 489516989, 990472392, 826100325, 241492975, 699128284, 82705347, 220086251, 43471696, 567070432, 42814933, 492460693, 725200706, 825416646, 888472237, 539118715, 315970344, 825268857, 762712770, 975642946, 367419772, 270700330, 246174809, 5571193, 457276187, 173712989, 624695810, 572948814, 859982821, 251291314, 597394351, 264014738, 679132832, 165787755, 859177005, 326689375, 10542783, 974535283, 888557381, 957367625, 671459857, 792726345, 409985431, 31535924, 4353523, 487995171, 407528357, 738561336, 844473757, 293959920, 596362642, 564206453, 994931890, 448662958, 495160983, 747174370, 335724957, 393881317, 591647815, 399382707, 330189207, 256686347, 239380416, 13970503, 83086391, 770517577, 735157685, 28602417, 820242159, 964991393, 394542477, 62404280, 736263531, 124502058, 654433456, 827511368, 340549921, 591000029, 996249458, 647651148, 361597668, 645220133, 873372929, 165207457, 60014328, 308788027, 80119268, 343630727, 451879617, 949704403, 343818468, 557780468, 105147136, 629419695, 241380493, 417187963, 679236208, 381717709, 357960194, 189811448, 966606384, 47091449, 453465896, 278075572, 712874926, 946381891, 804470503, 418528314, 406702360, 710928730, 327556200, 731313558, 996011998, 805833426, 394134232, 330103921, 956532385, 272248857, 302620491, 543166879, 726903398, 472655624, 285125000, 738113274, 272060784, 784299198, 888077186, 495399490, 710657203, 228851086, 660355682, 937717705, 928431946, 722377014, 9408660, 129158217, 299965190, 627720096, 908664091, 746337305, 639884827, 212645327, 560098950, 895984255, 381617133, 593890621, 686172115, 77064307, 741991395, 327351945, 488157588, 165494398, 273895902, 618771917, 362369752, 536502578, 451194580, 264082498, 860328751, 896556487, 729604272, 690703756, 957623012, 939957364, 209925585, 936465014, 322622472, 419477545, 173083264, 999727234, 872261183, 138737982, 40459851, 888084253, 404932251, 500902887, 583717975, 701620137, 529669042, 722646297, 419175991, 525016685, 298114673, 78585840, 311215578, 252718349, 362503213, 901385805, 92871938, 81617874, 810437219, 361012710, 184064772, 142508982, 937435203, 396742132, 692448455, 112845425, 470048273, 678578137, 176852820, 856568468, 739854978, 985879123, 930516678, 349569253, 992991393, 407318683, 857011551, 275682730, 580294377, 265599994, 136097010, 732709729, 447961274, 554984269, 204300311, 827813633, 157201662, 687803737, 185862104, 612030138, 945332087, 971160130, 66347099, 46177788, 210261251, 821159117, 507735523, 200087181, 228950604, 286589671, 428017589, 902297697, 77552342, 950835447, 766032703, 369925651, 835272069, 66779310, 345013199, 922675246, 274881724, 623185826, 441200027, 186943173, 300136411, 660989502, 551181188, 554477684, 659419644, 383891171, 401453909, 127959006, 657360438, 901066413, 806286109, 890578811, 149882952, 539207385, 908269480, 963705621, 437102244, 128811072, 620752763, 249012911, 23043335, 277087199, 307904911, 639723461, 566740738, 828524330, 828372065, 113222217, 813892922, 350456740, 619530546, 171859377, 42411313, 375205672, 4110306, 617678890, 875829920, 196719446, 84971941, 960129029, 354330557, 238901325, 944168954, 239246187, 853515971, 307462677, 803582328, 375385313, 411495089, 340149193, 363489558, 574656572, 417422585, 17688397, 169311267, 572012175, 815803568, 166640811, 406268282, 316509117, 743939456, 926261890, 354292053, 972550670, 75688254, 235654347, 131076596, 1722057, 923808899, 58324126, 810239443, 448219447, 487470492, 134225100, 32328803, 980763108, 16747641, 542710575, 741646145, 345807176, 861869411, 668650866, 862649021, 321296771, 741645345, 346436867, 33749007, 781473203, 158576983, 271579904, 807461796, 310357159, 766465443, 84867087, 186246773, 808268159, 954066206, 576566800, 960766384, 171476242, 4160503, 605583973, 885830574, 379165410, 322121190, 411765585, 476131255, 87471509, 670550077, 801423630, 819885013, 578286536, 254690419, 140702226, 47258773, 272369144, 348573101, 509072355, 901219116, 42470959, 609775270, 592576420, 437239044, 787005799, 703075064, 960426684, 130226823, 525126157, 352416950, 867374293, 293230178, 970163957, 407354881, 695284689, 92520986, 952477771, 940273135, 786111107, 841162800, 115852810, 334649406, 975679710, 468090655, 928036684, 275692423, 693899778, 140369408, 381244432, 920501795, 831270957, 914891729, 290651276, 996230516, 581646389, 409263522, 818892081, 605315078, 436330910, 889114906, 514849994, 855419611, 686219237, 838020354, 213922789, 929679750, 334236539, 422848030, 57405189, 11958360, 105627569, 703804363, 432210059, 731677422, 950454270, 381019873, 400450902, 319777813, 331368306, 664494948, 740315392, 788958345, 94547932, 642884032, 703834332, 927304115, 499244924, 230283614, 193686362, 638523287, 949452556, 547220373, 226200699, 586665866, 105781000, 523676359, 149220524, 160026727, 123512306, 241740661, 386256774, 791476741, 621639705, 488993409, 690106586, 769290035, 513659464, 454416088, 12619573, 589305523, 643659412, 668923826, 576295091, 572803708, 465582616, 495743339, 800825067, 566762319, 351726582, 597370357, 941433733, 417007761, 145811350, 209394050, 167898421, 666776325, 593596124, 930562783, 5040044, 20269235, 946204694, 628661571, 741760822, 902902850, 577004917, 699313457, 21238997, 731555480, 914189067, 612964513, 446423306, 396049515, 579250130, 185607255, 376344721, 425601162, 524719191, 536048067, 258640710, 844356045, 527540008, 651801826, 305867907, 400024693, 61218613, 195229055, 366760632, 966523561, 324066263, 837176368, 620267096, 761817928, 530653973, 350403912, 622087723, 312865768, 501384753, 501217595, 907392238, 460602908, 459438703, 831976081, 803546026, 517854844, 891388162, 781830479, 861171380, 276096502, 452131292, 160737786, 784492883, 663854888, 574376064, 999995278, 670535550, 497592542, 59022778, 619461689, 877509905, 378287681, 219757365, 781684031, 742755443, 598201212, 146675201, 626408245, 383725859, 286042777, 73412725, 728858824, 775968078, 941833314, 108406233, 550553033, 700457984, 448763253, 654806878, 665419639, 959871461, 609501189, 554058004, 791505976, 338394240, 49415942, 344902729, 180860979, 145517285, 215093429, 841554, 422017541, 894654790, 320037778, 489378636, 588343062, 592238318, 70077287, 40062575, 210648465, 887734776, 519738204, 205129138, 520077520, 516222786, 572321541, 514392433, 365546224, 375584600, 1416723, 201194330, 347571084, 772108691, 673980382, 40785111, 668389268, 568594289, 555399638, 309041455, 874006237, 590215893, 184657229, 132194749, 255056308, 388955112, 71041211, 528236276, 612194315, 890894706, 876461388, 740683970, 72388444, 779620939, 854055114, 354259369, 435455670, 863145461, 992866183, 314151502, 868235323, 559355984, 958579771, 328860150, 906747815, 736087233, 916408762, 614295204, 835902022, 145385787, 806444084, 130811967, 876484074, 14700914, 881979990, 682509003, 988407047, 536843463, 122397371, 898638446, 365718299, 731222328, 249203083, 342369123, 747815162, 627298437, 788513784, 770873655, 690130084, 113530671, 997047436, 265962980, 737278137, 537553397, 859734120, 238733023, 644188666, 139370354, 499936826, 858975930, 346785446, 67324201, 751968684, 661005387, 388313764, 707989807, 774822704, 215245238, 205721723, 193234735, 969414176, 152604116, 345304285, 701824669, 242856443, 515843026, 15347417, 153204622, 392345798, 165078993, 806536832, 94750412, 774316875, 75740532, 315262191, 701952801, 229036352, 617633616, 911112982, 744814292, 280124205, 960876277, 623068266, 733831048, 23192797, 700415710, 579493479, 369081556, 162736612, 105107262, 207433121, 606138765, 753213545, 121846793, 932038297, 150414129, 349749851, 651217281, 936465381, 28161316, 840909642, 174041171, 335822833, 664767186, 118885132, 377643944, 616658794, 706884143, 590657598, 27201744, 643745056, 51684075, 316779565, 297886445, 560408816, 35752087, 907960562, 523770419, 984830858, 707649602, 818245715, 575595603, 457070890, 47519946, 778189285, 116544979, 310867876, 649456528, 184872825, 860937140, 106661867, 709258301, 971484025, 996602858, 258195807, 78808769, 785879478, 226646500, 173243874, 266143811, 203298819, 950881971, 735193349, 267379043, 390199692, 250835803, 6313583, 833222964, 22653782, 796486382, 445704720, 26179210, 944460049, 607076257, 180458111, 256314495, 438961229, 82982062, 147212015, 20292666, 630976936, 659189946, 891373880, 860672940, 937367362, 833312333, 192821121, 266879405, 141832388, 402983357, 405049497, 729577383, 154182185, 128360984, 891092465, 21494095, 8819285, 111923315, 906217553, 609893685, 998602779, 457805575, 141447149, 847562769, 477909830, 873294053, 373779555, 391571767, 950472913, 932461589, 23722903, 708525876, 732990610, 362289751, 327010812, 905881484, 228816135, 67484265, 640066887, 655007688, 564053763, 712646890, 880160418, 197586097, 394213322, 849046908, 548031787, 810386089, 407298339, 429961173, 479285997, 953018966, 837922030, 966647657, 121413212, 961868952, 800048134, 45102811, 87599343, 70205632, 234826179, 350065848, 358257915, 488407299, 473126916, 935797154, 49043966, 327096364, 732953438, 476832342, 77183298, 291900112, 281571929, 932925152, 905313653, 825791590, 718278588, 92896415, 129411629, 717291605, 874375885, 638539430, 982531893, 812396331, 230520934, 23357769, 367074177, 161026612, 248032617, 150611699, 916539150, 757113466, 309103997, 79099618, 541653722, 881982362, 577647010, 468578773, 95298530, 79613451, 835234786, 376219779, 422146485, 560276314, 104356205, 1342389, 15353834, 980645456, 777941654, 180650754, 922145045, 924728508, 302265733, 217954886, 410221054, 816724727, 872067914, 113828339, 663323008, 795907452, 991191713, 760150362, 752915519, 850422105, 610766297, 825123341, 108860098, 370112183, 132004583, 896553704, 576054134, 13541692, 708339878, 545418615, 721872296, 256665109, 1607348, 409366172, 730443497, 458665520, 349721291, 356904805, 250223431, 49819993, 130740352, 461517173, 477592459, 603296291, 291745893, 263899305, 685200666, 418899353, 642112488, 100255463, 25701237, 674111261, 12025155, 702821920, 380627308, 997250220, 899956851, 774423224, 858229392, 922064343, 862487497, 746274828, 632114242, 261835932, 884207416, 288727330, 556576561, 205784699, 103017253, 358432135, 574742070, 608681256, 682380082, 379896762, 290683954, 823587634, 639179822, 618252869, 375290467, 673945207, 183919405, 721871079, 887844371, 98292588, 492194901, 781351951, 823252188, 627284067, 119252763, 967844988, 829609134, 195344150, 641668484, 39457297, 668196730, 561250404, 293411311, 910790202, 83270589, 755182386, 248586398, 758418022, 900406478, 67489470, 675425665, 778050545, 28450192, 377755269, 864075268, 572700161, 159671682, 189516084, 769692085, 982684692, 232171500, 955846837, 936498911, 60604561, 24817107, 290863396, 320998329, 975949546, 568038318, 981190313, 839934801, 731076705, 308765076, 49096444, 819186033, 121848308, 70048167, 433291522, 267715821, 205039677, 592805204, 319299929, 885698777, 511372058, 929917426, 125995414, 149593146, 378173517, 302916978, 392260726, 751594922, 402696501, 895475947, 442135723, 328589509, 513754209, 286390704, 709180855, 492694123, 166449611, 464697345, 526361930, 488788749, 928531443, 158484487, 837956847, 428447401, 864250592, 398249607, 869305947, 701822825, 743938133, 262454938, 639477906, 823531685, 624565409, 547453600, 716607163, 806726068, 481458249, 239251348, 870986740, 805274234, 294326136, 127686964, 597119402, 549132515, 605297229, 770281527, 148357605, 205384978, 651242353, 965017706, 402552297, 486551664, 112902824, 994657928, 833204318, 100259244, 953265919, 917913257, 169572574, 130576841, 377044599, 492524142, 697767640, 913104551, 10323877, 854551002, 184070460, 141705341, 37213362, 971900688, 638515304, 642255796, 534598067, 280654043, 886918634, 198479778, 801969393, 738096985, 725846998, 789502966, 353429063, 81959903, 503451428, 502892741, 639583507, 266210379, 257818524, 961709196, 756459501, 174365787, 959290232, 625277241, 187319629, 622669583, 778823768, 219913430, 766405926, 481760814, 579456342, 458888610, 585156669, 410860238, 306914197, 753019689, 794847260, 820699408, 698750276, 119911626, 96469984, 400732723, 972435836, 520100117, 993044448, 514252505, 28815651, 534081884, 250501681, 568185731, 899370670, 418614384, 218916756, 355712045, 800709750, 268575475, 301944096, 561825157, 184448060, 634721854, 533861926, 378212406, 772078093, 269433184, 126996252, 698777501, 721810714, 28087101, 687535443, 618074056, 664651926, 990624850, 65429409, 206178162, 379516774, 737428978, 993696277, 907080269, 890636506, 365954149, 372075589, 895539291, 200688630, 155093737, 217407844, 313369250, 281664062, 487411721, 782448068, 606642099, 408623587, 932294305, 431402982, 330435073, 81843943, 979806998, 199052785, 248061742, 694000650, 206143634, 497270481, 460595782, 592159296, 721565842, 949741474, 159068462, 317224176, 754896533, 315677303, 523947264, 390911335, 498970408, 926554262, 206207584, 29159701, 345630764, 900017854, 862775304, 285288725, 286757121, 921923860, 237932922, 550426579, 912594793, 939091280, 682666570, 432894167, 108345360, 346974721, 626010936, 727440122, 893700162, 24427209, 780211311, 215237705, 926933860, 514718056, 558913948, 546502064, 680001471, 331080809, 829837662, 940260271, 920065237, 329586397, 240802001, 66061750, 644707066, 454416644, 639583822, 189923386, 861059742, 918108818, 952514870, 313067234, 762961370, 617122400, 716367107, 416111129, 793769920, 994579454, 174294660, 248181693, 865607163, 999612287, 886616722, 812267661, 896452488, 268929903, 935083768, 625326191, 321815584, 758910465, 94325909, 424456375, 366318098, 576671933, 752702039, 607984122, 954793058, 528538097, 631521441, 785409695, 711247709, 129886807, 723174714, 579019024, 427531135, 792577934, 781814716, 301976476, 276836254, 423758968, 138461301, 217095310, 559241948, 251074859, 121758120, 672695387, 62634887, 678739134, 60803625, 264413498, 872794947, 542608089, 155102053, 891599423, 593557492, 156314271, 391257589, 438763959, 397186178, 334079305, 801519993, 572384721, 345572421, 422482995, 437290636, 756070197, 758153784, 299011331, 228449661, 905562385, 434695259, 442618304, 903574091, 816464082, 399504768, 43393125, 567699662, 131345620, 764297345, 726119381, 488990960, 386878970, 439910989, 375851945, 890203966, 645881115, 735114187, 413663934, 25616477, 587727201, 130229047, 567982580, 970916394, 426600189, 709198830, 503618645, 314738216, 875784367, 820105548, 786487762, 747375788, 100935413, 380531094, 870586371, 184424237, 180925452, 249080301, 300873502, 707095615, 991649326, 604409542, 746179093, 448056978, 222712467, 10652066, 295170028, 379912045, 356226814, 756706027, 756702184, 602355017, 507271882, 59477287, 567562787, 506417145, 746326779, 491088687, 900164466, 690226362, 174394369, 201451106, 905837076, 57510648, 520338877, 531968668, 897624432, 292988956, 106847123, 728612905, 782846108, 723426789, 178445313, 228282496, 531425874, 922829591, 618799612, 773976976, 651204481, 950326242, 203982938, 143930337, 105098311, 502859877, 332207266, 579771900, 940568866, 71774420, 349028765, 733676706, 986929313, 226123177, 620869389, 319563133, 446485371, 539266235, 722918988, 814852538, 539538060, 39938660, 438355010, 951593634, 663448841, 593198973, 79814677, 660590436, 677357699, 440613670, 593202513, 503089629, 760195487, 250838500, 919950306, 646537243, 927152562, 592441407, 538104302, 536409150, 63571155, 195702296, 918404527, 162808808, 693940238, 560230958, 737510986, 992392320, 844265228, 695521770, 300308712, 786523306, 487218310, 192343466, 661469699, 108679465, 430226867, 941561661, 461895340, 112417918, 736377990, 696227950, 240271069, 206256338, 935980941, 859978405, 353098420, 111547317, 152239363, 296988839, 477144360, 128393417, 77685469, 763115205, 546450049, 859618098, 567035474, 829775445, 372053443, 677584951, 854608609, 586334765, 303868057, 945647995, 450081540, 245322512, 50888693, 646961712, 809340243, 163667088, 967984985, 37105772, 230666976, 471431092, 865794920, 557360524, 196712220, 339655058, 984593717, 71799367, 836631493, 767861911, 195845936, 847825229, 513338989, 802246030, 100630025, 146623935, 496400989, 932211814, 234071598, 224569877, 212150251, 989658302, 773018140, 976829309, 210704071, 976454018, 227206920, 82585603, 20943243, 941517943, 980858113, 716249194, 468918057, 297765611, 189316142, 704333714, 98158910, 660412419, 774432518, 256872964, 178332466, 149690971, 905953659, 191707343, 673508706, 328690641, 152589756, 642170662, 375870459, 82332887, 99686233, 361876656, 531997253, 587656815, 636795244, 376732436, 281463785, 333131270, 647351778, 413343918, 530826653, 121568113, 646639273, 918388676, 180500470, 141528682, 795381584, 243632557, 949920568, 770960434, 23477918, 367109645, 280753972, 931871308, 777106938, 807302416, 119782236, 838050188, 517701944, 521018678, 279999069, 95294174, 913737779, 636716456, 213917257, 313642548, 724258807, 447114817, 435888466, 688936509, 47173272, 757534023, 459798670, 218477703, 224684154, 883265694, 862519344, 103648905, 389801582, 376781257, 649196382, 193076183, 176342182, 370017815, 415275631, 159459129, 577741346, 183493187, 934288505, 247335347, 680384923, 640793051, 446100812, 472090670, 104942002, 443836486, 490041392, 177861385, 182011718, 801415588, 809341777, 72587813, 979246912, 373413730, 543484643, 164487103, 622207939, 593024874, 889723386, 281975696, 224739623, 847452859, 27688987, 249712284, 49278176, 778315245, 61413908, 393049784, 885481747, 700978812, 723208366, 480023487, 158133910, 744919697, 806460295, 823887288, 210260880, 457677739, 661354635, 237870652, 806351141, 832699714, 595028474, 205208168, 971927854, 620022468, 261394736, 608445279, 70608879, 316478064, 600923836, 184037461, 511106281, 211892154, 577399998, 591623370, 330101496, 12593437, 354113973, 838697794, 583284694, 481393874, 687939971, 407908306, 836809663, 455605995, 788731391, 825055676, 787999762, 919830905, 695143520, 985655555, 914583133, 822069478, 827882170, 259953787, 36258899, 44924245, 482745229, 160721907, 441951657, 13756175, 788419518, 239467471, 374394446, 567140355, 179443822, 367630466, 626006099, 32115082, 770233251, 492727231, 478887944, 49498660, 732566538, 359927810, 694733241, 61383462, 691640937, 793612756, 136625897, 217858549, 226697256, 224263712, 425925466, 968665597, 674867775, 823074177, 57135845, 585582062, 715076040, 16222845, 866849959, 420382573, 576433211, 881826771, 682534407, 630957686, 559897318, 915979386, 542457716, 183018756, 533483784, 303313739, 836061103, 52095550, 703490829, 804568453, 727605640, 17741610, 750354895, 658319560, 602467989, 152247655, 640059348, 147546790, 802741668, 491599574, 359205192, 128978041, 335392585, 920059071, 724881286, 164761861, 74506138, 251655400, 376606047, 187632675, 954085460, 491543906, 314263706, 541062769, 386121910, 460000369, 239530270, 667753828, 766688938, 293938179, 184910094, 670113885, 893199925, 771504370, 948104827, 701269977, 641880425, 220216127, 731833509, 586288679, 196876265, 842847229, 258464438, 770351034, 651737610, 601857225, 845208530, 595359819, 882383666, 56413156, 804256367, 506536033, 677124433, 252185609, 964068805, 537509060, 671176618, 165315873, 41014665, 472336214, 898902122, 683936452, 198500860, 170436612, 706490309, 38423920, 112712878, 495319565, 892397346, 423861052, 906994181, 144585515, 277837207, 176663919, 182309856, 272310725, 147517632, 92438574, 215878046, 639965865, 740778766, 600302269, 172452913, 88162526, 868882029, 863756969, 920355219, 319549022, 290145457, 968719172, 223606840, 992979019, 286752499, 444628732, 234516285, 456064198, 222598220, 62019544, 246705815, 477455618, 311305598, 972631214, 58570703, 699338302, 856781226, 515276101, 717064938, 281106287, 963140726, 742666030, 542940631, 617610884, 718051984, 9458187, 281266719, 974025170, 71010849, 945000308, 957312201, 12661887, 952210413, 37586241, 244367147, 693355069, 768621069, 570128064, 286258546, 14209477, 656843801, 428674664, 208228544, 245281137, 773344534, 162726310, 829385596, 79419488, 29622322, 26364387, 236412837, 564124049, 578043092, 181981427, 378318581, 951698671, 646657929, 654453223, 97630280, 337799602, 466920219, 654768773, 40999192, 104101280, 596167394, 541048870, 961765887, 95775979, 611844052, 679343016, 49706730, 214281688, 336615021, 429098028, 187109385, 522822226, 999131590, 348409261, 928001355, 800795138, 115249263, 817916391, 598378394, 901810915, 15426892, 929183101, 836639467, 449226988, 803376748, 516864930, 595759449, 876179767, 302810570, 911105003, 754877076, 627357498, 277243518, 852714689, 845500606, 747059088, 826752809, 494131778, 90643925, 218330975, 473714548, 278485257, 325158152, 313443972, 864013402, 620460524, 171319262, 826599922, 302716081, 507641478, 644252176, 279360256, 811783829, 418522458, 563650588, 818568140, 828179919, 397989588, 398312466, 679213376, 901671329, 723516429, 901751708, 724950819, 972463050, 129760569, 548945517, 256587032, 683859186, 527168802, 870762572, 471671274, 228150215, 976998768, 397350704, 277022553, 352371755, 634518561, 944496870, 970417615, 565093552, 323075343, 695646928, 923049675, 127509861, 426939471, 80647168, 278587870, 986101073, 541892219, 153184724, 281448877, 915817759, 675929611, 660563444, 803466012, 619169162, 376148284, 598717220, 471163578, 660758257, 338496830, 840989232, 187014176, 197286497, 551485906, 501175098, 54454374, 30365751, 271075152, 424823263, 593152331, 969861594, 527487488, 559978081, 535208831, 439400614, 427620258, 884716390, 805154667, 442355131, 292627100, 556411349, 179758470, 129390911, 764136577, 671854115, 205764046, 202448424, 238833900, 773462265, 253384939, 812617559, 354045667, 688097513, 429441745, 732315839, 516989520, 703830955, 919763229, 75294885, 617500955, 172388021, 743020974, 470001001, 613497749, 646195932, 367451432, 882315779, 43497988, 487948579, 557252860, 232058132, 524476577, 839345455, 993776674, 420250222, 1913133, 454045963, 914470548, 774070945, 342734955, 173226677, 620101764, 304759028, 984123820, 81225448, 307537157, 424216080, 122575324, 500081254, 695099937, 811189310, 482832521, 752463613, 857278114, 809118614, 823548858, 195669101, 261692553, 42773179, 586548671, 240450526, 559459840, 798835970, 868765894, 999872234, 342758104, 17764630, 472872145, 196338709, 934444670, 888178235, 84660711, 839878120, 578087845, 698797046, 575891142, 316849797, 424624362, 780510560, 644352590, 626612877, 110517612, 237891092, 569186058, 386881298, 923874884, 173795807, 806669314, 341186257, 228287547, 246554493, 545970967, 410859780, 998136726, 993522176, 902292008, 863049491, 223587499, 19496433, 773060595, 405926224, 924269855, 231393751, 328588237, 765748592, 682696120, 757190467, 18792577, 386803083, 497830525, 395988661, 408935545, 69474536, 380255480, 766835024, 22681387, 762002283, 877392476, 532258465, 790444418, 472439415, 85883557, 44878408, 975894962, 748379242, 484876275, 445800852, 636377636, 990959012, 937235068, 330612604, 12467297, 282339212, 184661749, 193339062, 451228795, 538940041, 707576411, 867118255, 414696298, 703008715, 563315975, 308224864, 391356790, 923133549, 657896048, 433280274, 654098768, 218504177, 277676776, 248400497, 279072849, 168938385, 914725779, 199607979, 951772405, 38589679, 156599831, 478975954, 53681060, 461656714, 223350405, 469194693, 935552940, 496383908, 448465991, 185253607, 719878247, 820689070, 681472723, 47407593, 488612871, 537766625, 540819211, 728713922, 252352715, 746308276, 132742427, 637614102, 818555327, 113697671, 637530328, 418332040, 446157688, 387243488, 334661624, 409410725, 56015245, 882722365, 367295491, 901027463, 794551603, 420177205, 633556901, 214533284, 206157335, 464651555, 808338321, 990973969, 368172382, 888326931, 276141218, 951786507, 351330032, 254253330, 162972076, 433198264, 957833273, 552434934, 937716921, 299277434, 334046503, 947587349, 997835410, 147226679, 612135318, 650868657, 48608212, 638841584, 116562312, 67051100, 257074132, 552480989, 493649344, 128397634, 971327381, 740553511, 421439501, 284611909, 753006851, 908168862, 56138391, 662379622, 37639964, 231723248, 180986054, 114003435, 817174841, 709687984, 786055222, 636694325, 900653619, 98235204, 4711197, 516854899, 528389917, 587599108, 538460343, 2764429, 134983680, 221978572, 242313151, 199344927, 935549253, 380020379, 606425865, 951847987, 809348110, 880041450, 203170148, 971360092, 738718955, 619946809, 843667553, 770468189, 468756390, 339835011, 18736880, 556973580, 800215569, 463187887, 342354259, 313727781, 278073554, 704692555, 724449516, 911499786, 157842319, 119603932, 415291609, 430810296, 132546435, 181079145, 211586023, 626196615, 767649903, 395487822, 70511601, 696503364, 238839678, 283255737, 307431735, 130129005, 139211810, 785569410, 255589422, 187332572, 157519975, 281610763, 775352768, 373144456, 972532112, 419823028, 285053345, 464928355, 363682110, 469854815, 90401612, 413984341, 784175133, 553769787, 900472192, 358398467, 439896514, 649956686, 927503116, 477154221, 301288347, 668649156, 330976866, 261704175, 538154137, 392100474, 359441208, 183656866, 741697161, 544007107, 610320916, 908430466, 506991457, 683407968, 374300015, 548729042, 49450102, 627618692, 780220556, 822591767, 583816920, 654521963, 694013265, 401987244, 244292376, 326082751, 251283375, 93248080, 992759449, 56937713, 24465600, 108247816, 961829522, 789457735, 352685433, 337913227, 67902597, 750133939, 486610936, 338123792, 179907632, 535494034, 226127448, 875119800, 590247702, 580361870, 143520698, 810481745, 686505013, 762344956, 352984990, 92135135, 322748082, 283763199, 467105271, 117105077, 155498379, 238507790, 326895033, 669816161, 552889777, 396771481, 992458264, 785996055, 809239797, 817017877, 57094253, 965558634, 207470353, 855196839, 186851546, 127469170, 620433282, 243352928, 410521534, 190212699, 830120638, 571548048, 357836282, 660186128, 378058742, 350246209, 575398937, 46431318, 47752769, 602409341, 321279087, 401376194, 854196437, 659422639, 473520463, 862296335, 721525654, 858965248, 226733709, 85194717, 102555190, 260250087, 289514521, 235179832, 698968630, 647471236, 202503307, 580385309, 649909599, 742070822, 484246120, 365075406, 784896651, 144737114, 313886682, 733049240, 933702850, 310640161, 122097778, 675681822, 519495675, 910382534, 247269379, 658103888, 798878957, 775107953, 671672820, 672451421, 349972413, 124806330, 528396773, 372005098, 612279007, 787864930, 664002059, 562251608, 60958261, 560928871, 660934128, 53976395, 21576670, 820913125, 172248379, 658537841, 278384946, 27117462, 761099682, 226440057, 365933137, 728517659, 165109077, 418207544, 460599736, 49712905, 637453334, 944289156, 160156879, 727501276, 102937410, 843375939, 547936181, 672807900, 186620365, 316375162, 39238831, 251245059, 96480966, 631355815, 901320348, 979823934, 630892660, 323439069, 910291436, 201145450, 251559498, 520531822, 719773012, 639607695, 740067248, 771437766, 988203645, 605267457, 626403557, 219166347, 501467351, 625905676, 812950168, 464569225, 665449793, 715839673, 101220427, 324586669, 821202461, 586933322, 865305405, 308800566, 164707277, 173763732, 125958629, 842726979, 173504002, 468054664, 972425841, 811900999, 580363392, 147617601, 835509798, 586268817, 255766342, 710683549, 81054839, 853371585, 779155196, 211419676, 215702924, 841940332, 523658258, 106011703, 808359275, 368833996, 611079143, 644325712, 148509006, 276750666, 974094231, 910761251, 166254048, 189980545, 747661621, 649393683, 140168362, 112606454, 417041566, 532425453, 702189896, 818229909, 36582856, 376097954, 736240669, 959936089, 35098257, 353251615, 729146668, 52502076, 496370666, 156534192, 948596251, 593148087, 130375235, 771601255, 27723479, 814112238, 197353412, 838159472, 491869831, 553427608, 738204568, 367305902, 253851119, 641950056, 606707191, 101126064, 942332598, 914747161, 976250764, 747862552, 802137931, 593659481, 455638638, 711652350, 159254369, 820734447, 609361237, 317743622, 690056596, 120541526, 318554890, 866047389, 990423498, 26552026, 459608194, 509169633, 150646280, 800851394, 221294909, 940195473, 199772394, 708237922, 580215162, 201358189, 972625651, 562590992, 898786720, 848625244, 130211626, 998588457, 276062186, 770813342, 629020424, 296020606, 765637682, 494837709, 549351307, 51202478, 746257728, 132826123, 745360694, 164045193, 753502947, 951762166, 763745617, 147003822, 566873293, 689310305, 608389808, 891266120, 61881636, 794146598, 703680901, 345562574, 94844606, 527617208, 378625152, 837775172, 459255739, 952773263, 3910784, 620019536, 728902861, 29737133, 69000193, 471047579, 683560250, 883734875, 735542594, 433980112, 862184157, 806494463, 643927846, 1260790, 957737070, 438925264, 152068574, 440734046, 366965622, 326004607, 792741555, 480258936, 187758095, 78102796, 607499604, 942737999, 150345910, 489338894, 31431213, 96526654, 913927086, 660213893, 567300418, 128020074, 487168112, 155038325, 263963376, 677042663, 26344860, 235159292, 587885849, 366422141, 544144665, 198998295, 687944977, 272309646, 1558838, 140370765, 292674599, 886424664, 440903662, 434935529, 171364745, 475351052, 950326251, 846483214, 631050117, 186579712, 873312028, 463333178, 339375413, 565769586, 117268184, 352587014, 256978061, 192857391, 872802971, 457990054, 44488193, 573256176, 83728087, 103056749, 785579001, 315428427, 868168979, 153181406, 698657314, 448655731, 867942952, 10348205, 374511484, 124739575, 752195756, 144637140, 281096310, 548446730, 841716408, 230920634, 134975068, 673712028, 87905828, 588381542, 691269327, 185416091, 398606705, 154204, 781000575, 607260521, 490345209, 591993472, 96296926, 256705569, 622251118, 990525939, 345635967, 870712667, 342817748, 966923265, 779675456, 63012805, 941504268, 154067712, 30259265, 518675449, 970905121, 933425347, 539160890, 654218086, 777678030, 27135596, 536515440, 641940479, 505428068, 137495111, 184096727, 921463563, 77530425, 87171947, 610944741, 401130695, 829957065, 712011461, 254156195, 592106433, 3178536, 909861919, 683676992, 671911192, 836376054, 291600465, 564561664, 86267478, 595213415, 739154762, 828644225, 947838610, 389031844, 697740158, 923753059, 110317989, 981756799, 425617564, 395377178, 583408252, 947426712, 425724830, 168728654, 953580474, 422961103, 755438460, 591307945, 332981709, 91903585, 605172595, 300895246, 939613098, 903238262, 639761308, 788521612, 619795476, 834117676, 268016778, 63083761, 317729661, 537958082, 917249569, 426133166, 258333276, 665295092, 492789168, 481059807, 865583773, 136579696, 576010529, 95311269, 662109983, 30159655, 415833906, 527410808, 127784161, 907309728, 20492066, 370484898, 904276, 430833131, 58156061, 440884857, 13512197, 596764219, 216277803, 915251680, 70112810, 287633300, 989541579, 861315207, 874906441, 151973011, 479738366, 593707531, 591293349, 181434296, 495686347, 590457701, 130226981, 511155165, 105362323, 115619176, 448545746, 610364315, 80535625, 605479066, 856468648, 555572550, 484893856, 125171029, 828282631, 24773241, 52260854, 270645178, 627339677, 221435210, 72539087, 537869611, 246661668, 647484866, 699982624, 365206092, 550220071, 373889871, 306383593, 947251694, 949752938, 947418133, 264335760, 579410851, 582406686, 472265691, 962600000, 371579081, 313490243, 138513687, 165377208, 205834408, 402623809, 798206125, 88959978, 56982090, 86692718, 973703419, 232437734, 342255950, 315941605, 804762126, 971189258, 874321994, 715677407, 284049032, 937082522, 807553455, 650281605, 674384241, 620330757, 982560761, 770613120, 998549460, 561243961, 206978316, 743960018, 636674591, 244374138, 354913062, 849750121, 5560236, 775851908, 951891170, 552525312, 731325023, 259997041, 649341103, 960377011, 862863567, 844587856, 499081282, 553632003, 111528312, 664470570, 433329449, 950270396, 156582835, 467344570, 821551208, 973350710, 808207976, 546381753, 304533747, 741355803, 401661311, 910541552, 301145392, 647120912, 45789386, 776339013, 367147003, 221556320, 872217147, 475358444, 179411142, 512822315, 503491767, 417096999, 358070270, 642118631, 927791154, 716250120, 218403963, 299720485, 158491193, 723273760, 409675150, 140829728, 536626499, 634305565, 906301950, 446195249, 896743248, 152971623, 253715324, 857011953, 535614701, 61738417, 231705097, 66900874, 91541353, 651221428, 850483773, 551974400, 751365263, 967786418, 952350687, 773850385, 832276273, 175710382, 479105915, 272421331, 614885263, 83890396, 642469862, 123833323, 402036882, 525178302, 359682748, 370481361, 417789550, 755528834, 427846241, 968624206, 445237634, 830368376, 724369380, 143458206, 726162354, 293792799, 371629214, 616436096, 556734964, 227344632, 403173585, 467748545, 550212781, 393533866, 451115325, 55262707, 802055255, 859575865, 816585000, 354218330, 204512506, 705463578, 612215509, 93132747, 890371178, 325539314, 505076009, 615630441, 660480699, 122975311, 889130968, 414285555, 324148357, 748688082, 590959740, 284735164, 23254324, 683581633, 253034571, 398837349, 118548164, 318088348, 803123585, 228070291, 95192170, 177746189, 612859566, 492260627, 78566336, 315961823, 557397067, 872223060, 749431839, 73620436, 141041980, 371349471, 557368137, 30577247, 120960927, 436466255, 973792644, 904100640, 863498923, 885874753, 795770248, 550714389, 82033884, 792653857, 211453518, 521111429, 380788987, 394726702, 599357063, 449599058, 843913661, 923894328, 840770108, 676040156, 337761751, 556117949, 62278243, 582806182, 53930493, 623148086, 909837281, 799999355, 874297196, 683601041, 182070728, 695985152, 926250732, 814673942, 500590932, 888021422, 984303811, 719737476, 36715831, 196811810, 575035046, 403494161, 346201556, 938769320, 804897909, 301390119, 1263384, 420122719, 429792765, 916404256, 111581760, 873140541, 950038906, 226356606, 737234919, 913603791, 348374433, 45774736, 43605369, 337694975, 663735286, 396273012, 523029091, 645052881, 9901980, 827909503, 363424956, 862248704, 763352587, 668719364, 487656899, 705948471, 36816049, 446095347, 945534157, 738815911, 604696874, 55298873, 399546161, 399965498, 550088877, 229565403, 657388262, 372691227, 509794106, 859565767, 426254757, 461473581, 143448595, 991993666, 449698783, 36297451, 307551354, 746037862, 56760110, 457741093, 467275158, 278275219, 411190092, 237528705, 913524326, 418922309, 838858325, 971669630, 864218897, 655550124, 553795312, 554222208, 667260113, 599528533, 50423070, 268646598, 594248142, 920513190, 6237994, 452349752, 991412768, 412199671, 60643934, 572047614, 66233451, 40166888, 448667264, 15419032, 702602243, 210456209, 570727861, 168207178, 262340890, 285605665, 635957969, 711011944, 692038068, 865686695, 181942335, 3121641, 604353418, 627436721, 682297836, 154939108, 81128403, 817245092, 347257060, 585119056, 607020795, 790584184, 589877500, 762381128, 27228748, 550811872, 885132123, 54374852, 88413412, 261238660, 972185056, 696056202, 378902383, 312024803, 334722898, 525460340, 572363610, 458633758, 962397979, 572762989, 342709514, 630809155, 285855471, 568232519, 909037856, 794616394, 983536228, 43496949, 557905365, 306484841, 832560073, 775740442, 881813056, 451487157, 25535871, 864757162, 842332613, 18481143, 529536438, 326361243, 589197096, 792521603, 532033640, 47389378, 873650406, 708989137, 768562210, 103823319, 65945204, 784496483, 445089304, 672162276, 404169225, 286651231, 878875149, 650505516, 253746733, 865322303, 52690969, 694002328, 427759579, 415746536, 781742531, 335424638, 430013924, 490079771, 9943360, 399062439, 886330522, 687814063, 976213110, 371372842, 214373639, 527264517, 12173787, 163384275, 546868303, 540323733, 946453458, 226237810, 300221862, 412840051, 669294402, 641936613, 292645443, 315519911, 728352526, 458226052, 546785163, 263462741, 403752629, 230281430, 687889384, 624818007, 806072861, 361930601, 408387900, 328418229, 769393599, 949767289, 754950199, 406209966, 710392146, 593523789, 728357475, 549387164, 688603670, 483819332, 417376673, 207546210, 744024663, 772600826, 483049585, 886248443, 271342650, 216252862, 991394591, 656530294, 165288336, 229045636, 256062228, 106408122, 445451532, 632815157, 34376587, 198212080, 65683699, 714932516, 562296394, 350467107, 681119163, 500661421, 942201613, 33436726, 318498939, 67704704, 772430469, 975816378, 608781556, 366532602, 140232144, 966361080, 660191024, 83634447, 640500020, 690918435, 331708301, 372438838, 565835115, 808066971, 450832573, 218217728, 164129506, 521411904, 376980265, 256192596, 507584828, 258870903, 944570800, 676599072, 258832998, 913984417, 767030274, 552320992, 647625077, 916283361, 671776634, 685255274, 843840238, 25948010, 527558374, 593422299, 747487487, 122825539, 890070207, 700248798, 95460173, 193876453, 970660701, 105032705, 509446895, 163352843, 413157125, 168637737, 478314906, 830921297, 207021512, 677862497, 740715531, 6624579, 307788152, 699906878, 559109733, 972270512, 441367423, 832030151, 660952890, 513246692, 872818602, 689747068, 56455147, 954041746, 914778521, 724112037, 255475106, 250541777, 273675771, 745664323, 109313078, 562029126, 114022457, 273834881, 23240835, 38183968, 723848753, 630001789, 4101864, 771778324, 789401154, 245822201, 482972685, 638405196, 929109489, 522489938, 256962182, 858123508, 738377667, 755198136, 453669910, 175600977, 215419491, 975388309, 1341551, 732049942, 228388576, 193950768, 779212415, 209200986, 197396478, 398819315, 570642256, 675313605, 512923638, 455802113, 751368409, 792319384, 717305022, 983090558, 81196302, 419595775, 369590119, 392057145, 225551885, 117591869, 10987196, 383340271, 432964419, 425989569, 187089116, 943909683, 14997552, 995605691, 278566694, 82083968, 555887035, 816305135, 890641557, 245274445, 807293387, 231259532, 198652027, 794125132, 975194455, 278487549, 707715256, 214745101, 690168077, 774917214, 152991753, 534900948, 810958074, 703728244, 123525040, 738863204, 66685481, 246327294, 87236325, 430163101, 318493496, 607515299, 809485072, 18415703, 145332253, 799981218, 988309539, 920810524, 580764883, 871679443, 459915359, 686331534, 165321728, 219913782, 83533550, 185509961, 926348141, 666759786, 636715482, 52262111, 660751248, 626666374, 18728321, 915280576, 32705376, 521892735, 883712957, 449411792, 617647110, 952209142, 963086177, 44147852, 168661743, 359588306, 469136284, 384452900, 887052822, 165877397, 972801305, 583042150, 817623663, 630806586, 913071020, 436023233, 773577742, 269239176, 506825173, 797471073, 425565824, 868596770, 61810602, 472328253, 207343987, 706613889, 808120019, 308556276, 462301920, 249197357, 594191044, 590255708, 275078443, 132267816, 975439899, 498830245, 815524146, 853737533, 799020191, 268883223, 616159941, 902046336, 710727747, 543802411, 296705630, 652437341, 852892329, 673803490, 247686, 56673706, 747240110, 312584270, 848628545, 772143589, 920017422, 966072022, 809240159, 61846261, 885207646, 554080908, 394269600, 235763422, 169984595, 370038207, 669818483, 154972286, 874095156, 529461364, 843883814, 326233207, 930683155, 248470639, 988953775, 64747049, 998167888, 503078230, 775109019, 170863346, 106911199, 992411058, 293989174, 816498418, 782357901, 122944638, 726658681, 322203367, 766625116, 290987939, 409187408, 361289236, 265700234, 84954305, 987115437, 875509660, 695407535, 545983262, 734854605, 26260232, 651892459, 373531196, 393156367, 385793910, 926144629, 940089174, 614626622, 422246667, 889034293, 10157176, 965305133, 581883975, 788785988, 284548600, 272184811, 58066463, 243875477, 259312663, 564849730, 920478608, 638830717, 187048267, 158272394, 670180068, 906875759, 579708997, 915136613, 506026541, 606981038, 713710218, 252223951, 937559665, 758734935, 748553001, 442900274, 701974261, 418254280, 858603366, 604774668, 145289820, 654766922, 437555790, 356495277, 79914321, 68588378, 457051902, 70511012, 736044940, 558895232, 46404403, 319273954, 315143273, 543934163, 349335410, 76277153, 978287821, 419814361, 633883644, 185978006, 226229967, 358351668, 226348145, 884917733, 461247990, 291757446, 303906649, 272725723, 361263479, 824464670, 642200502, 657355565, 48958996, 329164789, 151923716, 678265507, 475803121, 113527682, 906508381, 174862924, 200463375, 540042909, 685235858, 486276306, 539136750, 771690258, 36620006, 226525121, 100522554, 295468063, 61026113, 380704974, 62227708, 463393930, 424036891, 67605917, 916975624, 129336240, 932152680, 680110289, 628555235, 198525727, 206174520, 27346133, 424054251, 374591262, 305602197, 283387367, 449425755, 155646449, 244254216, 64199014, 798096446, 943440238, 530995282, 92045871, 381418275, 989047448, 27372176, 355370600, 279520839, 181715184, 863623389, 858314765, 48389427, 15393510, 432341180, 121917398, 620207161, 916690744, 248390926, 444214925, 548706444, 337216591, 220463718, 418488644, 730701174, 441820320, 704203526, 834603621, 460985406, 738874912, 908327294, 44640929, 212671255, 565167684, 393814042, 735288712, 721206895, 518482816, 381140941, 417664478, 807165260, 189755908, 400186575, 303259190, 69185018, 469908871, 881632243, 896067877, 549724019, 236553338, 929142368, 115036899, 324746567, 471249309, 99237378, 386588466, 737799053, 898789757, 536034271, 850726624, 696340173, 679982626, 700495545, 254139539, 506626701, 742061832, 36646263, 813532022, 267953463, 991772917, 631499621, 261717487, 948874681, 112702910, 358090968, 775308156, 790469068, 373774125, 689435158, 113845537, 944309723, 103086222, 587437792, 442505825, 955659299, 822479969, 75929908, 414705383, 881874393, 796882167, 121016121, 480429108, 683439022, 165153694, 477300320, 168437019, 928454754, 228697590, 625987462, 792553058, 543375217, 575761543, 493078687, 275735428, 934847132, 151158514, 310989741, 485921552, 835219177, 819143563, 202177779, 214149743, 93873331, 249551044, 304588686, 728550248, 419058857, 492166808, 104093084, 464246976, 67803533, 369570385, 719503273, 663796880, 435975223, 598361030, 609847853, 128919527, 761942030, 981399429, 117242577, 923181498, 55149415, 874572728, 303048462, 287943100, 998991697, 19115703, 173800483, 211059632, 189241183, 996595127, 792473146, 582352480, 911040372, 366724361, 639367351, 915483368, 95471672, 426834906, 963060060, 464101347, 68273671, 2341270, 853552608, 799688823, 871374119, 256375927, 68388439, 127954007, 959344388, 348976726, 959258807, 733111030, 265717621, 65985958, 709037003, 684260638, 300291856, 654566806, 134579059, 885238268, 780253265, 877448542, 561997523, 500194154, 684820017, 519513159, 914706809, 83437914, 170929289, 393202383, 324027501, 227735062, 850375694, 30205220, 681358596, 30410756, 237304965, 323070818, 797537448, 25616963, 632003531, 619469237, 184976183, 58537164, 112382186, 569446008, 809389126, 509179169, 267814615, 226133980, 331442730, 188321025, 111020104, 728640900, 542188253, 139839698, 450509319, 127261619, 839171984, 647038920, 484874454, 199750942, 357061765, 645847161, 7560695, 63367623, 386152488, 25348094, 697882748, 226412164, 557756335, 320851051, 426094125, 586781322, 480684615, 157268079, 51987820, 671715772, 187320255, 814937799, 730244475, 530772095, 649736669, 407348304, 805891326, 772586122, 306255918, 294921104, 696569664, 330613594, 818468268, 703868881, 574950598, 117436502, 513572463, 688949047, 186581234, 242668426, 968908492, 58691872, 416168282, 297907324, 120623060, 509176547, 507482716, 519724103, 85972711, 925203982, 158659710, 865364490, 507145484, 393922874, 733006847, 45269021, 830801459, 150396250, 616289141, 578899217, 734134024, 328702650, 901486738, 3984002, 5705505, 335620742, 855000392, 770307290, 417196881, 750493321, 971381486, 207659583, 608270963, 875266615, 102981449, 870837391, 952780965, 60328358, 966216793, 444654308, 340461478, 650901286, 617201589, 606312959, 53990111, 233465169, 772964106, 777510565, 289021480, 372706848, 4468243, 628444786, 863310035, 88591576, 591644749, 463273284, 367312598, 791848167, 741414560, 265217350, 635358523, 123654254, 317294768, 649501454, 275916638, 631786015, 946840823, 310399512, 932911978, 6134969, 678245271, 279317599, 168338749, 94673018, 732029643, 708384871, 345169628, 270469369, 529782520, 449719415, 917199830, 184020461, 697235376, 554485284, 967122452, 102779432, 106014520, 384104117, 269946290, 538913778, 307803560, 464639564, 395498010, 437344058, 986703022, 667762188, 203379052, 308661339, 658763522, 164882446, 579143770, 639969073, 875867704, 146243780, 294343177, 894153118, 123164026, 616824629, 585243236, 787645256, 406014529, 831892166, 764639558, 49795792, 709210788, 143288280, 944589913, 670451458, 636604746, 199913816, 44711982, 702901136, 154201716, 93412218, 184123785, 451533852, 799368906, 602098033, 625313942, 468300853, 907696079, 49015703, 498364241, 622175095, 883151545, 223907478, 637868163, 942719089, 615128681, 632838897, 403604492, 565165379, 716239468, 342928942, 444059621, 634646320, 818731926, 397470242, 560074853, 57669244, 657353947, 680634498, 203222375, 597496360, 712920749, 102248430, 741380638, 795476400, 554103189, 891518000, 175817158, 9768620, 166220575, 350207135, 563014487, 697126335, 468549836, 366168742, 956876988, 77989735, 16803890, 492091314, 983588322, 702807493, 798242058, 81318862, 631065966, 54338346, 326600787, 893063098, 889086426, 337999978, 402779191, 2458783, 742951499, 554344512, 271482619, 262694572, 838149233, 956610653, 86591257, 692057217, 17525753, 943735255, 395062524, 314626230, 582099639, 146244666, 646809172, 440147634, 252038220, 992018464, 901246598, 762522401, 109482209, 212162395, 811523850, 414871731, 303284289, 83065352, 749400549, 803430711, 719348245, 52087598, 657730714, 644512696, 250892956, 390838192, 99479848, 571583078, 973246908, 4221601, 463549077, 118180061, 894384427, 150331299, 42029388, 193556976, 650164029, 716808554, 291519439, 206855953, 818172063, 953712438, 600825783, 87612831, 62580812, 573101481, 194210151, 733237450, 511978659, 338943466, 455926923, 370071606, 434808346, 499904136, 1578530, 399562183, 168389909, 270328016, 519542640, 440260315, 683575708, 636335887, 999596771, 646564854, 932417922, 697126744, 78790771, 152306815, 206824842, 92857537, 284078311, 839099450, 872089334, 344332718, 957990125, 345750444, 68907, 997994529, 328067693, 197231849, 199645918, 882493255, 744858955, 199109643, 290856376, 111335178, 202902698, 874557369, 385046566, 405424801, 764338524, 47703822, 377321496, 819327790, 462801230, 657478523, 939564217, 454610966, 408545189, 564934958, 89637812, 120912072, 1397468, 28896250, 143746241, 560952254, 550611439, 424971782, 37651571, 860608225, 780839734, 514584512, 839747604, 858538136, 744362034, 342836008, 267373989, 164083168, 136206635, 54542621, 712295402, 840871325, 851807982, 210618207, 472060599, 656410677, 161504117, 172020829, 83201788, 207585381, 206603015, 455156945, 206722047, 69974517, 862025303, 317225410, 577237162, 530800748, 301477573, 974890295, 241493267, 320458531, 918989201, 27562256, 662807951, 994848492, 841821070, 847341743, 97426581, 15783323, 690064837, 235663537, 845169862, 212780495, 241237562, 749375576, 267117956, 396067730, 986884027, 94677294, 758314287, 612343787, 334176097, 978649497, 344532713, 289535441, 863771748, 780292134, 905735440, 984331374, 767835467, 484577913, 415025655, 233562732, 577436977, 631498094, 411937822, 243720234, 718281124, 348234622, 357780913, 806032090, 155982709, 797821997, 662597701, 867748821, 441022999, 627093466, 379189743, 427316988, 31447649, 928195731, 871290142, 854549495, 940310473, 777041674, 881830767, 387691683, 166935569, 815690515, 824694783, 589713099, 92969066, 504630088, 304821076, 223324520, 974525671, 218688287, 510634710, 745910286, 955522673, 632044048, 322930166, 880097970, 34515278, 711504283, 71601451, 244264714, 704987399, 188764431, 124126857, 115459332, 778999183, 239412483, 296992451, 400939645, 820803394, 510838401, 894170600, 638538004, 329849232, 993805125, 398988409, 373435678, 981191906, 123738426, 176982384, 871581404, 588446734, 233584279, 507733047, 130363082, 824197818, 896479518, 831463631, 502601821, 720694724, 874320792, 200164110, 680470011, 867493222, 435811669, 972594802, 78084604, 918420610, 981271955, 615459740, 977985162, 586062411, 592450158, 635372564, 860177535, 920199220, 23089846, 742623858, 329261313, 720541688, 662367095, 635773995, 63766187, 37625105, 345867822, 368097248, 216646791, 234222315, 173126067, 2071620, 528587467, 220441984, 327565990, 767413440, 527745509, 81060519, 153414233, 178751194, 781332765, 993186497, 950873601, 205252280, 790284397, 398784543, 642239700, 457778342, 221203745, 28567299, 104255973, 239366319, 87157699, 372515433, 356957866, 800941371, 496931239, 776772148, 218811710, 449516592, 644389522, 973904951, 682340873, 898454458, 369376634, 856666725, 117680915, 155395253, 197325335, 443504520, 297642696, 653241672, 419805916, 571509748, 251807577, 860343707, 78309712, 497395866, 3107153, 748825575, 731413961, 465235985, 255669190, 119253188, 286309266, 514654832, 403118878, 153962305, 734465926, 897969513, 876218337, 424556148, 865559186, 858128903, 816470609, 623725530, 28671387, 811622071, 340023043, 67653398, 259560838, 528559547, 302614226, 843356540, 528213414, 787376593, 624363934, 861175746, 732385330, 691425954, 452274065, 868411829, 828348924, 699045547, 239737143, 964540669, 92293279, 159939784, 379890015, 135661886, 334895896, 94000218, 609174573, 230248439, 330328849, 94842560, 339637926, 67873318, 988944887, 878506567, 19794548, 995470246, 666084354, 25579417, 551239335, 105019642, 318202489, 56476001, 259533942, 869954844, 598344990, 280861458, 478895992, 291294099, 639964119, 499907884, 953428619, 452867496, 616216540, 964507910, 360486256, 149818312, 978921988, 63549404, 880177684, 59325767, 105141560, 85447942, 45105319, 40611515, 671745231, 521846637, 445650881, 896525484, 645681992, 120681477, 845589659, 693705759, 751179002, 414504541, 404635932, 650645753, 60233135, 150991810, 153508977, 935103259, 612537078, 744874571, 315336833, 596066484, 946366709, 691265672, 249006225, 151100770, 973627096, 679801847, 779792602, 609946083, 47012720, 468385780, 878252609, 358464170, 119610670, 94491688, 297033986, 272684836, 699605465, 78903846, 45448882, 580452385, 468023517, 156289568, 300256527, 482437761, 210553345, 732433437, 475611942, 222760217, 660519680, 960968145, 743088201, 934102399, 822950111, 467904702, 955851820, 629357975, 741229226, 898602388, 349341477, 323877098, 3370871, 981589194, 362809749, 418254680, 146071819, 761196847, 530555833, 94218756, 39687439, 74610854, 700708611, 235963412, 720409100, 739320716, 139380333, 20883922, 598956445, 673946598, 577984877, 719561268, 318332982, 264908801, 830120205, 414786847, 359981680, 712490848, 782559216, 342884817, 788483469, 150667055, 515161439, 830993671, 131180703, 653233033, 199932422, 998782256, 550851713, 56702765, 889107210, 105835060, 365878083, 994724248, 701578689, 998097250, 696739399, 977726160, 589951820, 649439579, 53841862, 593943647, 641539068, 64337365, 422643129, 152695446, 770144832, 799898377, 24948396, 138520954, 852892894, 97623505, 408991769, 611441866, 528759384, 513815251, 766410895, 822196014, 472129302, 480211517, 601538422, 826405944, 5965991, 89425933, 611367626, 42250955, 304156653, 191240172, 732400231, 327439064, 900906822, 71728537, 426469625, 589779995, 192509071, 302283674, 157617849, 516696474, 678485157, 281091661, 329454561, 95268910, 644153521, 94801079, 855841794, 222102572, 334804812, 827990203, 31726390, 866361833, 58866571, 916363208, 769650200, 951277649, 299075917, 995494051, 417447917, 884690628, 46450626, 361101810, 159444281, 434850816, 713763804, 257559431, 265050242, 192719451, 871707400, 625850660, 331333056, 609134780, 803065440, 294130503, 792732845, 560797148, 905037609, 801867836, 913745298, 517538610, 11306582, 11666448, 429951744, 35232843, 313001341, 524616045, 960683793, 276379506, 321856629, 534291179, 822493383, 488501677, 580355544, 989899512, 574860184, 719093185, 879851375, 731772308, 516089241, 772815674, 185736545, 208002740, 837692494, 796014127, 932552741, 729162581, 109205588, 518288738, 400827588, 893633517, 320080539, 582645896, 371475886, 422654542, 482153896, 331995211, 103757570, 424415355, 301025149, 750063904, 166319671, 667304843, 816573121, 58614808, 294025297, 829954656, 551841013, 113440689, 98135134, 128442058, 71580984, 168569526, 115651252, 134326576, 381249905, 123220264, 140430226, 303237503, 824129782, 341293914, 152899672, 76031228, 448212723, 665643043, 264824205, 741073356, 895049321, 871199102, 998934237, 995097557, 129637324, 984643534, 775932383, 152039893, 825483102, 860267048, 490333641, 21540183, 343160933, 936014042, 201599371, 950713498, 488990359, 332827180, 866462513, 897289942, 568656003, 737351142, 800828306, 96500538, 61945808, 594716179, 782642897, 627804663, 710504208, 584172822, 256010072, 27171885, 725391444, 728620645, 675682741, 922224046, 555625819, 786157190, 178274876, 591567902, 834799983, 797605070, 912854415, 468355615, 587849032, 141148822, 949111403, 64487515, 330851688, 703273305, 795845490, 949830945, 636592816, 576956323, 913065648, 53300688, 828014535, 628294855, 776258188, 471283132, 175228700, 427002246, 357022566, 86826134, 750971578, 752503690, 747879904, 729587557, 57194809, 148114144, 705564294, 780724888, 44658409, 376553807, 351010051, 827314634, 223014764, 972283383, 444532966, 824418069, 88457936, 872443682, 114913775, 83977637, 764653092, 231165011, 20608681, 177179856, 267600585, 267258902, 626287775, 708405250, 817412727, 382852014, 420678103, 339265904, 943198643, 611435473, 530885073, 868538150, 15034382, 729507749, 951349260, 317900535, 51617915, 907449103, 928113628, 528236094, 283684244, 756989197, 677110172, 842528857, 889744181, 594318087, 726488815, 862874197, 489493965, 489405934, 67316597, 98866000, 285109940, 361527616, 400488779, 806982986, 356298196, 376818697, 843921425, 921633233, 836106511, 934971888, 752868871, 264423151, 693592679, 138937614, 502928325, 963975450, 33086503, 182449377, 774308940, 883844529, 589414649, 487075898, 548397798, 252721690, 450578829, 670608699, 173629403, 191237173, 669250687, 532737872, 516603373, 753751091, 677944924, 221484645, 112892554, 547682133, 966889915, 92134416, 322828514, 188733628, 988471745, 584157224, 248507846, 760369427, 726614340, 168240441, 123065783, 300883366, 139284667, 14223461, 698713370, 835325969, 82504760, 830603341, 273654735, 164417465, 769240417, 577140326, 202966501, 753934918, 140700605, 429454516, 741922316, 432134883, 320797171, 175764515, 506445799, 402213870, 896134005, 656069329, 549232042, 45606345, 71531685, 226150096, 960447635, 349492954, 946423836, 170700562, 553412817, 697965710, 275628366, 333726328, 614147994, 497438148, 410207591, 142940450, 603738661, 13058948, 817686875, 407495698, 346128302, 264338939, 888092064, 932054891, 603764741, 528540693, 356277685, 251656572, 618356585, 967637438, 247402217, 849212558, 349216835, 554656824, 541840395, 195022282, 672612999, 623597166, 336349675, 285410162, 942418666, 915617831, 70493441, 982780213, 655809856, 493168926, 43931639, 537368858, 685667438, 351755460, 211006045, 539548235, 691901067, 55877949, 673336879, 780073805, 433563414, 624941405, 769235186, 141023366, 446281745, 857415853, 574153216, 949938974, 742026155, 975112426, 196065775, 261011361, 755281867, 928212881, 388180840, 678268799, 502221460, 412393671, 95127732, 31814485, 182618077, 347339558, 761042505, 573728198, 593378980, 434016377, 556261263, 694166949, 190858242, 727246081, 172554208, 372745953, 90342500, 940558536, 918136389, 229006550, 692583747, 142118027, 904519239, 619156448, 592324657, 832848281, 210934199, 128334353, 63168295, 298310796, 761136679, 91230637, 53501624, 946698290, 217902075, 306020741, 565770264, 577575477, 897944639, 456642087, 338732458, 947033887, 449146166, 126142435, 22221990, 921990494, 258822261, 622657386, 643422912, 807370080, 522211941, 303364678, 417068326, 423294127, 629851895, 95038696, 794001714, 219637, 31008864, 134397553, 318956349, 268122997, 544785274, 312883401, 805836641, 514963266, 136136417, 322746437, 441113787, 823098437, 568681696, 804967323, 812299290, 143847954, 531427634, 553142495, 9459599, 241792518, 40585455, 496989631, 926704891, 9822542, 64754155, 822874185, 595045929, 319539296, 709488235, 884197732, 738723580, 475067370, 287698433, 808544423, 87884813, 596286810, 642756151, 554722445, 2779158, 218717735, 47228779, 972389851, 285158769, 476159527, 397943531, 523867996, 470831300, 283735772, 15848437, 667473104, 410508651, 69400047, 126264693, 809778158, 303060091, 631120722, 733608557, 798846594, 655257041, 773116415, 124383577, 344293351, 904901004, 56600756, 299740642, 615358537, 856973810, 75235638, 352503810, 115082218, 146339258, 254524457, 470189527, 268326922, 293783467, 718481027, 564772932, 63126580, 468300839, 6633465, 490367776, 415715401, 69765036, 150012818, 454308105, 575839271, 467482441, 211098170, 893693939, 119992600, 198534530, 711993977, 902632498, 129365800, 620292065, 581547336, 371526047, 85976173, 73713517, 78560297, 346978601, 894652122, 281440884, 630950779, 755801081, 668858972, 865477231, 587203476, 303366998, 811551394, 61659372, 287162279, 877457710, 722568882, 948636325, 53564515, 467661123, 828566169, 411419545, 486433131, 951208570, 43124601, 794505997, 489742510, 804884823, 496114816, 311906294, 9576813, 194314961, 517559527, 701904527, 883613989, 112829514, 717714656, 318652662, 278820780, 191625563, 783270433, 736548973, 562367511, 569749347, 227848464, 395119015, 420756645, 412714517, 644467195, 576469676, 184266146, 95941775, 567418534, 652941148, 14065729, 873606470, 61674248, 654846992, 320056500, 68495554, 150754609, 547746910, 492669687, 40560917, 582063822, 998873529, 910233424, 920299036, 956180933, 747324718, 513983214, 948699255, 415911326, 887714907, 399666852, 262209895, 137511767, 21208737, 4210592, 630028752, 955730276, 388998258, 635081035, 762499544, 582570370, 849637818, 354632333, 842977837, 848076687, 316064094, 686820993, 33759547, 228876521, 778579829, 997985999, 196216182, 198146581, 984510375, 852295143, 350541383, 387254037, 588995288, 86947537, 394365331, 37874217, 725843917, 237799100, 267591845, 617533426, 931253701, 506931874, 394113497, 920463756, 829137669, 543907280, 374341917, 965190496, 182471688, 716243882, 944548529, 400093572, 656860457, 159490958, 414433658, 1133657, 771175763, 954898280, 648763463, 108282510, 870034242, 194642228, 591411907, 360162705, 795994594, 721490235, 260268071, 725641022, 80553166, 25847589, 574976269, 17136731, 954794822, 8465676, 475056644, 302649761, 366454725, 591774324, 114862902, 263279541, 244898666, 361204725, 944713531, 100888005, 214329173, 612593548, 521593601, 956642071, 533104985, 283999536, 343045808, 503727083, 814164924, 524022532, 161235165, 11798242, 44426795, 701663488, 370962338, 638459874, 492856060, 838674304, 812038642, 55502718, 240080629, 652013645, 451130556, 665005986, 547826364, 69724787, 603978111, 150045688, 473450658, 950041346, 962759669, 192453746, 534437591, 545862325, 54804488, 757185229, 485566262, 642607902, 464674466, 147738764, 42068905, 300824919, 151519516, 996504159, 694330035, 897147263, 488329747, 805576373, 482721717, 606210396, 428908346, 355132124, 257022813, 662623421, 875381851, 244292817, 917456975, 718227056, 529976905, 761286582, 384366749, 581305999, 748677229, 100648155, 735620290, 553535127, 23160075, 454131603, 456290676, 374210151, 534624394, 809741368, 503636351, 864984530, 857384664, 110950737, 217686264, 241262217, 455933334, 439397140, 695086678, 900585424, 419653073, 496746247, 764354511, 617824397, 115785168, 447042137, 738205803, 530945607, 400830511, 875289412, 478543662, 373509604, 7672992, 246206958, 100028727, 209074313, 101382148, 78419105, 703193780, 968533612, 111944858, 448566225, 776521228, 38827038, 354604231, 310912124, 826430618, 484923211, 570647226, 745846639, 633507417, 983540307, 52117726, 165372006, 5775868, 134944571, 642328868, 941041311, 134960166, 940278931, 749347680, 152168028, 110984637, 598991297, 905839151, 779311459, 896963765, 4282197, 191336787, 269129671, 592492463, 954936531, 635168074, 612409117, 358324670, 33578788, 854618250, 747053158, 265920331, 280301242, 289853830, 413724106, 188826467, 880353526, 373097002, 614778318, 778827379, 659981504, 182396473, 717899527, 842626294, 369947426, 140034790, 283128122, 344448421, 688616258, 152415190, 368847622, 652677586, 281153275, 837251103, 659045755, 569329682, 429278987, 1937114, 184548951, 382714166, 699350214, 833387479, 453922239, 472901197, 706434259, 10495759, 474278570, 52246564, 795643674, 804915740, 361127791, 115215691, 3659034, 828203175, 885067979, 503459643, 603548659, 731404805, 302215672, 629501643, 547490664, 681029574, 223672637, 198429442, 987594348, 780921858, 33238126, 70882342, 28960598, 648602541, 286610183, 840856646, 237257814, 29741226, 519370401, 142946131, 715272061, 438169917, 68560476, 293986268, 911004525, 402964136, 659897726, 569516052, 596755939, 437859971, 239105066, 458501178, 743391695, 76354951, 672207912, 974431681, 464181423, 147066931, 848452465, 470922437, 659651420, 204842960, 518133525, 935672977, 15065899, 816346509, 789754234, 450282096, 20470941, 740578332, 298747023, 712798324, 382640065, 415431159, 324319080, 529754781, 95394586, 190017515, 912035468, 936131239, 680381125, 706296747, 697084209, 836346002, 971856503, 123851213, 175528082, 60801199, 457623982, 365232791, 610893375, 23826318, 705936275, 297049962, 909850050, 452714550, 916202701, 251705112, 790817448, 401410453, 529136746, 599232551, 704276247, 714104136, 422648499, 309706145, 608901045, 367096940, 892327671, 764897778, 228697170, 360421136, 486239854, 808690388, 731491589, 137614323, 533589587, 357539280, 394853151, 759705304, 32986699, 873239439, 126853231, 991454255, 95857925, 792929905, 862692323, 155476384, 985639271, 68435055, 969455727, 487342747, 230453217, 422524699, 607980322, 143061150, 718791669, 201023791, 569043225, 756178920, 88431838, 964198974, 321569686, 968812864, 941890734, 163057106, 454965134, 641361341, 227345038, 354460082, 709819714, 222731518, 832815951, 619780665, 699169121, 219023076, 361645020, 643363697, 766594352, 689353822, 25366558, 441616564, 906392129, 183330636, 479784953, 130806224, 437021985, 964564269, 120580864, 167622785, 761534006, 226720790, 442433093, 661978919, 337614030, 399867004, 205678868, 391467624, 675966443, 658882310, 589196965, 905733, 396088188, 919768945, 211762684, 867984958, 772392522, 242953552, 503705591, 616618325, 887244535, 264527228, 627215691, 268067873, 394370004, 714709657, 860538255, 470087594, 29122963, 733404065, 855207245, 588718411, 926776356, 382731419, 803974120, 830021928, 493718260, 932561944, 954116526, 370174112, 550630790, 925257379, 398457061, 26234442, 123648414, 731936633, 329938704, 432349310, 112057391, 489851845, 91275071, 60051596, 247216770, 297912447, 135652529, 869555488, 163554468, 682523289, 626339069, 620024533, 638860030, 525539335, 104397441, 44907547, 560383259, 538643650, 770193228, 421007130, 102030749, 51062469, 456874056, 40340720, 566975712, 592700677, 20994768, 971951699, 801224666, 892946094, 701127980, 970526791, 130981692, 406238794, 125611834, 520466253, 757168217, 839970955, 112422811, 937290285, 465541821, 155842166, 349222602, 3220927, 10054001, 140232670, 152722708, 838448122, 751930641, 49564261, 127942543, 853753919, 504541501, 23599843, 450562268, 458043077, 234790446, 287564331, 175840019, 531268895, 469574412, 809411734, 223960322, 267875077, 748105675, 327666555, 418161294, 966247641, 256488127, 576054959, 772787653, 783983961, 378629609, 960047300, 392476366, 932461177, 796796230, 453472823, 102688653, 370008857, 807312098, 543768454, 490931575, 772721807, 317837000, 652611084, 829044480, 740554289, 57236664, 438478706, 442963180, 839103640, 423026026, 975697732, 709150590, 138371458, 132007616, 654274111, 702687230, 987729992, 290086818, 496073391, 350577862, 986085278, 412829401, 891902960, 728976629, 93786959, 480675727, 961010631, 524213546, 105786276, 309969094, 675935740, 672996396, 88508491, 62667275, 232848785, 342476201, 445190547, 596047024, 219420736, 297190484, 386066145, 645430525, 851345879, 730792331, 603379070, 529387594, 86684583, 715110599, 937648075, 565471845, 864475769, 347386294, 703453078, 704594433, 404707610, 697299398, 838907644, 265789536, 191673419, 218721085, 562130375, 642817703, 793708851, 314465899, 392693108, 289083822, 247862464, 901650367, 254481091, 164175357, 616082678, 204875023, 548526858, 824321192, 667884015, 570298097, 119079989, 426905998, 176878247, 359361120, 189325478, 6878874, 624000141, 118733127, 727540637, 492024715, 278843100, 678556790, 365137696, 615515746, 693916281, 116252489, 692473908, 436913683, 575652790, 941932312, 207692389, 53285816, 688945837, 982714410, 271796105, 830735764, 648412282, 250903187, 831908222, 357191174, 49310981, 954310834, 52108506, 872961349, 33324033, 789036529, 526561389, 29670325, 632436692, 878700696, 147059711, 535970737, 266589239, 831254457, 602574447, 806757038, 639700664, 69907060, 468382280, 453122403, 132288748, 29105443, 338314891, 628393012, 901686238, 784377188, 100570552, 610189182, 430972347, 861731829, 658126804, 980400247, 546581738, 908287644, 658940109, 386357455, 411150701, 231618444, 661489681, 970601893, 667085880, 524724372, 810913997, 563686675, 203601584, 120633776, 805026761, 558720445, 864665729, 427431188, 922187669, 661693117, 201429177, 889821157, 931000381, 632507316, 69329096, 997956290, 466029771, 63699567, 35034940, 423349924, 99624454, 139071617, 416895479, 185402925, 894324790, 136194422, 338685815, 857809596, 659240085, 95335519, 433286985, 347115737, 999106925, 855941696, 367215628, 293295819, 298963181, 778810963, 573089352, 970619900, 816635811, 281601799, 394834303, 555777164, 109927505, 97724979, 866206780, 907187972, 389337332, 474535122, 277084950, 959474109, 721761588, 164702149, 800445289, 290702744, 695973477, 449931174, 95643240, 772415936, 813820160, 957781385, 242240273, 112522169, 884455510, 993321311, 39795590, 149671289, 294133110, 947000117, 676117910, 657735818, 331402061, 36948144, 887703781, 608279358, 966428039, 20701351, 52542442, 842539891, 593601247, 636541334, 723032402, 947120076, 474925260, 301020493, 274564763, 541685835, 823641499, 497184504, 219768064, 85515020, 559231929, 518269849, 509268664, 567646171, 781124565, 757331478, 800909006, 387308409, 318239624, 785295799, 129574641, 484317987, 530026576, 669413867, 285812755, 842786585, 105008725, 388856408, 354423872, 933367852, 568619890, 432008061, 107277729, 62540403, 717610896, 200272092, 367271670, 530939253, 875652406, 120878733, 171414619, 672178448, 312564906, 781909090, 330132873, 960441181, 208956082, 138966619, 695759545, 491780377, 175834485, 922150690, 674387961, 759811736, 613385073, 38338809, 625477122, 686819443, 300896012, 966998277, 782173044, 804873256, 237465721, 460661085, 686025481, 907903644, 371320905, 325462464, 649781438, 112005930, 303600462, 795469145, 66217737, 561108682, 870192785, 819196033, 266068207, 794062450, 555083808, 545661654, 682637105, 979593736, 379620528, 196755378, 253724380, 819565264, 326976332, 355735355, 471721333, 402298661, 675198106, 243027719, 622363488, 326616790, 574204079, 140618438, 640066821, 403362363, 350068111, 376703477, 610718222, 527006658, 982042598, 150158756, 108375069, 620829874, 956632682, 234044081, 972564362, 448918582, 401740556, 347301825, 962301343, 621662735, 433703259, 540042530, 168082820, 572623933, 303334385, 785167053, 42924731, 174666671, 995706698, 417450989, 950130297, 642052011, 406872128, 424214957, 366556661, 69574083, 25129815, 848261659, 118751441, 286325278, 315799630, 336618553, 313018489, 284212089, 132612650, 855062558, 180634887, 628077339, 848213984, 653218421, 75910787, 110468337, 696378126, 367146327, 99432321, 205334279, 778383678, 780275519, 865482323, 961420622, 465121525, 841010558, 359935239, 574182188, 934169253, 16010236, 423399674, 225236538, 196592483, 287534722, 112239001, 842869156, 160108472, 222383377, 727296912, 205079554, 94492128, 371827163, 268386225, 268180249, 761197952, 906237738, 635121138, 10269875, 97885476, 451404423, 450642449, 383977952, 187141740, 837252430, 24575693, 896151168, 262739269, 206000686, 317293327, 273856737, 993033791, 159801720, 33657334, 630165423, 731909319, 224567786, 392270465, 47647798, 239892797, 709632602, 205625974, 490068683, 859456672, 880770659, 420305433, 673332038, 96917693, 793673224, 743588899, 280262453, 281982897, 850715526, 12004626, 259523749, 427375317, 796845692, 595169865, 395898449, 469756066, 577620256, 485891404, 605200077, 733177340, 555808747, 330965340, 548131477, 590938568, 544604312, 660166928, 140285880, 60953882, 751856114, 996918242, 445216051, 298328478, 144501400, 441944593, 718209605, 908966979, 839703924, 528194701, 709884883, 610284515, 115247912, 257248906, 462729124, 627231771, 633321558, 229348978, 771555959, 456619655, 77549645, 582044302, 439124494, 167071770, 679736238, 882106808, 64734308, 533294118, 722092405, 541160376, 703632646, 48701150, 372328693, 993184002, 680391953, 489764894, 165009951, 969111854, 856849763, 204636472, 228411938, 118342664, 813410269, 998104264, 354246516, 963104919, 496518901, 653532428, 105712215, 335385511, 285794185, 954592489, 793551527, 798988335, 217626587, 602888702, 295637374, 396148892, 474750642, 826485485, 196684406, 332184133, 930592752, 250384371, 714610663, 361268909, 370678984, 142676247, 538220894, 46107117, 142432983, 971531768, 548439584, 214668513, 326016672, 5027246, 58431796, 547222747, 658868972, 605393445, 724158548, 940403317, 474635136, 149312970, 334507321, 627143110, 257335009, 634717859, 649569138, 69244685, 804003568, 675931402, 934806865, 368721781, 186518658, 462505082, 35294739, 227398121, 691888775, 762626198, 734504209, 874609055, 311254525, 114223945, 873304858, 341075070, 79497601, 331643330, 178552676, 298246201, 866419667, 188008153, 942825192, 933414426, 455674908, 182017047, 627627334, 597549539, 28355614, 222898578, 73833485, 964952915, 901689015, 373754801, 825118661, 391637783, 472585219, 780253683, 367924946, 376270106, 474644709, 302369796, 271004407, 28172173, 966664699, 203252657, 946919434, 727971588, 2245589, 760546598, 887777704, 737009565, 916625350, 414087101, 529949093, 543596565, 543299444, 145769779, 480783324, 449184693, 291742723, 658366796, 889398709, 363094617, 288562274, 821630406, 259855167, 512752487, 562945598, 338102200, 644232214, 256946394, 633996642, 525370661, 33172455, 908526909, 174608876, 554068394, 985509835, 940619444, 555187999, 908173027, 974159985, 114976058, 26443441, 403979630, 633352508, 466910688, 931542954, 401222492, 453466288, 214049533, 508247630, 278634399, 349822103, 781029547, 645177876, 414023679, 512839350, 169484490, 412149050, 33824288, 957852286, 529646199, 741507457, 503232578, 772065963, 892264370, 8947406, 82697908, 137668095, 2852904, 849592349, 497435310, 98461172, 771829780, 25960744, 886156581, 473566121, 86689860, 129748377, 510853179, 333874183, 523567712, 10314556, 249795431, 411596729, 598480288, 565206805, 569361279, 159499535, 953174609, 230051657, 919333609, 980647090, 996174497, 30394299, 874666227, 409061092, 442528317, 222590525, 583155077, 519457494, 414201369, 144943668, 124539816, 693051880, 776940082, 90303098, 721757588, 758471085, 953407680, 655544558, 591510798, 495513662, 965452220, 15022080, 995166582, 386301220, 137638326, 848855324, 297344879, 913451145, 73784982, 622117731, 844353260, 802726226, 724889948, 994568335, 21152400, 17472044, 563147320, 713374492, 56167206, 278488908, 846876624, 200274917, 209304271, 157474056, 407756049, 138225539, 606388947, 765525192, 471240380, 735749073, 49073890, 814041990, 134778986, 29976989, 307696311, 174417053, 4839077, 186591490, 734185409, 331483083, 618665147, 463022931, 38212157, 815941539, 559552845, 901697239, 959625709, 856423847, 573792099, 65699896, 773085021, 559819778, 389558730, 694547450, 563694396, 911950213, 723437554, 455617952, 556237108, 677131646, 470655810, 624128788, 362291335, 696337115, 4319286, 789831112, 102360593, 223649622, 409803996, 558711791, 56313319, 410440565, 93939562, 102416715, 91513326, 645374271, 22180918, 689868287, 995958262, 6453145, 225764248, 214270274, 35276945, 609303617, 77888362, 333135070, 747762253, 647703331, 632389298, 170587820, 692361252, 897138775, 756090830, 331208404, 186919925, 556365840, 849857942, 255200726, 518401486, 301867575, 246097724, 751026341, 536360098, 682935868, 798560937, 975189162, 514378573, 948399580, 400230170, 413560152, 79488268, 972784242, 769498350, 532179632, 602424392, 418426470, 3539060, 796967963, 934763581, 275346060, 723301022, 400699809, 71084551, 200205405, 137861415, 814698844, 476044897, 809347015, 957956574, 198823302, 656999627, 74644300, 802791591, 308037515, 7838495, 440891184, 693637365, 336530274, 842141879, 992338849, 186723046, 305209539, 945697929, 829742248, 716065220, 942983692, 873737553, 523012920, 757172731, 483806324, 556125032, 156508460, 275882759, 92293762, 83140028, 512570852, 544312639, 366360895, 381259836, 326975252, 765643759, 160095817, 825065592, 411661040, 249357137, 13081433, 958857723, 278251918, 513657861, 355571752, 670087476, 767003174, 944772127, 650837151, 427049776, 6619270, 367353703, 203376636, 306317891, 1574219, 194480963, 391327587, 379779312, 357023064, 619151102, 480493038, 453933779, 872691126, 258914608, 510306916, 278337386, 23404686, 121827592, 135583285, 980893634, 157769699, 418583658, 584220539, 384049183, 780467381, 23088271, 142547309, 625239537, 400576925, 421391225, 832463617, 738255232, 338180208, 96750050, 505806364, 138045954, 724381888, 759023841, 391598403, 949450267, 925061045, 198710580, 35870525, 972157244, 549759582, 476126217, 236440135, 306202374, 408247920, 20939764, 891880006, 85821610, 167697328, 90917284, 16647091, 499023241, 959309921, 874561970, 586743098, 23183194, 69851155, 467452296, 920179680, 204184571, 227619017, 534506631, 920786040, 408800887, 960641257, 202759317, 3129482, 663625693, 105683528, 356559967, 503308842, 592084717, 384391931, 834658799, 686625514, 993911238, 4233577, 727602095, 79724211, 297573747, 750082793, 353127545, 785414509, 704275364, 453402488, 764475194, 314395510, 132506997, 679707030, 2950757, 54287386, 390671123, 803092079, 744228693, 54910483, 610261248, 654656278, 946609052, 948600754, 303497517, 440393258, 414574996, 872516198, 295756031, 556242573, 371977098, 409970020, 831284447, 624923900, 985975119, 657000350, 796809078, 405275155, 465150582, 925259853, 776413105, 132161166, 945356898, 487769231, 319719393, 845229347, 278275799, 21878817, 465584490, 501143136, 152082008, 342771820, 692209063, 550910239, 500222992, 784666242, 374432757, 509711513, 442923378, 918791562, 88026796, 479999925, 478565631, 85945059, 607229273, 128544788, 873542187, 679833668, 459319239, 4378744, 279392415, 775426119, 177595002, 692491534, 806815161, 241097352, 971362104, 730695694, 533299300, 231383625, 794615852, 719016719, 629581107, 544245684, 358444154, 884382902, 466027572, 232896593, 164010543, 13089982, 599077283, 136229046, 879380041, 978578789, 170503282, 30526736, 311532317, 248611557, 996066247, 578720273, 665493614, 359299262, 667127102, 320009341, 740395305, 323713355, 372467819, 726534637, 148788761, 571880045, 470002833, 991285981, 162672294, 972359392, 53631243, 203525839, 834129429, 852402115, 813756719, 565099541, 223767809, 283135344, 783266576, 467115260, 92156013, 774134729, 90286569, 91752391, 325434656, 484201252, 502661200, 17963587, 587933611, 888943045, 202774448, 824163467, 661529510, 549969382, 388459458, 345468161, 164820672, 638102815, 654074007, 802434037, 838786049, 364745838, 183574684, 518836746, 776583100, 228810515, 563149365, 798231663, 288791524, 642483371, 104014997, 381243014, 705741351, 584985482, 25108804, 624863431, 825762092, 137499178, 468554989, 414395460, 515457067, 122206856, 784448513, 728539177, 295306060, 363859037, 236602550, 916139484, 135773389, 650975135, 786595446, 124381352, 907260046, 689215354, 858907925, 891476390, 898027518, 983683609, 606353435, 174243341, 102706622, 33331912, 295971422, 555725421, 257668599, 436994948, 491531244, 122398437, 127854539, 598291067, 152537069, 980037062, 610593887, 713551254, 992369022, 261403728, 768756430, 910664220, 716041643, 13661757, 466234970, 308704361, 286923188, 284633760, 818062871, 99180722, 37386448, 195620096, 567629247, 819093708, 668981645, 801552231, 284397150, 797421926, 941901552, 419296890, 197966811, 600660709, 67181366, 648253750, 670205920, 250078349, 80915482, 233085261, 384719762, 651049756, 614290614, 224673359, 82979171, 29575154, 141321246, 993798013, 24148588, 684954283, 579900668, 130733510, 321554542, 618220794, 92615640, 618773241, 88538172, 457328573, 291268588, 917444124, 48660565, 988973394, 370910908, 926283363, 253763461, 111479641, 338282730, 895663909, 312971088, 26802, 625826831, 251084935, 134430103, 450886215, 732464229, 944456318, 214377588, 792241372, 10195169, 434024977, 889394168, 959038815, 493498430, 159745882, 187006341, 832341418, 295586460, 447514348, 663361772, 684314717, 544418033, 268355279, 465353559, 310855020, 787686898, 717205173, 265020649, 265354895, 455483542, 223868546, 54040567, 759652627, 210444407, 201354157, 100774243, 950337243, 333931640, 62284682, 792180099, 975101318, 339204695, 369560710, 601305149, 138113119, 600665541, 420811890, 666523098, 102407005, 902331856, 833403447, 807673980, 531414141, 97647738, 686497289, 337605276, 3300163, 631877637, 139439707, 393694606, 99315224, 758208580, 250984328, 803269462, 595276078, 451522512, 514540661, 579881401, 337902242, 556887527, 453280464, 472095347, 106214487, 276030758, 806314708, 922010400, 481683855, 730166131, 404054580, 892682360, 370564146, 809637049, 345209813, 858425314, 657326976, 116948054, 176797671, 251918468, 342004658, 231406095, 331364575, 816159566, 290262053, 956496110, 127412590, 471176664, 822506870, 43834425, 310456497, 504823090, 546240870, 351208080, 947681731, 754246139, 119057926, 668268388, 584597641, 988090613, 662140513, 359528532, 227476437, 133257393, 495041862, 266905265, 301026194, 947678438, 257662721, 982073974, 295894169, 868148526, 472823335, 869859722, 625124031, 801839136, 106286369, 149793645, 143872614, 108376176, 867941587, 394752399, 296892083, 138559861, 122262037, 593001734, 168734801, 403268192, 758112454, 561077742, 390606545, 986669232, 73370146, 573465117, 768191714, 888590742, 328220577, 168111959, 765989875, 339660218, 904441032, 122691831, 949037364, 227891367, 783567634, 13892948, 327691837, 784244859, 12815698, 863503987, 466393187, 346145548, 189597770, 495948258, 303367441, 233534124, 966071524, 810083228, 754757336, 54611188, 244848272, 521553738, 827454909, 242223845, 297953298, 621936864, 221192911, 318038105, 872029634, 359305896, 404101629, 634749021, 688597408, 70412030, 712712142, 774793097, 268511917, 550139353, 372592064, 635103994, 865727217, 349983406, 808193263, 772684515, 58944972, 865841330, 471911518, 361147468, 868763358, 388469449, 615269031, 885875666, 213289918, 117169359, 277096870, 545184653, 182775700, 107907808, 443568105, 272949977, 270747017, 355312362, 471897144, 666390772, 273942938, 800690995, 466265555, 348609147, 322974393, 747861409, 103344933, 660685071, 904261827, 918037482, 596757481, 79950356, 362780382, 992067425, 717369502, 900405206, 663468374, 278080927, 517587678, 468955754, 447455789, 885275224, 593299556, 638006671, 51050550, 36377101, 495761980, 372314190, 724540660, 141606417, 922875376, 955449348, 76270425, 321658324, 967025527, 584385402, 253571850, 608759072, 897395378, 725180150, 184505949, 775218817, 305677702, 4249027, 119941715, 356379691, 353495162, 425620857, 999006031, 942800208, 896273841, 148828740, 946058667, 548405301, 384402566, 140651797, 339696053, 946172680, 314794629, 220722210, 402506901, 283906492, 780616666, 869936848, 772997994, 629147349, 296655722, 243536409, 819533180, 266234875, 226489337, 839776144, 693017088, 609817284, 315111464, 884664545, 155353037, 310877300, 54680380, 196773358, 556774326, 984740972, 758431238, 560064538, 772181737, 754645810, 859373576, 233027191, 959695229, 981614352, 263009133, 779963901, 256483823, 158677668, 821822801, 719531110, 947140072, 320394444, 944087041, 819255565, 112474578, 405704144, 78412140, 938909254, 516732926, 171326552, 974408022, 527904500, 696379985, 522391966, 424719125, 289937346, 730673738, 319431875, 586858522, 382900841, 989907670, 56152252, 545913740, 325102629, 224137763, 715427767, 410920728, 144374780, 265078724, 154050584, 722178525, 165020842, 345503463, 467229867, 254185388, 988900710, 255605861, 469533240, 956735214, 403077779, 456081089, 455794876, 260481917, 577925696, 332012544, 838022769, 500049551, 774286573, 475862096, 276106977, 358111800, 676246962, 654203067, 437049944, 12343988, 222032039, 870712925, 407377266, 445994122, 5642683, 838407745, 90643359, 280419648, 478947794, 88880796, 829822973, 353748394, 550935646, 928319945, 503834001, 33974940, 505590641, 554543757, 828240673, 696791165, 730512859, 950348201, 658043834, 359181896, 931219992, 275312372, 151770524, 103768511, 448183007, 216760426, 984856591, 352680696, 371634069, 752356780, 334591065, 295883632, 241791724, 925049392, 917605542, 683416392, 850228974, 703119618, 371370292, 417555927, 976414893, 6472918, 195166222, 330715471, 699646676, 817281196, 252278408, 477550153, 461256178, 852412563, 902199106, 935934061, 575260093, 35434871, 953915916, 253138290, 472056404, 313837256, 72522519, 796715584, 58964419, 111494638, 485520295, 105894144, 54586550, 434508842, 502390445, 620593083, 975672477, 559517397, 609179108, 381114569, 973594239, 725484197, 363313997, 79883418, 611684850, 357585828, 447136560, 264400872, 954723997, 790610302, 439964188, 965284268, 938234570, 914516363, 394196949, 215962244, 844699301, 131243425, 91110073, 350129940, 277181735, 590367044, 888674790, 485662094, 703094325, 796067001, 998124898, 772924450, 630491161, 156117716, 75823054, 439437286, 887856852, 605806396, 479044049, 302009688, 555824465, 40572426, 489316764, 755690364, 539470819, 80812225, 852597923, 852018563, 207989195, 183121247, 574248282, 400263922, 435233398, 824490208, 936536038, 747692871, 747906712, 271034753, 879750480, 669375186, 119591854, 601984589, 496812852, 326789969, 949256616, 687254448, 795797134, 474455365, 767467938, 233133495, 619067151, 887235075, 141798306, 750546489, 142636726, 774935494, 979394862, 79437563, 804039136, 408399476, 888838413, 887271389, 906435468, 410549220, 367148067, 413976139, 58221986, 232380209, 452369661, 526912077, 519022527, 882351753, 376551583, 721360600, 747371498, 584547196, 961394834, 771346663, 362818828, 339986708, 495936294, 385771104, 879230702, 12020449, 945487270, 464708101, 595951949, 656603673, 287565064, 326525678, 482604859, 250785428, 636034396, 404194865, 990190974, 986600513, 419457408, 199323530, 748779030, 126144563, 241888055, 773980032, 114079140, 929741969, 89693477, 569469818, 415866137, 740816017, 944457991, 874613185, 849528284, 512865830, 294796116, 23133401, 884947423, 362148252, 735407733, 612559768, 744346524, 372511214, 181228619, 810877410, 245586023, 488665387, 237835358, 432038671, 539149179, 497815533, 268915788, 971576576, 579362576, 301064230, 290176860, 917033266, 29462485, 388234197, 72191565, 440941601, 515626844, 936297964, 103111143, 51079081, 364754912, 525723310, 88979747, 552616985, 917621957, 266733375, 305434047, 136070240, 489539969, 642850763, 872367951, 686086960, 828421532, 365331063, 102483794, 396206422, 33486691, 332187138, 83007141, 682193845, 552803748, 705754424, 507223092, 720940783, 477006305, 809845547, 777064072, 577252368, 54622512, 224781675, 267060696, 99281235, 498912793, 18627661, 262626234, 456567614, 927211208, 378717932, 848699014, 582444389, 628876469, 707145107, 248622053, 388768778, 406682354, 642143062, 999840032, 576634783, 12264605, 639221186, 355541179, 282648908, 116899253, 753101205, 996055470, 162668930, 385589386, 712253667, 546639391, 641644389, 777408898, 380435078, 353768552, 775343338, 222060269, 940450664, 737215033, 969157217, 84916151, 283949064, 60154463, 417277305, 273246735, 734961966, 621382468, 618688373, 170397794, 712492837, 122209589, 766832737, 886727592, 611655309, 215534548, 905816354, 28142860, 672737754, 246052577, 954463651, 355829875, 774761167, 761926427, 939909337, 246542781, 256053330, 157790335, 756201140, 518328367, 824000285, 743869178, 403400113, 456646391, 437482792, 137225002, 373226478, 463566988, 535256814, 942209421, 633521950, 597698796, 702827799, 97708850, 228532632, 230312030, 613435474, 110817923, 9051069, 540365492, 33395274, 640995313, 361029618, 97705170, 242656234, 899616792, 482315733, 345853852, 746524465, 374749697, 285583271, 184674830, 255561785, 123551091, 959184429, 652683264, 78588361, 993687904, 288467216, 987243548, 250211234, 131780353, 267802457, 280014442, 8902426, 285272582, 651812631, 263808163, 725386367, 494493666, 741324437, 659460411, 635310573, 745155474, 865232066, 302327704, 457031120, 154039206, 168735173, 790575420, 175935653, 641015204, 677474422, 990437134, 883872194, 18774841, 611100552, 684269242, 90256907, 74131584, 682350314, 61377044, 865904420, 584691493, 301854886, 612421939, 505966137, 987933869, 245234953, 501866788, 389690949, 334967736, 219629919, 236499064, 341115527, 341144733, 589361133, 511432447, 292685391, 974072231, 895851884, 557175747, 711025124, 264533749, 624322953, 759069767, 977520541, 520090982, 888396703, 6245393, 189275154, 334474360, 480444220, 532317403, 33211212, 698013021, 171735719, 312157803, 876727998, 216483209, 17451359, 799232989, 579409125, 443384143, 887255794, 706234073, 823263626, 799504315, 850514787, 402853812, 347745557, 995957981, 841250752, 272957529, 45311730, 997069946, 570891917, 977145130, 392165641, 843439777, 515669568, 464380439, 813071744, 992604562, 89368902, 271186450, 187073392, 497462707, 429368051, 21731223, 50240910, 144115814, 762113915, 529077481, 739274429, 851913828, 880888027, 157454228, 930701862, 358648204, 329879429, 188977223, 373956015, 21698327, 765757272, 95667819, 338764715, 23309432, 528903370, 935243996, 175096977, 715414158, 374380692, 63702550, 831795961, 91692633, 622109365, 617243374, 746788571, 969943102, 126833849, 45573965, 528386121, 754734607, 971338666, 936756085, 638635845, 31574292, 461321534, 276479450, 988540069, 531170958, 352706105, 912681245, 593814319, 142078713, 111087291, 15396193, 422725927, 649168568, 85662094, 955858783, 152584268, 175087220, 183931163, 826324652, 261596992, 732178503, 997879745, 677623103, 541900014, 686020508, 929782017, 973612123, 387037782, 740729196, 526150585, 612281677, 222073771, 844240512, 130422991, 940634436, 289658463, 105884846, 625711263, 347649742, 126549078, 722576240, 347658075, 114871361, 277070928, 612895070, 408312527, 377951537, 206420059, 690978425, 721903482, 428101022, 548181980, 275480418, 779202234, 534324759, 286311008, 508360732, 741631344, 588049850, 544032123, 389117746, 95243124, 610002492, 898247079, 141061030, 888733741, 395938588, 602679523, 271260017, 345195142, 189361893, 273346375, 905208204, 383013050, 454392107, 562107414, 262103703, 135085405, 798719942, 217489654, 753014647, 958121147, 484746811, 805069935, 683413808, 507922103, 272659666, 356539812, 633580247, 645699643, 981036173, 409989797, 357814538, 27810139, 409146286, 512188533, 520417895, 782111415, 529957762, 375278513, 724690139, 223244129, 800591985, 575098413, 11995842, 478320009, 558097363, 810176309, 686846206, 753496835, 800384843, 271675480, 70251975, 832904145, 197103225, 334782156, 807233636, 960297725, 586462577, 585808716, 872719373, 487362136, 1017490, 355461951, 367457050, 948943451, 726381566, 331213830, 487227235, 3719645, 811601496, 28294986, 342240154, 852898188, 275045834, 883506493, 325783281, 592456777, 916893875, 706652303, 834321339, 746112266, 539478489, 405426029, 625799013, 122772121, 273451351, 485440160, 711648756, 426909156, 80196773, 826538411, 750189718, 672809440, 613760596, 419535879, 896941078, 192651899, 363673321, 555667238, 392663504, 260628361, 442144216, 188179660, 839792202, 475360007, 754322630, 535555564, 590023503, 855646560, 963158170, 24082058, 666604866, 139972759, 970981346, 77499806, 398931992, 249971158, 882667035, 217759178, 478478326, 722602719, 909612951, 978367056, 59189261, 848559009, 33300824, 185619513, 518710312, 311309639, 778802410, 95142895, 330412381, 420064744, 646367587, 101465742, 844891740, 319400717, 760804297, 811519489, 93753233, 516520445, 599498486, 290463574, 308026445, 528204269, 370450294, 902943040, 681158445, 447950165, 412420394, 291391395, 740924885, 464486411, 979866689, 605334952, 128791245, 512257566, 729551149, 810091736, 678873524, 495480801, 453094540, 840370131, 810945797, 428747481, 430926493, 943728365, 434604435, 5678555, 723077592, 41326157, 464134268, 39538118, 75900227, 640558876, 83699757, 111989307, 225664731, 695160296, 830128476, 927414066, 664294281, 240686910, 979395990, 256772269, 766952673, 683074893, 943286786, 460338228, 9605788, 329752940, 121128456, 104864118, 400361386, 200431815, 215542147, 669143557, 79053341, 197273425, 145666636, 200446296, 410944924, 703639764, 945739290, 497352188, 292254199, 552894023, 141902862, 404225156, 399825012, 836515502, 198552142, 120657045, 427408410, 126475413, 321960697, 310331765, 332676647, 204392361, 838163250, 229516936, 562921931, 784632755, 630354394, 99983668, 359890490, 678749010, 376655840, 828186317, 987195113, 6085681, 560361912, 233859127, 168468932, 692661358, 86180958, 260445855, 668259657, 200378712, 280222556, 710993367, 851239120, 918992344, 254612132, 646615345, 501622314, 525479978, 341623729, 201289413, 472841468, 512139528, 442060648, 195183264, 177838863, 904176620, 420774032, 938206812, 457443476, 47613629, 395725411, 219614742, 537347603, 652098378, 742719464, 288022048, 183776710, 506422625, 11657154, 60751611, 110432051, 377773769, 883583743, 791926227, 413690648, 91869299, 683624796, 743098704, 316373281, 877188373, 785262535, 396768051, 726397211, 756764176, 406539205, 359541203, 944306046, 128074105, 352971060, 401019968, 734743147, 714148339, 326892091, 519582726, 16013321, 79702894, 936171845, 311927871, 47010850, 925705623, 442745003, 952989985, 103323338, 277819893, 973733943, 258937597, 854299623, 820404937, 755922904, 69475546, 254915288, 187679999, 657014252, 630238743, 918303380, 398385056, 42584814, 254692494, 714157638, 336919220, 264001602, 792986970, 970560392, 144091544, 826216360, 840759195, 839790315, 393356376, 678671395, 117329270, 43315325, 15918321, 801713729, 108238831, 171865285, 781483779, 164116876, 846441544, 672724662, 155481376, 63922284, 336696061, 264874968, 159013403, 509361777, 900982756, 795157696, 402901793, 211037769, 625894639, 696929807, 157134370, 678640377, 112971376, 240332188, 450127994, 768783384, 126868315, 802417919, 743101114, 2713717, 510111391, 577884350, 106892874, 213931641, 771736755, 634745557, 536312208, 68190812, 821623877, 754680438, 953018554, 35774793, 67722678, 15036665, 106955357, 802129602, 48317984, 485541604, 558467499, 858951745, 191447810, 468837311, 708052857, 187957426, 543236947, 894189810, 917286029, 217928493, 893893469, 513733716, 784279412, 77468135, 479216527, 990982216, 130255712, 393138570, 394437113, 929742630, 769263055, 153798280, 924849345, 699144200, 464366856, 79219083, 794980169, 971795028, 974221082, 868378468, 988463018, 417226811, 890445188, 442846243, 690463043, 481216461, 711710284, 819654041, 723691412, 44929371, 141680941, 342728581, 108764085, 967624907, 497879764, 636376359, 609441132, 441159142, 823344044, 617770666, 433081045, 960054358, 268553828, 302466316, 694487016, 461574760, 39888791, 365762306, 331868916, 784791928, 915148069, 133202339, 291896876, 457584558, 652491502, 636574402, 401390072, 548770598, 726406405, 956584701, 4587938, 535288852, 670223822, 775389761, 95321184, 45666113, 273290591, 516781243, 186029701, 304314767, 339680577, 644849331, 529607435, 675420877, 721734907, 898478585, 924913501, 590477345, 737887027, 336933564, 681243872, 50047850, 302079952, 275906485, 968678182, 299927506, 727212133, 167450393, 342259603, 509935956, 838885059, 753968585, 273259069, 448827091, 176163644, 875587836, 567445475, 60166618, 829940142, 619000647, 379817563, 322670752, 404046573, 163417773, 83240400, 419452707, 178395479, 736822092, 646067341, 946086910, 955555578, 242260081, 861446984, 527608239, 363140684, 31708986, 648339024, 260082691, 968839562, 126373007, 164577916, 653431754, 132046215, 941994021, 702593737, 448856551, 362581690, 713145821, 929012986, 551702166, 263437201, 817851613, 233124971, 625941827, 314985820, 364363080, 986125842, 957966219, 488000348, 610311944, 962724305, 856114899, 640134825, 678965186, 105177491, 961234823, 519362578, 575175437, 17005455, 729539819, 381156882, 728458331, 89433920, 92427682, 965117299, 307375788, 827657249, 989961358, 813693656, 950615781, 184028439, 888844964, 910021049, 106953268, 176801172, 399026806, 286058083, 939555037, 931388613, 922370352, 213004839, 931617624, 772089882, 170192073, 857593210, 439223651, 652025933, 66481435, 876405731, 4151809, 773915370, 285572597, 631551603, 127000907, 724510495, 885586533, 803800306, 839624643, 708544496, 366602313, 659595704, 301383874, 530943457, 699047760, 215705712, 416135145, 758829186, 921278196, 82625709, 795489764, 738744414, 68377609, 544077841, 316972553, 425456303, 471982164, 471671679, 240094710, 825838861, 107667078, 100555506, 950513526, 15445381, 401219764, 639924783, 564044679, 176950632, 239825490, 822585836, 584629026, 910262626, 425314965, 928043059, 30554177, 368839451, 883917379, 308619568, 577623229, 22057351, 305992653, 830114833, 350250997, 948975351, 23059666, 731031102, 772422744, 289463241, 946855570, 287621226, 972487952, 870263909, 476536675, 606066330, 815261863, 713695365, 161340506, 519661090, 51464691, 611176860, 193219867, 724458632, 928006593, 685920743, 357730337, 687801920, 466983418, 433482581, 440866050, 199474823, 145119222, 703618700, 549221351, 365038362, 736138080, 610621897, 184556643, 109544286, 407808218, 700640221, 932534929, 598127245, 50506281, 284963042, 553054801, 349809154, 146911966, 397441806, 808457099, 804175425, 901530442, 977662625, 195639614, 326350474, 80782081, 429398938, 60042889, 882379786, 978309420, 409500006, 805151207, 498408053, 974776742, 224066811, 261353655, 681802012, 355747270, 157975526, 907499773, 827537261, 27351677, 81886443, 168509412, 591098663, 91143832, 339087277, 704302850, 762875918, 477454323, 439373427, 739064552, 345479929, 601736726, 440591130, 696966640, 518003836, 887735214, 567653050, 380620730, 598903407, 982963302, 784472768, 226152073, 808300929, 105347778, 227919922, 607368944, 865155800, 447089239, 272100648, 163609195, 33893511, 938239039, 105641708, 241190311, 530555194, 954540847, 20531209, 798688349, 172465357, 389953147, 134750204, 975246142, 468539556, 718668074, 877052911, 771823438, 297665804, 607399622, 395223881, 513505749, 535319277, 311528659, 910711820, 518906657, 806604258, 214601345, 750620695, 103671337, 70885243, 671083061, 458443279, 426597097, 606135019, 734861977, 322937501, 965094288, 295096051, 989242053, 436279985, 173137805, 752981335, 161132238, 895455750, 67893908, 727174769, 502297125, 27674351, 926670067, 815913274, 105350952, 82264927, 258901901, 241839301, 204098860, 933903085, 760841352, 212988080, 55994035, 862291191, 902689151, 847242195, 5734324, 407486278, 377169027, 694128111, 455605243, 47158401, 85321277, 867939997, 520124139, 357430354, 949211241, 979103029, 434038145, 290087031, 640850303, 874538746, 288939607, 162442570, 941626621, 936271723, 694249081, 588338570, 925339357, 578987077, 860252554, 372673889, 923941383, 644178638, 559583277, 828818933, 798887626, 19630434, 618180336, 358493660, 580450664, 129688430, 447359203, 963410375, 244357058, 139031669, 453141732, 864249762, 807588272, 417610410, 431009129, 186134864, 953320204, 467843198, 410159498, 431349590, 940868430, 147443459, 465142619, 258479198, 439810188, 883095478, 899255705, 860423864, 392578417, 860201054, 64872247, 42486601, 546168376, 885495093, 781238354, 197176140, 817146792, 343887223, 270293279, 834476232, 715914486, 351611498, 380546119, 336003286, 296624241, 2566714, 60124712, 404407247, 117907604, 798042205, 137855485, 17170262, 576611637, 231525651, 341080939, 150621665, 466088230, 224943824, 207226820, 743651954, 427122092, 815529447, 939485333, 46120500, 975120323, 719880192, 337465508, 986398338, 581305405, 541628405, 124001352, 398636064, 473002458, 84292607, 564251894, 367094425, 314707343, 448347810, 58354442, 634084042, 497938861, 25957733, 900590575, 259869371, 905027868, 499087127, 175908206, 897741518, 885585653, 185807524, 95669485, 145262771, 122124966, 936703596, 185879020, 296209606, 247157464, 338548461, 619394431, 311689380, 561498505, 639473230, 473351282, 259889704, 241274937, 250127947, 350293005, 540763304, 425785303, 981576255, 793350754, 928277866, 196477698, 911075979, 620918047, 932500108, 623033257, 516939501, 890922568, 566292553, 455878680, 318452481, 180566550, 32089212, 553619129, 955406811, 232375246, 52420501, 241702942, 396245062, 904420966, 671891103, 361457942, 615250532, 210356100, 627168518, 510082334, 150926564, 276599771, 147321446, 558181697, 35744343, 546931577, 693637827, 965973088, 898227234, 943476883, 559395677, 53569784, 314882472, 114682964, 633713602, 310501361, 193811544, 594823059, 223523780, 764782993, 884906133, 671678011, 106305238, 113036083, 266266529, 671138281, 496677079, 38353992, 817834925, 897560719, 553884975, 742670441, 262302764, 168411890, 245762926, 540495844, 93921331, 773011071, 61217213, 351432781, 114896038, 530269675, 143751758, 257819862, 431983459, 191755684, 644648568, 350257172, 121974000, 462520981, 649619966, 997557930, 255367387, 299235356, 659354670, 642055273, 51221043, 307052989, 81969782, 332702630, 427815197, 912370363, 987291946, 965145934, 75902371, 635941275, 131548611, 811688714, 781209336, 524058816, 272195831, 375213155, 376026192, 393272550, 873998263, 574638417, 91431605, 792268784, 210141176, 174921821, 964949184, 151230475, 344775484, 84309935, 60872491, 844427712, 31868679, 833086874, 167658221, 834886812, 628415840, 317054670, 860804132, 671143580, 106836748, 807129533, 678409579, 412135036, 756907980, 203426460, 411033710, 473050847, 285012916, 20264500, 752605311, 154461777, 556217686, 892561970, 33617493, 11090123, 839336238, 631513075, 633699889, 73590133, 218545835, 982961791, 812081633, 961688897, 811453225, 402400859, 973046473, 56132813, 54232922, 833254626, 333270102, 997027807, 460547367, 128125547, 143584932, 952598888, 445902039, 428037064, 622257895, 607371635, 973626683, 414039374, 568293498, 23387120, 59157078, 950966319, 154532539, 967990688, 256771200, 117494629, 426877926, 877058767, 686809356, 108905567, 705432698, 972517599, 5270996, 510926180, 504870938, 273427679, 921014108, 396985051, 571667646, 699368016, 33532848, 174548745, 825443607, 735464066, 809914687, 14934135, 777449575, 100408495, 749220908, 315002411, 768485795, 342472390, 641864151, 431465217, 661082676, 637230044, 289397696, 925200487, 428062887, 974463570, 361844463, 829096432, 119530045, 226527049, 478685877, 27335131, 101875924, 260780163, 204862891, 767819459, 58834123, 658800178, 961007694, 94917624, 676020709, 418883298, 852474348, 321350403, 657842892, 471801265, 831664406, 247742270, 955489928, 927010753, 307289728, 711969523, 221819789, 591082624, 66489478, 596877802, 304738088, 995400532, 278405993, 827974811, 33808812, 608530945, 501484895, 643574467, 49784961, 898705604, 776474727, 291371685, 319946487, 191980198, 620102450, 894552860, 330951854, 673125016, 856024353, 620028956, 228181178, 222999326, 86365185, 795566916, 380893136, 200172436, 527725564, 999446906, 671786401, 617240022, 522914936, 595618515, 2377179, 713860557, 162067420, 984999357, 332253225, 734887117, 140211286, 766094569, 141023619, 238852034, 870028298, 863868983, 873845290, 297117645, 135734091, 564713047, 611880535, 781291438, 721776804, 748910083, 944221918, 582281310, 525144137, 191665411, 826438441, 579824856, 853357976, 296668117, 777506569, 185868247, 160068047, 968203631, 55979660, 645378386, 82841701, 473322009, 415076516, 658832565, 416927762, 340465534, 545574470, 760628918, 372717547, 767678386, 954133897, 112689346, 516969288, 96201420, 893026650, 722808085, 710209825, 503913114, 919695537, 473711096, 585149629, 599438231, 607203514, 168259364, 162164976, 768975780, 468352159, 928725004, 821600907, 49430914, 180043516, 13244561, 100312512, 561416450, 61169736, 631722015, 52911406, 419735938, 514517672, 752211044, 428906788, 224630057, 993207600, 530433988, 284359055, 634052239, 257703792, 934804092, 898862698, 246747418, 787135740, 264510677, 426273432, 825477179, 65542105, 633669483, 519849379, 456066156, 160301149, 919596716, 108467428, 232295738, 394049816, 528086680, 772974283, 929497438, 401888349, 627455832, 289312524, 391102849, 331784605, 786911952, 619199061, 575234327, 598284810, 126190201, 826287156, 136632457, 46941682, 165917915, 79451986, 803843792, 933414053, 821004427, 968494227, 734138028, 910091527, 996834305, 714753434, 353890784, 943868192, 963277463, 291019294, 604484329, 787641555, 377194622, 108268318, 47145894, 492205845, 984106979, 166611222, 470385816, 269535614, 674921721, 605456485, 275780304, 992293404, 546713982, 598396077, 937508704, 286448591, 838625149, 699573137, 862811947, 526922443, 27251769, 847873229, 918729407, 371360577, 911928866, 929056823, 849921002, 978168154, 818366717, 999760855, 383259510, 705163819, 180448100, 416834211, 18053606, 916064290, 348905453, 674629846, 651340100, 127020457, 761569283, 723557015, 156274627, 516286006, 645216793, 973096054, 861195377, 846105633, 695956460, 429978134, 916719962, 989849218, 788417847, 83373252, 289743496, 883747108, 625327506, 242864545, 338443287, 301125552, 795464189, 999538822, 795727733, 802035225, 391477993, 478870872, 797478215, 546475995, 812673634, 650347821, 688715824, 395767161, 820128156, 555287848, 849065976, 831436407, 143822602, 641984840, 772334219, 753378747, 115329086, 490594183, 3866816, 756927618, 117975398, 208563173, 376965664, 931454961, 193548117, 962376940, 85716545, 441038848, 91715964, 155742797, 252507746, 150504672, 958655793, 764582482, 594192924, 954954301, 985670071, 179690263, 912457272, 463933579, 847563860, 311032728, 104480524, 521868833, 427736807, 363711800, 49504140, 818744784, 850162462, 178601271, 780623515, 287294986, 318120543, 632837717, 319404926, 256346757, 632683442, 636136244, 660969965, 189287537, 877709551, 23971903, 457527663, 871915703, 673682885, 623840303, 223267949, 351980883, 262029334, 357551163, 768529339, 39897554, 348977903, 936044114, 856952592, 219653342, 684924316, 968245783, 65971285, 689287881, 37379013, 397592224, 609315024, 156738086, 819139924, 740556143, 716722658, 647724882, 737505979, 634965601, 818594448, 141098648, 621848521, 549361261, 808602626, 700170772, 45494994, 922051691, 214588198, 1207175, 183412268, 832821107, 15566627, 603576055, 981587660, 237974863, 781032253, 632565224, 358257294, 872671467, 4732699, 720366406, 680249833, 234304289, 909116448, 926986870, 43508566, 960475039, 6618370, 649969199, 252236357, 705628018, 237578733, 713941475, 649333345, 591465120, 557009814, 117269814, 361095779, 389976269, 433640934, 72825156, 330572845, 140550806, 127388890, 383365084, 541377031, 53267365, 246988991, 843668754, 37437213, 673931943, 719174911, 923227152, 104984216, 627764762, 26174087, 237354551, 381361256, 253114536, 836790412, 427221140, 579137846, 105553114, 393439039, 11755838, 824630644, 713833443, 273525816, 213092609, 394439667, 962406346, 50538109, 738576505, 451702680, 402573509, 859584149, 482402133, 78797992, 90161172, 559118707, 997569871, 536933061, 221608795, 274719736, 195748563, 564351063, 667905973, 676270441, 719278038, 660836010, 769541730, 904019596, 626947657, 904272398, 535259471, 359011044, 260084721, 623924729, 944691448, 439824276, 465486292, 26732858, 952341656, 421061862, 955672787, 879168080, 689990437, 446155536, 552881746, 224936523, 968887261, 102593717, 799120241, 648277599, 752102014, 464757969, 969672124, 244196761, 477349655, 625520240, 660611936, 597056538, 770529278, 435998007, 513832673, 560674823, 847558353, 4947584, 693235921, 961433609, 428307930, 669869315, 208005139, 616726726, 783856851, 139813198, 406594855, 954066242, 683851476, 962394236, 338950972, 905772428, 628187660, 406960327, 53388860, 689899276, 812258970, 848990670, 63724121, 399172680, 353616029, 70940854, 332032359, 489135827, 666273900, 634025338, 41146902, 966613581, 723565441, 682872329, 633734213, 575795925, 148545626, 413978292, 922701902, 239008672, 837835118, 205738248, 807689160, 407699210, 172866539, 903194796, 54198271, 411780110, 461488247, 183827147, 878487376, 807955327, 934019949, 894051063, 153471799, 591593097, 514109595, 834471408, 759385361, 504418916, 824068196, 478248500, 373407148, 610747160, 388788564, 972510933, 823684226, 589811930, 651030498, 181963391, 965997384, 746225049, 895796268, 617112155, 44253979, 324470018, 514227500, 7864302, 731129196, 939372599, 897043553, 975603680, 596898481, 729775332, 917373017, 397615785, 26815235, 179233900, 57262037, 700157820, 610918501, 861454632, 525986250, 731723212, 651079262, 952188682, 787813549, 370030449, 422907912, 195761391, 38879888, 824143558, 56218488, 68251711, 801659670, 801784480, 999512938, 751373792, 360081055, 181771617, 25277191, 648470738, 631419401, 95041700, 302890426, 224550341, 120155085, 30840434, 395743488, 497890881, 101658019, 394572579, 259826404, 932692290, 717933302, 605016484, 601426732, 658736116, 88829625, 726696493, 691807535, 371722208, 433202495, 624396456, 771188146, 284701456, 700357232, 916259370, 942866865, 806629428, 954972266, 752408308, 235337489, 194242534, 136252709, 814256159, 423192980, 638645885, 558194367, 255952258, 356365221, 436313473, 382360334, 622449974, 91676908, 945212732, 247300108, 392682534, 80627533, 616996492, 913326655, 107938295, 743155156, 515130761, 77809785, 871572922, 400271063, 599999742, 968426173, 487364405, 882703450, 226958451, 336087451, 436595239, 468558662, 956127568, 565850546, 825522717, 436170145, 787454301, 36874946, 998697886, 925219546, 74653148, 583166093, 513744330, 898561962, 487741958, 427579201, 934264679, 640896501, 670546506, 212924157, 547463019, 246355623, 835353791, 568045093, 304387102, 200052484, 148853302, 980820609, 934953215, 771101087, 35167987, 855075742, 365284255, 983076031, 868807985, 369551005, 501907142, 749571777, 40521132, 189169655, 922785908, 617190509, 884284209, 588402879, 209669491, 198524640, 121559662, 864373136, 636638421, 30512733, 778609583, 924585868, 318253317, 724598657, 446906269, 493149285, 965363342, 664606174, 164673459, 80424511, 942218416, 395425620, 682230879, 65251546, 835311400, 212429444, 310172839, 35445077, 174852697, 246707530, 164945124, 892668468, 377423052, 209777489, 205322668, 756750927, 594688432, 587208595, 139605493, 748448721, 485348038, 920372412, 191123866, 75256149, 165598545, 881107473, 487998043, 230401296, 75630688, 301125815, 360817863, 9661318, 969745295, 407456989, 257376691, 690660950, 681970426, 149443876, 597632031, 634315784, 427034449, 526008026, 830854027, 541717768, 647972257, 557005501, 904711865, 65143136, 587646957, 788742182, 854461208, 333956035, 315967676, 437567091, 499439812, 643840428, 297174481, 440272714, 636510124, 190250022, 574458290, 493479689, 104637812, 461512625, 37129397, 6028156, 368816976, 631071910, 936626669, 835738849, 662364278, 854695704, 696176195, 977985188, 340456947, 433355029, 778826416, 638063389, 482771125, 998752777, 972997935, 151802131, 663306804, 218552494, 921328485, 820674399, 445813203, 771617768, 414413743, 478847723, 776242984, 985767408, 540705318, 191843532, 952773790, 509500937, 241143118, 38102342, 129254953, 201491848, 182249585, 754939230, 935774395, 656132100, 515474560, 90364004, 309658457, 578269361, 605431674, 898300472, 950256266, 287668356, 121069584, 176924909, 812118035, 513137738, 16303976, 940919245, 873201899, 92217061, 687532355, 463661264, 886187509, 896897466, 64844394, 565733764, 28513649, 898964771, 74059362, 512267072, 245469087, 694138693, 826373591, 684096351, 532038809, 725245025, 74301497, 280905977, 834827628, 388227964, 100666200, 388673315, 528473001, 801966808, 68433018, 555782035, 965348929, 469078078, 24443634, 397606845, 674128782, 498327486, 444916199, 441343076, 895468497, 300080802, 960240867, 373610880, 560241538, 848236161, 673961121, 185853276, 588874153, 657038493, 844343630, 2480167, 585431126, 944690393, 145157699, 160544834, 607702334, 144139106, 700401754, 868340912, 55392083, 180060199, 308981141, 618354553, 247612775, 341227084, 21889755, 476925288, 140807619, 444855041, 848210083, 320168872, 743204087, 866752897, 558004290, 912523124, 307491192, 273868373, 900985301, 945761991, 84084164, 647084043, 944609991, 402563404, 7409146, 272625476, 939566637, 351968239, 587101764, 74943514, 660717862, 475498949, 415106664, 864708774, 66410847, 754941575, 693235817, 239551758, 244585705, 342377475, 765517029, 244757598, 354281720, 981049074, 231184444, 524880786, 97932670, 503958229, 116314684, 684947776, 244086664, 611485091, 33746522, 363578446, 190341075, 323231507, 39230888, 701446566, 446487677, 947677430, 154793986, 768090685, 481684294, 256554968, 620622603, 5781572, 849322375, 483771366, 604529220, 653935096, 947645938, 3056223, 650624451, 689870538, 225082076, 297924363, 220812199, 909884911, 372967915, 972517259, 238740473, 850946169, 852002780, 734494956, 624785756, 933426680, 865901368, 928267683, 829489658, 661403662, 729099795, 820743106, 308359490, 880276370, 442416115, 930067183, 670390954, 14121003, 183286612, 901154192, 565654333, 77615201, 953432653, 376912547, 469506294, 32333582, 628868171, 504787918, 873819778, 756208401, 444313594, 457127113, 356654268, 46100635, 760381055, 107430121, 824007657, 437985269, 321820914, 720064804, 87269430, 942705591, 109702648, 116916096, 832338244, 511255923, 575628916, 456610254, 248238183, 837864258, 482017241, 857457182, 479079094, 128930238, 801216297, 619505644, 701100877, 219773017, 988396634, 156336043, 190594824, 579143048, 786822109, 450307525, 682880378, 102791559, 935283776, 528482280, 322661924, 343941727, 910207393, 739009469, 682424545, 838947490, 784726716, 122783124, 524244237, 312771085, 185621426, 694971037, 240863863, 437099971, 487335599, 568734049, 280154858, 74136308, 209218288, 182527611, 609175881, 70898926, 398786729, 923015696, 432225148, 925743726, 522512902, 624120921, 894885556, 30083964, 745798546, 4914983, 140750008, 643647839, 710176892, 78046433, 528831729, 9827353, 374852506, 98765219, 177400801, 604595751, 902856139, 519313344, 252154770, 721827647, 588308984, 863889284, 37418918, 723655282, 515992254, 487587902, 832395319, 69480212, 986723240, 25446161, 982218425, 397621113, 363413344, 726793462, 574569503, 750747195, 520894994, 259526135, 721863832, 839121116, 323677176, 456307422, 127185657, 288380958, 445660533, 327255313, 598457088, 386187277, 149000515, 847005477, 959874260, 536040611, 542095317, 765482806, 200643926, 299614478, 898144547, 838371801, 941417611, 805333261, 804891675, 895613438, 397295052, 834620167, 451145525, 617548117, 268313777, 91646986, 618543566, 278416236, 539879857, 201773403, 817062584, 43979556, 107182814, 460502347, 205293786, 570472346, 741054920, 942238881, 56682444, 311100478, 578991951, 928694460, 643874122, 640143286, 845584762, 613658672, 758148656, 706680141, 476062881, 127436242, 925548909, 315049030, 875256450, 408667041, 318813553, 586242290, 902403805, 868374884, 164174600, 226485674, 850711313, 464317274, 219502684, 490318272, 881915564, 241747867, 63701721, 406680366, 129215011, 468895363, 287494294, 946636984, 21050146, 60969747, 550733458, 842849691, 324242499, 596912193, 781749454, 424434579, 178692299, 41004495, 674634595, 522286251, 57284252, 568503594, 370045035, 123406048, 762060536, 280010007, 202381549, 74496337, 67868807, 300433998, 441124267, 603178976, 117411491, 346371312, 135865042, 773735568, 962196071, 698786137, 324178251, 982893120, 859072225, 889464000, 561487562, 57249630, 118416359, 517442560, 574244156, 535003954, 681828617, 499088152, 829089612, 847601707, 731578008, 649948469, 173447065, 709119971, 796908421, 343090023, 80736940, 717322927, 938418371, 240652168, 820221135, 114977330, 440943823, 266861999, 183565408, 291254884, 964942477, 873150888, 84993111, 685088032, 393777548, 550900502, 814429509, 416094659, 148066771, 940291909, 155502901, 694307839, 199423322, 816664625, 412356991, 937117171, 275822685, 349227227, 488496724, 907609660, 251857119, 252432108, 85834635, 299716405, 751263379, 129032533, 977858696, 164143272, 944530985, 367704191, 950471232, 561885976, 590034771, 957665940, 276341469, 984743161, 883569545, 922257260, 436537005, 88453223, 267487071, 813864675, 486514815, 984378401, 650318652, 879919622, 350888252, 362667384, 672753035, 619706288, 587470884, 777920127, 35489176, 114275354, 934279301, 590479505, 446899825, 287350783, 741461454, 781631723, 167893318, 743221274, 19905201, 900560752, 891458656, 902815500, 220052673, 559740574, 943200464, 73496681, 881438704, 532888905, 157853392, 181372819, 62712023, 888291996, 46142742, 838887694, 453094925, 987731732, 901442193, 942551074, 14708937, 693715975, 599148692, 902463761, 954645400, 488605043, 840740407, 906431585, 57035546, 944142827, 658390331, 973000137, 484657738, 602318045, 174683528, 821470866, 666060025, 213223373, 702553254, 374763623, 70925328, 462735975, 4963777, 393271322, 33126199, 175304468, 784112547, 653297880, 101946138, 604505608, 763134235, 121476732, 291760134, 99933519, 470390410, 385678615, 414740250, 582566278, 908953411, 809175105, 993170623, 716432181, 529445977, 474074487, 951128290, 669483238, 660975828, 934764, 521790961, 799582352, 319706284, 603501529, 20971879, 587852367, 4647391, 91558411, 400145715, 209310146, 590326708, 239301226, 984567849, 988646156, 749131566, 786090598, 716647975, 883415758, 437647506, 289455108, 869099655, 999389673, 826147277, 706399713, 915240234, 75100787, 971326337, 952019079, 416150118, 688510843, 927119757, 586260822, 259266884, 717962809, 380194, 109645369, 886433956, 641107360, 839421904, 516365416, 113583376, 985757471, 340558356, 486099838, 942243326, 543138066, 9681700, 452752238, 216763802, 394438469, 594669426, 671698464, 777471299, 956246584, 822217430, 748674864, 420655829, 647762634, 948848938, 439557848, 409758667, 551719063, 393401735, 497154005, 971413360, 10557683, 695318102, 614349571, 891404031, 44685567, 627303470, 886016060, 366234776, 173158491, 451880355, 522587020, 153416109, 366230689, 42670862, 609151337, 468760139, 9713798, 95285851, 870835162, 437214056, 615722391, 370675022, 682115251, 18874212, 505322959, 624290943, 469611322, 528990801, 804916708, 671689075, 306923636, 363348618, 652921476, 842603530, 941782105, 835773798, 941256054, 857560835, 975022510, 313734699, 514068700, 607447705, 863621152, 845502734, 900274358, 55533445, 522348910, 921047808, 603994503, 536247285, 674708907, 572513695, 353944596, 865348045, 673528916, 155351017, 189817410, 977733505, 559027268, 869436500, 563152336, 102797034, 538876163, 116771134, 607973650, 104284662, 520102360, 734840276, 581836419, 926307392, 797564685, 596498449, 410502027, 106543286, 734839042, 38286107, 126433475, 885677202, 528165406, 909458851, 745930957, 801474807, 869048610, 401583996, 411784681, 413089678, 90135217, 462376035, 554361729, 545653740, 976497606, 125768206, 260077051, 631436559, 4255713, 114013991, 71790325, 64693169, 917321588, 782241657, 465142061, 713925770, 143951767, 78606601, 572799935, 478986421, 296773156, 455941631, 746018558, 36184207, 400143913, 584834541, 250644101, 331064754, 963541663, 777664141, 674516108, 593926417, 579953178, 270193848, 837637437, 816704663, 179325218, 963418067, 37390240, 282376946, 673492893, 456319100, 819078306, 160604707, 799794633, 782675304, 188898596, 505237529, 514339591, 362343983, 570986924, 769635288, 253783184, 384809138, 509249171, 353275101, 843335284, 753499370, 239022196, 96789623, 102658832, 762291499, 729366620, 852725217, 186026388, 905257127, 516468109, 531795733, 637865091, 548205127, 124917846, 392697266, 266808452, 298922740, 140994807, 26289693, 896246548, 386701882, 154511906, 824477495, 403024478, 697119392, 610453794, 320892936, 342943112, 240640213, 843645975, 933079921, 316376429, 383330094, 972591519, 575846044, 860006247, 489374186, 229435402, 299138462, 697543234, 176585257, 564024825, 134148676, 649977751, 99237092, 963514428, 366660178, 308918349, 429367231, 413131748, 351623239, 412145604, 62901370, 60629614, 296801846, 892187863, 231511621, 331919374, 797818955, 817466610, 973242761, 313016255, 15083681, 208522392, 902869917, 674390433, 318046321, 378094528, 269509893, 661458627, 851518644, 996914007, 333077758, 416802588, 84963490, 286514519, 31519047, 417853246, 824049685, 266523000, 917602453, 577186800, 258636910, 777716422, 906591023, 688262327, 641151842, 610471466, 136195464, 739350512, 756156376, 793904676, 962858006, 157907228, 13846592, 452036667, 751835294, 191689501, 840349703, 596773783, 672022149, 121454966, 519345548, 226209036, 932405741, 828865447, 134222604, 924442604, 213348592, 201120066, 196916968, 462877264, 903933621, 927688394, 634840956, 934925974, 274062903, 883273363, 499224725, 929511940, 232882108, 892671121, 987073827, 383805138, 957811226, 460942576, 177874871, 448191102, 843537103, 839776824, 548238253, 381297159, 813141667, 682459961, 107956482, 305809004, 878190334, 957466759, 771702292, 892324788, 83761116, 979989717, 858558342, 12324619, 584713961, 632603432, 793103119, 818382417, 911518576, 573204907, 518308168, 585232060, 629786127, 167729863, 35663000, 783543597, 373841326, 612253794, 271258180, 959649529, 918076882, 76761830, 100087304, 869145763, 940923630, 383083983, 554079323, 308897912, 162766157, 468630272, 477367283, 681394469, 647612580, 734275699, 328886945, 558843319, 235877977, 955091666, 569665948, 159391056, 174211264, 229782060, 27248555, 794629141, 949167498, 917712653, 285051763, 227365684, 169919545, 67424834, 199765942, 991531232, 767072611, 931804676, 146580901, 829650770, 423005406, 128087048, 323460565, 29972556, 843882118, 887100917, 117373248, 401938920, 270583421, 294264399, 392411707, 139707496, 728395103, 264369435, 323131495, 260398833, 993857929, 297649320, 469426442, 651775118, 343251262, 853899095, 355949795, 278161625, 422610536, 772702500, 54860979, 240881252, 38302286, 331563411, 961005333, 633361220, 805832562, 453392808, 564601339, 983108230, 806809648, 166134666, 842703047, 626500683, 494130618, 909672854, 172894387, 223968095, 315976111, 219639208, 104802260, 638272872, 97307735, 614818366, 388482436, 427882619, 316331429, 279162665, 68974461, 814868406, 735844964, 502646216, 402971636, 352033806, 713758100, 817558798, 399537930, 256053203, 550443126, 215434418, 873880435, 149774910, 646716515, 516582746, 118423161, 928013081, 655259572, 192166919, 761899800, 625584209, 790269049, 898107678, 355261320, 151017956, 927183660, 901046989, 978125493, 699665128, 506121159, 940067840, 329307444, 484709189, 179078036, 367539878, 196912629, 598191365, 650968175, 507455546, 140662363, 317944938, 860691378, 667804426, 118983643, 694871405, 756790655, 339504637, 191411358, 684972275, 805076591, 72954868, 954324318, 444926076, 612635024, 80472025, 165838897, 110288979, 607855292, 765549807, 705723348, 293708374, 601713690, 752720479, 722780511, 451171514, 760135362, 506773487, 511147268, 904944281, 50265339, 109021529, 4267929, 578041343, 666060082, 834698382, 951796527, 794400567, 211340585, 473879013, 578093871, 426855378, 655888390, 765773157, 423335472, 536784717, 785431551, 590665872, 689589066, 826454684, 903398157, 575670300, 662842376, 340449422, 464776110, 777864185, 536762891, 893089860, 467974665, 802030318, 952092388, 52364860, 673661390, 186820208, 785864861, 729537468, 817344929, 897462045, 300583856, 256301628, 654014091, 364647211, 107568830, 264616052, 836594567, 377392976, 69716454, 735663285, 628502636, 245416092, 987627180, 75877844, 836608087, 148890969, 466402640, 184824552, 161896476, 380077987, 738116693, 925632885, 989602071, 257997609, 939828880, 253287524, 959838798, 110731292, 34345880, 185899651, 954248550, 863393011, 282286369, 207447318, 837122152, 586802655, 340496603, 102479075, 826635185, 825281817, 650698092, 33438612, 12950803, 562501837, 95872077, 447346827, 384222998, 914984976, 629634895, 737509610, 623434359, 521877612, 544115447, 409638843, 571303277, 908284728, 625212919, 777663797, 261398798, 132267048, 134186971, 651437285, 501901760, 805973067, 233503060, 98848505, 486180288, 836815994, 479038499, 332036327, 854056013, 409256242, 602157300, 335614059, 52619776, 848193246, 604645290, 520063535, 351728791, 76632589, 211890222, 906157746, 924511775, 107446708, 159973930, 820489916, 231817059, 601301516, 440560157, 12933268, 669132670, 808373610, 824890609, 236442215, 20632954, 443156108, 44295285, 203761471, 468886899, 972075431, 301578469, 856113551, 879360048, 459737209, 750956022, 552423090, 449821356, 601667332, 460643414, 240050034, 940790192, 377402125, 450829162, 716880651, 124856574, 828419438, 417615779, 895166265, 348247944, 593636929, 101763891, 280498599, 242198648, 426199413, 368740667, 317882355, 976732846, 591651874, 286155702, 281600154, 55163115, 393734114, 268209051, 934561909, 623396324, 16024633, 225243403, 371860202, 284531835, 380023600, 403365318, 68510897, 297670185, 308351529, 476249297, 895546457, 556620130, 791123657, 159873121, 200766959, 511763872, 522614366, 17855435, 769557196, 272261992, 854397103, 244616186, 935456379, 42497208, 899213379, 313032796, 552184006, 866951889, 902324592, 230805713, 592420377, 120134695, 759794998, 342567821, 741666931, 732115005, 164041702, 220861529, 519368132, 633132168, 827106602, 270850742, 61171375, 988732049, 179100796, 4116131, 737206092, 806677693, 547901929, 446283571, 705743409, 126827665, 941666643, 270061621, 758050818, 338636704, 584054820, 173499400, 679959085, 794822335, 504839491, 101993911, 712997236, 54022831, 356154960, 639216695, 827723394, 906862441, 448645233, 248173559, 830456851, 43732023, 527020999, 99396276, 568932629, 931437159, 435045081, 200448241, 170900820, 31550315, 347148923, 586320307, 759055177, 663458515, 238620462, 634476728, 561748719, 743604791, 761189356, 494322720, 777109720, 306584257, 595176244, 909819988, 961858955, 447951857, 472902925, 373303117, 62459921, 801078357, 534818861, 566041820, 836457142, 115282334, 200597818, 102503136, 64190551, 840102170, 507313202, 391873976, 550278521, 106582782, 835356033, 27094824, 971043462, 511336849, 502736477, 603985111, 563172451, 574779458, 455220906, 488767983, 587019108, 968645153, 635835414, 881790154, 671198453, 797906853, 215629244, 918612364, 727968806, 438823214, 42142929, 780152617, 639350136, 101995894, 398590460, 475663585, 824791263, 657178983, 135528029, 279498641, 660433376, 870857251, 774853172, 977739928, 310386265, 148840556, 349581905, 849222426, 173199358, 626470090, 246250023, 853882092, 523811058, 616608936, 495959373, 798981276, 90332676, 883235787, 403264837, 581738883, 769665944, 727371298, 537907107, 768491552, 752515650, 233036088, 911944660, 99981895, 41450036, 177399482, 301801618, 854393684, 934005902, 957474632, 508397381, 612284548, 348583540, 651475609, 55024198, 253751100, 545903471, 131147411, 471544796, 720661855, 178624167, 774345914, 424752084, 791510751, 634461842, 39584525, 245819012, 97869673, 171969118, 300823256, 804693513, 89783357, 173472196, 738343478, 493500133, 357318864, 971319427, 988457794, 565314232, 948141068, 329518695, 44448860, 481853254, 924040126, 925020206, 505088956, 221730999, 328120468, 767091432, 806460938, 69577281, 45516403, 14373613, 8646318, 656633629, 642741126, 129039404, 514163459, 480839984, 835886102, 523609674, 714052681, 364704966, 799203845, 17978030, 25935293, 777726980, 207218216, 336260304, 253346013, 323353766, 218349471, 718104495, 593713853, 88495678, 549103385, 474582696, 424785846, 792395498, 279166132, 946156444, 505834506, 800482914, 396683495, 841978742, 119680208, 428740148, 292973238, 55281897, 271197487, 318292491, 583571859, 633693597, 816216556, 302547419, 430050107, 945571352, 751637669, 466472072, 503772768, 964583777, 932580679, 191315269, 256700926, 316742748, 885467729, 604433566, 473810862, 327115194, 394125865, 789943308, 978761074, 978630944, 404934949, 681849049, 410066015, 292161928, 335403467, 720125188, 304386924, 443506291, 938601180, 662002257, 879055663, 907479831, 183027987, 363467528, 860809152, 911079402, 771687594, 685286992, 638222487, 790109622, 4853430, 69124975, 408048088, 371813737, 107931039, 461700838, 674334374, 406202640, 913571569, 280851934, 257820760, 674020524, 533667161, 257210687, 891722501, 176277590, 565719126, 955447338, 505239267, 835627754, 3906038, 906504647, 959214439, 905993577, 117496797, 356705577, 413128754, 567644214, 396003573, 28244, 218271991, 142710070, 33012061, 702230754, 304521700, 529303569, 267336793, 268385732, 805257061, 535257034, 527007280, 241196995, 68766400, 854532469, 68470673, 985697767, 19685662, 995204332, 920535616, 589783340, 93075080, 488358133, 81080741, 69871556, 124586277, 564908852, 651407181, 779670132, 359191792, 562398944, 173737333, 328658137, 456742637, 60692810, 966077745, 593592970, 521157046, 196414849, 665860347, 315517934, 898675595, 348074581, 149698369, 195790409, 2782647, 774829277, 391730618, 307588143, 827863219, 558016826, 137369112, 828384337, 615086152, 748536570, 693716847, 311401976, 768308743, 370689494, 486979285, 349271534, 476551299, 552911081, 487882570, 550691372, 828234176, 116663976, 247611953, 142638662, 321303569, 497615768, 135282842, 475910355, 758003902, 522009435, 248539714, 803610662, 454617137, 497696447, 152133005, 123245609, 920403696, 554492744, 799622979, 348653403, 22324013, 866606414, 568598040, 280229000, 346339736, 228609493, 972242399, 531356648, 433706771, 342108644, 746974285, 700105442, 625504496, 853752434, 52844995, 183991145, 495669693, 434889799, 987509580, 363660962, 454550091, 287331365, 140594500, 441003799, 354613915, 767687746, 109051469, 93625101, 649090790, 395707268, 514486382, 420958355, 208905031, 788948443, 793401454, 848280977, 188656495, 832146816, 946141126, 771205804, 992244567, 330197294, 842103289, 489089040, 684322339, 223646171, 140864782, 515566405, 208626336, 10244747, 542045352, 575748788, 136828945, 969214219, 365758634, 507883341, 35393056, 112057917, 540202328, 557945483, 961684434, 14957837, 422388736, 383256063, 330583070, 993815066, 482867614, 692583121, 21201994, 938511471, 747730065, 746426309, 156314028, 574649662, 971474352, 773835223, 820596839, 131539172, 70534909, 386305608, 246383468, 469524275, 967507870, 445523506, 529431823, 225653792, 502677538, 187046411, 907807775, 22868511, 118241441, 355448411, 987684315, 803241387, 4722750, 136524734, 58027273, 139563084, 161923827, 602923401, 2079035, 20327479, 407720917, 709010916, 598660990, 911869444, 823752003, 301181110, 88351652, 883439663, 469907099, 386066389, 548625868, 252585316, 334093271, 30844916, 793996095, 983045835, 585724984, 287730, 163279379, 223557408, 518227493, 308831002, 800744514, 266959816, 557610561, 219319622, 520496859, 804234974, 905325615, 797787841, 660477827, 544798023, 978585350, 514661096, 746711587, 991402267, 6100414, 935321909, 614074675, 679640880, 575175107, 640805405, 1440207, 869422700, 606398154, 844716013, 320098844, 985435831, 193409833, 122812626, 858675525, 183811430, 608468523, 326981665, 535100691, 752314225, 459522734, 755751256, 665899668, 240678510, 868233002, 121326822, 449978351, 514103113, 685632689, 173564918, 424912831, 433576276, 505400018, 442373795, 837046061, 922391663, 306700500, 605122326, 839145405, 462015266, 928774884, 328937725, 383304671, 904168335, 276936045, 908575504, 128144999, 235005557, 594551408, 922731277, 508412759, 578029486, 331482028, 190471622, 292648527, 978599240, 823068601, 47178580, 479820547, 461357545, 829092408, 392967123, 710219841, 928368712, 549275288, 658721641, 139106428, 770300849, 916191638, 875379877, 777192028, 646421179, 528131343, 409790783, 506866585, 234527887, 340719189, 165268317, 237926987, 401677737, 117403894, 131078477, 563125250, 486471620, 772281869, 973153919, 393217439, 613514866, 57213597, 180438995, 866558332, 463059033, 284124597, 436251671, 445174744, 994760777, 317058483, 625832068, 393377353, 371950179, 721551834, 320393347, 366486621, 993750454, 360966567, 891922189, 795824010, 85074362, 250574113, 611935889, 937814118, 549050659, 361835285, 847353414, 164115521, 819573783, 48784824, 992570847, 508803973, 526796332, 567485451, 672287748, 650909253, 533376651, 142728223, 349238301, 480320100, 444903303, 190742081, 913313485, 354391188, 145175425, 786923183, 326337595, 382447673, 19636381, 247966063, 324880100, 283860698, 81734442, 854860153, 888521264, 484438076, 302127338, 437006473, 683896936, 429664571, 210394428, 755239313, 329042276, 601043750, 537987397, 517374778, 331649578, 997282503, 635250115, 840098893, 754126514, 470254024, 50277060, 623968149, 362622883, 622338494, 696362928, 751120852, 841797941, 318586874, 211424892, 260689410, 964080219, 727049021, 146013990, 123515515, 519527441, 797989813, 450012590, 57946585, 614840084, 327281862, 353525679, 268674394, 867212291, 252555578, 956043514, 713118107, 670318186, 522179156, 289415195, 831067703, 146587072, 567234676, 613162147, 788690466, 440769750, 58951686, 785426981, 750990277, 869802778, 219982102, 962492189, 358235725, 30260262, 126507282, 697264269, 114411850, 216273950, 916127622, 811211183, 118555323, 915653673, 785686415, 737932809, 39377865, 89806192, 842560895, 448637960, 552231367, 355611835, 530547700, 613920949, 580601350, 448537480, 864934990, 924624121, 251283098, 147729722, 151359298, 196536761, 122121659, 463678322, 349281863, 18479376, 450980010, 363808521, 704567963, 351088017, 367700701, 491177640, 202432217, 726329593, 394508207, 339924880, 33558962, 162084888, 52328072, 711595278, 514100643, 190580410, 863398261, 809765267, 54681000, 315630705, 400448324, 673793450, 144678162, 250216550, 816021880, 450403846, 8558980, 713812696, 77959169, 745347446, 895885472, 127986015, 959593465, 843461576, 58439061, 676448489, 717351426, 555127174, 412755048, 284811141, 129401350, 840565739, 682902224, 948412964, 374567192, 122749865, 472582897, 866456554, 761381388, 273014484, 837520851, 587283890, 515381668, 793398401, 496734824, 217382148, 420790990, 894438793, 631224260, 248162243, 999883202, 513474091, 608652265, 192671988, 969819837, 100800834, 187821261, 912825859, 158233805, 754947483, 997371305, 768936496, 986980757, 404663899, 173463995, 116210435, 856523778, 432996029, 385250055, 643364997, 942368085, 713830890, 23652549, 908358637, 912921536, 191906754, 975367496, 389955866, 435879617, 630290560, 323048229, 7779687, 321267335, 340284972, 574280143, 723783013, 265077614, 131308542, 776928377, 174390374, 555874413, 660716368, 313296796, 52266827, 11533117, 384307356, 519672559, 808124832, 915889716, 902234797, 405088763, 120245661, 429615586, 702736212, 281812473, 807732777, 561007175, 670614991, 332303930, 792711329, 848928529, 506503142, 757023287, 647946087, 327581343, 904798386, 454573600, 481789308, 729740694, 292617488, 530421398, 561675056, 652715752, 787453268, 673909034, 632072954, 50250737, 13626792, 77869609, 537528870, 435585195, 876276468, 426036206, 340707008, 443212348, 356927578, 305429367, 195679919, 248876033, 118155183, 3113845, 853245268, 599248801, 621707337, 481463969, 713740078, 744798626, 897538990, 110695246, 788009648, 643951371, 298047455, 48423719, 789674857, 545785806, 165025115, 632462636, 624477185, 465841467, 577857953, 684617055, 454273994, 22184752, 375963911, 406192965, 570669846, 742227781, 889445596, 137106323, 91934029, 914511895, 316256580, 952728290, 726208569, 703859842, 289057929, 250954584, 966749852, 982067284, 284476736, 877453769, 594973069, 769534647, 580968175, 472121323, 88559169, 685864350, 894084740, 372521778, 188794362, 119142774, 240965582, 101421851, 762855831, 732555575, 957728970, 87347321, 486133591, 159142458, 269899297, 600175608, 445557249, 248025402, 526270961, 455991738, 584859308, 352535638, 700236161, 719159801, 539439026, 670286911, 582353995, 392518643, 717371262, 164436710, 49434987, 418824103, 548998260, 803319833, 110883865, 511369278, 950434445, 100263830, 806853177, 414946763, 556358212, 734247131, 740748283, 156564542, 515110770, 747218318, 1498061, 832323021, 165357278, 658103568, 528013715, 904487704, 531236999, 558819306, 924144275, 633535182, 886580669, 806626475, 536733832, 749423036, 13535337, 161633875, 159540176, 712661279, 678570346, 819309982, 68606159, 573578914, 755386514, 35465819, 95187969, 416617081, 896674972, 552598607, 665036588, 800713433, 287180480, 805138033, 677570945, 75594626, 639314355, 264575503, 371197958, 71409054, 651003750, 467982745, 438520534, 905252806, 422058740, 282297771, 256013323, 22454071, 320578501, 75399992, 23606343, 653283846, 789868548, 272154554, 352528964, 92016600, 701710321, 410079702, 329245332, 134959636, 551492296, 780747424, 414999245, 689838118, 866203472, 359856794, 162380489, 745917491, 842322032, 740988448, 211613619, 732508142, 796854200, 593722846, 341121003, 398363281, 686505113, 465301558, 202995017, 431163600, 403009791, 415627199, 905334843, 923179341, 232502610, 863507052, 371507292, 179828881, 701895675, 324581463, 170635190, 525567420, 175769921, 617973037, 468789557, 445223705, 56046503, 216621542, 679212607, 402705893, 721632394, 544271024, 346286019, 54589283, 391551333, 691509458, 64040800, 640533053, 599980940, 77650814, 769057939, 994864110, 11888892, 113710300, 270036226, 633898476, 603399897, 605417984, 251008482, 420406922, 131115864, 372774432, 874151751, 943203773, 705766076, 167231839, 866606174, 197951730, 408121373, 838437913, 51490614, 690686263, 735117657, 784206944, 819391929, 557416004, 983348479, 893227330, 885857478, 386937417, 803774889, 834631994, 702799210, 565252625, 309888900, 871358877, 203832688, 583462528, 48840810, 311339361, 187758242, 451995885, 4069907, 528188759, 350912339, 488189119, 103449878, 377318914, 288177913, 605711655, 875572048, 975352038, 984780334, 532409084, 284263443, 59004274, 853584436, 847466105, 587068144, 864856108, 424388507, 162880645, 820349109, 409579507, 1064265, 728122388, 664803758, 54171052, 597457446, 84892094, 307657964, 288911258, 456607, 71603433, 195484615, 150291408, 368930716, 369411451, 96285010, 959203857, 919534004, 498183021, 175223597, 700400368, 328362745, 140659531, 367871584, 8384960, 207264759, 808707870, 794657371, 245204439, 180151216, 606798864, 947082059, 647779055, 279761945, 19803485, 758153088, 407228056, 336112906, 827522211, 359190975, 994229204, 421283047, 60237334, 171970781, 925119727, 390545327, 341955282, 52574165, 312475124, 28548625, 650090241, 891343280, 989917154, 927551777, 779552423, 694511410, 572049570, 718544788, 148494843, 952415068, 258521340, 582460802, 363671916, 167412683, 583977797, 257904646, 162074482, 877823925, 943964975, 195820489, 618710341, 512335027, 272101125, 170468441, 49540449, 867441937, 211064554, 276589498, 827160070, 677412628, 159334357, 517167128, 762136836, 92631185, 929099293, 189611537, 10162985, 143048978, 324992017, 454611188, 975733143, 929419951, 314829751, 796312403, 203993435, 159325914, 56414393, 304814637, 305629290, 842600827, 844599813, 385435511, 551711111, 863900333, 744811161, 794895609, 858786768, 687033257, 446788794, 487235428, 826923608, 797164884, 811407760, 292255284, 691835989, 70879386, 335455465, 490915608, 282110383, 191297065, 318348330, 426658464, 348328032, 597350555, 413199934, 364581660, 464496364, 130584928, 73118628, 525825510, 103978258, 904314279, 981335897, 264697239, 957858109, 259215085, 582466771, 808976922, 553297692, 424561962, 83429879, 752857452, 238766841, 978943229, 828774229, 315690388, 5236022, 551643281, 816549539, 512594675, 425046241, 53734276, 60643739, 425132015, 136112188, 499601432, 749145606, 711034290, 474117764, 422654300, 237212879, 666325677, 197086238, 846541544, 955729386, 177142607, 902229762, 975424918, 766369249, 600735765, 68794718, 185587301, 213601629, 738363310, 267876906, 360306930, 706311362, 262572166, 290791118, 638795199, 923537830, 428878817, 380349249, 517184281, 120375917, 806992876, 85416194, 255247038, 315775360, 758011125, 615052859, 183686325, 45286046, 646542626, 506309248, 596333782, 93907682, 621617795, 975600598, 869977003, 990613788, 665118478, 996096644, 619269591, 36703269, 454033770, 183041358, 875586924, 217306106, 278000341, 874634320, 846739375, 549272169, 39076595, 587630029, 738256490, 913152035, 550116894, 803621473, 234756781, 885579622, 253033264, 730718933, 890503243, 51664053, 189938564, 164453357, 430349758, 341082149, 905123851, 80427495, 330473925, 746672134, 581346028, 977738204, 635895339, 341523009, 18672678, 158888267, 106705666, 63649010, 13177489, 54972767, 584223297, 285110575, 583389274, 66481704, 383356705, 161459987, 496600305, 46694042, 839794126, 238573723, 705282668, 988622700, 77126480, 515265757, 607007270, 694136485, 980020793, 150831022, 770288211, 491285241, 798498327, 631091303, 584910655, 571335942, 731767094, 223213805, 56088022, 25770126, 324137874, 63295411, 741746038, 419266821, 67460150, 28229419, 939439337, 714601278, 40139978, 423823391, 901059680, 328475141, 36156642, 250355469, 961392592, 462781539, 637526341, 344090057, 916185844, 183651464, 205203185, 971455377, 856497326, 336744985, 532478434, 264367611, 58501554, 627539219, 804777444, 533167441, 31060232, 923285366, 434848228, 630289945, 177904990, 128450120, 841430839, 532471787, 411500973, 721534577, 208813346, 536558046, 721336477, 603161192, 637504309, 816564701, 725041135, 806251230, 705205476, 906549518, 784519288, 532090027, 451176481, 460674371, 618563174, 721609986, 141878270, 673052789, 515791, 968578291, 402526783, 851400985, 252408899, 661119348, 935715814, 925652386, 794929695, 300847380, 637148471, 251422959, 917749400, 669390697, 84360616, 881319400, 137634208, 430927155, 544735213, 796152862, 988669447, 587919995, 19039231, 397243616, 619500214, 374368041, 212496618, 785751657, 504363999, 783675468, 58109062, 456527245, 176600067, 464746788, 539525636, 974120502, 2196361, 37168794, 211222428, 29633955, 972343608, 750300475, 647501541, 489705113, 144348236, 120376446, 909730108, 983576844, 42149344, 680026507, 95892552, 449201742, 867278203, 500257547, 4089930, 795996936, 465739826, 364873000, 21022783, 938338517, 98339645, 548134514, 862304392, 556986970, 667856343, 699275815, 559843375, 562202156, 826098030, 345037321, 412182719, 889780449, 767474432, 352124925, 615745022, 51162617, 887799392, 783990394, 286711663, 585978631, 585806699, 208142555, 558655100, 88758698, 116150230, 924604672, 528556035, 682108618, 725708053, 883638524, 645647220, 593510485, 263622806, 686572808, 279048222, 447250688, 87314483, 189461519, 332790448, 772047053, 406313632, 620176865, 228119742, 981298268, 797440753, 881387846, 614584531, 802612738, 267991741, 37712361, 395571909, 339497244, 694984929, 696289863, 126160646, 749156066, 22976806, 663820969, 950134578, 636192158, 959262446, 197675564, 738169283, 378566175, 948862079, 569140734, 758688332, 742834992, 481158719, 547150064, 134431771, 856609477, 402163950, 126008897, 107547931, 818983519, 333237909, 32924730, 606269395, 311085079, 19561707, 6883491, 125983504, 643263502, 202246112, 929631867, 990181199, 198920103, 67935200, 456461929, 661342053, 255853086, 648081906, 167509990, 345775625, 293184169, 444209811, 604512507, 262203682, 452373123, 942789896, 708072607, 626346892, 885653408, 801530006, 139089867, 121543754, 420357235, 73537338, 375902339, 57275413, 674386702, 46025213, 889221796, 857658248, 586092052, 564734638, 668525806, 364495279, 852395155, 305755518, 304351531, 832735978, 877789895, 202893935, 144206341, 696251467, 319143973, 102853250, 708663464, 860450204, 921030329, 493909114, 755003043, 108078960, 948496441, 672012318, 226070809, 353427011, 121340810, 374127294, 384605081, 298548862, 580062999, 810945908, 113262655, 663363470, 225878331, 921367243, 14382517, 819831429, 294536905, 588635511, 168375448, 9525521, 753271367, 610032231, 560123896, 763148844, 684025792, 77962271, 918931505, 355744878, 831892855, 648985177, 803778091, 210407200, 929023297, 547533179, 412466417, 768291780, 606181811, 402599451, 412799900, 997131631, 251863070, 429375386, 554118372, 833715861, 188293390, 941973115, 896282530, 57496181, 121553842, 375686988, 999926415, 17215707, 315717889, 216355359, 920118252, 407556569, 131675287, 426896629, 64710279, 652921475, 900833498, 13606274, 471408115, 50721889, 843130099, 141137647, 615287599, 40932991, 897865276, 376112091, 687312966, 245423264, 749281933, 843685580, 97935135, 639527844, 430279392, 708455214, 591047669, 302520341, 709213837, 694038547, 224060837, 655264550, 301607836, 212904604, 3884052, 861814789, 4784592, 231299353, 440622191, 407351114, 10503698, 86396702, 23538578, 889180678, 918583294, 95470673, 19484927, 417909621, 355941292, 24232175, 631574633, 479758383, 557590902, 793445162, 37787728, 922688287, 549670192, 633631310, 48213020, 71067311, 702788498, 330026801, 413489396, 683133832, 827862696, 98007386, 903349596, 322926898, 933443395, 769737275, 400159902, 595739964, 499066962, 567231962, 150068115, 784789477, 370617650, 693252060, 183333408, 939095699, 972844611, 167342180, 714206655, 886544898, 1455556, 589254699, 58537120, 438570954, 11209084, 475847982, 142498685, 73557718, 627398589, 206553537, 687716355, 847301650, 473744101, 843120033, 19379489, 280771805, 448674169, 95241233, 513535958, 454036505, 327947380, 880210638, 460007530, 546988618, 123829201, 18270041, 452220294, 541885669, 944880199, 428588781, 120315669, 471190856, 786786593, 856194551, 348126778, 380342816, 164608961, 730795284, 930965006, 845245064, 904852214, 893527134, 906986326, 523785804, 222840149, 783892429, 888511422, 486947195, 585948881, 390977015, 912782937, 882657496, 641458511, 2182664, 994608713, 226984087, 481617826, 452427783, 464618708, 549839623, 485178568, 251351929, 344142183, 155442059, 488414439, 231558947, 618101703, 689963756, 521385637, 864597551, 617858218, 631982323, 159356308, 274403415, 86088631, 454170895, 362081195, 450331481, 595207497, 981181397, 705070274, 224053613, 286775240, 315074568, 648006741, 6520361, 158787631, 290029351, 366531835, 77916290, 470868415, 95637030, 786297872, 563219913, 32615573, 884919680, 654306789, 893564745, 318701647, 314343125, 566458328, 482701992, 472185696, 705690178, 908205419, 11530383, 977620946, 819975038, 557804403, 725996256, 904800633, 548172214, 422550610, 887775374, 395512, 868684197, 913220175, 610441530, 127583213, 674563137, 823678458, 720028863, 561596866, 702101955, 121394322, 474314509, 243588271, 327927253, 416242016, 555175302, 544113817, 196775085, 887742060, 570082888, 118598072, 675768506, 697768796, 852765525, 669424629, 870156655, 750529409, 862262764, 708976068, 612876277, 401992190, 491308412, 317277754, 340993668, 684649909, 737992191, 258029929, 819323016, 265402524, 414693564, 993744023, 421324169, 733086219, 458622145, 531021768, 101345015, 442225410, 918298910, 282042538, 875955513, 546239252, 665661704, 693790070, 406507812, 578512137, 879105740, 812103902, 948277124, 507889546, 87264987, 34800054, 394635796, 443115580, 476044649, 733390552, 285800826, 561371571, 314194487, 300048184, 208464315, 216763853, 364794431, 298030456, 95218669, 231207071, 516112462, 78804304, 865634744, 367957084, 234827920, 474867620, 671238214, 197911, 412789466, 696299030, 25156169, 5447143, 338731591, 375390139, 572545564, 531580307, 565093887, 13761282, 435334146, 740078367, 389715368, 48541695, 215571355, 232322593, 912349142, 738517144, 20543258, 350230235, 940844497, 590219154, 643439487, 283346058, 134440434, 187530867, 304132303, 83662444, 524145582, 46268430, 159062440, 612951754, 141582956, 679559249, 73689098, 591757601, 301987971, 902239766, 140096873, 252017356, 238842671, 591800410, 666839758, 685467358, 819632954, 601592692, 771167431, 801001765, 81897725, 605424387, 329617460, 889143001, 881111552, 30064110, 456793820, 975392461, 353001409, 943116148, 701230963, 616407467, 766380498, 587154729, 247113623, 974584233, 687190427, 153600806, 781655452, 130971586, 619225130, 652031049, 661761192, 948795414, 845199039, 138911245, 210930409, 738604077, 717543997, 413226667, 945613147, 350837174, 934072425, 529397044, 647500284, 795419666, 274203168, 62495707, 312906335, 658415691, 77768248, 492147859, 250716728, 120160654, 621979850, 360882249, 93476096, 840623839, 811641377, 708480933, 666252336, 102283979, 87812208, 114231555, 540257313, 744171945, 490065820, 625620072, 506716954, 737994685, 357937987, 99869724, 147026068, 336962923, 236456743, 311607542, 560489322, 991508028, 605716349, 140990420, 407378104, 213312586, 82656624, 189463739, 5731979, 140102324, 431902365, 56614957, 294599981, 541502951, 861632250, 311081915, 645273935, 171886367, 690181795, 784649683, 375851590, 252304302, 380304859, 52447602, 73667891, 527609408, 210950139, 791384022, 39393756, 230190173, 769165344, 782191266, 642448806, 833549710, 782531703, 374289096, 83343495, 93592022, 916492590, 42710083, 816936587, 786913724, 197468671, 963577124, 106089943, 769446930, 348920124, 689418796, 364687425, 891842141, 670056239, 255704990, 465712365, 510954833, 317912881, 588164607, 241239926, 256228942, 363091051, 117349979, 106589229, 959879510, 607175617, 750871820, 681895565, 351550441, 987146293, 887609297, 282501485, 898892874, 185450283, 99697056, 30294797, 136598652, 537047867, 550878310, 339901619, 477460868, 10729790, 394685146, 726108357, 943532504, 929009556, 502679933, 869592965, 637974769, 548674695, 719924496, 613167090, 818916069, 245273461, 283623624, 248072197, 656662180, 745586841, 584706763, 731716309, 313320833, 913739400, 487475296, 227995422, 79156108, 652069794, 3172073, 965758713, 919633694, 751077945, 580449469, 241945912, 637564013, 760725186, 563302955, 109183201, 298445679, 713480683, 950042190, 361688964, 297481825, 250583620, 937041551, 624869484, 758598598, 697399595, 1385588, 805460725, 306196234, 419954557, 36557777, 329026922, 40467033, 176964037, 802663755, 15296884, 957896499, 400714248, 216206125, 249878971, 131677032, 72987513, 347455256, 213311662, 30308431, 680771237, 916173334, 53781588, 547932843, 22262943, 263644108, 96670307, 704320194, 163942363, 858654998, 334621594, 918062814, 84251369, 9369413, 19273284, 871556009, 459587124, 263391412, 767864360, 631134034, 73069113, 325136605, 346837401, 762601072, 660648328, 352643281, 750457680, 292033786, 881931661, 753504161, 214175086, 91052730, 886076345, 577362205, 842149426, 637563289, 325997338, 671741851, 170342510, 544542286, 501442092, 152441070, 79428150, 688922994, 716888822, 420040656, 88715784, 842525203, 871990951, 444240926, 682670752, 846093540, 545950739, 412683135, 439541776, 4851908, 950600058, 530207868, 419036588, 36653749, 463591779, 973671187, 921624113, 932912577, 682160478, 851171297, 201861393, 129660461, 38339418, 243967220, 691480732, 890461712, 977903067, 827782698, 357429804, 805718637, 797892456, 332052539, 497155475, 234195235, 340986004, 897086314, 452570302, 215617717, 112285923, 387152042, 668376141, 538434571, 87634957, 171973752, 338488519, 370531032, 429781396, 618623738, 535377288, 244843111, 521919083, 7447394, 334514969, 108824143, 783054035, 245777708, 667372913, 638285106, 252530952, 654646527, 663984502, 857205351, 859467863, 23886735, 165600923, 83920770, 406716563, 711878910, 827448676, 444580221, 324111205, 880239244, 450807840, 277737905, 20893920, 151189533, 531804197, 577840878, 256734677, 342342598, 401725842, 856615115, 654923124, 360324440, 282541394, 664205132, 144335924, 671953863, 316879067, 200159232, 762154536, 519388119, 682213778, 205002054, 97677542, 16796509, 698215181, 77195979, 470190262, 815499275, 313843106, 205668302, 845658570, 723443721, 945832678, 727296173, 371513148, 461334404, 717004840, 100029103, 624152712, 455890673, 897060547, 442157290, 803068423, 109227984, 689108929, 477705957, 400582127, 889817038, 999680862, 874201937, 516920021, 358554849, 575406928, 661804907, 992723925, 392211939, 155268499, 531363776, 331863300, 643297813, 260233764, 232070007, 255729173, 622813264, 352834344, 370242479, 643642, 643660040, 814818480, 996425396, 403995234, 857454812, 46666344, 19524452, 805948940, 952132022, 311048956, 526071714, 770815862, 695587213, 449125589, 787475708, 734082522, 455641403, 625139490, 735204605, 220539184, 130074045, 805806644, 429483844, 499516371, 842408312, 499637766, 856063092, 323933094, 40487406, 773610069, 860899059, 230175531, 549526691, 257940658, 756051940, 621160632, 217437664, 13775178, 862088391, 160700990, 928036891, 501778234, 173606308, 112484109, 584967916, 575138216, 776935528, 425751986, 143279317, 427359312, 577342251, 324032283, 35482446, 848424975, 522258889, 525009391, 741428874, 552132499, 437335882, 253389060, 237601148, 97590597, 500823408, 151714685, 487768801, 408489080, 331860861, 995435458, 249887106, 492665635, 609098539, 388666959, 493833014, 406459155, 403207474, 735913372, 217891377, 137371754, 529956695, 23004729, 902311705, 89196574, 60599627, 373542083, 427288343, 148549200, 210212732, 472007085, 712452021, 972060779, 627571000, 591984325, 551780067, 34464828, 991232620, 366971725, 622709300, 668622028, 500625283, 384917104, 394013513, 920899262, 440731629, 217838160, 871869566, 185156805, 541026408, 867420795, 6620250, 711649462, 742522548, 646115660, 539204740, 573538416, 924798055, 994665597, 414773757, 572111570, 154909645, 413314785, 329315869, 591865914, 254116729, 56676250, 628665844, 107387630, 778249699, 542685621, 516878647, 484105992, 998041013, 192711184, 99460992, 557352849, 494861291, 336966251, 584300089, 946080491, 359877482, 972906416, 768483523, 74293108, 709894029, 660015618, 514256810, 134588350, 674146954, 298526818, 122889682, 851486380, 436397841, 41537415, 721956612, 685157069, 971467668, 923922426, 857365148, 159527789, 735423586, 309475237, 283276752, 361449606, 923872419, 804072893, 12703812, 917624553, 258859398, 417007768, 515926605, 426611673, 293191967, 116757510, 372424866, 356599821, 87802494, 723876547, 853946071, 698048166, 407514682, 381346139, 370148448, 208860644, 661972270, 7631392, 255375050, 627543215, 639909695, 953910083, 723914217, 671932709, 137095411, 258020750, 117282674, 956834540, 458802237, 256413569, 34218426, 887315476, 84579637, 443096283, 133835676, 407074992, 294381781, 978005474, 683160004, 956086699, 388277870, 670806584, 725666613, 510941979, 123288378, 106437580, 187898241, 535899836, 63837225, 238681181, 488358639, 837266185, 473745047, 566331135, 227938069, 159446756, 624867784, 778505295, 271745746, 843044456, 434901823, 779570320, 861385738, 484933786, 426269642, 342902819, 362223435, 578998592, 409247285, 737617979, 97927684, 859137900, 712375937, 509775710, 935219591, 270807157, 223523183, 128541079, 145995033, 128679164, 343098737, 810411899, 226760522, 272469946, 670666023, 337984609, 171962628, 443043876, 596234885, 167380992, 791325717, 357548777, 245978250, 432603290, 645531952, 893757789, 206829590, 785225367, 848089920, 666000362, 548118134, 735182591, 691479391, 756163493, 214493644, 281639567, 799388086, 742784703, 861699740, 923527420, 370382526, 626243493, 499012837, 842969844, 945654928, 803306724, 970146945, 180473430, 525461115, 867098302, 814334512, 17950786, 531283545, 586952674, 457828710, 6303463, 179573409, 119180585, 133545076, 882779623, 876922109, 939992692, 76367727, 46392593, 136748952, 437952891, 803326925, 724603842, 408884911, 629181773, 735422731, 775936934, 511686925, 339432922, 71980793, 92337480, 936459234, 172596610, 331125628, 846052132, 971661733, 222513475, 874646556, 733211487, 493533347, 916661983, 6234298, 426953771, 930437366, 310069624, 572772580, 468658316, 831326858, 17807353, 268832964, 800766245, 797680061, 451947165, 629552296, 484098778, 682233184, 783032231, 522497756, 333201045, 430030824, 869674954, 934405129, 353695631, 408523480, 42120626, 850286753, 635120488, 173418809, 55090537, 221966138, 53640771, 594729034, 690454273, 720902570, 613905479, 911155794, 499125460, 830506043, 717559942, 857982224, 177852420, 752002100, 672092476, 111452721, 750504363, 625813062, 134135546, 486770612, 487178704, 172857836, 228962956, 510382936, 28869933, 135047273, 123603613, 618821730, 836614346, 562284171, 669390851, 258429715, 111618682, 907647146, 55868476, 692294543, 266144336, 805531912, 823281732, 178395080, 947546472, 719310330, 882464072, 423253260, 489904736, 747775470, 308013537, 18067916, 804613582, 657161369, 476710557, 972721949, 166791831, 77788604, 910287421, 73806271, 904825609, 65726586, 833275190, 314070097, 776612819, 673105969, 128028511, 141038747, 502908002, 216261632, 437761987, 281613477, 240661756, 629547358, 310382054, 813395932, 25106105, 459484006, 772017673, 819185806, 799343864, 290217771, 530642280, 446170254, 86880299, 494090809, 5529173, 59037265, 722181576, 474054662, 890388297, 187603474, 708631987, 296634762, 323732703, 441510474, 531925395, 413667481, 8130239, 82949621, 122254017, 505703677, 173826147, 652211269, 224882654, 744691815, 111489527, 393158505, 312587464, 308556464, 730094442, 204851902, 436127127, 645218235, 808751948, 873664179, 57399696, 339589318, 74862241, 517766174, 717226417, 518470300, 418418262, 184289171, 947307320, 291737747, 319095893, 759875535, 765951477, 908772535, 501345951, 90518298, 451696862, 434509180, 109570056, 342134865, 578469742, 636132282, 24917896, 950996074, 222104618, 186442741, 602743056, 619172466, 389518718, 134794099, 519401811, 569068839, 504226539, 827578595, 122380983, 906308778, 187114948, 668064372, 683272235, 31323124, 19054753, 973413119, 140659418, 371591845, 85452784, 635741625, 820566074, 522855192, 373678247, 299441975, 760643921, 292545509, 421738045, 634784980, 967750348, 526220142, 785495639, 483508149, 912652588, 67214985, 310952145, 248780061, 161554277, 311733629, 733489223, 307554410, 227423316, 416116587, 410475564, 288850260, 733833234, 451493567, 990627054, 500407468, 678537361, 255554749, 715888460, 252194861, 909408253, 860631398, 64874418, 878022956, 724825210, 954738995, 439348997, 831597143, 454922377, 212654997, 759570, 723311351, 131197009, 664606273, 895365655, 157510762, 775378642, 114524747, 370252969, 569455678, 517036829, 885017461, 866212222, 717798387, 479731361, 92276538, 741333894, 995355301, 451379494, 882088419, 705279707, 217021834, 116753174, 469282918, 294399813, 48194704, 15307114, 555296817, 149986660, 988378941, 326012774, 987107498, 154821470, 897937775, 360215862, 523867796, 515805536, 992915995, 504190684, 278883547, 267133893, 611220371, 626162839, 289214463, 207263544, 21921778, 920850022, 454415038, 109756135, 699877872, 697116451, 401911980, 777032384, 985452430, 382089998, 138462226, 989307716, 286610409, 701863534, 272441664, 474857990, 903139143, 667779314, 71136163, 816509900, 775846007, 677444449, 325479799, 338661137, 781499098, 872121463, 892227029, 130849340, 903290512, 551229024, 835050421, 925955070, 162960301, 705799242, 758872074, 489660366, 480135656, 538751334, 521528696, 396996424, 839910942, 963233502, 324738329, 559067898, 655057954, 812265702, 53950299, 599022071, 726775209, 739666441, 385263780, 875426269, 349448739, 292939654, 740813083, 763017916, 966610396, 235396534, 345953253, 21122814, 152347089, 281145934, 451233673, 915769204, 222249966, 663202679, 767985340, 171098894, 883058722, 880418520, 733343915, 288507051, 853643356, 125523625, 525155198, 597991, 303719826, 740239895, 284708958, 992343595, 91881470, 298016169, 350384620, 359213832, 697549611, 944174670, 552275067, 810661269, 882244626, 614146217, 464310826, 261819603, 411901237, 381011098, 700256932, 39975463, 725630177, 771044779, 472725591, 48442435, 739904486, 434255617, 26881058, 727070626, 989782361, 959544863, 841092477, 783693910, 846552889, 4971498, 649132079, 912347877, 421656595, 865071251, 302100273, 379708133, 602958695, 915263198, 930383775, 216864065, 93430322, 69430195, 356915364, 850018899, 240905838, 314408532, 131906928, 702117465, 88415019, 701965936, 336837718, 210940720, 701964121, 695379034, 991094537, 562792449, 27322845, 962950752, 272287919, 897985566, 432304440, 576567349, 905712256, 431716057, 387607587, 691748730, 707612389, 508209647, 38044283, 233804943, 7626539, 336354874, 753389637, 806882826, 115198018, 898017994, 405643696, 680486528, 618520395, 277887238, 626974844, 312116083, 853862213, 818073820, 774711033, 464849194, 964438463, 40501391, 537224568, 6022963, 900721565, 216681209, 745418864, 522296151, 785134800, 983221473, 944163245, 838108835, 217688309, 731234913, 96702736, 119771112, 95717056, 295197810, 344753144, 259736236, 560061377, 774148425, 989732269, 195570326, 321622502, 693526359, 321102851, 54817321, 754864168, 538599992, 320395341, 632494815, 383976558, 455957246, 621703228, 209621412, 452001247, 410792984, 771858854, 825721751, 7906944, 197009266, 777964645, 542078297, 663280456, 577087983, 642068517, 559654110, 486229459, 788516331, 497690196, 254306652, 645524793, 645894391, 662575747, 656472683, 21752048, 661880902, 861346874, 442194253, 906291022, 244766293, 712383311, 939911139, 938221742, 522341582, 340443487, 884121741, 222124929, 594794702, 699422441, 620599897, 946520662, 403085482, 919405131, 990824065, 967217835, 950773349, 127642454, 622330563, 89626190, 729536034, 694830010, 353261694, 956002349, 195367552, 572798073, 741149140, 726082262, 729994675, 313532900, 246802923, 737618489, 746522255, 493381615, 812640286, 815385220, 422902891, 44470188, 140303431, 517009008, 830664058, 87393405, 121940457, 80538188, 239846785, 39284265, 359250248, 359317437, 533759100, 667837736, 820122622, 333959643, 997504658, 901740026, 571006131, 145853815, 176517262, 420160662, 29299797, 729392233, 161524156, 597633823, 239435335, 597868529, 460542119, 361117790, 319155827, 121360617, 536868982, 462210240, 429589411, 78449619, 113035797, 99602065, 19138309, 209802369, 195102206, 268023867, 201721637, 777522735, 407015514, 164074996, 724955725, 618351933, 914455767, 538314180, 691917778, 258874392, 399758611, 241304507, 187200022, 310795325, 190987541, 81126699, 572935573, 131085516, 319180750, 56379446, 873339119, 172205536, 219619010, 104801832, 632696598, 818793892, 521927635, 610924859, 563932571, 106914467, 47369864, 51392109, 286628834, 415527984, 474546165, 404538676, 719722748, 680183541, 107451518, 910764238, 356293529, 211900596, 683936545, 436701331, 700305542, 721765147, 956127743, 962090723, 400095954, 473305511, 730976536, 579156990, 548245596, 319729880, 22006638, 631146282, 534409814, 518966614, 707692314, 162463571, 461586460, 638667896, 534769546, 483942380, 391779352, 542697086, 670333620, 54276904, 684068150, 982538689, 832691929, 938043726, 986811857, 76932318, 404429816, 243678551, 834215626, 154186605, 854971665, 672247517, 793173783, 873179570, 490534907, 494871306, 490491941, 824664384, 68612686, 856603846, 663752611, 603851212, 142143587, 647084914, 820937700, 393535803, 563712680, 751352907, 866554800, 746512419, 818642943, 746130168, 147131514, 720611436, 895140563, 701608295, 761698125, 419364201, 38622472, 635250190, 812079944, 528170346, 796742183, 629000690, 840930530, 990755987, 225717945, 6096473, 107166464, 587159469, 940452748, 683502454, 284718220, 638888120, 986823629, 424621738, 286002502, 923886755, 837601440, 436479720, 883321931, 212400077, 84343811, 594433398, 232602972, 411706845, 58239013, 960124222, 715270869, 337439664, 851855818, 146467174, 733838816, 86933039, 857499178, 94926064, 421682230, 633202201, 586448668, 270788634, 885799901, 267143807, 284771917, 623054728, 819852752, 322668552, 472630841, 126023343, 733512885, 57006572, 472185220, 848916436, 586372736, 140586999, 100798050, 727668954, 304781355, 18286096, 83688457, 855581148, 276643748, 555591199, 75193990, 220356710, 484516442, 487322364, 232321239, 314409304, 424888664, 444855104, 718014097, 295878006, 507162235, 145459265, 108303652, 492402948, 831914635, 110040502, 325976105, 285040187, 861443256, 186388050, 794170164, 735769834, 853375164, 899352049, 184897007, 51207762, 389041049, 668719878, 491722806, 672050722, 225539449, 48370819, 778965215, 761196731, 564448201, 287102539, 991518446, 555709102, 238514273, 126468640, 346637080, 640342, 876255496, 227778411, 887086122, 951642312, 658383965, 387567857, 701017358, 96133025, 526442193, 39363286, 654843532, 932019066, 52791620, 289899806, 132492939, 378474892, 853108611, 10536789, 887354348, 100392780, 29172133, 964463816, 941380131, 372593929, 328685842, 514932337, 239580185, 582771077, 188679585, 244314258, 883214, 882029049, 136229142, 440181293, 659684598, 345207451, 209837013, 165831311, 367539369, 510946714, 97264874, 84792435, 489421617, 947876694, 345981841, 814750774, 498751363, 509812584, 176056844, 199384022, 377438809, 71734298, 458550537, 162216822, 846234563, 32083519, 561540687, 271450347, 573760913, 23054491, 486551866, 708176113, 545054940, 730303868, 946752911, 898097592, 801980503, 193803535, 738062025, 132249392, 845013165, 89245132, 836561109, 836684708, 87722634, 823059794, 376055479, 436437778, 950371137, 479754188, 440570680, 368434694, 355851500, 417129157, 333004439, 875606246, 128827282, 905861252, 749464542, 976692161, 856737283, 224337812, 321595139, 971014074, 388952801, 537116131, 650509354, 282507516, 775063621, 211766803, 677911548, 924028240, 205277205, 889867325, 857192005, 96214936, 639575729, 177223155, 860484440, 645789872, 588959811, 465008050, 649468058, 12783376, 49565888, 377503550, 704130162, 752625437, 36333350, 134600366, 647579316, 827565862, 788096689, 495749788, 790383012, 66298270, 80186741, 701730185, 476827737, 344290233, 423828995, 734071423, 747509500, 968434707, 229471079, 866633212, 755426237, 396775694, 762479393, 924205838, 893388905, 374315730, 937381609, 946789913, 22422793, 598209905, 441381147, 100508387, 420209568, 493380103, 538598814, 410706676, 857254058, 823212159, 281271258, 124595404, 794941896, 225709888, 133894881, 202094706, 779551548, 36687403, 343002359, 202938297, 47845821, 439497238, 113534549, 993836179, 381605869, 38287682, 638144034, 384961915, 625952374, 895803110, 939552350, 931989380, 594756238, 86896043, 4476371, 200620444, 273381922, 515198858, 967516245, 344172438, 669670402, 593484157, 938208898, 660610991, 183374408, 999869451, 838880333, 114368650, 438722497, 169685040, 398284527, 296928632, 266426420, 712039823, 570349110, 805392418, 953868370, 834566154, 93927377, 18654787, 931358769, 608415607, 893858812, 875978175, 987823105, 622060480, 387840395, 444764206, 840340618, 821888958, 948029829, 764348226, 856915849, 660607827, 711365348, 249888296, 459931212, 631587405, 887995022, 262605203, 126390792, 378891836, 718555690, 11387043, 524791519, 912584618, 986664869, 855133424, 986137719, 814660128, 712348464, 773543533, 199784558, 453624286, 823724949, 654197057, 575805209, 22465468, 560351200, 934205288, 902646505, 598710569, 102963922, 108726978, 133179127, 731774159, 30999031, 14608324, 217960601, 567814349, 86840009, 410544741, 556072815, 726372795, 740142077, 768395414, 485795606, 662145899, 566973373, 324023470, 984424679, 571551177, 754189879, 509539432, 370381635, 12221226, 342618407, 588241548, 128470319, 787298456, 142142554, 771519326, 531906079, 606219804, 699919029, 790896276, 163628536, 131916199, 131582796, 551725110, 162756141, 323012598, 710406341, 831649752, 824110803, 200001609, 473065974, 118626445, 715344412, 395919787, 554460369, 556583161, 236370746, 173144909, 643915931, 24822291, 558466471, 129206596, 859204679, 886078021, 904196308, 848492402, 765262631, 399193745, 779369707, 899540028, 107366087, 896288149, 989716692, 458470929, 591824917, 171639004, 816235581, 410501137, 10328734, 258508522, 258928093, 987835603, 82622933, 37251170, 710768498, 327060689, 604132067, 744821382, 182543560, 701211587, 784440865, 872099873, 728661974, 756055088, 895123637, 583502856, 154135621, 375846676, 929700577, 195312775, 836243218, 893402969, 499316964, 384331403, 91739242, 230511450, 234908546, 951194191, 685463719, 672369015, 8591732, 421606504, 994164273, 231642760, 739183363, 291333220, 649452581, 325278615, 299816826, 298496222, 331240338, 716064635, 800157801, 924900761, 100002861, 850824126, 251274881, 810573405, 772944834, 387314549, 197129060, 291398181, 437283361, 426709266, 126872501, 256070220, 413878008, 794100285, 541979393, 562577971, 804554804, 858904420, 263995678, 440219778, 840227854, 857836140, 801441747, 330010659, 267679411, 196602178, 914064380, 648797638, 83691150, 973221213, 525930113, 710788644, 588904712, 454568806, 367880697, 734278103, 235244665, 881516791, 63308297, 328311799, 712099517, 640484167, 407757637, 423576467, 198213428, 657369589, 157008730, 694462989, 38016203, 664283743, 566265230, 957552147, 585469781, 878729925, 123283897, 371401540, 353589668, 783681170, 663104433, 380214533, 685206697, 273440283, 594320771, 85957129, 96311794, 875836702, 204154993, 666386391, 715472589, 913017246, 973484183, 574241592, 528617626, 463226868, 588065289, 600858743, 342557678, 396484004, 639677541, 915983874, 396242834, 802236180, 662100045, 994717362, 829359929, 82624681, 359278287, 980231182, 603373215, 782935958, 239455058, 687375205, 345703364, 35271873, 326827742, 542691403, 303286372, 923124583, 232711794, 861915624, 782685470, 443231754, 616253683, 40615286, 382408637, 775481427, 279593697, 334618563, 853367860, 950103033, 863858747, 670946915, 734062146, 990444469, 421594302, 529840467, 401180143, 695600764, 544860842, 614790974, 765564258, 483726591, 842737082, 577368052, 392709369, 204395246, 549502105, 305667103, 158963730, 893378081, 58789146, 310625959, 499555778, 93587, 574765447, 671214934, 510997651, 267576315, 16363114, 353452381, 318290623, 935422310, 990033076, 367697743, 206472232, 765782274, 174010513, 403849897, 85032655, 631339718, 315373280, 710924405, 640007919, 813317471, 669341530, 135270586, 27307807, 409610407, 886372765, 244880853, 635611423, 332734445, 121579684, 398985077, 814386065, 850271684, 983882324, 3113426, 748030310, 324921381, 122959497, 280005488, 425363359, 29459623, 111319179, 10207115, 558634318, 683913364, 841138938, 632234357, 249857093, 923951877, 362530454, 13774722, 699741895, 272465161, 973591919, 759784245, 75535176, 477486088, 582484229, 817467152, 564487475, 622520423, 603779404, 771109959, 27467153, 636290716, 823043340, 875427909, 418298615, 723236483, 72724371, 81905821, 793670717, 80101737, 503839691, 620046967, 508915286, 930557011, 723991493, 748542756, 393109702, 167755067, 428292515, 969108653, 464656327, 162961498, 303433350, 75208470, 407453106, 853502034, 875066993, 296100677, 777780093, 437372145, 924434051, 496902231, 102145325, 745480032, 553119587, 409946069, 348286530, 945847267, 541433023, 555134290, 249295696, 354599092, 148276785, 427132965, 747835349, 169595789, 961791109, 849728251, 668601919, 297300702, 506122006, 377228176, 901899043, 736088603, 687100763, 797502091, 63248853, 95293009, 248019177, 56897017, 32918564, 658306706, 321266059, 982220756, 332594198, 232946594, 464214519, 850548580, 642831215, 488088741, 973109032, 333728429, 86837813, 204155692, 99035314, 289403700, 617798760, 867292180, 401633552, 10632021, 395255280, 706904397, 445627590, 221611275, 732963760, 692262107, 685086818, 534556438, 415244651, 911783420, 990334226, 322811485, 781278460, 847438890, 500173071, 958723401, 819251475, 560830353, 112270609, 252806452, 186938096, 584463321, 276773482, 134538236, 17648178, 439351309, 147192221, 216621940, 936112052, 278339961, 32947708, 39039732, 278324860, 271558070, 754528190, 517773187, 792034230, 957275304, 24327563, 804601988, 983883678, 851433097, 536650674, 170055632, 389731590, 890049220, 744001240, 211412551, 948400959, 705431614, 564351180, 283841338, 775637162, 316498145, 140443180, 626558016, 700063619, 528065930, 765119219, 34570267, 36300001, 804044889, 418247823, 800837613, 632648533, 881901307, 102088175, 439124161, 216603347, 213459302, 22418429, 293020113, 772818769, 632749761, 12919466, 613498789, 962722463, 34761328, 261989538, 914102928, 963111010, 976672026, 968699190, 412451737, 342100374, 774461202, 405722125, 820147651, 923945413, 878990251, 840979183, 101722750, 401255939, 264072912, 94987716, 289778809, 668898693, 116779991, 907669464, 428226916, 244306465, 135796586, 322135415, 771292865, 475976687, 474146964, 178565543, 915054248, 88479425, 196138115, 645579002, 426508394, 311937265, 1633321, 548012166, 938555654, 143060254, 558332504, 65239750, 106784502, 360948834, 759828407, 816675686, 243295912, 885847243, 384693362, 879762178, 918540178, 98439086, 493871618, 723796105, 567832412, 141891609, 712901035, 579161618, 378623324, 677622264, 458535377, 367843870, 613453594, 364666621, 508929549, 190109504, 103126716, 406873840, 710221469, 569007468, 632388642, 415583820, 512922108, 337560010, 238585124, 481503504, 197800144, 949547444, 438926075, 181903280, 352515548, 987197422, 741903900, 723255722, 2877815, 528549205, 253181555, 957453774, 976059202, 676526638, 99427773, 730067617, 826489985, 419985441, 993960862, 889003320, 143687818, 130326880, 860958948, 9531557, 72293840, 689443177, 650946846, 361514173, 329036014, 917344491, 985959228, 352715460, 796313073, 821889896, 308955665, 464672140, 209084846, 241899601, 998539171, 98412887, 251424471, 468111615, 320010255, 609068161, 494015543, 137704139, 193417614, 875643299, 439235546, 321759095, 651253897, 29895155, 33827110, 202891541, 175584663, 843457348, 823919403, 621105621, 708796051, 73063292, 647111168, 752337850, 764854109, 232573403, 956840575, 197859504, 687414367, 262838322, 255739363, 543681389, 848006483, 716450898, 267196919, 921445195, 849639244, 908285621, 670001007, 380988952, 231364478, 293366893, 213770150, 126724603, 333464015, 945020444, 3096392, 765322298, 437165816, 982022454, 398670322, 260441940, 62744703, 13844313, 302556302, 902227738, 597992339, 692820955, 828503622, 24136669, 437260131, 165061996, 27821333, 611061557, 115770802, 807628609, 147138930, 966818012, 363401728, 989362491, 141653290, 756624585, 405880717, 787045487, 130113089, 247018620, 816505780, 737978909, 138336556, 19717666, 851511778, 160656185, 743001292, 673580770, 832978922, 11679580, 841551469, 73567220, 264905736, 410986849, 46768355, 642265346, 513821785, 303874330, 900319389, 956699296, 413136022, 366058272, 346302727, 600987145, 50896235, 82482047, 612744378, 823383903, 535600152, 714443084, 616206374, 82818359, 538416320, 61124843, 41823917, 208399872, 356909220, 129307256, 620653895, 923422236, 944595885, 341513983, 311645837, 815635289, 870990779, 700688754, 647033435, 570441673, 663758090, 665375270, 360631941, 645749245, 915737500, 470170472, 644878331, 132805531, 38635541, 964505155, 637535879, 871247824, 766945008, 643863409, 808325863, 227118845, 932255828, 943329173, 567995345, 481130098, 559543763, 363635008, 290771177, 385652410, 756996880, 25810468, 179334639, 74200409, 910058875, 588965933, 199050458, 670859976, 106777387, 258540389, 849411233, 902123762, 322943576, 954663564, 678372921, 387818349, 24530465, 134111767, 827319103, 401353590, 121266292, 858090697, 235170497, 843634116, 372269721, 141622814, 142626893, 553812724, 711642722, 676524264, 982213974, 652356647, 429837371, 952839867, 898578837, 773589495, 485405977, 307833730, 830424506, 416437242, 324420751, 648010923, 97165472, 727812363, 635612863, 223724830, 928122200, 437044460, 19049119, 624502997, 220946006, 679294013, 759692275, 189451026, 829035054, 188725819, 389567777, 61574997, 456002731, 773435353, 240449927, 972808418, 440971660, 767437680, 112245054, 864677117, 760122107, 656037047, 203076124, 550222476, 8715494, 712745129, 126585446, 361142130, 781688257, 729539971, 868681643, 86902866, 886040633, 91528540, 493082944, 691102501, 524577136, 204392477, 433056474, 74459052, 794147767, 613278827, 69520917, 935990524, 956540907, 956950731, 961084876, 142346982, 868203937, 39915912, 866668509, 302501964, 550108044, 417345932, 835547681, 10574508, 286723556, 118226749, 213298184, 459442082, 493577317, 183184897, 13183631, 749965073, 16082113, 704078635, 297181893, 379138617, 207359536, 826645876, 160821168, 206549932, 213413447, 762206029, 794330097, 805900423, 791875535, 851788657, 473369390, 5019590, 766933340, 592408319, 503886946, 273695337, 130022626, 234453069, 581380037, 785596724, 461851245, 941518314, 146726985, 764940696, 721439023, 596489130, 825889273, 305366197, 241803410, 416147553, 953247016, 711594447, 449543843, 798036064, 192023192, 161693853, 431053120, 144989949, 232887852, 93338230, 928517143, 227351087, 871685720, 875674283, 957396949, 768920881, 873353714, 260103103, 589874921, 413934249, 175884174, 148648425, 249357998, 883112264, 402875393, 199454803, 894615630, 729249012, 926116502, 309860028, 532011155, 583013444, 586875001, 204813871, 301522698, 732717169, 993064903, 759209899, 479643634, 631481496, 234715512, 180084174, 608959402, 124290661, 730828788, 971644280, 868303749, 494584497, 899957718, 832301033, 224459849, 599465199, 474852188, 772018238, 708442134, 311090502, 249904010, 915425304, 702722924, 703392253, 766122909, 671059791, 733426629, 603952706, 536633193, 234839651, 572606725, 265366205, 89410873, 891504482, 177470507, 420368832, 830226339, 43701758, 10436046, 741302837, 660793760, 711123687, 866107266, 466192773, 696571436, 383649299, 253162522, 846658159, 61824447, 678542978, 774230302, 369452187, 106245723, 235179563, 899912525, 657775133, 494999314, 250197993, 8780966, 473470138, 832921224, 664701193, 256885685, 597427809, 434829006, 952107675, 619632964, 614730157, 21508788, 222286935, 669595047, 22492463, 33480479, 140641744, 162815769, 418484294, 540957252, 113067229, 771625998, 247335022, 618158390, 565959167, 566093190, 962413993, 438517582, 88101480, 94805432, 177350721, 789018538, 869721448, 636065980, 76491972, 526307758, 100116781, 564268252, 925456733, 206926031, 40117869, 567721441, 284129189, 595575218, 443113646, 331726952, 718368293, 626802014, 124245225, 438574704, 719213003, 186849335, 539673806, 843446924, 735758066, 682278629, 137731194, 377169539, 609136298, 793100953, 981360811, 666133274, 30994236, 28842307, 207178577, 596341800, 819841326, 9488778, 245407971, 657787493, 227895910, 945607323, 532889052, 294940995, 774757815, 552725875, 281147851, 8220609, 714020570, 827675104, 200957306, 70800236, 615154244, 214123452, 413607831, 435556643, 918856749, 590391206, 884421150, 935271868, 805484798, 759989465, 351776455, 396635311, 315833226, 75761736, 233800131, 882040674, 595215391, 340483382, 94784085, 119781751, 982980471, 342494288, 471055246, 659487834, 159911711, 997905463, 118342457, 566877198, 813572085, 972898879, 101564965, 855611308, 811558467, 191082073, 698938287, 469590044, 237550595, 425138348, 857880945, 328845580, 709700434, 885793286, 776214353, 884264611, 581974400, 845060807, 648611268, 228545752, 384310795, 51851221, 601950025, 233179272, 13972242, 380141707, 6161991, 729817051, 468968682, 262923971, 344768907, 808731440, 312272615, 791053049, 928026969, 270430627, 613410777, 297116191, 934872535, 614359616, 351748332, 34841598, 204096049, 248818011, 483627223, 686981747, 64851789, 30355940, 107340628, 713492991, 475945043, 943762379, 51470488, 274617816, 918434326, 967539906, 9960391, 647096709, 870671695, 284036824, 195256249, 802360310, 758747265, 84409471, 472091497, 845021082, 746556848, 494710543, 3183234, 337465251, 145568610, 130817388, 386011207, 502690292, 323753213, 317727037, 759213248, 221248475, 495444814, 973506433, 617391151, 53292746, 381593192, 385035739, 138361640, 939912136, 362747712, 319290219, 51632964, 351333241, 99398118, 64384543, 636796185, 825476017, 611703624, 329523055, 888972273, 142454668, 873213030, 564501373, 238274389, 886622760, 991038296, 471327572, 288673186, 164481026, 294313334, 174631922, 958015244, 727784516, 355093404, 222039741, 676260336, 361087302, 560050763, 902797717, 306106009, 699868183, 169561723, 800517245, 152145578, 284015561, 532140528, 972681274, 369044568, 486320429, 820085736, 868329339, 708301963, 340712138, 853232939, 154792383, 355141670, 205267283, 98767705, 166824770, 794836594, 784388300, 317787271, 449795530, 606270852, 676811270, 355100151, 675298964, 319932367, 3979637, 5703240, 52575838, 915175672, 514124531, 996131467, 760613483, 721904279, 344509203, 437366028, 750455012, 281392524, 122965627, 626806845, 660931454, 566092012, 160922470, 749171113, 584572733, 706287283, 317791907, 938848431, 19507816, 970678483, 229685118, 338407941, 345991741, 575385466, 321273206, 316449194, 967226837, 977508451, 518490768, 182401862, 414633146, 103831885, 286116213, 773170122, 979220704, 11668335, 116695346, 86406546, 876782082, 199170765, 310740665, 278652891, 76505865, 293591316, 97037405, 549369903, 416482327, 261746564, 751983301, 756217620, 691186984, 481440632, 359117273, 529813237, 212074815, 691873855, 196125323, 620577542, 594993428, 85274947, 709315039, 104293799, 52975829, 510720081, 394840919, 676048279, 644848292, 554980997, 580477762, 551079875, 229456353, 201801700, 37075847, 220811838, 572215069, 328594004, 691211279, 405920547, 668397732, 418068789, 660843325, 493885415, 435894513, 969861602, 587040858, 562180335, 883320047, 692110642, 836093524, 118919332, 532099825, 123002159, 748456994, 729855077, 485600793, 85739305, 106760944, 91573169, 182478393, 853471073, 96057820, 501608503, 100481816, 343452486, 987012275, 238280583, 796046819, 6799607, 351452566, 588850020, 840476369, 759970958, 113986758, 495724605, 762562777, 425528197, 376366658, 484617777, 337729756, 191588987, 68687597, 331526091, 83320812, 532064120, 125128897, 3043667, 543082567, 79777788, 130927166, 739478821, 138865336, 806975536, 138621330, 251565828, 439436118, 414009063, 166433384, 817531892, 187550248, 176381894, 59816427, 357001767, 690897445, 822325898, 635222664, 905173951, 449696052, 649724479, 498201941, 935856279, 829801070, 852444469, 566146561, 738151313, 581790790, 942701190, 745594872, 277123073, 688072662, 157919513, 86501526, 596012613, 188910883, 981607915, 396530858, 439997751, 960403243, 933862785, 992635975, 761896074, 778733943, 733474824, 382298750, 779547377, 379295984, 45222728, 793316156, 292535745, 321434795, 488320652, 355626767, 474355426, 622093108, 311376144, 775566901, 178865806, 103696549, 175422751, 399490598, 445605495, 34196418, 625157259, 415083907, 28837441, 839136302, 409548241, 816889953, 78357668, 866365289, 177313005, 840005311, 669068786, 131498735, 889248577, 631128643, 161254128, 666088113, 430687171, 44348150, 209139038, 606488053, 821079442, 348540942, 601287885, 825768861, 954622027, 749958021, 810599834, 998722234, 273289056, 721569461, 238785754, 48413915, 107475657, 739072347, 724892904, 873510742, 329425141, 240430917, 109467417, 847802570, 892853386, 547102090, 710270224, 182221766, 146426304, 368294472, 716696792, 556514132, 668723337, 653381559, 199082178, 926413589, 319010140, 805878740, 210869267, 463671604, 408297125, 934721348, 445715380, 99894889, 737223699, 428463935, 817580614, 875224484, 787391965, 969059647, 718229330, 109746605, 660257825, 878037691, 389395330, 45796366, 358199037, 98054020, 928727027, 168280246, 485224229, 578390674, 142367908, 501718703, 9401630, 116796145, 988017857, 506112986, 306097244, 898470902, 166183458, 768999962, 780785138, 667013109, 814864737, 835818540, 290800018, 106037850, 264023459, 897463435, 628791911, 529694880, 899900375, 663695687, 865946883, 878915422, 485792710, 351826191, 134112359, 878348318, 114712065, 818018079, 968145016, 496178166, 80716071, 938720158, 566898123, 669847307, 230180053, 142757050, 137513344, 53226811, 20442883, 829789748, 449692049, 750068432, 794437590, 324386234, 549335550, 973990640, 783478128, 694706156, 116633977, 668337867, 688446952, 372835633, 226789162, 456869793, 97554850, 893773806, 108074825, 564164181, 178508470, 712227058, 125289244, 994867594, 233853414, 440232357, 84974815, 561533947, 607789403, 120987194, 417569521, 503285453, 10880317, 281345536, 597115486, 192385710, 772715416, 239442142, 164333731, 884807963, 231798682, 672967463, 484726372, 581769052, 586564323, 631756829, 731181998, 764950027, 402703700, 127354818, 470204690, 994846084, 373795026, 92264081, 415204840, 881411154, 977904798, 481984660, 207443873, 88290977, 950900051, 37947971, 69024573, 636782454, 447190373, 178239953, 888687147, 625570485, 585137573, 142329450, 492085560, 298271257, 673314500, 532097678, 260884868, 943687504, 972571729, 748274253, 955841533, 752010386, 544429464, 951772021, 830591353, 498656168, 23263853, 749516158, 12045170, 331089984, 741735061, 428948340, 551381557, 236630221, 793436138, 550313991, 390865276, 340011346, 527426032, 520400887, 468673327, 237000480, 589350680, 214860372, 643224437, 962536790, 488786949, 788388956, 892681727, 506745922, 295887576, 537555350, 132800561, 985322876, 103300972, 71648553, 128547205, 539866012, 70099799, 711579141, 967926941, 339440667, 132252943, 277252463, 148025442, 548108280, 527597617, 42535793, 31258977, 74174931, 109792965, 107037503, 716766791, 485517670, 181700269, 806438393, 746799478, 520764254, 709714724, 211850824, 177713895, 482991363, 694296077, 787738655, 123700616, 311729819, 411112065, 15942643, 201675635, 970738039, 711337880, 159155692, 469675751, 617766105, 147550165, 488578782, 791050391, 432330780, 653785286, 793329611, 531132643, 450496914, 184262969, 332792930, 614932472, 927624316, 124633374, 79527425, 366307659, 299062641, 171374488, 168867464, 379674944, 125155061, 871337818, 240632290, 411568611, 772350020, 750592963, 749319616, 565069890, 596873409, 709234155, 536815400, 558985742, 260377938, 905917260, 193420815, 481324761, 671076974, 517455601, 479289658, 679832852, 963631567, 273197068, 55830928, 632432352, 605895131, 491860438, 485900635, 71047027, 94863671, 264082297, 437028972, 690023867, 916013230, 821676173, 329464422, 559503790, 528307949, 652297852, 758649300, 892475988, 250633016, 285504607, 882110628, 233004761, 214534060, 452952689, 79111233, 381950439, 588641544, 106192636, 892693489, 187673437, 443086879, 758881662, 952773454, 143116686, 846111356, 107535103, 81951122, 223889091, 758998983, 107524525, 497835783, 665148257, 586925035, 878975863, 25850366, 542238778, 952968198, 158374301, 441648776, 337785661, 587089523, 715722050, 796055367, 673200157, 577523035, 611832712, 828975481, 544370092, 545311972, 312832843, 99207442, 602282474, 319879729, 185105916, 177803722, 67049533, 667025608, 809408656, 939976331, 518455271, 904809040, 909163777, 754612459, 160373983, 539181344, 533041126, 832019095, 66527236, 270873372, 683622179, 935625122, 163194853, 289804769, 853451379, 443493417, 542638589, 651252362, 357591241, 159474172, 268992840, 932903171, 705794561, 688001549, 872560209, 290064271, 759346987, 395715810, 321303829, 408703412, 375491319, 600004402, 438041658, 930961556, 828926676, 307982855, 31389777, 337768288, 430021507, 306973005, 693366376, 992207899, 378621963, 836187606, 475799336, 493993922, 433232920, 22991301, 300533101, 465858331, 201933340, 967501590, 936659398, 470005291, 208807234, 663018523, 57414643, 337586488, 431917752, 968501753, 338848254, 230060941, 633477826, 731050864, 132387064, 899959768, 40698516, 776948639, 946753446, 481936211, 728144770, 787422130, 761355720, 259879643, 216203065, 297467818, 661216357, 9655133, 576511025, 563770208, 73597746, 72061578, 315630154, 526733930, 51626417, 496126778, 308193238, 375929374, 760447962, 618653219, 291625441, 329460712, 416581795, 283158260, 870097790, 514614428, 224932116, 962915407, 520351052, 802241052, 966446930, 506214030, 568740636, 716772968, 609103386, 315944256, 164697534, 510395834, 559790206, 79989442, 273490094, 823052610, 534883143, 299458513, 671590556, 968846677, 114676221, 18224900, 409913146, 498825903, 458790035, 230632046, 444947940, 448589158, 992042937, 385322313, 514458127, 97460724, 826972663, 493855246, 578538532, 928061498, 470878808, 440010370, 449345759, 86259978, 964464308, 147277355, 265393078, 40406366, 305638218, 591248296, 997227358, 286771748, 947054646, 443565614, 235324071, 173721889, 729551250, 204423269, 66669347, 977033711, 622285499, 837919406, 88086789, 352159772, 568300910, 661170440, 36651071, 655134502, 623327034, 888665391, 784626895, 651357368, 968678727, 407214940, 157022181, 165376421, 913025949, 797301149, 96788561, 391087087, 396735878, 41689546, 869159650, 453496001, 994736828, 683524301, 849381502, 887063964, 204473051, 977315162, 88961882, 140919961, 256590503, 447965640, 877618327, 30416040, 229674134, 655303579, 85856250, 95005140, 797259698, 249004397, 996526674, 981191427, 731009986, 226998032, 781474124, 898544461, 866610105, 509269067, 124085398, 952045983, 228723176, 588460743, 439147458, 362229570, 709013580, 809855695, 472408892, 185470235, 281079096, 286488182, 295529166, 978547497, 791749480, 704593938, 674028004, 981580788, 303235994, 748995582, 711074575, 86345645, 965270414, 27547641, 25772171, 373472897, 805840741, 277527583, 11831327, 42422636, 701398740, 233588261, 978410427, 164554369, 47865131, 133721005, 510708059, 641925024, 983286568, 539046058, 116898544, 476540228, 559944945, 623606611, 772571542, 78061068, 15366223, 310867771, 347371920, 259695860, 733123941, 32837418, 718390603, 687709109, 841281211, 455890362, 611861241, 841107927, 453578772, 659766434, 388669125, 185685897, 64626587, 882921891, 773756403, 99666528, 145152957, 272017312, 135892933, 601794234, 585770717, 503642500, 960223625, 587203750, 990923919, 681436120, 260005417, 958800543, 754720914, 110348614, 134377837, 376655269, 565988530, 863806482, 78558818, 993357517, 831107832, 280071336, 185298647, 235394731, 204011378, 998289498, 576774641, 946994567, 150068109, 37367480, 282285753, 384493376, 854819010, 944788498, 32302095, 750254343, 791286211, 418755359, 931015041, 342352971, 742201610, 905783633, 420363469, 4991115, 193141038, 27068657, 702536853, 532720851, 142789709, 370713794, 376726309, 926545806, 817657569, 650447622, 684022549, 539800236, 58065255, 345477728, 776882193, 632758844, 715000683, 960942372, 55123402, 505846347, 699373791, 600721036, 463104561, 589187038, 234160992, 451992678, 119803436, 974478951, 204206283, 895776722, 563186693, 681980096, 69732416, 439164784, 688001799, 463271921, 346487707, 377423740, 866886242, 678851010, 862007248, 776044374, 461391060, 125142551, 140973022, 805430945, 525730892, 859475023, 897886216, 651472028, 825375084, 598665292, 853097580, 901562313, 410399347, 642075096, 543093635, 77245170, 192869528, 598924599, 415503235, 720661265, 412693013, 821335728, 839128974, 781163627, 789580782, 974985727, 354875135, 819232642, 893118187, 346619374, 461412383, 344289404, 586236567, 702821076, 473078953, 429846849, 762805954, 49893455, 224680395, 396513429, 510192132, 233235323, 501392058, 989858071, 435783512, 479448738, 62985713, 122126468, 620789000, 136833235, 903248636, 840195464, 32524504, 183103970, 275418129, 647205347, 602763646, 278900140, 761330644, 804103328, 992506708, 297551323, 793957928, 572349507, 410444914, 190728172, 937537627, 420999765, 225144539, 705163560, 465495258, 127354674, 237286619, 671360023, 627810056, 546532556, 58905212, 990738353, 242727664, 638373447, 606581181, 761591539, 294185303, 270869625, 90481830, 383262384, 655866576, 9335057, 380811675, 322038908, 393713075, 164293174, 789988898, 461405725, 497354242, 349621170, 549920952, 849341126, 162402404, 437873678, 389432107, 892786956, 231914373, 639250063, 121730177, 300770611, 434285145, 886959937, 547271706, 102333456, 150322067, 231377278, 964770493, 766583725, 647997915, 700469153, 452995630, 745711142, 173756320, 161550184, 665559220, 856021818, 173304921, 476952055, 172774212, 635850173, 400363240, 192698739, 884855387, 308703269, 365295568, 196650328, 609556517, 560998578, 361631971, 951646424, 345872638, 642529015, 607938633, 838199494, 904845185, 36482177, 298944863, 363880718, 46999042, 426470692, 826430894, 819889370, 862434390, 62734672, 423131112, 216151182, 821484269, 16632260, 269385126, 856329672, 800927349, 862332615, 104697816, 930842509, 601961159, 47274575, 170314276, 515311784, 206878824, 343550671, 135816285, 816335157, 137764313, 628840142, 522811955, 261005298, 461308734, 910308833, 63525632, 554608972, 339567732, 442546316, 298721657, 992204930, 379195182, 359963983, 493486391, 985328959, 919838702, 253039560, 462745421, 569513722, 404011851, 100322754, 920075754, 426436875, 498122370, 97223513, 415008412, 724797092, 193478271, 86062243, 301768862, 587533123, 51115534, 861499068, 983703049, 784053792, 107965203, 544769337, 722285034, 187372124, 43156774, 547312812, 960542199, 963421988, 425074510, 463100934, 148314464, 337252785, 921599176, 478673057, 899831797, 151876917, 326512411, 787934574, 537191618, 260956691, 356818389, 597231775, 213892882, 77089563, 718061716, 331410468, 29554601, 9105137, 910372412, 709082263, 266844064, 900678635, 841506996, 326521650, 882351399, 770668404, 714984351, 436444539, 171759254, 252575292, 949319654, 909871601, 605880418, 178351218, 296041799, 106357159, 11334689, 360388530, 170979566, 786256087, 655949664, 360445653, 825163202, 566144218, 287211844, 294695434, 800707655, 428516566, 82349278, 1513730, 869645462, 195436281, 943863714, 752281156, 890919313, 866217822, 212349232, 427253630, 208713803, 336359734, 650886044, 920727930, 858417103, 683961623, 561330179, 349656121, 996882057, 300383352, 117317432, 454640362, 790691206, 297313562, 338944291, 767195547, 9654694, 190015823, 882228869, 891416296, 711376963, 976563841, 250738925, 436759261, 832081939, 543181505, 12652324, 719578992, 655941169, 659436660, 395170313, 351442570, 790202583, 731529435, 238172120, 594338932, 617660043, 460408671, 793665921, 994692138, 761247825, 424116001, 361105849, 700321100, 389633646, 289292452, 374645850, 842502580, 48777746, 394023122, 283443215, 135640637, 422409135, 536735081, 209084632, 146904954, 258657239, 246344290, 737439395, 79259863, 647897930, 542800681, 293528484, 381851659, 877692189, 571009670, 843000755, 989758612, 599143928, 36277369, 620072705, 259404573, 686741635, 349963357, 200275310, 114853685, 681226069, 109803830, 261868438, 454002732, 646839715, 682927492, 455306351, 493202348, 481496718, 153003614, 257596610, 996475951, 358975743, 725075683, 367695390, 883608302, 473338961, 793006975, 576793504, 479730315, 671868995, 85174998, 669373197, 745066312, 301774371, 226903028, 440161265, 318348463, 289318170, 825613355, 981822670, 940935570, 420254866, 808798797, 374734765, 135526773, 185955919, 543077507, 36330248, 769778638, 761991095, 700328672, 907597735, 783075756, 814955543, 746117199, 995856594, 570633959, 611839280, 202882714, 679503710, 640668580, 780963218, 659747276, 346554419, 729907514, 503526684, 247620542, 502072449, 843447899, 251076614, 397535719, 707760528, 634713947, 348309511, 447838947, 714146092, 251135610, 729102283, 18067815, 845286182, 359024970, 444782805, 422288216, 550496408, 803372316, 308246837, 355539913, 425527065, 947069928, 591455399, 853912383, 697373399, 166260254, 575797622, 217030224, 713066950, 793828310, 313509278, 646781504, 921316841, 8288238, 78063613, 831021910, 257911749, 550734454, 862089265, 862702103, 509941772, 226365566, 81075519, 908500265, 193143978, 100934664, 60850665, 429104473, 14036086, 548732957, 276309549, 713750240, 692527920, 452458673, 97675723, 673013692, 6146452, 905913219, 699594741, 974475712, 743018215, 730449488, 961310274, 755357870, 582246469, 486064033, 873883950, 884958852, 712636477, 883527129, 793279214, 530233455, 212457632, 903681041, 989593713, 724201519, 709139499, 14766469, 188964355, 849178637, 902053305, 701293319, 169337026, 121551527, 866421801, 634296725, 563293153, 454195523, 608490619, 754649756, 960211167, 522917556, 455008773, 446212943, 704632127, 554818515, 732672658, 818154443, 647812258, 588453321, 872764781, 727394109, 282827928, 907152596, 381581635, 32836953, 291831822, 681416378, 296565197, 650236529, 978506961, 237628279, 442049718, 859018214, 252358072, 19876323, 655059675, 701937045, 775517730, 964790471, 640241971, 472900153, 249388588, 812469604, 541292630, 415977102, 399392757, 904835592, 800958124, 60534654, 257488042, 997491158, 915399565, 285839767, 437477008, 827916407, 418262054, 673397142, 640265141, 781465715, 139353327, 106911151, 989059545, 561937884, 879036536, 926432405, 479330104, 919880512, 650683500, 478610431, 560986366, 347376401, 637737146, 110953912, 857457337, 391764005, 976494687, 632660308, 921024647, 985147545, 636701795, 4489000, 65188949, 921673201, 697821131, 193526773, 917321933, 374797665, 962592992, 314887041, 433299954, 72500135, 887845758, 773526180, 936863473, 514968656, 212986168, 730847123, 376314381, 131542803, 713358820, 522011894, 422673631, 468838859, 530578164, 810746699, 643115407, 372210472, 624411881, 117286810, 771604716, 924416241, 220238837, 349856478, 440785215, 985488396, 796737453, 937270615, 57490506, 992743045, 431529498, 25676287, 846286374, 258031104, 539332299, 762350153, 203636094, 475776338, 704518567, 785979519, 840692764, 701922991, 575640950, 816079493, 658558077, 824664782, 414969191, 626327027, 882497385, 744751338, 811309754, 835032097, 804306609, 346484802, 819908136, 51360072, 87936829, 588813229, 571237463, 756279621, 131197148, 196761212, 586682185, 777570896, 186068422, 319696880, 426982428, 323161637, 817768454, 803601574, 814114087, 760613951, 233464055, 575289907, 124373489, 612136104, 100253413, 916600497, 532456812, 733030908, 832138447, 472130089, 724950915, 809230764, 229336617, 274063025, 346103744, 243170533, 388581795, 392737952, 984034038, 357635065, 9644038, 114883469, 187976818, 479635105, 192000579, 816608600, 309759489, 516049677, 667867321, 162740867, 586000593, 713242969, 490288711, 113558043, 970027878, 546386683, 425104968, 830682868, 76348024, 423881816, 415558711, 586549647, 145607826, 446738210, 984555781, 418336243, 439803557, 953391141, 488068154, 442422728, 150678321, 936208413, 224578758, 744301545, 140495320, 602881523, 334067954, 641562607, 938611891, 513144912, 41309900, 351562871, 317234065, 405119269, 902669073, 682756809, 461441405, 694558494, 627628275, 83560412, 517927837, 544366983, 112638806, 147355817, 732916880, 674361358, 326588048, 8922707, 957299214, 907198454, 309397959, 654217650, 704702046, 593023276, 919753245, 404575443, 838703436, 522698415, 106366518, 815029104, 380621314, 166070346, 848089860, 463299859, 686272355, 980518510, 462476509, 98838868, 771595022, 453174862, 317787366, 764404114, 619312369, 19457529, 191377603, 891874126, 82769594, 180226081, 800036338, 906534633, 583793729, 363317607, 394382778, 447663748, 425004675, 364430327, 890696254, 79757751, 725704926, 736719711, 757565609, 186115226, 89098457, 815289899, 936360444, 654495069, 974495081, 361733252, 878963864, 872293285, 871684325, 614025500, 966245100, 119971411, 561973374, 11795220, 160799619, 990752739, 306781904, 388342988, 700247036, 374388718, 80284970, 775341312, 48675002, 656912707, 42215521, 35763230, 694491618, 660880833, 291809634, 95554624, 264812750, 880006076, 869295036, 975623734, 642447063, 280372307, 508095761, 10302984, 155723628, 99458798, 654875014, 955316325, 275374975, 261430872, 808243975, 549345266, 607460048, 684560573, 636205339, 118910603, 222455587, 106590478, 126315663, 54763351, 653437449, 745268422, 688171473, 861926298, 677638171, 512642654, 666219366, 633893230, 942983131, 680324129, 318696854, 996835557, 985208111, 675908767, 245787446, 372585731, 831356740, 885218192, 536926778, 843440502, 707433562, 562101548, 760792649, 111288202, 141245921, 694139806, 221762693, 555819791, 956123647, 417804974, 361920528, 79767938, 101585075, 852088068, 57311784, 265459962, 821922662, 452684471, 5631530, 673330321, 532858314, 575087618, 448898265, 373361990, 357965046, 53421597, 880014188, 717245206, 189084474, 408825936, 872453532, 873946220, 738536084, 891896460, 141185246, 111864066, 423992440, 853431428, 425128439, 974314342, 135451562, 66887258, 859537966, 17615308, 593831358, 817822793, 797424316, 318331928, 106232649, 33687172, 262962413, 81134803, 803328284, 388507815, 464418993, 925362009, 470353106, 237171847, 470437132, 55103872, 163201473, 870774679, 109967396, 221489978, 32533184, 178290380, 425622630, 778211346, 927302433, 610350628, 150285049, 369770664, 374978638, 191357068, 728830894, 710315554, 300266585, 105340817, 609032739, 246391892, 942889798, 443049254, 599136805, 74560515, 302748595, 834486334, 753451703, 822873308, 775136722, 516595944, 485130549, 706068855, 822477359, 136532978, 157314574, 341501867, 232572229, 175578417, 50707498, 530936275, 891077181, 626793556, 983627825, 359214713, 398088894, 693328073, 94847666, 661003042, 951821784, 846527720, 582960296, 550590927, 155690391, 216722217, 705550155, 562210045, 487053389, 419911484, 390933857, 184641905, 837030444, 994573000, 764904683, 830344169, 629927318, 130434266, 578093297, 451998851, 21073731, 515579517, 78034590, 350199876, 450573128, 367313683, 707982635, 884290957, 231198902, 60923075, 885914953, 78662388, 324134437, 914907864, 415304450, 539348808, 841284960, 584773440, 920163586, 928491721, 129078001, 584008260, 39511485, 876413509, 603368407, 636989327, 353512833, 571325592, 466785802, 74676420, 590837382, 435550097, 706753689, 219633781, 688407641, 186197062, 310930369, 326836890, 622240534, 427405814, 211446665, 9754488, 46982737, 519150188, 662121788, 915931465, 878199306, 737921676, 571339034, 823863345, 561073464, 423722571, 187179115, 650931837, 449021848, 717738126, 569087817, 896996119, 319640176, 818190235, 798625797, 629332636, 379627020, 921051767, 194367868, 127828495, 378642580, 142411921, 194152511, 989503405, 391158276, 872787872, 653545716, 469238075, 364839320, 602164401, 963153173, 67714248, 886047915, 138881322, 199675923, 423694185, 734785849, 663852887, 876040855, 954133193, 749495021, 968473792, 354434032, 511973602, 203974420, 517473401, 799760629, 925625978, 251507223, 688792997, 852976400, 921769467, 169241715, 631002899, 408092794, 599129394, 78151745, 734920141, 527795782, 360046688, 828832090, 2199838, 858544576, 485760523, 923574112, 119654945, 43520402, 678517720, 963374614, 357215099, 305048045, 890059729, 220597366, 938492329, 202112051, 221863000, 244199936, 857393017, 29428243, 65935739, 301978803, 120095041, 256236628, 294141261, 112483282, 432074194, 833454064, 427217237, 130617017, 147489765, 325686392, 518469521, 968711335, 947363702, 774142586, 906384329, 532942851, 399249907, 777480366, 166238399, 93290290, 189085229, 463077183, 170569166, 404994943, 532652600, 801672045, 144418563, 461207717, 483975503, 87919998, 413722885, 556075015, 192029059, 825476816, 163615426, 803842720, 703599151, 923978527, 390851286, 271672382, 472552476, 884948050, 320143080, 344361890, 544615214, 662675730, 735339983, 462753312, 603577743, 770098743, 418674149, 590121723, 472033907, 260813265, 495449169, 510863586, 572169413, 303926215, 334475959, 894459870, 189295393, 94597570, 501762649, 792071064, 380237433, 456966372, 654517180, 563584078, 186002595, 645474672, 811018149, 322083614, 773690113, 396465706, 836018056, 492466742, 596889182, 914604256, 287242596, 524874720, 499343688, 728970952, 730224462, 753740617, 306544844, 673778214, 828565091, 690413118, 707782776, 65132317, 227278267, 233876939, 674951472, 799757717, 456565004, 788994289, 390233455, 797368452, 512454677, 212250790, 506801446, 298147805, 958565692, 925042572, 944085763, 500112976, 441334045, 803967836, 147238932, 886475283, 878321295, 28187919, 29789021, 909212425, 793808024, 77686052, 186524862, 149782761, 232751943, 730336935, 339014696, 541613942, 461041180, 815145463, 677251377, 688841614, 519834559, 815861578, 210234072, 482431035, 649492631, 295242936, 643429900, 146074440, 791072589, 14833420, 945018623, 191739418, 700956084, 347477176, 368521557, 45329050, 510290900, 409798458, 946015702, 732259375, 472214798, 308221349, 14024251, 617451592, 729592859, 129580787, 251132976, 763382685, 762960870, 368847370, 791465389, 34644645, 893122317, 809205638, 171071124, 95933531, 906335758, 179400391, 578920503, 268775092, 175524410, 545816300, 982608293, 615320162, 337138429, 160024463, 950760017, 188330695, 383210605, 274363988, 785766875, 513018603, 278330821, 767610138, 463967108, 48132923, 959307282, 173178812, 106273227, 751317760, 777775084, 823542485, 510816522, 171586076, 345913003, 461399495, 551139699, 296818054, 832141339, 714757833, 668841857, 6239059, 66375880, 539860191, 597857154, 98665655, 628501588, 535086477, 630994518, 507930018, 531580878, 865226366, 731738256, 935365869, 24352679, 193176389, 584115369, 222271366, 245160116, 658974155, 84672262, 978704989, 690373093, 863497439, 484828143, 877255404, 266352060, 762398352, 257690505, 939810511, 72875426, 253412351, 484223564, 223757294, 537911915, 145499986, 98344884, 350505255, 156514831, 328729540, 374451968, 756305373, 251015971, 652856223, 509882997, 550475531, 239576173, 929322420, 383871465, 100487323, 687817622, 838571719, 388345923, 436445106, 7885532, 974026499, 423169044, 356168374, 397323438, 462377064, 881897635, 114150420, 877823436, 667980386, 142675619, 842947371, 495753039, 30440570, 102485868, 856132228, 181344002, 947589104, 341501910, 651881894, 5865341, 674831911, 949352176, 400012594, 64732798, 106471599, 302279031, 802518204, 560774411, 689726674, 989560548, 422113715, 351180728, 825537537, 367011591, 170894491, 213915783, 500481032, 753467956, 956920694, 393646153, 202447988, 205375358, 341011555, 42702686, 573726800, 130118003, 230990849, 119288449, 798814985, 675320261, 632821417, 150701836, 725867308, 745930922, 782485640, 845406581, 282904555, 946201656, 510056627, 754865319, 133505161, 111776133, 964542694, 571267972, 427138231, 583335682, 235039620, 759689510, 509200186, 426257072, 643636168, 885775563, 957574886, 590676670, 379718424, 604446480, 232145973, 393019459, 430126488, 526870843, 807921792, 275274346, 742615616, 471173663, 433904255, 512472394, 161071692, 47150940, 644623638, 901577738, 219663947, 514032150, 914383714, 809060921, 660279998, 775566232, 696621472, 698118064, 127304149, 351581712, 5087985, 485175792, 482286817, 557676836, 646381666, 597043448, 943714531, 122745483, 162479035, 891628909, 922637342, 432652036, 212955457, 287132663, 183497530, 704578140, 283488569, 415000556, 248051612, 29198434, 317317699, 682850229, 658568098, 662264518, 819646552, 566369096, 798734251, 992903367, 360545857, 770117481, 191616289, 153114037, 258937109, 975439078, 896697306, 244884946, 251696193, 904491547, 88600270, 365063654, 368998843, 794183339, 930745090, 829376618, 268862790, 391472863, 686175191, 470766229, 236890649, 874501788, 647563389, 987435722, 984253514, 480673058, 928933408, 902923500, 420450563, 734594180, 101147111, 829453503, 257906018, 435030209, 392775392, 546886840, 55807219, 265589592, 20633644, 740545455, 687598057, 412887336, 28022988, 715183448, 327937018, 748833678, 463287049, 465251617, 969255483, 407182690, 293519242, 745241318, 628782531, 847711730, 620129620, 941729679, 924383382, 626568779, 255140266, 843762659, 305137455, 476539642, 801314593, 160371289, 376465919, 750008071, 254836121, 637666913, 4623445, 677339302, 192894294, 589422681, 82856760, 55620383, 54802667, 436163404, 545201919, 276977929, 126791454, 352360216, 478848834, 296194726, 846060791, 770279965, 356110416, 436469995, 696141908, 560241639, 206039978, 361639052, 963751447, 446597069, 569961949, 236117376, 162204406, 46791261, 442258682, 62889473, 373368274, 703456332, 765516730, 90163624, 942094242, 825285954, 934024972, 493497264, 298432370, 321088785, 749912996, 972081568, 395297053, 390043499, 908868394, 11904280, 172998691, 883758689, 920326576, 562020693, 610269420, 529939902, 672529315, 652934747, 360005869, 295243535, 587652232, 754893820, 249320260, 118366504, 552360960, 148287526, 926158729, 728179947, 240499881, 874092906, 215778848, 731526216, 895058098, 952603108, 706803245, 191913258, 687555788, 420083571, 254558296, 646905909, 204014386, 333572309, 493363471, 730632026, 389032755, 158304670, 329728434, 535486608, 315881556, 976221900, 482762471, 333783040, 452225678, 384669587, 750734493, 581634541, 640538435, 739993837, 682013924, 276294106, 12704395, 179494377, 871332924, 770671314, 262084448, 470312427, 654656994, 113538074, 390960552, 825151172, 464065271, 784477590, 516093706, 662668648, 720169380, 275718470, 796180415, 725243099, 747997405, 473583852, 534248180, 544869491, 280019157, 898528932, 839933722, 517327546, 324115693, 33512418, 589129627, 645663375, 339786439, 445205700, 321878697, 835666517, 188430161, 554115850, 83809604, 289480407, 652014086, 458092083, 881354002, 802841903, 371763024, 313018031, 888160089, 874565843, 204910655, 32709993, 748058090, 507759397, 669341356, 69056719, 25140097, 889564169, 81310379, 153765790, 519527849, 263071738, 846655343, 988246859, 23547256, 64274358, 309621772, 108091722, 44823037, 306018774, 375458271, 824348293, 637291909, 849569403, 488901391, 499324847, 90698282, 237153472, 740956963, 485385145, 895416057, 115231049, 583237280, 103559863, 96141361, 802459728, 683768088, 383459676, 402027244, 193973670, 655502744, 830079928, 359944782, 942091219, 621166010, 629102536, 158282962, 682825849, 584527540, 335657192, 768812641, 769354957, 810151248, 14428302, 918014017, 318111384, 892500980, 868058526, 107894078, 279538251, 574862512, 711465816, 391561161, 353558186, 558581617, 712599124, 199415579, 142705903, 423482618, 707665306, 94835936, 518070631, 771844394, 42331016, 241478274, 457825668, 701526314, 811461054, 298256107, 532835505, 705893376, 163035128, 932769786, 877915393, 148729522, 233736901, 797247115, 193514292, 79715625, 567316232, 949070633, 223404013, 146450084, 743159987, 984944857, 470724542, 351022513, 580337720, 861156281, 960783877, 988163582, 56205032, 657861261, 119928040, 933146084, 511151411, 214054184, 720952062, 74889359, 316345372, 189197953, 696073840, 540695748, 75698490, 165104884, 679725866, 420650185, 718699715, 963945751, 646317172, 26625004, 252346631, 6326784, 551259616, 745239928, 354265268, 379868289, 711567671, 713558376, 731286970, 579105455, 867918966, 687727352, 625444777, 92666031, 961817505, 610218336, 75135649, 631865402, 134775726, 934137480, 917689390, 412146838, 39621797, 709240423, 144341612, 823020667, 984062397, 427099887, 924357087, 975390144, 107653330, 848520369, 823978717, 553302030, 120258497, 808217116, 125872550, 206532672, 510791812, 128998629, 428661430, 86478712, 862702907, 89193944, 110447024, 541833339, 518927928, 661817757, 359826441, 990029790, 454439069, 188363543, 735287629, 339799374, 241024295, 895141187, 696354583, 372031987, 835014018, 652522659, 806270463, 184934619, 362439592, 718494745, 60904349, 107390773, 397483390, 761857634, 986271058, 558024332, 190278615, 308412513, 602878425, 679134443, 334113403, 119939461, 429633423, 941842105, 801183091, 257278011, 780044944, 262986606, 572757570, 873642366, 555369914, 858514273, 122621821, 410470942, 174216592, 328239892, 760252284, 269055786, 561779992, 742623797, 783352015, 258521569, 36706354, 355302536, 50312117, 867585367, 379317911, 35169262, 391865832, 192563536, 644252925, 985314360, 945851484, 864218193, 840102992, 710948752, 731908037, 183294757, 709886093, 34870060, 569724765, 502334582, 772889827, 286765004, 599366636, 34806415, 308206755, 244150557, 328643969, 84285611, 370617433, 441908180, 357813132, 989587954, 397089111, 216099352, 825526942, 329735761, 76821680, 108299908, 803154173, 644492201, 872730523, 414289756, 481989548, 894829821, 454256298, 448013175, 596336652, 636112830, 557663050, 88586296, 657226686, 366257035, 991818586, 45977711, 278334772, 428542779, 830536130, 872401720, 225216559, 427011929, 440832032, 232423610, 202980786, 786417221, 436903232, 317677208, 382237213, 796306773, 832205863, 953185660, 441222594, 244645732, 798657208, 377363307, 14648115, 887982420, 179918376, 61753173, 275830075, 136766512, 359187691, 951145550, 17058802, 842466289, 313273400, 138197374, 732098826, 820502450, 184766102, 887714849, 942220145, 93783981, 480391122, 564897458, 737492992, 820546126, 857762254, 310572772, 888431620, 577687433, 751804303, 703713661, 97423096, 869564822, 203930671, 662573479, 559014282, 694656174, 109619805, 177692062, 430570041, 293208523, 166824624, 225763182, 165748608, 115251272, 793991584, 127874452, 936139284, 270426309, 70939617, 143448150, 79595633, 654637863, 660059659, 525890005, 94271328, 589659189, 885568008, 440396376, 228310495, 592596625, 256569122, 590117724, 46236972, 435860259, 902392322, 888915267, 415165988, 355383313, 250024706, 782666244, 236068076, 599478943, 182305088, 110289236, 674190562, 528420000, 318216519, 775961110, 558385619, 84857305, 689239298, 768313078, 9858758, 429919545, 404618535, 162434848, 888409509, 845971391, 623749095, 934341361, 205464012, 322099004, 529196818, 361437204, 762920255, 559217615, 712657435, 982461612, 147733352, 96695180, 44747943, 749451861, 91407470, 741542438, 487661475, 898822858, 2712547, 351303445, 903833876, 577926809, 386540403, 440550637, 599036842, 593118009, 573548010, 953981606, 438367585, 556036186, 160631931, 144476531, 497636818, 537829269, 938647419, 648711480, 962911105, 122419856, 509265594, 93458552, 616286509, 320699713, 830129952, 790884095, 707354421, 297131210, 710159504, 897642251, 343087014, 622601107, 619718908, 940757977, 426712591, 722864827, 801971157, 425943160, 368461632, 335884685, 212562535, 100143164, 684557999, 216513708, 253484433, 785179545, 383423948, 157884726, 104412831, 172990370, 825879244, 933344630, 89193930, 759423480, 668970639, 443474682, 360666936, 113681364, 135526993, 962782833, 283216173, 930212195, 520825462, 621012610, 424586012, 402946653, 557803224, 508398581, 719820073, 273738884, 245693430, 974544575, 909608002, 802497009, 767073392, 232719969, 194635034, 53883987, 612393575, 862803394, 702146867, 614158348, 674023804, 22688994, 393922556, 336389831, 341045857, 170437245, 864200317, 467377735, 698406805, 216301208, 726314826, 816904475, 338606210, 145151939, 721805354, 305801697, 536757511, 856934447, 232981634, 998950298, 825299130, 117074878, 714673801, 602669359, 569313464, 915493288, 333444096, 925010480, 288281766, 326354132, 710666449, 670224741, 249329045, 537133684, 128380112, 296076186, 822181080, 170217508, 719034559, 241827561, 491543970, 841737540, 533062554, 590272935, 617777279, 8321195, 368226686, 125612212, 393481059, 867942649, 374990875, 644696211, 980375781, 257325825, 102485220, 218024700, 708844177, 520984295, 965164253, 128497323, 174435209, 225416749, 475449817, 86157745, 903573205, 62676266, 999651097, 187827466, 480978420, 438558990, 731800709, 147895340, 709410777, 207621195, 404243635, 511155198, 822295457, 972965181, 926864872, 725800386, 899105742, 740573865, 561840627, 618780807, 375092062, 739387054, 81056399, 192290041, 779750705, 571569199, 799033182, 907923189, 798261756, 381197804, 61258231, 416760798, 649657701, 427057664, 199574252, 731268725, 48741658, 199582188, 862216154, 121275805, 370814637, 428033053, 274307961, 209403150, 417428374, 581430597, 874214864, 362436318, 724701754, 770659112, 427342588, 7169680, 586736635, 216412437, 495290730, 247035007, 620744249, 617300848, 515575914, 184139770, 780053042, 147199860, 77711105, 596036543, 130778919, 789598639, 689083616, 437482557, 145420222, 674912486, 382929764, 202313664, 426282257, 734015296, 476721768, 268099782, 459151872, 425140250, 425382351, 253413718, 792228278, 243300472, 644533861, 154959103, 165976815, 845493762, 501516175, 298629022, 380014337, 237439781, 518202548, 361097802, 540543496, 958259792, 546853606, 113957800, 734121282, 109787225, 137862680, 746715286, 688279283, 788509967, 541102594, 196717648, 780812829, 949633099, 18753885, 471673117, 46063738, 4310394, 525686377, 460579465, 610198143, 74993847, 858783171, 799624099, 518501402, 101777365, 452051845, 627233389, 371924176, 981619161, 809095987, 454250912, 49253889, 531183506, 49094053, 767832575, 749718729, 234904330, 240057536, 912993648, 733138712, 67454908, 102412256, 534511509, 714014623, 750591692, 358242948, 698914308, 329170993, 638577338, 214199965, 401708544, 203714827, 15761679, 631965686, 24563524, 473822732, 446197987, 514987551, 716547059, 756062648, 894381928, 547132416, 297437330, 535313839, 115216942, 386569736, 139075661, 82129828, 684469533, 546723292, 817577296, 614510839, 877561441, 961201094, 968568753, 669329857, 917830423, 995141867, 156048176, 396256863, 576752276, 712865897, 480222744, 290088454, 338355137, 784924422, 558735332, 408872312, 405135255, 860923206, 649360449, 916173792, 856129031, 70771648, 495458871, 555660932, 359743672, 839855388, 78325628, 199918602, 366170004, 755987065, 310939322, 837898837, 362594955, 282145138, 994637217, 363474257, 35872067, 890731126, 328921366, 951598952, 879826282, 815376534, 111293821, 849807640, 508558397, 859527179, 669364924, 361374896, 555593563, 831733076, 918621025, 453450459, 364118525, 960731253, 606186967, 526127088, 434692658, 750941216, 254251628, 760138928, 338116656, 995653643, 669573976, 975571508, 867283968, 82266565, 821027547, 912993841, 216282737, 562785394, 824820749, 699761082, 405850222, 165257969, 43982116, 337487989, 85288207, 903870134, 477889168, 398294131, 877260236, 208946319, 623270141, 587142952, 968497694, 537473676, 389042821, 351444527, 78333607, 958659411, 956062376, 13970319, 121156751, 986809579, 372085348, 193647658, 852796549, 5964690, 965133144, 80815201, 636409274, 256780084, 993305992, 907516328, 221495058, 771967911, 625871828, 388212111, 404988229, 413856951, 62947790, 131873222, 938051463, 653498950, 221240136, 934502620, 416723984, 573421923, 454133935, 598788114, 588650938, 105529281, 206721864, 229823751, 113743272, 703380383, 408033873, 503385364, 154688569, 216002477, 320260507, 731798905, 649339934, 95722290, 604977220, 49777938, 415188908, 881562163, 503888374, 897437256, 690279279, 215447411, 224799896, 361769122, 230157215, 846508574, 162568319, 685006248, 314445334, 812662000, 590370376, 279370358, 603018559, 421181682, 610872879, 464473861, 622641185, 12007884, 963603635, 452981157, 428011682, 332378626, 38126152, 179858011, 536169851, 924034203, 475573729, 303378807, 288997523, 419480330, 383859487, 324170952, 688945504, 924192985, 961547806, 883893850, 533683426, 799320404, 314744693, 303631977, 739540811, 335768920, 89184592, 133378072, 437037933, 33453680, 112939092, 149019071, 579357913, 133648002, 808902351, 155640548, 421061742, 457086435, 386977664, 103425366, 732468855, 851981616, 867413392, 968527753, 718240507, 859675910, 392543612, 113812939, 428674482, 986252101, 793516901, 342898373, 938958208, 817170018, 968525020, 819517424, 498446647, 137360744, 18866470, 935356961, 626448561, 677196242, 322219784, 125805443, 596104821, 915709891, 533404350, 315459774, 138434297, 621797342, 109257705, 883791781, 4219220, 124831669, 892767167, 315242656, 636697622, 958510219, 823812249, 112828112, 959476400, 46220013, 37156486, 354793200, 619599485, 954001330, 189654506, 771685104, 778222573, 875227656, 982771887, 615455996, 32288707, 378077771, 236982339, 681624124, 13918967, 680352843, 696147487, 261419734, 73005788, 707534759, 382769920, 907277954, 976724625, 42307132, 407426291, 911084189, 430819448, 581342824, 345246534, 794477026, 346328848, 666383969, 419002151, 516766041, 599110332, 316831841, 655353816, 119485564, 93882866, 108611193, 411854227, 7066937, 954559435, 648487543, 604329275, 280218694, 554177373, 71215188, 155441048, 198727658, 154314698, 197254125, 582756073, 152552004, 708573406, 463953334, 138022478, 859415403, 700964464, 90143636, 959795111, 308796574, 539359961, 695132229, 52018842, 7869156, 754150615, 581600512, 431819488, 75869719, 550802762, 876506787, 352888672, 735649044, 71028723, 477502403, 674659526, 137000191, 867466954, 626159001, 86151185, 652163675, 875459737, 931747826, 827899151, 822847113, 444691524, 917283716, 538008540, 567887668, 942238825, 582789494, 900696339, 312179893, 519118629, 156722027, 588166313, 394695248, 623608245, 748454192, 624977311, 82077857, 914408336, 679286071, 463058966, 964466499, 439887762, 630055531, 414411936, 435955145, 486530787, 985345523, 131845973, 838171801, 15580441, 407579483, 250881447, 569935283, 195676201, 471682619, 136748040, 652985196, 845798274, 977277345, 969281985, 562769658, 954677164, 336645103, 846700035, 285227830, 453397000, 66246726, 372786750, 154514671, 225363784, 140519100, 24687124, 196750559, 463099077, 559003600, 336489278, 268740551, 9114222, 357265515, 347831369, 583238201, 63132763, 818981390, 80707007, 394908963, 496756482, 352926999, 913097545, 946064198, 685666693, 374182832, 565275100, 992963212, 98678926, 394042864, 907703474, 892097647, 39244483, 742158582, 648579740, 97567708, 845472327, 371509011, 692168526, 442052983, 358555355, 858690395, 507062175, 825495951, 846539122, 700772512, 484807297, 34618534, 173075709, 431307067, 287930543, 859133969, 849920311, 660956206, 951891196, 979111212, 154702810, 830059573, 691029743, 98030433, 629225990, 287454421, 541525369, 295665213, 579711639, 181707303, 270863340, 826206533, 129918529, 226949125, 393813251, 27632199, 219599102, 42533580, 906427937, 142523298, 210032413, 903611912, 45898977, 632282466, 170311728, 998318657, 782251127, 607252314, 334207179, 142840357, 575826507, 70011166, 151340577, 725782952, 597523408, 586920757, 592529654, 420145717, 483133709, 919399536, 854847708, 288529766, 504429740, 62778793, 223526246, 789307417, 554769911, 650793356, 632505518, 507388716, 819452503, 398978522, 292778334, 129662033, 242587223, 337804326, 317350863, 892107172, 591864272, 286095755, 578227659, 80740532, 352456221, 686798859, 505287351, 381946953, 275356746, 883240768, 72372131, 347498435, 327609495, 145020051, 710851393, 436270804, 803553855, 230958290, 381343268, 987714180, 993609078, 91828268, 40496139, 176926963, 175088491, 291588840, 399477269, 303732580, 579229267, 820426465, 41257135, 833532519, 40823139, 628465699, 49688976, 31578203, 364657981, 585081753, 803666943, 668280831, 234571486, 641600563, 762733126, 610818138, 197341048, 272608622, 509464408, 619127444, 736348753, 286157365, 644361130, 979817532, 200295736, 179934071, 881989235, 964815216, 838066074, 76045281, 613124107, 845896278, 485789107, 288835272, 230484028, 447081096, 474265689, 107641084, 923818902, 516317009, 500887889, 890078653, 60052627, 52863095, 270362545, 323929289, 239412132, 251183825, 429910781, 257122297, 109386714, 85383694, 617455578, 73516378, 320482474, 823752827, 569065284, 372311029, 652924147, 726189763, 643757153, 273322210, 949372126, 224707978, 292681603, 961759899, 811399092, 737071839, 677746745, 999342689, 969732344, 189852076, 13000244, 613414535, 177928398, 879316091, 366974990, 902089072, 939516654, 464478760, 911456267, 857057644, 258394710, 290913027, 715221496, 572782269, 156459868, 252295374, 527185866, 699351588, 417794960, 676032008, 99830089, 97719614, 851428761, 61255178, 909852889, 78552145, 42902976, 587698628, 292615921, 856360750, 766970949, 649594043, 599763752, 112763470, 281984507, 456968251, 635504646, 669124255, 968089339, 398857258, 651559390, 49429897, 693840498, 970522429, 182354286, 785991061, 312236519, 336775518, 572052240, 2720985, 940483566, 3266264, 787718820, 332615506, 179111803, 814014864, 440471327, 686274294, 337675153, 433224530, 923814779, 558496291, 793915653, 371064283, 121507131, 636362529, 451808565, 958066853, 917857359, 941231408, 73930420, 560517322, 549388134, 242196721, 826146804, 594868434, 641762579, 246884442, 629721184, 993370539, 37298935, 713440132, 364526921, 405369256, 853279684, 980857350, 444732569, 847199647, 646416097, 262182494, 850405072, 375830473, 375801357, 19516269, 849173279, 604942155, 581611017, 611277835, 766795375, 542232261, 965135419, 755936453, 365112338, 709286015, 31541771, 140050167, 583844122, 686950180, 558018088, 537932891, 391784405, 946178397, 711647927, 303783712, 904192393, 883597464, 73031737, 858269565, 949689554, 753172809, 286558384, 716472317, 857250539, 610118646, 529052243, 971724148, 686821008, 117350953, 204574936, 255552073, 420405835, 544507676, 582079831, 3434612, 184932051, 483686687, 516366757, 800927022, 968082037, 568157180, 234085412, 233468877, 562636549, 338817096, 62512519, 634099038, 125968689, 865328053, 171805415, 214879095, 9226319, 967119800, 155753314, 627317415, 724184613, 456754141, 383088794, 388048149, 348733286, 72487263, 545653332, 595163686, 238179454, 696852179, 136775774, 543089084, 575336218, 493389321, 57905433, 780393841, 28373297, 875649011, 60597705, 10501533, 769981057, 175473036, 454059480, 214447932, 766981010, 833771553, 699994713, 336114201, 228358652, 167219923, 626507358, 829513101, 545724343, 764125036, 819964160, 811145258, 733546061, 137516951, 836572101, 443913679, 423128644, 477039982, 44086094, 914979747, 425015143, 545945206, 350856623, 422882999, 542728376, 281472705, 146323965, 387539114, 887101322, 203928796, 557015044, 539385958, 160505770, 530050888, 920938189, 290251262, 19526307, 397188919, 333664364, 995279125, 189200254, 403498451, 859591333, 362474496, 994557218, 701788292, 949051372, 547760826, 533028076, 394415801, 719105695, 340535042, 176211141, 992722424, 26045749, 42702260, 736307368, 263277284, 590740589, 827123683, 871983320, 711390299, 818760622, 788269519, 346305754, 66908693, 410365062, 441253237, 406640661, 963914443, 587194277, 768278450, 827750999, 989044531, 59946125, 792592002, 602369575, 410248708, 177749731, 630491484, 661911639, 255971937, 593895713, 738453984, 932290444, 797665165, 921091967, 406733209, 713173564, 651484988, 982401752, 642896846, 712275321, 831209815, 852699150, 472753354, 287344590, 936240944, 831206703, 319293337, 34399520, 359515854, 626594229, 781038498, 465806003, 838190655, 680150058, 705506639, 605270192, 601821583, 438886076, 550841005, 947497369, 597570830, 699474285, 241873586, 701525400, 320134357, 183541137, 370326644, 948967689, 860305139, 407671131, 326040882, 669595634, 592411655, 895709392, 217757214, 555473407, 216641971, 23528645, 714948306, 813649979, 83885115, 274112601, 490636448, 864490134, 127818590, 544376055, 928393661, 771093415, 136568556, 100766791, 420283630, 889095275, 101687816, 834322627, 486530399, 520558689, 845589648, 393921403, 463135491, 856810967, 845238662, 978864674, 964502754, 373317924, 358265835, 636567811, 241636499, 783293004, 60275530, 246390175, 137046182, 394732566, 515710543, 841243459, 946727883, 767690507, 903781621, 547324798, 555499585, 292112372, 764800653, 383971334, 725118709, 758358350, 74343053, 290321764, 709753831, 961727254, 168944974, 164483605, 377520402, 63184171, 139884319, 234827181, 358034748, 712875470, 509365064, 203387578, 952587845, 965701034, 383217975, 445305780, 218396267, 562259632, 824145321, 370470991, 341762551, 710766547, 990520754, 514526360, 434163576, 77872344, 686492264, 21064751, 127405510, 75445008, 380604912, 595265163, 54308005, 895004898, 664540229, 552210857, 773156450, 598763949, 888554498, 223250727, 487776946, 1004849, 774886071, 482601251, 442683578, 688520956, 742214158, 790763854, 920969505, 993129003, 271269749, 637075292, 818445372, 721605926, 905003698, 219244526, 416379451, 916731989, 726588022, 567383859, 620600218, 44375163, 713741125, 233594139, 901958256, 73737415, 914528879, 177557364, 124271772, 201694637, 468664391, 644614497, 939541007, 278275413, 343909517, 586466301, 694693596, 94277030, 709783283, 254974856, 342910617, 629704015, 189273187, 897327588, 607620004, 142939548, 175585887, 652384065, 709864026, 877268801, 797778039, 818198196, 965787908, 324349236, 230071142, 176549925, 142310954, 567371671, 999043630, 425926098, 201620705, 365221887, 901539758, 987192568, 35857210, 636154234, 39524948, 513969655, 760250257, 861149844, 796804091, 100793722, 317526463, 855921597, 829715530, 797308981, 195353875, 814430976, 519201226, 483995969, 335820001, 730403515, 956295411, 271039610, 438852302, 339142415, 3098589, 689362615, 411893289, 327273672, 126646191, 697698265, 65817979, 927387394, 726493719, 271378715, 417906457, 679376495, 303165334, 796289975, 954520765, 498748873, 862324350, 332408280, 860568570, 207316986, 929451339, 230212808, 372598683, 216771952, 200821338, 393613509, 493269646, 636905778, 934124638, 510587586, 220477781, 444587291, 871051525, 395096920, 979256175, 206725288, 770510089, 369085609, 714498509, 2650289, 862009189, 762057157, 757153233, 495104670, 914680447, 487882646, 800309270, 88291968, 35916177, 932844104, 484462763, 358311909, 571260433, 991906925, 970995100, 961948568, 703600202, 765079278, 871048366, 486448876, 218799603, 485594672, 489727328, 990482433, 450153566, 62336841, 548334986, 535390219, 953448374, 880084929, 342380600, 215108339, 922924027, 690432480, 785397233, 58400038, 799799262, 766129224, 411271650, 691985514, 381715138, 421535494, 690656902, 43556730, 72397941, 422101676, 308818772, 593765517, 225437881, 408677824, 634379960, 71267728, 710752715, 679182931, 859542561, 473579746, 122628141, 205257820, 871893168, 341356720, 265659050, 330762252, 135663849, 775303884, 234886289, 934709789, 360323689, 463500635, 911847219, 361601045, 703758281, 790377891, 907188577, 476260980, 662712616, 932983767, 206862301, 581400931, 1530848, 354117037, 142951889, 526760368, 688566135, 402495204, 524756342, 229753913, 20526514, 453345809, 927377229, 748980693, 551710740, 818360440, 123224710, 384209785, 405535651, 293336655, 851339202, 123770648, 176437030, 730557898, 765251582, 852596847, 509487100, 850278726, 561834648, 925358556, 921898392, 149315038, 152388192, 91051579, 200492799, 145051700, 540282940, 178567734, 18660538, 15081249, 264282102, 369480355, 988236843, 841418606, 680196565, 799832616, 716415137, 274774922, 609715968, 760813266, 296717810, 632608492, 748345617, 188215522, 449647077, 290531101, 440034753, 561488800, 765664028, 290706087, 548573700, 889786316, 729277620, 98160245, 662349459, 942761055, 349747141, 169882815, 408654261, 979120637, 629296501, 622388221, 206122533, 253261021, 234351731, 441783122, 300292782, 366568555, 177913477, 886275902, 453991962, 121236578, 918700279, 276782381, 332428745, 628325053, 36312585, 297996158, 658832188, 723564913, 94252361, 332785893, 97541263, 613285026, 459417240, 180312047, 437640160, 422184487, 277447196, 477815263, 677858641, 851621339, 22047706, 277068487, 111859841, 604580126, 199090146, 867183836, 827363000, 84839888, 69898493, 641417979, 74680499, 348566259, 563998473, 409997274, 878459211, 900467847, 745843328, 473458089, 780692735, 102787690, 758196351, 470988426, 609714186, 974450846, 877155461, 536988221, 493069451, 1453580, 725803442, 922316235, 497450853, 138675997, 228190108, 99727895, 540356270, 375125959, 300017294, 976538266, 442929743, 556082892, 253282766, 387931054, 643946660, 415818108, 848412050, 107254365, 567225790, 846774202, 732925650, 300507432, 952371218, 499201049, 94339492, 49848278, 603185444, 313437640, 30559294, 453110321, 742921878, 31489104, 950201985, 137893033, 240451850, 756081087, 384724585, 673202438, 350500625, 304681919, 805937342, 783496485, 132714877, 466293006, 514324490, 144168475, 125290896, 89688038, 230390897, 336705247, 882376959, 587224376, 182704799, 25600937, 411947224, 485103606, 209713885, 632155908, 713547836, 650768792, 768255514, 562032464, 827474202, 98610936, 980224527, 929502240, 735751804, 856184223, 729924400, 462604268, 540151663, 758716552, 30909858, 985367816, 2987637, 395069485, 960287989, 34553694, 207189124, 441352475, 352094595, 968808598, 604341095, 423605230, 416501038, 858724793, 277541499, 813185970, 310349687, 910464479, 756149781, 254759034, 810590379, 949199574, 579423805, 34439604, 158310592, 475594217, 756856051, 27068424, 857286840, 351494439, 837494901, 658123850, 247665784, 74747809, 12120699, 618357918, 120873751, 904081756, 762310140, 460148798, 873761784, 40239606, 915233925, 571568951, 287868859, 649923592, 642239833, 233488362, 987542477, 276798158, 327208642, 256876300, 589241301, 958321030, 422696199, 374530894, 499502144, 782656580, 787340392, 619502197, 547692574, 427486486, 576224208, 429555873, 763934982, 585400520, 678924670, 479413996, 879049613, 454771049, 140790072, 737705552, 584148829, 967177466, 601472796, 558031960, 738168052, 261767222, 179577027, 490535465, 343665522, 66784508, 322863888, 113870301, 261945046, 190332957, 397238167, 852904102, 864710597, 457979672, 246688793, 515286074, 113946652, 464819157, 853989284, 76543177, 854487075, 404117048, 9456958, 97489937, 674065828, 685605622, 863825650, 352193762, 112423389, 736341751, 512750552, 776362773, 226406391, 710452630, 148110918, 334290521, 155556186, 582077371, 797824765, 860144610, 29837664, 402664700, 273036857, 295384986, 869468647, 512169570, 662284334, 348321704, 449654337, 615117886, 204240368, 737639325, 596491747, 1778297, 992742473, 797486845, 812883625, 691275240, 682141035, 632459859, 515103343, 840336448, 388801056, 892168071, 375748831, 832195705, 103613062, 88858393, 178792449, 607131057, 493792001, 566061698, 380511692, 292057129, 740094751, 560042352, 600729404, 107361027, 162039487, 884954959, 937322002, 557776239, 195228465, 499935567, 904078535, 685638759, 451284205, 38748604, 439895534, 507543511, 547482878, 150048083, 466027281, 498317433, 922799669, 245384579, 566291956, 37524328, 394963685, 188508654, 329924214, 783539204, 157453523, 544458923, 789204005, 723898481, 907875341, 343386510, 488856696, 380990891, 40967873, 108288561, 487360658, 487416954, 468762448, 368887450, 662678627, 250780491, 201872907, 786225119, 497709873, 889214914, 26471067, 792380984, 276474160, 215765593, 854211157, 571138447, 948692049, 506930195, 487843274, 170162978, 992498549, 438094991, 774805651, 360452057, 264850711, 858726636, 184755653, 601227390, 316543592, 270517491, 844840088, 644682121, 325920183, 63510358, 40924721, 201362442, 31459972, 666759663, 223210660, 483033461, 261505021, 670416609, 830324356, 69423645, 228346258, 144130957, 200104378, 416255458, 646363604, 748423128, 17669405, 728389107, 849439564, 393658932, 480516522, 377409374, 657639274, 702087086, 963578502, 208999513, 285846993, 499188836, 52387832, 208494369, 297854244, 361550784, 417205855, 298959188, 564889591, 171678957, 110802026, 792798175, 196408775, 182731561, 50118507, 503717502, 409283158, 347159088, 157888270, 982234182, 599070611, 980643417, 621936584, 223208489, 120900403, 565917355, 824907606, 310317795, 129042116, 195587952, 843766468, 756033729, 53502021, 525774634, 308332485, 696973954, 43387247, 743203554, 929938531, 931865379, 894621642, 893770610, 209064646, 146165254, 220620903, 955471756, 525508420, 230197674, 757023859, 140903645, 17960882, 134063743, 527186633, 520177450, 633371752, 394826332, 541179346, 168209535, 835536448, 864549299, 786288235, 404359034, 547750144, 570726841, 561658198, 515267032, 283576921, 672079993, 270310838, 904935060, 174064572, 522453297, 917662814, 695756459, 890068744, 632736145, 28818790, 746411531, 643225342, 19868075, 922393993, 197499284, 907093854, 329021792, 568072148, 432064132, 803855327, 768778359, 744146217, 285337675, 233027064, 235738280, 475069789, 343478427, 974924421, 534925483, 915324187, 404342408, 341314805, 500200359, 664796294, 905539260, 569742784, 650660889, 90036679, 505088271, 767517951, 837870211, 755814771, 691459591, 992893690, 465614303, 584540661, 292306160, 753332558, 758362959, 544812045, 187788867, 129314254, 613506261, 645565046, 748914596, 201265364, 661891426, 713295144, 775925245, 649660227, 270391344, 244390627, 26976186, 439343844, 606581913, 402469269, 194838366, 919249683, 556605026, 275027970, 521387327, 154113796, 7518592, 799154260, 695010464, 833953489, 987125409, 516309641, 77816421, 402969097, 147648365, 564384998, 916198004, 39007486, 381773405, 771344213, 791517741, 48325217, 726881247, 326935544, 87490294, 767356783, 51267217, 888400644, 59440086, 537316087, 992701890, 419747229, 292433093, 785041135, 868286229, 721946957, 665780205, 612395877, 982017549, 533891983, 849314125, 660216005, 205093549, 886638823, 924572913, 460896448, 695965718, 235459061, 328941207, 498658085, 478555930, 987710596, 177888993, 274251616, 759341908, 249071773, 583373250, 232773697, 967908345, 732341387, 497682800, 196756014, 885713951, 990562171, 721624828, 663126666, 122206826, 680872716, 678360006, 656043287, 388658986, 80228346, 802900682, 460344226, 962554285, 251877979, 931072675, 13251703, 229684721, 74512179, 408805872, 846127565, 746019186, 209165243, 196798342, 717835359, 680641736, 325302443, 926427294, 917624519, 240975095, 283842769, 285320633, 923637933, 962848481, 659560206, 274073990, 109517719, 766749744, 159233601, 463262705, 582798612, 332420045, 604803617, 99815403, 309263379, 801913377, 921169745, 507390195, 49351412, 891225042, 186378212, 745450315, 480140981, 604118933, 128803565, 173284915, 623154511, 174667270, 979847380, 360891841, 596192209, 541294967, 984565838, 243153998, 167359901, 472940817, 380902959, 115184265, 7496250, 251733383, 475422600, 493781920, 677275565, 775165701, 429018484, 706707561, 19671681, 24290291, 154894358, 393574615, 862311012, 258913498, 213097972, 412383745, 109564119, 791048503, 967319935, 472246493, 92591341, 498032641, 291626644, 369703820, 23191010, 427282293, 878901713, 188197462, 534720785, 775084629, 408808555, 585389623, 424058376, 729256668, 939747888, 261893656, 166175916, 336340250, 33677084, 882089024, 916749486, 620274169, 571025477, 760787486, 134463346, 260256750, 83835954, 353865745, 17637081, 150483063, 788400380, 288719002, 642624149, 243211747, 438484909, 911248810, 839159093, 387978842, 468363311, 798904821, 331356215, 408720815, 279641762, 396443139, 857431043, 524394243, 728180439, 695092217, 6728802, 729487612, 426166941, 818825619, 412888165, 205173498, 585898257, 158019819, 360563875, 401948224, 397710340, 100424040, 372567835, 337850659, 873232988, 211659814, 492305617, 527630034, 965808631, 336755757, 347408089, 170894892, 852799138, 475314713, 981967321, 848441035, 285282213, 898104402, 372843879, 866080483, 457590082, 722541367, 758059609, 663955067, 913945600, 751915428, 611167691, 117334755, 572447225, 933799485, 354615711, 182142631, 787008926, 142999279, 146579397, 614888274, 609204299, 322921411, 967063211, 534347223, 735928840, 854807349, 860154263, 593424647, 683695312, 305100128, 118864210, 339919170, 225250473, 520580709, 264673700, 402524164, 495370576, 119625939, 202485996, 280585741, 503762094, 875142290, 527859735, 311624963, 105696547, 747399731, 408280049, 431730291, 721763019, 171228557, 842902514, 642404769, 776160920, 893777101, 156627530, 243291, 349373974, 765087966, 774094700, 84837670, 726730378, 355829599, 169415420, 374154930, 805871024, 117318386, 465491036, 893448035, 342798795, 414142348, 252316068, 807265194, 815746496, 559406342, 478331686, 355944935, 166109699, 94744777, 903169835, 309464204, 367036110, 297449012, 113693814, 356161515, 150977603, 919299167, 139731632, 877255824, 497394566, 894601891, 180987131, 981886527, 605378692, 726995629, 737452495, 741994473, 219093102, 937316920, 616216209, 637575205, 222375085, 71921485, 802821842, 6935555, 621553245, 723256757, 191100975, 69800952, 31074772, 599198173, 141417353, 659474974, 263631939, 95607180, 10142881, 262761912, 765704743, 654631066, 122104034, 19724920, 437243160, 969207631, 7146199, 792984391, 37047653, 976980701, 550668751, 720156838, 745601903, 696348992, 313593250, 620244008, 320677745, 231391621, 590232360, 242874008, 678391481, 984601259, 361273373, 896060180, 946110504, 933750206, 908039357, 85014791, 241404147, 300985406, 158562082, 750397585, 195300358, 786077332, 368575103, 235079973, 643280990, 874330097, 838104001, 254104695, 472813792, 442046958, 901817507, 99987886, 691661010, 34846040, 634192313, 633256910, 341435033, 958121013, 808232179, 193807605, 702974730, 276330736, 496523737, 584451646, 361652597, 619197334, 167768962, 927063635, 784901840, 769906717, 363793795, 106302296, 276573604, 566494384, 134990942, 66753992, 41954520, 111369038, 997305486, 27448214, 254759449, 563931816, 575471912, 554623427, 753459153, 887582767, 719438466, 440940345, 186941394, 773592840, 905741581, 631594963, 664173991, 270503686, 340091128, 406701708, 564604679, 450490144, 114379061, 692289455, 520417602, 764783344, 655864683, 458747326, 991475650, 81985194, 964947830, 79535981, 52222489, 431547248, 575108764, 494455715, 580839031, 836846223, 247111433, 839639098, 155280010, 987577551, 357763881, 803316135, 677175043, 534061741, 110555568, 402225595, 101245545, 584903374, 359481630, 436801208, 841677764, 774625396, 353949202, 622432092, 862244028, 516533709, 956641035, 262156521, 993641842, 894887591, 494988406, 435308180, 502212487, 126184386, 680207901, 950664804, 365343632, 179217307, 120170478, 468602970, 119806436, 893119739, 937981712, 410669539, 503890205, 556513152, 772495378, 861904860, 312039747, 147818511, 348518600, 350928667, 821803495, 331540952, 322036758, 921683957, 252572236, 928944123, 842500201, 390453284, 793668457, 500184602, 9159102, 753614702, 155303542, 397739146, 663061359, 630250507, 154844524, 665978369, 415364063, 361103696, 686308792, 992169347, 641021828, 200573798, 128881871, 904151778, 110308868, 365017733, 507713337, 204336521, 288721272, 228366890, 485287135, 573434176, 633447792, 396553272, 366954688, 869603753, 569891912, 891119050, 356937369, 582049329, 955289468, 350500745, 963548576, 408978740, 147135909, 185386174, 567433724, 47076786, 285927185, 335279470, 637760856, 49152532, 145826676, 376582132, 21623559, 689378117, 476563805, 892123458, 996305259, 330418329, 11110467, 568605523, 979703399, 352663274, 911370165, 250801747, 637964410, 117867343, 673985295, 929958206, 376792683, 878192255, 928022992, 850372418, 526394119, 197011774, 786804199, 963649209, 261397347, 482492826, 752331645, 220340807, 165346486, 337104740, 919836091, 957840940, 321730959, 427914886, 933788775, 568069431, 716498802, 247213543, 640914069, 938107795, 305818259, 42659700, 46834563, 103810680, 238358164, 151068718, 486963496, 76651562, 771294677, 312071605, 562221750, 227882320, 796145732, 323786331, 263145416, 506017227, 962610919, 601824209, 323570436, 822643480, 931127127, 211184262, 420117361, 954449931, 619369427, 624727355, 790801172, 125399136, 479488557, 695648444, 206954400, 120238918, 186105244, 674965280, 598226841, 62839372, 366321901, 809403099, 151788028, 29828382, 824258489, 523918561, 565076286, 830930592, 233248570, 565495665, 306171271, 996475249, 256039483, 70600319, 420934999, 981670081, 8561225, 940251235, 204130644, 712809900, 888411709, 904047918, 183383453, 713465431, 133428936, 576879755, 562042927, 356821453, 22903182, 656948581, 45649600, 450958842, 913354713, 737623591, 456356020, 245530062, 29704831, 143505532, 998807255, 408151007, 669389686, 804285410, 415832335, 623157164, 880688919, 776754266, 521076192, 188776510, 611939070, 959487935, 608760182, 712441131, 560490454, 915766307, 830377031, 296963387, 2036989, 661213946, 339983886, 52400994, 74768106, 413028868, 271803580, 828320361, 757694521, 708182170, 158705170, 881909040, 427996893, 195763849, 179602305, 573240358, 349230970, 903789826, 588479259, 933799892, 484457149, 526356564, 897505385, 896568592, 829017898, 986228821, 994145242, 729753512, 207567606, 795150900, 697401979, 310205794, 518157387, 716640940, 702054192, 671516236, 835593866, 132381371, 922394143, 854321138, 26641278, 288345548, 569562661, 893374739, 922607743, 560760422, 68922219, 593491543, 154656349, 107813530, 523257106, 489856049, 171030973, 502054854, 306364414, 990117867, 756757248, 530862397, 686477562, 124588275, 471703247, 901747005, 59761733, 529362380, 587252688, 433785550, 739420563, 980421667, 317777187, 188995250, 296011612, 48010352, 794090563, 148248120, 850233010, 411810006, 463622610, 872368977, 403167054, 897446352, 167143701, 56116635, 894842726, 178700708, 789743111, 740621723, 31207345, 771566845, 159251234, 496034505, 831346329, 413623623, 114963052, 465233827, 148321755, 889416968, 358079469, 351954485, 827373390, 780336948, 552298162, 655108231, 974548979, 945778847, 563473607, 700847989, 507783183, 96528717, 535239795, 284031564, 702200285, 528635268, 59587954, 414261700, 881936920, 500511905, 125619221, 14452663, 122964142, 114968247, 270172815, 310370963, 229891866, 262071725, 637728823, 467250928, 382605208, 737557033, 684354820, 792326008, 654361563, 111090385, 439900336, 136006355, 800655151, 588884485, 243071811, 615019534, 208566806, 248717088, 118429648, 930859354, 321678701, 760322841, 907060451, 967500506, 319624540, 363529680, 91235816, 970634202, 430960463, 609416487, 643871339, 318696298, 888867896, 867763669, 148144905, 470112059, 712856948, 201064634, 438946802, 103123157, 469150263, 906209462, 946344563, 535191639, 443106913, 56152086, 346903884, 644151673, 875445357, 661009490, 989092979, 619169424, 949334297, 810873048, 170858833, 59653529, 359650450, 640326280, 428946327, 770837982, 634442379, 293655548, 551950508, 551648803, 834062451, 151173558, 333200299, 348647914, 984703426, 333596333, 858211804, 561851164, 806237886, 167165427, 837403292, 749805515, 628572576, 494655843, 366959825, 839488381, 840260167, 494138259, 297808612, 893194248, 124286964, 363891002, 809064066, 517963391, 885664494, 59160324, 754118117, 416839325, 195756071, 821439470, 548554567, 939357145, 552504900, 82440261, 258395798, 935624023, 71190970, 280790479, 555978146, 470172162, 34520064, 204587056, 778064587, 952790414, 561047196, 630210732, 619668130, 125507602, 80397813, 395822791, 383864227, 23378705, 51794298, 67750768, 850126393, 201855331, 697559359, 172025993, 905580798, 473186795, 183465560, 505883149, 684169657, 118418271, 230156695, 894857395, 163837297, 531074578, 559061344, 304165242, 490747400, 66485587, 596752912, 133742425, 965548111, 578236796, 903165249, 752435594, 130083264, 499875124, 123909349, 344388744, 599605843, 696168228, 614382534, 901908089, 633817464, 211154931, 147000631, 553776424, 324790148, 279178657, 839830495, 879237830, 304257069, 186748741, 210730427, 190599768, 748808881, 871865927, 717969038, 535978059, 358949544, 960218507, 855646915, 491743483, 487507393, 652488398, 832856949, 313311144, 587496292, 446265885, 688011135, 397385061, 106292696, 257239453, 579551372, 192128097, 220333209, 551825050, 130065547, 910741650, 129708968, 930890062, 757505171, 570922336, 172646426, 90858516, 990871622, 896098402, 805956707, 561337442, 339258466, 296588263, 682806413, 92324789, 774074227, 771763939, 625686167, 71789638, 798437213, 661455702, 603251630, 396815831, 452001521, 238577919, 453985900, 796153636, 906783031, 416360878, 942672055, 560502, 542954707, 482438181, 773470733, 741300610, 111450385, 812338903, 5487072, 779763712, 521666564, 12280389, 346882826, 703890662, 892551954, 485841806, 276850210, 338192111, 488328367, 168421843, 822948536, 729613428, 829563924, 459246234, 852975497, 566627607, 683708010, 181914040, 648963640, 373569200, 907619696, 959603391, 419968966, 532729869, 160865597, 498869816, 782302473, 587594814, 621310086, 297648197, 754826319, 345640377, 310014593, 627062299, 392186480, 943095832, 730178786, 895061623, 176584029, 325739235, 961636966, 987156653, 627432169, 106241720, 824381779, 322826000, 663212520, 191382508, 143179546, 354511491, 369913190, 498519639, 30149272, 65581840, 106236163, 546362796, 603742125, 202643957, 619040047, 771967871, 586954909, 947750245, 496980132, 447018734, 888802386, 177719059, 131630658, 339479359, 683315818, 593020947, 941283312, 194650087, 450157803, 154708017, 906223515, 633820410, 192202036, 158587839, 154610461, 726123810, 996168889, 483547130, 816615442, 355898710, 739000257, 393403002, 846198142, 654849791, 569102334, 937744526, 134765335, 18424328, 304817560, 251288947, 782041247, 429850178, 167653120, 373258807, 394422831, 736336049, 152983309, 571350204, 657407158, 992098086, 12961438, 908351643, 585811993, 679309305, 97255213, 204583774, 745869995, 506245299, 836960154, 555487591, 525265569, 486488756, 874064076, 460638694, 921352767, 806276623, 542884078, 189257429, 435177937, 225378817, 159190793, 539668114, 350660349, 48184874, 520591561, 613816561, 212351651, 509826047, 39636903, 884562169, 928474127, 441262243, 120548227, 862948313, 65028574, 169000667, 908836391, 507003960, 471285150, 143645322, 609493250, 135653081, 428437601, 684333942, 665367285, 921383746, 590323843, 776251016, 785630492, 815870714, 11467123, 352592544, 312263732, 285234175, 343326782, 348324488, 513995807, 508040357, 777113542, 951091777, 517402870, 637644471, 944922382, 413779289, 247968200, 458193942, 760291416, 354911155, 19070025, 245822249, 513088595, 649922224, 878634675, 209305763, 966250415, 840414919, 707248297, 399076743, 564099686, 854333093, 919756608, 634353213, 824078852, 849535750, 401876186, 673102838, 816261620, 959518090, 432870981, 455332540, 184490139, 629449375, 852594520, 316752706, 738688699, 553092442, 349366188, 631637879, 94590781, 830208458, 558025688, 455505955, 528470567, 430963901, 229802822, 244182196, 439885777, 737779146, 671349703, 107983419, 652183127, 737391546, 416694914, 46428632, 744839277, 788310232, 595752023, 158233343, 108187196, 552511378, 186119698, 659260408, 501758311, 499199030, 393224126, 670518502, 397048807, 234387995, 398680132, 611846997, 78383793, 659182628, 21093709, 300367961, 722045384, 791814408, 488517144, 890917224, 68187061, 438907607, 89337043, 352103997, 549214371, 884269453, 901155286, 927539970, 690032329, 253374797, 832515741, 515976604, 163779925, 201216582, 389580342, 541121509, 410349594, 531048127, 334350789, 720258708, 792356343, 739896567, 618357999, 352294268, 503518160, 821392572, 287431166, 639545430, 823168314, 307026971, 966037919, 985764237, 663108584, 553757560, 4341109, 654407770, 954935272, 779844989, 415830439, 768315642, 897167108, 643785475, 701552621, 452427360, 136436555, 673997088, 5673621, 507147925, 887886829, 263805579, 908867825, 117907310, 912217052, 153272806, 533464688, 418640017, 47692837, 673952602, 828197198, 512166334, 917227558, 438662946, 922889933, 630006721, 351249583, 25620101, 530276902, 917186543, 315126802, 126514347, 113814093, 953302838, 702023834, 276009714, 999850003, 84936663, 980757889, 118496758, 96832531, 35006274, 98031213, 645877692, 274448458, 249276093, 901360431, 999811172, 416265247, 324407250, 642950723, 779514959, 109209382, 956064847, 890077781, 835471026, 552521145, 608006448, 708261921, 620556702, 799844316, 358486079, 156421274, 30417672, 607035688, 265397862, 102458493, 269667822, 557036394, 541557777, 244576739, 475796991, 569363308, 889695654, 867259509, 84250926, 93710115, 869415849, 894241356, 655955794, 472635026, 997531599, 122565270, 18211049, 520911932, 905844007, 751629009, 940338956, 394678858, 191786217, 891650592, 561719551, 246766857, 400880546, 19054753, 657343654, 223812333, 5327902, 980713553, 780899248, 416005863, 767432963, 195441645, 156857569, 110345834, 254638977, 299710109, 718578167, 462314951, 90950307, 705040222, 718547439, 675497988, 793203853, 58165013, 135082490, 860633973, 675021861, 740961612, 244504750, 692729671, 468810569, 10109869, 842043443, 208593884, 545852697, 989034248, 315788225, 773137277, 214306982, 43924390, 270620929, 676584667, 886907645, 753864983, 522166492, 506755685, 784738470, 741146812, 509200737, 328194388, 88330115, 292803896, 794412343, 422253090, 497676400, 609502806, 506957503, 307162290, 338393498, 238955057, 464897857, 9694983, 965916061, 196739682, 89313150, 3004774, 239826176, 737832581, 467400795, 899358846, 175774063, 357574465, 308026850, 735716002, 903304201, 756325246, 712610092, 753421336, 572457816, 407334489, 513276442, 591742398, 65595398, 775233155, 277614544, 915039191, 423511113, 332840832, 246296063, 447620496, 94940561, 995227741, 496127760, 436546702, 261708418, 796785121, 776619704, 385831504, 237024445, 379006253, 615113148, 928527371, 137709036, 507646028, 866111104, 809146548, 287901617, 215293975, 778568726, 509014195, 670853524, 112504188, 408585370, 671621569, 333434837, 477713799, 454529581, 5370662, 116442963, 721220380, 591491209, 924975630, 133659786, 510852096, 166115606, 648294180, 554479298, 466658177, 769317744, 641486082, 135091669, 496606687, 253936845, 209103798, 368281422, 299719982, 492184935, 694811018, 765015080, 971255649, 166119812, 466964229, 961273385, 20871786, 411511297, 552979442, 142939488, 905178983, 848617703, 452660138, 431610392, 877581622, 400937345, 239131087, 761645203, 206895154, 567547753, 967073586, 388435628, 354141383, 216956207, 762850121, 986681408, 230323688, 796452571, 634270763, 688156504, 96756363, 729054437, 190678546, 632022567, 105108485, 473617091, 68715423, 991648071, 631205371, 737509449, 641874860, 568267702, 916151757, 578700538, 848478409, 38787185, 724873244, 511872723, 863872680, 945395930, 83787482, 526760120, 247728070, 632193527, 822121371, 375492926, 940763459, 306466361, 768653638, 422711968, 45470795, 578942469, 354096470, 258505563, 27777715, 197001921, 533814782, 398435349, 183938499, 879391393, 940201110, 557143784, 883292710, 973351512, 985184330, 975263815, 166613410, 801898611, 301157163, 646554907, 820764831, 268915697, 204757494, 999404135, 38573352, 376841334, 634703713, 407423456, 450646831, 315309115, 802168357, 155103734, 280227435, 916413715, 308180292, 54497083, 550978914, 940932120, 579322972, 412803393, 774269326, 618765908, 185336042, 595824003, 52256028, 61811449, 488024852, 460020474, 159743991, 319988881, 191001741, 124442620, 180311571, 341723764, 342368399, 84083583, 960114977, 483375440, 528859630, 713035442, 247954439, 889409403, 798369251, 874593304, 969607915, 873620638, 435904635, 96887427, 307035768, 876756406, 264823780, 820821967, 316659616, 268152011, 264436824, 828499712, 689920431, 648245366, 432276367, 384883299, 95891726, 123185057, 134964946, 479664032, 837568046, 156487816, 140505009, 489429671, 358604094, 322048270, 633341553, 890748396, 490526790, 207662437, 542484635, 236881541, 791098454, 440470978, 809597047, 119227929, 438040740, 918264969, 478505930, 153444458, 846128046, 570264549, 12757834, 93213380, 239466018, 901428185, 478247049, 767773274, 779997665, 663161874, 771471076, 131889902, 224700295, 69119347, 778928446, 290242546, 220900143, 482641315, 392016875, 763616911, 307446367, 445792133, 513363104, 617136989, 317775920, 94108073, 459462138, 424824665, 671587024, 885870674, 5592035, 73326943, 477918191, 376921053, 825545330, 938804136, 169523479, 729047496, 401138333, 653464787, 613254213, 171141043, 119499439, 763029052, 128953891, 378321681, 353089455, 926769273, 892390362, 384029967, 588075542, 291319894, 450482607, 507045341, 416652315, 14235798, 927248119, 964387930, 341778092, 4904033, 477206654, 109448714, 835864949, 666848687, 396743099, 701337638, 686843627, 584688755, 349479095, 714769792, 177900476, 485779600, 631953196, 171923259, 958361803, 512631027, 150462729, 892102100, 28933801, 863566214, 951235275, 965690567, 895773752, 783028928, 340202823, 913990755, 409521785, 172941467, 385400663, 110651598, 280524662, 122608601, 786544557, 962861710, 28718474, 671267307, 582408860, 777627451, 815655, 410762244, 936167693, 21293175, 57274010, 824173919, 764743855, 107178466, 876948704, 700565135, 781505695, 160910171, 630174148, 947622828, 507614358, 705702577, 127249627, 166417060, 608983170, 338602556, 315245071, 539682467, 59545020, 423306346, 970391448, 188865159, 850461178, 497493975, 713392801, 455568205, 442393343, 964623111, 420466744, 270684487, 229662437, 627542146, 449569012, 700616169, 784079762, 784476723, 549122327, 875263267, 632893451, 717304143, 823918420, 897147431, 869837697, 598343087, 719174759, 261978601, 586407675, 687071631, 409504491, 440626393, 168886132, 698812644, 887132519, 635195208, 634119601, 835153244, 652729070, 593048275, 436878393, 889655075, 833193455, 634255664, 983289239, 556158646, 653060944, 511327498, 198467895, 791712181, 662274973, 160275673, 784671161, 145517634, 857802443, 532841373, 695973673, 860631939, 320610875, 913535410, 594354554, 453333644, 745933056, 940736039, 109686413, 678024881, 889495964, 366855229, 705219429, 595221998, 641103846, 223543494, 526865776, 533506606, 454031750, 54499518, 677290520, 824430367, 221693726, 465248439, 172739941, 469658795, 68130181, 313005342, 442091731, 359210851, 299621555, 356307830, 22295235, 666305576, 622266923, 344337827, 165658509, 652037495, 501550314, 934592887, 798490895, 872132761, 747609964, 238639496, 840817221, 783231998, 877167674, 544220997, 243625454, 729401512, 478359033, 756615423, 391641029, 856482511, 227861057, 748565064, 852915328, 506612224, 834752900, 763838429, 338202842, 814912124, 591892372, 128661681, 934094994, 756575064, 453721288, 88422906, 635602321, 338334357, 239223545, 337092972, 476671606, 341428223, 137413326, 139131672, 892905220, 629364019, 849091202, 236790266, 329505574, 444460767, 20568624, 882248642, 2571008, 508417123, 531777958, 98515365, 899558091, 366851045, 375500438, 823336369, 185072236, 716367241, 879425602, 843030322, 829922287, 570456585, 549910778, 936616715, 339764094, 802778611, 479994705, 258167503, 211609914, 354193638, 361373432, 208127450, 669147958, 826210833, 705612307, 736094989, 832675084, 251454220, 141879804, 317138609, 107638312, 478012147, 272168494, 767578279, 221529469, 781754373, 105813015, 130798478, 410968860, 80185502, 625617539, 601848511, 355838495, 832857246, 911703546, 133411427, 469568635, 560925770, 900330414, 351548369, 3521477, 566349368, 648214794, 105609513, 138052287, 527544571, 458921545, 899347973, 669011974, 213036557, 337997768, 651554644, 582237327, 369908357, 288392361, 931443119, 395666848, 634908216, 297400652, 53749325, 985362747, 849770548, 943471335, 577124761, 741133499, 411393452, 439144223, 411107905, 675931188, 319514963, 979596665, 133022527, 828349289, 730068827, 440525399, 199516636, 286611426, 95976589, 571025998, 756915492, 197932383, 875148110, 222987792, 831159435, 348355885, 460891660, 206218143, 402871479, 83813266, 752561462, 709600121, 591353859, 935833269, 571499364, 344470817, 161531517, 157660765, 574147021, 722194645, 474544377, 586479999, 436254832, 963581782, 83386059, 364675001, 924879790, 892140219, 734061755, 63714833, 640144659, 561489995, 538224973, 98611417, 980310766, 83939986, 600038470, 637359607, 847434528, 797840770, 435045202, 352724430, 461737152, 225529477, 658663412, 525174222, 232830628, 239013097, 389208690, 862778801, 699304414, 974103199, 850857442, 102390193, 350817921, 19769815, 831552803, 300288574, 173333411, 329164610, 900841820, 799731376, 72906687, 281409880, 210822534, 773384747, 568208095, 98368083, 311027377, 772054171, 111607737, 998775245, 877965950, 290733275, 232324037, 511912666, 251004446, 944057988, 451918023, 823202324, 299577984, 614092414, 260429315, 182788002, 504076169, 487777101, 139161669, 28978957, 275264637, 225898355, 872101988, 716323700, 373421581, 253965309, 492186536, 266040325, 520337995, 770388705, 568140945, 647065312, 476512940, 700480455, 801498179, 802126142, 373571515, 309139971, 202957657, 793611974, 668845100, 524851603, 525580314, 795396431, 331495802, 947593319, 278941415, 46460631, 399495589, 869969661, 663459661, 660089309, 220427491, 76170475, 710923557, 883978192, 39378973, 791513838, 501692383, 665566328, 314670657, 873162949, 787055985, 989856616, 461642927, 756218097, 673134320, 550646990, 167978831, 50225130, 297968503, 261024236, 901966420, 735535302, 480005979, 454662903, 12284259, 332989719, 416696146, 515271406, 563878313, 632374245, 161487509, 839853148, 463756670, 640148867, 966165957, 983734178, 110418001, 929665664, 979457566, 756656205, 890679259, 166761221, 284327074, 548143379, 376951296, 423301823, 377083143, 394729917, 800172293, 150773581, 682562039, 426895370, 112219566, 762148519, 373765500, 620985558, 932118422, 803436498, 668130678, 532541389, 212465492, 435215084, 158206717, 41537335, 503965950, 458891305, 469296292, 991983343, 495971328, 233501683, 350615076, 505237700, 324847168, 326165811, 366364368, 240129627, 432376761, 388043699, 152534796, 643603723, 350136296, 967140723, 841749929, 768184502, 616739699, 570309872, 644191368, 404157378, 659097853, 776551810, 761009548, 881778884, 182658010, 699473127, 287736986, 529659709, 150145514, 987664547, 574303751, 742069178, 374237709, 500672267, 124880668, 3895767, 906774767, 866389653, 138466184, 205044671, 405986188, 381495968, 839167681, 79512218, 774735974, 852403513, 288563692, 132985625, 610694726, 142589782, 719163698, 647984266, 245202702, 394953902, 685589902, 370855310, 868642456, 365302141, 763344079, 995595732, 427368759, 55261273, 107112901, 288958615, 793074691, 324769595, 605602454, 518650577, 283481077, 425786462, 163353996, 889668473, 680023596, 820601010, 902353307, 234537997, 527015514, 374605913, 909696535, 784238847, 731923122, 248043141, 677813857, 535241674, 89867068, 470820513, 660983971, 402715209, 29077263, 507950105, 726730471, 214534764, 319835341, 477215941, 141035693, 271594671, 914200369, 48468211, 906995098, 801984257, 213884299, 976741911, 46407092, 644929628, 549347332, 410239912, 257511055, 417214772, 276780936, 567133738, 528754063, 834563967, 782074958, 910072082, 990358342, 830481457, 179270087, 359905609, 367251770, 56166012, 606347880, 559912710, 813222551, 44867473, 501168792, 766627230, 831638985, 166917183, 422896387, 235070050, 896975975, 869158698, 815216959, 438560061, 130190749, 215614604, 4124245, 210343113, 366385810, 500362783, 546193836, 43215051, 354975937, 726436418, 464437300, 659492013, 629558502, 173981846, 293171207, 638219006, 758724823, 23707600, 92011142, 542868481, 785832991, 45514816, 993115166, 284210122, 749322879, 386815938, 173410293, 264051670, 613763945, 696895445, 15086443, 64848866, 379968600, 197006680, 575664811, 328013895, 629264989, 538227647, 335517499, 361906969, 39427217, 283825337, 280275181, 952971143, 933337508, 706756096, 324166706, 271803859, 12504750, 19974332, 515570230, 250913556, 815366834, 901619452, 733106703, 568882338, 899483463, 390877069, 459953931, 85464906, 40505771, 624637120, 600674771, 626360229, 703887121, 419568224, 887163591, 601770453, 362619547, 826548447, 902137712, 132411985, 392301499, 22693515, 900769122, 904717469, 258760463, 693419132, 813690628, 393283760, 980872786, 769697529, 7937261, 343331663, 922598235, 959059855, 1919403, 905020291, 19537029, 447824694, 83576387, 210872580, 663973659, 97492767, 725318255, 761211030, 633397170, 673517225, 722515686, 396391501, 884040212, 483029354, 698317665, 681204005, 595415319, 698137425, 177041382, 385436595, 280657591, 786395036, 2316314, 555354425, 792487712, 522138828, 916373268, 978168103, 387366474, 606067889, 346962517, 288455207, 434297148, 186368362, 197930681, 978842432, 667898252, 425053863, 998275141, 935434408, 679017407, 526532744, 730682128, 588310224, 943028887, 726943702, 252340066, 950311849, 278960048, 182604689, 294114584, 149733440, 817520121, 646833490, 892135119, 69643032, 56898201, 40576712, 669412734, 397277190, 369002984, 250542402, 790687183, 264087273, 763015285, 619169001, 102928930, 996378917, 597315401, 775457810, 754194205, 692156911, 47229571, 584486795, 773461985, 473015636, 936723381, 770321978, 540594278, 855737579, 273731821, 19532456, 892209266, 930374199, 909484189, 226589693, 383606382, 437484438, 843353235, 180493494, 31074068, 987150103, 109152981, 239057981, 598176220, 578931775, 234123307, 694403138, 306927010, 86457531, 378027192, 678583736, 5740535, 462964852, 348471064, 863947755, 848364515, 781597259, 831935021, 970199383, 635344115, 407028321, 353130830, 90394691, 396530676, 816815406, 225421591, 495857643, 425141262, 844777245, 883132238, 165644105, 721002174, 523519010, 613006877, 791405040, 435038744, 430961716, 122223148, 773057392, 256979920, 562282275, 584839368, 222147190, 462961335, 445282659, 889525558, 708163082, 469537945, 891079184, 676983051, 256831379, 789475076, 152130578, 390325827, 798509711, 913740661, 811225104, 796351248, 477115385, 492105962, 684710404, 863057899, 489858720, 261062014, 16651325, 650920130, 394698582, 583075511, 131654334, 258869183, 465821411, 23269182, 763520875, 609521671, 939510917, 289960770, 45407208, 404623837, 971876729, 462397213, 619086302, 137987189, 902988465, 525576516, 170111880, 341656179, 905167467, 296019775, 430806458, 124363613, 978768218, 296389170, 627958005, 655964770, 625535984, 57425965, 93792867, 338947882, 114878362, 5171519, 242232656, 961163740, 260187243, 719149499, 221099926, 18403705, 269041831, 656151748, 229891540, 732777824, 964511683, 637028398, 878686546, 944145878, 402865511, 228019652, 169845547, 902352984, 958848549, 136748122, 959990382, 858140713, 294707128, 808418969, 334308342, 619928447, 328306850, 206451800, 435844773, 199025214, 541064359, 608019246, 925333268, 935604288, 500138604, 178924976, 368030885, 10904453, 367798779, 833833859, 372789296, 578207504, 112243667, 957684036, 513861505, 490140794, 762123701, 580727665, 983475088, 203846221, 226295203, 857727811, 820680867, 937536681, 433470260, 133424480, 563296038, 883486664, 431336871, 698542386, 685988732, 315469180, 957608564, 785674739, 445441879, 493439907, 635363348, 185686736, 720903134, 858079057, 96434374, 152021295, 126247417, 32651113, 93927807, 628227467, 175462847, 243278476, 387388337, 648499160, 141984621, 111421223, 588802843, 390372525, 871820060, 346368767, 318827524, 655329735, 2195018, 587284148, 846630632, 153270631, 588787264, 985076680, 795219954, 142664243, 414751783, 248276241, 756905909, 928698281, 72399084, 194373370, 264953813, 416751469, 61085048, 890921461, 57132686, 711153362, 796513629, 677622795, 883069101, 672622034, 954107116, 99760828, 300793912, 289468788, 552532652, 562657521, 974619910, 774845487, 157253812, 647097364, 969379611, 311838174, 313707515, 120493140, 78926016, 635465380, 696466420, 90732205, 8698593, 630052446, 298132652, 866913630, 366665770, 253077527, 594963777, 33381794, 635610504, 912902194, 187790098, 13181142, 541206956, 271446571, 255186211, 377768255, 167632508, 960823115, 566820915, 947274340, 533524180, 400013185, 828498796, 844880261, 503856382, 811938466, 40471060, 441452474, 280082831, 289343636, 400023726, 347292226, 500152893, 72150792, 615694946, 942066479, 211687170, 377510665, 289756261, 767304154, 553143144, 100544804, 908776349, 470657665, 127555862, 969747043, 10811584, 558683526, 391023227, 475245702, 334884370, 325001973, 577926949, 140909008, 827958606, 380865224, 517730849, 709616434, 177758485, 503019056, 124227149, 478856898, 227518239, 705353873, 525439791, 411567454, 151569478, 795451578, 519095346, 904421715, 953643655, 308959187, 965124903, 688599845, 731157625, 464700355, 932882395, 51431780, 67243725, 976739293, 552289707, 483784608, 423638223, 997563486, 696477750, 286648187, 854978098, 426837814, 827615551, 765239623, 842543176, 796591735, 838475420, 663292186, 610359737, 92664276, 31702427, 805248607, 155698316, 510229788, 549029033, 331713383, 306752838, 383545415, 302191626, 657284313, 280973126, 798862721, 308014264, 546031856, 517670544, 835865675, 701829425, 322029157, 81065154, 316495571, 54696325, 571191728, 5335867, 774691108, 40169435, 422519406, 60176515, 137394853, 789526718, 178305649, 56978192, 276222714, 427710483, 785407383, 418437007, 349364699, 835961586, 758701695, 771421772, 171920640, 399299845, 732219075, 42585112, 533779177, 783914356, 683015857, 316681019, 586329111, 715464328, 427082179, 11190868, 95455382, 612905135, 874129629, 526335048, 320810998, 351780057, 635206482, 146182981, 429273595, 895552847, 945921268, 677471298, 850503457, 88447012, 929712058, 302782058, 123955111, 732722521, 544950426, 226810990, 580817476, 684829679, 749592241, 542967851, 276411972, 898650506, 793161611, 807966269, 768820571, 284075625, 695522401, 956821185, 800125006, 75055031, 962932811, 26257358, 80251680, 769088021, 382052572, 678934760, 67420375, 874657805, 624688366, 605732326, 262265134, 925645698, 236270829, 110507421, 157839926, 59592681, 155890635, 188670235, 905843758, 754823048, 495026555, 176336234, 406142975, 645092306, 508933605, 242592364, 461092820, 825810846, 303658056, 960080476, 617869252, 482335596, 773025193, 466273659, 320307531, 95279953, 189056370, 501860144, 342617327, 306819175, 910836658, 169119665, 89516117, 895225223, 12007320, 358430892, 586190485, 34417219, 638866076, 591577651, 689244006, 26783403, 289046137, 825841765, 629605311, 887561206, 801058514, 764608296, 29599168, 22793186, 76735196, 79630950, 916635170, 263769362, 414568114, 464321917, 555397290, 820506634, 599208628, 96125595, 837792557, 707460949, 145540672, 352971819, 301603880, 522763502, 630935117, 927920989, 358939256, 464416006, 12854451, 838932152, 508239258, 148550208, 787821103, 493639467, 637763841, 398216541, 38732460, 494347236, 693723097, 77670697, 829696252, 226394751, 398827822, 620096317, 702277404, 377061960, 998901179, 311781290, 926688238, 761938581, 168791757, 766104021, 853691588, 773220657, 80636913, 997136156, 131316170, 837945065, 777454145, 955250471, 206075619, 979603247, 602643111, 500562628, 8136657, 362669890, 221957051, 492119150, 306144364, 30209899, 372451582, 856509579, 981398285, 11873727, 129049984, 974545956, 767929296, 475089603, 971886003, 511926360, 666866138, 855353642, 329926176, 219767328, 828070180, 422730265, 538056525, 711541834, 755512747, 979061006, 181046924, 322900187, 631351012, 600859123, 922706132, 798202824, 995404606, 310006911, 113307031, 974826372, 399919881, 20313367, 33632615, 741326540, 59387850, 432455066, 288671896, 97294062, 952708180, 206269297, 154657796, 231798498, 983950362, 416289491, 902831039, 615891540, 736329339, 276311493, 582300027, 724483915, 481157662, 158852983, 865733829, 28735187, 401607252, 940300393, 787883183, 835677038, 228773236, 634745171, 269668947, 780369317, 870560943, 419074246, 71220731, 768525566, 891335333, 214352838, 276461321, 691279459, 616134541, 504765210, 465319606, 381452371, 820450842, 643125613, 440816707, 373300518, 564389399, 218661447, 837758997, 222185815, 148685957, 335676136, 418487888, 709396918, 673791031, 469040997, 393649286, 832903243, 258130257, 973015684, 13234322, 811236120, 938049459, 945373125, 979729847, 762266503, 996917742, 964824262, 903329751, 529617363, 747599218, 990823627, 798390823, 353805927, 606445627, 584897498, 387001101, 902911576, 851679362, 948614433, 698723252, 242731621, 378798416, 182066888, 371213400, 999429233, 810646541, 687345911, 358541628, 787914706, 727608893, 475076882, 522033594, 13058470, 699360716, 865049020, 561198955, 648696344, 693576436, 799233467, 912461047, 709722394, 639739299, 856911528, 923166831, 615281606, 845987592, 740301524, 447244682, 309807842, 260895942, 777323689, 411645852, 105481718, 492880528, 56828371, 984487423, 939469865, 109854138, 462641880, 302569297, 753631886, 357492955, 791134853, 974253624, 919872955, 390245348, 833402767, 607915465, 419993766, 869859578, 255888493, 645972826, 614822923, 861496743, 453939774, 652327063, 636692058, 26961949, 393348929, 577208754, 570384349, 915464008, 555603908, 688080143, 739867290, 278667745, 852496861, 340240289, 274799760, 834123553, 676872267, 873358572, 747351498, 542857304, 877843704, 646459977, 316765278, 13930173, 634453191, 776784081, 515900594, 513100554, 391542313, 277921695, 830225473, 785380638, 271857327, 70542421, 842102462, 532670509, 818649580, 751543355, 121119619, 161668041, 67271312, 11587448, 746697016, 5815704, 921711072, 455808595, 611623731, 75143801, 747708738, 359458004, 289588999, 300164818, 7218314, 576126946, 355454873, 134085123, 568227460, 266095195, 895382647, 759100076, 186887897, 503804915, 698444275, 1303338, 452137144, 946822488, 956402565, 888320654, 971272546, 463405661, 985436841, 316483605, 483563761, 999417010, 409158569, 298782710, 270977266, 942134475, 934408220, 517190036, 468709465, 333404333, 403664744, 47084799, 36330309, 106144999, 266455191, 626970100, 853603880, 720670490, 111144959, 892912098, 233179826, 951407546, 484684930, 816685322, 14403859, 120167585, 100472012, 901721526, 905717422, 497610121, 245786690, 971912593, 595550001, 619178743, 651303552, 414328581, 532041263, 94258691, 652679665, 86609560, 271816928, 768918537, 506849117, 883072504, 159342653, 738381828, 807797342, 65167708, 579130706, 92369748, 194340084, 446759947, 154870070, 588974633, 198917824, 884453032, 911739598, 905587893, 27199943, 83269458, 209921886, 526370086, 195582269, 576265621, 579569864, 813758183, 688907048, 883112835, 679864341, 818278955, 58846261, 614856158, 847048235, 619491944, 466675950, 78789834, 133330722, 85048607, 412694965, 308957872, 916326502, 249420990, 27464433, 96548839, 52867228, 482257041, 25450655, 221395468, 331777688, 691107656, 256088944, 713890515, 651776348, 101440838, 566785316, 777461547, 228634008, 695324295, 970362837, 272266352, 776084922, 368279583, 306674439, 393434752, 315185721, 714747355, 449158848, 997891749, 575699223, 182930309, 313694453, 797437133, 292740822, 95560805, 489825763, 259806195, 529647674, 747149176, 957072515, 930826218, 679585112, 674318242, 761725325, 398470022, 108923066, 45358222, 257001088, 488737298, 241332224, 593950965, 438075066, 535411989, 518770077, 337421363, 690976482, 317299601, 229968987, 531544099, 477972526, 342858643, 90204496, 319804246, 161933161, 363480956, 631723618, 735494831, 500730910, 725016895, 237396589, 52731275, 613024988, 394139220, 69800914, 333125088, 74275999, 776228724, 933703839, 895745222, 666202886, 333351230, 515288710, 260228570, 613235948, 784408227, 920314402, 198983555, 883739329, 118119155, 1314806, 655870883, 170317759, 71965625, 29859368, 980426024, 25680078, 17978464, 107632410, 750798799, 434375292, 979585387, 167394995, 219295896, 441210394, 598073505, 629489128, 503029683, 872587973, 10702330, 798126599, 921818727, 979236600, 941612281, 710758608, 924291445, 976743214, 89713257, 265059590, 981230401, 843310683, 520938987, 291592371, 904386679, 319001396, 113607103, 725847323, 589987618, 794694413, 734197838, 167538740, 64441325, 613554745, 177713860, 926939769, 21763073, 557309378, 199008331, 254922143, 225195101, 421981080, 498384076, 774473617, 331234859, 865283235, 934930609, 905353017, 963705139, 651484089, 210724854, 423578566, 695541503, 17919456, 545249524, 65238734, 765457386, 327660920, 792104583, 646752630, 357839751, 12591903, 226954702, 768422548, 58765345, 956916646, 726903987, 211954004, 906500141, 106154614, 54748039, 414414390, 75149149, 972476262, 989209927, 330668258, 843836362, 320977684, 748846096, 44580453, 190809275, 978596989, 308659624, 275412907, 147180938, 547647937, 14690205, 806866898, 359958094, 56971225, 241209220, 112855212, 937691826, 538654852, 525096766, 620049389, 782660260, 720924466, 44559752, 714797745, 165733089, 546450930, 549937395, 986113491, 544164994, 839487137, 627292386, 367194578, 746782920, 348056578, 588657227, 786724684, 303346008, 226967049, 134363643, 524851289, 465256257, 391600851, 271816188, 415848525, 211445857, 346962517, 21379632, 347435685, 486524888, 751882964, 937956734, 368700789, 131983127, 287061992, 603820209, 645783901, 644259818, 670100040, 99107159, 872760311, 660081346, 667370232, 790345479, 306882574, 641444723, 82647803, 302909309, 79945067, 84803397, 968793904, 607659918, 492556144, 14697269, 964087087, 479901140, 921061463, 506497985, 466313742, 939127174, 814641983, 644859558, 657951941, 302252831, 236052260, 75297976, 579992712, 216630676, 479175455, 227724935, 734508726, 269402372, 132804373, 843732932, 672970359, 740183346, 819894740, 792788794, 272605491, 172489088, 978904410, 124025700, 764626958, 771078826, 930171120, 791434755, 905572640, 784788972, 944670367, 857769900, 839261637, 9594810, 21603400, 505674287, 880593418, 154019928, 521074491, 882577849, 456519813, 564021901, 393284413, 897061608, 830248440, 848871373, 583033859, 910679957, 791147321, 661202118, 339367669, 936626914, 59929433, 341109252, 157560603, 435863277, 577447333, 362128643, 864945983, 62389073, 756117584, 116578963, 181681040, 283250950, 693510016, 467333107, 575079923, 456568635, 16637679, 868389577, 463060698, 774341709, 890428627, 639933602, 208317379, 927303711, 183954074, 363686409, 722445291, 990613859, 623663050, 842011954, 218863088, 835816007, 715297021, 415331564, 789388359, 157484509, 485540153, 242294939, 849829400, 650545651, 710009614, 915979997, 151580704, 550927066, 298886974, 268424250, 369925581, 613571583, 499664023, 177851543, 52654554, 533753285, 959813892, 979201252, 777086219, 551576833, 208673905, 503915585, 353936619, 889404925, 272324092, 389528009, 999839191, 130872116, 709319892, 720091222, 353658467, 778246500, 402441242, 774166153, 736775515, 743919106, 982160236, 491154165, 506895893, 303042686, 943607163, 373677820, 587497446, 988628839, 227282748, 397954754, 15411863, 294599943, 480961678, 910117201, 904592286, 562812227, 552283067, 399829815, 574944305, 968694116, 965843832, 438930486, 5022343, 622134929, 76748049, 289234571, 836609726, 490012629, 329161652, 402442218, 419370560, 633737295, 521670862, 169724533, 433529267, 438529052, 106417334, 985734045, 114258302, 481620854, 166219356, 371301632, 615858922, 933295830, 880654542, 253209112, 881361464, 625265286, 39978427, 50074429, 455650705, 702022074, 984694110, 417789802, 289604331, 932424707, 241747896, 141277632, 70220177, 220028656, 545508748, 596462002, 744441721, 134043637, 195322384, 25789241, 122717981, 940299381, 68797754, 152668259, 537168582, 728233051, 582947482, 430997905, 876347615, 783872679, 900688430, 686403473, 561489812, 261083602, 627666963, 360067110, 571831207, 855971387, 188388797, 483195833, 755508928, 828663106, 471012789, 630524989, 427181794, 721394201, 209847638, 427365252, 503702343, 409903443, 298212081, 855741865, 655035223, 25376517, 528058808, 238829521, 795865551, 181357024, 400686450, 459670441, 923810071, 485069576, 751147503, 306231269, 708371113, 395848307, 415192636, 155378765, 920821998, 727464757, 147474184, 316956777, 170866426, 475750867, 446648156, 492020672, 800674799, 808868103, 364409530, 3958306, 40209234, 701370673, 243272041, 796117332, 270193136, 357124494, 235125490, 719232973, 965881857, 539054508, 236818300, 347858877, 895479324, 184256136, 988041309, 708220281, 810150827, 74556832, 6939617, 534133939, 124645090, 694728504, 65087308, 465808815, 632306117, 679374238, 856748840, 129155688, 684330629, 989716346, 291947844, 358112382, 698410832, 477052622, 292854700, 909225836, 760668181, 74781137, 116818899, 490232069, 941228501, 632429247, 744394, 875448560, 566145810, 498758025, 819964886, 225393135, 735342219, 400555715, 113323001, 293237924, 316772064, 447563558, 558932810, 3564697, 533368513, 171790746, 802073295, 289427371, 465765628, 674261253, 392922510, 813842718, 463625375, 634729950, 353043279, 34962369, 169243900, 442727126, 20373050, 571677244, 480462287, 200599331, 109675100, 303623931, 721862548, 853784309, 4944577, 908560390, 93320675, 613369062, 473647091, 643671963, 726017620, 835622224, 398190425, 829661237, 323183349, 195625860, 904370381, 789057007, 616104033, 236716704, 920610352, 721841561, 712525522, 275092143, 106962413, 748490581, 899509374, 958972274, 406645489, 25052616, 473566949, 987155700, 931655820, 523649957, 513212466, 515950560, 156447269, 28039913, 384141311, 123829138, 600887828, 560782307, 22521761, 510980104, 259179528, 399167589, 614648425, 696929265, 552834908, 273838022, 211669431, 815817727, 866551573, 384124621, 200703310, 489704623, 25068370, 668235513, 66961863, 991085611, 887680569, 167144758, 697311896, 394610774, 437419404, 957994445, 358944698, 373042858, 57888877, 701340018, 438154038, 371149142, 932365775, 536060517, 459232046, 762597796, 706952657, 155243101, 522378222, 273245356, 209992084, 880048493, 264330762, 177849144, 689318427, 934012886, 993864239, 499807429, 740397780, 450750511, 632216772, 927771836, 202940221, 591817134, 722388479, 410196766, 732073080, 390225839, 728967104, 438403863, 928231128, 105480813, 720316220, 236562869, 544055785, 855818479, 149351822, 984887029, 150670612, 906133314, 488738530, 390296853, 119336246, 514623874, 131943329, 43690192, 203360404, 639113947, 842272451, 534965890, 295759081, 616480439, 77866178, 836786394, 915754563, 981802762, 675768704, 451534341, 739295199, 530905473, 597794122, 717950814, 258732470, 997231761, 469133892, 166328026, 944491503, 188762526, 609447847, 352132729, 229717568, 50933973, 52107404, 958895022, 218752711, 816758689, 670653464, 644181198, 913228391, 254703025, 434939456, 228100669, 439175110, 708116522, 261391731, 171136552, 234530911, 366467989, 781924305, 435647087, 244213643, 63267264, 31182890, 880897696, 385314181, 719670585, 81492066, 908462286, 487802053, 927103466, 54505309, 177085070, 834823745, 129352465, 989013711, 445956925, 67370824, 218440862, 480616191, 769162777, 118639220, 890916187, 935750445, 481737372, 920077038, 294698869, 340130919, 757580753, 363912144, 44550535, 710447917, 752911899, 308464902, 15700549, 638002560, 495935540, 550044614, 519258823, 521152382, 20324966, 984783720, 135293298, 602170815, 61420738, 438325217, 121474002, 651356725, 24127248, 620011059, 25312717, 493272641, 983592838, 74557504, 166134329, 674693831, 538423007, 434482138, 552562935, 206016947, 138071284, 371965062, 549566018, 451140067, 900989560, 282719257, 147398415, 126729487, 120236564, 616682248, 957243273, 948759948, 444256596, 404902592, 897860326, 111318623, 537865175, 32750649, 634111448, 337406107, 751299649, 819691915, 946985872, 265367831, 335041076, 955732322, 838399646, 496113106, 952002986, 285740039, 790711204, 230585089, 241288847, 355448527, 633000175, 802541649, 640093780, 24167048, 500482046, 234458890, 549515174, 993937566, 934446227, 89188743, 437857081, 960518490, 389456969, 442718180, 961459893, 627386383, 971024398, 713327312, 204100312, 244239283, 234190138, 900377183, 841120815, 414853647, 886947927, 327915415, 520874931, 537768064, 378724138, 975452513, 761247015, 504875074, 377911946, 965421218, 3597172, 565263980, 537549910, 407354428, 190388071, 712269503, 246353043, 502172526, 421925677, 512747273, 772314420, 682103455, 468097468, 283060185, 648346784, 950168035, 78384702, 841127759, 407692749, 942767286, 497855207, 448835105, 785583580, 141266566, 557765110, 855224841, 407384142, 823116158, 341599514, 446405822, 692074716, 502405962, 488605958, 989163663, 39428288, 770272167, 710153203, 949272438, 188756395, 655724788, 665025175, 499976718, 647830479, 287492925, 824948783, 322837858, 691005959, 738456283, 76231328, 507486328, 878875245, 353934955, 611748891, 438955820, 20344676, 971958933, 556348114, 340725381, 496845277, 294559687, 549563057, 43942722, 468526640, 858217904, 786885232, 145848591, 261269689, 313228810, 989409821, 430075305, 905869119, 297832781, 359364525, 379445959, 595696756, 2726833, 452026848, 592914836, 720360237, 194308220, 466199533, 600076193, 766694664, 910366909, 738121379, 640195747, 245597010, 837280424, 587520798, 888942319, 173502759, 294746105, 849782813, 660192612, 48578573, 904827291, 55085557, 830144991, 958920936, 556497803, 586509666, 946149452, 383633545, 634031279, 477406574, 516734070, 321834935, 407565383, 873020056, 587992987, 391621719, 53320374, 998811058, 311345890, 661240675, 867110328, 427974875, 597132106, 127394151, 765815004, 265110505, 577192060, 285153351, 278071262, 720568443, 539431692, 169076822, 238215648, 5740443, 691837132, 224527249, 235569528, 41001320, 77377328, 598688529, 87713375, 594345093, 558394736, 481718931, 846880657, 378559572, 228887106, 747695952, 501187310, 543035060, 529143103, 62397247, 564697662, 20730445, 872787813, 424627998, 501072945, 978349855, 12833325, 173158458, 601579657, 650316173, 114784390, 977536467, 329119273, 601258183, 886617583, 579320262, 609499062, 147310476, 645023080, 506180405, 96760350, 985688818, 532916359, 851826637, 62274855, 910759494, 160748668, 134048105, 977738565, 695727079, 30548563, 390162674, 606788849, 406069849, 598940243, 730228903, 481297338, 241549237, 915985251, 577612905, 270360815, 195567679, 67170188, 914533713, 5456131, 977573581, 321639873, 427348242, 191596216, 563982191, 837524761, 558081798, 953252855, 29027491, 928173257, 42992490, 883817996, 250513479, 344333921, 355774576, 952424121, 911423891, 142221050, 466870660, 363927635, 986778225, 898883247, 631158224, 60082126, 811347403, 152529631, 994786011, 937691531, 75861085, 750357533, 608901857, 460771829, 565057119, 432570642, 262872518, 10452929, 999752473, 177869033, 886100984, 30663522, 985468000, 733295601, 759210545, 527001400, 194079878, 730859753, 580583154, 225247840, 766801410, 720221581, 4072751, 468256583, 747025047, 298565272, 935422603, 268669804, 647612038, 410838873, 13516392, 216386972, 631567485, 196120957, 604042428, 996116555, 112813558, 118151990, 336710, 759272980, 961881335, 124730586, 681845778, 167967264, 611994261, 912366543, 212775663, 607317630, 186387888, 10923832, 874144781, 468210691, 375625472, 188499871, 581576249, 769920666, 84612058, 925243996, 675472295, 117876212, 895713389, 330159047, 308133840, 579766125, 85831607, 501641346, 896813213, 160657167, 139590170, 678350882, 133291121, 733853112, 414451096, 995059960, 893382609, 189394922, 256267826, 526169776, 446597846, 438782695, 253451589, 574791815, 718712556, 511814195, 168428443, 323179978, 666832649, 214626074, 354490576, 130268154, 589399796, 715357110, 682753662, 75626490, 856351079, 229911278, 796356384, 261247558, 367818390, 731885525, 751291694, 691868831, 319572739, 735316807, 877434840, 138812504, 35533768, 515384542, 887235991, 502970914, 360528188, 160272198, 461446063, 347001621, 624112443, 35083895, 433108775, 692834177, 816245874, 216341000, 28382785, 737984920, 620737656, 394148746, 718863078, 576723877, 862866106, 731528691, 400097419, 220553715, 827239768, 781669201, 323554380, 861587256, 354778100, 137537716, 228720444, 249634478, 840308266, 45476595, 619844297, 599321858, 642279310, 646378008, 687735047, 992088191, 181697420, 330987892, 222753197, 125301344, 399802088, 345945142, 131018401, 222824179, 418638153, 147577682, 47905080, 992285378, 564246134, 108985672, 284056804, 417116769, 850586089, 770060146, 433406648, 438705091, 860229778, 669974017, 85742378, 857751676, 18523296, 664766901, 297943566, 849637043, 962807000, 979472127, 703468989, 851080753, 476113249, 243971369, 690688322, 777808421, 301960214, 115572116, 747408907, 722406108, 850208604, 606039383, 330053923, 703967495, 428020135, 985752246, 774887180, 717392934, 278656334, 229470446, 791163106, 612732073, 138011880, 315413086, 846002968, 455208289, 541326271, 417040254, 362013400, 577536744, 253706480, 966873188, 379702951, 996205416, 627385760, 542794793, 667584290, 754538437, 854436351, 975254079, 142283019, 100574540, 624264867, 31738104, 457070578, 667475270, 494582229, 356437103, 325067913, 760791434, 244106293, 919564974, 194404691, 50046265, 96489370, 829089796, 373998751, 12969404, 606707597, 853275659, 870239786, 826955395, 443896757, 585546180, 378475198, 733977225, 518540753, 917889187, 9370279, 514452136, 326007834, 187250430, 348125898, 718608089, 571722957, 821378585, 361861733, 475149544, 331236168, 787964266, 927563304, 688448074, 53759865, 129088187, 904220414, 309868897, 482833389, 437055898, 834821434, 354956736, 679458694, 527256301, 966173999, 423565759, 501328355, 674483039, 855559115, 549969944, 643148227, 118819534, 916601744, 426253736, 938020567, 216591235, 884291550, 65619928, 365862701, 977157042, 839112138, 756016511, 343617485, 859319468, 574183795, 553885439, 231195067, 13204058, 477411580, 170034361, 95612755, 76173611, 987347040, 543194069, 911394337, 408910208, 44793880, 911251151, 566327505, 964427343, 224743517, 382048904, 986245046, 991957518, 482079118, 730654567, 573922023, 934115451, 544953326, 360586088, 1126811, 974058558, 539004387, 525215261, 845329572, 18023599, 300210461, 750003980, 853251337, 909517530, 111958144, 334859959, 234117275, 614797019, 234551185, 551320300, 85466095, 203989952, 918911369, 137976140, 481529708, 696311130, 966232044, 72790881, 280150123, 261671612, 51298762, 465301380, 576661383, 749303328, 559108747, 708562549, 47672985, 916950319, 355835182, 450965966, 185021208, 260585624, 434103250, 964475799, 931117746, 555120091, 470042740, 347417589, 933741507, 593300864, 125701168, 470746022, 753373722, 944836698, 215701784, 938439610, 459744818, 826349595, 622490439, 554447595, 485751300, 131790475, 390825819, 849410640, 577334156, 395120842, 70197602, 631249282, 766952728, 997654164, 192804214, 401774451, 363842000, 744276951, 94171074, 438366636, 272749477, 38846124, 446574883, 356324719, 461486787, 233940657, 222390934, 143803705, 10980942, 549726942, 909479785, 182474114, 974347838, 633730901, 587654762, 988003282, 480456598, 55622329, 143382007, 265478654, 821587026, 256541060, 675882970, 27372001, 26715510, 600125717, 703250994, 953370352, 46656027, 463111214, 608516332, 652766552, 11835667, 310243567, 218474343, 659018138, 598996186, 323479685, 284520226, 878710928, 423488620, 74937952, 790155916, 597145410, 442963428, 984537001, 127701340, 52368130, 852694434, 903467135, 165689694, 992104607, 594385012, 119171394, 216873805, 617115132, 842390781, 149958427, 138274235, 681587061, 665546174, 836564362, 609120171, 986612050, 626694609, 619327540, 828110418, 396487217, 227594842, 181739026, 843823945, 599046142, 681491704, 743860347, 57138292, 919477927, 949144669, 319009342, 551194247, 225464746, 578667131, 523837154, 477192631, 418437386, 69637003, 916196834, 443353777, 298189381, 698175615, 36175982, 536024231, 145432579, 429346451, 760980955, 450085805, 984941589, 156752776, 591124425, 799610279, 340478180, 994623944, 647005900, 191728321, 843359670, 161306004, 690565492, 971005720, 116364887, 744650636, 412424248, 903854628, 671915958, 418385906, 299381003, 314376368, 605857635, 770386362, 343725942, 896323759, 971695231, 60197474, 678155694, 82705310, 29898208, 280278100, 22677175, 531015239, 145943025, 160901236, 75923088, 270323053, 258108882, 748267356, 446508534, 171820302, 891169654, 880491220, 921461385, 791771127, 493432684, 487743458, 83722855, 405479700, 570771185, 11530161, 397897055, 177026757, 518535556, 298689693, 800236368, 89101988, 395769527, 638409810, 992911378, 706320109, 785900169, 651551191, 370725312, 923992644, 447586697, 270184793, 805668140, 944535092, 53787002, 575290574, 805870483, 340453164, 474263504, 680560784, 117332378, 741972373, 234984965, 367483386, 303530368, 581672093, 585508815, 318531106, 14537308, 157523565, 547637378, 765747416, 430658802, 23341923, 323781067, 863630319, 451830580, 146017369, 374315606, 92943701, 736153614, 395015407, 556934150, 945271940, 293870471, 755646217, 391595272, 206279495, 922168060, 111445859, 817624539, 409636053, 494433798, 302464360, 327818083, 215138055, 472878864, 806017704, 450269044, 983791480, 624244433, 314906243, 798618751, 624497407, 704632096, 192246452, 367377206, 716198936, 271529747, 663989441, 92439241, 672933319, 608933959, 374299069, 991678693, 926317900, 965533587, 207598680, 418253901, 538236740, 668235038, 504378091, 736171529, 653017103, 63379366, 154006885, 609050190, 468560458, 891252233, 371729888, 428083002, 698755701, 487114773, 142230275, 752513267, 363884915, 180151625, 859202502, 969688535, 686566351, 684018812, 24483476, 28646075, 952556254, 881593840, 710200122, 954543371, 787015339, 27454053, 206617704, 880976708, 900996968, 97663371, 447842664, 904058052, 710909966, 175922232, 316174703, 633645595, 589930024, 863143554, 344386226, 47901130, 943900175, 343624862, 896034301, 762183646, 38494376, 445160143, 32325533, 74386520, 40749150, 845739031, 426696252, 675932537, 322632569, 255037707, 52639097, 497996902, 396144155, 44155123, 64636113, 180461689, 283381780, 925963686, 154418343, 818307263, 600314640, 718610567, 60094177, 260310866, 837581056, 25310401, 332785862, 29009643, 695496907, 827538757, 857177979, 258373837, 123289899, 35442979, 197604701, 989184015, 109023337, 507139572, 685580374, 297659784, 679350766, 124503585, 340586112, 710606342, 532952316, 626278108, 639450768, 937342098, 561907859, 216884717, 85377019, 91314093, 772771211, 320208447, 848211720, 474744040, 321068667, 360306752, 795473429, 905689757, 48499098, 440603852, 257393865, 207363949, 417693413, 186066481, 294619043, 949909882, 760607143, 894853675, 309565188, 757276800, 352746162, 317691185, 424790180, 356815555, 418968877, 801808837, 584776380, 458375331, 884922990, 424640202, 955661579, 221605235, 385246648, 259124235, 370734110, 809581661, 733837774, 850415773, 542071171, 762888903, 808491492, 804153283, 638528500, 583694002, 156202758, 321605925, 366974652, 484084075, 142506762, 484078523, 984225954, 440289727, 468411889, 381351054, 730787514, 507343788, 944617893, 497131475, 214969549, 944375119, 286962000, 648890985, 567584679, 264257611, 799265938, 346974698, 355714931, 332783871, 150129267, 931064848, 28746249, 710880098, 786298409, 505453097, 297621349, 996826022, 576410881, 384912784, 626017127, 365108843, 115983757, 478380973, 170932813, 102702704, 624594366, 590748261, 196501028, 625748603, 122706292, 248009455, 976624572, 105844655, 157033705, 791997912, 242986345, 908036429, 143385746, 669025552, 811662888, 38689137, 448845805, 848984038, 790755775, 716540089, 156225983, 495250665, 656896957, 150071397, 212796205, 134618234, 670984747, 461414326, 188127693, 281947246, 79474859, 854442434, 923683154, 479200562, 752561322, 318312295, 546145500, 445250614, 884822009, 535310568, 196636960, 483994347, 216856527, 404662388, 250514201, 461507594, 688427256, 864600290, 150826721, 317812586, 612073850, 307534248, 800188057, 910852100, 25166200, 375623581, 54963900, 181621151, 894507683, 877503424, 89078210, 738870182, 659871227, 744090903, 816405507, 306504776, 262983664, 220862229, 432824486, 338653627, 996940193, 600822915, 78653676, 966471475, 357273878, 533539110, 450125235, 564252309, 326782933, 833960591, 396711730, 979790595, 673714765, 955787736, 893599453, 882144702, 381913228, 62494403, 701060504, 774985287, 108067428, 340562457, 483570047, 470426731, 544930870, 469766347, 264300198, 926178936, 592743103, 53767873, 475693550, 844731794, 96186106, 418364147, 561244863, 221114620, 700029857, 850572359, 507132091, 216001369, 326949206, 741590143, 737395859, 346306084, 743404158, 709661022, 124449377, 240072742, 181900604, 170158954, 142382314, 815466814, 99764061, 230767720, 981939635, 849999291, 764405609, 272892170, 934120779, 617100485, 864988761, 815236854, 383935340, 815465816, 649809881, 526859761, 38941741, 11162526, 213680804, 685250266, 831439228, 879011090, 571551965, 785137090, 784933207, 347529863, 683705176, 420369270, 563854103, 450967064, 638801778, 821673117, 283759424, 26924407, 77905568, 848905132, 112553358, 22518699, 460615564, 428219937, 649473223, 136723827, 855270355, 482508303, 16207639, 568533375, 39866568, 985579852, 33770912, 814732097, 62754593, 653547925, 937482700, 259706381, 167079987, 215150094, 56518700, 178868040, 668946046, 985034588, 333834605, 36055608, 32556886, 398130822, 313873187, 252279703, 416824326, 215684622, 402223565, 58311376, 371412509, 555745970, 212606872, 847842000, 137746428, 304532289, 776827343, 911408130, 137708874, 743143024, 198296870, 224721880, 911877954, 569974391, 723570980, 929641011, 292353949, 397026671, 170838961, 913855480, 670290062, 381099506, 869497753, 846911003, 390139807, 142104158, 614859931, 173248001, 241207734, 435360388, 556666383, 118667880, 255117145, 81092036, 781655388, 813099897, 431076125, 76716286, 676884499, 656228120, 393270378, 321975561, 270713407, 662818150, 480272941, 169253688, 934098038, 488503951, 1258627, 128480479, 606522008, 831867100, 134152583, 978177819, 87172043, 627282697, 786650093, 375982630, 288295884, 155109851, 762352950, 445870914, 697002011, 738212640, 499269483, 826486081, 23867964, 666661404, 138017928, 404455132, 405549151, 798798167, 721231319, 59032946, 285933821, 922679632, 329837171, 304503386, 481755327, 774779262, 669046792, 117015298, 541262643, 596409418, 246786975, 275466183, 702236833, 369300903, 945482010, 429144841, 846322698, 243978312, 792312407, 401292408, 971084162, 271424910, 961206693, 483013145, 505673149, 243530000, 789795071, 636513810, 804283748, 640991869, 923917263, 434973231, 393197576, 539569220, 442190812, 306055655, 154119330, 40852481, 484851141, 679303558, 713137641, 598685517, 255073719, 195035006, 706444901, 670743411, 12588112, 187906693, 261264634, 595146731, 868078413, 815176688, 76513761, 574838786, 930437341, 243256460, 376653500, 932878848, 450624164, 667176137, 952570439, 861825040, 841432007, 870737199, 273713888, 689463567, 911461424, 577671470, 344939184, 312028484, 130950357, 861091348, 897311486, 491334435, 483999686, 71873433, 308329059, 491936390, 805735404, 606991518, 304757977, 968143805, 9418007, 693718288, 388659747, 365290662, 74778825, 476559804, 341918501, 192770602, 492924500, 984982690, 256134487, 999237046, 536444074, 110505706, 390985346, 632676378, 314403287, 546469361, 55029514, 220966899, 763610009, 119275949, 94597302, 624815903, 569098357, 464388828, 211550335, 967684527, 333255860, 596218321, 829746733, 893935774, 135733069, 444224814, 125040302, 950388202, 906736360, 495242671, 596018588, 786121052, 773388734, 83658976, 499895329, 395862373, 248886819, 461414772, 168685266, 328908162, 488521550, 572377703, 381463565, 768685446, 810312101, 629418425, 179921848, 80723656, 77129408, 619966785, 62645920, 924451815, 795378085, 863319385, 411272486, 526591426, 357379185, 162535868, 691072356, 316903018, 758440888, 897804876, 946248935, 135856097, 332100918, 567987462, 494216775, 876182539, 228327938, 973468236, 14657211, 595181696, 316908557, 809942827, 188055567, 241062387, 689085018, 568884400, 129459038, 459663139, 518322002, 454581595, 568246653, 583585915, 402368319, 984248032, 67201333, 491701349, 984257581, 349280248, 305259956, 143949216, 770118898, 969228546, 724337308, 240912492, 209895783, 344314680, 40938072, 615673292, 133171812, 546045234, 750163875, 598145662, 73706511, 694188674, 143101156, 826829041, 466409016, 189595204, 970269120, 567037830, 83897120, 268298223, 366201015, 823655146, 760980960, 201393427, 169291890, 754004906, 128881971, 816624344, 940900864, 870402153, 185272258, 160552854, 454673468, 590524618, 413661754, 849999731, 348926886, 363950480, 898309673, 989368836, 78936563, 925624810, 934819235, 813904691, 896645443, 996823509, 772667734, 221835841, 587860356, 887701003, 384272483, 571187617, 314085435, 369900501, 243336322, 217223240, 355450268, 900064041, 116935503, 297019746, 228259081, 110179657, 309460819, 340004089, 978122501, 602362029, 645948193, 116474987, 98523430, 583937701, 158642314, 786571882, 100821232, 848776645, 105080643, 918028466, 823961920, 264530355, 686600098, 400943775, 938248615, 447431535, 547694840, 27211026, 960615761, 681380917, 181601095, 154803678, 894019126, 655665065, 943618893, 962321621, 564777430, 255935481, 585160591, 49446091, 429986631, 7106256, 379032718, 815370129, 442223223, 810599818, 829518073, 500846988, 904950161, 908378067, 609972622, 815483780, 496063040, 900496505, 27992381, 306965622, 553043406, 724079957, 199739566, 920495465, 528864076, 167714032, 659610856, 482707531, 779869875, 973999201, 106218166, 187880277, 61556202, 13349351, 136133915, 473402042, 924039206, 848181009, 832525174, 497839158, 962341577, 406750703, 578609610, 549024155, 679999082, 791433315, 663560670, 470454086, 480471081, 527765202, 484163529, 621698988, 975124162, 150379744, 822867511, 498365207, 55932698, 179850069, 651178289, 300465853, 506084658, 586394336, 370894762, 808127850, 851193142, 763351272, 127505893, 12517271, 558794633, 773822516, 654129253, 745196755, 902128261, 98627727, 513811269, 651131516, 289004500, 648497004, 539140849, 340811579, 554316021, 490623072, 753528271, 540352790, 693212732, 863715412, 539231801, 12956480, 949628409, 991024402, 407890132, 883145154, 973348979, 52895610, 59641920, 672042215, 451899623, 169334973, 593601810, 820064742, 881623129, 998777953, 569012647, 298991358, 183764972, 290605336, 23678256, 414911685, 947221827, 22307553, 135925152, 974459464, 795578744, 45429430, 962135099, 822576021, 386358894, 735168031, 302606911, 113122226, 208912544, 691085970, 767085831, 982196631, 115786866, 463331198, 866345267, 802601220, 624534227, 985048007, 637132404, 50829904, 253964941, 381380167, 508802121, 358921261, 667956862, 236594876, 662684379, 111566795, 539629398, 84657973, 370005337, 239401006, 667891187, 865003018, 990533400, 501438887, 405091991, 625616534, 612545710, 773105562, 679072139, 793214063, 438834397, 882244800, 122719009, 186291502, 731177761, 440776721, 614840267, 510005329, 640231152, 499239661, 971596585, 200089786, 874711218, 780167101, 230847521, 453048368, 234876263, 566183479, 905281860, 50535289, 779760842, 756622801, 11861897, 24203685, 761064321, 152182601, 295573477, 311871089, 19388530, 95246339, 897595566, 966973066, 860498267, 940333730, 959980821, 245810455, 663585717, 741392096, 631256873, 591444899, 674791824, 701615484, 654137077, 820508309, 474187501, 94601642, 175367460, 352475832, 70813243, 763614412, 62632914, 407861042, 625689595, 176711261, 144744079, 18501107, 430436800, 191539830, 493289027, 908953662, 893856498, 611951445, 211754734, 954252396, 957365849, 830384003, 259233512, 455682250, 183812518, 284004972, 975130500, 234353378, 168653457, 247093864, 770175284, 630384846, 767353520, 21117691, 796379953, 713810572, 631816127, 822028086, 568857258, 313877017, 875687817, 627083679, 516159962, 717935151, 52563741, 266095254, 330524193, 670799145, 394171092, 402572073, 734864751, 798942254, 294060388, 748816178, 214274513, 220858698, 205850837, 513718631, 519214960, 936553373, 811314221, 440553089, 82405590, 601318004, 634130851, 960377456, 624362166, 619068451, 405927380, 194587343, 783466395, 734161941, 531730089, 289237911, 889477943, 342845015, 594622957, 400185460, 255725874, 149524192, 191887966, 83806972, 949853376, 552348603, 982047103, 940996450, 385600935, 730478848, 864525586, 775605489, 202137592, 812944592, 866887016, 458832007, 571813626, 295856471, 453930200, 406651878, 308997113, 468386750, 437982160, 54945833, 524890516, 944532781, 808507055, 15963636, 578405473, 481883215, 179392871, 464135894, 596319762, 249661645, 350139982, 63487953, 778200526, 619642320, 2226483, 60725891, 312686723, 872340599, 781997706, 243203695, 852552321, 410471908, 703292247, 672850009, 372731254, 466201161, 265545508, 44247586, 170814873, 11631951, 123009807, 318889397, 195627144, 292547811, 671775203, 277727479, 179326987, 440493628, 129426096, 121634017, 3306539, 27011000, 900450520, 473033743, 582470505, 276836809, 778685284, 797572125, 378541893, 131068581, 819123665, 76788598, 981821629, 888831752, 952466774, 22380426, 449999927, 477067092, 709999035, 220976801, 515661141, 36535452, 390257907, 618639687, 437561512, 388014836, 211990799, 100798049, 601586903, 487756422, 700506398, 773065432, 308475164, 820054734, 857273013, 351968330, 162690949, 638817732, 702704880, 776543614, 978295334, 861746072, 305884329, 564529890, 624471795, 872044194, 909097819, 229201953, 607909023, 700267844, 430263257, 558203554, 784386595, 537667863, 414725684, 355204731, 536941919, 254521514, 579064247, 636917144, 892376568, 812932701, 144684894, 227883929, 99209098, 840626330, 63958400, 183154609, 638236184, 342703948, 604969705, 825924498, 799999691, 176042291, 123374437, 649149920, 719658364, 11596502, 820356928, 762960489, 863293368, 216001657, 993638104, 930527485, 881911904, 176446374, 414157785, 540550308, 364058844, 303358518, 383239444, 359502408, 348858095, 439638486, 924375827, 745210188, 875663067, 377683061, 5294414, 511253455, 771714698, 601038041, 237730914, 910597773, 96901821, 944616135, 441421419, 459800523, 156854785, 520373741, 409541936, 341799565, 194494165, 580900994, 426608837, 442749257, 245054494, 65912420, 529913774, 689073379, 71140048, 434702682, 617412843, 801515353, 18503872, 996406112, 138294580, 646572925, 309478279, 756359080, 848909592, 6242677, 6058112, 354052116, 283260626, 675928939, 482326094, 751887326, 291522809, 336569630, 588763530, 16318540, 349263379, 140248930, 769899886, 222705128, 392571115, 6613716, 487997739, 510080009, 523802447, 434449601, 433308260, 748413197, 165451039, 614037753, 22044296, 13124429, 44424024, 225934121, 241502933, 34969730, 628988593, 648027131, 406329057, 129819061, 776404991, 839595412, 774340477, 827131663, 203321846, 623519542, 718354708, 425719083, 675000981, 470049478, 420098832, 716498519, 974120492, 950086442, 344086548, 105283892, 596115563, 186685678, 220801903, 215467372, 804636910, 675053405, 734412990, 285787711, 676625417, 624270543, 784592333, 563049720, 359301868, 294696990, 788864324, 376299094, 249470861, 752486027, 857567021, 819813894, 855061790, 273802879, 21337309, 35956915, 319937763, 340702214, 847824000, 984408446, 681388086, 325626564, 980865196, 30688604, 13933104, 695838757, 748951804, 274271761, 434969835, 195142749, 328352453, 903810981, 905734835, 408689688, 452332745, 616869391, 278932662, 19746523, 245626623, 916191578, 610725432, 407647225, 327870548, 292258240, 800787539, 426389162, 508878136, 855759122, 882465458, 522788873, 911067857, 382404903, 146921439, 931745648, 548527625, 335056583, 343592265, 593068068, 185162012, 905294370, 720959487, 373574171, 391759693, 135438128, 478758116, 736205643, 427319510, 624601551, 408053646, 473856335, 636417576, 568015134, 573533821, 704614390, 535608265, 687493801, 722433562, 444785132, 212977319, 469686101, 899821418, 591655951, 908272982, 895328534, 521157364, 271802614, 413128292, 696426607, 314209058, 916358914, 459183286, 3763841, 401565765, 817722715, 527893262, 766990589, 287562157, 63471639, 469727490, 223595688, 221397526, 723893863, 182667092, 833994030, 251737602, 538352327, 72007591, 389258013, 458832958, 917081935, 192299626, 985793532, 595224812, 497994539, 716620840, 119465678, 770434688, 468684571, 971619081, 921267602, 866345905, 622052953, 796275893, 556975492, 948730090, 994704270, 5451, 21388367, 819743463, 49886540, 880287725, 445486866, 420457915, 358686860, 335962831, 32016978, 126124913, 616868112, 430397271, 85457687, 458697312, 909466961, 901025110, 403368718, 42309129, 20935675, 520489137, 749392194, 265208254, 943491259, 460347429, 111349522, 435525859, 835698795, 838678305, 662253362, 851635812, 313446573, 385408848, 285450857, 794964187, 123606917, 888489122, 266722620, 227980392, 900639352, 867157889, 460355312, 779236460, 116034433, 226862175, 453827948, 751845844, 863787112, 759674565, 133500353, 701806781, 95732238, 395221784, 472395140, 942810533, 359308128, 681916606, 489835133, 572574738, 639437466, 308219514, 636468236, 637432850, 212774190, 14225556, 554559786, 101203409, 285584537, 587719332, 580791024, 437549755, 18560448, 246309499, 852648045, 415826751, 190292077, 456201517, 849768139, 317265747, 40698751, 110438327, 778170729, 887345958, 392263227, 871926122, 148645276, 247758792, 418201112, 530529080, 284421082, 338256742, 233523990, 760608831, 393752530, 66577273, 635502856, 209013504, 628290915, 841460280, 650198253, 708658128, 57548810, 663422283, 421158175, 787825730, 544092553, 566496723, 972658499, 719126557, 678462458, 488913294, 423559686, 659887179, 63758187, 696944024, 191789154, 966417183, 88900791, 242819335, 856397152, 37671727, 636957520, 586003864, 17711885, 355588648, 837928707, 492214325, 649786124, 235696476, 419852001, 105901323, 441618874, 607401639, 871729664, 322824259, 760191644, 369981363, 20308240, 132260411, 584535042, 997631648, 537758384, 643154628, 671324108, 714633250, 96881698, 311836526, 529741248, 271078229, 726177571, 516092424, 913131674, 145767047, 931704124, 506268524, 934884211, 308999088, 451175704, 177837244, 376714224, 692667537, 877505787, 536048799, 674311877, 670255696, 78863716, 973053581, 351397648, 618415064, 769978106, 578808313, 410047568, 826973812, 741140107, 945544631, 967144167, 705512422, 412539541, 631816344, 13844949, 551987707, 31649700, 266623046, 589591912, 67312836, 522679599, 994037853, 891093250, 801875595, 408874898, 249908869, 199855115, 182326585, 65447873, 43304958, 688696896, 852918975, 29457803, 620460629, 524543090, 902871048, 894723295, 48946669, 894453545, 672648358, 493755809, 26925784, 337860831, 651550049, 864358503, 239953127, 378674989, 938426050, 964218306, 786636101, 387950075, 348591827, 195780946, 309513983, 162505385, 299479918, 743170838, 616089840, 4629427, 663860635, 206530808, 493301743, 520795695, 715743635, 60275444, 133771952, 435257607, 577350815, 31878755, 626235565, 531821073, 621369130, 14918810, 877955897, 52285829, 482111654, 758264312, 71774503, 328929479, 240495491, 991443151, 364344769, 661029631, 965175067, 733134538, 509429937, 547442825, 55316833, 180594550, 174236013, 946248485, 688141629, 262165411, 361681900, 867576061, 344494307, 486925798, 197960815, 763734584, 233457619, 756845246, 536507183, 134767853, 520023243, 5249600, 695609618, 587586955, 641856055, 262461253, 998747739, 63796461, 579061142, 448693490, 470335259, 975376281, 62348590, 502327478, 887934180, 277671390, 55700527, 517978804, 476086966, 810025466, 416579848, 996310124, 878340297, 806890814, 474999700, 163720512, 921776889, 569389806, 266993258, 426378326, 468843207, 167423822, 13192155, 945921477, 561759084, 959360940, 803494373, 641873434, 789361714, 292208344, 150778150, 211846432, 386398977, 527431167, 342981484, 637994856, 232734734, 828909293, 396563953, 929843649, 873878600, 686619520, 633354005, 860508589, 530776987, 842826107, 159359460, 413364371, 318455385, 148746792, 55872321, 942871817, 680846182, 777277300, 109211618, 203995057, 328386045, 442612418, 583611321, 968024278, 202711464, 884741285, 262729553, 299935539, 257873823, 315011121, 773295512, 390118152, 835569614, 444735955, 474385653, 171559653, 540740507, 680815301, 799554360, 714406280, 851106452, 150861644, 525158085, 588040640, 24934673, 836673444, 146869215, 751813480, 718111045, 819176737, 82429331, 899305849, 783473191, 607914842, 828653209, 753161537, 320453453, 806249442, 412425784, 126419306, 793479317, 111229187, 446941232, 654230069, 806519288, 579689509, 136060595, 537716062, 894991678, 816359418, 236327769, 829332165, 988513605, 188038387, 722736465, 760310456, 646522094, 503869805, 417828525, 647778053, 718271697, 645559641, 250347753, 377952061, 956691227, 110529428, 932442436, 588214112, 803759511, 378802832, 313095237, 634600506, 315411254, 368456851, 99191823, 915323601, 535083664, 471984372, 107854429, 59545779, 98822874, 347855344, 618595812, 39633383, 65364126, 920820997, 665434078, 583471067, 266939431, 754755880, 930486360, 179891126, 866722375, 393036292, 697797824, 451835480, 132745311, 219180184, 774697413, 604738078, 913243668, 134444546, 306432694, 299695949, 76455921, 840022333, 800823782, 322911385, 897145029, 409389269, 412013884, 699818132, 416905145, 55432185, 530201486, 729868853, 758735932, 977766150, 449167461, 644725534, 880707652, 83816225, 962742923, 810384611, 461730774, 308536951, 137737846, 916370973, 508346837, 7947347, 712687865, 431943768, 48253826, 188760312, 354208703, 442260764, 115340459, 685291907, 894383482, 449664371, 563563259, 434625241, 129924932, 807202670, 830631477, 239302116, 704785707, 926382657, 286985399, 172583754, 56278402, 245125556, 434053777, 214543439, 850737750, 180354992, 691660390, 948983610, 842695555, 943462401, 188610217, 101727230, 751135106, 419645905, 974514677, 704650815, 871648690, 596391672, 713646182, 866949509, 18032943, 647539255, 196784932, 967529101, 575237605, 379973862, 962537720, 91408338, 867608392, 285229690, 433222992, 34035841, 166206918, 121673190, 618585856, 738325109, 204590783, 84995179, 956118351, 601706981, 736492663, 246987772, 204477313, 684410600, 534391142, 23992846, 828851467, 761908263, 609245082, 332174365, 58205600, 243738682, 844148981, 70931597, 836772188, 568617181, 289758840, 852248999, 919324245, 294594769, 235158028, 458114155, 857537513, 634314292, 949379362, 711380407, 134667184, 231049763, 626738661, 536813610, 766046157, 139044278, 693210396, 140747965, 791823960, 649761013, 138316888, 962481002, 330906265, 588730838, 895544205, 972585975, 460578729, 628058488, 875361941, 446333527, 523074082, 479446775, 919540190, 197278994, 797664533, 251523082, 794799353, 995751194, 563747359, 462607106, 758141902, 459995607, 105759109, 729814263, 218393614, 587337002, 18753197, 453329204, 523402909, 562866933, 800281797, 28235147, 582705938, 273586723, 33214029, 779254855, 609881579, 822359657, 48110023, 924890799, 454319290, 578927783, 912660594, 432111684, 393361063, 536825639, 236088344, 402639872, 656757773, 701905597, 700411738, 778891135, 223704817, 953997944, 957796838, 167681283, 52184291, 551303620, 466139233, 886171651, 739445628, 846610333, 119131626, 418385351, 974084249, 597064585, 973171232, 671977545, 594481980, 530970173, 114822117, 23953329, 416533850, 485670485, 629683595, 637494942, 628839211, 62995842, 202862925, 923695254, 752412479, 228218578, 74656354, 485207305, 962067457, 592178223, 440832620, 231393669, 788268414, 331093441, 473747184, 838980904, 680197394, 454493715, 717945255, 811312090, 714618831, 12441799, 776405525, 367132019, 85616229, 701327735, 206445471, 460120832, 336410113, 624136494, 276137526, 254338617, 318189595, 638984924, 589763919, 448746083, 403027243, 205007848, 300311654, 528512358, 182918960, 331923866, 52811545, 370823591, 180797898, 235374396, 296899525, 405023233, 720309995, 369420783, 338076867, 649483558, 434452240, 93797246, 407833263, 141601401, 695069683, 672481258, 868836875, 825191114, 473571925, 169601259, 307304096, 484065982, 555529522, 773366895, 261952094, 646005111, 218299921, 654732982, 283110652, 392977452, 873544141, 915467830, 398960008, 57595329, 153544604, 128229562, 977159567, 901514162, 928101, 596555770, 136685921, 785731998, 610623121, 876643524, 450230891, 691265603, 298603026, 560095829, 610754534, 258504340, 529262820, 981436596, 403302860, 220312179, 115493058, 925724461, 666597995, 958308977, 941870864, 491431304, 739811549, 814287061, 366209055, 916689745, 984169801, 758183710, 969846268, 102518935, 340415256, 644204350, 120734877, 854036415, 864386148, 122548795, 284757531, 744098878, 339087330, 746681854, 27144416, 136575169, 353567340, 78910736, 386113338, 191281693, 672060236, 51108535, 206713464, 806080566, 904623365, 253557284, 838667880, 264379242, 53491285, 136322583, 604542930, 554489095, 341506024, 241850919, 513214370, 117242843, 220133445, 101932629, 275827536, 786668882, 648815061, 138918912, 563634251, 231435046, 429235034, 88612452, 33710291, 636786940, 917541222, 780636653, 20600889, 949098017, 102517723, 818409257, 780195268, 788024980, 415139947, 352553828, 690841871, 846814366, 974641934, 691129629, 63590820, 291237246, 61071557, 736323427, 357549972, 868138781, 537499102, 326364590, 587220639, 418513751, 896669810, 698382245, 72594382, 725153444, 220038085, 871606542, 163921693, 120025253, 241770845, 47357217, 136507412, 676031655, 643155249, 208289238, 904527050, 475515817, 177817740, 583293815, 987224699, 520356245, 769806899, 783404363, 574325262, 98642872, 838488858, 375511738, 13957472, 169985029, 422478407, 178250965, 378753979, 460229118, 866572918, 791949771, 159510714, 376445279, 700931457, 42832532, 469227797, 126151691, 457350070, 593685429, 381224837, 12898428, 554870190, 23179211, 537171548, 738146582, 1769928, 700659726, 594764418, 188805195, 11976673, 182783567, 685407291, 751116966, 403060292, 977346470, 312485781, 532577219, 687526466, 424133918, 743812488, 73352732, 454226264, 717281815, 615884334, 541736179, 873239533, 945203317, 864028279, 692337077, 391962638, 305424767, 18257787, 850334498, 459066488, 126306004, 536436807, 347469579, 950384567, 758719393, 968891962, 39934437, 35499119, 674268127, 962230114, 3236798, 319653175, 572995629, 151082434, 304159341, 432473771, 971275277, 461816601, 957962599, 545119336, 284680151, 144333874, 618095902, 932917507, 278599805, 608910641, 205847165, 564775384, 623859354, 991150106, 286827510, 110812482, 445761050, 402493117, 9102165, 80809154, 503908438, 769295535, 417165630, 535392282, 116452195, 303464368, 145164424, 626490918, 156138666, 790252511, 812334394, 78023254, 973026316, 684464817, 672888129, 387748246, 670379810, 933804415, 203287496, 398958059, 868058097, 158918750, 697471963, 471171626, 938936777, 418574849, 684272680, 536664353, 195243872, 726497297, 53471695, 771544680, 504081930, 895964376, 754771551, 995118945, 616539886, 963061523, 97047003, 374176971, 474961123, 448338768, 710030859, 331562778, 254858465, 237599498, 960847172, 809898805, 636293623, 911832656, 199761742, 895961497, 509687837, 138529600, 323829549, 808277547, 438588633, 162431607, 870806826, 437483311, 389985504, 514672074, 933258571, 548897179, 43497189, 979097145, 12234182, 866275687, 769868182, 502224188, 193225240, 848361226, 255061959, 372499563, 551495041, 805719567, 949048178, 140195801, 971703109, 738299904, 525771832, 425092684, 655684237, 348458464, 951887441, 371720060, 398051868, 664503700, 760440369, 446784024, 761995375, 953062642, 597811767, 527247973, 4976502, 225333114, 468496402, 826238709, 63301609, 329428625, 317607049, 783503238, 712036410, 972362106, 454108165, 424886003, 686830782, 5577339, 936250257, 973965801, 2140444, 36448087, 468860114, 544621066, 426178303, 241562367, 206216472, 276307666, 700408058, 625863208, 79266763, 412093905, 399690643, 381839420, 467850144, 891184649, 501956241, 24373048, 262139692, 559109240, 804459599, 685326711, 404703091, 599124058, 705638160, 66010830, 572382694, 142393392, 755617027, 211256597, 157972323, 426272782, 170355761, 847696831, 686432641, 383382240, 282582534, 593709538, 320752146, 133156989, 886648903, 855759513, 85513480, 491658679, 725486533, 676320995, 114846874, 210181058, 267633091, 41505797, 802469150, 368384837, 332907465, 459876656, 350386959, 139301990, 476515542, 284084715, 608952961, 912412161, 497156205, 204280075, 930784971, 779122436, 639912989, 126609283, 254803045, 835189517, 130235340, 316733032, 108977237, 592160052, 37559923, 194568423, 914335770, 685720404, 107547937, 637317444, 953315988, 871460781, 22332913, 592472818, 476939353, 297916785, 439299040, 992445713, 152212871, 344276681, 822954572, 414689233, 644588139, 922214511, 181235967, 809186715, 534838706, 927285069, 376960469, 120421171, 944612098, 340608828, 141185974, 654039010, 301901081, 296186418, 137070738, 599074841, 97389257, 797992442, 433678538, 559504188, 996494166, 739448830, 475427719, 869762822, 394867932, 948262789, 452271808, 834513047, 199150185, 49650093, 828712800, 627921535, 363158976, 76454190, 146135990, 427597937, 669425666, 934284804, 522926621, 637831676, 483300813, 114082465, 545888377, 453056547, 949172295, 419258192, 514041620, 231384501, 107162413, 73173992, 844227465, 791239420, 837866605, 216244547, 826610670, 19449906, 468624328, 729637119, 836224906, 281505863, 705697748, 279335372, 582478498, 417570183, 690295152, 936613103, 941382488, 199769479, 29332370, 323861994, 429166102, 112235116, 272958779, 45111599, 422460962, 248191757, 935338823, 304617377, 568451880, 442521459, 432216121, 233999610, 635146751, 881002163, 131782129, 566256909, 411335999, 96899947, 981800344, 279218293, 646961444, 814063665, 667514231, 135908328, 634464926, 479559167, 13326366, 8053499, 901327496, 453296333, 737690369, 632593901, 16736277, 768217155, 398071355, 455319406, 20732209, 642669175, 702322195, 321919264, 943641048, 163523569, 604140947, 837388404, 746504612, 981439957, 669071566, 501080562, 735676194, 993993615, 660724997, 658015335, 679238625, 982401811, 505908363, 673436266, 709620947, 46276131, 148724631, 484351392, 891626508, 135667940, 588451983, 920108566, 210473120, 164587258, 257897584, 78366094, 132963361, 715418987, 482733481, 371780191, 413850129, 15539465, 536690171, 118445333, 325068590, 351406067, 292084841, 99114858, 294398919, 164521563, 274689230, 615947561, 392233866, 985684016, 334590391, 369483441, 434626832, 555283060, 499384303, 791918638, 454703383, 488556164, 876860330, 924345537, 28765313, 655633708, 889124475, 444366319, 426514394, 210665198, 438034637, 770416812, 573475298, 904958203, 879680280, 666883397, 412068834, 661612041, 943371819, 601381717, 209406950, 840725928, 151935684, 915005139, 363569388, 850895284, 806207458, 110967716, 41915685, 646848310, 377072799, 359707201, 613943867, 803593949, 710470490, 104448854, 971452585, 800074634, 741153947, 178462544, 368493638, 764001095, 298633485, 875307858, 840634400, 667643094, 662433945, 444892132, 728864651, 532977551, 889069664, 807924, 742002064, 866017576, 654011940, 360116974, 283588474, 926554740, 153631244, 492723950, 813957638, 106061139, 684115387, 317117289, 559313868, 300954149, 172098112, 745117159, 912973270, 352957873, 326936914, 51617341, 190367403, 855154936, 103124606, 409507018, 606395673, 786767335, 129979253, 613448143, 419384239, 212267072, 171258435, 303796924, 344583355, 908336288, 485870464, 639764421, 74829793, 264784508, 726395338, 372680437, 202248279, 333743230, 731416931, 188997414, 688025043, 5850816, 895405449, 274592023, 365763467, 47461045, 622161502, 55726973, 611743179, 373698512, 382501536, 854432535, 654911538, 936565555, 358261394, 338745461, 523140080, 180902944, 742266099, 515122874, 906478704, 18472792, 643495385, 212687378, 50306737, 162854659, 116210285, 215397323, 435304947, 858970704, 945142858, 293827102, 699132952, 239733461, 318999582, 89424477, 962962328, 670970111, 700199825, 594821401, 287849514, 651805837, 996426373, 603739389, 995484455, 80670999, 283902621, 905025733, 641494535, 440253166, 239773961, 963709201, 87595318, 842810197, 721349503, 378316046, 512241754, 716445867, 428229630, 156658108, 263208207, 404506438, 356637324, 331203229, 785352427, 231184022, 603592734, 173657167, 488530074, 520535989, 936765610, 856553595, 319830812, 187803920, 500330895, 446062724, 550827838, 662333613, 437902361, 867236970, 416574785, 201726601, 573567927, 868043551, 243801239, 745033756, 246537645, 471806556, 867238304, 958583866, 482867740, 576361648, 660624690, 535078703, 594913976, 903258780, 359908762, 900226174, 585340443, 916495363, 216485045, 265371628, 496435409, 726898377, 41144029, 302746813, 380489301, 605332707, 513513567, 677333326, 855863940, 673708101, 326537382, 372873872, 648703632, 307927537, 754280336, 62756143, 756163237, 639572402, 872453641, 445049794, 933385441, 998929831, 196088114, 896181348, 518154537, 163512885, 403332405, 207273960, 960858415, 11355527, 362597447, 655464361, 347233276, 878817314, 891229215, 501385125, 97030473, 839996025, 122006554, 152724566, 349729655, 761924896, 209630356, 617976090, 705655657, 670722120, 172272479, 693499243, 990491492, 262398490, 863904363, 923210683, 28682529, 759389037, 174370056, 988004597, 755673964, 834991350, 144921258, 420593340, 506311894, 973161848, 157079244, 135413222, 58304016, 496958845, 588566346, 535500549, 119836563, 343436158, 799624665, 597392933, 406080332, 328261411, 948115679, 600446251, 941059120, 607635504, 368194071, 584872438, 262462331, 426732312, 491416496, 195379450, 969148608, 339353658, 446461402, 466041038, 105972947, 79417410, 58560540, 300060929, 732410237, 151918892, 854732464, 994757575, 895358910, 153713943, 55951387, 8598408, 802408915, 107524404, 715749762, 211784814, 956756809, 946813397, 610348846, 36306237, 946624774, 841662139, 969945009, 759310763, 474127191, 88758597, 694652524, 141456515, 141156584, 161934615, 328601789, 151239441, 433913175, 124753, 939319358, 792831625, 104331331, 965759500, 144222653, 265703692, 622649950, 793680491, 641485277, 639262901, 935068163, 493022054, 506865658, 766466007, 128909819, 292847498, 548470070, 620197397, 189770322, 969859786, 137679954, 101547459, 745346962, 434736562, 881034880, 896325302, 373049874, 809467514, 530164831, 633387571, 197476040, 314216624, 329011377, 574011244, 119582829, 207882371, 796041543, 923655974, 34393238, 584968327, 927853862, 149250315, 742545690, 583840842, 583311892, 489656802, 448754094, 2834435, 857339246, 951899538, 736705098, 572840769, 328095335, 532707073, 792022036, 718214733, 713143237, 371481719, 268499181, 604110640, 524647235, 879705605, 924568170, 7835774, 958515330, 408752313, 626595107, 26987701, 725553471, 474571867, 483130638, 406157551, 708720495, 680646016, 383006931, 490687371, 535979899, 879403030, 420058062, 536275830, 516180757, 449225759, 227880059, 629632803, 459688318, 37597535, 647290604, 661729984, 379879, 673210808, 655786710, 114463277, 49543061, 898587159, 11730702, 186895213, 490977758, 968165117, 450026073, 358566779, 728050844, 471317450, 559436176, 650792609, 148400895, 751401074, 818289392, 585569299, 519520571, 220538992, 630081749, 733916306, 948852718, 592787813, 66817993, 826751458, 192995057, 414891696, 411627534, 636749010, 713172241, 380794287, 430100767, 271009912, 631231085, 15712776, 955533373, 263032839, 59274823, 145561183, 778962443, 409595079, 241368227, 305497116, 612047125, 170448961, 73980308, 475045977, 891218969, 414708731, 693222833, 459026369, 764089741, 344269105, 972445416, 142450416, 313522221, 587975819, 21963285, 243302684, 963521039, 951741230, 148124676, 522694615, 842622031, 132343563, 667177117, 901624028, 936088725, 516969275, 578853217, 195748012, 138548437, 308962539, 335439469, 571603870, 421392907, 872515199, 358251102, 400914164, 255811698, 328756209, 987857882, 947821767, 978124379, 143520806, 228549738, 277319837, 404772139, 740917155, 189823463, 364610517, 312257877, 506552745, 497851023, 402855307, 276279337, 274210177, 804559867, 471318350, 308464080, 309640295, 261565277, 775570410, 300809580, 217037388, 118942880, 290261894, 589251896, 972564721, 225120993, 276710948, 606196787, 493459965, 746678313, 143335555, 333199341, 356291417, 512846878, 715631057, 97601150, 244565172, 241035453, 804701305, 563072490, 653759253, 830304968, 763369009, 403908899, 37819216, 953811137, 493966603, 287797355, 233844590, 678028934, 284861956, 787513354, 425134604, 132488942, 641345361, 819423998, 575077797, 200592483, 2678552, 773880057, 633459454, 418563614, 392330851, 53212443, 112684611, 649380531, 328469427, 983813704, 615259884, 814402505, 935668118, 581255443, 729541466, 655588752, 547940385, 296523214, 198690732, 246785975, 37038678, 977056316, 190079920, 76964565, 730323231, 453821513, 457798402, 623681788, 805291730, 685126162, 321816683, 649250576, 302155794, 142455974, 505599982, 354378562, 929596157, 273283199, 463125059, 886143505, 420115678, 366762201, 154930404, 861281071, 170433470, 395481742, 422967595, 587784502, 656545184, 467303459, 318795281, 28748024, 817771840, 360241290, 575114910, 564917197, 946197544, 618544260, 562695341, 431249937, 234341302, 783954580, 7024662, 257034295, 457366561, 732256592, 616184899, 706997628, 156243262, 741336635, 546908373, 798077900, 694840547, 382900399, 6011952, 74351086, 482868741, 20890979, 844166201, 5406679, 695182597, 460949325, 948918620, 331990010, 250830343, 330993093, 413773690, 518079844, 671649230, 893777350, 433234593, 113262501, 447877602, 171748848, 786528553, 508517418, 206849124, 179607539, 873787404, 693804552, 133527269, 338498122, 648352384, 221852846, 53147155, 5039473, 518172082, 635210705, 450156488, 352542533, 58309066, 889341414, 339804847, 182104577, 986048056, 629396229, 88241540, 718131849, 680926054, 693248975, 960145606, 798684739, 689611077, 965278245, 606817738, 117064123, 135766461, 739869133, 26272425, 969218639, 51685576, 354166142, 21620455, 708455293, 579972830, 639037404, 545179844, 462306787, 41017015, 406597850, 957222892, 253527972, 646198619, 41776694, 931089216, 723025614, 126360990, 990637099, 423774546, 806233157, 804855073, 646341675, 504251829, 95978726, 92082401, 496686842, 402813376, 605453412, 562835197, 445997342, 675575871, 930738057, 659512908, 335853945, 264393594, 756491177, 623396826, 75463716, 804288438, 671546524, 515932979, 608570615, 175913080, 699535464, 873197485, 1235886, 754748928, 845619208, 7775689, 445300472, 950025231, 587977959, 121783002, 613480763, 563448530, 189533576, 774780941, 299658518, 415321340, 112042900, 405626181, 770359242, 230060980, 923793704, 511067252, 13926320, 753401249, 377714922, 106315129, 864640114, 32467658, 67145493, 942321434, 361682231, 471271200, 569440122, 481037197, 360152106, 962520811, 608334954, 254612331, 494273414, 494904107, 143927285, 294939700, 946235820, 473960484, 596130772, 675431275, 944655743, 108281304, 824777687, 199959754, 242834399, 688765874, 35889707, 678971377, 930501862, 645887731, 306404364, 120102038, 570107199, 221754217, 392551873, 837739481, 195447329, 669499174, 498493729, 127058810, 171270982, 693350777, 24750477, 621501128, 779020574, 137961706, 596481080, 505225841, 649416601, 330705626, 819330571, 100316246, 648884869, 367732051, 528042454, 615861941, 940936065, 654855678, 953366975, 187481608, 13072638, 811563545, 176862973, 522491762, 495515206, 549662553, 231145375, 36782719, 413277187, 444180605, 756986446, 203515708, 356450660, 222154044, 853252026, 529607447, 867300249, 732549380, 219730350, 718870401, 112120688, 770606473, 102332607, 962369809, 882034564, 651617852, 561265444, 268446713, 939250007, 969624108, 64451741, 952377938, 883373895, 132371322, 139707884, 641203269, 32987856, 984267863, 695377651, 57723811, 737422362, 430204648, 720248917, 964235271, 999265669, 565793202, 161475336, 872470203, 385556983, 640201530, 104663033, 718964960, 786588872, 940797799, 529448619, 163018069, 524103470, 376880209, 640251054, 97835934, 228739014, 548098012, 899736858, 339149079, 614779366, 947639599, 470642489, 417249951, 316961151, 414333711, 258341310, 360088804, 675046147, 470679507, 285802352, 57614758, 452835053, 525322379, 970191599, 89808854, 571026504, 456714222, 419922046, 592018774, 615747648, 695435219, 230282942, 282777475, 736393158, 19027186, 500857806, 328180103, 410335868, 421517559, 188003876, 848931266, 833227144, 329088548, 213052606, 373398306, 69897169, 517252605, 87024929, 719786334, 246381133, 564818808, 443340473, 952030767, 677881411, 28073688, 313720006, 258070858, 419197606, 678884472, 517474104, 441104056, 25877018, 998969973, 429423301, 58293248, 893615921, 831187574, 396327903, 69762474, 275664475, 331044192, 586204871, 106698065, 247457562, 661032380, 101932883, 447005962, 830147110, 269798384, 140963714, 577736926, 678331403, 12262090, 7718308, 382537070, 861072232, 433366443, 918335824, 598268800, 194624175, 815428099, 466058727, 931830544, 618703552, 810220066, 347643021, 478508217, 72972744, 538683457, 998761021, 657416269, 940321975, 469048308, 633557531, 858683477, 985474306, 510053092, 794978431, 836488913, 896719885, 23804625, 30806693, 157532818, 624146655, 476398805, 387193175, 244376833, 87650656, 888101216, 172038950, 852567177, 756587007, 905863962, 555013874, 328667493, 961773176, 321150165, 788629383, 700998117, 651260224, 965802674, 734859467, 79853966, 113427845, 608384883, 810082674, 219112661, 212980418, 124213121, 537871681, 888487471, 367407161, 330543173, 180677716, 495153276, 974566420, 961653137, 656949846, 251304735, 576177486, 749967326, 941263585, 28263370, 548196683, 189813118, 710001157, 164411129, 393696462, 834633907, 666732441, 260179634, 539904565, 189832686, 383401181, 487000708, 672805381, 207548254, 404084050, 604070349, 338899226, 833731952, 920558768, 436405367, 560084907, 879184661, 93690221, 599280644, 345063158, 611733895, 353608516, 792441748, 444101403, 537979629, 658345857, 838773947, 779864149, 834201101, 479653095, 691457214, 718337264, 491274972, 402520551, 104392337, 926884884, 395517545, 254933075, 727980238, 882106090, 347186957, 20608694, 280345993, 599682670, 287347521, 39854710, 684024577, 532733710, 940891925, 988151524, 63414860, 969363141, 732575580, 417204027, 381302365, 700029604, 703415918, 268410373, 224500928, 615496156, 200194768, 681646882, 755638019, 266681525, 802501579, 656022656, 415591448, 507732230, 943287867, 411045609, 286299838, 388388295, 501861736, 794699105, 450466659, 436375043, 425439174, 290704808, 429067527, 427946670, 664867137, 352539309, 458320186, 78714192, 447366161, 212681025, 588285688, 566049567, 245592497, 587298081, 662326130, 666706699, 702381884, 7592924, 138896928, 155057636, 776656461, 422402262, 57603399, 329846427, 818530855, 871148075, 877979407, 736669122, 170979261, 170583394, 933231858, 468321787, 22126824, 620955654, 462989135, 331827527, 781195440, 843241523, 553955086, 54608876, 595706087, 718793510, 73604859, 260899739, 821072403, 570358702, 683195371, 593278089, 12886136, 895685746, 369237408, 874556913, 597268509, 565632490, 373084816, 972892219, 284084779, 994471530, 951892323, 436655083, 184869456, 39590983, 950471416, 797947180, 792950891, 212173316, 972900026, 737709144, 20777465, 997520116, 627332892, 932808769, 678303614, 435019578, 726829720, 511500938, 514525836, 876805157, 914501926, 607581263, 127851827, 96501445, 610427742, 419727390, 750061395, 90478656, 494842949, 54431076, 858662555, 497395645, 493028117, 971284183, 716106554, 670509587, 289901395, 415463207, 126539911, 957463568, 353605623, 315642204, 374457039, 564502927, 518000656, 988345288, 931138660, 615697628, 749355521, 279016208, 121491804, 163872656, 350425773, 559543267, 839261249, 647395242, 954222185, 234723840, 650277200, 93871672, 187940418, 967206552, 449319428, 939717694, 538549072, 154602092, 672585063, 101605166, 556530089, 588194428, 560428735, 600059376, 505614677, 168977539, 725249056, 714022029, 619514652, 644722743, 385679800, 941790760, 811608986, 30901675, 677095131, 804262519, 424357828, 935482699, 499716783, 980412699, 519211457, 368290666, 950202144, 414258732, 620167270, 139456889, 594305651, 68112144, 900793613, 399183537, 375581465, 139077972, 706786733, 848676550, 568605333, 408921619, 833324418, 205158209, 958888669, 408778556, 674522081, 61404557, 66659955, 517119318, 220798575, 342410124, 942997198, 759359747, 453888785, 320436683, 747554144, 382103145, 868163749, 973141939, 456013886, 729708382, 554392993, 457645263, 668634903, 919073463, 461790106, 650462250, 189437569, 399436263, 502082567, 312593647, 225035721, 445911753, 135961367, 964992135, 839364616, 247428634, 776675884, 513764682, 294642958, 487608878, 59504588, 67829667, 268968665, 45154894, 875783464, 256848320, 197476740, 541799467, 578759351, 976674707, 965996471, 445125700, 314892022, 744787113, 410607235, 431423448, 122290488, 174230020, 490760509, 637890779, 38927948, 695445304, 659280339, 530814257, 520837155, 907755971, 188952565, 519565801, 568939429, 191522571, 729691675, 568079039, 18309712, 390048160, 33812139, 402634569, 167523322, 567199770, 830809055, 387882589, 743010101, 321667970, 223747632, 679685016, 740856529, 59848359, 7257301, 542869034, 536679854, 426876851, 974413622, 22802000, 76123639, 34253152, 357708838, 349233243, 130171244, 760365664, 715677036, 390826466, 485464569, 525268882, 692813758, 360974898, 441696132, 312207247, 486391436, 142114675, 658280508, 255704059, 423616460, 378383307, 295668321, 869418639, 4211304, 606455055, 396895987, 652902194, 248201178, 846175223, 307592875, 68689032, 109471583, 41585253, 618173530, 546610551, 650690402, 150713403, 62711242, 93682846, 919898919, 344382756, 548160845, 110202710, 302120498, 283762195, 607701279, 865483098, 429102743, 568890983, 158120607, 600070360, 996796751, 159666361, 919967250, 561799388, 652453184, 612136378, 577092472, 459147191, 460170206, 659757661, 681030567, 462976811, 597146215, 577999915, 149602264, 296550530, 595153335, 97753311, 762648008, 64087671, 436222693, 721013187, 632404607, 208527341, 276913648, 360289251, 510781128, 573748346, 209506769, 930171893, 103390511, 188577258, 993927050, 216961923, 456135489, 632370952, 163221303, 503172850, 93975624, 765584731, 761562242, 395870350, 556408824, 55181124, 499209900, 125463160, 54483587, 89983194, 432647433, 767068348, 670638831, 705597153, 299888368, 386170405, 833224111, 480277528, 730782444, 314599378, 664059384, 527695050, 596832188, 523719703, 540159396, 1827734, 343512877, 254059191, 790714859, 942919423, 241081502, 454132448, 435159111, 260902280, 81595491, 505694945, 67928147, 161318028, 341233204, 296806228, 449654063, 142664840, 110315501, 589804701, 244296235, 622667903, 970962840, 260284849, 486218971, 944837002, 813999962, 201469049, 217350655, 721812625, 349634930, 111528599, 904476691, 816155149, 89509770, 145160943, 816696022, 442672587, 518645662, 203758762, 683434830, 956774160, 251508525, 830837216, 313419712, 461464370, 606169250, 494435991, 147924710, 376345341, 655256284, 713194796, 103538203, 80962776, 592023070, 99817335, 302987006, 616607483, 381302266, 934511029, 972636400, 272903324, 720910635, 520213821, 458861488, 580680884, 693688209, 545322626, 754172978, 276489538, 107591087, 715137357, 470049812, 412495976, 429126691, 206087088, 760835382, 574016449, 25154295, 703303469, 420760337, 711166091, 78551339, 211201451, 919221365, 683716679, 495720350, 1489083, 127919248, 952559782, 574913105, 273767648, 452974357, 696803150, 735544443, 923605964, 230624645, 813323993, 432565911, 842651514, 328096372, 523034825, 824755677, 785888138, 992427019, 892400498, 185449677, 573940349, 80317066, 952652231, 372062501, 88712961, 925226644, 824178547, 806069142, 414696501, 972060445, 976047469, 1943241, 593948567, 85854949, 462510807, 733794811, 607882411, 199497035, 901089382, 103566478, 73423526, 353359450, 886510312, 29515623, 361454114, 335907138, 396664089, 604304169, 54193487, 843279880, 645213498, 709910955, 960077256, 237269686, 308053328, 85251357, 740726676, 130252148, 757630859, 62008964, 55622821, 840787843, 488855194, 323934134, 178437086, 755596706, 237579770, 781989734, 638405408, 28492153, 472071443, 768863297, 449197703, 829056366, 863630980, 685269673, 259472907, 578217443, 374532904, 54812020, 853338604, 257338514, 536893066, 561111444, 398153109, 188686358, 908746998, 19858409, 468950810, 337260851, 658829005, 47955174, 363073945, 942761098, 337828130, 830877831, 341319081, 645052767, 558254104, 475432900, 92897661, 736869237, 507115861, 453705290, 8103596, 621297911, 334949886, 89549364, 650068336, 166926536, 396620762, 944055544, 106128975, 328200689, 921640660, 187842384, 278523528, 667931202, 63316543, 798805414, 389246196, 759456462, 781862651, 203427557, 885312024, 507420363, 32435899, 650902630, 543212033, 284326977, 549382037, 401649743, 635488515, 240279670, 20532210, 745401998, 279452968, 604112438, 192010168, 410976398, 943355094, 606705879, 954451853, 309924074, 118242178, 823057346, 450193989, 142904542, 460650256, 560564885, 442891012, 376969095, 20287140, 648722379, 278707732, 117209374, 217559502, 34597079, 180732673, 75341315, 547706254, 432291901, 949467342, 594796136, 413284488, 189241423, 188041627, 804874822, 461851486, 494088151, 994394766, 23577820, 424181067, 624368325, 280815689, 923757504, 954440881, 437115018, 368355517, 438623365, 945607041, 664015520, 268251864, 10039328, 926018893, 949941948, 636774300, 882698447, 29903935, 11749110, 482921479, 5994153, 92419280, 675433980, 187967030, 522871804, 6560600, 485538232, 717934999, 47512681, 600134529, 364154985, 929961983, 210039990, 992389496, 886652754, 585469472, 708340350, 147692530, 728252743, 780881376, 778996304, 344614999, 862656006, 290273929, 61527365, 240402157, 697029112, 874941917, 69732831, 509932152, 122032276, 453943424, 753323179, 357816985, 237566569, 806822296, 176346524, 889628870, 451920125, 436797016, 47009747, 827783438, 164301943, 378855140, 773982429, 403317048, 978777250, 856975997, 102381675, 263681982, 105431600, 392945628, 191147829, 410959457, 352639845, 693127258, 604552840, 290493741, 12938023, 782099757, 526194415, 843390096, 476798929, 645265394, 925964622, 34878746, 591501842, 71703717, 976619772, 204761005, 103732350, 751236564, 926802506, 37288273, 869522497, 766248350, 774142686, 676229664, 857674426, 76521517, 208235942, 507355293, 586553827, 685828354, 108575516, 299057852, 155157682, 768522426, 134774150, 346709638, 516474602, 632160355, 343374737, 891607539, 750737100, 792015439, 765772907, 265010066, 67069619, 105548256, 411777512, 322754819, 288439374, 287714508, 366796672, 101070776, 157038394, 9844160, 844144089, 378993199, 949904936, 898475096, 59730013, 454628782, 813987969, 218487630, 123332815, 548131200, 313119730, 678002330, 528647702, 42190126, 921956980, 484396219, 105696027, 312080216, 364652758, 126930845, 70688533, 429593213, 942127361, 28026149, 988803528, 149540358, 72352263, 198331891, 966030806, 318514174, 653683902, 408013344, 319763927, 272980332, 436859647, 660404189, 454092514, 576029198, 23454836, 333841160, 410890535, 108841435, 106097731, 560779128, 744997752, 49190282, 21862704, 12296944, 315295697, 318529598, 862140561, 19730801, 871831935, 97818175, 280342881, 826474825, 631737687, 188181695, 916889024, 323960931, 116278491, 411763512, 945593964, 75620691, 253743109, 356901230, 74491, 461054191, 676224826, 899985858, 845906432, 416058238, 515440476, 395773905, 798359484, 250794975, 642980335, 211944980, 595445056, 84146634, 65105911, 476238921, 661894951, 398878288, 196789467, 471907544, 304816424, 95596574, 634376441, 182169178, 703562960, 511957000, 687358401, 629465076, 515072607, 308883369, 388190008, 62450068, 67879479, 739189054, 281683990, 381182432, 224503331, 87094570, 338271053, 166002021, 575824828, 710383364, 363830087, 317693526, 763695560, 444389091, 579977050, 621292506, 292171269, 292036142, 576908307, 583158825, 355141763, 26569236, 900368538, 424912772, 297803740, 401465098, 692951565, 675614906, 487572644, 628278290, 245504108, 777142957, 132725311, 108269053, 217465599, 269412591, 468720599, 599053337, 54776237, 483125667, 450537345, 983301403, 214983269, 480505186, 365836245, 539034751, 246994365, 178130738, 880124086, 71621815, 176828227, 106982176, 414203362, 780390979, 521956409, 920724803, 596177494, 490056152, 958227187, 261272311, 285649190, 300332085, 441304985, 240464391, 533649392, 164238207, 502114127, 331594292, 298934149, 947669621, 36751468, 232522956, 741957135, 238678731, 835647820, 512663447, 622029974, 991843804, 536217485, 352734832, 838182897, 215689599, 486477496, 287584769, 714126903, 370223203, 619271833, 590834869, 462693107, 955149778, 910383191, 239414719, 372593387, 554289349, 407608616, 831634986, 597245795, 201235601, 827562794, 622103496, 322527681, 835031358, 131615771, 512222838, 604527335, 705351655, 813184053, 82116070, 663014810, 364896329, 550609700, 687126791, 238474644, 287184742, 323887654, 634876308, 467773750, 562857153, 198099198, 167047672, 491333821, 460577234, 770241682, 704386002, 587002638, 452318744, 326462931, 444057587, 975586497, 385201391, 481913313, 132476205, 569399784, 347397156, 119448826, 496990273, 944347738, 932211089, 331708225, 713392877, 759466099, 258212480, 301576651, 915298979, 257119860, 763561276, 809372108, 665090309, 149701804, 594211649, 325639206, 298523674, 520986936, 814054495, 97740115, 856838477, 255841214, 897575341, 850972062, 121307254, 48812244, 701609591, 621161859, 872845322, 135688387, 175200093, 630484481, 120429717, 405822240, 818492399, 333561585, 620603847, 770001654, 247363681, 839816985, 853031016, 630698442, 218699840, 948490508, 890784741, 340850183, 811334721, 370837256, 875285081, 346867064, 759138882, 44896094, 860240021, 996786680, 203095330, 663479406, 55627309, 679023496, 813841007, 801648280, 853477103, 109264626, 45529671, 831357322, 674888319, 688589802, 278490369, 90713271, 521838323, 563946099, 638454800, 274324920, 471110778, 720349522, 891361376, 58837066, 126968899, 132779449, 372878697, 550212995, 768271789, 388388921, 490611293, 520729888, 714010503, 425367677, 980499590, 53682826, 495814758, 420209720, 425398878, 637592680, 802478359, 74146929, 59204571, 687020073, 600045690, 915772320, 104776854, 767876472, 261305102, 173080802, 889442235, 700394821, 913551944, 163358995, 356012385, 20836437, 889116796, 675684916, 669545631, 873234091, 43643591, 510913886, 896915606, 670586605, 613337861, 274447604, 810969909, 839071190, 842027954, 348907324, 88169643, 95965620, 389162190, 365294233, 353038016, 937646503, 256765092, 629695370, 63027373, 781300611, 359253006, 933728524, 582093218, 863710005, 466720740, 913645571, 73393635, 768988105, 382849926, 422095214, 657963948, 97538044, 692109490, 220102113, 835937404, 797274440, 329842730, 133698736, 400147858, 26257416, 259742917, 62181145, 904229089, 388469144, 519008913, 215499732, 866810355, 121597512, 369821025, 941069709, 218655641, 160226328, 409153117, 336544517, 101259216, 489175794, 300287376, 992784245, 749164341, 2445580, 89046366, 388248785, 66474015, 346576524, 227382280, 63271439, 727220011, 744583940, 108069042, 31350640, 790439316, 823055234, 929789968, 387337050, 751556105, 145534419, 519287566, 352444842, 330076346, 840679099, 593565633, 736330035, 24958015, 976674700, 893633365, 317059470, 533037162, 894170894, 927997023, 754581161, 991362642, 364472771, 208485181, 322378908, 361671838, 173979241, 81552606, 209426265, 834925895, 556019333, 198221426, 170669184, 384994908, 80428378, 704881807, 3593661, 6573334, 144754552, 114947552, 461728654, 451694388, 964977072, 238226403, 585543415, 472709928, 195004430, 107335633, 1506421, 189522516, 192666685, 297647017, 530803825, 936143496, 796374115, 33331044, 877735110, 373495429, 256780854, 666405337, 266424732, 642194561, 218778538, 933301884, 560458711, 862667019, 641270826, 597489802, 825055454, 310991037, 886716246, 801331300, 819686132, 377716810, 538967083, 721233431, 540443917, 736405181, 108878961, 614085225, 609650688, 793930364, 750643081, 964600424, 58043472, 475618636, 216180544, 561389226, 899874894, 890924761, 390586212, 115841647, 444324272, 968327932, 897277973, 306121267, 757235260, 981547317, 984408976, 933568848, 782478810, 503705698, 227520156, 366931172, 802643943, 586174083, 268766476, 278658148, 37789721, 855010202, 864026513, 780859044, 890812990, 368123493, 771935899, 623584376, 625916325, 624700824, 386228782, 114220512, 507684639, 340450878, 297399858, 45731979, 786502574, 346322754, 345148341, 977686173, 381465141, 960637916, 452569653, 404815054, 971199706, 231132982, 319193096, 341019585, 435491198, 52940167, 890561479, 134154826, 729804631, 174736103, 155227399, 143146097, 388636857, 323059754, 367354052, 329389346, 222308289, 366840704, 775083788, 881243409, 718043524, 602841187, 282168672, 996385689, 646079310, 227344377, 71242692, 46212885, 838422408, 428386912, 664362693, 100226579, 544958506, 824252857, 19555337, 197705844, 3370325, 20915689, 620549380, 955517319, 369067648, 158922429, 787727323, 693109087, 906417445, 442401453, 118666206, 212861101, 699529174, 693802742, 775385644, 153536184, 309748861, 205434461, 572291399, 358580593, 255183429, 345737914, 615682211, 860712112, 165165201, 674424704, 878020737, 32346616, 33146329, 389321732, 547301754, 614722937, 636962093, 296216623, 936539595, 487557205, 148332466, 113187609, 192088392, 701326689, 668156251, 473199433, 110849130, 493153163, 651492432, 486136285, 584213745, 983857765, 102083034, 179594138, 639270791, 533560064, 52237668, 617203425, 942172480, 948509668, 207264349, 980993235, 882855042, 331402061, 325265725, 943263833, 138095142, 790230557, 460522616, 332759364, 215231904, 696654532, 895661065, 485737571, 768338443, 143834007, 78369031, 715480182, 693304751, 352750107, 497185408, 2523751, 942447795, 300229745, 366247638, 979614797, 457280837, 963792885, 691321472, 743819903, 543788388, 582935739, 491631260, 722900042, 560189706, 364130304, 434732407, 60869560, 240234989, 327131400, 431354404, 584870517, 426661355, 341572312, 496353025, 256219850, 179538208, 903373229, 262869646, 243539230, 45745999, 215034504, 219065284, 325162518, 145914071, 756078132, 15082699, 249267847, 724457743, 131756655, 709646699, 719684624, 448066462, 174534914, 237294283, 748572127, 732240040, 760127555, 152306910, 590786293, 354965083, 704223824, 656864509, 200374705, 2383527, 452395401, 611883578, 702291743, 28505247, 660251665, 581619957, 492688829, 714298256, 689841673, 260247621, 905630266, 654225147, 543682463, 420906249, 216940023, 295195823, 972740617, 56721378, 824712797, 819681621, 978746224, 770375314, 951445894, 883044334, 740303190, 123859735, 658396848, 306381452, 793349926, 242463072, 942836885, 801427657, 148508709, 554498083, 553057726, 397332994, 125026222, 392847144, 175666647, 654252491, 342320257, 577296451, 885432146, 107299371, 551511668, 984317166, 530511670, 462401524, 428062502, 883017289, 882702968, 254456105, 205997673, 842550803, 883475577, 51583597, 257508423, 169601296, 400333457, 551645008, 192117576, 84841898, 99631549, 33596512, 224702761, 811524188, 667180317, 146653430, 508120889, 206559501, 69242418, 627241156, 487344554, 330354300, 742646173, 229226978, 966146983, 341149966, 579037588, 968431926, 924871227, 969773792, 655567459, 833370721, 481360755, 187527263, 938923514, 859136319, 341243051, 323888544, 328098446, 485872718, 143493190, 127354097, 558364639, 940054105, 245522026, 312419188, 535690438, 604357574, 603202724, 238375522, 451369855, 551622989, 777113536, 353551108, 148824621, 897163892, 787118567, 835224753, 868124404, 978863311, 318984169, 516507005, 786243998, 756725958, 519329520, 382069550, 726336105, 673036944, 314855287, 809979333, 857615322, 497763965, 632086525, 506845477, 429090790, 939618221, 340583166, 530479476, 422177190, 51846929, 133174439, 999396899, 280030502, 832076716, 123684871, 930810433, 401218833, 216824866, 161760394, 322801574, 413989659, 399632867, 405322007, 274936556, 415787731, 178403620, 589775356, 290509818, 1601168, 144754912, 143545673, 373928266, 368590723, 878872932, 97010082, 600303422, 705718608, 902996225, 790289993, 87617603, 624692735, 825189477, 715272771, 556408060, 401207721, 337386383, 916549505, 563513543, 79951149, 552089828, 815068660, 130738413, 11673128, 386126425, 933528386, 58175310, 964007685, 892528561, 564738022, 674705551, 438209291, 178102526, 615044425, 556943805, 812673853, 807368096, 284142562, 886263918, 130311560, 15890729, 944567519, 222452928, 216414152, 466215237, 142021951, 16708020, 563449197, 651349363, 247087142, 664239003, 154194589, 364609849, 371122379, 170254603, 634904674, 749839009, 182497156, 126840791, 888781594, 364322195, 970994422, 801257174, 633513663, 809688600, 241600422, 164467942, 305190218, 470914282, 34861712, 217859685, 911379349, 669307726, 654280506, 687427573, 86894855, 827724312, 505143355, 876224905, 184027147, 472225952, 942661575, 759292581, 211679644, 262274951, 779460004, 509335415, 222788471, 890122298, 2485663, 457665923, 943755770, 302538453, 840242731, 816058606, 761123380, 999309343, 883258988, 126298867, 732641819, 263165112, 963564214, 68520911, 345626042, 896294063, 700530502, 24099753, 994019818, 181983119, 202853918, 341250889, 538910168, 931148305, 511343367, 292780224, 918370088, 114772976, 901218520, 427136681, 447266585, 141521387, 934492809, 164704934, 113228195, 864807970, 575177924, 55857009, 237638244, 352920568, 272892643, 448511894, 947639874, 473477295, 980573371, 832876567, 334488506, 180502246, 2667579, 926665041, 493853260, 908430489, 767168278, 496559748, 232989943, 266544120, 749282697, 690366929, 937139268, 233068594, 831929174, 736739566, 727045468, 965773062, 371713766, 661706358, 979640337, 607841724, 612573592, 337131509, 122530384, 346218166, 252738386, 402912045, 650099766, 589424664, 81672649, 342581915, 368197438, 583738839, 50024709, 824583477, 915916573, 279240560, 790247458, 148060909, 919816496, 216976280, 177696024, 673713296, 623364768, 252499773, 308706932, 734633216, 683751755, 329116579, 576084207, 307699920, 718036261, 207495697, 718824263, 467510407, 604823437, 560787959, 237520535, 200288283, 972596876, 76041606, 404206687, 388291571, 758236157, 475568166, 475269504, 703208960, 213125488, 304925875, 502024460, 233120100, 930681011, 260235569, 534784773, 459685507, 351343802, 552396959, 753404014, 217165295, 929798959, 320628615, 795057070, 707534466, 138166761, 899116919, 418097506, 330595338, 839062347, 298487868, 175306744, 165776804, 57775889, 629015561, 838168884, 764475714, 860993265, 305178868, 75508475, 872411436, 819931085, 266973893, 793306073, 401603803, 777150241, 536363636, 139947850, 922371896, 752902245, 102256873, 907289116, 290881460, 113101821, 400500599, 894313620, 911494699, 239336965, 944458417, 512154529, 886405457, 160329315, 730082805, 85485640, 99262117, 611245911, 704135901, 434894127, 849356200, 831961923, 375123350, 259481359, 523297796, 669473132, 142420477, 776309401, 523684234, 706139880, 472202510, 689611632, 959583568, 976517997, 904880718, 68276919, 964232683, 652509757, 86329083, 439739195, 253834810, 539377712, 221754327, 619743674, 805569353, 622923257, 332163490, 207568608, 501753456, 54831042, 168242744, 253588700, 356703694, 706830327, 60964459, 256051364, 444735418, 443350605, 778741678, 480965483, 448239926, 825414080, 361418670, 778509057, 766004579, 949666109, 180237364, 720493277, 889353474, 609610535, 643973157, 299202854, 841892295, 923691777, 256096429, 174952113, 37460992, 579635160, 930008193, 674772619, 223516959, 229232679, 877028463, 934688075, 36673116, 695967154, 701633702, 642075008, 930139426, 566911508, 789317256, 846376915, 516290108, 306063274, 169921887, 28663614, 94398885, 66035640, 455852177, 959317061, 575941490, 715419348, 913017952, 297555982, 318473550, 459066456, 570968712, 681546928, 112548413, 838295220, 847734635, 964279083, 553568080, 387997512, 373410940, 562825422, 132025854, 537333869, 903874802, 529750167, 821765812, 135162531, 810993747, 629049966, 932315768, 759525251, 276365297, 206587206, 421837164, 923536030, 364735029, 383830653, 706426910, 597353050, 912534172, 408520016, 241381474, 241959948, 536939940, 58809499, 819547366, 57143611, 768468372, 815771249, 624232541, 227518437, 241975940, 588806495, 140319253, 513104836, 800619733, 184823257, 592576364, 323451691, 595372536, 45330000, 299675436, 405134548, 579137606, 475131579, 416297046, 766734725, 287540872, 636347073, 930603949, 822285694, 920249163, 254442680, 958829309, 601831420, 870720724, 87291397, 742381866, 2228039, 353775504, 419403740, 614699305, 575177325, 858031502, 390153394, 667231167, 567415415, 229643799, 456195978, 728795127, 108203092, 820895212, 224531809, 382719967, 713011118, 821354012, 506570790, 334414589, 578416645, 251787310, 38547919, 370034031, 288451980, 191857427, 272695304, 703941354, 790194270, 221349815, 105621231, 820066783, 243458598, 244395440, 310989609, 909875910, 815092113, 898862982, 241159448, 1296261, 452049123, 149478599, 343661398, 248083261, 633418014, 553161072, 664630466, 97610452, 965474329, 946391479, 203230743, 205961880, 232915649, 734262918, 423821462, 133643776, 747079142, 303219204, 806389553, 246554436, 44527246, 247570725, 383841522, 851527552, 340236384, 292862879, 769897558, 103663194, 763486975, 739692368, 401500295, 795508782, 109523558, 61633284, 434619539, 438516970, 992915766, 388568812, 267489593, 130757655, 186140258, 286667871, 952323471, 752237878, 935848017, 878307741, 109018889, 601394567, 563482529, 571999777, 322626077, 390909376, 846096402, 600190399, 735143653, 196835312, 233498935, 437596815, 178633224, 484556384, 144762194, 590861648, 46661593, 361771628, 602207099, 203561652, 150419743, 130284977, 564834683, 810698675, 476041763, 13636022, 355284560, 710289813, 536185256, 899216126, 609060768, 68988526, 497756395, 562852365, 947561840, 434860180, 748728941, 256552555, 476843760, 576388339, 79097457, 286291504, 943030870, 185050331, 225573288, 74761609, 934719307, 897073749, 496878800, 367622760, 884236366, 328496395, 919260032, 584022119, 469228965, 318167713, 181561505, 662284707, 429180824, 300203570, 771659821, 724977173, 787883979, 301894567, 585785234, 881804964, 274799149, 331230395, 307487166, 302843983, 846587780, 44447204, 202469318, 36206237, 511684632, 277516549, 307472079, 939080385, 225766701, 849930939, 311384788, 472394583, 527915803, 832195220, 200077877, 796096062, 516491784, 708719819, 342934450, 812498928, 526206335, 389347399, 148204903, 15454129, 984873711, 428957646, 512757933, 269747731, 606281997, 313802008, 855946928, 513112949, 683315728, 539858367, 91354308, 879165180, 340090554, 43228532, 708742219, 911530212, 149971695, 988428945, 131583109, 735401458, 365829087, 211828031, 421143619, 601238749, 476819781, 335582459, 671069547, 768184350, 989155159, 805870337, 388145753, 807171417, 642895230, 419971784, 167123588, 819677966, 111163060, 352757236, 858616860, 786441520, 563078389, 835716764, 876846931, 177740995, 328312724, 258150732, 999457331, 381137206, 773002559, 930941119, 33331064, 571808822, 860224325, 5169680, 44572311, 428506129, 715544445, 95366896, 760678428, 914902051, 822799281, 51839294, 270529588, 606751816, 358002938, 994201837, 661340921, 29504257, 82806294, 786556737, 687179247, 71880628, 860013534, 590758571, 478196158, 889139433, 607486470, 673083735, 792292981, 210148629, 871020208, 296988135, 233098230, 463974030, 202080817, 643689123, 681727633, 141195606, 249765139, 711030920, 417679139, 745849483, 492218423, 220908611, 613301584, 368211950, 314933825, 871266213, 968142539, 332040435, 334231192, 921237534, 378894771, 664142716, 229317303, 697854093, 774119586, 148802767, 382102830, 366670070, 789535873, 534122571, 309711560, 94011939, 589926549, 188834194, 115535191, 711162082, 555925720, 7002979, 204269970, 393755795, 83598919, 889087085, 231054541, 616367603, 332172663, 846354361, 762904132, 483978370, 388053245, 349375464, 120420667, 965019387, 992698407, 608212998, 123029673, 646705046, 700986443, 140089200, 608882686, 828866257, 839379649, 157327266, 652885627, 195294517, 720232077, 708097578, 835011664, 714642895, 774567496, 789382768, 691386834, 118687277, 875135935, 71172363, 894427614, 567968557, 652801945, 779084789, 757904635, 650130426, 923491064, 685599842, 569616529, 892586384, 941009696, 597647632, 224218049, 771556670, 840143713, 568434477, 427421857, 834610506, 109965859, 488724535, 527432403, 991424658, 466773105, 328668150, 243222109, 719929839, 304734422, 173288498, 984566971, 522176431, 466762075, 395098292, 593833827, 98854392, 276443183, 507344064, 675117556, 149691642, 37771841, 474639929, 220141075, 602080023, 457835165, 546781840, 674934648, 661852974, 75086349, 468540557, 965844612, 775126601, 771689260, 429699114, 371626800, 370841970, 525603562, 322408121, 690021656, 926277651, 792721379, 16272622, 35485842, 210387990, 898597928, 108645744, 2122338, 411426190, 82592546, 245267840, 315012850, 229946792, 35764774, 273148739, 814845359, 711749648, 175399244, 696448135, 341232351, 576764631, 473822515, 970752050, 335225912, 737781582, 382496644, 7594891, 705643247, 650504436, 253528048, 614337705, 143988244, 375320933, 776355647, 34118973, 409615468, 290052317, 747616370, 991319298, 77343623, 492351330, 889219555, 571052103, 264197346, 247410103, 653749837, 517908997, 644968678, 259191940, 779786323, 116813849, 645593174, 747223943, 669162150, 743898321, 373779841, 5589128, 485343360, 955151562, 19124982, 913191265, 959180333, 941395844, 57177975, 247733200, 348242644, 932809486, 220801027, 314342817, 849078913, 689837274, 828320817, 812512107, 935871982, 491117533, 705969573, 883338164, 191921328, 431054839, 955886323, 610036057, 733194257, 165461689, 636722801, 332074028, 465750804, 468435845, 281400399, 282961663, 746820271, 630074460, 917511048, 764910893, 421072816, 300235348, 552676462, 309288173, 699634446, 590918152, 684936405, 967946280, 967174568, 512619680, 99143832, 509732001, 183734492, 495372619, 691135819, 648986742, 531741064, 464867561, 714753942, 197139021, 535870931, 614757446, 869709312, 870406399, 67617404, 9532461, 665321242, 727950511, 416493618, 987460764, 267632368, 911455087, 676717286, 321418732, 11414781, 326943209, 721435123, 635384222, 349346928, 963909163, 60519145, 916205082, 370407446, 466782439, 574824633, 926709069, 740768506, 113442229, 7099927, 84276494, 840923872, 172624922, 191484246, 933722128, 592540553, 628852234, 354826023, 23853996, 489562495, 870293185, 57272384, 216692016, 496486622, 151222573, 56892477, 69034191, 541218678, 772923674, 887714933, 996255454, 489434690, 753229808, 153655952, 359026852, 372931952, 995642003, 462555795, 573333976, 97599821, 833230391, 155796415, 880422019, 498213570, 623747778, 10257600, 393879633, 133079599, 236923018, 16209432, 967195347, 884797525, 265378276, 873268277, 663377583, 491378097, 300579224, 550160857, 469099337, 83868101, 748082505, 49856278, 565885323, 290601848, 756941219, 576053152, 38689647, 753409730, 845067880, 737596433, 737716690, 326247243, 30917059, 663643978, 800967165, 655075700, 379185499, 396183545, 17045327, 443155730, 290198922, 174686966, 558767936, 100406785, 147259422, 778019993, 277061718, 226951249, 26011274, 15131696, 535899174, 195883282, 975962472, 784007110, 92945434, 523330577, 966222974, 611528047, 16453396, 162138411, 124157487, 304154289, 909044262, 856171425, 337183716, 98122241, 863543840, 531080568, 541100194, 246561842, 277479130, 135229144, 878675223, 189501363, 292224679, 54657174, 242082221, 922715502, 681909321, 409630571, 392113409, 402072938, 599517801, 943374964, 501999289, 272167844, 417319790, 165328261, 300527810, 844672458, 216509946, 141248846, 151663122, 150795969, 400378226, 204280555, 987794009, 56750015, 521960578, 664746724, 506197840, 613830596, 393932286, 440269670, 70201417, 160493840, 996595899, 275357254, 351930528, 486991418, 945286016, 549429112, 412112715, 555782806, 162316099, 296837100, 206012207, 25357440, 481480845, 151977343, 357652412, 248345190, 533804092, 722314689, 176960096, 982616939, 275331478, 797803913, 13590981, 104029170, 436774925, 589004145, 316468010, 461980739, 170244783, 981474134, 716620545, 277327619, 603363148, 355457043, 663178978, 981669626, 477396845, 241670793, 532933152, 574585592, 131785969, 311376382, 603434083, 481091976, 192072288, 99957937, 169751692, 712626952, 129418392, 307211730, 910058086, 845955868, 385565675, 46699667, 864248098, 551437871, 197447398, 966503550, 217043248, 413667088, 895134918, 656726631, 957185869, 951787169, 143911377, 905649549, 978293390, 238054220, 924931296, 594201964, 716282060, 77895784, 725070524, 159931695, 628579595, 469318889, 455314685, 12780779, 652005745, 831500225, 716871523, 568703431, 341115995, 612982744, 317635473, 480886618, 881743556, 987465115, 299557621, 166997973, 497051603, 517146577, 337993194, 263795916, 220726857, 954944514, 727356457, 160869937, 742894002, 484894289, 873105749, 264300683, 470101030, 828410616, 649834954, 131310764, 708815372, 340464412, 284525032, 948060390, 718750297, 608238287, 819121332, 690457673, 442092316, 311572830, 889430496, 605093391, 150639231, 458908945, 77062919, 160065624, 538556792, 425544731, 883991837, 497783498, 255807027, 311584357, 501770813, 269053359, 970462178, 726903766, 775357828, 36082331, 325059679, 182992512, 255348018, 696651389, 617717502, 346072263, 720856940, 562149168, 197332779, 402881934, 114039203, 678561105, 955531152, 846893828, 111671648, 833589533, 275772851, 561794370, 302337714, 75522716, 652442405, 759656840, 670438152, 875738200, 717154166, 88492204, 360820963, 731214487, 826149847, 60136248, 492581032, 48401069, 582886153, 746082421, 628459051, 301513073, 964931427, 943822349, 881602448, 471077261, 899039051, 537271100, 125285514, 364863463, 304738885, 810734949, 217525536, 622262443, 298060722, 255484731, 77270943, 903089531, 369231310, 76156529, 740081942, 414904814, 780670037, 347410204, 590085941, 111809332, 163678961, 762224814, 456650521, 512545263, 248460257, 924684394, 135093636, 305759105, 792431560, 297965023, 73160054, 60953215, 356429391, 838476535, 769244685, 819076971, 355140181, 989750865, 60697465, 238913001, 171875699, 715041701, 129116169, 914905188, 444205677, 538507012, 894534372, 726501558, 746750356, 463645596, 447093311, 955572002, 303904900, 820498411, 614198317, 299601807, 672475985, 178329893, 386898082, 507951567, 90565613, 408052189, 206031063, 735769477, 512330187, 658469434, 988204162, 360136538, 857806660, 8455218, 725382235, 423369085, 174745676, 391247427, 659798470, 481576274, 721609002, 696155145, 134764146, 543546156, 981562542, 112395501, 949402400, 675883947, 309908241, 212495333, 347638318, 441209541, 429208245, 810701423, 905161622, 338946563, 285410195, 177610725, 349822007, 384801457, 71583996, 679740398, 992348606, 624275578, 970495818, 202958244, 549899989, 355193618, 891539908, 380565576, 485567079, 786777132, 175571018, 350228502, 186642900, 670911587, 623604626, 35961283, 197941849, 444438724, 651175756, 365739718, 853779461, 15479468, 343423745, 408758931, 270847298, 115704228, 441298396, 856469504, 711561693, 754271585, 23230733, 603922514, 790928213, 172902891, 790489409, 288302827, 496632360, 127693902, 139212275, 856095775, 578240697, 830556423, 211371312, 216137333, 574601624, 643039625, 47447139, 451853615, 526473527, 324910681, 833191106, 940216557, 256952189, 438936023, 118832893, 866666735, 692895981, 202717367, 838461080, 793432999, 333566924, 142056040, 500648794, 394128810, 683669364, 625600654, 116238339, 250517781, 182900485, 427175538, 684114567, 54652850, 517991841, 208053068, 321004655, 869524981, 503126253, 15557551, 986350531, 172638625, 462310546, 692730350, 830874415, 538007466, 467568665, 688214734, 35635582, 910572150, 551848542, 737790899, 314129203, 848213256, 795562662, 890237924, 144281277, 959918406, 326788360, 516676508, 127183260, 129295268, 14861176, 849229381, 278317776, 588361935, 739228600, 458668599, 921049505, 89684662, 305769415, 952522839, 174783528, 108113333, 200231713, 752854707, 875611991, 562106566, 884732125, 84445640, 773011082, 311306365, 285960302, 243351270, 444429032, 612119425, 605613360, 148132650, 727859972, 775426506, 218757739, 965869805, 186283139, 265651912, 552284647, 531621238, 308091299, 285858091, 496561622, 356903067, 105598590, 834172098, 337784026, 184429501, 103680041, 260411022, 866912870, 268222471, 882691939, 885800129, 216761758, 720517285, 471827117, 503656485, 379784579, 193611947, 230617499, 393598069, 147872704, 47832212, 795154177, 334416484, 812608691, 880233927, 318271661, 389366914, 825446723, 846128679, 786364948, 146390401, 359052760, 658841513, 188786748, 193229739, 317841406, 397940755, 779133883, 433548372, 63169169, 68198992, 347732960, 895531743, 340262530, 883829645, 577687667, 809082901, 974856984, 147195649, 211503847, 964963305, 326018069, 666639000, 731789399, 402456596, 136500214, 866543620, 509551470, 382859698, 420308931, 65053306, 860155374, 587342532, 141352738, 85276281, 364810473, 943359649, 903331516, 664664903, 72762453, 233735741, 621234292, 889690254, 761570973, 351172749, 983178971, 687758375, 761151584, 197501459, 809638294, 326961600, 920557209, 292709367, 89133171, 857600178, 57601131, 846460825, 51023366, 655520080, 922782738, 399704722, 617942162, 960947717, 429122176, 97534186, 186054681, 343987988, 705646722, 309696483, 235932081, 493382332, 726182976, 318921176, 354494666, 738291736, 888761660, 697356338, 584807198, 266813260, 975682510, 866908729, 240093246, 859579902, 419350290, 723804590, 248681241, 815836032, 510995374, 531738829, 7294828, 708931767, 471288353, 275554581, 618558978, 816952183, 187278273, 749390099, 703631527, 604621831, 429506151, 154142891, 302263749, 611545796, 846996636, 43594794, 801839565, 921413438, 525828007, 122589475, 176277933, 903890452, 799404702, 308100551, 150631897, 305282410, 810160102, 19465048, 395391701, 311613343, 648529542, 629343567, 718329806, 559516352, 357111461, 274287963, 8396295, 725989407, 327415991, 190099864, 105927111, 377603136, 450288513, 133656877, 500766126, 851238139, 884020449, 325151013, 743169062, 902497773, 652079030, 668378518, 368995896, 386607899, 691214199, 346704290, 647945835, 161377006, 924157048, 474027284, 96591334, 459468867, 319762330, 829990219, 582794329, 720027533, 542448290, 712524913, 317718028, 409626144, 566929994, 154869526, 762725987, 114903451, 34519031, 230779239, 273692280, 500305727, 245412385, 946397573, 52926862, 178810396, 626767046, 179518163, 23796736, 111524030, 400570064, 179070689, 543990876, 844081156, 274898140, 973996279, 701255714, 277361320, 287179620, 782401892, 646999208, 110750671, 495036513, 537220560, 508259917, 70677560, 256037934, 159185267, 568087093, 885847818, 696253671, 304208261, 822676334, 317873669, 940468425, 994816474, 684051003, 67601297, 401219950, 261683736, 245892788, 782852866, 171908151, 951625960, 45067575, 174071999, 553856152, 524671144, 579325786, 76781989, 198115961, 754188767, 516706797, 433475716, 757620603, 121182807, 214891664, 783574129, 848486995, 776850156, 552864948, 702330954, 559557619, 349584080, 232934983, 604905862, 908307233, 357069126, 439021576, 785155835, 464802891, 947499991, 935236956, 921709856, 557576206, 459424110, 874578471, 538500711, 404985096, 961299571, 662645529, 187108129, 707013682, 564861756, 139054917, 254934715, 108146740, 332654662, 618218064, 326797180, 446502064, 635943360, 242264112, 624446528, 419804928, 657372576, 496590563, 487422112, 520487459, 65002759, 954926411, 420739264, 4629750, 307770915, 76050249, 178083942, 613797993, 905776840, 595481503, 403495519, 537391643, 196618850, 555136813, 623974333, 788305609, 156975859, 496600549, 696842923, 212423308, 186174568, 455889854, 824159707, 877694475, 87778188, 592755245, 325440794, 700036990, 34435983, 100302179, 445082027, 763969412, 647203902, 900999318, 780639300, 605114802, 679171390, 735548210, 732261499, 161093461, 686410673, 413103646, 728683711, 536976503, 381454765, 565448107, 718075155, 778796721, 637835073, 800609433, 452390068, 761330317, 312139148, 888760704, 678280849, 308320574, 49932207, 483223159, 588307426, 893664014, 517592341, 530807511, 285954986, 468545089, 689707523, 800292117, 772152244, 7990946, 891084183, 129210434, 951134505, 819426818, 500608988, 955321609, 514431922, 463864482, 629546791, 181577976, 271996530, 535077051, 229462337, 478501101, 345534216, 465204493, 583777110, 717878463, 292950875, 244663870, 768202612, 39017386, 321258634, 318946714, 180481276, 895538835, 397071999, 667920254, 411635159, 875946097, 747823292, 261573979, 323812523, 301870962, 556806316, 261836318, 208149186, 370451018, 319893586, 869934944, 481834746, 584462390, 425569080, 222748252, 198928317, 285395565, 229135683, 507914373, 351151814, 855402136, 691906968, 426792279, 384295637, 815344288, 299476620, 621787210, 72688715, 573638719, 118159492, 813317062, 994846028, 4518752, 798829121, 765741657, 16192504, 602114207, 216799126, 958166645, 31378869, 959813391, 38799008, 555998006, 497116372, 27872651, 800158934, 667857678, 982254864, 635789645, 168248783, 417541716, 121571114, 124069427, 436448702, 714468125, 695824381, 238411132, 362919883, 845521108, 642908282, 369896308, 795794078, 600607153, 170322601, 37316977, 499898838, 926569982, 990917842, 469875189, 104152639, 99860091, 279168211, 935503027, 368338079, 330131944, 475639669, 948780662, 847346418, 579235732, 124880009, 530392900, 795897982, 768824022, 954123240, 462406279, 924424797, 271196728, 503132798, 112346724, 118022598, 203211167, 307096610, 570181950, 614159128, 867605898, 410742420, 314167217, 361318670, 899673072, 398413446, 822289399, 225042271, 111860077, 898337153, 39966731, 945479122, 660408043, 845059975, 143399043, 806008074, 413451096, 414416193, 882411200, 16467106, 790011171, 226695776, 725643439, 40797494, 150773881, 983952594, 604341536, 730296585, 462680154, 251211854, 290187860, 799818218, 906571088, 254653050, 675372550, 22801816, 126530220, 14992927, 112264564, 197089011, 172244655, 614451555, 768365014, 910822113, 992760204, 129105921, 430226591, 897497459, 931249745, 396653738, 422624723, 984091384, 987436359, 341613038, 580252753, 783511148, 757908942, 978700651, 927146214, 584752419, 673605257, 657736746, 324743661, 976406808, 359282989, 427280636, 179512188, 909630560, 754288656, 188828236, 606197728, 758084015, 663095475, 934501590, 927520701, 900522789, 330291429, 503860088, 399510835, 307728662, 173252641, 190927166, 533564841, 701766501, 844110625, 148396215, 861656275, 661961990, 64951157, 991494201, 233129004, 193781672, 968119667, 875042747, 617016784, 480017654, 478798824, 141272492, 745543379, 69825142, 415018371, 381816417, 368776100, 159288793, 888985412, 25290786, 209986561, 574212323, 959608734, 995090267, 818328775, 673706716, 658366558, 758679706, 458933821, 461397169, 972451593, 761393454, 916773126, 220517251, 225025006, 283461914, 555531728, 809655698, 508845674, 429550590, 427426595, 945744151, 593790337, 188549867, 476709000, 51051831, 798837119, 572177077, 925240360, 335418319, 131390798, 99192267, 758080151, 207985688, 563466124, 131095658, 342935963, 978176437, 470369552, 299131973, 801073091, 776822740, 456306989, 628620799, 820493540, 787041232, 6243147, 234409988, 950735830, 628679782, 469878802, 72828184, 641006927, 145431804, 602398804, 998999125, 458603689, 337191743, 208454223, 425335525, 486375173, 989392470, 528634601, 194727811, 448152245, 946919045, 757048922, 521692152, 338281894, 892459725, 424895829, 333941973, 473741293, 247440605, 40670577, 692498579, 18670188, 653396756, 423016873, 801403100, 956227446, 636510628, 768939005, 278377353, 716953529, 191407110, 91905230, 172073469, 347664546, 272555482, 753808787, 451551423, 832087710, 443615580, 520424033, 776052281, 607462583, 724575925, 317633901, 812609719, 2123362, 27338353, 536282733, 556556246, 793860415, 71892544, 408921483, 490926112, 290977205, 139922581, 942851221, 485979213, 425565270, 498526273, 477252590, 735288530, 320511031, 643534400, 948761843, 6062060, 338082334, 253569001, 69953406, 746691762, 155047173, 633969955, 867499129, 75974374, 664091355, 343328002, 829788132, 127356930, 945528225, 930054458, 189130372, 69641007, 633813815, 372877113, 422463142, 159493494, 662290207, 582961340, 259523895, 265534659, 947062497, 39193004, 169607885, 798633839, 572503040, 59268612, 83391474, 879046339, 214542828, 501727947, 59607806, 840194374, 793431503, 507318085, 536940569, 615228298, 813658951, 711058619, 678188919, 996405125, 537014986, 864962841, 865219172, 926127086, 351716147, 5532763, 599119923, 104044892, 863462685, 59128067, 650009465, 469558120, 730585965, 826619064, 125531271, 508194600, 629206389, 93682068, 929897225, 503854469, 694922612, 723810797, 504102898, 457409913, 875128004, 886435398, 994570782, 547788137, 544245401, 792116850, 934845653, 224117300, 409765727, 232696031, 970537147, 885716035, 257918310, 21766258, 440238376, 585103, 175180772, 961001575, 217336654, 750104600, 663067202, 593124946, 702360918, 205878464, 675604149, 624848659, 37621198, 353523419, 44604915, 414411983, 822466911, 284229964, 693200442, 201085636, 66652553, 678600220, 857513784, 265681564, 2634919, 830262353, 419942391, 518243928, 973816995, 508762293, 915895590, 955592045, 647055065, 397133921, 18404091, 318704917, 234618765, 414279541, 338562826, 172562464, 751637284, 404663270, 411900230, 697542074, 500432460, 446304358, 843049679, 127682874, 688213872, 718669293, 573669660, 139164543, 940154519, 711262562, 359787702, 281862412, 171028332, 513025326, 680936782, 5840703, 540144934, 205943106, 875660770, 966797941, 140616484, 363784210, 692978019, 746911363, 973865916, 21801190, 437893652, 171042937, 304330193, 120141866, 312031003, 604213879, 186753555, 443861318, 260166074, 878561332, 378505876, 545709446, 526078568, 542512918, 764011468, 740588089, 127430507, 748464746, 128475758, 628497294, 567766730, 763651187, 520372201, 918350055, 122606408, 996516682, 343718057, 243224024, 530779607, 816268678, 155627972, 469029077, 590312590, 955278863, 464546808, 750730596, 981183498, 372919482, 178917821, 983361403, 669249557, 530656676, 542347487, 300382153, 640703376, 862693477, 915807583, 754319238, 667931297, 277695713, 567509215, 304775440, 156804645, 748620999, 96842103, 395624317, 877820303, 352429059, 963328853, 596971381, 334477253, 542714249, 149069517, 18922218, 725596522, 195552591, 77586151, 574212434, 487673267, 400189355, 602993115, 42068555, 333323319, 724609620, 92001005, 849146586, 912888814, 117718205, 418477790, 916351977, 860568965, 989748234, 588527144, 762189401, 662701463, 395672053, 301918579, 566820522, 148782127, 72278525, 330759668, 846810129, 842230373, 97869517, 593999050, 761648581, 94611834, 747092268, 369346441, 367912108, 329416244, 247606616, 616608785, 325832252, 349374731, 991740801, 842111329, 662880403, 623283953, 92052232, 27096275, 727899619, 173471258, 42210095, 393821421, 437672781, 975131583, 170427152, 126579046, 974766557, 846276687, 776250462, 577975466, 86805397, 147274409, 661951435, 920700474, 185920969, 881524519, 232349359, 32094884, 629279004, 724170033, 321859424, 561341086, 832264344, 941690320, 884457614, 215014820, 48778200, 38317258, 430264388, 247498361, 660811849, 731699823, 468608115, 122680988, 996623292, 448138703, 921259446, 170588224, 426518798, 740754664, 146092905, 774532843, 999598186, 228862194, 728701430, 709041649, 451448124, 12673110, 398077222, 10145558, 574000842, 307962802, 164633735, 674594144, 737643842, 483477931, 89231851, 419530854, 945206210, 810942446, 227845366, 279357143, 85522573, 672232296, 273864431, 582784037, 458572422, 230471286, 842313932, 492004802, 84349535, 688251683, 75533206, 221111379, 392875447, 960730521, 904367201, 31061810, 163296581, 950873878, 725153848, 34762116, 671222165, 421995968, 849169075, 618703, 186087838, 20310161, 922578010, 566849685, 706955468, 502341830, 423849812, 117956418, 812811910, 977188191, 490623796, 896035879, 953758371, 20300728, 492115445, 143626011, 523202449, 501639598, 780326204, 657805533, 136989631, 68057135, 709013701, 497984592, 291850040, 874372123, 758688953, 421531785, 932379707, 139446219, 734803972, 968566756, 556417757, 5463962, 46411771, 341517340, 989855559, 399889963, 12508339, 455826521, 95298546, 345834111, 595281212, 334367367, 863876879, 991293576, 879939102, 976284344, 327078879, 641312125, 302125856, 634283529, 687025996, 577241716, 686084243, 408475343, 883194009, 457590867, 712527060, 776312645, 371182687, 655550945, 904302794, 848856568, 177566205, 452421150, 792891423, 502564371, 12889411, 672824632, 536746953, 948121097, 456829368, 63791442, 288392371, 965655874, 289551684, 807489352, 638193304, 833786542, 88939464, 499826737, 382636595, 267970667, 728557945, 387542058, 251870225, 366082874, 364439185, 609281689, 995299790, 879469353, 750492966, 851180596, 800537934, 438221990, 702619853, 769710889, 543253597, 481424686, 904952991, 397822114, 654196327, 609656351, 618809948, 92345007, 996960062, 430542233, 274110731, 443261276, 78953965, 521766202, 449397073, 908735073, 150108952, 884455242, 678736953, 47316804, 372658521, 431370285, 362278592, 426954851, 216869521, 404442097, 467814045, 591484208, 758169339, 745515792, 545531735, 409355490, 547694681, 363879947, 857024914, 839823687, 577714911, 602666929, 789701545, 662097372, 590304211, 488943070, 782049498, 930522465, 528568704, 591409651, 374185178, 854180997, 896823216, 262625983, 468893523, 303729596, 559170176, 490341118, 163740787, 372403262, 793491979, 139993592, 918225282, 756453821, 815732063, 909032269, 25113064, 891333392, 159127127, 1166393, 840245859, 414020533, 872426908, 141314563, 599041324, 180593413, 550974040, 136434290, 347624591, 865955613, 576917179, 694539698, 767459286, 630089274, 840961655, 467525953, 311803922, 641187733, 894988761, 981966925, 692981462, 528350338, 511788360, 686673388, 496634318, 772298426, 956085350, 235110236, 927824853, 313660530, 545523335, 369114990, 747756670, 189413897, 449317398, 573911904, 279377462, 473420217, 643309154, 414783725, 164413347, 766472341, 375564352, 3070629, 783875228, 409896611, 620724521, 717720069, 105232794, 152674724, 497805196, 524588767, 464225067, 970217473, 27051937, 829336033, 530677974, 77942200, 200871418, 918048605, 116441112, 842100203, 682209119, 796679807, 551970413, 292813998, 496884177, 228168826, 9002, 383761188, 513332114, 913591088, 356842389, 455309386, 887256484, 148048177, 184943520, 141366146, 761916048, 721320700, 461241056, 243950689, 627919217, 496343154, 444789023, 445794174, 311082572, 730964663, 577240561, 557284531, 347120217, 572751935, 4921833, 550731064, 221923920, 496648484, 87553845, 385255773, 356147595, 272202509, 780854366, 618502161, 39069566, 448268177, 829110970, 812097036, 753466775, 109630295, 798328618, 303059905, 239205094, 284656879, 249367507, 608231062, 195847211, 781017573, 253165658, 364562267, 623126018, 895615591, 487970847, 697707141, 170265960, 885068400, 893254717, 559726357, 1625722, 191849768, 86403235, 944948865, 711287377, 509372874, 185075115, 263250385, 754380540, 744979383, 48338350, 477748441, 74163673, 554244567, 744001177, 491204009, 499167714, 275080218, 42811197, 127401543, 291964823, 435802911, 185924818, 851621651, 731399711, 90274020, 51651798, 942737439, 681779844, 500067834, 997289118, 808878014, 720550440, 407688098, 90088994, 239063903, 872579987, 349566142, 658303479, 966234619, 597640461, 543582196, 465551875, 339429028, 976633173, 939276382, 803128839, 363687141, 302126418, 215903652, 523858361, 456141849, 462360439, 270365611, 902323608, 445521165, 149947423, 487001555, 685945721, 806614383, 145709319, 736237874, 23114099, 271897495, 190128443, 727457086, 555390860, 121482675, 533558919, 952750520, 469122751, 934969770, 491308568, 705394374, 892220170, 108141040, 294173749, 901700058, 871271319, 824412339, 337978955, 24394837, 753634970, 152819050, 845039934, 807180174, 323303595, 504170844, 543650945, 270297895, 193028536, 372658885, 195277657, 205676421, 458111431, 771677452, 577712004, 49159036, 460373024, 719279543, 798868864, 146605061, 822525096, 14472305, 822619403, 563945019, 346501367, 601868326, 553246801, 639400837, 640347548, 442234200, 466561620, 150968772, 955125415, 622490706, 676473055, 303332390, 293535747, 933557448, 599965471, 211034719, 75069761, 699038114, 832590975, 452150111, 853147935, 992377657, 700993901, 307082110, 544751495, 716508988, 419366757, 682063811, 371970282, 175535122, 874395662, 17655787, 832206554, 78031515, 964041370, 142723098, 699620165, 544828487, 486760567, 893112412, 225584953, 284461527, 522313086, 615269937, 20352993, 998736261, 856470927, 64219025, 732735432, 642080958, 640073139, 317465248, 221688300, 469219361, 957972089, 85933514, 309735718, 911102816, 919907858, 115070615, 31178058, 809167645, 361874744, 716383781, 480809679, 386923615, 702025629, 167320151, 310824358, 996494116, 383543104, 546923513, 266944815, 290868920, 517845663, 479200236, 401992149, 110210030, 552607676, 416810290, 722059195, 787209513, 454211899, 319759993, 674575966, 25092225, 87974530, 655701461, 593224292, 258675015, 209081994, 894771806, 87051924, 290039463, 507171741, 352715725, 159428593, 186398754, 495212279, 779470533, 300707805, 234460664, 727204214, 130037421, 882959932, 758321565, 630000930, 826034847, 100529471, 629418312, 572432275, 440918324, 539272300, 331939506, 501178961, 745971046, 942123480, 747654398, 252648179, 902643569, 308451146, 961635599, 117343205, 337324300, 259762997, 772600192, 153682409, 880015690, 893690754, 95232546, 266759478, 176918940, 246275248, 658271850, 186293453, 705672649, 263683978, 626051807, 467188187, 755849838, 902633748, 284720267, 119406929, 589176202, 565836626, 169210125, 914694063, 27087277, 904342663, 896243485, 392325398, 869953005, 540760968, 783881365, 862921147, 683359121, 962570141, 993364908, 536976461, 218326330, 557688875, 748497088, 743017227, 49996398, 990968603, 182370275, 594366378, 331019805, 428954271, 981533720, 998669756, 324620898, 422336972, 257057593, 205141622, 823122865, 956147916, 560168918, 473936456, 904993326, 488784121, 301860067, 625218397, 962960254, 72667017, 494867512, 643134705, 908909256, 843385977, 376213047, 820918674, 155902114, 340807960, 113102222, 523850777, 920655438, 574264621, 721748374, 716844176, 457106805, 549174571, 586595665, 260751247, 99869410, 64967688, 170386860, 945605958, 2915646, 738266814, 496235126, 660365807, 797254075, 247375808, 83189665, 515785932, 742330380, 854999632, 931217773, 106218651, 51171932, 79122323, 34616279, 778602816, 38340453, 848723342, 907765499, 426598038, 818669292, 437852841, 641524398, 618285238, 382443397, 509513851, 447373631, 85109722, 213516420, 287187410, 771249058, 656683894, 552769153, 411178129, 170283963, 236503713, 811999692, 293138810, 848704297, 571967652, 225851700, 789302443, 278377369, 55089922, 524984109, 427848608, 490227808, 128866594, 769035968, 930770487, 257675443, 298729820, 350534085, 295903782, 117467621, 873468370, 900277207, 357735603, 672529134, 918404338, 67333850, 911697447, 837324141, 32987125, 477107079, 872857954, 728787683, 602294721, 241923443, 852271160, 279305574, 61326840, 811129267, 246988302, 92847434, 407860813, 283304568, 113096657, 359089795, 896667524, 50395879, 120164435, 785671334, 720469839, 29754442, 750142462, 118461623, 221555599, 51579543, 553279296, 864881889, 857743765, 811495702, 115036409, 721050568, 632058297, 248472613, 248313994, 556099364, 675399271, 733738264, 650146153, 823912111, 544669965, 78239247, 94364951, 888401524, 123996681, 558421372, 604797640, 795804512, 454745770, 87281718, 713762860, 128151714, 307660553, 761349882, 686412703, 25200201, 57527945, 66281162, 127406537, 164259536, 407793240, 805317675, 874195984, 599920498, 230744498, 150849751, 46962750, 785895519, 223072980, 502484905, 871896324, 25570927, 90644733, 550595474, 331869624, 362997251, 626292815, 796979405, 253724420, 175250430, 236373374, 939118812, 783385614, 617935164, 345998203, 675008799, 879167502, 207307221, 341267643, 474317959, 484214276, 677276874, 214765600, 162189579, 666508096, 288176750, 951645052, 248768513, 290891530, 912639250, 117183593, 964139787, 330721584, 107568697, 79586558, 177305256, 492490449, 82667534, 879083243, 235588250, 348038932, 109488160, 676706706, 377998612, 564634646, 567730182, 239885339, 642627798, 866781427, 452001806, 416563953, 123510513, 212551691, 382351088, 842106733, 551745212, 177421195, 555406372, 798234763, 663878793, 620921762, 795864421, 880032894, 44381369, 19975347, 121616413, 758251504, 172223215, 389952527, 409879132, 887986114, 505659008, 721058070, 42418411, 736869077, 755403688, 970632666, 906530692, 398649991, 39768877, 21591863, 314430225, 950596894, 584739521, 293754949, 566589556, 863419433, 98086370, 410910778, 674511838, 557950069, 153171618, 451214835, 946172638, 483605291, 941441799, 830668948, 381506259, 550538814, 934551268, 95435329, 344808081, 14397811, 631152940, 281594650, 761716086, 617646974, 474524945, 131168378, 418869157, 804522082, 548804490, 59483564, 696576852, 288068411, 827821, 340371111, 103482864, 652972291, 211771275, 828376763, 284256111, 270964189, 173489491, 956489270, 481662032, 579351483, 26499681, 749038880, 734188304, 551072551, 923958103, 487405309, 598958747, 313354043, 442854807, 348805306, 408244560, 940915858, 557713163, 735365586, 802402329, 693450653, 435181457, 192256430, 243158623, 923696962, 539951334, 751580904, 879217608, 148859772, 928162926, 348487723, 453346500, 265954316, 153692291, 586855476, 873795937, 315595392, 683110827, 150406926, 68609308, 859989796, 36062431, 118016838, 516267916, 751436649, 531973380, 708293748, 862623012, 687119256, 299060494, 665064111, 449743174, 384920207, 210687345, 279685575, 632824075, 981323839, 736849445, 929213759, 931124089, 627625020, 504334589, 663535492, 332513200, 90241144, 348938537, 936694387, 469595529, 589409476, 611533102, 177047815, 259418737, 206915403, 788703518, 237631503, 328527492, 332886237, 208258966, 475568666, 367149003, 47280511, 745508534, 395204189, 301858471, 74941891, 609374951, 640516019, 804974838, 944011773, 977949257, 867863831, 662435172, 25002908, 984433969, 651171458, 680042261, 308491114, 792304972, 877840026, 212163272, 624573832, 225444674, 736834575, 297592630, 163249895, 866801280, 673600643, 668149643, 730097564, 870604351, 23028511, 326701115, 801693710, 620185204, 598629248, 510299550, 773077218, 292294698, 825415848, 42952968, 464518246, 221993879, 845045871, 864108824, 917410073, 890221131, 376969467, 587603135, 548146119, 492748216, 227484187, 925724008, 264203574, 119367923, 409642187, 920034397, 224044508, 75103657, 528504116, 263007961, 244760518, 31060442, 602872839, 101544490, 220737007, 534642351, 507584900, 545711974, 951619010, 450732023, 736293985, 497186547, 693795481, 388597647, 541993474, 593172412, 424481725, 986986960, 813723136, 317811654, 390089347, 424312192, 18389420, 414751865, 247872031, 472378444, 30106405, 819092800, 877672426, 271152285, 244873466, 193675075, 39504709, 93020264, 784813255, 184003574, 99171110, 871377247, 97535070, 197769064, 182091377, 255486331, 911247066, 604820161, 794209216, 566617041, 267105416, 632208258, 742913615, 500593146, 923435524, 344462488, 231510265, 927884456, 318340821, 929581859, 911201998, 101374620, 816488781, 665631462, 807052637, 514143740, 252741212, 305621260, 123191259, 593027293, 256806244, 978128865, 450506218, 217473858, 148133862, 857385816, 80227371, 333614925, 237986514, 66555395, 718029246, 929257101, 960731843, 195024002, 78777010, 27156837, 263930958, 795576591, 152669485, 889684631, 244638891, 882639335, 735806932, 11033883, 965668168, 664779084, 663144957, 939821228, 774831927, 195862315, 134770606, 386001729, 520388848, 432356118, 845307934, 45372364, 951010539, 883740350, 372678819, 664683921, 521944839, 391306128, 495706584, 122410736, 644112771, 352965300, 530056459, 895717333, 30398820, 873301074, 38023842, 142393430, 343086050, 616339272, 571334809, 289408906, 715675417, 448462735, 835320769, 600065195, 575101960, 42833064, 686249313, 779688248, 538476535, 904065507, 392193762, 147147345, 432617469, 166349766, 182705766, 250858257, 299181802, 959034232, 829440998, 758451243, 871743259, 10849845, 452580721, 61893308, 314831240, 187476990, 846325599, 455236546, 900354678, 269408184, 205083881, 430817783, 897442298, 453784565, 518856868, 992136493, 101334000, 873190966, 842794440, 400867773, 5870275, 588661789, 647339774, 198368833, 349757968, 218523480, 317276918, 747191122, 80812693, 448932261, 624440051, 555441369, 871777857, 275975199, 486710100, 184894478, 384705526, 674821004, 280145306, 380622836, 159627859, 627988039, 993095061, 291873488, 603066658, 19536019, 513529811, 366756216, 675738536, 275170660, 411885395, 783072420, 869117975, 345758753, 78848921, 391406991, 743639241, 806275253, 315789899, 555545216, 50029190, 648113469, 990213328, 824624122, 205898194, 729176262, 364827422, 125990223, 66120001, 493114454, 492924446, 976085250, 307121221, 286131962, 150916213, 857668228, 161612510, 559565295, 627754256, 523021692, 816618358, 30675506, 848101652, 892865662, 266124541, 415019035, 678471210, 382967344, 561809370, 635014401, 495741783, 395643318, 431852287, 342919530, 868841626, 78921080, 710226696, 736474807, 803945855, 498045042, 264103921, 249753894, 495180175, 818507572, 239823810, 716317451, 985980127, 823226831, 275432655, 234899543, 870663309, 291961274, 657162898, 597432744, 939756506, 172567516, 165107711, 914749612, 318224819, 821136643, 70992016, 125809735, 390877847, 827364090, 209216292, 941318369, 639694675, 104425881, 968045102, 31689536, 646918343, 326568365, 176738539, 192650295, 890113478, 89256854, 125684452, 443303487, 368970322, 245477783, 205143903, 74634896, 646143854, 2313269, 852169294, 999624965, 194020037, 258517926, 539669781, 611579159, 923623707, 326491279, 381823261, 244952588, 787701204, 756990093, 440642180, 26146631, 580141655, 746429499, 273932111, 309739984, 135288941, 921548395, 696019574, 923068893, 565289436, 5920449, 388136116, 171002567, 609108149, 241582811, 654088587, 716767179, 698877526, 114555046, 511440154, 345824280, 195657750, 80400500, 552373333, 585575265, 743185539, 966720440, 351599822, 563929045, 781918842, 83976513, 286092446, 410334549, 452153750, 687366019, 388848442, 623507801, 852834266, 949531581, 389347394, 783691325, 170384420, 783851466, 422966893, 742529629, 537249372, 616935711, 49807692, 713369949, 974385793, 834813126, 908231872, 350741531, 897258593, 136111780, 853347563, 185165477, 246499107, 950203405, 743912083, 455451075, 97756295, 306848189, 912915684, 708212232, 772775890, 240863921, 910278623, 444241, 405928325, 459886060, 702490861, 982653969, 935919093, 135561545, 19196304, 127255552, 435110386, 387326281, 506738300, 847324585, 628323197, 967475008, 82057568, 267379329, 563167247, 287977126, 11613202, 993563246, 228170723, 3711614, 319651328, 311041799, 461831748, 827941228, 951926315, 148951144, 59499195, 935991822, 998558186, 611420172, 142660744, 858160176, 410204174, 912614255, 244974856, 263087375, 791283669, 290751547, 290256008, 612636638, 14574967, 465706520, 35371889, 768776531, 114109610, 27023131, 198720726, 382283197, 681405322, 495233533, 504317482, 704287780, 265180206, 580582765, 138240277, 166318033, 653198184, 53161715, 523108395, 838164081, 205309029, 661017815, 186327553, 300528245, 474952187, 557111666, 412869369, 166301947, 20805975, 405056961, 984326663, 516814594, 416390658, 729392748, 830105295, 862393823, 621788606, 816913911, 105497473, 746538819, 285026806, 797661511, 385559853, 467829901, 870646227, 966371443, 767744801, 604633064, 176233498, 154321858, 618618471, 700729818, 969847607, 559688108, 6069540, 115779919, 109662183, 685458938, 215932132, 545641585, 750887340, 214319895, 388611284, 208218483, 999982131, 449627664, 232593753, 397664975, 832447820, 990271980, 959119301, 199131798, 860953254, 956574771, 25773477, 340952798, 290281031, 553615917, 544178837, 734243137, 907080184, 183151985, 484230941, 409862441, 808129224, 266806365, 126943207, 106532225, 909321473, 115804095, 144284677, 461509902, 822557857, 182311579, 601501455, 305693427, 546667162, 682103742, 985944518, 202447347, 250501979, 972550162, 595316537, 35104362, 102217869, 57015151, 782382350, 384962670, 166246264, 360333362, 360632586, 642827928, 347503719, 707600067, 428209044, 128313657, 829500081, 884739430, 165902203, 926591539, 128760563, 916743667, 682508992, 935821757, 447237097, 77623459, 718018189, 401286300, 50749631, 769777622, 819247412, 902311276, 822365049, 694569300, 143008467, 753957160, 669854591, 990520841, 358732310, 82830351, 76306150, 478470292, 614483473, 874270888, 614797745, 312998575, 986278631, 344102598, 284509359, 154158302, 686234744, 703432404, 987715323, 137777378, 31225042, 471454937, 861124055, 317804670, 301241975, 114382669, 275869364, 438941008, 345893624, 650238664, 497107673, 790491995, 103824822, 329367215, 528080265, 626811197, 622346995, 410841461, 242413217, 907946963, 533779989, 709946650, 993907011, 293454115, 708188369, 38302016, 857462812, 382189423, 422745415, 527266187, 560751020, 310123056, 266605567, 381652587, 871364642, 488871430, 389085493, 36291785, 525559348, 388277587, 31889009, 220485010, 721327090, 327012956, 651808614, 927451193, 392183692, 58607752, 23613589, 235424435, 340377563, 962293871, 931624124, 933914858, 571934780, 391841281, 995700919, 344630468, 149978509, 127372469, 276832381, 595843366, 131659518, 995121456, 471238989, 221462727, 706356188, 485105361, 645433543, 462250243, 339317158, 908569807, 663474848, 957897853, 237389024, 371842692, 704416310, 416578563, 832709593, 930066582, 51288805, 924215645, 422345248, 3068943, 106239383, 661595305, 16475489, 12921008, 408969709, 843240842, 691359896, 44046765, 187721156, 262012672, 246085476, 656443535, 588202743, 79503016, 150921774, 733834081, 265900360, 64601423, 133592104, 170405818, 985270691, 590777625, 684593968, 426813443, 575367758, 220901308, 772561085, 397897571, 384822983, 687763354, 282623928, 407409243, 15173252, 927797836, 72629927, 790025466, 637023786, 219575020, 628969976, 271645179, 682266456, 900699959, 69378091, 41681673, 339585563, 261099743, 724910607, 203374654, 64827993, 201085634, 833977908, 208990193, 351985728, 368863205, 217621627, 369282667, 540015136, 148027243, 234635117, 175968244, 701711659, 52917361, 268173190, 562401159, 47631761, 543877061, 110339088, 248356027, 979588027, 270475586, 664897175, 947840869, 641175256, 88020873, 15813981, 602014817, 490617635, 263512432, 51079302, 968580420, 155274822, 147684866, 277304896, 620888505, 304877134, 715973390, 764233623, 759539863, 366174595, 534907434, 851886977, 491226509, 286490658, 685119428, 917273914, 968581542, 778598134, 578403709, 815114056, 352762447, 824384865, 700384250, 111756178, 437965590, 117972775, 264516547, 389747933, 180598028, 443228745, 30354006, 802016089, 436494137, 825568300, 659106260, 408233127, 976477357, 456329418, 510968540, 248019834, 501351006, 162397500, 963292711, 61945607, 402886570, 214503111, 916931425, 378354174, 785008377, 568250709, 973455278, 277150506, 778158299, 999145362, 817793615, 686503534, 655364057, 375948474, 348623360, 61417618, 529282367, 235162711, 899204330, 449696083, 303446738, 925205970, 490479981, 838580420, 719897783, 17591268, 234719133, 178861737, 445342137, 904421055, 536104414, 656484906, 681037550, 227970722, 526412622, 449277937, 36085994, 439244001, 109821134, 994150499, 509872584, 119823672, 326963936, 52732917, 431748140, 321905514, 137809379, 645878746, 519534654, 897586530, 707315307, 23776677, 412800467, 475513538, 861054591, 942787348, 597970241, 134146543, 298454400, 886112739, 518850354, 152536848, 356487057, 392083231, 58215072, 408898878, 346874228, 500795789, 716379264, 79741940, 978178023, 243965288, 900635733, 382506510, 844085181, 268124695, 666886043, 548495813, 360254306, 47998703, 382850456, 554610249, 384569646, 27794740, 577279012, 550944737, 266734548, 801850761, 673172805, 326343749, 45856294, 786988732, 272126137, 349845080, 399011056, 747487824, 317072123, 405467994, 232942155, 483908011, 610576462, 258722770, 162344529, 708808867, 357302648, 823480786, 599123050, 179478503, 695854423, 647959013, 474585868, 568267149, 15797705, 851308527, 643738530, 169189291, 112365917, 825403954, 169657891, 816145596, 94223817, 998921609, 186490579, 689834965, 533798040, 736980973, 417861317, 65814282, 767603947, 129900067, 778296804, 917936420, 594094937, 400020488, 472540212, 431642718, 733861173, 587926658, 983615765, 625790395, 6405753, 852823918, 195734144, 925620283, 86933551, 916292888, 412415225, 838870777, 894847173, 781993892, 543869157, 172585867, 847897073, 194801793, 582377752, 1609793, 376446338, 802963627, 985009524, 866191905, 114843858, 568126239, 863709467, 378393874, 64604884, 519480530, 649266676, 964448947, 218955192, 3129725, 993762963, 370576823, 872937030, 627463598, 884820605, 911788997, 44147335, 965346069, 262207674, 919390586, 272444205, 367627476, 322344725, 512978915, 749085510, 881623431, 410050626, 720326991, 319039700, 672911448, 493339595, 138142653, 87582784, 931069442, 591296875, 351329834, 483860229, 308912961, 65038711, 182518278, 284098738, 362543550, 87699277, 37426830, 424173221, 122593672, 249305782, 53003257, 586454737, 745527100, 335483646, 396998387, 330533795, 176428988, 118896331, 710582452, 671489129, 57846998, 443640433, 923675813, 298171528, 831373905, 226399210, 591702844, 528903128, 757837089, 473443828, 816231013, 398391536, 316283100, 26385697, 518706341, 261783009, 159545207, 102441409, 420844610, 315642074, 123608202, 675484341, 963234415, 456268539, 495792823, 979018725, 731237640, 506657551, 566942489, 157008177, 259284106, 808091446, 168196143, 218060779, 346755943, 273790584, 864232653, 121874096, 204963873, 721436257, 541829714, 355999115, 839041842, 69002561, 871330038, 703316259, 899460867, 746880000, 443930531, 196428636, 943431923, 759496263, 969009680, 19940848, 853952590, 29075341, 853115720, 316810362, 273633078, 711380037, 842934275, 746814529, 726074735, 847695905, 123424555, 907086748, 340653784, 729397221, 887657472, 150518156, 762192886, 946263030, 468666973, 405780857, 300701116, 939723287, 683643266, 793762994, 496025935, 296850116, 821888180, 357667239, 519174949, 835465593, 535532581, 589542288, 157026342, 357063226, 799061860, 667083480, 863663799, 538760595, 153632530, 509838929, 835599105, 412745801, 828907032, 27545674, 932074494, 275087641, 439576775, 894662930, 658943279, 523329967, 209554010, 80558055, 402361577, 224600465, 710064427, 356502077, 630117178, 371652380, 861881399, 442633776, 61120851, 536485084, 158072531, 704828727, 649541888, 703986629, 802663209, 909471264, 160265643, 122035306, 260657388, 427004404, 569383247, 980222219, 345387609, 817561999, 224425902, 326373409, 520580041, 626185341, 252298501, 30205640, 112114095, 96744032, 522983605, 694971737, 58426113, 276967103, 808167946, 808975816, 583173934, 277497371, 561054644, 314912706, 520128355, 995192265, 776829028, 942182012, 709700489, 113328378, 594587973, 101463065, 61939557, 987707728, 868342533, 269225513, 974314092, 577343361, 433281548, 340354381, 906429776, 141160947, 752625782, 656674117, 153678124, 480068883, 482815544, 984388946, 487125484, 781614926, 81117549, 816622588, 101545424, 789973057, 507287449, 76983201, 149538976, 51809920, 729733734, 197213790, 637229128, 305041585, 883775641, 824513531, 289992210, 593015712, 197137827, 979680691, 892964752, 177206371, 117958025, 878750624, 21193918, 608595484, 828901742, 33210012, 434216237, 628480786, 802680611, 691861473, 777564316, 975260603, 806834058, 725357479, 993287975, 627974974, 528040199, 729207799, 572045275, 302450099, 574307121, 495256212, 792491683, 387195438, 396443654, 295858218, 777331467, 143294264, 264556938, 639097429, 445789422, 501192593, 153159498, 444967170, 548441918, 777624732, 821313259, 88891623, 987712510, 890816313, 422516989, 150105376, 444858090, 273700106, 11747370, 94212506, 594771269, 594707124, 593449384, 572518008, 353985124, 955414452, 209203546, 465723106, 977811415, 494478407, 887746154, 474175724, 563100928, 942512059, 305257230, 313027567, 461757553, 352811419, 64077880, 139593834, 847364679, 176525770, 353474902, 149647468, 870478878, 382862288, 728969408, 613611041, 779588692, 773141396, 283044674, 306179080, 484024241, 813700969, 471705700, 497562701, 342138707, 937403561, 311123652, 66724132, 800743653, 859116764, 843676270, 875944567, 194070815, 538764726, 16134459, 68528235, 633404970, 862972980, 581654685, 955440042, 552841500, 939025069, 805831243, 713654603, 347737651, 481188946, 873908689, 348351206, 301702917, 267986686, 638032508, 737345704, 534865941, 326161710, 747719877, 737018073, 310974831, 822380845, 336515966, 151026183, 780337178, 548748119, 73627987, 414028475, 224153933, 441721357, 717873814, 276147797, 258915886, 97729527, 978552536, 509893314, 31661604, 835184571, 320527343, 530483121, 14282598, 118022686, 991143762, 890671420, 502962225, 733794719, 461641918, 797547775, 568471497, 461902678, 182026684, 83896393, 603608244, 464431713, 612235636, 367330362, 405466187, 275723792, 387588722, 578833426, 612443884, 711609830, 751879212, 682083682, 718200942, 338269365, 215294920, 103703303, 923483392, 687221694, 57101337, 239673640, 466288023, 545061098, 557907021, 60651104, 617972156, 449078939, 618142282, 664355728, 730000640, 535089007, 928461272, 300591610, 580153917, 825521176, 767370846, 995345528, 435434380, 853267792, 356438840, 217498573, 207342346, 401350251, 208274496, 981597479, 445193278, 670514568, 714559726, 785763111, 428232625, 394283990, 472764255, 168878482, 195695330, 545627511, 14937665, 900556562, 382571818, 292370146, 158432772, 245833194, 708377545, 4428207, 158233769, 114327770, 453720450, 783010611, 440621064, 499086630, 944550675, 391888760, 965725635, 24650058, 527244752, 193259265, 901534771, 735623551, 536595756, 180000103, 965267056, 355270923, 877562169, 797085745, 554773855, 959752016, 373372613, 250328407, 988466485, 367775232, 603616214, 41295181, 20078679, 336621416, 77643804, 634047072, 351956613, 923168160, 73435134, 187619423, 729915251, 398368183, 562461257, 927345361, 536039882, 502664912, 178386305, 166987892, 252408222, 885986485, 5059778, 686810112, 327199735, 320242676, 824044145, 948701618, 364506608, 997665934, 155740110, 83873719, 318873339, 212811905, 236807453, 542356179, 491877932, 982822368, 278709608, 942974960, 356574063, 408965232, 457621974, 52554688, 585403049, 931366986, 669672410, 47864438, 395626722, 280342025, 459652589, 298145453, 374429329, 878160719, 489958641, 500355584, 124045034, 677048076, 215636566, 178833959, 599759748, 57626498, 592396355, 338420989, 761036761, 544914058, 290663841, 344430383, 773783267, 819738212, 348960205, 135247064, 524775977, 820092487, 432039675, 569608134, 393537843, 497366089, 64476465, 323134564, 130031605, 18462870, 676295051, 324020603, 360705468, 56791678, 413816196, 35028734, 820247737, 70753032, 512279751, 405821237, 426432029, 117987054, 882396610, 792061945, 738431152, 384529642, 471537789, 250500779, 730696194, 672789467, 786566712, 804421022, 297834570, 286541483, 609383454, 377366512, 641095078, 25602869, 678648724, 999160317, 624952790, 218895294, 832998484, 213597675, 981109014, 89664694, 422007755, 990935483, 978273942, 387380626, 252245742, 70293588, 827268635, 828408041, 876817035, 579279130, 92226746, 857311438, 132043424, 808186922, 409020236, 60170179, 156121724, 95112452, 695679443, 590592738, 864069279, 531408081, 257167651, 643892992, 340556485, 678811397, 951607611, 811538058, 23732209, 74223644, 332418840, 479067586, 898886617, 485966866, 609418612, 942861682, 811899138, 935630154, 869102143, 649608730, 308429633, 797830483, 604871566, 227469251, 266591981, 682948507, 731647422, 156485296, 910838158, 974392654, 192930099, 320837702, 136978344, 155520202, 161054255, 817091988, 368147310, 768045830, 652539036, 253927335, 100738957, 56953418, 362575098, 37700042, 658350809, 257647244, 443122291, 378365594, 566458467, 539911913, 838267214, 221787561, 490117007, 704147468, 388864643, 722072017, 395232103, 27118076, 137049222, 402631763, 88776301, 692660182, 89902633, 935865892, 444139243, 55438404, 185643914, 111614362, 295232961, 467915126, 719866986, 907053448, 394472097, 552523438, 952449051, 983340722, 643457566, 889232252, 246407159, 469955525, 49772188, 480219879, 742304669, 776488764, 538985411, 956316982, 877794038, 446132342, 713903930, 33664499, 968608997, 571494274, 363642119, 598279810, 974497150, 936227417, 528828052, 625705029, 13570105, 764478132, 451628070, 368993938, 206341221, 640848858, 869384070, 8417876, 830838851, 210555593, 413974866, 391811094, 709204222, 588628993, 861227918, 313127737, 569198441, 323785964, 301065880, 701929844, 290232744, 182205042, 28974837, 219616934, 242733682, 688121141, 751149453, 949334341, 755823040, 308710298, 128361709, 458677189, 461459692, 212761364, 35467879, 72944143, 207556157, 968622277, 669509521, 239502366, 962590003, 334207434, 784642451, 4109455, 317741316, 998141182, 661359310, 498675645, 19755168, 651130992, 225800952, 452753633, 154725218, 64920166, 338033430, 931559326, 779427466, 268795033, 410706552, 938663646, 525382061, 742541224, 303214108, 761258156, 639272546, 636105991, 732584240, 902497796, 885537942, 417833537, 5851744, 653968976, 967650457, 461498684, 174409034, 399796865, 739326519, 665329727, 493587186, 681811587, 17224243, 21223856, 708523865, 762951960, 317051640, 126552626, 174630180, 638543773, 786640932, 372267071, 953442629, 125472930, 312985014, 536765866, 934276619, 464980113, 90161528, 267167609, 186123959, 325986714, 473280829, 405384688, 2442789, 582632637, 387963461, 128287828, 32639181, 917922938, 543153830, 922558363, 67018370, 837225839, 195229937, 56238945, 255869909, 773598180, 805818231, 734585654, 472123716, 622236759, 739480571, 377296096, 293090566, 392463909, 644517261, 849931749, 924326660, 959550464, 651228013, 776663308, 664605959, 142367692, 818801260, 395824616, 139593472, 536780660, 531400903, 628984907, 539279725, 21385419, 379107316, 536894148, 604272774, 92524053, 729999567, 800819072, 881707523, 51642502, 307695359, 999260576, 798000683, 181226543, 140860022, 487392510, 72218192, 646817894, 710619467, 902150735, 103270906, 796534161, 976500066, 789009779, 230469178, 779657914, 260781576, 60398603, 856247980, 99630394, 12108748, 583079228, 764575806, 653141463, 636451587, 759367608, 322675751, 338289022, 795341712, 664784742, 401170379, 988285352, 270316285, 683673543, 729543107, 883518685, 320516478, 635851664, 395496384, 840915559, 94011541, 935137028, 830156603, 686937946, 621497798, 507318485, 925061797, 239819169, 429912602, 124842310, 802735720, 1729697, 173868093, 639056145, 689719650, 599069285, 173122950, 745560123, 449182731, 171126656, 56583022, 20365731, 523161310, 206190353, 898119337, 17475565, 439055109, 130011694, 238788848, 804209188, 920317243, 333702747, 699267056, 755972765, 402311988, 88577603, 627565459, 782366459, 267824975, 907995242, 865371324, 3129538, 335619750, 720251401, 170588951, 886033227, 699197565, 930265594, 705540429, 235994815, 243521613, 498361171, 341674566, 71211896, 191847674, 234587428, 592084407, 380137030, 448586252, 293720670, 369902633, 560196654, 913923242, 635064285, 813163793, 286705699, 141222943, 802551766, 592541466, 850138134, 23949938, 447509616, 963669331, 19860305, 965005323, 255454121, 714418737, 666048457, 691630944, 470426733, 328361249, 152909713, 278654647, 531403957, 42242495, 662451098, 285188447, 485499333, 195797838, 230814982, 901614650, 981959542, 235323892, 292632990, 963902839, 631210721, 939578841, 740805914, 714326562, 526256009, 633668377, 546748886, 929513111, 194500454, 157765335, 316138015, 532606572, 141365351, 659709709, 390784716, 430914383, 447981479, 544587698, 880511917, 17630480, 192515646, 952208638, 55129882, 254497613, 98473120, 326969117, 410371952, 573265637, 892814804, 889307814, 379916124, 166996816, 500790050, 694619558, 180865399, 327573452, 469093104, 291718830, 683801648, 764982473, 285162760, 238965693, 730012811, 136504334, 78170351, 738645973, 35721794, 531768227, 546306579, 268126822, 539063128, 368181146, 552350303, 356767658, 862822558, 236825035, 245901062, 950005620, 14272786, 200207543, 745789251, 590823229, 438748045, 899250165, 328806623, 859796185, 942471112, 176076458, 674765215, 19539085, 76532989, 521279274, 99198139, 143062465, 66948799, 839478317, 333850025, 778398179, 361047842, 372121859, 721311553, 888749003, 986162915, 510455078, 613948132, 362966672, 786569819, 729674678, 479113208, 719500671, 843560278, 842029480, 752593896, 57119722, 50734047, 784841271, 83112053, 346682949, 935680565, 41562189, 115571888, 59491888, 168662982, 654072449, 511994066, 116660306, 850692134, 679470741, 992210947, 657378163, 742672450, 278336229, 677121144, 908414218, 630648354, 968696043, 113110274, 835065915, 969456603, 28072703, 713010007, 660059669, 372795845, 251497008, 897055738, 758305605, 718445758, 543340135, 185972592, 982501156, 802656158, 700424345, 46908401, 227393848, 375444774, 310992686, 996382757, 669044641, 573386550, 896005558, 238874829, 556826250, 503158441, 730369368, 888722919, 239165838, 414191492, 803754171, 443964965, 115113672, 949019574, 236823349, 819541128, 928147781, 246055766, 741493104, 747100188, 170821001, 454988125, 757065924, 820810995, 953309630, 289371300, 984475870, 885086103, 702663197, 414942882, 589460940, 205973394, 662525664, 30437093, 394071667, 779120928, 846053967, 540181623, 469937197, 746094437, 774799598, 951774328, 440493853, 733152648, 513855226, 542253873, 494028959, 787970505, 598676294, 548897609, 78903400, 829208183, 244412972, 171023288, 420952831, 765095522, 634272689, 548952917, 646270899, 133901598, 793626108, 51793302, 29779102, 252161636, 228356130, 865244004, 826238101, 153431864, 518325333, 918119949, 888195203, 941074053, 924212342, 254961087, 796019736, 970305177, 115678514, 464344689, 487691067, 207255571, 165272427, 617465197, 415124320, 424431245, 697698512, 899733962, 3979885, 734265526, 381512308, 194822081, 296395107, 746761812, 376461751, 767196768, 900682671, 954010667, 309664387, 536650624, 109884722, 212340879, 188792233, 615078929, 141934992, 708794412, 804374719, 123947989, 701689831, 527403824, 405711996, 195292771, 121802953, 593658881, 417430339, 473481859, 760742509, 175371718, 988287313, 886190826, 900766972, 321987960, 420719472, 657248979, 554338386, 914524338, 556644170, 687575951, 762458092, 445566847, 646254269, 257840641, 179264137, 995142802, 802086362, 576229512, 482541705, 205745820, 902985362, 349822933, 27464766, 545731439, 659547241, 811574564, 632142380, 318169391, 97024412, 207961425, 603093340, 308011588, 687673887, 881287051, 733881551, 580304198, 177428038, 417609178, 741000905, 996273996, 475629284, 584732100, 98819287, 306839484, 570984312, 598579955, 660955940, 381914220, 819199284, 626093526, 534361636, 784838936, 636905183, 585492871, 131433179, 428312739, 651982950, 560710293, 783992636, 991802116, 901325956, 305805360, 251205002, 515496459, 862190542, 171474791, 304248990, 700485000, 200606709, 784869043, 541992052, 582551198, 157123878, 781731331, 388293750, 412782038, 385549998, 376228983, 551846128, 231482179, 530153971, 344277548, 793490234, 520755418, 330533344, 356678361, 215307584, 306605571, 459400413, 383441568, 964644560, 689204216, 979534710, 694883277, 965821147, 882275955, 615628262, 107916253, 391497593, 9029457, 660483627, 679689666, 32354205, 94349732, 758622883, 749286009, 325103582, 319022032, 549019161, 906720308, 575212719, 11280971, 974294009, 62535786, 270142806, 179058980, 960322226, 182612352, 261406643, 982717996, 598346227, 961288636, 920230032, 464778886, 867104876, 715286265, 364934480, 487042644, 496387487, 273612604, 203436576, 43098925, 394138281, 740504995, 608945865, 679904145, 153892287, 522703485, 482968943, 44809067, 127926427, 417952047, 899153797, 751472330, 486643482, 296376856, 941520378, 985439073, 703980778, 449600305, 603014422, 845585679, 265916130, 331490323, 270119943, 75121069, 569820853, 861745936, 663432421, 190819602, 942622055, 736977845, 499820068, 611036901, 711984913, 786180879, 350744649, 889572168, 144795605, 390878343, 277311681, 103720044, 402629173, 266116318, 447735225, 537889768, 780078962, 507263575, 194091628, 285234818, 946340962, 113301419, 637414582, 858892215, 605660492, 680113019, 621432269, 411072448, 743652931, 240039860, 981928607, 239586485, 322251677, 598177901, 325964389, 398078498, 411878298, 816377536, 879026140, 649252204, 412540602, 247076479, 894214702, 196325404, 370576798, 700774592, 489638773, 807960496, 773216246, 380095825, 918679592, 492368130, 188468508, 555527322, 458864951, 218175635, 743714974, 862842146, 429017336, 279679773, 501343645, 441986467, 903321921, 55179465, 741122043, 321524860, 39469002, 752583443, 255270804, 931082886, 167514543, 469501974, 831368157, 997857475, 691564117, 642213397, 629622913, 220837497, 610358152, 958159760, 850511113, 677662577, 879942913, 255658527, 139532984, 798420669, 924401063, 668918235, 723217074, 252383548, 6673831, 712236308, 503426254, 229867529, 545756299, 203804140, 149791956, 558286977, 798782293, 97567502, 978564211, 326091304, 363288125, 43482112, 957510168, 95679015, 564065146, 328794173, 472338718, 560282895, 618874742, 800340987, 437908685, 366652048, 563917046, 688973070, 676115523, 452810144, 321677750, 579155289, 670483367, 227916689, 637820078, 829978986, 246344704, 345223314, 914555104, 634747171, 831697677, 650456685, 891846250, 530995014, 499124977, 245264558, 307826710, 643091678, 998086563, 680964793, 547153061, 805882457, 665143592, 143530140, 632524070, 152514254, 398304176, 72650651, 273581399, 615205844, 491504052, 301936896, 301985817, 381780544, 271614315, 798823072, 482666467, 270289148, 774696900, 640068783, 373151502, 964093129, 764029570, 600791217, 327105083, 586721014, 736565627, 977060998, 646607249, 196457366, 218616532, 34967473, 412135164, 340695486, 563101252, 185073377, 976019444, 548274596, 311687507, 305768053, 540472840, 501891911, 614999659, 785907891, 483195987, 103069815, 371862288, 607342500, 289857346, 97731085, 633826744, 430635605, 669934483, 870011241, 697766946, 804605383, 834595582, 86282460, 835202211, 115832469, 222698650, 86847157, 351911942, 594236547, 875293882, 38673256, 383363764, 953522812, 124664193, 162866332, 225590596, 620962003, 928174993, 681513907, 970111983, 582061051, 979686355, 384865854, 454809486, 871481082, 193162923, 666837951, 871116344, 630373326, 897295235, 42620851, 831202886, 962032380, 192626465, 538247075, 128819974, 931570693, 88909646, 904935165, 640647603, 230229059, 614639897, 430247420, 923375597, 840057971, 333292990, 162345315, 951870967, 305684979, 896380867, 358124531, 420176211, 169581374, 865209279, 310613339, 946958266, 728397752, 533810552, 744757210, 532936875, 848678862, 578784974, 487552485, 412044578, 691678155, 415881600, 797270150, 622375844, 219902901, 504251965, 154390411, 208077071, 542408049, 429731458, 921766567, 235783823, 909923268, 353817604, 643492915, 950474199, 320153945, 472230699, 192422216, 921471720, 523841352, 504773272, 839209353, 983935429, 470137805, 137055291, 526452230, 931956992, 862505089, 140873535, 231754514, 398093753, 655554302, 738967249, 894677799, 777043008, 808513542, 436115965, 899445577, 812636492, 514049413, 449311849, 470700296, 177276212, 306649411, 714806793, 652921286, 383553817, 145324776, 480388301, 899982764, 114880376, 985398376, 393184494, 94602249, 764166191, 992088079, 937928657, 994831160, 911214364, 814915382, 149323257, 59276107, 367983490, 942730567, 225958578, 181072723, 902091773, 791276341, 43001654, 529116146, 501812291, 486072657, 655869411, 211437458, 566784889, 571082261, 691681829, 674921493, 336615848, 999615778, 985970902, 733512902, 770431106, 394183496, 782241879, 838971841, 469332774, 463673626, 576105107, 253333626, 836074580, 336213675, 23806137, 704665430, 255236481, 647811926, 705183733, 542096975, 122149066, 443680675, 821867819, 267147373, 871464469, 910586399, 263621266, 447322422, 492780857, 345296599, 738051177, 489460014, 949235438, 567741578, 748469729, 99034078, 613594474, 435295578, 613516580, 644271997, 732548457, 20548156, 817605713, 625347009, 294639829, 938691721, 420854372, 200494490, 431716587, 186354312, 402860548, 420360958, 957332725, 222795859, 317442170, 302901822, 39296985, 729493432, 831320067, 488236640, 967185818, 975529763, 601312450, 994907778, 909208557, 659924122, 522286840, 346888176, 585613906, 800544180, 81783355, 807739560, 272075584, 996924212, 999562263, 56549727, 281460756, 766076671, 320752584, 991050311, 461767360, 262124853, 447469490, 906951946, 211700529, 387753327, 720025191, 546584665, 410833694, 354503912, 486358245, 121170792, 962422074, 611749844, 249004017, 617238107, 671470407, 357809670, 818587256, 789091930, 89042670, 42348708, 901713486, 229683267, 847697958, 905677129, 823204548, 414566596, 770208465, 434680123, 689745649, 980559951, 989194916, 44482386, 10072216, 1876236, 12926208, 315972978, 896673949, 419659177, 509594898, 756756022, 481360692, 278529682, 297688650, 897251121, 877118880, 535715338, 985297603, 309943621, 450682681, 813210698, 18667641, 69407381, 531174463, 670827214, 604060516, 985797527, 678452097, 601710151, 716889037, 643429900, 244411962, 137431665, 730228911, 510592494, 673110625, 941164368, 565960456, 12041488, 945929971, 286010059, 540117814, 786727687, 279367435, 484235407, 310080102, 880947352, 108524130, 301389874, 88018721, 814233558, 793015391, 152355414, 207178444, 437907115, 535993381, 909309652, 816244140, 705983374, 146526548, 749329537, 258128717, 137471209, 32195544, 817073072, 441292564, 531219489, 921784089, 563324200, 637153828, 53554588, 956591090, 750916313, 143249087, 653996009, 781300326, 580953060, 166612221, 988245441, 333201871, 903238346, 183120945, 444264076, 355344220, 803992898, 494346377, 84031416, 414196592, 449279932, 652235740, 211450786, 111850320, 564382767, 521583718, 339558136, 4216530, 409469668, 577752902, 954672617, 569509660, 17285165, 10903163, 830077833, 638121187, 745488910, 928050827, 244078465, 877418291, 803126650, 718623475, 112744617, 500850820, 794052108, 446362045, 623542259, 150886374, 729763252, 877974434, 183060596, 940694168, 906525190, 80722024, 646611494, 856707670, 669793843, 297105856, 911539436, 968527777, 683491913, 316019825, 286471034, 455683029, 193897826, 932827636, 252854050, 435552121, 84226789, 533741047, 192481530, 50399850, 11624682, 963401273, 807187590, 552929750, 790869438, 671199226, 731477809, 159084017, 710823486, 540036907, 105336736, 800023279, 625265725, 511711973, 1102488, 649745982, 43720471, 560481743, 268798099, 23166152, 589901811, 15473993, 673286759, 989931288, 789553782, 855262265, 332277602, 875090158, 296434727, 850410259, 782959957, 996933907, 531574885, 896307326, 135233308, 220956133, 997739626, 616557782, 472127963, 624165502, 491716442, 797531014, 359705318, 567002848, 501919197, 641823953, 363921033, 426117102, 113485203, 52204937, 583042669, 175872172, 254013967, 411983187, 311366764, 38377174, 641446278, 565141599, 135119152, 896514940, 798613178, 859006414, 282578710, 600808458, 76489896, 188836570, 479043421, 162534015, 337370355, 714861939, 322142079, 455989086, 326344376, 139792322, 948960491, 485502046, 211060251, 313817110, 726571596, 691406393, 349705923, 965909385, 116583862, 902734263, 579194323, 80448990, 703994858, 675219185, 762861603, 844117929, 919573445, 733552650, 268991866, 313102387, 227471219, 908503247, 933671759, 440163456, 526625190, 474188372, 125305430, 903909878, 6649952, 713757799, 345266165, 61647477, 582907349, 831055320, 581806417, 338032190, 168333603, 738985555, 780711105, 902946188, 283667672, 157092601, 385128392, 991684410, 216086222, 251394536, 700537247, 312894834, 788263053, 676376542, 716435853, 633646839, 520748471, 931546857, 6141580, 402980246, 481961422, 525248735, 912743020, 430811796, 347561404, 614296042, 646204201, 582988885, 743517091, 134501340, 903123432, 226577528, 658702364, 163047848, 93304710, 468046644, 94627669, 854525972, 241744676, 679150782, 250859640, 12067377, 448586520, 813630714, 608134046, 795613742, 240621719, 476907678, 842226628, 812551963, 233025317, 206424133, 750112557, 939037553, 498447110, 794567927, 208445971, 152620600, 4191693, 313682925, 603313259, 139815883, 883074304, 504582331, 684912556, 568110614, 800999791, 146361373, 168838824, 712956285, 194203785, 39720313, 26582715, 430908956, 388488644, 366721780, 486258045, 415040526, 658546352, 221651997, 199572939, 601075301, 992280017, 916618535, 973436190, 99067514, 526023013, 754697881, 365902454, 129768790, 575996782, 617719632, 780571723, 868856595, 536146785, 371217388, 307163006, 793405940, 755180542, 944141438, 494840545, 589341553, 616047103, 67467537, 655609308, 712592568, 558725398, 358761422, 918260011, 840619383, 547199598, 784276270, 864059457, 645723629, 369324790, 451912972, 85497856, 205128002, 100476368, 809534303, 529790089, 680074835, 154193031, 203570645, 902722736, 185646008, 152318865, 995907602, 835014239, 348826482, 289773143, 601338395, 529258960, 184423589, 869921518, 328747025, 74772488, 713545013, 486924060, 780210602, 383887955, 113153072, 973437945, 646782502, 410843039, 264585006, 530679810, 815868544, 192608559, 838327322, 149364836, 299275137, 118009157, 166823843, 452925384, 606184611, 623542727, 801434546, 141119934, 701730570, 985329385, 727595924, 44363648, 621538446, 474672651, 318610341, 150236847, 973646155, 431586086, 299043116, 246354524, 185742668, 770040294, 367782160, 320564786, 814543874, 796019999, 918605829, 363844322, 843668554, 224597959, 662046040, 7470391, 792346682, 728393240, 210640179, 963471392, 690674632, 871392618, 681859702, 504456696, 548057026, 897243490, 943009073, 541107552, 436897666, 451776479, 648539580, 420802727, 607132608, 457352297, 892291421, 679521994, 506666830, 981051652, 854886942, 219925035, 73088205, 912609785, 449996427, 236959748, 925877036, 753578714, 445128538, 460518651, 397081320, 933250661, 818512958, 223136239, 530836886, 137699630, 253701693, 774870726, 468942556, 881940685, 760364767, 887162358, 906946134, 121909913, 862071112, 868349776, 800093873, 796346939, 428485305, 406085237, 939547589, 360189478, 710106558, 708859361, 381915696, 830199936, 912263133, 314729984, 176310145, 383096287, 620797326, 180753340, 408657889, 822689497, 244127059, 421836576, 684207483, 481023763, 715354240, 356657331, 636325439, 108038870, 528861049, 766633322, 134621708, 586474522, 920916478, 64467511, 655971433, 675434749, 606583417, 594902966, 694887943, 544871557, 205559012, 10644127, 614733962, 823084081, 872496030, 430841590, 984997365, 764956340, 126162875, 986465626, 666535361, 816326930, 201482769, 650859439, 978684192, 371135591, 751554934, 299779581, 809700107, 796266075, 801689412, 652092380, 650535037, 483674233, 207261648, 423336008, 985025487, 706052647, 911692752, 78429952, 338366830, 860549513, 32744794, 878901920, 556381842, 527338078, 333955603, 206142212, 581605796, 743453178, 30038344, 272114661, 106570188, 328128734, 517848446, 755064292, 428223415, 4765392, 896951277, 98858983, 117765450, 329010168, 522590660, 337704245, 780904560, 303607458, 646553137, 649637174, 23055776, 390501556, 116753412, 382540458, 520762439, 265114649, 12316716, 887011575, 273054026, 920031300, 525647637, 922113464, 742547673, 230181150, 309005449, 295108096, 422642957, 658429068, 430551297, 355590285, 994920080, 519134832, 997238983, 653153425, 830979648, 744821097, 254305502, 66327595, 771606400, 632361926, 948170520, 882642156, 213363997, 533889186, 47624813, 883757861, 519796513, 127438503, 930080988, 96578747, 842973683, 155326116, 238611455, 289324931, 650270235, 275685084, 904590931, 882683993, 636175886, 571509842, 466444673, 427855773, 847211993, 366276380, 897172936, 175649775, 166640004, 698487903, 904519633, 712952916, 157033825, 736981864, 388328772, 119618470, 791072676, 642879340, 98134756, 457054610, 934074677, 619357350, 781155571, 756267639, 700178439, 470591204, 133803060, 869900319, 943370486, 400299595, 515645301, 848632632, 105542902, 687131701, 67445378, 52983265, 699459632, 657577783, 609098046, 999895748, 443735751, 666781907, 687906333, 61903826, 375415805, 772027376, 17320594, 117944693, 780236860, 576044577, 482384512, 208701323, 756782480, 672052283, 646234285, 336429985, 868803575, 216904612, 338761092, 347670003, 646170566, 499855316, 168922745, 163364880, 289506466, 261185918, 892080408, 912375692, 937436969, 180531187, 469589512, 323140719, 345189286, 797800309, 534057537, 639672598, 109643603, 577810266, 71547236, 130007223, 982304417, 234441019, 651790644, 34717666, 174491682, 490399777, 29515787, 387044068, 968277679, 327731141, 544132199, 172724471, 482444842, 995260581, 846017654, 484816769, 494657117, 742165162, 955391639, 993701892, 747245356, 981398460, 316853419, 282477237, 271245385, 564497599, 306152648, 428630198, 357829377, 864851903, 830891378, 518108542, 916688665, 446319060, 979631890, 897549993, 343781351, 584415696, 570626055, 410465747, 862405264, 637070170, 697750135, 988243966, 879755885, 117936898, 730715676, 585343999, 615737641, 651505725, 64812626, 342617416, 625390245, 786665076, 76599369, 137591643, 640527855, 151276807, 82877723, 402537373, 849465552, 190364861, 71248406, 156074777, 272116623, 233229000, 654858485, 915360762, 867390005, 83821230, 240345358, 97328507, 551565175, 799640544, 518258040, 174293115, 774229775, 795003215, 668450821, 738453621, 337895098, 982134160, 421154505, 970220939, 77830142, 126119314, 760065544, 451130247, 180251354, 828429471, 505277421, 695952325, 247813824, 55952036, 107011039, 390136916, 132025427, 50638886, 601982997, 311499825, 606221296, 767186474, 499754051, 266866177, 174914203, 197129670, 806230840, 361717617, 887205626, 991422349, 624597401, 488927321, 224992417, 551222570, 810974434, 146860590, 608399760, 162962958, 769278087, 301032470, 190065526, 532344524, 187996919, 437179967, 489449000, 765363278, 808426610, 388508289, 407458730, 157310379, 275229388, 943603696, 961757735, 500155350, 362823283, 80509141, 745358538, 334048707, 986674667, 481653514, 720088066, 794767352, 570164911, 670388047, 293523859, 811905565, 167607800, 662589301, 275029508, 724623591, 130518543, 597926138, 356135704, 256538779, 157993304, 482281190, 250016918, 37252878, 855741536, 621085920, 529320168, 548929905, 515069835, 81568554, 286845984, 795203796, 442156456, 294853036, 116011853, 881676509, 510644087, 257196626, 678452186, 824063243, 506178954, 319619580, 342136843, 815378008, 582173040, 191895289, 181483612, 494444333, 647702176, 239765168, 737953276, 705202469, 802685435, 699502734, 105696703, 395977294, 303255753, 307151628, 989172048, 457689886, 956565142, 890839300, 648178330, 297906636, 665050899, 422189880, 510140791, 25169979, 22086542, 597555734, 690488585, 723328802, 127160205, 739788036, 54062713, 501879612, 33377388, 851948736, 138458204, 706748313, 518390351, 179326422, 640005648, 391285626, 835424489, 893454682, 316875620, 448521294, 48487466, 936172792, 258348270, 257200825, 897799140, 331421345, 681180025, 36233726, 595782953, 190154382, 873903714, 579805099, 803591905, 988526337, 200603205, 207985480, 213076704, 450061271, 516833659, 245938435, 318244649, 830152852, 337878206, 770247061, 591499562, 741869341, 998031507, 29757644, 69481142, 853193126, 152486965, 31385676, 57102545, 726713246, 400023977, 366741112, 465624259, 554628581, 346586740, 725216711, 40823318, 407014742, 365693399, 92065192, 456929731, 495368501, 719165837, 754941306, 555183089, 370718721, 477057718, 555638946, 870661501, 222295668, 621130725, 349007763, 908887530, 298861753, 274642104, 135296703, 525698820, 664045039, 798839003, 488481387, 718556807, 102515726, 820907145, 98239695, 252814421, 807509093, 484890912, 385028023, 498242295, 680728154, 673358634, 575190108, 69900760, 248299124, 867819168, 768624893, 272926716, 774025317, 741731942, 498638567, 899609622, 543383746, 39398391, 991746406, 266943739, 6249874, 525742344, 432816904, 437586062, 177430192, 353951612, 793415326, 485966776, 451262695, 822900058, 974473111, 985770767, 35256174, 608175228, 111012505, 626963382, 859255086, 667074611, 476081105, 25005585, 656677104, 943447938, 310999786, 662302678, 307871379, 496092397, 703687193, 261853127, 920945583, 583453699, 353315955, 93449561, 400856294, 497448462, 419527384, 503165916, 570402054, 770442242, 888394804, 24018167, 384989422, 526396764, 267828414, 892667165, 852979539, 921126340, 388109862, 302632821, 67218402, 520183305, 631865, 42473583, 875811567, 587678118, 995824694, 307403913, 477413003, 43637045, 643086566, 934508781, 194434863, 278519238, 65697684, 734699017, 74345095, 647440944, 487324053, 471288259, 404305515, 725484860, 501593144, 473402617, 875357233, 927703205, 378525897, 460643399, 995457954, 983732107, 110351933, 382207218, 776842911, 436892789, 776478026, 317492757, 709901514, 293404794, 408349571, 698847777, 554047371, 171083783, 492991451, 996610847, 762323685, 113510329, 30397663, 838880002, 431091943, 762375964, 172607798, 457232270, 677099064, 45278460, 343643509, 282625258, 536386012, 623572129, 343557864, 207070604, 861780848, 330391583, 511833104, 965356500, 587941588, 337025890, 993047653, 893757507, 672069728, 775613381, 598565832, 326239915, 105977085, 730819118, 578500584, 398057537, 694244654, 196234371, 683922872, 102803749, 975923839, 494999817, 796753065, 863892375, 178765463, 595478050, 245851555, 144123548, 486316682, 72750528, 971034115, 791098315, 625161960, 981414822, 547863718, 809825678, 619238372, 518295366, 771946608, 781731531, 421288664, 810681132, 327301511, 68400981, 961865539, 303987364, 812935869, 629615935, 992087106, 384044584, 764838825, 422725808, 753265590, 631445652, 462290739, 506992702, 472954955, 166943075, 455996332, 330052972, 183166519, 767450388, 151919399, 777694151, 115624868, 693126730, 412742918, 276339699, 909723994, 394123835, 985644098, 231096412, 455939495, 740444731, 48714941, 77890466, 829855699, 418294928, 664555361, 206530268, 828001660, 874766053, 173358247, 87577803, 592437381, 710160379, 960044147, 913323848, 701377318, 46124061, 54918782, 420168371, 332471514, 985092099, 823399348, 148399866, 307383818, 16213463, 504372371, 873625182, 491035599, 355905572, 604229139, 223841323, 832213544, 809051856, 576426116, 246562658, 303648726, 475713113, 608345795, 713411653, 888314094, 791340526, 957322683, 26686115, 51274608, 739073967, 467320292, 212273973, 27844327, 312936692, 250128509, 958172002, 939444925, 24829943, 789897700, 507218351, 990421421, 345219169, 458579551, 999240212, 62418172, 302875064, 602065114, 489975482, 878639391, 300376549, 934341092, 398829507, 555651244, 569867008, 67830210, 116511934, 976691791, 211950031, 749615015, 206366932, 439818204, 489308365, 676442434, 212643114, 415783683, 246774938, 670542717, 18229470, 770718221, 575125493, 927650943, 945829304, 705015784, 518411848, 830943364, 456938958, 159519816, 884411123, 994404654, 880211885, 965379788, 268527564, 801818286, 463878275, 346570963, 296150583, 533421253, 519799584, 261107120, 783578107, 75750668, 323045039, 842065704, 553132250, 934115055, 172493117, 538664758, 512418833, 762587782, 911160168, 923967341, 248955833, 470174105, 647715169, 414552925, 995787501, 176515683, 322124607, 494349245, 404491574, 17216156, 889146321, 719918986, 244003005, 69526277, 695234226, 891023596, 585643813, 100434614, 608979324, 139781049, 917796181, 551474055, 874197933, 516895152, 816721310, 358740415, 492566391, 902326068, 249923216, 467968550, 653410255, 70654445, 380836438, 233868101, 466952143, 38058659, 143801568, 445048836, 350920626, 484240715, 952709258, 762473188, 218610389, 261956298, 21050248, 418963634, 415553761, 496409839, 527711721, 674519839, 843545729, 409402862, 77673808, 979049110, 918664627, 560700313, 629109723, 233956118, 901021113, 159067317, 89409801, 32571748, 129959394, 361073304, 417040468, 950492025, 207292303, 790947402, 572854057, 465102550, 355581225, 947651879, 890480655, 658086407, 568202192, 633151036, 904720416, 160157293, 648138244, 382366937, 16670061, 590902725, 628488936, 615628483, 710398817, 316899145, 820020039, 878797957, 579239004, 68407657, 257158384, 687972923, 368350212, 183696140, 65715779, 243837687, 417290533, 839661178, 808931610, 711708609, 960681546, 927390508, 322942423, 111333242, 482124557, 241502646, 353908716, 46258546, 179195093, 802890799, 485078041, 182647679, 519492079, 489804609, 595355196, 677020555, 976007475, 136361609, 123681008, 386329250, 996829780, 718018578, 827574023, 766047874, 552808213, 151079121, 671571059, 701964781, 611817126, 782061936, 418257922, 65065911, 203739513, 498954865, 514866542, 240946480, 700023022, 72041340, 612723580, 585572021, 398615193, 645978474, 533267271, 957736093, 303625272, 16044192, 334142717, 593750782, 725026017, 709596173, 445444613, 39014455, 551926971, 438923583, 252232395, 652149870, 171242181, 662343698, 829821118, 620437081, 863574996, 553581994, 655462169, 793786933, 966681584, 279613643, 436537708, 758154659, 233406500, 172493877, 174761113, 652961074, 720739691, 698553783, 747641610, 88165354, 929433707, 63511742, 173769838, 849646351, 837219068, 838766033, 115908575, 821430693, 719797024, 86977358, 883285888, 381497789, 281148014, 466806421, 346048288, 487431479, 754295499, 343779927, 883719395, 136352912, 374892514, 577691385, 443382753, 513771230, 201295366, 129400269, 589116209, 365044718, 875909379, 867537118, 230125326, 224437041, 594977356, 544791242, 9309556, 2403225, 67329345, 113974143, 642521759, 531456406, 547053106, 916954886, 762993534, 25827077, 501109909, 378502384, 209059283, 523060594, 666768822, 237304759, 702984439, 731413650, 799665299, 853614503, 393660400, 180808946, 731750044, 836567176, 136492363, 397960194, 825719167, 531226240, 65845448, 911491861, 521893743, 465942080, 104309263, 921015595, 466323383, 680318523, 145693972, 660226238, 2002506, 389946126, 621208232, 541499088, 29130143, 957437004, 91616250, 995991480, 292507020, 518811718, 645439120, 642088395, 56278298, 45014158, 732864960, 243021652, 785767518, 595740221, 447430378, 442037466, 252310817, 126463849, 166078043, 920439658, 692501619, 967062902, 109703786, 159358652, 292888350, 286946163, 794465073, 953896184, 488696367, 694447833, 514077884, 623698384, 889122540, 988330414, 719823643, 43099113, 783347634, 671180022, 227811921, 34734668, 831445387, 172104314, 718903769, 726053943, 430235276, 612957612, 536751428, 420009525, 140318079, 599216181, 510389499, 798001035, 176714560, 983429806, 4677472, 817201122, 887199114, 229220400, 109743706, 807522285, 796087868, 669220175, 601686973, 81102324, 602514165, 73663214, 752319520, 662264236, 659862950, 637704911, 754783782, 92575578, 987404276, 949971578, 835385227, 931470303, 880576948, 618263818, 296196519, 113105588, 767714964, 2278594, 353673830, 305173248, 711802783, 277857267, 336268075, 580185159, 904664696, 229692712, 398114547, 945075489, 800710525, 170378046, 785456337, 564328581, 994896889, 667945259, 81001836, 349635475, 700002131, 546577256, 523288510, 178830909, 240298462, 84919439, 223369076, 224624250, 177534472, 717814797, 377129908, 181061434, 450944266, 932216735, 148782910, 584803947, 354754710, 737323285, 354999978, 158087133, 403063225, 962796625, 194293808, 918848289, 402965168, 667782082, 112424708, 670411841, 294868685, 801715899, 932495574, 408765928, 591638641, 822866402, 68263756, 220210485, 638843804, 597246151, 366206532, 253487013, 321148092, 629169193, 802954307, 840715490, 170104554, 177789020, 203018664, 758495139, 838387061, 681785218, 651264158, 358689434, 250791885, 810478601, 721794311, 344711552, 372846269, 423598305, 150952440, 84748862, 646502257, 863921611, 644845902, 277811761, 521487702, 364861491, 95604818, 455611392, 724318205, 650255808, 153628075, 327581629, 477706750, 750700531, 351309982, 244853671, 600837550, 404174399, 549152188, 574079186, 709846238, 623164232, 259257009, 162263739, 810210546, 918124580, 144571337, 56788400, 147905858, 545729866, 201411566, 599456185, 471622779, 919007752, 241080123, 682835498, 983937044, 446435730, 945906122, 589737193, 745709079, 512476683, 963627819, 221027097, 350768254, 375727501, 647316329, 18683035, 349547850, 286667764, 16293965, 446083949, 981094735, 870927667, 868739110, 976661508, 65175929, 472726220, 578139078, 815300038, 394781459, 333888493, 471377795, 58901649, 735836776, 408504573, 148214577, 881363648, 464661601, 534174692, 380691076, 895416727, 602877364, 866918970, 566691272, 576641452, 482543394, 460418436, 386704507, 816884897, 983259294, 117135735, 677645174, 234213350, 816419238, 943285126, 438214421, 423243125, 27865639, 757982447, 991362237, 592722701, 805752136, 935959959, 342668517, 317421329, 128037771, 840852495, 889166971, 748591259, 760492811, 496882038, 878296790, 849442641, 850883852, 65236171, 309272990, 583222921, 465397108, 285670366, 304452688, 557657084, 880389805, 38641105, 154228269, 856397665, 316154076, 687898914, 979320295, 638298592, 459222319, 752088173, 922102754, 114176958, 307032142, 676622702, 523860672, 658004157, 721684275, 17195963, 798482930, 244434269, 352554861, 687326174, 366473399, 543754571, 736830796, 519908879, 831000168, 51643123, 997008977, 230670829, 580627594, 279305748, 315248836, 669440377, 169524490, 39199662, 296718757, 771893518, 918588919, 827816302, 196339611, 502277162, 990006215, 983852595, 882289341, 308527219, 537569531, 915782909, 702111537, 550704520, 557828253, 943698148, 248418936, 342955751, 933197852, 340708015, 496074483, 196531117, 337796894, 81549277, 51086747, 753467781, 627767204, 689486741, 175123045, 610898300, 31905517, 440962231, 181523729, 823983124, 231811186, 33296080, 847182087, 699255409, 958890142, 303676846, 462048041, 558807079, 216810094, 819465833, 248355457, 186660198, 759307899, 711783195, 228017511, 805108908, 835032343, 505821695, 312222322, 646057774, 268275680, 427320464, 828525775, 684616028, 512062368, 732444731, 590402042, 937541389, 827410738, 263859008, 264133543, 48811408, 274824270, 317370719, 903210025, 965159828, 286933033, 20439728, 547380658, 487372701, 753492677, 78901656, 585010131, 289998581, 968890289, 76190630, 842697153, 948092837, 90707981, 105540581, 521186842, 596708234, 202486108, 318456535, 51046344, 47323987, 630682720, 388059705, 906762321, 772664000, 271319623, 14953562, 305819364, 638503283, 326860453, 263627347, 181910737, 289239205, 578571383, 901793231, 18876324, 770705189, 142064615, 916913729, 395193970, 250020153, 18744907, 736832061, 151920930, 341648633, 177045183, 186598794, 549474461, 486699745, 602504200, 667460303, 652473499, 505572411, 692860583, 593697343, 621654860, 394110136, 796158926, 313985101, 136154999, 281335981, 438855673, 201569225, 162349639, 755011712, 655934239, 825405401, 723024708, 654813557, 991335689, 130106891, 133673409, 461861464, 980669085, 162133069, 803292025, 808452056, 230956484, 727279753, 375662963, 182329649, 78642792, 174795892, 145421651, 583974269, 412805246, 70489617, 162412821, 759849388, 326291212, 47796241, 910063256, 784650205, 347364078, 372181798, 584482250, 152824871, 206494068, 24226320, 726132935, 420496386, 862292314, 227082843, 559714901, 557205438, 426979968, 494489599, 502235324, 1711233, 294512699, 289442098, 755596690, 823002055, 146867568, 939604013, 776068590, 337101256, 726027215, 927277631, 101217214, 2515924, 401913403, 160036808, 577545223, 610757467, 674452980, 514749692, 199524, 222878231, 462852188, 630981576, 511133957, 953247907, 716652086, 665797138, 995982466, 197985782, 109395425, 362333439, 203926749, 841505612, 453667724, 930855094, 138607912, 284857710, 891402800, 808647926, 372376871, 451961478, 30335963, 212408542, 931647748, 880732298, 909292898, 715618793, 340196968, 627092366, 991879998, 487061701, 959082597, 803594579, 132378013, 404322236, 534025560, 863166986, 874609411, 971361212, 435274099, 808426375, 758540072, 618314760, 542863883, 369970344, 924780878, 251028711, 855973225, 968439363, 688679248, 761133170, 773706712, 160145093, 154955355, 85535639, 113676056, 779428221, 890892940, 236765627, 936041824, 422337656, 733034539, 97889174, 789154270, 988986140, 283635521, 686870549, 566448216, 926944547, 130856677, 477818075, 999051991, 142908712, 780469103, 955418446, 12671596, 203508303, 396308488, 15958049, 80942206, 998856618, 286366185, 773185030, 337242896, 247068161, 572397404, 959747069, 780375337, 920473359, 762358669, 96348666, 191628956, 359912500, 894377997, 383531122, 992513374, 863114411, 123223475, 331117281, 111454815, 146068159, 17998919, 792081960, 324095230, 740738385, 4538105, 23760733, 361416907, 112179756, 640495097, 711389633, 393175299, 904470866, 849687846, 166196956, 854521106, 769661475, 431616954, 47225919, 357753241, 100502841, 435870170, 522505406, 787143188, 777281050, 544006450, 115850087, 776187856, 756841900, 728363744, 487879185, 480237569, 626136148, 680884811, 198794370, 600833948, 312835782, 86755558, 226055073, 84841663, 799070048, 110725383, 507796270, 121213442, 914122816, 236639969, 91225487, 509205021, 241955340, 554195290, 102788987, 532764824, 235979035, 998199025, 519521535, 708147275, 370965510, 717195102, 287307171, 901568896, 196770293, 789106566, 788021202, 320815433, 829344743, 510897421, 226210105, 889983693, 748420295, 269793495, 605485694, 998344298, 417777609, 315159805, 595333107, 266213833, 817869714, 84565829, 26254617, 978680066, 642599485, 901946470, 883737561, 490388772, 620297946, 769128005, 471259975, 878969186, 915349389, 489046350, 942542467, 658807378, 585809855, 28095267, 32487163, 124850969, 475871183, 847426710, 540954617, 845394691, 253340775, 14449069, 221867263, 215042554, 88127131, 396013609, 207768642, 828687069, 323677791, 172338493, 390096979, 435490697, 720454955, 597604713, 655675881, 103210493, 66790975, 385988438, 721779116, 23253398, 114728284, 742143852, 227586237, 130918121, 715557492, 7489087, 15348326, 686882858, 985097392, 477011273, 471349465, 948082076, 56048970, 95307897, 879641798, 236062681, 418679563, 595683699, 833377412, 241666732, 500347542, 179639676, 748742510, 358838083, 700083763, 491514724, 363817309, 796484073, 352543013, 692281114, 853957450, 848210620, 160490076, 646460693, 676518066, 532161387, 568097782, 955767818, 573567415, 224496004, 6956404, 711161963, 720761647, 862038307, 283740191, 463515502, 500709594, 250943765, 26005570, 966322209, 231094183, 553690511, 533821231, 938893141, 959012379, 36426698, 759199812, 674926136, 997232536, 215452537, 712321224, 522709672, 851734082, 183284157, 685126017, 316258728, 351785484, 26090119, 847797045, 261812345, 475486673, 556190962, 105807444, 464714838, 827565151, 502851926, 179000117, 38179848, 831576208, 955753969, 575065051, 903029051, 286214098, 530212463, 158068856, 559040597, 442502743, 162096310, 14441422, 549209899, 687095400, 187906450, 589159800, 874658086, 744488200, 683596034, 13475911, 600132368, 619066920, 764773595, 381069003, 348340709, 675278253, 371895550, 581459614, 614028431, 639445191, 794266771, 256171548, 745242270, 123406029, 608590605, 827544780, 720304329, 468994185, 556249330, 627413, 483246293, 54452325, 104175791, 555424203, 166577823, 488132449, 453713239, 130091690, 780607593, 880774575, 13466214, 625531798, 732519845, 86631301, 510777233, 33188062, 399558906, 355647493]))
+
+test4 :: Test
+test4 = TestCase (assertEqual "for (continuousSubarrays [413731335, 708336615, 580085319, 965787266, 153396535, 591706899, 72721949, 674953891, 25636195, 948911655, 310850223, 386611508, 121141727, 808100, 298392873, 256726253, 175205914, 187915309, 657868217, 431814216, 270931564, 482808416, 846581830, 969190130, 202954751, 344941064, 305956776, 519071697, 98968590, 316288473, 771386513, 321406714, 666237611, 369058382, 125237637, 797497392, 5605464, 40734473, 275360753, 238178478, 800575742, 719846386, 716241553, 915332913, 721102739, 941978111, 645458450, 171452992, 829709893, 754359272, 673003152, 644744845, 216541790, 734948943, 683613208, 838534829, 603081028, 815431649, 352087711, 140211730, 293284204, 22469334, 897099441, 791488292, 99266880, 979355467, 373745765, 90037547, 961655046, 309461745, 193364737, 124234102, 582986, 857155781, 228344949, 278300939, 171852962, 238194209, 602079420, 325459203, 761636070, 560540757, 683762146, 536611697, 108084330, 89997168, 174648446, 699417636, 368273871, 239270231, 391868945, 609215741, 700049755, 809741386, 817163827, 871100123, 346868100, 861099090, 644271475, 394272061, 490454401, 644394657, 881767225, 834599122, 287498283, 375092578, 420342855, 4000933, 211111295, 212319923, 781867875, 267537512, 341625517, 413656489, 801281415, 594434, 801007943, 321374765, 907027605, 605118147, 336984727, 279791512, 871713172, 485049515, 153294539, 197724101, 978374901, 553433438, 962255541, 915612957, 249146722, 98268937, 762756724, 345221529, 29371830, 214098867, 322318837, 111719620, 673731698, 561512126, 450358741, 930383888, 694012077, 721782616, 915076595, 700166359, 957949767, 620792132, 357407477, 144854746, 967423508, 376914401, 149002547, 512037393, 356617712, 823634069, 917894576, 234526984, 833909698, 801274627, 237940936, 361945441, 840951465, 88002496, 113299508, 183236224, 223963566, 192532708, 955943454, 582845092, 684863998, 974926659, 434490852, 666925621, 951922254, 948781769, 269592311, 986648341, 785123125, 838865814, 943287768, 584171302, 28570371, 631314234, 781596115, 443217680, 333204827, 241415409, 213999286, 413781985, 310232141, 999044622, 628588643, 978380099, 824326324, 797681320, 156693224, 112145784, 947601358, 950562974, 494537697, 402120769, 7114010, 937456540, 567410413, 128875397, 521652145, 730976213, 867588791, 635633782, 39059846, 110144999, 670754947, 86063238, 728593109, 354849737, 957362000, 748743772, 770989822, 567276943, 791676823, 252069739, 956291521, 293971084, 732418410, 573495473, 473709615, 151288094, 178720569, 744989963, 775285848, 106362128, 746619571, 630679516, 335103311, 886547599, 427348844, 788963434, 720701036, 316032412, 488895813, 508908871, 980926474, 38871807, 25448939, 743692941, 975164034, 305042452, 386000934, 292726712, 271695008, 870759, 105884490, 94235554, 315968749, 913527536, 925914200, 744330646, 958804076, 145076876, 441496119, 402285014, 172213728, 169337806, 861042534, 586556348, 199614766, 236678927, 914626419, 656747484, 536165158, 199529608, 396479791, 69286094, 19800830, 903654001, 236553158, 747469314, 777537787, 270415574, 149388146, 74400287, 408750353, 289661278, 321944803, 65274776, 792999794, 663706642, 175482094, 813034331, 992430157, 287882232, 438487982, 427977428, 612396567, 119920863, 940603084, 465669645, 162707962, 462939356, 878376176, 930982098, 606577721, 926425328, 406992069, 669793207, 545976193, 728185279, 796354077, 542883079, 181147355, 465623475, 686865566, 663350157, 63513768, 137935593, 917565590, 886870659, 11445436, 800849397, 470104196, 920935548, 495365622, 956450015, 448479631, 3029746, 829993242, 637419854, 275364113, 366817830, 225756186, 827038380, 237179227, 950321772, 751840365, 118100349, 248412969, 265898443, 715451284, 917768105, 304928619, 842114964, 385856998, 321836303, 299829327, 840288592, 330976027, 109072258, 788020064, 792750432, 556960388, 916688334, 200152808, 996937287, 855926397, 676215528, 212492739, 649660265, 970060576, 267597002, 167781870, 206955139, 430916249, 748609618, 515896812, 803033637, 793689075, 548534581, 538324103, 183411531, 201243818, 599537504, 700391144, 557911654, 51996414, 548944151, 158261211, 616006451, 111582550, 621224415, 340902531, 943885077, 743256658, 196911496, 872411722, 976923959, 955308225, 833507771, 24017746, 540185215, 163122054, 943017611, 855797206, 816165484, 374728161, 982580543, 494547501, 715216836, 871502321, 182940591, 709230709, 557987404, 392819334, 906114528, 398796636, 565543554, 537027209, 187854476, 279930917, 363397967, 229580194, 24015436, 39306439, 668000971, 422475936, 959728478, 429088887, 344077326, 419642544, 30275043, 894648164, 681893497, 60418295, 923875981, 478237376, 53166924, 256824820, 120238770, 76801085, 850766631, 343951556, 551986164, 15782546, 612560189, 817881999, 902536232, 483356197, 768100923, 835058136, 80866190, 856731801, 332392883, 369822756, 599059558, 153250436, 677183121, 799588468, 276867444, 571407204, 347549505, 278312466, 966210989, 200557664, 150037612, 417386225, 824570285, 342316941, 490373184, 484095345, 885418724, 106013468, 902998002, 576464868, 212026191, 134921934, 264730231, 173416926, 426686639, 496806619, 219824633, 93790039, 650501396, 883577034, 109886354, 19184042, 583601582, 214197200, 8849132, 908027782, 473886796, 207044992, 76840755, 835555470, 998541685, 78688441, 2827655, 714460831, 806380957, 556238150, 702580286, 567714041, 243230630, 86720563, 62701673, 215853615, 78188446, 691994899, 116965365, 900179597, 512174404, 757720584, 302245326, 929726034, 773131145, 122947131, 768574752, 461913631, 545297838, 711952955, 799755660, 667207693, 387016143, 753348286, 158279966, 716779547, 609894386, 437866035, 97646589, 753477047, 281498129, 591705538, 46827770, 32682921, 858190303, 665669424, 45444551, 223380929, 878307807, 736007544, 861020535, 590178625, 634284662, 399756223, 87368198, 886429843, 686766055, 276174149, 521120704, 613108288, 849052145, 146646259, 250221263, 612027197, 623760543, 206748793, 922383026, 270229216, 151607509, 716259767, 968705433, 123403254, 866296346, 564391485, 963039068, 356790218, 988067875, 418524951, 893380393, 171779163, 64755481, 548151237, 788971640, 841725143, 927643523, 786340731, 630290254, 176806686, 605885633, 892104570, 501043790, 345946105, 679562320, 665783998, 217185772, 381219151, 882628296, 608473379, 332805512, 56566108, 925585918, 83015590, 254176096, 932334129, 288039543, 457713543, 846359446, 193969957, 636900718, 329621267, 639165997, 963448136, 223944067, 895146022, 557647432, 646539153, 232139458, 32228366, 333162038, 451494641, 629478700, 30768043, 118435128, 182388584, 283986470, 884752985, 45516620, 264728776, 93124502, 232682795, 407730356, 454644103, 560670331, 206494864, 665484115, 747835656, 869491083, 554345470, 29516098, 852742245, 42655265, 425852606, 50663716, 516189766, 321400450, 718188085, 203454416, 278541624, 597682318, 587039170, 296368722, 732535579, 110714948, 937555221, 347954526, 724477753, 620055420, 284402158, 146124168, 763015906, 953936077, 673788060, 825563655, 735934087, 426531771, 517511130, 932554319, 189329293, 292900931, 55161390, 310959308, 483535385, 997199345, 973244766, 612355413, 954308705, 984859433, 359607273, 743175474, 35022266, 959417310, 136718697, 926594041, 516356542, 74705318, 337746782, 896018366, 899482249, 300926791, 696835683, 673231212, 562571404, 776555855, 939619077, 838564848, 636538558, 253050192, 683060504, 984688992, 307974244, 283372334, 778956955, 689761985, 406481107, 14291891, 347227620, 69625173, 579166626, 41424192, 879126995, 456955392, 663010276, 717612835, 963318115, 736922174, 484654684, 791843641, 38579674, 795825389, 497339006, 434806962, 652390131, 345940390, 93907458, 645962363, 284085320, 163961521, 675082385, 107379399, 235054852, 306850097, 267194775, 12475538, 398394422, 945322302, 85066595, 58335379, 93083420, 937646795, 265322953, 414848641, 628546849, 885605272, 611960029, 71300872, 707529456, 203519640, 904855747, 947758838, 469804206, 528116603, 982081061, 373012403, 180752230, 747937832, 446414086, 462683272, 885011593, 754054680, 713881233, 135380616, 551436332, 758717175, 455031398, 146912511, 649989274, 358754299, 248111693, 839059227, 729934034, 665481302, 850532818, 269804145, 651283525, 477837349, 937048296, 485581230, 483691200, 121639719, 674411996, 42051473, 254999016, 334506778, 345294312, 356534241, 623031843, 627940204, 455563997, 852758338, 665197802, 381757926, 439627824, 648049707, 135323521, 109739298, 888047617, 563577448, 432935334, 864669427, 950560113, 633179031, 780669622, 907134460, 198717665, 890665536, 457587904, 184484965, 81276651, 769854047, 45405839, 208140976, 637347877, 228873096, 465752861, 280407394, 752168231, 711650345, 88894179, 697828595, 213659810, 568041834, 347149794, 915180944, 716092361, 766407138, 149345188, 101330956, 597732507, 19821446, 689477539, 371841395, 139447671, 144679961, 784762364, 808896792, 172847976, 853629079, 628430389, 488459291, 300400394, 891468567, 815692958, 523045758, 177388290, 773739145, 397110752, 958194515, 640761148, 646682357, 677658927, 947047201, 158130416, 345388562, 849454439, 476040908, 67076603, 74483251, 270237006, 434145305, 679391888, 239209888, 575743537, 947020258, 29982786, 65339228, 293454639, 795063205, 246857433, 783907320, 393630647, 568762951, 306074758, 922988635, 694819402, 970879428, 455679704, 212376216, 997776697, 855423864, 677069322, 310592112, 91567111, 921453754, 225429190, 371350941, 235957205, 707966988, 501175677, 565691995, 738955477, 33396184, 162724691, 731371019, 399931965, 561248316, 976210094, 409571727, 573027417, 517715106, 369660110, 178210695, 560019596, 252599420, 415898413, 328290766, 386753946, 719202808, 180165193, 925409999, 597842541, 664280152, 994655470, 989054279, 221977146, 608096993, 177671408, 127619823, 388409434, 363703327, 865203222, 802778059, 219558153, 303955686, 626020841, 578270154, 457779398, 481976299, 781708969, 944998681, 667066644, 507859378, 691276117, 375307211, 300374293, 694615978, 88932354, 954566837, 570053458, 325505751, 392936053, 141709077, 714641953, 340246795, 158983891, 856453030, 476861855, 560448974, 221576372, 772448208, 57062508, 132293472, 498376038, 416156538, 865353333, 154858954, 927836276, 907216222, 846558843, 676462152, 434378702, 866314004, 670415126, 904861588, 850418999, 302975282, 984827028, 345577260, 554134319, 544854958, 565596774, 310366024, 17910569, 918313569, 334051047, 899956946, 382511654, 160117597, 720442857, 379556402, 877458950, 292765966, 699918481, 550858665, 111545290, 820881785, 993301842, 308445312, 136113246, 919317248, 76541674, 467027571, 593287573, 342598357, 478869556, 453782080, 535498761, 512863157, 340014702, 827734938, 449353949, 729077402, 22276351, 736766269, 393531337, 745679509, 279935525, 493997536, 832023340, 996919625, 606430248, 252205601, 527759321, 825971028, 848848206, 718311826, 783199109, 384897174, 432343008, 107686214, 610382970, 627198023, 929646503, 358786231, 800923701, 256403902, 631903868, 958679879, 606442146, 521617517, 138742386, 526546010, 943515984, 931671476, 812513572, 786285022, 8034113, 405396209, 95714134, 92277382, 477747542, 799940327, 896793430, 494787896, 592010774, 8371281, 53712796, 640875897, 272634160, 154239003, 166722024, 326851209, 664982616, 183225438, 777672419, 695421105, 532798499, 185272727, 269208992, 54031602, 303491895, 508076960, 38161764, 669458990, 763700802, 133768885, 66571419, 332765184, 286080219, 410370061, 865414802, 106340020, 607411838, 686468455, 980674668, 572196789, 350654464, 263288280, 591573645, 272716357, 661662832, 17301381, 846253425, 276239867, 710925627, 345850488, 172748944, 720276497, 830664775, 208822833, 269604920, 309099484, 982317947, 314986552, 773287077, 750600270, 833813410, 273508835, 581329099, 649800751, 988757236, 268663805, 233155640, 439200021, 704711916, 340428817, 88324629, 739318435, 805208225, 30214482, 11667106, 880231600, 296234196, 202527775, 272785462, 85570851, 206930524, 158405208, 744852941, 496308108, 430260873, 581774515, 389483578, 644217884, 978644595, 309731298, 823169165, 868280281, 221049982, 978450207, 856046889, 206461635, 701897057, 433780053, 481339485, 61330756, 799145541, 911167866, 207488723, 610636375, 405869894, 102341409, 623531841, 371294189, 482933052, 821832287, 395455790, 365373327, 859899797, 188750301, 157327886, 201708214, 981655148, 568593284, 11447376, 704056583, 853691294, 929765718, 867689661, 652778673, 678736806, 29907996, 587751788, 430040407, 167489770, 206790429, 32739086, 998488865, 731108511, 145848401, 802725720, 632434616, 570700852, 531114033, 247323014, 509584135, 854169338, 984936008, 812785848, 780268263, 293665316, 933357329, 900522410, 216913150, 658392842, 82729587, 928020201, 246542059, 629954375, 676441382, 640169483, 609881129, 893816886, 762131991, 395270473, 402346057, 192443411, 219215208, 76092517, 676589808, 987095262, 105540739, 754070186, 87970786, 936906968, 479684644, 157227726, 843034713, 780789152, 991684617, 989012687, 713638928, 845462838, 633572721, 527597588, 187970877, 551924609, 908104139, 356526509, 947973846, 287531904, 368884759, 754952633, 795545133, 67745136, 781670999, 519061099, 944914594, 656745076, 679249536, 847332578, 294172234, 816163130, 555879280, 970069641, 863387397, 38409322, 355818671, 760099475, 531856656, 53936327, 279823079, 948140990, 965518126, 353922218, 200829283, 603711874, 755229679, 321801256, 430960874, 602148374, 885553559, 789093929, 711154245, 664739264, 228600828, 307829014, 103639007, 651476143, 8138101, 823388907, 878957621, 691461309, 659327330, 489912293, 413049832, 177972834, 275307680, 876023238, 768807355, 826587272, 736672976, 216435475, 487349073, 607079682, 883922293, 23948295, 886188621, 546760920, 207095748, 321301745, 290036870, 669825611, 621498370, 301925206, 925691420, 335354994, 429424789, 591585472, 524613200, 339984036, 900359720, 92923328, 905892915, 201371015, 690420231, 90619015, 246443495, 186347028, 805764862, 353280814, 285368182, 354402441, 323023485, 396364199, 718622780, 832184, 600785897, 115313110, 762948544, 451458935, 416157136, 780261318, 946846801, 488731555, 467329511, 741703242, 2309424, 58553289, 147950607, 543848335, 482709470, 483232376, 933160747, 905623908, 271978875, 731550634, 92537489, 931298197, 372604386, 820892540, 706933772, 866427648, 681435659, 87791021, 962277540, 702302773, 612418274, 566586339, 531418163, 212012934, 22420066, 116294017, 427298032, 588188941, 480754582, 958970820, 635445821, 461684313, 25237641, 707708114, 285421054, 636979498, 534488517, 134537996, 573651066, 778211996, 297152349, 981990991, 94330261, 267544507, 607774534, 742960351, 750790892, 687665011, 609432555, 127056040, 909313271, 310864816, 560698465, 929854496, 90637042, 171798607, 474091866, 190333634, 132192401, 307675697, 198564991, 467104529, 749218248, 741646970, 338239943, 318088786, 134256018, 623326505, 162204385, 445071719, 84376471, 268984039, 824635759, 805378017, 239093820, 929355962, 12335178, 753620269, 603878675, 51159571, 400555138, 927041300, 835504522, 726171350, 400983102, 358150636, 344665908, 481756721, 251242336, 295043691, 415962542, 913758599, 111517785, 423761433, 503053658, 194884323, 588078540, 718140888, 523613132, 450351051, 503526620, 830037658, 633231798, 473969186, 996141499, 823443876, 515858164, 555740081, 776437847, 865403087, 82734522, 926236247, 99468669, 405108225, 594580402, 761994997, 240304348, 201507122, 113462820, 364781613, 869402824, 350507036, 623640033, 216653571, 689337138, 725853496, 969462378, 880140140, 607518758, 755946679, 813607781, 255698977, 966036932, 878926096, 634115631, 244456837, 894683587, 817240970, 58220318, 590517693, 585765159, 180430852, 481887488, 36188242, 17773085, 810327385, 822915204, 560296126, 202928704, 749254079, 526905804, 646756794, 866888268, 580018090, 489031494, 559663258, 272580501, 374898828, 158268266, 822549379, 948421906, 81866449, 959990529, 405420587, 19196530, 58709529, 119084269, 411145061, 712341084, 255804011, 177348066, 331079796, 890849643, 43516975, 732280588, 958155787, 768865587, 895149677, 923408197, 711202999, 619168110, 155600920, 537719386, 401231278, 73183990, 134329509, 183280529, 602112261, 902666659, 605190591, 86090875, 477295210, 234408494, 135196569, 423482189, 129847032, 671983693, 531267536, 374671287, 582156388, 978417623, 158967063, 824847733, 459921769, 990416567, 883473999, 600771904, 321708529, 97704799, 674009918, 256895128, 745572001, 785990678, 694379085, 785393692, 139499981, 316773317, 740087705, 362998006, 793949399, 529138921, 779903627, 179654716, 617366173, 583651712, 803138787, 414570553, 270609377, 259193200, 149093106, 932521885, 443906154, 869471485, 728773909, 987078272, 66387044, 994341389, 31811108, 605436569, 181588170, 851740847, 428750091, 635341282, 615303444, 341613923, 987286694, 63810661, 601736867, 367423763, 358750294, 21385945, 536549389, 224073134, 908074312, 311971782, 41858382, 929576924, 289753986, 920029407, 645000994, 220997854, 951531687, 467513694, 798040859, 145395042, 840760159, 710479528, 174421049, 788076005, 265542245, 82774055, 766809571, 478516002, 947413061, 511230509, 121591704, 12416809, 491944114, 832717451, 630629565, 881620877, 50408117, 757642856, 93616113, 578449110, 864041138, 218140648, 739573473, 247690670, 692977352, 114903635, 212749017, 367107123, 883831586, 336508136, 536592435, 721478117, 544508468, 626728182, 227415688, 545452112, 92260591, 209274476, 364600612, 218264139, 331598817, 121975173, 596595040, 144819563, 384696635, 111906949, 199066296, 852544130, 287666918, 466408994, 215037610, 776148646, 143302235, 614490586, 545193971, 218330004, 891563472, 98679046, 147710475, 622255911, 778571501, 441003607, 586419318, 479857603, 402575157, 382983304, 186263041, 428129570, 936566321, 375652041, 888048904, 676814082, 395646379, 678684668, 95081400, 337695960, 198388430, 746629561, 490103305, 136224723, 954782470, 905609914, 192764728, 620837778, 341043461, 449567709, 16148897, 48960736, 13137924, 15160714, 973551303, 530093381, 670145556, 980662824, 842445131, 587948548, 644743872, 17712348, 623960213, 941611645, 437897142, 740568060, 206999374, 280438024, 632798957, 822889511, 24591569, 865144193, 69254796, 238651238, 865514563, 192944549, 344505079, 974756231, 791556700, 154327527, 941380658, 927831565, 336508836, 362901036, 252011646, 1802074, 737579607, 209112523, 260213570, 686582618, 642956391, 275306945, 601678177, 958575484, 634003392, 676395873, 767602218, 207325742, 205166807, 359581837, 414668788, 311790101, 73377179, 320995330, 726351541, 841097334, 308136066, 929338548, 459183296, 552363253, 155033258, 687391407, 40369502, 399707430, 441850841, 928123680, 296462381, 323214466, 945967722, 469077259, 792909966, 156590061, 756510015, 933403491, 893219035, 928875948, 526315862, 756896513, 751166815, 408446317, 838531174, 593831202, 304298775, 405070986, 811446196, 466032385, 87128607, 869784367, 299500460, 397039652, 664783085, 483631800, 451850920, 148108505, 976320197, 308000602, 186726641, 214510746, 96698232, 222484140, 638792388, 727309438, 768100598, 405772613, 672335026, 3125548, 98583732, 280294416, 489498907, 775363202, 951900602, 978863160, 440305503, 349402480, 323847643, 993961069, 918551710, 328072514, 231206965, 789247867, 131367812, 125618915, 563084042, 399203963, 119243107, 714903829, 860774111, 766900018, 905725290, 394311739, 228650509, 642996197, 36153257, 356140251, 224629587, 844745104, 253968060, 565111557, 343040941, 466115334, 973312213, 915150604, 355238148, 658840592, 785423118, 763722188, 294086193, 173809863, 348517867, 877667141, 617188337, 491224323, 528789539, 255288740, 258499173, 898343497, 453918864, 903826549, 80434292, 150757602, 833945549, 891464350, 565992242, 334700943, 802336872, 450473690, 280270859, 892946581, 138153471, 327100304, 276572296, 67549691, 315737078, 577199727, 191010696, 703245924, 618788711, 316382655, 607061435, 834859554, 246070374, 248666652, 97086396, 108551426, 297094355, 253631200, 558433434, 868304448, 384265042, 955085543, 829446894, 684460743, 43936312, 63833416, 885065419, 34494294, 972177440, 758022393, 528532090, 387387983, 13062534, 303265324, 182270410, 755188342, 636100451, 118980129, 538704446, 644397469, 154122018, 840724502, 667511591, 132284721, 872377154, 282160554, 330958291, 801103067, 248827678, 76319661, 360294209, 387233283, 656832441, 62019489, 157320427, 758412986, 746719372, 698161212, 787018660, 246835661, 879814196, 957764678, 56055627, 166318443, 767075391, 163396082, 440001027, 793918403, 927579793, 616208632, 525499036, 985362048, 170581666, 673114281, 422560901, 921245163, 888505653, 244862466, 755687979, 308131593, 322954592, 467364254, 39570734, 791368480, 771068163, 982980768, 695192613, 526092979, 275401837, 830590155, 379416756, 705426232, 125828588, 713321239, 603390198, 15373925, 131499536, 590990244, 585320324, 965297198, 277110107, 89571726, 983954663, 447140540, 138215602, 41359650, 340236648, 463967801, 576198859, 436040623, 545039097, 670427915, 498140518, 262231666, 785004014, 616942953, 782191947, 716466633, 50315160, 274931836, 715714153, 137181297, 974215292, 625900950, 318857650, 557069969, 403350402, 778843347, 78915141, 352003917, 152225373, 711724823, 133786300, 429811808, 5438497, 413350144, 324805175, 582928216, 502067412, 302536569, 79915926, 262206749, 830636980, 340167017, 648355063, 459945291, 69864440, 847941719, 841450818, 211302260, 780475703, 551431815, 190898234, 628878910, 979545553, 996435985, 273410093, 138758589, 522669360, 974307676, 801135424, 446094044, 273298907, 764601587, 595204710, 866936437, 908376941, 853199017, 601488548, 891377764, 57827911, 753350571, 61600406, 476006156, 436672052, 245304427, 171539891, 32740722, 609297442, 421062638, 779577674, 790914027, 843741481, 615519891, 323576434, 893093779, 153724207, 475861604, 6976568, 769960428, 669697249, 721652390, 358065158, 644258115, 534961471, 107840586, 764810077, 181890870, 509493009, 81132472, 175634367, 461570493, 284398396, 379500647, 31782829, 261217061, 39552613, 975723746, 981134081, 926465682, 233412795, 544255630, 839767794, 64611268, 631704423, 680504505, 78609955, 753654362, 245745949, 321809324, 91326980, 480139299, 50870750, 452780641, 984163580, 4236369, 667656910, 250444181, 712760650, 443775310, 590502920, 784436719, 785506507, 744319456, 402604512, 467141403, 341414353, 601815337, 472568202, 13704160, 929527657, 599092153, 863038896, 749376125, 579346166, 229013417, 977245189, 104048011, 726079062, 931757071, 799461439, 93987121, 651680291, 78792256, 979254270, 427703181, 397690189, 527556296, 729361637, 19301146, 542611347, 859009938, 332461453, 848947886, 762489565, 852310890, 523779121, 310655147, 377435140, 468309975, 244718386, 440811636, 940037896, 72243965, 257215034, 651548705, 794286323, 433276852, 958232382, 171790538, 53418648, 5226118, 404018104, 873291369, 321807151, 354792113, 830690912, 945527872, 216470404, 653811890, 981144316, 607414712, 769539250, 107671818, 102570011, 15684039, 723952448, 731979623, 956953138, 739380293, 270919429, 750088466, 849781831, 171522685, 536354176, 998052961, 49757192, 705930442, 538187851, 180343305, 93957807, 51247223, 829840308, 687895586, 932170852, 661679460, 627791416, 946826259, 822589554, 598170312, 997796557, 676041757, 935813390, 685161801, 72425486, 953974810, 68525757, 805082254, 671588514, 932607493, 195369808, 758163333, 144572205, 834002385, 634082125, 666887480, 767454091, 562150940, 421096460, 328638399, 858926615, 525790239, 18726584, 71769579, 899265887, 411248251, 14775613, 867023116, 894563930, 371093961, 874678144, 505523406, 259706359, 324979771, 96440357, 875200784, 447029881, 664176421, 648670116, 699728729, 770533919, 826712206, 590162638, 499972005, 544415193, 763403045, 354065558, 103404943, 38978182, 7406911, 214214861, 749820134, 180696438, 999592382, 307101157, 227210948, 712461226, 42968507, 385099071, 920384324, 912156961, 578168437, 94503362, 745370693, 65370187, 603830078, 77457120, 25896102, 929685720, 949156158, 179804062, 307568501, 59127807, 677398118, 862806293, 476821206, 81176497, 929610983, 39732898, 578236375, 639982924, 640438440, 831806694, 228031358, 525957489, 768896195, 544179047, 866408305, 24590029, 376315026, 932223558, 101309346, 490341441, 608094837, 605479312, 600859610, 920336984, 727802194, 175767973, 249461792, 764795797, 614232673, 590809348, 190710589, 873215413, 701324209, 917237583, 1731674, 394484315, 428901387, 234256603, 754488229, 103196521, 248706088, 68765620, 527384784, 342104021, 394604600, 490251877, 469174900, 236666888, 645885702, 365041806, 306551573, 954086918, 742465961, 995407332, 714449098, 509575481, 474634533, 246230853, 667404858, 289452952, 623024559, 736680837, 7442503, 707957993, 739040070, 152413642, 556011186, 229488458, 939621870, 7237687, 596633048, 408582621, 93036351, 80692053, 383751390, 316267179, 255243279, 614669856, 148848957, 295959764, 470285261, 232377397, 992310871, 257337028, 988345371, 925194406, 43555239, 65467475, 33796906, 977861317, 726995273, 474282957, 695235422, 603818422, 574636901, 558445752, 936682400, 365476516, 955594632, 129417742, 287640817, 755116368, 211028797, 284622888, 460148494, 278417708, 747896528, 959979600, 52347904, 468664021, 668098190, 178468240, 212440378, 457536872, 83317756, 367541293, 45815078, 821700934, 226374771, 405427776, 203468470, 525432368, 697041097, 878138151, 800263551, 422160301, 673741626, 796808293, 936402809, 516169132, 578193752, 48967098, 305133504, 519921419, 303358112, 302277149, 860037263, 331739118, 251834639, 681478197, 69524498, 638683975, 979972053, 83179028, 992175419, 132347387, 653548081, 252770919, 566825843, 537120507, 563440436, 915705427, 150125138, 487477572, 695675221, 257871215, 936637989, 213038009, 420818744, 102340823, 490224339, 104540989, 429620596, 488217832, 618241335, 263368657, 208178493, 12656915, 226301817, 579690099, 437525627, 730471811, 807381802, 502291137, 57087345, 770850407, 720563914, 551926373, 721227768, 411716355, 653223238, 619272163, 703732323, 913201082, 203097163, 953305689, 446216475, 834971408, 140150400, 784580486, 287153946, 166384116, 184461532, 997697827, 715435092, 909805532, 116036325, 301482013, 904281551, 253632579, 260778270, 732953283, 911561950, 927555493, 764405091, 864188781, 858491089, 338247600, 439969305, 108181624, 616215446, 952627178, 485712980, 530233813, 773032350, 796087558, 693829210, 892534993, 195611180, 549985227, 120545299, 986627163, 648915710, 430118229, 401773568, 518695409, 522303580, 521200064, 459573665, 46205646, 244694493, 706791537, 546897494, 766199773, 837214879, 183208372, 841896853, 19164614, 501483054, 47034683, 21126811, 11466994, 375253198, 520340304, 30816161, 871991497, 668325563, 904812791, 146969289, 724403480, 147549355, 878258453, 494536387, 143054553, 270512101, 88060187, 661606791, 537175661, 537649568, 577045877, 926110588, 415697537, 613043118, 987409038, 291454344, 527578521, 176708589, 245275724, 345758515, 547432103, 101757866, 94632346, 957630514, 906451498, 642062563, 182260848, 57525291, 780274072, 575651658, 76640948, 199400711, 897729922, 697697653, 199556364, 429479274, 328497702, 873839638, 142527996, 203705833, 417561122, 484111084, 203216550, 897917032, 302398380, 400501993, 266678110, 894837846, 612299932, 809230351, 433577237, 442926805, 889969425, 815903584, 415341747, 807110349, 164217573, 844063373, 711626795, 377370379, 156244635, 894197295, 579596616, 286625420, 510754596, 774517766, 83798465, 776896517, 947867479, 540909478, 710908554, 551139106, 975495304, 813874578, 585430929, 818186404, 159539853, 478908433, 892422638, 387067082, 793858278, 590144539, 266614725, 843893829, 849840219, 443475922, 813577456, 254783140, 397313325, 575872401, 470275326, 204661822, 73415800, 273405868, 898678826, 300830628, 239149688, 706391567, 596545640, 810034994, 787084644, 843859430, 513265632, 373440212, 112064910, 697220977, 399304434, 973369703, 526028940, 242617561, 991795768, 995590828, 427415979, 798668023, 510514058, 148812132, 903439542, 899872756, 903545712, 43926251, 711026041, 954892974, 683081780, 468071581, 357607931, 563861743, 504844890, 319480376, 737069045, 308225544, 838281808, 743281821, 852372975, 610773857, 213637643, 863223267, 9421902, 759375075, 497446434, 847147110, 336300724, 461918508, 516373509, 453829632, 507297300, 95817747, 463389723, 226361518, 944418704, 473105483, 1527779, 529938978, 236585930, 541762011, 551867197, 960165783, 27081612, 121164421, 344605869, 223417372, 859607334, 202698258, 389222938, 817968970, 89250665, 860972900, 967039504, 541183532, 458256227, 256052562, 274704336, 626036135, 889993317, 977550305, 286490719, 950296491, 454054345, 666980239, 618286493, 879706816, 17716767, 94531918, 313995279, 231159396, 267325271, 872465324, 266501164, 951627183, 971070863, 837657732, 5374977, 883714029, 580020514, 141173494, 108991354, 861658220, 914643906, 505193627, 989350304, 495682089, 806054513, 949735837, 120431880, 352965807, 897069118, 289083241, 968510870, 728267628, 167609296, 441844469, 96248380, 833750665, 840465737, 557464208, 496976525, 888557258, 557079170, 401610993, 889317974, 136220416, 142567249, 70584221, 770068981, 472260082, 249852565, 368226378, 98484400, 15798912, 146162118, 31975181, 799183742, 191355821, 507046224, 794572734, 415062640, 831080016, 517321774, 446918846, 840566947, 125702654, 590179266, 809761059, 298487296, 31622693, 348549270, 773320262, 869766847, 157175907, 915369349, 272073512, 19034270, 655464547, 179223368, 977053451, 646395281, 809725086, 73706101, 772144321, 275638864, 115094120, 625844468, 108142176, 893514685, 799726753, 845793799, 493926696, 855979954, 861480416, 41441872, 432743455, 598794099, 97478927, 399788796, 958201080, 509400797, 618698509, 790524978, 882242602, 174831825, 655391951, 812590664, 611676506, 186242081, 909394611, 900000867, 664604597, 414145815, 16208849, 638803672, 801436941, 467400904, 300147197, 586386640, 79902003, 980043479, 706693141, 119503701, 363057655, 727633406, 276448348, 953918554, 487723756, 294977747, 945302675, 509623863, 297228199, 776603487, 759415145, 637534440, 373015984, 959469054, 334153534, 993112395, 372226063, 264698150, 220360696, 434942417, 324320465, 378520103, 500931840, 892977552, 574509978, 506485282, 734039431, 638935762, 322164552, 608016614, 392124708, 231644165, 746964540, 74583030, 459745720, 450579642, 758967766, 38281233, 219532041, 322709463, 898136470, 578656799, 283869314, 601566489, 745863301, 88139288, 395854420, 61088540, 787626705, 235893245, 171771551, 878019312, 617197601, 495626450, 350764946, 924707455, 54949103, 332359554, 243213712, 479902117, 683012595, 149302909, 117260532, 66804229, 623510732, 134619558, 15297747, 57585451, 578946902, 275355572, 749723880, 184754230, 39937725, 964452393, 765940992, 281303363, 382733425, 713117284, 333292058, 9986507, 548334795, 499935347, 706437490, 941436442, 185545079, 398808089, 954212374, 935308349, 668933747, 357978719, 115218609, 331249665, 262813627, 882235884, 300798048, 436082707, 465053988, 810567423, 533932226, 148357548, 980613483, 628555460, 750662000, 46517353, 105929001, 245055160, 629080519, 216815656, 119411069, 773966705, 302905776, 861329884, 152507319, 286531793, 969541736, 186459772, 371556685, 216445422, 639405852, 620271226, 337057501, 558545888, 389255095, 907178897, 552689190, 231180651, 929859379, 178092341, 908647647, 520783892, 723496518, 129584616, 303905254, 181453841, 137434685, 605589113, 754609274, 145491282, 661832805, 471044486, 607362589, 972763723, 610486665, 956320498, 342370159, 965320573, 85583333, 52584375, 603543279, 640044567, 869501421, 236135960, 992640951, 228473795, 798857839, 515731563, 610118402, 93976213, 482335623, 933867184, 891395091, 678588782, 144298317, 480244966, 978082757, 89026779, 152629134, 214973733, 18246584, 90880035, 163903251, 705622160, 613122215, 382792552, 405463394, 62001998, 183372477, 884705076, 944692426, 841304619, 853975907, 143949907, 387032322, 750614322, 229800533, 186833229, 674937824, 572624868, 338691328, 468158772, 57709314, 653555002, 477777335, 899463806, 647068391, 719143299, 999571506, 118352181, 702689888, 705744067, 347303310, 13831087, 623347257, 913085005, 982166867, 519761203, 791527702, 589002666, 860380423, 513184780, 91873923, 947471826, 221916558, 205560938, 365275377, 212701267, 616285264, 769492665, 335809363, 865581593, 628975548, 303655284, 406081981, 559724811, 837011703, 591830558, 76829321, 960928299, 639602228, 952194190, 826625327, 744426466, 670501789, 415533635, 587684370, 282261414, 4300707, 622301382, 55038870, 35990469, 54921783, 558281322, 365364612, 147843427, 341510324, 893934385, 521108668, 23059992, 316331565, 689481910, 609366468, 450156720, 531858890, 383379745, 906159452, 101507460, 113019745, 210466778, 405650227, 38122283, 116990067, 270178820, 224368253, 385361073, 225183903, 133206972, 963870667, 419150888, 24158292, 379431466, 242163178, 365924029, 231491787, 626778605, 955941574, 521747901, 414564013, 430971213, 534382035, 12661998, 672485075, 700541287, 53505652, 161289397, 763291328, 99921887, 323823106, 656615764, 844924584, 797064377, 542785177, 675521733, 49629005, 553511212, 435787776, 399463766, 747127122, 121166355, 300244423, 199995943, 20728135, 842659864, 247291715, 785349965, 542191801, 752249527, 547677993, 717842517, 870515210, 399022711, 415433793, 179880231, 898051335, 50914259, 920103010, 915339240, 718353063, 191510128, 50626020, 208493820, 931119991, 277083900, 787672570, 203265068, 549600461, 411131906, 87869401, 245183582, 224464359, 483768091, 905693722, 846874659, 639459170, 601649048, 550105884, 982475937, 437693911, 696621056, 841943728, 918891036, 87696158, 575997747, 318893366, 267072292, 15799069, 747869880, 863878947, 776862807, 850623909, 463236545, 497932982, 146803223, 489814231, 943467622, 115775767, 315588510, 934038526, 374392113, 771917541, 631932532, 154008664, 905019369, 347608640, 620737388, 272009292, 710544374, 597325103, 777519043, 257174144, 621611843, 376804255, 285022176, 255767850, 739200421, 615337076, 762436815, 358487743, 559826208, 967424982, 277167634, 132392810, 458777184, 490286676, 557858486, 474843625, 326842365, 912976529, 1772911, 513084242, 850944001, 572898304, 718248659, 515290696, 107116413, 152435449, 252937676, 730621367, 849525019, 913975423, 319069088, 945877399, 49232863, 638388085, 534796961, 289761734, 392985425, 147491049, 500297018, 428829208, 557190085, 753200120, 278645015, 149344789, 198546306, 228373074, 266527267, 366504096, 891139688, 776063938, 592524046, 15623342, 915503829, 460961070, 368119931, 418233441, 234586214, 953424289, 467728520, 549309610, 60783529, 329518423, 452011368, 731386652, 18801987, 955816316, 177048398, 891755010, 738101430, 886390572, 932026239, 311723479, 592802192, 26862749, 732520170, 460423782, 910459760, 572196093, 260263664, 668400746, 746381845, 429429508, 343606063, 303556673, 156285634, 166724299, 320907010, 35434550, 636956689, 206431964, 528698824, 677100792, 797274590, 762926653, 196839497, 659284630, 135308669, 760849921, 389314515, 420468477, 187846650, 743793220, 632138865, 548895918, 77553709, 761140630, 396661975, 210008634, 471704282, 630866309, 427854917, 560008390, 112139405, 224128300, 870052165, 203007247, 178218504, 593065188, 311773465, 843264111, 863637453, 576983867, 672137099, 375606766, 513249163, 576048274, 297030427, 223109128, 124504477, 355410316, 581394080, 310219432, 707233072, 924903041, 816431525, 285119506, 283502295, 954009333, 504112778, 576134972, 801160723, 137616696, 396600015, 307547683, 973448058, 331279303, 368001390, 280293146, 253782850, 583639868, 992987950, 156179994, 50733967, 395432975, 283921690, 90418343, 60601303, 875239499, 564178350, 677852843, 565704633, 505857408, 418398461, 967394873, 545944896, 76489697, 544536296, 922855937, 579990147, 139594330, 660807744, 349618723, 104406354, 912771398, 260406988, 914202177, 850679865, 310031188, 153055098, 294744130, 47121286, 179046424, 801108209, 160964729, 666134698, 744346568, 554445732, 625484056, 471180832, 510282473, 797374080, 974905583, 191218348, 272344806, 410328844, 124518793, 912246473, 693916134, 599007824, 287549821, 84720114, 778874609, 868649460, 417812467, 85192026, 730638490, 333771548, 428844292, 205146835, 318839122, 262809544, 149481760, 324915185, 598046934, 45139050, 531175725, 592439203, 643898432, 996082917, 650674191, 317402339, 269798513, 633561405, 456448079, 491677825, 749057285, 29084824, 352175499, 831685171, 61526259, 288511375, 55704263, 225084032, 118130013, 392454528, 654612005, 199101710, 432612736, 277125387, 885937576, 85937817, 905866763, 125766569, 734124951, 640443647, 631231152, 528408077, 756308651, 608894852, 542746417, 399476487, 587993006, 314996247, 277069841, 161000197, 730906723, 37689357, 692585705, 487890944, 744413486, 557049054, 383132495, 52841388, 615879504, 253987563, 917362696, 144188443, 179300638, 716394815, 574063746, 933364097, 560533115, 707056590, 505229475, 985596027, 497843829, 490326213, 655546820, 347486070, 926407851, 80230587, 992106855, 280390747, 888136061, 27895490, 467368985, 240434463, 246993006, 791624750, 858514565, 833361762, 657727886, 595712069, 281229208, 450477234, 95183191, 647022609, 725160869, 399099420, 116930593, 200459363, 880806946, 900243092, 491200449, 473295037, 540086306, 765655459, 295258173, 344238937, 78243922, 656477947, 372754042, 418453062, 370248261, 467900501, 696490739, 263457432, 874322166, 598303607, 287744504, 674970062, 708528246, 372068490, 101895817, 690621023, 349422252, 231612541, 497517743, 605595783, 532179645, 981389639, 592561266, 815474675, 539566828, 102455061, 591858828, 126408893, 336044076, 866657144, 157169176, 930996847, 100539211, 499389296, 109260986, 891366579, 930224964, 98828757, 96236247, 398061676, 414446402, 938490885, 56893574, 700392215, 110946570, 981096212, 719586090, 699827021, 19835259, 720802002, 174217437, 776120075, 739541791, 869122103, 156894679, 777605994, 711748602, 327903595, 921471339, 189185986, 406838333, 563585847, 717315085, 840868281, 401126440, 623557179, 765435289, 130312295, 43951268, 677666913, 895538548, 177962823, 201448091, 230315326, 365958700, 972727586, 326172513, 868946635, 44652887, 379925712, 327350523, 700184464, 300519822, 644604260, 740145919, 661365513, 333698349, 514035114, 859527213, 271711531, 683933935, 629303498, 144506972, 470515193, 162318345, 361468988, 773681403, 951061808, 618054892, 170325268, 541789267, 879940958, 835631004, 228332363, 285941, 893489786, 707683348, 95338226, 306290205, 802405981, 293220340, 967511979, 593726390, 835193546, 76873636, 239104489, 98862539, 730794137, 483217075, 565334732, 620839406, 488761639, 306143438, 443844020, 191707075, 673806132, 371244124, 426322917, 690821801, 126313746, 368560425, 293999434, 238721923, 198407199, 259064807, 477745889, 669810485, 396775991, 917671963, 15555009, 961291894, 521275086, 118553165, 376450715, 436208891, 754192196, 960953410, 691003753, 277420959, 48223675, 895557693, 478440090, 845184988, 812492659, 716399281, 27282094, 594466981, 147543633, 191024744, 290864892, 192183368, 813367972, 563033685, 586187140, 196464330, 850801020, 300870970, 311947313, 681362461, 726142239, 239308072, 84012810, 241603802, 399718378, 901032097, 788930297, 975620475, 310650235, 137819782, 395221412, 242337596, 136332832, 262323761, 428955394, 616825046, 272608443, 942188421, 351541622, 373663972, 366026932, 569044135, 828867394, 839860756, 483606735, 140373407, 144133406, 571177100, 864133331, 483809534, 352462943, 476034081, 529590755, 811034676, 746270821, 63369749, 593688894, 278165128, 103746320, 170691917, 19098123, 596619039, 733097272, 370704721, 74535413, 940664464, 911538679, 943462332, 990306562, 793048101, 883432874, 203865682, 812420040, 306138712, 15553831, 37449603, 702612837, 841902965, 553941631, 52531429, 87602367, 800571677, 156944672, 340656687, 918148385, 756066090, 232089177, 797358606, 11236890, 848237973, 346750968, 670799950, 366501871, 73330622, 463396541, 52145811, 379061612, 356916657, 610924441, 566352168, 725712905, 525071540, 206556595, 298352204, 44052589, 265974787, 275331917, 695797905, 236938505, 970002970, 134849121, 669972523, 434179031, 347090745, 618225984, 282486983, 394331970, 395437230, 891404949, 239975401, 381980526, 698192817, 57060436, 912971099, 1104871, 688263907, 769198324, 739575598, 532631463, 277667949, 488947190, 810198691, 112549138, 179305582, 607773893, 579013424, 631392285, 308428974, 389438297, 591531061, 180081068, 520212290, 92817517, 984792271, 12197746, 133241620, 695914295, 815965749, 112737698, 860534153, 788005873, 868408275, 54048520, 324533105, 629384182, 11898576, 392656807, 304838938, 413892374, 605813142, 312625830, 879283147, 192493615, 636534893, 463717629, 645643993, 830319623, 907497711, 823984702, 86873495, 920329741, 491053552, 423509659, 557383937, 778140718, 991559738, 646331066, 642645796, 886317432, 601782135, 363069773, 633534588, 680004349, 5506516, 352975882, 248267268, 834087074, 5575808, 427613276, 221977159, 957545479, 440878596, 954122460, 566713065, 38054480, 807511120, 782891013, 118534672, 990036140, 756153848, 924333944, 831527806, 61823242, 506972240, 613113528, 952310587, 556625734, 683356635, 696578339, 308493989, 228232333, 254453124, 84225461, 516290794, 618679557, 63691765, 82224094, 189056772, 651814557, 310067314, 411763322, 313912349, 771320262, 585579114, 835544241, 566485107, 199009778, 811706051, 49495028, 770981261, 937563672, 126680902, 307838732, 735950129, 147051542, 783045385, 425661477, 809741678, 332129043, 916678174, 916297229, 41482767, 773422713, 509037150, 162414232, 859539910, 382275890, 768158897, 851882864, 572779052, 707660612, 759552950, 859138674, 744382295, 598537750, 463579059, 928534585, 927950208, 27660847, 393383234, 969474592, 847359283, 88414963, 78209647, 309163297, 209855851, 475442276, 918685620, 16036468, 908610682, 793486974, 220496231, 876286281, 827700253, 338635890, 597355864, 478125313, 566259565, 115026999, 152905599, 303008714, 684090569, 743078996, 365804458, 737716842, 581805374, 626757933, 987982263, 827845161, 670029535, 498692509, 370595370, 487234609, 269344736, 43501911, 354128066, 995753311, 925192574, 473304733, 475029048, 917514567, 545020447, 182588338, 316642599, 540035951, 710961242, 742498418, 200711020, 482141596, 528466631, 164571917, 364449942, 638092211, 928867457, 678394005, 117255268, 543985032, 21121661, 644159109, 690671240, 514290553, 751875578, 775725131, 968972849, 410235833, 735133656, 715008253, 364031466, 207104415, 151283030, 23444391, 216083821, 73608470, 467491573, 420886604, 50701033, 831624965, 901547242, 306395377, 920532100, 512930979, 584219632, 262671541, 816160110, 500472581, 359917036, 85225092, 37667080, 874009806, 333750265, 474803208, 939582417, 490443030, 645950492, 283156254, 333587925, 256037181, 926248492, 468107860, 989910206, 434995802, 766214484, 370383737, 785508012, 409728347, 608335758, 510392824, 920361764, 969876396, 636914114, 95252305, 100191734, 36173505, 27805966, 834499176, 660561955, 312717301, 601214298, 48976578, 472893250, 854365496, 687013775, 773108756, 524092691, 983822957, 563185784, 733135463, 169468789, 214071123, 152554683, 467244838, 22667157, 361612776, 242948948, 252024594, 264733615, 278320296, 966951663, 731039245, 197132228, 205967878, 396124526, 572104711, 194711647, 770982717, 649778360, 478972332, 485678989, 126031989, 747808032, 102685464, 897423638, 654318373, 713286421, 42805601, 261475668, 940193704, 608088613, 274559573, 880583996, 877527645, 30940592, 893336236, 369814210, 683937337, 769666312, 955283060, 63840162, 462408574, 843128182, 161046360, 698061185, 980141729, 528676729, 919743605, 891850484, 644700472, 976350749, 96713437, 278410059, 725487639, 872786715, 541185537, 272754980, 677276423, 818277073, 630709988, 552477150, 587882654, 59769224, 176952810, 84975297, 410928016, 892029106, 737940824, 67810171, 195073261, 195157966, 699229991, 936830384, 180098283, 692177846, 985614429, 132708799, 47802949, 849189905, 396463653, 724340207, 603195581, 882855528, 256420034, 907230641, 114614650, 865378449, 54887380, 380315265, 295423966, 594675328, 942021674, 719211937, 282157453, 929531439, 263721499, 226350975, 130912517, 361019368, 536655775, 634210679, 956542764, 395242952, 381757080, 896676803, 803874536, 39789419, 534445837, 649318209, 934512768, 866084407, 141057543, 89557182, 204571306, 792224623, 110354180, 837562932, 781192414, 759660174, 172855296, 138540970, 143289602, 940477484, 867244995, 319323162, 16774888, 59612102, 807984357, 373157449, 983604742, 942405255, 370545574, 265235934, 274414353, 645346254, 856009522, 394825362, 66481913, 222543930, 786061006, 542800434, 346806501, 189450334, 826953360, 347159917, 518762996, 836791944, 998740850, 712499532, 315831163, 757727979, 723627023, 387537087, 405816256, 577825543, 69360811, 61929574, 620518498, 786880442, 843535719, 215843910, 897220267, 511761079, 956738162, 912015716, 122989910, 628348925, 293239366, 202666848, 347050567, 686699606, 384236781, 345352557, 819954936, 216552392, 531106131, 249911840, 555205344, 366954680, 819926029, 622726900, 185122681, 441409960, 971546689, 758698717, 209327028, 277196068, 651920682, 852911804, 851535604, 253828078, 784488503, 813762030, 774332440, 367309249, 152868437, 75282501, 164225170, 672823555, 1230038, 267859240, 158682053, 252715353, 911371111, 922560963, 450537084, 319324917, 703164389, 487141598, 827642598, 614296453, 193382142, 740785872, 168669451, 215317641, 553899248, 442078367, 843495411, 991934280, 500692530, 582647689, 932908371, 603150283, 475490546, 863569191, 139042763, 631362140, 773855432, 9150349, 129297103, 566197830, 153907030, 932373923, 906364255, 888814144, 426871596, 68518236, 237186696, 851825653, 156323578, 691105797, 822812352, 564102818, 216579488, 834504136, 800457605, 498649279, 563118693, 325257047, 27007110, 446704535, 519911842, 101115933, 481204166, 343590592, 543798202, 459546572, 236313195, 98056285, 548627976, 53277049, 718833042, 394320418, 765983229, 616782805, 793202281, 972154404, 313073578, 602423570, 539068897, 525574887, 870524230, 571749019, 172333482, 231328568, 145138809, 177214316, 322689601, 291869508, 676869190, 358501339, 96898989, 157525579, 981044687, 561850784, 963306212, 241399009, 764667128, 389517295, 967327681, 783301124, 180762432, 159116051, 53140745, 873628167, 704300289, 907604399, 403961346, 389835228, 498822546, 40954945, 200880142, 33479471, 294838480, 710211435, 100342333, 602333477, 455056551, 781881911, 308254759, 508430053, 5811619, 645688052, 723960366, 189715197, 318809790, 778488277, 670258603, 31951275, 927419314, 533290433, 321403497, 523285899, 52449590, 966096408, 177759055, 865018282, 81622668, 53304684, 779766787, 708840784, 953969764, 876506150, 516318203, 650674743, 700953952, 88103930, 957683302, 419298108, 830577308, 975580626, 827142080, 320387144, 526836597, 29675036, 638043948, 876121399, 537475455, 838568518, 75527340, 526262929, 896382073, 323725624, 466350507, 780919481, 430973228, 663369859, 553516764, 530961408, 277393522, 385454956, 222951035, 897813165, 665881060, 714712819, 950662016, 988133715, 175817449, 67193695, 376682613, 43277371, 657764447, 903101183, 343298758, 962624195, 415635200, 351011256, 723966447, 873769944, 388429630, 13211224, 459591479, 44341284, 126689855, 53775432, 540743190, 618571597, 119466451, 541598416, 99115196, 56357955, 413990134, 47114026, 937861216, 309558882, 577017282, 889544058, 741327943, 687227320, 650325684, 680958775, 759428777, 332205975, 78157991, 666818073, 582620429, 356943533, 411443297, 432838758, 816701474, 820291493, 847076025, 340500498, 91072411, 835370134, 512167732, 93246501, 358154151, 463171905, 401954336, 950885536, 718594046, 590903248, 277825683, 892830411, 390166379, 246405220, 433094069, 148845067, 232825918, 735310337, 432196201, 690821613, 388400107, 304900480, 442482405, 89895880, 977623098, 42632262, 306259543, 156945412, 721975735, 36244449, 626415551, 489809637, 241735711, 967709573, 178526721, 678570076, 73046032, 741033635, 792940510, 859190055, 841603056, 101452188, 383715960, 319715800, 86082595, 729369540, 868398080, 275258298, 20806708, 788471862, 988070579, 904501400, 338957186, 228987994, 863180072, 309462935, 681344246, 52548574, 620255515, 610051515, 229579350, 949618550, 815092042, 15544693, 990598730, 745206334, 768638460, 341951176, 246999699, 697590418, 731754856, 897410496, 783602124, 993543742, 843978476, 77242337, 151664580, 767954544, 265176803, 135080949, 57778153, 15989824, 289866931, 763187548, 218544593, 368851616, 490372082, 556536560, 659385009, 644648856, 624934009, 852920475, 178585496, 93269012, 792279158, 626340418, 551593359, 828850068, 222906042, 90202078, 356581464, 823941997, 340442656, 962443689, 306595059, 938400478, 492371426, 646455238, 377297038, 594095724, 109499173, 824210190, 43538918, 963847913, 435756906, 317075841, 431717018, 545368972, 289110758, 121606890, 230597099, 615996798, 634782985, 296357464, 247311045, 150859256, 556781281, 501871284, 800756672, 225363557, 896298536, 916710734, 810603388, 225785540, 217332984, 206577415, 688636890, 197320106, 936177002, 489409898, 624688510, 15647597, 88954419, 412171864, 50788299, 781072320, 340716411, 42999228, 190020789, 100972794, 432571848, 679114552, 603703787, 302924522, 332843169, 644145079, 560866840, 972035087, 858543619, 936276974, 929923683, 725480141, 473141804, 972352876, 154679073, 281581319, 686767561, 177096450, 221606952, 482362079, 462058513, 145474512, 857278040, 187410810, 764104147, 399195264, 659198386, 937506584, 917357643, 323730959, 300884011, 866312733, 59161809, 588259172, 274069139, 255213666, 582434311, 794716601, 376594002, 700150452, 812245969, 472467418, 238748949, 289571551, 797979105, 90676458, 922872360, 458354469, 153918366, 466901206, 185573410, 720109808, 853347799, 600897957, 120599403, 767167948, 473012115, 758560286, 310257459, 161937632, 127245634, 784637798, 8668123, 629596857, 346645041, 769340481, 161101631, 489576036, 853522805, 718338868, 451929074, 260756934, 518247939, 525530986, 248032360, 659303699, 328496966, 291402796, 854196927, 448073951, 724520338, 837970643, 626030502, 475092838, 531889594, 717769313, 313796626, 64032398, 612360496, 313452720, 336533847, 279346835, 472096512, 209723547, 165099060, 288796504, 963924989, 900188869, 602907121, 13936698, 403960352, 317593859, 316591141, 806742973, 745423713, 802654433, 993442541, 546609605, 193435676, 602596315, 635340616, 67957998, 480932293, 818607463, 412768728, 223145945, 144487039, 387282628, 833313625, 97252252, 707135113, 780621754, 30927757, 855372443, 965059448, 415807168, 755798169, 838249432, 199066597, 545386750, 905468221, 844429459, 147588490, 432917297, 401383514, 729378535, 610922360, 246774922, 540541383, 203352131, 78353121, 767430862, 902524987, 477063845, 838043718, 906869364, 152354697, 493099362, 127743859, 544889534, 693951180, 524113252, 16175367, 302078648, 948431688, 740840648, 920866508, 915245961, 98793287, 606943341, 712694501, 427104626, 663725009, 460043604, 805269167, 804683304, 87338534, 539643585, 440225615, 484916745, 337761147, 621600906, 547105259, 523074099, 844047046, 314783860, 289374155, 778508458, 538209616, 388854342, 342280142, 123186818, 759325582, 160844114, 124321021, 775467813, 808122631, 273677482, 518086767, 990466808, 496801143, 754694823, 974740016, 885653911, 578336499, 654342763, 644257834, 655163207, 401621333, 176021798, 287926135, 43204708, 831423388, 321357599, 143685336, 134204116, 236698490, 668535058, 369570131, 436149821, 329419385, 540431909, 243946530, 810433653, 143248083, 709237482, 128323008, 275571363, 835131299, 431633455, 3137859, 434789999, 526274777, 305083313, 179386838, 806655088, 389673255, 149659963, 155835821, 107441218, 882276540, 54952432, 846956364, 501596261, 213629046, 838734053, 931539474, 81321963, 742889824, 401903147, 354305799, 604073447, 291506371, 232742838, 183490737, 591568244, 975373824, 344935720, 649512796, 915607973, 199640661, 637585586, 256401026, 868336324, 696870181, 313834403, 194576840, 372391102, 56547008, 559313365, 73217677, 568692122, 2737266, 399757504, 426127294, 613535367, 518268268, 851191055, 856352722, 928902439, 132977089, 734024529, 185110733, 115191042, 391229883, 900796327, 848922482, 360840917, 444861647, 152573478, 657920186, 480909196, 419994257, 985967052, 493396870, 543167596, 404058236, 610003986, 689301469, 956190190, 3642622, 322806197, 632511215, 984662546, 739950445, 108944566, 398244127, 65370022, 455851812, 696124046, 276407443, 540438809, 870275117, 321188772, 954332780, 993193066, 654465384, 507366353, 264459737, 763856328, 978147303, 637992358, 71127048, 845497107, 78207973, 63046799, 925882285, 4678668, 249983234, 766543285, 967521086, 324393253, 458584729, 139191645, 229830864, 699518186, 108051555, 503749896, 171193052, 570336694, 848971477, 590789341, 164655376, 274264200, 411327140, 748563986, 859007589, 737746812, 293856511, 521586832, 108237995, 485790990, 485020165, 788008671, 494001489, 323595632, 973256087, 768385986, 596104068, 317427254, 910436217, 424723997, 830212616, 480918870, 970926712, 160933902, 642444783, 110918310, 797368988, 44893382, 207597971, 835605505, 608645587, 945869577, 894817945, 153569903, 228862572, 602188290, 750639212, 547110227, 268501203, 506082177, 477409251, 763523760, 240418075, 956728620, 59558283, 943872697, 480843629, 592139544, 284917784, 523911111, 702010549, 336778047, 221783608, 72742646, 166667857, 325639320, 995350168, 894633936, 349629171, 257170309, 476727980, 12387856, 946814259, 531660713, 499214500, 136626082, 616992215, 295496237, 726388216, 555249273, 64982015, 346466020, 415262015, 594299419, 178516571, 623585953, 113982326, 840622394, 833536949, 272136155, 813797179, 499936856, 760042666, 307721873, 60810073, 894985141, 106370919, 54447832, 882944523, 194613383, 820374978, 484794694, 375195469, 737743548, 737001698, 133788582, 65202996, 586717815, 717281852, 437187949, 142421237, 64276113, 646156054, 898318102, 200292977, 154615367, 723728563, 265624535, 420202858, 278049583, 272752942, 796041896, 441014103, 297732232, 539720736, 300425584, 53309009, 711490559, 640327592, 244413655, 375655484, 476701381, 567254973, 408757339, 810428487, 265126937, 124486577, 901884481, 232814226, 638133154, 942757132, 910805816, 293361528, 616013719, 139945919, 562186919, 266744048, 653630512, 56851206, 60951514, 676913292, 565865689, 724660163, 141868000, 149146142, 277840828, 508009037, 808531970, 511304672, 103609052, 709515171, 513528138, 83045695, 816914904, 686111342, 448476860, 874642883, 125084247, 464592964, 563092022, 638999481, 1604651, 505929596, 462580833, 167097441, 69912596, 4997298, 727560348, 882106167, 630735045, 697050309, 868899940, 895984747, 737782465, 73821733, 499757138, 290822470, 831392938, 374740277, 454200764, 379740965, 197165590, 792792255, 630486528, 121254878, 890423016, 47664943, 919643171, 725812658, 705042144, 199915761, 330011065, 118291944, 8464491, 184061835, 466566699, 772108671, 254161855, 986055577, 59417387, 829626253, 263991003, 556163962, 572103513, 935121868, 822714470, 268921629, 49947668, 288497195, 736012263, 477669661, 318533621, 276740459, 340309788, 89582039, 685085237, 908705857, 661282170, 387404597, 221894240, 517162683, 837768779, 873538714, 126555284, 186046551, 392409127, 265289305, 133280389, 395806360, 239296596, 670579742, 690567807, 938409901, 785568990, 916114038, 965536741, 94218658, 966299964, 569994716, 34062965, 724460403, 169953664, 874333688, 720515895, 968194896, 568886977, 572680516, 778675080, 427658786, 698323601, 296533918, 678327308, 18183408, 622714840, 708675916, 124724639, 26013723, 107835341, 747583869, 409143626, 342494344, 106143205, 420382749, 549748743, 391107215, 756388941, 405364195, 28835429, 520347455, 106225697, 717580298, 608969066, 685648214, 379733475, 72809735, 560468763, 725779892, 784558702, 44678500, 197107108, 53372176, 289385492, 798377626, 524649099, 219438706, 385443054, 182601337, 602299447, 732655657, 306359239, 520585293, 374743128, 492169519, 320460134, 39853754, 724861117, 850435464, 349803196, 659613652, 323741517, 466301597, 237336818, 238439606, 129736117, 576854922, 429519199, 282410270, 908529486, 804482055, 38545303, 398854293, 156775062, 899356288, 974540524, 773860217, 822920637, 311416041, 53670501, 661247680, 970181506, 363470261, 555970489, 573115249, 625958653, 143439888, 113401391, 924234445, 905450553, 110149582, 809524990, 672343712, 139933652, 822394195, 624160781, 726770014, 859362478, 663147276, 656523406, 791360051, 799897721, 547201576, 468161953, 607085981, 895046444, 302270533, 659943919, 17209080, 21556307, 108615266, 925960068, 565325203, 578323636, 776226738, 955186673, 814749619, 374372813, 678872330, 869185848, 454756168, 196569508, 133625416, 490911059, 65783430, 140148074, 129159592, 349375243, 267752960, 55340532, 889073931, 87034383, 45651745, 625289635, 466955304, 763985607, 986665356, 673485980, 689424590, 781149041, 893601578, 749049857, 34906576, 537310413, 863136218, 351623714, 518388743, 642915804, 187604080, 655306030, 34401087, 712128353, 456199668, 517255924, 259178711, 393213645, 856824142, 675189376, 389336567, 429243499, 28538754, 834526290, 219988220, 565621489, 41093376, 166833757, 884704084, 91668076, 874839814, 210621794, 394398552, 202510634, 362685312, 426866008, 983253801, 709882798, 478768536, 72429126, 904484467, 218297951, 932147194, 926371645, 698649517, 516491235, 433641877, 575610104, 980407389, 772104505, 275291366, 454114999, 596343783, 993337401, 257481715, 279568177, 555193064, 496446775, 965795534, 472159185, 805411717, 251218896, 266289913, 898153140, 51098938, 181774214, 663612009, 803357422, 61386084, 473527014, 441499200, 204268996, 807133992, 937491280, 677280175, 406642783, 688249301, 145041661, 390205972, 323217351, 5683955, 952910262, 19173734, 419701617, 211611007, 29157460, 121445978, 165232685, 303846859, 209737183, 399600244, 566869275, 141780625, 971621914, 637419163, 257021914, 553655128, 762148360, 853509109, 760239517, 502525775, 74553975, 256858597, 228098535, 365679000, 785057392, 166256966, 359233879, 616195367, 289326620, 317711453, 321996748, 862175827, 625383592, 545569629, 15265270, 501101900, 351606395, 646164806, 516831147, 717488829, 416391755, 815129147, 129336572, 821815164, 905857882, 707609803, 867827931, 313383788, 654420384, 924716155, 398344460, 678281353, 158968085, 796802696, 615361994, 944047102, 869485166, 60206883, 863060697, 932757645, 867565160, 525604193, 85111453, 448938334, 845492308, 77029377, 892082827, 397902651, 972251226, 264402825, 608288274, 98398775, 107999466, 789249385, 309571143, 900860098, 899141196, 960237839, 785652432, 329298408, 133678965, 650559859, 501847323, 87417761, 687794779, 629578563, 593081041, 470041647, 90149650, 695279105, 167220859, 196772578, 526868627, 942180086, 134184662, 534771371, 584609548, 331671810, 155531698, 526757271, 124528000, 770101855, 895034066, 802836077, 653594644, 842656023, 216933808, 473399149, 711137627, 274345806, 418116899, 524128545, 646151240, 592560789, 455104440, 988051643, 98874901, 131914701, 858819964, 145799073, 20390206, 475800034, 330006626, 134777736, 472523623, 600914378, 640324194, 858512908, 849822636, 707098436, 853173090, 121172499, 444046809, 475972539, 118177489, 471994107, 365784627, 265775086, 378303572, 901537796, 347699826, 381250215, 365866987, 616876152, 777310963, 934674119, 357834862, 592381117, 694068432, 425026471, 401498119, 844587669, 760516052, 925100821, 862693117, 658160578, 818470484, 125285488, 935180932, 856763958, 764429253, 485569780, 158735656, 298914389, 658033282, 732580675, 639580599, 285619929, 392673711, 90322037, 352500613, 521927483, 539738653, 849632447, 195912977, 54173428, 52434977, 675905064, 621519044, 128459147, 611280970, 407582628, 281563564, 309103660, 674923491, 738661350, 98763403, 644486043, 111177412, 535748213, 178456688, 334729141, 580832295, 361696526, 775897311, 282826454, 607639408, 233962153, 934543400, 447928999, 833543139, 867339160, 562509032, 497006601, 32559108, 762732268, 74440003, 939857152, 690786118, 731993577, 921985686, 881964558, 122048537, 406030698, 948014362, 112268705, 190526896, 262200095, 294800186, 726157902, 319249110, 810780000, 765409479, 426239531, 552359108, 700599379, 343819520, 190208432, 434567719, 328256646, 180594051, 563977496, 264969663, 428831206, 339390138, 185258299, 865190447, 748465807, 175758169, 4208124, 571232647, 540071776, 705349153, 515490195, 291425848, 759811872, 805520169, 493435797, 625494037, 190043939, 642781455, 391454352, 321498528, 596404515, 505591801, 414719889, 996857182, 385373404, 851526354, 381383298, 902650377, 839468396, 817831703, 19225801, 342189827, 467571944, 678393881, 8089954, 378499423, 66931307, 289408823, 565824511, 856922752, 564502260, 434733800, 187974016, 589759936, 535576049, 156053778, 650825977, 56133681, 634341837, 329290433, 966696303, 866176738, 453048789, 339707191, 541734643, 870812987, 638765446, 320944527, 615917643, 340078461, 478570720, 395200919, 430015327, 453772585, 695343644, 534056246, 30139103, 998419430, 233963916, 408256648, 368361664, 146943775, 679491927, 78629167, 393494578, 130752009, 516661090, 829902129, 394428886, 594114454, 379200056, 227996907, 866619560, 27906234, 222949521, 968061653, 445357554, 705094656, 377553605, 177948902, 697148936, 156206524, 958107913, 416341105, 974689348, 342798747, 418462084, 453948740, 862345476, 894818500, 971480855, 417621650, 506634457, 726944297, 388877853, 810162300, 336214657, 493018432, 308344303, 16061014, 689059342, 462125030, 585951832, 711686869, 909325161, 285580765, 564180682, 159381871, 397019529, 125033427, 178588897, 143270112, 906366991, 337934824, 302704339, 56503692, 682998706, 232504277, 595875997, 228253611, 71060060, 882333542, 357020849, 411673236, 585237163, 871575538, 534862278, 453716660, 106127189, 923955529, 336429848, 295307992, 790730845, 389505660, 930702314, 836584897, 676593267, 465328217, 333436537, 269357935, 39406558, 290770561, 510526453, 469736187, 919767265, 245808562, 567398551, 476840645, 944035018, 626284867, 270196613, 834665413, 775684170, 695061807, 13229780, 399799742, 314608800, 975002722, 212359963, 537516905, 371332671, 50733022, 955211182, 321919922, 567289030, 795931381, 681171524, 110660639, 577085483, 689323073, 887177188, 392919460, 195347049, 75730065, 575308590, 763450446, 708991810, 10719628, 841486588, 920223454, 723076547, 780696049, 747206469, 235399312, 403455139, 975567058, 998634929, 285668112, 528508814, 189506557, 756663447, 474524705, 308567062, 726522021, 725020614, 262258687, 747496013, 313209184, 279765632, 870981776, 491522212, 965961267, 443138652, 247215150, 103039056, 291753265, 526969030, 284771233, 542025393, 715861943, 686531003, 229106415, 17306320, 775333142, 303173853, 408347462, 617151027, 658889792, 642987575, 99759956, 453639086, 208935770, 834317565, 251328452, 62088662, 214311744, 252693214, 796753593, 603158273, 795910626, 381866713, 875049915, 299855583, 26796427, 995261413, 977948826, 85347387, 50693364, 723314368, 169705513, 78518769, 338004922, 461357498, 525434776, 301919126, 213309618, 669393286, 860443166, 714973382, 303089605, 210978771, 661869884, 793447178, 753865983, 610363200, 296599351, 365509569, 944793031, 902485884, 208889832, 957564080, 561273570, 549266265, 787643738, 193130431, 699632743, 581522860, 841095037, 511305421, 188239334, 485458510, 829780300, 206038873, 94972523, 733620101, 931989605, 456947955, 22141720, 449206925, 189778031, 445131687, 494639334, 194733433, 617890442, 646842365, 912301828, 594173740, 117873108, 788251814, 910025252, 356230451, 105127475, 541846892, 277955727, 204421231, 666653071, 58086921, 945701463, 982302812, 300391042, 131182463, 118322914, 427747055, 201233722, 813626283, 160125414, 283682284, 655219220, 576413111, 46915687, 871708661, 239185973, 265808326, 191419749, 246805811, 913219225, 592862050, 447413946, 293599766, 702752882, 891428800, 722934609, 587872700, 886958603, 599203313, 663383933, 813062860, 105743090, 794669998, 517796660, 896201981, 191392234, 675817205, 311710795, 442360593, 193719911, 820254291, 203226041, 572094859, 288894377, 902784100, 884322249, 178325640, 54440734, 793723255, 845076001, 398349722, 512832904, 141390358, 305682791, 840087697, 830512874, 894191021, 201764948, 841049275, 679505429, 424893202, 981061035, 830628823, 838888126, 18331805, 842405636, 330998004, 469729597, 240777782, 184195169, 938499026, 592202073, 887556894, 787408350, 516696606, 321641263, 996341223, 417034105, 673173549, 63561355, 225321493, 89143979, 757598142, 411181452, 142904570, 260155785, 512411045, 49799876, 1476666, 994866743, 148629251, 328341302, 222308253, 263875691, 182464477, 908466702, 636232771, 775862025, 274823873, 806845316, 969383372, 261457522, 156449515, 757475300, 184319976, 944841740, 137305048, 610271382, 46681366, 170802223, 111678616, 370272733, 8368336, 950163906, 547420321, 636624270, 126758613, 892760073, 635170383, 530963466, 199814110, 379281415, 78765178, 324001909, 505043921, 93425771, 510834232, 143800369, 987117703, 431046710, 850913935, 174378698, 323625660, 399319005, 826410753, 154545983, 225052182, 510148024, 404186794, 186700667, 152542711, 23699799, 709910676, 863669688, 462735961, 614203064, 713291034, 830499772, 339149652, 284875556, 308491292, 466545837, 427536830, 798395949, 531302424, 283654336, 121242552, 41643204, 381164628, 204449576, 575821928, 192301967, 608711724, 934836920, 868121146, 129875372, 577522712, 622646982, 58813729, 296635190, 81035425, 254151878, 993587324, 815270728, 77271901, 380157581, 971522559, 484845202, 922284634, 430399751, 798038903, 972003681, 177194969, 643146642, 187059252, 114589680, 518614219, 369259915, 334631095, 531965641, 566659870, 631608090, 743006179, 600544954, 659718275, 769859011, 846880655, 943264530, 515796567, 803104440, 635810146, 159060670, 738678137, 669396473, 197650020, 796899563, 232759414, 488057121, 375357953, 448580537, 752253228, 169513716, 463296522, 352140403, 947011520, 531872899, 959037290, 817345344, 698599503, 721632651, 114081525, 380636937, 65150967, 869082887, 320845218, 29229435, 604028497, 942531185, 975120933, 720989189, 635825996, 707061016, 185200321, 871777234, 563548610, 811952901, 902205133, 417496129, 603487083, 581055799, 189584018, 745850042, 945541349, 893340135, 54182444, 600742066, 333559225, 378958195, 669867962, 874924805, 280227448, 128028953, 986536245, 763394039, 110198855, 427734517, 953107770, 487948989, 550540502, 92862681, 867689131, 251559940, 293048614, 282026084, 360689892, 999286919, 268081865, 287227810, 940148688, 471316912, 181131666, 232666076, 188074824, 454813949, 970740601, 303568794, 467462736, 477031739, 669338548, 966128379, 722811079, 800735784, 6538219, 535275281, 402462427, 247591480, 613588854, 633484693, 201695730, 882920648, 507940102, 875495940, 371507512, 778395105, 836305085, 832167626, 278220477, 692752982, 672886908, 793103394, 202020296, 303006845, 695459619, 483170546, 698673619, 286559263, 893595737, 813777204, 185673457, 933172984, 831655135, 138735033, 448040911, 652666699, 204613170, 5492382, 842922450, 275303003, 544173006, 64418536, 823712873, 500448354, 357209295, 519593904, 375555631, 781686821, 383629858, 710261736, 231158140, 126593220, 568764558, 202364344, 401961048, 905025154, 345591710, 864611387, 130667493, 377945377, 576073452, 502479732, 377757179, 696281921, 817982671, 214163622, 402107446, 761178971, 65994307, 391295278, 666931448, 739356003, 876544992, 511660415, 208828199, 501141668, 343099021, 457946110, 536436818, 685991290, 279625077, 193024461, 227668906, 437952891, 195563297, 354340281, 418472814, 297949839, 709322637, 368239410, 425072301, 747063408, 183438024, 319528034, 305071488, 685874390, 708287361, 333521756, 445411404, 887886868, 757471672, 208439709, 932148833, 990471272, 892360416, 859201856, 69096872, 586640706, 813823847, 556803089, 784218790, 79487678, 352852440, 968842245, 374117984, 285778428, 932715932, 857821119, 845106740, 317941791, 554804816, 374108892, 741475428, 936875819, 61308171, 688188261, 717026960, 330656478, 443454213, 179896350, 522970004, 143124704, 951157748, 500210502, 785977592, 391969017, 340419897, 488926711, 28724308, 558085901, 704932967, 471959853, 56028894, 378345877, 788281975, 811415298, 345291851, 689877618, 560897514, 735353325, 409139438, 370495269, 302898187, 232204811, 437774930, 396148470, 942244096, 10647697, 25565753, 110478724, 86894995, 896214138, 364667500, 400200358, 334172208, 275169438, 509281400, 372962949, 948180805, 834206081, 675390071, 842728472, 518615266, 129823567, 378163107, 704119106, 635934147, 303923299, 892038575, 585825437, 691281593, 639961528, 376179961, 702997435, 835113437, 781887710, 641584406, 632698971, 970676432, 659265827, 549084803, 575666392, 797225740, 12932379, 385842655, 267274603, 880883789, 230338137, 513227115, 324570632, 22218947, 421791298, 974677136, 681905162, 785149434, 551442438, 874460584, 264337014, 723144518, 146299440, 808965511, 754268964, 448555105, 701737974, 166410046, 528856151, 663401605, 103935013, 816478583, 161000152, 222553981, 320993873, 220806676, 453660539, 411447279, 111705795, 204233889, 929810853, 586796753, 352550337, 713594001, 225298581, 10139490, 400498627, 964247425, 425953274, 350077507, 872039229, 597153840, 711354406, 615753269, 671822292, 619482799, 247695605, 954579656, 580806371, 336050476, 674162247, 227988867, 694189603, 969692937, 65699568, 2252853, 495787372, 709000758, 321929569, 562248196, 138031867, 766357780, 299107657, 254513001, 753560646, 387810166, 58647563, 454403831, 583454184, 993957826, 484351279, 729012276, 824480785, 958859210, 296058351, 800997881, 181514233, 422449096, 764720857, 217575730, 956153070, 28881340, 488547202, 124643294, 692153839, 566659565, 306145080, 153887057, 687307998, 164594580, 477999568, 718325532, 625710386, 966928188, 970847329, 762307727, 154611275, 587221436, 949724266, 8034642, 976435744, 736207794, 559103851, 546569843, 512957462, 35125294, 683331008, 17054060, 253160086, 344412146, 162972071, 459310226, 649008887, 109671513, 365167071, 744452107, 635996250, 70698565, 245870117, 425237399, 166235817, 334753954, 650399335, 113402260, 330999614, 409994455, 60161567, 788407317, 300551843, 578253985, 297147924, 33916060, 862186143, 286160439, 362603943, 725249791, 160841872, 147207102, 795761685, 342826869, 221102975, 774477722, 738484014, 290102242, 852279608, 619709733, 781661300, 891450446, 100538881, 362554822, 707244154, 392108875, 779511426, 533960079, 911735270, 829472093, 434745693, 282441396, 803863267, 914367555, 916918019, 810891723, 697523243, 589774057, 463010228, 662701636, 618880387, 807690646, 284327105, 525676001, 228130393, 417768587, 413963185, 69745103, 9059251, 906708345, 965048229, 323571389, 98520415, 449088234, 82754549, 791308737, 518523435, 849599974, 670938269, 396818745, 186942677, 119848070, 309464255, 941796416, 334888484, 683442591, 815876166, 445722969, 84114950, 250346948, 613319340, 668298709, 432076958, 570116792, 25832953, 132508509, 957726849, 114179669, 124834221, 323348368, 745663429, 106048038, 948781195, 721580145, 34475102, 274065723, 468036484, 143572659, 528469374, 737262227, 77265938, 381585550, 330425918, 348099133, 507673072, 973273373, 217828574, 507938442, 232078079, 537604600, 877839647, 131963796, 84042627, 98155903, 20311724, 310740088, 520008671, 745446088, 147611840, 89691120, 273029009, 57190843, 665067058, 222778708, 41475109, 694574024, 73031119, 160364593, 585912843, 980504727, 829703109, 237193717, 176006782, 238457798, 322125968, 703119909, 923650724, 343607399, 281995439, 143551721, 301404160, 262202505, 15384442, 559127777, 515148167, 165714895, 541567525, 544839256, 800815474, 109559114, 981516955, 961329928, 626823592, 963282452, 102571986, 11314559, 110111081, 405311188, 944276432, 602571993, 23910740, 375404658, 550708696, 693093481, 500011428, 887210255, 710224558, 251281437, 528965060, 175082312, 606132787, 164565941, 847761205, 366002822, 490735822, 857324918, 905990016, 477652478, 898554901, 245539280, 30848145, 514302620, 561164019, 468295002, 988303116, 151073026, 670437955, 259571115, 329028545, 544060074, 547391933, 630992424, 531946311, 255161267, 180644911, 370909004, 29341887, 573803485, 519010539, 295540832, 280646936, 149821373, 914046176, 260356395, 699390923, 908612199, 533480458, 801416213, 534920723, 617760277, 994137969, 611916252, 837743202, 278608785, 965301743, 48904701, 338077251, 770049560, 543068055, 49669207, 368302486, 397721554, 548434632, 82338129, 600214852, 991835163, 135182554, 101192785, 14014828, 624483249, 310765441, 474337863, 978883766, 253639946, 864335034, 235069084, 368636636, 716798195, 39156798, 320793416, 611251447, 316032650, 7130102, 300856115, 46279372, 883034483, 594781542, 935440520, 423686957, 905339038, 886657553, 684633069, 118880604, 595284124, 910040201, 423307681, 526685487, 866888987, 57074295, 530580289, 611026943, 258495475, 580423720, 291288393, 588628242, 909317452, 995215212, 395902669, 563569951, 26761099, 280659543, 931522481, 901962795, 955005642, 815723720, 143641825, 678577890, 359251907, 302704454, 391561699, 60681641, 693082780, 586287515, 220726170, 899304232, 289553322, 663983918, 27685868, 653419298, 782582101, 744272766, 19635059, 377698221, 667046423, 207530994, 256406816, 584845772, 426721923, 870423527, 731269565, 142385478, 65779618, 632432141, 126628645, 733430348, 421080328, 162777713, 224423935, 854118413, 851006775, 580775646, 669734884, 280980953, 409783892, 638422313, 441786740, 784039573, 58069166, 125676850, 580457137, 645114191, 795467221, 706852691, 100786592, 341259730, 43268139, 911492125, 130792895, 365593254, 107622249, 988603461, 970872759, 164452233, 887862579, 250239331, 948923265, 266427561, 874894003, 510444782, 358493179, 253436816, 713755474, 823490420, 546650972, 721319761, 433923983, 897577249, 410786046, 825512080, 844459763, 645374554, 755087901, 243172940, 770288934, 98165890, 374072082, 194541093, 347940045, 586952710, 419038556, 643003824, 193800277, 72466930, 508552018, 603220286, 157535158, 552293035, 172169610, 691861294, 905921022, 452886303, 905810889, 621421988, 702643356, 810703539, 11133350, 577342151, 556176130, 980341297, 386172827, 111246281, 262392072, 868403856, 782482396, 3467838, 920572010, 153361944, 304645340, 620641745, 609398557, 231006511, 904045233, 963838675, 197657485, 684115649, 184811774, 296241028, 880501664, 56017053, 178859235, 270370935, 688613243, 227135026, 153644466, 417885829, 746950843, 223498963, 32114526, 329267263, 414031028, 346332871, 266862266, 170220008, 264519711, 636873935, 11515019, 108727573, 252802724, 546550234, 463674314, 172665547, 168190286, 862225356, 195668778, 205187942, 877030858, 884769379, 209553628, 99565018, 90648192, 914297919, 72528992, 515907805, 829025189, 708635890, 214902408, 425019109, 954467259, 673371408, 548447487, 944011904, 282006531, 566780799, 450814771, 976818080, 913010549, 856084411, 629375842, 31682771, 475815743, 930296473, 687960129, 939434943, 620140297, 875309581, 982120626, 255543126, 988282284, 942543795, 267024169, 855292577, 710484688, 244211173, 914168318, 870354168, 572805983, 769091269, 936289798, 867755346, 242963298, 48015979, 314032374, 288712527, 8772496, 715575711, 646945697, 30337776, 775495373, 592609705, 775698866, 376549734, 234003878, 893499151, 372322537, 918870272, 316026637, 872631706, 107099967, 913431542, 464802120, 810236239, 671018349, 683081682, 310692753, 913751810, 82225631, 643156396, 471665254, 663491845, 801683807, 932536522, 463542768, 396591441, 809153293, 20834393, 981260314, 70529453, 194576461, 957892011, 584885485, 949666977, 905318178, 543514681, 650897979, 323448479, 808239907, 848570589, 238288063, 892757728, 973034666, 604996624, 97120201, 583514810, 754274399, 828955604, 864783221, 129123079, 590726133, 130888609, 246388007, 650934054, 60062697, 501338146, 515140471, 999015735, 256367050, 274804401, 83201365, 898147489, 66030660, 74284137, 738562070, 789553750, 674455462, 831251208, 891282104, 79025032, 378306933, 213540441, 740533254, 911765594, 492368782, 929111631, 510499613, 143527902, 570464019, 717212691, 573046495, 98850349, 987492413, 992445564, 342614270, 183126416, 222607152, 754811096, 480955889, 697471808, 912246212, 11358519, 511830582, 906240906, 653997785, 969498193, 708784275, 1651451, 858556920, 238833359, 17259473, 514346741, 506251626, 2188553, 784470056, 217146060, 960204138, 707383855, 185008040, 248967091, 603177148, 961277005, 905390584, 331413289, 953946404, 634977100, 165863932, 718554492, 639118345, 722426255, 726537626, 768650038, 889341836, 877401726, 741061050, 363143289, 845604572, 371774784, 312511153, 441309941, 931195920, 121433030, 801965913, 405314733, 443130317, 34261251, 223852945, 342408105, 257931072, 433094524, 647982677, 476440951, 55057208, 430976525, 882451366, 501340811, 822104872, 482675131, 883027000, 439511755, 690209557, 107127964, 724545290, 897038130, 358176403, 767526676, 71747807, 784770199, 194243762, 788388144, 353696787, 222080016, 378448368, 5800506, 480395884, 124326046, 566945637, 105744091, 651543864, 300464773, 264328543, 875362243, 325858136, 662884394, 543469348, 486330112, 201790397, 714701905, 17471795, 794207728, 323040827, 496210341, 117029536, 757318886, 66023671, 994320826, 390084569, 7609049, 989047178, 929454549, 632175330, 464054107, 154766676, 997499519, 161555070, 210260232, 223206508, 506745820, 537082467, 86431633, 163532141, 550188887, 389529194, 418073444, 630639760, 968549206, 164894105, 170033973, 585163740, 752475975, 789594420, 287979157, 618525499, 674932629, 102066681, 870649733, 782538308, 181637234, 179576016, 210623619, 32649935, 905909399, 448946110, 475516184, 566229156, 129047283, 865955249, 928124079, 690833298, 424898245, 608124378, 290484402, 182607414, 811018738, 963292778, 461740964, 7859230, 146411337, 509321006, 352905519, 675014422, 301328564, 313777976, 307395658, 907005914, 170194239, 638766391, 226463383, 321971013, 201187180, 347210344, 37527796, 764485871, 707663127, 45401516, 867441868, 64400055, 71530246, 992402597, 446152613, 630355260, 549925579, 154484106, 99500796, 450977719, 403552810, 79047693, 560954874, 205857379, 915657874, 119180669, 993561038, 249742926, 992339459, 846621219, 633973561, 734062714, 548436015, 523816558, 992554138, 302131497, 411142900, 545958423, 979659030, 726054181, 610896919, 673441834, 291364559, 195131810, 253350418, 521248625, 597792024, 123152044, 631474936, 891891481, 945434758, 300129615, 223450977, 983093477, 570077055, 72564173, 295593051, 144280366, 460578104, 137977698, 726482693, 619092339, 343304619, 937869951, 395018238, 242895827, 565703067, 323975133, 731964669, 923642172, 667479858, 970650812, 130042204, 924262522, 786690576, 120440360, 193577670, 285263553, 4110201, 112074810, 47469185, 148231887, 110028303, 983578908, 57161853, 192310071, 67030193, 916291040, 791888272, 686739157, 464083780, 431751653, 858121232, 833430606, 368010856, 432034387, 486928273, 9979131, 913370176, 326324566, 579577877, 545519390, 255038888, 74827808, 161829602, 9314951, 820240265, 362567122, 706277025, 937758995, 190923454, 189937641, 79016800, 968720596, 328961880, 774661832, 262620680, 896929039, 289382886, 29688040, 569172341, 785242981, 606307739, 542468607, 791221312, 807291726, 684787619, 998746266, 656983062, 67353081, 629120156, 864036779, 180212650, 520683136, 356887515, 128357978, 280099242, 988755379, 209258393, 744789886, 660257090, 138293490, 168675196, 284800975, 658341401, 96135158, 752175902, 306751521, 58915572, 997143060, 217076801, 2448239, 527266123, 112640114, 323298518, 471813938, 684238656, 298540332, 982009572, 289216980, 928353871, 258408222, 56266870, 202595244, 649227559, 431120072, 679014346, 807752559, 29346483, 77036141, 306830909, 385040443, 920357732, 566291188, 724345393, 167313070, 611467938, 341473405, 468094232, 624830102, 388534505, 599298976, 651276536, 505472148, 460880069, 199204319, 633328214, 75828092, 881074136, 265864206, 157865931, 679949084, 359335862, 562450371, 728788467, 831273476, 584131340, 629221935, 997873195, 612344691, 979379215, 246499147, 233528746, 236312359, 181181983, 870302610, 671574941, 570423193, 87665262, 795002378, 299318633, 724839544, 383776712, 129183868, 352486786, 46122183, 507485985, 516756764, 7000548, 721729303, 637777772, 198274343, 448303037, 697623750, 617520877, 956114185, 274821449, 638170887, 513329047, 800154160, 321489129, 547366342, 66094603, 603171134, 118976572, 501543320, 519239336, 519949476, 389759501, 680565506, 71491258, 515913005, 939744682, 678363667, 85765388, 872603263, 31137346, 635438863, 763708663, 550609368, 906456289, 839592500, 380843569, 983730127, 455972118, 151699957, 926195631, 108246383, 259797120, 643359549, 790562064, 271961235, 286329088, 747495754, 962290167, 380611818, 744986190, 364431841, 293535259, 107988351, 786314364, 624660049, 314933286, 451229666, 543249365, 989891680, 87749619, 195637914, 342524124, 556908375, 159502901, 764868190, 675217792, 372683282, 82545083, 452198659, 176637684, 447083821, 740133772, 54648884, 822680364, 580592465, 95353830, 112705613, 609523732, 982907184, 646503295, 712687191, 99634123, 309250597, 270422358, 179783274, 134779492, 845346053, 520972613, 419184307, 734390729, 658716005, 455183997, 460891306, 446785684, 123769045, 913561815, 103667072, 621858071, 676389082, 434796738, 139835346, 436839893, 948100919, 308322100, 307508217, 12089416, 220213884, 578842381, 991226707, 54267310, 594467748, 444606975, 376215344, 151254182, 643461801, 971841674, 101941488, 892622833, 377990290, 914369003, 431535676, 996506628, 312058785, 72040559, 909693826, 514117621, 713350649, 498275398, 832697034, 530631655, 800437465, 778690036, 594974040, 889990747, 285292390, 590749338, 119253369, 613280936, 686408118, 540132267, 872670446, 177331931, 901620662, 955814356, 410020975, 176518866, 135758423, 214732260, 670228121, 700256742, 329866914, 207106187, 423624747, 313418751, 154182215, 500482590, 771542710, 919125971, 422635417, 196709384, 285995452, 853481320, 401796190, 51134210, 518625425, 148026359, 523389801, 976293584, 740871752, 694349536, 624325494, 616566279, 837831006, 623098467, 851204649, 768618529, 178185240, 615836825, 873636069, 253375452, 72237237, 396388042, 670106545, 317432856, 655955177, 69250414, 832271956, 302325823, 903116080, 273987363, 895895505, 715034731, 281436620, 785337144, 787673271, 58656481, 835933541, 607683662, 587809516, 477688055, 488679437, 348251650, 981417290, 353833420, 163886192, 478924054, 427516455, 921364245, 387092158, 205306404, 658692135, 944357178, 518112250, 390198569, 880154961, 571564362, 950167718, 266212462, 746360397, 668373321, 422571536, 83905542, 594698478, 630376332, 579041199, 471744519, 959995220, 692195421, 635738904, 650086145, 322160655, 497147022, 986532275, 241795070, 613893198, 827441333, 531461479, 374941697, 798124926, 259386377, 153429168, 10054967, 92710600, 297419678, 189027474, 107227119, 847316279, 661576281, 411383787, 462362931, 500860338, 531886033, 705333395, 428784554, 821464242, 918977553, 239745022, 170523464, 796457479, 342187179, 341832502, 881349889, 944946524, 803669796, 24932496, 779266289, 907809710, 318214068, 552609484, 632049945, 158123505, 48556835, 863713679, 677325563, 134902862, 768168940, 730850613, 411743549, 900187034, 925212202, 898853195, 223778832, 543058841, 242000589, 612684545, 517253273, 204429273, 581796069, 160832072, 239426176, 256150276, 15262852, 937369429, 205756336, 280143624, 844798499, 497131058, 385029232, 671990228, 621169070, 500970852, 909193838, 577578510, 546392818, 79609537, 976530226, 156714390, 287036682, 755810543, 948017972, 155329425, 578274653, 503079257, 598465749, 390086486, 120035795, 605005039, 668686690, 600173688, 821840132, 776094284, 276180434, 465619111, 35126223, 208601329, 618012443, 295149803, 646845649, 930280544, 421182331, 46795126, 869832119, 706342502, 583450787, 115894908, 380145207, 570229621, 443901726, 791089220, 970809137, 621788254, 737158990, 112243429, 351504035, 932390003, 658560783, 822060186, 538006496, 259789626, 44605240, 603020580, 233199772, 369059649, 141541140, 5851112, 624932162, 26503526, 915353171, 395811366, 964362226, 762594398, 497752223, 453892137, 25111977, 571215081, 944886052, 413836522, 879526665, 940322681, 813265247, 374045376, 897850211, 732249503, 769240522, 749592175, 532633692, 753914219, 209892310, 91260031, 655684428, 693140848, 651393476, 1566209, 793624413, 375586535, 890588624, 814740341, 648387963, 615265215, 726158582, 705880264, 948504501, 618468393, 901981709, 266308187, 456364492, 79979372, 221506126, 522772635, 345359365, 571808812, 137778919, 933032842, 451369205, 567148022, 132429850, 305200351, 45119773, 789262650, 811887706, 59988970, 139538378, 518305929, 371909120, 358560701, 368624982, 729607691, 554334200, 65794198, 361089994, 771669160, 330994527, 871957916, 264647721, 724965853, 852248656, 358223517, 944170157, 825990779, 994429328, 420343764, 685105148, 830875786, 336138763, 479204731, 837190993, 153665899, 311452782, 152626736, 919786348, 779018510, 628825334, 986571788, 130166333, 712596195, 747325708, 490522724, 47928992, 623624465, 598211896, 528686234, 231500958, 923120545, 784050979, 830234585, 822144694, 293818966, 865639204, 183254222, 499555269, 790030041, 454615151, 224902305, 498222488, 459156249, 845377085, 535326588, 254234362, 458546732, 707615011, 349950399, 114393151, 528840627, 450330609, 586083518, 586401832, 857206728, 645667725, 606261191, 138229959, 977043812, 560195089, 289741584, 522622044, 569641675, 508919607, 140247980, 465979808, 873508970, 61275921, 192658072, 467740007, 122457980, 266775964, 117983595, 481498709, 714164833, 438822695, 682182001, 764713071, 948842975, 492352963, 748794115, 477037755, 770158787, 431684757, 399056643, 175250387, 653977438, 982251198, 791589256, 597077020, 515466827, 660727360, 744265123, 699762977, 468273214, 717920427, 977811637, 17295544, 485412584, 955653541, 946288627, 638371201, 807382042, 507366852, 712687619, 655921843, 322648008, 834997890, 213187876, 821916460, 881863521, 807020525, 907598365, 337455788, 244875674, 772592640, 600394377, 136355183, 746818967, 450692105, 329243090, 603584826, 655176979, 923907009, 779750167, 233348619, 550077087, 888742577, 710570413, 971871168, 552825474, 811433605, 465182535, 430711008, 269897340, 836298026, 245339883, 44603836, 391534620, 715021260, 264774255, 882207133, 314768854, 22791152, 761870346, 744100789, 220324234, 558226479, 909001131, 641011842, 760646560, 595023385, 187315107, 495406312, 363218327, 570798546, 427887821, 607667856, 594461663, 520707277, 807702400, 334608448, 225124083, 591805076, 904497165, 362256570, 656694368, 549144289, 808446998, 579740458, 53062711, 624038512, 547645870, 775629739, 779293590, 370165279, 785685877, 305892908, 195899848, 207496376, 928611629, 290294943, 507919815, 446687017, 732526913, 101492293, 856296892, 432867262, 576186436, 402446762, 369456373, 599649023, 486939074, 425943566, 332647745, 355500314, 757181475, 443834820, 489908245, 221431986, 798507379, 542523852, 392530986, 345168491, 404116557, 855957849, 216520279, 166768853, 713251959, 968367823, 334970417, 181138906, 143364883, 556797898, 261774212, 285900954, 923177495, 652467067, 843522407, 673338531, 954812393, 144515076, 433168616, 100457434, 197777844, 272038290, 840095777, 320682734, 525003494, 898496675, 270007159, 274388867, 461952967, 361650675, 255532177, 134256907, 554429003, 229809589, 880060062, 249872599, 379827621, 548854579, 438419757, 221227228, 394136675, 45725447, 561403176, 958391041, 393232485, 263068688, 265438366, 424599304, 503391028, 635144936, 586177659, 997659941, 650958807, 497990351, 81434297, 925412142, 545062321, 907924849, 154430608, 780745714, 900796565, 519963662, 997685621, 750988545, 42752783, 158351606, 491278582, 811862031, 231660106, 525501159, 633106361, 966317411, 766855088, 703418146, 817797809, 450042273, 932832885, 180641814, 967396929, 190842170, 648047583, 935754989, 336839009, 390924247, 812349437, 394502469, 4590354, 810932907, 299162387, 833092198, 639278702, 822368606, 488403292, 815117844, 454860739, 280604167, 889416813, 781021574, 366096585, 144968181, 127690879, 247742159, 367541851, 780146041, 358295533, 975573347, 516024447, 738184110, 569745923, 840048428, 788601269, 608645739, 786460501, 488022081, 454273689, 492767455, 275381778, 105532937, 874272580, 286153393, 813885079, 784816436, 263690324, 41871146, 252096507, 184848591, 965632287, 252707786, 508358707, 422991248, 373940210, 996029294, 554793251, 340414391, 538487413, 959854820, 133565312, 228041104, 257374956, 16611568, 758518261, 107570607, 867802392, 484042372, 786445501, 766224458, 848739548, 738236982, 824069126, 254494117, 702139252, 395505084, 714422446, 426312492, 312590708, 646254434, 598576926, 489718779, 775084909, 905021385, 28072072, 950517870, 169600266, 997752584, 920390699, 77686045, 651301282, 421435641, 236030525, 896276504, 71431628, 678964018, 484468426, 383066993, 856156209, 611387296, 42864166, 25060204, 85825254, 144402381, 593481901, 935370886, 684463218, 91279349, 605761403, 336422521, 670376253, 377678962, 193791049, 148614979, 417488555, 983251342, 453578822, 730156029, 470133701, 648939336, 479147392, 184133228, 970292507, 669815791, 221470917, 762312104, 828607037, 657412451, 365116514, 353725436, 604147431, 128366214, 165993139, 439746679, 804147206, 834059720, 128419088, 201144969, 424448588, 491966688, 868701518, 915175243, 350671214, 349819095, 473236039, 749619912, 476193073, 755962005, 837969655, 982355965, 812889892, 342763524, 88253398, 27260136, 93131742, 866658826, 427025948, 139565966, 345495661, 397928768, 293399866, 378266924, 528729131, 562356627, 615920294, 231960720, 314550797, 741983866, 827745351, 437485977, 463465279, 903844759, 477581973, 187739015, 631291254, 42508503, 550991362, 47451744, 750720221, 767783585, 563045360, 878826552, 245797050, 92834700, 552250981, 440548081, 772266562, 3255797, 199146188, 876518239, 185820781, 758852515, 924687034, 420843941, 50454684, 745647987, 699785760, 324579243, 195989932, 298093235, 168344581, 103704176, 772343011, 355193995, 604294703, 230076914, 235800982, 965478310, 781189498, 750493550, 761080425, 131097300, 220717253, 668489519, 411336001, 226669116, 864508661, 227851847, 762290279, 495333557, 638229174, 919351296, 670196457, 33657753, 432650198, 646093454, 537383092, 980022312, 598753929, 734787605, 917155859, 219021243, 980022055, 269067064, 776583118, 149094130, 514138983, 850426542, 307520978, 482757247, 268392174, 607338163, 152555836, 507284326, 285929982, 888131650, 510374479, 674431977, 369987320, 451450027, 763924936, 538138601, 690805388, 849594916, 633589027, 937038176, 491455092, 951357550, 238448445, 540333417, 432015532, 69670641, 803556959, 38362808, 603438852, 788071033, 176860302, 187776501, 787350628, 857400488, 694771492, 788923335, 72943742, 348171704, 6937219, 311275897, 725969901, 864749724, 264886453, 270363310, 934876034, 235148726, 386831867, 483268833, 157130996, 142984839, 457063065, 139184428, 302109889, 367171922, 837761235, 549274047, 224418777, 870267632, 208193490, 488285169, 852447224, 507301052, 45225153, 46224249, 924256500, 994390340, 760161781, 76440546, 153425317, 520081158, 317710456, 919349362, 339854178, 905448642, 459956182, 8973104, 100192450, 620445893, 803087594, 754654562, 360026240, 824563880, 131603969, 540891273, 735193709, 994343257, 227720404, 455788400, 393233979, 23111734, 713284323, 478560671, 8298919, 669166660, 911684983, 849874186, 862180172, 311496400, 817157046, 920424691, 540167601, 198968000, 117019164, 518721132, 366496262, 820836798, 631968815, 342936842, 152775910, 680670466, 972402561, 992846393, 485951075, 194100817, 699579258, 730283090, 302263875, 497279864, 819643733, 645523528, 357054383, 332616724, 709937519, 114910197, 830346743, 863100637, 330511121, 451222411, 796152112, 296632974, 431312315, 802269911, 384048380, 852927576, 961942307, 833151806, 225410087, 86895951, 764776818, 34010383, 219198233, 166920800, 372269005, 833376338, 623873901, 854709870, 371199030, 490419406, 436984047, 435252748, 371782348, 728644992, 719645325, 759496656, 547266030, 242712487, 473725186, 166582119, 306558253, 351736703, 482972289, 745605422, 763649274, 848291010, 134521238, 822918813, 70559577, 169118030, 633838309, 287432670, 801147883, 891175225, 509084210, 73769140, 550755342, 806145346, 658957964, 299641265, 62025854, 564456547, 968813879, 432804960, 308698793, 373925099, 320614906, 500718496, 136853297, 738459928, 542130425, 728820527, 444764726, 948100284, 424857548, 832004192, 350652329, 495702710, 709518584, 232724247, 902059401, 521078473, 421778039, 368752854, 859413162, 305228196, 569612959, 119478576, 440939924, 336556669, 261837223, 454458371, 520640162, 439056500, 112851905, 998294024, 78011366, 453448739, 302871366, 339704222, 108838781, 103878981, 64776946, 148823679, 385969505, 520961502, 182901508, 468065929, 351016973, 314484154, 154941739, 455109765, 760701208, 719822996, 816587809, 43960368, 244146286, 625605355, 101149226, 124858314, 82047885, 26907490, 528419479, 18201173, 430420596, 956358821, 389090998, 789721765, 680171442, 984264344, 209885149, 640332817, 760804843, 584776255, 180409136, 138423134, 325709960, 879311377, 47679525, 894576264, 413399275, 959832635, 863640295, 13820699, 300580016, 659025744, 494867159, 933143916, 822920348, 178813374, 759299732, 789471099, 820190118, 496599515, 528007880, 785784734, 8914162, 43878697, 649902576, 917140509, 461088305, 439717817, 810124900, 116815509, 372137600, 834308431, 612644741, 399525031, 599777196, 129949141, 952217753, 171808098, 158692196, 201484294, 856515821, 898348168, 677072565, 518213247, 593385160, 48129692, 587503115, 108953611, 95818029, 390480872, 381008174, 843611590, 787741708, 146334505, 984488266, 86158400, 700151169, 333340323, 396976975, 308747539, 732319739, 111398730, 113517701, 96868199, 192794002, 882186080, 772600199, 138860098, 833178375, 991318904, 679272344, 645755335, 315277129, 470874546, 340903216, 665276379, 541453974, 936499501, 68492445, 159830857, 555515333, 90352805, 942468123, 649287938, 146679523, 168552478, 549284820, 40581880, 315799543, 636176607, 785469953, 248459588, 991426005, 45281277, 364817769, 782737803, 417670028, 200183740, 960650569, 425180911, 902347648, 918643232, 98165938, 665365073, 830330706, 779459856, 620234398, 621265505, 350332919, 360514942, 393320082, 178205209, 363756069, 681800704, 860836831, 412464790, 907254805, 683436192, 386708006, 81966382, 831895588, 438322346, 771335941, 851195299, 262903444, 362016520, 577700910, 524529851, 395853554, 29581453, 514235576, 916323139, 166069873, 552278366, 104787462, 162558930, 859281432, 558312887, 273555689, 926454675, 35523670, 503009445, 384405345, 313391919, 300935107, 775803617, 199983144, 677375829, 255235157, 437308268, 38992385, 691498147, 393760961, 459290330, 570045263, 512280920, 173091726, 915870991, 107987562, 360034250, 511964762, 520548405, 358290560, 507755374, 787378854, 626460760, 344984838, 323262078, 147694093, 415185826, 955567800, 534524188, 298180166, 619674268, 542017515, 498565332, 912458161, 427589188, 218463444, 772691156, 909025008, 250866499, 980261899, 726950920, 957754135, 998664042, 24038709, 177262083, 904723467, 686634388, 710786294, 945460309, 400081307, 142203517, 120528766, 264439996, 715952108, 236130930, 81412663, 360711334, 616911473, 662901255, 674504723, 173898834, 290178335, 199708283, 66948803, 219407456, 799514441, 790629518, 852009907, 267446458, 201735813, 246692568, 88578940, 521331956, 333072496, 808671993, 775564396, 157066897, 909177288, 126066613, 630024195, 119830083, 143172716, 224276862, 374845680, 993832865, 196328254, 778680365, 100146975, 634478234, 470117916, 923060320, 875662124, 329693426, 396949326, 734130223, 875530075, 270905123, 507985957, 747726108, 258393733, 960250955, 650320393, 900663748, 646155245, 447349909, 338573777, 365496379, 499911870, 655192304, 946619342, 860709321, 888012973, 596901158, 161487796, 155253723, 379866869, 361850807, 470434032, 198435307, 390451624, 742197696, 404274257, 787795677, 217164200, 987882578, 558085540, 813496129, 960070920, 79661137, 992813029, 69551410, 821447401, 255386188, 830832473, 140200704, 933279552, 989816054, 794192466, 929962900, 303037916, 825539962, 388030892, 968769404, 293369937, 50697572, 260294443, 363093927, 79610849, 395494978, 620029582, 10447421, 840208677, 61534920, 688940886, 597338548, 962242671, 829058615, 958565296, 170622305, 237673359, 719011736, 205901300, 458203576, 709980094, 452238074, 982797047, 979381043, 255585552, 941869452, 404232752, 658131405, 72855095, 101559157, 28500704, 491876639, 267160413, 140384823, 550593393, 256089395, 868551562, 681505822, 483686217, 98199660, 677816132, 32656871, 773200316, 558203967, 706463633, 607418347, 767817049, 738161395, 81670994, 885981387, 321859977, 735150361, 811633825, 752686176, 425341719, 335446305, 362976768, 14219295, 242572822, 829850439, 986768223, 739801907, 786741123, 53905209, 492954185, 899575040, 354738683, 400346132, 773910718, 787349171, 987756595, 703241585, 466753437, 810102731, 313891511, 127768627, 963055664, 167532012, 139380704, 210757637, 80275374, 725562526, 158612911, 768673548, 399239777, 296046228, 18733021, 259443899, 951401692, 304578130, 361593173, 968880228, 499478253, 905944420, 641956050, 634436054, 872858913, 756246700, 636891894, 143677994, 507846322, 65983489, 866552315, 911721324, 199578617, 138010139, 895872459, 558060259, 836837413, 382085674, 86137130, 48469849, 175712288, 939144087, 844615659, 527693142, 631501139, 264272292, 103792046, 135559902, 463648554, 1754102, 884054363, 593355846, 864901717, 715092347, 337104853, 231826461, 293325247, 8241697, 717840439, 742059191, 63575367, 869761246, 226848070, 832080329, 377080516, 5642107, 170699949, 650518782, 454357150, 200931146, 213628795, 455060744, 629510578, 510463964, 64326392, 572478373, 526014792, 318866774, 834954897, 582861853, 137587638, 220143913, 514485305, 546627850, 315178293, 779178878, 970060564, 834426878, 170969055, 265144765, 49469628, 621147583, 121717237, 164032844, 716776424, 847118718, 286106460, 476259318, 166963335, 845987665, 905718101, 505234515, 436801819, 991078762, 829358308, 388702699, 358874564, 84569656, 119198226, 751879906, 59425510, 53755153, 96483122, 128874317, 785923040, 197760964, 961812638, 754247836, 423564667, 808920603, 552389783, 171942634, 249773904, 473893618, 566004619, 942065045, 345329399, 289859020, 792461122, 100924548, 396539988, 243521503, 291604159, 475206596, 620423071, 780660364, 699372649, 490130952, 191872937, 893361484, 307439183, 483700259, 433380111, 39630991, 327046384, 134668244, 777618401, 127853473, 731602649, 147770991, 880346335, 867055264, 141750688, 94168423, 159398680, 592365508, 258046208, 758684531, 472764697, 230273351, 46609993, 275451259, 638261768, 986116432, 21861487, 438816689, 327259985, 133899256, 848039307, 186421485, 196239338, 751634526, 510698909, 37997141, 136870089, 87051574, 648901360, 151109939, 702782002, 507566740, 295509734, 354496162, 500413155, 762073381, 350949112, 638445805, 902416976, 61864546, 877818778, 612752543, 221352455, 181868205, 707856918, 571531280, 231020087, 306994965, 953914262, 807668272, 740783552, 358400930, 618031279, 964094800, 200899302, 700871962, 627552883, 349930543, 720427034, 324554368, 737330987, 297177904, 767931131, 601237654, 667706333, 510549261, 901250, 984603966, 266067613, 499232717, 459576860, 228652703, 467892087, 377486701, 446681606, 217619426, 961747451, 77623422, 284499960, 863849290, 148298889, 5766965, 53047027, 582129751, 132435067, 67862006, 732465581, 481681919, 154798153, 836489341, 422258299, 677772155, 144079050, 905270656, 153620695, 381513406, 174006804, 642431609, 645292212, 368577674, 512384516, 592924743, 824877668, 12187023, 76098338, 167973054, 4175822, 765694364, 401845221, 623748023, 743269201, 624096452, 802219001, 980797320, 687389908, 1641175, 257560397, 224005916, 5757118, 421050715, 933578683, 550951237, 383393590, 967667083, 691506177, 76074166, 67972827, 224293580, 601375087, 820123677, 354274896, 130420624, 630332979, 260228986, 92988385, 572937219, 542733311, 490100049, 787891310, 21709148, 344331186, 253880059, 329020633, 625679960, 41394059, 137005743, 199797943, 879681033, 926281704, 365239271, 665174094, 413204795, 308451438, 410401654, 855179034, 116432526, 677993097, 413656998, 669406381, 764908501, 762876935, 125969056, 820408234, 511156870, 120717446, 915674521, 950522694, 168364222, 718341641, 89009193, 254773655, 861948472, 842554878, 407836941, 695684950, 225954080, 990153269, 231036689, 907142842, 880675161, 600738779, 30737639, 64753456, 296121201, 387198333, 364384185, 963338121, 804121042, 465278358, 102120752, 196698776, 755377151, 872418735, 795181554, 29866952, 366687047, 560521084, 681577557, 171320119, 218696537, 299448767, 970597238, 961091948, 348579406, 73560350, 939944829, 962888709, 685500516, 240579040, 672799886, 985694464, 839818862, 512790724, 628299, 806149903, 209611415, 104450300, 161704848, 878899090, 567190449, 984321512, 599268611, 36879775, 508565300, 859736727, 926936074, 498014353, 622438077, 375335333, 53578623, 759585154, 755649259, 449173842, 340263663, 36452316, 535071986, 948580699, 27720542, 619965027, 103937113, 710342102, 346355046, 847927408, 312878937, 461969785, 186734596, 402022606, 144666165, 725038312, 261714105, 179967034, 349956713, 228079307, 767557268, 259058593, 556821401, 726966268, 114097716, 538198586, 539185104, 615348821, 717792358, 623589418, 870679150, 633168651, 877468075, 983908722, 941758621, 218799449, 925929385, 67538920, 578159526, 445969297, 108095976, 474125159, 288017579, 660452066, 35612659, 618080948, 916892000, 601316618, 757720727, 269949934, 68199084, 186037875, 895851576, 982013657, 367298973, 664255233, 651208853, 480910196, 428079022, 69357082, 508419878, 403856734, 275690710, 905575404, 700553418, 554856034, 668454989, 30356231, 86803912, 607840019, 815542939, 622216808, 247119823, 424743733, 681632127, 210910930, 721250991, 902313831, 327607253, 988704284, 404030313, 775774728, 312521766, 127537644, 22812932, 440905526, 772569430, 28732923, 119704297, 240063637, 794937227, 854101791, 853823464, 221833202, 37609028, 461274490, 519538841, 708223574, 318122068, 743248294, 185908539, 117759162, 479098346, 725733145, 960128788, 428545806, 627195637, 602246812, 469444844, 196195829, 876901340, 166910037, 652651280, 784760124, 200664105, 893510456, 46219243, 837640357, 864815689, 609788395, 89677844, 142763953, 898949995, 670882754, 682869166, 381539847, 864954356, 650173316, 423920660, 843663169, 831116037, 746969347, 957639114, 577377652, 152366954, 587236938, 819936316, 434949335, 462683938, 35327949, 456496230, 322261150, 989484498, 153591426, 816615737, 324624638, 490646020, 930775454, 320633695, 27672208, 994828255, 324699394, 264102322, 128762602, 951577337, 741879785, 107538821, 192079047, 136368, 44518687, 372120248, 879797815, 15584384, 933528438, 466698897, 214882618, 862540561, 908963326, 94673093, 273026276, 544194584, 748189688, 658497914, 161565874, 927269561, 622245138, 640379728, 967134458, 77812262, 698434408, 307845102, 242320976, 867276153, 128008212, 976440348, 649432958, 294675452, 95885645, 450962849, 1513466, 477524414, 579289190, 58601743, 296610706, 443191431, 102939821, 133760022, 16174890, 404299584, 65438711, 283963186, 14055203, 261443111, 830279042, 636555881, 522841483, 88213601, 897646669, 246858781, 794830555, 509285475, 876290521, 890146949, 336816781, 192072742, 680339100, 455947903, 970547620, 714586287, 221935623, 445788640, 418663288, 169655716, 86305772, 377732984, 443719075, 513386363, 100178245, 316690852, 812831228, 424395511, 713812552, 344597802, 418083371, 511948109, 345762631, 14045632, 442734880, 535471851, 24471037, 865148236, 126351841, 199289363, 314555202, 37738322, 105601064, 973169994, 816071539, 425725865, 219263197, 23554247, 801170499, 520672802, 766614977, 733565832, 137089103, 922897795, 102788601, 14760328, 37514022, 870270148, 949667867, 75663806, 603997080, 825010353, 372583433, 289857345, 929459501, 248591661, 539723384, 987892953, 152400915, 966164648, 75548906, 97729278, 357740532, 94945706, 603470307, 538252491, 583487202, 869329446, 775440966, 716036780, 904197169, 805506979, 411230000, 927249874, 274623055, 709669351, 864970397, 80025650, 310512220, 691041334, 636028807, 452346486, 378966118, 864501115, 585600286, 866911327, 710195334, 290406890, 149718084, 252629020, 486165459, 978465374, 772182845, 741335579, 510452860, 413260391, 846207585, 431304571, 982355791, 356526620, 614536026, 874974282, 535928387, 50945352, 662803302, 698044481, 935586519, 736529289, 54847429, 403375537, 178622302, 16700161, 465501131, 602055289, 802137624, 418783723, 820512994, 763468433, 695380423, 284195836, 988177919, 712089514, 120711347, 20203365, 885958823, 324996709, 796729946, 941178094, 641919839, 416454155, 64852608, 687779729, 319164378, 692269278, 294318511, 24265579, 745306824, 310643251, 413268661, 380440536, 441088151, 998029552, 810777697, 220051058, 453239696, 939276594, 913826228, 866401893, 562178425, 726502014, 190790, 182907004, 226544348, 709417742, 315196883, 996758676, 604040966, 77003213, 323873716, 160923281, 688797098, 625974536, 533128992, 286817373, 806447309, 674883756, 473859315, 680156199, 955553605, 563873175, 715289405, 741930801, 419956180, 435139337, 692750488, 151598665, 314976398, 939996163, 565804938, 719743437, 114848735, 551376072, 37788132, 454472060, 292807419, 135190474, 310250368, 181425178, 640990782, 235290540, 315687328, 994403922, 892816795, 360959184, 314515598, 769906139, 658529107, 997344471, 559037456, 187042385, 33441802, 320405371, 378274234, 701689249, 370730844, 458597005, 31647897, 499673416, 305944895, 342889882, 745299825, 54989551, 252324367, 942134927, 865366748, 880147043, 85472432, 213757478, 559088340, 524813245, 697106555, 235808096, 974865539, 629432578, 262470819, 312597995, 145352878, 270253473, 281601943, 773005029, 359051247, 251214385, 811379355, 481267910, 38896873, 881894689, 196215345, 877153584, 244968508, 498225681, 430382083, 200896771, 772278013, 829791905, 806094000, 148255458, 171283794, 170088444, 352692220, 789933496, 430866825, 600657910, 259762747, 99723763, 849822203, 743742943, 778703812, 201040914, 903397582, 8634915, 876048101, 221783715, 886375285, 121913480, 455296511, 632727766, 350087416, 738097003, 988750606, 915520177, 147606819, 865063990, 438244332, 258839073, 116491429, 915828762, 413663958, 62294999, 196005612, 644802175, 873659572, 568091089, 176123254, 401278698, 522040568, 723763651, 391116815, 58279614, 503731559, 879106417, 323445773, 998978336, 296742413, 168673808, 291977504, 580766503, 466546115, 399127808, 821213187, 975374074, 633212003, 636011935, 379306772, 880316891, 465452763, 573863068, 511391672, 215349216, 943510852, 652792043, 280359799, 765269848, 112097141, 881657054, 721613107, 950798335, 529210349, 170008187, 345750928, 230231424, 458069181, 554089564, 972157932, 733726735, 724477718, 520860235, 807599967, 609247742, 634809555, 92091249, 298178693, 324468711, 787923786, 903732639, 581373770, 655898510, 936168841, 943285154, 731576905, 370072686, 333131550, 790038413, 576800840, 983118315, 9545579, 101161544, 38709964, 791425228, 999552009, 112104949, 661274944, 744195930, 31201295, 537498003, 641445481, 260299856, 156044053, 225211225, 827117935, 785075044, 962100503, 465173904, 716164077, 410081794, 130559159, 726316186, 985526352, 715997034, 807614462, 199123787, 388222968, 679057825, 570646718, 195487218, 439127122, 659151257, 842068991, 876046760, 154028716, 52940731, 435712807, 991523237, 263739758, 534655279, 987991414, 282466413, 707320567, 813992508, 526312862, 440673102, 980076409, 943432306, 267964628, 85253830, 501710756, 238878772, 445965670, 587454850, 741894036, 750578503, 464208721, 742311075, 509377580, 618787213, 152273174, 651255116, 955605931, 110029630, 853453626, 138090005, 845105451, 824042533, 377439621, 600745380, 190983269, 338226774, 297898359, 646792454, 917310354, 255721909, 399363664, 758712792, 706264999, 279020095, 240768125, 146096485, 319349662, 317032616, 736397875, 203107293, 315753416, 200023280, 274188817, 677768309, 926008356, 111411097, 913574053, 908883082, 794622060, 112404619, 968884502, 474221650, 996598046, 222779187, 832049730, 655642900, 509837417, 104382145, 454615217, 875894137, 841699415, 292781145, 621726784, 361151304, 481130359, 948064567, 776559324, 511620232, 878356810, 869559988, 183052101, 122407479, 337147442, 570951813, 660611510, 177232061, 949773392, 576999176, 667406324, 616766488, 405907553, 891549446, 528129091, 372564206, 843853193, 743875402, 699154631, 3728906, 192427827, 127577299, 623330746, 629202123, 285113953, 412911188, 559056730, 865739546, 487159641, 850075372, 74225778, 514575643, 239848102, 36167014, 844193628, 992212681, 405446563, 896720178, 984885374, 833244098, 23002433, 848668870, 581795576, 450649001, 952819865, 656286429, 192077096, 16714468, 573919626, 137775460, 153498686, 843873498, 396282421, 673617197, 825015589, 15158435, 230016774, 613748661, 83907757, 12101194, 799779380, 592994721, 133509040, 659440368, 474927252, 166104181, 179245989, 912614947, 466417455, 698129598, 227555592, 406745222, 357861664, 460196880, 560358206, 328963702, 658630354, 185115662, 12588910, 115249929, 154907273, 39238338, 798456322, 636076189, 249091271, 504352516, 642112893, 261690667, 321584151, 532999921, 769430187, 320885915, 551223059, 780871092, 958142560, 579066385, 722188340, 783157363, 75348747, 483485658, 276995261, 377162859, 889799808, 433515996, 456180893, 34054517, 683175067, 709847001, 396703449, 476419604, 727972314, 313480325, 966154525, 324899959, 196321782, 883481755, 706985211, 839631356, 845799034, 874378702, 904024642, 547273148, 878608836, 24592016, 86400766, 287648511, 485566089, 376508053, 520576788, 683396146, 383115663, 748919806, 850556146, 591096817, 229376747, 263440731, 694607840, 604976986, 496149818, 151672659, 895348190, 156157254, 500830004, 313656027, 954052944, 313378385, 245116555, 128878539, 498194156, 977995791, 9179908, 258949498, 494211597, 632001267, 162160023, 26849764, 137915720, 717759610, 57834200, 193095056, 384748678, 212914555, 187628942, 459389821, 66906177, 870647564, 520576219, 699846957, 172228385, 460378520, 410430349, 652933927, 977982210, 433974164, 143282888, 459014005, 482080737, 639138800, 76348095, 201907954, 618568443, 859782429, 922448719, 941642798, 525016770, 829450362, 738365383, 780381484, 15566440, 622975522, 131477002, 363473338, 907831944, 923966421, 175526301, 665636052, 642154260, 536437243, 653275870, 102892721, 668764292, 625923375, 17235872, 990514918, 700031043, 507825924, 166335487, 389974967, 754921276, 15410219, 384878083, 167745662, 320285234, 999589554, 648172509, 187809486, 321609465, 948992267, 389541319, 545306838, 300333080, 797377479, 437126453, 579125238, 630531701, 34124535, 44432382, 326260208, 513647302, 64899699, 205025603, 96672056, 168444566, 336819364, 949081872, 25570228, 609957027, 916068675, 551740208, 388862007, 754814810, 331392991, 210654832, 374497639, 269905365, 646975743, 428433851, 408546345, 774731210, 457544413, 415447228, 900545933, 417073843, 395708827, 908205165, 298067916, 605663224, 862952292, 319835730, 29339629, 372224836, 84633855, 712239672, 460360892, 594352828, 580757309, 820097489, 785895564, 593800909, 759161834, 970747139, 74518126, 59310720, 844841797, 457578117, 978488584, 445724587, 687541942, 779738474, 552106753, 872194395, 427164159, 132688135, 551869447, 518294865, 515514177, 712987547, 268018263, 693663735, 857464273, 290672050, 827559110, 867316964, 433779250, 729298227, 925645017, 280468498, 748100007, 34342459, 876449610, 620956833, 739423238, 296635864, 318434975, 153570483, 321083806, 818883935, 385570821, 444429816, 230208698, 107586150, 360010742, 121973798, 407271237, 33716308, 741745098, 25619487, 286551254, 562991503, 265406628, 940408978, 285363106, 196126290, 881543780, 639739069, 619510246, 973472818, 562770281, 230395630, 649416183, 787678418, 943291450, 181004619, 702810206, 883522455, 429569016, 256666062, 116576853, 510938443, 955328657, 609525224, 633213104, 962743649, 884977484, 949410652, 299709902, 607336615, 677586775, 571898555, 802233848, 556754061, 660612774, 164686710, 72538203, 15743479, 898559574, 70298781, 820538137, 806007450, 464979272, 11729107, 76448403, 938626764, 602374900, 206143541, 116584108, 934331780, 385695320, 586434624, 302460713, 707999398, 126804709, 739359188, 599442871, 598086236, 913296963, 481945159, 91143098, 764339847, 997291907, 387571584, 623425779, 15219512, 95183113, 859644165, 615177011, 963807200, 218690730, 651554833, 120183226, 152888446, 394763769, 497167888, 260520495, 459145904, 203772259, 164562603, 986315090, 216730162, 410317122, 406478990, 692391699, 184455770, 566436467, 404833569, 100748957, 302034717, 402218867, 417923093, 660426531, 236121669, 574210073, 607910583, 604729770, 915428440, 756576781, 109334213, 202613706, 284114113, 120430006, 547252931, 808743496, 524319665, 472004981, 862979789, 793755043, 929087563, 839513656, 600601352, 53609750, 48430095, 154918174, 305662563, 543706531, 260870792, 938258793, 945981360, 175281123, 967726971, 571993476, 903502395, 320956129, 188844197, 705827323, 970023184, 329835052, 609890730, 67504262, 203642753, 226264053, 229986421, 732561368, 981748095, 788337510, 547395112, 290376748, 515903893, 146280411, 215341408, 214621074, 705059859, 182933886, 209679274, 248294991, 395529905, 294956998, 638172920, 276031904, 398823438, 936418395, 385304031, 468540455, 430802930, 814195576, 101958716, 351343432, 661476280, 574578333, 669979095, 201284737, 853609654, 218395119, 187527139, 503732125, 776179057, 710904304, 954037317, 462526767, 9363696, 562507199, 565102876, 523833944, 426715730, 263154708, 124845798, 317488876, 386662887, 445394145, 194780153, 471675495, 950697508, 95919351, 104254091, 964876396, 675821321, 734157083, 237985842, 481375249, 107137786, 813241838, 154979674, 67859096, 414798235, 151204026, 148028332, 474274608, 525899639, 387973866, 486835351, 132597307, 529894295, 858677519, 374958234, 94391860, 722804890, 6283233, 81167880, 914976374, 508438608, 405875239, 547620279, 302900305, 60452166, 707631188, 209398027, 80349536, 16111172, 814464344, 694728741, 239359263, 431354255, 954411278, 637973687, 695899906, 448664520, 333112807, 32780515, 614238148, 611081379, 919555535, 768940456, 860253171, 948388273, 379077075, 31191248, 677346860, 796119318, 291346737, 11022551, 126095195, 668836490, 707211409, 897534939, 374399960, 929390576, 764174143, 150323499, 620844294, 671674318, 780677573, 443778428, 663583394, 77396886, 928406973, 179897896, 550683596, 560220114, 424601567, 83213011, 412315973, 355052149, 330453686, 903921245, 981768209, 766456527, 853643819, 584051731, 535009250, 652921278, 400015173, 304725983, 435634293, 760866705, 613681116, 503306502, 102427690, 395253925, 752789066, 434327707, 993499715, 545455215, 908742344, 805661753, 758752295, 194448106, 44051155, 614277559, 308190113, 361214834, 289063811, 423487738, 327897978, 93483468, 101305108, 781397609, 36940286, 53923503, 993676693, 977136717, 493860226, 186809598, 958911233, 865531596, 963905101, 403757203, 789100927, 650374880, 341790280, 143617155, 958155419, 944465258, 833408346, 614281708, 280644542, 428596523, 215641907, 393078711, 274358971, 843271526, 263114435, 580448050, 888554498, 69663760, 224456741, 378348229, 400575549, 175603428, 407955538, 994129104, 894607140, 534180955, 693243011, 323805130, 593816603, 999509848, 458726229, 78363806, 871615027, 238545790, 566910404, 164875911, 847913148, 155033886, 890649291, 420230378, 273598488, 136651078, 403034455, 457573253, 625290420, 369134075, 118972513, 88952743, 292342164, 11879516, 274166601, 873356290, 558031998, 515598114, 356447692, 122972162, 158089453, 528641357, 637344387, 452429901, 932414022, 100746593, 868503880, 733354667, 630182551, 727531987, 474792577, 992176435, 509128871, 472289909, 180913422, 954526850, 40892348, 643743171, 890708651, 518760537, 305227017, 519264630, 157673080, 376857428, 172600364, 756447837, 57217709, 301231781, 342830890, 917237930, 731825733, 998596740, 460595081, 742201819, 638318387, 852533653, 420662416, 857394897, 689876567, 134092269, 62460721, 659474663, 695190750, 954216938, 275123182, 267097198, 78124117, 963225932, 666699681, 127684556, 441050005, 93841393, 931216447, 680396817, 177527270, 786606270, 381660141, 601996792, 950755851, 722234198, 506619620, 925317214, 601282674, 262040676, 65764054, 871712071, 154531340, 611894450, 33526667, 165776186, 608811783, 768041518, 652120931, 216054150, 502670312, 844598754, 719188256, 734736754, 214804351, 318095063, 339001649, 668528630, 437354387, 374317415, 280490696, 8402771, 583525900, 142952813, 497402140, 550577531, 97871920, 402208797, 256639464, 51901328, 688230539, 38617931, 450357585, 381194778, 175529080, 602653999, 477644383, 681590139, 47010903, 491365124, 351996654, 752657505, 563128459, 51047724, 409136212, 365536175, 778449391, 519234004, 383721628, 745965090, 733380170, 855347303, 219235262, 457759636, 506047680, 261789807, 452330831, 590730849, 570442628, 292313337, 271530765, 852759670, 541767254, 46736526, 3526122, 941736274, 215833866, 428731246, 400036320, 307250349, 444452029, 599222804, 200253817, 401603762, 614467046, 591506867, 693533038, 845774161, 944088074, 603457196, 273674949, 578901838, 128165652, 504474402, 55980713, 555927710, 812800052, 674080017, 724028412, 36509195, 504114620, 641817379, 944243245, 832589758, 844374579, 843370732, 841491400, 414643625, 786260754, 416796677, 786268412, 927434512, 913792454, 749210312, 800947126, 926538377, 519822111, 108655348, 194971637, 596541711, 355533495, 11121376, 72830841, 779831659, 491271370, 884692845, 701516054, 805516542, 28994794, 951973247, 656444411, 93380524, 657758518, 41769286, 582031208, 139005745, 114331346, 357433876, 674546608, 180968563, 977909030, 468391120, 790337313, 564289451, 77062520, 824930143, 330248673, 61502732, 125362727, 577959674, 917675478, 200358453, 374982080, 72828093, 887339428, 801620158, 417167417, 94804801, 451104066, 932170943, 857732836, 932416371, 881876649, 874941684, 119389878, 19143656, 798417116, 112132568, 73689316, 433502206, 603819866, 172442695, 382856549, 530223461, 991402499, 151307720, 962190821, 579466119, 954733558, 143837780, 384537829, 783374621, 722292641, 353121064, 596073003, 21130288, 667341769, 635509088, 375299918, 208241899, 507137062, 729407605, 777203274, 953134920, 732079978, 103030848, 264443087, 345333179, 205530407, 639242239, 75890531, 923764931, 357274641, 962127764, 785249883, 589735589, 77685529, 900513217, 401834886, 782081513, 550641764, 347649355, 63648774, 42473079, 753368100, 506613324, 272055031, 368895168, 826172441, 768120256, 958842292, 331359212, 686316735, 26586791, 907079293, 114606242, 40712690, 62951746, 499416360, 75126429, 878417664, 335023755, 911848326, 682278097, 982674221, 232828300, 12173682, 256028523, 513902684, 461973504, 82116152, 643641776, 251002494, 421782412, 95873735, 318800181, 752821889, 437363870, 439910773, 90346616, 562082216, 283132044, 89916784, 599859217, 719104436, 953263632, 36222327, 870229560, 368717045, 699212590, 779134844, 728113442, 769315313, 502974809, 593802086, 198494907, 775705600, 563872884, 639728245, 683406368, 990348097, 751733707, 798294319, 504162113, 415155032, 836912820, 999267407, 11860047, 677721270, 689325339, 420073710, 124771960, 60650918, 193203151, 190970303, 262703370, 215059379, 483987805, 562291078, 532959625, 154667402, 280885105, 776967665, 896538097, 917605925, 957944418, 92992736, 499703623, 483494772, 517312660, 801132488, 830875902, 163635611, 409789702, 640653632, 811396420, 206262502, 969099797, 706353886, 263875078, 374246096, 131812928, 484721152, 202547968, 579071862, 311714164, 388212401, 341364160, 23650398, 227993409, 661605476, 881446826, 138313795, 889138846, 644725334, 762618689, 76174270, 581232686, 866080505, 669263145, 1324666, 86323789, 580084250, 114131107, 882294971, 372293024, 813187966, 824021336, 172731897, 882234330, 836276993, 315641880, 783492509, 193323119, 192710091, 983199676, 855943641, 37696838, 724387477, 247352229, 775447045, 980960065, 103311349, 101086741, 435599433, 860824524, 723256510, 578704398, 289654539, 740743338, 766150735, 486755583, 230193663, 203791119, 909343999, 115214148, 301664791, 857368323, 335746820, 358969532, 731049214, 203201371, 355514671, 725149691, 657050133, 122932308, 242021558, 373775892, 961425505, 880592232, 927104959, 902355756, 965660006, 594244133, 727400455, 790030483, 399636519, 722317118, 111237539, 639121746, 543411210, 245411248, 4942904, 647998655, 610423205, 341829751, 449494838, 681546222, 15116317, 553223134, 132367023, 311555879, 509411899, 958503259, 387742132, 897321224, 775165682, 451060255, 389934557, 219871745, 249701027, 878467604, 588257441, 899970551, 237057919, 583585388, 595586637, 145210603, 757459293, 575323068, 83225276, 685851693, 547014394, 169090207, 158113987, 998779352, 72290739, 496379030, 864355719, 505597227, 380090748, 313829525, 276710489, 582526121, 965127125, 79946352, 283290785, 836860506, 365309736, 712656531, 720462907, 291303169, 48026431, 762642853, 638755598, 430461183, 404729394, 597803063, 570984202, 925273496, 46045204, 781277739, 904415856, 86025224, 11670901, 102157489, 353808716, 273676938, 669699740, 472121917, 629345854, 617387242, 116607220, 203717965, 864906411, 342990453, 956868027, 873833504, 729528558, 712813102, 521590537, 227584805, 585504707, 165877549, 652537896, 435006498, 275755460, 821275172, 690025747, 217518635, 459327624, 269252331, 813789994, 218418610, 760653847, 694250070, 702875987, 763549813, 39152798, 585546813, 807954360, 193325149, 533788390, 814801484, 407986234, 421982907, 550368461, 43828533, 83751042, 410166544, 633066149, 289880345, 335997119, 742165865, 591600589, 896637886, 550276803, 303388699, 106032940, 514236885, 741000, 604237519, 321496191, 168434609, 185162926, 485181552, 23617647, 698588112, 54253714, 986407181, 56165275, 687762445, 865152976, 277525633, 623160713, 845331689, 497797220, 514872812, 730478703, 356838649, 624497124, 152525167, 904212609, 916125136, 69771034, 168790133, 504739255, 545088549, 689680166, 652433114, 655983999, 830846104, 702709904, 913054211, 919371142, 849633618, 120627396, 457753104, 364998938, 835239255, 996591933, 611546031, 857010311, 246198527, 424943625, 655288037, 644419410, 53488720, 104836843, 504564215, 631471630, 542612804, 444472060, 136403629, 491460448, 658721853, 986070055, 983949898, 597379483, 872244865, 489779403, 548894891, 432610091, 644821129, 819087040, 212376528, 826271184, 603654476, 115019471, 340607034, 989244913, 332234024, 943449127, 994740666, 867950388, 967129375, 55314299, 892981474, 154214207, 11463568, 867004311, 493614465, 913739809, 259281808, 593379218, 28509559, 651684791, 518785103, 488338085, 568714035, 875196709, 186039453, 437109186, 463072603, 213459497, 864866136, 346778592, 510437946, 698609308, 251733587, 42812709, 760842637, 672766285, 844205204, 229507204, 599175422, 219536638, 217345449, 496521777, 465432866, 309977207, 344462087, 257622084, 941517145, 103725308, 734046005, 662868872, 94089541, 498074970, 599737135, 477638143, 137328649, 727590847, 659588724, 132045023, 643770359, 909457032, 654043891, 617327258, 167893636, 579195537, 10691652, 584781631, 588668147, 530848613, 191327968, 715904380, 614335872, 809847980, 236506545, 107284798, 271829006, 963386676, 746107473, 84896757, 684731363, 794085041, 759028919, 774948909, 859737868, 859205060, 290990286, 763695877, 459887838, 712667391, 877411266, 368902430, 810969208, 33103615, 408322565, 417830264, 699545402, 116131757, 85573496, 257315905, 100684833, 731637438, 455593208, 387355876, 879262786, 141981784, 196692756, 984957351, 138195184, 580972917, 42659366, 498673329, 513074158, 224380357, 101252167, 258107032, 273903345, 138425785, 452374425, 568057057, 203156788, 22307072, 36863752, 160164783, 113116010, 294182565, 420394520, 497074044, 820893932, 589865405, 308510439, 607037209, 163550500, 547699370, 525331274, 746596083, 290758568, 600885994, 885404701, 967846749, 757686659, 681404931, 721960121, 148255659, 921983383, 986662720, 418991541, 891982381, 299495534, 252486659, 767031125, 82177577, 176788952, 228718162, 860458684, 408282963, 463396357, 576681349, 758768101, 380002407, 880473303, 188974776, 427594852, 54651603, 188363690, 884404092, 888691394, 884855296, 88377493, 569623669, 147487508, 652371899, 477640239, 218994763, 900722460, 308463869, 619848495, 887742107, 49430541, 237916230, 144524521, 155321613, 848896400, 643731533, 276631978, 377136194, 338516979, 44782683, 59551720, 22059063, 11417117, 568287128, 365510514, 492781724, 890960618, 291204431, 264500704, 44796355, 612988664, 649894723, 266429432, 930410395, 648366574, 332149948, 672702468, 414226126, 416546410, 100174965, 640614963, 679059635, 831229691, 91318813, 124795674, 147493545, 715838549, 414436248, 827880429, 244903351, 179062113, 543748725, 61368530, 613691224, 600688765, 814433781, 591303154, 589357245, 174399789, 741087890, 781607323, 926959056, 185722169, 401635318, 620399877, 269209259, 365840486, 446785275, 710003014, 960880742, 331611378, 136835597, 226822348, 702857273, 54918201, 603734958, 487211313, 558458664, 942962874, 208669945, 872458532, 582585513, 198486654, 794821080, 443706185, 308022316, 62874883, 496708371, 707407335, 286558131, 892833823, 741090574, 48766459, 148905351, 459387068, 747950176, 593002195, 164451411, 868360538, 953808913, 136345247, 954067342, 306546891, 103396710, 675239335, 235027438, 295474443, 522598855, 321444862, 658887558, 535420894, 261440519, 181136431, 715042432, 827000337, 274656634, 944852299, 106944309, 850578292, 753972383, 876727356, 194638349, 433433428, 725143282, 500186622, 32008858, 472126443, 908041509, 696882483, 348196647, 57415631, 830056181, 915594092, 971963923, 496780280, 879987140, 51195141, 171194056, 936838190, 495283579, 527075414, 954150524, 692886554, 996501084, 704287156, 210295922, 828761003, 384231296, 282845331, 285457086, 109520499, 38511264, 153700676, 57970481, 543760032, 38431498, 916529700, 443972221, 698730293, 830156018, 315498345, 808117606, 922284120, 304771371, 459897213, 70984710, 184728616, 10228356, 37157839, 112706015, 483268013, 291665557, 393474139, 655926617, 115962472, 517021692, 739419744, 41465045, 899653124, 697028159, 960901846, 457655354, 660749561, 119191490, 591962542, 158620584, 369936259, 72850582, 211770581, 46388055, 566385223, 950796385, 772219010, 500948779, 369092085, 436001983, 840986407, 408691860, 981125374, 418408985, 163971902, 688560997, 925582038, 183454932, 399957002, 375150239, 399624638, 373392627, 640263578, 825277396, 16054354, 228315716, 687325047, 866326612, 198071754, 257593554, 680076376, 424479921, 615979637, 40691332, 223048730, 267236346, 912684453, 357107196, 251264265, 184787957, 116699880, 297429752, 80644218, 349605765, 466946975, 162614080, 765983625, 144798283, 621402039, 139143498, 61640338, 299452707, 947239294, 153112370, 951084603, 252341642, 9256144, 5363779, 982550865, 597581359, 967283876, 890877554, 697179344, 843193203, 207665948, 764300323, 849739076, 760520068, 299767068, 329258394, 490910741, 947232175, 749670398, 414260201, 447269635, 384071473, 198344721, 457533806, 367621769, 76813418, 932664353, 183544970, 484888238, 717742795, 12363692, 95203969, 457541127, 786197880, 55096675, 511837946, 950402891, 764416409, 939488939, 783600437, 36863071, 770809938, 206857269, 145838751, 998236392, 179572012, 31377073, 633152837, 796909245, 442637029, 551047345, 695245511, 962759979, 344088121, 273989884, 83482427, 172445160, 996751338, 848001052, 677851105, 133077309, 606828062, 951615373, 374784151, 34263917, 24001323, 536306379, 800709041, 541045274, 819571038, 492339749, 199821325, 686077938, 372067950, 688598769, 618945936, 881882647, 602682617, 136293800, 897920575, 105352081, 98388145, 720875509, 170803946, 908966878, 881000269, 873510117, 241520735, 824215315, 128607399, 7328897, 869085043, 537136169, 388904416, 365561659, 187471024, 247702166, 384412518, 467967661, 201322007, 914340918, 39485020, 504049779, 36338550, 930843788, 296604556, 29102342, 331940126, 273597875, 909741412, 366274775, 407747767, 59921482, 812656938, 233090663, 199568068, 650922184, 508017943, 452059161, 135479816, 463573106, 814317210, 811024958, 595072358, 601544086, 138171329, 198688730, 969062974, 578494166, 954128020, 956380917, 890500789, 17961335, 458453453, 98762315, 949598717, 26464658, 797161262, 870066732, 502845543, 983025902, 49799171, 724108195, 730394506, 761752756, 278091107, 955639156, 269440808, 646829544, 783707526, 438096453, 554399815, 313713944, 249442422, 5875001, 403361200, 744454165, 94950522, 671063371, 59416481, 353992202, 346886243, 872913344, 851921857, 725274791, 907008788, 847312803, 267778449, 889269255, 605780001, 112589874, 889957533, 58696463, 296169882, 902577312, 963848818, 650796079, 86752935, 773397549, 192512408, 275922211, 106272291, 984163166, 238344217, 325875518, 618422164, 926535852, 75339954, 28026045, 188773680, 222912981, 888003171, 30218660, 709373213, 257371274, 956838066, 124135810, 749158049, 334947817, 682420113, 736980145, 866424571, 802482438, 955753912, 903762957, 688702108, 990045998, 838149313, 475317011, 855384076, 424876854, 705039228, 205102928, 682506479, 712972337, 553785874, 996820573, 235289221, 378645217, 250940883, 399635808, 323421299, 441279243, 993609738, 847127772, 264914189, 571461192, 968962449, 890836679, 473281102, 690131248, 527428776, 212296459, 881000475, 743153208, 940788300, 401440071, 797245299, 25892000, 671009057, 223776151, 810672109, 647569985, 341837708, 66369105, 241384482, 770241753, 962057038, 429073655, 586033020, 641518709, 187349297, 498045289, 799077624, 335151242, 348793284, 476985267, 731057990, 925248003, 203948978, 880754920, 18211685, 527036867, 83509930, 154841882, 899257668, 934332126, 966161573, 658932734, 336405341, 625522751, 400965072, 635102902, 981038382, 112438657, 183658835, 350373066, 854175534, 928050500, 220216765, 345756417, 213596285, 694104845, 712984122, 177769596, 101378097, 755259014, 170232172, 33010391, 445731474, 682313753, 210792749, 928219640, 161804515, 457070794, 243940709, 999422485, 62357675, 677305767, 799566305, 256366758, 718561800, 522447283, 892431174, 752779620, 839630734, 674473247, 821141736, 445696039, 482277838, 556548765, 547963877, 919917278, 843892034, 68000371, 98039503, 788502953, 652469514, 290428525, 79920572, 152777653, 124202543, 647448126, 293476546, 58790877, 826287245, 97612527, 421205260, 89247945, 303822970, 943397257, 997205025, 783408089, 497937870, 156406501, 976012931, 41883256, 923680944, 726879100, 135907818, 648462178, 19614846, 263271018, 213150468, 758254971, 730564433, 331021598, 792387378, 480776255, 805791403, 4147998, 863456112, 565002724, 64224915, 273736960, 189435554, 450840036, 713361719, 752310638, 165416133, 735091636, 302702511, 786327632, 539024188, 457886859, 360097980, 699510643, 365842122, 839542393, 302392290, 207008214, 654995679, 347838400, 45513521, 118570262, 565915016, 80321779, 896314320, 947603528, 550372470, 967487582, 663764309, 340550734, 457350875, 283962262, 836242737, 899452089, 883792457, 375476994, 520154675, 309461717, 24695042, 805151601, 744420282, 560860255, 958235923, 319950784, 4370193, 330861832, 43669714, 966847495, 986196204, 962607216, 574118904, 131065891, 806912120, 288497184, 342711042, 887158421, 630123214, 521313688, 105636722, 2655171, 447884461, 715874520, 287760155, 584477795, 139499764, 821503500, 913451682, 437232054, 919748915, 438077464, 328464159, 950269223, 604842971, 219119524, 677563304, 267585330, 130894815, 447246374, 35188383, 579934949, 575501066, 754879699, 408057314, 582495362, 99890820, 369111510, 353840634, 520159517, 996319034, 330200363, 505910364, 490358340, 98573330, 746774513, 976089548, 326261148, 211606290, 301974681, 32453376, 187628855, 706220154, 266456704, 771025575, 767156255, 131509619, 133099766, 36694657, 143759499, 72916699, 260778307, 677234543, 616996725, 511017898, 91795485, 841354865, 101665934, 716505498, 116654216, 52955875, 737284050, 814413935, 486575248, 9225306, 377908004, 506155221, 173173061, 718908532, 111904304, 654951314, 326477433, 487309868, 287417449, 198145797, 45566920, 218344393, 594358997, 876710482, 511420617, 954631763, 29166989, 850492719, 423527165, 498115909, 225975364, 393018627, 414532528, 676434769, 906265432, 815693708, 46597158, 881720419, 301463197, 433345913, 332610144, 559850456, 156461569, 12364193, 722681750, 596073144, 491980362, 400314950, 791799445, 881639712, 144914710, 87980605, 679558406, 382980567, 51603628, 704923440, 936828833, 319327707, 988402311, 336575481, 817964043, 484540266, 588690096, 203040295, 86302114, 901868979, 715704755, 535573880, 565327555, 944550021, 675048032, 830134317, 929201513, 107313110, 845175834, 693359038, 831439917, 245571616, 458515901, 776932486, 923331647, 809801747, 148157887, 309997250, 743596641, 890587055, 785609264, 822928229, 802216009, 771666979, 807336347, 680293660, 394111599, 979158359, 929587947, 747251656, 338936103, 931886508, 238626038, 710454406, 181847399, 307705614, 765709447, 281852735, 485390733, 55271567, 445314599, 926240899, 746405811, 568999617, 276280178, 894251877, 972011301, 995999422, 744453707, 136487775, 348528870, 952148338, 265626889, 600721204, 63965895, 547567387, 141707828, 925880695, 149632675, 957257134, 442855224, 16447293, 1012486, 925520772, 615924640, 274750649, 176715892, 713624269, 946377145, 312371273, 149006194, 322432733, 649099672, 700606494, 359837420, 626242082, 962897007, 77221009, 242672328, 308460184, 550656049, 733454960, 687614371, 471679182, 155730734, 526123019, 167330397, 496370944, 385114149, 583451367, 566123946, 765616622, 625192242, 170722215, 566506152, 27656839, 420519921, 822770969, 203591839, 385178148, 31031511, 395592333, 299559057, 399287312, 64907625, 188324304, 539492040, 771584479, 205842279, 191054617, 709549916, 808014420, 778809154, 645115392, 805745505, 20498154, 923634785, 186611421, 688362263, 620067806, 685896917, 405011648, 760372680, 799720770, 877636012, 404230945, 327663549, 675135255, 982073326, 536765066, 118344189, 197461494, 646990416, 123959371, 79407616, 703044508, 559255963, 547391222, 176414949, 748131916, 419779476, 55241075, 114522351, 63169617, 225702573, 829262729, 57812417, 987729207, 671635717, 543152592, 471377320, 854427222, 844195203, 803553350, 834449193, 257710068, 495310482, 150154245, 804767582, 894590612, 302024537, 542022378, 881232818, 153927464, 831522290, 629504277, 777577052, 586819313, 800500688, 310613952, 285434120, 322352221, 659437239, 312283533, 74111071, 101577379, 165657841, 365909806, 850205639, 815014067, 32749396, 407814276, 820957496, 714794593, 667682930, 195066389, 49183169, 575931182, 277368613, 927261022, 99554512, 824188652, 804066039, 629022409, 777274462, 609370460, 314672508, 382293768, 641968462, 855704489, 845958760, 486783107, 261072940, 383242908, 667431563, 687205682, 623897420, 397771480, 633160544, 210814186, 639679568, 344980745, 650612714, 380594087, 83191867, 524526447, 892456242, 691605294, 657434012, 226656536, 265859394, 743384154, 789521566, 342064142, 984342519, 181939781, 566268652, 24851836, 950682048, 627323616, 380522292, 89355887, 959947357, 372772991, 848607859, 79388386, 378993121, 262566860, 581817379, 133746910, 473050738, 368229370, 218813564, 885729487, 409589929, 579410253, 507875756, 448072226, 392139462, 111479524, 107377107, 589529402, 257198334, 817061131, 311255115, 274780460, 145040133, 998166310, 607028316, 582180129, 441308942, 102938014, 247731102, 853945771, 298227442, 221264617, 511752174, 766543916, 50499969, 165772526, 384219624, 115829091, 2367421, 311011379, 472805209, 561281389, 474171987, 748418254, 28335805, 136455944, 702837490, 332639635, 383908050, 855068671, 352844135, 535891421, 562272017, 770537657, 404906905, 244769737, 303337422, 511037117, 93527889, 415022741, 794877517, 679957810, 424438605, 320701136, 94298694, 166317979, 174593, 389544816, 307592242, 239802673, 266491468, 115991046, 895449873, 350083675, 70291856, 265955930, 424096749, 257592064, 456360793, 684307654, 991028140, 351972866, 458307761, 782666670, 265645204, 156066507, 23868504, 853497616, 22277401, 265352303, 532489728, 842814903, 291253772, 876669091, 961336801, 552523548, 97451596, 847767697, 313408264, 546622186, 288930722, 678242749, 14715369, 603212967, 281694459, 962390248, 516800226, 335841047, 124004008, 202794648, 260290609, 492978206, 566058267, 93390045, 822338887, 608136009, 556739265, 658400649, 516167877, 625693403, 858689197, 948956101, 103606966, 442631603, 599235113, 821452389, 489106798, 587224174, 208161660, 660159015, 792635278, 629279545, 50108619, 251405775, 218803989, 642134028, 531643663, 803782501, 126116728, 674571683, 542427750, 953196139, 569450726, 945241715, 924221720, 494771469, 448635326, 949470686, 688917131, 379596859, 574429623, 654497424, 713697258, 275009290, 989527747, 346253453, 905547881, 5328474, 350699177, 27455170, 164384294, 611007739, 255539035, 82610485, 352191779, 520221923, 166323663, 584103542, 391559100, 606355616, 874384028, 520595192, 136510305, 575669013, 121931018, 320268548, 717590146, 887668689, 790321793, 321318078, 264499229, 343358706, 485899112, 464062975, 553556753, 87398585, 508931938, 148674359, 392140704, 649563745, 311852860, 486518897, 665997808, 869675394, 418139858, 772482595, 227760986, 522808311, 469733987, 362412726, 639895434, 580947112, 853456300, 401366332, 217909416, 397304907, 194218515, 227275450, 959184033, 42692381, 223239278, 51074202, 820382348, 144304974, 424949994, 333102520, 977514706, 242413955, 45922446, 793686541, 809616010, 736350201, 94882249, 907619930, 18000221, 823814338, 768347536, 448380996, 684827590, 744682623, 519354778, 612366425, 207375437, 867384610, 355762829, 955028745, 242280132, 421739389, 111930569, 61578250, 692623722, 176819069, 421864372, 656829903, 907963139, 434635513, 648142759, 233755860, 711255407, 556000186, 312114340, 696497583, 525604982, 583211195, 305270208, 924006671, 802073061, 385907806, 232882645, 507620552, 742376418, 491133034, 979290930, 684667940, 845526429, 174114750, 875995657, 694252185, 507814305, 392505782, 309918901, 138217640, 143915156, 714178550, 910922611, 72681514, 543728367, 858805609, 901069307, 421235914, 347684762, 11326293, 638713344, 710891495, 866878958, 949757627, 828463297, 113326110, 237854690, 40645808, 581456260, 182621670, 868910465, 892934075, 485407748, 661436725, 657885281, 230659343, 439634489, 287298576, 529481175, 336648287, 880156439, 567987037, 639159217, 924252316, 71372731, 512096368, 125124149, 192388811, 770682452, 333730594, 131779816, 248590847, 220932961, 817238918, 9112328, 665310274, 21894608, 945469452, 406772486, 558859579, 584693790, 453283447, 960593469, 386002234, 782677814, 567303967, 418504810, 253988569, 760607100, 957424428, 115498050, 800415877, 97065195, 91063595, 922688448, 599369805, 632179925, 938073734, 24934265, 347256350, 935712743, 8892311, 428918144, 781329861, 193466861, 399056844, 329353385, 442521379, 402003438, 321254447, 250407839, 317490634, 156271654, 52540908, 746767154, 988158222, 952822414, 391446051, 364744932, 891163783, 916575741, 137590607, 322304420, 429546370, 868171115, 848724281, 350917578, 27187418, 638712021, 274537567, 198954824, 544242543, 471665800, 108113253, 468410363, 223915439, 544651337, 27566092, 884705913, 824399386, 952793361, 166727744, 272460793, 176216274, 260702129, 541630648, 257763599, 379569049, 740745560, 537642830, 601710073, 993889590, 232243982, 577904117, 477009042, 343034145, 188106603, 860151377, 65969627, 706097285, 933103743, 409696314, 862653049, 745287317, 564705448, 49919969, 918651739, 684984753, 371448031, 282351455, 648622124, 971513679, 776167169, 374782771, 304061260, 203620868, 960948075, 413714610, 487424637, 354915955, 408170403, 114535677, 83399390, 87837462, 315024123, 741381059, 652355331, 300857269, 511742102, 245333041, 874780354, 358883510, 421558622, 154921053, 909647103, 379251750, 112948350, 275332583, 20261495, 648315402, 475794599, 72172620, 559996483, 267803103, 772042821, 503791142, 137152032, 808331643, 383253068, 329702180, 621861527, 865335763, 452284975, 94654169, 618503811, 600539069, 55019338, 9199585, 136976437, 890106114, 310509021, 469679665, 159245851, 16694420, 629914913, 814948333, 971679887, 156800207, 76389826, 837415856, 673454053, 257647030, 348447079, 998546970, 410983318, 824166951, 633453973, 134189369, 25951043, 119926895, 506605979, 303809204, 319210862, 731961940, 77263495, 515734132, 379863116, 725039007, 677975235, 375872688, 277141929, 487024445, 807825025, 938283193, 522931358, 166873324, 931124172, 384959464, 539283199, 21130792, 939075793, 162083306, 880348607, 702969219, 652259334, 433844700, 97877026, 845383503, 951601084, 532447415, 15701709, 102865367, 252512806, 507659276, 882532886, 204035579, 77223968, 85262455, 63685061, 476154358, 470234898, 493304517, 807253609, 556241519, 967245257, 737680086, 721755254, 564136978, 142648193, 570282230, 258185363, 259599759, 72808483, 769946502, 82164097, 842899924, 842779106, 772796744, 118151770, 603686263, 252483591, 573041396, 161608137, 891061865, 12148980, 3132992, 140153934, 676340648, 505103390, 713865228, 996057486, 964902015, 634694077, 645916121, 216463960, 998578644, 830907424, 484646154, 155650075, 149797316, 636027012, 628214476, 994922679, 943055928, 99032617, 741244721, 19112929, 401899545, 769559701, 570681216, 814791755, 418221227, 991632177, 711745191, 907463145, 814784181, 124718019, 359305435, 464489813, 355724391, 949943664, 610441245, 673124619, 169463948, 332533738, 105590575, 448351410, 378839252, 428155041, 506876306, 141115645, 327541578, 574136045, 856172002, 920387330, 39637288, 516386315, 721213185, 652253501, 949557497, 840886450, 988613749, 771684756, 607942710, 667222148, 651859707, 604403750, 948037901, 947439121, 702719523, 805211212, 469431128, 774465653, 431494590, 448654297, 257236322, 184014875, 861699969, 966924629, 515256098, 842143360, 10979407, 147869792, 266213963, 296984948, 830910586, 905008730, 679172113, 382214135, 364138373, 220335412, 772447657, 542742972, 460522524, 624460256, 224746692, 175879881, 722951998, 59430356, 471760728, 616405508, 657872798, 713757023, 416050428, 178772039, 452996443, 396761309, 624754636, 506835889, 198718057, 59568812, 180825111, 281811274, 512099533, 683569413, 132667282, 26694933, 206067911, 633028265, 975555803, 664834465, 859592919, 2092919, 988377135, 337358698, 490732997, 323898306, 282909677, 781941410, 560493898, 984775412, 244760483, 16950638, 249460451, 231669105, 665975801, 49711181, 648215497, 995118057, 106405882, 80192668, 442706891, 38913491, 657343114, 748576883, 317354035, 332293273, 40919614, 962218937, 160003371, 365499399, 546276713, 784804772, 879203035, 666009196, 383036546, 148085161, 498580742, 408158912, 100542125, 919615166, 699074192, 335238095, 938571496, 954245333, 16797974, 672948892, 566360057, 966243698, 231397941, 6841622, 307927711, 526622671, 108107125, 561470341, 827664373, 43745898, 910488158, 517183776, 352309669, 524712287, 131894282, 891368910, 797843497, 500722744, 475223692, 385622953, 113373146, 544758096, 89449256, 580124250, 903211032, 336761014, 925988394, 632132359, 920786780, 781487612, 695940963, 283055038, 274613142, 819434512, 679286066, 161014099, 869344106, 980391205, 565688282, 763566690, 552714879, 285772718, 980667010, 681682390, 980403014, 201873071, 156527312, 485843912, 474032276, 534755443, 982246948, 688358366, 653158331, 951310587, 824437726, 339752512, 197481138, 571238134, 831793252, 920368751, 464088550, 10044520, 575646634, 458562328, 2463168, 922642254, 53118944, 569780729, 226505881, 273242521, 3747953, 488261998, 332244300, 923643392, 963781658, 35064071, 409295007, 737810338, 102829021, 477804603, 468587202, 94162050, 897494305, 483586061, 666918802, 774970022, 643861862, 908763928, 78940338, 147459273, 310421260, 781988236, 811372016, 221428736, 453275640, 354544005, 942270834, 767647119, 672599557, 740840205, 771038670, 760401275, 519097686, 757511930, 355120760, 169456949, 693602823, 230484995, 412436124, 581745292, 157234485, 717038671, 204482390, 54310059, 295898021, 23542459, 854638491, 256245636, 710810834, 24062096, 38406881, 572598651, 315411401, 326035697, 433413938, 6934338, 258213164, 319822325, 805776355, 469702886, 183621607, 588613059, 22872772, 973202594, 426259034, 249416213, 598104853, 811778909, 752053666, 874860909, 995191255, 717223639, 74003888, 191646178, 649017213, 147743350, 712568738, 102755377, 89297589, 748701590, 78485848, 268012485, 427136352, 10768067, 130858380, 70575757, 12759554, 676485131, 528920732, 546619471, 647035637, 73009510, 430623900, 440901304, 563840660, 263105867, 762366571, 372282300, 744282613, 614712730, 627970641, 144974754, 915829522, 708251194, 296966673, 99682665, 559879529, 900728319, 665495880, 679216189, 132753726, 596146911, 302519734, 129133811, 208336943, 545696878, 334708524, 982427984, 326869079, 434592937, 458486353, 395707077, 238885676, 375230382, 974502180, 387226914, 631420781, 641489697, 207986154, 891528722, 228929079, 481455946, 946817086, 861215048, 889110188, 657470669, 653865456, 895804587, 981930787, 326255366, 28509411, 921887237, 187498572, 453926427, 235801906, 430316652, 410661488, 443048691, 156257064, 558192262, 326669244, 32006769, 758405829, 867047520, 698148327, 350024993, 395065382, 420696878, 90262026, 754398689, 316388702, 241681320, 606340730, 30563290, 121030958, 385443014, 76722806, 550854881, 357772907, 787539405, 930114797, 74235013, 53828148, 982292997, 904269365, 414214512, 606592673, 897700268, 618921090, 302979222, 93922354, 738106922, 790387865, 948623582, 267362248, 583310450, 770022364, 787796485, 235283489, 693130416, 738982517, 660944922, 328974591, 71121356, 322403720, 884364535, 63433428, 800819319, 504665681, 210672182, 450478704, 60958641, 885611293, 149546624, 775730397, 729602160, 782174638, 640673740, 920798543, 773104281, 658041104, 516131797, 145395563, 534300267, 91876666, 70740999, 65624868, 208205280, 584970717, 916520998, 432502864, 443120508, 227465431, 704409253, 602984463, 891944368, 862988358, 170540466, 969861920, 482270336, 791079692, 577119380, 908918704, 32082250, 641875440, 163527046, 679966980, 11763937, 640754868, 8258014, 498129533, 939304914, 420778900, 204482935, 361760433, 915698657, 447110693, 90005292, 151049943, 435081578, 834868844, 873093574, 288936286, 712945673, 348642412, 875713234, 99614747, 232462595, 524682314, 562103172, 876989413, 483269550, 999609699, 169830031, 713117376, 965697637, 20239571, 225758166, 903535883, 374079828, 253771625, 868818423, 541339087, 46942653, 409357230, 511376734, 691245812, 464279741, 514069645, 118678563, 158598711, 805950994, 139679048, 760245860, 444183, 821571781, 219788733, 775170490, 147018538, 456500815, 781400660, 278765722, 242784448, 529240759, 459762610, 87328849, 679979825, 106538133, 542046588, 74758521, 82653175, 154020037, 814313796, 885728863, 134250889, 400707306, 69012541, 740725445, 787215384, 324255418, 831269772, 350551019, 477333973, 976371196, 231444016, 665401895, 424003476, 73778677, 958532511, 623713776, 282379763, 488844712, 276865665, 828406296, 506177294, 394668715, 451148759, 794754040, 204641626, 683690922, 890962714, 744664964, 428532173, 615962344, 872583214, 182244238, 644692567, 504545728, 287676979, 463729129, 620048412, 692410111, 447092074, 931046600, 505715250, 41907491, 563274602, 845146003, 628171043, 328578123, 864180832, 618099785, 730264251, 814607000, 165853774, 185436173, 609533906, 692707255, 270736675, 29019359, 435497882, 655967911, 710672006, 616077275, 220730677, 377535116, 267627227, 611374490, 474087001, 790284767, 845225066, 923038372, 829463259, 204426960, 351569485, 947564201, 501920111, 961835301, 985051472, 580124237, 711637807, 843961731, 113936248, 933526727, 784190617, 905871788, 693592011, 941243778, 837510101, 844216780, 706794313, 920401188, 889083302, 64026971, 161670171, 601006344, 310648226, 260226635, 946882589, 520040788, 265202141, 464470970, 123445432, 94596385, 473632843, 198772038, 821681351, 226512127, 54151318, 650840644, 319756097, 681926872, 238441518, 461600469, 670269757, 964985891, 91173576, 19815433, 134526539, 916019356, 791709371, 911131257, 852095026, 432154215, 18795776, 36765767, 903941066, 230782634, 14485278, 685462709, 413231623, 157360440, 904202745, 185339885, 300384331, 178325625, 704937606, 306416028, 646681345, 712835004, 917761156, 360832415, 361813304, 332146855, 227320892, 987308335, 176353816, 841033537, 202971603, 33988533, 153988220, 742770943, 987901658, 512476690, 762345161, 517741626, 402708342, 327408797, 840568507, 935057889, 723913172, 665137809, 296724441, 711676104, 534899259, 245269356, 20466150, 837188529, 101027265, 787885177, 223006481, 959673520, 738606173, 206608367, 855973134, 204024839, 449220299, 249312034, 984953386, 194468865, 605319418, 652639866, 705031148, 436366908, 939401348, 976133584, 499780581, 325993926, 302626630, 508915681, 730245254, 10855096, 117564498, 358028272, 65706377, 733195896, 813052643, 179023695, 244898547, 510371782, 133176351, 646003779, 383461411, 477177968, 78971816, 198720150, 723935961, 256004754, 464702135, 612381065, 877696164, 224273695, 259840265, 789471016, 802730620, 304231569, 206873051, 428027609, 539339670, 532659459, 200447979, 163913108, 95999872, 880665755, 335611471, 556822603, 943446432, 845876775, 410743986, 277799891, 673275401, 353006731, 128073372, 571214183, 296219002, 267368169, 651799078, 760948274, 29918579, 117789741, 349610255, 918851194, 116903705, 920063679, 69430973, 882052704, 204207097, 672257556, 981661706, 57883684, 658150236, 348021039, 231074407, 209496169, 984693675, 907514560, 351813812, 583020688, 85715072, 762339238, 84021212, 198036193, 562143209, 296317778, 430470388, 60097471, 500004535, 350546737, 153843844, 5162870, 929602912, 497762452, 925812926, 854868191, 192153749, 504747170, 217711973, 458172402, 225778221, 595407557, 380260469, 596617299, 745432459, 795486718, 839075978, 156300902, 693333394, 381997715, 63374101, 94279717, 174366963, 310625195, 173889480, 854767337, 594229641, 243882919, 56748180, 672541334, 691896907, 21508322, 703407706, 752606219, 44475923, 872870919, 95680161, 785717086, 646556049, 503372333, 670494213, 223624782, 641547364, 846116001, 895362711, 129198008, 56494186, 93321223, 979766843, 779811242, 762698193, 206205300, 254698645, 995826742, 828901204, 164014293, 602798096, 684485452, 676241545, 375566612, 13741541, 533461482, 590781961, 746192714, 38570482, 626886055, 468401313, 216253320, 499658690, 411173234, 452885947, 833255196, 476103436, 857759466, 480324297, 672518813, 954279774, 575508521, 450234252, 686310950, 434630947, 449604567, 817410996, 391036102, 746577379, 735404594, 432329065, 722353206, 448231107, 426881862, 422013430, 648170724, 879372482, 540423409, 398686392, 414654241, 950490915, 350800691, 660528578, 623052166, 393852759, 655815078, 725383636, 606891047, 372821736, 127095834, 103745670, 817693365, 968030415, 869044305, 717288729, 339611649, 580584959, 266309627, 850433717, 575832531, 19909616, 889215460, 706783942, 874382670, 83631618, 376455699, 756829362, 701685073, 45860067, 702544542, 697943443, 537133654, 77559212, 245625181, 986532722, 809868992, 727421633, 176925806, 754086282, 726594002, 454140940, 416974818, 408023045, 460772075, 615198392, 533361006, 518140758, 17144931, 802365626, 923449252, 532920938, 376298069, 493486392, 757683207, 872120739, 880557660, 806614015, 87577539, 655270983, 772832340, 806752711, 616473969, 541966185, 803674710, 671260847, 31806718, 977599834, 718115430, 117741410, 310634690, 31260465, 220794242, 323699294, 606299787, 12451463, 349642080, 225627172, 494224432, 995920593, 578570587, 541325730, 607006767, 942873136, 653777872, 764898245, 685301382, 468595858, 296465279, 738742491, 256866872, 234632488, 518772213, 727059795, 36048654, 837263275, 672234638, 583537796, 284538590, 209736878, 907655008, 536930828, 463796715, 392898656, 143286259, 512161555, 164505205, 299654308, 629099174, 39025237, 599162100, 813765034, 632109916, 457490633, 637688106, 791386669, 515111128, 87091655, 581644586, 521555587, 928281895, 499276459, 671372076, 360940216, 904319375, 266275316, 162491200, 449754561, 90386962, 175878599, 62532370, 156718875, 138869011, 704796982, 161565104, 897513235, 360018352, 736621532, 925648584, 398970764, 343034136, 228124188, 695975888, 653920606, 723928403, 545179233, 354943304, 96899462, 539161102, 76774562, 848155736, 824009099, 79042692, 605125323, 387670201, 770161055, 848359847, 794200275, 151035011, 543079422, 827583484, 605813526, 54926168, 379125994, 452726874, 674643433, 235799421, 521388105, 892991124, 628571215, 491215354, 558070874, 37488656, 11434335, 642178394, 733636153, 835571704, 177179527, 545295526, 109193016, 597510512, 819786166, 783729396, 394110241, 398122918, 157315047, 233351415, 156759936, 198591553, 90696858, 523593450, 533590771, 744433408, 425612365, 464613551, 231680588, 965910490, 647234837, 106042149, 828299354, 522111046, 2469940, 283653736, 433036686, 817726229, 869896847, 568112837, 785459532, 346845126, 15397926, 486446761, 697112012, 467822622, 695222925, 585246468, 962983570, 733453084, 743365278, 213458637, 573508129, 65616807, 795717057, 622252640, 160650977, 656256515, 408703293, 313392453, 778351653, 250667734, 822549377, 16530247, 467378349, 774888868, 158360708, 479412723, 971818131, 593703772, 46291126, 2558779, 3228184, 978471398, 530339957, 920829925, 35017471, 256630908, 52704956, 883690039, 583368899, 453523934, 846408854, 197217373, 853452421, 810141282, 441347032, 756168543, 31154015, 211944515, 156415743, 733046031, 566943074, 102320811, 234990582, 585471199, 95836413, 143442908, 429799179, 541590241, 9669593, 241286746, 507735921, 311941628, 503881128, 941084556, 293879435, 761661097, 664112573, 846038725, 301889514, 714610667, 898731997, 897206231, 246280890, 975055014, 205101102, 621911861, 175845448, 145828544, 78377609, 279771640, 792452251, 564075561, 448884020, 414466901, 312765262, 583203850, 734998825, 29477951, 134146871, 513988661, 866806726, 769587021, 695975301, 874303028, 23668097, 186419191, 347309189, 598347435, 538736184, 192090556, 360378836, 91337668, 601013277, 741518938, 505414431, 381489917, 804808785, 127411285, 394917322, 430194671, 799681715, 290507930, 143013368, 133732367, 8181551, 123280320, 32820614, 454525438, 532904873, 872354131, 546122045, 61803641, 369154955, 692841022, 400483069, 976854131, 728122161, 754083376, 349250425, 482583982, 988201272, 760387406, 88113192, 619484530, 883445421, 348770543, 888627075, 181550778, 564271207, 421721432, 399162427, 826214130, 129036003, 69710486, 972277669, 862450297, 855630877, 602973476, 572368955, 270146316, 880407106, 739145102, 619815685, 325005011, 503950437, 506447594, 983446286, 298549562, 899168486, 382286278, 900748382, 345708495, 357798383, 777728590, 17108229, 583820289, 474900826, 93968957, 308974662, 248902693, 545398954, 34478476, 886520842, 686565172, 740473189, 237073353, 795289459, 26960251, 807461566, 482631557, 858100702, 22324038, 924198463, 934759844, 478106299, 473122790, 158057599, 296891234, 125952218, 887875777, 633403511, 717867609, 792215481, 82940337, 484384971, 451417431, 640020668, 293157053, 360099952, 979271387, 80279947, 712171932, 299883613, 81220602, 445998107, 880634770, 547820208, 879656103, 500428543, 939192689, 193106141, 750026716, 56125957, 534500560, 615359392, 948553787, 738719150, 691833572, 749926490, 133969289, 159939301, 106604119, 285729824, 701872110, 597122627, 62325443, 303301146, 592718344, 6744491, 985816055, 113618367, 524537496, 781468138, 896823381, 292838920, 374419958, 471555855, 677886680, 459131942, 219778735, 883291579, 446899661, 638798411, 445158339, 267090132, 851736777, 393093579, 864275650, 706520854, 526803940, 563112259, 265327338, 318871059, 241461398, 582044374, 69015060, 994804516, 301278941, 777151024, 381024395, 340263783, 525235406, 636680333, 636886117, 934518113, 137186923, 49900761, 79317545, 363070987, 736017769, 541669152, 834549908, 655634101, 43689533, 488556352, 846661743, 581610257, 492440007, 259656371, 69687482, 244222736, 493752527, 871115665, 357508250, 461142929, 129731047, 348124999, 768318297, 969663737, 533803618, 824244744, 738672072, 162024191, 732465172, 977647920, 161270837, 353385850, 876252026, 726037822, 40391381, 706436649, 940593782, 555213490, 226617543, 492787311, 500362154, 915133167, 33728553, 971822948, 668278397, 760978683, 132768472, 299903243, 238323055, 318478598, 286745300, 485430946, 717954039, 892421576, 570264864, 558757904, 338452072, 463029786, 675810341, 391340686, 21656789, 834333949, 941586056, 843434526, 641223367, 875950660, 389079973, 404152651, 375326771, 729484622, 688349326, 913192695, 80685989, 56765421, 860292112, 304016101, 553108086, 892240581, 673239024, 172609026, 74033588, 612904827, 180467526, 606685997, 886978836, 958757568, 456054058, 681436707, 244410377, 484070934, 449349627, 402286284, 680104516, 623921198, 49763657, 684860217, 17865000, 368019477, 740884351, 79585503, 344869439, 274375640, 588836884, 194688716, 354825530, 630903398, 247498336, 690326432, 184849708, 771651982, 761705307, 353227566, 809911976, 574097937, 179178601, 959062006, 990206177, 267717471, 320646780, 848047033, 574950047, 286567244, 832678160, 898742207, 718194247, 207440483, 998583962, 296380298, 987324494, 47726452, 945634488, 474498761, 228863936, 782777129, 542556405, 224856954, 251988130, 400348212, 227200346, 588745512, 365259745, 946189068, 918268223, 970097944, 545085833, 586490744, 662118266, 463206184, 791398510, 108833047, 981073050, 387511522, 243348159, 919442465, 614270806, 325816923, 856367979, 205023916, 488517693, 856005978, 323394994, 569334202, 979325140, 978519092, 391915458, 761701549, 7317908, 134255887, 235332414, 991334722, 918060120, 696949913, 633509854, 949030564, 896937961, 3072426, 527994237, 861012625, 849867528, 221276797, 700831049, 69813203, 924740282, 449739409, 123762709, 687433664, 566014931, 132428474, 785267444, 884320381, 218308376, 998518791, 210202194, 48144614, 388100773, 567449814, 398337394, 575923164, 834187212, 314041857, 85100080, 136970524, 112671441, 995405516, 788909937, 231029797, 951629087, 831733892, 102802741, 749977653, 1117214, 567823917, 468355617, 961704816, 706498861, 565089136, 160811356, 981174472, 278867507, 107181784, 254161462, 330571095, 818422061, 131914777, 354429468, 805668349, 853357855, 839401858, 225167305, 166782432, 998406030, 881252802, 57177963, 861986599, 141253215, 8015602, 937280598, 817875775, 360842600, 88132222, 930975881, 289053227, 769428708, 740697874, 709287585, 132397315, 896105718, 677612343, 679691478, 155892471, 980791118, 228498798, 450687830, 751619101, 521951615, 483092269, 954460478, 111264109, 889680184, 967751960, 238958053, 577575187, 23685008, 940063529, 237573213, 444408211, 646341739, 501254755, 118016000, 665196896, 254361607, 826008236, 130537092, 30617564, 704621590, 94070945, 612769975, 437896635, 272958949, 378672941, 551413092, 747391335, 788355116, 747109824, 332543117, 904883656, 538643515, 42778332, 611432435, 169994279, 979035204, 878764784, 879473977, 571059375, 329657200, 952712757, 287731052, 74867181, 512458274, 107972316, 159191484, 228091854, 710924495, 242627319, 993606189, 265039965, 850807780, 62933954, 932664845, 574330321, 463718211, 990516275, 935102163, 824790405, 311616201, 788107165, 404914161, 893405147, 159474655, 659763679, 195337605, 509318030, 309894317, 851487609, 669670726, 439161718, 691024134, 163051202, 489366260, 980804984, 768013979, 701743824, 855043125, 952533963, 153842557, 684426219, 72471576, 773272209, 404157363, 166135784, 596856531, 929363057, 793834811, 897485147, 952914932, 187334321, 733832579, 668272672, 106182340, 583150851, 138328754, 305759748, 566642741, 730556549, 509351483, 803254536, 220578456, 341377858, 453167665, 971297743, 400840472, 746940340, 482857653, 290055497, 927067145, 81157907, 477214334, 171703950, 329168519, 944653665, 669645412, 532415318, 363582766, 788587703, 644206213, 36107871, 515154681, 100602372, 396889730, 133669903, 61923040, 568057788, 69602192, 880904659, 482362943, 571670956, 739667709, 215172563, 771915180, 15622173, 464165959, 317955376, 978351080, 347862425, 435897468, 382268707, 490269231, 634460800, 28019778, 832279348, 299911338, 632768139, 156303520, 462148974, 658416121, 68529168, 695482069, 276327205, 167604013, 184952202, 897966389, 774325815, 520643202, 154931996, 138568481, 685963546, 310674812, 360608209, 326759696, 798400676, 836943916, 831217555, 641203505, 467703036, 746795325, 782430403, 320139072, 235599787, 521206309, 793342272, 420703806, 368103478, 156481047, 478501687, 334856688, 695734792, 914355492, 835733377, 250601256, 706667716, 888505801, 777556331, 55153110, 654767896, 768877266, 864538283, 510812069, 758206537, 360476091, 239184741, 668102428, 434414460, 531378825, 698589528, 661223436, 118397733, 512597367, 530726269, 309866029, 666845349, 427191538, 569679518, 910634891, 677907206, 1353047, 356816655, 12170654, 105820036, 717906969, 676210436, 699077655, 266172784, 834858361, 200569310, 134109523, 876431465, 189159732, 573629775, 811192688, 621158633, 800946173, 989345722, 40084964, 986280267, 316004723, 55277116, 810687020, 156407661, 885776864, 503288117, 989104387, 114502761, 981683157, 571368354, 122556604, 525448723, 472735322, 944647190, 650762279, 18316721, 201609956, 781584321, 37503642, 34721467, 707984845, 325667144, 353819276, 564366453, 966004294, 537952324, 417677685, 88564418, 960896863, 78219662, 296181568, 576405235, 440089300, 817556677, 239606243, 844934758, 181770281, 943975393, 179344178, 961131817, 681095930, 170040171, 364545678, 148639265, 833310415, 491481732, 998650741, 288485065, 870725293, 288095598, 167449433, 376563971, 292880715, 395466594, 614134383, 132134549, 541380166, 124873559, 684949737, 327982407, 415626210, 306952272, 382618251, 882396515, 176655992, 537873331, 273118588, 219022107, 702516166, 431635185, 690169978, 642759211, 414957550, 699648235, 488116276, 457797100, 290318995, 521743592, 483675035, 280172905, 71581430, 517590201, 253135660, 596239547, 928454188, 768528509, 237342074, 269109689, 81692367, 162524064, 933879764, 481734900, 785767693, 378712802, 976565252, 30726929, 342574464, 210279903, 880643208, 401721512, 708335086, 677947954, 856958228, 291363410, 844420955, 545720364, 958004021, 543849623, 431070505, 11408528, 587155159, 627223100, 941719836, 589169004, 395903031, 816883159, 898154390, 765049873, 455117068, 609918090, 317936732, 675485794, 294008353, 337832830, 16332535, 390006550, 890492137, 649310098, 941593342, 909640943, 456533246, 13524209, 518842673, 188237039, 362462282, 544312878, 863270727, 862516644, 590993450, 706563399, 868082289, 675349860, 176589952, 863454767, 471727462, 636001388, 757707612, 418517216, 552814977, 701084988, 579901691, 1657188, 375653121, 388336640, 901988186, 271811990, 255799313, 238419681, 976119911, 638921731, 14565447, 476372879, 814275530, 456213660, 802057810, 565899079, 942061687, 18026508, 30012548, 7616092, 385642768, 74753039, 963422517, 162570061, 889667136, 982132217, 272585372, 488785112, 658076780, 916292889, 242289142, 444842515, 892462148, 209959286, 727433864, 414004504, 8512523, 418141306, 153074839, 445674399, 817329023, 847887231, 72970020, 393097587, 16222175, 619462409, 510363825, 455375158, 676932399, 730809251, 531026065, 82447576, 996431185, 441880526, 871831954, 50018250, 126408566, 28162193, 167093290, 710409230, 568802278, 676572418, 395799696, 30700446, 975700260, 689021265, 288839718, 376652836, 539649829, 548655468, 715634756, 709136707, 771522628, 895261236, 78750778, 666029298, 22164963, 619921957, 91010246, 237592109, 377579635, 804094879, 984764683, 251609394, 408639500, 168435455, 566841799, 280864452, 515448934, 43035610, 594516496, 50656945, 721157675, 437881285, 958439999, 433941986, 392227925, 624490385, 534906661, 513069413, 587412894, 993452444, 925228805, 106473241, 613982284, 880655731, 628270250, 989812015, 798696341, 757860605, 793879892, 7492385, 349080525, 621229026, 130035162, 241601699, 927952119, 883773772, 544088049, 299779606, 537745145, 151795170, 80196093, 848393464, 276594882, 823772600, 45762979, 633826077, 415582216, 36788505, 939323917, 179629240, 874523852, 351996216, 291817691, 302334683, 581878483, 739569579, 180999125, 935808360, 981062909, 57446029, 226756825, 724458242, 966214363, 749799704, 714529170, 584735379, 640938149, 607588359, 469490237, 161174359, 387547639, 256846636, 339801875, 489192617, 814169214, 636429426, 941092022, 482128443, 826514248, 114294458, 775053648, 907828094, 117157503, 707547334, 359456109, 661522131, 529693990, 333426869, 317335569, 820471850, 691543020, 464468813, 231031143, 309063955, 295910171, 943400615, 570924218, 166020375, 243176684, 870178670, 133039349, 789596782, 803325052, 550343882, 706852511, 413126365, 632653582, 678818396, 891721080, 883072010, 616145086, 992996560, 539541052, 331201217, 792080153, 787966396, 679568340, 749211753, 947881643, 604652055, 480974040, 504113582, 431494716, 813078200, 935555300, 940315135, 727166638, 757088521, 660567844, 910999608, 565643350, 961945360, 289464253, 849551674, 359850088, 652739145, 370494472, 654253493, 968423503, 53779160, 321566851, 939443906, 985565154, 811128748, 270047557, 433256792, 106808350, 366209971, 857275671, 666322881, 99237376, 792884797, 406768440, 90783719, 965204751, 519675024, 181153463, 107105426, 92239694, 428410640, 883135127, 315533361, 56814583, 138112039, 443616238, 480018993, 878332899, 649635881, 58249294, 237455521, 245029057, 135478917, 47471195, 904905360, 103112590, 564009463, 524346087, 768890894, 867444058, 196280733, 566893493, 603892522, 901450379, 512504061, 750033590, 358629892, 780891769, 120275273, 260321229, 698499500, 33290807, 105395915, 515706441, 529578953, 713094272, 826700746, 962382009, 442788772, 367902793, 591730369, 707569869, 215229806, 300506507, 818200955, 230537364, 32141207, 541083843, 266089531, 116914158, 575623823, 442808438, 482960501, 197150512, 27323596, 549768515, 142160762, 818657669, 89502517, 532608560, 210805743, 686334450, 990940555, 402336223, 660081294, 281485435, 908603095, 339887374, 455647316, 359968292, 361243919, 486154734, 628614921, 102963475, 987537865, 153636456, 875650457, 540119006, 928207135, 471852502, 606915555, 230370312, 338737999, 466617988, 633855192, 611335239, 873579202, 975986278, 798155897, 176277888, 63347062, 516514153, 87463239, 295666810, 194706100, 425253384, 848477143, 922581045, 993090519, 293926533, 192007018, 875367840, 96188932, 181222246, 68648957, 513705774, 700423436, 580288714, 799875265, 751092257, 31361802, 732259752, 486701122, 22060856, 120733592, 373839697, 993415521, 303097028, 712122173, 641724796, 540421856, 345661285, 909112592, 213368079, 201577626, 111635810, 29574019, 781723274, 885043482, 389647485, 759008276, 856600109, 44386974, 676535525, 96880054, 713573080, 364200365, 432955395, 988106045, 198798314, 996122219, 715294196, 108453506, 137531542, 481839910, 753644315, 62117585, 238889327, 425084964, 771147250, 535138197, 152252751, 811582366, 822381568, 903012588, 348304745, 436787079, 818265690, 580718791, 933181979, 312663881, 899661324, 919012158, 104193774, 217424310, 674702425, 243239248, 667548350, 721117435, 477189979, 627792528, 851895739, 880780400, 568862894, 580416463, 647628214, 975787460, 183476244, 258651403, 19875284, 512211074, 290372411, 716058700, 849803107, 494690368, 30970634, 513257249, 215524131, 787500294, 425215919, 949518730, 105953907, 23137188, 561536791, 724153002, 575379348, 622735652, 8002363, 657438093, 893818636, 523353333, 798426396, 300080924, 945009196, 977173311, 406954176, 219429825, 313621544, 112385730, 32554711, 992034844, 737978755, 497009041, 859816036, 520423280, 896401840, 238961591, 640662030, 945271521, 646947271, 296325082, 401380731, 148597473, 210964288, 568305145, 790296591, 968869725, 828713031, 544826190, 401155681, 658575659, 933435793, 151592780, 910160919, 291729351, 37627663, 60394241, 758928351, 963958128, 688406179, 630003799, 292120275, 961987590, 780011689, 149420699, 70508778, 151170219, 251691212, 497030316, 817212177, 848586395, 378530675, 161500872, 925851616, 301156659, 682492689, 393283465, 293072395, 593062264, 832976577, 830126687, 694413773, 387315572, 189069478, 834140019, 909331535, 912433663, 823682875, 219238203, 959412534, 244878429, 180814329, 513897313, 459032545, 15474310, 290536038, 951495861, 815051933, 690230564, 43271729, 170240404, 729938476, 278364788, 557125204, 323060300, 3408960, 738426466, 605672759, 115318261, 420332948, 221705021, 112705091, 35282615, 323106684, 750193017, 643531883, 220117998, 16176953, 883305015, 289718864, 211636765, 359772645, 625126319, 501887634, 559252266, 927815796, 550980093, 100629283, 540717079, 95924642, 589675445, 596585536, 70303784, 824564124, 465688997, 400500665, 381167249, 331617975, 410285032, 256160174, 160554478, 933246785, 622274762, 793400961, 120049546, 167771467, 454951962, 609050902, 839733263, 697050474, 25300849, 992892849, 999313956, 447855688, 587492879, 559589683, 364565575, 751333643, 49914274, 834142560, 159075775, 500939772, 548686970, 65832371, 367654627, 37696907, 976830166, 379134519, 519476863, 946748180, 534776218, 855771030, 921687030, 22201687, 865872768, 710851841, 925234304, 860286128, 174111606, 229261374, 41209901, 6178635, 309642676, 992024715, 294714155, 538602426, 195672691, 150769986, 455960147, 930663702, 646707292, 482150906, 639720370, 975169846, 163825658, 616468153, 397363126, 417962549, 377053510, 91109704, 71019740, 374398639, 610962604, 70816934, 416227388, 601890309, 680665673, 984941452, 602530397, 456023575, 67148831, 907307001, 852763935, 193776358, 338021445, 988224853, 996004752, 103525552, 718953861, 693578576, 887087224, 456900770, 810093553, 736983622, 303857749, 436250712, 363792188, 871889533, 387285266, 7777518, 371393610, 761538749, 291742070, 536653956, 980296166, 80239158, 334071385, 636033044, 390730923, 49362564, 122382823, 294775472, 841966700, 602366772, 625323120, 821097218, 998900132, 813445637, 152698458, 198782494, 802787696, 612682549, 122249717, 422739745, 43786716, 716489887, 932233963, 320232251, 947532398, 105064326, 537013871, 803845880, 648777857, 720023084, 377738458, 297868125, 308794386, 383709053, 952839378, 159384982, 116794368, 355315547, 348752175, 896983097, 821370765, 3784808, 733885916, 214792102, 910698225, 674303649, 672362452, 434154159, 453999252, 424589265, 109528737, 420834920, 692767295, 757282418, 425683478, 554323792, 708422076, 196885550, 268884053, 316900091, 169539609, 547331447, 594569026, 636608586, 174917861, 967501482, 125318250, 416396636, 394964459, 90986633, 483666125, 496373247, 888095511, 109979007, 357283255, 421661131, 760269030, 190842563, 562954767, 919940832, 421097497, 63773814, 622026111, 179865880, 928893181, 951684043, 775311716, 682300438, 773160911, 402738977, 105222257, 26548885, 235943130, 545475664, 135600213, 91550808, 613855, 812106429, 796933038, 566657205, 814211623, 152315147, 41156437, 408612413, 456315162, 906230924, 176170508, 915998444, 225974809, 519810622, 903089250, 451002814, 492252300, 78941172, 618398976, 288163103, 921199248, 917163621, 538280150, 965010093, 968576760, 242440302, 705593839, 944678008, 26296029, 87899320, 785609157, 997216269, 620658665, 785436748, 30635577, 907298350, 976338500, 789216033, 534631831, 121707133, 621890833, 174297568, 927631386, 226762738, 105292699, 228603250, 419698591, 882865225, 899710501, 627547781, 486694638, 821973500, 391653378, 726591058, 529119713, 485383406, 559102127, 399627398, 244142219, 673947199, 901758617, 713062407, 823075020, 455091625, 834052821, 541694138, 588488732, 473817183, 783349167, 871909633, 9571279, 969133532, 929913573, 499940456, 546333121, 823917435, 420388000, 841240144, 19565454, 605001346, 767293813, 851434475, 9453559, 748750941, 861445748, 703011773, 34488766, 460902152, 261215764, 784602513, 597900415, 419654787, 128875984, 160131590, 717712377, 56220589, 336078316, 593180566, 380032776, 495254473, 34031030, 869296805, 595805085, 400311494, 329073877, 837014305, 26415242, 135563303, 180711741, 398408180, 58104009, 325694104, 207974761, 436312005, 258769252, 859393177, 516932521, 193706325, 574763339, 694906510, 191037349, 660777544, 933224382, 659440571, 333093695, 710328286, 894602657, 511055460, 504469738, 742362820, 206877476, 197983682, 597177387, 289996409, 131786151, 911059318, 127856666, 804534936, 767586021, 164356394, 273983566, 174872921, 510723647, 592915933, 720454856, 111699111, 540308073, 573349462, 729916880, 141422586, 721229118, 987554466, 531981885, 791888374, 382081083, 750920223, 424572571, 261493165, 515142511, 942729810, 979818030, 757030121, 19701367, 999354683, 187967299, 382527809, 225644678, 13692285, 461452553, 618315205, 667946139, 975373265, 22569379, 263683376, 973100361, 844899495, 893683432, 266026407, 19899580, 212785691, 204904722, 909252856, 201106623, 851100174, 327518484, 87487074, 720687907, 895918813, 389206705, 366568068, 304934860, 16829079, 810509866, 937305323, 746331024, 310762423, 214872398, 209104580, 196262441, 410779262, 566117950, 336789814, 517413850, 737626109, 971300575, 523823386, 98599637, 949612225, 393533198, 132013638, 362812488, 428941294, 385050704, 890924810, 700041411, 317267765, 393381875, 273954056, 393047128, 706617234, 941440214, 137713000, 955986814, 217590386, 179682768, 82252365, 650826015, 225263170, 840691803, 495679928, 193577970, 255361643, 892021169, 923386873, 762090147, 912857627, 934867514, 843550769, 754516061, 564366842, 266873677, 120551078, 391500180, 789372143, 488879848, 234778957, 472328396, 444013222, 157562691, 295563766, 145127422, 539865128, 735236176, 325407597, 836757965, 602321970, 751153493, 653443633, 754205890, 361355359, 374397477, 474533339, 91547556, 721900733, 47293697, 188805118, 175153161, 594463271, 94889160, 245755311, 401103166, 862934641, 123226825, 205177353, 298761428, 138225830, 50287135, 446530577, 788930187, 888648625, 341961655, 91455938, 454292192, 196186771, 170257127, 803962441, 83314645, 734483576, 589069268, 434161352, 583284721, 830469751, 40260858, 492512329, 238438721, 656988421, 292048821, 146285058, 664637663, 92545315, 679213501, 229051694, 957321480, 982631174, 925208831, 271512500, 523932260, 94069570, 897408191, 616698973, 182595132, 416153850, 265457690, 921327746, 378630280, 368371961, 834901900, 935830607, 101437912, 603468588, 437119400, 972072106, 4293052, 577491523, 671178374, 425484301, 544359538, 539463524, 386494403, 432006199, 850802308, 815576277, 70944196, 776793504, 127133956, 231679397, 458693319, 69232014, 646197188, 745190017, 593621002, 543875909, 553607170, 241184105, 7574210, 12649035, 486540634, 804409384, 117414845, 87727512, 303950562, 757290060, 356234318, 949480864, 631981937, 969035737, 584737430, 445935375, 450243227, 982338537, 853145588, 37696692, 884062650, 708987973, 399179763, 436303405, 79423889, 654373527, 143944884, 489891385, 119980270, 503335954, 23282136, 375781591, 45128008, 820025737, 820027669, 939242258, 972039090, 349180897, 537771654, 372022189, 216841522, 738588817, 831069965, 657639468, 234632059, 925889962, 861629584, 71271112, 429345742, 664070004, 691878380, 737691706, 157704079, 513109455, 605382893, 834032802, 747228818, 357885502, 328187276, 618868006, 48868652, 754050745, 831580162, 397204041, 180762015, 514330405, 23763580, 996520820, 170854224, 868456143, 926294048, 52948941, 773725795, 232798967, 597019274, 765525423, 663085701, 31341860, 914619380, 80633296, 117359842, 765510442, 75009314, 968130411, 811859777, 9201382, 542789848, 336823988, 972416534, 403938119, 502826142, 692923313, 59307404, 624895466, 550841016, 893293828, 268776634, 429271238, 102176989, 340694694, 977618186, 614126917, 551004741, 968360746, 135048096, 831711390, 213193783, 578807921, 363759187, 949757445, 985948364, 316520942, 569884202, 586004003, 377368532, 308323562, 584422845, 383104707, 970673962, 720346370, 461627482, 54936076, 480713241, 999703691, 143373077, 153300944, 881944866, 568337532, 506054981, 61271871, 387000736, 145703661, 860295298, 999835690, 510615694, 76563435, 447348600, 542651107, 312504333, 476461471, 574513593, 537673229, 911313413, 739918496, 462071764, 364209847, 107377823, 362112061, 396234413, 954247802, 54893402, 249343232, 520234613, 966777782, 51759673, 947412900, 29423591, 176975187, 720867304, 945119953, 422419107, 149533811, 266308964, 968089487, 440480474, 710755509, 953642052, 389268144, 257131851, 564483486, 114528947, 768396179, 524324541, 984382919, 335503421, 46850093, 365742746, 731503795, 519001093, 553399948, 605267111, 71652307, 945129887, 703935223, 218518705, 804976348, 296231131, 66528468, 114108608, 539318565, 207316950, 613627424, 620219147, 113433563, 937283583, 416392401, 974731222, 159189201, 985324841, 812500684, 324245623, 609085459, 668202776, 66066614, 264281310, 495828046, 857558116, 863599912, 657346588, 746818425, 972151277, 976528831, 319309381, 931932019, 481440087, 472283044, 898698870, 17669710, 613529290, 279439819, 996179445, 476693561, 305643113, 538953106, 324070794, 385594448, 766583235, 248147907, 975984376, 412309986, 183880618, 250425263, 647370362, 633127652, 686323380, 661752677, 453813502, 64654642, 468987080, 233539897, 902976488, 359434182, 509884978, 843223323, 711455470, 246010004, 774174351, 131962624, 728871248, 72540501, 82868203, 730649883, 598563549, 751579824, 867000765, 288213956, 133682867, 9470412, 376984477, 934722240, 359928093, 71559917, 209806562, 66958133, 87167664, 811470411, 425187979, 355048349, 130116851, 80648277, 673636755, 715161457, 398586621, 591958173, 858919910, 662349493, 737734315, 537406078, 638873646, 714344856, 279960686, 550881399, 829617117, 474618016, 542005131, 588750483, 482274686, 754645711, 954494106, 632428228, 163590411, 83948525, 596189409, 351304613, 598078136, 546975281, 868303361, 131947622, 493623899, 520954018, 587752554, 496932600, 734199903, 16886643, 598146284, 278904507, 78816436, 934491006, 296249598, 150171923, 853175452, 55854347, 989469782, 577054733, 129291488, 227465155, 555177200, 906462762, 162224183, 269482008, 130412147, 211885050, 168862533, 51889106, 620270408, 503576354, 232482042, 361222834, 310341817, 260431350, 51464046, 342893030, 926111512, 546109431, 651573368, 29101600, 64119475, 849863149, 390107607, 456635217, 441258071, 784112276, 680917517, 249246950, 752763510, 718438880, 897407960, 765166555, 936037986, 833486183, 838460404, 967490533, 363859117, 419233314, 805519137, 722171177, 453534760, 927844976, 65987679, 794672750, 309627764, 588690968, 196045552, 848534308, 411713633, 561505038, 16037435, 456054443, 202611801, 500786060, 223133517, 805823459, 961248620, 18187503, 660489309, 842499027, 734430365, 824189968, 57866462, 381860410, 43218280, 944382062, 531548701, 670345410, 391036191, 443781716, 586349495, 583416095, 82889267, 116708340, 533126355, 697020802, 22022437, 7458104, 558422274, 126709934, 31421028, 766831422, 116089188, 697613468, 596494655, 981407553, 809250028, 319644579, 802719595, 887560018, 330852683, 545465175, 583290027, 318093246, 902466142, 282022854, 863812858, 216565239, 456368800, 891980124, 854393271, 992407700, 311850005, 838830312, 73840954, 595919312, 904701332, 644970715, 92038373, 768902538, 571847250, 974194827, 162576192, 498623217, 968379826, 759096323, 261368968, 482213634, 860971817, 371019433, 100663536, 610199004, 276802798, 917041128, 381062984, 950195767, 726049338, 886451591, 103900473, 362491735, 358392281, 165101235, 197827286, 638804388, 399714138, 916845126, 467731770, 453569183, 988093030, 276945325, 589187470, 320006638, 50705137, 501947987, 105661090, 917695865, 706058914, 500496391, 591650350, 451720252, 569665773, 86259026, 809639852, 862519815, 54809845, 87551005, 203183764, 655027807, 74696771, 394796445, 458721247, 11224217, 195893828, 232642138, 972514039, 590573004, 125767976, 3854875, 112542807, 461165146, 768105777, 167108202, 534350304, 81746573, 708397460, 765896163, 211769581, 379548951, 766291094, 859576056, 220634782, 481950927, 201047193, 906830070, 8920551, 159536625, 323796434, 701178082, 968277410, 158734162, 995274604, 985772351, 851754787, 677067486, 342501148, 427818736, 987233651, 346588298, 190247203, 200338169, 679510221, 888687573, 917865697, 866204750, 690559812, 265657660, 906518146, 418251138, 129887856, 35122017, 379297359, 567306290, 561226791, 829185296, 431506921, 595973792, 30367955, 794874337, 561740925, 814577055, 396592267, 214686118, 876107986, 149336141, 784608991, 883763092, 929563296, 18600289, 942975775, 926152448, 880742860, 168723244, 680029430, 115379128, 261888232, 919957012, 62622424, 726562426, 639651320, 198379926, 792661358, 378350899, 611083939, 876994827, 221788063, 991678869, 248491701, 505772123, 898863649, 140648934, 662661734, 379788546, 553465001, 531462977, 117827494, 222633928, 181607996, 406258422, 203955494, 45365876, 948706533, 114336646, 748745882, 854774114, 671449080, 255968560, 629891256, 981522539, 474419934, 283187877, 236674093, 817196739, 431493922, 791477226, 384645606, 571268470, 914896069, 70844146, 928229504, 811911038, 923530808, 107896933, 269791500, 262091862, 879418318, 996169887, 576682604, 990533756, 520414986, 4402877, 814800969, 788057177, 790506614, 646912151, 882778185, 907597905, 961634489, 502359443, 828438954, 495233243, 627704198, 133015727, 138904920, 759586314, 179806868, 988142163, 812321403, 456964577, 754160947, 65864228, 645227478, 524938879, 551309265, 823340630, 948807910, 288670696, 460686906, 922611282, 198731262, 204187301, 81322258, 510906694, 615889690, 810947002, 436058862, 599407431, 592491637, 990267795, 92693605, 461540960, 573024023, 888405528, 816527608, 585932129, 443944724, 572564443, 793571708, 132730973, 708514726, 113621602, 950836933, 884458968, 409473677, 538445758, 271151543, 851016209, 554961809, 231413480, 672791642, 191442804, 605411792, 626421475, 216106340, 595352205, 959268076, 550569565, 486314575, 111933674, 730581916, 659164685, 502546235, 567533237, 982475899, 301094228, 107546226, 4340079, 766860415, 844796830, 630350725, 357554218, 243012467, 988534448, 959997993, 229342974, 935849681, 803136006, 320885289, 111663027, 189206895, 204545863, 985833412, 331893995, 611813248, 606500868, 908688140, 520930866, 995278456, 715284226, 284102393, 548262152, 435234384, 157948656, 58135154, 606252018, 775978589, 528300451, 95102029, 924719734, 149423935, 568316249, 480239207, 533446461, 511804628, 516102828, 829905468, 216181961, 602447591, 954786080, 319141107, 773107943, 371699665, 827528933, 149326382, 863403554, 86643841, 272988086, 441035844, 727985690, 11767993, 531226227, 244468916, 959038750, 780168238, 7662979, 245815814, 407673508, 325400665, 904051112, 681124225, 109036733, 818525149, 443204513, 454876798, 709254660, 450129776, 462532843, 397050699, 147089689, 615422381, 575047869, 613976564, 247607139, 103545660, 283772020, 365957947, 416175337, 552659309, 323349501, 638823338, 405600180, 887296816, 170020470, 546088027, 423424615, 434413357, 487899076, 792137063, 749082894, 653519921, 600344473, 876854506, 484002284, 440746931, 570958527, 837271054, 188348645, 428197684, 800734864, 39561443, 255738938, 871074482, 478115204, 303308416, 80556302, 377977356, 964061967, 752974708, 565489464, 621314862, 647407440, 180254426, 759117311, 352357561, 863381189, 426504581, 489748551, 205881135, 695188265, 434823991, 45522645, 208828776, 19697144, 533401403, 627589296, 815009975, 359181282, 590385085, 82381564, 968945316, 230093798, 539984649, 89259097, 960617925, 702911473, 316459209, 399770410, 898941377, 41793969, 770669523, 292423691, 162720800, 428978585, 426481288, 268337496, 294440331, 111612341, 863369262, 626851177, 398543708, 968176016, 237174674, 439904483, 259585892, 5140761, 309303741, 745647630, 576904609, 974893447, 19274581, 767065312, 86281886, 157126137, 697430619, 872559626, 953865059, 786727333, 81827700, 823533299, 734339144, 34442404, 44571558, 470325047, 185864392, 194524362, 657990328, 912989062, 178966586, 327822690, 129979977, 784107795, 695322750, 132047462, 577284535, 350838352, 532281016, 517965294, 843301947, 427332173, 107636827, 59520956, 646447689, 52677900, 421597711, 913930259, 583882651, 903673190, 315314383, 408274447, 85738071, 1922619, 90131946, 839485608, 217751311, 151579775, 399582540, 237626928, 454863827, 142119925, 88204220, 360238524, 208563901, 781322569, 495459580, 394503044, 601582786, 650193065, 272057133, 628393477, 403747104, 670906903, 937080958, 583067833, 433510269, 768335785, 43887513, 819562216, 347217970, 606401489, 563758396, 285699898, 885023435, 617158397, 472285793, 3766002, 399590917, 681534594, 402692289, 401136525, 542266584, 890357948, 775642291, 660250793, 818326200, 217925902, 19185214, 848794061, 698652348, 845434457, 81446839, 967268903, 187234970, 152784613, 594811286, 65111715, 369289910, 911034128, 436489190, 735013164, 402830751, 67585349, 935637749, 784291978, 835166602, 388938700, 719913379, 195887834, 892881077, 973592435, 31563508, 727710847, 69985215, 183783947, 144334682, 697699696, 77458593, 678980904, 78170669, 244038315, 739500498, 949067401, 67684867, 370107146, 883247053, 690011254, 43616646, 821387304, 272505701, 855547940, 925374369, 414029148, 295351252, 816176911, 783475067, 177438753, 637929881, 860291895, 552469634, 239997453, 148689540, 340137285, 552133406, 486928153, 748695617, 911770413, 553029201, 779510176, 641695935, 930353637, 589302909, 260298685, 227598089, 544836779, 800788537, 874515653, 137967319, 683127109, 69553547, 428255654, 297871722, 875068743, 19356841, 358309172, 861592679, 544715022, 208502229, 20877687, 768236286, 519367575, 643272158, 986792335, 47663498, 349574242, 106853276, 909254988, 350443223, 446041417, 627767716, 439071015, 334739966, 863177343, 661645594, 400467834, 636585569, 533554868, 451168356, 106067452, 324584349, 411378367, 828753585, 912666092, 676406646, 199040739, 652094042, 784775007, 460494937, 621083256, 484437569, 116318323, 318823965, 994208976, 110434485, 588901821, 516556662, 77894907, 54530593, 701755787, 891303431, 886758146, 494030927, 688333645, 12499359, 483625558, 544304838, 438376247, 318197683, 254420156, 519680360, 39457032, 255784404, 218984050, 434840983, 998133249, 497583048, 5774127, 270683617, 88188894, 276599180, 727202502, 270109310, 142018876, 713543974, 534840480, 594163248, 104005828, 634882329, 282195701, 775983667, 492419708, 414848981, 557149224, 325862841, 855885436, 218539009, 7647437, 339493683, 685804392, 398085306, 400870996, 20977994, 358517923, 850656181, 905600340, 390197579, 949806584, 479408345, 866284436, 308054113, 211852099, 472385818, 846255070, 472346416, 357898478, 335940240, 343081180, 198745424, 12251544, 842099639, 76267709, 175376799, 941613813, 426989434, 413996659, 231582218, 914689555, 135927717, 775244846, 739319742, 288464357, 904373812, 253725181, 716261074, 891136927, 731290386, 219798960, 20325298, 501623475, 30093643, 18104533, 595834479, 557113869, 277357545, 351999219, 689293795, 343004364, 220709015, 212810615, 35711355, 879984789, 296675943, 653942756, 980124288, 79631509, 466899966, 439118249, 197051655, 604822909, 339091244, 473747760, 834220512, 861763201, 78204804, 381410843, 44431189, 155021751, 297466020, 103509264, 982119632, 685478851, 415974295, 181728932, 284883091, 255894671, 476602574, 49488425, 380039779, 708071302, 58195826, 57096014, 60711992, 568820996, 812698920, 706880260, 740828890, 463930206, 646484466, 56988037, 510831493, 655783115, 617265625, 443845796, 937978954, 316493956, 69748197, 559740651, 806049346, 272784594, 672082037, 60382568, 84946934, 967940151, 679650173, 876236735, 47403467, 159533191, 416141753, 878364435, 911045565, 846305591, 896461492, 365682230, 600744986, 866513647, 20176543, 972542086, 888480755, 550184109, 354658704, 36904392, 889792911, 617722963, 872517218, 591928473, 564610346, 349832670, 764036199, 153061468, 651248353, 125693600, 626619651, 531923867, 397896346, 481578558, 16504817, 250525600, 310322323, 232216261, 277473252, 257996910, 396033996, 159633241, 880886116, 771925804, 9848698, 111408388, 415947328, 32911014, 804103474, 464203621, 144792073, 55631865, 104974798, 162386048, 208786569, 484366893, 528501660, 764464228, 168364144, 344225645, 804669885, 517699308, 852496080, 261507299, 84972372, 62229049, 790803172, 623522497, 12775405, 903195562, 734422496, 10282324, 977910019, 360446800, 816224564, 500725804, 660341125, 637413052, 266961852, 868936011, 539745700, 939834226, 270650762, 77401272, 322090889, 426728005, 426028106, 93179805, 432822797, 351383498, 644307270, 575045618, 603391452, 419499338, 172809886, 960694415, 504991067, 807647368, 729740308, 454180056, 586347711, 407089099, 451793273, 138677654, 706152102, 379963039, 434376581, 927018544, 823883222, 104494403, 645396742, 79270869, 979596722, 386980284, 506462053, 171090930, 598548632, 309270239, 667579438, 407915877, 595916451, 957538876, 272621326, 925552237, 2850932, 932216643, 101967391, 715823643, 505667310, 820669523, 687556018, 48314249, 389537976, 20106632, 656182415, 773495147, 801798207, 614959912, 918211177, 777586570, 674153161, 984409342, 649378413, 388689752, 380687430, 421441560, 529887990, 673828241, 934844944, 720619789, 795233592, 55825430, 470006546, 7336120, 328219109, 120826475, 698293192, 520751476, 999635899, 267741204, 340754730, 876242159, 767984238, 796145734, 672018321, 119996481, 471330944, 261606644, 150874407, 393691220, 585205168, 209129681, 138439555, 659685406, 475444805, 102630536, 151731650, 503696915, 572005713, 550071249, 262691515, 776288995, 560273522, 121200056, 734211170, 306001405, 996463951, 903988482, 301862572, 2967137, 883030533, 479443812, 934894557, 612078156, 790586243, 144685489, 993757075, 574946740, 353533653, 836227497, 859048390, 984129451, 51108354, 343520327, 351035967, 481177231, 242261825, 864372667, 97488515, 213665580, 421920094, 912396548, 817631680, 323626127, 177162791, 127056614, 835236154, 873442862, 256628247, 221299506, 852701087, 408498221, 210743493, 659038034, 431322008, 355376307, 955880691, 115762161, 997083566, 341006083, 422384837, 745226449, 441742410, 174129338, 416181936, 301692840, 908637666, 617694707, 101956809, 979958136, 235084777, 223815251, 8016132, 630452074, 998284679, 740337092, 609076966, 214317809, 458519281, 376892616, 85850446, 154653425, 204967147, 54947917, 680473604, 437395672, 849555451, 539916828, 430704999, 66634966, 112095886, 823196337, 335369944, 800437314, 461504857, 313828844, 256722315, 425323694, 896679685, 323106242, 385832156, 457746494, 847508186, 286730192, 233751633, 164529796, 234940673, 59475012, 905981007, 378275440, 222174057, 439341968, 817210374, 473829362, 913140429, 250146755, 401437578, 520347746, 545475334, 530983996, 667237538, 727029386, 120131462, 911985765, 146743002, 245030381, 665311953, 916158662, 26562999, 214473696, 957017903, 609574851, 95714912, 725125261, 70081802, 911675592, 409604420, 329273843, 273410293, 422133470, 453895401, 409910178, 204913620, 446298906, 7109163, 931165033, 954608491, 393632608, 807295459, 261370216, 302514861, 501668700, 165141081, 646049614, 451305124, 709298853, 945546797, 98893035, 760097682, 420809390, 683138577, 884485042, 533132080, 52685044, 89689904, 861810379, 456368524, 467741389, 357419164, 3693724, 854001406, 879836986, 778018854, 571838854, 58959921, 565903771, 777197822, 352859232, 870021941, 106506980, 259051848, 497881793, 597500360, 668227493, 233951381, 41790821, 527246806, 233175705, 738101307, 530100353, 134243757, 779803206, 893226007, 37429814, 913776801, 55414029, 642853278, 353019687, 997681668, 686251004, 352031744, 79547067, 140440560, 165729807, 950370659, 282558121, 621048351, 655572980, 646272722, 407738380, 612811896, 601897170, 626909363, 793076272, 25199102, 908455201, 706356964, 272845280, 962925676, 5866998, 120023850, 133161029, 913061558, 862680452, 919325076, 735070298, 755509133, 488549130, 167097860, 663374198, 958558114, 237797084, 738876722, 69897176, 622036908, 20773703, 198911393, 882276648, 213474517, 663879043, 298933443, 539105291, 673633430, 401509436, 762502164, 451109272, 761587652, 562746939, 852902984, 696317930, 639349593, 614968982, 464551421, 72389666, 973367762, 392799204, 604231659, 655840797, 154843791, 672664957, 528774345, 875322047, 134315584, 702289357, 696329815, 930596281, 780499103, 826487285, 812403644, 84109844, 265555797, 214702768, 673128025, 972878785, 566505595, 696537364, 240381881, 626093658, 439651814, 411097261, 44138197, 563679206, 213671936, 386277771, 852121757, 268984298, 384539785, 432153400, 39123336, 20061071, 113238402, 273233902, 563262824, 359263262, 301215010, 776331397, 534434523, 32111681, 708643402, 79270473, 492220422, 448906532, 240149550, 285071050, 830679570, 442334689, 547589248, 273166447, 293603265, 917728090, 154885404, 704186889, 280962986, 331947899, 107563918, 157581709, 550548875, 828520255, 972712775, 241100250, 600337807, 434291152, 438328130, 868016050, 971072701, 117760425, 583827634, 566894257, 669369169, 960856252, 244542890, 939423815, 442492299, 679618046, 114206061, 765678173, 614217440, 885789173, 874147525, 114193954, 639073207, 36282682, 662318695, 81401973, 307460332, 151815230, 792244099, 588692784, 796646594, 105459461, 627220796, 176727226, 35812346, 829757651, 449016539, 762519514, 48324276, 667837562, 801939567, 503091892, 323615365, 386089691, 348923232, 185290190, 306456258, 102529322, 241565984, 467509772, 470796288, 558539956, 475405728, 96143340, 728414541, 194943790, 333478252, 245999982, 385332591, 108428943, 725471738, 656643240, 664685056, 368806377, 641141657, 905211907, 94157687, 574779326, 161319103, 667336384, 963309223, 118050397, 621154537, 626459250, 517130106, 251789890, 837208416, 140051916, 831456440, 747530017, 651615975, 542061173, 858942148, 802827342, 837497770, 302197066, 161216407, 739151491, 699012657, 699777759, 294932766, 850383600, 780459623, 626672487, 871393900, 83151519, 111159718, 583768878, 128731021, 858678479, 520115293, 574683867, 721681443, 818199190, 499756442, 713261972, 602469347, 588343083, 772807447, 714224221, 511437051, 431922344, 813823153, 419839852, 724210079, 312589211, 822837075, 438173502, 324826140, 23332216, 913037906, 693399833, 606829358, 531476968, 401148591, 48322304, 902852426, 862864779, 640027679, 734529508, 685267902, 814563804, 182081708, 434016391, 187261589, 162449424, 746632311, 911282068, 25909645, 879793864, 320691492, 869609801, 30386503, 36949865, 821997009, 784744975, 348709313, 801577727, 759825091, 918605367, 263001650, 611074450, 390066065, 975304497, 833188341, 807186857, 302075169, 571413862, 852841876, 727139522, 137163392, 94834425, 494286255, 395025956, 872445131, 473629020, 779751256, 442945011, 595287504, 564070805, 967136974, 699481149, 538349798, 990460938, 227591845, 992455486, 548118845, 754204834, 728064738, 603335429, 203725445, 16995429, 860820789, 781857029, 757787644, 678927853, 522481343, 695726243, 171134351, 493202818, 508581586, 399493312, 743745851, 367907266, 569185189, 334914428, 409358203, 583800104, 614518027, 684660762, 575832, 84581676, 696573066, 300054100, 861641350, 805471511, 566386651, 859308511, 955579608, 795853687, 399302433, 922699334, 107011939, 330681331, 531111174, 613161787, 588447838, 776468559, 319031988, 897444086, 904050267, 44163812, 793533073, 129119245, 79640010, 80457533, 715494396, 163011946, 666996981, 623957701, 948683850, 646836834, 45914075, 751909710, 393597030, 989813117, 53976933, 58852914, 407051678, 237759429, 591126181, 552615834, 258926681, 397002565, 712255454, 460756184, 555968941, 82551046, 397908341, 975637687, 226315469, 613995726, 761569069, 691707774, 232158030, 516991800, 861202540, 604615899, 482615942, 42169926, 415927194, 176547303, 283256849, 466679486, 871346863, 803667359, 127784679, 403070481, 251376881, 288304714, 237565063, 635937530, 837677030, 973430536, 138622287, 345801904, 566908256, 207177715, 765399502, 186676109, 308814751, 999385648, 283548388, 925754910, 477304251, 301331491, 469556020, 851016568, 921441632, 950958756, 934150407, 777927592, 206037758, 707553691, 532837600, 277751833, 239616929, 215502565, 400499284, 759022669, 684853999, 579304186, 825319189, 982605613, 557362588, 864889364, 818001390, 262246786, 666190354, 303037119, 634058718, 458250180, 730089384, 25073099, 201942263, 371400416, 455099861, 480574689, 838908508, 78937132, 650686309, 134227920, 611215201, 662554011, 417283355, 69853065, 826949645, 891557007, 195499529, 634090769, 224524134, 557334479, 657915709, 103678193, 826842833, 597643731, 963011767, 832278762, 710240957, 944055420, 109440396, 534805631, 86756687, 263558710, 531054638, 759695553, 429034301, 194042189, 723770632, 226463842, 959398312, 594781355, 381289548, 987440787, 240466640, 289352068, 209633412, 84088109, 221406416, 261534703, 487262113, 893555699, 49727026, 758270531, 440537927, 693422199, 125709750, 694556174, 524262602, 136776658, 222599299, 282197189, 316303308, 881595146, 311829581, 685211921, 660411260, 107858599, 649385801, 160764717, 463709625, 239557001, 450710191, 655041183, 233864053, 721870953, 720674397, 612582625, 30237916, 332824078, 927775495, 429255452, 315826481, 44924671, 1632733, 427349153, 299446153, 536876098, 794702743, 571765087, 937955674, 879867155, 38268995, 948776618, 830918249, 421916984, 93474830, 366358544, 71673456, 160592027, 825980392, 97331393, 926344840, 291628927, 764275797, 62976013, 862901408, 778186302, 218566311, 507546530, 403691673, 402276011, 489594848, 72859078, 929263493, 985535621, 491990909, 40310327, 639147636, 109283815, 614489813, 152849722, 985346813, 550108062, 615077055, 331015757, 262712602, 923347104, 991210218, 35634196, 416254915, 69705296, 29164375, 906825081, 480680483, 639854940, 326317508, 745836601, 920679994, 468841364, 889349557, 658222426, 89914959, 222324311, 808749231, 286389297, 500293440, 999131491, 658274684, 170054527, 609522251, 350391180, 797925628, 933002381, 676038769, 69680793, 200293054, 175443543, 972069963, 937761872, 787227143, 972448618, 544377855, 597421304, 113072731, 43878668, 626305961, 428290313, 214228782, 268868660, 487196138, 250829040, 851886275, 324614011, 792849914, 248864575, 830669461, 176179204, 234297500, 690942664, 684491603, 527921792, 932188830, 704973666, 746280595, 711769802, 320866376, 942701559, 767508423, 14403596, 309979060, 739160281, 749485580, 817225519, 529906225, 1142328, 258508388, 292136958, 489424182, 620510235, 805788649, 537540126, 141900479, 265990217, 878897486, 811007010, 221247335, 136057364, 132385717, 663304201, 705502213, 159518189, 62428701, 896269668, 565330184, 523216562, 308874536, 401056765, 421797868, 558290064, 251506405, 677369110, 871955689, 804859693, 414125018, 518154459, 716471676, 828714958, 929640771, 851886835, 28864389, 13329733, 436416482, 892515573, 703609216, 302110312, 873889910, 89743727, 189945587, 377477672, 225405651, 695626637, 471369624, 122456937, 582448871, 699335272, 28199052, 558150224, 357619669, 367398709, 690872423, 151493886, 146550356, 415646465, 970717198, 30688595, 916347249, 688123457, 772741299, 257742295, 16874089, 613611520, 977352271, 244690699, 983032262, 464891062, 127552597, 217927317, 703447646, 417562767, 813248281, 446517485, 795732289, 376956185, 905642438, 937927833, 199794998, 983062219, 709445263, 876619589, 858399344, 826898086, 185065764, 888959001, 6753513, 983157419, 978176091, 467673220, 841158021, 65760688, 441862907, 225514888, 414710599, 48483932, 357765080, 455300000, 573009950, 114054312, 630263741, 942846532, 608134306, 485310252, 656209820, 695474766, 532939744, 867105412, 325437139, 923580059, 131705618, 108276195, 958710003, 625676290, 245607319, 724375610, 169969437, 109631770, 408869434, 74777037, 343337651, 864273026, 963233796, 611031576, 262466173, 388503915, 473057168, 91780949, 64076062, 165364076, 280500121, 25482147, 404464413, 186447069, 863420168, 315743204, 319631421, 737802783, 999023723, 868070650, 347098762, 342376240, 127664225, 883140574, 943350526, 906501003, 796710086, 689405738, 15682480, 142103341, 130196063, 803607098, 979724576, 662988846, 173320091, 632428762, 64490504, 331002556, 138769136, 733308826, 721673361, 514428221, 421757756, 495084702, 443217709, 91779166, 168063047, 653259349, 659920567, 523958696, 110564873, 38109922, 695630571, 220177351, 850042884, 634320746, 865702399, 852431006, 117803561, 634874846, 922687852, 835948236, 994704580, 759656552, 303231365, 443059814, 850646492, 858103444, 84971821, 488574348, 353176569, 434615677, 574481059, 979660060, 379856429, 217819498, 233195388, 403029131, 964035749, 508466420, 815448090, 632544668, 490475444, 378456235, 48336836, 656107281, 285194907, 563958842, 844279581, 319783385, 38134797, 606268558, 709664562, 150615120, 791928493, 872140223, 726922407, 920168155, 395440568, 339324359, 37197099, 832755052, 39524151, 216349392, 640740033, 586217933, 992543156, 29361668, 743797058, 300668788, 31805339, 61161378, 207564607, 752813300, 281613063, 351305187, 264533014, 120946241, 414888638, 763059773, 236341819, 153782726, 467791887, 102796823, 913755259, 28611466, 625487617, 400799812, 354955600, 954800329, 147425650, 345307262, 414047907, 299916843, 809553400, 622724863, 563077761, 409248405, 217181086, 154165808, 387939180, 66919547, 263192439, 52482756, 100986340, 611388948, 959266272, 299654808, 73991986, 432843148, 506818650, 314083677, 626793674, 990875964, 133357865, 100737104, 565138255, 447835122, 646016895, 129639526, 865203133, 243949290, 180635629, 455804564, 620172148, 774127262, 586600978, 45493328, 982667994, 334670139, 589171730, 104718985, 236218869, 943510201, 187272946, 11806464, 257200591, 226688115, 931999703, 802772525, 68554126, 426554423, 284561093, 528223042, 633638208, 141421337, 518606315, 362429031, 656441999, 710120582, 669143937, 125036247, 16382720, 651473338, 593577370, 78221298, 294785061, 814926071, 100018350, 412182430, 272879389, 79512662, 590394388, 541446497, 557608324, 144820076, 902995173, 641678122, 451051454, 952661211, 456454436, 769811394, 979806610, 697132782, 209790219, 915828287, 524077709, 930434222, 649803731, 753915091, 119030227, 925041698, 591558273, 559324551, 680042590, 856937310, 332831608, 732450608, 315349113, 651846899, 836164793, 561362650, 665556097, 242256528, 961688656, 660636940, 543349559, 68253275, 968519451, 612859112, 366433954, 289292399, 368903169, 739068016, 511485827, 38375135, 92897007, 808255138, 321966660, 521630559, 366991230, 107976879, 863584012, 291846078, 971738005, 580909849, 972071470, 307152252, 437075702, 734978222, 678217304, 89889168, 412756984, 30794476, 129228774, 229966969, 881992849, 886949055, 342076186, 945521303, 466537662, 442928461, 524043244, 866433946, 69723368, 84819776, 956442870, 826203662, 596192829, 155556651, 326438216, 642567058, 506074538, 985879459, 415328555, 825977083, 356526561, 412833909, 983475287, 402844668, 222673328, 667746111, 88335, 334670335, 186244458, 705803593, 149610274, 578128623, 656565232, 821037087, 493369825, 333606060, 713062893, 52867007, 50453348, 72012328, 124708094, 316292502, 494121237, 618518228, 936229617, 396833072, 701226853, 460130898, 460420957, 425879218, 897549123, 365618042, 535534433, 386313888, 279446014, 98908916, 911069855, 197404652, 323965096, 703242353, 950613079, 622073237, 790866534, 683714703, 365397913, 627884163, 496115425, 238238419, 331380084, 448316261, 814197834, 864835816, 657283935, 632585702, 730338847, 162987065, 420666371, 601255937, 751592984, 682995408, 672578076, 676003829, 260867174, 814204727, 60658645, 874973292, 542403524, 538641613, 715979569, 517727372, 360560699, 933072414, 409835321, 994175753, 624490943, 425573674, 856114331, 499028367, 496706754, 384402113, 875296052, 320736484, 985358062, 137606207, 635016806, 895064952, 910471231, 286731309, 583639987, 312254013, 23351156, 223573833, 231697587, 913972019, 588856968, 289164451, 952657985, 56514426, 443961193, 748385507, 783305454, 227503834, 918796591, 211350830, 926959253, 307469751, 937490055, 652599567, 804542573, 683175920, 583120721, 348232648, 252793995, 905129641, 545840268, 135262932, 279796030, 697961521, 912946580, 677180053, 558865595, 892120597, 732538916, 239622552, 659529771, 64348669, 194646212, 799512265, 380084958, 997828410, 443069777, 319116170, 859655, 760466474, 102433733, 397852824, 445257080, 255190290, 710414135, 879518521, 866933000, 505433697, 768443657, 614584561, 13114318, 41067678, 751625699, 246377897, 121730467, 464573398, 961529099, 695150345, 596470153, 70299717, 329567356, 360739005, 891708866, 321887923, 528588112, 869050551, 432183062, 551308129, 889102543, 64056587, 814105749, 572849910, 514942417, 256362972, 895551660, 111152934, 46202697, 522605913, 319169115, 482996753, 540976797, 90594092, 277816433, 619986931, 644946253, 785542655, 393118180, 562435030, 299358641, 865988389, 279569714, 317306404, 367811344, 994319821, 69771629, 365322102, 676624544, 869878468, 947011790, 259446984, 798553214, 193157736, 82004334, 240904228, 306241642, 608522820, 441950066, 72584146, 46955653, 874884561, 215898194, 160981070, 454524520, 470765465, 732686821, 162614854, 800720567, 11393600, 61747714, 267991038, 408159318, 253256961, 695410822, 906477182, 638048170, 52192456, 797050481, 31414012, 914355121, 836022385, 579401981, 444541348, 130310304, 597434549, 216333820, 705433333, 920473825, 674064691, 318799030, 719267304, 110914796, 855493851, 797029490, 789915141, 131560992, 726332702, 297539891, 276154017, 664756231, 317467178, 926510643, 873485250, 156373017, 897072599, 86354322, 102952679, 113599135, 350571070, 190103607, 820326638, 564642599, 954792737, 621794314, 569099223, 109760971, 694271918, 407637669, 653580050, 446869863, 22622101, 407383992, 678539798, 648661199, 627676734, 47253040, 137969364, 386710064, 92123346, 778485489, 155339330, 169205834, 451290497, 678816085, 682924058, 195107805, 379695210, 438749049, 404098797, 689127754, 277009286, 972012276, 620034900, 937045546, 126988228, 880181901, 645719463, 7484471, 183521962, 243113618, 794877893, 739381923, 785285842, 860597950, 557679723, 420421739, 135577877, 797955392, 259967586, 10284984, 319743978, 212226708, 57161610, 631996999, 44664747, 375825475, 518807641, 49850652, 593627241, 667261356, 873366556, 220620718, 730051929, 780645822, 639171262, 118982350, 516881388, 697238823, 111159130, 5309780, 94615398, 744978639, 646328127, 322422428, 861151214, 744957294, 533446258, 586921489, 279567194, 634356441, 13354743, 968033930, 784016190, 963335521, 390928660, 561807264, 656514967, 537954042, 417717415, 681562930, 206744976, 232869441, 291813145, 631667697, 380938134, 609139059, 927497046, 259066983, 44304759, 482519440, 433381055, 212838454, 255114963, 676814328, 534083123, 114515705, 658559578, 677336240, 819197877, 469745866, 327975716, 253589930, 230633489, 356295266, 490159376, 978858616, 55543276, 268478496, 487512416, 407075560, 225931026, 124608654, 27609072, 926069567, 150496858, 454482375, 601087380, 416732994, 603174813, 811044233, 964304594, 71086763, 974753871, 838075457, 921599061, 205972975, 409965194, 72838056, 292290751, 53682127, 182033517, 127696384, 670598146, 819599190, 318587142, 909002182, 195599617, 577596322, 259828490, 167798037, 458966039, 786594878, 357303948, 429479640, 745432357, 184849031, 251353720, 557904512, 298548708, 220028369, 339142691, 247609685, 236627203, 609234625, 466842732, 787887082, 51850892, 905760001, 187672640, 675367682, 329645424, 338150060, 569144281, 641343174, 419830881, 554578661, 568089090, 200828316, 749123665, 723837373, 664234571, 384976114, 540311658, 624903566, 329303896, 356923995, 215647556, 512846226, 934960870, 915227807, 893357593, 628580842, 138941801, 499039833, 145729775, 924146523, 192771927, 424711046, 650156042, 485894293, 447550896, 873012795, 181343395, 394447265, 662082518, 377161172, 80522759, 929687211, 146060910, 212747210, 384759104, 872206866, 72895856, 987114098, 282636087, 835920041, 461401168, 604939327, 34607047, 554576062, 123802863, 385191337, 897493567, 173325079, 627255978, 461574670, 957565805, 577493571, 259339878, 801704543, 577823155, 27751917, 303801050, 905144614, 18800650, 765608591, 23461802, 394673264, 481402720, 440709996, 791094131, 826399675, 348779381, 737296056, 647561172, 887497770, 535825711, 627559243, 701261119, 490593800, 911616880, 875009832, 633530613, 849099437, 513216190, 974014316, 334827231, 551649428, 321019835, 259800720, 909298892, 2989620, 289912454, 123233798, 166671367, 592503741, 459661918, 736546448, 558150914, 165459991, 96092449, 842355536, 114668567, 84946560, 137337230, 503873974, 823903357, 690902118, 690626675, 626897175, 164607283, 320889242, 50011343, 127755353, 430451680, 300211173, 427592558, 328410620, 226799466, 574417349, 854231673, 350680094, 675775762, 177508305, 620542375, 143947090, 416184710, 887184828, 895119644, 652848913, 153104910, 919880955, 883005557, 787837531, 216705858, 756964219, 270155939, 232113706, 171910521, 244713279, 819551208, 797188853, 714238660, 941802280, 731701702, 547181071, 366982297, 489483443, 469586935, 996289406, 918974786, 771079459, 658655802, 283641500, 551862865, 2351208, 841219132, 702142668, 421063136, 979635820, 898228114, 596467748, 106193108, 125005636, 132099025, 208870913, 35046893, 113352656, 428530969, 195723454, 711429404, 641959542, 809958628, 743897236, 259479536, 227146695, 253342035, 61838387, 5795974, 423948939, 854407646, 66679715, 819541670, 982856870, 779745640, 424009568, 678339871, 270516766, 673337752, 770973685, 20942047, 30944454, 453219694, 917241787, 836822204, 627177389, 584114513, 413031704, 422075571, 38663092, 610854081, 743200341, 464997624, 703571229, 136046584, 994945642, 568951029, 385882524, 765717828, 476509896, 940774087, 127219979, 186570447, 709676610, 489585499, 1443236, 597599525, 322795455, 342348303, 474424537, 593169833, 742690936, 625851396, 411749664, 350233742, 80237999, 538058327, 39263825, 333349607, 875895564, 18747541, 444239139, 965276407, 666501965, 920214448, 85320486, 919559051, 92676310, 946942202, 813780944, 184868264, 836615685, 426961616, 656944087, 390292997, 776322841, 444774502, 799062032, 773675673, 469943891, 867788472, 604395078, 398762254, 114826469, 560177600, 631547006, 185882407, 586606962, 277309594, 328219927, 801181339, 98624434, 471654779, 814972017, 476202924, 762447762, 387936519, 555272470, 657758930, 679362272, 258080662, 51146410, 300217713, 581637852, 888315118, 383516978, 399828867, 969535486, 675905811, 31466996, 302303187, 77068864, 157281984, 166431492, 369433553, 717900129, 795643852, 414455989, 478177603, 824658223, 691652692, 377296825, 170109237, 625296438, 635765545, 62921760, 684432833, 454730336, 788369280, 371065401, 679626059, 396261570, 848030403, 796328586, 807830466, 166503944, 58903384, 754929429, 785731882, 258898570, 325158677, 911851784, 881641879, 242285897, 74214998, 877514547, 283643987, 570003855, 672502650, 635011935, 384251142, 742272896, 671682847, 182786576, 235181706, 119850480, 928337602, 956480100, 385775917, 756474847, 80113207, 298287164, 481212861, 579690928, 619058875, 927351804, 656379429, 817890360, 406204759, 90389579, 274033354, 224695927, 542152915, 150434443, 843586896, 293148839, 154552108, 645768578, 288541661, 600938933, 197726130, 875108493, 156011402, 823560887, 609682975, 230304845, 948083694, 91734809, 832432120, 391705039, 372425210, 304451490, 813269367, 301247837, 753118233, 467555492, 405519905, 250686002, 298338313, 340027905, 753744201, 742890590, 803775433, 232789500, 259411870, 795513084, 367178795, 340840830, 225548531, 533916112, 717231374, 296856585, 448298873, 218987194, 297521247, 632568643, 58610839, 205930254, 809079897, 168478252, 182378498, 591510822, 421923122, 482270448, 911925825, 846502901, 589631102, 41847154, 216377025, 231226297, 27005902, 637769424, 255163945, 502841172, 622962497, 655161523, 75953562, 167580681, 543464759, 477808433, 352505861, 562525485, 269529512, 553773987, 403207609, 351198466, 391127893, 969124675, 720844546, 650646949, 709807198, 696739881, 941643240, 560668841, 197009119, 842696359, 478965105, 405021624, 416249347, 462494658, 551509551, 7712305, 975878289, 442681025, 993139279, 759536424, 543389648, 176666397, 501543846, 708344410, 577239237, 610206485, 723784393, 106792669, 529996148, 148341243, 252758591, 104845275, 164578758, 554993768, 341862314, 570471669, 158267010, 675262496, 932698519, 110763450, 781341649, 110310876, 941157979, 335312233, 258714923, 676977836, 998414953, 738699134, 744135135, 859372106, 43429391, 575377689, 204724476, 107009627, 947911586, 15869346, 185038225, 444621971, 563099458, 986588469, 181151652, 113726489, 802213203, 218527562, 796958915, 783882962, 780502635, 49275560, 231598484, 362894780, 276183626, 625756056, 439591964, 908850264, 372220574, 635558262, 173393292, 805333557, 411584307, 577734571, 657025679, 55542705, 552564650, 750785670, 849141994, 719578091, 917739002, 89908785, 69455345, 568377575, 580260708, 908439174, 897744100, 282636764, 623985599, 160118743, 48683448, 272830682, 603536167, 319262460, 75681071, 887491630, 825789688, 730043097, 941109105, 417295007, 953560569, 463694234, 239006976, 370067410, 809420022, 442306713, 345805294, 290326251, 663008784, 804091273, 144706462, 49277925, 692802773, 139154327, 248501979, 212967463, 229923910, 816521422, 338249787, 736145999, 929710810, 792077164, 848377612, 369579188, 716557408, 565126946, 504184837, 669561120, 958230595, 136120636, 82785331, 967169522, 368370448, 82788764, 349907686, 880706675, 314768269, 602917099, 292040982, 689780537, 775555000, 186388852, 53356013, 259084139, 889727743, 977935918, 590902354, 564318905, 888146839, 434348180, 162753917, 306934182, 657605837, 281826696, 156231281, 178503497, 960122313, 118852907, 678748511, 816320858, 20189644, 550428175, 579870494, 585488079, 504063431, 628328306, 753047340, 614501165, 504162618, 454987754, 861229313, 20160608, 501696146, 806409907, 6919524, 933765222, 508417063, 750077412, 922599538, 129059489, 42034339, 658971765, 990659241, 753959682, 235322914, 467435340, 60561543, 659495361, 331518899, 941342485, 238453278, 269713234, 35418962, 615509261, 596688092, 209502521, 870976832, 489625610, 137566968, 7339360, 950115254, 887409324, 124228550, 264631775, 836728561, 385563947, 520875683, 769607608, 620859571, 770663243, 901597618, 831253556, 409038628, 949321001, 97493248, 985622540, 745249637, 121263802, 418578966, 401434237, 943632838, 870388272, 656892166, 70607572, 481100706, 891547394, 661208723, 686294341, 50301254, 928125430, 647796178, 219009988, 256894817, 757659514, 35710526, 543669638, 649380493, 87812898, 886341723, 653448763, 831185727, 59237524, 880073479, 426967573, 682752710, 393475179, 791402228, 100429173, 895043820, 519685094, 435289464, 63268264, 222981613, 586934130, 219946627, 326014124, 720844972, 69205971, 751185606, 984191240, 905429109, 932822023, 447268020, 920422821, 748584619, 4630263, 634656595, 447385985, 956848726, 261006887, 54989379, 404841551, 697667794, 74532632, 732600633, 601728695, 768454286, 919088173, 979915187, 267299213, 898496394, 951293113, 497152370, 239385211, 224400973, 800734808, 590240940, 601681780, 358271366, 201591433, 191817467, 29991814, 456587997, 698747433, 488217725, 747660236, 928936298, 128542204, 741443821, 225023819, 735034740, 70724770, 1646273, 988490251, 245322182, 482837911, 552467882, 853119315, 686318174, 618746117, 928227495, 333582023, 300243931, 336478037, 986394858, 788013784, 911264017, 541449491, 874561718, 924167550, 24330452, 708056581, 933697008, 801901448, 366141358, 990467090, 723730440, 686255749, 451054324, 575963693, 995500499, 270875822, 484587253, 56066232, 232872965, 880421704, 492937357, 324017720, 965225281, 57164794, 666520521, 418964865, 328039111, 343888249, 741245988, 557328849, 405327858, 102171260, 464451944, 136565691, 735941584, 9426223, 546773591, 185343008, 58159322, 57720213, 518236562, 854747925, 335118930, 547457860, 334386770, 684316156, 577948686, 578554494, 449501710, 483329038, 13115415, 10576036, 598112184, 369967193, 439275446, 48486010, 951811357, 10956486, 210391001, 665911484, 370913759, 969912885, 191297205, 171338558, 987401292, 306686616, 380225618, 557150079, 908958890, 92407071, 622849368, 901605450, 501324825, 411893001, 486231194, 76794408, 151944512, 895214832, 370720469, 175464887, 967403099, 195754213, 45207711, 382329183, 365128656, 244368179, 296917725, 60342057, 356988798, 707735928, 844591244, 697253443, 763401059, 883614664, 713510305, 769360856, 898069158, 455795300, 993624297, 637229075, 912348098, 461576850, 331296406, 391385762, 376072761, 767221291, 887280720, 563397679, 996624332, 552796969, 390587838, 784414927, 251439043, 623413502, 398755555, 857660575, 865296809, 298532027, 604387977, 792774909, 134896495, 887684076, 652331234, 430157182, 523386290, 809655682, 388286779, 775644888, 761828453, 767616630, 211517247, 882379655, 214128765, 73659053, 84672046, 888096838, 818836160, 610136320, 566776336, 53591649, 161440735, 848208206, 678210677, 895039787, 249525153, 275801780, 385811820, 36587030, 544909242, 137037701, 403009653, 811217222, 916071867, 11036614, 334238332, 448465205, 878746344, 115402531, 667282659, 412706944, 942913411, 203924151, 245317671, 670120514, 332087399, 116256747, 908736290, 837807539, 691432118, 494539906, 123015003, 613080528, 674381879, 10045797, 407579800, 607064713, 623203825, 538873656, 567451080, 107072883, 325783589, 932514673, 465210199, 185099822, 718441180, 283895976, 197619583, 175023908, 649455062, 944312074, 515927006, 726912101, 339327562, 543916862, 829906194, 108809742, 26366797, 154802754, 674713035, 82991680, 791066841, 811252369, 39694931, 470385497, 889067910, 693919051, 100461462, 604076231, 915400240, 597691644, 850823921, 350938437, 202841347, 434629485, 890691573, 366442987, 83261931, 404186868, 627403505, 165444841, 819619854, 329928806, 952909364, 353866108, 736173093, 260606388, 735748986, 566646948, 492054274, 138349980, 540224499, 614211567, 98241539, 516768194, 98039352, 231507108, 325037696, 859297363, 766527945, 732588903, 159042797, 333471430, 670882081, 110713335, 246626641, 668787373, 302156527, 807633970, 646236761, 469328975, 661117685, 571716013, 774810694, 203427768, 119938479, 315003547, 602432579, 564776564, 390950344, 946446471, 247002363, 861299576, 921249430, 11567576, 833509471, 957965625, 287442462, 946468092, 559613549, 820115485, 786665940, 365413169, 37335069, 595802888, 351460393, 995403477, 258531273, 429947783, 458128753, 58521654, 531297797, 999713614, 98999647, 499889442, 300066058, 949672483, 219968673, 405867023, 844785871, 125305984, 88483777, 730030604, 966010260, 653186265, 936250054, 338125684, 304312684, 248760642, 996374552, 757017067, 11992666, 465590865, 296632425, 179198389, 939794171, 563761330, 396727205, 615303663, 809783226, 878916310, 472632942, 387105198, 559978693, 508878350, 866002959, 222880250, 555629180, 657701745, 245655496, 194031571, 250352452, 36348499, 593289180, 160503410, 341368159, 506849603, 419989635, 692592449, 67959855, 30722487, 726862569, 68011459, 887272636, 648246519, 302143968, 11166347, 501832105, 10752737, 936581358, 539301720, 141661947, 695743148, 526622548, 834091317, 719885165, 124351451, 663179605, 317123440, 296772198, 237218234, 332528047, 163055049, 209966672, 765570226, 287898654, 661527397, 156627488, 480977593, 671071696, 590745910, 134963852, 275216327, 996818326, 613796596, 194438333, 336656011, 544374207, 973475813, 539688027, 678455136, 690657547, 921908014, 528290630, 839967283, 151584452, 732596874, 495843446, 941381590, 780490369, 834553417, 253507148, 909617857, 346199140, 892463506, 18736290, 244182566, 183614392, 244448021, 102536197, 465531758, 721454136, 804154265, 578459212, 727191744, 234526706, 458036611, 745324145, 212809774, 939329167, 558322793, 686237182, 465690551, 758727832, 58470321, 621548009, 258051478, 614680952, 476194201, 601734746, 796977021, 118504284, 31390794, 358923814, 480852403, 3831085, 513577593, 424368251, 339598414, 269514604, 766718771, 944318412, 858994897, 75289284, 170410253, 29519955, 520515730, 469687788, 633303116, 990497355, 325167870, 550847730, 140751732, 450575616, 396515781, 794958108, 776549143, 706957470, 921813304, 811361222, 630910650, 174701961, 590526177, 676602876, 149261647, 554566391, 633755129, 19095875, 608484778, 234138702, 381591406, 651403233, 747566384, 933067885, 253523396, 307356742, 476004520, 145586731, 177759478, 135780158, 953245998, 76384609, 241435306, 881403715, 905244188, 842422005, 617983850, 944381610, 462246273, 966492081, 934429864, 842987250, 950935989, 711424157, 299546742, 688827548, 738190854, 574413117, 676095553, 574015896, 741718254, 751481621, 432357116, 260864806, 655998961, 770761456, 273941326, 360473044, 612348390, 173057240, 287242032, 282187659, 246877878, 232522499, 320126814, 533270196, 812909366, 885771285, 210485997, 525414848, 878486975, 119227042, 35191770, 983810980, 568853996, 912903439, 951261852, 898466728, 594765429, 695111842, 364844759, 79135125, 815421010, 159164806, 819188100, 662592801, 340074258, 654452447, 980546017, 984931806, 337189927, 57207171, 685347986, 78391590, 840114054, 388067325, 270561656, 89513581, 806317090, 465287692, 590492558, 130903401, 531698006, 484540677, 188143912, 384258830, 499491235, 109879738, 482698812, 307338820, 20239785, 978046260, 497384198, 271422425, 330764669, 376647163, 9176567, 860505292, 873555595, 701885829, 801750355, 15249149, 576471011, 639194711, 334565762, 282666503, 694138710, 839544612, 76912267, 806768370, 610392575, 37668266, 603920674, 109729765, 39904926, 870253981, 828795385, 43315484, 846228159, 925372794, 591546770, 727650437, 29313655, 896657059, 155687473, 146535940, 946416071, 520977226, 856571671, 259836483, 372385906, 299298268, 975818880, 103283100, 768893544, 259509164, 174994002, 758521052, 855717334, 541686312, 7425253, 470343952, 293224257, 250328388, 464955853, 496008969, 635530890, 440218795, 341341651, 665732677, 405265387, 426222437, 3947841, 407419729, 97480774, 127344215, 909068964, 849833706, 529960859, 343823784, 611955269, 474280356, 272371842, 280586939, 830284240, 730114546, 214504356, 529484749, 283432734, 771021693, 590571037, 385747656, 105246842, 247171286, 686422536, 268902733, 392441581, 729372664, 838304016, 599309744, 61581289, 196659566, 212614129, 728984451, 877740502, 201905088, 833843956, 766594710, 435965004, 255002512, 42360721, 904498354, 411931602, 493645517, 696369003, 187987848, 451882113, 164605146, 283967550, 547320866, 480633457, 1299001, 321704953, 537484900, 584055665, 359024926, 634252726, 76617499, 330759207, 356552268, 159389287, 337637485, 264529225, 769990461, 821483268, 22148366, 552443306, 641229743, 234331060, 859954010, 715736194, 552313519, 36161416, 89615507, 498023992, 469097902, 48162655, 788692501, 964961643, 546146478, 829238469, 879369307, 666749872, 408001223, 210660707, 474723880, 121949222, 721458644, 192201422, 857939053, 734935884, 117198776, 606842697, 994561447, 574979338, 769082795, 446013358, 742967125, 64239212, 202995410, 315694411, 183405440, 679759000, 270539944, 811105729, 292315539, 906899587, 280744119, 606467387, 462030700, 746254058, 659323293, 766081454, 38267246, 456606642, 670466142, 611187577, 43090301, 989708596, 541495606, 610164392, 596757947, 397028009, 202452449, 453432144, 257271054, 249461136, 889228834, 642555183, 806462418, 213483831, 370901056, 383531085, 238523389, 555589373, 5693737, 565832111, 67838823, 542629599, 469752695, 763553783, 225724499, 503579017, 842153626, 629651635, 160059973, 495122142, 376107435, 55085150, 739608819, 387833257, 110649110, 87390086, 622032501, 597633210, 82367321, 830075364, 336915180, 952037378, 367766169, 421108110, 622635197, 314112723, 968868271, 544987487, 565451730, 873197017, 754811042, 483569513, 302996654, 674681588, 352377702, 611631305, 328705710, 627155364, 692501139, 993050003, 119532424, 214491664, 247121279, 358658426, 818429743, 856165331, 799705485, 144024234, 293821803, 471678405, 338076307, 183020553, 491755920, 595439578, 660371979, 215288345, 937690577, 650678750, 475679817, 693495245, 682119011, 40560331, 111716401, 252304787, 347789101, 268095774, 654787606, 219462147, 617898975, 353421514, 287543074, 766942663, 969905272, 996944087, 59711287, 913856124, 775957987, 810206445, 798953936, 920805202, 466271564, 838582192, 39953631, 174603894, 707833403, 711421540, 559830401, 774604248, 727309384, 340014326, 603691269, 25680302, 159202113, 12038004, 973851087, 905123966, 456523239, 806674471, 600645790, 676200356, 797459051, 263226093, 507288770, 626007092, 556336735, 791517384, 802031381, 151430317, 325565776, 32092493, 479848819, 810641526, 383602726, 806345027, 926287297, 212227890, 113632177, 552086256, 561608274, 244186468, 750840, 585730999, 924955668, 549591702, 800370574, 315814447, 350522845, 428484917, 793118133, 522035145, 320976403, 742412662, 621914769, 619717456, 699178694, 687730625, 579374595, 876131746, 411859937, 582328394, 330937169, 497490757, 113085072, 807984205, 992693614, 730573982, 724644708, 604156133, 154531105, 158427135, 39918226, 208742503, 877095193, 989288285, 630780755, 291973768, 302385181, 552271705, 800040276, 193631038, 25411189, 23750324, 249236863, 274847442, 94753056, 984934910, 69708770, 263668668, 708226628, 584382563, 725463466, 646148221, 25454904, 495826739, 338674582, 555287824, 599001674, 239776311, 234665347, 522583573, 315309528, 597023464, 486980241, 620585710, 540012947, 829347998, 973426039, 36251066, 924474611, 371877586, 105709527, 20355310, 296623048, 8681913, 255470560, 753760163, 189014032, 650769280, 707402044, 860178461, 311683190, 546266491, 612266525, 903877790, 52652479, 874685874, 178768599, 361337981, 446441514, 520243841, 76656683, 336740445, 327813340, 424955018, 30068513, 657456522, 537396280, 839471187, 495245471, 685558612, 206038180, 161246892, 437425318, 513679949, 790541044, 290643843, 229152522, 116577826, 304758814, 843252054, 669705382, 880492994, 474231497, 37682950, 923932366, 684337931, 813711285, 985198700, 211925007, 458878698, 324036284, 26543284, 845200635, 194576126, 190916518, 529311819, 300479499, 870179003, 113723487, 936246105, 152622744, 10098302, 785739258, 776941730, 395675425, 477692753, 9263165, 723842599, 682054099, 495471914, 7481196, 150075988, 542492627, 45175025, 393203383, 324574162, 395694465, 518789983, 846901542, 439123617, 316625308, 107630930, 991837225, 623546062, 919994084, 781781174, 815972076, 102050828, 542645605, 801193873, 910662098, 887732950, 746209937, 567445644, 806690673, 760035245, 572473191, 264869670, 647599095, 243877351, 1353848, 326209968, 262377499, 180353252, 888486055, 431688388, 675487938, 808527844, 285683359, 446293649, 711752628, 553730287, 724957797, 741162757, 523971866, 903895371, 668502709, 193485263, 295334399, 410235527, 736024415, 862157568, 881939394, 854086950, 28644884, 829747754, 569587319, 483754247, 145238645, 457785109, 467140132, 143372630, 171964588, 275087755, 368479768, 631257597, 719244068, 167172395, 518514482, 374998459, 174331902, 242661333, 502065849, 169725571, 318813790, 410092787, 930361256, 2486283, 667338533, 296810959, 324151549, 465283585, 422039950, 899306415, 577795395, 199501441, 912991967, 797701654, 944263050, 460856642, 605338817, 255359096, 30082307, 49247185, 691804645, 921431431, 702424182, 923873660, 690869875, 923365188, 994416348, 8676347, 718061096, 972396822, 182996061, 329534080, 259134745, 68882078, 393141110, 859312728, 370667051, 467039490, 663286810, 503549375, 654601063, 924530153, 503457844, 324978174, 243948338, 834332536, 460320243, 587980831, 674201502, 548119845, 171064255, 729525559, 286783746, 556107828, 659595673, 157035742, 10258734, 653612821, 24108591, 362770291, 684463683, 259478504, 387721633, 436258639, 320957677, 828059032, 833574393, 735649958, 750849079, 627276906, 567058147, 239953108, 748867012, 387318925, 366702714, 202467147, 88869886, 376987173, 682373011, 934597318, 8470206, 657027809, 494858858, 623883278, 53310706, 753181664, 128252348, 203294714, 3945365, 177474520, 893616760, 300928881, 68584444, 276845256, 253331389, 253692135, 668311241, 287815267, 534223352, 194130824, 937469401, 220888060, 378762635, 777471997, 406937073, 444621155, 373361949, 591204408, 790981586, 10199957, 23160845, 156764152, 545552236, 113653949, 430064816, 378637048, 281688139, 94565633, 285725339, 992609330, 764309975, 446723939, 544743618, 563492303, 773917756, 893593926, 978432444, 591596816, 652377504, 741415639, 57258649, 402829177, 389285709, 864106942, 684869504, 833772901, 483990062, 241114631, 817081975, 851753574, 999109104, 860298678, 83233396, 513197245, 185979143, 934958465, 218108309, 29578176, 284294739, 476431239, 525767337, 146150520, 244767377, 915460633, 690605255, 859627521, 12562443, 918095146, 762617457, 67520946, 433646552, 254120591, 403137450, 771252359, 709897261, 797869027, 995838291, 517507426, 113053227, 382009942, 711902976, 470526830, 412417627, 197036329, 403487589, 825589871, 925589747, 959329972, 524552226, 29975656, 404035257, 531284928, 254699136, 734748447, 282180072, 802641836, 480780321, 878512025, 273327235, 490930805, 122829386, 923350174, 821889593, 616104525, 127645522, 136011118, 189654373, 547648497, 581480620, 400792261, 692975594, 354770751, 651840329, 221031817, 46716762, 767013349, 2528200, 416446468, 667187047, 190920536, 130867549, 389333627, 28284594, 545080443, 481139364, 459751129, 533452530, 489959799, 615162771, 764873470, 462745199, 290221854, 731607064, 828552404, 663905868, 835021716, 6956270, 763383014, 268836822, 58061797, 189126688, 143661550, 136630063, 54446550, 651108974, 720841986, 152587614, 486410113, 925046485, 535083474, 128855595, 349836891, 767944207, 726513138, 586066542, 585632363, 829009223, 617155304, 582702173, 696607142, 627228534, 557276853, 50049287, 238000725, 741891942, 41852039, 148335577, 397682760, 992159034, 872641514, 928067139, 427831561, 113016813, 793171338, 359691993, 176430776, 764981033, 891857951, 776585532, 523488444, 24111494, 637519766, 391112863, 492066006, 785612887, 838229454, 849884020, 698041297, 729251585, 852100419, 943054443, 465149341, 587202368, 914306213, 71906378, 376841879, 2861545, 710579949, 930965874, 127415752, 687267442, 233328595, 898022964, 570604831, 717992782, 51653393, 120180821, 710350296, 573037528, 97975767, 582259549, 634149433, 404678577, 602464738, 345449473, 832950675, 402536829, 718612514, 84364489, 16241861, 300805525, 646974989, 18445921, 744908426, 119643164, 781201112, 26519550, 723898831, 537509879, 126901086, 791303924, 846018818, 235843116, 10059655, 669049877, 662093815, 738816788, 832983839, 305323098, 839224520, 363890444, 98412317, 524229664, 834637074, 840397600, 244544554, 678903044, 829605435, 685874112, 116652824, 939981785, 540311495, 569250356, 961992556, 493173324, 594645290, 371633678, 686444067, 300029488, 384307788, 423441105, 692995897, 195614961, 410815423, 749369576, 975346651, 333380334, 181162270, 519964274, 882265311, 614531574, 813099491, 228390825, 326250577, 316427528, 780990263, 681621365, 876522107, 75133858, 509739746, 837674930, 789848650, 141850046, 270348851, 438419618, 241656976, 46593641, 955585999, 70115463, 725855892, 52018955, 61813051, 155533818, 611158047, 975792737, 806090480, 701050730, 552271846, 669986368, 206389212, 239776916, 991566926, 748287356, 121129205, 134697115, 551498157, 730795919, 173220804, 188642533, 136427829, 594458509, 755669231, 589094863, 783090009, 88369562, 63019336, 155312205, 793751468, 16013005, 560085963, 570036824, 44707393, 220882799, 400841256, 739127931, 790840581, 983592959, 773056409, 310921889, 811904898, 31472515, 49775023, 719626767, 123318308, 398063375, 29726708, 841646926, 667666288, 123973850, 245261486, 264164135, 266553248, 640785347, 461436204, 823620881, 783356097, 925072022, 585438415, 220108709, 181414833, 223389527, 421266624, 705630089, 818670161, 356977191, 581322523, 542184916, 811554847, 849567780, 83533997, 782721575, 991612446, 431983088, 347894750, 676536032, 416590105, 226777627, 129855563, 198042931, 893567457, 269181497, 704794579, 884170011, 754001612, 175543958, 623087829, 227090400, 900379202, 65173502, 732461984, 924291554, 775469008, 462798883, 293852522, 156933781, 54247789, 748268968, 959604814, 321185779, 102155795, 902554300, 335723132, 924543813, 503198363, 156904355, 921463083, 953021714, 41348158, 251357114, 675756923, 220503302, 974130525, 315387333, 622960253, 281990096, 734696309, 994519662, 120892389, 779033576, 877017349, 51019644, 643352505, 745054738, 404571729, 190535774, 964665715, 542206305, 490900025, 183032786, 556141274, 117579859, 290322016, 39444073, 401830795, 978655341, 918550245, 126203730, 445101671, 660785441, 991604560, 906620254, 804048625, 433190274, 132313111, 998068710, 53336019, 271221643, 686185210, 59053281, 807698197, 527467880, 307287037, 525134814, 745783578, 240477706, 187411622, 365800408, 54657038, 717871325, 522998505, 826300287, 937625639, 206807774, 385124374, 841882635, 456257041, 840270150, 502472220, 634167501, 60197698, 684469075, 324091166, 246537801, 911404939, 938963421, 856074482, 470517198, 455518708, 588803799, 174103168, 605169178, 936198349, 806686205, 614782649, 621944898, 642438491, 723130554, 116541384, 551215491, 510102981, 783898178, 216546291, 519531987, 321302529, 981670868, 663746942, 806814049, 157411822, 660622507, 626200512, 582293740, 833205103, 810942190, 126593377, 880999919, 540240373, 402444052, 282843462, 397314369, 677500021, 616425648, 79288720, 786639940, 398618490, 296197566, 577369521, 527680592, 438570544, 403798753, 369575555, 429534677, 970986005, 679032533, 260110126, 238755865, 327307011, 923594372, 76810710, 436176637, 358905244, 820682778, 785511513, 490613897, 580928416, 680884286, 324711951, 616866844, 39374026, 435151742, 448243066, 920599169, 256931703, 1378352, 123205655, 862226322, 726808544, 173157251, 80861403, 784968986, 123805292, 694601331, 550031962, 721640608, 536661073, 957470485, 992616542, 614849563, 864997100, 860350886, 629415263, 807302948, 50654537, 176520556, 256483336, 21057169, 140284803, 364396755, 808311208, 754096698, 317507729, 720234591, 121513484, 105109409, 408097275, 827961429, 74567277, 393220821, 168015973, 223080188, 78860942, 765871002, 24940744, 212519243, 33126979, 503446877, 719853557, 712121025, 799423134, 189718263, 102982747, 9090378, 867224821, 374030050, 747268257, 404787991, 302754031, 921061304, 898884600, 550877153, 397985000, 916771928, 281920640, 346754714, 711890060, 897549233, 591237469, 706880930, 208186776, 861209297, 892134799, 292943608, 441066878, 233628139, 758181059, 963770905, 285226616, 203585909, 503949114, 244625503, 51439362, 148257595, 802244300, 593754659, 390137410, 239804814, 975261661, 739550067, 53238290, 996958392, 917898632, 990227161, 782638064, 383069906, 870771427, 353607856, 467858814, 887190767, 16552162, 809252697, 869458550, 67232650, 392634309, 675700642, 838239836, 461603422, 567275394, 92362477, 368114508, 622687895, 233086634, 307123482, 936599887, 113514929, 110742724, 469988310, 391124793, 573743471, 337301160, 752490339, 748799081, 725602007, 715012736, 459366551, 316978874, 267882797, 795626777, 282541818, 582920649, 141855890, 976064780, 622635851, 765277908, 469567754, 968916273, 941988011, 155272561, 781624035, 608345624, 735361121, 857449631, 998653676, 787203642, 55801310, 378028684, 482803836, 510317322, 987377909, 721468274, 377644071, 777397289, 212008810, 950118485, 926497806, 564262703, 124722275, 527210741, 237055779, 83996116, 743395938, 879311123, 388473003, 354512244, 481981781, 352634819, 650079386, 52129161, 599118844, 255743451, 212986538, 318376355, 867985568, 27480865, 170512258, 422289265, 960355220, 967169398, 246861143, 519630938, 327863182, 246915178, 236606563, 246601499, 59287481, 943090185, 508211884, 167713353, 313713969, 283753266, 583841413, 406023418, 349817947, 207495040, 658270629, 447154838, 664281323, 536161455, 802694505, 785100287, 877142491, 735671758, 81141095, 318101189, 286747824, 322360792, 856616956, 523053496, 810371777, 570868729, 260744999, 374067624, 261152444, 316000407, 148960715, 705829965, 777199703, 427427282, 507984524, 522557366, 724887494, 407368112, 221457477, 806605871, 498800, 516860436, 205542805, 692814836, 810744140, 501441005, 401747357, 407949656, 591221566, 988171225, 54683455, 213602235, 420825020, 299673322, 639116724, 837166891, 29050374, 346970884, 912052244, 889721176, 554432358, 295829116, 259629941, 484382938, 608841527, 291147502, 225078302, 128416854, 924312472, 136952909, 663501488, 14385674, 171291340, 410115603, 239367818, 728664271, 225717247, 565770640, 86585542, 920553810, 352642761, 778959415, 636689111, 23465408, 705010825, 851526461, 550011577, 425818051, 37348765, 825483750, 647063284, 570934033, 604802294, 254938480, 657569754, 334657324, 213393460, 420461729, 33109290, 446335356, 741952748, 233032795, 586306174, 602333181, 741645410, 853953394, 224925232, 115882375, 252845491, 301077282, 187981426, 965583985, 247580297, 823200903, 909428087, 716577179, 633601763, 260876384, 564104053, 807040416, 188264882, 348781643, 803627117, 244990517, 273321004, 725318980, 615572396, 39498160, 730345484, 474315701, 867292753, 341814138, 832457604, 905754692, 231160048, 527208888, 117569761, 964143168, 531537027, 582660598, 634893196, 106488951, 848945447, 789358397, 800635778, 316180842, 477810384, 632105569, 30767581, 596253512, 638851157, 589026750, 626685040, 738476120, 635861273, 314656399, 614330164, 811731929, 715547184, 368494553, 562760133, 41816112, 626983763, 8194842, 757300378, 345687938, 95444761, 8971971, 330310294, 138356915, 844992711, 780811685, 863554316, 662350015, 981756217, 661955497, 512497854, 703673882, 280326017, 676478408, 778118767, 682607620, 794645990, 600398395, 318483546, 999860774, 42112281, 681169701, 389190111, 374479304, 165091218, 179654935, 192204407, 339942717, 514737876, 326465186, 118346620, 512710300, 445580637, 725811356, 377304039, 461932548, 180361052, 807554668, 913720589, 265417647, 848193485, 185943915, 64297811, 950493455, 787253268, 559585671, 341877152, 175927661, 334495796, 373652749, 617406918, 448976728, 791885299, 938738451, 51290715, 295362657, 511179269, 22809087, 670991333, 557855457, 803925120, 765720056, 639287938, 890492928, 640082325, 299594856, 832731543, 388835206, 380333394, 443300955, 272268885, 571256894, 487628466, 691066275, 210610707, 129572369, 869299345, 333074003, 331818166, 133897841, 364810809, 120629508, 640044402, 833482484, 145188128, 250615525, 521098445, 849284211, 679111535, 61138583, 462515827, 107309927, 147410124, 85890289, 318398374, 789104268, 131232588, 471014219, 604098990, 380347796, 783104114, 666053013, 871355714, 669707933, 684729362, 678982684, 905014723, 659892980, 29714059, 607467859, 54953648, 652402137, 349656086, 762828329, 175260487, 105234683, 339450770, 434469144, 71220204, 237299375, 23552303, 427174750, 193912752, 554412405, 403006898, 477540341, 324568645, 947199258, 944542423, 155212816, 788435576, 168303546, 605365603, 176348476, 907402882, 628923361, 954471946, 183235945, 412809346, 500977065, 395080997, 250472386, 804674550, 962748593, 515585346, 823543276, 146569904, 351409950, 472993284, 245757274, 880989445, 295414688, 873027126, 427140652, 991087376, 824675374, 650833659, 470600721, 284006109, 482634399, 445175628, 382763213, 59341009, 959366803, 115887586, 841149632, 801656037, 159396796, 870721109, 894684640, 870024808, 142151601, 976463540, 176548338, 514887022, 96806638, 399521456, 574615459, 639210481, 504723047, 796723492, 619572303, 116826919, 94579235, 116884583, 153919823, 135279771, 415762314, 817908996, 88828940, 191636900, 426281509, 226750315, 334043423, 326769652, 44865237, 857833884, 735101782, 794433634, 948588810, 936509079, 289768996, 453085666, 261597372, 488613416, 67758472, 639039031, 629940762, 900155892, 893599286, 807496848, 141035785, 782778812, 789147084, 820212575, 296645420, 79656364, 777498863, 118524662, 483148699, 723963625, 363829322, 912224501, 239986110, 887182951, 484684429, 138960745, 957646373, 290538004, 440171708, 388706232, 865681130, 729209873, 358156379, 927855997, 340320821, 269180127, 938533825, 84374690, 416394385, 555657978, 625197583, 983818431, 188416557, 261403282, 184150521, 442824203, 803456288, 547608601, 427387712, 275010112, 852538940, 323086781, 58981626, 386846320, 11278913, 89563679, 798411655, 402992873, 280588808, 116911295, 288761403, 995082758, 657556732, 485901727, 186883106, 701672336, 924718199, 609923523, 606301499, 520262188, 270989733, 480436847, 967682899, 330861062, 636803866, 991775943, 171307032, 166368071, 661030266, 512017247, 348145212, 138347781, 631368715, 789559899, 990751422, 494237128, 281065249, 7615764, 730338844, 519430596, 330110857, 35750085, 717076012, 107969491, 893002651, 971619526, 789969963, 919237823, 562307279, 281653231, 611899944, 325082975, 744507435, 50639652, 837082800, 93860132, 596145564, 438928275, 490370869, 885224095, 405179414, 123088757, 874938906, 969959067, 92166159, 699889154, 574961841, 983541352, 318441931, 529270311, 897074337, 571661292, 503894312, 237235732, 538368140, 181015687, 437216500, 388270648, 744903113, 652092497, 489021893, 789428177, 11518842, 140106741, 95994479, 645610049, 819553615, 206045389, 862032829, 49074325, 259461578, 65665383, 242709385, 818714001, 679539021, 742793720, 212362627, 322831866, 680828884, 897051368, 202707437, 602448191, 915181075, 638850499, 733525873, 48090948, 278357652, 108805153, 406270851, 482391470, 716730070, 751798375, 693582832, 338346987, 662641100, 90181056, 796463148, 15491621, 947727855, 401391797, 703770580, 188089902, 647585978, 736346528, 776731387, 900945780, 246799618, 392502427, 933419884, 262804187, 671946866, 64651740, 947082337, 263490444, 923914842, 575594277, 102174694, 802031105, 347492214, 853801553, 734552898, 114742428, 396374789, 744018915, 543683737, 137586380, 690225962, 96190117, 335851693, 239260890, 716578077, 979368567, 483539787, 803765079, 951093732, 295734572, 344632408, 674771583, 847826720, 107087323, 526444498, 212290010, 768165140, 585750021, 615909696, 703634135, 278155126, 721767600, 324525799, 635109063, 974568025, 229185519, 872348228, 846998436, 827400780, 329258480, 291177182, 607572311, 905841432, 389209918, 903761194, 216657559, 126103709, 436082951, 455131256, 20030753, 757727071, 784894297, 914929410, 174649086, 967855563, 50378868, 764852662, 124185849, 700620842, 454655766, 374270105, 711527338, 724012851, 245742454, 952575170, 356505130, 39749591, 154138480, 199024850, 783659183, 860259405, 714117923, 409183039, 585029155, 409237250, 779488707, 349294158, 246047000, 922645648, 174005549, 442272778, 449382032, 44422906, 861828586, 518370627, 646906342, 466552068, 313564982, 230468785, 491703384, 118907906, 342975989, 403044520, 986150796, 473960987, 988596066, 483056144, 899206886, 976220354, 393727457, 738631586, 35370017, 209638120, 663916348, 435648236, 359787862, 386042271, 838972743, 480436658, 717486816, 337560499, 856561019, 189009309, 691866877, 589908424, 690855758, 677043855, 52236294, 436942311, 138668715, 903881266, 644729156, 570880819, 851641829, 119130578, 158647249, 265067536, 319133278, 602881591, 575044966, 362670778, 701496650, 778913612, 800258318, 780771623, 871265949, 797052451, 307124640, 111567894, 510433264, 978617952, 438011365, 667369847, 258875161, 619057842, 403681504, 15036410, 522672305, 586707149, 327105814, 322191246, 200907823, 223097583, 998000572, 214975558, 189730824, 54242317, 151713854, 37541955, 772262903, 206820408, 70239638, 175495493, 804903289, 452176825, 485702295, 408031754, 369444439, 605991969, 768275146, 432871122, 593203761, 260875095, 535117890, 432772473, 468604422, 321045308, 284761307, 573821579, 981280943, 105413446, 724969841, 837388010, 563594099, 313714916, 875058114, 853900500, 314941784, 712833989, 682891818, 448259289, 849915877, 603256707, 336711246, 213445115, 662233881, 956868626, 312091558, 661954037, 307145295, 910499556, 357539613, 952564625, 301223959, 235023799, 809616831, 835059706, 541107604, 899684843, 159481304, 350845391, 183445280, 625343229, 897354688, 607674750, 980072154, 758873997, 720258613, 364512220, 352867464, 557207255, 68690418, 34746833, 208075392, 32104559, 340166799, 987626891, 882490464, 465427317, 561139561, 212020148, 934778728, 688780560, 162230586, 11971330, 204207346, 419325044, 460525608, 793243678, 127202430, 613961849, 606760899, 10541522, 677618950, 322500030, 224060262, 143124351, 762240382, 938467224, 581692656, 609097427, 886957669, 247419971, 229756663, 142209943, 934782713, 471522904, 859496502, 614574162, 843776901, 205266383, 398047214, 57288355, 532825942, 200137623, 470495078, 144524624, 170326815, 376015095, 533863867, 759673549, 998699328, 741941265, 516667024, 169375742, 961912723, 361564545, 810905419, 262778980, 818617122, 866746048, 350055198, 79455569, 205261501, 30507996, 600873300, 848653527, 769764347, 939986158, 977138688, 444563569, 661968506, 655885411, 98834877, 74018776, 68329601, 589462281, 100905093, 484075444, 932004257, 817855771, 443758370, 378798110, 286922747, 76274185, 10150141, 52709425, 353614094, 128742904, 158588337, 918401916, 609906979, 700645434, 941063004, 456281942, 352931440, 675107287, 778533508, 980313993, 603828476, 301556626, 52393242, 663081592, 572038496, 283174646, 202529124, 610274558, 666975754, 437269726, 932548569, 457470285, 768680411, 429334727, 543159409, 945879960, 694322962, 267777562, 337683334, 211323421, 524454134, 561237792, 548634924, 636213244, 336610837, 863838724, 505352823, 737092209, 308173744, 26816973, 892715213, 532592258, 770782103, 18622928, 806730039, 999589530, 696950731, 561519435, 749233635, 697751756, 793045245, 10530105, 213733422, 462718188, 203533897, 168461356, 56592899, 616317937, 571128460, 308712040, 364767615, 212558881, 147632306, 663275009, 10242970, 541348990, 116874199, 90471944, 627029576, 898907920, 531683895, 320836897, 847778265, 706685937, 358451669, 949264036, 106725023, 259243854, 440584444, 931306379, 409688476, 444747466, 169693624, 159824607, 151902134, 788435556, 621969997, 20034060, 359296648, 131477712, 23510418, 71349329, 423224598, 617575737, 769855159, 570396128, 638022111, 856095407, 338747191, 714293692, 783942519, 791649905, 896330191, 82598064, 323332464, 248076316, 537864339, 785484393, 185044856, 694587856, 220663768, 156993559, 803809791, 163713227, 78241483, 63459609, 852219716, 372348943, 153910385, 76181153, 18611722, 143752075, 797446352, 442717264, 429358222, 728905465, 655732300, 548559980, 890089888, 712937001, 547964127, 971802371, 589593282, 135410616, 414798473, 976976197, 246922560, 323642778, 112485706, 763674751, 214845162, 675731454, 661514323, 182964562, 859229256, 450660940, 243014003, 128099180, 420019047, 856121028, 404993399, 597692910, 762714258, 395485188, 376083143, 476028465, 979701564, 242754010, 41257038, 161340683, 256142972, 787489415, 367095526, 688020922, 337285489, 924587111, 502487129, 705919011, 434231190, 558754565, 62291718, 189199207, 340204150, 246259252, 531298199, 758049085, 231467839, 957339598, 748888965, 281708, 160379157, 456038638, 747327265, 427242777, 667172234, 715804440, 590029615, 188759074, 470590126, 461241144, 715405580, 692451459, 108256736, 86231335, 645124093, 770589730, 193075035, 693120435, 513004794, 868633932, 523097784, 162059453, 645357818, 818568614, 770066142, 140053890, 74348168, 866794075, 985620547, 529420181, 551581940, 258448379, 925264682, 37512218, 836344874, 492169271, 711412412, 341338229, 57369969, 562117697, 252689440, 555765588, 941919391, 545248167, 750896944, 497525939, 979434766, 34349308, 702125976, 431644789, 7534854, 279318784, 979533144, 242467133, 481612524, 766440538, 391476320, 225025370, 315918345, 780686365, 871771434, 666013411, 774543693, 191355517, 142234436, 951831670, 151530222, 352637166, 250844024, 967281828, 937359112, 334547754, 572096656, 839414090, 383703465, 590005873, 374754170, 330641551, 857122207, 294256817, 916719887, 382879295, 72598427, 32699200, 660056894, 728326288, 477209003, 873286887, 566960855, 243491282, 8787124, 460818212, 27345843, 983620271, 934028160, 104775365, 646849451, 769927682, 745545742, 856821237, 866330868, 446247615, 725538542, 405603064, 31232245, 150584408, 125357611, 465929638, 679513592, 604678829, 177306990, 564964163, 742374941, 69532808, 760634506, 101180948, 731010851, 280811032, 508861716, 398751391, 734919634, 218992181, 74238762, 786789689, 986910309, 41684574, 388791481, 928682614, 943817798, 395708186, 744931239, 451238942, 704283278, 328983643, 417098197, 300767095, 318176186, 993185216, 798822361, 887890169, 160392928, 989790632, 960382009, 311767421, 643533816, 764395459, 471139047, 374925480, 69200572, 497588713, 355469423, 111454915, 976381007, 835642213, 573759419, 903537791, 295911053, 216639958, 170374734, 755872914, 499500598, 109732792, 140779883, 658225161, 557510067, 634950527, 337146289, 21663321, 61548589, 17324940, 498680761, 400656237, 934586170, 632432153, 101496090, 397722235, 222029780, 471138321, 235809453, 7750640, 288424380, 229913019, 971234797, 437201747, 657168457, 557876862, 574282910, 349258255, 923755638, 439911445, 73089678, 139894962, 956953073, 692262289, 671080128, 351030678, 172789877, 958217376, 606565252, 387497466, 516609532, 332382153, 472653680, 856904874, 118370612, 527373378, 54449274, 82145388, 522236790, 413478456, 822588007, 428622596, 579107894, 235944912, 107316345, 292786660, 44302588, 895345529, 599649088, 673335957, 782494371, 526554597, 533156686, 627478078, 474769492, 772508830, 280580678, 68355712, 683801907, 180479012, 703392650, 37778140, 223314981, 664241539, 154865145, 953664582, 674212168, 910311027, 17782610, 518044648, 657771781, 594388300, 56746861, 725818611, 861851453, 674155634, 618613956, 583570024, 943720556, 980778381, 666474265, 552481453, 640310826, 713260841, 941292631, 901798245, 200287261, 809947964, 268406650, 539594846, 949547469, 528741271, 153345135, 279413164, 609880628, 986037675, 379125257, 503342114, 57687379, 626056123, 276024130, 978431993, 198888593, 933116522, 403494470, 6928119, 885536173, 821580891, 974375702, 261090512, 755816186, 618690194, 67219275, 393322988, 881518238, 752071913, 283520128, 652155102, 674434609, 484551103, 624832366, 752868357, 512097841, 379244051, 445132024, 974460660, 363028579, 6874969, 250953489, 705997960, 48991132, 476638206, 843845249, 465596430, 194105032, 656575431, 654881973, 900563095, 80279676, 381439151, 609359732, 891709823, 715516057, 228216541, 847694029, 821315035, 360541477, 363845282, 987023658, 505837585, 209209190, 236444598, 953035814, 315490609, 980838820, 228307374, 644561617, 196270943, 9254941, 532817167, 273924567, 884155247, 601202434, 308150367, 834668736, 876534523, 838149513, 606322725, 227778444, 167683437, 191517783, 145435289, 274083749, 535703768, 812367731, 431891234, 698781132, 661511992, 351932088, 974009259, 633830826, 165957337, 418280078, 997414259, 368480267, 637227862, 233543771, 491635629, 693015505, 929079886, 448451892, 793729464, 184535925, 40599160, 553583001, 239196061, 324110871, 675155179, 220440163, 128438268, 277863447, 944990152, 178693379, 978682455, 166763445, 534196012, 151311001, 306723006, 128460992, 39237382, 175347244, 376413562, 419148593, 821441359, 316366575, 656785837, 186487943, 931889246, 682323257, 635603200, 262023278, 980330556, 950479837, 195045250, 112688703, 12679190, 34059048, 893639030, 614920146, 172557405, 246644828, 81480109, 282908560, 129594521, 224203557, 332528784, 170238950, 968822602, 639962940, 305505806, 778672338, 159776724, 433032717, 402623453, 688048747, 519673379, 791614817, 833738802, 723908027, 634816206, 91868556, 494758300, 861615915, 588071767, 712717132, 441384025, 664269990, 584962110, 420589044, 429778924, 856583103, 857212530, 104379549, 323036744, 993895849, 341234903, 295557155, 160542746, 766670956, 775739221, 519900558, 25881699, 108879159, 41485711, 305758089, 232072624, 491383580, 659564379, 789176775, 864796159, 318293600, 733285122, 885263820, 874955210, 413929246, 705871216, 249463673, 564356735, 986557035, 341969050, 613810143, 291446674, 566502473, 598395702, 898031857, 505579680, 361012711, 647508560, 247417847, 401831307, 148704542, 385352661, 147977102, 777942575, 411629724, 905271507, 397094785, 969600445, 45755440, 254915025, 410220775, 93483053, 684824053, 894518190, 621707319, 268542349, 551227172, 531265861, 894619580, 423728630, 54193442, 893011623, 325406729, 516927609, 573046494, 867793214, 75405460, 693236639, 959445383, 154383084, 95273405, 401999555, 725242222, 141017084, 286914405, 438528218, 70293461, 195065644, 333990115, 407783656, 783446028, 2718859, 615529927, 961938888, 608764422, 431641245, 772297762, 644113138, 32940002, 236793275, 931468514, 574942940, 493347008, 313995593, 841597018, 472273311, 636264222, 94800549, 356146909, 806666173, 465366862, 136687333, 509478966, 393778975, 57087691, 217478205, 856652678, 928623875, 522910316, 675064571, 905980428, 955432379, 963700290, 192010413, 138414571, 751295162, 627267739, 562919220, 505173893, 694985004, 452463796, 595893908, 316611872, 238485372, 88548817, 448382113, 765603069, 505940461, 689720889, 45735490, 653727364, 478330070, 169123248, 935841814, 924247522, 434163582, 27562616, 138793333, 542552482, 970788689, 370873414, 133978434, 770491668, 650286552, 501963448, 913588062, 866512185, 120255658, 936933347, 575710004, 742762026, 353305672, 810887194, 628365981, 648458010, 976809617, 494013201, 458032947, 149462249, 316609080, 192545031, 81156001, 462179430, 77629050, 990200624, 482445380, 633414481, 30919382, 198373081, 826670428, 78780518, 500799070, 244731095, 731851006, 714799389, 478090528, 683395212, 220561791, 57677640, 581684318, 24592425, 807224603, 253923794, 6648737, 641815160, 946515629, 601189007, 295429589, 724166194, 103904872, 895479827, 459849278, 181590841, 597362604, 213238411, 426348150, 497527986, 900475387, 254685085, 371576512, 526145244, 983503716, 662183889, 761137791, 472761606, 150872941, 588067951, 627816084, 34039018, 230224992, 802999123, 149621444, 560788397, 742565733, 303163718, 744034431, 464943601, 254249756, 553700034, 722290998, 356024927, 825862682, 394803470, 124235317, 126375142, 458281212, 167836352, 682499975, 680669224, 651982925, 15846862, 38973407, 379090352, 164858392, 343924897, 947097498, 690986656, 429871319, 207274775, 638018159, 275472469, 665721478, 81313317, 964954965, 5652119, 57835003, 455987719, 405609314, 10652910, 129502143, 656292835, 292339942, 807802627, 661911371, 182866301, 9614639, 35291383, 34143555, 236889110, 112488112, 390946784, 919510703, 526791905, 596423793, 777427963, 525126199, 685293182, 621550648, 588240691, 73290389, 397584867, 30306696, 84789863, 399633369, 569638017, 961457575, 134153532, 794522547, 430686756, 961658782, 8314073, 146805770, 473978514, 130841861, 595136075, 517019641, 174534059, 774452736, 460972639, 330680974, 471300943, 242130090, 501049571, 383907314, 18244414, 925917097, 3499151, 184166853, 991353060, 477466196, 61732065, 654069549, 861391821, 169048962, 158945643, 905870925, 434183747, 566267316, 310778060, 768418109, 260314359, 873192777, 370778554, 883214671, 842218534, 698444901, 794451012, 252503505, 354587135, 49969439, 118413335, 491312063, 285801589, 151179962, 880912908, 467120575, 380898564, 35781682, 46226363, 107864371, 674688589, 218777394, 332618017, 417727475, 62360458, 805487739, 903000237, 406822638, 8444485, 317444833, 570144854, 201277147, 252818364, 265594487, 928712547, 753765319, 44913413, 398548478, 449330892, 994246, 218534696, 473764093, 391775216, 737505453, 932344134, 577715135, 683129262, 551421305, 274722668, 832058276, 546335462, 340031771, 504443909, 45603197, 66319610, 952448177, 278348156, 478690854, 64301139, 100265770, 619103327, 138592617, 699861147, 601941794, 530133207, 652322072, 381043150, 142886516, 772277414, 69469121, 867496664, 973485975, 841921732, 774037486, 813260857, 574275896, 950229980, 2429869, 187137962, 917087000, 14413231, 675373787, 419441974, 607437476, 203539393, 930967964, 870820072, 403849167, 930483985, 590949548, 240192998, 686820273, 312838503, 818449881, 232260230, 358981851, 918851287, 15818095, 176690302, 10054499, 608789773, 705916783, 929215594, 63324756, 660465474, 357764737, 79972289, 945229909, 741139638, 506401654, 581578948, 323479599, 434310178, 708657990, 433584891, 996512177, 547245284, 543965365, 509077262, 337770930, 441787141, 949307032, 100007861, 417326601, 287323006, 308480604, 855960009, 889511173, 920221349, 959703408, 453225351, 69551540, 871859359, 184595549, 594760432, 877916111, 936240980, 749509577, 602518914, 99513824, 211537733, 503743879, 914846533, 55307954, 550399533, 272385891, 480041265, 75919434, 220065607, 889405185, 873760112, 961939743, 627407044, 7637873, 990829265, 189548478, 857273633, 412403858, 319408915, 115397293, 470525240, 438044769, 388161925, 81221404, 343272193, 168773078, 414451980, 927169641, 840432092, 60200394, 287938449, 795715272, 103322605, 342531602, 429124392, 804413389, 850634660, 11194999, 520448403, 943934586, 732085757, 936418042, 320333736, 689445464, 346809456, 756848603, 61557733, 136623175, 748145390, 546592825, 41839616, 811967140, 625398456, 265614930, 828807344, 780796487, 58990671, 216059173, 805632215, 36971330, 865153510, 466344612, 625371751, 155703511, 403433621, 867609387, 133270048, 957249520, 557258079, 722048102, 103390112, 285914716, 688695462, 14889747, 21825532, 848465385, 847284451, 689945476, 609440999, 505304158, 385561927, 472701890, 731590588, 524632271, 957033094, 735397318, 431386154, 38741870, 607232941, 732662979, 405839283, 870043538, 593022820, 531163555, 390074488, 590443214, 427400915, 468155080, 98198300, 459539122, 728999819, 741603743, 849546455, 242371107, 473193379, 274476848, 832302239, 280073036, 62152143, 839448346, 141824282, 623238828, 742242125, 185531734, 483202674, 878019727, 16752256, 963041291, 492202018, 384359103, 577813656, 293771873, 377164994, 275864029, 591155379, 532202419, 60521339, 982902983, 271593107, 353499620, 488996538, 536796034, 597486273, 938422163, 979072282, 696256158, 774146843, 508747583, 349838551, 539626011, 909820265, 540231806, 268467466, 426775704, 360011330, 217643095, 785266779, 656046786, 146912279, 642111574, 126309692, 63464792, 804443804, 722000858, 284256700, 214862883, 514106659, 689616573, 953826865, 298043131, 374698265, 547862100, 438351110, 501557323, 6129727, 126773850, 14072773, 655938717, 710586504, 133854259, 86941392, 56745710, 241845514, 184145766, 782259519, 347597373, 636764334, 16609372, 743841760, 548120262, 49431529, 898793315, 799298252, 479355751, 825194621, 310899884, 331611391, 566646319, 807883733, 517129940, 515938140, 733831381, 256386165, 736995747, 686120613, 966306429, 582998755, 55934710, 521003609, 267320874, 967655392, 525803263, 640505915, 982330372, 296839831, 876544264, 744601599, 710686106, 805012920, 555330192, 990241991, 876252153, 552172492, 530064934, 140030733, 965787233, 246518895, 710998686, 115434236, 613596595, 314812599, 109094555, 172652523, 736723794, 310728266, 703590408, 207549285, 310888248, 411690089, 517121388, 251549134, 689441821, 439706738, 460609898, 179746000, 939234441, 218749407, 343138620, 282104146, 603663822, 576233223, 42800157, 896132805, 754703490, 458469521, 490350175, 286781349, 873432803, 675516680, 45617457, 773821869, 860722992, 384068175, 116877532, 875767891, 330728248, 521761184, 747436269, 343445706, 331982156, 693539793, 423865207, 78546411, 727930859, 177170751, 59590166, 404000933, 942230814, 233526134, 240486942, 791300523, 52884721, 503581288, 987180327, 860614582, 101121765, 558620090, 564027921, 342865253, 201929667, 481213172, 822253060, 948216668, 414079308, 42449612, 49783742, 650272608, 637716619, 288975219, 400084104, 854553232, 758102546, 779793185, 560329893, 460365468, 510395043, 27537479, 934905343, 739246393, 54953035, 745765655, 225243724, 197815441, 585376039, 553208326, 542473993, 798701891, 200769929, 773024395, 394986224, 856262911, 417246375, 739176610, 930577819, 484504752, 306620225, 15621692, 541382508, 369083814, 692397, 501500906, 380744893, 87947670, 191344390, 4077235, 743865683, 664489456, 298719208, 938004182, 231367576, 647202152, 883331645, 529744469, 856625485, 125122127, 485921030, 423619858, 711984330, 552898347, 225710203, 998979190, 398243972, 681149413, 462697954, 831502859, 915299904, 346880581, 122978255, 626238894, 773600477, 939786137, 591806048, 915165803, 498763939, 114814837, 101947980, 441782771, 977571301, 488527168, 92606068, 81217753, 506771393, 149250969, 757114504, 921918855, 539167192, 688695788, 900210907, 942083600, 380940844, 668345257, 325013060, 105849145, 372188296, 733026061, 913919282, 192799489, 315631900, 185339978, 380221455, 265466568, 451759051, 364643351, 203591307, 394905865, 496498951, 387985854, 257370413, 757270258, 776916265, 464924170, 672253182, 685607618, 861189577, 454751282, 854187117, 436624941, 996597851, 780448920, 510926924, 921431998, 761878626, 736577108, 777911635, 583440432, 35943737, 652549544, 675561674, 626065631, 215709573, 109510431, 930799406, 215849034, 201379357, 513049615, 386030881, 589919353, 364274609, 324050709, 319168128, 874837522, 797863137, 359613078, 477473574, 4008190, 235856689, 38080743, 419105419, 717840501, 412476512, 218906034, 946200794, 126664968, 279532420, 10935145, 285625031, 247213061, 799426257, 440773759, 504444523, 393982016, 944057572, 901772685, 520558016, 457434162, 850273402, 693089251, 623308373, 691002275, 716673987, 763840263, 775950234, 75699646, 109693652, 413677083, 79329986, 990633290, 623156852, 184835268, 328127669, 345549715, 996113406, 320617475, 83944293, 866874687, 690432371, 336212778, 108712148, 882212362, 544256218, 25944592, 604741511, 176997982, 249781612, 619260866, 911634710, 429403664, 829192628, 207393763, 828713249, 264300551, 677347448, 36105324, 819603495, 167808657, 222084465, 887409209, 301666820, 472668016, 299918680, 678228690, 553278684, 347505782, 614453871, 609444444, 504086630, 146767029, 350623220, 842310530, 295471744, 61966062, 995828364, 404471237, 171706462, 871832720, 749340886, 810447015, 165391194, 31484329, 562211656, 871400322, 629543470, 15618314, 932800824, 20998827, 913338310, 538031792, 494221503, 538754386, 117892948, 108804231, 260503398, 796904156, 236996635, 259327804, 865257547, 430505754, 743314894, 49580071, 55203105, 748854594, 14530801, 555210778, 481999594, 627159452, 716652777, 510171631, 754202806, 67823423, 798780979, 741963456, 182136443, 451000972, 849575084, 636185519, 918749173, 518909674, 744236732, 719808085, 325828790, 997946625, 812331768, 574159737, 816731726, 119665845, 92143569, 411319501, 815001129, 707427224, 557669191, 719254203, 589101653, 58670420, 891480517, 429272299, 98290621, 70996104, 544756970, 114046580, 204682070, 368495530, 865154696, 724421540, 383615286, 156479286, 763327095, 934443394, 315972798, 259680518, 607890589, 905498598, 678432401, 222325312, 491137753, 347553486, 261960740, 83440771, 826038604, 625939262, 843495031, 456551997, 665399128, 348048258, 637146193, 375648054, 992241725, 624690957, 192455667, 226991159, 112336004, 102415435, 94766586, 357316942, 958508289, 109431600, 378686952, 223110976, 365387093, 61790558, 4305345, 310479177, 620222449, 273974713, 492539519, 421552689, 634064587, 428545232, 36759194, 688008460, 650818686, 605205452, 907320328, 40731160, 835361205, 971397789, 803554846, 968668888, 268427766, 832442624, 262546396, 60385062, 874408589, 253428235, 824310062, 637937891, 751278161, 537610047, 773123986, 777663096, 235932097, 191042306, 60387045, 959395889, 335934931, 545651919, 631973753, 64328894, 151924662, 902841180, 518629371, 106372226, 607400728, 417862232, 484763043, 48382581, 7238106, 873986446, 496492409, 838480870, 327608294, 598002963, 732081293, 848459801, 52710376, 191494163, 10034804, 944895442, 694093035, 520439146, 341400096, 444016344, 40333641, 864475497, 478982999, 877753800, 211130860, 386075565, 532641885, 746410110, 26511846, 439800408, 676618816, 186060085, 738260876, 673950048, 631110822, 143242456, 853210207, 333146392, 177698261, 225875153, 872990838, 108186180, 603743634, 580998998, 676431138, 975801615, 559819598, 465184647, 425797421, 469370768, 571353559, 436037778, 458740016, 472613564, 578039894, 278203449, 92384578, 939028913, 2610393, 4685679, 553893037, 110810620, 442359464, 507257727, 433197926, 870915119, 354035288, 240640403, 964431858, 68764901, 878372096, 564141506, 839282659, 781044717, 651138230, 174714550, 657829470, 707127707, 327118806, 290654483, 987421374, 469931230, 210978542, 970343452, 618517645, 625746015, 506944666, 733026174, 410555968, 330093717, 125541689, 170430635, 451184975, 315657565, 347749123, 291113714, 219714648, 701350571, 694094538, 245040473, 311765590, 193670467, 41349642, 544700076, 864321874, 406380460, 29093898, 768000128, 867175163, 164161404, 82579138, 129798057, 173496475, 499968, 305823159, 298906017, 548712060, 808205467, 540187711, 243405053, 484846261, 780457000, 316392083, 144063002, 513202899, 820339603, 886763602, 780455108, 31570907, 309037081, 297912821, 205200811, 483836632, 141187810, 563180374, 226082717, 616268183, 266623128, 71716190, 56218417, 462688011, 278562666, 254508093, 12907112, 484587893, 343510996, 77818150, 781459062, 247887727, 963792585, 570210730, 330814795, 137635205, 335435199, 609717095, 516267557, 954613012, 18640835, 899463031, 5381238, 203119750, 775592130, 169488739, 212373519, 879232312, 474425822, 648987251, 144136652, 715548053, 627105628, 359154330, 923911573, 457234803, 660105343, 380760875, 64943931, 680729019, 373005026, 756841016, 604040149, 513434184, 399048364, 412131708, 526512018, 737764716, 437549843, 124651879, 146339268, 629990338, 88174945, 636285431, 612383982, 636818299, 61442849, 135261181, 824410190, 670066409, 547052861, 225501824, 465557955, 913516493, 706347186, 451747018, 629495110, 293143200, 362072734, 514092985, 331306986, 879007223, 398825355, 31280976, 364029104, 466972992, 225573984, 683684129, 295127707, 692487117, 354498439, 300385785, 183467775, 695375073, 175391772, 462259009, 370561361, 432845065, 428155631, 377203975, 29199072, 302569894, 153495087, 737490044, 212686665, 913118944, 734649581, 749029946, 522379753, 885725981, 292515587, 811209122, 709282792, 452520489, 537071427, 530717233, 663290400, 452339825, 739878071, 293684009, 413203968, 980234894, 840218977, 847896624, 759571188, 592739820, 704988836, 471315132, 724100691, 139785401, 780068022, 797409837, 274482270, 197083337, 736719892, 288913058, 702436445, 897611858, 78530999, 212968490, 955044941, 761912531, 175000405, 150933446, 194757998, 617127022, 445598301, 975755247, 314214018, 664159586, 788275013, 838097427, 786750770, 570554307, 28431834, 291248139, 967021, 838120797, 376691541, 917162576, 369592343, 139847660, 748220124, 740354800, 721264546, 560067999, 672147147, 515952403, 387159939, 386230554, 998883730, 402477236, 609388772, 229545479, 638399609, 961063483, 941202497, 425049714, 65636938, 549139890, 536488189, 47581705, 748415721, 787541121, 748973777, 657351309, 612151374, 895070220, 952641990, 345503879, 870560007, 517880366, 551503116, 637567067, 662041833, 551875100, 744607830, 518523952, 686118059, 292517752, 461033110, 243801198, 184177760, 917381610, 508594634, 622815777, 200517875, 307967170, 293682463, 442524763, 658391749, 358778425, 84651907, 792276831, 397953175, 998601867, 357636412, 979967701, 506546606, 864539464, 214334619, 233357200, 234772717, 717277520, 193598121, 329751059, 96036989, 904047526, 261761569, 60421522, 813719462, 684679691, 742738791, 854976801, 880666899, 131626387, 752310513, 722703350, 211832185, 15785901, 345922588, 444606484, 657688263, 85574049, 766389887, 783986778, 85179165, 620858762, 324410091, 761454578, 284860430, 995203058, 139583991, 952564753, 936725044, 377390086, 227931860, 96502543, 620979746, 770202432, 591384898, 89307983, 623223432, 542011215, 103097426, 157565491, 737500924, 178629117, 926298481, 319923850, 229653554, 585947167, 280693975, 224360660, 984173369, 50937479, 504251750, 315233352, 577829310, 805372831, 741266914, 661554790, 239112590, 54537709, 850444762, 384061259, 223182865, 508291491, 789188968, 699965037, 283772547, 420626274, 140946215, 525394009, 535204655, 525736822, 568361031, 814574304, 648909831, 269389260, 321966068, 9472952, 641215355, 545712360, 39457190, 115738225, 498459872, 562607671, 512809458, 48698146, 951465845, 365831359, 982160987, 187566830, 58410623, 574149634, 140231968, 838453375, 882789140, 846391837, 314156340, 379893743, 471382384, 210024446, 649553122, 330794535, 956122932, 636572538, 38569331, 358732948, 992451061, 707534191, 492974669, 625981163, 678419963, 736737933, 866586096, 526565619, 423774982, 117259611, 997575977, 736278719, 949451336, 746051048, 829994523, 18506121, 612394437, 471002382, 107848717, 954553124, 507536560, 453546252, 333518583, 32661411, 663225706, 749321607, 179334377, 179160560, 631013870, 559759066, 684212958, 642835206, 461709819, 592255908, 285752133, 202932748, 905828149, 631507431, 4158795, 335426559, 42635911, 553891742, 497514549, 785963639, 244675652, 818581092, 395258477, 307720089, 326037131, 42338700, 896183243, 616788491, 895821559, 764525210, 995869956, 993446121, 565168035, 963369738, 425959158, 970864975, 671127793, 947098313, 807714391, 974854388, 396940136, 702534544, 32748840, 124784343, 823120796, 864352422, 637512592, 551938814, 13128439, 578394109, 839010744, 983871087, 773664886, 1550709, 841928390, 910335699, 466124260, 150406453, 955717001, 921487234, 813846183, 743577532, 141941943, 603805065, 80486056, 215132518, 812016259, 672931678, 70813492, 841941315, 392719040, 538522713, 3881057, 549140222, 139986275, 523921705, 581574162, 788073208, 576413306, 229030938, 588761220, 197713161, 767910132, 837735216, 893861676, 549487501, 702763806, 358248891, 609143780, 975300789, 210178585, 87162199, 202208269, 675093787, 514131697, 402875834, 710026571, 490914429, 831339899, 340355125, 730008929, 640251617, 356031243, 699848215, 485472865, 573381499, 98110951, 379412077, 115638441, 769127166, 765922120, 910908633, 101061257, 323515174, 389711123, 49242413, 575768851, 276245998, 942486583, 788078478, 46340893, 81571564, 501503208, 915315025, 937775741, 938899149, 79054886, 717539293, 734547381, 217437422, 977579716, 451286770, 127464693, 867708006, 372973865, 634391465, 715352992, 658666838, 179521342, 640294833, 750906312, 310899783, 540427794, 102698722, 850790133, 167745272, 825672054, 595596789, 372236915, 926750521, 848924191, 126748025, 952458664, 137585089, 401306460, 443587943, 447358777, 436104745, 577422922, 722806353, 378684339, 351851556, 383303700, 582352223, 641930375, 61630033, 219365875, 638604540, 236212292, 384590886, 955551269, 288082880, 188808217, 352384269, 812225720, 616859620, 458364680, 396235850, 701129792, 549239513, 846226569, 231484844, 557679211, 273452421, 837246911, 379188180, 329013427, 96829316, 230718796, 25948862, 9134047, 152952310, 243048751, 623655566, 321353120, 999870014, 87047716, 164508200, 272988433, 588328863, 492718644, 548770352, 326762970, 237264758, 236519748, 67949725, 457387111, 275728104, 637372539, 197202325, 429185166, 562794583, 980008803, 155016222, 293815421, 809852146, 3845547, 367428216, 634870224, 927901867, 466228224, 242480189, 720641003, 855724400, 546821104, 659675497, 646454278, 887594794, 601444395, 817367868, 480323440, 758422877, 333764985, 205270944, 441251510, 299477142, 253054788, 169562772, 612732292, 621638462, 383866295, 955188137, 768485969, 638187000, 775324004, 104185875, 671417977, 742683216, 536484586, 69394759, 624450231, 244698819, 37680127, 818110967, 442698165, 225597303, 61194339, 945102988, 204054666, 526280179, 336726725, 640828786, 351099568, 689899781, 503761316, 251976856, 103166071, 140954666, 107688329, 984039089, 851338740, 589034534, 628156587, 833586081, 838543932, 197365677, 453883250, 930196208, 318480696, 266359321, 110794534, 430246273, 906015050, 396988163, 541799060, 153537979, 609824192, 664071885, 816178952, 9279150, 350320948, 374626915, 565893743, 434904912, 334673425, 110734824, 468266583, 960854404, 681228509, 437417365, 419772637, 597398472, 69517602, 878936972, 892583931, 239171785, 197052267, 720550197, 677983155, 54711141, 138571903, 725223167, 812085287, 168602114, 154767525, 670868973, 74945734, 215085729, 174253080, 376143870, 29592049, 382740636, 928173946, 913427823, 378824356, 434736962, 14910100, 609162599, 954949855, 547613079, 672436860, 136735194, 592012357, 319434436, 936487938, 74758540, 655716703, 431079800, 25074647, 310807184, 600616085, 223497135, 384908221, 401620180, 250918782, 63763380, 412362426, 958512209, 941903727, 838408387, 32570081, 842444367, 258805329, 20382997, 335369157, 840337056, 788572685, 863125298, 934790333, 999168694, 68844124, 857008303, 857824860, 48797412, 568670590, 99486127, 17413746, 485817491, 890033118, 545530197, 712968237, 932247843, 157688188, 248563181, 347811279, 609386350, 438732276, 282030187, 124587605, 630470127, 453902209, 392714533, 910149686, 6635204, 861565695, 323455929, 69711607, 831789236, 992936820, 428995323, 656350347, 753717044, 28007109, 303447694, 296940302, 116798105, 173527802, 665186050, 258437651, 790910137, 991933796, 817228884, 636462771, 269991927, 746779027, 424110266, 34425389, 699890465, 332913508, 389426304, 620118516, 62315091, 768381800, 288480875, 422618667, 612204754, 566237086, 300690020, 576370635, 877795535, 86791427, 292844023, 848526189, 75375825, 137114126, 351103153, 844826490, 594780965, 21085488, 270008381, 817177773, 34530276, 873225548, 477813160, 834679627, 709130464, 613718879, 233642887, 260442059, 727278502, 245577337, 96967654, 262239625, 564810052, 754128515, 131757319, 703234080, 265491480, 959940221, 403699864, 433811200, 580250451, 289188711, 382783134, 91057065, 127900959, 663625752, 148567402, 919647835, 879442284, 286597822, 85395546, 225405721, 647582027, 169841590, 770892834, 102088978, 846374229, 491817505, 190250902, 175660702, 488798846, 422931688, 583436289, 554029681, 97356660, 390187478, 98179225, 142863020, 13692329, 677507862, 6435541, 42689595, 850413912, 800296380, 677180272, 807323114, 847103310, 448042816, 874206164, 123065255, 894559862, 73061306, 537075223, 572998584, 321882901, 454033297, 2052489, 331365434, 975478485, 63758720, 31031667, 293613910, 248275063, 434085693, 628505793, 135165651, 969801883, 195571695, 939121701, 211445163, 423218450, 15264023, 915528896, 796150655, 708608752, 169837642, 507526394, 513608222, 857176044, 51228990, 867923624, 815991917, 714572536, 740384167, 675390141, 37571474, 257702414, 626603897, 624242324, 143621020, 955879228, 320775505, 628196240, 985728023, 826954929, 834165336, 275251261, 367361683, 827494741, 497728372, 240903387, 118933400, 811283606, 339811870, 506013119, 525822938, 101199817, 829842907, 471531998, 689654450, 135505086, 459203836, 507527360, 245262234, 619443734, 245384529, 930173217, 515392401, 262027844, 171162755, 75533323, 479766044, 212603065, 255166034, 746513188, 69212527, 242677643, 477679830, 342929616, 18062275, 35492604, 778388300, 830730628, 774449364, 713134588, 897820265, 8948985, 861566664, 253177568, 938215750, 703042633, 442667937, 274179389, 538713735, 272751086, 26585804, 398185084, 766297598, 178308568, 948688720, 333402137, 167068773, 98069347, 902762806, 475475181, 813660334, 274242164, 910662500, 56274373, 517592720, 27143157, 682378421, 804577780, 822951821, 325320065, 44214267, 511680524, 273514209, 860547191, 392672688, 815549243, 281346877, 796917207, 44515563, 667798424, 141517582, 217114233, 624653411, 393783039, 551427481, 868499465, 827747595, 919295557, 248485522, 402935120, 386423196, 732099781, 494723488, 542395053, 382346261, 957036004, 93921264, 803780782, 407073092, 570603648, 614041971, 882819664, 679173544, 705281557, 122974294, 361707443, 497198841, 746820702, 430207482, 188573407, 578015223, 577887473, 754969378, 316478045, 624082389, 745171124, 820997863, 827183381, 791986936, 266139088, 788424202, 261569952, 644506021, 78681443, 632641948, 663539107, 49097432, 677446282, 684956117, 710109073, 209971784, 365997678, 613038703, 196809611, 67635391, 611368268, 173188865, 549119267, 419243951, 453298955, 566088049, 457950573, 785784890, 23929829, 621868223, 313331624, 484333931, 488794875, 557523, 279318780, 461519983, 548458715, 215896769, 927642951, 858670753, 746100237, 679494766, 486081103, 243089475, 436007176, 259772918, 20788162, 124103304, 26139658, 666391366, 407158639, 990766968, 206237329, 855734867, 449589140, 723971508, 56478377, 38681841, 779859288, 151377452, 864668216, 395657597, 838996110, 2498570, 353446622, 395967181, 192785250, 798048498, 905033611, 802855058, 61229527, 603262794, 639393186, 957748880, 620483904, 524755218, 137745062, 445962324, 146490423, 170449865, 433949431, 352463001, 645888222, 265433513, 772837145, 153324928, 778075313, 645516531, 828969776, 985932887, 438613359, 405691445, 23591592, 758031943, 523492251, 16843642, 119331958, 940116572, 271014826, 781444956, 211221182, 392615259, 990898408, 855569320, 781972992, 179522095, 342927407, 993019132, 282170151, 756161708, 133221633, 721905697, 531956518, 239677572, 840470937, 579668806, 989870252, 302544437, 510079230, 883693527, 230771716, 353325845, 96899219, 577736068, 459871823, 39938136, 850180423, 334443444, 781890400, 810456120, 58485325, 403949393, 335084656, 553960667, 756067717, 801062389, 6325920, 921402263, 371242765, 609483512, 57425236, 878245101, 133081987, 588492371, 220043624, 185381741, 572540816, 353471780, 107612092, 15899773, 591210541, 993989607, 625592778, 728839444, 24317184, 417050473, 975003690, 591518999, 713349484, 734289208, 760701102, 420615743, 326264486, 308361262, 520175117, 473748443, 239851444, 267520828, 166370643, 278885937, 99260731, 286348557, 445135301, 367695840, 35572444, 464551993, 641359784, 844431371, 909587725, 162227517, 819712977, 221461406, 848111182, 252333717, 140384756, 725683241, 521126167, 798430780, 507065928, 819123015, 280467795, 893435654, 288136895, 254701349, 457136386, 535973874, 469162005, 647317607, 120318, 475638011, 365296730, 187864589, 709770139, 593739849, 917354549, 305425277, 348475187, 261870110, 534741536, 167050534, 359625826, 521400141, 896785440, 727620794, 613860888, 930168958, 227981000, 579631744, 408752319, 269864989, 107499628, 565917349, 332842906, 872942650, 57582624, 384034541, 639924105, 823513916, 531325887, 189762584, 202489661, 41485507, 46716642, 18329321, 733253589, 179470869, 253563091, 818413245, 136755010, 646398211, 157935129, 253602525, 407851607, 179661587, 415575779, 786134497, 475110334, 129024868, 896745876, 384589045, 574883891, 306719403, 510353001, 782034272, 957895795, 30032533, 697217275, 697608162, 892483064, 322865562, 578747016, 804871161, 824567306, 130040221, 575974207, 653877023, 198288975, 434614393, 542060626, 417603512, 481310274, 108730820, 817706236, 918654519, 199492053, 36604479, 611359128, 973541436, 261834821, 706407406, 463024274, 285151783, 52671386, 434601391, 599431278, 642370981, 905462225, 501030873, 126784142, 811328805, 539429804, 395919086, 320692905, 978187901, 638509211, 549760786, 992809942, 26707693, 553585272, 698653735, 748574616, 787147519, 250715538, 446145511, 269068647, 307173253, 70320932, 515420086, 191857660, 114631613, 995040535, 917042061, 239320496, 312692840, 609484904, 586704151, 120449880, 214965447, 597551280, 750463378, 68988211, 666320692, 346152493, 46188014, 575532596, 81321208, 358027539, 702080166, 701582943, 479173461, 690191292, 478734064, 273039787, 350609092, 695827354, 81109302, 485531760, 923323743, 457215663, 428144995, 45018790, 103511005, 950295661, 662944396, 951292320, 117519939, 968461625, 313200839, 201997895, 161407402, 853193476, 878797758, 910890969, 354088176, 391996341, 256083851, 158128203, 867337311, 185525607, 570342523, 844665199, 953385255, 396875361, 183691626, 641479325, 600560125, 70703086, 166972501, 252244542, 223207846, 665076047, 337108704, 765438557, 660501323, 388256581, 537135786, 899131036, 11923692, 160691433, 38510666, 169758912, 882729739, 587174735, 5158211, 122263956, 510587659, 6927142, 187006109, 483159940, 556075364, 958366792, 719694518, 526078695, 769021464, 504206250, 954314397, 522362015, 700066903, 783043311, 897643046, 150945705, 912629039, 786967947, 225824341, 51956382, 431147666, 733544996, 840279494, 879998140, 492543203, 661856170, 32847056, 10012184, 300529345, 119053925, 558999439, 317490747, 934972241, 152011153, 328936516, 188519945, 26983750, 61856822, 589141921, 964265855, 89898403, 751399524, 434114931, 865364970, 555971959, 10846639, 204545457, 337236425, 89585300, 561519869, 430910131, 123634999, 693044791, 182201602, 467539947, 960114853, 228220361, 776575897, 554123960, 651303691, 11304799, 522933523, 916704716, 282729799, 519017006, 993541611, 977437957, 411610585, 813663462, 171430900, 74135779, 349704302, 383854543, 733566761, 760438377, 557659310, 214614119, 35019381, 247368387, 220258959, 67282633, 848877242, 802314144, 926433055, 966350626, 794672922, 117771002, 523565720, 369088164, 957293937, 78581215, 416723054, 653534420, 883615395, 371055678, 576794107, 236647144, 533674282, 496481591, 1858288, 901548087, 207700358, 84996898, 913437482, 75370388, 790703438, 884720994, 287859359, 912828995, 272857508, 546480395, 386807234, 773028264, 312790349, 667401923, 270467970, 405405375, 911181749, 452036813, 73766945, 595728085, 231867476, 477073965, 861845142, 997340667, 562159463, 791555177, 933036962, 919630617, 991890122, 533641508, 111913788, 347137837, 770430685, 966596215, 789517761, 15622591, 878880933, 838429723, 87536533, 107089871, 958156581, 317457945, 470937298, 658549520, 120526017, 398911736, 495648158, 962634974, 683123276, 233174638, 593623029, 59533463, 555292373, 916074943, 715203445, 308551417, 132491457, 606822484, 242377876, 721923700, 279766898, 677013424, 67801523, 392174584, 760692157, 616306868, 830863895, 568984885, 885758057, 646072871, 389488213, 936012736, 825035475, 694273067, 609707201, 549498832, 769202902, 80124465, 619862295, 941125442, 466961056, 752992179, 617524395, 939376758, 416696347, 272063925, 916581207, 467999185, 330877532, 97902217, 456135207, 588016342, 318409197, 955702828, 169452209, 372815601, 953558177, 173229027, 160254603, 756815397, 126003671, 816465337, 211616926, 870729289, 541224173, 802616614, 54709015, 715060157, 954917809, 783693485, 240002319, 415571143, 961123860, 432360387, 308706712, 570147447, 971411368, 218601449, 245822791, 933117531, 538900362, 789771776, 778767732, 881981565, 2171709, 91058936, 349935, 804923425, 943907680, 73735608, 468730637, 321088188, 295225997, 47626116, 36940025, 527621538, 343337000, 710544430, 37101403, 536356459, 898041863, 473031820, 889408928, 152729163, 491844199, 845213191, 274236498, 874356988, 902372994, 936190360, 888703259, 373734435, 563851888, 718212328, 857856993, 564684149, 254268355, 163235630, 149113695, 770328982, 716736240, 766985340, 59903882, 780538290, 74479001, 225646898, 912993383, 218081275, 841303278, 728186031, 862678295, 582317845, 881655659, 177687753, 544693300, 797152398, 872117037, 830570083, 647237096, 580406384, 781605449, 773554334, 944175382, 799099842, 252136386, 885675640, 412256345, 874467817, 199323912, 884450225, 843859051, 594796009, 961664368, 515624147, 334235956, 12361102, 223189653, 846897278, 479520599, 868462039, 42034203, 831006067, 327404487, 534987655, 388396566, 104041967, 355441909, 59894135, 82707415, 967046403, 649875926, 419474534, 435077726, 541363248, 941242725, 893560512, 243281097, 778738059, 856009358, 319002965, 300200209, 193521391, 202981200, 130253348, 473288080, 754261944, 498561823, 84827017, 405566605, 848841686, 464233867, 984137267, 86639515, 453927738, 491775099, 71232775, 879986297, 717437812, 741982847, 8062941, 670427683, 600259310, 708058928, 774072585, 809949064, 55477819, 140225475, 212521753, 262100160, 733846325, 401219402, 483657504, 108712263, 10503386, 182953143, 731632464, 327131055, 499937269, 489486672, 775729580, 714559532, 819764837, 195210883, 676757033, 278092395, 869717525, 402793089, 435118905, 471251760, 703343820, 299747453, 807816277, 428123688, 419448862, 622822223, 160391833, 386639940, 498754764, 378918212, 697589037, 788662017, 109506059, 192531657, 974326274, 536312718, 483465799, 851114781, 896831391, 398436070, 857930105, 965616903, 614521135, 216697747, 571146680, 960896542, 702901998, 540602827, 400361722, 846965474, 888631206, 643751999, 675541445, 485751060, 187694699, 462202152, 865310951, 59781561, 244877341, 99274728, 467335368, 444790894, 5567144, 395532890, 555006646, 948895852, 159908597, 133669404, 75352645, 189885262, 560462158, 539850819, 43170558, 639071736, 646367358, 735268699, 351500746, 667241845, 170085078, 120377703, 592565979, 280065133, 737931129, 151968289, 578735175, 897264863, 387075981, 734597353, 752095936, 940743876, 242230953, 556826752, 342725598, 4721096, 531862486, 849129999, 896392726, 6342478, 418043147, 486035657, 628950689, 850180306, 948994322, 372092321, 625238421, 567363698, 539196290, 526296138, 12706298, 58515732, 337109340, 798470902, 57252624, 724778577, 394680796, 863457044, 366176197, 56221240, 688009425, 766140808, 328079678, 634580081, 593373068, 470828070, 481159050, 188456000, 282129875, 809618718, 859464505, 540454863, 463207390, 976563894, 201715787, 986165136, 385500172, 41380112, 763885449, 884268468, 111264046, 789814842, 667363603, 26322085, 744351232, 82473533, 625533815, 184145441, 756955870, 872372479, 370709281, 241455063, 549664644, 867143693, 960969109, 704506294, 554781426, 49778194, 660749300, 548171400, 875039668, 385779779, 863526881, 658267180, 670232887, 503867155, 825889451, 711768163, 246621855, 676599418, 738841524, 353931903, 34105393, 563003939, 848458237, 299079677, 362381651, 503946704, 347220264, 874876181, 430842083, 574587111, 785038614, 502458002, 718553527, 523664363, 116419814, 904631294, 437231847, 588589362, 830651577, 704416367, 799007579, 32067635, 94219231, 43872758, 732775954, 38817096, 159901299, 444817461, 203789332, 445315631, 431255791, 408220484, 328531714, 839346179, 626508774, 211971343, 497067986, 240376743, 799096399, 421208381, 871106738, 354581200, 932452661, 609008477, 612119059, 100188677, 714532105, 958342624, 132325422, 414544624, 711658614, 725417414, 930413852, 256083514, 74897575, 150446782, 557746025, 528359618, 903726824, 668027820, 160652674, 179226853, 711606165, 193773722, 802605335, 306521583, 792619204, 368353470, 227863351, 854154250, 571549569, 422895019, 742258062, 152094040, 119397132, 317332463, 117582013, 735871658, 494764336, 818751523, 234393230, 406150099, 246569089, 336742939, 43506076, 9848608, 571727029, 577549082, 911096008, 90465415, 686417072, 164839079, 287734714, 824779232, 217469687, 147010559, 116243704, 222287066, 97823835, 38981940, 336614317, 151510992, 384744713, 104335089, 449977337, 513161640, 702387889, 735265894, 704002361, 171917604, 940488507, 968348011, 382830436, 164914051, 47841526, 724144225, 945113984, 840478969, 787684385, 541087663, 2905855, 202057743, 609027729, 999730800, 851678147, 13833280, 477974309, 549363365, 532201526, 854327072, 42111298, 318201422, 766125018, 707557058, 469213603, 797107466, 830378085, 344619898, 20856266, 373012285, 983722550, 562064044, 945137175, 569025303, 145290462, 285168370, 669771565, 214065904, 580794192, 106154151, 508691512, 396537576, 251198906, 839639905, 964155345, 226630458, 593651134, 649821181, 888177631, 493774941, 979513262, 152381291, 782835333, 68216806, 230994378, 934878586, 974279909, 403163364, 127324601, 86418867, 363622604, 383688361, 645331973, 508705659, 533696655, 10005118, 144276874, 135846490, 555696728, 878428897, 980338673, 891800111, 729663674, 244541345, 172035791, 764141256, 415277096, 566102423, 921843805, 598473984, 502763684, 720363114, 565433776, 819966662, 97639557, 760982938, 845841440, 135175727, 88936035, 491090623, 813435009, 766261290, 85176016, 741676546, 718231202, 54211188, 613079118, 197663380, 743496898, 908651404, 949835881, 32909751, 85044823, 863779289, 223737846, 538724405, 800244582, 830670255, 858194762, 646462951, 257004273, 13025605, 378403635, 91688935, 446488929, 630545711, 533862143, 650537370, 306778488, 72406012, 227908630, 136997627, 818789142, 459251902, 607777845, 446396194, 114885597, 419576991, 112482372, 683674368, 528115127, 90541176, 334503802, 696006243, 574751749, 862224702, 657911917, 753165389, 401856875, 430631390, 209680790, 828915735, 19086366, 491859245, 481053743, 936468176, 360301136, 237221204, 95057610, 186504414, 132218554, 808207454, 654657347, 558429341, 858606565, 216541342, 733592862, 762973629, 369481370, 6324306, 193557867, 307481267, 72225424, 115824109, 388535739, 875803527, 877902768, 890236637, 961380950, 56558330, 306036357, 862509839, 446155857, 983730946, 995260499, 773020227, 604508352, 86976353, 14001677, 303729037, 262045149, 602562941, 276385243, 420893252, 708705522, 564929347, 764734359, 978457649, 468899806, 820456781, 347103238, 506657763, 103865918, 842439302, 655053308, 132762840, 716998792, 226754384, 939345853, 638063201, 69962432, 901469971, 28071391, 501138347, 985039491, 137866633, 14051098, 711230156, 750481955, 915644724, 683137553, 740611188, 939755159, 363040105, 215961952, 161658761, 250781284, 61823986, 822252214, 90423811, 197391399, 203172233, 831252831, 477714172, 509616381, 920839323, 682317378, 229437546, 30422330, 340084229, 988062507, 593694750, 113769047, 826290198, 714956037, 662675346, 17757340, 853203887, 195882311, 138838726, 927416232, 87118235, 4341200, 77895441, 63210943, 979217839, 163082085, 770992870, 177243362, 70630825, 28712913, 101158351, 358005439, 650220222, 653879835, 266542922, 586678281, 809682379, 999369391, 281451402, 450684615, 763810154, 832141040, 511771133, 360815586, 508028108, 309226550, 270168837, 361000253, 768713895, 512406781, 196670020, 323201860, 184942979, 601365855, 19137790, 786617588, 830160229, 5022381, 844627839, 790242521, 865197320, 111782754, 847272790, 219433596, 189783728, 677102088, 349070582, 407493964, 892515093, 734711289, 766600969, 248443644, 592680248, 890056943, 653289695, 457456230, 43479012, 395363032, 689201132, 463611020, 720827079, 867972935, 659549528, 310690033, 224484294, 680012075, 927650248, 359224158, 362134727, 81877790, 6815054, 787970813, 54132520, 899821061, 957075868, 457803905, 994306291, 725421818, 841698368, 355514317, 730016997, 733903115, 109996418, 615475395, 733849602, 397240321, 833493284, 999810962, 578383827, 162040480, 732334477, 719071483, 903323189, 632592474, 744270450, 807135932, 350525961, 484851919, 611494255, 625171574, 393109183, 793287197, 568146363, 811795101, 828431120, 24815619, 856507956, 411678543, 638642948, 442490537, 853887136, 348219153, 546343844, 866814601, 824839820, 80467910, 973461565, 534603948, 347702886, 206812807, 555201770, 45932776, 146318638, 164709843, 18342781, 988207192, 735848649, 651160749, 971575307, 890738882, 913672384, 263375302, 53215299, 731455109, 797466464, 297591314, 345760984, 855650552, 345687322, 470088391, 340629334, 288229450, 8818989, 392781387, 872535548, 556472018, 892028814, 506173235, 191595416, 32805203, 240147443, 689011930, 446750865, 946111848, 283180816, 847948631, 106757588, 808798019, 98725503, 611138979, 814125984, 829867194, 597771754, 883993878, 270661896, 955150245, 573880775, 760301744, 599284746, 68902830, 98426273, 748617881, 588927948, 414993610, 125616437, 425727979, 544164754, 828151451, 265575418, 77391184, 169371871, 266895414, 719968822, 951371929, 551814784, 962004700, 311408428, 632840044, 268544745, 348652669, 73204906, 285554433, 467442181, 156469858, 717254017, 867963227, 45600629, 898238964, 865193772, 14234056, 111851284, 754291285, 600691164, 155520737, 193171356, 161757616, 377698120, 537997050, 894240154, 463915501, 299499621, 777557073, 668404899, 952249218, 829645371, 668729582, 715850635, 582890446, 126921111, 947266792, 651332951, 595868889, 672037109, 170032474, 424332154, 544483167, 711681114, 65863724, 41043927, 547614159, 824348643, 640140984, 423635380, 57789229, 299215518, 761486321, 961403790, 49995334, 181509951, 807294030, 948723610, 898750716, 386916277, 387609465, 923212446, 108539549, 858376963, 137577542, 10041128, 240252493, 416176651, 977206448, 416062730, 897854239, 539570232, 815097618, 970902167, 472086092, 824133073, 378017894, 116013685, 521337952, 347423409, 186219553, 2672731, 237214125, 164817386, 494128754, 408385972, 682490263, 229375645, 320483179, 977738919, 64918207, 751643804, 390727039, 565173938, 752882940, 312693670, 334128664, 437691619, 959371904, 690549093, 384911268, 37769198, 313218312, 735327368, 865607311, 328963200, 485959265, 237256720, 298136882, 256432466, 738015760, 138776279, 351147733, 775904490, 594695739, 148720899, 480613071, 911896091, 780914864, 526778711, 655584350, 603344005, 152776216, 325711747, 577373432, 457554966, 619247138, 838235565, 297923010, 384806101, 905569534, 206638811, 686734582, 229246150, 349944972, 552137060, 33268040, 849867959, 339517704, 371319060, 296766874, 586112413, 613218613, 793845309, 269093294, 228213007, 519383511, 109049617, 111233096, 411401589, 90167238, 790774217, 440834400, 10282222, 649403696, 705138235, 496039627, 654506630, 187408740, 560375992, 165662669, 874737097, 418967682, 526677580, 299780037, 914504635, 806894081, 127048194, 178466863, 778264933, 634910240, 125805046, 59021581, 464540618, 602340821, 501915777, 645994006, 273883775, 571739822, 452246871, 621470422, 215880978, 605810253, 424364346, 778675059, 512120458, 564173814, 740852495, 734979, 913826247, 816928255, 854625991, 91567632, 766397120, 563899092, 72194112, 603130118, 768140955, 922572757, 525387278, 549297349, 744910600, 350488832, 293812736, 483517644, 68297164, 289996484, 568921045, 494946629, 899254236, 988121680, 16939479, 477146586, 529022029, 808877631, 255195475, 464953194, 211787757, 910950025, 509253967, 261049824, 819918065, 805108560, 96866729, 719270792, 823746217, 990908510, 872575411, 776739651, 236412794, 379157703, 178681375, 863350710, 637229057, 364421795, 958501759, 474906222, 93416458, 757576931, 692353928, 65720221, 533525431, 968372271, 372232274, 28894149, 283130376, 914897182, 675856315, 493707306, 4851512, 127572903, 684688957, 834885973, 202858390, 27133126, 83534539, 633074308, 639858018, 814976301, 445030019, 222077622, 506674014, 638783245, 758658646, 695196529, 455830785, 502031298, 426221388, 176022553, 182281360, 685646697, 769649791, 415312776, 357232799, 820151709, 14871740, 97419160, 291207176, 383930063, 872748970, 329513752, 899180528, 814859293, 244466821, 37200173, 189687928, 182374609, 108434949, 613642580, 666191221, 686411773, 909663382, 523209093, 540974132, 616816474, 374416684, 570433819, 568658225, 464015205, 2493915, 539498767, 277855521, 106640490, 170235390, 833168690, 252941064, 499627644, 311875344, 603402434, 303232621, 703348106, 164432629, 213060330, 425121548, 267397950, 570490869, 484955758, 233299368, 693894349, 396517130, 758205155, 911183562, 273907710, 303720724, 708404775, 630216646, 746989138, 790324962, 328114443, 119651626, 504020558, 420720593, 341610613, 450980626, 471028072, 276917983, 208490011, 272644317, 229238480, 45937922, 903947527, 360953056, 683568795, 731361533, 297055273, 132425725, 745394836, 841536742, 641845478, 639597758, 657794935, 100487195, 60132671, 380491646, 226735480, 933908500, 278553355, 493134792, 716163966, 684683843, 96951533, 589926379, 834682082, 868107249, 333758803, 972469559, 357753297, 147988249, 156012254, 247022930, 645158713, 655283276, 214183096, 738872732, 534135258, 380181043, 515671964, 807288564, 783893707, 106749038, 509836999, 763905058, 351648150, 478758310, 653955933, 694143297, 951310405, 626411157, 60977503, 358203194, 854111819, 697862020, 808826516, 173347159, 172691581, 728126663, 678929657, 694403152, 415842944, 514571277, 209801547, 199995791, 362941867, 857503663, 70750322, 986716586, 533282920, 375177208, 230730821, 49304473, 769785497, 322594474, 965222751, 427359002, 961825669, 56917650, 514094444, 894840021, 235936298, 5066562, 537737400, 166246998, 525019801, 539638845, 453723276, 526168086, 901758004, 742134835, 459508062, 430472946, 472881606, 150235067, 424216246, 323644603, 705448611, 48095770, 929382194, 130971811, 399041126, 191376243, 745683471, 781411493, 174018490, 932002126, 444121426, 217676149, 230443947, 586896524, 216123837, 392536487, 134697473, 757002259, 126711098, 115053, 868139443, 359270286, 891072164, 643172370, 256389054, 696250989, 874976664, 243912631, 792719294, 99709519, 470584091, 951434779, 996288908, 484579657, 502024214, 655574893, 939266848, 894899820, 310971626, 181761008, 769697388, 466222996, 953276170, 867908727, 949809579, 46938621, 972020530, 144546474, 654147725, 425954274, 377709221, 892875942, 647689730, 916098244, 734356354, 654274781, 233615290, 316232134, 277689697, 483978150, 846424118, 604304357, 52009596, 657443526, 698891562, 413823841, 959911907, 425218606, 465379798, 988519973, 683291111, 781401759, 743010302, 58305401, 591032606, 186318887, 631235494, 708800244, 527875684, 481448372, 940581742, 905375778, 227015602, 441243962, 421028568, 87934933, 695746265, 124852762, 692351980, 408924842, 679093951, 606352107, 765422020, 579044413, 844690216, 913165806, 653940501, 55402321, 666337666, 401746611, 799418238, 40032139, 55138563, 557569706, 980602054, 89706977, 169375333, 276048958, 13114391, 108640527, 266087164, 847545633, 117451734, 11391210, 756116576, 399313777, 595189956, 832237743, 76220779, 69716339, 61911736, 740965143, 957590302, 896645567, 90953293, 599581075, 699778007, 6451958, 525024557, 943472695, 448431511, 947499788, 238960600, 48063582, 781102445, 598501845, 832142741, 424912835, 681603314, 111991617, 237575742, 487835635, 310487870, 235438739, 374600591, 345901369, 296547555, 170364144, 554608765, 977899923, 470270120, 544438004, 488832457, 662799491, 416700528, 642491100, 539052181, 242908843, 464007083, 928515538, 641724617, 795379603, 668076617, 777836533, 421386259, 825050543, 374130836, 640140445, 800390681, 991921698, 31997363, 926751678, 724784616, 522113326, 730057048, 358744444, 522077981, 429130500, 506514562, 940983637, 567258078, 832874740, 405565625, 853763392, 43686520, 698285129, 86089714, 630724579, 904627071, 85464978, 210943608, 41397655, 215638016, 111338655, 839696857, 26251128, 490434156, 701564918, 424964618, 57141625, 275895833, 384382577, 60395938, 371782056, 978297660, 249358903, 120235952, 154369612, 724934210, 670376369, 164022320, 285097697, 294943095, 347593798, 239068793, 221374769, 911888925, 20810260, 332106836, 640930275, 95822139, 1571993, 857472911, 505560884, 134575040, 192300340, 216800821, 916722277, 22697206, 63092652, 126932824, 272898142, 978278714, 863336602, 307257414, 644789132, 114949687, 803123112, 936806656, 622383655, 98645538, 799440340, 798235890, 878331360, 744176258, 613194875, 955177586, 571424086, 123261161, 388334883, 22161920, 830208349, 222479395, 657022868, 629997484, 650837708, 436611625, 502956115, 858342921, 767141198, 562043633, 154452049, 732399631, 886837771, 915392338, 97463820, 833755489, 815743615, 876690189, 754387721, 596934133, 237758340, 607116416, 578004649, 295812424, 387351519, 248063391, 828957947, 1550994, 776291279, 626926862, 383173201, 124062736, 381941393, 88375767, 628349375, 228404250, 810446242, 339874162, 288674757, 30274780, 573959479, 311136749, 649514199, 510522767, 116464740, 700517948, 173495814, 60711956, 73649675, 466086525, 713505871, 50245889, 761309518, 896494345, 205290016, 398301842, 541729999, 639678325, 539101654, 841894603, 789326330, 620573150, 95480033, 425444394, 464780613, 14567395, 567446450, 358955387, 754997130, 344779860, 994686926, 479105276, 781249480, 552550701, 541023558, 559550067, 186215723, 845108855, 585371176, 346453600, 622647901, 291909496, 304646781, 546342238, 403462827, 567770394, 892012882, 671807324, 610996877, 628356398, 500972723, 251721401, 757622414, 578744132, 41566093, 9568131, 18352636, 88567796, 849312380, 474459981, 855209670, 376845396, 617717670, 461377953, 898393064, 677685131, 853714850, 889087342, 691111191, 652897809, 9629863, 846284216, 250013301, 681831615, 146216915, 74441364, 44783228, 149685860, 982578065, 155567299, 190022990, 850704534, 836388533, 597196207, 756593216, 841175392, 687798653, 739389988, 734568027, 119179462, 625144506, 848311679, 407165036, 612966752, 222443754, 717903465, 858963226, 779095569, 29576749, 23450977, 396596171, 330689083, 296585309, 894198556, 268808083, 79031758, 463746971, 785735619, 453078891, 572862374, 948022947, 326894415, 504270119, 310073495, 27267677, 508616153, 187970481, 105307744, 369310499, 834261881, 569395278, 416503699, 322101103, 145496130, 33195306, 301653691, 57948658, 523720429, 874749261, 249140430, 117623766, 807109538, 427178967, 162606081, 378210922, 169888597, 939799642, 117199998, 452904852, 122981576, 73820623, 197142045, 278056391, 236750944, 190856587, 124521692, 383483540, 870736136, 265390031, 902240416, 437596301, 32132324, 852149148, 372407666, 928227112, 715295008, 55130584, 276247578, 606487756, 108154824, 994727654, 108895351, 766250899, 412822602, 76179954, 847030443, 341593517, 972216081, 625283404, 124182160, 125781969, 770409923, 883526511, 573419987, 786431992, 476181233, 242298802, 993917602, 63128982, 201099333, 972419967, 498453655, 434307071, 594093257, 325199559, 764372691, 970931812, 218432404, 455107601, 469627287, 343738169, 721363964, 274813908, 342867048, 659546741, 229858823, 630855536, 227482130, 191487859, 899395453, 46299454, 669641858, 923792841, 655108394, 664367402, 602526320, 753894114, 475465625, 298622488, 710297840, 812077387, 536543915, 503427692, 265335817, 544833914, 344781073, 335608224, 253432638, 514317276, 558200155, 290148653, 143565795, 332531400, 92969872, 299839582, 699073611, 184200003, 916822299, 383203031, 311209714, 258914924, 839187152, 711744075, 651214908, 713550902, 441877562, 420316239, 907821188, 271030378, 804524425, 128415226, 858498825, 152613717, 11512781, 939130778, 692488873, 316668234, 274751254, 521722106, 317949444, 320029798, 507956819, 977129996, 298083709, 108994110, 684317112, 380056639, 144209675, 15342600, 447044468, 765423875, 48236296, 174826807, 658821509, 764772643, 889994168, 309392498, 223069150, 287830877, 430174418, 44103118, 27519562, 984923190, 684730172, 854503209, 419778214, 624666155, 270862172, 712587673, 120689347, 452053366, 333894647, 102761822, 121739403, 70021915, 902051317, 462099698, 998048893, 125394992, 68415845, 77675755, 103172688, 335872898, 635883541, 733654249, 160769416, 344575352, 131401880, 506025979, 748148989, 339407135, 17650055, 158931775, 98483801, 230211253, 362670497, 907102110, 30027368, 422739660, 865655468, 438526248, 857875444, 917146138, 405463502, 934653188, 948280556, 906147263, 467743883, 821038711, 126953928, 711335709, 795905877, 11738083, 560510584, 77624907, 280870332, 97316667, 568125745, 291531802, 842517797, 670786251, 148039660, 662838808, 644807830, 307005460, 905002073, 102117, 979690884, 121507443, 535874430, 915927883, 783875096, 772908659, 150258119, 554097668, 771162127, 795120707, 907263678, 377352943, 512206045, 802229876, 613970044, 922132088, 959884541, 195919579, 234957261, 756346462, 86922170, 630496699, 980744464, 887628692, 135489759, 262207956, 108756335, 402008450, 491626817, 200622718, 47062561, 384948491, 583912654, 497365817, 699099633, 32596187, 26432515, 216004672, 551022481, 565280290, 579221053, 673751391, 482116187, 35082062, 704514749, 87260487, 197460734, 722916692, 61113360, 340664545, 809561966, 741967525, 314239966, 780821427, 148376317, 577942357, 223400499, 14676614, 399985208, 186444345, 833550255, 923992473, 210554629, 296822347, 223343935, 473803445, 264649424, 211651339, 330608627, 806313703, 890351729, 833091865, 792908217, 502817965, 289862184, 871358122, 185285186, 356021130, 536996290, 274244797, 387175493, 22257786, 421680652, 516474669, 945147399, 648356888, 833214657, 589949452, 100575166, 933309403, 481348456, 101423446, 80467341, 705000864, 445830455, 496810453, 442005704, 222394244, 409126554, 536927672, 444532098, 698708316, 322794606, 42789316, 933549386, 544181836, 835864049, 946031837, 707996345, 587933135, 13404017, 817236937, 454279812, 873845621, 631728400, 450812793, 243815532, 620311627, 788863482, 824227245, 501932579, 980905275, 537728820, 334102732, 295727372, 377406913, 54121080, 177432473, 779935932, 836740143, 337962597, 497632721, 929191435, 382555045, 459554767, 211282907, 811017252, 905404774, 28751095, 612862368, 702008322, 964396433, 583590436, 412777007, 793180054, 230081580, 943387628, 480598207, 623083957, 450770058, 684873961, 992130610, 441834380, 592039282, 467947766, 157846133, 462752014, 221814503, 837618991, 123993926, 82846209, 386751184, 985446222, 69681307, 142821884, 705821086, 734535115, 302716064, 918581344, 597589854, 979744541, 780801590, 151258415, 243034333, 239523754, 313413537, 535062165, 987610145, 279388201, 413402183, 105118646, 994678408, 595518022, 893264470, 7417830, 29797095, 845804301, 496751681, 572463388, 589587821, 673241557, 21681909, 527075932, 735298391, 291486978, 153414423, 955731850, 394656414, 504455013, 602586638, 637419903, 552072418, 744786479, 182079054, 516090542, 55491040, 860505264, 265298337, 910170102, 148606277, 550711, 607449069, 627439041, 711229389, 400867143, 424323405, 114257153, 72529876, 511538404, 211256457, 657732567, 485383523, 547772476, 547358131, 163132628, 205849393, 65393657, 328404506, 304144094, 823318138, 212474880, 75012680, 128569206, 60448465, 628809620, 742831879, 54377260, 229268320, 508761910, 997417432, 532507571, 546257816, 775654435, 142993702, 249584721, 949102043, 575853896, 699315409, 142763379, 798850650, 689353203, 882075789, 503968858, 92439900, 955548076, 231713117, 465665225, 466065889, 393895450, 640623601, 98743282, 269656946, 536613385, 504555471, 339593568, 386667000, 18716008, 183050910, 754388904, 403854704, 220374593, 835351990, 917362804, 93211943, 592881293, 850174752, 507600220, 118861554, 611403710, 548850607, 118153251, 687864045, 686090623, 609436203, 159582640, 43355598, 411966569, 252462984, 427929900, 661444374, 906160928, 187694341, 631642231, 248270882, 872526568, 31187265, 606118115, 665042027, 445286874, 851674831, 584286173, 863563866, 855450125, 869440466, 739538267, 928009841, 46440357, 502663000, 430070375, 192526732, 31874965, 903062980, 382954155, 99090212, 996881890, 990785198, 903604446, 698467356, 689333110, 700654846, 55985401, 938640394, 232949478, 536865646, 298638779, 365760104, 493984238, 187048744, 772564891, 221382283, 26186949, 497620193, 956684631, 847688900, 794356533, 433613864, 927520671, 529879643, 616219167, 226237514, 275097770, 444190359, 699467156, 114473728, 597862221, 365473972, 852565186, 217690366, 951917084, 334048142, 379477186, 27997477, 471780069, 298482411, 861703550, 880374312, 713684835, 260106274, 427812218, 544283034, 863526030, 143727961, 425242482, 421171099, 579058349, 491153067, 753284777, 843699358, 916524733, 221081765, 367418885, 534403386, 262407867, 543578996, 80818438, 70951183, 678909670, 468795248, 557483631, 468769780, 150177164, 677608207, 554731952, 271257442, 563831344, 112369539, 127008074, 587603809, 200603435, 701198375, 26557324, 474202748, 984144946, 255756859, 749146472, 377941006, 605371998, 593708874, 917524006, 371614878, 743622904, 511807870, 835668962, 358792619, 185324611, 581942111, 618806695, 456858673, 411154485, 701154380, 575569289, 443661543, 460171001, 87549866, 981433104, 800410752, 185573811, 813217933, 232721518, 422708343, 538107507, 217611337, 610048458, 987093930, 232072260, 82754929, 712384275, 2786805, 783219078, 698644674, 573266768, 85958837, 308946455, 548828271, 287490875, 498974622, 962049388, 12874718, 861300395, 788513573, 914025665, 84575144, 563249867, 507032375, 600255876, 376751574, 105694271, 724386688, 759500505, 278236706, 99261945, 695291043, 70200538, 436152179, 430745886, 778174756, 737530107, 246662136, 429761447, 791600337, 777754281, 468862342, 759190538, 128049729, 734583859, 971610497, 583250102, 48232392, 552219440, 839160534, 862049099, 65657432, 479461291, 767376095, 760807519, 127344486, 198325667, 630831439, 796300787, 381056694, 102915665, 362444112, 52718319, 60112500, 628290008, 387598945, 326938880, 371633937, 442672959, 14924415, 830002670, 5402449, 479001138, 126893908, 152933587, 653119137, 396189589, 32587858, 147497141, 622125894, 971081348, 160558586, 398991125, 238809427, 451575568, 975578324, 466056822, 212132492, 803331093, 172203591, 744840716, 291778247, 386046365, 236414231, 838046457, 756067586, 348862889, 108431964, 637330101, 915570232, 204930104, 483588234, 660881673, 833161033, 923167737, 823748946, 881610956, 298385138, 569150964, 284413680, 750628659, 977144252, 441828026, 734662739, 657527458, 95148126, 470385839, 965726511, 213638782, 348560487, 80161183, 281421848, 797136782, 801589810, 364802334, 867239737, 167549135, 348455648, 612588607, 602222808, 269754597, 82021429, 860912224, 540358324, 533848707, 1663625, 943789921, 994103700, 761923860, 414763804, 609404966, 445716060, 50521175, 437672112, 93080132, 756852947, 153650599, 187332027, 181371707, 822722155, 71926247, 68227547, 716404947, 561875674, 373443029, 363785794, 178282051, 597078228, 302442205, 792967657, 902922246, 815355688, 101052735, 64451464, 206271470, 467239626, 27572433, 730045697, 789132546, 158542177, 452195896, 489527629, 185785094, 560819405, 451849829, 40198825, 803879645, 93282749, 804321461, 93831396, 274517867, 705471621, 102972677, 387281324, 842262796, 178665010, 336853449, 969928579, 460034963, 263791127, 454786864, 612544492, 365176543, 469927936, 594215866, 995536217, 885063704, 211530428, 473415159, 37147314, 258307045, 661641928, 288126494, 783407021, 996852781, 911217928, 489652823, 51017878, 908904759, 51986151, 803672625, 857437564, 496137798, 30149546, 903658032, 172784717, 295499493, 915433889, 150243570, 717051074, 990201906, 9132803, 394801138, 685561079, 692166514, 952374907, 498049150, 107253974, 894845502, 397224391, 492403405, 812638217, 30786333, 802178024, 451338840, 415147449, 983324397, 385624237, 243498995, 127672590, 502375938, 664518170, 48467405, 389113596, 4474627, 157932724, 177464993, 866636716, 950245277, 263041178, 656402356, 605641331, 495544485, 116388505, 307287636, 708550557, 906548173, 411887450, 913647044, 798471602, 286061659, 976456296, 108784299, 18696377, 762880782, 462418643, 204245298, 971613961, 142291277, 906960429, 548372594, 690489728, 853749016, 242543477, 32289461, 874164142, 70452467, 604089835, 1341973, 964185035, 917166572, 550196171, 761594272, 620566452, 61035675, 260018754, 931420600, 499625628, 259790475, 9693130, 982468431, 317378819, 325141551, 777671027, 18064195, 200113735, 703945737, 448211270, 229330282, 636535269, 2492629, 95087756, 84143037, 54211884, 843512513, 755078917, 239593831, 843906871, 145422074, 26616642, 117556511, 335550359, 53340257, 188897110, 226789277, 772597829, 952914736, 553000377, 308693149, 819232713, 504158979, 672694087, 129020052, 913618956, 31087628, 12091558, 916697904, 449193493, 114122927, 209367711, 647579183, 182477319, 789253944, 927297270, 165279368, 420889228, 888790417, 21784247, 115343255, 973993941, 727060753, 850063060, 269751479, 95425835, 964065018, 523282656, 405589149, 772765391, 340302667, 890136265, 283292665, 546698202, 989559670, 737137916, 923147199, 183957401, 192978258, 189434419, 759529449, 174218234, 164810975, 606912945, 459223749, 456388180, 412049780, 789934571, 327206118, 666789787, 350906399, 631172824, 641243294, 123746251, 70932494, 841873730, 195630248, 861839883, 984103063, 685107299, 822614627, 866095524, 631094696, 961022913, 590480772, 294304843, 646241887, 116934945, 609049700, 20725361, 227602979, 805091251, 268654597, 785876780, 472409626, 536808849, 754691167, 194356215, 107171381, 2880023, 456832705, 280261077, 831019323, 997828482, 759094429, 654088655, 470097007, 841700280, 19543394, 933463141, 35492276, 772106970, 745924732, 477628475, 204059872, 709574458, 109180162, 455436527, 113527887, 589753855, 64090089, 867812833, 921233803, 863945408, 455217386, 349456195, 471700479, 210792697, 977432664, 337214254, 79218757, 446340576, 716306479, 170145914, 406086831, 829303634, 867615331, 506838418, 416230002, 611868420, 772295133, 922751639, 981419135, 44842464, 43987051, 96654235, 942411568, 329108060, 6316197, 995583793, 736108837, 452555357, 327056104, 651881158, 562595976, 86648982, 366811158, 209031286, 407124425, 122013472, 824528362, 984821247, 683693460, 73008278, 384563378, 171043810, 736283913, 292396415, 339032515, 199981852, 752300446, 4732387, 230335129, 657187462, 574812300, 310686240, 67631309, 300882348, 157014510, 548920462, 238945636, 198833601, 970375609, 64484990, 836846530, 287040875, 89122495, 639708554, 364189694, 398363045, 299520774, 648883862, 761466178, 99196379, 151178488, 767483132, 881560900, 785403252, 630620891, 354131885, 992104494, 714228281, 349166385, 868010963, 367587778, 126621826, 179132663, 468084160, 111258767, 127956917, 352284708, 296197177, 431848960, 959074166, 878132058, 103194743, 475244318, 469846826, 166468299, 816791008, 19103245, 423703346, 845831112, 876171765, 402203026, 70797383, 376209559, 554300052, 476570954, 208779860, 410781991, 959649652, 498149855, 743274323, 608556278, 67642028, 288029635, 593389850, 645467604, 139145958, 441673867, 691269098, 662155350, 207027061, 93805382, 519000743, 212417602, 528324909, 479352134, 323074134, 433029390, 81464130, 698502328, 653460537, 657964318, 788613723, 211316966, 697568450, 384932735, 513262351, 933635291, 698793933, 74109858, 351107727, 458465006, 64009026, 619700931, 638372753, 812659218, 417724236, 311272381, 356175554, 855770544, 842714713, 293945836, 404135702, 875881088, 561918389, 543056012, 552974044, 447766610, 237437930, 328714154, 325467462, 33867673, 615839298, 471891443, 989410506, 787738187, 49307100, 475915086, 703457969, 153074060, 32272054, 321941683, 997657072, 670370406, 572670962, 349024146, 414784721, 941606646, 883027884, 814560973, 326659499, 691864088, 556008031, 336978785, 962602386, 839382890, 494233291, 909769539, 351258565, 240698854, 511256941, 353898293, 163089633, 269788296, 577693874, 712027283, 706362795, 440854514, 783894872, 690477947, 18436334, 146052250, 646257436, 348097726, 983349089, 483747684, 563044737, 450755163, 855282076, 686080119, 538999184, 566069905, 730215846, 19776543, 732743795, 113950847, 709310298, 767459128, 623674767, 192803424, 311828444, 633332532, 465535625, 139734057, 783507155, 991084923, 404626513, 493811622, 50729136, 147959457, 300005264, 627509132, 991984257, 43285289, 123408021, 339002812, 6442330, 40168824, 995610208, 823156152, 137327698, 674334257, 568965138, 468993588, 679442740, 538305224, 492549043, 787182647, 319239553, 350901919, 787968536, 357226434, 331749326, 70564748, 771681235, 410663800, 896943772, 646544713, 874137591, 216188898, 343984111, 773084220, 726745540, 398067119, 199468967, 585868074, 25961489, 500695429, 989461266, 121573285, 790179037, 213010435, 521766615, 86547792, 894909729, 489385449, 170643496, 35847729, 19320805, 492855592, 743207707, 592702471, 319734901, 128221613, 525339826, 269199749, 686641834, 170585131, 53263260, 909790347, 322079170, 887766056, 566474497, 899610144, 594299463, 65488099, 253760287, 255957005, 408370103, 643606868, 184063258, 349314977, 717521204, 775544013, 691344900, 225752669, 182398353, 128411811, 164375273, 487393422, 93785379, 489806204, 89570248, 846472334, 831539871, 645020385, 53130637, 241009500, 661512133, 927025869, 14791444, 657782639, 499786962, 961947570, 905695879, 889253410, 407370681, 623844946, 890810903, 253539852, 748963926, 119034505, 864159548, 750805705, 689724202, 450116139, 818704301, 479718014, 112504023, 286253109, 123733959, 378218282, 393610880, 176410741, 70302748, 463436044, 944913479, 185758270, 373724659, 918662294, 400349959, 641567297, 959395052, 169489353, 139799116, 789276735, 521574740, 787901250, 544148090, 366881168, 924007307, 724620443, 144061441, 589906820, 467678243, 636782546, 549990135, 599887231, 300700479, 829091243, 733818773, 201401033, 7244160, 11553420, 662927308, 500263678, 905054490, 783200036, 911904073, 200784470, 950224498, 694891057, 623521635, 105475825, 967106642, 994515796, 985241658, 925519025, 798517936, 825056698, 259899342, 322489882, 511787252, 383107365, 941260153, 382972505, 962814236, 608756627, 926571706, 286495217, 876790071, 199533558, 144835798, 462661283, 156096027, 241955116, 441411820, 354235452, 753245641, 757497145, 724591365, 362072743, 446059002, 840839407, 121158062, 704842565, 895178492, 339384571, 131622645, 887036686, 663783842, 874125293, 965362061, 387827664, 812435164, 131760913, 642646565, 493401004, 612136242, 771900662, 182569964, 670445404, 149858458, 532524168, 881434921, 631164701, 728408894, 129383526, 413081944, 59372567, 102679410, 926904487, 672143526, 817721021, 361016125, 792639577, 337389253, 600717499, 189200865, 595521319, 616380678, 165360987, 198787050, 504677557, 541145199, 604760555, 516406898, 220853071, 667870934, 661335854, 118942040, 338991649, 136148740, 795010415, 151262017, 93304104, 134821879, 253653887, 256861757, 675331235, 597314108, 275989695, 329674755, 9554267, 54025976, 940680952, 34770037, 320072902, 993938943, 89527372, 234497428, 598747178, 98639246, 658373476, 353399588, 964723799, 44392584, 726330607, 804391587, 77644147, 91810584, 716265710, 208985950, 956459216, 125352141, 39565889, 570790418, 999508368, 214983911, 506148375, 1830495, 510862771, 613604370, 893443212, 379497383, 93803389, 899913808, 381283022, 709513887, 194619626, 329991324, 78526345, 950439664, 905949153, 313288224, 164241010, 463315704, 91247292, 715772595, 701723929, 546570225, 470361048, 963014288, 85419086, 354057375, 438976318, 454365080, 86857882, 730205728, 865422924, 294812948, 844451220, 154000613, 729459795, 297949160, 917459813, 131316783, 528022606, 759982883, 711532674, 400454218, 277840994, 828948352, 863507030, 233377297, 997831067, 895136436, 803073800, 535758296, 819127355, 425722882, 37825977, 456946713, 313487464, 942231049, 667335359, 823958951, 630662182, 268322708, 757236929, 334097918, 790977093, 374484815, 712338406, 443126062, 47550849, 34885942, 420771583, 389652981, 928033691, 568641930, 218793859, 769859899, 582018664, 656773374, 861095043, 494943623, 747769398, 788793474, 797221580, 740187084, 800424962, 43411955, 831068666, 987480050, 851862503, 324652663, 505481015, 501412158, 526878656, 585903468, 636585410, 869150159, 122285485, 391014296, 323462361, 648186533, 437562337, 830706630, 633730711, 487384309, 282637221, 414144823, 719628351, 423708291, 707665418, 944231503, 776275213, 5727132, 903728392, 413125398, 690182629, 803602248, 333282596, 11367105, 244462650, 764914559, 609785263, 497636887, 201501716, 165570983, 206973115, 983356136, 525217798, 340640558, 27839764, 551539338, 42859006, 128624748, 902688434, 250173152, 119745670, 562177080, 66379953, 252345987, 156984854, 765318750, 608433502, 459621515, 227103320, 876284005, 761254141, 427165774, 92636386, 913419165, 769445800, 4737033, 220368607, 165159109, 948149168, 194673369, 791747464, 595191901, 494803458, 575968485, 897326320, 485961647, 303177652, 435169151, 961105254, 473893641, 786488664, 327961475, 199911801, 70313714, 134366967, 383977927, 451794604, 317289429, 68871036, 585726630, 100701868, 441223547, 194415462, 518852541, 7732306, 292557169, 667841823, 17061579, 439986594, 716555218, 256931101, 324700067, 377523696, 865999332, 666319565, 85077601, 566605840, 436284767, 731359232, 319619808, 721694381, 315100832, 680606983, 148253136, 344015631, 255935660, 135090679, 751255722, 208813107, 447032024, 943753744, 317456000, 39261297, 121812475, 519119517, 920515611, 619900050, 881870880, 496976303, 649665773, 393296258, 347997265, 301661894, 150030699, 519011061, 885786132, 447053672, 965734572, 32590280, 632044402, 40853537, 597414551, 496382433, 861641306, 362585790, 770878143, 330910457, 608891230, 271793534, 260065285, 749820792, 947792540, 214599342, 466207845, 495644254, 48653050, 325558804, 884726568, 42048855, 14920080, 796880940, 380680947, 658726321, 563698445, 387112943, 855377395, 619788393, 71946350, 258031921, 452196951, 928121771, 622026369, 347389218, 725211679, 756516438, 482376879, 902727364, 282704559, 55306934, 517619852, 836073444, 317959502, 905928742, 291885742, 226974811, 780889766, 217520909, 135615153, 997345511, 705178997, 4240295, 62781769, 783213975, 57209856, 360543485, 292519030, 334195795, 976518151, 506598610, 849151253, 60240374, 348258984, 515371581, 800784023, 24037111, 602096834, 709240161, 307709798, 650217832, 13430132, 761548158, 717975634, 999443620, 637853664, 625095127, 454376941, 637440609, 287586763, 334647973, 980645610, 422494714, 626290215, 346481503, 643293753, 730766914, 608893154, 929852117, 660566422, 48426236, 306885361, 255310417, 920057578, 385613169, 155955548, 139247653, 980976702, 367478384, 399574776, 278967053, 466060271, 261359021, 871488412, 553405687, 871266891, 615631311, 87822237, 822101501, 792200950, 118906384, 594841654, 939431791, 65195004, 848063644, 405439026, 986006204, 637145860, 920845304, 483484701, 159691455, 894601000, 539803375, 204400391, 357818744, 61458778, 453772285, 509821462, 163741611, 204105020, 904871383, 227797265, 49068354, 239623486, 543453994, 902827596, 214368868, 534559344, 717186469, 473772708, 342743418, 105787933, 573262939, 100956792, 90594381, 639253991, 399560554, 763740700, 951852462, 606132629, 140244965, 401034041, 819290077, 747828409, 99414241, 334657969, 650313812, 901796010, 805822583, 8291026, 930173250, 86660904, 598274135, 741217387, 360511327, 163975600, 530233829, 784456925, 225893227, 871515415, 781947096, 185932030, 749559795, 639393243, 717969245, 26987564, 999368190, 140600628, 473643487, 377185764, 779976882, 686544156, 55056651, 954295305, 760289446, 30137113, 869413687, 683140231, 920314600, 639744752, 548602345, 345139341, 558838483, 382843061, 220279155, 840132385, 656809855, 998155886, 809036415, 372746251, 672315731, 238832869, 769981208, 868980441, 3964372, 876183182, 69313736, 864460811, 845777556, 95636063, 305026418, 77488030, 198976519, 591871301, 328410898, 539910226, 498800524, 977501391, 305560979, 413454649, 806793662, 308893296, 812231008, 561346538, 888596620, 674849160, 831318399, 309749266, 146842613, 85584801, 832594969, 628849979, 280354748, 412851900, 257151579, 934117154, 556655878, 458473368, 753739473, 201792188, 868048164, 43536808, 423197373, 772193444, 898126744, 726933234, 260156046, 315198333, 382717065, 633196870, 552681771, 985251576, 698468686, 393598031, 416481180, 654908337, 453975102, 264915130, 355337780, 473696724, 769999711, 246001679, 107580871, 242079551, 1272129, 834023017, 442737321, 320710013, 222639325, 178595053, 99127957, 391285722, 776940988, 940699372, 884069994, 966590688, 950421472, 155221452, 773669840, 118931447, 242691820, 248786395, 672770470, 787954565, 51077013, 802129078, 886859711, 176052542, 675793993, 119469312, 400711049, 288207980, 317733333, 689233408, 570166904, 108477116, 304851076, 667253862, 759748576, 245299192, 657291825, 805467083, 669054868, 81641053, 623612928, 847975179, 650066018, 106940312, 727793810, 533336539, 333547088, 629783912, 888343521, 507107968, 384396453, 497563114, 708338395, 262066367, 20427459, 99094704, 774796182, 205780778, 934622725, 366471655, 353625590, 883484224, 152471479, 775646384, 923614331, 459177118, 368071042, 637570408, 35672561, 51110147, 397304920, 304223916, 216289100, 56698398, 728921564, 930819362, 523406059, 928256513, 397919304, 67449908, 590513425, 499395881, 537396649, 727085587, 947712556, 55437744, 991509230, 903979098, 459484847, 919364549, 335621908, 406656205, 153844077, 282510536, 714868578, 703115129, 127160406, 501666036, 780306807, 655654022, 589076451, 167464093, 484984905, 459239244, 845012639, 10402988, 695259675, 253309331, 146643427, 236467539, 46968156, 79973324, 764826659, 509530489, 381662960, 417661553, 282384446, 191192903, 706451423, 568731543, 594003873, 128817606, 986449483, 794351301, 977764100, 274327776, 939495312, 863528059, 438154536, 156246229, 917579284, 804932037, 199616525, 737640750, 988798782, 472724472, 967867814, 116693786, 356246460, 603026390, 322089185, 359331761, 267724635, 768996912, 200668538, 563928225, 622037151, 105505973, 941365443, 912542580, 172158711, 654452275, 819436926, 385688339, 894889043, 695387219, 473488116, 979632077, 522604533, 574114548, 29787800, 938007984, 15317607, 45997433, 193034224, 581551815, 353543020, 965722020, 669216545, 607629366, 966016416, 561855598, 310376809, 475443042, 81299601, 213600371, 542790812, 476768449, 12823542, 972224798, 606350844, 231817187, 159195073, 30861869, 862775512, 119541047, 972057392, 622492715, 770295861, 809926379, 797819739, 961632593, 238954227, 659497680, 146868662, 579702500, 59154041, 173375436, 481675429, 416478138, 785029441, 33006471, 867714383, 567523569, 150595408, 879548633, 947719531, 510643047, 572327714, 775246930, 85093749, 36598201, 821658628, 159713297, 989924650, 982922473, 622454946, 644840667, 36257877, 40669088, 333995089, 699619925, 931960470, 936986607, 878916429, 463105969, 298952159, 629988994, 518990958, 370077195, 180474042, 425494600, 523369608, 34251923, 102298117, 477988840, 696955262, 559178320, 863300296, 552108156, 223890319, 203413201, 842210914, 730957504, 956664642, 893908120, 697802272, 621980562, 836446058, 559888488, 694099383, 860947541, 230241667, 338144420, 226610846, 306040113, 833870836, 138585956, 232778950, 916826726, 121536612, 333899767, 356693083, 12737312, 845385229, 488673485, 435644630, 376303353, 523247955, 922163663, 954264428, 906106591, 847821630, 765288684, 690068939, 352313403, 222701697, 988346977, 562927392, 683761500, 290525432, 645726461, 40679495, 463618594, 232044563, 562261499, 591542643, 480216817, 603505580, 840587235, 236337802, 186764883, 335536337, 113072064, 604468985, 40058034, 870663440, 81733071, 486802668, 384890701, 443764963, 677241050, 56249540, 471884446, 462646481, 620174218, 349728049, 441532578, 309070380, 58268238, 529633260, 338261973, 63565086, 154480063, 71638770, 838098231, 201042539, 585459785, 302741145, 969637667, 626242866, 691915447, 514708332, 465606153, 468561114, 740558380, 52102678, 53644179, 356462146, 58253716, 918644374, 115722343, 929154863, 656212177, 525975939, 133527040, 453656070, 84097424, 556903574, 926610626, 564499236, 715513991, 49114183, 603484514, 928122885, 210556678, 485338726, 623149659, 490713745, 86867867, 394883865, 418334673, 667101544, 41794986, 673632058, 707617170, 763347616, 793572168, 406151962, 818883741, 964923422, 537388663, 702255211, 800766116, 101278506, 989795625, 958854967, 418549854, 640375469, 104978782, 425327609, 203528494, 327022161, 527987114, 326735567, 15593794, 791227673, 241150071, 330012733, 730738620, 832854377, 830204392, 724967690, 16471897, 616011050, 687336165, 713200655, 165167995, 182133124, 176568493, 431692960, 321783101, 856003309, 943327501, 144167625, 646894869, 325142180, 741185248, 42026832, 180112960, 143296012, 17983380, 459333438, 321484168, 886740663, 661296443, 475503403, 375620223, 317388745, 984231132, 372129810, 725660832, 74883177, 514462654, 933618258, 239436472, 399926409, 659664229, 587133613, 421428672, 82123937, 405392910, 485416338, 245733506, 155749169, 518347950, 889988349, 750862373, 235658914, 487873352, 936301477, 673367039, 3744476, 312448868, 575560935, 929025991, 686529101, 764045348, 870063339, 243701947, 46149716, 770399883, 148052133, 573613111, 541756363, 188982830, 467492118, 922095873, 158994555, 148457074, 711375750, 508437527, 280039718, 618269476, 699546541, 767671431, 636885237, 874666321, 256861491, 184738688, 517813397, 770074545, 129319528, 658153434, 735208317, 848378474, 545882322, 478916031, 791056633, 264833321, 839639649, 166397837, 79154968, 874917251, 340229964, 914971082, 437734844, 70763438, 376809198, 217336168, 342635024, 600313809, 407257561, 450739080, 229851494, 394565457, 292921821, 73201143, 461468105, 20683034, 185391034, 796553397, 191691824, 889569223, 348537467, 666887274, 740984656, 496420487, 946218219, 279943961, 337847257, 642716785, 938012261, 947126638, 293472223, 6853201, 500024576, 557579617, 774194436, 341604837, 64522216, 424998991, 911056852, 835800809, 385190970, 101341835, 429501012, 714712746, 413945031, 656836328, 670421116, 855323592, 527296686, 531902983, 726583011, 752132134, 787387869, 113726720, 65773883, 239452044, 628963805, 444746046, 757326595, 655429142, 147917151, 940104273, 782292889, 792778335, 182516282, 245337938, 639088844, 511078281, 691871691, 927493999, 763299362, 511799661, 577520650, 478824143, 961247666, 108758482, 922693704, 318430650, 23774529, 14815898, 619877237, 939573988, 737027925, 490883271, 76661621, 974339810, 936844288, 149021067, 551615295, 283265813, 371474154, 580838524, 251565705, 861666706, 76276418, 595278132, 108767054, 122505759, 657374792, 502290358, 165108036, 306541638, 370991590, 844011315, 440205473, 659603378, 565477491, 866000968, 443037598, 42640126, 943213111, 343185305, 62098379, 749803486, 398964403, 563798679, 127844554, 630978417, 814142843, 116534069, 301032146, 606037151, 262053961, 312409123, 662094667, 680595509, 291230393, 411224718, 30002813, 832844214, 779951967, 86189698, 982418104, 485914651, 200879493, 380516057, 970160877, 561665144, 392718010, 433336958, 153489251, 279216939, 372050869, 854933703, 184869664, 179082821, 864187943, 167333047, 679171604, 342168795, 46305694, 133766843, 318474505, 758299548, 701064981, 15351785, 395766713, 557538075, 760540930, 91091692, 750637706, 663709669, 580128284, 920002310, 112528280, 725981303, 207624290, 17866602, 848919947, 276677938, 361948481, 96302837, 256742278, 586381567, 618390516, 890808562, 874258535, 521050272, 542692344, 161127638, 149277684, 225925476, 71592079, 86224677, 606354662, 1359784, 60931459, 467806574, 334659208, 960376185, 60032566, 390091012, 369043539, 805722202, 476628711, 941673649, 268428342, 224463005, 169907601, 656392558, 906229539, 646334981, 70270720, 328364099, 639605063, 280212543, 912467907, 324971838, 153777957, 913630477, 560870849, 240298894, 814330379, 205383282, 641760334, 363722593, 69837834, 172809878, 446316780, 772027092, 708344159, 864374269, 195774083, 14505393, 690945756, 633223151, 61096477, 881734101, 90905653, 684675302, 786390648, 907272451, 624122103, 502934019, 281543411, 240041796, 398457215, 827096929, 273615457, 408189042, 252327484, 806503217, 78483397, 466584192, 654048051, 538303266, 407582589, 352089919, 299052818, 252819414, 762216813, 68565372, 794341730, 463962909, 513562642, 560169752, 540083927, 501673845, 650225326, 317909362, 976440511, 292627398, 43854890, 417987478, 351729685, 572199574, 119384876, 303784656, 3935687, 964624063, 200254569, 391969730, 388526743, 582110362, 473479844, 132116668, 826093618, 842587090, 230752332, 540618618, 358167451, 563259802, 694737016, 648099449, 34532892, 458514169, 694532678, 65506741, 962059417, 344900593, 873023359, 89458129, 288020641, 955084221, 336229224, 594034855, 943529529, 736010414, 281170394, 649947636, 689958371, 342664110, 448302606, 638913052, 829788528, 128805900, 592264316, 708042352, 634957532, 295369056, 622167982, 215371606, 39806602, 869494830, 391114782, 455520735, 773342829, 262394886, 678038231, 661551635, 479873124, 828333087, 214582282, 189069815, 318044445, 801014194, 284082800, 232415889, 151344286, 725060191, 447922746, 622685782, 115748661, 810224392, 291122373, 647319031, 631065926, 918713579, 105117575, 542034560, 793334581, 507121527, 260043033, 884862149, 761128536, 821163402, 737154072, 644298962, 467149284, 603670043, 863443470, 223332213, 557491260, 737622069, 86666155, 820459866, 492756342, 656456410, 500238244, 75554053, 263295506, 218216621, 878217215, 257860507, 88262273, 492254399, 387675100, 891040540, 897963412, 333082867, 265836381, 194407491, 744637434, 391294459, 809353264, 762780382, 64832258, 338062011, 470040203, 4009213, 500631374, 741243312, 779509557, 492357834, 542936970, 625794478, 939845814, 143867823, 812663566, 397563416, 924826282, 620632838, 939874596, 180562159, 964747116, 488489155, 199164773, 469186575, 470353995, 441514559, 12830066, 642945923, 794258648, 217962374, 689242968, 551401957, 760249867, 152138324, 254341133, 189830026, 920524378, 407153927, 491301312, 646849770, 136923764, 33143185, 769157792, 44265676, 938589327, 805688306, 701642260, 261710881, 194176067, 285673952, 767817426, 456395010, 684454009, 355282491, 884650312, 859569066, 141914772, 946025030, 812944244, 372994397, 634983976, 780726202, 555178852, 400664130, 389485698, 5482789, 263801809, 972699879, 356000619, 899476265, 291278987, 696809429, 364651264, 855787300, 484542862, 220769114, 801751221, 511451930, 578435259, 596614547, 702613380, 985081229, 925575646, 662252739, 655036117, 778635914, 927359272, 25425434, 377830153, 352625260, 729747268, 687501785, 717980991, 874871791, 338258900, 205635790, 836777528, 975857914, 769077205, 638539459, 122739054, 874683377, 102304544, 604308856, 597344041, 84287776, 493618054, 558562767, 648026090, 561866199, 201553505, 85441767, 672423598, 90179469, 307931298, 325434873, 731484491, 459703868, 435705316, 784387915, 545384518, 776901476, 424386203, 371327346, 31288142, 25442480, 900002095, 784068122, 147622697, 21647647, 59738181, 112419068, 590967575, 888862589, 341843497, 886067466, 411962846, 215061741, 715672008, 237415990, 9746881, 289913999, 241731244, 852829064, 96528216, 603347096, 14398554, 385304577, 53467603, 30243285, 646858473, 544133241, 362197002, 331159497, 655434355, 736429192, 248767923, 697636101, 652061753, 723623541, 114422792, 354614467, 389767792, 975330147, 733094550, 892654737, 481748809, 355412917, 95602166, 74014736, 555150720, 452660572, 772002207, 63700638, 921619045, 878295211, 990918787, 238355255, 95385251, 638571946, 501951889, 750743054, 699396472, 849078591, 190353747, 77790864, 977343510, 936871772, 295038760, 746967104, 839523183, 935166161, 790536266, 189029506, 278861001, 356488416, 995875300, 870268076, 541535151, 431731831, 221984490, 746722906, 213622200, 76910324, 530209127, 418458240, 751192568, 889467789, 616108636, 95732237, 406260104, 966453697, 287936378, 482790935, 27734855, 517986404, 999283099, 669811582, 760262942, 907836269, 970556743, 312915236, 444065497, 865462304, 843423798, 89161073, 682551540, 204877621, 913124916, 588333694, 297403731, 610902349, 355793447, 182496368, 286272652, 194329039, 438892959, 348860635, 880618569, 626640320, 413513638, 751359068, 956839421, 738328573, 574271021, 266008860, 383149682, 197312503, 688149067, 290384672, 915899594, 130427330, 282742505, 886506149, 201488098, 167895609, 669746834, 897637956, 570960924, 785486924, 386775320, 128603468, 83793700, 705911929, 998276116, 128670396, 543349108, 670732386, 151829741, 43193976, 129262986, 774689216, 895587689, 711536001, 762108862, 909677500, 949522973, 702351275, 424198719, 396807064, 197710589, 513897924, 985299046, 64769814, 31974864, 947869199, 22933592, 457267985, 334976277, 652550636, 49878909, 607444129, 443815243, 864727468, 719389792, 858151049, 257895499, 27060872, 617814819, 350188941, 663640429, 588479712, 699357870, 336398142, 455129307, 510438721, 876717083, 162200637, 152705495, 184585887, 900579906, 66251441, 36504593, 815561438, 580587588, 362417268, 532994023, 676661094, 585052934, 619800981, 829126911, 553386709, 466201807, 970129910, 462548233, 283688667, 193323320, 635302287, 437753627, 918578845, 890626061, 536007441, 988831289, 891558528, 559405764, 119020836, 525450748, 933869879, 927995150, 377746070, 858628370, 613509911, 626411997, 830417021, 52130853, 590509436, 783583442, 925053370, 887542279, 449282987, 675607039, 632805285, 626138232, 169071531, 831329039, 243431695, 971049457, 677630232, 747911043, 19729834, 252608176, 311275805, 963375483, 70055219, 668376734, 738948060, 451069846, 997998233, 285308450, 12889275, 639494014, 141865579, 938034205, 980199125, 603347856, 680693939, 749524387, 508218632, 67509512, 159772484, 982086714, 619375349, 690368426, 663871475, 248260384, 233397250, 599875892, 570612429, 260512743, 295083251, 585817685, 476100019, 689149558, 289284961, 565587276, 30245563, 136223304, 737246297, 802455624, 716909424, 383473777, 895918845, 828336780, 371878223, 279109048, 652140009, 912671880, 5051642, 635291450, 434052018, 173173438, 982316298, 440193070, 648082298, 351420879, 827536354, 52031930, 375214524, 625593681, 898479373, 390713088, 680824567, 261290067, 416052793, 954841593, 402161974, 475076450, 176224775, 583037519, 266115318, 666634439, 543253264, 976032253, 462713264, 281649847, 878723115, 748469233, 87087922, 229802340, 34608902, 480220675, 778423760, 870014672, 393045653, 839268220, 399520508, 286554939, 447866797, 693279533, 514306660, 162363220, 47117927, 82037214, 990604358, 367097064, 814694672, 835465473, 268729872, 791568160, 467278201, 550083576, 896161117, 529775954, 324812669, 335944836, 819209428, 588588556, 618521210, 91213046, 705375079, 912231038, 63600173, 134773426, 190900092, 6456499, 157169722, 473593087, 709198116, 90524967, 329957185, 616594118, 176412862, 829082205, 837444426, 923503799, 723625860, 685243892, 361736373, 210828135, 556044010, 628011388, 233978752, 401551127, 767872185, 995949976, 275913848, 217045412, 678651646, 3981532, 820460570, 176941227, 318833606, 529921086, 354114745, 289971104, 530150500, 64241668, 960814808, 737582380, 853465117, 343372647, 908821099, 529345298, 748275402, 595602541, 553067027, 487109877, 124856792, 547434064, 589469647, 672060999, 875580601, 268261496, 79183330, 84720692, 894559277, 285179638, 255997848, 153887222, 811456385, 250950583, 802025285, 910450107, 430004758, 18921785, 335274002, 714587760, 408944501, 712905480, 530754968, 304590543, 78000643, 23675883, 452030185, 68958464, 368305647, 969921263, 829016341, 715133654, 965161937, 98694574, 548066475, 728055933, 731989315, 384163449, 762467737, 101393330, 575099493, 15851084, 461616413, 804681234, 732464930, 28442421, 186249276, 871690384, 814207523, 923745992, 847360143, 129658939, 463845160, 874543960, 749976844, 127868007, 851522791, 913780219, 381147861, 987785410, 779422572, 252428464, 993269925, 812398347, 416713613, 261067128, 170343153, 196496897, 50895776, 273708852, 801793864, 67611529, 655793256, 236957846, 720310989, 240747922, 816377160, 578396687, 284935700, 147770240, 188672303, 142580246, 88251136, 463124928, 461119331, 172523562, 341958548, 696532302, 763173939, 680174198, 489484590, 331712216, 683578482, 299306413, 127346185, 454246286, 478455564, 778563688, 575788118, 965676751, 428605434, 735898184, 527140236, 150735969, 27463651, 248358835, 265956286, 401173059, 358692046, 890783059, 62079301, 85430933, 558838803, 933500759, 262119687, 209960465, 576362074, 28884892, 400990375, 605527303, 506234702, 440741445, 427199949, 294196286, 965083136, 624339902, 799773018, 950865324, 200273067, 595633931, 139867547, 189526218, 950831604, 612927636, 805134066, 36992458, 530605755, 294918965, 25064318, 506803859, 572085521, 596491091, 502177337, 700816641, 50214348, 787848803, 319776054, 227291901, 985606288, 356019795, 439759316, 589481964, 816920428, 685130827, 783954805, 970525815, 309608021, 889650618, 978810192, 711538786, 931483058, 173022177, 871931055, 242475325, 447528421, 478880983, 524262079, 710926241, 875977136, 911405559, 58158751, 574842471, 324809743, 92817493, 161090728, 369332447, 845977761, 199679758, 493136090, 708634589, 714393651, 217062252, 833176992, 621598162, 621046605, 733384295, 206692695, 963211640, 421966545, 491034132, 281405120, 675954303, 423340070, 823669074, 999577725, 190205754, 885144685, 702657826, 718740728, 218632632, 557436029, 761747151, 139173298, 190075646, 578331696, 432249636, 530336374, 535106786, 281619342, 865303374, 325608237, 722448638, 391597525, 936188006, 112783927, 943731224, 510068608, 159372713, 807932804, 740410061, 257827071, 981789016, 872837518, 870741042, 496300858, 566803717, 187903123, 979822602, 339376247, 485129919, 496453792, 404790296, 339729649, 155938195, 427523850, 868383967, 53394608, 226463739, 670325014, 570492260, 545667206, 701460116, 249653900, 414346629, 420273969, 777164837, 72486724, 464218366, 170527894, 374615089, 865067246, 14708141, 541604417, 723695202, 967690519, 467073441, 295959183, 257047020, 408403574, 121005292, 11722430, 922021024, 796380815, 464870168, 617679916, 84869296, 207949205, 439526282, 44549390, 523740502, 598009206, 350964640, 690275639, 670946990, 852012342, 876711195, 804094721, 199278656, 335768657, 382247099, 878537743, 407710885, 535705823, 684049386, 817478425, 342050446, 376257211, 767988634, 429418073, 433062377, 658392712, 776493678, 989897640, 38976536, 887788662, 602910609, 546316404, 929057299, 349644634, 438187392, 25384066, 605652217, 723459198, 343327008, 821455527, 227351727, 8918525, 759406388, 530855527, 638658347, 237021560, 325040584, 314975266, 985296565, 41673603, 14321380, 369672356, 230040537, 706377916, 705636376, 518147391, 404654084, 621880137, 758319485, 114660733, 509137063, 234073312, 447644945, 780514950, 458285840, 406591426, 572136119, 192449265, 113018312, 473650396, 535531065, 938969623, 482988444, 584437318, 275936143, 577905434, 146011379, 482837470, 30393113, 95819645, 191990444, 877877479, 640585059, 493431648, 745298944, 15404396, 184800509, 494297753, 696696637, 419198308, 437238658, 438561693, 752099826, 251999983, 285389885, 830903245, 95167023, 435700747, 207892669, 701748574, 896206438, 983993604, 694154385, 768499443, 37897269, 12348313, 379657233, 947894986, 601589732, 722447049, 272506549, 383174892, 184090618, 184295368, 569779223, 270667154, 653819554, 837977810, 575211397, 561068671, 411555227, 172143860, 434118365, 333693987, 862585191, 975542568, 649295278, 397888525, 595144798, 417725402, 858527040, 157870779, 42582991, 976031725, 493536332, 471695089, 299711084, 136828510, 954661529, 223211651, 800325297, 221855684, 207382985, 944610623, 115654998, 786420523, 997419538, 867489176, 435798537, 211456841, 188223981, 666929783, 56681695, 344349997, 596562923, 273765707, 127899232, 229955300, 945318929, 691615993, 106423319, 875489218, 773194455, 341662702, 840063315, 742800414, 932954318, 611845960, 552342349, 619952123, 618209559, 915244647, 804762247, 289720860, 818569523, 164893994, 2580834, 193886937, 868479401, 868173285, 250739786, 827519380, 293036423, 112040144, 657633554, 911125499, 936136325, 341577972, 474648436, 629494607, 152759492, 737073791, 370339489, 17750565, 599611758, 764842883, 674490900, 107009347, 387855165, 632426749, 629733332, 988495776, 154392544, 284545084, 837155673, 5071993, 999320904, 972902891, 895176911, 30413211, 91281021, 278860344, 899264968, 788128652, 490812337, 655063087, 23447359, 551708783, 612226556, 489694490, 170215412, 557481040, 455064796, 787467635, 74689831, 783779371, 823398890, 718355254, 499412471, 58939436, 568604541, 345749887, 859306826, 901839612, 683904626, 99064861, 296533154, 81246277, 30946024, 800299297, 907057536, 631233749, 911020322, 124546008, 158708981, 63919872, 990193306, 898411603, 618563169, 972314541, 308647828, 855569586, 754135141, 324409434, 502215168, 799638483, 272320670, 533387092, 637103364, 719820010, 26950750, 619882604, 685582832, 368149432, 84004494, 116342909, 282619488, 651694783, 217623751, 126475475, 544419428, 161974110, 482123085, 242719944, 844235645, 618652417, 408370382, 459405138, 362485424, 837165414, 316402022, 312166462, 231958943, 699706833, 638217344, 333481695, 973172177, 83983537, 609706486, 743564236, 269603870, 346854147, 225832521, 787705712, 810940361, 368993161, 935055237, 653244182, 333822770, 590681483, 253420700, 609446654, 420820519, 406405512, 440298577, 502777867, 190238133, 619962478, 290710283, 234160674, 114277790, 206454741, 737710056, 966498373, 171901212, 180075735, 573744895, 93495885, 500822191, 933199820, 367110595, 199666747, 590601473, 993191321, 414516594, 508839014, 599255286, 620591837, 341622764, 488082133, 36900762, 991459757, 795721541, 355822293, 792607269, 780806314, 479051126, 101110971, 110671866, 294600188, 516206110, 496505464, 981876814, 789451304, 689002828, 632969598, 775036490, 324212542, 579577818, 319109299, 2182556, 191933146, 464566042, 835512509, 357084213, 450595979, 566038584, 544850951, 688782648, 831982643, 924910302, 179882912, 921527278, 411385633, 222461576, 57741363, 461065886, 836576978, 848497600, 577771024, 272229778, 18654928, 364783560, 182614593, 564602136, 533911524, 647134181, 784684764, 929714595, 800928845, 310949690, 116280549, 428710629, 571668633, 472617526, 902737026, 211522710, 987525482, 133132092, 204215307, 472290569, 229849079, 623982957, 719977208, 168287680, 852021118, 547246675, 704564432, 265035230, 43913232, 287572553, 634658850, 980291631, 640665145, 921233424, 18350031, 891609736, 780746257, 236386289, 867197947, 292843667, 153698354, 743069386, 212625398, 727871928, 283226620, 855113407, 907196575, 535539218, 978664074, 381411235, 38299917, 202306241, 541858260, 570841109, 377977074, 829999593, 367360142, 101971839, 659730412, 268444278, 126416702, 409237206, 149152406, 989393648, 124234454, 840685151, 403620137, 400498870, 671461411, 980295708, 288336605, 946846647, 949546994, 422757248, 537741789, 310772072, 681474738, 886237847, 686128223, 353840926, 522127783, 323307365, 564161355, 570296496, 214558333, 246166173, 618956923, 455946972, 380957574, 908172637, 364783194, 451545120, 624919547, 643843788, 185155356, 249616071, 634008970, 801653342, 830719864, 689246389, 374836366, 869109573, 294407124, 774583375, 616881676, 690628588, 925825189, 255336298, 214632956, 124537026, 941407833, 495846065, 340572641, 44797188, 476135772, 511723199, 88321568, 3744020, 141081836, 701485724, 508087657, 51328599, 527606294, 108303581, 646432688, 529872327, 97032787, 907934562, 302354679, 629203216, 148675346, 875329743, 989974142, 681737909, 506766179, 556826412, 514961945, 140370386, 757110169, 13462753, 945905083, 334658465, 141225362, 885684619, 496240220, 934233947, 361113178, 633100304, 762537491, 845421721, 606118371, 787073043, 406054639, 810964439, 730910575, 188213552, 367359306, 260887750, 99908368, 679312131, 706431763, 408811303, 398079878, 647610614, 392711969, 665955831, 219774562, 272908039, 658300894, 187114536, 932536085, 363904427, 983081900, 172568646, 45792108, 435146202, 489694729, 792127637, 708626560, 883526780, 42428379, 746311474, 804061240, 274496315, 325973483, 583998717, 654896394, 804363845, 22291739, 39337047, 2107467, 161745704, 641590509, 954097243, 547741453, 903339081, 486314280, 224910014, 896363402, 297103232, 439430040, 68726540, 995834002, 954530972, 963514877, 683317288, 166591072, 448396849, 714281120, 581600092, 580876433, 439178817, 968536853, 514276226, 861086561, 779070026, 53001936, 531615061, 365765521, 125067923, 412341575, 381258067, 50537169, 336248079, 508907419, 21088390, 244380403, 292121878, 747557253, 73942123, 954026097, 824330205, 589153358, 277532141, 485252549, 131760269, 870452587, 84157081, 364082777, 756455335, 829233969, 58003694, 536333357, 913119996, 715689059, 385299691, 867388083, 678238898, 483573067, 960167258, 671333578, 36010284, 165009246, 471356051, 105364044, 888007734, 98505330, 227350598, 42386119, 121404061, 772789942, 750448416, 365828676, 865102638, 519189661, 937033850, 452753604, 660656149, 372255082, 225463848, 169026855, 43774834, 483203722, 798030244, 282071687, 868209981, 966653568, 343479275, 579878450, 394530494, 534049474, 247433306, 714483163, 221798915, 356124767, 776163319, 970577966, 326753647, 485359016, 519528439, 20209643, 187778268, 866397837, 211214405, 762936034, 587448681, 992093778, 793844481, 539376166, 268897397, 214126780, 305441250, 75668667, 58482824, 742292470, 282186801, 700937039, 264489154, 582947284, 80838762, 379878069, 83964482, 710032802, 153993613, 196233871, 808295654, 501014310, 731059779, 68757176, 140415635, 51610150, 119351162, 908392649, 354518119, 442080663, 198025159, 122424262, 110166583, 169061447, 707374482, 941210189, 44780290, 195481907, 597025936, 751882447, 957978214, 200787933, 841564008, 421780896, 25740690, 386404245, 547440751, 320078411, 701860506, 822861958, 124304338, 691908401, 499446533, 220096730, 666936427, 599331875, 722291946, 745374295, 864384824, 393635309, 450107019, 453278075, 63926956, 19130856, 465645981, 25961407, 733124794, 375503853, 208646809, 953455471, 563299726, 350587582, 424805634, 655918770, 321702027, 293058634, 989697142, 870127475, 528038787, 115450150, 777535543, 931254527, 760519424, 74027740, 13635784, 58218582, 996527107, 908823656, 452594815, 451768888, 97559108, 864356103, 622052636, 195570832, 140720929, 455761753, 17113427, 452472358, 179478961, 435824012, 950398558, 668325941, 272032021, 615686602, 808311434, 715651067, 174377813, 60365394, 377742351, 875549856, 612312622, 28130378, 138243383, 451453114, 267356858, 503668237, 991653297, 873037039, 625904217, 517169424, 154736882, 900639605, 668719448, 143516245, 108785212, 39631023, 812009542, 836992355, 28298176, 383405029, 912458920, 393770320, 642851902, 395069152, 290303980, 637418112, 527285856, 659024956, 738182137, 458005193, 940577301, 67091450, 885401890, 653803785, 380137078, 881837920, 500492343, 780204642, 659859031, 474303266, 761421389, 349747443, 503157161, 761249009, 944827112, 509423709, 873298442, 821717920, 267319364, 328944004, 689290205, 589044084, 892553425, 911561884, 860840314, 853993219, 396408205, 398079164, 696689918, 585979524, 846013177, 318295354, 516123355, 700100848, 373546495, 462945963, 655030919, 70981359, 259462542, 670236809, 93613390, 456192738, 948903343, 718356070, 196993427, 359528558, 268991923, 300600500, 788994995, 943206968, 545087299, 465284809, 321309617, 99268435, 586865063, 48055334, 150036204, 931696339, 423343261, 484426917, 427412908, 434234198, 272743304, 259899330, 296761060, 373984516, 996342712, 332197557, 386036185, 702394889, 390460731, 779584686, 485768416, 256260492, 811128850, 60849049, 499449998, 172955466, 503926220, 904744626, 365482311, 608782289, 425574202, 963533197, 37485566, 987145743, 847946723, 990918778, 154260906, 47273787, 207378175, 668920406, 148100057, 147185149, 834086274, 478391782, 638921439, 788803371, 76266921, 631700596, 760704667, 181381517, 738067681, 45181563, 455965557, 353704446, 222316617, 857055610, 820088703, 945213191, 506238651, 768167304, 915006478, 288916475, 91416901, 446471532, 516297678, 290094890, 742052261, 350529811, 707277277, 319247473, 72571808, 500799323, 758631940, 863369924, 11266170, 807800476, 339631343, 526222586, 148553315, 556966035, 399652962, 342890555, 449509988, 86445637, 563654756, 576127354, 404725597, 469610944, 608068965, 540545348, 367236443, 714114241, 379592937, 290259177, 619881886, 216835874, 86905138, 332253769, 36659528, 367043756, 87959195, 648469392, 48965734, 231864605, 438873743, 598607244, 537628130, 134020880, 971645059, 674478177, 462502001, 837449651, 815274607, 41865964, 332654136, 290508408, 813908616, 279727898, 581941718, 7823284, 967859940, 918174821, 561745017, 910497992, 433266171, 766898853, 844888701, 83472065, 880065196, 898557867, 113082233, 937090092, 91885958, 565643610, 998501781, 913245937, 421758233, 972634121, 206662083, 464513648, 815910642, 653545774, 666334321, 495593213, 100242510, 469267380, 267352473, 586995995, 744093191, 152263722, 250031731, 11153, 110128285, 190952838, 427862391, 428368479, 633893845, 382940783, 771869067, 484293273, 689744126, 121706499, 942489305, 70080257, 796998161, 377066978, 212420199, 660228575, 952170753, 132840969, 508855167, 936249382, 146662761, 957462551, 7942588, 579987484, 596083794, 579534845, 495065006, 460028333, 939129179, 909457599, 851477029, 992068700, 124001483, 21940703, 91592655, 517048540, 343760285, 688284609, 841928403, 385662358, 242570178, 542523297, 194863701, 780079054, 371874400, 286331196, 462149519, 136886264, 154938333, 836711125, 496734396, 208744931, 709490181, 426484854, 725269618, 665876718, 911892820, 455400199, 707619974, 355850883, 379749823, 481626061, 454864272, 76498440, 692925876, 593123857, 678242983, 386781633, 909695067, 870568688, 330492999, 191771292, 762942868, 932625871, 878593090, 9653263, 466099419, 374103418, 999467176, 504109765, 614069052, 904882529, 566046275, 452574155, 679542237, 487487686, 670969655, 990914847, 728486219, 404331556, 86944462, 944837518, 267923648, 401634565, 736736972, 433931499, 823447648, 108038892, 380154280, 561081242, 971585640, 501152218, 829610234, 491687523, 802620296, 499958895, 480126804, 336765539, 522809545, 996276021, 833178374, 721786968, 294778131, 992325829, 935451973, 153819989, 509689040, 201728679, 443559669, 422432551, 113388213, 724375477, 377149605, 973345778, 605813569, 826504658, 954802549, 819710027, 453858863, 277235560, 154370465, 924770907, 744185799, 541099146, 124914929, 894442597, 305598208, 470569789, 247198711, 413243567, 197849708, 146596556, 179360005, 413481102, 103783442, 681300303, 104153603, 340618522, 79917284, 641330658, 690751491, 938832103, 129331137, 591882417, 850285938, 745428229, 890461572, 705132936, 158164802, 103883536, 505897949, 871971717, 745965781, 412841821, 547559505, 212064718, 802232916, 833196985, 75552472, 916269495, 708257845, 490088334, 770725418, 706166973, 648236087, 603239738, 12194743, 382975162, 899620807, 172251639, 570201933, 348517684, 121204380, 24012630, 741170901, 889989534, 350154860, 545728669, 845256522, 818688449, 658647351, 128728758, 164582188, 288876014, 690828200, 958678752, 698130303, 329564441, 810062630, 736221328, 667114760, 975381913, 699008486, 59729452, 330893226, 129580215, 821558765, 435274725, 602228634, 690674252, 17913203, 184076174, 856928278, 67714707, 423951463, 148706337, 169227737, 469223228, 75702307, 560699038, 982201991, 2724609, 968528661, 398749272, 715386253, 703631548, 698483014, 13794642, 873732846, 587626512, 882803420, 995026339, 353724121, 229256288, 649600541, 37713757, 125884066, 817447936, 860383675, 702204914, 115990556, 877048836, 9469403, 754101141, 483202752, 811339125, 623393545, 698042480, 754379407, 117014550, 338934313, 448269748, 497366479, 291958148, 495552981, 220662864, 898126305, 551889487, 789043568, 592550649, 614888080, 204912579, 18823413, 506581027, 992457717, 532356157, 526192364, 457426084, 952245470, 800143002, 880931867, 485725043, 558207744, 853969417, 553850779, 565962734, 390378126, 794408768, 206194146, 409862992, 161288802, 154263751, 893075618, 882089811, 115993229, 473554195, 192267861, 452434112, 684499669, 191363005, 774686205, 864800042, 451946743, 414905812, 168294710, 209141588, 201346786, 134415318, 865296860, 296296975, 579886144, 338808739, 173038872, 761503897, 317220000, 793753109, 254538440, 491778754, 326426628, 361531183, 406042356, 152456492, 162966165, 743773483, 621828533, 582558237, 248406323, 870627766, 244095092, 200430156, 315958736, 49434710, 148675974, 412757324, 242772589, 650344744, 383622962, 45783127, 283238947, 743069908, 780339278, 683000764, 830043676, 146065876, 313995874, 870355060, 231760361, 242154300, 499165134, 166456310, 159468393, 589279058, 739791188, 791834272, 447669581, 386960086, 716926584, 541821101, 402397730, 818959761, 962295099, 336957677, 727946112, 811445997, 539506049, 751798355, 666598596, 13728323, 132203814, 267934301, 828927374, 820002843, 132924014, 279110496, 645674142, 477331249, 838335709, 397603766, 745127974, 575448696, 953120399, 977828993, 409468637, 45967043, 345612390, 335216186, 888819848, 781434339, 343297806, 237092541, 453053428, 761359435, 668514283, 922656840, 516723031, 455413707, 787884465, 273527773, 767104882, 961981153, 959445639, 869464333, 71712473, 693619437, 693736726, 381270513, 716849996, 340587831, 62250695, 448863840, 120455186, 268275347, 837349633, 933168505, 146113520, 414302408, 524609585, 432115386, 766891389, 306608621, 827672473, 522842106, 183309760, 462721105, 446976280, 365869505, 648679337, 279653976, 326122224, 704060859, 839739783, 542729854, 622583293, 68163845, 393085175, 389591174, 635494202, 982547984, 378419039, 379196511, 308259705, 149627196, 844175542, 239685054, 823469706, 507695572, 377613488, 747201789, 766521594, 717463642, 824783807, 928956986, 789898655, 510104437, 288086429, 791700040, 510015724, 183788841, 77904465, 542664714, 690293333, 558158061, 872550315, 6383112, 984059246, 102613720, 649460857, 985643582, 988058928, 639269139, 240527813, 873596162, 14270732, 672926056, 582703801, 93842119, 966552892, 113754297, 407310234, 368501132, 363680523, 253798913, 461683712, 516887665, 197066964, 340998035, 218315513, 351306041, 982987128, 673859963, 517798841, 8669033, 191152548, 348996550, 763779851, 152255958, 4059484, 180639182, 335283738, 881632018, 721652402, 738904745, 13080287, 716907019, 895492110, 6315309, 230797123, 539132227, 398552015, 397390876, 259479816, 987039094, 79738884, 534117418, 878709631, 315114374, 284640757, 957702221, 253050611, 654167521, 933897808, 394581108, 713511225, 386021492, 602326888, 702904311, 916420950, 255751304, 582741680, 299840342, 214757414, 573646520, 276399639, 286362337, 591761009, 750609878, 462112925, 50133047, 681606777, 631615622, 784430185, 115538036, 779344669, 780110126, 375145594, 871447420, 30539700, 229960667, 976164059, 764909721, 204037110, 783957693, 909156512, 940104262, 291227645, 27925299, 686368903, 666266490, 409136480, 916337948, 537682872, 959297147, 209197097, 781570802, 475116991, 284175255, 593264705, 8417522, 664730397, 734919686, 138413602, 12270399, 432604276, 327366498, 925806274, 528776701, 811367490, 605385445, 541403778, 319964492, 40942881, 200431238, 995594810, 787999619, 177417974, 677265453, 263678381, 925897164, 940983468, 500106795, 708727897, 450484839, 722296080, 604805362, 327430574, 924750223, 718461006, 311986426, 613552907, 691304181, 399968475, 676136362, 266762616, 827223343, 524488777, 682635285, 364520553, 247494821, 838355705, 896383079, 27913746, 187333965, 379791099, 120945202, 996021486, 544054792, 181600708, 546110868, 744957167, 466234898, 641348425, 650317351, 848651459, 239000600, 498381679, 812190994, 517614815, 312411447, 432484553, 473295921, 207660605, 48196060, 59833697, 27908828, 418362272, 921138195, 127376516, 633701808, 716429344, 585234350, 79992884, 442187376, 5421384, 434588534, 395598229, 669190019, 515396478, 684602891, 781754032, 237046300, 869589607, 960628063, 120424909, 43318443, 923841513, 319283592, 771878669, 534588938, 428047607, 741484767, 910437705, 158127516, 788877572, 276410035, 270943577, 605342770, 650479751, 109471922, 679107142, 195290301, 130821246, 881872837, 613240767, 152136492, 514802202, 137339972, 906709429, 76410957, 168526, 455516635, 794269163, 83455763, 586268303, 414485773, 432402998, 827757391, 449307787, 217708317, 337675430, 138345105, 349920423, 406747539, 897789203, 226029221, 827999752, 864775550, 833366000, 557295192, 292392602, 57608010, 153522353, 326192159, 241951800, 664557479, 490090455, 603805343, 348562387, 495188263, 496261283, 128090598, 645058163, 123909450, 73296963, 534191465, 177643359, 220194860, 845176293, 790983288, 366121649, 17335067, 822590193, 951031239, 417683735, 177355684, 907833852, 422045125, 120230845, 231559907, 122980594, 57938289, 922726254, 776174059, 189253086, 320408371, 261033072, 99687162, 419838243, 102626573, 200054346, 631028129, 853887839, 679009060, 321206799, 708734300, 144190542, 893689633, 379544685, 363109245, 241378081, 740039738, 929856872, 229686536, 477581422, 654864346, 474785436, 827660952, 509068545, 295269690, 951551447, 981446914, 686105461, 237163676, 159997381, 677637676, 135323603, 68766022, 558306891, 433961828, 370991013, 31528625, 935407620, 804911255, 287217179, 338448439, 892614852, 307364310, 503458154, 61011331, 762592491, 59552215, 850395787, 153253118, 575270796, 238486897, 367722612, 522266138, 507425964, 959480114, 641439382, 394783687, 978019914, 644867269, 801579639, 700723750, 103042244, 101361338, 517678263, 521813144, 696084485, 941933556, 833765011, 972408556, 99806880, 859897950, 738532286, 707586008, 197242096, 427096653, 483402828, 136053581, 581817418, 121920079, 147850304, 696818543, 636499283, 806228352, 950733810, 606412478, 190478187, 822898970, 56843381, 623558662, 791466368, 244932110, 787875732, 394279032, 472949015, 90558355, 164288909, 337534714, 329526757, 725253998, 794318226, 418093424, 583249440, 415211424, 923294013, 217994771, 799611946, 935801687, 549927280, 817019084, 664125294, 556125462, 488260530, 723045782, 417978419, 62933416, 517725233, 136071639, 50912642, 899813488, 277643437, 612758308, 391976800, 659105010, 285123462, 548391552, 700030825, 976094673, 966384944, 464656716, 151871762, 37094761, 460813530, 944537335, 451876658, 518396734, 224719037, 426411557, 123915442, 327621681, 707113519, 771031288, 27393800, 470524680, 668778083, 655461203, 470715801, 992193644, 186644974, 172132452, 722924438, 70043286, 66706750, 584739813, 54104091, 130173859, 343109397, 490846227, 57908964, 856084525, 970226844, 824359108, 973342568, 667645118, 958010249, 116383757, 651061606, 220200311, 633337876, 961418, 560455304, 657121774, 12402945, 414233562, 127079761, 46320586, 262533732, 560561658, 850839618, 855835448, 770202735, 102952171, 838629375, 336687854, 625459139, 339985846, 920569099, 994043313, 586281226, 57162969, 299775573, 54247414, 456217868, 480512009, 589427878, 806494631, 782986063, 660883619, 502320205, 600054744, 793107197, 984095367, 463038851, 32293738, 523459407, 624767950, 968086608, 391029024, 723503053, 266992763, 99754029, 765620390, 822909347, 906950845, 23155549, 65952427, 752338006, 61680591, 232941952, 726349655, 668231440, 991595750, 63437411, 186906923, 315033927, 153969652, 924332694, 524420734, 130738105, 994094876, 955262908, 517782667, 657122441, 320270478, 43972352, 561886671, 961403513, 977007523, 60467640, 192725497, 583129215, 644342838, 478151254, 791424648, 119325452, 977408696, 118389541, 999656200, 281636910, 593792526, 143204401, 740047217, 824089947, 71162730, 650457494, 537042431, 844476142, 215382336, 880617131, 767475365, 126250075, 472306731, 833009941, 641085774, 848704434, 150823637, 741370626, 898810209, 861865700, 841307006, 96037424, 707065650, 959914958, 896947050, 698051761, 469970600, 833108645, 928744615, 655812340, 870469224, 440310085, 952587150, 635739163, 595730288, 915478160, 995232569, 467652172, 240065826, 403623050, 569570644, 983117052, 247258879, 133812056, 864436656, 92179324, 523989778, 930090368, 482716219, 96329075, 813486660, 929333005, 899794518, 674353801, 840219954, 296281529, 93548949, 481928535, 432344974, 631239345, 349695977, 88341800, 946453682, 283357481, 875403518, 974809, 220527751, 863538609, 597890034, 180430265, 304999933, 221475387, 482506992, 886016216, 779230574, 235643811, 403841679, 289843779, 104441648, 101851623, 680746230, 538516641, 757939756, 160088695, 749508069, 16234207, 84731774, 486874225, 765487846, 639447578, 350752124, 769204284, 1635383, 421632659, 332350377, 871007879, 638932112, 583415356, 535811703, 272338948, 387586045, 78693690, 896228194, 615041111, 42097876, 113282137, 928930365, 176766198, 727796964, 888786724, 686105862, 301973878, 558387818, 904722274, 471032791, 307164329, 479964126, 844449107, 680186138, 581660667, 383758639, 635983302, 723355267, 665619393, 756625722, 58256211, 495856611, 301792020, 83944703, 134132850, 849718118, 130989568, 919291980, 291314354, 399537582, 872942299, 241522552, 765266679, 778489625, 966232604, 287628208, 86353495, 918399362, 522682184, 95416834, 60338491, 114633698, 608635945, 267034084, 905728425, 446255917, 161553393, 63173537, 575852475, 375830173, 480053566, 517095035, 90020855, 851046837, 242648259, 202684195, 134979206, 875598803, 976262908, 988428992, 560348129, 140396895, 455692505, 982567711, 518244456, 474334049, 468232097, 269187945, 566864531, 8468062, 6394145, 302310214, 211448131, 305781591, 413712005, 629241207, 261119487, 28829089, 875010301, 524803161, 580372691, 61729141, 53067615, 99868768, 293579407, 31791401, 111601246, 231086808, 305783987, 371765661, 979851030, 545598163, 644239565, 316617805, 602974321, 347442496, 620084798, 838277488, 62743509, 494386334, 383632740, 346519392, 958287202, 777907391, 949247961, 852872826, 491286878, 162920404, 454836992, 433827208, 814560440, 265394326, 248091504, 618689854, 129230132, 630475393, 494039950, 135346561, 89805417, 312386334, 254848179, 14894512, 187354450, 415232632, 56006560, 667179989, 292354244, 932418115, 374758742, 13903924, 502944877, 689426814, 290641778, 934770985, 209275366, 783552260, 189987715, 39699815, 970645055, 186728623, 724422085, 272029356, 197889677, 145596160, 593513376, 312474846, 846133741, 212751315, 143244158, 549941342, 916187119, 286142242, 132436109, 185368535, 307164701, 278333973, 69360398, 494923316, 192121575, 887425829, 455434029, 551520524, 931520372, 762722942, 434641474, 691846587, 335971299, 450630936, 512224930, 555062209, 908536874, 210795477, 390418938, 272362069, 203196360, 934600649, 208709892, 722616825, 766509753, 854484229, 862059956, 343223474, 578070511, 412802121, 363894881, 496238877, 189979161, 482530793, 785479632, 653471959, 584014693, 348027879, 420804891, 438770726, 426721399, 804527894, 486018254, 503479598, 922238314, 459288472, 92164625, 970985633, 466454289, 706541225, 160351289, 386516460, 322710343, 882414767, 615734146, 347530363, 62401614, 247216475, 904904478, 778705661, 120854555, 805410184, 283716702, 279494851, 793029133, 704379125, 231875891, 513582210, 988818109, 42646964, 669347423, 373190213, 115819910, 908996499, 196907340, 560872563, 445290542, 863797763, 493253029, 710466474, 515545883, 116922579, 718927082, 520032416, 583124878, 296780927, 822474335, 868094655, 832711306, 967382570, 56225180, 241641552, 771529859, 343601223, 649591839, 657724456, 752558413, 960194731, 212162006, 11086433, 710942674, 176330583, 604161164, 517467236, 62572089, 610692971, 831377003, 795980680, 295194098, 997081520, 956187001, 592831106, 517234630, 967804351, 779010379, 193925979, 258877875, 294712622, 527665398, 12337131, 629935377, 652390343, 928015733, 952506395, 828955756, 632470525, 657001679, 602116906, 929040718, 115087064, 773951283, 627631871, 746806640, 766837604, 629271262, 366790883, 653147133, 619147864, 349836074, 313187484, 795240016, 415470051, 341998331, 451813058, 941317089, 885505646, 945321125, 213961808, 173801211, 195352422, 683660615, 452050038, 506354949, 159727440, 656314872, 858683287, 964314792, 186543674, 321939266, 121423394, 849635657, 292058919, 840426749, 123461351, 785089074, 422576416, 164673309, 944913582, 225891260, 505862777, 762941234, 170305254, 951873847, 605734274, 236380618, 652899999, 108525465, 294674327, 460607415, 424280218, 641481544, 372968680, 386071694, 253610464, 798148429, 458992587, 983107562, 750234791, 177044547, 497889029, 201473749, 373727519, 836907914, 669989253, 970200815, 333931870, 548634797, 938528597, 898368170, 818405061, 965877369, 201937459, 792467262, 90105878, 546130687, 147082783, 71689351, 815280445, 947810089, 365944688, 517754089, 540487058, 996429565, 336328265, 4279367, 20595454, 228614822, 11620632, 442479024, 615654743, 85520668, 315089519, 145721074, 756758265, 528140140, 561800605, 187227799, 130124682, 386523545, 580889990, 197033853, 340575298, 549056164, 472634157, 31994297, 83609050, 283677772, 337527211, 937817717, 408434558, 539558439, 534484642, 89697242, 294447626, 549830236, 229738105, 277944556, 322388042, 609233315, 521265361, 409517731, 686593130, 269472125, 786533699, 406240116, 421720679, 337370486, 718564906, 506732004, 509814802, 77528981, 756112632, 901799108, 251370348, 613011132, 1533290, 823264720, 669546072, 561410631, 964928273, 114866610, 148673966, 517324244, 614013057, 146127022, 72150145, 937341683, 842778993, 595629884, 271926740, 745351571, 300916282, 197021984, 811352317, 267223755, 906263755, 673879445, 865907213, 57163750, 136547781, 772596413, 689814585, 611085397, 812727833, 143383814, 627611636, 265414200, 995940866, 301640900, 758651528, 84553643, 141798616, 70173673, 638935456, 802136889, 766272567, 786133214, 234506545, 472478113, 769904445, 824702635, 156844601, 947112784, 734020070, 518863403, 528967991, 877680080, 989802319, 993129370, 786128257, 371406094, 780948479, 935798652, 587519252, 805974960, 318683708, 998795986, 321716761, 980147317, 481406499, 485300820, 113113437, 350285413, 433824563, 714861899, 917671271, 770604630, 533350123, 530740401, 704612081, 225103590, 385156353, 787399617, 671906301, 959402965, 94630415, 940887712, 585572459, 966393811, 938429485, 227371661, 162794696, 4581021, 779493031, 356226531, 15097445, 866645350, 423845767, 934731703, 523589449, 533251972, 54110914, 519521425, 594388205, 407574971, 824597520, 833403702, 941686285, 35416773, 489744233, 975022251, 689653537, 865740552, 59505371, 684536497, 477178860, 389756938, 364371469, 552895415, 554468484, 48867960, 564649059, 623183027, 397565875, 434381657, 414455405, 982300248, 295347423, 248418845, 441682369, 506835718, 32245833, 151127073, 497295698, 355276352, 750000575, 518551835, 98401413, 699250636, 238580342, 539405631, 29722630, 739250072, 965273315, 52631324, 265087949, 279378543, 773796911, 431293528, 820929858, 792383838, 846307513, 320232613, 796824005, 592720426, 870345448, 173270341, 653604667, 856631119, 954155169, 394251484, 640731451, 319729587, 675327626, 350493252, 771829860, 250958719, 478420121, 832272668, 146852764, 407671414, 938797049, 848955390, 300763014, 219461449, 413524086, 670532453, 296964827, 246474964, 131004637, 103230508, 331193715, 293815069, 625062994, 917346169, 909380673, 795745425, 696233426, 929103970, 571950526, 477754895, 237732697, 716052788, 261858590, 966719082, 535605819, 251511137, 386763080, 545399661, 334299544, 964664337, 776539428, 724107575, 319427252, 890103224, 836158258, 399551825, 531194488, 385715230, 690991597, 45749978, 213703189, 245857709, 771876344, 653956789, 254732547, 40550219, 803947578, 700107366, 402698682, 589459652, 467447589, 944607682, 600366200, 97073290, 47486680, 162736740, 496123349, 920855891, 609380675, 242754473, 660098331, 936168145, 741905131, 464699305, 451918993, 301928103, 907709350, 706504467, 309452398, 778988634, 51715737, 468182841, 301044830, 31824152, 312750862, 604225343, 679052600, 955080684, 367499327, 846007753, 375619467, 488739129, 58421502, 285771206, 996505682, 137513535, 267638560, 968136878, 26364637, 124729440, 125937566, 766809417, 616466980, 328900534, 105787014, 994359061, 835088122, 379934816, 432497060, 878856740, 74765893, 676835310, 723331281, 763820720, 352485237, 679778463, 953035903, 738011990, 803672233, 802791451, 7873139, 397490105, 473996106, 954187249, 742532623, 466169122, 93896396, 515394048, 555052180, 441472894, 859853017, 496759089, 980038069, 863111282, 542119355, 472162202, 949630998, 398762776, 721824106, 26225345, 449331071, 307973019, 210881958, 365057165, 751119693, 640205675, 434517355, 868194771, 344701251, 23582239, 336077529, 802116200, 630453960, 465543579, 523547605, 374683212, 93548028, 402180941, 548348840, 328334544, 371017161, 441266105, 946866763, 301379717, 591360727, 997157221, 81135280, 208686697, 22027904, 229455372, 648432372, 319241519, 397663434, 422294579, 705406077, 148275159, 14063770, 885389552, 76025027, 821680411, 554833071, 333667669, 402340413, 891925756, 956110637, 87855126, 769187164, 154190905, 366584511, 358937279, 951862484, 339907767, 744302742, 764535540, 588035567, 498800364, 432503675, 368383501, 410642495, 896006486, 535353050, 376464779, 675896530, 829027191, 580153959, 708101564, 833128796, 926761723, 28891550, 38528110, 193552648, 411526491, 734326396, 356515541, 452563365, 541250929, 442751075, 440729291, 877380376, 577510107, 227830596, 224778402, 688608141, 937320049, 771790704, 475240267, 882638527, 425381656, 425511673, 639007844, 701175769, 98489894, 27351416, 100318291, 751847812, 498793170, 99389115, 329514932, 427400955, 724025882, 900570595, 368041047, 566169721, 506474699, 520886218, 554125202, 690439391, 991720736, 24511970, 557191887, 954243481, 382668703, 793266891, 189667065, 927023165, 797962990, 140814859, 538141711, 608305892, 300394857, 543380135, 14295727, 589990516, 759878628, 945880572, 973620552, 211589347, 675264266, 947023027, 661319328, 912695114, 261249434, 784993590, 63633715, 880259108, 974871507, 258966483, 579340999, 339445094, 562934265, 451902518, 946272880, 804870390, 480835170, 823176182, 178600516, 688435756, 406737385, 834104337, 591848310, 798710456, 928828496, 482194444, 244196633, 995473136, 37193003, 676190687, 942119741, 249435829, 238532004, 289783302, 786549283, 2257120, 678699105, 536576769, 763277983, 934679703, 695509039, 240740964, 240720672, 580797714, 203278761, 345566206, 660013302, 56809904, 198161129, 213386370, 789119928, 311808015, 595717406, 579297337, 60016309, 976591037, 60158170, 902064, 15880382, 761109210, 348036779, 14109877, 694243125, 588197985, 313657861, 648467753, 897503769, 700954394, 940277821, 257078044, 55415190, 733999783, 166464797, 78246114, 171898583, 454135721, 191108574, 34083353, 875641231, 168470204, 870091976, 684288028, 9456707, 153275183, 522721516, 746176481, 887924270, 330573404, 841768245, 834558642, 905950682, 840129182, 745968643, 580177587, 523910513, 19419138, 570501719, 619651713, 16092292, 258889740, 796361241, 760019579, 670197562, 630897333, 417951006, 283272279, 813793785, 614221162, 911976659, 593590255, 232594796, 478499296, 650916385, 658587792, 974173756, 147906101, 212154556, 222264042, 533175098, 920832941, 822451121, 414902705, 696318086, 952581337, 901909113, 92567403, 362099716, 667143867, 328610514, 961147863, 840029465, 461828563, 224186253, 740780341, 749106052, 92644846, 15302730, 499026158, 343549314, 221206098, 932999437, 862480670, 471381897, 678230840, 603163946, 514467929, 713321464, 334024143, 929411493, 167983393, 783190198, 675248849, 512505442, 890315863, 475051367, 421144895, 312515764, 754602120, 378953077, 133283645, 937612192, 688365286, 55865648, 980925067, 874564958, 357791832, 480976495, 96218846, 446561309, 316481415, 853054770, 142216783, 301792445, 375207329, 184060219, 209032368, 243627062, 648628051, 687237896, 855139904, 146218942, 908126067, 622840978, 751707552, 68304508, 146560599, 80732484, 10194546, 908679904, 862533742, 966743373, 763683391, 129584920, 516088378, 510798804, 843395876, 877863332, 517849916, 222690449, 795604780, 575300245, 388131776, 589296587, 23894419, 964333388, 390795194, 890635183, 794853936, 131597636, 415257016, 14544034, 914242708, 139347370, 382340784, 590659318, 55297208, 885091097, 671886962, 36274694, 559884782, 744683000, 134659564, 30193291, 518284604, 750070866, 640649656, 682208107, 374123324, 471980309, 13053336, 377917517, 521793540, 228116600, 255438699, 579747832, 904461881, 979731338, 739209518, 645943167, 758229396, 172425010, 520144309, 101274084, 507336306, 810645837, 225921400, 237451256, 908617177, 564292997, 228626146, 826344301, 378850609, 449772558, 508028847, 166300590, 728892653, 757570705, 921705664, 107127238, 470368893, 218418837, 326148972, 508085037, 973819971, 327615747, 792895490, 737968165, 976853859, 68854484, 663473516, 439635334, 489163943, 269554601, 435590125, 954381465, 448635301, 530394500, 887390453, 128281846, 51786737, 942594199, 717948617, 121694064, 494373398, 969644116, 769135689, 917975986, 9518210, 64294325, 319024771, 86939313, 555389311, 152514134, 819841364, 116629348, 302831024, 606267080, 466881798, 302374009, 430606363, 915796563, 823236243, 280980174, 175499763, 465352408, 314946626, 172469926, 111262165, 443256385, 877535834, 888468636, 44480204, 808523249, 933005397, 509181982, 771240328, 124324572, 691039257, 14376615, 967744272, 414683557, 526568589, 119615836, 898471937, 821896923, 817768783, 500940006, 667351995, 746417953, 205342063, 73791091, 301907128, 157832280, 771127844, 823464668, 7050280, 440141230, 447196165, 191804541, 452026885, 87347166, 276831040, 60045288, 734465819, 164560833, 199230799, 349216876, 428543293, 772522955, 347184953, 62340406, 54577140, 272726833, 794454806, 985751704, 341174474, 621985059, 692859155, 469189763, 321043343, 329478061, 343608954, 592782592, 879104522, 63173355, 413290636, 56255892, 929609503, 879749990, 702807091, 927760758, 746586888, 539058098, 127047623, 239033011, 555807535, 283062377, 272971449, 251977715, 80040060, 174738522, 983248882, 165602321, 67218160, 224964621, 894042159, 410101927, 520955589, 806873074, 308033648, 835263458, 11964240, 336858967, 198715807, 372278844, 843790923, 402207080, 241351895, 748877352, 702886910, 606916897, 769495286, 889412313, 172815805, 762669762, 296465696, 219756279, 323192882, 645319337, 590478084, 606671802, 251977841, 460687979, 434785849, 954050586, 841685742, 20399223, 683568183, 596291616, 222321052, 329184104, 520255361, 405636904, 680569303, 966936172, 2048902, 51321264, 408628815, 894248043, 436922851, 319754195, 727113161, 476616401, 857769200, 406587878, 924680356, 752826071, 230077605, 677605001, 264662666, 607106695, 586631397, 986808348, 469370556, 70085022, 426516234, 251182268, 414082164, 244381621, 330413331, 929098136, 80892264, 878086419, 492077920, 211750697, 295452807, 882560159, 873420655, 611155739, 37938835, 920898531, 867955246, 335742551, 169973162, 733695946, 899652780, 65354334, 513302150, 304859099, 944194106, 126428089, 533595542, 572286561, 572817065, 924129706, 512976948, 127706863, 655094408, 271484831, 59690887, 625625794, 719702453, 601881560, 26280177, 12826551, 434333704, 149322577, 946892, 228689746, 980028706, 612494720, 303269874, 805912980, 548784306, 248100075, 424988228, 434538075, 519525678, 163030788, 411733318, 149518659, 634610110, 963465495, 678635478, 299284051, 608728547, 57203784, 965957016, 348207775, 150465499, 622587473, 626159819, 727250521, 159473586, 310533752, 67604276, 6992121, 960546640, 497030182, 426800915, 362409769, 198309179, 950727197, 695291089, 858723360, 872424174, 694334802, 998242489, 153829638, 261957956, 454542500, 316850589, 133337107, 514296367, 566734301, 310276074, 732946036, 109393293, 504517443, 915565144, 729463989, 362313073, 791790612, 756466459, 516395724, 548841960, 484787855, 994349084, 273038906, 994344029, 463272649, 152190637, 324301955, 557013589, 537671846, 888951343, 569588101, 822295623, 376548403, 459744175, 585521210, 954883760, 415081894, 826748512, 275511322, 490179019, 713930620, 746237, 125480658, 355914301, 627386086, 359614204, 187679463, 458727138, 509337130, 720419508, 58203052, 598479400, 241316185, 720647261, 382379848, 134706195, 976724859, 494054017, 165646682, 567960211, 517333590, 395550406, 701129212, 138553764, 683192621, 856132938, 353182813, 57828966, 181110510, 465980733, 533815878, 264810815, 331412050, 695365486, 947107563, 326771338, 596304680, 22158227, 6670759, 990264379, 967329095, 936842637, 955347795, 662122280, 12693830, 604017445, 270313430, 91974997, 247320526, 617666345, 720259304, 58451946, 29744343, 192137035, 738404027, 511916560, 528845611, 454311591, 83679200, 366570854, 348963616, 870996352, 868643132, 705136876, 528773588, 944317986, 941716288, 170235720, 526696882, 132634591, 972883494, 545874471, 897858649, 831653916, 63034044, 865383685, 542396385, 962428933, 568126518, 856890714, 797913437, 327657627, 364411612, 755505612, 50236349, 40016991, 69792312, 738409476, 550599219, 105554865, 670576834, 77455355, 539797974, 990877549, 699145389, 31870300, 206738055, 253079346, 749151778, 922455218, 620775454, 130485804, 211003054, 893890126, 317507371, 518662031, 92822295, 663843101, 331004880, 646317636, 781547271, 757749220, 997994399, 824097332, 835179408, 13738075, 821404475, 59953151, 928145401, 646760556, 310421871, 43800793, 836234925, 531517423, 198561868, 73958816, 814908803, 741333490, 643904472, 342283273, 98136919, 911393175, 621890864, 511103918, 642836605, 748456357, 674186792, 686286317, 754140421, 383712724, 452194725, 938128470, 765609892, 9607337, 991986013, 259317782, 567677073, 328711132, 945159156, 115963880, 910713214, 342533198, 312727257, 460310499, 319021190, 195211438, 838290641, 995675913, 478638520, 678344285, 819357656, 415631089, 177935645, 715668543, 366522241, 358259913, 488403757, 284976732, 551858262, 343882609, 277524925, 513650818, 670606644, 174359279, 15423420, 209074737, 350967879, 172323808, 915013738, 975761405, 641999276, 344094963, 717243355, 397347308, 495044478, 352282483, 632105594, 81811089, 417307237, 265640170, 468402651, 778665612, 723922796, 786983335, 176544514, 621681549, 242168688, 793254374, 360102198, 414752517, 705913477, 901100375, 56003452, 37112402, 938276104, 515527046, 253702484, 859350576, 841699507, 679132054, 26112171, 897358843, 264580886, 253271422, 514363696, 389670369, 918288823, 58352290, 98953823, 203088076, 194384723, 716158423, 587504682, 320442818, 235576884, 315589357, 462633427, 432690509, 389525182, 910073710, 181551227, 961197495, 327375353, 945812093, 376634970, 865788441, 414864486, 963789136, 477369402, 184599622, 818835974, 467106331, 548651336, 765745264, 802851563, 792792510, 145956838, 684802090, 175885440, 48280565, 946953465, 177462135, 473299857, 669950820, 671489323, 54690604, 639154441, 619592864, 418238618, 716348553, 537845770, 424111546, 208853211, 825341873, 981584837, 884568145, 939064630, 312359819, 628189716, 980047108, 14986749, 570387115, 126856329, 667479246, 334356844, 999055161, 631580953, 526174432, 783242006, 979554426, 639895372, 296437341, 350160235, 50513678, 238876291, 931829502, 841688776, 405893732, 534237697, 396166044, 296984326, 952220262, 831646295, 414542155, 950434743, 530911894, 167290509, 233185898, 587677945, 73480356, 188731292, 737356128, 672516091, 964334774, 330003006, 66652634, 409632877, 637355033, 711157134, 216188909, 120949580, 99364819, 796376480, 127525604, 835306969, 782466538, 106381940, 767348642, 791100091, 140117976, 900004355, 928311389, 37896739, 824471064, 698658816, 75199025, 453832080, 964065320, 479441732, 48498386, 359537374, 556282640, 982926515, 152213167, 448569151, 34690048, 198255908, 606846508, 678582925, 720471076, 299754597, 920486028, 598023207, 906262473, 995533234, 510307266, 46475440, 28130763, 771228584, 826416278, 178212109, 928844055, 412294773, 546296101, 903272750, 463828510, 638793132, 271705431, 856304699, 102943141, 771301637, 886650807, 206898336, 282971329, 628560570, 216670945, 295555075, 751025620, 281973141, 625925863, 993680445, 763652032, 173031885, 581132074, 940958641, 365025678, 441970972, 66324262, 637762286, 398055552, 874160490, 216625476, 256441388, 849959895, 833494030, 217331780, 134901704, 907796108, 451872200, 589770021, 613447149, 900565375, 194883287, 341561845, 741538323, 202668516, 463251182, 545063407, 222918866, 317646046, 301717703, 576375614, 125144275, 204673009, 138500570, 465298058, 640779906, 637634004, 838794711, 615233021, 808921497, 72483026, 594072831, 513053724, 290130930, 670700014, 23522210, 984085690, 926940319, 227192753, 228353138, 56337011, 56130582, 767521208, 782717244, 300421657, 261685452, 115917502, 358950163, 172960688, 454893754, 429822436, 922614676, 326638566, 465280430, 587768084, 434296543, 779676699, 837356517, 637452633, 364462788, 838852413, 274874084, 670467839, 188786469, 602910269, 613534599, 539242350, 922434937, 825000668, 735778057, 480522814, 335710264, 577148841, 831093955, 647043905, 904410894, 404529907, 796907053, 424169401, 665087527, 401970565, 343938374, 378979166, 54674949, 390321442, 724951541, 756953391, 396398586, 701157989, 985834462, 906946132, 964401681, 894842130, 339321777, 919606116, 522192152, 972991656, 422386471, 200312331, 150905159, 766012621, 871065101, 72971619, 965969456, 829709813, 275019204, 289360907, 25430325, 41777150, 917816034, 916161228, 919043088, 559518624, 328444646, 302563185, 641628438, 186445076, 413663177, 959285055, 702307844, 27188490, 84628711, 275388490, 208612511, 880542666, 524337071, 803227066, 302186441, 3660638, 811639965, 686853810, 700296120, 22280092, 151041591, 258502789, 594767031, 399443376, 505987089, 792721615, 843728448, 426242825, 655605834, 827903434, 44340485, 196726400, 714808826, 990125736, 99866432, 264061257, 280881241, 227188682, 248562956, 984384437, 446242873, 687769035, 137956344, 454343231, 6120987, 96212152, 489823679, 520390155, 18258860, 386162393, 891731336, 601317206, 217664175, 584771173, 865039260, 523128650, 890384891, 626603006, 713050153, 19251700, 64360651, 739027732, 877106206, 433990206, 493855428, 281468583, 238090089, 260463297, 971410501, 948963573, 408414405, 777147169, 46181592, 680900763, 979645559, 405368904, 886874668, 711988553, 95086840, 376466356, 193693888, 307365775, 584122559, 300118876, 732987512, 726285547, 804008572, 166229281, 27902531, 576033161, 866725504, 817978616, 672959185, 434730844, 455524665, 404253779, 246680481, 997693045, 37745303, 7148668, 602019710, 13323541, 6024350, 528429358, 85528071, 945453745, 451614657, 750475690, 382128810, 403490826, 980002248, 570744830, 852022493, 894158274, 357669867, 836833724, 986707506, 578606177, 138309459, 66782715, 311024283, 750267030, 504603850, 696647334, 27249722, 30335445, 41206962, 349552485, 219904247, 290080942, 94646194, 219724512, 616850423, 177267021, 296273208, 511393870, 649674544, 254920253, 266848564, 844074547, 512575590, 574145542, 872113266, 781685688, 377778098, 653053238, 478809208, 707304328, 283760308, 548728323, 968079197, 725214811, 949963310, 846026363, 643764104, 769701128, 356507109, 306091373, 869376349, 320712985, 96587637, 728684354, 114907248, 947621925, 14697176, 531487270, 973996084, 379343269, 828055784, 891246854, 811505585, 437538516, 726970776, 697685081, 209332693, 992343337, 272979526, 278765567, 532593636, 764355234, 366879499, 312231328, 131716007, 144267521, 202859153, 909717019, 353834977, 258308116, 241303056, 819662767, 752210436, 459054320, 892455249, 70024528, 250148725, 211895525, 640459125, 683605310, 579068604, 335894915, 173563906, 843683895, 771944464, 69336949, 204862446, 496074095, 900619526, 728801523, 649083124, 467788876, 902571532, 671856759, 22746435, 2910804, 312938647, 38087464, 442067973, 14627452, 184726907, 165030835, 788722590, 43855710, 438098924, 900797666, 865558259, 205197759, 464827865, 492615690, 242201014, 754820224, 152786404, 549865641, 272628090, 210344732, 778357193, 768904557, 142995041, 151868529, 532237874, 694952147, 420647955, 8252014, 572650083, 534962823, 374099287, 165444, 580762256, 487817228, 247947122, 362709000, 666966489, 362249916, 184354943, 479511704, 414232409, 244062394, 62887607, 510068523, 944076660, 515690931, 744997334, 110677166, 154202259, 158476924, 122841637, 901295026, 191118209, 394703231, 88021555, 472651142, 853824098, 175298765, 698935575, 896032410, 998820146, 173306968, 437165094, 129810951, 675549624, 140232996, 244832309, 742859321, 578335643, 263535593, 305415401, 624142032, 795974687, 626985383, 369535331, 744188253, 810336102, 121464410, 493962958, 226919066, 661005490, 530149081, 693172790, 396491549, 275755026, 575898842, 621279928, 731197091, 658680863, 139297313, 754115331, 450591742, 835619443, 848990996, 521540353, 388823597, 918844422, 630332597, 460064941, 339854293, 395446216, 675209013, 41590497, 109357749, 421322340, 614860159, 972203967, 836552165, 871975543, 609456402, 244564896, 295538500, 117587950, 790275322, 513361267, 921859192, 152454863, 311452655, 858593458, 771888592, 246847651, 662064136, 754536624, 134420069, 746205930, 794783849, 141207430, 784178627, 376008413, 832329732, 254856274, 414638178, 723313426, 529195959, 18131049, 345741658, 979876768, 92082284, 45937001, 506645362, 877191769, 758163954, 859948021, 287935729, 648699120, 153564485, 108809440, 200584769, 722614058, 863285980, 140933829, 514570541, 440764697, 189356167, 565630937, 39341162, 881121036, 279734517, 272384531, 587056411, 847861645, 686632725, 230039656, 702659945, 289381904, 441639069, 505139807, 469700263, 39794497, 387067905, 679684973, 884533453, 182320161, 328981443, 865915565, 902458239, 762558073, 552436945, 625018172, 264854118, 638119824, 719937093, 266315892, 198681644, 833010432, 935214774, 269876590, 508818284, 236258999, 92937247, 617349146, 697907363, 690604641, 537807880, 867960744, 748835641, 36043620, 373878250, 699245657, 816705302, 926492210, 623863704, 472074381, 863919542, 974805556, 214956214, 126308290, 210758258, 763731087, 835366751, 958822268, 841685668, 802839321, 557783657, 710430413, 550149667, 238948248, 291930890, 630285196, 37125254, 99584381, 681609345, 846589738, 201836612, 113894293, 149387279, 515882648, 435338732, 613782390, 274253163, 78944885, 89919922, 953082172, 481079125, 894640433, 750201354, 67636522, 270383746, 280649313, 158795738, 676523756, 201922843, 153142117, 355766465, 613161556, 292514893, 688494123, 416850486, 316198418, 497562440, 645698717, 980463437, 586786289, 757263526, 896081017, 362867946, 296859307, 219095767, 562253455, 779917856, 364100514, 74840243, 749860007, 960927933, 516802610, 137156839, 977394680, 659271176, 586441872, 976015837, 139740216, 300332373, 57150028, 578649844, 560065874, 413012005, 383019623, 29400863, 470013882, 594803700, 199921297, 975946562, 769863257, 701064564, 239918087, 841950084, 2056740, 526112721, 306125780, 332576229, 869770046, 439416532, 729237644, 218396882, 842500268, 574994705, 743566472, 738536268, 270001668, 550210669, 957248209, 915016822, 651603393, 885122696, 57057087, 673572564, 102674974, 420778800, 231169173, 774193205, 974247095, 930558752, 889172169, 320838060, 151392503, 744986238, 934853183, 946187782, 666472109, 401489899, 722654671, 843840969, 314976232, 412979731, 345252835, 354055802, 676066696, 558218880, 922816907, 415202529, 30057660, 174410475, 504533022, 84614776, 961212766, 870210934, 482943352, 60410624, 984539760, 913816967, 806243908, 971013171, 52874268, 579361629, 20794239, 154708630, 908163597, 791438294, 869538331, 731397432, 292085977, 564574300, 381246053, 655134432, 515493574, 587375105, 254511157, 558864511, 572090822, 553008523, 58625498, 771342885, 682243896, 250751274, 353346885, 870992267, 211713122, 135036828, 7198723, 425405052, 124000418, 141570161, 55734534, 392534543, 142394288, 739252727, 648838775, 587849427, 315582943, 630361331, 324286383, 491072892, 326932652, 261114120, 979680031, 540282376, 553946235, 652639058, 559527751, 674721326, 764635257, 340321658, 902611694, 402678577, 596024254, 815865170, 178113743, 739058213, 26961127, 811765397, 63961893, 871339207, 811841272, 308876067, 964559527, 727905765, 990494458, 549075687, 99547387, 137004483, 377685136, 810477288, 227072345, 33185697, 502168714, 722537360, 856761281, 890371489, 122415874, 83969872, 647922300, 743074934, 750792359, 42457769, 823785658, 432597977, 289472364, 878966233, 581246338, 83477091, 652637422, 321085086, 715722191, 327265003, 757551328, 113813862, 96400442, 203870650, 353654673, 251947408, 41785737, 793138390, 823173432, 677068000, 470772116, 934975374, 105007027, 231029631, 249400066, 646913906, 864213872, 124633308, 925113311, 638062259, 284946934, 292853942, 870422265, 195491143, 439477638, 102695621, 156074983, 902123308, 944031028, 598955773, 833140826, 539883641, 269056462, 485543099, 254376262, 15333653, 545923333, 852896476, 33174296, 426712250, 895290414, 555185358, 72857748, 260559405, 180740931, 297842857, 718935518, 836913796, 208296191, 704490442, 167606285, 58549068, 225959880, 22791859, 362651851, 831674651, 821917752, 240151325, 259128874, 210135094, 619256494, 988201139, 570538950, 113633989, 215692145, 293207825, 260249880, 998551392, 308592383, 217879347, 127782428, 643724061, 820009145, 726214358, 525145647, 740627634, 169981222, 492460320, 490320819, 787665351, 290708634, 977321072, 484166473, 596574556, 549556778, 130290628, 438120950, 939127532, 395913868, 623316105, 393685347, 433407311, 936052481, 885262104, 996964549, 465960310, 708579207, 37163633, 708943714, 884975533, 61591400, 325110605, 293012411, 898778608, 580226007, 339521371, 795876536, 62136645, 535548187, 318645080, 169369508, 241327805, 69523277, 429175196, 222547086, 709385096, 581445955, 397699882, 195533677, 842690042, 445504303, 439388107, 450778870, 68066479, 983912433, 958402853, 436333472, 991229135, 720614812, 929896011, 864867577, 59290352, 890754590, 934742489, 159785595, 819855428, 70680828, 38688753, 618240444, 729266083, 72388874, 919742755, 626896271, 19548264, 240782095, 148643758, 133469027, 770747237, 722587802, 6956529, 181375780, 316605305, 652339715, 693839861, 988786398, 255337187, 207179444, 809164942, 579413823, 334362959, 394157809, 916729555, 598799166, 889165911, 592169893, 925327251, 223283589, 101890220, 11075233, 154499898, 771328568, 992753824, 799575779, 428114705, 416970961, 200033441, 711219053, 960983674, 8544653, 817769963, 839034995, 844311189, 492142360, 947039749, 528825751, 558624801, 467618196, 952943774, 400358837, 655439133, 867503513, 3888453, 924196298, 413157768, 165489655, 191603616, 404881802, 653579467, 639291275, 560080363, 516683615, 106300221, 192633232, 119134770, 82934324, 67209156, 511565501, 165834502, 563458409, 717178241, 372115772, 744398683, 57515213, 858751757, 217516810, 21347330, 6915492, 776747959, 816406073, 712593952, 89047865, 189350371, 958947882, 521050690, 534145190, 109162789, 39633680, 404940060, 818760353, 150087177, 31776780, 425097585, 159564805, 974350432, 214506200, 15002731, 441680200, 50569300, 681513106, 544701725, 628021962, 422867980, 911696981, 66535431, 520397280, 490716201, 409363981, 666262609, 11220844, 732892698, 151724591, 711909609, 37430157, 916383761, 146111271, 999033220, 916153540, 337912659, 389907296, 306121157, 170723904, 407371377, 547405169, 372106523, 613284836, 214753713, 339804730, 745915146, 244402230, 352676566, 283366996, 500292232, 345008197, 270299203, 381314654, 320288771, 270504023, 535254023, 361476317, 412350260, 769012809, 192251999, 65488881, 692236445, 35721893, 749171197, 936182899, 885571794, 915366155, 162086291, 840311958, 271807529, 868235612, 499856344, 89725570, 446273365, 886273506, 386817283, 490254474, 644929811, 141326327, 105740722, 908566324, 908338528, 998246610, 971433214, 957446656, 275900530, 741101723, 326904352, 557345200, 662436100, 601738122, 887813006, 620980408, 247152637, 325561054, 749700514, 336905306, 614665297, 608528303, 486743974, 927873482, 101275894, 757544391, 697416417, 213454096, 777961355, 25147944, 576018173, 451647840, 138992300, 344726388, 678037965, 849886105, 912229651, 941827988, 520522324, 576358784, 489110742, 670634017, 112013576, 594355036, 695317252, 717429928, 559699696, 262534870, 546003297, 354784424, 451467123, 664433320, 414263303, 577292629, 129590358, 373840986, 644603209, 653700690, 385439848, 828248287, 687005520, 992310745, 589790308, 599072506, 864595731, 384291825, 487642477, 259588167, 682697588, 105133793, 400556611, 916015767, 416523175, 746355812, 563224559, 764853892, 546528195, 185642722, 591895779, 327827738, 413560092, 563708026, 748727080, 313403567, 781761119, 843263459, 942331113, 993152583, 695212882, 378975291, 348598602, 884300044, 720935629, 846619359, 640309537, 680054409, 480966761, 150357982, 77250311, 577013955, 870877565, 477648563, 522676558, 553063972, 144841344, 567750479, 359031656, 531210601, 678467827, 219781898, 895929445, 277930127, 768683773, 853476641, 68163572, 458364515, 570658823, 284928809, 51410924, 199864303, 760139626, 696384139, 957141997, 535136732, 564708320, 971280347, 126372607, 803764971, 272932346, 524693371, 468189297, 205004396, 705820256, 822413156, 680786157, 277783412, 994184147, 534932853, 788470665, 736217728, 935061020, 240674799, 281745163, 262133228, 527687446, 720218823, 611227220, 161553346, 88263261, 504534450, 759722238, 573040244, 293568726, 365897340, 30028305, 676218476, 209360763, 977886773, 519278240, 953570687, 12531504, 272200521, 167924803, 550271946, 443228927, 771542415, 733096238, 626076896, 499878150, 59519102, 596775049, 61707471, 247753425, 331296672, 56550024, 87278855, 966899669, 33564902, 563038003, 365728616, 794980682, 747532191, 308399612, 361806686, 470772771, 661663749, 553200696, 292927487, 704651277, 70820831, 399721119, 762072558, 44306085, 961669221, 576846349, 92375324, 659671328, 126319980, 805981138, 275530251, 841673882, 58431893, 252996740, 203521051, 232101218, 937446163, 194349276, 807859220, 876482859, 445577411, 437633718, 161068819, 87184689, 514992216, 123042081, 725168316, 71646449, 334646665, 435507276, 567274533, 239724250, 179860651, 151503, 570758677, 232433162, 294404440, 403174746, 413863586, 424373189, 563420762, 919031755, 587264571, 830681986, 263939125, 371855807, 38684118, 64021454, 518056480, 248863651, 573818616, 550533289, 558318857, 400331911, 774908898, 126437618, 942378244, 574648114, 620634491, 663383379, 214377271, 236763306, 50925289, 838726397, 762846790, 841069509, 420083118, 457956948, 422595276, 766258064, 979632110, 943807664, 230224940, 990214497, 306406586, 255164482, 557223475, 543306586, 539852413, 928859583, 18492259, 472141761, 33579728, 408671261, 68540177, 18074118, 868439228, 646366305, 350066286, 957039972, 289965914, 746249309, 998161486, 445075057, 86055627, 496056497, 639353598, 617373181, 117753643, 968035693, 469924518, 578857837, 205418740, 83021724, 849278674, 581583839, 358189527, 454199278, 281524701, 294523744, 905170527, 203915181, 263884153, 403812220, 751302524, 18485203, 599036526, 892849375, 19655588, 371092017, 472372081, 315895230, 931864812, 692332100, 627138938, 168839818, 290185636, 61137265, 354401068, 970626599, 870260043, 319518638, 20628756, 976431159, 487148287, 181420728, 414235286, 251802610, 629042405, 878290883, 769798760, 175764079, 260707190, 712892490, 411764075, 30421444, 948930090, 398821775, 703906776, 441591462, 546409947, 435223911, 50279713, 91716790, 224893887, 906735442, 76418303, 392329676, 242953377, 430970158, 626469287, 778670280, 43828382, 690096936, 193463718, 484943545, 30248846, 752545756, 892142362, 194484035, 698124945, 5284337, 464112279, 924268999, 18048716, 522817733, 286078181, 571834703, 95556114, 317419566, 655517692, 938333995, 626160564, 511945301, 70583425, 987582109, 418789016, 814240674, 93546647, 350620366, 47040022, 94918848, 545501224, 159315431, 315900086, 893200400, 161936330, 796058460, 34727393, 275513869, 410918333, 183570136, 298016509, 435423004, 501986268, 571491490, 538999173, 109981426, 344666036, 427692046, 39540521, 434624614, 679425497, 437943834, 29570648, 259856034, 480375093, 525008519, 832893594, 215997382, 858016227, 618186107, 513671994, 366042139, 830020826, 97938740, 133257568, 739501265, 697530164, 473874339, 908280513, 6355405, 587610178, 623247587, 220552827, 108934659, 695189137, 110830846, 563720750, 418155929, 579046311, 698005815, 693031154, 657969673, 921748102, 277998204, 847868901, 580493912, 268300384, 300220651, 790634454, 451105018, 97408023, 839212957, 878255291, 357922489, 925822010, 992400, 183589034, 67307234, 532091568, 495287462, 360572421, 107577422, 572663310, 89651493, 705155271, 647247625, 342020044, 209498386, 117007974, 347976255, 436819409, 534134932, 645993182, 212816827, 872114535, 260069933, 90827359, 624069389, 625221912, 848551496, 286184383, 937989000, 458986672, 741846177, 572477287, 589128225, 27244714, 288468004, 393650848, 976452296, 77327723, 915365661, 281217977, 65414742, 57330196, 369695238, 584786818, 93998080, 455937088, 648233078, 734536313, 66772268, 977928786, 559837882, 983771728, 841447231, 99838963, 137898076, 61258889, 782471175, 638444387, 66178837, 611993189, 767944823, 696400221, 480042636, 864603583, 984158792, 136473356, 691157625, 457171234, 191296432, 713714225, 944199630, 322162662, 2470038, 13581986, 326412724, 167855811, 263760877, 110502438, 264598380, 236446604, 414259108, 972095032, 623327585, 590180007, 559102133, 585201429, 536036601, 810943066, 993927040, 60081089, 644519555, 744990242, 652819019, 700501173, 449250777, 497021266, 988189779, 277995672, 911587854, 134336067, 282405555, 303808371, 139899060, 655323455, 423629417, 547175786, 937069961, 388903331, 762843755, 232669174, 207091870, 697710711, 229225790, 387892295, 200284107, 448872659, 866470094, 765095609, 398824726, 975543170, 577025609, 803682177, 408383151, 835767654, 486450345, 461760774, 987747225, 564342940, 416324361, 869581201, 744090442, 195585896, 201855989, 572496991, 942006569, 459815135, 318683691, 37605683, 950339233, 808632975, 469435785, 989527733, 667502424, 121696212, 805494968, 318618382, 295804413, 242250158, 952713097, 978726076, 704459674, 111341541, 96026793, 579978372, 125232039, 871992809, 397610646, 699255457, 652311042, 74364815, 957569816, 737185336, 212035978, 2793173, 10234925, 218070059, 77405261, 108023031, 196108113, 771333679, 888623204, 63887180, 507105057, 56027229, 304943695, 786538821, 346654670, 284575079, 444414364, 396426524, 248700167, 412318046, 507301183, 913210382, 79767343, 782344712, 314584522, 671698722, 720567670, 63906529, 331763382, 580260237, 210548344, 523846549, 163007036, 573288939, 123593559, 718434732, 163497310, 848922928, 549888876, 657484397, 982397651, 412145858, 357059393, 267826871, 630919619, 242810244, 969288946, 319919454, 153279185, 734101094, 522111155, 52372199, 661742028, 345415481, 115696496, 756018867, 472423458, 355202914, 498621837, 865207885, 353056929, 513517750, 760900240, 271040046, 583874354, 469430770, 379094773, 349085827, 149886127, 73263224, 801042887, 971353727, 902446187, 857784671, 759469328, 787727067, 215050418, 145027869, 582032450, 488060221, 745110850, 770587948, 548210474, 285868799, 328517682, 681207984, 480131136, 508221606, 696772319, 121690470, 446335507, 455281692, 442699830, 393689076, 639532024, 418873558, 487477457, 587330323, 496239310, 832918374, 26784889, 692815943, 322838457, 68406286, 851585179, 811860890, 217464418, 47926309, 583334012, 981849787, 424081278, 846226402, 834734133, 16978019, 818288449, 813428858, 529242657, 128001291, 589781950, 672382319, 888452893, 724677030, 758668450, 777759011, 141350475, 814408429, 199416883, 330190215, 343185508, 529467502, 450220127, 497585145, 269491816, 357774572, 440790074, 548681066, 183048844, 371893011, 339147499, 259897649, 258978969, 275916932, 395498551, 712934069, 636328846, 715755978, 291895457, 667663134, 454421516, 284660379, 986369695, 365130221, 360090809, 420767572, 674657985, 410263344, 263146067, 971630833, 659492936, 831254124, 275273022, 568163145, 982385638, 458997148, 652705520, 482292772, 615572939, 369949257, 463000762, 697890193, 38223380, 470187425, 994048952, 376533151, 480752429, 896066220, 58264501, 219009110, 87586175, 374037153, 651499062, 238004558, 730448938, 382796974, 819459500, 528387157, 904142186, 946674411, 423198855, 303941970, 95368602, 585078108, 520899474, 424672930, 365086778, 450938816, 882444419, 342205986, 166013457, 948304909, 175794620, 511841464, 158663029, 271585611, 903706479, 273133352, 844580937, 106549204, 722709157, 947031292, 158146366, 575477879, 406848999, 884939718, 507474455, 303943135, 246568993, 538931088, 72155800, 339623110, 319212676, 110648110, 379161759, 358267932, 958307362, 208347124, 232028392, 575001302, 723682585, 844897502, 449327140, 125340679, 2677847, 732449516, 536873838, 560050164, 719012020, 117066196, 159364132, 221088992, 762700494, 937025242, 728356399, 938024993, 881173365, 79132140, 358395201, 941883706, 182289434, 118776158, 396900808, 562518465, 506572799, 441692968, 525636278, 823715019, 84608973, 278974721, 947170410, 674387666, 467416630, 702822863, 261709382, 553473949, 67094895, 143932339, 398914922, 798086456, 946025060, 537876502, 951862026, 353709769, 687535877, 636570715, 815919554, 954792220, 866583653, 218319573, 766746388, 675337075, 59856501, 686127337, 284506829, 920616014, 583100752, 340348809, 841300682, 339312201, 127034180, 84566628, 717702551, 511640395, 930269892, 100702891, 529125247, 21914649, 312412400, 928086577, 410019209, 92818825, 549929494, 981444929, 25900458, 716198526, 295153565, 615095929, 730361626, 836795933, 999545402, 851013151, 591392566, 956602277, 625175700, 441958224, 649324586, 925649371, 197424524, 587705118, 208501610, 387209147, 489878338, 18945482, 381867631, 525719109, 591263005, 778076016, 33535872, 791210570, 933105466, 97089417, 928856265, 346421912, 491097472, 109204323, 798599800, 732591864, 852265908, 351294478, 432217407, 630692369, 5011476, 409276478, 921752962, 616089812, 165350285, 315932043, 824417652, 919799186, 323123050, 472453189, 204799721, 407436764, 302316048, 848764993, 363963145, 433460168, 434590594, 236498487, 171804394, 782220782, 447540696, 593949628, 842943995, 188193299, 881910628, 96403731, 857697932, 999898392, 597014922, 118539428, 835675037, 768537707, 661485358, 895838105, 69666030, 266644198, 484582237, 360666734, 995273906, 343504041, 179995299, 12413511, 890092222, 245239949, 95218218, 213157463, 966892720, 366018052, 911053937, 755351139, 712997567, 210109939, 724320166, 694737449, 258807253, 786641617, 66183870, 820708459, 505899913, 325916036, 588597585, 565158937, 120473543, 307953110, 34960871, 444689233, 307158408, 488980048, 510068046, 335016346, 481661027, 759718310, 557273190, 437252777, 93072630, 65396633, 2168909, 14984443, 30751135, 126873377, 209876525, 522250578, 439843228, 759991122, 314039797, 490374192, 55727678, 492203637, 366111372, 438386789, 963332486, 694429120, 563841227, 717088283, 572085090, 887707528, 169585901, 405721606, 869546682, 605108745, 355129221, 198265080, 128098387, 138533744, 521109220, 640787981, 645344901, 91838048, 16145318, 730532757, 371755034, 560522754, 925264220, 230870361, 868421141, 779818311, 843813731, 494634056, 780759664, 474669722, 915867174, 335682517, 991963247, 524858308, 561800985, 302554884, 920424520, 257662327, 682566932, 936374822, 266471240, 310380347, 170498703, 183692950, 879678860, 117715818, 429644780, 8421027, 808260029, 912054695, 577106254, 265154265, 483792650, 324293057, 422124216, 759403666, 524146374, 930744328, 597123765, 61532749, 669832498, 648974750, 127831384, 365747858, 95886359, 989986237, 626322693, 520679505, 289321280, 256316534, 750284110, 306897398, 209036119, 487741136, 712325978, 201582003, 689574486, 275607296, 84853598, 496834237, 909623884, 830153048, 994799468, 232851956, 964839038, 302248526, 857206791, 461416520, 966257722, 338980713, 792000569, 939055669, 599204077, 751007869, 518026988, 313738798, 280876621, 694638724, 774501906, 411007642, 717070929, 809992569, 424058777, 654108211, 949497042, 856058012, 515088415, 150033402, 184190208, 604045479, 79432257, 755844963, 564988677, 902641037, 250113289, 454223112, 43614, 642456501, 368337520, 781161371, 417174977, 408175278, 810892531, 816744006, 680813996, 699982517, 967194655, 330316636, 22151650, 402825535, 512598379, 376093944, 72130687, 476417016, 971294027, 287561268, 342924520, 801267926, 612670901, 131686014, 82817689, 530671356, 17996151, 681501249, 278540267, 834188144, 753833403, 623264375, 691656979, 17171308, 530223678, 473646122, 401556701, 534632722, 655784896, 63729468, 501302301, 865179996, 204760471, 477759126, 357007774, 465463607, 379109392, 160119059, 968277734, 328786761, 99376881, 841704279, 557973981, 483748540, 13287179, 55555250, 625402004, 149937363, 334866841, 198834809, 33852911, 215845275, 997145595, 669091445, 331838443, 937133476, 95481512, 899004604, 509718973, 454788132, 329552724, 662510361, 729254642, 867905749, 544701067, 463125631, 5775454, 417616342, 838597086, 670091629, 328375564, 875517021, 141997903, 423232496, 935050938, 214342220, 934873548, 584306877, 952273339, 225509920, 530638965, 785865628, 453471363, 644944805, 385372788, 367021902, 356704394, 434226196, 366464984, 361147813, 266772563, 775620960, 405032188, 374036509, 950182870, 150619861, 568103889, 398386436, 833139533, 309799367, 199389843, 332788285, 845520973, 948221092, 559397304, 240452089, 193507897, 780366737, 378822265, 958423909, 766930706, 502345468, 111525421, 729609648, 864069779, 133365739, 636538493, 956792313, 377028856, 887929496, 139905059, 885947813, 663017618, 682620004, 961072651, 425218808, 111670217, 587484806, 491936132, 810713262, 66870563, 512750352, 119126864, 942670458, 967781113, 299741075, 957151730, 865503763, 625332449, 714780286, 16332042, 839196601, 417438781, 942595743, 308696363, 111454419, 795996272, 34526303, 793975111, 6282553, 408867075, 436264893, 461654711, 618962101, 530022632, 829647388, 156872641, 187710743, 970417786, 71976312, 610361693, 949479604, 246548379, 60479703, 42451571, 656802860, 772289577, 14518986, 195282734, 370587337, 133553451, 64416399, 442890948, 485741959, 699998431, 241657904, 58633389, 920623010, 289516918, 623982319, 628132245, 324686655, 207837984, 142786353, 492564506, 433210785, 831953417, 685746843, 842556764, 206951696, 206731260, 249203418, 668174154, 543635027, 502227111, 545762778, 620695418, 952518958, 313357760, 597833754, 850279114, 930604267, 138743961, 425430882, 132596380, 30383291, 374084580, 410697054, 702052459, 638782283, 363685741, 913792401, 123347115, 461827128, 638599332, 215244093, 321021363, 476016363, 1461675, 45979772, 937705394, 639380550, 172207016, 405063498, 414093361, 449212281, 697463256, 446953401, 397567661, 399641177, 795707329, 552662821, 45437688, 888941280, 636399790, 437665209, 386894403, 609108199, 496016833, 287646015, 571821346, 853173417, 334521050, 550092012, 180411843, 854161700, 637774807, 172130141, 473306557, 681612487, 352832744, 122586686, 637694400, 692879737, 591291682, 981786908, 978517379, 978259274, 153218609, 108983698, 344589107, 431225067, 283773337, 16874998, 789471476, 681745664, 723252806, 486355568, 135080642, 725199571, 133989025, 553655325, 789001098, 417229735, 698712627, 465916496, 128890711, 932365923, 442489840, 20348537, 379270386, 721960128, 654718826, 880264207, 824562947, 57870886, 183643859, 55544912, 871806385, 307234173, 674377438, 616547204, 29048767, 622707378, 638501651, 42575826, 794491021, 254065296, 634986747, 839890980, 153718278, 81502635, 262782705, 308343245, 150454410, 489692326, 846350010, 490531363, 610165739, 185061216, 909633745, 732526928, 372873343, 62061389, 936605100, 868811995, 376397259, 21427269, 61081961, 590623202, 83386566, 770277784, 530604088, 705449490, 603515148, 240188204, 79556189, 73213164, 318974944, 501978821, 842647372, 630258014, 797137689, 242297588, 831306680, 337483316, 984607008, 83592413, 957993560, 319370199, 969893588, 801948141, 413072584, 860681067, 482809105, 116048314, 332080979, 786629740, 121772985, 297211291, 552511225, 687308825, 637586830, 393696551, 581992644, 854933264, 602100001, 275234771, 947943033, 403659762, 670060606, 413988580, 724443366, 535512391, 234695318, 294536528, 580114306, 473667100, 154686180, 194815987, 59119057, 590502875, 33435055, 784492567, 565680445, 48365162, 67648197, 538783754, 27807752, 523451656, 81936984, 716476866, 76564714, 76983929, 701628465, 797651206, 760977945, 110264943, 107205470, 806386059, 224017925, 524662792, 915142691, 82382194, 74191064, 624795494, 465732245, 23317184, 995398586, 5792809, 832318002, 8233686, 343410017, 683201362, 708229493, 46592239, 889600085, 391346744, 693712764, 985578382, 421460321, 799018305, 899495022, 169384173, 711315909, 932606066, 407112087, 107212997, 127173274, 549331434, 165822476, 412842413, 709751620, 129586311, 103648263, 528382316, 401740975, 889725580, 759519193, 259012337, 234722774, 132693213, 840487560, 771044427, 408869996, 346410317, 639252735, 526956413, 175324229, 144301283, 124795321, 123676424, 942884026, 850147778, 657792443, 703425942, 388641, 121438034, 161285757, 505869942, 582008538, 762252199, 68467190, 761693379, 540902078, 486788932, 396987106, 79480612, 924049794, 55517531, 932001218, 118323420, 81699984, 562273810, 225841391, 215324278, 450212108, 579759726, 425763496, 867973372, 935809193, 700281229, 519562061, 790131948, 545400591, 760138174, 534717199, 715562907, 299164471, 54709790, 262449949, 941957997, 193636201, 938484018, 556684314, 790642728, 830955502, 782613257, 835499476, 350615220, 442547349, 878006573, 519599805, 602795433, 614442068, 760561439, 565453429, 486318914, 518558747, 897194988, 691660475, 869738414, 459965580, 827276447, 153273058, 181643091, 114025849, 1596374, 568360265, 777838208, 248214415, 939142246, 572654076, 293714797, 127585250, 215102787, 753244412, 116111454, 866651814, 297331625, 45598963, 530605481, 601746773, 319119198, 961383471, 431373450, 599883305, 702058050, 754629590, 232351653, 89083252, 4574979, 304661738, 78974751, 347372914, 841813221, 25677573, 779670565, 664323172, 971423606, 512356403, 472045475, 904238933, 123209771, 104165480, 725285974, 789654972, 645203660, 556542973, 833307576, 171009585, 497911565, 990187581, 134569211, 78256141, 668549834, 616112711, 974264265, 770377850, 283930706, 463433618, 923306117, 145452656, 623405779, 345415410, 804373929, 761750569, 714922274, 202706760, 538576753, 194921375, 495708910, 770207467, 551934885, 971870355, 399191316, 873340881, 511993981, 952024808, 15967464, 991863829, 840984318, 340722335, 35068426, 665027986, 269576584, 421989073, 184789442, 490460084, 636718701, 734553327, 740300451, 553853712, 187881444, 293542311, 528727756, 433462447, 61708221, 154513484, 827155805, 24662583, 248824353, 608998986, 410428764, 533117898, 435377543, 705885726, 829633463, 530328957, 204163889, 295289789, 186615962, 664728932, 858453621, 13969806, 829531987, 870241367, 854031354, 147716673, 93578702, 806507977, 717387749, 891453664, 677772263, 616945855, 793614240, 422967955, 962773593, 417104144, 257595027, 443949157, 561511625, 697535945, 423220917, 788259437, 317140086, 640742596, 590472774, 897867833, 682229424, 466191145, 3286040, 322360756, 463155731, 340016784, 638440711, 914846263, 420071060, 560456275, 32699863, 445791861, 716569373, 844238808, 118404009, 274633291, 793470737, 875877453, 612831002, 478611077, 389404729, 984735129, 210044671, 677434432, 99212266, 555957124, 528654183, 946372062, 940568699, 519281209, 868818722, 61387056, 17179453, 580340148, 306219069, 875414750, 955694467, 495935794, 38727398, 506119234, 770184454, 65799012, 733658408, 491521380, 350513747, 942135894, 673462299, 133519114, 954360097, 159382527, 483507782, 232026997, 329447804, 539750538, 718822257, 930205765, 414553174, 348770025, 923940396, 910764897, 772069724, 312804504, 963270649, 393704375, 348722496, 843132185, 846578065, 238537683, 374867953, 781497167, 428140821, 924784363, 788810705, 699801749, 609208482, 284093996, 4841993, 202941407, 456683576, 347922901, 552394559, 44348543, 376038478, 434962180, 136766865, 961571482, 285039048, 776735211, 707825865, 985816210, 472392173, 228075409, 759065925, 372412296, 822877538, 723929673, 654629205, 595097851, 213998061, 950254485, 425270556, 928896428, 684833265, 222829854, 869698823, 258978845, 30359610, 380197016, 533078636, 551011009, 797944108, 490252043, 324941535, 99343242, 291253012, 958108281, 214470748, 999776105, 443717896, 972165388, 290684236, 685281391, 641344667, 672862760, 231413481, 244287049, 211039333, 821458999, 839048171, 379112572, 929163769, 17510751, 916627320, 33312156, 461537528, 379441438, 949035690, 31249030, 633409942, 594860507, 371089371, 242691666, 481651210, 524772094, 93040546, 227772914, 988718422, 838006517, 465077336, 568222577, 101273288, 385433529, 607047303, 732634826, 70054198, 498495849, 579073114, 72815786, 723859431, 314954920, 947694418, 377829628, 325596677, 897618957, 406212686, 976495119, 357751523, 849136431, 643586696, 903003536, 815051188, 12641752, 670853784, 775177740, 476881609, 958465789, 215316849, 274376079, 354055668, 588790232, 236267761, 877988149, 352588320, 226212203, 382128129, 569246807, 330814637, 153966813, 504036207, 445062820, 431074388, 658722163, 640153769, 203489672, 149975235, 997608347, 740535378, 835239994, 469505316, 698607500, 633449601, 351552265, 838793348, 455992601, 999578770, 173174167, 854569504, 87226380, 291693081, 912116389, 319858932, 74190199, 536724871, 938076228, 919005043, 417569782, 519587181, 668222107, 857958197, 725224235, 738017825, 821723288, 366792492, 510883716, 634435156, 759563938, 400585911, 97940889, 522928089, 191430059, 17230388, 537893800, 805024730, 669064498, 55267594, 893703880, 643761884, 970251683, 849330385, 308594921, 728157639, 381446512, 687812549, 383805660, 788042453, 229884002, 60798482, 733122943, 262519653, 616174204, 995217253, 141226324, 986127160, 284085874, 209313203, 219724967, 438750232, 295998030, 693303032, 934096628, 854194175, 764422687, 18643011, 442279491, 484225500, 790428137, 764602025, 327903317, 808009378, 560360004, 197408817, 26776564, 649269144, 505095170, 555886797, 974323566, 300334098, 901184289, 113438782, 418156785, 399172642, 497022088, 283066583, 99694225, 754493533, 4626074, 397334157, 268800401, 494661111, 225974292, 682167577, 888525629, 401494760, 665252168, 469677720, 830085621, 142771085, 466856913, 325449205, 69342485, 651545484, 150810890, 994639298, 440247596, 520889768, 932521486, 874116308, 650958254, 161649247, 620555027, 549149914, 234997699, 71705103, 739600504, 32530367, 95210306, 683452818, 784379630, 639596358, 789792380, 466181360, 72828722, 899667307, 744863366, 994931162, 74493590, 270740105, 800354380, 77604074, 135386577, 560841760, 585631463, 695060118, 232548117, 791299059, 538151673, 734135121, 279209507, 668173333, 338792078, 968814800, 81626120, 512042870, 651222164, 915125029, 735213630, 167477314, 406726827, 752478031, 895178620, 9997475, 629321996, 833524832, 489862241, 841860187, 920706301, 490013097, 14122966, 284077980, 508796954, 410881166, 729462168, 607862465, 821410572, 211771836, 861486524, 632549589, 421276415, 786993019, 575964929, 597033708, 177969270, 218707697, 781769451, 463121241, 90535066, 927344202, 770028211, 996628732, 383143781, 858205208, 29420819, 617365603, 145136155, 198875222, 615580822, 898740800, 772663707, 472234099, 165151568, 443368163, 211968138, 451245898, 428075435, 165679922, 113344164, 3769855, 256653320, 133413631, 727469610, 486098748, 929334483, 639555445, 404596006, 548065924, 370813574, 341669324, 602949654, 380358515, 96822051, 1118486, 955916092, 395056355, 884860820, 6242584, 442811196, 812572264, 251842308, 691734781, 32638324, 681779439, 184437081, 987773983, 355271956, 876520174, 406595733, 701059084, 489274932, 157064002, 850937718, 507074627, 121735021, 382612933, 791755985, 328727520, 896650475, 588363506, 646619326, 699859986, 295954559, 834581413, 243407255, 665206123, 897120812, 957834345, 305037159, 307666379, 605404139, 274462227, 948929917, 136731124, 472543423, 174276837, 641696790, 801595518, 104336176, 253646590, 697319475, 648842081, 559902726, 604182215, 340515188, 35574323, 866080631, 949314673, 404499509, 153299264, 602402663, 373360244, 949905973, 908560456, 257336820, 651656023, 924285265, 222579498, 602856062, 392357233, 820715156, 679150839, 944909752, 201402736, 202384080, 398979465, 119666651, 755090724, 655001157, 473768283, 454874096, 960019491, 969051576, 701814879, 27311654, 520726070, 616493762, 198470870, 271619428, 519113916, 567373459, 140374598, 443606072, 126088796, 313639336, 154154570, 535744725, 300206938, 688037478, 840720462, 856364404, 26844060, 231464148, 555392595, 359412081, 263165960, 70702783, 586942872, 206829641, 63642528, 50443961, 174809771, 921917196, 177047358, 409891197, 744846198, 8345575, 841438745, 809130017, 180412223, 274114380, 427735312, 736725133, 112327009, 511326341, 183181306, 770868250, 468515026, 707490145, 781410399, 400277117, 680160404, 442077734, 514067810, 445439973, 225787582, 343739749, 387253165, 266138195, 320647158, 158291461, 669299015, 995450661, 969909759, 146401451, 77668703, 666235744, 329678966, 51982323, 226685844, 676867557, 280273550, 208041703, 709663427, 287045650, 425345898, 1419665, 486528884, 745518479, 497879972, 377137535, 503374775, 255720956, 227903624, 41969282, 286855215, 511030851, 606418448, 208380838, 897597973, 989983803, 661769362, 483923248, 417626442, 284621584, 751926330, 296090221, 646720605, 444924874, 882902277, 427465935, 225319662, 398086012, 323837887, 915753333, 945679534, 679651724, 60322251, 150302013, 67845969, 72569382, 243891548, 879874884, 138719871, 936435206, 890886609, 852825054, 708069430, 550940926, 932052985, 855032299, 368591102, 640019862, 390698750, 193507395, 196834733, 622074266, 126987687, 411409845, 604743306, 365411382, 460884794, 258449759, 242264399, 237604742, 874070633, 322017826, 192571166, 510958501, 778629522, 590984385, 382593067, 210497301, 263658383, 760181537, 993102983, 951158322, 605952329, 491253944, 911150791, 250995514, 410586035, 984374254, 751149040, 148485143, 525178075, 484690925, 541227806, 808248307, 149813515, 114009163, 893595037, 427141771, 219671241, 998828348, 490171770, 865853087, 891377259, 102490793, 75385506, 231389788, 181241267, 229091804, 121846366, 456833835, 836131835, 577639435, 293216123, 330098476, 820380636, 561293306, 289059809, 462548246, 202234955, 353976428, 96170721, 232461330, 267076346, 373029426, 917661456, 333864179, 656997944, 530215512, 238489139, 341518824, 548513016, 222542320, 478902131, 826357635, 911434805, 142031190, 458879636, 146481294, 663899257, 902994568, 173084382, 145551260, 555907732, 473868283, 900963359, 252924287, 980943230, 262913852, 609767902, 507956769, 263288185, 725993154, 37224988, 331248183, 444569867, 686316938, 503317446, 110753999, 319594477, 26467614, 106202392, 264577672, 314043839, 271461966, 433787989, 825293630, 754367303, 583320638, 460296893, 589812197, 429561124, 518683091, 938742938, 119412706, 374165363, 938284209, 305949983, 804270010, 574394643, 991744311, 118443661, 822879414, 328227190, 910036176, 17933687, 703760776, 561289408, 177049757, 684934702, 914704245, 207001642, 866918731, 823178253, 300884385, 562530673, 894888474, 910244844, 801151327, 647319703, 379453284, 123445171, 176281675, 494467837, 942048165, 250332363, 459953736, 440588952, 896721180, 175107811, 54092084, 429556569, 5843311, 606754169, 100100912, 749292426, 395672109, 256915470, 675549833, 278599767, 827463273, 205778696, 370152831, 954397288, 2164284, 567110357, 473106855, 771994664, 714608428, 895042302, 557506954, 932448618, 721137930, 234869816, 501862426, 735547089, 805023335, 747757381, 689361061, 533458854, 237647205, 821818219, 41426574, 328475030, 99495784, 836698770, 835286273, 410322052, 984523554, 58814160, 80738940, 112189037, 828986607, 945517327, 819555420, 683393828, 294570418, 735516857, 914859422, 339363622, 56567986, 730086057, 406731681, 871977797, 625550332, 778201973, 656013319, 127922228, 769992406, 685136657, 266053156, 649667035, 565278183, 60696089, 30818042, 679111362, 740685406, 479067710, 689859720, 988885107, 722100653, 755827653, 271051363, 252810337, 844530659, 589680383, 690086097, 565648112, 543705890, 167608035, 171833127, 131978869, 284792339, 597313695, 996716791, 318240269, 998940055, 977339257, 306408485, 608957671, 127164840, 796665191, 245245236, 498784847, 193224771, 475805254, 339071655, 627409825, 390653256, 802894785, 789937067, 435010543, 217239892, 544297688, 933216027, 183063337, 623802049, 466710905, 90157274, 44544327, 438484299, 130389846, 78482038, 635189788, 491464602, 271858489, 316674054, 80818423, 827382936, 300282340, 937879262, 973575199, 963836998, 577340561, 870558739, 35043234, 705638627, 788801211, 416353104, 746577685, 122470636, 161039091, 149250509, 795299898, 854803459, 580148041, 218832186, 758111499, 866919925, 560304820, 99138667, 304103801, 846468106, 291081113, 578967674, 957899648, 536051432, 837572095, 994298351, 248835685, 826798370, 529669552, 610699440, 678600867, 720621194, 202533857, 797090424, 819840461, 70430494, 696059918, 684876147, 982207358, 750507000, 185901059, 95651986, 649978527, 816638198, 160443269, 827910783, 778120241, 745249043, 591985312, 109083386, 477751891, 984513252, 709976694, 297773412, 851524947, 681053614, 780899882, 445100108, 501998733, 320622053, 351416832, 885205159, 73224995, 335461910, 565216084, 861169419, 207633613, 403287215, 74111710, 286342053, 292022703, 513527225, 187584824, 133691723, 499210600, 213443258, 287471122, 618393242, 738878188, 68938031, 383425363, 613406592, 372008077, 742253956, 775739693, 26905992, 630436120, 491637199, 79810719, 826872396, 765664145, 756001255, 810916261, 563901103, 702313094, 51720547, 36752729, 631293777, 868634755, 606974473, 921875943, 826921024, 413858819, 934407288, 767664397, 667206188, 892320422, 440717390, 22454585, 370729048, 507540039, 648928118, 953208674, 153422897, 558453816, 504370340, 339062949, 775367377, 886597678, 229207474, 359999767, 212504605, 329514343, 521070166, 584691212, 522097630, 730005150, 573159893, 580693080, 170111128, 983988501, 753808708, 530703933, 739300643, 511253787, 337731073, 998135795, 268398175, 291119040, 44379789, 53534450, 370608071, 687487187, 463754231, 756637967, 54947543, 484519653, 664651257, 554403348, 962917791, 132434921, 996938050, 856629197, 62188486, 430657152, 960621340, 546370441, 423576078, 90983461, 913272721, 260585594, 949017436, 81799541, 98457753, 382697235, 516091999, 837529383, 354168323, 410562672, 365610323, 466594698, 60086798, 425769179, 118004119, 117673719, 800871825, 854056186, 189130560, 267959020, 203337893, 585359150, 528188684, 979702187, 872766516, 335187621, 572539606, 76300765, 758091312, 826040959, 415544877, 920007767, 751131862, 413309020, 902212650, 39852873, 421505984, 211105902, 482979776, 99264944, 237961538, 454133948, 448477408, 261957290, 704682300, 502543717, 722587503, 741236490, 889941655, 748929382, 355129153, 993908356, 386253100, 376162772, 155936180, 964753134, 55319350, 143651904, 959500652, 307388582, 960796260, 606856621, 318252918, 994909220, 105127913, 318127686, 799498817, 269695535, 177855059, 374334745, 101091784, 179714580, 534119571, 2662042, 505599163, 303240296, 748255283, 485523776, 97067949, 517300224, 225825648, 137197996, 58932629, 491265072, 411585349, 243238379, 471830434, 403795694, 582371192, 210682627, 459978366, 730496243, 352447278, 311870834, 435709580, 356141122, 104290588, 152268445, 689192412, 540340939, 534626279, 562119192, 413011350, 460847845, 337407045, 703427412, 196425942, 498543882, 509698972, 351204807, 19254399, 950074222, 60481259, 41783015, 78845838, 256144984, 179427146, 236688369, 354860826, 670209283, 117602006, 662134056, 69062043, 740870758, 709944041, 807363351, 432499275, 388460379, 986157557, 850476402, 888686808, 248355584, 829545927, 730601385, 452586541, 952048301, 331345140, 690333466, 705933849, 160462644, 912052275, 441326150, 957628992, 380564357, 177907216, 518045293, 501584658, 769326267, 2354527, 74765302, 891332527, 681320715, 296975873, 110672121, 61462801, 876871907, 685445422, 4464673, 29779098, 709580428, 46414917, 310656980, 815461442, 768858403, 54152391, 489389243, 890073646, 455533508, 696230023, 156008759, 492306516, 496724495, 320187812, 87045073, 738092783, 502597072, 513166093, 42432789, 111620166, 342011923, 692512176, 207560766, 771364723, 956617771, 567874447, 604943608, 868326724, 725320718, 412038251, 957229689, 20059922, 156771823, 531615597, 377845091, 153296965, 884643913, 462562114, 727234276, 968921668, 869764333, 724395186, 312868471, 712540966, 174103664, 189317693, 897242971, 515410779, 254781283, 450798394, 873892950, 62033777, 847758349, 352819556, 817200848, 428736930, 764350038, 780249694, 567118560, 916654001, 403365416, 996621133, 390785595, 206792668, 804141086, 100851526, 914001120, 557464861, 455942232, 148082850, 320184729, 836790673, 296551729, 16576373, 23496179, 54502873, 439838260, 294925297, 79819362, 622115519, 60978142, 493042697, 143112142, 13543209, 650593766, 786514394, 70620262, 829768261, 283563898, 304002706, 327040436, 112976741, 191284388, 594973539, 34259798, 531628570, 812422387, 293752457, 261783231, 482201721, 304258099, 204108154, 913599340, 771564423, 614810393, 551875327, 552856056, 486549859, 352643674, 489382476, 222203947, 34676663, 353345602, 405567283, 37740605, 719960226, 731888158, 540640824, 616047759, 867338996, 66868419, 811895180, 528657494, 583178565, 954867971, 36912817, 303227950, 681030327, 858082812, 876423342, 472599820, 732273192, 202487463, 160761547, 143399114, 64440160, 938634614, 89743644, 11624246, 550801273, 715237723, 349025082, 312565365, 347772011, 343653802, 953487178, 146998113, 791889478, 422862016, 32852289, 236239741, 982936018, 928162002, 46696594, 966825204, 714176533, 483897977, 488149535, 275126528, 134086093, 310840895, 940476028, 503605009, 283398146, 285418422, 733538371, 848939887, 586540347, 566607436, 73169051, 596232300, 648502571, 504156304, 716327546, 365400430, 165267403, 270668493, 110688632, 746841988, 826770218, 584808155, 629840771, 959857660, 571115888, 419783503, 264771973, 559932797, 713272185, 327059055, 491869853, 126870212, 943624357, 341523760, 881776263, 197709695, 563533211, 161991913, 596081138, 936847804, 880883051, 763894956, 649991543, 202432193, 981229383, 566540972, 697875864, 549769751, 584793347, 87872993, 437187257, 498951566, 780374348, 812494860, 198364843, 112236126, 4434574, 26308296, 284809245, 644265592, 716574721, 469809694, 47212815, 930293702, 769816223, 851524070, 974557707, 417927067, 988014075, 548894841, 944934471, 534380646, 916201076, 507742046, 183344156, 555003962, 730731882, 338631254, 213456991, 835848787, 463135004, 163719207, 547583795, 172018018, 551463748, 798642454, 241294735, 912689910, 327531143, 874208931, 881209635, 927979016, 155973364, 382575366, 276507351, 717305005, 235255131, 417722772, 301679359, 238171167, 196467628, 991079336, 355352441, 870684474, 624157850, 58826251, 727523258, 571358482, 469433131, 381156092, 918402430, 579019735, 123760131, 749017982, 7902194, 72020105, 17229512, 848595009, 296674496, 789046217, 926955835, 273930538, 18623572, 716460555, 132658981, 955901730, 28370841, 845380532, 517777163, 792371242, 680710926, 249267160, 364122774, 134338990, 740494115, 173915097, 659543286, 1485915, 352617189, 849143308, 35220108, 358992585, 483078019, 750079469, 50382622, 552232343, 47514277, 744390590, 204165518, 273089341, 949572632, 537264966, 802513036, 992183283, 563255606, 234650509, 965216042, 469195486, 743664524, 297681891, 592837399, 381502985, 401408884, 573590229, 69807257, 789857387, 234632127, 892790860, 987228509, 562062125, 353072107, 303513245, 508343118, 861457663, 691259846, 408040444, 105499650, 975807021, 833229321, 826704432, 231459788, 110374165, 359794964, 795020559, 885788309, 944409392, 281026772, 717644537, 142959124, 47344550, 397053606, 143124640, 331699547, 947549452, 302837089, 42070615, 634262406, 264289754, 545486565, 711066942, 795044404, 322583336, 723693266, 717523301, 486716260, 262864483, 403046285, 252218198, 455423920, 70131662, 183838862, 151325702, 771592565, 511425883, 478537264, 836619313, 436473956, 514921220, 979889841, 213928783, 512405017, 638014610, 337357992, 303167201, 335471463, 234275375, 722551790, 97773847, 38002053, 263456329, 439480896, 402944023, 180297267, 134721440, 170909688, 508346464, 251469673, 145287981, 721450817, 838861921, 696240752, 326178725, 51109783, 447139878, 921621522, 628372391, 448278910, 38552630, 701141761, 970994769, 44155232, 96112281, 790563874, 260165122, 698261937, 362410678, 656409726, 978379578, 177760713, 367373710, 204255750, 59702440, 99688330, 438494480, 806598393, 190953048, 350801135, 42704133, 725137975, 32150981, 413273570, 25375826, 381388630, 80106413, 640908171, 689781470, 348988253, 745813771, 573398239, 67501696, 713778019, 995042047, 162470258, 54748706, 710379897, 507429422, 643332074, 969025571, 217696222, 27342122, 318211121, 915210972, 611154364, 643439001, 959481397, 433512782, 826934947, 161178457, 72551132, 753420119, 771258215, 850001796, 450179159, 607495265, 497969333, 418343914, 881995633, 11545807, 804327193, 387454741, 148522831, 271320338, 875179811, 875197437, 727507637, 522804663, 3446556, 514217354, 818476421, 359153621, 143607968, 211916325, 612499820, 85604557, 301288365, 801612197, 964974767, 342097550, 538901963, 440973359, 807146163, 80075582, 320052621, 979660077, 397206430, 62423570, 248533194, 927327549, 135964089, 317354882, 725939951, 449709189, 991849147, 302323154, 845445725, 877710623, 48745123, 281960231, 351901037, 394776954, 877097293, 652275962, 839063531, 378191472, 581997797, 282350815, 265370047, 905611198, 710594388, 158936117, 865801692, 866585384, 390245912, 787349240, 500075554, 453923759, 782912311, 371759605, 388331703, 814279542, 689597862, 611375634, 103378527, 714982719, 916251166, 299014930, 912761223, 946612162, 100484425, 299860204, 493794850, 27972709, 574551456, 135006052, 618085924, 889307304, 563797693, 897709078, 76787998, 267892918, 335610078, 181719055, 350076104, 805118734, 405784662, 575796573, 950324999, 498749742, 15908423, 678607014, 158693669, 387340010, 743336020, 205694108, 658260049, 240773263, 567519358, 733797760, 459076840, 108551197, 551842044, 821441194, 650986461, 450357785, 792989760, 32620599, 182038843, 670129088, 126427264, 418769502, 444468600, 43147711, 652638983, 610421507, 49792595, 875380084, 695801476, 726743202, 46818457, 853602206, 188362529, 464197583, 177407883, 893033934, 980403255, 759397935, 16588686, 796941254, 168145411, 552900316, 590180409, 389212311, 760147014, 914040915, 255640206, 964621421, 314041082, 301159850, 990913388, 823242406, 224150399, 511663028, 83794996, 725258912, 982255769, 387301512, 61044918, 604206715, 6560635, 159003373, 876065923, 446458685, 575819420, 595707192, 515396707, 977399506, 46243335, 678188680, 861252723, 295499368, 2403139, 59428282, 978041180, 841329095, 838569452, 172413884, 686592205, 364878866, 903413213, 540325791, 628297897, 659994300, 14327929, 92242101, 704084998, 563861770, 888718518, 486453265, 843416941, 923148550, 596845218, 168014666, 937261383, 434164362, 460076957, 504638254, 781029187, 500031230, 192344848, 905126583, 801164972, 36962633, 799009782, 714834576, 598872362, 394999835, 708517593, 333901620, 95535125, 952630806, 27608092, 293135020, 494720277, 133660921, 957123208, 257324240, 413915064, 130731254, 442856784, 303012228, 542439690, 735719642, 298099117, 200171449, 736276902, 872647012, 990034475, 62094518, 325971064, 41742423, 931395718, 989550689, 773128436, 759777896, 890389535, 35777385, 143149843, 405263773, 437817131, 676086317, 998863129, 77826230, 75452282, 794677396, 905163618, 255901761, 621933811, 260169603, 660151089, 251332905, 578717666, 881444813, 615405590, 123720284, 529124547, 770526156, 993872760, 484469853, 572811385, 732782192, 258758951, 732396703, 828635931, 548055559, 888768533, 727443345, 566718095, 677814307, 227924775, 190101187, 243210363, 359218445, 214159932, 813589143, 896351428, 708242100, 880178317, 511402059, 228707181, 678425026, 936587129, 928103065, 643237395, 679554959, 245576905, 772031417, 499476389, 637959694, 961913239, 883745675, 511961423, 989622873, 98185944, 552152707, 455826834, 458043980, 963808855, 975911847, 746007704, 819155874, 878642872, 695738095, 618663713, 949279228, 980100962, 793310588, 121138824, 769838415, 339332915, 694724109, 23758255, 841431865, 813624776, 899607254, 943905277, 938634110, 684112090, 110543979, 146741571, 50995361, 293070168, 485327105, 308561943, 757296883, 875128196, 96792046, 269805462, 735719240, 87242995, 644878879, 316499840, 369383257, 715063590, 522365187, 69370398, 628879089, 403054925, 929626750, 674766610, 172236677, 794064729, 604488596, 922916520, 72737291, 741891931, 972622550, 402549104, 786486198, 287508226, 948988935, 113987743, 582851672, 449940500, 763087817, 367676502, 195273923, 352049570, 24825186, 141433577, 838274923, 596323450, 471562200, 517569326, 760050218, 28926339, 778042322, 546981570, 127491680, 862255330, 29867446, 394065726, 195911953, 781401443, 504070639, 419382622, 736500216, 750644628, 776402254, 948438021, 550482791, 183683835, 374064047, 264930782, 996142570, 462216985, 159698236, 534997270, 957659958, 652435467, 385282047, 632702530, 686636003, 496329990, 588308517, 306167660, 915276882, 660264085, 261206539, 529577767, 526043379, 960527825, 371472137, 143676938, 468687928, 763070459, 900326149, 747698078, 960890996, 659972215, 640638845, 932279137, 680389901, 432892663, 962683918, 236756674, 778051773, 956869579, 1864928, 176042658, 941338650, 113407588, 598546948, 221292248, 862553852, 817497039, 876630419, 588138775, 486586696, 530658755, 488754115, 925026579, 748713072, 951595903, 141495507, 316806354, 262928959, 686156531, 577060825, 620020764, 55122958, 250923065, 151216116, 69928311, 503298422, 658333042, 357841527, 229431227, 600298001, 996265243, 584895494, 318657894, 879571698, 896795154, 886208711, 289896059, 434529256, 366654896, 685369052, 10158723, 909205214, 763208513, 652782790, 971484869, 780369892, 617642165, 223842894, 135471044, 150643872, 588884754, 916035068, 773790979, 658913006, 348128187, 835334282, 469632201, 896883549, 225718400, 930694631, 548746683, 126220038, 683787517, 412506219, 233298896, 167805799, 337681339, 280224351, 667844210, 773517688, 63351775, 987180971, 321854021, 923154014, 336248902, 900068433, 303905794, 161353114, 938345246, 41175877, 416314606, 752708250, 475789286, 632730991, 229233958, 740533274, 72765360, 70184957, 306187474, 295147514, 845469061, 699516525, 967305005, 273040619, 234392177, 518780922, 993147839, 34470897, 430058336, 965412926, 155696676, 905855881, 640023894, 692195872, 547009835, 640942550, 224326714, 721935623, 714643218, 722088582, 873585914, 540273932, 473874320, 349040499, 117943897, 687298970, 741273642, 989936930, 202009241, 438385979, 623982603, 44218362, 849356684, 368584983, 257509090, 41556264, 703173890, 397118505, 489176745, 94049903, 830648559, 237843559, 156503529, 958454600, 211394390, 81836913, 563888047, 164872458, 550543095, 548873346, 469194972, 731584198, 557556445, 950902226, 604221875, 263103555, 41203706, 703440297, 815560508, 362997023, 47327310, 213268570, 198239150, 686234695, 828177661, 254018183, 847755255, 561459186, 109893133, 527528842, 548232939, 996215599, 381073207, 47310263, 778461447, 724775851, 137464861, 398507028, 233902132, 922365606, 443949593, 753912916, 293083426, 320370985, 165333391, 883445137, 990945525, 728536063, 249591004, 202500290, 604698034, 264843630, 775305845, 100598745, 413088633, 597646407, 509158444, 257792266, 107649747, 409731741, 22114873, 119007590, 135556896, 485923556, 482017091, 61925401, 80733447, 521040661, 960358823, 573433162, 693326284, 587229693, 577398563, 770292102, 442548455, 16186533, 815007675, 979726830, 11419931, 918322745, 222591662, 149499837, 692412536, 609644521, 666979184, 14307163, 667354471, 343122859, 948228710, 666778160, 261443494, 340746107, 901511799, 109002019, 773147263, 45977041, 423016367, 853863415, 820303653, 123329754, 396563912, 371167663, 5174532, 591171828, 612946599, 655823739, 799022885, 221543722, 999025968, 427023907, 616779060, 543906488, 964900222, 766265513, 341183172, 504675079, 733475147, 618991188, 684419770, 424705378, 543362883, 486796195, 755850608, 319341040, 28895222, 493750344, 127371669, 586559122, 763184998, 850335179, 745631429, 738964534, 724601597, 535927203, 599840601, 779771727, 86462472, 523342504, 761368795, 727686122, 293606588, 979292766, 229750365, 562688691, 808116415, 293770669, 441142124, 663284380, 250589369, 122452513, 533741283, 632056635, 973161809, 825678961, 737784484, 228636052, 70787389, 938786943, 356478742, 497536600, 905171869, 576763735, 668168745, 303524093, 13728102, 568475085, 130340752, 151682600, 122756996, 774706136, 68116481, 11078552, 311623321, 796971660, 802195981, 714738303, 732069753, 495482396, 82680899, 723178060, 920016478, 660359656, 284338357, 934260049, 750233210, 442501992, 145277922, 787106515, 556983803, 913098816, 160657621, 446512121, 838272604, 542632262, 804053690, 131442646, 705329977, 213468155, 764236929, 320877037, 381665354, 731189516, 628434050, 592667030, 766967476, 728109825, 368906849, 798029692, 420832609, 632033476, 800727529, 282253708, 468786234, 95777256, 357452923, 270480590, 754484317, 468231130, 938856586, 897804419, 533195164, 818633313, 323041572, 92406074, 7348017, 624860376, 496061253, 925290011, 955328203, 198946938, 322323360, 124747525, 190819177, 22684122, 499602772, 419448565, 641227954, 662172938, 703467210, 1852176, 679402470, 766491616, 853870808, 373406034, 670829864, 681511546, 205518726, 326725184, 275818422, 304521169, 862566852, 765511949, 59425234, 547890217, 916634345, 260341415, 708066847, 641490687, 104919555, 314952705, 150133418, 736205191, 252950931, 701605690, 139056781, 143679253, 687959433, 349525669, 346385928, 147660628, 700838464, 767943134, 671065992, 751008901, 150929656, 269609358, 535064972, 99766405, 848970262, 264371149, 335796848, 719218818, 9940227, 824290150, 986114192, 808445529, 424904670, 324279123, 220351840, 324290984, 833970024, 767665757, 559241827, 185165582, 140601521, 371780144, 793231567, 19894892, 430883585, 699991969, 889057858, 78929471, 149634271, 135069669, 120810408, 935661469, 683389647, 959037732, 778754578, 400424986, 817760206, 280428126, 214201670, 669318707, 714734433, 97333924, 384127674, 345122746, 141818128, 541931210, 985551490, 462789767, 478669034, 532793487, 558722969, 864795904, 725225090, 353538775, 926719358, 436671202, 591282431, 162099606, 998505748, 128994065, 908107409, 235558687, 585367523, 687337610, 977404339, 402638533, 710941136, 752780150, 424407648, 874828482, 919367474, 109746069, 619604742, 842015298, 534573590, 277644816, 776422371, 44957069, 153150338, 810400200, 521917051, 395006583, 640896140, 732232983, 11586803, 753322675, 599272868, 279864049, 695356348, 380051579, 746256011, 184162653, 818432170, 378633177, 527723407, 438043093, 425184002, 248857035, 240253943, 544859581, 974319774, 610800957, 995837925, 967977540, 241841313, 707513632, 770945505, 2773393, 617972447, 524660504, 986559697, 614537706, 109843413, 840751530, 800274315, 879427851, 636959428, 464854741, 752595672, 600003994, 56520576, 760893470, 136306590, 876395109, 692286217, 502841047, 423380576, 61090198, 894866861, 560995886, 214348358, 39884570, 712571316, 425079536, 694569095, 704361322, 877671755, 831089344, 159204254, 848018792, 330229320, 965656881, 690165615, 985303270, 767209802, 696087630, 904657214, 142984579, 542793650, 715330369, 414910452, 250382445, 42810572, 986162704, 990023361, 164643856, 101797138, 602476779, 336642993, 600318339, 313830982, 236358810, 205323882, 638712614, 771922573, 588916727, 845136229, 536523287, 192579719, 841630137, 217180380, 119603173, 833597815, 292095677, 320102446, 14905830, 83603725, 186390955, 725883945, 400795847, 144232290, 211174276, 19969981, 773005708, 231197211, 793221499, 110039785, 255782499, 229367973, 379108767, 135023214, 403590337, 766536063, 318087147, 437306221, 443159520, 53231197, 187914733, 186485914, 947430477, 824880312, 99845325, 586310739, 147880745, 757689942, 480225865, 884196104, 724458463, 437300611, 528418070, 794761615, 81053361, 260935829, 433993397, 486730705, 409208184, 227898548, 166952317, 326203202, 804441387, 970435240, 213109729, 299376038, 608484533, 614086434, 569726618, 642417041, 939807507, 501528654, 521631135, 642174676, 768013133, 32664160, 284562482, 463754885, 528806925, 734919163, 474628748, 601194090, 249544527, 771510533, 645822504, 219348256, 308851395, 487048350, 354027557, 529222429, 233041875, 796744258, 344722296, 54456119, 966170966, 444614173, 106160788, 92379911, 542153412, 932589788, 21084285, 66689461, 435968342, 284961973, 294348860, 302741628, 545766375, 274948478, 658770497, 372058635, 389839982, 814102898, 763128115, 553904866, 794171112, 727875519, 317183668, 521352642, 580884019, 830802225, 985392151, 797419239, 629907440, 637403157, 418749339, 261634107, 463480826, 374311457, 479057829, 140194937, 40370952, 300461749, 389921145, 282864210, 471704331, 622484842, 907092139, 919889922, 887950227, 85008962, 124813194, 562004291, 897476454, 993609390, 404455091, 206455668, 243914991, 414149464, 64360883, 318681081, 848085621, 681839858, 967338519, 318545130, 458081651, 209603701, 917362653, 564129151, 833454844, 58462927, 940068900, 833518678, 220223820, 339608426, 391518142, 299640446, 769413547, 495099294, 401146699, 507155190, 118029580, 735427658, 677145253, 855991427, 277340214, 679562578, 826011061, 266456921, 265927684, 777632559, 810447415, 643970436, 372767736, 321921330, 451658917, 867577908, 181474705, 683271196, 279862204, 789125808, 298236469, 986691883, 930082443, 232896174, 298169652, 367684932, 318634145, 798891381, 98818838, 705157878, 167773018, 75154030, 202385048, 315947231, 735818772, 806517444, 330913934, 797794677, 396553846, 136074564, 101598923, 658865658, 351358164, 727537208, 925896815, 73336052, 316107707, 616332995, 929450055, 994943597, 997132741, 723060435, 320006446, 374771345, 335247825, 834151687, 498083513, 701705956, 386598606, 302167781, 675221844, 675117933, 578222047, 737243707, 704885387, 739217281, 809988831, 390797612, 745954865, 677885937, 391719278, 666004980, 642750899, 454836291, 964117552, 762298815, 535051889, 79469651, 135488966, 935527747, 728181968, 598017374, 232778268, 819798847, 701308356, 657166794, 647647231, 376664798, 300645991, 741459030, 861564258, 710762354, 50971726, 329060413, 324196205, 626600453, 608408865, 772816592, 407112287, 376708593, 876193677, 886854642, 74760775, 35784394, 712288626, 643612706, 437347958, 592694728, 578940060, 390272813, 541448221, 875382927, 457952254, 322453710, 408058610, 566599132, 18886587, 743645638, 228724009, 738709622, 850491059, 744659002, 294186725, 845792042, 925495606, 153124415, 287462864, 794054943, 195333208, 322361003, 572593617, 86804752, 66769471, 132085725, 308606842, 614117544, 361700944, 256597380, 144681895, 272949560, 6859641, 307359239, 533564250, 496470802, 551335910, 433102387, 45805144, 885594589, 455145636, 32686903, 34556333, 176412464, 884193066, 482503837, 903104170, 442038892, 37281303, 253761603, 419253466, 966537319, 439651181, 228478121, 804736847, 199182714, 309477271, 815705171, 511124741, 135187980, 53348787, 14619523, 389280165, 588465017, 304942713, 108788547, 572786800, 331692029, 118166083, 533690604, 962043242, 530590007, 211766443, 995108204, 317883054, 446335474, 13653370, 151359685, 43405803, 702208488, 474292709, 866748661, 410157439, 311602955, 642160460, 587369861, 536644904, 440559880, 894780571, 79925606, 837947309, 905687497, 253322863, 268972503, 118232929, 645801423, 97235104, 380554238, 395002598, 470194092, 845062624, 520119405, 50649832, 481785253, 725124531, 938125894, 391603298, 266153685, 328188582, 472665690, 893333876, 86934475, 174029777, 454087773, 874963800, 991495711, 224468844, 872581620, 651803981, 523586516, 508438322, 823886942, 816836362, 840054325, 963670520, 900145393, 337063505, 333570810, 182227852, 486169920, 600941438, 349268875, 156123866, 136390574, 773664267, 890005139, 945843524, 618995132, 848920491, 152661243, 982385936, 363201339, 530140041, 32290103, 93273673, 559952565, 632851955, 915567826, 556840431, 458635736, 830120820, 670525962, 504513389, 389372953, 718326486, 612056870, 665752457, 211491411, 846779777, 824718181, 495924958, 692398841, 959054757, 23557249, 414022349, 814350440, 425282957, 80292023, 199274393, 224843545, 246520811, 206618574, 992652418, 612469681, 408484592, 376838628, 38405177, 778505846, 151771996, 904547726, 19727132, 713202228, 989466118, 430267299, 977421269, 691089740, 376751903, 515990152, 650376375, 861894823, 145115471, 55672274, 734369547, 964193207, 468953012, 445495317, 535704766, 408699544, 166283998, 139941389, 237212303, 447265928, 616581199, 574107788, 649982766, 883967291, 36274920, 627580659, 997115144, 737259321, 84091577, 715916418, 900775314, 578508115, 208560649, 115498904, 265565893, 719720048, 748950174, 327250058, 106475586, 212863650, 622778591, 30337435, 907043881, 997311675, 834291850, 964202613, 507767464, 829570922, 795307828, 494170145, 108744165, 96938833, 513387679, 461489248, 696110062, 170139187, 3227602, 188419447, 496815981, 857654973, 259949843, 360529700, 301037714, 210858298, 743934717, 766306082, 743378069, 882730339, 502774557, 819756889, 639263650, 20626285, 676808621, 20354810, 641918017, 736814330, 59789319, 376067608, 358490539, 469175327, 63404781, 504772403, 586790040, 565798435, 362711253, 752184707, 951541265, 609110988, 463690330, 755539008, 78066373, 673193711, 139748648, 636283218, 184106540, 267258503, 15263995, 601958933, 781284644, 494561805, 287653110, 590253963, 505752075, 653929099, 127063079, 589447023, 727395196, 730111825, 952375782, 248930184, 749255835, 982449204, 747599487, 870611105, 360968813, 552874133, 201539611, 594720335, 346599828, 401045034, 453592701, 86757586, 952272348, 366218126, 519317258, 170437409, 509156379, 8129882, 489170057, 510178445, 542872261, 983045333, 66542734, 179668892, 182339457, 286072885, 522541154, 156717941, 436268971, 981623728, 243445503, 795015877, 43936776, 625331171, 538984196, 365219156, 980305313, 101442336, 962398703, 429336051, 253548586, 353754098, 864657896, 663626869, 22800267, 221718636, 842227589, 904034798, 662689385, 863239320, 251478649, 83530103, 267225908, 504095527, 366659290, 986917293, 378949772, 573918055, 804074442, 28963827, 877801936, 134114486, 683582861, 986964220, 910531177, 455811316, 412804165, 952817834, 878699020, 155980752, 791532949, 621904697, 343576206, 162766437, 5607776, 553591409, 461501391, 47614227, 778357318, 483128717, 159409865, 838757241, 332130875, 338431934, 279874014, 111336782, 230379611, 145468718, 666095199, 582843105, 138164651, 384220008, 224690943, 219604087, 913653740, 266555964, 32825627, 675131353, 68910217, 812466110, 407644144, 733609521, 313197533, 670180321, 291282653, 851322428, 842607525, 69158326, 644683224, 895320340, 196982786, 235702588, 24974190, 788372399, 408003321, 126442540, 359616978, 611354299, 983763378, 446134050, 336699380, 616577570, 871189094, 326474133, 810492588, 909916585, 395807651, 916566056, 13413641, 89832354, 799073494, 110348738, 938972123, 470874532, 964750208, 854265487, 660134753, 708790854, 688918173, 138891916, 886382749, 223659308, 329224850, 337793546, 429982678, 637264789, 236351526, 179134911, 641404727, 813049033, 897176197, 796695739, 446597720, 750385352, 349207654, 370147998, 145231668, 90937993, 692660077, 895878886, 848808502, 739870579, 549181382, 178374293, 449736225, 47741791, 77945718, 370737785, 556076713, 208643494, 429788360, 32166231, 223354216, 17220225, 774782561, 18161840, 626404037, 326918465, 21158233, 289135566, 678438564, 465378370, 457159316, 273108098, 533518841, 269648071, 706486889, 475718713, 388581831, 69773757, 312978516, 234047424, 551252908, 768791974, 290950419, 128361396, 221288489, 771184635, 109991697, 59034412, 646574489, 663064871, 134020825, 900619915, 646865896, 314854956, 482429410, 863152067, 334158461, 100422004, 374804504, 575883956, 939347278, 697044614, 563802389, 551073818, 68406001, 80560985, 447397234, 46433886, 361793631, 9922670, 510111369, 566426459, 640523265, 983318793, 831528365, 637846054, 799921018, 989381502, 925350665, 205751204, 349294927, 950764778, 960347811, 74932193, 754959053, 953937891, 431377926, 599696603, 934568857, 69960290, 673938518, 478937548, 876173022, 947758506, 368878899, 239193094, 859414828, 670428817, 590208953, 966311952, 366046174, 238501698, 758610045, 175376800, 497086777, 353332811, 690645448, 373785761, 62249379, 263910698, 41659919, 768985816, 259526346, 581297435, 9116755, 719734226, 188398697, 978270757, 199170175, 606529753, 346838945, 784158581, 186420207, 140893477, 492586742, 702559751, 507887020, 582854242, 842813212, 58516652, 451599527, 609065459, 755882003, 233957277, 576993846, 85620898, 74056383, 288521624, 646341670, 247577538, 336048000, 163310897, 607926585, 948549899, 195578539, 787853801, 841921349, 504189152, 506939826, 85190012, 52902058, 308930491, 961700861, 790508361, 204187681, 544832705, 212112639, 621873681, 819683184, 784174519, 59106329, 925738236, 689909544, 231501733, 963501959, 934153605, 40074772, 664380679, 118367355, 839889348, 509277770, 8847783, 136655527, 493080778, 392884551, 488214790, 73740874, 228863003, 979105535, 713021563, 509867357, 704064117, 663027828, 800423748, 545228551, 580665472, 322418656, 977245905, 765248190, 951015523, 190331532, 98038073, 289472084, 774789763, 809720008, 360769345, 374928879, 799501989, 613666037, 328362611, 977121845, 279586948, 761518660, 104593005, 428596923, 500966732, 122461611, 133416156, 531369538, 441579339, 561087057, 541401335, 484551478, 962933909, 68828815, 936262422, 245192795, 302108729, 574804815, 736772182, 534283273, 164177857, 25870604, 951483887, 588166945, 589931645, 975390755, 872467997, 599678330, 464797505, 817348087, 376252548, 176091685, 989508962, 574577914, 959741275, 977829102, 181920390, 770240365, 535067416, 508163218, 472321680, 591967885, 726403076, 470480205, 892244149, 745115632, 809117891, 840869599, 522610393, 39366727, 621260115, 717342009, 462326160, 382647137, 144060920, 576714448, 347349925, 300746360, 149577339, 36076501, 361008706, 249020640, 980626600, 636806777, 474857013, 373943378, 972747975, 936227862, 782525928, 520855724, 706109284, 724031189, 621285377, 793941717, 594439918, 596022720, 423053126, 715539454, 658023840, 981037499, 900853822, 593076953, 312938548, 621751578, 128577187, 868964449, 370300345, 204233601, 759407020, 730487272, 939429511, 760360169, 607099419, 234153769, 794403822, 973717478, 712319924, 825817032, 797810328, 58866618, 728749947, 921727999, 712719588, 941390903, 502079886, 357537801, 34558441, 839903620, 737032587, 690314283, 184292713, 566645704, 748997692, 874448775, 895240876, 924336378, 163030313, 404514069, 755798542, 888128182, 230860570, 650351870, 859823840, 588641293, 963381129, 586188270, 325491592, 990348641, 550024371, 346105434, 54338953, 793847088, 590837772, 364789743, 66517391, 599678650, 404648195, 986403122, 400828672, 379826444, 93073034, 798202695, 948199485, 714822736, 420265248, 292025334, 852670803, 119652695, 6606489, 932703888, 522556738, 833677381, 762788956, 214181591, 315978937, 352251616, 955740766, 947441999, 30237661, 466782735, 504703568, 41764012, 680117786, 988670382, 349917913, 439230303, 779641867, 238176247, 323670141, 645509058, 43437344, 14838556, 662998229, 939103706, 972738981, 748044544, 713008489, 942955268, 35804957, 825012336, 831958908, 277297462, 656991762, 388517540, 94607425, 706921427, 839535921, 136731811, 701997233, 777391626, 380426638, 231791464, 364306933, 224630061, 985802659, 556848798, 260432290, 616502258, 923805925, 802796589, 602764088, 402465867, 108075762, 578459907, 411352971, 638461704, 819914019, 678700331, 119248952, 730903122, 577979127, 962072683, 521973496, 729988248, 541877104, 913177136, 400208668, 347035522, 529595463, 251424564, 533313977, 22475977, 106957132, 861872378, 995192314, 447261267, 658190210, 532692232, 620227724, 566026272, 24116753, 998333736, 11501490, 670680749, 329768777, 149715320, 794868264, 391746953, 330068789, 307322419, 249174033, 394267228, 233279729, 84287000, 729892112, 124624239, 682906059, 551094950, 716081689, 355690625, 67015773, 895958517, 144628419, 814004160, 983335457, 216952369, 714948515, 655707309, 849817174, 515758708, 92191059, 246444143, 242776055, 801707408, 967120967, 536171252, 285719234, 198404249, 497392979, 72219855, 973161060, 173184891, 71824281, 856813078, 827102161, 158013431, 655185139, 846195372, 850895874, 986407185, 987852535, 341770458, 247410980, 566673889, 96060634, 646113030, 76480317, 784602436, 735448001, 914843745, 518308140, 919120788, 973740814, 653853583, 390656106, 561738876, 414030318, 801746413, 868651505, 406778313, 666991066, 336058286, 242661779, 174787314, 354954591, 523429725, 334257202, 805322691, 497841642, 423797828, 335242058, 514620193, 779657426, 458600046, 56503647, 741670705, 702436589, 904185919, 458162468, 616550242, 566505940, 320146058, 634233842, 892033784, 677431498, 329374425, 528469945, 101644620, 541245319, 362323162, 862548172, 215363395, 339856918, 769333535, 465965061, 521366376, 798224113, 603007989, 283873806, 652484383, 85156567, 253390545, 566617675, 144777563, 388755797, 829554604, 795086383, 321652635, 152023942, 337516377, 182885998, 289843418, 833943168, 78822898, 619646641, 925518432, 418386802, 878701817, 113022893, 768488409, 847597656, 500390984, 973929644, 611932748, 861971546, 409973463, 682697733, 175075390, 745062616, 734111998, 659729631, 85827156, 470581355, 317215293, 685419000, 850245144, 512390821, 623610047, 197636379, 78913203, 184307390, 445651469, 54216151, 373746002, 814057587, 636993994, 510301635, 75169271, 801241368, 521360958, 155608949, 653318400, 735070407, 882112988, 234904159, 707451243, 165607957, 18298824, 644464980, 836669301, 458572658, 863379402, 607893209, 303304990, 400711305, 350202415, 772711671, 85562967, 520417813, 719153116, 801880482, 764952491, 905686983, 46800229, 362276183, 793320715, 942622583, 28477967, 483867128, 997852191, 770683831, 824162142, 686420546, 21006633, 83914096, 109939866, 132575583, 857850770, 954124235, 379303337, 464609206, 738524200, 255374020, 781768297, 387360208, 527124036, 588280960, 217926332, 669759414, 109806802, 293129429, 588011701, 369938881, 536412684, 600306029, 264535428, 177108850, 397315142, 288419401, 435139305, 368733747, 405435077, 574219769, 428458307, 797372882, 678967488, 684473439, 979571950, 617514840, 856811950, 43683265, 515404807, 415550465, 341147280, 483764641, 688306296, 190147823, 603025837, 663537828, 503734429, 272195385, 84295341, 524441915, 977981106, 274845540, 935186661, 929889741, 601703154, 282942465, 832373333, 286194255, 118850994, 159245110, 747869597, 592498920, 705017285, 15672379, 476278257, 196185957, 730175958, 239299541, 850975211, 165931132, 232159600, 608582730, 219106843, 820085563, 928101393, 547071346, 135459848, 111064620, 578150358, 669865282, 762777801, 137546177, 921314788, 279166616, 913418356, 684362628, 421568778, 368481929, 767024213, 405888725, 395518758, 521606038, 97275232, 88502510, 884572837, 461028363, 710582613, 196720887, 122571153, 26827230, 522520046, 700907017, 623668052, 65624186, 465615059, 23740015, 288068727, 161130849, 633996895, 521352717, 891914162, 736717189, 250904272, 188093774, 227979479, 805459651, 826472644, 591963918, 244324070, 546228642, 94967459, 819934443, 160123850, 213324842, 197610859, 185961750, 534171404, 831084729, 525660906, 713449163, 52244499, 104916178, 704457237, 497315992, 804506785, 991307728, 505725950, 161097587, 254634232, 964977009, 859797017, 63919266, 199242516, 669995827, 70395628, 407226633, 646801574, 852846786, 134819584, 968511605, 578436727, 113465095, 414130209, 219556131, 940065303, 550110580, 518664680, 533739764, 654827226, 117333355, 632415088, 221318246, 745153814, 578810069, 665043401, 212844218, 589688770, 1205503, 160504413, 840689855, 234858627, 654189047, 61011111, 906593389, 237108709, 914848934, 262582740, 195527104, 928644740, 303752501, 342327150, 630261739, 975170849, 235251731, 545752590, 352613047, 492175523, 12261076, 497195032, 850200854, 260713353, 825829736, 257477582, 589387562, 928405293, 206157591, 949181802, 360849585, 46741251, 295170199, 706295111, 533005651, 913306632, 430406394, 741165857, 80021536, 796900536, 120961904, 945295298, 503699377, 823026863, 864076956, 145683753, 163558109, 256599978, 422673187, 447914234, 142468997, 31147789, 818965358, 594543813, 296303157, 249567419, 363369253, 338085283, 29628428, 356155356, 51345863, 456529078, 454784804, 698937652, 585822628, 74265788, 175260154, 458538002, 230939120, 232923485, 469548796, 838239513, 96086155, 628023891, 227459915, 425460631, 993421207, 264262663, 275206241, 172747344, 151804428, 565451014, 89812929, 490047659, 432136891, 705658100, 822208812, 771627003, 947267948, 33541487, 639644191, 613739182, 236816760, 748852163, 601725339, 269944973, 92981780, 215717120, 773829412, 803903030, 577144986, 299162002, 962516923, 801058070, 447283735, 863351163, 451532659, 706986630, 202514234, 281319266, 754320382, 142719597, 294399743, 549907959, 640829798, 909892845, 302510270, 939178705, 566223859, 80213564, 88440945, 373137426, 351286323, 862895698, 918248913, 849726982, 180089737, 173106597, 410742198, 432492815, 661614304, 547529598, 983521541, 198071539, 126017389, 370338220, 541782419, 218443222, 830989933, 352969273, 387380376, 140055440, 841195049, 552898958, 166452525, 560206661, 829341339, 753650047, 123074525, 628131242, 332790821, 840548027, 72009381, 384904738, 609014728, 96424802, 460002418, 595243342, 837870170, 69695324, 878134806, 544095881, 61215947, 503654930, 816059001, 619468219, 276779715, 598800030, 897738735, 103810351, 93089515, 714224793, 881448085, 371175153, 843733907, 362560589, 20289362, 620895065, 84695449, 869708050, 675467852, 129037906, 382975751, 625823232, 356284245, 76015016, 327012849, 436684624, 141933157, 803595559, 327182174, 537684153, 781397188, 77662475, 420165865, 700286416, 796299995, 320951803, 731905165, 749115377, 984320390, 393545864, 624095621, 955450889, 489947084, 236203250, 80857222, 470995416, 951285508, 787951557, 646472072, 761708369, 812139984, 788466185, 31384586, 839766709, 562775948, 139952842, 919745781, 820719003, 706596706, 399043067, 444197511, 575249403, 312553277, 796552355, 325460064, 567306718, 482185227, 898980249, 223432726, 899496448, 621613996, 350837707, 965679026, 487872058, 737161698, 804657984, 408251822, 783478500, 337445798, 555204131, 735108006, 766183939, 209973681, 372720545, 571674581, 416301187, 696277719, 163534652, 999818146, 30590342, 798589899, 694460848, 655814183, 244366492, 906589106, 610862786, 356838282, 926475778, 937122236, 459395723, 452086887, 588973167, 986964719, 724940159, 522712810, 808932525, 916436498, 776846029, 311562741, 242803330, 599380320, 725446071, 23527501, 60421952, 227194823, 973365632, 106210932, 327262111, 708491323, 741124486, 547238252, 475699520, 306510071, 359402814, 344777535, 204543331, 162599917, 491636895, 530685425, 914844145, 880792222, 853366643, 76578823, 214209159, 423847362, 537485380, 683016635, 705096175, 244533398, 966239035, 776000687, 240691101, 588731100, 541684456, 688172583, 121664892, 587126223, 132445809, 834711812, 583908185, 919947384, 381015076, 662856505, 459182314, 736962031, 106640340, 675526035, 951509132, 823697235, 780974982, 252259208, 719029395, 887690181, 200965479, 535180573, 411851227, 323830535, 470094292, 597218120, 857679632, 352157050, 223935420, 334915641, 281997926, 163353768, 38734013, 825453155, 718940329, 8894949, 43398744, 322438157, 467639557, 629607849, 764612699, 620392049, 636202752, 692796995, 493952614, 588475927, 641719531, 745731048, 500883891, 957185974, 211676195, 848581709, 705847154, 337470133, 368884221, 386404580, 800215375, 355322806, 472879812, 154798360, 900468319, 970839863, 520786401, 216812551, 263838503, 472833607, 932924772, 398018424, 463334328, 671492619, 585815892, 223362314, 596263207, 263536048, 751186654, 460313819, 459759862, 793458978, 315934395, 410097766, 278863467, 721237419, 543877132, 860850304, 824053240, 281103572, 180739911, 520622343, 948181537, 44061155, 329406026, 338418155, 414983035, 919201749, 490882694, 97030014, 855327287, 516933976, 483067880, 281127190, 774444700, 911361611, 355166865, 323963799, 719114777, 480826569, 814281471, 560821782, 880389161, 423475300, 158387097, 821219147, 857069543, 942343282, 541211718, 742509905, 565682167, 306730301, 920437478, 545348230, 78788805, 15028511, 32353416, 611567357, 805587935, 57927175, 905287540, 719098155, 863122272, 911582827, 201907424, 596349675, 131811626, 978112330, 37621103, 106460903, 174457679, 470245255, 960035489, 797359122, 140608219, 409057087, 135655817, 533428842, 676024043, 581130494, 367129118, 850386483, 352174614, 576878962, 972849878, 341284562, 90193885, 844628504, 536644203, 314742620, 174242389, 647992802, 869317044, 239701096, 736300129, 395770260, 686276701, 495900547, 670036213, 460216635, 839481527, 982167539, 361086645, 879651012, 210755006, 158278358, 206501915, 39670966, 775122954, 938088269, 879076197, 476452809, 780612357, 836275479, 162467215, 154449238, 570108767, 517523912, 747041056, 919886302, 305429155, 647880599, 784800816, 537037751, 269123222, 752473138, 434872937, 127054663, 208307331, 674291944, 798338580, 872993269, 401172157, 31513175, 436215317, 94739545, 692244682, 142217625, 543687030, 779438820, 260664801, 278246468, 891315789, 777025612, 189794774, 247932195, 780769623, 962461114, 854533354, 353186769, 219402309, 266800681, 426437118, 825889612, 613862892, 172510535, 926733085, 767124053, 624930091, 282795377, 983304557, 402987150, 420304250, 470365548, 125109793, 942616507, 467659665, 725967424, 682431588, 618490700, 938358190, 748137126, 689737946, 4942446, 263020789, 911156563, 281590747, 41413862, 763724202, 168786374, 373541948, 491963028, 796476560, 380638949, 550618271, 366212392, 802540677, 935837858, 145813078, 26551902, 859908998, 741089122, 879324755, 774152183, 553397969, 522102872, 293403961, 496186193, 631764415, 268840672, 283489883, 411464941, 417291627, 619799331, 312625436, 46831119, 773932673, 849779692, 973613102, 992126841, 414905241, 853962336, 804524588, 656105290, 858541579, 110395939, 206785479, 829208443, 183957528, 662731055, 35781770, 640217982, 420058710, 658375432, 68313201, 818028128, 239760537, 416142135, 953810793, 651614027, 514216357, 858989787, 494487095, 735211620, 765594898, 117435281, 587467512, 590070964, 813815613, 402712935, 15804354, 573914241, 214613148, 389224738, 568673621, 318959288, 602779843, 975574291, 74691537, 959635651, 252439638, 458082297, 39603552, 437297350, 566696572, 983331453, 117707221, 145705636, 779143775, 103787887, 270487562, 913375199, 243993549, 548463479, 914311520, 672330954, 830288691, 367161313, 638779056, 637671261, 303322069, 110959627, 943604802, 256169981, 227095755, 852797938, 838255511, 320953904, 863953526, 14441141, 575279566, 652156657, 217747379, 640053737, 175095416, 726275715, 837783160, 787174557, 409652156, 658790882, 573847387, 563901990, 234563918, 346661955, 961591811, 548185110, 786115667, 863049700, 638957012, 255114875, 288038496, 467032482, 645092113, 285548672, 363713616, 709716174, 444432200, 349084066, 82825929, 335786001, 616960071, 94503766, 795986773, 670604306, 368981550, 962109534, 371121631, 978466398, 363776812, 147204146, 206603939, 970039684, 396604988, 825699245, 56015433, 268981307, 307848633, 218727401, 240449452, 672875355, 259329744, 633364459, 986812469, 537775898, 612099368, 948242363, 345422280, 64429111, 119958242, 265279604, 703981293, 728174100, 270394721, 241347597, 356142330, 392246814, 633952461, 80359525, 980557227, 13963311, 793218427, 773011997, 768939585, 160713692, 97359885, 600189868, 109537383, 141566816, 304099723, 410747366, 990859695, 571907447, 569525856, 160859009, 670484355, 94417313, 667780536, 211780454, 882817429, 939658049, 626881189, 85035934, 595811313, 119578134, 153477526, 348389219, 599139347, 810176540, 721797530, 45900141, 478292114, 472864149, 193745932, 174149504, 558550562, 336485346, 242936727, 797941325, 467779889, 67391197, 258002084, 672875761, 986502880, 803458934, 782388664, 658024277, 443439585, 637118359, 10708628, 723242867, 163909084, 190466057, 407304098, 344872169, 850881357, 870774508, 937426353, 746032366, 502326025, 507091560, 236814921, 118350398, 481434759, 242804907, 565890242, 190519382, 410660303, 588180180, 675786818, 722252171, 501379885, 234148779, 24567701, 460241959, 211612603, 610829177, 707635138, 495982828, 311356747, 676330764, 423686324, 210432426, 111667295, 532322683, 219051364, 53355005, 520742946, 677177485, 870308358, 643578492, 297412394, 361790111, 955721067, 465286596, 910137683, 967273597, 934646496, 848374296, 519076556, 827220311, 789421408, 682391161, 43176800, 373390629, 370848051, 263315065, 15886559, 564272732, 826186489, 210193161, 857009991, 693843285, 527193553, 980097975, 221732978, 368733403, 433713321, 400078335, 280043999, 396627078, 943522696, 753382638, 964705984, 439332446, 853231912, 322972353, 669093723, 807342982, 810615643, 213434947, 30829992, 647675765, 287910199, 693320793, 163599032, 553608597, 979987352, 981974890, 653222345, 299330987, 672380744, 287036926, 129620954, 376428456, 622849467, 591525864, 287801742, 280103233, 733202303, 542327826, 180788796, 178480325, 514037798, 243243436, 277296602, 583188153, 88015190, 617692891, 922350820, 689738783, 648558829, 909650186, 278357792, 99840689, 908065991, 4133076, 307386486, 524163825, 72061263, 999981445, 295494703, 823642500, 542062986, 64961814, 957708038, 184238574, 784326259, 53216514, 809426915, 641804990, 46852664, 420412893, 55772494, 815936469, 175592968, 841048870, 29556582, 528830101, 466328442, 376322738, 92636757, 295787911, 391760878, 834893100, 763465822, 720294276, 93196459, 902156859, 198773285, 220538805, 126924682, 212057933, 360608998, 185176868, 276048725, 991750874, 144127136, 93566557, 189186444, 477514444, 574352595, 681964141, 497737123, 553366449, 599682129, 979480401, 182409325, 833739461, 157961150, 8730803, 952392629, 199845907, 960144569, 735691596, 565130880, 969651824, 171198865, 16322468, 29402316, 751687860, 359039166, 44581967, 815367014, 131680226, 806823958, 177198440, 535040465, 997929829, 154269949, 950687581, 383218593, 225875551, 382275501, 387880351, 724419137, 810234302, 642549271, 700160866, 18954364, 643635344, 183207586, 994045675, 751660840, 365704413, 904391275, 906548375, 671881352, 425291797, 576231991, 180039557, 562107834, 953131346, 401378341, 142370840, 800468520, 398077556, 745693500, 483284968, 539154772, 314418625, 409057558, 486971174, 930523094, 509799054, 323276014, 284891457, 780601687, 783547720, 857462857, 735845676, 722312980, 358858486, 358472564, 718065027, 434985987, 610464787, 127157462, 645482942, 490616668, 878140225, 905288030, 144553343, 363290074, 679564299, 456123394, 302053432, 7602845, 565164468, 583675342, 161754167, 34634311, 262987207, 374560957, 941883138, 705765419, 741289921, 386670602, 595171422, 884591359, 661174588, 823047701, 902087911, 246808704, 991963729, 810723157, 50581737, 50044883, 829273524, 161201354, 963304716, 610541674, 175684872, 676681373, 822577802, 404182165, 627557884, 547419690, 29817491, 680807216, 41816711, 553065112, 329281831, 314673508, 96553913, 406153979, 385817558, 390526660, 680536405, 888451440, 916840300, 577119544, 911266607, 264878686, 149611057, 964508023, 510563214, 534109757, 749434426, 894462047, 365707856, 142447672, 702021582, 644121059, 658628533, 371362380, 59450686, 115070802, 108378513, 347560450, 926817322, 818007524, 368503529, 559649548, 250939915, 528795017, 809171668, 531907075, 194678611, 199297853, 840267548, 852215441, 998894252, 116420853, 331398744, 74396763, 831374325, 776545662, 526629691, 823355449, 852987596, 593986123, 92767775, 846069418, 412471494, 558952815, 639740835, 745679212, 129667448, 653690657, 451524786, 985160071, 364011670, 540100995, 620740063, 929627077, 879445384, 100095230, 70101277, 538767854, 268264276, 894240445, 649029039, 820365425, 28508104, 585982120, 490651238, 158421322, 282650139, 839726149, 239019088, 304462128, 424508392, 244741592, 419244172, 363150362, 973050140, 104803004, 560526869, 186503479, 21350359, 128419587, 401231856, 865957279, 583517521, 249527829, 417777058, 255248238, 233657211, 565734902, 113420933, 866383523, 479927232, 794268506, 382414683, 417591916, 78724690, 964099856, 246666106, 663099924, 184187188, 658613119, 302437027, 814930597, 82629294, 420319466, 642496658, 59654667, 57461854, 992705241, 854176511, 781599418, 587777507, 806242756, 866251509, 156570209, 134587058, 901107894, 617280358, 163913920, 666394012, 614518567, 262078199, 142945736, 890121858, 20498891, 307872700, 958733433, 771855648, 339002116, 563610907, 161399295, 192568234, 918523610, 768273020, 320816796, 658388130, 51282694, 492894004, 711746737, 464952785, 618619932, 383091350, 442916880, 534701918, 770711640, 117731315, 483602500, 980922083, 182620579, 178612007, 862161198, 945781629, 974486301, 912985638, 178488106, 952054663, 909218827, 244769709, 378896775, 927144357, 250737180, 154170471, 744036805, 67565630, 457395778, 825397579, 78386245, 353226931, 956555384, 726207995, 46971139, 259439853, 929439874, 897528676, 809619552, 873892332, 119083417, 296130849, 736104563, 881734593, 526149644, 650624930, 554112084, 427255767, 398100561, 556241854, 925409812, 496427354, 958537554, 396657903, 866413574, 764082278, 867725691, 653702133, 99390033, 542809069, 449222511, 919644825, 28700361, 573354905, 975105083, 544622038, 537623730, 565328320, 449531348, 958220438, 814574469, 465853871, 938938818, 208373782, 773463231, 543669568, 942789229, 323691953, 491874096, 921510591, 595186686, 524484096, 638422726, 602345981, 352960859, 49523598, 773629778, 684660963, 244259969, 939665931, 10596288, 604356278, 846896300, 181620986, 223792705, 686624666, 780581640, 428025568, 615771193, 95321515, 276458527, 730462245, 644726237, 550410456, 630374433, 300245745, 649608022, 250186836, 127425849, 406462910, 648730017, 529710393, 165095522, 143563104, 220092519, 383153221, 451415377, 486972268, 393504228, 234133649, 286755888, 154666315, 983009318, 731914249, 591579530, 56266533, 91359610, 797844628, 577035618, 803517689, 758123472, 384617433, 687159085, 649971856, 454632629, 144243192, 219008605, 881995064, 342870932, 506021753, 603117490, 742378514, 513400117, 604803804, 55189343, 350804581, 968428086, 77156058, 913111470, 779977742, 256462332, 438059737, 496675243, 121055665, 828836194, 729235708, 781587847, 454102447, 58537287, 840422835, 284951511, 718042544, 298775901, 95932705, 413396004, 286580264, 960746293, 869957259, 925007921, 57397366, 522147118, 254214867, 966686370, 790620384, 467627508, 772515657, 333142049, 190017255, 480280901, 775097262, 317696848, 560382850, 998565101, 282008891, 555832848, 544342054, 366343965, 149795364, 552970489, 645016142, 802549851, 921936899, 698836293, 407033171, 304567963, 424187228, 271044928, 514758285, 45607267, 290859745, 673919041, 625115665, 476641996, 40532445, 734599524, 937209074, 720234909, 947753530, 650567335, 674231553, 945737749, 792417282, 213755601, 730397958, 64303528, 11976964, 158066957, 420047220, 320339291, 281883473, 888422798, 938331720, 188321974, 510680176, 529410167, 461247574, 830381276, 136474091, 753347846, 272743796, 665675734, 27451731, 156493566, 574479815, 468333379, 868676668, 73957572, 333113017, 115764098, 542752275, 52719274, 774051935, 450342108, 72289532, 541687715, 582942742, 146312683, 146389159, 748986964, 617814802, 168815113, 965192032, 539013257, 618299748, 138250924, 861194857, 646040875, 125676496, 67312538, 814871860, 108782677, 783361775, 167934627, 641872053, 374117621, 9692201, 577620620, 19412498, 694822684, 615297108, 692324845, 378501662, 425292053, 25631995, 509852689, 795950306, 103064591, 655913053, 394306621, 995325610, 762702547, 586650947, 801234012, 611174621, 744358133, 173051397, 289149114, 885686410, 237884042, 294119725, 729872000, 399604603, 278156472, 132696919, 854033218, 602336713, 953577017, 521666925, 716466894, 123046358, 585258265, 680333081, 819146074, 559702697, 527823916, 978906157, 845408480, 812346283, 261138038, 145312564, 356360483, 982599539, 749474021, 494284289, 600246826, 561518628, 830228150, 903911633, 850313484, 675300140, 293540771, 890247459, 971756287, 509054693, 215845192, 210696044, 690285270, 49891029, 825614827, 10165680, 570685384, 156782597, 890585997, 485640635, 334389570, 253777361, 417142567, 144784930, 608892419, 325991910, 115988406, 237672942, 313008861, 318749265, 509565234, 783258417, 767537149, 200819086, 309421949, 415987542, 912762144, 794529584, 825636848, 188359868, 665419151, 95180987, 437446570, 908272215, 296221519, 162998963, 909813533, 836757726, 848417103, 706564920, 90042413, 853133616, 984712966, 871213053, 485778581, 412011459, 355596087, 994015127, 416371548, 779702692, 127750119, 846498412, 933983954, 744423957, 634742557, 128642495, 666434252, 655314368, 219517247, 95759154, 712219353, 547611372, 32407404, 837400830, 946113140, 330236336, 512899320, 211788064, 461071695, 210684988, 187689706, 413803561, 434369327, 556492164, 629173491, 637889340, 920254562, 332887816, 626764750, 614725985, 796599158, 100054413, 919543541, 552164045, 929424292, 174611751, 338467885, 371190620, 906311848, 429899036, 933307343, 489862351, 36104735, 328850501, 55699439, 158404075, 730949335, 707322679, 365946589, 473891462, 789431683, 649679540, 695223318, 873679337, 346352325, 795518031, 55122742, 494728288, 761195333, 599241594, 761568526, 683213338, 283747250, 106947901, 751458363, 25602653, 167662317, 149888653, 792752598, 976344331, 202629758, 665406583, 885994869, 706421791, 474567984, 873332783, 6203682, 628801924, 566435523, 285649968, 781299694, 119333112, 887661924, 89377258, 517687814, 855544692, 979194040, 753208631, 866522938, 594214260, 442855147, 674322900, 89585416, 966144529, 790312204, 952102412, 168034003, 396972340, 207680527, 558026016, 465726421, 933355393, 922880570, 205703752, 344078714, 51622632, 211367278, 573955916, 304897268, 893964107, 313362634, 813377718, 878951986, 249291892, 399164183, 718198170, 50141523, 296429879, 410924606, 508482618, 752588268, 811178133, 556324834, 289689633, 643754287, 521710546, 421811372, 540138273, 515056109, 255108007, 770525762, 425670326, 919140088, 72057263, 734977956, 64054074, 983444141, 686173426, 296476194, 539802244, 363361692, 740329862, 753110032, 543825884, 321762144, 416538620, 236864066, 52142470, 243316820, 882569809, 576723077, 577883710, 359820757, 93433849, 870231678, 779360023, 469471261, 706339551, 267572254, 788080077, 495506579, 330030769, 498153617, 199201287, 733848076, 872621042, 943120463, 610028234, 93036599, 6797612, 823919509, 879226979, 314157475, 96176735, 322471631, 571978152, 279975597, 281392319, 295457155, 251364909, 567929723, 815621761, 771204360, 766731491, 249113918, 934042574, 708159224, 986698375, 130225562, 655421411, 632318562, 625638698, 974632788, 307493896, 188708864, 156470409, 965964337, 552964204, 141569499, 239983567, 219971399, 303685561, 848629731, 476507339, 639904129, 571209174, 683032828, 915468167, 551967720, 23483150, 546611530, 686284668, 443380294, 940344369, 323162181, 70674107, 189964320, 427444162, 470630046, 154778052, 598678055, 933583516, 636916878, 9625663, 589434365, 106545596, 265755641, 472138741, 241024230, 783340238, 431386065, 329464736, 970101503, 25546605, 26436634, 617640975, 996870859, 978519694, 838892565, 987970896, 373161572, 43883187, 673070697, 646330886, 647683569, 42791612, 496976744, 518902287, 478766257, 51141251, 711407706, 364519973, 689310314, 917773244, 434700541, 11491299, 297023522, 310831096, 398824187, 880659520, 514399664, 76947395, 989044418, 223272132, 988675194, 903512135, 30774038, 826862013, 165562541, 245735019, 568951976, 7728379, 653987381, 794504516, 406661924, 155162155, 66942263, 594826449, 57290123, 767818171, 372842842, 444733811, 143692472, 952191129, 596126188, 717370849, 657985705, 145167965, 21538054, 608298968, 118629471, 633761764, 19509920, 421192205, 689363035, 642640597, 167581328, 682377929, 267100737, 219495261, 591672047, 236304164, 977771340, 719262950, 543883912, 702472669, 718911028, 408337583, 895820369, 324789553, 302488678, 542524353, 550564952, 545591336, 383783500, 241165597, 517513782, 524779774, 342429826, 275242228, 758559939, 316472874, 96219333, 111322382, 739399534, 114283473, 137166015, 377193869, 728543116, 427038991, 541264707, 582131381, 98722179, 887524273, 987626493, 165063500, 985073798, 699893197, 917881011, 55576774, 47418513, 934711848, 250596533, 604940034, 596354087, 889495092, 400883918, 309547740, 105601457, 475073304, 254132493, 210431228, 202057939, 437472417, 568771219, 427105269, 720407778, 373101830, 331471998, 51838367, 863688588, 227942747, 69455917, 377928118, 699598124, 744195419, 784967560, 335260124, 543502417, 215209827, 617115046, 29757783, 93311729, 978638352, 356149727, 574961103, 335870881, 141814507, 34002254, 47736348, 983377182, 891321787, 333354979, 801327675, 818563921, 800555958, 862736316, 140195727, 734152751, 12472764, 775869066, 18638373, 344783593, 817587252, 28975286, 196839409, 548184, 305852302, 657547598, 262798795, 413032665, 955455111, 913339266, 844566799, 290939624, 893238651, 816014378, 365682678, 529049175, 584872951, 950160367, 721031153, 540409332, 359207958, 239886424, 807211014, 227957170, 574891764, 473030679, 667505279, 905482016, 371897740, 759047223, 227532201, 315683370, 855989563, 91808598, 443881816, 911370144, 349331294, 613428579, 236418677, 615720526, 125773613, 633255466, 212323199, 78585983, 226025437, 982860143, 38017436, 626869660, 393599150, 730151090, 490881659, 58932972, 485217460, 91124667, 134381317, 700143205, 956660881, 238510547, 603802290, 457200876, 49619548, 789859149, 281147300, 621541272, 963005123, 213189050, 92187652, 747627059, 469658790, 610197414, 197453591, 949018110, 220693762, 704638572, 803483136, 62562887, 763249074, 160535107, 899001616, 815257496, 357421509, 377327916, 180850543, 798477751, 24835817, 113828251, 793468368, 804759796, 858524861, 222973968, 73154680, 872794728, 598656845, 435391072, 933331273, 99974138, 564875103, 759098863, 212938849, 568704071, 461091735, 581553072, 839331250, 879009297, 506607817, 655607424, 118941037, 177733202, 743700168, 790958645, 248398201, 362961356, 444575185, 812262363, 507728828, 702244949, 764449969, 327164259, 749039199, 767293570, 894969893, 240704508, 979931472, 351683951, 256390840, 370740728, 838643541, 456996131, 632856509, 363843449, 2216755, 696792482, 536025976, 586564508, 888709311, 999605820, 528579306, 769625726, 667487646, 681167266, 720674706, 599557549, 253856267, 411553754, 445501027, 357118892, 28472119, 875523387, 334003777, 534833324, 217471257, 834950312, 670908483, 337508362, 642306618, 575657894, 636447964, 746614902, 326214147, 937651393, 205600090, 501649259, 264208458, 465982092, 693919450, 512784603, 573577874, 156264536, 275126165, 8275935, 462520164, 945226108, 686461680, 325651129, 472026850, 472384348, 7805562, 681110120, 820177657, 272556532, 842105703, 433736551, 581936143, 40740889, 111099756, 70835949, 222860785, 74433951, 423094029, 79671973, 230400767, 892234017, 273893231, 830738359, 494157140, 721231605, 500174465, 110797458, 723298910, 190892154, 756641766, 694554004, 540977295, 376513842, 35183184, 26220324, 355044804, 580228980, 431768358, 488319586, 768996392, 668080533, 989233701, 278925851, 259897757, 975362650, 352699276, 223707548, 265723509, 94493760, 878013939, 517427197, 501173554, 76772771, 615173959, 862407790, 941947685, 786188948, 787538055, 526082725, 405038957, 24177842, 396452139, 89368400, 571530493, 666527234, 341482633, 112322852, 916030106, 708565932, 963119891, 874245104, 630708149, 940032387, 329283066, 249566184, 118451624, 984914692, 727148914, 422242299, 119582340, 757183335, 926148392, 451722499, 274150693, 336713834, 722106735, 338784209, 915110058, 302394311, 526733133, 969472177, 732811116, 373488996, 431928003, 765226594, 724366017, 560255511, 516874130, 882920409, 443028183, 461282979, 698800800, 917285643, 707439597, 268302462, 737024400, 71825918, 158225008, 133529066, 478003726, 478094666, 730284609, 956086494, 159933664, 602170391, 989323918, 965104801, 35670433, 738269230, 594362728, 132739752, 715397181, 148548444, 411555774, 460253617, 196380562, 55993539, 521458552, 113840630, 536441264, 358831401, 824691444, 617873317, 263041019, 491031851, 85035413, 296321264, 703273562, 547025981, 323038547, 388915668, 322013892, 953479618, 573439790, 335705190, 635572740, 66192784, 799238090, 622503245, 487836844, 558379526, 20780752, 193391989, 237876989, 745865795, 175494231, 37555059, 902284383, 413907760, 65063961, 484257006, 358463236, 55737518, 771753689, 177012311, 159534726, 775001072, 276884918, 79065073, 146958408, 726361758, 49234455, 371574056, 553358761, 638187517, 225215064, 488875979, 721941009, 592344339, 916530741, 977711490, 836159214, 57970723, 634946090, 717105688, 338665225, 530782719, 217403247, 93254487, 278774973, 36049412, 45679997, 110102100, 354611918, 365760517, 960159472, 548650744, 230144312, 597541080, 66790925, 616045221, 656136972, 594075633, 635477741, 464282657, 78356072, 402673171, 363573539, 599303219, 782452454, 417651035, 960051638, 346987383, 399625267, 310362782, 599661617, 38351027, 922023422, 246507964, 134312677, 257147904, 770631258, 174000068, 861477341, 569564868, 671396827, 496784542, 988627087, 711065168, 438853866, 871960292, 547935579, 670358884, 17251125, 56764830, 828324579, 695089673, 251654631, 605213800, 47430822, 999019087, 632353996, 944757325, 428164488, 632733322, 329815669, 209536347, 168084310, 264871800, 959042984, 295319566, 690109179, 168695387, 479623191, 409922100, 10250415, 753899292, 927464901, 969460835, 633489737, 11215839, 370184481, 943846160, 16325015, 927721369, 152889009, 595697618, 42546141, 56761125, 348515622, 911185129, 160216482, 305212516, 924119457, 281989837, 160187903, 606172922, 296116151, 796195972, 206227094, 676233205, 312384875, 55961684, 315668903, 17850090, 638331588, 407705514, 143181071, 359468388, 589428767, 562825544, 890881884, 93109190, 52130843, 788496190, 800543848, 496509777, 57956870, 141776239, 382149247, 614226107, 858804715, 658907226, 785462462, 548283306, 868232142, 605287734, 858822345, 573456097, 911312540, 126468775, 811503140, 24308769, 935392938, 33322147, 446395840, 694797764, 382671669, 394126008, 271110076, 979918011, 599901870, 349272727, 722316178, 461401409, 561291837, 343789407, 821175965, 868782660, 292018996, 18770777, 493579927, 305361764, 323413259, 346363929, 601068274, 547311140, 771756668, 614885908, 940214310, 530250210, 912920480, 993934951, 6265973, 625114577, 921422450, 838952948, 445870429, 134244481, 128730168, 756722095, 309108109, 618419673, 660569067, 988769160, 996375062, 123541133, 768759054, 833369431, 37727092, 77449146, 115353629, 809189981, 791044226, 856354807, 307250188, 549545172, 882815954, 422739977, 217304884, 611834233, 637326925, 848223807, 616137335, 929940458, 589308292, 936230437, 844793931, 579390514, 677635113, 762245026, 73574120, 848959137, 103665135, 488931541, 246346405, 925805049, 405954587, 46282007, 664371372, 192759699, 465803988, 277638479, 585451385, 525374319, 538204347, 923719258, 158028742, 536932082, 659548293, 707474193, 782412812, 823260897, 527882541, 385184278, 847380141, 399561244, 83076117, 725285638, 678713145, 436271658, 873482751, 909628774, 875275874, 421418802, 856818560, 122238451, 57915934, 527277572, 251054110, 631939456, 235236476, 320186036, 524464085, 74439796, 522209249, 815757739, 381951287, 600062579, 749408051, 841315842, 936107146, 365828247, 491240285, 415608833, 426395217, 18212196, 785445792, 464838673, 537923817, 576191992, 84067833, 903729163, 443903021, 346668831, 176742942, 478237905, 703853709, 235772549, 845019388, 374522687, 555509340, 375096457, 95493065, 831289088, 291566018, 733191877, 861677507, 65327936, 822734920, 309909449, 568004012, 764740318, 557704095, 289566051, 124555032, 5276818, 334011482, 33275389, 328660940, 951788708, 219605694, 674990875, 79919695, 529947382, 492848129, 405049906, 916600465, 81917405, 699884596, 423939227, 192712924, 834851533, 955536764, 834248121, 658093102, 522228354, 628531249, 63948908, 910208642, 925652388, 608274854, 287684622, 354724678, 765008580, 563063053, 113382061, 397186080, 427560811, 607994863, 910811498, 831440682, 889761968, 179718466, 707816594, 829511056, 546589263, 167687745, 138923082, 54840422, 650520112, 491094799, 467384055, 536679183, 354110483, 216551143, 33891536, 766890654, 436731266, 402819561, 514760700, 6109064, 30449093, 816893322, 495290878, 51388847, 36663290, 31759515, 274054543, 419194230, 470091783, 49330406, 693541537, 845965013, 825290173, 180640972, 737245021, 443737210, 154951533, 308307527, 165588734, 845684564, 573884777, 486243976, 498837382, 19695713, 427428452, 898211281, 585453770, 386755330, 848528823, 593882392, 703146453, 484858322, 311317488, 472144423, 194838824, 279228642, 136753107, 68167459, 869213530, 217904147, 566051958, 47408775, 292123772, 89664772, 985043050, 363604069, 645790951, 287044443, 691189021, 463218398, 679338077, 583321243, 709726853, 231159648, 829564715, 951939330, 577870127, 829450703, 143445151, 454225399, 48709642, 785803277, 986252388, 77702624, 603236635, 671718115, 130442965, 99758170, 858719979, 517160968, 900099394, 878161626, 826437855, 998857845, 194643822, 505784954, 20046395, 511566279, 231709344, 811382068, 642411816, 832990484, 99659142, 506860531, 977017318, 948635753, 380586462, 707351879, 299956703, 736090327, 758301100, 600503646, 268707211, 626966846, 167772420, 203438442, 566464207, 124615836, 423170678, 682864572, 275371068, 22618705, 703273059, 417955042, 70032202, 118836433, 208538317, 812331708, 88353179, 781525001, 439052757, 283407064, 397982144, 334027532, 629628673, 270181054, 509930463, 177699464, 579301744, 434087723, 247272936, 701262604, 60397663, 214730500, 769062713, 932491874, 612781788, 841306808, 928659905, 875347768, 699394982, 292069721, 91596423, 346262425, 884653204, 973325796, 822978292, 663106873, 164468714, 942088715, 550759932, 98129688, 169108238, 430909857, 853785925, 512125390, 931203052, 192337154, 977976736, 785036092, 219087966, 100157614, 908880940, 409722092, 771688257, 218159873, 8418683, 697539260, 611610489, 78506401, 640193905, 814297941, 436410104, 276249243, 364452453, 230775087, 136349039, 957237297, 726885665, 526570856, 752139328, 80873387, 135672832, 301961042, 34087503, 16821881, 593909355, 889233415, 916088279, 623881534, 710995755, 489308471, 120937170, 437334406, 931458649, 227430100, 709098939, 183488405, 72792385, 502203471, 322436677, 700114741, 442690953, 854059166, 403913103, 573386399, 322532435, 638105124, 866323134, 931037233, 700681418, 386258889, 452867364, 376236469, 739418858, 549414863, 29858887, 249766817, 581214415, 721501897, 122293768, 121228552, 292908799, 607448196, 764305071, 825803539, 759907594, 315216832, 525328984, 79611459, 783564636, 666848587, 718736660, 273129423, 311663696, 505493731, 545441944, 934104720, 912920876, 643518317, 102552504, 832441239, 997897799, 47642648, 506343709, 217794004, 676144589, 302403049, 306800389, 265919820, 374863286, 273220066, 196692585, 568288050, 112454784, 704026112, 820737063, 823760411, 807087713, 327901149, 486377352, 652795015, 853411512, 182783965, 909507526, 180711925, 762077774, 303974940, 203323642, 775422546, 507225555, 662136865, 6738917, 154936523, 504108699, 20958011, 905729249, 82188064, 529635468, 720768542, 182996754, 793663921, 428965408, 523106349, 648545451, 930881627, 39924523, 40499957, 554110921, 626747808, 567688440, 312645270, 44584882, 620480486, 502327902, 130880488, 620694174, 965893733, 917464563, 740076884, 258254956, 591754722, 473387823, 411982919, 633737428, 956991853, 342183718, 900892530, 962770486, 237471627, 417388470, 378507098, 570508686, 417141838, 378666202, 44789741, 326855089, 113760620, 119455044, 10491243, 145111799, 114690467, 306931757, 108251931, 252300787, 352875816, 968155501, 801715414, 724573086, 506881303, 705016313, 618760624, 2416789, 15396409, 566454503, 436913796, 818599674, 30901323, 925320075, 678065624, 973970803, 739198382, 675031675, 441162590, 719588571, 563453196, 609395080, 164279981, 826553713, 524322494, 967791482, 163511391, 155213779, 475023217, 26329551, 543149877, 834875704, 606640152, 79701247, 678451866, 595437835, 612014995, 959194639, 884143074, 523234555, 638385722, 665968246, 131246719, 283321239, 213719862, 247678745, 318522884, 14856084, 932804288, 269631398, 759683945, 61153403, 67020659, 110591671, 222778250, 666831535, 910695203, 722881777, 675569715, 137781564, 505353374, 557187752, 512907190, 294716949, 250728925, 989955148, 325185107, 794853549, 584055546, 881890956, 968793289, 550051138, 756866792, 273078374, 891488987, 406091026, 748471644, 589282527, 191654326, 159956254, 564045290, 823284879, 647862112, 660848646, 509217824, 494192646, 364819699, 916608562, 296333716, 748999425, 653007519, 993327289, 848107309, 564628873, 513000711, 479927923, 364729177, 22769456, 642543168, 873594365, 733867788, 503719482, 92737775, 439027937, 513445878, 682265246, 624157218, 192278901, 471633060, 742825418, 332979678, 982231659, 659078827, 215832323, 568743257, 851158261, 999354081, 278318786, 457413033, 837061118, 509482394, 767761702, 731554703, 789576486, 915375469, 692022110, 690710623, 933149505, 304407096, 689557369, 237992824, 442354931, 743724327, 54676738, 102577570, 970589171, 123390121, 531616117, 439524589, 806755578, 559786799, 661387224, 353272419, 863567878, 127798719, 404097036, 986087101, 280768106, 656853789, 793720351, 583201899, 875520832, 51498595, 959286395, 812663540, 132863818, 791330060, 205025687, 602518044, 189529466, 977969980, 94459151, 668264168, 637356217, 67706140, 293582881, 413924389, 191252778, 925806627, 763512590, 452430745, 238319395, 328906275, 844157094, 743071706, 217647065, 996527116, 229661635, 953914586, 463040888, 310439782, 34433326, 858813859, 64121378, 317980396, 627508415, 796234098, 20323570, 623177083, 408423739, 742627246, 145536930, 100285974, 395063048, 783814233, 59467402, 19987039, 959073257, 472363783, 739392442, 503988848, 163779530, 451435659, 837897409, 103197842, 67765461, 60837715, 342876810, 336007185, 777874246, 706668982, 479055520, 447882505, 8809307, 212311978, 10790118, 970149578, 498546578, 245621590, 821518259, 805970582, 263706187, 803627053, 968150752, 385635497, 362458611, 43131100, 908553154, 867851531, 884619423, 591892310, 713587488, 988946601, 127263447, 539094416, 599276782, 659144169, 702979611, 346829331, 441795657, 792319818, 171961094, 236680694, 525793883, 285361908, 833667169, 34654606, 612526245, 218289644, 932342984, 99952837, 945238473, 654574515, 329139376, 682960113, 520829676, 955222381, 931424968, 157983956, 162273228, 717997769, 783444391, 999855926, 893547530, 437453422, 499281854, 732080113, 986995264, 167293382, 239047252, 665763039, 435221465, 277245023, 312767110, 766018110, 587157035, 840505126, 98280197, 229095385, 675163900, 7386852, 87532752, 635125709, 554474547, 525672296, 917970588, 11443414, 638444797, 598624820, 668969177, 23266974, 973495168, 628917669, 741409032, 51598815, 604430686, 367201030, 269361533, 566739145, 665547669, 115625420, 631881969, 509486220, 774728517, 321175506, 136168316, 192930065, 541352615, 511931163, 438682048, 748685529, 313799243, 753799194, 955659598, 974522431, 88081834, 476726915, 178816396, 132115938, 420611673, 207959146, 578338244, 576637748, 250817311, 864284931, 655161773, 211147056, 35843851, 490607515, 753801632, 64262206, 102684114, 826757904, 283276773, 341417563, 681424904, 381701499, 938313309, 36587205, 109445044, 778425006, 750868328, 506026555, 910628915, 224982426, 653669191, 9179817, 581634149, 571262118, 303300894, 638227844, 270317184, 269646356, 679171244, 197825918, 861892700, 625977139, 6964641, 778938995, 50794234, 364439226, 175506745, 396161332, 764831051, 937805853, 668596314, 620270267, 65761163, 703906482, 34366292, 122757229, 416082915, 479216585, 832702982, 509249038, 966179939, 590719850, 165470549, 250272954, 767655757, 282843884, 862295668, 438423906, 240909259, 730518851, 490142749, 326324831, 394592799, 964597993, 864465774, 129492586, 872778574, 179689726, 770941329, 608503950, 348866529, 837774257, 194919060, 9437885, 721964126, 490239775, 469135529, 130668593, 904552239, 840882231, 998143929, 88085817, 181961158, 836399841, 571429949, 429411492, 604995118, 311484928, 178749476, 12892435, 514750855, 981516258, 949803911, 975059858, 949915112, 737652963, 169425691, 271053765, 276104558, 164624188, 591889328, 320910312, 273825882, 158088149, 279159392, 830368972, 418551202, 373025015, 189031234, 958790222, 758915474, 63850957, 454008109, 504066675, 508679694, 392879675, 864080206, 987878667, 22867196, 50226211, 278868928, 990415267, 405471239, 335731803, 853778391, 576749734, 979725648, 879936160, 658209802, 640390398, 410208882, 85554768, 421481073, 872844757, 909136992, 212956724, 825346854, 905350239, 285971806, 976931990, 663337449, 203519690, 961769174, 796649615, 158806296, 742800165, 827694180, 26559346, 958855042, 363828870, 463724989, 278310912, 274910274, 843935868, 805371550, 186561279, 185728557, 219083659, 817920915, 925689206, 212941045, 432598650, 600652067, 842855656, 22473782, 834709449, 578422290, 137217753, 452347764, 554432756, 119419428, 152548376, 593347551, 493933735, 502778249, 791332232, 840776510, 679425959, 821962652, 731241492, 22619431, 695032010, 71989174, 306108483, 861121367, 217351283, 251272732, 840929824, 279563215, 485414665, 521027435, 749439297, 22715054, 132146450, 535376111, 172526378, 184845810, 515608665, 379409315, 941029934, 852139951, 44584496, 946225084, 878944783, 334324371, 590167450, 654412148, 945280025, 771403200, 833577166, 67885549, 162660784, 328930657, 125003699, 612776268, 684599673, 367425318, 571552556, 642247780, 811829084, 55221258, 687194453, 990087760, 270955382, 149604069, 200123651, 879935964, 572201045, 748222880, 383118578, 517393649, 392945652, 778813400, 913953875, 780615377, 305862597, 810668457, 822288939, 728877423, 457031254, 248116769, 78798857, 894724986, 341068877, 980585188, 776129605, 767281333, 144023823, 69504337, 845035941, 492657552, 73207814, 505706156, 243243239, 334636675, 954320202, 567389390, 482522287, 930180865, 825854078, 829201295, 422561313, 826496409, 28636623, 368731985, 314643282, 875965227, 111470736, 761904779, 274763716, 130221145, 784367923, 538596337, 250434430, 158870183, 303084754, 143392898, 80916499, 833083285, 166823857, 920070660, 954750241, 831258239, 469651847, 178088176, 809551418, 319300430, 682269008, 909800061, 800555957, 630565504, 639672756, 727330158, 709740431, 438176999, 843933686, 455695437, 859756389, 5796298, 349210376, 894660391, 741548284, 458030184, 536597890, 750439623, 255978424, 171882553, 981843785, 349136029, 207552884, 428463842, 551810216, 807699105, 30415878, 484221727, 595039453, 263773983, 581152495, 832525073, 672649455, 485934588, 775450896, 290393767, 964749709, 179105761, 769713492, 653011588, 114753059, 57318721, 68659613, 135190263, 913265154, 817631016, 871398952, 807934835, 130827051, 284319126, 455041596, 440228254, 882207953, 472199579, 175205383, 431268081, 859384541, 726407004, 492500884, 605654621, 459876512, 844100363, 905487650, 366438357, 506471258, 149287669, 905294375, 411501801, 450225560, 479709458, 620428096, 836275816, 511419759, 259301602, 383322415, 432341202, 215882916, 397770932, 850590997, 650275278, 756556649, 300310761, 764215704, 226846973, 95173446, 283717682, 648173109, 690668578, 917441398, 17575413, 474688732, 298029785, 86320917, 369502826, 542831356, 545743885, 841289350, 783511867, 527327846, 156174296, 486483286, 36026679, 274041628, 968031292, 583424107, 679163547, 141441347, 468092452, 383521958, 610815364, 501810038, 557610884, 57226197, 690978741, 991532447, 464239726, 233696478, 176080371, 872428102, 958904406, 18017326, 592098343, 822259426, 99856976, 755434751, 308345578, 479461278, 511024191, 630953252, 49894651, 811148529, 493733572, 398483170, 753137451, 393301757, 849963772, 52730059, 690140356, 195924384, 187202281, 784754781, 804322231, 754115370, 260067489, 334584715, 553382200, 443450573, 684006918, 425798640, 387581570, 483267611, 171882706, 731989510, 856138920, 587969594, 882782638, 236515097, 966105258, 600478312, 517969724, 414225879, 734737205, 539027569, 822745155, 219128590, 190980985, 198371222, 984987356, 207827629, 20992102, 376984638, 633721511, 693597091, 938791060, 895847790, 395174103, 931616637, 398331033, 965283552, 977406030, 829551037, 4801309, 496969418, 151679923, 697269379, 521883181, 8748408, 662993020, 441545392, 708581851, 49820919, 770905379, 366979386, 613130952, 363933976, 935224248, 80417773, 393026022, 16261872, 749740606, 515159234, 242529245, 233892468, 50482462, 122657218, 448795102, 723477682, 140546591, 947617519, 233651019, 438655273, 276397493, 153636131, 195520379, 940748516, 113038492, 222097702, 382345631, 35037906, 410895532, 473989488, 850830014, 129126315, 707855026, 34619546, 759878935, 820898811, 549323815, 259699173, 812058432, 650250511, 690052964, 701272419, 376111281, 55541672, 741953212, 483413668, 633077554, 972648667, 865182641, 586515671, 936083819, 404205594, 970427750, 620048749, 208439677, 528291855, 314645759, 498195048, 971044479, 377160636, 546143046, 98395227, 542103117, 493094396, 514047993, 428127320, 443932175, 564281082, 674704577, 971169262, 907793536, 399206981, 704775057, 585054038, 484856348, 612956160, 816132067, 819747858, 592919646, 5989927, 687420466, 462707753, 300985703, 806360371, 227898719, 873183093, 434168614, 811563798, 365865146, 318193608, 513842346, 452483811, 368956459, 347347378, 633595364, 6228494, 470759808, 983908225, 125321019, 741814485, 579434226, 208901377, 127253749, 817583353, 878098151, 34823705, 939879626, 137558661, 997758135, 672937874, 350210433, 156713066, 500651344, 89712970, 272598786, 112722209, 682176197, 481002139, 124156775, 954019919, 628654348, 636534296, 657702623, 425090392, 590647014, 865436448, 854422117, 279055881, 896413338, 303678613, 606872378, 575811142, 14097120, 42389412, 27195835, 911809632, 178760679, 388070636, 294349849, 333483026, 467201658, 75452699, 633779876, 477296949, 841093876, 705982463, 951864769, 294045877, 128580108, 968141302, 668126894, 465398028, 481547690, 730140753, 795022015, 9366052, 617001291, 161315906, 761532055, 198073595, 770611033, 761962841, 245670878, 960405086, 34891917, 904729273, 323990374, 390600661, 348930325, 76891711, 742303021, 760813398, 684649067, 980679238, 576483132, 967510002, 672872695, 899094652, 633653806, 808412089, 325357936, 191770420, 30363877, 965473326, 750046900, 957060149, 699928340, 656961759, 206884064, 654446689, 251858829, 54794110, 61748494, 483806899, 86028853, 3654578, 133969311, 433688323, 175647327, 520129763, 43729573, 982455008, 150277621, 183259202, 359204421, 920415229, 422617454, 252714444, 922450343, 633399289, 618142280, 82897951, 216752840, 913327223, 644649938, 104264293, 747394016, 884144496, 942862075, 696323425, 567615652, 397812061, 909616852, 730520162, 142923116, 361162411, 261861688, 56604923, 472035997, 936016743, 916841452, 565385271, 185409964, 396383179, 223487609, 239261136, 369586962, 934072282, 587615126, 329627509, 875212266, 235743164, 611131605, 477271146, 569169619, 231884176, 606129556, 134695630, 41570614, 359774355, 427240724, 722841406, 664995741, 785739428, 97804284, 575353740, 677956140, 984983602, 780542193, 762736347, 590956742, 580031933, 815082539, 370262625, 873156641, 777787875, 345783474, 507090547, 470094980, 203166988, 373961021, 566585441, 168828915, 107495946, 108075973, 816739055, 467994824, 438217653, 524648042, 237699748, 971252258, 629811137, 478352669, 679032509, 160448957, 810778900, 860949063, 41460396, 624452737, 291360350, 538371758, 145314417, 340783257, 639853270, 895596034, 80203845, 408760529, 867609298, 856309936, 765902062, 607247061, 695804953, 154083131, 256682593, 122967500, 34357695, 105710732, 278211725, 511598862, 689716131, 805316414, 526239088, 590120308, 497162397, 849835778, 713939659, 27706041, 305521914, 26854282, 698123545, 794683886, 760497071, 489774239, 53651399, 632998730, 631135611, 184719597, 188733914, 943863901, 358815477, 390081470, 702972398, 659274012, 113317461, 538492171, 284936815, 891754318, 779397322, 857726401, 56830393, 819326574, 355010624, 575754637, 284235991, 319570823, 573079211, 925311383, 355422574, 783090816, 466518536, 449181912, 918722066, 800244365, 339532352, 210364560, 141037114, 529501605, 216631180, 189442294, 419639916, 435002054, 792537938, 212043895, 488532420, 865053162, 906716420, 604137240, 175238897, 884658828, 961582792, 174714252, 432326132, 966571022, 935935429, 33828041, 852041882, 291608219, 774602687, 104072000, 947708990, 828447272, 350100855, 614107629, 905097788, 228043542, 833693784, 353979751, 766338135, 967883999, 78676913, 621883883, 216122238, 555852941, 699967727, 222023318, 776477859, 263606807, 964911173, 796277376, 390322286, 333874821, 418977676, 483662934, 821437853, 695553193, 942989832, 941767318, 641716502, 280054820, 597471705, 931030912, 552152359, 7357720, 637331234, 523159970, 333440956, 982067427, 194573339, 906205346, 513054944, 737467506, 817797046, 446009807, 863240725, 914878502, 723839775, 229084213, 153017569, 210700057, 33715509, 115546036, 25932320, 636721632, 419311347, 860255925, 584555773, 994507746, 885066880, 318734714, 684931715, 372742357, 832045796, 802107415, 268872606, 859744178, 66300388, 555071293, 219119569, 309556522, 657431594, 658631874, 929176600, 970860260, 398012950, 86346441, 262872419, 283925630, 270983892, 449749279, 620220112, 729890999, 291234825, 518709535, 931323992, 106056154, 761945077, 395270459, 445890684, 6871582, 434796824, 81635923, 223940424, 589611770, 60594576, 335554954, 61272695, 148457394, 309559207, 949759811, 213823302, 851297001, 924337403, 365970618, 386436212, 855151715, 706867443, 396884616, 164738468, 539187743, 326010419, 618438310, 175474676, 262603254, 833676476, 696091586, 309683748, 471819350, 104085709, 673510858, 298154793, 545051353, 462245510, 498384487, 175993990, 442883331, 825913798, 281836603, 40901168, 196538300, 14559273, 683253860, 938317469, 369653247, 840213449, 994312428, 295805110, 344010286, 778222995, 747459484, 765163099, 398251475, 2764359, 906231392, 841374732, 902466732, 512331108, 594270891, 317593010, 722477700, 490177837, 226231433, 498975971, 492152800, 122851047, 255127276, 729926868, 311904649, 742362298, 479088109, 889329059, 369651773, 216677683, 852744732, 550654743, 897909975, 50056430, 976578042, 898306519, 732550073, 589531444, 972509850, 326285011, 555771132, 810209296, 447473278, 285792660, 930666322, 782691714, 115388437, 881825021, 923263919, 137217030, 81055805, 552641347, 917408609, 386148707, 929471501, 321607599, 84029617, 161605610, 87752417, 606038575, 611323561, 480685096, 832269135, 723109667, 578628205, 133988708, 263791081, 364300926, 281974026, 268551029, 972204889, 820291250, 583981374, 622444915, 959697889, 12643166, 737857547, 44764333, 378503240, 502986041, 784702412, 285816657, 384231906, 722320791, 411774531, 722353803, 657159196, 117070836, 944546899, 717425608, 549472494, 960518429, 14898641, 679327424, 265638529, 454057009, 371206389, 961197520, 287552688, 392118032, 4883898, 112592411, 24951202, 411349641, 637556859, 425267309, 821515495, 676752805, 236781346, 438328380, 366884663, 983016445, 551260607, 567042811, 816893785, 296720208, 424867086, 394723147, 229494697, 984769025, 998070159, 540644571, 638829724, 294255191, 18284747, 820491441, 491755562, 999311965, 214763565, 242744425, 904251993, 385140749, 865252875, 72533987, 662473874, 486855925, 407888231, 592945573, 506964279, 508655557, 768341643, 263217881, 89322541, 664291514, 823863881, 232781, 403837898, 87532616, 539704332, 12522299, 649362100, 285770831, 673868849, 604201049, 2708235, 262428793, 948930235, 273657867, 956044062, 846999808, 97034182, 937751387, 552877003, 596711476, 638755010, 859942609, 922050100, 659006385, 803239564, 617242043, 815199422, 128967492, 660051357, 95206958, 302447176, 343264510, 998569124, 466324446, 377847954, 450549466, 622984326, 86555242, 364514768, 933257282, 858764124, 857590707, 732799059, 927282076, 399646349, 613301035, 754123974, 944041265, 549973193, 563996227, 917666883, 386812758, 796559134, 552726402, 718809059, 524156786, 106683123, 793305498, 720151957, 837567831, 941307088, 250723791, 396393864, 872007441, 351962262, 614192063, 415866742, 296372192, 969765167, 720177557, 352915219, 796930970, 8617327, 201387534, 379949883, 49609947, 424451997, 722636357, 107089626, 186472168, 734829552, 733214426, 774210902, 681287227, 387052438, 668400535, 261726265, 671690029, 403785700, 207655674, 851554383, 996638653, 313947906, 503714724, 83405367, 923462367, 580977380, 566734190, 136741266, 681715905, 48941474, 800870658, 938066308, 138222969, 241251062, 954209998, 61019611, 512981133, 499797894, 681749780, 648471619, 803133417, 63808241, 185890599, 548518720, 741217472, 811019279, 676097245, 746738089, 589086059, 73827457, 640275009, 842560223, 828700160, 693265947, 214282394, 54418960, 60368956, 423462634, 610142053, 840322604, 80325594, 526742330, 341576748, 567585106, 420677448, 719731488, 976674705, 394791953, 462383265, 356181372, 290662478, 748598942, 943203473, 727084264, 442445364, 336776153, 854944937, 716042639, 671691429, 750535783, 245140257, 791099968, 571246774, 599180406, 530190239, 884033307, 698605572, 933605655, 42335382, 545709297, 939679238, 164532253, 915067051, 761003800, 108113478, 104990914, 931660058, 89576232, 391052029, 210468173, 670646264, 434310475, 952897229, 224806560, 222986884, 849690455, 813906271, 548942464, 112871517, 513753228, 781398003, 321538135, 295100041, 638097686, 425679185, 235065810, 849484443, 484056076, 777231276, 765778463, 367558028, 186173140, 125505844, 272099644, 994815320, 472934083, 990474216, 314525737, 253226850, 822167898, 404356770, 499070865, 92766678, 523281194, 258812723, 609387891, 693966027, 817442119, 798654910, 698552539, 464366030, 397418498, 929421026, 742466873, 985742834, 136860193, 805846709, 697483484, 414296276, 179328687, 530977974, 696798347, 926342244, 987934313, 183872911, 489184921, 388415639, 611537587, 616305461, 316397924, 124811265, 562495894, 279282102, 894616789, 585753144, 972743160, 780888287, 490620340, 722044660, 471435976, 566270748, 824816264, 978547594, 739746547, 960265796, 905813453, 861041090, 290481247, 974647477, 234275258, 406176655, 812357528, 332526181, 403281791, 759584031, 314075622, 570478528, 44832735, 794934941, 322043288, 645724774, 143818744, 756413916, 7776126, 809190208, 77193308, 325356732, 588486959, 279093409, 367798911, 888709348, 852555214, 912086750, 389773058, 13204754, 569841391, 605876888, 569442891, 83631956, 401137297, 938554274, 28334601, 775367805, 905929070, 466535994, 795502922, 828901959, 931363130, 664806379, 447220211, 797271066, 387611948, 392874921, 955637897, 157753454, 749163898, 979944120, 261694802, 951460161, 97249705, 497009367, 56302400, 708048139, 496614643, 59556103, 254047389, 57999747, 711175364, 42392900, 763078862, 355052725, 758759122, 72719546, 659363019, 497376738, 730709015, 391566232, 56332878, 923069625, 514604751, 597876220, 127074870, 185924719, 198561236, 679720441, 752432147, 924025949, 345465373, 934390687, 867746166, 630474530, 434630079, 218440004, 21824737, 599259976, 961363252, 398344214, 199677645, 945019413, 240914342, 489844621, 886995255, 367900278, 103570734, 373362189, 531465061, 133503009, 953586097, 988486603, 179292626, 490612826, 162616071, 737477974, 735604607, 907375240, 852800614, 193311382, 792151422, 526853936, 873605146, 516218244, 520818037, 559624625, 916582103, 384226624, 187463441, 753367726, 901268768, 531496085, 788278005, 851150411, 388488237, 508394591, 79293494, 872148651, 670305597, 946797271, 586541005, 440592801, 708448533, 518538843, 764833273, 804384722, 845084219, 754417683, 568653535, 192866086, 663798935, 59903643, 957806300, 134799742, 405259946, 878098442, 505230758, 361131357, 989607415, 862433566, 616711722, 663278209, 577556286, 697780506, 802391572, 878816387, 907597556, 342680066, 363160773, 570116807, 859887511, 967545467, 748406833, 745951985, 469448976, 461240296, 600424983, 539157184, 189940643, 515984268, 252879045, 273108200, 485211722, 56597135, 566193671, 653470761, 508193430, 164238202, 601339648, 972694408, 156372739, 579221273, 437669543, 66928754, 658099380, 339769261, 61199967, 992420677, 180141981, 579727546, 372625060, 893614826, 978140084, 108754822, 625977969, 120855919, 858583275, 210301372, 75765574, 799981265, 946659739, 312173750, 705014954, 345786761, 455959124, 683848837, 375075746, 522944837, 262678737, 154369069, 1932397, 47629132, 317369897, 891543789, 664682444, 589167109, 435268586, 762869958, 17818710, 411088516, 934001886, 979165516, 282732512, 842246650, 993340850, 765425655, 724804372, 886746082, 751827670, 353071356, 431048081, 389815687, 512764227, 904988474, 61378335, 799552355, 554357712, 503619173, 618324717, 305713871, 969228173, 8971801, 315780447, 593087085, 46082320, 569857061, 448123052, 71240306, 60079330, 958872018, 677413172, 215903261, 550548849, 496138400, 698585358, 316917204, 334406884, 706566408, 461931047, 159940101, 810112699, 770360568, 234304677, 628994578, 84884633, 831492234, 41824528, 344231990, 341716178, 334146947, 968411162, 959042899, 518922281, 43195485, 670575844, 469854356, 502097074, 103116892, 894314474, 900852041, 159816184, 183904483, 996918418, 647873817, 603415973, 651736262, 802134685, 464548165, 668414206, 223263759, 219937482, 74266175, 703690050, 550268367, 675859109, 619558211, 539879687, 331984098, 334896150, 254264418, 954906023, 436369613, 644734969, 7952555, 323748106, 444453808, 489120966, 205504540, 371785160, 962621321, 314572748, 158443756, 551139381, 539092408, 535157151, 453095133, 191986808, 139927512, 415532646, 578269353, 786938330, 133867599, 112291463, 501971306, 112572791, 271482219, 426477566, 334957912, 731604744, 283123620, 624530577, 145754527, 414463439, 835762552, 569253204, 647021417, 899611019, 648139483, 783546271, 722905929, 406870660, 220177151, 257115156, 989677424, 638564669, 794084726, 163248205, 494811602, 485359753, 878178186, 905114050, 237505183, 413421504, 630267926, 308994482, 52808018, 713243187, 886124452, 375251636, 414226073, 40309713, 470177119, 557420156, 58370453, 426761388, 814100151, 217594056, 768130432, 709256511, 936804933, 812388850, 473934854, 694624081, 250368687, 55473314, 320914611, 346005728, 980124676, 196710866, 495497961, 316320903, 222841387, 200414894, 361871595, 570676266, 951820647, 232363225, 646297520, 659833850, 239985993, 302264576, 177292934, 565641901, 275425144, 962329430, 695027910, 91654031, 119851400, 159195441, 161557392, 387833074, 983930143, 718526330, 974397906, 991245105, 464544522, 510965658, 660361392, 690958748, 794563892, 740799425, 484560525, 4975228, 890130447, 850649030, 973278645, 883604377, 943514809, 422394729, 474644286, 188600423, 909994864, 387985365, 836100452, 980216127, 35184911, 89584203, 41284190, 809588584, 392834609, 406053847, 262945161, 368719118, 689543145, 723313341, 594833771, 854113230, 801962759, 924263868, 179516333, 689370038, 619129435, 463288876, 940310939, 850205608, 294426239, 410434640, 255788608, 202280852, 979943287, 413416606, 670548431, 601842811, 297768388, 593535978, 412553773, 387847945, 696058314, 120000101, 160892382, 249870248, 817268310, 352648107, 603015120, 200726343, 757294834, 488465117, 877828288, 193027225, 816160229, 918698090, 877723588, 830661574, 947067086, 487237879, 412602533, 599087470, 586968550, 625614989, 976783116, 27669499, 925968038, 577413827, 628904109, 865419653, 985824032, 417314997, 388736640, 282237953, 181721274, 506660923, 934852039, 394830638, 676881626, 591829351, 316281968, 676580215, 934774637, 837844194, 250307987, 536586006, 319945492, 242190462, 854670927, 389609116, 435859088, 54306686, 182899514, 347404925, 404709504, 601291171, 273157726, 928901958, 380439931, 84392595, 728179056, 147307391, 748173702, 105978490, 824260486, 606222038, 230908235, 507853113, 374022223, 138039267, 379039132, 268494881, 682465295, 118179462, 445033808, 207036343, 945707873, 653283208, 701420, 32979493, 554651617, 723606642, 538038442, 802908060, 534120775, 662254246, 767375862, 459533641, 313612339, 55572160, 368357473, 595196330, 176527275, 526779516, 770398183, 929915984, 359308751, 341583644, 557120741, 539272575, 835866461, 642111893, 95934015, 782705810, 843133868, 931728013, 254937444, 866949171, 590256782, 725184175, 507028199, 914095705, 802593991, 245221950, 844617518, 583681378, 226022250, 297999574, 456146036, 568404957, 754243669, 351863031, 760727938, 140551108, 436342057, 134058670, 22778186, 810164820, 343319659, 71377554, 144972039, 316964560, 338607310, 839478251, 338370840, 611782131, 658871924, 797845843, 296296199, 321092285, 875646346, 510332912, 789545552, 686387788, 833358684, 61401878, 685550006, 499742443, 504455074, 30710842, 65989194, 697636528, 577552338, 351416185, 112366516, 685074539, 526585281, 108019800, 603606439, 398630793, 716404250, 112927684, 787789448, 608187924, 752243255, 860666686, 994180153, 216737475, 166810229, 607926265, 285228604, 356003135, 686409319, 324755593, 638362380, 327146865, 423303343, 839097067, 995275294, 794019411, 715047648, 259778943, 778412581, 532066866, 655613924, 610464553, 200879679, 213449908, 902813096, 657405833, 243672469, 713663871, 646042560, 768234283, 38657351, 881307265, 581846181, 1194837, 724116728, 426260600, 580201212, 579594214, 982488008, 941639829, 530600100, 656407930, 506200392, 507911364, 313639085, 429685755, 99490968, 240441659, 964709950, 186469766, 667489, 849569187, 846920699, 388249274, 219981868, 167083871, 335665084, 799592699, 507230387, 209591964, 447741012, 117728935, 231283373, 250299824, 565693581, 498780095, 926751486, 593973994, 667245156, 125018511, 287500832, 485003355, 519181311, 585439586, 751412067, 583729669, 347020779, 144517951, 541927388, 8976695, 966831212, 610478203, 671208605, 192406388, 52371145, 995764314, 700861945, 265776751, 223697058, 391512192, 940847903, 629210334, 498355621, 116921497, 281825305, 118912899, 71504280, 842293733, 741408152, 963656941, 756614071, 724243497, 583417533, 985223564, 211271657, 700745312, 574406665, 187503581, 155868548, 756413655, 887372007, 215345000, 513372428, 547237403, 193670815, 365162818, 25689577, 963517278, 564696413, 670258591, 825140395, 611919805, 189767611, 226843709, 82106259, 158348193, 284281044, 836891674, 195677744, 81146603, 900031102, 340536360, 825245509, 61875865, 24976904, 525032746, 464538035, 168859021, 5253876, 781683986, 975622472, 476142016, 429003333, 504460684, 636174451, 87732818, 349002446, 921100371, 698482495, 82638598, 256185424, 715666019, 996006851, 75736575, 269192115, 868392192, 742569718, 852200546, 81338158, 318387291, 511322034, 456630312, 930531977, 849413002, 756603499, 837111241, 774741060, 677776139, 112240494, 256370949, 921919692, 476101483, 284462102, 176740877, 481263366, 154261008, 631089872, 22426236, 192013105, 287675435, 958214780, 663778953, 515106458, 502558378, 436831035, 867614321, 912100958, 624183560, 21848125, 564694168, 930036774, 581350659, 495395489, 161621939, 816030100, 48020324, 603822551, 899301731, 597292237, 220944366, 872995943, 555046389, 699855543, 949833631, 510955891, 170328831, 959114800, 244371862, 870046704, 807787720, 293926675, 155557956, 416250671, 939843133, 202631677, 123983523, 268053880, 274964110, 495411284, 418559713, 855373173, 753859992, 741789692, 663827225, 679872007, 154369040, 882183665, 849463056, 482392694, 852752099, 308404077, 758494431, 979191618, 306856633, 440723308, 229918791, 518583705, 402544924, 357665724, 777091753, 93701372, 794782341, 179290858, 450619505, 774441643, 182837969, 583388944, 807270143, 179331156, 164307532, 120385381, 403675468, 188971425, 96686328, 30676204, 600749118, 662245870, 656634224, 200781149, 927859499, 476063090, 140035651, 506460728, 183904040, 889657059, 910883559, 974219083, 828687641, 235264056, 652658202, 812386303, 909375772, 264082892, 67400816, 110103142, 627388424, 9119544, 166512409, 734759070, 304730875, 303609215, 587148515, 644272817, 405507746, 389837295, 538026175, 352934206, 356541679, 66233068, 92984368, 185057855, 41162295, 660723986, 69911455, 959136456, 644817879, 339604125, 915527276, 115260813, 24734560, 678416148, 399550475, 802110870, 861183443, 949690083, 989383391, 726905705, 333691155, 892336500, 134987850, 140049604, 108818016, 959038740, 502124659, 972194563, 979040303, 146371198, 610978133, 953640991, 48689143, 489584557, 178298253, 14151795, 778646568, 204051352, 709419780, 976818193, 344671654, 676066647, 787799296, 975941793, 28226348, 72144130, 395027402, 393872797, 574698018, 575864379, 538024997, 220031105, 244014619, 832700112, 493643062, 250912016, 483372239, 893517567, 360806162, 676042004, 432381047, 712324969, 568122308, 810001484, 820306000, 550686506, 758846219, 487209294, 147190730, 632518840, 481636198, 154528739, 156628209, 440935704, 632325171, 490032030, 460447179, 30559327, 699272373, 424458230, 63040552, 233681173, 632838827, 967073057, 505265606, 677765657, 429033922, 679469304, 468405202, 574402831, 419150830, 460999301, 629986801, 856991174, 486829970, 141736206, 827158052, 290077018, 289752770, 533428486, 264474724, 809489780, 518223420, 846693426, 284635790, 171434074, 733665808, 542331970, 850343871, 478553060, 791655681, 835912982, 508612241, 185510916, 641385212, 366933385, 103815404, 416972346, 721604448, 910636835, 46616831, 64536639, 953789269, 424400047, 722422212, 916189094, 428558205, 38860125, 957705234, 708037860, 491511604, 761045167, 109979314, 670307346, 454989889, 171650330, 564692364, 280306803, 418709819, 137875667, 342030048, 229367152, 149120049, 501718429, 33831039, 506580859, 952853273, 929724643, 145058205, 934461306, 22423321, 249488177, 870968334, 688902745, 612277208, 396146631, 470195023, 770832369, 212653200, 74176796, 368273873, 161898549, 690475854, 839855339, 498084105, 621405520, 217360716, 372215960, 919851856, 63174563, 662487135, 367268789, 50129130, 387037923, 480977403, 260227256, 731179737, 804578246, 972236660, 17783449, 879809581, 713907094, 104747130, 841525181, 224986061, 810501101, 948385464, 901738545, 672641988, 565067218, 810612010, 711500682, 186640645, 511933045, 408335877, 695811672, 280711254, 691415576, 938378229, 634843296, 886312030, 436029567, 610139166, 506987121, 258795039, 211454350, 514500975, 906376134, 267253159, 813354546, 886754846, 595669412, 382945381, 418941655, 833568736, 573119539, 238761165, 700009996, 984594784, 18845703, 34561892, 534356968, 158502379, 88702501, 572499964, 181267077, 94709473, 133139866, 923193180, 712314096, 254120230, 245058981, 133342451, 861453434, 603754123, 318528569, 503504253, 523209062, 345972302, 558142250, 450337033, 84089248, 356417917, 82994929, 399397684, 300945663, 691227340, 113423128, 264733736, 887143386, 132275156, 900852156, 345172505, 785737662, 329442469, 905218181, 591326656, 903103463, 328396309, 242327075, 931769756, 640253689, 373480107, 139412350, 926531359, 265492926, 833627124, 272831272, 853389730, 513445221, 1083346, 42816399, 32880107, 450530462, 383586345, 664051344, 25821752, 400354820, 663027080, 339372648, 740168775, 425312513, 655191119, 682605126, 389436614, 952854995, 769091326, 710729549, 369037303, 38695168, 150473237, 274250503, 500285072, 350558561, 393953017, 402075170, 789300753, 514993484, 345301010, 953143676, 389133399, 107789759, 881596862, 112238186, 181343293, 924831285, 49281199, 632592620, 158095034, 893863227, 839310784, 362464046, 655773048, 50079996, 175112238, 442878970, 125160968, 156850834, 344979195, 480777122, 708832936, 433513978, 775297917, 222736147, 853224447, 103387810, 985213480, 691082501, 241330695, 817424227, 662649345, 679517422, 555067904, 148359905, 719997440, 848400644, 976553663, 444451710, 447409797, 672319064, 770882174, 906486338, 307044604, 594830345, 227346800, 92137219, 676048349, 66369241, 852351550, 799987348, 86167374, 611772364, 926842479, 17141979, 51444996, 151385823, 715360328, 568934839, 92890082, 165849915, 866435016, 448231458, 791707869, 157879270, 687208620, 317622211, 586096249, 595863012, 838681272, 146773905, 412052187, 134776613, 518239280, 55723686, 206532512, 801428806, 368436552, 998121702, 791740334, 103467128, 24521703, 563028423, 931245924, 618541461, 241515132, 433440179, 325705698, 594512658, 687343628, 261523587, 554090248, 179731704, 249136034, 639881113, 427969142, 828488849, 251262875, 990829092, 512759032, 177221410, 485324910, 247674333, 789414142, 697572706, 547477822, 420690378, 224665220, 510905314, 776830129, 942087061, 22293421, 687092476, 647412509, 475201343, 794474071, 631368484, 532702089, 623877233, 23320229, 463491761, 997355758, 315270126, 561938481, 473827980, 676202987, 682999697, 643667190, 928667813, 413308059, 109129679, 240399566, 303786633, 21242048, 701653363, 628255087, 589380695, 970619062, 567622777, 498929707, 391786289, 120872345, 953825468, 178697409, 180706907, 103108761, 914847987, 891776452, 764962593, 290207687, 973578085, 397995109, 310447090, 149935340, 533652285, 545861260, 472324674, 792481982, 782720842, 943216484, 871199018, 367121275, 498206727, 133375414, 921176830, 169657730, 204047610, 895788829, 25245392, 196507033, 402978710, 532307792, 246581599, 619639777, 977683775, 351965387, 944747563, 892768094, 332182077, 305097613, 764922091, 699626423, 883694056, 114218404, 499347017, 48343851, 454321315, 938317708, 874743528, 414202812, 432531817, 996502035, 111894910, 621011237, 821140869, 246896833, 361704938, 927646394, 384823902, 80615493, 585160186, 778004616, 770121707, 515651099, 218054173, 67604229, 168657039, 388051413, 791606017, 716016852, 255284347, 951556050, 424024570, 536446051, 485337530, 619147274, 232383920, 451656243, 327224282, 658300683, 134923492, 118503889, 88709321, 576312939, 362720008, 154979174, 866195828, 44557524, 343772391, 467427385, 463157453, 567221328, 50259238, 256626825, 908461889, 856014399, 888671571, 986100554, 792517767, 705561226, 658919579, 11648289, 105838993, 179388303, 377957652, 92716195, 891556069, 175153150, 322508867, 471772642, 297442455, 186432210, 977148835, 802934790, 193686272, 367206893, 693522728, 755277403, 506990944, 990043328, 262348022, 848238682, 426331918, 221016101, 763521620, 792326270, 729030620, 463621173, 625429167, 502373169, 361042224, 361303993, 85556684, 354677242, 698050116, 987066419, 300436851, 500058453, 118118312, 534854497, 396539753, 86469022, 413496464, 570461401, 828540998, 713945669, 539291484, 517820579, 509272202, 544622201, 928524402, 269694940, 932484981, 566257689, 173210067, 955787170, 67157565, 581031594, 811900638, 586839078, 339468890, 515099470, 242485208, 824353508, 986183975, 255872684, 742036283, 546249310, 939530200, 946415828, 465252525, 227516877, 348781836, 638320049, 869840678, 392281551, 727547485, 726520252, 925065447, 391896874, 945067143, 626528808, 463391501, 39956033, 399416140, 792047759, 189183408, 223108090, 577419666, 188886490, 409314372, 344739709, 91842682, 802660577, 775385922, 585907193, 173670578, 442785603, 339943873, 725004801, 745078031, 485678433, 337698141, 147044095, 616979992, 872825833, 412038078, 785708293, 369183324, 724710034, 47783561, 672767096, 543267225, 923524173, 765964990, 382464210, 264061885, 540875496, 434451230, 30586776, 756418148, 80043325, 449063426, 709401689, 444575640, 247407390, 28980203, 771115960, 30107921, 772252249, 846775980, 819004021, 676221381, 478470256, 703337569, 209156355, 541695803, 269639210, 505451560, 555395133, 635800952, 235995615, 790852180, 87324308, 382998712, 594511060, 891707440, 190396687, 176596908, 43156633, 941954410, 648400988, 922583347, 114767362, 945546002, 314813137, 13005418, 478495844, 422601859, 837013936, 482365461, 977488859, 823289449, 198806996, 882632843, 452464798, 178242855, 277193015, 287740621, 219725053, 480087204, 852465188, 836342315, 858049576, 931068591, 242628187, 804452383, 379457474, 415349151, 34134877, 75525069, 883484808, 770930294, 103699448, 225148477, 860126035, 530205962, 896105485, 893585601, 149446642, 579246069, 657233871, 659241552, 314344696, 353997273, 266178639, 33890620, 622815764, 192872543, 176848281, 825968276, 656335882, 260275325, 196563879, 79708479, 698323720, 230781939, 568052089, 875190194, 839714946, 8271146, 497432465, 133297543, 248922555, 400973094, 474882865, 324042463, 714439939, 804994151, 76220808, 37259698, 733059336, 520533796, 437097754, 795386139, 922586058, 239423412, 542722559, 524284603, 448889212, 963669499, 693547942, 618989640, 300376980, 471944681, 872437016, 607328568, 689862877, 124588470, 510073941, 679932744, 871989319, 720087774, 456013189, 158761481, 107755167, 777484687, 952528269, 484906621, 73029698, 825833843, 893572445, 716610155, 685080223, 819207557, 55487669, 371022081, 957075576, 206901571, 128995626, 473408054, 170213467, 41859960, 153983680, 410983926, 282980694, 929205508, 755523825, 280602845, 462896114, 690331456, 61544344, 873908359, 567498314, 727506942, 877234580, 803580141, 366006584, 440399415, 811255390, 419562144, 685640372, 753520228, 739046441, 863913911, 522318220, 383725776, 922705083, 135128764, 123307110, 95678323, 671206121, 480326273, 817961646, 352946656, 683373929, 613342425, 982493079, 208124636, 357262010, 39908237, 704626811, 472249052, 58786907, 444260276, 841677020, 40282331, 111642996, 497822646, 891845811, 77155903, 174839970, 285907120, 867652085, 977183814, 50166451, 537129325, 360557594, 30589204, 191517878, 728178150, 45774327, 358398763, 217651242, 279650020, 960242923, 564023353, 604478452, 264898023, 701263051, 482765319, 517073597, 312169125, 980681078, 946245793, 460498969, 541007327, 763764596, 369828957, 111146985, 675455423, 428592252, 576619190, 773311791, 206889353, 1858521, 629550396, 576164047, 994284256, 877643220, 116186676, 550340145, 632651028, 962709771, 324695728, 184419501, 65132283, 399391901, 886632022, 489068778, 907708960, 857079288, 509314508, 767693237, 962143335, 513923425, 172341046, 431372955, 176499864, 616384639, 643731481, 659508590, 278830990, 177290528, 598169567, 474576583, 774740257, 43461888, 215929927, 27839118, 737403200, 549313680, 401571084, 802731273, 52439810, 639416391, 247800509, 586960320, 145335884, 553050034, 504033443, 789279436, 207527954, 972812852, 398447149, 470087868, 910477183, 706075787, 845297024, 604393848, 511675477, 153243637, 172964335, 836686006, 766775813, 17969507, 624329194, 28640917, 795472736, 345797014, 536946009, 437203843, 542990698, 235123816, 219389445, 946191066, 530003724, 825049178, 883782320, 233139128, 747664920, 159131373, 218058481, 501498126, 480628427, 377744906, 360017490, 4599842, 763699440, 612199955, 507017155, 580517880, 195041880, 581655641, 417569233, 691342521, 795537087, 817436904, 83464536, 402207893, 48526753, 641626766, 783378967, 486666582, 573904754, 837811313, 426843753, 685948879, 849589385, 100734396, 701788250, 316236400, 624157031, 595728406, 182603686, 739976280, 52013139, 180497979, 235256275, 83968124, 780257230, 755889544, 580154480, 896340973, 505643332, 220421801, 970195177, 821188353, 925809722, 603121721, 775563878, 408645271, 637195277, 531996986, 131951884, 188234394, 543644842, 323841614, 4669286, 458891516, 785549304, 860488210, 529090837, 61591599, 978989798, 64128009, 580438561, 434617, 549941087, 500739301, 546865034, 564938155, 655329200, 306673431, 551802106, 183974247, 402611875, 454079597, 683836713, 173660424, 208096617, 670700095, 301105128, 428209056, 23269986, 820836390, 306464030, 700065088, 529546486, 511913502, 86039739, 874202823, 232839817, 686925845, 536565574, 913600253, 655562178, 376795612, 430887132, 344960895, 802060467, 281552131, 14313634, 246889436, 397326514, 955315695, 162569141, 866212734, 931225625, 197910259, 281821694, 858390270, 301558087, 343900381, 193763921, 946111126, 855696787, 204837982, 51001967, 778910105, 336079431, 936027010, 221487219, 146753504, 855018575, 986713871, 66349425, 388969986, 970208674, 922633362, 105860839, 143579857, 697883007, 355998729, 510902691, 456029307, 876306243, 881596365, 255546830, 200794913, 323774204, 559186197, 416069278, 373366073, 649062686, 901925058, 153214038, 814408936, 445243575, 703250814, 530599227, 558714306, 755998654, 314751303, 637241561, 801447096, 982434867, 748246341, 839395071, 468253021, 634066618, 161423699, 929407304, 697948052, 500992041, 45169671, 437363728, 819436689, 945945975, 429148767, 428484734, 640016665, 416293388, 696276974, 314857212, 787099318, 589672242, 106034264, 552624940, 193843183, 114926839, 496784110, 779304648, 789153836, 859877683, 117857303, 233653577, 197372845, 909562627, 575477611, 222448729, 274867843, 987782811, 674874032, 506115429, 91898881, 67831303, 192874664, 485177365, 259553545, 723227732, 542122434, 240440942, 589555874, 262053801, 735930088, 819992317, 940343737, 354344814, 153123596, 113653838, 91614143, 930692310, 435690203, 792963494, 970668837, 191883722, 521507088, 99881613, 844117840, 79698466, 387659479, 667089400, 719691651, 51222470, 271198767, 116578498, 490465099, 363115593, 224175914, 438633568, 338611434, 562460801, 919482815, 857770504, 137409336, 766973915, 540897678, 326373823, 669830074, 238095916, 290531937, 174656734, 865750678, 570481728, 893364613, 445144264, 146259860, 205133219, 393446158, 440055069, 911151685, 519676163, 391113001, 895631812, 836078273, 469047516, 860907448, 283246223, 990592237, 81041995, 410726404, 472554693, 538586876, 397895190, 214423856, 46014977, 166935877, 748505723, 673814494, 773209835, 455686601, 285392771, 871220947, 532647412, 210388814, 535507879, 425893357, 936249270, 511428404, 733504190, 488978310, 68310736, 313234724, 464010732, 91355636, 460023193, 877935795, 229955517, 4880217, 910817706, 7918478, 133426021, 551872990, 302050897, 160668425, 154655165, 778955078, 670307870, 369170730, 899692172, 117936743, 827644163, 235492811, 6975128, 166426112, 457620664, 550426157, 300288703, 158036572, 801926692, 356965713, 32980788, 770636361, 951955391, 902222840, 295510504, 650132753, 352675966, 591183248, 57689310, 542385088, 858456354, 545610857, 887721536, 992677326, 313633132, 510513056, 422188751, 979677131, 309665170, 604417226, 427338505, 756356927, 545660883, 928509258, 254002522, 511583052, 638391146, 602313980, 641102283, 498313092, 906614485, 431912746, 632236205, 110906326, 11434797, 770174732, 639451530, 748835801, 263263255, 929415803, 637860715, 683859254, 933935983, 452168911, 217815193, 552344341, 829976894, 924114238, 450621199, 835431675, 227905664, 700985106, 158281954, 430008815, 210011347, 675606623, 803428910, 808448783, 405665992, 396869453, 220282403, 550911802, 694503555, 6020860, 63202391, 873673379, 502707829, 388681233, 593020488, 700138282, 232579659, 910337697, 450908024, 161312554, 376576220, 731591286, 524601264, 187132358, 810250886, 143281726, 770405281, 414267488, 417902791, 460311684, 644455231, 182425244, 165918109, 375315508, 91245628, 467386188, 367132303, 101557410, 129661789, 741265207, 983971385, 299963259, 176615294, 990841721, 297755749, 752158305, 714691560, 600801383, 596310924, 961973781, 522784858, 952973395, 620308790, 540907136, 199891293, 371936865, 757222258, 662893399, 906248154, 261689317, 578889047, 434330099, 961677920, 359898020, 827783042, 315835458, 728740340, 697650896, 692884790, 32091554, 4895993, 391389244, 396767415, 822752752, 683131990, 450183243, 880996415, 356978343, 553707856, 676313995, 640846151, 387458261, 75470749, 316211098, 678780813, 233158909, 68842945, 270435605, 716140720, 810531682, 474602774, 546628457, 60063610, 401672175, 763318775, 951906710, 264292163, 610880530, 630917876, 533273300, 493510665, 113959938, 616910386, 625413362, 717130036, 617493458, 814475753, 874754357, 662415142, 43756929, 153351095, 421934175, 421217369, 673899712, 150339664, 75690215, 971819766, 638966464, 908935710, 24347656, 38878655, 396641918, 939612598, 129638095, 202324437, 745068693, 755760581, 598958022, 951518347, 402327480, 259819519, 963936492, 709554503, 360132883, 111161579, 369191749, 180571619, 984748125, 681495005, 649568324, 520675781, 84825880, 320491579, 226565505, 348015602, 491494349, 884006807, 219334300, 680838709, 494474319, 336292223, 181889074, 314153474, 262457449, 340795658, 350212683, 567498181, 547923925, 346988838, 558843786, 302003702, 890502445, 572606073, 26234391, 910200592, 199689834, 386731372, 347602207, 835600446, 568971933, 248909861, 688971337, 175547514, 444407653, 968093800, 313899831, 464465091, 464797103, 944109860, 223661678, 636611165, 372938032, 332683147, 410115821, 889934310, 748319446, 70611199, 515244521, 95536253, 957923924, 627772664, 157261551, 273545487, 961420637, 352405528, 82599182, 267969423, 317468430, 977029261, 529677032, 194700360, 220370751, 389120743, 616313227, 20052784, 891551388, 117572729, 989454960, 111832743, 809522295, 850160525, 500588312, 85356595, 567143664, 375058752, 37715614, 797544957, 729121731, 728053634, 735241176, 587469906, 682977679, 738490039, 649233463, 566356354, 216942959, 625962443, 162005011, 958450, 844412329, 7766177, 519688816, 137483937, 232547599, 876870507, 319878491, 297843482, 661582061, 796516549, 124215089, 694296659, 243650922, 652422666, 515643363, 994660867, 830707321, 487121289, 494426613, 177591038, 243255062, 994574944, 227321500, 60973858, 353156192, 389696161, 763251468, 833865564, 353553218, 636625812, 240802029, 179872000, 83990205, 718153908, 467571371, 678034169, 369749190, 961580824, 30948862, 822460898, 423094653, 712535888, 635499538, 465381164, 731032655, 97788148, 146975682, 223260408, 974184348, 43535914, 444837567, 84992460, 754115521, 172649296, 170809303, 369128350, 596412290, 896418960, 409953170, 956438401, 800506382, 267181255, 187537565, 248894095, 249002195, 516699693, 158674657, 222528881, 634818839, 19637748, 289385958, 344077786, 125244249, 880015720, 742919271, 747284343, 455690045, 734401708, 288094953, 927656907, 976677473, 757275672, 642092852, 335719371, 543650979, 66417331, 729611199, 139193587, 414895728, 715848195, 178265431, 411108817, 326922939, 830495338, 787321721, 529073008, 954102462, 921550345, 355657777, 321197797, 258516482, 212422097, 367416405, 533912345, 51283149, 828128931, 202245659, 528092845, 64916053, 947738828, 920451580, 133284386, 593351445, 938289451, 351466166, 438649250, 943205113, 392228215, 67913884, 936320498, 36156904, 526656089, 859016191, 854798693, 138243035, 155956801, 203548298, 184216462, 232830157, 178896234, 853531059, 121647360, 28360431, 663938059, 550318240, 139681926, 411098125, 809191494, 9869704, 316645398, 646671232, 406191046, 527835964, 414880370, 558339213, 206039048, 899490719, 64769839, 711487135, 728239108, 379292826, 914962017, 512600176, 202633540, 809469112, 659106644, 211000738, 963038874, 64920713, 97402853, 461984447, 686703313, 456626397, 727526908, 748690819, 110907065, 127445893, 590242054, 208626363, 777425254, 895597025, 697214477, 251187911, 390629465, 644636480, 39842796, 589137810, 577664549, 773080973, 321220689, 741958674, 298005059, 999136415, 344885183, 136548444, 218724621, 84022976, 539461690, 206465010, 372999564, 389631359, 640898717, 857967784, 658009036, 903031300, 756402289, 222776247, 716333167, 501941090, 200896482, 333568171, 869592913, 945860733, 455155212, 968466874, 784233281, 596275233, 853837635, 157021605, 268069090, 813677724, 735692968, 244229826, 374818623, 557529313, 973151867, 711863827, 830455263, 387150270, 483532982, 605946778, 925657330, 751215508, 794475860, 526018907, 165891067, 982908503, 909797118, 914838851, 194578196, 393280347, 275662416, 747588175, 802598465, 377570191, 408214024, 985120430, 813173515, 883918032, 285125264, 721882894, 922552000, 102030883, 701827069, 273382032, 977921054, 193101501, 636104234, 939552731, 645777883, 619660433, 543562896, 862077727, 721790508, 150575405, 891728093, 386926372, 81577195, 702500911, 917784518, 957600157, 20957299, 694769074, 774982625, 384890556, 166274549, 541543466, 147057234, 25024953, 454734480, 399917628, 842904145, 368216882, 172423551, 669010744, 472163724, 339850830, 195999118, 935292849, 715500090, 241546277, 601922235, 456891985, 921354614, 146448220, 742573627, 404660493, 23039859, 81872365, 665465177, 221172138, 162690282, 78027931, 524363102, 669433204, 814169175, 432162376, 835079496, 525507782, 72516948, 823455172, 666632452, 785572315, 719371514, 716705307, 586864749, 995374836, 595255660, 945724333, 728896130, 584708278, 30899272, 187364606, 173728282, 230426893, 858377795, 434979081, 715056472, 252829192, 245004820, 58188436, 639823531, 588800093, 941432722, 746174694, 526006380, 1958, 479744852, 462502264, 429330463, 542470693, 331263214, 645031246, 379379156, 127240803, 190677416, 239776697, 52718927, 693267871, 541512151, 104136877, 392589197, 957209983, 378560468, 152748934, 569874279, 925819158, 234075257, 164319788, 301650204, 681849036, 420700939, 554849216, 106421995, 15097217, 150379017, 784270808, 82690133, 24097920, 106064211, 772894514, 268484678, 670016575, 772389510, 80610121, 593121281, 197895986, 942909121, 355358747, 25367399, 544405038, 381942609, 856925130, 266100680, 507466104, 960199942, 359338121, 277476733, 708569503, 150730259, 952313618, 278628267, 385913012, 970415092, 285407119, 510654327, 819208144, 130041473, 494160996, 940220770, 536235432, 842677544, 344039374, 23582132, 928827788, 316852531, 495311962, 872484948, 577812301, 403953051, 227778988, 911600304, 443115943, 946403669, 841601401, 483800017, 535280198, 684169826, 333391457, 882830418, 711312944, 701154573, 298263834, 200428464, 570942451, 973946290, 517264814, 521144879, 887668960, 451403939, 724890825, 446869309, 350761348, 36650082, 746110305, 831541912, 964244859, 141989707, 452601252, 518363412, 733120851, 229486164, 719947905, 205984342, 433490592, 161707260, 27376149, 739660220, 889716281, 217131743, 689686484, 421731112, 412285883, 158363325, 940881309, 37149388, 55818439, 861867604, 467528040, 833613457, 611268775, 910798823, 431282016, 431605101, 833191802, 653997821, 45339660, 453409106, 161691509, 991387701, 550569599, 860637959, 423526771, 632106124, 837520462, 803457184, 470371210, 708520807, 105942629, 475376416, 568000214, 386716756, 727941887, 998159332, 855557059, 471228581, 676893914, 135915545, 829559600, 54940739, 628527045, 41962397, 83730689, 392283535, 116906011, 37819840, 319587596, 448050875, 357182550, 311585833, 590194695, 567322957, 744956905, 476709531, 364836315, 686983024, 106663910, 384479621, 552374696, 777973016, 982743825, 463917137, 776296335, 65193492, 216328234, 600247580, 430276259, 499503531, 598437562, 53159799, 267302943, 157719371, 475084574, 669420330, 202597296, 964557115, 658635188, 922114932, 180385258, 971144122, 93607581, 73873084, 245990404, 804407980, 512944784, 947492282, 40664386, 438194674, 975648859, 607774415, 373808096, 802849308, 997000119, 482181269, 27357450, 339098524, 922135997, 133240092, 75859775, 557966796, 739511044, 632754624, 310138246, 258263012, 382956774, 618444027, 12096907, 158280345, 634837113, 590669773, 644208890, 36622098, 822674695, 502128290, 595551847, 641502665, 943265166, 200670750, 857052272, 700198883, 781722652, 611799401, 268262581, 790239433, 77628568, 222040384, 791417745, 672849684, 519807835, 984156859, 820493560, 389728834, 570370117, 563333242, 813944190, 840318060, 818394233, 728203735, 667074542, 68443062, 571876346, 865863664, 515424298, 70284705, 89225825, 796024953, 211299516, 638986858, 19206486, 245064993, 459232596, 762755868, 925548269, 176264672, 428904928, 514998171, 914337318, 597234558, 811121118, 646161365, 33444346, 46993444, 657321838, 876369593, 704093583, 793943104, 861449567, 995385523, 477644299, 466329479, 127909550, 746389073, 835823272, 967604279, 66865028, 213239399, 702493183, 144961253, 965624821, 266271161, 495190302, 594015762, 436799730, 631071172, 29221119, 22948761, 648402220, 183770157, 853359994, 767614022, 37618073, 642171407, 362110653, 391872580, 244809005, 433759967, 69277507, 254473129, 796192773, 67913432, 511390264, 328152966, 830916949, 328002463, 171380057, 539340368, 246885562, 118475182, 175531845, 431019291, 668346118, 917342657, 876785734, 776825460, 747791085, 535394670, 376224528, 980277137, 275066526, 107106766, 363445511, 433246373, 376548375, 424628738, 675780691, 380817906, 43653205, 397271550, 818212546, 698528160, 392084342, 863092423, 919532478, 849157910, 380086335, 722440649, 486391551, 788286127, 30415521, 670555908, 555012147, 60973911, 418278927, 464952233, 382509398, 100017474, 983009253, 581207262, 165311622, 615392887, 831027031, 979263881, 417913442, 775516469, 513631643, 806177370, 62819836, 510271010, 13505684, 296538808, 147599904, 378628670, 93871363, 463906755, 75635412, 769041273, 723131327, 936878565, 484948047, 47728735, 477733590, 223654107, 694300695, 34095272, 20527544, 419045776, 481902851, 868692715, 783673456, 283535204, 56434250, 393668933, 312441180, 365390394, 736278267, 182537019, 429676919, 549152525, 998058890, 724570387, 174004904, 631224329, 458793397, 621178479, 769478069, 979797085, 244695033, 873886272, 884669902, 584790574, 670248620, 180600872, 410133841, 432993964, 423345414, 744222719, 104354657, 494579510, 829917913, 551807122, 929864822, 595267116, 480936141, 283223566, 389063548, 877009072, 79722379, 47227362, 800064967, 283946672, 170664274, 710654503, 548729310, 403713930, 429939433, 428211802, 791359895, 70106574, 719984296, 982584364, 485344188, 708739680, 684145348, 447940746, 733132311, 53651676, 365595475, 237000270, 379144276, 398249496, 110549441, 709642956, 880614504, 114611470, 450558842, 167818502, 522418406, 957289737, 319232254, 261438802, 714759520, 248420252, 705170553, 548203726, 866752171, 929080744, 955528359, 416815139, 924498222, 174611323, 20768661, 83848121, 958755281, 821183011, 612301920, 632863849, 230806172, 771846666, 934013582, 862125288, 292956065, 661678154, 716501101, 532087038, 814171628, 916686117, 131617618, 280995974, 571531431, 516144896, 952847541, 274237677, 355069352, 961976964, 99537590, 514918914, 83101038, 437304430, 760155502, 269686436, 268164490, 569876070, 344893, 131604046, 898759912, 943570576, 238006123, 884319254, 282315028, 974520135, 372057733, 25671586, 490760034, 681611186, 909405517, 635099769, 404502661, 719532465, 591547886, 316192465, 616258829, 274942579, 671331590, 333771723, 261635649, 146167920, 547854058, 427365141, 891018211, 71213464, 208671706, 492615399, 740412641, 722793765, 875607931, 71600452, 648772497, 48820374, 912188134, 896185613, 770545785, 576993909, 116284926, 80213553, 445171747, 118177936, 73179701, 670173081, 350493744, 422607862, 420988921, 261843199, 148856786, 629814130, 605116683, 705958541, 615801998, 240606235, 830530355, 664221750, 630545768, 145051380, 636018365, 27058603, 694644091, 940911461, 67706917, 33346146, 15340200, 335230335, 694971091, 214386961, 353281746, 228345711, 700480486, 443781397, 477432894, 225377796, 926461958, 945636381, 507930292, 672403721, 887619114, 921770428, 572657525, 964029437, 390070113, 638716065, 646479814, 890288101, 771582782, 871146570, 41151076, 966928134, 92865487, 539898182, 21076988, 57537011, 991346991, 228957946, 464600575, 382525153, 300641998, 832664474, 824359508, 137134524, 680028965, 614581756, 689634529, 328166671, 982052474, 449672674, 723325838, 342096595, 78348297, 113489583, 908282164, 727036755, 395918906, 130017047, 684926379, 76871560, 708751226, 673646537, 542158035, 497794195, 751050710, 579484380, 516396499, 349684726, 471728143, 694775557, 342003732, 379819112, 776775123, 764639508, 145249619, 632054073, 554432423, 373163070, 500874082, 645203606, 521493659, 75520575, 398238042, 729563595, 572809314, 894871430, 492183280, 825986750, 444274904, 475642189, 909726612, 562234435, 491467592, 999398990, 540760673, 717289750, 378137303, 598798820, 172747652, 737577853, 410832015, 228850555, 245446282, 906758776, 367540169, 48428128, 570277426, 194224495, 345456259, 150513113, 517196863, 578141764, 519055590, 234861056, 534953977, 786758554, 947600810, 910483202, 257276548, 56008296, 155665743, 775652795, 419738443, 112580916, 177434521, 713144450, 317885711, 130107322, 651853735, 293492120, 413691750, 461504436, 910658565, 335072923, 423367279, 879185886, 734825706, 425220340, 97072690, 576990488, 677782717, 48451478, 557805596, 593821291, 804262439, 950695923, 784568353, 630880490, 526397929, 856056900, 913272195, 458060316, 774639946, 721445809, 637712864, 304725532, 818228795, 295306783, 184546077, 141734298, 347906254, 49774416, 404260940, 616087943, 58205351, 851299527, 514815267, 846868849, 250008246, 671909215, 874932052, 105658829, 596133242, 615781967, 601034059, 200800576, 472609936, 618548730, 922440066, 811764485, 711032875, 119874175, 280312923, 31459506, 9328223, 888128280, 948210273, 884711945, 331245572, 783388565, 394468564, 922306515, 448639455, 424031696, 144673781, 888725445, 773412260, 55980651, 749457542, 949476026, 887283899, 635915248, 954298766, 126817445, 119282390, 296748366, 343411938, 517092783, 561087250, 81894328, 885376708, 952294369, 385046332, 505282341, 240520897, 739154540, 586332761, 964068643, 773779750, 837504911, 467004867, 277879514, 547544565, 706654946, 299607742, 364969530, 381748974, 973352579, 972417896, 901835154, 434983800, 725812239, 491361808, 476469188, 996748598, 485612692, 194615889, 110881479, 317577000, 88733356, 602652087, 997248819, 283276911, 236710787, 512684294, 899174116, 763326719, 100366286, 594004121, 129853275, 659454778, 713288482, 163448601, 822658367, 818571197, 217880612, 744578961, 763877722, 128244015, 269348839, 955580501, 323173465, 520327744, 769538827, 583069894, 822591628, 884415917, 960497857, 175971242, 83679696, 721747313, 345824965, 514058454, 451760551, 685422560, 399517771, 189497699, 591031879, 38722151, 538283024, 384127219, 624120671, 416021080, 936977166, 690347391, 214097696, 155012691, 525905417, 662701552, 676657682, 721417575, 160607534, 459144413, 691902812, 168673408, 392841164, 891729707, 716616226, 120032522, 852704988, 443518315, 848085029, 690072265, 137858086, 588933600, 70274567, 201276973, 8227829, 172480978, 218313439, 977158825, 970629418, 736127962, 40574060, 970839634, 392973445, 579743524, 51024189, 518070205, 487905691, 548703481, 713898972, 152238557, 621488599, 392088466, 396299744, 442898194, 611137602, 556270919, 307914059, 446282217, 597901705, 122121477, 613159157, 810369457, 572334902, 153845079, 302325750, 176149717, 594991824, 937830030, 448500360, 779333101, 871936371, 242325635, 981431182, 107514097, 353815769, 421272989, 375617414, 879761144, 229730160, 338797494, 723923767, 685019054, 275922886, 972879223, 201638664, 482877178, 361160724, 966947203, 915675323, 728861657, 172117816, 436106606, 478536049, 944028874, 965517561, 951110269, 512502652, 805433621, 460296730, 713636389, 270316450, 564268748, 995015860, 274474456, 405239036, 259956535, 901624971, 543809857, 226588531, 411121587, 975934121, 862478931, 472943243, 780627626, 968013732, 389496674, 722615386, 222109894, 751411932, 868093594, 518040041, 944125701, 718279046, 255600702, 898133028, 927428912, 556640216, 838238074, 13995751, 343443251, 361576984, 425468183, 106220729, 734991052, 124294278, 829387760, 6736488, 138856701, 726659744, 329581173, 886553308, 123694507, 519932012, 814568176, 499495310, 185253810, 748930601, 167638809, 814832327, 348542050, 341382591, 597484306, 77686481, 882004056, 167963533, 194520587, 354019464, 696454755, 331910011, 545476836, 171161904, 681893847, 475070948, 500870727, 960905888, 989037829, 643528959, 11412721, 266157382, 769242692, 819613727, 959858575, 355004319, 350579535, 461214221, 199006927, 545363272, 528884010, 867854176, 639117112, 739805362, 303773281, 760180308, 562865710, 259821382, 411419702, 969259030, 702574339, 242702561, 171224733, 134168394, 416376064, 438964874, 952158997, 433642414, 667329746, 921801799, 950053359, 960742877, 342460801, 728353746, 877996260, 709392336, 100316307, 772495649, 948596130, 818734629, 132773911, 914623182, 700261400, 600464596, 947673081, 288626711, 622915801, 108004534, 39559279, 891927177, 616417063, 833276595, 583795698, 17784128, 642922285, 231440286, 384990378, 934631639, 772428670, 275317067, 453359734, 125394974, 647628493, 982930061, 410635836, 124569477, 963408839, 513244618, 516705100, 257982258, 278738716, 276217595, 374024569, 945197424, 311082578, 91401546, 424908563, 29787843, 687447094, 947321993, 35887176, 897415583, 176500769, 106785452, 525650564, 364048765, 456709834, 725710367, 927708211, 915724142, 55725238, 438815885, 965967140, 166616372, 276527202, 888056674, 630106586, 476779036, 98919123, 747644827, 633137544, 767158948, 959072818, 767005742, 820174844, 540285966, 414863431, 942185355, 759716271, 86469010, 427027088, 747120285, 381360095, 921576020, 940036995, 404017953, 955523216, 57440028, 943690952, 838677234, 53701121, 46782032, 996699820, 410893343, 994262070, 156493209, 663790423, 345668250, 245138641, 14295014, 240913354, 272731573, 504022188, 859654138, 510740021, 466139760, 476737305, 667822759, 150228754, 858787789, 495060068, 145935811, 180008060, 732974186, 477476877, 931308206, 920075435, 164656465, 545685736, 243150944, 995687426, 405640124, 942506737, 551442674, 127228789, 347458641, 444928614, 251599645, 652445058, 737551138, 318874287, 961279942, 285470135, 152836401, 886113196, 418904552, 668561088, 379314623, 950332430, 789983493, 490685682, 340310627, 415843335, 186006161, 300628480, 524882353, 702756858, 678824408, 48401376, 454418887, 405336472, 678947615, 168258766, 955715135, 561801735, 164780700, 358313606, 301236783, 233326040, 297488280, 563945631, 68859479, 256824360, 984877417, 312582346, 868950722, 14624992, 298388671, 877470011, 894010913, 904336345, 272503859, 11525090, 906562198, 424999605, 630326123, 600617657, 208423538, 328141015, 263925084, 404192646, 269702861, 273620166, 623609974, 455825440, 83009717, 90326863, 257809756, 325398573, 322906266, 704375931, 653062202, 463138628, 523585717, 528171821, 127566739, 631110592, 858756467, 984822527, 415812759, 832117515, 355231067, 686918562, 30199803, 790339594, 536261496, 319221198, 819036472, 400193195, 879428092, 739880850, 542706540, 692945917, 741700013, 911950049, 327770572, 330924155, 45086869, 261286564, 770326979, 423123221, 653403901, 144406925, 827176854, 528095320, 986104727, 667214927, 218909653, 386051073, 276134300, 659665910, 474310752, 746923623, 877751285, 150487373, 568063767, 957944171, 517531112, 827241901, 288534597, 474266633, 830478552, 391288881, 263517083, 794600872, 696574290, 390192905, 965091249, 873253893, 763560636, 313450348, 69814691, 732625710, 396932100, 128157031, 534900914, 723030206, 926766072, 409525245, 635434259, 683362315, 308255824, 644286965, 398932930, 688647753, 347142775, 823611942, 564727045, 87660128, 806093818, 339915871, 17967514, 406349623, 677105533, 525133380, 663457084, 151673230, 789952213, 314714063, 232968781, 462652433, 651618742, 368094446, 687781706, 443197508, 404394107, 767210684, 980809152, 515373605, 893470917, 382559794, 281762146, 957666449, 319940871, 940787720, 524324154, 696774250, 40296214, 956806407, 829096326, 962830958, 162955450, 928364793, 531223515, 911415567, 235539474, 673211251, 892761485, 421116467, 832140783, 102957669, 579824057, 74604898, 920440161, 705130257, 752648096, 23712587, 308440218, 824579015, 367884477, 151397390, 298292171, 140987740, 566688696, 830780580, 158276255, 401077323, 607950100, 839288633, 694640126, 392011698, 152901038, 703332390, 117132907, 825038395, 539066717, 79694135, 483101461, 252281086, 567565459, 685709104, 398776393, 646752380, 137954988, 267851897, 430047488, 442206444, 585987371, 106898415, 293123576, 379250030, 14880713, 427484884, 993348935, 155387962, 720970279, 86403567, 53385600, 993264607, 874497978, 777186005, 264556129, 868534972, 656054146, 446616186, 128178606, 531925803, 537658690, 444661112, 885962291, 327994647, 669047021, 797532099, 889010038, 111123626, 7817020, 30772459, 41906382, 780838506, 76517460, 270782936, 660708132, 149109201, 832742318, 650335446, 881008384, 25034670, 436851563, 749818627, 435787441, 248646612, 627319704, 85262326, 694065322, 332537284, 22961639, 297333860, 133854856, 811652375, 455245724, 157716576, 677134525, 979292090, 339162588, 12209183, 565107436, 505717868, 801004815, 626813607, 215198819, 305967988, 901704235, 532258330, 86837751, 889122965, 456404790, 482414208, 258059997, 14402699, 254949290, 492266460, 414732582, 590111719, 663516878, 61981418, 361800885, 33031380, 706398217, 406082658, 470412424, 703563842, 750820104, 999035304, 377079067, 246328184, 888754610, 356484610, 402493928, 701061501, 191792703, 588118805, 249172487, 120589510, 561540636, 387952176, 752440551, 470694655, 388736782, 71717417, 644841026, 297573176, 851683786, 168554124, 394132345, 543359417, 502942422, 822988329, 770420818, 84222441, 235797053, 402223637, 534725329, 761980501, 187299207, 207328243, 146345985, 498276394, 907125371, 310500133, 148072701, 732886324, 875776524, 69057930, 586586276, 545740710, 876505374, 69812515, 525853588, 331497948, 272292610, 905052975, 59123867, 82474557, 573761953, 626516409, 756572815, 889041414, 616599665, 569046529, 144620977, 12131880, 386427267, 744307539, 811424916, 497676352, 838833946, 750680537, 727486287, 875312219, 161705314, 96068709, 601720412, 186376048, 927396875, 137498898, 321688995, 449781873, 485893276, 371016724, 180381087, 77441386, 172402131, 763861041, 885157949, 925072166, 278724772, 625632843, 282596552, 836332055, 411944457, 722429157, 21707720, 234007917, 74435024, 556614465, 651459763, 925843293, 286912744, 16112817, 15145827, 643589854, 875142562, 889994196, 991024969, 800700388, 960714507, 683310431, 354641879, 383222955, 161296450, 217521434, 984413807, 21770976, 399838318, 743730184, 411590726, 736100500, 715776375, 669484737, 88886538, 526964247, 747752232, 815317965, 813051319, 83422359, 50976537, 442449158, 604191491, 159244205, 856266421, 359274198, 477029150, 888268437, 516870855, 108961603, 442455987, 415679375, 20376685, 573559924, 751660822, 14595742, 414240621, 747188287, 153313934, 896726148, 962472116, 255186706, 903194400, 454568771, 159054198, 567630756, 606500961, 836766944, 832771434, 231960788, 547933287, 679291107, 75049388, 389804341, 66351917, 531029043, 49655388, 400565315, 940283160, 330271880, 434429373, 106107941, 313493344, 398346407, 447583581, 135811983, 502538314, 387647711, 210670935, 826415045, 986518893, 37111910, 574750922, 773111003, 1111797, 523432925, 993927813, 394523861, 740800974, 662774506, 383155971, 506996163, 254696404, 608659928, 655885548, 965059920, 846436180, 927596358, 60338495, 729926782, 823750503, 523126706, 191591965, 492379334, 823069035, 95386240, 711569148, 557616540, 264337872, 66190198, 986626953, 215336043, 704690787, 293518818, 477352181, 495395488, 557279141, 426219766, 857007431, 323680409, 475350579, 549028588, 603947182, 982664968, 445868661, 232411922, 246409607, 576992137, 516543771, 947795721, 105748213, 548346974, 973210290, 229376822, 808835795, 528089839, 718600147, 277341834, 669482004, 261937402, 711189762, 116677611, 856010057, 838250469, 388440245, 847961863, 931878532, 954515745, 376475218, 353571332, 105664274, 594760340, 526504469, 619597916, 751847552, 714745551, 136666034, 364809804, 313591434, 185712007, 899304358, 83101259, 676781050, 761556063, 121534381, 508020856, 746482621, 520139793, 356164618, 506882821, 119795552, 213179788, 794599981, 84820695, 854713366, 452419675, 305295909, 287244189, 467847255, 473057716, 179629741, 521891933, 540993266, 240374646, 372570593, 734197413, 579023117, 556644739, 264839762, 537548662, 455603315, 496727140, 5861713, 24697704, 43164008, 913138429, 319422881, 703574960, 33982260, 309922162, 107928389, 987899983, 726173255, 421903051, 971675887, 817858391, 651150241, 407910979, 152677162, 944825572, 385332262, 122716067, 781709591, 838860726, 31513314, 642902281, 315944727, 175367775, 107184033, 518520597, 653926664, 899314611, 44797798, 690064889, 18151495, 906130718, 97076335, 498657693, 141135070, 891265736, 144943099, 563210395, 633810518, 867610816, 284258365, 695983038, 428210304, 18829415, 168746948, 162389553, 80051344, 855288218, 190600893, 805750365, 540434069, 719061364, 641366544, 97266810, 302311488, 510633283, 399136634, 341620868, 399929560, 699782030, 182213882, 368207540, 169550210, 752661066, 266261061, 883925024, 131016399, 650876497, 281059901, 73445545, 761457029, 22735002, 649701659, 141286061, 657028281, 806285744, 784599091, 280887203, 10449716, 506613058, 699183085, 522756576, 503025200, 207795612, 628579529, 439006378, 299072036, 801038893, 856103273, 569899351, 446838466, 656881705, 979677087, 358100772, 351453724, 627471575, 288731226, 252404710, 715345080, 120735797, 935144522, 677666110, 78591497, 691350292, 278818736, 282057965, 399461964, 532130104, 35618041, 112363137, 784885731, 152765164, 221414102, 6070970, 561310010, 271276233, 54989676, 72175799, 768703740, 272194376, 365325135, 204778141, 456302232, 971096674, 491411576, 843550846, 315307566, 398836757, 48628847, 685175877, 781100001, 703085825, 140794743, 133924705, 798863563, 319607704, 999163286, 370875315, 443242973, 509390916, 584021769, 742029695, 262559021, 906899657, 850850898, 399418116, 107906093, 186731045, 731399993, 480400310, 281003779, 930636185, 886315421, 606227150, 889777232, 179539585, 145105729, 805738850, 52098544, 748460496, 311577816, 594384448, 393633438, 899356374, 799030567, 627197184, 426131279, 325895813, 780376570, 921247279, 385391252, 724681706, 366675153, 178637344, 838377758, 374197683, 115724703, 849804979, 78694545, 997311390, 78718781, 734425707, 810762486, 694893571, 815423631, 288612404, 450208233, 917358984, 11887704, 332364342, 44876917, 899487119, 413346825, 693058391, 488889320, 832878372, 211080222, 657428480, 994036037, 340778665, 756319265, 288159401, 787491524, 978986288, 928974735, 849364599, 147377334, 442280892, 366022705, 10269902, 369484578, 959935144, 914686811, 461856524, 103244095, 935421730, 310585190, 207407215, 324685839, 665744626, 578181605, 776050212, 900938601, 106209174, 280326138, 171209380, 682474053, 271995098, 306503766, 582418103, 434140884, 226900665, 402272867, 667662745, 195825780, 721859096, 993475237, 196550427, 240903150, 662206831, 889021831, 999723617, 947885906, 702033246, 228159158, 484356963, 254662208, 353484021, 375945499, 735092130, 692292898, 80505075, 11027904, 961062619, 820813110, 283110677, 550478501, 932291413, 805515194, 542581557, 505850663, 803642322, 619285717, 156871076, 194542932, 7147069, 896217178, 124484100, 71451414, 901275434, 984753844, 928299205, 520304902, 118240315, 350413709, 710411178, 373858559, 861530615, 278769522, 505660702, 492558912, 371945289, 307632072, 789018759, 137680047, 523366522, 490950851, 481290908, 997176137, 616216247, 325346123, 911230190, 687545103, 351436330, 673042351, 867175996, 997737551, 903804977, 64733042, 757575064, 959048683, 593522530, 879350786, 376081016, 579423379, 853537519, 174104771, 154772825, 247970416, 977554519, 442156403, 685316823, 635762929, 774202202, 768972205, 930455498, 137635900, 681394653, 813150980, 266927445, 49873020, 600886895, 923035344, 164442010, 327248915, 179715698, 231543836, 97165915, 15354307, 783019377, 337234946, 264615867, 166904931, 129498473, 549245965, 312045758, 101312828, 22797582, 580752370, 409021727, 943919548, 401569321, 810162885, 401670620, 184475351, 469549624, 780155018, 364188328, 457490383, 163362327, 300263647, 879023276, 698609641, 628008279, 564922116, 172516218, 6994774, 143199971, 523854661, 247714264, 953290383, 497841623, 776473070, 623590170, 705573173, 60341577, 346019249, 656200784, 199522119, 618503721, 795277967, 784059581, 505056042, 861264265, 513289101, 519765067, 968841978, 285644423, 29874174, 86712492, 341240972, 860016686, 414530062, 377901124, 485564686, 177704571, 791704242, 763045640, 761159855, 404862267, 801013800, 944219555, 901139845, 993613636, 314252246, 671801902, 70672440, 53987881, 289940084, 403065084, 108163952, 106482753, 870012392, 53844910, 85911784, 712580764, 356708858, 171367686, 900323572, 250454525, 97608162, 528306495, 254704274, 990498601, 543741273, 824456817, 27827532, 954310105, 222421642, 627251742, 910031857, 936177808, 382895057, 416660341, 32272862, 544484664, 491751920, 40503669, 836107242, 648963865, 464059926, 769121444, 855591539, 302534919, 601850006, 611972881, 979140165, 243885749, 553381052, 177827438, 276292410, 310817152, 196102137, 448025393, 278242050, 552387217, 514454091, 296907616, 751916847, 158318124, 104927627, 594666848, 106094293, 577943062, 297881084, 122858655, 439927697, 943847776, 601018198, 920816673, 7833495, 317766236, 885771904, 562233713, 991174270, 700648107, 976762517, 257599700, 860376300, 833391590, 584328417, 517063940, 21841580, 544797064, 144575552, 907664515, 780266224, 748956983, 680232503, 114060339, 323307037, 555870016, 200176913, 674776853, 491174803, 345971411, 534396930, 710626944, 39585295, 700401104, 216025996, 769458332, 143549653, 518896678, 75095695, 541827037, 734278939, 976496190, 319207084, 425556778, 217413700, 276464843, 76372051, 907008012, 355157062, 861965249, 828580717, 619005291, 329153204, 192727045, 138408735, 591169047, 941756171, 122560494, 329181840, 639761772, 765343243, 547981003, 960903026, 131425969, 501382071, 988804151, 145240815, 328491694, 650948794, 261873629, 166111997, 27031805, 51047979, 230903203, 917429588, 23685465, 696922636, 878695966, 954789255, 996702095, 427361609, 21474313, 883385287, 649158820, 675196292, 419525433, 71373872, 723194946, 542378666, 567757265, 485309602, 29760490, 691536351, 95163562, 545072265, 946407347, 147413137, 813982725, 537424949, 631631259, 44904659, 387402489, 677960330, 170087925, 937734942, 781629179, 541692631, 62421520, 100854188, 234888039, 80944970, 877169879, 187322918, 980368428, 846878170, 938426324, 497044097, 419778987, 431329883, 60993369, 937445486, 927538087, 883408671, 866887315, 709862119, 532249558, 679122353, 346318832, 886515141, 154385004, 197911829, 580387930, 803192671, 904538838, 439495268, 895007130, 563876511, 337772411, 281276821, 214318091, 395190965, 937129647, 472358985, 562944790, 533992102, 215810828, 201029225, 212787292, 571498367, 373002366, 278681913, 780591610, 453657736, 565545091, 782922710, 739894293, 931805207, 686170151, 780523613, 321633963, 243453729, 980754933, 831846176, 322235095, 193437521, 849909314, 921182061, 484972433, 725269632, 732885076, 66812282, 122894856, 929151703, 187595784, 134116581, 405803818, 442364939, 147003020, 92408618, 847070081, 651487847, 18889494, 550827308, 409951280, 858593666, 192217490, 670443020, 752357743, 305168092, 166856463, 320828923, 600354393, 9151187, 324215799, 118799590, 509362873, 409237999, 523620319, 964118977, 437886697, 868760, 730269549, 970928679, 896711052, 699744316, 744355277, 780695676, 988460097, 248042345, 609536109, 185380247, 829478819, 70054733, 210291982, 731069034, 906397317, 688256037, 81942410, 274437196, 746660227, 427196992, 311405989, 461269573, 128066913, 81077290, 796035387, 625362010, 821756001, 484854027, 761183841, 122750543, 689596821, 724998853, 442455763, 51027302, 359866654, 725709704, 422025525, 340512836, 950051684, 198869419, 732379310, 765937352, 536417451, 494367704, 499966404, 934726126, 226794318, 956325335, 835983637, 417455383, 812016890, 763917785, 291753974, 677097552, 694715637, 244057803, 625201829, 489843658, 979610644, 897940676, 235424080, 980764901, 533312088, 815592789, 388724773, 719792457, 572717977, 310728315, 952598118, 487702974, 652463645, 979515199, 543099113, 893678873, 150827214, 58866747, 521861308, 857018344, 722558201, 529529902, 514228500, 58222062, 630151167, 436200350, 131296429, 298441148, 315735211, 513164879, 554086935, 703319410, 263973575, 587423010, 395647631, 494916675, 167417422, 687402163, 423467647, 415543798, 507490895, 329395860, 575479110, 692004574, 275342736, 189790036, 539157909, 446961227, 633055809, 190239455, 43631111, 689442577, 318873066, 738999267, 879394535, 82440124, 166623378, 786334110, 421777394, 13513984, 451723395, 126055454, 904670639, 638916246, 582710358, 280392613, 273704305, 16188584, 966736517, 605185, 735842104, 166555488, 977732994, 565184098, 667366990, 178661842, 730135640, 457953765, 883059544, 438078173, 215014496, 921882335, 264126019, 358423547, 507014858, 258266998, 692222822, 753546375, 41722277, 449339851, 357497165, 140186266, 690832852, 336058965, 24803933, 998157017, 698338470, 38199032, 189826742, 171063555, 87058476, 875306352, 449953410, 658202295, 620191206, 972748440, 621665431, 248315349, 261326789, 800892136, 793364002, 910782251, 81304722, 123799170, 857029897, 626568518, 679631642, 170961959, 259348304, 485368065, 315539667, 36095790, 28466984, 395405504, 171987162, 737247054, 682223014, 195034510, 978452094, 291989702, 382236832, 233254197, 489488245, 32178482, 439289114, 712986594, 281385482, 810346514, 391197789, 511001418, 172460317, 970855701, 857505648, 498428410, 696149869, 331226060, 512844951, 13269286, 562704826, 973039986, 308555470, 777565042, 114388112, 901616199, 990068299, 786985466, 363630169, 529012109, 639692828, 138743113, 148970961, 648889664, 495751395, 224003026, 460207433, 56498021, 926191018, 990235439, 607352562, 276080160, 282559839, 598361928, 143240789, 307383483, 691974670, 990700420, 815195158, 720803819, 436220021, 32487082, 395888814, 724559831, 482423541, 548098427, 262227806, 739915593, 314777385, 563707263, 802338755, 659469613, 141295569, 538716373, 501302430, 404228012, 564524981, 674595966, 993046706, 592752447, 412310540, 569271209, 644793491, 40198801, 451847501, 610051844, 274519416, 204389269, 200855202, 171465805, 122570720, 854170518, 189116675, 347395192, 993406692, 714538101, 380071202, 375967981, 616743949, 374076178, 596072537, 315655688, 986446374, 242748733, 952336456, 259346963, 380523286, 23889051, 615373744, 69752800, 194202427, 669079342, 235594221, 183428934, 605313912, 995341743, 125009622, 604017710, 865232116, 275275124, 304959689, 508172991, 49851109, 729514785, 759602737, 138503813, 274397638, 138852959, 451258444, 604027077, 266533781, 770581028, 626816203, 603864139, 59555279, 775097753, 386760846, 160075255, 22869792, 9745514, 760442514, 660577727, 836191914, 787026539, 119816321, 783056780, 217494854, 854876924, 904807225, 164037708, 605207839, 764872635, 964831755, 391933795, 129597731, 819712474, 354902394, 651272833, 294158639, 237667193, 226916118, 698867120, 71616113, 609314023, 395749002, 687655596, 1038879, 334586720, 6479409, 536101844, 176492603, 469297374, 241197491, 889160166, 406214891, 88702251, 849498063, 288582376, 228244642, 86444501, 908262873, 446586115, 947971571, 236852110, 565245818, 113832286, 800134225, 257255971, 887372192, 613380748, 65758732, 121790430, 237723810, 160511707, 741074949, 252411386, 5588254, 28713888, 252716133, 945560242, 177393363, 285665531, 881603906, 364067044, 480725775, 108119785, 501950019, 45172228, 312036158, 38887388, 710346215, 483857157, 974145493, 100298348, 192234961, 153382091, 784459819, 819197244, 3133952, 712005737, 411431119, 568056499, 728048119, 716325364, 162806686, 86512612, 715309877, 398096757, 857955816, 88573818, 4888639, 685144025, 325270325, 13127231, 67710628, 33006383, 466564138, 682513907, 526923255, 810060451, 452370930, 654230844, 287394957, 471427831, 98730964, 889099179, 993853989, 306695677, 181463606, 765467532, 381674290, 361767369, 733855377, 959533490, 376660512, 776167775, 873162851, 564356999, 486358325, 529332882, 804296216, 440856478, 344596366, 12314977, 501941014, 103645938, 15053082, 530467748, 68073367, 371361185, 58318443, 300531894, 105569488, 92854023, 497568995, 302377329, 894656160, 952973070, 206163011, 467957611, 416267288, 734321393, 766162209, 328102320, 801069738, 816046357, 284407505, 225937325, 143877575, 638054557, 391728259, 579021874, 18934388, 383725342, 150423150, 806496568, 41061338, 557601072, 225411280, 914909141, 280663201, 260120862, 354316099, 234070254, 467039061, 462870081, 990021631, 196076633, 762685683, 195545853, 601767486, 435578818, 347108811, 59881544, 789381570, 272425869, 538169121, 329909867, 186984736, 856260997, 966782253, 872597951, 756566473, 567539701, 286533273, 729146797, 965695685, 413623775, 161222991, 97433187, 420213599, 891548367, 642315399, 540200060, 547933618, 615968353, 378368009, 267890899, 345046476, 393215657, 799498876, 84712457, 653497333, 953154960, 382949496, 808871721, 694963347, 658361016, 156742459, 155045205, 879324396, 397028636, 847020647, 60648701, 663823726, 567638642, 739205467, 392579963, 709010640, 255645359, 536822818, 513165142, 742368718, 614528169, 593370177, 835724989, 382664364, 846484694, 578713665, 556274652, 383858790, 938379915, 287642629, 798999108, 648273434, 256671192, 235726737, 643102124, 302719076, 677789802, 680582044, 289598120, 683910897, 618736954, 546128995, 505542972, 56135382, 513046424, 46549129, 952349465, 845497502, 767079949, 236473210, 188608607, 443534576, 364602264, 889137864, 207927632, 456575117, 635770123, 249694245, 886010241, 366879421, 776562069, 293293689, 72998959, 76584932, 286346904, 117762677, 646793573, 713174784, 29329309, 638995511, 556001867, 398694620, 64660322, 437263738, 859790003, 52938907, 929421277, 109938633, 165531932, 720911641, 555370350, 576048360, 898801139, 238225605, 270182515, 947418983, 899159636, 21713951, 77170778, 38468174, 831236825, 373038364, 453178040, 248330307, 559022242, 630617757, 188396131, 322647286, 748986686, 609920330, 76489453, 714240865, 670418022, 634533027, 562352416, 777360977, 737545590, 799894466, 315034411, 280789717, 699173147, 793051330, 172586507, 988793204, 227244692, 928329922, 819528454, 593040436, 416410793, 657491203, 422768058, 891393446, 422476664, 456073044, 761783391, 8950330, 683743172, 372624872, 621892519, 361933024, 553314448, 357582721, 282820157, 269733505, 37405465, 820379708, 618078850, 959954637, 589862371, 891346219, 265244327, 783439524, 388997403, 796050043, 827535554, 60810228, 992256735, 421781383, 38152656, 465847031, 922293882, 32272927, 16924869, 240291409, 907108434, 781471784, 865707676, 825626936, 444981750, 837450821, 973080770, 474262415, 647336498, 964370482, 947838725, 793437804, 944023608, 233381644, 315076250, 268248928, 841493610, 145138665, 424669224, 712213930, 887988483, 96460297, 313851041, 364884669, 197298275, 284604261, 592858347, 2075343, 833448195, 442031603, 143337141, 909014726, 838707588, 673776879, 237121756, 61869106, 876970989, 183036766, 613489220, 838333895, 135564412, 12405562, 427409659, 389416737, 546886974, 821388532, 399667271, 10115913, 141684574, 745883999, 48313711, 6590517, 142977355, 703459138, 972608568, 290156512, 494759953, 104739161, 110780388, 476133300, 861108460, 691515089, 367789010, 298721563, 300467797, 69640173, 731390672, 49282990, 558280754, 240412973, 94830923, 892592396, 409911396, 543275288, 597766798, 112267386, 326885162, 124051648, 19660270, 618788976, 577738003, 623948654, 613153309, 448841157, 162395592, 127878628, 569779745, 436012301, 983540486, 343354573, 35510153, 498302457, 408028103, 376258412, 975884994, 927380001, 446067314, 891034030, 406824264, 893412766, 879661267, 262264433, 797280423, 169880433, 246411894, 969559200, 999748328, 384090371, 827866749, 894454748, 489027107, 345572331, 431389732, 961661392, 332507513, 355432793, 107347557, 238084605, 918920583, 97684390, 896185956, 60548293, 88156466, 129205667, 137242629, 140970777, 934567897, 179399278, 503119566, 662535078, 455259266, 703029099, 247033655, 252008781, 860340754, 43544047, 316188792, 785622133, 838858491, 725196949, 43172630, 792007328, 143769527, 554001053, 11014222, 925695116, 149609398, 622245056, 864121314, 599588570, 964657230, 858869282, 25821699, 347513860, 977312620, 516342339, 561559404, 553667025, 885779956, 740150857, 225919607, 97708667, 663820050, 167459691, 393864413, 736060706, 912060804, 720669876, 968430375, 597131250, 277474508, 751661181, 624494340, 337452648, 260594848, 152238690, 314531680, 22563405, 567449545, 570290551, 794016679, 669818615, 612415177, 269251929, 222892157, 77328247, 341992212, 781951196, 841261942, 322164168, 825789778, 142276966, 422399944, 23319945, 455235923, 793195271, 810904677, 246954686, 96836603, 954208315, 840976239, 365289189, 734111881, 612216414, 721801060, 882436541, 783255937, 828656905, 842064479, 152250987, 624448295, 426190853, 921453627, 725471750, 844060780, 272409354, 422132965, 373705438, 184134426, 572385700, 797663067, 381914595, 280267774, 395743065, 170457392, 618958668, 972105274, 367589541, 635163512, 546588552, 733719244, 655537469, 280539387, 121639774, 219968596, 516032292, 864150506, 459711926, 738049856, 374243167, 531897836, 696817475, 247419906, 610492730, 726726565, 545023069, 341718292, 36107744, 425482550, 919431850, 494271316, 194489745, 506445366, 315572111, 182444468, 84502571, 827570514, 813967709, 129161077, 572166785, 263969858, 986135893, 121864900, 544547310, 542263575, 891628801, 392400060, 999021343, 226304116, 171873397, 874244388, 153753094, 978028958, 128999961, 165458888, 64182763, 475346051, 305433400, 957939041, 263458662, 543612623, 789810787, 359458757, 202150670, 722971538, 850845860, 785254867, 957699357, 93630241, 664388223, 995473552, 869250451, 662940349, 809270922, 653068814, 400847576, 998458755, 602592050, 874352063, 539871208, 133317712, 427582732, 378653068, 557424699, 551383444, 75677133, 385729944, 558481481, 974238218, 787199545, 28046850, 25124385, 771008702, 892738285, 26403297, 701127371, 344790106, 164066687, 645204653, 514046176, 165166401, 571912177, 189726885, 744400512, 725136018, 922960939, 476964226, 183615986, 532937481, 296560617, 158660682, 775072798, 318014131, 87872803, 65066721, 625205688, 752360777, 192912819, 17587961, 275373371, 557574822, 729558905, 382170795, 148566599, 878202606, 154683890, 42800454, 839396993, 227311543, 128604656, 901614563, 505453437, 666142549, 271377427, 668279528, 148774081, 883423396, 392108787, 334941690, 305193415, 851046694, 448435143, 618731826, 356559174, 569670892, 725215762, 120097410, 640979658, 521960815, 204226719, 667628625, 876040020, 686080495, 295106661, 824048975, 676227338, 60206023, 467499238, 3123613, 432318485, 605501075, 411247368, 780818142, 151435068, 211597401, 928568485, 55980710, 785282330, 608361079, 121393406, 653261471, 792318686, 407129532, 805081711, 884108467, 46674579, 599379977, 490246923, 727468783, 657311088, 350330933, 804377045, 7610595, 346283498, 914809243, 21276487, 156560213, 205836220, 392186097, 692533175, 256388476, 694031306, 922921366, 581013949, 409436852, 431512766, 943553357, 538754187, 637263832, 124514277, 718842154, 226680801, 59969987, 617243679, 447513542, 152022591, 45211736, 446862720, 588508361, 559810773, 426242216, 956690638, 259819517, 863866819, 409729514, 325257317, 845533197, 70777570, 457265305, 38739421, 435541708, 717994842, 763053129, 316013592, 232526264, 813756165, 815997314, 935086234, 299467623, 700562225, 358608426, 854347938, 410643380, 26154659, 137279553, 971839551, 977521961, 202098206, 498752687, 939137734, 166486414, 283348330, 87861314, 898737457, 776251891, 782334858, 687776576, 586619910, 859507133, 669757900, 600830788, 717667828, 786364664, 467070083, 838206857, 685963897, 152844271, 834285156, 19781709, 153892263, 108355814, 869871091, 487084538, 42152894, 587091510, 973734429, 118944736, 833546688, 997941078, 778867965, 115553528, 57196929, 518989238, 32404314, 523484664, 975155550, 371859196, 69769576, 649618594, 646645694, 418437664, 760599709, 470612773, 171550646, 758964466, 952783573, 566038942, 133715763, 497006485, 770250171, 297253851, 525828775, 406903183, 604505048, 821325378, 18596742, 591270613, 646394303, 949445, 386616639, 515095414, 233222138, 335100624, 151177654, 543207282, 566124181, 703882814, 842563781, 592523260, 481123935, 10679009, 384996551, 88143477, 794965517, 165640259, 323308963, 424639876, 517558431, 941890920, 563223399, 539475167, 183967840, 159951756, 134966665, 450726961, 107767345, 534655535, 843012967, 768250778, 858775387, 915709842, 452981920, 552323402, 425775120, 82748517, 516119695, 923708372, 679064051, 84903211, 74429371, 343545972, 96215826, 418203980, 266533317, 260370507, 731183177, 541442243, 290226644, 510617523, 573373321, 17894810, 890149699, 791099246, 44702004, 370279833, 410192107, 561868279, 757002224, 53797562, 168074496, 533294742, 399708752, 384786687, 31650624, 488600801, 441073258, 985333900, 790343333, 266779490, 76159696, 744000901, 937168398, 841915451, 530748868, 738563925, 111966896, 467489718, 176700426, 117976935, 513527277, 310375793, 90600497, 93171621, 604071736, 675154965, 817781510, 628837956, 388127847, 144321421, 176127521, 483268465, 554251156, 28103884, 598215586, 265024238, 945953396, 686235635, 882803294, 474612951, 767767142, 623129149, 169856839, 345419500, 143030288, 257481155, 708403841, 320780620, 788735101, 321564779, 216964599, 618098528, 1739454, 986273379, 876220332, 792402926, 180581146, 648786257, 15534248, 671273964, 527928292, 814420514, 931232615, 906248666, 595702792, 713900069, 752767950, 803155749, 133934580, 28237492, 305367141, 133193751, 530757059, 426481790, 110057234, 648594007, 74650655, 955198191, 855192590, 874385837, 596537114, 430127697, 108816368, 497225810, 318255970, 518503151, 407042213, 925539138, 500294105, 190812560, 682674323, 640176663, 849255216, 101231093, 274146550, 390213149, 142903097, 694643214, 684449943, 428791064, 672788147, 566525954, 953986774, 459145100, 89920884, 560958763, 274599298, 133984398, 812390540, 813018107, 23124214, 384731538, 737671000, 429396288, 374301665, 140116877, 247680322, 705957305, 321477566, 154785593, 339873502, 736378020, 859995727, 965694949, 625421623, 889331118, 390547761, 800327418, 767844228, 934082352, 404260356, 666758867, 391887152, 804976308, 832804748, 674501797, 879407665, 429393622, 739726895, 416038773, 21444234, 394770483, 5389913, 564947550, 847270558, 413957460, 523003455, 94075286, 593235674, 733450906, 717484389, 663488342, 568164610, 868277991, 310403540, 779683615, 212393820, 849968809, 918896686, 994923470, 908278723, 646845556, 325068325, 175505608, 428267075, 307633080, 77149702, 956082016, 875214040, 619963980, 533981106, 868618176, 472123848, 530441244, 205422569, 196533449, 475633432, 579090789, 703164848, 12869346, 930760116, 438277275, 346230381, 711010013, 971112261, 77781285, 197129761, 492988204, 334954038, 513519110, 548862099, 673049424, 466254932, 141767001, 628522472, 487147805, 196230386, 548163700, 19525495, 396301018, 202257619, 598797242, 551314581, 425512448, 80817348, 717846489, 330034602, 330602516, 949010332, 151278639, 287636672, 286985908, 957796783, 926554239, 565323972, 69805639, 379778241, 155633318, 778345679, 57130281, 583254041, 431817577, 119982068, 145362963, 763099076, 600545501, 368567435, 516731510, 660908924, 825997714, 98264328, 916872205, 482535230, 575811296, 413577619, 929653249, 167323421, 831113783, 165394640, 305298277, 748188213, 412413753, 390449666, 208271985, 464121130, 435565884, 601565201, 330271472, 9805749, 476491711, 769426265, 94980073, 84888109, 541787076, 645150266, 176056137, 348376327, 201197043, 561151641, 390525600, 58563420, 648515989, 544919012, 6374542, 361737439, 769191617, 746267424, 986062802, 647932145, 694841391, 757278368, 698996101, 783975820, 963228469, 739312089, 750488155, 625340341, 481061088, 582915163, 557405892, 160978943, 49027742, 570506441, 279184513, 559617002, 884689427, 331260434, 561943754, 659701149, 13521230, 269861200, 465438535, 414963660, 260351235, 615206284, 22987255, 373713119, 989643229, 462794845, 841373420, 793648426, 689862652, 431862135, 515158620, 907671692, 252861163, 75962683, 324743059, 109651070, 122231047, 861695220, 949900666, 111657605, 340029945, 750775081, 743301263, 522708338, 733250962, 45469927, 746762169, 442144189, 92737397, 203370794, 808324701, 995296402, 886333667, 21045763, 968824590, 315812454, 433416303, 397518113, 661756647, 665996821, 280768907, 55496314, 62789534, 96667421, 311262795, 414763911, 607336705, 430731748, 573181241, 832689681, 921856481, 997916216, 754219255, 614746984, 245882767, 244795793, 184091179, 20294712, 906040454, 820013994, 126398, 174143455, 645013367, 637271421, 519031774, 329863761, 810083469, 913068927, 326023927, 399672736, 336659137, 405089130, 905063978, 914002695, 411510847, 720798797, 583851634, 548348213, 211898053, 800023638, 891373152, 728720849, 715513758, 376857753, 218610096, 884416707, 228559141, 16428912, 373683130, 476096933, 304355713, 952268771, 452086021, 580692650, 298249414, 547435969, 407169257, 147153438, 895933765, 471816602, 747606417, 681544983, 946808150, 517218615, 568498116, 475745676, 341112772, 806390443, 123394172, 725791210, 830755668, 254744631, 735217522, 978511300, 749208488, 587912008, 911952324, 342924919, 221774881, 430678947, 800217803, 18658762, 587509766, 887352779, 650205231, 988995474, 886518436, 175242783, 611470329, 828721808, 201548487, 669131527, 68541894, 475408519, 722448924, 798685023, 858861714, 533320902, 594669921, 673984394, 583325363, 100243908, 280475273, 464327534, 264753686, 450059429, 823758976, 88758937, 659284670, 184407921, 515882506, 881234616, 655566539, 730694100, 84262147, 933173327, 190185637, 873371834, 907881497, 495801247, 93847099, 102388760, 881560428, 866557307, 98863117, 992720055, 194188293, 902930642, 520999805, 856346173, 515791440, 714085294, 382469487, 456475202, 219429564, 932079280, 684004576, 866400899, 751750696, 10394689, 413936319, 335674410, 550256580, 82409787, 421669629, 567409406, 468326495, 772554252, 409132740, 479468303, 541524899, 470579547, 388728038, 18058534, 553713413, 820274706, 507212585, 924425232, 587914240, 297907561, 732170780, 826802852, 962039174, 314789168, 745533305, 713550267, 429115180, 981015931, 119523004, 462467952, 693290073, 525183166, 160014523, 548275957, 108749219, 863109294, 478798920, 781033736, 896884882, 354571884, 499946143, 604953206, 707135457, 960709805, 371644, 726407050, 743900716, 450862803, 319501780, 212855034, 609338781, 484234335, 617436576, 252229965, 794414690, 374667571, 143705731, 259490979, 80491355, 578891147, 807481322, 795609594, 286044049, 637771722, 329346168, 828936548, 860710537, 43521261, 675101534, 428503351, 965647864, 385605782, 35365558, 69009574, 620101598, 24448726, 754432615, 227775014, 23043207, 192097769, 84913585, 799999844, 836290540, 864107702, 195108140, 478641369, 779903296, 553771900, 932239809, 833379281, 282570078, 260834726, 985887528, 559381044, 871816638, 465538162, 305074371, 534951628, 747725895, 214050370, 434099076, 333144056, 850430845, 292136416, 54311874, 875600733, 559443580, 24898882, 879172133, 878628314, 737478569, 459759138, 383481741, 291196584, 764114630, 175261149, 388400003, 771958661, 488794635, 642576096, 374909455, 563225805, 598859208, 907984915, 700317622, 731275242, 978889720, 387219744, 59337858, 674362482, 138483923, 781382256, 662490316, 14446228, 206731632, 44517849, 622434319, 727591295, 2030702, 145189054, 445189403, 584258047, 718771582, 200760019, 830716513, 209739329, 876744918, 232225161, 468254971, 517261578, 799937660, 807072655, 111592634, 68446445, 226674156, 728936229, 228037370, 542491144, 114359892, 280129992, 846091257, 667228019, 167942450, 494725086, 671974136, 614488391, 619505778, 713178374, 229424032, 804332676, 906774859, 428368582, 239493666, 978509828, 276500418, 619227605, 763619467, 318150750, 707080672, 429615871, 283906113, 926086933, 21787960, 946290072, 138776480, 609458039, 423037733, 92989616, 693394317, 750255391, 318119310, 827325213, 204491938, 870326531, 336135176, 458568320, 217125137, 707330566, 586046741, 510945360, 672179039, 882992955, 660226296, 249734315, 460963464, 260740863, 387485121, 533477444, 829484530, 254710245, 687285260, 675225955, 49450508, 933396766, 286984317, 78814429, 697375294, 180531523, 126266492, 163424336, 965744791, 548658442, 670364314, 158609458, 545967743, 607479737, 534032031, 757540074, 334652182, 234884528, 320781894, 110640926, 610657211, 930713321, 379146203, 344771713, 235552630, 102697584, 474954785, 657227725, 185815963, 625506272, 802643078, 259402637, 74022562, 447322505, 542340405, 381156376, 420300475, 271267431, 76247478, 1037096, 342639085, 602359352, 592212644, 268474184, 838319807, 594382379, 749701190, 874884869, 620444770, 899436315, 221852562, 86708153, 803520601, 479619209, 275533326, 527261152, 24737067, 970949255, 524556148, 810005832, 737907884, 173159116, 248509162, 602715244, 234744721, 213374871, 284562739, 71600292, 992768388, 950666793, 925143060, 380501043, 851563748, 69796453, 823367043, 188615074, 799073991, 54593723, 46691080, 126530152, 582325058, 643690380, 759648473, 588945749, 234917306, 386671336, 24390369, 872017064, 669869696, 400906489, 810166757, 198571376, 333466111, 987535032, 298914222, 9104436, 42254869, 218357870, 497676527, 243195341, 933518363, 822595385, 474190187, 846638892, 257835937, 104901385, 147440677, 340438547, 508406464, 616436114, 351323622, 596098501, 593615204, 957006851, 440950114, 250926684, 692197290, 551088026, 483295970, 85296948, 545839596, 137548448, 577626925, 738069150, 975267278, 985090835, 476774085, 879241177, 983196568, 745770222, 396745682, 592346449, 656298550, 635813626, 449868860, 415109598, 657282870, 770049378, 100300184, 828370833, 841948778, 204764325, 779508966, 58957202, 779736428, 55622092, 699985522, 782802804, 564341341, 400534912, 289284553, 386736361, 10465441, 5737442, 297967759, 502823425, 822487894, 72313977, 225626944, 20513366, 108929526, 607118958, 969435315, 12564543, 566596839, 142643157, 981190087, 948147040, 541631485, 485114948, 510761708, 997715562, 303754547, 422270876, 715699865, 796732507, 218833340, 538194760, 980623153, 608191519, 784937479, 302234688, 257584217, 356692867, 653171800, 38690464, 738966198, 295549448, 533250839, 63152001, 302876563, 756038515, 891440023, 564170037, 33605722, 48054040, 719955702, 403329310, 415419235, 747132963, 472975809, 339240821, 751223816, 381352391, 120738605, 783154418, 586147718, 144200159, 481543492, 45057972, 245177870, 449539331, 857332904, 67672868, 499782274, 400236293, 504511688, 752898372, 342129177, 973178352, 300249907, 561122341, 635207847, 327492347, 580514432, 613365397, 473038701, 526380205, 298506725, 375106204, 135562995, 5558166, 241545839, 83147683, 365947353, 126887961, 86107783, 906661031, 717814396, 6030185, 587863558, 869215132, 410589969, 656230109, 515283542, 990068493, 19500818, 940124925, 334283943, 341148322, 730987678, 149251031, 465189712, 35753195, 181667237, 718627781, 551350460, 294085287, 998062834, 687171390, 440417558, 260660568, 256456963, 173286123, 165577075, 252990616, 96816550, 998883680, 101845254, 809734698, 275934573, 799572586, 761625872, 123187779, 460094424, 663392335, 335126774, 850070939, 854999325, 780184920, 36756263, 466322169, 895024627, 203722533, 464079809, 756530670, 986042611, 918297851, 998636546, 194216613, 225076191, 871241355, 188121100, 458747435, 162984434, 924195, 628229240, 966361250, 90914124, 895434155, 231806630, 840312514, 718757317, 708022374, 195499584, 505831636, 340250478, 272532988, 666438592, 511952191, 484352325, 541170434, 851702413, 392435733, 960921507, 727163473, 715065297, 722887525, 157325552, 76537151, 916805366, 739836340, 526073806, 52564014, 603857096, 752038571, 798245592, 168972999, 945903841, 449885112, 228916421, 85790551, 731477363, 493354905, 997696337, 812363035, 941481425, 921622378, 865613764, 901895356, 535753482, 117563951, 579753227, 804723907, 971400807, 533432436, 749455702, 640692683, 504828106, 612273182, 885852840, 625606035, 723132352, 486408203, 901475905, 10294593, 528222438, 566319066, 275528367, 146900178, 192422710, 694481158, 2411676, 114157006, 199764118, 276133451, 203086809, 378004186, 955189728, 730819734, 224361847, 757397519, 772247497, 610546072, 740993864, 948916975, 432011820, 194718347, 341265835, 308545303, 216990261, 351218464, 421229639, 543573844, 159805567, 433477934, 728562013, 565412384, 660024411, 647300498, 50320269, 194972029, 551146531, 465029853, 932863763, 650105045, 848814264, 468226577, 748774021, 505576531, 482819932, 283946969, 787750360, 67672302, 88854574, 468831720, 828568788, 914726275, 580346697, 991267223, 161417262, 866066234, 873859640, 371901394, 876800861, 534687312, 34409423, 313235170, 571496940, 79515229, 503313538, 518915929, 265013117, 514612991, 658076123, 64967574, 857424887, 855319071, 181759201, 245501566, 423526924, 435817195, 363128806, 70830659, 841781162, 422732324, 423020470, 723887142, 304598103, 183162885, 964369580, 385797980, 181217533, 581143418, 599274425, 461660935, 51185028, 927424407, 122802114, 134761301, 976074526, 471314284, 309031037, 299880487, 595461537, 615849478, 749303606, 416163084, 682367829, 741837186, 408006481, 677440643, 828079620, 315231205, 738066905, 862196318, 772475459, 434365275, 29785231, 26556306, 490342109, 318751496, 120328776, 572473093, 493397615, 535093956, 137836418, 381763508, 793961720, 60761203, 435919, 743668271, 588021863, 109318051, 772318998, 97647125, 892300701, 686308019, 301639038, 572214987, 791890999, 166324368, 438485993, 788738812, 239475011, 380805978, 166923619, 41150339, 561646541, 315235499, 46801339, 642128077, 710032980, 445607838, 231060973, 856868460, 431866651, 461532122, 554829729, 804090512, 924541976, 3553285, 281770699, 233149010, 465841348, 329975495, 804302827, 71354872, 103168910, 243686383, 676908695, 591164460, 448406685, 830351066, 504654440, 583013951, 888053024, 29334340, 308076148, 357545526, 978790409, 802661059, 379376424, 410012834, 937434007, 821496902, 624630212, 459612166, 55035634, 738705509, 841764340, 281334857, 13813325, 908655323, 558798752, 32754814, 25153591, 940121062, 490327123, 936296837, 83312785, 175799938, 405457906, 667817809, 541641430, 65935467, 611649462, 259881811, 459327606, 761633945, 948899208, 581707672, 700069836, 409557473, 628244320, 821182310, 402651838, 765219360, 831345335, 641024574, 419131833, 231010283, 375125431, 386085464, 420194301, 646738223, 860128496, 56074603, 554654327, 889589109, 547358187, 13694140, 358128442, 522947701, 114393503, 480953780, 652544843, 514342109, 165744003, 449432101, 691182025, 32211816, 201609502, 953778723, 842240936, 591118275, 66369697, 711527349, 156714315, 736677390, 584720923, 10449065, 757740841, 752927677, 760500470, 283713420, 144746051, 925832671, 132657651, 851363353, 866275624, 746022256, 982846139, 244668596, 558235454, 697586679, 52822042, 616800456, 28171664, 62001361, 675650032, 851653440, 397227487, 930402797, 129900309, 595060140, 763677145, 505062000, 850335362, 81450747, 538160990, 710431745, 5263649, 113351514, 821208069, 598383704, 865897504, 626631562, 441766021, 957064908, 62872823, 57838426, 777244737, 151428974, 265460418, 457109486, 644053295, 883019010, 985909655, 704140830, 230079619, 726027258, 292683, 448221228, 635515482, 423201379, 992346281, 676552408, 460655475, 383830065, 209046692, 848341581, 642078984, 780475489, 524870766, 144814273, 248197865, 190806276, 591452523, 931440879, 370141432, 611960411, 780515039, 465074224, 552353212, 18053522, 47077437, 480213866, 115238271, 165198872, 469604725, 697377376, 297681903, 173225767, 604917948, 608976295, 170550754, 989637845, 724226541, 420587531, 176057172, 707867567, 190785073, 999007447, 236992522, 917244832, 874161868, 549758361, 75081478, 954160229, 280161792, 607883447, 254303672, 101701578, 421330032, 910777984, 295325039, 481073763, 715373558, 35221157, 731455799, 761419152, 371348939, 247456145, 329963691, 600066153, 977533689, 956536959, 327976985, 668147859, 914318433, 166047794, 150019267, 739793118, 568796048, 223985076, 630555746, 886367856, 449766888, 528145246, 849408814, 880142430, 166810634, 29354883, 268004055, 186500623, 657913635, 438481589, 329354704, 797255999, 312529890, 465868777, 555565427, 812979244, 451063934, 900846099, 804621976, 936298913, 205353453, 787924275, 715200668, 678870843, 321438419, 623754229, 813543888, 73698122, 84338888, 56988708, 538463497, 717378686, 400889952, 956514712, 524095332, 269186414, 93278545, 685346789, 813599436, 825371030, 837785813, 67011576, 966586768, 490097547, 708133253, 820441644, 238448156, 626362054, 682046757, 540883368, 626276746, 303820628, 851367382, 316265608, 644128299, 266000812, 376659412, 836977402, 627192730, 962657417, 74704161, 39383790, 702915661, 553241178, 441549278, 157230877, 19157522, 85347778, 77860278, 53942706, 462699429, 237503609, 144862104, 760520253, 594274566, 960245161, 378462891, 999789997, 515038745, 677221435, 140146051, 143089556, 806761971, 712797968, 742689570, 458271579, 297979077, 915237857, 890306143, 824689473, 699877399, 554746892, 710140849, 409396529, 976871914, 639445115, 239240971, 241139765, 404045962, 458020250, 807916714, 554806331, 220091311, 292236554, 138889187, 177906523, 120360570, 239024630, 747840369, 435111797, 334147145, 828903060, 516193229, 871830841, 252330124, 486676708, 218669420, 739789150, 856954502, 666852814, 856690389, 344911435, 476226993, 256804638, 408458139, 309697270, 688620610, 751795784, 906251710, 70378518, 421901648, 423089935, 684341436, 991234940, 971455081, 339826746, 655398735, 177366935, 919107683, 795701080, 911044276, 174614953, 18210176, 137080178, 471556323, 192746949, 505456262, 774418133, 252559193, 65146588, 846064683, 800719105, 475402315, 709472614, 937377085, 924367161, 769621634, 473963953, 471857394, 715052761, 383137386, 576835487, 221363912, 65385892, 376712725, 183304550, 176005803, 352824566, 262018865, 860754519, 574293743, 98847027, 316499344, 586136828, 537252227, 769616879, 852009990, 443119961, 213882916, 649360831, 603076659, 896127783, 840845054, 44859205, 759889313, 255315400, 120145333, 71783670, 131788600, 949155960, 712408825, 56079504, 376609321, 30025570, 264909088, 938573746, 299864319, 910938941, 576712961, 138560869, 214307082, 631887622, 58518897, 127040537, 618278152, 729395076, 913451477, 452822207, 160153925, 315213012, 451055449, 335358119, 551706402, 782487802, 575777513, 851116423, 396667945, 671140224, 951193156, 303078567, 233535935, 537334391, 290017350, 427761441, 261317762, 572194498, 79463172, 491864154, 823689051, 846719374, 214323943, 604677161, 286113118, 209333363, 984173469, 686192409, 854990860, 92580437, 545786489, 243797129, 842352387, 106861178, 20533317, 846866680, 154752522, 46627498, 905092065, 112196, 299637, 958985218, 953654412, 996002092, 304715647, 392617653, 948913678, 838022163, 666139215, 990628967, 505483582, 13508762, 932609761, 50327245, 846537776, 661890470, 956545272, 50409495, 754730070, 870931605, 207863377, 108049268, 429717296, 305287530, 870644795, 366924870, 951257041, 583622161, 261079607, 129703276, 954029183, 821580060, 401848443, 565564915, 570627690, 467987242, 30608258, 328516103, 37993054, 203628152, 939155506, 328733924, 496103455, 559873118, 218361831, 832865970, 17005262, 826617130, 904243672, 29210576, 369611000, 22287254, 114801494, 137634774, 653634065, 498179644, 268288701, 595607117, 330426919, 809754252, 802750180, 999882259, 755989653, 661772537, 444492213, 543579390, 905529044, 912136076, 673376691, 727233973, 125844358, 254887923, 228029816, 200884561, 780767002, 530716216, 171239914, 129772458, 315561467, 183521551, 946656463, 728788777, 921436729, 92685250, 865205865, 90568284, 919535057, 756682557, 241027247, 496123527, 986686686, 622353091, 816531309, 641788641, 113863053, 824067199, 175917024, 945518523, 378763368, 765437765, 566214200, 905111981, 336065633, 964896530, 229729320, 264724499, 919807349, 402990775, 862894669, 328144965, 293226084, 753516422, 975263547, 436250986, 754949620, 235599301, 76416058, 162755405, 36460248, 327077211, 886401182, 76319599, 722675368, 15723177, 682007307, 103167861, 562479365, 226743732, 28672937, 592801503, 172154553, 906183274, 985646043, 100560061, 621730335, 336286168, 415185279, 646825602, 516497177, 961205757, 649709727, 276291185, 563866038, 251934214, 404407379, 201707822, 315134183, 249898647, 845458949, 249808810, 820350289, 958046407, 808483550, 834601705, 960860877, 362231871, 729135286, 56050104, 916397243, 43502541, 742074780, 468050630, 983192592, 521388556, 521705118, 977907340, 418205653, 311325120, 553621935, 282316769, 391798058, 822361849, 252740974, 461523576, 770079300, 574087539, 123519746, 56744740, 632493722, 872560557, 899196234, 573997690, 66892146, 634157034, 848795551, 576204029, 934928695, 420734646, 786245857, 858900441, 194159381, 49599675, 645151056, 13834884, 746095992, 251297453, 137815873, 276825305, 83478808, 415452751, 627491810, 500696707, 215421927, 569683404, 7315607, 476677816, 553279272, 870905158, 656079766, 715956957, 470604357, 633304086, 447442103, 389665651, 883434394, 369486533, 383585845, 425063276, 656829679, 3149353, 611379346, 665538510, 167898998, 514367815, 894402293, 961329947, 762491758, 544600686, 580185081, 698926463, 606059538, 50592532, 502797252, 835755700, 691872830, 225546165, 720900551, 441681401, 833351745, 416569219, 439665373, 380232098, 55905686, 105478414, 199512684, 920533599, 369081545, 398399604, 44258562, 870462807, 858711053, 807030750, 597624967, 271641954, 841324805, 170768472, 848099668, 58233066, 522308922, 18490830, 930659160, 275917698, 921881562, 917305946, 855442377, 995728982, 700743290, 640129649, 796806617, 852901832, 548436388, 895590995, 73436958, 248048912, 729633410, 788092345, 976173698, 69365275, 750000106, 231112576, 310621448, 872577522, 839515904, 766400388, 462375429, 891578682, 692313596, 378147677, 340085948, 980709520, 750038540, 223682458, 264145409, 977324712, 424408416, 83305555, 884412584, 347202360, 564886574, 544349421, 567850346, 459022203, 780707538, 132472997, 651729288, 468942219, 481477233, 312762752, 708203638, 469477097, 264716281, 323856517, 283556647, 345747631, 325638637, 627490152, 652058578, 194437580, 228350139, 242177010, 682792262, 843197226, 532684615, 398492937, 582811868, 960024370, 3682272, 541541574, 173609987, 921728544, 692554983, 389344105, 777700577, 730547442, 826787612, 962814732, 438300416, 529579866, 594688593, 156694815, 627686985, 855031500, 31644694, 96488222, 134082955, 707709593, 607750350, 22689561, 879135776, 679133237, 926060167, 31382625, 736840376, 985484680, 951369344, 392009873, 126616281, 949945405, 93081454, 12666341, 136082075, 123809054, 922038926, 748581935, 830478038, 405831082, 521778741, 175857563, 577794762, 721455112, 383875519, 756280643, 408204345, 737629043, 749558627, 602290816, 641060327, 75532022, 708860993, 778578947, 153269542, 776843632, 496038364, 922902241, 725186811, 344339446, 62375307, 179087082, 536565888, 355473280, 92670008, 898950539, 225375705, 849257077, 846738997, 229355181, 28959720, 700976574, 602412523, 69822858, 720127373, 463584384, 205872666, 326555065, 659948270, 75384339, 23512863, 488383871, 834840985, 768666741, 81639340, 944222223, 977470708, 700833526, 200785773, 969731118, 271208636, 173033101, 758481502, 656826263, 909943206, 55876508, 561507577, 965685084, 311676854, 559979159, 774768246, 43887246, 806268245, 853642353, 987938803, 261981652, 250941057, 583312314, 538444293, 13555052, 160655765, 343808538, 820829676, 490615677, 455879672, 992125904, 604424219, 411715709, 191984023, 810807789, 189458942, 397451293, 215015058, 900632027, 939317370, 32131876, 371816645, 583892115, 500603678, 352207975, 327700254, 129051291, 121558358, 702080593, 30960284, 304001634, 453883094, 263876970, 126125236, 350502928, 337770019, 201403672, 103397166, 55793389, 610930754, 683959231, 155749740, 810719793, 695139445, 229632327, 453902410, 231059761, 277856389, 136217145, 595790665, 830252833, 166478312, 707203500, 673583692, 200683664, 940157830, 551650320, 224316319, 550408584, 562947013, 67402908, 883226423, 486367892, 917452981, 467827665, 71729281, 700758438, 366271748, 471514062, 803372351, 196582062, 148624990, 122685977, 111083022, 837318354, 357710970, 584286555, 890564308, 690421114, 39146276, 708554139, 576243697, 594285058, 859057347, 400611209, 582910284, 147284829, 40394114, 805970330, 756863230, 325865573, 100888483, 356923159, 88377138, 636390268, 523434050, 368152087, 624620911, 579431353, 42497043, 969820791, 299374822, 308159813, 702175154, 939335999, 456804068, 761602804, 943952152, 997960914, 479018906, 860745522, 554536931, 149810208, 495559878, 857893405, 25721712, 534519131, 544308690, 32299516, 188350752, 972140613, 655297387, 257296921, 917764592, 335672895, 280112458, 325358770, 607886021, 293396687, 188670220, 835349532, 890719274, 184008301, 707433688, 38456533, 887664779, 756760519, 882256116, 978353484, 264497750, 152421396, 521376097, 803685029, 597054891, 802781125, 396403851, 504697923, 91482447, 268405498, 549995692, 551306558, 358047053, 723338970, 515716889, 398558332, 244403812, 463457169, 123666112, 505452231, 855514358, 901432864, 341412349, 14461591, 758180969, 966753962, 647028359, 808997039, 938766646, 487492906, 516654777, 72680100, 111521284, 52485651, 12415555, 760356278, 425994613, 667255866, 690981038, 790293942, 834770437, 649385860, 416399555, 871392417, 247490400, 435762999, 328613005, 184355384, 253426420, 391886819, 523644636, 297265913, 438550475, 418261452, 532418530, 857765117, 585071133, 919004433, 358601121, 476249662, 699880980, 655916721, 468653762, 387409869, 920452553, 921279852, 260019161, 113284527, 871709053, 958114481, 501500363, 440003328, 513405792, 95510357, 786732787, 709988093, 321287583, 887042288, 44150923, 779942807, 54525564, 792932326, 344066674, 476623299, 551038752, 143835553, 199052933, 819277571, 349489093, 263085058, 35096467, 705374463, 590501466, 448354092, 635017452, 587910394, 500844935, 400636400, 585228434, 192754503, 794340948, 453773147, 187174836, 643711159, 319272695, 908856553, 192860718, 401898617, 919924294, 64667169, 139515306, 340432089, 969703697, 874792247, 434625948, 221246614, 748172402, 630583578, 614532122, 794315068, 706727110, 910548502, 336155991, 750454626, 402837668, 12697623, 329681015, 273807737, 502759985, 425288080, 902748163, 485834251, 620534362, 863518169, 835003766, 284927718, 338536546, 20561896, 222795812, 245147887, 880655975, 174868338, 416200790, 626684292, 247184873, 857121725, 973289228, 253320204, 201557228, 822321103, 197458093, 14844656, 509796552, 936617439, 592838062, 906237408, 261344098, 531646160, 303351859, 785849058, 860382814, 554082673, 949009612, 126467059, 810482477, 663764488, 571523311, 795694619, 782326409, 104361127, 272416162, 213123402, 702204906, 624352306, 354169893, 787576070, 626113079, 405737501, 644873493, 272345896, 543712582, 596540508, 168217505, 272709232, 330573796, 203685204, 302278414, 738187848, 425899921, 684264826, 316570898, 444051648, 692090960, 855758863, 995080675, 568771600, 823156484, 66740492, 481695330, 51974606, 701690716, 474102222, 475785291, 769990123, 661160432, 595256715, 574812299, 654440248, 98803644, 928201015, 960328389, 684898983, 315013302, 139869957, 24915240, 3327391, 504233458, 719864300, 681960816, 573612168, 606992275, 533432116, 295670418, 945518849, 105651347, 38904965, 886932361, 603389563, 242067801, 35808766, 860453644, 934194387, 640536761, 11289302, 265442880, 17875945, 749340994, 742185679, 438688316, 798298457, 249657105, 848926801, 329381330, 764840396, 593585385, 944333965, 412487490, 153144171, 782783295, 798540285, 285437524, 673833636, 180518430, 316423825, 677448673, 573867014, 669055326, 600682247, 864390637, 754626024, 664383295, 944319188, 950222490, 640079717, 722034505, 245102806, 370341, 614727322, 638716774, 975417037, 794012652, 187917292, 270626440, 804279034, 437630378, 514739973, 593759895, 733882943, 359213002, 798719033, 652726125, 298339457, 659843174, 460104375, 381089534, 650612100, 185717258, 428424159, 95942198, 235157387, 945979648, 405497162, 156669756, 556813634, 766100816, 445630904, 336472665, 30361939, 621154778, 932609491, 46497215, 216071175, 14083277, 89555529, 729334321, 484494032, 940734432, 781643290, 763625848, 387054702, 920403942, 675539297, 174425054, 725116467, 927926536, 480359565, 86840971, 614263012, 307820388, 923811961, 556143527, 162115507, 448855786, 646450586, 443432899, 632091540, 419008352, 466221681, 735492634, 960692825, 382541874, 592446403, 368482601, 491676940, 982953211, 366144489, 345258442, 963405787, 515688992, 860675361, 143401098, 94082829, 707206925, 151207314, 781234212, 222700841, 523779611, 151216736, 999524801, 301081266, 75155613, 692790736, 708029103, 111119756, 449069957, 465097396, 620487442, 127143948, 261124522, 261506679, 303449270, 549125968, 770971328, 511720863, 453047503, 725735678, 767628809, 105599169, 299842834, 214008243, 359908293, 162631409, 10365878, 915129137, 901414871, 512015043, 139292103, 738126349, 659331747, 645832921, 856312599, 675626293, 317600409, 220197527, 656543482, 687296054, 185464825, 317914996, 6786333, 815093757, 556744207, 616176295, 778371215, 285773040, 322746971, 657830045, 751379694, 243084447, 452185644, 828335303, 908896480, 989115992, 263856708, 118931166, 887386521, 216721561, 499166340, 417858314, 579208406, 50902572, 965903349, 882045655, 599817827, 109603552, 766176808, 593687305, 32237903, 443799839, 375924343, 253007611, 822371475, 176051481, 236858610, 324188904, 238383252, 982724940, 280550866, 465577771, 676680134, 105197358, 378651515, 380094159, 77092831, 580002729, 672434637, 713354491, 458945257, 286382361, 808766109, 453641881, 235715524, 81306744, 329381221, 860538083, 929289283, 295237387, 536837977, 590161724, 650000477, 950168814, 226583369, 432854682, 785626293, 507697490, 93740552, 64380398, 686537629, 139958898, 591427240, 869325601, 232247266, 680534858, 715044575, 207612560, 707820890, 265557402, 23597233, 333420463, 104855902, 268362180, 997183233, 861625804, 489000164, 129006841, 671428203, 392068678, 920890315, 384091965, 482159835, 60560458, 23331273, 922416045, 958922310, 696965753, 39029891, 585043915, 503178364, 408319234, 99895195, 776333395, 343207165, 965161290, 313428793, 392884010, 794715218, 828029117, 988037434, 722617191, 178831418, 590307004, 768216725, 956036514, 497056124, 301056276, 550706736, 181028595, 989654714, 323579353, 62843817, 101353434, 485720308, 229437677, 844110627, 896490978, 588493838, 745795723, 360503327, 770966554, 20853207, 154898569, 909746246, 972072696, 828680471, 358192988, 52940671, 479522307, 375247654, 373895078, 145385344, 521079278, 994480575, 395003018, 527329108, 181736575, 235737143, 852098233, 862066536, 586835017, 852518001, 880317169, 564304326, 827997520, 120717853, 535836825, 129227870, 255580066, 638769489, 928231225, 809510793, 157254495, 584274839, 588192060, 965473119, 168133090, 225625917, 650420338, 795559173, 142888362, 363973227, 635562520, 504587634, 314477625, 585578446, 552135074, 476298191, 518789654, 294229216, 752188167, 768694030, 532171191, 769907525, 97819289, 634700441, 593080915, 726308460, 715340765, 488032457, 377980928, 180098346, 57624264, 94704566, 347567153, 285369683, 539644556, 391756821, 839765483, 490497563, 548928943, 599003444, 427583169, 574957892, 188450771, 626950102, 466792327, 798362000, 664567071, 460952522, 711663779, 731800991, 237964336, 176285041, 416369888, 4811902, 371781935, 342373965, 526734537, 182525197, 502545048, 603679606, 88271057, 721554294, 325714682, 487609392, 652514006, 738087946, 868034025, 42095323, 523696837, 819998166, 326586990, 887181837, 282184313, 555043394, 574333765, 985659103, 75896914, 272043476, 578467640, 186783044, 667756373, 303681052, 750168624, 570328983, 219074870, 290923010, 326701642, 427682597, 114765056, 293460151, 260504630, 677079279, 136799069, 983649762, 323244950, 650334982, 538198163, 297197099, 79550470, 324411624, 104250671, 444079167, 274272984, 452337385, 884351633, 276438210, 648970476, 710233351, 887946651, 617260135, 432707, 415558277, 549334312, 218592370, 451701990, 112894421, 768432515, 743031143, 816216242, 20441344, 335324430, 416168274, 396355587, 639550204, 156213013, 645077861, 861998967, 357809780, 19732213, 189312310, 877973659, 424517645, 528848367, 20491617, 90356921, 911308032, 167638020, 471744547, 141427407, 966500949, 451357804, 40928490, 283877779, 843801933, 999146454, 755296802, 765770991, 270435468, 215900742, 516595976, 307149994, 164694938, 415673216, 823965642, 328939624, 456184575, 241794084, 997688795, 239228966, 757076469, 446792919, 697030618, 860717887, 142353364, 345253514, 387137624, 333367922, 382343136, 353897647, 164047905, 151839930, 458558305, 110736036, 716061851, 721211157, 345059634, 982146594, 345627108, 105917876, 602898134, 47064089, 285569692, 569800832, 179221649, 61388578, 501513428, 23575322, 795221002, 61897167, 144053055, 953331385, 44186969, 317469024, 432661467, 695896867, 208608683, 876360916, 550493793, 558870302, 359003314, 942326196, 20753216, 786958411, 432835606, 316645705, 473169149, 557990056, 259878585, 893245072, 782002623, 205011263, 443161086, 229300296, 763698940, 335210098, 987528918, 488116168, 72866843, 257486222, 857581597, 227969005, 543593435, 276114744, 463412339, 317985327, 632053938, 54683420, 836313861, 245871923, 951602923, 34506969, 617218091, 797084729, 210052371, 950493172, 203852702, 295208819, 397310424, 143770456, 525612819, 764982533, 746814756, 421536763, 970933121, 188574366, 317733612, 613854847, 884990256, 112707046, 526901204, 20174694, 577531537, 499367341, 767898116, 369468643, 813127810, 614179515, 207270520, 614991490, 718624615, 708358199, 533269592, 25596282, 926864664, 50202150, 900377730, 600655245, 856198576, 521745716, 113175124, 76879721, 703080383, 750792369, 54354237, 158229527, 826972470, 86620541, 231512828, 35719184, 285848032, 381313012, 430182972, 397784744, 290285431, 147930931, 857884080, 749614548, 230805231, 750500414, 741368356, 509127710, 250449003, 652843003, 779704416, 987207096, 835158721, 416430411, 855312022, 956819922, 715917123, 72204936, 942920788, 41314005, 40165625, 301873442, 926760794, 804129737, 912538096, 663905383, 893675117, 66353581, 533073677, 786598178, 801382681, 256169131, 608365922, 732050880, 971751166, 496086158, 354347180, 396406029, 911490803, 981205104, 783764430, 185643897, 753816186, 414055342, 999332386, 200324334, 91175970, 597603860, 375098602, 425059099, 127037801, 305479748, 961322178, 463733629, 851381816, 766286128, 338071229, 126546228, 536764684, 779891875, 965149261, 349680873, 805293306, 981590963, 133617221, 145711304, 717611295, 577315218, 580088322, 642507661, 851354295, 351790329, 845295499, 520672491, 958979377, 883011649, 451893744, 584530711, 608298560, 702933921, 35735590, 380048048, 706839851, 916113857, 2995882, 928003108, 707614588, 562634020, 638468944, 780323649, 229686680, 191318790, 262365354, 152824907, 241197789, 324015943, 823543821, 903099581, 749478660, 308860658, 282157358, 208500181, 319866734, 633746609, 688998323, 552898151, 186647199, 879745896, 615983645, 900124210, 522123035, 192644410, 292854209, 371031081, 197963206, 336735156, 27850315, 436926620, 393476078, 838932336, 163174924, 981015940, 222442984, 673218469, 828681798, 425931436, 10753166, 513730984, 107906718, 189627153, 109807840, 689069877, 237043119, 140164364, 454697480, 531552405, 55344622, 948921201, 483579204, 160804612, 678109401, 741788538, 910841448, 747481925, 770655095, 970891811, 380472818, 708103094, 734752022, 230730591, 357956153, 827370516, 197639843, 756176534, 244490907, 380944695, 107937052, 958028095, 574839888, 949216965, 612005329, 29486519, 560410136, 742753883, 557902670, 33855007, 415021238, 331984733, 914255889, 513621284, 486871405, 922836059, 736416147, 244067830, 865196088, 352616712, 949655815, 406761668, 637790167, 571195043, 228352096, 669838374, 979087355, 309631908, 541579609, 993913770, 835667557, 869548927, 852036816, 756801256, 769513486, 385018677, 129503778, 410307686, 687614385, 509248084, 833126123, 947140672, 441347616, 291781189, 803879176, 508550394, 639705140, 654598553, 125453077, 310997921, 380987503, 919756559, 359874798, 840038576, 738898693, 920180799, 755772666, 978192386, 124633010, 833818411, 722110167, 370398563, 189654626, 449567764, 605628064, 144970051, 533896610, 593871553, 758264410, 891683111, 983992117, 506511711, 791256241, 309636705, 756208008, 411505732, 226214474, 936569746, 518007580, 377805058, 21109514, 234241084, 477312461, 982205995, 827728157, 427884633, 379028102, 7089713, 546055320, 896239475, 130767171, 9398098, 276214540, 4372550, 266345018, 756210376, 273133719, 895728944, 364322660, 380218439, 196739442, 975511089, 472386146, 234987013, 422428022, 557131588, 986434205, 150839948, 379423659, 941195030, 467562984, 219281908, 999309996, 869469723, 358049298, 75830726, 412495991, 471432900, 824912183, 337559659, 180954684, 32935218, 906900381, 87223350, 982802948, 317469512, 614766643, 972943366, 902675390, 470632698, 399613386, 648646160, 132879332, 76606226, 386686828, 237420607, 65634409, 672647678, 357072612, 47302329, 803432752, 503881102, 721070545, 246528412, 771286641, 556142873, 250631187, 276979004, 72662868, 229450146, 725817839, 162811472, 792776833, 136537516, 541111601, 815531206, 130862232, 61522483, 506300652, 277017611, 133392045, 549045298, 941839351, 111101917, 509278170, 594921731, 120013364, 916980974, 590742366, 706185040, 726829942, 430625870, 67311630, 622860316, 977525558, 778843887, 88878046, 387939575, 295376451, 960612686, 687848413, 159662348, 368350085, 883320801, 590817381, 638861467, 983286265, 868019301, 305567690, 65837794, 426034142, 170605912, 487638198, 224759256, 392365940, 442672107, 925910478, 55202163, 658157668, 170517056, 572739976, 758493152, 669634321, 952620677, 699409230, 682528442, 684809153, 560309969, 711380956, 921208330, 470088796, 786870393, 374992763, 790994853, 51196335, 915037065, 621284154, 871443864, 582364150, 659193104, 937861885, 996421422, 186447754, 434579767, 398245414, 49787170, 618771511, 506180380, 973858954, 433993854, 610500047, 430783206, 654070170, 460186941, 89596185, 740320376, 632604130, 416051297, 898126603, 651197279, 306787561, 605895844, 879461207, 115406586, 841746311, 52036494, 816231293, 950827591, 976704133, 624314954, 632623617, 644836317, 420591215, 484802984, 713781307, 753410294, 201947059, 149834152, 413683080, 467308961, 484902564, 669942970, 588533537, 902213154, 912254243, 948462401, 887096076, 995951367, 691942781, 758426458, 282207013, 294982209, 283621065, 900151617, 525427826, 298683475, 139194442, 279677546, 735804134, 745233451, 526597005, 31571598, 124842070, 257372617, 19787018, 144650860, 9498228, 119756978, 677872555, 97516314, 116961418, 53965360, 555984527, 633952548, 39518381, 10862546, 689130289, 592701477, 365465448, 261712076, 343016200, 491821624, 10614421, 336974512, 938918388, 218232405, 994440509, 154633452, 65442284, 444539728, 231691712, 346912799, 318464624, 717379954, 939106763, 330874142, 375377299, 622237746, 533271132, 918010420, 848192107, 673641086, 843620542, 125037337, 139669001, 907850210, 818468422, 880291735, 890276985, 70686367, 654841458, 911496167, 592155098, 264658713, 462637969, 102785578, 973466325, 766413303, 906131303, 395762989, 356770764, 485388122, 757605420, 200998747, 61749296, 329648083, 569921571, 792214096, 31767319, 516098162, 400241649, 356962887, 496741690, 788789882, 632169825, 351404910, 323302834, 50988672, 638040096, 509948228, 789555593, 164424725, 275746535, 380366308, 895227591, 681211108, 306210514, 342408271, 273747133, 664861659, 609081285, 333953396, 221249826, 923209879, 681808320, 279771049, 643464188, 518370665, 99108270, 73615477, 551676282, 671149026, 905951958, 335826908, 86525995, 25344208, 679451044, 862999747, 384392717, 731765786, 512568277, 557720614, 33478673, 167886131, 617498305, 965232735, 976523688, 848327979, 101845194, 121418150, 124940735, 334205371, 890511073, 657968076, 347890685, 915394179, 127844287, 983301781, 714634393, 239798050, 185393326, 75877105, 325557316, 629560044, 289952016, 929915911, 285117439, 33711837, 505894315, 984283206, 187186441, 537956696, 674226315, 52188017, 655620300, 866499822, 233603473, 191077678, 812242720, 502624167, 729351922, 562376952, 52406675, 170560507, 783598862, 307964838, 129552262, 494218743, 301706072, 919583913, 385237560, 468598701, 449956929, 136523748, 21669073, 184180012, 125712901, 606448000, 220352341, 141147447, 717248571, 760137717, 200750523, 771341040, 767836068, 72982472, 585032941, 212465788, 588356602, 639435325, 117948839, 506963762, 258660274, 161448830, 344125197, 697001200, 178568955, 488300467, 908983863, 425969393, 989187781, 357316644, 748972060, 983771976, 251078721, 539879040, 80573018, 412992147, 112213226, 801292119, 62454405, 49800964, 20766066, 605237874, 432807539, 348929471, 607016881, 913868058, 771484261, 165089478, 791827224, 616916364, 691117776, 360041028, 861541741, 953180695, 98874953, 311854813, 87292361, 906717094, 333515024, 159220399, 762492519, 76346981, 287074530, 871520009, 938235174, 932400676, 505304517, 377025689, 31245674, 320422759, 507239784, 33739167, 231172750, 44843432, 669873635, 389369295, 796892858, 87035567, 834905162, 107205219, 243091404, 198874246, 751051736, 725964943, 582302157, 342483472, 984778762, 657645058, 505444911, 972467433, 58726968, 928800042, 49107721, 448185713, 548686008, 35224026, 947247875, 97737428, 783044116, 144511943, 800711874, 283467033, 858717144, 794612661, 739761623, 607953813, 428757734, 899075216, 839118224, 288211373, 901078791, 749824013, 621793571, 937019300, 404148801, 582575386, 617126581, 671998963, 442807944, 86141702, 417957743, 442242536, 995714005, 991807270, 840945109, 278758115, 265930048, 35195111, 612548250, 724127720, 372055509, 328817719, 269320951, 477918782, 940255201, 660424529, 272479241, 949914855, 828319726, 90656885, 166206766, 295914138, 381714305, 727234267, 747820219, 324208858, 210810504, 510833921, 39168019, 486894459, 438960169, 6043567, 60834360, 957665371, 937949768, 680578039, 874334167, 485556726, 876390123, 345620401, 724001028, 731248734, 847999848, 263613528, 877279388, 689245934, 192616418, 676546207, 271920507, 325264364, 150264846, 132588342, 967195595, 254321700, 727209483, 916086425, 897288698, 858363012, 358784708, 410441185, 374913035, 322194900, 267677220, 256869087, 629845812, 227735982, 726959577, 762328558, 604965181, 963696048, 119339068, 894428054, 886174579, 77365310, 218861570, 44695210, 510560066, 637811002, 680279967, 478710279, 36620338, 798399069, 783569797, 222176580, 206385717, 345974343, 434018061, 831140699, 12591537, 277312379, 567929026, 724344501, 744532518, 627316148, 537037140, 455281232, 967552820, 935641412, 108661016, 225168713, 357828473, 525943886, 577213576, 240551993, 307586548, 463742043, 825617220, 235700626, 778003789, 577421288, 463253859, 434083927, 869120427, 824512860, 980598123, 602117032, 716448768, 527472027, 995701770, 269931932, 813325890, 415801387, 712591304, 95972444, 557127431, 749463129, 267461509, 361964268, 927595464, 172453196, 657609904, 893905759, 987744562, 991281514, 243890980, 196289223, 131154991, 855920234, 59670267, 584377875, 403583607, 824388852, 341067071, 319942097, 168013782, 22617933, 226772846, 383564235, 310407318, 25687593, 915476143, 101235082, 527484763, 507151178, 723353343, 125265866, 372594950, 357035462, 24910223, 276891579, 346959973, 810304388, 912148206, 876694174, 806308933, 726865950, 281246458, 719426441, 428330680, 483080191, 694571071, 804990146, 433479760, 400171068, 112639525, 58541536, 431301202, 974268235, 261263688, 416940081, 970719795, 305320288, 809096027, 242230863, 509688520, 44562697, 921823201, 197311048, 869470493, 563743266, 23575482, 641954863, 523968708, 447898244, 54874030, 982672674, 290017990, 310409058, 496330559, 188140356, 114533835, 652688692, 867515487, 165824271, 56235083, 664013452, 873609810, 370415077, 508278825, 42409370, 927684900, 963854096, 254963920, 429985736, 793130842, 166276441, 414177709, 615600490, 688529898, 942692061, 322366815, 436234898, 473724141, 362668769, 347368654, 632370485, 992198558, 183958496, 681129945, 678310818, 87345402, 722220774, 511000100, 93691228, 969187452, 466341116, 959739199, 919696834, 46016233, 972132432, 843965627, 854686336, 570574575, 476653003, 637190730, 9802935, 391078599, 406945821, 599819755, 444862305, 837374881, 105353080, 847419213, 104069217, 825475032, 897002037, 218085293, 713191592, 261400185, 88612834, 340154489, 38404672, 340802290, 662221692, 215123316, 386138781, 158171976, 205915399, 44528806, 860436107, 464676416, 441192090, 519880977, 773388399, 267255666, 198177585, 862680761, 898922425, 211268062, 827987056, 646030582, 5202313, 455796465, 382565924, 494751524, 15043948, 265095310, 737400033, 702177600, 247872402, 540819600, 853853314, 269119425, 559328773, 104033327, 403593589, 6276946, 837796314, 456176212, 832382157, 580954821, 618092527, 265422825, 425603157, 904858436, 666441218, 405708993, 424999175, 16320312, 227803425, 434329047, 232236419, 891832693, 155350803, 83798073, 320106016, 152817708, 291957507, 477600017, 266426733, 200446453, 340583347, 129482871, 908427074, 121533534, 809291017, 140321173, 857630771, 596965956, 996902531, 991092450, 475951458, 484447835, 356719067, 425373756, 985327648, 264094432, 316323936, 563233578, 881529553, 525384343, 975823266, 260024582, 914190868, 632668231, 354618179, 122528312, 819689964, 16070054, 341292636, 549977880, 764951302, 791759663, 74585299, 318743875, 737470236, 870054828, 611031071, 495249183, 143029515, 406280608, 220527538, 496282164, 163920873, 97482156, 393432568, 565118769, 935705097, 481748975, 484702563, 298191781, 745321522, 201785271, 519598368, 542315458, 231105058, 721696943, 131435917, 788514490, 931760806, 998871696, 377407005, 923308926, 754862951, 517375695, 37531454, 155765150, 157919682, 726006586, 770858071, 357639394, 136586633, 968633647, 69472018, 263856452, 766468715, 545906460, 888131232, 957881409, 751188432, 237611461, 949005476, 385246112, 408560238, 212836220, 658397537, 824178548, 778368842, 483046123, 919707691, 138236182, 379853246, 157354142, 496676622, 928052076, 167156822, 916042570, 384843901, 303118094, 280164845, 177884466, 540407171, 860736697, 315263684, 159844051, 684202291, 368189445, 981652770, 118490903, 848190025, 33509730, 147034517, 404723935, 982977794, 6575537, 236603211, 274482246, 327487696, 299874105, 684480745, 501836217, 209088416, 112679239, 810706360, 800279930, 638525669, 123241835, 873181044, 574232237, 367513164, 978878334, 231264170, 978310186, 247945857, 995680594, 279271030, 761599505, 542360300, 485713521, 716166265, 482428663, 352825918, 616555623, 316326878, 154685228, 347123702, 983595415, 347631623, 402040455, 511724393, 841313344, 746179042, 47384908, 850046291, 431752752, 508900948, 310548294, 827556610, 841503591, 138243340, 109504356, 756507993, 143149478, 289829822, 743824066, 773141033, 379045786, 399699318, 174050426, 659023556, 354802023, 400142258, 870387367, 558484895, 793594152, 289289173, 716860287, 99287050, 566104760, 621050858, 968737677, 9286678, 194569962, 853200669, 239176733, 836863664, 298908844, 687556763, 52103658, 456029821, 992556450, 881165383, 187216789, 596743483, 970208628, 632550627, 300335108, 574054515, 718458455, 613016418, 366654491, 603979794, 823490250, 521767945, 788319387, 124023144, 932100120, 997303344, 718712824, 131651236, 63477754, 824862235, 548185104, 563258383, 386748278, 426333617, 465579148, 135922212, 184902459, 503847286, 248423739, 629386095, 247627229, 851155612, 3213692, 276397511, 923584945, 109721175, 858356278, 857985155, 222413139, 118239718, 377279864, 458147138, 707568925, 250806443, 431788223, 268782812, 12454790, 106388022, 165729344, 359657097, 91462362, 58059025, 371561980, 274539839, 973251987, 469848676, 909459248, 406464900, 449617826, 601378772, 293757865, 809420996, 322508190, 455116150, 628058320, 773681949, 864176211, 745049378, 31913114, 285242219, 100631903, 670807571, 633149764, 149038374, 67697022, 957884170, 885019927, 885353939, 481266110, 487154812, 69467403, 769200162, 92927442, 947966248, 869466520, 642673585, 693146968, 736052730, 36122708, 222404234, 854341588, 34590618, 242224037, 744575842, 773108902, 683638165, 198411035, 835119965, 149171791, 97307964, 99636212, 168338884, 815474129, 758000718, 8401984, 554684786, 629175248, 668563821, 514909009, 120465656, 43912183, 695941568, 901547397, 367343299, 515421631, 972961170, 861878893, 340034831, 165642857, 767469497, 883193352, 493539676, 369589477, 463709625, 305700411, 416223766, 435392017, 201494210, 737020501, 396217022, 165932836, 360372300, 530688241, 750351641, 71265309, 638241335, 725389754, 47964576, 176542909, 374952730, 904637825, 298243196, 806103369, 972469260, 635369482, 142914624, 564172056, 734815605, 346581310, 35691953, 353092445, 353898784, 23540850, 28718, 424798251, 958973541, 980886438, 775579219, 489498761, 385242608, 498326857, 959141090, 475967884, 716748966, 290005446, 295185096, 968875408, 890984899, 941802898, 717671621, 515582758, 745442814, 804950924, 652589608, 310576689, 950755742, 583534268, 109350503, 898010212, 399926441, 547435010, 570893268, 556810156, 524645391, 567097554, 784109423, 141206726, 561925838, 896751957, 725892804, 299950571, 144065904, 862603212, 625188461, 778991009, 969376031, 988824975, 911780770, 199181448, 887258140, 570855022, 795527087, 274788179, 568950446, 465475912, 537445235, 843159615, 769964194, 266551735, 79227977, 549590593, 123554100, 242949547, 646825547, 49339445, 411713125, 913863128, 755951191, 8218741, 698587729, 981992503, 459054941, 608496525, 739694388, 631934345, 202341792, 590939722, 270422032, 836204283, 669871216, 102769184, 157156748, 313858923, 480781579, 114187897, 645888225, 541102180, 789160594, 451471655, 4060879, 548127564, 720906368, 278171895, 872537673, 664972776, 468566971, 787417352, 199187615, 531143323, 450297193, 122006420, 471414576, 679701625, 492222692, 810419631, 897801394, 126852766, 607682448, 48468784, 911957931, 827603573, 242979621, 887344563, 332521506, 17850357, 586431462, 36688826, 409913292, 907216388, 982942912, 165544121, 803478317, 402858233, 641561103, 287246871, 708043565, 219032040, 276396115, 570130781, 333333520, 570183283, 835135129, 913099649, 696979695, 850264952, 447800758, 659787336, 818896009, 819509818, 545462610, 389746798, 501076962, 712257437, 766617878, 854967464, 408580069, 848458761, 703212719, 367405729, 165409075, 882898801, 576907222, 745172753, 536798735, 718844822, 584087000, 773491223, 336933552, 812810257, 944333585, 696583528, 954347361, 100707279, 44699249, 856659467, 918711568, 816570598, 261600758, 884399751, 331074471, 880098966, 917881173, 42872016, 136590917, 548449679, 217073024, 372825789, 23197147, 709364524, 970025986, 570421076, 222103953, 10784865, 657730144, 336789282, 578584206, 503703130, 889850857, 116102054, 95559709, 133695080, 802050293, 957969466, 795182850, 126474473, 435184832, 146285215, 985870390, 932616177, 856168231, 112721485, 67552184, 104846341, 19524885, 975681429, 259912916, 974067053, 281207654, 627189101, 536668229, 192480185, 439348407, 490192215, 264384099, 665617633, 947324199, 804165028, 357889219, 933864378, 473822830, 959641909, 887702478, 404843415, 743516297, 862255670, 806962546, 326186784, 275094596, 958981574, 184710520, 266678898, 720090435, 240245789, 221554559, 44648690, 57221537, 571386582, 145926347, 475665645, 217977202, 294434208, 1000556, 878690996, 982560600, 382658818, 821382914, 900321573, 893387899, 776554701, 852708386, 167738329, 345882832, 822660958, 8550088, 692558077, 535534860, 622468226, 739755324, 137002878, 501740752, 208149620, 409522998, 792416080, 125577315, 215217632, 171486326, 853305859, 680629663, 570048808, 107207630, 212546001, 259848439, 485622170, 66728976, 171267374, 747204922, 851980099, 412044440, 396600081, 871070501, 474463314, 308748402, 18852292, 270249962, 832594899, 540706493, 459428993, 538662586, 574172508, 248396029, 808184926, 760794306, 957640140, 586385949, 647217396, 180793807, 660186119, 616809724, 86567255, 805639306, 342464845, 460158168, 384090456, 459732530, 58726460, 151334945, 252806686, 9413074, 429028486, 381107239, 720193856, 571400168, 334919714, 936388409, 71642427, 499900881, 104455259, 772008100, 980935349, 379456361, 693744247, 132936197, 258534885, 578821958, 189137677, 640271217, 422990297, 832468299, 677399995, 754046702, 52025212, 819154278, 143218648, 212521900, 878508927, 784307357, 342346513, 350230339, 1541877, 510213478, 834153020, 41852535, 881033414, 215089344, 165562066, 34195428, 449294949, 748207596, 235702037, 221458330, 196602435, 303059289, 111330286, 63028018, 481599499, 364661949, 997115167, 476786255, 888020177, 40553467, 214767562, 787933337, 998443336, 596515537, 536117784, 348164066, 534003406, 554104286, 248552438, 287220012, 187214619, 808705393, 557394046, 505804040, 940929403, 358069326, 268782549, 223189889, 377094472, 813379186, 369199814, 923311866, 220643525, 61659886, 887356576, 360226010, 471354275, 219650345, 175854558, 214489840, 981526259, 731984674, 379741610, 35941470, 746069062, 414763430, 247656694, 710541619, 833196192, 801542093, 737128951, 3405972, 340043651, 35576087, 158606056, 274764426, 76602329, 503781531, 424150449, 81919257, 160709731, 330180283, 490554136, 64903404, 89330712, 677476146, 192651700, 198261297, 721037544, 237038674, 719368575, 138102910, 214098294, 141488700, 790841095, 958072328, 890756275, 759114536, 393202250, 310312265, 278559250, 494379670, 70653635, 987299098, 338210897, 54573434, 715029911, 108018437, 970971832, 979384006, 631161989, 335344023, 113926385, 927192405, 66118048, 984450482, 378541734, 402360132, 394647725, 574303488, 882832810, 169713763, 599444812, 527677230, 328829274, 862328498, 329891960, 757993183, 631187618, 826028845, 651152408, 293871820, 23820443, 844734576, 592040655, 907282711, 167084140, 985796347, 623908897, 195027418, 746944339, 176027694, 943902823, 633054325, 724825691, 514281387, 951814150, 39638840, 761365014, 286632256, 220532155, 436896180, 234859567, 157397662, 923431898, 701825971, 321163988, 297419174, 379156598, 602010204, 993075887, 357854539, 204332446, 767814778, 679746544, 369383406, 17004920, 852106715, 125603561, 146594146, 271078245, 878228830, 847932528, 231397658, 133265059, 788849456, 382209386, 388241140, 596187568, 370905840, 131578117, 985862068, 741365615, 433221929, 750815029, 533468383, 145067501, 779309059, 667900401, 851577210, 416940039, 992844517, 880933051, 177094443, 699248049, 573610680, 773395271, 666406173, 771406361, 688263526, 371832544, 932759653, 624326480, 708309925, 410528586, 10714641, 129479984, 639621718, 893425627, 3714651, 63010595, 120830609, 74589909, 137962743, 756894618, 719411601, 530606738, 974457984, 645448440, 490277050, 475048515, 343557346, 431136010, 503203796, 525492313, 550084382, 56946569, 312756056, 612573807, 516883431, 884704482, 34205611, 182589922, 169051347, 354267342, 990266902, 978451169, 84017101, 333021681, 26077586, 94782634, 832647603, 8593248, 368183402, 153034738, 255822434, 581063224, 923198485, 878629787, 823283739, 87557219, 834096950, 836092579, 232540856, 630783434, 192921569, 162416942, 607774404, 355020294, 65302049, 159116742, 490431921, 360123900, 851224969, 124513058, 376989026, 785086985, 527255559, 213468829, 732901285, 142582436, 381498496, 549213237, 625519157, 101833185, 851749836, 304273739, 927993567, 17415440, 369103004, 283915938, 327616221, 310751126, 294525860, 901698370, 986442782, 459024508, 684826556, 668241171, 615107324, 711518947, 475622480, 939409251, 556576397, 22941611, 952898471, 709191774, 890981381, 730932662, 128302101, 674219807, 434588322, 90988453, 298445808, 754573374, 752780501, 512784202, 222766658, 366330042, 101327584, 288399158, 315987315, 614860366, 781675333, 221351195, 317732963, 839526568, 7478759, 42433496, 784546372, 79851701, 745680229, 897733828, 661819230, 946734617, 442749894, 233708607, 139432000, 787671339, 171749968, 349294767, 57744762, 614542085, 275389466, 501905979, 387590557, 188458098, 304930418, 446497563, 243666958, 496937048, 494570841, 265147494, 883684813, 87291710, 668825958, 830191807, 478849539, 732748512, 775864361, 389129597, 411076348, 567517818, 461382583, 487216002, 154152343, 494430592, 145637982, 151861159, 894817857, 629596392, 884729850, 605261406, 373474851, 403906977, 93551635, 285534607, 898465285, 375819421, 918276349, 516993110, 23495003, 496147704, 969180966, 906340624, 786361214, 703466773, 794907939, 817172063, 860320689, 853181729, 540880371, 849708088, 686540052, 560239001, 44982166, 285555058, 954523382, 310176542, 453436456, 493666779, 107181628, 700689008, 106875519, 166644453, 89236258, 396109078, 404825345, 844059277, 667206210, 231257890, 990775321, 667173592, 361965547, 429819063, 850969303, 6773773, 186474188, 695957122, 807378882, 266942706, 175684766, 64941195, 123638451, 38472501, 99445075, 4490830, 791344751, 688029186, 235422816, 679246415, 976096826, 55358734, 820229065, 593675715, 71179407, 880620106, 632711220, 445437871, 118122175, 20713820, 679020939, 586778742, 452212170, 658780578, 965121495, 650781520, 234051892, 341459992, 554556507, 13199193, 318311096, 302644962, 283890783, 1228935, 157015633, 491578834, 259857393, 533330737, 265673477, 654572800, 742970685, 934430897, 703512306, 701322495, 254610808, 346732148, 332337796, 607301575, 409813286, 966944873, 542599361, 906779699, 811845131, 279776807, 599609316, 570259075, 681710559, 369479264, 774534558, 821126399, 833806206, 893653786, 761181029, 469905307, 385588411, 9356635, 341470629, 838924198, 750770396, 618843651, 97225757, 884096244, 556184919, 560389907, 574870566, 397142354, 960153864, 540551823, 123302825, 572356052, 256553420, 632306169, 127931026, 716941002, 347624921, 201623428, 370205530, 556424589, 953340340, 215943549, 768492924, 865569851, 531675643, 499923227, 929509759, 745147853, 509455022, 806130858, 627388795, 934509478, 330383349, 523241216, 795205541, 890066092, 292134984, 559662803, 143496690, 41426042, 845566055, 311044510, 979190646, 556116651, 763182676, 846470052, 523742680, 685991769, 342666102, 353862793, 310268389, 324704861, 248522546, 563237688, 624163467, 244658585, 710155394, 236825599, 44828619, 865010628, 211437817, 207849550, 801617176, 469600429, 100954313, 330455082, 74344335, 537619389, 62568311, 829975012, 119875899, 502813665, 54469436, 696833723, 184933527, 145931055, 785196795, 576560722, 207054704, 987118638, 918721571, 903284597, 635007684, 32376320, 158582284, 935431231, 740494774, 709921183, 125282021, 734469339, 502305550, 358619632, 588367885, 378999869, 229784330, 482908288, 200015583, 917495282, 927948162, 608034697, 808431135, 527077222, 162543765, 389950857, 245601267, 249715419, 693027971, 190580856, 529089171, 955684526, 30761537, 938337593, 788577458, 549209636, 827045404, 122308318, 620861323, 971676255, 416840020, 294457424, 524558544, 556815065, 630892050, 967268905, 646360522, 429093749, 273629798, 491769510, 776972562, 7734440, 487016701, 464277815, 610398444, 170422712, 229016657, 714740048, 969069237, 80291050, 417641256, 952187770, 749983779, 648689790, 971140131, 951554088, 110361135, 366812247, 670286064, 351934350, 610789935, 892359063, 659538584, 809272917, 656853450, 834218956, 318381406, 421005852, 413973609, 964864024, 916374071, 48815337, 956932078, 298839761, 35653598, 993186141, 487819763, 266278852, 792289374, 65889596, 534911118, 683820678, 310945474, 369513047, 816802574, 930482893, 282430064, 218572025, 673462611, 247612459, 684708154, 572468102, 78534906, 779316880, 507584866, 241685928, 164169297, 925984571, 174048503, 725036003, 63721295, 23128493, 632477591, 323650721, 695154822, 194815714, 933300586, 98743115, 596527852, 794127852, 174663265, 26675663, 577862324, 434246016, 475233835, 849652896, 337638356, 755871629, 378866778, 279433078, 458464603, 235726524, 689767644, 663552183, 479240095, 743699136, 1551776, 279898168, 501372710, 374933359, 826435099, 8175993, 890212870, 68744776, 973300857, 677629842, 88200270, 933487038, 762800394, 782106240, 151044457, 533720302, 799661973, 397849546, 88133299, 856166069, 590641145, 938138799, 552221599, 856165278, 106746042, 435431789, 887586851, 274130423, 301977160, 282110657, 422720366, 63100393, 836615808, 52153984, 683905059, 144404794, 331665548, 915011335, 105012790, 447454686, 357783838, 875737347, 853022616, 609779392, 954358568, 828758691, 919695041, 821980278, 719841089, 513058110, 500117508, 691134165, 111958252, 260657777, 47521105, 576190368, 11416701, 498700255, 525863304, 187271885, 695854420, 780001328, 474696969, 660336750, 976279, 936448695, 336923507, 995705773, 740731110, 91954536, 46524664, 547873000, 731668621, 574726627, 53508645, 580644244, 504400694, 355885033, 212200417, 292060053, 721009357, 604932419, 828091150, 442201412, 957751886, 456865160, 474264098, 942382573, 724048394, 567218207, 596139930, 967007667, 6976490, 481022909, 992658387, 744364349, 782509587, 154080186, 491415374, 211057430, 988623305, 150094915, 858625639, 553935388, 173781337, 758264515, 797758048, 847819239, 139204073, 84946734, 798288654, 183143418, 292591740, 634366539, 905776888, 567587532, 28774873, 861809891, 247948385, 209496849, 735476781, 919054970, 917666215, 384789988, 9405156, 310680777, 720327586, 472862776, 767167017, 747931361, 549003538, 631150854, 973701016, 180281488, 616568088, 90667890, 679572702, 559637559, 583057280, 398005624, 551840589, 356926652, 789186824, 405464848, 15855738, 516904191, 931856246, 138626346, 947532730, 160004293, 586485329, 337827731, 249529441, 274382660, 940941230, 374608875, 796114469, 109815469, 255424270, 209459078, 721260654, 804775505, 743419612, 940965880, 813683566, 785512948, 477500721, 443873003, 997970841, 547656156, 501144940, 44044120, 279860481, 354881895, 67974289, 469155118, 646752721, 112881596, 336464623, 914370859, 541329107, 452319818, 981186137, 76415342, 866394731, 647347225, 657613976, 770247281, 922442524, 523943271, 154817027, 829453276, 341631851, 608260265, 261958915, 884099235, 694750566, 399062646, 55218908, 474919318, 368407786, 612370865, 196261766, 562103499, 394263241, 136041586, 50700713, 104487259, 15643690, 243739335, 333577808, 864834510, 760649220, 782472408, 559317505, 578147399, 232975951, 949630153, 946609233, 239169302, 805474850, 756450437, 870746657, 53599790, 883074342, 978572656, 949544208, 810415210, 232493696, 287063042, 243810909, 560083151, 692496045, 774535598, 886547501, 594208752, 19574102, 387866859, 998638168, 444421985, 56718857, 201937506, 411609663, 431426699, 701971109, 588504082, 521227883, 288287516, 701295201, 739013258, 128260857, 157937036, 2010706, 204934616, 439544293, 897335874, 925992026, 614992827, 704147094, 31292326, 492336414, 496741569, 474654476, 673289472, 780264004, 554125649, 608139985, 910533551, 462689313, 427302618, 991952813, 597279719, 802119662, 680409240, 661521314, 355510685, 479405186, 169634660, 377796466, 681215581, 868204754, 701301770, 253489987, 103958717, 701991666, 470932786, 718332831, 533644680, 889126107, 118427686, 437674136, 560875488, 870552891, 681471823, 312454442, 983972702, 335926877, 709383622, 696312396, 830298633, 915267542, 865016947, 151504467, 767067373, 135607095, 854146658, 812297810, 234009625, 641652256, 33493370, 964453271, 680177852, 328632033, 597693601, 825374583, 129698432, 250016781, 173471724, 821215868, 220923948, 341339895, 614249027, 163370239, 865736103, 908205791, 689752686, 416535782, 283833081, 311280613, 816065217, 796022191, 8261439, 893252687, 156737660, 117972525, 616978539, 384275684, 610460554, 187400435, 987124637, 55644850, 699910867, 17798292, 799048448, 785729311, 195410061, 916944281, 394164138, 61242258, 136943995, 344282091, 528517552, 936372020, 907043818, 526152330, 889409042, 462583088, 196058575, 730454168, 627453206, 451806947, 217546901, 726916522, 706468262, 977833796, 403505682, 393180594, 409376252, 96619979, 646818252, 759042070, 440010399, 26308652, 411545709, 92522462, 63062851, 588991652, 605243743, 168193572, 457306881, 784347270, 467008195, 312875941, 464375563, 512129654, 811206820, 832124657, 801343610, 749240671, 833980918, 949514338, 888364692, 659916832, 319931532, 446011569, 128937992, 876449682, 537823053, 863707177, 778742945, 18306368, 350585057, 845788762, 306685906, 438218788, 462850061, 536750675, 665252813, 99691739, 776023518, 182801723, 342832160, 574007435, 671000306, 462024901, 795626555, 302240773, 769196176, 896328332, 94706012, 898460771, 181064708, 687646575, 152662523, 696499801, 40703024, 607033206, 164843429, 725958153, 774477278, 92262644, 781547125, 823444984, 743007169, 213759787, 280052686, 720085456, 209839653, 873121446, 422160085, 829344107, 838121484, 354665639, 107493385, 964756622, 535166902, 303477351, 211742814, 772749777, 698034051, 157071044, 804407641, 427675637, 785942803, 949415464, 154127114, 30098708, 749287282, 188353078, 898485691, 144634957, 692241844, 718007256, 516150208, 912727040, 571568107, 579986861, 246304731, 840055097, 650322180, 869430374, 455700030, 386299014, 899100048, 702791154, 859972151, 921975412, 766146299, 123679859, 234935742, 875254790, 77814264, 398949811, 907223173, 793925867, 756964770, 814758421, 938357067, 896338412, 178348049, 873969024, 994140536, 820357558, 240252064, 488306796, 590861819, 892445763, 178678957, 98483017, 925591378, 112531289, 51571533, 695073544, 891838944, 966463330, 787354041, 728225907, 43071244, 858465760, 130244035, 980887407, 379789115, 338919195, 195982898, 905236641, 689670931, 64769482, 232547789, 464460119, 987700239, 631841976, 84386232, 538496526, 389551239, 470484674, 460146738, 109407787, 151104974, 823283777, 764441227, 90920845, 46221725, 237076013, 351973006, 7903460, 987811492, 502815862, 663466929, 437757438, 930587838, 453307935, 558648753, 454087112, 352255142, 951963038, 975148548, 319965736, 442562334, 493703645, 831867658, 378346829, 504580909, 213407439, 767892112, 917536618, 626391451, 457874303, 807026671, 929000092, 983713274, 326151518, 143070111, 538243030, 533371242, 795133057, 558409093, 830612607, 369442831, 755017518, 833507695, 975248272, 250299487, 791211489, 140254936, 287005262, 848219658, 91274008, 626150658, 874929966, 962532441, 956002451, 406009986, 423813439, 81743332, 228094661, 423469579, 345001700, 70560160, 368426159, 768975562, 236393880, 348357000, 224701291, 545543681, 692955476, 460709, 742113784, 895559538, 164905151, 788033458, 302851936, 374069328, 481155426, 330495016, 41780555, 404184867, 972005894, 520087309, 997660400, 935571478, 604174982, 722295443, 483990398, 647866467, 950706706, 547307078, 567834046, 578884376, 499352220, 897515918, 973294927, 750905718, 113014535, 421666852, 73428360, 147020467, 427371985, 479871569, 209565897, 584103778, 737151119, 682485184, 353372796, 524977646, 377432209, 628509911, 274204113, 516880141, 896802397, 745978046, 613939662, 131948140, 151118714, 91677207, 308222504, 182951039, 243551083, 309993029, 175943503, 800754446, 671924585, 614107503, 975067455, 112524705, 665209749, 764174716, 720894773, 828701220, 262932296, 592111389, 716105955, 222843637, 774751547, 831119407, 657403416, 629690869, 279743355, 434102277, 198077782, 247588480, 504341100, 880650505, 943225266, 689938807, 821271575, 250564788, 845814816, 491971751, 72512596, 286749860, 415806025, 514721878, 114336826, 487835836, 469078553, 485444551, 369065415, 993424357, 435842106, 236429485, 695964642, 94793882, 46686284, 413864990, 230848657, 494851051, 493078759, 556685490, 968983290, 699597989, 586650677, 420506989, 183664468, 92383573, 143402097, 174364449, 63809687, 710431114, 608307860, 665338706, 552031992, 428357134, 700532311, 925087343, 432607249, 308410791, 873803508, 110742232, 211584121, 638091092, 149861068, 821773925, 360978187, 962903730, 210638870, 694405369, 129939290, 573431044, 967924742, 995542745, 6365403, 696370699, 767041697, 841764373, 428526787, 495694144, 21515924, 830153345, 700372964, 747994226, 632241784, 638927930, 450864013, 522836496, 300412698, 850360354, 471572092, 11259953, 21908912, 1313369, 237207033, 699301647, 823399357, 717143708, 889946592, 572492446, 198217297, 244845101, 256429795, 94095038, 704341354, 165614294, 141063919, 546618388, 831246815, 170172517, 116820845, 947685984, 374661840, 209882153, 974718059, 911350875, 725704363, 432492916, 139114436, 335170019, 302505017, 829090549, 227548976, 247429891, 107271139, 880901941, 228810456, 418389409, 797348677, 797109494, 165607959, 557019439, 25536870, 33392691, 227340845, 286120848, 301484778, 325885666, 698958846, 451238547, 273868253, 955387944, 429334559, 209893223, 182490461, 906866272, 987718328, 8231629, 881799857, 59884538, 661231067, 997338626, 730195496, 377155730, 849223164, 221132793, 795191699, 267049092, 419669233, 704585374, 468550177, 670580605, 716132547, 193661728, 317210060, 218821517, 110844683, 265758222, 118913563, 933255475, 744647765, 911877215, 749917316, 941146550, 660297618, 721068745, 620503634, 415609664, 289644162, 678055198, 880252821, 44055116, 459515403, 233039203, 482160961, 200314359, 196507663, 187878148, 226564697, 492252364, 633458514, 940530100, 136881998, 590143999, 263908731, 383292279, 199931650, 643888338, 438678960, 452620567, 73270510, 386136594, 172261329, 713051932, 437151896, 44322318, 266597318, 998283624, 61955781, 826463668, 692682752, 522518368, 605472634, 972690868, 854495675, 447488749, 450910193, 469125622, 635138902, 684423148, 770628567, 900009795, 122529139, 59467301, 189454664, 12882652, 965152198, 163420181, 165792122, 18901476, 544263265, 396973680, 602578240, 679333377, 388733766, 794429378, 27006630, 262015145, 895629665, 853513915, 379928899, 546069586, 303639690, 717186156, 276679197, 248374856, 8462663, 369949531, 917818545, 648940028, 636536462, 625472149, 124982214, 128795178, 466634814, 702594051, 50608768, 383901531, 902192348, 230111025, 528089232, 506480715, 641852101, 664436527, 119938701, 576750808, 262235328, 975872791, 482345373, 274556454, 371234759, 245580968, 498990393, 738390637, 780324895, 36792311, 275363734, 3811362, 204115683, 325378682, 311846876, 866180406, 483750228, 907662883, 493513010, 210458129, 494190226, 312031004, 496645993, 736065398, 810833745, 812267613, 431780287, 565931855, 393035662, 908744240, 528948335, 91973186, 236173487, 191686020, 349138829, 47211774, 183895004, 679483208, 692386655, 37535971, 988761504, 576256392, 226226067, 311822155, 78533580, 588986170, 507197361, 843548772, 374860197, 371925087, 833219135, 744512181, 237534049, 142199972, 630243599, 642491605, 675899711, 821922142, 537635081, 630104993, 275893426, 779363556, 922188385, 659097791, 66771311, 736766481, 508974570, 466304410, 698148847, 650538937, 880730329, 572267887, 520693728, 932745177, 988843851, 620218350, 90802953, 994806785, 323008981, 516300071, 583229270, 712291531, 878784571, 813387634, 674852724, 224928063, 100714997, 999923608, 219809889, 714013024, 823941040, 63523896, 53113439, 5014811, 745233489, 571381398, 22941446, 812036071, 478401094, 571337350, 726815561, 864040882, 218295386, 106895782, 930338817, 795586948, 345223859, 459304198, 708585723, 260168432, 183143942, 216511232, 591610642, 715107604, 774170046, 130447626, 956619532, 512126588, 174514311, 964547351, 784128931, 501349861, 876213271, 449714378, 219644239, 216659144, 922012653, 53276300, 137132020, 981013755, 742872920, 941451064, 218422675, 867348142, 744946817, 361025736, 363776180, 271276164, 440085626, 792318510, 628021658, 569891713, 360404481, 190007327, 619416960, 588061164, 931521868, 308554222, 152966718, 612016748, 486621939, 788976107, 669829673, 969432859, 635461457, 670090410, 147578540, 230993204, 995748921, 718376399, 620667654, 924448321, 39605413, 153278446, 53567549, 854336123, 272218857, 516474611, 219394229, 395132938, 141717138, 561916258, 600896755, 172340670, 117738784, 90790698, 683144595, 492379513, 308894896, 355066351, 943294839, 907308398, 78742926, 492361462, 88591593, 446868611, 393094008, 878331835, 89094382, 9447908, 624311765, 504804114, 928323940, 940144033, 592136682, 732502437, 633544079, 138221072, 692009296, 428868800, 892105329, 330984666, 511201186, 543217166, 865164625, 246758637, 33703174, 812458928, 209655781, 375728763, 496544109, 325504987, 553555796, 798781383, 316313223, 839041212, 20646568, 702970859, 605498798, 184885416, 50628202, 135693160, 517523570, 432863173, 749884529, 887804110, 604583571, 374772341, 278603687, 210501610, 725444989, 942633080, 261633069, 548539077, 425764466, 135621009, 133245119, 531612480, 880936364, 112625887, 602116730, 288392508, 816841335, 272052165, 115693144, 826392907, 471386275, 294666288, 421824407, 816592849, 330958731, 787762396, 959274247, 527559904, 642793867, 950778422, 446392171, 506292001, 703738918, 553055641, 183442711, 265839343, 30278171, 293790729, 845316708, 561245965, 768138623, 451408575, 874635574, 264969638, 67097457, 377827442, 198795189, 239304805, 544453698, 962645034, 183271016, 861836397, 845256116, 967949828, 435015295, 12516562, 955266694, 987264080, 678582307, 690383812, 777539453, 636239746, 497764238, 87263282, 753028963, 814942575, 220585102, 455860359, 114201980, 25830580, 843746705, 225858179, 878176470, 80679080, 453216424, 509682769, 166610764, 539757893, 827963066, 682258094, 578750162, 193893998, 780082397, 880798840, 743143682, 125825848, 447834695, 721968840, 770530464, 81867226, 865553081, 504978664, 166215602, 585563758, 864551832, 912562499, 281293140, 879277896, 574585651, 826889156, 703380298, 217371669, 991866910, 356115874, 487503192, 107481002, 782704156, 126868909, 835932298, 510149640, 679804107, 503174169, 562786774, 376309229, 283517876, 349748943, 632350465, 278763012, 503121771, 833143794, 917908247, 815015931, 29645062, 587284319, 501463681, 350630191, 302993741, 449326699, 739466872, 67612954, 633601661, 64126066, 579062039, 122043560, 859615155, 923239637, 317730916, 583110547, 959056967, 6696303, 599991249, 991274886, 928607870, 518187618, 47029686, 839937829, 567988102, 434793665, 114310245, 655340521, 279985382, 393709510, 258003678, 901678811, 784295642, 116379281, 420438555, 855689819, 431526050, 673352530, 154923141, 522570812, 553848666, 324889945, 601225170, 659240559, 567268825, 214095048, 549477675, 327819778, 313797624, 649700313, 73153647, 943877686, 14493823, 396668670, 905884513, 728970362, 297784971, 347817718, 682022348, 658190909, 121517784, 987540280, 870656749, 778824091, 175427814, 656208873, 351700906, 595506275, 2070877, 975771533, 479710506, 800807274, 753782249, 21788844, 606228205, 437471154, 567606100, 235158929, 383281708, 128254023, 698346411, 169631940, 715887120, 715968222, 605442399, 572491598, 270574340, 381776241, 612745608, 696897128, 934306932, 267597392, 501321029, 223849150, 329628142, 988806196, 206314977, 233419262, 971670410, 52817118, 185308448, 810213576, 297763240, 109952652, 83357389, 257541243, 894846897, 593154657, 884112040, 188485032, 606951943, 546798849, 121258489, 136290603, 371328349, 640235814, 749957201, 594046220, 952049918, 330697540, 591061718, 525448770, 68567384, 461838924, 381122289, 294643352, 119837678, 98396029, 919060553, 579703749, 324970243, 773421187, 40636308, 997546032, 501545286, 438382465, 125671313, 857160042, 353834660, 830847496, 213300937, 524174516, 750146834, 744572991, 36140723, 642204288, 67205357, 4125776, 138664175, 719119101, 642378178, 596941128, 766414189, 923685316, 766969622, 125808920, 291596353, 146860281, 390582054, 68191183, 484242778, 829476193, 41854978, 972033400, 804949735, 365177000, 297569815, 781257897, 224751800, 386180050, 345236367, 265527853, 783669290, 165591178, 484212279, 246442186, 277007688, 418003245, 896116278, 607555793, 349056354, 57211918, 231221673, 780400901, 301000424, 907281274, 949906950, 681608158, 423821654, 196233158, 35034157, 441236357, 79978577, 531892525, 127340347, 788006756, 405983511, 889140125, 27998503, 174396083, 511080838, 621036142, 386745451, 321230005, 977638100, 716884986, 163889456, 554231245, 492963714, 15462887, 953397387, 802209258, 875490446, 926477126, 91995644, 779709869, 278623720, 616232571, 405309125, 738814783, 742461372, 677795955, 210053232, 750299359, 567346360, 228568816, 931153006, 608743838, 660698847, 590403136, 527779481, 181669830, 332314821, 947002221, 679369911, 115938431, 239266666, 716824324, 928569281, 327966229, 210648532, 392614204, 162776733, 68732992, 181911652, 905311306, 537458890, 664967335, 225599264, 398352745, 545168708, 305722042, 194098772, 900124216, 445001036, 74695682, 514759764, 368386982, 452513111, 294950108, 743207134, 297132146, 338385293, 130807140, 76918757, 633425387, 215595432, 908896930, 397116908, 401999305, 817691940, 867598816, 793830524, 957021271, 565827999, 821784343, 717535250, 225974006, 74804170, 619960190, 452434002, 651723190, 759314414, 896736524, 574595921, 817327048, 321207274, 132892702, 277151205, 537289820, 644207272, 967851301, 499389799, 821967757, 716616503, 718521124, 575793595, 214726865, 671503360, 778432511, 812007213, 163973890, 939873467, 196898663, 76736071, 284548758, 831156965, 172128668, 494577710, 320301407, 159913151, 555361711, 212512957, 609113661, 724182533, 679183658, 840564296, 774580740, 715287293, 293744179, 657605031, 609144767, 509457564, 171644507, 309323891, 361986594, 283570262, 398089030, 312473140, 726605024, 28469279, 540014545, 916333016, 957470950, 155449865, 371453949, 529089418, 540718659, 209894404, 39360854, 31579013, 382810232, 190879903, 495649625, 369827352, 453054142, 853375180, 680079175, 981672152, 626927845, 212833373, 235068538, 735830383, 830312582, 348175529, 133879909, 232211277, 812742335, 911869083, 402416055, 425025880, 571880233, 762595206, 626636371, 331457037, 168124247, 574979652, 41773725, 353615278, 312892411, 153848877, 531146816, 748170218, 325099565, 706860202, 747009004, 642622120, 598024192, 95683776, 769425481, 622521973, 345724990, 721828341, 58629196, 143309023, 825890, 814189260, 723616358, 688066823, 252821583, 64952990, 792376698, 817067333, 586752767, 834737401, 149470942, 665230323, 791365887, 776002424, 607584429, 93906111, 662750905, 109430207, 261886718, 9039193, 513290697, 699967273, 924520221, 835269155, 631978442, 395143460, 434715686, 750976825, 396974332, 39709464, 156388669, 578249388, 469942343, 658083349, 910263166, 566386676, 206206358, 159676634, 25592718, 864095148, 285063821, 861757352, 394657437, 89649829, 28042943, 739971799, 902519074, 155086573, 618230983, 386350294, 533733642, 972623861, 291590180, 810282619, 161600806, 409576560, 516336811, 158690942, 959604559, 550742198, 40738153, 256534802, 632537480, 717923002, 130396523, 28192557, 148073718, 23815708, 371812300, 129038488, 901087641, 408813387, 326889011, 955160595, 164424095, 820694036, 622714352, 269346265, 708538366, 878405099, 884028500, 400668534, 536947171, 492864609, 882964842, 569494336, 51917661, 490895192, 933567081, 129409654, 808688960, 257628139, 554561856, 699836438, 937833088, 795625021, 645876260, 952198118, 785205277, 841085773, 941697317, 779604663, 449923628, 249050667, 290473202, 804137599, 606360604, 349350658, 951275670, 821986678, 767346489, 597856053, 357203028, 404258480, 463646039, 824068763, 206220167, 936151083, 711702838, 683588803, 114948152, 37412952, 150014553, 927738425, 24265082, 743987549, 781168046, 370952563, 135840161, 518532960, 539367351, 651104043, 144607248, 415223745, 269852882, 121156510, 633715725, 31733569, 458919711, 939115489, 301958608, 458726423, 578103401, 575383582, 812101284, 249542067, 580016282, 405472181, 416560202, 464042949, 324695477, 359170582, 645381748, 546774536, 54508317, 819216996, 381092952, 828313981, 555049401, 13664274, 665056959, 107048897, 432987862, 348096869, 423702801, 209895908, 390147573, 835374231, 576253872, 831878989, 221056465, 227243442, 622681294, 616517620, 866157429, 419132204, 372090580, 857245003, 37175056, 979804249, 775864733, 974678652, 141931291, 44263895, 524470386, 339557682, 636857343, 862775292, 953785747, 613145648, 451560513, 692576967, 929200004, 929815725, 446547226, 463065057, 536051961, 610833058, 796037446, 968714583, 824472526, 970042950, 533584831, 170160633, 159247147, 9952168, 819424274, 313536657, 448030810, 259845959, 433397987, 794248265, 298835417, 44502151, 586016238, 762695261, 742825517, 982951154, 575077066, 413233128, 702649444, 175111533, 961678828, 997507101, 436770720, 724635805, 153070038, 180825085, 586419419, 288518150, 440420596, 856288880, 835333122, 176751496, 880446660, 989044950, 690506915, 451571462, 506630838, 927286444, 93986907, 122209307, 615415524, 874332393, 556094720, 241590365, 151346725, 670282326, 321339003, 963493963, 960087711, 779260492, 432297231, 860286471, 581490021, 952290364, 458437289, 597119239, 954137764, 622094105, 400049297, 424131738, 324020632, 934206243, 235897184, 314344413, 762909836, 762649578, 384777856, 628857848, 22786366, 266455471, 574921876, 289882686, 401528332, 288666709, 159619667, 575883695, 553620051, 854200072, 186239959, 239911785, 607300643, 596251775, 529937506, 749218487, 945917742, 479793703, 787699842, 690092166, 872072440, 928751013, 800120863, 834960255, 268551996, 576986815, 894847955, 129902756, 701323062, 15389427, 918985272, 892131873, 924968615, 39700989, 11649907, 99772004, 17308991, 993976987, 56711974, 646143713, 113824738, 112245793, 443635670, 226628781, 169934468, 616299148, 15673869, 8309641, 162299276, 462249668, 102428558, 44582622, 637512185, 679555504, 627993596, 245565064, 868832010, 877848211, 427835922, 531500584, 473504829, 87019576, 152648830, 717914935, 416944010, 902690344, 891917529, 277363499, 281216775, 402762427, 180949555, 874179038, 42508409, 594269393, 834382147, 551235065, 523850100, 12947706, 736152309, 568749620, 218587757, 200771704, 758647030, 81468523, 4842717, 961181259, 906039876, 715332108, 274248891, 115487398, 847999641, 903028624, 769829849, 706918448, 444608530, 903657843, 27493671, 14990157, 545692099, 802805013, 88576094, 640766928, 428610503, 803815108, 704974858, 894906642, 59226474, 28288401, 945013281, 767833855, 798214103, 267252624, 636259057, 508092720, 428239835, 742677608, 2439174, 749606635, 741168390, 903897694, 743789688, 712799103, 547787318, 821244384, 400054621, 826001268, 803845792, 815005312, 77719526, 883271084, 219430520, 73845715, 272428970, 228534430, 628277897, 162409891, 418426950, 830039189, 761710766, 191300655, 601038383, 287520684, 748502053, 186902957, 716282190, 600771373, 950210807, 705938598, 66421712, 104682045, 843518846, 348663091, 246613015, 473377429, 440306816, 691851338, 163422658, 135392796, 513339727, 88437287, 283214185, 117249459, 907156062, 451325657, 579647163, 513000091, 907803361, 551471442, 744358487, 591426222, 206499962, 100118887, 790249174, 73640003, 881917340, 388059987, 882675404, 950922759, 414377121, 781261037, 744167379, 179543548, 910757461, 971248617, 717898913, 770850511, 92008503, 676051468, 323395771, 785693339, 590710852, 5269715, 638467150, 222414983, 761259521, 263644731, 38435090, 511761572, 359786646, 922954018, 244924683, 583067706, 283046571, 318633875, 683594615, 666490526, 701580911, 113006477, 798971016, 601110540, 16906631, 925876997, 182600417, 402025416, 748769228, 952500551, 723955009, 721345133, 437098362, 110577320, 288452032, 157120269, 308808178, 529982934, 537116596, 851753399, 808073596, 281853983, 991840640, 674971920, 881953508, 826863160, 546397811, 993533771, 80415042, 537197012, 243843839, 305803329, 352030961, 961785935, 332682600, 522714297, 670726800, 415785964, 414333185, 366481188, 330700239, 552485501, 488988260, 374517983, 178014519, 491500745, 961531466, 469771503, 384094484, 696470383, 1583705, 22183990, 643154122, 788192510, 962850295, 609310538, 685004814, 832517167, 728213123, 63686736, 979223902, 834494380, 181440619, 657899494, 227121691, 113344051, 633328785, 180707565, 883367870, 619055916, 652349918, 287095263, 978242925, 413225775, 250453632, 881310348, 82635622, 538371953, 71119403, 567086062, 80160234, 392028501, 717832063, 900341668, 907540174, 708221231, 687052798, 619676292, 64403326, 364013495, 488213672, 493438603, 44656594, 887622596, 829650988, 874730563, 846056808, 42506429, 123224704, 111028720, 588987917, 799900783, 707350819, 418758247, 812018916, 642951045, 84909618, 865254743, 926896719, 327629618, 765175105, 735941069, 510166249, 626817214, 609508845, 106648879, 763596967, 767909762, 967382870, 214890611, 553410984, 287554472, 145093584, 899949989, 193975568, 202875350, 845684647, 267851993, 826063948, 685599133, 873902606, 631356665, 118030382, 33334080, 502602925, 493210461, 816193125, 579913274, 110984405, 610961636, 761687267, 410416790, 435693342, 629997227, 164809679, 957304169, 370578787, 124686334, 21220731, 876539917, 159511308, 574256011, 300148823, 614528235, 757067953, 942950561, 38648470, 67906110, 675401474, 258953685, 617595723, 550691700, 679155176, 68573179, 881330857, 497216607, 706764695, 875954171, 658466735, 451614616, 300245762, 450860146, 589061005, 244839524, 959407569, 985586018, 296670292, 709965248, 914841911, 542396223, 347632801, 884057525, 514841062, 204946906, 554069851, 830301336, 483666392, 165280700, 330294986, 586303412, 34248106, 972488007, 485734804, 759938017, 590180324, 380045223, 15436325, 384275927, 97195916, 145718696, 300273528, 758403722, 935394897, 234777236, 586936993, 560650825, 523436251, 441771068, 118128251, 325113714, 656265903, 23111360, 483963218, 250105333, 908932371, 429614994, 648812152, 666788826, 806817543, 39216877, 317026644, 13149264, 750683427, 965553329, 992555529, 644920271, 757324615, 713931409, 246271877, 527010715, 337508046, 767089782, 523531950, 180015000, 449043181, 168432003, 721113458, 131756109, 399835172, 202509715, 945410608, 515974067, 483523586, 813867785, 206319613, 643252161, 902938147, 27252470, 946801989, 189182959, 159315701, 622667801, 942901221, 18658460, 643182287, 748601029, 916630433, 515202432, 541822294, 490971823, 530862167, 277304438, 446091273, 727132672, 920918242, 456929764, 893538826, 61265612, 730521667, 333094080, 92060112, 162815476, 569780040, 362610810, 934934642, 150642458, 51447094, 849629843, 72127359, 134579543, 192371021, 764147145, 813401205, 516338716, 211192747, 830456339, 315151643, 183851735, 771589163, 612047116, 371106527, 21749065, 872889024, 315026277, 630211598, 827070751, 70444289, 759115596, 24169723, 887563122, 361695342, 115655086, 369266977, 60705341, 255587088, 637283561, 69087771, 263951836, 759199658, 13507410, 136101367, 16109069, 919947339, 191841266, 588723785, 201889482, 949297695, 717540462, 318021352, 193650596, 183275909, 333173039, 527173649, 842074749, 550002418, 179952870, 626674461, 291613731, 615229788, 14486008, 316631117, 573287626, 454516140, 987976300, 538767871, 337197221, 166804802, 882200475, 127183682, 260065299, 590933118, 413717900, 928297924, 415530617, 171086543, 178099140, 452647438, 659248471, 283268239, 199164336, 381825121, 704599129, 339061850, 441725606, 389514807, 51072246, 194007188, 510465589, 553206777, 633434569, 113247224, 883598158, 572947164, 878877284, 712099936, 339805514, 313994784, 640938479, 173677435, 992569385, 783085622, 623553391, 435835005, 343903441, 96104921, 262662568, 305211414, 30565407, 506835811, 735317518, 453705602, 79290317, 832425189, 201105056, 555458035, 630438554, 624606872, 66965768, 541136598, 843364341, 475268689, 756621547, 919285650, 153174558, 352561669, 345018536, 747020173, 369147457, 973308422, 392634587, 230391055, 567813958, 713041210, 172095041, 352419211, 224854977, 128265078, 248988860, 81236577, 663424496, 831493283, 155868659, 155836124, 318897640, 641430780, 768635540, 408074355, 112189313, 665061357, 527573143, 468080283, 999768743, 406406275, 165188462, 794283235, 99159762, 970306951, 776722693, 480726934, 48794286, 616045663, 258502479, 219407776, 151179595, 50981966, 121648099, 108069070, 166213286, 824441367, 950939170, 157330157, 411008035, 96057948, 44215181, 258584038, 488607597, 139125461, 382854237, 315536005, 217814871, 613279475, 614455582, 764117195, 884808815, 511529663, 982092343, 886771941, 603087237, 932245203, 711298610, 743282816, 81159987, 471342526, 845021454, 521401269, 462513459, 420269535, 805495038, 727924505, 886709727, 991398140, 868847330, 489891233, 957974302, 558047692, 927084616, 441893649, 963296200, 846736618, 943832132, 283400623, 70031515, 168371958, 332149133, 276380531, 339120395, 553060644, 556860226, 690680199, 837696296, 63371623, 671232174, 729706264, 972601447, 529555264, 211827356, 943880909, 700916112, 957436496, 306010335, 621906997, 965381997, 290665655, 597939401, 630452944, 48513625, 970223215, 882285212, 702055516, 643431697, 259615324, 391776781, 886243789, 399395712, 540376530, 609957011, 726833358, 710199777, 628526273, 832983653, 927328561, 935209970, 26031796, 719174013, 146124733, 138676243, 273707899, 887988609, 51127571, 791944843, 62595646, 231164695, 190065327, 519589919, 2329264, 492875963, 475861242, 442535825, 915267607, 328539363, 287032537, 511610638, 300972538, 318465722, 695832435, 491331863, 988467464, 983128228, 981119767, 430715017, 157014598, 254184255, 16050588, 772493819, 939047053, 499897037, 645524809, 873476113, 317288956, 247739974, 663517262, 735321871, 832517881, 763299126, 815803438, 415349498, 177538022, 237300062, 422013515, 775233240, 682424736, 173716402, 597197435, 996996242, 656150124, 109676711, 903450580, 150990268, 279120600, 829615733, 371069691, 285973627, 876537974, 513631017, 758650342, 522771496, 475217274, 45972264, 188644787, 108090278, 129018787, 70958552, 249724789, 702492723, 130329956, 256094481, 280907095, 693666270, 192290369, 906491185, 904396433, 272782617, 136844455, 536637023, 695112980, 667687494, 948176209, 989410435, 717516111, 813686931, 822199803, 748521836, 948034419, 669278472, 364899689, 376517839, 415776764, 495295662, 479158829, 273309370, 640962946, 21863655, 4315998, 823378891, 25738483, 445394456, 293504968, 455272040, 72289534, 466492431, 549030951, 746989625, 280885104, 666399241, 659813619, 795353530, 250282815, 508321826, 197263951, 703060970, 188312302, 263211491, 842310407, 845323764, 978391274, 521880420, 998274346, 458801062, 28089567, 708002692, 350435798, 23689222, 676952507, 697988607, 791410901, 848690607, 669769986, 891043796, 938295354, 850431481, 303438399, 306330846, 756101554, 898101419, 770590456, 158285116, 465533556, 620002371, 211902696, 883921854, 598974678, 379756487, 627330828, 388403353, 340334317, 136248430, 388901678, 300947638, 550246562, 374553154, 831416859, 199444202, 574230784, 387653674, 706329225, 224061290, 629678850, 620078680, 511218713, 963293195, 861282955, 961110425, 797602945, 941417355, 419068777, 680027716, 684417422, 956965902, 222087615, 968663187, 749716899, 791747513, 970683390, 942794353, 905827099, 759463425, 276111828, 584756656, 509049689, 145915352, 982407253, 717076292, 151819852, 297894513, 536945118, 150740403, 386565889, 411666225, 687831472, 728419337, 985870277, 191199784, 783121525, 918757323, 78650926, 53717984, 508431094, 347458503, 867189443, 563455724, 333899351, 372566314, 631487702, 97968749, 968728769, 795406969, 793090894, 886225833, 841357745, 605381537, 855601392, 931479819, 926622, 674510558, 235089443, 741175589, 339016268, 151404678, 161495470, 872276632, 187114651, 352558494, 700810341, 33024602, 563211421, 582125574, 957594447, 104300184, 358035823, 251768866, 144626978, 665180429, 133104565, 832638411, 519133900, 708922851, 947826984, 561372509, 532328495, 283688560, 209506761, 962509609, 337441019, 499054196, 292959752, 934460524, 924699784, 56728859, 28755420, 137065576, 906475255, 655676060, 843612142, 241195091, 134514673, 649990343, 392546882, 499143461, 61506941, 118510070, 919496059, 752386681, 420942050, 664473640, 705032092, 485348254, 224675256, 867129249, 565026036, 236157117, 761768670, 771135932, 435602587, 879499103, 149028609, 179988077, 698980555, 128996723, 966129512, 994052923, 516108103, 603969804, 265793478, 740727276, 817887329, 64830778, 218890536, 763640261, 719701214, 63364671, 989842862, 437510348, 812016498, 900526605, 720055949, 44137216, 242650098, 403504381, 510842706, 108466202, 262046316, 607378571, 322686985, 316748123, 836111015, 923504313, 591444188, 929438884, 48121616, 520656715, 483344743, 2089530, 826484169, 751970465, 138221029, 330637178, 56093289, 28231304, 836150296, 875743625, 892136450, 906490518, 481424975, 941374599, 666591712, 746411878, 10551292, 228478194, 797691051, 981519065, 770785029, 491140198, 165592312, 469386452, 215504391, 264023381, 29203370, 758475899, 303362040, 95255139, 791009718, 431504737, 997655930, 686994828, 177031892, 161533041, 159373091, 726191906, 666516717, 738088845, 866278013, 825174005, 881862209, 220334820, 427965514, 669701052, 938412128, 929012366, 319896180, 944112425, 299344042, 712047258, 424249509, 893603331, 537708128, 427870910, 254414240, 286184932, 448959818, 157874624, 468470635, 753356164, 968852841, 903937074, 447312108, 624193377, 751032626, 679984871, 896224473, 300061289, 757775039, 100172012, 458040048, 480710144, 161538771, 930870146, 262828557, 378760529, 807298619, 497825759, 188472289, 16275444, 754694178, 756419569, 121903924, 367334547, 247659208, 617045571, 486482096, 177664340, 808832353, 727128850, 627103836, 788092127, 993044763, 329120852, 796845941, 286507317, 73840332, 98834952, 609669236, 673012257, 985685110, 484388384, 641215660, 690288891, 237189315, 684637113, 179641411, 100331450, 331318316, 320843516, 549431504, 765840615, 328216515, 499564971, 762141222, 928710768, 274162562, 184053561, 850949297, 286146758, 822021344, 155186342, 975349220, 124468906, 495558640, 603285867, 635006432, 177537791, 102523120, 358080645, 267916067, 75113016, 781091937, 262665368, 818022230, 908145483, 985786459, 83542778, 285862644, 701024, 223387442, 603373332, 500238030, 662028404, 557138008, 368247014, 337332903, 836246026, 59003475, 484004362, 229346100, 381268190, 51166262, 882726196, 804392576, 81989607, 199679486, 80936194, 576200959, 588669522, 824999805, 732307562, 465225378, 208280015, 301350517, 915418767, 576742002, 199068798, 135102407, 931428333, 408738149, 159041809, 354974549, 578508521, 365565098, 897419592, 163441799, 674500763, 695188151, 509721208, 99410021, 880739969, 228648227, 869163128, 453346186, 989668561, 213979623, 774123644, 436057723, 436108306, 527986371, 266144440, 636256570, 130457020, 721428720, 75903805, 652419605, 501290030, 751629322, 98819160, 598343021, 838434152, 999173783, 247184217, 396227206, 780047759, 585708205, 150955365, 105092109, 103168614, 321020788, 471654648, 364846270, 231509586, 285675553, 18419438, 856628920, 246742890, 99529525, 810157420, 999860879, 9003164, 684289090, 865189625, 725043678, 198327214, 970995574, 155069860, 625558459, 491815008, 327773628, 440960533, 129493015, 439433491, 20498003, 842694683, 114767266, 855890429, 979832780, 245681065, 694259752, 868089873, 987946936, 265241888, 198114079, 503045708, 250554613, 314555943, 270952605, 244541626, 864587328, 950559007, 398020073, 910152574, 405950526, 231212022, 111572241, 440528770, 548985243, 411554141, 568540191, 85116445, 530486059, 428468178, 564357179, 309766846, 900387031, 156958503, 913626442, 88361044, 54756339, 670816493, 164660984, 595298990, 587433528, 897040980, 856493758, 514933611, 198456565, 661539701, 574726041, 726500560, 736654544, 649236251, 608058376, 742722383, 259856865, 703994172, 669784166, 459971722, 199893038, 538456393, 570956859, 416595518, 424529724, 792597242, 334575418, 952509459, 516981291, 424345184, 565904611, 912970447, 573596954, 841888718, 941454670, 382720959, 501224895, 68733364, 50556876, 644825354, 19485895, 959189903, 750781636, 770000594, 768664257, 862773553, 367375060, 50842267, 432821625, 289237387, 138965772, 228563814, 816253013, 169100888, 855986225, 788437864, 450253806, 267258656, 475441407, 228018622, 634398114, 627552688, 690082812, 187352278, 10428869, 937808725, 993608995, 294150630, 587359373, 238941491, 654894540, 846537603, 187868275, 433071999, 836854912, 694152355, 680278275, 799129550, 846343787, 445084253, 268814499, 810736789, 446802086, 727037107, 182973428, 742163433, 469817622, 850965026, 22978511, 484892425, 820448838, 948234123, 614284664, 220333402, 426488316, 32255569, 912453093, 968377957, 139360531, 531771441, 460008478, 409026578, 831614422, 788241275, 124362459, 287602880, 972828472, 416264584, 323694571, 180656937, 165286214, 440232326, 480672268, 695329869, 661447941, 736187875, 821461431, 765136968, 443949095, 534726887, 231510919, 93266545, 442752160, 850311855, 497394559, 912823985, 180979417, 15845495, 373699942, 631517619, 187379277, 86133974, 563189363, 797652649, 959932543, 959273354, 660452751, 869170653, 484132630, 894192129, 861089638, 938337960, 89943687, 626180797, 890394776, 742297469, 728416712, 457779972, 269930117, 511977927, 832226980, 402962045, 499506786, 688079183, 747033015, 31113961, 828276312, 380772609, 435091649, 976900994, 316455998, 400829672, 176503567, 413496175, 664270360, 239517064, 773558585, 67179314, 9869024, 16713172, 231025067, 320689586, 456045667, 888905079, 191769735, 29040822, 175037663, 298369271, 12025163, 808967491, 854256722, 453625573, 437969500, 594303869, 253235713, 102429935, 287016229, 302270909, 862490438, 404327846, 695221840, 128032703, 932948327, 162966570, 909401610, 136399068, 879791767, 361638783, 888084598, 676078831, 386286752, 659035773, 86223095, 963465492, 868098079, 667737647, 517048047, 945534088, 746977782, 837473, 151537704, 404377935, 576829694, 838950094, 313085024, 237641187, 569600573, 194868935, 730029284, 675871702, 803021464, 321559674, 355731636, 129964682, 851854721, 724867987, 380277089, 532146146, 108010557, 37926617, 298224348, 470048607, 513592544, 226036964, 598145770, 610173814, 79225172, 545402821, 799647254, 337321499, 585174163, 193214014, 709480227, 468803214, 18031388, 31835365, 242062720, 436755629, 423652860, 54253089, 76391265, 903278212, 174275524, 110151425, 447502947, 646678253, 16308611, 959337089, 492513499, 20143745, 417214155, 81436072, 144453044, 133204352, 199781039, 224690483, 168839985, 880879623, 707682267, 619752583, 901660299, 369163868, 407636464, 620502727, 468575884, 384306311, 154936545, 901675078, 226855618, 587663258, 326562486, 663122779, 303430538, 678308644, 604330620, 417758099, 218973353, 501004101, 305700825, 135876569, 617265509, 631279522, 359049206, 659060025, 522302539, 732000855, 62405425, 484662731, 248296700, 803109834, 830613774, 299679415, 774025842, 837242042, 977629317, 839813645, 885345413, 901567618, 26799632, 840991168, 361283105, 305102854, 226062154, 355930433, 17271219, 900197701, 873699162, 489034046, 250025796, 4312099, 726140012, 363233706, 387455329, 689025253, 263148444, 535144802, 119610252, 127379851, 990099235, 471643585, 853200745, 526658780, 167043913, 720819850, 304184545, 518523337, 906874615, 763704358, 529743753, 226138570, 699197659, 703863611, 701260127, 560476520, 65389337, 146496090, 840594075, 186692512, 843505391, 851708424, 254974512, 485873974, 502395073, 43725734, 9036192, 279010257, 907888034, 118316255, 510685196, 503099155, 700159823, 376166506, 300849396, 335102044, 864239161, 328161172, 793683069, 477799463, 185230744, 53314503, 441868898, 533607399, 151952642, 783378065, 453407293, 210015609, 884050996, 607178653, 267401067, 132749357, 499015594, 535022229, 353718776, 515812298, 785263492, 332709882, 476446758, 815191659, 830413907, 121501204, 132201022, 26944477, 312434619, 286525963, 335077284, 684856201, 223330445, 705348676, 597132704, 686720626, 562918725, 716290965, 847882767, 894573524, 101598321, 20238498, 724486010, 463401940, 528611339, 220825462, 761256413, 636749463, 208309411, 368254788, 205600943, 45316275, 273877363, 721808961, 525993439, 77075712, 867169830, 20860213, 454976847, 1903821, 898270647, 246323903, 975674800, 560731028, 459947987, 523189674, 349132931, 921902521, 753566337, 673948702, 220713394, 89588354, 140298623, 684396723, 80923063, 1453032, 394719234, 830882906, 885921549, 685212579, 867170147, 485929648, 858571656, 707049703, 592448364, 519977949, 590550300, 535943906, 231749369, 856431322, 337875389, 701135843, 678431068, 184869685, 177232215, 268745259, 229764405, 71269897, 576226971, 400375015, 549689997, 671790751, 909125653, 273618459, 934998046, 758012770, 881048188, 677987464, 813079447, 885735743, 736504113, 626535983, 758198046, 149895848, 102388730, 125051002, 141261553, 649939793, 304907335, 286189903, 147661095, 785702603, 951040105, 379439540, 671201810, 78709379, 522202553, 750333909, 548443527, 202203763, 299557501, 546312407, 23961861, 5004597, 579122407, 622761914, 257657742, 112456594, 7500674, 979479909, 159749077, 153791664, 485111253, 16531775, 179692159, 803769235, 972268225, 600670120, 592839520, 550482391, 882007388, 605758975, 430459133, 198716690, 998945587, 156410320, 544780833, 359507465, 599447768, 268013733, 461939352, 166243000, 954052748, 656397885, 990413059, 964358259, 532827604, 230511191, 653612559, 732000574, 157537915, 586848813, 359314928, 904207471, 962710492, 440923520, 206433869, 577388550, 103528063, 338209138, 640425522, 463677457, 693217376, 74143342, 347600686, 356382246, 728010707, 448091395, 873610017, 945677029, 638687003, 430155381, 567467061, 23880215, 169614149, 469139335, 887289949, 343474252, 829772355, 180382863, 840136255, 484168544, 705737079, 194625957, 73155670, 502272846, 927810334, 38404448, 48563440, 891923934, 637978659, 807859122, 905093622, 263014049, 379848894, 204646160, 685599987, 389002139, 107248888, 559157918, 573476643, 205014829, 428441930, 253113997, 119808717, 263556555, 459537218, 63363506, 90944162, 84434294, 739281960, 329881675, 307245170, 350148491, 879766951, 499443283, 150840312, 363841547, 845098647, 474737136, 200397283, 88122441, 642846926, 616992862, 408469076, 859159038, 89498507, 310620228, 496742330, 692347486, 794411084, 407946444, 737202105, 310473734, 30317030, 666656284, 466411491, 590402934, 456112027, 314143392, 336417661, 505795890, 650208252, 172376531, 110367317, 767819875, 591628663, 792995708, 436655172, 625051441, 881978423, 534908026, 108274296, 407219129, 745173053, 994340351, 548602473, 778667905, 33188327, 709504856, 777228369, 181340480, 224643881, 549564667, 485672441, 735576857, 242494420, 982117666, 556299319, 959267996, 551331982, 999944155, 395265331, 311627937, 830706334, 100112801, 845629908, 444861243, 803900805, 199928389, 859896831, 536780041, 277323573, 897782549, 276121491, 829541258, 251447675, 214775906, 476093284, 955954872, 284837462, 337008866, 361605712, 113867125, 44057119, 725956334, 773009940, 798186048, 480217945, 909282605, 670045, 549240463, 660968983, 180432874, 605974113, 713303037, 176976674, 294796202, 647546581, 291192229, 448010115, 858603909, 352945279, 210570629, 888290397, 427623640, 826922425, 166656505, 109438459, 66900743, 971509983, 26774190, 652806420, 203164896, 837089892, 408299435, 969852549, 537963053, 801744638, 748354893, 838862142, 214559464, 386842070, 154926455, 347787676, 375544511, 318515719, 618152000, 522170008, 193273324, 617733365, 188400877, 34105661, 69599238, 515192212, 105034453, 220236755, 324607453, 514255559, 22052678, 834493414, 714840805, 984979445, 433887812, 532657777, 646898879, 86766815, 19047898, 666361044, 492028378, 758597927, 893839207, 476009005, 91969779, 88830607, 580670162, 609182792, 158286035, 24264918, 557803951, 448990752, 973520659, 914756944, 325414626, 91094144, 449585780, 949259561, 611789724, 342025726, 848632061, 588235189, 365882819, 613894553, 1281261, 801373027, 875675309, 44370651, 553467085, 829617096, 881733940, 838023124, 265554292, 891617519, 498641153, 293074204, 358723895, 402200470, 31396712, 668971949, 627536541, 393922994, 557702951, 733725502, 867516213, 85337382, 807804486, 463084854, 44626272, 165227710, 257936543, 981087142, 354874796, 312244442, 708727970, 989397110, 792276454, 964669724, 598180747, 762992194, 100072987, 806915380, 199269425, 363595979, 930271222, 225531747, 524654862, 255558606, 270052714, 992463756, 717325763, 430454396, 297935387, 822946901, 112356658, 540285064, 800698307, 358540645, 232034502, 7033907, 561330536, 229619034, 488872959, 587958656, 115591270, 292442473, 922433881, 157768331, 713589863, 290112246, 117474769, 149119603, 7861024, 801357877, 698612652, 777638001, 561205473, 532038320, 483420333, 221290463, 202781664, 455142854, 863376138, 208834130, 512061624, 183867390, 191623029, 559770826, 370969056, 898006682, 350224358, 990579715, 307835467, 150950116, 787010974, 644614988, 260694330, 893970273, 217061935, 230878776, 910870666, 724998560, 534835015, 233087738, 543435955, 293280934, 183371410, 277003421, 271210343, 993180209, 945429560, 220872478, 833883846, 140094327, 23676880, 845400118, 685073777, 440497830, 611891886, 316986182, 360774180, 466076404, 639933186, 87583273, 992575297, 733955601, 987472821, 726999833, 88440813, 624583606, 519967768, 608828661, 321302962, 617052176, 91060516, 381298224, 346882404, 193685481, 615335843, 631367632, 632252430, 490381647, 421909616, 251088428, 303716001, 146308667, 123046144, 918289326, 432283751, 972428077, 957735628, 84605215, 462312972, 994093076, 338665499, 489721290, 70929116, 122157328, 550290556, 621704155, 680130454, 442189787, 834719043, 61669027, 527461040, 380186862, 85126660, 431473712, 806389334, 654991472, 368637674, 811588729, 610868190, 314676305, 46264034, 52596837, 535179635, 774973744, 83391244, 667299711, 884944430, 449712006, 209436312, 411131074, 270158540, 395117081, 392236619, 934175523, 511611281, 365470357, 302510838, 969912075, 841609071, 669756184, 172695415, 309502917, 249129780, 364903617, 332886564, 579000693, 379221284, 476262065, 115550512, 759227759, 537285548, 661009855, 922440438, 207269265, 142432579, 511077487, 935356312, 827526423, 802839691, 191039706, 502104837, 643690747, 395532681, 702147665, 665558630, 176709380, 615120997, 893250945, 537739023, 282121934, 27311522, 234481652, 13996766, 312741007, 111139485, 273412619, 709439992, 916271619, 277572625, 683116526, 984705575, 310369074, 895022045, 148701404, 694291032, 763458295, 577060359, 31891723, 808868275, 557931746, 408253637, 237405341, 425963367, 590040333, 610691588, 724313629, 784980933, 944527864, 136491283, 938509231, 686964970, 293570377, 320325406, 235439922, 940012797, 896214780, 849735508, 50423311, 889658482, 69390565, 415279507, 968580723, 753337398, 26128275, 984691913, 501487112, 865741470, 116205352, 216651516, 140740012, 298674646, 182363508, 312941827, 452282443, 345698324, 416646118, 483006047, 796923801, 505012598, 179873062, 677449130, 792637348, 986787183, 740001469, 909793378, 397693810, 225920798, 220264509, 202299712, 683766710, 447419594, 189672775, 453824081, 147425955, 77063024, 215736978, 502051474, 484485139, 576931963, 895970502, 942280680, 829825908, 383711535, 408703838, 660150305, 462695579, 45200997, 359737778, 38540232, 130077364, 676857101, 859839436, 545381883, 276083817, 105144784, 405797433, 688390704, 305353004, 985127471, 961271118, 125246624, 847964315, 344875157, 320106122, 59750873, 813073999, 953158387, 219553617, 320211910, 286318344, 948991458, 560945247, 123411595, 124274859, 865198152, 512231113, 295617190, 530833397, 394692216, 732476149, 728815502, 745377567, 602714203, 383049507, 894380441, 707917555, 893808478, 762584507, 623780786, 198072889, 458915623, 207409270, 691754956, 229591764, 279777530, 883825432, 881007942, 522586896, 400477475, 916258767, 694072890, 81593916, 443170279, 976699281, 55331692, 660174038, 895247532, 248935868, 772787854, 704222423, 352502936, 85485771, 28112699, 747792697, 425614366, 959374918, 108659902, 65813598, 313581616, 771854207, 336325254, 595262148, 514228025, 954907663, 422225389, 517381386, 431312662, 988833062, 53614438, 845181968, 848399261, 284235910, 562733438, 329475380, 781316199, 388386342, 490426741, 32708447, 699049621, 963178005, 288949809, 423363067, 884356374, 633707471, 317402609, 914541866, 640612042, 102860544, 996725734, 239833476, 363656463, 434368038, 969253977, 821220949, 531708983, 998360963, 737683386, 307597737, 100455677, 441631454, 587094613, 876598901, 656687337, 15940317, 181186907, 491894204, 361100592, 359282209, 631504136, 793956423, 217168982, 758434020, 105371195, 543792682, 2810505, 521396816, 566659946, 19328085, 209136362, 132346353, 568570158, 935158206, 472367907, 143861031, 621544264, 15261229, 225023387, 387283010, 415068800, 797501515, 735662909, 585280889, 865302962, 956722796, 863912592, 812999216, 953177692, 522526016, 933457706, 369878246, 717268034, 749548810, 45611623, 150620439, 322784368, 755071818, 911079220, 263816085, 21399865, 830679692, 745088646, 286888683, 983957615, 474470891, 709452260, 235636723, 113560232, 749144008, 6023180, 68629004, 450849210, 768721012, 307514486, 49911961, 180369613, 403158969, 450425374, 605363548, 110373404, 418051062, 999135530, 280197064, 648601115, 422029787, 277127732, 9364126, 801653961, 67448061, 161069103, 442044400, 99485671, 337186944, 156590096, 900725647, 985365749, 569995196, 410335300, 745740429, 700775565, 836971796, 106976914, 564913327, 788150924, 32869402, 808608604, 849768704, 667326539, 349899881, 95523753, 911364722, 493694357, 876496354, 952639833, 270241355, 643479809, 845045917, 542029743, 946569514, 329975835, 693567034, 669277708, 202152686, 459211089, 573374863, 780250135, 436322974, 323865335, 210939470, 998850234, 139435686, 326309672, 346261019, 451257421, 602732199, 859797073, 268692262, 153542735, 560460620, 953259110, 52164776, 338257298, 347594487, 635937946, 449257976, 110806041, 815950024, 942390655, 385758542, 530409316, 545060115, 4618461, 339042761, 365872377, 979027052, 871107563, 546531139, 762075568, 726908301, 406096986, 17005641, 752415716, 350146263, 311569851, 699472417, 181106819, 435203313, 447464053, 249245900, 191220648, 245011333, 127526353, 643085334, 215693714, 788071387, 696089578, 884854730, 787463780, 751345959, 309225389, 124912247, 607303804, 641153014, 762946986, 984961924, 708295566, 33781503, 322812894, 305434589, 430457952, 325102082, 55124059, 309577987, 911377165, 277486315, 288433571, 105049429, 568665647, 180162080, 333896964, 711613464, 900383682, 844860867, 870099389, 126339866, 281105241, 309790361, 128121623, 913704393, 898654699, 604021576, 526134440, 105518469, 467942230, 924189514, 910274165, 843114776, 591886253, 839740714, 150699784, 8265044, 646435830, 826460155, 616692993, 787975343, 306300037, 72291291, 573128480, 842547543, 331099576, 848363238, 547503297, 452568984, 142102322, 156559878, 303565892, 530229922, 895515762, 686779588, 928025512, 817283873, 8356857, 919813013, 227022899, 645405806, 837923974, 751795669, 77102191, 542464295, 472370018, 275042131, 477634474, 86435414, 742377832, 892115115, 807230103, 266772250, 491938244, 804515533, 941575406, 159463968, 361270637, 275795712, 773601772, 765847059, 174053232, 751594066, 328437205, 829814373, 986837513, 551199157, 347188683, 196181940, 142966938, 247881044, 954335967, 625450824, 692987952, 906654723, 566148286, 119266778, 32277853, 585098462, 597364562, 16066152, 514932397, 351147396, 862247811, 462352993, 270372337, 448537742, 226644319, 167742167, 434129798, 245854363, 245296052, 491149405, 360629267, 876580260, 925126699, 229091151, 802911274, 518908614, 103700575, 144957406, 355378834, 560786946, 185018596, 664184782, 645388669, 637558527, 25349984, 764907373, 862158190, 217392987, 342186325, 598784528, 484945380, 629482247, 541771823, 477472176, 502709247, 15037076, 970159473, 354232500, 383247444, 791887737, 61956400, 821142925, 590345181, 611776210, 967778158, 371469746, 634874492, 451057703, 644454574, 159555037, 767904024, 963617511, 909584929, 663284319, 135869378, 325963617, 987358982, 388290532, 73869960, 723248364, 627822089, 289608610, 509370640, 936272135, 56694132, 871965444, 276821091, 243322974, 789220935, 909360408, 108244897, 445371373, 718815723, 899545204, 815728255, 9809377, 958811723, 93755571, 145912881, 827641725, 795598819, 250941746, 925511213, 747886555, 238496297, 248316762, 540271983, 238710792, 795126197, 349437860, 131432569, 394443761, 935404135, 503456398, 352776369, 826441788, 289798174, 989755753, 246718087, 86038313, 798916982, 348209066, 365777555, 614859935, 558227743, 471916555, 218861711, 610198927, 625694937, 576401271, 938600345, 574342898, 354193817, 101648197, 295176544, 271542729, 402648052, 397302494, 957410364, 672852396, 919754253, 29120888, 572565292, 598384503, 48604501, 591800481, 607795741, 962974649, 360704292, 697031858, 243604215, 684191387, 216613857, 98452961, 84674912, 640382065, 288114214, 268220841, 571284325, 10290148, 143631661, 189427196, 218793845, 690943134, 938489265, 850784848, 790078410, 690199469, 311056499, 874898481, 181359038, 730038630, 535972977, 976609238, 14957487, 664230835, 14937134, 768219184, 993034373, 370628184, 396361484, 258200585, 693619766, 890908489, 431417705, 944725121, 910126739, 200873881, 17371681, 627929316, 478390309, 635050857, 641890709, 129564667, 348184506, 510116066, 734733445, 477678774, 166022080, 805292828, 551152216, 261729070, 656265687, 718284007, 672583619, 31172101, 86673781, 754070781, 284040575, 347513831, 126416220, 165273497, 433699640, 128212903, 893661256, 783925700, 48746233, 195211976, 615684438, 634882248, 817723056, 129988611, 634503132, 534431399, 903662745, 617623528, 927557310, 18069385, 252310250, 240752760, 625649892, 783764089, 630807662, 901842620, 987588565, 452233437, 598818043, 43529061, 114378635, 570626488, 928804995, 192557727, 580980604, 923426029, 509226486, 499731238, 932121392, 834640561, 120520725, 620611413, 458079845, 365921687, 85128583, 414357682, 415564149, 473133864, 704008642, 50386138, 847953200, 213428192, 114324675, 82411813, 551121920, 489791424, 717478777, 92059208, 478914940, 216393510, 406303741, 94337437, 659410974, 749521019, 494967163, 257039837, 159003908, 818238321, 508756219, 115201414, 172094801, 287967626, 83125314, 354898893, 144190239, 980404896, 961205290, 506144532, 329986476, 347938306, 362167724, 630009261, 397693839, 568395533, 135474949, 461162005, 244713821, 266461737, 772759315, 231290765, 580982588, 212609619, 255972936, 83689263, 804394253, 742997603, 563181112, 237952357, 216003687, 290624072, 216785423, 240281852, 394090433, 873304812, 627836065, 612636015, 575028025, 847904982, 305619329, 298512708, 538171836, 555256840, 359947164, 192409836, 422415079, 677422009, 925434845, 384877329, 902758485, 530389695, 936836708, 680542433, 980314998, 983730526, 961294167, 130063656, 879144990, 647152725, 837899759, 928517489, 987699476, 195720130, 673593960, 915757943, 333503050, 593995595, 346333369, 251871842, 582447389, 416169132, 223759677, 957136823, 944988282, 334297104, 215354334, 383653440, 364121335, 8940651, 479925279, 901681853, 371773763, 833938346, 517087021, 213151022, 780992340, 246819400, 206117637, 182073018, 218911165, 101442633, 338432781, 177409966, 224528315, 562813502, 680216149, 267562050, 939793266, 586512837, 465163490, 803554319, 720542260, 487685889, 138830096, 666425126, 804741628, 589441497, 33725235, 300600493, 291493401, 306492041, 993451810, 391748853, 662695483, 818700109, 418532288, 415154350, 149487965, 436867162, 378634562, 638977883, 468175747, 580882273, 510198020, 990502227, 674379021, 770298609, 734126342, 880993255, 199715104, 655292646, 80353527, 404027456, 52077217, 892135174, 75848033, 271422882, 748733615, 478927046, 504629584, 515723428, 962777972, 879771507, 714760099, 802396561, 756511660, 221069449, 234679878, 188087791, 57195105, 755952971, 832729373, 441707193, 975233735, 167015173, 590537578, 223990992, 956401068, 117727916, 750546816, 814339618, 332691164, 278877878, 735151416, 762937634, 963925923, 241394329, 120871810, 182817857, 25461625, 195409328, 520928939, 504234202, 191885612, 430851210, 844180516, 973356459, 504624966, 865116599, 337592187, 535838311, 336989659, 905961574, 512155015, 47972041, 80467223, 782518869, 303892313, 304038619, 98524105, 948860214, 51693470, 785990769, 725702555, 22949119, 633640214, 170170618, 610657799, 479280993, 162529854, 403400007, 880261800, 140112000, 140769581, 469003657, 151629767, 284279023, 483517703, 554241366, 955019708, 191473946, 304769306, 159002524, 942790057, 537128405, 39313898, 165271957, 764979259, 170922159, 190396436, 301955174, 828478388, 605214433, 618440128, 785547360, 789994183, 724439339, 815700362, 297943016, 779496447, 761957261, 494459298, 362300426, 25011070, 952863427, 636909175, 153066809, 602963069, 794192115, 592804656, 607575717, 80912339, 320118446, 832154624, 977738957, 281838791, 770810560, 160637789, 88622027, 91655331, 131558388, 246279037, 325758018, 647873813, 327980229, 745956504, 454608333, 275510551, 491035996, 578341759, 309144260, 84836637, 268629677, 166851233, 372946402, 12419308, 976496431, 715046849, 586673159, 310547180, 88216885, 257410658, 63586039, 253400022, 307985163, 43176416, 688141789, 588611307, 147105381, 411337967, 194773937, 354459455, 534749237, 394268812, 713792482, 694076963, 564014545, 156562250, 621489217, 199683817, 656928358, 427904333, 729622413, 476571840, 875175104, 447821191, 187597352, 855568586, 938533744, 960077559, 987351300, 751834356, 368990799, 538673986, 26459726, 963707588, 503005786, 826938348, 297216454, 878035280, 322310301, 824331842, 701147636, 260393537, 497763875, 670710319, 328137830, 669610837, 937834082, 952108329, 886002414, 46032256, 317207170, 934096665, 165246418, 206401549, 778951930, 837145491, 770451866, 528012900, 265739794, 292540064, 453977860, 754215841, 31158343, 349216516, 481495923, 180848663, 993415071, 187183720, 995599333, 172011220, 771245882, 916847250, 70478627, 971645781, 219542310, 342086402, 473950571, 5226309, 179617926, 619125803, 387308979, 386054124, 529481778, 394209203, 724163144, 29400080, 227877673, 143571309, 747967869, 852808355, 446372167, 543497908, 265160091, 998621848, 841971698, 851466475, 257035279, 256578719, 647302425, 62503983, 996411803, 926568855, 819007069, 657950186, 983324785, 576441043, 623199867, 537188185, 446891452, 283948012, 186442965, 595460487, 342976417, 227154825, 206207722, 136200738, 187218581, 944569487, 446144924, 38002808, 576729709, 25115909, 240880092, 231962738, 997292212, 824101218, 64589779, 764525884, 325943967, 482033544, 786835514, 468077066, 745285798, 89845414, 489327368, 33413890, 526863614, 540750421, 709258798, 874730369, 848275150, 651079146, 818525875, 221864260, 913287067, 312339048, 508206963, 269730987, 217855008, 543131096, 357416223, 312914935, 827876353, 434367049, 246649131, 747327083, 51931521, 855822902, 100656849, 557554307, 777229278, 101778752, 830457685, 18104466, 595195718, 435105223, 425630333, 608940757, 784307580, 192380825, 16531918, 407821122, 333437378, 581065934, 428333391, 465796673, 560397201, 838466003, 748687449, 243210495, 37796678, 345906143, 845201683, 533199200, 68930685, 385628937, 298209485, 392215354, 788128097, 957372215, 709171262, 779395409, 623490766, 948366413, 684937011, 805587259, 849729774, 16608749, 598465802, 841362937, 814283321, 183039986, 529789023, 558871141, 803359673, 425186335, 298629295, 639947466, 57614983, 566661328, 349724837, 857352648, 761579972, 51309842, 229965283, 442562766, 449318615, 414406357, 377763855, 496122699, 79683390, 597366209, 769156337, 861895411, 319743119, 98416621, 626060155, 12650534, 479077853, 175483352, 630477276, 258867261, 832838845, 446961507, 622629336, 742711464, 601343299, 494028546, 857971679, 553800783, 565418133, 558270702, 179068516, 165270152, 392811392, 660747989, 657638430, 649902464, 166684273, 592784489, 621356018, 284220266, 175603685, 234798010, 944307798, 550133543, 688785449, 983211217, 3400319, 794137631, 380584588, 98618518, 127820915, 375197361, 459044907, 10459186, 242783452, 692743622, 107031393, 577341584, 672151369, 384152192, 487565311, 222775268, 953420475, 277088336, 249703365, 401537684, 512328625, 484295890, 926303689, 374032541, 636392084, 823276380, 404813070, 550848860, 922132397, 385656555, 692764390, 318412899, 529451229, 174211112, 11793432, 893999550, 232044510, 620097962, 366866360, 992017684, 546719028, 545999242, 66338379, 356504101, 236120395, 302945458, 924073589, 891570266, 94556048, 612724268, 947373679, 902581814, 617325942, 229092067, 94123395, 153233395, 417573418, 881418503, 670883041, 197558948, 386919768, 815747839, 879694835, 665731319, 382656064, 689226478, 93615480, 321114165, 330254782, 559210212, 692269773, 10826923, 792370210, 517909570, 694422547, 847824243, 722248802, 477720044, 129327830, 669230352, 452977061, 773954657, 381111807, 239803715, 23369709, 409125506, 199324327, 922875078, 87662977, 467052613, 107682950, 783322772, 919738839, 249719858, 981921318, 965529115, 266099709, 7966177, 946162642, 346174810, 215590407, 275139131, 277226162, 325993220, 278689395, 81461489, 846718424, 889133130, 151570321, 869530719, 389822789, 455524763, 270274010, 650289255, 519554541, 361145631, 182639902, 167016260, 432007969, 61186492, 89371261, 517056150, 286731171, 754522057, 252077569, 591208022, 647731507, 516074255, 128803673, 862773453, 254322828, 390364794, 599270231, 990997577, 653394014, 572099633, 197044235, 955684283, 720084376, 555607736, 38018300, 903948056, 959501105, 637369840, 737107330, 227664256, 125969019, 623987746, 706463806, 546432385, 150085747, 548695310, 876511279, 711347932, 948360786, 202798205, 930090943, 534536595, 583999182, 316639362, 597449902, 59704669, 870811958, 859143383, 400965438, 510119998, 226383868, 490587205, 266984757, 87762420, 926418658, 332446558, 840223342, 553715693, 392037171, 274169506, 663002709, 40710596, 35685209, 896187320, 711579885, 844522980, 947257175, 595694624, 994826246, 802507403, 983126902, 952249574, 81166143, 343644327, 535687009, 421988160, 851316754, 307588133, 800332875, 120396882, 996978618, 969205346, 552993814, 951450118, 445974328, 398402369, 528920036, 810849820, 299954419, 476621993, 181252309, 616780198, 88447564, 776880191, 400217795, 666094871, 94718293, 107630860, 844135555, 414465723, 745126650, 75641238, 243170712, 949391735, 502681535, 23668648, 442498517, 172378349, 602303658, 807573757, 66248686, 302732102, 624419868, 526783119, 214759879, 56938848, 773989963, 6116688, 529841719, 791766255, 355991306, 452011847, 274887655, 919057665, 864871858, 917343711, 578369119, 361234802, 95351090, 860040594, 330241482, 132637235, 155390119, 70423475, 644954261, 604751333, 735667371, 422975210, 529911598, 545990160, 215568029, 784022917, 392679125, 150836434, 465546536, 276444712, 710618327, 458954173, 832088356, 746271789, 54477633, 521737764, 240717864, 495840303, 951620346, 760039808, 659102293, 688323712, 854617182, 492826493, 607041633, 300831073, 450471733, 801705878, 333577406, 478315774, 83066062, 495433048, 272973630, 505717658, 97135636, 822021397, 716926942, 570903994, 827377353, 76844756, 747320126, 258374912, 890704745, 103282482, 144709901, 250436031, 607267693, 232252368, 815372524, 463139871, 246680768, 475146291, 826993682, 14821143, 582618000, 534341663, 631404550, 541434981, 665611801, 439472516, 897865317, 484282471, 561614622, 180373148, 860996285, 530278936, 115871409, 817624707, 791959598, 665648441, 773590979, 353891532, 43897111, 549244181, 525385983, 356649028, 855581819, 730085270, 781276214, 553287764, 480390338, 315727600, 589134012, 349934365, 37358253, 133571856, 809362542, 512602058, 984259663, 964892106, 830181682, 193362496, 289208475, 858078775, 335502210, 668040627, 123040187, 723809350, 392230477, 349842690, 176407357, 519890462, 803398589, 844127922, 279530764, 777503580, 825807028, 874698322, 654595778, 299084787, 448570056, 998702756, 878871152, 144487626, 280164554, 541342381, 683395342, 704525843, 635099071, 871444074, 854755313, 545241191, 416677760, 908439008, 6280612, 113360698, 825184506, 498428555, 659322838, 206692702, 819773326, 78509813, 575568871, 494708703, 692886408, 198462687, 994113725, 185696109, 819841991, 924678596, 441790433, 160318877, 126342606, 132039028, 890339217, 35197293, 483412951, 290801064, 910545488, 236863515, 46764274, 464051392, 705349721, 56030673, 373758335, 542470180, 379511807, 807549296, 566007825, 62442422, 816879187, 335245083, 627558082, 670926079, 913404550, 981645396, 607214853, 111429998, 360143626, 820880153, 700969905, 390915578, 81704698, 606305205, 818997036, 839579420, 205823519, 155585230, 145122266, 964846227, 268585342, 450880808, 290929733, 701570811, 422554362, 176081897, 921511615, 101089094, 288879064, 468402799, 234186782, 332112040, 832983691, 926725338, 327837559, 991436149, 518001660, 474487819, 656995807, 899615488, 180818148, 499714157, 959395358, 274988400, 388367489, 439505828, 696162650, 510738466, 986082850, 229346437, 255240424, 293639399, 194808292, 13506092, 609265792, 464637850, 75227982, 840962626, 267354439, 336203474, 439461853, 840341864, 721752873, 776852512, 592626781, 135552747, 495942883, 255544023, 844365536, 800862206, 971108705, 717545873, 513717583, 793406444, 439190925, 321561537, 700764137, 250605404, 335229767, 583566674, 489981661, 757774134, 655977442, 243651798, 967095277, 10153428, 836309965, 309872372, 342038642, 349645730, 792751025, 990921299, 760149052, 567740315, 271399569, 175397879, 33450913, 651436244, 481824213, 403282862, 194689102, 143928749, 640446543, 650847561, 165382333, 21330574, 559749504, 282940989, 635452680, 198970804, 787741454, 224206403, 116876475, 888283066, 155625883, 860938482, 99088315, 484939080, 364475419, 153539142, 226078558, 750222544, 213606507, 688894008, 276468095, 278536363, 309485454, 494814303, 565847172, 185128670, 474807123, 433802845, 898356688, 43128309, 943678481, 969260612, 22405733, 710265235, 117100653, 838713994, 728511539, 888476942, 495013699, 520660543, 580415397, 712448051, 742683544, 462624548, 480195166, 360713853, 296023939, 136173400, 767333058, 887881473, 565244375, 692747906, 432832017, 25138485, 638412308, 130522256, 576208056, 84298855, 410520161, 416427322, 389088761, 624078853, 902418781, 760646470, 258257149, 899910699, 776203807, 19849935, 646493819, 560776196, 546763519, 823332256, 734592445, 614286546, 616045382, 989454045, 17075584, 7877742, 502817732, 224907449, 855294437, 101417127, 807471111, 560027782, 533618440, 678982159, 848796093, 689859567, 190011906, 5785746, 42930470, 192270620, 880400034, 838024067, 121561205, 290767336, 111960881, 853019340, 341175094, 766270350, 188758306, 727467556, 136319432, 576969623, 280426212, 623323983, 774448576, 588954976, 315027230, 803856696, 29941095, 431948971, 142281161, 925124433, 861392125, 80891864, 972043980, 629020667, 561805004, 312315151, 476215536, 771343174, 987329546, 357825065, 336891650, 411555915, 343813589, 195820445, 882645414, 410720520, 753478695, 663992720, 774220252, 749137259, 930691248, 434923257, 161093539, 770837781, 354312961, 193395774, 367123461, 565354245, 679270793, 397628751, 217121216, 11760875, 403564348, 71150102, 368592024, 897815353, 994505662, 408127559, 13668410, 69820824, 69774071, 861606001, 604655326, 121848283, 363261206, 533544368, 538663570, 172311982, 220197600, 172089912, 165169436, 429935475, 65008037, 699439776, 273839877, 490141238, 490067959, 444898877, 393713858, 176355122, 59295682, 892326741, 281583835, 687723650, 870182540, 346071449, 332969843, 335722873, 337845984, 45176399, 24415806, 2308862, 1110263, 952816287, 413596322, 457602184, 608181126, 138846196, 683156584, 648555388, 136354769, 70181525, 911269767, 348803783, 586386836, 95395008, 639691462, 197246507, 784316873, 351344494, 516118995, 133439447, 209032763, 754815525, 844000344, 579497382, 543598008, 669010574, 810144603, 990464876, 974778641, 697366177, 327010262, 370312488, 560846170, 792223978, 70777692, 730059355, 645250397, 267577093, 38654537, 752518626, 382980134, 931773562, 481034793, 391116196, 978295062, 460741013, 36044394, 427642224, 654541956, 229620044, 480648144, 220672935, 74255693, 164517499, 848528607, 698706905, 270106207, 72249359, 728454879, 401029097, 749737699, 540722419, 515623264, 186253746, 447327384, 667749960, 257643019, 53384358, 244082175, 319549014, 824197936, 312631521, 223966894, 407534855, 232784358, 271917418, 921835724, 796371425, 768552953, 771116236, 720631769, 176115214, 463104294, 32601129, 873101983, 726488097, 905506187, 772022708, 790766539, 277549142, 258224017, 534233396, 457451484, 984765991, 666356229, 285112732, 105240204, 928779057, 733734550, 426028638, 85012999, 607498383, 350044059, 192726117, 785458212, 5138745, 638384576, 530395046, 160725892, 734577696, 298137775, 647176944, 636168408, 916717020, 145883949, 21835951, 609989524, 624600036, 130858009, 196338930, 205677297, 242576008, 182054034, 173135017, 310635461, 239132350, 820851500, 952663487, 842340211, 870203762, 136114077, 875790965, 997698949, 398343918, 120520969, 730588957, 512775855, 8402306, 149806096, 944510804, 590083469, 73224200, 638298925, 377854673, 108235234, 523684573, 737188402, 2401175, 346457936, 172703383, 68480745, 645510646, 29654483, 134565318, 758053746, 173563088, 30554840, 677360534, 923509332, 473173031, 395834641, 895652708, 605630278, 508175810, 764267340, 286758227, 744444264, 379175927, 449921848, 733348406, 580120246, 517256243, 809596999, 389739963, 149587825, 518270340, 781470036, 338561638, 390916754, 176754554, 761794037, 291256125, 837185091, 732116166, 43956658, 150478758, 774125829, 643082844, 433448966, 145624080, 658759579, 975189687, 182969393, 969020183, 514460413, 407090123, 806351506, 546163661, 456190832, 767790206, 497309281, 279638005, 353159068, 188343504, 276622066, 11211935, 845988772, 129716351, 179604516, 901713398, 807188467, 221256876, 372100198, 210494116, 3705926, 424688858, 241869215, 463164360, 789967778, 906824777, 30644170, 922593312, 870508102, 295177668, 871995365, 945281750, 819341940, 739946801, 12044988, 154891550, 478628932, 972747958, 904619787, 377180378, 731784350, 399165286, 818350623, 864683908, 829864725, 859057886, 870464298, 550186631, 806230328, 156856889, 902361490, 150111030, 427978050, 635787880, 202050879, 942161080, 109182608, 896550699, 225527937, 1389135, 745689842, 86486564, 864162564, 5496036, 777358075, 770648663, 79851200, 949768534, 180911475, 432703028, 450220864, 512693889, 78978195, 536102254, 846388768, 709182546, 684179252, 588229545, 465688588, 62689190, 231436507, 444025359, 446536019, 498654777, 254235486, 757735073, 3308698, 204293927, 166774429, 206945668, 669447860, 587798803, 968552651, 702979778, 509986268, 421595208, 658693753, 311193363, 667210544, 522571593, 622115838, 276192827, 342369481, 249829775, 310669449, 143289847, 192370577, 276004383, 46471923, 517907769, 38643304, 859472548, 63585522, 426083874, 59218909, 808048523, 857310500, 634284520, 914991031, 768015314, 338364133, 56784469, 549295962, 905736217, 850548589, 436109554, 602310229, 280527687, 581026012, 250260519, 94920251, 687195072, 715605344, 812827227, 121047329, 820041695, 944980421, 761843831, 669681665, 893838821, 636433333, 658601084, 775978999, 693736, 828142745, 793907544, 443095282, 667829409, 966972183, 107051237, 835205102, 174982423, 976935799, 166285456, 616988179, 384074994, 798097663, 115797299, 109600134, 678026262, 164419564, 900720457, 890698898, 246533756, 744699434, 976145004, 859338715, 380534428, 239842175, 327532138, 560228431, 835422064, 86109188, 436136807, 562260015, 714422856, 652486483, 491382413, 248558592, 47127165, 420724437, 835853533, 700496733, 198441067, 847132235, 808758721, 969536979, 842604953, 19246681, 756169129, 87299869, 113484450, 213818009, 653256432, 460648611, 486615476, 786937206, 825708047, 144959874, 483005513, 315277484, 458118120, 987810880, 440448650, 450597398, 56606046, 622491683, 9315294, 402591289, 57507108, 540247114, 973140542, 901497821, 117059023, 923403284, 254770802, 337402255, 630798921, 44869992, 503635697, 653696614, 97691172, 692823490, 671486158, 215593409, 128049096, 51064024, 151859051, 989625046, 534568785, 511865523, 804590410, 152789747, 578002812, 400643391, 746641972, 373386205, 447966762, 216855307, 747531637, 629084795, 928318330, 386974745, 680022877, 721786378, 920395528, 597250466, 586201335, 188508906, 893020783, 208741505, 789442410, 138210386, 182816013, 839489682, 818535254, 27724923, 271657370, 52380605, 756435266, 259760562, 173264985, 578466608, 211415241, 277351160, 994433619, 605014110, 109737936, 951816885, 151872984, 437301871, 657772697, 701015346, 246627780, 639946642, 941448178, 562440403, 512597988, 641431519, 736319869, 95465603, 652165150, 324041869, 624372657, 959333724, 518346217, 757774499, 133957495, 25561867, 624193394, 595748537, 485385180, 133084757, 520071223, 4078826, 386659126, 496469866, 410370106, 515826958, 15107574, 928205991, 210199455, 872281929, 175547467, 599313571, 198410993, 524338695, 47629775, 323066904, 154106020, 89360205, 573686797, 115368814, 744836769, 407702832, 263786877, 503687133, 423034065, 814447664, 407373376, 89879452, 496409771, 635738873, 971649889, 278605005, 394342115, 247223851, 480025538, 332259578, 870606627, 853005124, 564178469, 76818035, 522787291, 363424451, 812925302, 941133394, 334980263, 288203814, 635000445, 718067192, 804859112, 506098587, 337624030, 855847919, 743511920, 766591741, 645185534, 666495062, 221502231, 956728792, 725035143, 734771055, 794004193, 54537202, 685441472, 312704634, 885657144, 394300099, 62867819, 185463588, 758479248, 811173547, 443026100, 934869180, 836211246, 329303403, 543539182, 804216019, 764975672, 867375998, 447868317, 510966542, 183996175, 770858499, 972270739, 38602002, 80079651, 631160166, 872300994, 281068346, 240997335, 558428456, 635393236, 314092356, 542158996, 361794680, 842118593, 969462755, 248845624, 97040434, 191026469, 506195424, 681539665, 471462363, 407031392, 394239462, 216587559, 499172272, 332717233, 528497883, 28397583, 127451318, 537488132, 233106459, 558910329, 568846298, 980238965, 663990665, 991044814, 469848397, 126594089, 752774484, 246840169, 363050684, 343002256, 489655997, 831774883, 4605452, 461419582, 657440698, 778869258, 862580707, 704169785, 237590485, 280719657, 917848606, 399201251, 768310924, 249798911, 360027216, 58620968, 283331155, 113392644, 33209187, 388100300, 956342490, 176128181, 646260884, 819012799, 425679597, 555714305, 159394301, 126727581, 615741944, 320363259, 285920844, 389710134, 716652518, 991139425, 94780009, 795769534, 329150150, 441979373, 310264309, 153137156, 440310659, 553597873, 246448927, 475695860, 862712468, 472822574, 942394929, 406325217, 233899864, 600655502, 546895948, 91896043, 298293314, 279708236, 599795103, 657181092, 868248663, 344244185, 635095366, 900328988, 957509567, 689693786, 89137671, 688078491, 477664330, 93445246, 352223023, 285209396, 266489448, 663740026, 290760952, 75807891, 342104663, 300477385, 611318327, 879011528, 348294053, 106086231, 196436721, 42553867, 674326498, 918025986, 382097348, 914538075, 820088277, 315177560, 650795975, 596956149, 785016165, 22574245, 609766522, 249342345, 964856558, 255079135, 785320619, 145692231, 858090755, 212951446, 968821233, 975005936, 618307056, 554840295, 740845099, 605303152, 494750071, 706309797, 652583336, 292329740, 816031908, 155579626, 268639277, 609245446, 219889746, 465165351, 631815232, 131531526, 13062478, 701402590, 353034034, 708865671, 982572526, 342768651, 217796881, 139746151, 711073949, 472232627, 34719165, 657057018, 300804329, 52433178, 432447337, 513173551, 128419472, 201276156, 164603585, 626836740, 253252588, 71654233, 297537668, 512351823, 253067471, 93486612, 220517698, 533772073, 582928145, 838113231, 733856907, 132050272, 462980761, 89920112, 660850401, 654018630, 731325839, 50814153, 218810352, 869687628, 880218715, 568822158, 288206695, 623106814, 198425640, 259896039, 444148507, 220412651, 268566089, 381656228, 23542994, 80244718, 257392574, 175154459, 652689485, 352631251, 370828596, 329552457, 133958828, 365912312, 727582147, 666037923, 776103972, 929325084, 198793300, 943852189, 302232495, 183812047, 936180550, 969000266, 766663961, 960600688, 918582507, 999670056, 474277182, 461748444, 65009359, 677365030, 614150512, 222438345, 288914363, 592560582, 423273195, 159464902, 137919624, 320902459, 631475294, 16946477, 107593784, 214540730, 244393720, 349479952, 987091129, 305316328, 977991030, 498549103, 693936549, 331120182, 258373419, 742637117, 698882706, 147205499, 85413634, 943554505, 767016789, 428963028, 919921355, 926169821, 289139767, 976246311, 638471844, 726514588, 185575664, 976506294, 930935783, 7899030, 858614604, 326844489, 474869443, 909620800, 116140043, 979361369, 177465659, 661377982, 598710411, 127139069, 191418322, 380466962, 653272896, 287567, 354652750, 912145420, 705625688, 374660379, 231343714, 97771001, 891876637, 53540505, 791667094, 995482807, 727637761, 547983572, 687092037, 69708130, 294217809, 527532069, 721068029, 551453732, 681760971, 334068170, 789247970, 426438702, 724012901, 249139531, 535951019, 332756504, 966797289, 860662712, 278702911, 326782086, 895619691, 920798038, 766140628, 576588310, 147296278, 668850596, 439382457, 429270355, 351998820, 524971900, 783004434, 387712173, 54031826, 870318582, 856012804, 817396913, 810177487, 207892957, 905753750, 27885911, 325103519, 452119173, 625567570, 212572397, 942205709, 336507021, 558807126, 968498395, 985132655, 245327149, 49752084, 211900974, 604855819, 925583760, 986598087, 70632960, 761113431, 530594780, 305809806, 393660218, 200868866, 433560330, 997359107, 398706127, 825555234, 946863011, 506217884, 334725323, 51045542, 920916934, 594106530, 487871743, 891651139, 110176725, 703652962, 117816983, 106505360, 192616634, 55941559, 617941944, 805930388, 860552337, 379574871, 629395935, 469476311, 808933250, 582355342, 430107227, 435443400, 342970580, 848085481, 385172863, 83448568, 652475389, 526083523, 527130743, 97221104, 36167930, 288003986, 830630121, 908895299, 359910037, 721699672, 958988655, 507214951, 340135063, 333733639, 13674951, 138530490, 504238845, 853597669, 161475782, 580665957, 178508105, 166111720, 555115016, 991760302, 197485259, 958992996, 15071677, 864308161, 806582627, 885848752, 789825399, 281935088, 892310960, 850547536, 98481415, 864729687, 273563786, 501402503, 344154933, 371795490, 463630762, 320674404, 11605312, 687678118, 934722196, 269842525, 364241091, 315653646, 171093501, 116825016, 183062633, 489071224, 111624964, 145418424, 76991024, 87698922, 681416157, 139233010, 667310734, 119779365, 932494558, 66147144, 122135069, 467002453, 722638346, 60268554, 589256691, 648832531, 734269159, 882220814, 571233622, 336704681, 190599105, 436244589, 875907342, 789462854, 393904393, 407069785, 31089499, 448813227, 629879357, 67443796, 145861820, 197807204, 657770049, 411923142, 705851411, 235274928, 967830490, 461363596, 443579187, 566376270, 304414, 862248824, 349509086, 278475478, 635642462, 237584288, 897702621, 893664663, 318171311, 262992297, 142347879, 841650248, 136917324, 358280765, 193390502, 140045350, 651227451, 215213895, 897345550, 635899844, 797985757, 192931770, 154401131, 725433345, 769010047, 714105431, 652404413, 412773010, 456397176, 659475790, 299563795, 614472636, 600074790, 235998625, 931589204, 890163044, 139305752, 854292755, 783643341, 96761775, 656652556, 20269319, 597959250, 781095220, 488335754, 25384289, 204738305, 330416051, 937952425, 378552079, 291837768, 684930158, 14292337, 774441313, 611889643, 741677935, 300904028, 205082077, 498876817, 46089641, 909831286, 323949211, 824866843, 391993628, 575000635, 128568245, 526646865, 406300608, 345148979, 175895067, 627665111, 652871345, 692092032, 677330810, 519371210, 543410910, 366080754, 737187250, 397416980, 768852204, 987061801, 676183914, 379982656, 684601580, 811927041, 802592418, 226626562, 972281546, 808144621, 158223357, 358913911, 388441209, 265855738, 534857947, 71389615, 103563839, 895063949, 746667408, 56927546, 550920539, 785598733, 525132464, 892093376, 908206382, 585287656, 157284192, 24407730, 919188293, 577685415, 67780334, 320443842, 309094982, 754227585, 610293052, 738040831, 735632300, 74161859, 637987813, 574366903, 73270901, 500225322, 37986315, 280581782, 788866758, 721731761, 928927961, 159385996, 406039767, 10269003, 388473429, 321262537, 322101785, 4454131, 22478206, 184223057, 168137925, 147693657, 809017438, 801431587, 701682566, 258792508, 656559852, 985334602, 990809436, 311274748, 308399634, 221681015, 550316610, 184623302, 300892135, 9156375, 426367270, 800641282, 351118770, 222110769, 284776345, 49516993, 837633972, 64611873, 588156718, 668443287, 858197351, 777464681, 426267762, 561354310, 688175593, 565505951, 279429625, 106183627, 276852201, 311951390, 624204001, 112472391, 503958006, 390597914, 377471304, 593586712, 757513889, 779390823, 891189507, 798915371, 508053736, 754573014, 808056502, 229942823, 463296574, 587119901, 197470912, 828879754, 727876786, 350586107, 653181222, 772746795, 320171518, 500923081, 245425157, 447068054, 46252616, 297556685, 284867168, 632569906, 551055123, 617070632, 851735271, 584875245, 941473359, 92457493, 419046933, 716985430, 486071397, 169289939, 316572219, 776539700, 207386897, 588027400, 904565878, 755780876, 796074629, 359992320, 192597500, 976686470, 517789524, 949350410, 357708322, 667423706, 402310034, 152801561, 250749506, 524999951, 122639864, 568007236, 964185058, 206706624, 642410358, 272227710, 577265040, 466729325, 830979122, 823567773, 642286475, 282027237, 236467373, 856165086, 835380102, 496387654, 214254360, 347384772, 893096173, 891014026, 604944140, 196083220, 105676788, 638228703, 540527190, 286965229, 883210063, 357988770, 713614905, 2415257, 882829514, 565608495, 394942872, 165977547, 135077290, 116979442, 458679475, 238495905, 150470735, 253963263, 218221515, 792276584, 29151071, 58585203, 929358967, 37910278, 380784330, 930003338, 451465363, 620841717, 669185416, 139853995, 456998220, 892342453, 847146100, 489536906, 643326749, 377595067, 718977239, 497382465, 896532284, 521571148, 16602370, 398812482, 746514321, 414042438, 341521608, 288987276, 705099078, 679975330, 525056116, 481073871, 241397964, 51056266, 863844404, 672199294, 542337208, 349722977, 670149923, 155617117, 93932276, 978200644, 909605408, 949524, 236845855, 881442384, 373821431, 238050740, 836801837, 855088726, 285742946, 231590600, 441957455, 402402291, 969433560, 854266729, 870087258, 164095154, 295513901, 416008440, 165195909, 854077648, 667431042, 914884595, 465830385, 306148058, 231186323, 617587540, 581490937, 422637192, 248249036, 438171634, 72733819, 916923059, 107700046, 176542828, 585195119, 330353529, 770127666, 407383679, 570939418, 244728604, 338014930, 916190883, 127657387, 71614756, 473988455, 218481192, 409776282, 526748624, 497383607, 323352893, 530918187, 620389662, 9537962, 423750522, 652080908, 491551459, 517358132, 458631573, 89806489, 24385933, 629493568, 789712206, 151670169, 541501250, 789025020, 671085286, 897889047, 684930145, 673314981, 602797516, 73449458, 193457294, 185897371, 789589234, 185622204, 236137593, 477722702, 855345928, 442489430, 992123228, 903212654, 777536059, 262506086, 88297112, 656852473, 259300817, 830380056, 651814246, 914288113, 157910472, 438177584, 423134229, 513684977, 996136822, 600695361, 984628366, 41943515, 944917173, 528175458, 620789411, 814963688, 517241114, 782189967, 159252370, 937461142, 446451027, 708943124, 283370569, 209880085, 975707674, 744799044, 774843026, 313493944, 658322991, 371347758, 559831878, 157873389, 76212297, 915488512, 209401681, 908025223, 674940310, 52017183, 436045571, 46505590, 985097990, 680580557, 53937397, 618160033, 135988050, 56049002, 208387808, 891759332, 810418977, 863839983, 523622609, 500481015, 576135350, 10686203, 397417576, 481061629, 307662951, 312257494, 412485832, 621056891, 166611899, 262210239, 612077120, 133164938, 777569592, 630958344, 362873899, 164976356, 975194448, 749756135, 331809667, 278159528, 261395577, 174450093, 634805739, 64617891, 415756338, 4033163, 296645456, 424023797, 606543189, 478874339, 932178832, 136167200, 117189166, 175040482, 275138410, 31240964, 210160888, 974210525, 50629182, 474006426, 836700293, 460268598, 740719631, 455562818, 241118244, 136760592, 302731236, 738895019, 879914491, 349647808, 636994844, 599936812, 603839800, 346492377, 255058321, 73426869, 692243806, 682641966, 610619140, 446996751, 226953813, 580434985, 578050365, 642595361, 295967921, 693526601, 725416747, 116820808, 967477909, 280134595, 676612089, 517671519, 886594447, 973282362, 42339583, 936627064, 351932549, 668065889, 457516096, 889707932, 379745708, 115949646, 606345711, 388388876, 929880595, 362797861, 292238510, 607623289, 999594967, 874919334, 144860211, 386599856, 1699482, 840456647, 631518436, 687906856, 315952961, 760886266, 924265028, 441000508, 785521306, 305348237, 804669723, 772022373, 346186082, 203723401, 62185566, 804519812, 205328884, 923972370, 677246876, 803806231, 684612587, 761287270, 61132722, 359167983, 462627054, 815230130, 220374470, 117201013, 610636630, 394208197, 162900354, 506015199, 509423294, 217609335, 598086442, 851937448, 934757772, 796171910, 928811611, 846218472, 141915387, 589103505, 649492027, 602417276, 560014173, 965219668, 302163396, 487808272, 907482829, 787556591, 556776248, 978234014, 670008374, 529147861, 839702292, 754792377, 941318093, 131369778, 412845893, 908694034, 51970414, 602383219, 676162990, 644000689, 273258960, 323426017, 474965518, 381190287, 281186382, 240045859, 960377245, 68926098, 463286963, 107785425, 480511115, 281811699, 630214041, 865975392, 274127532, 96302395, 345491867, 600984131, 490247554, 363535522, 955301509, 649414343, 993595317, 328949371, 126683430, 27733669, 849697016, 668655944, 687434558, 721856075, 970429213, 274602014, 37941595, 92715425, 939775532, 235816672, 538449238, 487884414, 897708869, 220744621, 465977582, 390223989, 303867819, 557870569, 460155638, 906426832, 233231481, 631578455, 172033823, 397181613, 708489667, 624154057, 592717130, 743753275, 927559361, 46559424, 781029749, 621293546, 314523301, 364021933, 393832400, 232535495, 653981191, 743515017, 408512419, 812789950, 542131408, 669602774, 820508123, 411303526, 967821621, 573436353, 172407870, 556795710, 213671521, 669382439, 194987885, 495976913, 184501617, 763969279, 457516106, 851141699, 204667598, 640960415, 811094628, 374352816, 362928109, 809559039, 262674637, 321875492, 260531771, 914962737, 285690992, 459879912, 621934918, 385119381, 549830117, 95859292, 698460511, 202780296, 855989941, 902381118, 687007344, 682821441, 753952454, 433030274, 317830055, 715908362, 48732071, 796526682, 873943675, 706181622, 547361635, 820389503, 972727888, 564844188, 695398538, 273826648, 498457570, 310324366, 446701056, 982922131, 221899762, 568182924, 534335303, 400733422, 156843792, 670223029, 331574138, 481115886, 247452622, 55453661, 941563227, 727627211, 987212824, 705277452, 485962762, 738491202, 689938383, 82773730, 939375215, 830788976, 327499772, 104342946, 298409296, 416064314, 634395576, 878104321, 461452271, 469061094, 818111640, 498049425, 628020232, 799957654, 152493078, 925287039, 943681057, 194908240, 280982264, 853350962, 697193578, 437097163, 242188743, 456468022, 269987675, 423564240, 513854789, 727689198, 874387254, 24539819, 993601316, 932352756, 895100345, 876464800, 484200097, 622354267, 592742184, 462697102, 810512243, 541459545, 506154150, 791120556, 540491394, 565214336, 626701378, 375118197, 512031448, 438955807, 846326154, 938794283, 698135355, 931342836, 377032737, 339112292, 121252305, 44108835, 893722320, 13396583, 299528066, 579300010, 82255694, 612397499, 744706789, 956369312, 526920010, 208170799, 268890016, 978221661, 377157514, 191016943, 856523648, 855790498, 220342995, 456564892, 772439147, 813592500, 646476092, 15491034, 288743148, 673548325, 128225695, 124937329, 224736652, 855253658, 406295837, 503001797, 64341232, 199844385, 24735455, 473482603, 793357233, 547437412, 386133014, 67065209, 921557597, 25488678, 591053067, 20836806, 66860595, 778732217, 283014430, 163834046, 723423164, 973334764, 57513605, 477923463, 139531424, 330796118, 787039958, 20228544, 6985631, 438279912, 507608779, 308053256, 305763699, 967600782, 755669267, 822324539, 471476584, 831831905, 974648749, 991523837, 521092141, 30882130, 830014723, 281782048, 938982501, 408279789, 200422319, 341675477, 923195793, 788763010, 959748271, 943630278, 793818463, 31311048, 585869070, 329545744, 58284824, 380148932, 266892488, 421766414, 634991287, 776966072, 651605209, 248208428, 229612741, 671786951, 125084578, 532290406, 605551977, 129804760, 502058978, 922644095, 470407, 496351205, 628049112, 992581783, 537671028, 201747235, 691218163, 578430352, 911628151, 559274919, 847941020, 206145775, 41656465, 649503890, 843629834, 969978694, 433326934, 582062925, 463806228, 96451201, 865439889, 429395407, 899592530, 670809477, 114416573, 337308289, 349168879, 469402379, 898913332, 562836958, 946610587, 683378794, 553574917, 414203968, 805133006, 224569257, 136712074, 400636967, 576270155, 5344381, 104198047, 891983151, 51007234, 669603234, 907457848, 794477741, 224303538, 605753086, 585731704, 191577548, 186251870, 144574837, 246814917, 732912938, 497061552, 757918293, 658058121, 776047801, 473882865, 905965614, 18796417, 348212555, 42686486, 371970187, 141908636, 589459939, 781437982, 266678843, 842067654, 697074511, 935860800, 514849716, 846810992, 914473210, 451887945, 998238630, 109924734, 691095849, 472407506, 836115877, 615758817, 638388913, 909099757, 672593003, 904315729, 576553929, 96808214, 630695532, 237838587, 918670395, 820555471, 315336915, 549736799, 294626038, 917900469, 367382499, 496537949, 141825855, 765280396, 825802453, 986094170, 435781376, 706614652, 585075021, 188977555, 890805043, 940722746, 368449044, 181646535, 151581907, 968207178, 34015246, 170404396, 32446332, 69243485, 704925550, 828384700, 274617426, 916512673, 978986278, 415793016, 861562806, 135487096, 480153477, 993113813, 433472514, 945280237, 926859660, 632905962, 900459005, 977093823, 851853757, 826623315, 22001001, 796399941, 331667535, 450227314, 631347968, 641792584, 905994513, 643846830, 876934116, 363031276, 947113432, 710060026, 935607465, 522126001, 712255058, 940212107, 366562826, 182996922, 170275342, 154878327, 765436522, 366731965, 253854004, 301980160, 796343563, 715845727, 941103185, 800891133, 783171966, 522019036, 747063004, 601250875, 911193769, 562202160, 468467012, 564232967, 68124835, 422127491, 485225648, 855283433, 276572321, 501415457, 992395225, 328698124, 926227273, 106341374, 351704308, 722228780, 278384473, 914460965, 19023395, 115018861, 82368655, 841267305, 14037648, 62992766, 921676638, 393059044, 606987157, 609817997, 1583504, 856393709, 136308473, 635969522, 464713096, 180518477, 166603379, 939290322, 692144922, 183916469, 901759790, 904065859, 229288030, 41005128, 185832591, 735739475, 960659505, 330954967, 892557588, 314373365, 811921889, 839984868, 88985159, 667246963, 682830338, 923618163, 206990570, 105610067, 304273574, 906828488, 915804743, 197609782, 384082648, 547050412, 762668844, 150217486, 997085028, 983455126, 847056495, 910163732, 485644031, 750692193, 296161443, 965300228, 445528678, 507085306, 523007323, 269038543, 28239427, 412090614, 847845288, 390672668, 58163751, 260862379, 13028972, 441745897, 212183930, 101720293, 82513313, 256526524, 908180411, 244299519, 862195814, 317086139, 11015140, 660704122, 682186282, 313943155, 348042738, 793818179, 889111686, 202411186, 388877845, 864689946, 667703714, 363270490, 223666338, 373144406, 13763356, 713612531, 971516247, 957950300, 498765648, 659684233, 697638235, 136575037, 976322873, 33649936, 301710157, 642899776, 485470483, 585121657, 831067190, 910604999, 343531530, 240869511, 586366689, 519242158, 41712328, 265004350, 998805458, 419691613, 432417500, 663695849, 536751273, 955722068, 17978667, 561481452, 51281261, 626595938, 551621618, 696756282, 101513253, 532699155, 360533315, 467385310, 935824910, 282370173, 170923127, 893750926, 16270915, 62734620, 325702641, 963767826, 566963047, 431493823, 795823543, 108688544, 645056965, 676994545, 200328285, 769503249, 189488537, 55617085, 506292678, 773722534, 641560389, 432609475, 769778940, 253556555, 588146310, 684136538, 78124794, 183425707, 183511777, 906199417, 189279392, 427402138, 632149794, 173565810, 953626710, 189754459, 324233253, 158113224, 945676087, 859108298, 8946951, 100880408, 612412139, 476432352, 881745196, 951365388, 123472835, 565638008, 947572037, 968585181, 882780878, 90040014, 778579773, 164137269, 673926607, 703711966, 942631818, 501578155, 274585477, 560219349, 363437247, 3789861, 509813286, 90968478, 502448417, 71700231, 121024400, 397727666, 30262975, 245025931, 21524531, 859439691, 432745084, 523385617, 423639439, 999880629, 956764113, 338718367, 453073080, 679589368, 734280427, 755980123, 654863818, 236365483, 773589820, 872894174, 784344977, 703154416, 248713614, 848313626, 782899390, 970734164, 494027309, 866695645, 273909687, 436042573, 706770029, 530226271, 982672952, 321796119, 187554338, 183097622, 897648124, 419484472, 110675630, 269950440, 261057644, 413520402, 274518237, 616438252, 941943897, 570798084, 408410814, 484656372, 242122967, 348091784, 286183382, 521462947, 173735224, 595106191, 950003997, 129342147, 299068448, 364422219, 514193088, 15701787, 819871850, 361034880, 323440427, 661129888, 51457852, 6087163, 532710995, 671111438, 305997058, 385409939, 64711600, 763399581, 566324045, 777456631, 586548880, 89591274, 714631738, 311431678, 353478258, 72049903, 662330948, 999933483, 136498104, 678763605, 445570509, 917459013, 292508552, 219161926, 481408827, 716415224, 935269007, 100417798, 767799942, 473015403, 854549668, 206508837, 368244973, 362905078, 837216484, 694008919, 407415965, 716431104, 65947961, 57025631, 733339194, 914430847, 334515284, 231720669, 352880787, 668798278, 183680492, 855511051, 532177371, 281084894, 431119066, 615405291, 878312881, 233479684, 244469059, 823956809, 897858567, 957255251, 536638444, 275565917, 241936775, 410396607, 388194722, 672131613, 558760843, 883957452, 404180216, 710267018, 545536032, 25174411, 849873347, 593780860, 240713189, 160024224, 302867295, 463400948, 558088844, 321555345, 47916230, 825119524, 436955918, 943774082, 92823595, 345943124, 842593213, 884662371, 741747402, 230323542, 875079028, 87983554, 68888792, 547097374, 627883738, 275945139, 830353940, 559648795, 567479938, 219665348, 744925210, 1163997, 534092314, 442506950, 420619766, 710563332, 505809331, 426730663, 935036050, 64941741, 697804818, 606660355, 685987419, 719714660, 610617127, 878759734, 24972854, 191580518, 998975053, 121303272, 275914368, 127720450, 653094330, 875749998, 299828168, 232659630, 44914060, 93263882, 801862212, 737475492, 74385252, 156920367, 681766353, 340913296, 699008683, 734623133, 415844565, 944495967, 672920866, 766891511, 767594762, 574319952, 226540889, 523424404, 981407949, 529184836, 462730063, 34328460, 363385295, 187695724, 132189977, 66603120, 592723454, 992694973, 509538324, 330671153, 344255798, 535581700, 709312207, 973492318, 838250325, 388718532, 632402871, 432577368, 49946823, 435770116, 106288852, 981315996, 22632722, 210110134, 660659803, 560209583, 930422039, 945303113, 140798752, 944916888, 693730187, 60990064, 105893799, 39022610, 548052896, 378923552, 223214203, 847393047, 577108062, 507518546, 963144246, 890793353, 197234647, 702154090, 101209457, 710868315, 935249167, 30573853, 286223791, 562385943, 82702114, 550084825, 521653672, 423348505, 980479586, 433458885, 652521797, 815835203, 857896213, 150277480, 732682719, 456899269, 851975779, 320351423, 491250521, 970235745, 480322230, 418889988, 610773350, 294596588, 591365247, 373579525, 853979328, 4751977, 984754926, 765956895, 13100905, 316796957, 398885858, 841281036, 831903522, 192846690, 366580510, 368996525, 661424861, 34030728, 55540846, 499062437, 636816111, 332779647, 887540155, 686828846, 9443882, 35098624, 130965322, 407327428, 803573143, 755448642, 30836627, 805904208, 986554620, 327187473, 594883085, 923273408, 986286285, 298690846, 176015404, 950767596, 622600844, 66188996, 232323184, 538880094, 984766983, 54255148, 32481802, 327482959, 239928001, 440520915, 440336843, 320667910, 505234672, 782393333, 576889536, 313502095, 905666236, 441351914, 230380912, 357038327, 762126010, 473918298, 133006831, 73127677, 99123113, 724765120, 671941182, 410466277, 417349613, 361713204, 488413940, 758809788, 810409899, 185489272, 970734562, 313521540, 245315146, 737144408, 391108563, 907655659, 177381120, 418351101, 87953075, 206123025, 596535639, 250034171, 855681349, 467342866, 261630004, 859923581, 50024525, 826619881, 418391686, 345997591, 988420069, 105473816, 62589645, 558828775, 719647968, 629130337, 109201882, 421252253, 613028452, 630833549, 725873419, 632314721, 491876937, 876658597, 419461057, 386158705, 297446356, 503862103, 655852639, 965498146, 923976228, 754626573, 494682905, 898843954, 686406786, 167635410, 236423139, 729154638, 504691365, 960261551, 98418571, 193865033, 175624526, 432305250, 400704260, 625737985, 934029091, 835677162, 551568858, 753984660, 493505892, 874380909, 953453117, 569382676, 696936412, 160476772, 494818142, 487472152, 29630998, 135606328, 875400494, 278814602, 456461507, 382307401, 729304058, 966527349, 947833165, 136448477, 156557075, 196397538, 240873095, 689835897, 178863759, 783832795, 245103035, 93040579, 772538741, 213270407, 673934981, 639178540, 493592145, 468629718, 674559007, 464683924, 627690893, 217476312, 459627876, 814503673, 686199576, 857235082, 448043401, 181637154, 346293237, 994418657, 984137459, 726332281, 247761364, 978273323, 865494300, 917672842, 69941958, 216104441, 413889783, 971287737, 722209236, 181840039, 656552048, 853173528, 423345991, 986830923, 665935135, 127350482, 66302556, 680736473, 126276018, 269341437, 992270865, 736250190, 540563043, 682297769, 255937194, 989721217, 204671764, 612113371, 911281153, 511839224, 793694231, 305098171, 757813010, 697336108, 524098067, 364375814, 291599192, 807152784, 94366511, 737606082, 697949670, 194230622, 606687813, 633197229, 935110119, 613145859, 532048859, 883880876, 372409458, 60987564, 855753217, 744367968, 832419846, 59622005, 783899609, 497843877, 617880397, 403903540, 686487357, 50539587, 988004764, 161837810, 666440447, 242042563, 377899570, 886989760, 929870399, 624918243, 677842746, 132041497, 835639494, 251884449, 550169386, 708525526, 916465605, 832512317, 709345885, 284435651, 368154784, 974272608, 719607964, 925550781, 155856877, 651933758, 711448155, 242319241, 883315027, 468027123, 892563390, 92147669, 606274404, 911243333, 555120181, 32742985, 242550783, 346454172, 346929928, 603520579, 331058136, 501535527, 779324186, 626383133, 179010621, 817826033, 402716486, 554696923, 236619191, 278921870, 779452361, 109287852, 199186619, 175292215, 450642113, 548974564, 250969917, 547621510, 901715078, 796931585, 753582648, 85800934, 975418251, 495603444, 510539119, 727113784, 126730162, 83237648, 987541737, 483162227, 616224367, 772901236, 443208187, 122099225, 356927666, 820158698, 416385766, 311399582, 325140764, 319873117, 956114600, 963236767, 161450969, 762166755, 980969756, 767901876, 990992147, 835906733, 108206914, 22021430, 776903613, 266902868, 221865653, 588408267, 624554942, 179390801, 985718936, 753502992, 664748023, 761637338, 826111598, 594817127, 403430837, 577677656, 624416964, 60891121, 814554950, 961244461, 940541328, 564259884, 566398946, 401718792, 897735064, 610558018, 218836720, 632403250, 311870293, 133368587, 246533847, 360377244, 115474691, 330500694, 985718642, 625551480, 240441890, 947103770, 635043276, 870431806, 130367354, 343231803, 207495573, 557289394, 260759235, 852267286, 135704509, 81173508, 99182474, 195215613, 423000582, 920597624, 975992923, 510627398, 256030214, 94103446, 988985776, 555562116, 616015568, 731712387, 710454343, 156606440, 900409622, 976201911, 104361900, 448154852, 273186309, 579310826, 27340896, 764818310, 20488705, 462406228, 653865425, 818312834, 80304313, 233244692, 21607464, 769487868, 158340002, 229337847, 401439086, 91730997, 240263237, 498061283, 372913682, 374044781, 671972699, 186972594, 408306235, 562351472, 880112348, 990472377, 635471666, 215435701, 960775991, 537287261, 139584569, 390944107, 904406787, 800263495, 8895680, 726211712, 448016388, 333889584, 163873675, 532821617, 174630534, 27246886, 695021913, 845168212, 346178383, 68242307, 663420037, 921107521, 41171673, 225545349, 553665894, 261254410, 461651765, 208252577, 107042483, 171890929, 207178899, 820978157, 330089199, 126650900, 194430489, 645010638, 594603091, 269911620, 28737411, 588714785, 100859050, 95891332, 202081623, 124172794, 449603405, 650142299, 95517178, 428677520, 578919730, 961671094, 213167430, 265803020, 413202029, 520813965, 281752288, 453929719, 122159989, 86200106, 796653325, 851722865, 377553853, 391484004, 20008306, 969969417, 110308429, 923139882, 806496370, 771277337, 974903706, 291933904, 241540790, 32458624, 379823801, 659120265, 643483174, 4944852, 856557697, 688913176, 598173776, 225213861, 151642369, 560405324, 54229939, 546280962, 346679668, 767109581, 169776170, 774158258, 771855608, 638011520, 520315710, 189344266, 948473196, 744645731, 514863902, 330601213, 637852210, 786881263, 418079892, 827151055, 571921393, 305809390, 725003833, 520201266, 720612255, 783123652, 567761917, 164021820, 81385975, 161746849, 293708299, 769283586, 796429170, 816976036, 5775140, 772340937, 652540534, 846862983, 42214918, 637393928, 47248297, 232592911, 267807946, 957825646, 61884298, 143879444, 483077413, 758092892, 956409163, 732131826, 561911229, 191804120, 468129690, 631210514, 366105210, 694038551, 709834817, 579073049, 407785286, 66623727, 34748292, 740943089, 794526870, 272216422, 181816987, 22881532, 688436155, 732109206, 98658720, 596821099, 459132157, 26252120, 441137705, 995786848, 276107011, 531259757, 690849081, 974115399, 934777877, 549314407, 442933001, 225414833, 317631316, 733762705, 268381403, 204002038, 846854697, 846617504, 700203544, 476409282, 512376809, 106801653, 693060332, 72941097, 164755981, 429738206, 971634857, 507482922, 77645189, 67502369, 730622526, 343009639, 571131616, 751282675, 976940959, 442408054, 230669336, 405599190, 101990011, 14211332, 975361338, 800227319, 619322926, 629337768, 576154641, 379756193, 988421215, 600423429, 596245896, 797614550, 694261730, 170756951, 726273200, 318253823, 780533818, 195722794, 304571097, 364913842, 903552751, 496504950, 808491671, 171064584, 674762254, 483802750, 734781432, 477341953, 48722971, 150403874, 452453080, 90649533, 663693932, 611742088, 621308028, 638682783, 498249138, 474108965, 977205207, 620818352, 480364632, 948531396, 390571028, 255944515, 623233094, 895730522, 418795555, 682995262, 40614385, 564902989, 821905649, 593535728, 497992986, 43321427, 65820805, 508482539, 87867533, 213911864, 184563580, 678901277, 977065590, 52195263, 98627381, 393360374, 628942280, 483565843, 124014029, 813439648, 187216391, 593780444, 457361700, 417026274, 84032016, 136200345, 170188764, 819215367, 11405211, 43023771, 209571250, 666374202, 855368310, 501830264, 791797641, 929793257, 847863456, 527418602, 71652798, 275795919, 12906991, 425744300, 758937695, 517547214, 702125494, 101098000, 54239609, 700974229, 669000465, 379623891, 459892641, 171713287, 701206017, 220288099, 777292264, 798032875, 346255540, 998580297, 292581728, 64026849, 153594556, 292882853, 652176359, 199516444, 835097759, 832499449, 481162190, 191798076, 521044532, 389133556, 435857852, 559434344, 685561284, 485310456, 935266880, 832923285, 523797941, 39037806, 815616024, 566644230, 167388722, 842278767, 968864325, 571312815, 230093827, 846632390, 591388618, 943024626, 600097526, 860190183, 270717357, 669694798, 988735124, 17411299, 89549327, 641086538, 456092061, 185938594, 327979217, 747300113, 479058260, 156861079, 73498548, 168799861, 936735465, 668600779, 222869848, 371110147, 166177491, 286564470, 264271415, 181848610, 951352408, 11778067, 302930785, 16415030, 683508369, 880230391, 375448040, 798255156, 146881824, 572561362, 793864223, 908935987, 102646810, 321830427, 267451589, 425820278, 70201156, 71273411, 337185657, 687775170, 603688846, 981482665, 214820511, 800655184, 129605344, 334641698, 156827732, 459917784, 224740528, 883480206, 312806111, 974206597, 332048520, 554124460, 523932859, 440090940, 497261088, 918664683, 270895612, 662323432, 657977051, 685420783, 929898288, 389646222, 222571459, 9606225, 471934716, 640585022, 260462266, 696482184, 629685392, 516897915, 478415980, 318432000, 569126286, 785759850, 281466721, 175210464, 31364752, 432914270, 867378203, 31956005, 501172318, 673267130, 697435538, 556740518, 932946722, 747784347, 729673903, 348068857, 169499782, 858543127, 674467607, 12895210, 159089161, 938165269, 969128207, 539617457, 14302123, 571972171, 531392894, 586374304, 344091734, 642775616, 330811573, 719155021, 815539190, 536926546, 456497821, 526215840, 915974366, 355054243, 436545594, 177412570, 795279154, 268502538, 671439106, 73548829, 125782392, 33192447, 556673871, 192531078, 42143212, 68571599, 574106012, 679519299, 976821728, 662896500, 236065724, 795324456, 256074949, 200628516, 778489208, 42408071, 878986965, 259908662, 108843150, 536645878, 892223497, 25104686, 406834451, 265617859, 655863356, 716794280, 965757501, 181170224, 858691110, 468175542, 562280309, 871884475, 326715108, 960523710, 527094199, 116855448, 963744591, 553436399, 701553627, 201382253, 118200974, 672999069, 612346670, 839851767, 83807990, 751280796, 23563524, 276468484, 934576314, 549211305, 761825340, 481577684, 711279015, 623704507, 978747221, 404409076, 806992231, 403263818, 341560608, 150555650, 904236288, 255222196, 808047449, 806616617, 7087873, 349098502, 165009575, 346438575, 251045878, 249938882, 768019308, 864558315, 574583620, 203760415, 187395482, 635040581, 352142599, 594549664, 914875054, 385889012, 698971176, 943554370, 624545402, 891504344, 946245844, 398201465, 993760394, 737438895, 821166571, 916185790, 650637458, 357212947, 261416824, 177924386, 376975265, 732672085, 344253626, 462488288, 102506159, 519978852, 51779944, 868169466, 871074149, 47739261, 826891809, 124483958, 161501525, 75873342, 190160279, 890114857, 152745915, 291548222, 81080677, 293348550, 121695394, 199677510, 163376024, 261096402, 122946147, 745877817, 144868763, 616835385, 857604419, 146725968, 704056820, 236283912, 439193484, 530573764, 605202410, 766164997, 388431369, 391184358, 26954585, 751860024, 839986598, 709346940, 314170957, 399102667, 641254588, 333227153, 299556713, 364683851, 736525360, 501503364, 259758971, 177082955, 439268655, 279246628, 586075088, 759768908, 161071997, 58569629, 947751459, 968360091, 280740316, 701512203, 226658006, 184111309, 22143038, 172555180, 462707392, 334611976, 520757003, 458038454, 186799533, 772960764, 971511477, 319033556, 946836994, 517925862, 664248087, 605330462, 40400324, 456893554, 41584934, 532827382, 965830690, 985147965, 953082380, 821701106, 918302862, 542953426, 22790682, 587688554, 466655270, 235182448, 541618745, 70519441, 203286183, 91197828, 962825038, 424881366, 858694633, 566823087, 219327021, 242746558, 461415983, 424375546, 40310668, 83359557, 235816754, 225661982, 856527417, 912519612, 530231145, 487326699, 276586691, 755680897, 3857066, 680059035, 799373267, 549407311, 436985269, 27700951, 534444145, 65866987, 270695281, 937137158, 74948966, 377571673, 319808629, 467833625, 682083202, 622072621, 895053315, 476712301, 653853046, 284877966, 787753971, 300484984, 939546917, 527744102, 975247249, 759877165, 837950095, 927051395, 134008188, 74486376, 741814192, 503219867, 250031519, 537439711, 845462024, 288490416, 8676211, 993657065, 194962033, 265634743, 40774401, 16541725, 64869459, 815380446, 969674170, 852699538, 657990131, 778235215, 539225470, 999706375, 492205020, 522172330, 745369084, 707035099, 380100724, 610357854, 783189241, 350899960, 644682037, 452025361, 65583772, 430720463, 412512879, 833421022, 311828991, 996762520, 769408027, 460983706, 9877600, 6744655, 543037853, 623948880, 36087308, 39443160, 192052802, 666000834, 346414931, 539725506, 253887598, 568888953, 870503991, 670108679, 885638533, 788054968, 305416405, 451768046, 123305268, 164999777, 267386647, 601993671, 956971664, 924763918, 90590239, 784240385, 119280600, 601460970, 815223629, 765363625, 600099690, 808656561, 175547202, 596887170, 945485585, 250106484, 968815383, 849490710, 472183078, 331111867, 895090675, 653744342, 560165824, 191154381, 285384052, 154000277, 59234350, 196306371, 584412741, 865907751, 659324958, 278635861, 902395685, 896061746, 820152496, 735676511, 823590218, 783455284, 726963222, 264238832, 234642039, 553733166, 934003466, 996874021, 701089705, 64518123, 311906857, 966193976, 183027545, 123178790, 376584078, 566768296, 110559825, 113225090, 294744658, 552479347, 50430503, 505970450, 902943670, 569024286, 924716818, 926294184, 521536010, 753329880, 365433909, 573032704, 631040776, 920620340, 129803188, 316673594, 991931916, 298275228, 861571353, 908061327, 905927623, 660303795, 264357542, 627994033, 387320686, 644853917, 59716024, 358997283, 646399246, 906992587, 958804642, 438802342, 402960731, 333215374, 499112242, 703144273, 84272422, 64279765, 834911839, 65884340, 828838070, 169971490, 812045020, 450031527, 768257878, 879666513, 351759276, 993244164, 102044417, 747060416, 998157798, 379776890, 130786058, 673668674, 901861190, 19661974, 209966186, 959519713, 784405710, 514749493, 845228835, 813249156, 627963045, 803781032, 408988559, 244063654, 113017032, 349551196, 886102365, 794111053, 257951391, 178797380, 598688206, 879276586, 24751076, 297479872, 283270622, 334225042, 218845081, 253605645, 94299670, 254484595, 661047011, 393203519, 723926514, 508231472, 586246039, 412893418, 550176180, 546046282, 117252519, 542244402, 333429535, 298359336, 922399879, 95121038, 605628108, 437716142, 364320915, 649356341, 509263547, 908838012, 534123262, 586456912, 171487373, 327937119, 95443280, 108950052, 751263299, 204560740, 942985312, 720842742, 164618259, 268436560, 418323862, 138097014, 336923533, 523102144, 191583605, 610219873, 907022101, 832105517, 866041233, 53462664, 588285270, 884886305, 261788837, 487070391, 326166270, 679854079, 527711497, 705422764, 123087942, 628944978, 203751044, 220054470, 45154028, 184029547, 886890351, 870603640, 270508898, 747521893, 814920149, 699644954, 972356759, 429635179, 418242937, 323092032, 436040887, 283357846, 380304967, 16214890, 237552788, 388132406, 891897266, 54128994, 647660653, 843456082, 984419693, 100043178, 283893990, 33756145, 627711187, 267399634, 976676715, 691458827, 985264394, 324662512, 687530586, 949658183, 766189733, 694306043, 755447547, 248187956, 977574514, 523026187, 475540919, 426571973, 764213911, 385467764, 364244654, 240664322, 522213575, 912765460, 600905238, 152723868, 590595602, 734474005, 996163141, 746805230, 532573161, 489109845, 347127663, 598166782, 769902465, 198840919, 481068029, 234542067, 920387094, 864255459, 828274079, 442870841, 141858880, 603882557, 77558380, 836789423, 624316351, 488838321, 279205715, 820672542, 449804961, 420333953, 691432914, 35053409, 102941324, 119043311, 185083685, 819293739, 713697593, 455988577, 4876281, 892906703, 457239572, 315998819, 783011132, 160821517, 629171711, 698477467, 337687049, 605192005, 77382360, 703527730, 277297745, 359038982, 914104139, 658154920, 492081770, 484307255, 302796981, 148478604, 775169310, 667303975, 959313300, 917701187, 148562083, 210352090, 626217599, 945015883, 710543134, 939074431, 325523457, 577183555, 942560225, 75730080, 711523446, 635633438, 168105511, 296971077, 687848331, 687748475, 352037246, 500478179, 775367279, 132184556, 173786431, 759800814, 408107070, 81341598, 669657930, 906479453, 901376421, 552978852, 647117144, 566214490, 320069188, 807215899, 781786813, 333305064, 974376278, 531383147, 381730159, 312995539, 592831843, 10072067, 695328369, 252402332, 639597500, 255165229, 797715658, 860976404, 386654985, 541467068, 912052151, 582076002, 671600109, 156645909, 199947497, 889515222, 508593627, 946077164, 369159304, 175092532, 172696022, 732310443, 170150250, 315017783, 988034364, 157839988, 801945276, 471314692, 620907268, 702054206, 856046470, 771424946, 979309613, 964631592, 992054302, 548709587, 881764633, 863068128, 435882412, 1852416, 164315172, 491957896, 788044514, 397498534, 680762352, 998744468, 822436132, 384826046, 5620569, 34353125, 153710568, 273875542, 135854696, 138966699, 445243932, 770762567, 166956041, 383440391, 59318132, 100353506, 923414871, 107618212, 523517719, 129748702, 717413290, 943278873, 168609636, 462437596, 93981904, 879689929, 623522731, 332674062, 107675078, 503350170, 420408437, 893046047, 617748031, 944003971, 668201338, 423982176, 252739019, 662555634, 211361393, 122831564, 794467997, 214752295, 659709420, 960772852, 501467766, 327316822, 431438403, 965273976, 576217216, 658267775, 665204375, 916332754, 742581083, 927306345, 327174909, 860088976, 476965288, 193653543, 23309650, 573830297, 90073358, 108106868, 25377088, 235735456, 216826611, 435424617, 814991996, 179543498, 15435028, 339627225, 688392641, 912712244, 736306177, 223813763, 937230393, 26193197, 800435677, 867683901, 476586230, 538712972, 251539801, 938588868, 749278949, 791831595, 565931546, 109341789, 480122053, 29134873, 394584186, 1445730, 297599239, 481011379, 50707396, 257574066, 117677697, 701293097, 906643824, 363523421, 364693331, 585241267, 104847617, 971640559, 466530289, 348834459, 892915326, 959568463, 962484035, 704810871, 879791457, 92065218, 91197459, 611322879, 173906089, 590907422, 491780867, 657742467, 275766352, 714829459, 246021763, 861380600, 185273487, 627757424, 991169442, 896747186, 874989408, 940128179, 107130827, 529364463, 886339571, 323612597, 669351565, 244667631, 711147423, 888069489, 810386388, 444037122, 810529196, 543606489, 167594281, 451785312, 70000250, 739382085, 596913228, 423665291, 866716583, 720126987, 252224767, 142518073, 977550432, 555799186, 91058852, 760572969, 161357030, 891828770, 6655443, 617438839, 484235838, 269142134, 833874929, 356527967, 776231571, 529819431, 884326244, 312485764, 838344573, 687999567, 836696831, 313829265, 110326339, 974925648, 956255573, 606864754, 372043752, 616354889, 448435351, 775272927, 692964231, 43516237, 325250388, 224477996, 475063511, 831884709, 70743865, 541543006, 292358299, 535266294, 659948340, 664627898, 53142386, 739801719, 606460217, 961914158, 191332276, 387203008, 397750259, 111833269, 243962527, 267060047, 319306591, 61608294, 563840708, 172989520, 7242417, 807143916, 125643393, 329733974, 786095262, 242481676, 563003378, 429453132, 222062050, 606204872, 212313453, 258875124, 160531296, 914535210, 988984797, 94142069, 597477091, 611761601, 578340510, 699397635, 534275242, 54276460, 551769811, 127590179, 852779743, 89243852, 960069743, 211319213, 460559998, 801426476, 325283407, 655340436, 825558121, 801876872, 930874439, 113375210, 905649598, 939602777, 612403731, 871979248, 755677349, 686174232, 791205623, 143599087, 787647267, 80733356, 899007344, 691152908, 214509185, 43803905, 810455755, 501567843, 897430196, 702502492, 349459595, 361298264, 795559208, 479416249, 446186735, 114998754, 798770877, 858526750, 853310892, 78547174, 641895942, 718663621, 872265761, 186882876, 326071555, 384473149, 882649147, 269862764, 194661254, 12757321, 626628351, 196432143, 479915780, 520252438, 246026292, 685544659, 294032334, 541607500, 880068714, 509320717, 681134976, 968008730, 33223756, 299981609, 701975447, 541705987, 797641114, 298944689, 727233460, 825740998, 749508682, 509643038, 208136873, 237300739, 371232536, 582688389, 575099407, 50754795, 663731682, 455945420, 393675836, 103182220, 967249877, 144741488, 242423436, 535324498, 629630384, 775572129, 524024243, 852144918, 695825377, 774986085, 974591567, 756165631, 258025996, 728557475, 136682845, 177858719, 260070327, 879295966, 503164547, 321018696, 659941725, 939691702, 278337218, 144780641, 962952600, 401992382, 307922801, 997651806, 70399502, 777332975, 407915225, 102836027, 251508777, 448496919, 382121097, 857641836, 179210187, 598077591, 979421303, 636311752, 258492197, 676574743, 712759359, 507091924, 441376310, 125497789, 550221479, 641226386, 448843600, 712092621, 779041174, 88389270, 881279749, 667616233, 917141349, 510061687, 314036313, 16586647, 415096765, 618916212, 209668628, 175802687, 457052152, 267936141, 789441161, 548049068, 545407340, 366721025, 173931187, 827021172, 634024038, 17692917, 667908623, 932881476, 662595357, 977537435, 836086199, 174067021, 275937452, 811282001, 118350161, 5322931, 958641017, 529732382, 128236388, 745220834, 325690647, 55958690, 97203653, 752041532, 622217053, 629900069, 950751916, 733723303, 956513129, 7907868, 541438757, 799296966, 986944809, 633859812, 494304765, 16554912, 679897361, 83316573, 17866320, 375358794, 336122645, 344179367, 478404039, 177672946, 558771145, 559577, 194874303, 340443655, 784337535, 421609301, 635755654, 379194589, 564788253, 919090518, 978893303, 417393740, 70419061, 672502643, 341858533, 554021501, 992479350, 199925032, 927009488, 440503682, 548852319, 897823599, 185157257, 796752211, 410108291, 175314778, 227928428, 558091605, 231408686, 314834951, 215832948, 475339558, 202673651, 405405586, 970798565, 559823603, 145576384, 183694740, 137643450, 638857338, 444682747, 441925413, 849856713, 840483936, 772921804, 439097456, 673541786, 652081022, 278141875, 606795047, 618201514, 234463000, 743306438, 559558853, 449499604, 653682753, 981015357, 532038782, 401022134, 436293158, 711373005, 510549040, 278746421, 165598794, 404706834, 80300914, 666319320, 498938346, 839459094, 858091942, 375510425, 58819998, 453646864, 512266131, 745576673, 738582559, 501819774, 609815977, 269248967, 723257163, 345316929, 533190455, 879156363, 871275594, 286580132, 226389380, 618211375, 50444353, 37008864, 497196712, 431927953, 287007658, 944926923, 398002342, 427745904, 897880282, 413228618, 69843500, 567839008, 25644904, 103004312, 692678476, 524557032, 560078779, 379815034, 991039148, 52059168, 393851503, 632372225, 206461319, 482639593, 664459007, 130411793, 794030187, 568381968, 903836573, 932333026, 402480283, 994983515, 930359407, 953290276, 478586455, 732264931, 481179807, 978630828, 408059644, 214974704, 747156890, 251227236, 38112193, 875772566, 43515470, 171801081, 446328520, 808474317, 718866866, 953870522, 661848417, 352244885, 947207427, 951214004, 538418310, 877025821, 559721137, 7228886, 684355936, 554703179, 901703587, 858465562, 256617271, 423635916, 454654210, 612217753, 892325828, 20559458, 302611046, 967805483, 961960960, 201567358, 242614457, 633248399, 379094921, 868977326, 708422348, 947869623, 672604054, 6446828, 88179527, 805388645, 677329900, 15651987, 648852228, 473229600, 783528682, 781290557, 690864122, 213567855, 717488052, 103662961, 860370530, 538237342, 345883821, 946084249, 723653106, 529065226, 551129738, 312797108, 518805624, 270225998, 34871024, 764011692, 948868441, 527132448, 473590338, 788366745, 884189515, 470861997, 220783209, 691421209, 59297726, 590599480, 994456381, 491168179, 517597160, 102725064, 83887658, 419889115, 730365644, 939355348, 554712596, 338704774, 805775136, 208963416, 450831248, 176925848, 300172088, 123407976, 983391596, 451300119, 71853921, 518828896, 62581166, 128081308, 989590415, 824614220, 412680904, 61377677, 524654150, 975331274, 486554354, 216911344, 348726246, 186506810, 747667201, 410153134, 901629515, 325508620, 308367977, 517868643, 73118853, 241744146, 379501625, 683379902, 117047358, 956184967, 717179501, 698554976, 169791067, 550332291, 331181916, 107759440, 982980276, 263149790, 586637722, 44119416, 461532420, 419061755, 711202727, 185056643, 599737747, 158683327, 758769154, 305004553, 595050187, 654417844, 81745168, 52727236, 981432108, 894187381, 455900713, 239558999, 177024491, 972782403, 692129605, 413343028, 719188459, 672063039, 724958193, 562562640, 556841811, 793129625, 363407536, 234635191, 324192313, 509423090, 367103293, 917475156, 16455836, 129223589, 407005545, 535910401, 40448684, 935403525, 629899030, 361726731, 678614049, 864371951, 528031093, 377494023, 171770081, 205014221, 596125236, 604814963, 43595962, 628379630, 862301476, 801188185, 507499080, 287994922, 632303504, 722196062, 873160048, 669354230, 11647510, 825426713, 682270082, 309409546, 144278710, 724142323, 835264214, 32402806, 371829099, 337915296, 240303033, 210389152, 968003680, 754739543, 621731936, 456985803, 9317204, 87755611, 110863501, 636503295, 358003208, 826308307, 844101178, 418134666, 306514828, 768088082, 745381186, 486807537, 431999794, 487169055, 786509654, 513986228, 133981400, 526772372, 486204303, 302109835, 813305258, 401356178, 57300504, 204221663, 950247615, 103973026, 25009885, 148691899, 627004598, 397519712, 840122292, 591760747, 188869017, 165051914, 487977904, 202753296, 524582812, 29855096, 237424047, 15012675, 312309348, 171069733, 622196327, 444567184, 668742741, 372267088, 696017488, 732756648, 816076129, 153908772, 890981861, 907866277, 194504781, 11740086, 60274378, 904106198, 202131772, 175066337, 991388360, 584317066, 963179613, 398430259, 353092873, 541909489, 401147621, 347518268, 535681605, 662066595, 672934042, 768581862, 200944880, 330738237, 761962514, 922740785, 765710842, 283582997, 149652225, 511514663, 315986010, 602501717, 414461739, 322233480, 839211546, 902709117, 579969092, 959629362, 882900643, 96247250, 302690537, 146278538, 286869891, 31829485, 875397916, 348447783, 829790434, 127727527, 41213231, 798416246, 264968258, 902223912, 628801250, 858811373, 757739461, 285810012, 368205443, 539974414, 483391630, 281754463, 935601390, 541043992, 884330520, 133731753, 936152308, 822079165, 749982410, 465350972, 25453918, 400760525, 999461851, 218482853, 60120526, 347296180, 295141487, 299465626, 385711015, 210669745, 2406984, 581461398, 316736126, 185508777, 785946804, 44382874, 364153762, 119932291, 449531271, 950812167, 640221454, 154498907, 411199600, 125170517, 958399459, 38852681, 430498337, 159357346, 553272429, 190270430, 506372995, 322647766, 24493640, 864967126, 557140536, 735242101, 233206806, 562604940, 609917295, 767982524, 175131199, 204017970, 228656675, 5968437, 790676845, 907371286, 376778287, 22503101, 941845307, 724046408, 432318378, 902864102, 837498007, 181608220, 835583359, 330665622, 28135972, 203681453, 188635450, 450526496, 975637366, 795804730, 595055172, 54788111, 376449267, 608718002, 92100690, 474937331, 72663143, 486087457, 254965026, 90601139, 540827028, 942456318, 516309593, 796203920, 813463719, 949107317, 196189261, 754736756, 21704855, 467075695, 509723251, 48553248, 195898949, 393846852, 630074826, 457640585, 779059529, 286912159, 174034155, 626514365, 417483310, 620994945, 645738224, 934700234, 53161576, 756906045, 960164109, 350152456, 995389655, 148735919, 345018851, 892339102, 282752334, 20109577, 844674620, 508695186, 355785954, 817728608, 610887938, 273019979, 327299331, 486225843, 701034576, 117324744, 372504065, 784051834, 49237352, 559975004, 517642902, 662451758, 315568959, 375088931, 72862305, 617918049, 315003345, 961432878, 622346229, 322532032, 627716689, 944159676, 592476203, 105363703, 306813613, 146035413, 654687315, 553803987, 508951543, 93643531, 610790152, 533072128, 519374868, 564851180, 383209221, 387801705, 231135326, 239174494, 656868544, 618739913, 747048269, 137378469, 291642319, 578122856, 345644903, 215303674, 633574869, 627455956, 101615137, 951459439, 858693982, 149047132, 585831876, 560873857, 675480432, 307727646, 988865255, 823044506, 414528567, 117505124, 750005946, 43758862, 619597098, 596284793, 50922465, 5016994, 980230395, 257499346, 32752845, 575268590, 59610119, 858348210, 360778691, 315087567, 562374336, 940801329, 130494738, 391568964, 949938361, 60563185, 764092671, 301283620, 720388956, 922180542, 5258144, 879056921, 864766825, 595574996, 993643527, 398279558, 91422758, 839461445, 507638893, 137552906, 38755041, 970621522, 398205125, 963346512, 292727734, 553999911, 247007502, 205107784, 960423102, 878302529, 805647546, 861820533, 29267418, 52875423, 957082154, 625136026, 230570210, 993549439, 941894834, 391629385, 895675980, 907738630, 891279331, 32434058, 247120356, 342420306, 51555521, 11692720, 371674013, 499468091, 237603582, 117802813, 830740863, 361224987, 172866755, 240390964, 663787922, 983257894, 827053225, 487398720, 527138164, 432837246, 131674771, 288879602, 923139386, 28041449, 312561358, 156906511, 272233322, 496632542, 916557813, 8349736, 628027020, 691561357, 585798449, 801549714, 915072552, 11912336, 992790565, 865703833, 830466290, 303330678, 881549796, 663354181, 48136280, 189276270, 591708726, 160875661, 876328276, 121224716, 538139109, 205726075, 152531397, 181543049, 604279424, 764405271, 223953415, 933045311, 562468955, 491417175, 422564755, 735592695, 643523627, 444012677, 420818224, 595191168, 521966112, 764586243, 830044124, 826661557, 669660053, 379316438, 256963316, 649261511, 862369214, 457851475, 762160804, 271773378, 646445289, 690099114, 363543151, 750620967, 354424578, 959015548, 168198264, 231724811, 999744020, 860055474, 77484536, 255259854, 76634582, 542112930, 351483049, 646603152, 814819977, 913435179, 915633398, 824602273, 99803957, 554319045, 77731927, 602053829, 259660713, 160866581, 255203539, 397169253, 859240739, 743925202, 556686610, 579271172, 414291464, 789548271, 22903334, 32321354, 962704255, 366218841, 925026268, 422797733, 234295107, 962264354, 801213261, 64060182, 904123601, 287857393, 397688485, 950812461, 401975829, 813030457, 591481434, 30398683, 257786959, 414466754, 288894077, 475674607, 771923640, 28414914, 896576196, 371958462, 756184522, 389310446, 814912651, 486525117, 51254943, 271551672, 532571204, 778303114, 259629248, 839258362, 506814498, 80175775, 299354503, 248144371, 107897492, 307485281, 536151419, 992783967, 119536128, 618772961, 573735382, 68376771, 929009955, 190198078, 406664648, 120958616, 930411300, 12825062, 799929704, 98803792, 668210754, 281800740, 350543835, 936421194, 780171618, 336642298, 256184150, 657044450, 773136581, 965444327, 64462146, 781634791, 774658068, 456072767, 127274676, 724416560, 321422816, 610113746, 56306914, 620009733, 749358889, 254355898, 264518737, 640805670, 76008684, 456012169, 855039523, 442214833, 538520294, 156298306, 279565961, 967876927, 32674137, 529176814, 204029607, 975609975, 896954772, 818089070, 335820263, 702295037, 502900714, 265050843, 530310505, 664159700, 495208196, 133522091, 167128728, 951711767, 278564631, 71253052, 41028593, 956391277, 905302486, 929532217, 434574728, 91171336, 713326744, 371506685, 58076832, 325881827, 539146852, 631525415, 398082841, 769095414, 719769996, 809861637, 611054037, 57613323, 261245203, 540649686, 236733429, 513086343, 806717299, 840775644, 575476850, 601943811, 896680266, 99017412, 578641053, 829169515, 847015214, 55908740, 376583650, 980542689, 181390577, 859986197, 603750545, 820690187, 112672210, 59493889, 575559677, 518009530, 549255776, 474524751, 963692666, 711136996, 795026360, 457209894, 77326721, 369703366, 506061066, 815841084, 566363680, 865130317, 148079996, 124881135, 870399768, 401930936, 848114597, 732807637, 17927393, 257996806, 264398390, 511061802, 201163752, 371791751, 651054853, 77410948, 259732365, 978756730, 190138255, 193081586, 309095450, 662205784, 615528682, 531271872, 5483725, 476634902, 511194148, 268097839, 736144998, 164214560, 562677792, 744956597, 95504510, 856417102, 887353596, 720262100, 7101052, 931410837, 689192376, 873118600, 289035009, 572369519, 573196592, 502578508, 735678857, 180278090, 292857590, 460098863, 284382440, 252357516, 705435254, 162847964, 78993972, 77126617, 461958120, 519900658, 639592151, 277380959, 527664356, 37969883, 610384187, 413777241, 939805343, 180042752, 181122547, 998775649, 254741866, 676201257, 767889369, 705955164, 226095289, 90322618, 695258205, 644011525, 59712963, 113469249, 606590453, 501458370, 963041882, 271876898, 378416906, 921264282, 282573482, 827427078, 73439649, 701127856, 874855383, 590961220, 149075962, 108630392, 608641256, 980325616, 704314176, 425246883, 939090032, 168376682, 597197365, 178991549, 628886170, 343596401, 126337709, 7554571, 112589084, 359007918, 246062491, 862866068, 114089506, 35421084, 595876665, 924477932, 214871049, 255342658, 39999061, 814415810, 295511812, 265017874, 725436780, 427021105, 139580018, 483380461, 81139115, 549073676, 382012034, 921445713, 661407367, 902102304, 591976665, 362790181, 179734096, 121300279, 966108470, 841593118, 153523298, 976621106, 693716854, 276118911, 526954575, 347892488, 134651309, 20416077, 437878487, 785804111, 756146831, 124836582, 96705858, 494595338, 194702129, 775107815, 226316839, 215730521, 664039810, 861353363, 183041380, 912173215, 34879296, 892273486, 282400367, 517723204, 42605110, 276057963, 548542528, 374633107, 978742692, 195514101, 330197273, 573749270, 125368457, 396715888, 725550057, 736915551, 994267569, 483756828, 477596342, 479444396, 40486610, 292056139, 721502610, 517608918, 682820634, 471078031, 631036730, 840823854, 352702906, 59526453, 14545521, 302520091, 174521734, 452009463, 977065192, 743564918, 499026713, 460275772, 972286054, 603679568, 736793751, 489242143, 307450185, 955919945, 320139247, 908186758, 404584874, 522759903, 248479111, 793561280, 143893372, 594433061, 946316841, 253289561, 736846032, 442935635, 62058915, 498949640, 127907058, 697112436, 809093559, 497834387, 984408426, 600948562, 192023813, 202233679, 192921193, 406215458, 480617311, 455073941, 45605782, 780842075, 164715106, 841010608, 861443493, 316857479, 366216857, 809527122, 11470977, 730411431, 970280338, 266301363, 263241352, 873537252, 6077464, 983727980, 521156667, 231978387, 105692871, 706180450, 695777432, 189319175, 861750585, 16352268, 497474279, 258577967, 578037511, 710213063, 205769460, 334414012, 255845719, 918882547, 816769047, 709325505, 797952467, 533798067, 731811428, 255935108, 249723484, 793757932, 677682358, 358832579, 274966374, 94727662, 382865002, 69803861, 666826737, 54272767, 537198865, 233173019, 595428530, 592013288, 226278179, 581275474, 746732190, 781592446, 817827649, 368060376, 650567824, 847504534, 51738770, 94597894, 637981032, 694493056, 422959088, 460599721, 157215362, 672275103, 983928719, 943706205, 69591292, 952986554, 372214911, 911774341, 995092635, 117802691, 141725951, 891298644, 234637300, 926751332, 414698587, 843349266, 382262656, 866782419, 55889861, 517910798, 941426939, 203009710, 456957282, 251244144, 784114946, 247350462, 128720747, 679408113, 755255895, 644340526, 560691636, 89584655, 33871593, 973209354, 835296607, 642305236, 425250749, 954190097, 33952287, 471328863, 702950817, 107855375, 890293587, 639385460, 333957130, 771289246, 471681815, 533086663, 119987395, 683817348, 219217039, 748668964, 995212213, 208403339, 156855171, 576549959, 238744229, 920795341, 351159002, 813739772, 985078560, 438343227, 603562276, 934070811, 420400527, 774930695, 758798996, 851545351, 48928959, 997376116, 606403486, 256516825, 68850457, 354788115, 471515700, 426292710, 884616058, 119917684, 784698588, 301726768, 349335280, 398638442, 655375503, 903944328, 669734964, 250037089, 911777200, 639332410, 551410025, 791667505, 603998633, 78239619, 209128864, 655831219, 5043918, 304957607, 550534882, 576670288, 888484262, 799119897, 210937734, 160027237, 223239315, 508435028, 771802922, 401115999, 328444905, 437817055, 560049792, 461768353, 451492661, 379788286, 811216722, 670740185, 279005274, 80182467, 627159416, 859393261, 424865080, 652014790, 93659125, 149769258, 356105623, 548495026, 814155731, 760595503, 111058190, 110655435, 607424794, 460530526, 887888937, 120172909, 419419781, 135671669, 975010152, 168875433, 492806129, 377242073, 740309765, 804749648, 207632229, 389707995, 532845444, 277803518, 176432029, 49836901, 698787384, 747108481, 895496364, 304798001, 134586559, 274990157, 479681769, 632605384, 258587637, 973626290, 124429481, 893130965, 454248526, 284590651, 571581398, 824288374, 410763591, 828535513, 202505648, 727415352, 169719909, 227253972, 501754114, 987357642, 477823866, 468272496, 518544315, 410954317, 47537949, 533792240, 436697554, 818805982, 453136928, 598579543, 494105029, 600796109, 972457429, 293862581, 747560030, 888382886, 458566653, 258874668, 456627482, 375014693, 324096660, 633836940, 440434490, 868729782, 302243493, 139908389, 576203677, 647551244, 522393231, 895388027, 345256188, 23417286, 489928795, 817085884, 746545209, 654329433, 770638836, 808020201, 927038168, 215487305, 579717611, 607039030, 575417823, 227622358, 303900789, 769375927, 971496213, 289770230, 436033357, 518817680, 509825334, 651660491, 728373804, 666374795, 393888885, 872659877, 974071296, 691766445, 575175949, 429804200, 232455844, 801897623, 117256747, 842636587, 175690347, 557679644, 189052079, 552962276, 524062649, 97889546, 902449314, 301032276, 486948332, 90955054, 869183447, 788815559, 730854370, 400592285, 216540251, 709043204, 930072590, 156780989, 29576710, 230575816, 146602223, 364797828, 814884376, 797309327, 237629030, 293477716, 360775756, 63665792, 873142416, 389826062, 960679113, 256301651, 508840116, 708479237, 273061405, 771145108, 159355675, 499448954, 243573910, 607861145, 645973778, 231783828, 141515968, 776087307, 266841542, 300112388, 814061483, 813729892, 383286466, 769370420, 377014219, 260208484, 957069003, 766118946, 991633449, 680644149, 782789191, 652053257, 296783991, 234416091, 809458434, 711416567, 85425245, 483271535, 978388468, 714571462, 760554747, 805069905, 5606514, 89244345, 82346900, 637028448, 722314143, 982816547, 99803234, 44622874, 194500949, 928970600, 293292358, 550093273, 250007047, 928237002, 756671694, 534300462, 32646962, 838939734, 712556580, 613508750, 94874004, 487271893, 990167259, 102121266, 826956466, 472115392, 227764930, 59550664, 374949125, 141692069, 906150732, 36267737, 835630387, 285807370, 835300667, 827126375, 173469168, 307528119, 113234152, 800552292, 942300485, 56669459, 591643316, 531187705, 805442367, 844302203, 224892316, 349930384, 775314954, 454643684, 608521508, 778942650, 776476991, 938214193, 744290280, 604862014, 547109464, 898406584, 393518465, 995087164, 663268465, 262112309, 363754020, 477473771, 398464182, 720396620, 851560091, 271692803, 573013419, 470149433, 680655532, 104818721, 164364568, 573771236, 897132771, 748505643, 368798699, 377892031, 567130, 55859335, 692738346, 584314050, 876595508, 108783381, 387271084, 982932212, 892641066, 201987154, 397295112, 753755474, 305483726, 364343177, 545186164, 548266634, 976890532, 962690011, 118804492, 448126614, 944830570, 56547954, 337604248, 956231830, 660089070, 384869801, 477971664, 95318411, 164393552, 869821784, 925108665, 359903576, 4849009, 754045892, 227184540, 836495952, 805809058, 4679196, 464770701, 730079138, 895019447, 81199570, 244273753, 83659996, 840433872, 314829498, 169279104, 395576775, 989592780, 687782566, 520648062, 268744013, 46448012, 931745978, 90221225, 525028094, 774970259, 843835828, 693364703, 820224577, 596913921, 522466403, 439020277, 180925344, 626438788, 863946873, 84505559, 358539491, 267999778, 450362962, 237317920, 546261134, 645033897, 388325504, 34205937, 810267591, 798891251, 778468690, 715785097, 888035575, 914325868, 427653155, 780911249, 637458334, 293346522, 930873792, 679875871, 275977736, 629010489, 368049440, 495598221, 122370223, 358307834, 112971499, 643379955, 50679170, 116665544, 661946540, 50229316, 573484163, 415394339, 336993480, 365511242, 16035553, 718892172, 488897489, 109822658, 545258157, 147854984, 178387432, 930568030, 159055667, 253487834, 750616009, 757846358, 257208663, 934419161, 689767548, 483186660, 722185861, 585310325, 126315604, 2583880, 359631844, 186682051, 718202108, 980012495, 766486654, 387306634, 911209278, 735544321, 320820227, 208071328, 704275644, 398507040, 40411739, 263186021, 946349834, 330641455, 290916211, 689824446, 754870696, 341722598, 146037384, 546654725, 366997915, 502349425, 568407446, 284980915, 143880057, 934685262, 705491185, 141487753, 321186801, 266271454, 185181335, 857189647, 560755103, 127699290, 238950430, 952635620, 968198655, 302041780, 291592258, 64530486, 576218945, 449676918, 137280061, 657165710, 662865107, 637538543, 459906301, 759821104, 315543270, 587318215, 333820907, 713500128, 910901919, 449244971, 293674973, 705383583, 265175961, 36118566, 199134601, 422561856, 660621343, 718166710, 860952834, 868949805, 491702025, 621053336, 584301808, 315615171, 111695361, 344729624, 314257027, 141652065, 18646987, 912206868, 967684290, 297802971, 17181104, 68474486, 580122736, 5969378, 521906999, 677061894, 421987951, 903303563, 137235517, 165624820, 464948645, 166895181, 943939806, 834673676, 948286049, 17758899, 532942141, 312576708, 508548860, 991803699, 606036366, 862857769, 142758377, 646305224, 296620679, 9500210, 622921512, 758453611, 965289795, 834533157, 361979435, 542251335, 630634504, 890822267, 165983170, 583346324, 855938726, 733250840, 753983179, 488741817, 593290547, 825117013, 593738708, 517456207, 146427374, 728712280, 863558124, 352348641, 385656737, 551001005, 438611489, 922188678, 123121348, 282342986, 342538182, 215668537, 101223111, 945671168, 164490157, 737381402, 251465805, 624666322, 964714615, 362587115, 585722448, 789016579, 916401902, 184415571, 42043198, 400959678, 190056902, 515590997, 714641854, 863817663, 137922231, 644552466, 427273246, 75534268, 655846160, 622726664, 972001775, 226570986, 264525915, 787612814, 182478617, 438748550, 516735491, 879927395, 788557710, 804793328, 45798591, 267188480, 294993046, 708936586, 891149355, 780225822, 366454319, 645568883, 481469336, 742061754, 759101867, 353758339, 960252966, 52443770, 652418954, 461299219, 339018950, 498385635, 660473693, 375019357, 517510871, 577584317, 321504794, 821546748, 222442344, 322733018, 541437927, 997940056, 190125245, 994650878, 183480572, 252822170, 212988660, 659723836, 660076136, 563708746, 716546319, 560616528, 552352722, 293873851, 872432692, 859324936, 377847974, 931864878, 607892107, 176540761, 452427134, 51293411, 508209391, 98668425, 83779691, 317840737, 708736647, 982351450, 610395582, 917950956, 769592638, 485224719, 226449750, 227559115, 509630142, 961868940, 694963042, 720780348, 480890342, 630699963, 210700043, 428792767, 194280778, 562631381, 913921988, 173082321, 926120386, 29632022, 635579872, 52068516, 54965636, 182816115, 541031348, 525016971, 102128987, 148062078, 123179108, 473539399, 27869688, 855085227, 479247596, 734783130, 737145052, 210784858, 904167620, 412422412, 106903888, 345246844, 976783385, 900389199, 859028698, 961420601, 854734922, 859690130, 772586926, 69001700, 30639881, 653668664, 657206039, 44443131, 741944224, 921055394, 112715683, 834456051, 657287390, 1030658, 391822988, 505533534, 327761673, 989395665, 816649256, 296678881, 614965122, 455946144, 523614012, 449460252, 104496629, 348140360, 283946882, 736151536, 466554474, 368246523, 587883870, 136153616, 797453832, 319435921, 596073109, 989242815, 919164101, 775163847, 383667661, 381073960, 370477531, 287393946, 370492750, 559398844, 339245000, 858643741, 497028477, 64836380, 279140607, 47796429, 504027632, 990135795, 621238694, 850632490, 937715798, 838669212, 767588179, 95325395, 570296361, 811002509, 178258960, 259017281, 725171311, 422049758, 848676516, 514078262, 606801302, 595768936, 609926199, 615626472, 587892303, 456765476, 115902432, 843189920, 552435087, 13990796, 199540635, 92207234, 569923587, 132524807, 327829504, 356239049, 969722812, 626877747, 500975107, 816065654, 364273931, 546770134, 942002419, 330951136, 605083591, 657612912, 734665795, 204218708, 245721612, 287327962, 535510252, 530058540, 166694063, 735748306, 816830816, 524906400, 334980804, 550643022, 41789410, 702410642, 48230091, 954255156, 465149796, 167643298, 52438898, 190867379, 410780391, 731599185, 4090987, 560010343, 90027553, 743166011, 574749040, 34055007, 470931080, 622407903, 640747350, 993308285, 887609471, 599434895, 973691677, 394642226, 48590054, 865284653, 774751435, 440313776, 574652083, 108370211, 398026364, 724495658, 469573485, 799251033, 505507372, 156655341, 892118705, 57668409, 420791399, 131473314, 946664708, 240247861, 816019097, 353183837, 821950715, 288132308, 71470263, 947224665, 512004800, 209325625, 732840130, 897771831, 750002142, 800261464, 66155885, 218811119, 742841669, 957339326, 44007707, 996528305, 820915345, 737741325, 137834248, 733127788, 808904015, 442408401, 362150040, 278050636, 607110708, 339149538, 309745923, 348145844, 893260856, 986886650, 301631738, 460686593, 361080017, 449552964, 882513151, 455196565, 661645634, 756748966, 290731437, 514858960, 300104694, 323475811, 553196688, 584041730, 193205293, 965926351, 814857170, 699872286, 437647557, 402690916, 694086813, 107793168, 895173665, 433048522, 474078035, 973636183, 229390083, 492427246, 590684709, 483698619, 2940872, 959885270, 566203366, 330891852, 637761937, 883882686, 486972064, 81865364, 568491113, 925870821, 87567649, 454589664, 154114431, 73040788, 180454152, 927251905, 897183620, 834516102, 220089923, 766477533, 369094913, 548405457, 953417908, 506514986, 322681457, 290704619, 284344000, 616508682, 392277935, 125020264, 371732499, 386665706, 486053502, 513920805, 739873022, 949758922, 727035544, 103583570, 781045231, 153547052, 848798218, 672111278, 646637583, 71495993, 715327297, 994571871, 271547140, 469756028, 913229707, 966210041, 424682353, 678531305, 700147971, 757377165, 218249312, 44967346, 216718328, 616834613, 181268831, 694039728, 520468977, 78929261, 853274255, 768767094, 454187051, 986193840, 32884857, 980076344, 115443135, 487807666, 812450272, 565501521, 605597612, 751533555, 137399182, 244259858, 435047161, 10334748, 587368167, 92590756, 529758255, 140794966, 581810281, 86799375, 942139969, 913997089, 38282758, 598810991, 601484062, 456250421, 568408096, 67309113, 338233663, 855831951, 351425551, 217983886, 835249893, 668740987, 437989023, 503911336, 24796162, 885742192, 79565977, 332874901, 825458177, 843138969, 864621720, 249434941, 405504075, 641360433, 556431557, 143843593, 47154079, 777801356, 689022128, 963975553, 327329945, 200992624, 491024909, 727536872, 728000602, 61106224, 511853470, 881791636, 195433727, 393674581, 543638065, 493004211, 161704992, 127743858, 667176728, 524707177, 807156591, 235309762, 963136467, 988589347, 852876491, 701177983, 177596229, 117703927, 419263978, 746070350, 558270435, 536163174, 87589174, 981426978, 49455715, 986877700, 88223199, 83738671, 199659149, 106733555, 582417773, 594415209, 760784600, 103284846, 864235389, 207237794, 217923570, 821983783, 134546820, 353129739, 929882432, 690300989, 324719993, 328883082, 13746328, 471165318, 287086367, 513691746, 437530423, 587845894, 284308926, 966066322, 279064725, 491572914, 390063670, 532650211, 236612416, 245926934, 18340177, 877228155, 76934445, 494436288, 680976578, 12045170, 173397696, 599143851, 361072550, 100743272, 332276997, 955747935, 136017041, 300299861, 714948254, 263586685, 341215577, 957250478, 876913290, 432466953, 728975655, 267820788, 499963870, 134998110, 712361844, 199045113, 298604341, 730764857, 260533569, 119526652, 879167998, 916434306, 942193301, 558615004, 606366914, 366418056, 890078634, 713417995, 552822429, 655676002, 414804518, 37102261, 369111888, 474967573, 447660312, 214142129, 696735527, 814375121, 927811638, 354498746, 758779660, 639832378, 303915138, 495413469, 574847282, 167424056, 71214294, 500414700, 777006835, 243300839, 935847888, 145730481, 172734650, 39017296, 876666152, 746332723, 806658767, 896997163, 838460812, 103416099, 383415651, 893213433, 55047005, 532995547, 204287553, 277781145, 706176394, 773751978, 64899558, 949394114, 508809501, 854448001, 813963175, 922797266, 241783520, 235590469, 226800975, 52547638, 123917812, 579284143, 958690193, 88371153, 10417644, 891180239, 788320487, 890974927, 345617698, 59420416, 902090029, 846792897, 684971278, 922078133, 547383795, 445917752, 383384050, 38741254, 457076274, 331404732, 935438575, 708507382, 436637561, 483930891, 996695440, 843728261, 705667485, 335045334, 277682081, 283894858, 621651814, 90449228, 594675746, 934180408, 755819595, 573511866, 686671126, 260020919, 749034870, 46080191, 342769672, 313267974, 602768265, 536958821, 907927067, 931328295, 184142026, 338972824, 859754790, 437933188, 454211339, 343944979, 592958888, 519850967, 827699978, 258783432, 138189220, 896654221, 226745110, 751668198, 820266906, 512154911, 531086970, 694348865, 457217139, 415801097, 154851079, 271496429, 721467028, 4009457, 285929886, 26459165, 621466951, 361878799, 960729774, 570912474, 984679741, 656832130, 855256996, 268645139, 822596348, 797811791, 834906976, 22578204, 53869663, 929741575, 866605515, 298103852, 185531472, 519375508, 28853711, 918443336, 561466670, 67166864, 18280984, 279212417, 850917127, 701814014, 344982817, 381320196, 709213328, 329661992, 105559151, 671830958, 387113613, 437747026, 285524025, 839862668, 134624770, 337700827, 618648328, 718834909, 742766986, 826440392, 700345807, 360644947, 500509514, 82218480, 487670122, 646434478, 330708869, 482586566, 959210168, 319201610, 216214230, 989266089, 539759718, 73225226, 904608781, 866799379, 982850385, 134457606, 459327325, 989462680, 587659454, 975494678, 761459927, 187016454, 946111401, 888821243, 124123082, 333148722, 104195231, 319684656, 790507598, 792222779, 717337095, 506269311, 864851969, 240788519, 248653387, 308504051, 65070303, 541504558, 10030380, 476479826, 836841388, 576749791, 876593120, 775082017, 435743404, 347455387, 765316989, 662251847, 638101005, 732563578, 985339678, 289011452, 683567993, 346918044, 85472402, 304323264, 556148718, 261055790, 656122327, 62706042, 91778777, 89311981, 532971522, 350745306, 562950254, 957395778, 586990738, 274543776, 568769397, 939922962, 110094579, 484172321, 521629636, 523533664, 900927463, 612231754, 947982486, 631866042, 855837424, 781869579, 926943017, 430937806, 182545105, 390563727, 801778313, 94278497, 255079206, 645648150, 371267391, 401440945, 789881304, 904538395, 978648759, 990284689, 950426428, 785255009, 662086654, 356533504, 816800111, 749733249, 377640738, 583049345, 165559349, 512788269, 95181556, 555190553, 541981978, 764062927, 220477404, 830984271, 901802749, 812692925, 731530637, 219482532, 547309746, 869905491, 514100743, 545493654, 452629557, 817790865, 936076829, 491292902, 912749961, 407805157, 36386195, 634525154, 900165276, 289208890, 341986719, 839976105, 338336278, 297141907, 620442273, 350442992, 711428948, 421093578, 211296844, 993958731, 386197124, 229721091, 870541834, 332399425, 252391390, 397901505, 491570309, 141325682, 324660688, 427818217, 944224535, 290502497, 480229494, 682790976, 948717696, 970937663, 843713231, 343634305, 5289188, 680320070, 842424097, 680023642, 10553223, 480858303, 387690537, 406301966, 974946471, 474699655, 631179737, 443653760, 412774966, 942368672, 93078662, 408506990, 90303341, 823637012, 444094614, 376478343, 191211624, 766028162, 758443546, 633946261, 732763867, 914969982, 170254950, 875670581, 259407377, 197005524, 924732459, 331465040, 174585452, 850187929, 642583851, 190937653, 327617814, 351644234, 350665663, 18012520, 665629414, 157141786, 837570430, 320589151, 768447714, 654726747, 659985400, 969972419, 143478692, 387313909, 74102244, 250553629, 824714692, 94352337, 560146761, 125585848, 264731637, 712491885, 362919678, 639941958, 646865384, 702063458, 426980542, 275757228, 263347417, 111922005, 36370637, 70274384, 505487588, 184694926, 116826758, 81259008, 473865152, 258407673, 5239706, 847230732, 750640496, 163802180, 223292447, 139649048, 597209009, 305186999, 596195655, 877281499, 173670745, 386262522, 489809994, 169463312, 320209396, 548250984, 802833698, 779547182, 579746694, 656897970, 253046105, 797987449, 389632532, 753389466, 880779712, 318696169, 325021236, 773420027, 203058257, 18285210, 19901511, 390740257, 703324244, 287869108, 880281290, 220847063, 116761709, 676247381, 35267507, 412246804, 662230323, 853546490, 979663972, 959307920, 898348754, 210591657, 540311085, 300080766, 98414606, 33718052, 987350769, 64379484, 94802310, 44792219, 439206017, 803898137, 80201635, 327216841, 954220684, 361994331, 273451076, 398153703, 363469629, 935566376, 528525645, 300682946, 454776975, 874358242, 515452753, 547372499, 119880058, 743023054, 851929797, 241543307, 487342339, 599609882, 721813957, 743872900, 130909806, 196625989, 932199440, 973402166, 795950025, 398277281, 475101519, 220365916, 629779594, 502544780, 727353428, 571292659, 452911958, 723210497, 318772155, 793792894, 90698849, 904067235, 633700388, 229857094, 790302448, 51959922, 113667129, 366229834, 428985913, 587736299, 559694602, 129763549, 788423154, 134739344, 670897303, 402328038, 41038782, 895008532, 531630217, 788457079, 353247597, 855693687, 161664222, 588557248, 800105051, 763901120, 636603771, 492370667, 863953769, 335958112, 278297477, 723068632, 845380677, 995931973, 401432027, 86743051, 825539280, 532144523, 715947996, 880407972, 793180015, 186842235, 848652786, 584601132, 322690467, 897821662, 46844859, 870853527, 962934256, 491457563, 335664587, 978439816, 124712548, 460203135, 964682432, 69428616, 554256346, 663348144, 263224793, 970321471, 626841717, 585433770, 867858890, 22867142, 817135209, 668438505, 754678274, 178124003, 612963047, 699839953, 149343915, 2518386, 629752686, 142109997, 287071359, 732610742, 328078194, 87813798, 74292482, 648297702, 860151823, 578530718, 599386602, 210364557, 167760569, 192996258, 990574342, 267310927, 627839069, 192542214, 311783652, 970970736, 916418145, 974361422, 240867096, 705843110, 42918927, 260834697, 454697697, 355405484, 479460147, 479465952, 762583144, 313215430, 415599026, 29636153, 410040115, 454026692, 177740335, 385167316, 10701418, 860944331, 29594624, 849179549, 5234398, 140915240, 293235470, 752662454, 546863896, 300856168, 901638585, 680570223, 22436454, 180438563, 231338089, 945230831, 622349329, 272079581, 623943469, 192328261, 390626461, 242140403, 37537807, 483507012, 630631593, 176694346, 510422597, 91909954, 186974170, 167659547, 290908763, 710501960, 40668161, 393446215, 309267020, 478887059, 203148881, 442601084, 215339550, 698978993, 653260703, 566072046, 240084403, 110051077, 12800240, 4313193, 883806191, 648022827, 199239797, 703856470, 211180792, 831715398, 609687999, 579557894, 665258180, 209104273, 250260460, 406868379, 622512573, 848343546, 10994522, 203190025, 657919345, 80644087, 965552206, 220424094, 884065657, 106842894, 246052984, 287824943, 341755742, 748926733, 131683691, 559359465, 143657816, 727286521, 438985687, 685059618, 523712231, 54444965, 268061549, 669189596, 919948475, 10925329, 579635523, 666178541, 527492162, 828532198, 43945238, 756208569, 94941958, 237156632, 434187287, 183572812, 587996323, 222888155, 723877676, 206736677, 54940178, 986580153, 481470471, 774174917, 24999926, 762946222, 399281064, 149479316, 639259336, 111127657, 440673702, 624913127, 447901006, 444190377, 281796848, 826093934, 896304359, 367430493, 50131456, 611594935, 927991976, 435385715, 201497913, 351436582, 421448861, 487440495, 679839673, 393678096, 438704551, 381325508, 287169722, 237903995, 595222517, 310172320, 552771229, 330909376, 88650017, 172490692, 41399368, 439594118, 535301850, 356431300, 400705498, 873822525, 922210872, 759218545, 438576294, 888340185, 181079470, 460967033, 588974543, 133818731, 960904505, 166002680, 694292641, 73554581, 471365694, 587603773, 104766887, 329834426, 345651442, 121478764, 616859833, 358149204, 929207717, 848664033, 80379821, 698719520, 435980760, 241682195, 480644775, 99954636, 571424101, 189841044, 783806869, 780927512, 485914986, 871856020, 562602171, 727557040, 300823292, 128994397, 942660645, 696814648, 776446798, 394806849, 699966813, 870273618, 253405396, 61526336, 847171887, 317939955, 807189858, 326213245, 935265200, 136477125, 615984552, 558988609, 825904843, 996989454, 166345195, 338763009, 774860209, 470599328, 736143068, 456125161, 190721065, 642756197, 648538105, 769103356, 941656308, 775923173, 638351277, 41068850, 754832028, 489884274, 611748130, 422911874, 157604088, 760804465, 446420275, 629336200, 410630443, 5265606, 929240986, 72875215, 501287494, 415588899, 891179687, 821601673, 488123556, 890322956, 192782033, 986138890, 954064636, 637713465, 229730569, 643012900, 83715858, 934535652, 229679791, 231405231, 834837539, 650892426, 826041207, 480133028, 94085576, 630623008, 584342159, 281838339, 704775720, 427620282, 170858497, 391476850, 448879500, 582546058, 383978145, 968746288, 433654178, 716129917, 710758093, 58530496, 357952895, 708577626, 794201013, 293295188, 734214003, 6982465, 779040325, 406734072, 839745480, 76710636, 36719612, 736817796, 157971575, 753570076, 721525527, 938872220, 235491071, 311900255, 992637244, 571911982, 831519387, 703174812, 526163873, 460787023, 661670129, 63337743, 868632562, 877521026, 684096410, 955394432, 435616721, 438442308, 265485524, 312779316, 216382548, 847323780, 619004355, 728448408, 877960851, 687995767, 314530507, 744533234, 350580413, 568958864, 211959544, 506924665, 781093571, 825444681, 651590644, 155166099, 660855920, 945833256, 427493200, 931789237, 9990374, 927504813, 169759111, 653739003, 227274636, 589835541, 211097203, 800195886, 123370551, 206571626, 861813933, 458018878, 335361380, 942942077, 913315986, 222762739, 734169259, 404032353, 296161952, 453563930, 571301492, 277768389, 292913668, 852379827, 347178776, 992846086, 871177359, 282076557, 112018226, 784279879, 316897027, 364259228, 339200620, 645757912, 491593549, 454667804, 950191275, 524797093, 921106395, 578182586, 916698224, 505061888, 484948266, 159557474, 171812207, 778384706, 804760988, 94741258, 152653137, 35544750, 877025065, 588580548, 451725442, 789546873, 818574586, 88321255, 71441800, 404960023, 624030855, 847884267, 641623047, 742208344, 612975423, 364270633, 437080854, 487175359, 401274220, 612376426, 853995062, 797862558, 764201968, 27297369, 82215489, 100297733, 844447871, 360720329, 490222650, 505051968, 436602253, 317332571, 730757435, 106997514, 362527989, 623750056, 803900527, 995381898, 600104756, 121512467, 993724939, 102976123, 787292490, 148233709, 239475988, 671264854, 415489565, 605253474, 447857891, 2219245, 656880787, 742089881, 305152293, 931320391, 849585608, 916043366, 186969269, 874305529, 440293359, 890459180, 732586442, 430762872, 249858324, 133568971, 572187431, 649502665, 411459312, 993656390, 91453112, 196036183, 195021753, 999031859, 409583625, 476358163, 672179547, 175016017, 825731741, 607640606, 781859762, 259518930, 957912271, 635781340, 536115403, 737063649, 355202725, 552974103, 197846915, 408639680, 120653890, 614131033, 666669878, 246916045, 835700614, 331865146, 41452484, 97229661, 169412140, 632170769, 119358299, 577269592, 125163135, 368206421, 858515173, 455716278, 590917187, 518749759, 283957093, 123141767, 40546500, 304286877, 354266919, 513167071, 910515800, 218199673, 51812111, 797831708, 668681237, 507456199, 304157501, 672445030, 388903091, 876963024, 282505389, 17306740, 90601224, 553276131, 588707280, 796014994, 291358826, 124275162, 195583900, 792895389, 778778076, 856157008, 140180858, 712167216, 422467075, 29575986, 226478964, 707512522, 121071829, 324921564, 326022464, 410002625, 233893416, 984911980, 541364462, 408798011, 372542713, 198625437, 869472544, 574528281, 463549977, 196436049, 13053924, 862776254, 663683181, 551082289, 434136458, 340811886, 896518822, 505177015, 582653457, 54714846, 740133752, 572002112, 578033377, 959956795, 715140026, 797708350, 441501270, 937197653, 945043904, 105096007, 640128986, 618344780, 318934313, 712810752, 902923108, 932096298, 554269433, 865429996, 235005481, 776740271, 62876935, 876416443, 844435101, 246980822, 820773320, 4620981, 686414928, 673693099, 262449609, 513164825, 17788565, 159086684, 912339533, 331844657, 136453624, 972860832, 970171661, 711536695, 569394284, 639149926, 366089639, 704674177, 189206381, 695020019, 80283969, 718652073, 169592022, 136939901, 903509771, 944364138, 364220656, 517418405, 563484263, 415108693, 188173487, 654527894, 913405866, 341834987, 257760674, 485821812, 989932748, 374023615, 4641799, 469158805, 198445864, 616872619, 109805196, 85266588, 491323228, 631471846, 178143869, 328665617, 994070327, 363748716, 893046339, 653958976, 888271743, 162903301, 505628034, 23148659, 672970526, 914903164, 444624047, 754132264, 350271105, 336374455, 567935516, 56379500, 867165002, 982734861, 687442667, 128513546, 396125699, 419058188, 288209085, 552515526, 64488965, 56408182, 513964508, 441504167, 929609672, 460875866, 98412256, 72048688, 80146100, 486688281, 944996192, 548593993, 148450290, 762900984, 520596545, 847476239, 901228027, 361605943, 649795019, 44956546, 494938176, 727471104, 401438214, 12000439, 693479624, 618424712, 189414454, 316462351, 561281076, 445222715, 389718447, 563726196, 305990171, 666399949, 281473508, 257517755, 868143122, 76126897, 388884355, 565852030, 982815755, 697803217, 386020416, 482960902, 36003782, 177782706, 639360955, 343461607, 407237584, 744811379, 377510793, 971985250, 123845867, 628346871, 317870596, 15324772, 622652538, 767579850, 836703909, 274243607, 245257216, 346080411, 554386104, 173661955, 469167672, 672775979, 805022944, 738033083, 953606753, 420932286, 387642314, 312927301, 544727408, 677043093, 235066183, 765563299, 737959455, 323829187, 649197178, 466591243, 354684893, 769553783, 600169867, 126015878, 912578930, 908448537, 751443548, 64782758, 869749742, 945858965, 927700649, 195417241, 366765425, 218342135, 271039684, 988678915, 808789847, 521403260, 270890023, 45653107, 143862138, 2223705, 596645047, 704579293, 426645733, 748929343, 963907799, 333849739, 628385925, 871798299, 10802346, 389788457, 304733795, 85386247, 263954563, 543076917, 987186194, 499994550, 396429660, 327317655, 750758453, 122170907, 15579994, 663173401, 624726230, 441148491, 309302989, 999118031, 410370784, 908356982, 141303645, 618170149, 472317022, 241883167, 238371076, 664974564, 53394948, 678061832, 303351365, 868060461, 992565092, 990392471, 458046846, 502966270, 449705735, 116401463, 205136196, 87634324, 85746580, 262474018, 420448325, 186333339, 932982329, 189084422, 410594036, 995620004, 446982214, 671093834, 248201801, 709997569, 914882005, 173031135, 104211755, 968777932, 706525446, 914254777, 500037702, 945603186, 246160970, 426090379, 93810342, 873721661, 47608883, 350073684, 930391855, 20505484, 473521925, 741943777, 700577479, 545082122, 500067972, 809122877, 258519285, 277282432, 634388242, 688136919, 834570421, 324274899, 683315881, 529665461, 164396073, 872361966, 848847433, 117964072, 964087346, 6899392, 499559785, 217669223, 215925404, 208045659, 788310054, 259989686, 412815360, 357681939, 46173613, 543224374, 601563008, 481129250, 625777457, 412273193, 730681536, 129564105, 540955803, 391248158, 402025095, 870994251, 650941623, 163531677, 281581809, 290497373, 311039079, 835997147, 170688431, 707937918, 975415534, 609505352, 334976265, 659500722, 303188853, 980736628, 659075906, 533836218, 343177901, 98318384, 29366025, 247807382, 227862183, 894981439, 722697201, 862061563, 333672420, 255789005, 202304538, 716984184, 917089510, 970320277, 340191772, 9221698, 395303667, 238814321, 400895588, 153179670, 44852915, 300914801, 878528211, 751439950, 576239034, 255276143, 426038180, 90277775, 189104000, 772565113, 602143145, 870039125, 806241687, 204959118, 327833340, 316039021, 582681407, 69222034, 126184959, 726011407, 462559737, 749454813, 601329495, 849012599, 213151497, 339217013, 219432479, 452840227, 273729228, 215765975, 806934334, 165620550, 995282090, 211246093, 888354728, 6314430, 248618352, 366566245, 793337195, 52818036, 353684178, 256898721, 493666787, 962005155, 964203500, 424335749, 213384055, 842343703, 599819385, 843686374, 905293137, 438930397, 173981573, 816728314, 553505623, 609857487, 9373195, 678019312, 443295117, 972061987, 607068663, 632822529, 923355218, 101761235, 707947968, 319813941, 356328224, 758940588, 298577398, 42554416, 70977550, 206655519, 85060775, 698921138, 736883120, 300404492, 640758591, 935624221, 242395287, 509990769, 988352101, 467405319, 459580032, 869053075, 570534108, 784340416, 670684445, 539659082, 475511678, 509162982, 382617474, 720372936, 45237078, 655872761, 321353419, 856388953, 121261650, 281719366, 913421592, 445751827, 704589003, 704893128, 198001747, 854779597, 420549944, 558896949, 676240151, 759183957, 408359777, 493508520, 652275421, 560410837, 354750505, 349537617, 746395884, 405735943, 358007310, 809616048, 781039384, 371834993, 104198767, 276952338, 307088821, 643719698, 990618857, 13404953, 237596345, 618047007, 775319289, 492430457, 667772680, 51952437, 41940865, 613111346, 797733445, 824155293, 403664499, 870427361, 706160105, 437981903, 504964852, 793568105, 48220953, 655736424, 146570431, 37611569, 679866402, 537860034, 633952930, 209877715, 40122823, 553518087, 286909798, 360305566, 421094346, 694207326, 379985769, 573202393, 226161456, 315233143, 988108041, 548209397, 975066640, 741539074, 638668207, 770160410, 704087737, 341088682, 755534729, 351084881, 910818124, 989363984, 511395510, 772943715, 142603367, 376859575, 777928205, 275029436, 418653835, 449371080, 983764714, 839116801, 84977498, 477225707, 630693092, 687758641, 600086242, 749925715, 408908055, 859463460, 661466904, 756192716, 251661025, 455407480, 44603931, 469177257, 522875425, 131387051, 905989876, 98735798, 297200979, 138846101, 791910679, 635195396, 618467862, 659032500, 682024102, 655550778, 283108417, 903365827, 841128239, 348472609, 529208124, 322164728, 670395204, 553672228, 485415686, 309463065, 684138469, 304083844, 357908813, 440162540, 315642098, 840253232, 532892884, 220502344, 32129853, 347925003, 660605797, 225671013, 953747600, 48084179, 558482137, 809720028, 685628676, 639427498, 368961935, 272128877, 712878510, 914862654, 254974920, 90279966, 486249988, 324486576, 826839267, 384048111, 739076839, 268255474, 273089648, 509276447, 669143066, 644293557, 26528681, 979578124, 78928151, 938023182, 416832254, 480230870, 286163681, 295090170, 70052976, 138096066, 707369237, 369900852, 678899437, 375011183, 842278746, 375350647, 803268912, 490289085, 840446510, 537227573, 892654654, 679585417, 928546065, 734571632, 53454473, 977385674, 847303289, 448190564, 443681451, 640187208, 53720483, 925473810, 250658583, 349474254, 990140522, 86543711, 369411292, 144457984, 18534454, 706889420, 794610970, 613541931, 730556536, 96983702, 588349004, 630819828, 336347364, 706249525, 966613524, 923984923, 341804860, 372292108, 845598165, 84123764, 208309347, 441774473, 525912301, 315908844, 194132762, 788475820, 835167295, 566153430, 751721252, 401229852, 674713168, 532353523, 77632469, 642557144, 222474304, 936269133, 980620551, 428307693, 972912007, 434124545, 265569450, 754071354, 821013607, 923385224, 706930216, 537089345, 527131211, 277860063, 779030207, 760311775, 167664254, 109406896, 147530909, 965998493, 11295779, 497098950, 198023184, 976790327, 448091509, 427427718, 481363051, 971733020, 36128915, 923120129, 333721952, 88035446, 827914485, 988179635, 526726868, 162618037, 60619333, 274347793, 765853082, 980816181, 953568509, 739845515, 434251687, 769931181, 39899148, 123869212, 158292324, 795439280, 172082555, 655787536, 977857732, 661113074, 139451207, 160621216, 759148103, 51555999, 831377257, 774586618, 649162478, 459557982, 859284046, 188717713, 421510700, 959386814, 95176103, 832818623, 912112832, 653614000, 89638957, 320014180, 66912471, 181249885, 808898497, 673604638, 872298954, 563251025, 339852237, 231947272, 695479339, 155377417, 423938064, 397378734, 32410785, 179375849, 240760980, 359999192, 287216312, 391948864, 820452175, 82233407, 774568344, 337526289, 173192770, 300828867, 287944772, 871122680, 638649166, 196554392, 695956301, 54999484, 917518491, 937567211, 545716316, 138619194, 835584064, 547288387, 708059858, 280742541, 913433716, 183716089, 981078052, 8726152, 750967409, 613587558, 710076379, 294691857, 396767116, 913506449, 931136742, 413229884, 908515463, 723621303, 112543123, 720887516, 777241552, 255030118, 571185080, 945038867, 637128357, 102206429, 603926348, 718045150, 305591271, 225068308, 361513931, 707512826, 288938289, 269116324, 210215062, 866133350, 493797150, 648616850, 346734378, 279473116, 370279094, 666118751, 482956918, 49970649, 355750819, 448616034, 16732616, 785118237, 193036058, 78500326, 318233721, 442330201, 897897564, 418727528, 351401602, 128021743, 64190729, 635752529, 599070910, 925561284, 191306219, 37824320, 678072264, 449659270, 212555109, 372162533, 145678700, 370293600, 408850479, 176344194, 642277157, 246278045, 504680212, 29008655, 331939794, 309837337, 331580007, 129809303, 175480622, 799266310, 100553564, 670870403, 895525316, 331632601, 763724207, 246754761, 538553245, 501153882, 62562321, 440716443, 272156734, 170558858, 706141076, 580089238, 658682815, 96117443, 417807388, 113519183, 639368537, 400065919, 657113965, 918310729, 662876057, 174769053, 335543604, 975822381, 109218837, 573834470, 574128206, 890693728, 321181888, 251494245, 662150082, 895869625, 537108936, 941137, 254314158, 17265292, 63202366, 171516380, 278945492, 600799293, 971190456, 577436146, 60436479, 403952264, 433851903, 920206922, 553285288, 767838428, 105254329, 496287479, 756037158, 119405828, 179922544, 715310173, 303679971, 914766439, 145281561, 259997846, 365532491, 528671550, 553135392, 918293895, 270358388, 36322026, 299934422, 138299178, 95741312, 87205708, 177431674, 86615803, 757453380, 337341203, 600489337, 934348391, 289474459, 348968837, 408591207, 659040188, 759517995, 27200229, 608850193, 614423387, 563721594, 377731843, 54650509, 48666057, 602552420, 655233191, 712757251, 542918264, 327288039, 417929882, 511761726, 746693635, 650671534, 360821194, 458627735, 647704766, 545536912, 811702407, 739227086, 252864723, 530843864, 308515308, 394990324, 39051726, 615455843, 878943541, 779435411, 182169202, 29296817, 678915540, 155426868, 484415306, 477515057, 794511607, 230518268, 539756100, 50760132, 539541287, 318722917, 162780350, 621766503, 994503625, 794215500, 876962645, 178698996, 379993525, 440274795, 971871029, 161818793, 891477292, 64229491, 926036098, 485339354, 987310144, 78657991, 301273978, 51511457, 493394108, 222501433, 859054619, 865818727, 796461111, 230461315, 24656447, 924645322, 406590413, 724435932, 199653864, 876886723, 189394896, 377978395, 639762163, 415206018, 366203807, 115857552, 730458041, 417002505, 641566156, 573077463, 661341281, 311057921, 568529171, 247714875, 829162231, 868271220, 637545156, 978885695, 468870551, 691210915, 371624664, 205240478, 243307141, 738556000, 75770446, 240541962, 879152038, 288829374, 297755714, 731086592, 647020745, 269814587, 281341075, 177287469, 397225143, 843875584, 10720423, 548349103, 281657632, 822684418, 256633901, 329054124, 860632519, 305183857, 211226059, 588908107, 576566499, 795428791, 74045673, 442064211, 985937886, 257301628, 867277608, 506150149, 627232805, 140575824, 821354131, 415763872, 551012563, 830602779, 954656899, 235717231, 115698213, 276987141, 28463431, 432763895, 455648027, 592791943, 795943793, 447882805, 299701804, 284635031, 95399554, 432693706, 499240800, 268042594, 377812909, 448726957, 812917528, 55268715, 406813457, 783379732, 110299831, 608777105, 325820356, 575875663, 345383077, 268581643, 664134519, 891704432, 33588181, 237555799, 823352862, 560579208, 634136911, 832456612, 777484516, 623750032, 980393779, 534540352, 469635270, 670771446, 989058021, 583251232, 231860007, 704645071, 75667327, 700877508, 220784493, 773207189, 401817434, 973950758, 276981912, 219804796, 112541903, 386676357, 390965775, 737358837, 675651234, 596160544, 545488026, 876472650, 31148164, 288604889, 588094112, 522178373, 971671429, 792141597, 731708545, 890402478, 599162114, 836535653, 835303135, 345310767, 284020826, 285725989, 180624172, 518100188, 400670717, 562634997, 133400078, 662057787, 655093699, 441965273, 603214694, 783210713, 854600952, 883285386, 90471009, 871603144, 705717285, 791150727, 3046974, 992291954, 265339517, 402100166, 932778872, 41246238, 651855194, 426351904, 236570599, 971421379, 536086636, 147164568, 877060831, 876520580, 267314609, 212163625, 855789240, 616502042, 57403665, 868403835, 779942405, 270147401, 767938764, 327881559, 952840016, 623046284, 489995535, 247398813, 633183728, 248132556, 645407077, 535234539, 797636359, 261955501, 795292490, 451685333, 661892131, 131261825, 934279728, 905389301, 91513155, 463540868, 557540286, 576933742, 603506184, 743236618, 389084373, 900174734, 788849873, 600455506, 637167962, 855976252, 314336436, 73901858, 355118786, 360679297, 264843971, 723716451, 465264849, 614440198, 8096358, 319401491, 26104038, 466391983, 789727267, 435801242, 82770876, 83636291, 902081376, 652624017, 776981435, 116612567, 768340398, 76492646, 828593660, 763965420, 769137942, 375499090, 502552588, 543774199, 373939520, 414108858, 666831108, 188107135, 784329079, 564860767, 626931349, 653167089, 235765231, 501561950, 916465243, 771524659, 12586771, 113777759, 21263503, 811295570, 741767401, 710077068, 839310816, 781958654, 91298905, 756030071, 179056601, 69998034, 162957762, 108200613, 470434275, 311020688, 594344597, 418713573, 295379432, 74544399, 187008632, 302760563, 622632187, 726639479, 350021602, 246163574, 966848464, 862177225, 747589186, 882943647, 208776012, 402184160, 805215536, 126566328, 226522219, 513898173, 116197083, 93171898, 46258155, 552968738, 857948919, 812688414, 122715537, 992167063, 533610085, 287067334, 458451057, 409664950, 458995259, 121350032, 741277002, 468946704, 634824875, 663046513, 867876479, 546301291, 85185180, 40867285, 883414960, 3714136, 768428063, 563849605, 280506204, 370946765, 466410142, 168186769, 921913214, 572887961, 174863643, 596714263, 210325011, 9314519, 969848265, 999190316, 272949552, 474298602, 910844150, 389317654, 639001003, 495298467, 382589012, 833518815, 708703844, 625882747, 490432307, 812633821, 9355725, 553171636, 206480780, 277619881, 940418200, 986787085, 769223417, 555267035, 263714466, 18784083, 187764967, 340602065, 111172952, 600182648, 236056629, 403758176, 6144386, 321550223, 167502567, 586585376, 510156977, 129408915, 748975306, 782386993, 545988257, 451500249, 556751061, 576151702, 67989906, 842288916, 432719152, 434932575, 547799459, 643638394, 30359108, 313732742, 436563454, 715188309, 390227762, 125483610, 840889392, 713598196, 718623191, 284770837, 459232784, 6557511, 642673484, 644168306, 105717080, 229526330, 207630088, 973362655, 509717688, 20598438, 638317999, 677818289, 430927803, 350762833, 329803854, 338066278, 361398156, 133980828, 72386739, 51123340, 209686206, 103462785, 586955407, 445620649, 339816761, 769570467, 331079507, 673857758, 534167457, 434754968, 785512746, 691381391, 316124475, 890403661, 624806118, 433850340, 270985772, 424775652, 293791928, 410905424, 659030203, 352651410, 447467133, 461743049, 749679684, 293590961, 931961374, 780784124, 14744686, 332098779, 848370887, 730433531, 634018458, 176443895, 717365221, 132830163, 965733904, 245620751, 239615615, 499717224, 861886846, 585036267, 901274051, 988881293, 396710353, 142791794, 711665581, 469665203, 233223261, 504139985, 13549732, 401900828, 51899483, 659574567, 296934629, 54341542, 822628867, 977900622, 866425832, 95322824, 865375162, 481653939, 640118639, 546398597, 787928983, 153116190, 7890339, 837179917, 987190896, 414857312, 99048215, 412199189, 325786520, 113690598, 690333639, 256139227, 326538858, 118944527, 373799282, 138736325, 743864324, 618894257, 836107323, 584632087, 869429017, 462105091, 765486256, 943478841, 228974191, 159794583, 386726175, 161282771, 439775362, 557110513, 120091090, 162756608, 194978562, 263978100, 906477531, 487002914, 858595354, 11128778, 82920486, 637605959, 541478550, 163990560, 237506834, 332675752, 887570784, 976714717, 564615134, 904860238, 360354602, 515896080, 461277188, 842390577, 562564595, 643536648, 318532347, 343164702, 441369742, 806963165, 618022631, 92791139, 396493963, 831252962, 636315725, 781073868, 731243977, 557316963, 374673606, 188685812, 551200660, 359299322, 514257805, 232447154, 279581939, 296811393, 404543333, 185298756, 876534483, 946020637, 159756971, 149591198, 420356938, 122235137, 285046753, 671542840, 609831342, 109655895, 273289923, 599499080, 728468931, 962494903, 824209126, 233753018, 699428182, 42945786, 330547966, 251344057, 874310721, 445373735, 383110298, 406768097, 719931186, 795631208, 833844968, 61006805, 244420387, 21449557, 912478578, 215426564, 106813455, 515950828, 2914751, 911035306, 941425048, 846413766, 398897115, 304163593, 202396511, 454698480, 515150333, 250383836, 897226341, 10849447, 698882713, 300622731, 772958088, 546566715, 649691677, 621512880, 661107554, 329290799, 555593004, 322134199, 404818733, 167399599, 572535364, 764061200, 191726217, 494304860, 138671949, 823697097, 152084302, 371449896, 204396184, 624766429, 513129350, 301193550, 537867939, 396124409, 219588692, 964205677, 439517392, 989598665, 388522003, 363776039, 396065424, 909649020, 375066434, 937359922, 466873352, 131928877, 427319735, 224029730, 359036787, 287850565, 206977132, 499497275, 109630211, 268732118, 348934305, 384331743, 336334831, 927902017, 751100875, 777044861, 41026251, 160033630, 992028455, 329441096, 655503647, 105077357, 465940353, 777933302, 535127989, 123262302, 238540346, 41676836, 834099172, 411935566, 777467875, 664107237, 152717713, 780407217, 824242724, 113402742, 326455324, 827948385, 722854397, 175427269, 875393760, 539888382, 663175279, 899490126, 816901135, 868826640, 697839142, 105986992, 227499744, 463038007, 166642760, 736744391, 306030301, 982998451, 897274723, 751874378, 390424526, 226205722, 992788828, 930803562, 738755090, 579960456, 967630497, 562230231, 689477639, 879085704, 769267834, 386301566, 156146970, 58161548, 820243881, 388321741, 714461998, 370600975, 914368008, 775198736, 637285907, 387537422, 210325548, 308849245, 874114449, 87864165, 773758093, 283365288, 851800500, 219209400, 806983471, 184858672, 263149355, 277866284, 911673464, 763529536, 331472970, 329848563, 299489443, 41792417, 34674845, 520203229, 213954546, 446582179, 449432098, 805394810, 206893201, 153337902, 314547708, 529079165, 810036622, 351330494, 364306015, 71887071, 128022064, 169803339, 274423528, 676652169, 923073549, 417507770, 423557583, 297500000, 329529966, 92409938, 605648515, 355671204, 694658521, 419762706, 8140361, 42342403, 48714514, 396745722, 507775512, 949782029, 389710784, 116665317, 29726704, 281007213, 862273421, 163223781, 230871548, 947006787, 35813445, 928151802, 955752783, 417285858, 118097085, 177195936, 407388562, 758458654, 280070695, 828471624, 891060444, 786882692, 116006488, 196584612, 708963433, 103098665, 594208228, 959428928, 469535450, 686679120, 324234248, 42345272, 666503648, 251706353, 8303103, 370749534, 518276445, 530350986, 732725001, 922222392, 806082634, 37313033, 507794333, 98053961, 576909686, 370556621, 410459451, 298117869, 421638294, 938882547, 291332587, 704790360, 743728525, 283216145, 703844667, 26723361, 868505140, 257916643, 601849262, 772205879, 237754601, 631392290, 900153531, 563649373, 335047330, 967887412, 78730240, 152661603, 194184373, 249971807, 987245665, 157084102, 614498694, 898201098, 555881854, 694702349, 342823079, 352577520, 245082624, 1581677, 723390937, 70142527, 2065162, 66099391, 472867402, 563477019, 431419881, 464260960, 255367496, 889304308, 561298268, 912480395, 111708649, 321759591, 143364510, 764953443, 364724436, 452339841, 819084851, 20560233, 917783541, 136279261, 572393877, 445768943, 219875492, 508269450, 61087201, 467232008, 307179481, 635087817, 473653196, 439386763, 135486545, 968300345, 175020991, 341381500, 148472514, 886093849, 151509505, 991979317, 549998682, 223982027, 257940633, 764216406, 595741274, 337091458, 545549109, 971069844, 774378765, 566959720, 437960496, 933240778, 375813240, 982487122, 224582456, 563632329, 974633371, 16350761, 434038189, 775509790, 533381137, 857928627, 907987564, 857762284, 91439263, 802654194, 663807112, 203541530, 788653192, 920691951, 110271210, 495419496, 414206711, 469728833, 276947197, 363590632, 902926807, 204036779, 316264410, 961761373, 665282294, 263956003, 747042645, 613558244, 723708381, 543111765, 350451526, 277092971, 933093340, 206628597, 765961159, 531754018, 679670183, 894414218, 214658020, 781429161, 324586529, 30982263, 464632855, 37337237, 707732187, 571986934, 463613958, 550929066, 147642583, 879554088, 64120354, 169812065, 436756204, 554519762, 919843496, 214172941, 827320015, 263110272, 46001680, 958207461, 317565710, 136140038, 518002376, 566216856, 885493377, 277158913, 726506286, 604307224, 177720503, 575687020, 298910839, 569287344, 6659238, 774805585, 621951162, 746694866, 661661024, 282117922, 261971274, 512721575, 712351480, 214715443, 207749189, 14825152, 593548783, 2440577, 672450624, 602174900, 411391093, 385722512, 481697722, 964379736, 380398585, 62368687, 238353061, 807525634, 882599823, 461025285, 121590738, 696666474, 775549810, 366426458, 773153210, 105223235, 580615927, 850827911, 289779820, 180025989, 701674271, 973238422, 217052557, 344211654, 788131078, 456776969, 120546208, 4151142, 470571732, 839087374, 807882719, 954480260, 18901838, 326160095, 570848513, 346037180, 188165046, 693004402, 470944888, 312719166, 346392315, 135724206, 951402425, 475471072, 971887670, 350734566, 942689093, 483432758, 586784451, 220372237, 205203689, 846656621, 908139981, 133123166, 52212397, 626581154, 597576475, 227222877, 992451347, 267048668, 326846905, 106528960, 913826137, 932982784, 612674828, 811130890, 825721575, 786295998, 661449169, 22884355, 376430100, 481655693, 972878561, 601704476, 529260878, 820013367, 178932192, 992813835, 421272263, 266647573, 909722184, 717026967, 929731457, 261160402, 801633749, 546189833, 890026846, 473377365, 721438873, 817172228, 45095059, 401162276, 388027540, 424299236, 781860075, 539161282, 452183980, 259740568, 134696461, 412831179, 449129845, 575514717, 19778899, 94524438, 151891497, 233349780, 774585770, 425401148, 412720002, 137410542, 656650694, 321942738, 540637815, 310440399, 953630048, 97047545, 23056736, 981220384, 419147698, 820246722, 697279542, 654153199, 2948593, 105720717, 819028158, 805043311, 692173736, 559607950, 557970884, 541729264, 693975971, 667336919, 787096475, 751413012, 160022918, 597968589, 399188786, 59675475, 644482128, 330593832, 613232154, 767553588, 779473924, 434196055, 346508558, 220071324, 522482702, 321578510, 356229910, 291285156, 970719365, 340806269, 666899715, 594829758, 698141445, 890629856, 986722628, 487223836, 970728538, 568760606, 787935348, 380609891, 99639588, 971497787, 50336317, 375971610, 65105556, 945672928, 345754444, 867724635, 718456868, 20637232, 81791460, 889397552, 300611358, 478961809, 558909547, 125109835, 642381054, 418463176, 11414284, 146926438, 97027493, 381831349, 97869899, 716351583, 50241917, 565520004, 850491753, 162404019, 462351549, 209109719, 765774246, 275217973, 762912002, 857616643, 540500148, 441160088, 198082320, 730418806, 817295308, 530888892, 865312105, 753610033, 563101356, 448585127, 628679502, 153929301, 371488309, 869538930, 747079502, 257259766, 780553392, 635300141, 67956686, 359402, 187913987, 604170339, 453050956, 580602162, 80638792, 655549558, 806759797, 745612777, 814636492, 321772048, 244988733, 672940104, 920525763, 794186300, 408789205, 771783587, 974857333, 792249510, 550508217, 666160698, 886747961, 3052019, 899479072, 116686650, 987652372, 448096120, 986821913, 565774851, 757501927, 294125096, 248167319, 93058107, 925534535, 790477515, 428242946, 246772316, 582703590, 15189108, 371976260, 970108103, 438054841, 702919363, 932439418, 300158073, 531474245, 996048716, 279843638, 210112238, 470247911, 505258417, 402057377, 465933360, 652274089, 965146690, 525777369, 319366556, 471748709, 959957656, 137608780, 820266493, 853381275, 83310252, 960272705, 576772574, 797456418, 894181234, 303395279, 284895517, 570331947, 799404076, 232324999, 223812397, 286473527, 830930910, 209117239, 764237971, 727706954, 4386967, 127291858, 109711383, 109924955, 563625930, 995564796, 875396912, 39840585, 923549420, 409728682, 806411435, 718349646, 86210966, 148318666, 450281598, 647253338, 204766448, 961602013, 423192701, 562655686, 207441755, 938137281, 535311598, 85336986, 777315832, 738803557, 527397568, 751456547, 428321883, 335566231, 774245296, 129250638, 602359189, 203904506, 718493743, 142657418, 543246995, 364411826, 210704410, 579320430, 791632602, 692883495, 559988341, 645602654, 326481139, 460620155, 690334557, 62216840, 538594234, 961593030, 208806152, 970506244, 255593985, 898700491, 868387478, 216374226, 103286192, 600232124, 820955052, 844462259, 784392646, 64845145, 606769536, 928900605, 647121477, 57346889, 824827870, 773209267, 456016136, 731629115, 610813724, 649232991, 890595155, 597258576, 570158461, 168774108, 869373154, 426529152, 848174835, 669149160, 547790336, 292621315, 205098341, 430705284, 512758036, 194914601, 745912383, 248026521, 317964204, 617419374, 517012733, 246608553, 510698818, 610601381, 418773372, 749741437, 266384283, 53032518, 561777295, 989902076, 23517476, 301394566, 285724630, 238079747, 170984421, 871806686, 264255740, 300589767, 197690950, 937876962, 654369314, 885345665, 803158653, 562977052, 617996948, 147861127, 940969091, 373576487, 231362555, 106285543, 760058691, 763185154, 534664057, 957017019, 300806828, 301672870, 898235400, 160351858, 737978300, 563277807, 652960544, 26446438, 300526577, 337019827, 169692615, 464451528, 498383000, 695524860, 443622530, 637379759, 187131053, 91567940, 174487717, 619723997, 547364236, 667077769, 861990837, 269656878, 98239251, 409722580, 93214370, 510934257, 176253950, 770498901, 33225028, 494995430, 666720890, 477902856, 379434004, 755291533, 421866741, 346000807, 664928344, 786808572, 917262612, 880619154, 32426004, 165926654, 610190817, 266970212, 401056129, 103510962, 447074635, 870941425, 62380403, 547593384, 302302810, 652824020, 606093356, 240644399, 875381852, 740291944, 253559985, 606696884, 151000920, 467331636, 31202911, 155490673, 663817458, 377999151, 1202978, 850331938, 74869728, 551883914, 920830669, 923465842, 40369669, 901524141, 598161442, 245959235, 406343396, 187197659, 478358674, 818902748, 14852300, 870811099, 602230009, 475779198, 423563725, 964897639, 546031067, 252973472, 853767649, 282542915, 465365034, 541808252, 337768915, 677603800, 310052899, 817647524, 640306506, 601043822, 191099917, 852178392, 827656916, 316167971, 928140873, 815408675, 572884737, 661924736, 459582575, 899910863, 381092208, 589274959, 293344719, 812818281, 613019060, 821756533, 787049947, 774637461, 398814198, 127042689, 515828983, 318358769, 615692647, 163869257, 163550962, 721228118, 208394584, 430286796, 777236245, 748942905, 479460062, 540690464, 120804780, 780179181, 266690257, 34139461, 882208391, 906235214, 37405308, 599460695, 666325146, 768034167, 485328521, 66390264, 641800235, 923682188, 773137668, 368686628, 742021801, 802984996, 371801825, 680713585, 811156106, 208512914, 730599765, 569167144, 35826841, 20867106, 634456305, 786126635, 476224625, 489368764, 360028860, 628356821, 513652489, 214137796, 189169816, 433563221, 55664707, 685140934, 510181168, 538881087, 688304025, 781897878, 923653472, 908505969, 728665047, 592314449, 699571796, 914973404, 608448117, 479035443, 189275097, 839779111, 64107724, 340321731, 375684040, 179509274, 131653792, 382961195, 585427756, 255333041, 579264099, 159186886, 852471505, 913225043, 522740304, 414512485, 270370471, 516225795, 947450214, 457352891, 204656580, 520979202, 280686702, 458579057, 185004457, 417961308, 535247220, 656761047, 356469613, 781365628, 618954957, 723560122, 567864708, 315320993, 808384131, 672059919, 914014486, 166343283, 365547589, 502332140, 356451832, 956440540, 472717424, 953039619, 946227621, 460497152, 153948692, 512257834, 389153918, 592328096, 432058417, 602045197, 632412603, 14158220, 618262499, 374105115, 986008294, 726378960, 775017641, 773324952, 763671330, 837984636, 616220226, 812066444, 892565384, 514584655, 645593685, 621139244, 868949481, 564036570, 250634364, 314848196, 715833577, 832753563, 81680222, 824483448, 61700502, 605080294, 369801760, 3248820, 526763027, 302852710, 728346284, 721885740, 653341827, 29103960, 118931899, 310095724, 981698283, 210061538, 131112369, 614365487, 638235870, 691653944, 350125336, 15930801, 926625016, 733354693, 149756121, 877962137, 448971267, 19573197, 938463329, 192515095, 808654488, 358853301, 474154394, 276651061, 570640546, 46343989, 285044464, 288713843, 983609851, 734622337, 200242622, 209942700, 596271683, 401003114, 523245245, 537724475, 814400904, 317495439, 43697263, 365150297, 588583722, 75927967, 379301571, 134304407, 552445583, 398283575, 383323473, 441254621, 324484825, 223886238, 818448918, 939767640, 198537723, 506977989, 230098251, 18905789, 430886078, 679913389, 380003133, 399880487, 190080471, 628244236, 217154135, 528452494, 6890056, 638650739, 115873244, 797582810, 766259355, 955978037, 158401294, 674409560, 283585397, 158906637, 146403289, 915214954, 957550233, 326039577, 360452432, 321011519, 2271982, 181069798, 257118254, 338415423, 944673295, 826690248, 937723918, 743923088, 41214603, 88741218, 250634938, 998224143, 388044729, 759997979, 330837383, 301063574, 269271290, 610465667, 915317784, 910633214, 433324256, 882489380, 158966296, 728343707, 402396489, 615795273, 718875292, 740201908, 48813943, 276853870, 624174156, 924197343, 265269960, 700665139, 738142107, 574460402, 508448722, 689801229, 973148615, 287106921, 882765074, 929925575, 863635172, 720956675, 321585424, 40249219, 551874871, 172904248, 193861833, 452709497, 967624288, 686710575, 423694170, 987596292, 49530383, 55706228, 240817895, 63003905, 25602046, 775352126, 147425848, 505025881, 539470670, 526853730, 634113208, 251251349, 548832878, 46972559, 766851314, 715350392, 398730473, 374668866, 757554316, 720067928, 380650405, 314335707, 768607525, 831733223, 730404990, 781085386, 672882661, 63771359, 929777319, 364258032, 546303160, 374900480, 497716982, 925827842, 634815625, 835725471, 887638937, 712103599, 987654990, 515774225, 673572914, 259503703, 550813538, 510465757, 459574870, 192608702, 489027698, 486418116, 216345600, 110869332, 878077053, 969185552, 368650433, 540658942, 954034723, 912064423, 853439231, 53774917, 451903469, 370749863, 818317926, 640556497, 664659507, 208616989, 723908874, 111773710, 886305277, 849163411, 936529921, 97583656, 764433319, 342485953, 48696074, 241572854, 354350611, 492572847, 6078557, 967198210, 626354288, 441017580, 192944363, 135566638, 688471103, 820551076, 656445780, 575978498, 809356074, 146981425, 178592106, 180997765, 579889945, 356524849, 810104366, 992376595, 315395857, 37531820, 196983858, 255551005, 257767661, 862669882, 247940827, 434180160, 27240242, 289516017, 589001461, 637223198, 739789738, 577989959, 209849083, 116895602, 48804747, 273596560, 914641724, 654110642, 732540679, 264392763, 85173298, 848622698, 976334029, 478496915, 517058824, 778912631, 589708062, 227467890, 541348094, 863039552, 327126703, 291819267, 418851986, 282129386, 17023297, 602317448, 335848811, 88596799, 724180108, 215200080, 931972076, 592828021, 181409274, 712827760, 514842050, 97446384, 810799975, 948801714, 822021087, 686286006, 498486931, 914707295, 915983801, 768745901, 844711223, 102219035, 644702811, 786199675, 944473435, 109979896, 729930971, 509152820, 772332834, 171056589, 501838243, 224958778, 216415601, 936713966, 457316493, 404302522, 735425814, 560349465, 610136811, 898307910, 505826035, 298770609, 528903767, 339650430, 35783073, 331528708, 166249046, 237332526, 460600553, 997754824, 223074830, 803106273, 937338525, 30113373, 966190404, 810980292, 752102314, 464505838, 555464487, 23556330, 647539420, 386012733, 574372684, 183585083, 730136389, 361647425, 999253102, 527034774, 857676502, 834266351, 231932994, 224105359, 230657773, 556421691, 577209207, 824039076, 989821104, 411704709, 647836427, 114715376, 840987758, 951042577, 4936769, 331904490, 21480228, 311113193, 279590938, 423408622, 841866910, 679459443, 46368475, 176618601, 377373695, 533830484, 218221434, 228695031, 560027837, 319567975, 216302020, 869388586, 578944768, 744960178, 924153841, 40357448, 260764232, 710845380, 418809155, 846798879, 287325867, 564900335, 713704625, 376532438, 63818582, 979370712, 397798810, 5980722, 919992843, 763963761, 936539272, 901980033, 942859306, 796338703, 886994369, 162666103, 492386887, 675311826, 246432248, 653307709, 272302021, 499504893, 912510703, 627343985, 168143899, 422731860, 314748579, 341873090, 99848483, 669244702, 506922670, 420125015, 51756244, 994679178, 735212569, 275946462, 24281534, 643750813, 266049893, 280883705, 724129118, 835280522, 320330683, 321563824, 515265244, 694192290, 451974424, 507323235, 502305595, 290029369, 828753335, 230421213, 211829755, 145230, 345855048, 18382634, 744155929, 121622810, 560747409, 190422595, 894866428, 251454281, 423491752, 588007420, 198007123, 174124940, 499390280, 656023163, 409183636, 507546586, 512257090, 404463066, 113618359, 94905315, 339141806, 608432500, 626714441, 476970393, 511674116, 97125866, 387824398, 189786602, 191286372, 762191151, 219495580, 128366919, 466504380, 862290760, 166113136, 78169848, 137764192, 826901875, 500398471, 84715519, 551185848, 849249217, 377059285, 186989719, 837151743, 679352061, 605199527, 952699587, 161141844, 292341651, 347312277, 434131217, 716140098, 249965201, 834765696, 957953630, 40000941, 618083245, 176434616, 493673847, 421771501, 371525732, 152188433, 698130054, 736373520, 469294158, 308086282, 245728474, 729111515, 709441900, 840624333, 371204511, 864938880, 167749467, 790620678, 657140258, 882137117, 710949470, 634445306, 307676433, 885983139, 769168263, 250899457, 130777882, 141792860, 846443585, 57941922, 138209788, 896460309, 280301418, 755777096, 280008293, 577225435, 7517119, 990452384, 539995974, 526523154, 347023029, 591387882, 987375812, 605372585, 827613542, 537214042, 75839524, 321669707, 205470136, 863383153, 271152564, 654641744, 571280878, 854367446, 26191740, 906849096, 812590967, 638784816, 124691245, 571928180, 833693661, 375629400, 714314342, 768527695, 762263362, 377094552, 120351782, 843356478, 145717040, 190842080, 832296543, 59218614, 566849679, 162811751, 212656248, 135290567, 657141256, 111623422, 115292825, 306910284, 42750062, 2294236, 985985068, 823244797, 539110827, 421262627, 341980682, 883953931, 314791370, 462522898, 708186504, 602648918, 175179731, 159400643, 77356647, 933858466, 859478758, 687507916, 37253674, 294447218, 418081771, 872335120, 351290082, 952587157, 29544332, 851041854, 392605690, 818210406, 347446231, 662851004, 24145563, 697555899, 508510248, 987849630, 878363576, 430377317, 949015413, 952004125, 152163511, 967221117, 835628271, 835728424, 556102126, 257938836, 421221023, 186472036, 287195340, 11031171, 181017789, 490854205, 885244784, 477732491, 658181975, 300188279, 273971313, 960704055, 17048340, 322591827, 242894356, 823337876, 603343602, 933065926, 880936497, 984954628, 404415165, 961011953, 892387539, 662143602, 82465011, 653479000, 702141920, 866148049, 924447282, 849975296, 387917521, 652829049, 683691166, 511694704, 953716473, 314941498, 559914515, 468345218, 484602363, 58531181, 307704500, 314581623, 328153407, 867575999, 194936018, 458687093, 801076364, 495330258, 632580119, 976583389, 342176143, 80249886, 535040574, 862714958, 221975520, 780449618, 556275456, 696437389, 874871775, 418254240, 690569201, 961902370, 427605618, 690276721, 902685144, 660158019, 984417301, 489074124, 537903403, 357399153, 554302351, 426132482, 986872514, 245327955, 615067387, 636373169, 480828608, 989129537, 642995815, 198596650, 724647031, 244765912, 589959226, 543462367, 469758901, 154753991, 396622178, 143256623, 291482039, 817727147, 3883586, 258535221, 47502251, 203053484, 366918046, 929597054, 52758824, 805739561, 257902284, 276663370, 959221961, 579739676, 875186569, 730292922, 845638373, 39687089, 553260390, 32535734, 172826370, 634193348, 558251883, 545262252, 652085917, 128145314, 707848583, 683068316, 350846508, 73405587, 90595986, 56982108, 833244158, 299625395, 424705524, 365045255, 678313349, 833265268, 70169099, 28546599, 937570140, 240748795, 868028244, 843984050, 261344791, 788613100, 253719026, 910562123, 136973095, 329320948, 925494989, 779421653, 943617937, 426114188, 780488726, 174793236, 353858311, 315258846, 47681715, 126074241, 124162051, 165312452, 555541963, 427197970, 889100463, 398592856, 435029457, 980142208, 793094280, 873611745, 534796884, 409874375, 665869714, 778975291, 15528443, 561370695, 349165833, 683397191, 618637591, 412619063, 149807217, 476304807, 33520691, 536105909, 566393069, 395875512, 869054700, 159711318, 612301493, 642471286, 456373054, 839172252, 858558374, 336204422, 864685751, 199573819, 655842029, 676659119, 492855996, 735886024, 329764554, 339019756, 130321880, 937405064, 372629162, 931806245, 129699836, 993921352, 77840251, 436367102, 885554544, 227107447, 612672540, 356698114, 814098391, 544970994, 955806053, 821402835, 920406057, 488499233, 704688636, 175530048, 834014009, 534997173, 779044760, 112657841, 667439958, 371291041, 963884032, 893918289, 117387609, 130764825, 21708697, 794431324, 177030862, 617195862, 250776985, 904626163, 825998380, 52943670, 401240976, 115409684, 714572197, 143630282, 377354458, 404839938, 457109052, 624974094, 671831731, 617462901, 10604849, 776572485, 89516745, 74293073, 281087007, 459477933, 676013262, 840165776, 806153620, 719700577, 840450742, 902058025, 800439150, 289190466, 89998853, 681053496, 719407377, 98554564, 553992365, 747374569, 377789815, 556233103, 938442849, 287949838, 892748688, 795399657, 779603223, 179153493, 748599429, 791802503, 393764153, 981291959, 841022311, 856013625, 181716128, 802648115, 398820034, 750486446, 875448556, 636662647, 335737961, 118767047, 189748706, 12298860, 812059362, 233064527, 403413819, 337898461, 646893973, 945840372, 85856341, 289550623, 855445134, 293481819, 926661040, 783624586, 669737870, 811100921, 895138898, 221521220, 21105195, 897593500, 140111528, 851828413, 432696519, 526677611, 982958525, 323677930, 679746345, 245335250, 831716772, 314849655, 770539631, 129837136, 310037644, 334963148, 47583262, 286562790, 723126761, 51422184, 531846349, 944541647, 368222753, 670360822, 275202717, 109172990, 377871173, 433066820, 787953496, 874010044, 526915618, 29439658, 47354278, 92186370, 722560253, 205305795, 645401961, 256052171, 627093163, 954423447, 676159445, 129683385, 696822628, 222905759, 687746383, 197658738, 961308477, 507262524, 756156474, 371246817, 253041316, 940499370, 570288010, 56421608, 616660579, 302185342, 770265643, 875760857, 246179134, 837507022, 793148263, 355122724, 579406104, 772009096, 755884476, 215812498, 202760604, 125939614, 639466991, 252638214, 808966455, 784014732, 698380397, 571069341, 977425208, 33051139, 404994290, 935724726, 261316030, 875148697, 839205319, 742750397, 447397739, 156259168, 249805310, 215223673, 706360604, 285160064, 491149964, 713854132, 937093998, 709643196, 547818809, 303866769, 943011578, 538596151, 660605911, 521771604, 503542987, 791743884, 682370551, 612165726, 303368810, 882225342, 475927449, 622250219, 845778530, 700640048, 528841406, 830418693, 675135780, 535671387, 129006361, 116351356, 564544035, 932097809, 669583433, 754952510, 361367724, 186601698, 413880241, 826474121, 276203797, 918128869, 249712507, 63965657, 807484413, 719311328, 981785380, 608178879, 755579893, 445365947, 51343312, 159345941, 226681689, 125809993, 529408891, 167316873, 238728057, 903533930, 403849818, 372525681, 580311482, 799561418, 693240986, 797446820, 938963616, 430272884, 404297008, 471710039, 347465475, 657045828, 367931393, 632925403, 795576940, 928588820, 75909946, 724561553, 52912442, 762659618, 323284092, 785401801, 87010651, 530118229, 253743588, 818093099, 277494613, 14108788, 344283264, 592400270, 309222475, 199468786, 897284452, 4318153, 643881543, 121059906, 332377461, 557895463, 974114508, 154223342, 748269438, 460282083, 872387065, 970501921, 455940713, 4883938, 249470239, 659629555, 959348774, 747039175, 563019267, 928950515, 968926837, 806791734, 734394098, 531686756, 657386253, 719818870, 16581471, 38481585, 874782848, 195876195, 995052808, 972015240, 459603210, 536004440, 255601172, 165700720, 623222004, 901890848, 380717359, 206763149, 96354281, 991325895, 259922751, 901747563, 739158418, 349254107, 101764917, 537543240, 432147591, 822930523, 441286442, 90873668, 544948702, 813652621, 545276857, 499305218, 666432523, 124875155, 357416938, 549619336, 608176945, 986363991, 623140142, 696796896, 443288967, 885071637, 863712155, 926714085, 849047961, 114119616, 593017223, 682376496, 387139719, 398853231, 800901894, 131951818, 409699499, 969705763, 810354986, 434544928, 861360383, 939798518, 657021489, 285539121, 63310474, 138291423, 376469932, 128701490, 620985969, 412312368, 560981731, 979640361, 695013802, 443463364, 901172140, 155808342, 594685398, 569805699, 737909985, 179654197, 930024273, 227768532, 402500583, 787928336, 457495034, 30445372, 738772156, 690115520, 475850775, 148784300, 284991895, 700305509, 814596833, 147289365, 448538638, 327574096, 530374261, 688208712, 94299390, 986169391, 395287674, 350308057, 938414427, 947032501, 904127128, 142303010, 876574404, 172162837, 396753057, 886781005, 767697791, 816666407, 952096822, 824011386, 266662343, 698711748, 314951894, 883745992, 944218935, 25578206, 808587035, 797414170, 431844708, 624650999, 113935436, 488677946, 798388216, 881513976, 33348892, 155329647, 532899391, 986755456, 909854243, 450511590, 131088400, 922982041, 617460689, 73493607, 794872935, 985163536, 637531591, 780726120, 957304953, 56596736, 149541747, 915816336, 272034283, 306702096, 633924846, 97520842, 633645848, 345495241, 509722346, 797111981, 187579867, 30311861, 249391733, 383945935, 532180125, 212543406, 982261028, 384820052, 538956335, 411375851, 585975334, 725815894, 389785224, 818069680, 925349379, 888492522, 756418002, 659524643, 309515938, 391644579, 785988076, 267471504, 221771908, 74249329, 942943888, 554790450, 697380679, 780815205, 872672110, 893534022, 817906467, 128555416, 375217041, 844021679, 151957268, 844953700, 37284326, 568418666, 333253781, 385086758, 503943299, 296898349, 732772615, 773138144, 743711733, 313044789, 628413434, 403714264, 25258278, 96180037, 948500042, 48180561, 57278286, 17550169, 118171405, 124622023, 393685638, 132855323, 603631068, 30882764, 345525286, 529622693, 850125481, 52373887, 723467927, 175565120, 217879031, 634403661, 219530523, 725241749, 927004793, 86381794, 710673175, 588965460, 493708448, 270951827, 199828457, 173859784, 383374200, 14949171, 262133267, 319712133, 512756161, 799533049, 792656612, 744629523, 598129383, 978409470, 79978090, 487803020, 256415570, 220996727, 651000591, 736723553, 293905856, 134582332, 514809140, 245082604, 520762209, 688667446, 654363382, 670443926, 152663614, 12143697, 169550936, 242682785, 726971880, 949007795, 321983699, 609275753, 532221004, 796849476, 194319362, 807136924, 331654262, 81118988, 541249737, 797000145, 90269248, 57974030, 971027708, 363948313, 321951285, 98447824, 890541482, 57376644, 948911091, 60395872, 797011125, 720766111, 630837950, 684267868, 383272506, 881844627, 225902940, 304728763, 270003366, 759099802, 909650514, 651531263, 637998611, 46395745, 699626645, 563837498, 922956598, 497607921, 694551987, 775075701, 599647185, 993049749, 819869464, 111916957, 272994423, 771450886, 282625080, 1844160, 983240240, 768667359, 594068647, 920385390, 292498853, 430641416, 153190129, 607688018, 545659842, 918419340, 78872170, 562207603, 221928898, 175694794, 35221763, 832378290, 743012442, 254708658, 561520157, 784175061, 135877408, 577360246, 45548928, 146203251, 777302439, 777590903, 597408559, 5808299, 291428080, 470328569, 740917277, 5813290, 25483074, 988119521, 399999091, 842554744, 683125763, 294502590, 133558598, 204198482, 47274319, 381307350, 967227291, 383781115, 954143772, 738188106, 189724190, 371148298, 508323686, 497628968, 613657328, 335369, 259825484, 625661965, 197051704, 945198159, 975636477, 845871311, 806859031, 691006044, 692313531, 473254503, 331545100, 885566736, 304971663, 608798850, 73444100, 480384294, 440129935, 696562715, 605210091, 589954352, 641351647, 560948388, 535290689, 255020748, 297035677, 341042875, 507863140, 741559331, 418515544, 593797437, 684099055, 321987751, 938909530, 185743481, 663965229, 949155788, 635732839, 127127553, 64901778, 657351176, 562071328, 239419013, 161096614, 568651631, 356166563, 617014448, 551074318, 379798241, 863084500, 852726073, 264609455, 837533405, 270922513, 161139003, 415319590, 783802321, 5031626, 187797688, 912876756, 834126125, 227591582, 895036031, 594543098, 699425561, 112237392, 115423458, 463468419, 199807987, 453925180, 411479709, 630774468, 147418341, 564921944, 327580089, 838727724, 623147126, 64283724, 552167407, 955315702, 345880972, 853057470, 901417888, 898764577, 159533645, 155839837, 779452974, 154676214, 163629488, 687059497, 117684109, 898752257, 68201281, 576694061, 73824106, 472676746, 621621661, 643024991, 82952798, 945426126, 807200946, 898325330, 608513135, 387536225, 961524747, 931072157, 168329531, 127549199, 955409454, 438135920, 302956484, 530224469, 700465027, 337889365, 57528050, 107990398, 24851639, 975780555, 52044980, 791872661, 300832026, 13961281, 238593903, 457368937, 946150924, 765007149, 591623430, 54257711, 959097473, 477166966, 105719150, 830847284, 61129702, 468261053, 356617173, 545867930, 237548324, 358957789, 165847298, 554463439, 67339985, 326605948, 310878106, 354136293, 652938266, 39430769, 957531331, 876791387, 374492804, 303291768, 636933481, 391155960, 143536163, 359908146, 719769170, 57954034, 279898607, 23186821, 919183666, 422824912, 988281560, 617787460, 531409881, 605819266, 157658047, 516296115, 900036877, 214424214, 215001816, 903419896, 735777265, 20116211, 443466078, 551441330, 269243624, 363421320, 347738214, 500886858, 942689776, 653757008, 226114809, 288665264, 270898884, 91076081, 974058663, 318080126, 39148750, 702590044, 18271284, 772660288, 811871642, 122104023, 871282274, 863838473, 754909875, 26604588, 686987730, 800474474, 41632799, 734792299, 201645319, 881219996, 722145061, 397917035, 544430716, 46451589, 162702682, 865036641, 641920296, 513418293, 272360851, 281949859, 230752185, 244462359, 23910658, 587619188, 247966823, 185058615, 725565460, 105445817, 641606032, 152985089, 430053420, 431716837, 660378549, 238621109, 144036116, 2763406, 329712241, 448990125, 332080412, 395437898, 739313235, 858196579, 653319733, 559526906, 450303153, 164540720, 251470117, 848938246, 972469408, 46845627, 547847220, 122105797, 453812549, 600614712, 624634724, 801039743, 818870551, 518077461, 865331466, 52202498, 982626501, 219346246, 916053394, 922015923, 950283847, 648595899, 203138212, 747271317, 196261511, 568601775, 867723329, 452823989, 865963472, 574552719, 624727075, 761809469, 189976222, 215563742, 821692245, 285711105, 462449508, 272846969, 784213862, 984702658, 962141547, 478121604, 639336968, 576303175, 871332914, 911692593, 119570973, 507780723, 979910, 928335810, 583636547, 653251198, 390764441, 132752887, 668467838, 110577121, 500346193, 294325352, 333456673, 288092323, 632704131, 653116005, 290056527, 481014820, 909070554, 353682881, 84258068, 145040857, 550409923, 720743163, 852583462, 147474883, 415048866, 299893618, 578321124, 736006706, 161639700, 246539906, 120900127, 218002362, 116726740, 206232581, 110308541, 621431093, 363112009, 646426347, 327812963, 775691707, 11103800, 249210508, 859435729, 146407873, 742921762, 291492161, 604565191, 790252019, 380145475, 346246062, 964920775, 573733868, 381661464, 937972550, 234758129, 459869106, 574245783, 453321809, 151623251, 188900736, 877503674, 352161345, 800427145, 515261340, 893733917, 816330322, 873567103, 701347479, 718731992, 726585167, 835506805, 24171716, 270839827, 854692971, 15053694, 50562527, 190369663, 957933526, 2260856, 347938083, 938859724, 295229014, 662250032, 105040779, 144061828, 290661728, 421125532, 245471765, 969449993, 534979395, 134123483, 277928042, 160012422, 467229706, 365154168, 900745279, 761445681, 694015625, 751415399, 162319836, 121470544, 688454105, 465225369, 556053773, 535143717, 697512536, 589107584, 310187072, 369220290, 174697364, 316053840, 506729916, 102129504, 869487368, 72220267, 126076244, 58569425, 664938980, 600369445, 359193028, 745483056, 537145430, 733880936, 974136392, 799629552, 327759651, 31533900, 163492163, 670798020, 19142414, 252768144, 396025496, 536390572, 502045470, 362713349, 769684954, 631975774, 74719376, 155969892, 420327444, 498944560, 847609650, 842962293, 748829874, 912181008, 769253409, 912686006, 271288175, 35284088, 26614605, 184879637, 882881217, 314345145, 657296674, 185128259, 62724637, 530287, 700083884, 167937427, 90195875, 763434383, 446273080, 722671352, 851296481, 714583399, 732238412, 613358615, 771648302, 147599212, 62679099, 366831185, 692618135, 549428853, 397480992, 536423402, 826536392, 700017638, 428694186, 357028478, 652809557, 654217526, 254884790, 318442124, 890435470, 620730038, 339644998, 231641041, 972074470, 736930560, 513834649, 705171386, 827688757, 361500053, 820305147, 770723031, 780955, 697477635, 66676887, 224635772, 250413350, 883597045, 370034031, 78845437, 117485005, 650523452, 707261234, 53071220, 542665826, 492239443, 844620403, 151062914, 530429828, 570866386, 889836986, 852513028, 877124812, 491004399, 360965082, 437373410, 407506986, 159525689, 780031148, 85733013, 924200688, 381492392, 101537629, 21736723, 413545682, 626610953, 288859424, 636257262, 244911088, 327930743, 552600575, 450916319, 292172862, 111568563, 328054286, 621325332, 110885019, 713733385, 139232734, 217877043, 691880311, 906286969, 462398705, 199077325, 198514309, 575894576, 413180450, 692508570, 738364271, 19584346, 859648493, 429149089, 708483768, 289673097, 665730767, 206618689, 764712994, 819544936, 530208807, 701819098, 938986220, 578808324, 854730420, 471272344, 348422816, 907648145, 457531000, 555652466, 954595763, 552878318, 641939828, 391432533, 302965386, 606427723, 245959535, 854776446, 788701819, 200151338, 77012033, 605046571, 712554824, 368364350, 714978723, 896783878, 867627063, 8584548, 258852571, 967373145, 91327816, 432539367, 563891573, 794229538, 138277336, 711652997, 380973487, 149986082, 288711081, 845067409, 171807646, 769080387, 555352149, 265756569, 100840055, 804676883, 690084897, 779403310, 82961748, 781473762, 489370710, 939174123, 765328324, 152310374, 100299706, 870232567, 963542919, 130338559, 740553948, 791902866, 587333292, 508825600, 594171935, 982354004, 882159737, 284315533, 179151131, 369033959, 449272510, 767741449, 673505889, 989385120, 337920991, 15660234, 396752821, 148349578, 285974198, 317382005, 133240701, 698978192, 728816717, 171294009, 690312637, 483218852, 662050539, 769840835, 344456009, 972578508, 338653518, 805311140, 814893340, 796675584, 656771686, 170934305, 272496550, 304907609, 975401230, 954460639, 297144908, 423193541, 110509106, 707395592, 914470342, 969054254, 184935120, 748703052, 541619675, 427154610, 951600460, 641311944, 877195214, 530502804, 722380253, 957116176, 718728225, 44103054, 639157331, 742888930, 223081513, 284640294, 524793185, 72122501, 59484958, 330509048, 62111782, 557933650, 144145139, 720065138, 692078360, 597132724, 30693001, 749013776, 390240974, 74647718, 830626889, 259622477, 161304771, 946712287, 759525765, 854279957, 117541280, 121996987, 51392376, 906696946, 898860936, 255715231, 341027263, 194181884, 509388182, 878712007, 755369175, 17430653, 965240750, 778299497, 977158150, 642631349, 365891664, 835644530, 500899206, 823999743, 524359889, 782318744, 622172946, 95302439, 276123578, 213949625, 463128181, 763366080, 675644857, 49118259, 181707296, 173682493, 472296127, 943706741, 29747313, 558205571, 807792471, 982469523, 888895550, 280095919, 144414826, 740024061, 631268064, 31842639, 999662811, 904213138, 645597386, 735455498, 209235993, 523365218, 417389799, 941544742, 252333819, 185641133, 938751612, 48138381, 849423651, 615717270, 2528872, 606351833, 785380885, 304178513, 662371401, 480196532, 563714740, 739705873, 943301552, 602357327, 878528257, 762921713, 17708275, 243739161, 171636480, 999300979, 447987337, 238991707, 10539946, 562478844, 366022264, 687376929, 884552468, 754708236, 912344342, 631222881, 516431503, 45942841, 80177411, 730335104, 310585447, 492159536, 516981549, 717136469, 156586399, 279035673, 783180725, 299713497, 239655709, 14786469, 893392982, 609532634, 737883707, 263941297, 154174705, 747787579, 849656058, 881531169, 523800979, 97740276, 283304360, 159585456, 603217453, 84257009, 300264051, 272475898, 367033472, 890265714, 549288198, 772885318, 416489615, 982567727, 633876378, 468248495, 216975175, 136262387, 368690762, 493878769, 837756443, 668695019, 416105972, 697430960, 960926588, 535652424, 829384200, 444816866, 841672778, 920953051, 738844667, 28595855, 737823458, 523246641, 157547106, 401625148, 107879701, 296899301, 305812732, 803464919, 83104665, 726143838, 249524492, 98356338, 518017985, 480597985, 83982020, 740865235, 34082604, 188508559, 940331458, 347856047, 597322723, 871172084, 186111641, 57461295, 985992109, 649054792, 987894440, 121307412, 584984779, 282109077, 50331366, 814639378, 607417699, 797430778, 1058819, 843180137, 664040153, 221862435, 968683063, 225633120, 210548545, 166157141, 353764242, 892969953, 676725262, 245653305, 213287393, 120066203, 941592634, 715938171, 639963546, 721581934, 575728008, 557068999, 623995712, 963809622, 316467968, 417254522, 42278312, 429658844, 510840518, 173329206, 169456487, 804795272, 832127929, 65810408, 856518700, 507775275, 861007118, 409048664, 819567372, 160505175, 374763342, 923211881, 680275763, 297273889, 683410323, 349001992, 638717036, 75153625, 602548323, 14741048, 30582010, 579131825, 957811148, 614562951, 861682289, 660431911, 177982955, 652015059, 778192330, 641476241, 230878512, 980570989, 823149, 185753908, 757891053, 201645271, 136045480, 894766834, 927187040, 229459753, 287199854, 215824438, 458400491, 177298367, 64705957, 187260203, 730575853, 475026459, 910487868, 865755568, 430234683, 640178423, 249273473, 810452768, 930179087, 644627278, 378830354, 193259653, 243772523, 583534284, 787210757, 445383178, 25685025, 481432463, 345962351, 9190545, 240614507, 979847697, 928153083, 27359590, 488477314, 322489045, 68587082, 190285529, 206060136, 25183306, 311648274, 451628438, 854554284, 774038386, 688570847, 440233028, 354666620, 874809860, 56961400, 79834666, 246831228, 594134244, 413411021, 251102180, 703418987, 408391475, 123011697, 283637015, 657947859, 600746510, 416678228, 107822035, 279018423, 954550049, 482560537, 75811712, 147565199, 460859713, 708982326, 288755090, 341282562, 929467208, 805445805, 970670161, 434457307, 765368298, 796151554, 534155176, 293076276, 875800008, 497764664, 928827517, 221354076, 302483171, 724851675, 975172556, 447527932, 510158851, 557024194, 947725099, 498429246, 583050761, 214366268, 214773247, 747090352, 974290543, 374419351, 859927140, 24045668, 780352394, 173057938, 10498764, 152777800, 7844111, 43085717, 739526774, 666132624, 702673658, 957430420, 181894542, 537498439, 590260381, 857552061, 84064351, 225981968, 20217064, 62594820, 763813892, 991616215, 469784560, 327880345, 466834111, 868702891, 827822198, 813673464, 196020146, 333671578, 374290142, 246983095, 912150970, 484232596, 814708586, 631381914, 781286449, 381380822, 387700786, 304635540, 81043707, 232831261, 246190564, 600322547, 833441179, 513675274, 50890338, 254793680, 286115509, 219306535, 627854703, 480785920, 527597728, 489848799, 196049659, 712649370, 994301970, 227708729, 70015627, 669296040, 707749805, 680209734, 247597089, 485871854, 566226000, 558326192, 263399944, 133187913, 735589778, 836873548, 995883365, 228415791, 672218552, 36855774, 252964051, 970863793, 303097268, 394947798, 799487543, 357409701, 214958741, 40161183, 915628194, 74766847, 115871839, 605784334, 360649669, 214610502, 878840343, 938036402, 996776324, 985214436, 447274438, 849828214, 646850957, 815054348, 913412805, 734587898, 310066171, 887590613, 64486114, 587892022, 617564425, 339872591, 962776779, 541882791, 7811216, 303985327, 720473073, 872536419, 333160468, 526186826, 154405307, 220450032, 810843246, 769622606, 662053066, 936535133, 501101019, 716658374, 124407954, 489799089, 688810166, 475762460, 984056555, 232724666, 513104465, 566918310, 216886041, 784121606, 263337931, 563401748, 88057169, 783152413, 136278278, 60545538, 279493384, 67848431, 628970480, 80422784, 668673172, 952570847, 329147601, 608371001, 40171099, 101263523, 949414005, 838882185, 573464640, 913954502, 264477261, 651042643, 851338352, 989423919, 517178592, 750296087, 101168766, 841545322, 262593476, 503877813, 25113448, 970990514, 520236493, 93167908, 550763532, 339145020, 409635705, 726997377, 598051813, 351795997, 145333015, 550859864, 205128740, 797633888, 706853469, 703272855, 877115521, 700797112, 274758313, 449058010, 575893836, 282656675, 975334060, 320941533, 511194773, 894534591, 445828646, 713249419, 414650708, 559143706, 998160648, 327322320, 806413689, 550021368, 858849018, 598738894, 639054255, 895513264, 471099497, 89951434, 374670405, 774905755, 185379680, 367065075, 253648061, 748429239, 196120237, 32590725, 384558039, 440545357, 580940746, 630614721, 244927136, 413376052, 595665197, 320682122, 245164188, 215172560, 713320797, 172185151, 303743554, 416890457, 308504989, 31308922, 964610082, 894582476, 538240752, 504596225, 544380627, 753245640, 679285428, 192841047, 328319048, 471300935, 580269789, 582618550, 614477795, 562457858, 474694021, 592270769, 561298353, 732723875, 928485139, 686808874, 472763824, 889369834, 68246615, 783504164, 544001540, 999121700, 611668958, 980407129, 696912049, 692426293, 727029910, 620292887, 395534924, 202280495, 777199456, 875582463, 284103922, 187076981, 847749567, 903065302, 741389899, 675971289, 140499299, 178811635, 27263421, 800867847, 395145116, 66798157, 388091650, 901694029, 747090245, 884788794, 256490631, 587074545, 841331675, 611261404, 974902841, 332553842, 304821864, 407193435, 92485845, 877929591, 21312148, 112591880, 968892212, 534385952, 149530684, 580956619, 155772074, 40955697, 293393657, 904948797, 902807352, 199939913, 286839295, 140609466, 277521932, 648955807, 164383622, 175273617, 899213625, 442115655, 981699674, 786997128, 901452715, 163949297, 114201349, 243084218, 661245076, 365255861, 521650014, 389861975, 747134740, 907567432, 274264618, 506168907, 205894289, 676111593, 951680724, 406294868, 95827805, 936785955, 369662663, 917770106, 49631711, 210562725, 291161228, 322529256, 68666709, 942503192, 279012452, 735474489, 146417506, 901835647, 109696432, 632863083, 528116008, 10058212, 172614010, 407366770, 66389818, 170840603, 815986284, 521940212, 493671002, 186397384, 145869243, 972613097, 905207863, 96180957, 948906738, 105921375, 221585447, 544900304, 559123203, 49241133, 857207710, 915389351, 115757980, 504534196, 787465838, 644243874, 575056843, 528231467, 733936998, 153318519, 502604972, 718464293, 990149086, 33718640, 71948038, 401355033, 446925541, 162535291, 523114236, 926050596, 708440631, 604032815, 3312113, 895048623, 519008014, 75841816, 779131225, 396137160, 725362378, 996496845, 400036795, 169293920, 683054123, 359227360, 85389716, 571034589, 615555882, 827830688, 182318708, 63399022, 332486621, 938964666, 881218816, 716744192, 752372862, 152769088, 906431751, 623505706, 713150913, 110838280, 823473128, 236542472, 727789958, 626274357, 207930456, 775550228, 476419691, 151146679, 264757778, 203718402, 936597025, 540756823, 782072955, 937144945, 365137980, 515106445, 504703831, 782174015, 157333309, 997883927, 600818982, 338026534, 972567221, 254343502, 972496774, 147622321, 543032696, 148210846, 277387706, 26962444, 513439796, 815592025, 883089626, 340461306, 765187354, 25139628, 612981934, 869478335, 507251691, 458783783, 861613890, 150071039, 573365217, 687461510, 215147668, 569336016, 427755545, 120804340, 533602702, 257880606, 243825301, 425820188, 179996808, 159919222, 20773746, 750896606, 372473346, 443905558, 52777096, 925398106, 892602974, 536550792, 249072124, 463887921, 116336059, 966932366, 394536789, 115152217, 621929932, 523952786, 937215616, 72167527, 815891789, 366616322, 920045664, 578952860, 386555747, 174100613, 961484460, 267810332, 218633879, 580426562, 474526585, 858973969, 991953836, 73856924, 69085101, 52172530, 489771390, 896374852, 289779283, 853412581, 718522450, 520611553, 695392959, 524927187, 266253283, 393774699, 9080756, 303950250, 315276286, 392660410, 793886181, 862737991, 915928469, 697369425, 709689661, 251142924, 544437917, 324752238, 724809701, 302711667, 96504055, 891618427, 541560475, 459756736, 87683218, 322040373, 556934819, 460208498, 121367180, 274436394, 923802581, 315894119, 911681164, 852039935, 415704813, 325863300, 145788204, 298194353, 14300437, 209301065, 92486953, 221926363, 376872637, 782268162, 783620029, 101516993, 114608700, 613316652, 543172300, 672120730, 227231114, 896387252, 321718411, 122372962, 868200118, 916929641, 921218032, 594525672, 990653493, 292502085, 471659254, 158821416, 674924857, 176098528, 5175459, 878139168, 218453250, 787396854, 657975744, 113209817, 57706219, 126730029, 66263753, 893482064, 14339412, 854342145, 749741683, 281497213, 347677813, 850597458, 793919412, 499514872, 628261312, 939449384, 774419275, 545705863, 577541435, 582302412, 578906638, 324910212, 406421100, 736929734, 154004361, 838352800, 602222541, 44999859, 721906311, 123033182, 597119224, 396371507, 397905732, 685016360, 577840816, 904741822, 377776228, 610002988, 686704251, 574613800, 270442545, 967698632, 237152043, 869394488, 470755564, 983694315, 977648085, 612378323, 152162844, 368507384, 470092530, 702130803, 783561003, 682423981, 87702812, 9884061, 580678054, 521402089, 150050715, 717689080, 717854976, 768800254, 373778234, 663187426, 690523948, 358780099, 267218371, 122410794, 875357658, 885209429, 641043613, 765854306, 707530278, 754398286, 164008949, 233311813, 164482382, 241030046, 92179998, 105190978, 346985157, 492611435, 14060941, 582548250, 683260302, 698363934, 249195810, 458725556, 887742027, 959735645, 58424727, 960119504, 913848988, 431068902, 155733623, 420228147, 732933102, 906437447, 226762676, 914815038, 78522387, 401016415, 430479404, 373994386, 180166242, 460678565, 491282562, 583592933, 661497927, 272697030, 615462830, 818480692, 157704423, 454038021, 322646299, 939726426, 760537471, 952217740, 900432681, 221587439, 63955070, 916476614, 927518966, 125576432, 494816959, 663352124, 949480835, 481215781, 319882571, 596489643, 554480587, 153754651, 185007264, 146757568, 362250926, 893069636, 972186061, 466464713, 625199848, 252752498, 683513777, 505049176, 143577523, 520882855, 997345766, 179647677, 397433222, 849468779, 643395641, 553193530, 691351450, 923553326, 164205768, 736900198, 539899796, 812700836, 126546022, 355774824, 341328201, 453080677, 438912389, 400828783, 814377781, 36357777, 972777442, 847438580, 444090785, 321509903, 102932533, 859233003, 145940239, 626627904, 490250368, 874016922, 136325156, 26378559, 748244880, 749560048, 534475657, 931425758, 509463716, 107830810, 639200610, 260451225, 637324055, 186486243, 712276447, 549838179, 730799376, 484246655, 405387636, 945312860, 48950903, 243460697, 449010103, 73228044, 79440741, 619603598, 407485317, 651543679, 604192861, 180511088, 684644061, 521482947, 129294089, 275683493, 840792922, 580366969, 713151468, 401846047, 508162869, 770462477, 189707571, 492461183, 577821626, 899892721, 30267051, 792225991, 255958816, 484689854, 98018887, 441240377, 689787753, 76474737, 854806007, 409202531, 267247422, 103744926, 360928176, 79695443, 20597184, 682738919, 727206361, 640426987, 912022283, 944990728, 362948979, 371905153, 130127062, 925722970, 675624472, 237203198, 228470782, 738842112, 657619066, 482651728, 370957879, 80500014, 542905792, 824079230, 798176829, 870830864, 293636709, 533943409, 310858390, 292358384, 101712724, 813946829, 43182054, 334645815, 253921347, 942606446, 31442838, 475249830, 395062553, 83808451, 874530548, 498613552, 165461583, 819224926, 550688932, 501715316, 554837534, 820093269, 784122504, 255424812, 1081882, 804341490, 418979129, 29838670, 169714352, 995418081, 710699504, 247231126, 654252158, 406640353, 5954554, 899066316, 188410451, 988950482, 768183224, 763118680, 584894479, 594197625, 716387422, 604824289, 680159355, 306774317, 308761125, 725817718, 758909232, 858954661, 218339602, 968051836, 839776100, 274452600, 406683013, 577563758, 928071352, 457812644, 254507290, 597683907, 4010325, 454416665, 804849713, 770576076, 458607821, 249457011, 847069905, 431474968, 235307613, 833740754, 132015845, 205074981, 528944081, 94072284, 792771999, 244560380, 962495000, 456768040, 95224687, 724089935, 744385253, 975845938, 921764592, 928414002, 181447977, 845669950, 292953684, 342900506, 988039705, 791226290, 225846072, 704725754, 375635333, 689890795, 376413002, 919756731, 1839982, 224106705, 823079071, 375528286, 571443726, 131510099, 742937864, 990822229, 685889689, 410171494, 804674773, 364003534, 639186181, 452339637, 49223137, 113922173, 819679946, 218040538, 883322995, 782796703, 57154167, 732323014, 971562992, 213660041, 378742683, 918247605, 958875567, 3495003, 401805931, 212498444, 34134670, 908287997, 411002023, 451491166, 538882614, 549001309, 574267416, 349091693, 624635886, 216995349, 477606345, 160521636, 195612595, 902478083, 661096349, 607875922, 486998155, 662128699, 254327615, 450760543, 416060934, 501672355, 66997675, 142337022, 361788685, 180167815, 28852057, 700045886, 344098297, 930179918, 425376569, 146104427, 696798801, 146772764, 517999871, 34879348, 548182546, 34146834, 691758497, 50848326, 433993386, 868545534, 487297434, 499753551, 23904451, 257485803, 857755558, 827592947, 80301637, 468280797, 377375348, 975827562, 986593419, 483659910, 816580871, 996402484, 957662681, 217017618, 284899511, 360769730, 784760225, 609867027, 768303477, 465644257, 767929942, 169999437, 663635048, 681341151, 703192969, 248469762, 601669017, 924963870, 601310460, 961634780, 744962727, 9823178, 652984889, 412086197, 567215957, 667180649, 839845953, 981929622, 18592808, 410750525, 161533608, 556851708, 326454362, 971755456, 980806772, 821759082, 624520118, 406943131, 16204871, 732047681, 129389687, 170524272, 184243024, 129042299, 980825801, 617574143, 935893611, 989347277, 820031986, 630985553, 645402579, 538419871, 812365107, 417580094, 44437385, 11895061, 338332760, 276344423, 740060895, 906005832, 991295653, 575442355, 252677775, 388951234, 855886537, 323767990, 570721040, 766631751, 931326393, 994988010, 471186498, 678987620, 570662059, 967535714, 774247009, 729203800, 15033759, 222075846, 277743892, 512347825, 924498761, 60635466, 835933821, 147052004, 777241745, 44854682, 440154871, 24690496, 233738584, 56308577, 598007086, 963814576, 561719994, 818672972, 780569219, 564241230, 689263344, 668008912, 790557134, 806786815, 28588306, 295365233, 119238593, 147915534, 639803943, 841289049, 447205977, 226912415, 105515054, 41235325, 805913791, 349872414, 150993643, 53677628, 361870764, 893255497, 268701280, 910184408, 88803822, 259125827, 891916340, 642511329, 319813050, 794116009, 301694523, 600751248, 211125843, 784055521, 971299574, 636836323, 867626206, 493576363, 443582901, 186877774, 136524037, 243076189, 22973421, 200676866, 328692513, 420508317, 451373669, 160301946, 349471833, 966657640, 962719709, 874989659, 280676244, 920104613, 159001571, 42580632, 168151822, 278662634, 55401924, 138104133, 626433971, 496354767, 103772982, 32285699, 586273910, 571133272, 506497659, 380909199, 703333945, 528523985, 872532356, 469855684, 161160737, 94940528, 909625591, 815645282, 965983354, 693463067, 61975531, 147449717, 338790683, 343964729, 516945226, 518102604, 431322663, 720800910, 15118579, 815503891, 184138894, 69778478, 100864742, 689329746, 939551956, 946151636, 775326698, 310364574, 368539007, 459961408, 172638014, 629486367, 37316388, 323483178, 309419569, 263866543, 300112668, 993212917, 311331533, 348689239, 831344165, 199659349, 3129267, 51309861, 741499058, 111994286, 300925606, 786444082, 971562325, 265159696, 358667389, 487148100, 225955226, 440434595, 285239998, 792057782, 82848978, 171504470, 218454092, 616540252, 379268562, 588336457, 998007040, 226384480, 638257244, 80076913, 176947599, 470967767, 477790323, 924013282, 457524220, 336388565, 849970676, 193820907, 357919452, 785214207, 893567055, 720163328, 285229595, 175140092, 283853122, 628750529, 174123081, 861571311, 357976802, 257864974, 777615348, 569793544, 98070929, 676988906, 970394269, 998528423, 920311700, 548863396, 571481906, 30031208, 48162182, 315370888, 163987457, 488670509, 798059948, 590095690, 602425902, 572145445, 54583146, 352670036, 71458305, 524384731, 419882720, 627645908, 500674250, 411438206, 315487110, 347926083, 350553012, 812909793, 424702408, 745527501, 385533634, 650198382, 585910632, 203800018, 678341767, 315924129, 470275672, 374076421, 438390347, 192311479, 293429756, 846100744, 484992012, 79219228, 948593872, 148208407, 541661350, 383950217, 117767843, 267981443, 359546755, 510694585, 18652205, 915974379, 340016967, 316856932, 437087477, 440423998, 169573632, 252707841, 106889569, 243442399, 329472778, 728138703, 789657403, 198742171, 263431290, 601107140, 252565080, 267854602, 564648396, 362616408, 210691155, 350601392, 983130132, 453268996, 866306649, 336528819, 667061855, 205525074, 416068902, 72582702, 660370770, 21602478, 753978849, 214325740, 631993153, 13848952, 996994544, 124881499, 513808143, 462036449, 950411648, 938909904, 956914538, 401882325, 669815741, 442411536, 118477579, 782681610, 496799526, 259084482, 960603022, 8907660, 785510435, 280199889, 660974826, 391337252, 749431530, 996809580, 79583184, 735831170, 538699411, 3986019, 636863483, 607328870, 688231029, 731941397, 561263428, 923145536, 441266641, 397923396, 557841264, 564647729, 489836187, 185622162, 196538638, 902101049, 157556786, 312756430, 581287801, 905420444, 490683697, 280310144, 257071399, 788487953, 580841493, 580083473, 184913948, 469132892, 689726950, 247317255, 673386147, 933323572, 649976355, 582460493, 932776911, 978146704, 808566567, 131029178, 389151934, 377068530, 199725285, 401619154, 42900393, 445950256, 401021112, 670501212, 732136025, 291004243, 4280844, 144352032, 478437570, 136163062, 22439260, 738144182, 931008168, 632395809, 132860274, 271756303, 450485010, 430172904, 388951162, 916914248, 347124586, 30112647, 48430589, 549341266, 904671958, 325320312, 187505977, 847544548, 592423680, 161520612, 581247334, 622935983, 784235700, 130701899, 859397094, 420304286, 840548713, 851906099, 847825628, 558690474, 610894224, 409971589, 248449143, 753602440, 514229638, 875473387, 496771298, 238457611, 45913475, 705483282, 109035065, 812219169, 82945314, 686587182, 486315004, 515341846, 216430206, 371476833, 111020143, 987820446, 791638954, 189922730, 22289530, 504207376, 870289042, 522679937, 867944916, 241391437, 834340588, 335012142, 262910187, 734266063, 206172810, 426335011, 119983324, 174942817, 962253968, 561241667, 171284412, 636491079, 357164637, 757989294, 960188280, 297065958, 959613695, 366715119, 480805495, 680886198, 108434486, 658315368, 580781234, 298961435, 819648743, 448396682, 191769405, 413070021, 338450512, 793560713, 429350602, 5953061, 941928046, 986034853, 439545101, 964065261, 716612277, 582886884, 66263778, 391684569, 528441565, 922878964, 2368064, 847605978, 42857652, 656572241, 178917208, 819134315, 94677158, 77002932, 350045529, 797949268, 282995595, 94995093, 210941196, 630012810, 344612556, 752579800, 603312683, 134802298, 729330124, 684517737, 449255516, 732221964, 293508036, 830984827, 385150800, 425460074, 478225360, 953499577, 146273966, 535693555, 344786213, 782594615, 103596855, 532758843, 34613721, 155606245, 630807778, 889977184, 727949107, 323956778, 390745971, 179413685, 79501805, 970192987, 817448127, 733513172, 248076636, 958838442, 947924997, 56893442, 909701229, 599283497, 682630601, 848320509, 501929787, 806692048, 52230183, 896284241, 912833243, 925609230, 932936646, 692440016, 301874917, 185843502, 181644767, 727983272, 192332519, 670580547, 724973757, 591182077, 268460855, 735353334, 904235917, 188317922, 888930327, 309973167, 735630348, 764771721, 193606761, 20257391, 160163731, 394112810, 292556318, 236168651, 163911726, 120772552, 103920549, 973229692, 525147934, 887349451, 529528346, 681690824, 114054868, 701527180, 656479372, 47211740, 741707115, 667820215, 595062964, 134087781, 855107355, 976735985, 743817889, 222642477, 243084474, 269817752, 442614723, 685444912, 386159202, 682847519, 969327149, 643072027, 39613122, 329364727, 232843747, 444298841, 967209354, 641040939, 153142999, 498123212, 428851597, 849405915, 440639129, 871117178, 123596374, 81346658, 596215404, 906809881, 750479568, 567423275, 428882919, 544165548, 381462852, 26193817, 959211050, 212308337, 582721686, 195377886, 762519256, 31797886, 229761351, 647752443, 137400388, 711254972, 203521234, 874425518, 239562455, 947730476, 782944731, 174336441, 677112082, 97896315, 188683074, 995286011, 96243316, 366262804, 638476876, 413083525, 35070240, 983217102, 132945753, 176218134, 324538820, 469584297, 452525437, 285552678, 428454109, 249897492, 302435334, 942682025, 96680475, 628200075, 625315780, 323819912, 678361023, 471787648, 328490738, 287017865, 766087988, 104027778, 108620917, 549973126, 618670330, 684525546, 336399626, 817890626, 945553112, 546826216, 854261902, 213992804, 682834780, 227463102, 585275290, 603586903, 651670470, 947771924, 117214732, 518661633, 183387238, 248633075, 708735526, 562836699, 263981144, 564995479, 392835919, 656309098, 749484942, 989728035, 376119257, 962953474, 537921204, 281854422, 427358976, 966975887, 798653632, 532681544, 681364101, 721792974, 140288494, 502219879, 347902674, 559097166, 358783724, 709031787, 714634975, 956991303, 736448743, 312927464, 485319514, 563809517, 926212704, 778041080, 149258548, 874929181, 668642067, 234384280, 728838419, 103680275, 397840246, 984156124, 661898714, 796767660, 145421386, 839082528, 114697275, 180154324, 814022372, 312263593, 755598747, 147623557, 16294144, 213960942, 545488542, 313286999, 316314685, 155297346, 13783134, 535429706, 708444258, 93717437, 760755940, 880601217, 916921836, 175871975, 724729278, 637843082, 544964304, 814581098, 216771338, 601826716, 598466968, 453646955, 565333411, 463808592, 605619067, 79120383, 109341503, 920539882, 40448815, 264943981, 964941306, 535840515, 703724999, 392781304, 988846519, 146880848, 581516940, 461266736, 991942970, 351330773, 697310691, 275606735, 458196520, 538229558, 837311516, 320157928, 563841407, 443067420, 790259551, 937906063, 7734929, 629418218, 739972635, 253901870, 183927010, 594572049, 728960919, 374361201, 840045557, 481619677, 273079652, 2350465, 435355504, 83955938, 643126125, 803640365, 803729988, 623422534, 267249059, 26857414, 553460825, 524688064, 624494055, 95881198, 925034096, 2162590, 748495905, 810877147, 837111984, 132060726, 671523574, 201777605, 734685911, 324222066, 136012495, 745040898, 361327749, 712032021, 842382115, 235854152, 359031475, 386863477, 866670761, 235885664, 552572804, 657718486, 636140542, 929971793, 549125356, 655924750, 189815157, 846139984, 119076093, 146136363, 718109164, 199851215, 548904570, 917872396, 148761533, 612515835, 840088362, 420294069, 687144102, 395852367, 930249590, 359331082, 153013724, 810582189, 449456506, 255615884, 851499307, 300133549, 232994488, 600441166, 559242926, 953890971, 992881096, 651532658, 697194348, 861022377, 141951983, 715556227, 608870981, 822163138, 282846174, 309699916, 748617148, 825019626, 120516327, 547514923, 603699724, 499746069, 187287594, 796048187, 612887460, 246424092, 995999823, 225459940, 83960964, 758501974, 618085698, 544264334, 737887618, 63079131, 313131524, 453601555, 699137881, 580843061, 133225620, 71056546, 705450987, 754601523, 185556287, 295904860, 329592280, 225944404, 217627313, 371596510, 417268664, 700900190, 312972669, 903298303, 828271073, 559088294, 231974096, 344725102, 125767321, 528663412, 869516935, 943491247, 682127376, 306784321, 235294015, 301436899, 269292283, 816555679, 818126727, 393584521, 954516685, 344308938, 691826372, 278811066, 323303841, 332696304, 264936089, 488226740, 537166370, 724505685, 864681293, 988496260, 156143476, 597599288, 983070127, 581904290, 466934858, 364036565, 278930480, 926994905, 703371818, 772030825, 291619437, 419033482, 855161445, 299000591, 206283340, 960010587, 964323976, 989838508, 363854560, 596777835, 380853670, 366039001, 790439445, 935594359, 271674448, 230202471, 356539077, 245939830, 291836878, 709083562, 827374318, 467936050, 974766537, 899956474, 245152841, 134424980, 736463811, 746016845, 83795152, 789487271, 700611465, 646641584, 259346301, 362747979, 684366287, 51027934, 895278873, 481643936, 414101397, 931723679, 749222736, 251404085, 145667451, 707808044, 182242583, 141134924, 991902258, 77114999, 118980938, 842411594, 381208299, 231692597, 451232892, 912310119, 739076790, 341406312, 502643091, 155839684, 790200132, 370367613, 108957014, 102705540, 875568064, 588967951, 645400124, 845748347, 124346572, 201849797, 879850709, 60638398, 707878279, 633573623, 387949453, 589407593, 399939845, 340223721, 95958947, 798133771, 123577506, 690181918, 204689593, 723775556, 912655457, 675418641, 122373652, 342538857, 381045431, 210575632, 842829131, 289371934, 834062245, 87043014, 200804860, 642849830, 567598452, 152815598, 459440899, 237530418, 674542604, 956067033, 38367871, 905619929, 631789795, 282780494, 869335178, 900012177, 818885498, 224157346, 238512723, 52167014, 70098021, 900131785, 652237166, 142393312, 967410949, 48852687, 549505062, 151315131, 68107520, 481137284, 954372332, 349869726, 428867625, 661640439, 988392345, 562477770, 471393170, 590252585, 228283375, 882605925, 830431892, 56890864, 168720210, 67310399, 685321690, 231948257, 86815193, 351832357, 797204161, 306207862, 328799709, 280990138, 875638044, 903264057, 209458804, 612555855, 979321801, 111855627, 619822053, 248120975, 559092919, 703083443, 51404116, 161811033, 223545428, 401506770, 378865307, 804471811, 697678865, 894828203, 155496351, 809953324, 960051295, 509918443, 563499961, 384296715, 499056058, 774329241, 783285144, 569217708, 819543058, 21200376, 729790186, 959570454, 867112589, 317749624, 256766039, 980091400, 406701926, 838098067, 461138118, 676348862, 215072648, 625298807, 405887456, 612803826, 975445130, 746688059, 278737402, 701864808, 166514608, 896654911, 821765968, 525342111, 774106881, 235920200, 325168445, 700692214, 48332305, 160900224, 413821769, 439197063, 896268668, 811703619, 37660191, 393699640, 463788166, 617838295, 358278376, 798780230, 810650097, 720768406, 253191197, 743693715, 757890924, 32278360, 178775255, 286534826, 639642998, 61596883, 649262900, 618602688, 731365106, 446542385, 549782976, 614246769, 742633799, 870879290, 387598235, 821561904, 622268470, 555922322, 425016015, 178527934, 529314711, 189222790, 343391814, 742601893, 48855808, 834439768, 738259912, 986824397, 44205841, 465282457, 362436617, 281557170, 697252055, 421622548, 793275891, 472121631, 729724370, 113334202, 172107389, 945774381, 80163070, 659737062, 452243356, 741304242, 557020488, 25998478, 445754513, 843321643, 142655784, 926691461, 956266541, 299200232, 325041263, 582963906, 182884428, 810208714, 776663497, 935796134, 246794724, 753957204, 878846825, 605702752, 492279222, 514118294, 434581593, 307023033, 828379793, 863497756, 980708014, 307150294, 911378286, 751505071, 665564608, 263964219, 237983645, 440132621, 670225984, 833912890, 524153067, 554516693, 703913003, 375427253, 205811627, 711783980, 267010959, 255321173, 920653275, 678343582, 471694598, 917324156, 642458584, 43941735, 486824068, 208768226, 494618621, 808674675, 966711433, 531185651, 252954246, 496252267, 943661490, 540824821, 891995746, 597152184, 251646910, 778651072, 551825246, 231105659, 596865601, 274733551, 429630594, 320866759, 427879147, 412398869, 71647561, 748208189, 157662435, 872492150, 851710541, 919755601, 196422947, 819099367, 849479766, 221853201, 282854892, 774145641, 112487324, 126044274, 787461569, 112445786, 476172515, 443450430, 508778771, 5395576, 772173898, 21910541, 124237776, 180203760, 314337557, 744528824, 637484454, 8702526, 562019173, 173531669, 347089809, 321561942, 704271528, 965129958, 527464356, 465609029, 883248213, 41728750, 273360639, 149351226, 686622141, 842813077, 512184982, 18022676, 833705669, 39758546, 472058205, 182954011, 944480471, 599202214, 411924464, 722367505, 477484445, 88572130, 996774307, 908728271, 955738218, 322769162, 158627028, 473591086, 995793318, 631779904, 245479192, 278051091, 371823437, 566022223, 457146103, 535755660, 448174498, 280352182, 68680985, 730835832, 135910580, 387227277, 875288473, 443489763, 872466314, 923362864, 598554013, 409025615, 353050524, 257698493, 18631209, 900098477, 651152100, 364598234, 915113325, 478937968, 961732421, 406552237, 964167033, 203316272, 974350904, 523570237, 401100451, 438133214, 470177957, 686792903, 155498072, 738550700, 753626332, 853876646, 750451198, 962348170, 826185480, 734782443, 560061063, 575826394, 823818562, 717979669, 84388530, 951398669, 883458798, 226832531, 620795519, 92525922, 108589328, 843355577, 650157608, 520909801, 655283859, 305787552, 375750882, 28722234, 605010248, 449110059, 447652199, 793646031, 563131306, 971666324, 652448576, 376880295, 788743601, 735468533, 31965161, 310835020, 838042887, 925753086, 960112390, 545636609, 483477384, 761412924, 647930495, 422924217, 534777769, 357689055, 362449103, 680323028, 830205766, 590466975, 961173972, 659629864, 577257930, 181635739, 723387461, 614772090, 114533602, 224753571, 798622135, 665797216, 469430367, 888315891, 137048142, 387441032, 791558534, 158618858, 724555995, 829899136, 118945686, 408346658, 66074953, 836198994, 200733677, 990058841, 977021988, 645597388, 432968258, 602367819, 70608267, 85198549, 429248497, 515499713, 264751801, 829430041, 247121299, 560448993, 335526998, 552800864, 56619218, 126128790, 333810257, 834598653, 673858949, 917703774, 490596899, 597851871, 949283412, 375560421, 852190511, 110031150, 777373336, 573910543, 623960704, 317057846, 761329138, 898886450, 586190734, 368970180, 93611430, 49463570, 584113656, 48581324, 498627749, 625553709, 337168010, 635562267, 827020488, 366124443, 269775528, 996406510, 121939195, 155654252, 945666556, 653271735, 703643132, 375171106, 344743950, 32766206, 220872711, 847373337, 77796023, 851662626, 690615951, 165062786, 285135414, 47560482, 232866427, 600653309, 610921009, 946608452, 370659752, 299790833, 556797077, 317392431, 728996921, 882039312, 812101131, 541300161, 91291937, 989542177, 397362663, 973531403, 585584450, 981982480, 316039418, 662551037, 226915103, 203312039, 143976765, 701906082, 444690820, 802868661, 396580790, 479768532, 131383596, 371185447, 879643865, 130426830, 260811502, 448547222, 922420153, 383368891, 758309537, 40083386, 785278508, 617301368, 535537491, 117875822, 193695507, 124504197, 990371664, 49468839, 707942762, 256810044, 593974449, 233599970, 31655224, 904044611, 906498658, 617446460, 625281483, 89528403, 53993303, 926473334, 814352834, 654304568, 648489131, 737846091, 738205639, 296718864, 44141185, 650029042, 902426598, 866500627, 129073753, 321274121, 246275242, 441183119, 565390718, 705057017, 402143260, 755711259, 765500561, 974247985, 232362235, 945257581, 573646992, 675480090, 48897954, 966969220, 539643045, 125642860, 967919172, 177385483, 264547766, 448730589, 733759180, 100479216, 962184608, 449324466, 527173438, 620232651, 1044952, 874791617, 799175430, 898296760, 220025969, 747480294, 828226551, 659770121, 985165667, 916201836, 227931653, 770252648, 93338716, 72106530, 663457739, 891661893, 178804041, 412580526, 973077257, 650521984, 316426544, 853350714, 907065887, 705009272, 316153240, 992177255, 992846158, 771923063, 900470907, 493143686, 243324252, 24066574, 202750130, 40908373, 313466710, 803559886, 481696294, 686598392, 892411813, 450625766, 470761109, 113762999, 246395466, 352718947, 647615773, 947930311, 140405987, 341230165, 782699586, 395590923, 897340652, 276748572, 159229100, 563231986, 306441809, 951344915, 963418938, 858735686, 284719727, 25037538, 39519376, 328287270, 669581793, 340974699, 408799646, 237651490, 499872735, 391283659, 188930278, 14579922, 436349321, 39741399, 219903454, 316386652, 790332018, 496992050, 470225844, 392107810, 542286639, 683503552, 332990074, 501545268, 797877595, 851307077, 191451209, 593189406, 976476183, 918321591, 340620296, 558449182, 302661099, 582112417, 844539054, 352913972, 853947180, 681440402, 480309828, 312390779, 784437523, 845403649, 915154630, 41737835, 418090345, 906117797, 349325996, 610038593, 724067955, 356683495, 993853901, 462716332, 148537044, 73972169, 55868155, 203298394, 906864604, 916946577, 815084987, 353891572, 906977314, 782787956, 938121265, 133361503, 472549069, 652414305, 974730419, 426577822, 692131182, 216483115, 33029046, 512325951, 762412000, 550037408, 250169400, 482454718, 924596609, 295013073, 252338038, 495012452, 895549135, 748123400, 816076489, 994413346, 781832298, 951782049, 317176914, 430667904, 191375258, 447442954, 365645416, 393784330, 181436151, 713216279, 980911505, 504089297, 65076019, 732200793, 74283652, 489241661, 969314584, 31956688, 842248434, 812446840, 368730011, 448106162, 847435078, 549798870, 912049413, 324857159, 204461086, 97965855, 864245858, 946407091, 786731601, 187637036, 638243015, 547325436, 819807071, 470771042, 240526815, 659446570, 253216426, 529583416, 544137363, 678584562, 262948389, 813002202, 193256116, 709494303, 818194550, 321957140, 158070998, 401790555, 632402171, 405718294, 234198655, 449015725, 494852498, 434910352, 612575771, 196481955, 417211510, 52952574, 244013989, 304062532, 479964333, 846729316, 362553474, 428455502, 905540917, 466451311, 690422856, 347383216, 686096120, 166727250, 372543626, 803971123, 413072049, 744530051, 312646817, 651860642, 315617765, 198084912, 929952566, 676044212, 990101537, 846609042, 869201595, 491651700, 691213736, 177812976, 496589603, 3930285, 142498882, 351086654, 711706061, 513485816, 209016986, 198161565, 318175126, 358678168, 813550908, 791699733, 512842910, 761190592, 731977554, 101762387, 37165904, 563710129, 360917323, 771155987, 91700843, 333685346, 210741277, 351212133, 894445529, 990359789, 415394517, 709048551, 389320136, 897199670, 424202332, 902697222, 635339264, 213404382, 342834996, 730302689, 367146097, 841718042, 4313027, 806444681, 940519228, 979508489, 773507913, 599663776, 967439090, 629420342, 108327119, 35524987, 82559623, 717646284, 805656152, 123938029, 751486783, 89742755, 346532241, 375983428, 362705648, 656151728, 848359521, 960892428, 40268492, 724016588, 311541664, 924532927, 315322301, 46946254, 880835131, 725337175, 233766344, 747956046, 770317769, 933188723, 946460600, 864177419, 202009922, 272683751, 996809314, 404589018, 505837882, 400155825, 764075525, 500977568, 304999105, 54297704, 308255967, 437865517, 593531618, 895412304, 780615091, 68238547, 892242202, 383510860, 835955153, 288007681, 290077607, 725158530, 991253866, 293788780, 499353262, 276190170, 164662264, 814684918, 761601858, 797778622, 176538697, 485855967, 242199137, 922649146, 863508678, 978802026, 327919610, 26942222, 748722068, 124246020, 250811278, 72880381, 586980827, 920279872, 743185684, 440647170, 115741740, 276079905, 957864927, 774267402, 81995601, 432648533, 662176181, 963624365, 947057721, 654054611, 531487020, 719409054, 384158510, 579991564, 199667250, 776044571, 987282549, 649542720, 37020691, 295051253, 846724699, 359612190, 10653281, 637124217, 234492826, 540541846, 578177177, 517822507, 378166291, 867677699, 958440377, 965863764, 610905036, 584303209, 778017021, 240318797, 967976383, 248393477, 673311159, 535544123, 508829646, 947511145, 440416839, 398664266, 775721188, 17901182, 928525010, 822322956, 76724319, 623014478, 941705693, 693690529, 799833328, 288626941, 121536345, 29787496, 23272066, 913803437, 148025489, 506731940, 330899927, 936065945, 185207104, 81412404, 583456663, 92789617, 794426427, 554662868, 914244242, 641814454, 563110357, 521580857, 796274956, 17062014, 453680425, 825067718, 701019445, 488772760, 166482561, 845662949, 790848412, 607962624, 926785143, 100325840, 845605469, 536504365, 172738902, 950150836, 157103574, 624217053, 972972993, 229128307, 890024802, 99440111, 655833077, 272720878, 8001316, 386306681, 459407657, 206806525, 41044464, 504743238, 681902765, 551407904, 822265562, 119818230, 554751426, 872237620, 80765587, 526814195, 496555341, 362743275, 360166747, 362542046, 354383497, 210238766, 949475353, 116519027, 18026523, 141501759, 15744217, 483895806, 220949684, 91981485, 745007573, 816690628, 197997175, 679239484, 178139322, 17349598, 283982061, 969216171, 27927395, 908842560, 55970964, 66320655, 493289383, 51484036, 852337796, 461920546, 609830269, 706227887, 755299913, 316028802, 575294921, 237296973, 646033459, 954387313, 462794767, 938122610, 291992001, 179594118, 398210788, 572467529, 383985280, 522418100, 272067301, 214265724, 64405836, 716238503, 326584263, 959114841, 623204110, 957154855, 882436799, 564820758, 404911711, 948342613, 562074516, 187915643, 797667724, 286119742, 568673987, 199580791, 927453448, 820890341, 631624447, 411314520, 30920346, 155179461, 350791222, 503803958, 192577269, 481384043, 686254086, 559243539, 813885471, 555679068, 613294239, 955566132, 921243835, 555379746, 771984614, 619044282, 970100264, 631210990, 652446036, 581930927, 331033046, 987366180, 330874759, 962816051, 710078737, 459100782, 998577944, 109955824, 603549286, 452016882, 248992001, 907855893, 777689396, 220815425, 402526451, 971033199, 147585342, 269555788, 834701407, 16162240, 546823124, 630286757, 337582940, 349941940, 154747071, 119298487, 915857289, 190022260, 561795271, 553656373, 642416680, 319951043, 675516184, 946555758, 266939045, 144293774, 316645655, 436315339, 424686353, 509774882, 549240197, 202859084, 133531691, 393378295, 481901600, 368771988, 117382665, 810378115, 506524290, 690937952, 747441025, 386328964, 832528737, 342202166, 37409419, 559784531, 385545445, 717082393, 506362074, 118629356, 662734406, 132705240, 354586972, 69079272, 985016754, 488442277, 861389226, 616325334, 586913331, 897835779, 487999350, 696381688, 634577099, 627943557, 768398396, 368364344, 159548776, 368661906, 729559801, 652533871, 847380326, 537829281, 820589246, 735099440, 546023179, 770712513, 195096214, 51184676, 621271140, 77438003, 882970418, 85707975, 806947528, 253849811, 21737272, 584277278, 105047871, 778216078, 457377967, 367761904, 811455424, 897662859, 896918474, 953042559, 354996489, 6668198, 712435861, 313406227, 281123611, 872355882, 344591957, 387924436, 435208021, 284088565, 757485750, 428421091, 479725110, 435927011, 249390634, 828260862, 352897681, 691655779, 612760446, 557450231, 802356457, 150103935, 731250212, 621814512, 901783826, 759710384, 62099085, 497986814, 228689319, 693566725, 821415287, 609701179, 320669350, 901620111, 740576246, 892970886, 669029416, 282096076, 695132706, 614510480, 378360626, 413541925, 724723496, 94799794, 983704806, 778959870, 773072900, 645418474, 172206643, 496822157, 187570827, 636596108, 433258131, 693429919, 488058061, 305507874, 518749294, 504415133, 935823450, 864300094, 563827653, 702396493, 320403650, 153989627, 870023628, 279172692, 362036116, 843808498, 754112598, 835536626, 662973361, 926787260, 978833465, 370156026, 642846463, 612649586, 242945524, 324870280, 389294411, 91821006, 659346231, 568761778, 577646570, 668614049, 610191416, 801266223, 147325505, 202607579, 235877965, 521206449, 18072391, 491247920, 964209704, 871159144, 787595859, 470433385, 666756521, 111238272, 906974373, 619644987, 943309867, 971924635, 682491172, 610970958, 816464478, 551506153, 380296301, 845384560, 777178168, 627304729, 180782487, 257273385, 604623722, 549464867, 742955570, 140449242, 169698540, 939828557, 850804295, 874790260, 312562046, 239497357, 668948721, 673831269, 505813233, 854342981, 848276653, 78116846, 969973819, 187005413, 884876445, 786527118, 755741896, 975523179, 861218223, 72594163, 856342236, 955061670, 71671901, 593910759, 969252391, 962466252, 38276276, 633591851, 846019485, 23190085, 342341451, 612766864, 445533771, 265894038, 537389916, 166353085, 70005218, 863606089, 589031221, 482954853, 39851757, 471010607, 169118392, 467840606, 230535089, 384666057, 84948039, 566091314, 733625701, 243760688, 435349717, 967714962, 645221178, 463066682, 562759383, 525873423, 19386117, 725253617, 292729873, 918693485, 859835812, 787339212, 135322753, 699413896, 875357017, 175303933, 873464431, 300576286, 626326142, 397910744, 323942517, 300471274, 915629920, 21517828, 804960766, 791876703, 120572867, 873499367, 473882044, 987757669, 282881450, 95736448, 421292146, 714393695, 548569995, 376936567, 492453765, 480203167, 958575214, 349018917, 904050928, 163635792, 913991929, 975460601, 184743683, 736625113, 283011688, 150664529, 641802421, 497677548, 162207721, 468207625, 617276271, 971106208, 255731169, 37858198, 418024471, 865332320, 64177044, 536711568, 721723407, 547517058, 427782311, 513592727, 176914790, 953382157, 434835583, 503627301, 120568472, 823696867, 79104825, 625926819, 606348074, 921013876, 928090699, 703668918, 741217763, 648726166, 459005552, 193865966, 639402930, 391985929, 449265012, 918430314, 247871683, 526427781, 721251751, 575577921, 635735967, 160331015, 233239742, 414323421, 405041892, 423269481, 198896906, 794218155, 189728460, 870059533, 472499936, 305274527, 723668632, 955063944, 444927978, 671727165, 845825536, 661838267, 702583072, 128134689, 581116945, 578896201, 719162822, 864623712, 637926046, 649258254, 101257691, 882453998, 131309609, 179015066, 545450681, 514087456, 110801357, 312574922, 95844684, 974524591, 842610944, 451195769, 637728200, 837231725, 994849953, 115344083, 200931877, 693666554, 998179997, 943087158, 653619255, 584810700, 270750505, 35533163, 350605234, 824429397, 700395125, 610765952, 522958969, 250455713, 546099478, 732790117, 806679854, 370390324, 703127494, 605872653, 664916820, 697795677, 109285000, 12848291, 532125980, 930371759, 249008428, 504468020, 554182561, 152600045, 762724492, 521295193, 886043211, 276584874, 545862236, 341460909, 939995827, 421727484, 238783037, 603908067, 148336664, 924953064, 413346826, 472543538, 550008973, 440221293, 713306025, 690039055, 347809902, 132728802, 290599296, 366753108, 520884267, 577759492, 570052878, 58429172, 875302319, 824983291, 603667506, 685978649, 153547422, 695755808, 278672294, 778223620, 702153480, 154267155, 802710558, 834562236, 572544908, 820033270, 707853596, 929407866, 423996964, 638724431, 799301883, 445927712, 256211254, 45009795, 964602840, 614887086, 473764531, 837203556, 780870684, 198614492, 457100505, 118101105, 495015067, 404215164, 405963468, 879392327, 125063008, 337277397, 776761253, 387315726, 43255347, 289117850, 429721568, 833863090, 222855094, 733641616, 28916669, 654893178, 915685612, 790422521, 938926337, 711829846, 786695410, 199284649, 106983614, 785313535, 56824911, 666430714, 229034434, 867956206, 705437038, 311123410, 578238881, 625014416, 520587004, 28530274, 799492901, 519512425, 354354371, 359203934, 514037109, 579287066, 40980093, 798543539, 86417691, 623355981, 381866757, 922861308, 878081616, 504912285, 660888746, 118746150, 576676168, 206081698, 507473097, 584674059, 290605157, 491761076, 299110119, 9955174, 275454371, 392094021, 93319559, 223706189, 580266070, 908032828, 438271143, 428493344, 708933469, 20931259, 745337821, 52421785, 610288959, 71586602, 989659869, 342634610, 706586853, 631961315, 48986496, 312644007, 29766387, 834637363, 931945956, 460144696, 332035306, 786464081, 519715711, 140909116, 599066810, 525874842, 71173980, 407878913, 211554331, 636512351, 520133172, 873237549, 195016256, 976366731, 99996747, 67452709, 913600950, 257002624, 909637757, 567717873, 189602049, 885571169, 498002808, 168531706, 226972467, 582358104, 952602958, 957189485, 120601339, 647456831, 118376096, 822977980, 140262582, 478483929, 34894687, 952692666, 92611159, 339100333, 587067700, 694754188, 499023511, 398949014, 194530494, 503891134, 590144570, 886207477, 447895591, 456368129, 959528930, 33608168, 389718730, 808971229, 300743435, 868960284, 885760553, 510273656, 112921352, 778655718, 647806864, 456490073, 624096489, 646563031, 448403357, 929520491, 891166314, 609350543, 728330103, 278876507, 725933572, 100835178, 657142542, 450272937, 719438672, 665888034, 737955839, 222943908, 884821469, 985571424, 855411249, 62772463, 996688002, 475598332, 79079839, 904904146, 62894403, 633970161, 993814930, 990993344, 924172907, 972750798, 113184466, 135320443, 359322552, 104163950, 742715925, 879737918, 378847336, 274506204, 832370787, 991570048, 519150075, 478013526, 88848534, 969332950, 37288029, 696767609, 571942006, 675431001, 389323006, 617322853, 790580784, 388318327, 532313247, 907234407, 798742378, 609153752, 146245811, 130912812, 272152077, 479563218, 354968638, 345831936, 589166114, 268442094, 994261268, 460267230, 299625075, 985041278, 969638247, 467935713, 911095004, 494386141, 564815076, 601899392, 991105543, 269209594, 420541135, 338860761, 97609409, 197350252, 320212008, 538243644, 900677213, 392093095, 229727661, 290440207, 945731494, 264527472, 314641158, 201504846, 712821515, 397150366, 271527131, 382308257, 293827215, 677016548, 495822352, 742947971, 819303177, 821452071, 401724294, 71005403, 682268247, 610890273, 591195824, 865455197, 776828260, 141848417, 500825731, 480240463, 634818064, 640032449, 191860491, 428907065, 318018757, 817389079, 359687806, 573648856, 533958869, 740311800, 820227601, 86672685, 22987391, 749849501, 341859539, 818166859, 70993488, 707811098, 89724463, 115828962, 749488545, 151344794, 230705064, 530832728, 517707839, 647826881, 859533781, 883479686, 845500091, 704740477, 581245383, 386975655, 779783744, 395610082, 272447383, 204963666, 399428703, 911011983, 152799301, 283296552, 951542196, 702188635, 326132295, 3518524, 772401578, 914225041, 380946398, 514687327, 146843590, 491000627, 999145088, 922738654, 452494896, 190968935, 885010551, 601628037, 943242211, 502058206, 615485575, 763189649, 899244519, 624615923, 84602775, 894472852, 282740949, 24679282, 296728458, 171757072, 786211783, 400358269, 736916675, 915329710, 601321199, 438365468, 573205988, 697733728, 79423685, 174722553, 810295102, 423887149, 726560267, 701487460, 854738798, 361803767, 917926019, 382667243, 16857553, 770326447, 766454410, 925784730, 874537095, 422442738, 789163678, 518659278, 555171414, 137871610, 812321722, 787421783, 114427480, 608366963, 475651937, 259548850, 11257041, 105644045, 31030178, 200203792, 626072257, 881334152, 741024777, 246136840, 485612512, 290094502, 785608395, 364709515, 111401157, 448080266, 848748527, 202744637, 406207528, 951971976, 196498792, 219994638, 430753246, 41907921, 50090755, 507288974, 851100191, 150711034, 185184434, 363715005, 208372238, 442238695, 184775073, 330350084, 120056672, 911016541, 590098192, 292211370, 945864024, 595006327, 717549070, 453423086, 468229912, 510094179, 376925322, 801382017, 716185894, 866452845, 582785185, 937305364, 917679636, 675396144, 419710425, 203832656, 964444087, 978169792, 531013164, 433446551, 243074267, 555600441, 326626753, 676174870, 894295117, 87113997, 530887097, 565402930, 808346054, 731390034, 979424833, 945717731, 440783878, 14531218, 755145220, 397246327, 120678701, 491372993, 921306915, 173281061, 830988627, 695978989, 846905594, 721145678, 510756224, 467272661, 769762270, 523636362, 673605071, 641043672, 590034667, 772854796, 938943598, 547426985, 254491766, 501178618, 177416255, 825361164, 34815177, 449638180, 174911001, 501447468, 512828912, 341285144, 344359783, 576074197, 913849585, 207899745, 720944505, 666483169, 267852718, 25184021, 72214146, 913460738, 716315843, 582704602, 139527057, 194090549, 667803162, 976906640, 335051167, 817145750, 861104511, 190788338, 568443359, 793546061, 67955850, 645797138, 297456168, 462934768, 528562812, 790199250, 958239958, 575191807, 858772587, 30848023, 698502171, 668299072, 165842207, 845955454, 912517236, 383700310, 865379880, 507401442, 438831369, 761926130, 818389257, 287294174, 87140657, 51031261, 554711503, 101929939, 29117506, 554037463, 807331168, 668692818, 18987664, 807178993, 257773416, 858874415, 907912829, 68353, 376100604, 36135161, 205399011, 794573956, 132655420, 929044057, 103484174, 264933920, 241963438, 390128691, 131727401, 891818842, 380653782, 424036044, 750689140, 313280798, 159118049, 767204834, 316241615, 288378557, 743423444, 588801799, 41574277, 716344635, 955069987, 83979304, 931847016, 382153601, 407517223, 486743294, 313929828, 871591406, 946712695, 287892013, 988656924, 517690992, 92470230, 327528683, 778976042, 746690211, 785948116, 306413103, 579966325, 74269445, 681277427, 967012008, 451371480, 671029794, 320073901, 522310164, 476177866, 726815925, 676188664, 962201388, 394948713, 40819039, 555469125, 244769131, 773174749, 682308862, 363034845, 380280564, 818714433, 909003905, 497634380, 255580416, 197230403, 382868310, 708344239, 597555315, 727419602, 173559312, 719483213, 478438391, 865806353, 813666220, 619905416, 185710089, 464344289, 508100892, 421434456, 861675336, 882066241, 518005474, 207866915, 902107627, 470228399, 876344503, 284327746, 276995605, 807950067, 157278841, 797490110, 4318800, 979706900, 975161979, 108085643, 683530388, 619727982, 125393545, 269000322, 146545772, 93321641, 966940616, 610229022, 552020660, 967631481, 508325585, 828406570, 854437374, 587553575, 603566518, 691648842, 425491557, 924610976, 846353104, 754913294, 789764036, 403013936, 571715756, 66521120, 305571473, 816554478, 639773753, 27330548, 607821141, 599756211, 759617660, 47933479, 617397433, 270978467, 592437766, 189464596, 900039752, 387842213, 616195169, 509392946, 528987973, 502224993, 761059692, 756699584, 685902791, 992268991, 41870877, 632578205, 262155416, 257478846, 558436028, 971893265, 750985053, 774569189, 735338571, 625886341, 120948397, 652204704, 351926629, 57787725, 781755630, 852095836, 631986123, 468418515, 622166523, 121175670, 618256315, 795064942, 62391244, 75052207, 330593728, 774438442, 901635317, 995728790, 35449154, 977756089, 102222121, 536299436, 540336919, 665274156, 275895242, 435190332, 720410208, 51516113, 107847961, 617865613, 603041039, 97554505, 449853057, 992863026, 840853492, 287108516, 804613569, 536006520, 772405165, 620211195, 232413628, 128811559, 122881008, 991376475, 875267741, 532113662, 321693338, 975641371, 828848217, 518673573, 650212667, 950702252, 866785110, 902089554, 923694752, 421682746, 444991769, 780386297, 568398661, 760846942, 669726259, 424324973, 890220435, 989005638, 951243561, 571152291, 640320153, 129189337, 879292177, 758013977, 118523487, 947449045, 641568029, 926562039, 538009004, 738974908, 389545399, 975850450, 478549053, 885570328, 919903061, 548839221, 596395846, 679356941, 528544934, 664668733, 701827492, 117556191, 179941844, 433181650, 774470648, 30854782, 290528406, 468734480, 712337616, 772616748, 215428280, 99089571, 515908312, 406120275, 207769475, 33563275, 406690076, 113820851, 891849259, 609173176, 75147826, 140291627, 326972887, 769256361, 681967320, 276629243, 286826516, 64950423, 269008316, 809590292, 850939526, 58235649, 614939252, 424457157, 647537659, 358164984, 259016052, 303516427, 785984454, 601184931, 106030312, 5998727, 524504942, 812721732, 461157005, 178354396, 152409885, 516128535, 430199091, 168784559, 662354451, 655147867, 408356280, 187876856, 333515959, 601742036, 610390451, 196384652, 117989949, 650953252, 319813300, 23505050, 304530196, 313942510, 485769893, 830218644, 231045314, 619542891, 437965636, 44142073, 930451503, 187993125, 828840567, 914262260, 213381201, 733082963, 858152055, 15830047, 71270292, 220377931, 40124663, 849009757, 819907193, 791092435, 939876008, 65465234, 933036655, 414625652, 450827207, 656416985, 13444627, 598078943, 677025309, 361089149, 752988884, 834009648, 861506231, 770689207, 884130674, 177224345, 126612580, 789658899, 197956090, 915432131, 567012012, 625435560, 39745947, 113233257, 216878086, 764194283, 997352143, 992561115, 413179692, 741821098, 72198651, 845618824, 137099838, 152133575, 981003388, 545338440, 188568305, 41850756, 84836088, 485289799, 256649750, 815859077, 68143914, 698307063, 341770448, 831413786, 624812339, 839594974, 54603881, 827342920, 371916940, 64291861, 272802423, 595917184, 744552636, 145634024, 525806521, 273973587, 25103711, 357701569, 980437449, 11070297, 517708261, 321408826, 673471887, 987678893, 678824354, 180931897, 462753148, 166585117, 291764414, 312377805, 643609168, 699621565, 603420805, 674729788, 998413532, 33125482, 608908312, 789750750, 589034474, 415906930, 118897538, 586005049, 943865621, 221449237, 234385985, 619537389, 1186247, 748847028, 926973788, 397884075, 7631353, 470189532, 790612651, 662590249, 61841815, 102404571, 951719831, 493833038, 928184439, 443559631, 582039032, 537321667, 561701442, 352735562, 352281458, 561924203, 280540477, 146829736, 963498014, 240636694, 131357028, 305241902, 822732649, 994638145, 332115396, 667609932, 450752317, 120435524, 707879740, 140088111, 397844865, 477290642, 60185019, 81319104, 945057898, 904560343, 21211633, 189105354, 419211917, 658739095, 893774394, 333034316, 513776832, 982939692, 297688013, 366356244, 837697635, 385102842, 136481595, 133364596, 341798919, 519790827, 486874168, 968104306, 193761680, 616547434, 149414574, 503670303, 200884236, 22111753, 111156035, 672306792, 924894651, 326363250, 592093242, 439239193, 299249244, 769820040, 457033942, 412266044, 599768636, 881067733, 664392363, 744229233, 783673056, 522971663, 228860040, 346009862, 477608503, 979729505, 877812343, 472043434, 633095925, 156513369, 30062947, 93285489, 193316791, 810704334, 118258351, 657248994, 563149132, 481417454, 747715626, 823544454, 914145156, 691603228, 513384532, 832889769, 125946987, 475227931, 323210055, 88918569, 687479879, 188136847, 609867159, 771171326, 192609276, 218324003, 635857258, 830657881, 420054612, 659122980, 871737936, 803841644, 429712012, 456911862, 575360313, 474394394, 259342497, 777085595, 554873611, 72962591, 624853492, 130894031, 265773281, 335423979, 822523384, 852360455, 327410962, 970159470, 396262082, 559115473, 779473230, 957412248, 186592317, 713599983, 178937507, 632714033, 226757799, 361460316, 133814744, 318035156, 234564798, 292069194, 903468572, 640668711, 294600696, 762345603, 233738339, 761018882, 288143083, 871731021, 773927439, 284535941, 933853741, 34432855, 938049524, 558738492, 819107606, 220280890, 895246359, 78828891, 743247843, 188567307, 19833054, 744596923, 171180871, 453784529, 218020953, 249620197, 816791359, 324420951, 636927373, 19054373, 868174598, 4355293, 641901100, 765856767, 826232190, 615251323, 970684552, 317949202, 601216717, 731741473, 154589951, 838303922, 953724917, 726742331, 577700610, 896925714, 280269018, 114304879, 910803962, 375596911, 629852087, 587446813, 38935200, 489862645, 579644669, 12283158, 182627015, 55840171, 423769604, 480578028, 903644510, 804091518, 283620714, 657356463, 978530664, 82336603, 993304068, 324122030, 454509334, 19895682, 95719307, 661256154, 876394318, 646208499, 661968105, 323498608, 946548248, 789816041, 197474453, 558898719, 442635269, 200139859, 530812448, 158576940, 107653415, 758942285, 22710561, 927179081, 180345622, 95202538, 741789352, 53378518, 212105777, 891065864, 793237648, 584039370, 140370585, 444473979, 832823310, 736340801, 141431900, 684251461, 737884440, 64600103, 67493804, 316947288, 36127328, 422846580, 254806306, 959974242, 363084500, 275016657, 774677510, 272530965, 221088930, 451929653, 648398410, 966212964, 26514894, 700054519, 564060002, 173154949, 548896317, 518853891, 729528925, 68639878, 120838831, 79695456, 199013502, 672718369, 746464966, 445915479, 328105355, 317515236, 155510639, 370953136, 244418330, 155775032, 492062139, 791604821, 836361670, 684943906, 132293828, 472738961, 956607402, 763133326, 987520991, 556938279, 818308314, 28933877, 683792694, 90657377, 850189010, 498898825, 79206298, 141403914, 319375102, 706272799, 94896082, 560374497, 122825253, 434254997, 859064159, 81524346, 557043698, 551688060, 222762730, 390892170, 530719797, 993640707, 372561442, 29421243, 911054073, 239218148, 637355454, 233682680, 872032393, 276706807, 53544508, 299315427, 958134144, 543418959, 674184203, 112014589, 705022222, 488743945, 398360412, 678835383, 951879122, 725768319, 936183593, 208857879, 626302446, 612272487, 259795790, 91089748, 898979919, 580266391, 864820321, 232922327, 208846404, 160817685, 266315228, 540523620, 670384726, 636421928, 644561734, 137590652, 314421670, 636809183, 341291561, 912864361, 909035092, 874725509, 167396857, 388937965, 674225805, 129443234, 277501519, 45687734, 44804509, 125744423, 993152338, 200780290, 906659590, 830761169, 790566273, 573912290, 686982357, 19702721, 923276430, 149632289, 935500406, 929691314, 665773647, 531790934, 232851863, 66213004, 118340452, 991017212, 317358342, 27956076, 13221345, 722612922, 860850509, 801955404, 765265641, 352886477, 458462487, 846411042, 728413619, 586491435, 672498905, 57657946, 101828401, 452917513, 385957775, 801297834, 695327033, 869245891, 700454700, 51270968, 253608342, 976897813, 802284854, 565513441, 795363854, 486709571, 747292926, 981950132, 640455566, 390422546, 497852234, 622592028, 540218103, 824887535, 990218735, 220076724, 378928853, 164268993, 963462847, 338301145, 710065694, 402185533, 838763933, 79744760, 494361190, 769798700, 164005068, 750199638, 269746755, 73842374, 603921487, 310664487, 567517584, 347681186, 189504983, 643868484, 709403032, 828820041, 194735467, 733367762, 184887149, 477372069, 299675960, 8395370, 382433302, 951552110, 590678861, 79736603, 74348035, 119686723, 395283306, 555304268, 818358750, 414511910, 787750678, 617950923, 939761953, 197890299, 301290470, 525957913, 396360155, 35399970, 952798086, 229542092, 857788948, 79937065, 128834332, 433649424, 434552019, 744753323, 561411632, 750224422, 260224890, 485434863, 489915407, 228002011, 96170397, 629148245, 701504531, 271199076, 441768933, 180546012, 586874693, 835613994, 381225573, 334856528, 971472027, 993979985, 765012803, 186741209, 267675016, 375423615, 344462019, 945720107, 477099813, 390480024, 827151220, 881236429, 92694358, 39222831, 318843096, 94939668, 218005496, 995327216, 350509376, 179925556, 547187468, 593585828, 108462428, 864505417, 123803778, 537407147, 902546594, 426357508, 595603850, 67493906, 685464778, 805734498, 29267652, 479914180, 300808718, 516732131, 207787285, 338333397, 230992269, 181632445, 239965700, 652089195, 711660289, 732537723, 855328161, 846496804, 39567455, 987601267, 753259347, 856128157, 981658469, 539032052, 578720581, 366695758, 523439258, 192537769, 582806534, 249448233, 398800722, 11904593, 744753035, 277834366, 277865664, 640915789, 409827550, 480624867, 609199377, 259918069, 778018804, 192594720, 550083197, 459102990, 620972998, 710971277, 569069792, 598425016, 369472302, 370395730, 320248429, 482728948, 192468496, 914458993, 9448055, 832636262, 898183483, 800795616, 942917201, 4171502, 675058863, 518298336, 270953523, 692933140, 962958126, 247754802, 185611670, 665355487, 35326058, 196567445, 503295848, 535368318, 713870620, 478393132, 781202959, 26932171, 404173774, 204331621, 313197734, 634064940, 273637417, 282415107, 827912513, 109472962, 522836548, 693224464, 38963521, 619693818, 520992177, 37552929, 680292682, 972624794, 287322258, 147238666, 321437383, 696327606, 758818367, 160016805, 878925869, 12232036, 844254493, 756327217, 495109781, 718539194, 246368887, 365815947, 108668320, 546530911, 491436539, 54860055, 775855580, 226825588, 677154762, 168226368, 194776602, 941362910, 642540889, 39026546, 260070523, 262362690, 76662964, 631651786, 227657016, 378186487, 229236878, 989379242, 100917755, 236384820, 718486526, 98491189, 526679650, 995479748, 830769638, 35052012, 193365688, 928948818, 312013173, 366819567, 430026728, 441858553, 220322598, 175797784, 40192402, 850835732, 764103479, 13976796, 745377364, 267069685, 885060478, 142932452, 24981134, 713758849, 425227132, 417418718, 24979809, 144916300, 541183748, 302538632, 249791451, 149887997, 791852479, 250211025, 454652053, 396037901, 408639631, 627742012, 446095105, 914119014, 661316897, 376249992, 471397889, 961580133, 797649882, 832328157, 404357179, 95927791, 507276151, 635029975, 840460466, 344025028, 557406477, 566976025, 553558909, 189784698, 885377587, 785833439, 963143788, 835949268, 837171578, 837423977, 229858130, 375827991, 639086375, 673938889, 801036245, 603150999, 859533376, 303693909, 165750742, 101736101, 44962066, 812183820, 20034004, 565676334, 486500422, 690784690, 430908764, 538504407, 565550800, 261329427, 400867259, 140344272, 954963531, 814216125, 854893105, 708493273, 309518176, 325039017, 392223151, 149890151, 2570484, 77396348, 112383121, 67587523, 189606719, 984286081, 10166760, 690285657, 169310679, 714521256, 158809663, 522340591, 52186408, 430506517, 987408567, 87113233, 211123549, 185813879, 158283034, 928075430, 945123210, 500851468, 317679964, 837704647, 364615168, 388497501, 129241941, 120158914, 868595154, 552526683, 758938460, 504245792, 818237080, 245788574, 453509523, 879584038, 468810754, 743811965, 219249841, 247350374, 889753066, 695800277, 343905504, 879294432, 203697904, 168219166, 597661349, 661033502, 747619395, 425538637, 952013166, 737783239, 64076401, 225877397, 645018837, 470710533, 30345458, 604724824, 514154450, 179065553, 559238074, 184571933, 921495981, 851729940, 852213070, 387918754, 295228856, 113748673, 642756948, 404121794, 863041410, 30895111, 433582645, 600631810, 726972432, 961953308, 372259151, 992163604, 469363729, 544273752, 246564363, 385234583, 441290501, 353763655, 646584852, 520957923, 509088399, 697769596, 107512710, 4353361, 844157934, 980590015, 914136245, 109198922, 413173019, 234614725, 949018194, 281787570, 664332680, 46659825, 955705176, 396404341, 714363253, 756514237, 370869913, 198185134, 524712743, 562167593, 706474033, 692673683, 3809732, 139830304, 76213547, 598174536, 578784211, 175345233, 618963870, 507984877, 82378147, 609994887, 654865785, 552906786, 84050059, 406153845, 232576594, 356103228, 881031056, 597717047, 951336685, 653059834, 537505788, 592946598, 863313224, 462700394, 7565974, 343277152, 592645386, 686038530, 316418660, 42996242, 9544842, 642464432, 391747474, 755309845, 969359652, 419591220, 586192161, 78992214, 805986613, 79730069, 208597993, 918611715, 731757659, 18826634, 682042033, 232716276, 396031720, 442476755, 298880666, 261047211, 339889354, 977439183, 391157391, 514563260, 857666421, 738865380, 20010223, 643077257, 424662836, 186173674, 531908674, 725421607, 143866119, 616830440, 706274011, 684212741, 481249652, 82076646, 615961498, 603619087, 905454447, 446357941, 538427833, 552945206, 635370511, 449884311, 881629174, 133868731, 73319731, 816768317, 318225939, 925045668, 364365329, 352874125, 705448270, 832345397, 161884488, 752991258, 643223666, 479447742, 392808097, 568145029, 236564792, 563145363, 11329162, 559998455, 42620340, 636917042, 719262629, 840578500, 865164398, 738510658, 976784572, 949309453, 554113214, 453351499, 367772228, 453494929, 533259073, 242062533, 798294018, 943075740, 923180172, 83939874, 568960024, 262031770, 782220365, 120180219, 197144870, 64152971, 286540757, 450966864, 469826834, 99317822, 712705642, 212853978, 438061544, 758011841, 964545783, 132561705, 653980767, 116042332, 137792445, 249676313, 430785599, 704223678, 553477108, 151752306, 441922834, 650473712, 464364956, 258429454, 498005470, 717061498, 451978027, 178490485, 177951319, 890135395, 751590851, 104446103, 424704730, 800268132, 301414623, 74394557, 320262203, 85469201, 993202095, 116676482, 900417322, 702319285, 30570004, 899554061, 255572462, 506014628, 163532454, 380831154, 560198201, 499231663, 507143444, 845662777, 907027900, 138931338, 949806221, 943769827, 2215736, 46251876, 265765753, 181135357, 279941595, 941179821, 680561721, 276131264, 701635187, 830568200, 353128576, 787489156, 434323776, 690788099, 516280199, 401746661, 225390782, 502213851, 179692106, 177258320, 240766205, 700086171, 416523754, 698553501, 716007063, 757476010, 848256624, 501024685, 351017168, 154424179, 246356860, 260450513, 473867065, 605971045, 117848904, 549608083, 580437695, 346687622, 600824136, 98200822, 383148975, 495291782, 950988198, 440667096, 936190536, 263662692, 63976438, 413731032, 619267232, 161865296, 213801117, 117814333, 127553413, 84077516, 91787324, 496779700, 645084222, 649752779, 811877646, 663949324, 851837808, 234264807, 91544456, 844165891, 625508050, 570001941, 438685626, 166151797, 270611031, 332019547, 520211793, 931438959, 623793356, 828576109, 158931910, 301086302, 304624790, 898976137, 372475286, 414998854, 76392194, 10942261, 364804524, 441096066, 686718398, 530138060, 643042677, 119856675, 714395309, 541344147, 835831009, 818553871, 759409935, 901041597, 580490511, 215116515, 635850396, 225158471, 355850010, 197658166, 994010128, 901611050, 932090294, 853886988, 836009001, 524090586, 947234119, 240267261, 133484838, 28553568, 481248819, 773823019, 191506014, 403878365, 812342991, 510446725, 904172864, 497303236, 835549880, 329273473, 488602634, 653834526, 862666660, 678105687, 747480123, 704765712, 176726391, 594735329, 99126988, 995329288, 127828418, 889169528, 668889775, 213081280, 503982235, 706708564, 383441555, 843852229, 606104326, 131256033, 820404179, 598403048, 247583281, 127339108, 480251154, 322927581, 301723581, 577295697, 387665408, 514942445, 643216778, 620869848, 320750514, 416484105, 270791965, 545472196, 68129122, 75267416, 604055789, 540910528, 624866329, 278088262, 243841847, 490716496, 711533028, 481946100, 343911717, 620439055, 623832419, 297267067, 469038279, 529927368, 436585049, 11833712, 909982202, 34258174, 781700027, 998665674, 916021165, 561839542, 795864534, 204750891, 323214477, 109227457, 154098434, 973449834, 709356569, 102676052, 516217777, 428886172, 399369504, 396035960, 203623029, 972093729, 612430394, 157282376, 932588183, 162156887, 990154848, 951852142, 993162758, 576253483, 377961583, 836965452, 880023393, 407489308, 299540337, 715701703, 493016707, 169987259, 663646179, 991747035, 285966290, 10881209, 772726364, 641075907, 86610868, 557725688, 605000267, 629609703, 792030202, 455585075, 894841517, 84867395, 210497120, 741696959, 699715395, 216307811, 813273782, 844125448, 711432853, 633480656, 203545259, 851135107, 191160871, 238186113, 146273760, 830123087, 210204497, 221851671, 161074474, 95102110, 73398792, 928805988, 514041827, 24322366, 663909456, 766390133, 648073226, 977715558, 555466006, 583066138, 960107037, 705858356, 666770994, 510721632, 401444617, 985344089, 799915986, 238989421, 334312224, 579003280, 302286652, 324524132, 632520334, 968144398, 373132975, 736127038, 222602236, 637863014, 490958763, 411682425, 17203469, 910858608, 158670465, 424598627, 49331288, 359767119, 764806687, 923262066, 653991990, 552449857, 733903788, 346404766, 616817445, 47838526, 505961833, 573074891, 471554243, 94123104, 975392695, 828700141, 135253167, 796258830, 438811860, 515451624, 118734845, 900296449, 602881408, 268991915, 124542697, 412433960, 674133797, 132905421, 68634910, 831201318, 771853253, 396633937, 681971950, 571952729, 653920920, 264232443, 580300737, 893917714, 610777815, 567083691, 388705789, 295387620, 840648817, 184936010, 183745879, 287055169, 806197083, 217635225, 149883758, 902963958, 846785923, 610350938, 617197787, 945803497, 136861863, 169161890, 677975882, 164624755, 944044242, 19957543, 415490198, 57393653, 36715982, 187497999, 45111075, 773853478, 387154395, 360360043, 862195284, 274977725, 793492618, 540575745, 614592397, 680486457, 214479731, 386528898, 541677081, 809936681, 819008354, 962126081, 452209925, 181351338, 52892756, 13239811, 195175480, 480412762, 198047708, 528466123, 372411232, 334592616, 116281014, 736125436, 378555733, 718676610, 592941640, 783917350, 351998632, 409903652, 347660969, 360571244, 432794553, 347056994, 880076961, 487749705, 736609564, 117775326, 171628051, 229799048, 903381983, 207526193, 962612091, 168899183, 901788689, 20427632, 790541102, 64875282, 955855478, 279699666, 453410097, 942480367, 13325360, 74420330, 349060571, 772683833, 41449642, 823383302, 913903426, 613203541, 292779263, 82245702, 243572727, 410688660, 690454579, 799154124, 636959621, 693333011, 775309748, 544538918, 465911795, 765535514, 251901606, 68253403, 431237621, 245557824, 459316181, 48023858, 837930112, 490725934, 175665848, 138239139, 465252079, 784999450, 124160056, 499610538, 890691613, 407589373, 982146128, 977752063, 717271824, 325677793, 450896648, 736488361, 151056058, 774963882, 743115104, 551403587, 515423005, 743911425, 264563126, 345228446, 768733669, 134291634, 474457333, 199802475, 88158068, 125853859, 52136069, 762301200, 220702050, 205736246, 957710731, 20753311, 564530552, 351922182, 721206805, 28972260, 27710003, 143360620, 223744362, 43906062, 955513832, 627038753, 684329395, 631869437, 481393996, 784587928, 114535721, 42100020, 996456818, 84694922, 511018722, 751206815, 761067864, 137600225, 641111775, 400462674, 644787699, 78924879, 772419901, 554237771, 16846428, 133411773, 901394943, 428591606, 956403709, 255620889, 881209329, 370536613, 198051165, 277835584, 659144067, 573423225, 388248920, 156312078, 512999248, 974642168, 251222922, 401449876, 159806322, 300767581, 666871082, 276530176, 716573734, 765561623, 569161374, 601834360, 457970240, 579941788, 326580683, 611670511, 570015466, 103589576, 946169793, 877053449, 69370152, 457304011, 487634334, 834295614, 576839857, 289466357, 320427266, 199675035, 865842682, 429652539, 131074329, 408875583, 910387522, 674069750, 400107824, 319442724, 368652077, 450603056, 830764752, 954252778, 24031500, 441792651, 510337389, 413014851, 636685711, 129555466, 123373630, 329737764, 128732386, 815366321, 343374037, 927129943, 999170480, 968164889, 216382601, 748043076, 387492577, 8063183, 296266172, 680623209, 24161058, 282181252, 281976918, 579580250, 212833724, 896386102, 995161250, 566258261, 691615447, 480178041, 39586125, 373238458, 508059739, 781040367, 550279180, 422969400, 543006975, 748756858, 567076719, 678360527, 140170588, 112767940, 227563285, 113638687, 622873816, 958564901, 753791160, 130425324, 491039529, 515134871, 953446970, 196652335, 589391880, 238761621, 415772145, 989401531, 202073237, 269687991, 129947736, 803878448, 224511488, 417423467, 287303952, 347286334, 19666399, 83864368, 305009071, 180263335, 352668175, 940888133, 40675742, 391780588, 730928961, 45264729, 83617232, 622678347, 388182741, 220801017, 720535036, 858195298, 843312639, 720679688, 404606474, 813793448, 242656828, 257221449, 225263107, 437151647, 411881457, 149706878, 935498664, 509761742, 416589282, 466429163, 769381155, 801997049, 670418798, 388386899, 239043019, 670692938, 17779286, 297338382, 426407054, 755178739, 511157187, 472906658, 227303399, 49674400, 947414049, 865783845, 485591260, 134576867, 387586533, 644470902, 431048116, 624265729, 249109634, 546290953, 253433909, 801376376, 135987271, 586879582, 959656145, 674200929, 228201336, 270785441, 718704730, 977039153, 581670109, 113875927, 170847349, 59547601, 366351226, 221462984, 585360363, 126246280, 235047700, 931978651, 442385841, 162490578, 952617196, 685655094, 219379367, 877964270, 435883276, 343593856, 579458336, 485107287, 467181057, 855665851, 622149699, 144791767, 389935856, 963362813, 779131582, 262828637, 744343257, 259042338, 409929870, 27463721, 857614525, 82170948, 818887213, 581145712, 512442982, 780653576, 336936456, 711793705, 223200541, 917524747, 896910889, 456450958, 559101853, 41199592, 992446983, 61184599, 891313776, 851136312, 244399950, 604280468, 43129417, 995337511, 929130644, 510115821, 688828446, 514158360, 450314739, 944869097, 741251405, 345398748, 203899644, 262453607, 738877944, 866266807, 830825942, 224065317, 105020451, 648412507, 578190951, 769636679, 119071975, 662422710, 426164714, 896102292, 164860890, 660360786, 449482159, 69947533, 182212349, 786506934, 180900931, 576930655, 124362633, 967465459, 330041432, 866043221, 865500053, 617563979, 521516916, 820809715, 560538033, 135649780, 187751347, 42310637, 334763517, 868157714, 509671104, 830154079, 618022753, 415627848, 591726002, 758407230, 901167863, 633618370, 678201739, 56720346, 115689859, 496826585, 77974404, 362696755, 454370218, 876137937, 142556136, 106089455, 494117574, 990871721, 238158684, 602007626, 680810727, 434662778, 243808095, 872203783, 769805938, 831052391, 587106998, 860166301, 954345842, 715542816, 394000284, 355675601, 938401490, 756963813, 853077077, 865264478, 648603052, 126692884, 932218680, 499605822, 229487579, 654857550, 985425690, 10724738, 276811695, 114947550, 255923816, 828721179, 27216823, 896690071, 845970283, 132657655, 819198057, 512479940, 785436270, 329167001, 941262374, 128236649, 573170189, 802845498, 295009653, 975167420, 98135176, 495201121, 782752340, 755799155, 491065156, 724469591, 160599318, 340215728, 601092889, 577843146, 961966636, 957205065, 990169838, 537959348, 11612887, 868186087, 494604457, 825666729, 831777830, 718412307, 281755422, 285271244, 621642724, 28552566, 302018296, 346794233, 49618988, 540897688, 999356371, 551308293, 559293890, 12844526, 323880327, 223564946, 480215833, 977244387, 332881858, 504240733, 69078041, 787734876, 929822382, 540957424, 613615999, 253609112, 373826709, 821468723, 13749677, 411366717, 61577722, 917737449, 613228729, 51114877, 195397056, 904188602, 314135597, 256327164, 742182598, 128189753, 784471324, 151028590, 819791037, 125121737, 670106091, 200267500, 582098134, 451128162, 679993500, 618174473, 413276923, 904864464, 986498563, 855830764, 993218996, 896467589, 49984081, 52890843, 985408948, 616151139, 347950453, 496060071, 726543190, 367472925, 642263748, 246497331, 859685627, 443491024, 530737175, 554145289, 64284170, 506393850, 904673227, 539339407, 657919107, 391777029, 604242305, 352129750, 567645060, 249091623, 10920858, 171940620, 147819116, 737814263, 425568189, 160210012, 370335974, 939803904, 157837801, 341913530, 562763206, 514188755, 179849911, 234163298, 401256952, 497116443, 853686616, 715279776, 562928190, 501162838, 973989916, 94088193, 776711738, 234318552, 207846253, 822616858, 610266342, 611041831, 392711278, 278213824, 360777707, 421842259, 731241480, 381976156, 805763914, 536749486, 995929491, 727855293, 680077144, 322194363, 584584774, 687501290, 753199803, 295218307, 613572807, 415442471, 346245760, 635292526, 929931245, 677645222, 255646696, 853111716, 869110745, 681244073, 707863195, 719935020, 170070552, 445712741, 603368423, 478656808, 109199408, 273269459, 112034796, 202495675, 900009426, 897386616, 166292266, 760855832, 269006687, 350203518, 892493590, 581403191, 133115286, 196970394, 67208859, 20895082, 802587039, 559784329, 58232541, 740283967, 569161574, 171566233, 649260580, 686409143, 80509102, 982351066, 756005477, 426015499, 152288189, 844021452, 233671790, 568674414, 705966211, 762784458, 411796085, 660834650, 106660923, 856357025, 176632510, 135497634, 705294756, 678143016, 410081204, 343469639, 956883004, 946833604, 978049024, 271338832, 63285654, 781751320, 408883740, 299782378, 827816470, 390967301, 632309601, 172327129, 400236993, 669793567, 594358469, 828832935, 560348474, 680432968, 992538625, 580106584, 987477635, 91352903, 113817334, 425905169, 5653723, 335592971, 588135826, 592940579, 666667994, 664088827, 164324478, 850008884, 825729234, 519811043, 92006825, 852420820, 863721517, 376603663, 690434479, 464782046, 408435957, 410076310, 338495811, 489271809, 386145061, 911776722, 638434646, 422353554, 868841015, 724580266, 125907457, 374837418, 432785441, 710424478, 607439367, 891399258, 564675560, 463930190, 516043139, 140634698, 702682662, 383077777, 994197459, 577236444, 24068696, 443869467, 851456881, 102680463, 847931820, 337042514, 837031926, 449968828, 964609093, 516117737, 286941482, 315552200, 260913442, 240655364, 357835023, 270122746, 753464219, 485731944, 379260874, 318064609, 383026285, 868791314, 538794102, 65776310, 456507716, 630318141, 821749620, 167427153, 93048447, 599408023, 628216022, 856626963, 594304974, 225072422, 196987752, 533896419, 609144113, 215422242, 610416008, 266486218, 755165418, 5588754, 231084245, 568783318, 21760100, 539772731, 488989953, 807191208, 441198968, 79166961, 682344576, 920874900, 589886139, 238946485, 92701937, 675021849, 138188763, 341554781, 695630531, 395579009, 184090111, 796722307, 423905079, 422644276, 400353212, 531181971, 654947221, 933331765, 827287279, 65953194, 612137667, 973975366, 798377496, 796048626, 531447863, 452261119, 613202164, 405945685, 10768147, 722264958, 699967470, 71196800, 990273415, 128104298, 1572187, 515484266, 610907566, 782502411, 90041948, 825266799, 893689556, 515354570, 342078763, 449937545, 46788300, 861384705, 303644837, 885858797, 269047819, 902492503, 989784050, 519012518, 281685760, 555853639, 470795634, 868702884, 673481741, 794973254, 287187283, 943280008, 468439656, 909599894, 661092171, 254121163, 779225894, 943947176, 283135024, 67542385, 575081536, 942400443, 616103746, 315264446, 691245394, 338765418, 137392063, 636714171, 20742275, 995482811, 714270265, 322940278, 443839245, 473931811, 788983174, 38511774, 830262468, 331502938, 269736134, 408612195, 540769439, 192165215, 834113119, 244589851, 145004240, 159187470, 308416803, 721038751, 343015873, 187278969, 120578709, 123453538, 723929131, 620938676, 513423445, 366545173, 851100840, 621427579, 591865265, 732891744, 911635391, 504657794, 58146358, 164737614, 589526357, 642411959, 651820696, 441501203, 637106038, 743793969, 453307334, 350327729, 127529889, 615521578, 849842294, 817072478, 915440095, 915563969, 825798927, 402915594, 490641805, 167457644, 779031114, 652959876, 804992988, 952977433, 85826132, 390335419, 878555126, 94106321, 745667577, 34070933, 374438161, 44552877, 828935426, 338114805, 878905387, 630196847, 375650837, 871288654, 249628253, 545675790, 724260007, 336614169, 887648051, 938953924, 625724786, 264448121, 684029257, 42731856, 374024472, 462460815, 960597604, 529835600, 811144546, 101648796, 221582373, 920543121, 992634067, 765449221, 488362980, 973315534, 754584342, 403655422, 73020675, 557887432, 441708121, 492233411, 163047537, 172823869, 740713513, 858680134, 904597207, 647230726, 801804459, 170743948, 623846328, 945051053, 293709287, 860723153, 821292002, 367822775, 357843361, 988234544, 717761181, 552859133, 459818045, 70414324, 764625989, 994660554, 42457691, 840115939, 808752244, 541396746, 896248129, 592444475, 248802462, 748307470, 439783499, 234642317, 788640870, 806063173, 693323916, 622956645, 618331006, 868382260, 286735363, 807452734, 1831494, 322175432, 850358136, 329771940, 555357211, 929364831, 92271618, 674502065, 595080169, 101648602, 13692461, 497376562, 620798169, 189312659, 911448371, 556063568, 120485134, 510864467, 78599572, 304043834, 183408810, 647152556, 18582163, 535397348, 451877312, 524303195, 868238743, 514247367, 491921841, 478987176, 185089922, 217882113, 32154029, 32645372, 800168654, 934941351, 631765803, 958833826, 151128701, 416507191, 351424902, 95976518, 883379285, 77454540, 90522610, 679638838, 103816421, 63693020, 962122852, 987055622, 926360872, 20774208, 88699291, 136109667, 263104216, 842969579, 687452202, 717966806, 153686592, 268752329, 798632545, 887611084, 375968202, 201387705, 445333263, 379971413, 835221660, 471428513, 698194025, 537166645, 671246018, 551999051, 670385784, 520067201, 18254184, 649611376, 128601041, 983389510, 848108113, 669402525, 802408807, 892717655, 357844880, 221175636, 719960826, 594868980, 839371547, 71482749, 882682265, 731491298, 961802294, 649473451, 944500387, 96698705, 915752940, 765778814, 335203419, 800969379, 990018191, 28869862, 901944668, 946148335, 511877469, 806225446, 504945117, 618041703, 168106989, 170224202, 848004333, 42630905, 369316596, 412867520, 402788439, 930143793, 560205078, 516097110, 47310991, 458717047, 434761447, 217986867, 405158407, 482483810, 501229557, 82557542, 705132434, 297499464, 103847, 654922936, 370748456, 612793768, 177408662, 902803209, 662829086, 107453472, 587812063, 296258828, 137950578, 873010851, 662183253, 396362085, 484813478, 6389232, 864615027, 920068008, 177505851, 574821480, 783077735, 274489798, 258333936, 186907087, 66377494, 237098834, 790585734, 399854894, 156959830, 978882095, 205818092, 706267974, 259471569, 156040394, 995800449, 362379418, 518865430, 492673552, 173510066, 926502002, 4850915, 678104611, 348386618, 351606762, 271564106, 5230826, 473912173, 640971245, 586297108, 410596950, 522066239, 254967840, 641918835, 455260747, 41235756, 27065300, 96371202, 382763078, 130898242, 604855435, 292160718, 66467040, 324634475, 200561726, 44879055, 696172916, 339079082, 158449969, 803807586, 472309279, 99604716, 49342924, 415150489, 920757689, 75316062, 854360838, 136671167, 341310932, 357849806, 334886161, 218642234, 274123715, 871124150, 750309254, 468258313, 348104506, 975412421, 582302809, 130366616, 567857022, 25609836, 308055698, 326509327, 493409306, 130125066, 846887654, 608602476, 863190692, 466729366, 120056417, 466191554, 841223939, 467004459, 207721624, 778454369, 109333349, 122822652, 110815381, 474180055, 629936199, 13631685, 77688366, 931945301, 444661141, 413592969, 546423107, 861402383, 280076997, 788446543, 717791870, 661796783, 964001009, 150686025, 250484406, 731330428, 425811355, 118810566, 387511142, 953929342, 276955634, 979606099, 470545853, 211437355, 837683813, 120883545, 755900811, 309828152, 338658307, 837855228, 377094933, 592019364, 623395790, 106261809, 668227238, 963733491, 665449596, 140006078, 732584940, 502817284, 734468190, 922176775, 633127270, 832736107, 954896342, 105491157, 47536256, 509811800, 436310101, 225400667, 999059131, 206495121, 270530629, 924285803, 469558477, 972024392, 638826172, 307803688, 210609981, 889363455, 513151769, 630428280, 545087571, 564133366, 884009262, 530783328, 448454371, 272826122, 524477482, 883786649, 974148297, 221000849, 212535749, 996295367, 922943409, 893235409, 375847468, 931517217, 140579008, 118701344, 904183613, 805741520, 573446906, 198563486, 709297168, 714658062, 371744454, 141712512, 273582577, 537344754, 816487291, 805407665, 111128174, 864897705, 313285897, 143080484, 600159709, 260411502, 851937049, 578864434, 6987509, 180899473, 864261480, 397152742, 44096061, 901685908, 634961620, 538402591, 348079279, 793434643, 559315147, 399616382, 806241820, 96275679, 95340678, 854970309, 563755062, 730772090, 19057344, 202907651, 367854990, 748368019, 548446243, 703117609, 893964082, 916648413, 757179633, 362508502, 411022593, 702221998, 289555465, 236577127, 761230317, 90864142, 804424730, 231830773, 404013701, 21575411, 828103781, 132770371, 250520445, 551820924, 445225982, 963232197, 704207618, 155925033, 563574677, 394173729, 590113805, 513000087, 72493086, 399943929, 232786968, 233020745, 146366806, 509333756, 67712378, 865656825, 787499691, 718316945, 170012044, 178561215, 6187717, 989304521, 617851954, 592617357, 647125336, 39831771, 191699611, 964679545, 512266591, 890080878, 29845027, 80599519, 627792001, 168253028, 471082912, 516187306, 555380899, 761264117, 562107546, 603081773, 759706778, 953253095, 252695570, 442133684, 291538349, 616034323, 555101288, 116154759, 655494341, 987306407, 167398405, 313805093, 125812564, 804025166, 119146628, 921524933, 415106267, 699450195, 585063801, 105083187, 103179993, 831701738, 65083527, 890501606, 723257832, 403128265, 675513398, 928693681, 234489942, 493192486, 644951015, 958511751, 91780026, 492836745, 516017701, 991411105, 502159308, 65573484, 736073705, 83721630, 554854396, 615801963, 830254765, 419287575, 71531643, 145316977, 5953234, 984878428, 5958478, 767653192, 69765561, 866064157, 100517817, 436374222, 744213392, 850703306, 459063239, 490834774, 218074655, 503919010, 524498853, 163217401, 872622980, 738972266, 508919929, 185597033, 476230551, 187015624, 359589679, 719062191, 204114833, 210005049, 532287004, 745617921, 205174414, 654135254, 143389168, 143285918, 745897274, 91574410, 740070416, 806813654, 959960762, 534474811, 324130264, 433955674, 83743968, 115798870, 204170071, 911124473, 992782490, 397584727, 289140431, 90796386, 981917511, 613310810, 368287370, 655603775, 212147659, 831478867, 527522006, 347563522, 952813334, 832555491, 143823113, 778976664, 507048630, 991650215, 834794626, 957383415, 538741353, 669599669, 721949440, 928924344, 820412715, 359648348, 296980747, 296673781, 203557231, 750500086, 95116466, 978943620, 742488043, 193181395, 66125604, 724838871, 892093404, 323385064, 775202645, 578364831, 790949704, 132007904, 651991843, 27566159, 870865814, 696317730, 825459777, 620613373, 660498274, 485347967, 179014980, 479992519, 438968610, 165947377, 547586057, 717331785, 778015918, 739824756, 888033091, 308660753, 292734602, 349437478, 896487128, 585556918, 4368643, 112781041, 519006896, 349617809, 746075483, 869917694, 248999853, 878942712, 34818780, 8924499, 389585497, 14700458, 713822251, 413800940, 859187465, 730870497, 309343405, 903951097, 299654501, 35485800, 386793394, 500223649, 592355845, 171340083, 194991175, 263702661, 547326774, 342037025, 700663182, 640643752, 755106537, 64606153, 912998415, 541057818, 821272097, 522618014, 635077119, 406335705, 169482339, 577754541, 547028214, 566091516, 927377676, 434033893, 841352554, 776912461, 617050551, 704057162, 777563926, 767343073, 579237171, 200863035, 266654105, 931091602, 848858707, 58435277, 476417496, 361746404, 873355723, 230143981, 595575387, 247833505, 480280841, 853821754, 870371100, 118631591, 801864093, 393806780, 201074315, 95559659, 92043410, 690653170, 29021302, 318247683, 685319881, 936472164, 395170668, 494974680, 469956961, 135699347, 284917338, 662010360, 223443770, 736287867, 533246416, 875085386, 750705677, 948066842, 342707089, 945349979, 464687976, 645089433, 254388690, 229526915, 19702356, 449160710, 147532796, 80072934, 550537863, 359451834, 268987766, 742869714, 716877429, 901844286, 71328464, 724476869, 739466572, 125183006, 63895764, 938593885, 869924595, 481397714, 648544074, 179444622, 737795986, 286060192, 819523374, 615922312, 242161826, 164548247, 415488641, 734277622, 736771957, 176281113, 868769390, 160241353, 123799421, 983039895, 468842361, 745879856, 212445169, 986841578, 193466893, 68645512, 215707719, 62587197, 781977045, 104875318, 104002903, 356742139, 179133845, 595886651, 940331889, 752356316, 793360406, 466691149, 283641502, 481017365, 882357875, 259596164, 578780503, 802830518, 331586276, 105805103, 86762051, 770236173, 856117112, 797768968, 521083311, 368017840, 307064337, 202528900, 153212412, 348606926, 767931534, 911324104, 562129742, 294677794, 605340488, 335914873, 629718733, 761656219, 599334657, 807952957, 500261897, 538941354, 404270912, 75163726, 646206179, 113007956, 15034565, 765865793, 432828878, 528579980, 935071531, 5441345, 892658477, 524124317, 709029789, 972207681, 856012623, 599574242, 194048614, 514421465, 625387639, 121306242, 196363314, 558630420, 380790085, 217006171, 436664947, 178517152, 747521116, 590617007, 320437541, 129748803, 466439063, 984354422, 591341975, 811468058, 863960287, 350863909, 26870133, 116800540, 201385516, 825236293, 830267689, 982326710, 721025283, 925357580, 899149610, 134646773, 197183806, 131467992, 163882496, 756108813, 723418698, 328454316, 271390574, 541506527, 328971182, 515471040, 372630721, 120586683, 905578323, 961058400, 124524577, 919242947, 950899838, 731493056, 223403028, 568507856, 162814962, 922243874, 634492609, 693254352, 374518011, 958559539, 777870265, 999963579, 570258020, 82218923, 348148182, 999160936, 302865939, 2895141, 836564971, 478324626, 265258277, 571175425, 185720148, 742450386, 318389562, 685026831, 144719388, 514230998, 222805693, 450912345, 741036615, 629805722, 650645932, 616804566, 422833893, 522139719, 223933367, 298574858, 581916634, 997867888, 972711823, 246704148, 285943955, 719835532, 16871216, 302860592, 533534432, 163375680, 784207651, 326133399, 481647449, 212903947, 637698021, 828929124, 639018732, 202678520, 601729385, 209365694, 462446915, 347033958, 100429171, 413841950, 115744729, 784139474, 617414456, 174787055, 758641147, 231646514, 524324307, 431373272, 78530762, 416222699, 120632316, 402765731, 925705600, 812010576, 640675362, 453841126, 643077563, 100391697, 895150350, 18884431, 770781143, 233959873, 211840359, 703366995, 454142762, 683807283, 12797375, 194546604, 439599005, 174653792, 632432419, 684331318, 595132702, 727773633, 546833873, 934002311, 783370837, 69245561, 760441067, 685483524, 848461277, 908135486, 926535366, 650871529, 875920432, 438079853, 40223898, 419631893, 201278466, 692506120, 463411904, 873748048, 775450678, 23669713, 787819789, 727738336, 256955915, 59462329, 774266353, 566039555, 708677781, 665095786, 27043998, 269373692, 126826124, 197641360, 335576191, 565540913, 270824504, 306623760, 78274323, 805020688, 304584936, 407566469, 921637097, 263190110, 642483460, 567788112, 958335374, 597888384, 585144564, 596672686, 365690253, 547799534, 537728422, 975030759, 675397898, 545060276, 556883943, 709153779, 870151682, 716020453, 184741470, 572300541, 28206807, 16489295, 769618223, 507211926, 147331555, 805886414, 516004932, 846661971, 279521165, 924182045, 285444265, 148835582, 558514447, 231334068, 261093528, 50526602, 241189350, 71554144, 974583780, 931476517, 477549337, 976537328, 230318722, 948671629, 710021283, 241997541, 201000930, 207748484, 191342710, 497211950, 687124841, 666202894, 79455596, 927357622, 803706141, 507044471, 890433624, 362087713, 939255269, 943975618, 603128659, 611822797, 536993080, 293307231, 165261329, 170725509, 611869809, 721902697, 977527932, 799355625, 913850654, 422756901, 483411235, 316600310, 248077831, 152061841, 919228294, 974712707, 776165460, 532983923, 312356887, 215797277, 785754902, 960276867, 214040904, 753018336, 316015000, 941271662, 855983207, 81579854, 535480668, 662667290, 89988334, 710727630, 211045253, 473026046, 44612662, 174459135, 735202536, 178716966, 221384851, 816126626, 378442327, 45503075, 228016206, 149554491, 158992587, 655794243, 981813552, 662698712, 977567821, 261040223, 904318693, 430321192, 221610438, 466682696, 896160328, 905653624, 22203059, 983982860, 787394226, 191829527, 662409791, 190080060, 822870208, 423341044, 212489454, 898371169, 244743086, 223192387, 17991093, 438190266, 931216258, 839434883, 657080491, 214517039, 775523539, 978189241, 257241379, 53532759, 883510945, 236810755, 45076858, 134227463, 750047025, 161338165, 186260324, 699756906, 332456529, 836955508, 693801155, 381241869, 165192556, 12776219, 768142636, 242642522, 188996082, 347476786, 953201610, 484524797, 320812346, 636690132, 449742791, 983884471, 210689776, 307527447, 74133683, 127557152, 166698810, 559217522, 124424893, 479651802, 616111733, 409105638, 655861862, 687625640, 653146747, 698874564, 904344681, 641123182, 301305347, 250766918, 182722317, 39499781, 475432396, 118394986, 670933353, 370533996, 707849690, 788692383, 391198504, 180097230, 711392189, 643655493, 808088640, 13585317, 238754624, 303069482, 643702159, 941669454, 758237172, 41409385, 887670201, 8129707, 614898672, 63614664, 755061232, 337657509, 621129166, 461524193, 203441772, 341272485, 600362415, 732861765, 989959980, 872636705, 220268626, 405347546, 311886874, 246563312, 884600936, 185526839, 877720335, 772956078, 183090423, 795589681, 865962481, 170647263, 454738801, 798989553, 887028107, 697525115, 804357730, 592720519, 136949865, 129982425, 507828228, 1297216, 619027139, 146965991, 959336385, 542990624, 852527870, 469993187, 993487976, 437625545, 859045014, 781792831, 971093766, 223241000, 78596226, 343498080, 885154924, 685846626, 602034056, 329099595, 964422698, 224728250, 410443364, 289706063, 359939421, 239597446, 26729057, 353792892, 438641288, 78337642, 797831900, 927414859, 190640457, 697113229, 967850109, 208895249, 994643003, 161497627, 509410060, 242252424, 901324021, 632704974, 470042217, 660016901, 987129384, 408862682, 984027052, 56965958, 688129549, 489669566, 285532497, 621522252, 181736676, 310613023, 166037227, 674032520, 329412385, 883503915, 972596839, 843018565, 449255215, 713915945, 945772195, 460078018, 169471234, 391567834, 228606240, 156142118, 229224908, 375101730, 278726818, 602442879, 529286284, 777324485, 734366902, 484486300, 973295209, 767482156, 619971794, 308935146, 416276398, 34144513, 751071749, 268608950, 864856911, 829889140, 258697061, 942546915, 209690592, 43626553, 955550833, 267466057, 874240666, 98102614, 330083312, 417981837, 381641556, 312734828, 253318650, 610318292, 432521338, 222138046, 738894232, 292224810, 394657839, 535612442, 425732983, 738153195, 617181610, 841465301, 861453400, 441280097, 632633288, 224730120, 24007918, 867730228, 329941200, 618429553, 593345751, 538464982, 175468013, 412122851, 665257960, 63745601, 474371634, 235179452, 50883112, 884657204, 31349811, 682110243, 359612849, 46016039, 664246046, 792978923, 734418939, 330319038, 98083339, 490257748, 32660832, 816675469, 805977380, 121703767, 644256305, 818684943, 36878100, 652944991, 997784578, 395979868, 468021195, 502022376, 979825513, 209322054, 794818890, 683064929, 830593927, 223724496, 513043808, 300343163, 397432583, 441068104, 8684197, 907090308, 12080615, 596281981, 547872157, 520791114, 492952726, 528379040, 620331641, 914028092, 889170033, 948870172, 332131555, 777724090, 38375371, 33216854, 771762233, 736321489, 389555137, 262411708, 847622342, 520412622, 8416064, 563337376, 382982057, 37771547, 490582602, 254338909, 636591633, 318669368, 560757503, 366077053, 21804197, 670022231, 844946034, 846183793, 236857304, 987045422, 406294830, 747913598, 922090014, 651561737, 757028211, 106770556, 424280244, 802253198, 448972592, 377995719, 828929417, 187674371, 973915261, 142048943, 942439303, 795300611, 13106512, 366923747, 16213284, 465928878, 628599964, 693249313, 520057223, 783315533, 547275049, 250216341, 325720216, 4661181, 66072140, 534929085, 709223077, 147945553, 95767723, 418429198, 299580696, 348179271, 415077091, 220235705, 243306392, 256444708, 306780574, 931887481, 414765026, 399485389, 319911036, 241537989, 359549167, 403511810, 215575485, 933543673, 264108189, 451033062, 720271351, 618272531, 740048011, 782591297, 104848746, 494673301, 682031218, 647816889, 477582337, 543664352, 959746321, 149165741, 691104653, 850753575, 936078986, 820761350, 318530856, 295930250, 196693812, 509773235, 35229825, 578492018, 983789079, 79034151, 719928147, 986718122, 95114209, 997216010, 376115654, 439844770, 705783596, 276669753, 580382552, 263414678, 118771689, 615523865, 141409699, 382611395, 955547095, 388551877, 693127514, 620204267, 739970174, 327087136, 519264664, 700148917, 677165594, 394692344, 241722269, 513074597, 983037358, 37097385, 352514861, 759540396, 794496762, 886778205, 814006141, 358843104, 1738787, 50110608, 617963322, 527472002, 821327695, 944814784, 52323909, 336175034, 860714368, 891099840, 27832029, 811480796, 35926226, 18907073, 129395552, 420878383, 937631977, 371990310, 10377648, 318638594, 959864480, 503119743, 821717342, 772921635, 372163021, 277041834, 22822333, 441591535, 878640339, 590861896, 663631191, 751872740, 237784893, 140115458, 208617699, 202264090, 355223675, 663850511, 482856396, 75157493, 337021868, 653652282, 446246632, 758061472, 1396894, 908509532, 959977471, 771380994, 105716258, 885095861, 878513929, 443626711, 531813337, 478660090, 886385283, 193468745, 625513704, 776046710, 647726649, 797136983, 664501404, 527822357, 718299999, 370602316, 190875161, 393854664, 152976170, 612732544, 284346147, 961431200, 758229293, 577116988, 863659902, 167199896, 42759500, 300286355, 708082604, 805071668, 559902144, 655487483, 107189914, 496881845, 11181170, 789910964, 459926857, 364460032, 834312252, 818181481, 809912154, 820980270, 130540342, 294736623, 255810137, 917200433, 600299393, 639373563, 180590444, 743978679, 454530819, 796013151, 366632222, 710626188, 621158264, 413763796, 251713013, 615627531, 37204100, 994972589, 850440448, 94197712, 941518615, 866514857, 390773380, 416669172, 281280817, 869075152, 178140304, 809064971, 13559380, 132758677, 84146393, 756773628, 564455727, 383416607, 82349518, 244658090, 722401923, 88100720, 121091500, 241758431, 648455974, 11696492, 267470993, 538729712, 493853020, 274408598, 696966688, 493459778, 808195637, 225538942, 942015422, 362429390, 598407105, 733628757, 104017402, 921002166, 334543959, 384775083, 499811151, 783423012, 387187956, 969440332, 993607801, 708768854, 488511485, 87399400, 472706349, 340963897, 803593702, 86789879, 21951242, 879279283, 711848219, 573632171, 760241672, 945271241, 476087930, 351107519, 547459508, 725837858, 403014207, 337794687, 179619366, 551179103, 450430038, 254139928, 759089942, 247062252, 368662112, 294300631, 664023269, 98290852, 949298713, 966356642, 78637562, 388519799, 226326651, 43513139, 179217101, 137242286, 359455725, 864428453, 300312711, 84249141, 330823060, 416476126, 532014793, 902418473, 533746810, 80254927, 477276952, 652646015, 252770320, 519466815, 363001835, 111023993, 111912337, 460729892, 173186665, 182133752, 868903867, 424252683, 526255478, 258911605, 340974214, 739864831, 404195383, 660755039, 786497928, 813096237, 817263268, 423994895, 407555294, 841307267, 381694361, 621633639, 634272723, 4656833, 756165838, 665238163, 565983613, 243806279, 650063084, 317867428, 538176822, 7060021, 285829435, 155868153, 711156217, 707537726, 371540346, 75576866, 48652299, 660494545, 940884576, 185911222, 71504773, 745619449, 28252421, 9731328, 625137352, 852526637, 272817457, 61361065, 431060959, 886397484, 37675059, 510213010, 495999201, 981745649, 84242920, 220215147, 907820279, 658040358, 277975218, 144019474, 486298564, 305514074, 522723166, 195186630, 676045249, 962465090, 733298879, 628253302, 499306608, 196602723, 117262567, 336467666, 344378112, 669094293, 343783125, 588977548, 206667727, 209623420, 494782568, 917686632, 997652132, 511452841, 961251972, 318659890, 535664368, 689356034, 733290070, 928322311, 761127690, 239287050, 946614212, 447656435, 637591974, 759526532, 923679796, 942706928, 492584497, 211037778, 626322929, 372222268, 715622012, 770367779, 485727711, 390213504, 944891236, 481503588, 568212508, 315838978, 784029237, 311893136, 903027235, 376497833, 943928735, 120684279, 334840251, 855998878, 19308741, 977962296, 519262519, 418634343, 382399721, 331123565, 72024208, 734818103, 653069588, 883902241, 130732422, 487040269, 637715360, 511870710, 164631289, 279352933, 83844931, 764929914, 116995494, 865459684, 558902680, 812631473, 166523788, 316016920, 445456460, 387194332, 145466424, 776797343, 95226589, 748257430, 890850169, 644204577, 566745454, 383268023, 162381935, 751983326, 790349002, 634465955, 687059591, 180685111, 270822204, 420862078, 818348277, 54974327, 827940598, 692786976, 604303892, 139587990, 704560727, 286178546, 714998825, 226062316, 624047810, 634281830, 667471417, 625790123, 87903816, 494010837, 742279292, 544230859, 594181801, 806137729, 331785930, 996469677, 605689189, 695958506, 139838746, 205924064, 409330857, 615124121, 237597386, 955813527, 909748741, 966517668, 348291836, 893903113, 158649333, 796098757, 687957045, 510907219, 438495875, 126531612, 69349572, 42310312, 50620081, 304175110, 325432571, 32025068, 112392018, 72923083, 384469030, 679262910, 276054185, 175176050, 495843830, 291775816, 625752256, 628108428, 971495642, 780604961, 904706349, 13719832, 179158871, 607808380, 169099512, 455606875, 815528872, 399005454, 992980027, 96048752, 769282309, 21666650, 524664896, 246438423, 967954296, 443966367, 1999294, 91580088, 357832704, 235863773, 349568016, 902719162, 311593459, 616705820, 685177049, 875218149, 577179998, 601900731, 451625410, 217823248, 877760739, 416077252, 866596190, 784066678, 457536769, 4269541, 139711789, 330380433, 26622584, 508552066, 55797452, 812125022, 288607425, 100250618, 459231268, 448672134, 856370468, 697179326, 861369964, 644427341, 671512085, 50052013, 618828715, 194770389, 918661402, 549810850, 269661275, 864514822, 319725214, 464940142, 840289639, 927625787, 315371796, 234319332, 499969150, 519720296, 29118084, 722122668, 242957267, 495275791, 711660842, 300197321, 433098424, 277598303, 469902535, 567613293, 634622987, 923900810, 588829655, 311379572, 343808136, 692471382, 776143757, 87530745, 412585676, 164002588, 794404169, 146735653, 679297084, 123702729, 573993111, 653801409, 673411285, 132180091, 775029960, 245790889, 530850712, 727129343, 435730392, 692905767, 831162309, 862594990, 839874394, 756322279, 791045590, 242322580, 417714658, 347624944, 465124778, 437997246, 939077815, 256498549, 308593589, 603376444, 752670900, 436924069, 18666190, 97205440, 397293671, 51097342, 559807350, 777792006, 674592048, 577341554, 421493414, 535327720, 983563044, 409122330, 500567856, 978408808, 942814197, 424679342, 8593935, 230400378, 402986296, 428644987, 105542296, 431129441, 287231776, 89772855, 235762476, 432987896, 217024959, 969518535, 475363277, 313814388, 839326592, 193670839, 92652826, 443641051, 386465401, 680220836, 292276093, 237174783, 856960710, 888959614, 395004940, 605015946, 551803663, 275257026, 1827731, 869840541, 183548212, 638692226, 136915996, 413571894, 510664489, 215150850, 555890943, 799245461, 369455378, 412838154, 947545981, 444612290, 33330428, 933573939, 875777800, 578511376, 602914835, 924876221, 156225553, 616176014, 398034520, 629858260, 996265436, 694591437, 208349524, 544048425, 359973373, 990314841, 548444790, 570798024, 594781307, 393784992, 80862154, 348122437, 81752521, 927145338, 889252219, 725189158, 570937427, 291452974, 264563340, 984044253, 147047245, 490033768, 940523933, 395577397, 537845692, 861512113, 342357466, 372810598, 678874394, 518863615, 813197076, 346997044, 650224988, 523504953, 83989065, 687600767, 923016660, 556406583, 895746062, 31388502, 98911528, 56761227, 508747789, 342505302, 595812416, 821159364, 32426144, 551008317, 2601432, 328090592, 967245866, 600109596, 821450879, 9463934, 296011052, 605979156, 951048136, 680325869, 149051985, 272501962, 558953154, 624546146, 488586788, 923075441, 434217473, 525758976, 135700150, 134153249, 589246060, 193811489, 345835687, 116658648, 864216186, 798668852, 186799154, 347534, 597858948, 756679923, 233240908, 399188094, 633932548, 203882119, 36641250, 739541205, 506716614, 828051115, 255383511, 731799298, 834568292, 491150645, 457818272, 890667284, 893838449, 263955559, 493879868, 31337211, 411525262, 580296946, 250611106, 374910284, 100024283, 474677951, 225514255, 869864303, 670280856, 935441918, 643457016, 377299633, 714115628, 663020586, 777578162, 282872826, 480849778, 166958911, 507652276, 230247485, 885312793, 249693746, 349327944, 564201315, 789019017, 216283124, 443773725, 970770262, 888559019, 368244946, 945076738, 343133211, 968256259, 889832400, 162256862, 10942625, 27562289, 704150478, 16993835, 580813670, 575410295, 711429401, 358367022, 428059044, 508540506, 40510789, 231625508, 367024274, 594443118, 597205845, 475960950, 566097509, 87720678, 267307002, 830859471, 806120356, 751635738, 910482178, 84977401, 262774469, 517074748, 296555029, 860652810, 117444811, 285489371, 656799282, 169771699, 840205279, 192048904, 398889805, 801663298, 131327513, 174483756, 685605395, 660814811, 538884071, 26601008, 2177810, 732061992, 726739604, 594341327, 528923051, 377090859, 548970639, 554860025, 983186198, 598626348, 683287187, 525495031, 886573199, 851107935, 901335562, 257166979, 610506320, 853864378, 575326132, 814541587, 435331328, 760617241, 916907961, 628608010, 9687791, 879447764, 545908414, 40594796, 231292526, 110314736, 733070198, 215418460, 350626683, 37392132, 394696562, 267604931, 831261185, 162845862, 52289145, 298389690, 129490735, 745817816, 686384241, 283045460, 741462739, 658743565, 469970740, 3733623, 51131832, 862575936, 272872995, 104586139, 253041389, 376741310, 623148201, 392806448, 957312265, 525920174, 619771690, 92517843, 71998890, 532525138, 799836601, 894761205, 777944174, 998119805, 908067505, 960907103, 170467469, 433412842, 706408373, 899318553, 574232494, 397668619, 724395938, 373900148, 654359332, 29190375, 430689943, 537324461, 964479876, 648687713, 692959099, 291549369, 118351976, 31468736, 511944677, 433038799, 225827357, 877420201, 604202435, 100372361, 119560538, 500305077, 110890704, 528926735, 63898737, 304887385, 200351776, 16622586, 888390380, 524418087, 61720582, 168980055, 641537383, 782928729, 446275845, 388706080, 795672351, 84196511, 352867747, 90387016, 687357743, 141535383, 535897179, 199150852, 770211770, 714930526, 813753797, 358169623, 509583301, 323800088, 329081171, 627663778, 542629583, 893572152, 808897029, 21676936, 321444111, 890040771, 419031499, 57174432, 958086138, 62970998, 132639614, 884649741, 475442008, 322484730, 538916343, 972659109, 318991613, 813558426, 784412990, 539734417, 353766044, 424146614, 922987671, 987832222, 318773916, 817435968, 883342491, 93313430, 693726703, 193940505, 763490119, 122716231, 537459198, 992797103, 402758600, 959698805, 28418269, 756829588, 716934077, 670044153, 673016943, 224754607, 355654555, 499097807, 185270360, 252683420, 318046600, 839557368, 121355806, 959136107, 302058514, 369294302, 30124490, 739053370, 875762155, 545584084, 481945030, 408573010, 258169717, 713174126, 525403420, 867728455, 810101285, 354039966, 710174797, 123925783, 810675694, 653673843, 218459093, 553352566, 801447018, 676904661, 767484399, 168613594, 720748306, 986259969, 825187006, 807808193, 430305832, 977061181, 148655633, 720982973, 622445999, 786052482, 982197373, 341724441, 533375774, 958630913, 978810689, 724908783, 988443599, 837509084, 32219604, 385431374, 226358341, 613740258, 379769458, 323042276, 618754013, 692011117, 281179859, 990739015, 986516624, 320044899, 300192694, 168176107, 960975833, 446091819, 927535613, 434451288, 71538578, 65848552, 601136830, 283724599, 689202374, 558353034, 968919317, 160357291, 28771210, 896752953, 115432121, 945712699, 253295630, 714189343, 507578414, 729906778, 998674608, 376486880, 951255478, 173019428, 75626088, 291330388, 361215161, 649997081, 27545766, 944048088, 790642193, 820770770, 210794370, 569317222, 90303921, 348507024, 536809692, 819514333, 785653548, 401859531, 396594993, 496173659, 608928623, 360190803, 691586465, 964987427, 504737390, 940541748, 165090036, 860558064, 711731631, 85488753, 792807829, 350476045, 548948506, 389287872, 520203243, 939426549, 346554620, 846130404, 977352801, 498043624, 970801881, 842514970, 946335129, 992910584, 272740605, 81806327, 570216787, 323149721, 369041490, 976835016, 715962143, 473490759, 468502922, 194654360, 943208710, 985654813, 598758468, 663693760, 718579099, 726068100, 979237301, 820548764, 905598620, 523878984, 709621459, 581098296, 929715571, 277182700, 496801991, 171039728, 844699439, 425838233, 513537340, 689629615, 129970430, 843702445, 318946513, 391733750, 828383550, 690096739, 436054728, 187810346, 178389, 457167612, 936996915, 551639640, 5846035, 860397392, 36949753, 167955141, 551124183, 684789382, 80832814, 120767799, 748447041, 464463337, 393517151, 298334742, 788983270, 963923651, 721196022, 623739990, 62979180, 799492302, 280149323, 680898054, 768729512, 397914353, 339349649, 89254434, 650633299, 854264318, 9386729, 96230876, 287843541, 291448783, 913316075, 756143629, 710664248, 792317781, 100300069, 338517818, 470504383, 237931559, 641167002, 902235020, 472967571, 641973029, 587136478, 53257935, 338798995, 262509285, 506237480, 11454084, 72074919, 356729920, 279046712, 893517716, 958553895, 151910978, 750219293, 791261489, 510523452, 218494203, 756814018, 708683240, 683156593, 459261790, 723803377, 430184209, 98738853, 809689732, 390904412, 558154883, 16810141, 177351201, 949976257, 818495985, 977104639, 531161826, 160719882, 242824412, 567086834, 757732385, 194690372, 30981804, 647225383, 330903628, 95314536, 580577116, 703930795, 70776127, 108617582, 192861382, 57480222, 330300381, 273096522, 286798446, 784563241, 633866021, 840448211, 833971239, 532077371, 34282928, 584825606, 771596988, 830419943, 276806154, 446201731, 134645697, 806647140, 585766932, 396198879, 450973815, 678896424, 88556859, 216768618, 9030966, 377765831, 831818853, 661402550, 113376235, 170865500, 73946406, 145993264, 944491310, 416486181, 965862657, 853358054, 720107105, 807684122, 840862688, 831552701, 150353338, 289572399, 771604333, 957531002, 642601263, 252441534, 813379727, 333001789, 799609735, 969102360, 800722971, 359019986, 180253457, 282770854, 517559247, 264434155, 584346127, 384760024, 810486019, 406057963, 232220164, 386526091, 180474093, 879270738, 320801874, 807668896, 30065608, 49148940, 409055888, 290825524, 938569767, 381374941, 64268734, 449300468, 217572059, 32764480, 907147030, 763806728, 963508555, 894192635, 667901383, 187319332, 63315270, 904640673, 186186258, 848168570, 29693325, 31568166, 707739554, 921380400, 112667663, 772820711, 531802648, 380028295, 712814889, 695616945, 73414720, 862083694, 868284747, 48472463, 880710654, 636815059, 603158531, 811261678, 362270723, 968370954, 295673964, 213895956, 13672225, 658452344, 185198747, 10939697, 111607572, 132902160, 871087419, 719248039, 991270288, 529020287, 982852062, 601183052, 457632554, 26144114, 382718073, 484903874, 277164567, 345415366, 380482255, 915795511, 213351207, 412248132, 833045706, 16656250, 494855585, 432512645, 752402418, 903313188, 116668958, 390116708, 83003780, 371643102, 733245495, 56786792, 598505650, 908252362, 310815448, 911391064, 841337174, 720629046, 37362186, 246512286, 864383596, 239955567, 572125433, 727011545, 889972784, 421156585, 696763820, 43513614, 768320761, 140014801, 733060491, 352805615, 807737034, 643187100, 960747867, 644711498, 524858653, 434349476, 333210577, 524832081, 233525669, 141608495, 507902054, 211307056, 515152835, 999382385, 700390881, 50879954, 914547479, 511545823, 93717192, 129810177, 177381126, 380447798, 917694128, 680252483, 139431398, 662298739, 729808606, 791968970, 454254072, 228129159, 644615650, 688003839, 150984680, 186804538, 647073938, 449563575, 225885461, 650510806, 655412978, 318912192, 909617993, 810597461, 214510079, 942205639, 380893663, 151642678, 413963359, 289888282, 183683368, 898490576, 14593444, 907568468, 612935153, 349395179, 339255690, 723062246, 17665630, 536038589, 600580428, 706759499, 237710657, 48602062, 163876870, 644710735, 902102474, 969216310, 903703587, 516011592, 283442362, 933525067, 795143459, 322806744, 417135748, 142625094, 489995324, 627570474, 914650037, 435368511, 590825506, 915782858, 425811107, 282249650, 654080931, 989744328, 41439886, 285791079, 681389548, 371412355, 680044976, 973418393, 339204829, 281126655, 8066977, 636037358, 374311292, 420045245, 957823748, 793672699, 131648991, 110286370, 684884228, 640459948, 671037555, 942729905, 749917081, 332731366, 341433391, 856332981, 717566720, 176598030, 561387074, 260205614, 791676625, 977875312, 158099195, 932483633, 661052097, 75616315, 402023943, 622630966, 966082147, 114831530, 368446918, 983384961, 107529112, 151623176, 347735278, 976306294, 833784128, 504302504, 471896788, 281074202, 753754833, 50880773, 191187901, 794222434, 763015896, 740953357, 213807339, 587504997, 336224476, 356624371, 463172081, 556685452, 806986642, 684621910, 685767379, 133203477, 896386396, 172277519, 953764759, 279711630, 988591852, 383800093, 393618362, 744776328, 988710201, 777809274, 474282693, 292371774, 655803016, 427515150, 200068539, 536056906, 267899770, 978897615, 932745638, 23535974, 911728439, 135110054, 101854150, 827400101, 981329957, 168047412, 66992994, 41428311, 139203394, 572000707, 850594011, 912677251, 149158682, 676597898, 570999380, 258310731, 948951857, 352973301, 656499135, 462524481, 52008397, 309840264, 74060455, 816766249, 502445540, 978612904, 367869586, 141763556, 284235098, 125108287, 699361872, 314445990, 35091782, 7613634, 206137822, 231354981, 607690276, 742127027, 96641129, 524899947, 728702811, 924839953, 287425686, 969702835, 833961310, 857977531, 729039394, 407403875, 224404625, 384004608, 335068173, 952902123, 697036412, 866022476, 8805393, 18195363, 608287548, 192835053, 230605879, 649881132, 547798210, 68844484, 803441561, 229477871, 838297731, 862547618, 211000726, 99110347, 295553795, 578484841, 616353020, 861890374, 609475303, 442937948, 315838278, 191383817, 498981832, 723098701, 877491535, 862798902, 60763151, 586990806, 808950578, 642944658, 516653324, 11009758, 970574247, 281701348, 657884340, 134031783, 444408013, 392734749, 641997054, 427255170, 342403090, 879459562, 991283817, 554869371, 897341502, 537130783, 134609461, 866640280, 773369730, 990505085, 357737369, 862035498, 754223881, 204650576, 489658717, 599839898, 221408866, 875151890, 119586588, 616839026, 631827160, 592181816, 514076151, 863427531, 735834407, 958885028, 355476397, 807909950, 442918088, 245441307, 904388717, 968919259, 738631437, 242147484, 66624870, 300313478, 300592386, 509493852, 306030235, 990071527, 866121822, 704785869, 855093344, 985288152, 978157199, 106100404, 800239170, 433698139, 269137109, 476489242, 56479193, 745257585, 402207595, 999703049, 189517239, 481595187, 976754521, 908372202, 77918038, 215199638, 852353644, 991864228, 173697627, 604517310, 207497856, 764633311, 966693628, 949241644, 172193512, 392935787, 400515113, 270590491, 365795203, 757123802, 824246620, 486691927, 624275437, 851693753, 992601663, 257262673, 165670786, 387766211, 798848030, 509541284, 658576651, 573126393, 103654910, 550343325, 34915842, 187921791, 893025971, 534635790, 754560061, 682387083, 352556639, 427293067, 644424007, 807641912, 156697438, 588593467, 815567150, 559251333, 627167377, 171121396, 352165490, 156972319, 998526231, 80894314, 375992578, 777700068, 942357362, 63553054, 136165269, 404471230, 991187489, 886481513, 374270943, 808431138, 690017518, 709953910, 974387008, 45209372, 280033642, 24935874, 134223175, 74813421, 571988679, 101795767, 273305871, 590474190, 793279387, 327037430, 974476626, 618365560, 907359888, 971828562, 910420034, 403728229, 726967423, 624190226, 648672440, 164180821, 991245222, 859615046, 478577875, 322001978, 878243800, 127676739, 699747955, 25344265, 845017156, 433842728, 31940292, 642675248, 640164987, 450630488, 372439814, 199584275, 247162042, 355370250, 219815792, 819384742, 977107706, 612862470, 705318466, 677474842, 357207313, 173312387, 385004993, 652120036, 606662918, 472485912, 173908182, 103850283, 656698187, 26458390, 662938914, 219770858, 359603318, 320600395, 812953112, 784243307, 515008440, 192035988, 97233275, 62664174, 44420034, 756045242, 697044354, 306690774, 967748873, 650763199, 456264025, 112876478, 227655047, 714644464, 759881671, 415263421, 145704879, 265226236, 179245300, 584448338, 786868978, 777930829, 816845311, 457515499, 6356144, 384970527, 973253077, 154171857, 457551835, 996499984, 175458671, 315533653, 118385025, 686068090, 128960988, 136482992, 825381546, 458933728, 826102058, 536981578, 925147859, 488657133, 243499607, 76734917, 130485461, 196137242, 714775894, 213895668, 964674963, 158936017, 651760668, 69276653, 957318116, 332015205, 541701613, 9327603, 332793181, 364278566, 335372252, 864753442, 89950097, 965790534, 252334030, 294611692, 426986254, 893070498, 63897006, 72779481, 926722646, 271465376, 203400850, 532791352, 661895773, 299501189, 830078238, 952889430, 704503949, 268244967, 360227433, 138871662, 999905128, 929147265, 206552001, 124261396, 290510500, 845792959, 465434092, 457342551, 504524517, 504294066, 476008084, 580906199, 776941451, 898509124, 22159961, 190405551, 733825520, 577399405, 742221288, 117047792, 718683141, 573393974, 675179954, 79664439, 840260737, 942702021, 425507550, 841051000, 415229381, 150817953, 472718408, 888785269, 10383905, 423295280, 140062946, 581067096, 205219547, 606820767, 290832609, 617473042, 930312931, 442153357, 58118983, 864749857, 750937094, 593200634, 674134571, 24734862, 775716824, 694650418, 912421190, 385371526, 76923387, 557849777, 434252555, 952274832, 788908359, 256582123, 778725243, 210844397, 575411076, 231016532, 199849448, 720848558, 820005705, 364450693, 764517533, 488235882, 851820855, 405109715, 277787487, 147721503, 544914971, 491203230, 697897250, 300017663, 887121662, 481500212, 510548480, 717469553, 454316318, 588911962, 66939277, 136435194, 738475200, 555834576, 749586347, 793925912, 542377600, 725613364, 526150137, 349921090, 246121008, 643817236, 641776021, 257340798, 762785349, 566790695, 975218974, 720065834, 598331602, 693677126, 694834118, 299335997, 691213745, 924308981, 900605984, 12563288, 252864822, 4795025, 231855517, 889088813, 424434076, 789865225, 978603876, 508586783, 956008287, 884635739, 304095507, 876470102, 531941854, 794186711, 318598930, 570260988, 864901937, 554170521, 679492880, 169197213, 21223631, 201379034, 318937622, 506421751, 459096078, 918287107, 605853777, 544257612, 528718262, 65434841, 424853080, 172215585, 885210109, 873592285, 480079760, 194222640, 650547659, 316799650, 651658766, 401576480, 929713423, 939239356, 163799335, 790508583, 566140178, 135379711, 647461003, 350424979, 869884378, 253584236, 914798243, 900530967, 121879908, 618024158, 991863649, 824715879, 960610001, 876098450, 792873602, 889285822, 48244229, 137905533, 194972363, 995232400, 323360100, 996634770, 45415861, 627475156, 91288366, 54383516, 815228673, 311980673, 278849543, 119293782, 773216332, 958329382, 774487099, 840319937, 724356825, 134651421, 625234433, 224762057, 540109041, 986456775, 574097070, 173044372, 688892911, 836638986, 503939283, 952139913, 255150014, 939508698, 925225447, 759836046, 588219392, 106506049, 750958346, 387565560, 9587423, 441472422, 733050538, 807872632, 627372907, 82433711, 907617479, 977821548, 932524446, 159033448, 657795795, 364218784, 7452197, 70261052, 327227019, 240163647, 668916487, 852436194, 720068343, 768858665, 125664218, 47724672, 881402304, 630863796, 943503514, 152730682, 295990036, 178217136, 119757621, 883619189, 333452395, 231550579, 958670728, 501360412, 553602047, 59849587, 788225878, 156470367, 278984666, 596422504, 198156000, 279119079, 220565538, 295208193, 468785881, 989376477, 536639733, 587797769, 829565916, 665856423, 773388263, 491809459, 544083359, 484503272, 266674446, 732747022, 422726996, 618586808, 970425575, 285012304, 953764511, 654032233, 422692043, 201394076, 993889648, 72562110, 266771542, 899158118, 67325674, 299562366, 996900181, 579119656, 315597886, 475433331, 605894978, 894869178, 69289373, 166949962, 945229278, 995502918, 77620385, 894026647, 1140180, 525201908, 958152543, 161920162, 47941701, 509530537, 753241634, 626565470, 291570224, 574845715, 806539822, 485798031, 579542283, 335929098, 850443702, 735854197, 78793918, 695662296, 389008580, 975166401, 126557359, 667755725, 878920818, 822176557, 335149510, 416913212, 176954486, 375365867, 204128446, 126747226, 971090374, 262374833, 865038902, 59397185, 473311355, 737270652, 515155925, 220296370, 328790490, 769213223, 238791836, 411720090, 767798299, 874534737, 690052515, 448852897, 111558252, 781517461, 70824242, 555218849, 163969758, 99859162, 655255794, 31459848, 536365815, 152422368, 219917265, 219398479, 708500052, 614025521, 618087731, 227030371, 452906413, 520530598, 395405120, 714570567, 858782670, 875100007, 28594681, 590585990, 475241588, 908162505, 658670905, 510204037, 15678560, 635022879, 97567117, 17738315, 834950235, 483952928, 586823646, 519653674, 517061577, 523352893, 273681271, 339488461, 888942365, 469431070, 336520990, 741973577, 948491313, 970652124, 942084193, 472579232, 652790494, 980443870, 617366837, 805740706, 937374493, 898262045, 233282822, 376516786, 471701632, 410119332, 395637425, 707192300, 817780668, 656633447, 441131980, 339502835, 648889412, 386676241, 716784576, 786540950, 53439464, 327579616, 338191277, 47387614, 80976197, 646242108, 770339012, 228083015, 776093508, 294378752, 94327186, 520159269, 411352320, 225853987, 39170003, 733991755, 893040309, 900239556, 141003937, 793943664, 163523360, 245103034, 905117537, 463876886, 723999852, 40676761, 698178233, 281179793, 755114713, 966137881, 373683905, 554974332, 274488152, 586423515, 388354970, 800811027, 483487994, 102339506, 255677212, 46485530, 340503432, 168766321, 582942662, 182151811, 869269818, 720274937, 413865913, 311705852, 752795096, 225305931, 767645282, 879602793, 981873702, 633151794, 464322695, 871889403, 120797509, 557019306, 162538943, 207060485, 974281350, 743450375, 385852862, 633260250, 842261591, 654814907, 285292685, 171800370, 381194895, 120084661, 703627110, 285926371, 530514730, 387206379, 281390570, 170575199, 702516668, 105812482, 372846547, 147680562, 165432477, 831367530, 609290036, 590157782, 950277372, 679603309, 825204961, 764693296, 521457044, 465198166, 930688062, 727187334, 816509530, 962740325, 369826584, 726925763, 54543311, 582121043, 478019400, 847878185, 46662299, 625175652, 827281549, 402830592, 358643268, 865964286, 207668915, 321564478, 324744944, 19381972, 558414746, 627060711, 437238959, 678437431, 56348268, 38062589, 904233036, 281142684, 646109706, 45345272, 755864105, 588778789, 584977738, 96845958, 589569433, 961718777, 559665184, 604232887, 314356042, 901150853, 884959133, 688095791, 177059026, 962960672, 951981738, 700917485, 684640743, 609881311, 5866040, 781196069, 910091238, 899725556, 257502273, 71856604, 342505075, 434233161, 61449295, 174790840, 983857156, 207529877, 992580306, 220711322, 953511584, 153975731, 357274757, 303407239, 959124204, 342962270, 751326366, 284906235, 550981694, 532126053, 901880569, 202409853, 50387041, 848526135, 180659014, 462936616, 86448329, 805286929, 432595240, 139953269, 23987456, 909282381, 456968555, 233149603, 986920265, 292806821, 647361597, 109010573, 84196307, 910076493, 17221826, 831033961, 414498780, 855614469, 11557460, 302953619, 107401987, 405788525, 280037162, 229178834, 511277053, 551245746, 735121756, 694239103, 249053923, 32280602, 990061944, 393057915, 283963231, 267536251, 258608188, 524677539, 259261730, 92340883, 129522353, 88755555, 582613026, 970336595, 324612297, 394378180, 833996358, 54665420, 303450036, 563432515, 19159866, 591211177, 656266471, 355567531, 899964335, 784438194, 673083717, 226604012, 644142670, 5270117, 525642091, 353630421, 848680619, 186066950, 480479881, 828234435, 575284408, 293370703, 819899444, 413907536, 794344062, 690346577, 369752653, 309089482, 238225664, 121323316, 37624528, 668680676, 281302436, 326104531, 742841720, 809293233, 27566545, 249666650, 162610151, 840712406, 51799936, 144759137, 145108939, 669690204, 125484174, 301911372, 553178437, 656615604, 573475792, 526212945, 237275970, 578901040, 538148928, 764298410, 650824234, 831295213, 620968307, 523430535, 775717986, 407502645, 750025151, 778150837, 259332986, 803423323, 213922652, 213015998, 952925204, 4778185, 235425962, 256710139, 32460460, 866359548, 449296215, 784104078, 332752071, 914814044, 938443974, 203370191, 814355324, 509378241, 956347280, 989202281, 278305900, 973989630, 673544508, 132012989, 791974625, 513091592, 279736921, 802818415, 169939530, 339601069, 507495300, 790805401, 591061974, 626919325, 679783371, 988962336, 216620794, 236265932, 597252954, 395594014, 280033836, 474416390, 634788514, 920389927, 192938974, 602847991, 413722901, 448780884, 953686715, 804494288, 186950156, 55701861, 636115082, 354166339, 282489905, 9207792, 197788341, 673229655, 125653912, 319024504, 188342261, 955311124, 504593987, 414089836, 738973205, 72620727, 607796283, 796900170, 501430097, 900424001, 851798908, 418974087, 444721669, 377662481, 432838887, 559205089, 534727171, 48070046, 899379919, 975018995, 744934772, 440756132, 750985430, 70177720, 267853929, 653712622, 921599967, 331818032, 679086634, 150445478, 901946301, 127545865, 668512036, 931741287, 241556819, 719689734, 364137602, 53606727, 315052832, 171486700, 375063986, 552924690, 403986359, 883047858, 30037072, 370467725, 975795756, 206289139, 990741558, 861185956, 498671028, 300933860, 807196563, 803811048, 884279796, 749985533, 964881722, 681974228, 745169164, 188666053, 397029756, 535516306, 138655193, 957460599, 915928806, 979468529, 390397629, 974443578, 217103168, 143922150, 846394650, 220627051, 240315661, 92403626, 935873286, 361298821, 539625736, 188770673, 891498722, 420786726, 512604613, 590487653, 665906781, 169234336, 911893821, 565456366, 842348452, 293840968, 177424116, 76922978, 598571940, 689267581, 401836141, 724215277, 169813697, 511564131, 663223201, 331561911, 690069199, 331965540, 959900942, 129198797, 873391339, 957740423, 695410670, 678441949, 334636047, 271354556, 680883260, 702022173, 829873591, 116180875, 347377518, 785257163, 310360502, 748146261, 693218536, 349353757, 103553344, 15386643, 215329538, 25742085, 782424322, 793001903, 886309013, 78453845, 654748408, 485540354, 300583553, 643477137, 814843047, 488312339, 422596818, 533769993, 624079426, 376270178, 885586631, 910745121, 406326706, 651034229, 945986871, 390064788, 321973268, 183082176, 486723422, 992500146, 513275376, 381504298, 941935378, 622767573, 566753028, 114469196, 695072566, 177556310, 749843415, 894344649, 612507419, 43682101, 16207285, 68372558, 720787435, 333412195, 812878450, 648599748, 505626768, 850104833, 789088845, 227783436, 245286120, 259318404, 457598721, 72462829, 502449778, 962991473, 269045645, 323655169, 848912997, 583748577, 969863176, 33593903, 600518228, 970489235, 635147900, 791807389, 183050226, 936774078, 121805868, 250150651, 90303292, 149502165, 197762836, 636700465, 780415384, 215781252, 518946395, 60989490, 557725781, 110762453, 813521985, 793394695, 136032405, 498702897, 561222917, 814638836, 126763465, 887092034, 657468523, 60539862, 275171972, 394782715, 203246617, 591192195, 517784145, 485329479, 960594924, 67824617, 985005383, 645377949, 265006138, 965354193, 493997765, 225549308, 424775398, 873422677, 100835877, 523361186, 634604850, 679520485, 343423085, 610824136, 667600080, 711010205, 677778021, 465092210, 577025022, 367102946, 544897681, 249145118, 483116080, 930727221, 121954705, 320182857, 106706148, 231033, 424160064, 478510533, 171317026, 320023488, 562993326, 537271712, 180066821, 219321751, 937130203, 98536165, 524648869, 764828169, 160172181, 32557975, 941423760, 428433102, 709936115, 483515314, 504702594, 841976325, 193967310, 23549085, 8961430, 181825729, 604676784, 416747268, 865733406, 452134522, 854334811, 256469379, 168972269, 888333947, 573935886, 825508019, 308822870, 307969133, 883590616, 717092192, 146609754, 313399444, 296960034, 24908682, 579015318, 823745985, 319639932, 336437521, 976261568, 588170038, 325088270, 303886179, 284628535, 506179186, 936850059, 829888271, 712020424, 929266749, 444552150, 733340315, 919067338, 546155584, 89169203, 217145688, 251909564, 249068836, 198166527, 92825061, 550770686, 121525901, 980682541, 554282612, 320540684, 884866828, 639489386, 937583969, 215136796, 29878957, 23722858, 866591837, 969035846, 911591563, 574422297, 3424448, 698748719, 939135691, 257455081, 382762986, 531509906, 253866805, 107510532, 435157112, 814573395, 730396555, 11367446, 288942927, 730005602, 590175915, 159950765, 482870548, 81237797, 43009777, 889331697, 66071791, 177439150, 369625244, 825303469, 317217692, 87361907, 275282806, 911375369, 181630695, 760677413, 143260425, 349107194, 461224181, 230162936, 343052527, 324486171, 344254484, 876831446, 406207612, 428205027, 232961625, 959374905, 951668576, 99168876, 385564193, 407321048, 513667200, 571263011, 155320525, 620274999, 672963704, 241177613, 840198719, 352430211, 741407388, 540399546, 549524813, 241608476, 609089510, 174041641, 22863352, 444665667, 269539533, 558653886, 641643568, 77483527, 786462278, 711697495, 676134350, 153560882, 215030443, 510248763, 742331728, 608695290, 556874509, 691199902, 61154259, 723627372, 964369221, 134288146, 565414397, 65185071, 853027148, 538756287, 362477559, 48799809, 137714018, 973993976, 26328690, 438449421, 331577259, 437490261, 18946228, 629779669, 782384052, 871068398, 774582973, 175763900, 547228391, 536115484, 141842148, 717751375, 174254948, 452864353, 438088888, 254558168, 909196631, 141585594, 692792087, 439956384, 317450193, 325075520, 901431402, 746887660, 249061803, 591630530, 179491900, 559256155, 250257176, 671019755, 832424875, 542730931, 297195046, 411014496, 352333860, 892517270, 459728845, 102660699, 77582024, 288041902, 601380320, 941858594, 283104766, 261574529, 744829524, 166667572, 147760694, 853988465, 131583158, 705417872, 332985959, 31651600, 228868744, 988847727, 249160160, 149749516, 144102726, 589848741, 315115545, 98882182, 419475081, 27046666, 944675895, 436442430, 331603110, 332114422, 993305516, 69896596, 967646236, 254361862, 622197377, 869499096, 93472426, 572269644, 989716289, 601598391, 977281619, 731819764, 880190352, 328537997, 768896136, 700445272, 928631462, 393585850, 29728348, 812426533, 25323752, 153063185, 891776445, 99893081, 884235874, 942110105, 228468580, 994506564, 129253231, 390953916, 18956713, 270731907, 87896119, 698763577, 536883840, 548939344, 815266445, 68367104, 447943571, 210655171, 561780610, 105806013, 464039795, 932069601, 777513439, 456513627, 829042458, 45366162, 78136330, 246532393, 465887098, 465510640, 723310345, 661234260, 120274148, 870537063, 763813112, 626785529, 952109023, 480432150, 116967287, 792320079, 719301494, 2562960, 308461832, 776856310, 33352174, 905337125, 280530001, 215534536, 425102639, 505942559, 907743463, 552188163, 673654924, 614388519, 17324689, 123425783, 596552474, 928485931, 404729194, 538704601, 696403858, 79257069, 155092539, 201693396, 581717945, 220712087, 516336652, 657741969, 620468902, 36503701, 646270002, 118949219, 630301927, 265156886, 716485342, 94510341, 162426105, 34925758, 700869516, 532221934, 289924537, 25312697, 542009508, 842707888, 409246034, 188797304, 546508972, 990265216, 531527362, 435479677, 591428663, 373630375, 366037618, 147901390, 396575650, 940847636, 347720993, 736378813, 549533335, 933870204, 634418557, 205184835, 632869096, 537709672, 686821183, 197977660, 861270636, 316866349, 219725342, 648924640, 228880347, 614947878, 780479872, 577552148, 867139034, 840425368, 888775363, 618096470, 518842869, 824075846, 555889774, 788070602, 29810384, 321309829, 962525180, 322804676, 615799287, 227944357, 5096871, 245564478, 22278174, 601731907, 643940705, 526482374, 498828666, 470779528, 989898175, 830983724, 261406310, 263130428, 238194031, 203996986, 785641862, 291558998, 857064994, 338952021, 319498750, 949619229, 536948095, 807497503, 238075631, 617561090, 741574656, 710491704, 236997805, 58180248, 225886919, 72716140, 756120188, 845102963, 330451665, 312121167, 300878438, 210005627, 710288616, 437587705, 696407718, 553144838, 184840820, 622600436, 559368969, 152790184, 223648996, 637999997, 701809930, 109109081, 648032328, 136301601, 690630137, 754894264, 95822067, 260494022, 363595969, 227177783, 683689074, 435737127, 174966694, 654311344, 621832122, 577605459, 257565699, 935377403, 14124796, 494646272, 55985068, 918180308, 392412028, 205007186, 538662109, 282510694, 971558980, 12096228, 600081332, 450100925, 169902331, 210253559, 67816274, 331325359, 513039530, 36454466, 244533546, 2101919, 722357543, 618167475, 474432105, 855090678, 487737425, 463139987, 124570382, 969499792, 458320303, 898733939, 149514219, 137209395, 204918537, 439489863, 446528036, 403153331, 878643306, 314766412, 880861432, 596514147, 195771695, 477183650, 667937075, 240759864, 252652922, 80341095, 494616756, 103901156, 998436863, 549896291, 895602023, 94994006, 745094695, 115399021, 689264916, 479973382, 966450796, 380279219, 844280274, 289884649, 293909259, 427405175, 921481605, 324484350, 605277109, 816242478, 538349514, 472056539, 74244594, 362360172, 856552378, 47347708, 767980260, 884441039, 12736037, 226673257, 659524527, 781807920, 233917950, 415472207, 609642902, 339714777, 103029629, 257708386, 359518804, 617050359, 816504226, 815883486, 820533849, 152197070, 875101907, 229351715, 942582181, 215575258, 591935841, 377896713, 975732118, 15726249, 57722077, 688250597, 434330006, 820368376, 962872070, 586161611, 213874477, 848139005, 652950877, 182491261, 442379062, 49782964, 741332333, 671167545, 191056821, 570274827, 881408158, 152443220, 651692882, 721325510, 166658817, 489621768, 910481578, 775827268, 541741185, 300159377, 694718194, 600324345, 325169269, 341642452, 963081612, 529915727, 686071250, 120684955, 814294505, 189067314, 156488849, 882801209, 18639796, 248021817, 870014183, 137571360, 787544295, 709022008, 493683204, 70426506, 607733680, 651452035, 420879340, 173019047, 967604820, 539748903, 313081807, 459827505, 437591657, 711491033, 430692346, 375674342, 816240105, 991666799, 82734144, 55838637, 555254508, 320739930, 337067692, 166344325, 89210077, 4611185, 545297314, 900648727, 711594180, 2007998, 424197145, 692767789, 683386915, 864907329, 49009270, 963129036, 89151931, 720844890, 344842305, 492171665, 67697682, 396976053, 374952972, 520940834, 35243450, 180391856, 594160937, 988791225, 972759390, 306035108, 723030436, 166351997, 447616777, 629178524, 350975420, 843358589, 164566706, 162998628, 995087174, 935274272, 636258620, 746045412, 734770299, 495160232, 738369726, 788703573, 444024769, 977058350, 501457967, 52504538, 696008365, 579759568, 975733758, 637184230, 833981422, 741546856, 367691905, 261757826, 210256446, 166072384, 720181679, 776864341, 58690804, 664574081, 393847953, 720940138, 813443698, 299935989, 73993409, 406635153, 62828285, 513242227, 92633998, 218041615, 732702428, 959863649, 182580009, 868842411, 177596073, 570261750, 221555135, 189694933, 507406603, 416872275, 451038762, 356395556, 21406758, 595651788, 648616311, 457167191, 427602022, 288767453, 584139649, 163737922, 524761180, 325425379, 571259768, 219047112, 244474962, 806476882, 70950022, 658599965, 258239512, 489901847, 742094937, 895265129, 760891463, 746769918, 351027406, 297694662, 321611068, 121742129, 890136363, 687465250, 723685941, 839362754, 854477663, 852766369, 213892507, 340525724, 742112115, 315502968, 295399225, 982768669, 895005412, 469984542, 595750218, 457298504, 541564400, 184505512, 573173889, 910298325, 532688026, 372973167, 759907120, 872637955])," 90410 (continuousSubarrays [413731335, 708336615, 580085319, 965787266, 153396535, 591706899, 72721949, 674953891, 25636195, 948911655, 310850223, 386611508, 121141727, 808100, 298392873, 256726253, 175205914, 187915309, 657868217, 431814216, 270931564, 482808416, 846581830, 969190130, 202954751, 344941064, 305956776, 519071697, 98968590, 316288473, 771386513, 321406714, 666237611, 369058382, 125237637, 797497392, 5605464, 40734473, 275360753, 238178478, 800575742, 719846386, 716241553, 915332913, 721102739, 941978111, 645458450, 171452992, 829709893, 754359272, 673003152, 644744845, 216541790, 734948943, 683613208, 838534829, 603081028, 815431649, 352087711, 140211730, 293284204, 22469334, 897099441, 791488292, 99266880, 979355467, 373745765, 90037547, 961655046, 309461745, 193364737, 124234102, 582986, 857155781, 228344949, 278300939, 171852962, 238194209, 602079420, 325459203, 761636070, 560540757, 683762146, 536611697, 108084330, 89997168, 174648446, 699417636, 368273871, 239270231, 391868945, 609215741, 700049755, 809741386, 817163827, 871100123, 346868100, 861099090, 644271475, 394272061, 490454401, 644394657, 881767225, 834599122, 287498283, 375092578, 420342855, 4000933, 211111295, 212319923, 781867875, 267537512, 341625517, 413656489, 801281415, 594434, 801007943, 321374765, 907027605, 605118147, 336984727, 279791512, 871713172, 485049515, 153294539, 197724101, 978374901, 553433438, 962255541, 915612957, 249146722, 98268937, 762756724, 345221529, 29371830, 214098867, 322318837, 111719620, 673731698, 561512126, 450358741, 930383888, 694012077, 721782616, 915076595, 700166359, 957949767, 620792132, 357407477, 144854746, 967423508, 376914401, 149002547, 512037393, 356617712, 823634069, 917894576, 234526984, 833909698, 801274627, 237940936, 361945441, 840951465, 88002496, 113299508, 183236224, 223963566, 192532708, 955943454, 582845092, 684863998, 974926659, 434490852, 666925621, 951922254, 948781769, 269592311, 986648341, 785123125, 838865814, 943287768, 584171302, 28570371, 631314234, 781596115, 443217680, 333204827, 241415409, 213999286, 413781985, 310232141, 999044622, 628588643, 978380099, 824326324, 797681320, 156693224, 112145784, 947601358, 950562974, 494537697, 402120769, 7114010, 937456540, 567410413, 128875397, 521652145, 730976213, 867588791, 635633782, 39059846, 110144999, 670754947, 86063238, 728593109, 354849737, 957362000, 748743772, 770989822, 567276943, 791676823, 252069739, 956291521, 293971084, 732418410, 573495473, 473709615, 151288094, 178720569, 744989963, 775285848, 106362128, 746619571, 630679516, 335103311, 886547599, 427348844, 788963434, 720701036, 316032412, 488895813, 508908871, 980926474, 38871807, 25448939, 743692941, 975164034, 305042452, 386000934, 292726712, 271695008, 870759, 105884490, 94235554, 315968749, 913527536, 925914200, 744330646, 958804076, 145076876, 441496119, 402285014, 172213728, 169337806, 861042534, 586556348, 199614766, 236678927, 914626419, 656747484, 536165158, 199529608, 396479791, 69286094, 19800830, 903654001, 236553158, 747469314, 777537787, 270415574, 149388146, 74400287, 408750353, 289661278, 321944803, 65274776, 792999794, 663706642, 175482094, 813034331, 992430157, 287882232, 438487982, 427977428, 612396567, 119920863, 940603084, 465669645, 162707962, 462939356, 878376176, 930982098, 606577721, 926425328, 406992069, 669793207, 545976193, 728185279, 796354077, 542883079, 181147355, 465623475, 686865566, 663350157, 63513768, 137935593, 917565590, 886870659, 11445436, 800849397, 470104196, 920935548, 495365622, 956450015, 448479631, 3029746, 829993242, 637419854, 275364113, 366817830, 225756186, 827038380, 237179227, 950321772, 751840365, 118100349, 248412969, 265898443, 715451284, 917768105, 304928619, 842114964, 385856998, 321836303, 299829327, 840288592, 330976027, 109072258, 788020064, 792750432, 556960388, 916688334, 200152808, 996937287, 855926397, 676215528, 212492739, 649660265, 970060576, 267597002, 167781870, 206955139, 430916249, 748609618, 515896812, 803033637, 793689075, 548534581, 538324103, 183411531, 201243818, 599537504, 700391144, 557911654, 51996414, 548944151, 158261211, 616006451, 111582550, 621224415, 340902531, 943885077, 743256658, 196911496, 872411722, 976923959, 955308225, 833507771, 24017746, 540185215, 163122054, 943017611, 855797206, 816165484, 374728161, 982580543, 494547501, 715216836, 871502321, 182940591, 709230709, 557987404, 392819334, 906114528, 398796636, 565543554, 537027209, 187854476, 279930917, 363397967, 229580194, 24015436, 39306439, 668000971, 422475936, 959728478, 429088887, 344077326, 419642544, 30275043, 894648164, 681893497, 60418295, 923875981, 478237376, 53166924, 256824820, 120238770, 76801085, 850766631, 343951556, 551986164, 15782546, 612560189, 817881999, 902536232, 483356197, 768100923, 835058136, 80866190, 856731801, 332392883, 369822756, 599059558, 153250436, 677183121, 799588468, 276867444, 571407204, 347549505, 278312466, 966210989, 200557664, 150037612, 417386225, 824570285, 342316941, 490373184, 484095345, 885418724, 106013468, 902998002, 576464868, 212026191, 134921934, 264730231, 173416926, 426686639, 496806619, 219824633, 93790039, 650501396, 883577034, 109886354, 19184042, 583601582, 214197200, 8849132, 908027782, 473886796, 207044992, 76840755, 835555470, 998541685, 78688441, 2827655, 714460831, 806380957, 556238150, 702580286, 567714041, 243230630, 86720563, 62701673, 215853615, 78188446, 691994899, 116965365, 900179597, 512174404, 757720584, 302245326, 929726034, 773131145, 122947131, 768574752, 461913631, 545297838, 711952955, 799755660, 667207693, 387016143, 753348286, 158279966, 716779547, 609894386, 437866035, 97646589, 753477047, 281498129, 591705538, 46827770, 32682921, 858190303, 665669424, 45444551, 223380929, 878307807, 736007544, 861020535, 590178625, 634284662, 399756223, 87368198, 886429843, 686766055, 276174149, 521120704, 613108288, 849052145, 146646259, 250221263, 612027197, 623760543, 206748793, 922383026, 270229216, 151607509, 716259767, 968705433, 123403254, 866296346, 564391485, 963039068, 356790218, 988067875, 418524951, 893380393, 171779163, 64755481, 548151237, 788971640, 841725143, 927643523, 786340731, 630290254, 176806686, 605885633, 892104570, 501043790, 345946105, 679562320, 665783998, 217185772, 381219151, 882628296, 608473379, 332805512, 56566108, 925585918, 83015590, 254176096, 932334129, 288039543, 457713543, 846359446, 193969957, 636900718, 329621267, 639165997, 963448136, 223944067, 895146022, 557647432, 646539153, 232139458, 32228366, 333162038, 451494641, 629478700, 30768043, 118435128, 182388584, 283986470, 884752985, 45516620, 264728776, 93124502, 232682795, 407730356, 454644103, 560670331, 206494864, 665484115, 747835656, 869491083, 554345470, 29516098, 852742245, 42655265, 425852606, 50663716, 516189766, 321400450, 718188085, 203454416, 278541624, 597682318, 587039170, 296368722, 732535579, 110714948, 937555221, 347954526, 724477753, 620055420, 284402158, 146124168, 763015906, 953936077, 673788060, 825563655, 735934087, 426531771, 517511130, 932554319, 189329293, 292900931, 55161390, 310959308, 483535385, 997199345, 973244766, 612355413, 954308705, 984859433, 359607273, 743175474, 35022266, 959417310, 136718697, 926594041, 516356542, 74705318, 337746782, 896018366, 899482249, 300926791, 696835683, 673231212, 562571404, 776555855, 939619077, 838564848, 636538558, 253050192, 683060504, 984688992, 307974244, 283372334, 778956955, 689761985, 406481107, 14291891, 347227620, 69625173, 579166626, 41424192, 879126995, 456955392, 663010276, 717612835, 963318115, 736922174, 484654684, 791843641, 38579674, 795825389, 497339006, 434806962, 652390131, 345940390, 93907458, 645962363, 284085320, 163961521, 675082385, 107379399, 235054852, 306850097, 267194775, 12475538, 398394422, 945322302, 85066595, 58335379, 93083420, 937646795, 265322953, 414848641, 628546849, 885605272, 611960029, 71300872, 707529456, 203519640, 904855747, 947758838, 469804206, 528116603, 982081061, 373012403, 180752230, 747937832, 446414086, 462683272, 885011593, 754054680, 713881233, 135380616, 551436332, 758717175, 455031398, 146912511, 649989274, 358754299, 248111693, 839059227, 729934034, 665481302, 850532818, 269804145, 651283525, 477837349, 937048296, 485581230, 483691200, 121639719, 674411996, 42051473, 254999016, 334506778, 345294312, 356534241, 623031843, 627940204, 455563997, 852758338, 665197802, 381757926, 439627824, 648049707, 135323521, 109739298, 888047617, 563577448, 432935334, 864669427, 950560113, 633179031, 780669622, 907134460, 198717665, 890665536, 457587904, 184484965, 81276651, 769854047, 45405839, 208140976, 637347877, 228873096, 465752861, 280407394, 752168231, 711650345, 88894179, 697828595, 213659810, 568041834, 347149794, 915180944, 716092361, 766407138, 149345188, 101330956, 597732507, 19821446, 689477539, 371841395, 139447671, 144679961, 784762364, 808896792, 172847976, 853629079, 628430389, 488459291, 300400394, 891468567, 815692958, 523045758, 177388290, 773739145, 397110752, 958194515, 640761148, 646682357, 677658927, 947047201, 158130416, 345388562, 849454439, 476040908, 67076603, 74483251, 270237006, 434145305, 679391888, 239209888, 575743537, 947020258, 29982786, 65339228, 293454639, 795063205, 246857433, 783907320, 393630647, 568762951, 306074758, 922988635, 694819402, 970879428, 455679704, 212376216, 997776697, 855423864, 677069322, 310592112, 91567111, 921453754, 225429190, 371350941, 235957205, 707966988, 501175677, 565691995, 738955477, 33396184, 162724691, 731371019, 399931965, 561248316, 976210094, 409571727, 573027417, 517715106, 369660110, 178210695, 560019596, 252599420, 415898413, 328290766, 386753946, 719202808, 180165193, 925409999, 597842541, 664280152, 994655470, 989054279, 221977146, 608096993, 177671408, 127619823, 388409434, 363703327, 865203222, 802778059, 219558153, 303955686, 626020841, 578270154, 457779398, 481976299, 781708969, 944998681, 667066644, 507859378, 691276117, 375307211, 300374293, 694615978, 88932354, 954566837, 570053458, 325505751, 392936053, 141709077, 714641953, 340246795, 158983891, 856453030, 476861855, 560448974, 221576372, 772448208, 57062508, 132293472, 498376038, 416156538, 865353333, 154858954, 927836276, 907216222, 846558843, 676462152, 434378702, 866314004, 670415126, 904861588, 850418999, 302975282, 984827028, 345577260, 554134319, 544854958, 565596774, 310366024, 17910569, 918313569, 334051047, 899956946, 382511654, 160117597, 720442857, 379556402, 877458950, 292765966, 699918481, 550858665, 111545290, 820881785, 993301842, 308445312, 136113246, 919317248, 76541674, 467027571, 593287573, 342598357, 478869556, 453782080, 535498761, 512863157, 340014702, 827734938, 449353949, 729077402, 22276351, 736766269, 393531337, 745679509, 279935525, 493997536, 832023340, 996919625, 606430248, 252205601, 527759321, 825971028, 848848206, 718311826, 783199109, 384897174, 432343008, 107686214, 610382970, 627198023, 929646503, 358786231, 800923701, 256403902, 631903868, 958679879, 606442146, 521617517, 138742386, 526546010, 943515984, 931671476, 812513572, 786285022, 8034113, 405396209, 95714134, 92277382, 477747542, 799940327, 896793430, 494787896, 592010774, 8371281, 53712796, 640875897, 272634160, 154239003, 166722024, 326851209, 664982616, 183225438, 777672419, 695421105, 532798499, 185272727, 269208992, 54031602, 303491895, 508076960, 38161764, 669458990, 763700802, 133768885, 66571419, 332765184, 286080219, 410370061, 865414802, 106340020, 607411838, 686468455, 980674668, 572196789, 350654464, 263288280, 591573645, 272716357, 661662832, 17301381, 846253425, 276239867, 710925627, 345850488, 172748944, 720276497, 830664775, 208822833, 269604920, 309099484, 982317947, 314986552, 773287077, 750600270, 833813410, 273508835, 581329099, 649800751, 988757236, 268663805, 233155640, 439200021, 704711916, 340428817, 88324629, 739318435, 805208225, 30214482, 11667106, 880231600, 296234196, 202527775, 272785462, 85570851, 206930524, 158405208, 744852941, 496308108, 430260873, 581774515, 389483578, 644217884, 978644595, 309731298, 823169165, 868280281, 221049982, 978450207, 856046889, 206461635, 701897057, 433780053, 481339485, 61330756, 799145541, 911167866, 207488723, 610636375, 405869894, 102341409, 623531841, 371294189, 482933052, 821832287, 395455790, 365373327, 859899797, 188750301, 157327886, 201708214, 981655148, 568593284, 11447376, 704056583, 853691294, 929765718, 867689661, 652778673, 678736806, 29907996, 587751788, 430040407, 167489770, 206790429, 32739086, 998488865, 731108511, 145848401, 802725720, 632434616, 570700852, 531114033, 247323014, 509584135, 854169338, 984936008, 812785848, 780268263, 293665316, 933357329, 900522410, 216913150, 658392842, 82729587, 928020201, 246542059, 629954375, 676441382, 640169483, 609881129, 893816886, 762131991, 395270473, 402346057, 192443411, 219215208, 76092517, 676589808, 987095262, 105540739, 754070186, 87970786, 936906968, 479684644, 157227726, 843034713, 780789152, 991684617, 989012687, 713638928, 845462838, 633572721, 527597588, 187970877, 551924609, 908104139, 356526509, 947973846, 287531904, 368884759, 754952633, 795545133, 67745136, 781670999, 519061099, 944914594, 656745076, 679249536, 847332578, 294172234, 816163130, 555879280, 970069641, 863387397, 38409322, 355818671, 760099475, 531856656, 53936327, 279823079, 948140990, 965518126, 353922218, 200829283, 603711874, 755229679, 321801256, 430960874, 602148374, 885553559, 789093929, 711154245, 664739264, 228600828, 307829014, 103639007, 651476143, 8138101, 823388907, 878957621, 691461309, 659327330, 489912293, 413049832, 177972834, 275307680, 876023238, 768807355, 826587272, 736672976, 216435475, 487349073, 607079682, 883922293, 23948295, 886188621, 546760920, 207095748, 321301745, 290036870, 669825611, 621498370, 301925206, 925691420, 335354994, 429424789, 591585472, 524613200, 339984036, 900359720, 92923328, 905892915, 201371015, 690420231, 90619015, 246443495, 186347028, 805764862, 353280814, 285368182, 354402441, 323023485, 396364199, 718622780, 832184, 600785897, 115313110, 762948544, 451458935, 416157136, 780261318, 946846801, 488731555, 467329511, 741703242, 2309424, 58553289, 147950607, 543848335, 482709470, 483232376, 933160747, 905623908, 271978875, 731550634, 92537489, 931298197, 372604386, 820892540, 706933772, 866427648, 681435659, 87791021, 962277540, 702302773, 612418274, 566586339, 531418163, 212012934, 22420066, 116294017, 427298032, 588188941, 480754582, 958970820, 635445821, 461684313, 25237641, 707708114, 285421054, 636979498, 534488517, 134537996, 573651066, 778211996, 297152349, 981990991, 94330261, 267544507, 607774534, 742960351, 750790892, 687665011, 609432555, 127056040, 909313271, 310864816, 560698465, 929854496, 90637042, 171798607, 474091866, 190333634, 132192401, 307675697, 198564991, 467104529, 749218248, 741646970, 338239943, 318088786, 134256018, 623326505, 162204385, 445071719, 84376471, 268984039, 824635759, 805378017, 239093820, 929355962, 12335178, 753620269, 603878675, 51159571, 400555138, 927041300, 835504522, 726171350, 400983102, 358150636, 344665908, 481756721, 251242336, 295043691, 415962542, 913758599, 111517785, 423761433, 503053658, 194884323, 588078540, 718140888, 523613132, 450351051, 503526620, 830037658, 633231798, 473969186, 996141499, 823443876, 515858164, 555740081, 776437847, 865403087, 82734522, 926236247, 99468669, 405108225, 594580402, 761994997, 240304348, 201507122, 113462820, 364781613, 869402824, 350507036, 623640033, 216653571, 689337138, 725853496, 969462378, 880140140, 607518758, 755946679, 813607781, 255698977, 966036932, 878926096, 634115631, 244456837, 894683587, 817240970, 58220318, 590517693, 585765159, 180430852, 481887488, 36188242, 17773085, 810327385, 822915204, 560296126, 202928704, 749254079, 526905804, 646756794, 866888268, 580018090, 489031494, 559663258, 272580501, 374898828, 158268266, 822549379, 948421906, 81866449, 959990529, 405420587, 19196530, 58709529, 119084269, 411145061, 712341084, 255804011, 177348066, 331079796, 890849643, 43516975, 732280588, 958155787, 768865587, 895149677, 923408197, 711202999, 619168110, 155600920, 537719386, 401231278, 73183990, 134329509, 183280529, 602112261, 902666659, 605190591, 86090875, 477295210, 234408494, 135196569, 423482189, 129847032, 671983693, 531267536, 374671287, 582156388, 978417623, 158967063, 824847733, 459921769, 990416567, 883473999, 600771904, 321708529, 97704799, 674009918, 256895128, 745572001, 785990678, 694379085, 785393692, 139499981, 316773317, 740087705, 362998006, 793949399, 529138921, 779903627, 179654716, 617366173, 583651712, 803138787, 414570553, 270609377, 259193200, 149093106, 932521885, 443906154, 869471485, 728773909, 987078272, 66387044, 994341389, 31811108, 605436569, 181588170, 851740847, 428750091, 635341282, 615303444, 341613923, 987286694, 63810661, 601736867, 367423763, 358750294, 21385945, 536549389, 224073134, 908074312, 311971782, 41858382, 929576924, 289753986, 920029407, 645000994, 220997854, 951531687, 467513694, 798040859, 145395042, 840760159, 710479528, 174421049, 788076005, 265542245, 82774055, 766809571, 478516002, 947413061, 511230509, 121591704, 12416809, 491944114, 832717451, 630629565, 881620877, 50408117, 757642856, 93616113, 578449110, 864041138, 218140648, 739573473, 247690670, 692977352, 114903635, 212749017, 367107123, 883831586, 336508136, 536592435, 721478117, 544508468, 626728182, 227415688, 545452112, 92260591, 209274476, 364600612, 218264139, 331598817, 121975173, 596595040, 144819563, 384696635, 111906949, 199066296, 852544130, 287666918, 466408994, 215037610, 776148646, 143302235, 614490586, 545193971, 218330004, 891563472, 98679046, 147710475, 622255911, 778571501, 441003607, 586419318, 479857603, 402575157, 382983304, 186263041, 428129570, 936566321, 375652041, 888048904, 676814082, 395646379, 678684668, 95081400, 337695960, 198388430, 746629561, 490103305, 136224723, 954782470, 905609914, 192764728, 620837778, 341043461, 449567709, 16148897, 48960736, 13137924, 15160714, 973551303, 530093381, 670145556, 980662824, 842445131, 587948548, 644743872, 17712348, 623960213, 941611645, 437897142, 740568060, 206999374, 280438024, 632798957, 822889511, 24591569, 865144193, 69254796, 238651238, 865514563, 192944549, 344505079, 974756231, 791556700, 154327527, 941380658, 927831565, 336508836, 362901036, 252011646, 1802074, 737579607, 209112523, 260213570, 686582618, 642956391, 275306945, 601678177, 958575484, 634003392, 676395873, 767602218, 207325742, 205166807, 359581837, 414668788, 311790101, 73377179, 320995330, 726351541, 841097334, 308136066, 929338548, 459183296, 552363253, 155033258, 687391407, 40369502, 399707430, 441850841, 928123680, 296462381, 323214466, 945967722, 469077259, 792909966, 156590061, 756510015, 933403491, 893219035, 928875948, 526315862, 756896513, 751166815, 408446317, 838531174, 593831202, 304298775, 405070986, 811446196, 466032385, 87128607, 869784367, 299500460, 397039652, 664783085, 483631800, 451850920, 148108505, 976320197, 308000602, 186726641, 214510746, 96698232, 222484140, 638792388, 727309438, 768100598, 405772613, 672335026, 3125548, 98583732, 280294416, 489498907, 775363202, 951900602, 978863160, 440305503, 349402480, 323847643, 993961069, 918551710, 328072514, 231206965, 789247867, 131367812, 125618915, 563084042, 399203963, 119243107, 714903829, 860774111, 766900018, 905725290, 394311739, 228650509, 642996197, 36153257, 356140251, 224629587, 844745104, 253968060, 565111557, 343040941, 466115334, 973312213, 915150604, 355238148, 658840592, 785423118, 763722188, 294086193, 173809863, 348517867, 877667141, 617188337, 491224323, 528789539, 255288740, 258499173, 898343497, 453918864, 903826549, 80434292, 150757602, 833945549, 891464350, 565992242, 334700943, 802336872, 450473690, 280270859, 892946581, 138153471, 327100304, 276572296, 67549691, 315737078, 577199727, 191010696, 703245924, 618788711, 316382655, 607061435, 834859554, 246070374, 248666652, 97086396, 108551426, 297094355, 253631200, 558433434, 868304448, 384265042, 955085543, 829446894, 684460743, 43936312, 63833416, 885065419, 34494294, 972177440, 758022393, 528532090, 387387983, 13062534, 303265324, 182270410, 755188342, 636100451, 118980129, 538704446, 644397469, 154122018, 840724502, 667511591, 132284721, 872377154, 282160554, 330958291, 801103067, 248827678, 76319661, 360294209, 387233283, 656832441, 62019489, 157320427, 758412986, 746719372, 698161212, 787018660, 246835661, 879814196, 957764678, 56055627, 166318443, 767075391, 163396082, 440001027, 793918403, 927579793, 616208632, 525499036, 985362048, 170581666, 673114281, 422560901, 921245163, 888505653, 244862466, 755687979, 308131593, 322954592, 467364254, 39570734, 791368480, 771068163, 982980768, 695192613, 526092979, 275401837, 830590155, 379416756, 705426232, 125828588, 713321239, 603390198, 15373925, 131499536, 590990244, 585320324, 965297198, 277110107, 89571726, 983954663, 447140540, 138215602, 41359650, 340236648, 463967801, 576198859, 436040623, 545039097, 670427915, 498140518, 262231666, 785004014, 616942953, 782191947, 716466633, 50315160, 274931836, 715714153, 137181297, 974215292, 625900950, 318857650, 557069969, 403350402, 778843347, 78915141, 352003917, 152225373, 711724823, 133786300, 429811808, 5438497, 413350144, 324805175, 582928216, 502067412, 302536569, 79915926, 262206749, 830636980, 340167017, 648355063, 459945291, 69864440, 847941719, 841450818, 211302260, 780475703, 551431815, 190898234, 628878910, 979545553, 996435985, 273410093, 138758589, 522669360, 974307676, 801135424, 446094044, 273298907, 764601587, 595204710, 866936437, 908376941, 853199017, 601488548, 891377764, 57827911, 753350571, 61600406, 476006156, 436672052, 245304427, 171539891, 32740722, 609297442, 421062638, 779577674, 790914027, 843741481, 615519891, 323576434, 893093779, 153724207, 475861604, 6976568, 769960428, 669697249, 721652390, 358065158, 644258115, 534961471, 107840586, 764810077, 181890870, 509493009, 81132472, 175634367, 461570493, 284398396, 379500647, 31782829, 261217061, 39552613, 975723746, 981134081, 926465682, 233412795, 544255630, 839767794, 64611268, 631704423, 680504505, 78609955, 753654362, 245745949, 321809324, 91326980, 480139299, 50870750, 452780641, 984163580, 4236369, 667656910, 250444181, 712760650, 443775310, 590502920, 784436719, 785506507, 744319456, 402604512, 467141403, 341414353, 601815337, 472568202, 13704160, 929527657, 599092153, 863038896, 749376125, 579346166, 229013417, 977245189, 104048011, 726079062, 931757071, 799461439, 93987121, 651680291, 78792256, 979254270, 427703181, 397690189, 527556296, 729361637, 19301146, 542611347, 859009938, 332461453, 848947886, 762489565, 852310890, 523779121, 310655147, 377435140, 468309975, 244718386, 440811636, 940037896, 72243965, 257215034, 651548705, 794286323, 433276852, 958232382, 171790538, 53418648, 5226118, 404018104, 873291369, 321807151, 354792113, 830690912, 945527872, 216470404, 653811890, 981144316, 607414712, 769539250, 107671818, 102570011, 15684039, 723952448, 731979623, 956953138, 739380293, 270919429, 750088466, 849781831, 171522685, 536354176, 998052961, 49757192, 705930442, 538187851, 180343305, 93957807, 51247223, 829840308, 687895586, 932170852, 661679460, 627791416, 946826259, 822589554, 598170312, 997796557, 676041757, 935813390, 685161801, 72425486, 953974810, 68525757, 805082254, 671588514, 932607493, 195369808, 758163333, 144572205, 834002385, 634082125, 666887480, 767454091, 562150940, 421096460, 328638399, 858926615, 525790239, 18726584, 71769579, 899265887, 411248251, 14775613, 867023116, 894563930, 371093961, 874678144, 505523406, 259706359, 324979771, 96440357, 875200784, 447029881, 664176421, 648670116, 699728729, 770533919, 826712206, 590162638, 499972005, 544415193, 763403045, 354065558, 103404943, 38978182, 7406911, 214214861, 749820134, 180696438, 999592382, 307101157, 227210948, 712461226, 42968507, 385099071, 920384324, 912156961, 578168437, 94503362, 745370693, 65370187, 603830078, 77457120, 25896102, 929685720, 949156158, 179804062, 307568501, 59127807, 677398118, 862806293, 476821206, 81176497, 929610983, 39732898, 578236375, 639982924, 640438440, 831806694, 228031358, 525957489, 768896195, 544179047, 866408305, 24590029, 376315026, 932223558, 101309346, 490341441, 608094837, 605479312, 600859610, 920336984, 727802194, 175767973, 249461792, 764795797, 614232673, 590809348, 190710589, 873215413, 701324209, 917237583, 1731674, 394484315, 428901387, 234256603, 754488229, 103196521, 248706088, 68765620, 527384784, 342104021, 394604600, 490251877, 469174900, 236666888, 645885702, 365041806, 306551573, 954086918, 742465961, 995407332, 714449098, 509575481, 474634533, 246230853, 667404858, 289452952, 623024559, 736680837, 7442503, 707957993, 739040070, 152413642, 556011186, 229488458, 939621870, 7237687, 596633048, 408582621, 93036351, 80692053, 383751390, 316267179, 255243279, 614669856, 148848957, 295959764, 470285261, 232377397, 992310871, 257337028, 988345371, 925194406, 43555239, 65467475, 33796906, 977861317, 726995273, 474282957, 695235422, 603818422, 574636901, 558445752, 936682400, 365476516, 955594632, 129417742, 287640817, 755116368, 211028797, 284622888, 460148494, 278417708, 747896528, 959979600, 52347904, 468664021, 668098190, 178468240, 212440378, 457536872, 83317756, 367541293, 45815078, 821700934, 226374771, 405427776, 203468470, 525432368, 697041097, 878138151, 800263551, 422160301, 673741626, 796808293, 936402809, 516169132, 578193752, 48967098, 305133504, 519921419, 303358112, 302277149, 860037263, 331739118, 251834639, 681478197, 69524498, 638683975, 979972053, 83179028, 992175419, 132347387, 653548081, 252770919, 566825843, 537120507, 563440436, 915705427, 150125138, 487477572, 695675221, 257871215, 936637989, 213038009, 420818744, 102340823, 490224339, 104540989, 429620596, 488217832, 618241335, 263368657, 208178493, 12656915, 226301817, 579690099, 437525627, 730471811, 807381802, 502291137, 57087345, 770850407, 720563914, 551926373, 721227768, 411716355, 653223238, 619272163, 703732323, 913201082, 203097163, 953305689, 446216475, 834971408, 140150400, 784580486, 287153946, 166384116, 184461532, 997697827, 715435092, 909805532, 116036325, 301482013, 904281551, 253632579, 260778270, 732953283, 911561950, 927555493, 764405091, 864188781, 858491089, 338247600, 439969305, 108181624, 616215446, 952627178, 485712980, 530233813, 773032350, 796087558, 693829210, 892534993, 195611180, 549985227, 120545299, 986627163, 648915710, 430118229, 401773568, 518695409, 522303580, 521200064, 459573665, 46205646, 244694493, 706791537, 546897494, 766199773, 837214879, 183208372, 841896853, 19164614, 501483054, 47034683, 21126811, 11466994, 375253198, 520340304, 30816161, 871991497, 668325563, 904812791, 146969289, 724403480, 147549355, 878258453, 494536387, 143054553, 270512101, 88060187, 661606791, 537175661, 537649568, 577045877, 926110588, 415697537, 613043118, 987409038, 291454344, 527578521, 176708589, 245275724, 345758515, 547432103, 101757866, 94632346, 957630514, 906451498, 642062563, 182260848, 57525291, 780274072, 575651658, 76640948, 199400711, 897729922, 697697653, 199556364, 429479274, 328497702, 873839638, 142527996, 203705833, 417561122, 484111084, 203216550, 897917032, 302398380, 400501993, 266678110, 894837846, 612299932, 809230351, 433577237, 442926805, 889969425, 815903584, 415341747, 807110349, 164217573, 844063373, 711626795, 377370379, 156244635, 894197295, 579596616, 286625420, 510754596, 774517766, 83798465, 776896517, 947867479, 540909478, 710908554, 551139106, 975495304, 813874578, 585430929, 818186404, 159539853, 478908433, 892422638, 387067082, 793858278, 590144539, 266614725, 843893829, 849840219, 443475922, 813577456, 254783140, 397313325, 575872401, 470275326, 204661822, 73415800, 273405868, 898678826, 300830628, 239149688, 706391567, 596545640, 810034994, 787084644, 843859430, 513265632, 373440212, 112064910, 697220977, 399304434, 973369703, 526028940, 242617561, 991795768, 995590828, 427415979, 798668023, 510514058, 148812132, 903439542, 899872756, 903545712, 43926251, 711026041, 954892974, 683081780, 468071581, 357607931, 563861743, 504844890, 319480376, 737069045, 308225544, 838281808, 743281821, 852372975, 610773857, 213637643, 863223267, 9421902, 759375075, 497446434, 847147110, 336300724, 461918508, 516373509, 453829632, 507297300, 95817747, 463389723, 226361518, 944418704, 473105483, 1527779, 529938978, 236585930, 541762011, 551867197, 960165783, 27081612, 121164421, 344605869, 223417372, 859607334, 202698258, 389222938, 817968970, 89250665, 860972900, 967039504, 541183532, 458256227, 256052562, 274704336, 626036135, 889993317, 977550305, 286490719, 950296491, 454054345, 666980239, 618286493, 879706816, 17716767, 94531918, 313995279, 231159396, 267325271, 872465324, 266501164, 951627183, 971070863, 837657732, 5374977, 883714029, 580020514, 141173494, 108991354, 861658220, 914643906, 505193627, 989350304, 495682089, 806054513, 949735837, 120431880, 352965807, 897069118, 289083241, 968510870, 728267628, 167609296, 441844469, 96248380, 833750665, 840465737, 557464208, 496976525, 888557258, 557079170, 401610993, 889317974, 136220416, 142567249, 70584221, 770068981, 472260082, 249852565, 368226378, 98484400, 15798912, 146162118, 31975181, 799183742, 191355821, 507046224, 794572734, 415062640, 831080016, 517321774, 446918846, 840566947, 125702654, 590179266, 809761059, 298487296, 31622693, 348549270, 773320262, 869766847, 157175907, 915369349, 272073512, 19034270, 655464547, 179223368, 977053451, 646395281, 809725086, 73706101, 772144321, 275638864, 115094120, 625844468, 108142176, 893514685, 799726753, 845793799, 493926696, 855979954, 861480416, 41441872, 432743455, 598794099, 97478927, 399788796, 958201080, 509400797, 618698509, 790524978, 882242602, 174831825, 655391951, 812590664, 611676506, 186242081, 909394611, 900000867, 664604597, 414145815, 16208849, 638803672, 801436941, 467400904, 300147197, 586386640, 79902003, 980043479, 706693141, 119503701, 363057655, 727633406, 276448348, 953918554, 487723756, 294977747, 945302675, 509623863, 297228199, 776603487, 759415145, 637534440, 373015984, 959469054, 334153534, 993112395, 372226063, 264698150, 220360696, 434942417, 324320465, 378520103, 500931840, 892977552, 574509978, 506485282, 734039431, 638935762, 322164552, 608016614, 392124708, 231644165, 746964540, 74583030, 459745720, 450579642, 758967766, 38281233, 219532041, 322709463, 898136470, 578656799, 283869314, 601566489, 745863301, 88139288, 395854420, 61088540, 787626705, 235893245, 171771551, 878019312, 617197601, 495626450, 350764946, 924707455, 54949103, 332359554, 243213712, 479902117, 683012595, 149302909, 117260532, 66804229, 623510732, 134619558, 15297747, 57585451, 578946902, 275355572, 749723880, 184754230, 39937725, 964452393, 765940992, 281303363, 382733425, 713117284, 333292058, 9986507, 548334795, 499935347, 706437490, 941436442, 185545079, 398808089, 954212374, 935308349, 668933747, 357978719, 115218609, 331249665, 262813627, 882235884, 300798048, 436082707, 465053988, 810567423, 533932226, 148357548, 980613483, 628555460, 750662000, 46517353, 105929001, 245055160, 629080519, 216815656, 119411069, 773966705, 302905776, 861329884, 152507319, 286531793, 969541736, 186459772, 371556685, 216445422, 639405852, 620271226, 337057501, 558545888, 389255095, 907178897, 552689190, 231180651, 929859379, 178092341, 908647647, 520783892, 723496518, 129584616, 303905254, 181453841, 137434685, 605589113, 754609274, 145491282, 661832805, 471044486, 607362589, 972763723, 610486665, 956320498, 342370159, 965320573, 85583333, 52584375, 603543279, 640044567, 869501421, 236135960, 992640951, 228473795, 798857839, 515731563, 610118402, 93976213, 482335623, 933867184, 891395091, 678588782, 144298317, 480244966, 978082757, 89026779, 152629134, 214973733, 18246584, 90880035, 163903251, 705622160, 613122215, 382792552, 405463394, 62001998, 183372477, 884705076, 944692426, 841304619, 853975907, 143949907, 387032322, 750614322, 229800533, 186833229, 674937824, 572624868, 338691328, 468158772, 57709314, 653555002, 477777335, 899463806, 647068391, 719143299, 999571506, 118352181, 702689888, 705744067, 347303310, 13831087, 623347257, 913085005, 982166867, 519761203, 791527702, 589002666, 860380423, 513184780, 91873923, 947471826, 221916558, 205560938, 365275377, 212701267, 616285264, 769492665, 335809363, 865581593, 628975548, 303655284, 406081981, 559724811, 837011703, 591830558, 76829321, 960928299, 639602228, 952194190, 826625327, 744426466, 670501789, 415533635, 587684370, 282261414, 4300707, 622301382, 55038870, 35990469, 54921783, 558281322, 365364612, 147843427, 341510324, 893934385, 521108668, 23059992, 316331565, 689481910, 609366468, 450156720, 531858890, 383379745, 906159452, 101507460, 113019745, 210466778, 405650227, 38122283, 116990067, 270178820, 224368253, 385361073, 225183903, 133206972, 963870667, 419150888, 24158292, 379431466, 242163178, 365924029, 231491787, 626778605, 955941574, 521747901, 414564013, 430971213, 534382035, 12661998, 672485075, 700541287, 53505652, 161289397, 763291328, 99921887, 323823106, 656615764, 844924584, 797064377, 542785177, 675521733, 49629005, 553511212, 435787776, 399463766, 747127122, 121166355, 300244423, 199995943, 20728135, 842659864, 247291715, 785349965, 542191801, 752249527, 547677993, 717842517, 870515210, 399022711, 415433793, 179880231, 898051335, 50914259, 920103010, 915339240, 718353063, 191510128, 50626020, 208493820, 931119991, 277083900, 787672570, 203265068, 549600461, 411131906, 87869401, 245183582, 224464359, 483768091, 905693722, 846874659, 639459170, 601649048, 550105884, 982475937, 437693911, 696621056, 841943728, 918891036, 87696158, 575997747, 318893366, 267072292, 15799069, 747869880, 863878947, 776862807, 850623909, 463236545, 497932982, 146803223, 489814231, 943467622, 115775767, 315588510, 934038526, 374392113, 771917541, 631932532, 154008664, 905019369, 347608640, 620737388, 272009292, 710544374, 597325103, 777519043, 257174144, 621611843, 376804255, 285022176, 255767850, 739200421, 615337076, 762436815, 358487743, 559826208, 967424982, 277167634, 132392810, 458777184, 490286676, 557858486, 474843625, 326842365, 912976529, 1772911, 513084242, 850944001, 572898304, 718248659, 515290696, 107116413, 152435449, 252937676, 730621367, 849525019, 913975423, 319069088, 945877399, 49232863, 638388085, 534796961, 289761734, 392985425, 147491049, 500297018, 428829208, 557190085, 753200120, 278645015, 149344789, 198546306, 228373074, 266527267, 366504096, 891139688, 776063938, 592524046, 15623342, 915503829, 460961070, 368119931, 418233441, 234586214, 953424289, 467728520, 549309610, 60783529, 329518423, 452011368, 731386652, 18801987, 955816316, 177048398, 891755010, 738101430, 886390572, 932026239, 311723479, 592802192, 26862749, 732520170, 460423782, 910459760, 572196093, 260263664, 668400746, 746381845, 429429508, 343606063, 303556673, 156285634, 166724299, 320907010, 35434550, 636956689, 206431964, 528698824, 677100792, 797274590, 762926653, 196839497, 659284630, 135308669, 760849921, 389314515, 420468477, 187846650, 743793220, 632138865, 548895918, 77553709, 761140630, 396661975, 210008634, 471704282, 630866309, 427854917, 560008390, 112139405, 224128300, 870052165, 203007247, 178218504, 593065188, 311773465, 843264111, 863637453, 576983867, 672137099, 375606766, 513249163, 576048274, 297030427, 223109128, 124504477, 355410316, 581394080, 310219432, 707233072, 924903041, 816431525, 285119506, 283502295, 954009333, 504112778, 576134972, 801160723, 137616696, 396600015, 307547683, 973448058, 331279303, 368001390, 280293146, 253782850, 583639868, 992987950, 156179994, 50733967, 395432975, 283921690, 90418343, 60601303, 875239499, 564178350, 677852843, 565704633, 505857408, 418398461, 967394873, 545944896, 76489697, 544536296, 922855937, 579990147, 139594330, 660807744, 349618723, 104406354, 912771398, 260406988, 914202177, 850679865, 310031188, 153055098, 294744130, 47121286, 179046424, 801108209, 160964729, 666134698, 744346568, 554445732, 625484056, 471180832, 510282473, 797374080, 974905583, 191218348, 272344806, 410328844, 124518793, 912246473, 693916134, 599007824, 287549821, 84720114, 778874609, 868649460, 417812467, 85192026, 730638490, 333771548, 428844292, 205146835, 318839122, 262809544, 149481760, 324915185, 598046934, 45139050, 531175725, 592439203, 643898432, 996082917, 650674191, 317402339, 269798513, 633561405, 456448079, 491677825, 749057285, 29084824, 352175499, 831685171, 61526259, 288511375, 55704263, 225084032, 118130013, 392454528, 654612005, 199101710, 432612736, 277125387, 885937576, 85937817, 905866763, 125766569, 734124951, 640443647, 631231152, 528408077, 756308651, 608894852, 542746417, 399476487, 587993006, 314996247, 277069841, 161000197, 730906723, 37689357, 692585705, 487890944, 744413486, 557049054, 383132495, 52841388, 615879504, 253987563, 917362696, 144188443, 179300638, 716394815, 574063746, 933364097, 560533115, 707056590, 505229475, 985596027, 497843829, 490326213, 655546820, 347486070, 926407851, 80230587, 992106855, 280390747, 888136061, 27895490, 467368985, 240434463, 246993006, 791624750, 858514565, 833361762, 657727886, 595712069, 281229208, 450477234, 95183191, 647022609, 725160869, 399099420, 116930593, 200459363, 880806946, 900243092, 491200449, 473295037, 540086306, 765655459, 295258173, 344238937, 78243922, 656477947, 372754042, 418453062, 370248261, 467900501, 696490739, 263457432, 874322166, 598303607, 287744504, 674970062, 708528246, 372068490, 101895817, 690621023, 349422252, 231612541, 497517743, 605595783, 532179645, 981389639, 592561266, 815474675, 539566828, 102455061, 591858828, 126408893, 336044076, 866657144, 157169176, 930996847, 100539211, 499389296, 109260986, 891366579, 930224964, 98828757, 96236247, 398061676, 414446402, 938490885, 56893574, 700392215, 110946570, 981096212, 719586090, 699827021, 19835259, 720802002, 174217437, 776120075, 739541791, 869122103, 156894679, 777605994, 711748602, 327903595, 921471339, 189185986, 406838333, 563585847, 717315085, 840868281, 401126440, 623557179, 765435289, 130312295, 43951268, 677666913, 895538548, 177962823, 201448091, 230315326, 365958700, 972727586, 326172513, 868946635, 44652887, 379925712, 327350523, 700184464, 300519822, 644604260, 740145919, 661365513, 333698349, 514035114, 859527213, 271711531, 683933935, 629303498, 144506972, 470515193, 162318345, 361468988, 773681403, 951061808, 618054892, 170325268, 541789267, 879940958, 835631004, 228332363, 285941, 893489786, 707683348, 95338226, 306290205, 802405981, 293220340, 967511979, 593726390, 835193546, 76873636, 239104489, 98862539, 730794137, 483217075, 565334732, 620839406, 488761639, 306143438, 443844020, 191707075, 673806132, 371244124, 426322917, 690821801, 126313746, 368560425, 293999434, 238721923, 198407199, 259064807, 477745889, 669810485, 396775991, 917671963, 15555009, 961291894, 521275086, 118553165, 376450715, 436208891, 754192196, 960953410, 691003753, 277420959, 48223675, 895557693, 478440090, 845184988, 812492659, 716399281, 27282094, 594466981, 147543633, 191024744, 290864892, 192183368, 813367972, 563033685, 586187140, 196464330, 850801020, 300870970, 311947313, 681362461, 726142239, 239308072, 84012810, 241603802, 399718378, 901032097, 788930297, 975620475, 310650235, 137819782, 395221412, 242337596, 136332832, 262323761, 428955394, 616825046, 272608443, 942188421, 351541622, 373663972, 366026932, 569044135, 828867394, 839860756, 483606735, 140373407, 144133406, 571177100, 864133331, 483809534, 352462943, 476034081, 529590755, 811034676, 746270821, 63369749, 593688894, 278165128, 103746320, 170691917, 19098123, 596619039, 733097272, 370704721, 74535413, 940664464, 911538679, 943462332, 990306562, 793048101, 883432874, 203865682, 812420040, 306138712, 15553831, 37449603, 702612837, 841902965, 553941631, 52531429, 87602367, 800571677, 156944672, 340656687, 918148385, 756066090, 232089177, 797358606, 11236890, 848237973, 346750968, 670799950, 366501871, 73330622, 463396541, 52145811, 379061612, 356916657, 610924441, 566352168, 725712905, 525071540, 206556595, 298352204, 44052589, 265974787, 275331917, 695797905, 236938505, 970002970, 134849121, 669972523, 434179031, 347090745, 618225984, 282486983, 394331970, 395437230, 891404949, 239975401, 381980526, 698192817, 57060436, 912971099, 1104871, 688263907, 769198324, 739575598, 532631463, 277667949, 488947190, 810198691, 112549138, 179305582, 607773893, 579013424, 631392285, 308428974, 389438297, 591531061, 180081068, 520212290, 92817517, 984792271, 12197746, 133241620, 695914295, 815965749, 112737698, 860534153, 788005873, 868408275, 54048520, 324533105, 629384182, 11898576, 392656807, 304838938, 413892374, 605813142, 312625830, 879283147, 192493615, 636534893, 463717629, 645643993, 830319623, 907497711, 823984702, 86873495, 920329741, 491053552, 423509659, 557383937, 778140718, 991559738, 646331066, 642645796, 886317432, 601782135, 363069773, 633534588, 680004349, 5506516, 352975882, 248267268, 834087074, 5575808, 427613276, 221977159, 957545479, 440878596, 954122460, 566713065, 38054480, 807511120, 782891013, 118534672, 990036140, 756153848, 924333944, 831527806, 61823242, 506972240, 613113528, 952310587, 556625734, 683356635, 696578339, 308493989, 228232333, 254453124, 84225461, 516290794, 618679557, 63691765, 82224094, 189056772, 651814557, 310067314, 411763322, 313912349, 771320262, 585579114, 835544241, 566485107, 199009778, 811706051, 49495028, 770981261, 937563672, 126680902, 307838732, 735950129, 147051542, 783045385, 425661477, 809741678, 332129043, 916678174, 916297229, 41482767, 773422713, 509037150, 162414232, 859539910, 382275890, 768158897, 851882864, 572779052, 707660612, 759552950, 859138674, 744382295, 598537750, 463579059, 928534585, 927950208, 27660847, 393383234, 969474592, 847359283, 88414963, 78209647, 309163297, 209855851, 475442276, 918685620, 16036468, 908610682, 793486974, 220496231, 876286281, 827700253, 338635890, 597355864, 478125313, 566259565, 115026999, 152905599, 303008714, 684090569, 743078996, 365804458, 737716842, 581805374, 626757933, 987982263, 827845161, 670029535, 498692509, 370595370, 487234609, 269344736, 43501911, 354128066, 995753311, 925192574, 473304733, 475029048, 917514567, 545020447, 182588338, 316642599, 540035951, 710961242, 742498418, 200711020, 482141596, 528466631, 164571917, 364449942, 638092211, 928867457, 678394005, 117255268, 543985032, 21121661, 644159109, 690671240, 514290553, 751875578, 775725131, 968972849, 410235833, 735133656, 715008253, 364031466, 207104415, 151283030, 23444391, 216083821, 73608470, 467491573, 420886604, 50701033, 831624965, 901547242, 306395377, 920532100, 512930979, 584219632, 262671541, 816160110, 500472581, 359917036, 85225092, 37667080, 874009806, 333750265, 474803208, 939582417, 490443030, 645950492, 283156254, 333587925, 256037181, 926248492, 468107860, 989910206, 434995802, 766214484, 370383737, 785508012, 409728347, 608335758, 510392824, 920361764, 969876396, 636914114, 95252305, 100191734, 36173505, 27805966, 834499176, 660561955, 312717301, 601214298, 48976578, 472893250, 854365496, 687013775, 773108756, 524092691, 983822957, 563185784, 733135463, 169468789, 214071123, 152554683, 467244838, 22667157, 361612776, 242948948, 252024594, 264733615, 278320296, 966951663, 731039245, 197132228, 205967878, 396124526, 572104711, 194711647, 770982717, 649778360, 478972332, 485678989, 126031989, 747808032, 102685464, 897423638, 654318373, 713286421, 42805601, 261475668, 940193704, 608088613, 274559573, 880583996, 877527645, 30940592, 893336236, 369814210, 683937337, 769666312, 955283060, 63840162, 462408574, 843128182, 161046360, 698061185, 980141729, 528676729, 919743605, 891850484, 644700472, 976350749, 96713437, 278410059, 725487639, 872786715, 541185537, 272754980, 677276423, 818277073, 630709988, 552477150, 587882654, 59769224, 176952810, 84975297, 410928016, 892029106, 737940824, 67810171, 195073261, 195157966, 699229991, 936830384, 180098283, 692177846, 985614429, 132708799, 47802949, 849189905, 396463653, 724340207, 603195581, 882855528, 256420034, 907230641, 114614650, 865378449, 54887380, 380315265, 295423966, 594675328, 942021674, 719211937, 282157453, 929531439, 263721499, 226350975, 130912517, 361019368, 536655775, 634210679, 956542764, 395242952, 381757080, 896676803, 803874536, 39789419, 534445837, 649318209, 934512768, 866084407, 141057543, 89557182, 204571306, 792224623, 110354180, 837562932, 781192414, 759660174, 172855296, 138540970, 143289602, 940477484, 867244995, 319323162, 16774888, 59612102, 807984357, 373157449, 983604742, 942405255, 370545574, 265235934, 274414353, 645346254, 856009522, 394825362, 66481913, 222543930, 786061006, 542800434, 346806501, 189450334, 826953360, 347159917, 518762996, 836791944, 998740850, 712499532, 315831163, 757727979, 723627023, 387537087, 405816256, 577825543, 69360811, 61929574, 620518498, 786880442, 843535719, 215843910, 897220267, 511761079, 956738162, 912015716, 122989910, 628348925, 293239366, 202666848, 347050567, 686699606, 384236781, 345352557, 819954936, 216552392, 531106131, 249911840, 555205344, 366954680, 819926029, 622726900, 185122681, 441409960, 971546689, 758698717, 209327028, 277196068, 651920682, 852911804, 851535604, 253828078, 784488503, 813762030, 774332440, 367309249, 152868437, 75282501, 164225170, 672823555, 1230038, 267859240, 158682053, 252715353, 911371111, 922560963, 450537084, 319324917, 703164389, 487141598, 827642598, 614296453, 193382142, 740785872, 168669451, 215317641, 553899248, 442078367, 843495411, 991934280, 500692530, 582647689, 932908371, 603150283, 475490546, 863569191, 139042763, 631362140, 773855432, 9150349, 129297103, 566197830, 153907030, 932373923, 906364255, 888814144, 426871596, 68518236, 237186696, 851825653, 156323578, 691105797, 822812352, 564102818, 216579488, 834504136, 800457605, 498649279, 563118693, 325257047, 27007110, 446704535, 519911842, 101115933, 481204166, 343590592, 543798202, 459546572, 236313195, 98056285, 548627976, 53277049, 718833042, 394320418, 765983229, 616782805, 793202281, 972154404, 313073578, 602423570, 539068897, 525574887, 870524230, 571749019, 172333482, 231328568, 145138809, 177214316, 322689601, 291869508, 676869190, 358501339, 96898989, 157525579, 981044687, 561850784, 963306212, 241399009, 764667128, 389517295, 967327681, 783301124, 180762432, 159116051, 53140745, 873628167, 704300289, 907604399, 403961346, 389835228, 498822546, 40954945, 200880142, 33479471, 294838480, 710211435, 100342333, 602333477, 455056551, 781881911, 308254759, 508430053, 5811619, 645688052, 723960366, 189715197, 318809790, 778488277, 670258603, 31951275, 927419314, 533290433, 321403497, 523285899, 52449590, 966096408, 177759055, 865018282, 81622668, 53304684, 779766787, 708840784, 953969764, 876506150, 516318203, 650674743, 700953952, 88103930, 957683302, 419298108, 830577308, 975580626, 827142080, 320387144, 526836597, 29675036, 638043948, 876121399, 537475455, 838568518, 75527340, 526262929, 896382073, 323725624, 466350507, 780919481, 430973228, 663369859, 553516764, 530961408, 277393522, 385454956, 222951035, 897813165, 665881060, 714712819, 950662016, 988133715, 175817449, 67193695, 376682613, 43277371, 657764447, 903101183, 343298758, 962624195, 415635200, 351011256, 723966447, 873769944, 388429630, 13211224, 459591479, 44341284, 126689855, 53775432, 540743190, 618571597, 119466451, 541598416, 99115196, 56357955, 413990134, 47114026, 937861216, 309558882, 577017282, 889544058, 741327943, 687227320, 650325684, 680958775, 759428777, 332205975, 78157991, 666818073, 582620429, 356943533, 411443297, 432838758, 816701474, 820291493, 847076025, 340500498, 91072411, 835370134, 512167732, 93246501, 358154151, 463171905, 401954336, 950885536, 718594046, 590903248, 277825683, 892830411, 390166379, 246405220, 433094069, 148845067, 232825918, 735310337, 432196201, 690821613, 388400107, 304900480, 442482405, 89895880, 977623098, 42632262, 306259543, 156945412, 721975735, 36244449, 626415551, 489809637, 241735711, 967709573, 178526721, 678570076, 73046032, 741033635, 792940510, 859190055, 841603056, 101452188, 383715960, 319715800, 86082595, 729369540, 868398080, 275258298, 20806708, 788471862, 988070579, 904501400, 338957186, 228987994, 863180072, 309462935, 681344246, 52548574, 620255515, 610051515, 229579350, 949618550, 815092042, 15544693, 990598730, 745206334, 768638460, 341951176, 246999699, 697590418, 731754856, 897410496, 783602124, 993543742, 843978476, 77242337, 151664580, 767954544, 265176803, 135080949, 57778153, 15989824, 289866931, 763187548, 218544593, 368851616, 490372082, 556536560, 659385009, 644648856, 624934009, 852920475, 178585496, 93269012, 792279158, 626340418, 551593359, 828850068, 222906042, 90202078, 356581464, 823941997, 340442656, 962443689, 306595059, 938400478, 492371426, 646455238, 377297038, 594095724, 109499173, 824210190, 43538918, 963847913, 435756906, 317075841, 431717018, 545368972, 289110758, 121606890, 230597099, 615996798, 634782985, 296357464, 247311045, 150859256, 556781281, 501871284, 800756672, 225363557, 896298536, 916710734, 810603388, 225785540, 217332984, 206577415, 688636890, 197320106, 936177002, 489409898, 624688510, 15647597, 88954419, 412171864, 50788299, 781072320, 340716411, 42999228, 190020789, 100972794, 432571848, 679114552, 603703787, 302924522, 332843169, 644145079, 560866840, 972035087, 858543619, 936276974, 929923683, 725480141, 473141804, 972352876, 154679073, 281581319, 686767561, 177096450, 221606952, 482362079, 462058513, 145474512, 857278040, 187410810, 764104147, 399195264, 659198386, 937506584, 917357643, 323730959, 300884011, 866312733, 59161809, 588259172, 274069139, 255213666, 582434311, 794716601, 376594002, 700150452, 812245969, 472467418, 238748949, 289571551, 797979105, 90676458, 922872360, 458354469, 153918366, 466901206, 185573410, 720109808, 853347799, 600897957, 120599403, 767167948, 473012115, 758560286, 310257459, 161937632, 127245634, 784637798, 8668123, 629596857, 346645041, 769340481, 161101631, 489576036, 853522805, 718338868, 451929074, 260756934, 518247939, 525530986, 248032360, 659303699, 328496966, 291402796, 854196927, 448073951, 724520338, 837970643, 626030502, 475092838, 531889594, 717769313, 313796626, 64032398, 612360496, 313452720, 336533847, 279346835, 472096512, 209723547, 165099060, 288796504, 963924989, 900188869, 602907121, 13936698, 403960352, 317593859, 316591141, 806742973, 745423713, 802654433, 993442541, 546609605, 193435676, 602596315, 635340616, 67957998, 480932293, 818607463, 412768728, 223145945, 144487039, 387282628, 833313625, 97252252, 707135113, 780621754, 30927757, 855372443, 965059448, 415807168, 755798169, 838249432, 199066597, 545386750, 905468221, 844429459, 147588490, 432917297, 401383514, 729378535, 610922360, 246774922, 540541383, 203352131, 78353121, 767430862, 902524987, 477063845, 838043718, 906869364, 152354697, 493099362, 127743859, 544889534, 693951180, 524113252, 16175367, 302078648, 948431688, 740840648, 920866508, 915245961, 98793287, 606943341, 712694501, 427104626, 663725009, 460043604, 805269167, 804683304, 87338534, 539643585, 440225615, 484916745, 337761147, 621600906, 547105259, 523074099, 844047046, 314783860, 289374155, 778508458, 538209616, 388854342, 342280142, 123186818, 759325582, 160844114, 124321021, 775467813, 808122631, 273677482, 518086767, 990466808, 496801143, 754694823, 974740016, 885653911, 578336499, 654342763, 644257834, 655163207, 401621333, 176021798, 287926135, 43204708, 831423388, 321357599, 143685336, 134204116, 236698490, 668535058, 369570131, 436149821, 329419385, 540431909, 243946530, 810433653, 143248083, 709237482, 128323008, 275571363, 835131299, 431633455, 3137859, 434789999, 526274777, 305083313, 179386838, 806655088, 389673255, 149659963, 155835821, 107441218, 882276540, 54952432, 846956364, 501596261, 213629046, 838734053, 931539474, 81321963, 742889824, 401903147, 354305799, 604073447, 291506371, 232742838, 183490737, 591568244, 975373824, 344935720, 649512796, 915607973, 199640661, 637585586, 256401026, 868336324, 696870181, 313834403, 194576840, 372391102, 56547008, 559313365, 73217677, 568692122, 2737266, 399757504, 426127294, 613535367, 518268268, 851191055, 856352722, 928902439, 132977089, 734024529, 185110733, 115191042, 391229883, 900796327, 848922482, 360840917, 444861647, 152573478, 657920186, 480909196, 419994257, 985967052, 493396870, 543167596, 404058236, 610003986, 689301469, 956190190, 3642622, 322806197, 632511215, 984662546, 739950445, 108944566, 398244127, 65370022, 455851812, 696124046, 276407443, 540438809, 870275117, 321188772, 954332780, 993193066, 654465384, 507366353, 264459737, 763856328, 978147303, 637992358, 71127048, 845497107, 78207973, 63046799, 925882285, 4678668, 249983234, 766543285, 967521086, 324393253, 458584729, 139191645, 229830864, 699518186, 108051555, 503749896, 171193052, 570336694, 848971477, 590789341, 164655376, 274264200, 411327140, 748563986, 859007589, 737746812, 293856511, 521586832, 108237995, 485790990, 485020165, 788008671, 494001489, 323595632, 973256087, 768385986, 596104068, 317427254, 910436217, 424723997, 830212616, 480918870, 970926712, 160933902, 642444783, 110918310, 797368988, 44893382, 207597971, 835605505, 608645587, 945869577, 894817945, 153569903, 228862572, 602188290, 750639212, 547110227, 268501203, 506082177, 477409251, 763523760, 240418075, 956728620, 59558283, 943872697, 480843629, 592139544, 284917784, 523911111, 702010549, 336778047, 221783608, 72742646, 166667857, 325639320, 995350168, 894633936, 349629171, 257170309, 476727980, 12387856, 946814259, 531660713, 499214500, 136626082, 616992215, 295496237, 726388216, 555249273, 64982015, 346466020, 415262015, 594299419, 178516571, 623585953, 113982326, 840622394, 833536949, 272136155, 813797179, 499936856, 760042666, 307721873, 60810073, 894985141, 106370919, 54447832, 882944523, 194613383, 820374978, 484794694, 375195469, 737743548, 737001698, 133788582, 65202996, 586717815, 717281852, 437187949, 142421237, 64276113, 646156054, 898318102, 200292977, 154615367, 723728563, 265624535, 420202858, 278049583, 272752942, 796041896, 441014103, 297732232, 539720736, 300425584, 53309009, 711490559, 640327592, 244413655, 375655484, 476701381, 567254973, 408757339, 810428487, 265126937, 124486577, 901884481, 232814226, 638133154, 942757132, 910805816, 293361528, 616013719, 139945919, 562186919, 266744048, 653630512, 56851206, 60951514, 676913292, 565865689, 724660163, 141868000, 149146142, 277840828, 508009037, 808531970, 511304672, 103609052, 709515171, 513528138, 83045695, 816914904, 686111342, 448476860, 874642883, 125084247, 464592964, 563092022, 638999481, 1604651, 505929596, 462580833, 167097441, 69912596, 4997298, 727560348, 882106167, 630735045, 697050309, 868899940, 895984747, 737782465, 73821733, 499757138, 290822470, 831392938, 374740277, 454200764, 379740965, 197165590, 792792255, 630486528, 121254878, 890423016, 47664943, 919643171, 725812658, 705042144, 199915761, 330011065, 118291944, 8464491, 184061835, 466566699, 772108671, 254161855, 986055577, 59417387, 829626253, 263991003, 556163962, 572103513, 935121868, 822714470, 268921629, 49947668, 288497195, 736012263, 477669661, 318533621, 276740459, 340309788, 89582039, 685085237, 908705857, 661282170, 387404597, 221894240, 517162683, 837768779, 873538714, 126555284, 186046551, 392409127, 265289305, 133280389, 395806360, 239296596, 670579742, 690567807, 938409901, 785568990, 916114038, 965536741, 94218658, 966299964, 569994716, 34062965, 724460403, 169953664, 874333688, 720515895, 968194896, 568886977, 572680516, 778675080, 427658786, 698323601, 296533918, 678327308, 18183408, 622714840, 708675916, 124724639, 26013723, 107835341, 747583869, 409143626, 342494344, 106143205, 420382749, 549748743, 391107215, 756388941, 405364195, 28835429, 520347455, 106225697, 717580298, 608969066, 685648214, 379733475, 72809735, 560468763, 725779892, 784558702, 44678500, 197107108, 53372176, 289385492, 798377626, 524649099, 219438706, 385443054, 182601337, 602299447, 732655657, 306359239, 520585293, 374743128, 492169519, 320460134, 39853754, 724861117, 850435464, 349803196, 659613652, 323741517, 466301597, 237336818, 238439606, 129736117, 576854922, 429519199, 282410270, 908529486, 804482055, 38545303, 398854293, 156775062, 899356288, 974540524, 773860217, 822920637, 311416041, 53670501, 661247680, 970181506, 363470261, 555970489, 573115249, 625958653, 143439888, 113401391, 924234445, 905450553, 110149582, 809524990, 672343712, 139933652, 822394195, 624160781, 726770014, 859362478, 663147276, 656523406, 791360051, 799897721, 547201576, 468161953, 607085981, 895046444, 302270533, 659943919, 17209080, 21556307, 108615266, 925960068, 565325203, 578323636, 776226738, 955186673, 814749619, 374372813, 678872330, 869185848, 454756168, 196569508, 133625416, 490911059, 65783430, 140148074, 129159592, 349375243, 267752960, 55340532, 889073931, 87034383, 45651745, 625289635, 466955304, 763985607, 986665356, 673485980, 689424590, 781149041, 893601578, 749049857, 34906576, 537310413, 863136218, 351623714, 518388743, 642915804, 187604080, 655306030, 34401087, 712128353, 456199668, 517255924, 259178711, 393213645, 856824142, 675189376, 389336567, 429243499, 28538754, 834526290, 219988220, 565621489, 41093376, 166833757, 884704084, 91668076, 874839814, 210621794, 394398552, 202510634, 362685312, 426866008, 983253801, 709882798, 478768536, 72429126, 904484467, 218297951, 932147194, 926371645, 698649517, 516491235, 433641877, 575610104, 980407389, 772104505, 275291366, 454114999, 596343783, 993337401, 257481715, 279568177, 555193064, 496446775, 965795534, 472159185, 805411717, 251218896, 266289913, 898153140, 51098938, 181774214, 663612009, 803357422, 61386084, 473527014, 441499200, 204268996, 807133992, 937491280, 677280175, 406642783, 688249301, 145041661, 390205972, 323217351, 5683955, 952910262, 19173734, 419701617, 211611007, 29157460, 121445978, 165232685, 303846859, 209737183, 399600244, 566869275, 141780625, 971621914, 637419163, 257021914, 553655128, 762148360, 853509109, 760239517, 502525775, 74553975, 256858597, 228098535, 365679000, 785057392, 166256966, 359233879, 616195367, 289326620, 317711453, 321996748, 862175827, 625383592, 545569629, 15265270, 501101900, 351606395, 646164806, 516831147, 717488829, 416391755, 815129147, 129336572, 821815164, 905857882, 707609803, 867827931, 313383788, 654420384, 924716155, 398344460, 678281353, 158968085, 796802696, 615361994, 944047102, 869485166, 60206883, 863060697, 932757645, 867565160, 525604193, 85111453, 448938334, 845492308, 77029377, 892082827, 397902651, 972251226, 264402825, 608288274, 98398775, 107999466, 789249385, 309571143, 900860098, 899141196, 960237839, 785652432, 329298408, 133678965, 650559859, 501847323, 87417761, 687794779, 629578563, 593081041, 470041647, 90149650, 695279105, 167220859, 196772578, 526868627, 942180086, 134184662, 534771371, 584609548, 331671810, 155531698, 526757271, 124528000, 770101855, 895034066, 802836077, 653594644, 842656023, 216933808, 473399149, 711137627, 274345806, 418116899, 524128545, 646151240, 592560789, 455104440, 988051643, 98874901, 131914701, 858819964, 145799073, 20390206, 475800034, 330006626, 134777736, 472523623, 600914378, 640324194, 858512908, 849822636, 707098436, 853173090, 121172499, 444046809, 475972539, 118177489, 471994107, 365784627, 265775086, 378303572, 901537796, 347699826, 381250215, 365866987, 616876152, 777310963, 934674119, 357834862, 592381117, 694068432, 425026471, 401498119, 844587669, 760516052, 925100821, 862693117, 658160578, 818470484, 125285488, 935180932, 856763958, 764429253, 485569780, 158735656, 298914389, 658033282, 732580675, 639580599, 285619929, 392673711, 90322037, 352500613, 521927483, 539738653, 849632447, 195912977, 54173428, 52434977, 675905064, 621519044, 128459147, 611280970, 407582628, 281563564, 309103660, 674923491, 738661350, 98763403, 644486043, 111177412, 535748213, 178456688, 334729141, 580832295, 361696526, 775897311, 282826454, 607639408, 233962153, 934543400, 447928999, 833543139, 867339160, 562509032, 497006601, 32559108, 762732268, 74440003, 939857152, 690786118, 731993577, 921985686, 881964558, 122048537, 406030698, 948014362, 112268705, 190526896, 262200095, 294800186, 726157902, 319249110, 810780000, 765409479, 426239531, 552359108, 700599379, 343819520, 190208432, 434567719, 328256646, 180594051, 563977496, 264969663, 428831206, 339390138, 185258299, 865190447, 748465807, 175758169, 4208124, 571232647, 540071776, 705349153, 515490195, 291425848, 759811872, 805520169, 493435797, 625494037, 190043939, 642781455, 391454352, 321498528, 596404515, 505591801, 414719889, 996857182, 385373404, 851526354, 381383298, 902650377, 839468396, 817831703, 19225801, 342189827, 467571944, 678393881, 8089954, 378499423, 66931307, 289408823, 565824511, 856922752, 564502260, 434733800, 187974016, 589759936, 535576049, 156053778, 650825977, 56133681, 634341837, 329290433, 966696303, 866176738, 453048789, 339707191, 541734643, 870812987, 638765446, 320944527, 615917643, 340078461, 478570720, 395200919, 430015327, 453772585, 695343644, 534056246, 30139103, 998419430, 233963916, 408256648, 368361664, 146943775, 679491927, 78629167, 393494578, 130752009, 516661090, 829902129, 394428886, 594114454, 379200056, 227996907, 866619560, 27906234, 222949521, 968061653, 445357554, 705094656, 377553605, 177948902, 697148936, 156206524, 958107913, 416341105, 974689348, 342798747, 418462084, 453948740, 862345476, 894818500, 971480855, 417621650, 506634457, 726944297, 388877853, 810162300, 336214657, 493018432, 308344303, 16061014, 689059342, 462125030, 585951832, 711686869, 909325161, 285580765, 564180682, 159381871, 397019529, 125033427, 178588897, 143270112, 906366991, 337934824, 302704339, 56503692, 682998706, 232504277, 595875997, 228253611, 71060060, 882333542, 357020849, 411673236, 585237163, 871575538, 534862278, 453716660, 106127189, 923955529, 336429848, 295307992, 790730845, 389505660, 930702314, 836584897, 676593267, 465328217, 333436537, 269357935, 39406558, 290770561, 510526453, 469736187, 919767265, 245808562, 567398551, 476840645, 944035018, 626284867, 270196613, 834665413, 775684170, 695061807, 13229780, 399799742, 314608800, 975002722, 212359963, 537516905, 371332671, 50733022, 955211182, 321919922, 567289030, 795931381, 681171524, 110660639, 577085483, 689323073, 887177188, 392919460, 195347049, 75730065, 575308590, 763450446, 708991810, 10719628, 841486588, 920223454, 723076547, 780696049, 747206469, 235399312, 403455139, 975567058, 998634929, 285668112, 528508814, 189506557, 756663447, 474524705, 308567062, 726522021, 725020614, 262258687, 747496013, 313209184, 279765632, 870981776, 491522212, 965961267, 443138652, 247215150, 103039056, 291753265, 526969030, 284771233, 542025393, 715861943, 686531003, 229106415, 17306320, 775333142, 303173853, 408347462, 617151027, 658889792, 642987575, 99759956, 453639086, 208935770, 834317565, 251328452, 62088662, 214311744, 252693214, 796753593, 603158273, 795910626, 381866713, 875049915, 299855583, 26796427, 995261413, 977948826, 85347387, 50693364, 723314368, 169705513, 78518769, 338004922, 461357498, 525434776, 301919126, 213309618, 669393286, 860443166, 714973382, 303089605, 210978771, 661869884, 793447178, 753865983, 610363200, 296599351, 365509569, 944793031, 902485884, 208889832, 957564080, 561273570, 549266265, 787643738, 193130431, 699632743, 581522860, 841095037, 511305421, 188239334, 485458510, 829780300, 206038873, 94972523, 733620101, 931989605, 456947955, 22141720, 449206925, 189778031, 445131687, 494639334, 194733433, 617890442, 646842365, 912301828, 594173740, 117873108, 788251814, 910025252, 356230451, 105127475, 541846892, 277955727, 204421231, 666653071, 58086921, 945701463, 982302812, 300391042, 131182463, 118322914, 427747055, 201233722, 813626283, 160125414, 283682284, 655219220, 576413111, 46915687, 871708661, 239185973, 265808326, 191419749, 246805811, 913219225, 592862050, 447413946, 293599766, 702752882, 891428800, 722934609, 587872700, 886958603, 599203313, 663383933, 813062860, 105743090, 794669998, 517796660, 896201981, 191392234, 675817205, 311710795, 442360593, 193719911, 820254291, 203226041, 572094859, 288894377, 902784100, 884322249, 178325640, 54440734, 793723255, 845076001, 398349722, 512832904, 141390358, 305682791, 840087697, 830512874, 894191021, 201764948, 841049275, 679505429, 424893202, 981061035, 830628823, 838888126, 18331805, 842405636, 330998004, 469729597, 240777782, 184195169, 938499026, 592202073, 887556894, 787408350, 516696606, 321641263, 996341223, 417034105, 673173549, 63561355, 225321493, 89143979, 757598142, 411181452, 142904570, 260155785, 512411045, 49799876, 1476666, 994866743, 148629251, 328341302, 222308253, 263875691, 182464477, 908466702, 636232771, 775862025, 274823873, 806845316, 969383372, 261457522, 156449515, 757475300, 184319976, 944841740, 137305048, 610271382, 46681366, 170802223, 111678616, 370272733, 8368336, 950163906, 547420321, 636624270, 126758613, 892760073, 635170383, 530963466, 199814110, 379281415, 78765178, 324001909, 505043921, 93425771, 510834232, 143800369, 987117703, 431046710, 850913935, 174378698, 323625660, 399319005, 826410753, 154545983, 225052182, 510148024, 404186794, 186700667, 152542711, 23699799, 709910676, 863669688, 462735961, 614203064, 713291034, 830499772, 339149652, 284875556, 308491292, 466545837, 427536830, 798395949, 531302424, 283654336, 121242552, 41643204, 381164628, 204449576, 575821928, 192301967, 608711724, 934836920, 868121146, 129875372, 577522712, 622646982, 58813729, 296635190, 81035425, 254151878, 993587324, 815270728, 77271901, 380157581, 971522559, 484845202, 922284634, 430399751, 798038903, 972003681, 177194969, 643146642, 187059252, 114589680, 518614219, 369259915, 334631095, 531965641, 566659870, 631608090, 743006179, 600544954, 659718275, 769859011, 846880655, 943264530, 515796567, 803104440, 635810146, 159060670, 738678137, 669396473, 197650020, 796899563, 232759414, 488057121, 375357953, 448580537, 752253228, 169513716, 463296522, 352140403, 947011520, 531872899, 959037290, 817345344, 698599503, 721632651, 114081525, 380636937, 65150967, 869082887, 320845218, 29229435, 604028497, 942531185, 975120933, 720989189, 635825996, 707061016, 185200321, 871777234, 563548610, 811952901, 902205133, 417496129, 603487083, 581055799, 189584018, 745850042, 945541349, 893340135, 54182444, 600742066, 333559225, 378958195, 669867962, 874924805, 280227448, 128028953, 986536245, 763394039, 110198855, 427734517, 953107770, 487948989, 550540502, 92862681, 867689131, 251559940, 293048614, 282026084, 360689892, 999286919, 268081865, 287227810, 940148688, 471316912, 181131666, 232666076, 188074824, 454813949, 970740601, 303568794, 467462736, 477031739, 669338548, 966128379, 722811079, 800735784, 6538219, 535275281, 402462427, 247591480, 613588854, 633484693, 201695730, 882920648, 507940102, 875495940, 371507512, 778395105, 836305085, 832167626, 278220477, 692752982, 672886908, 793103394, 202020296, 303006845, 695459619, 483170546, 698673619, 286559263, 893595737, 813777204, 185673457, 933172984, 831655135, 138735033, 448040911, 652666699, 204613170, 5492382, 842922450, 275303003, 544173006, 64418536, 823712873, 500448354, 357209295, 519593904, 375555631, 781686821, 383629858, 710261736, 231158140, 126593220, 568764558, 202364344, 401961048, 905025154, 345591710, 864611387, 130667493, 377945377, 576073452, 502479732, 377757179, 696281921, 817982671, 214163622, 402107446, 761178971, 65994307, 391295278, 666931448, 739356003, 876544992, 511660415, 208828199, 501141668, 343099021, 457946110, 536436818, 685991290, 279625077, 193024461, 227668906, 437952891, 195563297, 354340281, 418472814, 297949839, 709322637, 368239410, 425072301, 747063408, 183438024, 319528034, 305071488, 685874390, 708287361, 333521756, 445411404, 887886868, 757471672, 208439709, 932148833, 990471272, 892360416, 859201856, 69096872, 586640706, 813823847, 556803089, 784218790, 79487678, 352852440, 968842245, 374117984, 285778428, 932715932, 857821119, 845106740, 317941791, 554804816, 374108892, 741475428, 936875819, 61308171, 688188261, 717026960, 330656478, 443454213, 179896350, 522970004, 143124704, 951157748, 500210502, 785977592, 391969017, 340419897, 488926711, 28724308, 558085901, 704932967, 471959853, 56028894, 378345877, 788281975, 811415298, 345291851, 689877618, 560897514, 735353325, 409139438, 370495269, 302898187, 232204811, 437774930, 396148470, 942244096, 10647697, 25565753, 110478724, 86894995, 896214138, 364667500, 400200358, 334172208, 275169438, 509281400, 372962949, 948180805, 834206081, 675390071, 842728472, 518615266, 129823567, 378163107, 704119106, 635934147, 303923299, 892038575, 585825437, 691281593, 639961528, 376179961, 702997435, 835113437, 781887710, 641584406, 632698971, 970676432, 659265827, 549084803, 575666392, 797225740, 12932379, 385842655, 267274603, 880883789, 230338137, 513227115, 324570632, 22218947, 421791298, 974677136, 681905162, 785149434, 551442438, 874460584, 264337014, 723144518, 146299440, 808965511, 754268964, 448555105, 701737974, 166410046, 528856151, 663401605, 103935013, 816478583, 161000152, 222553981, 320993873, 220806676, 453660539, 411447279, 111705795, 204233889, 929810853, 586796753, 352550337, 713594001, 225298581, 10139490, 400498627, 964247425, 425953274, 350077507, 872039229, 597153840, 711354406, 615753269, 671822292, 619482799, 247695605, 954579656, 580806371, 336050476, 674162247, 227988867, 694189603, 969692937, 65699568, 2252853, 495787372, 709000758, 321929569, 562248196, 138031867, 766357780, 299107657, 254513001, 753560646, 387810166, 58647563, 454403831, 583454184, 993957826, 484351279, 729012276, 824480785, 958859210, 296058351, 800997881, 181514233, 422449096, 764720857, 217575730, 956153070, 28881340, 488547202, 124643294, 692153839, 566659565, 306145080, 153887057, 687307998, 164594580, 477999568, 718325532, 625710386, 966928188, 970847329, 762307727, 154611275, 587221436, 949724266, 8034642, 976435744, 736207794, 559103851, 546569843, 512957462, 35125294, 683331008, 17054060, 253160086, 344412146, 162972071, 459310226, 649008887, 109671513, 365167071, 744452107, 635996250, 70698565, 245870117, 425237399, 166235817, 334753954, 650399335, 113402260, 330999614, 409994455, 60161567, 788407317, 300551843, 578253985, 297147924, 33916060, 862186143, 286160439, 362603943, 725249791, 160841872, 147207102, 795761685, 342826869, 221102975, 774477722, 738484014, 290102242, 852279608, 619709733, 781661300, 891450446, 100538881, 362554822, 707244154, 392108875, 779511426, 533960079, 911735270, 829472093, 434745693, 282441396, 803863267, 914367555, 916918019, 810891723, 697523243, 589774057, 463010228, 662701636, 618880387, 807690646, 284327105, 525676001, 228130393, 417768587, 413963185, 69745103, 9059251, 906708345, 965048229, 323571389, 98520415, 449088234, 82754549, 791308737, 518523435, 849599974, 670938269, 396818745, 186942677, 119848070, 309464255, 941796416, 334888484, 683442591, 815876166, 445722969, 84114950, 250346948, 613319340, 668298709, 432076958, 570116792, 25832953, 132508509, 957726849, 114179669, 124834221, 323348368, 745663429, 106048038, 948781195, 721580145, 34475102, 274065723, 468036484, 143572659, 528469374, 737262227, 77265938, 381585550, 330425918, 348099133, 507673072, 973273373, 217828574, 507938442, 232078079, 537604600, 877839647, 131963796, 84042627, 98155903, 20311724, 310740088, 520008671, 745446088, 147611840, 89691120, 273029009, 57190843, 665067058, 222778708, 41475109, 694574024, 73031119, 160364593, 585912843, 980504727, 829703109, 237193717, 176006782, 238457798, 322125968, 703119909, 923650724, 343607399, 281995439, 143551721, 301404160, 262202505, 15384442, 559127777, 515148167, 165714895, 541567525, 544839256, 800815474, 109559114, 981516955, 961329928, 626823592, 963282452, 102571986, 11314559, 110111081, 405311188, 944276432, 602571993, 23910740, 375404658, 550708696, 693093481, 500011428, 887210255, 710224558, 251281437, 528965060, 175082312, 606132787, 164565941, 847761205, 366002822, 490735822, 857324918, 905990016, 477652478, 898554901, 245539280, 30848145, 514302620, 561164019, 468295002, 988303116, 151073026, 670437955, 259571115, 329028545, 544060074, 547391933, 630992424, 531946311, 255161267, 180644911, 370909004, 29341887, 573803485, 519010539, 295540832, 280646936, 149821373, 914046176, 260356395, 699390923, 908612199, 533480458, 801416213, 534920723, 617760277, 994137969, 611916252, 837743202, 278608785, 965301743, 48904701, 338077251, 770049560, 543068055, 49669207, 368302486, 397721554, 548434632, 82338129, 600214852, 991835163, 135182554, 101192785, 14014828, 624483249, 310765441, 474337863, 978883766, 253639946, 864335034, 235069084, 368636636, 716798195, 39156798, 320793416, 611251447, 316032650, 7130102, 300856115, 46279372, 883034483, 594781542, 935440520, 423686957, 905339038, 886657553, 684633069, 118880604, 595284124, 910040201, 423307681, 526685487, 866888987, 57074295, 530580289, 611026943, 258495475, 580423720, 291288393, 588628242, 909317452, 995215212, 395902669, 563569951, 26761099, 280659543, 931522481, 901962795, 955005642, 815723720, 143641825, 678577890, 359251907, 302704454, 391561699, 60681641, 693082780, 586287515, 220726170, 899304232, 289553322, 663983918, 27685868, 653419298, 782582101, 744272766, 19635059, 377698221, 667046423, 207530994, 256406816, 584845772, 426721923, 870423527, 731269565, 142385478, 65779618, 632432141, 126628645, 733430348, 421080328, 162777713, 224423935, 854118413, 851006775, 580775646, 669734884, 280980953, 409783892, 638422313, 441786740, 784039573, 58069166, 125676850, 580457137, 645114191, 795467221, 706852691, 100786592, 341259730, 43268139, 911492125, 130792895, 365593254, 107622249, 988603461, 970872759, 164452233, 887862579, 250239331, 948923265, 266427561, 874894003, 510444782, 358493179, 253436816, 713755474, 823490420, 546650972, 721319761, 433923983, 897577249, 410786046, 825512080, 844459763, 645374554, 755087901, 243172940, 770288934, 98165890, 374072082, 194541093, 347940045, 586952710, 419038556, 643003824, 193800277, 72466930, 508552018, 603220286, 157535158, 552293035, 172169610, 691861294, 905921022, 452886303, 905810889, 621421988, 702643356, 810703539, 11133350, 577342151, 556176130, 980341297, 386172827, 111246281, 262392072, 868403856, 782482396, 3467838, 920572010, 153361944, 304645340, 620641745, 609398557, 231006511, 904045233, 963838675, 197657485, 684115649, 184811774, 296241028, 880501664, 56017053, 178859235, 270370935, 688613243, 227135026, 153644466, 417885829, 746950843, 223498963, 32114526, 329267263, 414031028, 346332871, 266862266, 170220008, 264519711, 636873935, 11515019, 108727573, 252802724, 546550234, 463674314, 172665547, 168190286, 862225356, 195668778, 205187942, 877030858, 884769379, 209553628, 99565018, 90648192, 914297919, 72528992, 515907805, 829025189, 708635890, 214902408, 425019109, 954467259, 673371408, 548447487, 944011904, 282006531, 566780799, 450814771, 976818080, 913010549, 856084411, 629375842, 31682771, 475815743, 930296473, 687960129, 939434943, 620140297, 875309581, 982120626, 255543126, 988282284, 942543795, 267024169, 855292577, 710484688, 244211173, 914168318, 870354168, 572805983, 769091269, 936289798, 867755346, 242963298, 48015979, 314032374, 288712527, 8772496, 715575711, 646945697, 30337776, 775495373, 592609705, 775698866, 376549734, 234003878, 893499151, 372322537, 918870272, 316026637, 872631706, 107099967, 913431542, 464802120, 810236239, 671018349, 683081682, 310692753, 913751810, 82225631, 643156396, 471665254, 663491845, 801683807, 932536522, 463542768, 396591441, 809153293, 20834393, 981260314, 70529453, 194576461, 957892011, 584885485, 949666977, 905318178, 543514681, 650897979, 323448479, 808239907, 848570589, 238288063, 892757728, 973034666, 604996624, 97120201, 583514810, 754274399, 828955604, 864783221, 129123079, 590726133, 130888609, 246388007, 650934054, 60062697, 501338146, 515140471, 999015735, 256367050, 274804401, 83201365, 898147489, 66030660, 74284137, 738562070, 789553750, 674455462, 831251208, 891282104, 79025032, 378306933, 213540441, 740533254, 911765594, 492368782, 929111631, 510499613, 143527902, 570464019, 717212691, 573046495, 98850349, 987492413, 992445564, 342614270, 183126416, 222607152, 754811096, 480955889, 697471808, 912246212, 11358519, 511830582, 906240906, 653997785, 969498193, 708784275, 1651451, 858556920, 238833359, 17259473, 514346741, 506251626, 2188553, 784470056, 217146060, 960204138, 707383855, 185008040, 248967091, 603177148, 961277005, 905390584, 331413289, 953946404, 634977100, 165863932, 718554492, 639118345, 722426255, 726537626, 768650038, 889341836, 877401726, 741061050, 363143289, 845604572, 371774784, 312511153, 441309941, 931195920, 121433030, 801965913, 405314733, 443130317, 34261251, 223852945, 342408105, 257931072, 433094524, 647982677, 476440951, 55057208, 430976525, 882451366, 501340811, 822104872, 482675131, 883027000, 439511755, 690209557, 107127964, 724545290, 897038130, 358176403, 767526676, 71747807, 784770199, 194243762, 788388144, 353696787, 222080016, 378448368, 5800506, 480395884, 124326046, 566945637, 105744091, 651543864, 300464773, 264328543, 875362243, 325858136, 662884394, 543469348, 486330112, 201790397, 714701905, 17471795, 794207728, 323040827, 496210341, 117029536, 757318886, 66023671, 994320826, 390084569, 7609049, 989047178, 929454549, 632175330, 464054107, 154766676, 997499519, 161555070, 210260232, 223206508, 506745820, 537082467, 86431633, 163532141, 550188887, 389529194, 418073444, 630639760, 968549206, 164894105, 170033973, 585163740, 752475975, 789594420, 287979157, 618525499, 674932629, 102066681, 870649733, 782538308, 181637234, 179576016, 210623619, 32649935, 905909399, 448946110, 475516184, 566229156, 129047283, 865955249, 928124079, 690833298, 424898245, 608124378, 290484402, 182607414, 811018738, 963292778, 461740964, 7859230, 146411337, 509321006, 352905519, 675014422, 301328564, 313777976, 307395658, 907005914, 170194239, 638766391, 226463383, 321971013, 201187180, 347210344, 37527796, 764485871, 707663127, 45401516, 867441868, 64400055, 71530246, 992402597, 446152613, 630355260, 549925579, 154484106, 99500796, 450977719, 403552810, 79047693, 560954874, 205857379, 915657874, 119180669, 993561038, 249742926, 992339459, 846621219, 633973561, 734062714, 548436015, 523816558, 992554138, 302131497, 411142900, 545958423, 979659030, 726054181, 610896919, 673441834, 291364559, 195131810, 253350418, 521248625, 597792024, 123152044, 631474936, 891891481, 945434758, 300129615, 223450977, 983093477, 570077055, 72564173, 295593051, 144280366, 460578104, 137977698, 726482693, 619092339, 343304619, 937869951, 395018238, 242895827, 565703067, 323975133, 731964669, 923642172, 667479858, 970650812, 130042204, 924262522, 786690576, 120440360, 193577670, 285263553, 4110201, 112074810, 47469185, 148231887, 110028303, 983578908, 57161853, 192310071, 67030193, 916291040, 791888272, 686739157, 464083780, 431751653, 858121232, 833430606, 368010856, 432034387, 486928273, 9979131, 913370176, 326324566, 579577877, 545519390, 255038888, 74827808, 161829602, 9314951, 820240265, 362567122, 706277025, 937758995, 190923454, 189937641, 79016800, 968720596, 328961880, 774661832, 262620680, 896929039, 289382886, 29688040, 569172341, 785242981, 606307739, 542468607, 791221312, 807291726, 684787619, 998746266, 656983062, 67353081, 629120156, 864036779, 180212650, 520683136, 356887515, 128357978, 280099242, 988755379, 209258393, 744789886, 660257090, 138293490, 168675196, 284800975, 658341401, 96135158, 752175902, 306751521, 58915572, 997143060, 217076801, 2448239, 527266123, 112640114, 323298518, 471813938, 684238656, 298540332, 982009572, 289216980, 928353871, 258408222, 56266870, 202595244, 649227559, 431120072, 679014346, 807752559, 29346483, 77036141, 306830909, 385040443, 920357732, 566291188, 724345393, 167313070, 611467938, 341473405, 468094232, 624830102, 388534505, 599298976, 651276536, 505472148, 460880069, 199204319, 633328214, 75828092, 881074136, 265864206, 157865931, 679949084, 359335862, 562450371, 728788467, 831273476, 584131340, 629221935, 997873195, 612344691, 979379215, 246499147, 233528746, 236312359, 181181983, 870302610, 671574941, 570423193, 87665262, 795002378, 299318633, 724839544, 383776712, 129183868, 352486786, 46122183, 507485985, 516756764, 7000548, 721729303, 637777772, 198274343, 448303037, 697623750, 617520877, 956114185, 274821449, 638170887, 513329047, 800154160, 321489129, 547366342, 66094603, 603171134, 118976572, 501543320, 519239336, 519949476, 389759501, 680565506, 71491258, 515913005, 939744682, 678363667, 85765388, 872603263, 31137346, 635438863, 763708663, 550609368, 906456289, 839592500, 380843569, 983730127, 455972118, 151699957, 926195631, 108246383, 259797120, 643359549, 790562064, 271961235, 286329088, 747495754, 962290167, 380611818, 744986190, 364431841, 293535259, 107988351, 786314364, 624660049, 314933286, 451229666, 543249365, 989891680, 87749619, 195637914, 342524124, 556908375, 159502901, 764868190, 675217792, 372683282, 82545083, 452198659, 176637684, 447083821, 740133772, 54648884, 822680364, 580592465, 95353830, 112705613, 609523732, 982907184, 646503295, 712687191, 99634123, 309250597, 270422358, 179783274, 134779492, 845346053, 520972613, 419184307, 734390729, 658716005, 455183997, 460891306, 446785684, 123769045, 913561815, 103667072, 621858071, 676389082, 434796738, 139835346, 436839893, 948100919, 308322100, 307508217, 12089416, 220213884, 578842381, 991226707, 54267310, 594467748, 444606975, 376215344, 151254182, 643461801, 971841674, 101941488, 892622833, 377990290, 914369003, 431535676, 996506628, 312058785, 72040559, 909693826, 514117621, 713350649, 498275398, 832697034, 530631655, 800437465, 778690036, 594974040, 889990747, 285292390, 590749338, 119253369, 613280936, 686408118, 540132267, 872670446, 177331931, 901620662, 955814356, 410020975, 176518866, 135758423, 214732260, 670228121, 700256742, 329866914, 207106187, 423624747, 313418751, 154182215, 500482590, 771542710, 919125971, 422635417, 196709384, 285995452, 853481320, 401796190, 51134210, 518625425, 148026359, 523389801, 976293584, 740871752, 694349536, 624325494, 616566279, 837831006, 623098467, 851204649, 768618529, 178185240, 615836825, 873636069, 253375452, 72237237, 396388042, 670106545, 317432856, 655955177, 69250414, 832271956, 302325823, 903116080, 273987363, 895895505, 715034731, 281436620, 785337144, 787673271, 58656481, 835933541, 607683662, 587809516, 477688055, 488679437, 348251650, 981417290, 353833420, 163886192, 478924054, 427516455, 921364245, 387092158, 205306404, 658692135, 944357178, 518112250, 390198569, 880154961, 571564362, 950167718, 266212462, 746360397, 668373321, 422571536, 83905542, 594698478, 630376332, 579041199, 471744519, 959995220, 692195421, 635738904, 650086145, 322160655, 497147022, 986532275, 241795070, 613893198, 827441333, 531461479, 374941697, 798124926, 259386377, 153429168, 10054967, 92710600, 297419678, 189027474, 107227119, 847316279, 661576281, 411383787, 462362931, 500860338, 531886033, 705333395, 428784554, 821464242, 918977553, 239745022, 170523464, 796457479, 342187179, 341832502, 881349889, 944946524, 803669796, 24932496, 779266289, 907809710, 318214068, 552609484, 632049945, 158123505, 48556835, 863713679, 677325563, 134902862, 768168940, 730850613, 411743549, 900187034, 925212202, 898853195, 223778832, 543058841, 242000589, 612684545, 517253273, 204429273, 581796069, 160832072, 239426176, 256150276, 15262852, 937369429, 205756336, 280143624, 844798499, 497131058, 385029232, 671990228, 621169070, 500970852, 909193838, 577578510, 546392818, 79609537, 976530226, 156714390, 287036682, 755810543, 948017972, 155329425, 578274653, 503079257, 598465749, 390086486, 120035795, 605005039, 668686690, 600173688, 821840132, 776094284, 276180434, 465619111, 35126223, 208601329, 618012443, 295149803, 646845649, 930280544, 421182331, 46795126, 869832119, 706342502, 583450787, 115894908, 380145207, 570229621, 443901726, 791089220, 970809137, 621788254, 737158990, 112243429, 351504035, 932390003, 658560783, 822060186, 538006496, 259789626, 44605240, 603020580, 233199772, 369059649, 141541140, 5851112, 624932162, 26503526, 915353171, 395811366, 964362226, 762594398, 497752223, 453892137, 25111977, 571215081, 944886052, 413836522, 879526665, 940322681, 813265247, 374045376, 897850211, 732249503, 769240522, 749592175, 532633692, 753914219, 209892310, 91260031, 655684428, 693140848, 651393476, 1566209, 793624413, 375586535, 890588624, 814740341, 648387963, 615265215, 726158582, 705880264, 948504501, 618468393, 901981709, 266308187, 456364492, 79979372, 221506126, 522772635, 345359365, 571808812, 137778919, 933032842, 451369205, 567148022, 132429850, 305200351, 45119773, 789262650, 811887706, 59988970, 139538378, 518305929, 371909120, 358560701, 368624982, 729607691, 554334200, 65794198, 361089994, 771669160, 330994527, 871957916, 264647721, 724965853, 852248656, 358223517, 944170157, 825990779, 994429328, 420343764, 685105148, 830875786, 336138763, 479204731, 837190993, 153665899, 311452782, 152626736, 919786348, 779018510, 628825334, 986571788, 130166333, 712596195, 747325708, 490522724, 47928992, 623624465, 598211896, 528686234, 231500958, 923120545, 784050979, 830234585, 822144694, 293818966, 865639204, 183254222, 499555269, 790030041, 454615151, 224902305, 498222488, 459156249, 845377085, 535326588, 254234362, 458546732, 707615011, 349950399, 114393151, 528840627, 450330609, 586083518, 586401832, 857206728, 645667725, 606261191, 138229959, 977043812, 560195089, 289741584, 522622044, 569641675, 508919607, 140247980, 465979808, 873508970, 61275921, 192658072, 467740007, 122457980, 266775964, 117983595, 481498709, 714164833, 438822695, 682182001, 764713071, 948842975, 492352963, 748794115, 477037755, 770158787, 431684757, 399056643, 175250387, 653977438, 982251198, 791589256, 597077020, 515466827, 660727360, 744265123, 699762977, 468273214, 717920427, 977811637, 17295544, 485412584, 955653541, 946288627, 638371201, 807382042, 507366852, 712687619, 655921843, 322648008, 834997890, 213187876, 821916460, 881863521, 807020525, 907598365, 337455788, 244875674, 772592640, 600394377, 136355183, 746818967, 450692105, 329243090, 603584826, 655176979, 923907009, 779750167, 233348619, 550077087, 888742577, 710570413, 971871168, 552825474, 811433605, 465182535, 430711008, 269897340, 836298026, 245339883, 44603836, 391534620, 715021260, 264774255, 882207133, 314768854, 22791152, 761870346, 744100789, 220324234, 558226479, 909001131, 641011842, 760646560, 595023385, 187315107, 495406312, 363218327, 570798546, 427887821, 607667856, 594461663, 520707277, 807702400, 334608448, 225124083, 591805076, 904497165, 362256570, 656694368, 549144289, 808446998, 579740458, 53062711, 624038512, 547645870, 775629739, 779293590, 370165279, 785685877, 305892908, 195899848, 207496376, 928611629, 290294943, 507919815, 446687017, 732526913, 101492293, 856296892, 432867262, 576186436, 402446762, 369456373, 599649023, 486939074, 425943566, 332647745, 355500314, 757181475, 443834820, 489908245, 221431986, 798507379, 542523852, 392530986, 345168491, 404116557, 855957849, 216520279, 166768853, 713251959, 968367823, 334970417, 181138906, 143364883, 556797898, 261774212, 285900954, 923177495, 652467067, 843522407, 673338531, 954812393, 144515076, 433168616, 100457434, 197777844, 272038290, 840095777, 320682734, 525003494, 898496675, 270007159, 274388867, 461952967, 361650675, 255532177, 134256907, 554429003, 229809589, 880060062, 249872599, 379827621, 548854579, 438419757, 221227228, 394136675, 45725447, 561403176, 958391041, 393232485, 263068688, 265438366, 424599304, 503391028, 635144936, 586177659, 997659941, 650958807, 497990351, 81434297, 925412142, 545062321, 907924849, 154430608, 780745714, 900796565, 519963662, 997685621, 750988545, 42752783, 158351606, 491278582, 811862031, 231660106, 525501159, 633106361, 966317411, 766855088, 703418146, 817797809, 450042273, 932832885, 180641814, 967396929, 190842170, 648047583, 935754989, 336839009, 390924247, 812349437, 394502469, 4590354, 810932907, 299162387, 833092198, 639278702, 822368606, 488403292, 815117844, 454860739, 280604167, 889416813, 781021574, 366096585, 144968181, 127690879, 247742159, 367541851, 780146041, 358295533, 975573347, 516024447, 738184110, 569745923, 840048428, 788601269, 608645739, 786460501, 488022081, 454273689, 492767455, 275381778, 105532937, 874272580, 286153393, 813885079, 784816436, 263690324, 41871146, 252096507, 184848591, 965632287, 252707786, 508358707, 422991248, 373940210, 996029294, 554793251, 340414391, 538487413, 959854820, 133565312, 228041104, 257374956, 16611568, 758518261, 107570607, 867802392, 484042372, 786445501, 766224458, 848739548, 738236982, 824069126, 254494117, 702139252, 395505084, 714422446, 426312492, 312590708, 646254434, 598576926, 489718779, 775084909, 905021385, 28072072, 950517870, 169600266, 997752584, 920390699, 77686045, 651301282, 421435641, 236030525, 896276504, 71431628, 678964018, 484468426, 383066993, 856156209, 611387296, 42864166, 25060204, 85825254, 144402381, 593481901, 935370886, 684463218, 91279349, 605761403, 336422521, 670376253, 377678962, 193791049, 148614979, 417488555, 983251342, 453578822, 730156029, 470133701, 648939336, 479147392, 184133228, 970292507, 669815791, 221470917, 762312104, 828607037, 657412451, 365116514, 353725436, 604147431, 128366214, 165993139, 439746679, 804147206, 834059720, 128419088, 201144969, 424448588, 491966688, 868701518, 915175243, 350671214, 349819095, 473236039, 749619912, 476193073, 755962005, 837969655, 982355965, 812889892, 342763524, 88253398, 27260136, 93131742, 866658826, 427025948, 139565966, 345495661, 397928768, 293399866, 378266924, 528729131, 562356627, 615920294, 231960720, 314550797, 741983866, 827745351, 437485977, 463465279, 903844759, 477581973, 187739015, 631291254, 42508503, 550991362, 47451744, 750720221, 767783585, 563045360, 878826552, 245797050, 92834700, 552250981, 440548081, 772266562, 3255797, 199146188, 876518239, 185820781, 758852515, 924687034, 420843941, 50454684, 745647987, 699785760, 324579243, 195989932, 298093235, 168344581, 103704176, 772343011, 355193995, 604294703, 230076914, 235800982, 965478310, 781189498, 750493550, 761080425, 131097300, 220717253, 668489519, 411336001, 226669116, 864508661, 227851847, 762290279, 495333557, 638229174, 919351296, 670196457, 33657753, 432650198, 646093454, 537383092, 980022312, 598753929, 734787605, 917155859, 219021243, 980022055, 269067064, 776583118, 149094130, 514138983, 850426542, 307520978, 482757247, 268392174, 607338163, 152555836, 507284326, 285929982, 888131650, 510374479, 674431977, 369987320, 451450027, 763924936, 538138601, 690805388, 849594916, 633589027, 937038176, 491455092, 951357550, 238448445, 540333417, 432015532, 69670641, 803556959, 38362808, 603438852, 788071033, 176860302, 187776501, 787350628, 857400488, 694771492, 788923335, 72943742, 348171704, 6937219, 311275897, 725969901, 864749724, 264886453, 270363310, 934876034, 235148726, 386831867, 483268833, 157130996, 142984839, 457063065, 139184428, 302109889, 367171922, 837761235, 549274047, 224418777, 870267632, 208193490, 488285169, 852447224, 507301052, 45225153, 46224249, 924256500, 994390340, 760161781, 76440546, 153425317, 520081158, 317710456, 919349362, 339854178, 905448642, 459956182, 8973104, 100192450, 620445893, 803087594, 754654562, 360026240, 824563880, 131603969, 540891273, 735193709, 994343257, 227720404, 455788400, 393233979, 23111734, 713284323, 478560671, 8298919, 669166660, 911684983, 849874186, 862180172, 311496400, 817157046, 920424691, 540167601, 198968000, 117019164, 518721132, 366496262, 820836798, 631968815, 342936842, 152775910, 680670466, 972402561, 992846393, 485951075, 194100817, 699579258, 730283090, 302263875, 497279864, 819643733, 645523528, 357054383, 332616724, 709937519, 114910197, 830346743, 863100637, 330511121, 451222411, 796152112, 296632974, 431312315, 802269911, 384048380, 852927576, 961942307, 833151806, 225410087, 86895951, 764776818, 34010383, 219198233, 166920800, 372269005, 833376338, 623873901, 854709870, 371199030, 490419406, 436984047, 435252748, 371782348, 728644992, 719645325, 759496656, 547266030, 242712487, 473725186, 166582119, 306558253, 351736703, 482972289, 745605422, 763649274, 848291010, 134521238, 822918813, 70559577, 169118030, 633838309, 287432670, 801147883, 891175225, 509084210, 73769140, 550755342, 806145346, 658957964, 299641265, 62025854, 564456547, 968813879, 432804960, 308698793, 373925099, 320614906, 500718496, 136853297, 738459928, 542130425, 728820527, 444764726, 948100284, 424857548, 832004192, 350652329, 495702710, 709518584, 232724247, 902059401, 521078473, 421778039, 368752854, 859413162, 305228196, 569612959, 119478576, 440939924, 336556669, 261837223, 454458371, 520640162, 439056500, 112851905, 998294024, 78011366, 453448739, 302871366, 339704222, 108838781, 103878981, 64776946, 148823679, 385969505, 520961502, 182901508, 468065929, 351016973, 314484154, 154941739, 455109765, 760701208, 719822996, 816587809, 43960368, 244146286, 625605355, 101149226, 124858314, 82047885, 26907490, 528419479, 18201173, 430420596, 956358821, 389090998, 789721765, 680171442, 984264344, 209885149, 640332817, 760804843, 584776255, 180409136, 138423134, 325709960, 879311377, 47679525, 894576264, 413399275, 959832635, 863640295, 13820699, 300580016, 659025744, 494867159, 933143916, 822920348, 178813374, 759299732, 789471099, 820190118, 496599515, 528007880, 785784734, 8914162, 43878697, 649902576, 917140509, 461088305, 439717817, 810124900, 116815509, 372137600, 834308431, 612644741, 399525031, 599777196, 129949141, 952217753, 171808098, 158692196, 201484294, 856515821, 898348168, 677072565, 518213247, 593385160, 48129692, 587503115, 108953611, 95818029, 390480872, 381008174, 843611590, 787741708, 146334505, 984488266, 86158400, 700151169, 333340323, 396976975, 308747539, 732319739, 111398730, 113517701, 96868199, 192794002, 882186080, 772600199, 138860098, 833178375, 991318904, 679272344, 645755335, 315277129, 470874546, 340903216, 665276379, 541453974, 936499501, 68492445, 159830857, 555515333, 90352805, 942468123, 649287938, 146679523, 168552478, 549284820, 40581880, 315799543, 636176607, 785469953, 248459588, 991426005, 45281277, 364817769, 782737803, 417670028, 200183740, 960650569, 425180911, 902347648, 918643232, 98165938, 665365073, 830330706, 779459856, 620234398, 621265505, 350332919, 360514942, 393320082, 178205209, 363756069, 681800704, 860836831, 412464790, 907254805, 683436192, 386708006, 81966382, 831895588, 438322346, 771335941, 851195299, 262903444, 362016520, 577700910, 524529851, 395853554, 29581453, 514235576, 916323139, 166069873, 552278366, 104787462, 162558930, 859281432, 558312887, 273555689, 926454675, 35523670, 503009445, 384405345, 313391919, 300935107, 775803617, 199983144, 677375829, 255235157, 437308268, 38992385, 691498147, 393760961, 459290330, 570045263, 512280920, 173091726, 915870991, 107987562, 360034250, 511964762, 520548405, 358290560, 507755374, 787378854, 626460760, 344984838, 323262078, 147694093, 415185826, 955567800, 534524188, 298180166, 619674268, 542017515, 498565332, 912458161, 427589188, 218463444, 772691156, 909025008, 250866499, 980261899, 726950920, 957754135, 998664042, 24038709, 177262083, 904723467, 686634388, 710786294, 945460309, 400081307, 142203517, 120528766, 264439996, 715952108, 236130930, 81412663, 360711334, 616911473, 662901255, 674504723, 173898834, 290178335, 199708283, 66948803, 219407456, 799514441, 790629518, 852009907, 267446458, 201735813, 246692568, 88578940, 521331956, 333072496, 808671993, 775564396, 157066897, 909177288, 126066613, 630024195, 119830083, 143172716, 224276862, 374845680, 993832865, 196328254, 778680365, 100146975, 634478234, 470117916, 923060320, 875662124, 329693426, 396949326, 734130223, 875530075, 270905123, 507985957, 747726108, 258393733, 960250955, 650320393, 900663748, 646155245, 447349909, 338573777, 365496379, 499911870, 655192304, 946619342, 860709321, 888012973, 596901158, 161487796, 155253723, 379866869, 361850807, 470434032, 198435307, 390451624, 742197696, 404274257, 787795677, 217164200, 987882578, 558085540, 813496129, 960070920, 79661137, 992813029, 69551410, 821447401, 255386188, 830832473, 140200704, 933279552, 989816054, 794192466, 929962900, 303037916, 825539962, 388030892, 968769404, 293369937, 50697572, 260294443, 363093927, 79610849, 395494978, 620029582, 10447421, 840208677, 61534920, 688940886, 597338548, 962242671, 829058615, 958565296, 170622305, 237673359, 719011736, 205901300, 458203576, 709980094, 452238074, 982797047, 979381043, 255585552, 941869452, 404232752, 658131405, 72855095, 101559157, 28500704, 491876639, 267160413, 140384823, 550593393, 256089395, 868551562, 681505822, 483686217, 98199660, 677816132, 32656871, 773200316, 558203967, 706463633, 607418347, 767817049, 738161395, 81670994, 885981387, 321859977, 735150361, 811633825, 752686176, 425341719, 335446305, 362976768, 14219295, 242572822, 829850439, 986768223, 739801907, 786741123, 53905209, 492954185, 899575040, 354738683, 400346132, 773910718, 787349171, 987756595, 703241585, 466753437, 810102731, 313891511, 127768627, 963055664, 167532012, 139380704, 210757637, 80275374, 725562526, 158612911, 768673548, 399239777, 296046228, 18733021, 259443899, 951401692, 304578130, 361593173, 968880228, 499478253, 905944420, 641956050, 634436054, 872858913, 756246700, 636891894, 143677994, 507846322, 65983489, 866552315, 911721324, 199578617, 138010139, 895872459, 558060259, 836837413, 382085674, 86137130, 48469849, 175712288, 939144087, 844615659, 527693142, 631501139, 264272292, 103792046, 135559902, 463648554, 1754102, 884054363, 593355846, 864901717, 715092347, 337104853, 231826461, 293325247, 8241697, 717840439, 742059191, 63575367, 869761246, 226848070, 832080329, 377080516, 5642107, 170699949, 650518782, 454357150, 200931146, 213628795, 455060744, 629510578, 510463964, 64326392, 572478373, 526014792, 318866774, 834954897, 582861853, 137587638, 220143913, 514485305, 546627850, 315178293, 779178878, 970060564, 834426878, 170969055, 265144765, 49469628, 621147583, 121717237, 164032844, 716776424, 847118718, 286106460, 476259318, 166963335, 845987665, 905718101, 505234515, 436801819, 991078762, 829358308, 388702699, 358874564, 84569656, 119198226, 751879906, 59425510, 53755153, 96483122, 128874317, 785923040, 197760964, 961812638, 754247836, 423564667, 808920603, 552389783, 171942634, 249773904, 473893618, 566004619, 942065045, 345329399, 289859020, 792461122, 100924548, 396539988, 243521503, 291604159, 475206596, 620423071, 780660364, 699372649, 490130952, 191872937, 893361484, 307439183, 483700259, 433380111, 39630991, 327046384, 134668244, 777618401, 127853473, 731602649, 147770991, 880346335, 867055264, 141750688, 94168423, 159398680, 592365508, 258046208, 758684531, 472764697, 230273351, 46609993, 275451259, 638261768, 986116432, 21861487, 438816689, 327259985, 133899256, 848039307, 186421485, 196239338, 751634526, 510698909, 37997141, 136870089, 87051574, 648901360, 151109939, 702782002, 507566740, 295509734, 354496162, 500413155, 762073381, 350949112, 638445805, 902416976, 61864546, 877818778, 612752543, 221352455, 181868205, 707856918, 571531280, 231020087, 306994965, 953914262, 807668272, 740783552, 358400930, 618031279, 964094800, 200899302, 700871962, 627552883, 349930543, 720427034, 324554368, 737330987, 297177904, 767931131, 601237654, 667706333, 510549261, 901250, 984603966, 266067613, 499232717, 459576860, 228652703, 467892087, 377486701, 446681606, 217619426, 961747451, 77623422, 284499960, 863849290, 148298889, 5766965, 53047027, 582129751, 132435067, 67862006, 732465581, 481681919, 154798153, 836489341, 422258299, 677772155, 144079050, 905270656, 153620695, 381513406, 174006804, 642431609, 645292212, 368577674, 512384516, 592924743, 824877668, 12187023, 76098338, 167973054, 4175822, 765694364, 401845221, 623748023, 743269201, 624096452, 802219001, 980797320, 687389908, 1641175, 257560397, 224005916, 5757118, 421050715, 933578683, 550951237, 383393590, 967667083, 691506177, 76074166, 67972827, 224293580, 601375087, 820123677, 354274896, 130420624, 630332979, 260228986, 92988385, 572937219, 542733311, 490100049, 787891310, 21709148, 344331186, 253880059, 329020633, 625679960, 41394059, 137005743, 199797943, 879681033, 926281704, 365239271, 665174094, 413204795, 308451438, 410401654, 855179034, 116432526, 677993097, 413656998, 669406381, 764908501, 762876935, 125969056, 820408234, 511156870, 120717446, 915674521, 950522694, 168364222, 718341641, 89009193, 254773655, 861948472, 842554878, 407836941, 695684950, 225954080, 990153269, 231036689, 907142842, 880675161, 600738779, 30737639, 64753456, 296121201, 387198333, 364384185, 963338121, 804121042, 465278358, 102120752, 196698776, 755377151, 872418735, 795181554, 29866952, 366687047, 560521084, 681577557, 171320119, 218696537, 299448767, 970597238, 961091948, 348579406, 73560350, 939944829, 962888709, 685500516, 240579040, 672799886, 985694464, 839818862, 512790724, 628299, 806149903, 209611415, 104450300, 161704848, 878899090, 567190449, 984321512, 599268611, 36879775, 508565300, 859736727, 926936074, 498014353, 622438077, 375335333, 53578623, 759585154, 755649259, 449173842, 340263663, 36452316, 535071986, 948580699, 27720542, 619965027, 103937113, 710342102, 346355046, 847927408, 312878937, 461969785, 186734596, 402022606, 144666165, 725038312, 261714105, 179967034, 349956713, 228079307, 767557268, 259058593, 556821401, 726966268, 114097716, 538198586, 539185104, 615348821, 717792358, 623589418, 870679150, 633168651, 877468075, 983908722, 941758621, 218799449, 925929385, 67538920, 578159526, 445969297, 108095976, 474125159, 288017579, 660452066, 35612659, 618080948, 916892000, 601316618, 757720727, 269949934, 68199084, 186037875, 895851576, 982013657, 367298973, 664255233, 651208853, 480910196, 428079022, 69357082, 508419878, 403856734, 275690710, 905575404, 700553418, 554856034, 668454989, 30356231, 86803912, 607840019, 815542939, 622216808, 247119823, 424743733, 681632127, 210910930, 721250991, 902313831, 327607253, 988704284, 404030313, 775774728, 312521766, 127537644, 22812932, 440905526, 772569430, 28732923, 119704297, 240063637, 794937227, 854101791, 853823464, 221833202, 37609028, 461274490, 519538841, 708223574, 318122068, 743248294, 185908539, 117759162, 479098346, 725733145, 960128788, 428545806, 627195637, 602246812, 469444844, 196195829, 876901340, 166910037, 652651280, 784760124, 200664105, 893510456, 46219243, 837640357, 864815689, 609788395, 89677844, 142763953, 898949995, 670882754, 682869166, 381539847, 864954356, 650173316, 423920660, 843663169, 831116037, 746969347, 957639114, 577377652, 152366954, 587236938, 819936316, 434949335, 462683938, 35327949, 456496230, 322261150, 989484498, 153591426, 816615737, 324624638, 490646020, 930775454, 320633695, 27672208, 994828255, 324699394, 264102322, 128762602, 951577337, 741879785, 107538821, 192079047, 136368, 44518687, 372120248, 879797815, 15584384, 933528438, 466698897, 214882618, 862540561, 908963326, 94673093, 273026276, 544194584, 748189688, 658497914, 161565874, 927269561, 622245138, 640379728, 967134458, 77812262, 698434408, 307845102, 242320976, 867276153, 128008212, 976440348, 649432958, 294675452, 95885645, 450962849, 1513466, 477524414, 579289190, 58601743, 296610706, 443191431, 102939821, 133760022, 16174890, 404299584, 65438711, 283963186, 14055203, 261443111, 830279042, 636555881, 522841483, 88213601, 897646669, 246858781, 794830555, 509285475, 876290521, 890146949, 336816781, 192072742, 680339100, 455947903, 970547620, 714586287, 221935623, 445788640, 418663288, 169655716, 86305772, 377732984, 443719075, 513386363, 100178245, 316690852, 812831228, 424395511, 713812552, 344597802, 418083371, 511948109, 345762631, 14045632, 442734880, 535471851, 24471037, 865148236, 126351841, 199289363, 314555202, 37738322, 105601064, 973169994, 816071539, 425725865, 219263197, 23554247, 801170499, 520672802, 766614977, 733565832, 137089103, 922897795, 102788601, 14760328, 37514022, 870270148, 949667867, 75663806, 603997080, 825010353, 372583433, 289857345, 929459501, 248591661, 539723384, 987892953, 152400915, 966164648, 75548906, 97729278, 357740532, 94945706, 603470307, 538252491, 583487202, 869329446, 775440966, 716036780, 904197169, 805506979, 411230000, 927249874, 274623055, 709669351, 864970397, 80025650, 310512220, 691041334, 636028807, 452346486, 378966118, 864501115, 585600286, 866911327, 710195334, 290406890, 149718084, 252629020, 486165459, 978465374, 772182845, 741335579, 510452860, 413260391, 846207585, 431304571, 982355791, 356526620, 614536026, 874974282, 535928387, 50945352, 662803302, 698044481, 935586519, 736529289, 54847429, 403375537, 178622302, 16700161, 465501131, 602055289, 802137624, 418783723, 820512994, 763468433, 695380423, 284195836, 988177919, 712089514, 120711347, 20203365, 885958823, 324996709, 796729946, 941178094, 641919839, 416454155, 64852608, 687779729, 319164378, 692269278, 294318511, 24265579, 745306824, 310643251, 413268661, 380440536, 441088151, 998029552, 810777697, 220051058, 453239696, 939276594, 913826228, 866401893, 562178425, 726502014, 190790, 182907004, 226544348, 709417742, 315196883, 996758676, 604040966, 77003213, 323873716, 160923281, 688797098, 625974536, 533128992, 286817373, 806447309, 674883756, 473859315, 680156199, 955553605, 563873175, 715289405, 741930801, 419956180, 435139337, 692750488, 151598665, 314976398, 939996163, 565804938, 719743437, 114848735, 551376072, 37788132, 454472060, 292807419, 135190474, 310250368, 181425178, 640990782, 235290540, 315687328, 994403922, 892816795, 360959184, 314515598, 769906139, 658529107, 997344471, 559037456, 187042385, 33441802, 320405371, 378274234, 701689249, 370730844, 458597005, 31647897, 499673416, 305944895, 342889882, 745299825, 54989551, 252324367, 942134927, 865366748, 880147043, 85472432, 213757478, 559088340, 524813245, 697106555, 235808096, 974865539, 629432578, 262470819, 312597995, 145352878, 270253473, 281601943, 773005029, 359051247, 251214385, 811379355, 481267910, 38896873, 881894689, 196215345, 877153584, 244968508, 498225681, 430382083, 200896771, 772278013, 829791905, 806094000, 148255458, 171283794, 170088444, 352692220, 789933496, 430866825, 600657910, 259762747, 99723763, 849822203, 743742943, 778703812, 201040914, 903397582, 8634915, 876048101, 221783715, 886375285, 121913480, 455296511, 632727766, 350087416, 738097003, 988750606, 915520177, 147606819, 865063990, 438244332, 258839073, 116491429, 915828762, 413663958, 62294999, 196005612, 644802175, 873659572, 568091089, 176123254, 401278698, 522040568, 723763651, 391116815, 58279614, 503731559, 879106417, 323445773, 998978336, 296742413, 168673808, 291977504, 580766503, 466546115, 399127808, 821213187, 975374074, 633212003, 636011935, 379306772, 880316891, 465452763, 573863068, 511391672, 215349216, 943510852, 652792043, 280359799, 765269848, 112097141, 881657054, 721613107, 950798335, 529210349, 170008187, 345750928, 230231424, 458069181, 554089564, 972157932, 733726735, 724477718, 520860235, 807599967, 609247742, 634809555, 92091249, 298178693, 324468711, 787923786, 903732639, 581373770, 655898510, 936168841, 943285154, 731576905, 370072686, 333131550, 790038413, 576800840, 983118315, 9545579, 101161544, 38709964, 791425228, 999552009, 112104949, 661274944, 744195930, 31201295, 537498003, 641445481, 260299856, 156044053, 225211225, 827117935, 785075044, 962100503, 465173904, 716164077, 410081794, 130559159, 726316186, 985526352, 715997034, 807614462, 199123787, 388222968, 679057825, 570646718, 195487218, 439127122, 659151257, 842068991, 876046760, 154028716, 52940731, 435712807, 991523237, 263739758, 534655279, 987991414, 282466413, 707320567, 813992508, 526312862, 440673102, 980076409, 943432306, 267964628, 85253830, 501710756, 238878772, 445965670, 587454850, 741894036, 750578503, 464208721, 742311075, 509377580, 618787213, 152273174, 651255116, 955605931, 110029630, 853453626, 138090005, 845105451, 824042533, 377439621, 600745380, 190983269, 338226774, 297898359, 646792454, 917310354, 255721909, 399363664, 758712792, 706264999, 279020095, 240768125, 146096485, 319349662, 317032616, 736397875, 203107293, 315753416, 200023280, 274188817, 677768309, 926008356, 111411097, 913574053, 908883082, 794622060, 112404619, 968884502, 474221650, 996598046, 222779187, 832049730, 655642900, 509837417, 104382145, 454615217, 875894137, 841699415, 292781145, 621726784, 361151304, 481130359, 948064567, 776559324, 511620232, 878356810, 869559988, 183052101, 122407479, 337147442, 570951813, 660611510, 177232061, 949773392, 576999176, 667406324, 616766488, 405907553, 891549446, 528129091, 372564206, 843853193, 743875402, 699154631, 3728906, 192427827, 127577299, 623330746, 629202123, 285113953, 412911188, 559056730, 865739546, 487159641, 850075372, 74225778, 514575643, 239848102, 36167014, 844193628, 992212681, 405446563, 896720178, 984885374, 833244098, 23002433, 848668870, 581795576, 450649001, 952819865, 656286429, 192077096, 16714468, 573919626, 137775460, 153498686, 843873498, 396282421, 673617197, 825015589, 15158435, 230016774, 613748661, 83907757, 12101194, 799779380, 592994721, 133509040, 659440368, 474927252, 166104181, 179245989, 912614947, 466417455, 698129598, 227555592, 406745222, 357861664, 460196880, 560358206, 328963702, 658630354, 185115662, 12588910, 115249929, 154907273, 39238338, 798456322, 636076189, 249091271, 504352516, 642112893, 261690667, 321584151, 532999921, 769430187, 320885915, 551223059, 780871092, 958142560, 579066385, 722188340, 783157363, 75348747, 483485658, 276995261, 377162859, 889799808, 433515996, 456180893, 34054517, 683175067, 709847001, 396703449, 476419604, 727972314, 313480325, 966154525, 324899959, 196321782, 883481755, 706985211, 839631356, 845799034, 874378702, 904024642, 547273148, 878608836, 24592016, 86400766, 287648511, 485566089, 376508053, 520576788, 683396146, 383115663, 748919806, 850556146, 591096817, 229376747, 263440731, 694607840, 604976986, 496149818, 151672659, 895348190, 156157254, 500830004, 313656027, 954052944, 313378385, 245116555, 128878539, 498194156, 977995791, 9179908, 258949498, 494211597, 632001267, 162160023, 26849764, 137915720, 717759610, 57834200, 193095056, 384748678, 212914555, 187628942, 459389821, 66906177, 870647564, 520576219, 699846957, 172228385, 460378520, 410430349, 652933927, 977982210, 433974164, 143282888, 459014005, 482080737, 639138800, 76348095, 201907954, 618568443, 859782429, 922448719, 941642798, 525016770, 829450362, 738365383, 780381484, 15566440, 622975522, 131477002, 363473338, 907831944, 923966421, 175526301, 665636052, 642154260, 536437243, 653275870, 102892721, 668764292, 625923375, 17235872, 990514918, 700031043, 507825924, 166335487, 389974967, 754921276, 15410219, 384878083, 167745662, 320285234, 999589554, 648172509, 187809486, 321609465, 948992267, 389541319, 545306838, 300333080, 797377479, 437126453, 579125238, 630531701, 34124535, 44432382, 326260208, 513647302, 64899699, 205025603, 96672056, 168444566, 336819364, 949081872, 25570228, 609957027, 916068675, 551740208, 388862007, 754814810, 331392991, 210654832, 374497639, 269905365, 646975743, 428433851, 408546345, 774731210, 457544413, 415447228, 900545933, 417073843, 395708827, 908205165, 298067916, 605663224, 862952292, 319835730, 29339629, 372224836, 84633855, 712239672, 460360892, 594352828, 580757309, 820097489, 785895564, 593800909, 759161834, 970747139, 74518126, 59310720, 844841797, 457578117, 978488584, 445724587, 687541942, 779738474, 552106753, 872194395, 427164159, 132688135, 551869447, 518294865, 515514177, 712987547, 268018263, 693663735, 857464273, 290672050, 827559110, 867316964, 433779250, 729298227, 925645017, 280468498, 748100007, 34342459, 876449610, 620956833, 739423238, 296635864, 318434975, 153570483, 321083806, 818883935, 385570821, 444429816, 230208698, 107586150, 360010742, 121973798, 407271237, 33716308, 741745098, 25619487, 286551254, 562991503, 265406628, 940408978, 285363106, 196126290, 881543780, 639739069, 619510246, 973472818, 562770281, 230395630, 649416183, 787678418, 943291450, 181004619, 702810206, 883522455, 429569016, 256666062, 116576853, 510938443, 955328657, 609525224, 633213104, 962743649, 884977484, 949410652, 299709902, 607336615, 677586775, 571898555, 802233848, 556754061, 660612774, 164686710, 72538203, 15743479, 898559574, 70298781, 820538137, 806007450, 464979272, 11729107, 76448403, 938626764, 602374900, 206143541, 116584108, 934331780, 385695320, 586434624, 302460713, 707999398, 126804709, 739359188, 599442871, 598086236, 913296963, 481945159, 91143098, 764339847, 997291907, 387571584, 623425779, 15219512, 95183113, 859644165, 615177011, 963807200, 218690730, 651554833, 120183226, 152888446, 394763769, 497167888, 260520495, 459145904, 203772259, 164562603, 986315090, 216730162, 410317122, 406478990, 692391699, 184455770, 566436467, 404833569, 100748957, 302034717, 402218867, 417923093, 660426531, 236121669, 574210073, 607910583, 604729770, 915428440, 756576781, 109334213, 202613706, 284114113, 120430006, 547252931, 808743496, 524319665, 472004981, 862979789, 793755043, 929087563, 839513656, 600601352, 53609750, 48430095, 154918174, 305662563, 543706531, 260870792, 938258793, 945981360, 175281123, 967726971, 571993476, 903502395, 320956129, 188844197, 705827323, 970023184, 329835052, 609890730, 67504262, 203642753, 226264053, 229986421, 732561368, 981748095, 788337510, 547395112, 290376748, 515903893, 146280411, 215341408, 214621074, 705059859, 182933886, 209679274, 248294991, 395529905, 294956998, 638172920, 276031904, 398823438, 936418395, 385304031, 468540455, 430802930, 814195576, 101958716, 351343432, 661476280, 574578333, 669979095, 201284737, 853609654, 218395119, 187527139, 503732125, 776179057, 710904304, 954037317, 462526767, 9363696, 562507199, 565102876, 523833944, 426715730, 263154708, 124845798, 317488876, 386662887, 445394145, 194780153, 471675495, 950697508, 95919351, 104254091, 964876396, 675821321, 734157083, 237985842, 481375249, 107137786, 813241838, 154979674, 67859096, 414798235, 151204026, 148028332, 474274608, 525899639, 387973866, 486835351, 132597307, 529894295, 858677519, 374958234, 94391860, 722804890, 6283233, 81167880, 914976374, 508438608, 405875239, 547620279, 302900305, 60452166, 707631188, 209398027, 80349536, 16111172, 814464344, 694728741, 239359263, 431354255, 954411278, 637973687, 695899906, 448664520, 333112807, 32780515, 614238148, 611081379, 919555535, 768940456, 860253171, 948388273, 379077075, 31191248, 677346860, 796119318, 291346737, 11022551, 126095195, 668836490, 707211409, 897534939, 374399960, 929390576, 764174143, 150323499, 620844294, 671674318, 780677573, 443778428, 663583394, 77396886, 928406973, 179897896, 550683596, 560220114, 424601567, 83213011, 412315973, 355052149, 330453686, 903921245, 981768209, 766456527, 853643819, 584051731, 535009250, 652921278, 400015173, 304725983, 435634293, 760866705, 613681116, 503306502, 102427690, 395253925, 752789066, 434327707, 993499715, 545455215, 908742344, 805661753, 758752295, 194448106, 44051155, 614277559, 308190113, 361214834, 289063811, 423487738, 327897978, 93483468, 101305108, 781397609, 36940286, 53923503, 993676693, 977136717, 493860226, 186809598, 958911233, 865531596, 963905101, 403757203, 789100927, 650374880, 341790280, 143617155, 958155419, 944465258, 833408346, 614281708, 280644542, 428596523, 215641907, 393078711, 274358971, 843271526, 263114435, 580448050, 888554498, 69663760, 224456741, 378348229, 400575549, 175603428, 407955538, 994129104, 894607140, 534180955, 693243011, 323805130, 593816603, 999509848, 458726229, 78363806, 871615027, 238545790, 566910404, 164875911, 847913148, 155033886, 890649291, 420230378, 273598488, 136651078, 403034455, 457573253, 625290420, 369134075, 118972513, 88952743, 292342164, 11879516, 274166601, 873356290, 558031998, 515598114, 356447692, 122972162, 158089453, 528641357, 637344387, 452429901, 932414022, 100746593, 868503880, 733354667, 630182551, 727531987, 474792577, 992176435, 509128871, 472289909, 180913422, 954526850, 40892348, 643743171, 890708651, 518760537, 305227017, 519264630, 157673080, 376857428, 172600364, 756447837, 57217709, 301231781, 342830890, 917237930, 731825733, 998596740, 460595081, 742201819, 638318387, 852533653, 420662416, 857394897, 689876567, 134092269, 62460721, 659474663, 695190750, 954216938, 275123182, 267097198, 78124117, 963225932, 666699681, 127684556, 441050005, 93841393, 931216447, 680396817, 177527270, 786606270, 381660141, 601996792, 950755851, 722234198, 506619620, 925317214, 601282674, 262040676, 65764054, 871712071, 154531340, 611894450, 33526667, 165776186, 608811783, 768041518, 652120931, 216054150, 502670312, 844598754, 719188256, 734736754, 214804351, 318095063, 339001649, 668528630, 437354387, 374317415, 280490696, 8402771, 583525900, 142952813, 497402140, 550577531, 97871920, 402208797, 256639464, 51901328, 688230539, 38617931, 450357585, 381194778, 175529080, 602653999, 477644383, 681590139, 47010903, 491365124, 351996654, 752657505, 563128459, 51047724, 409136212, 365536175, 778449391, 519234004, 383721628, 745965090, 733380170, 855347303, 219235262, 457759636, 506047680, 261789807, 452330831, 590730849, 570442628, 292313337, 271530765, 852759670, 541767254, 46736526, 3526122, 941736274, 215833866, 428731246, 400036320, 307250349, 444452029, 599222804, 200253817, 401603762, 614467046, 591506867, 693533038, 845774161, 944088074, 603457196, 273674949, 578901838, 128165652, 504474402, 55980713, 555927710, 812800052, 674080017, 724028412, 36509195, 504114620, 641817379, 944243245, 832589758, 844374579, 843370732, 841491400, 414643625, 786260754, 416796677, 786268412, 927434512, 913792454, 749210312, 800947126, 926538377, 519822111, 108655348, 194971637, 596541711, 355533495, 11121376, 72830841, 779831659, 491271370, 884692845, 701516054, 805516542, 28994794, 951973247, 656444411, 93380524, 657758518, 41769286, 582031208, 139005745, 114331346, 357433876, 674546608, 180968563, 977909030, 468391120, 790337313, 564289451, 77062520, 824930143, 330248673, 61502732, 125362727, 577959674, 917675478, 200358453, 374982080, 72828093, 887339428, 801620158, 417167417, 94804801, 451104066, 932170943, 857732836, 932416371, 881876649, 874941684, 119389878, 19143656, 798417116, 112132568, 73689316, 433502206, 603819866, 172442695, 382856549, 530223461, 991402499, 151307720, 962190821, 579466119, 954733558, 143837780, 384537829, 783374621, 722292641, 353121064, 596073003, 21130288, 667341769, 635509088, 375299918, 208241899, 507137062, 729407605, 777203274, 953134920, 732079978, 103030848, 264443087, 345333179, 205530407, 639242239, 75890531, 923764931, 357274641, 962127764, 785249883, 589735589, 77685529, 900513217, 401834886, 782081513, 550641764, 347649355, 63648774, 42473079, 753368100, 506613324, 272055031, 368895168, 826172441, 768120256, 958842292, 331359212, 686316735, 26586791, 907079293, 114606242, 40712690, 62951746, 499416360, 75126429, 878417664, 335023755, 911848326, 682278097, 982674221, 232828300, 12173682, 256028523, 513902684, 461973504, 82116152, 643641776, 251002494, 421782412, 95873735, 318800181, 752821889, 437363870, 439910773, 90346616, 562082216, 283132044, 89916784, 599859217, 719104436, 953263632, 36222327, 870229560, 368717045, 699212590, 779134844, 728113442, 769315313, 502974809, 593802086, 198494907, 775705600, 563872884, 639728245, 683406368, 990348097, 751733707, 798294319, 504162113, 415155032, 836912820, 999267407, 11860047, 677721270, 689325339, 420073710, 124771960, 60650918, 193203151, 190970303, 262703370, 215059379, 483987805, 562291078, 532959625, 154667402, 280885105, 776967665, 896538097, 917605925, 957944418, 92992736, 499703623, 483494772, 517312660, 801132488, 830875902, 163635611, 409789702, 640653632, 811396420, 206262502, 969099797, 706353886, 263875078, 374246096, 131812928, 484721152, 202547968, 579071862, 311714164, 388212401, 341364160, 23650398, 227993409, 661605476, 881446826, 138313795, 889138846, 644725334, 762618689, 76174270, 581232686, 866080505, 669263145, 1324666, 86323789, 580084250, 114131107, 882294971, 372293024, 813187966, 824021336, 172731897, 882234330, 836276993, 315641880, 783492509, 193323119, 192710091, 983199676, 855943641, 37696838, 724387477, 247352229, 775447045, 980960065, 103311349, 101086741, 435599433, 860824524, 723256510, 578704398, 289654539, 740743338, 766150735, 486755583, 230193663, 203791119, 909343999, 115214148, 301664791, 857368323, 335746820, 358969532, 731049214, 203201371, 355514671, 725149691, 657050133, 122932308, 242021558, 373775892, 961425505, 880592232, 927104959, 902355756, 965660006, 594244133, 727400455, 790030483, 399636519, 722317118, 111237539, 639121746, 543411210, 245411248, 4942904, 647998655, 610423205, 341829751, 449494838, 681546222, 15116317, 553223134, 132367023, 311555879, 509411899, 958503259, 387742132, 897321224, 775165682, 451060255, 389934557, 219871745, 249701027, 878467604, 588257441, 899970551, 237057919, 583585388, 595586637, 145210603, 757459293, 575323068, 83225276, 685851693, 547014394, 169090207, 158113987, 998779352, 72290739, 496379030, 864355719, 505597227, 380090748, 313829525, 276710489, 582526121, 965127125, 79946352, 283290785, 836860506, 365309736, 712656531, 720462907, 291303169, 48026431, 762642853, 638755598, 430461183, 404729394, 597803063, 570984202, 925273496, 46045204, 781277739, 904415856, 86025224, 11670901, 102157489, 353808716, 273676938, 669699740, 472121917, 629345854, 617387242, 116607220, 203717965, 864906411, 342990453, 956868027, 873833504, 729528558, 712813102, 521590537, 227584805, 585504707, 165877549, 652537896, 435006498, 275755460, 821275172, 690025747, 217518635, 459327624, 269252331, 813789994, 218418610, 760653847, 694250070, 702875987, 763549813, 39152798, 585546813, 807954360, 193325149, 533788390, 814801484, 407986234, 421982907, 550368461, 43828533, 83751042, 410166544, 633066149, 289880345, 335997119, 742165865, 591600589, 896637886, 550276803, 303388699, 106032940, 514236885, 741000, 604237519, 321496191, 168434609, 185162926, 485181552, 23617647, 698588112, 54253714, 986407181, 56165275, 687762445, 865152976, 277525633, 623160713, 845331689, 497797220, 514872812, 730478703, 356838649, 624497124, 152525167, 904212609, 916125136, 69771034, 168790133, 504739255, 545088549, 689680166, 652433114, 655983999, 830846104, 702709904, 913054211, 919371142, 849633618, 120627396, 457753104, 364998938, 835239255, 996591933, 611546031, 857010311, 246198527, 424943625, 655288037, 644419410, 53488720, 104836843, 504564215, 631471630, 542612804, 444472060, 136403629, 491460448, 658721853, 986070055, 983949898, 597379483, 872244865, 489779403, 548894891, 432610091, 644821129, 819087040, 212376528, 826271184, 603654476, 115019471, 340607034, 989244913, 332234024, 943449127, 994740666, 867950388, 967129375, 55314299, 892981474, 154214207, 11463568, 867004311, 493614465, 913739809, 259281808, 593379218, 28509559, 651684791, 518785103, 488338085, 568714035, 875196709, 186039453, 437109186, 463072603, 213459497, 864866136, 346778592, 510437946, 698609308, 251733587, 42812709, 760842637, 672766285, 844205204, 229507204, 599175422, 219536638, 217345449, 496521777, 465432866, 309977207, 344462087, 257622084, 941517145, 103725308, 734046005, 662868872, 94089541, 498074970, 599737135, 477638143, 137328649, 727590847, 659588724, 132045023, 643770359, 909457032, 654043891, 617327258, 167893636, 579195537, 10691652, 584781631, 588668147, 530848613, 191327968, 715904380, 614335872, 809847980, 236506545, 107284798, 271829006, 963386676, 746107473, 84896757, 684731363, 794085041, 759028919, 774948909, 859737868, 859205060, 290990286, 763695877, 459887838, 712667391, 877411266, 368902430, 810969208, 33103615, 408322565, 417830264, 699545402, 116131757, 85573496, 257315905, 100684833, 731637438, 455593208, 387355876, 879262786, 141981784, 196692756, 984957351, 138195184, 580972917, 42659366, 498673329, 513074158, 224380357, 101252167, 258107032, 273903345, 138425785, 452374425, 568057057, 203156788, 22307072, 36863752, 160164783, 113116010, 294182565, 420394520, 497074044, 820893932, 589865405, 308510439, 607037209, 163550500, 547699370, 525331274, 746596083, 290758568, 600885994, 885404701, 967846749, 757686659, 681404931, 721960121, 148255659, 921983383, 986662720, 418991541, 891982381, 299495534, 252486659, 767031125, 82177577, 176788952, 228718162, 860458684, 408282963, 463396357, 576681349, 758768101, 380002407, 880473303, 188974776, 427594852, 54651603, 188363690, 884404092, 888691394, 884855296, 88377493, 569623669, 147487508, 652371899, 477640239, 218994763, 900722460, 308463869, 619848495, 887742107, 49430541, 237916230, 144524521, 155321613, 848896400, 643731533, 276631978, 377136194, 338516979, 44782683, 59551720, 22059063, 11417117, 568287128, 365510514, 492781724, 890960618, 291204431, 264500704, 44796355, 612988664, 649894723, 266429432, 930410395, 648366574, 332149948, 672702468, 414226126, 416546410, 100174965, 640614963, 679059635, 831229691, 91318813, 124795674, 147493545, 715838549, 414436248, 827880429, 244903351, 179062113, 543748725, 61368530, 613691224, 600688765, 814433781, 591303154, 589357245, 174399789, 741087890, 781607323, 926959056, 185722169, 401635318, 620399877, 269209259, 365840486, 446785275, 710003014, 960880742, 331611378, 136835597, 226822348, 702857273, 54918201, 603734958, 487211313, 558458664, 942962874, 208669945, 872458532, 582585513, 198486654, 794821080, 443706185, 308022316, 62874883, 496708371, 707407335, 286558131, 892833823, 741090574, 48766459, 148905351, 459387068, 747950176, 593002195, 164451411, 868360538, 953808913, 136345247, 954067342, 306546891, 103396710, 675239335, 235027438, 295474443, 522598855, 321444862, 658887558, 535420894, 261440519, 181136431, 715042432, 827000337, 274656634, 944852299, 106944309, 850578292, 753972383, 876727356, 194638349, 433433428, 725143282, 500186622, 32008858, 472126443, 908041509, 696882483, 348196647, 57415631, 830056181, 915594092, 971963923, 496780280, 879987140, 51195141, 171194056, 936838190, 495283579, 527075414, 954150524, 692886554, 996501084, 704287156, 210295922, 828761003, 384231296, 282845331, 285457086, 109520499, 38511264, 153700676, 57970481, 543760032, 38431498, 916529700, 443972221, 698730293, 830156018, 315498345, 808117606, 922284120, 304771371, 459897213, 70984710, 184728616, 10228356, 37157839, 112706015, 483268013, 291665557, 393474139, 655926617, 115962472, 517021692, 739419744, 41465045, 899653124, 697028159, 960901846, 457655354, 660749561, 119191490, 591962542, 158620584, 369936259, 72850582, 211770581, 46388055, 566385223, 950796385, 772219010, 500948779, 369092085, 436001983, 840986407, 408691860, 981125374, 418408985, 163971902, 688560997, 925582038, 183454932, 399957002, 375150239, 399624638, 373392627, 640263578, 825277396, 16054354, 228315716, 687325047, 866326612, 198071754, 257593554, 680076376, 424479921, 615979637, 40691332, 223048730, 267236346, 912684453, 357107196, 251264265, 184787957, 116699880, 297429752, 80644218, 349605765, 466946975, 162614080, 765983625, 144798283, 621402039, 139143498, 61640338, 299452707, 947239294, 153112370, 951084603, 252341642, 9256144, 5363779, 982550865, 597581359, 967283876, 890877554, 697179344, 843193203, 207665948, 764300323, 849739076, 760520068, 299767068, 329258394, 490910741, 947232175, 749670398, 414260201, 447269635, 384071473, 198344721, 457533806, 367621769, 76813418, 932664353, 183544970, 484888238, 717742795, 12363692, 95203969, 457541127, 786197880, 55096675, 511837946, 950402891, 764416409, 939488939, 783600437, 36863071, 770809938, 206857269, 145838751, 998236392, 179572012, 31377073, 633152837, 796909245, 442637029, 551047345, 695245511, 962759979, 344088121, 273989884, 83482427, 172445160, 996751338, 848001052, 677851105, 133077309, 606828062, 951615373, 374784151, 34263917, 24001323, 536306379, 800709041, 541045274, 819571038, 492339749, 199821325, 686077938, 372067950, 688598769, 618945936, 881882647, 602682617, 136293800, 897920575, 105352081, 98388145, 720875509, 170803946, 908966878, 881000269, 873510117, 241520735, 824215315, 128607399, 7328897, 869085043, 537136169, 388904416, 365561659, 187471024, 247702166, 384412518, 467967661, 201322007, 914340918, 39485020, 504049779, 36338550, 930843788, 296604556, 29102342, 331940126, 273597875, 909741412, 366274775, 407747767, 59921482, 812656938, 233090663, 199568068, 650922184, 508017943, 452059161, 135479816, 463573106, 814317210, 811024958, 595072358, 601544086, 138171329, 198688730, 969062974, 578494166, 954128020, 956380917, 890500789, 17961335, 458453453, 98762315, 949598717, 26464658, 797161262, 870066732, 502845543, 983025902, 49799171, 724108195, 730394506, 761752756, 278091107, 955639156, 269440808, 646829544, 783707526, 438096453, 554399815, 313713944, 249442422, 5875001, 403361200, 744454165, 94950522, 671063371, 59416481, 353992202, 346886243, 872913344, 851921857, 725274791, 907008788, 847312803, 267778449, 889269255, 605780001, 112589874, 889957533, 58696463, 296169882, 902577312, 963848818, 650796079, 86752935, 773397549, 192512408, 275922211, 106272291, 984163166, 238344217, 325875518, 618422164, 926535852, 75339954, 28026045, 188773680, 222912981, 888003171, 30218660, 709373213, 257371274, 956838066, 124135810, 749158049, 334947817, 682420113, 736980145, 866424571, 802482438, 955753912, 903762957, 688702108, 990045998, 838149313, 475317011, 855384076, 424876854, 705039228, 205102928, 682506479, 712972337, 553785874, 996820573, 235289221, 378645217, 250940883, 399635808, 323421299, 441279243, 993609738, 847127772, 264914189, 571461192, 968962449, 890836679, 473281102, 690131248, 527428776, 212296459, 881000475, 743153208, 940788300, 401440071, 797245299, 25892000, 671009057, 223776151, 810672109, 647569985, 341837708, 66369105, 241384482, 770241753, 962057038, 429073655, 586033020, 641518709, 187349297, 498045289, 799077624, 335151242, 348793284, 476985267, 731057990, 925248003, 203948978, 880754920, 18211685, 527036867, 83509930, 154841882, 899257668, 934332126, 966161573, 658932734, 336405341, 625522751, 400965072, 635102902, 981038382, 112438657, 183658835, 350373066, 854175534, 928050500, 220216765, 345756417, 213596285, 694104845, 712984122, 177769596, 101378097, 755259014, 170232172, 33010391, 445731474, 682313753, 210792749, 928219640, 161804515, 457070794, 243940709, 999422485, 62357675, 677305767, 799566305, 256366758, 718561800, 522447283, 892431174, 752779620, 839630734, 674473247, 821141736, 445696039, 482277838, 556548765, 547963877, 919917278, 843892034, 68000371, 98039503, 788502953, 652469514, 290428525, 79920572, 152777653, 124202543, 647448126, 293476546, 58790877, 826287245, 97612527, 421205260, 89247945, 303822970, 943397257, 997205025, 783408089, 497937870, 156406501, 976012931, 41883256, 923680944, 726879100, 135907818, 648462178, 19614846, 263271018, 213150468, 758254971, 730564433, 331021598, 792387378, 480776255, 805791403, 4147998, 863456112, 565002724, 64224915, 273736960, 189435554, 450840036, 713361719, 752310638, 165416133, 735091636, 302702511, 786327632, 539024188, 457886859, 360097980, 699510643, 365842122, 839542393, 302392290, 207008214, 654995679, 347838400, 45513521, 118570262, 565915016, 80321779, 896314320, 947603528, 550372470, 967487582, 663764309, 340550734, 457350875, 283962262, 836242737, 899452089, 883792457, 375476994, 520154675, 309461717, 24695042, 805151601, 744420282, 560860255, 958235923, 319950784, 4370193, 330861832, 43669714, 966847495, 986196204, 962607216, 574118904, 131065891, 806912120, 288497184, 342711042, 887158421, 630123214, 521313688, 105636722, 2655171, 447884461, 715874520, 287760155, 584477795, 139499764, 821503500, 913451682, 437232054, 919748915, 438077464, 328464159, 950269223, 604842971, 219119524, 677563304, 267585330, 130894815, 447246374, 35188383, 579934949, 575501066, 754879699, 408057314, 582495362, 99890820, 369111510, 353840634, 520159517, 996319034, 330200363, 505910364, 490358340, 98573330, 746774513, 976089548, 326261148, 211606290, 301974681, 32453376, 187628855, 706220154, 266456704, 771025575, 767156255, 131509619, 133099766, 36694657, 143759499, 72916699, 260778307, 677234543, 616996725, 511017898, 91795485, 841354865, 101665934, 716505498, 116654216, 52955875, 737284050, 814413935, 486575248, 9225306, 377908004, 506155221, 173173061, 718908532, 111904304, 654951314, 326477433, 487309868, 287417449, 198145797, 45566920, 218344393, 594358997, 876710482, 511420617, 954631763, 29166989, 850492719, 423527165, 498115909, 225975364, 393018627, 414532528, 676434769, 906265432, 815693708, 46597158, 881720419, 301463197, 433345913, 332610144, 559850456, 156461569, 12364193, 722681750, 596073144, 491980362, 400314950, 791799445, 881639712, 144914710, 87980605, 679558406, 382980567, 51603628, 704923440, 936828833, 319327707, 988402311, 336575481, 817964043, 484540266, 588690096, 203040295, 86302114, 901868979, 715704755, 535573880, 565327555, 944550021, 675048032, 830134317, 929201513, 107313110, 845175834, 693359038, 831439917, 245571616, 458515901, 776932486, 923331647, 809801747, 148157887, 309997250, 743596641, 890587055, 785609264, 822928229, 802216009, 771666979, 807336347, 680293660, 394111599, 979158359, 929587947, 747251656, 338936103, 931886508, 238626038, 710454406, 181847399, 307705614, 765709447, 281852735, 485390733, 55271567, 445314599, 926240899, 746405811, 568999617, 276280178, 894251877, 972011301, 995999422, 744453707, 136487775, 348528870, 952148338, 265626889, 600721204, 63965895, 547567387, 141707828, 925880695, 149632675, 957257134, 442855224, 16447293, 1012486, 925520772, 615924640, 274750649, 176715892, 713624269, 946377145, 312371273, 149006194, 322432733, 649099672, 700606494, 359837420, 626242082, 962897007, 77221009, 242672328, 308460184, 550656049, 733454960, 687614371, 471679182, 155730734, 526123019, 167330397, 496370944, 385114149, 583451367, 566123946, 765616622, 625192242, 170722215, 566506152, 27656839, 420519921, 822770969, 203591839, 385178148, 31031511, 395592333, 299559057, 399287312, 64907625, 188324304, 539492040, 771584479, 205842279, 191054617, 709549916, 808014420, 778809154, 645115392, 805745505, 20498154, 923634785, 186611421, 688362263, 620067806, 685896917, 405011648, 760372680, 799720770, 877636012, 404230945, 327663549, 675135255, 982073326, 536765066, 118344189, 197461494, 646990416, 123959371, 79407616, 703044508, 559255963, 547391222, 176414949, 748131916, 419779476, 55241075, 114522351, 63169617, 225702573, 829262729, 57812417, 987729207, 671635717, 543152592, 471377320, 854427222, 844195203, 803553350, 834449193, 257710068, 495310482, 150154245, 804767582, 894590612, 302024537, 542022378, 881232818, 153927464, 831522290, 629504277, 777577052, 586819313, 800500688, 310613952, 285434120, 322352221, 659437239, 312283533, 74111071, 101577379, 165657841, 365909806, 850205639, 815014067, 32749396, 407814276, 820957496, 714794593, 667682930, 195066389, 49183169, 575931182, 277368613, 927261022, 99554512, 824188652, 804066039, 629022409, 777274462, 609370460, 314672508, 382293768, 641968462, 855704489, 845958760, 486783107, 261072940, 383242908, 667431563, 687205682, 623897420, 397771480, 633160544, 210814186, 639679568, 344980745, 650612714, 380594087, 83191867, 524526447, 892456242, 691605294, 657434012, 226656536, 265859394, 743384154, 789521566, 342064142, 984342519, 181939781, 566268652, 24851836, 950682048, 627323616, 380522292, 89355887, 959947357, 372772991, 848607859, 79388386, 378993121, 262566860, 581817379, 133746910, 473050738, 368229370, 218813564, 885729487, 409589929, 579410253, 507875756, 448072226, 392139462, 111479524, 107377107, 589529402, 257198334, 817061131, 311255115, 274780460, 145040133, 998166310, 607028316, 582180129, 441308942, 102938014, 247731102, 853945771, 298227442, 221264617, 511752174, 766543916, 50499969, 165772526, 384219624, 115829091, 2367421, 311011379, 472805209, 561281389, 474171987, 748418254, 28335805, 136455944, 702837490, 332639635, 383908050, 855068671, 352844135, 535891421, 562272017, 770537657, 404906905, 244769737, 303337422, 511037117, 93527889, 415022741, 794877517, 679957810, 424438605, 320701136, 94298694, 166317979, 174593, 389544816, 307592242, 239802673, 266491468, 115991046, 895449873, 350083675, 70291856, 265955930, 424096749, 257592064, 456360793, 684307654, 991028140, 351972866, 458307761, 782666670, 265645204, 156066507, 23868504, 853497616, 22277401, 265352303, 532489728, 842814903, 291253772, 876669091, 961336801, 552523548, 97451596, 847767697, 313408264, 546622186, 288930722, 678242749, 14715369, 603212967, 281694459, 962390248, 516800226, 335841047, 124004008, 202794648, 260290609, 492978206, 566058267, 93390045, 822338887, 608136009, 556739265, 658400649, 516167877, 625693403, 858689197, 948956101, 103606966, 442631603, 599235113, 821452389, 489106798, 587224174, 208161660, 660159015, 792635278, 629279545, 50108619, 251405775, 218803989, 642134028, 531643663, 803782501, 126116728, 674571683, 542427750, 953196139, 569450726, 945241715, 924221720, 494771469, 448635326, 949470686, 688917131, 379596859, 574429623, 654497424, 713697258, 275009290, 989527747, 346253453, 905547881, 5328474, 350699177, 27455170, 164384294, 611007739, 255539035, 82610485, 352191779, 520221923, 166323663, 584103542, 391559100, 606355616, 874384028, 520595192, 136510305, 575669013, 121931018, 320268548, 717590146, 887668689, 790321793, 321318078, 264499229, 343358706, 485899112, 464062975, 553556753, 87398585, 508931938, 148674359, 392140704, 649563745, 311852860, 486518897, 665997808, 869675394, 418139858, 772482595, 227760986, 522808311, 469733987, 362412726, 639895434, 580947112, 853456300, 401366332, 217909416, 397304907, 194218515, 227275450, 959184033, 42692381, 223239278, 51074202, 820382348, 144304974, 424949994, 333102520, 977514706, 242413955, 45922446, 793686541, 809616010, 736350201, 94882249, 907619930, 18000221, 823814338, 768347536, 448380996, 684827590, 744682623, 519354778, 612366425, 207375437, 867384610, 355762829, 955028745, 242280132, 421739389, 111930569, 61578250, 692623722, 176819069, 421864372, 656829903, 907963139, 434635513, 648142759, 233755860, 711255407, 556000186, 312114340, 696497583, 525604982, 583211195, 305270208, 924006671, 802073061, 385907806, 232882645, 507620552, 742376418, 491133034, 979290930, 684667940, 845526429, 174114750, 875995657, 694252185, 507814305, 392505782, 309918901, 138217640, 143915156, 714178550, 910922611, 72681514, 543728367, 858805609, 901069307, 421235914, 347684762, 11326293, 638713344, 710891495, 866878958, 949757627, 828463297, 113326110, 237854690, 40645808, 581456260, 182621670, 868910465, 892934075, 485407748, 661436725, 657885281, 230659343, 439634489, 287298576, 529481175, 336648287, 880156439, 567987037, 639159217, 924252316, 71372731, 512096368, 125124149, 192388811, 770682452, 333730594, 131779816, 248590847, 220932961, 817238918, 9112328, 665310274, 21894608, 945469452, 406772486, 558859579, 584693790, 453283447, 960593469, 386002234, 782677814, 567303967, 418504810, 253988569, 760607100, 957424428, 115498050, 800415877, 97065195, 91063595, 922688448, 599369805, 632179925, 938073734, 24934265, 347256350, 935712743, 8892311, 428918144, 781329861, 193466861, 399056844, 329353385, 442521379, 402003438, 321254447, 250407839, 317490634, 156271654, 52540908, 746767154, 988158222, 952822414, 391446051, 364744932, 891163783, 916575741, 137590607, 322304420, 429546370, 868171115, 848724281, 350917578, 27187418, 638712021, 274537567, 198954824, 544242543, 471665800, 108113253, 468410363, 223915439, 544651337, 27566092, 884705913, 824399386, 952793361, 166727744, 272460793, 176216274, 260702129, 541630648, 257763599, 379569049, 740745560, 537642830, 601710073, 993889590, 232243982, 577904117, 477009042, 343034145, 188106603, 860151377, 65969627, 706097285, 933103743, 409696314, 862653049, 745287317, 564705448, 49919969, 918651739, 684984753, 371448031, 282351455, 648622124, 971513679, 776167169, 374782771, 304061260, 203620868, 960948075, 413714610, 487424637, 354915955, 408170403, 114535677, 83399390, 87837462, 315024123, 741381059, 652355331, 300857269, 511742102, 245333041, 874780354, 358883510, 421558622, 154921053, 909647103, 379251750, 112948350, 275332583, 20261495, 648315402, 475794599, 72172620, 559996483, 267803103, 772042821, 503791142, 137152032, 808331643, 383253068, 329702180, 621861527, 865335763, 452284975, 94654169, 618503811, 600539069, 55019338, 9199585, 136976437, 890106114, 310509021, 469679665, 159245851, 16694420, 629914913, 814948333, 971679887, 156800207, 76389826, 837415856, 673454053, 257647030, 348447079, 998546970, 410983318, 824166951, 633453973, 134189369, 25951043, 119926895, 506605979, 303809204, 319210862, 731961940, 77263495, 515734132, 379863116, 725039007, 677975235, 375872688, 277141929, 487024445, 807825025, 938283193, 522931358, 166873324, 931124172, 384959464, 539283199, 21130792, 939075793, 162083306, 880348607, 702969219, 652259334, 433844700, 97877026, 845383503, 951601084, 532447415, 15701709, 102865367, 252512806, 507659276, 882532886, 204035579, 77223968, 85262455, 63685061, 476154358, 470234898, 493304517, 807253609, 556241519, 967245257, 737680086, 721755254, 564136978, 142648193, 570282230, 258185363, 259599759, 72808483, 769946502, 82164097, 842899924, 842779106, 772796744, 118151770, 603686263, 252483591, 573041396, 161608137, 891061865, 12148980, 3132992, 140153934, 676340648, 505103390, 713865228, 996057486, 964902015, 634694077, 645916121, 216463960, 998578644, 830907424, 484646154, 155650075, 149797316, 636027012, 628214476, 994922679, 943055928, 99032617, 741244721, 19112929, 401899545, 769559701, 570681216, 814791755, 418221227, 991632177, 711745191, 907463145, 814784181, 124718019, 359305435, 464489813, 355724391, 949943664, 610441245, 673124619, 169463948, 332533738, 105590575, 448351410, 378839252, 428155041, 506876306, 141115645, 327541578, 574136045, 856172002, 920387330, 39637288, 516386315, 721213185, 652253501, 949557497, 840886450, 988613749, 771684756, 607942710, 667222148, 651859707, 604403750, 948037901, 947439121, 702719523, 805211212, 469431128, 774465653, 431494590, 448654297, 257236322, 184014875, 861699969, 966924629, 515256098, 842143360, 10979407, 147869792, 266213963, 296984948, 830910586, 905008730, 679172113, 382214135, 364138373, 220335412, 772447657, 542742972, 460522524, 624460256, 224746692, 175879881, 722951998, 59430356, 471760728, 616405508, 657872798, 713757023, 416050428, 178772039, 452996443, 396761309, 624754636, 506835889, 198718057, 59568812, 180825111, 281811274, 512099533, 683569413, 132667282, 26694933, 206067911, 633028265, 975555803, 664834465, 859592919, 2092919, 988377135, 337358698, 490732997, 323898306, 282909677, 781941410, 560493898, 984775412, 244760483, 16950638, 249460451, 231669105, 665975801, 49711181, 648215497, 995118057, 106405882, 80192668, 442706891, 38913491, 657343114, 748576883, 317354035, 332293273, 40919614, 962218937, 160003371, 365499399, 546276713, 784804772, 879203035, 666009196, 383036546, 148085161, 498580742, 408158912, 100542125, 919615166, 699074192, 335238095, 938571496, 954245333, 16797974, 672948892, 566360057, 966243698, 231397941, 6841622, 307927711, 526622671, 108107125, 561470341, 827664373, 43745898, 910488158, 517183776, 352309669, 524712287, 131894282, 891368910, 797843497, 500722744, 475223692, 385622953, 113373146, 544758096, 89449256, 580124250, 903211032, 336761014, 925988394, 632132359, 920786780, 781487612, 695940963, 283055038, 274613142, 819434512, 679286066, 161014099, 869344106, 980391205, 565688282, 763566690, 552714879, 285772718, 980667010, 681682390, 980403014, 201873071, 156527312, 485843912, 474032276, 534755443, 982246948, 688358366, 653158331, 951310587, 824437726, 339752512, 197481138, 571238134, 831793252, 920368751, 464088550, 10044520, 575646634, 458562328, 2463168, 922642254, 53118944, 569780729, 226505881, 273242521, 3747953, 488261998, 332244300, 923643392, 963781658, 35064071, 409295007, 737810338, 102829021, 477804603, 468587202, 94162050, 897494305, 483586061, 666918802, 774970022, 643861862, 908763928, 78940338, 147459273, 310421260, 781988236, 811372016, 221428736, 453275640, 354544005, 942270834, 767647119, 672599557, 740840205, 771038670, 760401275, 519097686, 757511930, 355120760, 169456949, 693602823, 230484995, 412436124, 581745292, 157234485, 717038671, 204482390, 54310059, 295898021, 23542459, 854638491, 256245636, 710810834, 24062096, 38406881, 572598651, 315411401, 326035697, 433413938, 6934338, 258213164, 319822325, 805776355, 469702886, 183621607, 588613059, 22872772, 973202594, 426259034, 249416213, 598104853, 811778909, 752053666, 874860909, 995191255, 717223639, 74003888, 191646178, 649017213, 147743350, 712568738, 102755377, 89297589, 748701590, 78485848, 268012485, 427136352, 10768067, 130858380, 70575757, 12759554, 676485131, 528920732, 546619471, 647035637, 73009510, 430623900, 440901304, 563840660, 263105867, 762366571, 372282300, 744282613, 614712730, 627970641, 144974754, 915829522, 708251194, 296966673, 99682665, 559879529, 900728319, 665495880, 679216189, 132753726, 596146911, 302519734, 129133811, 208336943, 545696878, 334708524, 982427984, 326869079, 434592937, 458486353, 395707077, 238885676, 375230382, 974502180, 387226914, 631420781, 641489697, 207986154, 891528722, 228929079, 481455946, 946817086, 861215048, 889110188, 657470669, 653865456, 895804587, 981930787, 326255366, 28509411, 921887237, 187498572, 453926427, 235801906, 430316652, 410661488, 443048691, 156257064, 558192262, 326669244, 32006769, 758405829, 867047520, 698148327, 350024993, 395065382, 420696878, 90262026, 754398689, 316388702, 241681320, 606340730, 30563290, 121030958, 385443014, 76722806, 550854881, 357772907, 787539405, 930114797, 74235013, 53828148, 982292997, 904269365, 414214512, 606592673, 897700268, 618921090, 302979222, 93922354, 738106922, 790387865, 948623582, 267362248, 583310450, 770022364, 787796485, 235283489, 693130416, 738982517, 660944922, 328974591, 71121356, 322403720, 884364535, 63433428, 800819319, 504665681, 210672182, 450478704, 60958641, 885611293, 149546624, 775730397, 729602160, 782174638, 640673740, 920798543, 773104281, 658041104, 516131797, 145395563, 534300267, 91876666, 70740999, 65624868, 208205280, 584970717, 916520998, 432502864, 443120508, 227465431, 704409253, 602984463, 891944368, 862988358, 170540466, 969861920, 482270336, 791079692, 577119380, 908918704, 32082250, 641875440, 163527046, 679966980, 11763937, 640754868, 8258014, 498129533, 939304914, 420778900, 204482935, 361760433, 915698657, 447110693, 90005292, 151049943, 435081578, 834868844, 873093574, 288936286, 712945673, 348642412, 875713234, 99614747, 232462595, 524682314, 562103172, 876989413, 483269550, 999609699, 169830031, 713117376, 965697637, 20239571, 225758166, 903535883, 374079828, 253771625, 868818423, 541339087, 46942653, 409357230, 511376734, 691245812, 464279741, 514069645, 118678563, 158598711, 805950994, 139679048, 760245860, 444183, 821571781, 219788733, 775170490, 147018538, 456500815, 781400660, 278765722, 242784448, 529240759, 459762610, 87328849, 679979825, 106538133, 542046588, 74758521, 82653175, 154020037, 814313796, 885728863, 134250889, 400707306, 69012541, 740725445, 787215384, 324255418, 831269772, 350551019, 477333973, 976371196, 231444016, 665401895, 424003476, 73778677, 958532511, 623713776, 282379763, 488844712, 276865665, 828406296, 506177294, 394668715, 451148759, 794754040, 204641626, 683690922, 890962714, 744664964, 428532173, 615962344, 872583214, 182244238, 644692567, 504545728, 287676979, 463729129, 620048412, 692410111, 447092074, 931046600, 505715250, 41907491, 563274602, 845146003, 628171043, 328578123, 864180832, 618099785, 730264251, 814607000, 165853774, 185436173, 609533906, 692707255, 270736675, 29019359, 435497882, 655967911, 710672006, 616077275, 220730677, 377535116, 267627227, 611374490, 474087001, 790284767, 845225066, 923038372, 829463259, 204426960, 351569485, 947564201, 501920111, 961835301, 985051472, 580124237, 711637807, 843961731, 113936248, 933526727, 784190617, 905871788, 693592011, 941243778, 837510101, 844216780, 706794313, 920401188, 889083302, 64026971, 161670171, 601006344, 310648226, 260226635, 946882589, 520040788, 265202141, 464470970, 123445432, 94596385, 473632843, 198772038, 821681351, 226512127, 54151318, 650840644, 319756097, 681926872, 238441518, 461600469, 670269757, 964985891, 91173576, 19815433, 134526539, 916019356, 791709371, 911131257, 852095026, 432154215, 18795776, 36765767, 903941066, 230782634, 14485278, 685462709, 413231623, 157360440, 904202745, 185339885, 300384331, 178325625, 704937606, 306416028, 646681345, 712835004, 917761156, 360832415, 361813304, 332146855, 227320892, 987308335, 176353816, 841033537, 202971603, 33988533, 153988220, 742770943, 987901658, 512476690, 762345161, 517741626, 402708342, 327408797, 840568507, 935057889, 723913172, 665137809, 296724441, 711676104, 534899259, 245269356, 20466150, 837188529, 101027265, 787885177, 223006481, 959673520, 738606173, 206608367, 855973134, 204024839, 449220299, 249312034, 984953386, 194468865, 605319418, 652639866, 705031148, 436366908, 939401348, 976133584, 499780581, 325993926, 302626630, 508915681, 730245254, 10855096, 117564498, 358028272, 65706377, 733195896, 813052643, 179023695, 244898547, 510371782, 133176351, 646003779, 383461411, 477177968, 78971816, 198720150, 723935961, 256004754, 464702135, 612381065, 877696164, 224273695, 259840265, 789471016, 802730620, 304231569, 206873051, 428027609, 539339670, 532659459, 200447979, 163913108, 95999872, 880665755, 335611471, 556822603, 943446432, 845876775, 410743986, 277799891, 673275401, 353006731, 128073372, 571214183, 296219002, 267368169, 651799078, 760948274, 29918579, 117789741, 349610255, 918851194, 116903705, 920063679, 69430973, 882052704, 204207097, 672257556, 981661706, 57883684, 658150236, 348021039, 231074407, 209496169, 984693675, 907514560, 351813812, 583020688, 85715072, 762339238, 84021212, 198036193, 562143209, 296317778, 430470388, 60097471, 500004535, 350546737, 153843844, 5162870, 929602912, 497762452, 925812926, 854868191, 192153749, 504747170, 217711973, 458172402, 225778221, 595407557, 380260469, 596617299, 745432459, 795486718, 839075978, 156300902, 693333394, 381997715, 63374101, 94279717, 174366963, 310625195, 173889480, 854767337, 594229641, 243882919, 56748180, 672541334, 691896907, 21508322, 703407706, 752606219, 44475923, 872870919, 95680161, 785717086, 646556049, 503372333, 670494213, 223624782, 641547364, 846116001, 895362711, 129198008, 56494186, 93321223, 979766843, 779811242, 762698193, 206205300, 254698645, 995826742, 828901204, 164014293, 602798096, 684485452, 676241545, 375566612, 13741541, 533461482, 590781961, 746192714, 38570482, 626886055, 468401313, 216253320, 499658690, 411173234, 452885947, 833255196, 476103436, 857759466, 480324297, 672518813, 954279774, 575508521, 450234252, 686310950, 434630947, 449604567, 817410996, 391036102, 746577379, 735404594, 432329065, 722353206, 448231107, 426881862, 422013430, 648170724, 879372482, 540423409, 398686392, 414654241, 950490915, 350800691, 660528578, 623052166, 393852759, 655815078, 725383636, 606891047, 372821736, 127095834, 103745670, 817693365, 968030415, 869044305, 717288729, 339611649, 580584959, 266309627, 850433717, 575832531, 19909616, 889215460, 706783942, 874382670, 83631618, 376455699, 756829362, 701685073, 45860067, 702544542, 697943443, 537133654, 77559212, 245625181, 986532722, 809868992, 727421633, 176925806, 754086282, 726594002, 454140940, 416974818, 408023045, 460772075, 615198392, 533361006, 518140758, 17144931, 802365626, 923449252, 532920938, 376298069, 493486392, 757683207, 872120739, 880557660, 806614015, 87577539, 655270983, 772832340, 806752711, 616473969, 541966185, 803674710, 671260847, 31806718, 977599834, 718115430, 117741410, 310634690, 31260465, 220794242, 323699294, 606299787, 12451463, 349642080, 225627172, 494224432, 995920593, 578570587, 541325730, 607006767, 942873136, 653777872, 764898245, 685301382, 468595858, 296465279, 738742491, 256866872, 234632488, 518772213, 727059795, 36048654, 837263275, 672234638, 583537796, 284538590, 209736878, 907655008, 536930828, 463796715, 392898656, 143286259, 512161555, 164505205, 299654308, 629099174, 39025237, 599162100, 813765034, 632109916, 457490633, 637688106, 791386669, 515111128, 87091655, 581644586, 521555587, 928281895, 499276459, 671372076, 360940216, 904319375, 266275316, 162491200, 449754561, 90386962, 175878599, 62532370, 156718875, 138869011, 704796982, 161565104, 897513235, 360018352, 736621532, 925648584, 398970764, 343034136, 228124188, 695975888, 653920606, 723928403, 545179233, 354943304, 96899462, 539161102, 76774562, 848155736, 824009099, 79042692, 605125323, 387670201, 770161055, 848359847, 794200275, 151035011, 543079422, 827583484, 605813526, 54926168, 379125994, 452726874, 674643433, 235799421, 521388105, 892991124, 628571215, 491215354, 558070874, 37488656, 11434335, 642178394, 733636153, 835571704, 177179527, 545295526, 109193016, 597510512, 819786166, 783729396, 394110241, 398122918, 157315047, 233351415, 156759936, 198591553, 90696858, 523593450, 533590771, 744433408, 425612365, 464613551, 231680588, 965910490, 647234837, 106042149, 828299354, 522111046, 2469940, 283653736, 433036686, 817726229, 869896847, 568112837, 785459532, 346845126, 15397926, 486446761, 697112012, 467822622, 695222925, 585246468, 962983570, 733453084, 743365278, 213458637, 573508129, 65616807, 795717057, 622252640, 160650977, 656256515, 408703293, 313392453, 778351653, 250667734, 822549377, 16530247, 467378349, 774888868, 158360708, 479412723, 971818131, 593703772, 46291126, 2558779, 3228184, 978471398, 530339957, 920829925, 35017471, 256630908, 52704956, 883690039, 583368899, 453523934, 846408854, 197217373, 853452421, 810141282, 441347032, 756168543, 31154015, 211944515, 156415743, 733046031, 566943074, 102320811, 234990582, 585471199, 95836413, 143442908, 429799179, 541590241, 9669593, 241286746, 507735921, 311941628, 503881128, 941084556, 293879435, 761661097, 664112573, 846038725, 301889514, 714610667, 898731997, 897206231, 246280890, 975055014, 205101102, 621911861, 175845448, 145828544, 78377609, 279771640, 792452251, 564075561, 448884020, 414466901, 312765262, 583203850, 734998825, 29477951, 134146871, 513988661, 866806726, 769587021, 695975301, 874303028, 23668097, 186419191, 347309189, 598347435, 538736184, 192090556, 360378836, 91337668, 601013277, 741518938, 505414431, 381489917, 804808785, 127411285, 394917322, 430194671, 799681715, 290507930, 143013368, 133732367, 8181551, 123280320, 32820614, 454525438, 532904873, 872354131, 546122045, 61803641, 369154955, 692841022, 400483069, 976854131, 728122161, 754083376, 349250425, 482583982, 988201272, 760387406, 88113192, 619484530, 883445421, 348770543, 888627075, 181550778, 564271207, 421721432, 399162427, 826214130, 129036003, 69710486, 972277669, 862450297, 855630877, 602973476, 572368955, 270146316, 880407106, 739145102, 619815685, 325005011, 503950437, 506447594, 983446286, 298549562, 899168486, 382286278, 900748382, 345708495, 357798383, 777728590, 17108229, 583820289, 474900826, 93968957, 308974662, 248902693, 545398954, 34478476, 886520842, 686565172, 740473189, 237073353, 795289459, 26960251, 807461566, 482631557, 858100702, 22324038, 924198463, 934759844, 478106299, 473122790, 158057599, 296891234, 125952218, 887875777, 633403511, 717867609, 792215481, 82940337, 484384971, 451417431, 640020668, 293157053, 360099952, 979271387, 80279947, 712171932, 299883613, 81220602, 445998107, 880634770, 547820208, 879656103, 500428543, 939192689, 193106141, 750026716, 56125957, 534500560, 615359392, 948553787, 738719150, 691833572, 749926490, 133969289, 159939301, 106604119, 285729824, 701872110, 597122627, 62325443, 303301146, 592718344, 6744491, 985816055, 113618367, 524537496, 781468138, 896823381, 292838920, 374419958, 471555855, 677886680, 459131942, 219778735, 883291579, 446899661, 638798411, 445158339, 267090132, 851736777, 393093579, 864275650, 706520854, 526803940, 563112259, 265327338, 318871059, 241461398, 582044374, 69015060, 994804516, 301278941, 777151024, 381024395, 340263783, 525235406, 636680333, 636886117, 934518113, 137186923, 49900761, 79317545, 363070987, 736017769, 541669152, 834549908, 655634101, 43689533, 488556352, 846661743, 581610257, 492440007, 259656371, 69687482, 244222736, 493752527, 871115665, 357508250, 461142929, 129731047, 348124999, 768318297, 969663737, 533803618, 824244744, 738672072, 162024191, 732465172, 977647920, 161270837, 353385850, 876252026, 726037822, 40391381, 706436649, 940593782, 555213490, 226617543, 492787311, 500362154, 915133167, 33728553, 971822948, 668278397, 760978683, 132768472, 299903243, 238323055, 318478598, 286745300, 485430946, 717954039, 892421576, 570264864, 558757904, 338452072, 463029786, 675810341, 391340686, 21656789, 834333949, 941586056, 843434526, 641223367, 875950660, 389079973, 404152651, 375326771, 729484622, 688349326, 913192695, 80685989, 56765421, 860292112, 304016101, 553108086, 892240581, 673239024, 172609026, 74033588, 612904827, 180467526, 606685997, 886978836, 958757568, 456054058, 681436707, 244410377, 484070934, 449349627, 402286284, 680104516, 623921198, 49763657, 684860217, 17865000, 368019477, 740884351, 79585503, 344869439, 274375640, 588836884, 194688716, 354825530, 630903398, 247498336, 690326432, 184849708, 771651982, 761705307, 353227566, 809911976, 574097937, 179178601, 959062006, 990206177, 267717471, 320646780, 848047033, 574950047, 286567244, 832678160, 898742207, 718194247, 207440483, 998583962, 296380298, 987324494, 47726452, 945634488, 474498761, 228863936, 782777129, 542556405, 224856954, 251988130, 400348212, 227200346, 588745512, 365259745, 946189068, 918268223, 970097944, 545085833, 586490744, 662118266, 463206184, 791398510, 108833047, 981073050, 387511522, 243348159, 919442465, 614270806, 325816923, 856367979, 205023916, 488517693, 856005978, 323394994, 569334202, 979325140, 978519092, 391915458, 761701549, 7317908, 134255887, 235332414, 991334722, 918060120, 696949913, 633509854, 949030564, 896937961, 3072426, 527994237, 861012625, 849867528, 221276797, 700831049, 69813203, 924740282, 449739409, 123762709, 687433664, 566014931, 132428474, 785267444, 884320381, 218308376, 998518791, 210202194, 48144614, 388100773, 567449814, 398337394, 575923164, 834187212, 314041857, 85100080, 136970524, 112671441, 995405516, 788909937, 231029797, 951629087, 831733892, 102802741, 749977653, 1117214, 567823917, 468355617, 961704816, 706498861, 565089136, 160811356, 981174472, 278867507, 107181784, 254161462, 330571095, 818422061, 131914777, 354429468, 805668349, 853357855, 839401858, 225167305, 166782432, 998406030, 881252802, 57177963, 861986599, 141253215, 8015602, 937280598, 817875775, 360842600, 88132222, 930975881, 289053227, 769428708, 740697874, 709287585, 132397315, 896105718, 677612343, 679691478, 155892471, 980791118, 228498798, 450687830, 751619101, 521951615, 483092269, 954460478, 111264109, 889680184, 967751960, 238958053, 577575187, 23685008, 940063529, 237573213, 444408211, 646341739, 501254755, 118016000, 665196896, 254361607, 826008236, 130537092, 30617564, 704621590, 94070945, 612769975, 437896635, 272958949, 378672941, 551413092, 747391335, 788355116, 747109824, 332543117, 904883656, 538643515, 42778332, 611432435, 169994279, 979035204, 878764784, 879473977, 571059375, 329657200, 952712757, 287731052, 74867181, 512458274, 107972316, 159191484, 228091854, 710924495, 242627319, 993606189, 265039965, 850807780, 62933954, 932664845, 574330321, 463718211, 990516275, 935102163, 824790405, 311616201, 788107165, 404914161, 893405147, 159474655, 659763679, 195337605, 509318030, 309894317, 851487609, 669670726, 439161718, 691024134, 163051202, 489366260, 980804984, 768013979, 701743824, 855043125, 952533963, 153842557, 684426219, 72471576, 773272209, 404157363, 166135784, 596856531, 929363057, 793834811, 897485147, 952914932, 187334321, 733832579, 668272672, 106182340, 583150851, 138328754, 305759748, 566642741, 730556549, 509351483, 803254536, 220578456, 341377858, 453167665, 971297743, 400840472, 746940340, 482857653, 290055497, 927067145, 81157907, 477214334, 171703950, 329168519, 944653665, 669645412, 532415318, 363582766, 788587703, 644206213, 36107871, 515154681, 100602372, 396889730, 133669903, 61923040, 568057788, 69602192, 880904659, 482362943, 571670956, 739667709, 215172563, 771915180, 15622173, 464165959, 317955376, 978351080, 347862425, 435897468, 382268707, 490269231, 634460800, 28019778, 832279348, 299911338, 632768139, 156303520, 462148974, 658416121, 68529168, 695482069, 276327205, 167604013, 184952202, 897966389, 774325815, 520643202, 154931996, 138568481, 685963546, 310674812, 360608209, 326759696, 798400676, 836943916, 831217555, 641203505, 467703036, 746795325, 782430403, 320139072, 235599787, 521206309, 793342272, 420703806, 368103478, 156481047, 478501687, 334856688, 695734792, 914355492, 835733377, 250601256, 706667716, 888505801, 777556331, 55153110, 654767896, 768877266, 864538283, 510812069, 758206537, 360476091, 239184741, 668102428, 434414460, 531378825, 698589528, 661223436, 118397733, 512597367, 530726269, 309866029, 666845349, 427191538, 569679518, 910634891, 677907206, 1353047, 356816655, 12170654, 105820036, 717906969, 676210436, 699077655, 266172784, 834858361, 200569310, 134109523, 876431465, 189159732, 573629775, 811192688, 621158633, 800946173, 989345722, 40084964, 986280267, 316004723, 55277116, 810687020, 156407661, 885776864, 503288117, 989104387, 114502761, 981683157, 571368354, 122556604, 525448723, 472735322, 944647190, 650762279, 18316721, 201609956, 781584321, 37503642, 34721467, 707984845, 325667144, 353819276, 564366453, 966004294, 537952324, 417677685, 88564418, 960896863, 78219662, 296181568, 576405235, 440089300, 817556677, 239606243, 844934758, 181770281, 943975393, 179344178, 961131817, 681095930, 170040171, 364545678, 148639265, 833310415, 491481732, 998650741, 288485065, 870725293, 288095598, 167449433, 376563971, 292880715, 395466594, 614134383, 132134549, 541380166, 124873559, 684949737, 327982407, 415626210, 306952272, 382618251, 882396515, 176655992, 537873331, 273118588, 219022107, 702516166, 431635185, 690169978, 642759211, 414957550, 699648235, 488116276, 457797100, 290318995, 521743592, 483675035, 280172905, 71581430, 517590201, 253135660, 596239547, 928454188, 768528509, 237342074, 269109689, 81692367, 162524064, 933879764, 481734900, 785767693, 378712802, 976565252, 30726929, 342574464, 210279903, 880643208, 401721512, 708335086, 677947954, 856958228, 291363410, 844420955, 545720364, 958004021, 543849623, 431070505, 11408528, 587155159, 627223100, 941719836, 589169004, 395903031, 816883159, 898154390, 765049873, 455117068, 609918090, 317936732, 675485794, 294008353, 337832830, 16332535, 390006550, 890492137, 649310098, 941593342, 909640943, 456533246, 13524209, 518842673, 188237039, 362462282, 544312878, 863270727, 862516644, 590993450, 706563399, 868082289, 675349860, 176589952, 863454767, 471727462, 636001388, 757707612, 418517216, 552814977, 701084988, 579901691, 1657188, 375653121, 388336640, 901988186, 271811990, 255799313, 238419681, 976119911, 638921731, 14565447, 476372879, 814275530, 456213660, 802057810, 565899079, 942061687, 18026508, 30012548, 7616092, 385642768, 74753039, 963422517, 162570061, 889667136, 982132217, 272585372, 488785112, 658076780, 916292889, 242289142, 444842515, 892462148, 209959286, 727433864, 414004504, 8512523, 418141306, 153074839, 445674399, 817329023, 847887231, 72970020, 393097587, 16222175, 619462409, 510363825, 455375158, 676932399, 730809251, 531026065, 82447576, 996431185, 441880526, 871831954, 50018250, 126408566, 28162193, 167093290, 710409230, 568802278, 676572418, 395799696, 30700446, 975700260, 689021265, 288839718, 376652836, 539649829, 548655468, 715634756, 709136707, 771522628, 895261236, 78750778, 666029298, 22164963, 619921957, 91010246, 237592109, 377579635, 804094879, 984764683, 251609394, 408639500, 168435455, 566841799, 280864452, 515448934, 43035610, 594516496, 50656945, 721157675, 437881285, 958439999, 433941986, 392227925, 624490385, 534906661, 513069413, 587412894, 993452444, 925228805, 106473241, 613982284, 880655731, 628270250, 989812015, 798696341, 757860605, 793879892, 7492385, 349080525, 621229026, 130035162, 241601699, 927952119, 883773772, 544088049, 299779606, 537745145, 151795170, 80196093, 848393464, 276594882, 823772600, 45762979, 633826077, 415582216, 36788505, 939323917, 179629240, 874523852, 351996216, 291817691, 302334683, 581878483, 739569579, 180999125, 935808360, 981062909, 57446029, 226756825, 724458242, 966214363, 749799704, 714529170, 584735379, 640938149, 607588359, 469490237, 161174359, 387547639, 256846636, 339801875, 489192617, 814169214, 636429426, 941092022, 482128443, 826514248, 114294458, 775053648, 907828094, 117157503, 707547334, 359456109, 661522131, 529693990, 333426869, 317335569, 820471850, 691543020, 464468813, 231031143, 309063955, 295910171, 943400615, 570924218, 166020375, 243176684, 870178670, 133039349, 789596782, 803325052, 550343882, 706852511, 413126365, 632653582, 678818396, 891721080, 883072010, 616145086, 992996560, 539541052, 331201217, 792080153, 787966396, 679568340, 749211753, 947881643, 604652055, 480974040, 504113582, 431494716, 813078200, 935555300, 940315135, 727166638, 757088521, 660567844, 910999608, 565643350, 961945360, 289464253, 849551674, 359850088, 652739145, 370494472, 654253493, 968423503, 53779160, 321566851, 939443906, 985565154, 811128748, 270047557, 433256792, 106808350, 366209971, 857275671, 666322881, 99237376, 792884797, 406768440, 90783719, 965204751, 519675024, 181153463, 107105426, 92239694, 428410640, 883135127, 315533361, 56814583, 138112039, 443616238, 480018993, 878332899, 649635881, 58249294, 237455521, 245029057, 135478917, 47471195, 904905360, 103112590, 564009463, 524346087, 768890894, 867444058, 196280733, 566893493, 603892522, 901450379, 512504061, 750033590, 358629892, 780891769, 120275273, 260321229, 698499500, 33290807, 105395915, 515706441, 529578953, 713094272, 826700746, 962382009, 442788772, 367902793, 591730369, 707569869, 215229806, 300506507, 818200955, 230537364, 32141207, 541083843, 266089531, 116914158, 575623823, 442808438, 482960501, 197150512, 27323596, 549768515, 142160762, 818657669, 89502517, 532608560, 210805743, 686334450, 990940555, 402336223, 660081294, 281485435, 908603095, 339887374, 455647316, 359968292, 361243919, 486154734, 628614921, 102963475, 987537865, 153636456, 875650457, 540119006, 928207135, 471852502, 606915555, 230370312, 338737999, 466617988, 633855192, 611335239, 873579202, 975986278, 798155897, 176277888, 63347062, 516514153, 87463239, 295666810, 194706100, 425253384, 848477143, 922581045, 993090519, 293926533, 192007018, 875367840, 96188932, 181222246, 68648957, 513705774, 700423436, 580288714, 799875265, 751092257, 31361802, 732259752, 486701122, 22060856, 120733592, 373839697, 993415521, 303097028, 712122173, 641724796, 540421856, 345661285, 909112592, 213368079, 201577626, 111635810, 29574019, 781723274, 885043482, 389647485, 759008276, 856600109, 44386974, 676535525, 96880054, 713573080, 364200365, 432955395, 988106045, 198798314, 996122219, 715294196, 108453506, 137531542, 481839910, 753644315, 62117585, 238889327, 425084964, 771147250, 535138197, 152252751, 811582366, 822381568, 903012588, 348304745, 436787079, 818265690, 580718791, 933181979, 312663881, 899661324, 919012158, 104193774, 217424310, 674702425, 243239248, 667548350, 721117435, 477189979, 627792528, 851895739, 880780400, 568862894, 580416463, 647628214, 975787460, 183476244, 258651403, 19875284, 512211074, 290372411, 716058700, 849803107, 494690368, 30970634, 513257249, 215524131, 787500294, 425215919, 949518730, 105953907, 23137188, 561536791, 724153002, 575379348, 622735652, 8002363, 657438093, 893818636, 523353333, 798426396, 300080924, 945009196, 977173311, 406954176, 219429825, 313621544, 112385730, 32554711, 992034844, 737978755, 497009041, 859816036, 520423280, 896401840, 238961591, 640662030, 945271521, 646947271, 296325082, 401380731, 148597473, 210964288, 568305145, 790296591, 968869725, 828713031, 544826190, 401155681, 658575659, 933435793, 151592780, 910160919, 291729351, 37627663, 60394241, 758928351, 963958128, 688406179, 630003799, 292120275, 961987590, 780011689, 149420699, 70508778, 151170219, 251691212, 497030316, 817212177, 848586395, 378530675, 161500872, 925851616, 301156659, 682492689, 393283465, 293072395, 593062264, 832976577, 830126687, 694413773, 387315572, 189069478, 834140019, 909331535, 912433663, 823682875, 219238203, 959412534, 244878429, 180814329, 513897313, 459032545, 15474310, 290536038, 951495861, 815051933, 690230564, 43271729, 170240404, 729938476, 278364788, 557125204, 323060300, 3408960, 738426466, 605672759, 115318261, 420332948, 221705021, 112705091, 35282615, 323106684, 750193017, 643531883, 220117998, 16176953, 883305015, 289718864, 211636765, 359772645, 625126319, 501887634, 559252266, 927815796, 550980093, 100629283, 540717079, 95924642, 589675445, 596585536, 70303784, 824564124, 465688997, 400500665, 381167249, 331617975, 410285032, 256160174, 160554478, 933246785, 622274762, 793400961, 120049546, 167771467, 454951962, 609050902, 839733263, 697050474, 25300849, 992892849, 999313956, 447855688, 587492879, 559589683, 364565575, 751333643, 49914274, 834142560, 159075775, 500939772, 548686970, 65832371, 367654627, 37696907, 976830166, 379134519, 519476863, 946748180, 534776218, 855771030, 921687030, 22201687, 865872768, 710851841, 925234304, 860286128, 174111606, 229261374, 41209901, 6178635, 309642676, 992024715, 294714155, 538602426, 195672691, 150769986, 455960147, 930663702, 646707292, 482150906, 639720370, 975169846, 163825658, 616468153, 397363126, 417962549, 377053510, 91109704, 71019740, 374398639, 610962604, 70816934, 416227388, 601890309, 680665673, 984941452, 602530397, 456023575, 67148831, 907307001, 852763935, 193776358, 338021445, 988224853, 996004752, 103525552, 718953861, 693578576, 887087224, 456900770, 810093553, 736983622, 303857749, 436250712, 363792188, 871889533, 387285266, 7777518, 371393610, 761538749, 291742070, 536653956, 980296166, 80239158, 334071385, 636033044, 390730923, 49362564, 122382823, 294775472, 841966700, 602366772, 625323120, 821097218, 998900132, 813445637, 152698458, 198782494, 802787696, 612682549, 122249717, 422739745, 43786716, 716489887, 932233963, 320232251, 947532398, 105064326, 537013871, 803845880, 648777857, 720023084, 377738458, 297868125, 308794386, 383709053, 952839378, 159384982, 116794368, 355315547, 348752175, 896983097, 821370765, 3784808, 733885916, 214792102, 910698225, 674303649, 672362452, 434154159, 453999252, 424589265, 109528737, 420834920, 692767295, 757282418, 425683478, 554323792, 708422076, 196885550, 268884053, 316900091, 169539609, 547331447, 594569026, 636608586, 174917861, 967501482, 125318250, 416396636, 394964459, 90986633, 483666125, 496373247, 888095511, 109979007, 357283255, 421661131, 760269030, 190842563, 562954767, 919940832, 421097497, 63773814, 622026111, 179865880, 928893181, 951684043, 775311716, 682300438, 773160911, 402738977, 105222257, 26548885, 235943130, 545475664, 135600213, 91550808, 613855, 812106429, 796933038, 566657205, 814211623, 152315147, 41156437, 408612413, 456315162, 906230924, 176170508, 915998444, 225974809, 519810622, 903089250, 451002814, 492252300, 78941172, 618398976, 288163103, 921199248, 917163621, 538280150, 965010093, 968576760, 242440302, 705593839, 944678008, 26296029, 87899320, 785609157, 997216269, 620658665, 785436748, 30635577, 907298350, 976338500, 789216033, 534631831, 121707133, 621890833, 174297568, 927631386, 226762738, 105292699, 228603250, 419698591, 882865225, 899710501, 627547781, 486694638, 821973500, 391653378, 726591058, 529119713, 485383406, 559102127, 399627398, 244142219, 673947199, 901758617, 713062407, 823075020, 455091625, 834052821, 541694138, 588488732, 473817183, 783349167, 871909633, 9571279, 969133532, 929913573, 499940456, 546333121, 823917435, 420388000, 841240144, 19565454, 605001346, 767293813, 851434475, 9453559, 748750941, 861445748, 703011773, 34488766, 460902152, 261215764, 784602513, 597900415, 419654787, 128875984, 160131590, 717712377, 56220589, 336078316, 593180566, 380032776, 495254473, 34031030, 869296805, 595805085, 400311494, 329073877, 837014305, 26415242, 135563303, 180711741, 398408180, 58104009, 325694104, 207974761, 436312005, 258769252, 859393177, 516932521, 193706325, 574763339, 694906510, 191037349, 660777544, 933224382, 659440571, 333093695, 710328286, 894602657, 511055460, 504469738, 742362820, 206877476, 197983682, 597177387, 289996409, 131786151, 911059318, 127856666, 804534936, 767586021, 164356394, 273983566, 174872921, 510723647, 592915933, 720454856, 111699111, 540308073, 573349462, 729916880, 141422586, 721229118, 987554466, 531981885, 791888374, 382081083, 750920223, 424572571, 261493165, 515142511, 942729810, 979818030, 757030121, 19701367, 999354683, 187967299, 382527809, 225644678, 13692285, 461452553, 618315205, 667946139, 975373265, 22569379, 263683376, 973100361, 844899495, 893683432, 266026407, 19899580, 212785691, 204904722, 909252856, 201106623, 851100174, 327518484, 87487074, 720687907, 895918813, 389206705, 366568068, 304934860, 16829079, 810509866, 937305323, 746331024, 310762423, 214872398, 209104580, 196262441, 410779262, 566117950, 336789814, 517413850, 737626109, 971300575, 523823386, 98599637, 949612225, 393533198, 132013638, 362812488, 428941294, 385050704, 890924810, 700041411, 317267765, 393381875, 273954056, 393047128, 706617234, 941440214, 137713000, 955986814, 217590386, 179682768, 82252365, 650826015, 225263170, 840691803, 495679928, 193577970, 255361643, 892021169, 923386873, 762090147, 912857627, 934867514, 843550769, 754516061, 564366842, 266873677, 120551078, 391500180, 789372143, 488879848, 234778957, 472328396, 444013222, 157562691, 295563766, 145127422, 539865128, 735236176, 325407597, 836757965, 602321970, 751153493, 653443633, 754205890, 361355359, 374397477, 474533339, 91547556, 721900733, 47293697, 188805118, 175153161, 594463271, 94889160, 245755311, 401103166, 862934641, 123226825, 205177353, 298761428, 138225830, 50287135, 446530577, 788930187, 888648625, 341961655, 91455938, 454292192, 196186771, 170257127, 803962441, 83314645, 734483576, 589069268, 434161352, 583284721, 830469751, 40260858, 492512329, 238438721, 656988421, 292048821, 146285058, 664637663, 92545315, 679213501, 229051694, 957321480, 982631174, 925208831, 271512500, 523932260, 94069570, 897408191, 616698973, 182595132, 416153850, 265457690, 921327746, 378630280, 368371961, 834901900, 935830607, 101437912, 603468588, 437119400, 972072106, 4293052, 577491523, 671178374, 425484301, 544359538, 539463524, 386494403, 432006199, 850802308, 815576277, 70944196, 776793504, 127133956, 231679397, 458693319, 69232014, 646197188, 745190017, 593621002, 543875909, 553607170, 241184105, 7574210, 12649035, 486540634, 804409384, 117414845, 87727512, 303950562, 757290060, 356234318, 949480864, 631981937, 969035737, 584737430, 445935375, 450243227, 982338537, 853145588, 37696692, 884062650, 708987973, 399179763, 436303405, 79423889, 654373527, 143944884, 489891385, 119980270, 503335954, 23282136, 375781591, 45128008, 820025737, 820027669, 939242258, 972039090, 349180897, 537771654, 372022189, 216841522, 738588817, 831069965, 657639468, 234632059, 925889962, 861629584, 71271112, 429345742, 664070004, 691878380, 737691706, 157704079, 513109455, 605382893, 834032802, 747228818, 357885502, 328187276, 618868006, 48868652, 754050745, 831580162, 397204041, 180762015, 514330405, 23763580, 996520820, 170854224, 868456143, 926294048, 52948941, 773725795, 232798967, 597019274, 765525423, 663085701, 31341860, 914619380, 80633296, 117359842, 765510442, 75009314, 968130411, 811859777, 9201382, 542789848, 336823988, 972416534, 403938119, 502826142, 692923313, 59307404, 624895466, 550841016, 893293828, 268776634, 429271238, 102176989, 340694694, 977618186, 614126917, 551004741, 968360746, 135048096, 831711390, 213193783, 578807921, 363759187, 949757445, 985948364, 316520942, 569884202, 586004003, 377368532, 308323562, 584422845, 383104707, 970673962, 720346370, 461627482, 54936076, 480713241, 999703691, 143373077, 153300944, 881944866, 568337532, 506054981, 61271871, 387000736, 145703661, 860295298, 999835690, 510615694, 76563435, 447348600, 542651107, 312504333, 476461471, 574513593, 537673229, 911313413, 739918496, 462071764, 364209847, 107377823, 362112061, 396234413, 954247802, 54893402, 249343232, 520234613, 966777782, 51759673, 947412900, 29423591, 176975187, 720867304, 945119953, 422419107, 149533811, 266308964, 968089487, 440480474, 710755509, 953642052, 389268144, 257131851, 564483486, 114528947, 768396179, 524324541, 984382919, 335503421, 46850093, 365742746, 731503795, 519001093, 553399948, 605267111, 71652307, 945129887, 703935223, 218518705, 804976348, 296231131, 66528468, 114108608, 539318565, 207316950, 613627424, 620219147, 113433563, 937283583, 416392401, 974731222, 159189201, 985324841, 812500684, 324245623, 609085459, 668202776, 66066614, 264281310, 495828046, 857558116, 863599912, 657346588, 746818425, 972151277, 976528831, 319309381, 931932019, 481440087, 472283044, 898698870, 17669710, 613529290, 279439819, 996179445, 476693561, 305643113, 538953106, 324070794, 385594448, 766583235, 248147907, 975984376, 412309986, 183880618, 250425263, 647370362, 633127652, 686323380, 661752677, 453813502, 64654642, 468987080, 233539897, 902976488, 359434182, 509884978, 843223323, 711455470, 246010004, 774174351, 131962624, 728871248, 72540501, 82868203, 730649883, 598563549, 751579824, 867000765, 288213956, 133682867, 9470412, 376984477, 934722240, 359928093, 71559917, 209806562, 66958133, 87167664, 811470411, 425187979, 355048349, 130116851, 80648277, 673636755, 715161457, 398586621, 591958173, 858919910, 662349493, 737734315, 537406078, 638873646, 714344856, 279960686, 550881399, 829617117, 474618016, 542005131, 588750483, 482274686, 754645711, 954494106, 632428228, 163590411, 83948525, 596189409, 351304613, 598078136, 546975281, 868303361, 131947622, 493623899, 520954018, 587752554, 496932600, 734199903, 16886643, 598146284, 278904507, 78816436, 934491006, 296249598, 150171923, 853175452, 55854347, 989469782, 577054733, 129291488, 227465155, 555177200, 906462762, 162224183, 269482008, 130412147, 211885050, 168862533, 51889106, 620270408, 503576354, 232482042, 361222834, 310341817, 260431350, 51464046, 342893030, 926111512, 546109431, 651573368, 29101600, 64119475, 849863149, 390107607, 456635217, 441258071, 784112276, 680917517, 249246950, 752763510, 718438880, 897407960, 765166555, 936037986, 833486183, 838460404, 967490533, 363859117, 419233314, 805519137, 722171177, 453534760, 927844976, 65987679, 794672750, 309627764, 588690968, 196045552, 848534308, 411713633, 561505038, 16037435, 456054443, 202611801, 500786060, 223133517, 805823459, 961248620, 18187503, 660489309, 842499027, 734430365, 824189968, 57866462, 381860410, 43218280, 944382062, 531548701, 670345410, 391036191, 443781716, 586349495, 583416095, 82889267, 116708340, 533126355, 697020802, 22022437, 7458104, 558422274, 126709934, 31421028, 766831422, 116089188, 697613468, 596494655, 981407553, 809250028, 319644579, 802719595, 887560018, 330852683, 545465175, 583290027, 318093246, 902466142, 282022854, 863812858, 216565239, 456368800, 891980124, 854393271, 992407700, 311850005, 838830312, 73840954, 595919312, 904701332, 644970715, 92038373, 768902538, 571847250, 974194827, 162576192, 498623217, 968379826, 759096323, 261368968, 482213634, 860971817, 371019433, 100663536, 610199004, 276802798, 917041128, 381062984, 950195767, 726049338, 886451591, 103900473, 362491735, 358392281, 165101235, 197827286, 638804388, 399714138, 916845126, 467731770, 453569183, 988093030, 276945325, 589187470, 320006638, 50705137, 501947987, 105661090, 917695865, 706058914, 500496391, 591650350, 451720252, 569665773, 86259026, 809639852, 862519815, 54809845, 87551005, 203183764, 655027807, 74696771, 394796445, 458721247, 11224217, 195893828, 232642138, 972514039, 590573004, 125767976, 3854875, 112542807, 461165146, 768105777, 167108202, 534350304, 81746573, 708397460, 765896163, 211769581, 379548951, 766291094, 859576056, 220634782, 481950927, 201047193, 906830070, 8920551, 159536625, 323796434, 701178082, 968277410, 158734162, 995274604, 985772351, 851754787, 677067486, 342501148, 427818736, 987233651, 346588298, 190247203, 200338169, 679510221, 888687573, 917865697, 866204750, 690559812, 265657660, 906518146, 418251138, 129887856, 35122017, 379297359, 567306290, 561226791, 829185296, 431506921, 595973792, 30367955, 794874337, 561740925, 814577055, 396592267, 214686118, 876107986, 149336141, 784608991, 883763092, 929563296, 18600289, 942975775, 926152448, 880742860, 168723244, 680029430, 115379128, 261888232, 919957012, 62622424, 726562426, 639651320, 198379926, 792661358, 378350899, 611083939, 876994827, 221788063, 991678869, 248491701, 505772123, 898863649, 140648934, 662661734, 379788546, 553465001, 531462977, 117827494, 222633928, 181607996, 406258422, 203955494, 45365876, 948706533, 114336646, 748745882, 854774114, 671449080, 255968560, 629891256, 981522539, 474419934, 283187877, 236674093, 817196739, 431493922, 791477226, 384645606, 571268470, 914896069, 70844146, 928229504, 811911038, 923530808, 107896933, 269791500, 262091862, 879418318, 996169887, 576682604, 990533756, 520414986, 4402877, 814800969, 788057177, 790506614, 646912151, 882778185, 907597905, 961634489, 502359443, 828438954, 495233243, 627704198, 133015727, 138904920, 759586314, 179806868, 988142163, 812321403, 456964577, 754160947, 65864228, 645227478, 524938879, 551309265, 823340630, 948807910, 288670696, 460686906, 922611282, 198731262, 204187301, 81322258, 510906694, 615889690, 810947002, 436058862, 599407431, 592491637, 990267795, 92693605, 461540960, 573024023, 888405528, 816527608, 585932129, 443944724, 572564443, 793571708, 132730973, 708514726, 113621602, 950836933, 884458968, 409473677, 538445758, 271151543, 851016209, 554961809, 231413480, 672791642, 191442804, 605411792, 626421475, 216106340, 595352205, 959268076, 550569565, 486314575, 111933674, 730581916, 659164685, 502546235, 567533237, 982475899, 301094228, 107546226, 4340079, 766860415, 844796830, 630350725, 357554218, 243012467, 988534448, 959997993, 229342974, 935849681, 803136006, 320885289, 111663027, 189206895, 204545863, 985833412, 331893995, 611813248, 606500868, 908688140, 520930866, 995278456, 715284226, 284102393, 548262152, 435234384, 157948656, 58135154, 606252018, 775978589, 528300451, 95102029, 924719734, 149423935, 568316249, 480239207, 533446461, 511804628, 516102828, 829905468, 216181961, 602447591, 954786080, 319141107, 773107943, 371699665, 827528933, 149326382, 863403554, 86643841, 272988086, 441035844, 727985690, 11767993, 531226227, 244468916, 959038750, 780168238, 7662979, 245815814, 407673508, 325400665, 904051112, 681124225, 109036733, 818525149, 443204513, 454876798, 709254660, 450129776, 462532843, 397050699, 147089689, 615422381, 575047869, 613976564, 247607139, 103545660, 283772020, 365957947, 416175337, 552659309, 323349501, 638823338, 405600180, 887296816, 170020470, 546088027, 423424615, 434413357, 487899076, 792137063, 749082894, 653519921, 600344473, 876854506, 484002284, 440746931, 570958527, 837271054, 188348645, 428197684, 800734864, 39561443, 255738938, 871074482, 478115204, 303308416, 80556302, 377977356, 964061967, 752974708, 565489464, 621314862, 647407440, 180254426, 759117311, 352357561, 863381189, 426504581, 489748551, 205881135, 695188265, 434823991, 45522645, 208828776, 19697144, 533401403, 627589296, 815009975, 359181282, 590385085, 82381564, 968945316, 230093798, 539984649, 89259097, 960617925, 702911473, 316459209, 399770410, 898941377, 41793969, 770669523, 292423691, 162720800, 428978585, 426481288, 268337496, 294440331, 111612341, 863369262, 626851177, 398543708, 968176016, 237174674, 439904483, 259585892, 5140761, 309303741, 745647630, 576904609, 974893447, 19274581, 767065312, 86281886, 157126137, 697430619, 872559626, 953865059, 786727333, 81827700, 823533299, 734339144, 34442404, 44571558, 470325047, 185864392, 194524362, 657990328, 912989062, 178966586, 327822690, 129979977, 784107795, 695322750, 132047462, 577284535, 350838352, 532281016, 517965294, 843301947, 427332173, 107636827, 59520956, 646447689, 52677900, 421597711, 913930259, 583882651, 903673190, 315314383, 408274447, 85738071, 1922619, 90131946, 839485608, 217751311, 151579775, 399582540, 237626928, 454863827, 142119925, 88204220, 360238524, 208563901, 781322569, 495459580, 394503044, 601582786, 650193065, 272057133, 628393477, 403747104, 670906903, 937080958, 583067833, 433510269, 768335785, 43887513, 819562216, 347217970, 606401489, 563758396, 285699898, 885023435, 617158397, 472285793, 3766002, 399590917, 681534594, 402692289, 401136525, 542266584, 890357948, 775642291, 660250793, 818326200, 217925902, 19185214, 848794061, 698652348, 845434457, 81446839, 967268903, 187234970, 152784613, 594811286, 65111715, 369289910, 911034128, 436489190, 735013164, 402830751, 67585349, 935637749, 784291978, 835166602, 388938700, 719913379, 195887834, 892881077, 973592435, 31563508, 727710847, 69985215, 183783947, 144334682, 697699696, 77458593, 678980904, 78170669, 244038315, 739500498, 949067401, 67684867, 370107146, 883247053, 690011254, 43616646, 821387304, 272505701, 855547940, 925374369, 414029148, 295351252, 816176911, 783475067, 177438753, 637929881, 860291895, 552469634, 239997453, 148689540, 340137285, 552133406, 486928153, 748695617, 911770413, 553029201, 779510176, 641695935, 930353637, 589302909, 260298685, 227598089, 544836779, 800788537, 874515653, 137967319, 683127109, 69553547, 428255654, 297871722, 875068743, 19356841, 358309172, 861592679, 544715022, 208502229, 20877687, 768236286, 519367575, 643272158, 986792335, 47663498, 349574242, 106853276, 909254988, 350443223, 446041417, 627767716, 439071015, 334739966, 863177343, 661645594, 400467834, 636585569, 533554868, 451168356, 106067452, 324584349, 411378367, 828753585, 912666092, 676406646, 199040739, 652094042, 784775007, 460494937, 621083256, 484437569, 116318323, 318823965, 994208976, 110434485, 588901821, 516556662, 77894907, 54530593, 701755787, 891303431, 886758146, 494030927, 688333645, 12499359, 483625558, 544304838, 438376247, 318197683, 254420156, 519680360, 39457032, 255784404, 218984050, 434840983, 998133249, 497583048, 5774127, 270683617, 88188894, 276599180, 727202502, 270109310, 142018876, 713543974, 534840480, 594163248, 104005828, 634882329, 282195701, 775983667, 492419708, 414848981, 557149224, 325862841, 855885436, 218539009, 7647437, 339493683, 685804392, 398085306, 400870996, 20977994, 358517923, 850656181, 905600340, 390197579, 949806584, 479408345, 866284436, 308054113, 211852099, 472385818, 846255070, 472346416, 357898478, 335940240, 343081180, 198745424, 12251544, 842099639, 76267709, 175376799, 941613813, 426989434, 413996659, 231582218, 914689555, 135927717, 775244846, 739319742, 288464357, 904373812, 253725181, 716261074, 891136927, 731290386, 219798960, 20325298, 501623475, 30093643, 18104533, 595834479, 557113869, 277357545, 351999219, 689293795, 343004364, 220709015, 212810615, 35711355, 879984789, 296675943, 653942756, 980124288, 79631509, 466899966, 439118249, 197051655, 604822909, 339091244, 473747760, 834220512, 861763201, 78204804, 381410843, 44431189, 155021751, 297466020, 103509264, 982119632, 685478851, 415974295, 181728932, 284883091, 255894671, 476602574, 49488425, 380039779, 708071302, 58195826, 57096014, 60711992, 568820996, 812698920, 706880260, 740828890, 463930206, 646484466, 56988037, 510831493, 655783115, 617265625, 443845796, 937978954, 316493956, 69748197, 559740651, 806049346, 272784594, 672082037, 60382568, 84946934, 967940151, 679650173, 876236735, 47403467, 159533191, 416141753, 878364435, 911045565, 846305591, 896461492, 365682230, 600744986, 866513647, 20176543, 972542086, 888480755, 550184109, 354658704, 36904392, 889792911, 617722963, 872517218, 591928473, 564610346, 349832670, 764036199, 153061468, 651248353, 125693600, 626619651, 531923867, 397896346, 481578558, 16504817, 250525600, 310322323, 232216261, 277473252, 257996910, 396033996, 159633241, 880886116, 771925804, 9848698, 111408388, 415947328, 32911014, 804103474, 464203621, 144792073, 55631865, 104974798, 162386048, 208786569, 484366893, 528501660, 764464228, 168364144, 344225645, 804669885, 517699308, 852496080, 261507299, 84972372, 62229049, 790803172, 623522497, 12775405, 903195562, 734422496, 10282324, 977910019, 360446800, 816224564, 500725804, 660341125, 637413052, 266961852, 868936011, 539745700, 939834226, 270650762, 77401272, 322090889, 426728005, 426028106, 93179805, 432822797, 351383498, 644307270, 575045618, 603391452, 419499338, 172809886, 960694415, 504991067, 807647368, 729740308, 454180056, 586347711, 407089099, 451793273, 138677654, 706152102, 379963039, 434376581, 927018544, 823883222, 104494403, 645396742, 79270869, 979596722, 386980284, 506462053, 171090930, 598548632, 309270239, 667579438, 407915877, 595916451, 957538876, 272621326, 925552237, 2850932, 932216643, 101967391, 715823643, 505667310, 820669523, 687556018, 48314249, 389537976, 20106632, 656182415, 773495147, 801798207, 614959912, 918211177, 777586570, 674153161, 984409342, 649378413, 388689752, 380687430, 421441560, 529887990, 673828241, 934844944, 720619789, 795233592, 55825430, 470006546, 7336120, 328219109, 120826475, 698293192, 520751476, 999635899, 267741204, 340754730, 876242159, 767984238, 796145734, 672018321, 119996481, 471330944, 261606644, 150874407, 393691220, 585205168, 209129681, 138439555, 659685406, 475444805, 102630536, 151731650, 503696915, 572005713, 550071249, 262691515, 776288995, 560273522, 121200056, 734211170, 306001405, 996463951, 903988482, 301862572, 2967137, 883030533, 479443812, 934894557, 612078156, 790586243, 144685489, 993757075, 574946740, 353533653, 836227497, 859048390, 984129451, 51108354, 343520327, 351035967, 481177231, 242261825, 864372667, 97488515, 213665580, 421920094, 912396548, 817631680, 323626127, 177162791, 127056614, 835236154, 873442862, 256628247, 221299506, 852701087, 408498221, 210743493, 659038034, 431322008, 355376307, 955880691, 115762161, 997083566, 341006083, 422384837, 745226449, 441742410, 174129338, 416181936, 301692840, 908637666, 617694707, 101956809, 979958136, 235084777, 223815251, 8016132, 630452074, 998284679, 740337092, 609076966, 214317809, 458519281, 376892616, 85850446, 154653425, 204967147, 54947917, 680473604, 437395672, 849555451, 539916828, 430704999, 66634966, 112095886, 823196337, 335369944, 800437314, 461504857, 313828844, 256722315, 425323694, 896679685, 323106242, 385832156, 457746494, 847508186, 286730192, 233751633, 164529796, 234940673, 59475012, 905981007, 378275440, 222174057, 439341968, 817210374, 473829362, 913140429, 250146755, 401437578, 520347746, 545475334, 530983996, 667237538, 727029386, 120131462, 911985765, 146743002, 245030381, 665311953, 916158662, 26562999, 214473696, 957017903, 609574851, 95714912, 725125261, 70081802, 911675592, 409604420, 329273843, 273410293, 422133470, 453895401, 409910178, 204913620, 446298906, 7109163, 931165033, 954608491, 393632608, 807295459, 261370216, 302514861, 501668700, 165141081, 646049614, 451305124, 709298853, 945546797, 98893035, 760097682, 420809390, 683138577, 884485042, 533132080, 52685044, 89689904, 861810379, 456368524, 467741389, 357419164, 3693724, 854001406, 879836986, 778018854, 571838854, 58959921, 565903771, 777197822, 352859232, 870021941, 106506980, 259051848, 497881793, 597500360, 668227493, 233951381, 41790821, 527246806, 233175705, 738101307, 530100353, 134243757, 779803206, 893226007, 37429814, 913776801, 55414029, 642853278, 353019687, 997681668, 686251004, 352031744, 79547067, 140440560, 165729807, 950370659, 282558121, 621048351, 655572980, 646272722, 407738380, 612811896, 601897170, 626909363, 793076272, 25199102, 908455201, 706356964, 272845280, 962925676, 5866998, 120023850, 133161029, 913061558, 862680452, 919325076, 735070298, 755509133, 488549130, 167097860, 663374198, 958558114, 237797084, 738876722, 69897176, 622036908, 20773703, 198911393, 882276648, 213474517, 663879043, 298933443, 539105291, 673633430, 401509436, 762502164, 451109272, 761587652, 562746939, 852902984, 696317930, 639349593, 614968982, 464551421, 72389666, 973367762, 392799204, 604231659, 655840797, 154843791, 672664957, 528774345, 875322047, 134315584, 702289357, 696329815, 930596281, 780499103, 826487285, 812403644, 84109844, 265555797, 214702768, 673128025, 972878785, 566505595, 696537364, 240381881, 626093658, 439651814, 411097261, 44138197, 563679206, 213671936, 386277771, 852121757, 268984298, 384539785, 432153400, 39123336, 20061071, 113238402, 273233902, 563262824, 359263262, 301215010, 776331397, 534434523, 32111681, 708643402, 79270473, 492220422, 448906532, 240149550, 285071050, 830679570, 442334689, 547589248, 273166447, 293603265, 917728090, 154885404, 704186889, 280962986, 331947899, 107563918, 157581709, 550548875, 828520255, 972712775, 241100250, 600337807, 434291152, 438328130, 868016050, 971072701, 117760425, 583827634, 566894257, 669369169, 960856252, 244542890, 939423815, 442492299, 679618046, 114206061, 765678173, 614217440, 885789173, 874147525, 114193954, 639073207, 36282682, 662318695, 81401973, 307460332, 151815230, 792244099, 588692784, 796646594, 105459461, 627220796, 176727226, 35812346, 829757651, 449016539, 762519514, 48324276, 667837562, 801939567, 503091892, 323615365, 386089691, 348923232, 185290190, 306456258, 102529322, 241565984, 467509772, 470796288, 558539956, 475405728, 96143340, 728414541, 194943790, 333478252, 245999982, 385332591, 108428943, 725471738, 656643240, 664685056, 368806377, 641141657, 905211907, 94157687, 574779326, 161319103, 667336384, 963309223, 118050397, 621154537, 626459250, 517130106, 251789890, 837208416, 140051916, 831456440, 747530017, 651615975, 542061173, 858942148, 802827342, 837497770, 302197066, 161216407, 739151491, 699012657, 699777759, 294932766, 850383600, 780459623, 626672487, 871393900, 83151519, 111159718, 583768878, 128731021, 858678479, 520115293, 574683867, 721681443, 818199190, 499756442, 713261972, 602469347, 588343083, 772807447, 714224221, 511437051, 431922344, 813823153, 419839852, 724210079, 312589211, 822837075, 438173502, 324826140, 23332216, 913037906, 693399833, 606829358, 531476968, 401148591, 48322304, 902852426, 862864779, 640027679, 734529508, 685267902, 814563804, 182081708, 434016391, 187261589, 162449424, 746632311, 911282068, 25909645, 879793864, 320691492, 869609801, 30386503, 36949865, 821997009, 784744975, 348709313, 801577727, 759825091, 918605367, 263001650, 611074450, 390066065, 975304497, 833188341, 807186857, 302075169, 571413862, 852841876, 727139522, 137163392, 94834425, 494286255, 395025956, 872445131, 473629020, 779751256, 442945011, 595287504, 564070805, 967136974, 699481149, 538349798, 990460938, 227591845, 992455486, 548118845, 754204834, 728064738, 603335429, 203725445, 16995429, 860820789, 781857029, 757787644, 678927853, 522481343, 695726243, 171134351, 493202818, 508581586, 399493312, 743745851, 367907266, 569185189, 334914428, 409358203, 583800104, 614518027, 684660762, 575832, 84581676, 696573066, 300054100, 861641350, 805471511, 566386651, 859308511, 955579608, 795853687, 399302433, 922699334, 107011939, 330681331, 531111174, 613161787, 588447838, 776468559, 319031988, 897444086, 904050267, 44163812, 793533073, 129119245, 79640010, 80457533, 715494396, 163011946, 666996981, 623957701, 948683850, 646836834, 45914075, 751909710, 393597030, 989813117, 53976933, 58852914, 407051678, 237759429, 591126181, 552615834, 258926681, 397002565, 712255454, 460756184, 555968941, 82551046, 397908341, 975637687, 226315469, 613995726, 761569069, 691707774, 232158030, 516991800, 861202540, 604615899, 482615942, 42169926, 415927194, 176547303, 283256849, 466679486, 871346863, 803667359, 127784679, 403070481, 251376881, 288304714, 237565063, 635937530, 837677030, 973430536, 138622287, 345801904, 566908256, 207177715, 765399502, 186676109, 308814751, 999385648, 283548388, 925754910, 477304251, 301331491, 469556020, 851016568, 921441632, 950958756, 934150407, 777927592, 206037758, 707553691, 532837600, 277751833, 239616929, 215502565, 400499284, 759022669, 684853999, 579304186, 825319189, 982605613, 557362588, 864889364, 818001390, 262246786, 666190354, 303037119, 634058718, 458250180, 730089384, 25073099, 201942263, 371400416, 455099861, 480574689, 838908508, 78937132, 650686309, 134227920, 611215201, 662554011, 417283355, 69853065, 826949645, 891557007, 195499529, 634090769, 224524134, 557334479, 657915709, 103678193, 826842833, 597643731, 963011767, 832278762, 710240957, 944055420, 109440396, 534805631, 86756687, 263558710, 531054638, 759695553, 429034301, 194042189, 723770632, 226463842, 959398312, 594781355, 381289548, 987440787, 240466640, 289352068, 209633412, 84088109, 221406416, 261534703, 487262113, 893555699, 49727026, 758270531, 440537927, 693422199, 125709750, 694556174, 524262602, 136776658, 222599299, 282197189, 316303308, 881595146, 311829581, 685211921, 660411260, 107858599, 649385801, 160764717, 463709625, 239557001, 450710191, 655041183, 233864053, 721870953, 720674397, 612582625, 30237916, 332824078, 927775495, 429255452, 315826481, 44924671, 1632733, 427349153, 299446153, 536876098, 794702743, 571765087, 937955674, 879867155, 38268995, 948776618, 830918249, 421916984, 93474830, 366358544, 71673456, 160592027, 825980392, 97331393, 926344840, 291628927, 764275797, 62976013, 862901408, 778186302, 218566311, 507546530, 403691673, 402276011, 489594848, 72859078, 929263493, 985535621, 491990909, 40310327, 639147636, 109283815, 614489813, 152849722, 985346813, 550108062, 615077055, 331015757, 262712602, 923347104, 991210218, 35634196, 416254915, 69705296, 29164375, 906825081, 480680483, 639854940, 326317508, 745836601, 920679994, 468841364, 889349557, 658222426, 89914959, 222324311, 808749231, 286389297, 500293440, 999131491, 658274684, 170054527, 609522251, 350391180, 797925628, 933002381, 676038769, 69680793, 200293054, 175443543, 972069963, 937761872, 787227143, 972448618, 544377855, 597421304, 113072731, 43878668, 626305961, 428290313, 214228782, 268868660, 487196138, 250829040, 851886275, 324614011, 792849914, 248864575, 830669461, 176179204, 234297500, 690942664, 684491603, 527921792, 932188830, 704973666, 746280595, 711769802, 320866376, 942701559, 767508423, 14403596, 309979060, 739160281, 749485580, 817225519, 529906225, 1142328, 258508388, 292136958, 489424182, 620510235, 805788649, 537540126, 141900479, 265990217, 878897486, 811007010, 221247335, 136057364, 132385717, 663304201, 705502213, 159518189, 62428701, 896269668, 565330184, 523216562, 308874536, 401056765, 421797868, 558290064, 251506405, 677369110, 871955689, 804859693, 414125018, 518154459, 716471676, 828714958, 929640771, 851886835, 28864389, 13329733, 436416482, 892515573, 703609216, 302110312, 873889910, 89743727, 189945587, 377477672, 225405651, 695626637, 471369624, 122456937, 582448871, 699335272, 28199052, 558150224, 357619669, 367398709, 690872423, 151493886, 146550356, 415646465, 970717198, 30688595, 916347249, 688123457, 772741299, 257742295, 16874089, 613611520, 977352271, 244690699, 983032262, 464891062, 127552597, 217927317, 703447646, 417562767, 813248281, 446517485, 795732289, 376956185, 905642438, 937927833, 199794998, 983062219, 709445263, 876619589, 858399344, 826898086, 185065764, 888959001, 6753513, 983157419, 978176091, 467673220, 841158021, 65760688, 441862907, 225514888, 414710599, 48483932, 357765080, 455300000, 573009950, 114054312, 630263741, 942846532, 608134306, 485310252, 656209820, 695474766, 532939744, 867105412, 325437139, 923580059, 131705618, 108276195, 958710003, 625676290, 245607319, 724375610, 169969437, 109631770, 408869434, 74777037, 343337651, 864273026, 963233796, 611031576, 262466173, 388503915, 473057168, 91780949, 64076062, 165364076, 280500121, 25482147, 404464413, 186447069, 863420168, 315743204, 319631421, 737802783, 999023723, 868070650, 347098762, 342376240, 127664225, 883140574, 943350526, 906501003, 796710086, 689405738, 15682480, 142103341, 130196063, 803607098, 979724576, 662988846, 173320091, 632428762, 64490504, 331002556, 138769136, 733308826, 721673361, 514428221, 421757756, 495084702, 443217709, 91779166, 168063047, 653259349, 659920567, 523958696, 110564873, 38109922, 695630571, 220177351, 850042884, 634320746, 865702399, 852431006, 117803561, 634874846, 922687852, 835948236, 994704580, 759656552, 303231365, 443059814, 850646492, 858103444, 84971821, 488574348, 353176569, 434615677, 574481059, 979660060, 379856429, 217819498, 233195388, 403029131, 964035749, 508466420, 815448090, 632544668, 490475444, 378456235, 48336836, 656107281, 285194907, 563958842, 844279581, 319783385, 38134797, 606268558, 709664562, 150615120, 791928493, 872140223, 726922407, 920168155, 395440568, 339324359, 37197099, 832755052, 39524151, 216349392, 640740033, 586217933, 992543156, 29361668, 743797058, 300668788, 31805339, 61161378, 207564607, 752813300, 281613063, 351305187, 264533014, 120946241, 414888638, 763059773, 236341819, 153782726, 467791887, 102796823, 913755259, 28611466, 625487617, 400799812, 354955600, 954800329, 147425650, 345307262, 414047907, 299916843, 809553400, 622724863, 563077761, 409248405, 217181086, 154165808, 387939180, 66919547, 263192439, 52482756, 100986340, 611388948, 959266272, 299654808, 73991986, 432843148, 506818650, 314083677, 626793674, 990875964, 133357865, 100737104, 565138255, 447835122, 646016895, 129639526, 865203133, 243949290, 180635629, 455804564, 620172148, 774127262, 586600978, 45493328, 982667994, 334670139, 589171730, 104718985, 236218869, 943510201, 187272946, 11806464, 257200591, 226688115, 931999703, 802772525, 68554126, 426554423, 284561093, 528223042, 633638208, 141421337, 518606315, 362429031, 656441999, 710120582, 669143937, 125036247, 16382720, 651473338, 593577370, 78221298, 294785061, 814926071, 100018350, 412182430, 272879389, 79512662, 590394388, 541446497, 557608324, 144820076, 902995173, 641678122, 451051454, 952661211, 456454436, 769811394, 979806610, 697132782, 209790219, 915828287, 524077709, 930434222, 649803731, 753915091, 119030227, 925041698, 591558273, 559324551, 680042590, 856937310, 332831608, 732450608, 315349113, 651846899, 836164793, 561362650, 665556097, 242256528, 961688656, 660636940, 543349559, 68253275, 968519451, 612859112, 366433954, 289292399, 368903169, 739068016, 511485827, 38375135, 92897007, 808255138, 321966660, 521630559, 366991230, 107976879, 863584012, 291846078, 971738005, 580909849, 972071470, 307152252, 437075702, 734978222, 678217304, 89889168, 412756984, 30794476, 129228774, 229966969, 881992849, 886949055, 342076186, 945521303, 466537662, 442928461, 524043244, 866433946, 69723368, 84819776, 956442870, 826203662, 596192829, 155556651, 326438216, 642567058, 506074538, 985879459, 415328555, 825977083, 356526561, 412833909, 983475287, 402844668, 222673328, 667746111, 88335, 334670335, 186244458, 705803593, 149610274, 578128623, 656565232, 821037087, 493369825, 333606060, 713062893, 52867007, 50453348, 72012328, 124708094, 316292502, 494121237, 618518228, 936229617, 396833072, 701226853, 460130898, 460420957, 425879218, 897549123, 365618042, 535534433, 386313888, 279446014, 98908916, 911069855, 197404652, 323965096, 703242353, 950613079, 622073237, 790866534, 683714703, 365397913, 627884163, 496115425, 238238419, 331380084, 448316261, 814197834, 864835816, 657283935, 632585702, 730338847, 162987065, 420666371, 601255937, 751592984, 682995408, 672578076, 676003829, 260867174, 814204727, 60658645, 874973292, 542403524, 538641613, 715979569, 517727372, 360560699, 933072414, 409835321, 994175753, 624490943, 425573674, 856114331, 499028367, 496706754, 384402113, 875296052, 320736484, 985358062, 137606207, 635016806, 895064952, 910471231, 286731309, 583639987, 312254013, 23351156, 223573833, 231697587, 913972019, 588856968, 289164451, 952657985, 56514426, 443961193, 748385507, 783305454, 227503834, 918796591, 211350830, 926959253, 307469751, 937490055, 652599567, 804542573, 683175920, 583120721, 348232648, 252793995, 905129641, 545840268, 135262932, 279796030, 697961521, 912946580, 677180053, 558865595, 892120597, 732538916, 239622552, 659529771, 64348669, 194646212, 799512265, 380084958, 997828410, 443069777, 319116170, 859655, 760466474, 102433733, 397852824, 445257080, 255190290, 710414135, 879518521, 866933000, 505433697, 768443657, 614584561, 13114318, 41067678, 751625699, 246377897, 121730467, 464573398, 961529099, 695150345, 596470153, 70299717, 329567356, 360739005, 891708866, 321887923, 528588112, 869050551, 432183062, 551308129, 889102543, 64056587, 814105749, 572849910, 514942417, 256362972, 895551660, 111152934, 46202697, 522605913, 319169115, 482996753, 540976797, 90594092, 277816433, 619986931, 644946253, 785542655, 393118180, 562435030, 299358641, 865988389, 279569714, 317306404, 367811344, 994319821, 69771629, 365322102, 676624544, 869878468, 947011790, 259446984, 798553214, 193157736, 82004334, 240904228, 306241642, 608522820, 441950066, 72584146, 46955653, 874884561, 215898194, 160981070, 454524520, 470765465, 732686821, 162614854, 800720567, 11393600, 61747714, 267991038, 408159318, 253256961, 695410822, 906477182, 638048170, 52192456, 797050481, 31414012, 914355121, 836022385, 579401981, 444541348, 130310304, 597434549, 216333820, 705433333, 920473825, 674064691, 318799030, 719267304, 110914796, 855493851, 797029490, 789915141, 131560992, 726332702, 297539891, 276154017, 664756231, 317467178, 926510643, 873485250, 156373017, 897072599, 86354322, 102952679, 113599135, 350571070, 190103607, 820326638, 564642599, 954792737, 621794314, 569099223, 109760971, 694271918, 407637669, 653580050, 446869863, 22622101, 407383992, 678539798, 648661199, 627676734, 47253040, 137969364, 386710064, 92123346, 778485489, 155339330, 169205834, 451290497, 678816085, 682924058, 195107805, 379695210, 438749049, 404098797, 689127754, 277009286, 972012276, 620034900, 937045546, 126988228, 880181901, 645719463, 7484471, 183521962, 243113618, 794877893, 739381923, 785285842, 860597950, 557679723, 420421739, 135577877, 797955392, 259967586, 10284984, 319743978, 212226708, 57161610, 631996999, 44664747, 375825475, 518807641, 49850652, 593627241, 667261356, 873366556, 220620718, 730051929, 780645822, 639171262, 118982350, 516881388, 697238823, 111159130, 5309780, 94615398, 744978639, 646328127, 322422428, 861151214, 744957294, 533446258, 586921489, 279567194, 634356441, 13354743, 968033930, 784016190, 963335521, 390928660, 561807264, 656514967, 537954042, 417717415, 681562930, 206744976, 232869441, 291813145, 631667697, 380938134, 609139059, 927497046, 259066983, 44304759, 482519440, 433381055, 212838454, 255114963, 676814328, 534083123, 114515705, 658559578, 677336240, 819197877, 469745866, 327975716, 253589930, 230633489, 356295266, 490159376, 978858616, 55543276, 268478496, 487512416, 407075560, 225931026, 124608654, 27609072, 926069567, 150496858, 454482375, 601087380, 416732994, 603174813, 811044233, 964304594, 71086763, 974753871, 838075457, 921599061, 205972975, 409965194, 72838056, 292290751, 53682127, 182033517, 127696384, 670598146, 819599190, 318587142, 909002182, 195599617, 577596322, 259828490, 167798037, 458966039, 786594878, 357303948, 429479640, 745432357, 184849031, 251353720, 557904512, 298548708, 220028369, 339142691, 247609685, 236627203, 609234625, 466842732, 787887082, 51850892, 905760001, 187672640, 675367682, 329645424, 338150060, 569144281, 641343174, 419830881, 554578661, 568089090, 200828316, 749123665, 723837373, 664234571, 384976114, 540311658, 624903566, 329303896, 356923995, 215647556, 512846226, 934960870, 915227807, 893357593, 628580842, 138941801, 499039833, 145729775, 924146523, 192771927, 424711046, 650156042, 485894293, 447550896, 873012795, 181343395, 394447265, 662082518, 377161172, 80522759, 929687211, 146060910, 212747210, 384759104, 872206866, 72895856, 987114098, 282636087, 835920041, 461401168, 604939327, 34607047, 554576062, 123802863, 385191337, 897493567, 173325079, 627255978, 461574670, 957565805, 577493571, 259339878, 801704543, 577823155, 27751917, 303801050, 905144614, 18800650, 765608591, 23461802, 394673264, 481402720, 440709996, 791094131, 826399675, 348779381, 737296056, 647561172, 887497770, 535825711, 627559243, 701261119, 490593800, 911616880, 875009832, 633530613, 849099437, 513216190, 974014316, 334827231, 551649428, 321019835, 259800720, 909298892, 2989620, 289912454, 123233798, 166671367, 592503741, 459661918, 736546448, 558150914, 165459991, 96092449, 842355536, 114668567, 84946560, 137337230, 503873974, 823903357, 690902118, 690626675, 626897175, 164607283, 320889242, 50011343, 127755353, 430451680, 300211173, 427592558, 328410620, 226799466, 574417349, 854231673, 350680094, 675775762, 177508305, 620542375, 143947090, 416184710, 887184828, 895119644, 652848913, 153104910, 919880955, 883005557, 787837531, 216705858, 756964219, 270155939, 232113706, 171910521, 244713279, 819551208, 797188853, 714238660, 941802280, 731701702, 547181071, 366982297, 489483443, 469586935, 996289406, 918974786, 771079459, 658655802, 283641500, 551862865, 2351208, 841219132, 702142668, 421063136, 979635820, 898228114, 596467748, 106193108, 125005636, 132099025, 208870913, 35046893, 113352656, 428530969, 195723454, 711429404, 641959542, 809958628, 743897236, 259479536, 227146695, 253342035, 61838387, 5795974, 423948939, 854407646, 66679715, 819541670, 982856870, 779745640, 424009568, 678339871, 270516766, 673337752, 770973685, 20942047, 30944454, 453219694, 917241787, 836822204, 627177389, 584114513, 413031704, 422075571, 38663092, 610854081, 743200341, 464997624, 703571229, 136046584, 994945642, 568951029, 385882524, 765717828, 476509896, 940774087, 127219979, 186570447, 709676610, 489585499, 1443236, 597599525, 322795455, 342348303, 474424537, 593169833, 742690936, 625851396, 411749664, 350233742, 80237999, 538058327, 39263825, 333349607, 875895564, 18747541, 444239139, 965276407, 666501965, 920214448, 85320486, 919559051, 92676310, 946942202, 813780944, 184868264, 836615685, 426961616, 656944087, 390292997, 776322841, 444774502, 799062032, 773675673, 469943891, 867788472, 604395078, 398762254, 114826469, 560177600, 631547006, 185882407, 586606962, 277309594, 328219927, 801181339, 98624434, 471654779, 814972017, 476202924, 762447762, 387936519, 555272470, 657758930, 679362272, 258080662, 51146410, 300217713, 581637852, 888315118, 383516978, 399828867, 969535486, 675905811, 31466996, 302303187, 77068864, 157281984, 166431492, 369433553, 717900129, 795643852, 414455989, 478177603, 824658223, 691652692, 377296825, 170109237, 625296438, 635765545, 62921760, 684432833, 454730336, 788369280, 371065401, 679626059, 396261570, 848030403, 796328586, 807830466, 166503944, 58903384, 754929429, 785731882, 258898570, 325158677, 911851784, 881641879, 242285897, 74214998, 877514547, 283643987, 570003855, 672502650, 635011935, 384251142, 742272896, 671682847, 182786576, 235181706, 119850480, 928337602, 956480100, 385775917, 756474847, 80113207, 298287164, 481212861, 579690928, 619058875, 927351804, 656379429, 817890360, 406204759, 90389579, 274033354, 224695927, 542152915, 150434443, 843586896, 293148839, 154552108, 645768578, 288541661, 600938933, 197726130, 875108493, 156011402, 823560887, 609682975, 230304845, 948083694, 91734809, 832432120, 391705039, 372425210, 304451490, 813269367, 301247837, 753118233, 467555492, 405519905, 250686002, 298338313, 340027905, 753744201, 742890590, 803775433, 232789500, 259411870, 795513084, 367178795, 340840830, 225548531, 533916112, 717231374, 296856585, 448298873, 218987194, 297521247, 632568643, 58610839, 205930254, 809079897, 168478252, 182378498, 591510822, 421923122, 482270448, 911925825, 846502901, 589631102, 41847154, 216377025, 231226297, 27005902, 637769424, 255163945, 502841172, 622962497, 655161523, 75953562, 167580681, 543464759, 477808433, 352505861, 562525485, 269529512, 553773987, 403207609, 351198466, 391127893, 969124675, 720844546, 650646949, 709807198, 696739881, 941643240, 560668841, 197009119, 842696359, 478965105, 405021624, 416249347, 462494658, 551509551, 7712305, 975878289, 442681025, 993139279, 759536424, 543389648, 176666397, 501543846, 708344410, 577239237, 610206485, 723784393, 106792669, 529996148, 148341243, 252758591, 104845275, 164578758, 554993768, 341862314, 570471669, 158267010, 675262496, 932698519, 110763450, 781341649, 110310876, 941157979, 335312233, 258714923, 676977836, 998414953, 738699134, 744135135, 859372106, 43429391, 575377689, 204724476, 107009627, 947911586, 15869346, 185038225, 444621971, 563099458, 986588469, 181151652, 113726489, 802213203, 218527562, 796958915, 783882962, 780502635, 49275560, 231598484, 362894780, 276183626, 625756056, 439591964, 908850264, 372220574, 635558262, 173393292, 805333557, 411584307, 577734571, 657025679, 55542705, 552564650, 750785670, 849141994, 719578091, 917739002, 89908785, 69455345, 568377575, 580260708, 908439174, 897744100, 282636764, 623985599, 160118743, 48683448, 272830682, 603536167, 319262460, 75681071, 887491630, 825789688, 730043097, 941109105, 417295007, 953560569, 463694234, 239006976, 370067410, 809420022, 442306713, 345805294, 290326251, 663008784, 804091273, 144706462, 49277925, 692802773, 139154327, 248501979, 212967463, 229923910, 816521422, 338249787, 736145999, 929710810, 792077164, 848377612, 369579188, 716557408, 565126946, 504184837, 669561120, 958230595, 136120636, 82785331, 967169522, 368370448, 82788764, 349907686, 880706675, 314768269, 602917099, 292040982, 689780537, 775555000, 186388852, 53356013, 259084139, 889727743, 977935918, 590902354, 564318905, 888146839, 434348180, 162753917, 306934182, 657605837, 281826696, 156231281, 178503497, 960122313, 118852907, 678748511, 816320858, 20189644, 550428175, 579870494, 585488079, 504063431, 628328306, 753047340, 614501165, 504162618, 454987754, 861229313, 20160608, 501696146, 806409907, 6919524, 933765222, 508417063, 750077412, 922599538, 129059489, 42034339, 658971765, 990659241, 753959682, 235322914, 467435340, 60561543, 659495361, 331518899, 941342485, 238453278, 269713234, 35418962, 615509261, 596688092, 209502521, 870976832, 489625610, 137566968, 7339360, 950115254, 887409324, 124228550, 264631775, 836728561, 385563947, 520875683, 769607608, 620859571, 770663243, 901597618, 831253556, 409038628, 949321001, 97493248, 985622540, 745249637, 121263802, 418578966, 401434237, 943632838, 870388272, 656892166, 70607572, 481100706, 891547394, 661208723, 686294341, 50301254, 928125430, 647796178, 219009988, 256894817, 757659514, 35710526, 543669638, 649380493, 87812898, 886341723, 653448763, 831185727, 59237524, 880073479, 426967573, 682752710, 393475179, 791402228, 100429173, 895043820, 519685094, 435289464, 63268264, 222981613, 586934130, 219946627, 326014124, 720844972, 69205971, 751185606, 984191240, 905429109, 932822023, 447268020, 920422821, 748584619, 4630263, 634656595, 447385985, 956848726, 261006887, 54989379, 404841551, 697667794, 74532632, 732600633, 601728695, 768454286, 919088173, 979915187, 267299213, 898496394, 951293113, 497152370, 239385211, 224400973, 800734808, 590240940, 601681780, 358271366, 201591433, 191817467, 29991814, 456587997, 698747433, 488217725, 747660236, 928936298, 128542204, 741443821, 225023819, 735034740, 70724770, 1646273, 988490251, 245322182, 482837911, 552467882, 853119315, 686318174, 618746117, 928227495, 333582023, 300243931, 336478037, 986394858, 788013784, 911264017, 541449491, 874561718, 924167550, 24330452, 708056581, 933697008, 801901448, 366141358, 990467090, 723730440, 686255749, 451054324, 575963693, 995500499, 270875822, 484587253, 56066232, 232872965, 880421704, 492937357, 324017720, 965225281, 57164794, 666520521, 418964865, 328039111, 343888249, 741245988, 557328849, 405327858, 102171260, 464451944, 136565691, 735941584, 9426223, 546773591, 185343008, 58159322, 57720213, 518236562, 854747925, 335118930, 547457860, 334386770, 684316156, 577948686, 578554494, 449501710, 483329038, 13115415, 10576036, 598112184, 369967193, 439275446, 48486010, 951811357, 10956486, 210391001, 665911484, 370913759, 969912885, 191297205, 171338558, 987401292, 306686616, 380225618, 557150079, 908958890, 92407071, 622849368, 901605450, 501324825, 411893001, 486231194, 76794408, 151944512, 895214832, 370720469, 175464887, 967403099, 195754213, 45207711, 382329183, 365128656, 244368179, 296917725, 60342057, 356988798, 707735928, 844591244, 697253443, 763401059, 883614664, 713510305, 769360856, 898069158, 455795300, 993624297, 637229075, 912348098, 461576850, 331296406, 391385762, 376072761, 767221291, 887280720, 563397679, 996624332, 552796969, 390587838, 784414927, 251439043, 623413502, 398755555, 857660575, 865296809, 298532027, 604387977, 792774909, 134896495, 887684076, 652331234, 430157182, 523386290, 809655682, 388286779, 775644888, 761828453, 767616630, 211517247, 882379655, 214128765, 73659053, 84672046, 888096838, 818836160, 610136320, 566776336, 53591649, 161440735, 848208206, 678210677, 895039787, 249525153, 275801780, 385811820, 36587030, 544909242, 137037701, 403009653, 811217222, 916071867, 11036614, 334238332, 448465205, 878746344, 115402531, 667282659, 412706944, 942913411, 203924151, 245317671, 670120514, 332087399, 116256747, 908736290, 837807539, 691432118, 494539906, 123015003, 613080528, 674381879, 10045797, 407579800, 607064713, 623203825, 538873656, 567451080, 107072883, 325783589, 932514673, 465210199, 185099822, 718441180, 283895976, 197619583, 175023908, 649455062, 944312074, 515927006, 726912101, 339327562, 543916862, 829906194, 108809742, 26366797, 154802754, 674713035, 82991680, 791066841, 811252369, 39694931, 470385497, 889067910, 693919051, 100461462, 604076231, 915400240, 597691644, 850823921, 350938437, 202841347, 434629485, 890691573, 366442987, 83261931, 404186868, 627403505, 165444841, 819619854, 329928806, 952909364, 353866108, 736173093, 260606388, 735748986, 566646948, 492054274, 138349980, 540224499, 614211567, 98241539, 516768194, 98039352, 231507108, 325037696, 859297363, 766527945, 732588903, 159042797, 333471430, 670882081, 110713335, 246626641, 668787373, 302156527, 807633970, 646236761, 469328975, 661117685, 571716013, 774810694, 203427768, 119938479, 315003547, 602432579, 564776564, 390950344, 946446471, 247002363, 861299576, 921249430, 11567576, 833509471, 957965625, 287442462, 946468092, 559613549, 820115485, 786665940, 365413169, 37335069, 595802888, 351460393, 995403477, 258531273, 429947783, 458128753, 58521654, 531297797, 999713614, 98999647, 499889442, 300066058, 949672483, 219968673, 405867023, 844785871, 125305984, 88483777, 730030604, 966010260, 653186265, 936250054, 338125684, 304312684, 248760642, 996374552, 757017067, 11992666, 465590865, 296632425, 179198389, 939794171, 563761330, 396727205, 615303663, 809783226, 878916310, 472632942, 387105198, 559978693, 508878350, 866002959, 222880250, 555629180, 657701745, 245655496, 194031571, 250352452, 36348499, 593289180, 160503410, 341368159, 506849603, 419989635, 692592449, 67959855, 30722487, 726862569, 68011459, 887272636, 648246519, 302143968, 11166347, 501832105, 10752737, 936581358, 539301720, 141661947, 695743148, 526622548, 834091317, 719885165, 124351451, 663179605, 317123440, 296772198, 237218234, 332528047, 163055049, 209966672, 765570226, 287898654, 661527397, 156627488, 480977593, 671071696, 590745910, 134963852, 275216327, 996818326, 613796596, 194438333, 336656011, 544374207, 973475813, 539688027, 678455136, 690657547, 921908014, 528290630, 839967283, 151584452, 732596874, 495843446, 941381590, 780490369, 834553417, 253507148, 909617857, 346199140, 892463506, 18736290, 244182566, 183614392, 244448021, 102536197, 465531758, 721454136, 804154265, 578459212, 727191744, 234526706, 458036611, 745324145, 212809774, 939329167, 558322793, 686237182, 465690551, 758727832, 58470321, 621548009, 258051478, 614680952, 476194201, 601734746, 796977021, 118504284, 31390794, 358923814, 480852403, 3831085, 513577593, 424368251, 339598414, 269514604, 766718771, 944318412, 858994897, 75289284, 170410253, 29519955, 520515730, 469687788, 633303116, 990497355, 325167870, 550847730, 140751732, 450575616, 396515781, 794958108, 776549143, 706957470, 921813304, 811361222, 630910650, 174701961, 590526177, 676602876, 149261647, 554566391, 633755129, 19095875, 608484778, 234138702, 381591406, 651403233, 747566384, 933067885, 253523396, 307356742, 476004520, 145586731, 177759478, 135780158, 953245998, 76384609, 241435306, 881403715, 905244188, 842422005, 617983850, 944381610, 462246273, 966492081, 934429864, 842987250, 950935989, 711424157, 299546742, 688827548, 738190854, 574413117, 676095553, 574015896, 741718254, 751481621, 432357116, 260864806, 655998961, 770761456, 273941326, 360473044, 612348390, 173057240, 287242032, 282187659, 246877878, 232522499, 320126814, 533270196, 812909366, 885771285, 210485997, 525414848, 878486975, 119227042, 35191770, 983810980, 568853996, 912903439, 951261852, 898466728, 594765429, 695111842, 364844759, 79135125, 815421010, 159164806, 819188100, 662592801, 340074258, 654452447, 980546017, 984931806, 337189927, 57207171, 685347986, 78391590, 840114054, 388067325, 270561656, 89513581, 806317090, 465287692, 590492558, 130903401, 531698006, 484540677, 188143912, 384258830, 499491235, 109879738, 482698812, 307338820, 20239785, 978046260, 497384198, 271422425, 330764669, 376647163, 9176567, 860505292, 873555595, 701885829, 801750355, 15249149, 576471011, 639194711, 334565762, 282666503, 694138710, 839544612, 76912267, 806768370, 610392575, 37668266, 603920674, 109729765, 39904926, 870253981, 828795385, 43315484, 846228159, 925372794, 591546770, 727650437, 29313655, 896657059, 155687473, 146535940, 946416071, 520977226, 856571671, 259836483, 372385906, 299298268, 975818880, 103283100, 768893544, 259509164, 174994002, 758521052, 855717334, 541686312, 7425253, 470343952, 293224257, 250328388, 464955853, 496008969, 635530890, 440218795, 341341651, 665732677, 405265387, 426222437, 3947841, 407419729, 97480774, 127344215, 909068964, 849833706, 529960859, 343823784, 611955269, 474280356, 272371842, 280586939, 830284240, 730114546, 214504356, 529484749, 283432734, 771021693, 590571037, 385747656, 105246842, 247171286, 686422536, 268902733, 392441581, 729372664, 838304016, 599309744, 61581289, 196659566, 212614129, 728984451, 877740502, 201905088, 833843956, 766594710, 435965004, 255002512, 42360721, 904498354, 411931602, 493645517, 696369003, 187987848, 451882113, 164605146, 283967550, 547320866, 480633457, 1299001, 321704953, 537484900, 584055665, 359024926, 634252726, 76617499, 330759207, 356552268, 159389287, 337637485, 264529225, 769990461, 821483268, 22148366, 552443306, 641229743, 234331060, 859954010, 715736194, 552313519, 36161416, 89615507, 498023992, 469097902, 48162655, 788692501, 964961643, 546146478, 829238469, 879369307, 666749872, 408001223, 210660707, 474723880, 121949222, 721458644, 192201422, 857939053, 734935884, 117198776, 606842697, 994561447, 574979338, 769082795, 446013358, 742967125, 64239212, 202995410, 315694411, 183405440, 679759000, 270539944, 811105729, 292315539, 906899587, 280744119, 606467387, 462030700, 746254058, 659323293, 766081454, 38267246, 456606642, 670466142, 611187577, 43090301, 989708596, 541495606, 610164392, 596757947, 397028009, 202452449, 453432144, 257271054, 249461136, 889228834, 642555183, 806462418, 213483831, 370901056, 383531085, 238523389, 555589373, 5693737, 565832111, 67838823, 542629599, 469752695, 763553783, 225724499, 503579017, 842153626, 629651635, 160059973, 495122142, 376107435, 55085150, 739608819, 387833257, 110649110, 87390086, 622032501, 597633210, 82367321, 830075364, 336915180, 952037378, 367766169, 421108110, 622635197, 314112723, 968868271, 544987487, 565451730, 873197017, 754811042, 483569513, 302996654, 674681588, 352377702, 611631305, 328705710, 627155364, 692501139, 993050003, 119532424, 214491664, 247121279, 358658426, 818429743, 856165331, 799705485, 144024234, 293821803, 471678405, 338076307, 183020553, 491755920, 595439578, 660371979, 215288345, 937690577, 650678750, 475679817, 693495245, 682119011, 40560331, 111716401, 252304787, 347789101, 268095774, 654787606, 219462147, 617898975, 353421514, 287543074, 766942663, 969905272, 996944087, 59711287, 913856124, 775957987, 810206445, 798953936, 920805202, 466271564, 838582192, 39953631, 174603894, 707833403, 711421540, 559830401, 774604248, 727309384, 340014326, 603691269, 25680302, 159202113, 12038004, 973851087, 905123966, 456523239, 806674471, 600645790, 676200356, 797459051, 263226093, 507288770, 626007092, 556336735, 791517384, 802031381, 151430317, 325565776, 32092493, 479848819, 810641526, 383602726, 806345027, 926287297, 212227890, 113632177, 552086256, 561608274, 244186468, 750840, 585730999, 924955668, 549591702, 800370574, 315814447, 350522845, 428484917, 793118133, 522035145, 320976403, 742412662, 621914769, 619717456, 699178694, 687730625, 579374595, 876131746, 411859937, 582328394, 330937169, 497490757, 113085072, 807984205, 992693614, 730573982, 724644708, 604156133, 154531105, 158427135, 39918226, 208742503, 877095193, 989288285, 630780755, 291973768, 302385181, 552271705, 800040276, 193631038, 25411189, 23750324, 249236863, 274847442, 94753056, 984934910, 69708770, 263668668, 708226628, 584382563, 725463466, 646148221, 25454904, 495826739, 338674582, 555287824, 599001674, 239776311, 234665347, 522583573, 315309528, 597023464, 486980241, 620585710, 540012947, 829347998, 973426039, 36251066, 924474611, 371877586, 105709527, 20355310, 296623048, 8681913, 255470560, 753760163, 189014032, 650769280, 707402044, 860178461, 311683190, 546266491, 612266525, 903877790, 52652479, 874685874, 178768599, 361337981, 446441514, 520243841, 76656683, 336740445, 327813340, 424955018, 30068513, 657456522, 537396280, 839471187, 495245471, 685558612, 206038180, 161246892, 437425318, 513679949, 790541044, 290643843, 229152522, 116577826, 304758814, 843252054, 669705382, 880492994, 474231497, 37682950, 923932366, 684337931, 813711285, 985198700, 211925007, 458878698, 324036284, 26543284, 845200635, 194576126, 190916518, 529311819, 300479499, 870179003, 113723487, 936246105, 152622744, 10098302, 785739258, 776941730, 395675425, 477692753, 9263165, 723842599, 682054099, 495471914, 7481196, 150075988, 542492627, 45175025, 393203383, 324574162, 395694465, 518789983, 846901542, 439123617, 316625308, 107630930, 991837225, 623546062, 919994084, 781781174, 815972076, 102050828, 542645605, 801193873, 910662098, 887732950, 746209937, 567445644, 806690673, 760035245, 572473191, 264869670, 647599095, 243877351, 1353848, 326209968, 262377499, 180353252, 888486055, 431688388, 675487938, 808527844, 285683359, 446293649, 711752628, 553730287, 724957797, 741162757, 523971866, 903895371, 668502709, 193485263, 295334399, 410235527, 736024415, 862157568, 881939394, 854086950, 28644884, 829747754, 569587319, 483754247, 145238645, 457785109, 467140132, 143372630, 171964588, 275087755, 368479768, 631257597, 719244068, 167172395, 518514482, 374998459, 174331902, 242661333, 502065849, 169725571, 318813790, 410092787, 930361256, 2486283, 667338533, 296810959, 324151549, 465283585, 422039950, 899306415, 577795395, 199501441, 912991967, 797701654, 944263050, 460856642, 605338817, 255359096, 30082307, 49247185, 691804645, 921431431, 702424182, 923873660, 690869875, 923365188, 994416348, 8676347, 718061096, 972396822, 182996061, 329534080, 259134745, 68882078, 393141110, 859312728, 370667051, 467039490, 663286810, 503549375, 654601063, 924530153, 503457844, 324978174, 243948338, 834332536, 460320243, 587980831, 674201502, 548119845, 171064255, 729525559, 286783746, 556107828, 659595673, 157035742, 10258734, 653612821, 24108591, 362770291, 684463683, 259478504, 387721633, 436258639, 320957677, 828059032, 833574393, 735649958, 750849079, 627276906, 567058147, 239953108, 748867012, 387318925, 366702714, 202467147, 88869886, 376987173, 682373011, 934597318, 8470206, 657027809, 494858858, 623883278, 53310706, 753181664, 128252348, 203294714, 3945365, 177474520, 893616760, 300928881, 68584444, 276845256, 253331389, 253692135, 668311241, 287815267, 534223352, 194130824, 937469401, 220888060, 378762635, 777471997, 406937073, 444621155, 373361949, 591204408, 790981586, 10199957, 23160845, 156764152, 545552236, 113653949, 430064816, 378637048, 281688139, 94565633, 285725339, 992609330, 764309975, 446723939, 544743618, 563492303, 773917756, 893593926, 978432444, 591596816, 652377504, 741415639, 57258649, 402829177, 389285709, 864106942, 684869504, 833772901, 483990062, 241114631, 817081975, 851753574, 999109104, 860298678, 83233396, 513197245, 185979143, 934958465, 218108309, 29578176, 284294739, 476431239, 525767337, 146150520, 244767377, 915460633, 690605255, 859627521, 12562443, 918095146, 762617457, 67520946, 433646552, 254120591, 403137450, 771252359, 709897261, 797869027, 995838291, 517507426, 113053227, 382009942, 711902976, 470526830, 412417627, 197036329, 403487589, 825589871, 925589747, 959329972, 524552226, 29975656, 404035257, 531284928, 254699136, 734748447, 282180072, 802641836, 480780321, 878512025, 273327235, 490930805, 122829386, 923350174, 821889593, 616104525, 127645522, 136011118, 189654373, 547648497, 581480620, 400792261, 692975594, 354770751, 651840329, 221031817, 46716762, 767013349, 2528200, 416446468, 667187047, 190920536, 130867549, 389333627, 28284594, 545080443, 481139364, 459751129, 533452530, 489959799, 615162771, 764873470, 462745199, 290221854, 731607064, 828552404, 663905868, 835021716, 6956270, 763383014, 268836822, 58061797, 189126688, 143661550, 136630063, 54446550, 651108974, 720841986, 152587614, 486410113, 925046485, 535083474, 128855595, 349836891, 767944207, 726513138, 586066542, 585632363, 829009223, 617155304, 582702173, 696607142, 627228534, 557276853, 50049287, 238000725, 741891942, 41852039, 148335577, 397682760, 992159034, 872641514, 928067139, 427831561, 113016813, 793171338, 359691993, 176430776, 764981033, 891857951, 776585532, 523488444, 24111494, 637519766, 391112863, 492066006, 785612887, 838229454, 849884020, 698041297, 729251585, 852100419, 943054443, 465149341, 587202368, 914306213, 71906378, 376841879, 2861545, 710579949, 930965874, 127415752, 687267442, 233328595, 898022964, 570604831, 717992782, 51653393, 120180821, 710350296, 573037528, 97975767, 582259549, 634149433, 404678577, 602464738, 345449473, 832950675, 402536829, 718612514, 84364489, 16241861, 300805525, 646974989, 18445921, 744908426, 119643164, 781201112, 26519550, 723898831, 537509879, 126901086, 791303924, 846018818, 235843116, 10059655, 669049877, 662093815, 738816788, 832983839, 305323098, 839224520, 363890444, 98412317, 524229664, 834637074, 840397600, 244544554, 678903044, 829605435, 685874112, 116652824, 939981785, 540311495, 569250356, 961992556, 493173324, 594645290, 371633678, 686444067, 300029488, 384307788, 423441105, 692995897, 195614961, 410815423, 749369576, 975346651, 333380334, 181162270, 519964274, 882265311, 614531574, 813099491, 228390825, 326250577, 316427528, 780990263, 681621365, 876522107, 75133858, 509739746, 837674930, 789848650, 141850046, 270348851, 438419618, 241656976, 46593641, 955585999, 70115463, 725855892, 52018955, 61813051, 155533818, 611158047, 975792737, 806090480, 701050730, 552271846, 669986368, 206389212, 239776916, 991566926, 748287356, 121129205, 134697115, 551498157, 730795919, 173220804, 188642533, 136427829, 594458509, 755669231, 589094863, 783090009, 88369562, 63019336, 155312205, 793751468, 16013005, 560085963, 570036824, 44707393, 220882799, 400841256, 739127931, 790840581, 983592959, 773056409, 310921889, 811904898, 31472515, 49775023, 719626767, 123318308, 398063375, 29726708, 841646926, 667666288, 123973850, 245261486, 264164135, 266553248, 640785347, 461436204, 823620881, 783356097, 925072022, 585438415, 220108709, 181414833, 223389527, 421266624, 705630089, 818670161, 356977191, 581322523, 542184916, 811554847, 849567780, 83533997, 782721575, 991612446, 431983088, 347894750, 676536032, 416590105, 226777627, 129855563, 198042931, 893567457, 269181497, 704794579, 884170011, 754001612, 175543958, 623087829, 227090400, 900379202, 65173502, 732461984, 924291554, 775469008, 462798883, 293852522, 156933781, 54247789, 748268968, 959604814, 321185779, 102155795, 902554300, 335723132, 924543813, 503198363, 156904355, 921463083, 953021714, 41348158, 251357114, 675756923, 220503302, 974130525, 315387333, 622960253, 281990096, 734696309, 994519662, 120892389, 779033576, 877017349, 51019644, 643352505, 745054738, 404571729, 190535774, 964665715, 542206305, 490900025, 183032786, 556141274, 117579859, 290322016, 39444073, 401830795, 978655341, 918550245, 126203730, 445101671, 660785441, 991604560, 906620254, 804048625, 433190274, 132313111, 998068710, 53336019, 271221643, 686185210, 59053281, 807698197, 527467880, 307287037, 525134814, 745783578, 240477706, 187411622, 365800408, 54657038, 717871325, 522998505, 826300287, 937625639, 206807774, 385124374, 841882635, 456257041, 840270150, 502472220, 634167501, 60197698, 684469075, 324091166, 246537801, 911404939, 938963421, 856074482, 470517198, 455518708, 588803799, 174103168, 605169178, 936198349, 806686205, 614782649, 621944898, 642438491, 723130554, 116541384, 551215491, 510102981, 783898178, 216546291, 519531987, 321302529, 981670868, 663746942, 806814049, 157411822, 660622507, 626200512, 582293740, 833205103, 810942190, 126593377, 880999919, 540240373, 402444052, 282843462, 397314369, 677500021, 616425648, 79288720, 786639940, 398618490, 296197566, 577369521, 527680592, 438570544, 403798753, 369575555, 429534677, 970986005, 679032533, 260110126, 238755865, 327307011, 923594372, 76810710, 436176637, 358905244, 820682778, 785511513, 490613897, 580928416, 680884286, 324711951, 616866844, 39374026, 435151742, 448243066, 920599169, 256931703, 1378352, 123205655, 862226322, 726808544, 173157251, 80861403, 784968986, 123805292, 694601331, 550031962, 721640608, 536661073, 957470485, 992616542, 614849563, 864997100, 860350886, 629415263, 807302948, 50654537, 176520556, 256483336, 21057169, 140284803, 364396755, 808311208, 754096698, 317507729, 720234591, 121513484, 105109409, 408097275, 827961429, 74567277, 393220821, 168015973, 223080188, 78860942, 765871002, 24940744, 212519243, 33126979, 503446877, 719853557, 712121025, 799423134, 189718263, 102982747, 9090378, 867224821, 374030050, 747268257, 404787991, 302754031, 921061304, 898884600, 550877153, 397985000, 916771928, 281920640, 346754714, 711890060, 897549233, 591237469, 706880930, 208186776, 861209297, 892134799, 292943608, 441066878, 233628139, 758181059, 963770905, 285226616, 203585909, 503949114, 244625503, 51439362, 148257595, 802244300, 593754659, 390137410, 239804814, 975261661, 739550067, 53238290, 996958392, 917898632, 990227161, 782638064, 383069906, 870771427, 353607856, 467858814, 887190767, 16552162, 809252697, 869458550, 67232650, 392634309, 675700642, 838239836, 461603422, 567275394, 92362477, 368114508, 622687895, 233086634, 307123482, 936599887, 113514929, 110742724, 469988310, 391124793, 573743471, 337301160, 752490339, 748799081, 725602007, 715012736, 459366551, 316978874, 267882797, 795626777, 282541818, 582920649, 141855890, 976064780, 622635851, 765277908, 469567754, 968916273, 941988011, 155272561, 781624035, 608345624, 735361121, 857449631, 998653676, 787203642, 55801310, 378028684, 482803836, 510317322, 987377909, 721468274, 377644071, 777397289, 212008810, 950118485, 926497806, 564262703, 124722275, 527210741, 237055779, 83996116, 743395938, 879311123, 388473003, 354512244, 481981781, 352634819, 650079386, 52129161, 599118844, 255743451, 212986538, 318376355, 867985568, 27480865, 170512258, 422289265, 960355220, 967169398, 246861143, 519630938, 327863182, 246915178, 236606563, 246601499, 59287481, 943090185, 508211884, 167713353, 313713969, 283753266, 583841413, 406023418, 349817947, 207495040, 658270629, 447154838, 664281323, 536161455, 802694505, 785100287, 877142491, 735671758, 81141095, 318101189, 286747824, 322360792, 856616956, 523053496, 810371777, 570868729, 260744999, 374067624, 261152444, 316000407, 148960715, 705829965, 777199703, 427427282, 507984524, 522557366, 724887494, 407368112, 221457477, 806605871, 498800, 516860436, 205542805, 692814836, 810744140, 501441005, 401747357, 407949656, 591221566, 988171225, 54683455, 213602235, 420825020, 299673322, 639116724, 837166891, 29050374, 346970884, 912052244, 889721176, 554432358, 295829116, 259629941, 484382938, 608841527, 291147502, 225078302, 128416854, 924312472, 136952909, 663501488, 14385674, 171291340, 410115603, 239367818, 728664271, 225717247, 565770640, 86585542, 920553810, 352642761, 778959415, 636689111, 23465408, 705010825, 851526461, 550011577, 425818051, 37348765, 825483750, 647063284, 570934033, 604802294, 254938480, 657569754, 334657324, 213393460, 420461729, 33109290, 446335356, 741952748, 233032795, 586306174, 602333181, 741645410, 853953394, 224925232, 115882375, 252845491, 301077282, 187981426, 965583985, 247580297, 823200903, 909428087, 716577179, 633601763, 260876384, 564104053, 807040416, 188264882, 348781643, 803627117, 244990517, 273321004, 725318980, 615572396, 39498160, 730345484, 474315701, 867292753, 341814138, 832457604, 905754692, 231160048, 527208888, 117569761, 964143168, 531537027, 582660598, 634893196, 106488951, 848945447, 789358397, 800635778, 316180842, 477810384, 632105569, 30767581, 596253512, 638851157, 589026750, 626685040, 738476120, 635861273, 314656399, 614330164, 811731929, 715547184, 368494553, 562760133, 41816112, 626983763, 8194842, 757300378, 345687938, 95444761, 8971971, 330310294, 138356915, 844992711, 780811685, 863554316, 662350015, 981756217, 661955497, 512497854, 703673882, 280326017, 676478408, 778118767, 682607620, 794645990, 600398395, 318483546, 999860774, 42112281, 681169701, 389190111, 374479304, 165091218, 179654935, 192204407, 339942717, 514737876, 326465186, 118346620, 512710300, 445580637, 725811356, 377304039, 461932548, 180361052, 807554668, 913720589, 265417647, 848193485, 185943915, 64297811, 950493455, 787253268, 559585671, 341877152, 175927661, 334495796, 373652749, 617406918, 448976728, 791885299, 938738451, 51290715, 295362657, 511179269, 22809087, 670991333, 557855457, 803925120, 765720056, 639287938, 890492928, 640082325, 299594856, 832731543, 388835206, 380333394, 443300955, 272268885, 571256894, 487628466, 691066275, 210610707, 129572369, 869299345, 333074003, 331818166, 133897841, 364810809, 120629508, 640044402, 833482484, 145188128, 250615525, 521098445, 849284211, 679111535, 61138583, 462515827, 107309927, 147410124, 85890289, 318398374, 789104268, 131232588, 471014219, 604098990, 380347796, 783104114, 666053013, 871355714, 669707933, 684729362, 678982684, 905014723, 659892980, 29714059, 607467859, 54953648, 652402137, 349656086, 762828329, 175260487, 105234683, 339450770, 434469144, 71220204, 237299375, 23552303, 427174750, 193912752, 554412405, 403006898, 477540341, 324568645, 947199258, 944542423, 155212816, 788435576, 168303546, 605365603, 176348476, 907402882, 628923361, 954471946, 183235945, 412809346, 500977065, 395080997, 250472386, 804674550, 962748593, 515585346, 823543276, 146569904, 351409950, 472993284, 245757274, 880989445, 295414688, 873027126, 427140652, 991087376, 824675374, 650833659, 470600721, 284006109, 482634399, 445175628, 382763213, 59341009, 959366803, 115887586, 841149632, 801656037, 159396796, 870721109, 894684640, 870024808, 142151601, 976463540, 176548338, 514887022, 96806638, 399521456, 574615459, 639210481, 504723047, 796723492, 619572303, 116826919, 94579235, 116884583, 153919823, 135279771, 415762314, 817908996, 88828940, 191636900, 426281509, 226750315, 334043423, 326769652, 44865237, 857833884, 735101782, 794433634, 948588810, 936509079, 289768996, 453085666, 261597372, 488613416, 67758472, 639039031, 629940762, 900155892, 893599286, 807496848, 141035785, 782778812, 789147084, 820212575, 296645420, 79656364, 777498863, 118524662, 483148699, 723963625, 363829322, 912224501, 239986110, 887182951, 484684429, 138960745, 957646373, 290538004, 440171708, 388706232, 865681130, 729209873, 358156379, 927855997, 340320821, 269180127, 938533825, 84374690, 416394385, 555657978, 625197583, 983818431, 188416557, 261403282, 184150521, 442824203, 803456288, 547608601, 427387712, 275010112, 852538940, 323086781, 58981626, 386846320, 11278913, 89563679, 798411655, 402992873, 280588808, 116911295, 288761403, 995082758, 657556732, 485901727, 186883106, 701672336, 924718199, 609923523, 606301499, 520262188, 270989733, 480436847, 967682899, 330861062, 636803866, 991775943, 171307032, 166368071, 661030266, 512017247, 348145212, 138347781, 631368715, 789559899, 990751422, 494237128, 281065249, 7615764, 730338844, 519430596, 330110857, 35750085, 717076012, 107969491, 893002651, 971619526, 789969963, 919237823, 562307279, 281653231, 611899944, 325082975, 744507435, 50639652, 837082800, 93860132, 596145564, 438928275, 490370869, 885224095, 405179414, 123088757, 874938906, 969959067, 92166159, 699889154, 574961841, 983541352, 318441931, 529270311, 897074337, 571661292, 503894312, 237235732, 538368140, 181015687, 437216500, 388270648, 744903113, 652092497, 489021893, 789428177, 11518842, 140106741, 95994479, 645610049, 819553615, 206045389, 862032829, 49074325, 259461578, 65665383, 242709385, 818714001, 679539021, 742793720, 212362627, 322831866, 680828884, 897051368, 202707437, 602448191, 915181075, 638850499, 733525873, 48090948, 278357652, 108805153, 406270851, 482391470, 716730070, 751798375, 693582832, 338346987, 662641100, 90181056, 796463148, 15491621, 947727855, 401391797, 703770580, 188089902, 647585978, 736346528, 776731387, 900945780, 246799618, 392502427, 933419884, 262804187, 671946866, 64651740, 947082337, 263490444, 923914842, 575594277, 102174694, 802031105, 347492214, 853801553, 734552898, 114742428, 396374789, 744018915, 543683737, 137586380, 690225962, 96190117, 335851693, 239260890, 716578077, 979368567, 483539787, 803765079, 951093732, 295734572, 344632408, 674771583, 847826720, 107087323, 526444498, 212290010, 768165140, 585750021, 615909696, 703634135, 278155126, 721767600, 324525799, 635109063, 974568025, 229185519, 872348228, 846998436, 827400780, 329258480, 291177182, 607572311, 905841432, 389209918, 903761194, 216657559, 126103709, 436082951, 455131256, 20030753, 757727071, 784894297, 914929410, 174649086, 967855563, 50378868, 764852662, 124185849, 700620842, 454655766, 374270105, 711527338, 724012851, 245742454, 952575170, 356505130, 39749591, 154138480, 199024850, 783659183, 860259405, 714117923, 409183039, 585029155, 409237250, 779488707, 349294158, 246047000, 922645648, 174005549, 442272778, 449382032, 44422906, 861828586, 518370627, 646906342, 466552068, 313564982, 230468785, 491703384, 118907906, 342975989, 403044520, 986150796, 473960987, 988596066, 483056144, 899206886, 976220354, 393727457, 738631586, 35370017, 209638120, 663916348, 435648236, 359787862, 386042271, 838972743, 480436658, 717486816, 337560499, 856561019, 189009309, 691866877, 589908424, 690855758, 677043855, 52236294, 436942311, 138668715, 903881266, 644729156, 570880819, 851641829, 119130578, 158647249, 265067536, 319133278, 602881591, 575044966, 362670778, 701496650, 778913612, 800258318, 780771623, 871265949, 797052451, 307124640, 111567894, 510433264, 978617952, 438011365, 667369847, 258875161, 619057842, 403681504, 15036410, 522672305, 586707149, 327105814, 322191246, 200907823, 223097583, 998000572, 214975558, 189730824, 54242317, 151713854, 37541955, 772262903, 206820408, 70239638, 175495493, 804903289, 452176825, 485702295, 408031754, 369444439, 605991969, 768275146, 432871122, 593203761, 260875095, 535117890, 432772473, 468604422, 321045308, 284761307, 573821579, 981280943, 105413446, 724969841, 837388010, 563594099, 313714916, 875058114, 853900500, 314941784, 712833989, 682891818, 448259289, 849915877, 603256707, 336711246, 213445115, 662233881, 956868626, 312091558, 661954037, 307145295, 910499556, 357539613, 952564625, 301223959, 235023799, 809616831, 835059706, 541107604, 899684843, 159481304, 350845391, 183445280, 625343229, 897354688, 607674750, 980072154, 758873997, 720258613, 364512220, 352867464, 557207255, 68690418, 34746833, 208075392, 32104559, 340166799, 987626891, 882490464, 465427317, 561139561, 212020148, 934778728, 688780560, 162230586, 11971330, 204207346, 419325044, 460525608, 793243678, 127202430, 613961849, 606760899, 10541522, 677618950, 322500030, 224060262, 143124351, 762240382, 938467224, 581692656, 609097427, 886957669, 247419971, 229756663, 142209943, 934782713, 471522904, 859496502, 614574162, 843776901, 205266383, 398047214, 57288355, 532825942, 200137623, 470495078, 144524624, 170326815, 376015095, 533863867, 759673549, 998699328, 741941265, 516667024, 169375742, 961912723, 361564545, 810905419, 262778980, 818617122, 866746048, 350055198, 79455569, 205261501, 30507996, 600873300, 848653527, 769764347, 939986158, 977138688, 444563569, 661968506, 655885411, 98834877, 74018776, 68329601, 589462281, 100905093, 484075444, 932004257, 817855771, 443758370, 378798110, 286922747, 76274185, 10150141, 52709425, 353614094, 128742904, 158588337, 918401916, 609906979, 700645434, 941063004, 456281942, 352931440, 675107287, 778533508, 980313993, 603828476, 301556626, 52393242, 663081592, 572038496, 283174646, 202529124, 610274558, 666975754, 437269726, 932548569, 457470285, 768680411, 429334727, 543159409, 945879960, 694322962, 267777562, 337683334, 211323421, 524454134, 561237792, 548634924, 636213244, 336610837, 863838724, 505352823, 737092209, 308173744, 26816973, 892715213, 532592258, 770782103, 18622928, 806730039, 999589530, 696950731, 561519435, 749233635, 697751756, 793045245, 10530105, 213733422, 462718188, 203533897, 168461356, 56592899, 616317937, 571128460, 308712040, 364767615, 212558881, 147632306, 663275009, 10242970, 541348990, 116874199, 90471944, 627029576, 898907920, 531683895, 320836897, 847778265, 706685937, 358451669, 949264036, 106725023, 259243854, 440584444, 931306379, 409688476, 444747466, 169693624, 159824607, 151902134, 788435556, 621969997, 20034060, 359296648, 131477712, 23510418, 71349329, 423224598, 617575737, 769855159, 570396128, 638022111, 856095407, 338747191, 714293692, 783942519, 791649905, 896330191, 82598064, 323332464, 248076316, 537864339, 785484393, 185044856, 694587856, 220663768, 156993559, 803809791, 163713227, 78241483, 63459609, 852219716, 372348943, 153910385, 76181153, 18611722, 143752075, 797446352, 442717264, 429358222, 728905465, 655732300, 548559980, 890089888, 712937001, 547964127, 971802371, 589593282, 135410616, 414798473, 976976197, 246922560, 323642778, 112485706, 763674751, 214845162, 675731454, 661514323, 182964562, 859229256, 450660940, 243014003, 128099180, 420019047, 856121028, 404993399, 597692910, 762714258, 395485188, 376083143, 476028465, 979701564, 242754010, 41257038, 161340683, 256142972, 787489415, 367095526, 688020922, 337285489, 924587111, 502487129, 705919011, 434231190, 558754565, 62291718, 189199207, 340204150, 246259252, 531298199, 758049085, 231467839, 957339598, 748888965, 281708, 160379157, 456038638, 747327265, 427242777, 667172234, 715804440, 590029615, 188759074, 470590126, 461241144, 715405580, 692451459, 108256736, 86231335, 645124093, 770589730, 193075035, 693120435, 513004794, 868633932, 523097784, 162059453, 645357818, 818568614, 770066142, 140053890, 74348168, 866794075, 985620547, 529420181, 551581940, 258448379, 925264682, 37512218, 836344874, 492169271, 711412412, 341338229, 57369969, 562117697, 252689440, 555765588, 941919391, 545248167, 750896944, 497525939, 979434766, 34349308, 702125976, 431644789, 7534854, 279318784, 979533144, 242467133, 481612524, 766440538, 391476320, 225025370, 315918345, 780686365, 871771434, 666013411, 774543693, 191355517, 142234436, 951831670, 151530222, 352637166, 250844024, 967281828, 937359112, 334547754, 572096656, 839414090, 383703465, 590005873, 374754170, 330641551, 857122207, 294256817, 916719887, 382879295, 72598427, 32699200, 660056894, 728326288, 477209003, 873286887, 566960855, 243491282, 8787124, 460818212, 27345843, 983620271, 934028160, 104775365, 646849451, 769927682, 745545742, 856821237, 866330868, 446247615, 725538542, 405603064, 31232245, 150584408, 125357611, 465929638, 679513592, 604678829, 177306990, 564964163, 742374941, 69532808, 760634506, 101180948, 731010851, 280811032, 508861716, 398751391, 734919634, 218992181, 74238762, 786789689, 986910309, 41684574, 388791481, 928682614, 943817798, 395708186, 744931239, 451238942, 704283278, 328983643, 417098197, 300767095, 318176186, 993185216, 798822361, 887890169, 160392928, 989790632, 960382009, 311767421, 643533816, 764395459, 471139047, 374925480, 69200572, 497588713, 355469423, 111454915, 976381007, 835642213, 573759419, 903537791, 295911053, 216639958, 170374734, 755872914, 499500598, 109732792, 140779883, 658225161, 557510067, 634950527, 337146289, 21663321, 61548589, 17324940, 498680761, 400656237, 934586170, 632432153, 101496090, 397722235, 222029780, 471138321, 235809453, 7750640, 288424380, 229913019, 971234797, 437201747, 657168457, 557876862, 574282910, 349258255, 923755638, 439911445, 73089678, 139894962, 956953073, 692262289, 671080128, 351030678, 172789877, 958217376, 606565252, 387497466, 516609532, 332382153, 472653680, 856904874, 118370612, 527373378, 54449274, 82145388, 522236790, 413478456, 822588007, 428622596, 579107894, 235944912, 107316345, 292786660, 44302588, 895345529, 599649088, 673335957, 782494371, 526554597, 533156686, 627478078, 474769492, 772508830, 280580678, 68355712, 683801907, 180479012, 703392650, 37778140, 223314981, 664241539, 154865145, 953664582, 674212168, 910311027, 17782610, 518044648, 657771781, 594388300, 56746861, 725818611, 861851453, 674155634, 618613956, 583570024, 943720556, 980778381, 666474265, 552481453, 640310826, 713260841, 941292631, 901798245, 200287261, 809947964, 268406650, 539594846, 949547469, 528741271, 153345135, 279413164, 609880628, 986037675, 379125257, 503342114, 57687379, 626056123, 276024130, 978431993, 198888593, 933116522, 403494470, 6928119, 885536173, 821580891, 974375702, 261090512, 755816186, 618690194, 67219275, 393322988, 881518238, 752071913, 283520128, 652155102, 674434609, 484551103, 624832366, 752868357, 512097841, 379244051, 445132024, 974460660, 363028579, 6874969, 250953489, 705997960, 48991132, 476638206, 843845249, 465596430, 194105032, 656575431, 654881973, 900563095, 80279676, 381439151, 609359732, 891709823, 715516057, 228216541, 847694029, 821315035, 360541477, 363845282, 987023658, 505837585, 209209190, 236444598, 953035814, 315490609, 980838820, 228307374, 644561617, 196270943, 9254941, 532817167, 273924567, 884155247, 601202434, 308150367, 834668736, 876534523, 838149513, 606322725, 227778444, 167683437, 191517783, 145435289, 274083749, 535703768, 812367731, 431891234, 698781132, 661511992, 351932088, 974009259, 633830826, 165957337, 418280078, 997414259, 368480267, 637227862, 233543771, 491635629, 693015505, 929079886, 448451892, 793729464, 184535925, 40599160, 553583001, 239196061, 324110871, 675155179, 220440163, 128438268, 277863447, 944990152, 178693379, 978682455, 166763445, 534196012, 151311001, 306723006, 128460992, 39237382, 175347244, 376413562, 419148593, 821441359, 316366575, 656785837, 186487943, 931889246, 682323257, 635603200, 262023278, 980330556, 950479837, 195045250, 112688703, 12679190, 34059048, 893639030, 614920146, 172557405, 246644828, 81480109, 282908560, 129594521, 224203557, 332528784, 170238950, 968822602, 639962940, 305505806, 778672338, 159776724, 433032717, 402623453, 688048747, 519673379, 791614817, 833738802, 723908027, 634816206, 91868556, 494758300, 861615915, 588071767, 712717132, 441384025, 664269990, 584962110, 420589044, 429778924, 856583103, 857212530, 104379549, 323036744, 993895849, 341234903, 295557155, 160542746, 766670956, 775739221, 519900558, 25881699, 108879159, 41485711, 305758089, 232072624, 491383580, 659564379, 789176775, 864796159, 318293600, 733285122, 885263820, 874955210, 413929246, 705871216, 249463673, 564356735, 986557035, 341969050, 613810143, 291446674, 566502473, 598395702, 898031857, 505579680, 361012711, 647508560, 247417847, 401831307, 148704542, 385352661, 147977102, 777942575, 411629724, 905271507, 397094785, 969600445, 45755440, 254915025, 410220775, 93483053, 684824053, 894518190, 621707319, 268542349, 551227172, 531265861, 894619580, 423728630, 54193442, 893011623, 325406729, 516927609, 573046494, 867793214, 75405460, 693236639, 959445383, 154383084, 95273405, 401999555, 725242222, 141017084, 286914405, 438528218, 70293461, 195065644, 333990115, 407783656, 783446028, 2718859, 615529927, 961938888, 608764422, 431641245, 772297762, 644113138, 32940002, 236793275, 931468514, 574942940, 493347008, 313995593, 841597018, 472273311, 636264222, 94800549, 356146909, 806666173, 465366862, 136687333, 509478966, 393778975, 57087691, 217478205, 856652678, 928623875, 522910316, 675064571, 905980428, 955432379, 963700290, 192010413, 138414571, 751295162, 627267739, 562919220, 505173893, 694985004, 452463796, 595893908, 316611872, 238485372, 88548817, 448382113, 765603069, 505940461, 689720889, 45735490, 653727364, 478330070, 169123248, 935841814, 924247522, 434163582, 27562616, 138793333, 542552482, 970788689, 370873414, 133978434, 770491668, 650286552, 501963448, 913588062, 866512185, 120255658, 936933347, 575710004, 742762026, 353305672, 810887194, 628365981, 648458010, 976809617, 494013201, 458032947, 149462249, 316609080, 192545031, 81156001, 462179430, 77629050, 990200624, 482445380, 633414481, 30919382, 198373081, 826670428, 78780518, 500799070, 244731095, 731851006, 714799389, 478090528, 683395212, 220561791, 57677640, 581684318, 24592425, 807224603, 253923794, 6648737, 641815160, 946515629, 601189007, 295429589, 724166194, 103904872, 895479827, 459849278, 181590841, 597362604, 213238411, 426348150, 497527986, 900475387, 254685085, 371576512, 526145244, 983503716, 662183889, 761137791, 472761606, 150872941, 588067951, 627816084, 34039018, 230224992, 802999123, 149621444, 560788397, 742565733, 303163718, 744034431, 464943601, 254249756, 553700034, 722290998, 356024927, 825862682, 394803470, 124235317, 126375142, 458281212, 167836352, 682499975, 680669224, 651982925, 15846862, 38973407, 379090352, 164858392, 343924897, 947097498, 690986656, 429871319, 207274775, 638018159, 275472469, 665721478, 81313317, 964954965, 5652119, 57835003, 455987719, 405609314, 10652910, 129502143, 656292835, 292339942, 807802627, 661911371, 182866301, 9614639, 35291383, 34143555, 236889110, 112488112, 390946784, 919510703, 526791905, 596423793, 777427963, 525126199, 685293182, 621550648, 588240691, 73290389, 397584867, 30306696, 84789863, 399633369, 569638017, 961457575, 134153532, 794522547, 430686756, 961658782, 8314073, 146805770, 473978514, 130841861, 595136075, 517019641, 174534059, 774452736, 460972639, 330680974, 471300943, 242130090, 501049571, 383907314, 18244414, 925917097, 3499151, 184166853, 991353060, 477466196, 61732065, 654069549, 861391821, 169048962, 158945643, 905870925, 434183747, 566267316, 310778060, 768418109, 260314359, 873192777, 370778554, 883214671, 842218534, 698444901, 794451012, 252503505, 354587135, 49969439, 118413335, 491312063, 285801589, 151179962, 880912908, 467120575, 380898564, 35781682, 46226363, 107864371, 674688589, 218777394, 332618017, 417727475, 62360458, 805487739, 903000237, 406822638, 8444485, 317444833, 570144854, 201277147, 252818364, 265594487, 928712547, 753765319, 44913413, 398548478, 449330892, 994246, 218534696, 473764093, 391775216, 737505453, 932344134, 577715135, 683129262, 551421305, 274722668, 832058276, 546335462, 340031771, 504443909, 45603197, 66319610, 952448177, 278348156, 478690854, 64301139, 100265770, 619103327, 138592617, 699861147, 601941794, 530133207, 652322072, 381043150, 142886516, 772277414, 69469121, 867496664, 973485975, 841921732, 774037486, 813260857, 574275896, 950229980, 2429869, 187137962, 917087000, 14413231, 675373787, 419441974, 607437476, 203539393, 930967964, 870820072, 403849167, 930483985, 590949548, 240192998, 686820273, 312838503, 818449881, 232260230, 358981851, 918851287, 15818095, 176690302, 10054499, 608789773, 705916783, 929215594, 63324756, 660465474, 357764737, 79972289, 945229909, 741139638, 506401654, 581578948, 323479599, 434310178, 708657990, 433584891, 996512177, 547245284, 543965365, 509077262, 337770930, 441787141, 949307032, 100007861, 417326601, 287323006, 308480604, 855960009, 889511173, 920221349, 959703408, 453225351, 69551540, 871859359, 184595549, 594760432, 877916111, 936240980, 749509577, 602518914, 99513824, 211537733, 503743879, 914846533, 55307954, 550399533, 272385891, 480041265, 75919434, 220065607, 889405185, 873760112, 961939743, 627407044, 7637873, 990829265, 189548478, 857273633, 412403858, 319408915, 115397293, 470525240, 438044769, 388161925, 81221404, 343272193, 168773078, 414451980, 927169641, 840432092, 60200394, 287938449, 795715272, 103322605, 342531602, 429124392, 804413389, 850634660, 11194999, 520448403, 943934586, 732085757, 936418042, 320333736, 689445464, 346809456, 756848603, 61557733, 136623175, 748145390, 546592825, 41839616, 811967140, 625398456, 265614930, 828807344, 780796487, 58990671, 216059173, 805632215, 36971330, 865153510, 466344612, 625371751, 155703511, 403433621, 867609387, 133270048, 957249520, 557258079, 722048102, 103390112, 285914716, 688695462, 14889747, 21825532, 848465385, 847284451, 689945476, 609440999, 505304158, 385561927, 472701890, 731590588, 524632271, 957033094, 735397318, 431386154, 38741870, 607232941, 732662979, 405839283, 870043538, 593022820, 531163555, 390074488, 590443214, 427400915, 468155080, 98198300, 459539122, 728999819, 741603743, 849546455, 242371107, 473193379, 274476848, 832302239, 280073036, 62152143, 839448346, 141824282, 623238828, 742242125, 185531734, 483202674, 878019727, 16752256, 963041291, 492202018, 384359103, 577813656, 293771873, 377164994, 275864029, 591155379, 532202419, 60521339, 982902983, 271593107, 353499620, 488996538, 536796034, 597486273, 938422163, 979072282, 696256158, 774146843, 508747583, 349838551, 539626011, 909820265, 540231806, 268467466, 426775704, 360011330, 217643095, 785266779, 656046786, 146912279, 642111574, 126309692, 63464792, 804443804, 722000858, 284256700, 214862883, 514106659, 689616573, 953826865, 298043131, 374698265, 547862100, 438351110, 501557323, 6129727, 126773850, 14072773, 655938717, 710586504, 133854259, 86941392, 56745710, 241845514, 184145766, 782259519, 347597373, 636764334, 16609372, 743841760, 548120262, 49431529, 898793315, 799298252, 479355751, 825194621, 310899884, 331611391, 566646319, 807883733, 517129940, 515938140, 733831381, 256386165, 736995747, 686120613, 966306429, 582998755, 55934710, 521003609, 267320874, 967655392, 525803263, 640505915, 982330372, 296839831, 876544264, 744601599, 710686106, 805012920, 555330192, 990241991, 876252153, 552172492, 530064934, 140030733, 965787233, 246518895, 710998686, 115434236, 613596595, 314812599, 109094555, 172652523, 736723794, 310728266, 703590408, 207549285, 310888248, 411690089, 517121388, 251549134, 689441821, 439706738, 460609898, 179746000, 939234441, 218749407, 343138620, 282104146, 603663822, 576233223, 42800157, 896132805, 754703490, 458469521, 490350175, 286781349, 873432803, 675516680, 45617457, 773821869, 860722992, 384068175, 116877532, 875767891, 330728248, 521761184, 747436269, 343445706, 331982156, 693539793, 423865207, 78546411, 727930859, 177170751, 59590166, 404000933, 942230814, 233526134, 240486942, 791300523, 52884721, 503581288, 987180327, 860614582, 101121765, 558620090, 564027921, 342865253, 201929667, 481213172, 822253060, 948216668, 414079308, 42449612, 49783742, 650272608, 637716619, 288975219, 400084104, 854553232, 758102546, 779793185, 560329893, 460365468, 510395043, 27537479, 934905343, 739246393, 54953035, 745765655, 225243724, 197815441, 585376039, 553208326, 542473993, 798701891, 200769929, 773024395, 394986224, 856262911, 417246375, 739176610, 930577819, 484504752, 306620225, 15621692, 541382508, 369083814, 692397, 501500906, 380744893, 87947670, 191344390, 4077235, 743865683, 664489456, 298719208, 938004182, 231367576, 647202152, 883331645, 529744469, 856625485, 125122127, 485921030, 423619858, 711984330, 552898347, 225710203, 998979190, 398243972, 681149413, 462697954, 831502859, 915299904, 346880581, 122978255, 626238894, 773600477, 939786137, 591806048, 915165803, 498763939, 114814837, 101947980, 441782771, 977571301, 488527168, 92606068, 81217753, 506771393, 149250969, 757114504, 921918855, 539167192, 688695788, 900210907, 942083600, 380940844, 668345257, 325013060, 105849145, 372188296, 733026061, 913919282, 192799489, 315631900, 185339978, 380221455, 265466568, 451759051, 364643351, 203591307, 394905865, 496498951, 387985854, 257370413, 757270258, 776916265, 464924170, 672253182, 685607618, 861189577, 454751282, 854187117, 436624941, 996597851, 780448920, 510926924, 921431998, 761878626, 736577108, 777911635, 583440432, 35943737, 652549544, 675561674, 626065631, 215709573, 109510431, 930799406, 215849034, 201379357, 513049615, 386030881, 589919353, 364274609, 324050709, 319168128, 874837522, 797863137, 359613078, 477473574, 4008190, 235856689, 38080743, 419105419, 717840501, 412476512, 218906034, 946200794, 126664968, 279532420, 10935145, 285625031, 247213061, 799426257, 440773759, 504444523, 393982016, 944057572, 901772685, 520558016, 457434162, 850273402, 693089251, 623308373, 691002275, 716673987, 763840263, 775950234, 75699646, 109693652, 413677083, 79329986, 990633290, 623156852, 184835268, 328127669, 345549715, 996113406, 320617475, 83944293, 866874687, 690432371, 336212778, 108712148, 882212362, 544256218, 25944592, 604741511, 176997982, 249781612, 619260866, 911634710, 429403664, 829192628, 207393763, 828713249, 264300551, 677347448, 36105324, 819603495, 167808657, 222084465, 887409209, 301666820, 472668016, 299918680, 678228690, 553278684, 347505782, 614453871, 609444444, 504086630, 146767029, 350623220, 842310530, 295471744, 61966062, 995828364, 404471237, 171706462, 871832720, 749340886, 810447015, 165391194, 31484329, 562211656, 871400322, 629543470, 15618314, 932800824, 20998827, 913338310, 538031792, 494221503, 538754386, 117892948, 108804231, 260503398, 796904156, 236996635, 259327804, 865257547, 430505754, 743314894, 49580071, 55203105, 748854594, 14530801, 555210778, 481999594, 627159452, 716652777, 510171631, 754202806, 67823423, 798780979, 741963456, 182136443, 451000972, 849575084, 636185519, 918749173, 518909674, 744236732, 719808085, 325828790, 997946625, 812331768, 574159737, 816731726, 119665845, 92143569, 411319501, 815001129, 707427224, 557669191, 719254203, 589101653, 58670420, 891480517, 429272299, 98290621, 70996104, 544756970, 114046580, 204682070, 368495530, 865154696, 724421540, 383615286, 156479286, 763327095, 934443394, 315972798, 259680518, 607890589, 905498598, 678432401, 222325312, 491137753, 347553486, 261960740, 83440771, 826038604, 625939262, 843495031, 456551997, 665399128, 348048258, 637146193, 375648054, 992241725, 624690957, 192455667, 226991159, 112336004, 102415435, 94766586, 357316942, 958508289, 109431600, 378686952, 223110976, 365387093, 61790558, 4305345, 310479177, 620222449, 273974713, 492539519, 421552689, 634064587, 428545232, 36759194, 688008460, 650818686, 605205452, 907320328, 40731160, 835361205, 971397789, 803554846, 968668888, 268427766, 832442624, 262546396, 60385062, 874408589, 253428235, 824310062, 637937891, 751278161, 537610047, 773123986, 777663096, 235932097, 191042306, 60387045, 959395889, 335934931, 545651919, 631973753, 64328894, 151924662, 902841180, 518629371, 106372226, 607400728, 417862232, 484763043, 48382581, 7238106, 873986446, 496492409, 838480870, 327608294, 598002963, 732081293, 848459801, 52710376, 191494163, 10034804, 944895442, 694093035, 520439146, 341400096, 444016344, 40333641, 864475497, 478982999, 877753800, 211130860, 386075565, 532641885, 746410110, 26511846, 439800408, 676618816, 186060085, 738260876, 673950048, 631110822, 143242456, 853210207, 333146392, 177698261, 225875153, 872990838, 108186180, 603743634, 580998998, 676431138, 975801615, 559819598, 465184647, 425797421, 469370768, 571353559, 436037778, 458740016, 472613564, 578039894, 278203449, 92384578, 939028913, 2610393, 4685679, 553893037, 110810620, 442359464, 507257727, 433197926, 870915119, 354035288, 240640403, 964431858, 68764901, 878372096, 564141506, 839282659, 781044717, 651138230, 174714550, 657829470, 707127707, 327118806, 290654483, 987421374, 469931230, 210978542, 970343452, 618517645, 625746015, 506944666, 733026174, 410555968, 330093717, 125541689, 170430635, 451184975, 315657565, 347749123, 291113714, 219714648, 701350571, 694094538, 245040473, 311765590, 193670467, 41349642, 544700076, 864321874, 406380460, 29093898, 768000128, 867175163, 164161404, 82579138, 129798057, 173496475, 499968, 305823159, 298906017, 548712060, 808205467, 540187711, 243405053, 484846261, 780457000, 316392083, 144063002, 513202899, 820339603, 886763602, 780455108, 31570907, 309037081, 297912821, 205200811, 483836632, 141187810, 563180374, 226082717, 616268183, 266623128, 71716190, 56218417, 462688011, 278562666, 254508093, 12907112, 484587893, 343510996, 77818150, 781459062, 247887727, 963792585, 570210730, 330814795, 137635205, 335435199, 609717095, 516267557, 954613012, 18640835, 899463031, 5381238, 203119750, 775592130, 169488739, 212373519, 879232312, 474425822, 648987251, 144136652, 715548053, 627105628, 359154330, 923911573, 457234803, 660105343, 380760875, 64943931, 680729019, 373005026, 756841016, 604040149, 513434184, 399048364, 412131708, 526512018, 737764716, 437549843, 124651879, 146339268, 629990338, 88174945, 636285431, 612383982, 636818299, 61442849, 135261181, 824410190, 670066409, 547052861, 225501824, 465557955, 913516493, 706347186, 451747018, 629495110, 293143200, 362072734, 514092985, 331306986, 879007223, 398825355, 31280976, 364029104, 466972992, 225573984, 683684129, 295127707, 692487117, 354498439, 300385785, 183467775, 695375073, 175391772, 462259009, 370561361, 432845065, 428155631, 377203975, 29199072, 302569894, 153495087, 737490044, 212686665, 913118944, 734649581, 749029946, 522379753, 885725981, 292515587, 811209122, 709282792, 452520489, 537071427, 530717233, 663290400, 452339825, 739878071, 293684009, 413203968, 980234894, 840218977, 847896624, 759571188, 592739820, 704988836, 471315132, 724100691, 139785401, 780068022, 797409837, 274482270, 197083337, 736719892, 288913058, 702436445, 897611858, 78530999, 212968490, 955044941, 761912531, 175000405, 150933446, 194757998, 617127022, 445598301, 975755247, 314214018, 664159586, 788275013, 838097427, 786750770, 570554307, 28431834, 291248139, 967021, 838120797, 376691541, 917162576, 369592343, 139847660, 748220124, 740354800, 721264546, 560067999, 672147147, 515952403, 387159939, 386230554, 998883730, 402477236, 609388772, 229545479, 638399609, 961063483, 941202497, 425049714, 65636938, 549139890, 536488189, 47581705, 748415721, 787541121, 748973777, 657351309, 612151374, 895070220, 952641990, 345503879, 870560007, 517880366, 551503116, 637567067, 662041833, 551875100, 744607830, 518523952, 686118059, 292517752, 461033110, 243801198, 184177760, 917381610, 508594634, 622815777, 200517875, 307967170, 293682463, 442524763, 658391749, 358778425, 84651907, 792276831, 397953175, 998601867, 357636412, 979967701, 506546606, 864539464, 214334619, 233357200, 234772717, 717277520, 193598121, 329751059, 96036989, 904047526, 261761569, 60421522, 813719462, 684679691, 742738791, 854976801, 880666899, 131626387, 752310513, 722703350, 211832185, 15785901, 345922588, 444606484, 657688263, 85574049, 766389887, 783986778, 85179165, 620858762, 324410091, 761454578, 284860430, 995203058, 139583991, 952564753, 936725044, 377390086, 227931860, 96502543, 620979746, 770202432, 591384898, 89307983, 623223432, 542011215, 103097426, 157565491, 737500924, 178629117, 926298481, 319923850, 229653554, 585947167, 280693975, 224360660, 984173369, 50937479, 504251750, 315233352, 577829310, 805372831, 741266914, 661554790, 239112590, 54537709, 850444762, 384061259, 223182865, 508291491, 789188968, 699965037, 283772547, 420626274, 140946215, 525394009, 535204655, 525736822, 568361031, 814574304, 648909831, 269389260, 321966068, 9472952, 641215355, 545712360, 39457190, 115738225, 498459872, 562607671, 512809458, 48698146, 951465845, 365831359, 982160987, 187566830, 58410623, 574149634, 140231968, 838453375, 882789140, 846391837, 314156340, 379893743, 471382384, 210024446, 649553122, 330794535, 956122932, 636572538, 38569331, 358732948, 992451061, 707534191, 492974669, 625981163, 678419963, 736737933, 866586096, 526565619, 423774982, 117259611, 997575977, 736278719, 949451336, 746051048, 829994523, 18506121, 612394437, 471002382, 107848717, 954553124, 507536560, 453546252, 333518583, 32661411, 663225706, 749321607, 179334377, 179160560, 631013870, 559759066, 684212958, 642835206, 461709819, 592255908, 285752133, 202932748, 905828149, 631507431, 4158795, 335426559, 42635911, 553891742, 497514549, 785963639, 244675652, 818581092, 395258477, 307720089, 326037131, 42338700, 896183243, 616788491, 895821559, 764525210, 995869956, 993446121, 565168035, 963369738, 425959158, 970864975, 671127793, 947098313, 807714391, 974854388, 396940136, 702534544, 32748840, 124784343, 823120796, 864352422, 637512592, 551938814, 13128439, 578394109, 839010744, 983871087, 773664886, 1550709, 841928390, 910335699, 466124260, 150406453, 955717001, 921487234, 813846183, 743577532, 141941943, 603805065, 80486056, 215132518, 812016259, 672931678, 70813492, 841941315, 392719040, 538522713, 3881057, 549140222, 139986275, 523921705, 581574162, 788073208, 576413306, 229030938, 588761220, 197713161, 767910132, 837735216, 893861676, 549487501, 702763806, 358248891, 609143780, 975300789, 210178585, 87162199, 202208269, 675093787, 514131697, 402875834, 710026571, 490914429, 831339899, 340355125, 730008929, 640251617, 356031243, 699848215, 485472865, 573381499, 98110951, 379412077, 115638441, 769127166, 765922120, 910908633, 101061257, 323515174, 389711123, 49242413, 575768851, 276245998, 942486583, 788078478, 46340893, 81571564, 501503208, 915315025, 937775741, 938899149, 79054886, 717539293, 734547381, 217437422, 977579716, 451286770, 127464693, 867708006, 372973865, 634391465, 715352992, 658666838, 179521342, 640294833, 750906312, 310899783, 540427794, 102698722, 850790133, 167745272, 825672054, 595596789, 372236915, 926750521, 848924191, 126748025, 952458664, 137585089, 401306460, 443587943, 447358777, 436104745, 577422922, 722806353, 378684339, 351851556, 383303700, 582352223, 641930375, 61630033, 219365875, 638604540, 236212292, 384590886, 955551269, 288082880, 188808217, 352384269, 812225720, 616859620, 458364680, 396235850, 701129792, 549239513, 846226569, 231484844, 557679211, 273452421, 837246911, 379188180, 329013427, 96829316, 230718796, 25948862, 9134047, 152952310, 243048751, 623655566, 321353120, 999870014, 87047716, 164508200, 272988433, 588328863, 492718644, 548770352, 326762970, 237264758, 236519748, 67949725, 457387111, 275728104, 637372539, 197202325, 429185166, 562794583, 980008803, 155016222, 293815421, 809852146, 3845547, 367428216, 634870224, 927901867, 466228224, 242480189, 720641003, 855724400, 546821104, 659675497, 646454278, 887594794, 601444395, 817367868, 480323440, 758422877, 333764985, 205270944, 441251510, 299477142, 253054788, 169562772, 612732292, 621638462, 383866295, 955188137, 768485969, 638187000, 775324004, 104185875, 671417977, 742683216, 536484586, 69394759, 624450231, 244698819, 37680127, 818110967, 442698165, 225597303, 61194339, 945102988, 204054666, 526280179, 336726725, 640828786, 351099568, 689899781, 503761316, 251976856, 103166071, 140954666, 107688329, 984039089, 851338740, 589034534, 628156587, 833586081, 838543932, 197365677, 453883250, 930196208, 318480696, 266359321, 110794534, 430246273, 906015050, 396988163, 541799060, 153537979, 609824192, 664071885, 816178952, 9279150, 350320948, 374626915, 565893743, 434904912, 334673425, 110734824, 468266583, 960854404, 681228509, 437417365, 419772637, 597398472, 69517602, 878936972, 892583931, 239171785, 197052267, 720550197, 677983155, 54711141, 138571903, 725223167, 812085287, 168602114, 154767525, 670868973, 74945734, 215085729, 174253080, 376143870, 29592049, 382740636, 928173946, 913427823, 378824356, 434736962, 14910100, 609162599, 954949855, 547613079, 672436860, 136735194, 592012357, 319434436, 936487938, 74758540, 655716703, 431079800, 25074647, 310807184, 600616085, 223497135, 384908221, 401620180, 250918782, 63763380, 412362426, 958512209, 941903727, 838408387, 32570081, 842444367, 258805329, 20382997, 335369157, 840337056, 788572685, 863125298, 934790333, 999168694, 68844124, 857008303, 857824860, 48797412, 568670590, 99486127, 17413746, 485817491, 890033118, 545530197, 712968237, 932247843, 157688188, 248563181, 347811279, 609386350, 438732276, 282030187, 124587605, 630470127, 453902209, 392714533, 910149686, 6635204, 861565695, 323455929, 69711607, 831789236, 992936820, 428995323, 656350347, 753717044, 28007109, 303447694, 296940302, 116798105, 173527802, 665186050, 258437651, 790910137, 991933796, 817228884, 636462771, 269991927, 746779027, 424110266, 34425389, 699890465, 332913508, 389426304, 620118516, 62315091, 768381800, 288480875, 422618667, 612204754, 566237086, 300690020, 576370635, 877795535, 86791427, 292844023, 848526189, 75375825, 137114126, 351103153, 844826490, 594780965, 21085488, 270008381, 817177773, 34530276, 873225548, 477813160, 834679627, 709130464, 613718879, 233642887, 260442059, 727278502, 245577337, 96967654, 262239625, 564810052, 754128515, 131757319, 703234080, 265491480, 959940221, 403699864, 433811200, 580250451, 289188711, 382783134, 91057065, 127900959, 663625752, 148567402, 919647835, 879442284, 286597822, 85395546, 225405721, 647582027, 169841590, 770892834, 102088978, 846374229, 491817505, 190250902, 175660702, 488798846, 422931688, 583436289, 554029681, 97356660, 390187478, 98179225, 142863020, 13692329, 677507862, 6435541, 42689595, 850413912, 800296380, 677180272, 807323114, 847103310, 448042816, 874206164, 123065255, 894559862, 73061306, 537075223, 572998584, 321882901, 454033297, 2052489, 331365434, 975478485, 63758720, 31031667, 293613910, 248275063, 434085693, 628505793, 135165651, 969801883, 195571695, 939121701, 211445163, 423218450, 15264023, 915528896, 796150655, 708608752, 169837642, 507526394, 513608222, 857176044, 51228990, 867923624, 815991917, 714572536, 740384167, 675390141, 37571474, 257702414, 626603897, 624242324, 143621020, 955879228, 320775505, 628196240, 985728023, 826954929, 834165336, 275251261, 367361683, 827494741, 497728372, 240903387, 118933400, 811283606, 339811870, 506013119, 525822938, 101199817, 829842907, 471531998, 689654450, 135505086, 459203836, 507527360, 245262234, 619443734, 245384529, 930173217, 515392401, 262027844, 171162755, 75533323, 479766044, 212603065, 255166034, 746513188, 69212527, 242677643, 477679830, 342929616, 18062275, 35492604, 778388300, 830730628, 774449364, 713134588, 897820265, 8948985, 861566664, 253177568, 938215750, 703042633, 442667937, 274179389, 538713735, 272751086, 26585804, 398185084, 766297598, 178308568, 948688720, 333402137, 167068773, 98069347, 902762806, 475475181, 813660334, 274242164, 910662500, 56274373, 517592720, 27143157, 682378421, 804577780, 822951821, 325320065, 44214267, 511680524, 273514209, 860547191, 392672688, 815549243, 281346877, 796917207, 44515563, 667798424, 141517582, 217114233, 624653411, 393783039, 551427481, 868499465, 827747595, 919295557, 248485522, 402935120, 386423196, 732099781, 494723488, 542395053, 382346261, 957036004, 93921264, 803780782, 407073092, 570603648, 614041971, 882819664, 679173544, 705281557, 122974294, 361707443, 497198841, 746820702, 430207482, 188573407, 578015223, 577887473, 754969378, 316478045, 624082389, 745171124, 820997863, 827183381, 791986936, 266139088, 788424202, 261569952, 644506021, 78681443, 632641948, 663539107, 49097432, 677446282, 684956117, 710109073, 209971784, 365997678, 613038703, 196809611, 67635391, 611368268, 173188865, 549119267, 419243951, 453298955, 566088049, 457950573, 785784890, 23929829, 621868223, 313331624, 484333931, 488794875, 557523, 279318780, 461519983, 548458715, 215896769, 927642951, 858670753, 746100237, 679494766, 486081103, 243089475, 436007176, 259772918, 20788162, 124103304, 26139658, 666391366, 407158639, 990766968, 206237329, 855734867, 449589140, 723971508, 56478377, 38681841, 779859288, 151377452, 864668216, 395657597, 838996110, 2498570, 353446622, 395967181, 192785250, 798048498, 905033611, 802855058, 61229527, 603262794, 639393186, 957748880, 620483904, 524755218, 137745062, 445962324, 146490423, 170449865, 433949431, 352463001, 645888222, 265433513, 772837145, 153324928, 778075313, 645516531, 828969776, 985932887, 438613359, 405691445, 23591592, 758031943, 523492251, 16843642, 119331958, 940116572, 271014826, 781444956, 211221182, 392615259, 990898408, 855569320, 781972992, 179522095, 342927407, 993019132, 282170151, 756161708, 133221633, 721905697, 531956518, 239677572, 840470937, 579668806, 989870252, 302544437, 510079230, 883693527, 230771716, 353325845, 96899219, 577736068, 459871823, 39938136, 850180423, 334443444, 781890400, 810456120, 58485325, 403949393, 335084656, 553960667, 756067717, 801062389, 6325920, 921402263, 371242765, 609483512, 57425236, 878245101, 133081987, 588492371, 220043624, 185381741, 572540816, 353471780, 107612092, 15899773, 591210541, 993989607, 625592778, 728839444, 24317184, 417050473, 975003690, 591518999, 713349484, 734289208, 760701102, 420615743, 326264486, 308361262, 520175117, 473748443, 239851444, 267520828, 166370643, 278885937, 99260731, 286348557, 445135301, 367695840, 35572444, 464551993, 641359784, 844431371, 909587725, 162227517, 819712977, 221461406, 848111182, 252333717, 140384756, 725683241, 521126167, 798430780, 507065928, 819123015, 280467795, 893435654, 288136895, 254701349, 457136386, 535973874, 469162005, 647317607, 120318, 475638011, 365296730, 187864589, 709770139, 593739849, 917354549, 305425277, 348475187, 261870110, 534741536, 167050534, 359625826, 521400141, 896785440, 727620794, 613860888, 930168958, 227981000, 579631744, 408752319, 269864989, 107499628, 565917349, 332842906, 872942650, 57582624, 384034541, 639924105, 823513916, 531325887, 189762584, 202489661, 41485507, 46716642, 18329321, 733253589, 179470869, 253563091, 818413245, 136755010, 646398211, 157935129, 253602525, 407851607, 179661587, 415575779, 786134497, 475110334, 129024868, 896745876, 384589045, 574883891, 306719403, 510353001, 782034272, 957895795, 30032533, 697217275, 697608162, 892483064, 322865562, 578747016, 804871161, 824567306, 130040221, 575974207, 653877023, 198288975, 434614393, 542060626, 417603512, 481310274, 108730820, 817706236, 918654519, 199492053, 36604479, 611359128, 973541436, 261834821, 706407406, 463024274, 285151783, 52671386, 434601391, 599431278, 642370981, 905462225, 501030873, 126784142, 811328805, 539429804, 395919086, 320692905, 978187901, 638509211, 549760786, 992809942, 26707693, 553585272, 698653735, 748574616, 787147519, 250715538, 446145511, 269068647, 307173253, 70320932, 515420086, 191857660, 114631613, 995040535, 917042061, 239320496, 312692840, 609484904, 586704151, 120449880, 214965447, 597551280, 750463378, 68988211, 666320692, 346152493, 46188014, 575532596, 81321208, 358027539, 702080166, 701582943, 479173461, 690191292, 478734064, 273039787, 350609092, 695827354, 81109302, 485531760, 923323743, 457215663, 428144995, 45018790, 103511005, 950295661, 662944396, 951292320, 117519939, 968461625, 313200839, 201997895, 161407402, 853193476, 878797758, 910890969, 354088176, 391996341, 256083851, 158128203, 867337311, 185525607, 570342523, 844665199, 953385255, 396875361, 183691626, 641479325, 600560125, 70703086, 166972501, 252244542, 223207846, 665076047, 337108704, 765438557, 660501323, 388256581, 537135786, 899131036, 11923692, 160691433, 38510666, 169758912, 882729739, 587174735, 5158211, 122263956, 510587659, 6927142, 187006109, 483159940, 556075364, 958366792, 719694518, 526078695, 769021464, 504206250, 954314397, 522362015, 700066903, 783043311, 897643046, 150945705, 912629039, 786967947, 225824341, 51956382, 431147666, 733544996, 840279494, 879998140, 492543203, 661856170, 32847056, 10012184, 300529345, 119053925, 558999439, 317490747, 934972241, 152011153, 328936516, 188519945, 26983750, 61856822, 589141921, 964265855, 89898403, 751399524, 434114931, 865364970, 555971959, 10846639, 204545457, 337236425, 89585300, 561519869, 430910131, 123634999, 693044791, 182201602, 467539947, 960114853, 228220361, 776575897, 554123960, 651303691, 11304799, 522933523, 916704716, 282729799, 519017006, 993541611, 977437957, 411610585, 813663462, 171430900, 74135779, 349704302, 383854543, 733566761, 760438377, 557659310, 214614119, 35019381, 247368387, 220258959, 67282633, 848877242, 802314144, 926433055, 966350626, 794672922, 117771002, 523565720, 369088164, 957293937, 78581215, 416723054, 653534420, 883615395, 371055678, 576794107, 236647144, 533674282, 496481591, 1858288, 901548087, 207700358, 84996898, 913437482, 75370388, 790703438, 884720994, 287859359, 912828995, 272857508, 546480395, 386807234, 773028264, 312790349, 667401923, 270467970, 405405375, 911181749, 452036813, 73766945, 595728085, 231867476, 477073965, 861845142, 997340667, 562159463, 791555177, 933036962, 919630617, 991890122, 533641508, 111913788, 347137837, 770430685, 966596215, 789517761, 15622591, 878880933, 838429723, 87536533, 107089871, 958156581, 317457945, 470937298, 658549520, 120526017, 398911736, 495648158, 962634974, 683123276, 233174638, 593623029, 59533463, 555292373, 916074943, 715203445, 308551417, 132491457, 606822484, 242377876, 721923700, 279766898, 677013424, 67801523, 392174584, 760692157, 616306868, 830863895, 568984885, 885758057, 646072871, 389488213, 936012736, 825035475, 694273067, 609707201, 549498832, 769202902, 80124465, 619862295, 941125442, 466961056, 752992179, 617524395, 939376758, 416696347, 272063925, 916581207, 467999185, 330877532, 97902217, 456135207, 588016342, 318409197, 955702828, 169452209, 372815601, 953558177, 173229027, 160254603, 756815397, 126003671, 816465337, 211616926, 870729289, 541224173, 802616614, 54709015, 715060157, 954917809, 783693485, 240002319, 415571143, 961123860, 432360387, 308706712, 570147447, 971411368, 218601449, 245822791, 933117531, 538900362, 789771776, 778767732, 881981565, 2171709, 91058936, 349935, 804923425, 943907680, 73735608, 468730637, 321088188, 295225997, 47626116, 36940025, 527621538, 343337000, 710544430, 37101403, 536356459, 898041863, 473031820, 889408928, 152729163, 491844199, 845213191, 274236498, 874356988, 902372994, 936190360, 888703259, 373734435, 563851888, 718212328, 857856993, 564684149, 254268355, 163235630, 149113695, 770328982, 716736240, 766985340, 59903882, 780538290, 74479001, 225646898, 912993383, 218081275, 841303278, 728186031, 862678295, 582317845, 881655659, 177687753, 544693300, 797152398, 872117037, 830570083, 647237096, 580406384, 781605449, 773554334, 944175382, 799099842, 252136386, 885675640, 412256345, 874467817, 199323912, 884450225, 843859051, 594796009, 961664368, 515624147, 334235956, 12361102, 223189653, 846897278, 479520599, 868462039, 42034203, 831006067, 327404487, 534987655, 388396566, 104041967, 355441909, 59894135, 82707415, 967046403, 649875926, 419474534, 435077726, 541363248, 941242725, 893560512, 243281097, 778738059, 856009358, 319002965, 300200209, 193521391, 202981200, 130253348, 473288080, 754261944, 498561823, 84827017, 405566605, 848841686, 464233867, 984137267, 86639515, 453927738, 491775099, 71232775, 879986297, 717437812, 741982847, 8062941, 670427683, 600259310, 708058928, 774072585, 809949064, 55477819, 140225475, 212521753, 262100160, 733846325, 401219402, 483657504, 108712263, 10503386, 182953143, 731632464, 327131055, 499937269, 489486672, 775729580, 714559532, 819764837, 195210883, 676757033, 278092395, 869717525, 402793089, 435118905, 471251760, 703343820, 299747453, 807816277, 428123688, 419448862, 622822223, 160391833, 386639940, 498754764, 378918212, 697589037, 788662017, 109506059, 192531657, 974326274, 536312718, 483465799, 851114781, 896831391, 398436070, 857930105, 965616903, 614521135, 216697747, 571146680, 960896542, 702901998, 540602827, 400361722, 846965474, 888631206, 643751999, 675541445, 485751060, 187694699, 462202152, 865310951, 59781561, 244877341, 99274728, 467335368, 444790894, 5567144, 395532890, 555006646, 948895852, 159908597, 133669404, 75352645, 189885262, 560462158, 539850819, 43170558, 639071736, 646367358, 735268699, 351500746, 667241845, 170085078, 120377703, 592565979, 280065133, 737931129, 151968289, 578735175, 897264863, 387075981, 734597353, 752095936, 940743876, 242230953, 556826752, 342725598, 4721096, 531862486, 849129999, 896392726, 6342478, 418043147, 486035657, 628950689, 850180306, 948994322, 372092321, 625238421, 567363698, 539196290, 526296138, 12706298, 58515732, 337109340, 798470902, 57252624, 724778577, 394680796, 863457044, 366176197, 56221240, 688009425, 766140808, 328079678, 634580081, 593373068, 470828070, 481159050, 188456000, 282129875, 809618718, 859464505, 540454863, 463207390, 976563894, 201715787, 986165136, 385500172, 41380112, 763885449, 884268468, 111264046, 789814842, 667363603, 26322085, 744351232, 82473533, 625533815, 184145441, 756955870, 872372479, 370709281, 241455063, 549664644, 867143693, 960969109, 704506294, 554781426, 49778194, 660749300, 548171400, 875039668, 385779779, 863526881, 658267180, 670232887, 503867155, 825889451, 711768163, 246621855, 676599418, 738841524, 353931903, 34105393, 563003939, 848458237, 299079677, 362381651, 503946704, 347220264, 874876181, 430842083, 574587111, 785038614, 502458002, 718553527, 523664363, 116419814, 904631294, 437231847, 588589362, 830651577, 704416367, 799007579, 32067635, 94219231, 43872758, 732775954, 38817096, 159901299, 444817461, 203789332, 445315631, 431255791, 408220484, 328531714, 839346179, 626508774, 211971343, 497067986, 240376743, 799096399, 421208381, 871106738, 354581200, 932452661, 609008477, 612119059, 100188677, 714532105, 958342624, 132325422, 414544624, 711658614, 725417414, 930413852, 256083514, 74897575, 150446782, 557746025, 528359618, 903726824, 668027820, 160652674, 179226853, 711606165, 193773722, 802605335, 306521583, 792619204, 368353470, 227863351, 854154250, 571549569, 422895019, 742258062, 152094040, 119397132, 317332463, 117582013, 735871658, 494764336, 818751523, 234393230, 406150099, 246569089, 336742939, 43506076, 9848608, 571727029, 577549082, 911096008, 90465415, 686417072, 164839079, 287734714, 824779232, 217469687, 147010559, 116243704, 222287066, 97823835, 38981940, 336614317, 151510992, 384744713, 104335089, 449977337, 513161640, 702387889, 735265894, 704002361, 171917604, 940488507, 968348011, 382830436, 164914051, 47841526, 724144225, 945113984, 840478969, 787684385, 541087663, 2905855, 202057743, 609027729, 999730800, 851678147, 13833280, 477974309, 549363365, 532201526, 854327072, 42111298, 318201422, 766125018, 707557058, 469213603, 797107466, 830378085, 344619898, 20856266, 373012285, 983722550, 562064044, 945137175, 569025303, 145290462, 285168370, 669771565, 214065904, 580794192, 106154151, 508691512, 396537576, 251198906, 839639905, 964155345, 226630458, 593651134, 649821181, 888177631, 493774941, 979513262, 152381291, 782835333, 68216806, 230994378, 934878586, 974279909, 403163364, 127324601, 86418867, 363622604, 383688361, 645331973, 508705659, 533696655, 10005118, 144276874, 135846490, 555696728, 878428897, 980338673, 891800111, 729663674, 244541345, 172035791, 764141256, 415277096, 566102423, 921843805, 598473984, 502763684, 720363114, 565433776, 819966662, 97639557, 760982938, 845841440, 135175727, 88936035, 491090623, 813435009, 766261290, 85176016, 741676546, 718231202, 54211188, 613079118, 197663380, 743496898, 908651404, 949835881, 32909751, 85044823, 863779289, 223737846, 538724405, 800244582, 830670255, 858194762, 646462951, 257004273, 13025605, 378403635, 91688935, 446488929, 630545711, 533862143, 650537370, 306778488, 72406012, 227908630, 136997627, 818789142, 459251902, 607777845, 446396194, 114885597, 419576991, 112482372, 683674368, 528115127, 90541176, 334503802, 696006243, 574751749, 862224702, 657911917, 753165389, 401856875, 430631390, 209680790, 828915735, 19086366, 491859245, 481053743, 936468176, 360301136, 237221204, 95057610, 186504414, 132218554, 808207454, 654657347, 558429341, 858606565, 216541342, 733592862, 762973629, 369481370, 6324306, 193557867, 307481267, 72225424, 115824109, 388535739, 875803527, 877902768, 890236637, 961380950, 56558330, 306036357, 862509839, 446155857, 983730946, 995260499, 773020227, 604508352, 86976353, 14001677, 303729037, 262045149, 602562941, 276385243, 420893252, 708705522, 564929347, 764734359, 978457649, 468899806, 820456781, 347103238, 506657763, 103865918, 842439302, 655053308, 132762840, 716998792, 226754384, 939345853, 638063201, 69962432, 901469971, 28071391, 501138347, 985039491, 137866633, 14051098, 711230156, 750481955, 915644724, 683137553, 740611188, 939755159, 363040105, 215961952, 161658761, 250781284, 61823986, 822252214, 90423811, 197391399, 203172233, 831252831, 477714172, 509616381, 920839323, 682317378, 229437546, 30422330, 340084229, 988062507, 593694750, 113769047, 826290198, 714956037, 662675346, 17757340, 853203887, 195882311, 138838726, 927416232, 87118235, 4341200, 77895441, 63210943, 979217839, 163082085, 770992870, 177243362, 70630825, 28712913, 101158351, 358005439, 650220222, 653879835, 266542922, 586678281, 809682379, 999369391, 281451402, 450684615, 763810154, 832141040, 511771133, 360815586, 508028108, 309226550, 270168837, 361000253, 768713895, 512406781, 196670020, 323201860, 184942979, 601365855, 19137790, 786617588, 830160229, 5022381, 844627839, 790242521, 865197320, 111782754, 847272790, 219433596, 189783728, 677102088, 349070582, 407493964, 892515093, 734711289, 766600969, 248443644, 592680248, 890056943, 653289695, 457456230, 43479012, 395363032, 689201132, 463611020, 720827079, 867972935, 659549528, 310690033, 224484294, 680012075, 927650248, 359224158, 362134727, 81877790, 6815054, 787970813, 54132520, 899821061, 957075868, 457803905, 994306291, 725421818, 841698368, 355514317, 730016997, 733903115, 109996418, 615475395, 733849602, 397240321, 833493284, 999810962, 578383827, 162040480, 732334477, 719071483, 903323189, 632592474, 744270450, 807135932, 350525961, 484851919, 611494255, 625171574, 393109183, 793287197, 568146363, 811795101, 828431120, 24815619, 856507956, 411678543, 638642948, 442490537, 853887136, 348219153, 546343844, 866814601, 824839820, 80467910, 973461565, 534603948, 347702886, 206812807, 555201770, 45932776, 146318638, 164709843, 18342781, 988207192, 735848649, 651160749, 971575307, 890738882, 913672384, 263375302, 53215299, 731455109, 797466464, 297591314, 345760984, 855650552, 345687322, 470088391, 340629334, 288229450, 8818989, 392781387, 872535548, 556472018, 892028814, 506173235, 191595416, 32805203, 240147443, 689011930, 446750865, 946111848, 283180816, 847948631, 106757588, 808798019, 98725503, 611138979, 814125984, 829867194, 597771754, 883993878, 270661896, 955150245, 573880775, 760301744, 599284746, 68902830, 98426273, 748617881, 588927948, 414993610, 125616437, 425727979, 544164754, 828151451, 265575418, 77391184, 169371871, 266895414, 719968822, 951371929, 551814784, 962004700, 311408428, 632840044, 268544745, 348652669, 73204906, 285554433, 467442181, 156469858, 717254017, 867963227, 45600629, 898238964, 865193772, 14234056, 111851284, 754291285, 600691164, 155520737, 193171356, 161757616, 377698120, 537997050, 894240154, 463915501, 299499621, 777557073, 668404899, 952249218, 829645371, 668729582, 715850635, 582890446, 126921111, 947266792, 651332951, 595868889, 672037109, 170032474, 424332154, 544483167, 711681114, 65863724, 41043927, 547614159, 824348643, 640140984, 423635380, 57789229, 299215518, 761486321, 961403790, 49995334, 181509951, 807294030, 948723610, 898750716, 386916277, 387609465, 923212446, 108539549, 858376963, 137577542, 10041128, 240252493, 416176651, 977206448, 416062730, 897854239, 539570232, 815097618, 970902167, 472086092, 824133073, 378017894, 116013685, 521337952, 347423409, 186219553, 2672731, 237214125, 164817386, 494128754, 408385972, 682490263, 229375645, 320483179, 977738919, 64918207, 751643804, 390727039, 565173938, 752882940, 312693670, 334128664, 437691619, 959371904, 690549093, 384911268, 37769198, 313218312, 735327368, 865607311, 328963200, 485959265, 237256720, 298136882, 256432466, 738015760, 138776279, 351147733, 775904490, 594695739, 148720899, 480613071, 911896091, 780914864, 526778711, 655584350, 603344005, 152776216, 325711747, 577373432, 457554966, 619247138, 838235565, 297923010, 384806101, 905569534, 206638811, 686734582, 229246150, 349944972, 552137060, 33268040, 849867959, 339517704, 371319060, 296766874, 586112413, 613218613, 793845309, 269093294, 228213007, 519383511, 109049617, 111233096, 411401589, 90167238, 790774217, 440834400, 10282222, 649403696, 705138235, 496039627, 654506630, 187408740, 560375992, 165662669, 874737097, 418967682, 526677580, 299780037, 914504635, 806894081, 127048194, 178466863, 778264933, 634910240, 125805046, 59021581, 464540618, 602340821, 501915777, 645994006, 273883775, 571739822, 452246871, 621470422, 215880978, 605810253, 424364346, 778675059, 512120458, 564173814, 740852495, 734979, 913826247, 816928255, 854625991, 91567632, 766397120, 563899092, 72194112, 603130118, 768140955, 922572757, 525387278, 549297349, 744910600, 350488832, 293812736, 483517644, 68297164, 289996484, 568921045, 494946629, 899254236, 988121680, 16939479, 477146586, 529022029, 808877631, 255195475, 464953194, 211787757, 910950025, 509253967, 261049824, 819918065, 805108560, 96866729, 719270792, 823746217, 990908510, 872575411, 776739651, 236412794, 379157703, 178681375, 863350710, 637229057, 364421795, 958501759, 474906222, 93416458, 757576931, 692353928, 65720221, 533525431, 968372271, 372232274, 28894149, 283130376, 914897182, 675856315, 493707306, 4851512, 127572903, 684688957, 834885973, 202858390, 27133126, 83534539, 633074308, 639858018, 814976301, 445030019, 222077622, 506674014, 638783245, 758658646, 695196529, 455830785, 502031298, 426221388, 176022553, 182281360, 685646697, 769649791, 415312776, 357232799, 820151709, 14871740, 97419160, 291207176, 383930063, 872748970, 329513752, 899180528, 814859293, 244466821, 37200173, 189687928, 182374609, 108434949, 613642580, 666191221, 686411773, 909663382, 523209093, 540974132, 616816474, 374416684, 570433819, 568658225, 464015205, 2493915, 539498767, 277855521, 106640490, 170235390, 833168690, 252941064, 499627644, 311875344, 603402434, 303232621, 703348106, 164432629, 213060330, 425121548, 267397950, 570490869, 484955758, 233299368, 693894349, 396517130, 758205155, 911183562, 273907710, 303720724, 708404775, 630216646, 746989138, 790324962, 328114443, 119651626, 504020558, 420720593, 341610613, 450980626, 471028072, 276917983, 208490011, 272644317, 229238480, 45937922, 903947527, 360953056, 683568795, 731361533, 297055273, 132425725, 745394836, 841536742, 641845478, 639597758, 657794935, 100487195, 60132671, 380491646, 226735480, 933908500, 278553355, 493134792, 716163966, 684683843, 96951533, 589926379, 834682082, 868107249, 333758803, 972469559, 357753297, 147988249, 156012254, 247022930, 645158713, 655283276, 214183096, 738872732, 534135258, 380181043, 515671964, 807288564, 783893707, 106749038, 509836999, 763905058, 351648150, 478758310, 653955933, 694143297, 951310405, 626411157, 60977503, 358203194, 854111819, 697862020, 808826516, 173347159, 172691581, 728126663, 678929657, 694403152, 415842944, 514571277, 209801547, 199995791, 362941867, 857503663, 70750322, 986716586, 533282920, 375177208, 230730821, 49304473, 769785497, 322594474, 965222751, 427359002, 961825669, 56917650, 514094444, 894840021, 235936298, 5066562, 537737400, 166246998, 525019801, 539638845, 453723276, 526168086, 901758004, 742134835, 459508062, 430472946, 472881606, 150235067, 424216246, 323644603, 705448611, 48095770, 929382194, 130971811, 399041126, 191376243, 745683471, 781411493, 174018490, 932002126, 444121426, 217676149, 230443947, 586896524, 216123837, 392536487, 134697473, 757002259, 126711098, 115053, 868139443, 359270286, 891072164, 643172370, 256389054, 696250989, 874976664, 243912631, 792719294, 99709519, 470584091, 951434779, 996288908, 484579657, 502024214, 655574893, 939266848, 894899820, 310971626, 181761008, 769697388, 466222996, 953276170, 867908727, 949809579, 46938621, 972020530, 144546474, 654147725, 425954274, 377709221, 892875942, 647689730, 916098244, 734356354, 654274781, 233615290, 316232134, 277689697, 483978150, 846424118, 604304357, 52009596, 657443526, 698891562, 413823841, 959911907, 425218606, 465379798, 988519973, 683291111, 781401759, 743010302, 58305401, 591032606, 186318887, 631235494, 708800244, 527875684, 481448372, 940581742, 905375778, 227015602, 441243962, 421028568, 87934933, 695746265, 124852762, 692351980, 408924842, 679093951, 606352107, 765422020, 579044413, 844690216, 913165806, 653940501, 55402321, 666337666, 401746611, 799418238, 40032139, 55138563, 557569706, 980602054, 89706977, 169375333, 276048958, 13114391, 108640527, 266087164, 847545633, 117451734, 11391210, 756116576, 399313777, 595189956, 832237743, 76220779, 69716339, 61911736, 740965143, 957590302, 896645567, 90953293, 599581075, 699778007, 6451958, 525024557, 943472695, 448431511, 947499788, 238960600, 48063582, 781102445, 598501845, 832142741, 424912835, 681603314, 111991617, 237575742, 487835635, 310487870, 235438739, 374600591, 345901369, 296547555, 170364144, 554608765, 977899923, 470270120, 544438004, 488832457, 662799491, 416700528, 642491100, 539052181, 242908843, 464007083, 928515538, 641724617, 795379603, 668076617, 777836533, 421386259, 825050543, 374130836, 640140445, 800390681, 991921698, 31997363, 926751678, 724784616, 522113326, 730057048, 358744444, 522077981, 429130500, 506514562, 940983637, 567258078, 832874740, 405565625, 853763392, 43686520, 698285129, 86089714, 630724579, 904627071, 85464978, 210943608, 41397655, 215638016, 111338655, 839696857, 26251128, 490434156, 701564918, 424964618, 57141625, 275895833, 384382577, 60395938, 371782056, 978297660, 249358903, 120235952, 154369612, 724934210, 670376369, 164022320, 285097697, 294943095, 347593798, 239068793, 221374769, 911888925, 20810260, 332106836, 640930275, 95822139, 1571993, 857472911, 505560884, 134575040, 192300340, 216800821, 916722277, 22697206, 63092652, 126932824, 272898142, 978278714, 863336602, 307257414, 644789132, 114949687, 803123112, 936806656, 622383655, 98645538, 799440340, 798235890, 878331360, 744176258, 613194875, 955177586, 571424086, 123261161, 388334883, 22161920, 830208349, 222479395, 657022868, 629997484, 650837708, 436611625, 502956115, 858342921, 767141198, 562043633, 154452049, 732399631, 886837771, 915392338, 97463820, 833755489, 815743615, 876690189, 754387721, 596934133, 237758340, 607116416, 578004649, 295812424, 387351519, 248063391, 828957947, 1550994, 776291279, 626926862, 383173201, 124062736, 381941393, 88375767, 628349375, 228404250, 810446242, 339874162, 288674757, 30274780, 573959479, 311136749, 649514199, 510522767, 116464740, 700517948, 173495814, 60711956, 73649675, 466086525, 713505871, 50245889, 761309518, 896494345, 205290016, 398301842, 541729999, 639678325, 539101654, 841894603, 789326330, 620573150, 95480033, 425444394, 464780613, 14567395, 567446450, 358955387, 754997130, 344779860, 994686926, 479105276, 781249480, 552550701, 541023558, 559550067, 186215723, 845108855, 585371176, 346453600, 622647901, 291909496, 304646781, 546342238, 403462827, 567770394, 892012882, 671807324, 610996877, 628356398, 500972723, 251721401, 757622414, 578744132, 41566093, 9568131, 18352636, 88567796, 849312380, 474459981, 855209670, 376845396, 617717670, 461377953, 898393064, 677685131, 853714850, 889087342, 691111191, 652897809, 9629863, 846284216, 250013301, 681831615, 146216915, 74441364, 44783228, 149685860, 982578065, 155567299, 190022990, 850704534, 836388533, 597196207, 756593216, 841175392, 687798653, 739389988, 734568027, 119179462, 625144506, 848311679, 407165036, 612966752, 222443754, 717903465, 858963226, 779095569, 29576749, 23450977, 396596171, 330689083, 296585309, 894198556, 268808083, 79031758, 463746971, 785735619, 453078891, 572862374, 948022947, 326894415, 504270119, 310073495, 27267677, 508616153, 187970481, 105307744, 369310499, 834261881, 569395278, 416503699, 322101103, 145496130, 33195306, 301653691, 57948658, 523720429, 874749261, 249140430, 117623766, 807109538, 427178967, 162606081, 378210922, 169888597, 939799642, 117199998, 452904852, 122981576, 73820623, 197142045, 278056391, 236750944, 190856587, 124521692, 383483540, 870736136, 265390031, 902240416, 437596301, 32132324, 852149148, 372407666, 928227112, 715295008, 55130584, 276247578, 606487756, 108154824, 994727654, 108895351, 766250899, 412822602, 76179954, 847030443, 341593517, 972216081, 625283404, 124182160, 125781969, 770409923, 883526511, 573419987, 786431992, 476181233, 242298802, 993917602, 63128982, 201099333, 972419967, 498453655, 434307071, 594093257, 325199559, 764372691, 970931812, 218432404, 455107601, 469627287, 343738169, 721363964, 274813908, 342867048, 659546741, 229858823, 630855536, 227482130, 191487859, 899395453, 46299454, 669641858, 923792841, 655108394, 664367402, 602526320, 753894114, 475465625, 298622488, 710297840, 812077387, 536543915, 503427692, 265335817, 544833914, 344781073, 335608224, 253432638, 514317276, 558200155, 290148653, 143565795, 332531400, 92969872, 299839582, 699073611, 184200003, 916822299, 383203031, 311209714, 258914924, 839187152, 711744075, 651214908, 713550902, 441877562, 420316239, 907821188, 271030378, 804524425, 128415226, 858498825, 152613717, 11512781, 939130778, 692488873, 316668234, 274751254, 521722106, 317949444, 320029798, 507956819, 977129996, 298083709, 108994110, 684317112, 380056639, 144209675, 15342600, 447044468, 765423875, 48236296, 174826807, 658821509, 764772643, 889994168, 309392498, 223069150, 287830877, 430174418, 44103118, 27519562, 984923190, 684730172, 854503209, 419778214, 624666155, 270862172, 712587673, 120689347, 452053366, 333894647, 102761822, 121739403, 70021915, 902051317, 462099698, 998048893, 125394992, 68415845, 77675755, 103172688, 335872898, 635883541, 733654249, 160769416, 344575352, 131401880, 506025979, 748148989, 339407135, 17650055, 158931775, 98483801, 230211253, 362670497, 907102110, 30027368, 422739660, 865655468, 438526248, 857875444, 917146138, 405463502, 934653188, 948280556, 906147263, 467743883, 821038711, 126953928, 711335709, 795905877, 11738083, 560510584, 77624907, 280870332, 97316667, 568125745, 291531802, 842517797, 670786251, 148039660, 662838808, 644807830, 307005460, 905002073, 102117, 979690884, 121507443, 535874430, 915927883, 783875096, 772908659, 150258119, 554097668, 771162127, 795120707, 907263678, 377352943, 512206045, 802229876, 613970044, 922132088, 959884541, 195919579, 234957261, 756346462, 86922170, 630496699, 980744464, 887628692, 135489759, 262207956, 108756335, 402008450, 491626817, 200622718, 47062561, 384948491, 583912654, 497365817, 699099633, 32596187, 26432515, 216004672, 551022481, 565280290, 579221053, 673751391, 482116187, 35082062, 704514749, 87260487, 197460734, 722916692, 61113360, 340664545, 809561966, 741967525, 314239966, 780821427, 148376317, 577942357, 223400499, 14676614, 399985208, 186444345, 833550255, 923992473, 210554629, 296822347, 223343935, 473803445, 264649424, 211651339, 330608627, 806313703, 890351729, 833091865, 792908217, 502817965, 289862184, 871358122, 185285186, 356021130, 536996290, 274244797, 387175493, 22257786, 421680652, 516474669, 945147399, 648356888, 833214657, 589949452, 100575166, 933309403, 481348456, 101423446, 80467341, 705000864, 445830455, 496810453, 442005704, 222394244, 409126554, 536927672, 444532098, 698708316, 322794606, 42789316, 933549386, 544181836, 835864049, 946031837, 707996345, 587933135, 13404017, 817236937, 454279812, 873845621, 631728400, 450812793, 243815532, 620311627, 788863482, 824227245, 501932579, 980905275, 537728820, 334102732, 295727372, 377406913, 54121080, 177432473, 779935932, 836740143, 337962597, 497632721, 929191435, 382555045, 459554767, 211282907, 811017252, 905404774, 28751095, 612862368, 702008322, 964396433, 583590436, 412777007, 793180054, 230081580, 943387628, 480598207, 623083957, 450770058, 684873961, 992130610, 441834380, 592039282, 467947766, 157846133, 462752014, 221814503, 837618991, 123993926, 82846209, 386751184, 985446222, 69681307, 142821884, 705821086, 734535115, 302716064, 918581344, 597589854, 979744541, 780801590, 151258415, 243034333, 239523754, 313413537, 535062165, 987610145, 279388201, 413402183, 105118646, 994678408, 595518022, 893264470, 7417830, 29797095, 845804301, 496751681, 572463388, 589587821, 673241557, 21681909, 527075932, 735298391, 291486978, 153414423, 955731850, 394656414, 504455013, 602586638, 637419903, 552072418, 744786479, 182079054, 516090542, 55491040, 860505264, 265298337, 910170102, 148606277, 550711, 607449069, 627439041, 711229389, 400867143, 424323405, 114257153, 72529876, 511538404, 211256457, 657732567, 485383523, 547772476, 547358131, 163132628, 205849393, 65393657, 328404506, 304144094, 823318138, 212474880, 75012680, 128569206, 60448465, 628809620, 742831879, 54377260, 229268320, 508761910, 997417432, 532507571, 546257816, 775654435, 142993702, 249584721, 949102043, 575853896, 699315409, 142763379, 798850650, 689353203, 882075789, 503968858, 92439900, 955548076, 231713117, 465665225, 466065889, 393895450, 640623601, 98743282, 269656946, 536613385, 504555471, 339593568, 386667000, 18716008, 183050910, 754388904, 403854704, 220374593, 835351990, 917362804, 93211943, 592881293, 850174752, 507600220, 118861554, 611403710, 548850607, 118153251, 687864045, 686090623, 609436203, 159582640, 43355598, 411966569, 252462984, 427929900, 661444374, 906160928, 187694341, 631642231, 248270882, 872526568, 31187265, 606118115, 665042027, 445286874, 851674831, 584286173, 863563866, 855450125, 869440466, 739538267, 928009841, 46440357, 502663000, 430070375, 192526732, 31874965, 903062980, 382954155, 99090212, 996881890, 990785198, 903604446, 698467356, 689333110, 700654846, 55985401, 938640394, 232949478, 536865646, 298638779, 365760104, 493984238, 187048744, 772564891, 221382283, 26186949, 497620193, 956684631, 847688900, 794356533, 433613864, 927520671, 529879643, 616219167, 226237514, 275097770, 444190359, 699467156, 114473728, 597862221, 365473972, 852565186, 217690366, 951917084, 334048142, 379477186, 27997477, 471780069, 298482411, 861703550, 880374312, 713684835, 260106274, 427812218, 544283034, 863526030, 143727961, 425242482, 421171099, 579058349, 491153067, 753284777, 843699358, 916524733, 221081765, 367418885, 534403386, 262407867, 543578996, 80818438, 70951183, 678909670, 468795248, 557483631, 468769780, 150177164, 677608207, 554731952, 271257442, 563831344, 112369539, 127008074, 587603809, 200603435, 701198375, 26557324, 474202748, 984144946, 255756859, 749146472, 377941006, 605371998, 593708874, 917524006, 371614878, 743622904, 511807870, 835668962, 358792619, 185324611, 581942111, 618806695, 456858673, 411154485, 701154380, 575569289, 443661543, 460171001, 87549866, 981433104, 800410752, 185573811, 813217933, 232721518, 422708343, 538107507, 217611337, 610048458, 987093930, 232072260, 82754929, 712384275, 2786805, 783219078, 698644674, 573266768, 85958837, 308946455, 548828271, 287490875, 498974622, 962049388, 12874718, 861300395, 788513573, 914025665, 84575144, 563249867, 507032375, 600255876, 376751574, 105694271, 724386688, 759500505, 278236706, 99261945, 695291043, 70200538, 436152179, 430745886, 778174756, 737530107, 246662136, 429761447, 791600337, 777754281, 468862342, 759190538, 128049729, 734583859, 971610497, 583250102, 48232392, 552219440, 839160534, 862049099, 65657432, 479461291, 767376095, 760807519, 127344486, 198325667, 630831439, 796300787, 381056694, 102915665, 362444112, 52718319, 60112500, 628290008, 387598945, 326938880, 371633937, 442672959, 14924415, 830002670, 5402449, 479001138, 126893908, 152933587, 653119137, 396189589, 32587858, 147497141, 622125894, 971081348, 160558586, 398991125, 238809427, 451575568, 975578324, 466056822, 212132492, 803331093, 172203591, 744840716, 291778247, 386046365, 236414231, 838046457, 756067586, 348862889, 108431964, 637330101, 915570232, 204930104, 483588234, 660881673, 833161033, 923167737, 823748946, 881610956, 298385138, 569150964, 284413680, 750628659, 977144252, 441828026, 734662739, 657527458, 95148126, 470385839, 965726511, 213638782, 348560487, 80161183, 281421848, 797136782, 801589810, 364802334, 867239737, 167549135, 348455648, 612588607, 602222808, 269754597, 82021429, 860912224, 540358324, 533848707, 1663625, 943789921, 994103700, 761923860, 414763804, 609404966, 445716060, 50521175, 437672112, 93080132, 756852947, 153650599, 187332027, 181371707, 822722155, 71926247, 68227547, 716404947, 561875674, 373443029, 363785794, 178282051, 597078228, 302442205, 792967657, 902922246, 815355688, 101052735, 64451464, 206271470, 467239626, 27572433, 730045697, 789132546, 158542177, 452195896, 489527629, 185785094, 560819405, 451849829, 40198825, 803879645, 93282749, 804321461, 93831396, 274517867, 705471621, 102972677, 387281324, 842262796, 178665010, 336853449, 969928579, 460034963, 263791127, 454786864, 612544492, 365176543, 469927936, 594215866, 995536217, 885063704, 211530428, 473415159, 37147314, 258307045, 661641928, 288126494, 783407021, 996852781, 911217928, 489652823, 51017878, 908904759, 51986151, 803672625, 857437564, 496137798, 30149546, 903658032, 172784717, 295499493, 915433889, 150243570, 717051074, 990201906, 9132803, 394801138, 685561079, 692166514, 952374907, 498049150, 107253974, 894845502, 397224391, 492403405, 812638217, 30786333, 802178024, 451338840, 415147449, 983324397, 385624237, 243498995, 127672590, 502375938, 664518170, 48467405, 389113596, 4474627, 157932724, 177464993, 866636716, 950245277, 263041178, 656402356, 605641331, 495544485, 116388505, 307287636, 708550557, 906548173, 411887450, 913647044, 798471602, 286061659, 976456296, 108784299, 18696377, 762880782, 462418643, 204245298, 971613961, 142291277, 906960429, 548372594, 690489728, 853749016, 242543477, 32289461, 874164142, 70452467, 604089835, 1341973, 964185035, 917166572, 550196171, 761594272, 620566452, 61035675, 260018754, 931420600, 499625628, 259790475, 9693130, 982468431, 317378819, 325141551, 777671027, 18064195, 200113735, 703945737, 448211270, 229330282, 636535269, 2492629, 95087756, 84143037, 54211884, 843512513, 755078917, 239593831, 843906871, 145422074, 26616642, 117556511, 335550359, 53340257, 188897110, 226789277, 772597829, 952914736, 553000377, 308693149, 819232713, 504158979, 672694087, 129020052, 913618956, 31087628, 12091558, 916697904, 449193493, 114122927, 209367711, 647579183, 182477319, 789253944, 927297270, 165279368, 420889228, 888790417, 21784247, 115343255, 973993941, 727060753, 850063060, 269751479, 95425835, 964065018, 523282656, 405589149, 772765391, 340302667, 890136265, 283292665, 546698202, 989559670, 737137916, 923147199, 183957401, 192978258, 189434419, 759529449, 174218234, 164810975, 606912945, 459223749, 456388180, 412049780, 789934571, 327206118, 666789787, 350906399, 631172824, 641243294, 123746251, 70932494, 841873730, 195630248, 861839883, 984103063, 685107299, 822614627, 866095524, 631094696, 961022913, 590480772, 294304843, 646241887, 116934945, 609049700, 20725361, 227602979, 805091251, 268654597, 785876780, 472409626, 536808849, 754691167, 194356215, 107171381, 2880023, 456832705, 280261077, 831019323, 997828482, 759094429, 654088655, 470097007, 841700280, 19543394, 933463141, 35492276, 772106970, 745924732, 477628475, 204059872, 709574458, 109180162, 455436527, 113527887, 589753855, 64090089, 867812833, 921233803, 863945408, 455217386, 349456195, 471700479, 210792697, 977432664, 337214254, 79218757, 446340576, 716306479, 170145914, 406086831, 829303634, 867615331, 506838418, 416230002, 611868420, 772295133, 922751639, 981419135, 44842464, 43987051, 96654235, 942411568, 329108060, 6316197, 995583793, 736108837, 452555357, 327056104, 651881158, 562595976, 86648982, 366811158, 209031286, 407124425, 122013472, 824528362, 984821247, 683693460, 73008278, 384563378, 171043810, 736283913, 292396415, 339032515, 199981852, 752300446, 4732387, 230335129, 657187462, 574812300, 310686240, 67631309, 300882348, 157014510, 548920462, 238945636, 198833601, 970375609, 64484990, 836846530, 287040875, 89122495, 639708554, 364189694, 398363045, 299520774, 648883862, 761466178, 99196379, 151178488, 767483132, 881560900, 785403252, 630620891, 354131885, 992104494, 714228281, 349166385, 868010963, 367587778, 126621826, 179132663, 468084160, 111258767, 127956917, 352284708, 296197177, 431848960, 959074166, 878132058, 103194743, 475244318, 469846826, 166468299, 816791008, 19103245, 423703346, 845831112, 876171765, 402203026, 70797383, 376209559, 554300052, 476570954, 208779860, 410781991, 959649652, 498149855, 743274323, 608556278, 67642028, 288029635, 593389850, 645467604, 139145958, 441673867, 691269098, 662155350, 207027061, 93805382, 519000743, 212417602, 528324909, 479352134, 323074134, 433029390, 81464130, 698502328, 653460537, 657964318, 788613723, 211316966, 697568450, 384932735, 513262351, 933635291, 698793933, 74109858, 351107727, 458465006, 64009026, 619700931, 638372753, 812659218, 417724236, 311272381, 356175554, 855770544, 842714713, 293945836, 404135702, 875881088, 561918389, 543056012, 552974044, 447766610, 237437930, 328714154, 325467462, 33867673, 615839298, 471891443, 989410506, 787738187, 49307100, 475915086, 703457969, 153074060, 32272054, 321941683, 997657072, 670370406, 572670962, 349024146, 414784721, 941606646, 883027884, 814560973, 326659499, 691864088, 556008031, 336978785, 962602386, 839382890, 494233291, 909769539, 351258565, 240698854, 511256941, 353898293, 163089633, 269788296, 577693874, 712027283, 706362795, 440854514, 783894872, 690477947, 18436334, 146052250, 646257436, 348097726, 983349089, 483747684, 563044737, 450755163, 855282076, 686080119, 538999184, 566069905, 730215846, 19776543, 732743795, 113950847, 709310298, 767459128, 623674767, 192803424, 311828444, 633332532, 465535625, 139734057, 783507155, 991084923, 404626513, 493811622, 50729136, 147959457, 300005264, 627509132, 991984257, 43285289, 123408021, 339002812, 6442330, 40168824, 995610208, 823156152, 137327698, 674334257, 568965138, 468993588, 679442740, 538305224, 492549043, 787182647, 319239553, 350901919, 787968536, 357226434, 331749326, 70564748, 771681235, 410663800, 896943772, 646544713, 874137591, 216188898, 343984111, 773084220, 726745540, 398067119, 199468967, 585868074, 25961489, 500695429, 989461266, 121573285, 790179037, 213010435, 521766615, 86547792, 894909729, 489385449, 170643496, 35847729, 19320805, 492855592, 743207707, 592702471, 319734901, 128221613, 525339826, 269199749, 686641834, 170585131, 53263260, 909790347, 322079170, 887766056, 566474497, 899610144, 594299463, 65488099, 253760287, 255957005, 408370103, 643606868, 184063258, 349314977, 717521204, 775544013, 691344900, 225752669, 182398353, 128411811, 164375273, 487393422, 93785379, 489806204, 89570248, 846472334, 831539871, 645020385, 53130637, 241009500, 661512133, 927025869, 14791444, 657782639, 499786962, 961947570, 905695879, 889253410, 407370681, 623844946, 890810903, 253539852, 748963926, 119034505, 864159548, 750805705, 689724202, 450116139, 818704301, 479718014, 112504023, 286253109, 123733959, 378218282, 393610880, 176410741, 70302748, 463436044, 944913479, 185758270, 373724659, 918662294, 400349959, 641567297, 959395052, 169489353, 139799116, 789276735, 521574740, 787901250, 544148090, 366881168, 924007307, 724620443, 144061441, 589906820, 467678243, 636782546, 549990135, 599887231, 300700479, 829091243, 733818773, 201401033, 7244160, 11553420, 662927308, 500263678, 905054490, 783200036, 911904073, 200784470, 950224498, 694891057, 623521635, 105475825, 967106642, 994515796, 985241658, 925519025, 798517936, 825056698, 259899342, 322489882, 511787252, 383107365, 941260153, 382972505, 962814236, 608756627, 926571706, 286495217, 876790071, 199533558, 144835798, 462661283, 156096027, 241955116, 441411820, 354235452, 753245641, 757497145, 724591365, 362072743, 446059002, 840839407, 121158062, 704842565, 895178492, 339384571, 131622645, 887036686, 663783842, 874125293, 965362061, 387827664, 812435164, 131760913, 642646565, 493401004, 612136242, 771900662, 182569964, 670445404, 149858458, 532524168, 881434921, 631164701, 728408894, 129383526, 413081944, 59372567, 102679410, 926904487, 672143526, 817721021, 361016125, 792639577, 337389253, 600717499, 189200865, 595521319, 616380678, 165360987, 198787050, 504677557, 541145199, 604760555, 516406898, 220853071, 667870934, 661335854, 118942040, 338991649, 136148740, 795010415, 151262017, 93304104, 134821879, 253653887, 256861757, 675331235, 597314108, 275989695, 329674755, 9554267, 54025976, 940680952, 34770037, 320072902, 993938943, 89527372, 234497428, 598747178, 98639246, 658373476, 353399588, 964723799, 44392584, 726330607, 804391587, 77644147, 91810584, 716265710, 208985950, 956459216, 125352141, 39565889, 570790418, 999508368, 214983911, 506148375, 1830495, 510862771, 613604370, 893443212, 379497383, 93803389, 899913808, 381283022, 709513887, 194619626, 329991324, 78526345, 950439664, 905949153, 313288224, 164241010, 463315704, 91247292, 715772595, 701723929, 546570225, 470361048, 963014288, 85419086, 354057375, 438976318, 454365080, 86857882, 730205728, 865422924, 294812948, 844451220, 154000613, 729459795, 297949160, 917459813, 131316783, 528022606, 759982883, 711532674, 400454218, 277840994, 828948352, 863507030, 233377297, 997831067, 895136436, 803073800, 535758296, 819127355, 425722882, 37825977, 456946713, 313487464, 942231049, 667335359, 823958951, 630662182, 268322708, 757236929, 334097918, 790977093, 374484815, 712338406, 443126062, 47550849, 34885942, 420771583, 389652981, 928033691, 568641930, 218793859, 769859899, 582018664, 656773374, 861095043, 494943623, 747769398, 788793474, 797221580, 740187084, 800424962, 43411955, 831068666, 987480050, 851862503, 324652663, 505481015, 501412158, 526878656, 585903468, 636585410, 869150159, 122285485, 391014296, 323462361, 648186533, 437562337, 830706630, 633730711, 487384309, 282637221, 414144823, 719628351, 423708291, 707665418, 944231503, 776275213, 5727132, 903728392, 413125398, 690182629, 803602248, 333282596, 11367105, 244462650, 764914559, 609785263, 497636887, 201501716, 165570983, 206973115, 983356136, 525217798, 340640558, 27839764, 551539338, 42859006, 128624748, 902688434, 250173152, 119745670, 562177080, 66379953, 252345987, 156984854, 765318750, 608433502, 459621515, 227103320, 876284005, 761254141, 427165774, 92636386, 913419165, 769445800, 4737033, 220368607, 165159109, 948149168, 194673369, 791747464, 595191901, 494803458, 575968485, 897326320, 485961647, 303177652, 435169151, 961105254, 473893641, 786488664, 327961475, 199911801, 70313714, 134366967, 383977927, 451794604, 317289429, 68871036, 585726630, 100701868, 441223547, 194415462, 518852541, 7732306, 292557169, 667841823, 17061579, 439986594, 716555218, 256931101, 324700067, 377523696, 865999332, 666319565, 85077601, 566605840, 436284767, 731359232, 319619808, 721694381, 315100832, 680606983, 148253136, 344015631, 255935660, 135090679, 751255722, 208813107, 447032024, 943753744, 317456000, 39261297, 121812475, 519119517, 920515611, 619900050, 881870880, 496976303, 649665773, 393296258, 347997265, 301661894, 150030699, 519011061, 885786132, 447053672, 965734572, 32590280, 632044402, 40853537, 597414551, 496382433, 861641306, 362585790, 770878143, 330910457, 608891230, 271793534, 260065285, 749820792, 947792540, 214599342, 466207845, 495644254, 48653050, 325558804, 884726568, 42048855, 14920080, 796880940, 380680947, 658726321, 563698445, 387112943, 855377395, 619788393, 71946350, 258031921, 452196951, 928121771, 622026369, 347389218, 725211679, 756516438, 482376879, 902727364, 282704559, 55306934, 517619852, 836073444, 317959502, 905928742, 291885742, 226974811, 780889766, 217520909, 135615153, 997345511, 705178997, 4240295, 62781769, 783213975, 57209856, 360543485, 292519030, 334195795, 976518151, 506598610, 849151253, 60240374, 348258984, 515371581, 800784023, 24037111, 602096834, 709240161, 307709798, 650217832, 13430132, 761548158, 717975634, 999443620, 637853664, 625095127, 454376941, 637440609, 287586763, 334647973, 980645610, 422494714, 626290215, 346481503, 643293753, 730766914, 608893154, 929852117, 660566422, 48426236, 306885361, 255310417, 920057578, 385613169, 155955548, 139247653, 980976702, 367478384, 399574776, 278967053, 466060271, 261359021, 871488412, 553405687, 871266891, 615631311, 87822237, 822101501, 792200950, 118906384, 594841654, 939431791, 65195004, 848063644, 405439026, 986006204, 637145860, 920845304, 483484701, 159691455, 894601000, 539803375, 204400391, 357818744, 61458778, 453772285, 509821462, 163741611, 204105020, 904871383, 227797265, 49068354, 239623486, 543453994, 902827596, 214368868, 534559344, 717186469, 473772708, 342743418, 105787933, 573262939, 100956792, 90594381, 639253991, 399560554, 763740700, 951852462, 606132629, 140244965, 401034041, 819290077, 747828409, 99414241, 334657969, 650313812, 901796010, 805822583, 8291026, 930173250, 86660904, 598274135, 741217387, 360511327, 163975600, 530233829, 784456925, 225893227, 871515415, 781947096, 185932030, 749559795, 639393243, 717969245, 26987564, 999368190, 140600628, 473643487, 377185764, 779976882, 686544156, 55056651, 954295305, 760289446, 30137113, 869413687, 683140231, 920314600, 639744752, 548602345, 345139341, 558838483, 382843061, 220279155, 840132385, 656809855, 998155886, 809036415, 372746251, 672315731, 238832869, 769981208, 868980441, 3964372, 876183182, 69313736, 864460811, 845777556, 95636063, 305026418, 77488030, 198976519, 591871301, 328410898, 539910226, 498800524, 977501391, 305560979, 413454649, 806793662, 308893296, 812231008, 561346538, 888596620, 674849160, 831318399, 309749266, 146842613, 85584801, 832594969, 628849979, 280354748, 412851900, 257151579, 934117154, 556655878, 458473368, 753739473, 201792188, 868048164, 43536808, 423197373, 772193444, 898126744, 726933234, 260156046, 315198333, 382717065, 633196870, 552681771, 985251576, 698468686, 393598031, 416481180, 654908337, 453975102, 264915130, 355337780, 473696724, 769999711, 246001679, 107580871, 242079551, 1272129, 834023017, 442737321, 320710013, 222639325, 178595053, 99127957, 391285722, 776940988, 940699372, 884069994, 966590688, 950421472, 155221452, 773669840, 118931447, 242691820, 248786395, 672770470, 787954565, 51077013, 802129078, 886859711, 176052542, 675793993, 119469312, 400711049, 288207980, 317733333, 689233408, 570166904, 108477116, 304851076, 667253862, 759748576, 245299192, 657291825, 805467083, 669054868, 81641053, 623612928, 847975179, 650066018, 106940312, 727793810, 533336539, 333547088, 629783912, 888343521, 507107968, 384396453, 497563114, 708338395, 262066367, 20427459, 99094704, 774796182, 205780778, 934622725, 366471655, 353625590, 883484224, 152471479, 775646384, 923614331, 459177118, 368071042, 637570408, 35672561, 51110147, 397304920, 304223916, 216289100, 56698398, 728921564, 930819362, 523406059, 928256513, 397919304, 67449908, 590513425, 499395881, 537396649, 727085587, 947712556, 55437744, 991509230, 903979098, 459484847, 919364549, 335621908, 406656205, 153844077, 282510536, 714868578, 703115129, 127160406, 501666036, 780306807, 655654022, 589076451, 167464093, 484984905, 459239244, 845012639, 10402988, 695259675, 253309331, 146643427, 236467539, 46968156, 79973324, 764826659, 509530489, 381662960, 417661553, 282384446, 191192903, 706451423, 568731543, 594003873, 128817606, 986449483, 794351301, 977764100, 274327776, 939495312, 863528059, 438154536, 156246229, 917579284, 804932037, 199616525, 737640750, 988798782, 472724472, 967867814, 116693786, 356246460, 603026390, 322089185, 359331761, 267724635, 768996912, 200668538, 563928225, 622037151, 105505973, 941365443, 912542580, 172158711, 654452275, 819436926, 385688339, 894889043, 695387219, 473488116, 979632077, 522604533, 574114548, 29787800, 938007984, 15317607, 45997433, 193034224, 581551815, 353543020, 965722020, 669216545, 607629366, 966016416, 561855598, 310376809, 475443042, 81299601, 213600371, 542790812, 476768449, 12823542, 972224798, 606350844, 231817187, 159195073, 30861869, 862775512, 119541047, 972057392, 622492715, 770295861, 809926379, 797819739, 961632593, 238954227, 659497680, 146868662, 579702500, 59154041, 173375436, 481675429, 416478138, 785029441, 33006471, 867714383, 567523569, 150595408, 879548633, 947719531, 510643047, 572327714, 775246930, 85093749, 36598201, 821658628, 159713297, 989924650, 982922473, 622454946, 644840667, 36257877, 40669088, 333995089, 699619925, 931960470, 936986607, 878916429, 463105969, 298952159, 629988994, 518990958, 370077195, 180474042, 425494600, 523369608, 34251923, 102298117, 477988840, 696955262, 559178320, 863300296, 552108156, 223890319, 203413201, 842210914, 730957504, 956664642, 893908120, 697802272, 621980562, 836446058, 559888488, 694099383, 860947541, 230241667, 338144420, 226610846, 306040113, 833870836, 138585956, 232778950, 916826726, 121536612, 333899767, 356693083, 12737312, 845385229, 488673485, 435644630, 376303353, 523247955, 922163663, 954264428, 906106591, 847821630, 765288684, 690068939, 352313403, 222701697, 988346977, 562927392, 683761500, 290525432, 645726461, 40679495, 463618594, 232044563, 562261499, 591542643, 480216817, 603505580, 840587235, 236337802, 186764883, 335536337, 113072064, 604468985, 40058034, 870663440, 81733071, 486802668, 384890701, 443764963, 677241050, 56249540, 471884446, 462646481, 620174218, 349728049, 441532578, 309070380, 58268238, 529633260, 338261973, 63565086, 154480063, 71638770, 838098231, 201042539, 585459785, 302741145, 969637667, 626242866, 691915447, 514708332, 465606153, 468561114, 740558380, 52102678, 53644179, 356462146, 58253716, 918644374, 115722343, 929154863, 656212177, 525975939, 133527040, 453656070, 84097424, 556903574, 926610626, 564499236, 715513991, 49114183, 603484514, 928122885, 210556678, 485338726, 623149659, 490713745, 86867867, 394883865, 418334673, 667101544, 41794986, 673632058, 707617170, 763347616, 793572168, 406151962, 818883741, 964923422, 537388663, 702255211, 800766116, 101278506, 989795625, 958854967, 418549854, 640375469, 104978782, 425327609, 203528494, 327022161, 527987114, 326735567, 15593794, 791227673, 241150071, 330012733, 730738620, 832854377, 830204392, 724967690, 16471897, 616011050, 687336165, 713200655, 165167995, 182133124, 176568493, 431692960, 321783101, 856003309, 943327501, 144167625, 646894869, 325142180, 741185248, 42026832, 180112960, 143296012, 17983380, 459333438, 321484168, 886740663, 661296443, 475503403, 375620223, 317388745, 984231132, 372129810, 725660832, 74883177, 514462654, 933618258, 239436472, 399926409, 659664229, 587133613, 421428672, 82123937, 405392910, 485416338, 245733506, 155749169, 518347950, 889988349, 750862373, 235658914, 487873352, 936301477, 673367039, 3744476, 312448868, 575560935, 929025991, 686529101, 764045348, 870063339, 243701947, 46149716, 770399883, 148052133, 573613111, 541756363, 188982830, 467492118, 922095873, 158994555, 148457074, 711375750, 508437527, 280039718, 618269476, 699546541, 767671431, 636885237, 874666321, 256861491, 184738688, 517813397, 770074545, 129319528, 658153434, 735208317, 848378474, 545882322, 478916031, 791056633, 264833321, 839639649, 166397837, 79154968, 874917251, 340229964, 914971082, 437734844, 70763438, 376809198, 217336168, 342635024, 600313809, 407257561, 450739080, 229851494, 394565457, 292921821, 73201143, 461468105, 20683034, 185391034, 796553397, 191691824, 889569223, 348537467, 666887274, 740984656, 496420487, 946218219, 279943961, 337847257, 642716785, 938012261, 947126638, 293472223, 6853201, 500024576, 557579617, 774194436, 341604837, 64522216, 424998991, 911056852, 835800809, 385190970, 101341835, 429501012, 714712746, 413945031, 656836328, 670421116, 855323592, 527296686, 531902983, 726583011, 752132134, 787387869, 113726720, 65773883, 239452044, 628963805, 444746046, 757326595, 655429142, 147917151, 940104273, 782292889, 792778335, 182516282, 245337938, 639088844, 511078281, 691871691, 927493999, 763299362, 511799661, 577520650, 478824143, 961247666, 108758482, 922693704, 318430650, 23774529, 14815898, 619877237, 939573988, 737027925, 490883271, 76661621, 974339810, 936844288, 149021067, 551615295, 283265813, 371474154, 580838524, 251565705, 861666706, 76276418, 595278132, 108767054, 122505759, 657374792, 502290358, 165108036, 306541638, 370991590, 844011315, 440205473, 659603378, 565477491, 866000968, 443037598, 42640126, 943213111, 343185305, 62098379, 749803486, 398964403, 563798679, 127844554, 630978417, 814142843, 116534069, 301032146, 606037151, 262053961, 312409123, 662094667, 680595509, 291230393, 411224718, 30002813, 832844214, 779951967, 86189698, 982418104, 485914651, 200879493, 380516057, 970160877, 561665144, 392718010, 433336958, 153489251, 279216939, 372050869, 854933703, 184869664, 179082821, 864187943, 167333047, 679171604, 342168795, 46305694, 133766843, 318474505, 758299548, 701064981, 15351785, 395766713, 557538075, 760540930, 91091692, 750637706, 663709669, 580128284, 920002310, 112528280, 725981303, 207624290, 17866602, 848919947, 276677938, 361948481, 96302837, 256742278, 586381567, 618390516, 890808562, 874258535, 521050272, 542692344, 161127638, 149277684, 225925476, 71592079, 86224677, 606354662, 1359784, 60931459, 467806574, 334659208, 960376185, 60032566, 390091012, 369043539, 805722202, 476628711, 941673649, 268428342, 224463005, 169907601, 656392558, 906229539, 646334981, 70270720, 328364099, 639605063, 280212543, 912467907, 324971838, 153777957, 913630477, 560870849, 240298894, 814330379, 205383282, 641760334, 363722593, 69837834, 172809878, 446316780, 772027092, 708344159, 864374269, 195774083, 14505393, 690945756, 633223151, 61096477, 881734101, 90905653, 684675302, 786390648, 907272451, 624122103, 502934019, 281543411, 240041796, 398457215, 827096929, 273615457, 408189042, 252327484, 806503217, 78483397, 466584192, 654048051, 538303266, 407582589, 352089919, 299052818, 252819414, 762216813, 68565372, 794341730, 463962909, 513562642, 560169752, 540083927, 501673845, 650225326, 317909362, 976440511, 292627398, 43854890, 417987478, 351729685, 572199574, 119384876, 303784656, 3935687, 964624063, 200254569, 391969730, 388526743, 582110362, 473479844, 132116668, 826093618, 842587090, 230752332, 540618618, 358167451, 563259802, 694737016, 648099449, 34532892, 458514169, 694532678, 65506741, 962059417, 344900593, 873023359, 89458129, 288020641, 955084221, 336229224, 594034855, 943529529, 736010414, 281170394, 649947636, 689958371, 342664110, 448302606, 638913052, 829788528, 128805900, 592264316, 708042352, 634957532, 295369056, 622167982, 215371606, 39806602, 869494830, 391114782, 455520735, 773342829, 262394886, 678038231, 661551635, 479873124, 828333087, 214582282, 189069815, 318044445, 801014194, 284082800, 232415889, 151344286, 725060191, 447922746, 622685782, 115748661, 810224392, 291122373, 647319031, 631065926, 918713579, 105117575, 542034560, 793334581, 507121527, 260043033, 884862149, 761128536, 821163402, 737154072, 644298962, 467149284, 603670043, 863443470, 223332213, 557491260, 737622069, 86666155, 820459866, 492756342, 656456410, 500238244, 75554053, 263295506, 218216621, 878217215, 257860507, 88262273, 492254399, 387675100, 891040540, 897963412, 333082867, 265836381, 194407491, 744637434, 391294459, 809353264, 762780382, 64832258, 338062011, 470040203, 4009213, 500631374, 741243312, 779509557, 492357834, 542936970, 625794478, 939845814, 143867823, 812663566, 397563416, 924826282, 620632838, 939874596, 180562159, 964747116, 488489155, 199164773, 469186575, 470353995, 441514559, 12830066, 642945923, 794258648, 217962374, 689242968, 551401957, 760249867, 152138324, 254341133, 189830026, 920524378, 407153927, 491301312, 646849770, 136923764, 33143185, 769157792, 44265676, 938589327, 805688306, 701642260, 261710881, 194176067, 285673952, 767817426, 456395010, 684454009, 355282491, 884650312, 859569066, 141914772, 946025030, 812944244, 372994397, 634983976, 780726202, 555178852, 400664130, 389485698, 5482789, 263801809, 972699879, 356000619, 899476265, 291278987, 696809429, 364651264, 855787300, 484542862, 220769114, 801751221, 511451930, 578435259, 596614547, 702613380, 985081229, 925575646, 662252739, 655036117, 778635914, 927359272, 25425434, 377830153, 352625260, 729747268, 687501785, 717980991, 874871791, 338258900, 205635790, 836777528, 975857914, 769077205, 638539459, 122739054, 874683377, 102304544, 604308856, 597344041, 84287776, 493618054, 558562767, 648026090, 561866199, 201553505, 85441767, 672423598, 90179469, 307931298, 325434873, 731484491, 459703868, 435705316, 784387915, 545384518, 776901476, 424386203, 371327346, 31288142, 25442480, 900002095, 784068122, 147622697, 21647647, 59738181, 112419068, 590967575, 888862589, 341843497, 886067466, 411962846, 215061741, 715672008, 237415990, 9746881, 289913999, 241731244, 852829064, 96528216, 603347096, 14398554, 385304577, 53467603, 30243285, 646858473, 544133241, 362197002, 331159497, 655434355, 736429192, 248767923, 697636101, 652061753, 723623541, 114422792, 354614467, 389767792, 975330147, 733094550, 892654737, 481748809, 355412917, 95602166, 74014736, 555150720, 452660572, 772002207, 63700638, 921619045, 878295211, 990918787, 238355255, 95385251, 638571946, 501951889, 750743054, 699396472, 849078591, 190353747, 77790864, 977343510, 936871772, 295038760, 746967104, 839523183, 935166161, 790536266, 189029506, 278861001, 356488416, 995875300, 870268076, 541535151, 431731831, 221984490, 746722906, 213622200, 76910324, 530209127, 418458240, 751192568, 889467789, 616108636, 95732237, 406260104, 966453697, 287936378, 482790935, 27734855, 517986404, 999283099, 669811582, 760262942, 907836269, 970556743, 312915236, 444065497, 865462304, 843423798, 89161073, 682551540, 204877621, 913124916, 588333694, 297403731, 610902349, 355793447, 182496368, 286272652, 194329039, 438892959, 348860635, 880618569, 626640320, 413513638, 751359068, 956839421, 738328573, 574271021, 266008860, 383149682, 197312503, 688149067, 290384672, 915899594, 130427330, 282742505, 886506149, 201488098, 167895609, 669746834, 897637956, 570960924, 785486924, 386775320, 128603468, 83793700, 705911929, 998276116, 128670396, 543349108, 670732386, 151829741, 43193976, 129262986, 774689216, 895587689, 711536001, 762108862, 909677500, 949522973, 702351275, 424198719, 396807064, 197710589, 513897924, 985299046, 64769814, 31974864, 947869199, 22933592, 457267985, 334976277, 652550636, 49878909, 607444129, 443815243, 864727468, 719389792, 858151049, 257895499, 27060872, 617814819, 350188941, 663640429, 588479712, 699357870, 336398142, 455129307, 510438721, 876717083, 162200637, 152705495, 184585887, 900579906, 66251441, 36504593, 815561438, 580587588, 362417268, 532994023, 676661094, 585052934, 619800981, 829126911, 553386709, 466201807, 970129910, 462548233, 283688667, 193323320, 635302287, 437753627, 918578845, 890626061, 536007441, 988831289, 891558528, 559405764, 119020836, 525450748, 933869879, 927995150, 377746070, 858628370, 613509911, 626411997, 830417021, 52130853, 590509436, 783583442, 925053370, 887542279, 449282987, 675607039, 632805285, 626138232, 169071531, 831329039, 243431695, 971049457, 677630232, 747911043, 19729834, 252608176, 311275805, 963375483, 70055219, 668376734, 738948060, 451069846, 997998233, 285308450, 12889275, 639494014, 141865579, 938034205, 980199125, 603347856, 680693939, 749524387, 508218632, 67509512, 159772484, 982086714, 619375349, 690368426, 663871475, 248260384, 233397250, 599875892, 570612429, 260512743, 295083251, 585817685, 476100019, 689149558, 289284961, 565587276, 30245563, 136223304, 737246297, 802455624, 716909424, 383473777, 895918845, 828336780, 371878223, 279109048, 652140009, 912671880, 5051642, 635291450, 434052018, 173173438, 982316298, 440193070, 648082298, 351420879, 827536354, 52031930, 375214524, 625593681, 898479373, 390713088, 680824567, 261290067, 416052793, 954841593, 402161974, 475076450, 176224775, 583037519, 266115318, 666634439, 543253264, 976032253, 462713264, 281649847, 878723115, 748469233, 87087922, 229802340, 34608902, 480220675, 778423760, 870014672, 393045653, 839268220, 399520508, 286554939, 447866797, 693279533, 514306660, 162363220, 47117927, 82037214, 990604358, 367097064, 814694672, 835465473, 268729872, 791568160, 467278201, 550083576, 896161117, 529775954, 324812669, 335944836, 819209428, 588588556, 618521210, 91213046, 705375079, 912231038, 63600173, 134773426, 190900092, 6456499, 157169722, 473593087, 709198116, 90524967, 329957185, 616594118, 176412862, 829082205, 837444426, 923503799, 723625860, 685243892, 361736373, 210828135, 556044010, 628011388, 233978752, 401551127, 767872185, 995949976, 275913848, 217045412, 678651646, 3981532, 820460570, 176941227, 318833606, 529921086, 354114745, 289971104, 530150500, 64241668, 960814808, 737582380, 853465117, 343372647, 908821099, 529345298, 748275402, 595602541, 553067027, 487109877, 124856792, 547434064, 589469647, 672060999, 875580601, 268261496, 79183330, 84720692, 894559277, 285179638, 255997848, 153887222, 811456385, 250950583, 802025285, 910450107, 430004758, 18921785, 335274002, 714587760, 408944501, 712905480, 530754968, 304590543, 78000643, 23675883, 452030185, 68958464, 368305647, 969921263, 829016341, 715133654, 965161937, 98694574, 548066475, 728055933, 731989315, 384163449, 762467737, 101393330, 575099493, 15851084, 461616413, 804681234, 732464930, 28442421, 186249276, 871690384, 814207523, 923745992, 847360143, 129658939, 463845160, 874543960, 749976844, 127868007, 851522791, 913780219, 381147861, 987785410, 779422572, 252428464, 993269925, 812398347, 416713613, 261067128, 170343153, 196496897, 50895776, 273708852, 801793864, 67611529, 655793256, 236957846, 720310989, 240747922, 816377160, 578396687, 284935700, 147770240, 188672303, 142580246, 88251136, 463124928, 461119331, 172523562, 341958548, 696532302, 763173939, 680174198, 489484590, 331712216, 683578482, 299306413, 127346185, 454246286, 478455564, 778563688, 575788118, 965676751, 428605434, 735898184, 527140236, 150735969, 27463651, 248358835, 265956286, 401173059, 358692046, 890783059, 62079301, 85430933, 558838803, 933500759, 262119687, 209960465, 576362074, 28884892, 400990375, 605527303, 506234702, 440741445, 427199949, 294196286, 965083136, 624339902, 799773018, 950865324, 200273067, 595633931, 139867547, 189526218, 950831604, 612927636, 805134066, 36992458, 530605755, 294918965, 25064318, 506803859, 572085521, 596491091, 502177337, 700816641, 50214348, 787848803, 319776054, 227291901, 985606288, 356019795, 439759316, 589481964, 816920428, 685130827, 783954805, 970525815, 309608021, 889650618, 978810192, 711538786, 931483058, 173022177, 871931055, 242475325, 447528421, 478880983, 524262079, 710926241, 875977136, 911405559, 58158751, 574842471, 324809743, 92817493, 161090728, 369332447, 845977761, 199679758, 493136090, 708634589, 714393651, 217062252, 833176992, 621598162, 621046605, 733384295, 206692695, 963211640, 421966545, 491034132, 281405120, 675954303, 423340070, 823669074, 999577725, 190205754, 885144685, 702657826, 718740728, 218632632, 557436029, 761747151, 139173298, 190075646, 578331696, 432249636, 530336374, 535106786, 281619342, 865303374, 325608237, 722448638, 391597525, 936188006, 112783927, 943731224, 510068608, 159372713, 807932804, 740410061, 257827071, 981789016, 872837518, 870741042, 496300858, 566803717, 187903123, 979822602, 339376247, 485129919, 496453792, 404790296, 339729649, 155938195, 427523850, 868383967, 53394608, 226463739, 670325014, 570492260, 545667206, 701460116, 249653900, 414346629, 420273969, 777164837, 72486724, 464218366, 170527894, 374615089, 865067246, 14708141, 541604417, 723695202, 967690519, 467073441, 295959183, 257047020, 408403574, 121005292, 11722430, 922021024, 796380815, 464870168, 617679916, 84869296, 207949205, 439526282, 44549390, 523740502, 598009206, 350964640, 690275639, 670946990, 852012342, 876711195, 804094721, 199278656, 335768657, 382247099, 878537743, 407710885, 535705823, 684049386, 817478425, 342050446, 376257211, 767988634, 429418073, 433062377, 658392712, 776493678, 989897640, 38976536, 887788662, 602910609, 546316404, 929057299, 349644634, 438187392, 25384066, 605652217, 723459198, 343327008, 821455527, 227351727, 8918525, 759406388, 530855527, 638658347, 237021560, 325040584, 314975266, 985296565, 41673603, 14321380, 369672356, 230040537, 706377916, 705636376, 518147391, 404654084, 621880137, 758319485, 114660733, 509137063, 234073312, 447644945, 780514950, 458285840, 406591426, 572136119, 192449265, 113018312, 473650396, 535531065, 938969623, 482988444, 584437318, 275936143, 577905434, 146011379, 482837470, 30393113, 95819645, 191990444, 877877479, 640585059, 493431648, 745298944, 15404396, 184800509, 494297753, 696696637, 419198308, 437238658, 438561693, 752099826, 251999983, 285389885, 830903245, 95167023, 435700747, 207892669, 701748574, 896206438, 983993604, 694154385, 768499443, 37897269, 12348313, 379657233, 947894986, 601589732, 722447049, 272506549, 383174892, 184090618, 184295368, 569779223, 270667154, 653819554, 837977810, 575211397, 561068671, 411555227, 172143860, 434118365, 333693987, 862585191, 975542568, 649295278, 397888525, 595144798, 417725402, 858527040, 157870779, 42582991, 976031725, 493536332, 471695089, 299711084, 136828510, 954661529, 223211651, 800325297, 221855684, 207382985, 944610623, 115654998, 786420523, 997419538, 867489176, 435798537, 211456841, 188223981, 666929783, 56681695, 344349997, 596562923, 273765707, 127899232, 229955300, 945318929, 691615993, 106423319, 875489218, 773194455, 341662702, 840063315, 742800414, 932954318, 611845960, 552342349, 619952123, 618209559, 915244647, 804762247, 289720860, 818569523, 164893994, 2580834, 193886937, 868479401, 868173285, 250739786, 827519380, 293036423, 112040144, 657633554, 911125499, 936136325, 341577972, 474648436, 629494607, 152759492, 737073791, 370339489, 17750565, 599611758, 764842883, 674490900, 107009347, 387855165, 632426749, 629733332, 988495776, 154392544, 284545084, 837155673, 5071993, 999320904, 972902891, 895176911, 30413211, 91281021, 278860344, 899264968, 788128652, 490812337, 655063087, 23447359, 551708783, 612226556, 489694490, 170215412, 557481040, 455064796, 787467635, 74689831, 783779371, 823398890, 718355254, 499412471, 58939436, 568604541, 345749887, 859306826, 901839612, 683904626, 99064861, 296533154, 81246277, 30946024, 800299297, 907057536, 631233749, 911020322, 124546008, 158708981, 63919872, 990193306, 898411603, 618563169, 972314541, 308647828, 855569586, 754135141, 324409434, 502215168, 799638483, 272320670, 533387092, 637103364, 719820010, 26950750, 619882604, 685582832, 368149432, 84004494, 116342909, 282619488, 651694783, 217623751, 126475475, 544419428, 161974110, 482123085, 242719944, 844235645, 618652417, 408370382, 459405138, 362485424, 837165414, 316402022, 312166462, 231958943, 699706833, 638217344, 333481695, 973172177, 83983537, 609706486, 743564236, 269603870, 346854147, 225832521, 787705712, 810940361, 368993161, 935055237, 653244182, 333822770, 590681483, 253420700, 609446654, 420820519, 406405512, 440298577, 502777867, 190238133, 619962478, 290710283, 234160674, 114277790, 206454741, 737710056, 966498373, 171901212, 180075735, 573744895, 93495885, 500822191, 933199820, 367110595, 199666747, 590601473, 993191321, 414516594, 508839014, 599255286, 620591837, 341622764, 488082133, 36900762, 991459757, 795721541, 355822293, 792607269, 780806314, 479051126, 101110971, 110671866, 294600188, 516206110, 496505464, 981876814, 789451304, 689002828, 632969598, 775036490, 324212542, 579577818, 319109299, 2182556, 191933146, 464566042, 835512509, 357084213, 450595979, 566038584, 544850951, 688782648, 831982643, 924910302, 179882912, 921527278, 411385633, 222461576, 57741363, 461065886, 836576978, 848497600, 577771024, 272229778, 18654928, 364783560, 182614593, 564602136, 533911524, 647134181, 784684764, 929714595, 800928845, 310949690, 116280549, 428710629, 571668633, 472617526, 902737026, 211522710, 987525482, 133132092, 204215307, 472290569, 229849079, 623982957, 719977208, 168287680, 852021118, 547246675, 704564432, 265035230, 43913232, 287572553, 634658850, 980291631, 640665145, 921233424, 18350031, 891609736, 780746257, 236386289, 867197947, 292843667, 153698354, 743069386, 212625398, 727871928, 283226620, 855113407, 907196575, 535539218, 978664074, 381411235, 38299917, 202306241, 541858260, 570841109, 377977074, 829999593, 367360142, 101971839, 659730412, 268444278, 126416702, 409237206, 149152406, 989393648, 124234454, 840685151, 403620137, 400498870, 671461411, 980295708, 288336605, 946846647, 949546994, 422757248, 537741789, 310772072, 681474738, 886237847, 686128223, 353840926, 522127783, 323307365, 564161355, 570296496, 214558333, 246166173, 618956923, 455946972, 380957574, 908172637, 364783194, 451545120, 624919547, 643843788, 185155356, 249616071, 634008970, 801653342, 830719864, 689246389, 374836366, 869109573, 294407124, 774583375, 616881676, 690628588, 925825189, 255336298, 214632956, 124537026, 941407833, 495846065, 340572641, 44797188, 476135772, 511723199, 88321568, 3744020, 141081836, 701485724, 508087657, 51328599, 527606294, 108303581, 646432688, 529872327, 97032787, 907934562, 302354679, 629203216, 148675346, 875329743, 989974142, 681737909, 506766179, 556826412, 514961945, 140370386, 757110169, 13462753, 945905083, 334658465, 141225362, 885684619, 496240220, 934233947, 361113178, 633100304, 762537491, 845421721, 606118371, 787073043, 406054639, 810964439, 730910575, 188213552, 367359306, 260887750, 99908368, 679312131, 706431763, 408811303, 398079878, 647610614, 392711969, 665955831, 219774562, 272908039, 658300894, 187114536, 932536085, 363904427, 983081900, 172568646, 45792108, 435146202, 489694729, 792127637, 708626560, 883526780, 42428379, 746311474, 804061240, 274496315, 325973483, 583998717, 654896394, 804363845, 22291739, 39337047, 2107467, 161745704, 641590509, 954097243, 547741453, 903339081, 486314280, 224910014, 896363402, 297103232, 439430040, 68726540, 995834002, 954530972, 963514877, 683317288, 166591072, 448396849, 714281120, 581600092, 580876433, 439178817, 968536853, 514276226, 861086561, 779070026, 53001936, 531615061, 365765521, 125067923, 412341575, 381258067, 50537169, 336248079, 508907419, 21088390, 244380403, 292121878, 747557253, 73942123, 954026097, 824330205, 589153358, 277532141, 485252549, 131760269, 870452587, 84157081, 364082777, 756455335, 829233969, 58003694, 536333357, 913119996, 715689059, 385299691, 867388083, 678238898, 483573067, 960167258, 671333578, 36010284, 165009246, 471356051, 105364044, 888007734, 98505330, 227350598, 42386119, 121404061, 772789942, 750448416, 365828676, 865102638, 519189661, 937033850, 452753604, 660656149, 372255082, 225463848, 169026855, 43774834, 483203722, 798030244, 282071687, 868209981, 966653568, 343479275, 579878450, 394530494, 534049474, 247433306, 714483163, 221798915, 356124767, 776163319, 970577966, 326753647, 485359016, 519528439, 20209643, 187778268, 866397837, 211214405, 762936034, 587448681, 992093778, 793844481, 539376166, 268897397, 214126780, 305441250, 75668667, 58482824, 742292470, 282186801, 700937039, 264489154, 582947284, 80838762, 379878069, 83964482, 710032802, 153993613, 196233871, 808295654, 501014310, 731059779, 68757176, 140415635, 51610150, 119351162, 908392649, 354518119, 442080663, 198025159, 122424262, 110166583, 169061447, 707374482, 941210189, 44780290, 195481907, 597025936, 751882447, 957978214, 200787933, 841564008, 421780896, 25740690, 386404245, 547440751, 320078411, 701860506, 822861958, 124304338, 691908401, 499446533, 220096730, 666936427, 599331875, 722291946, 745374295, 864384824, 393635309, 450107019, 453278075, 63926956, 19130856, 465645981, 25961407, 733124794, 375503853, 208646809, 953455471, 563299726, 350587582, 424805634, 655918770, 321702027, 293058634, 989697142, 870127475, 528038787, 115450150, 777535543, 931254527, 760519424, 74027740, 13635784, 58218582, 996527107, 908823656, 452594815, 451768888, 97559108, 864356103, 622052636, 195570832, 140720929, 455761753, 17113427, 452472358, 179478961, 435824012, 950398558, 668325941, 272032021, 615686602, 808311434, 715651067, 174377813, 60365394, 377742351, 875549856, 612312622, 28130378, 138243383, 451453114, 267356858, 503668237, 991653297, 873037039, 625904217, 517169424, 154736882, 900639605, 668719448, 143516245, 108785212, 39631023, 812009542, 836992355, 28298176, 383405029, 912458920, 393770320, 642851902, 395069152, 290303980, 637418112, 527285856, 659024956, 738182137, 458005193, 940577301, 67091450, 885401890, 653803785, 380137078, 881837920, 500492343, 780204642, 659859031, 474303266, 761421389, 349747443, 503157161, 761249009, 944827112, 509423709, 873298442, 821717920, 267319364, 328944004, 689290205, 589044084, 892553425, 911561884, 860840314, 853993219, 396408205, 398079164, 696689918, 585979524, 846013177, 318295354, 516123355, 700100848, 373546495, 462945963, 655030919, 70981359, 259462542, 670236809, 93613390, 456192738, 948903343, 718356070, 196993427, 359528558, 268991923, 300600500, 788994995, 943206968, 545087299, 465284809, 321309617, 99268435, 586865063, 48055334, 150036204, 931696339, 423343261, 484426917, 427412908, 434234198, 272743304, 259899330, 296761060, 373984516, 996342712, 332197557, 386036185, 702394889, 390460731, 779584686, 485768416, 256260492, 811128850, 60849049, 499449998, 172955466, 503926220, 904744626, 365482311, 608782289, 425574202, 963533197, 37485566, 987145743, 847946723, 990918778, 154260906, 47273787, 207378175, 668920406, 148100057, 147185149, 834086274, 478391782, 638921439, 788803371, 76266921, 631700596, 760704667, 181381517, 738067681, 45181563, 455965557, 353704446, 222316617, 857055610, 820088703, 945213191, 506238651, 768167304, 915006478, 288916475, 91416901, 446471532, 516297678, 290094890, 742052261, 350529811, 707277277, 319247473, 72571808, 500799323, 758631940, 863369924, 11266170, 807800476, 339631343, 526222586, 148553315, 556966035, 399652962, 342890555, 449509988, 86445637, 563654756, 576127354, 404725597, 469610944, 608068965, 540545348, 367236443, 714114241, 379592937, 290259177, 619881886, 216835874, 86905138, 332253769, 36659528, 367043756, 87959195, 648469392, 48965734, 231864605, 438873743, 598607244, 537628130, 134020880, 971645059, 674478177, 462502001, 837449651, 815274607, 41865964, 332654136, 290508408, 813908616, 279727898, 581941718, 7823284, 967859940, 918174821, 561745017, 910497992, 433266171, 766898853, 844888701, 83472065, 880065196, 898557867, 113082233, 937090092, 91885958, 565643610, 998501781, 913245937, 421758233, 972634121, 206662083, 464513648, 815910642, 653545774, 666334321, 495593213, 100242510, 469267380, 267352473, 586995995, 744093191, 152263722, 250031731, 11153, 110128285, 190952838, 427862391, 428368479, 633893845, 382940783, 771869067, 484293273, 689744126, 121706499, 942489305, 70080257, 796998161, 377066978, 212420199, 660228575, 952170753, 132840969, 508855167, 936249382, 146662761, 957462551, 7942588, 579987484, 596083794, 579534845, 495065006, 460028333, 939129179, 909457599, 851477029, 992068700, 124001483, 21940703, 91592655, 517048540, 343760285, 688284609, 841928403, 385662358, 242570178, 542523297, 194863701, 780079054, 371874400, 286331196, 462149519, 136886264, 154938333, 836711125, 496734396, 208744931, 709490181, 426484854, 725269618, 665876718, 911892820, 455400199, 707619974, 355850883, 379749823, 481626061, 454864272, 76498440, 692925876, 593123857, 678242983, 386781633, 909695067, 870568688, 330492999, 191771292, 762942868, 932625871, 878593090, 9653263, 466099419, 374103418, 999467176, 504109765, 614069052, 904882529, 566046275, 452574155, 679542237, 487487686, 670969655, 990914847, 728486219, 404331556, 86944462, 944837518, 267923648, 401634565, 736736972, 433931499, 823447648, 108038892, 380154280, 561081242, 971585640, 501152218, 829610234, 491687523, 802620296, 499958895, 480126804, 336765539, 522809545, 996276021, 833178374, 721786968, 294778131, 992325829, 935451973, 153819989, 509689040, 201728679, 443559669, 422432551, 113388213, 724375477, 377149605, 973345778, 605813569, 826504658, 954802549, 819710027, 453858863, 277235560, 154370465, 924770907, 744185799, 541099146, 124914929, 894442597, 305598208, 470569789, 247198711, 413243567, 197849708, 146596556, 179360005, 413481102, 103783442, 681300303, 104153603, 340618522, 79917284, 641330658, 690751491, 938832103, 129331137, 591882417, 850285938, 745428229, 890461572, 705132936, 158164802, 103883536, 505897949, 871971717, 745965781, 412841821, 547559505, 212064718, 802232916, 833196985, 75552472, 916269495, 708257845, 490088334, 770725418, 706166973, 648236087, 603239738, 12194743, 382975162, 899620807, 172251639, 570201933, 348517684, 121204380, 24012630, 741170901, 889989534, 350154860, 545728669, 845256522, 818688449, 658647351, 128728758, 164582188, 288876014, 690828200, 958678752, 698130303, 329564441, 810062630, 736221328, 667114760, 975381913, 699008486, 59729452, 330893226, 129580215, 821558765, 435274725, 602228634, 690674252, 17913203, 184076174, 856928278, 67714707, 423951463, 148706337, 169227737, 469223228, 75702307, 560699038, 982201991, 2724609, 968528661, 398749272, 715386253, 703631548, 698483014, 13794642, 873732846, 587626512, 882803420, 995026339, 353724121, 229256288, 649600541, 37713757, 125884066, 817447936, 860383675, 702204914, 115990556, 877048836, 9469403, 754101141, 483202752, 811339125, 623393545, 698042480, 754379407, 117014550, 338934313, 448269748, 497366479, 291958148, 495552981, 220662864, 898126305, 551889487, 789043568, 592550649, 614888080, 204912579, 18823413, 506581027, 992457717, 532356157, 526192364, 457426084, 952245470, 800143002, 880931867, 485725043, 558207744, 853969417, 553850779, 565962734, 390378126, 794408768, 206194146, 409862992, 161288802, 154263751, 893075618, 882089811, 115993229, 473554195, 192267861, 452434112, 684499669, 191363005, 774686205, 864800042, 451946743, 414905812, 168294710, 209141588, 201346786, 134415318, 865296860, 296296975, 579886144, 338808739, 173038872, 761503897, 317220000, 793753109, 254538440, 491778754, 326426628, 361531183, 406042356, 152456492, 162966165, 743773483, 621828533, 582558237, 248406323, 870627766, 244095092, 200430156, 315958736, 49434710, 148675974, 412757324, 242772589, 650344744, 383622962, 45783127, 283238947, 743069908, 780339278, 683000764, 830043676, 146065876, 313995874, 870355060, 231760361, 242154300, 499165134, 166456310, 159468393, 589279058, 739791188, 791834272, 447669581, 386960086, 716926584, 541821101, 402397730, 818959761, 962295099, 336957677, 727946112, 811445997, 539506049, 751798355, 666598596, 13728323, 132203814, 267934301, 828927374, 820002843, 132924014, 279110496, 645674142, 477331249, 838335709, 397603766, 745127974, 575448696, 953120399, 977828993, 409468637, 45967043, 345612390, 335216186, 888819848, 781434339, 343297806, 237092541, 453053428, 761359435, 668514283, 922656840, 516723031, 455413707, 787884465, 273527773, 767104882, 961981153, 959445639, 869464333, 71712473, 693619437, 693736726, 381270513, 716849996, 340587831, 62250695, 448863840, 120455186, 268275347, 837349633, 933168505, 146113520, 414302408, 524609585, 432115386, 766891389, 306608621, 827672473, 522842106, 183309760, 462721105, 446976280, 365869505, 648679337, 279653976, 326122224, 704060859, 839739783, 542729854, 622583293, 68163845, 393085175, 389591174, 635494202, 982547984, 378419039, 379196511, 308259705, 149627196, 844175542, 239685054, 823469706, 507695572, 377613488, 747201789, 766521594, 717463642, 824783807, 928956986, 789898655, 510104437, 288086429, 791700040, 510015724, 183788841, 77904465, 542664714, 690293333, 558158061, 872550315, 6383112, 984059246, 102613720, 649460857, 985643582, 988058928, 639269139, 240527813, 873596162, 14270732, 672926056, 582703801, 93842119, 966552892, 113754297, 407310234, 368501132, 363680523, 253798913, 461683712, 516887665, 197066964, 340998035, 218315513, 351306041, 982987128, 673859963, 517798841, 8669033, 191152548, 348996550, 763779851, 152255958, 4059484, 180639182, 335283738, 881632018, 721652402, 738904745, 13080287, 716907019, 895492110, 6315309, 230797123, 539132227, 398552015, 397390876, 259479816, 987039094, 79738884, 534117418, 878709631, 315114374, 284640757, 957702221, 253050611, 654167521, 933897808, 394581108, 713511225, 386021492, 602326888, 702904311, 916420950, 255751304, 582741680, 299840342, 214757414, 573646520, 276399639, 286362337, 591761009, 750609878, 462112925, 50133047, 681606777, 631615622, 784430185, 115538036, 779344669, 780110126, 375145594, 871447420, 30539700, 229960667, 976164059, 764909721, 204037110, 783957693, 909156512, 940104262, 291227645, 27925299, 686368903, 666266490, 409136480, 916337948, 537682872, 959297147, 209197097, 781570802, 475116991, 284175255, 593264705, 8417522, 664730397, 734919686, 138413602, 12270399, 432604276, 327366498, 925806274, 528776701, 811367490, 605385445, 541403778, 319964492, 40942881, 200431238, 995594810, 787999619, 177417974, 677265453, 263678381, 925897164, 940983468, 500106795, 708727897, 450484839, 722296080, 604805362, 327430574, 924750223, 718461006, 311986426, 613552907, 691304181, 399968475, 676136362, 266762616, 827223343, 524488777, 682635285, 364520553, 247494821, 838355705, 896383079, 27913746, 187333965, 379791099, 120945202, 996021486, 544054792, 181600708, 546110868, 744957167, 466234898, 641348425, 650317351, 848651459, 239000600, 498381679, 812190994, 517614815, 312411447, 432484553, 473295921, 207660605, 48196060, 59833697, 27908828, 418362272, 921138195, 127376516, 633701808, 716429344, 585234350, 79992884, 442187376, 5421384, 434588534, 395598229, 669190019, 515396478, 684602891, 781754032, 237046300, 869589607, 960628063, 120424909, 43318443, 923841513, 319283592, 771878669, 534588938, 428047607, 741484767, 910437705, 158127516, 788877572, 276410035, 270943577, 605342770, 650479751, 109471922, 679107142, 195290301, 130821246, 881872837, 613240767, 152136492, 514802202, 137339972, 906709429, 76410957, 168526, 455516635, 794269163, 83455763, 586268303, 414485773, 432402998, 827757391, 449307787, 217708317, 337675430, 138345105, 349920423, 406747539, 897789203, 226029221, 827999752, 864775550, 833366000, 557295192, 292392602, 57608010, 153522353, 326192159, 241951800, 664557479, 490090455, 603805343, 348562387, 495188263, 496261283, 128090598, 645058163, 123909450, 73296963, 534191465, 177643359, 220194860, 845176293, 790983288, 366121649, 17335067, 822590193, 951031239, 417683735, 177355684, 907833852, 422045125, 120230845, 231559907, 122980594, 57938289, 922726254, 776174059, 189253086, 320408371, 261033072, 99687162, 419838243, 102626573, 200054346, 631028129, 853887839, 679009060, 321206799, 708734300, 144190542, 893689633, 379544685, 363109245, 241378081, 740039738, 929856872, 229686536, 477581422, 654864346, 474785436, 827660952, 509068545, 295269690, 951551447, 981446914, 686105461, 237163676, 159997381, 677637676, 135323603, 68766022, 558306891, 433961828, 370991013, 31528625, 935407620, 804911255, 287217179, 338448439, 892614852, 307364310, 503458154, 61011331, 762592491, 59552215, 850395787, 153253118, 575270796, 238486897, 367722612, 522266138, 507425964, 959480114, 641439382, 394783687, 978019914, 644867269, 801579639, 700723750, 103042244, 101361338, 517678263, 521813144, 696084485, 941933556, 833765011, 972408556, 99806880, 859897950, 738532286, 707586008, 197242096, 427096653, 483402828, 136053581, 581817418, 121920079, 147850304, 696818543, 636499283, 806228352, 950733810, 606412478, 190478187, 822898970, 56843381, 623558662, 791466368, 244932110, 787875732, 394279032, 472949015, 90558355, 164288909, 337534714, 329526757, 725253998, 794318226, 418093424, 583249440, 415211424, 923294013, 217994771, 799611946, 935801687, 549927280, 817019084, 664125294, 556125462, 488260530, 723045782, 417978419, 62933416, 517725233, 136071639, 50912642, 899813488, 277643437, 612758308, 391976800, 659105010, 285123462, 548391552, 700030825, 976094673, 966384944, 464656716, 151871762, 37094761, 460813530, 944537335, 451876658, 518396734, 224719037, 426411557, 123915442, 327621681, 707113519, 771031288, 27393800, 470524680, 668778083, 655461203, 470715801, 992193644, 186644974, 172132452, 722924438, 70043286, 66706750, 584739813, 54104091, 130173859, 343109397, 490846227, 57908964, 856084525, 970226844, 824359108, 973342568, 667645118, 958010249, 116383757, 651061606, 220200311, 633337876, 961418, 560455304, 657121774, 12402945, 414233562, 127079761, 46320586, 262533732, 560561658, 850839618, 855835448, 770202735, 102952171, 838629375, 336687854, 625459139, 339985846, 920569099, 994043313, 586281226, 57162969, 299775573, 54247414, 456217868, 480512009, 589427878, 806494631, 782986063, 660883619, 502320205, 600054744, 793107197, 984095367, 463038851, 32293738, 523459407, 624767950, 968086608, 391029024, 723503053, 266992763, 99754029, 765620390, 822909347, 906950845, 23155549, 65952427, 752338006, 61680591, 232941952, 726349655, 668231440, 991595750, 63437411, 186906923, 315033927, 153969652, 924332694, 524420734, 130738105, 994094876, 955262908, 517782667, 657122441, 320270478, 43972352, 561886671, 961403513, 977007523, 60467640, 192725497, 583129215, 644342838, 478151254, 791424648, 119325452, 977408696, 118389541, 999656200, 281636910, 593792526, 143204401, 740047217, 824089947, 71162730, 650457494, 537042431, 844476142, 215382336, 880617131, 767475365, 126250075, 472306731, 833009941, 641085774, 848704434, 150823637, 741370626, 898810209, 861865700, 841307006, 96037424, 707065650, 959914958, 896947050, 698051761, 469970600, 833108645, 928744615, 655812340, 870469224, 440310085, 952587150, 635739163, 595730288, 915478160, 995232569, 467652172, 240065826, 403623050, 569570644, 983117052, 247258879, 133812056, 864436656, 92179324, 523989778, 930090368, 482716219, 96329075, 813486660, 929333005, 899794518, 674353801, 840219954, 296281529, 93548949, 481928535, 432344974, 631239345, 349695977, 88341800, 946453682, 283357481, 875403518, 974809, 220527751, 863538609, 597890034, 180430265, 304999933, 221475387, 482506992, 886016216, 779230574, 235643811, 403841679, 289843779, 104441648, 101851623, 680746230, 538516641, 757939756, 160088695, 749508069, 16234207, 84731774, 486874225, 765487846, 639447578, 350752124, 769204284, 1635383, 421632659, 332350377, 871007879, 638932112, 583415356, 535811703, 272338948, 387586045, 78693690, 896228194, 615041111, 42097876, 113282137, 928930365, 176766198, 727796964, 888786724, 686105862, 301973878, 558387818, 904722274, 471032791, 307164329, 479964126, 844449107, 680186138, 581660667, 383758639, 635983302, 723355267, 665619393, 756625722, 58256211, 495856611, 301792020, 83944703, 134132850, 849718118, 130989568, 919291980, 291314354, 399537582, 872942299, 241522552, 765266679, 778489625, 966232604, 287628208, 86353495, 918399362, 522682184, 95416834, 60338491, 114633698, 608635945, 267034084, 905728425, 446255917, 161553393, 63173537, 575852475, 375830173, 480053566, 517095035, 90020855, 851046837, 242648259, 202684195, 134979206, 875598803, 976262908, 988428992, 560348129, 140396895, 455692505, 982567711, 518244456, 474334049, 468232097, 269187945, 566864531, 8468062, 6394145, 302310214, 211448131, 305781591, 413712005, 629241207, 261119487, 28829089, 875010301, 524803161, 580372691, 61729141, 53067615, 99868768, 293579407, 31791401, 111601246, 231086808, 305783987, 371765661, 979851030, 545598163, 644239565, 316617805, 602974321, 347442496, 620084798, 838277488, 62743509, 494386334, 383632740, 346519392, 958287202, 777907391, 949247961, 852872826, 491286878, 162920404, 454836992, 433827208, 814560440, 265394326, 248091504, 618689854, 129230132, 630475393, 494039950, 135346561, 89805417, 312386334, 254848179, 14894512, 187354450, 415232632, 56006560, 667179989, 292354244, 932418115, 374758742, 13903924, 502944877, 689426814, 290641778, 934770985, 209275366, 783552260, 189987715, 39699815, 970645055, 186728623, 724422085, 272029356, 197889677, 145596160, 593513376, 312474846, 846133741, 212751315, 143244158, 549941342, 916187119, 286142242, 132436109, 185368535, 307164701, 278333973, 69360398, 494923316, 192121575, 887425829, 455434029, 551520524, 931520372, 762722942, 434641474, 691846587, 335971299, 450630936, 512224930, 555062209, 908536874, 210795477, 390418938, 272362069, 203196360, 934600649, 208709892, 722616825, 766509753, 854484229, 862059956, 343223474, 578070511, 412802121, 363894881, 496238877, 189979161, 482530793, 785479632, 653471959, 584014693, 348027879, 420804891, 438770726, 426721399, 804527894, 486018254, 503479598, 922238314, 459288472, 92164625, 970985633, 466454289, 706541225, 160351289, 386516460, 322710343, 882414767, 615734146, 347530363, 62401614, 247216475, 904904478, 778705661, 120854555, 805410184, 283716702, 279494851, 793029133, 704379125, 231875891, 513582210, 988818109, 42646964, 669347423, 373190213, 115819910, 908996499, 196907340, 560872563, 445290542, 863797763, 493253029, 710466474, 515545883, 116922579, 718927082, 520032416, 583124878, 296780927, 822474335, 868094655, 832711306, 967382570, 56225180, 241641552, 771529859, 343601223, 649591839, 657724456, 752558413, 960194731, 212162006, 11086433, 710942674, 176330583, 604161164, 517467236, 62572089, 610692971, 831377003, 795980680, 295194098, 997081520, 956187001, 592831106, 517234630, 967804351, 779010379, 193925979, 258877875, 294712622, 527665398, 12337131, 629935377, 652390343, 928015733, 952506395, 828955756, 632470525, 657001679, 602116906, 929040718, 115087064, 773951283, 627631871, 746806640, 766837604, 629271262, 366790883, 653147133, 619147864, 349836074, 313187484, 795240016, 415470051, 341998331, 451813058, 941317089, 885505646, 945321125, 213961808, 173801211, 195352422, 683660615, 452050038, 506354949, 159727440, 656314872, 858683287, 964314792, 186543674, 321939266, 121423394, 849635657, 292058919, 840426749, 123461351, 785089074, 422576416, 164673309, 944913582, 225891260, 505862777, 762941234, 170305254, 951873847, 605734274, 236380618, 652899999, 108525465, 294674327, 460607415, 424280218, 641481544, 372968680, 386071694, 253610464, 798148429, 458992587, 983107562, 750234791, 177044547, 497889029, 201473749, 373727519, 836907914, 669989253, 970200815, 333931870, 548634797, 938528597, 898368170, 818405061, 965877369, 201937459, 792467262, 90105878, 546130687, 147082783, 71689351, 815280445, 947810089, 365944688, 517754089, 540487058, 996429565, 336328265, 4279367, 20595454, 228614822, 11620632, 442479024, 615654743, 85520668, 315089519, 145721074, 756758265, 528140140, 561800605, 187227799, 130124682, 386523545, 580889990, 197033853, 340575298, 549056164, 472634157, 31994297, 83609050, 283677772, 337527211, 937817717, 408434558, 539558439, 534484642, 89697242, 294447626, 549830236, 229738105, 277944556, 322388042, 609233315, 521265361, 409517731, 686593130, 269472125, 786533699, 406240116, 421720679, 337370486, 718564906, 506732004, 509814802, 77528981, 756112632, 901799108, 251370348, 613011132, 1533290, 823264720, 669546072, 561410631, 964928273, 114866610, 148673966, 517324244, 614013057, 146127022, 72150145, 937341683, 842778993, 595629884, 271926740, 745351571, 300916282, 197021984, 811352317, 267223755, 906263755, 673879445, 865907213, 57163750, 136547781, 772596413, 689814585, 611085397, 812727833, 143383814, 627611636, 265414200, 995940866, 301640900, 758651528, 84553643, 141798616, 70173673, 638935456, 802136889, 766272567, 786133214, 234506545, 472478113, 769904445, 824702635, 156844601, 947112784, 734020070, 518863403, 528967991, 877680080, 989802319, 993129370, 786128257, 371406094, 780948479, 935798652, 587519252, 805974960, 318683708, 998795986, 321716761, 980147317, 481406499, 485300820, 113113437, 350285413, 433824563, 714861899, 917671271, 770604630, 533350123, 530740401, 704612081, 225103590, 385156353, 787399617, 671906301, 959402965, 94630415, 940887712, 585572459, 966393811, 938429485, 227371661, 162794696, 4581021, 779493031, 356226531, 15097445, 866645350, 423845767, 934731703, 523589449, 533251972, 54110914, 519521425, 594388205, 407574971, 824597520, 833403702, 941686285, 35416773, 489744233, 975022251, 689653537, 865740552, 59505371, 684536497, 477178860, 389756938, 364371469, 552895415, 554468484, 48867960, 564649059, 623183027, 397565875, 434381657, 414455405, 982300248, 295347423, 248418845, 441682369, 506835718, 32245833, 151127073, 497295698, 355276352, 750000575, 518551835, 98401413, 699250636, 238580342, 539405631, 29722630, 739250072, 965273315, 52631324, 265087949, 279378543, 773796911, 431293528, 820929858, 792383838, 846307513, 320232613, 796824005, 592720426, 870345448, 173270341, 653604667, 856631119, 954155169, 394251484, 640731451, 319729587, 675327626, 350493252, 771829860, 250958719, 478420121, 832272668, 146852764, 407671414, 938797049, 848955390, 300763014, 219461449, 413524086, 670532453, 296964827, 246474964, 131004637, 103230508, 331193715, 293815069, 625062994, 917346169, 909380673, 795745425, 696233426, 929103970, 571950526, 477754895, 237732697, 716052788, 261858590, 966719082, 535605819, 251511137, 386763080, 545399661, 334299544, 964664337, 776539428, 724107575, 319427252, 890103224, 836158258, 399551825, 531194488, 385715230, 690991597, 45749978, 213703189, 245857709, 771876344, 653956789, 254732547, 40550219, 803947578, 700107366, 402698682, 589459652, 467447589, 944607682, 600366200, 97073290, 47486680, 162736740, 496123349, 920855891, 609380675, 242754473, 660098331, 936168145, 741905131, 464699305, 451918993, 301928103, 907709350, 706504467, 309452398, 778988634, 51715737, 468182841, 301044830, 31824152, 312750862, 604225343, 679052600, 955080684, 367499327, 846007753, 375619467, 488739129, 58421502, 285771206, 996505682, 137513535, 267638560, 968136878, 26364637, 124729440, 125937566, 766809417, 616466980, 328900534, 105787014, 994359061, 835088122, 379934816, 432497060, 878856740, 74765893, 676835310, 723331281, 763820720, 352485237, 679778463, 953035903, 738011990, 803672233, 802791451, 7873139, 397490105, 473996106, 954187249, 742532623, 466169122, 93896396, 515394048, 555052180, 441472894, 859853017, 496759089, 980038069, 863111282, 542119355, 472162202, 949630998, 398762776, 721824106, 26225345, 449331071, 307973019, 210881958, 365057165, 751119693, 640205675, 434517355, 868194771, 344701251, 23582239, 336077529, 802116200, 630453960, 465543579, 523547605, 374683212, 93548028, 402180941, 548348840, 328334544, 371017161, 441266105, 946866763, 301379717, 591360727, 997157221, 81135280, 208686697, 22027904, 229455372, 648432372, 319241519, 397663434, 422294579, 705406077, 148275159, 14063770, 885389552, 76025027, 821680411, 554833071, 333667669, 402340413, 891925756, 956110637, 87855126, 769187164, 154190905, 366584511, 358937279, 951862484, 339907767, 744302742, 764535540, 588035567, 498800364, 432503675, 368383501, 410642495, 896006486, 535353050, 376464779, 675896530, 829027191, 580153959, 708101564, 833128796, 926761723, 28891550, 38528110, 193552648, 411526491, 734326396, 356515541, 452563365, 541250929, 442751075, 440729291, 877380376, 577510107, 227830596, 224778402, 688608141, 937320049, 771790704, 475240267, 882638527, 425381656, 425511673, 639007844, 701175769, 98489894, 27351416, 100318291, 751847812, 498793170, 99389115, 329514932, 427400955, 724025882, 900570595, 368041047, 566169721, 506474699, 520886218, 554125202, 690439391, 991720736, 24511970, 557191887, 954243481, 382668703, 793266891, 189667065, 927023165, 797962990, 140814859, 538141711, 608305892, 300394857, 543380135, 14295727, 589990516, 759878628, 945880572, 973620552, 211589347, 675264266, 947023027, 661319328, 912695114, 261249434, 784993590, 63633715, 880259108, 974871507, 258966483, 579340999, 339445094, 562934265, 451902518, 946272880, 804870390, 480835170, 823176182, 178600516, 688435756, 406737385, 834104337, 591848310, 798710456, 928828496, 482194444, 244196633, 995473136, 37193003, 676190687, 942119741, 249435829, 238532004, 289783302, 786549283, 2257120, 678699105, 536576769, 763277983, 934679703, 695509039, 240740964, 240720672, 580797714, 203278761, 345566206, 660013302, 56809904, 198161129, 213386370, 789119928, 311808015, 595717406, 579297337, 60016309, 976591037, 60158170, 902064, 15880382, 761109210, 348036779, 14109877, 694243125, 588197985, 313657861, 648467753, 897503769, 700954394, 940277821, 257078044, 55415190, 733999783, 166464797, 78246114, 171898583, 454135721, 191108574, 34083353, 875641231, 168470204, 870091976, 684288028, 9456707, 153275183, 522721516, 746176481, 887924270, 330573404, 841768245, 834558642, 905950682, 840129182, 745968643, 580177587, 523910513, 19419138, 570501719, 619651713, 16092292, 258889740, 796361241, 760019579, 670197562, 630897333, 417951006, 283272279, 813793785, 614221162, 911976659, 593590255, 232594796, 478499296, 650916385, 658587792, 974173756, 147906101, 212154556, 222264042, 533175098, 920832941, 822451121, 414902705, 696318086, 952581337, 901909113, 92567403, 362099716, 667143867, 328610514, 961147863, 840029465, 461828563, 224186253, 740780341, 749106052, 92644846, 15302730, 499026158, 343549314, 221206098, 932999437, 862480670, 471381897, 678230840, 603163946, 514467929, 713321464, 334024143, 929411493, 167983393, 783190198, 675248849, 512505442, 890315863, 475051367, 421144895, 312515764, 754602120, 378953077, 133283645, 937612192, 688365286, 55865648, 980925067, 874564958, 357791832, 480976495, 96218846, 446561309, 316481415, 853054770, 142216783, 301792445, 375207329, 184060219, 209032368, 243627062, 648628051, 687237896, 855139904, 146218942, 908126067, 622840978, 751707552, 68304508, 146560599, 80732484, 10194546, 908679904, 862533742, 966743373, 763683391, 129584920, 516088378, 510798804, 843395876, 877863332, 517849916, 222690449, 795604780, 575300245, 388131776, 589296587, 23894419, 964333388, 390795194, 890635183, 794853936, 131597636, 415257016, 14544034, 914242708, 139347370, 382340784, 590659318, 55297208, 885091097, 671886962, 36274694, 559884782, 744683000, 134659564, 30193291, 518284604, 750070866, 640649656, 682208107, 374123324, 471980309, 13053336, 377917517, 521793540, 228116600, 255438699, 579747832, 904461881, 979731338, 739209518, 645943167, 758229396, 172425010, 520144309, 101274084, 507336306, 810645837, 225921400, 237451256, 908617177, 564292997, 228626146, 826344301, 378850609, 449772558, 508028847, 166300590, 728892653, 757570705, 921705664, 107127238, 470368893, 218418837, 326148972, 508085037, 973819971, 327615747, 792895490, 737968165, 976853859, 68854484, 663473516, 439635334, 489163943, 269554601, 435590125, 954381465, 448635301, 530394500, 887390453, 128281846, 51786737, 942594199, 717948617, 121694064, 494373398, 969644116, 769135689, 917975986, 9518210, 64294325, 319024771, 86939313, 555389311, 152514134, 819841364, 116629348, 302831024, 606267080, 466881798, 302374009, 430606363, 915796563, 823236243, 280980174, 175499763, 465352408, 314946626, 172469926, 111262165, 443256385, 877535834, 888468636, 44480204, 808523249, 933005397, 509181982, 771240328, 124324572, 691039257, 14376615, 967744272, 414683557, 526568589, 119615836, 898471937, 821896923, 817768783, 500940006, 667351995, 746417953, 205342063, 73791091, 301907128, 157832280, 771127844, 823464668, 7050280, 440141230, 447196165, 191804541, 452026885, 87347166, 276831040, 60045288, 734465819, 164560833, 199230799, 349216876, 428543293, 772522955, 347184953, 62340406, 54577140, 272726833, 794454806, 985751704, 341174474, 621985059, 692859155, 469189763, 321043343, 329478061, 343608954, 592782592, 879104522, 63173355, 413290636, 56255892, 929609503, 879749990, 702807091, 927760758, 746586888, 539058098, 127047623, 239033011, 555807535, 283062377, 272971449, 251977715, 80040060, 174738522, 983248882, 165602321, 67218160, 224964621, 894042159, 410101927, 520955589, 806873074, 308033648, 835263458, 11964240, 336858967, 198715807, 372278844, 843790923, 402207080, 241351895, 748877352, 702886910, 606916897, 769495286, 889412313, 172815805, 762669762, 296465696, 219756279, 323192882, 645319337, 590478084, 606671802, 251977841, 460687979, 434785849, 954050586, 841685742, 20399223, 683568183, 596291616, 222321052, 329184104, 520255361, 405636904, 680569303, 966936172, 2048902, 51321264, 408628815, 894248043, 436922851, 319754195, 727113161, 476616401, 857769200, 406587878, 924680356, 752826071, 230077605, 677605001, 264662666, 607106695, 586631397, 986808348, 469370556, 70085022, 426516234, 251182268, 414082164, 244381621, 330413331, 929098136, 80892264, 878086419, 492077920, 211750697, 295452807, 882560159, 873420655, 611155739, 37938835, 920898531, 867955246, 335742551, 169973162, 733695946, 899652780, 65354334, 513302150, 304859099, 944194106, 126428089, 533595542, 572286561, 572817065, 924129706, 512976948, 127706863, 655094408, 271484831, 59690887, 625625794, 719702453, 601881560, 26280177, 12826551, 434333704, 149322577, 946892, 228689746, 980028706, 612494720, 303269874, 805912980, 548784306, 248100075, 424988228, 434538075, 519525678, 163030788, 411733318, 149518659, 634610110, 963465495, 678635478, 299284051, 608728547, 57203784, 965957016, 348207775, 150465499, 622587473, 626159819, 727250521, 159473586, 310533752, 67604276, 6992121, 960546640, 497030182, 426800915, 362409769, 198309179, 950727197, 695291089, 858723360, 872424174, 694334802, 998242489, 153829638, 261957956, 454542500, 316850589, 133337107, 514296367, 566734301, 310276074, 732946036, 109393293, 504517443, 915565144, 729463989, 362313073, 791790612, 756466459, 516395724, 548841960, 484787855, 994349084, 273038906, 994344029, 463272649, 152190637, 324301955, 557013589, 537671846, 888951343, 569588101, 822295623, 376548403, 459744175, 585521210, 954883760, 415081894, 826748512, 275511322, 490179019, 713930620, 746237, 125480658, 355914301, 627386086, 359614204, 187679463, 458727138, 509337130, 720419508, 58203052, 598479400, 241316185, 720647261, 382379848, 134706195, 976724859, 494054017, 165646682, 567960211, 517333590, 395550406, 701129212, 138553764, 683192621, 856132938, 353182813, 57828966, 181110510, 465980733, 533815878, 264810815, 331412050, 695365486, 947107563, 326771338, 596304680, 22158227, 6670759, 990264379, 967329095, 936842637, 955347795, 662122280, 12693830, 604017445, 270313430, 91974997, 247320526, 617666345, 720259304, 58451946, 29744343, 192137035, 738404027, 511916560, 528845611, 454311591, 83679200, 366570854, 348963616, 870996352, 868643132, 705136876, 528773588, 944317986, 941716288, 170235720, 526696882, 132634591, 972883494, 545874471, 897858649, 831653916, 63034044, 865383685, 542396385, 962428933, 568126518, 856890714, 797913437, 327657627, 364411612, 755505612, 50236349, 40016991, 69792312, 738409476, 550599219, 105554865, 670576834, 77455355, 539797974, 990877549, 699145389, 31870300, 206738055, 253079346, 749151778, 922455218, 620775454, 130485804, 211003054, 893890126, 317507371, 518662031, 92822295, 663843101, 331004880, 646317636, 781547271, 757749220, 997994399, 824097332, 835179408, 13738075, 821404475, 59953151, 928145401, 646760556, 310421871, 43800793, 836234925, 531517423, 198561868, 73958816, 814908803, 741333490, 643904472, 342283273, 98136919, 911393175, 621890864, 511103918, 642836605, 748456357, 674186792, 686286317, 754140421, 383712724, 452194725, 938128470, 765609892, 9607337, 991986013, 259317782, 567677073, 328711132, 945159156, 115963880, 910713214, 342533198, 312727257, 460310499, 319021190, 195211438, 838290641, 995675913, 478638520, 678344285, 819357656, 415631089, 177935645, 715668543, 366522241, 358259913, 488403757, 284976732, 551858262, 343882609, 277524925, 513650818, 670606644, 174359279, 15423420, 209074737, 350967879, 172323808, 915013738, 975761405, 641999276, 344094963, 717243355, 397347308, 495044478, 352282483, 632105594, 81811089, 417307237, 265640170, 468402651, 778665612, 723922796, 786983335, 176544514, 621681549, 242168688, 793254374, 360102198, 414752517, 705913477, 901100375, 56003452, 37112402, 938276104, 515527046, 253702484, 859350576, 841699507, 679132054, 26112171, 897358843, 264580886, 253271422, 514363696, 389670369, 918288823, 58352290, 98953823, 203088076, 194384723, 716158423, 587504682, 320442818, 235576884, 315589357, 462633427, 432690509, 389525182, 910073710, 181551227, 961197495, 327375353, 945812093, 376634970, 865788441, 414864486, 963789136, 477369402, 184599622, 818835974, 467106331, 548651336, 765745264, 802851563, 792792510, 145956838, 684802090, 175885440, 48280565, 946953465, 177462135, 473299857, 669950820, 671489323, 54690604, 639154441, 619592864, 418238618, 716348553, 537845770, 424111546, 208853211, 825341873, 981584837, 884568145, 939064630, 312359819, 628189716, 980047108, 14986749, 570387115, 126856329, 667479246, 334356844, 999055161, 631580953, 526174432, 783242006, 979554426, 639895372, 296437341, 350160235, 50513678, 238876291, 931829502, 841688776, 405893732, 534237697, 396166044, 296984326, 952220262, 831646295, 414542155, 950434743, 530911894, 167290509, 233185898, 587677945, 73480356, 188731292, 737356128, 672516091, 964334774, 330003006, 66652634, 409632877, 637355033, 711157134, 216188909, 120949580, 99364819, 796376480, 127525604, 835306969, 782466538, 106381940, 767348642, 791100091, 140117976, 900004355, 928311389, 37896739, 824471064, 698658816, 75199025, 453832080, 964065320, 479441732, 48498386, 359537374, 556282640, 982926515, 152213167, 448569151, 34690048, 198255908, 606846508, 678582925, 720471076, 299754597, 920486028, 598023207, 906262473, 995533234, 510307266, 46475440, 28130763, 771228584, 826416278, 178212109, 928844055, 412294773, 546296101, 903272750, 463828510, 638793132, 271705431, 856304699, 102943141, 771301637, 886650807, 206898336, 282971329, 628560570, 216670945, 295555075, 751025620, 281973141, 625925863, 993680445, 763652032, 173031885, 581132074, 940958641, 365025678, 441970972, 66324262, 637762286, 398055552, 874160490, 216625476, 256441388, 849959895, 833494030, 217331780, 134901704, 907796108, 451872200, 589770021, 613447149, 900565375, 194883287, 341561845, 741538323, 202668516, 463251182, 545063407, 222918866, 317646046, 301717703, 576375614, 125144275, 204673009, 138500570, 465298058, 640779906, 637634004, 838794711, 615233021, 808921497, 72483026, 594072831, 513053724, 290130930, 670700014, 23522210, 984085690, 926940319, 227192753, 228353138, 56337011, 56130582, 767521208, 782717244, 300421657, 261685452, 115917502, 358950163, 172960688, 454893754, 429822436, 922614676, 326638566, 465280430, 587768084, 434296543, 779676699, 837356517, 637452633, 364462788, 838852413, 274874084, 670467839, 188786469, 602910269, 613534599, 539242350, 922434937, 825000668, 735778057, 480522814, 335710264, 577148841, 831093955, 647043905, 904410894, 404529907, 796907053, 424169401, 665087527, 401970565, 343938374, 378979166, 54674949, 390321442, 724951541, 756953391, 396398586, 701157989, 985834462, 906946132, 964401681, 894842130, 339321777, 919606116, 522192152, 972991656, 422386471, 200312331, 150905159, 766012621, 871065101, 72971619, 965969456, 829709813, 275019204, 289360907, 25430325, 41777150, 917816034, 916161228, 919043088, 559518624, 328444646, 302563185, 641628438, 186445076, 413663177, 959285055, 702307844, 27188490, 84628711, 275388490, 208612511, 880542666, 524337071, 803227066, 302186441, 3660638, 811639965, 686853810, 700296120, 22280092, 151041591, 258502789, 594767031, 399443376, 505987089, 792721615, 843728448, 426242825, 655605834, 827903434, 44340485, 196726400, 714808826, 990125736, 99866432, 264061257, 280881241, 227188682, 248562956, 984384437, 446242873, 687769035, 137956344, 454343231, 6120987, 96212152, 489823679, 520390155, 18258860, 386162393, 891731336, 601317206, 217664175, 584771173, 865039260, 523128650, 890384891, 626603006, 713050153, 19251700, 64360651, 739027732, 877106206, 433990206, 493855428, 281468583, 238090089, 260463297, 971410501, 948963573, 408414405, 777147169, 46181592, 680900763, 979645559, 405368904, 886874668, 711988553, 95086840, 376466356, 193693888, 307365775, 584122559, 300118876, 732987512, 726285547, 804008572, 166229281, 27902531, 576033161, 866725504, 817978616, 672959185, 434730844, 455524665, 404253779, 246680481, 997693045, 37745303, 7148668, 602019710, 13323541, 6024350, 528429358, 85528071, 945453745, 451614657, 750475690, 382128810, 403490826, 980002248, 570744830, 852022493, 894158274, 357669867, 836833724, 986707506, 578606177, 138309459, 66782715, 311024283, 750267030, 504603850, 696647334, 27249722, 30335445, 41206962, 349552485, 219904247, 290080942, 94646194, 219724512, 616850423, 177267021, 296273208, 511393870, 649674544, 254920253, 266848564, 844074547, 512575590, 574145542, 872113266, 781685688, 377778098, 653053238, 478809208, 707304328, 283760308, 548728323, 968079197, 725214811, 949963310, 846026363, 643764104, 769701128, 356507109, 306091373, 869376349, 320712985, 96587637, 728684354, 114907248, 947621925, 14697176, 531487270, 973996084, 379343269, 828055784, 891246854, 811505585, 437538516, 726970776, 697685081, 209332693, 992343337, 272979526, 278765567, 532593636, 764355234, 366879499, 312231328, 131716007, 144267521, 202859153, 909717019, 353834977, 258308116, 241303056, 819662767, 752210436, 459054320, 892455249, 70024528, 250148725, 211895525, 640459125, 683605310, 579068604, 335894915, 173563906, 843683895, 771944464, 69336949, 204862446, 496074095, 900619526, 728801523, 649083124, 467788876, 902571532, 671856759, 22746435, 2910804, 312938647, 38087464, 442067973, 14627452, 184726907, 165030835, 788722590, 43855710, 438098924, 900797666, 865558259, 205197759, 464827865, 492615690, 242201014, 754820224, 152786404, 549865641, 272628090, 210344732, 778357193, 768904557, 142995041, 151868529, 532237874, 694952147, 420647955, 8252014, 572650083, 534962823, 374099287, 165444, 580762256, 487817228, 247947122, 362709000, 666966489, 362249916, 184354943, 479511704, 414232409, 244062394, 62887607, 510068523, 944076660, 515690931, 744997334, 110677166, 154202259, 158476924, 122841637, 901295026, 191118209, 394703231, 88021555, 472651142, 853824098, 175298765, 698935575, 896032410, 998820146, 173306968, 437165094, 129810951, 675549624, 140232996, 244832309, 742859321, 578335643, 263535593, 305415401, 624142032, 795974687, 626985383, 369535331, 744188253, 810336102, 121464410, 493962958, 226919066, 661005490, 530149081, 693172790, 396491549, 275755026, 575898842, 621279928, 731197091, 658680863, 139297313, 754115331, 450591742, 835619443, 848990996, 521540353, 388823597, 918844422, 630332597, 460064941, 339854293, 395446216, 675209013, 41590497, 109357749, 421322340, 614860159, 972203967, 836552165, 871975543, 609456402, 244564896, 295538500, 117587950, 790275322, 513361267, 921859192, 152454863, 311452655, 858593458, 771888592, 246847651, 662064136, 754536624, 134420069, 746205930, 794783849, 141207430, 784178627, 376008413, 832329732, 254856274, 414638178, 723313426, 529195959, 18131049, 345741658, 979876768, 92082284, 45937001, 506645362, 877191769, 758163954, 859948021, 287935729, 648699120, 153564485, 108809440, 200584769, 722614058, 863285980, 140933829, 514570541, 440764697, 189356167, 565630937, 39341162, 881121036, 279734517, 272384531, 587056411, 847861645, 686632725, 230039656, 702659945, 289381904, 441639069, 505139807, 469700263, 39794497, 387067905, 679684973, 884533453, 182320161, 328981443, 865915565, 902458239, 762558073, 552436945, 625018172, 264854118, 638119824, 719937093, 266315892, 198681644, 833010432, 935214774, 269876590, 508818284, 236258999, 92937247, 617349146, 697907363, 690604641, 537807880, 867960744, 748835641, 36043620, 373878250, 699245657, 816705302, 926492210, 623863704, 472074381, 863919542, 974805556, 214956214, 126308290, 210758258, 763731087, 835366751, 958822268, 841685668, 802839321, 557783657, 710430413, 550149667, 238948248, 291930890, 630285196, 37125254, 99584381, 681609345, 846589738, 201836612, 113894293, 149387279, 515882648, 435338732, 613782390, 274253163, 78944885, 89919922, 953082172, 481079125, 894640433, 750201354, 67636522, 270383746, 280649313, 158795738, 676523756, 201922843, 153142117, 355766465, 613161556, 292514893, 688494123, 416850486, 316198418, 497562440, 645698717, 980463437, 586786289, 757263526, 896081017, 362867946, 296859307, 219095767, 562253455, 779917856, 364100514, 74840243, 749860007, 960927933, 516802610, 137156839, 977394680, 659271176, 586441872, 976015837, 139740216, 300332373, 57150028, 578649844, 560065874, 413012005, 383019623, 29400863, 470013882, 594803700, 199921297, 975946562, 769863257, 701064564, 239918087, 841950084, 2056740, 526112721, 306125780, 332576229, 869770046, 439416532, 729237644, 218396882, 842500268, 574994705, 743566472, 738536268, 270001668, 550210669, 957248209, 915016822, 651603393, 885122696, 57057087, 673572564, 102674974, 420778800, 231169173, 774193205, 974247095, 930558752, 889172169, 320838060, 151392503, 744986238, 934853183, 946187782, 666472109, 401489899, 722654671, 843840969, 314976232, 412979731, 345252835, 354055802, 676066696, 558218880, 922816907, 415202529, 30057660, 174410475, 504533022, 84614776, 961212766, 870210934, 482943352, 60410624, 984539760, 913816967, 806243908, 971013171, 52874268, 579361629, 20794239, 154708630, 908163597, 791438294, 869538331, 731397432, 292085977, 564574300, 381246053, 655134432, 515493574, 587375105, 254511157, 558864511, 572090822, 553008523, 58625498, 771342885, 682243896, 250751274, 353346885, 870992267, 211713122, 135036828, 7198723, 425405052, 124000418, 141570161, 55734534, 392534543, 142394288, 739252727, 648838775, 587849427, 315582943, 630361331, 324286383, 491072892, 326932652, 261114120, 979680031, 540282376, 553946235, 652639058, 559527751, 674721326, 764635257, 340321658, 902611694, 402678577, 596024254, 815865170, 178113743, 739058213, 26961127, 811765397, 63961893, 871339207, 811841272, 308876067, 964559527, 727905765, 990494458, 549075687, 99547387, 137004483, 377685136, 810477288, 227072345, 33185697, 502168714, 722537360, 856761281, 890371489, 122415874, 83969872, 647922300, 743074934, 750792359, 42457769, 823785658, 432597977, 289472364, 878966233, 581246338, 83477091, 652637422, 321085086, 715722191, 327265003, 757551328, 113813862, 96400442, 203870650, 353654673, 251947408, 41785737, 793138390, 823173432, 677068000, 470772116, 934975374, 105007027, 231029631, 249400066, 646913906, 864213872, 124633308, 925113311, 638062259, 284946934, 292853942, 870422265, 195491143, 439477638, 102695621, 156074983, 902123308, 944031028, 598955773, 833140826, 539883641, 269056462, 485543099, 254376262, 15333653, 545923333, 852896476, 33174296, 426712250, 895290414, 555185358, 72857748, 260559405, 180740931, 297842857, 718935518, 836913796, 208296191, 704490442, 167606285, 58549068, 225959880, 22791859, 362651851, 831674651, 821917752, 240151325, 259128874, 210135094, 619256494, 988201139, 570538950, 113633989, 215692145, 293207825, 260249880, 998551392, 308592383, 217879347, 127782428, 643724061, 820009145, 726214358, 525145647, 740627634, 169981222, 492460320, 490320819, 787665351, 290708634, 977321072, 484166473, 596574556, 549556778, 130290628, 438120950, 939127532, 395913868, 623316105, 393685347, 433407311, 936052481, 885262104, 996964549, 465960310, 708579207, 37163633, 708943714, 884975533, 61591400, 325110605, 293012411, 898778608, 580226007, 339521371, 795876536, 62136645, 535548187, 318645080, 169369508, 241327805, 69523277, 429175196, 222547086, 709385096, 581445955, 397699882, 195533677, 842690042, 445504303, 439388107, 450778870, 68066479, 983912433, 958402853, 436333472, 991229135, 720614812, 929896011, 864867577, 59290352, 890754590, 934742489, 159785595, 819855428, 70680828, 38688753, 618240444, 729266083, 72388874, 919742755, 626896271, 19548264, 240782095, 148643758, 133469027, 770747237, 722587802, 6956529, 181375780, 316605305, 652339715, 693839861, 988786398, 255337187, 207179444, 809164942, 579413823, 334362959, 394157809, 916729555, 598799166, 889165911, 592169893, 925327251, 223283589, 101890220, 11075233, 154499898, 771328568, 992753824, 799575779, 428114705, 416970961, 200033441, 711219053, 960983674, 8544653, 817769963, 839034995, 844311189, 492142360, 947039749, 528825751, 558624801, 467618196, 952943774, 400358837, 655439133, 867503513, 3888453, 924196298, 413157768, 165489655, 191603616, 404881802, 653579467, 639291275, 560080363, 516683615, 106300221, 192633232, 119134770, 82934324, 67209156, 511565501, 165834502, 563458409, 717178241, 372115772, 744398683, 57515213, 858751757, 217516810, 21347330, 6915492, 776747959, 816406073, 712593952, 89047865, 189350371, 958947882, 521050690, 534145190, 109162789, 39633680, 404940060, 818760353, 150087177, 31776780, 425097585, 159564805, 974350432, 214506200, 15002731, 441680200, 50569300, 681513106, 544701725, 628021962, 422867980, 911696981, 66535431, 520397280, 490716201, 409363981, 666262609, 11220844, 732892698, 151724591, 711909609, 37430157, 916383761, 146111271, 999033220, 916153540, 337912659, 389907296, 306121157, 170723904, 407371377, 547405169, 372106523, 613284836, 214753713, 339804730, 745915146, 244402230, 352676566, 283366996, 500292232, 345008197, 270299203, 381314654, 320288771, 270504023, 535254023, 361476317, 412350260, 769012809, 192251999, 65488881, 692236445, 35721893, 749171197, 936182899, 885571794, 915366155, 162086291, 840311958, 271807529, 868235612, 499856344, 89725570, 446273365, 886273506, 386817283, 490254474, 644929811, 141326327, 105740722, 908566324, 908338528, 998246610, 971433214, 957446656, 275900530, 741101723, 326904352, 557345200, 662436100, 601738122, 887813006, 620980408, 247152637, 325561054, 749700514, 336905306, 614665297, 608528303, 486743974, 927873482, 101275894, 757544391, 697416417, 213454096, 777961355, 25147944, 576018173, 451647840, 138992300, 344726388, 678037965, 849886105, 912229651, 941827988, 520522324, 576358784, 489110742, 670634017, 112013576, 594355036, 695317252, 717429928, 559699696, 262534870, 546003297, 354784424, 451467123, 664433320, 414263303, 577292629, 129590358, 373840986, 644603209, 653700690, 385439848, 828248287, 687005520, 992310745, 589790308, 599072506, 864595731, 384291825, 487642477, 259588167, 682697588, 105133793, 400556611, 916015767, 416523175, 746355812, 563224559, 764853892, 546528195, 185642722, 591895779, 327827738, 413560092, 563708026, 748727080, 313403567, 781761119, 843263459, 942331113, 993152583, 695212882, 378975291, 348598602, 884300044, 720935629, 846619359, 640309537, 680054409, 480966761, 150357982, 77250311, 577013955, 870877565, 477648563, 522676558, 553063972, 144841344, 567750479, 359031656, 531210601, 678467827, 219781898, 895929445, 277930127, 768683773, 853476641, 68163572, 458364515, 570658823, 284928809, 51410924, 199864303, 760139626, 696384139, 957141997, 535136732, 564708320, 971280347, 126372607, 803764971, 272932346, 524693371, 468189297, 205004396, 705820256, 822413156, 680786157, 277783412, 994184147, 534932853, 788470665, 736217728, 935061020, 240674799, 281745163, 262133228, 527687446, 720218823, 611227220, 161553346, 88263261, 504534450, 759722238, 573040244, 293568726, 365897340, 30028305, 676218476, 209360763, 977886773, 519278240, 953570687, 12531504, 272200521, 167924803, 550271946, 443228927, 771542415, 733096238, 626076896, 499878150, 59519102, 596775049, 61707471, 247753425, 331296672, 56550024, 87278855, 966899669, 33564902, 563038003, 365728616, 794980682, 747532191, 308399612, 361806686, 470772771, 661663749, 553200696, 292927487, 704651277, 70820831, 399721119, 762072558, 44306085, 961669221, 576846349, 92375324, 659671328, 126319980, 805981138, 275530251, 841673882, 58431893, 252996740, 203521051, 232101218, 937446163, 194349276, 807859220, 876482859, 445577411, 437633718, 161068819, 87184689, 514992216, 123042081, 725168316, 71646449, 334646665, 435507276, 567274533, 239724250, 179860651, 151503, 570758677, 232433162, 294404440, 403174746, 413863586, 424373189, 563420762, 919031755, 587264571, 830681986, 263939125, 371855807, 38684118, 64021454, 518056480, 248863651, 573818616, 550533289, 558318857, 400331911, 774908898, 126437618, 942378244, 574648114, 620634491, 663383379, 214377271, 236763306, 50925289, 838726397, 762846790, 841069509, 420083118, 457956948, 422595276, 766258064, 979632110, 943807664, 230224940, 990214497, 306406586, 255164482, 557223475, 543306586, 539852413, 928859583, 18492259, 472141761, 33579728, 408671261, 68540177, 18074118, 868439228, 646366305, 350066286, 957039972, 289965914, 746249309, 998161486, 445075057, 86055627, 496056497, 639353598, 617373181, 117753643, 968035693, 469924518, 578857837, 205418740, 83021724, 849278674, 581583839, 358189527, 454199278, 281524701, 294523744, 905170527, 203915181, 263884153, 403812220, 751302524, 18485203, 599036526, 892849375, 19655588, 371092017, 472372081, 315895230, 931864812, 692332100, 627138938, 168839818, 290185636, 61137265, 354401068, 970626599, 870260043, 319518638, 20628756, 976431159, 487148287, 181420728, 414235286, 251802610, 629042405, 878290883, 769798760, 175764079, 260707190, 712892490, 411764075, 30421444, 948930090, 398821775, 703906776, 441591462, 546409947, 435223911, 50279713, 91716790, 224893887, 906735442, 76418303, 392329676, 242953377, 430970158, 626469287, 778670280, 43828382, 690096936, 193463718, 484943545, 30248846, 752545756, 892142362, 194484035, 698124945, 5284337, 464112279, 924268999, 18048716, 522817733, 286078181, 571834703, 95556114, 317419566, 655517692, 938333995, 626160564, 511945301, 70583425, 987582109, 418789016, 814240674, 93546647, 350620366, 47040022, 94918848, 545501224, 159315431, 315900086, 893200400, 161936330, 796058460, 34727393, 275513869, 410918333, 183570136, 298016509, 435423004, 501986268, 571491490, 538999173, 109981426, 344666036, 427692046, 39540521, 434624614, 679425497, 437943834, 29570648, 259856034, 480375093, 525008519, 832893594, 215997382, 858016227, 618186107, 513671994, 366042139, 830020826, 97938740, 133257568, 739501265, 697530164, 473874339, 908280513, 6355405, 587610178, 623247587, 220552827, 108934659, 695189137, 110830846, 563720750, 418155929, 579046311, 698005815, 693031154, 657969673, 921748102, 277998204, 847868901, 580493912, 268300384, 300220651, 790634454, 451105018, 97408023, 839212957, 878255291, 357922489, 925822010, 992400, 183589034, 67307234, 532091568, 495287462, 360572421, 107577422, 572663310, 89651493, 705155271, 647247625, 342020044, 209498386, 117007974, 347976255, 436819409, 534134932, 645993182, 212816827, 872114535, 260069933, 90827359, 624069389, 625221912, 848551496, 286184383, 937989000, 458986672, 741846177, 572477287, 589128225, 27244714, 288468004, 393650848, 976452296, 77327723, 915365661, 281217977, 65414742, 57330196, 369695238, 584786818, 93998080, 455937088, 648233078, 734536313, 66772268, 977928786, 559837882, 983771728, 841447231, 99838963, 137898076, 61258889, 782471175, 638444387, 66178837, 611993189, 767944823, 696400221, 480042636, 864603583, 984158792, 136473356, 691157625, 457171234, 191296432, 713714225, 944199630, 322162662, 2470038, 13581986, 326412724, 167855811, 263760877, 110502438, 264598380, 236446604, 414259108, 972095032, 623327585, 590180007, 559102133, 585201429, 536036601, 810943066, 993927040, 60081089, 644519555, 744990242, 652819019, 700501173, 449250777, 497021266, 988189779, 277995672, 911587854, 134336067, 282405555, 303808371, 139899060, 655323455, 423629417, 547175786, 937069961, 388903331, 762843755, 232669174, 207091870, 697710711, 229225790, 387892295, 200284107, 448872659, 866470094, 765095609, 398824726, 975543170, 577025609, 803682177, 408383151, 835767654, 486450345, 461760774, 987747225, 564342940, 416324361, 869581201, 744090442, 195585896, 201855989, 572496991, 942006569, 459815135, 318683691, 37605683, 950339233, 808632975, 469435785, 989527733, 667502424, 121696212, 805494968, 318618382, 295804413, 242250158, 952713097, 978726076, 704459674, 111341541, 96026793, 579978372, 125232039, 871992809, 397610646, 699255457, 652311042, 74364815, 957569816, 737185336, 212035978, 2793173, 10234925, 218070059, 77405261, 108023031, 196108113, 771333679, 888623204, 63887180, 507105057, 56027229, 304943695, 786538821, 346654670, 284575079, 444414364, 396426524, 248700167, 412318046, 507301183, 913210382, 79767343, 782344712, 314584522, 671698722, 720567670, 63906529, 331763382, 580260237, 210548344, 523846549, 163007036, 573288939, 123593559, 718434732, 163497310, 848922928, 549888876, 657484397, 982397651, 412145858, 357059393, 267826871, 630919619, 242810244, 969288946, 319919454, 153279185, 734101094, 522111155, 52372199, 661742028, 345415481, 115696496, 756018867, 472423458, 355202914, 498621837, 865207885, 353056929, 513517750, 760900240, 271040046, 583874354, 469430770, 379094773, 349085827, 149886127, 73263224, 801042887, 971353727, 902446187, 857784671, 759469328, 787727067, 215050418, 145027869, 582032450, 488060221, 745110850, 770587948, 548210474, 285868799, 328517682, 681207984, 480131136, 508221606, 696772319, 121690470, 446335507, 455281692, 442699830, 393689076, 639532024, 418873558, 487477457, 587330323, 496239310, 832918374, 26784889, 692815943, 322838457, 68406286, 851585179, 811860890, 217464418, 47926309, 583334012, 981849787, 424081278, 846226402, 834734133, 16978019, 818288449, 813428858, 529242657, 128001291, 589781950, 672382319, 888452893, 724677030, 758668450, 777759011, 141350475, 814408429, 199416883, 330190215, 343185508, 529467502, 450220127, 497585145, 269491816, 357774572, 440790074, 548681066, 183048844, 371893011, 339147499, 259897649, 258978969, 275916932, 395498551, 712934069, 636328846, 715755978, 291895457, 667663134, 454421516, 284660379, 986369695, 365130221, 360090809, 420767572, 674657985, 410263344, 263146067, 971630833, 659492936, 831254124, 275273022, 568163145, 982385638, 458997148, 652705520, 482292772, 615572939, 369949257, 463000762, 697890193, 38223380, 470187425, 994048952, 376533151, 480752429, 896066220, 58264501, 219009110, 87586175, 374037153, 651499062, 238004558, 730448938, 382796974, 819459500, 528387157, 904142186, 946674411, 423198855, 303941970, 95368602, 585078108, 520899474, 424672930, 365086778, 450938816, 882444419, 342205986, 166013457, 948304909, 175794620, 511841464, 158663029, 271585611, 903706479, 273133352, 844580937, 106549204, 722709157, 947031292, 158146366, 575477879, 406848999, 884939718, 507474455, 303943135, 246568993, 538931088, 72155800, 339623110, 319212676, 110648110, 379161759, 358267932, 958307362, 208347124, 232028392, 575001302, 723682585, 844897502, 449327140, 125340679, 2677847, 732449516, 536873838, 560050164, 719012020, 117066196, 159364132, 221088992, 762700494, 937025242, 728356399, 938024993, 881173365, 79132140, 358395201, 941883706, 182289434, 118776158, 396900808, 562518465, 506572799, 441692968, 525636278, 823715019, 84608973, 278974721, 947170410, 674387666, 467416630, 702822863, 261709382, 553473949, 67094895, 143932339, 398914922, 798086456, 946025060, 537876502, 951862026, 353709769, 687535877, 636570715, 815919554, 954792220, 866583653, 218319573, 766746388, 675337075, 59856501, 686127337, 284506829, 920616014, 583100752, 340348809, 841300682, 339312201, 127034180, 84566628, 717702551, 511640395, 930269892, 100702891, 529125247, 21914649, 312412400, 928086577, 410019209, 92818825, 549929494, 981444929, 25900458, 716198526, 295153565, 615095929, 730361626, 836795933, 999545402, 851013151, 591392566, 956602277, 625175700, 441958224, 649324586, 925649371, 197424524, 587705118, 208501610, 387209147, 489878338, 18945482, 381867631, 525719109, 591263005, 778076016, 33535872, 791210570, 933105466, 97089417, 928856265, 346421912, 491097472, 109204323, 798599800, 732591864, 852265908, 351294478, 432217407, 630692369, 5011476, 409276478, 921752962, 616089812, 165350285, 315932043, 824417652, 919799186, 323123050, 472453189, 204799721, 407436764, 302316048, 848764993, 363963145, 433460168, 434590594, 236498487, 171804394, 782220782, 447540696, 593949628, 842943995, 188193299, 881910628, 96403731, 857697932, 999898392, 597014922, 118539428, 835675037, 768537707, 661485358, 895838105, 69666030, 266644198, 484582237, 360666734, 995273906, 343504041, 179995299, 12413511, 890092222, 245239949, 95218218, 213157463, 966892720, 366018052, 911053937, 755351139, 712997567, 210109939, 724320166, 694737449, 258807253, 786641617, 66183870, 820708459, 505899913, 325916036, 588597585, 565158937, 120473543, 307953110, 34960871, 444689233, 307158408, 488980048, 510068046, 335016346, 481661027, 759718310, 557273190, 437252777, 93072630, 65396633, 2168909, 14984443, 30751135, 126873377, 209876525, 522250578, 439843228, 759991122, 314039797, 490374192, 55727678, 492203637, 366111372, 438386789, 963332486, 694429120, 563841227, 717088283, 572085090, 887707528, 169585901, 405721606, 869546682, 605108745, 355129221, 198265080, 128098387, 138533744, 521109220, 640787981, 645344901, 91838048, 16145318, 730532757, 371755034, 560522754, 925264220, 230870361, 868421141, 779818311, 843813731, 494634056, 780759664, 474669722, 915867174, 335682517, 991963247, 524858308, 561800985, 302554884, 920424520, 257662327, 682566932, 936374822, 266471240, 310380347, 170498703, 183692950, 879678860, 117715818, 429644780, 8421027, 808260029, 912054695, 577106254, 265154265, 483792650, 324293057, 422124216, 759403666, 524146374, 930744328, 597123765, 61532749, 669832498, 648974750, 127831384, 365747858, 95886359, 989986237, 626322693, 520679505, 289321280, 256316534, 750284110, 306897398, 209036119, 487741136, 712325978, 201582003, 689574486, 275607296, 84853598, 496834237, 909623884, 830153048, 994799468, 232851956, 964839038, 302248526, 857206791, 461416520, 966257722, 338980713, 792000569, 939055669, 599204077, 751007869, 518026988, 313738798, 280876621, 694638724, 774501906, 411007642, 717070929, 809992569, 424058777, 654108211, 949497042, 856058012, 515088415, 150033402, 184190208, 604045479, 79432257, 755844963, 564988677, 902641037, 250113289, 454223112, 43614, 642456501, 368337520, 781161371, 417174977, 408175278, 810892531, 816744006, 680813996, 699982517, 967194655, 330316636, 22151650, 402825535, 512598379, 376093944, 72130687, 476417016, 971294027, 287561268, 342924520, 801267926, 612670901, 131686014, 82817689, 530671356, 17996151, 681501249, 278540267, 834188144, 753833403, 623264375, 691656979, 17171308, 530223678, 473646122, 401556701, 534632722, 655784896, 63729468, 501302301, 865179996, 204760471, 477759126, 357007774, 465463607, 379109392, 160119059, 968277734, 328786761, 99376881, 841704279, 557973981, 483748540, 13287179, 55555250, 625402004, 149937363, 334866841, 198834809, 33852911, 215845275, 997145595, 669091445, 331838443, 937133476, 95481512, 899004604, 509718973, 454788132, 329552724, 662510361, 729254642, 867905749, 544701067, 463125631, 5775454, 417616342, 838597086, 670091629, 328375564, 875517021, 141997903, 423232496, 935050938, 214342220, 934873548, 584306877, 952273339, 225509920, 530638965, 785865628, 453471363, 644944805, 385372788, 367021902, 356704394, 434226196, 366464984, 361147813, 266772563, 775620960, 405032188, 374036509, 950182870, 150619861, 568103889, 398386436, 833139533, 309799367, 199389843, 332788285, 845520973, 948221092, 559397304, 240452089, 193507897, 780366737, 378822265, 958423909, 766930706, 502345468, 111525421, 729609648, 864069779, 133365739, 636538493, 956792313, 377028856, 887929496, 139905059, 885947813, 663017618, 682620004, 961072651, 425218808, 111670217, 587484806, 491936132, 810713262, 66870563, 512750352, 119126864, 942670458, 967781113, 299741075, 957151730, 865503763, 625332449, 714780286, 16332042, 839196601, 417438781, 942595743, 308696363, 111454419, 795996272, 34526303, 793975111, 6282553, 408867075, 436264893, 461654711, 618962101, 530022632, 829647388, 156872641, 187710743, 970417786, 71976312, 610361693, 949479604, 246548379, 60479703, 42451571, 656802860, 772289577, 14518986, 195282734, 370587337, 133553451, 64416399, 442890948, 485741959, 699998431, 241657904, 58633389, 920623010, 289516918, 623982319, 628132245, 324686655, 207837984, 142786353, 492564506, 433210785, 831953417, 685746843, 842556764, 206951696, 206731260, 249203418, 668174154, 543635027, 502227111, 545762778, 620695418, 952518958, 313357760, 597833754, 850279114, 930604267, 138743961, 425430882, 132596380, 30383291, 374084580, 410697054, 702052459, 638782283, 363685741, 913792401, 123347115, 461827128, 638599332, 215244093, 321021363, 476016363, 1461675, 45979772, 937705394, 639380550, 172207016, 405063498, 414093361, 449212281, 697463256, 446953401, 397567661, 399641177, 795707329, 552662821, 45437688, 888941280, 636399790, 437665209, 386894403, 609108199, 496016833, 287646015, 571821346, 853173417, 334521050, 550092012, 180411843, 854161700, 637774807, 172130141, 473306557, 681612487, 352832744, 122586686, 637694400, 692879737, 591291682, 981786908, 978517379, 978259274, 153218609, 108983698, 344589107, 431225067, 283773337, 16874998, 789471476, 681745664, 723252806, 486355568, 135080642, 725199571, 133989025, 553655325, 789001098, 417229735, 698712627, 465916496, 128890711, 932365923, 442489840, 20348537, 379270386, 721960128, 654718826, 880264207, 824562947, 57870886, 183643859, 55544912, 871806385, 307234173, 674377438, 616547204, 29048767, 622707378, 638501651, 42575826, 794491021, 254065296, 634986747, 839890980, 153718278, 81502635, 262782705, 308343245, 150454410, 489692326, 846350010, 490531363, 610165739, 185061216, 909633745, 732526928, 372873343, 62061389, 936605100, 868811995, 376397259, 21427269, 61081961, 590623202, 83386566, 770277784, 530604088, 705449490, 603515148, 240188204, 79556189, 73213164, 318974944, 501978821, 842647372, 630258014, 797137689, 242297588, 831306680, 337483316, 984607008, 83592413, 957993560, 319370199, 969893588, 801948141, 413072584, 860681067, 482809105, 116048314, 332080979, 786629740, 121772985, 297211291, 552511225, 687308825, 637586830, 393696551, 581992644, 854933264, 602100001, 275234771, 947943033, 403659762, 670060606, 413988580, 724443366, 535512391, 234695318, 294536528, 580114306, 473667100, 154686180, 194815987, 59119057, 590502875, 33435055, 784492567, 565680445, 48365162, 67648197, 538783754, 27807752, 523451656, 81936984, 716476866, 76564714, 76983929, 701628465, 797651206, 760977945, 110264943, 107205470, 806386059, 224017925, 524662792, 915142691, 82382194, 74191064, 624795494, 465732245, 23317184, 995398586, 5792809, 832318002, 8233686, 343410017, 683201362, 708229493, 46592239, 889600085, 391346744, 693712764, 985578382, 421460321, 799018305, 899495022, 169384173, 711315909, 932606066, 407112087, 107212997, 127173274, 549331434, 165822476, 412842413, 709751620, 129586311, 103648263, 528382316, 401740975, 889725580, 759519193, 259012337, 234722774, 132693213, 840487560, 771044427, 408869996, 346410317, 639252735, 526956413, 175324229, 144301283, 124795321, 123676424, 942884026, 850147778, 657792443, 703425942, 388641, 121438034, 161285757, 505869942, 582008538, 762252199, 68467190, 761693379, 540902078, 486788932, 396987106, 79480612, 924049794, 55517531, 932001218, 118323420, 81699984, 562273810, 225841391, 215324278, 450212108, 579759726, 425763496, 867973372, 935809193, 700281229, 519562061, 790131948, 545400591, 760138174, 534717199, 715562907, 299164471, 54709790, 262449949, 941957997, 193636201, 938484018, 556684314, 790642728, 830955502, 782613257, 835499476, 350615220, 442547349, 878006573, 519599805, 602795433, 614442068, 760561439, 565453429, 486318914, 518558747, 897194988, 691660475, 869738414, 459965580, 827276447, 153273058, 181643091, 114025849, 1596374, 568360265, 777838208, 248214415, 939142246, 572654076, 293714797, 127585250, 215102787, 753244412, 116111454, 866651814, 297331625, 45598963, 530605481, 601746773, 319119198, 961383471, 431373450, 599883305, 702058050, 754629590, 232351653, 89083252, 4574979, 304661738, 78974751, 347372914, 841813221, 25677573, 779670565, 664323172, 971423606, 512356403, 472045475, 904238933, 123209771, 104165480, 725285974, 789654972, 645203660, 556542973, 833307576, 171009585, 497911565, 990187581, 134569211, 78256141, 668549834, 616112711, 974264265, 770377850, 283930706, 463433618, 923306117, 145452656, 623405779, 345415410, 804373929, 761750569, 714922274, 202706760, 538576753, 194921375, 495708910, 770207467, 551934885, 971870355, 399191316, 873340881, 511993981, 952024808, 15967464, 991863829, 840984318, 340722335, 35068426, 665027986, 269576584, 421989073, 184789442, 490460084, 636718701, 734553327, 740300451, 553853712, 187881444, 293542311, 528727756, 433462447, 61708221, 154513484, 827155805, 24662583, 248824353, 608998986, 410428764, 533117898, 435377543, 705885726, 829633463, 530328957, 204163889, 295289789, 186615962, 664728932, 858453621, 13969806, 829531987, 870241367, 854031354, 147716673, 93578702, 806507977, 717387749, 891453664, 677772263, 616945855, 793614240, 422967955, 962773593, 417104144, 257595027, 443949157, 561511625, 697535945, 423220917, 788259437, 317140086, 640742596, 590472774, 897867833, 682229424, 466191145, 3286040, 322360756, 463155731, 340016784, 638440711, 914846263, 420071060, 560456275, 32699863, 445791861, 716569373, 844238808, 118404009, 274633291, 793470737, 875877453, 612831002, 478611077, 389404729, 984735129, 210044671, 677434432, 99212266, 555957124, 528654183, 946372062, 940568699, 519281209, 868818722, 61387056, 17179453, 580340148, 306219069, 875414750, 955694467, 495935794, 38727398, 506119234, 770184454, 65799012, 733658408, 491521380, 350513747, 942135894, 673462299, 133519114, 954360097, 159382527, 483507782, 232026997, 329447804, 539750538, 718822257, 930205765, 414553174, 348770025, 923940396, 910764897, 772069724, 312804504, 963270649, 393704375, 348722496, 843132185, 846578065, 238537683, 374867953, 781497167, 428140821, 924784363, 788810705, 699801749, 609208482, 284093996, 4841993, 202941407, 456683576, 347922901, 552394559, 44348543, 376038478, 434962180, 136766865, 961571482, 285039048, 776735211, 707825865, 985816210, 472392173, 228075409, 759065925, 372412296, 822877538, 723929673, 654629205, 595097851, 213998061, 950254485, 425270556, 928896428, 684833265, 222829854, 869698823, 258978845, 30359610, 380197016, 533078636, 551011009, 797944108, 490252043, 324941535, 99343242, 291253012, 958108281, 214470748, 999776105, 443717896, 972165388, 290684236, 685281391, 641344667, 672862760, 231413481, 244287049, 211039333, 821458999, 839048171, 379112572, 929163769, 17510751, 916627320, 33312156, 461537528, 379441438, 949035690, 31249030, 633409942, 594860507, 371089371, 242691666, 481651210, 524772094, 93040546, 227772914, 988718422, 838006517, 465077336, 568222577, 101273288, 385433529, 607047303, 732634826, 70054198, 498495849, 579073114, 72815786, 723859431, 314954920, 947694418, 377829628, 325596677, 897618957, 406212686, 976495119, 357751523, 849136431, 643586696, 903003536, 815051188, 12641752, 670853784, 775177740, 476881609, 958465789, 215316849, 274376079, 354055668, 588790232, 236267761, 877988149, 352588320, 226212203, 382128129, 569246807, 330814637, 153966813, 504036207, 445062820, 431074388, 658722163, 640153769, 203489672, 149975235, 997608347, 740535378, 835239994, 469505316, 698607500, 633449601, 351552265, 838793348, 455992601, 999578770, 173174167, 854569504, 87226380, 291693081, 912116389, 319858932, 74190199, 536724871, 938076228, 919005043, 417569782, 519587181, 668222107, 857958197, 725224235, 738017825, 821723288, 366792492, 510883716, 634435156, 759563938, 400585911, 97940889, 522928089, 191430059, 17230388, 537893800, 805024730, 669064498, 55267594, 893703880, 643761884, 970251683, 849330385, 308594921, 728157639, 381446512, 687812549, 383805660, 788042453, 229884002, 60798482, 733122943, 262519653, 616174204, 995217253, 141226324, 986127160, 284085874, 209313203, 219724967, 438750232, 295998030, 693303032, 934096628, 854194175, 764422687, 18643011, 442279491, 484225500, 790428137, 764602025, 327903317, 808009378, 560360004, 197408817, 26776564, 649269144, 505095170, 555886797, 974323566, 300334098, 901184289, 113438782, 418156785, 399172642, 497022088, 283066583, 99694225, 754493533, 4626074, 397334157, 268800401, 494661111, 225974292, 682167577, 888525629, 401494760, 665252168, 469677720, 830085621, 142771085, 466856913, 325449205, 69342485, 651545484, 150810890, 994639298, 440247596, 520889768, 932521486, 874116308, 650958254, 161649247, 620555027, 549149914, 234997699, 71705103, 739600504, 32530367, 95210306, 683452818, 784379630, 639596358, 789792380, 466181360, 72828722, 899667307, 744863366, 994931162, 74493590, 270740105, 800354380, 77604074, 135386577, 560841760, 585631463, 695060118, 232548117, 791299059, 538151673, 734135121, 279209507, 668173333, 338792078, 968814800, 81626120, 512042870, 651222164, 915125029, 735213630, 167477314, 406726827, 752478031, 895178620, 9997475, 629321996, 833524832, 489862241, 841860187, 920706301, 490013097, 14122966, 284077980, 508796954, 410881166, 729462168, 607862465, 821410572, 211771836, 861486524, 632549589, 421276415, 786993019, 575964929, 597033708, 177969270, 218707697, 781769451, 463121241, 90535066, 927344202, 770028211, 996628732, 383143781, 858205208, 29420819, 617365603, 145136155, 198875222, 615580822, 898740800, 772663707, 472234099, 165151568, 443368163, 211968138, 451245898, 428075435, 165679922, 113344164, 3769855, 256653320, 133413631, 727469610, 486098748, 929334483, 639555445, 404596006, 548065924, 370813574, 341669324, 602949654, 380358515, 96822051, 1118486, 955916092, 395056355, 884860820, 6242584, 442811196, 812572264, 251842308, 691734781, 32638324, 681779439, 184437081, 987773983, 355271956, 876520174, 406595733, 701059084, 489274932, 157064002, 850937718, 507074627, 121735021, 382612933, 791755985, 328727520, 896650475, 588363506, 646619326, 699859986, 295954559, 834581413, 243407255, 665206123, 897120812, 957834345, 305037159, 307666379, 605404139, 274462227, 948929917, 136731124, 472543423, 174276837, 641696790, 801595518, 104336176, 253646590, 697319475, 648842081, 559902726, 604182215, 340515188, 35574323, 866080631, 949314673, 404499509, 153299264, 602402663, 373360244, 949905973, 908560456, 257336820, 651656023, 924285265, 222579498, 602856062, 392357233, 820715156, 679150839, 944909752, 201402736, 202384080, 398979465, 119666651, 755090724, 655001157, 473768283, 454874096, 960019491, 969051576, 701814879, 27311654, 520726070, 616493762, 198470870, 271619428, 519113916, 567373459, 140374598, 443606072, 126088796, 313639336, 154154570, 535744725, 300206938, 688037478, 840720462, 856364404, 26844060, 231464148, 555392595, 359412081, 263165960, 70702783, 586942872, 206829641, 63642528, 50443961, 174809771, 921917196, 177047358, 409891197, 744846198, 8345575, 841438745, 809130017, 180412223, 274114380, 427735312, 736725133, 112327009, 511326341, 183181306, 770868250, 468515026, 707490145, 781410399, 400277117, 680160404, 442077734, 514067810, 445439973, 225787582, 343739749, 387253165, 266138195, 320647158, 158291461, 669299015, 995450661, 969909759, 146401451, 77668703, 666235744, 329678966, 51982323, 226685844, 676867557, 280273550, 208041703, 709663427, 287045650, 425345898, 1419665, 486528884, 745518479, 497879972, 377137535, 503374775, 255720956, 227903624, 41969282, 286855215, 511030851, 606418448, 208380838, 897597973, 989983803, 661769362, 483923248, 417626442, 284621584, 751926330, 296090221, 646720605, 444924874, 882902277, 427465935, 225319662, 398086012, 323837887, 915753333, 945679534, 679651724, 60322251, 150302013, 67845969, 72569382, 243891548, 879874884, 138719871, 936435206, 890886609, 852825054, 708069430, 550940926, 932052985, 855032299, 368591102, 640019862, 390698750, 193507395, 196834733, 622074266, 126987687, 411409845, 604743306, 365411382, 460884794, 258449759, 242264399, 237604742, 874070633, 322017826, 192571166, 510958501, 778629522, 590984385, 382593067, 210497301, 263658383, 760181537, 993102983, 951158322, 605952329, 491253944, 911150791, 250995514, 410586035, 984374254, 751149040, 148485143, 525178075, 484690925, 541227806, 808248307, 149813515, 114009163, 893595037, 427141771, 219671241, 998828348, 490171770, 865853087, 891377259, 102490793, 75385506, 231389788, 181241267, 229091804, 121846366, 456833835, 836131835, 577639435, 293216123, 330098476, 820380636, 561293306, 289059809, 462548246, 202234955, 353976428, 96170721, 232461330, 267076346, 373029426, 917661456, 333864179, 656997944, 530215512, 238489139, 341518824, 548513016, 222542320, 478902131, 826357635, 911434805, 142031190, 458879636, 146481294, 663899257, 902994568, 173084382, 145551260, 555907732, 473868283, 900963359, 252924287, 980943230, 262913852, 609767902, 507956769, 263288185, 725993154, 37224988, 331248183, 444569867, 686316938, 503317446, 110753999, 319594477, 26467614, 106202392, 264577672, 314043839, 271461966, 433787989, 825293630, 754367303, 583320638, 460296893, 589812197, 429561124, 518683091, 938742938, 119412706, 374165363, 938284209, 305949983, 804270010, 574394643, 991744311, 118443661, 822879414, 328227190, 910036176, 17933687, 703760776, 561289408, 177049757, 684934702, 914704245, 207001642, 866918731, 823178253, 300884385, 562530673, 894888474, 910244844, 801151327, 647319703, 379453284, 123445171, 176281675, 494467837, 942048165, 250332363, 459953736, 440588952, 896721180, 175107811, 54092084, 429556569, 5843311, 606754169, 100100912, 749292426, 395672109, 256915470, 675549833, 278599767, 827463273, 205778696, 370152831, 954397288, 2164284, 567110357, 473106855, 771994664, 714608428, 895042302, 557506954, 932448618, 721137930, 234869816, 501862426, 735547089, 805023335, 747757381, 689361061, 533458854, 237647205, 821818219, 41426574, 328475030, 99495784, 836698770, 835286273, 410322052, 984523554, 58814160, 80738940, 112189037, 828986607, 945517327, 819555420, 683393828, 294570418, 735516857, 914859422, 339363622, 56567986, 730086057, 406731681, 871977797, 625550332, 778201973, 656013319, 127922228, 769992406, 685136657, 266053156, 649667035, 565278183, 60696089, 30818042, 679111362, 740685406, 479067710, 689859720, 988885107, 722100653, 755827653, 271051363, 252810337, 844530659, 589680383, 690086097, 565648112, 543705890, 167608035, 171833127, 131978869, 284792339, 597313695, 996716791, 318240269, 998940055, 977339257, 306408485, 608957671, 127164840, 796665191, 245245236, 498784847, 193224771, 475805254, 339071655, 627409825, 390653256, 802894785, 789937067, 435010543, 217239892, 544297688, 933216027, 183063337, 623802049, 466710905, 90157274, 44544327, 438484299, 130389846, 78482038, 635189788, 491464602, 271858489, 316674054, 80818423, 827382936, 300282340, 937879262, 973575199, 963836998, 577340561, 870558739, 35043234, 705638627, 788801211, 416353104, 746577685, 122470636, 161039091, 149250509, 795299898, 854803459, 580148041, 218832186, 758111499, 866919925, 560304820, 99138667, 304103801, 846468106, 291081113, 578967674, 957899648, 536051432, 837572095, 994298351, 248835685, 826798370, 529669552, 610699440, 678600867, 720621194, 202533857, 797090424, 819840461, 70430494, 696059918, 684876147, 982207358, 750507000, 185901059, 95651986, 649978527, 816638198, 160443269, 827910783, 778120241, 745249043, 591985312, 109083386, 477751891, 984513252, 709976694, 297773412, 851524947, 681053614, 780899882, 445100108, 501998733, 320622053, 351416832, 885205159, 73224995, 335461910, 565216084, 861169419, 207633613, 403287215, 74111710, 286342053, 292022703, 513527225, 187584824, 133691723, 499210600, 213443258, 287471122, 618393242, 738878188, 68938031, 383425363, 613406592, 372008077, 742253956, 775739693, 26905992, 630436120, 491637199, 79810719, 826872396, 765664145, 756001255, 810916261, 563901103, 702313094, 51720547, 36752729, 631293777, 868634755, 606974473, 921875943, 826921024, 413858819, 934407288, 767664397, 667206188, 892320422, 440717390, 22454585, 370729048, 507540039, 648928118, 953208674, 153422897, 558453816, 504370340, 339062949, 775367377, 886597678, 229207474, 359999767, 212504605, 329514343, 521070166, 584691212, 522097630, 730005150, 573159893, 580693080, 170111128, 983988501, 753808708, 530703933, 739300643, 511253787, 337731073, 998135795, 268398175, 291119040, 44379789, 53534450, 370608071, 687487187, 463754231, 756637967, 54947543, 484519653, 664651257, 554403348, 962917791, 132434921, 996938050, 856629197, 62188486, 430657152, 960621340, 546370441, 423576078, 90983461, 913272721, 260585594, 949017436, 81799541, 98457753, 382697235, 516091999, 837529383, 354168323, 410562672, 365610323, 466594698, 60086798, 425769179, 118004119, 117673719, 800871825, 854056186, 189130560, 267959020, 203337893, 585359150, 528188684, 979702187, 872766516, 335187621, 572539606, 76300765, 758091312, 826040959, 415544877, 920007767, 751131862, 413309020, 902212650, 39852873, 421505984, 211105902, 482979776, 99264944, 237961538, 454133948, 448477408, 261957290, 704682300, 502543717, 722587503, 741236490, 889941655, 748929382, 355129153, 993908356, 386253100, 376162772, 155936180, 964753134, 55319350, 143651904, 959500652, 307388582, 960796260, 606856621, 318252918, 994909220, 105127913, 318127686, 799498817, 269695535, 177855059, 374334745, 101091784, 179714580, 534119571, 2662042, 505599163, 303240296, 748255283, 485523776, 97067949, 517300224, 225825648, 137197996, 58932629, 491265072, 411585349, 243238379, 471830434, 403795694, 582371192, 210682627, 459978366, 730496243, 352447278, 311870834, 435709580, 356141122, 104290588, 152268445, 689192412, 540340939, 534626279, 562119192, 413011350, 460847845, 337407045, 703427412, 196425942, 498543882, 509698972, 351204807, 19254399, 950074222, 60481259, 41783015, 78845838, 256144984, 179427146, 236688369, 354860826, 670209283, 117602006, 662134056, 69062043, 740870758, 709944041, 807363351, 432499275, 388460379, 986157557, 850476402, 888686808, 248355584, 829545927, 730601385, 452586541, 952048301, 331345140, 690333466, 705933849, 160462644, 912052275, 441326150, 957628992, 380564357, 177907216, 518045293, 501584658, 769326267, 2354527, 74765302, 891332527, 681320715, 296975873, 110672121, 61462801, 876871907, 685445422, 4464673, 29779098, 709580428, 46414917, 310656980, 815461442, 768858403, 54152391, 489389243, 890073646, 455533508, 696230023, 156008759, 492306516, 496724495, 320187812, 87045073, 738092783, 502597072, 513166093, 42432789, 111620166, 342011923, 692512176, 207560766, 771364723, 956617771, 567874447, 604943608, 868326724, 725320718, 412038251, 957229689, 20059922, 156771823, 531615597, 377845091, 153296965, 884643913, 462562114, 727234276, 968921668, 869764333, 724395186, 312868471, 712540966, 174103664, 189317693, 897242971, 515410779, 254781283, 450798394, 873892950, 62033777, 847758349, 352819556, 817200848, 428736930, 764350038, 780249694, 567118560, 916654001, 403365416, 996621133, 390785595, 206792668, 804141086, 100851526, 914001120, 557464861, 455942232, 148082850, 320184729, 836790673, 296551729, 16576373, 23496179, 54502873, 439838260, 294925297, 79819362, 622115519, 60978142, 493042697, 143112142, 13543209, 650593766, 786514394, 70620262, 829768261, 283563898, 304002706, 327040436, 112976741, 191284388, 594973539, 34259798, 531628570, 812422387, 293752457, 261783231, 482201721, 304258099, 204108154, 913599340, 771564423, 614810393, 551875327, 552856056, 486549859, 352643674, 489382476, 222203947, 34676663, 353345602, 405567283, 37740605, 719960226, 731888158, 540640824, 616047759, 867338996, 66868419, 811895180, 528657494, 583178565, 954867971, 36912817, 303227950, 681030327, 858082812, 876423342, 472599820, 732273192, 202487463, 160761547, 143399114, 64440160, 938634614, 89743644, 11624246, 550801273, 715237723, 349025082, 312565365, 347772011, 343653802, 953487178, 146998113, 791889478, 422862016, 32852289, 236239741, 982936018, 928162002, 46696594, 966825204, 714176533, 483897977, 488149535, 275126528, 134086093, 310840895, 940476028, 503605009, 283398146, 285418422, 733538371, 848939887, 586540347, 566607436, 73169051, 596232300, 648502571, 504156304, 716327546, 365400430, 165267403, 270668493, 110688632, 746841988, 826770218, 584808155, 629840771, 959857660, 571115888, 419783503, 264771973, 559932797, 713272185, 327059055, 491869853, 126870212, 943624357, 341523760, 881776263, 197709695, 563533211, 161991913, 596081138, 936847804, 880883051, 763894956, 649991543, 202432193, 981229383, 566540972, 697875864, 549769751, 584793347, 87872993, 437187257, 498951566, 780374348, 812494860, 198364843, 112236126, 4434574, 26308296, 284809245, 644265592, 716574721, 469809694, 47212815, 930293702, 769816223, 851524070, 974557707, 417927067, 988014075, 548894841, 944934471, 534380646, 916201076, 507742046, 183344156, 555003962, 730731882, 338631254, 213456991, 835848787, 463135004, 163719207, 547583795, 172018018, 551463748, 798642454, 241294735, 912689910, 327531143, 874208931, 881209635, 927979016, 155973364, 382575366, 276507351, 717305005, 235255131, 417722772, 301679359, 238171167, 196467628, 991079336, 355352441, 870684474, 624157850, 58826251, 727523258, 571358482, 469433131, 381156092, 918402430, 579019735, 123760131, 749017982, 7902194, 72020105, 17229512, 848595009, 296674496, 789046217, 926955835, 273930538, 18623572, 716460555, 132658981, 955901730, 28370841, 845380532, 517777163, 792371242, 680710926, 249267160, 364122774, 134338990, 740494115, 173915097, 659543286, 1485915, 352617189, 849143308, 35220108, 358992585, 483078019, 750079469, 50382622, 552232343, 47514277, 744390590, 204165518, 273089341, 949572632, 537264966, 802513036, 992183283, 563255606, 234650509, 965216042, 469195486, 743664524, 297681891, 592837399, 381502985, 401408884, 573590229, 69807257, 789857387, 234632127, 892790860, 987228509, 562062125, 353072107, 303513245, 508343118, 861457663, 691259846, 408040444, 105499650, 975807021, 833229321, 826704432, 231459788, 110374165, 359794964, 795020559, 885788309, 944409392, 281026772, 717644537, 142959124, 47344550, 397053606, 143124640, 331699547, 947549452, 302837089, 42070615, 634262406, 264289754, 545486565, 711066942, 795044404, 322583336, 723693266, 717523301, 486716260, 262864483, 403046285, 252218198, 455423920, 70131662, 183838862, 151325702, 771592565, 511425883, 478537264, 836619313, 436473956, 514921220, 979889841, 213928783, 512405017, 638014610, 337357992, 303167201, 335471463, 234275375, 722551790, 97773847, 38002053, 263456329, 439480896, 402944023, 180297267, 134721440, 170909688, 508346464, 251469673, 145287981, 721450817, 838861921, 696240752, 326178725, 51109783, 447139878, 921621522, 628372391, 448278910, 38552630, 701141761, 970994769, 44155232, 96112281, 790563874, 260165122, 698261937, 362410678, 656409726, 978379578, 177760713, 367373710, 204255750, 59702440, 99688330, 438494480, 806598393, 190953048, 350801135, 42704133, 725137975, 32150981, 413273570, 25375826, 381388630, 80106413, 640908171, 689781470, 348988253, 745813771, 573398239, 67501696, 713778019, 995042047, 162470258, 54748706, 710379897, 507429422, 643332074, 969025571, 217696222, 27342122, 318211121, 915210972, 611154364, 643439001, 959481397, 433512782, 826934947, 161178457, 72551132, 753420119, 771258215, 850001796, 450179159, 607495265, 497969333, 418343914, 881995633, 11545807, 804327193, 387454741, 148522831, 271320338, 875179811, 875197437, 727507637, 522804663, 3446556, 514217354, 818476421, 359153621, 143607968, 211916325, 612499820, 85604557, 301288365, 801612197, 964974767, 342097550, 538901963, 440973359, 807146163, 80075582, 320052621, 979660077, 397206430, 62423570, 248533194, 927327549, 135964089, 317354882, 725939951, 449709189, 991849147, 302323154, 845445725, 877710623, 48745123, 281960231, 351901037, 394776954, 877097293, 652275962, 839063531, 378191472, 581997797, 282350815, 265370047, 905611198, 710594388, 158936117, 865801692, 866585384, 390245912, 787349240, 500075554, 453923759, 782912311, 371759605, 388331703, 814279542, 689597862, 611375634, 103378527, 714982719, 916251166, 299014930, 912761223, 946612162, 100484425, 299860204, 493794850, 27972709, 574551456, 135006052, 618085924, 889307304, 563797693, 897709078, 76787998, 267892918, 335610078, 181719055, 350076104, 805118734, 405784662, 575796573, 950324999, 498749742, 15908423, 678607014, 158693669, 387340010, 743336020, 205694108, 658260049, 240773263, 567519358, 733797760, 459076840, 108551197, 551842044, 821441194, 650986461, 450357785, 792989760, 32620599, 182038843, 670129088, 126427264, 418769502, 444468600, 43147711, 652638983, 610421507, 49792595, 875380084, 695801476, 726743202, 46818457, 853602206, 188362529, 464197583, 177407883, 893033934, 980403255, 759397935, 16588686, 796941254, 168145411, 552900316, 590180409, 389212311, 760147014, 914040915, 255640206, 964621421, 314041082, 301159850, 990913388, 823242406, 224150399, 511663028, 83794996, 725258912, 982255769, 387301512, 61044918, 604206715, 6560635, 159003373, 876065923, 446458685, 575819420, 595707192, 515396707, 977399506, 46243335, 678188680, 861252723, 295499368, 2403139, 59428282, 978041180, 841329095, 838569452, 172413884, 686592205, 364878866, 903413213, 540325791, 628297897, 659994300, 14327929, 92242101, 704084998, 563861770, 888718518, 486453265, 843416941, 923148550, 596845218, 168014666, 937261383, 434164362, 460076957, 504638254, 781029187, 500031230, 192344848, 905126583, 801164972, 36962633, 799009782, 714834576, 598872362, 394999835, 708517593, 333901620, 95535125, 952630806, 27608092, 293135020, 494720277, 133660921, 957123208, 257324240, 413915064, 130731254, 442856784, 303012228, 542439690, 735719642, 298099117, 200171449, 736276902, 872647012, 990034475, 62094518, 325971064, 41742423, 931395718, 989550689, 773128436, 759777896, 890389535, 35777385, 143149843, 405263773, 437817131, 676086317, 998863129, 77826230, 75452282, 794677396, 905163618, 255901761, 621933811, 260169603, 660151089, 251332905, 578717666, 881444813, 615405590, 123720284, 529124547, 770526156, 993872760, 484469853, 572811385, 732782192, 258758951, 732396703, 828635931, 548055559, 888768533, 727443345, 566718095, 677814307, 227924775, 190101187, 243210363, 359218445, 214159932, 813589143, 896351428, 708242100, 880178317, 511402059, 228707181, 678425026, 936587129, 928103065, 643237395, 679554959, 245576905, 772031417, 499476389, 637959694, 961913239, 883745675, 511961423, 989622873, 98185944, 552152707, 455826834, 458043980, 963808855, 975911847, 746007704, 819155874, 878642872, 695738095, 618663713, 949279228, 980100962, 793310588, 121138824, 769838415, 339332915, 694724109, 23758255, 841431865, 813624776, 899607254, 943905277, 938634110, 684112090, 110543979, 146741571, 50995361, 293070168, 485327105, 308561943, 757296883, 875128196, 96792046, 269805462, 735719240, 87242995, 644878879, 316499840, 369383257, 715063590, 522365187, 69370398, 628879089, 403054925, 929626750, 674766610, 172236677, 794064729, 604488596, 922916520, 72737291, 741891931, 972622550, 402549104, 786486198, 287508226, 948988935, 113987743, 582851672, 449940500, 763087817, 367676502, 195273923, 352049570, 24825186, 141433577, 838274923, 596323450, 471562200, 517569326, 760050218, 28926339, 778042322, 546981570, 127491680, 862255330, 29867446, 394065726, 195911953, 781401443, 504070639, 419382622, 736500216, 750644628, 776402254, 948438021, 550482791, 183683835, 374064047, 264930782, 996142570, 462216985, 159698236, 534997270, 957659958, 652435467, 385282047, 632702530, 686636003, 496329990, 588308517, 306167660, 915276882, 660264085, 261206539, 529577767, 526043379, 960527825, 371472137, 143676938, 468687928, 763070459, 900326149, 747698078, 960890996, 659972215, 640638845, 932279137, 680389901, 432892663, 962683918, 236756674, 778051773, 956869579, 1864928, 176042658, 941338650, 113407588, 598546948, 221292248, 862553852, 817497039, 876630419, 588138775, 486586696, 530658755, 488754115, 925026579, 748713072, 951595903, 141495507, 316806354, 262928959, 686156531, 577060825, 620020764, 55122958, 250923065, 151216116, 69928311, 503298422, 658333042, 357841527, 229431227, 600298001, 996265243, 584895494, 318657894, 879571698, 896795154, 886208711, 289896059, 434529256, 366654896, 685369052, 10158723, 909205214, 763208513, 652782790, 971484869, 780369892, 617642165, 223842894, 135471044, 150643872, 588884754, 916035068, 773790979, 658913006, 348128187, 835334282, 469632201, 896883549, 225718400, 930694631, 548746683, 126220038, 683787517, 412506219, 233298896, 167805799, 337681339, 280224351, 667844210, 773517688, 63351775, 987180971, 321854021, 923154014, 336248902, 900068433, 303905794, 161353114, 938345246, 41175877, 416314606, 752708250, 475789286, 632730991, 229233958, 740533274, 72765360, 70184957, 306187474, 295147514, 845469061, 699516525, 967305005, 273040619, 234392177, 518780922, 993147839, 34470897, 430058336, 965412926, 155696676, 905855881, 640023894, 692195872, 547009835, 640942550, 224326714, 721935623, 714643218, 722088582, 873585914, 540273932, 473874320, 349040499, 117943897, 687298970, 741273642, 989936930, 202009241, 438385979, 623982603, 44218362, 849356684, 368584983, 257509090, 41556264, 703173890, 397118505, 489176745, 94049903, 830648559, 237843559, 156503529, 958454600, 211394390, 81836913, 563888047, 164872458, 550543095, 548873346, 469194972, 731584198, 557556445, 950902226, 604221875, 263103555, 41203706, 703440297, 815560508, 362997023, 47327310, 213268570, 198239150, 686234695, 828177661, 254018183, 847755255, 561459186, 109893133, 527528842, 548232939, 996215599, 381073207, 47310263, 778461447, 724775851, 137464861, 398507028, 233902132, 922365606, 443949593, 753912916, 293083426, 320370985, 165333391, 883445137, 990945525, 728536063, 249591004, 202500290, 604698034, 264843630, 775305845, 100598745, 413088633, 597646407, 509158444, 257792266, 107649747, 409731741, 22114873, 119007590, 135556896, 485923556, 482017091, 61925401, 80733447, 521040661, 960358823, 573433162, 693326284, 587229693, 577398563, 770292102, 442548455, 16186533, 815007675, 979726830, 11419931, 918322745, 222591662, 149499837, 692412536, 609644521, 666979184, 14307163, 667354471, 343122859, 948228710, 666778160, 261443494, 340746107, 901511799, 109002019, 773147263, 45977041, 423016367, 853863415, 820303653, 123329754, 396563912, 371167663, 5174532, 591171828, 612946599, 655823739, 799022885, 221543722, 999025968, 427023907, 616779060, 543906488, 964900222, 766265513, 341183172, 504675079, 733475147, 618991188, 684419770, 424705378, 543362883, 486796195, 755850608, 319341040, 28895222, 493750344, 127371669, 586559122, 763184998, 850335179, 745631429, 738964534, 724601597, 535927203, 599840601, 779771727, 86462472, 523342504, 761368795, 727686122, 293606588, 979292766, 229750365, 562688691, 808116415, 293770669, 441142124, 663284380, 250589369, 122452513, 533741283, 632056635, 973161809, 825678961, 737784484, 228636052, 70787389, 938786943, 356478742, 497536600, 905171869, 576763735, 668168745, 303524093, 13728102, 568475085, 130340752, 151682600, 122756996, 774706136, 68116481, 11078552, 311623321, 796971660, 802195981, 714738303, 732069753, 495482396, 82680899, 723178060, 920016478, 660359656, 284338357, 934260049, 750233210, 442501992, 145277922, 787106515, 556983803, 913098816, 160657621, 446512121, 838272604, 542632262, 804053690, 131442646, 705329977, 213468155, 764236929, 320877037, 381665354, 731189516, 628434050, 592667030, 766967476, 728109825, 368906849, 798029692, 420832609, 632033476, 800727529, 282253708, 468786234, 95777256, 357452923, 270480590, 754484317, 468231130, 938856586, 897804419, 533195164, 818633313, 323041572, 92406074, 7348017, 624860376, 496061253, 925290011, 955328203, 198946938, 322323360, 124747525, 190819177, 22684122, 499602772, 419448565, 641227954, 662172938, 703467210, 1852176, 679402470, 766491616, 853870808, 373406034, 670829864, 681511546, 205518726, 326725184, 275818422, 304521169, 862566852, 765511949, 59425234, 547890217, 916634345, 260341415, 708066847, 641490687, 104919555, 314952705, 150133418, 736205191, 252950931, 701605690, 139056781, 143679253, 687959433, 349525669, 346385928, 147660628, 700838464, 767943134, 671065992, 751008901, 150929656, 269609358, 535064972, 99766405, 848970262, 264371149, 335796848, 719218818, 9940227, 824290150, 986114192, 808445529, 424904670, 324279123, 220351840, 324290984, 833970024, 767665757, 559241827, 185165582, 140601521, 371780144, 793231567, 19894892, 430883585, 699991969, 889057858, 78929471, 149634271, 135069669, 120810408, 935661469, 683389647, 959037732, 778754578, 400424986, 817760206, 280428126, 214201670, 669318707, 714734433, 97333924, 384127674, 345122746, 141818128, 541931210, 985551490, 462789767, 478669034, 532793487, 558722969, 864795904, 725225090, 353538775, 926719358, 436671202, 591282431, 162099606, 998505748, 128994065, 908107409, 235558687, 585367523, 687337610, 977404339, 402638533, 710941136, 752780150, 424407648, 874828482, 919367474, 109746069, 619604742, 842015298, 534573590, 277644816, 776422371, 44957069, 153150338, 810400200, 521917051, 395006583, 640896140, 732232983, 11586803, 753322675, 599272868, 279864049, 695356348, 380051579, 746256011, 184162653, 818432170, 378633177, 527723407, 438043093, 425184002, 248857035, 240253943, 544859581, 974319774, 610800957, 995837925, 967977540, 241841313, 707513632, 770945505, 2773393, 617972447, 524660504, 986559697, 614537706, 109843413, 840751530, 800274315, 879427851, 636959428, 464854741, 752595672, 600003994, 56520576, 760893470, 136306590, 876395109, 692286217, 502841047, 423380576, 61090198, 894866861, 560995886, 214348358, 39884570, 712571316, 425079536, 694569095, 704361322, 877671755, 831089344, 159204254, 848018792, 330229320, 965656881, 690165615, 985303270, 767209802, 696087630, 904657214, 142984579, 542793650, 715330369, 414910452, 250382445, 42810572, 986162704, 990023361, 164643856, 101797138, 602476779, 336642993, 600318339, 313830982, 236358810, 205323882, 638712614, 771922573, 588916727, 845136229, 536523287, 192579719, 841630137, 217180380, 119603173, 833597815, 292095677, 320102446, 14905830, 83603725, 186390955, 725883945, 400795847, 144232290, 211174276, 19969981, 773005708, 231197211, 793221499, 110039785, 255782499, 229367973, 379108767, 135023214, 403590337, 766536063, 318087147, 437306221, 443159520, 53231197, 187914733, 186485914, 947430477, 824880312, 99845325, 586310739, 147880745, 757689942, 480225865, 884196104, 724458463, 437300611, 528418070, 794761615, 81053361, 260935829, 433993397, 486730705, 409208184, 227898548, 166952317, 326203202, 804441387, 970435240, 213109729, 299376038, 608484533, 614086434, 569726618, 642417041, 939807507, 501528654, 521631135, 642174676, 768013133, 32664160, 284562482, 463754885, 528806925, 734919163, 474628748, 601194090, 249544527, 771510533, 645822504, 219348256, 308851395, 487048350, 354027557, 529222429, 233041875, 796744258, 344722296, 54456119, 966170966, 444614173, 106160788, 92379911, 542153412, 932589788, 21084285, 66689461, 435968342, 284961973, 294348860, 302741628, 545766375, 274948478, 658770497, 372058635, 389839982, 814102898, 763128115, 553904866, 794171112, 727875519, 317183668, 521352642, 580884019, 830802225, 985392151, 797419239, 629907440, 637403157, 418749339, 261634107, 463480826, 374311457, 479057829, 140194937, 40370952, 300461749, 389921145, 282864210, 471704331, 622484842, 907092139, 919889922, 887950227, 85008962, 124813194, 562004291, 897476454, 993609390, 404455091, 206455668, 243914991, 414149464, 64360883, 318681081, 848085621, 681839858, 967338519, 318545130, 458081651, 209603701, 917362653, 564129151, 833454844, 58462927, 940068900, 833518678, 220223820, 339608426, 391518142, 299640446, 769413547, 495099294, 401146699, 507155190, 118029580, 735427658, 677145253, 855991427, 277340214, 679562578, 826011061, 266456921, 265927684, 777632559, 810447415, 643970436, 372767736, 321921330, 451658917, 867577908, 181474705, 683271196, 279862204, 789125808, 298236469, 986691883, 930082443, 232896174, 298169652, 367684932, 318634145, 798891381, 98818838, 705157878, 167773018, 75154030, 202385048, 315947231, 735818772, 806517444, 330913934, 797794677, 396553846, 136074564, 101598923, 658865658, 351358164, 727537208, 925896815, 73336052, 316107707, 616332995, 929450055, 994943597, 997132741, 723060435, 320006446, 374771345, 335247825, 834151687, 498083513, 701705956, 386598606, 302167781, 675221844, 675117933, 578222047, 737243707, 704885387, 739217281, 809988831, 390797612, 745954865, 677885937, 391719278, 666004980, 642750899, 454836291, 964117552, 762298815, 535051889, 79469651, 135488966, 935527747, 728181968, 598017374, 232778268, 819798847, 701308356, 657166794, 647647231, 376664798, 300645991, 741459030, 861564258, 710762354, 50971726, 329060413, 324196205, 626600453, 608408865, 772816592, 407112287, 376708593, 876193677, 886854642, 74760775, 35784394, 712288626, 643612706, 437347958, 592694728, 578940060, 390272813, 541448221, 875382927, 457952254, 322453710, 408058610, 566599132, 18886587, 743645638, 228724009, 738709622, 850491059, 744659002, 294186725, 845792042, 925495606, 153124415, 287462864, 794054943, 195333208, 322361003, 572593617, 86804752, 66769471, 132085725, 308606842, 614117544, 361700944, 256597380, 144681895, 272949560, 6859641, 307359239, 533564250, 496470802, 551335910, 433102387, 45805144, 885594589, 455145636, 32686903, 34556333, 176412464, 884193066, 482503837, 903104170, 442038892, 37281303, 253761603, 419253466, 966537319, 439651181, 228478121, 804736847, 199182714, 309477271, 815705171, 511124741, 135187980, 53348787, 14619523, 389280165, 588465017, 304942713, 108788547, 572786800, 331692029, 118166083, 533690604, 962043242, 530590007, 211766443, 995108204, 317883054, 446335474, 13653370, 151359685, 43405803, 702208488, 474292709, 866748661, 410157439, 311602955, 642160460, 587369861, 536644904, 440559880, 894780571, 79925606, 837947309, 905687497, 253322863, 268972503, 118232929, 645801423, 97235104, 380554238, 395002598, 470194092, 845062624, 520119405, 50649832, 481785253, 725124531, 938125894, 391603298, 266153685, 328188582, 472665690, 893333876, 86934475, 174029777, 454087773, 874963800, 991495711, 224468844, 872581620, 651803981, 523586516, 508438322, 823886942, 816836362, 840054325, 963670520, 900145393, 337063505, 333570810, 182227852, 486169920, 600941438, 349268875, 156123866, 136390574, 773664267, 890005139, 945843524, 618995132, 848920491, 152661243, 982385936, 363201339, 530140041, 32290103, 93273673, 559952565, 632851955, 915567826, 556840431, 458635736, 830120820, 670525962, 504513389, 389372953, 718326486, 612056870, 665752457, 211491411, 846779777, 824718181, 495924958, 692398841, 959054757, 23557249, 414022349, 814350440, 425282957, 80292023, 199274393, 224843545, 246520811, 206618574, 992652418, 612469681, 408484592, 376838628, 38405177, 778505846, 151771996, 904547726, 19727132, 713202228, 989466118, 430267299, 977421269, 691089740, 376751903, 515990152, 650376375, 861894823, 145115471, 55672274, 734369547, 964193207, 468953012, 445495317, 535704766, 408699544, 166283998, 139941389, 237212303, 447265928, 616581199, 574107788, 649982766, 883967291, 36274920, 627580659, 997115144, 737259321, 84091577, 715916418, 900775314, 578508115, 208560649, 115498904, 265565893, 719720048, 748950174, 327250058, 106475586, 212863650, 622778591, 30337435, 907043881, 997311675, 834291850, 964202613, 507767464, 829570922, 795307828, 494170145, 108744165, 96938833, 513387679, 461489248, 696110062, 170139187, 3227602, 188419447, 496815981, 857654973, 259949843, 360529700, 301037714, 210858298, 743934717, 766306082, 743378069, 882730339, 502774557, 819756889, 639263650, 20626285, 676808621, 20354810, 641918017, 736814330, 59789319, 376067608, 358490539, 469175327, 63404781, 504772403, 586790040, 565798435, 362711253, 752184707, 951541265, 609110988, 463690330, 755539008, 78066373, 673193711, 139748648, 636283218, 184106540, 267258503, 15263995, 601958933, 781284644, 494561805, 287653110, 590253963, 505752075, 653929099, 127063079, 589447023, 727395196, 730111825, 952375782, 248930184, 749255835, 982449204, 747599487, 870611105, 360968813, 552874133, 201539611, 594720335, 346599828, 401045034, 453592701, 86757586, 952272348, 366218126, 519317258, 170437409, 509156379, 8129882, 489170057, 510178445, 542872261, 983045333, 66542734, 179668892, 182339457, 286072885, 522541154, 156717941, 436268971, 981623728, 243445503, 795015877, 43936776, 625331171, 538984196, 365219156, 980305313, 101442336, 962398703, 429336051, 253548586, 353754098, 864657896, 663626869, 22800267, 221718636, 842227589, 904034798, 662689385, 863239320, 251478649, 83530103, 267225908, 504095527, 366659290, 986917293, 378949772, 573918055, 804074442, 28963827, 877801936, 134114486, 683582861, 986964220, 910531177, 455811316, 412804165, 952817834, 878699020, 155980752, 791532949, 621904697, 343576206, 162766437, 5607776, 553591409, 461501391, 47614227, 778357318, 483128717, 159409865, 838757241, 332130875, 338431934, 279874014, 111336782, 230379611, 145468718, 666095199, 582843105, 138164651, 384220008, 224690943, 219604087, 913653740, 266555964, 32825627, 675131353, 68910217, 812466110, 407644144, 733609521, 313197533, 670180321, 291282653, 851322428, 842607525, 69158326, 644683224, 895320340, 196982786, 235702588, 24974190, 788372399, 408003321, 126442540, 359616978, 611354299, 983763378, 446134050, 336699380, 616577570, 871189094, 326474133, 810492588, 909916585, 395807651, 916566056, 13413641, 89832354, 799073494, 110348738, 938972123, 470874532, 964750208, 854265487, 660134753, 708790854, 688918173, 138891916, 886382749, 223659308, 329224850, 337793546, 429982678, 637264789, 236351526, 179134911, 641404727, 813049033, 897176197, 796695739, 446597720, 750385352, 349207654, 370147998, 145231668, 90937993, 692660077, 895878886, 848808502, 739870579, 549181382, 178374293, 449736225, 47741791, 77945718, 370737785, 556076713, 208643494, 429788360, 32166231, 223354216, 17220225, 774782561, 18161840, 626404037, 326918465, 21158233, 289135566, 678438564, 465378370, 457159316, 273108098, 533518841, 269648071, 706486889, 475718713, 388581831, 69773757, 312978516, 234047424, 551252908, 768791974, 290950419, 128361396, 221288489, 771184635, 109991697, 59034412, 646574489, 663064871, 134020825, 900619915, 646865896, 314854956, 482429410, 863152067, 334158461, 100422004, 374804504, 575883956, 939347278, 697044614, 563802389, 551073818, 68406001, 80560985, 447397234, 46433886, 361793631, 9922670, 510111369, 566426459, 640523265, 983318793, 831528365, 637846054, 799921018, 989381502, 925350665, 205751204, 349294927, 950764778, 960347811, 74932193, 754959053, 953937891, 431377926, 599696603, 934568857, 69960290, 673938518, 478937548, 876173022, 947758506, 368878899, 239193094, 859414828, 670428817, 590208953, 966311952, 366046174, 238501698, 758610045, 175376800, 497086777, 353332811, 690645448, 373785761, 62249379, 263910698, 41659919, 768985816, 259526346, 581297435, 9116755, 719734226, 188398697, 978270757, 199170175, 606529753, 346838945, 784158581, 186420207, 140893477, 492586742, 702559751, 507887020, 582854242, 842813212, 58516652, 451599527, 609065459, 755882003, 233957277, 576993846, 85620898, 74056383, 288521624, 646341670, 247577538, 336048000, 163310897, 607926585, 948549899, 195578539, 787853801, 841921349, 504189152, 506939826, 85190012, 52902058, 308930491, 961700861, 790508361, 204187681, 544832705, 212112639, 621873681, 819683184, 784174519, 59106329, 925738236, 689909544, 231501733, 963501959, 934153605, 40074772, 664380679, 118367355, 839889348, 509277770, 8847783, 136655527, 493080778, 392884551, 488214790, 73740874, 228863003, 979105535, 713021563, 509867357, 704064117, 663027828, 800423748, 545228551, 580665472, 322418656, 977245905, 765248190, 951015523, 190331532, 98038073, 289472084, 774789763, 809720008, 360769345, 374928879, 799501989, 613666037, 328362611, 977121845, 279586948, 761518660, 104593005, 428596923, 500966732, 122461611, 133416156, 531369538, 441579339, 561087057, 541401335, 484551478, 962933909, 68828815, 936262422, 245192795, 302108729, 574804815, 736772182, 534283273, 164177857, 25870604, 951483887, 588166945, 589931645, 975390755, 872467997, 599678330, 464797505, 817348087, 376252548, 176091685, 989508962, 574577914, 959741275, 977829102, 181920390, 770240365, 535067416, 508163218, 472321680, 591967885, 726403076, 470480205, 892244149, 745115632, 809117891, 840869599, 522610393, 39366727, 621260115, 717342009, 462326160, 382647137, 144060920, 576714448, 347349925, 300746360, 149577339, 36076501, 361008706, 249020640, 980626600, 636806777, 474857013, 373943378, 972747975, 936227862, 782525928, 520855724, 706109284, 724031189, 621285377, 793941717, 594439918, 596022720, 423053126, 715539454, 658023840, 981037499, 900853822, 593076953, 312938548, 621751578, 128577187, 868964449, 370300345, 204233601, 759407020, 730487272, 939429511, 760360169, 607099419, 234153769, 794403822, 973717478, 712319924, 825817032, 797810328, 58866618, 728749947, 921727999, 712719588, 941390903, 502079886, 357537801, 34558441, 839903620, 737032587, 690314283, 184292713, 566645704, 748997692, 874448775, 895240876, 924336378, 163030313, 404514069, 755798542, 888128182, 230860570, 650351870, 859823840, 588641293, 963381129, 586188270, 325491592, 990348641, 550024371, 346105434, 54338953, 793847088, 590837772, 364789743, 66517391, 599678650, 404648195, 986403122, 400828672, 379826444, 93073034, 798202695, 948199485, 714822736, 420265248, 292025334, 852670803, 119652695, 6606489, 932703888, 522556738, 833677381, 762788956, 214181591, 315978937, 352251616, 955740766, 947441999, 30237661, 466782735, 504703568, 41764012, 680117786, 988670382, 349917913, 439230303, 779641867, 238176247, 323670141, 645509058, 43437344, 14838556, 662998229, 939103706, 972738981, 748044544, 713008489, 942955268, 35804957, 825012336, 831958908, 277297462, 656991762, 388517540, 94607425, 706921427, 839535921, 136731811, 701997233, 777391626, 380426638, 231791464, 364306933, 224630061, 985802659, 556848798, 260432290, 616502258, 923805925, 802796589, 602764088, 402465867, 108075762, 578459907, 411352971, 638461704, 819914019, 678700331, 119248952, 730903122, 577979127, 962072683, 521973496, 729988248, 541877104, 913177136, 400208668, 347035522, 529595463, 251424564, 533313977, 22475977, 106957132, 861872378, 995192314, 447261267, 658190210, 532692232, 620227724, 566026272, 24116753, 998333736, 11501490, 670680749, 329768777, 149715320, 794868264, 391746953, 330068789, 307322419, 249174033, 394267228, 233279729, 84287000, 729892112, 124624239, 682906059, 551094950, 716081689, 355690625, 67015773, 895958517, 144628419, 814004160, 983335457, 216952369, 714948515, 655707309, 849817174, 515758708, 92191059, 246444143, 242776055, 801707408, 967120967, 536171252, 285719234, 198404249, 497392979, 72219855, 973161060, 173184891, 71824281, 856813078, 827102161, 158013431, 655185139, 846195372, 850895874, 986407185, 987852535, 341770458, 247410980, 566673889, 96060634, 646113030, 76480317, 784602436, 735448001, 914843745, 518308140, 919120788, 973740814, 653853583, 390656106, 561738876, 414030318, 801746413, 868651505, 406778313, 666991066, 336058286, 242661779, 174787314, 354954591, 523429725, 334257202, 805322691, 497841642, 423797828, 335242058, 514620193, 779657426, 458600046, 56503647, 741670705, 702436589, 904185919, 458162468, 616550242, 566505940, 320146058, 634233842, 892033784, 677431498, 329374425, 528469945, 101644620, 541245319, 362323162, 862548172, 215363395, 339856918, 769333535, 465965061, 521366376, 798224113, 603007989, 283873806, 652484383, 85156567, 253390545, 566617675, 144777563, 388755797, 829554604, 795086383, 321652635, 152023942, 337516377, 182885998, 289843418, 833943168, 78822898, 619646641, 925518432, 418386802, 878701817, 113022893, 768488409, 847597656, 500390984, 973929644, 611932748, 861971546, 409973463, 682697733, 175075390, 745062616, 734111998, 659729631, 85827156, 470581355, 317215293, 685419000, 850245144, 512390821, 623610047, 197636379, 78913203, 184307390, 445651469, 54216151, 373746002, 814057587, 636993994, 510301635, 75169271, 801241368, 521360958, 155608949, 653318400, 735070407, 882112988, 234904159, 707451243, 165607957, 18298824, 644464980, 836669301, 458572658, 863379402, 607893209, 303304990, 400711305, 350202415, 772711671, 85562967, 520417813, 719153116, 801880482, 764952491, 905686983, 46800229, 362276183, 793320715, 942622583, 28477967, 483867128, 997852191, 770683831, 824162142, 686420546, 21006633, 83914096, 109939866, 132575583, 857850770, 954124235, 379303337, 464609206, 738524200, 255374020, 781768297, 387360208, 527124036, 588280960, 217926332, 669759414, 109806802, 293129429, 588011701, 369938881, 536412684, 600306029, 264535428, 177108850, 397315142, 288419401, 435139305, 368733747, 405435077, 574219769, 428458307, 797372882, 678967488, 684473439, 979571950, 617514840, 856811950, 43683265, 515404807, 415550465, 341147280, 483764641, 688306296, 190147823, 603025837, 663537828, 503734429, 272195385, 84295341, 524441915, 977981106, 274845540, 935186661, 929889741, 601703154, 282942465, 832373333, 286194255, 118850994, 159245110, 747869597, 592498920, 705017285, 15672379, 476278257, 196185957, 730175958, 239299541, 850975211, 165931132, 232159600, 608582730, 219106843, 820085563, 928101393, 547071346, 135459848, 111064620, 578150358, 669865282, 762777801, 137546177, 921314788, 279166616, 913418356, 684362628, 421568778, 368481929, 767024213, 405888725, 395518758, 521606038, 97275232, 88502510, 884572837, 461028363, 710582613, 196720887, 122571153, 26827230, 522520046, 700907017, 623668052, 65624186, 465615059, 23740015, 288068727, 161130849, 633996895, 521352717, 891914162, 736717189, 250904272, 188093774, 227979479, 805459651, 826472644, 591963918, 244324070, 546228642, 94967459, 819934443, 160123850, 213324842, 197610859, 185961750, 534171404, 831084729, 525660906, 713449163, 52244499, 104916178, 704457237, 497315992, 804506785, 991307728, 505725950, 161097587, 254634232, 964977009, 859797017, 63919266, 199242516, 669995827, 70395628, 407226633, 646801574, 852846786, 134819584, 968511605, 578436727, 113465095, 414130209, 219556131, 940065303, 550110580, 518664680, 533739764, 654827226, 117333355, 632415088, 221318246, 745153814, 578810069, 665043401, 212844218, 589688770, 1205503, 160504413, 840689855, 234858627, 654189047, 61011111, 906593389, 237108709, 914848934, 262582740, 195527104, 928644740, 303752501, 342327150, 630261739, 975170849, 235251731, 545752590, 352613047, 492175523, 12261076, 497195032, 850200854, 260713353, 825829736, 257477582, 589387562, 928405293, 206157591, 949181802, 360849585, 46741251, 295170199, 706295111, 533005651, 913306632, 430406394, 741165857, 80021536, 796900536, 120961904, 945295298, 503699377, 823026863, 864076956, 145683753, 163558109, 256599978, 422673187, 447914234, 142468997, 31147789, 818965358, 594543813, 296303157, 249567419, 363369253, 338085283, 29628428, 356155356, 51345863, 456529078, 454784804, 698937652, 585822628, 74265788, 175260154, 458538002, 230939120, 232923485, 469548796, 838239513, 96086155, 628023891, 227459915, 425460631, 993421207, 264262663, 275206241, 172747344, 151804428, 565451014, 89812929, 490047659, 432136891, 705658100, 822208812, 771627003, 947267948, 33541487, 639644191, 613739182, 236816760, 748852163, 601725339, 269944973, 92981780, 215717120, 773829412, 803903030, 577144986, 299162002, 962516923, 801058070, 447283735, 863351163, 451532659, 706986630, 202514234, 281319266, 754320382, 142719597, 294399743, 549907959, 640829798, 909892845, 302510270, 939178705, 566223859, 80213564, 88440945, 373137426, 351286323, 862895698, 918248913, 849726982, 180089737, 173106597, 410742198, 432492815, 661614304, 547529598, 983521541, 198071539, 126017389, 370338220, 541782419, 218443222, 830989933, 352969273, 387380376, 140055440, 841195049, 552898958, 166452525, 560206661, 829341339, 753650047, 123074525, 628131242, 332790821, 840548027, 72009381, 384904738, 609014728, 96424802, 460002418, 595243342, 837870170, 69695324, 878134806, 544095881, 61215947, 503654930, 816059001, 619468219, 276779715, 598800030, 897738735, 103810351, 93089515, 714224793, 881448085, 371175153, 843733907, 362560589, 20289362, 620895065, 84695449, 869708050, 675467852, 129037906, 382975751, 625823232, 356284245, 76015016, 327012849, 436684624, 141933157, 803595559, 327182174, 537684153, 781397188, 77662475, 420165865, 700286416, 796299995, 320951803, 731905165, 749115377, 984320390, 393545864, 624095621, 955450889, 489947084, 236203250, 80857222, 470995416, 951285508, 787951557, 646472072, 761708369, 812139984, 788466185, 31384586, 839766709, 562775948, 139952842, 919745781, 820719003, 706596706, 399043067, 444197511, 575249403, 312553277, 796552355, 325460064, 567306718, 482185227, 898980249, 223432726, 899496448, 621613996, 350837707, 965679026, 487872058, 737161698, 804657984, 408251822, 783478500, 337445798, 555204131, 735108006, 766183939, 209973681, 372720545, 571674581, 416301187, 696277719, 163534652, 999818146, 30590342, 798589899, 694460848, 655814183, 244366492, 906589106, 610862786, 356838282, 926475778, 937122236, 459395723, 452086887, 588973167, 986964719, 724940159, 522712810, 808932525, 916436498, 776846029, 311562741, 242803330, 599380320, 725446071, 23527501, 60421952, 227194823, 973365632, 106210932, 327262111, 708491323, 741124486, 547238252, 475699520, 306510071, 359402814, 344777535, 204543331, 162599917, 491636895, 530685425, 914844145, 880792222, 853366643, 76578823, 214209159, 423847362, 537485380, 683016635, 705096175, 244533398, 966239035, 776000687, 240691101, 588731100, 541684456, 688172583, 121664892, 587126223, 132445809, 834711812, 583908185, 919947384, 381015076, 662856505, 459182314, 736962031, 106640340, 675526035, 951509132, 823697235, 780974982, 252259208, 719029395, 887690181, 200965479, 535180573, 411851227, 323830535, 470094292, 597218120, 857679632, 352157050, 223935420, 334915641, 281997926, 163353768, 38734013, 825453155, 718940329, 8894949, 43398744, 322438157, 467639557, 629607849, 764612699, 620392049, 636202752, 692796995, 493952614, 588475927, 641719531, 745731048, 500883891, 957185974, 211676195, 848581709, 705847154, 337470133, 368884221, 386404580, 800215375, 355322806, 472879812, 154798360, 900468319, 970839863, 520786401, 216812551, 263838503, 472833607, 932924772, 398018424, 463334328, 671492619, 585815892, 223362314, 596263207, 263536048, 751186654, 460313819, 459759862, 793458978, 315934395, 410097766, 278863467, 721237419, 543877132, 860850304, 824053240, 281103572, 180739911, 520622343, 948181537, 44061155, 329406026, 338418155, 414983035, 919201749, 490882694, 97030014, 855327287, 516933976, 483067880, 281127190, 774444700, 911361611, 355166865, 323963799, 719114777, 480826569, 814281471, 560821782, 880389161, 423475300, 158387097, 821219147, 857069543, 942343282, 541211718, 742509905, 565682167, 306730301, 920437478, 545348230, 78788805, 15028511, 32353416, 611567357, 805587935, 57927175, 905287540, 719098155, 863122272, 911582827, 201907424, 596349675, 131811626, 978112330, 37621103, 106460903, 174457679, 470245255, 960035489, 797359122, 140608219, 409057087, 135655817, 533428842, 676024043, 581130494, 367129118, 850386483, 352174614, 576878962, 972849878, 341284562, 90193885, 844628504, 536644203, 314742620, 174242389, 647992802, 869317044, 239701096, 736300129, 395770260, 686276701, 495900547, 670036213, 460216635, 839481527, 982167539, 361086645, 879651012, 210755006, 158278358, 206501915, 39670966, 775122954, 938088269, 879076197, 476452809, 780612357, 836275479, 162467215, 154449238, 570108767, 517523912, 747041056, 919886302, 305429155, 647880599, 784800816, 537037751, 269123222, 752473138, 434872937, 127054663, 208307331, 674291944, 798338580, 872993269, 401172157, 31513175, 436215317, 94739545, 692244682, 142217625, 543687030, 779438820, 260664801, 278246468, 891315789, 777025612, 189794774, 247932195, 780769623, 962461114, 854533354, 353186769, 219402309, 266800681, 426437118, 825889612, 613862892, 172510535, 926733085, 767124053, 624930091, 282795377, 983304557, 402987150, 420304250, 470365548, 125109793, 942616507, 467659665, 725967424, 682431588, 618490700, 938358190, 748137126, 689737946, 4942446, 263020789, 911156563, 281590747, 41413862, 763724202, 168786374, 373541948, 491963028, 796476560, 380638949, 550618271, 366212392, 802540677, 935837858, 145813078, 26551902, 859908998, 741089122, 879324755, 774152183, 553397969, 522102872, 293403961, 496186193, 631764415, 268840672, 283489883, 411464941, 417291627, 619799331, 312625436, 46831119, 773932673, 849779692, 973613102, 992126841, 414905241, 853962336, 804524588, 656105290, 858541579, 110395939, 206785479, 829208443, 183957528, 662731055, 35781770, 640217982, 420058710, 658375432, 68313201, 818028128, 239760537, 416142135, 953810793, 651614027, 514216357, 858989787, 494487095, 735211620, 765594898, 117435281, 587467512, 590070964, 813815613, 402712935, 15804354, 573914241, 214613148, 389224738, 568673621, 318959288, 602779843, 975574291, 74691537, 959635651, 252439638, 458082297, 39603552, 437297350, 566696572, 983331453, 117707221, 145705636, 779143775, 103787887, 270487562, 913375199, 243993549, 548463479, 914311520, 672330954, 830288691, 367161313, 638779056, 637671261, 303322069, 110959627, 943604802, 256169981, 227095755, 852797938, 838255511, 320953904, 863953526, 14441141, 575279566, 652156657, 217747379, 640053737, 175095416, 726275715, 837783160, 787174557, 409652156, 658790882, 573847387, 563901990, 234563918, 346661955, 961591811, 548185110, 786115667, 863049700, 638957012, 255114875, 288038496, 467032482, 645092113, 285548672, 363713616, 709716174, 444432200, 349084066, 82825929, 335786001, 616960071, 94503766, 795986773, 670604306, 368981550, 962109534, 371121631, 978466398, 363776812, 147204146, 206603939, 970039684, 396604988, 825699245, 56015433, 268981307, 307848633, 218727401, 240449452, 672875355, 259329744, 633364459, 986812469, 537775898, 612099368, 948242363, 345422280, 64429111, 119958242, 265279604, 703981293, 728174100, 270394721, 241347597, 356142330, 392246814, 633952461, 80359525, 980557227, 13963311, 793218427, 773011997, 768939585, 160713692, 97359885, 600189868, 109537383, 141566816, 304099723, 410747366, 990859695, 571907447, 569525856, 160859009, 670484355, 94417313, 667780536, 211780454, 882817429, 939658049, 626881189, 85035934, 595811313, 119578134, 153477526, 348389219, 599139347, 810176540, 721797530, 45900141, 478292114, 472864149, 193745932, 174149504, 558550562, 336485346, 242936727, 797941325, 467779889, 67391197, 258002084, 672875761, 986502880, 803458934, 782388664, 658024277, 443439585, 637118359, 10708628, 723242867, 163909084, 190466057, 407304098, 344872169, 850881357, 870774508, 937426353, 746032366, 502326025, 507091560, 236814921, 118350398, 481434759, 242804907, 565890242, 190519382, 410660303, 588180180, 675786818, 722252171, 501379885, 234148779, 24567701, 460241959, 211612603, 610829177, 707635138, 495982828, 311356747, 676330764, 423686324, 210432426, 111667295, 532322683, 219051364, 53355005, 520742946, 677177485, 870308358, 643578492, 297412394, 361790111, 955721067, 465286596, 910137683, 967273597, 934646496, 848374296, 519076556, 827220311, 789421408, 682391161, 43176800, 373390629, 370848051, 263315065, 15886559, 564272732, 826186489, 210193161, 857009991, 693843285, 527193553, 980097975, 221732978, 368733403, 433713321, 400078335, 280043999, 396627078, 943522696, 753382638, 964705984, 439332446, 853231912, 322972353, 669093723, 807342982, 810615643, 213434947, 30829992, 647675765, 287910199, 693320793, 163599032, 553608597, 979987352, 981974890, 653222345, 299330987, 672380744, 287036926, 129620954, 376428456, 622849467, 591525864, 287801742, 280103233, 733202303, 542327826, 180788796, 178480325, 514037798, 243243436, 277296602, 583188153, 88015190, 617692891, 922350820, 689738783, 648558829, 909650186, 278357792, 99840689, 908065991, 4133076, 307386486, 524163825, 72061263, 999981445, 295494703, 823642500, 542062986, 64961814, 957708038, 184238574, 784326259, 53216514, 809426915, 641804990, 46852664, 420412893, 55772494, 815936469, 175592968, 841048870, 29556582, 528830101, 466328442, 376322738, 92636757, 295787911, 391760878, 834893100, 763465822, 720294276, 93196459, 902156859, 198773285, 220538805, 126924682, 212057933, 360608998, 185176868, 276048725, 991750874, 144127136, 93566557, 189186444, 477514444, 574352595, 681964141, 497737123, 553366449, 599682129, 979480401, 182409325, 833739461, 157961150, 8730803, 952392629, 199845907, 960144569, 735691596, 565130880, 969651824, 171198865, 16322468, 29402316, 751687860, 359039166, 44581967, 815367014, 131680226, 806823958, 177198440, 535040465, 997929829, 154269949, 950687581, 383218593, 225875551, 382275501, 387880351, 724419137, 810234302, 642549271, 700160866, 18954364, 643635344, 183207586, 994045675, 751660840, 365704413, 904391275, 906548375, 671881352, 425291797, 576231991, 180039557, 562107834, 953131346, 401378341, 142370840, 800468520, 398077556, 745693500, 483284968, 539154772, 314418625, 409057558, 486971174, 930523094, 509799054, 323276014, 284891457, 780601687, 783547720, 857462857, 735845676, 722312980, 358858486, 358472564, 718065027, 434985987, 610464787, 127157462, 645482942, 490616668, 878140225, 905288030, 144553343, 363290074, 679564299, 456123394, 302053432, 7602845, 565164468, 583675342, 161754167, 34634311, 262987207, 374560957, 941883138, 705765419, 741289921, 386670602, 595171422, 884591359, 661174588, 823047701, 902087911, 246808704, 991963729, 810723157, 50581737, 50044883, 829273524, 161201354, 963304716, 610541674, 175684872, 676681373, 822577802, 404182165, 627557884, 547419690, 29817491, 680807216, 41816711, 553065112, 329281831, 314673508, 96553913, 406153979, 385817558, 390526660, 680536405, 888451440, 916840300, 577119544, 911266607, 264878686, 149611057, 964508023, 510563214, 534109757, 749434426, 894462047, 365707856, 142447672, 702021582, 644121059, 658628533, 371362380, 59450686, 115070802, 108378513, 347560450, 926817322, 818007524, 368503529, 559649548, 250939915, 528795017, 809171668, 531907075, 194678611, 199297853, 840267548, 852215441, 998894252, 116420853, 331398744, 74396763, 831374325, 776545662, 526629691, 823355449, 852987596, 593986123, 92767775, 846069418, 412471494, 558952815, 639740835, 745679212, 129667448, 653690657, 451524786, 985160071, 364011670, 540100995, 620740063, 929627077, 879445384, 100095230, 70101277, 538767854, 268264276, 894240445, 649029039, 820365425, 28508104, 585982120, 490651238, 158421322, 282650139, 839726149, 239019088, 304462128, 424508392, 244741592, 419244172, 363150362, 973050140, 104803004, 560526869, 186503479, 21350359, 128419587, 401231856, 865957279, 583517521, 249527829, 417777058, 255248238, 233657211, 565734902, 113420933, 866383523, 479927232, 794268506, 382414683, 417591916, 78724690, 964099856, 246666106, 663099924, 184187188, 658613119, 302437027, 814930597, 82629294, 420319466, 642496658, 59654667, 57461854, 992705241, 854176511, 781599418, 587777507, 806242756, 866251509, 156570209, 134587058, 901107894, 617280358, 163913920, 666394012, 614518567, 262078199, 142945736, 890121858, 20498891, 307872700, 958733433, 771855648, 339002116, 563610907, 161399295, 192568234, 918523610, 768273020, 320816796, 658388130, 51282694, 492894004, 711746737, 464952785, 618619932, 383091350, 442916880, 534701918, 770711640, 117731315, 483602500, 980922083, 182620579, 178612007, 862161198, 945781629, 974486301, 912985638, 178488106, 952054663, 909218827, 244769709, 378896775, 927144357, 250737180, 154170471, 744036805, 67565630, 457395778, 825397579, 78386245, 353226931, 956555384, 726207995, 46971139, 259439853, 929439874, 897528676, 809619552, 873892332, 119083417, 296130849, 736104563, 881734593, 526149644, 650624930, 554112084, 427255767, 398100561, 556241854, 925409812, 496427354, 958537554, 396657903, 866413574, 764082278, 867725691, 653702133, 99390033, 542809069, 449222511, 919644825, 28700361, 573354905, 975105083, 544622038, 537623730, 565328320, 449531348, 958220438, 814574469, 465853871, 938938818, 208373782, 773463231, 543669568, 942789229, 323691953, 491874096, 921510591, 595186686, 524484096, 638422726, 602345981, 352960859, 49523598, 773629778, 684660963, 244259969, 939665931, 10596288, 604356278, 846896300, 181620986, 223792705, 686624666, 780581640, 428025568, 615771193, 95321515, 276458527, 730462245, 644726237, 550410456, 630374433, 300245745, 649608022, 250186836, 127425849, 406462910, 648730017, 529710393, 165095522, 143563104, 220092519, 383153221, 451415377, 486972268, 393504228, 234133649, 286755888, 154666315, 983009318, 731914249, 591579530, 56266533, 91359610, 797844628, 577035618, 803517689, 758123472, 384617433, 687159085, 649971856, 454632629, 144243192, 219008605, 881995064, 342870932, 506021753, 603117490, 742378514, 513400117, 604803804, 55189343, 350804581, 968428086, 77156058, 913111470, 779977742, 256462332, 438059737, 496675243, 121055665, 828836194, 729235708, 781587847, 454102447, 58537287, 840422835, 284951511, 718042544, 298775901, 95932705, 413396004, 286580264, 960746293, 869957259, 925007921, 57397366, 522147118, 254214867, 966686370, 790620384, 467627508, 772515657, 333142049, 190017255, 480280901, 775097262, 317696848, 560382850, 998565101, 282008891, 555832848, 544342054, 366343965, 149795364, 552970489, 645016142, 802549851, 921936899, 698836293, 407033171, 304567963, 424187228, 271044928, 514758285, 45607267, 290859745, 673919041, 625115665, 476641996, 40532445, 734599524, 937209074, 720234909, 947753530, 650567335, 674231553, 945737749, 792417282, 213755601, 730397958, 64303528, 11976964, 158066957, 420047220, 320339291, 281883473, 888422798, 938331720, 188321974, 510680176, 529410167, 461247574, 830381276, 136474091, 753347846, 272743796, 665675734, 27451731, 156493566, 574479815, 468333379, 868676668, 73957572, 333113017, 115764098, 542752275, 52719274, 774051935, 450342108, 72289532, 541687715, 582942742, 146312683, 146389159, 748986964, 617814802, 168815113, 965192032, 539013257, 618299748, 138250924, 861194857, 646040875, 125676496, 67312538, 814871860, 108782677, 783361775, 167934627, 641872053, 374117621, 9692201, 577620620, 19412498, 694822684, 615297108, 692324845, 378501662, 425292053, 25631995, 509852689, 795950306, 103064591, 655913053, 394306621, 995325610, 762702547, 586650947, 801234012, 611174621, 744358133, 173051397, 289149114, 885686410, 237884042, 294119725, 729872000, 399604603, 278156472, 132696919, 854033218, 602336713, 953577017, 521666925, 716466894, 123046358, 585258265, 680333081, 819146074, 559702697, 527823916, 978906157, 845408480, 812346283, 261138038, 145312564, 356360483, 982599539, 749474021, 494284289, 600246826, 561518628, 830228150, 903911633, 850313484, 675300140, 293540771, 890247459, 971756287, 509054693, 215845192, 210696044, 690285270, 49891029, 825614827, 10165680, 570685384, 156782597, 890585997, 485640635, 334389570, 253777361, 417142567, 144784930, 608892419, 325991910, 115988406, 237672942, 313008861, 318749265, 509565234, 783258417, 767537149, 200819086, 309421949, 415987542, 912762144, 794529584, 825636848, 188359868, 665419151, 95180987, 437446570, 908272215, 296221519, 162998963, 909813533, 836757726, 848417103, 706564920, 90042413, 853133616, 984712966, 871213053, 485778581, 412011459, 355596087, 994015127, 416371548, 779702692, 127750119, 846498412, 933983954, 744423957, 634742557, 128642495, 666434252, 655314368, 219517247, 95759154, 712219353, 547611372, 32407404, 837400830, 946113140, 330236336, 512899320, 211788064, 461071695, 210684988, 187689706, 413803561, 434369327, 556492164, 629173491, 637889340, 920254562, 332887816, 626764750, 614725985, 796599158, 100054413, 919543541, 552164045, 929424292, 174611751, 338467885, 371190620, 906311848, 429899036, 933307343, 489862351, 36104735, 328850501, 55699439, 158404075, 730949335, 707322679, 365946589, 473891462, 789431683, 649679540, 695223318, 873679337, 346352325, 795518031, 55122742, 494728288, 761195333, 599241594, 761568526, 683213338, 283747250, 106947901, 751458363, 25602653, 167662317, 149888653, 792752598, 976344331, 202629758, 665406583, 885994869, 706421791, 474567984, 873332783, 6203682, 628801924, 566435523, 285649968, 781299694, 119333112, 887661924, 89377258, 517687814, 855544692, 979194040, 753208631, 866522938, 594214260, 442855147, 674322900, 89585416, 966144529, 790312204, 952102412, 168034003, 396972340, 207680527, 558026016, 465726421, 933355393, 922880570, 205703752, 344078714, 51622632, 211367278, 573955916, 304897268, 893964107, 313362634, 813377718, 878951986, 249291892, 399164183, 718198170, 50141523, 296429879, 410924606, 508482618, 752588268, 811178133, 556324834, 289689633, 643754287, 521710546, 421811372, 540138273, 515056109, 255108007, 770525762, 425670326, 919140088, 72057263, 734977956, 64054074, 983444141, 686173426, 296476194, 539802244, 363361692, 740329862, 753110032, 543825884, 321762144, 416538620, 236864066, 52142470, 243316820, 882569809, 576723077, 577883710, 359820757, 93433849, 870231678, 779360023, 469471261, 706339551, 267572254, 788080077, 495506579, 330030769, 498153617, 199201287, 733848076, 872621042, 943120463, 610028234, 93036599, 6797612, 823919509, 879226979, 314157475, 96176735, 322471631, 571978152, 279975597, 281392319, 295457155, 251364909, 567929723, 815621761, 771204360, 766731491, 249113918, 934042574, 708159224, 986698375, 130225562, 655421411, 632318562, 625638698, 974632788, 307493896, 188708864, 156470409, 965964337, 552964204, 141569499, 239983567, 219971399, 303685561, 848629731, 476507339, 639904129, 571209174, 683032828, 915468167, 551967720, 23483150, 546611530, 686284668, 443380294, 940344369, 323162181, 70674107, 189964320, 427444162, 470630046, 154778052, 598678055, 933583516, 636916878, 9625663, 589434365, 106545596, 265755641, 472138741, 241024230, 783340238, 431386065, 329464736, 970101503, 25546605, 26436634, 617640975, 996870859, 978519694, 838892565, 987970896, 373161572, 43883187, 673070697, 646330886, 647683569, 42791612, 496976744, 518902287, 478766257, 51141251, 711407706, 364519973, 689310314, 917773244, 434700541, 11491299, 297023522, 310831096, 398824187, 880659520, 514399664, 76947395, 989044418, 223272132, 988675194, 903512135, 30774038, 826862013, 165562541, 245735019, 568951976, 7728379, 653987381, 794504516, 406661924, 155162155, 66942263, 594826449, 57290123, 767818171, 372842842, 444733811, 143692472, 952191129, 596126188, 717370849, 657985705, 145167965, 21538054, 608298968, 118629471, 633761764, 19509920, 421192205, 689363035, 642640597, 167581328, 682377929, 267100737, 219495261, 591672047, 236304164, 977771340, 719262950, 543883912, 702472669, 718911028, 408337583, 895820369, 324789553, 302488678, 542524353, 550564952, 545591336, 383783500, 241165597, 517513782, 524779774, 342429826, 275242228, 758559939, 316472874, 96219333, 111322382, 739399534, 114283473, 137166015, 377193869, 728543116, 427038991, 541264707, 582131381, 98722179, 887524273, 987626493, 165063500, 985073798, 699893197, 917881011, 55576774, 47418513, 934711848, 250596533, 604940034, 596354087, 889495092, 400883918, 309547740, 105601457, 475073304, 254132493, 210431228, 202057939, 437472417, 568771219, 427105269, 720407778, 373101830, 331471998, 51838367, 863688588, 227942747, 69455917, 377928118, 699598124, 744195419, 784967560, 335260124, 543502417, 215209827, 617115046, 29757783, 93311729, 978638352, 356149727, 574961103, 335870881, 141814507, 34002254, 47736348, 983377182, 891321787, 333354979, 801327675, 818563921, 800555958, 862736316, 140195727, 734152751, 12472764, 775869066, 18638373, 344783593, 817587252, 28975286, 196839409, 548184, 305852302, 657547598, 262798795, 413032665, 955455111, 913339266, 844566799, 290939624, 893238651, 816014378, 365682678, 529049175, 584872951, 950160367, 721031153, 540409332, 359207958, 239886424, 807211014, 227957170, 574891764, 473030679, 667505279, 905482016, 371897740, 759047223, 227532201, 315683370, 855989563, 91808598, 443881816, 911370144, 349331294, 613428579, 236418677, 615720526, 125773613, 633255466, 212323199, 78585983, 226025437, 982860143, 38017436, 626869660, 393599150, 730151090, 490881659, 58932972, 485217460, 91124667, 134381317, 700143205, 956660881, 238510547, 603802290, 457200876, 49619548, 789859149, 281147300, 621541272, 963005123, 213189050, 92187652, 747627059, 469658790, 610197414, 197453591, 949018110, 220693762, 704638572, 803483136, 62562887, 763249074, 160535107, 899001616, 815257496, 357421509, 377327916, 180850543, 798477751, 24835817, 113828251, 793468368, 804759796, 858524861, 222973968, 73154680, 872794728, 598656845, 435391072, 933331273, 99974138, 564875103, 759098863, 212938849, 568704071, 461091735, 581553072, 839331250, 879009297, 506607817, 655607424, 118941037, 177733202, 743700168, 790958645, 248398201, 362961356, 444575185, 812262363, 507728828, 702244949, 764449969, 327164259, 749039199, 767293570, 894969893, 240704508, 979931472, 351683951, 256390840, 370740728, 838643541, 456996131, 632856509, 363843449, 2216755, 696792482, 536025976, 586564508, 888709311, 999605820, 528579306, 769625726, 667487646, 681167266, 720674706, 599557549, 253856267, 411553754, 445501027, 357118892, 28472119, 875523387, 334003777, 534833324, 217471257, 834950312, 670908483, 337508362, 642306618, 575657894, 636447964, 746614902, 326214147, 937651393, 205600090, 501649259, 264208458, 465982092, 693919450, 512784603, 573577874, 156264536, 275126165, 8275935, 462520164, 945226108, 686461680, 325651129, 472026850, 472384348, 7805562, 681110120, 820177657, 272556532, 842105703, 433736551, 581936143, 40740889, 111099756, 70835949, 222860785, 74433951, 423094029, 79671973, 230400767, 892234017, 273893231, 830738359, 494157140, 721231605, 500174465, 110797458, 723298910, 190892154, 756641766, 694554004, 540977295, 376513842, 35183184, 26220324, 355044804, 580228980, 431768358, 488319586, 768996392, 668080533, 989233701, 278925851, 259897757, 975362650, 352699276, 223707548, 265723509, 94493760, 878013939, 517427197, 501173554, 76772771, 615173959, 862407790, 941947685, 786188948, 787538055, 526082725, 405038957, 24177842, 396452139, 89368400, 571530493, 666527234, 341482633, 112322852, 916030106, 708565932, 963119891, 874245104, 630708149, 940032387, 329283066, 249566184, 118451624, 984914692, 727148914, 422242299, 119582340, 757183335, 926148392, 451722499, 274150693, 336713834, 722106735, 338784209, 915110058, 302394311, 526733133, 969472177, 732811116, 373488996, 431928003, 765226594, 724366017, 560255511, 516874130, 882920409, 443028183, 461282979, 698800800, 917285643, 707439597, 268302462, 737024400, 71825918, 158225008, 133529066, 478003726, 478094666, 730284609, 956086494, 159933664, 602170391, 989323918, 965104801, 35670433, 738269230, 594362728, 132739752, 715397181, 148548444, 411555774, 460253617, 196380562, 55993539, 521458552, 113840630, 536441264, 358831401, 824691444, 617873317, 263041019, 491031851, 85035413, 296321264, 703273562, 547025981, 323038547, 388915668, 322013892, 953479618, 573439790, 335705190, 635572740, 66192784, 799238090, 622503245, 487836844, 558379526, 20780752, 193391989, 237876989, 745865795, 175494231, 37555059, 902284383, 413907760, 65063961, 484257006, 358463236, 55737518, 771753689, 177012311, 159534726, 775001072, 276884918, 79065073, 146958408, 726361758, 49234455, 371574056, 553358761, 638187517, 225215064, 488875979, 721941009, 592344339, 916530741, 977711490, 836159214, 57970723, 634946090, 717105688, 338665225, 530782719, 217403247, 93254487, 278774973, 36049412, 45679997, 110102100, 354611918, 365760517, 960159472, 548650744, 230144312, 597541080, 66790925, 616045221, 656136972, 594075633, 635477741, 464282657, 78356072, 402673171, 363573539, 599303219, 782452454, 417651035, 960051638, 346987383, 399625267, 310362782, 599661617, 38351027, 922023422, 246507964, 134312677, 257147904, 770631258, 174000068, 861477341, 569564868, 671396827, 496784542, 988627087, 711065168, 438853866, 871960292, 547935579, 670358884, 17251125, 56764830, 828324579, 695089673, 251654631, 605213800, 47430822, 999019087, 632353996, 944757325, 428164488, 632733322, 329815669, 209536347, 168084310, 264871800, 959042984, 295319566, 690109179, 168695387, 479623191, 409922100, 10250415, 753899292, 927464901, 969460835, 633489737, 11215839, 370184481, 943846160, 16325015, 927721369, 152889009, 595697618, 42546141, 56761125, 348515622, 911185129, 160216482, 305212516, 924119457, 281989837, 160187903, 606172922, 296116151, 796195972, 206227094, 676233205, 312384875, 55961684, 315668903, 17850090, 638331588, 407705514, 143181071, 359468388, 589428767, 562825544, 890881884, 93109190, 52130843, 788496190, 800543848, 496509777, 57956870, 141776239, 382149247, 614226107, 858804715, 658907226, 785462462, 548283306, 868232142, 605287734, 858822345, 573456097, 911312540, 126468775, 811503140, 24308769, 935392938, 33322147, 446395840, 694797764, 382671669, 394126008, 271110076, 979918011, 599901870, 349272727, 722316178, 461401409, 561291837, 343789407, 821175965, 868782660, 292018996, 18770777, 493579927, 305361764, 323413259, 346363929, 601068274, 547311140, 771756668, 614885908, 940214310, 530250210, 912920480, 993934951, 6265973, 625114577, 921422450, 838952948, 445870429, 134244481, 128730168, 756722095, 309108109, 618419673, 660569067, 988769160, 996375062, 123541133, 768759054, 833369431, 37727092, 77449146, 115353629, 809189981, 791044226, 856354807, 307250188, 549545172, 882815954, 422739977, 217304884, 611834233, 637326925, 848223807, 616137335, 929940458, 589308292, 936230437, 844793931, 579390514, 677635113, 762245026, 73574120, 848959137, 103665135, 488931541, 246346405, 925805049, 405954587, 46282007, 664371372, 192759699, 465803988, 277638479, 585451385, 525374319, 538204347, 923719258, 158028742, 536932082, 659548293, 707474193, 782412812, 823260897, 527882541, 385184278, 847380141, 399561244, 83076117, 725285638, 678713145, 436271658, 873482751, 909628774, 875275874, 421418802, 856818560, 122238451, 57915934, 527277572, 251054110, 631939456, 235236476, 320186036, 524464085, 74439796, 522209249, 815757739, 381951287, 600062579, 749408051, 841315842, 936107146, 365828247, 491240285, 415608833, 426395217, 18212196, 785445792, 464838673, 537923817, 576191992, 84067833, 903729163, 443903021, 346668831, 176742942, 478237905, 703853709, 235772549, 845019388, 374522687, 555509340, 375096457, 95493065, 831289088, 291566018, 733191877, 861677507, 65327936, 822734920, 309909449, 568004012, 764740318, 557704095, 289566051, 124555032, 5276818, 334011482, 33275389, 328660940, 951788708, 219605694, 674990875, 79919695, 529947382, 492848129, 405049906, 916600465, 81917405, 699884596, 423939227, 192712924, 834851533, 955536764, 834248121, 658093102, 522228354, 628531249, 63948908, 910208642, 925652388, 608274854, 287684622, 354724678, 765008580, 563063053, 113382061, 397186080, 427560811, 607994863, 910811498, 831440682, 889761968, 179718466, 707816594, 829511056, 546589263, 167687745, 138923082, 54840422, 650520112, 491094799, 467384055, 536679183, 354110483, 216551143, 33891536, 766890654, 436731266, 402819561, 514760700, 6109064, 30449093, 816893322, 495290878, 51388847, 36663290, 31759515, 274054543, 419194230, 470091783, 49330406, 693541537, 845965013, 825290173, 180640972, 737245021, 443737210, 154951533, 308307527, 165588734, 845684564, 573884777, 486243976, 498837382, 19695713, 427428452, 898211281, 585453770, 386755330, 848528823, 593882392, 703146453, 484858322, 311317488, 472144423, 194838824, 279228642, 136753107, 68167459, 869213530, 217904147, 566051958, 47408775, 292123772, 89664772, 985043050, 363604069, 645790951, 287044443, 691189021, 463218398, 679338077, 583321243, 709726853, 231159648, 829564715, 951939330, 577870127, 829450703, 143445151, 454225399, 48709642, 785803277, 986252388, 77702624, 603236635, 671718115, 130442965, 99758170, 858719979, 517160968, 900099394, 878161626, 826437855, 998857845, 194643822, 505784954, 20046395, 511566279, 231709344, 811382068, 642411816, 832990484, 99659142, 506860531, 977017318, 948635753, 380586462, 707351879, 299956703, 736090327, 758301100, 600503646, 268707211, 626966846, 167772420, 203438442, 566464207, 124615836, 423170678, 682864572, 275371068, 22618705, 703273059, 417955042, 70032202, 118836433, 208538317, 812331708, 88353179, 781525001, 439052757, 283407064, 397982144, 334027532, 629628673, 270181054, 509930463, 177699464, 579301744, 434087723, 247272936, 701262604, 60397663, 214730500, 769062713, 932491874, 612781788, 841306808, 928659905, 875347768, 699394982, 292069721, 91596423, 346262425, 884653204, 973325796, 822978292, 663106873, 164468714, 942088715, 550759932, 98129688, 169108238, 430909857, 853785925, 512125390, 931203052, 192337154, 977976736, 785036092, 219087966, 100157614, 908880940, 409722092, 771688257, 218159873, 8418683, 697539260, 611610489, 78506401, 640193905, 814297941, 436410104, 276249243, 364452453, 230775087, 136349039, 957237297, 726885665, 526570856, 752139328, 80873387, 135672832, 301961042, 34087503, 16821881, 593909355, 889233415, 916088279, 623881534, 710995755, 489308471, 120937170, 437334406, 931458649, 227430100, 709098939, 183488405, 72792385, 502203471, 322436677, 700114741, 442690953, 854059166, 403913103, 573386399, 322532435, 638105124, 866323134, 931037233, 700681418, 386258889, 452867364, 376236469, 739418858, 549414863, 29858887, 249766817, 581214415, 721501897, 122293768, 121228552, 292908799, 607448196, 764305071, 825803539, 759907594, 315216832, 525328984, 79611459, 783564636, 666848587, 718736660, 273129423, 311663696, 505493731, 545441944, 934104720, 912920876, 643518317, 102552504, 832441239, 997897799, 47642648, 506343709, 217794004, 676144589, 302403049, 306800389, 265919820, 374863286, 273220066, 196692585, 568288050, 112454784, 704026112, 820737063, 823760411, 807087713, 327901149, 486377352, 652795015, 853411512, 182783965, 909507526, 180711925, 762077774, 303974940, 203323642, 775422546, 507225555, 662136865, 6738917, 154936523, 504108699, 20958011, 905729249, 82188064, 529635468, 720768542, 182996754, 793663921, 428965408, 523106349, 648545451, 930881627, 39924523, 40499957, 554110921, 626747808, 567688440, 312645270, 44584882, 620480486, 502327902, 130880488, 620694174, 965893733, 917464563, 740076884, 258254956, 591754722, 473387823, 411982919, 633737428, 956991853, 342183718, 900892530, 962770486, 237471627, 417388470, 378507098, 570508686, 417141838, 378666202, 44789741, 326855089, 113760620, 119455044, 10491243, 145111799, 114690467, 306931757, 108251931, 252300787, 352875816, 968155501, 801715414, 724573086, 506881303, 705016313, 618760624, 2416789, 15396409, 566454503, 436913796, 818599674, 30901323, 925320075, 678065624, 973970803, 739198382, 675031675, 441162590, 719588571, 563453196, 609395080, 164279981, 826553713, 524322494, 967791482, 163511391, 155213779, 475023217, 26329551, 543149877, 834875704, 606640152, 79701247, 678451866, 595437835, 612014995, 959194639, 884143074, 523234555, 638385722, 665968246, 131246719, 283321239, 213719862, 247678745, 318522884, 14856084, 932804288, 269631398, 759683945, 61153403, 67020659, 110591671, 222778250, 666831535, 910695203, 722881777, 675569715, 137781564, 505353374, 557187752, 512907190, 294716949, 250728925, 989955148, 325185107, 794853549, 584055546, 881890956, 968793289, 550051138, 756866792, 273078374, 891488987, 406091026, 748471644, 589282527, 191654326, 159956254, 564045290, 823284879, 647862112, 660848646, 509217824, 494192646, 364819699, 916608562, 296333716, 748999425, 653007519, 993327289, 848107309, 564628873, 513000711, 479927923, 364729177, 22769456, 642543168, 873594365, 733867788, 503719482, 92737775, 439027937, 513445878, 682265246, 624157218, 192278901, 471633060, 742825418, 332979678, 982231659, 659078827, 215832323, 568743257, 851158261, 999354081, 278318786, 457413033, 837061118, 509482394, 767761702, 731554703, 789576486, 915375469, 692022110, 690710623, 933149505, 304407096, 689557369, 237992824, 442354931, 743724327, 54676738, 102577570, 970589171, 123390121, 531616117, 439524589, 806755578, 559786799, 661387224, 353272419, 863567878, 127798719, 404097036, 986087101, 280768106, 656853789, 793720351, 583201899, 875520832, 51498595, 959286395, 812663540, 132863818, 791330060, 205025687, 602518044, 189529466, 977969980, 94459151, 668264168, 637356217, 67706140, 293582881, 413924389, 191252778, 925806627, 763512590, 452430745, 238319395, 328906275, 844157094, 743071706, 217647065, 996527116, 229661635, 953914586, 463040888, 310439782, 34433326, 858813859, 64121378, 317980396, 627508415, 796234098, 20323570, 623177083, 408423739, 742627246, 145536930, 100285974, 395063048, 783814233, 59467402, 19987039, 959073257, 472363783, 739392442, 503988848, 163779530, 451435659, 837897409, 103197842, 67765461, 60837715, 342876810, 336007185, 777874246, 706668982, 479055520, 447882505, 8809307, 212311978, 10790118, 970149578, 498546578, 245621590, 821518259, 805970582, 263706187, 803627053, 968150752, 385635497, 362458611, 43131100, 908553154, 867851531, 884619423, 591892310, 713587488, 988946601, 127263447, 539094416, 599276782, 659144169, 702979611, 346829331, 441795657, 792319818, 171961094, 236680694, 525793883, 285361908, 833667169, 34654606, 612526245, 218289644, 932342984, 99952837, 945238473, 654574515, 329139376, 682960113, 520829676, 955222381, 931424968, 157983956, 162273228, 717997769, 783444391, 999855926, 893547530, 437453422, 499281854, 732080113, 986995264, 167293382, 239047252, 665763039, 435221465, 277245023, 312767110, 766018110, 587157035, 840505126, 98280197, 229095385, 675163900, 7386852, 87532752, 635125709, 554474547, 525672296, 917970588, 11443414, 638444797, 598624820, 668969177, 23266974, 973495168, 628917669, 741409032, 51598815, 604430686, 367201030, 269361533, 566739145, 665547669, 115625420, 631881969, 509486220, 774728517, 321175506, 136168316, 192930065, 541352615, 511931163, 438682048, 748685529, 313799243, 753799194, 955659598, 974522431, 88081834, 476726915, 178816396, 132115938, 420611673, 207959146, 578338244, 576637748, 250817311, 864284931, 655161773, 211147056, 35843851, 490607515, 753801632, 64262206, 102684114, 826757904, 283276773, 341417563, 681424904, 381701499, 938313309, 36587205, 109445044, 778425006, 750868328, 506026555, 910628915, 224982426, 653669191, 9179817, 581634149, 571262118, 303300894, 638227844, 270317184, 269646356, 679171244, 197825918, 861892700, 625977139, 6964641, 778938995, 50794234, 364439226, 175506745, 396161332, 764831051, 937805853, 668596314, 620270267, 65761163, 703906482, 34366292, 122757229, 416082915, 479216585, 832702982, 509249038, 966179939, 590719850, 165470549, 250272954, 767655757, 282843884, 862295668, 438423906, 240909259, 730518851, 490142749, 326324831, 394592799, 964597993, 864465774, 129492586, 872778574, 179689726, 770941329, 608503950, 348866529, 837774257, 194919060, 9437885, 721964126, 490239775, 469135529, 130668593, 904552239, 840882231, 998143929, 88085817, 181961158, 836399841, 571429949, 429411492, 604995118, 311484928, 178749476, 12892435, 514750855, 981516258, 949803911, 975059858, 949915112, 737652963, 169425691, 271053765, 276104558, 164624188, 591889328, 320910312, 273825882, 158088149, 279159392, 830368972, 418551202, 373025015, 189031234, 958790222, 758915474, 63850957, 454008109, 504066675, 508679694, 392879675, 864080206, 987878667, 22867196, 50226211, 278868928, 990415267, 405471239, 335731803, 853778391, 576749734, 979725648, 879936160, 658209802, 640390398, 410208882, 85554768, 421481073, 872844757, 909136992, 212956724, 825346854, 905350239, 285971806, 976931990, 663337449, 203519690, 961769174, 796649615, 158806296, 742800165, 827694180, 26559346, 958855042, 363828870, 463724989, 278310912, 274910274, 843935868, 805371550, 186561279, 185728557, 219083659, 817920915, 925689206, 212941045, 432598650, 600652067, 842855656, 22473782, 834709449, 578422290, 137217753, 452347764, 554432756, 119419428, 152548376, 593347551, 493933735, 502778249, 791332232, 840776510, 679425959, 821962652, 731241492, 22619431, 695032010, 71989174, 306108483, 861121367, 217351283, 251272732, 840929824, 279563215, 485414665, 521027435, 749439297, 22715054, 132146450, 535376111, 172526378, 184845810, 515608665, 379409315, 941029934, 852139951, 44584496, 946225084, 878944783, 334324371, 590167450, 654412148, 945280025, 771403200, 833577166, 67885549, 162660784, 328930657, 125003699, 612776268, 684599673, 367425318, 571552556, 642247780, 811829084, 55221258, 687194453, 990087760, 270955382, 149604069, 200123651, 879935964, 572201045, 748222880, 383118578, 517393649, 392945652, 778813400, 913953875, 780615377, 305862597, 810668457, 822288939, 728877423, 457031254, 248116769, 78798857, 894724986, 341068877, 980585188, 776129605, 767281333, 144023823, 69504337, 845035941, 492657552, 73207814, 505706156, 243243239, 334636675, 954320202, 567389390, 482522287, 930180865, 825854078, 829201295, 422561313, 826496409, 28636623, 368731985, 314643282, 875965227, 111470736, 761904779, 274763716, 130221145, 784367923, 538596337, 250434430, 158870183, 303084754, 143392898, 80916499, 833083285, 166823857, 920070660, 954750241, 831258239, 469651847, 178088176, 809551418, 319300430, 682269008, 909800061, 800555957, 630565504, 639672756, 727330158, 709740431, 438176999, 843933686, 455695437, 859756389, 5796298, 349210376, 894660391, 741548284, 458030184, 536597890, 750439623, 255978424, 171882553, 981843785, 349136029, 207552884, 428463842, 551810216, 807699105, 30415878, 484221727, 595039453, 263773983, 581152495, 832525073, 672649455, 485934588, 775450896, 290393767, 964749709, 179105761, 769713492, 653011588, 114753059, 57318721, 68659613, 135190263, 913265154, 817631016, 871398952, 807934835, 130827051, 284319126, 455041596, 440228254, 882207953, 472199579, 175205383, 431268081, 859384541, 726407004, 492500884, 605654621, 459876512, 844100363, 905487650, 366438357, 506471258, 149287669, 905294375, 411501801, 450225560, 479709458, 620428096, 836275816, 511419759, 259301602, 383322415, 432341202, 215882916, 397770932, 850590997, 650275278, 756556649, 300310761, 764215704, 226846973, 95173446, 283717682, 648173109, 690668578, 917441398, 17575413, 474688732, 298029785, 86320917, 369502826, 542831356, 545743885, 841289350, 783511867, 527327846, 156174296, 486483286, 36026679, 274041628, 968031292, 583424107, 679163547, 141441347, 468092452, 383521958, 610815364, 501810038, 557610884, 57226197, 690978741, 991532447, 464239726, 233696478, 176080371, 872428102, 958904406, 18017326, 592098343, 822259426, 99856976, 755434751, 308345578, 479461278, 511024191, 630953252, 49894651, 811148529, 493733572, 398483170, 753137451, 393301757, 849963772, 52730059, 690140356, 195924384, 187202281, 784754781, 804322231, 754115370, 260067489, 334584715, 553382200, 443450573, 684006918, 425798640, 387581570, 483267611, 171882706, 731989510, 856138920, 587969594, 882782638, 236515097, 966105258, 600478312, 517969724, 414225879, 734737205, 539027569, 822745155, 219128590, 190980985, 198371222, 984987356, 207827629, 20992102, 376984638, 633721511, 693597091, 938791060, 895847790, 395174103, 931616637, 398331033, 965283552, 977406030, 829551037, 4801309, 496969418, 151679923, 697269379, 521883181, 8748408, 662993020, 441545392, 708581851, 49820919, 770905379, 366979386, 613130952, 363933976, 935224248, 80417773, 393026022, 16261872, 749740606, 515159234, 242529245, 233892468, 50482462, 122657218, 448795102, 723477682, 140546591, 947617519, 233651019, 438655273, 276397493, 153636131, 195520379, 940748516, 113038492, 222097702, 382345631, 35037906, 410895532, 473989488, 850830014, 129126315, 707855026, 34619546, 759878935, 820898811, 549323815, 259699173, 812058432, 650250511, 690052964, 701272419, 376111281, 55541672, 741953212, 483413668, 633077554, 972648667, 865182641, 586515671, 936083819, 404205594, 970427750, 620048749, 208439677, 528291855, 314645759, 498195048, 971044479, 377160636, 546143046, 98395227, 542103117, 493094396, 514047993, 428127320, 443932175, 564281082, 674704577, 971169262, 907793536, 399206981, 704775057, 585054038, 484856348, 612956160, 816132067, 819747858, 592919646, 5989927, 687420466, 462707753, 300985703, 806360371, 227898719, 873183093, 434168614, 811563798, 365865146, 318193608, 513842346, 452483811, 368956459, 347347378, 633595364, 6228494, 470759808, 983908225, 125321019, 741814485, 579434226, 208901377, 127253749, 817583353, 878098151, 34823705, 939879626, 137558661, 997758135, 672937874, 350210433, 156713066, 500651344, 89712970, 272598786, 112722209, 682176197, 481002139, 124156775, 954019919, 628654348, 636534296, 657702623, 425090392, 590647014, 865436448, 854422117, 279055881, 896413338, 303678613, 606872378, 575811142, 14097120, 42389412, 27195835, 911809632, 178760679, 388070636, 294349849, 333483026, 467201658, 75452699, 633779876, 477296949, 841093876, 705982463, 951864769, 294045877, 128580108, 968141302, 668126894, 465398028, 481547690, 730140753, 795022015, 9366052, 617001291, 161315906, 761532055, 198073595, 770611033, 761962841, 245670878, 960405086, 34891917, 904729273, 323990374, 390600661, 348930325, 76891711, 742303021, 760813398, 684649067, 980679238, 576483132, 967510002, 672872695, 899094652, 633653806, 808412089, 325357936, 191770420, 30363877, 965473326, 750046900, 957060149, 699928340, 656961759, 206884064, 654446689, 251858829, 54794110, 61748494, 483806899, 86028853, 3654578, 133969311, 433688323, 175647327, 520129763, 43729573, 982455008, 150277621, 183259202, 359204421, 920415229, 422617454, 252714444, 922450343, 633399289, 618142280, 82897951, 216752840, 913327223, 644649938, 104264293, 747394016, 884144496, 942862075, 696323425, 567615652, 397812061, 909616852, 730520162, 142923116, 361162411, 261861688, 56604923, 472035997, 936016743, 916841452, 565385271, 185409964, 396383179, 223487609, 239261136, 369586962, 934072282, 587615126, 329627509, 875212266, 235743164, 611131605, 477271146, 569169619, 231884176, 606129556, 134695630, 41570614, 359774355, 427240724, 722841406, 664995741, 785739428, 97804284, 575353740, 677956140, 984983602, 780542193, 762736347, 590956742, 580031933, 815082539, 370262625, 873156641, 777787875, 345783474, 507090547, 470094980, 203166988, 373961021, 566585441, 168828915, 107495946, 108075973, 816739055, 467994824, 438217653, 524648042, 237699748, 971252258, 629811137, 478352669, 679032509, 160448957, 810778900, 860949063, 41460396, 624452737, 291360350, 538371758, 145314417, 340783257, 639853270, 895596034, 80203845, 408760529, 867609298, 856309936, 765902062, 607247061, 695804953, 154083131, 256682593, 122967500, 34357695, 105710732, 278211725, 511598862, 689716131, 805316414, 526239088, 590120308, 497162397, 849835778, 713939659, 27706041, 305521914, 26854282, 698123545, 794683886, 760497071, 489774239, 53651399, 632998730, 631135611, 184719597, 188733914, 943863901, 358815477, 390081470, 702972398, 659274012, 113317461, 538492171, 284936815, 891754318, 779397322, 857726401, 56830393, 819326574, 355010624, 575754637, 284235991, 319570823, 573079211, 925311383, 355422574, 783090816, 466518536, 449181912, 918722066, 800244365, 339532352, 210364560, 141037114, 529501605, 216631180, 189442294, 419639916, 435002054, 792537938, 212043895, 488532420, 865053162, 906716420, 604137240, 175238897, 884658828, 961582792, 174714252, 432326132, 966571022, 935935429, 33828041, 852041882, 291608219, 774602687, 104072000, 947708990, 828447272, 350100855, 614107629, 905097788, 228043542, 833693784, 353979751, 766338135, 967883999, 78676913, 621883883, 216122238, 555852941, 699967727, 222023318, 776477859, 263606807, 964911173, 796277376, 390322286, 333874821, 418977676, 483662934, 821437853, 695553193, 942989832, 941767318, 641716502, 280054820, 597471705, 931030912, 552152359, 7357720, 637331234, 523159970, 333440956, 982067427, 194573339, 906205346, 513054944, 737467506, 817797046, 446009807, 863240725, 914878502, 723839775, 229084213, 153017569, 210700057, 33715509, 115546036, 25932320, 636721632, 419311347, 860255925, 584555773, 994507746, 885066880, 318734714, 684931715, 372742357, 832045796, 802107415, 268872606, 859744178, 66300388, 555071293, 219119569, 309556522, 657431594, 658631874, 929176600, 970860260, 398012950, 86346441, 262872419, 283925630, 270983892, 449749279, 620220112, 729890999, 291234825, 518709535, 931323992, 106056154, 761945077, 395270459, 445890684, 6871582, 434796824, 81635923, 223940424, 589611770, 60594576, 335554954, 61272695, 148457394, 309559207, 949759811, 213823302, 851297001, 924337403, 365970618, 386436212, 855151715, 706867443, 396884616, 164738468, 539187743, 326010419, 618438310, 175474676, 262603254, 833676476, 696091586, 309683748, 471819350, 104085709, 673510858, 298154793, 545051353, 462245510, 498384487, 175993990, 442883331, 825913798, 281836603, 40901168, 196538300, 14559273, 683253860, 938317469, 369653247, 840213449, 994312428, 295805110, 344010286, 778222995, 747459484, 765163099, 398251475, 2764359, 906231392, 841374732, 902466732, 512331108, 594270891, 317593010, 722477700, 490177837, 226231433, 498975971, 492152800, 122851047, 255127276, 729926868, 311904649, 742362298, 479088109, 889329059, 369651773, 216677683, 852744732, 550654743, 897909975, 50056430, 976578042, 898306519, 732550073, 589531444, 972509850, 326285011, 555771132, 810209296, 447473278, 285792660, 930666322, 782691714, 115388437, 881825021, 923263919, 137217030, 81055805, 552641347, 917408609, 386148707, 929471501, 321607599, 84029617, 161605610, 87752417, 606038575, 611323561, 480685096, 832269135, 723109667, 578628205, 133988708, 263791081, 364300926, 281974026, 268551029, 972204889, 820291250, 583981374, 622444915, 959697889, 12643166, 737857547, 44764333, 378503240, 502986041, 784702412, 285816657, 384231906, 722320791, 411774531, 722353803, 657159196, 117070836, 944546899, 717425608, 549472494, 960518429, 14898641, 679327424, 265638529, 454057009, 371206389, 961197520, 287552688, 392118032, 4883898, 112592411, 24951202, 411349641, 637556859, 425267309, 821515495, 676752805, 236781346, 438328380, 366884663, 983016445, 551260607, 567042811, 816893785, 296720208, 424867086, 394723147, 229494697, 984769025, 998070159, 540644571, 638829724, 294255191, 18284747, 820491441, 491755562, 999311965, 214763565, 242744425, 904251993, 385140749, 865252875, 72533987, 662473874, 486855925, 407888231, 592945573, 506964279, 508655557, 768341643, 263217881, 89322541, 664291514, 823863881, 232781, 403837898, 87532616, 539704332, 12522299, 649362100, 285770831, 673868849, 604201049, 2708235, 262428793, 948930235, 273657867, 956044062, 846999808, 97034182, 937751387, 552877003, 596711476, 638755010, 859942609, 922050100, 659006385, 803239564, 617242043, 815199422, 128967492, 660051357, 95206958, 302447176, 343264510, 998569124, 466324446, 377847954, 450549466, 622984326, 86555242, 364514768, 933257282, 858764124, 857590707, 732799059, 927282076, 399646349, 613301035, 754123974, 944041265, 549973193, 563996227, 917666883, 386812758, 796559134, 552726402, 718809059, 524156786, 106683123, 793305498, 720151957, 837567831, 941307088, 250723791, 396393864, 872007441, 351962262, 614192063, 415866742, 296372192, 969765167, 720177557, 352915219, 796930970, 8617327, 201387534, 379949883, 49609947, 424451997, 722636357, 107089626, 186472168, 734829552, 733214426, 774210902, 681287227, 387052438, 668400535, 261726265, 671690029, 403785700, 207655674, 851554383, 996638653, 313947906, 503714724, 83405367, 923462367, 580977380, 566734190, 136741266, 681715905, 48941474, 800870658, 938066308, 138222969, 241251062, 954209998, 61019611, 512981133, 499797894, 681749780, 648471619, 803133417, 63808241, 185890599, 548518720, 741217472, 811019279, 676097245, 746738089, 589086059, 73827457, 640275009, 842560223, 828700160, 693265947, 214282394, 54418960, 60368956, 423462634, 610142053, 840322604, 80325594, 526742330, 341576748, 567585106, 420677448, 719731488, 976674705, 394791953, 462383265, 356181372, 290662478, 748598942, 943203473, 727084264, 442445364, 336776153, 854944937, 716042639, 671691429, 750535783, 245140257, 791099968, 571246774, 599180406, 530190239, 884033307, 698605572, 933605655, 42335382, 545709297, 939679238, 164532253, 915067051, 761003800, 108113478, 104990914, 931660058, 89576232, 391052029, 210468173, 670646264, 434310475, 952897229, 224806560, 222986884, 849690455, 813906271, 548942464, 112871517, 513753228, 781398003, 321538135, 295100041, 638097686, 425679185, 235065810, 849484443, 484056076, 777231276, 765778463, 367558028, 186173140, 125505844, 272099644, 994815320, 472934083, 990474216, 314525737, 253226850, 822167898, 404356770, 499070865, 92766678, 523281194, 258812723, 609387891, 693966027, 817442119, 798654910, 698552539, 464366030, 397418498, 929421026, 742466873, 985742834, 136860193, 805846709, 697483484, 414296276, 179328687, 530977974, 696798347, 926342244, 987934313, 183872911, 489184921, 388415639, 611537587, 616305461, 316397924, 124811265, 562495894, 279282102, 894616789, 585753144, 972743160, 780888287, 490620340, 722044660, 471435976, 566270748, 824816264, 978547594, 739746547, 960265796, 905813453, 861041090, 290481247, 974647477, 234275258, 406176655, 812357528, 332526181, 403281791, 759584031, 314075622, 570478528, 44832735, 794934941, 322043288, 645724774, 143818744, 756413916, 7776126, 809190208, 77193308, 325356732, 588486959, 279093409, 367798911, 888709348, 852555214, 912086750, 389773058, 13204754, 569841391, 605876888, 569442891, 83631956, 401137297, 938554274, 28334601, 775367805, 905929070, 466535994, 795502922, 828901959, 931363130, 664806379, 447220211, 797271066, 387611948, 392874921, 955637897, 157753454, 749163898, 979944120, 261694802, 951460161, 97249705, 497009367, 56302400, 708048139, 496614643, 59556103, 254047389, 57999747, 711175364, 42392900, 763078862, 355052725, 758759122, 72719546, 659363019, 497376738, 730709015, 391566232, 56332878, 923069625, 514604751, 597876220, 127074870, 185924719, 198561236, 679720441, 752432147, 924025949, 345465373, 934390687, 867746166, 630474530, 434630079, 218440004, 21824737, 599259976, 961363252, 398344214, 199677645, 945019413, 240914342, 489844621, 886995255, 367900278, 103570734, 373362189, 531465061, 133503009, 953586097, 988486603, 179292626, 490612826, 162616071, 737477974, 735604607, 907375240, 852800614, 193311382, 792151422, 526853936, 873605146, 516218244, 520818037, 559624625, 916582103, 384226624, 187463441, 753367726, 901268768, 531496085, 788278005, 851150411, 388488237, 508394591, 79293494, 872148651, 670305597, 946797271, 586541005, 440592801, 708448533, 518538843, 764833273, 804384722, 845084219, 754417683, 568653535, 192866086, 663798935, 59903643, 957806300, 134799742, 405259946, 878098442, 505230758, 361131357, 989607415, 862433566, 616711722, 663278209, 577556286, 697780506, 802391572, 878816387, 907597556, 342680066, 363160773, 570116807, 859887511, 967545467, 748406833, 745951985, 469448976, 461240296, 600424983, 539157184, 189940643, 515984268, 252879045, 273108200, 485211722, 56597135, 566193671, 653470761, 508193430, 164238202, 601339648, 972694408, 156372739, 579221273, 437669543, 66928754, 658099380, 339769261, 61199967, 992420677, 180141981, 579727546, 372625060, 893614826, 978140084, 108754822, 625977969, 120855919, 858583275, 210301372, 75765574, 799981265, 946659739, 312173750, 705014954, 345786761, 455959124, 683848837, 375075746, 522944837, 262678737, 154369069, 1932397, 47629132, 317369897, 891543789, 664682444, 589167109, 435268586, 762869958, 17818710, 411088516, 934001886, 979165516, 282732512, 842246650, 993340850, 765425655, 724804372, 886746082, 751827670, 353071356, 431048081, 389815687, 512764227, 904988474, 61378335, 799552355, 554357712, 503619173, 618324717, 305713871, 969228173, 8971801, 315780447, 593087085, 46082320, 569857061, 448123052, 71240306, 60079330, 958872018, 677413172, 215903261, 550548849, 496138400, 698585358, 316917204, 334406884, 706566408, 461931047, 159940101, 810112699, 770360568, 234304677, 628994578, 84884633, 831492234, 41824528, 344231990, 341716178, 334146947, 968411162, 959042899, 518922281, 43195485, 670575844, 469854356, 502097074, 103116892, 894314474, 900852041, 159816184, 183904483, 996918418, 647873817, 603415973, 651736262, 802134685, 464548165, 668414206, 223263759, 219937482, 74266175, 703690050, 550268367, 675859109, 619558211, 539879687, 331984098, 334896150, 254264418, 954906023, 436369613, 644734969, 7952555, 323748106, 444453808, 489120966, 205504540, 371785160, 962621321, 314572748, 158443756, 551139381, 539092408, 535157151, 453095133, 191986808, 139927512, 415532646, 578269353, 786938330, 133867599, 112291463, 501971306, 112572791, 271482219, 426477566, 334957912, 731604744, 283123620, 624530577, 145754527, 414463439, 835762552, 569253204, 647021417, 899611019, 648139483, 783546271, 722905929, 406870660, 220177151, 257115156, 989677424, 638564669, 794084726, 163248205, 494811602, 485359753, 878178186, 905114050, 237505183, 413421504, 630267926, 308994482, 52808018, 713243187, 886124452, 375251636, 414226073, 40309713, 470177119, 557420156, 58370453, 426761388, 814100151, 217594056, 768130432, 709256511, 936804933, 812388850, 473934854, 694624081, 250368687, 55473314, 320914611, 346005728, 980124676, 196710866, 495497961, 316320903, 222841387, 200414894, 361871595, 570676266, 951820647, 232363225, 646297520, 659833850, 239985993, 302264576, 177292934, 565641901, 275425144, 962329430, 695027910, 91654031, 119851400, 159195441, 161557392, 387833074, 983930143, 718526330, 974397906, 991245105, 464544522, 510965658, 660361392, 690958748, 794563892, 740799425, 484560525, 4975228, 890130447, 850649030, 973278645, 883604377, 943514809, 422394729, 474644286, 188600423, 909994864, 387985365, 836100452, 980216127, 35184911, 89584203, 41284190, 809588584, 392834609, 406053847, 262945161, 368719118, 689543145, 723313341, 594833771, 854113230, 801962759, 924263868, 179516333, 689370038, 619129435, 463288876, 940310939, 850205608, 294426239, 410434640, 255788608, 202280852, 979943287, 413416606, 670548431, 601842811, 297768388, 593535978, 412553773, 387847945, 696058314, 120000101, 160892382, 249870248, 817268310, 352648107, 603015120, 200726343, 757294834, 488465117, 877828288, 193027225, 816160229, 918698090, 877723588, 830661574, 947067086, 487237879, 412602533, 599087470, 586968550, 625614989, 976783116, 27669499, 925968038, 577413827, 628904109, 865419653, 985824032, 417314997, 388736640, 282237953, 181721274, 506660923, 934852039, 394830638, 676881626, 591829351, 316281968, 676580215, 934774637, 837844194, 250307987, 536586006, 319945492, 242190462, 854670927, 389609116, 435859088, 54306686, 182899514, 347404925, 404709504, 601291171, 273157726, 928901958, 380439931, 84392595, 728179056, 147307391, 748173702, 105978490, 824260486, 606222038, 230908235, 507853113, 374022223, 138039267, 379039132, 268494881, 682465295, 118179462, 445033808, 207036343, 945707873, 653283208, 701420, 32979493, 554651617, 723606642, 538038442, 802908060, 534120775, 662254246, 767375862, 459533641, 313612339, 55572160, 368357473, 595196330, 176527275, 526779516, 770398183, 929915984, 359308751, 341583644, 557120741, 539272575, 835866461, 642111893, 95934015, 782705810, 843133868, 931728013, 254937444, 866949171, 590256782, 725184175, 507028199, 914095705, 802593991, 245221950, 844617518, 583681378, 226022250, 297999574, 456146036, 568404957, 754243669, 351863031, 760727938, 140551108, 436342057, 134058670, 22778186, 810164820, 343319659, 71377554, 144972039, 316964560, 338607310, 839478251, 338370840, 611782131, 658871924, 797845843, 296296199, 321092285, 875646346, 510332912, 789545552, 686387788, 833358684, 61401878, 685550006, 499742443, 504455074, 30710842, 65989194, 697636528, 577552338, 351416185, 112366516, 685074539, 526585281, 108019800, 603606439, 398630793, 716404250, 112927684, 787789448, 608187924, 752243255, 860666686, 994180153, 216737475, 166810229, 607926265, 285228604, 356003135, 686409319, 324755593, 638362380, 327146865, 423303343, 839097067, 995275294, 794019411, 715047648, 259778943, 778412581, 532066866, 655613924, 610464553, 200879679, 213449908, 902813096, 657405833, 243672469, 713663871, 646042560, 768234283, 38657351, 881307265, 581846181, 1194837, 724116728, 426260600, 580201212, 579594214, 982488008, 941639829, 530600100, 656407930, 506200392, 507911364, 313639085, 429685755, 99490968, 240441659, 964709950, 186469766, 667489, 849569187, 846920699, 388249274, 219981868, 167083871, 335665084, 799592699, 507230387, 209591964, 447741012, 117728935, 231283373, 250299824, 565693581, 498780095, 926751486, 593973994, 667245156, 125018511, 287500832, 485003355, 519181311, 585439586, 751412067, 583729669, 347020779, 144517951, 541927388, 8976695, 966831212, 610478203, 671208605, 192406388, 52371145, 995764314, 700861945, 265776751, 223697058, 391512192, 940847903, 629210334, 498355621, 116921497, 281825305, 118912899, 71504280, 842293733, 741408152, 963656941, 756614071, 724243497, 583417533, 985223564, 211271657, 700745312, 574406665, 187503581, 155868548, 756413655, 887372007, 215345000, 513372428, 547237403, 193670815, 365162818, 25689577, 963517278, 564696413, 670258591, 825140395, 611919805, 189767611, 226843709, 82106259, 158348193, 284281044, 836891674, 195677744, 81146603, 900031102, 340536360, 825245509, 61875865, 24976904, 525032746, 464538035, 168859021, 5253876, 781683986, 975622472, 476142016, 429003333, 504460684, 636174451, 87732818, 349002446, 921100371, 698482495, 82638598, 256185424, 715666019, 996006851, 75736575, 269192115, 868392192, 742569718, 852200546, 81338158, 318387291, 511322034, 456630312, 930531977, 849413002, 756603499, 837111241, 774741060, 677776139, 112240494, 256370949, 921919692, 476101483, 284462102, 176740877, 481263366, 154261008, 631089872, 22426236, 192013105, 287675435, 958214780, 663778953, 515106458, 502558378, 436831035, 867614321, 912100958, 624183560, 21848125, 564694168, 930036774, 581350659, 495395489, 161621939, 816030100, 48020324, 603822551, 899301731, 597292237, 220944366, 872995943, 555046389, 699855543, 949833631, 510955891, 170328831, 959114800, 244371862, 870046704, 807787720, 293926675, 155557956, 416250671, 939843133, 202631677, 123983523, 268053880, 274964110, 495411284, 418559713, 855373173, 753859992, 741789692, 663827225, 679872007, 154369040, 882183665, 849463056, 482392694, 852752099, 308404077, 758494431, 979191618, 306856633, 440723308, 229918791, 518583705, 402544924, 357665724, 777091753, 93701372, 794782341, 179290858, 450619505, 774441643, 182837969, 583388944, 807270143, 179331156, 164307532, 120385381, 403675468, 188971425, 96686328, 30676204, 600749118, 662245870, 656634224, 200781149, 927859499, 476063090, 140035651, 506460728, 183904040, 889657059, 910883559, 974219083, 828687641, 235264056, 652658202, 812386303, 909375772, 264082892, 67400816, 110103142, 627388424, 9119544, 166512409, 734759070, 304730875, 303609215, 587148515, 644272817, 405507746, 389837295, 538026175, 352934206, 356541679, 66233068, 92984368, 185057855, 41162295, 660723986, 69911455, 959136456, 644817879, 339604125, 915527276, 115260813, 24734560, 678416148, 399550475, 802110870, 861183443, 949690083, 989383391, 726905705, 333691155, 892336500, 134987850, 140049604, 108818016, 959038740, 502124659, 972194563, 979040303, 146371198, 610978133, 953640991, 48689143, 489584557, 178298253, 14151795, 778646568, 204051352, 709419780, 976818193, 344671654, 676066647, 787799296, 975941793, 28226348, 72144130, 395027402, 393872797, 574698018, 575864379, 538024997, 220031105, 244014619, 832700112, 493643062, 250912016, 483372239, 893517567, 360806162, 676042004, 432381047, 712324969, 568122308, 810001484, 820306000, 550686506, 758846219, 487209294, 147190730, 632518840, 481636198, 154528739, 156628209, 440935704, 632325171, 490032030, 460447179, 30559327, 699272373, 424458230, 63040552, 233681173, 632838827, 967073057, 505265606, 677765657, 429033922, 679469304, 468405202, 574402831, 419150830, 460999301, 629986801, 856991174, 486829970, 141736206, 827158052, 290077018, 289752770, 533428486, 264474724, 809489780, 518223420, 846693426, 284635790, 171434074, 733665808, 542331970, 850343871, 478553060, 791655681, 835912982, 508612241, 185510916, 641385212, 366933385, 103815404, 416972346, 721604448, 910636835, 46616831, 64536639, 953789269, 424400047, 722422212, 916189094, 428558205, 38860125, 957705234, 708037860, 491511604, 761045167, 109979314, 670307346, 454989889, 171650330, 564692364, 280306803, 418709819, 137875667, 342030048, 229367152, 149120049, 501718429, 33831039, 506580859, 952853273, 929724643, 145058205, 934461306, 22423321, 249488177, 870968334, 688902745, 612277208, 396146631, 470195023, 770832369, 212653200, 74176796, 368273873, 161898549, 690475854, 839855339, 498084105, 621405520, 217360716, 372215960, 919851856, 63174563, 662487135, 367268789, 50129130, 387037923, 480977403, 260227256, 731179737, 804578246, 972236660, 17783449, 879809581, 713907094, 104747130, 841525181, 224986061, 810501101, 948385464, 901738545, 672641988, 565067218, 810612010, 711500682, 186640645, 511933045, 408335877, 695811672, 280711254, 691415576, 938378229, 634843296, 886312030, 436029567, 610139166, 506987121, 258795039, 211454350, 514500975, 906376134, 267253159, 813354546, 886754846, 595669412, 382945381, 418941655, 833568736, 573119539, 238761165, 700009996, 984594784, 18845703, 34561892, 534356968, 158502379, 88702501, 572499964, 181267077, 94709473, 133139866, 923193180, 712314096, 254120230, 245058981, 133342451, 861453434, 603754123, 318528569, 503504253, 523209062, 345972302, 558142250, 450337033, 84089248, 356417917, 82994929, 399397684, 300945663, 691227340, 113423128, 264733736, 887143386, 132275156, 900852156, 345172505, 785737662, 329442469, 905218181, 591326656, 903103463, 328396309, 242327075, 931769756, 640253689, 373480107, 139412350, 926531359, 265492926, 833627124, 272831272, 853389730, 513445221, 1083346, 42816399, 32880107, 450530462, 383586345, 664051344, 25821752, 400354820, 663027080, 339372648, 740168775, 425312513, 655191119, 682605126, 389436614, 952854995, 769091326, 710729549, 369037303, 38695168, 150473237, 274250503, 500285072, 350558561, 393953017, 402075170, 789300753, 514993484, 345301010, 953143676, 389133399, 107789759, 881596862, 112238186, 181343293, 924831285, 49281199, 632592620, 158095034, 893863227, 839310784, 362464046, 655773048, 50079996, 175112238, 442878970, 125160968, 156850834, 344979195, 480777122, 708832936, 433513978, 775297917, 222736147, 853224447, 103387810, 985213480, 691082501, 241330695, 817424227, 662649345, 679517422, 555067904, 148359905, 719997440, 848400644, 976553663, 444451710, 447409797, 672319064, 770882174, 906486338, 307044604, 594830345, 227346800, 92137219, 676048349, 66369241, 852351550, 799987348, 86167374, 611772364, 926842479, 17141979, 51444996, 151385823, 715360328, 568934839, 92890082, 165849915, 866435016, 448231458, 791707869, 157879270, 687208620, 317622211, 586096249, 595863012, 838681272, 146773905, 412052187, 134776613, 518239280, 55723686, 206532512, 801428806, 368436552, 998121702, 791740334, 103467128, 24521703, 563028423, 931245924, 618541461, 241515132, 433440179, 325705698, 594512658, 687343628, 261523587, 554090248, 179731704, 249136034, 639881113, 427969142, 828488849, 251262875, 990829092, 512759032, 177221410, 485324910, 247674333, 789414142, 697572706, 547477822, 420690378, 224665220, 510905314, 776830129, 942087061, 22293421, 687092476, 647412509, 475201343, 794474071, 631368484, 532702089, 623877233, 23320229, 463491761, 997355758, 315270126, 561938481, 473827980, 676202987, 682999697, 643667190, 928667813, 413308059, 109129679, 240399566, 303786633, 21242048, 701653363, 628255087, 589380695, 970619062, 567622777, 498929707, 391786289, 120872345, 953825468, 178697409, 180706907, 103108761, 914847987, 891776452, 764962593, 290207687, 973578085, 397995109, 310447090, 149935340, 533652285, 545861260, 472324674, 792481982, 782720842, 943216484, 871199018, 367121275, 498206727, 133375414, 921176830, 169657730, 204047610, 895788829, 25245392, 196507033, 402978710, 532307792, 246581599, 619639777, 977683775, 351965387, 944747563, 892768094, 332182077, 305097613, 764922091, 699626423, 883694056, 114218404, 499347017, 48343851, 454321315, 938317708, 874743528, 414202812, 432531817, 996502035, 111894910, 621011237, 821140869, 246896833, 361704938, 927646394, 384823902, 80615493, 585160186, 778004616, 770121707, 515651099, 218054173, 67604229, 168657039, 388051413, 791606017, 716016852, 255284347, 951556050, 424024570, 536446051, 485337530, 619147274, 232383920, 451656243, 327224282, 658300683, 134923492, 118503889, 88709321, 576312939, 362720008, 154979174, 866195828, 44557524, 343772391, 467427385, 463157453, 567221328, 50259238, 256626825, 908461889, 856014399, 888671571, 986100554, 792517767, 705561226, 658919579, 11648289, 105838993, 179388303, 377957652, 92716195, 891556069, 175153150, 322508867, 471772642, 297442455, 186432210, 977148835, 802934790, 193686272, 367206893, 693522728, 755277403, 506990944, 990043328, 262348022, 848238682, 426331918, 221016101, 763521620, 792326270, 729030620, 463621173, 625429167, 502373169, 361042224, 361303993, 85556684, 354677242, 698050116, 987066419, 300436851, 500058453, 118118312, 534854497, 396539753, 86469022, 413496464, 570461401, 828540998, 713945669, 539291484, 517820579, 509272202, 544622201, 928524402, 269694940, 932484981, 566257689, 173210067, 955787170, 67157565, 581031594, 811900638, 586839078, 339468890, 515099470, 242485208, 824353508, 986183975, 255872684, 742036283, 546249310, 939530200, 946415828, 465252525, 227516877, 348781836, 638320049, 869840678, 392281551, 727547485, 726520252, 925065447, 391896874, 945067143, 626528808, 463391501, 39956033, 399416140, 792047759, 189183408, 223108090, 577419666, 188886490, 409314372, 344739709, 91842682, 802660577, 775385922, 585907193, 173670578, 442785603, 339943873, 725004801, 745078031, 485678433, 337698141, 147044095, 616979992, 872825833, 412038078, 785708293, 369183324, 724710034, 47783561, 672767096, 543267225, 923524173, 765964990, 382464210, 264061885, 540875496, 434451230, 30586776, 756418148, 80043325, 449063426, 709401689, 444575640, 247407390, 28980203, 771115960, 30107921, 772252249, 846775980, 819004021, 676221381, 478470256, 703337569, 209156355, 541695803, 269639210, 505451560, 555395133, 635800952, 235995615, 790852180, 87324308, 382998712, 594511060, 891707440, 190396687, 176596908, 43156633, 941954410, 648400988, 922583347, 114767362, 945546002, 314813137, 13005418, 478495844, 422601859, 837013936, 482365461, 977488859, 823289449, 198806996, 882632843, 452464798, 178242855, 277193015, 287740621, 219725053, 480087204, 852465188, 836342315, 858049576, 931068591, 242628187, 804452383, 379457474, 415349151, 34134877, 75525069, 883484808, 770930294, 103699448, 225148477, 860126035, 530205962, 896105485, 893585601, 149446642, 579246069, 657233871, 659241552, 314344696, 353997273, 266178639, 33890620, 622815764, 192872543, 176848281, 825968276, 656335882, 260275325, 196563879, 79708479, 698323720, 230781939, 568052089, 875190194, 839714946, 8271146, 497432465, 133297543, 248922555, 400973094, 474882865, 324042463, 714439939, 804994151, 76220808, 37259698, 733059336, 520533796, 437097754, 795386139, 922586058, 239423412, 542722559, 524284603, 448889212, 963669499, 693547942, 618989640, 300376980, 471944681, 872437016, 607328568, 689862877, 124588470, 510073941, 679932744, 871989319, 720087774, 456013189, 158761481, 107755167, 777484687, 952528269, 484906621, 73029698, 825833843, 893572445, 716610155, 685080223, 819207557, 55487669, 371022081, 957075576, 206901571, 128995626, 473408054, 170213467, 41859960, 153983680, 410983926, 282980694, 929205508, 755523825, 280602845, 462896114, 690331456, 61544344, 873908359, 567498314, 727506942, 877234580, 803580141, 366006584, 440399415, 811255390, 419562144, 685640372, 753520228, 739046441, 863913911, 522318220, 383725776, 922705083, 135128764, 123307110, 95678323, 671206121, 480326273, 817961646, 352946656, 683373929, 613342425, 982493079, 208124636, 357262010, 39908237, 704626811, 472249052, 58786907, 444260276, 841677020, 40282331, 111642996, 497822646, 891845811, 77155903, 174839970, 285907120, 867652085, 977183814, 50166451, 537129325, 360557594, 30589204, 191517878, 728178150, 45774327, 358398763, 217651242, 279650020, 960242923, 564023353, 604478452, 264898023, 701263051, 482765319, 517073597, 312169125, 980681078, 946245793, 460498969, 541007327, 763764596, 369828957, 111146985, 675455423, 428592252, 576619190, 773311791, 206889353, 1858521, 629550396, 576164047, 994284256, 877643220, 116186676, 550340145, 632651028, 962709771, 324695728, 184419501, 65132283, 399391901, 886632022, 489068778, 907708960, 857079288, 509314508, 767693237, 962143335, 513923425, 172341046, 431372955, 176499864, 616384639, 643731481, 659508590, 278830990, 177290528, 598169567, 474576583, 774740257, 43461888, 215929927, 27839118, 737403200, 549313680, 401571084, 802731273, 52439810, 639416391, 247800509, 586960320, 145335884, 553050034, 504033443, 789279436, 207527954, 972812852, 398447149, 470087868, 910477183, 706075787, 845297024, 604393848, 511675477, 153243637, 172964335, 836686006, 766775813, 17969507, 624329194, 28640917, 795472736, 345797014, 536946009, 437203843, 542990698, 235123816, 219389445, 946191066, 530003724, 825049178, 883782320, 233139128, 747664920, 159131373, 218058481, 501498126, 480628427, 377744906, 360017490, 4599842, 763699440, 612199955, 507017155, 580517880, 195041880, 581655641, 417569233, 691342521, 795537087, 817436904, 83464536, 402207893, 48526753, 641626766, 783378967, 486666582, 573904754, 837811313, 426843753, 685948879, 849589385, 100734396, 701788250, 316236400, 624157031, 595728406, 182603686, 739976280, 52013139, 180497979, 235256275, 83968124, 780257230, 755889544, 580154480, 896340973, 505643332, 220421801, 970195177, 821188353, 925809722, 603121721, 775563878, 408645271, 637195277, 531996986, 131951884, 188234394, 543644842, 323841614, 4669286, 458891516, 785549304, 860488210, 529090837, 61591599, 978989798, 64128009, 580438561, 434617, 549941087, 500739301, 546865034, 564938155, 655329200, 306673431, 551802106, 183974247, 402611875, 454079597, 683836713, 173660424, 208096617, 670700095, 301105128, 428209056, 23269986, 820836390, 306464030, 700065088, 529546486, 511913502, 86039739, 874202823, 232839817, 686925845, 536565574, 913600253, 655562178, 376795612, 430887132, 344960895, 802060467, 281552131, 14313634, 246889436, 397326514, 955315695, 162569141, 866212734, 931225625, 197910259, 281821694, 858390270, 301558087, 343900381, 193763921, 946111126, 855696787, 204837982, 51001967, 778910105, 336079431, 936027010, 221487219, 146753504, 855018575, 986713871, 66349425, 388969986, 970208674, 922633362, 105860839, 143579857, 697883007, 355998729, 510902691, 456029307, 876306243, 881596365, 255546830, 200794913, 323774204, 559186197, 416069278, 373366073, 649062686, 901925058, 153214038, 814408936, 445243575, 703250814, 530599227, 558714306, 755998654, 314751303, 637241561, 801447096, 982434867, 748246341, 839395071, 468253021, 634066618, 161423699, 929407304, 697948052, 500992041, 45169671, 437363728, 819436689, 945945975, 429148767, 428484734, 640016665, 416293388, 696276974, 314857212, 787099318, 589672242, 106034264, 552624940, 193843183, 114926839, 496784110, 779304648, 789153836, 859877683, 117857303, 233653577, 197372845, 909562627, 575477611, 222448729, 274867843, 987782811, 674874032, 506115429, 91898881, 67831303, 192874664, 485177365, 259553545, 723227732, 542122434, 240440942, 589555874, 262053801, 735930088, 819992317, 940343737, 354344814, 153123596, 113653838, 91614143, 930692310, 435690203, 792963494, 970668837, 191883722, 521507088, 99881613, 844117840, 79698466, 387659479, 667089400, 719691651, 51222470, 271198767, 116578498, 490465099, 363115593, 224175914, 438633568, 338611434, 562460801, 919482815, 857770504, 137409336, 766973915, 540897678, 326373823, 669830074, 238095916, 290531937, 174656734, 865750678, 570481728, 893364613, 445144264, 146259860, 205133219, 393446158, 440055069, 911151685, 519676163, 391113001, 895631812, 836078273, 469047516, 860907448, 283246223, 990592237, 81041995, 410726404, 472554693, 538586876, 397895190, 214423856, 46014977, 166935877, 748505723, 673814494, 773209835, 455686601, 285392771, 871220947, 532647412, 210388814, 535507879, 425893357, 936249270, 511428404, 733504190, 488978310, 68310736, 313234724, 464010732, 91355636, 460023193, 877935795, 229955517, 4880217, 910817706, 7918478, 133426021, 551872990, 302050897, 160668425, 154655165, 778955078, 670307870, 369170730, 899692172, 117936743, 827644163, 235492811, 6975128, 166426112, 457620664, 550426157, 300288703, 158036572, 801926692, 356965713, 32980788, 770636361, 951955391, 902222840, 295510504, 650132753, 352675966, 591183248, 57689310, 542385088, 858456354, 545610857, 887721536, 992677326, 313633132, 510513056, 422188751, 979677131, 309665170, 604417226, 427338505, 756356927, 545660883, 928509258, 254002522, 511583052, 638391146, 602313980, 641102283, 498313092, 906614485, 431912746, 632236205, 110906326, 11434797, 770174732, 639451530, 748835801, 263263255, 929415803, 637860715, 683859254, 933935983, 452168911, 217815193, 552344341, 829976894, 924114238, 450621199, 835431675, 227905664, 700985106, 158281954, 430008815, 210011347, 675606623, 803428910, 808448783, 405665992, 396869453, 220282403, 550911802, 694503555, 6020860, 63202391, 873673379, 502707829, 388681233, 593020488, 700138282, 232579659, 910337697, 450908024, 161312554, 376576220, 731591286, 524601264, 187132358, 810250886, 143281726, 770405281, 414267488, 417902791, 460311684, 644455231, 182425244, 165918109, 375315508, 91245628, 467386188, 367132303, 101557410, 129661789, 741265207, 983971385, 299963259, 176615294, 990841721, 297755749, 752158305, 714691560, 600801383, 596310924, 961973781, 522784858, 952973395, 620308790, 540907136, 199891293, 371936865, 757222258, 662893399, 906248154, 261689317, 578889047, 434330099, 961677920, 359898020, 827783042, 315835458, 728740340, 697650896, 692884790, 32091554, 4895993, 391389244, 396767415, 822752752, 683131990, 450183243, 880996415, 356978343, 553707856, 676313995, 640846151, 387458261, 75470749, 316211098, 678780813, 233158909, 68842945, 270435605, 716140720, 810531682, 474602774, 546628457, 60063610, 401672175, 763318775, 951906710, 264292163, 610880530, 630917876, 533273300, 493510665, 113959938, 616910386, 625413362, 717130036, 617493458, 814475753, 874754357, 662415142, 43756929, 153351095, 421934175, 421217369, 673899712, 150339664, 75690215, 971819766, 638966464, 908935710, 24347656, 38878655, 396641918, 939612598, 129638095, 202324437, 745068693, 755760581, 598958022, 951518347, 402327480, 259819519, 963936492, 709554503, 360132883, 111161579, 369191749, 180571619, 984748125, 681495005, 649568324, 520675781, 84825880, 320491579, 226565505, 348015602, 491494349, 884006807, 219334300, 680838709, 494474319, 336292223, 181889074, 314153474, 262457449, 340795658, 350212683, 567498181, 547923925, 346988838, 558843786, 302003702, 890502445, 572606073, 26234391, 910200592, 199689834, 386731372, 347602207, 835600446, 568971933, 248909861, 688971337, 175547514, 444407653, 968093800, 313899831, 464465091, 464797103, 944109860, 223661678, 636611165, 372938032, 332683147, 410115821, 889934310, 748319446, 70611199, 515244521, 95536253, 957923924, 627772664, 157261551, 273545487, 961420637, 352405528, 82599182, 267969423, 317468430, 977029261, 529677032, 194700360, 220370751, 389120743, 616313227, 20052784, 891551388, 117572729, 989454960, 111832743, 809522295, 850160525, 500588312, 85356595, 567143664, 375058752, 37715614, 797544957, 729121731, 728053634, 735241176, 587469906, 682977679, 738490039, 649233463, 566356354, 216942959, 625962443, 162005011, 958450, 844412329, 7766177, 519688816, 137483937, 232547599, 876870507, 319878491, 297843482, 661582061, 796516549, 124215089, 694296659, 243650922, 652422666, 515643363, 994660867, 830707321, 487121289, 494426613, 177591038, 243255062, 994574944, 227321500, 60973858, 353156192, 389696161, 763251468, 833865564, 353553218, 636625812, 240802029, 179872000, 83990205, 718153908, 467571371, 678034169, 369749190, 961580824, 30948862, 822460898, 423094653, 712535888, 635499538, 465381164, 731032655, 97788148, 146975682, 223260408, 974184348, 43535914, 444837567, 84992460, 754115521, 172649296, 170809303, 369128350, 596412290, 896418960, 409953170, 956438401, 800506382, 267181255, 187537565, 248894095, 249002195, 516699693, 158674657, 222528881, 634818839, 19637748, 289385958, 344077786, 125244249, 880015720, 742919271, 747284343, 455690045, 734401708, 288094953, 927656907, 976677473, 757275672, 642092852, 335719371, 543650979, 66417331, 729611199, 139193587, 414895728, 715848195, 178265431, 411108817, 326922939, 830495338, 787321721, 529073008, 954102462, 921550345, 355657777, 321197797, 258516482, 212422097, 367416405, 533912345, 51283149, 828128931, 202245659, 528092845, 64916053, 947738828, 920451580, 133284386, 593351445, 938289451, 351466166, 438649250, 943205113, 392228215, 67913884, 936320498, 36156904, 526656089, 859016191, 854798693, 138243035, 155956801, 203548298, 184216462, 232830157, 178896234, 853531059, 121647360, 28360431, 663938059, 550318240, 139681926, 411098125, 809191494, 9869704, 316645398, 646671232, 406191046, 527835964, 414880370, 558339213, 206039048, 899490719, 64769839, 711487135, 728239108, 379292826, 914962017, 512600176, 202633540, 809469112, 659106644, 211000738, 963038874, 64920713, 97402853, 461984447, 686703313, 456626397, 727526908, 748690819, 110907065, 127445893, 590242054, 208626363, 777425254, 895597025, 697214477, 251187911, 390629465, 644636480, 39842796, 589137810, 577664549, 773080973, 321220689, 741958674, 298005059, 999136415, 344885183, 136548444, 218724621, 84022976, 539461690, 206465010, 372999564, 389631359, 640898717, 857967784, 658009036, 903031300, 756402289, 222776247, 716333167, 501941090, 200896482, 333568171, 869592913, 945860733, 455155212, 968466874, 784233281, 596275233, 853837635, 157021605, 268069090, 813677724, 735692968, 244229826, 374818623, 557529313, 973151867, 711863827, 830455263, 387150270, 483532982, 605946778, 925657330, 751215508, 794475860, 526018907, 165891067, 982908503, 909797118, 914838851, 194578196, 393280347, 275662416, 747588175, 802598465, 377570191, 408214024, 985120430, 813173515, 883918032, 285125264, 721882894, 922552000, 102030883, 701827069, 273382032, 977921054, 193101501, 636104234, 939552731, 645777883, 619660433, 543562896, 862077727, 721790508, 150575405, 891728093, 386926372, 81577195, 702500911, 917784518, 957600157, 20957299, 694769074, 774982625, 384890556, 166274549, 541543466, 147057234, 25024953, 454734480, 399917628, 842904145, 368216882, 172423551, 669010744, 472163724, 339850830, 195999118, 935292849, 715500090, 241546277, 601922235, 456891985, 921354614, 146448220, 742573627, 404660493, 23039859, 81872365, 665465177, 221172138, 162690282, 78027931, 524363102, 669433204, 814169175, 432162376, 835079496, 525507782, 72516948, 823455172, 666632452, 785572315, 719371514, 716705307, 586864749, 995374836, 595255660, 945724333, 728896130, 584708278, 30899272, 187364606, 173728282, 230426893, 858377795, 434979081, 715056472, 252829192, 245004820, 58188436, 639823531, 588800093, 941432722, 746174694, 526006380, 1958, 479744852, 462502264, 429330463, 542470693, 331263214, 645031246, 379379156, 127240803, 190677416, 239776697, 52718927, 693267871, 541512151, 104136877, 392589197, 957209983, 378560468, 152748934, 569874279, 925819158, 234075257, 164319788, 301650204, 681849036, 420700939, 554849216, 106421995, 15097217, 150379017, 784270808, 82690133, 24097920, 106064211, 772894514, 268484678, 670016575, 772389510, 80610121, 593121281, 197895986, 942909121, 355358747, 25367399, 544405038, 381942609, 856925130, 266100680, 507466104, 960199942, 359338121, 277476733, 708569503, 150730259, 952313618, 278628267, 385913012, 970415092, 285407119, 510654327, 819208144, 130041473, 494160996, 940220770, 536235432, 842677544, 344039374, 23582132, 928827788, 316852531, 495311962, 872484948, 577812301, 403953051, 227778988, 911600304, 443115943, 946403669, 841601401, 483800017, 535280198, 684169826, 333391457, 882830418, 711312944, 701154573, 298263834, 200428464, 570942451, 973946290, 517264814, 521144879, 887668960, 451403939, 724890825, 446869309, 350761348, 36650082, 746110305, 831541912, 964244859, 141989707, 452601252, 518363412, 733120851, 229486164, 719947905, 205984342, 433490592, 161707260, 27376149, 739660220, 889716281, 217131743, 689686484, 421731112, 412285883, 158363325, 940881309, 37149388, 55818439, 861867604, 467528040, 833613457, 611268775, 910798823, 431282016, 431605101, 833191802, 653997821, 45339660, 453409106, 161691509, 991387701, 550569599, 860637959, 423526771, 632106124, 837520462, 803457184, 470371210, 708520807, 105942629, 475376416, 568000214, 386716756, 727941887, 998159332, 855557059, 471228581, 676893914, 135915545, 829559600, 54940739, 628527045, 41962397, 83730689, 392283535, 116906011, 37819840, 319587596, 448050875, 357182550, 311585833, 590194695, 567322957, 744956905, 476709531, 364836315, 686983024, 106663910, 384479621, 552374696, 777973016, 982743825, 463917137, 776296335, 65193492, 216328234, 600247580, 430276259, 499503531, 598437562, 53159799, 267302943, 157719371, 475084574, 669420330, 202597296, 964557115, 658635188, 922114932, 180385258, 971144122, 93607581, 73873084, 245990404, 804407980, 512944784, 947492282, 40664386, 438194674, 975648859, 607774415, 373808096, 802849308, 997000119, 482181269, 27357450, 339098524, 922135997, 133240092, 75859775, 557966796, 739511044, 632754624, 310138246, 258263012, 382956774, 618444027, 12096907, 158280345, 634837113, 590669773, 644208890, 36622098, 822674695, 502128290, 595551847, 641502665, 943265166, 200670750, 857052272, 700198883, 781722652, 611799401, 268262581, 790239433, 77628568, 222040384, 791417745, 672849684, 519807835, 984156859, 820493560, 389728834, 570370117, 563333242, 813944190, 840318060, 818394233, 728203735, 667074542, 68443062, 571876346, 865863664, 515424298, 70284705, 89225825, 796024953, 211299516, 638986858, 19206486, 245064993, 459232596, 762755868, 925548269, 176264672, 428904928, 514998171, 914337318, 597234558, 811121118, 646161365, 33444346, 46993444, 657321838, 876369593, 704093583, 793943104, 861449567, 995385523, 477644299, 466329479, 127909550, 746389073, 835823272, 967604279, 66865028, 213239399, 702493183, 144961253, 965624821, 266271161, 495190302, 594015762, 436799730, 631071172, 29221119, 22948761, 648402220, 183770157, 853359994, 767614022, 37618073, 642171407, 362110653, 391872580, 244809005, 433759967, 69277507, 254473129, 796192773, 67913432, 511390264, 328152966, 830916949, 328002463, 171380057, 539340368, 246885562, 118475182, 175531845, 431019291, 668346118, 917342657, 876785734, 776825460, 747791085, 535394670, 376224528, 980277137, 275066526, 107106766, 363445511, 433246373, 376548375, 424628738, 675780691, 380817906, 43653205, 397271550, 818212546, 698528160, 392084342, 863092423, 919532478, 849157910, 380086335, 722440649, 486391551, 788286127, 30415521, 670555908, 555012147, 60973911, 418278927, 464952233, 382509398, 100017474, 983009253, 581207262, 165311622, 615392887, 831027031, 979263881, 417913442, 775516469, 513631643, 806177370, 62819836, 510271010, 13505684, 296538808, 147599904, 378628670, 93871363, 463906755, 75635412, 769041273, 723131327, 936878565, 484948047, 47728735, 477733590, 223654107, 694300695, 34095272, 20527544, 419045776, 481902851, 868692715, 783673456, 283535204, 56434250, 393668933, 312441180, 365390394, 736278267, 182537019, 429676919, 549152525, 998058890, 724570387, 174004904, 631224329, 458793397, 621178479, 769478069, 979797085, 244695033, 873886272, 884669902, 584790574, 670248620, 180600872, 410133841, 432993964, 423345414, 744222719, 104354657, 494579510, 829917913, 551807122, 929864822, 595267116, 480936141, 283223566, 389063548, 877009072, 79722379, 47227362, 800064967, 283946672, 170664274, 710654503, 548729310, 403713930, 429939433, 428211802, 791359895, 70106574, 719984296, 982584364, 485344188, 708739680, 684145348, 447940746, 733132311, 53651676, 365595475, 237000270, 379144276, 398249496, 110549441, 709642956, 880614504, 114611470, 450558842, 167818502, 522418406, 957289737, 319232254, 261438802, 714759520, 248420252, 705170553, 548203726, 866752171, 929080744, 955528359, 416815139, 924498222, 174611323, 20768661, 83848121, 958755281, 821183011, 612301920, 632863849, 230806172, 771846666, 934013582, 862125288, 292956065, 661678154, 716501101, 532087038, 814171628, 916686117, 131617618, 280995974, 571531431, 516144896, 952847541, 274237677, 355069352, 961976964, 99537590, 514918914, 83101038, 437304430, 760155502, 269686436, 268164490, 569876070, 344893, 131604046, 898759912, 943570576, 238006123, 884319254, 282315028, 974520135, 372057733, 25671586, 490760034, 681611186, 909405517, 635099769, 404502661, 719532465, 591547886, 316192465, 616258829, 274942579, 671331590, 333771723, 261635649, 146167920, 547854058, 427365141, 891018211, 71213464, 208671706, 492615399, 740412641, 722793765, 875607931, 71600452, 648772497, 48820374, 912188134, 896185613, 770545785, 576993909, 116284926, 80213553, 445171747, 118177936, 73179701, 670173081, 350493744, 422607862, 420988921, 261843199, 148856786, 629814130, 605116683, 705958541, 615801998, 240606235, 830530355, 664221750, 630545768, 145051380, 636018365, 27058603, 694644091, 940911461, 67706917, 33346146, 15340200, 335230335, 694971091, 214386961, 353281746, 228345711, 700480486, 443781397, 477432894, 225377796, 926461958, 945636381, 507930292, 672403721, 887619114, 921770428, 572657525, 964029437, 390070113, 638716065, 646479814, 890288101, 771582782, 871146570, 41151076, 966928134, 92865487, 539898182, 21076988, 57537011, 991346991, 228957946, 464600575, 382525153, 300641998, 832664474, 824359508, 137134524, 680028965, 614581756, 689634529, 328166671, 982052474, 449672674, 723325838, 342096595, 78348297, 113489583, 908282164, 727036755, 395918906, 130017047, 684926379, 76871560, 708751226, 673646537, 542158035, 497794195, 751050710, 579484380, 516396499, 349684726, 471728143, 694775557, 342003732, 379819112, 776775123, 764639508, 145249619, 632054073, 554432423, 373163070, 500874082, 645203606, 521493659, 75520575, 398238042, 729563595, 572809314, 894871430, 492183280, 825986750, 444274904, 475642189, 909726612, 562234435, 491467592, 999398990, 540760673, 717289750, 378137303, 598798820, 172747652, 737577853, 410832015, 228850555, 245446282, 906758776, 367540169, 48428128, 570277426, 194224495, 345456259, 150513113, 517196863, 578141764, 519055590, 234861056, 534953977, 786758554, 947600810, 910483202, 257276548, 56008296, 155665743, 775652795, 419738443, 112580916, 177434521, 713144450, 317885711, 130107322, 651853735, 293492120, 413691750, 461504436, 910658565, 335072923, 423367279, 879185886, 734825706, 425220340, 97072690, 576990488, 677782717, 48451478, 557805596, 593821291, 804262439, 950695923, 784568353, 630880490, 526397929, 856056900, 913272195, 458060316, 774639946, 721445809, 637712864, 304725532, 818228795, 295306783, 184546077, 141734298, 347906254, 49774416, 404260940, 616087943, 58205351, 851299527, 514815267, 846868849, 250008246, 671909215, 874932052, 105658829, 596133242, 615781967, 601034059, 200800576, 472609936, 618548730, 922440066, 811764485, 711032875, 119874175, 280312923, 31459506, 9328223, 888128280, 948210273, 884711945, 331245572, 783388565, 394468564, 922306515, 448639455, 424031696, 144673781, 888725445, 773412260, 55980651, 749457542, 949476026, 887283899, 635915248, 954298766, 126817445, 119282390, 296748366, 343411938, 517092783, 561087250, 81894328, 885376708, 952294369, 385046332, 505282341, 240520897, 739154540, 586332761, 964068643, 773779750, 837504911, 467004867, 277879514, 547544565, 706654946, 299607742, 364969530, 381748974, 973352579, 972417896, 901835154, 434983800, 725812239, 491361808, 476469188, 996748598, 485612692, 194615889, 110881479, 317577000, 88733356, 602652087, 997248819, 283276911, 236710787, 512684294, 899174116, 763326719, 100366286, 594004121, 129853275, 659454778, 713288482, 163448601, 822658367, 818571197, 217880612, 744578961, 763877722, 128244015, 269348839, 955580501, 323173465, 520327744, 769538827, 583069894, 822591628, 884415917, 960497857, 175971242, 83679696, 721747313, 345824965, 514058454, 451760551, 685422560, 399517771, 189497699, 591031879, 38722151, 538283024, 384127219, 624120671, 416021080, 936977166, 690347391, 214097696, 155012691, 525905417, 662701552, 676657682, 721417575, 160607534, 459144413, 691902812, 168673408, 392841164, 891729707, 716616226, 120032522, 852704988, 443518315, 848085029, 690072265, 137858086, 588933600, 70274567, 201276973, 8227829, 172480978, 218313439, 977158825, 970629418, 736127962, 40574060, 970839634, 392973445, 579743524, 51024189, 518070205, 487905691, 548703481, 713898972, 152238557, 621488599, 392088466, 396299744, 442898194, 611137602, 556270919, 307914059, 446282217, 597901705, 122121477, 613159157, 810369457, 572334902, 153845079, 302325750, 176149717, 594991824, 937830030, 448500360, 779333101, 871936371, 242325635, 981431182, 107514097, 353815769, 421272989, 375617414, 879761144, 229730160, 338797494, 723923767, 685019054, 275922886, 972879223, 201638664, 482877178, 361160724, 966947203, 915675323, 728861657, 172117816, 436106606, 478536049, 944028874, 965517561, 951110269, 512502652, 805433621, 460296730, 713636389, 270316450, 564268748, 995015860, 274474456, 405239036, 259956535, 901624971, 543809857, 226588531, 411121587, 975934121, 862478931, 472943243, 780627626, 968013732, 389496674, 722615386, 222109894, 751411932, 868093594, 518040041, 944125701, 718279046, 255600702, 898133028, 927428912, 556640216, 838238074, 13995751, 343443251, 361576984, 425468183, 106220729, 734991052, 124294278, 829387760, 6736488, 138856701, 726659744, 329581173, 886553308, 123694507, 519932012, 814568176, 499495310, 185253810, 748930601, 167638809, 814832327, 348542050, 341382591, 597484306, 77686481, 882004056, 167963533, 194520587, 354019464, 696454755, 331910011, 545476836, 171161904, 681893847, 475070948, 500870727, 960905888, 989037829, 643528959, 11412721, 266157382, 769242692, 819613727, 959858575, 355004319, 350579535, 461214221, 199006927, 545363272, 528884010, 867854176, 639117112, 739805362, 303773281, 760180308, 562865710, 259821382, 411419702, 969259030, 702574339, 242702561, 171224733, 134168394, 416376064, 438964874, 952158997, 433642414, 667329746, 921801799, 950053359, 960742877, 342460801, 728353746, 877996260, 709392336, 100316307, 772495649, 948596130, 818734629, 132773911, 914623182, 700261400, 600464596, 947673081, 288626711, 622915801, 108004534, 39559279, 891927177, 616417063, 833276595, 583795698, 17784128, 642922285, 231440286, 384990378, 934631639, 772428670, 275317067, 453359734, 125394974, 647628493, 982930061, 410635836, 124569477, 963408839, 513244618, 516705100, 257982258, 278738716, 276217595, 374024569, 945197424, 311082578, 91401546, 424908563, 29787843, 687447094, 947321993, 35887176, 897415583, 176500769, 106785452, 525650564, 364048765, 456709834, 725710367, 927708211, 915724142, 55725238, 438815885, 965967140, 166616372, 276527202, 888056674, 630106586, 476779036, 98919123, 747644827, 633137544, 767158948, 959072818, 767005742, 820174844, 540285966, 414863431, 942185355, 759716271, 86469010, 427027088, 747120285, 381360095, 921576020, 940036995, 404017953, 955523216, 57440028, 943690952, 838677234, 53701121, 46782032, 996699820, 410893343, 994262070, 156493209, 663790423, 345668250, 245138641, 14295014, 240913354, 272731573, 504022188, 859654138, 510740021, 466139760, 476737305, 667822759, 150228754, 858787789, 495060068, 145935811, 180008060, 732974186, 477476877, 931308206, 920075435, 164656465, 545685736, 243150944, 995687426, 405640124, 942506737, 551442674, 127228789, 347458641, 444928614, 251599645, 652445058, 737551138, 318874287, 961279942, 285470135, 152836401, 886113196, 418904552, 668561088, 379314623, 950332430, 789983493, 490685682, 340310627, 415843335, 186006161, 300628480, 524882353, 702756858, 678824408, 48401376, 454418887, 405336472, 678947615, 168258766, 955715135, 561801735, 164780700, 358313606, 301236783, 233326040, 297488280, 563945631, 68859479, 256824360, 984877417, 312582346, 868950722, 14624992, 298388671, 877470011, 894010913, 904336345, 272503859, 11525090, 906562198, 424999605, 630326123, 600617657, 208423538, 328141015, 263925084, 404192646, 269702861, 273620166, 623609974, 455825440, 83009717, 90326863, 257809756, 325398573, 322906266, 704375931, 653062202, 463138628, 523585717, 528171821, 127566739, 631110592, 858756467, 984822527, 415812759, 832117515, 355231067, 686918562, 30199803, 790339594, 536261496, 319221198, 819036472, 400193195, 879428092, 739880850, 542706540, 692945917, 741700013, 911950049, 327770572, 330924155, 45086869, 261286564, 770326979, 423123221, 653403901, 144406925, 827176854, 528095320, 986104727, 667214927, 218909653, 386051073, 276134300, 659665910, 474310752, 746923623, 877751285, 150487373, 568063767, 957944171, 517531112, 827241901, 288534597, 474266633, 830478552, 391288881, 263517083, 794600872, 696574290, 390192905, 965091249, 873253893, 763560636, 313450348, 69814691, 732625710, 396932100, 128157031, 534900914, 723030206, 926766072, 409525245, 635434259, 683362315, 308255824, 644286965, 398932930, 688647753, 347142775, 823611942, 564727045, 87660128, 806093818, 339915871, 17967514, 406349623, 677105533, 525133380, 663457084, 151673230, 789952213, 314714063, 232968781, 462652433, 651618742, 368094446, 687781706, 443197508, 404394107, 767210684, 980809152, 515373605, 893470917, 382559794, 281762146, 957666449, 319940871, 940787720, 524324154, 696774250, 40296214, 956806407, 829096326, 962830958, 162955450, 928364793, 531223515, 911415567, 235539474, 673211251, 892761485, 421116467, 832140783, 102957669, 579824057, 74604898, 920440161, 705130257, 752648096, 23712587, 308440218, 824579015, 367884477, 151397390, 298292171, 140987740, 566688696, 830780580, 158276255, 401077323, 607950100, 839288633, 694640126, 392011698, 152901038, 703332390, 117132907, 825038395, 539066717, 79694135, 483101461, 252281086, 567565459, 685709104, 398776393, 646752380, 137954988, 267851897, 430047488, 442206444, 585987371, 106898415, 293123576, 379250030, 14880713, 427484884, 993348935, 155387962, 720970279, 86403567, 53385600, 993264607, 874497978, 777186005, 264556129, 868534972, 656054146, 446616186, 128178606, 531925803, 537658690, 444661112, 885962291, 327994647, 669047021, 797532099, 889010038, 111123626, 7817020, 30772459, 41906382, 780838506, 76517460, 270782936, 660708132, 149109201, 832742318, 650335446, 881008384, 25034670, 436851563, 749818627, 435787441, 248646612, 627319704, 85262326, 694065322, 332537284, 22961639, 297333860, 133854856, 811652375, 455245724, 157716576, 677134525, 979292090, 339162588, 12209183, 565107436, 505717868, 801004815, 626813607, 215198819, 305967988, 901704235, 532258330, 86837751, 889122965, 456404790, 482414208, 258059997, 14402699, 254949290, 492266460, 414732582, 590111719, 663516878, 61981418, 361800885, 33031380, 706398217, 406082658, 470412424, 703563842, 750820104, 999035304, 377079067, 246328184, 888754610, 356484610, 402493928, 701061501, 191792703, 588118805, 249172487, 120589510, 561540636, 387952176, 752440551, 470694655, 388736782, 71717417, 644841026, 297573176, 851683786, 168554124, 394132345, 543359417, 502942422, 822988329, 770420818, 84222441, 235797053, 402223637, 534725329, 761980501, 187299207, 207328243, 146345985, 498276394, 907125371, 310500133, 148072701, 732886324, 875776524, 69057930, 586586276, 545740710, 876505374, 69812515, 525853588, 331497948, 272292610, 905052975, 59123867, 82474557, 573761953, 626516409, 756572815, 889041414, 616599665, 569046529, 144620977, 12131880, 386427267, 744307539, 811424916, 497676352, 838833946, 750680537, 727486287, 875312219, 161705314, 96068709, 601720412, 186376048, 927396875, 137498898, 321688995, 449781873, 485893276, 371016724, 180381087, 77441386, 172402131, 763861041, 885157949, 925072166, 278724772, 625632843, 282596552, 836332055, 411944457, 722429157, 21707720, 234007917, 74435024, 556614465, 651459763, 925843293, 286912744, 16112817, 15145827, 643589854, 875142562, 889994196, 991024969, 800700388, 960714507, 683310431, 354641879, 383222955, 161296450, 217521434, 984413807, 21770976, 399838318, 743730184, 411590726, 736100500, 715776375, 669484737, 88886538, 526964247, 747752232, 815317965, 813051319, 83422359, 50976537, 442449158, 604191491, 159244205, 856266421, 359274198, 477029150, 888268437, 516870855, 108961603, 442455987, 415679375, 20376685, 573559924, 751660822, 14595742, 414240621, 747188287, 153313934, 896726148, 962472116, 255186706, 903194400, 454568771, 159054198, 567630756, 606500961, 836766944, 832771434, 231960788, 547933287, 679291107, 75049388, 389804341, 66351917, 531029043, 49655388, 400565315, 940283160, 330271880, 434429373, 106107941, 313493344, 398346407, 447583581, 135811983, 502538314, 387647711, 210670935, 826415045, 986518893, 37111910, 574750922, 773111003, 1111797, 523432925, 993927813, 394523861, 740800974, 662774506, 383155971, 506996163, 254696404, 608659928, 655885548, 965059920, 846436180, 927596358, 60338495, 729926782, 823750503, 523126706, 191591965, 492379334, 823069035, 95386240, 711569148, 557616540, 264337872, 66190198, 986626953, 215336043, 704690787, 293518818, 477352181, 495395488, 557279141, 426219766, 857007431, 323680409, 475350579, 549028588, 603947182, 982664968, 445868661, 232411922, 246409607, 576992137, 516543771, 947795721, 105748213, 548346974, 973210290, 229376822, 808835795, 528089839, 718600147, 277341834, 669482004, 261937402, 711189762, 116677611, 856010057, 838250469, 388440245, 847961863, 931878532, 954515745, 376475218, 353571332, 105664274, 594760340, 526504469, 619597916, 751847552, 714745551, 136666034, 364809804, 313591434, 185712007, 899304358, 83101259, 676781050, 761556063, 121534381, 508020856, 746482621, 520139793, 356164618, 506882821, 119795552, 213179788, 794599981, 84820695, 854713366, 452419675, 305295909, 287244189, 467847255, 473057716, 179629741, 521891933, 540993266, 240374646, 372570593, 734197413, 579023117, 556644739, 264839762, 537548662, 455603315, 496727140, 5861713, 24697704, 43164008, 913138429, 319422881, 703574960, 33982260, 309922162, 107928389, 987899983, 726173255, 421903051, 971675887, 817858391, 651150241, 407910979, 152677162, 944825572, 385332262, 122716067, 781709591, 838860726, 31513314, 642902281, 315944727, 175367775, 107184033, 518520597, 653926664, 899314611, 44797798, 690064889, 18151495, 906130718, 97076335, 498657693, 141135070, 891265736, 144943099, 563210395, 633810518, 867610816, 284258365, 695983038, 428210304, 18829415, 168746948, 162389553, 80051344, 855288218, 190600893, 805750365, 540434069, 719061364, 641366544, 97266810, 302311488, 510633283, 399136634, 341620868, 399929560, 699782030, 182213882, 368207540, 169550210, 752661066, 266261061, 883925024, 131016399, 650876497, 281059901, 73445545, 761457029, 22735002, 649701659, 141286061, 657028281, 806285744, 784599091, 280887203, 10449716, 506613058, 699183085, 522756576, 503025200, 207795612, 628579529, 439006378, 299072036, 801038893, 856103273, 569899351, 446838466, 656881705, 979677087, 358100772, 351453724, 627471575, 288731226, 252404710, 715345080, 120735797, 935144522, 677666110, 78591497, 691350292, 278818736, 282057965, 399461964, 532130104, 35618041, 112363137, 784885731, 152765164, 221414102, 6070970, 561310010, 271276233, 54989676, 72175799, 768703740, 272194376, 365325135, 204778141, 456302232, 971096674, 491411576, 843550846, 315307566, 398836757, 48628847, 685175877, 781100001, 703085825, 140794743, 133924705, 798863563, 319607704, 999163286, 370875315, 443242973, 509390916, 584021769, 742029695, 262559021, 906899657, 850850898, 399418116, 107906093, 186731045, 731399993, 480400310, 281003779, 930636185, 886315421, 606227150, 889777232, 179539585, 145105729, 805738850, 52098544, 748460496, 311577816, 594384448, 393633438, 899356374, 799030567, 627197184, 426131279, 325895813, 780376570, 921247279, 385391252, 724681706, 366675153, 178637344, 838377758, 374197683, 115724703, 849804979, 78694545, 997311390, 78718781, 734425707, 810762486, 694893571, 815423631, 288612404, 450208233, 917358984, 11887704, 332364342, 44876917, 899487119, 413346825, 693058391, 488889320, 832878372, 211080222, 657428480, 994036037, 340778665, 756319265, 288159401, 787491524, 978986288, 928974735, 849364599, 147377334, 442280892, 366022705, 10269902, 369484578, 959935144, 914686811, 461856524, 103244095, 935421730, 310585190, 207407215, 324685839, 665744626, 578181605, 776050212, 900938601, 106209174, 280326138, 171209380, 682474053, 271995098, 306503766, 582418103, 434140884, 226900665, 402272867, 667662745, 195825780, 721859096, 993475237, 196550427, 240903150, 662206831, 889021831, 999723617, 947885906, 702033246, 228159158, 484356963, 254662208, 353484021, 375945499, 735092130, 692292898, 80505075, 11027904, 961062619, 820813110, 283110677, 550478501, 932291413, 805515194, 542581557, 505850663, 803642322, 619285717, 156871076, 194542932, 7147069, 896217178, 124484100, 71451414, 901275434, 984753844, 928299205, 520304902, 118240315, 350413709, 710411178, 373858559, 861530615, 278769522, 505660702, 492558912, 371945289, 307632072, 789018759, 137680047, 523366522, 490950851, 481290908, 997176137, 616216247, 325346123, 911230190, 687545103, 351436330, 673042351, 867175996, 997737551, 903804977, 64733042, 757575064, 959048683, 593522530, 879350786, 376081016, 579423379, 853537519, 174104771, 154772825, 247970416, 977554519, 442156403, 685316823, 635762929, 774202202, 768972205, 930455498, 137635900, 681394653, 813150980, 266927445, 49873020, 600886895, 923035344, 164442010, 327248915, 179715698, 231543836, 97165915, 15354307, 783019377, 337234946, 264615867, 166904931, 129498473, 549245965, 312045758, 101312828, 22797582, 580752370, 409021727, 943919548, 401569321, 810162885, 401670620, 184475351, 469549624, 780155018, 364188328, 457490383, 163362327, 300263647, 879023276, 698609641, 628008279, 564922116, 172516218, 6994774, 143199971, 523854661, 247714264, 953290383, 497841623, 776473070, 623590170, 705573173, 60341577, 346019249, 656200784, 199522119, 618503721, 795277967, 784059581, 505056042, 861264265, 513289101, 519765067, 968841978, 285644423, 29874174, 86712492, 341240972, 860016686, 414530062, 377901124, 485564686, 177704571, 791704242, 763045640, 761159855, 404862267, 801013800, 944219555, 901139845, 993613636, 314252246, 671801902, 70672440, 53987881, 289940084, 403065084, 108163952, 106482753, 870012392, 53844910, 85911784, 712580764, 356708858, 171367686, 900323572, 250454525, 97608162, 528306495, 254704274, 990498601, 543741273, 824456817, 27827532, 954310105, 222421642, 627251742, 910031857, 936177808, 382895057, 416660341, 32272862, 544484664, 491751920, 40503669, 836107242, 648963865, 464059926, 769121444, 855591539, 302534919, 601850006, 611972881, 979140165, 243885749, 553381052, 177827438, 276292410, 310817152, 196102137, 448025393, 278242050, 552387217, 514454091, 296907616, 751916847, 158318124, 104927627, 594666848, 106094293, 577943062, 297881084, 122858655, 439927697, 943847776, 601018198, 920816673, 7833495, 317766236, 885771904, 562233713, 991174270, 700648107, 976762517, 257599700, 860376300, 833391590, 584328417, 517063940, 21841580, 544797064, 144575552, 907664515, 780266224, 748956983, 680232503, 114060339, 323307037, 555870016, 200176913, 674776853, 491174803, 345971411, 534396930, 710626944, 39585295, 700401104, 216025996, 769458332, 143549653, 518896678, 75095695, 541827037, 734278939, 976496190, 319207084, 425556778, 217413700, 276464843, 76372051, 907008012, 355157062, 861965249, 828580717, 619005291, 329153204, 192727045, 138408735, 591169047, 941756171, 122560494, 329181840, 639761772, 765343243, 547981003, 960903026, 131425969, 501382071, 988804151, 145240815, 328491694, 650948794, 261873629, 166111997, 27031805, 51047979, 230903203, 917429588, 23685465, 696922636, 878695966, 954789255, 996702095, 427361609, 21474313, 883385287, 649158820, 675196292, 419525433, 71373872, 723194946, 542378666, 567757265, 485309602, 29760490, 691536351, 95163562, 545072265, 946407347, 147413137, 813982725, 537424949, 631631259, 44904659, 387402489, 677960330, 170087925, 937734942, 781629179, 541692631, 62421520, 100854188, 234888039, 80944970, 877169879, 187322918, 980368428, 846878170, 938426324, 497044097, 419778987, 431329883, 60993369, 937445486, 927538087, 883408671, 866887315, 709862119, 532249558, 679122353, 346318832, 886515141, 154385004, 197911829, 580387930, 803192671, 904538838, 439495268, 895007130, 563876511, 337772411, 281276821, 214318091, 395190965, 937129647, 472358985, 562944790, 533992102, 215810828, 201029225, 212787292, 571498367, 373002366, 278681913, 780591610, 453657736, 565545091, 782922710, 739894293, 931805207, 686170151, 780523613, 321633963, 243453729, 980754933, 831846176, 322235095, 193437521, 849909314, 921182061, 484972433, 725269632, 732885076, 66812282, 122894856, 929151703, 187595784, 134116581, 405803818, 442364939, 147003020, 92408618, 847070081, 651487847, 18889494, 550827308, 409951280, 858593666, 192217490, 670443020, 752357743, 305168092, 166856463, 320828923, 600354393, 9151187, 324215799, 118799590, 509362873, 409237999, 523620319, 964118977, 437886697, 868760, 730269549, 970928679, 896711052, 699744316, 744355277, 780695676, 988460097, 248042345, 609536109, 185380247, 829478819, 70054733, 210291982, 731069034, 906397317, 688256037, 81942410, 274437196, 746660227, 427196992, 311405989, 461269573, 128066913, 81077290, 796035387, 625362010, 821756001, 484854027, 761183841, 122750543, 689596821, 724998853, 442455763, 51027302, 359866654, 725709704, 422025525, 340512836, 950051684, 198869419, 732379310, 765937352, 536417451, 494367704, 499966404, 934726126, 226794318, 956325335, 835983637, 417455383, 812016890, 763917785, 291753974, 677097552, 694715637, 244057803, 625201829, 489843658, 979610644, 897940676, 235424080, 980764901, 533312088, 815592789, 388724773, 719792457, 572717977, 310728315, 952598118, 487702974, 652463645, 979515199, 543099113, 893678873, 150827214, 58866747, 521861308, 857018344, 722558201, 529529902, 514228500, 58222062, 630151167, 436200350, 131296429, 298441148, 315735211, 513164879, 554086935, 703319410, 263973575, 587423010, 395647631, 494916675, 167417422, 687402163, 423467647, 415543798, 507490895, 329395860, 575479110, 692004574, 275342736, 189790036, 539157909, 446961227, 633055809, 190239455, 43631111, 689442577, 318873066, 738999267, 879394535, 82440124, 166623378, 786334110, 421777394, 13513984, 451723395, 126055454, 904670639, 638916246, 582710358, 280392613, 273704305, 16188584, 966736517, 605185, 735842104, 166555488, 977732994, 565184098, 667366990, 178661842, 730135640, 457953765, 883059544, 438078173, 215014496, 921882335, 264126019, 358423547, 507014858, 258266998, 692222822, 753546375, 41722277, 449339851, 357497165, 140186266, 690832852, 336058965, 24803933, 998157017, 698338470, 38199032, 189826742, 171063555, 87058476, 875306352, 449953410, 658202295, 620191206, 972748440, 621665431, 248315349, 261326789, 800892136, 793364002, 910782251, 81304722, 123799170, 857029897, 626568518, 679631642, 170961959, 259348304, 485368065, 315539667, 36095790, 28466984, 395405504, 171987162, 737247054, 682223014, 195034510, 978452094, 291989702, 382236832, 233254197, 489488245, 32178482, 439289114, 712986594, 281385482, 810346514, 391197789, 511001418, 172460317, 970855701, 857505648, 498428410, 696149869, 331226060, 512844951, 13269286, 562704826, 973039986, 308555470, 777565042, 114388112, 901616199, 990068299, 786985466, 363630169, 529012109, 639692828, 138743113, 148970961, 648889664, 495751395, 224003026, 460207433, 56498021, 926191018, 990235439, 607352562, 276080160, 282559839, 598361928, 143240789, 307383483, 691974670, 990700420, 815195158, 720803819, 436220021, 32487082, 395888814, 724559831, 482423541, 548098427, 262227806, 739915593, 314777385, 563707263, 802338755, 659469613, 141295569, 538716373, 501302430, 404228012, 564524981, 674595966, 993046706, 592752447, 412310540, 569271209, 644793491, 40198801, 451847501, 610051844, 274519416, 204389269, 200855202, 171465805, 122570720, 854170518, 189116675, 347395192, 993406692, 714538101, 380071202, 375967981, 616743949, 374076178, 596072537, 315655688, 986446374, 242748733, 952336456, 259346963, 380523286, 23889051, 615373744, 69752800, 194202427, 669079342, 235594221, 183428934, 605313912, 995341743, 125009622, 604017710, 865232116, 275275124, 304959689, 508172991, 49851109, 729514785, 759602737, 138503813, 274397638, 138852959, 451258444, 604027077, 266533781, 770581028, 626816203, 603864139, 59555279, 775097753, 386760846, 160075255, 22869792, 9745514, 760442514, 660577727, 836191914, 787026539, 119816321, 783056780, 217494854, 854876924, 904807225, 164037708, 605207839, 764872635, 964831755, 391933795, 129597731, 819712474, 354902394, 651272833, 294158639, 237667193, 226916118, 698867120, 71616113, 609314023, 395749002, 687655596, 1038879, 334586720, 6479409, 536101844, 176492603, 469297374, 241197491, 889160166, 406214891, 88702251, 849498063, 288582376, 228244642, 86444501, 908262873, 446586115, 947971571, 236852110, 565245818, 113832286, 800134225, 257255971, 887372192, 613380748, 65758732, 121790430, 237723810, 160511707, 741074949, 252411386, 5588254, 28713888, 252716133, 945560242, 177393363, 285665531, 881603906, 364067044, 480725775, 108119785, 501950019, 45172228, 312036158, 38887388, 710346215, 483857157, 974145493, 100298348, 192234961, 153382091, 784459819, 819197244, 3133952, 712005737, 411431119, 568056499, 728048119, 716325364, 162806686, 86512612, 715309877, 398096757, 857955816, 88573818, 4888639, 685144025, 325270325, 13127231, 67710628, 33006383, 466564138, 682513907, 526923255, 810060451, 452370930, 654230844, 287394957, 471427831, 98730964, 889099179, 993853989, 306695677, 181463606, 765467532, 381674290, 361767369, 733855377, 959533490, 376660512, 776167775, 873162851, 564356999, 486358325, 529332882, 804296216, 440856478, 344596366, 12314977, 501941014, 103645938, 15053082, 530467748, 68073367, 371361185, 58318443, 300531894, 105569488, 92854023, 497568995, 302377329, 894656160, 952973070, 206163011, 467957611, 416267288, 734321393, 766162209, 328102320, 801069738, 816046357, 284407505, 225937325, 143877575, 638054557, 391728259, 579021874, 18934388, 383725342, 150423150, 806496568, 41061338, 557601072, 225411280, 914909141, 280663201, 260120862, 354316099, 234070254, 467039061, 462870081, 990021631, 196076633, 762685683, 195545853, 601767486, 435578818, 347108811, 59881544, 789381570, 272425869, 538169121, 329909867, 186984736, 856260997, 966782253, 872597951, 756566473, 567539701, 286533273, 729146797, 965695685, 413623775, 161222991, 97433187, 420213599, 891548367, 642315399, 540200060, 547933618, 615968353, 378368009, 267890899, 345046476, 393215657, 799498876, 84712457, 653497333, 953154960, 382949496, 808871721, 694963347, 658361016, 156742459, 155045205, 879324396, 397028636, 847020647, 60648701, 663823726, 567638642, 739205467, 392579963, 709010640, 255645359, 536822818, 513165142, 742368718, 614528169, 593370177, 835724989, 382664364, 846484694, 578713665, 556274652, 383858790, 938379915, 287642629, 798999108, 648273434, 256671192, 235726737, 643102124, 302719076, 677789802, 680582044, 289598120, 683910897, 618736954, 546128995, 505542972, 56135382, 513046424, 46549129, 952349465, 845497502, 767079949, 236473210, 188608607, 443534576, 364602264, 889137864, 207927632, 456575117, 635770123, 249694245, 886010241, 366879421, 776562069, 293293689, 72998959, 76584932, 286346904, 117762677, 646793573, 713174784, 29329309, 638995511, 556001867, 398694620, 64660322, 437263738, 859790003, 52938907, 929421277, 109938633, 165531932, 720911641, 555370350, 576048360, 898801139, 238225605, 270182515, 947418983, 899159636, 21713951, 77170778, 38468174, 831236825, 373038364, 453178040, 248330307, 559022242, 630617757, 188396131, 322647286, 748986686, 609920330, 76489453, 714240865, 670418022, 634533027, 562352416, 777360977, 737545590, 799894466, 315034411, 280789717, 699173147, 793051330, 172586507, 988793204, 227244692, 928329922, 819528454, 593040436, 416410793, 657491203, 422768058, 891393446, 422476664, 456073044, 761783391, 8950330, 683743172, 372624872, 621892519, 361933024, 553314448, 357582721, 282820157, 269733505, 37405465, 820379708, 618078850, 959954637, 589862371, 891346219, 265244327, 783439524, 388997403, 796050043, 827535554, 60810228, 992256735, 421781383, 38152656, 465847031, 922293882, 32272927, 16924869, 240291409, 907108434, 781471784, 865707676, 825626936, 444981750, 837450821, 973080770, 474262415, 647336498, 964370482, 947838725, 793437804, 944023608, 233381644, 315076250, 268248928, 841493610, 145138665, 424669224, 712213930, 887988483, 96460297, 313851041, 364884669, 197298275, 284604261, 592858347, 2075343, 833448195, 442031603, 143337141, 909014726, 838707588, 673776879, 237121756, 61869106, 876970989, 183036766, 613489220, 838333895, 135564412, 12405562, 427409659, 389416737, 546886974, 821388532, 399667271, 10115913, 141684574, 745883999, 48313711, 6590517, 142977355, 703459138, 972608568, 290156512, 494759953, 104739161, 110780388, 476133300, 861108460, 691515089, 367789010, 298721563, 300467797, 69640173, 731390672, 49282990, 558280754, 240412973, 94830923, 892592396, 409911396, 543275288, 597766798, 112267386, 326885162, 124051648, 19660270, 618788976, 577738003, 623948654, 613153309, 448841157, 162395592, 127878628, 569779745, 436012301, 983540486, 343354573, 35510153, 498302457, 408028103, 376258412, 975884994, 927380001, 446067314, 891034030, 406824264, 893412766, 879661267, 262264433, 797280423, 169880433, 246411894, 969559200, 999748328, 384090371, 827866749, 894454748, 489027107, 345572331, 431389732, 961661392, 332507513, 355432793, 107347557, 238084605, 918920583, 97684390, 896185956, 60548293, 88156466, 129205667, 137242629, 140970777, 934567897, 179399278, 503119566, 662535078, 455259266, 703029099, 247033655, 252008781, 860340754, 43544047, 316188792, 785622133, 838858491, 725196949, 43172630, 792007328, 143769527, 554001053, 11014222, 925695116, 149609398, 622245056, 864121314, 599588570, 964657230, 858869282, 25821699, 347513860, 977312620, 516342339, 561559404, 553667025, 885779956, 740150857, 225919607, 97708667, 663820050, 167459691, 393864413, 736060706, 912060804, 720669876, 968430375, 597131250, 277474508, 751661181, 624494340, 337452648, 260594848, 152238690, 314531680, 22563405, 567449545, 570290551, 794016679, 669818615, 612415177, 269251929, 222892157, 77328247, 341992212, 781951196, 841261942, 322164168, 825789778, 142276966, 422399944, 23319945, 455235923, 793195271, 810904677, 246954686, 96836603, 954208315, 840976239, 365289189, 734111881, 612216414, 721801060, 882436541, 783255937, 828656905, 842064479, 152250987, 624448295, 426190853, 921453627, 725471750, 844060780, 272409354, 422132965, 373705438, 184134426, 572385700, 797663067, 381914595, 280267774, 395743065, 170457392, 618958668, 972105274, 367589541, 635163512, 546588552, 733719244, 655537469, 280539387, 121639774, 219968596, 516032292, 864150506, 459711926, 738049856, 374243167, 531897836, 696817475, 247419906, 610492730, 726726565, 545023069, 341718292, 36107744, 425482550, 919431850, 494271316, 194489745, 506445366, 315572111, 182444468, 84502571, 827570514, 813967709, 129161077, 572166785, 263969858, 986135893, 121864900, 544547310, 542263575, 891628801, 392400060, 999021343, 226304116, 171873397, 874244388, 153753094, 978028958, 128999961, 165458888, 64182763, 475346051, 305433400, 957939041, 263458662, 543612623, 789810787, 359458757, 202150670, 722971538, 850845860, 785254867, 957699357, 93630241, 664388223, 995473552, 869250451, 662940349, 809270922, 653068814, 400847576, 998458755, 602592050, 874352063, 539871208, 133317712, 427582732, 378653068, 557424699, 551383444, 75677133, 385729944, 558481481, 974238218, 787199545, 28046850, 25124385, 771008702, 892738285, 26403297, 701127371, 344790106, 164066687, 645204653, 514046176, 165166401, 571912177, 189726885, 744400512, 725136018, 922960939, 476964226, 183615986, 532937481, 296560617, 158660682, 775072798, 318014131, 87872803, 65066721, 625205688, 752360777, 192912819, 17587961, 275373371, 557574822, 729558905, 382170795, 148566599, 878202606, 154683890, 42800454, 839396993, 227311543, 128604656, 901614563, 505453437, 666142549, 271377427, 668279528, 148774081, 883423396, 392108787, 334941690, 305193415, 851046694, 448435143, 618731826, 356559174, 569670892, 725215762, 120097410, 640979658, 521960815, 204226719, 667628625, 876040020, 686080495, 295106661, 824048975, 676227338, 60206023, 467499238, 3123613, 432318485, 605501075, 411247368, 780818142, 151435068, 211597401, 928568485, 55980710, 785282330, 608361079, 121393406, 653261471, 792318686, 407129532, 805081711, 884108467, 46674579, 599379977, 490246923, 727468783, 657311088, 350330933, 804377045, 7610595, 346283498, 914809243, 21276487, 156560213, 205836220, 392186097, 692533175, 256388476, 694031306, 922921366, 581013949, 409436852, 431512766, 943553357, 538754187, 637263832, 124514277, 718842154, 226680801, 59969987, 617243679, 447513542, 152022591, 45211736, 446862720, 588508361, 559810773, 426242216, 956690638, 259819517, 863866819, 409729514, 325257317, 845533197, 70777570, 457265305, 38739421, 435541708, 717994842, 763053129, 316013592, 232526264, 813756165, 815997314, 935086234, 299467623, 700562225, 358608426, 854347938, 410643380, 26154659, 137279553, 971839551, 977521961, 202098206, 498752687, 939137734, 166486414, 283348330, 87861314, 898737457, 776251891, 782334858, 687776576, 586619910, 859507133, 669757900, 600830788, 717667828, 786364664, 467070083, 838206857, 685963897, 152844271, 834285156, 19781709, 153892263, 108355814, 869871091, 487084538, 42152894, 587091510, 973734429, 118944736, 833546688, 997941078, 778867965, 115553528, 57196929, 518989238, 32404314, 523484664, 975155550, 371859196, 69769576, 649618594, 646645694, 418437664, 760599709, 470612773, 171550646, 758964466, 952783573, 566038942, 133715763, 497006485, 770250171, 297253851, 525828775, 406903183, 604505048, 821325378, 18596742, 591270613, 646394303, 949445, 386616639, 515095414, 233222138, 335100624, 151177654, 543207282, 566124181, 703882814, 842563781, 592523260, 481123935, 10679009, 384996551, 88143477, 794965517, 165640259, 323308963, 424639876, 517558431, 941890920, 563223399, 539475167, 183967840, 159951756, 134966665, 450726961, 107767345, 534655535, 843012967, 768250778, 858775387, 915709842, 452981920, 552323402, 425775120, 82748517, 516119695, 923708372, 679064051, 84903211, 74429371, 343545972, 96215826, 418203980, 266533317, 260370507, 731183177, 541442243, 290226644, 510617523, 573373321, 17894810, 890149699, 791099246, 44702004, 370279833, 410192107, 561868279, 757002224, 53797562, 168074496, 533294742, 399708752, 384786687, 31650624, 488600801, 441073258, 985333900, 790343333, 266779490, 76159696, 744000901, 937168398, 841915451, 530748868, 738563925, 111966896, 467489718, 176700426, 117976935, 513527277, 310375793, 90600497, 93171621, 604071736, 675154965, 817781510, 628837956, 388127847, 144321421, 176127521, 483268465, 554251156, 28103884, 598215586, 265024238, 945953396, 686235635, 882803294, 474612951, 767767142, 623129149, 169856839, 345419500, 143030288, 257481155, 708403841, 320780620, 788735101, 321564779, 216964599, 618098528, 1739454, 986273379, 876220332, 792402926, 180581146, 648786257, 15534248, 671273964, 527928292, 814420514, 931232615, 906248666, 595702792, 713900069, 752767950, 803155749, 133934580, 28237492, 305367141, 133193751, 530757059, 426481790, 110057234, 648594007, 74650655, 955198191, 855192590, 874385837, 596537114, 430127697, 108816368, 497225810, 318255970, 518503151, 407042213, 925539138, 500294105, 190812560, 682674323, 640176663, 849255216, 101231093, 274146550, 390213149, 142903097, 694643214, 684449943, 428791064, 672788147, 566525954, 953986774, 459145100, 89920884, 560958763, 274599298, 133984398, 812390540, 813018107, 23124214, 384731538, 737671000, 429396288, 374301665, 140116877, 247680322, 705957305, 321477566, 154785593, 339873502, 736378020, 859995727, 965694949, 625421623, 889331118, 390547761, 800327418, 767844228, 934082352, 404260356, 666758867, 391887152, 804976308, 832804748, 674501797, 879407665, 429393622, 739726895, 416038773, 21444234, 394770483, 5389913, 564947550, 847270558, 413957460, 523003455, 94075286, 593235674, 733450906, 717484389, 663488342, 568164610, 868277991, 310403540, 779683615, 212393820, 849968809, 918896686, 994923470, 908278723, 646845556, 325068325, 175505608, 428267075, 307633080, 77149702, 956082016, 875214040, 619963980, 533981106, 868618176, 472123848, 530441244, 205422569, 196533449, 475633432, 579090789, 703164848, 12869346, 930760116, 438277275, 346230381, 711010013, 971112261, 77781285, 197129761, 492988204, 334954038, 513519110, 548862099, 673049424, 466254932, 141767001, 628522472, 487147805, 196230386, 548163700, 19525495, 396301018, 202257619, 598797242, 551314581, 425512448, 80817348, 717846489, 330034602, 330602516, 949010332, 151278639, 287636672, 286985908, 957796783, 926554239, 565323972, 69805639, 379778241, 155633318, 778345679, 57130281, 583254041, 431817577, 119982068, 145362963, 763099076, 600545501, 368567435, 516731510, 660908924, 825997714, 98264328, 916872205, 482535230, 575811296, 413577619, 929653249, 167323421, 831113783, 165394640, 305298277, 748188213, 412413753, 390449666, 208271985, 464121130, 435565884, 601565201, 330271472, 9805749, 476491711, 769426265, 94980073, 84888109, 541787076, 645150266, 176056137, 348376327, 201197043, 561151641, 390525600, 58563420, 648515989, 544919012, 6374542, 361737439, 769191617, 746267424, 986062802, 647932145, 694841391, 757278368, 698996101, 783975820, 963228469, 739312089, 750488155, 625340341, 481061088, 582915163, 557405892, 160978943, 49027742, 570506441, 279184513, 559617002, 884689427, 331260434, 561943754, 659701149, 13521230, 269861200, 465438535, 414963660, 260351235, 615206284, 22987255, 373713119, 989643229, 462794845, 841373420, 793648426, 689862652, 431862135, 515158620, 907671692, 252861163, 75962683, 324743059, 109651070, 122231047, 861695220, 949900666, 111657605, 340029945, 750775081, 743301263, 522708338, 733250962, 45469927, 746762169, 442144189, 92737397, 203370794, 808324701, 995296402, 886333667, 21045763, 968824590, 315812454, 433416303, 397518113, 661756647, 665996821, 280768907, 55496314, 62789534, 96667421, 311262795, 414763911, 607336705, 430731748, 573181241, 832689681, 921856481, 997916216, 754219255, 614746984, 245882767, 244795793, 184091179, 20294712, 906040454, 820013994, 126398, 174143455, 645013367, 637271421, 519031774, 329863761, 810083469, 913068927, 326023927, 399672736, 336659137, 405089130, 905063978, 914002695, 411510847, 720798797, 583851634, 548348213, 211898053, 800023638, 891373152, 728720849, 715513758, 376857753, 218610096, 884416707, 228559141, 16428912, 373683130, 476096933, 304355713, 952268771, 452086021, 580692650, 298249414, 547435969, 407169257, 147153438, 895933765, 471816602, 747606417, 681544983, 946808150, 517218615, 568498116, 475745676, 341112772, 806390443, 123394172, 725791210, 830755668, 254744631, 735217522, 978511300, 749208488, 587912008, 911952324, 342924919, 221774881, 430678947, 800217803, 18658762, 587509766, 887352779, 650205231, 988995474, 886518436, 175242783, 611470329, 828721808, 201548487, 669131527, 68541894, 475408519, 722448924, 798685023, 858861714, 533320902, 594669921, 673984394, 583325363, 100243908, 280475273, 464327534, 264753686, 450059429, 823758976, 88758937, 659284670, 184407921, 515882506, 881234616, 655566539, 730694100, 84262147, 933173327, 190185637, 873371834, 907881497, 495801247, 93847099, 102388760, 881560428, 866557307, 98863117, 992720055, 194188293, 902930642, 520999805, 856346173, 515791440, 714085294, 382469487, 456475202, 219429564, 932079280, 684004576, 866400899, 751750696, 10394689, 413936319, 335674410, 550256580, 82409787, 421669629, 567409406, 468326495, 772554252, 409132740, 479468303, 541524899, 470579547, 388728038, 18058534, 553713413, 820274706, 507212585, 924425232, 587914240, 297907561, 732170780, 826802852, 962039174, 314789168, 745533305, 713550267, 429115180, 981015931, 119523004, 462467952, 693290073, 525183166, 160014523, 548275957, 108749219, 863109294, 478798920, 781033736, 896884882, 354571884, 499946143, 604953206, 707135457, 960709805, 371644, 726407050, 743900716, 450862803, 319501780, 212855034, 609338781, 484234335, 617436576, 252229965, 794414690, 374667571, 143705731, 259490979, 80491355, 578891147, 807481322, 795609594, 286044049, 637771722, 329346168, 828936548, 860710537, 43521261, 675101534, 428503351, 965647864, 385605782, 35365558, 69009574, 620101598, 24448726, 754432615, 227775014, 23043207, 192097769, 84913585, 799999844, 836290540, 864107702, 195108140, 478641369, 779903296, 553771900, 932239809, 833379281, 282570078, 260834726, 985887528, 559381044, 871816638, 465538162, 305074371, 534951628, 747725895, 214050370, 434099076, 333144056, 850430845, 292136416, 54311874, 875600733, 559443580, 24898882, 879172133, 878628314, 737478569, 459759138, 383481741, 291196584, 764114630, 175261149, 388400003, 771958661, 488794635, 642576096, 374909455, 563225805, 598859208, 907984915, 700317622, 731275242, 978889720, 387219744, 59337858, 674362482, 138483923, 781382256, 662490316, 14446228, 206731632, 44517849, 622434319, 727591295, 2030702, 145189054, 445189403, 584258047, 718771582, 200760019, 830716513, 209739329, 876744918, 232225161, 468254971, 517261578, 799937660, 807072655, 111592634, 68446445, 226674156, 728936229, 228037370, 542491144, 114359892, 280129992, 846091257, 667228019, 167942450, 494725086, 671974136, 614488391, 619505778, 713178374, 229424032, 804332676, 906774859, 428368582, 239493666, 978509828, 276500418, 619227605, 763619467, 318150750, 707080672, 429615871, 283906113, 926086933, 21787960, 946290072, 138776480, 609458039, 423037733, 92989616, 693394317, 750255391, 318119310, 827325213, 204491938, 870326531, 336135176, 458568320, 217125137, 707330566, 586046741, 510945360, 672179039, 882992955, 660226296, 249734315, 460963464, 260740863, 387485121, 533477444, 829484530, 254710245, 687285260, 675225955, 49450508, 933396766, 286984317, 78814429, 697375294, 180531523, 126266492, 163424336, 965744791, 548658442, 670364314, 158609458, 545967743, 607479737, 534032031, 757540074, 334652182, 234884528, 320781894, 110640926, 610657211, 930713321, 379146203, 344771713, 235552630, 102697584, 474954785, 657227725, 185815963, 625506272, 802643078, 259402637, 74022562, 447322505, 542340405, 381156376, 420300475, 271267431, 76247478, 1037096, 342639085, 602359352, 592212644, 268474184, 838319807, 594382379, 749701190, 874884869, 620444770, 899436315, 221852562, 86708153, 803520601, 479619209, 275533326, 527261152, 24737067, 970949255, 524556148, 810005832, 737907884, 173159116, 248509162, 602715244, 234744721, 213374871, 284562739, 71600292, 992768388, 950666793, 925143060, 380501043, 851563748, 69796453, 823367043, 188615074, 799073991, 54593723, 46691080, 126530152, 582325058, 643690380, 759648473, 588945749, 234917306, 386671336, 24390369, 872017064, 669869696, 400906489, 810166757, 198571376, 333466111, 987535032, 298914222, 9104436, 42254869, 218357870, 497676527, 243195341, 933518363, 822595385, 474190187, 846638892, 257835937, 104901385, 147440677, 340438547, 508406464, 616436114, 351323622, 596098501, 593615204, 957006851, 440950114, 250926684, 692197290, 551088026, 483295970, 85296948, 545839596, 137548448, 577626925, 738069150, 975267278, 985090835, 476774085, 879241177, 983196568, 745770222, 396745682, 592346449, 656298550, 635813626, 449868860, 415109598, 657282870, 770049378, 100300184, 828370833, 841948778, 204764325, 779508966, 58957202, 779736428, 55622092, 699985522, 782802804, 564341341, 400534912, 289284553, 386736361, 10465441, 5737442, 297967759, 502823425, 822487894, 72313977, 225626944, 20513366, 108929526, 607118958, 969435315, 12564543, 566596839, 142643157, 981190087, 948147040, 541631485, 485114948, 510761708, 997715562, 303754547, 422270876, 715699865, 796732507, 218833340, 538194760, 980623153, 608191519, 784937479, 302234688, 257584217, 356692867, 653171800, 38690464, 738966198, 295549448, 533250839, 63152001, 302876563, 756038515, 891440023, 564170037, 33605722, 48054040, 719955702, 403329310, 415419235, 747132963, 472975809, 339240821, 751223816, 381352391, 120738605, 783154418, 586147718, 144200159, 481543492, 45057972, 245177870, 449539331, 857332904, 67672868, 499782274, 400236293, 504511688, 752898372, 342129177, 973178352, 300249907, 561122341, 635207847, 327492347, 580514432, 613365397, 473038701, 526380205, 298506725, 375106204, 135562995, 5558166, 241545839, 83147683, 365947353, 126887961, 86107783, 906661031, 717814396, 6030185, 587863558, 869215132, 410589969, 656230109, 515283542, 990068493, 19500818, 940124925, 334283943, 341148322, 730987678, 149251031, 465189712, 35753195, 181667237, 718627781, 551350460, 294085287, 998062834, 687171390, 440417558, 260660568, 256456963, 173286123, 165577075, 252990616, 96816550, 998883680, 101845254, 809734698, 275934573, 799572586, 761625872, 123187779, 460094424, 663392335, 335126774, 850070939, 854999325, 780184920, 36756263, 466322169, 895024627, 203722533, 464079809, 756530670, 986042611, 918297851, 998636546, 194216613, 225076191, 871241355, 188121100, 458747435, 162984434, 924195, 628229240, 966361250, 90914124, 895434155, 231806630, 840312514, 718757317, 708022374, 195499584, 505831636, 340250478, 272532988, 666438592, 511952191, 484352325, 541170434, 851702413, 392435733, 960921507, 727163473, 715065297, 722887525, 157325552, 76537151, 916805366, 739836340, 526073806, 52564014, 603857096, 752038571, 798245592, 168972999, 945903841, 449885112, 228916421, 85790551, 731477363, 493354905, 997696337, 812363035, 941481425, 921622378, 865613764, 901895356, 535753482, 117563951, 579753227, 804723907, 971400807, 533432436, 749455702, 640692683, 504828106, 612273182, 885852840, 625606035, 723132352, 486408203, 901475905, 10294593, 528222438, 566319066, 275528367, 146900178, 192422710, 694481158, 2411676, 114157006, 199764118, 276133451, 203086809, 378004186, 955189728, 730819734, 224361847, 757397519, 772247497, 610546072, 740993864, 948916975, 432011820, 194718347, 341265835, 308545303, 216990261, 351218464, 421229639, 543573844, 159805567, 433477934, 728562013, 565412384, 660024411, 647300498, 50320269, 194972029, 551146531, 465029853, 932863763, 650105045, 848814264, 468226577, 748774021, 505576531, 482819932, 283946969, 787750360, 67672302, 88854574, 468831720, 828568788, 914726275, 580346697, 991267223, 161417262, 866066234, 873859640, 371901394, 876800861, 534687312, 34409423, 313235170, 571496940, 79515229, 503313538, 518915929, 265013117, 514612991, 658076123, 64967574, 857424887, 855319071, 181759201, 245501566, 423526924, 435817195, 363128806, 70830659, 841781162, 422732324, 423020470, 723887142, 304598103, 183162885, 964369580, 385797980, 181217533, 581143418, 599274425, 461660935, 51185028, 927424407, 122802114, 134761301, 976074526, 471314284, 309031037, 299880487, 595461537, 615849478, 749303606, 416163084, 682367829, 741837186, 408006481, 677440643, 828079620, 315231205, 738066905, 862196318, 772475459, 434365275, 29785231, 26556306, 490342109, 318751496, 120328776, 572473093, 493397615, 535093956, 137836418, 381763508, 793961720, 60761203, 435919, 743668271, 588021863, 109318051, 772318998, 97647125, 892300701, 686308019, 301639038, 572214987, 791890999, 166324368, 438485993, 788738812, 239475011, 380805978, 166923619, 41150339, 561646541, 315235499, 46801339, 642128077, 710032980, 445607838, 231060973, 856868460, 431866651, 461532122, 554829729, 804090512, 924541976, 3553285, 281770699, 233149010, 465841348, 329975495, 804302827, 71354872, 103168910, 243686383, 676908695, 591164460, 448406685, 830351066, 504654440, 583013951, 888053024, 29334340, 308076148, 357545526, 978790409, 802661059, 379376424, 410012834, 937434007, 821496902, 624630212, 459612166, 55035634, 738705509, 841764340, 281334857, 13813325, 908655323, 558798752, 32754814, 25153591, 940121062, 490327123, 936296837, 83312785, 175799938, 405457906, 667817809, 541641430, 65935467, 611649462, 259881811, 459327606, 761633945, 948899208, 581707672, 700069836, 409557473, 628244320, 821182310, 402651838, 765219360, 831345335, 641024574, 419131833, 231010283, 375125431, 386085464, 420194301, 646738223, 860128496, 56074603, 554654327, 889589109, 547358187, 13694140, 358128442, 522947701, 114393503, 480953780, 652544843, 514342109, 165744003, 449432101, 691182025, 32211816, 201609502, 953778723, 842240936, 591118275, 66369697, 711527349, 156714315, 736677390, 584720923, 10449065, 757740841, 752927677, 760500470, 283713420, 144746051, 925832671, 132657651, 851363353, 866275624, 746022256, 982846139, 244668596, 558235454, 697586679, 52822042, 616800456, 28171664, 62001361, 675650032, 851653440, 397227487, 930402797, 129900309, 595060140, 763677145, 505062000, 850335362, 81450747, 538160990, 710431745, 5263649, 113351514, 821208069, 598383704, 865897504, 626631562, 441766021, 957064908, 62872823, 57838426, 777244737, 151428974, 265460418, 457109486, 644053295, 883019010, 985909655, 704140830, 230079619, 726027258, 292683, 448221228, 635515482, 423201379, 992346281, 676552408, 460655475, 383830065, 209046692, 848341581, 642078984, 780475489, 524870766, 144814273, 248197865, 190806276, 591452523, 931440879, 370141432, 611960411, 780515039, 465074224, 552353212, 18053522, 47077437, 480213866, 115238271, 165198872, 469604725, 697377376, 297681903, 173225767, 604917948, 608976295, 170550754, 989637845, 724226541, 420587531, 176057172, 707867567, 190785073, 999007447, 236992522, 917244832, 874161868, 549758361, 75081478, 954160229, 280161792, 607883447, 254303672, 101701578, 421330032, 910777984, 295325039, 481073763, 715373558, 35221157, 731455799, 761419152, 371348939, 247456145, 329963691, 600066153, 977533689, 956536959, 327976985, 668147859, 914318433, 166047794, 150019267, 739793118, 568796048, 223985076, 630555746, 886367856, 449766888, 528145246, 849408814, 880142430, 166810634, 29354883, 268004055, 186500623, 657913635, 438481589, 329354704, 797255999, 312529890, 465868777, 555565427, 812979244, 451063934, 900846099, 804621976, 936298913, 205353453, 787924275, 715200668, 678870843, 321438419, 623754229, 813543888, 73698122, 84338888, 56988708, 538463497, 717378686, 400889952, 956514712, 524095332, 269186414, 93278545, 685346789, 813599436, 825371030, 837785813, 67011576, 966586768, 490097547, 708133253, 820441644, 238448156, 626362054, 682046757, 540883368, 626276746, 303820628, 851367382, 316265608, 644128299, 266000812, 376659412, 836977402, 627192730, 962657417, 74704161, 39383790, 702915661, 553241178, 441549278, 157230877, 19157522, 85347778, 77860278, 53942706, 462699429, 237503609, 144862104, 760520253, 594274566, 960245161, 378462891, 999789997, 515038745, 677221435, 140146051, 143089556, 806761971, 712797968, 742689570, 458271579, 297979077, 915237857, 890306143, 824689473, 699877399, 554746892, 710140849, 409396529, 976871914, 639445115, 239240971, 241139765, 404045962, 458020250, 807916714, 554806331, 220091311, 292236554, 138889187, 177906523, 120360570, 239024630, 747840369, 435111797, 334147145, 828903060, 516193229, 871830841, 252330124, 486676708, 218669420, 739789150, 856954502, 666852814, 856690389, 344911435, 476226993, 256804638, 408458139, 309697270, 688620610, 751795784, 906251710, 70378518, 421901648, 423089935, 684341436, 991234940, 971455081, 339826746, 655398735, 177366935, 919107683, 795701080, 911044276, 174614953, 18210176, 137080178, 471556323, 192746949, 505456262, 774418133, 252559193, 65146588, 846064683, 800719105, 475402315, 709472614, 937377085, 924367161, 769621634, 473963953, 471857394, 715052761, 383137386, 576835487, 221363912, 65385892, 376712725, 183304550, 176005803, 352824566, 262018865, 860754519, 574293743, 98847027, 316499344, 586136828, 537252227, 769616879, 852009990, 443119961, 213882916, 649360831, 603076659, 896127783, 840845054, 44859205, 759889313, 255315400, 120145333, 71783670, 131788600, 949155960, 712408825, 56079504, 376609321, 30025570, 264909088, 938573746, 299864319, 910938941, 576712961, 138560869, 214307082, 631887622, 58518897, 127040537, 618278152, 729395076, 913451477, 452822207, 160153925, 315213012, 451055449, 335358119, 551706402, 782487802, 575777513, 851116423, 396667945, 671140224, 951193156, 303078567, 233535935, 537334391, 290017350, 427761441, 261317762, 572194498, 79463172, 491864154, 823689051, 846719374, 214323943, 604677161, 286113118, 209333363, 984173469, 686192409, 854990860, 92580437, 545786489, 243797129, 842352387, 106861178, 20533317, 846866680, 154752522, 46627498, 905092065, 112196, 299637, 958985218, 953654412, 996002092, 304715647, 392617653, 948913678, 838022163, 666139215, 990628967, 505483582, 13508762, 932609761, 50327245, 846537776, 661890470, 956545272, 50409495, 754730070, 870931605, 207863377, 108049268, 429717296, 305287530, 870644795, 366924870, 951257041, 583622161, 261079607, 129703276, 954029183, 821580060, 401848443, 565564915, 570627690, 467987242, 30608258, 328516103, 37993054, 203628152, 939155506, 328733924, 496103455, 559873118, 218361831, 832865970, 17005262, 826617130, 904243672, 29210576, 369611000, 22287254, 114801494, 137634774, 653634065, 498179644, 268288701, 595607117, 330426919, 809754252, 802750180, 999882259, 755989653, 661772537, 444492213, 543579390, 905529044, 912136076, 673376691, 727233973, 125844358, 254887923, 228029816, 200884561, 780767002, 530716216, 171239914, 129772458, 315561467, 183521551, 946656463, 728788777, 921436729, 92685250, 865205865, 90568284, 919535057, 756682557, 241027247, 496123527, 986686686, 622353091, 816531309, 641788641, 113863053, 824067199, 175917024, 945518523, 378763368, 765437765, 566214200, 905111981, 336065633, 964896530, 229729320, 264724499, 919807349, 402990775, 862894669, 328144965, 293226084, 753516422, 975263547, 436250986, 754949620, 235599301, 76416058, 162755405, 36460248, 327077211, 886401182, 76319599, 722675368, 15723177, 682007307, 103167861, 562479365, 226743732, 28672937, 592801503, 172154553, 906183274, 985646043, 100560061, 621730335, 336286168, 415185279, 646825602, 516497177, 961205757, 649709727, 276291185, 563866038, 251934214, 404407379, 201707822, 315134183, 249898647, 845458949, 249808810, 820350289, 958046407, 808483550, 834601705, 960860877, 362231871, 729135286, 56050104, 916397243, 43502541, 742074780, 468050630, 983192592, 521388556, 521705118, 977907340, 418205653, 311325120, 553621935, 282316769, 391798058, 822361849, 252740974, 461523576, 770079300, 574087539, 123519746, 56744740, 632493722, 872560557, 899196234, 573997690, 66892146, 634157034, 848795551, 576204029, 934928695, 420734646, 786245857, 858900441, 194159381, 49599675, 645151056, 13834884, 746095992, 251297453, 137815873, 276825305, 83478808, 415452751, 627491810, 500696707, 215421927, 569683404, 7315607, 476677816, 553279272, 870905158, 656079766, 715956957, 470604357, 633304086, 447442103, 389665651, 883434394, 369486533, 383585845, 425063276, 656829679, 3149353, 611379346, 665538510, 167898998, 514367815, 894402293, 961329947, 762491758, 544600686, 580185081, 698926463, 606059538, 50592532, 502797252, 835755700, 691872830, 225546165, 720900551, 441681401, 833351745, 416569219, 439665373, 380232098, 55905686, 105478414, 199512684, 920533599, 369081545, 398399604, 44258562, 870462807, 858711053, 807030750, 597624967, 271641954, 841324805, 170768472, 848099668, 58233066, 522308922, 18490830, 930659160, 275917698, 921881562, 917305946, 855442377, 995728982, 700743290, 640129649, 796806617, 852901832, 548436388, 895590995, 73436958, 248048912, 729633410, 788092345, 976173698, 69365275, 750000106, 231112576, 310621448, 872577522, 839515904, 766400388, 462375429, 891578682, 692313596, 378147677, 340085948, 980709520, 750038540, 223682458, 264145409, 977324712, 424408416, 83305555, 884412584, 347202360, 564886574, 544349421, 567850346, 459022203, 780707538, 132472997, 651729288, 468942219, 481477233, 312762752, 708203638, 469477097, 264716281, 323856517, 283556647, 345747631, 325638637, 627490152, 652058578, 194437580, 228350139, 242177010, 682792262, 843197226, 532684615, 398492937, 582811868, 960024370, 3682272, 541541574, 173609987, 921728544, 692554983, 389344105, 777700577, 730547442, 826787612, 962814732, 438300416, 529579866, 594688593, 156694815, 627686985, 855031500, 31644694, 96488222, 134082955, 707709593, 607750350, 22689561, 879135776, 679133237, 926060167, 31382625, 736840376, 985484680, 951369344, 392009873, 126616281, 949945405, 93081454, 12666341, 136082075, 123809054, 922038926, 748581935, 830478038, 405831082, 521778741, 175857563, 577794762, 721455112, 383875519, 756280643, 408204345, 737629043, 749558627, 602290816, 641060327, 75532022, 708860993, 778578947, 153269542, 776843632, 496038364, 922902241, 725186811, 344339446, 62375307, 179087082, 536565888, 355473280, 92670008, 898950539, 225375705, 849257077, 846738997, 229355181, 28959720, 700976574, 602412523, 69822858, 720127373, 463584384, 205872666, 326555065, 659948270, 75384339, 23512863, 488383871, 834840985, 768666741, 81639340, 944222223, 977470708, 700833526, 200785773, 969731118, 271208636, 173033101, 758481502, 656826263, 909943206, 55876508, 561507577, 965685084, 311676854, 559979159, 774768246, 43887246, 806268245, 853642353, 987938803, 261981652, 250941057, 583312314, 538444293, 13555052, 160655765, 343808538, 820829676, 490615677, 455879672, 992125904, 604424219, 411715709, 191984023, 810807789, 189458942, 397451293, 215015058, 900632027, 939317370, 32131876, 371816645, 583892115, 500603678, 352207975, 327700254, 129051291, 121558358, 702080593, 30960284, 304001634, 453883094, 263876970, 126125236, 350502928, 337770019, 201403672, 103397166, 55793389, 610930754, 683959231, 155749740, 810719793, 695139445, 229632327, 453902410, 231059761, 277856389, 136217145, 595790665, 830252833, 166478312, 707203500, 673583692, 200683664, 940157830, 551650320, 224316319, 550408584, 562947013, 67402908, 883226423, 486367892, 917452981, 467827665, 71729281, 700758438, 366271748, 471514062, 803372351, 196582062, 148624990, 122685977, 111083022, 837318354, 357710970, 584286555, 890564308, 690421114, 39146276, 708554139, 576243697, 594285058, 859057347, 400611209, 582910284, 147284829, 40394114, 805970330, 756863230, 325865573, 100888483, 356923159, 88377138, 636390268, 523434050, 368152087, 624620911, 579431353, 42497043, 969820791, 299374822, 308159813, 702175154, 939335999, 456804068, 761602804, 943952152, 997960914, 479018906, 860745522, 554536931, 149810208, 495559878, 857893405, 25721712, 534519131, 544308690, 32299516, 188350752, 972140613, 655297387, 257296921, 917764592, 335672895, 280112458, 325358770, 607886021, 293396687, 188670220, 835349532, 890719274, 184008301, 707433688, 38456533, 887664779, 756760519, 882256116, 978353484, 264497750, 152421396, 521376097, 803685029, 597054891, 802781125, 396403851, 504697923, 91482447, 268405498, 549995692, 551306558, 358047053, 723338970, 515716889, 398558332, 244403812, 463457169, 123666112, 505452231, 855514358, 901432864, 341412349, 14461591, 758180969, 966753962, 647028359, 808997039, 938766646, 487492906, 516654777, 72680100, 111521284, 52485651, 12415555, 760356278, 425994613, 667255866, 690981038, 790293942, 834770437, 649385860, 416399555, 871392417, 247490400, 435762999, 328613005, 184355384, 253426420, 391886819, 523644636, 297265913, 438550475, 418261452, 532418530, 857765117, 585071133, 919004433, 358601121, 476249662, 699880980, 655916721, 468653762, 387409869, 920452553, 921279852, 260019161, 113284527, 871709053, 958114481, 501500363, 440003328, 513405792, 95510357, 786732787, 709988093, 321287583, 887042288, 44150923, 779942807, 54525564, 792932326, 344066674, 476623299, 551038752, 143835553, 199052933, 819277571, 349489093, 263085058, 35096467, 705374463, 590501466, 448354092, 635017452, 587910394, 500844935, 400636400, 585228434, 192754503, 794340948, 453773147, 187174836, 643711159, 319272695, 908856553, 192860718, 401898617, 919924294, 64667169, 139515306, 340432089, 969703697, 874792247, 434625948, 221246614, 748172402, 630583578, 614532122, 794315068, 706727110, 910548502, 336155991, 750454626, 402837668, 12697623, 329681015, 273807737, 502759985, 425288080, 902748163, 485834251, 620534362, 863518169, 835003766, 284927718, 338536546, 20561896, 222795812, 245147887, 880655975, 174868338, 416200790, 626684292, 247184873, 857121725, 973289228, 253320204, 201557228, 822321103, 197458093, 14844656, 509796552, 936617439, 592838062, 906237408, 261344098, 531646160, 303351859, 785849058, 860382814, 554082673, 949009612, 126467059, 810482477, 663764488, 571523311, 795694619, 782326409, 104361127, 272416162, 213123402, 702204906, 624352306, 354169893, 787576070, 626113079, 405737501, 644873493, 272345896, 543712582, 596540508, 168217505, 272709232, 330573796, 203685204, 302278414, 738187848, 425899921, 684264826, 316570898, 444051648, 692090960, 855758863, 995080675, 568771600, 823156484, 66740492, 481695330, 51974606, 701690716, 474102222, 475785291, 769990123, 661160432, 595256715, 574812299, 654440248, 98803644, 928201015, 960328389, 684898983, 315013302, 139869957, 24915240, 3327391, 504233458, 719864300, 681960816, 573612168, 606992275, 533432116, 295670418, 945518849, 105651347, 38904965, 886932361, 603389563, 242067801, 35808766, 860453644, 934194387, 640536761, 11289302, 265442880, 17875945, 749340994, 742185679, 438688316, 798298457, 249657105, 848926801, 329381330, 764840396, 593585385, 944333965, 412487490, 153144171, 782783295, 798540285, 285437524, 673833636, 180518430, 316423825, 677448673, 573867014, 669055326, 600682247, 864390637, 754626024, 664383295, 944319188, 950222490, 640079717, 722034505, 245102806, 370341, 614727322, 638716774, 975417037, 794012652, 187917292, 270626440, 804279034, 437630378, 514739973, 593759895, 733882943, 359213002, 798719033, 652726125, 298339457, 659843174, 460104375, 381089534, 650612100, 185717258, 428424159, 95942198, 235157387, 945979648, 405497162, 156669756, 556813634, 766100816, 445630904, 336472665, 30361939, 621154778, 932609491, 46497215, 216071175, 14083277, 89555529, 729334321, 484494032, 940734432, 781643290, 763625848, 387054702, 920403942, 675539297, 174425054, 725116467, 927926536, 480359565, 86840971, 614263012, 307820388, 923811961, 556143527, 162115507, 448855786, 646450586, 443432899, 632091540, 419008352, 466221681, 735492634, 960692825, 382541874, 592446403, 368482601, 491676940, 982953211, 366144489, 345258442, 963405787, 515688992, 860675361, 143401098, 94082829, 707206925, 151207314, 781234212, 222700841, 523779611, 151216736, 999524801, 301081266, 75155613, 692790736, 708029103, 111119756, 449069957, 465097396, 620487442, 127143948, 261124522, 261506679, 303449270, 549125968, 770971328, 511720863, 453047503, 725735678, 767628809, 105599169, 299842834, 214008243, 359908293, 162631409, 10365878, 915129137, 901414871, 512015043, 139292103, 738126349, 659331747, 645832921, 856312599, 675626293, 317600409, 220197527, 656543482, 687296054, 185464825, 317914996, 6786333, 815093757, 556744207, 616176295, 778371215, 285773040, 322746971, 657830045, 751379694, 243084447, 452185644, 828335303, 908896480, 989115992, 263856708, 118931166, 887386521, 216721561, 499166340, 417858314, 579208406, 50902572, 965903349, 882045655, 599817827, 109603552, 766176808, 593687305, 32237903, 443799839, 375924343, 253007611, 822371475, 176051481, 236858610, 324188904, 238383252, 982724940, 280550866, 465577771, 676680134, 105197358, 378651515, 380094159, 77092831, 580002729, 672434637, 713354491, 458945257, 286382361, 808766109, 453641881, 235715524, 81306744, 329381221, 860538083, 929289283, 295237387, 536837977, 590161724, 650000477, 950168814, 226583369, 432854682, 785626293, 507697490, 93740552, 64380398, 686537629, 139958898, 591427240, 869325601, 232247266, 680534858, 715044575, 207612560, 707820890, 265557402, 23597233, 333420463, 104855902, 268362180, 997183233, 861625804, 489000164, 129006841, 671428203, 392068678, 920890315, 384091965, 482159835, 60560458, 23331273, 922416045, 958922310, 696965753, 39029891, 585043915, 503178364, 408319234, 99895195, 776333395, 343207165, 965161290, 313428793, 392884010, 794715218, 828029117, 988037434, 722617191, 178831418, 590307004, 768216725, 956036514, 497056124, 301056276, 550706736, 181028595, 989654714, 323579353, 62843817, 101353434, 485720308, 229437677, 844110627, 896490978, 588493838, 745795723, 360503327, 770966554, 20853207, 154898569, 909746246, 972072696, 828680471, 358192988, 52940671, 479522307, 375247654, 373895078, 145385344, 521079278, 994480575, 395003018, 527329108, 181736575, 235737143, 852098233, 862066536, 586835017, 852518001, 880317169, 564304326, 827997520, 120717853, 535836825, 129227870, 255580066, 638769489, 928231225, 809510793, 157254495, 584274839, 588192060, 965473119, 168133090, 225625917, 650420338, 795559173, 142888362, 363973227, 635562520, 504587634, 314477625, 585578446, 552135074, 476298191, 518789654, 294229216, 752188167, 768694030, 532171191, 769907525, 97819289, 634700441, 593080915, 726308460, 715340765, 488032457, 377980928, 180098346, 57624264, 94704566, 347567153, 285369683, 539644556, 391756821, 839765483, 490497563, 548928943, 599003444, 427583169, 574957892, 188450771, 626950102, 466792327, 798362000, 664567071, 460952522, 711663779, 731800991, 237964336, 176285041, 416369888, 4811902, 371781935, 342373965, 526734537, 182525197, 502545048, 603679606, 88271057, 721554294, 325714682, 487609392, 652514006, 738087946, 868034025, 42095323, 523696837, 819998166, 326586990, 887181837, 282184313, 555043394, 574333765, 985659103, 75896914, 272043476, 578467640, 186783044, 667756373, 303681052, 750168624, 570328983, 219074870, 290923010, 326701642, 427682597, 114765056, 293460151, 260504630, 677079279, 136799069, 983649762, 323244950, 650334982, 538198163, 297197099, 79550470, 324411624, 104250671, 444079167, 274272984, 452337385, 884351633, 276438210, 648970476, 710233351, 887946651, 617260135, 432707, 415558277, 549334312, 218592370, 451701990, 112894421, 768432515, 743031143, 816216242, 20441344, 335324430, 416168274, 396355587, 639550204, 156213013, 645077861, 861998967, 357809780, 19732213, 189312310, 877973659, 424517645, 528848367, 20491617, 90356921, 911308032, 167638020, 471744547, 141427407, 966500949, 451357804, 40928490, 283877779, 843801933, 999146454, 755296802, 765770991, 270435468, 215900742, 516595976, 307149994, 164694938, 415673216, 823965642, 328939624, 456184575, 241794084, 997688795, 239228966, 757076469, 446792919, 697030618, 860717887, 142353364, 345253514, 387137624, 333367922, 382343136, 353897647, 164047905, 151839930, 458558305, 110736036, 716061851, 721211157, 345059634, 982146594, 345627108, 105917876, 602898134, 47064089, 285569692, 569800832, 179221649, 61388578, 501513428, 23575322, 795221002, 61897167, 144053055, 953331385, 44186969, 317469024, 432661467, 695896867, 208608683, 876360916, 550493793, 558870302, 359003314, 942326196, 20753216, 786958411, 432835606, 316645705, 473169149, 557990056, 259878585, 893245072, 782002623, 205011263, 443161086, 229300296, 763698940, 335210098, 987528918, 488116168, 72866843, 257486222, 857581597, 227969005, 543593435, 276114744, 463412339, 317985327, 632053938, 54683420, 836313861, 245871923, 951602923, 34506969, 617218091, 797084729, 210052371, 950493172, 203852702, 295208819, 397310424, 143770456, 525612819, 764982533, 746814756, 421536763, 970933121, 188574366, 317733612, 613854847, 884990256, 112707046, 526901204, 20174694, 577531537, 499367341, 767898116, 369468643, 813127810, 614179515, 207270520, 614991490, 718624615, 708358199, 533269592, 25596282, 926864664, 50202150, 900377730, 600655245, 856198576, 521745716, 113175124, 76879721, 703080383, 750792369, 54354237, 158229527, 826972470, 86620541, 231512828, 35719184, 285848032, 381313012, 430182972, 397784744, 290285431, 147930931, 857884080, 749614548, 230805231, 750500414, 741368356, 509127710, 250449003, 652843003, 779704416, 987207096, 835158721, 416430411, 855312022, 956819922, 715917123, 72204936, 942920788, 41314005, 40165625, 301873442, 926760794, 804129737, 912538096, 663905383, 893675117, 66353581, 533073677, 786598178, 801382681, 256169131, 608365922, 732050880, 971751166, 496086158, 354347180, 396406029, 911490803, 981205104, 783764430, 185643897, 753816186, 414055342, 999332386, 200324334, 91175970, 597603860, 375098602, 425059099, 127037801, 305479748, 961322178, 463733629, 851381816, 766286128, 338071229, 126546228, 536764684, 779891875, 965149261, 349680873, 805293306, 981590963, 133617221, 145711304, 717611295, 577315218, 580088322, 642507661, 851354295, 351790329, 845295499, 520672491, 958979377, 883011649, 451893744, 584530711, 608298560, 702933921, 35735590, 380048048, 706839851, 916113857, 2995882, 928003108, 707614588, 562634020, 638468944, 780323649, 229686680, 191318790, 262365354, 152824907, 241197789, 324015943, 823543821, 903099581, 749478660, 308860658, 282157358, 208500181, 319866734, 633746609, 688998323, 552898151, 186647199, 879745896, 615983645, 900124210, 522123035, 192644410, 292854209, 371031081, 197963206, 336735156, 27850315, 436926620, 393476078, 838932336, 163174924, 981015940, 222442984, 673218469, 828681798, 425931436, 10753166, 513730984, 107906718, 189627153, 109807840, 689069877, 237043119, 140164364, 454697480, 531552405, 55344622, 948921201, 483579204, 160804612, 678109401, 741788538, 910841448, 747481925, 770655095, 970891811, 380472818, 708103094, 734752022, 230730591, 357956153, 827370516, 197639843, 756176534, 244490907, 380944695, 107937052, 958028095, 574839888, 949216965, 612005329, 29486519, 560410136, 742753883, 557902670, 33855007, 415021238, 331984733, 914255889, 513621284, 486871405, 922836059, 736416147, 244067830, 865196088, 352616712, 949655815, 406761668, 637790167, 571195043, 228352096, 669838374, 979087355, 309631908, 541579609, 993913770, 835667557, 869548927, 852036816, 756801256, 769513486, 385018677, 129503778, 410307686, 687614385, 509248084, 833126123, 947140672, 441347616, 291781189, 803879176, 508550394, 639705140, 654598553, 125453077, 310997921, 380987503, 919756559, 359874798, 840038576, 738898693, 920180799, 755772666, 978192386, 124633010, 833818411, 722110167, 370398563, 189654626, 449567764, 605628064, 144970051, 533896610, 593871553, 758264410, 891683111, 983992117, 506511711, 791256241, 309636705, 756208008, 411505732, 226214474, 936569746, 518007580, 377805058, 21109514, 234241084, 477312461, 982205995, 827728157, 427884633, 379028102, 7089713, 546055320, 896239475, 130767171, 9398098, 276214540, 4372550, 266345018, 756210376, 273133719, 895728944, 364322660, 380218439, 196739442, 975511089, 472386146, 234987013, 422428022, 557131588, 986434205, 150839948, 379423659, 941195030, 467562984, 219281908, 999309996, 869469723, 358049298, 75830726, 412495991, 471432900, 824912183, 337559659, 180954684, 32935218, 906900381, 87223350, 982802948, 317469512, 614766643, 972943366, 902675390, 470632698, 399613386, 648646160, 132879332, 76606226, 386686828, 237420607, 65634409, 672647678, 357072612, 47302329, 803432752, 503881102, 721070545, 246528412, 771286641, 556142873, 250631187, 276979004, 72662868, 229450146, 725817839, 162811472, 792776833, 136537516, 541111601, 815531206, 130862232, 61522483, 506300652, 277017611, 133392045, 549045298, 941839351, 111101917, 509278170, 594921731, 120013364, 916980974, 590742366, 706185040, 726829942, 430625870, 67311630, 622860316, 977525558, 778843887, 88878046, 387939575, 295376451, 960612686, 687848413, 159662348, 368350085, 883320801, 590817381, 638861467, 983286265, 868019301, 305567690, 65837794, 426034142, 170605912, 487638198, 224759256, 392365940, 442672107, 925910478, 55202163, 658157668, 170517056, 572739976, 758493152, 669634321, 952620677, 699409230, 682528442, 684809153, 560309969, 711380956, 921208330, 470088796, 786870393, 374992763, 790994853, 51196335, 915037065, 621284154, 871443864, 582364150, 659193104, 937861885, 996421422, 186447754, 434579767, 398245414, 49787170, 618771511, 506180380, 973858954, 433993854, 610500047, 430783206, 654070170, 460186941, 89596185, 740320376, 632604130, 416051297, 898126603, 651197279, 306787561, 605895844, 879461207, 115406586, 841746311, 52036494, 816231293, 950827591, 976704133, 624314954, 632623617, 644836317, 420591215, 484802984, 713781307, 753410294, 201947059, 149834152, 413683080, 467308961, 484902564, 669942970, 588533537, 902213154, 912254243, 948462401, 887096076, 995951367, 691942781, 758426458, 282207013, 294982209, 283621065, 900151617, 525427826, 298683475, 139194442, 279677546, 735804134, 745233451, 526597005, 31571598, 124842070, 257372617, 19787018, 144650860, 9498228, 119756978, 677872555, 97516314, 116961418, 53965360, 555984527, 633952548, 39518381, 10862546, 689130289, 592701477, 365465448, 261712076, 343016200, 491821624, 10614421, 336974512, 938918388, 218232405, 994440509, 154633452, 65442284, 444539728, 231691712, 346912799, 318464624, 717379954, 939106763, 330874142, 375377299, 622237746, 533271132, 918010420, 848192107, 673641086, 843620542, 125037337, 139669001, 907850210, 818468422, 880291735, 890276985, 70686367, 654841458, 911496167, 592155098, 264658713, 462637969, 102785578, 973466325, 766413303, 906131303, 395762989, 356770764, 485388122, 757605420, 200998747, 61749296, 329648083, 569921571, 792214096, 31767319, 516098162, 400241649, 356962887, 496741690, 788789882, 632169825, 351404910, 323302834, 50988672, 638040096, 509948228, 789555593, 164424725, 275746535, 380366308, 895227591, 681211108, 306210514, 342408271, 273747133, 664861659, 609081285, 333953396, 221249826, 923209879, 681808320, 279771049, 643464188, 518370665, 99108270, 73615477, 551676282, 671149026, 905951958, 335826908, 86525995, 25344208, 679451044, 862999747, 384392717, 731765786, 512568277, 557720614, 33478673, 167886131, 617498305, 965232735, 976523688, 848327979, 101845194, 121418150, 124940735, 334205371, 890511073, 657968076, 347890685, 915394179, 127844287, 983301781, 714634393, 239798050, 185393326, 75877105, 325557316, 629560044, 289952016, 929915911, 285117439, 33711837, 505894315, 984283206, 187186441, 537956696, 674226315, 52188017, 655620300, 866499822, 233603473, 191077678, 812242720, 502624167, 729351922, 562376952, 52406675, 170560507, 783598862, 307964838, 129552262, 494218743, 301706072, 919583913, 385237560, 468598701, 449956929, 136523748, 21669073, 184180012, 125712901, 606448000, 220352341, 141147447, 717248571, 760137717, 200750523, 771341040, 767836068, 72982472, 585032941, 212465788, 588356602, 639435325, 117948839, 506963762, 258660274, 161448830, 344125197, 697001200, 178568955, 488300467, 908983863, 425969393, 989187781, 357316644, 748972060, 983771976, 251078721, 539879040, 80573018, 412992147, 112213226, 801292119, 62454405, 49800964, 20766066, 605237874, 432807539, 348929471, 607016881, 913868058, 771484261, 165089478, 791827224, 616916364, 691117776, 360041028, 861541741, 953180695, 98874953, 311854813, 87292361, 906717094, 333515024, 159220399, 762492519, 76346981, 287074530, 871520009, 938235174, 932400676, 505304517, 377025689, 31245674, 320422759, 507239784, 33739167, 231172750, 44843432, 669873635, 389369295, 796892858, 87035567, 834905162, 107205219, 243091404, 198874246, 751051736, 725964943, 582302157, 342483472, 984778762, 657645058, 505444911, 972467433, 58726968, 928800042, 49107721, 448185713, 548686008, 35224026, 947247875, 97737428, 783044116, 144511943, 800711874, 283467033, 858717144, 794612661, 739761623, 607953813, 428757734, 899075216, 839118224, 288211373, 901078791, 749824013, 621793571, 937019300, 404148801, 582575386, 617126581, 671998963, 442807944, 86141702, 417957743, 442242536, 995714005, 991807270, 840945109, 278758115, 265930048, 35195111, 612548250, 724127720, 372055509, 328817719, 269320951, 477918782, 940255201, 660424529, 272479241, 949914855, 828319726, 90656885, 166206766, 295914138, 381714305, 727234267, 747820219, 324208858, 210810504, 510833921, 39168019, 486894459, 438960169, 6043567, 60834360, 957665371, 937949768, 680578039, 874334167, 485556726, 876390123, 345620401, 724001028, 731248734, 847999848, 263613528, 877279388, 689245934, 192616418, 676546207, 271920507, 325264364, 150264846, 132588342, 967195595, 254321700, 727209483, 916086425, 897288698, 858363012, 358784708, 410441185, 374913035, 322194900, 267677220, 256869087, 629845812, 227735982, 726959577, 762328558, 604965181, 963696048, 119339068, 894428054, 886174579, 77365310, 218861570, 44695210, 510560066, 637811002, 680279967, 478710279, 36620338, 798399069, 783569797, 222176580, 206385717, 345974343, 434018061, 831140699, 12591537, 277312379, 567929026, 724344501, 744532518, 627316148, 537037140, 455281232, 967552820, 935641412, 108661016, 225168713, 357828473, 525943886, 577213576, 240551993, 307586548, 463742043, 825617220, 235700626, 778003789, 577421288, 463253859, 434083927, 869120427, 824512860, 980598123, 602117032, 716448768, 527472027, 995701770, 269931932, 813325890, 415801387, 712591304, 95972444, 557127431, 749463129, 267461509, 361964268, 927595464, 172453196, 657609904, 893905759, 987744562, 991281514, 243890980, 196289223, 131154991, 855920234, 59670267, 584377875, 403583607, 824388852, 341067071, 319942097, 168013782, 22617933, 226772846, 383564235, 310407318, 25687593, 915476143, 101235082, 527484763, 507151178, 723353343, 125265866, 372594950, 357035462, 24910223, 276891579, 346959973, 810304388, 912148206, 876694174, 806308933, 726865950, 281246458, 719426441, 428330680, 483080191, 694571071, 804990146, 433479760, 400171068, 112639525, 58541536, 431301202, 974268235, 261263688, 416940081, 970719795, 305320288, 809096027, 242230863, 509688520, 44562697, 921823201, 197311048, 869470493, 563743266, 23575482, 641954863, 523968708, 447898244, 54874030, 982672674, 290017990, 310409058, 496330559, 188140356, 114533835, 652688692, 867515487, 165824271, 56235083, 664013452, 873609810, 370415077, 508278825, 42409370, 927684900, 963854096, 254963920, 429985736, 793130842, 166276441, 414177709, 615600490, 688529898, 942692061, 322366815, 436234898, 473724141, 362668769, 347368654, 632370485, 992198558, 183958496, 681129945, 678310818, 87345402, 722220774, 511000100, 93691228, 969187452, 466341116, 959739199, 919696834, 46016233, 972132432, 843965627, 854686336, 570574575, 476653003, 637190730, 9802935, 391078599, 406945821, 599819755, 444862305, 837374881, 105353080, 847419213, 104069217, 825475032, 897002037, 218085293, 713191592, 261400185, 88612834, 340154489, 38404672, 340802290, 662221692, 215123316, 386138781, 158171976, 205915399, 44528806, 860436107, 464676416, 441192090, 519880977, 773388399, 267255666, 198177585, 862680761, 898922425, 211268062, 827987056, 646030582, 5202313, 455796465, 382565924, 494751524, 15043948, 265095310, 737400033, 702177600, 247872402, 540819600, 853853314, 269119425, 559328773, 104033327, 403593589, 6276946, 837796314, 456176212, 832382157, 580954821, 618092527, 265422825, 425603157, 904858436, 666441218, 405708993, 424999175, 16320312, 227803425, 434329047, 232236419, 891832693, 155350803, 83798073, 320106016, 152817708, 291957507, 477600017, 266426733, 200446453, 340583347, 129482871, 908427074, 121533534, 809291017, 140321173, 857630771, 596965956, 996902531, 991092450, 475951458, 484447835, 356719067, 425373756, 985327648, 264094432, 316323936, 563233578, 881529553, 525384343, 975823266, 260024582, 914190868, 632668231, 354618179, 122528312, 819689964, 16070054, 341292636, 549977880, 764951302, 791759663, 74585299, 318743875, 737470236, 870054828, 611031071, 495249183, 143029515, 406280608, 220527538, 496282164, 163920873, 97482156, 393432568, 565118769, 935705097, 481748975, 484702563, 298191781, 745321522, 201785271, 519598368, 542315458, 231105058, 721696943, 131435917, 788514490, 931760806, 998871696, 377407005, 923308926, 754862951, 517375695, 37531454, 155765150, 157919682, 726006586, 770858071, 357639394, 136586633, 968633647, 69472018, 263856452, 766468715, 545906460, 888131232, 957881409, 751188432, 237611461, 949005476, 385246112, 408560238, 212836220, 658397537, 824178548, 778368842, 483046123, 919707691, 138236182, 379853246, 157354142, 496676622, 928052076, 167156822, 916042570, 384843901, 303118094, 280164845, 177884466, 540407171, 860736697, 315263684, 159844051, 684202291, 368189445, 981652770, 118490903, 848190025, 33509730, 147034517, 404723935, 982977794, 6575537, 236603211, 274482246, 327487696, 299874105, 684480745, 501836217, 209088416, 112679239, 810706360, 800279930, 638525669, 123241835, 873181044, 574232237, 367513164, 978878334, 231264170, 978310186, 247945857, 995680594, 279271030, 761599505, 542360300, 485713521, 716166265, 482428663, 352825918, 616555623, 316326878, 154685228, 347123702, 983595415, 347631623, 402040455, 511724393, 841313344, 746179042, 47384908, 850046291, 431752752, 508900948, 310548294, 827556610, 841503591, 138243340, 109504356, 756507993, 143149478, 289829822, 743824066, 773141033, 379045786, 399699318, 174050426, 659023556, 354802023, 400142258, 870387367, 558484895, 793594152, 289289173, 716860287, 99287050, 566104760, 621050858, 968737677, 9286678, 194569962, 853200669, 239176733, 836863664, 298908844, 687556763, 52103658, 456029821, 992556450, 881165383, 187216789, 596743483, 970208628, 632550627, 300335108, 574054515, 718458455, 613016418, 366654491, 603979794, 823490250, 521767945, 788319387, 124023144, 932100120, 997303344, 718712824, 131651236, 63477754, 824862235, 548185104, 563258383, 386748278, 426333617, 465579148, 135922212, 184902459, 503847286, 248423739, 629386095, 247627229, 851155612, 3213692, 276397511, 923584945, 109721175, 858356278, 857985155, 222413139, 118239718, 377279864, 458147138, 707568925, 250806443, 431788223, 268782812, 12454790, 106388022, 165729344, 359657097, 91462362, 58059025, 371561980, 274539839, 973251987, 469848676, 909459248, 406464900, 449617826, 601378772, 293757865, 809420996, 322508190, 455116150, 628058320, 773681949, 864176211, 745049378, 31913114, 285242219, 100631903, 670807571, 633149764, 149038374, 67697022, 957884170, 885019927, 885353939, 481266110, 487154812, 69467403, 769200162, 92927442, 947966248, 869466520, 642673585, 693146968, 736052730, 36122708, 222404234, 854341588, 34590618, 242224037, 744575842, 773108902, 683638165, 198411035, 835119965, 149171791, 97307964, 99636212, 168338884, 815474129, 758000718, 8401984, 554684786, 629175248, 668563821, 514909009, 120465656, 43912183, 695941568, 901547397, 367343299, 515421631, 972961170, 861878893, 340034831, 165642857, 767469497, 883193352, 493539676, 369589477, 463709625, 305700411, 416223766, 435392017, 201494210, 737020501, 396217022, 165932836, 360372300, 530688241, 750351641, 71265309, 638241335, 725389754, 47964576, 176542909, 374952730, 904637825, 298243196, 806103369, 972469260, 635369482, 142914624, 564172056, 734815605, 346581310, 35691953, 353092445, 353898784, 23540850, 28718, 424798251, 958973541, 980886438, 775579219, 489498761, 385242608, 498326857, 959141090, 475967884, 716748966, 290005446, 295185096, 968875408, 890984899, 941802898, 717671621, 515582758, 745442814, 804950924, 652589608, 310576689, 950755742, 583534268, 109350503, 898010212, 399926441, 547435010, 570893268, 556810156, 524645391, 567097554, 784109423, 141206726, 561925838, 896751957, 725892804, 299950571, 144065904, 862603212, 625188461, 778991009, 969376031, 988824975, 911780770, 199181448, 887258140, 570855022, 795527087, 274788179, 568950446, 465475912, 537445235, 843159615, 769964194, 266551735, 79227977, 549590593, 123554100, 242949547, 646825547, 49339445, 411713125, 913863128, 755951191, 8218741, 698587729, 981992503, 459054941, 608496525, 739694388, 631934345, 202341792, 590939722, 270422032, 836204283, 669871216, 102769184, 157156748, 313858923, 480781579, 114187897, 645888225, 541102180, 789160594, 451471655, 4060879, 548127564, 720906368, 278171895, 872537673, 664972776, 468566971, 787417352, 199187615, 531143323, 450297193, 122006420, 471414576, 679701625, 492222692, 810419631, 897801394, 126852766, 607682448, 48468784, 911957931, 827603573, 242979621, 887344563, 332521506, 17850357, 586431462, 36688826, 409913292, 907216388, 982942912, 165544121, 803478317, 402858233, 641561103, 287246871, 708043565, 219032040, 276396115, 570130781, 333333520, 570183283, 835135129, 913099649, 696979695, 850264952, 447800758, 659787336, 818896009, 819509818, 545462610, 389746798, 501076962, 712257437, 766617878, 854967464, 408580069, 848458761, 703212719, 367405729, 165409075, 882898801, 576907222, 745172753, 536798735, 718844822, 584087000, 773491223, 336933552, 812810257, 944333585, 696583528, 954347361, 100707279, 44699249, 856659467, 918711568, 816570598, 261600758, 884399751, 331074471, 880098966, 917881173, 42872016, 136590917, 548449679, 217073024, 372825789, 23197147, 709364524, 970025986, 570421076, 222103953, 10784865, 657730144, 336789282, 578584206, 503703130, 889850857, 116102054, 95559709, 133695080, 802050293, 957969466, 795182850, 126474473, 435184832, 146285215, 985870390, 932616177, 856168231, 112721485, 67552184, 104846341, 19524885, 975681429, 259912916, 974067053, 281207654, 627189101, 536668229, 192480185, 439348407, 490192215, 264384099, 665617633, 947324199, 804165028, 357889219, 933864378, 473822830, 959641909, 887702478, 404843415, 743516297, 862255670, 806962546, 326186784, 275094596, 958981574, 184710520, 266678898, 720090435, 240245789, 221554559, 44648690, 57221537, 571386582, 145926347, 475665645, 217977202, 294434208, 1000556, 878690996, 982560600, 382658818, 821382914, 900321573, 893387899, 776554701, 852708386, 167738329, 345882832, 822660958, 8550088, 692558077, 535534860, 622468226, 739755324, 137002878, 501740752, 208149620, 409522998, 792416080, 125577315, 215217632, 171486326, 853305859, 680629663, 570048808, 107207630, 212546001, 259848439, 485622170, 66728976, 171267374, 747204922, 851980099, 412044440, 396600081, 871070501, 474463314, 308748402, 18852292, 270249962, 832594899, 540706493, 459428993, 538662586, 574172508, 248396029, 808184926, 760794306, 957640140, 586385949, 647217396, 180793807, 660186119, 616809724, 86567255, 805639306, 342464845, 460158168, 384090456, 459732530, 58726460, 151334945, 252806686, 9413074, 429028486, 381107239, 720193856, 571400168, 334919714, 936388409, 71642427, 499900881, 104455259, 772008100, 980935349, 379456361, 693744247, 132936197, 258534885, 578821958, 189137677, 640271217, 422990297, 832468299, 677399995, 754046702, 52025212, 819154278, 143218648, 212521900, 878508927, 784307357, 342346513, 350230339, 1541877, 510213478, 834153020, 41852535, 881033414, 215089344, 165562066, 34195428, 449294949, 748207596, 235702037, 221458330, 196602435, 303059289, 111330286, 63028018, 481599499, 364661949, 997115167, 476786255, 888020177, 40553467, 214767562, 787933337, 998443336, 596515537, 536117784, 348164066, 534003406, 554104286, 248552438, 287220012, 187214619, 808705393, 557394046, 505804040, 940929403, 358069326, 268782549, 223189889, 377094472, 813379186, 369199814, 923311866, 220643525, 61659886, 887356576, 360226010, 471354275, 219650345, 175854558, 214489840, 981526259, 731984674, 379741610, 35941470, 746069062, 414763430, 247656694, 710541619, 833196192, 801542093, 737128951, 3405972, 340043651, 35576087, 158606056, 274764426, 76602329, 503781531, 424150449, 81919257, 160709731, 330180283, 490554136, 64903404, 89330712, 677476146, 192651700, 198261297, 721037544, 237038674, 719368575, 138102910, 214098294, 141488700, 790841095, 958072328, 890756275, 759114536, 393202250, 310312265, 278559250, 494379670, 70653635, 987299098, 338210897, 54573434, 715029911, 108018437, 970971832, 979384006, 631161989, 335344023, 113926385, 927192405, 66118048, 984450482, 378541734, 402360132, 394647725, 574303488, 882832810, 169713763, 599444812, 527677230, 328829274, 862328498, 329891960, 757993183, 631187618, 826028845, 651152408, 293871820, 23820443, 844734576, 592040655, 907282711, 167084140, 985796347, 623908897, 195027418, 746944339, 176027694, 943902823, 633054325, 724825691, 514281387, 951814150, 39638840, 761365014, 286632256, 220532155, 436896180, 234859567, 157397662, 923431898, 701825971, 321163988, 297419174, 379156598, 602010204, 993075887, 357854539, 204332446, 767814778, 679746544, 369383406, 17004920, 852106715, 125603561, 146594146, 271078245, 878228830, 847932528, 231397658, 133265059, 788849456, 382209386, 388241140, 596187568, 370905840, 131578117, 985862068, 741365615, 433221929, 750815029, 533468383, 145067501, 779309059, 667900401, 851577210, 416940039, 992844517, 880933051, 177094443, 699248049, 573610680, 773395271, 666406173, 771406361, 688263526, 371832544, 932759653, 624326480, 708309925, 410528586, 10714641, 129479984, 639621718, 893425627, 3714651, 63010595, 120830609, 74589909, 137962743, 756894618, 719411601, 530606738, 974457984, 645448440, 490277050, 475048515, 343557346, 431136010, 503203796, 525492313, 550084382, 56946569, 312756056, 612573807, 516883431, 884704482, 34205611, 182589922, 169051347, 354267342, 990266902, 978451169, 84017101, 333021681, 26077586, 94782634, 832647603, 8593248, 368183402, 153034738, 255822434, 581063224, 923198485, 878629787, 823283739, 87557219, 834096950, 836092579, 232540856, 630783434, 192921569, 162416942, 607774404, 355020294, 65302049, 159116742, 490431921, 360123900, 851224969, 124513058, 376989026, 785086985, 527255559, 213468829, 732901285, 142582436, 381498496, 549213237, 625519157, 101833185, 851749836, 304273739, 927993567, 17415440, 369103004, 283915938, 327616221, 310751126, 294525860, 901698370, 986442782, 459024508, 684826556, 668241171, 615107324, 711518947, 475622480, 939409251, 556576397, 22941611, 952898471, 709191774, 890981381, 730932662, 128302101, 674219807, 434588322, 90988453, 298445808, 754573374, 752780501, 512784202, 222766658, 366330042, 101327584, 288399158, 315987315, 614860366, 781675333, 221351195, 317732963, 839526568, 7478759, 42433496, 784546372, 79851701, 745680229, 897733828, 661819230, 946734617, 442749894, 233708607, 139432000, 787671339, 171749968, 349294767, 57744762, 614542085, 275389466, 501905979, 387590557, 188458098, 304930418, 446497563, 243666958, 496937048, 494570841, 265147494, 883684813, 87291710, 668825958, 830191807, 478849539, 732748512, 775864361, 389129597, 411076348, 567517818, 461382583, 487216002, 154152343, 494430592, 145637982, 151861159, 894817857, 629596392, 884729850, 605261406, 373474851, 403906977, 93551635, 285534607, 898465285, 375819421, 918276349, 516993110, 23495003, 496147704, 969180966, 906340624, 786361214, 703466773, 794907939, 817172063, 860320689, 853181729, 540880371, 849708088, 686540052, 560239001, 44982166, 285555058, 954523382, 310176542, 453436456, 493666779, 107181628, 700689008, 106875519, 166644453, 89236258, 396109078, 404825345, 844059277, 667206210, 231257890, 990775321, 667173592, 361965547, 429819063, 850969303, 6773773, 186474188, 695957122, 807378882, 266942706, 175684766, 64941195, 123638451, 38472501, 99445075, 4490830, 791344751, 688029186, 235422816, 679246415, 976096826, 55358734, 820229065, 593675715, 71179407, 880620106, 632711220, 445437871, 118122175, 20713820, 679020939, 586778742, 452212170, 658780578, 965121495, 650781520, 234051892, 341459992, 554556507, 13199193, 318311096, 302644962, 283890783, 1228935, 157015633, 491578834, 259857393, 533330737, 265673477, 654572800, 742970685, 934430897, 703512306, 701322495, 254610808, 346732148, 332337796, 607301575, 409813286, 966944873, 542599361, 906779699, 811845131, 279776807, 599609316, 570259075, 681710559, 369479264, 774534558, 821126399, 833806206, 893653786, 761181029, 469905307, 385588411, 9356635, 341470629, 838924198, 750770396, 618843651, 97225757, 884096244, 556184919, 560389907, 574870566, 397142354, 960153864, 540551823, 123302825, 572356052, 256553420, 632306169, 127931026, 716941002, 347624921, 201623428, 370205530, 556424589, 953340340, 215943549, 768492924, 865569851, 531675643, 499923227, 929509759, 745147853, 509455022, 806130858, 627388795, 934509478, 330383349, 523241216, 795205541, 890066092, 292134984, 559662803, 143496690, 41426042, 845566055, 311044510, 979190646, 556116651, 763182676, 846470052, 523742680, 685991769, 342666102, 353862793, 310268389, 324704861, 248522546, 563237688, 624163467, 244658585, 710155394, 236825599, 44828619, 865010628, 211437817, 207849550, 801617176, 469600429, 100954313, 330455082, 74344335, 537619389, 62568311, 829975012, 119875899, 502813665, 54469436, 696833723, 184933527, 145931055, 785196795, 576560722, 207054704, 987118638, 918721571, 903284597, 635007684, 32376320, 158582284, 935431231, 740494774, 709921183, 125282021, 734469339, 502305550, 358619632, 588367885, 378999869, 229784330, 482908288, 200015583, 917495282, 927948162, 608034697, 808431135, 527077222, 162543765, 389950857, 245601267, 249715419, 693027971, 190580856, 529089171, 955684526, 30761537, 938337593, 788577458, 549209636, 827045404, 122308318, 620861323, 971676255, 416840020, 294457424, 524558544, 556815065, 630892050, 967268905, 646360522, 429093749, 273629798, 491769510, 776972562, 7734440, 487016701, 464277815, 610398444, 170422712, 229016657, 714740048, 969069237, 80291050, 417641256, 952187770, 749983779, 648689790, 971140131, 951554088, 110361135, 366812247, 670286064, 351934350, 610789935, 892359063, 659538584, 809272917, 656853450, 834218956, 318381406, 421005852, 413973609, 964864024, 916374071, 48815337, 956932078, 298839761, 35653598, 993186141, 487819763, 266278852, 792289374, 65889596, 534911118, 683820678, 310945474, 369513047, 816802574, 930482893, 282430064, 218572025, 673462611, 247612459, 684708154, 572468102, 78534906, 779316880, 507584866, 241685928, 164169297, 925984571, 174048503, 725036003, 63721295, 23128493, 632477591, 323650721, 695154822, 194815714, 933300586, 98743115, 596527852, 794127852, 174663265, 26675663, 577862324, 434246016, 475233835, 849652896, 337638356, 755871629, 378866778, 279433078, 458464603, 235726524, 689767644, 663552183, 479240095, 743699136, 1551776, 279898168, 501372710, 374933359, 826435099, 8175993, 890212870, 68744776, 973300857, 677629842, 88200270, 933487038, 762800394, 782106240, 151044457, 533720302, 799661973, 397849546, 88133299, 856166069, 590641145, 938138799, 552221599, 856165278, 106746042, 435431789, 887586851, 274130423, 301977160, 282110657, 422720366, 63100393, 836615808, 52153984, 683905059, 144404794, 331665548, 915011335, 105012790, 447454686, 357783838, 875737347, 853022616, 609779392, 954358568, 828758691, 919695041, 821980278, 719841089, 513058110, 500117508, 691134165, 111958252, 260657777, 47521105, 576190368, 11416701, 498700255, 525863304, 187271885, 695854420, 780001328, 474696969, 660336750, 976279, 936448695, 336923507, 995705773, 740731110, 91954536, 46524664, 547873000, 731668621, 574726627, 53508645, 580644244, 504400694, 355885033, 212200417, 292060053, 721009357, 604932419, 828091150, 442201412, 957751886, 456865160, 474264098, 942382573, 724048394, 567218207, 596139930, 967007667, 6976490, 481022909, 992658387, 744364349, 782509587, 154080186, 491415374, 211057430, 988623305, 150094915, 858625639, 553935388, 173781337, 758264515, 797758048, 847819239, 139204073, 84946734, 798288654, 183143418, 292591740, 634366539, 905776888, 567587532, 28774873, 861809891, 247948385, 209496849, 735476781, 919054970, 917666215, 384789988, 9405156, 310680777, 720327586, 472862776, 767167017, 747931361, 549003538, 631150854, 973701016, 180281488, 616568088, 90667890, 679572702, 559637559, 583057280, 398005624, 551840589, 356926652, 789186824, 405464848, 15855738, 516904191, 931856246, 138626346, 947532730, 160004293, 586485329, 337827731, 249529441, 274382660, 940941230, 374608875, 796114469, 109815469, 255424270, 209459078, 721260654, 804775505, 743419612, 940965880, 813683566, 785512948, 477500721, 443873003, 997970841, 547656156, 501144940, 44044120, 279860481, 354881895, 67974289, 469155118, 646752721, 112881596, 336464623, 914370859, 541329107, 452319818, 981186137, 76415342, 866394731, 647347225, 657613976, 770247281, 922442524, 523943271, 154817027, 829453276, 341631851, 608260265, 261958915, 884099235, 694750566, 399062646, 55218908, 474919318, 368407786, 612370865, 196261766, 562103499, 394263241, 136041586, 50700713, 104487259, 15643690, 243739335, 333577808, 864834510, 760649220, 782472408, 559317505, 578147399, 232975951, 949630153, 946609233, 239169302, 805474850, 756450437, 870746657, 53599790, 883074342, 978572656, 949544208, 810415210, 232493696, 287063042, 243810909, 560083151, 692496045, 774535598, 886547501, 594208752, 19574102, 387866859, 998638168, 444421985, 56718857, 201937506, 411609663, 431426699, 701971109, 588504082, 521227883, 288287516, 701295201, 739013258, 128260857, 157937036, 2010706, 204934616, 439544293, 897335874, 925992026, 614992827, 704147094, 31292326, 492336414, 496741569, 474654476, 673289472, 780264004, 554125649, 608139985, 910533551, 462689313, 427302618, 991952813, 597279719, 802119662, 680409240, 661521314, 355510685, 479405186, 169634660, 377796466, 681215581, 868204754, 701301770, 253489987, 103958717, 701991666, 470932786, 718332831, 533644680, 889126107, 118427686, 437674136, 560875488, 870552891, 681471823, 312454442, 983972702, 335926877, 709383622, 696312396, 830298633, 915267542, 865016947, 151504467, 767067373, 135607095, 854146658, 812297810, 234009625, 641652256, 33493370, 964453271, 680177852, 328632033, 597693601, 825374583, 129698432, 250016781, 173471724, 821215868, 220923948, 341339895, 614249027, 163370239, 865736103, 908205791, 689752686, 416535782, 283833081, 311280613, 816065217, 796022191, 8261439, 893252687, 156737660, 117972525, 616978539, 384275684, 610460554, 187400435, 987124637, 55644850, 699910867, 17798292, 799048448, 785729311, 195410061, 916944281, 394164138, 61242258, 136943995, 344282091, 528517552, 936372020, 907043818, 526152330, 889409042, 462583088, 196058575, 730454168, 627453206, 451806947, 217546901, 726916522, 706468262, 977833796, 403505682, 393180594, 409376252, 96619979, 646818252, 759042070, 440010399, 26308652, 411545709, 92522462, 63062851, 588991652, 605243743, 168193572, 457306881, 784347270, 467008195, 312875941, 464375563, 512129654, 811206820, 832124657, 801343610, 749240671, 833980918, 949514338, 888364692, 659916832, 319931532, 446011569, 128937992, 876449682, 537823053, 863707177, 778742945, 18306368, 350585057, 845788762, 306685906, 438218788, 462850061, 536750675, 665252813, 99691739, 776023518, 182801723, 342832160, 574007435, 671000306, 462024901, 795626555, 302240773, 769196176, 896328332, 94706012, 898460771, 181064708, 687646575, 152662523, 696499801, 40703024, 607033206, 164843429, 725958153, 774477278, 92262644, 781547125, 823444984, 743007169, 213759787, 280052686, 720085456, 209839653, 873121446, 422160085, 829344107, 838121484, 354665639, 107493385, 964756622, 535166902, 303477351, 211742814, 772749777, 698034051, 157071044, 804407641, 427675637, 785942803, 949415464, 154127114, 30098708, 749287282, 188353078, 898485691, 144634957, 692241844, 718007256, 516150208, 912727040, 571568107, 579986861, 246304731, 840055097, 650322180, 869430374, 455700030, 386299014, 899100048, 702791154, 859972151, 921975412, 766146299, 123679859, 234935742, 875254790, 77814264, 398949811, 907223173, 793925867, 756964770, 814758421, 938357067, 896338412, 178348049, 873969024, 994140536, 820357558, 240252064, 488306796, 590861819, 892445763, 178678957, 98483017, 925591378, 112531289, 51571533, 695073544, 891838944, 966463330, 787354041, 728225907, 43071244, 858465760, 130244035, 980887407, 379789115, 338919195, 195982898, 905236641, 689670931, 64769482, 232547789, 464460119, 987700239, 631841976, 84386232, 538496526, 389551239, 470484674, 460146738, 109407787, 151104974, 823283777, 764441227, 90920845, 46221725, 237076013, 351973006, 7903460, 987811492, 502815862, 663466929, 437757438, 930587838, 453307935, 558648753, 454087112, 352255142, 951963038, 975148548, 319965736, 442562334, 493703645, 831867658, 378346829, 504580909, 213407439, 767892112, 917536618, 626391451, 457874303, 807026671, 929000092, 983713274, 326151518, 143070111, 538243030, 533371242, 795133057, 558409093, 830612607, 369442831, 755017518, 833507695, 975248272, 250299487, 791211489, 140254936, 287005262, 848219658, 91274008, 626150658, 874929966, 962532441, 956002451, 406009986, 423813439, 81743332, 228094661, 423469579, 345001700, 70560160, 368426159, 768975562, 236393880, 348357000, 224701291, 545543681, 692955476, 460709, 742113784, 895559538, 164905151, 788033458, 302851936, 374069328, 481155426, 330495016, 41780555, 404184867, 972005894, 520087309, 997660400, 935571478, 604174982, 722295443, 483990398, 647866467, 950706706, 547307078, 567834046, 578884376, 499352220, 897515918, 973294927, 750905718, 113014535, 421666852, 73428360, 147020467, 427371985, 479871569, 209565897, 584103778, 737151119, 682485184, 353372796, 524977646, 377432209, 628509911, 274204113, 516880141, 896802397, 745978046, 613939662, 131948140, 151118714, 91677207, 308222504, 182951039, 243551083, 309993029, 175943503, 800754446, 671924585, 614107503, 975067455, 112524705, 665209749, 764174716, 720894773, 828701220, 262932296, 592111389, 716105955, 222843637, 774751547, 831119407, 657403416, 629690869, 279743355, 434102277, 198077782, 247588480, 504341100, 880650505, 943225266, 689938807, 821271575, 250564788, 845814816, 491971751, 72512596, 286749860, 415806025, 514721878, 114336826, 487835836, 469078553, 485444551, 369065415, 993424357, 435842106, 236429485, 695964642, 94793882, 46686284, 413864990, 230848657, 494851051, 493078759, 556685490, 968983290, 699597989, 586650677, 420506989, 183664468, 92383573, 143402097, 174364449, 63809687, 710431114, 608307860, 665338706, 552031992, 428357134, 700532311, 925087343, 432607249, 308410791, 873803508, 110742232, 211584121, 638091092, 149861068, 821773925, 360978187, 962903730, 210638870, 694405369, 129939290, 573431044, 967924742, 995542745, 6365403, 696370699, 767041697, 841764373, 428526787, 495694144, 21515924, 830153345, 700372964, 747994226, 632241784, 638927930, 450864013, 522836496, 300412698, 850360354, 471572092, 11259953, 21908912, 1313369, 237207033, 699301647, 823399357, 717143708, 889946592, 572492446, 198217297, 244845101, 256429795, 94095038, 704341354, 165614294, 141063919, 546618388, 831246815, 170172517, 116820845, 947685984, 374661840, 209882153, 974718059, 911350875, 725704363, 432492916, 139114436, 335170019, 302505017, 829090549, 227548976, 247429891, 107271139, 880901941, 228810456, 418389409, 797348677, 797109494, 165607959, 557019439, 25536870, 33392691, 227340845, 286120848, 301484778, 325885666, 698958846, 451238547, 273868253, 955387944, 429334559, 209893223, 182490461, 906866272, 987718328, 8231629, 881799857, 59884538, 661231067, 997338626, 730195496, 377155730, 849223164, 221132793, 795191699, 267049092, 419669233, 704585374, 468550177, 670580605, 716132547, 193661728, 317210060, 218821517, 110844683, 265758222, 118913563, 933255475, 744647765, 911877215, 749917316, 941146550, 660297618, 721068745, 620503634, 415609664, 289644162, 678055198, 880252821, 44055116, 459515403, 233039203, 482160961, 200314359, 196507663, 187878148, 226564697, 492252364, 633458514, 940530100, 136881998, 590143999, 263908731, 383292279, 199931650, 643888338, 438678960, 452620567, 73270510, 386136594, 172261329, 713051932, 437151896, 44322318, 266597318, 998283624, 61955781, 826463668, 692682752, 522518368, 605472634, 972690868, 854495675, 447488749, 450910193, 469125622, 635138902, 684423148, 770628567, 900009795, 122529139, 59467301, 189454664, 12882652, 965152198, 163420181, 165792122, 18901476, 544263265, 396973680, 602578240, 679333377, 388733766, 794429378, 27006630, 262015145, 895629665, 853513915, 379928899, 546069586, 303639690, 717186156, 276679197, 248374856, 8462663, 369949531, 917818545, 648940028, 636536462, 625472149, 124982214, 128795178, 466634814, 702594051, 50608768, 383901531, 902192348, 230111025, 528089232, 506480715, 641852101, 664436527, 119938701, 576750808, 262235328, 975872791, 482345373, 274556454, 371234759, 245580968, 498990393, 738390637, 780324895, 36792311, 275363734, 3811362, 204115683, 325378682, 311846876, 866180406, 483750228, 907662883, 493513010, 210458129, 494190226, 312031004, 496645993, 736065398, 810833745, 812267613, 431780287, 565931855, 393035662, 908744240, 528948335, 91973186, 236173487, 191686020, 349138829, 47211774, 183895004, 679483208, 692386655, 37535971, 988761504, 576256392, 226226067, 311822155, 78533580, 588986170, 507197361, 843548772, 374860197, 371925087, 833219135, 744512181, 237534049, 142199972, 630243599, 642491605, 675899711, 821922142, 537635081, 630104993, 275893426, 779363556, 922188385, 659097791, 66771311, 736766481, 508974570, 466304410, 698148847, 650538937, 880730329, 572267887, 520693728, 932745177, 988843851, 620218350, 90802953, 994806785, 323008981, 516300071, 583229270, 712291531, 878784571, 813387634, 674852724, 224928063, 100714997, 999923608, 219809889, 714013024, 823941040, 63523896, 53113439, 5014811, 745233489, 571381398, 22941446, 812036071, 478401094, 571337350, 726815561, 864040882, 218295386, 106895782, 930338817, 795586948, 345223859, 459304198, 708585723, 260168432, 183143942, 216511232, 591610642, 715107604, 774170046, 130447626, 956619532, 512126588, 174514311, 964547351, 784128931, 501349861, 876213271, 449714378, 219644239, 216659144, 922012653, 53276300, 137132020, 981013755, 742872920, 941451064, 218422675, 867348142, 744946817, 361025736, 363776180, 271276164, 440085626, 792318510, 628021658, 569891713, 360404481, 190007327, 619416960, 588061164, 931521868, 308554222, 152966718, 612016748, 486621939, 788976107, 669829673, 969432859, 635461457, 670090410, 147578540, 230993204, 995748921, 718376399, 620667654, 924448321, 39605413, 153278446, 53567549, 854336123, 272218857, 516474611, 219394229, 395132938, 141717138, 561916258, 600896755, 172340670, 117738784, 90790698, 683144595, 492379513, 308894896, 355066351, 943294839, 907308398, 78742926, 492361462, 88591593, 446868611, 393094008, 878331835, 89094382, 9447908, 624311765, 504804114, 928323940, 940144033, 592136682, 732502437, 633544079, 138221072, 692009296, 428868800, 892105329, 330984666, 511201186, 543217166, 865164625, 246758637, 33703174, 812458928, 209655781, 375728763, 496544109, 325504987, 553555796, 798781383, 316313223, 839041212, 20646568, 702970859, 605498798, 184885416, 50628202, 135693160, 517523570, 432863173, 749884529, 887804110, 604583571, 374772341, 278603687, 210501610, 725444989, 942633080, 261633069, 548539077, 425764466, 135621009, 133245119, 531612480, 880936364, 112625887, 602116730, 288392508, 816841335, 272052165, 115693144, 826392907, 471386275, 294666288, 421824407, 816592849, 330958731, 787762396, 959274247, 527559904, 642793867, 950778422, 446392171, 506292001, 703738918, 553055641, 183442711, 265839343, 30278171, 293790729, 845316708, 561245965, 768138623, 451408575, 874635574, 264969638, 67097457, 377827442, 198795189, 239304805, 544453698, 962645034, 183271016, 861836397, 845256116, 967949828, 435015295, 12516562, 955266694, 987264080, 678582307, 690383812, 777539453, 636239746, 497764238, 87263282, 753028963, 814942575, 220585102, 455860359, 114201980, 25830580, 843746705, 225858179, 878176470, 80679080, 453216424, 509682769, 166610764, 539757893, 827963066, 682258094, 578750162, 193893998, 780082397, 880798840, 743143682, 125825848, 447834695, 721968840, 770530464, 81867226, 865553081, 504978664, 166215602, 585563758, 864551832, 912562499, 281293140, 879277896, 574585651, 826889156, 703380298, 217371669, 991866910, 356115874, 487503192, 107481002, 782704156, 126868909, 835932298, 510149640, 679804107, 503174169, 562786774, 376309229, 283517876, 349748943, 632350465, 278763012, 503121771, 833143794, 917908247, 815015931, 29645062, 587284319, 501463681, 350630191, 302993741, 449326699, 739466872, 67612954, 633601661, 64126066, 579062039, 122043560, 859615155, 923239637, 317730916, 583110547, 959056967, 6696303, 599991249, 991274886, 928607870, 518187618, 47029686, 839937829, 567988102, 434793665, 114310245, 655340521, 279985382, 393709510, 258003678, 901678811, 784295642, 116379281, 420438555, 855689819, 431526050, 673352530, 154923141, 522570812, 553848666, 324889945, 601225170, 659240559, 567268825, 214095048, 549477675, 327819778, 313797624, 649700313, 73153647, 943877686, 14493823, 396668670, 905884513, 728970362, 297784971, 347817718, 682022348, 658190909, 121517784, 987540280, 870656749, 778824091, 175427814, 656208873, 351700906, 595506275, 2070877, 975771533, 479710506, 800807274, 753782249, 21788844, 606228205, 437471154, 567606100, 235158929, 383281708, 128254023, 698346411, 169631940, 715887120, 715968222, 605442399, 572491598, 270574340, 381776241, 612745608, 696897128, 934306932, 267597392, 501321029, 223849150, 329628142, 988806196, 206314977, 233419262, 971670410, 52817118, 185308448, 810213576, 297763240, 109952652, 83357389, 257541243, 894846897, 593154657, 884112040, 188485032, 606951943, 546798849, 121258489, 136290603, 371328349, 640235814, 749957201, 594046220, 952049918, 330697540, 591061718, 525448770, 68567384, 461838924, 381122289, 294643352, 119837678, 98396029, 919060553, 579703749, 324970243, 773421187, 40636308, 997546032, 501545286, 438382465, 125671313, 857160042, 353834660, 830847496, 213300937, 524174516, 750146834, 744572991, 36140723, 642204288, 67205357, 4125776, 138664175, 719119101, 642378178, 596941128, 766414189, 923685316, 766969622, 125808920, 291596353, 146860281, 390582054, 68191183, 484242778, 829476193, 41854978, 972033400, 804949735, 365177000, 297569815, 781257897, 224751800, 386180050, 345236367, 265527853, 783669290, 165591178, 484212279, 246442186, 277007688, 418003245, 896116278, 607555793, 349056354, 57211918, 231221673, 780400901, 301000424, 907281274, 949906950, 681608158, 423821654, 196233158, 35034157, 441236357, 79978577, 531892525, 127340347, 788006756, 405983511, 889140125, 27998503, 174396083, 511080838, 621036142, 386745451, 321230005, 977638100, 716884986, 163889456, 554231245, 492963714, 15462887, 953397387, 802209258, 875490446, 926477126, 91995644, 779709869, 278623720, 616232571, 405309125, 738814783, 742461372, 677795955, 210053232, 750299359, 567346360, 228568816, 931153006, 608743838, 660698847, 590403136, 527779481, 181669830, 332314821, 947002221, 679369911, 115938431, 239266666, 716824324, 928569281, 327966229, 210648532, 392614204, 162776733, 68732992, 181911652, 905311306, 537458890, 664967335, 225599264, 398352745, 545168708, 305722042, 194098772, 900124216, 445001036, 74695682, 514759764, 368386982, 452513111, 294950108, 743207134, 297132146, 338385293, 130807140, 76918757, 633425387, 215595432, 908896930, 397116908, 401999305, 817691940, 867598816, 793830524, 957021271, 565827999, 821784343, 717535250, 225974006, 74804170, 619960190, 452434002, 651723190, 759314414, 896736524, 574595921, 817327048, 321207274, 132892702, 277151205, 537289820, 644207272, 967851301, 499389799, 821967757, 716616503, 718521124, 575793595, 214726865, 671503360, 778432511, 812007213, 163973890, 939873467, 196898663, 76736071, 284548758, 831156965, 172128668, 494577710, 320301407, 159913151, 555361711, 212512957, 609113661, 724182533, 679183658, 840564296, 774580740, 715287293, 293744179, 657605031, 609144767, 509457564, 171644507, 309323891, 361986594, 283570262, 398089030, 312473140, 726605024, 28469279, 540014545, 916333016, 957470950, 155449865, 371453949, 529089418, 540718659, 209894404, 39360854, 31579013, 382810232, 190879903, 495649625, 369827352, 453054142, 853375180, 680079175, 981672152, 626927845, 212833373, 235068538, 735830383, 830312582, 348175529, 133879909, 232211277, 812742335, 911869083, 402416055, 425025880, 571880233, 762595206, 626636371, 331457037, 168124247, 574979652, 41773725, 353615278, 312892411, 153848877, 531146816, 748170218, 325099565, 706860202, 747009004, 642622120, 598024192, 95683776, 769425481, 622521973, 345724990, 721828341, 58629196, 143309023, 825890, 814189260, 723616358, 688066823, 252821583, 64952990, 792376698, 817067333, 586752767, 834737401, 149470942, 665230323, 791365887, 776002424, 607584429, 93906111, 662750905, 109430207, 261886718, 9039193, 513290697, 699967273, 924520221, 835269155, 631978442, 395143460, 434715686, 750976825, 396974332, 39709464, 156388669, 578249388, 469942343, 658083349, 910263166, 566386676, 206206358, 159676634, 25592718, 864095148, 285063821, 861757352, 394657437, 89649829, 28042943, 739971799, 902519074, 155086573, 618230983, 386350294, 533733642, 972623861, 291590180, 810282619, 161600806, 409576560, 516336811, 158690942, 959604559, 550742198, 40738153, 256534802, 632537480, 717923002, 130396523, 28192557, 148073718, 23815708, 371812300, 129038488, 901087641, 408813387, 326889011, 955160595, 164424095, 820694036, 622714352, 269346265, 708538366, 878405099, 884028500, 400668534, 536947171, 492864609, 882964842, 569494336, 51917661, 490895192, 933567081, 129409654, 808688960, 257628139, 554561856, 699836438, 937833088, 795625021, 645876260, 952198118, 785205277, 841085773, 941697317, 779604663, 449923628, 249050667, 290473202, 804137599, 606360604, 349350658, 951275670, 821986678, 767346489, 597856053, 357203028, 404258480, 463646039, 824068763, 206220167, 936151083, 711702838, 683588803, 114948152, 37412952, 150014553, 927738425, 24265082, 743987549, 781168046, 370952563, 135840161, 518532960, 539367351, 651104043, 144607248, 415223745, 269852882, 121156510, 633715725, 31733569, 458919711, 939115489, 301958608, 458726423, 578103401, 575383582, 812101284, 249542067, 580016282, 405472181, 416560202, 464042949, 324695477, 359170582, 645381748, 546774536, 54508317, 819216996, 381092952, 828313981, 555049401, 13664274, 665056959, 107048897, 432987862, 348096869, 423702801, 209895908, 390147573, 835374231, 576253872, 831878989, 221056465, 227243442, 622681294, 616517620, 866157429, 419132204, 372090580, 857245003, 37175056, 979804249, 775864733, 974678652, 141931291, 44263895, 524470386, 339557682, 636857343, 862775292, 953785747, 613145648, 451560513, 692576967, 929200004, 929815725, 446547226, 463065057, 536051961, 610833058, 796037446, 968714583, 824472526, 970042950, 533584831, 170160633, 159247147, 9952168, 819424274, 313536657, 448030810, 259845959, 433397987, 794248265, 298835417, 44502151, 586016238, 762695261, 742825517, 982951154, 575077066, 413233128, 702649444, 175111533, 961678828, 997507101, 436770720, 724635805, 153070038, 180825085, 586419419, 288518150, 440420596, 856288880, 835333122, 176751496, 880446660, 989044950, 690506915, 451571462, 506630838, 927286444, 93986907, 122209307, 615415524, 874332393, 556094720, 241590365, 151346725, 670282326, 321339003, 963493963, 960087711, 779260492, 432297231, 860286471, 581490021, 952290364, 458437289, 597119239, 954137764, 622094105, 400049297, 424131738, 324020632, 934206243, 235897184, 314344413, 762909836, 762649578, 384777856, 628857848, 22786366, 266455471, 574921876, 289882686, 401528332, 288666709, 159619667, 575883695, 553620051, 854200072, 186239959, 239911785, 607300643, 596251775, 529937506, 749218487, 945917742, 479793703, 787699842, 690092166, 872072440, 928751013, 800120863, 834960255, 268551996, 576986815, 894847955, 129902756, 701323062, 15389427, 918985272, 892131873, 924968615, 39700989, 11649907, 99772004, 17308991, 993976987, 56711974, 646143713, 113824738, 112245793, 443635670, 226628781, 169934468, 616299148, 15673869, 8309641, 162299276, 462249668, 102428558, 44582622, 637512185, 679555504, 627993596, 245565064, 868832010, 877848211, 427835922, 531500584, 473504829, 87019576, 152648830, 717914935, 416944010, 902690344, 891917529, 277363499, 281216775, 402762427, 180949555, 874179038, 42508409, 594269393, 834382147, 551235065, 523850100, 12947706, 736152309, 568749620, 218587757, 200771704, 758647030, 81468523, 4842717, 961181259, 906039876, 715332108, 274248891, 115487398, 847999641, 903028624, 769829849, 706918448, 444608530, 903657843, 27493671, 14990157, 545692099, 802805013, 88576094, 640766928, 428610503, 803815108, 704974858, 894906642, 59226474, 28288401, 945013281, 767833855, 798214103, 267252624, 636259057, 508092720, 428239835, 742677608, 2439174, 749606635, 741168390, 903897694, 743789688, 712799103, 547787318, 821244384, 400054621, 826001268, 803845792, 815005312, 77719526, 883271084, 219430520, 73845715, 272428970, 228534430, 628277897, 162409891, 418426950, 830039189, 761710766, 191300655, 601038383, 287520684, 748502053, 186902957, 716282190, 600771373, 950210807, 705938598, 66421712, 104682045, 843518846, 348663091, 246613015, 473377429, 440306816, 691851338, 163422658, 135392796, 513339727, 88437287, 283214185, 117249459, 907156062, 451325657, 579647163, 513000091, 907803361, 551471442, 744358487, 591426222, 206499962, 100118887, 790249174, 73640003, 881917340, 388059987, 882675404, 950922759, 414377121, 781261037, 744167379, 179543548, 910757461, 971248617, 717898913, 770850511, 92008503, 676051468, 323395771, 785693339, 590710852, 5269715, 638467150, 222414983, 761259521, 263644731, 38435090, 511761572, 359786646, 922954018, 244924683, 583067706, 283046571, 318633875, 683594615, 666490526, 701580911, 113006477, 798971016, 601110540, 16906631, 925876997, 182600417, 402025416, 748769228, 952500551, 723955009, 721345133, 437098362, 110577320, 288452032, 157120269, 308808178, 529982934, 537116596, 851753399, 808073596, 281853983, 991840640, 674971920, 881953508, 826863160, 546397811, 993533771, 80415042, 537197012, 243843839, 305803329, 352030961, 961785935, 332682600, 522714297, 670726800, 415785964, 414333185, 366481188, 330700239, 552485501, 488988260, 374517983, 178014519, 491500745, 961531466, 469771503, 384094484, 696470383, 1583705, 22183990, 643154122, 788192510, 962850295, 609310538, 685004814, 832517167, 728213123, 63686736, 979223902, 834494380, 181440619, 657899494, 227121691, 113344051, 633328785, 180707565, 883367870, 619055916, 652349918, 287095263, 978242925, 413225775, 250453632, 881310348, 82635622, 538371953, 71119403, 567086062, 80160234, 392028501, 717832063, 900341668, 907540174, 708221231, 687052798, 619676292, 64403326, 364013495, 488213672, 493438603, 44656594, 887622596, 829650988, 874730563, 846056808, 42506429, 123224704, 111028720, 588987917, 799900783, 707350819, 418758247, 812018916, 642951045, 84909618, 865254743, 926896719, 327629618, 765175105, 735941069, 510166249, 626817214, 609508845, 106648879, 763596967, 767909762, 967382870, 214890611, 553410984, 287554472, 145093584, 899949989, 193975568, 202875350, 845684647, 267851993, 826063948, 685599133, 873902606, 631356665, 118030382, 33334080, 502602925, 493210461, 816193125, 579913274, 110984405, 610961636, 761687267, 410416790, 435693342, 629997227, 164809679, 957304169, 370578787, 124686334, 21220731, 876539917, 159511308, 574256011, 300148823, 614528235, 757067953, 942950561, 38648470, 67906110, 675401474, 258953685, 617595723, 550691700, 679155176, 68573179, 881330857, 497216607, 706764695, 875954171, 658466735, 451614616, 300245762, 450860146, 589061005, 244839524, 959407569, 985586018, 296670292, 709965248, 914841911, 542396223, 347632801, 884057525, 514841062, 204946906, 554069851, 830301336, 483666392, 165280700, 330294986, 586303412, 34248106, 972488007, 485734804, 759938017, 590180324, 380045223, 15436325, 384275927, 97195916, 145718696, 300273528, 758403722, 935394897, 234777236, 586936993, 560650825, 523436251, 441771068, 118128251, 325113714, 656265903, 23111360, 483963218, 250105333, 908932371, 429614994, 648812152, 666788826, 806817543, 39216877, 317026644, 13149264, 750683427, 965553329, 992555529, 644920271, 757324615, 713931409, 246271877, 527010715, 337508046, 767089782, 523531950, 180015000, 449043181, 168432003, 721113458, 131756109, 399835172, 202509715, 945410608, 515974067, 483523586, 813867785, 206319613, 643252161, 902938147, 27252470, 946801989, 189182959, 159315701, 622667801, 942901221, 18658460, 643182287, 748601029, 916630433, 515202432, 541822294, 490971823, 530862167, 277304438, 446091273, 727132672, 920918242, 456929764, 893538826, 61265612, 730521667, 333094080, 92060112, 162815476, 569780040, 362610810, 934934642, 150642458, 51447094, 849629843, 72127359, 134579543, 192371021, 764147145, 813401205, 516338716, 211192747, 830456339, 315151643, 183851735, 771589163, 612047116, 371106527, 21749065, 872889024, 315026277, 630211598, 827070751, 70444289, 759115596, 24169723, 887563122, 361695342, 115655086, 369266977, 60705341, 255587088, 637283561, 69087771, 263951836, 759199658, 13507410, 136101367, 16109069, 919947339, 191841266, 588723785, 201889482, 949297695, 717540462, 318021352, 193650596, 183275909, 333173039, 527173649, 842074749, 550002418, 179952870, 626674461, 291613731, 615229788, 14486008, 316631117, 573287626, 454516140, 987976300, 538767871, 337197221, 166804802, 882200475, 127183682, 260065299, 590933118, 413717900, 928297924, 415530617, 171086543, 178099140, 452647438, 659248471, 283268239, 199164336, 381825121, 704599129, 339061850, 441725606, 389514807, 51072246, 194007188, 510465589, 553206777, 633434569, 113247224, 883598158, 572947164, 878877284, 712099936, 339805514, 313994784, 640938479, 173677435, 992569385, 783085622, 623553391, 435835005, 343903441, 96104921, 262662568, 305211414, 30565407, 506835811, 735317518, 453705602, 79290317, 832425189, 201105056, 555458035, 630438554, 624606872, 66965768, 541136598, 843364341, 475268689, 756621547, 919285650, 153174558, 352561669, 345018536, 747020173, 369147457, 973308422, 392634587, 230391055, 567813958, 713041210, 172095041, 352419211, 224854977, 128265078, 248988860, 81236577, 663424496, 831493283, 155868659, 155836124, 318897640, 641430780, 768635540, 408074355, 112189313, 665061357, 527573143, 468080283, 999768743, 406406275, 165188462, 794283235, 99159762, 970306951, 776722693, 480726934, 48794286, 616045663, 258502479, 219407776, 151179595, 50981966, 121648099, 108069070, 166213286, 824441367, 950939170, 157330157, 411008035, 96057948, 44215181, 258584038, 488607597, 139125461, 382854237, 315536005, 217814871, 613279475, 614455582, 764117195, 884808815, 511529663, 982092343, 886771941, 603087237, 932245203, 711298610, 743282816, 81159987, 471342526, 845021454, 521401269, 462513459, 420269535, 805495038, 727924505, 886709727, 991398140, 868847330, 489891233, 957974302, 558047692, 927084616, 441893649, 963296200, 846736618, 943832132, 283400623, 70031515, 168371958, 332149133, 276380531, 339120395, 553060644, 556860226, 690680199, 837696296, 63371623, 671232174, 729706264, 972601447, 529555264, 211827356, 943880909, 700916112, 957436496, 306010335, 621906997, 965381997, 290665655, 597939401, 630452944, 48513625, 970223215, 882285212, 702055516, 643431697, 259615324, 391776781, 886243789, 399395712, 540376530, 609957011, 726833358, 710199777, 628526273, 832983653, 927328561, 935209970, 26031796, 719174013, 146124733, 138676243, 273707899, 887988609, 51127571, 791944843, 62595646, 231164695, 190065327, 519589919, 2329264, 492875963, 475861242, 442535825, 915267607, 328539363, 287032537, 511610638, 300972538, 318465722, 695832435, 491331863, 988467464, 983128228, 981119767, 430715017, 157014598, 254184255, 16050588, 772493819, 939047053, 499897037, 645524809, 873476113, 317288956, 247739974, 663517262, 735321871, 832517881, 763299126, 815803438, 415349498, 177538022, 237300062, 422013515, 775233240, 682424736, 173716402, 597197435, 996996242, 656150124, 109676711, 903450580, 150990268, 279120600, 829615733, 371069691, 285973627, 876537974, 513631017, 758650342, 522771496, 475217274, 45972264, 188644787, 108090278, 129018787, 70958552, 249724789, 702492723, 130329956, 256094481, 280907095, 693666270, 192290369, 906491185, 904396433, 272782617, 136844455, 536637023, 695112980, 667687494, 948176209, 989410435, 717516111, 813686931, 822199803, 748521836, 948034419, 669278472, 364899689, 376517839, 415776764, 495295662, 479158829, 273309370, 640962946, 21863655, 4315998, 823378891, 25738483, 445394456, 293504968, 455272040, 72289534, 466492431, 549030951, 746989625, 280885104, 666399241, 659813619, 795353530, 250282815, 508321826, 197263951, 703060970, 188312302, 263211491, 842310407, 845323764, 978391274, 521880420, 998274346, 458801062, 28089567, 708002692, 350435798, 23689222, 676952507, 697988607, 791410901, 848690607, 669769986, 891043796, 938295354, 850431481, 303438399, 306330846, 756101554, 898101419, 770590456, 158285116, 465533556, 620002371, 211902696, 883921854, 598974678, 379756487, 627330828, 388403353, 340334317, 136248430, 388901678, 300947638, 550246562, 374553154, 831416859, 199444202, 574230784, 387653674, 706329225, 224061290, 629678850, 620078680, 511218713, 963293195, 861282955, 961110425, 797602945, 941417355, 419068777, 680027716, 684417422, 956965902, 222087615, 968663187, 749716899, 791747513, 970683390, 942794353, 905827099, 759463425, 276111828, 584756656, 509049689, 145915352, 982407253, 717076292, 151819852, 297894513, 536945118, 150740403, 386565889, 411666225, 687831472, 728419337, 985870277, 191199784, 783121525, 918757323, 78650926, 53717984, 508431094, 347458503, 867189443, 563455724, 333899351, 372566314, 631487702, 97968749, 968728769, 795406969, 793090894, 886225833, 841357745, 605381537, 855601392, 931479819, 926622, 674510558, 235089443, 741175589, 339016268, 151404678, 161495470, 872276632, 187114651, 352558494, 700810341, 33024602, 563211421, 582125574, 957594447, 104300184, 358035823, 251768866, 144626978, 665180429, 133104565, 832638411, 519133900, 708922851, 947826984, 561372509, 532328495, 283688560, 209506761, 962509609, 337441019, 499054196, 292959752, 934460524, 924699784, 56728859, 28755420, 137065576, 906475255, 655676060, 843612142, 241195091, 134514673, 649990343, 392546882, 499143461, 61506941, 118510070, 919496059, 752386681, 420942050, 664473640, 705032092, 485348254, 224675256, 867129249, 565026036, 236157117, 761768670, 771135932, 435602587, 879499103, 149028609, 179988077, 698980555, 128996723, 966129512, 994052923, 516108103, 603969804, 265793478, 740727276, 817887329, 64830778, 218890536, 763640261, 719701214, 63364671, 989842862, 437510348, 812016498, 900526605, 720055949, 44137216, 242650098, 403504381, 510842706, 108466202, 262046316, 607378571, 322686985, 316748123, 836111015, 923504313, 591444188, 929438884, 48121616, 520656715, 483344743, 2089530, 826484169, 751970465, 138221029, 330637178, 56093289, 28231304, 836150296, 875743625, 892136450, 906490518, 481424975, 941374599, 666591712, 746411878, 10551292, 228478194, 797691051, 981519065, 770785029, 491140198, 165592312, 469386452, 215504391, 264023381, 29203370, 758475899, 303362040, 95255139, 791009718, 431504737, 997655930, 686994828, 177031892, 161533041, 159373091, 726191906, 666516717, 738088845, 866278013, 825174005, 881862209, 220334820, 427965514, 669701052, 938412128, 929012366, 319896180, 944112425, 299344042, 712047258, 424249509, 893603331, 537708128, 427870910, 254414240, 286184932, 448959818, 157874624, 468470635, 753356164, 968852841, 903937074, 447312108, 624193377, 751032626, 679984871, 896224473, 300061289, 757775039, 100172012, 458040048, 480710144, 161538771, 930870146, 262828557, 378760529, 807298619, 497825759, 188472289, 16275444, 754694178, 756419569, 121903924, 367334547, 247659208, 617045571, 486482096, 177664340, 808832353, 727128850, 627103836, 788092127, 993044763, 329120852, 796845941, 286507317, 73840332, 98834952, 609669236, 673012257, 985685110, 484388384, 641215660, 690288891, 237189315, 684637113, 179641411, 100331450, 331318316, 320843516, 549431504, 765840615, 328216515, 499564971, 762141222, 928710768, 274162562, 184053561, 850949297, 286146758, 822021344, 155186342, 975349220, 124468906, 495558640, 603285867, 635006432, 177537791, 102523120, 358080645, 267916067, 75113016, 781091937, 262665368, 818022230, 908145483, 985786459, 83542778, 285862644, 701024, 223387442, 603373332, 500238030, 662028404, 557138008, 368247014, 337332903, 836246026, 59003475, 484004362, 229346100, 381268190, 51166262, 882726196, 804392576, 81989607, 199679486, 80936194, 576200959, 588669522, 824999805, 732307562, 465225378, 208280015, 301350517, 915418767, 576742002, 199068798, 135102407, 931428333, 408738149, 159041809, 354974549, 578508521, 365565098, 897419592, 163441799, 674500763, 695188151, 509721208, 99410021, 880739969, 228648227, 869163128, 453346186, 989668561, 213979623, 774123644, 436057723, 436108306, 527986371, 266144440, 636256570, 130457020, 721428720, 75903805, 652419605, 501290030, 751629322, 98819160, 598343021, 838434152, 999173783, 247184217, 396227206, 780047759, 585708205, 150955365, 105092109, 103168614, 321020788, 471654648, 364846270, 231509586, 285675553, 18419438, 856628920, 246742890, 99529525, 810157420, 999860879, 9003164, 684289090, 865189625, 725043678, 198327214, 970995574, 155069860, 625558459, 491815008, 327773628, 440960533, 129493015, 439433491, 20498003, 842694683, 114767266, 855890429, 979832780, 245681065, 694259752, 868089873, 987946936, 265241888, 198114079, 503045708, 250554613, 314555943, 270952605, 244541626, 864587328, 950559007, 398020073, 910152574, 405950526, 231212022, 111572241, 440528770, 548985243, 411554141, 568540191, 85116445, 530486059, 428468178, 564357179, 309766846, 900387031, 156958503, 913626442, 88361044, 54756339, 670816493, 164660984, 595298990, 587433528, 897040980, 856493758, 514933611, 198456565, 661539701, 574726041, 726500560, 736654544, 649236251, 608058376, 742722383, 259856865, 703994172, 669784166, 459971722, 199893038, 538456393, 570956859, 416595518, 424529724, 792597242, 334575418, 952509459, 516981291, 424345184, 565904611, 912970447, 573596954, 841888718, 941454670, 382720959, 501224895, 68733364, 50556876, 644825354, 19485895, 959189903, 750781636, 770000594, 768664257, 862773553, 367375060, 50842267, 432821625, 289237387, 138965772, 228563814, 816253013, 169100888, 855986225, 788437864, 450253806, 267258656, 475441407, 228018622, 634398114, 627552688, 690082812, 187352278, 10428869, 937808725, 993608995, 294150630, 587359373, 238941491, 654894540, 846537603, 187868275, 433071999, 836854912, 694152355, 680278275, 799129550, 846343787, 445084253, 268814499, 810736789, 446802086, 727037107, 182973428, 742163433, 469817622, 850965026, 22978511, 484892425, 820448838, 948234123, 614284664, 220333402, 426488316, 32255569, 912453093, 968377957, 139360531, 531771441, 460008478, 409026578, 831614422, 788241275, 124362459, 287602880, 972828472, 416264584, 323694571, 180656937, 165286214, 440232326, 480672268, 695329869, 661447941, 736187875, 821461431, 765136968, 443949095, 534726887, 231510919, 93266545, 442752160, 850311855, 497394559, 912823985, 180979417, 15845495, 373699942, 631517619, 187379277, 86133974, 563189363, 797652649, 959932543, 959273354, 660452751, 869170653, 484132630, 894192129, 861089638, 938337960, 89943687, 626180797, 890394776, 742297469, 728416712, 457779972, 269930117, 511977927, 832226980, 402962045, 499506786, 688079183, 747033015, 31113961, 828276312, 380772609, 435091649, 976900994, 316455998, 400829672, 176503567, 413496175, 664270360, 239517064, 773558585, 67179314, 9869024, 16713172, 231025067, 320689586, 456045667, 888905079, 191769735, 29040822, 175037663, 298369271, 12025163, 808967491, 854256722, 453625573, 437969500, 594303869, 253235713, 102429935, 287016229, 302270909, 862490438, 404327846, 695221840, 128032703, 932948327, 162966570, 909401610, 136399068, 879791767, 361638783, 888084598, 676078831, 386286752, 659035773, 86223095, 963465492, 868098079, 667737647, 517048047, 945534088, 746977782, 837473, 151537704, 404377935, 576829694, 838950094, 313085024, 237641187, 569600573, 194868935, 730029284, 675871702, 803021464, 321559674, 355731636, 129964682, 851854721, 724867987, 380277089, 532146146, 108010557, 37926617, 298224348, 470048607, 513592544, 226036964, 598145770, 610173814, 79225172, 545402821, 799647254, 337321499, 585174163, 193214014, 709480227, 468803214, 18031388, 31835365, 242062720, 436755629, 423652860, 54253089, 76391265, 903278212, 174275524, 110151425, 447502947, 646678253, 16308611, 959337089, 492513499, 20143745, 417214155, 81436072, 144453044, 133204352, 199781039, 224690483, 168839985, 880879623, 707682267, 619752583, 901660299, 369163868, 407636464, 620502727, 468575884, 384306311, 154936545, 901675078, 226855618, 587663258, 326562486, 663122779, 303430538, 678308644, 604330620, 417758099, 218973353, 501004101, 305700825, 135876569, 617265509, 631279522, 359049206, 659060025, 522302539, 732000855, 62405425, 484662731, 248296700, 803109834, 830613774, 299679415, 774025842, 837242042, 977629317, 839813645, 885345413, 901567618, 26799632, 840991168, 361283105, 305102854, 226062154, 355930433, 17271219, 900197701, 873699162, 489034046, 250025796, 4312099, 726140012, 363233706, 387455329, 689025253, 263148444, 535144802, 119610252, 127379851, 990099235, 471643585, 853200745, 526658780, 167043913, 720819850, 304184545, 518523337, 906874615, 763704358, 529743753, 226138570, 699197659, 703863611, 701260127, 560476520, 65389337, 146496090, 840594075, 186692512, 843505391, 851708424, 254974512, 485873974, 502395073, 43725734, 9036192, 279010257, 907888034, 118316255, 510685196, 503099155, 700159823, 376166506, 300849396, 335102044, 864239161, 328161172, 793683069, 477799463, 185230744, 53314503, 441868898, 533607399, 151952642, 783378065, 453407293, 210015609, 884050996, 607178653, 267401067, 132749357, 499015594, 535022229, 353718776, 515812298, 785263492, 332709882, 476446758, 815191659, 830413907, 121501204, 132201022, 26944477, 312434619, 286525963, 335077284, 684856201, 223330445, 705348676, 597132704, 686720626, 562918725, 716290965, 847882767, 894573524, 101598321, 20238498, 724486010, 463401940, 528611339, 220825462, 761256413, 636749463, 208309411, 368254788, 205600943, 45316275, 273877363, 721808961, 525993439, 77075712, 867169830, 20860213, 454976847, 1903821, 898270647, 246323903, 975674800, 560731028, 459947987, 523189674, 349132931, 921902521, 753566337, 673948702, 220713394, 89588354, 140298623, 684396723, 80923063, 1453032, 394719234, 830882906, 885921549, 685212579, 867170147, 485929648, 858571656, 707049703, 592448364, 519977949, 590550300, 535943906, 231749369, 856431322, 337875389, 701135843, 678431068, 184869685, 177232215, 268745259, 229764405, 71269897, 576226971, 400375015, 549689997, 671790751, 909125653, 273618459, 934998046, 758012770, 881048188, 677987464, 813079447, 885735743, 736504113, 626535983, 758198046, 149895848, 102388730, 125051002, 141261553, 649939793, 304907335, 286189903, 147661095, 785702603, 951040105, 379439540, 671201810, 78709379, 522202553, 750333909, 548443527, 202203763, 299557501, 546312407, 23961861, 5004597, 579122407, 622761914, 257657742, 112456594, 7500674, 979479909, 159749077, 153791664, 485111253, 16531775, 179692159, 803769235, 972268225, 600670120, 592839520, 550482391, 882007388, 605758975, 430459133, 198716690, 998945587, 156410320, 544780833, 359507465, 599447768, 268013733, 461939352, 166243000, 954052748, 656397885, 990413059, 964358259, 532827604, 230511191, 653612559, 732000574, 157537915, 586848813, 359314928, 904207471, 962710492, 440923520, 206433869, 577388550, 103528063, 338209138, 640425522, 463677457, 693217376, 74143342, 347600686, 356382246, 728010707, 448091395, 873610017, 945677029, 638687003, 430155381, 567467061, 23880215, 169614149, 469139335, 887289949, 343474252, 829772355, 180382863, 840136255, 484168544, 705737079, 194625957, 73155670, 502272846, 927810334, 38404448, 48563440, 891923934, 637978659, 807859122, 905093622, 263014049, 379848894, 204646160, 685599987, 389002139, 107248888, 559157918, 573476643, 205014829, 428441930, 253113997, 119808717, 263556555, 459537218, 63363506, 90944162, 84434294, 739281960, 329881675, 307245170, 350148491, 879766951, 499443283, 150840312, 363841547, 845098647, 474737136, 200397283, 88122441, 642846926, 616992862, 408469076, 859159038, 89498507, 310620228, 496742330, 692347486, 794411084, 407946444, 737202105, 310473734, 30317030, 666656284, 466411491, 590402934, 456112027, 314143392, 336417661, 505795890, 650208252, 172376531, 110367317, 767819875, 591628663, 792995708, 436655172, 625051441, 881978423, 534908026, 108274296, 407219129, 745173053, 994340351, 548602473, 778667905, 33188327, 709504856, 777228369, 181340480, 224643881, 549564667, 485672441, 735576857, 242494420, 982117666, 556299319, 959267996, 551331982, 999944155, 395265331, 311627937, 830706334, 100112801, 845629908, 444861243, 803900805, 199928389, 859896831, 536780041, 277323573, 897782549, 276121491, 829541258, 251447675, 214775906, 476093284, 955954872, 284837462, 337008866, 361605712, 113867125, 44057119, 725956334, 773009940, 798186048, 480217945, 909282605, 670045, 549240463, 660968983, 180432874, 605974113, 713303037, 176976674, 294796202, 647546581, 291192229, 448010115, 858603909, 352945279, 210570629, 888290397, 427623640, 826922425, 166656505, 109438459, 66900743, 971509983, 26774190, 652806420, 203164896, 837089892, 408299435, 969852549, 537963053, 801744638, 748354893, 838862142, 214559464, 386842070, 154926455, 347787676, 375544511, 318515719, 618152000, 522170008, 193273324, 617733365, 188400877, 34105661, 69599238, 515192212, 105034453, 220236755, 324607453, 514255559, 22052678, 834493414, 714840805, 984979445, 433887812, 532657777, 646898879, 86766815, 19047898, 666361044, 492028378, 758597927, 893839207, 476009005, 91969779, 88830607, 580670162, 609182792, 158286035, 24264918, 557803951, 448990752, 973520659, 914756944, 325414626, 91094144, 449585780, 949259561, 611789724, 342025726, 848632061, 588235189, 365882819, 613894553, 1281261, 801373027, 875675309, 44370651, 553467085, 829617096, 881733940, 838023124, 265554292, 891617519, 498641153, 293074204, 358723895, 402200470, 31396712, 668971949, 627536541, 393922994, 557702951, 733725502, 867516213, 85337382, 807804486, 463084854, 44626272, 165227710, 257936543, 981087142, 354874796, 312244442, 708727970, 989397110, 792276454, 964669724, 598180747, 762992194, 100072987, 806915380, 199269425, 363595979, 930271222, 225531747, 524654862, 255558606, 270052714, 992463756, 717325763, 430454396, 297935387, 822946901, 112356658, 540285064, 800698307, 358540645, 232034502, 7033907, 561330536, 229619034, 488872959, 587958656, 115591270, 292442473, 922433881, 157768331, 713589863, 290112246, 117474769, 149119603, 7861024, 801357877, 698612652, 777638001, 561205473, 532038320, 483420333, 221290463, 202781664, 455142854, 863376138, 208834130, 512061624, 183867390, 191623029, 559770826, 370969056, 898006682, 350224358, 990579715, 307835467, 150950116, 787010974, 644614988, 260694330, 893970273, 217061935, 230878776, 910870666, 724998560, 534835015, 233087738, 543435955, 293280934, 183371410, 277003421, 271210343, 993180209, 945429560, 220872478, 833883846, 140094327, 23676880, 845400118, 685073777, 440497830, 611891886, 316986182, 360774180, 466076404, 639933186, 87583273, 992575297, 733955601, 987472821, 726999833, 88440813, 624583606, 519967768, 608828661, 321302962, 617052176, 91060516, 381298224, 346882404, 193685481, 615335843, 631367632, 632252430, 490381647, 421909616, 251088428, 303716001, 146308667, 123046144, 918289326, 432283751, 972428077, 957735628, 84605215, 462312972, 994093076, 338665499, 489721290, 70929116, 122157328, 550290556, 621704155, 680130454, 442189787, 834719043, 61669027, 527461040, 380186862, 85126660, 431473712, 806389334, 654991472, 368637674, 811588729, 610868190, 314676305, 46264034, 52596837, 535179635, 774973744, 83391244, 667299711, 884944430, 449712006, 209436312, 411131074, 270158540, 395117081, 392236619, 934175523, 511611281, 365470357, 302510838, 969912075, 841609071, 669756184, 172695415, 309502917, 249129780, 364903617, 332886564, 579000693, 379221284, 476262065, 115550512, 759227759, 537285548, 661009855, 922440438, 207269265, 142432579, 511077487, 935356312, 827526423, 802839691, 191039706, 502104837, 643690747, 395532681, 702147665, 665558630, 176709380, 615120997, 893250945, 537739023, 282121934, 27311522, 234481652, 13996766, 312741007, 111139485, 273412619, 709439992, 916271619, 277572625, 683116526, 984705575, 310369074, 895022045, 148701404, 694291032, 763458295, 577060359, 31891723, 808868275, 557931746, 408253637, 237405341, 425963367, 590040333, 610691588, 724313629, 784980933, 944527864, 136491283, 938509231, 686964970, 293570377, 320325406, 235439922, 940012797, 896214780, 849735508, 50423311, 889658482, 69390565, 415279507, 968580723, 753337398, 26128275, 984691913, 501487112, 865741470, 116205352, 216651516, 140740012, 298674646, 182363508, 312941827, 452282443, 345698324, 416646118, 483006047, 796923801, 505012598, 179873062, 677449130, 792637348, 986787183, 740001469, 909793378, 397693810, 225920798, 220264509, 202299712, 683766710, 447419594, 189672775, 453824081, 147425955, 77063024, 215736978, 502051474, 484485139, 576931963, 895970502, 942280680, 829825908, 383711535, 408703838, 660150305, 462695579, 45200997, 359737778, 38540232, 130077364, 676857101, 859839436, 545381883, 276083817, 105144784, 405797433, 688390704, 305353004, 985127471, 961271118, 125246624, 847964315, 344875157, 320106122, 59750873, 813073999, 953158387, 219553617, 320211910, 286318344, 948991458, 560945247, 123411595, 124274859, 865198152, 512231113, 295617190, 530833397, 394692216, 732476149, 728815502, 745377567, 602714203, 383049507, 894380441, 707917555, 893808478, 762584507, 623780786, 198072889, 458915623, 207409270, 691754956, 229591764, 279777530, 883825432, 881007942, 522586896, 400477475, 916258767, 694072890, 81593916, 443170279, 976699281, 55331692, 660174038, 895247532, 248935868, 772787854, 704222423, 352502936, 85485771, 28112699, 747792697, 425614366, 959374918, 108659902, 65813598, 313581616, 771854207, 336325254, 595262148, 514228025, 954907663, 422225389, 517381386, 431312662, 988833062, 53614438, 845181968, 848399261, 284235910, 562733438, 329475380, 781316199, 388386342, 490426741, 32708447, 699049621, 963178005, 288949809, 423363067, 884356374, 633707471, 317402609, 914541866, 640612042, 102860544, 996725734, 239833476, 363656463, 434368038, 969253977, 821220949, 531708983, 998360963, 737683386, 307597737, 100455677, 441631454, 587094613, 876598901, 656687337, 15940317, 181186907, 491894204, 361100592, 359282209, 631504136, 793956423, 217168982, 758434020, 105371195, 543792682, 2810505, 521396816, 566659946, 19328085, 209136362, 132346353, 568570158, 935158206, 472367907, 143861031, 621544264, 15261229, 225023387, 387283010, 415068800, 797501515, 735662909, 585280889, 865302962, 956722796, 863912592, 812999216, 953177692, 522526016, 933457706, 369878246, 717268034, 749548810, 45611623, 150620439, 322784368, 755071818, 911079220, 263816085, 21399865, 830679692, 745088646, 286888683, 983957615, 474470891, 709452260, 235636723, 113560232, 749144008, 6023180, 68629004, 450849210, 768721012, 307514486, 49911961, 180369613, 403158969, 450425374, 605363548, 110373404, 418051062, 999135530, 280197064, 648601115, 422029787, 277127732, 9364126, 801653961, 67448061, 161069103, 442044400, 99485671, 337186944, 156590096, 900725647, 985365749, 569995196, 410335300, 745740429, 700775565, 836971796, 106976914, 564913327, 788150924, 32869402, 808608604, 849768704, 667326539, 349899881, 95523753, 911364722, 493694357, 876496354, 952639833, 270241355, 643479809, 845045917, 542029743, 946569514, 329975835, 693567034, 669277708, 202152686, 459211089, 573374863, 780250135, 436322974, 323865335, 210939470, 998850234, 139435686, 326309672, 346261019, 451257421, 602732199, 859797073, 268692262, 153542735, 560460620, 953259110, 52164776, 338257298, 347594487, 635937946, 449257976, 110806041, 815950024, 942390655, 385758542, 530409316, 545060115, 4618461, 339042761, 365872377, 979027052, 871107563, 546531139, 762075568, 726908301, 406096986, 17005641, 752415716, 350146263, 311569851, 699472417, 181106819, 435203313, 447464053, 249245900, 191220648, 245011333, 127526353, 643085334, 215693714, 788071387, 696089578, 884854730, 787463780, 751345959, 309225389, 124912247, 607303804, 641153014, 762946986, 984961924, 708295566, 33781503, 322812894, 305434589, 430457952, 325102082, 55124059, 309577987, 911377165, 277486315, 288433571, 105049429, 568665647, 180162080, 333896964, 711613464, 900383682, 844860867, 870099389, 126339866, 281105241, 309790361, 128121623, 913704393, 898654699, 604021576, 526134440, 105518469, 467942230, 924189514, 910274165, 843114776, 591886253, 839740714, 150699784, 8265044, 646435830, 826460155, 616692993, 787975343, 306300037, 72291291, 573128480, 842547543, 331099576, 848363238, 547503297, 452568984, 142102322, 156559878, 303565892, 530229922, 895515762, 686779588, 928025512, 817283873, 8356857, 919813013, 227022899, 645405806, 837923974, 751795669, 77102191, 542464295, 472370018, 275042131, 477634474, 86435414, 742377832, 892115115, 807230103, 266772250, 491938244, 804515533, 941575406, 159463968, 361270637, 275795712, 773601772, 765847059, 174053232, 751594066, 328437205, 829814373, 986837513, 551199157, 347188683, 196181940, 142966938, 247881044, 954335967, 625450824, 692987952, 906654723, 566148286, 119266778, 32277853, 585098462, 597364562, 16066152, 514932397, 351147396, 862247811, 462352993, 270372337, 448537742, 226644319, 167742167, 434129798, 245854363, 245296052, 491149405, 360629267, 876580260, 925126699, 229091151, 802911274, 518908614, 103700575, 144957406, 355378834, 560786946, 185018596, 664184782, 645388669, 637558527, 25349984, 764907373, 862158190, 217392987, 342186325, 598784528, 484945380, 629482247, 541771823, 477472176, 502709247, 15037076, 970159473, 354232500, 383247444, 791887737, 61956400, 821142925, 590345181, 611776210, 967778158, 371469746, 634874492, 451057703, 644454574, 159555037, 767904024, 963617511, 909584929, 663284319, 135869378, 325963617, 987358982, 388290532, 73869960, 723248364, 627822089, 289608610, 509370640, 936272135, 56694132, 871965444, 276821091, 243322974, 789220935, 909360408, 108244897, 445371373, 718815723, 899545204, 815728255, 9809377, 958811723, 93755571, 145912881, 827641725, 795598819, 250941746, 925511213, 747886555, 238496297, 248316762, 540271983, 238710792, 795126197, 349437860, 131432569, 394443761, 935404135, 503456398, 352776369, 826441788, 289798174, 989755753, 246718087, 86038313, 798916982, 348209066, 365777555, 614859935, 558227743, 471916555, 218861711, 610198927, 625694937, 576401271, 938600345, 574342898, 354193817, 101648197, 295176544, 271542729, 402648052, 397302494, 957410364, 672852396, 919754253, 29120888, 572565292, 598384503, 48604501, 591800481, 607795741, 962974649, 360704292, 697031858, 243604215, 684191387, 216613857, 98452961, 84674912, 640382065, 288114214, 268220841, 571284325, 10290148, 143631661, 189427196, 218793845, 690943134, 938489265, 850784848, 790078410, 690199469, 311056499, 874898481, 181359038, 730038630, 535972977, 976609238, 14957487, 664230835, 14937134, 768219184, 993034373, 370628184, 396361484, 258200585, 693619766, 890908489, 431417705, 944725121, 910126739, 200873881, 17371681, 627929316, 478390309, 635050857, 641890709, 129564667, 348184506, 510116066, 734733445, 477678774, 166022080, 805292828, 551152216, 261729070, 656265687, 718284007, 672583619, 31172101, 86673781, 754070781, 284040575, 347513831, 126416220, 165273497, 433699640, 128212903, 893661256, 783925700, 48746233, 195211976, 615684438, 634882248, 817723056, 129988611, 634503132, 534431399, 903662745, 617623528, 927557310, 18069385, 252310250, 240752760, 625649892, 783764089, 630807662, 901842620, 987588565, 452233437, 598818043, 43529061, 114378635, 570626488, 928804995, 192557727, 580980604, 923426029, 509226486, 499731238, 932121392, 834640561, 120520725, 620611413, 458079845, 365921687, 85128583, 414357682, 415564149, 473133864, 704008642, 50386138, 847953200, 213428192, 114324675, 82411813, 551121920, 489791424, 717478777, 92059208, 478914940, 216393510, 406303741, 94337437, 659410974, 749521019, 494967163, 257039837, 159003908, 818238321, 508756219, 115201414, 172094801, 287967626, 83125314, 354898893, 144190239, 980404896, 961205290, 506144532, 329986476, 347938306, 362167724, 630009261, 397693839, 568395533, 135474949, 461162005, 244713821, 266461737, 772759315, 231290765, 580982588, 212609619, 255972936, 83689263, 804394253, 742997603, 563181112, 237952357, 216003687, 290624072, 216785423, 240281852, 394090433, 873304812, 627836065, 612636015, 575028025, 847904982, 305619329, 298512708, 538171836, 555256840, 359947164, 192409836, 422415079, 677422009, 925434845, 384877329, 902758485, 530389695, 936836708, 680542433, 980314998, 983730526, 961294167, 130063656, 879144990, 647152725, 837899759, 928517489, 987699476, 195720130, 673593960, 915757943, 333503050, 593995595, 346333369, 251871842, 582447389, 416169132, 223759677, 957136823, 944988282, 334297104, 215354334, 383653440, 364121335, 8940651, 479925279, 901681853, 371773763, 833938346, 517087021, 213151022, 780992340, 246819400, 206117637, 182073018, 218911165, 101442633, 338432781, 177409966, 224528315, 562813502, 680216149, 267562050, 939793266, 586512837, 465163490, 803554319, 720542260, 487685889, 138830096, 666425126, 804741628, 589441497, 33725235, 300600493, 291493401, 306492041, 993451810, 391748853, 662695483, 818700109, 418532288, 415154350, 149487965, 436867162, 378634562, 638977883, 468175747, 580882273, 510198020, 990502227, 674379021, 770298609, 734126342, 880993255, 199715104, 655292646, 80353527, 404027456, 52077217, 892135174, 75848033, 271422882, 748733615, 478927046, 504629584, 515723428, 962777972, 879771507, 714760099, 802396561, 756511660, 221069449, 234679878, 188087791, 57195105, 755952971, 832729373, 441707193, 975233735, 167015173, 590537578, 223990992, 956401068, 117727916, 750546816, 814339618, 332691164, 278877878, 735151416, 762937634, 963925923, 241394329, 120871810, 182817857, 25461625, 195409328, 520928939, 504234202, 191885612, 430851210, 844180516, 973356459, 504624966, 865116599, 337592187, 535838311, 336989659, 905961574, 512155015, 47972041, 80467223, 782518869, 303892313, 304038619, 98524105, 948860214, 51693470, 785990769, 725702555, 22949119, 633640214, 170170618, 610657799, 479280993, 162529854, 403400007, 880261800, 140112000, 140769581, 469003657, 151629767, 284279023, 483517703, 554241366, 955019708, 191473946, 304769306, 159002524, 942790057, 537128405, 39313898, 165271957, 764979259, 170922159, 190396436, 301955174, 828478388, 605214433, 618440128, 785547360, 789994183, 724439339, 815700362, 297943016, 779496447, 761957261, 494459298, 362300426, 25011070, 952863427, 636909175, 153066809, 602963069, 794192115, 592804656, 607575717, 80912339, 320118446, 832154624, 977738957, 281838791, 770810560, 160637789, 88622027, 91655331, 131558388, 246279037, 325758018, 647873813, 327980229, 745956504, 454608333, 275510551, 491035996, 578341759, 309144260, 84836637, 268629677, 166851233, 372946402, 12419308, 976496431, 715046849, 586673159, 310547180, 88216885, 257410658, 63586039, 253400022, 307985163, 43176416, 688141789, 588611307, 147105381, 411337967, 194773937, 354459455, 534749237, 394268812, 713792482, 694076963, 564014545, 156562250, 621489217, 199683817, 656928358, 427904333, 729622413, 476571840, 875175104, 447821191, 187597352, 855568586, 938533744, 960077559, 987351300, 751834356, 368990799, 538673986, 26459726, 963707588, 503005786, 826938348, 297216454, 878035280, 322310301, 824331842, 701147636, 260393537, 497763875, 670710319, 328137830, 669610837, 937834082, 952108329, 886002414, 46032256, 317207170, 934096665, 165246418, 206401549, 778951930, 837145491, 770451866, 528012900, 265739794, 292540064, 453977860, 754215841, 31158343, 349216516, 481495923, 180848663, 993415071, 187183720, 995599333, 172011220, 771245882, 916847250, 70478627, 971645781, 219542310, 342086402, 473950571, 5226309, 179617926, 619125803, 387308979, 386054124, 529481778, 394209203, 724163144, 29400080, 227877673, 143571309, 747967869, 852808355, 446372167, 543497908, 265160091, 998621848, 841971698, 851466475, 257035279, 256578719, 647302425, 62503983, 996411803, 926568855, 819007069, 657950186, 983324785, 576441043, 623199867, 537188185, 446891452, 283948012, 186442965, 595460487, 342976417, 227154825, 206207722, 136200738, 187218581, 944569487, 446144924, 38002808, 576729709, 25115909, 240880092, 231962738, 997292212, 824101218, 64589779, 764525884, 325943967, 482033544, 786835514, 468077066, 745285798, 89845414, 489327368, 33413890, 526863614, 540750421, 709258798, 874730369, 848275150, 651079146, 818525875, 221864260, 913287067, 312339048, 508206963, 269730987, 217855008, 543131096, 357416223, 312914935, 827876353, 434367049, 246649131, 747327083, 51931521, 855822902, 100656849, 557554307, 777229278, 101778752, 830457685, 18104466, 595195718, 435105223, 425630333, 608940757, 784307580, 192380825, 16531918, 407821122, 333437378, 581065934, 428333391, 465796673, 560397201, 838466003, 748687449, 243210495, 37796678, 345906143, 845201683, 533199200, 68930685, 385628937, 298209485, 392215354, 788128097, 957372215, 709171262, 779395409, 623490766, 948366413, 684937011, 805587259, 849729774, 16608749, 598465802, 841362937, 814283321, 183039986, 529789023, 558871141, 803359673, 425186335, 298629295, 639947466, 57614983, 566661328, 349724837, 857352648, 761579972, 51309842, 229965283, 442562766, 449318615, 414406357, 377763855, 496122699, 79683390, 597366209, 769156337, 861895411, 319743119, 98416621, 626060155, 12650534, 479077853, 175483352, 630477276, 258867261, 832838845, 446961507, 622629336, 742711464, 601343299, 494028546, 857971679, 553800783, 565418133, 558270702, 179068516, 165270152, 392811392, 660747989, 657638430, 649902464, 166684273, 592784489, 621356018, 284220266, 175603685, 234798010, 944307798, 550133543, 688785449, 983211217, 3400319, 794137631, 380584588, 98618518, 127820915, 375197361, 459044907, 10459186, 242783452, 692743622, 107031393, 577341584, 672151369, 384152192, 487565311, 222775268, 953420475, 277088336, 249703365, 401537684, 512328625, 484295890, 926303689, 374032541, 636392084, 823276380, 404813070, 550848860, 922132397, 385656555, 692764390, 318412899, 529451229, 174211112, 11793432, 893999550, 232044510, 620097962, 366866360, 992017684, 546719028, 545999242, 66338379, 356504101, 236120395, 302945458, 924073589, 891570266, 94556048, 612724268, 947373679, 902581814, 617325942, 229092067, 94123395, 153233395, 417573418, 881418503, 670883041, 197558948, 386919768, 815747839, 879694835, 665731319, 382656064, 689226478, 93615480, 321114165, 330254782, 559210212, 692269773, 10826923, 792370210, 517909570, 694422547, 847824243, 722248802, 477720044, 129327830, 669230352, 452977061, 773954657, 381111807, 239803715, 23369709, 409125506, 199324327, 922875078, 87662977, 467052613, 107682950, 783322772, 919738839, 249719858, 981921318, 965529115, 266099709, 7966177, 946162642, 346174810, 215590407, 275139131, 277226162, 325993220, 278689395, 81461489, 846718424, 889133130, 151570321, 869530719, 389822789, 455524763, 270274010, 650289255, 519554541, 361145631, 182639902, 167016260, 432007969, 61186492, 89371261, 517056150, 286731171, 754522057, 252077569, 591208022, 647731507, 516074255, 128803673, 862773453, 254322828, 390364794, 599270231, 990997577, 653394014, 572099633, 197044235, 955684283, 720084376, 555607736, 38018300, 903948056, 959501105, 637369840, 737107330, 227664256, 125969019, 623987746, 706463806, 546432385, 150085747, 548695310, 876511279, 711347932, 948360786, 202798205, 930090943, 534536595, 583999182, 316639362, 597449902, 59704669, 870811958, 859143383, 400965438, 510119998, 226383868, 490587205, 266984757, 87762420, 926418658, 332446558, 840223342, 553715693, 392037171, 274169506, 663002709, 40710596, 35685209, 896187320, 711579885, 844522980, 947257175, 595694624, 994826246, 802507403, 983126902, 952249574, 81166143, 343644327, 535687009, 421988160, 851316754, 307588133, 800332875, 120396882, 996978618, 969205346, 552993814, 951450118, 445974328, 398402369, 528920036, 810849820, 299954419, 476621993, 181252309, 616780198, 88447564, 776880191, 400217795, 666094871, 94718293, 107630860, 844135555, 414465723, 745126650, 75641238, 243170712, 949391735, 502681535, 23668648, 442498517, 172378349, 602303658, 807573757, 66248686, 302732102, 624419868, 526783119, 214759879, 56938848, 773989963, 6116688, 529841719, 791766255, 355991306, 452011847, 274887655, 919057665, 864871858, 917343711, 578369119, 361234802, 95351090, 860040594, 330241482, 132637235, 155390119, 70423475, 644954261, 604751333, 735667371, 422975210, 529911598, 545990160, 215568029, 784022917, 392679125, 150836434, 465546536, 276444712, 710618327, 458954173, 832088356, 746271789, 54477633, 521737764, 240717864, 495840303, 951620346, 760039808, 659102293, 688323712, 854617182, 492826493, 607041633, 300831073, 450471733, 801705878, 333577406, 478315774, 83066062, 495433048, 272973630, 505717658, 97135636, 822021397, 716926942, 570903994, 827377353, 76844756, 747320126, 258374912, 890704745, 103282482, 144709901, 250436031, 607267693, 232252368, 815372524, 463139871, 246680768, 475146291, 826993682, 14821143, 582618000, 534341663, 631404550, 541434981, 665611801, 439472516, 897865317, 484282471, 561614622, 180373148, 860996285, 530278936, 115871409, 817624707, 791959598, 665648441, 773590979, 353891532, 43897111, 549244181, 525385983, 356649028, 855581819, 730085270, 781276214, 553287764, 480390338, 315727600, 589134012, 349934365, 37358253, 133571856, 809362542, 512602058, 984259663, 964892106, 830181682, 193362496, 289208475, 858078775, 335502210, 668040627, 123040187, 723809350, 392230477, 349842690, 176407357, 519890462, 803398589, 844127922, 279530764, 777503580, 825807028, 874698322, 654595778, 299084787, 448570056, 998702756, 878871152, 144487626, 280164554, 541342381, 683395342, 704525843, 635099071, 871444074, 854755313, 545241191, 416677760, 908439008, 6280612, 113360698, 825184506, 498428555, 659322838, 206692702, 819773326, 78509813, 575568871, 494708703, 692886408, 198462687, 994113725, 185696109, 819841991, 924678596, 441790433, 160318877, 126342606, 132039028, 890339217, 35197293, 483412951, 290801064, 910545488, 236863515, 46764274, 464051392, 705349721, 56030673, 373758335, 542470180, 379511807, 807549296, 566007825, 62442422, 816879187, 335245083, 627558082, 670926079, 913404550, 981645396, 607214853, 111429998, 360143626, 820880153, 700969905, 390915578, 81704698, 606305205, 818997036, 839579420, 205823519, 155585230, 145122266, 964846227, 268585342, 450880808, 290929733, 701570811, 422554362, 176081897, 921511615, 101089094, 288879064, 468402799, 234186782, 332112040, 832983691, 926725338, 327837559, 991436149, 518001660, 474487819, 656995807, 899615488, 180818148, 499714157, 959395358, 274988400, 388367489, 439505828, 696162650, 510738466, 986082850, 229346437, 255240424, 293639399, 194808292, 13506092, 609265792, 464637850, 75227982, 840962626, 267354439, 336203474, 439461853, 840341864, 721752873, 776852512, 592626781, 135552747, 495942883, 255544023, 844365536, 800862206, 971108705, 717545873, 513717583, 793406444, 439190925, 321561537, 700764137, 250605404, 335229767, 583566674, 489981661, 757774134, 655977442, 243651798, 967095277, 10153428, 836309965, 309872372, 342038642, 349645730, 792751025, 990921299, 760149052, 567740315, 271399569, 175397879, 33450913, 651436244, 481824213, 403282862, 194689102, 143928749, 640446543, 650847561, 165382333, 21330574, 559749504, 282940989, 635452680, 198970804, 787741454, 224206403, 116876475, 888283066, 155625883, 860938482, 99088315, 484939080, 364475419, 153539142, 226078558, 750222544, 213606507, 688894008, 276468095, 278536363, 309485454, 494814303, 565847172, 185128670, 474807123, 433802845, 898356688, 43128309, 943678481, 969260612, 22405733, 710265235, 117100653, 838713994, 728511539, 888476942, 495013699, 520660543, 580415397, 712448051, 742683544, 462624548, 480195166, 360713853, 296023939, 136173400, 767333058, 887881473, 565244375, 692747906, 432832017, 25138485, 638412308, 130522256, 576208056, 84298855, 410520161, 416427322, 389088761, 624078853, 902418781, 760646470, 258257149, 899910699, 776203807, 19849935, 646493819, 560776196, 546763519, 823332256, 734592445, 614286546, 616045382, 989454045, 17075584, 7877742, 502817732, 224907449, 855294437, 101417127, 807471111, 560027782, 533618440, 678982159, 848796093, 689859567, 190011906, 5785746, 42930470, 192270620, 880400034, 838024067, 121561205, 290767336, 111960881, 853019340, 341175094, 766270350, 188758306, 727467556, 136319432, 576969623, 280426212, 623323983, 774448576, 588954976, 315027230, 803856696, 29941095, 431948971, 142281161, 925124433, 861392125, 80891864, 972043980, 629020667, 561805004, 312315151, 476215536, 771343174, 987329546, 357825065, 336891650, 411555915, 343813589, 195820445, 882645414, 410720520, 753478695, 663992720, 774220252, 749137259, 930691248, 434923257, 161093539, 770837781, 354312961, 193395774, 367123461, 565354245, 679270793, 397628751, 217121216, 11760875, 403564348, 71150102, 368592024, 897815353, 994505662, 408127559, 13668410, 69820824, 69774071, 861606001, 604655326, 121848283, 363261206, 533544368, 538663570, 172311982, 220197600, 172089912, 165169436, 429935475, 65008037, 699439776, 273839877, 490141238, 490067959, 444898877, 393713858, 176355122, 59295682, 892326741, 281583835, 687723650, 870182540, 346071449, 332969843, 335722873, 337845984, 45176399, 24415806, 2308862, 1110263, 952816287, 413596322, 457602184, 608181126, 138846196, 683156584, 648555388, 136354769, 70181525, 911269767, 348803783, 586386836, 95395008, 639691462, 197246507, 784316873, 351344494, 516118995, 133439447, 209032763, 754815525, 844000344, 579497382, 543598008, 669010574, 810144603, 990464876, 974778641, 697366177, 327010262, 370312488, 560846170, 792223978, 70777692, 730059355, 645250397, 267577093, 38654537, 752518626, 382980134, 931773562, 481034793, 391116196, 978295062, 460741013, 36044394, 427642224, 654541956, 229620044, 480648144, 220672935, 74255693, 164517499, 848528607, 698706905, 270106207, 72249359, 728454879, 401029097, 749737699, 540722419, 515623264, 186253746, 447327384, 667749960, 257643019, 53384358, 244082175, 319549014, 824197936, 312631521, 223966894, 407534855, 232784358, 271917418, 921835724, 796371425, 768552953, 771116236, 720631769, 176115214, 463104294, 32601129, 873101983, 726488097, 905506187, 772022708, 790766539, 277549142, 258224017, 534233396, 457451484, 984765991, 666356229, 285112732, 105240204, 928779057, 733734550, 426028638, 85012999, 607498383, 350044059, 192726117, 785458212, 5138745, 638384576, 530395046, 160725892, 734577696, 298137775, 647176944, 636168408, 916717020, 145883949, 21835951, 609989524, 624600036, 130858009, 196338930, 205677297, 242576008, 182054034, 173135017, 310635461, 239132350, 820851500, 952663487, 842340211, 870203762, 136114077, 875790965, 997698949, 398343918, 120520969, 730588957, 512775855, 8402306, 149806096, 944510804, 590083469, 73224200, 638298925, 377854673, 108235234, 523684573, 737188402, 2401175, 346457936, 172703383, 68480745, 645510646, 29654483, 134565318, 758053746, 173563088, 30554840, 677360534, 923509332, 473173031, 395834641, 895652708, 605630278, 508175810, 764267340, 286758227, 744444264, 379175927, 449921848, 733348406, 580120246, 517256243, 809596999, 389739963, 149587825, 518270340, 781470036, 338561638, 390916754, 176754554, 761794037, 291256125, 837185091, 732116166, 43956658, 150478758, 774125829, 643082844, 433448966, 145624080, 658759579, 975189687, 182969393, 969020183, 514460413, 407090123, 806351506, 546163661, 456190832, 767790206, 497309281, 279638005, 353159068, 188343504, 276622066, 11211935, 845988772, 129716351, 179604516, 901713398, 807188467, 221256876, 372100198, 210494116, 3705926, 424688858, 241869215, 463164360, 789967778, 906824777, 30644170, 922593312, 870508102, 295177668, 871995365, 945281750, 819341940, 739946801, 12044988, 154891550, 478628932, 972747958, 904619787, 377180378, 731784350, 399165286, 818350623, 864683908, 829864725, 859057886, 870464298, 550186631, 806230328, 156856889, 902361490, 150111030, 427978050, 635787880, 202050879, 942161080, 109182608, 896550699, 225527937, 1389135, 745689842, 86486564, 864162564, 5496036, 777358075, 770648663, 79851200, 949768534, 180911475, 432703028, 450220864, 512693889, 78978195, 536102254, 846388768, 709182546, 684179252, 588229545, 465688588, 62689190, 231436507, 444025359, 446536019, 498654777, 254235486, 757735073, 3308698, 204293927, 166774429, 206945668, 669447860, 587798803, 968552651, 702979778, 509986268, 421595208, 658693753, 311193363, 667210544, 522571593, 622115838, 276192827, 342369481, 249829775, 310669449, 143289847, 192370577, 276004383, 46471923, 517907769, 38643304, 859472548, 63585522, 426083874, 59218909, 808048523, 857310500, 634284520, 914991031, 768015314, 338364133, 56784469, 549295962, 905736217, 850548589, 436109554, 602310229, 280527687, 581026012, 250260519, 94920251, 687195072, 715605344, 812827227, 121047329, 820041695, 944980421, 761843831, 669681665, 893838821, 636433333, 658601084, 775978999, 693736, 828142745, 793907544, 443095282, 667829409, 966972183, 107051237, 835205102, 174982423, 976935799, 166285456, 616988179, 384074994, 798097663, 115797299, 109600134, 678026262, 164419564, 900720457, 890698898, 246533756, 744699434, 976145004, 859338715, 380534428, 239842175, 327532138, 560228431, 835422064, 86109188, 436136807, 562260015, 714422856, 652486483, 491382413, 248558592, 47127165, 420724437, 835853533, 700496733, 198441067, 847132235, 808758721, 969536979, 842604953, 19246681, 756169129, 87299869, 113484450, 213818009, 653256432, 460648611, 486615476, 786937206, 825708047, 144959874, 483005513, 315277484, 458118120, 987810880, 440448650, 450597398, 56606046, 622491683, 9315294, 402591289, 57507108, 540247114, 973140542, 901497821, 117059023, 923403284, 254770802, 337402255, 630798921, 44869992, 503635697, 653696614, 97691172, 692823490, 671486158, 215593409, 128049096, 51064024, 151859051, 989625046, 534568785, 511865523, 804590410, 152789747, 578002812, 400643391, 746641972, 373386205, 447966762, 216855307, 747531637, 629084795, 928318330, 386974745, 680022877, 721786378, 920395528, 597250466, 586201335, 188508906, 893020783, 208741505, 789442410, 138210386, 182816013, 839489682, 818535254, 27724923, 271657370, 52380605, 756435266, 259760562, 173264985, 578466608, 211415241, 277351160, 994433619, 605014110, 109737936, 951816885, 151872984, 437301871, 657772697, 701015346, 246627780, 639946642, 941448178, 562440403, 512597988, 641431519, 736319869, 95465603, 652165150, 324041869, 624372657, 959333724, 518346217, 757774499, 133957495, 25561867, 624193394, 595748537, 485385180, 133084757, 520071223, 4078826, 386659126, 496469866, 410370106, 515826958, 15107574, 928205991, 210199455, 872281929, 175547467, 599313571, 198410993, 524338695, 47629775, 323066904, 154106020, 89360205, 573686797, 115368814, 744836769, 407702832, 263786877, 503687133, 423034065, 814447664, 407373376, 89879452, 496409771, 635738873, 971649889, 278605005, 394342115, 247223851, 480025538, 332259578, 870606627, 853005124, 564178469, 76818035, 522787291, 363424451, 812925302, 941133394, 334980263, 288203814, 635000445, 718067192, 804859112, 506098587, 337624030, 855847919, 743511920, 766591741, 645185534, 666495062, 221502231, 956728792, 725035143, 734771055, 794004193, 54537202, 685441472, 312704634, 885657144, 394300099, 62867819, 185463588, 758479248, 811173547, 443026100, 934869180, 836211246, 329303403, 543539182, 804216019, 764975672, 867375998, 447868317, 510966542, 183996175, 770858499, 972270739, 38602002, 80079651, 631160166, 872300994, 281068346, 240997335, 558428456, 635393236, 314092356, 542158996, 361794680, 842118593, 969462755, 248845624, 97040434, 191026469, 506195424, 681539665, 471462363, 407031392, 394239462, 216587559, 499172272, 332717233, 528497883, 28397583, 127451318, 537488132, 233106459, 558910329, 568846298, 980238965, 663990665, 991044814, 469848397, 126594089, 752774484, 246840169, 363050684, 343002256, 489655997, 831774883, 4605452, 461419582, 657440698, 778869258, 862580707, 704169785, 237590485, 280719657, 917848606, 399201251, 768310924, 249798911, 360027216, 58620968, 283331155, 113392644, 33209187, 388100300, 956342490, 176128181, 646260884, 819012799, 425679597, 555714305, 159394301, 126727581, 615741944, 320363259, 285920844, 389710134, 716652518, 991139425, 94780009, 795769534, 329150150, 441979373, 310264309, 153137156, 440310659, 553597873, 246448927, 475695860, 862712468, 472822574, 942394929, 406325217, 233899864, 600655502, 546895948, 91896043, 298293314, 279708236, 599795103, 657181092, 868248663, 344244185, 635095366, 900328988, 957509567, 689693786, 89137671, 688078491, 477664330, 93445246, 352223023, 285209396, 266489448, 663740026, 290760952, 75807891, 342104663, 300477385, 611318327, 879011528, 348294053, 106086231, 196436721, 42553867, 674326498, 918025986, 382097348, 914538075, 820088277, 315177560, 650795975, 596956149, 785016165, 22574245, 609766522, 249342345, 964856558, 255079135, 785320619, 145692231, 858090755, 212951446, 968821233, 975005936, 618307056, 554840295, 740845099, 605303152, 494750071, 706309797, 652583336, 292329740, 816031908, 155579626, 268639277, 609245446, 219889746, 465165351, 631815232, 131531526, 13062478, 701402590, 353034034, 708865671, 982572526, 342768651, 217796881, 139746151, 711073949, 472232627, 34719165, 657057018, 300804329, 52433178, 432447337, 513173551, 128419472, 201276156, 164603585, 626836740, 253252588, 71654233, 297537668, 512351823, 253067471, 93486612, 220517698, 533772073, 582928145, 838113231, 733856907, 132050272, 462980761, 89920112, 660850401, 654018630, 731325839, 50814153, 218810352, 869687628, 880218715, 568822158, 288206695, 623106814, 198425640, 259896039, 444148507, 220412651, 268566089, 381656228, 23542994, 80244718, 257392574, 175154459, 652689485, 352631251, 370828596, 329552457, 133958828, 365912312, 727582147, 666037923, 776103972, 929325084, 198793300, 943852189, 302232495, 183812047, 936180550, 969000266, 766663961, 960600688, 918582507, 999670056, 474277182, 461748444, 65009359, 677365030, 614150512, 222438345, 288914363, 592560582, 423273195, 159464902, 137919624, 320902459, 631475294, 16946477, 107593784, 214540730, 244393720, 349479952, 987091129, 305316328, 977991030, 498549103, 693936549, 331120182, 258373419, 742637117, 698882706, 147205499, 85413634, 943554505, 767016789, 428963028, 919921355, 926169821, 289139767, 976246311, 638471844, 726514588, 185575664, 976506294, 930935783, 7899030, 858614604, 326844489, 474869443, 909620800, 116140043, 979361369, 177465659, 661377982, 598710411, 127139069, 191418322, 380466962, 653272896, 287567, 354652750, 912145420, 705625688, 374660379, 231343714, 97771001, 891876637, 53540505, 791667094, 995482807, 727637761, 547983572, 687092037, 69708130, 294217809, 527532069, 721068029, 551453732, 681760971, 334068170, 789247970, 426438702, 724012901, 249139531, 535951019, 332756504, 966797289, 860662712, 278702911, 326782086, 895619691, 920798038, 766140628, 576588310, 147296278, 668850596, 439382457, 429270355, 351998820, 524971900, 783004434, 387712173, 54031826, 870318582, 856012804, 817396913, 810177487, 207892957, 905753750, 27885911, 325103519, 452119173, 625567570, 212572397, 942205709, 336507021, 558807126, 968498395, 985132655, 245327149, 49752084, 211900974, 604855819, 925583760, 986598087, 70632960, 761113431, 530594780, 305809806, 393660218, 200868866, 433560330, 997359107, 398706127, 825555234, 946863011, 506217884, 334725323, 51045542, 920916934, 594106530, 487871743, 891651139, 110176725, 703652962, 117816983, 106505360, 192616634, 55941559, 617941944, 805930388, 860552337, 379574871, 629395935, 469476311, 808933250, 582355342, 430107227, 435443400, 342970580, 848085481, 385172863, 83448568, 652475389, 526083523, 527130743, 97221104, 36167930, 288003986, 830630121, 908895299, 359910037, 721699672, 958988655, 507214951, 340135063, 333733639, 13674951, 138530490, 504238845, 853597669, 161475782, 580665957, 178508105, 166111720, 555115016, 991760302, 197485259, 958992996, 15071677, 864308161, 806582627, 885848752, 789825399, 281935088, 892310960, 850547536, 98481415, 864729687, 273563786, 501402503, 344154933, 371795490, 463630762, 320674404, 11605312, 687678118, 934722196, 269842525, 364241091, 315653646, 171093501, 116825016, 183062633, 489071224, 111624964, 145418424, 76991024, 87698922, 681416157, 139233010, 667310734, 119779365, 932494558, 66147144, 122135069, 467002453, 722638346, 60268554, 589256691, 648832531, 734269159, 882220814, 571233622, 336704681, 190599105, 436244589, 875907342, 789462854, 393904393, 407069785, 31089499, 448813227, 629879357, 67443796, 145861820, 197807204, 657770049, 411923142, 705851411, 235274928, 967830490, 461363596, 443579187, 566376270, 304414, 862248824, 349509086, 278475478, 635642462, 237584288, 897702621, 893664663, 318171311, 262992297, 142347879, 841650248, 136917324, 358280765, 193390502, 140045350, 651227451, 215213895, 897345550, 635899844, 797985757, 192931770, 154401131, 725433345, 769010047, 714105431, 652404413, 412773010, 456397176, 659475790, 299563795, 614472636, 600074790, 235998625, 931589204, 890163044, 139305752, 854292755, 783643341, 96761775, 656652556, 20269319, 597959250, 781095220, 488335754, 25384289, 204738305, 330416051, 937952425, 378552079, 291837768, 684930158, 14292337, 774441313, 611889643, 741677935, 300904028, 205082077, 498876817, 46089641, 909831286, 323949211, 824866843, 391993628, 575000635, 128568245, 526646865, 406300608, 345148979, 175895067, 627665111, 652871345, 692092032, 677330810, 519371210, 543410910, 366080754, 737187250, 397416980, 768852204, 987061801, 676183914, 379982656, 684601580, 811927041, 802592418, 226626562, 972281546, 808144621, 158223357, 358913911, 388441209, 265855738, 534857947, 71389615, 103563839, 895063949, 746667408, 56927546, 550920539, 785598733, 525132464, 892093376, 908206382, 585287656, 157284192, 24407730, 919188293, 577685415, 67780334, 320443842, 309094982, 754227585, 610293052, 738040831, 735632300, 74161859, 637987813, 574366903, 73270901, 500225322, 37986315, 280581782, 788866758, 721731761, 928927961, 159385996, 406039767, 10269003, 388473429, 321262537, 322101785, 4454131, 22478206, 184223057, 168137925, 147693657, 809017438, 801431587, 701682566, 258792508, 656559852, 985334602, 990809436, 311274748, 308399634, 221681015, 550316610, 184623302, 300892135, 9156375, 426367270, 800641282, 351118770, 222110769, 284776345, 49516993, 837633972, 64611873, 588156718, 668443287, 858197351, 777464681, 426267762, 561354310, 688175593, 565505951, 279429625, 106183627, 276852201, 311951390, 624204001, 112472391, 503958006, 390597914, 377471304, 593586712, 757513889, 779390823, 891189507, 798915371, 508053736, 754573014, 808056502, 229942823, 463296574, 587119901, 197470912, 828879754, 727876786, 350586107, 653181222, 772746795, 320171518, 500923081, 245425157, 447068054, 46252616, 297556685, 284867168, 632569906, 551055123, 617070632, 851735271, 584875245, 941473359, 92457493, 419046933, 716985430, 486071397, 169289939, 316572219, 776539700, 207386897, 588027400, 904565878, 755780876, 796074629, 359992320, 192597500, 976686470, 517789524, 949350410, 357708322, 667423706, 402310034, 152801561, 250749506, 524999951, 122639864, 568007236, 964185058, 206706624, 642410358, 272227710, 577265040, 466729325, 830979122, 823567773, 642286475, 282027237, 236467373, 856165086, 835380102, 496387654, 214254360, 347384772, 893096173, 891014026, 604944140, 196083220, 105676788, 638228703, 540527190, 286965229, 883210063, 357988770, 713614905, 2415257, 882829514, 565608495, 394942872, 165977547, 135077290, 116979442, 458679475, 238495905, 150470735, 253963263, 218221515, 792276584, 29151071, 58585203, 929358967, 37910278, 380784330, 930003338, 451465363, 620841717, 669185416, 139853995, 456998220, 892342453, 847146100, 489536906, 643326749, 377595067, 718977239, 497382465, 896532284, 521571148, 16602370, 398812482, 746514321, 414042438, 341521608, 288987276, 705099078, 679975330, 525056116, 481073871, 241397964, 51056266, 863844404, 672199294, 542337208, 349722977, 670149923, 155617117, 93932276, 978200644, 909605408, 949524, 236845855, 881442384, 373821431, 238050740, 836801837, 855088726, 285742946, 231590600, 441957455, 402402291, 969433560, 854266729, 870087258, 164095154, 295513901, 416008440, 165195909, 854077648, 667431042, 914884595, 465830385, 306148058, 231186323, 617587540, 581490937, 422637192, 248249036, 438171634, 72733819, 916923059, 107700046, 176542828, 585195119, 330353529, 770127666, 407383679, 570939418, 244728604, 338014930, 916190883, 127657387, 71614756, 473988455, 218481192, 409776282, 526748624, 497383607, 323352893, 530918187, 620389662, 9537962, 423750522, 652080908, 491551459, 517358132, 458631573, 89806489, 24385933, 629493568, 789712206, 151670169, 541501250, 789025020, 671085286, 897889047, 684930145, 673314981, 602797516, 73449458, 193457294, 185897371, 789589234, 185622204, 236137593, 477722702, 855345928, 442489430, 992123228, 903212654, 777536059, 262506086, 88297112, 656852473, 259300817, 830380056, 651814246, 914288113, 157910472, 438177584, 423134229, 513684977, 996136822, 600695361, 984628366, 41943515, 944917173, 528175458, 620789411, 814963688, 517241114, 782189967, 159252370, 937461142, 446451027, 708943124, 283370569, 209880085, 975707674, 744799044, 774843026, 313493944, 658322991, 371347758, 559831878, 157873389, 76212297, 915488512, 209401681, 908025223, 674940310, 52017183, 436045571, 46505590, 985097990, 680580557, 53937397, 618160033, 135988050, 56049002, 208387808, 891759332, 810418977, 863839983, 523622609, 500481015, 576135350, 10686203, 397417576, 481061629, 307662951, 312257494, 412485832, 621056891, 166611899, 262210239, 612077120, 133164938, 777569592, 630958344, 362873899, 164976356, 975194448, 749756135, 331809667, 278159528, 261395577, 174450093, 634805739, 64617891, 415756338, 4033163, 296645456, 424023797, 606543189, 478874339, 932178832, 136167200, 117189166, 175040482, 275138410, 31240964, 210160888, 974210525, 50629182, 474006426, 836700293, 460268598, 740719631, 455562818, 241118244, 136760592, 302731236, 738895019, 879914491, 349647808, 636994844, 599936812, 603839800, 346492377, 255058321, 73426869, 692243806, 682641966, 610619140, 446996751, 226953813, 580434985, 578050365, 642595361, 295967921, 693526601, 725416747, 116820808, 967477909, 280134595, 676612089, 517671519, 886594447, 973282362, 42339583, 936627064, 351932549, 668065889, 457516096, 889707932, 379745708, 115949646, 606345711, 388388876, 929880595, 362797861, 292238510, 607623289, 999594967, 874919334, 144860211, 386599856, 1699482, 840456647, 631518436, 687906856, 315952961, 760886266, 924265028, 441000508, 785521306, 305348237, 804669723, 772022373, 346186082, 203723401, 62185566, 804519812, 205328884, 923972370, 677246876, 803806231, 684612587, 761287270, 61132722, 359167983, 462627054, 815230130, 220374470, 117201013, 610636630, 394208197, 162900354, 506015199, 509423294, 217609335, 598086442, 851937448, 934757772, 796171910, 928811611, 846218472, 141915387, 589103505, 649492027, 602417276, 560014173, 965219668, 302163396, 487808272, 907482829, 787556591, 556776248, 978234014, 670008374, 529147861, 839702292, 754792377, 941318093, 131369778, 412845893, 908694034, 51970414, 602383219, 676162990, 644000689, 273258960, 323426017, 474965518, 381190287, 281186382, 240045859, 960377245, 68926098, 463286963, 107785425, 480511115, 281811699, 630214041, 865975392, 274127532, 96302395, 345491867, 600984131, 490247554, 363535522, 955301509, 649414343, 993595317, 328949371, 126683430, 27733669, 849697016, 668655944, 687434558, 721856075, 970429213, 274602014, 37941595, 92715425, 939775532, 235816672, 538449238, 487884414, 897708869, 220744621, 465977582, 390223989, 303867819, 557870569, 460155638, 906426832, 233231481, 631578455, 172033823, 397181613, 708489667, 624154057, 592717130, 743753275, 927559361, 46559424, 781029749, 621293546, 314523301, 364021933, 393832400, 232535495, 653981191, 743515017, 408512419, 812789950, 542131408, 669602774, 820508123, 411303526, 967821621, 573436353, 172407870, 556795710, 213671521, 669382439, 194987885, 495976913, 184501617, 763969279, 457516106, 851141699, 204667598, 640960415, 811094628, 374352816, 362928109, 809559039, 262674637, 321875492, 260531771, 914962737, 285690992, 459879912, 621934918, 385119381, 549830117, 95859292, 698460511, 202780296, 855989941, 902381118, 687007344, 682821441, 753952454, 433030274, 317830055, 715908362, 48732071, 796526682, 873943675, 706181622, 547361635, 820389503, 972727888, 564844188, 695398538, 273826648, 498457570, 310324366, 446701056, 982922131, 221899762, 568182924, 534335303, 400733422, 156843792, 670223029, 331574138, 481115886, 247452622, 55453661, 941563227, 727627211, 987212824, 705277452, 485962762, 738491202, 689938383, 82773730, 939375215, 830788976, 327499772, 104342946, 298409296, 416064314, 634395576, 878104321, 461452271, 469061094, 818111640, 498049425, 628020232, 799957654, 152493078, 925287039, 943681057, 194908240, 280982264, 853350962, 697193578, 437097163, 242188743, 456468022, 269987675, 423564240, 513854789, 727689198, 874387254, 24539819, 993601316, 932352756, 895100345, 876464800, 484200097, 622354267, 592742184, 462697102, 810512243, 541459545, 506154150, 791120556, 540491394, 565214336, 626701378, 375118197, 512031448, 438955807, 846326154, 938794283, 698135355, 931342836, 377032737, 339112292, 121252305, 44108835, 893722320, 13396583, 299528066, 579300010, 82255694, 612397499, 744706789, 956369312, 526920010, 208170799, 268890016, 978221661, 377157514, 191016943, 856523648, 855790498, 220342995, 456564892, 772439147, 813592500, 646476092, 15491034, 288743148, 673548325, 128225695, 124937329, 224736652, 855253658, 406295837, 503001797, 64341232, 199844385, 24735455, 473482603, 793357233, 547437412, 386133014, 67065209, 921557597, 25488678, 591053067, 20836806, 66860595, 778732217, 283014430, 163834046, 723423164, 973334764, 57513605, 477923463, 139531424, 330796118, 787039958, 20228544, 6985631, 438279912, 507608779, 308053256, 305763699, 967600782, 755669267, 822324539, 471476584, 831831905, 974648749, 991523837, 521092141, 30882130, 830014723, 281782048, 938982501, 408279789, 200422319, 341675477, 923195793, 788763010, 959748271, 943630278, 793818463, 31311048, 585869070, 329545744, 58284824, 380148932, 266892488, 421766414, 634991287, 776966072, 651605209, 248208428, 229612741, 671786951, 125084578, 532290406, 605551977, 129804760, 502058978, 922644095, 470407, 496351205, 628049112, 992581783, 537671028, 201747235, 691218163, 578430352, 911628151, 559274919, 847941020, 206145775, 41656465, 649503890, 843629834, 969978694, 433326934, 582062925, 463806228, 96451201, 865439889, 429395407, 899592530, 670809477, 114416573, 337308289, 349168879, 469402379, 898913332, 562836958, 946610587, 683378794, 553574917, 414203968, 805133006, 224569257, 136712074, 400636967, 576270155, 5344381, 104198047, 891983151, 51007234, 669603234, 907457848, 794477741, 224303538, 605753086, 585731704, 191577548, 186251870, 144574837, 246814917, 732912938, 497061552, 757918293, 658058121, 776047801, 473882865, 905965614, 18796417, 348212555, 42686486, 371970187, 141908636, 589459939, 781437982, 266678843, 842067654, 697074511, 935860800, 514849716, 846810992, 914473210, 451887945, 998238630, 109924734, 691095849, 472407506, 836115877, 615758817, 638388913, 909099757, 672593003, 904315729, 576553929, 96808214, 630695532, 237838587, 918670395, 820555471, 315336915, 549736799, 294626038, 917900469, 367382499, 496537949, 141825855, 765280396, 825802453, 986094170, 435781376, 706614652, 585075021, 188977555, 890805043, 940722746, 368449044, 181646535, 151581907, 968207178, 34015246, 170404396, 32446332, 69243485, 704925550, 828384700, 274617426, 916512673, 978986278, 415793016, 861562806, 135487096, 480153477, 993113813, 433472514, 945280237, 926859660, 632905962, 900459005, 977093823, 851853757, 826623315, 22001001, 796399941, 331667535, 450227314, 631347968, 641792584, 905994513, 643846830, 876934116, 363031276, 947113432, 710060026, 935607465, 522126001, 712255058, 940212107, 366562826, 182996922, 170275342, 154878327, 765436522, 366731965, 253854004, 301980160, 796343563, 715845727, 941103185, 800891133, 783171966, 522019036, 747063004, 601250875, 911193769, 562202160, 468467012, 564232967, 68124835, 422127491, 485225648, 855283433, 276572321, 501415457, 992395225, 328698124, 926227273, 106341374, 351704308, 722228780, 278384473, 914460965, 19023395, 115018861, 82368655, 841267305, 14037648, 62992766, 921676638, 393059044, 606987157, 609817997, 1583504, 856393709, 136308473, 635969522, 464713096, 180518477, 166603379, 939290322, 692144922, 183916469, 901759790, 904065859, 229288030, 41005128, 185832591, 735739475, 960659505, 330954967, 892557588, 314373365, 811921889, 839984868, 88985159, 667246963, 682830338, 923618163, 206990570, 105610067, 304273574, 906828488, 915804743, 197609782, 384082648, 547050412, 762668844, 150217486, 997085028, 983455126, 847056495, 910163732, 485644031, 750692193, 296161443, 965300228, 445528678, 507085306, 523007323, 269038543, 28239427, 412090614, 847845288, 390672668, 58163751, 260862379, 13028972, 441745897, 212183930, 101720293, 82513313, 256526524, 908180411, 244299519, 862195814, 317086139, 11015140, 660704122, 682186282, 313943155, 348042738, 793818179, 889111686, 202411186, 388877845, 864689946, 667703714, 363270490, 223666338, 373144406, 13763356, 713612531, 971516247, 957950300, 498765648, 659684233, 697638235, 136575037, 976322873, 33649936, 301710157, 642899776, 485470483, 585121657, 831067190, 910604999, 343531530, 240869511, 586366689, 519242158, 41712328, 265004350, 998805458, 419691613, 432417500, 663695849, 536751273, 955722068, 17978667, 561481452, 51281261, 626595938, 551621618, 696756282, 101513253, 532699155, 360533315, 467385310, 935824910, 282370173, 170923127, 893750926, 16270915, 62734620, 325702641, 963767826, 566963047, 431493823, 795823543, 108688544, 645056965, 676994545, 200328285, 769503249, 189488537, 55617085, 506292678, 773722534, 641560389, 432609475, 769778940, 253556555, 588146310, 684136538, 78124794, 183425707, 183511777, 906199417, 189279392, 427402138, 632149794, 173565810, 953626710, 189754459, 324233253, 158113224, 945676087, 859108298, 8946951, 100880408, 612412139, 476432352, 881745196, 951365388, 123472835, 565638008, 947572037, 968585181, 882780878, 90040014, 778579773, 164137269, 673926607, 703711966, 942631818, 501578155, 274585477, 560219349, 363437247, 3789861, 509813286, 90968478, 502448417, 71700231, 121024400, 397727666, 30262975, 245025931, 21524531, 859439691, 432745084, 523385617, 423639439, 999880629, 956764113, 338718367, 453073080, 679589368, 734280427, 755980123, 654863818, 236365483, 773589820, 872894174, 784344977, 703154416, 248713614, 848313626, 782899390, 970734164, 494027309, 866695645, 273909687, 436042573, 706770029, 530226271, 982672952, 321796119, 187554338, 183097622, 897648124, 419484472, 110675630, 269950440, 261057644, 413520402, 274518237, 616438252, 941943897, 570798084, 408410814, 484656372, 242122967, 348091784, 286183382, 521462947, 173735224, 595106191, 950003997, 129342147, 299068448, 364422219, 514193088, 15701787, 819871850, 361034880, 323440427, 661129888, 51457852, 6087163, 532710995, 671111438, 305997058, 385409939, 64711600, 763399581, 566324045, 777456631, 586548880, 89591274, 714631738, 311431678, 353478258, 72049903, 662330948, 999933483, 136498104, 678763605, 445570509, 917459013, 292508552, 219161926, 481408827, 716415224, 935269007, 100417798, 767799942, 473015403, 854549668, 206508837, 368244973, 362905078, 837216484, 694008919, 407415965, 716431104, 65947961, 57025631, 733339194, 914430847, 334515284, 231720669, 352880787, 668798278, 183680492, 855511051, 532177371, 281084894, 431119066, 615405291, 878312881, 233479684, 244469059, 823956809, 897858567, 957255251, 536638444, 275565917, 241936775, 410396607, 388194722, 672131613, 558760843, 883957452, 404180216, 710267018, 545536032, 25174411, 849873347, 593780860, 240713189, 160024224, 302867295, 463400948, 558088844, 321555345, 47916230, 825119524, 436955918, 943774082, 92823595, 345943124, 842593213, 884662371, 741747402, 230323542, 875079028, 87983554, 68888792, 547097374, 627883738, 275945139, 830353940, 559648795, 567479938, 219665348, 744925210, 1163997, 534092314, 442506950, 420619766, 710563332, 505809331, 426730663, 935036050, 64941741, 697804818, 606660355, 685987419, 719714660, 610617127, 878759734, 24972854, 191580518, 998975053, 121303272, 275914368, 127720450, 653094330, 875749998, 299828168, 232659630, 44914060, 93263882, 801862212, 737475492, 74385252, 156920367, 681766353, 340913296, 699008683, 734623133, 415844565, 944495967, 672920866, 766891511, 767594762, 574319952, 226540889, 523424404, 981407949, 529184836, 462730063, 34328460, 363385295, 187695724, 132189977, 66603120, 592723454, 992694973, 509538324, 330671153, 344255798, 535581700, 709312207, 973492318, 838250325, 388718532, 632402871, 432577368, 49946823, 435770116, 106288852, 981315996, 22632722, 210110134, 660659803, 560209583, 930422039, 945303113, 140798752, 944916888, 693730187, 60990064, 105893799, 39022610, 548052896, 378923552, 223214203, 847393047, 577108062, 507518546, 963144246, 890793353, 197234647, 702154090, 101209457, 710868315, 935249167, 30573853, 286223791, 562385943, 82702114, 550084825, 521653672, 423348505, 980479586, 433458885, 652521797, 815835203, 857896213, 150277480, 732682719, 456899269, 851975779, 320351423, 491250521, 970235745, 480322230, 418889988, 610773350, 294596588, 591365247, 373579525, 853979328, 4751977, 984754926, 765956895, 13100905, 316796957, 398885858, 841281036, 831903522, 192846690, 366580510, 368996525, 661424861, 34030728, 55540846, 499062437, 636816111, 332779647, 887540155, 686828846, 9443882, 35098624, 130965322, 407327428, 803573143, 755448642, 30836627, 805904208, 986554620, 327187473, 594883085, 923273408, 986286285, 298690846, 176015404, 950767596, 622600844, 66188996, 232323184, 538880094, 984766983, 54255148, 32481802, 327482959, 239928001, 440520915, 440336843, 320667910, 505234672, 782393333, 576889536, 313502095, 905666236, 441351914, 230380912, 357038327, 762126010, 473918298, 133006831, 73127677, 99123113, 724765120, 671941182, 410466277, 417349613, 361713204, 488413940, 758809788, 810409899, 185489272, 970734562, 313521540, 245315146, 737144408, 391108563, 907655659, 177381120, 418351101, 87953075, 206123025, 596535639, 250034171, 855681349, 467342866, 261630004, 859923581, 50024525, 826619881, 418391686, 345997591, 988420069, 105473816, 62589645, 558828775, 719647968, 629130337, 109201882, 421252253, 613028452, 630833549, 725873419, 632314721, 491876937, 876658597, 419461057, 386158705, 297446356, 503862103, 655852639, 965498146, 923976228, 754626573, 494682905, 898843954, 686406786, 167635410, 236423139, 729154638, 504691365, 960261551, 98418571, 193865033, 175624526, 432305250, 400704260, 625737985, 934029091, 835677162, 551568858, 753984660, 493505892, 874380909, 953453117, 569382676, 696936412, 160476772, 494818142, 487472152, 29630998, 135606328, 875400494, 278814602, 456461507, 382307401, 729304058, 966527349, 947833165, 136448477, 156557075, 196397538, 240873095, 689835897, 178863759, 783832795, 245103035, 93040579, 772538741, 213270407, 673934981, 639178540, 493592145, 468629718, 674559007, 464683924, 627690893, 217476312, 459627876, 814503673, 686199576, 857235082, 448043401, 181637154, 346293237, 994418657, 984137459, 726332281, 247761364, 978273323, 865494300, 917672842, 69941958, 216104441, 413889783, 971287737, 722209236, 181840039, 656552048, 853173528, 423345991, 986830923, 665935135, 127350482, 66302556, 680736473, 126276018, 269341437, 992270865, 736250190, 540563043, 682297769, 255937194, 989721217, 204671764, 612113371, 911281153, 511839224, 793694231, 305098171, 757813010, 697336108, 524098067, 364375814, 291599192, 807152784, 94366511, 737606082, 697949670, 194230622, 606687813, 633197229, 935110119, 613145859, 532048859, 883880876, 372409458, 60987564, 855753217, 744367968, 832419846, 59622005, 783899609, 497843877, 617880397, 403903540, 686487357, 50539587, 988004764, 161837810, 666440447, 242042563, 377899570, 886989760, 929870399, 624918243, 677842746, 132041497, 835639494, 251884449, 550169386, 708525526, 916465605, 832512317, 709345885, 284435651, 368154784, 974272608, 719607964, 925550781, 155856877, 651933758, 711448155, 242319241, 883315027, 468027123, 892563390, 92147669, 606274404, 911243333, 555120181, 32742985, 242550783, 346454172, 346929928, 603520579, 331058136, 501535527, 779324186, 626383133, 179010621, 817826033, 402716486, 554696923, 236619191, 278921870, 779452361, 109287852, 199186619, 175292215, 450642113, 548974564, 250969917, 547621510, 901715078, 796931585, 753582648, 85800934, 975418251, 495603444, 510539119, 727113784, 126730162, 83237648, 987541737, 483162227, 616224367, 772901236, 443208187, 122099225, 356927666, 820158698, 416385766, 311399582, 325140764, 319873117, 956114600, 963236767, 161450969, 762166755, 980969756, 767901876, 990992147, 835906733, 108206914, 22021430, 776903613, 266902868, 221865653, 588408267, 624554942, 179390801, 985718936, 753502992, 664748023, 761637338, 826111598, 594817127, 403430837, 577677656, 624416964, 60891121, 814554950, 961244461, 940541328, 564259884, 566398946, 401718792, 897735064, 610558018, 218836720, 632403250, 311870293, 133368587, 246533847, 360377244, 115474691, 330500694, 985718642, 625551480, 240441890, 947103770, 635043276, 870431806, 130367354, 343231803, 207495573, 557289394, 260759235, 852267286, 135704509, 81173508, 99182474, 195215613, 423000582, 920597624, 975992923, 510627398, 256030214, 94103446, 988985776, 555562116, 616015568, 731712387, 710454343, 156606440, 900409622, 976201911, 104361900, 448154852, 273186309, 579310826, 27340896, 764818310, 20488705, 462406228, 653865425, 818312834, 80304313, 233244692, 21607464, 769487868, 158340002, 229337847, 401439086, 91730997, 240263237, 498061283, 372913682, 374044781, 671972699, 186972594, 408306235, 562351472, 880112348, 990472377, 635471666, 215435701, 960775991, 537287261, 139584569, 390944107, 904406787, 800263495, 8895680, 726211712, 448016388, 333889584, 163873675, 532821617, 174630534, 27246886, 695021913, 845168212, 346178383, 68242307, 663420037, 921107521, 41171673, 225545349, 553665894, 261254410, 461651765, 208252577, 107042483, 171890929, 207178899, 820978157, 330089199, 126650900, 194430489, 645010638, 594603091, 269911620, 28737411, 588714785, 100859050, 95891332, 202081623, 124172794, 449603405, 650142299, 95517178, 428677520, 578919730, 961671094, 213167430, 265803020, 413202029, 520813965, 281752288, 453929719, 122159989, 86200106, 796653325, 851722865, 377553853, 391484004, 20008306, 969969417, 110308429, 923139882, 806496370, 771277337, 974903706, 291933904, 241540790, 32458624, 379823801, 659120265, 643483174, 4944852, 856557697, 688913176, 598173776, 225213861, 151642369, 560405324, 54229939, 546280962, 346679668, 767109581, 169776170, 774158258, 771855608, 638011520, 520315710, 189344266, 948473196, 744645731, 514863902, 330601213, 637852210, 786881263, 418079892, 827151055, 571921393, 305809390, 725003833, 520201266, 720612255, 783123652, 567761917, 164021820, 81385975, 161746849, 293708299, 769283586, 796429170, 816976036, 5775140, 772340937, 652540534, 846862983, 42214918, 637393928, 47248297, 232592911, 267807946, 957825646, 61884298, 143879444, 483077413, 758092892, 956409163, 732131826, 561911229, 191804120, 468129690, 631210514, 366105210, 694038551, 709834817, 579073049, 407785286, 66623727, 34748292, 740943089, 794526870, 272216422, 181816987, 22881532, 688436155, 732109206, 98658720, 596821099, 459132157, 26252120, 441137705, 995786848, 276107011, 531259757, 690849081, 974115399, 934777877, 549314407, 442933001, 225414833, 317631316, 733762705, 268381403, 204002038, 846854697, 846617504, 700203544, 476409282, 512376809, 106801653, 693060332, 72941097, 164755981, 429738206, 971634857, 507482922, 77645189, 67502369, 730622526, 343009639, 571131616, 751282675, 976940959, 442408054, 230669336, 405599190, 101990011, 14211332, 975361338, 800227319, 619322926, 629337768, 576154641, 379756193, 988421215, 600423429, 596245896, 797614550, 694261730, 170756951, 726273200, 318253823, 780533818, 195722794, 304571097, 364913842, 903552751, 496504950, 808491671, 171064584, 674762254, 483802750, 734781432, 477341953, 48722971, 150403874, 452453080, 90649533, 663693932, 611742088, 621308028, 638682783, 498249138, 474108965, 977205207, 620818352, 480364632, 948531396, 390571028, 255944515, 623233094, 895730522, 418795555, 682995262, 40614385, 564902989, 821905649, 593535728, 497992986, 43321427, 65820805, 508482539, 87867533, 213911864, 184563580, 678901277, 977065590, 52195263, 98627381, 393360374, 628942280, 483565843, 124014029, 813439648, 187216391, 593780444, 457361700, 417026274, 84032016, 136200345, 170188764, 819215367, 11405211, 43023771, 209571250, 666374202, 855368310, 501830264, 791797641, 929793257, 847863456, 527418602, 71652798, 275795919, 12906991, 425744300, 758937695, 517547214, 702125494, 101098000, 54239609, 700974229, 669000465, 379623891, 459892641, 171713287, 701206017, 220288099, 777292264, 798032875, 346255540, 998580297, 292581728, 64026849, 153594556, 292882853, 652176359, 199516444, 835097759, 832499449, 481162190, 191798076, 521044532, 389133556, 435857852, 559434344, 685561284, 485310456, 935266880, 832923285, 523797941, 39037806, 815616024, 566644230, 167388722, 842278767, 968864325, 571312815, 230093827, 846632390, 591388618, 943024626, 600097526, 860190183, 270717357, 669694798, 988735124, 17411299, 89549327, 641086538, 456092061, 185938594, 327979217, 747300113, 479058260, 156861079, 73498548, 168799861, 936735465, 668600779, 222869848, 371110147, 166177491, 286564470, 264271415, 181848610, 951352408, 11778067, 302930785, 16415030, 683508369, 880230391, 375448040, 798255156, 146881824, 572561362, 793864223, 908935987, 102646810, 321830427, 267451589, 425820278, 70201156, 71273411, 337185657, 687775170, 603688846, 981482665, 214820511, 800655184, 129605344, 334641698, 156827732, 459917784, 224740528, 883480206, 312806111, 974206597, 332048520, 554124460, 523932859, 440090940, 497261088, 918664683, 270895612, 662323432, 657977051, 685420783, 929898288, 389646222, 222571459, 9606225, 471934716, 640585022, 260462266, 696482184, 629685392, 516897915, 478415980, 318432000, 569126286, 785759850, 281466721, 175210464, 31364752, 432914270, 867378203, 31956005, 501172318, 673267130, 697435538, 556740518, 932946722, 747784347, 729673903, 348068857, 169499782, 858543127, 674467607, 12895210, 159089161, 938165269, 969128207, 539617457, 14302123, 571972171, 531392894, 586374304, 344091734, 642775616, 330811573, 719155021, 815539190, 536926546, 456497821, 526215840, 915974366, 355054243, 436545594, 177412570, 795279154, 268502538, 671439106, 73548829, 125782392, 33192447, 556673871, 192531078, 42143212, 68571599, 574106012, 679519299, 976821728, 662896500, 236065724, 795324456, 256074949, 200628516, 778489208, 42408071, 878986965, 259908662, 108843150, 536645878, 892223497, 25104686, 406834451, 265617859, 655863356, 716794280, 965757501, 181170224, 858691110, 468175542, 562280309, 871884475, 326715108, 960523710, 527094199, 116855448, 963744591, 553436399, 701553627, 201382253, 118200974, 672999069, 612346670, 839851767, 83807990, 751280796, 23563524, 276468484, 934576314, 549211305, 761825340, 481577684, 711279015, 623704507, 978747221, 404409076, 806992231, 403263818, 341560608, 150555650, 904236288, 255222196, 808047449, 806616617, 7087873, 349098502, 165009575, 346438575, 251045878, 249938882, 768019308, 864558315, 574583620, 203760415, 187395482, 635040581, 352142599, 594549664, 914875054, 385889012, 698971176, 943554370, 624545402, 891504344, 946245844, 398201465, 993760394, 737438895, 821166571, 916185790, 650637458, 357212947, 261416824, 177924386, 376975265, 732672085, 344253626, 462488288, 102506159, 519978852, 51779944, 868169466, 871074149, 47739261, 826891809, 124483958, 161501525, 75873342, 190160279, 890114857, 152745915, 291548222, 81080677, 293348550, 121695394, 199677510, 163376024, 261096402, 122946147, 745877817, 144868763, 616835385, 857604419, 146725968, 704056820, 236283912, 439193484, 530573764, 605202410, 766164997, 388431369, 391184358, 26954585, 751860024, 839986598, 709346940, 314170957, 399102667, 641254588, 333227153, 299556713, 364683851, 736525360, 501503364, 259758971, 177082955, 439268655, 279246628, 586075088, 759768908, 161071997, 58569629, 947751459, 968360091, 280740316, 701512203, 226658006, 184111309, 22143038, 172555180, 462707392, 334611976, 520757003, 458038454, 186799533, 772960764, 971511477, 319033556, 946836994, 517925862, 664248087, 605330462, 40400324, 456893554, 41584934, 532827382, 965830690, 985147965, 953082380, 821701106, 918302862, 542953426, 22790682, 587688554, 466655270, 235182448, 541618745, 70519441, 203286183, 91197828, 962825038, 424881366, 858694633, 566823087, 219327021, 242746558, 461415983, 424375546, 40310668, 83359557, 235816754, 225661982, 856527417, 912519612, 530231145, 487326699, 276586691, 755680897, 3857066, 680059035, 799373267, 549407311, 436985269, 27700951, 534444145, 65866987, 270695281, 937137158, 74948966, 377571673, 319808629, 467833625, 682083202, 622072621, 895053315, 476712301, 653853046, 284877966, 787753971, 300484984, 939546917, 527744102, 975247249, 759877165, 837950095, 927051395, 134008188, 74486376, 741814192, 503219867, 250031519, 537439711, 845462024, 288490416, 8676211, 993657065, 194962033, 265634743, 40774401, 16541725, 64869459, 815380446, 969674170, 852699538, 657990131, 778235215, 539225470, 999706375, 492205020, 522172330, 745369084, 707035099, 380100724, 610357854, 783189241, 350899960, 644682037, 452025361, 65583772, 430720463, 412512879, 833421022, 311828991, 996762520, 769408027, 460983706, 9877600, 6744655, 543037853, 623948880, 36087308, 39443160, 192052802, 666000834, 346414931, 539725506, 253887598, 568888953, 870503991, 670108679, 885638533, 788054968, 305416405, 451768046, 123305268, 164999777, 267386647, 601993671, 956971664, 924763918, 90590239, 784240385, 119280600, 601460970, 815223629, 765363625, 600099690, 808656561, 175547202, 596887170, 945485585, 250106484, 968815383, 849490710, 472183078, 331111867, 895090675, 653744342, 560165824, 191154381, 285384052, 154000277, 59234350, 196306371, 584412741, 865907751, 659324958, 278635861, 902395685, 896061746, 820152496, 735676511, 823590218, 783455284, 726963222, 264238832, 234642039, 553733166, 934003466, 996874021, 701089705, 64518123, 311906857, 966193976, 183027545, 123178790, 376584078, 566768296, 110559825, 113225090, 294744658, 552479347, 50430503, 505970450, 902943670, 569024286, 924716818, 926294184, 521536010, 753329880, 365433909, 573032704, 631040776, 920620340, 129803188, 316673594, 991931916, 298275228, 861571353, 908061327, 905927623, 660303795, 264357542, 627994033, 387320686, 644853917, 59716024, 358997283, 646399246, 906992587, 958804642, 438802342, 402960731, 333215374, 499112242, 703144273, 84272422, 64279765, 834911839, 65884340, 828838070, 169971490, 812045020, 450031527, 768257878, 879666513, 351759276, 993244164, 102044417, 747060416, 998157798, 379776890, 130786058, 673668674, 901861190, 19661974, 209966186, 959519713, 784405710, 514749493, 845228835, 813249156, 627963045, 803781032, 408988559, 244063654, 113017032, 349551196, 886102365, 794111053, 257951391, 178797380, 598688206, 879276586, 24751076, 297479872, 283270622, 334225042, 218845081, 253605645, 94299670, 254484595, 661047011, 393203519, 723926514, 508231472, 586246039, 412893418, 550176180, 546046282, 117252519, 542244402, 333429535, 298359336, 922399879, 95121038, 605628108, 437716142, 364320915, 649356341, 509263547, 908838012, 534123262, 586456912, 171487373, 327937119, 95443280, 108950052, 751263299, 204560740, 942985312, 720842742, 164618259, 268436560, 418323862, 138097014, 336923533, 523102144, 191583605, 610219873, 907022101, 832105517, 866041233, 53462664, 588285270, 884886305, 261788837, 487070391, 326166270, 679854079, 527711497, 705422764, 123087942, 628944978, 203751044, 220054470, 45154028, 184029547, 886890351, 870603640, 270508898, 747521893, 814920149, 699644954, 972356759, 429635179, 418242937, 323092032, 436040887, 283357846, 380304967, 16214890, 237552788, 388132406, 891897266, 54128994, 647660653, 843456082, 984419693, 100043178, 283893990, 33756145, 627711187, 267399634, 976676715, 691458827, 985264394, 324662512, 687530586, 949658183, 766189733, 694306043, 755447547, 248187956, 977574514, 523026187, 475540919, 426571973, 764213911, 385467764, 364244654, 240664322, 522213575, 912765460, 600905238, 152723868, 590595602, 734474005, 996163141, 746805230, 532573161, 489109845, 347127663, 598166782, 769902465, 198840919, 481068029, 234542067, 920387094, 864255459, 828274079, 442870841, 141858880, 603882557, 77558380, 836789423, 624316351, 488838321, 279205715, 820672542, 449804961, 420333953, 691432914, 35053409, 102941324, 119043311, 185083685, 819293739, 713697593, 455988577, 4876281, 892906703, 457239572, 315998819, 783011132, 160821517, 629171711, 698477467, 337687049, 605192005, 77382360, 703527730, 277297745, 359038982, 914104139, 658154920, 492081770, 484307255, 302796981, 148478604, 775169310, 667303975, 959313300, 917701187, 148562083, 210352090, 626217599, 945015883, 710543134, 939074431, 325523457, 577183555, 942560225, 75730080, 711523446, 635633438, 168105511, 296971077, 687848331, 687748475, 352037246, 500478179, 775367279, 132184556, 173786431, 759800814, 408107070, 81341598, 669657930, 906479453, 901376421, 552978852, 647117144, 566214490, 320069188, 807215899, 781786813, 333305064, 974376278, 531383147, 381730159, 312995539, 592831843, 10072067, 695328369, 252402332, 639597500, 255165229, 797715658, 860976404, 386654985, 541467068, 912052151, 582076002, 671600109, 156645909, 199947497, 889515222, 508593627, 946077164, 369159304, 175092532, 172696022, 732310443, 170150250, 315017783, 988034364, 157839988, 801945276, 471314692, 620907268, 702054206, 856046470, 771424946, 979309613, 964631592, 992054302, 548709587, 881764633, 863068128, 435882412, 1852416, 164315172, 491957896, 788044514, 397498534, 680762352, 998744468, 822436132, 384826046, 5620569, 34353125, 153710568, 273875542, 135854696, 138966699, 445243932, 770762567, 166956041, 383440391, 59318132, 100353506, 923414871, 107618212, 523517719, 129748702, 717413290, 943278873, 168609636, 462437596, 93981904, 879689929, 623522731, 332674062, 107675078, 503350170, 420408437, 893046047, 617748031, 944003971, 668201338, 423982176, 252739019, 662555634, 211361393, 122831564, 794467997, 214752295, 659709420, 960772852, 501467766, 327316822, 431438403, 965273976, 576217216, 658267775, 665204375, 916332754, 742581083, 927306345, 327174909, 860088976, 476965288, 193653543, 23309650, 573830297, 90073358, 108106868, 25377088, 235735456, 216826611, 435424617, 814991996, 179543498, 15435028, 339627225, 688392641, 912712244, 736306177, 223813763, 937230393, 26193197, 800435677, 867683901, 476586230, 538712972, 251539801, 938588868, 749278949, 791831595, 565931546, 109341789, 480122053, 29134873, 394584186, 1445730, 297599239, 481011379, 50707396, 257574066, 117677697, 701293097, 906643824, 363523421, 364693331, 585241267, 104847617, 971640559, 466530289, 348834459, 892915326, 959568463, 962484035, 704810871, 879791457, 92065218, 91197459, 611322879, 173906089, 590907422, 491780867, 657742467, 275766352, 714829459, 246021763, 861380600, 185273487, 627757424, 991169442, 896747186, 874989408, 940128179, 107130827, 529364463, 886339571, 323612597, 669351565, 244667631, 711147423, 888069489, 810386388, 444037122, 810529196, 543606489, 167594281, 451785312, 70000250, 739382085, 596913228, 423665291, 866716583, 720126987, 252224767, 142518073, 977550432, 555799186, 91058852, 760572969, 161357030, 891828770, 6655443, 617438839, 484235838, 269142134, 833874929, 356527967, 776231571, 529819431, 884326244, 312485764, 838344573, 687999567, 836696831, 313829265, 110326339, 974925648, 956255573, 606864754, 372043752, 616354889, 448435351, 775272927, 692964231, 43516237, 325250388, 224477996, 475063511, 831884709, 70743865, 541543006, 292358299, 535266294, 659948340, 664627898, 53142386, 739801719, 606460217, 961914158, 191332276, 387203008, 397750259, 111833269, 243962527, 267060047, 319306591, 61608294, 563840708, 172989520, 7242417, 807143916, 125643393, 329733974, 786095262, 242481676, 563003378, 429453132, 222062050, 606204872, 212313453, 258875124, 160531296, 914535210, 988984797, 94142069, 597477091, 611761601, 578340510, 699397635, 534275242, 54276460, 551769811, 127590179, 852779743, 89243852, 960069743, 211319213, 460559998, 801426476, 325283407, 655340436, 825558121, 801876872, 930874439, 113375210, 905649598, 939602777, 612403731, 871979248, 755677349, 686174232, 791205623, 143599087, 787647267, 80733356, 899007344, 691152908, 214509185, 43803905, 810455755, 501567843, 897430196, 702502492, 349459595, 361298264, 795559208, 479416249, 446186735, 114998754, 798770877, 858526750, 853310892, 78547174, 641895942, 718663621, 872265761, 186882876, 326071555, 384473149, 882649147, 269862764, 194661254, 12757321, 626628351, 196432143, 479915780, 520252438, 246026292, 685544659, 294032334, 541607500, 880068714, 509320717, 681134976, 968008730, 33223756, 299981609, 701975447, 541705987, 797641114, 298944689, 727233460, 825740998, 749508682, 509643038, 208136873, 237300739, 371232536, 582688389, 575099407, 50754795, 663731682, 455945420, 393675836, 103182220, 967249877, 144741488, 242423436, 535324498, 629630384, 775572129, 524024243, 852144918, 695825377, 774986085, 974591567, 756165631, 258025996, 728557475, 136682845, 177858719, 260070327, 879295966, 503164547, 321018696, 659941725, 939691702, 278337218, 144780641, 962952600, 401992382, 307922801, 997651806, 70399502, 777332975, 407915225, 102836027, 251508777, 448496919, 382121097, 857641836, 179210187, 598077591, 979421303, 636311752, 258492197, 676574743, 712759359, 507091924, 441376310, 125497789, 550221479, 641226386, 448843600, 712092621, 779041174, 88389270, 881279749, 667616233, 917141349, 510061687, 314036313, 16586647, 415096765, 618916212, 209668628, 175802687, 457052152, 267936141, 789441161, 548049068, 545407340, 366721025, 173931187, 827021172, 634024038, 17692917, 667908623, 932881476, 662595357, 977537435, 836086199, 174067021, 275937452, 811282001, 118350161, 5322931, 958641017, 529732382, 128236388, 745220834, 325690647, 55958690, 97203653, 752041532, 622217053, 629900069, 950751916, 733723303, 956513129, 7907868, 541438757, 799296966, 986944809, 633859812, 494304765, 16554912, 679897361, 83316573, 17866320, 375358794, 336122645, 344179367, 478404039, 177672946, 558771145, 559577, 194874303, 340443655, 784337535, 421609301, 635755654, 379194589, 564788253, 919090518, 978893303, 417393740, 70419061, 672502643, 341858533, 554021501, 992479350, 199925032, 927009488, 440503682, 548852319, 897823599, 185157257, 796752211, 410108291, 175314778, 227928428, 558091605, 231408686, 314834951, 215832948, 475339558, 202673651, 405405586, 970798565, 559823603, 145576384, 183694740, 137643450, 638857338, 444682747, 441925413, 849856713, 840483936, 772921804, 439097456, 673541786, 652081022, 278141875, 606795047, 618201514, 234463000, 743306438, 559558853, 449499604, 653682753, 981015357, 532038782, 401022134, 436293158, 711373005, 510549040, 278746421, 165598794, 404706834, 80300914, 666319320, 498938346, 839459094, 858091942, 375510425, 58819998, 453646864, 512266131, 745576673, 738582559, 501819774, 609815977, 269248967, 723257163, 345316929, 533190455, 879156363, 871275594, 286580132, 226389380, 618211375, 50444353, 37008864, 497196712, 431927953, 287007658, 944926923, 398002342, 427745904, 897880282, 413228618, 69843500, 567839008, 25644904, 103004312, 692678476, 524557032, 560078779, 379815034, 991039148, 52059168, 393851503, 632372225, 206461319, 482639593, 664459007, 130411793, 794030187, 568381968, 903836573, 932333026, 402480283, 994983515, 930359407, 953290276, 478586455, 732264931, 481179807, 978630828, 408059644, 214974704, 747156890, 251227236, 38112193, 875772566, 43515470, 171801081, 446328520, 808474317, 718866866, 953870522, 661848417, 352244885, 947207427, 951214004, 538418310, 877025821, 559721137, 7228886, 684355936, 554703179, 901703587, 858465562, 256617271, 423635916, 454654210, 612217753, 892325828, 20559458, 302611046, 967805483, 961960960, 201567358, 242614457, 633248399, 379094921, 868977326, 708422348, 947869623, 672604054, 6446828, 88179527, 805388645, 677329900, 15651987, 648852228, 473229600, 783528682, 781290557, 690864122, 213567855, 717488052, 103662961, 860370530, 538237342, 345883821, 946084249, 723653106, 529065226, 551129738, 312797108, 518805624, 270225998, 34871024, 764011692, 948868441, 527132448, 473590338, 788366745, 884189515, 470861997, 220783209, 691421209, 59297726, 590599480, 994456381, 491168179, 517597160, 102725064, 83887658, 419889115, 730365644, 939355348, 554712596, 338704774, 805775136, 208963416, 450831248, 176925848, 300172088, 123407976, 983391596, 451300119, 71853921, 518828896, 62581166, 128081308, 989590415, 824614220, 412680904, 61377677, 524654150, 975331274, 486554354, 216911344, 348726246, 186506810, 747667201, 410153134, 901629515, 325508620, 308367977, 517868643, 73118853, 241744146, 379501625, 683379902, 117047358, 956184967, 717179501, 698554976, 169791067, 550332291, 331181916, 107759440, 982980276, 263149790, 586637722, 44119416, 461532420, 419061755, 711202727, 185056643, 599737747, 158683327, 758769154, 305004553, 595050187, 654417844, 81745168, 52727236, 981432108, 894187381, 455900713, 239558999, 177024491, 972782403, 692129605, 413343028, 719188459, 672063039, 724958193, 562562640, 556841811, 793129625, 363407536, 234635191, 324192313, 509423090, 367103293, 917475156, 16455836, 129223589, 407005545, 535910401, 40448684, 935403525, 629899030, 361726731, 678614049, 864371951, 528031093, 377494023, 171770081, 205014221, 596125236, 604814963, 43595962, 628379630, 862301476, 801188185, 507499080, 287994922, 632303504, 722196062, 873160048, 669354230, 11647510, 825426713, 682270082, 309409546, 144278710, 724142323, 835264214, 32402806, 371829099, 337915296, 240303033, 210389152, 968003680, 754739543, 621731936, 456985803, 9317204, 87755611, 110863501, 636503295, 358003208, 826308307, 844101178, 418134666, 306514828, 768088082, 745381186, 486807537, 431999794, 487169055, 786509654, 513986228, 133981400, 526772372, 486204303, 302109835, 813305258, 401356178, 57300504, 204221663, 950247615, 103973026, 25009885, 148691899, 627004598, 397519712, 840122292, 591760747, 188869017, 165051914, 487977904, 202753296, 524582812, 29855096, 237424047, 15012675, 312309348, 171069733, 622196327, 444567184, 668742741, 372267088, 696017488, 732756648, 816076129, 153908772, 890981861, 907866277, 194504781, 11740086, 60274378, 904106198, 202131772, 175066337, 991388360, 584317066, 963179613, 398430259, 353092873, 541909489, 401147621, 347518268, 535681605, 662066595, 672934042, 768581862, 200944880, 330738237, 761962514, 922740785, 765710842, 283582997, 149652225, 511514663, 315986010, 602501717, 414461739, 322233480, 839211546, 902709117, 579969092, 959629362, 882900643, 96247250, 302690537, 146278538, 286869891, 31829485, 875397916, 348447783, 829790434, 127727527, 41213231, 798416246, 264968258, 902223912, 628801250, 858811373, 757739461, 285810012, 368205443, 539974414, 483391630, 281754463, 935601390, 541043992, 884330520, 133731753, 936152308, 822079165, 749982410, 465350972, 25453918, 400760525, 999461851, 218482853, 60120526, 347296180, 295141487, 299465626, 385711015, 210669745, 2406984, 581461398, 316736126, 185508777, 785946804, 44382874, 364153762, 119932291, 449531271, 950812167, 640221454, 154498907, 411199600, 125170517, 958399459, 38852681, 430498337, 159357346, 553272429, 190270430, 506372995, 322647766, 24493640, 864967126, 557140536, 735242101, 233206806, 562604940, 609917295, 767982524, 175131199, 204017970, 228656675, 5968437, 790676845, 907371286, 376778287, 22503101, 941845307, 724046408, 432318378, 902864102, 837498007, 181608220, 835583359, 330665622, 28135972, 203681453, 188635450, 450526496, 975637366, 795804730, 595055172, 54788111, 376449267, 608718002, 92100690, 474937331, 72663143, 486087457, 254965026, 90601139, 540827028, 942456318, 516309593, 796203920, 813463719, 949107317, 196189261, 754736756, 21704855, 467075695, 509723251, 48553248, 195898949, 393846852, 630074826, 457640585, 779059529, 286912159, 174034155, 626514365, 417483310, 620994945, 645738224, 934700234, 53161576, 756906045, 960164109, 350152456, 995389655, 148735919, 345018851, 892339102, 282752334, 20109577, 844674620, 508695186, 355785954, 817728608, 610887938, 273019979, 327299331, 486225843, 701034576, 117324744, 372504065, 784051834, 49237352, 559975004, 517642902, 662451758, 315568959, 375088931, 72862305, 617918049, 315003345, 961432878, 622346229, 322532032, 627716689, 944159676, 592476203, 105363703, 306813613, 146035413, 654687315, 553803987, 508951543, 93643531, 610790152, 533072128, 519374868, 564851180, 383209221, 387801705, 231135326, 239174494, 656868544, 618739913, 747048269, 137378469, 291642319, 578122856, 345644903, 215303674, 633574869, 627455956, 101615137, 951459439, 858693982, 149047132, 585831876, 560873857, 675480432, 307727646, 988865255, 823044506, 414528567, 117505124, 750005946, 43758862, 619597098, 596284793, 50922465, 5016994, 980230395, 257499346, 32752845, 575268590, 59610119, 858348210, 360778691, 315087567, 562374336, 940801329, 130494738, 391568964, 949938361, 60563185, 764092671, 301283620, 720388956, 922180542, 5258144, 879056921, 864766825, 595574996, 993643527, 398279558, 91422758, 839461445, 507638893, 137552906, 38755041, 970621522, 398205125, 963346512, 292727734, 553999911, 247007502, 205107784, 960423102, 878302529, 805647546, 861820533, 29267418, 52875423, 957082154, 625136026, 230570210, 993549439, 941894834, 391629385, 895675980, 907738630, 891279331, 32434058, 247120356, 342420306, 51555521, 11692720, 371674013, 499468091, 237603582, 117802813, 830740863, 361224987, 172866755, 240390964, 663787922, 983257894, 827053225, 487398720, 527138164, 432837246, 131674771, 288879602, 923139386, 28041449, 312561358, 156906511, 272233322, 496632542, 916557813, 8349736, 628027020, 691561357, 585798449, 801549714, 915072552, 11912336, 992790565, 865703833, 830466290, 303330678, 881549796, 663354181, 48136280, 189276270, 591708726, 160875661, 876328276, 121224716, 538139109, 205726075, 152531397, 181543049, 604279424, 764405271, 223953415, 933045311, 562468955, 491417175, 422564755, 735592695, 643523627, 444012677, 420818224, 595191168, 521966112, 764586243, 830044124, 826661557, 669660053, 379316438, 256963316, 649261511, 862369214, 457851475, 762160804, 271773378, 646445289, 690099114, 363543151, 750620967, 354424578, 959015548, 168198264, 231724811, 999744020, 860055474, 77484536, 255259854, 76634582, 542112930, 351483049, 646603152, 814819977, 913435179, 915633398, 824602273, 99803957, 554319045, 77731927, 602053829, 259660713, 160866581, 255203539, 397169253, 859240739, 743925202, 556686610, 579271172, 414291464, 789548271, 22903334, 32321354, 962704255, 366218841, 925026268, 422797733, 234295107, 962264354, 801213261, 64060182, 904123601, 287857393, 397688485, 950812461, 401975829, 813030457, 591481434, 30398683, 257786959, 414466754, 288894077, 475674607, 771923640, 28414914, 896576196, 371958462, 756184522, 389310446, 814912651, 486525117, 51254943, 271551672, 532571204, 778303114, 259629248, 839258362, 506814498, 80175775, 299354503, 248144371, 107897492, 307485281, 536151419, 992783967, 119536128, 618772961, 573735382, 68376771, 929009955, 190198078, 406664648, 120958616, 930411300, 12825062, 799929704, 98803792, 668210754, 281800740, 350543835, 936421194, 780171618, 336642298, 256184150, 657044450, 773136581, 965444327, 64462146, 781634791, 774658068, 456072767, 127274676, 724416560, 321422816, 610113746, 56306914, 620009733, 749358889, 254355898, 264518737, 640805670, 76008684, 456012169, 855039523, 442214833, 538520294, 156298306, 279565961, 967876927, 32674137, 529176814, 204029607, 975609975, 896954772, 818089070, 335820263, 702295037, 502900714, 265050843, 530310505, 664159700, 495208196, 133522091, 167128728, 951711767, 278564631, 71253052, 41028593, 956391277, 905302486, 929532217, 434574728, 91171336, 713326744, 371506685, 58076832, 325881827, 539146852, 631525415, 398082841, 769095414, 719769996, 809861637, 611054037, 57613323, 261245203, 540649686, 236733429, 513086343, 806717299, 840775644, 575476850, 601943811, 896680266, 99017412, 578641053, 829169515, 847015214, 55908740, 376583650, 980542689, 181390577, 859986197, 603750545, 820690187, 112672210, 59493889, 575559677, 518009530, 549255776, 474524751, 963692666, 711136996, 795026360, 457209894, 77326721, 369703366, 506061066, 815841084, 566363680, 865130317, 148079996, 124881135, 870399768, 401930936, 848114597, 732807637, 17927393, 257996806, 264398390, 511061802, 201163752, 371791751, 651054853, 77410948, 259732365, 978756730, 190138255, 193081586, 309095450, 662205784, 615528682, 531271872, 5483725, 476634902, 511194148, 268097839, 736144998, 164214560, 562677792, 744956597, 95504510, 856417102, 887353596, 720262100, 7101052, 931410837, 689192376, 873118600, 289035009, 572369519, 573196592, 502578508, 735678857, 180278090, 292857590, 460098863, 284382440, 252357516, 705435254, 162847964, 78993972, 77126617, 461958120, 519900658, 639592151, 277380959, 527664356, 37969883, 610384187, 413777241, 939805343, 180042752, 181122547, 998775649, 254741866, 676201257, 767889369, 705955164, 226095289, 90322618, 695258205, 644011525, 59712963, 113469249, 606590453, 501458370, 963041882, 271876898, 378416906, 921264282, 282573482, 827427078, 73439649, 701127856, 874855383, 590961220, 149075962, 108630392, 608641256, 980325616, 704314176, 425246883, 939090032, 168376682, 597197365, 178991549, 628886170, 343596401, 126337709, 7554571, 112589084, 359007918, 246062491, 862866068, 114089506, 35421084, 595876665, 924477932, 214871049, 255342658, 39999061, 814415810, 295511812, 265017874, 725436780, 427021105, 139580018, 483380461, 81139115, 549073676, 382012034, 921445713, 661407367, 902102304, 591976665, 362790181, 179734096, 121300279, 966108470, 841593118, 153523298, 976621106, 693716854, 276118911, 526954575, 347892488, 134651309, 20416077, 437878487, 785804111, 756146831, 124836582, 96705858, 494595338, 194702129, 775107815, 226316839, 215730521, 664039810, 861353363, 183041380, 912173215, 34879296, 892273486, 282400367, 517723204, 42605110, 276057963, 548542528, 374633107, 978742692, 195514101, 330197273, 573749270, 125368457, 396715888, 725550057, 736915551, 994267569, 483756828, 477596342, 479444396, 40486610, 292056139, 721502610, 517608918, 682820634, 471078031, 631036730, 840823854, 352702906, 59526453, 14545521, 302520091, 174521734, 452009463, 977065192, 743564918, 499026713, 460275772, 972286054, 603679568, 736793751, 489242143, 307450185, 955919945, 320139247, 908186758, 404584874, 522759903, 248479111, 793561280, 143893372, 594433061, 946316841, 253289561, 736846032, 442935635, 62058915, 498949640, 127907058, 697112436, 809093559, 497834387, 984408426, 600948562, 192023813, 202233679, 192921193, 406215458, 480617311, 455073941, 45605782, 780842075, 164715106, 841010608, 861443493, 316857479, 366216857, 809527122, 11470977, 730411431, 970280338, 266301363, 263241352, 873537252, 6077464, 983727980, 521156667, 231978387, 105692871, 706180450, 695777432, 189319175, 861750585, 16352268, 497474279, 258577967, 578037511, 710213063, 205769460, 334414012, 255845719, 918882547, 816769047, 709325505, 797952467, 533798067, 731811428, 255935108, 249723484, 793757932, 677682358, 358832579, 274966374, 94727662, 382865002, 69803861, 666826737, 54272767, 537198865, 233173019, 595428530, 592013288, 226278179, 581275474, 746732190, 781592446, 817827649, 368060376, 650567824, 847504534, 51738770, 94597894, 637981032, 694493056, 422959088, 460599721, 157215362, 672275103, 983928719, 943706205, 69591292, 952986554, 372214911, 911774341, 995092635, 117802691, 141725951, 891298644, 234637300, 926751332, 414698587, 843349266, 382262656, 866782419, 55889861, 517910798, 941426939, 203009710, 456957282, 251244144, 784114946, 247350462, 128720747, 679408113, 755255895, 644340526, 560691636, 89584655, 33871593, 973209354, 835296607, 642305236, 425250749, 954190097, 33952287, 471328863, 702950817, 107855375, 890293587, 639385460, 333957130, 771289246, 471681815, 533086663, 119987395, 683817348, 219217039, 748668964, 995212213, 208403339, 156855171, 576549959, 238744229, 920795341, 351159002, 813739772, 985078560, 438343227, 603562276, 934070811, 420400527, 774930695, 758798996, 851545351, 48928959, 997376116, 606403486, 256516825, 68850457, 354788115, 471515700, 426292710, 884616058, 119917684, 784698588, 301726768, 349335280, 398638442, 655375503, 903944328, 669734964, 250037089, 911777200, 639332410, 551410025, 791667505, 603998633, 78239619, 209128864, 655831219, 5043918, 304957607, 550534882, 576670288, 888484262, 799119897, 210937734, 160027237, 223239315, 508435028, 771802922, 401115999, 328444905, 437817055, 560049792, 461768353, 451492661, 379788286, 811216722, 670740185, 279005274, 80182467, 627159416, 859393261, 424865080, 652014790, 93659125, 149769258, 356105623, 548495026, 814155731, 760595503, 111058190, 110655435, 607424794, 460530526, 887888937, 120172909, 419419781, 135671669, 975010152, 168875433, 492806129, 377242073, 740309765, 804749648, 207632229, 389707995, 532845444, 277803518, 176432029, 49836901, 698787384, 747108481, 895496364, 304798001, 134586559, 274990157, 479681769, 632605384, 258587637, 973626290, 124429481, 893130965, 454248526, 284590651, 571581398, 824288374, 410763591, 828535513, 202505648, 727415352, 169719909, 227253972, 501754114, 987357642, 477823866, 468272496, 518544315, 410954317, 47537949, 533792240, 436697554, 818805982, 453136928, 598579543, 494105029, 600796109, 972457429, 293862581, 747560030, 888382886, 458566653, 258874668, 456627482, 375014693, 324096660, 633836940, 440434490, 868729782, 302243493, 139908389, 576203677, 647551244, 522393231, 895388027, 345256188, 23417286, 489928795, 817085884, 746545209, 654329433, 770638836, 808020201, 927038168, 215487305, 579717611, 607039030, 575417823, 227622358, 303900789, 769375927, 971496213, 289770230, 436033357, 518817680, 509825334, 651660491, 728373804, 666374795, 393888885, 872659877, 974071296, 691766445, 575175949, 429804200, 232455844, 801897623, 117256747, 842636587, 175690347, 557679644, 189052079, 552962276, 524062649, 97889546, 902449314, 301032276, 486948332, 90955054, 869183447, 788815559, 730854370, 400592285, 216540251, 709043204, 930072590, 156780989, 29576710, 230575816, 146602223, 364797828, 814884376, 797309327, 237629030, 293477716, 360775756, 63665792, 873142416, 389826062, 960679113, 256301651, 508840116, 708479237, 273061405, 771145108, 159355675, 499448954, 243573910, 607861145, 645973778, 231783828, 141515968, 776087307, 266841542, 300112388, 814061483, 813729892, 383286466, 769370420, 377014219, 260208484, 957069003, 766118946, 991633449, 680644149, 782789191, 652053257, 296783991, 234416091, 809458434, 711416567, 85425245, 483271535, 978388468, 714571462, 760554747, 805069905, 5606514, 89244345, 82346900, 637028448, 722314143, 982816547, 99803234, 44622874, 194500949, 928970600, 293292358, 550093273, 250007047, 928237002, 756671694, 534300462, 32646962, 838939734, 712556580, 613508750, 94874004, 487271893, 990167259, 102121266, 826956466, 472115392, 227764930, 59550664, 374949125, 141692069, 906150732, 36267737, 835630387, 285807370, 835300667, 827126375, 173469168, 307528119, 113234152, 800552292, 942300485, 56669459, 591643316, 531187705, 805442367, 844302203, 224892316, 349930384, 775314954, 454643684, 608521508, 778942650, 776476991, 938214193, 744290280, 604862014, 547109464, 898406584, 393518465, 995087164, 663268465, 262112309, 363754020, 477473771, 398464182, 720396620, 851560091, 271692803, 573013419, 470149433, 680655532, 104818721, 164364568, 573771236, 897132771, 748505643, 368798699, 377892031, 567130, 55859335, 692738346, 584314050, 876595508, 108783381, 387271084, 982932212, 892641066, 201987154, 397295112, 753755474, 305483726, 364343177, 545186164, 548266634, 976890532, 962690011, 118804492, 448126614, 944830570, 56547954, 337604248, 956231830, 660089070, 384869801, 477971664, 95318411, 164393552, 869821784, 925108665, 359903576, 4849009, 754045892, 227184540, 836495952, 805809058, 4679196, 464770701, 730079138, 895019447, 81199570, 244273753, 83659996, 840433872, 314829498, 169279104, 395576775, 989592780, 687782566, 520648062, 268744013, 46448012, 931745978, 90221225, 525028094, 774970259, 843835828, 693364703, 820224577, 596913921, 522466403, 439020277, 180925344, 626438788, 863946873, 84505559, 358539491, 267999778, 450362962, 237317920, 546261134, 645033897, 388325504, 34205937, 810267591, 798891251, 778468690, 715785097, 888035575, 914325868, 427653155, 780911249, 637458334, 293346522, 930873792, 679875871, 275977736, 629010489, 368049440, 495598221, 122370223, 358307834, 112971499, 643379955, 50679170, 116665544, 661946540, 50229316, 573484163, 415394339, 336993480, 365511242, 16035553, 718892172, 488897489, 109822658, 545258157, 147854984, 178387432, 930568030, 159055667, 253487834, 750616009, 757846358, 257208663, 934419161, 689767548, 483186660, 722185861, 585310325, 126315604, 2583880, 359631844, 186682051, 718202108, 980012495, 766486654, 387306634, 911209278, 735544321, 320820227, 208071328, 704275644, 398507040, 40411739, 263186021, 946349834, 330641455, 290916211, 689824446, 754870696, 341722598, 146037384, 546654725, 366997915, 502349425, 568407446, 284980915, 143880057, 934685262, 705491185, 141487753, 321186801, 266271454, 185181335, 857189647, 560755103, 127699290, 238950430, 952635620, 968198655, 302041780, 291592258, 64530486, 576218945, 449676918, 137280061, 657165710, 662865107, 637538543, 459906301, 759821104, 315543270, 587318215, 333820907, 713500128, 910901919, 449244971, 293674973, 705383583, 265175961, 36118566, 199134601, 422561856, 660621343, 718166710, 860952834, 868949805, 491702025, 621053336, 584301808, 315615171, 111695361, 344729624, 314257027, 141652065, 18646987, 912206868, 967684290, 297802971, 17181104, 68474486, 580122736, 5969378, 521906999, 677061894, 421987951, 903303563, 137235517, 165624820, 464948645, 166895181, 943939806, 834673676, 948286049, 17758899, 532942141, 312576708, 508548860, 991803699, 606036366, 862857769, 142758377, 646305224, 296620679, 9500210, 622921512, 758453611, 965289795, 834533157, 361979435, 542251335, 630634504, 890822267, 165983170, 583346324, 855938726, 733250840, 753983179, 488741817, 593290547, 825117013, 593738708, 517456207, 146427374, 728712280, 863558124, 352348641, 385656737, 551001005, 438611489, 922188678, 123121348, 282342986, 342538182, 215668537, 101223111, 945671168, 164490157, 737381402, 251465805, 624666322, 964714615, 362587115, 585722448, 789016579, 916401902, 184415571, 42043198, 400959678, 190056902, 515590997, 714641854, 863817663, 137922231, 644552466, 427273246, 75534268, 655846160, 622726664, 972001775, 226570986, 264525915, 787612814, 182478617, 438748550, 516735491, 879927395, 788557710, 804793328, 45798591, 267188480, 294993046, 708936586, 891149355, 780225822, 366454319, 645568883, 481469336, 742061754, 759101867, 353758339, 960252966, 52443770, 652418954, 461299219, 339018950, 498385635, 660473693, 375019357, 517510871, 577584317, 321504794, 821546748, 222442344, 322733018, 541437927, 997940056, 190125245, 994650878, 183480572, 252822170, 212988660, 659723836, 660076136, 563708746, 716546319, 560616528, 552352722, 293873851, 872432692, 859324936, 377847974, 931864878, 607892107, 176540761, 452427134, 51293411, 508209391, 98668425, 83779691, 317840737, 708736647, 982351450, 610395582, 917950956, 769592638, 485224719, 226449750, 227559115, 509630142, 961868940, 694963042, 720780348, 480890342, 630699963, 210700043, 428792767, 194280778, 562631381, 913921988, 173082321, 926120386, 29632022, 635579872, 52068516, 54965636, 182816115, 541031348, 525016971, 102128987, 148062078, 123179108, 473539399, 27869688, 855085227, 479247596, 734783130, 737145052, 210784858, 904167620, 412422412, 106903888, 345246844, 976783385, 900389199, 859028698, 961420601, 854734922, 859690130, 772586926, 69001700, 30639881, 653668664, 657206039, 44443131, 741944224, 921055394, 112715683, 834456051, 657287390, 1030658, 391822988, 505533534, 327761673, 989395665, 816649256, 296678881, 614965122, 455946144, 523614012, 449460252, 104496629, 348140360, 283946882, 736151536, 466554474, 368246523, 587883870, 136153616, 797453832, 319435921, 596073109, 989242815, 919164101, 775163847, 383667661, 381073960, 370477531, 287393946, 370492750, 559398844, 339245000, 858643741, 497028477, 64836380, 279140607, 47796429, 504027632, 990135795, 621238694, 850632490, 937715798, 838669212, 767588179, 95325395, 570296361, 811002509, 178258960, 259017281, 725171311, 422049758, 848676516, 514078262, 606801302, 595768936, 609926199, 615626472, 587892303, 456765476, 115902432, 843189920, 552435087, 13990796, 199540635, 92207234, 569923587, 132524807, 327829504, 356239049, 969722812, 626877747, 500975107, 816065654, 364273931, 546770134, 942002419, 330951136, 605083591, 657612912, 734665795, 204218708, 245721612, 287327962, 535510252, 530058540, 166694063, 735748306, 816830816, 524906400, 334980804, 550643022, 41789410, 702410642, 48230091, 954255156, 465149796, 167643298, 52438898, 190867379, 410780391, 731599185, 4090987, 560010343, 90027553, 743166011, 574749040, 34055007, 470931080, 622407903, 640747350, 993308285, 887609471, 599434895, 973691677, 394642226, 48590054, 865284653, 774751435, 440313776, 574652083, 108370211, 398026364, 724495658, 469573485, 799251033, 505507372, 156655341, 892118705, 57668409, 420791399, 131473314, 946664708, 240247861, 816019097, 353183837, 821950715, 288132308, 71470263, 947224665, 512004800, 209325625, 732840130, 897771831, 750002142, 800261464, 66155885, 218811119, 742841669, 957339326, 44007707, 996528305, 820915345, 737741325, 137834248, 733127788, 808904015, 442408401, 362150040, 278050636, 607110708, 339149538, 309745923, 348145844, 893260856, 986886650, 301631738, 460686593, 361080017, 449552964, 882513151, 455196565, 661645634, 756748966, 290731437, 514858960, 300104694, 323475811, 553196688, 584041730, 193205293, 965926351, 814857170, 699872286, 437647557, 402690916, 694086813, 107793168, 895173665, 433048522, 474078035, 973636183, 229390083, 492427246, 590684709, 483698619, 2940872, 959885270, 566203366, 330891852, 637761937, 883882686, 486972064, 81865364, 568491113, 925870821, 87567649, 454589664, 154114431, 73040788, 180454152, 927251905, 897183620, 834516102, 220089923, 766477533, 369094913, 548405457, 953417908, 506514986, 322681457, 290704619, 284344000, 616508682, 392277935, 125020264, 371732499, 386665706, 486053502, 513920805, 739873022, 949758922, 727035544, 103583570, 781045231, 153547052, 848798218, 672111278, 646637583, 71495993, 715327297, 994571871, 271547140, 469756028, 913229707, 966210041, 424682353, 678531305, 700147971, 757377165, 218249312, 44967346, 216718328, 616834613, 181268831, 694039728, 520468977, 78929261, 853274255, 768767094, 454187051, 986193840, 32884857, 980076344, 115443135, 487807666, 812450272, 565501521, 605597612, 751533555, 137399182, 244259858, 435047161, 10334748, 587368167, 92590756, 529758255, 140794966, 581810281, 86799375, 942139969, 913997089, 38282758, 598810991, 601484062, 456250421, 568408096, 67309113, 338233663, 855831951, 351425551, 217983886, 835249893, 668740987, 437989023, 503911336, 24796162, 885742192, 79565977, 332874901, 825458177, 843138969, 864621720, 249434941, 405504075, 641360433, 556431557, 143843593, 47154079, 777801356, 689022128, 963975553, 327329945, 200992624, 491024909, 727536872, 728000602, 61106224, 511853470, 881791636, 195433727, 393674581, 543638065, 493004211, 161704992, 127743858, 667176728, 524707177, 807156591, 235309762, 963136467, 988589347, 852876491, 701177983, 177596229, 117703927, 419263978, 746070350, 558270435, 536163174, 87589174, 981426978, 49455715, 986877700, 88223199, 83738671, 199659149, 106733555, 582417773, 594415209, 760784600, 103284846, 864235389, 207237794, 217923570, 821983783, 134546820, 353129739, 929882432, 690300989, 324719993, 328883082, 13746328, 471165318, 287086367, 513691746, 437530423, 587845894, 284308926, 966066322, 279064725, 491572914, 390063670, 532650211, 236612416, 245926934, 18340177, 877228155, 76934445, 494436288, 680976578, 12045170, 173397696, 599143851, 361072550, 100743272, 332276997, 955747935, 136017041, 300299861, 714948254, 263586685, 341215577, 957250478, 876913290, 432466953, 728975655, 267820788, 499963870, 134998110, 712361844, 199045113, 298604341, 730764857, 260533569, 119526652, 879167998, 916434306, 942193301, 558615004, 606366914, 366418056, 890078634, 713417995, 552822429, 655676002, 414804518, 37102261, 369111888, 474967573, 447660312, 214142129, 696735527, 814375121, 927811638, 354498746, 758779660, 639832378, 303915138, 495413469, 574847282, 167424056, 71214294, 500414700, 777006835, 243300839, 935847888, 145730481, 172734650, 39017296, 876666152, 746332723, 806658767, 896997163, 838460812, 103416099, 383415651, 893213433, 55047005, 532995547, 204287553, 277781145, 706176394, 773751978, 64899558, 949394114, 508809501, 854448001, 813963175, 922797266, 241783520, 235590469, 226800975, 52547638, 123917812, 579284143, 958690193, 88371153, 10417644, 891180239, 788320487, 890974927, 345617698, 59420416, 902090029, 846792897, 684971278, 922078133, 547383795, 445917752, 383384050, 38741254, 457076274, 331404732, 935438575, 708507382, 436637561, 483930891, 996695440, 843728261, 705667485, 335045334, 277682081, 283894858, 621651814, 90449228, 594675746, 934180408, 755819595, 573511866, 686671126, 260020919, 749034870, 46080191, 342769672, 313267974, 602768265, 536958821, 907927067, 931328295, 184142026, 338972824, 859754790, 437933188, 454211339, 343944979, 592958888, 519850967, 827699978, 258783432, 138189220, 896654221, 226745110, 751668198, 820266906, 512154911, 531086970, 694348865, 457217139, 415801097, 154851079, 271496429, 721467028, 4009457, 285929886, 26459165, 621466951, 361878799, 960729774, 570912474, 984679741, 656832130, 855256996, 268645139, 822596348, 797811791, 834906976, 22578204, 53869663, 929741575, 866605515, 298103852, 185531472, 519375508, 28853711, 918443336, 561466670, 67166864, 18280984, 279212417, 850917127, 701814014, 344982817, 381320196, 709213328, 329661992, 105559151, 671830958, 387113613, 437747026, 285524025, 839862668, 134624770, 337700827, 618648328, 718834909, 742766986, 826440392, 700345807, 360644947, 500509514, 82218480, 487670122, 646434478, 330708869, 482586566, 959210168, 319201610, 216214230, 989266089, 539759718, 73225226, 904608781, 866799379, 982850385, 134457606, 459327325, 989462680, 587659454, 975494678, 761459927, 187016454, 946111401, 888821243, 124123082, 333148722, 104195231, 319684656, 790507598, 792222779, 717337095, 506269311, 864851969, 240788519, 248653387, 308504051, 65070303, 541504558, 10030380, 476479826, 836841388, 576749791, 876593120, 775082017, 435743404, 347455387, 765316989, 662251847, 638101005, 732563578, 985339678, 289011452, 683567993, 346918044, 85472402, 304323264, 556148718, 261055790, 656122327, 62706042, 91778777, 89311981, 532971522, 350745306, 562950254, 957395778, 586990738, 274543776, 568769397, 939922962, 110094579, 484172321, 521629636, 523533664, 900927463, 612231754, 947982486, 631866042, 855837424, 781869579, 926943017, 430937806, 182545105, 390563727, 801778313, 94278497, 255079206, 645648150, 371267391, 401440945, 789881304, 904538395, 978648759, 990284689, 950426428, 785255009, 662086654, 356533504, 816800111, 749733249, 377640738, 583049345, 165559349, 512788269, 95181556, 555190553, 541981978, 764062927, 220477404, 830984271, 901802749, 812692925, 731530637, 219482532, 547309746, 869905491, 514100743, 545493654, 452629557, 817790865, 936076829, 491292902, 912749961, 407805157, 36386195, 634525154, 900165276, 289208890, 341986719, 839976105, 338336278, 297141907, 620442273, 350442992, 711428948, 421093578, 211296844, 993958731, 386197124, 229721091, 870541834, 332399425, 252391390, 397901505, 491570309, 141325682, 324660688, 427818217, 944224535, 290502497, 480229494, 682790976, 948717696, 970937663, 843713231, 343634305, 5289188, 680320070, 842424097, 680023642, 10553223, 480858303, 387690537, 406301966, 974946471, 474699655, 631179737, 443653760, 412774966, 942368672, 93078662, 408506990, 90303341, 823637012, 444094614, 376478343, 191211624, 766028162, 758443546, 633946261, 732763867, 914969982, 170254950, 875670581, 259407377, 197005524, 924732459, 331465040, 174585452, 850187929, 642583851, 190937653, 327617814, 351644234, 350665663, 18012520, 665629414, 157141786, 837570430, 320589151, 768447714, 654726747, 659985400, 969972419, 143478692, 387313909, 74102244, 250553629, 824714692, 94352337, 560146761, 125585848, 264731637, 712491885, 362919678, 639941958, 646865384, 702063458, 426980542, 275757228, 263347417, 111922005, 36370637, 70274384, 505487588, 184694926, 116826758, 81259008, 473865152, 258407673, 5239706, 847230732, 750640496, 163802180, 223292447, 139649048, 597209009, 305186999, 596195655, 877281499, 173670745, 386262522, 489809994, 169463312, 320209396, 548250984, 802833698, 779547182, 579746694, 656897970, 253046105, 797987449, 389632532, 753389466, 880779712, 318696169, 325021236, 773420027, 203058257, 18285210, 19901511, 390740257, 703324244, 287869108, 880281290, 220847063, 116761709, 676247381, 35267507, 412246804, 662230323, 853546490, 979663972, 959307920, 898348754, 210591657, 540311085, 300080766, 98414606, 33718052, 987350769, 64379484, 94802310, 44792219, 439206017, 803898137, 80201635, 327216841, 954220684, 361994331, 273451076, 398153703, 363469629, 935566376, 528525645, 300682946, 454776975, 874358242, 515452753, 547372499, 119880058, 743023054, 851929797, 241543307, 487342339, 599609882, 721813957, 743872900, 130909806, 196625989, 932199440, 973402166, 795950025, 398277281, 475101519, 220365916, 629779594, 502544780, 727353428, 571292659, 452911958, 723210497, 318772155, 793792894, 90698849, 904067235, 633700388, 229857094, 790302448, 51959922, 113667129, 366229834, 428985913, 587736299, 559694602, 129763549, 788423154, 134739344, 670897303, 402328038, 41038782, 895008532, 531630217, 788457079, 353247597, 855693687, 161664222, 588557248, 800105051, 763901120, 636603771, 492370667, 863953769, 335958112, 278297477, 723068632, 845380677, 995931973, 401432027, 86743051, 825539280, 532144523, 715947996, 880407972, 793180015, 186842235, 848652786, 584601132, 322690467, 897821662, 46844859, 870853527, 962934256, 491457563, 335664587, 978439816, 124712548, 460203135, 964682432, 69428616, 554256346, 663348144, 263224793, 970321471, 626841717, 585433770, 867858890, 22867142, 817135209, 668438505, 754678274, 178124003, 612963047, 699839953, 149343915, 2518386, 629752686, 142109997, 287071359, 732610742, 328078194, 87813798, 74292482, 648297702, 860151823, 578530718, 599386602, 210364557, 167760569, 192996258, 990574342, 267310927, 627839069, 192542214, 311783652, 970970736, 916418145, 974361422, 240867096, 705843110, 42918927, 260834697, 454697697, 355405484, 479460147, 479465952, 762583144, 313215430, 415599026, 29636153, 410040115, 454026692, 177740335, 385167316, 10701418, 860944331, 29594624, 849179549, 5234398, 140915240, 293235470, 752662454, 546863896, 300856168, 901638585, 680570223, 22436454, 180438563, 231338089, 945230831, 622349329, 272079581, 623943469, 192328261, 390626461, 242140403, 37537807, 483507012, 630631593, 176694346, 510422597, 91909954, 186974170, 167659547, 290908763, 710501960, 40668161, 393446215, 309267020, 478887059, 203148881, 442601084, 215339550, 698978993, 653260703, 566072046, 240084403, 110051077, 12800240, 4313193, 883806191, 648022827, 199239797, 703856470, 211180792, 831715398, 609687999, 579557894, 665258180, 209104273, 250260460, 406868379, 622512573, 848343546, 10994522, 203190025, 657919345, 80644087, 965552206, 220424094, 884065657, 106842894, 246052984, 287824943, 341755742, 748926733, 131683691, 559359465, 143657816, 727286521, 438985687, 685059618, 523712231, 54444965, 268061549, 669189596, 919948475, 10925329, 579635523, 666178541, 527492162, 828532198, 43945238, 756208569, 94941958, 237156632, 434187287, 183572812, 587996323, 222888155, 723877676, 206736677, 54940178, 986580153, 481470471, 774174917, 24999926, 762946222, 399281064, 149479316, 639259336, 111127657, 440673702, 624913127, 447901006, 444190377, 281796848, 826093934, 896304359, 367430493, 50131456, 611594935, 927991976, 435385715, 201497913, 351436582, 421448861, 487440495, 679839673, 393678096, 438704551, 381325508, 287169722, 237903995, 595222517, 310172320, 552771229, 330909376, 88650017, 172490692, 41399368, 439594118, 535301850, 356431300, 400705498, 873822525, 922210872, 759218545, 438576294, 888340185, 181079470, 460967033, 588974543, 133818731, 960904505, 166002680, 694292641, 73554581, 471365694, 587603773, 104766887, 329834426, 345651442, 121478764, 616859833, 358149204, 929207717, 848664033, 80379821, 698719520, 435980760, 241682195, 480644775, 99954636, 571424101, 189841044, 783806869, 780927512, 485914986, 871856020, 562602171, 727557040, 300823292, 128994397, 942660645, 696814648, 776446798, 394806849, 699966813, 870273618, 253405396, 61526336, 847171887, 317939955, 807189858, 326213245, 935265200, 136477125, 615984552, 558988609, 825904843, 996989454, 166345195, 338763009, 774860209, 470599328, 736143068, 456125161, 190721065, 642756197, 648538105, 769103356, 941656308, 775923173, 638351277, 41068850, 754832028, 489884274, 611748130, 422911874, 157604088, 760804465, 446420275, 629336200, 410630443, 5265606, 929240986, 72875215, 501287494, 415588899, 891179687, 821601673, 488123556, 890322956, 192782033, 986138890, 954064636, 637713465, 229730569, 643012900, 83715858, 934535652, 229679791, 231405231, 834837539, 650892426, 826041207, 480133028, 94085576, 630623008, 584342159, 281838339, 704775720, 427620282, 170858497, 391476850, 448879500, 582546058, 383978145, 968746288, 433654178, 716129917, 710758093, 58530496, 357952895, 708577626, 794201013, 293295188, 734214003, 6982465, 779040325, 406734072, 839745480, 76710636, 36719612, 736817796, 157971575, 753570076, 721525527, 938872220, 235491071, 311900255, 992637244, 571911982, 831519387, 703174812, 526163873, 460787023, 661670129, 63337743, 868632562, 877521026, 684096410, 955394432, 435616721, 438442308, 265485524, 312779316, 216382548, 847323780, 619004355, 728448408, 877960851, 687995767, 314530507, 744533234, 350580413, 568958864, 211959544, 506924665, 781093571, 825444681, 651590644, 155166099, 660855920, 945833256, 427493200, 931789237, 9990374, 927504813, 169759111, 653739003, 227274636, 589835541, 211097203, 800195886, 123370551, 206571626, 861813933, 458018878, 335361380, 942942077, 913315986, 222762739, 734169259, 404032353, 296161952, 453563930, 571301492, 277768389, 292913668, 852379827, 347178776, 992846086, 871177359, 282076557, 112018226, 784279879, 316897027, 364259228, 339200620, 645757912, 491593549, 454667804, 950191275, 524797093, 921106395, 578182586, 916698224, 505061888, 484948266, 159557474, 171812207, 778384706, 804760988, 94741258, 152653137, 35544750, 877025065, 588580548, 451725442, 789546873, 818574586, 88321255, 71441800, 404960023, 624030855, 847884267, 641623047, 742208344, 612975423, 364270633, 437080854, 487175359, 401274220, 612376426, 853995062, 797862558, 764201968, 27297369, 82215489, 100297733, 844447871, 360720329, 490222650, 505051968, 436602253, 317332571, 730757435, 106997514, 362527989, 623750056, 803900527, 995381898, 600104756, 121512467, 993724939, 102976123, 787292490, 148233709, 239475988, 671264854, 415489565, 605253474, 447857891, 2219245, 656880787, 742089881, 305152293, 931320391, 849585608, 916043366, 186969269, 874305529, 440293359, 890459180, 732586442, 430762872, 249858324, 133568971, 572187431, 649502665, 411459312, 993656390, 91453112, 196036183, 195021753, 999031859, 409583625, 476358163, 672179547, 175016017, 825731741, 607640606, 781859762, 259518930, 957912271, 635781340, 536115403, 737063649, 355202725, 552974103, 197846915, 408639680, 120653890, 614131033, 666669878, 246916045, 835700614, 331865146, 41452484, 97229661, 169412140, 632170769, 119358299, 577269592, 125163135, 368206421, 858515173, 455716278, 590917187, 518749759, 283957093, 123141767, 40546500, 304286877, 354266919, 513167071, 910515800, 218199673, 51812111, 797831708, 668681237, 507456199, 304157501, 672445030, 388903091, 876963024, 282505389, 17306740, 90601224, 553276131, 588707280, 796014994, 291358826, 124275162, 195583900, 792895389, 778778076, 856157008, 140180858, 712167216, 422467075, 29575986, 226478964, 707512522, 121071829, 324921564, 326022464, 410002625, 233893416, 984911980, 541364462, 408798011, 372542713, 198625437, 869472544, 574528281, 463549977, 196436049, 13053924, 862776254, 663683181, 551082289, 434136458, 340811886, 896518822, 505177015, 582653457, 54714846, 740133752, 572002112, 578033377, 959956795, 715140026, 797708350, 441501270, 937197653, 945043904, 105096007, 640128986, 618344780, 318934313, 712810752, 902923108, 932096298, 554269433, 865429996, 235005481, 776740271, 62876935, 876416443, 844435101, 246980822, 820773320, 4620981, 686414928, 673693099, 262449609, 513164825, 17788565, 159086684, 912339533, 331844657, 136453624, 972860832, 970171661, 711536695, 569394284, 639149926, 366089639, 704674177, 189206381, 695020019, 80283969, 718652073, 169592022, 136939901, 903509771, 944364138, 364220656, 517418405, 563484263, 415108693, 188173487, 654527894, 913405866, 341834987, 257760674, 485821812, 989932748, 374023615, 4641799, 469158805, 198445864, 616872619, 109805196, 85266588, 491323228, 631471846, 178143869, 328665617, 994070327, 363748716, 893046339, 653958976, 888271743, 162903301, 505628034, 23148659, 672970526, 914903164, 444624047, 754132264, 350271105, 336374455, 567935516, 56379500, 867165002, 982734861, 687442667, 128513546, 396125699, 419058188, 288209085, 552515526, 64488965, 56408182, 513964508, 441504167, 929609672, 460875866, 98412256, 72048688, 80146100, 486688281, 944996192, 548593993, 148450290, 762900984, 520596545, 847476239, 901228027, 361605943, 649795019, 44956546, 494938176, 727471104, 401438214, 12000439, 693479624, 618424712, 189414454, 316462351, 561281076, 445222715, 389718447, 563726196, 305990171, 666399949, 281473508, 257517755, 868143122, 76126897, 388884355, 565852030, 982815755, 697803217, 386020416, 482960902, 36003782, 177782706, 639360955, 343461607, 407237584, 744811379, 377510793, 971985250, 123845867, 628346871, 317870596, 15324772, 622652538, 767579850, 836703909, 274243607, 245257216, 346080411, 554386104, 173661955, 469167672, 672775979, 805022944, 738033083, 953606753, 420932286, 387642314, 312927301, 544727408, 677043093, 235066183, 765563299, 737959455, 323829187, 649197178, 466591243, 354684893, 769553783, 600169867, 126015878, 912578930, 908448537, 751443548, 64782758, 869749742, 945858965, 927700649, 195417241, 366765425, 218342135, 271039684, 988678915, 808789847, 521403260, 270890023, 45653107, 143862138, 2223705, 596645047, 704579293, 426645733, 748929343, 963907799, 333849739, 628385925, 871798299, 10802346, 389788457, 304733795, 85386247, 263954563, 543076917, 987186194, 499994550, 396429660, 327317655, 750758453, 122170907, 15579994, 663173401, 624726230, 441148491, 309302989, 999118031, 410370784, 908356982, 141303645, 618170149, 472317022, 241883167, 238371076, 664974564, 53394948, 678061832, 303351365, 868060461, 992565092, 990392471, 458046846, 502966270, 449705735, 116401463, 205136196, 87634324, 85746580, 262474018, 420448325, 186333339, 932982329, 189084422, 410594036, 995620004, 446982214, 671093834, 248201801, 709997569, 914882005, 173031135, 104211755, 968777932, 706525446, 914254777, 500037702, 945603186, 246160970, 426090379, 93810342, 873721661, 47608883, 350073684, 930391855, 20505484, 473521925, 741943777, 700577479, 545082122, 500067972, 809122877, 258519285, 277282432, 634388242, 688136919, 834570421, 324274899, 683315881, 529665461, 164396073, 872361966, 848847433, 117964072, 964087346, 6899392, 499559785, 217669223, 215925404, 208045659, 788310054, 259989686, 412815360, 357681939, 46173613, 543224374, 601563008, 481129250, 625777457, 412273193, 730681536, 129564105, 540955803, 391248158, 402025095, 870994251, 650941623, 163531677, 281581809, 290497373, 311039079, 835997147, 170688431, 707937918, 975415534, 609505352, 334976265, 659500722, 303188853, 980736628, 659075906, 533836218, 343177901, 98318384, 29366025, 247807382, 227862183, 894981439, 722697201, 862061563, 333672420, 255789005, 202304538, 716984184, 917089510, 970320277, 340191772, 9221698, 395303667, 238814321, 400895588, 153179670, 44852915, 300914801, 878528211, 751439950, 576239034, 255276143, 426038180, 90277775, 189104000, 772565113, 602143145, 870039125, 806241687, 204959118, 327833340, 316039021, 582681407, 69222034, 126184959, 726011407, 462559737, 749454813, 601329495, 849012599, 213151497, 339217013, 219432479, 452840227, 273729228, 215765975, 806934334, 165620550, 995282090, 211246093, 888354728, 6314430, 248618352, 366566245, 793337195, 52818036, 353684178, 256898721, 493666787, 962005155, 964203500, 424335749, 213384055, 842343703, 599819385, 843686374, 905293137, 438930397, 173981573, 816728314, 553505623, 609857487, 9373195, 678019312, 443295117, 972061987, 607068663, 632822529, 923355218, 101761235, 707947968, 319813941, 356328224, 758940588, 298577398, 42554416, 70977550, 206655519, 85060775, 698921138, 736883120, 300404492, 640758591, 935624221, 242395287, 509990769, 988352101, 467405319, 459580032, 869053075, 570534108, 784340416, 670684445, 539659082, 475511678, 509162982, 382617474, 720372936, 45237078, 655872761, 321353419, 856388953, 121261650, 281719366, 913421592, 445751827, 704589003, 704893128, 198001747, 854779597, 420549944, 558896949, 676240151, 759183957, 408359777, 493508520, 652275421, 560410837, 354750505, 349537617, 746395884, 405735943, 358007310, 809616048, 781039384, 371834993, 104198767, 276952338, 307088821, 643719698, 990618857, 13404953, 237596345, 618047007, 775319289, 492430457, 667772680, 51952437, 41940865, 613111346, 797733445, 824155293, 403664499, 870427361, 706160105, 437981903, 504964852, 793568105, 48220953, 655736424, 146570431, 37611569, 679866402, 537860034, 633952930, 209877715, 40122823, 553518087, 286909798, 360305566, 421094346, 694207326, 379985769, 573202393, 226161456, 315233143, 988108041, 548209397, 975066640, 741539074, 638668207, 770160410, 704087737, 341088682, 755534729, 351084881, 910818124, 989363984, 511395510, 772943715, 142603367, 376859575, 777928205, 275029436, 418653835, 449371080, 983764714, 839116801, 84977498, 477225707, 630693092, 687758641, 600086242, 749925715, 408908055, 859463460, 661466904, 756192716, 251661025, 455407480, 44603931, 469177257, 522875425, 131387051, 905989876, 98735798, 297200979, 138846101, 791910679, 635195396, 618467862, 659032500, 682024102, 655550778, 283108417, 903365827, 841128239, 348472609, 529208124, 322164728, 670395204, 553672228, 485415686, 309463065, 684138469, 304083844, 357908813, 440162540, 315642098, 840253232, 532892884, 220502344, 32129853, 347925003, 660605797, 225671013, 953747600, 48084179, 558482137, 809720028, 685628676, 639427498, 368961935, 272128877, 712878510, 914862654, 254974920, 90279966, 486249988, 324486576, 826839267, 384048111, 739076839, 268255474, 273089648, 509276447, 669143066, 644293557, 26528681, 979578124, 78928151, 938023182, 416832254, 480230870, 286163681, 295090170, 70052976, 138096066, 707369237, 369900852, 678899437, 375011183, 842278746, 375350647, 803268912, 490289085, 840446510, 537227573, 892654654, 679585417, 928546065, 734571632, 53454473, 977385674, 847303289, 448190564, 443681451, 640187208, 53720483, 925473810, 250658583, 349474254, 990140522, 86543711, 369411292, 144457984, 18534454, 706889420, 794610970, 613541931, 730556536, 96983702, 588349004, 630819828, 336347364, 706249525, 966613524, 923984923, 341804860, 372292108, 845598165, 84123764, 208309347, 441774473, 525912301, 315908844, 194132762, 788475820, 835167295, 566153430, 751721252, 401229852, 674713168, 532353523, 77632469, 642557144, 222474304, 936269133, 980620551, 428307693, 972912007, 434124545, 265569450, 754071354, 821013607, 923385224, 706930216, 537089345, 527131211, 277860063, 779030207, 760311775, 167664254, 109406896, 147530909, 965998493, 11295779, 497098950, 198023184, 976790327, 448091509, 427427718, 481363051, 971733020, 36128915, 923120129, 333721952, 88035446, 827914485, 988179635, 526726868, 162618037, 60619333, 274347793, 765853082, 980816181, 953568509, 739845515, 434251687, 769931181, 39899148, 123869212, 158292324, 795439280, 172082555, 655787536, 977857732, 661113074, 139451207, 160621216, 759148103, 51555999, 831377257, 774586618, 649162478, 459557982, 859284046, 188717713, 421510700, 959386814, 95176103, 832818623, 912112832, 653614000, 89638957, 320014180, 66912471, 181249885, 808898497, 673604638, 872298954, 563251025, 339852237, 231947272, 695479339, 155377417, 423938064, 397378734, 32410785, 179375849, 240760980, 359999192, 287216312, 391948864, 820452175, 82233407, 774568344, 337526289, 173192770, 300828867, 287944772, 871122680, 638649166, 196554392, 695956301, 54999484, 917518491, 937567211, 545716316, 138619194, 835584064, 547288387, 708059858, 280742541, 913433716, 183716089, 981078052, 8726152, 750967409, 613587558, 710076379, 294691857, 396767116, 913506449, 931136742, 413229884, 908515463, 723621303, 112543123, 720887516, 777241552, 255030118, 571185080, 945038867, 637128357, 102206429, 603926348, 718045150, 305591271, 225068308, 361513931, 707512826, 288938289, 269116324, 210215062, 866133350, 493797150, 648616850, 346734378, 279473116, 370279094, 666118751, 482956918, 49970649, 355750819, 448616034, 16732616, 785118237, 193036058, 78500326, 318233721, 442330201, 897897564, 418727528, 351401602, 128021743, 64190729, 635752529, 599070910, 925561284, 191306219, 37824320, 678072264, 449659270, 212555109, 372162533, 145678700, 370293600, 408850479, 176344194, 642277157, 246278045, 504680212, 29008655, 331939794, 309837337, 331580007, 129809303, 175480622, 799266310, 100553564, 670870403, 895525316, 331632601, 763724207, 246754761, 538553245, 501153882, 62562321, 440716443, 272156734, 170558858, 706141076, 580089238, 658682815, 96117443, 417807388, 113519183, 639368537, 400065919, 657113965, 918310729, 662876057, 174769053, 335543604, 975822381, 109218837, 573834470, 574128206, 890693728, 321181888, 251494245, 662150082, 895869625, 537108936, 941137, 254314158, 17265292, 63202366, 171516380, 278945492, 600799293, 971190456, 577436146, 60436479, 403952264, 433851903, 920206922, 553285288, 767838428, 105254329, 496287479, 756037158, 119405828, 179922544, 715310173, 303679971, 914766439, 145281561, 259997846, 365532491, 528671550, 553135392, 918293895, 270358388, 36322026, 299934422, 138299178, 95741312, 87205708, 177431674, 86615803, 757453380, 337341203, 600489337, 934348391, 289474459, 348968837, 408591207, 659040188, 759517995, 27200229, 608850193, 614423387, 563721594, 377731843, 54650509, 48666057, 602552420, 655233191, 712757251, 542918264, 327288039, 417929882, 511761726, 746693635, 650671534, 360821194, 458627735, 647704766, 545536912, 811702407, 739227086, 252864723, 530843864, 308515308, 394990324, 39051726, 615455843, 878943541, 779435411, 182169202, 29296817, 678915540, 155426868, 484415306, 477515057, 794511607, 230518268, 539756100, 50760132, 539541287, 318722917, 162780350, 621766503, 994503625, 794215500, 876962645, 178698996, 379993525, 440274795, 971871029, 161818793, 891477292, 64229491, 926036098, 485339354, 987310144, 78657991, 301273978, 51511457, 493394108, 222501433, 859054619, 865818727, 796461111, 230461315, 24656447, 924645322, 406590413, 724435932, 199653864, 876886723, 189394896, 377978395, 639762163, 415206018, 366203807, 115857552, 730458041, 417002505, 641566156, 573077463, 661341281, 311057921, 568529171, 247714875, 829162231, 868271220, 637545156, 978885695, 468870551, 691210915, 371624664, 205240478, 243307141, 738556000, 75770446, 240541962, 879152038, 288829374, 297755714, 731086592, 647020745, 269814587, 281341075, 177287469, 397225143, 843875584, 10720423, 548349103, 281657632, 822684418, 256633901, 329054124, 860632519, 305183857, 211226059, 588908107, 576566499, 795428791, 74045673, 442064211, 985937886, 257301628, 867277608, 506150149, 627232805, 140575824, 821354131, 415763872, 551012563, 830602779, 954656899, 235717231, 115698213, 276987141, 28463431, 432763895, 455648027, 592791943, 795943793, 447882805, 299701804, 284635031, 95399554, 432693706, 499240800, 268042594, 377812909, 448726957, 812917528, 55268715, 406813457, 783379732, 110299831, 608777105, 325820356, 575875663, 345383077, 268581643, 664134519, 891704432, 33588181, 237555799, 823352862, 560579208, 634136911, 832456612, 777484516, 623750032, 980393779, 534540352, 469635270, 670771446, 989058021, 583251232, 231860007, 704645071, 75667327, 700877508, 220784493, 773207189, 401817434, 973950758, 276981912, 219804796, 112541903, 386676357, 390965775, 737358837, 675651234, 596160544, 545488026, 876472650, 31148164, 288604889, 588094112, 522178373, 971671429, 792141597, 731708545, 890402478, 599162114, 836535653, 835303135, 345310767, 284020826, 285725989, 180624172, 518100188, 400670717, 562634997, 133400078, 662057787, 655093699, 441965273, 603214694, 783210713, 854600952, 883285386, 90471009, 871603144, 705717285, 791150727, 3046974, 992291954, 265339517, 402100166, 932778872, 41246238, 651855194, 426351904, 236570599, 971421379, 536086636, 147164568, 877060831, 876520580, 267314609, 212163625, 855789240, 616502042, 57403665, 868403835, 779942405, 270147401, 767938764, 327881559, 952840016, 623046284, 489995535, 247398813, 633183728, 248132556, 645407077, 535234539, 797636359, 261955501, 795292490, 451685333, 661892131, 131261825, 934279728, 905389301, 91513155, 463540868, 557540286, 576933742, 603506184, 743236618, 389084373, 900174734, 788849873, 600455506, 637167962, 855976252, 314336436, 73901858, 355118786, 360679297, 264843971, 723716451, 465264849, 614440198, 8096358, 319401491, 26104038, 466391983, 789727267, 435801242, 82770876, 83636291, 902081376, 652624017, 776981435, 116612567, 768340398, 76492646, 828593660, 763965420, 769137942, 375499090, 502552588, 543774199, 373939520, 414108858, 666831108, 188107135, 784329079, 564860767, 626931349, 653167089, 235765231, 501561950, 916465243, 771524659, 12586771, 113777759, 21263503, 811295570, 741767401, 710077068, 839310816, 781958654, 91298905, 756030071, 179056601, 69998034, 162957762, 108200613, 470434275, 311020688, 594344597, 418713573, 295379432, 74544399, 187008632, 302760563, 622632187, 726639479, 350021602, 246163574, 966848464, 862177225, 747589186, 882943647, 208776012, 402184160, 805215536, 126566328, 226522219, 513898173, 116197083, 93171898, 46258155, 552968738, 857948919, 812688414, 122715537, 992167063, 533610085, 287067334, 458451057, 409664950, 458995259, 121350032, 741277002, 468946704, 634824875, 663046513, 867876479, 546301291, 85185180, 40867285, 883414960, 3714136, 768428063, 563849605, 280506204, 370946765, 466410142, 168186769, 921913214, 572887961, 174863643, 596714263, 210325011, 9314519, 969848265, 999190316, 272949552, 474298602, 910844150, 389317654, 639001003, 495298467, 382589012, 833518815, 708703844, 625882747, 490432307, 812633821, 9355725, 553171636, 206480780, 277619881, 940418200, 986787085, 769223417, 555267035, 263714466, 18784083, 187764967, 340602065, 111172952, 600182648, 236056629, 403758176, 6144386, 321550223, 167502567, 586585376, 510156977, 129408915, 748975306, 782386993, 545988257, 451500249, 556751061, 576151702, 67989906, 842288916, 432719152, 434932575, 547799459, 643638394, 30359108, 313732742, 436563454, 715188309, 390227762, 125483610, 840889392, 713598196, 718623191, 284770837, 459232784, 6557511, 642673484, 644168306, 105717080, 229526330, 207630088, 973362655, 509717688, 20598438, 638317999, 677818289, 430927803, 350762833, 329803854, 338066278, 361398156, 133980828, 72386739, 51123340, 209686206, 103462785, 586955407, 445620649, 339816761, 769570467, 331079507, 673857758, 534167457, 434754968, 785512746, 691381391, 316124475, 890403661, 624806118, 433850340, 270985772, 424775652, 293791928, 410905424, 659030203, 352651410, 447467133, 461743049, 749679684, 293590961, 931961374, 780784124, 14744686, 332098779, 848370887, 730433531, 634018458, 176443895, 717365221, 132830163, 965733904, 245620751, 239615615, 499717224, 861886846, 585036267, 901274051, 988881293, 396710353, 142791794, 711665581, 469665203, 233223261, 504139985, 13549732, 401900828, 51899483, 659574567, 296934629, 54341542, 822628867, 977900622, 866425832, 95322824, 865375162, 481653939, 640118639, 546398597, 787928983, 153116190, 7890339, 837179917, 987190896, 414857312, 99048215, 412199189, 325786520, 113690598, 690333639, 256139227, 326538858, 118944527, 373799282, 138736325, 743864324, 618894257, 836107323, 584632087, 869429017, 462105091, 765486256, 943478841, 228974191, 159794583, 386726175, 161282771, 439775362, 557110513, 120091090, 162756608, 194978562, 263978100, 906477531, 487002914, 858595354, 11128778, 82920486, 637605959, 541478550, 163990560, 237506834, 332675752, 887570784, 976714717, 564615134, 904860238, 360354602, 515896080, 461277188, 842390577, 562564595, 643536648, 318532347, 343164702, 441369742, 806963165, 618022631, 92791139, 396493963, 831252962, 636315725, 781073868, 731243977, 557316963, 374673606, 188685812, 551200660, 359299322, 514257805, 232447154, 279581939, 296811393, 404543333, 185298756, 876534483, 946020637, 159756971, 149591198, 420356938, 122235137, 285046753, 671542840, 609831342, 109655895, 273289923, 599499080, 728468931, 962494903, 824209126, 233753018, 699428182, 42945786, 330547966, 251344057, 874310721, 445373735, 383110298, 406768097, 719931186, 795631208, 833844968, 61006805, 244420387, 21449557, 912478578, 215426564, 106813455, 515950828, 2914751, 911035306, 941425048, 846413766, 398897115, 304163593, 202396511, 454698480, 515150333, 250383836, 897226341, 10849447, 698882713, 300622731, 772958088, 546566715, 649691677, 621512880, 661107554, 329290799, 555593004, 322134199, 404818733, 167399599, 572535364, 764061200, 191726217, 494304860, 138671949, 823697097, 152084302, 371449896, 204396184, 624766429, 513129350, 301193550, 537867939, 396124409, 219588692, 964205677, 439517392, 989598665, 388522003, 363776039, 396065424, 909649020, 375066434, 937359922, 466873352, 131928877, 427319735, 224029730, 359036787, 287850565, 206977132, 499497275, 109630211, 268732118, 348934305, 384331743, 336334831, 927902017, 751100875, 777044861, 41026251, 160033630, 992028455, 329441096, 655503647, 105077357, 465940353, 777933302, 535127989, 123262302, 238540346, 41676836, 834099172, 411935566, 777467875, 664107237, 152717713, 780407217, 824242724, 113402742, 326455324, 827948385, 722854397, 175427269, 875393760, 539888382, 663175279, 899490126, 816901135, 868826640, 697839142, 105986992, 227499744, 463038007, 166642760, 736744391, 306030301, 982998451, 897274723, 751874378, 390424526, 226205722, 992788828, 930803562, 738755090, 579960456, 967630497, 562230231, 689477639, 879085704, 769267834, 386301566, 156146970, 58161548, 820243881, 388321741, 714461998, 370600975, 914368008, 775198736, 637285907, 387537422, 210325548, 308849245, 874114449, 87864165, 773758093, 283365288, 851800500, 219209400, 806983471, 184858672, 263149355, 277866284, 911673464, 763529536, 331472970, 329848563, 299489443, 41792417, 34674845, 520203229, 213954546, 446582179, 449432098, 805394810, 206893201, 153337902, 314547708, 529079165, 810036622, 351330494, 364306015, 71887071, 128022064, 169803339, 274423528, 676652169, 923073549, 417507770, 423557583, 297500000, 329529966, 92409938, 605648515, 355671204, 694658521, 419762706, 8140361, 42342403, 48714514, 396745722, 507775512, 949782029, 389710784, 116665317, 29726704, 281007213, 862273421, 163223781, 230871548, 947006787, 35813445, 928151802, 955752783, 417285858, 118097085, 177195936, 407388562, 758458654, 280070695, 828471624, 891060444, 786882692, 116006488, 196584612, 708963433, 103098665, 594208228, 959428928, 469535450, 686679120, 324234248, 42345272, 666503648, 251706353, 8303103, 370749534, 518276445, 530350986, 732725001, 922222392, 806082634, 37313033, 507794333, 98053961, 576909686, 370556621, 410459451, 298117869, 421638294, 938882547, 291332587, 704790360, 743728525, 283216145, 703844667, 26723361, 868505140, 257916643, 601849262, 772205879, 237754601, 631392290, 900153531, 563649373, 335047330, 967887412, 78730240, 152661603, 194184373, 249971807, 987245665, 157084102, 614498694, 898201098, 555881854, 694702349, 342823079, 352577520, 245082624, 1581677, 723390937, 70142527, 2065162, 66099391, 472867402, 563477019, 431419881, 464260960, 255367496, 889304308, 561298268, 912480395, 111708649, 321759591, 143364510, 764953443, 364724436, 452339841, 819084851, 20560233, 917783541, 136279261, 572393877, 445768943, 219875492, 508269450, 61087201, 467232008, 307179481, 635087817, 473653196, 439386763, 135486545, 968300345, 175020991, 341381500, 148472514, 886093849, 151509505, 991979317, 549998682, 223982027, 257940633, 764216406, 595741274, 337091458, 545549109, 971069844, 774378765, 566959720, 437960496, 933240778, 375813240, 982487122, 224582456, 563632329, 974633371, 16350761, 434038189, 775509790, 533381137, 857928627, 907987564, 857762284, 91439263, 802654194, 663807112, 203541530, 788653192, 920691951, 110271210, 495419496, 414206711, 469728833, 276947197, 363590632, 902926807, 204036779, 316264410, 961761373, 665282294, 263956003, 747042645, 613558244, 723708381, 543111765, 350451526, 277092971, 933093340, 206628597, 765961159, 531754018, 679670183, 894414218, 214658020, 781429161, 324586529, 30982263, 464632855, 37337237, 707732187, 571986934, 463613958, 550929066, 147642583, 879554088, 64120354, 169812065, 436756204, 554519762, 919843496, 214172941, 827320015, 263110272, 46001680, 958207461, 317565710, 136140038, 518002376, 566216856, 885493377, 277158913, 726506286, 604307224, 177720503, 575687020, 298910839, 569287344, 6659238, 774805585, 621951162, 746694866, 661661024, 282117922, 261971274, 512721575, 712351480, 214715443, 207749189, 14825152, 593548783, 2440577, 672450624, 602174900, 411391093, 385722512, 481697722, 964379736, 380398585, 62368687, 238353061, 807525634, 882599823, 461025285, 121590738, 696666474, 775549810, 366426458, 773153210, 105223235, 580615927, 850827911, 289779820, 180025989, 701674271, 973238422, 217052557, 344211654, 788131078, 456776969, 120546208, 4151142, 470571732, 839087374, 807882719, 954480260, 18901838, 326160095, 570848513, 346037180, 188165046, 693004402, 470944888, 312719166, 346392315, 135724206, 951402425, 475471072, 971887670, 350734566, 942689093, 483432758, 586784451, 220372237, 205203689, 846656621, 908139981, 133123166, 52212397, 626581154, 597576475, 227222877, 992451347, 267048668, 326846905, 106528960, 913826137, 932982784, 612674828, 811130890, 825721575, 786295998, 661449169, 22884355, 376430100, 481655693, 972878561, 601704476, 529260878, 820013367, 178932192, 992813835, 421272263, 266647573, 909722184, 717026967, 929731457, 261160402, 801633749, 546189833, 890026846, 473377365, 721438873, 817172228, 45095059, 401162276, 388027540, 424299236, 781860075, 539161282, 452183980, 259740568, 134696461, 412831179, 449129845, 575514717, 19778899, 94524438, 151891497, 233349780, 774585770, 425401148, 412720002, 137410542, 656650694, 321942738, 540637815, 310440399, 953630048, 97047545, 23056736, 981220384, 419147698, 820246722, 697279542, 654153199, 2948593, 105720717, 819028158, 805043311, 692173736, 559607950, 557970884, 541729264, 693975971, 667336919, 787096475, 751413012, 160022918, 597968589, 399188786, 59675475, 644482128, 330593832, 613232154, 767553588, 779473924, 434196055, 346508558, 220071324, 522482702, 321578510, 356229910, 291285156, 970719365, 340806269, 666899715, 594829758, 698141445, 890629856, 986722628, 487223836, 970728538, 568760606, 787935348, 380609891, 99639588, 971497787, 50336317, 375971610, 65105556, 945672928, 345754444, 867724635, 718456868, 20637232, 81791460, 889397552, 300611358, 478961809, 558909547, 125109835, 642381054, 418463176, 11414284, 146926438, 97027493, 381831349, 97869899, 716351583, 50241917, 565520004, 850491753, 162404019, 462351549, 209109719, 765774246, 275217973, 762912002, 857616643, 540500148, 441160088, 198082320, 730418806, 817295308, 530888892, 865312105, 753610033, 563101356, 448585127, 628679502, 153929301, 371488309, 869538930, 747079502, 257259766, 780553392, 635300141, 67956686, 359402, 187913987, 604170339, 453050956, 580602162, 80638792, 655549558, 806759797, 745612777, 814636492, 321772048, 244988733, 672940104, 920525763, 794186300, 408789205, 771783587, 974857333, 792249510, 550508217, 666160698, 886747961, 3052019, 899479072, 116686650, 987652372, 448096120, 986821913, 565774851, 757501927, 294125096, 248167319, 93058107, 925534535, 790477515, 428242946, 246772316, 582703590, 15189108, 371976260, 970108103, 438054841, 702919363, 932439418, 300158073, 531474245, 996048716, 279843638, 210112238, 470247911, 505258417, 402057377, 465933360, 652274089, 965146690, 525777369, 319366556, 471748709, 959957656, 137608780, 820266493, 853381275, 83310252, 960272705, 576772574, 797456418, 894181234, 303395279, 284895517, 570331947, 799404076, 232324999, 223812397, 286473527, 830930910, 209117239, 764237971, 727706954, 4386967, 127291858, 109711383, 109924955, 563625930, 995564796, 875396912, 39840585, 923549420, 409728682, 806411435, 718349646, 86210966, 148318666, 450281598, 647253338, 204766448, 961602013, 423192701, 562655686, 207441755, 938137281, 535311598, 85336986, 777315832, 738803557, 527397568, 751456547, 428321883, 335566231, 774245296, 129250638, 602359189, 203904506, 718493743, 142657418, 543246995, 364411826, 210704410, 579320430, 791632602, 692883495, 559988341, 645602654, 326481139, 460620155, 690334557, 62216840, 538594234, 961593030, 208806152, 970506244, 255593985, 898700491, 868387478, 216374226, 103286192, 600232124, 820955052, 844462259, 784392646, 64845145, 606769536, 928900605, 647121477, 57346889, 824827870, 773209267, 456016136, 731629115, 610813724, 649232991, 890595155, 597258576, 570158461, 168774108, 869373154, 426529152, 848174835, 669149160, 547790336, 292621315, 205098341, 430705284, 512758036, 194914601, 745912383, 248026521, 317964204, 617419374, 517012733, 246608553, 510698818, 610601381, 418773372, 749741437, 266384283, 53032518, 561777295, 989902076, 23517476, 301394566, 285724630, 238079747, 170984421, 871806686, 264255740, 300589767, 197690950, 937876962, 654369314, 885345665, 803158653, 562977052, 617996948, 147861127, 940969091, 373576487, 231362555, 106285543, 760058691, 763185154, 534664057, 957017019, 300806828, 301672870, 898235400, 160351858, 737978300, 563277807, 652960544, 26446438, 300526577, 337019827, 169692615, 464451528, 498383000, 695524860, 443622530, 637379759, 187131053, 91567940, 174487717, 619723997, 547364236, 667077769, 861990837, 269656878, 98239251, 409722580, 93214370, 510934257, 176253950, 770498901, 33225028, 494995430, 666720890, 477902856, 379434004, 755291533, 421866741, 346000807, 664928344, 786808572, 917262612, 880619154, 32426004, 165926654, 610190817, 266970212, 401056129, 103510962, 447074635, 870941425, 62380403, 547593384, 302302810, 652824020, 606093356, 240644399, 875381852, 740291944, 253559985, 606696884, 151000920, 467331636, 31202911, 155490673, 663817458, 377999151, 1202978, 850331938, 74869728, 551883914, 920830669, 923465842, 40369669, 901524141, 598161442, 245959235, 406343396, 187197659, 478358674, 818902748, 14852300, 870811099, 602230009, 475779198, 423563725, 964897639, 546031067, 252973472, 853767649, 282542915, 465365034, 541808252, 337768915, 677603800, 310052899, 817647524, 640306506, 601043822, 191099917, 852178392, 827656916, 316167971, 928140873, 815408675, 572884737, 661924736, 459582575, 899910863, 381092208, 589274959, 293344719, 812818281, 613019060, 821756533, 787049947, 774637461, 398814198, 127042689, 515828983, 318358769, 615692647, 163869257, 163550962, 721228118, 208394584, 430286796, 777236245, 748942905, 479460062, 540690464, 120804780, 780179181, 266690257, 34139461, 882208391, 906235214, 37405308, 599460695, 666325146, 768034167, 485328521, 66390264, 641800235, 923682188, 773137668, 368686628, 742021801, 802984996, 371801825, 680713585, 811156106, 208512914, 730599765, 569167144, 35826841, 20867106, 634456305, 786126635, 476224625, 489368764, 360028860, 628356821, 513652489, 214137796, 189169816, 433563221, 55664707, 685140934, 510181168, 538881087, 688304025, 781897878, 923653472, 908505969, 728665047, 592314449, 699571796, 914973404, 608448117, 479035443, 189275097, 839779111, 64107724, 340321731, 375684040, 179509274, 131653792, 382961195, 585427756, 255333041, 579264099, 159186886, 852471505, 913225043, 522740304, 414512485, 270370471, 516225795, 947450214, 457352891, 204656580, 520979202, 280686702, 458579057, 185004457, 417961308, 535247220, 656761047, 356469613, 781365628, 618954957, 723560122, 567864708, 315320993, 808384131, 672059919, 914014486, 166343283, 365547589, 502332140, 356451832, 956440540, 472717424, 953039619, 946227621, 460497152, 153948692, 512257834, 389153918, 592328096, 432058417, 602045197, 632412603, 14158220, 618262499, 374105115, 986008294, 726378960, 775017641, 773324952, 763671330, 837984636, 616220226, 812066444, 892565384, 514584655, 645593685, 621139244, 868949481, 564036570, 250634364, 314848196, 715833577, 832753563, 81680222, 824483448, 61700502, 605080294, 369801760, 3248820, 526763027, 302852710, 728346284, 721885740, 653341827, 29103960, 118931899, 310095724, 981698283, 210061538, 131112369, 614365487, 638235870, 691653944, 350125336, 15930801, 926625016, 733354693, 149756121, 877962137, 448971267, 19573197, 938463329, 192515095, 808654488, 358853301, 474154394, 276651061, 570640546, 46343989, 285044464, 288713843, 983609851, 734622337, 200242622, 209942700, 596271683, 401003114, 523245245, 537724475, 814400904, 317495439, 43697263, 365150297, 588583722, 75927967, 379301571, 134304407, 552445583, 398283575, 383323473, 441254621, 324484825, 223886238, 818448918, 939767640, 198537723, 506977989, 230098251, 18905789, 430886078, 679913389, 380003133, 399880487, 190080471, 628244236, 217154135, 528452494, 6890056, 638650739, 115873244, 797582810, 766259355, 955978037, 158401294, 674409560, 283585397, 158906637, 146403289, 915214954, 957550233, 326039577, 360452432, 321011519, 2271982, 181069798, 257118254, 338415423, 944673295, 826690248, 937723918, 743923088, 41214603, 88741218, 250634938, 998224143, 388044729, 759997979, 330837383, 301063574, 269271290, 610465667, 915317784, 910633214, 433324256, 882489380, 158966296, 728343707, 402396489, 615795273, 718875292, 740201908, 48813943, 276853870, 624174156, 924197343, 265269960, 700665139, 738142107, 574460402, 508448722, 689801229, 973148615, 287106921, 882765074, 929925575, 863635172, 720956675, 321585424, 40249219, 551874871, 172904248, 193861833, 452709497, 967624288, 686710575, 423694170, 987596292, 49530383, 55706228, 240817895, 63003905, 25602046, 775352126, 147425848, 505025881, 539470670, 526853730, 634113208, 251251349, 548832878, 46972559, 766851314, 715350392, 398730473, 374668866, 757554316, 720067928, 380650405, 314335707, 768607525, 831733223, 730404990, 781085386, 672882661, 63771359, 929777319, 364258032, 546303160, 374900480, 497716982, 925827842, 634815625, 835725471, 887638937, 712103599, 987654990, 515774225, 673572914, 259503703, 550813538, 510465757, 459574870, 192608702, 489027698, 486418116, 216345600, 110869332, 878077053, 969185552, 368650433, 540658942, 954034723, 912064423, 853439231, 53774917, 451903469, 370749863, 818317926, 640556497, 664659507, 208616989, 723908874, 111773710, 886305277, 849163411, 936529921, 97583656, 764433319, 342485953, 48696074, 241572854, 354350611, 492572847, 6078557, 967198210, 626354288, 441017580, 192944363, 135566638, 688471103, 820551076, 656445780, 575978498, 809356074, 146981425, 178592106, 180997765, 579889945, 356524849, 810104366, 992376595, 315395857, 37531820, 196983858, 255551005, 257767661, 862669882, 247940827, 434180160, 27240242, 289516017, 589001461, 637223198, 739789738, 577989959, 209849083, 116895602, 48804747, 273596560, 914641724, 654110642, 732540679, 264392763, 85173298, 848622698, 976334029, 478496915, 517058824, 778912631, 589708062, 227467890, 541348094, 863039552, 327126703, 291819267, 418851986, 282129386, 17023297, 602317448, 335848811, 88596799, 724180108, 215200080, 931972076, 592828021, 181409274, 712827760, 514842050, 97446384, 810799975, 948801714, 822021087, 686286006, 498486931, 914707295, 915983801, 768745901, 844711223, 102219035, 644702811, 786199675, 944473435, 109979896, 729930971, 509152820, 772332834, 171056589, 501838243, 224958778, 216415601, 936713966, 457316493, 404302522, 735425814, 560349465, 610136811, 898307910, 505826035, 298770609, 528903767, 339650430, 35783073, 331528708, 166249046, 237332526, 460600553, 997754824, 223074830, 803106273, 937338525, 30113373, 966190404, 810980292, 752102314, 464505838, 555464487, 23556330, 647539420, 386012733, 574372684, 183585083, 730136389, 361647425, 999253102, 527034774, 857676502, 834266351, 231932994, 224105359, 230657773, 556421691, 577209207, 824039076, 989821104, 411704709, 647836427, 114715376, 840987758, 951042577, 4936769, 331904490, 21480228, 311113193, 279590938, 423408622, 841866910, 679459443, 46368475, 176618601, 377373695, 533830484, 218221434, 228695031, 560027837, 319567975, 216302020, 869388586, 578944768, 744960178, 924153841, 40357448, 260764232, 710845380, 418809155, 846798879, 287325867, 564900335, 713704625, 376532438, 63818582, 979370712, 397798810, 5980722, 919992843, 763963761, 936539272, 901980033, 942859306, 796338703, 886994369, 162666103, 492386887, 675311826, 246432248, 653307709, 272302021, 499504893, 912510703, 627343985, 168143899, 422731860, 314748579, 341873090, 99848483, 669244702, 506922670, 420125015, 51756244, 994679178, 735212569, 275946462, 24281534, 643750813, 266049893, 280883705, 724129118, 835280522, 320330683, 321563824, 515265244, 694192290, 451974424, 507323235, 502305595, 290029369, 828753335, 230421213, 211829755, 145230, 345855048, 18382634, 744155929, 121622810, 560747409, 190422595, 894866428, 251454281, 423491752, 588007420, 198007123, 174124940, 499390280, 656023163, 409183636, 507546586, 512257090, 404463066, 113618359, 94905315, 339141806, 608432500, 626714441, 476970393, 511674116, 97125866, 387824398, 189786602, 191286372, 762191151, 219495580, 128366919, 466504380, 862290760, 166113136, 78169848, 137764192, 826901875, 500398471, 84715519, 551185848, 849249217, 377059285, 186989719, 837151743, 679352061, 605199527, 952699587, 161141844, 292341651, 347312277, 434131217, 716140098, 249965201, 834765696, 957953630, 40000941, 618083245, 176434616, 493673847, 421771501, 371525732, 152188433, 698130054, 736373520, 469294158, 308086282, 245728474, 729111515, 709441900, 840624333, 371204511, 864938880, 167749467, 790620678, 657140258, 882137117, 710949470, 634445306, 307676433, 885983139, 769168263, 250899457, 130777882, 141792860, 846443585, 57941922, 138209788, 896460309, 280301418, 755777096, 280008293, 577225435, 7517119, 990452384, 539995974, 526523154, 347023029, 591387882, 987375812, 605372585, 827613542, 537214042, 75839524, 321669707, 205470136, 863383153, 271152564, 654641744, 571280878, 854367446, 26191740, 906849096, 812590967, 638784816, 124691245, 571928180, 833693661, 375629400, 714314342, 768527695, 762263362, 377094552, 120351782, 843356478, 145717040, 190842080, 832296543, 59218614, 566849679, 162811751, 212656248, 135290567, 657141256, 111623422, 115292825, 306910284, 42750062, 2294236, 985985068, 823244797, 539110827, 421262627, 341980682, 883953931, 314791370, 462522898, 708186504, 602648918, 175179731, 159400643, 77356647, 933858466, 859478758, 687507916, 37253674, 294447218, 418081771, 872335120, 351290082, 952587157, 29544332, 851041854, 392605690, 818210406, 347446231, 662851004, 24145563, 697555899, 508510248, 987849630, 878363576, 430377317, 949015413, 952004125, 152163511, 967221117, 835628271, 835728424, 556102126, 257938836, 421221023, 186472036, 287195340, 11031171, 181017789, 490854205, 885244784, 477732491, 658181975, 300188279, 273971313, 960704055, 17048340, 322591827, 242894356, 823337876, 603343602, 933065926, 880936497, 984954628, 404415165, 961011953, 892387539, 662143602, 82465011, 653479000, 702141920, 866148049, 924447282, 849975296, 387917521, 652829049, 683691166, 511694704, 953716473, 314941498, 559914515, 468345218, 484602363, 58531181, 307704500, 314581623, 328153407, 867575999, 194936018, 458687093, 801076364, 495330258, 632580119, 976583389, 342176143, 80249886, 535040574, 862714958, 221975520, 780449618, 556275456, 696437389, 874871775, 418254240, 690569201, 961902370, 427605618, 690276721, 902685144, 660158019, 984417301, 489074124, 537903403, 357399153, 554302351, 426132482, 986872514, 245327955, 615067387, 636373169, 480828608, 989129537, 642995815, 198596650, 724647031, 244765912, 589959226, 543462367, 469758901, 154753991, 396622178, 143256623, 291482039, 817727147, 3883586, 258535221, 47502251, 203053484, 366918046, 929597054, 52758824, 805739561, 257902284, 276663370, 959221961, 579739676, 875186569, 730292922, 845638373, 39687089, 553260390, 32535734, 172826370, 634193348, 558251883, 545262252, 652085917, 128145314, 707848583, 683068316, 350846508, 73405587, 90595986, 56982108, 833244158, 299625395, 424705524, 365045255, 678313349, 833265268, 70169099, 28546599, 937570140, 240748795, 868028244, 843984050, 261344791, 788613100, 253719026, 910562123, 136973095, 329320948, 925494989, 779421653, 943617937, 426114188, 780488726, 174793236, 353858311, 315258846, 47681715, 126074241, 124162051, 165312452, 555541963, 427197970, 889100463, 398592856, 435029457, 980142208, 793094280, 873611745, 534796884, 409874375, 665869714, 778975291, 15528443, 561370695, 349165833, 683397191, 618637591, 412619063, 149807217, 476304807, 33520691, 536105909, 566393069, 395875512, 869054700, 159711318, 612301493, 642471286, 456373054, 839172252, 858558374, 336204422, 864685751, 199573819, 655842029, 676659119, 492855996, 735886024, 329764554, 339019756, 130321880, 937405064, 372629162, 931806245, 129699836, 993921352, 77840251, 436367102, 885554544, 227107447, 612672540, 356698114, 814098391, 544970994, 955806053, 821402835, 920406057, 488499233, 704688636, 175530048, 834014009, 534997173, 779044760, 112657841, 667439958, 371291041, 963884032, 893918289, 117387609, 130764825, 21708697, 794431324, 177030862, 617195862, 250776985, 904626163, 825998380, 52943670, 401240976, 115409684, 714572197, 143630282, 377354458, 404839938, 457109052, 624974094, 671831731, 617462901, 10604849, 776572485, 89516745, 74293073, 281087007, 459477933, 676013262, 840165776, 806153620, 719700577, 840450742, 902058025, 800439150, 289190466, 89998853, 681053496, 719407377, 98554564, 553992365, 747374569, 377789815, 556233103, 938442849, 287949838, 892748688, 795399657, 779603223, 179153493, 748599429, 791802503, 393764153, 981291959, 841022311, 856013625, 181716128, 802648115, 398820034, 750486446, 875448556, 636662647, 335737961, 118767047, 189748706, 12298860, 812059362, 233064527, 403413819, 337898461, 646893973, 945840372, 85856341, 289550623, 855445134, 293481819, 926661040, 783624586, 669737870, 811100921, 895138898, 221521220, 21105195, 897593500, 140111528, 851828413, 432696519, 526677611, 982958525, 323677930, 679746345, 245335250, 831716772, 314849655, 770539631, 129837136, 310037644, 334963148, 47583262, 286562790, 723126761, 51422184, 531846349, 944541647, 368222753, 670360822, 275202717, 109172990, 377871173, 433066820, 787953496, 874010044, 526915618, 29439658, 47354278, 92186370, 722560253, 205305795, 645401961, 256052171, 627093163, 954423447, 676159445, 129683385, 696822628, 222905759, 687746383, 197658738, 961308477, 507262524, 756156474, 371246817, 253041316, 940499370, 570288010, 56421608, 616660579, 302185342, 770265643, 875760857, 246179134, 837507022, 793148263, 355122724, 579406104, 772009096, 755884476, 215812498, 202760604, 125939614, 639466991, 252638214, 808966455, 784014732, 698380397, 571069341, 977425208, 33051139, 404994290, 935724726, 261316030, 875148697, 839205319, 742750397, 447397739, 156259168, 249805310, 215223673, 706360604, 285160064, 491149964, 713854132, 937093998, 709643196, 547818809, 303866769, 943011578, 538596151, 660605911, 521771604, 503542987, 791743884, 682370551, 612165726, 303368810, 882225342, 475927449, 622250219, 845778530, 700640048, 528841406, 830418693, 675135780, 535671387, 129006361, 116351356, 564544035, 932097809, 669583433, 754952510, 361367724, 186601698, 413880241, 826474121, 276203797, 918128869, 249712507, 63965657, 807484413, 719311328, 981785380, 608178879, 755579893, 445365947, 51343312, 159345941, 226681689, 125809993, 529408891, 167316873, 238728057, 903533930, 403849818, 372525681, 580311482, 799561418, 693240986, 797446820, 938963616, 430272884, 404297008, 471710039, 347465475, 657045828, 367931393, 632925403, 795576940, 928588820, 75909946, 724561553, 52912442, 762659618, 323284092, 785401801, 87010651, 530118229, 253743588, 818093099, 277494613, 14108788, 344283264, 592400270, 309222475, 199468786, 897284452, 4318153, 643881543, 121059906, 332377461, 557895463, 974114508, 154223342, 748269438, 460282083, 872387065, 970501921, 455940713, 4883938, 249470239, 659629555, 959348774, 747039175, 563019267, 928950515, 968926837, 806791734, 734394098, 531686756, 657386253, 719818870, 16581471, 38481585, 874782848, 195876195, 995052808, 972015240, 459603210, 536004440, 255601172, 165700720, 623222004, 901890848, 380717359, 206763149, 96354281, 991325895, 259922751, 901747563, 739158418, 349254107, 101764917, 537543240, 432147591, 822930523, 441286442, 90873668, 544948702, 813652621, 545276857, 499305218, 666432523, 124875155, 357416938, 549619336, 608176945, 986363991, 623140142, 696796896, 443288967, 885071637, 863712155, 926714085, 849047961, 114119616, 593017223, 682376496, 387139719, 398853231, 800901894, 131951818, 409699499, 969705763, 810354986, 434544928, 861360383, 939798518, 657021489, 285539121, 63310474, 138291423, 376469932, 128701490, 620985969, 412312368, 560981731, 979640361, 695013802, 443463364, 901172140, 155808342, 594685398, 569805699, 737909985, 179654197, 930024273, 227768532, 402500583, 787928336, 457495034, 30445372, 738772156, 690115520, 475850775, 148784300, 284991895, 700305509, 814596833, 147289365, 448538638, 327574096, 530374261, 688208712, 94299390, 986169391, 395287674, 350308057, 938414427, 947032501, 904127128, 142303010, 876574404, 172162837, 396753057, 886781005, 767697791, 816666407, 952096822, 824011386, 266662343, 698711748, 314951894, 883745992, 944218935, 25578206, 808587035, 797414170, 431844708, 624650999, 113935436, 488677946, 798388216, 881513976, 33348892, 155329647, 532899391, 986755456, 909854243, 450511590, 131088400, 922982041, 617460689, 73493607, 794872935, 985163536, 637531591, 780726120, 957304953, 56596736, 149541747, 915816336, 272034283, 306702096, 633924846, 97520842, 633645848, 345495241, 509722346, 797111981, 187579867, 30311861, 249391733, 383945935, 532180125, 212543406, 982261028, 384820052, 538956335, 411375851, 585975334, 725815894, 389785224, 818069680, 925349379, 888492522, 756418002, 659524643, 309515938, 391644579, 785988076, 267471504, 221771908, 74249329, 942943888, 554790450, 697380679, 780815205, 872672110, 893534022, 817906467, 128555416, 375217041, 844021679, 151957268, 844953700, 37284326, 568418666, 333253781, 385086758, 503943299, 296898349, 732772615, 773138144, 743711733, 313044789, 628413434, 403714264, 25258278, 96180037, 948500042, 48180561, 57278286, 17550169, 118171405, 124622023, 393685638, 132855323, 603631068, 30882764, 345525286, 529622693, 850125481, 52373887, 723467927, 175565120, 217879031, 634403661, 219530523, 725241749, 927004793, 86381794, 710673175, 588965460, 493708448, 270951827, 199828457, 173859784, 383374200, 14949171, 262133267, 319712133, 512756161, 799533049, 792656612, 744629523, 598129383, 978409470, 79978090, 487803020, 256415570, 220996727, 651000591, 736723553, 293905856, 134582332, 514809140, 245082604, 520762209, 688667446, 654363382, 670443926, 152663614, 12143697, 169550936, 242682785, 726971880, 949007795, 321983699, 609275753, 532221004, 796849476, 194319362, 807136924, 331654262, 81118988, 541249737, 797000145, 90269248, 57974030, 971027708, 363948313, 321951285, 98447824, 890541482, 57376644, 948911091, 60395872, 797011125, 720766111, 630837950, 684267868, 383272506, 881844627, 225902940, 304728763, 270003366, 759099802, 909650514, 651531263, 637998611, 46395745, 699626645, 563837498, 922956598, 497607921, 694551987, 775075701, 599647185, 993049749, 819869464, 111916957, 272994423, 771450886, 282625080, 1844160, 983240240, 768667359, 594068647, 920385390, 292498853, 430641416, 153190129, 607688018, 545659842, 918419340, 78872170, 562207603, 221928898, 175694794, 35221763, 832378290, 743012442, 254708658, 561520157, 784175061, 135877408, 577360246, 45548928, 146203251, 777302439, 777590903, 597408559, 5808299, 291428080, 470328569, 740917277, 5813290, 25483074, 988119521, 399999091, 842554744, 683125763, 294502590, 133558598, 204198482, 47274319, 381307350, 967227291, 383781115, 954143772, 738188106, 189724190, 371148298, 508323686, 497628968, 613657328, 335369, 259825484, 625661965, 197051704, 945198159, 975636477, 845871311, 806859031, 691006044, 692313531, 473254503, 331545100, 885566736, 304971663, 608798850, 73444100, 480384294, 440129935, 696562715, 605210091, 589954352, 641351647, 560948388, 535290689, 255020748, 297035677, 341042875, 507863140, 741559331, 418515544, 593797437, 684099055, 321987751, 938909530, 185743481, 663965229, 949155788, 635732839, 127127553, 64901778, 657351176, 562071328, 239419013, 161096614, 568651631, 356166563, 617014448, 551074318, 379798241, 863084500, 852726073, 264609455, 837533405, 270922513, 161139003, 415319590, 783802321, 5031626, 187797688, 912876756, 834126125, 227591582, 895036031, 594543098, 699425561, 112237392, 115423458, 463468419, 199807987, 453925180, 411479709, 630774468, 147418341, 564921944, 327580089, 838727724, 623147126, 64283724, 552167407, 955315702, 345880972, 853057470, 901417888, 898764577, 159533645, 155839837, 779452974, 154676214, 163629488, 687059497, 117684109, 898752257, 68201281, 576694061, 73824106, 472676746, 621621661, 643024991, 82952798, 945426126, 807200946, 898325330, 608513135, 387536225, 961524747, 931072157, 168329531, 127549199, 955409454, 438135920, 302956484, 530224469, 700465027, 337889365, 57528050, 107990398, 24851639, 975780555, 52044980, 791872661, 300832026, 13961281, 238593903, 457368937, 946150924, 765007149, 591623430, 54257711, 959097473, 477166966, 105719150, 830847284, 61129702, 468261053, 356617173, 545867930, 237548324, 358957789, 165847298, 554463439, 67339985, 326605948, 310878106, 354136293, 652938266, 39430769, 957531331, 876791387, 374492804, 303291768, 636933481, 391155960, 143536163, 359908146, 719769170, 57954034, 279898607, 23186821, 919183666, 422824912, 988281560, 617787460, 531409881, 605819266, 157658047, 516296115, 900036877, 214424214, 215001816, 903419896, 735777265, 20116211, 443466078, 551441330, 269243624, 363421320, 347738214, 500886858, 942689776, 653757008, 226114809, 288665264, 270898884, 91076081, 974058663, 318080126, 39148750, 702590044, 18271284, 772660288, 811871642, 122104023, 871282274, 863838473, 754909875, 26604588, 686987730, 800474474, 41632799, 734792299, 201645319, 881219996, 722145061, 397917035, 544430716, 46451589, 162702682, 865036641, 641920296, 513418293, 272360851, 281949859, 230752185, 244462359, 23910658, 587619188, 247966823, 185058615, 725565460, 105445817, 641606032, 152985089, 430053420, 431716837, 660378549, 238621109, 144036116, 2763406, 329712241, 448990125, 332080412, 395437898, 739313235, 858196579, 653319733, 559526906, 450303153, 164540720, 251470117, 848938246, 972469408, 46845627, 547847220, 122105797, 453812549, 600614712, 624634724, 801039743, 818870551, 518077461, 865331466, 52202498, 982626501, 219346246, 916053394, 922015923, 950283847, 648595899, 203138212, 747271317, 196261511, 568601775, 867723329, 452823989, 865963472, 574552719, 624727075, 761809469, 189976222, 215563742, 821692245, 285711105, 462449508, 272846969, 784213862, 984702658, 962141547, 478121604, 639336968, 576303175, 871332914, 911692593, 119570973, 507780723, 979910, 928335810, 583636547, 653251198, 390764441, 132752887, 668467838, 110577121, 500346193, 294325352, 333456673, 288092323, 632704131, 653116005, 290056527, 481014820, 909070554, 353682881, 84258068, 145040857, 550409923, 720743163, 852583462, 147474883, 415048866, 299893618, 578321124, 736006706, 161639700, 246539906, 120900127, 218002362, 116726740, 206232581, 110308541, 621431093, 363112009, 646426347, 327812963, 775691707, 11103800, 249210508, 859435729, 146407873, 742921762, 291492161, 604565191, 790252019, 380145475, 346246062, 964920775, 573733868, 381661464, 937972550, 234758129, 459869106, 574245783, 453321809, 151623251, 188900736, 877503674, 352161345, 800427145, 515261340, 893733917, 816330322, 873567103, 701347479, 718731992, 726585167, 835506805, 24171716, 270839827, 854692971, 15053694, 50562527, 190369663, 957933526, 2260856, 347938083, 938859724, 295229014, 662250032, 105040779, 144061828, 290661728, 421125532, 245471765, 969449993, 534979395, 134123483, 277928042, 160012422, 467229706, 365154168, 900745279, 761445681, 694015625, 751415399, 162319836, 121470544, 688454105, 465225369, 556053773, 535143717, 697512536, 589107584, 310187072, 369220290, 174697364, 316053840, 506729916, 102129504, 869487368, 72220267, 126076244, 58569425, 664938980, 600369445, 359193028, 745483056, 537145430, 733880936, 974136392, 799629552, 327759651, 31533900, 163492163, 670798020, 19142414, 252768144, 396025496, 536390572, 502045470, 362713349, 769684954, 631975774, 74719376, 155969892, 420327444, 498944560, 847609650, 842962293, 748829874, 912181008, 769253409, 912686006, 271288175, 35284088, 26614605, 184879637, 882881217, 314345145, 657296674, 185128259, 62724637, 530287, 700083884, 167937427, 90195875, 763434383, 446273080, 722671352, 851296481, 714583399, 732238412, 613358615, 771648302, 147599212, 62679099, 366831185, 692618135, 549428853, 397480992, 536423402, 826536392, 700017638, 428694186, 357028478, 652809557, 654217526, 254884790, 318442124, 890435470, 620730038, 339644998, 231641041, 972074470, 736930560, 513834649, 705171386, 827688757, 361500053, 820305147, 770723031, 780955, 697477635, 66676887, 224635772, 250413350, 883597045, 370034031, 78845437, 117485005, 650523452, 707261234, 53071220, 542665826, 492239443, 844620403, 151062914, 530429828, 570866386, 889836986, 852513028, 877124812, 491004399, 360965082, 437373410, 407506986, 159525689, 780031148, 85733013, 924200688, 381492392, 101537629, 21736723, 413545682, 626610953, 288859424, 636257262, 244911088, 327930743, 552600575, 450916319, 292172862, 111568563, 328054286, 621325332, 110885019, 713733385, 139232734, 217877043, 691880311, 906286969, 462398705, 199077325, 198514309, 575894576, 413180450, 692508570, 738364271, 19584346, 859648493, 429149089, 708483768, 289673097, 665730767, 206618689, 764712994, 819544936, 530208807, 701819098, 938986220, 578808324, 854730420, 471272344, 348422816, 907648145, 457531000, 555652466, 954595763, 552878318, 641939828, 391432533, 302965386, 606427723, 245959535, 854776446, 788701819, 200151338, 77012033, 605046571, 712554824, 368364350, 714978723, 896783878, 867627063, 8584548, 258852571, 967373145, 91327816, 432539367, 563891573, 794229538, 138277336, 711652997, 380973487, 149986082, 288711081, 845067409, 171807646, 769080387, 555352149, 265756569, 100840055, 804676883, 690084897, 779403310, 82961748, 781473762, 489370710, 939174123, 765328324, 152310374, 100299706, 870232567, 963542919, 130338559, 740553948, 791902866, 587333292, 508825600, 594171935, 982354004, 882159737, 284315533, 179151131, 369033959, 449272510, 767741449, 673505889, 989385120, 337920991, 15660234, 396752821, 148349578, 285974198, 317382005, 133240701, 698978192, 728816717, 171294009, 690312637, 483218852, 662050539, 769840835, 344456009, 972578508, 338653518, 805311140, 814893340, 796675584, 656771686, 170934305, 272496550, 304907609, 975401230, 954460639, 297144908, 423193541, 110509106, 707395592, 914470342, 969054254, 184935120, 748703052, 541619675, 427154610, 951600460, 641311944, 877195214, 530502804, 722380253, 957116176, 718728225, 44103054, 639157331, 742888930, 223081513, 284640294, 524793185, 72122501, 59484958, 330509048, 62111782, 557933650, 144145139, 720065138, 692078360, 597132724, 30693001, 749013776, 390240974, 74647718, 830626889, 259622477, 161304771, 946712287, 759525765, 854279957, 117541280, 121996987, 51392376, 906696946, 898860936, 255715231, 341027263, 194181884, 509388182, 878712007, 755369175, 17430653, 965240750, 778299497, 977158150, 642631349, 365891664, 835644530, 500899206, 823999743, 524359889, 782318744, 622172946, 95302439, 276123578, 213949625, 463128181, 763366080, 675644857, 49118259, 181707296, 173682493, 472296127, 943706741, 29747313, 558205571, 807792471, 982469523, 888895550, 280095919, 144414826, 740024061, 631268064, 31842639, 999662811, 904213138, 645597386, 735455498, 209235993, 523365218, 417389799, 941544742, 252333819, 185641133, 938751612, 48138381, 849423651, 615717270, 2528872, 606351833, 785380885, 304178513, 662371401, 480196532, 563714740, 739705873, 943301552, 602357327, 878528257, 762921713, 17708275, 243739161, 171636480, 999300979, 447987337, 238991707, 10539946, 562478844, 366022264, 687376929, 884552468, 754708236, 912344342, 631222881, 516431503, 45942841, 80177411, 730335104, 310585447, 492159536, 516981549, 717136469, 156586399, 279035673, 783180725, 299713497, 239655709, 14786469, 893392982, 609532634, 737883707, 263941297, 154174705, 747787579, 849656058, 881531169, 523800979, 97740276, 283304360, 159585456, 603217453, 84257009, 300264051, 272475898, 367033472, 890265714, 549288198, 772885318, 416489615, 982567727, 633876378, 468248495, 216975175, 136262387, 368690762, 493878769, 837756443, 668695019, 416105972, 697430960, 960926588, 535652424, 829384200, 444816866, 841672778, 920953051, 738844667, 28595855, 737823458, 523246641, 157547106, 401625148, 107879701, 296899301, 305812732, 803464919, 83104665, 726143838, 249524492, 98356338, 518017985, 480597985, 83982020, 740865235, 34082604, 188508559, 940331458, 347856047, 597322723, 871172084, 186111641, 57461295, 985992109, 649054792, 987894440, 121307412, 584984779, 282109077, 50331366, 814639378, 607417699, 797430778, 1058819, 843180137, 664040153, 221862435, 968683063, 225633120, 210548545, 166157141, 353764242, 892969953, 676725262, 245653305, 213287393, 120066203, 941592634, 715938171, 639963546, 721581934, 575728008, 557068999, 623995712, 963809622, 316467968, 417254522, 42278312, 429658844, 510840518, 173329206, 169456487, 804795272, 832127929, 65810408, 856518700, 507775275, 861007118, 409048664, 819567372, 160505175, 374763342, 923211881, 680275763, 297273889, 683410323, 349001992, 638717036, 75153625, 602548323, 14741048, 30582010, 579131825, 957811148, 614562951, 861682289, 660431911, 177982955, 652015059, 778192330, 641476241, 230878512, 980570989, 823149, 185753908, 757891053, 201645271, 136045480, 894766834, 927187040, 229459753, 287199854, 215824438, 458400491, 177298367, 64705957, 187260203, 730575853, 475026459, 910487868, 865755568, 430234683, 640178423, 249273473, 810452768, 930179087, 644627278, 378830354, 193259653, 243772523, 583534284, 787210757, 445383178, 25685025, 481432463, 345962351, 9190545, 240614507, 979847697, 928153083, 27359590, 488477314, 322489045, 68587082, 190285529, 206060136, 25183306, 311648274, 451628438, 854554284, 774038386, 688570847, 440233028, 354666620, 874809860, 56961400, 79834666, 246831228, 594134244, 413411021, 251102180, 703418987, 408391475, 123011697, 283637015, 657947859, 600746510, 416678228, 107822035, 279018423, 954550049, 482560537, 75811712, 147565199, 460859713, 708982326, 288755090, 341282562, 929467208, 805445805, 970670161, 434457307, 765368298, 796151554, 534155176, 293076276, 875800008, 497764664, 928827517, 221354076, 302483171, 724851675, 975172556, 447527932, 510158851, 557024194, 947725099, 498429246, 583050761, 214366268, 214773247, 747090352, 974290543, 374419351, 859927140, 24045668, 780352394, 173057938, 10498764, 152777800, 7844111, 43085717, 739526774, 666132624, 702673658, 957430420, 181894542, 537498439, 590260381, 857552061, 84064351, 225981968, 20217064, 62594820, 763813892, 991616215, 469784560, 327880345, 466834111, 868702891, 827822198, 813673464, 196020146, 333671578, 374290142, 246983095, 912150970, 484232596, 814708586, 631381914, 781286449, 381380822, 387700786, 304635540, 81043707, 232831261, 246190564, 600322547, 833441179, 513675274, 50890338, 254793680, 286115509, 219306535, 627854703, 480785920, 527597728, 489848799, 196049659, 712649370, 994301970, 227708729, 70015627, 669296040, 707749805, 680209734, 247597089, 485871854, 566226000, 558326192, 263399944, 133187913, 735589778, 836873548, 995883365, 228415791, 672218552, 36855774, 252964051, 970863793, 303097268, 394947798, 799487543, 357409701, 214958741, 40161183, 915628194, 74766847, 115871839, 605784334, 360649669, 214610502, 878840343, 938036402, 996776324, 985214436, 447274438, 849828214, 646850957, 815054348, 913412805, 734587898, 310066171, 887590613, 64486114, 587892022, 617564425, 339872591, 962776779, 541882791, 7811216, 303985327, 720473073, 872536419, 333160468, 526186826, 154405307, 220450032, 810843246, 769622606, 662053066, 936535133, 501101019, 716658374, 124407954, 489799089, 688810166, 475762460, 984056555, 232724666, 513104465, 566918310, 216886041, 784121606, 263337931, 563401748, 88057169, 783152413, 136278278, 60545538, 279493384, 67848431, 628970480, 80422784, 668673172, 952570847, 329147601, 608371001, 40171099, 101263523, 949414005, 838882185, 573464640, 913954502, 264477261, 651042643, 851338352, 989423919, 517178592, 750296087, 101168766, 841545322, 262593476, 503877813, 25113448, 970990514, 520236493, 93167908, 550763532, 339145020, 409635705, 726997377, 598051813, 351795997, 145333015, 550859864, 205128740, 797633888, 706853469, 703272855, 877115521, 700797112, 274758313, 449058010, 575893836, 282656675, 975334060, 320941533, 511194773, 894534591, 445828646, 713249419, 414650708, 559143706, 998160648, 327322320, 806413689, 550021368, 858849018, 598738894, 639054255, 895513264, 471099497, 89951434, 374670405, 774905755, 185379680, 367065075, 253648061, 748429239, 196120237, 32590725, 384558039, 440545357, 580940746, 630614721, 244927136, 413376052, 595665197, 320682122, 245164188, 215172560, 713320797, 172185151, 303743554, 416890457, 308504989, 31308922, 964610082, 894582476, 538240752, 504596225, 544380627, 753245640, 679285428, 192841047, 328319048, 471300935, 580269789, 582618550, 614477795, 562457858, 474694021, 592270769, 561298353, 732723875, 928485139, 686808874, 472763824, 889369834, 68246615, 783504164, 544001540, 999121700, 611668958, 980407129, 696912049, 692426293, 727029910, 620292887, 395534924, 202280495, 777199456, 875582463, 284103922, 187076981, 847749567, 903065302, 741389899, 675971289, 140499299, 178811635, 27263421, 800867847, 395145116, 66798157, 388091650, 901694029, 747090245, 884788794, 256490631, 587074545, 841331675, 611261404, 974902841, 332553842, 304821864, 407193435, 92485845, 877929591, 21312148, 112591880, 968892212, 534385952, 149530684, 580956619, 155772074, 40955697, 293393657, 904948797, 902807352, 199939913, 286839295, 140609466, 277521932, 648955807, 164383622, 175273617, 899213625, 442115655, 981699674, 786997128, 901452715, 163949297, 114201349, 243084218, 661245076, 365255861, 521650014, 389861975, 747134740, 907567432, 274264618, 506168907, 205894289, 676111593, 951680724, 406294868, 95827805, 936785955, 369662663, 917770106, 49631711, 210562725, 291161228, 322529256, 68666709, 942503192, 279012452, 735474489, 146417506, 901835647, 109696432, 632863083, 528116008, 10058212, 172614010, 407366770, 66389818, 170840603, 815986284, 521940212, 493671002, 186397384, 145869243, 972613097, 905207863, 96180957, 948906738, 105921375, 221585447, 544900304, 559123203, 49241133, 857207710, 915389351, 115757980, 504534196, 787465838, 644243874, 575056843, 528231467, 733936998, 153318519, 502604972, 718464293, 990149086, 33718640, 71948038, 401355033, 446925541, 162535291, 523114236, 926050596, 708440631, 604032815, 3312113, 895048623, 519008014, 75841816, 779131225, 396137160, 725362378, 996496845, 400036795, 169293920, 683054123, 359227360, 85389716, 571034589, 615555882, 827830688, 182318708, 63399022, 332486621, 938964666, 881218816, 716744192, 752372862, 152769088, 906431751, 623505706, 713150913, 110838280, 823473128, 236542472, 727789958, 626274357, 207930456, 775550228, 476419691, 151146679, 264757778, 203718402, 936597025, 540756823, 782072955, 937144945, 365137980, 515106445, 504703831, 782174015, 157333309, 997883927, 600818982, 338026534, 972567221, 254343502, 972496774, 147622321, 543032696, 148210846, 277387706, 26962444, 513439796, 815592025, 883089626, 340461306, 765187354, 25139628, 612981934, 869478335, 507251691, 458783783, 861613890, 150071039, 573365217, 687461510, 215147668, 569336016, 427755545, 120804340, 533602702, 257880606, 243825301, 425820188, 179996808, 159919222, 20773746, 750896606, 372473346, 443905558, 52777096, 925398106, 892602974, 536550792, 249072124, 463887921, 116336059, 966932366, 394536789, 115152217, 621929932, 523952786, 937215616, 72167527, 815891789, 366616322, 920045664, 578952860, 386555747, 174100613, 961484460, 267810332, 218633879, 580426562, 474526585, 858973969, 991953836, 73856924, 69085101, 52172530, 489771390, 896374852, 289779283, 853412581, 718522450, 520611553, 695392959, 524927187, 266253283, 393774699, 9080756, 303950250, 315276286, 392660410, 793886181, 862737991, 915928469, 697369425, 709689661, 251142924, 544437917, 324752238, 724809701, 302711667, 96504055, 891618427, 541560475, 459756736, 87683218, 322040373, 556934819, 460208498, 121367180, 274436394, 923802581, 315894119, 911681164, 852039935, 415704813, 325863300, 145788204, 298194353, 14300437, 209301065, 92486953, 221926363, 376872637, 782268162, 783620029, 101516993, 114608700, 613316652, 543172300, 672120730, 227231114, 896387252, 321718411, 122372962, 868200118, 916929641, 921218032, 594525672, 990653493, 292502085, 471659254, 158821416, 674924857, 176098528, 5175459, 878139168, 218453250, 787396854, 657975744, 113209817, 57706219, 126730029, 66263753, 893482064, 14339412, 854342145, 749741683, 281497213, 347677813, 850597458, 793919412, 499514872, 628261312, 939449384, 774419275, 545705863, 577541435, 582302412, 578906638, 324910212, 406421100, 736929734, 154004361, 838352800, 602222541, 44999859, 721906311, 123033182, 597119224, 396371507, 397905732, 685016360, 577840816, 904741822, 377776228, 610002988, 686704251, 574613800, 270442545, 967698632, 237152043, 869394488, 470755564, 983694315, 977648085, 612378323, 152162844, 368507384, 470092530, 702130803, 783561003, 682423981, 87702812, 9884061, 580678054, 521402089, 150050715, 717689080, 717854976, 768800254, 373778234, 663187426, 690523948, 358780099, 267218371, 122410794, 875357658, 885209429, 641043613, 765854306, 707530278, 754398286, 164008949, 233311813, 164482382, 241030046, 92179998, 105190978, 346985157, 492611435, 14060941, 582548250, 683260302, 698363934, 249195810, 458725556, 887742027, 959735645, 58424727, 960119504, 913848988, 431068902, 155733623, 420228147, 732933102, 906437447, 226762676, 914815038, 78522387, 401016415, 430479404, 373994386, 180166242, 460678565, 491282562, 583592933, 661497927, 272697030, 615462830, 818480692, 157704423, 454038021, 322646299, 939726426, 760537471, 952217740, 900432681, 221587439, 63955070, 916476614, 927518966, 125576432, 494816959, 663352124, 949480835, 481215781, 319882571, 596489643, 554480587, 153754651, 185007264, 146757568, 362250926, 893069636, 972186061, 466464713, 625199848, 252752498, 683513777, 505049176, 143577523, 520882855, 997345766, 179647677, 397433222, 849468779, 643395641, 553193530, 691351450, 923553326, 164205768, 736900198, 539899796, 812700836, 126546022, 355774824, 341328201, 453080677, 438912389, 400828783, 814377781, 36357777, 972777442, 847438580, 444090785, 321509903, 102932533, 859233003, 145940239, 626627904, 490250368, 874016922, 136325156, 26378559, 748244880, 749560048, 534475657, 931425758, 509463716, 107830810, 639200610, 260451225, 637324055, 186486243, 712276447, 549838179, 730799376, 484246655, 405387636, 945312860, 48950903, 243460697, 449010103, 73228044, 79440741, 619603598, 407485317, 651543679, 604192861, 180511088, 684644061, 521482947, 129294089, 275683493, 840792922, 580366969, 713151468, 401846047, 508162869, 770462477, 189707571, 492461183, 577821626, 899892721, 30267051, 792225991, 255958816, 484689854, 98018887, 441240377, 689787753, 76474737, 854806007, 409202531, 267247422, 103744926, 360928176, 79695443, 20597184, 682738919, 727206361, 640426987, 912022283, 944990728, 362948979, 371905153, 130127062, 925722970, 675624472, 237203198, 228470782, 738842112, 657619066, 482651728, 370957879, 80500014, 542905792, 824079230, 798176829, 870830864, 293636709, 533943409, 310858390, 292358384, 101712724, 813946829, 43182054, 334645815, 253921347, 942606446, 31442838, 475249830, 395062553, 83808451, 874530548, 498613552, 165461583, 819224926, 550688932, 501715316, 554837534, 820093269, 784122504, 255424812, 1081882, 804341490, 418979129, 29838670, 169714352, 995418081, 710699504, 247231126, 654252158, 406640353, 5954554, 899066316, 188410451, 988950482, 768183224, 763118680, 584894479, 594197625, 716387422, 604824289, 680159355, 306774317, 308761125, 725817718, 758909232, 858954661, 218339602, 968051836, 839776100, 274452600, 406683013, 577563758, 928071352, 457812644, 254507290, 597683907, 4010325, 454416665, 804849713, 770576076, 458607821, 249457011, 847069905, 431474968, 235307613, 833740754, 132015845, 205074981, 528944081, 94072284, 792771999, 244560380, 962495000, 456768040, 95224687, 724089935, 744385253, 975845938, 921764592, 928414002, 181447977, 845669950, 292953684, 342900506, 988039705, 791226290, 225846072, 704725754, 375635333, 689890795, 376413002, 919756731, 1839982, 224106705, 823079071, 375528286, 571443726, 131510099, 742937864, 990822229, 685889689, 410171494, 804674773, 364003534, 639186181, 452339637, 49223137, 113922173, 819679946, 218040538, 883322995, 782796703, 57154167, 732323014, 971562992, 213660041, 378742683, 918247605, 958875567, 3495003, 401805931, 212498444, 34134670, 908287997, 411002023, 451491166, 538882614, 549001309, 574267416, 349091693, 624635886, 216995349, 477606345, 160521636, 195612595, 902478083, 661096349, 607875922, 486998155, 662128699, 254327615, 450760543, 416060934, 501672355, 66997675, 142337022, 361788685, 180167815, 28852057, 700045886, 344098297, 930179918, 425376569, 146104427, 696798801, 146772764, 517999871, 34879348, 548182546, 34146834, 691758497, 50848326, 433993386, 868545534, 487297434, 499753551, 23904451, 257485803, 857755558, 827592947, 80301637, 468280797, 377375348, 975827562, 986593419, 483659910, 816580871, 996402484, 957662681, 217017618, 284899511, 360769730, 784760225, 609867027, 768303477, 465644257, 767929942, 169999437, 663635048, 681341151, 703192969, 248469762, 601669017, 924963870, 601310460, 961634780, 744962727, 9823178, 652984889, 412086197, 567215957, 667180649, 839845953, 981929622, 18592808, 410750525, 161533608, 556851708, 326454362, 971755456, 980806772, 821759082, 624520118, 406943131, 16204871, 732047681, 129389687, 170524272, 184243024, 129042299, 980825801, 617574143, 935893611, 989347277, 820031986, 630985553, 645402579, 538419871, 812365107, 417580094, 44437385, 11895061, 338332760, 276344423, 740060895, 906005832, 991295653, 575442355, 252677775, 388951234, 855886537, 323767990, 570721040, 766631751, 931326393, 994988010, 471186498, 678987620, 570662059, 967535714, 774247009, 729203800, 15033759, 222075846, 277743892, 512347825, 924498761, 60635466, 835933821, 147052004, 777241745, 44854682, 440154871, 24690496, 233738584, 56308577, 598007086, 963814576, 561719994, 818672972, 780569219, 564241230, 689263344, 668008912, 790557134, 806786815, 28588306, 295365233, 119238593, 147915534, 639803943, 841289049, 447205977, 226912415, 105515054, 41235325, 805913791, 349872414, 150993643, 53677628, 361870764, 893255497, 268701280, 910184408, 88803822, 259125827, 891916340, 642511329, 319813050, 794116009, 301694523, 600751248, 211125843, 784055521, 971299574, 636836323, 867626206, 493576363, 443582901, 186877774, 136524037, 243076189, 22973421, 200676866, 328692513, 420508317, 451373669, 160301946, 349471833, 966657640, 962719709, 874989659, 280676244, 920104613, 159001571, 42580632, 168151822, 278662634, 55401924, 138104133, 626433971, 496354767, 103772982, 32285699, 586273910, 571133272, 506497659, 380909199, 703333945, 528523985, 872532356, 469855684, 161160737, 94940528, 909625591, 815645282, 965983354, 693463067, 61975531, 147449717, 338790683, 343964729, 516945226, 518102604, 431322663, 720800910, 15118579, 815503891, 184138894, 69778478, 100864742, 689329746, 939551956, 946151636, 775326698, 310364574, 368539007, 459961408, 172638014, 629486367, 37316388, 323483178, 309419569, 263866543, 300112668, 993212917, 311331533, 348689239, 831344165, 199659349, 3129267, 51309861, 741499058, 111994286, 300925606, 786444082, 971562325, 265159696, 358667389, 487148100, 225955226, 440434595, 285239998, 792057782, 82848978, 171504470, 218454092, 616540252, 379268562, 588336457, 998007040, 226384480, 638257244, 80076913, 176947599, 470967767, 477790323, 924013282, 457524220, 336388565, 849970676, 193820907, 357919452, 785214207, 893567055, 720163328, 285229595, 175140092, 283853122, 628750529, 174123081, 861571311, 357976802, 257864974, 777615348, 569793544, 98070929, 676988906, 970394269, 998528423, 920311700, 548863396, 571481906, 30031208, 48162182, 315370888, 163987457, 488670509, 798059948, 590095690, 602425902, 572145445, 54583146, 352670036, 71458305, 524384731, 419882720, 627645908, 500674250, 411438206, 315487110, 347926083, 350553012, 812909793, 424702408, 745527501, 385533634, 650198382, 585910632, 203800018, 678341767, 315924129, 470275672, 374076421, 438390347, 192311479, 293429756, 846100744, 484992012, 79219228, 948593872, 148208407, 541661350, 383950217, 117767843, 267981443, 359546755, 510694585, 18652205, 915974379, 340016967, 316856932, 437087477, 440423998, 169573632, 252707841, 106889569, 243442399, 329472778, 728138703, 789657403, 198742171, 263431290, 601107140, 252565080, 267854602, 564648396, 362616408, 210691155, 350601392, 983130132, 453268996, 866306649, 336528819, 667061855, 205525074, 416068902, 72582702, 660370770, 21602478, 753978849, 214325740, 631993153, 13848952, 996994544, 124881499, 513808143, 462036449, 950411648, 938909904, 956914538, 401882325, 669815741, 442411536, 118477579, 782681610, 496799526, 259084482, 960603022, 8907660, 785510435, 280199889, 660974826, 391337252, 749431530, 996809580, 79583184, 735831170, 538699411, 3986019, 636863483, 607328870, 688231029, 731941397, 561263428, 923145536, 441266641, 397923396, 557841264, 564647729, 489836187, 185622162, 196538638, 902101049, 157556786, 312756430, 581287801, 905420444, 490683697, 280310144, 257071399, 788487953, 580841493, 580083473, 184913948, 469132892, 689726950, 247317255, 673386147, 933323572, 649976355, 582460493, 932776911, 978146704, 808566567, 131029178, 389151934, 377068530, 199725285, 401619154, 42900393, 445950256, 401021112, 670501212, 732136025, 291004243, 4280844, 144352032, 478437570, 136163062, 22439260, 738144182, 931008168, 632395809, 132860274, 271756303, 450485010, 430172904, 388951162, 916914248, 347124586, 30112647, 48430589, 549341266, 904671958, 325320312, 187505977, 847544548, 592423680, 161520612, 581247334, 622935983, 784235700, 130701899, 859397094, 420304286, 840548713, 851906099, 847825628, 558690474, 610894224, 409971589, 248449143, 753602440, 514229638, 875473387, 496771298, 238457611, 45913475, 705483282, 109035065, 812219169, 82945314, 686587182, 486315004, 515341846, 216430206, 371476833, 111020143, 987820446, 791638954, 189922730, 22289530, 504207376, 870289042, 522679937, 867944916, 241391437, 834340588, 335012142, 262910187, 734266063, 206172810, 426335011, 119983324, 174942817, 962253968, 561241667, 171284412, 636491079, 357164637, 757989294, 960188280, 297065958, 959613695, 366715119, 480805495, 680886198, 108434486, 658315368, 580781234, 298961435, 819648743, 448396682, 191769405, 413070021, 338450512, 793560713, 429350602, 5953061, 941928046, 986034853, 439545101, 964065261, 716612277, 582886884, 66263778, 391684569, 528441565, 922878964, 2368064, 847605978, 42857652, 656572241, 178917208, 819134315, 94677158, 77002932, 350045529, 797949268, 282995595, 94995093, 210941196, 630012810, 344612556, 752579800, 603312683, 134802298, 729330124, 684517737, 449255516, 732221964, 293508036, 830984827, 385150800, 425460074, 478225360, 953499577, 146273966, 535693555, 344786213, 782594615, 103596855, 532758843, 34613721, 155606245, 630807778, 889977184, 727949107, 323956778, 390745971, 179413685, 79501805, 970192987, 817448127, 733513172, 248076636, 958838442, 947924997, 56893442, 909701229, 599283497, 682630601, 848320509, 501929787, 806692048, 52230183, 896284241, 912833243, 925609230, 932936646, 692440016, 301874917, 185843502, 181644767, 727983272, 192332519, 670580547, 724973757, 591182077, 268460855, 735353334, 904235917, 188317922, 888930327, 309973167, 735630348, 764771721, 193606761, 20257391, 160163731, 394112810, 292556318, 236168651, 163911726, 120772552, 103920549, 973229692, 525147934, 887349451, 529528346, 681690824, 114054868, 701527180, 656479372, 47211740, 741707115, 667820215, 595062964, 134087781, 855107355, 976735985, 743817889, 222642477, 243084474, 269817752, 442614723, 685444912, 386159202, 682847519, 969327149, 643072027, 39613122, 329364727, 232843747, 444298841, 967209354, 641040939, 153142999, 498123212, 428851597, 849405915, 440639129, 871117178, 123596374, 81346658, 596215404, 906809881, 750479568, 567423275, 428882919, 544165548, 381462852, 26193817, 959211050, 212308337, 582721686, 195377886, 762519256, 31797886, 229761351, 647752443, 137400388, 711254972, 203521234, 874425518, 239562455, 947730476, 782944731, 174336441, 677112082, 97896315, 188683074, 995286011, 96243316, 366262804, 638476876, 413083525, 35070240, 983217102, 132945753, 176218134, 324538820, 469584297, 452525437, 285552678, 428454109, 249897492, 302435334, 942682025, 96680475, 628200075, 625315780, 323819912, 678361023, 471787648, 328490738, 287017865, 766087988, 104027778, 108620917, 549973126, 618670330, 684525546, 336399626, 817890626, 945553112, 546826216, 854261902, 213992804, 682834780, 227463102, 585275290, 603586903, 651670470, 947771924, 117214732, 518661633, 183387238, 248633075, 708735526, 562836699, 263981144, 564995479, 392835919, 656309098, 749484942, 989728035, 376119257, 962953474, 537921204, 281854422, 427358976, 966975887, 798653632, 532681544, 681364101, 721792974, 140288494, 502219879, 347902674, 559097166, 358783724, 709031787, 714634975, 956991303, 736448743, 312927464, 485319514, 563809517, 926212704, 778041080, 149258548, 874929181, 668642067, 234384280, 728838419, 103680275, 397840246, 984156124, 661898714, 796767660, 145421386, 839082528, 114697275, 180154324, 814022372, 312263593, 755598747, 147623557, 16294144, 213960942, 545488542, 313286999, 316314685, 155297346, 13783134, 535429706, 708444258, 93717437, 760755940, 880601217, 916921836, 175871975, 724729278, 637843082, 544964304, 814581098, 216771338, 601826716, 598466968, 453646955, 565333411, 463808592, 605619067, 79120383, 109341503, 920539882, 40448815, 264943981, 964941306, 535840515, 703724999, 392781304, 988846519, 146880848, 581516940, 461266736, 991942970, 351330773, 697310691, 275606735, 458196520, 538229558, 837311516, 320157928, 563841407, 443067420, 790259551, 937906063, 7734929, 629418218, 739972635, 253901870, 183927010, 594572049, 728960919, 374361201, 840045557, 481619677, 273079652, 2350465, 435355504, 83955938, 643126125, 803640365, 803729988, 623422534, 267249059, 26857414, 553460825, 524688064, 624494055, 95881198, 925034096, 2162590, 748495905, 810877147, 837111984, 132060726, 671523574, 201777605, 734685911, 324222066, 136012495, 745040898, 361327749, 712032021, 842382115, 235854152, 359031475, 386863477, 866670761, 235885664, 552572804, 657718486, 636140542, 929971793, 549125356, 655924750, 189815157, 846139984, 119076093, 146136363, 718109164, 199851215, 548904570, 917872396, 148761533, 612515835, 840088362, 420294069, 687144102, 395852367, 930249590, 359331082, 153013724, 810582189, 449456506, 255615884, 851499307, 300133549, 232994488, 600441166, 559242926, 953890971, 992881096, 651532658, 697194348, 861022377, 141951983, 715556227, 608870981, 822163138, 282846174, 309699916, 748617148, 825019626, 120516327, 547514923, 603699724, 499746069, 187287594, 796048187, 612887460, 246424092, 995999823, 225459940, 83960964, 758501974, 618085698, 544264334, 737887618, 63079131, 313131524, 453601555, 699137881, 580843061, 133225620, 71056546, 705450987, 754601523, 185556287, 295904860, 329592280, 225944404, 217627313, 371596510, 417268664, 700900190, 312972669, 903298303, 828271073, 559088294, 231974096, 344725102, 125767321, 528663412, 869516935, 943491247, 682127376, 306784321, 235294015, 301436899, 269292283, 816555679, 818126727, 393584521, 954516685, 344308938, 691826372, 278811066, 323303841, 332696304, 264936089, 488226740, 537166370, 724505685, 864681293, 988496260, 156143476, 597599288, 983070127, 581904290, 466934858, 364036565, 278930480, 926994905, 703371818, 772030825, 291619437, 419033482, 855161445, 299000591, 206283340, 960010587, 964323976, 989838508, 363854560, 596777835, 380853670, 366039001, 790439445, 935594359, 271674448, 230202471, 356539077, 245939830, 291836878, 709083562, 827374318, 467936050, 974766537, 899956474, 245152841, 134424980, 736463811, 746016845, 83795152, 789487271, 700611465, 646641584, 259346301, 362747979, 684366287, 51027934, 895278873, 481643936, 414101397, 931723679, 749222736, 251404085, 145667451, 707808044, 182242583, 141134924, 991902258, 77114999, 118980938, 842411594, 381208299, 231692597, 451232892, 912310119, 739076790, 341406312, 502643091, 155839684, 790200132, 370367613, 108957014, 102705540, 875568064, 588967951, 645400124, 845748347, 124346572, 201849797, 879850709, 60638398, 707878279, 633573623, 387949453, 589407593, 399939845, 340223721, 95958947, 798133771, 123577506, 690181918, 204689593, 723775556, 912655457, 675418641, 122373652, 342538857, 381045431, 210575632, 842829131, 289371934, 834062245, 87043014, 200804860, 642849830, 567598452, 152815598, 459440899, 237530418, 674542604, 956067033, 38367871, 905619929, 631789795, 282780494, 869335178, 900012177, 818885498, 224157346, 238512723, 52167014, 70098021, 900131785, 652237166, 142393312, 967410949, 48852687, 549505062, 151315131, 68107520, 481137284, 954372332, 349869726, 428867625, 661640439, 988392345, 562477770, 471393170, 590252585, 228283375, 882605925, 830431892, 56890864, 168720210, 67310399, 685321690, 231948257, 86815193, 351832357, 797204161, 306207862, 328799709, 280990138, 875638044, 903264057, 209458804, 612555855, 979321801, 111855627, 619822053, 248120975, 559092919, 703083443, 51404116, 161811033, 223545428, 401506770, 378865307, 804471811, 697678865, 894828203, 155496351, 809953324, 960051295, 509918443, 563499961, 384296715, 499056058, 774329241, 783285144, 569217708, 819543058, 21200376, 729790186, 959570454, 867112589, 317749624, 256766039, 980091400, 406701926, 838098067, 461138118, 676348862, 215072648, 625298807, 405887456, 612803826, 975445130, 746688059, 278737402, 701864808, 166514608, 896654911, 821765968, 525342111, 774106881, 235920200, 325168445, 700692214, 48332305, 160900224, 413821769, 439197063, 896268668, 811703619, 37660191, 393699640, 463788166, 617838295, 358278376, 798780230, 810650097, 720768406, 253191197, 743693715, 757890924, 32278360, 178775255, 286534826, 639642998, 61596883, 649262900, 618602688, 731365106, 446542385, 549782976, 614246769, 742633799, 870879290, 387598235, 821561904, 622268470, 555922322, 425016015, 178527934, 529314711, 189222790, 343391814, 742601893, 48855808, 834439768, 738259912, 986824397, 44205841, 465282457, 362436617, 281557170, 697252055, 421622548, 793275891, 472121631, 729724370, 113334202, 172107389, 945774381, 80163070, 659737062, 452243356, 741304242, 557020488, 25998478, 445754513, 843321643, 142655784, 926691461, 956266541, 299200232, 325041263, 582963906, 182884428, 810208714, 776663497, 935796134, 246794724, 753957204, 878846825, 605702752, 492279222, 514118294, 434581593, 307023033, 828379793, 863497756, 980708014, 307150294, 911378286, 751505071, 665564608, 263964219, 237983645, 440132621, 670225984, 833912890, 524153067, 554516693, 703913003, 375427253, 205811627, 711783980, 267010959, 255321173, 920653275, 678343582, 471694598, 917324156, 642458584, 43941735, 486824068, 208768226, 494618621, 808674675, 966711433, 531185651, 252954246, 496252267, 943661490, 540824821, 891995746, 597152184, 251646910, 778651072, 551825246, 231105659, 596865601, 274733551, 429630594, 320866759, 427879147, 412398869, 71647561, 748208189, 157662435, 872492150, 851710541, 919755601, 196422947, 819099367, 849479766, 221853201, 282854892, 774145641, 112487324, 126044274, 787461569, 112445786, 476172515, 443450430, 508778771, 5395576, 772173898, 21910541, 124237776, 180203760, 314337557, 744528824, 637484454, 8702526, 562019173, 173531669, 347089809, 321561942, 704271528, 965129958, 527464356, 465609029, 883248213, 41728750, 273360639, 149351226, 686622141, 842813077, 512184982, 18022676, 833705669, 39758546, 472058205, 182954011, 944480471, 599202214, 411924464, 722367505, 477484445, 88572130, 996774307, 908728271, 955738218, 322769162, 158627028, 473591086, 995793318, 631779904, 245479192, 278051091, 371823437, 566022223, 457146103, 535755660, 448174498, 280352182, 68680985, 730835832, 135910580, 387227277, 875288473, 443489763, 872466314, 923362864, 598554013, 409025615, 353050524, 257698493, 18631209, 900098477, 651152100, 364598234, 915113325, 478937968, 961732421, 406552237, 964167033, 203316272, 974350904, 523570237, 401100451, 438133214, 470177957, 686792903, 155498072, 738550700, 753626332, 853876646, 750451198, 962348170, 826185480, 734782443, 560061063, 575826394, 823818562, 717979669, 84388530, 951398669, 883458798, 226832531, 620795519, 92525922, 108589328, 843355577, 650157608, 520909801, 655283859, 305787552, 375750882, 28722234, 605010248, 449110059, 447652199, 793646031, 563131306, 971666324, 652448576, 376880295, 788743601, 735468533, 31965161, 310835020, 838042887, 925753086, 960112390, 545636609, 483477384, 761412924, 647930495, 422924217, 534777769, 357689055, 362449103, 680323028, 830205766, 590466975, 961173972, 659629864, 577257930, 181635739, 723387461, 614772090, 114533602, 224753571, 798622135, 665797216, 469430367, 888315891, 137048142, 387441032, 791558534, 158618858, 724555995, 829899136, 118945686, 408346658, 66074953, 836198994, 200733677, 990058841, 977021988, 645597388, 432968258, 602367819, 70608267, 85198549, 429248497, 515499713, 264751801, 829430041, 247121299, 560448993, 335526998, 552800864, 56619218, 126128790, 333810257, 834598653, 673858949, 917703774, 490596899, 597851871, 949283412, 375560421, 852190511, 110031150, 777373336, 573910543, 623960704, 317057846, 761329138, 898886450, 586190734, 368970180, 93611430, 49463570, 584113656, 48581324, 498627749, 625553709, 337168010, 635562267, 827020488, 366124443, 269775528, 996406510, 121939195, 155654252, 945666556, 653271735, 703643132, 375171106, 344743950, 32766206, 220872711, 847373337, 77796023, 851662626, 690615951, 165062786, 285135414, 47560482, 232866427, 600653309, 610921009, 946608452, 370659752, 299790833, 556797077, 317392431, 728996921, 882039312, 812101131, 541300161, 91291937, 989542177, 397362663, 973531403, 585584450, 981982480, 316039418, 662551037, 226915103, 203312039, 143976765, 701906082, 444690820, 802868661, 396580790, 479768532, 131383596, 371185447, 879643865, 130426830, 260811502, 448547222, 922420153, 383368891, 758309537, 40083386, 785278508, 617301368, 535537491, 117875822, 193695507, 124504197, 990371664, 49468839, 707942762, 256810044, 593974449, 233599970, 31655224, 904044611, 906498658, 617446460, 625281483, 89528403, 53993303, 926473334, 814352834, 654304568, 648489131, 737846091, 738205639, 296718864, 44141185, 650029042, 902426598, 866500627, 129073753, 321274121, 246275242, 441183119, 565390718, 705057017, 402143260, 755711259, 765500561, 974247985, 232362235, 945257581, 573646992, 675480090, 48897954, 966969220, 539643045, 125642860, 967919172, 177385483, 264547766, 448730589, 733759180, 100479216, 962184608, 449324466, 527173438, 620232651, 1044952, 874791617, 799175430, 898296760, 220025969, 747480294, 828226551, 659770121, 985165667, 916201836, 227931653, 770252648, 93338716, 72106530, 663457739, 891661893, 178804041, 412580526, 973077257, 650521984, 316426544, 853350714, 907065887, 705009272, 316153240, 992177255, 992846158, 771923063, 900470907, 493143686, 243324252, 24066574, 202750130, 40908373, 313466710, 803559886, 481696294, 686598392, 892411813, 450625766, 470761109, 113762999, 246395466, 352718947, 647615773, 947930311, 140405987, 341230165, 782699586, 395590923, 897340652, 276748572, 159229100, 563231986, 306441809, 951344915, 963418938, 858735686, 284719727, 25037538, 39519376, 328287270, 669581793, 340974699, 408799646, 237651490, 499872735, 391283659, 188930278, 14579922, 436349321, 39741399, 219903454, 316386652, 790332018, 496992050, 470225844, 392107810, 542286639, 683503552, 332990074, 501545268, 797877595, 851307077, 191451209, 593189406, 976476183, 918321591, 340620296, 558449182, 302661099, 582112417, 844539054, 352913972, 853947180, 681440402, 480309828, 312390779, 784437523, 845403649, 915154630, 41737835, 418090345, 906117797, 349325996, 610038593, 724067955, 356683495, 993853901, 462716332, 148537044, 73972169, 55868155, 203298394, 906864604, 916946577, 815084987, 353891572, 906977314, 782787956, 938121265, 133361503, 472549069, 652414305, 974730419, 426577822, 692131182, 216483115, 33029046, 512325951, 762412000, 550037408, 250169400, 482454718, 924596609, 295013073, 252338038, 495012452, 895549135, 748123400, 816076489, 994413346, 781832298, 951782049, 317176914, 430667904, 191375258, 447442954, 365645416, 393784330, 181436151, 713216279, 980911505, 504089297, 65076019, 732200793, 74283652, 489241661, 969314584, 31956688, 842248434, 812446840, 368730011, 448106162, 847435078, 549798870, 912049413, 324857159, 204461086, 97965855, 864245858, 946407091, 786731601, 187637036, 638243015, 547325436, 819807071, 470771042, 240526815, 659446570, 253216426, 529583416, 544137363, 678584562, 262948389, 813002202, 193256116, 709494303, 818194550, 321957140, 158070998, 401790555, 632402171, 405718294, 234198655, 449015725, 494852498, 434910352, 612575771, 196481955, 417211510, 52952574, 244013989, 304062532, 479964333, 846729316, 362553474, 428455502, 905540917, 466451311, 690422856, 347383216, 686096120, 166727250, 372543626, 803971123, 413072049, 744530051, 312646817, 651860642, 315617765, 198084912, 929952566, 676044212, 990101537, 846609042, 869201595, 491651700, 691213736, 177812976, 496589603, 3930285, 142498882, 351086654, 711706061, 513485816, 209016986, 198161565, 318175126, 358678168, 813550908, 791699733, 512842910, 761190592, 731977554, 101762387, 37165904, 563710129, 360917323, 771155987, 91700843, 333685346, 210741277, 351212133, 894445529, 990359789, 415394517, 709048551, 389320136, 897199670, 424202332, 902697222, 635339264, 213404382, 342834996, 730302689, 367146097, 841718042, 4313027, 806444681, 940519228, 979508489, 773507913, 599663776, 967439090, 629420342, 108327119, 35524987, 82559623, 717646284, 805656152, 123938029, 751486783, 89742755, 346532241, 375983428, 362705648, 656151728, 848359521, 960892428, 40268492, 724016588, 311541664, 924532927, 315322301, 46946254, 880835131, 725337175, 233766344, 747956046, 770317769, 933188723, 946460600, 864177419, 202009922, 272683751, 996809314, 404589018, 505837882, 400155825, 764075525, 500977568, 304999105, 54297704, 308255967, 437865517, 593531618, 895412304, 780615091, 68238547, 892242202, 383510860, 835955153, 288007681, 290077607, 725158530, 991253866, 293788780, 499353262, 276190170, 164662264, 814684918, 761601858, 797778622, 176538697, 485855967, 242199137, 922649146, 863508678, 978802026, 327919610, 26942222, 748722068, 124246020, 250811278, 72880381, 586980827, 920279872, 743185684, 440647170, 115741740, 276079905, 957864927, 774267402, 81995601, 432648533, 662176181, 963624365, 947057721, 654054611, 531487020, 719409054, 384158510, 579991564, 199667250, 776044571, 987282549, 649542720, 37020691, 295051253, 846724699, 359612190, 10653281, 637124217, 234492826, 540541846, 578177177, 517822507, 378166291, 867677699, 958440377, 965863764, 610905036, 584303209, 778017021, 240318797, 967976383, 248393477, 673311159, 535544123, 508829646, 947511145, 440416839, 398664266, 775721188, 17901182, 928525010, 822322956, 76724319, 623014478, 941705693, 693690529, 799833328, 288626941, 121536345, 29787496, 23272066, 913803437, 148025489, 506731940, 330899927, 936065945, 185207104, 81412404, 583456663, 92789617, 794426427, 554662868, 914244242, 641814454, 563110357, 521580857, 796274956, 17062014, 453680425, 825067718, 701019445, 488772760, 166482561, 845662949, 790848412, 607962624, 926785143, 100325840, 845605469, 536504365, 172738902, 950150836, 157103574, 624217053, 972972993, 229128307, 890024802, 99440111, 655833077, 272720878, 8001316, 386306681, 459407657, 206806525, 41044464, 504743238, 681902765, 551407904, 822265562, 119818230, 554751426, 872237620, 80765587, 526814195, 496555341, 362743275, 360166747, 362542046, 354383497, 210238766, 949475353, 116519027, 18026523, 141501759, 15744217, 483895806, 220949684, 91981485, 745007573, 816690628, 197997175, 679239484, 178139322, 17349598, 283982061, 969216171, 27927395, 908842560, 55970964, 66320655, 493289383, 51484036, 852337796, 461920546, 609830269, 706227887, 755299913, 316028802, 575294921, 237296973, 646033459, 954387313, 462794767, 938122610, 291992001, 179594118, 398210788, 572467529, 383985280, 522418100, 272067301, 214265724, 64405836, 716238503, 326584263, 959114841, 623204110, 957154855, 882436799, 564820758, 404911711, 948342613, 562074516, 187915643, 797667724, 286119742, 568673987, 199580791, 927453448, 820890341, 631624447, 411314520, 30920346, 155179461, 350791222, 503803958, 192577269, 481384043, 686254086, 559243539, 813885471, 555679068, 613294239, 955566132, 921243835, 555379746, 771984614, 619044282, 970100264, 631210990, 652446036, 581930927, 331033046, 987366180, 330874759, 962816051, 710078737, 459100782, 998577944, 109955824, 603549286, 452016882, 248992001, 907855893, 777689396, 220815425, 402526451, 971033199, 147585342, 269555788, 834701407, 16162240, 546823124, 630286757, 337582940, 349941940, 154747071, 119298487, 915857289, 190022260, 561795271, 553656373, 642416680, 319951043, 675516184, 946555758, 266939045, 144293774, 316645655, 436315339, 424686353, 509774882, 549240197, 202859084, 133531691, 393378295, 481901600, 368771988, 117382665, 810378115, 506524290, 690937952, 747441025, 386328964, 832528737, 342202166, 37409419, 559784531, 385545445, 717082393, 506362074, 118629356, 662734406, 132705240, 354586972, 69079272, 985016754, 488442277, 861389226, 616325334, 586913331, 897835779, 487999350, 696381688, 634577099, 627943557, 768398396, 368364344, 159548776, 368661906, 729559801, 652533871, 847380326, 537829281, 820589246, 735099440, 546023179, 770712513, 195096214, 51184676, 621271140, 77438003, 882970418, 85707975, 806947528, 253849811, 21737272, 584277278, 105047871, 778216078, 457377967, 367761904, 811455424, 897662859, 896918474, 953042559, 354996489, 6668198, 712435861, 313406227, 281123611, 872355882, 344591957, 387924436, 435208021, 284088565, 757485750, 428421091, 479725110, 435927011, 249390634, 828260862, 352897681, 691655779, 612760446, 557450231, 802356457, 150103935, 731250212, 621814512, 901783826, 759710384, 62099085, 497986814, 228689319, 693566725, 821415287, 609701179, 320669350, 901620111, 740576246, 892970886, 669029416, 282096076, 695132706, 614510480, 378360626, 413541925, 724723496, 94799794, 983704806, 778959870, 773072900, 645418474, 172206643, 496822157, 187570827, 636596108, 433258131, 693429919, 488058061, 305507874, 518749294, 504415133, 935823450, 864300094, 563827653, 702396493, 320403650, 153989627, 870023628, 279172692, 362036116, 843808498, 754112598, 835536626, 662973361, 926787260, 978833465, 370156026, 642846463, 612649586, 242945524, 324870280, 389294411, 91821006, 659346231, 568761778, 577646570, 668614049, 610191416, 801266223, 147325505, 202607579, 235877965, 521206449, 18072391, 491247920, 964209704, 871159144, 787595859, 470433385, 666756521, 111238272, 906974373, 619644987, 943309867, 971924635, 682491172, 610970958, 816464478, 551506153, 380296301, 845384560, 777178168, 627304729, 180782487, 257273385, 604623722, 549464867, 742955570, 140449242, 169698540, 939828557, 850804295, 874790260, 312562046, 239497357, 668948721, 673831269, 505813233, 854342981, 848276653, 78116846, 969973819, 187005413, 884876445, 786527118, 755741896, 975523179, 861218223, 72594163, 856342236, 955061670, 71671901, 593910759, 969252391, 962466252, 38276276, 633591851, 846019485, 23190085, 342341451, 612766864, 445533771, 265894038, 537389916, 166353085, 70005218, 863606089, 589031221, 482954853, 39851757, 471010607, 169118392, 467840606, 230535089, 384666057, 84948039, 566091314, 733625701, 243760688, 435349717, 967714962, 645221178, 463066682, 562759383, 525873423, 19386117, 725253617, 292729873, 918693485, 859835812, 787339212, 135322753, 699413896, 875357017, 175303933, 873464431, 300576286, 626326142, 397910744, 323942517, 300471274, 915629920, 21517828, 804960766, 791876703, 120572867, 873499367, 473882044, 987757669, 282881450, 95736448, 421292146, 714393695, 548569995, 376936567, 492453765, 480203167, 958575214, 349018917, 904050928, 163635792, 913991929, 975460601, 184743683, 736625113, 283011688, 150664529, 641802421, 497677548, 162207721, 468207625, 617276271, 971106208, 255731169, 37858198, 418024471, 865332320, 64177044, 536711568, 721723407, 547517058, 427782311, 513592727, 176914790, 953382157, 434835583, 503627301, 120568472, 823696867, 79104825, 625926819, 606348074, 921013876, 928090699, 703668918, 741217763, 648726166, 459005552, 193865966, 639402930, 391985929, 449265012, 918430314, 247871683, 526427781, 721251751, 575577921, 635735967, 160331015, 233239742, 414323421, 405041892, 423269481, 198896906, 794218155, 189728460, 870059533, 472499936, 305274527, 723668632, 955063944, 444927978, 671727165, 845825536, 661838267, 702583072, 128134689, 581116945, 578896201, 719162822, 864623712, 637926046, 649258254, 101257691, 882453998, 131309609, 179015066, 545450681, 514087456, 110801357, 312574922, 95844684, 974524591, 842610944, 451195769, 637728200, 837231725, 994849953, 115344083, 200931877, 693666554, 998179997, 943087158, 653619255, 584810700, 270750505, 35533163, 350605234, 824429397, 700395125, 610765952, 522958969, 250455713, 546099478, 732790117, 806679854, 370390324, 703127494, 605872653, 664916820, 697795677, 109285000, 12848291, 532125980, 930371759, 249008428, 504468020, 554182561, 152600045, 762724492, 521295193, 886043211, 276584874, 545862236, 341460909, 939995827, 421727484, 238783037, 603908067, 148336664, 924953064, 413346826, 472543538, 550008973, 440221293, 713306025, 690039055, 347809902, 132728802, 290599296, 366753108, 520884267, 577759492, 570052878, 58429172, 875302319, 824983291, 603667506, 685978649, 153547422, 695755808, 278672294, 778223620, 702153480, 154267155, 802710558, 834562236, 572544908, 820033270, 707853596, 929407866, 423996964, 638724431, 799301883, 445927712, 256211254, 45009795, 964602840, 614887086, 473764531, 837203556, 780870684, 198614492, 457100505, 118101105, 495015067, 404215164, 405963468, 879392327, 125063008, 337277397, 776761253, 387315726, 43255347, 289117850, 429721568, 833863090, 222855094, 733641616, 28916669, 654893178, 915685612, 790422521, 938926337, 711829846, 786695410, 199284649, 106983614, 785313535, 56824911, 666430714, 229034434, 867956206, 705437038, 311123410, 578238881, 625014416, 520587004, 28530274, 799492901, 519512425, 354354371, 359203934, 514037109, 579287066, 40980093, 798543539, 86417691, 623355981, 381866757, 922861308, 878081616, 504912285, 660888746, 118746150, 576676168, 206081698, 507473097, 584674059, 290605157, 491761076, 299110119, 9955174, 275454371, 392094021, 93319559, 223706189, 580266070, 908032828, 438271143, 428493344, 708933469, 20931259, 745337821, 52421785, 610288959, 71586602, 989659869, 342634610, 706586853, 631961315, 48986496, 312644007, 29766387, 834637363, 931945956, 460144696, 332035306, 786464081, 519715711, 140909116, 599066810, 525874842, 71173980, 407878913, 211554331, 636512351, 520133172, 873237549, 195016256, 976366731, 99996747, 67452709, 913600950, 257002624, 909637757, 567717873, 189602049, 885571169, 498002808, 168531706, 226972467, 582358104, 952602958, 957189485, 120601339, 647456831, 118376096, 822977980, 140262582, 478483929, 34894687, 952692666, 92611159, 339100333, 587067700, 694754188, 499023511, 398949014, 194530494, 503891134, 590144570, 886207477, 447895591, 456368129, 959528930, 33608168, 389718730, 808971229, 300743435, 868960284, 885760553, 510273656, 112921352, 778655718, 647806864, 456490073, 624096489, 646563031, 448403357, 929520491, 891166314, 609350543, 728330103, 278876507, 725933572, 100835178, 657142542, 450272937, 719438672, 665888034, 737955839, 222943908, 884821469, 985571424, 855411249, 62772463, 996688002, 475598332, 79079839, 904904146, 62894403, 633970161, 993814930, 990993344, 924172907, 972750798, 113184466, 135320443, 359322552, 104163950, 742715925, 879737918, 378847336, 274506204, 832370787, 991570048, 519150075, 478013526, 88848534, 969332950, 37288029, 696767609, 571942006, 675431001, 389323006, 617322853, 790580784, 388318327, 532313247, 907234407, 798742378, 609153752, 146245811, 130912812, 272152077, 479563218, 354968638, 345831936, 589166114, 268442094, 994261268, 460267230, 299625075, 985041278, 969638247, 467935713, 911095004, 494386141, 564815076, 601899392, 991105543, 269209594, 420541135, 338860761, 97609409, 197350252, 320212008, 538243644, 900677213, 392093095, 229727661, 290440207, 945731494, 264527472, 314641158, 201504846, 712821515, 397150366, 271527131, 382308257, 293827215, 677016548, 495822352, 742947971, 819303177, 821452071, 401724294, 71005403, 682268247, 610890273, 591195824, 865455197, 776828260, 141848417, 500825731, 480240463, 634818064, 640032449, 191860491, 428907065, 318018757, 817389079, 359687806, 573648856, 533958869, 740311800, 820227601, 86672685, 22987391, 749849501, 341859539, 818166859, 70993488, 707811098, 89724463, 115828962, 749488545, 151344794, 230705064, 530832728, 517707839, 647826881, 859533781, 883479686, 845500091, 704740477, 581245383, 386975655, 779783744, 395610082, 272447383, 204963666, 399428703, 911011983, 152799301, 283296552, 951542196, 702188635, 326132295, 3518524, 772401578, 914225041, 380946398, 514687327, 146843590, 491000627, 999145088, 922738654, 452494896, 190968935, 885010551, 601628037, 943242211, 502058206, 615485575, 763189649, 899244519, 624615923, 84602775, 894472852, 282740949, 24679282, 296728458, 171757072, 786211783, 400358269, 736916675, 915329710, 601321199, 438365468, 573205988, 697733728, 79423685, 174722553, 810295102, 423887149, 726560267, 701487460, 854738798, 361803767, 917926019, 382667243, 16857553, 770326447, 766454410, 925784730, 874537095, 422442738, 789163678, 518659278, 555171414, 137871610, 812321722, 787421783, 114427480, 608366963, 475651937, 259548850, 11257041, 105644045, 31030178, 200203792, 626072257, 881334152, 741024777, 246136840, 485612512, 290094502, 785608395, 364709515, 111401157, 448080266, 848748527, 202744637, 406207528, 951971976, 196498792, 219994638, 430753246, 41907921, 50090755, 507288974, 851100191, 150711034, 185184434, 363715005, 208372238, 442238695, 184775073, 330350084, 120056672, 911016541, 590098192, 292211370, 945864024, 595006327, 717549070, 453423086, 468229912, 510094179, 376925322, 801382017, 716185894, 866452845, 582785185, 937305364, 917679636, 675396144, 419710425, 203832656, 964444087, 978169792, 531013164, 433446551, 243074267, 555600441, 326626753, 676174870, 894295117, 87113997, 530887097, 565402930, 808346054, 731390034, 979424833, 945717731, 440783878, 14531218, 755145220, 397246327, 120678701, 491372993, 921306915, 173281061, 830988627, 695978989, 846905594, 721145678, 510756224, 467272661, 769762270, 523636362, 673605071, 641043672, 590034667, 772854796, 938943598, 547426985, 254491766, 501178618, 177416255, 825361164, 34815177, 449638180, 174911001, 501447468, 512828912, 341285144, 344359783, 576074197, 913849585, 207899745, 720944505, 666483169, 267852718, 25184021, 72214146, 913460738, 716315843, 582704602, 139527057, 194090549, 667803162, 976906640, 335051167, 817145750, 861104511, 190788338, 568443359, 793546061, 67955850, 645797138, 297456168, 462934768, 528562812, 790199250, 958239958, 575191807, 858772587, 30848023, 698502171, 668299072, 165842207, 845955454, 912517236, 383700310, 865379880, 507401442, 438831369, 761926130, 818389257, 287294174, 87140657, 51031261, 554711503, 101929939, 29117506, 554037463, 807331168, 668692818, 18987664, 807178993, 257773416, 858874415, 907912829, 68353, 376100604, 36135161, 205399011, 794573956, 132655420, 929044057, 103484174, 264933920, 241963438, 390128691, 131727401, 891818842, 380653782, 424036044, 750689140, 313280798, 159118049, 767204834, 316241615, 288378557, 743423444, 588801799, 41574277, 716344635, 955069987, 83979304, 931847016, 382153601, 407517223, 486743294, 313929828, 871591406, 946712695, 287892013, 988656924, 517690992, 92470230, 327528683, 778976042, 746690211, 785948116, 306413103, 579966325, 74269445, 681277427, 967012008, 451371480, 671029794, 320073901, 522310164, 476177866, 726815925, 676188664, 962201388, 394948713, 40819039, 555469125, 244769131, 773174749, 682308862, 363034845, 380280564, 818714433, 909003905, 497634380, 255580416, 197230403, 382868310, 708344239, 597555315, 727419602, 173559312, 719483213, 478438391, 865806353, 813666220, 619905416, 185710089, 464344289, 508100892, 421434456, 861675336, 882066241, 518005474, 207866915, 902107627, 470228399, 876344503, 284327746, 276995605, 807950067, 157278841, 797490110, 4318800, 979706900, 975161979, 108085643, 683530388, 619727982, 125393545, 269000322, 146545772, 93321641, 966940616, 610229022, 552020660, 967631481, 508325585, 828406570, 854437374, 587553575, 603566518, 691648842, 425491557, 924610976, 846353104, 754913294, 789764036, 403013936, 571715756, 66521120, 305571473, 816554478, 639773753, 27330548, 607821141, 599756211, 759617660, 47933479, 617397433, 270978467, 592437766, 189464596, 900039752, 387842213, 616195169, 509392946, 528987973, 502224993, 761059692, 756699584, 685902791, 992268991, 41870877, 632578205, 262155416, 257478846, 558436028, 971893265, 750985053, 774569189, 735338571, 625886341, 120948397, 652204704, 351926629, 57787725, 781755630, 852095836, 631986123, 468418515, 622166523, 121175670, 618256315, 795064942, 62391244, 75052207, 330593728, 774438442, 901635317, 995728790, 35449154, 977756089, 102222121, 536299436, 540336919, 665274156, 275895242, 435190332, 720410208, 51516113, 107847961, 617865613, 603041039, 97554505, 449853057, 992863026, 840853492, 287108516, 804613569, 536006520, 772405165, 620211195, 232413628, 128811559, 122881008, 991376475, 875267741, 532113662, 321693338, 975641371, 828848217, 518673573, 650212667, 950702252, 866785110, 902089554, 923694752, 421682746, 444991769, 780386297, 568398661, 760846942, 669726259, 424324973, 890220435, 989005638, 951243561, 571152291, 640320153, 129189337, 879292177, 758013977, 118523487, 947449045, 641568029, 926562039, 538009004, 738974908, 389545399, 975850450, 478549053, 885570328, 919903061, 548839221, 596395846, 679356941, 528544934, 664668733, 701827492, 117556191, 179941844, 433181650, 774470648, 30854782, 290528406, 468734480, 712337616, 772616748, 215428280, 99089571, 515908312, 406120275, 207769475, 33563275, 406690076, 113820851, 891849259, 609173176, 75147826, 140291627, 326972887, 769256361, 681967320, 276629243, 286826516, 64950423, 269008316, 809590292, 850939526, 58235649, 614939252, 424457157, 647537659, 358164984, 259016052, 303516427, 785984454, 601184931, 106030312, 5998727, 524504942, 812721732, 461157005, 178354396, 152409885, 516128535, 430199091, 168784559, 662354451, 655147867, 408356280, 187876856, 333515959, 601742036, 610390451, 196384652, 117989949, 650953252, 319813300, 23505050, 304530196, 313942510, 485769893, 830218644, 231045314, 619542891, 437965636, 44142073, 930451503, 187993125, 828840567, 914262260, 213381201, 733082963, 858152055, 15830047, 71270292, 220377931, 40124663, 849009757, 819907193, 791092435, 939876008, 65465234, 933036655, 414625652, 450827207, 656416985, 13444627, 598078943, 677025309, 361089149, 752988884, 834009648, 861506231, 770689207, 884130674, 177224345, 126612580, 789658899, 197956090, 915432131, 567012012, 625435560, 39745947, 113233257, 216878086, 764194283, 997352143, 992561115, 413179692, 741821098, 72198651, 845618824, 137099838, 152133575, 981003388, 545338440, 188568305, 41850756, 84836088, 485289799, 256649750, 815859077, 68143914, 698307063, 341770448, 831413786, 624812339, 839594974, 54603881, 827342920, 371916940, 64291861, 272802423, 595917184, 744552636, 145634024, 525806521, 273973587, 25103711, 357701569, 980437449, 11070297, 517708261, 321408826, 673471887, 987678893, 678824354, 180931897, 462753148, 166585117, 291764414, 312377805, 643609168, 699621565, 603420805, 674729788, 998413532, 33125482, 608908312, 789750750, 589034474, 415906930, 118897538, 586005049, 943865621, 221449237, 234385985, 619537389, 1186247, 748847028, 926973788, 397884075, 7631353, 470189532, 790612651, 662590249, 61841815, 102404571, 951719831, 493833038, 928184439, 443559631, 582039032, 537321667, 561701442, 352735562, 352281458, 561924203, 280540477, 146829736, 963498014, 240636694, 131357028, 305241902, 822732649, 994638145, 332115396, 667609932, 450752317, 120435524, 707879740, 140088111, 397844865, 477290642, 60185019, 81319104, 945057898, 904560343, 21211633, 189105354, 419211917, 658739095, 893774394, 333034316, 513776832, 982939692, 297688013, 366356244, 837697635, 385102842, 136481595, 133364596, 341798919, 519790827, 486874168, 968104306, 193761680, 616547434, 149414574, 503670303, 200884236, 22111753, 111156035, 672306792, 924894651, 326363250, 592093242, 439239193, 299249244, 769820040, 457033942, 412266044, 599768636, 881067733, 664392363, 744229233, 783673056, 522971663, 228860040, 346009862, 477608503, 979729505, 877812343, 472043434, 633095925, 156513369, 30062947, 93285489, 193316791, 810704334, 118258351, 657248994, 563149132, 481417454, 747715626, 823544454, 914145156, 691603228, 513384532, 832889769, 125946987, 475227931, 323210055, 88918569, 687479879, 188136847, 609867159, 771171326, 192609276, 218324003, 635857258, 830657881, 420054612, 659122980, 871737936, 803841644, 429712012, 456911862, 575360313, 474394394, 259342497, 777085595, 554873611, 72962591, 624853492, 130894031, 265773281, 335423979, 822523384, 852360455, 327410962, 970159470, 396262082, 559115473, 779473230, 957412248, 186592317, 713599983, 178937507, 632714033, 226757799, 361460316, 133814744, 318035156, 234564798, 292069194, 903468572, 640668711, 294600696, 762345603, 233738339, 761018882, 288143083, 871731021, 773927439, 284535941, 933853741, 34432855, 938049524, 558738492, 819107606, 220280890, 895246359, 78828891, 743247843, 188567307, 19833054, 744596923, 171180871, 453784529, 218020953, 249620197, 816791359, 324420951, 636927373, 19054373, 868174598, 4355293, 641901100, 765856767, 826232190, 615251323, 970684552, 317949202, 601216717, 731741473, 154589951, 838303922, 953724917, 726742331, 577700610, 896925714, 280269018, 114304879, 910803962, 375596911, 629852087, 587446813, 38935200, 489862645, 579644669, 12283158, 182627015, 55840171, 423769604, 480578028, 903644510, 804091518, 283620714, 657356463, 978530664, 82336603, 993304068, 324122030, 454509334, 19895682, 95719307, 661256154, 876394318, 646208499, 661968105, 323498608, 946548248, 789816041, 197474453, 558898719, 442635269, 200139859, 530812448, 158576940, 107653415, 758942285, 22710561, 927179081, 180345622, 95202538, 741789352, 53378518, 212105777, 891065864, 793237648, 584039370, 140370585, 444473979, 832823310, 736340801, 141431900, 684251461, 737884440, 64600103, 67493804, 316947288, 36127328, 422846580, 254806306, 959974242, 363084500, 275016657, 774677510, 272530965, 221088930, 451929653, 648398410, 966212964, 26514894, 700054519, 564060002, 173154949, 548896317, 518853891, 729528925, 68639878, 120838831, 79695456, 199013502, 672718369, 746464966, 445915479, 328105355, 317515236, 155510639, 370953136, 244418330, 155775032, 492062139, 791604821, 836361670, 684943906, 132293828, 472738961, 956607402, 763133326, 987520991, 556938279, 818308314, 28933877, 683792694, 90657377, 850189010, 498898825, 79206298, 141403914, 319375102, 706272799, 94896082, 560374497, 122825253, 434254997, 859064159, 81524346, 557043698, 551688060, 222762730, 390892170, 530719797, 993640707, 372561442, 29421243, 911054073, 239218148, 637355454, 233682680, 872032393, 276706807, 53544508, 299315427, 958134144, 543418959, 674184203, 112014589, 705022222, 488743945, 398360412, 678835383, 951879122, 725768319, 936183593, 208857879, 626302446, 612272487, 259795790, 91089748, 898979919, 580266391, 864820321, 232922327, 208846404, 160817685, 266315228, 540523620, 670384726, 636421928, 644561734, 137590652, 314421670, 636809183, 341291561, 912864361, 909035092, 874725509, 167396857, 388937965, 674225805, 129443234, 277501519, 45687734, 44804509, 125744423, 993152338, 200780290, 906659590, 830761169, 790566273, 573912290, 686982357, 19702721, 923276430, 149632289, 935500406, 929691314, 665773647, 531790934, 232851863, 66213004, 118340452, 991017212, 317358342, 27956076, 13221345, 722612922, 860850509, 801955404, 765265641, 352886477, 458462487, 846411042, 728413619, 586491435, 672498905, 57657946, 101828401, 452917513, 385957775, 801297834, 695327033, 869245891, 700454700, 51270968, 253608342, 976897813, 802284854, 565513441, 795363854, 486709571, 747292926, 981950132, 640455566, 390422546, 497852234, 622592028, 540218103, 824887535, 990218735, 220076724, 378928853, 164268993, 963462847, 338301145, 710065694, 402185533, 838763933, 79744760, 494361190, 769798700, 164005068, 750199638, 269746755, 73842374, 603921487, 310664487, 567517584, 347681186, 189504983, 643868484, 709403032, 828820041, 194735467, 733367762, 184887149, 477372069, 299675960, 8395370, 382433302, 951552110, 590678861, 79736603, 74348035, 119686723, 395283306, 555304268, 818358750, 414511910, 787750678, 617950923, 939761953, 197890299, 301290470, 525957913, 396360155, 35399970, 952798086, 229542092, 857788948, 79937065, 128834332, 433649424, 434552019, 744753323, 561411632, 750224422, 260224890, 485434863, 489915407, 228002011, 96170397, 629148245, 701504531, 271199076, 441768933, 180546012, 586874693, 835613994, 381225573, 334856528, 971472027, 993979985, 765012803, 186741209, 267675016, 375423615, 344462019, 945720107, 477099813, 390480024, 827151220, 881236429, 92694358, 39222831, 318843096, 94939668, 218005496, 995327216, 350509376, 179925556, 547187468, 593585828, 108462428, 864505417, 123803778, 537407147, 902546594, 426357508, 595603850, 67493906, 685464778, 805734498, 29267652, 479914180, 300808718, 516732131, 207787285, 338333397, 230992269, 181632445, 239965700, 652089195, 711660289, 732537723, 855328161, 846496804, 39567455, 987601267, 753259347, 856128157, 981658469, 539032052, 578720581, 366695758, 523439258, 192537769, 582806534, 249448233, 398800722, 11904593, 744753035, 277834366, 277865664, 640915789, 409827550, 480624867, 609199377, 259918069, 778018804, 192594720, 550083197, 459102990, 620972998, 710971277, 569069792, 598425016, 369472302, 370395730, 320248429, 482728948, 192468496, 914458993, 9448055, 832636262, 898183483, 800795616, 942917201, 4171502, 675058863, 518298336, 270953523, 692933140, 962958126, 247754802, 185611670, 665355487, 35326058, 196567445, 503295848, 535368318, 713870620, 478393132, 781202959, 26932171, 404173774, 204331621, 313197734, 634064940, 273637417, 282415107, 827912513, 109472962, 522836548, 693224464, 38963521, 619693818, 520992177, 37552929, 680292682, 972624794, 287322258, 147238666, 321437383, 696327606, 758818367, 160016805, 878925869, 12232036, 844254493, 756327217, 495109781, 718539194, 246368887, 365815947, 108668320, 546530911, 491436539, 54860055, 775855580, 226825588, 677154762, 168226368, 194776602, 941362910, 642540889, 39026546, 260070523, 262362690, 76662964, 631651786, 227657016, 378186487, 229236878, 989379242, 100917755, 236384820, 718486526, 98491189, 526679650, 995479748, 830769638, 35052012, 193365688, 928948818, 312013173, 366819567, 430026728, 441858553, 220322598, 175797784, 40192402, 850835732, 764103479, 13976796, 745377364, 267069685, 885060478, 142932452, 24981134, 713758849, 425227132, 417418718, 24979809, 144916300, 541183748, 302538632, 249791451, 149887997, 791852479, 250211025, 454652053, 396037901, 408639631, 627742012, 446095105, 914119014, 661316897, 376249992, 471397889, 961580133, 797649882, 832328157, 404357179, 95927791, 507276151, 635029975, 840460466, 344025028, 557406477, 566976025, 553558909, 189784698, 885377587, 785833439, 963143788, 835949268, 837171578, 837423977, 229858130, 375827991, 639086375, 673938889, 801036245, 603150999, 859533376, 303693909, 165750742, 101736101, 44962066, 812183820, 20034004, 565676334, 486500422, 690784690, 430908764, 538504407, 565550800, 261329427, 400867259, 140344272, 954963531, 814216125, 854893105, 708493273, 309518176, 325039017, 392223151, 149890151, 2570484, 77396348, 112383121, 67587523, 189606719, 984286081, 10166760, 690285657, 169310679, 714521256, 158809663, 522340591, 52186408, 430506517, 987408567, 87113233, 211123549, 185813879, 158283034, 928075430, 945123210, 500851468, 317679964, 837704647, 364615168, 388497501, 129241941, 120158914, 868595154, 552526683, 758938460, 504245792, 818237080, 245788574, 453509523, 879584038, 468810754, 743811965, 219249841, 247350374, 889753066, 695800277, 343905504, 879294432, 203697904, 168219166, 597661349, 661033502, 747619395, 425538637, 952013166, 737783239, 64076401, 225877397, 645018837, 470710533, 30345458, 604724824, 514154450, 179065553, 559238074, 184571933, 921495981, 851729940, 852213070, 387918754, 295228856, 113748673, 642756948, 404121794, 863041410, 30895111, 433582645, 600631810, 726972432, 961953308, 372259151, 992163604, 469363729, 544273752, 246564363, 385234583, 441290501, 353763655, 646584852, 520957923, 509088399, 697769596, 107512710, 4353361, 844157934, 980590015, 914136245, 109198922, 413173019, 234614725, 949018194, 281787570, 664332680, 46659825, 955705176, 396404341, 714363253, 756514237, 370869913, 198185134, 524712743, 562167593, 706474033, 692673683, 3809732, 139830304, 76213547, 598174536, 578784211, 175345233, 618963870, 507984877, 82378147, 609994887, 654865785, 552906786, 84050059, 406153845, 232576594, 356103228, 881031056, 597717047, 951336685, 653059834, 537505788, 592946598, 863313224, 462700394, 7565974, 343277152, 592645386, 686038530, 316418660, 42996242, 9544842, 642464432, 391747474, 755309845, 969359652, 419591220, 586192161, 78992214, 805986613, 79730069, 208597993, 918611715, 731757659, 18826634, 682042033, 232716276, 396031720, 442476755, 298880666, 261047211, 339889354, 977439183, 391157391, 514563260, 857666421, 738865380, 20010223, 643077257, 424662836, 186173674, 531908674, 725421607, 143866119, 616830440, 706274011, 684212741, 481249652, 82076646, 615961498, 603619087, 905454447, 446357941, 538427833, 552945206, 635370511, 449884311, 881629174, 133868731, 73319731, 816768317, 318225939, 925045668, 364365329, 352874125, 705448270, 832345397, 161884488, 752991258, 643223666, 479447742, 392808097, 568145029, 236564792, 563145363, 11329162, 559998455, 42620340, 636917042, 719262629, 840578500, 865164398, 738510658, 976784572, 949309453, 554113214, 453351499, 367772228, 453494929, 533259073, 242062533, 798294018, 943075740, 923180172, 83939874, 568960024, 262031770, 782220365, 120180219, 197144870, 64152971, 286540757, 450966864, 469826834, 99317822, 712705642, 212853978, 438061544, 758011841, 964545783, 132561705, 653980767, 116042332, 137792445, 249676313, 430785599, 704223678, 553477108, 151752306, 441922834, 650473712, 464364956, 258429454, 498005470, 717061498, 451978027, 178490485, 177951319, 890135395, 751590851, 104446103, 424704730, 800268132, 301414623, 74394557, 320262203, 85469201, 993202095, 116676482, 900417322, 702319285, 30570004, 899554061, 255572462, 506014628, 163532454, 380831154, 560198201, 499231663, 507143444, 845662777, 907027900, 138931338, 949806221, 943769827, 2215736, 46251876, 265765753, 181135357, 279941595, 941179821, 680561721, 276131264, 701635187, 830568200, 353128576, 787489156, 434323776, 690788099, 516280199, 401746661, 225390782, 502213851, 179692106, 177258320, 240766205, 700086171, 416523754, 698553501, 716007063, 757476010, 848256624, 501024685, 351017168, 154424179, 246356860, 260450513, 473867065, 605971045, 117848904, 549608083, 580437695, 346687622, 600824136, 98200822, 383148975, 495291782, 950988198, 440667096, 936190536, 263662692, 63976438, 413731032, 619267232, 161865296, 213801117, 117814333, 127553413, 84077516, 91787324, 496779700, 645084222, 649752779, 811877646, 663949324, 851837808, 234264807, 91544456, 844165891, 625508050, 570001941, 438685626, 166151797, 270611031, 332019547, 520211793, 931438959, 623793356, 828576109, 158931910, 301086302, 304624790, 898976137, 372475286, 414998854, 76392194, 10942261, 364804524, 441096066, 686718398, 530138060, 643042677, 119856675, 714395309, 541344147, 835831009, 818553871, 759409935, 901041597, 580490511, 215116515, 635850396, 225158471, 355850010, 197658166, 994010128, 901611050, 932090294, 853886988, 836009001, 524090586, 947234119, 240267261, 133484838, 28553568, 481248819, 773823019, 191506014, 403878365, 812342991, 510446725, 904172864, 497303236, 835549880, 329273473, 488602634, 653834526, 862666660, 678105687, 747480123, 704765712, 176726391, 594735329, 99126988, 995329288, 127828418, 889169528, 668889775, 213081280, 503982235, 706708564, 383441555, 843852229, 606104326, 131256033, 820404179, 598403048, 247583281, 127339108, 480251154, 322927581, 301723581, 577295697, 387665408, 514942445, 643216778, 620869848, 320750514, 416484105, 270791965, 545472196, 68129122, 75267416, 604055789, 540910528, 624866329, 278088262, 243841847, 490716496, 711533028, 481946100, 343911717, 620439055, 623832419, 297267067, 469038279, 529927368, 436585049, 11833712, 909982202, 34258174, 781700027, 998665674, 916021165, 561839542, 795864534, 204750891, 323214477, 109227457, 154098434, 973449834, 709356569, 102676052, 516217777, 428886172, 399369504, 396035960, 203623029, 972093729, 612430394, 157282376, 932588183, 162156887, 990154848, 951852142, 993162758, 576253483, 377961583, 836965452, 880023393, 407489308, 299540337, 715701703, 493016707, 169987259, 663646179, 991747035, 285966290, 10881209, 772726364, 641075907, 86610868, 557725688, 605000267, 629609703, 792030202, 455585075, 894841517, 84867395, 210497120, 741696959, 699715395, 216307811, 813273782, 844125448, 711432853, 633480656, 203545259, 851135107, 191160871, 238186113, 146273760, 830123087, 210204497, 221851671, 161074474, 95102110, 73398792, 928805988, 514041827, 24322366, 663909456, 766390133, 648073226, 977715558, 555466006, 583066138, 960107037, 705858356, 666770994, 510721632, 401444617, 985344089, 799915986, 238989421, 334312224, 579003280, 302286652, 324524132, 632520334, 968144398, 373132975, 736127038, 222602236, 637863014, 490958763, 411682425, 17203469, 910858608, 158670465, 424598627, 49331288, 359767119, 764806687, 923262066, 653991990, 552449857, 733903788, 346404766, 616817445, 47838526, 505961833, 573074891, 471554243, 94123104, 975392695, 828700141, 135253167, 796258830, 438811860, 515451624, 118734845, 900296449, 602881408, 268991915, 124542697, 412433960, 674133797, 132905421, 68634910, 831201318, 771853253, 396633937, 681971950, 571952729, 653920920, 264232443, 580300737, 893917714, 610777815, 567083691, 388705789, 295387620, 840648817, 184936010, 183745879, 287055169, 806197083, 217635225, 149883758, 902963958, 846785923, 610350938, 617197787, 945803497, 136861863, 169161890, 677975882, 164624755, 944044242, 19957543, 415490198, 57393653, 36715982, 187497999, 45111075, 773853478, 387154395, 360360043, 862195284, 274977725, 793492618, 540575745, 614592397, 680486457, 214479731, 386528898, 541677081, 809936681, 819008354, 962126081, 452209925, 181351338, 52892756, 13239811, 195175480, 480412762, 198047708, 528466123, 372411232, 334592616, 116281014, 736125436, 378555733, 718676610, 592941640, 783917350, 351998632, 409903652, 347660969, 360571244, 432794553, 347056994, 880076961, 487749705, 736609564, 117775326, 171628051, 229799048, 903381983, 207526193, 962612091, 168899183, 901788689, 20427632, 790541102, 64875282, 955855478, 279699666, 453410097, 942480367, 13325360, 74420330, 349060571, 772683833, 41449642, 823383302, 913903426, 613203541, 292779263, 82245702, 243572727, 410688660, 690454579, 799154124, 636959621, 693333011, 775309748, 544538918, 465911795, 765535514, 251901606, 68253403, 431237621, 245557824, 459316181, 48023858, 837930112, 490725934, 175665848, 138239139, 465252079, 784999450, 124160056, 499610538, 890691613, 407589373, 982146128, 977752063, 717271824, 325677793, 450896648, 736488361, 151056058, 774963882, 743115104, 551403587, 515423005, 743911425, 264563126, 345228446, 768733669, 134291634, 474457333, 199802475, 88158068, 125853859, 52136069, 762301200, 220702050, 205736246, 957710731, 20753311, 564530552, 351922182, 721206805, 28972260, 27710003, 143360620, 223744362, 43906062, 955513832, 627038753, 684329395, 631869437, 481393996, 784587928, 114535721, 42100020, 996456818, 84694922, 511018722, 751206815, 761067864, 137600225, 641111775, 400462674, 644787699, 78924879, 772419901, 554237771, 16846428, 133411773, 901394943, 428591606, 956403709, 255620889, 881209329, 370536613, 198051165, 277835584, 659144067, 573423225, 388248920, 156312078, 512999248, 974642168, 251222922, 401449876, 159806322, 300767581, 666871082, 276530176, 716573734, 765561623, 569161374, 601834360, 457970240, 579941788, 326580683, 611670511, 570015466, 103589576, 946169793, 877053449, 69370152, 457304011, 487634334, 834295614, 576839857, 289466357, 320427266, 199675035, 865842682, 429652539, 131074329, 408875583, 910387522, 674069750, 400107824, 319442724, 368652077, 450603056, 830764752, 954252778, 24031500, 441792651, 510337389, 413014851, 636685711, 129555466, 123373630, 329737764, 128732386, 815366321, 343374037, 927129943, 999170480, 968164889, 216382601, 748043076, 387492577, 8063183, 296266172, 680623209, 24161058, 282181252, 281976918, 579580250, 212833724, 896386102, 995161250, 566258261, 691615447, 480178041, 39586125, 373238458, 508059739, 781040367, 550279180, 422969400, 543006975, 748756858, 567076719, 678360527, 140170588, 112767940, 227563285, 113638687, 622873816, 958564901, 753791160, 130425324, 491039529, 515134871, 953446970, 196652335, 589391880, 238761621, 415772145, 989401531, 202073237, 269687991, 129947736, 803878448, 224511488, 417423467, 287303952, 347286334, 19666399, 83864368, 305009071, 180263335, 352668175, 940888133, 40675742, 391780588, 730928961, 45264729, 83617232, 622678347, 388182741, 220801017, 720535036, 858195298, 843312639, 720679688, 404606474, 813793448, 242656828, 257221449, 225263107, 437151647, 411881457, 149706878, 935498664, 509761742, 416589282, 466429163, 769381155, 801997049, 670418798, 388386899, 239043019, 670692938, 17779286, 297338382, 426407054, 755178739, 511157187, 472906658, 227303399, 49674400, 947414049, 865783845, 485591260, 134576867, 387586533, 644470902, 431048116, 624265729, 249109634, 546290953, 253433909, 801376376, 135987271, 586879582, 959656145, 674200929, 228201336, 270785441, 718704730, 977039153, 581670109, 113875927, 170847349, 59547601, 366351226, 221462984, 585360363, 126246280, 235047700, 931978651, 442385841, 162490578, 952617196, 685655094, 219379367, 877964270, 435883276, 343593856, 579458336, 485107287, 467181057, 855665851, 622149699, 144791767, 389935856, 963362813, 779131582, 262828637, 744343257, 259042338, 409929870, 27463721, 857614525, 82170948, 818887213, 581145712, 512442982, 780653576, 336936456, 711793705, 223200541, 917524747, 896910889, 456450958, 559101853, 41199592, 992446983, 61184599, 891313776, 851136312, 244399950, 604280468, 43129417, 995337511, 929130644, 510115821, 688828446, 514158360, 450314739, 944869097, 741251405, 345398748, 203899644, 262453607, 738877944, 866266807, 830825942, 224065317, 105020451, 648412507, 578190951, 769636679, 119071975, 662422710, 426164714, 896102292, 164860890, 660360786, 449482159, 69947533, 182212349, 786506934, 180900931, 576930655, 124362633, 967465459, 330041432, 866043221, 865500053, 617563979, 521516916, 820809715, 560538033, 135649780, 187751347, 42310637, 334763517, 868157714, 509671104, 830154079, 618022753, 415627848, 591726002, 758407230, 901167863, 633618370, 678201739, 56720346, 115689859, 496826585, 77974404, 362696755, 454370218, 876137937, 142556136, 106089455, 494117574, 990871721, 238158684, 602007626, 680810727, 434662778, 243808095, 872203783, 769805938, 831052391, 587106998, 860166301, 954345842, 715542816, 394000284, 355675601, 938401490, 756963813, 853077077, 865264478, 648603052, 126692884, 932218680, 499605822, 229487579, 654857550, 985425690, 10724738, 276811695, 114947550, 255923816, 828721179, 27216823, 896690071, 845970283, 132657655, 819198057, 512479940, 785436270, 329167001, 941262374, 128236649, 573170189, 802845498, 295009653, 975167420, 98135176, 495201121, 782752340, 755799155, 491065156, 724469591, 160599318, 340215728, 601092889, 577843146, 961966636, 957205065, 990169838, 537959348, 11612887, 868186087, 494604457, 825666729, 831777830, 718412307, 281755422, 285271244, 621642724, 28552566, 302018296, 346794233, 49618988, 540897688, 999356371, 551308293, 559293890, 12844526, 323880327, 223564946, 480215833, 977244387, 332881858, 504240733, 69078041, 787734876, 929822382, 540957424, 613615999, 253609112, 373826709, 821468723, 13749677, 411366717, 61577722, 917737449, 613228729, 51114877, 195397056, 904188602, 314135597, 256327164, 742182598, 128189753, 784471324, 151028590, 819791037, 125121737, 670106091, 200267500, 582098134, 451128162, 679993500, 618174473, 413276923, 904864464, 986498563, 855830764, 993218996, 896467589, 49984081, 52890843, 985408948, 616151139, 347950453, 496060071, 726543190, 367472925, 642263748, 246497331, 859685627, 443491024, 530737175, 554145289, 64284170, 506393850, 904673227, 539339407, 657919107, 391777029, 604242305, 352129750, 567645060, 249091623, 10920858, 171940620, 147819116, 737814263, 425568189, 160210012, 370335974, 939803904, 157837801, 341913530, 562763206, 514188755, 179849911, 234163298, 401256952, 497116443, 853686616, 715279776, 562928190, 501162838, 973989916, 94088193, 776711738, 234318552, 207846253, 822616858, 610266342, 611041831, 392711278, 278213824, 360777707, 421842259, 731241480, 381976156, 805763914, 536749486, 995929491, 727855293, 680077144, 322194363, 584584774, 687501290, 753199803, 295218307, 613572807, 415442471, 346245760, 635292526, 929931245, 677645222, 255646696, 853111716, 869110745, 681244073, 707863195, 719935020, 170070552, 445712741, 603368423, 478656808, 109199408, 273269459, 112034796, 202495675, 900009426, 897386616, 166292266, 760855832, 269006687, 350203518, 892493590, 581403191, 133115286, 196970394, 67208859, 20895082, 802587039, 559784329, 58232541, 740283967, 569161574, 171566233, 649260580, 686409143, 80509102, 982351066, 756005477, 426015499, 152288189, 844021452, 233671790, 568674414, 705966211, 762784458, 411796085, 660834650, 106660923, 856357025, 176632510, 135497634, 705294756, 678143016, 410081204, 343469639, 956883004, 946833604, 978049024, 271338832, 63285654, 781751320, 408883740, 299782378, 827816470, 390967301, 632309601, 172327129, 400236993, 669793567, 594358469, 828832935, 560348474, 680432968, 992538625, 580106584, 987477635, 91352903, 113817334, 425905169, 5653723, 335592971, 588135826, 592940579, 666667994, 664088827, 164324478, 850008884, 825729234, 519811043, 92006825, 852420820, 863721517, 376603663, 690434479, 464782046, 408435957, 410076310, 338495811, 489271809, 386145061, 911776722, 638434646, 422353554, 868841015, 724580266, 125907457, 374837418, 432785441, 710424478, 607439367, 891399258, 564675560, 463930190, 516043139, 140634698, 702682662, 383077777, 994197459, 577236444, 24068696, 443869467, 851456881, 102680463, 847931820, 337042514, 837031926, 449968828, 964609093, 516117737, 286941482, 315552200, 260913442, 240655364, 357835023, 270122746, 753464219, 485731944, 379260874, 318064609, 383026285, 868791314, 538794102, 65776310, 456507716, 630318141, 821749620, 167427153, 93048447, 599408023, 628216022, 856626963, 594304974, 225072422, 196987752, 533896419, 609144113, 215422242, 610416008, 266486218, 755165418, 5588754, 231084245, 568783318, 21760100, 539772731, 488989953, 807191208, 441198968, 79166961, 682344576, 920874900, 589886139, 238946485, 92701937, 675021849, 138188763, 341554781, 695630531, 395579009, 184090111, 796722307, 423905079, 422644276, 400353212, 531181971, 654947221, 933331765, 827287279, 65953194, 612137667, 973975366, 798377496, 796048626, 531447863, 452261119, 613202164, 405945685, 10768147, 722264958, 699967470, 71196800, 990273415, 128104298, 1572187, 515484266, 610907566, 782502411, 90041948, 825266799, 893689556, 515354570, 342078763, 449937545, 46788300, 861384705, 303644837, 885858797, 269047819, 902492503, 989784050, 519012518, 281685760, 555853639, 470795634, 868702884, 673481741, 794973254, 287187283, 943280008, 468439656, 909599894, 661092171, 254121163, 779225894, 943947176, 283135024, 67542385, 575081536, 942400443, 616103746, 315264446, 691245394, 338765418, 137392063, 636714171, 20742275, 995482811, 714270265, 322940278, 443839245, 473931811, 788983174, 38511774, 830262468, 331502938, 269736134, 408612195, 540769439, 192165215, 834113119, 244589851, 145004240, 159187470, 308416803, 721038751, 343015873, 187278969, 120578709, 123453538, 723929131, 620938676, 513423445, 366545173, 851100840, 621427579, 591865265, 732891744, 911635391, 504657794, 58146358, 164737614, 589526357, 642411959, 651820696, 441501203, 637106038, 743793969, 453307334, 350327729, 127529889, 615521578, 849842294, 817072478, 915440095, 915563969, 825798927, 402915594, 490641805, 167457644, 779031114, 652959876, 804992988, 952977433, 85826132, 390335419, 878555126, 94106321, 745667577, 34070933, 374438161, 44552877, 828935426, 338114805, 878905387, 630196847, 375650837, 871288654, 249628253, 545675790, 724260007, 336614169, 887648051, 938953924, 625724786, 264448121, 684029257, 42731856, 374024472, 462460815, 960597604, 529835600, 811144546, 101648796, 221582373, 920543121, 992634067, 765449221, 488362980, 973315534, 754584342, 403655422, 73020675, 557887432, 441708121, 492233411, 163047537, 172823869, 740713513, 858680134, 904597207, 647230726, 801804459, 170743948, 623846328, 945051053, 293709287, 860723153, 821292002, 367822775, 357843361, 988234544, 717761181, 552859133, 459818045, 70414324, 764625989, 994660554, 42457691, 840115939, 808752244, 541396746, 896248129, 592444475, 248802462, 748307470, 439783499, 234642317, 788640870, 806063173, 693323916, 622956645, 618331006, 868382260, 286735363, 807452734, 1831494, 322175432, 850358136, 329771940, 555357211, 929364831, 92271618, 674502065, 595080169, 101648602, 13692461, 497376562, 620798169, 189312659, 911448371, 556063568, 120485134, 510864467, 78599572, 304043834, 183408810, 647152556, 18582163, 535397348, 451877312, 524303195, 868238743, 514247367, 491921841, 478987176, 185089922, 217882113, 32154029, 32645372, 800168654, 934941351, 631765803, 958833826, 151128701, 416507191, 351424902, 95976518, 883379285, 77454540, 90522610, 679638838, 103816421, 63693020, 962122852, 987055622, 926360872, 20774208, 88699291, 136109667, 263104216, 842969579, 687452202, 717966806, 153686592, 268752329, 798632545, 887611084, 375968202, 201387705, 445333263, 379971413, 835221660, 471428513, 698194025, 537166645, 671246018, 551999051, 670385784, 520067201, 18254184, 649611376, 128601041, 983389510, 848108113, 669402525, 802408807, 892717655, 357844880, 221175636, 719960826, 594868980, 839371547, 71482749, 882682265, 731491298, 961802294, 649473451, 944500387, 96698705, 915752940, 765778814, 335203419, 800969379, 990018191, 28869862, 901944668, 946148335, 511877469, 806225446, 504945117, 618041703, 168106989, 170224202, 848004333, 42630905, 369316596, 412867520, 402788439, 930143793, 560205078, 516097110, 47310991, 458717047, 434761447, 217986867, 405158407, 482483810, 501229557, 82557542, 705132434, 297499464, 103847, 654922936, 370748456, 612793768, 177408662, 902803209, 662829086, 107453472, 587812063, 296258828, 137950578, 873010851, 662183253, 396362085, 484813478, 6389232, 864615027, 920068008, 177505851, 574821480, 783077735, 274489798, 258333936, 186907087, 66377494, 237098834, 790585734, 399854894, 156959830, 978882095, 205818092, 706267974, 259471569, 156040394, 995800449, 362379418, 518865430, 492673552, 173510066, 926502002, 4850915, 678104611, 348386618, 351606762, 271564106, 5230826, 473912173, 640971245, 586297108, 410596950, 522066239, 254967840, 641918835, 455260747, 41235756, 27065300, 96371202, 382763078, 130898242, 604855435, 292160718, 66467040, 324634475, 200561726, 44879055, 696172916, 339079082, 158449969, 803807586, 472309279, 99604716, 49342924, 415150489, 920757689, 75316062, 854360838, 136671167, 341310932, 357849806, 334886161, 218642234, 274123715, 871124150, 750309254, 468258313, 348104506, 975412421, 582302809, 130366616, 567857022, 25609836, 308055698, 326509327, 493409306, 130125066, 846887654, 608602476, 863190692, 466729366, 120056417, 466191554, 841223939, 467004459, 207721624, 778454369, 109333349, 122822652, 110815381, 474180055, 629936199, 13631685, 77688366, 931945301, 444661141, 413592969, 546423107, 861402383, 280076997, 788446543, 717791870, 661796783, 964001009, 150686025, 250484406, 731330428, 425811355, 118810566, 387511142, 953929342, 276955634, 979606099, 470545853, 211437355, 837683813, 120883545, 755900811, 309828152, 338658307, 837855228, 377094933, 592019364, 623395790, 106261809, 668227238, 963733491, 665449596, 140006078, 732584940, 502817284, 734468190, 922176775, 633127270, 832736107, 954896342, 105491157, 47536256, 509811800, 436310101, 225400667, 999059131, 206495121, 270530629, 924285803, 469558477, 972024392, 638826172, 307803688, 210609981, 889363455, 513151769, 630428280, 545087571, 564133366, 884009262, 530783328, 448454371, 272826122, 524477482, 883786649, 974148297, 221000849, 212535749, 996295367, 922943409, 893235409, 375847468, 931517217, 140579008, 118701344, 904183613, 805741520, 573446906, 198563486, 709297168, 714658062, 371744454, 141712512, 273582577, 537344754, 816487291, 805407665, 111128174, 864897705, 313285897, 143080484, 600159709, 260411502, 851937049, 578864434, 6987509, 180899473, 864261480, 397152742, 44096061, 901685908, 634961620, 538402591, 348079279, 793434643, 559315147, 399616382, 806241820, 96275679, 95340678, 854970309, 563755062, 730772090, 19057344, 202907651, 367854990, 748368019, 548446243, 703117609, 893964082, 916648413, 757179633, 362508502, 411022593, 702221998, 289555465, 236577127, 761230317, 90864142, 804424730, 231830773, 404013701, 21575411, 828103781, 132770371, 250520445, 551820924, 445225982, 963232197, 704207618, 155925033, 563574677, 394173729, 590113805, 513000087, 72493086, 399943929, 232786968, 233020745, 146366806, 509333756, 67712378, 865656825, 787499691, 718316945, 170012044, 178561215, 6187717, 989304521, 617851954, 592617357, 647125336, 39831771, 191699611, 964679545, 512266591, 890080878, 29845027, 80599519, 627792001, 168253028, 471082912, 516187306, 555380899, 761264117, 562107546, 603081773, 759706778, 953253095, 252695570, 442133684, 291538349, 616034323, 555101288, 116154759, 655494341, 987306407, 167398405, 313805093, 125812564, 804025166, 119146628, 921524933, 415106267, 699450195, 585063801, 105083187, 103179993, 831701738, 65083527, 890501606, 723257832, 403128265, 675513398, 928693681, 234489942, 493192486, 644951015, 958511751, 91780026, 492836745, 516017701, 991411105, 502159308, 65573484, 736073705, 83721630, 554854396, 615801963, 830254765, 419287575, 71531643, 145316977, 5953234, 984878428, 5958478, 767653192, 69765561, 866064157, 100517817, 436374222, 744213392, 850703306, 459063239, 490834774, 218074655, 503919010, 524498853, 163217401, 872622980, 738972266, 508919929, 185597033, 476230551, 187015624, 359589679, 719062191, 204114833, 210005049, 532287004, 745617921, 205174414, 654135254, 143389168, 143285918, 745897274, 91574410, 740070416, 806813654, 959960762, 534474811, 324130264, 433955674, 83743968, 115798870, 204170071, 911124473, 992782490, 397584727, 289140431, 90796386, 981917511, 613310810, 368287370, 655603775, 212147659, 831478867, 527522006, 347563522, 952813334, 832555491, 143823113, 778976664, 507048630, 991650215, 834794626, 957383415, 538741353, 669599669, 721949440, 928924344, 820412715, 359648348, 296980747, 296673781, 203557231, 750500086, 95116466, 978943620, 742488043, 193181395, 66125604, 724838871, 892093404, 323385064, 775202645, 578364831, 790949704, 132007904, 651991843, 27566159, 870865814, 696317730, 825459777, 620613373, 660498274, 485347967, 179014980, 479992519, 438968610, 165947377, 547586057, 717331785, 778015918, 739824756, 888033091, 308660753, 292734602, 349437478, 896487128, 585556918, 4368643, 112781041, 519006896, 349617809, 746075483, 869917694, 248999853, 878942712, 34818780, 8924499, 389585497, 14700458, 713822251, 413800940, 859187465, 730870497, 309343405, 903951097, 299654501, 35485800, 386793394, 500223649, 592355845, 171340083, 194991175, 263702661, 547326774, 342037025, 700663182, 640643752, 755106537, 64606153, 912998415, 541057818, 821272097, 522618014, 635077119, 406335705, 169482339, 577754541, 547028214, 566091516, 927377676, 434033893, 841352554, 776912461, 617050551, 704057162, 777563926, 767343073, 579237171, 200863035, 266654105, 931091602, 848858707, 58435277, 476417496, 361746404, 873355723, 230143981, 595575387, 247833505, 480280841, 853821754, 870371100, 118631591, 801864093, 393806780, 201074315, 95559659, 92043410, 690653170, 29021302, 318247683, 685319881, 936472164, 395170668, 494974680, 469956961, 135699347, 284917338, 662010360, 223443770, 736287867, 533246416, 875085386, 750705677, 948066842, 342707089, 945349979, 464687976, 645089433, 254388690, 229526915, 19702356, 449160710, 147532796, 80072934, 550537863, 359451834, 268987766, 742869714, 716877429, 901844286, 71328464, 724476869, 739466572, 125183006, 63895764, 938593885, 869924595, 481397714, 648544074, 179444622, 737795986, 286060192, 819523374, 615922312, 242161826, 164548247, 415488641, 734277622, 736771957, 176281113, 868769390, 160241353, 123799421, 983039895, 468842361, 745879856, 212445169, 986841578, 193466893, 68645512, 215707719, 62587197, 781977045, 104875318, 104002903, 356742139, 179133845, 595886651, 940331889, 752356316, 793360406, 466691149, 283641502, 481017365, 882357875, 259596164, 578780503, 802830518, 331586276, 105805103, 86762051, 770236173, 856117112, 797768968, 521083311, 368017840, 307064337, 202528900, 153212412, 348606926, 767931534, 911324104, 562129742, 294677794, 605340488, 335914873, 629718733, 761656219, 599334657, 807952957, 500261897, 538941354, 404270912, 75163726, 646206179, 113007956, 15034565, 765865793, 432828878, 528579980, 935071531, 5441345, 892658477, 524124317, 709029789, 972207681, 856012623, 599574242, 194048614, 514421465, 625387639, 121306242, 196363314, 558630420, 380790085, 217006171, 436664947, 178517152, 747521116, 590617007, 320437541, 129748803, 466439063, 984354422, 591341975, 811468058, 863960287, 350863909, 26870133, 116800540, 201385516, 825236293, 830267689, 982326710, 721025283, 925357580, 899149610, 134646773, 197183806, 131467992, 163882496, 756108813, 723418698, 328454316, 271390574, 541506527, 328971182, 515471040, 372630721, 120586683, 905578323, 961058400, 124524577, 919242947, 950899838, 731493056, 223403028, 568507856, 162814962, 922243874, 634492609, 693254352, 374518011, 958559539, 777870265, 999963579, 570258020, 82218923, 348148182, 999160936, 302865939, 2895141, 836564971, 478324626, 265258277, 571175425, 185720148, 742450386, 318389562, 685026831, 144719388, 514230998, 222805693, 450912345, 741036615, 629805722, 650645932, 616804566, 422833893, 522139719, 223933367, 298574858, 581916634, 997867888, 972711823, 246704148, 285943955, 719835532, 16871216, 302860592, 533534432, 163375680, 784207651, 326133399, 481647449, 212903947, 637698021, 828929124, 639018732, 202678520, 601729385, 209365694, 462446915, 347033958, 100429171, 413841950, 115744729, 784139474, 617414456, 174787055, 758641147, 231646514, 524324307, 431373272, 78530762, 416222699, 120632316, 402765731, 925705600, 812010576, 640675362, 453841126, 643077563, 100391697, 895150350, 18884431, 770781143, 233959873, 211840359, 703366995, 454142762, 683807283, 12797375, 194546604, 439599005, 174653792, 632432419, 684331318, 595132702, 727773633, 546833873, 934002311, 783370837, 69245561, 760441067, 685483524, 848461277, 908135486, 926535366, 650871529, 875920432, 438079853, 40223898, 419631893, 201278466, 692506120, 463411904, 873748048, 775450678, 23669713, 787819789, 727738336, 256955915, 59462329, 774266353, 566039555, 708677781, 665095786, 27043998, 269373692, 126826124, 197641360, 335576191, 565540913, 270824504, 306623760, 78274323, 805020688, 304584936, 407566469, 921637097, 263190110, 642483460, 567788112, 958335374, 597888384, 585144564, 596672686, 365690253, 547799534, 537728422, 975030759, 675397898, 545060276, 556883943, 709153779, 870151682, 716020453, 184741470, 572300541, 28206807, 16489295, 769618223, 507211926, 147331555, 805886414, 516004932, 846661971, 279521165, 924182045, 285444265, 148835582, 558514447, 231334068, 261093528, 50526602, 241189350, 71554144, 974583780, 931476517, 477549337, 976537328, 230318722, 948671629, 710021283, 241997541, 201000930, 207748484, 191342710, 497211950, 687124841, 666202894, 79455596, 927357622, 803706141, 507044471, 890433624, 362087713, 939255269, 943975618, 603128659, 611822797, 536993080, 293307231, 165261329, 170725509, 611869809, 721902697, 977527932, 799355625, 913850654, 422756901, 483411235, 316600310, 248077831, 152061841, 919228294, 974712707, 776165460, 532983923, 312356887, 215797277, 785754902, 960276867, 214040904, 753018336, 316015000, 941271662, 855983207, 81579854, 535480668, 662667290, 89988334, 710727630, 211045253, 473026046, 44612662, 174459135, 735202536, 178716966, 221384851, 816126626, 378442327, 45503075, 228016206, 149554491, 158992587, 655794243, 981813552, 662698712, 977567821, 261040223, 904318693, 430321192, 221610438, 466682696, 896160328, 905653624, 22203059, 983982860, 787394226, 191829527, 662409791, 190080060, 822870208, 423341044, 212489454, 898371169, 244743086, 223192387, 17991093, 438190266, 931216258, 839434883, 657080491, 214517039, 775523539, 978189241, 257241379, 53532759, 883510945, 236810755, 45076858, 134227463, 750047025, 161338165, 186260324, 699756906, 332456529, 836955508, 693801155, 381241869, 165192556, 12776219, 768142636, 242642522, 188996082, 347476786, 953201610, 484524797, 320812346, 636690132, 449742791, 983884471, 210689776, 307527447, 74133683, 127557152, 166698810, 559217522, 124424893, 479651802, 616111733, 409105638, 655861862, 687625640, 653146747, 698874564, 904344681, 641123182, 301305347, 250766918, 182722317, 39499781, 475432396, 118394986, 670933353, 370533996, 707849690, 788692383, 391198504, 180097230, 711392189, 643655493, 808088640, 13585317, 238754624, 303069482, 643702159, 941669454, 758237172, 41409385, 887670201, 8129707, 614898672, 63614664, 755061232, 337657509, 621129166, 461524193, 203441772, 341272485, 600362415, 732861765, 989959980, 872636705, 220268626, 405347546, 311886874, 246563312, 884600936, 185526839, 877720335, 772956078, 183090423, 795589681, 865962481, 170647263, 454738801, 798989553, 887028107, 697525115, 804357730, 592720519, 136949865, 129982425, 507828228, 1297216, 619027139, 146965991, 959336385, 542990624, 852527870, 469993187, 993487976, 437625545, 859045014, 781792831, 971093766, 223241000, 78596226, 343498080, 885154924, 685846626, 602034056, 329099595, 964422698, 224728250, 410443364, 289706063, 359939421, 239597446, 26729057, 353792892, 438641288, 78337642, 797831900, 927414859, 190640457, 697113229, 967850109, 208895249, 994643003, 161497627, 509410060, 242252424, 901324021, 632704974, 470042217, 660016901, 987129384, 408862682, 984027052, 56965958, 688129549, 489669566, 285532497, 621522252, 181736676, 310613023, 166037227, 674032520, 329412385, 883503915, 972596839, 843018565, 449255215, 713915945, 945772195, 460078018, 169471234, 391567834, 228606240, 156142118, 229224908, 375101730, 278726818, 602442879, 529286284, 777324485, 734366902, 484486300, 973295209, 767482156, 619971794, 308935146, 416276398, 34144513, 751071749, 268608950, 864856911, 829889140, 258697061, 942546915, 209690592, 43626553, 955550833, 267466057, 874240666, 98102614, 330083312, 417981837, 381641556, 312734828, 253318650, 610318292, 432521338, 222138046, 738894232, 292224810, 394657839, 535612442, 425732983, 738153195, 617181610, 841465301, 861453400, 441280097, 632633288, 224730120, 24007918, 867730228, 329941200, 618429553, 593345751, 538464982, 175468013, 412122851, 665257960, 63745601, 474371634, 235179452, 50883112, 884657204, 31349811, 682110243, 359612849, 46016039, 664246046, 792978923, 734418939, 330319038, 98083339, 490257748, 32660832, 816675469, 805977380, 121703767, 644256305, 818684943, 36878100, 652944991, 997784578, 395979868, 468021195, 502022376, 979825513, 209322054, 794818890, 683064929, 830593927, 223724496, 513043808, 300343163, 397432583, 441068104, 8684197, 907090308, 12080615, 596281981, 547872157, 520791114, 492952726, 528379040, 620331641, 914028092, 889170033, 948870172, 332131555, 777724090, 38375371, 33216854, 771762233, 736321489, 389555137, 262411708, 847622342, 520412622, 8416064, 563337376, 382982057, 37771547, 490582602, 254338909, 636591633, 318669368, 560757503, 366077053, 21804197, 670022231, 844946034, 846183793, 236857304, 987045422, 406294830, 747913598, 922090014, 651561737, 757028211, 106770556, 424280244, 802253198, 448972592, 377995719, 828929417, 187674371, 973915261, 142048943, 942439303, 795300611, 13106512, 366923747, 16213284, 465928878, 628599964, 693249313, 520057223, 783315533, 547275049, 250216341, 325720216, 4661181, 66072140, 534929085, 709223077, 147945553, 95767723, 418429198, 299580696, 348179271, 415077091, 220235705, 243306392, 256444708, 306780574, 931887481, 414765026, 399485389, 319911036, 241537989, 359549167, 403511810, 215575485, 933543673, 264108189, 451033062, 720271351, 618272531, 740048011, 782591297, 104848746, 494673301, 682031218, 647816889, 477582337, 543664352, 959746321, 149165741, 691104653, 850753575, 936078986, 820761350, 318530856, 295930250, 196693812, 509773235, 35229825, 578492018, 983789079, 79034151, 719928147, 986718122, 95114209, 997216010, 376115654, 439844770, 705783596, 276669753, 580382552, 263414678, 118771689, 615523865, 141409699, 382611395, 955547095, 388551877, 693127514, 620204267, 739970174, 327087136, 519264664, 700148917, 677165594, 394692344, 241722269, 513074597, 983037358, 37097385, 352514861, 759540396, 794496762, 886778205, 814006141, 358843104, 1738787, 50110608, 617963322, 527472002, 821327695, 944814784, 52323909, 336175034, 860714368, 891099840, 27832029, 811480796, 35926226, 18907073, 129395552, 420878383, 937631977, 371990310, 10377648, 318638594, 959864480, 503119743, 821717342, 772921635, 372163021, 277041834, 22822333, 441591535, 878640339, 590861896, 663631191, 751872740, 237784893, 140115458, 208617699, 202264090, 355223675, 663850511, 482856396, 75157493, 337021868, 653652282, 446246632, 758061472, 1396894, 908509532, 959977471, 771380994, 105716258, 885095861, 878513929, 443626711, 531813337, 478660090, 886385283, 193468745, 625513704, 776046710, 647726649, 797136983, 664501404, 527822357, 718299999, 370602316, 190875161, 393854664, 152976170, 612732544, 284346147, 961431200, 758229293, 577116988, 863659902, 167199896, 42759500, 300286355, 708082604, 805071668, 559902144, 655487483, 107189914, 496881845, 11181170, 789910964, 459926857, 364460032, 834312252, 818181481, 809912154, 820980270, 130540342, 294736623, 255810137, 917200433, 600299393, 639373563, 180590444, 743978679, 454530819, 796013151, 366632222, 710626188, 621158264, 413763796, 251713013, 615627531, 37204100, 994972589, 850440448, 94197712, 941518615, 866514857, 390773380, 416669172, 281280817, 869075152, 178140304, 809064971, 13559380, 132758677, 84146393, 756773628, 564455727, 383416607, 82349518, 244658090, 722401923, 88100720, 121091500, 241758431, 648455974, 11696492, 267470993, 538729712, 493853020, 274408598, 696966688, 493459778, 808195637, 225538942, 942015422, 362429390, 598407105, 733628757, 104017402, 921002166, 334543959, 384775083, 499811151, 783423012, 387187956, 969440332, 993607801, 708768854, 488511485, 87399400, 472706349, 340963897, 803593702, 86789879, 21951242, 879279283, 711848219, 573632171, 760241672, 945271241, 476087930, 351107519, 547459508, 725837858, 403014207, 337794687, 179619366, 551179103, 450430038, 254139928, 759089942, 247062252, 368662112, 294300631, 664023269, 98290852, 949298713, 966356642, 78637562, 388519799, 226326651, 43513139, 179217101, 137242286, 359455725, 864428453, 300312711, 84249141, 330823060, 416476126, 532014793, 902418473, 533746810, 80254927, 477276952, 652646015, 252770320, 519466815, 363001835, 111023993, 111912337, 460729892, 173186665, 182133752, 868903867, 424252683, 526255478, 258911605, 340974214, 739864831, 404195383, 660755039, 786497928, 813096237, 817263268, 423994895, 407555294, 841307267, 381694361, 621633639, 634272723, 4656833, 756165838, 665238163, 565983613, 243806279, 650063084, 317867428, 538176822, 7060021, 285829435, 155868153, 711156217, 707537726, 371540346, 75576866, 48652299, 660494545, 940884576, 185911222, 71504773, 745619449, 28252421, 9731328, 625137352, 852526637, 272817457, 61361065, 431060959, 886397484, 37675059, 510213010, 495999201, 981745649, 84242920, 220215147, 907820279, 658040358, 277975218, 144019474, 486298564, 305514074, 522723166, 195186630, 676045249, 962465090, 733298879, 628253302, 499306608, 196602723, 117262567, 336467666, 344378112, 669094293, 343783125, 588977548, 206667727, 209623420, 494782568, 917686632, 997652132, 511452841, 961251972, 318659890, 535664368, 689356034, 733290070, 928322311, 761127690, 239287050, 946614212, 447656435, 637591974, 759526532, 923679796, 942706928, 492584497, 211037778, 626322929, 372222268, 715622012, 770367779, 485727711, 390213504, 944891236, 481503588, 568212508, 315838978, 784029237, 311893136, 903027235, 376497833, 943928735, 120684279, 334840251, 855998878, 19308741, 977962296, 519262519, 418634343, 382399721, 331123565, 72024208, 734818103, 653069588, 883902241, 130732422, 487040269, 637715360, 511870710, 164631289, 279352933, 83844931, 764929914, 116995494, 865459684, 558902680, 812631473, 166523788, 316016920, 445456460, 387194332, 145466424, 776797343, 95226589, 748257430, 890850169, 644204577, 566745454, 383268023, 162381935, 751983326, 790349002, 634465955, 687059591, 180685111, 270822204, 420862078, 818348277, 54974327, 827940598, 692786976, 604303892, 139587990, 704560727, 286178546, 714998825, 226062316, 624047810, 634281830, 667471417, 625790123, 87903816, 494010837, 742279292, 544230859, 594181801, 806137729, 331785930, 996469677, 605689189, 695958506, 139838746, 205924064, 409330857, 615124121, 237597386, 955813527, 909748741, 966517668, 348291836, 893903113, 158649333, 796098757, 687957045, 510907219, 438495875, 126531612, 69349572, 42310312, 50620081, 304175110, 325432571, 32025068, 112392018, 72923083, 384469030, 679262910, 276054185, 175176050, 495843830, 291775816, 625752256, 628108428, 971495642, 780604961, 904706349, 13719832, 179158871, 607808380, 169099512, 455606875, 815528872, 399005454, 992980027, 96048752, 769282309, 21666650, 524664896, 246438423, 967954296, 443966367, 1999294, 91580088, 357832704, 235863773, 349568016, 902719162, 311593459, 616705820, 685177049, 875218149, 577179998, 601900731, 451625410, 217823248, 877760739, 416077252, 866596190, 784066678, 457536769, 4269541, 139711789, 330380433, 26622584, 508552066, 55797452, 812125022, 288607425, 100250618, 459231268, 448672134, 856370468, 697179326, 861369964, 644427341, 671512085, 50052013, 618828715, 194770389, 918661402, 549810850, 269661275, 864514822, 319725214, 464940142, 840289639, 927625787, 315371796, 234319332, 499969150, 519720296, 29118084, 722122668, 242957267, 495275791, 711660842, 300197321, 433098424, 277598303, 469902535, 567613293, 634622987, 923900810, 588829655, 311379572, 343808136, 692471382, 776143757, 87530745, 412585676, 164002588, 794404169, 146735653, 679297084, 123702729, 573993111, 653801409, 673411285, 132180091, 775029960, 245790889, 530850712, 727129343, 435730392, 692905767, 831162309, 862594990, 839874394, 756322279, 791045590, 242322580, 417714658, 347624944, 465124778, 437997246, 939077815, 256498549, 308593589, 603376444, 752670900, 436924069, 18666190, 97205440, 397293671, 51097342, 559807350, 777792006, 674592048, 577341554, 421493414, 535327720, 983563044, 409122330, 500567856, 978408808, 942814197, 424679342, 8593935, 230400378, 402986296, 428644987, 105542296, 431129441, 287231776, 89772855, 235762476, 432987896, 217024959, 969518535, 475363277, 313814388, 839326592, 193670839, 92652826, 443641051, 386465401, 680220836, 292276093, 237174783, 856960710, 888959614, 395004940, 605015946, 551803663, 275257026, 1827731, 869840541, 183548212, 638692226, 136915996, 413571894, 510664489, 215150850, 555890943, 799245461, 369455378, 412838154, 947545981, 444612290, 33330428, 933573939, 875777800, 578511376, 602914835, 924876221, 156225553, 616176014, 398034520, 629858260, 996265436, 694591437, 208349524, 544048425, 359973373, 990314841, 548444790, 570798024, 594781307, 393784992, 80862154, 348122437, 81752521, 927145338, 889252219, 725189158, 570937427, 291452974, 264563340, 984044253, 147047245, 490033768, 940523933, 395577397, 537845692, 861512113, 342357466, 372810598, 678874394, 518863615, 813197076, 346997044, 650224988, 523504953, 83989065, 687600767, 923016660, 556406583, 895746062, 31388502, 98911528, 56761227, 508747789, 342505302, 595812416, 821159364, 32426144, 551008317, 2601432, 328090592, 967245866, 600109596, 821450879, 9463934, 296011052, 605979156, 951048136, 680325869, 149051985, 272501962, 558953154, 624546146, 488586788, 923075441, 434217473, 525758976, 135700150, 134153249, 589246060, 193811489, 345835687, 116658648, 864216186, 798668852, 186799154, 347534, 597858948, 756679923, 233240908, 399188094, 633932548, 203882119, 36641250, 739541205, 506716614, 828051115, 255383511, 731799298, 834568292, 491150645, 457818272, 890667284, 893838449, 263955559, 493879868, 31337211, 411525262, 580296946, 250611106, 374910284, 100024283, 474677951, 225514255, 869864303, 670280856, 935441918, 643457016, 377299633, 714115628, 663020586, 777578162, 282872826, 480849778, 166958911, 507652276, 230247485, 885312793, 249693746, 349327944, 564201315, 789019017, 216283124, 443773725, 970770262, 888559019, 368244946, 945076738, 343133211, 968256259, 889832400, 162256862, 10942625, 27562289, 704150478, 16993835, 580813670, 575410295, 711429401, 358367022, 428059044, 508540506, 40510789, 231625508, 367024274, 594443118, 597205845, 475960950, 566097509, 87720678, 267307002, 830859471, 806120356, 751635738, 910482178, 84977401, 262774469, 517074748, 296555029, 860652810, 117444811, 285489371, 656799282, 169771699, 840205279, 192048904, 398889805, 801663298, 131327513, 174483756, 685605395, 660814811, 538884071, 26601008, 2177810, 732061992, 726739604, 594341327, 528923051, 377090859, 548970639, 554860025, 983186198, 598626348, 683287187, 525495031, 886573199, 851107935, 901335562, 257166979, 610506320, 853864378, 575326132, 814541587, 435331328, 760617241, 916907961, 628608010, 9687791, 879447764, 545908414, 40594796, 231292526, 110314736, 733070198, 215418460, 350626683, 37392132, 394696562, 267604931, 831261185, 162845862, 52289145, 298389690, 129490735, 745817816, 686384241, 283045460, 741462739, 658743565, 469970740, 3733623, 51131832, 862575936, 272872995, 104586139, 253041389, 376741310, 623148201, 392806448, 957312265, 525920174, 619771690, 92517843, 71998890, 532525138, 799836601, 894761205, 777944174, 998119805, 908067505, 960907103, 170467469, 433412842, 706408373, 899318553, 574232494, 397668619, 724395938, 373900148, 654359332, 29190375, 430689943, 537324461, 964479876, 648687713, 692959099, 291549369, 118351976, 31468736, 511944677, 433038799, 225827357, 877420201, 604202435, 100372361, 119560538, 500305077, 110890704, 528926735, 63898737, 304887385, 200351776, 16622586, 888390380, 524418087, 61720582, 168980055, 641537383, 782928729, 446275845, 388706080, 795672351, 84196511, 352867747, 90387016, 687357743, 141535383, 535897179, 199150852, 770211770, 714930526, 813753797, 358169623, 509583301, 323800088, 329081171, 627663778, 542629583, 893572152, 808897029, 21676936, 321444111, 890040771, 419031499, 57174432, 958086138, 62970998, 132639614, 884649741, 475442008, 322484730, 538916343, 972659109, 318991613, 813558426, 784412990, 539734417, 353766044, 424146614, 922987671, 987832222, 318773916, 817435968, 883342491, 93313430, 693726703, 193940505, 763490119, 122716231, 537459198, 992797103, 402758600, 959698805, 28418269, 756829588, 716934077, 670044153, 673016943, 224754607, 355654555, 499097807, 185270360, 252683420, 318046600, 839557368, 121355806, 959136107, 302058514, 369294302, 30124490, 739053370, 875762155, 545584084, 481945030, 408573010, 258169717, 713174126, 525403420, 867728455, 810101285, 354039966, 710174797, 123925783, 810675694, 653673843, 218459093, 553352566, 801447018, 676904661, 767484399, 168613594, 720748306, 986259969, 825187006, 807808193, 430305832, 977061181, 148655633, 720982973, 622445999, 786052482, 982197373, 341724441, 533375774, 958630913, 978810689, 724908783, 988443599, 837509084, 32219604, 385431374, 226358341, 613740258, 379769458, 323042276, 618754013, 692011117, 281179859, 990739015, 986516624, 320044899, 300192694, 168176107, 960975833, 446091819, 927535613, 434451288, 71538578, 65848552, 601136830, 283724599, 689202374, 558353034, 968919317, 160357291, 28771210, 896752953, 115432121, 945712699, 253295630, 714189343, 507578414, 729906778, 998674608, 376486880, 951255478, 173019428, 75626088, 291330388, 361215161, 649997081, 27545766, 944048088, 790642193, 820770770, 210794370, 569317222, 90303921, 348507024, 536809692, 819514333, 785653548, 401859531, 396594993, 496173659, 608928623, 360190803, 691586465, 964987427, 504737390, 940541748, 165090036, 860558064, 711731631, 85488753, 792807829, 350476045, 548948506, 389287872, 520203243, 939426549, 346554620, 846130404, 977352801, 498043624, 970801881, 842514970, 946335129, 992910584, 272740605, 81806327, 570216787, 323149721, 369041490, 976835016, 715962143, 473490759, 468502922, 194654360, 943208710, 985654813, 598758468, 663693760, 718579099, 726068100, 979237301, 820548764, 905598620, 523878984, 709621459, 581098296, 929715571, 277182700, 496801991, 171039728, 844699439, 425838233, 513537340, 689629615, 129970430, 843702445, 318946513, 391733750, 828383550, 690096739, 436054728, 187810346, 178389, 457167612, 936996915, 551639640, 5846035, 860397392, 36949753, 167955141, 551124183, 684789382, 80832814, 120767799, 748447041, 464463337, 393517151, 298334742, 788983270, 963923651, 721196022, 623739990, 62979180, 799492302, 280149323, 680898054, 768729512, 397914353, 339349649, 89254434, 650633299, 854264318, 9386729, 96230876, 287843541, 291448783, 913316075, 756143629, 710664248, 792317781, 100300069, 338517818, 470504383, 237931559, 641167002, 902235020, 472967571, 641973029, 587136478, 53257935, 338798995, 262509285, 506237480, 11454084, 72074919, 356729920, 279046712, 893517716, 958553895, 151910978, 750219293, 791261489, 510523452, 218494203, 756814018, 708683240, 683156593, 459261790, 723803377, 430184209, 98738853, 809689732, 390904412, 558154883, 16810141, 177351201, 949976257, 818495985, 977104639, 531161826, 160719882, 242824412, 567086834, 757732385, 194690372, 30981804, 647225383, 330903628, 95314536, 580577116, 703930795, 70776127, 108617582, 192861382, 57480222, 330300381, 273096522, 286798446, 784563241, 633866021, 840448211, 833971239, 532077371, 34282928, 584825606, 771596988, 830419943, 276806154, 446201731, 134645697, 806647140, 585766932, 396198879, 450973815, 678896424, 88556859, 216768618, 9030966, 377765831, 831818853, 661402550, 113376235, 170865500, 73946406, 145993264, 944491310, 416486181, 965862657, 853358054, 720107105, 807684122, 840862688, 831552701, 150353338, 289572399, 771604333, 957531002, 642601263, 252441534, 813379727, 333001789, 799609735, 969102360, 800722971, 359019986, 180253457, 282770854, 517559247, 264434155, 584346127, 384760024, 810486019, 406057963, 232220164, 386526091, 180474093, 879270738, 320801874, 807668896, 30065608, 49148940, 409055888, 290825524, 938569767, 381374941, 64268734, 449300468, 217572059, 32764480, 907147030, 763806728, 963508555, 894192635, 667901383, 187319332, 63315270, 904640673, 186186258, 848168570, 29693325, 31568166, 707739554, 921380400, 112667663, 772820711, 531802648, 380028295, 712814889, 695616945, 73414720, 862083694, 868284747, 48472463, 880710654, 636815059, 603158531, 811261678, 362270723, 968370954, 295673964, 213895956, 13672225, 658452344, 185198747, 10939697, 111607572, 132902160, 871087419, 719248039, 991270288, 529020287, 982852062, 601183052, 457632554, 26144114, 382718073, 484903874, 277164567, 345415366, 380482255, 915795511, 213351207, 412248132, 833045706, 16656250, 494855585, 432512645, 752402418, 903313188, 116668958, 390116708, 83003780, 371643102, 733245495, 56786792, 598505650, 908252362, 310815448, 911391064, 841337174, 720629046, 37362186, 246512286, 864383596, 239955567, 572125433, 727011545, 889972784, 421156585, 696763820, 43513614, 768320761, 140014801, 733060491, 352805615, 807737034, 643187100, 960747867, 644711498, 524858653, 434349476, 333210577, 524832081, 233525669, 141608495, 507902054, 211307056, 515152835, 999382385, 700390881, 50879954, 914547479, 511545823, 93717192, 129810177, 177381126, 380447798, 917694128, 680252483, 139431398, 662298739, 729808606, 791968970, 454254072, 228129159, 644615650, 688003839, 150984680, 186804538, 647073938, 449563575, 225885461, 650510806, 655412978, 318912192, 909617993, 810597461, 214510079, 942205639, 380893663, 151642678, 413963359, 289888282, 183683368, 898490576, 14593444, 907568468, 612935153, 349395179, 339255690, 723062246, 17665630, 536038589, 600580428, 706759499, 237710657, 48602062, 163876870, 644710735, 902102474, 969216310, 903703587, 516011592, 283442362, 933525067, 795143459, 322806744, 417135748, 142625094, 489995324, 627570474, 914650037, 435368511, 590825506, 915782858, 425811107, 282249650, 654080931, 989744328, 41439886, 285791079, 681389548, 371412355, 680044976, 973418393, 339204829, 281126655, 8066977, 636037358, 374311292, 420045245, 957823748, 793672699, 131648991, 110286370, 684884228, 640459948, 671037555, 942729905, 749917081, 332731366, 341433391, 856332981, 717566720, 176598030, 561387074, 260205614, 791676625, 977875312, 158099195, 932483633, 661052097, 75616315, 402023943, 622630966, 966082147, 114831530, 368446918, 983384961, 107529112, 151623176, 347735278, 976306294, 833784128, 504302504, 471896788, 281074202, 753754833, 50880773, 191187901, 794222434, 763015896, 740953357, 213807339, 587504997, 336224476, 356624371, 463172081, 556685452, 806986642, 684621910, 685767379, 133203477, 896386396, 172277519, 953764759, 279711630, 988591852, 383800093, 393618362, 744776328, 988710201, 777809274, 474282693, 292371774, 655803016, 427515150, 200068539, 536056906, 267899770, 978897615, 932745638, 23535974, 911728439, 135110054, 101854150, 827400101, 981329957, 168047412, 66992994, 41428311, 139203394, 572000707, 850594011, 912677251, 149158682, 676597898, 570999380, 258310731, 948951857, 352973301, 656499135, 462524481, 52008397, 309840264, 74060455, 816766249, 502445540, 978612904, 367869586, 141763556, 284235098, 125108287, 699361872, 314445990, 35091782, 7613634, 206137822, 231354981, 607690276, 742127027, 96641129, 524899947, 728702811, 924839953, 287425686, 969702835, 833961310, 857977531, 729039394, 407403875, 224404625, 384004608, 335068173, 952902123, 697036412, 866022476, 8805393, 18195363, 608287548, 192835053, 230605879, 649881132, 547798210, 68844484, 803441561, 229477871, 838297731, 862547618, 211000726, 99110347, 295553795, 578484841, 616353020, 861890374, 609475303, 442937948, 315838278, 191383817, 498981832, 723098701, 877491535, 862798902, 60763151, 586990806, 808950578, 642944658, 516653324, 11009758, 970574247, 281701348, 657884340, 134031783, 444408013, 392734749, 641997054, 427255170, 342403090, 879459562, 991283817, 554869371, 897341502, 537130783, 134609461, 866640280, 773369730, 990505085, 357737369, 862035498, 754223881, 204650576, 489658717, 599839898, 221408866, 875151890, 119586588, 616839026, 631827160, 592181816, 514076151, 863427531, 735834407, 958885028, 355476397, 807909950, 442918088, 245441307, 904388717, 968919259, 738631437, 242147484, 66624870, 300313478, 300592386, 509493852, 306030235, 990071527, 866121822, 704785869, 855093344, 985288152, 978157199, 106100404, 800239170, 433698139, 269137109, 476489242, 56479193, 745257585, 402207595, 999703049, 189517239, 481595187, 976754521, 908372202, 77918038, 215199638, 852353644, 991864228, 173697627, 604517310, 207497856, 764633311, 966693628, 949241644, 172193512, 392935787, 400515113, 270590491, 365795203, 757123802, 824246620, 486691927, 624275437, 851693753, 992601663, 257262673, 165670786, 387766211, 798848030, 509541284, 658576651, 573126393, 103654910, 550343325, 34915842, 187921791, 893025971, 534635790, 754560061, 682387083, 352556639, 427293067, 644424007, 807641912, 156697438, 588593467, 815567150, 559251333, 627167377, 171121396, 352165490, 156972319, 998526231, 80894314, 375992578, 777700068, 942357362, 63553054, 136165269, 404471230, 991187489, 886481513, 374270943, 808431138, 690017518, 709953910, 974387008, 45209372, 280033642, 24935874, 134223175, 74813421, 571988679, 101795767, 273305871, 590474190, 793279387, 327037430, 974476626, 618365560, 907359888, 971828562, 910420034, 403728229, 726967423, 624190226, 648672440, 164180821, 991245222, 859615046, 478577875, 322001978, 878243800, 127676739, 699747955, 25344265, 845017156, 433842728, 31940292, 642675248, 640164987, 450630488, 372439814, 199584275, 247162042, 355370250, 219815792, 819384742, 977107706, 612862470, 705318466, 677474842, 357207313, 173312387, 385004993, 652120036, 606662918, 472485912, 173908182, 103850283, 656698187, 26458390, 662938914, 219770858, 359603318, 320600395, 812953112, 784243307, 515008440, 192035988, 97233275, 62664174, 44420034, 756045242, 697044354, 306690774, 967748873, 650763199, 456264025, 112876478, 227655047, 714644464, 759881671, 415263421, 145704879, 265226236, 179245300, 584448338, 786868978, 777930829, 816845311, 457515499, 6356144, 384970527, 973253077, 154171857, 457551835, 996499984, 175458671, 315533653, 118385025, 686068090, 128960988, 136482992, 825381546, 458933728, 826102058, 536981578, 925147859, 488657133, 243499607, 76734917, 130485461, 196137242, 714775894, 213895668, 964674963, 158936017, 651760668, 69276653, 957318116, 332015205, 541701613, 9327603, 332793181, 364278566, 335372252, 864753442, 89950097, 965790534, 252334030, 294611692, 426986254, 893070498, 63897006, 72779481, 926722646, 271465376, 203400850, 532791352, 661895773, 299501189, 830078238, 952889430, 704503949, 268244967, 360227433, 138871662, 999905128, 929147265, 206552001, 124261396, 290510500, 845792959, 465434092, 457342551, 504524517, 504294066, 476008084, 580906199, 776941451, 898509124, 22159961, 190405551, 733825520, 577399405, 742221288, 117047792, 718683141, 573393974, 675179954, 79664439, 840260737, 942702021, 425507550, 841051000, 415229381, 150817953, 472718408, 888785269, 10383905, 423295280, 140062946, 581067096, 205219547, 606820767, 290832609, 617473042, 930312931, 442153357, 58118983, 864749857, 750937094, 593200634, 674134571, 24734862, 775716824, 694650418, 912421190, 385371526, 76923387, 557849777, 434252555, 952274832, 788908359, 256582123, 778725243, 210844397, 575411076, 231016532, 199849448, 720848558, 820005705, 364450693, 764517533, 488235882, 851820855, 405109715, 277787487, 147721503, 544914971, 491203230, 697897250, 300017663, 887121662, 481500212, 510548480, 717469553, 454316318, 588911962, 66939277, 136435194, 738475200, 555834576, 749586347, 793925912, 542377600, 725613364, 526150137, 349921090, 246121008, 643817236, 641776021, 257340798, 762785349, 566790695, 975218974, 720065834, 598331602, 693677126, 694834118, 299335997, 691213745, 924308981, 900605984, 12563288, 252864822, 4795025, 231855517, 889088813, 424434076, 789865225, 978603876, 508586783, 956008287, 884635739, 304095507, 876470102, 531941854, 794186711, 318598930, 570260988, 864901937, 554170521, 679492880, 169197213, 21223631, 201379034, 318937622, 506421751, 459096078, 918287107, 605853777, 544257612, 528718262, 65434841, 424853080, 172215585, 885210109, 873592285, 480079760, 194222640, 650547659, 316799650, 651658766, 401576480, 929713423, 939239356, 163799335, 790508583, 566140178, 135379711, 647461003, 350424979, 869884378, 253584236, 914798243, 900530967, 121879908, 618024158, 991863649, 824715879, 960610001, 876098450, 792873602, 889285822, 48244229, 137905533, 194972363, 995232400, 323360100, 996634770, 45415861, 627475156, 91288366, 54383516, 815228673, 311980673, 278849543, 119293782, 773216332, 958329382, 774487099, 840319937, 724356825, 134651421, 625234433, 224762057, 540109041, 986456775, 574097070, 173044372, 688892911, 836638986, 503939283, 952139913, 255150014, 939508698, 925225447, 759836046, 588219392, 106506049, 750958346, 387565560, 9587423, 441472422, 733050538, 807872632, 627372907, 82433711, 907617479, 977821548, 932524446, 159033448, 657795795, 364218784, 7452197, 70261052, 327227019, 240163647, 668916487, 852436194, 720068343, 768858665, 125664218, 47724672, 881402304, 630863796, 943503514, 152730682, 295990036, 178217136, 119757621, 883619189, 333452395, 231550579, 958670728, 501360412, 553602047, 59849587, 788225878, 156470367, 278984666, 596422504, 198156000, 279119079, 220565538, 295208193, 468785881, 989376477, 536639733, 587797769, 829565916, 665856423, 773388263, 491809459, 544083359, 484503272, 266674446, 732747022, 422726996, 618586808, 970425575, 285012304, 953764511, 654032233, 422692043, 201394076, 993889648, 72562110, 266771542, 899158118, 67325674, 299562366, 996900181, 579119656, 315597886, 475433331, 605894978, 894869178, 69289373, 166949962, 945229278, 995502918, 77620385, 894026647, 1140180, 525201908, 958152543, 161920162, 47941701, 509530537, 753241634, 626565470, 291570224, 574845715, 806539822, 485798031, 579542283, 335929098, 850443702, 735854197, 78793918, 695662296, 389008580, 975166401, 126557359, 667755725, 878920818, 822176557, 335149510, 416913212, 176954486, 375365867, 204128446, 126747226, 971090374, 262374833, 865038902, 59397185, 473311355, 737270652, 515155925, 220296370, 328790490, 769213223, 238791836, 411720090, 767798299, 874534737, 690052515, 448852897, 111558252, 781517461, 70824242, 555218849, 163969758, 99859162, 655255794, 31459848, 536365815, 152422368, 219917265, 219398479, 708500052, 614025521, 618087731, 227030371, 452906413, 520530598, 395405120, 714570567, 858782670, 875100007, 28594681, 590585990, 475241588, 908162505, 658670905, 510204037, 15678560, 635022879, 97567117, 17738315, 834950235, 483952928, 586823646, 519653674, 517061577, 523352893, 273681271, 339488461, 888942365, 469431070, 336520990, 741973577, 948491313, 970652124, 942084193, 472579232, 652790494, 980443870, 617366837, 805740706, 937374493, 898262045, 233282822, 376516786, 471701632, 410119332, 395637425, 707192300, 817780668, 656633447, 441131980, 339502835, 648889412, 386676241, 716784576, 786540950, 53439464, 327579616, 338191277, 47387614, 80976197, 646242108, 770339012, 228083015, 776093508, 294378752, 94327186, 520159269, 411352320, 225853987, 39170003, 733991755, 893040309, 900239556, 141003937, 793943664, 163523360, 245103034, 905117537, 463876886, 723999852, 40676761, 698178233, 281179793, 755114713, 966137881, 373683905, 554974332, 274488152, 586423515, 388354970, 800811027, 483487994, 102339506, 255677212, 46485530, 340503432, 168766321, 582942662, 182151811, 869269818, 720274937, 413865913, 311705852, 752795096, 225305931, 767645282, 879602793, 981873702, 633151794, 464322695, 871889403, 120797509, 557019306, 162538943, 207060485, 974281350, 743450375, 385852862, 633260250, 842261591, 654814907, 285292685, 171800370, 381194895, 120084661, 703627110, 285926371, 530514730, 387206379, 281390570, 170575199, 702516668, 105812482, 372846547, 147680562, 165432477, 831367530, 609290036, 590157782, 950277372, 679603309, 825204961, 764693296, 521457044, 465198166, 930688062, 727187334, 816509530, 962740325, 369826584, 726925763, 54543311, 582121043, 478019400, 847878185, 46662299, 625175652, 827281549, 402830592, 358643268, 865964286, 207668915, 321564478, 324744944, 19381972, 558414746, 627060711, 437238959, 678437431, 56348268, 38062589, 904233036, 281142684, 646109706, 45345272, 755864105, 588778789, 584977738, 96845958, 589569433, 961718777, 559665184, 604232887, 314356042, 901150853, 884959133, 688095791, 177059026, 962960672, 951981738, 700917485, 684640743, 609881311, 5866040, 781196069, 910091238, 899725556, 257502273, 71856604, 342505075, 434233161, 61449295, 174790840, 983857156, 207529877, 992580306, 220711322, 953511584, 153975731, 357274757, 303407239, 959124204, 342962270, 751326366, 284906235, 550981694, 532126053, 901880569, 202409853, 50387041, 848526135, 180659014, 462936616, 86448329, 805286929, 432595240, 139953269, 23987456, 909282381, 456968555, 233149603, 986920265, 292806821, 647361597, 109010573, 84196307, 910076493, 17221826, 831033961, 414498780, 855614469, 11557460, 302953619, 107401987, 405788525, 280037162, 229178834, 511277053, 551245746, 735121756, 694239103, 249053923, 32280602, 990061944, 393057915, 283963231, 267536251, 258608188, 524677539, 259261730, 92340883, 129522353, 88755555, 582613026, 970336595, 324612297, 394378180, 833996358, 54665420, 303450036, 563432515, 19159866, 591211177, 656266471, 355567531, 899964335, 784438194, 673083717, 226604012, 644142670, 5270117, 525642091, 353630421, 848680619, 186066950, 480479881, 828234435, 575284408, 293370703, 819899444, 413907536, 794344062, 690346577, 369752653, 309089482, 238225664, 121323316, 37624528, 668680676, 281302436, 326104531, 742841720, 809293233, 27566545, 249666650, 162610151, 840712406, 51799936, 144759137, 145108939, 669690204, 125484174, 301911372, 553178437, 656615604, 573475792, 526212945, 237275970, 578901040, 538148928, 764298410, 650824234, 831295213, 620968307, 523430535, 775717986, 407502645, 750025151, 778150837, 259332986, 803423323, 213922652, 213015998, 952925204, 4778185, 235425962, 256710139, 32460460, 866359548, 449296215, 784104078, 332752071, 914814044, 938443974, 203370191, 814355324, 509378241, 956347280, 989202281, 278305900, 973989630, 673544508, 132012989, 791974625, 513091592, 279736921, 802818415, 169939530, 339601069, 507495300, 790805401, 591061974, 626919325, 679783371, 988962336, 216620794, 236265932, 597252954, 395594014, 280033836, 474416390, 634788514, 920389927, 192938974, 602847991, 413722901, 448780884, 953686715, 804494288, 186950156, 55701861, 636115082, 354166339, 282489905, 9207792, 197788341, 673229655, 125653912, 319024504, 188342261, 955311124, 504593987, 414089836, 738973205, 72620727, 607796283, 796900170, 501430097, 900424001, 851798908, 418974087, 444721669, 377662481, 432838887, 559205089, 534727171, 48070046, 899379919, 975018995, 744934772, 440756132, 750985430, 70177720, 267853929, 653712622, 921599967, 331818032, 679086634, 150445478, 901946301, 127545865, 668512036, 931741287, 241556819, 719689734, 364137602, 53606727, 315052832, 171486700, 375063986, 552924690, 403986359, 883047858, 30037072, 370467725, 975795756, 206289139, 990741558, 861185956, 498671028, 300933860, 807196563, 803811048, 884279796, 749985533, 964881722, 681974228, 745169164, 188666053, 397029756, 535516306, 138655193, 957460599, 915928806, 979468529, 390397629, 974443578, 217103168, 143922150, 846394650, 220627051, 240315661, 92403626, 935873286, 361298821, 539625736, 188770673, 891498722, 420786726, 512604613, 590487653, 665906781, 169234336, 911893821, 565456366, 842348452, 293840968, 177424116, 76922978, 598571940, 689267581, 401836141, 724215277, 169813697, 511564131, 663223201, 331561911, 690069199, 331965540, 959900942, 129198797, 873391339, 957740423, 695410670, 678441949, 334636047, 271354556, 680883260, 702022173, 829873591, 116180875, 347377518, 785257163, 310360502, 748146261, 693218536, 349353757, 103553344, 15386643, 215329538, 25742085, 782424322, 793001903, 886309013, 78453845, 654748408, 485540354, 300583553, 643477137, 814843047, 488312339, 422596818, 533769993, 624079426, 376270178, 885586631, 910745121, 406326706, 651034229, 945986871, 390064788, 321973268, 183082176, 486723422, 992500146, 513275376, 381504298, 941935378, 622767573, 566753028, 114469196, 695072566, 177556310, 749843415, 894344649, 612507419, 43682101, 16207285, 68372558, 720787435, 333412195, 812878450, 648599748, 505626768, 850104833, 789088845, 227783436, 245286120, 259318404, 457598721, 72462829, 502449778, 962991473, 269045645, 323655169, 848912997, 583748577, 969863176, 33593903, 600518228, 970489235, 635147900, 791807389, 183050226, 936774078, 121805868, 250150651, 90303292, 149502165, 197762836, 636700465, 780415384, 215781252, 518946395, 60989490, 557725781, 110762453, 813521985, 793394695, 136032405, 498702897, 561222917, 814638836, 126763465, 887092034, 657468523, 60539862, 275171972, 394782715, 203246617, 591192195, 517784145, 485329479, 960594924, 67824617, 985005383, 645377949, 265006138, 965354193, 493997765, 225549308, 424775398, 873422677, 100835877, 523361186, 634604850, 679520485, 343423085, 610824136, 667600080, 711010205, 677778021, 465092210, 577025022, 367102946, 544897681, 249145118, 483116080, 930727221, 121954705, 320182857, 106706148, 231033, 424160064, 478510533, 171317026, 320023488, 562993326, 537271712, 180066821, 219321751, 937130203, 98536165, 524648869, 764828169, 160172181, 32557975, 941423760, 428433102, 709936115, 483515314, 504702594, 841976325, 193967310, 23549085, 8961430, 181825729, 604676784, 416747268, 865733406, 452134522, 854334811, 256469379, 168972269, 888333947, 573935886, 825508019, 308822870, 307969133, 883590616, 717092192, 146609754, 313399444, 296960034, 24908682, 579015318, 823745985, 319639932, 336437521, 976261568, 588170038, 325088270, 303886179, 284628535, 506179186, 936850059, 829888271, 712020424, 929266749, 444552150, 733340315, 919067338, 546155584, 89169203, 217145688, 251909564, 249068836, 198166527, 92825061, 550770686, 121525901, 980682541, 554282612, 320540684, 884866828, 639489386, 937583969, 215136796, 29878957, 23722858, 866591837, 969035846, 911591563, 574422297, 3424448, 698748719, 939135691, 257455081, 382762986, 531509906, 253866805, 107510532, 435157112, 814573395, 730396555, 11367446, 288942927, 730005602, 590175915, 159950765, 482870548, 81237797, 43009777, 889331697, 66071791, 177439150, 369625244, 825303469, 317217692, 87361907, 275282806, 911375369, 181630695, 760677413, 143260425, 349107194, 461224181, 230162936, 343052527, 324486171, 344254484, 876831446, 406207612, 428205027, 232961625, 959374905, 951668576, 99168876, 385564193, 407321048, 513667200, 571263011, 155320525, 620274999, 672963704, 241177613, 840198719, 352430211, 741407388, 540399546, 549524813, 241608476, 609089510, 174041641, 22863352, 444665667, 269539533, 558653886, 641643568, 77483527, 786462278, 711697495, 676134350, 153560882, 215030443, 510248763, 742331728, 608695290, 556874509, 691199902, 61154259, 723627372, 964369221, 134288146, 565414397, 65185071, 853027148, 538756287, 362477559, 48799809, 137714018, 973993976, 26328690, 438449421, 331577259, 437490261, 18946228, 629779669, 782384052, 871068398, 774582973, 175763900, 547228391, 536115484, 141842148, 717751375, 174254948, 452864353, 438088888, 254558168, 909196631, 141585594, 692792087, 439956384, 317450193, 325075520, 901431402, 746887660, 249061803, 591630530, 179491900, 559256155, 250257176, 671019755, 832424875, 542730931, 297195046, 411014496, 352333860, 892517270, 459728845, 102660699, 77582024, 288041902, 601380320, 941858594, 283104766, 261574529, 744829524, 166667572, 147760694, 853988465, 131583158, 705417872, 332985959, 31651600, 228868744, 988847727, 249160160, 149749516, 144102726, 589848741, 315115545, 98882182, 419475081, 27046666, 944675895, 436442430, 331603110, 332114422, 993305516, 69896596, 967646236, 254361862, 622197377, 869499096, 93472426, 572269644, 989716289, 601598391, 977281619, 731819764, 880190352, 328537997, 768896136, 700445272, 928631462, 393585850, 29728348, 812426533, 25323752, 153063185, 891776445, 99893081, 884235874, 942110105, 228468580, 994506564, 129253231, 390953916, 18956713, 270731907, 87896119, 698763577, 536883840, 548939344, 815266445, 68367104, 447943571, 210655171, 561780610, 105806013, 464039795, 932069601, 777513439, 456513627, 829042458, 45366162, 78136330, 246532393, 465887098, 465510640, 723310345, 661234260, 120274148, 870537063, 763813112, 626785529, 952109023, 480432150, 116967287, 792320079, 719301494, 2562960, 308461832, 776856310, 33352174, 905337125, 280530001, 215534536, 425102639, 505942559, 907743463, 552188163, 673654924, 614388519, 17324689, 123425783, 596552474, 928485931, 404729194, 538704601, 696403858, 79257069, 155092539, 201693396, 581717945, 220712087, 516336652, 657741969, 620468902, 36503701, 646270002, 118949219, 630301927, 265156886, 716485342, 94510341, 162426105, 34925758, 700869516, 532221934, 289924537, 25312697, 542009508, 842707888, 409246034, 188797304, 546508972, 990265216, 531527362, 435479677, 591428663, 373630375, 366037618, 147901390, 396575650, 940847636, 347720993, 736378813, 549533335, 933870204, 634418557, 205184835, 632869096, 537709672, 686821183, 197977660, 861270636, 316866349, 219725342, 648924640, 228880347, 614947878, 780479872, 577552148, 867139034, 840425368, 888775363, 618096470, 518842869, 824075846, 555889774, 788070602, 29810384, 321309829, 962525180, 322804676, 615799287, 227944357, 5096871, 245564478, 22278174, 601731907, 643940705, 526482374, 498828666, 470779528, 989898175, 830983724, 261406310, 263130428, 238194031, 203996986, 785641862, 291558998, 857064994, 338952021, 319498750, 949619229, 536948095, 807497503, 238075631, 617561090, 741574656, 710491704, 236997805, 58180248, 225886919, 72716140, 756120188, 845102963, 330451665, 312121167, 300878438, 210005627, 710288616, 437587705, 696407718, 553144838, 184840820, 622600436, 559368969, 152790184, 223648996, 637999997, 701809930, 109109081, 648032328, 136301601, 690630137, 754894264, 95822067, 260494022, 363595969, 227177783, 683689074, 435737127, 174966694, 654311344, 621832122, 577605459, 257565699, 935377403, 14124796, 494646272, 55985068, 918180308, 392412028, 205007186, 538662109, 282510694, 971558980, 12096228, 600081332, 450100925, 169902331, 210253559, 67816274, 331325359, 513039530, 36454466, 244533546, 2101919, 722357543, 618167475, 474432105, 855090678, 487737425, 463139987, 124570382, 969499792, 458320303, 898733939, 149514219, 137209395, 204918537, 439489863, 446528036, 403153331, 878643306, 314766412, 880861432, 596514147, 195771695, 477183650, 667937075, 240759864, 252652922, 80341095, 494616756, 103901156, 998436863, 549896291, 895602023, 94994006, 745094695, 115399021, 689264916, 479973382, 966450796, 380279219, 844280274, 289884649, 293909259, 427405175, 921481605, 324484350, 605277109, 816242478, 538349514, 472056539, 74244594, 362360172, 856552378, 47347708, 767980260, 884441039, 12736037, 226673257, 659524527, 781807920, 233917950, 415472207, 609642902, 339714777, 103029629, 257708386, 359518804, 617050359, 816504226, 815883486, 820533849, 152197070, 875101907, 229351715, 942582181, 215575258, 591935841, 377896713, 975732118, 15726249, 57722077, 688250597, 434330006, 820368376, 962872070, 586161611, 213874477, 848139005, 652950877, 182491261, 442379062, 49782964, 741332333, 671167545, 191056821, 570274827, 881408158, 152443220, 651692882, 721325510, 166658817, 489621768, 910481578, 775827268, 541741185, 300159377, 694718194, 600324345, 325169269, 341642452, 963081612, 529915727, 686071250, 120684955, 814294505, 189067314, 156488849, 882801209, 18639796, 248021817, 870014183, 137571360, 787544295, 709022008, 493683204, 70426506, 607733680, 651452035, 420879340, 173019047, 967604820, 539748903, 313081807, 459827505, 437591657, 711491033, 430692346, 375674342, 816240105, 991666799, 82734144, 55838637, 555254508, 320739930, 337067692, 166344325, 89210077, 4611185, 545297314, 900648727, 711594180, 2007998, 424197145, 692767789, 683386915, 864907329, 49009270, 963129036, 89151931, 720844890, 344842305, 492171665, 67697682, 396976053, 374952972, 520940834, 35243450, 180391856, 594160937, 988791225, 972759390, 306035108, 723030436, 166351997, 447616777, 629178524, 350975420, 843358589, 164566706, 162998628, 995087174, 935274272, 636258620, 746045412, 734770299, 495160232, 738369726, 788703573, 444024769, 977058350, 501457967, 52504538, 696008365, 579759568, 975733758, 637184230, 833981422, 741546856, 367691905, 261757826, 210256446, 166072384, 720181679, 776864341, 58690804, 664574081, 393847953, 720940138, 813443698, 299935989, 73993409, 406635153, 62828285, 513242227, 92633998, 218041615, 732702428, 959863649, 182580009, 868842411, 177596073, 570261750, 221555135, 189694933, 507406603, 416872275, 451038762, 356395556, 21406758, 595651788, 648616311, 457167191, 427602022, 288767453, 584139649, 163737922, 524761180, 325425379, 571259768, 219047112, 244474962, 806476882, 70950022, 658599965, 258239512, 489901847, 742094937, 895265129, 760891463, 746769918, 351027406, 297694662, 321611068, 121742129, 890136363, 687465250, 723685941, 839362754, 854477663, 852766369, 213892507, 340525724, 742112115, 315502968, 295399225, 982768669, 895005412, 469984542, 595750218, 457298504, 541564400, 184505512, 573173889, 910298325, 532688026, 372973167, 759907120, 872637955]))
+
+test5 :: Test
+test5 = TestCase (assertEqual "for (continuousSubarrays [545474762, 953787709, 674751628, 547108892, 139086321, 913984794, 455213752, 457371038, 837804203, 321301980, 622340159, 762005224, 508473801, 816102502, 114924508, 46789407, 657987508, 379771108, 196416467, 719296810, 495054479, 643462943, 12654004, 326443663, 440676053, 994855948, 95788762, 100456096, 270977958, 713933605, 740874937, 707881191, 521361591, 856258740, 718514932, 170403000, 175385464, 277230308, 624255322, 273359290, 953643451, 417501937, 798361803, 70944199, 962379022, 801126488, 109005986, 412779329, 318426048, 349405407, 598302991, 660867031, 1287363, 498039388, 655636954, 694997519, 513650074, 537106096, 30938447, 50239758, 504254037, 187552256, 870317830, 151919568, 869264851, 469086257, 222105663, 223490643, 893523557, 882450539, 549267987, 529469954, 823331810, 705347339, 65639947, 153171028, 265941837, 960051315, 292768994, 146881323, 628344033, 765468117, 857907900, 501562920, 787517433, 704861639, 11308443, 62725156, 607283388, 129346720, 348144468, 851306922, 344199521, 964292328, 128065732, 117805474, 467572364, 259778214, 319062270, 88533611, 126196412, 506345806, 441891684, 624403986, 870190098, 966167749, 858664638, 259225645, 985568593, 240806542, 796991554, 651969579, 924176268, 939796052, 377908036, 255806797, 181631657, 583668594, 429223101, 874833713, 412446693, 587837591, 958218101, 640627901, 177088445, 292216349, 193286102, 650633109, 853390624, 923312715, 362299943, 658210714, 804686394, 515526266, 451181064, 662930694, 626753689, 783555897, 12400310, 651814387, 938473743, 921168035, 391708552, 990604624, 979125847, 390093813, 825136930, 336454227, 376681215, 295643059, 419679702, 466493923, 73261819, 810794197, 487436405, 647687668, 233793725, 421738676, 898054550, 954533970, 103780920, 258582691, 866068063, 769182044, 998691651, 216046946, 570575460, 722218063, 359388980, 671059253, 883861116, 599293317, 30980739, 148289732, 358975391, 392969658, 746363205, 135600987, 710084864, 763429926, 323673486, 482258903, 499559815, 867845406, 483136077, 607104626, 16356966, 292267078, 422213889, 760807147, 567904255, 188239674, 673159479, 948735836, 882373507, 465742361, 506189533, 780640488, 752952151, 558539784, 486650725, 925079399, 291818571, 280039695, 314645165, 827470841, 73409681, 371218556, 216918091, 255693008, 667729327, 157759, 84608120, 127134321, 619916149, 327789042, 29728282, 876431758, 885622384, 482327881, 339660627, 352158148, 589081320, 396738219, 42795378, 803488061, 611767376, 960250059, 684476138, 197317093, 950355897, 406931811, 24349873, 970957800, 768442025, 754695890, 945932300, 136657174, 741180125, 807693202, 787725639, 360386485, 206012637, 519172129, 443867048, 81643105, 299588156, 218403345, 21451125, 616192657, 846590558, 443337316, 869802114, 421812875, 185371674, 257591463, 625879557, 78544716, 480628532, 627635990, 802455816, 921237920, 487488040, 561862634, 230240853, 773074864, 390584721, 232335660, 652529420, 448011690, 8324566, 335030889, 806053899, 940893509, 619360012, 723933263, 972239726, 714735400, 402518771, 742677165, 71418875, 296399566, 502505589, 827333130, 921605726, 143917835, 854959077, 895195342, 46950801, 675823938, 793162894, 446665270, 69742208, 418936131, 335363404, 614036870, 478481976, 971486173, 535186782, 838381379, 554100015, 598992997, 696657391, 870254447, 711831205, 176323343, 417694819, 151955415, 167281484, 448398683, 486830952, 593857530, 34967712, 824252004, 711386403, 402415956, 308979473, 623988414, 297692250, 684000792, 801637230, 25551290, 47406041, 339996352, 578815397, 997125839, 346630568, 445549892, 536888157, 712676461, 893316267, 811898762, 232287079, 341088297, 772011188, 693856715, 506001495, 856328082, 847418912, 575406390, 596785758, 774764468, 889530908, 966351783, 882592495, 340930891, 553807837, 123214609, 654854481, 978491472, 773065653, 776036754, 434109022, 219322095, 716182903, 628698585, 585623443, 125470931, 896459871, 730677023, 486053605, 365888700, 828118172, 896692557, 241894416, 63500807, 721254487, 117459765, 800286276, 329169937, 139984775, 456143947, 224908111, 600061356, 619292656, 58115536, 820843928, 685023287, 906494665, 480558257, 17825086, 621866055, 279233987, 655043510, 803392170, 251772159, 759906701, 444886526, 703414433, 85614203, 449268379, 293106900, 620959312, 845176523, 389202392, 788358775, 593593095, 922865226, 225037727, 183064595, 289253763, 118446192, 657233912, 364740200, 980925159, 693694199, 889243693, 403977707, 849606682, 872903781, 665011827, 343570614, 694238753, 115686435, 386119859, 540127512, 92791100, 810369430, 73933972, 311821610, 477772414, 927807719, 897029559, 742243851, 677803148, 98629375, 660516032, 342403461, 680146081, 867895850, 684963515, 77257011, 828987793, 478516366, 806952055, 870457563, 159392578, 939188936, 736487428, 437405433, 178709496, 841991515, 974735087, 130253428, 878145233, 526259799, 900845676, 374434377, 975849426, 757178258, 966787063, 302266026, 566020965, 61328760, 485590426, 238707687, 541324004, 998654768, 5456994, 117168740, 943595809, 926590565, 483231730, 535417750, 113506112, 938549495, 660732544, 274494701, 226314107, 625050478, 408899361, 635160847, 473933508, 383932427, 269667017, 998850970, 671265289, 44704132, 631168982, 904297704, 654040943, 649082038, 704955159, 23179026, 219543654, 886638783, 490363439, 708727854, 341920967, 171857227, 566349222, 326658879, 351134898, 878098244, 163527856, 444522521, 636185358, 165360294, 883016603, 307589084, 1127876, 297094573, 2266870, 773320646, 449377654, 411159915, 991928672, 865085084, 823684697, 526299204, 189163363, 450936725, 400494331, 984643951, 904036482, 633380680, 269002587, 145582883, 990288863, 818395328, 591997773, 653587918, 283333259, 657517832, 121590451, 406976514, 86341578, 295248803, 842841358, 318955430, 866162711, 369675805, 140687209, 304949464, 451470721, 831427057, 924145515, 933203451, 896902519, 188560232, 721521820, 108724259, 884227111, 610251465, 98122207, 990137877, 136448228, 271610438, 396784217, 391952157, 365569312, 517400730, 543789050, 248576794, 686942509, 91683708, 161802583, 678197563, 792922455, 883944849, 240477286, 909619908, 899484842, 31218726, 489212141, 128414243, 434785859, 301813582, 510916403, 606770772, 560480638, 924010217, 29758439, 573495626, 306790691, 656871980, 188519384, 591351428, 434265823, 319057051, 616827891, 618236668, 795953631, 401636033, 108600394, 765687252, 192922795, 47122622, 149055472, 312022541, 919094598, 968937120, 273189234, 588170831, 674991522, 995665825, 163566593, 631901094, 676082689, 245491590, 170263264, 313268266, 398558884, 654178111, 586145685, 55545839, 62681921, 652472126, 661456537, 943362938, 648407692, 874675248, 400391181, 617985661, 600650899, 500102731, 742685142, 431436545, 515024357, 894852168, 95010406, 393126650, 718767077, 143355012, 287816003, 445061639, 687716793, 986302907, 46160337, 328768315, 363690151, 442972337, 868444648, 981732261, 873563843, 973373342, 441344806, 440848829, 541238310, 385022583, 151948139, 663589540, 59689588, 717520943, 453600351, 509327393, 344240072, 775178739, 562700376, 258352741, 319843064, 472851438, 51278135, 146737094, 220689807, 700320382, 837332102, 762385525, 399959971, 340391529, 506350075, 309244592, 922326445, 308581072, 693856672, 435122256, 549415026, 943761953, 878234910, 38686776, 341990619, 332794128, 163334525, 436719687, 57646657, 917462331, 850315480, 380669479, 537835446, 204877363, 699662373, 39358988, 410026675, 94768102, 329948058, 721550840, 825553659, 304712541, 196325200, 607009647, 945395785, 967956293, 388320607, 133243535, 640342851, 445277384, 240854060, 469239245, 221896301, 325377114, 171457041, 925879675, 607293320, 53067765, 740263642, 898186869, 169410240, 948730095, 941019494, 294476646, 178250682, 305501864, 413087864, 924901626, 458315450, 958314557, 590331576, 75593805, 97061820, 145043190, 162473687, 951836985, 962466400, 167018333, 341206137, 134960982, 838815629, 382897871, 599308775, 101595843, 493804524, 230089706, 14722163, 350127480, 403371683, 613235294, 915894561, 834618526, 475187293, 27401342, 25363743, 932209539, 493936940, 524781045, 341384337, 885707986, 931029183, 988701420, 283148480, 935006656, 137668991, 874762225, 269100666, 90798739, 260988534, 126779018, 590532967, 97365741, 140736498, 714123802, 145722215, 722460160, 490322286, 811290287, 67742715, 713677709, 39743735, 332639627, 218125803, 713378338, 824495521, 802155217, 464190961, 508591532, 782584768, 62270081, 473801997, 780246306, 492962814, 596922368, 830159474, 982171716, 485473444, 748662054, 641029558, 211481352, 142625254, 754603067, 189617175, 441925744, 147899125, 860281759, 721251483, 864773403, 872633785, 33285556, 512721503, 163153735, 923076165, 499134592, 305679331, 52448476, 304471733, 904986224, 180173469, 873491106, 54145038, 850413878, 907977403, 729927922, 811633977, 904950176, 967333052, 873826354, 201838752, 805215738, 401471602, 198851990, 100308971, 820767311, 271177128, 626224830, 878636669, 766515865, 698046510, 94262611, 91220413, 34511572, 369678587, 136416738, 135295118, 835665387, 837010861, 1778766, 188983056, 520636238, 67932808, 842490299, 537076134, 257837150, 254214487, 640539077, 163653725, 365902396, 360638622, 747990900, 366004316, 518292904, 316433552, 864242416, 553070922, 855359306, 274710491, 30862493, 371214965, 74018785, 860725025, 23212647, 773378365, 244988883, 23911823, 995715530, 619254393, 873229435, 906485693, 802772084, 109348094, 337709190, 360376560, 620412528, 748806078, 96927764, 645692670, 515921770, 829497017, 319535006, 410349879, 365477827, 825984480, 420095159, 907728075, 453525347, 599004529, 524492831, 573007531, 588571259, 845043093, 659303990, 897664755, 689141490, 553464385, 612402452, 373088932, 290561218, 547062193, 182482668, 552490321, 631921117, 410498709, 897645415, 334252520, 853354392, 481839029, 499111479, 448327286, 758790177, 942150784, 810550498, 325945856, 864779657, 911600156, 737246429, 721670995, 370483014, 306381760, 582988068, 606736194, 528288688, 684396087, 981207893, 889223032, 452556604, 545934929, 432351484, 76192129, 24442032, 559427512, 118522351, 324985000, 602642254, 479431557, 820891887, 169957371, 692922048, 418135756, 575759197, 409144974, 546524375, 212836422, 869372143, 739934065, 103096338, 71683468, 166537114, 274182811, 152109497, 595401186, 943372376, 769966230, 376541867, 755512473, 826110380, 675752392, 767459616, 896331002, 624758059, 740305558, 560126549, 658826649, 539109044, 816910325, 566750152, 471067553, 688551621, 741199527, 52483806, 953002908, 730160068, 995900903, 331283408, 968015001, 4126543, 976093594, 862752300, 398483383, 659408192, 237199285, 348457285, 772972019, 480622739, 406044796, 751533503, 863596949, 571567136, 352641320, 668049650, 826962409, 690997860, 910314042, 713494248, 600901841, 688516875, 214834897, 177692862, 531026235, 990390602, 43541428, 617020987, 570722474, 162450513, 635827725, 63288761, 415548905, 286793206, 714088196, 940059162, 893899441, 749707054, 54067503, 27553999, 265237786, 264657154, 918428214, 542011994, 973059413, 979487296, 445331640, 21967865, 890594067, 768968716, 635514547, 575301384, 855634337, 367200514, 675846346, 642148298, 484407741, 221163342, 533925647, 843020373, 625603149, 916232486, 873072403, 779163460, 454060507, 75836, 7985462, 736721012, 383345697, 742346767, 660760312, 879114550, 29098064, 960655198, 426890371, 931812190, 428746353, 461046966, 494984288, 141134427, 811563191, 78726270, 588642920, 393699714, 142913769, 518877134, 604838140, 556676182, 152929184, 602798185, 910403651, 898625854, 626487224, 266034437, 725262406, 889614366, 597343152, 570666408, 218575288, 434917749, 516664, 944606220, 308338510, 871383776, 734925803, 297242798, 23889061, 627743907, 801456652, 575033010, 368240050, 672023672, 416777299, 789532761, 715855021, 70299680, 243983876, 33760751, 793001861, 750079838, 917145769, 643627426, 135779765, 721092021, 349580710, 937386887, 885945353, 528411233, 381325889, 774124795, 555778758, 377724189, 948995789, 430383986, 977767872, 411335735, 142426216, 80314555, 960647770, 840694797, 793202061, 329255107, 140086498, 532839916, 176196362, 57914219, 508464092, 992844662, 436809653, 212757427, 65689962, 366513380, 889148347, 837903010, 239554660, 779049456, 519381998, 395974210, 966870175, 474141784, 857071524, 688749281, 823683661, 256223060, 45021479, 70949872, 894833262, 211212585, 538535431, 414150849, 715635319, 586877556, 82270020, 556856608, 413749079, 681255945, 245554097, 408996897, 798777881, 964027279, 363846487, 290313722, 545523710, 991273368, 765412282, 617077811, 861215115, 26299008, 862797793, 59596791, 301896640, 761869449, 639849999, 800538240, 866748390, 993625200, 338906345, 470425459, 548423176, 536041050, 10782658, 382980242, 929027491, 738060623, 813836313, 658393818, 311258651, 960649848, 157822478, 514337768, 303480104, 84584675, 522762408, 473132591, 862805502, 349693312, 685105050, 200084935, 183456708, 337091315, 311170111, 601955385, 306355864, 36355775, 566661078, 901658014, 239156691, 24297902, 729470068, 52099623, 861296757, 87538180, 223653700, 558360570, 800466924, 964342519, 28164274, 97396457, 142583731, 37955214, 598490362, 65710058, 796478107, 319102805, 805443945, 128652129, 829657375, 744635191, 573704173, 423364048, 337376628, 912558285, 817468003, 818742040, 527484292, 745921998, 891911812, 457218573, 829125159, 566269154, 840080035, 612959021, 203165549, 19604136, 8674653, 402126667, 42695166, 189514194, 899650021, 348613324, 544024948, 462169960, 756134466, 508658848, 416201885, 77415861, 689685712, 940375657, 387694047, 184410804, 451594042, 677737450, 700266841, 790998449, 983438722, 706328626, 250762882, 647220267, 596114504, 522573431, 368335835, 116968162, 265467938, 433197341, 410593071, 689722571, 100882194, 250517565, 267394198, 654885954, 791220086, 385387395, 512629463, 427780382, 170956603, 560612281, 772076965, 720564842, 488615934, 496487939, 938725656, 344192520, 688755731, 110702180, 922350327, 273458122, 737158042, 781943315, 303792122, 340675387, 864307143, 806616164, 521146724, 388790616, 690256761, 60107634, 286219868, 596962067, 401129328, 3889485, 847924455, 979435561, 636654269, 910632239, 75718267, 430645998, 883062573, 78731248, 458560935, 210409424, 822159050, 391028691, 479458762, 807759689, 805467099, 391472631, 999061610, 863224004, 688267509, 179558502, 308937627, 171612608, 196507573, 8226690, 35218013, 651260077, 917416729, 283822888, 729020905, 489577865, 925303596, 246169850, 447609486, 305785839, 138918250, 535618005, 395080705, 840329533, 642433981, 923222229, 97518185, 943216342, 863719630, 837664589, 177492642, 613251889, 883509110, 864465797, 844094073, 421112860, 102956809, 553334773, 33367108, 400740021, 203737987, 316599432, 236017967, 410849848, 635198107, 771254195, 251259615, 459544712, 540355720, 484074381, 120134184, 780456768, 485597522, 617441391, 620328097, 781190683, 426842509, 693597921, 595298352, 178975374, 656798243, 151445934, 811132838, 235866953, 877793433, 786950615, 22681856, 920348392, 452775298, 986977771, 56345757, 766117314, 119243437, 510109445, 148064871, 103002707, 531949818, 966192244, 617095082, 639927510, 358547925, 2883468, 323176740, 33976940, 887381028, 639641104, 444391049, 825848115, 401579326, 49924231, 774504372, 878084802, 438736343, 280764838, 477861458, 305398000, 365919126, 117014660, 90530276, 223286082, 291332275, 194474090, 894003353, 565760011, 375913198, 153404764, 341017814, 313645146, 358356814, 552393957, 479675974, 64236486, 988652945, 940311595, 573275015, 588685691, 739444804, 715734849, 92919073, 95753635, 536207137, 946370747, 839488653, 498323784, 476451053, 72413659, 933210640, 457112560, 458752884, 180856524, 983236538, 557099459, 529995835, 926253994, 742849187, 342913171, 604768245, 838018587, 803865502, 200652393, 169706181, 614344516, 674422514, 308979502, 765984833, 348054262, 126912774, 707577036, 472653114, 423888161, 456193180, 66461691, 285685093, 540995782, 214301182, 22299842, 539000136, 11718239, 13206791, 91466661, 63830789, 844963994, 589466276, 226811295, 167471765, 853430338, 108591090, 51827920, 869173817, 301480866, 935946965, 919250600, 154795190, 425361886, 171870810, 316299095, 215697575, 155462995, 664565769, 609527593, 350858889, 766351396, 708760825, 144720506, 5326842, 351968601, 795875700, 633752781, 144309113, 269426973, 514590742, 478952952, 397068883, 483210, 903556971, 384232999, 384525706, 317350321, 673491018, 102183212, 367097956, 868164933, 999030445, 736378698, 217439879, 283982012, 438397539, 575564836, 753967089, 175708960, 412930649, 884483303, 923631348, 944453572, 37184601, 942236403, 616279693, 320226682, 762709977, 245927662, 479470077, 778597054, 765306649, 904549370, 727876269, 872620103, 170886370, 888444142, 855990907, 746741327, 623543118, 616767394, 274015708, 371264586, 938363172, 602136544, 5121907, 816193356, 278008691, 120457940, 292909843, 134407516, 266855193, 582265333, 487428920, 33903388, 883944844, 996644083, 144719175, 39689161, 424289042, 553754672, 117371262, 182849470, 573768345, 15512358, 438205647, 709504272, 245854884, 758552849, 911166829, 179552501, 933420287, 170398995, 750671721, 558518772, 739363661, 174590890, 988584173, 597670431, 988919279, 380917937, 235322464, 916511528, 964987293, 912235250, 460751322, 481062140, 517178602, 433118684, 884187269, 813047920, 260108521, 771891610, 67180856, 67692516, 946607800, 748465252, 807227704, 605986010, 639569963, 823459529, 774631666, 779371270, 391824543, 334621050, 425194741, 490986952, 405423883, 294658403, 855035557, 268810322, 908627670, 850662293, 544492775, 787998170, 836929703, 305979856, 207950875, 66843008, 916238441, 572189328, 966287456, 144131350, 889967423, 771031945, 394270857, 224536928, 695808640, 388137927, 771022337, 625631027, 303754181, 653353920, 964589853, 938425465, 755683021, 323880830, 750963488, 337444540, 47795552, 504231403, 362678177, 711224267, 239181312, 352082927, 844697922, 608690808, 567108619, 820648549, 831470735, 131819488, 452875939, 236504294, 812755420, 448395358, 127429881, 895215665, 136500513, 680103027, 709741933, 83237379, 31186693, 85280038, 225015595, 990263321, 17403044, 702768466, 371625217, 689428379, 926411632, 208823805, 937725433, 687037143, 254938728, 813469932, 87663854, 742699924, 357511406, 704424156, 273193473, 335307671, 452555265, 760105171, 286664170, 999193583, 311599503, 465829552, 675180690, 326904371, 85410941, 709871833, 624283060, 314883674, 700936741, 986713996, 294309855, 230899320, 383249980, 94270733, 837273005, 707287632, 567074790, 114619612, 31292085, 718908009, 810426882, 152494066, 832704914, 945591132, 126567325, 388012698, 501494863, 718251516, 420292959, 169090612, 816089214, 486041868, 408081394, 653652506, 624130979, 980270500, 499322388, 51461772, 20518627, 959149107, 946721170, 30358281, 153193848, 402188570, 382703386, 97311690, 943934004, 267493692, 676485361, 271088763, 189392, 849949014, 368141519, 364426571, 929718969, 411807418, 526643452, 47842799, 162637920, 512298819, 624946145, 288148069, 730546282, 223375135, 279669518, 342929454, 346568452, 626325245, 203796627, 337747070, 546891917, 193446517, 88258816, 355206206, 168611927, 378242113, 633047195, 968530242, 220672359, 642613345, 77669205, 680408968, 348361636, 756117845, 487840395, 614614203, 290965357, 61735792, 775505792, 744913573, 74812209, 472870216, 498746395, 978216286, 992911656, 493492912, 416336926, 92777874, 378133612, 766773580, 503914590, 964014124, 816870855, 332837871, 549028976, 243723848, 611509005, 622776867, 701613586, 927530077, 29286350, 599358839, 272131387, 103586743, 650687795, 311131803, 72046091, 68131563, 459227920, 218545147, 402032457, 317222954, 981607464, 420560723, 834304223, 877986590, 617532088, 501035956, 959751365, 360466345, 929031678, 416090738, 486185860, 706203269, 387536723, 239108411, 531218988, 513951010, 507598745, 616765115, 821162559, 928774996, 273176472, 467459755, 290104105, 192278967, 748449422, 654293301, 386210412, 327961863, 638157305, 151392660, 779705436, 942335051, 487000033, 148619671, 901344202, 666388055, 393066941, 54726027, 191645409, 684468687, 980175064, 464987474, 833480336, 695936859, 464097615, 402828229, 295634363, 853727004, 1661910, 958138899, 33754215, 431244903, 559227878, 183171949, 244173362, 428954133, 584028446, 583152145, 447569574, 556165918, 89814802, 978740599, 965800971, 618787714, 162891221, 284079827, 121087786, 136778506, 366529974, 66624914, 677243573, 620811433, 793088703, 335350530, 308776003, 510778331, 560004445, 548539507, 944485252, 929068866, 422083797, 259531117, 616175949, 338886401, 560067580, 56068534, 403938305, 244133026, 14701152, 872463625, 963999547, 480723683, 97051622, 817860493, 8632649, 587901920, 105791497, 503119781, 544039641, 468694243, 249831778, 410203092, 862064688, 179676223, 784850455, 217885201, 629649222, 262463805, 865377180, 597277248, 604703598, 556928608, 945023813, 622907090, 415827563, 39885883, 744104712, 416657176, 525432884, 140724163, 223387080, 641317504, 626482675, 675861094, 79295850, 724357963, 762270059, 474202963, 252982983, 309335964, 852023575, 18761755, 212480871, 291500510, 474320530, 985554089, 933603379, 738044811, 563917627, 903925207, 387100824, 427841910, 45834372, 92553571, 98102425, 446235023, 25095098, 89786949, 512483814, 492330064, 136816605, 30099403, 857366777, 104934903, 579573961, 660556988, 601268415, 26240169, 705633420, 819961837, 272848665, 950592612, 900366993, 985378679, 916037221, 171375585, 949992542, 299967623, 283407342, 586902371, 480730687, 4088114, 380394370, 846518041, 867835508, 381493660, 706952084, 349131763, 750459987, 214077262, 437482647, 213515026, 579824327, 498340209, 498202749, 625073265, 988972259, 177523029, 784369756, 411918352, 680773690, 57695851, 172042152, 523892175, 43706140, 582641462, 584292083, 688261450, 590012175, 575450050, 364291531, 695107845, 148741851, 583468807, 474626062, 258562553, 566000705, 212770026, 734185142, 267619855, 841904976, 796960237, 949019366, 500928349, 273616844, 601858185, 115202506, 254433683, 823657759, 925761178, 390652234, 20905617, 60797389, 376248729, 886385098, 117979069, 679843273, 381652609, 103936454, 786941909, 91286776, 761794271, 826854270, 113928621, 49796393, 403052800, 202560184, 849612874, 862639786, 954851896, 946197829, 347013707, 136982428, 952003383, 287436486, 238181924, 537279327, 28579892, 676414413, 160655288, 83043560, 667895652, 536182301, 685278090, 567135300, 27400168, 812549357, 725852630, 465160349, 921396435, 902934209, 727315626, 271807750, 234055703, 347941992, 217346896, 935937011, 989386614, 146767874, 870930333, 678406583, 186581172, 214804318, 792178530, 273792025, 191345509, 365145778, 301612373, 360215683, 379102492, 268158014, 956724493, 670556196, 506120037, 567746164, 113041681, 264033478, 601202897, 957627338, 840088178, 86824413, 445340116, 181509034, 416619273, 659185210, 870122037, 969490674, 350761605, 234399748, 536636448, 900739384, 974382167, 44417973, 102839031, 76166966, 278503326, 31102458, 943072102, 831756119, 960378827, 556842802, 306024335, 231584378, 503839857, 261105150, 129403563, 38240617, 566476727, 25028064, 65465971, 181578371, 837045496, 861095475, 732392588, 16785361, 261830968, 287649773, 192973925, 361958570, 875160560, 752728547, 218428289, 863595469, 295557775, 726614606, 922582021, 402740625, 307713163, 135184696, 526938641, 825723154, 473161125, 622463123, 415279809, 618053891, 981487310, 680772766, 206049248, 311165464, 456151871, 931405637, 876272495, 482680006, 530479461, 318895592, 253914388, 600544174, 434429887, 718953453, 821302784, 31339654, 502185703, 787212430, 786958035, 717125604, 89926190, 378926973, 260457654, 258326884, 333508196, 920081823, 888386730, 109721355, 317288849, 284888377, 871748095, 92999752, 129853916, 860626543, 961375327, 217319026, 767591300, 679515786, 861694653, 391141160, 88724233, 898719585, 193332111, 799380521, 160104301, 720185093, 812746383, 257409242, 913721848, 752988567, 972404785, 453738053, 143024510, 151131826, 171577136, 755425529, 648956078, 475703195, 193490964, 155830244, 401693373, 501547323, 149233723, 501253165, 796094513, 560557365, 674880158, 425847412, 789234724, 934522982, 235543747, 640964113, 868599905, 506939895, 26688794, 235455597, 119204086, 885724989, 418558546, 243624597, 979976483, 913358438, 654359926, 135937620, 569321168, 211509609, 307349745, 384998829, 563177493, 510387494, 322418416, 382155418, 179873810, 85818298, 40487879, 286977883, 264650851, 239246502, 433008, 795409932, 161143395, 851066705, 522577922, 51969475, 303097170, 525446882, 1260937, 813518302, 621876167, 768213354, 889225166, 564564166, 64079567, 855391565, 558931146, 818035247, 99770910, 278994908, 43228303, 281022961, 74639090, 36669996, 332255545, 409997028, 29504392, 515492845, 403369011, 594607407, 472078682, 319344991, 746437824, 611353666, 858373052, 617373639, 471994843, 763925526, 141853143, 369516300, 495755351, 133929659, 304278447, 340412102, 182609802, 194427504, 260506160, 912804989, 136246535, 19131913, 770883893, 222764940, 622729176, 999390488, 27942475, 292693708, 323781574, 480939154, 267234098, 44354366, 238789023, 756340601, 913622507, 810880044, 767373666, 952476974, 218531847, 337345311, 269719503, 124549413, 332859772, 913039131, 825371411, 550775739, 743858124, 250821189, 677756223, 65370794, 347351633, 85301263, 155371960, 758492635, 306945004, 507009987, 806625865, 587306687, 94151435, 445273913, 464176579, 594574641, 396701891, 68229526, 347861958, 49736786, 156968774, 486977742, 908771719, 387923681, 545191516, 589794745, 570976491, 983061156, 99594946, 863327089, 478535740, 173801790, 505716536, 980059937, 823448352, 310516801, 236536245, 596843812, 793446145, 509000348, 279449893, 371168424, 740725742, 220318780, 804525331, 148531381, 591440983, 787936188, 172089621, 839330789, 155362486, 176904476, 179920846, 462273540, 949684681, 116941022, 298917022, 963045832, 148226950, 313079294, 297045981, 272514387, 19472100, 787574941, 917085852, 685356712, 899339069, 452791686, 463182021, 63056345, 44241627, 536478890, 151523778, 395522268, 367864926, 838841020, 285726507, 554669659, 184905634, 742433109, 249409261, 781280163, 684857004, 460892738, 245052214, 312672979, 644463614, 44150004, 824160443, 195874280, 855248962, 169104717, 597163617, 103510010, 751954822, 374287915, 769316563, 113759039, 665659317, 661241451, 802341914, 11181895, 851763213, 135346535, 825844045, 638189759, 172707220, 188567925, 699433552, 790140084, 710954284, 5020665, 790507422, 909813702, 799202767, 789744445, 44956269, 988941546, 662253141, 471931895, 863889811, 858315485, 643220129, 609553047, 788851957, 813822809, 800287507, 293922598, 183525156, 870331995, 486472005, 722356426, 1426155, 466071882, 37128501, 21550214, 159863360, 904448010, 535656596, 134020476, 495084181, 155440139, 976719629, 767544431, 228240157, 726004533, 321958094, 385010040, 527642363, 336883841, 393828409, 552663231, 238746592, 874641217, 238295470, 490506067, 890256380, 313887046, 954571558, 625347754, 137036504, 299137324, 187974073, 984118908, 17567153, 677307178, 671898072, 593636359, 409297401, 470938340, 195383404, 663287121, 774337040, 168454574, 234914258, 591403157, 85601696, 120836858, 504575553, 301142091, 893963887, 762067181, 95759418, 200289891, 478819458, 582943946, 21537448, 996425170, 727074791, 239265113, 366577079, 635968060, 209879763, 384305484, 913054350, 347477148, 251727432, 461658224, 464731534, 979080068, 992882432, 565021945, 581353310, 66165450, 346489985, 462560156, 828518484, 389122463, 423075823, 619297788, 137971880, 747645232, 920305068, 377438381, 404712970, 655316265, 746386685, 862736878, 91442617, 877556098, 369810960, 504277209, 823766413, 507818138, 68788864, 159468632, 136847349, 348839851, 835510406, 159459664, 404903009, 401552292, 459435207, 628383693, 7539421, 515146380, 262182013, 659089754, 440013090, 300924598, 173328361, 803604029, 250969610, 191677037, 556387584, 472610737, 909624019, 629047472, 168708979, 769301010, 533755719, 319195838, 860266461, 298559175, 287451096, 309594172, 459704419, 829247412, 639996372, 41301244, 930750077, 249425630, 629210538, 14532017, 946954128, 982886385, 9672197, 262585052, 664742393, 749692050, 592716590, 626932772, 747161998, 482916310, 343875324, 274023813, 273160949, 423904105, 90029175, 874020739, 347848841, 219446851, 80505871, 917793532, 135853995, 631608006, 731641895, 526321382, 587101429, 890249558, 51830958, 766713682, 241537294, 620012991, 714012879, 958934633, 918409416, 309089925, 472080943, 246336413, 189852268, 396966351, 794652402, 677436245, 492197810, 438966600, 265407286, 970767471, 747527271, 415635650, 673595508, 109319236, 249603864, 698188341, 998080299, 10579186, 458689641, 333071021, 397600865, 837531047, 865092630, 207637421, 710313196, 485252187, 717954835, 94011131, 817893332, 922481624, 418417011, 547825706, 987001149, 467716181, 189803599, 933009911, 450364499, 366419009, 507471621, 297013854, 611625157, 913848205, 816940710, 363241574, 480376004, 632511988, 349268017, 99510975, 896800618, 20957257, 667136626, 682967420, 784432860, 936889935, 795903918, 709771676, 389322139, 709051292, 427393296, 565935890, 697876732, 299955216, 37364267, 939049548, 940010077, 831345644, 769648045, 7767575, 240758134, 871547295, 684371172, 340981263, 123073219, 654636490, 150638263, 906037085, 268941026, 825993582, 375449959, 888633615, 727905021, 434615509, 637455730, 875646512, 980782540, 115616482, 437050826, 625133362, 272940390, 53279330, 623642143, 650342096, 800562138, 373612502, 803727922, 134013241, 722570984, 925052253, 681045189, 595119700, 403399826, 793811892, 380288517, 452016335, 298884778, 418798496, 559519837, 446947295, 522268675, 746812883, 847977696, 440670840, 967253108, 883729101, 813625414, 470472376, 497893062, 565421185, 514770449, 37886862, 422107130, 877888262, 805448769, 317842972, 106716364, 457077222, 487386776, 619884017, 701647167, 323450706, 924675576, 610525255, 842585852, 652421730, 613903086, 677038111, 150424496, 659692947, 719704394, 916209547, 121672094, 529693614, 54797798, 355035678, 600808582, 367375414, 294615020, 543142894, 163510762, 20182205, 749075965, 401998900, 798941538, 766101146, 554427678, 116285338, 690396432, 953594662, 30152042, 265342790, 624927895, 406342314, 504305670, 144546567, 842780975, 215600692, 383314323, 601198807, 274737470, 838130097, 266973847, 320987561, 435707079, 860112419, 359254473, 497999205, 55304625, 805638418, 130798849, 690412174, 830031540, 407276482, 329203935, 553667410, 953334599, 145087607, 752962719, 263446847, 65441300, 546519690, 615474310, 110000670, 113613743, 794313965, 384112437, 979174410, 13444838, 286743230, 960285697, 540069925, 307282004, 148409652, 818464889, 883057580, 33644699, 436034836, 140356312, 2184607, 761906890, 884268489, 943341822, 420814233, 572487785, 292664984, 987956843, 717597808, 509417288, 767309817, 559812155, 695660327, 395390504, 534562117, 391757712, 7292167, 122059701, 957559000, 315275253, 778089919, 701002690, 181426825, 43522511, 874544364, 419889381, 184640792, 257743383, 169919953, 162725719, 530746589, 21806025, 476313762, 636951355, 800361405, 199108840, 382194066, 171850, 182032140, 882473899, 419825710, 230011401, 326551197, 538153943, 279350642, 975678077, 292781118, 229768421, 205974333, 228565731, 815782915, 517567123, 413415691, 754329842, 366819372, 491593618, 71984570, 779202181, 259947311, 585952820, 162426984, 952918457, 269362805, 337253256, 510218295, 649671982, 178624419, 94501319, 439764255, 113656980, 749911571, 87429388, 852778470, 526001577, 540223890, 631124558, 311330614, 497745293, 54532352, 771725480, 330326274, 953422291, 771513107, 447191508, 895359470, 584675952, 909682893, 842294783, 539964461, 543466915, 32259542, 429130140, 244716802, 588018096, 186919973, 13737814, 611496091, 614893652, 498994654, 352651128, 801803828, 919197043, 485607819, 108949943, 291446205, 972551903, 516407308, 413126928, 919424637, 896930886, 307862015, 814033447, 318545669, 808337199, 552441836, 142526986, 482161945, 333884475, 227902651, 375325318, 39716905, 761194257, 562130061, 199071171, 131669099, 834118162, 374503943, 518128121, 631198166, 684089095, 833168999, 299036033, 936907476, 480713720, 326609459, 696062255, 539999792, 341634517, 713933165, 60170184, 969838470, 98234515, 143644328, 447199661, 567459071, 173421784, 474477103, 591538911, 157378742, 970931835, 885372590, 593190162, 943680189, 843782140, 856553820, 961005059, 335999118, 132469133, 866426887, 39003681, 938035445, 64233449, 560301601, 659620340, 67489220, 854908012, 499436233, 396299190, 857356731, 420885009, 753668604, 579383007, 494250532, 754370691, 807814911, 393671176, 350419980, 763643068, 91942721, 298664625, 513244281, 8797265, 470654720, 617081822, 963548162, 234261667, 829281497, 314920608, 852863458, 490662676, 868882072, 628079678, 891799838, 1812998, 873499912, 38691623, 841533297, 167964955, 605066796, 924624422, 691771372, 439664955, 942670008, 654484888, 170748298, 747733646, 260786379, 842420800, 181424110, 815489453, 475734791, 700185636, 608358158, 226858118, 681415459, 96736907, 381944746, 827521318, 703542235, 155532871, 407634914, 372097683, 672932118, 612165085, 806007121, 613165029, 728944103, 729386837, 573812128, 98208085, 38742914, 660565653, 443433587, 942478662, 966984816, 252301134, 295644383, 508400964, 83194518, 726833898, 196571294, 330906682, 727945202, 291177859, 357257567, 876350021, 359804581, 882466846, 795423888, 933717538, 304795984, 818845402, 821064879, 710432881, 740586928, 111851235, 468896735, 250315980, 192487966, 953249374, 989150763, 755387932, 752385659, 724609614, 883040840, 826568048, 482726987, 421891126, 316418313, 658814755, 882765721, 433597764, 729608548, 349705465, 457684921, 770037177, 41844118, 914173109, 872405637, 623957606, 792914047, 970234671, 907160801, 313272429, 201980284, 4415540, 102294948, 463235521, 533767982, 858366441, 124631524, 854720101, 224014115, 179269573, 372916320, 367664179, 345584137, 440079604, 365731905, 906576589, 230396316, 696038073, 909298470, 820759515, 310697347, 394387811, 615547298, 277554074, 242064995, 186607097, 385874757, 366635781, 993019754, 551073392, 613802945, 351339310, 723933323, 216823676, 465630420, 808511690, 114580355, 607233196, 86344405, 902961958, 337238707, 670457623, 569227451, 473232309, 396057735, 489295628, 904032665, 96034423, 628704359, 187767876, 244720697, 96169740, 247451818, 157888538, 938261622, 532502908, 974541108, 16598964, 166183417, 32806768, 782528087, 581059701, 429308404, 487507376, 604568531, 502854853, 526553809, 149028214, 787161712, 721618473, 520562451, 429163690, 363157162, 220253999, 695225224, 982322828, 791164750, 337571118, 972845412, 582638093, 229689491, 970221085, 746856183, 920073521, 442360272, 933867718, 406917372, 820222333, 395566927, 74262648, 175459690, 348950108, 539590845, 521928331, 904073434, 479738473, 437525738, 593836748, 392311990, 985410115, 836419060, 567219940, 564571095, 322015210, 755193180, 675048605, 51872729, 997335598, 421763411, 224809678, 596705858, 494207959, 292840255, 384390431, 979223483, 423783352, 671024248, 291182996, 174291134, 113857815, 476449231, 598988087, 607520564, 241186112, 22518697, 287485696, 690042956, 597861321, 176692171, 363583340, 500981474, 529131136, 908673974, 226738800, 418333793, 382108029, 893220378, 425323068, 381068680, 791606499, 552518635, 814214360, 249422074, 971167094, 791650734, 972366174, 26095831, 952305754, 529716826, 87264678, 935598819, 139411762, 501010245, 820960210, 873972570, 381154881, 990483134, 305807054, 42694275, 332779388, 497658913, 826675642, 232820606, 186101300, 6452380, 131556289, 838356187, 242900912, 850609692, 390292465, 660518595, 625249774, 846890585, 167185603, 336847158, 104004260, 154733079, 85737883, 103773178, 527223041, 133049136, 480461050, 83233235, 432387866, 999455285, 562474336, 697237048, 564983857, 600563691, 755456968, 44454508, 601539069, 114678988, 467756875, 810206800, 367692613, 650823323, 832450066, 745362761, 440796599, 880985113, 263314425, 687540443, 131547277, 780405485, 608983333, 848629795, 121713727, 362244363, 20802011, 910794057, 657942580, 886873606, 749572972, 307550848, 991001286, 489857597, 451765092, 24809275, 401834863, 170047998, 669445711, 504031158, 707824005, 999635609, 378201136, 378164139, 867185612, 314606663, 754170687, 998551922, 35869012, 186699720, 411247520, 172236003, 366586508, 144939596, 866778617, 984875454, 454853169, 701985486, 636092747, 81700805, 153247666, 662888841, 505645766, 636735750, 96800926, 202773384, 121592492, 322859856, 602275330, 239591873, 75336373, 559535464, 750299632, 454604499, 309692294, 796412677, 492429571, 113770007, 93921921, 783255432, 158894702, 75289566, 38253721, 595188931, 225206247, 132825687, 83053018, 595960892, 84200213, 699640525, 173035739, 279346495, 840446828, 516415193, 476285079, 385936308, 381429656, 993492287, 777499323, 594569139, 19299769, 211946536, 323193473, 824004564, 28577311, 94173679, 95509250, 820897906, 669474889, 334962809, 229030035, 562798363, 194378149, 246339042, 280893132, 300305786, 951277337, 847652131, 32535455, 65399122, 881898648, 261940645, 443902890, 846479912, 449779450, 183159146, 400912971, 337079300, 20824019, 225133778, 276749314, 207861772, 90215278, 299106632, 505867044, 643516985, 526646587, 36706942, 738687372, 759633761, 253849571, 603903906, 804589932, 455301181, 463014322, 903006479, 562828633, 995624047, 745903908, 678991733, 489876267, 138401171, 848635772, 888164204, 739694927, 333582014, 248367592, 10721427, 357446407, 475434206, 320664224, 852006760, 678803159, 409826055, 717744813, 403299367, 963934599, 188580419, 209368084, 556102879, 109670284, 951323069, 984693169, 687725676, 545295012, 397147671, 372368649, 31046366, 779217099, 653421129, 203037957, 507225572, 457427594, 579724166, 42025757, 856843065, 139552008, 516148088, 516134979, 627741342, 630564797, 517878981, 707225372, 876224637, 472062017, 840849039, 692335505, 854080264, 975812067, 766960862, 455687168, 638096007, 404799545, 500240821, 615244280, 168298481, 889187427, 302653187, 325541097, 298196988, 702370838, 154390320, 548368091, 893741826, 456499954, 422473015, 377587600, 880675987, 972887979, 92848960, 439985665, 904178321, 518756855, 163439077, 501601045, 363576494, 107548285, 11079074, 346919542, 739876470, 35332562, 549592668, 13245524, 143062310, 650389392, 310000901, 137273781, 564696340, 17657246, 581107704, 662224915, 301333325, 844074554, 531132302, 667724130, 536413906, 27187851, 850600294, 321326826, 807319693, 256619042, 103256708, 755779642, 683467922, 646673062, 806091318, 818584041, 982805134, 622763658, 86972367, 204299098, 695723166, 238374877, 313058903, 599409902, 757769385, 935094903, 685387304, 551967586, 626401837, 27026799, 77264148, 958142238, 7021931, 902537294, 348505552, 156417532, 301182818, 380969143, 153256999, 432625203, 833405002, 983108878, 547444435, 624703926, 610310131, 301214259, 188384275, 413424852, 186605343, 928205672, 235866055, 91155011, 944142278, 844056060, 921357311, 547530392, 621366421, 868379621, 101890134, 744294122, 108400965, 585535431, 941223236, 202413414, 707964873, 954375981, 655806805, 148469318, 69933221, 481973396, 355094075, 291842012, 28583510, 520303777, 931691932, 373652373, 715224878, 340120109, 923074984, 656566333, 394603976, 193378397, 519399779, 242009600, 16249142, 205159838, 593127618, 133643239, 700501613, 507148355, 95810671, 518804081, 555480872, 838952366, 2722467, 232199376, 504242239, 992972387, 578617371, 175243675, 834856251, 84288631, 510090496, 527454853, 774153742, 451205376, 978473956, 672055800, 106895170, 658257324, 287447496, 703310011, 44245185, 281613759, 985117004, 806731670, 472746043, 131297326, 261766978, 93496296, 999631754, 930502436, 723861751, 447817714, 411571551, 580752396, 865672175, 460794428, 654252143, 705162682, 687675245, 522234030, 820100348, 398260854, 674209868, 1073287, 753762350, 125031358, 310295870, 726360835, 451312891, 569659846, 81852236, 648305201, 776455795, 937816883, 591725649, 958549189, 216967266, 982968757, 390179751, 208660960, 889006537, 756009824, 982146223, 554521392, 311129475, 500014701, 157545041, 20332501, 776257409, 948679308, 911461378, 278846990, 26078764, 567884673, 906617361, 999429812, 611685361, 291493954, 608793488, 900727214, 853224874, 66347913, 761303311, 965239635, 270941528, 137700479, 618612918, 65240759, 94973333, 434948543, 170983368, 353121657, 603331236, 494893572, 997580715, 401807424, 54371163, 794762770, 779150306, 407431856, 550733040, 650085067, 947941945, 984061253, 140142363, 248444734, 805084822, 278075736, 171120616, 191257921, 885867795, 382869907, 503122447, 343798655, 384161000, 514737082, 624615692, 707356725, 808810963, 226929570, 657378152, 495090263, 606067931, 852630001, 170937035, 712454612, 853122997, 42120808, 727284869, 341096867, 22916188, 747518081, 342960800, 541434116, 259919570, 349127, 993343309, 626957752, 294428033, 737854833, 708209238, 309401533, 89247876, 338569055, 218861075, 751517369, 605433330, 132254374, 306074196, 512702090, 752793226, 767048599, 504130315, 491045674, 341924584, 910608849, 637168597, 981983350, 522503466, 634761242, 842141589, 568824613, 330413190, 76174864, 151965562, 494736532, 745191988, 61228323, 410754245, 300684995, 901179527, 299612696, 795948597, 984356687, 315227548, 325340712, 720374318, 675427002, 106754704, 157232235, 273125698, 80246967, 154867932, 945585378, 532734615, 509582186, 296879847, 504462953, 965241506, 731614057, 43159677, 597928482, 330501085, 201375012, 293116718, 789470025, 412051075, 123429227, 975239366, 959980500, 355217012, 676088395, 860350698, 644343162, 42805924, 850842927, 617621396, 399950486, 579897164, 827421169, 938043968, 16870023, 369030755, 643319719, 49010457, 847888143, 392955385, 861540428, 521128128, 338350848, 821243982, 175778591, 116316082, 441043590, 498558857, 67113237, 365510371, 865564135, 895616843, 743361912, 755817912, 274680224, 667702203, 331649606, 296293474, 265490951, 797897015, 427017048, 513697670, 276335268, 797377010, 316447667, 59199545, 91552432, 251685847, 755105758, 533615198, 280849262, 571184940, 477250279, 692446598, 598228469, 216265570, 897172815, 512751725, 459802963, 47556047, 824621973, 801694655, 576844448, 71019235, 782710850, 540470220, 439892195, 305117831, 227232427, 471042743, 712756973, 123412983, 180832466, 675348514, 52408662, 175893445, 196900351, 256446609, 175193596, 726046383, 82372866, 983564175, 866158019, 471862971, 884272346, 390602269, 436928712, 614660183, 644288691, 422304872, 41869798, 181764762, 261535194, 426929939, 923357917, 87827360, 60596586, 247347948, 769012480, 479205598, 931963956, 967720718, 290070190, 247361720, 62988197, 230649759, 987472641, 196923581, 3020652, 265541235, 950332780, 218729854, 595953973, 585980485, 1049341, 472378275, 915531017, 966696050, 328274778, 332339825, 100782021, 669862095, 634015965, 431928420, 876412218, 471742221, 341240474, 26411080, 811219030, 954564390, 662428408, 637180214, 683937983, 991082328, 872685635, 274240436, 614234364, 84066481, 292074727, 269987752, 730504483, 59299152, 76097898, 33234435, 4707415, 321995643, 291177990, 219800510, 336158875, 306987359, 213596888, 804688165, 76352290, 866148290, 268983350, 515389464, 350744158, 232213927, 229038912, 411478417, 91276077, 76120473, 239865962, 72768319, 674391680, 293279925, 658195814, 145271473, 718192601, 442842733, 141455265, 411955230, 787858555, 341936714, 14896526, 108465692, 907801107, 363027072, 567540935, 749349823, 874020240, 335409888, 364388497, 81386145, 353465126, 28677775, 271651389, 109786821, 210181167, 810454502, 4119885, 471715295, 392262679, 272102105, 795880843, 341811774, 608510591, 154952936, 645254885, 756387854, 309306425, 182736007, 80538287, 671847088, 839015619, 109286328, 927619921, 465487020, 322896298, 762295577, 243062349, 927160927, 478436486, 981151512, 627651722, 297385933, 129442147, 764156526, 605525100, 582633598, 136131263, 274738902, 846923848, 966792777, 308713592, 719511657, 29870503, 948788382, 857738320, 489596091, 948565876, 88212201, 963598575, 218263680, 888716879, 863492698, 313352910, 224431206, 488039853, 746572565, 960599248, 807108758, 77343710, 165977337, 314360776, 860285583, 845450648, 331869266, 231444848, 485783936, 124786773, 692279043, 735881960, 86716194, 533038415, 395733870, 481907322, 79901425, 395413660, 636175044, 7972257, 667917360, 963383598, 190773384, 795533673, 885491635, 43106956, 309843017, 219121805, 609611326, 525457480, 455795613, 323573405, 20775239, 634898447, 392909801, 619959599, 4364973, 245444266, 311852750, 398931584, 836918116, 830431729, 6179725, 365396715, 236529057, 410446320, 986781053, 759817341, 412089055, 683781065, 220035735, 753353454, 839021563, 769140388, 27883023, 972739683, 78818518, 185360838, 623684733, 143053054, 638283146, 636167349, 349866027, 107063186, 878962912, 813174934, 758421025, 701540056, 85176722, 640681566, 78692219, 246051071, 172531813, 463400958, 688910160, 624785059, 48315934, 750709744, 303766313, 856783449, 931617088, 414135145, 702151870, 377205554, 671135489, 29653348, 49511929, 477881760, 436209714, 135628027, 802668726, 366100099, 403868931, 124967851, 32168004, 214985704, 978536328, 490086959, 460321464, 149576320, 97265789, 976450769, 438008389, 339072412, 656209103, 119614048, 418919804, 209521705, 914807537, 177205340, 581579776, 831491660, 359286813, 799422869, 738211743, 483675752, 764491357, 255929965, 185567232, 910323464, 712603003, 360588102, 308422388, 944043506, 630448956, 719358714, 369788555, 930512707, 797651110, 146319052, 268063276, 109011404, 801815204, 194773774, 598527292, 686878087, 953818032, 350190002, 132463614, 946165673, 914386438, 929622586, 31011207, 168685941, 37629321, 295071029, 453958026, 68973279, 274654257, 880904438, 911937400, 954331410, 491575905, 662685110, 33125488, 830650132, 250206619, 137772541, 164874543, 517084669, 781965160, 49569870, 281108956, 559037099, 987558578, 559638001, 225719175, 807159003, 440466585, 221791771, 893810416, 273962374, 591738945, 136459156, 111930935, 357113791, 77250565, 920201686, 27652921, 168061656, 509320230, 516236067, 228649175, 774019665, 303946537, 912568273, 763982616, 814731048, 771947795, 334699555, 628612266, 596320429, 359215528, 682801891, 610310506, 93248248, 546367917, 716583227, 509610741, 125797324, 202732687, 272679576, 1566601, 599410264, 579158307, 986106133, 226082651, 9196670, 452031023, 377595955, 367211206, 945739883, 934168080, 411854489, 541875469, 85079543, 643238705, 803234091, 930067972, 61248417, 932082998, 48275023, 699265683, 48090667, 40563186, 410666315, 310785172, 954924700, 64499823, 576291359, 803790065, 763516453, 319717553, 631613305, 134729877, 309260974, 570730339, 298896114, 624164835, 68189626, 201075232, 930238317, 832210948, 387221131, 379234378, 581078136, 163310224, 626566813, 651528636, 314905808, 13715252, 647461562, 425520697, 782160862, 13790874, 318687662, 626706735, 873305154, 222712864, 819672815, 276759749, 443233133, 827780705, 794394959, 133790435, 241515, 19590787, 54039318, 415013753, 147581836, 46625924, 92889757, 508140979, 155224236, 8908223, 725387605, 779871287, 909809433, 847217386, 244412946, 494377820, 91464815, 722049408, 854090353, 838274522, 292201407, 175902588, 405074835, 879817110, 278636758, 990291673, 501230063, 771141450, 466565035, 20134486, 998308196, 435346588, 583540864, 336495482, 516189271, 727287876, 121376351, 759083153, 130222151, 989673181, 312390828, 213376807, 251154842, 72828133, 347163791, 573150579, 44801007, 758426463, 771117180, 598612227, 466033922, 983961311, 836608657, 691703808, 462537714, 117702848, 142700122, 39927497, 400286121, 343350224, 448272113, 457717101, 660334804, 661323424, 800828097, 649898204, 238974644, 621253816, 237644022, 21394704, 18123825, 724149981, 302630605, 328909429, 541812005, 269743978, 902189488, 733845154, 379746703, 125592107, 356348040, 898544769, 742083643, 638662725, 861458055, 300704556, 57960267, 594348857, 273938190, 582957275, 45761410, 490665613, 374629510, 294037919, 904040790, 175524620, 823512783, 185239212, 542256019, 634630394, 762726173, 111593753, 392390659, 507474845, 614478438, 509120492, 967479295, 570781248, 204366439, 43729486, 305249271, 379815559, 326375174, 598175359, 77027376, 222130061, 689566924, 127085324, 841837324, 493629956, 308368220, 815004732, 94011610, 934500887, 532192852, 52085408, 101605081, 573464966, 902797262, 511750870, 533480792, 975644147, 838130212, 44067041, 775639688, 717380387, 677544053, 879614676, 849979561, 488806939, 292690755, 569430596, 399265537, 273423626, 451424875, 283165157, 51614068, 719900712, 251749337, 477550408, 729368883, 712658770, 442348107, 500498376, 533765664, 429132549, 869559432, 28391562, 565553705, 47536227, 105120973, 659717322, 211334714, 675586740, 672214740, 520625067, 59518038, 363774808, 412520611, 168758003, 125511572, 274552628, 998319631, 819850490, 127700024, 345733417, 866491539, 260958064, 747458265, 756555289, 467356946, 49025781, 888989615, 18955356, 943318907, 223375917, 472322509, 839264788, 962731500, 18373763, 674186799, 483691233, 287699619, 394382480, 249063594, 177133931, 509862015, 300434737, 517869700, 162903855, 887831408, 17081290, 832372463, 193902147, 618744624, 949572142, 400018469, 365338013, 993611400, 322078411, 14412190, 316317087, 461222651, 724835889, 216746160, 422324153, 758037318, 523416651, 25971966, 397736414, 947742921, 602889233, 253001174, 366678080, 335732288, 330947431, 606806497, 365220294, 1462533, 493351584, 15010989, 399621255, 599092291, 841883837, 19304563, 456186135, 449885657, 841039626, 177284185, 111779506, 147872243, 179645108, 956344328, 115186766, 812040138, 762983109, 772874994, 307718072, 264128625, 131825355, 220738025, 560712238, 426321346, 926309996, 694145216, 721149714, 974693059, 965643779, 822697210, 277136118, 738418906, 822884858, 469382809, 244975983, 72422893, 825364137, 780016878, 706408504, 769934716, 687462176, 722060755, 10435324, 566990662, 532170938, 383736607, 99254347, 575147745, 997568637, 720203232, 943868770, 436527114, 415693868, 259218282, 722085351, 518246840, 789285592, 898287526, 449102767, 793181179, 806927494, 859547188, 438742317, 940060614, 292255655, 958912907, 371037362, 201573712, 981341186, 288688140, 430325864, 320442932, 780183623, 577630137, 713001794, 303340728, 611301852, 428218252, 186955055, 278908837, 270473175, 183226485, 178703264, 771768930, 720853870, 88148198, 378287345, 339613481, 348088268, 245394542, 836716854, 759825472, 908951770, 237515786, 735892832, 211334542, 231098168, 216322645, 218098514, 631449621, 687141486, 265281288, 278197432, 69428162, 108040680, 328544366, 800536756, 970680472, 699575151, 898791987, 78968650, 16307726, 622702406, 448488082, 367967619, 577500600, 487433747, 350902033, 207444368, 6486453, 997194843, 91199240, 781881569, 565525725, 524532906, 950308773, 520693729, 734788432, 242228010, 818281151, 629790800, 648718418, 904644692, 121402358, 474885458, 980084251, 615086010, 463128921, 344573756, 525003540, 723318395, 976922538, 317083106, 283296013, 862407203, 167985345, 840442640, 350835330, 409934654, 849550879, 323058386, 772099836, 607885987, 699209238, 346998251, 52642402, 391352374, 780698389, 317688305, 655360324, 170564486, 991941413, 825350213, 279660862, 437709892, 460395511, 522703863, 282638873, 798741780, 303949678, 21507056, 440826544, 935580456, 566382606, 310315614, 816346169, 768483402, 621481847, 423729807, 792883632, 304454996, 114261947, 293553660, 99659489, 448387087, 199109541, 952110272, 836308647, 797452788, 192339000, 549022692, 871819452, 164626996, 378127861, 539590116, 358073785, 367549194, 840830866, 660700424, 427730165, 54297020, 356442819, 290476152, 220104825, 459576902, 999402942, 896686287, 445426452, 643790002, 513075886, 82525027, 169543716, 698723951, 759581233, 699779422, 683931787, 794687063, 829398661, 516972090, 602261659, 308926345, 677469924, 670347735, 945214899, 825680089, 8241522, 182300987, 402365909, 952625971, 476530458, 300288408, 345324021, 357096280, 710901085, 367581301, 394396551, 425243208, 344131463, 924836572, 285854297, 71337918, 105265701, 715685044, 516631475, 366651059, 657335452, 345644403, 948985305, 919964644, 635711434, 528617184, 11366851, 534289110, 675785459, 534705671, 76126783, 816006469, 995607326, 384685882, 199831315, 612393616, 528644132, 957754555, 209018611, 934033111, 978354087, 894623191, 418261699, 697116900, 44726549, 778752118, 766178863, 216824018, 703269954, 35429709, 542796113, 239394651, 582379406, 233127181, 406048947, 558900170, 204179245, 417179470, 771912667, 482475141, 422713235, 243589721, 466910617, 315029013, 519291465, 333177672, 70010498, 592445348, 751078960, 779163065, 277967051, 84403913, 534077, 394046359, 288873084, 981985836, 977690679, 873750047, 551270972, 164832864, 145061495, 416200494, 974295365, 344822591, 566522641, 394473699, 859961900, 446188157, 468269894, 334770446, 434540463, 525282703, 518008808, 138474383, 25529740, 182237390, 151235695, 26344826, 33531072, 445908646, 66380264, 595050779, 210308128, 602383865, 841614987, 759122598, 936076986, 977793448, 33324623, 789627345, 327289047, 311287224, 591140580, 516757792, 61023073, 341015749, 403758670, 447860175, 584666818, 670864171, 632952801, 416670365, 318826498, 496678871, 76700048, 402700754, 684300700, 531450029, 816085483, 665673479, 808178120, 412534582, 994907815, 96165668, 791820198, 32425513, 414852364, 894644088, 875719614, 20165962, 129529423, 309917181, 586839102, 252804809, 272937772, 405548376, 747082929, 918847590, 892213693, 448849161, 287943630, 560520722, 41099651, 344069311, 858964086, 769684170, 703576234, 391544911, 92824821, 615926077, 769602053, 916677045, 102206603, 318539689, 74144617, 703594238, 691287905, 942643365, 618831238, 933114262, 176965299, 383399242, 850203575, 33759475, 650444141, 375407612, 857817471, 778523635, 221032336, 777163111, 200514448, 703357632, 165062472, 554418890, 281181784, 21261289, 864941665, 576299760, 913282810, 802828768, 90390955, 895759223, 743317362, 917647131, 374328911, 755006595, 78037841, 203981221, 141915330, 123334474, 544662014, 894688957, 3129072, 954368147, 141821580, 247950886, 697919323, 73395494, 808137480, 767182913, 469678548, 595572320, 740725689, 337268045, 53922488, 414351769, 788250364, 451288814, 660008309, 277769666, 370460378, 202117331, 166543654, 909647841, 667049197, 133447098, 538465467, 750734303, 975797291, 781114222, 696021313, 864547752, 303517401, 416907372, 688001548, 420072397, 236845950, 699674629, 277380358, 676434434, 949337122, 138406650, 265935489, 286705836, 189162265, 285574170, 995700635, 598584002, 768369647, 43546280, 713026718, 927855402, 645725818, 261903090, 916533087, 624912356, 879589763, 206625452, 555431775, 955024790, 624556438, 936743494, 31358075, 838955981, 688128976, 999217717, 627490669, 996100033, 725827911, 580876210, 330838545, 66631684, 538614394, 489633817, 521347772, 434313671, 414628404, 910033903, 167448328, 315242897, 964579390, 457698856, 393133320, 912362879, 422170362, 625976039, 426071329, 395426705, 24146330, 402982785, 584732950, 951238810, 668978060, 896681061, 399958118, 372286825, 906345022, 361242009, 642826278, 602671653, 59921087, 470883790, 6171240, 221901154, 80530451, 940572475, 369272976, 159050404, 626040046, 789581909, 849195667, 961184889, 919727631, 983864478, 357121036, 827878426, 811879156, 171836076, 250128627, 933243951, 30589691, 225427713, 882202893, 566548791, 938475743, 127341287, 915741228, 766555079, 1587683, 116582782, 931155138, 574312519, 310839147, 314016824, 401561679, 428044190, 497317200, 872400778, 417863236, 954613895, 489975298, 597460299, 954001842, 207119449, 239738147, 371129008, 707484338, 954659810, 922336765, 542583172, 670247651, 636164531, 205599344, 62718669, 460037520, 196880465, 739780648, 212633100, 27012885, 736275764, 631100032, 10051694, 747146176, 746685209, 906101682, 638654241, 3665865, 451057269, 973533707, 273054449, 550430595, 6111708, 564292081, 58941981, 778661486, 670828682, 659013828, 309910666, 259254310, 158950106, 370078691, 863150754, 46272462, 397948660, 173077842, 846997377, 42851308, 95765996, 763537080, 703396496, 673249894, 691860202, 551891619, 837976032, 884398172, 73793849, 905707761, 317074207, 164652720, 470142916, 562619110, 512753340, 986492838, 642777847, 6354271, 359970889, 801994792, 845070482, 785934339, 360976462, 334116721, 992059265, 362900116, 245354145, 676033522, 505767025, 140117135, 233586667, 66056534, 278047158, 993172274, 509972581, 223966186, 972589452, 330989404, 254798936, 723919868, 592922515, 187272287, 187999862, 793225844, 312073504, 833592618, 106063724, 287152445, 692831144, 558874070, 136455, 734432171, 253967746, 277617807, 576753285, 359764178, 551347414, 693962746, 19094212, 67450498, 445978811, 37677300, 449619456, 145710235, 609178657, 355428884, 834651818, 801628964, 96016193, 564767128, 378598268, 203346166, 976963112, 381938699, 886140668, 778394259, 359673223, 377476822, 143427020, 934353337, 979958483, 635584437, 319117582, 178804381, 234172140, 851191527, 957856759, 819713313, 48368099, 313379989, 265141668, 27578257, 421889592, 873158703, 914122338, 523946218, 880484083, 707135768, 208939077, 318179490, 967159963, 629485146, 386213878, 801049463, 722273795, 991523032, 250267709, 126537048, 81496523, 640515931, 198373371, 624406397, 690392596, 136691034, 555056998, 555406152, 884538362, 123571657, 749630188, 800979894, 244587021, 83303463, 370619012, 619518176, 157275768, 11497896, 622720070, 671269785, 523282528, 804156335, 662596981, 194858145, 29610450, 476781315, 764794912, 854829465, 203694909, 815136602, 656488244, 90577211, 656491398, 601229421, 383190077, 62103533, 360943589, 538290737, 526682119, 670442866, 769246126, 227917602, 557877997, 274962456, 939530476, 872630531, 968579987, 266390249, 237029062, 407334818, 349939367, 369895639, 371741323, 824838518, 131948779, 285637578, 280763227, 354878016, 547578866, 689476647, 727212434, 824487586, 194384146, 98863431, 621469240, 926253645, 747369952, 212688618, 939484429, 120734020, 566618824, 614910812, 179381690, 171084273, 826779925, 942069745, 345361741, 280173662, 360116255, 697606655, 419345688, 537275267, 661058480, 47022952, 47462942, 509742274, 58329263, 773025156, 400566257, 745855834, 30907139, 506000243, 779257994, 246513674, 355884307, 166800364, 834782723, 396558241, 948565471, 577477205, 304789289, 11407914, 971190835, 381684561, 905575601, 909173908, 648280308, 485640651, 58122435, 384028336, 290523459, 696595799, 847206463, 214293134, 973786974, 25808633, 943138330, 689613278, 354657283, 918895405, 109585189, 492224537, 305621500, 844449536, 1981115, 810973767, 851395130, 719637352, 274906634, 877142623, 562281547, 167072742, 837587774, 444480348, 753273110, 494400930, 793335570, 495633575, 635973932, 177437975, 170486243, 255364801, 331484739, 465741292, 186863186, 171779898, 114244391, 725082975, 210555636, 743904882, 597860982, 253161427, 161114031, 634119906, 550759000, 836848822, 21689123, 369446673, 588286219, 55398026, 230573389, 731041143, 945731857, 220233530, 483267707, 967827554, 942676206, 98628368, 754374776, 114941647, 81140203, 416223918, 676441875, 675455920, 132599917, 426846667, 73361693, 185033784, 750489822, 39651952, 405973134, 465673550, 509036968, 818463127, 265241464, 917527218, 188951446, 504349793, 32883883, 848637096, 53285478, 547199763, 558653589, 128690823, 704496015, 622874009, 323620467, 564213773, 111470097, 589725659, 165858007, 502967771, 667204064, 571311880, 331891928, 18241935, 472560382, 172068734, 583812279, 794158111, 354478823, 257078024, 751880093, 593443902, 651965532, 75093005, 208425507, 156636638, 524092256, 183167082, 495736626, 794473942, 492658390, 166195496, 768407698, 768950583, 437172722, 35665201, 817233433, 80438376, 907797398, 749557771, 898026295, 683045057, 151519936, 827194715, 764204640, 217458895, 133776319, 144599035, 411921019, 704204086, 611453839, 374162114, 824891507, 164122143, 836589849, 605615611, 217859112, 902662874, 394831311, 637607254, 575169282, 800030381, 497002710, 650997486, 362524743, 747174634, 655357890, 305956891, 925098283, 523114204, 387867506, 889697959, 688435396, 165792841, 768286970, 389520063, 387448565, 118633801, 787226464, 650070003, 429046251, 163609428, 34668457, 45521116, 507464393, 393924576, 389093615, 372333314, 360527568, 965853717, 266071460, 660485360, 191997465, 916152290, 651805856, 598368600, 237711689, 38559696, 428570160, 974216749, 133675820, 6280369, 168162907, 569527871, 878645378, 156226192, 350193805, 331679186, 300322035, 482208536, 321889727, 24446613, 941566190, 908115494, 731258454, 161618923, 998974512, 326543059, 961746990, 74503316, 308675290, 469927472, 494480207, 936011220, 464596640, 624191746, 456928972, 739597217, 343796821, 478940258, 659655766, 596736287, 406440355, 807422328, 734603455, 973533709, 175194365, 6802303, 286586552, 448621027, 534532358, 96179426, 292135459, 407754378, 652593551, 631127561, 412208706, 408544449, 420583980, 583759519, 761581033, 319115566, 62674934, 279907075, 138681886, 421503296, 102404411, 295022457, 63742111, 187607382, 895411841, 680644612, 23632721, 540849616, 330412243, 150963154, 76280870, 501598607, 123651771, 952848533, 117513319, 97193703, 487513383, 386282671, 958151797, 289889111, 485698810, 104645018, 780481315, 38401948, 670669890, 639501121, 938114816, 219689111, 520213635, 262283309, 901302393, 145396696, 308235606, 724188792, 781008513, 719237187, 889455717, 591210483, 225588961, 27177056, 668694747, 815247160, 948883962, 580962229, 679734409, 469728341, 323015353, 221388750, 661419368, 389042475, 718632833, 77164446, 482039392, 337108227, 636911021, 182274850, 630942894, 140126897, 887542240, 472317092, 321141246, 814471726, 117989669, 54600151, 473343111, 700815318, 465520622, 20765598, 836280753, 216748760, 763550341, 127731477, 255967670, 259660875, 647270634, 477714936, 283381924, 52246746, 230281456, 984787639, 829501764, 972165415, 906448818, 969318173, 462507029, 92552300, 863123364, 765538974, 437440798, 756256034, 923776637, 32056350, 24811060, 886981298, 602058500, 264335022, 746931616, 411491479, 837213410, 820041357, 693066443, 611621254, 746392781, 855064473, 292305280, 388639735, 233304939, 966715940, 41113925, 403423047, 708150866, 568135508, 776887607, 374190086, 924389812, 714248582, 904221726, 152741436, 879016637, 864085822, 59878782, 339091149, 818546947, 988330764, 97271430, 441932814, 691402693, 225305253, 78986220, 316841370, 313930023, 141049949, 839597275, 244201107, 443706712, 96415466, 105961813, 840280439, 188656385, 211266547, 227850165, 924837827, 239145553, 526357369, 126252816, 374500394, 682798911, 493768817, 639718544, 106228260, 117340982, 649501511, 96618806, 162317011, 874923341, 549469094, 282734706, 815314049, 361274868, 512377781, 911884384, 131613660, 663684499, 419153345, 249152862, 322501649, 188572320, 498036905, 878038981, 593843880, 169870020, 616140121, 770874675, 100848267, 55104098, 329740501, 394034196, 572975122, 894579573, 998198764, 106549152, 227666644, 2836009, 765729681, 623818589, 927027639, 176660416, 513200766, 225882058, 857449297, 644087563, 881121435, 595379135, 507260066, 413532575, 716775216, 221341108, 36370262, 506327199, 415802787, 924595018, 654820986, 330125572, 262200142, 184486541, 510103948, 830605770, 134837001, 94269470, 478558788, 235182575, 60056264, 805417912, 88630908, 563426627, 218106157, 565231815, 419109602, 206642620, 918525837, 62112315, 422005459, 16639142, 312842017, 182910673, 76826371, 846928365, 356232375, 484898203, 337821222, 465872814, 944088378, 15087559, 128258020, 778049658, 284849438, 784457504, 46880140, 505785892, 746956277, 508179008, 447883665, 919324739, 608501290, 830995999, 485924863, 465375762, 482114104, 340130703, 17093569, 811399868, 70430942, 458342214, 210155644, 40316310, 329950439, 287198863, 534650769, 114407704, 130577434, 732230435, 499066347, 74131918, 550179784, 898442144, 764086520, 358950083, 766651477, 725557112, 473666552, 228164578, 436371007, 81359423, 530979699, 190238962, 447048702, 530559015, 560197666, 33071433, 728001303, 63608677, 93676469, 596005987, 848681828, 749544233, 717900358, 872554931, 856171127, 428183314, 303951902, 452565174, 107475052, 299238894, 645010815, 414789583, 773897863, 343830692, 376562730, 660394972, 486295161, 124868762, 669751826, 751470236, 634277053, 156396053, 498138641, 292729184, 573010447, 100913693, 369560033, 182003488, 511811917, 736236010, 437125361, 949374004, 490046333, 963246738, 259620333, 62521003, 774297932, 955152851, 349796873, 96644811, 684452761, 225123239, 495654107, 665507123, 644826919, 898484919, 221611021, 985274848, 131251482, 311112178, 70136389, 181540010, 734200283, 913073446, 464769328, 177172138, 5261052, 827149502, 474126408, 565820391, 219211892, 909448638, 241715063, 308749550, 14472089, 569050805, 343535526, 930181590, 833644264, 893491197, 271090975, 513530281, 940042284, 192547564, 402588308, 682207499, 41912788, 400557369, 256361116, 636869369, 23739839, 614110853, 604785610, 462690687, 74326839, 895282858, 887949286, 760621772, 334884756, 513525968, 156437406, 29951050, 397526164, 112040868, 833070821, 295693385, 132005261, 255298664, 92467741, 631210150, 759483409, 36629504, 898419620, 972486626, 191051388, 774826495, 913095695, 413846008, 616358602, 338284152, 166215278, 172269282, 212904639, 458350559, 545964413, 97697848, 755076026, 338637972, 49234415, 36442070, 329728118, 563346499, 532091694, 685054867, 604027800, 14829640, 182546154, 176340308, 5970052, 1529375, 962178547, 634141329, 465778999, 516715593, 853361205, 431091494, 501136499, 347458881, 572265056, 710173427, 45770766, 220881277, 676748598, 745303721, 558894565, 57210969, 643780362, 412898655, 478867975, 152215999, 569997057, 267873507, 249443369, 235410360, 428703886, 181261863, 241561832, 511995468, 68413166, 811839632, 303936858, 812875274, 654739770, 834689175, 951191218, 688404255, 204284885, 196593660, 64841274, 45386093, 673865389, 529302137, 220409501, 379534571, 813213470, 560408080, 547992729, 44453022, 331186382, 475814994, 64313694, 814578431, 514007812, 16672094, 802306469, 972459441, 1405550, 384064935, 595300303, 578709177, 434360356, 18570009, 492655091, 743778801, 676181087, 103725683, 480492340, 563294075, 617802667, 679123288, 785004296, 337531899, 780442449, 933421412, 266253070, 834571921, 532186986, 633963417, 893331951, 802755188, 596103921, 13785244, 4098596, 229324060, 345622909, 976191160, 204998233, 655690564, 255276044, 379248461, 397004064, 254245716, 184762418, 94922417, 992515947, 256114901, 422046468, 51468799, 52340223, 688582806, 687906851, 572036359, 819276210, 538339145, 553178285, 626307946, 732707498, 815952838, 687854363, 606507813, 748085220, 324390051, 167219874, 686451017, 15435942, 234405244, 259246610, 678499730, 689580899, 663503503, 353470968, 869455633, 690144856, 43720259, 957047650, 781346303, 489283000, 961001681, 768259120, 563994147, 298249992, 765666580, 586816110, 669859053, 164042926, 36223189, 366936781, 388461061, 385332579, 781593369, 872854379, 679735822, 309149234, 165421338, 118607777, 986229295, 548718956, 183337636, 437938332, 841444483, 110634513, 848880614, 308441849, 974393552, 874895908, 891697552, 534909088, 885995416, 230606857, 67928181, 969245224, 311475631, 88682426, 803392596, 628456979, 741452262, 666455945, 914324247, 126435115, 582512021, 519272548, 451281495, 445846504, 9340113, 857461169, 66787062, 759500984, 968040814, 142876765, 580470482, 423852676, 602328049, 139337477, 11517719, 703464644, 978035012, 146970103, 127319194, 936176880, 606045078, 242073569, 332581814, 948270084, 794393449, 421769255, 93068290, 935215521, 292073598, 321062439, 483426274, 780692179, 419041235, 64015594, 66295981, 676436652, 581821969, 960822588, 73672453, 579836988, 82330549, 516742276, 221577086, 425104969, 976741976, 236762320, 332853018, 545053451, 373746288, 717925409, 62024803, 100391442, 233542162, 130767988, 875196115, 665249421, 159270098, 626072642, 658319413, 751338394, 146901992, 207350173, 788318092, 101182383, 241154502, 971649735, 409785466, 698181415, 203642481, 812299850, 324022699, 962931526, 62539015, 688597261, 282811166, 663467257, 482006783, 187847878, 354765320, 134338525, 531267570, 877718625, 789444174, 744543442, 935859526, 904182496, 610004400, 515797688, 317200449, 591291342, 685184438, 118667186, 768625404, 219201766, 469258478, 403895575, 294611592, 876292847, 777345433, 379809622, 51052012, 292041340, 492392263, 767892361, 615218279, 999298346, 779972011, 900891841, 571241560, 307078275, 998736286, 642246553, 959601829, 320119988, 382511917, 662441686, 178480874, 247654954, 929544249, 344463283, 477424845, 451202124, 189567238, 400523867, 975841121, 392592330, 11305005, 792514394, 350777665, 221506667, 649603846, 903428383, 868488500, 992010851, 244213724, 522071303, 399331904, 752846266, 717446057, 784245358, 464632713, 713090267, 629901542, 5979383, 161049790, 707976485, 410108815, 555842951, 772616111, 220238375, 741365887, 799413046, 176572416, 851316727, 926962134, 223149574, 13540494, 378737186, 992998791, 590823221, 672504243, 761070300, 555175928, 500008875, 853134766, 866974787, 405924346, 540839602, 285927771, 824890779, 431436321, 484183082, 443026111, 896769395, 38004515, 665761414, 610806104, 873335971, 436742526, 797176470, 247162340, 143293563, 352355954, 590806481, 637428822, 706361473, 406562930, 888393574, 711896362, 57238668, 215002429, 866296990, 804173396, 144375390, 211537060, 534865171, 137994320, 177022526, 273808417, 552052594, 345234863, 33078003, 748187637, 603670321, 107893423, 904905425, 425626013, 501838856, 546161906, 734164157, 529104215, 792152139, 355093769, 761995153, 140357303, 83384383, 514916641, 174771544, 21125058, 624900121, 266162051, 605272175, 653629142, 681851646, 568736596, 132540582, 767448160, 799996207, 135942914, 655733352, 366303819, 793280790, 611307483, 916268811, 178812712, 840116499, 338407692, 682996055, 894778566, 167853599, 731381734, 916442293, 546891301, 667358817, 219974891, 505135635, 426043596, 810986119, 655034577, 257103093, 661292476, 185861926, 307767284, 153894013, 506821987, 508980076, 66632587, 571228972, 660551259, 246533494, 19579730, 576449067, 554374940, 153977045, 628969390, 226017798, 246351962, 388977965, 53900891, 354115890, 498658072, 756071954, 850359907, 93994583, 436697835, 720723736, 515721514, 613434902, 106865457, 505947037, 638403860, 808295164, 729253157, 880018396, 81162229, 711371909, 938192712, 945251039, 859134601, 261770885, 709373395, 553953846, 345946735, 272986839, 225462337, 595387169, 98283278, 462863000, 164134955, 227957351, 557935994, 367290060, 234615338, 383629127, 400474607, 423925389, 842745965, 32078394, 24310237, 634158729, 89400319, 591082560, 903585444, 776117466, 109950290, 684585224, 364465125, 804623536, 412109860, 711942302, 18311294, 245897873, 453014637, 55152324, 865389273, 149518297, 377974439, 833211359, 333945366, 769963559, 75356638, 645490890, 681127287, 391679875, 390282160, 371660941, 257553030, 52615770, 798331209, 887546323, 836556725, 152532505, 873006083, 126803876, 835365876, 109134314, 242953122, 129750628, 761392837, 779969953, 153392061, 476714365, 507910267, 764927499, 633279638, 669276538, 609436605, 725832898, 598418539, 370711033, 696251734, 232928331, 630167100, 257926743, 197299157, 101098435, 11895779, 389301816, 801476641, 70887541, 852310241, 309380863, 225539641, 679665913, 461241915, 553035879, 639447514, 200877404, 517417934, 164014871, 744383796, 54007431, 224962933, 738387277, 722292966, 156298937, 249747051, 984485339, 295141878, 901871191, 640921448, 942569742, 815469543, 656219174, 900546188, 632180714, 369072909, 162001296, 20760452, 564674219, 835753474, 10856907, 887290682, 43029118, 923480493, 860275255, 87039872, 776583885, 797943828, 720684466, 958498647, 984037133, 477909959, 321340543, 891179127, 220707342, 89717912, 383691709, 946552488, 69462298, 550589688, 799931487, 469893510, 268830432, 894299794, 305961871, 981052648, 572534218, 181346385, 105499890, 250194, 872667217, 956700602, 315409740, 802200404, 752690264, 121410575, 334993662, 196414735, 832492768, 10430822, 867400784, 356046982, 960588787, 359461879, 271850193, 979439225, 31497354, 866349260, 833557393, 658854508, 706833655, 708388751, 248058960, 142610128, 930394695, 799924094, 835865530, 229237829, 701905081, 412365567, 707752529, 357127092, 810034856, 846761987, 656934889, 783737450, 211880334, 569314146, 836198760, 741944298, 259229372, 840911744, 472239924, 788209950, 423830439, 489493141, 197526530, 115721397, 633897245, 768787423, 94659410, 281777707, 568557542, 719512776, 961443319, 971386178, 73647506, 47079709, 102893908, 384097448, 332681764, 36731856, 392588047, 764509957, 988628050, 690175947, 664984852, 985672183, 883168283, 531806955, 493968347, 877150840, 209032568, 271336061, 454810027, 475272578, 832406769, 62139852, 615806882, 212908758, 760462569, 288876513, 89154227, 730533561, 79779648, 603794215, 913442975, 44766524, 373544249, 531817658, 528441954, 486228888, 556657020, 269613074, 193296809, 764389271, 635160535, 190641955, 377186741, 108495269, 513151972, 589046392, 8602755, 50594510, 176129120, 873052628, 811199530, 647077247, 173554404, 53112316, 956513949, 478752432, 20470136, 125904903, 158014537, 716075221, 235589274, 482410508, 866212216, 790702026, 82815604, 77029717, 913465628, 222536605, 85054611, 306337598, 993575545, 977995019, 481851437, 920812533, 868626338, 782528655, 160180081, 18077935, 461059224, 560186127, 850018463, 424182941, 654163302, 222488716, 10256981, 847556410, 403050898, 508968671, 746240266, 333294953, 262243502, 118428282, 21564048, 15181469, 811054867, 992703648, 91839244, 147793301, 87850505, 500497479, 229523453, 870672814, 657004922, 217029909, 969353578, 116920950, 620054016, 842810726, 500984010, 677489002, 679168369, 41564173, 315250962, 868043614, 204039227, 565683346, 831533692, 806000751, 326332420, 391191059, 305020645, 941826191, 17186278, 824892410, 134307296, 788432171, 291957981, 878976367, 172348229, 213818755, 703021027, 303508303, 555336737, 358800521, 184889011, 830421811, 659712179, 306044163, 248837509, 457761546, 611085549, 267850848, 632506504, 296497750, 836215576, 189855820, 140032771, 146409046, 411628952, 749274722, 386590667, 459005739, 645936650, 401483197, 485950202, 516442988, 768244910, 961052450, 692361752, 793501724, 330883650, 143138272, 252531601, 512221284, 999049882, 315272965, 311766223, 417656279, 360721642, 714067250, 510577557, 10837148, 563844378, 347380557, 936695487, 696974712, 300025871, 81438137, 443964501, 510470680, 988913231, 404580211, 659377072, 694064696, 989397113, 662322212, 941588695, 89194804, 453469784, 920489560, 305552781, 741781491, 68173110, 362242289, 156518930, 316399963, 301533072, 126304930, 830853669, 961339731, 635118737, 675024543, 62491937, 799161690, 729766092, 560468978, 798423685, 702084912, 507047615, 951047110, 106712354, 426041823, 626350523, 582533119, 898470229, 752921218, 945176809, 629906760, 398341733, 456065360, 903773315, 987252827, 915091595, 263008477, 355972536, 977503906, 982438077, 74890398, 491482432, 42528573, 727628212, 514691220, 258058808, 540751102, 180193999, 889888881, 570583758, 418461411, 724001852, 559951606, 764716344, 998592253, 675745745, 441215420, 98157543, 896273590, 973382377, 778867677, 945485768, 582834337, 67171212, 331328640, 944809020, 482413825, 214790203, 514397300, 159079388, 830102444, 589394925, 124173729, 775617282, 970606297, 132275341, 991229881, 62712924, 107616951, 681252251, 904448150, 428671037, 651794328, 189459514, 605123256, 445978191, 22441708, 176819952, 413159888, 134087111, 855664427, 695622054, 330995284, 285858328, 686630429, 594779598, 622233660, 611350147, 718272547, 114704604, 927518455, 857911838, 603121300, 404478076, 625916027, 462289930, 997011482, 741125465, 730947637, 169307885, 655708396, 711616632, 735386893, 658579149, 569288636, 477798521, 681322620, 5804326, 995985714, 393474749, 853792403, 603601887, 78699766, 852329616, 24118142, 423357650, 385227354, 858799805, 690901980, 607122000, 149343097, 411395371, 394632816, 340423309, 733513440, 544661042, 87555993, 329665262, 59354086, 922980016, 557638742, 914737796, 620348434, 896429734, 547228135, 834738687, 660734821, 137167733, 830240000, 511622912, 807254286, 970536620, 641764585, 794529024, 192210347, 121389060, 497099197, 99361069, 227586650, 610153541, 866567829, 443762790, 95507701, 506147194, 654789716, 991266106, 571491373, 872338392, 768088112, 874278444, 971201339, 718587376, 348082345, 566757563, 443335132, 776132422, 778122976, 985347431, 190390745, 38541135, 674262698, 785024726, 27716429, 803143706, 433979900, 64636589, 238339954, 53235219, 210466020, 158379120, 875308463, 367740048, 372293868, 753720663, 399499405, 667224273, 971410951, 342962787, 933527037, 476132832, 125948861, 536317697, 48137010, 466080253, 197824550, 245035368, 341261197, 543233450, 55811546, 726681132, 964224160, 201779490, 893369030, 541353218, 725169368, 541133225, 159165321, 133885138, 698453426, 629988985, 551982076, 517004587, 254234687, 27790039, 383908732, 123069613, 131850383, 434176995, 531244357, 484850168, 498131765, 138598196, 113482497, 778416353, 94721209, 451190893, 159977821, 679427274, 995045116, 958321411, 434125642, 839961475, 478284216, 400450716, 246398862, 318671510, 642812879, 296582343, 950765967, 343118991, 91617403, 34576811, 923387482, 104329739, 39591161, 939073127, 63331887, 369188738, 20937291, 738295824, 257668192, 212518459, 215489932, 837601823, 67748386, 791453284, 486952502, 715655198, 228463830, 468638996, 872824691, 843251702, 538860972, 458216988, 920442338, 388365947, 10710475, 790052207, 22685895, 48412841, 35769442, 840260647, 169985529, 774933836, 423843688, 794733691, 618923052, 91571890, 878459848, 757822313, 322226255, 39230241, 511287672, 658309944, 548350442, 921103811, 520057964, 954295128, 169154439, 895254070, 137947369, 856039908, 610063352, 419194340, 191295383, 671742276, 890759003, 31053884, 540093289, 288155521, 446998247, 22620470, 351238993, 359958736, 690081398, 790214115, 305016075, 755215457, 12413933, 750311770, 939459555, 356723874, 810124083, 132591586, 698691709, 830210807, 598819465, 816740495, 298199236, 830979661, 581507527, 391735400, 127304331, 75969691, 425515929, 342000804, 837441500, 332714662, 487720495, 24021979, 271855128, 78172424, 797867928, 522686773, 899805025, 661130702, 104571001, 419588984, 402903791, 58225627, 945046951, 101827033, 76568176, 655312802, 339041752, 671884788, 937845125, 931238443, 78333452, 447946157, 53761225, 423078245, 739714513, 777798790, 750441296, 490786544, 250031627, 799261251, 695794988, 184906180, 500915905, 508933387, 680351870, 381061039, 439598959, 818993431, 74136503, 564349790, 296262842, 753937425, 690659817, 323597246, 796627366, 916447180, 528099324, 241346275, 492671062, 776968066, 599434574, 561767688, 959305266, 820244174, 896178473, 186492272, 434097897, 610770889, 282407166, 56902412, 118539099, 978003618, 659781461, 814234193, 711073211, 61894401, 846772277, 712450100, 485559319, 78523152, 420006520, 326529767, 374181464, 276626240, 681159684, 666046977, 849747130, 616598512, 333301045, 308968164, 37964435, 232947768, 221194741, 546430939, 954285163, 858869600, 686407358, 84622181, 344901455, 713907413, 389337144, 170607235, 621009310, 276654532, 175147120, 967940140, 249695378, 664559704, 736332312, 595607931, 697693134, 139094083, 307850955, 514541928, 383319958, 512110189, 258201574, 180723426, 91283469, 776554823, 184461148, 152517742, 980754664, 814319114, 662960156, 135636750, 253349385, 914580536, 724260895, 847118082, 893455798, 272683104, 795679817, 77221982, 442434877, 904692654, 632170992, 390703469, 204548856, 114993422, 691713169, 970452573, 873381791, 731143822, 922390374, 266599055, 838091957, 411062003, 604946661, 395202229, 236354630, 387045968, 780577325, 895974026, 987945395, 836125888, 391008272, 844164664, 195174595, 393744887, 136945234, 54058178, 685479689, 635656129, 588076011, 252630357, 680260544, 942668653, 576110681, 777784089, 400781048, 245151032, 599232983, 84605484, 376887935, 121879419, 548715822, 345814081, 945644841, 485115293, 733881951, 752498760, 123389173, 232798848, 606373153, 113144452, 825117190, 567523029, 828576190, 813279580, 647146307, 739524209, 757189893, 397229670, 977069384, 950657485, 351320591, 130511889, 969949796, 738285013, 942037191, 875674110, 990920465, 178910903, 150396007, 746898792, 356619246, 604170936, 742016544, 659500443, 358723473, 918281950, 896686420, 486006974, 293226973, 885358870, 103912401, 678932909, 770540150, 752128377, 675427074, 218740804, 204676430, 878227929, 995476366, 365592894, 199139734, 457604265, 76667367, 819385630, 636752133, 878506038, 737924420, 505560433, 116616396, 886626226, 313100396, 738912311, 184483883, 468340890, 175883540, 794292570, 121003624, 245504150, 409232597, 40486441, 840794260, 692448813, 511791252, 37874766, 514797059, 98359065, 636704286, 245313215, 908413906, 72225890, 198323405, 39130633, 452962301, 884138289, 249682604, 159919409, 216258396, 910688073, 469365220, 165186311, 788377882, 104248960, 474582802, 533077530, 349328721, 857262789, 364013446, 524293651, 812231331, 524801617, 136305717, 17262271, 833773371, 721741197, 796148446, 602845184, 536649611, 291707711, 930904869, 70381828, 470314283, 73741257, 105529821, 349537322, 41064579, 468986213, 13763716, 599047005, 76558911, 703427325, 975542232, 428966361, 65060644, 487485419, 843671971, 883628755, 638431181, 137595656, 767726132, 805244547, 626040445, 277370339, 565040317, 513850686, 261838657, 831264510, 96673899, 740814444, 632617390, 86038280, 835594485, 864228041, 213421548, 479094851, 291672568, 324190766, 322607217, 756529342, 840013612, 222968851, 954419095, 44175791, 777372623, 958988742, 160111145, 918780081, 509692894, 688206109, 899516405, 639400611, 659253409, 462586043, 728862471, 913486396, 909533112, 491905235, 530233669, 227911147, 698079473, 642851035, 78270570, 962022206, 596634037, 561163032, 260374947, 562540462, 985603099, 953968456, 847792980, 70625987, 791302155, 125568504, 301636553, 369625600, 10425614, 275779033, 762998874, 628768729, 930645909, 220475640, 306891181, 55253351, 973129249, 792543879, 439238002, 811524680, 507059579, 113022388, 725015106, 236371790, 772239300, 673758906, 251968381, 413749943, 409805687, 807267484, 460352962, 722778854, 223214669, 728823763, 615193826, 846639355, 946990330, 480619851, 81363707, 552242031, 107563147, 109057790, 993388625, 115610893, 624487351, 176474746, 815921015, 594808797, 114786312, 80144548, 951299457, 690934479, 958376920, 389759589, 999375660, 525894305, 723379227, 384112854, 415911529, 416451835, 136281654, 481276140, 733234650, 940359425, 862549002, 492155145, 590675586, 589368728, 748097317, 160851843, 732048379, 498063564, 964202493, 77999382, 854189027, 676813302, 562742030, 280188245, 888862876, 495100362, 261987036, 779813355, 264210001, 835294108, 197780764, 698252090, 817678929, 618917446, 564406902, 794777063, 385755569, 383039558, 273381028, 922152621, 268937618, 459910870, 238659074, 854781572, 327930904, 571238748, 103176967, 541115587, 508063707, 753635986, 540015383, 765165746, 505325940, 284579730, 305201001, 526308963, 297748097, 835265863, 637660592, 726792545, 491267142, 724531727, 479701701, 588358525, 504698732, 970020241, 772359792, 253570033, 37174916, 989968559, 678073022, 175782714, 348784243, 624914929, 813559065, 985301021, 489417008, 513227093, 46490565, 481289013, 731593200, 369824927, 858469495, 386360515, 384591650, 937733599, 279436260, 777763556, 925588680, 578157666, 926875682, 816877368, 830767316, 454967698, 699084137, 674783843, 54297999, 516129544, 836647065, 531295315, 546573346, 581317790, 853546781, 233455533, 604996028, 121109988, 721547583, 406080100, 706575243, 104596024, 907727441, 43392153, 300571075, 996728702, 852935969, 153658428, 6020672, 964941858, 25330383, 7866633, 344604267, 605213275, 178962401, 658212918, 271350544, 796897681, 429494524, 857864275, 974011975, 847872830, 775452450, 917225963, 109704557, 759506073, 831268874, 709883312, 38156034, 426348921, 869451254, 516442066, 76822665, 561177932, 864126808, 329882082, 271915229, 780381076, 771990193, 344153953, 850304097, 73052788, 15645850, 591022595, 703279888, 900736001, 126744175, 378365229, 604124390, 27487247, 874166292, 400173912, 511972980, 232217527, 495900806, 444196777, 759297535, 427204918, 444059020, 346903239, 3706344, 341040705, 539999428, 79185860, 71402853, 983851198, 600741494, 967706226, 129618235, 583187251, 843982144, 402034026, 736106487, 917181610, 661340524, 494527078, 233587837, 714831415, 723927379, 970173533, 88679741, 367899452, 40291140, 365954133, 121937660, 927210387, 531463348, 856873794, 535483815, 995502624, 820475571, 8993749, 620387526, 340660275, 456994156, 917527818, 574901170, 642880421, 114578242, 562881026, 501926433, 433018142, 655642449, 697780052, 664541924, 917355694, 299157800, 438645775, 958636280, 481877609, 700794867, 373887882, 730375075, 877371935, 936361566, 850279352, 524208145, 530669607, 757143840, 32109574, 521158400, 184831432, 899240264, 978932422, 189977470, 378080502, 447654, 522229206, 667148648, 901379921, 818699043, 521353419, 579170895, 305833511, 714568984, 656859123, 269665733, 566510367, 779431071, 320743651, 735483746, 775246984, 367781555, 843564786, 795043394, 285100527, 36246539, 207672564, 792862831, 337773666, 555698000, 341951371, 211106043, 971891172, 813144345, 786892549, 642215271, 56275173, 25338503, 729116423, 522676185, 795104372, 250174828, 858523887, 402032232, 649223526, 492611022, 476678411, 270291390, 15693461, 672482803, 414314904, 113593155, 16115990, 622735087, 798727072, 861355370, 490952186, 8413949, 398544633, 628323359, 512039870, 552574363, 550662316, 208591101, 36753241, 848315029, 585663894, 468917252, 264968041, 704560704, 444299723, 546141831, 335277318, 640659626, 752836734, 563139250, 469444984, 71087694, 684798095, 893464596, 576942019, 203924055, 820987409, 382415822, 679626818, 123985216, 88842557, 984175499, 414240522, 732967526, 774299612, 64232060, 406174935, 640098922, 240871602, 447066864, 702859506, 117374246, 627585030, 374732317, 963760316, 939466614, 544495906, 942340731, 613896666, 672115868, 293949932, 109168853, 228950000, 770564756, 507479639, 288009478, 368366821, 471066995, 742716230, 961648285, 739340962, 318705611, 51574483, 656497976, 703326415, 108218364, 194387320, 515963350, 448983811, 873569309, 646329706, 69593243, 920851821, 787677764, 913395298, 152130889, 821603723, 244041570, 121231151, 188478095, 868235379, 375543426, 592133057, 372714463, 400824957, 57714193, 751268044, 99332294, 639686713, 422560312, 290959192, 803486254, 120660798, 531198814, 468750334, 32314678, 998140098, 347475324, 96834955, 1355991, 606514038, 124294382, 709629342, 774777764, 939828501, 297803189, 929638475, 906243058, 282594119, 350183550, 444309239, 628139669, 135459612, 377382812, 961033459, 961147012, 218225179, 753858026, 47005387, 119268526, 84187319, 149147072, 889766736, 439108087, 840341551, 200212946, 836886434, 162179730, 260584946, 610323917, 508423210, 244615926, 357414516, 492326865, 161181687, 656183108, 288716694, 168351909, 770528902, 340418744, 117013911, 89074442, 807487104, 312441700, 186127758, 881409039, 289270704, 562759620, 157910656, 648771508, 217531951, 247706235, 510437717, 129763352, 950643033, 393563050, 337508032, 184660720, 875604818, 37905675, 210586726, 894292444, 350572261, 296073379, 688821974, 712063269, 10707447, 462546220, 772016108, 672672538, 804848961, 626378254, 56430630, 472284107, 580146152, 647229450, 256993129, 421621665, 671633012, 357073952, 964560756, 550883350, 444993969, 726248018, 427488178, 37555316, 147931183, 328863065, 855233192, 333584136, 259139624, 984720745, 541092362, 883128670, 176712093, 423342239, 771745231, 952348026, 582606195, 979451475, 670799243, 898649324, 848616293, 517365451, 58951977, 80909402, 192456033, 692871465, 310615392, 362082929, 768489982, 508684398, 151130194, 179103852, 984094223, 416665955, 3197287, 918505550, 470774392, 643055155, 961563237, 979616074, 183428144, 420670013, 996860754, 926047222, 77749779, 725228770, 163571365, 679153547, 541163985, 602977917, 398706665, 85734279, 480544008, 810751466, 45349027, 850717862, 278169551, 869270176, 51115166, 476095885, 382361110, 837251245, 957497082, 768993455, 184202269, 859950077, 509661320, 971405485, 236407553, 717640283, 853550856, 793401649, 632972843, 909682658, 862226290, 959357316, 204436647, 713995378, 536736742, 952991548, 680334804, 22851052, 19145618, 678117439, 307482116, 153205811, 766718687, 964924565, 461596038, 481898140, 807796086, 990743908, 309385038, 727862002, 690606822, 950315718, 939868946, 63072112, 373508041, 861087344, 283231653, 449783268, 826878613, 433561003, 745114644, 70792788, 941063268, 356245450, 597886681, 204204780, 577502657, 544004511, 739441349, 98430762, 109752920, 208720855, 751485650, 914816975, 202411389, 266740231, 889015861, 987968259, 793166087, 78291027, 436159791, 332827393, 945512881, 65873306, 215284504, 57062284, 926085448, 760926427, 826577551, 772216329, 505294290, 473704696, 473151561, 147413381, 73369974, 949287387, 373881244, 612176119, 555728566, 927731917, 891271868, 787874652, 811073755, 838624392, 827101728, 509631850, 783542116, 341999480, 331539832, 363976023, 11996466, 512118695, 754620592, 842433211, 723049155, 856901404, 467782503, 897382377, 871467267, 676835195, 779592808, 986030577, 950229067, 98856627, 39375374, 159381073, 804862932, 390091585, 313225029, 727030804, 237476435, 453155171, 54426713, 492816759, 297170383, 537963635, 352520704, 54148086, 219346969, 354260240, 231351122, 249185216, 698105901, 598186034, 882011708, 432936549, 51836104, 568586834, 126105841, 643224403, 840261875, 327780360, 758291799, 375032871, 597336859, 113493458, 566912634, 337555697, 527783271, 10041133, 265710726, 35698635, 610896758, 388514613, 981708100, 53607401, 459547942, 785979286, 623660961, 46231950, 126242943, 608356225, 763083892, 258566332, 608102914, 671356779, 1397073, 44191096, 142254083, 866826771, 374252863, 16311417, 245930015, 581904393, 35558652, 121691544, 299716204, 814414923, 187124662, 288638620, 768488458, 428907855, 620995281, 744470338, 922079879, 186815401, 452622815, 38418783, 790229019, 706586689, 774431088, 2069856, 989006064, 450477107, 851108427, 255326152, 694294806, 401630562, 463616380, 398575521, 703756461, 179716294, 505088941, 424974143, 981095788, 740110498, 524447931, 102550570, 132739284, 658235109, 504478075, 95818748, 722157035, 106449379, 208006394, 242222035, 381660331, 652366567, 347344272, 761002608, 171867326, 690343006, 936520495, 477014191, 68009875, 93501928, 675051693, 268276315, 672046771, 916233613, 128932755, 467200544, 472422948, 564987816, 102387602, 227526395, 246452909, 151828591, 606312585, 307058761, 557411488, 370424569, 89032340, 506960839, 276131785, 848436679, 698668327, 961654345, 991721365, 132064428, 378328657, 683910826, 144557409, 618959648, 71813783, 399218924, 212678075, 886061735, 2865853, 766195974, 617495153, 697270645, 155607141, 228414512, 405718991, 104985402, 909071179, 719606221, 59130199, 759881300, 819173588, 93768081, 179763928, 604625699, 200324591, 602849796, 134118583, 810082477, 172906198, 217610567, 755400621, 833493826, 127980123, 658450854, 533645031, 811217479, 677904482, 222588886, 994369236, 843399486, 682037897, 578574720, 12013653, 204027465, 335097035, 315111732, 327393925, 680248885, 684764707, 835874158, 267406330, 900481942, 235399952, 622706490, 67379273, 963645507, 152676412, 198743202, 788596366, 406237611, 398350904, 949576582, 339671528, 598893206, 354394093, 264843762, 495498317, 527089257, 350701406, 406388206, 927787491, 560024453, 351971093, 828163658, 431925229, 619757138, 478880167, 984592905, 349558988, 829534587, 528434776, 892058663, 713357141, 9248783, 664665037, 276164259, 169251560, 348585926, 593578992, 903340803, 795678795, 221497027, 502817542, 35618342, 400979603, 731499642, 979800271, 407196332, 564669933, 558074686, 395019049, 721535665, 282429539, 488573943, 933250501, 330225075, 253714937, 220211138, 786525006, 549734019, 436704871, 870829055, 427930525, 16053851, 381249136, 643992099, 718942760, 989322368, 811637293, 415185126, 610698231, 888423265, 969287506, 438838916, 138366119, 541166038, 725740666, 377786643, 999629503, 928821251, 717858768, 724920075, 534206307, 403189912, 25814084, 163157447, 995852111, 456392162, 329619306, 146068402, 774622685, 701958401, 334776578, 103309811, 859077450, 714206041, 261603469, 928108725, 233161654, 721712205, 418691156, 337794258, 33350305, 32783709, 478671630, 703418069, 483633424, 208876915, 8253054, 69344720, 267629391, 233035771, 900936142, 401854283, 898207822, 938679267, 171548771, 520574583, 680414306, 661398315, 671060407, 540265907, 375392893, 949280303, 170503459, 973796604, 394443654, 723412337, 621965119, 445066719, 739992977, 615769781, 628803367, 103976854, 732059094, 53872183, 653308759, 870478476, 759168560, 488233659, 695874565, 214916468, 412998035, 54685521, 767262040, 985575391, 828526876, 644118554, 332975218, 595312810, 186973604, 723321804, 428754024, 685089186, 564145918, 683210362, 499556515, 985674106, 478200070, 810247136, 743043645, 222372063, 577944618, 204891389, 984715786, 181978068, 107580593, 85864710, 898820447, 43260270, 670238221, 523819029, 935258583, 203004434, 209822519, 569184245, 124547344, 512467178, 612585270, 20558147, 787665538, 791659683, 556592210, 175416882, 726236651, 141701563, 93505999, 147888385, 667890873, 583212894, 190991870, 479980260, 22535723, 391387840, 787298780, 93058124, 936101750, 72668451, 785386012, 863717228, 253671867, 897394463, 659190734, 443333954, 990431285, 551591929, 403586515, 928965751, 589375983, 856589090, 157775197, 133642436, 25570232, 84428508, 950526822, 96988529, 328323095, 185367719, 706542042, 899842850, 636769822, 595295984, 940233645, 912091359, 781780697, 548878355, 320442790, 903909822, 744817791, 82712857, 311292230, 528478722, 851195908, 88996398, 594975340, 128749510, 630439515, 968357652, 362584692, 67868513, 271687586, 982282774, 342213665, 293425061, 753340052, 781288379, 862326112, 32287425, 810465226, 416192521, 356568718, 331897101, 62073572, 871994250, 976281386, 875031394, 885045984, 891552481, 769781381, 234451312, 250316431, 180768713, 787968012, 594817040, 270355675, 818937229, 498224599, 548928140, 427747260, 455196161, 748358340, 989509379, 170256002, 430399540, 931039665, 424937285, 534925473, 182359323, 804800300, 556090902, 978574296, 307760437, 128743253, 19546286, 372591902, 56476460, 378807165, 418131012, 1975259, 74266083, 366893828, 806572141, 898914921, 435551793, 447745191, 637469510, 608667604, 859775638, 780048638, 840703647, 96076104, 805801425, 132911822, 488434004, 888419383, 281461303, 741352674, 86883512, 179436460, 46739856, 449486812, 295611204, 373376670, 304706096, 621317838, 246601956, 782971335, 449932427, 602735723, 311972605, 678783495, 700605458, 659477371, 834391526, 18601016, 586362587, 490901537, 344509051, 465330652, 822594525, 97787032, 518638460, 180567077, 492342946, 681502684, 643288678, 839995143, 176684776, 774700403, 717789181, 219892753, 13451939, 622769565, 214378849, 959834404, 629321624, 685871848, 270452748, 564631983, 197332506, 899040303, 936217383, 219078467, 799154720, 88904390, 287259286, 724011468, 623998029, 838375649, 588760377, 45305176, 552776349, 761997798, 55251434, 370982493, 898693169, 875922357, 63984151, 95311674, 158500231, 88260203, 679039867, 588203913, 280985864, 81170408, 972732838, 569329138, 842422945, 964144042, 363884329, 442476882, 368325060, 849410477, 537395044, 42361596, 595752614, 386799936, 861032400, 519226592, 903921042, 941903541, 135654896, 13797163, 840139671, 855123775, 74421517, 85370095, 768702473, 999196352, 632409162, 456928651, 436943563, 536125058, 546473689, 27950220, 930611099, 376511084, 47344533, 391484562, 767764361, 158027473, 97344415, 913776575, 540078356, 425024917, 268116720, 383946210, 537071657, 960942985, 507482066, 162694725, 424479755, 780117668, 304404971, 596834114, 236152774, 390399303, 886920705, 819108898, 952953584, 637321964, 81231003, 908684549, 654429049, 222808824, 277516384, 360020886, 835492480, 542845951, 603571519, 757607617, 407803519, 711632309, 57237206, 464905454, 895667046, 50129213, 442237421, 986386359, 130602164, 454051425, 773866938, 793084241, 803832603, 491968114, 866966614, 250499328, 794209961, 626075246, 101205818, 246357195, 662030951, 82010131, 241383109, 382198310, 259458039, 915082633, 48449379, 258497781, 70924140, 490670183, 567025680, 140902695, 214370801, 52701903, 785270407, 212566968, 903054791, 557618184, 322043053, 521113507, 393021503, 223842012, 828266814, 19073475, 986148657, 189896, 852137807, 237369761, 540867931, 493461115, 830710061, 371944433, 157096, 822696117, 926792831, 790552149, 149542742, 875475311, 263341162, 498567280, 865771817, 24426181, 298509079, 808869834, 60115568, 421693840, 443106293, 697913829, 681516370, 72028738, 936920298, 580795652, 145193033, 536126271, 340120488, 641962635, 273390515, 818178222, 510376730, 621271252, 178700516, 511604306, 767984464, 232563748, 79360784, 551516419, 660450387, 732246157, 323532631, 57972064, 881156697, 811348802, 41610134, 496502972, 622635559, 552281061, 734722058, 906618907, 281873751, 167399539, 775040853, 424515249, 825651876, 387902414, 390643739, 178000583, 988311404, 286655957, 907679819, 889296929, 433097819, 186677888, 395362472, 202990718, 450677767, 466487998, 37563874, 222743976, 700041750, 395380169, 226730616, 349241250, 548353668, 906907064, 874858547, 273183590, 797519621, 710421006, 110305504, 879227816, 505676552, 430588341, 479981994, 407018250, 37158322, 898679763, 942668050, 451810890, 511803525, 243131301, 972617195, 380871258, 149724080, 730113767, 223250783, 377018910, 271593149, 30632044, 18737223, 721131972, 190646947, 906341616, 256470953, 555225760, 69210624, 20546185, 705457561, 870946224, 695044231, 75740133, 293277839, 548073334, 610948149, 454581225, 313542709, 596797497, 655644050, 711059264, 595940252, 55838734, 39068253, 985403689, 926243481, 889556477, 131371845, 431477747, 441250707, 650754096, 233464077, 357225275, 115575861, 485408887, 963342752, 887874952, 43276035, 37390807, 542295634, 630093221, 404363740, 202309720, 127617483, 508871205, 449013208, 479992365, 804967991, 407398113, 299535925, 366254929, 453815648, 313676804, 728230043, 825584643, 716636324, 821827781, 945839036, 66685331, 893280498, 358831257, 402324804, 350438085, 426811002, 238818649, 25087526, 186407362, 931153878, 691307129, 288532815, 976321592, 62431988, 312790221, 794085718, 77162742, 877485907, 436135753, 62927067, 773204109, 271403128, 778502611, 635084361, 509625953, 817339061, 513811268, 429634492, 846645891, 852697777, 215171906, 724880841, 956919279, 911273573, 549131361, 152048388, 429869467, 396017593, 851184803, 74572545, 768051318, 213400658, 99603573, 105343804, 190686520, 392185027, 522664017, 694120303, 209527911, 56675523, 444316040, 421651776, 395963385, 217347075, 44466288, 357871492, 489889351, 802920669, 649770023, 753739643, 859978225, 963409793, 429888298, 929571323, 470971619, 77745345, 426748370, 465020468, 332979674, 928220097, 958216976, 140939215, 97953022, 964696223, 141742684, 186289647, 658221883, 743049830, 429540660, 190093878, 323126355, 966801305, 521050710, 114677373, 601526094, 389507121, 885475379, 723904403, 318678456, 451276075, 429671970, 822529231, 103978968, 726439384, 25641118, 340592854, 730764981, 799798571, 420460023, 625664709, 558214991, 15631605, 336516352, 861268312, 455274745, 209034241, 971331903, 774974557, 966352428, 216278807, 568372964, 4569074, 146293084, 870601162, 26488570, 631552141, 475812731, 539529561, 421429405, 4085915, 115785344, 434786155, 787127920, 531612351, 145761904, 635394026, 542695510, 685791596, 400409757, 95598981, 620987461, 109737118, 782904117, 778061290, 187891702, 898535816, 852828980, 951849420, 383518035, 218442078, 698118555, 936670962, 438514166, 66122021, 361703311, 901427499, 301374907, 36870310, 524381545, 613442444, 273133321, 797574704, 130399509, 678199395, 620938578, 244314952, 442263189, 233744104, 661134990, 567701746, 52987426, 76320970, 528256173, 712897589, 996996707, 616682992, 361454069, 827876724, 271154061, 545750337, 867888301, 839348783, 335601096, 335855314, 731990300, 866615154, 671714353, 643745593, 663922261, 952182175, 820776176, 152327301, 220619567, 986342041, 902617828, 433696951, 791976096, 306493266, 398684713, 224889980, 557181767, 154964988, 964249440, 894263612, 771386961, 947657092, 896633415, 624113664, 776666912, 417002763, 822867570, 149912584, 923107944, 666877107, 419257748, 343808078, 890427121, 346737030, 387331302, 547738850, 617546179, 960355266, 323726074, 973348960, 914470856, 866866224, 197156719, 797468348, 3267625, 989009795, 676956016, 834391531, 784750313, 880272968, 896889303, 830233481, 312381255, 457981414, 416013086, 195418406, 481022794, 207621588, 948305360, 471476670, 596569751, 474149764, 625188397, 81569052, 204058906, 102913203, 523005083, 99850534, 887007649, 477325732, 366729538, 840650275, 422894148, 465628435, 48262607, 174151921, 328389529, 166418086, 93467312, 516314761, 303535388, 949576958, 699467047, 997393033, 664969059, 86020279, 644127831, 703951918, 745376176, 878340881, 695942934, 649286400, 890759179, 981187135, 180114670, 790882294, 931942407, 830764316, 880340001, 915748914, 854165826, 317736121, 537023024, 130450130, 908434251, 7172493, 899790325, 68355339, 374052090, 144214997, 512034747, 103225200, 194124971, 846739948, 960116612, 296730949, 60842416, 678976229, 671845545, 992328304, 496572428, 647666162, 258418641, 121980297, 694237378, 886711412, 153525843, 393624156, 784457684, 597772341, 52022688, 205455739, 407642958, 93272043, 301441897, 598827738, 397026192, 316739104, 630368699, 971845475, 802873170, 803214281, 754923550, 486089789, 369609056, 243515302, 432530790, 613983396, 217378905, 39099621, 94389371, 201601503, 859581589, 931603699, 585622738, 319566610, 706698384, 375586861, 29074246, 169999605, 124052168, 913609096, 794849736, 975370580, 551421987, 188565714, 74367152, 672260689, 950520037, 37223827, 986290506, 944017242, 159120925, 575833797, 246064892, 611927969, 302489586, 602165802, 143054344, 831451768, 758933894, 300654811, 979087327, 952680909, 397757719, 858700629, 493934399, 920534327, 424986968, 240148414, 507099643, 899011212, 279066076, 386758501, 209072178, 848492765, 936128695, 905905592, 665233712, 236227807, 130783677, 417564679, 529737034, 99817490, 989140438, 666177881, 879230083, 144481928, 141912285, 8551477, 700193690, 925038285, 537242138, 845656106, 592789320, 931127923, 883376641, 729433588, 123955691, 174758427, 56284211, 413297504, 502743670, 257750454, 196336751, 718983617, 383687403, 543053546, 628346681, 405366919, 574412387, 76867974, 789684161, 746044209, 174898702, 458109634, 441597067, 515979202, 709610505, 876838107, 463503401, 354026459, 415382132, 401391014, 806111107, 871499976, 185174559, 747903655, 646489773, 271836832, 397704293, 339286886, 333876780, 577625159, 943969644, 53072141, 750308594, 148331955, 465046877, 978487670, 950872562, 696143409, 421299664, 375324150, 432374317, 461812277, 644974279, 466393054, 801217303, 845410388, 462231472, 454202013, 714955848, 824678581, 803244917, 455337797, 345140497, 554091497, 310096135, 300761894, 25443080, 348213179, 935681192, 133544100, 124198249, 85653258, 847374360, 908877894, 588409206, 210349801, 182566729, 835820478, 819771514, 85504066, 154143941, 475066395, 126233919, 631941065, 397379307, 620768664, 237985565, 673261203, 650481886, 518073721, 153623019, 669650529, 374961475, 762626756, 98399667, 702230290, 153946466, 357600788, 452992422, 931713352, 763111978, 616545532, 877104525, 183783920, 198757960, 358711595, 130841201, 836724041, 262024974, 708067862, 968660340, 683219404, 67575654, 811713870, 8862311, 86214801, 223527303, 35863281, 193031781, 496361694, 577168638, 906284547, 124255417, 878833948, 616170392, 494293918, 528274238, 883630817, 352875295, 245143320, 538580646, 83679469, 523327031, 620220447, 162115359, 377937527, 240999938, 965235727, 935522536, 167343746, 895926522, 659802315, 770217285, 305263702, 468810669, 468352939, 905911531, 687810712, 574413858, 895818500, 344889040, 628292587, 977919306, 758369766, 455651981, 270946665, 817481968, 746340844, 321224011, 938683223, 977328259, 134089138, 640686426, 576977307, 378625114, 610877673, 195115064, 842666858, 541614679, 333880272, 244739958, 486761093, 679384644, 779951154, 235817065, 457338609, 427817159, 25503136, 664534121, 449587881, 675572262, 600210017, 12332011, 143235386, 56408211, 360272817, 455860456, 316503537, 532725032, 788569264, 981670581, 275310502, 715084069, 405855563, 629409485, 303657626, 604173340, 590435879, 166406610, 247083914, 311401810, 880589270, 120877495, 245743357, 268189366, 642956415, 34837734, 480352137, 302177736, 165045449, 922836688, 378566734, 760144548, 500231788, 451846440, 877809350, 914949319, 859416058, 151251459, 723247753, 69710364, 393962480, 275259098, 777318661, 606217229, 985555004, 62271450, 301500625, 388571345, 696523335, 20691345, 931201204, 521135709, 717376752, 590117762, 261667524, 492841088, 8206807, 98336501, 94692887, 455607120, 103271578, 492074748, 631915211, 844546782, 104884390, 168717512, 480939094, 978160398, 551677547, 520839364, 474977305, 735735412, 481225596, 361305453, 853673880, 184266164, 347198214, 194367044, 382632056, 998120094, 889539941, 89896848, 940871449, 642714453, 909002408, 971916430, 639295512, 124506374, 333949290, 656112456, 653231751, 838159632, 998186450, 952464663, 18170408, 51701563, 480872433, 713256671, 131472933, 435159083, 177524615, 255932662, 277319763, 358317304, 117590125, 382915062, 131036743, 323978274, 895745338, 833222874, 198382548, 818592512, 901728822, 355827384, 687656790, 411612913, 121155545, 236366847, 931634936, 132112060, 681141110, 242877421, 516094046, 491728967, 971842229, 787666781, 535880120, 763377167, 249254839, 969925391, 912922667, 720910551, 162657613, 666194006, 164180464, 693840185, 757338061, 895773073, 763336921, 988522379, 258295858, 833027114, 6403203, 605758479, 63573951, 771396359, 347111244, 824674386, 523653114, 546034112, 333953339, 708426511, 266891200, 630581970, 548103865, 909326326, 322663623, 653352504, 247816487, 934606289, 127627474, 112549027, 692600215, 166003825, 394871285, 999491229, 606963133, 337694030, 807310763, 860955343, 334518454, 605680958, 837331049, 306688006, 632545144, 30475479, 196093323, 777731741, 655209821, 506947041, 481020167, 854261200, 683864432, 303043470, 149597052, 567436446, 464378690, 774980032, 65716692, 269458797, 230794664, 25088439, 762867218, 536896527, 635404668, 122170865, 577709862, 917340976, 442551885, 448486142, 394597748, 202681413, 123792473, 407394101, 63954609, 363602778, 291454403, 800593900, 616245226, 80808730, 197986289, 88438162, 212358022, 676821469, 874576822, 844659928, 293432961, 228493470, 876943534, 831131595, 119546784, 587528815, 897412555, 669594425, 735303586, 454576372, 229844988, 399186351, 591257481, 3635458, 202260702, 602430835, 672797228, 972090572, 535196849, 627665501, 888190613, 320877873, 957325960, 768455100, 77583922, 57078780, 646648646, 156558123, 49710376, 812183747, 26376823, 950379041, 111340245, 774812180, 910350180, 172575394, 158892348, 535189598, 582872526, 419269502, 214555432, 328741641, 244941109, 542792685, 859890817, 331743555, 883957277, 656642733, 706309251, 760955856, 875406863, 992953360, 615774604, 159053692, 615180401, 86584893, 911159292, 315755788, 351819632, 102327562, 136458115, 408286650, 252789920, 423789731, 352509379, 769324300, 608829335, 389000939, 737073095, 938672679, 124025588, 512860975, 28619717, 251181966, 816406882, 506801475, 497780356, 115450205, 92141442, 447302057, 958341375, 147412508, 866595554, 19238659, 858724790, 432361759, 862943535, 62388817, 957918199, 862043617, 645823553, 860316607, 415853229, 138566999, 394895850, 795757439, 860962168, 676836652, 244785627, 701839426, 679823751, 923030299, 565354358, 740944252, 732580696, 554455007, 270126718, 139193759, 314492018, 839306545, 131882802, 119622971, 162994388, 662487349, 815589397, 392141096, 99367577, 6863519, 819442323, 986545811, 670556883, 280000122, 364510580, 732892077, 530807088, 37220044, 742870454, 727718438, 799255158, 855561094, 323372319, 452403154, 781841979, 861721310, 599738336, 140374579, 281626469, 960822539, 160336447, 93379420, 62102201, 819601216, 523626718, 295912375, 361046143, 59498997, 67138898, 369187726, 530694281, 47590362, 334616449, 844134905, 880141965, 340138943, 132046757, 816681821, 576717677, 172834626, 539574546, 548857878, 667149265, 112274813, 654174721, 140155485, 418802485, 30269822, 183492361, 71611519, 747320948, 690781933, 25046233, 402285177, 237346569, 380007724, 382996502, 87271021, 366615862, 232004847, 767572741, 806410431, 415592365, 364284482, 610179989, 677530099, 858700220, 139499154, 426044378, 886793242, 410999684, 379013686, 92501427, 628544541, 560913372, 812633423, 411717004, 61034440, 550023485, 87208890, 986187310, 667583945, 32887041, 951218692, 701091218, 170989837, 230056055, 11945872, 263037157, 163894622, 64400091, 716450329, 147355439, 172133386, 375783064, 325367355, 148149083, 566110201, 359217946, 495948764, 50846998, 490436049, 177481086, 41221509, 91259239, 388445297, 875446973, 616948565, 404441215, 500089600, 707047661, 500100541, 739400761, 506789718, 68124844, 701676847, 974537636, 71308628, 588959908, 622535497, 844660758, 173386876, 982818324, 861052538, 691757538, 859138998, 238777665, 339128579, 340194003, 846046097, 941663918, 829904307, 792663177, 281156043, 38022908, 548353773, 322782951, 469301841, 1868017, 240604061, 968125871, 831728464, 682270179, 777824579, 759561213, 949151979, 584290495, 661040715, 481769970, 827666004, 293839865, 44270795, 715915491, 980810928, 208176105, 743565001, 499807929, 721979270, 262845130, 87086722, 228776687, 110003514, 347758729, 251473841, 630352369, 61023499, 846111161, 266703498, 877153035, 955436647, 603176123, 808799003, 489626185, 880333910, 493141409, 426364417, 429618644, 728298515, 654795564, 305693260, 197052847, 915897489, 991252892, 445438275, 575465255, 965958985, 298782500, 291305069, 601594039, 542155896, 510810483, 557994645, 164188386, 63307973, 305812083, 470060441, 821526849, 992665935, 573804767, 411431772, 583529116, 648323161, 709580889, 572790702, 127004784, 235270674, 195696201, 913495328, 798862487, 133626985, 992646813, 71236054, 303295183, 417084418, 812907536, 725614822, 219874180, 601252008, 988328213, 649769809, 241513713, 519619499, 722826587, 504741107, 272943773, 480843246, 377377407, 572152038, 74246285, 566826206, 641333999, 476080636, 724830179, 830267324, 188510376, 388135272, 33675684, 6805221, 372208585, 826318532, 953410185, 715467996, 229670335, 897011920, 533523057, 861728575, 671135258, 288010080, 529004866, 435605620, 176206570, 899805749, 898061098, 540539632, 643133450, 452819121, 956553113, 906563866, 762469316, 894940359, 928127539, 960090293, 72891308, 317170354, 671989700, 413607935, 30561838, 910377257, 680233539, 670383504, 867061631, 433498516, 132144601, 800027174, 917931929, 517486945, 533692281, 121710005, 888745005, 855313892, 321711999, 191329372, 753097384, 668330269, 569240503, 284410320, 222047787, 105297614, 924738276, 466596987, 729781257, 911254799, 589625186, 891583740, 957090586, 616365552, 465840479, 65769771, 155323903, 844412463, 145439305, 318599493, 299092913, 596701607, 595440667, 211557055, 131925545, 852370497, 511247209, 976999240, 993825405, 502493297, 307821281, 894547366, 936024736, 40347232, 968438875, 224069518, 450433756, 798170970, 705995740, 795027569, 944369414, 260638421, 658679499, 981220190, 652340394, 701757498, 652876821, 376756194, 422185324, 213350036, 139503993, 623050408, 951689315, 195132408, 637593238, 132946891, 843192205, 256549951, 665663327, 880693471, 779492030, 22597984, 451409639, 853635317, 856430828, 166721174, 742914789, 576404518, 39397410, 462820744, 922178288, 708595921, 749185389, 648117715, 803634820, 85677732, 129519971, 822441511, 143613092, 107000764, 552824102, 722677742, 426995267, 142222971, 897431130, 448246337, 216532336, 746068825, 480339528, 28824685, 529587725, 70042980, 140893597, 473492639, 208576540, 627836549, 272655760, 993866097, 329196533, 340061684, 845084727, 183073494, 74322949, 576056931, 477373849, 315945708, 132203296, 1988593, 316791540, 24727042, 241100089, 59770117, 581686126, 377583931, 403487698, 302920385, 11196269, 804951842, 436319362, 806761309, 654836227, 834621231, 827845481, 317356352, 829062099, 160582745, 509806947, 335974201, 939554395, 279869100, 530891580, 179170526, 86062501, 261435641, 72473543, 227360039, 119096548, 234199550, 881027465, 154514328, 668235364, 848355101, 594276087, 848620389, 388129540, 304086043, 972587408, 824851270, 398883587, 121063308, 419523984, 122068416, 28495849, 391126811, 492579149, 334193456, 806005413, 277822329, 465256010, 16619499, 240333162, 647012846, 356000203, 988542129, 923002354, 702124075, 703461577, 226801569, 647247437, 372914616, 405823446, 439681526, 89178200, 599619453, 558778393, 940976267, 892627605, 361208398, 7486588, 811847798, 823723351, 107410531, 373544949, 564602348, 894435475, 422855397, 894296711, 193106563, 681431761, 312704412, 263008006, 811472676, 821346747, 759358423, 582184145, 80172253, 359757433, 843449966, 711935626, 438869852, 321102563, 704738076, 681898942, 941673654, 139113920, 761850660, 307662071, 597154566, 185620719, 779949426, 857020722, 660373529, 239667906, 332962794, 263561138, 164341798, 975619968, 842355894, 413484624, 79888577, 942247986, 962596891, 377731314, 462245359, 710821169, 759356426, 357992308, 721216663, 639630982, 531981641, 695916905, 464600767, 85265588, 304337794, 755584584, 182537415, 505017514, 757670149, 500927795, 191428826, 195139108, 50151371, 788719937, 561542082, 713007529, 425744272, 58039201, 238380675, 818650657, 764658622, 430051988, 108009748, 262738720, 940328552, 447227115, 628889130, 974455437, 412512029, 607414731, 747061952, 530595242, 641304692, 918300061, 479853846, 967147885, 146015429, 326353886, 42356452, 923582377, 185084397, 835944168, 627119031, 138615994, 486644713, 834485263, 871280457, 576670443, 112943167, 794206983, 558886950, 951952993, 92946971, 447951969, 630630272, 614396050, 650400148, 927415739, 389391219, 687707293, 924650327, 546755737, 377122392, 543623301, 518970615, 506014870, 969106752, 360428600, 333811234, 166971155, 891171388, 608546288, 148504328, 515718407, 136068624, 652090808, 532611126, 159051587, 639183609, 738241278, 697507722, 719299294, 396866933, 680856395, 496860452, 155970988, 601615384, 661454668, 229704258, 271000593, 314535908, 524845863, 44998905, 119189605, 444949863, 985251979, 680108622, 84230405, 810902569, 255933787, 200476009, 752288961, 695059403, 67978655, 30242110, 353789875, 508940545, 91309485, 605042824, 923577415, 596418244, 750521312, 389374489, 744553191, 609242549, 607743233, 191137580, 135833343, 13073271, 527146897, 791157349, 433699238, 200802090, 851865797, 924696749, 257191611, 842823614, 319225941, 709065594, 739205069, 483496856, 102670928, 502136087, 98705484, 532060658, 824752949, 978339321, 433124485, 97424338, 687866179, 98276026, 180513309, 274214252, 195189279, 244795967, 575786981, 1577268, 636285498, 318958583, 18736864, 356866219, 46298457, 242327033, 339481388, 97079284, 884903772, 546106518, 71980937, 517496092, 553206025, 353811494, 122834016, 415750004, 627559746, 748516255, 879481292, 37440133, 651582880, 992754685, 311713790, 744416198, 48292844, 761306491, 111762821, 189455534, 945249289, 65999483, 996053008, 777456557, 201762235, 365249220, 636373872, 681989472, 141608111, 78327039, 348854450, 164296494, 904275247, 520526858, 300742977, 431784206, 51588997, 59775797, 256135133, 834083987, 846045291, 55456038, 767325529, 708124280, 674919805, 136609383, 849255299, 920565049, 303452642, 317846268, 407118907, 103250462, 911646403, 136313190, 848897264, 267437167, 419574113, 211590680, 882769870, 253142275, 144919612, 253536666, 494175242, 343271565, 292164935, 479649210, 33864692, 393580285, 558034976, 260536714, 491666068, 153801954, 750502764, 556702038, 66932332, 498864989, 852621867, 539087913, 367153628, 45343652, 408286103, 74684167, 942080072, 496383611, 534716398, 414669393, 759093035, 200250748, 1550302, 979084743, 987087896, 335884304, 714448099, 860263707, 981010905, 167012941, 847787624, 633272925, 909963810, 713756179, 308020512, 815818532, 349724152, 5033611, 115184463, 546931713, 256563669, 111667287, 268995115, 303164771, 668426057, 328231656, 768988437, 137766465, 737080294, 16815702, 354202559, 341250368, 119578306, 43256918, 402522162, 631740459, 589773807, 773753314, 469742304, 505547235, 19124297, 650496595, 948699960, 248833532, 405521419, 888068116, 516494479, 132446111, 106932482, 945134520, 204314297, 98839245, 157741809, 311733833, 21042016, 582460549, 821235526, 88109167, 15840914, 456270867, 37777556, 963242650, 199511556, 687556787, 409832711, 979966162, 63427975, 161781285, 558357123, 352838560, 933706420, 319792054, 368055059, 895302354, 323947737, 353262610, 754654344, 898544547, 97254215, 581986472, 324636936, 215149827, 856172685, 199477821, 777835276, 212763359, 398498026, 493405779, 22086502, 248835005, 539429380, 111394479, 156546990, 798000022, 146971903, 11390249, 87054109, 778070922, 190157018, 51136291, 525601755, 652047249, 204625207, 955159361, 153410514, 77754178, 578045378, 90419937, 354592215, 724995567, 83197751, 768115793, 577831645, 24737215, 510265454, 764545007, 480266985, 222822371, 714149155, 798193307, 134503919, 193074903, 482123874, 16457049, 878364758, 994804865, 332738510, 316025805, 718749653, 245192692, 289169038, 534226813, 927527514, 788927813, 230746642, 628745875, 614092811, 203107889, 156825165, 381472907, 692772781, 714488608, 597073130, 987152426, 719930677, 802541267, 358738013, 164864849, 192148772, 131605610, 192749041, 250401277, 397271465, 423642600, 655619736, 848257999, 901451388, 65436397, 206105301, 958575920, 571538926, 24701775, 17962576, 509692501, 805112341, 568841302, 290132699, 671548356, 982872667, 45056966, 541020424, 274232922, 515732512, 982938806, 199797073, 704973236, 808514528, 968614006, 594080042, 648200428, 589255760, 920472535, 434896204, 4304874, 443912623, 31922821, 777777789, 827839349, 541052020, 360128270, 944044001, 967147216, 688928370, 794148966, 786070749, 478236244, 849456718, 291245794, 58217521, 75487451, 832621046, 304283844, 329927521, 213330079, 831140089, 991403027, 776860196, 742073915, 628803896, 452212807, 658804914, 436592135, 243224242, 414666725, 119478253, 131797461, 314129827, 45008622, 173116790, 321146173, 329929055, 437919231, 3646200, 999616106, 10781786, 584079677, 226459115, 741601457, 936953151, 953406278, 970595727, 419259228, 207446373, 279473056, 50821601, 129113294, 835513465, 997420875, 685289325, 319876517, 178742371, 572029261, 254851662, 473230960, 880422133, 252851152, 402476488, 610765521, 333560271, 558194300, 968554450, 655058466, 544077036, 863273645, 318705546, 440957446, 981128530, 709482383, 24463754, 521742059, 449395023, 915189408, 846764899, 788389432, 255266077, 824709844, 349911943, 29945912, 841456407, 763847605, 331832469, 8398434, 680818809, 710586193, 903194242, 81760546, 187329992, 19784040, 920652537, 308388270, 792059234, 469435596, 861449726, 770793487, 192577058, 457643168, 82360719, 135399871, 609457327, 1752737, 430928874, 310793350, 467162861, 192483992, 279685945, 752592560, 900600202, 484670056, 588701991, 738742570, 777389449, 563168630, 113708200, 383759595, 911848849, 335714400, 28267264, 730787981, 834781496, 842945479, 479244125, 659655039, 578894822, 193832490, 781388051, 393705446, 832619959, 376903937, 231980942, 502732709, 690908120, 207462847, 724076646, 524329743, 585109301, 57681674, 484064030, 415016276, 54505502, 144403467, 107920929, 360340461, 655587202, 461581159, 491641330, 766232967, 676716847, 633901904, 369473028, 755974217, 974466582, 484402024, 296044179, 700708664, 466365136, 987194237, 612915937, 116435910, 500661858, 627553617, 354523773, 503041941, 858219083, 200516963, 386026422, 124671132, 334611823, 451325605, 626313165, 243249951, 299335144, 704926394, 759626079, 86036522, 66664252, 161638289, 415474954, 927435131, 355785912, 576969037, 971669753, 174155856, 901858172, 976888269, 207367867, 600771198, 722248571, 93353650, 151314442, 414568150, 420565646, 178600338, 594698451, 728188325, 283961875, 780401341, 511250669, 541197084, 638837311, 513456433, 18577091, 344624800, 399201053, 521104846, 802652480, 266239342, 683824967, 640547356, 594150260, 870869426, 988681916, 268630517, 604490397, 378551991, 434675155, 920147380, 134608800, 862249909, 779632688, 90778386, 769508527, 742854726, 143390675, 57396524, 763244977, 747628520, 764002325, 887758855, 162085215, 923212761, 114239926, 230890772, 423909687, 649194657, 765870954, 212275025, 392112741, 92423765, 277052286, 752494153, 764595499, 343743126, 210923371, 820807604, 737734329, 411485797, 719096496, 995109706, 796190578, 108561363, 496746234, 834046321, 47425955, 451452167, 303983848, 933742837, 899921688, 694520631, 21122058, 890020507, 49823675, 109810756, 110944151, 496958229, 804392161, 631096307, 280413982, 580332092, 401727422, 822802848, 588154227, 977931296, 377144113, 335497071, 898885096, 484506554, 705804241, 207203296, 45869977, 651527074, 942638861, 338672249, 807275741, 459282255, 636951664, 324176288, 400125759, 653665868, 174103992, 996141561, 189149341, 58115081, 514895786, 692391307, 220652756, 118758545, 431737501, 736225798, 318716430, 167999269, 486463414, 930832008, 580472087, 859782625, 258894038, 646078961, 771131169, 112418058, 820860466, 98087706, 524500928, 563842016, 176996341, 676586883, 937386578, 704181139, 250761532, 874872121, 84479636, 452439385, 683225741, 71844415, 522592444, 215217177, 600487601, 506406133, 188192311, 202080610, 670969061, 405582990, 515638372, 227150808, 583002316, 100446865, 837574866, 370835474, 457849426, 757920592, 989922665, 289967708, 255324014, 123046160, 109948120, 843478379, 623943657, 931291732, 333342881, 528899844, 808983261, 406022715, 878206066, 50640690, 275428052, 539540546, 648907500, 681332297, 276405651, 576874225, 968626564, 950580175, 738538059, 195275628, 594606501, 595903491, 997375122, 957970945, 351079492, 481830021, 288666747, 645865143, 902007277, 202003745, 906982912, 821346419, 161913173, 249643097, 802307, 442535491, 876948542, 11368638, 251923406, 234564178, 247386464, 291096139, 820441192, 492632070, 515493460, 742543168, 273981926, 65783362, 295065328, 128392291, 702991167, 630540445, 486428493, 365400465, 50694642, 975155054, 802446544, 682258533, 914645128, 934338432, 639876503, 633266644, 499698974, 410855143, 451384478, 513962155, 688163376, 330117475, 816112741, 817328564, 269570531, 936039999, 580167299, 979167584, 449477199, 288133256, 430495857, 248378103, 154139308, 742054773, 965639655, 691763570, 457079261, 760613539, 526869229, 886546044, 102176759, 802602768, 910674082, 745201095, 590299345, 807090953, 674071738, 977600702, 369858403, 886903746, 180277721, 137447412, 48231698, 865071282, 87986513, 305950335, 298679079, 362082477, 105306931, 141251133, 262506976, 227715541, 9233687, 690570587, 865468096, 26332373, 464041304, 115266067, 640312839, 901504018, 400250031, 741498923, 664829986, 53110056, 640448114, 961826468, 842065975, 152778500, 151130227, 465718966, 824691780, 613082040, 690702683, 625059759, 3153555, 421095110, 238175138, 99674246, 243659028, 202598282, 822169783, 824535872, 412360563, 529148755, 485129469, 809608557, 843150241, 330867270, 673583455, 7520683, 589538619, 276653122, 503117922, 217912531, 931369631, 39501957, 467044641, 759232885, 632780278, 200785511, 249426731, 206566917, 133104128, 712230975, 936356675, 360663247, 210606916, 410434668, 528798370, 650001544, 319747674, 980070720, 168891630, 609032442, 103614938, 356749046, 885562068, 661674055, 133306546, 766824182, 962619998, 855643951, 525049061, 96338557, 498116240, 230359116, 148571596, 859161869, 918024410, 46429460, 887106154, 930154232, 39102759, 623397038, 961756214, 238264502, 154584908, 881758400, 793750541, 543888522, 479266067, 560453807, 178958019, 211204906, 628088234, 791009617, 302224087, 628237856, 967531329, 242045563, 58773004, 579116240, 521989584, 635396328, 963558492, 178926362, 462232090, 177794976, 512545607, 551398491, 820275990, 960386524, 143402705, 553028203, 598012734, 352741380, 449430293, 332223037, 788354416, 421201794, 883173821, 180609100, 541752282, 362523525, 70887403, 495674867, 878133259, 213094863, 384735465, 230719289, 91371944, 259692044, 965136237, 626937066, 105577493, 164483923, 939332245, 297863375, 746178940, 513900075, 506939528, 319378455, 228685413, 126760135, 409150513, 183866682, 110724344, 4464528, 626555379, 947944230, 791539410, 964267784, 396791558, 998758162, 768418885, 368599415, 897246651, 49168485, 364460862, 418198122, 865588825, 966395405, 616117672, 277026233, 384976735, 256165830, 822770663, 872225043, 655369134, 867164436, 281505351, 793059163, 598453204, 331899461, 99447372, 916684939, 10115978, 354402636, 524833285, 456981676, 216936, 633970386, 190643328, 268624703, 467320757, 404553457, 948007396, 742221146, 610195120, 364728249, 539083438, 960339597, 327957468, 731321707, 957539585, 93463143, 359958971, 833221526, 467527444, 649466433, 583310080, 685521438, 608921569, 551755268, 156276483, 620554269, 60286114, 105447483, 56288202, 494293604, 18482813, 316804290, 592190736, 943794166, 306579605, 713787468, 968303931, 8848973, 12996002, 178202364, 519541108, 358638379, 501739965, 548985079, 918011409, 568585680, 691899278, 762941907, 171175549, 89746373, 233210965, 10419835, 937302150, 634444967, 41245968, 558049249, 689685664, 841885138, 266742919, 166218952, 473483252, 868246228, 647678332, 914252977, 360658938, 585705565, 445367541, 489897541, 358156429, 189202323, 963941103, 703488722, 486443698, 793096444, 622169287, 431522462, 724226447, 529932431, 417677105, 775586110, 648971993, 84886554, 687882736, 143703384, 840350955, 10564955, 587140305, 919400478, 969746000, 28602753, 154527604, 595499512, 120266279, 808593953, 739675851, 522321155, 621111997, 511728552, 215987071, 250433540, 289169876, 197424996, 229937375, 275123839, 613206902, 449685670, 839250151, 516325077, 695900273, 9927709, 128014309, 399562974, 500525207, 657530197, 80971902, 517770948, 172868744, 92292288, 943480383, 146177280, 209410685, 931810237, 172300983, 453712199, 418219615, 753294636, 858099302, 446906020, 50315625, 348729961, 486819153, 528031568, 877824924, 741587688, 378343115, 459659318, 358599572, 272207617, 660945885, 812281098, 486369593, 98308485, 22879204, 488819487, 693239822, 613034070, 956845, 609081075, 328660295, 607155939, 592323552, 100292785, 561397589, 571877420, 374731747, 714807601, 898061356, 332039338, 661687063, 266003162, 648918002, 499138939, 197832888, 767995636, 903803470, 56946529, 243841580, 91483127, 868312644, 389727973, 483763606, 894466263, 807589259, 851407558, 401992025, 696449202, 792703448, 670670584, 551297457, 949161329, 578931252, 592202875, 85849288, 106589736, 981022427, 828490766, 291562890, 722400170, 957915970, 797047978, 175527056, 988123353, 462280656, 524285460, 32119028, 632894937, 219091465, 190343289, 719577249, 197518061, 393396223, 711339173, 976930437, 420064469, 389494978, 763681758, 898968509, 368176693, 781004969, 79885963, 877108206, 930457059, 929309220, 431113373, 106645450, 522490268, 204950432, 297601498, 840822041, 42788992, 388426951, 618862091, 539035746, 200139228, 478108437, 85392403, 143447220, 587402793, 572129795, 646047777, 363432306, 859087230, 211561185, 355554209, 759063641, 851023938, 8536451, 47160110, 295743470, 659771860, 389348670, 471230723, 548257914, 909125326, 829623391, 814571234, 335073079, 101675816, 723709165, 430141623, 805547969, 21863389, 107914405, 469422398, 488903643, 214629869, 591974321, 845608001, 446338459, 740025665, 408272753, 969816042, 82059823, 469895949, 250727455, 309363578, 512402038, 720863057, 119203804, 867359102, 233353581, 73376918, 603345589, 129774511, 254449326, 835622928, 631319821, 726760775, 299783245, 213806278, 495017295, 359697125, 881529974, 502704479, 109959829, 397074777, 399449153, 883863409, 537222306, 674710448, 206202196, 256048775, 420134229, 703938717, 317395221, 386415346, 151698906, 893405749, 118684636, 929158986, 962140323, 30481205, 840604534, 750289628, 338501479, 288351152, 45957503, 490989597, 258993666, 458087361, 187495842, 229449633, 277591623, 55787124, 40212025, 555632084, 355125899, 707221426, 260905319, 103455974, 921779247, 564104820, 453975120, 28679267, 844987910, 917870946, 833394997, 537405604, 42483903, 923673112, 408018313, 307594874, 52966144, 802768416, 646715969, 160285267, 399944068, 704555591, 33736132, 761441442, 281500261, 901208504, 408462618, 120251939, 801109245, 275921388, 36935760, 198031419, 89456626, 522493103, 190345008, 769564320, 851479813, 645527587, 467498864, 718419245, 961340978, 114644291, 847061787, 700514578, 752471444, 875686582, 630901708, 945659145, 784117504, 100780691, 961514782, 193475399, 40055170, 987634031, 711318467, 574050818, 269050476, 643172404, 740824366, 660517615, 239774490, 738629527, 441294003, 91274394, 804761591, 968238677, 676471901, 715307333, 255477761, 231056004, 151032983, 908668210, 665261491, 465689829, 199827911, 173293871, 502621403, 644193744, 457176626, 95586449, 559212922, 812907464, 306364125, 93932351, 504953662, 650904938, 262428421, 79736987, 405245927, 629617697, 473782892, 267633277, 804485252, 40750576, 718373238, 802284567, 899508943, 33391337, 161750596, 571097983, 144467481, 39243147, 142051540, 992504159, 61327913, 237758732, 975398246, 533614675, 821282541, 803778465, 666053596, 482474688, 287343026, 402110709, 361467820, 660682459, 766863962, 940971332, 133443376, 299322317, 403289380, 91773147, 578740420, 178337753, 626487223, 3329078, 133029916, 3445303, 180192376, 348345874, 382546435, 166253188, 762642188, 407937250, 357625136, 577200245, 379724244, 19232721, 345288519, 722704102, 223235722, 598922463, 881090280, 630053391, 718604012, 141511726, 273913253, 102354794, 476017907, 422540672, 695048655, 265734182, 240752030, 72436120, 74561677, 369765754, 986102028, 271213492, 144489834, 932666818, 473117188, 947829933, 341732375, 416832921, 206474181, 188913129, 998511470, 73646354, 299332842, 270671030, 77491204, 199382630, 620056299, 593621476, 205712819, 370899908, 27972373, 247878908, 471032089, 602821904, 36654639, 472210204, 1506888, 675608009, 188051949, 1167041, 532098903, 476252659, 669257691, 559553425, 715122734, 20547462, 536253493, 64166682, 494508143, 856419984, 546429105, 401304239, 483683742, 561236488, 925680184, 97940018, 739642396, 215456008, 179172199, 457743168, 454303229, 40214746, 666384953, 570926099, 317619550, 675864306, 585532696, 579862672, 529502563, 740576505, 385691413, 560222402, 93681395, 542474751, 950202120, 878048451, 808731428, 463878722, 831849211, 690138855, 104977773, 644018655, 81525857, 621911831, 722700955, 885090699, 165054401, 214052164, 53318648, 531691184, 780786743, 759193573, 810047374, 385843571, 636137416, 699791663, 918197910, 917669687, 604733759, 128077557, 282018282, 818485977, 404253604, 224796331, 830717554, 736892077, 237971203, 686952929, 832352844, 939385224, 864533054, 558246504, 332102058, 181428997, 170905489, 965822013, 311167709, 424290155, 324675837, 744974423, 923753558, 215435880, 661537145, 98598118, 401814655, 585513086, 500782111, 982056643, 280836371, 777948762, 62053892, 989591926, 558089027, 150308517, 102494307, 761855398, 491719540, 313833799, 787853830, 680999807, 285474868, 823831355, 487419754, 775390507, 774844102, 674678210, 107334650, 651914174, 731087618, 424443194, 779124300, 311082994, 66146814, 574712978, 195648032, 47340149, 740048564, 774440625, 912386616, 106712487, 990929093, 479657623, 579562917, 979925905, 896835207, 588948714, 924994467, 641703137, 103851144, 181744391, 903478053, 173534727, 835429479, 779727670, 518445180, 797801167, 84688954, 271757591, 243561365, 383869750, 12503155, 733977353, 328482802, 220455684, 325796704, 701277435, 225703491, 371908522, 315305513, 943278837, 417213490, 476407708, 204101784, 924105650, 956566869, 187723133, 674794433, 330150559, 145352675, 764384131, 523608159, 522652896, 240079428, 588212077, 826744362, 678228374, 713681319, 323625951, 626134311, 576030436, 172499205, 527153247, 849978068, 538483200, 307960863, 288873086, 708805257, 929145923, 796650440, 755467254, 516490791, 566444533, 179811163, 368151876, 375227087, 962418280, 844732958, 660975984, 864078849, 767284855, 110599079, 414761854, 814506949, 640661821, 753940276, 211161007, 122619936, 855029226, 846373552, 124254601, 976515689, 702139420, 289323689, 800855803, 895860146, 52670232, 236408258, 337587658, 20052478, 107643886, 821932709, 47777713, 424699248, 787285352, 11511992, 435779428, 37640569, 105997829, 555901379, 256164510, 394017575, 138177804, 72280161, 269242166, 705900441, 507045556, 875410672, 600076836, 366396719, 742936519, 826096577, 268159050, 108434341, 498995760, 52964357, 33585445, 163960723, 928550671, 367423573, 24222656, 574303907, 909532602, 579341391, 380140407, 166386321, 230546300, 520910726, 851814753, 454958295, 285031541, 117589106, 93524253, 433786619, 758377794, 119826477, 843242724, 573561994, 185503411, 711162233, 7833516, 897992628, 791063982, 842376379, 286786970, 28894124, 373799675, 731072534, 133306498, 518557782, 207121887, 133229360, 681637585, 454196646, 664997512, 643888558, 473008641, 79626084, 300700803, 191904399, 294943269, 650725754, 678191650, 369444142, 542419740, 995746712, 100493269, 213208444, 395996385, 153421443, 958461258, 45564257, 969273327, 259908894, 810923083, 98927862, 520543653, 195700116, 369892009, 767633128, 902866211, 310665207, 819037660, 8972278, 297942802, 31459453, 95988447, 563361072, 86692933, 81124319, 867978444, 383316498, 487051984, 62934898, 239833867, 552196833, 53955629, 172657428, 606474412, 335557460, 145557222, 644823371, 48857577, 45270372, 725657204, 897239268, 97006795, 99455912, 860385715, 618984039, 672552024, 323090996, 1130878, 971983578, 854323538, 550120983, 493765136, 512540169, 561639076, 510345063, 581009977, 50474279, 935374775, 789252348, 580877485, 254793747, 247650635, 171603249, 542555979, 388928136, 601735654, 990325645, 416595669, 485334449, 213389490, 725840032, 6462992, 408051361, 870301011, 888597507, 609682693, 940986890, 996838573, 449783687, 84467663, 110434429, 324095380, 493339444, 184782661, 316722012, 100792193, 828304402, 756504878, 83966780, 823557645, 546126079, 577093129, 543374338, 849555733, 910871853, 93692770, 563883649, 120131515, 480773657, 824738829, 772663671, 410735421, 356807837, 570974460, 668574348, 327972049, 370234855, 595632569, 681193488, 238224832, 583114028, 768501086, 385460389, 66838389, 646221508, 318319593, 928936405, 417756186, 363878096, 169957149, 469388416, 206113929, 688953663, 998234811, 312908002, 577528725, 863737144, 502698131, 678088765, 572716338, 49506241, 950917746, 985064567, 578032951, 775046937, 653979252, 28855707, 907658180, 103380183, 128592879, 402168262, 830451830, 552320941, 947382580, 405287281, 338298324, 874171231, 598853720, 312738333, 659912057, 83552159, 97149317, 885450385, 608808659, 307443193, 809488793, 334444846, 13540615, 764069004, 989411837, 989992867, 494376208, 185304716, 933025516, 515558383, 959573915, 108841997, 337676042, 894760342, 791444274, 421313607, 337925556, 770226917, 802806322, 362827296, 336345887, 552663403, 766035273, 152846983, 70085777, 525289153, 862330203, 281677461, 512692600, 394750755, 353567578, 252486796, 945051323, 545368762, 617985398, 661085622, 679889865, 203348884, 45884218, 597036160, 740552638, 974927841, 874985946, 941776850, 286236561, 967628725, 600622103, 260412816, 704410679, 368354222, 797512010, 109104239, 549187430, 383658072, 698882757, 981908961, 859206008, 745484739, 57199793, 972706842, 593761504, 942002813, 898482953, 476560035, 475965690, 693678800, 683701966, 333391163, 576355713, 810265280, 272429292, 558257999, 109464290, 179138554, 41466949, 176540931, 189861841, 981234983, 424636343, 124258832, 800922188, 418732796, 380582968, 905507432, 506342546, 808914618, 757178351, 587270257, 760521781, 911011621, 354844574, 124637577, 866964211, 76936541, 995624618, 449681445, 528960601, 296202055, 7345553, 222383668, 185814912, 119281004, 596424749, 518415262, 785769749, 638400725, 391979220, 345960069, 869376035, 807042212, 549559674, 526259562, 795429429, 881280355, 429003935, 995613209, 569463349, 877093595, 419656156, 835479133, 66941963, 259274570, 825432626, 454765865, 819550971, 560993317, 324416025, 602721331, 310489512, 263994145, 154753998, 745457465, 296265200, 605405662, 250004664, 726772805, 989003967, 908444294, 2920588, 582688591, 251601325, 443210894, 675453202, 540306057, 732456118, 395282948, 835086136, 852001992, 83764786, 40667549, 951979223, 808652033, 869454031, 905453644, 325720543, 996372842, 579542889, 619916537, 693010352, 489068235, 927058352, 610405815, 339728522, 235234812, 878570623, 852372411, 781151027, 553607427, 15363387, 717303588, 698589801, 597745275, 789292153, 880270263, 342877813, 688838394, 284787111, 619088937, 215590940, 694355700, 293942294, 383390671, 935896784, 275503424, 196619482, 893285648, 996765693, 522322373, 146765950, 456733515, 551795855, 77949424, 852104082, 111825070, 633615404, 239413760, 233191069, 574380711, 487199587, 900723693, 412684785, 279283213, 370635070, 736314697, 612268011, 622205130, 95438309, 752687355, 211208420, 919014092, 357355447, 919683657, 364605565, 695480980, 989316742, 344130607, 466273897, 842499131, 11997156, 951942443, 99086312, 185365541, 719618851, 223250053, 531648148, 524358945, 647562599, 761151530, 852435953, 700025611, 916514242, 781097730, 18965179, 73094835, 67009942, 868623138, 985274163, 905813142, 766811906, 326396497, 596910842, 378542348, 584198061, 261217027, 32571459, 531749954, 841916611, 480237711, 602064862, 684835787, 538121019, 802965947, 433618520, 589885902, 626474801, 674154450, 741087985, 531854984, 447766527, 866780667, 42336726, 914565176, 822599924, 176281041, 391936955, 433183131, 667990938, 83095976, 36239261, 597891560, 616093281, 5539284, 606304917, 577141687, 674393153, 313714352, 217655441, 561559108, 976206234, 137262940, 646906336, 716624919, 751223980, 618658735, 676580770, 406712107, 13866377, 619258417, 740252049, 78799433, 49195247, 30060546, 573665494, 968860567, 579977314, 411406301, 908988429, 717483905, 30487385, 409674069, 348889880, 536894554, 175243472, 672001272, 279723668, 225105401, 317982189, 61453406, 487580996, 596486437, 414801014, 120156595, 721921242, 485615087, 517512313, 998563768, 385496905, 447209845, 655020908, 489858077, 674990726, 239787862, 347298343, 245618144, 766957722, 869189848, 429135495, 334140348, 710850674, 64730003, 698676127, 961141339, 984087171, 733228099, 594763978, 103019364, 768957906, 418147016, 330657156, 356151898, 224529032, 396734064, 376763479, 527936717, 770677401, 228374783, 126384213, 934714492, 749662421, 708250738, 792394347, 603523181, 785978433, 609748589, 421821890, 19173848, 654740655, 255291638, 499622185, 978968167, 255392627, 488518263, 333984564, 49304163, 825206766, 346315378, 521189558, 688279418, 987150806, 846638527, 464217069, 776784899, 135981291, 105135949, 208289723, 646554056, 332293053, 442736141, 188226460, 215789208, 138174560, 592218878, 653613996, 900037555, 447860103, 717227196, 448725582, 60123482, 769184604, 323146137, 64756097, 782767668, 337782619, 445617802, 81836694, 144328560, 564462110, 685333335, 192038120, 191947512, 453391184, 598445831, 258686250, 987489337, 586958329, 329345726, 931328536, 355611485, 678166421, 342687338, 383412041, 795546264, 865592850, 874327994, 381911315, 694050430, 745616572, 23713184, 660564632, 77866698, 632123422, 639450650, 903327210, 241009825, 679477476, 712084634, 467313823, 544925538, 291840575, 892290046, 963064003, 838258507, 392722392, 59191994, 457691534, 569468050, 77122561, 387385228, 930025991, 235190867, 371859794, 441674240, 968833855, 925115259, 777264344, 645589091, 104939955, 815752445, 150235142, 627460803, 706095376, 177407119, 20126085, 537612254, 733398470, 800830806, 41806905, 332874224, 51656492, 378935836, 251743565, 510654415, 464392944, 544260210, 833754051, 195234792, 299761392, 925978906, 457196399, 503698712, 107707281, 62499352, 415364722, 495618004, 280067077, 61714292, 794471720, 118721274, 791617134, 234264639, 775707710, 613740901, 402118540, 770764445, 531948657, 764812423, 817709672, 775516771, 376800145, 724976445, 428222566, 275687964, 812158735, 800529615, 67720569, 112275127, 93017313, 569091474, 948224004, 73020223, 364028206, 478051176, 261123233, 727577865, 379562349, 721761824, 284636392, 899996212, 475008901, 51094687, 598945856, 163034792, 101270354, 158545962, 704249237, 570341606, 208632339, 215763178, 939746840, 789746151, 347981524, 130810868, 105559948, 10052307, 40379749, 956485618, 356426423, 904734098, 384562504, 35979345, 421313463, 798181183, 672386287, 33975308, 977917089, 106553803, 385127774, 658603049, 387971061, 574294014, 692442714, 888359348, 719902819, 271637867, 875949580, 87146486, 302234534, 84557591, 143298125, 233406675, 91604257, 478245644, 965849536, 909314012, 784622758, 710485916, 720180937, 28865996, 582629024, 191242812, 944239809, 256594268, 881543462, 66373940, 255145095, 203116237, 396237979, 548633450, 583695071, 845576177, 768835118, 96160897, 854420863, 906996306, 517320948, 278109403, 511594676, 599701949, 347104608, 928057125, 123672135, 31464331, 548156883, 520598517, 306098618, 840025741, 799153722, 125594930, 59734421, 30718316, 238449178, 479463034, 190922872, 58678430, 457338028, 385691409, 476574662, 872872802, 225080512, 538137607, 897838317, 1096368, 200768967, 333134346, 973724191, 203031742, 441405017, 524561663, 621331211, 516869709, 184389030, 422546122, 464233037, 136705980, 728662413, 425709861, 543848460, 498969960, 891941, 909292884, 94260512, 983060790, 64985685, 692128896, 901518431, 129847054, 645336449, 494020862, 217111084, 739727651, 380346460, 661926068, 805264711, 250873211, 80296717, 273596715, 463941095, 596253695, 377498853, 374529413, 236192566, 448450710, 458304190, 445586817, 934671396, 951316172, 548906586, 48612385, 494798144, 690156394, 858024161, 778858270, 660386928, 65816071, 366584952, 421337068, 439222200, 204512149, 580575632, 72295461, 562336296, 171532892, 881913285, 129273202, 542090702, 984487562, 512134183, 361973477, 858383931, 355291940, 598286070, 464495931, 270923827, 392311474, 811923288, 773431731, 551966809, 694703171, 470623217, 36222177, 912363586, 721144439, 863705054, 895346502, 360101391, 1057773, 575551143, 813757489, 706957740, 596941446, 575159600, 518894511, 765191701, 739083127, 352162624, 593879374, 280186941, 731538545, 837932608, 209341449, 963450938, 578636770, 294408018, 108209852, 945901723, 269907064, 879576225, 151916759, 913786088, 952755826, 596039178, 994857167, 725261826, 36947395, 254329752, 854505153, 192186150, 954581668, 576104495, 608243712, 601501019, 392219914, 473516887, 50140872, 709237172, 798846123, 305902072, 617175670, 246496903, 889324875, 83607783, 421443076, 442176836, 912117055, 775505045, 689776441, 44730679, 39233036, 514710124, 569352791, 504798947, 760396259, 868129724, 674686656, 504417300, 796832350, 808558254, 735009920, 753806670, 557188081, 994307511, 23191543, 265882485, 924350299, 806633003, 712490242, 769257315, 956159, 669864698, 949392879, 236238962, 245569993, 400163315, 388532812, 577888101, 829222178, 203324357, 305805743, 385401783, 993477192, 891434964, 827551902, 407493111, 925487433, 482724964, 716187107, 152801963, 545689470, 286012981, 978430321, 16081423, 30642163, 183667106, 787139011, 665215469, 198592326, 498814191, 991941883, 406301543, 765569060, 436089039, 747939681, 647402864, 104276176, 842308704, 756533946, 37176631, 850632460, 134480337, 909465770, 173660234, 74405402, 919140794, 392847545, 285164145, 914677522, 965238724, 420212580, 98840815, 140777567, 815689564, 888734912, 833014795, 491716891, 125392756, 607040999, 90588475, 121140212, 635219047, 312245967, 717883664, 185966426, 666195054, 14080036, 872948143, 705531232, 369122767, 868971826, 309278071, 475433933, 724133766, 164548688, 816199014, 176875097, 504746864, 518670801, 942612381, 169412591, 377165881, 856203854, 426555451, 186590900, 166310227, 537728486, 147583599, 524028789, 682046360, 944341933, 100803683, 388030076, 817072505, 854048073, 244827002, 124655865, 884032618, 777108077, 857548484, 966689005, 599074938, 953398496, 487915955, 737029682, 382288226, 999641713, 24479245, 319214931, 658969325, 321149409, 482207657, 855578624, 382738297, 152084148, 19030066, 718750031, 395013854, 813692538, 225278515, 753356335, 625314949, 10319456, 905975164, 230514397, 737558968, 142554687, 210791436, 762434637, 53139455, 744208977, 691429168, 613877584, 821442870, 864055646, 165922588, 538949985, 991324442, 482026728, 450337745, 229019450, 910098049, 267783092, 646311994, 148686709, 481769535, 427711825, 351537411, 361963638, 76367774, 561727633, 823939092, 227835647, 219570532, 154377598, 495577211, 941387373, 484088613, 153483587, 985464731, 649427575, 95217182, 825311755, 974559273, 332217377, 691775307, 713787960, 807643916, 601437997, 307189733, 416870973, 505366341, 964015118, 312477955, 150779455, 327779974, 612366315, 312802901, 897113267, 150021216, 863527594, 814008839, 96206996, 551437073, 908795568, 827087052, 565179602, 394682559, 989272027, 830830010, 778158965, 519323043, 423096842, 62728625, 542381516, 885963135, 849547406, 229136652, 80411291, 782355719, 486454622, 737646881, 468022605, 295615214, 283560683, 770553835, 642961277, 885635970, 92120198, 235210300, 198996690, 639808751, 488727741, 915804120, 765761331, 548415038, 269419593, 506733660, 712537102, 965867619, 547437437, 239738778, 24894528, 413013737, 413204118, 821439529, 310151141, 478066513, 354170399, 458009425, 589551259, 411229704, 488435910, 386217589, 703020251, 634337427, 409791403, 857652589, 823087444, 10792859, 463459162, 748195775, 924891440, 356567825, 173987539, 162069100, 555479034, 34299114, 494138058, 724171555, 751968496, 152756761, 725754099, 486412795, 978065974, 382914491, 652867614, 912106190, 644373146, 821119819, 401186403, 780239272, 703259082, 592129930, 839956086, 392517048, 302862578, 4202958, 556354926, 172331154, 675063187, 617894432, 305707039, 774371595, 366194315, 160964317, 944104077, 522814859, 345784715, 316498835, 840926624, 419799563, 200863888, 750027352, 579984398, 992818181, 105099840, 172760698, 288353491, 955534366, 961616277, 628029535, 779977522, 259273089, 302383727, 262292676, 469187699, 929106117, 301416520, 331216857, 263041463, 889593151, 663782352, 32703198, 607645779, 482073648, 949454102, 319437571, 760121969, 683532612, 764813576, 170396156, 840453955, 758879192, 382128093, 650812380, 443403703, 222043830, 701784268, 96959012, 380856183, 645482181, 879070201, 984212185, 987547942, 774950044, 744571855, 254067752, 626742781, 888725629, 992934995, 703628848, 800195717, 118063612, 61323368, 462780462, 79832285, 172941180, 770438425, 821383642, 504708824, 45866009, 139945967, 648178858, 774944009, 2290854, 340145240, 496835341, 251311895, 4014940, 309682075, 800264397, 311941786, 234759805, 292156367, 214581976, 608156970, 242092270, 462537137, 370547655, 47281654, 762044681, 45318250, 385415010, 31550598, 489056461, 942892597, 829627325, 41459462, 800223916, 645563231, 952797762, 253844153, 710725627, 234445175, 779468191, 612540609, 339936418, 886274682, 240578707, 607810886, 715797778, 366767916, 979914873, 384483358, 583381405, 871574190, 704787475, 240543561, 905094240, 580734156, 541428837, 806061442, 839176985, 630501646, 178266037, 236255770, 185563239, 611098694, 570594373, 71862607, 210015956, 950884496, 829796502, 543703918, 286896994, 633677691, 886551291, 979404013, 738728258, 253794042, 663212785, 559174449, 448424582, 517090892, 888834207, 574254484, 961863299, 323295496, 622936573, 46472058, 78287807, 875107966, 638163377, 346684215, 9263104, 990165992, 902284234, 274481740, 805695809, 672458663, 908783286, 65531672, 371304841, 161792504, 434364980, 900440081, 198855761, 373248848, 373189256, 708531671, 910812985, 196695467, 543097289, 318239319, 236489539, 403037290, 587760445, 215544422, 934976222, 443128086, 123995112, 343201889, 504000477, 637841283, 551200698, 8605913, 661152182, 414745296, 305983792, 747008903, 231495028, 43813556, 864259207, 906999308, 484276672, 262011104, 935806150, 398347619, 749145212, 238575016, 236182071, 496052592, 2918395, 260098390, 285763408, 345047467, 567945432, 285877496, 864165175, 452898767, 5472849, 32750441, 292911209, 132761940, 999180238, 76183694, 653606882, 913651064, 487942053, 181642367, 589656211, 74525157, 78893726, 419882564, 263985937, 328959797, 2801214, 58238074, 39594491, 274488803, 518930514, 36730028, 787140732, 536430970, 639005662, 155288663, 632162451, 729349495, 875644555, 375688525, 674221558, 904964211, 533957836, 935798560, 698532664, 624025322, 703240082, 181145974, 105270235, 485374538, 122103499, 166419326, 816440940, 372592950, 912678253, 375303042, 633313274, 875613607, 625266161, 644383146, 907260653, 630509859, 3664695, 15699693, 46927008, 160508324, 229490826, 509622211, 732768383, 80563664, 165670370, 787259783, 961702618, 3508396, 662581834, 983578185, 22454607, 957011870, 195051467, 703248341, 136180554, 143672365, 179935572, 194313556, 386575814, 539455002, 802371123, 551225485, 180646044, 2177733, 858205206, 805957222, 743872156, 115686623, 760536714, 273499229, 302794538, 943051520, 559934214, 234118829, 745304381, 703007443, 495552792, 595729163, 880004630, 444028443, 319238243, 736047233, 941899102, 735156551, 377419897, 281974908, 966269672, 283449197, 839911740, 5410528, 577639038, 684502268, 896760679, 264506405, 695278823, 888036793, 679552914, 960500501, 276878567, 451645825, 885172410, 749714322, 467023469, 547222190, 641309850, 941535577, 789917136, 33850681, 185017280, 636861250, 506973336, 979911627, 669689041, 548482880, 52911909, 15056346, 196242148, 497034770, 745463938, 83166201, 835827469, 55863867, 195282951, 46378517, 352105645, 562135566, 698594760, 988722550, 973020080, 168018070, 822949041, 894176898, 947057705, 256683109, 305580341, 963279900, 948349906, 320234188, 255821449, 318018386, 644687810, 110365825, 402496030, 333519274, 129364220, 11092815, 723257320, 495592184, 631309027, 880009188, 849935547, 464092293, 440137835, 229583781, 325272160, 252460281, 7925450, 286615879, 548063519, 681698591, 370939767, 787090109, 373501847, 784901333, 976655400, 969037023, 338817382, 557984004, 442955928, 224523477, 308233289, 385031063, 71538400, 751797223, 689076423, 355424952, 56645481, 16824821, 213266757, 974129263, 772637772, 638101616, 383289282, 690997561, 331296571, 400654523, 313556603, 76082353, 302591278, 564232560, 89510929, 491886698, 444877553, 157395646, 419934865, 484474219, 161649464, 281093131, 742786218, 524618137, 94122679, 852629817, 981980698, 26210962, 704089464, 587348353, 208623213, 151948789, 652687506, 743350743, 642809474, 697639577, 268715581, 223013805, 966616324, 165457371, 627085482, 688674127, 315330012, 611127023, 124560589, 646856942, 916705789, 926165619, 484359471, 947748845, 794631145, 111514400, 706294725, 217852618, 419051075, 493788174, 746392430, 241477982, 244284285, 412131589, 405906463, 161229615, 580308167, 983749128, 971703368, 901982613, 577986259, 623547041, 528053240, 307472792, 593443833, 320205639, 104252841, 625999972, 713641035, 145675459, 456392610, 392343285, 912837682, 710155571, 254531757, 257380464, 227833241, 874421715, 106425676, 892365521, 399628090, 454123833, 974115307, 361042589, 828960161, 13430404, 340220601, 584469476, 625275881, 663798829, 39170935, 718249402, 733511936, 18312224, 769849964, 182334389, 843432929, 998712293, 818439373, 139670982, 311856588, 585214175, 703946616, 708719769, 51518287, 202565097, 727864816, 351823905, 197407686, 305328983, 36991302, 712144578, 564967582, 386061421, 32379911, 404875066, 440537546, 208533688, 600445948, 658577900, 553932626, 751286527, 98360460, 521741871, 666432125, 239988898, 582319553, 556217651, 680458107, 48681980, 751208022, 113181054, 930278266, 142706301, 568930612, 558929952, 713586163, 255194722, 869472682, 452475170, 38394135, 978464772, 325897535, 641851056, 721468079, 756682349, 316689518, 733177541, 48039703, 835282705, 349026805, 921752074, 795032872, 950852447, 222812251, 83669459, 382256160, 236538630, 698285846, 426127580, 270837526, 701335351, 128538599, 268271576, 26653481, 739145792, 501421001, 575880540, 588656604, 292285650, 100809162, 516520849, 734841734, 620221489, 578229682, 1886363, 868418521, 229529468, 674556119, 487368543, 274908119, 565317382, 503490895, 498763871, 434118058, 202048033, 550274104, 115773412, 360794999, 573571486, 935446615, 830590025, 896045066, 695247867, 238199062, 262066940, 750665452, 833909504, 587559778, 163030207, 186329379, 868715944, 789451672, 448541550, 230624480, 963853823, 2883947, 513375703, 55707019, 366628270, 921499379, 802365401, 635490551, 807643846, 216166570, 987978292, 595407820, 118232324, 954152806, 89799231, 461173284, 693154341, 441026061, 542000805, 417419489, 925798481, 371773309, 241341162, 930871954, 616652399, 247440302, 378428018, 60539432, 210658390, 53017839, 629073753, 985364126, 970947909, 132100442, 819577283, 391218636, 47199857, 554195841, 157149007, 198581106, 567185780, 269960119, 379297520, 901221768, 279635365, 152152232, 702782438, 314760288, 669308942, 98808748, 557592456, 37997652, 911356891, 321844133, 927186779, 754187692, 826990335, 842530531, 307881668, 864903165, 745566228, 350033964, 37176350, 120937580, 504800822, 970914555, 468064942, 884894754, 827432623, 655268842, 824149707, 267137233, 376444107, 697669367, 497023341, 265964585, 274059656, 736142643, 39542051, 773066275, 601962983, 886489539, 464975908, 793927728, 358282689, 789163369, 687324285, 313744897, 57945227, 378476031, 989054139, 406230184, 132193368, 108120160, 162681552, 743575282, 869639420, 251197205, 640098922, 222981173, 713239299, 18329730, 861268598, 628377437, 978738018, 931013793, 226653929, 133213637, 614559577, 741040391, 828242595, 590112216, 230744959, 942282188, 16458030, 887832589, 770572104, 643716456, 507062062, 366395368, 177229063, 714555951, 280963750, 213312227, 769796387, 757334198, 955171085, 378260320, 727721109, 479198299, 720944930, 796909874, 783746303, 191248554, 343524679, 45961365, 423649900, 385409730, 771587366, 741333307, 23383200, 369866197, 965530449, 6180350, 904918337, 831387764, 118478783, 978099999, 956299431, 391384763, 412018417, 64414726, 779761465, 997691195, 735902755, 830762283, 98320621, 225795420, 913446888, 67698858, 762525780, 926177590, 715107954, 865225988, 144532007, 715735358, 429350917, 245767548, 494038144, 545271365, 298845170, 211391420, 758048017, 456376700, 705763254, 808926765, 224449051, 185244447, 649976475, 108640919, 185789919, 878400809, 764309454, 431918308, 977015446, 64999447, 995001287, 894858066, 510658032, 752139930, 451684991, 213749847, 555065171, 862859318, 241716797, 328905236, 397905208, 326501072, 858066532, 720888376, 591630177, 332871064, 493837579, 238523462, 315481760, 447580571, 308574787, 614195816, 379323307, 973614001, 644359838, 416913285, 665750735, 359860876, 57199542, 915647249, 595725390, 109639037, 745605518, 58716967, 542603627, 307988290, 677655425, 7792142, 33831841, 543312931, 292129146, 707967456, 644718710, 205511192, 763410504, 556755574, 957485705, 489288045, 553785613, 136958546, 940600193, 289276966, 71268704, 383329987, 404350687, 261848214, 514544828, 296481298, 651338752, 57817451, 311183765, 116832483, 739571022, 174991927, 240862125, 241667508, 665368089, 595301314, 799953201, 875687855, 143889597, 375140184, 380317752, 689116055, 955823867, 546702571, 255295869, 376718417, 23813433, 331443797, 328231276, 655193535, 874600009, 164072750, 355916405, 527279188, 267177353, 532445434, 368447684, 564608820, 580407020, 972805360, 205049401, 707340332, 872592723, 410856949, 45248952, 562122189, 501426967, 98884309, 872213852, 70760075, 856796943, 38925597, 141248556, 980789836, 345363490, 232037688, 388627111, 795662592, 529655799, 97223928, 907341273, 799069028, 540305609, 166026148, 72155212, 863518487, 984141170, 485215135, 858492811, 225707349, 34929090, 465589469, 402531366, 880555894, 445820754, 313118787, 765120794, 535619358, 968515105, 248490934, 561652734, 726796323, 298566871, 595550978, 289455360, 108896537, 338101408, 165160348, 330080735, 47415330, 784799001, 595243863, 207513278, 495981097, 88021848, 314283019, 804137627, 562605730, 776712272, 181405166, 632256513, 120833930, 590357072, 820985686, 268354169, 395166956, 49645517, 208638132, 214271934, 855229675, 228830826, 743368693, 247132575, 704081398, 562465429, 845937946, 410978599, 971062880, 510110685, 98205372, 462903466, 407285528, 584542020, 414531529, 318178836, 358579919, 929228046, 896276149, 64958837, 982803128, 996906056, 170928101, 417565216, 11404472, 660032101, 832912325, 130047737, 974522250, 706302133, 323342718, 474326956, 258803911, 91638016, 292544724, 954898686, 95963228, 422404987, 375219399, 785495108, 375221197, 754869574, 105172765, 635963052, 357588926, 209590306, 595602035, 170488820, 113594018, 151715544, 386151307, 120657271, 258288852, 192284020, 433201047, 322603664, 979920964, 193581294, 257456800, 931770146, 392765141, 157670266, 939958365, 350382357, 987259651, 405712574, 427642126, 636547836, 879382788, 697152615, 128634252, 437120957, 274374261, 339486994, 964997494, 733828623, 969091245, 92695216, 193571359, 1532690, 821798443, 636329728, 692774353, 976234995, 370233917, 943698691, 743487430, 528178055, 187812710, 507821419, 935014076, 605690001, 177125102, 298838724, 32052365, 833119048, 766145479, 508073842, 97028898, 842212037, 175815045, 544196273, 152967360, 442493635, 528143676, 221288243, 945079578, 431813259, 868796240, 64459937, 916512574, 939042485, 127532820, 714451101, 386839469, 552479123, 248987036, 337025316, 867697291, 847904381, 183940303, 49207826, 503372852, 319315531, 975686991, 703652120, 572419564, 884986310, 387566551, 231708921, 799099056, 402199547, 616568683, 588999110, 417483702, 807267918, 141925927, 262686484, 375698299, 323208772, 577354654, 542470092, 909922382, 376802368, 714502293, 386258217, 481459634, 927626285, 107678598, 554157798, 7934308, 848212950, 80996129, 392899332, 759239073, 582900183, 287054859, 802305193, 529155551, 442020888, 465099659, 186336261, 44954624, 694044427, 127806856, 640409227, 803728220, 946471200, 602198919, 450685535, 581564574, 482852732, 254064594, 373957508, 986117530, 442622365, 554471361, 359173776, 841254633, 195738361, 75886032, 788396695, 20428037, 93651515, 72358372, 136464916, 651723632, 563127125, 25490727, 173599858, 997501153, 987166235, 613192305, 435826972, 482466771, 205116129, 838999426, 200607887, 614489182, 264713778, 783627647, 990062426, 130910673, 607718694, 610377309, 573971785, 44762487, 835681954, 901110225, 810635240, 907611164, 18990065, 891266584, 443709899, 856361936, 333544319, 449821086, 391819344, 492571820, 569201419, 43290455, 715139587, 977360249, 911158090, 208880862, 120246831, 325012151, 933168271, 59056896, 452251614, 42677113, 329291183, 507672703, 828848904, 805074800, 927800487, 112119792, 671013909, 280205230, 304046225, 233620113, 82697693, 603202922, 431708257, 924598392, 771690178, 162826872, 556646653, 754736670, 691737621, 893738106, 828481698, 847417499, 711097283, 335748196, 648357347, 253025199, 401170055, 175724403, 176989383, 329081393, 821902026, 668264335, 931168239, 31404023, 264373266, 209633728, 281695773, 900023297, 304588401, 112910078, 535724287, 512675127, 211323872, 424940210, 940956705, 852411436, 720955844, 276896509, 775331342, 843433286, 93024939, 126634849, 237184412, 942062873, 791406974, 124699996, 579130417, 725044404, 366851505, 528133958, 337290560, 932310854, 734525480, 223812483, 834958217, 674476081, 818888091, 63761621, 254695498, 805113726, 840952636, 570419319, 487364464, 726128723, 796227572, 794725038, 950841452, 394301434, 791909502, 544663440, 399423788, 854629610, 723654707, 106580963, 952996021, 783544010, 533572122, 323567763, 219718785, 144002928, 348711, 268688938, 811586929, 599960972, 225211524, 527867956, 336262974, 92080553, 737311714, 196860926, 598253403, 190309270, 565120269, 465452917, 731607347, 272736106, 503430147, 212730386, 904925581, 720277894, 260795263, 210596187, 694790634, 624776087, 671663944, 847511013, 683925203, 636072522, 702102668, 447575011, 851687143, 883015212, 439516260, 16750807, 485427525, 888327453, 221465665, 909695686, 780635295, 932254232, 203119849, 320378411, 668426417, 763693420, 471444790, 241684027, 982953794, 960328452, 997520736, 913929868, 924579815, 777271518, 205492851, 221105073, 417782751, 117922847, 446445473, 501688424, 569325831, 353735051, 100947722, 552928046, 550517992, 409502063, 956136319, 35561079, 319349605, 285689093, 340466719, 699578802, 316307848, 485863505, 884645562, 228275908, 892506654, 31171149, 806590153, 796510306, 200902063, 738864517, 226777850, 111505909, 387592741, 865027458, 513133876, 910770118, 692239882, 659768857, 407995501, 132054630, 414570827, 767478608, 767363709, 237939981, 167125796, 457778291, 436383327, 247025420, 427653923, 687809316, 542568515, 258138862, 429591349, 831078643, 691563804, 6076712, 32832048, 651801971, 832436927, 383723073, 516565758, 663885240, 634741769, 156052531, 386969098, 896948673, 62889360, 806506987, 989947807, 959873038, 561568856, 907200468, 336886056, 399053830, 293312423, 883103631, 269935595, 847651833, 79170664, 547333795, 376080999, 593947268, 187421151, 264310614, 657721321, 621107862, 493669992, 764718750, 232810153, 752127194, 342901750, 357453511, 698109784, 859753082, 489914655, 955400174, 519959228, 246128707, 402468393, 685729119, 69856467, 367165748, 138369385, 562354182, 262904273, 10199255, 477488697, 132021531, 739029924, 779281102, 63612578, 626669690, 897048978, 419058738, 601638816, 744011098, 576599564, 812800558, 561703165, 39063056, 479380867, 929458705, 451396871, 307851439, 13291917, 491960891, 720528393, 408003208, 948856978, 216061878, 45363753, 431877031, 631572742, 486743468, 754614879, 938257294, 263274600, 103073283, 624897259, 634425191, 772325148, 827981337, 239509894, 408247025, 451882216, 474576441, 35104984, 293481671, 932372206, 416207244, 423187228, 886949683, 424331940, 448827726, 338304841, 675688993, 682176060, 474347768, 874258027, 680756980, 872130223, 109959412, 229729139, 354010016, 205799359, 438538723, 110254676, 371094555, 291120096, 450255246, 641644943, 850492225, 298814161, 988770042, 304274002, 716843243, 866866936, 974204375, 806858506, 826482270, 794173391, 878088530, 856980379, 908736049, 487913784, 142531387, 358480247, 727393711, 609738411, 426290335, 112548255, 211014775, 209912135, 41133458, 35264820, 743422796, 164235339, 13758379, 953981087, 196733812, 701044552, 712119106, 871012964, 380621390, 426359759, 218396581, 696874394, 704436303, 441930125, 222108652, 317952760, 961443205, 630423306, 258285433, 562451173, 982711292, 810991713, 683327677, 493663435, 314871021, 716089855, 758511951, 406227696, 67761985, 651785462, 185683564, 263942043, 266487354, 877115452, 279581012, 564191654, 188659276, 565082849, 412460785, 644728891, 155611384, 947081884, 126227509, 300457549, 909107582, 734620264, 516285455, 475335700, 516547497, 22021010, 371484309, 13475656, 271775417, 240483396, 493507914, 251423575, 342383990, 495373032, 5646399, 559212030, 430495522, 746456282, 354419228, 308384321, 350513233, 537447859, 500997406, 112435378, 667185557, 358906711, 900407852, 325662938, 203365486, 287355104, 370227382, 948358472, 987413314, 632990611, 657630885, 985825811, 629071056, 392255905, 469519912, 152864550, 116324934, 896431336, 691886714, 220560258, 425470610, 126003363, 84407098, 192485033, 932678841, 225344184, 93908835, 921156465, 124830866, 997347540, 761390909, 182793301, 454895537, 551960614, 893629668, 763497900, 535489631, 901662949, 954715266, 655343788, 677661529, 695166119, 560716517, 603966178, 145107468, 621524376, 814733835, 621754418, 253617223, 326101572, 315225228, 682773281, 160514706, 363140981, 374193828, 222509896, 750780404, 673939334, 44143854, 94775450, 600235672, 68006694, 595204676, 543329678, 81916148, 500736663, 129304543, 59061803, 499771112, 184890948, 190205673, 386598581, 295062338, 420816574, 37465154, 663297757, 464682612, 424405978, 758902354, 474916087, 933979147, 818096702, 225532561, 194927230, 314379252, 348071739, 87576268, 404194126, 267546512, 414736173, 617817923, 523619556, 478369149, 839782358, 359701547, 290668765, 703427987, 355012053, 859392856, 687592704, 176163227, 966835656, 612730629, 850873501, 190900846, 1891782, 524348898, 843974712, 211926064, 711720847, 633514798, 651269086, 410030874, 561395294, 146011348, 942009467, 416449875, 442660810, 181053991, 275742831, 652219209, 587357577, 150583521, 175388851, 345735968, 870165551, 389517571, 417320093, 646833144, 39564564, 769306564, 847798749, 970327769, 148952539, 609517647, 78626713, 602969360, 912406833, 35184725, 407763477, 669360706, 513627859, 509484005, 814053844, 638591226, 239576871, 464961419, 859658791, 651839026, 871909042, 703465773, 830668544, 625480185, 54495912, 788286887, 286583073, 976295257, 225449454, 948681774, 443799554, 408335956, 623171282, 415363920, 467324352, 637361797, 41845785, 118858588, 905230900, 564201581, 478525902, 642649869, 809525144, 243304164, 370453202, 646373885, 791607163, 353127986, 87017951, 734063559, 411032701, 510185216, 60574322, 785080230, 927780460, 754693760, 272295819, 723996102, 398311808, 989380209, 600664571, 88397500, 625587845, 757337620, 600716059, 599453541, 48968802, 717154486, 160413947, 891968562, 233147788, 397846850, 851156951, 566889001, 100689184, 936478328, 797168865, 112635655, 988527615, 899075102, 794410288, 946657162, 550117697, 16711288, 745502969, 54751684, 208385516, 496782678, 6378482, 127938444, 803582092, 150282643, 472657363, 733417184, 759187749, 771343629, 453959644, 430864872, 882857389, 61117358, 187677199, 196620473, 924991771, 49630299, 79319450, 58320803, 811931935, 225293095, 961932961, 993014260, 146275865, 211750788, 141385755, 770732726, 65941134, 706252289, 43959019, 160326808, 763935726, 537542646, 455346968, 461727655, 184611323, 527313282, 396804095, 738275751, 847313622, 948534327, 470864984, 25156089, 81392770, 819635414, 433728046, 144133770, 920310188, 738824642, 866233095, 921653029, 901746821, 976566935, 563071924, 120697329, 583292608, 933985142, 142641853, 707653767, 489574686, 915653857, 543162187, 617929391, 839854517, 973096839, 901497380, 741758313, 477510583, 915075561, 997372955, 508054407, 841129465, 630539801, 314899931, 561387300, 265990603, 14274272, 157883278, 364268551, 261234686, 394755980, 541905605, 389962084, 742985486, 355539146, 636431347, 673422000, 192057606, 985241812, 831606645, 323375306, 268007203, 905243081, 52617681, 573858557, 752330170, 657868708, 293933037, 223594690, 490177861, 612473742, 148821926, 58392760, 825680570, 175510101, 519072272, 904529413, 523252638, 622737136, 33796199, 981217879, 331716646, 370274270, 125522874, 297759193, 900818297, 188037002, 431699080, 843119457, 541810826, 270548794, 973680675, 96626912, 56282126, 381033187, 725758999, 511556944, 444079168, 778786714, 497731571, 666381886, 115999073, 687550808, 425091007, 38990048, 459250090, 113048245, 305012308, 470004084, 544426322, 521937044, 626223896, 339654645, 35654721, 669625512, 679733418, 512857064, 599635822, 774362890, 747016601, 939787033, 304356189, 61159262, 205499617, 42001673, 360718450, 719619452, 281089549, 911484458, 533004272, 72386455, 178136088, 642393312, 681808155, 723069963, 887977296, 163133222, 380089394, 148275063, 877008944, 824766232, 714021273, 516302020, 793928247, 481327365, 334567959, 423445627, 806623044, 953655596, 14065101, 371252093, 386139764, 898270893, 517755493, 249149395, 655755150, 519952720, 491777117, 796647443, 404478568, 851005565, 349242215, 973522156, 699618675, 164158207, 134038287, 686754625, 562714158, 79731415, 460347518, 534499456, 743767373, 774702764, 295045999, 455165743, 99120201, 344979336, 944351340, 121307847, 700239121, 371106627, 802510563, 850749961, 214288743, 160938373, 861653320, 451705561, 947571976, 220909594, 425801429, 747743094, 72356034, 265926179, 19199909, 275908414, 749001187, 967114232, 661614699, 334248838, 600158563, 326656177, 967108898, 344242533, 289540119, 902119423, 288790031, 726253927, 783854038, 397864115, 334226459, 611851006, 410117386, 73297332, 652302941, 978439712, 899070495, 143873593, 916563119, 912036141, 551666623, 23809432, 49873486, 322957604, 447387940, 968328567, 693172442, 710939025, 59387796, 406074838, 574527647, 649444778, 967610412, 387340105, 265175917, 558285840, 358861257, 689552937, 635803044, 348262385, 180328739, 946917215, 786487668, 582308299, 633229103, 214061194, 155209472, 381314344, 673018610, 967006291, 963991669, 759351162, 663025199, 672682769, 527509032, 603306862, 159648545, 404879826, 815401195, 698039461, 439353284, 667496857, 59980597, 934601845, 647355926, 194635046, 520329193, 234858707, 696394106, 447099840, 236084788, 741940097, 66071739, 333905813, 311346847, 644537586, 497092124, 347530796, 546018082, 798852350, 573216603, 726528025, 176023366, 404222370, 602390702, 819439551, 912128174, 266327760, 845241323, 591440729, 452414445, 729829912, 265636544, 966213428, 675912053, 44336523, 764380926, 634801842, 321842824, 25799519, 732972498, 463836137, 802604609, 645393705, 622224703, 50769918, 978921986, 952469435, 144685679, 639931826, 363846651, 238431255, 251477467, 800311621, 354068641, 563795406, 766744495, 786539066, 759229923, 862359618, 937907376, 846531304, 281321793, 158533597, 641852703, 956115567, 180758139, 370286763, 641534736, 330244002, 364769202, 189250198, 344523794, 50425702, 888177386, 4144815, 39263721, 767176840, 65062159, 448424742, 816460173, 371906214, 672564225, 491452664, 583906590, 742790472, 317756115, 959378306, 687183102, 93799278, 712677415, 47230610, 870730357, 641841558, 985181744, 207766310, 473377581, 953867832, 873534481, 424054657, 218357420, 489960398, 46376143, 656381227, 491006218, 940258407, 882218991, 639613783, 806211473, 11272344, 511214862, 719160497, 122553512, 343684464, 229783308, 245131914, 922431825, 456315985, 931899094, 987633945, 21981495, 296999037, 226376658, 574518781, 678681355, 949456264, 111447694, 37810589, 773801808, 371488005, 663554740, 198082193, 201913472, 853177769, 526291953, 471622984, 568351086, 114604701, 990067011, 957948439, 185602036, 285814266, 380477347, 450486296, 357716969, 770704096, 527524998, 272263555, 192386529, 668941030, 582376850, 807533510, 232698175, 208225109, 528093328, 380327528, 875957400, 856721425, 567320092, 140167172, 111312331, 882274370, 325844268, 417562397, 691817927, 589295667, 704660467, 692990959, 847093212, 382085392, 133209757, 974308956, 515651534, 53452380, 782181343, 651130190, 481400685, 457202460, 57774375, 200795668, 205520849, 401002981, 135119115, 423036096, 392371803, 745604673, 178348777, 965654400, 471250961, 705076072, 226545755, 131675127, 89118592, 561530346, 111420977, 788480146, 360600984, 880526132, 116720867, 924356194, 852977914, 520401761, 29987231, 654613487, 85333479, 689407513, 848048785, 495212763, 47112295, 764244987, 800364611, 204057160, 715329745, 981606051, 708777512, 961194380, 781562061, 840221360, 349290197, 893482026, 278177817, 511770756, 239578576, 460817467, 295023894, 90130210, 734325785, 738261950, 484410745, 591139251, 207429271, 529137997, 33379445, 696281680, 834729647, 393927454, 366366315, 417485863, 454455727, 926928521, 337967342, 733596178, 646060709, 121941044, 891438943, 162957710, 769451022, 21714015, 463324960, 778643247, 694601077, 517434273, 753491974, 440368241, 291097727, 754324982, 932644380, 945720753, 504573513, 413019921, 490841710, 721854867, 857985960, 439408572, 706554284, 56874718, 784163326, 709811136, 502901492, 322414340, 589037580, 220077169, 770378102, 339387201, 151258623, 489906356, 674983662, 53785518, 687724056, 139509225, 694509727, 573036610, 878352757, 745423666, 484011725, 543265643, 639858284, 973594854, 950219043, 649109976, 505333301, 303045276, 369846903, 490593262, 338808024, 606841703, 576000177, 507407788, 863577833, 594235814, 883340541, 397357863, 665045157, 679057623, 967068678, 153176947, 851949599, 674683131, 70063117, 633892267, 182222343, 380971579, 700754812, 595637943, 643172489, 618581184, 952496533, 24414398, 329468785, 180998970, 217466443, 620173167, 541787068, 972237781, 358904055, 527053260, 999067793, 503568617, 998601816, 763802925, 386345379, 578974443, 933429597, 936742647, 79354351, 281460937, 769146704, 875531807, 309444046, 420210685, 761813642, 787037967, 79337549, 420222635, 827083818, 645862952, 529851802, 916278843, 423443727, 864250716, 241841336, 361692275, 499590268, 547507923, 980789910, 218142558, 506880171, 638398651, 956614798, 317298138, 264511288, 624520946, 355301476, 427990870, 213492919, 407596281, 588052435, 511812170, 733017120, 731074092, 612809753, 163406548, 287945191, 914645414, 233439113, 733240348, 317366568, 690817672, 434229962, 784851770, 488158715, 329812462, 816034479, 235464015, 480986860, 746730495, 326587445, 407587130, 868241354, 999681351, 59638102, 195814973, 634363797, 574665349, 166091056, 825221483, 78310006, 183126816, 476745249, 245740804, 139233000, 522295560, 711498495, 333215572, 341769974, 438648640, 373376152, 412650513, 756060417, 857613200, 846701223, 525834583, 461505844, 595856986, 801443328, 309951105, 434397408, 623691225, 349592507, 566475983, 795818425, 402118701, 5657466, 67644717, 158688772, 22887247, 508006197, 528712867, 224941202, 719170196, 271700379, 622258884, 363608887, 525161922, 852193174, 668876605, 902115121, 805295698, 55310320, 729060417, 788740098, 502207389, 750893446, 856809665, 706138306, 662478671, 306177051, 640975971, 249335681, 854040659, 829705226, 808892414, 922183589, 295534604, 619568649, 854450401, 42383252, 94691042, 800708868, 64452472, 453991593, 698668561, 445605713, 952640987, 331161356, 911367067, 384077272, 618919896, 160460273, 466688497, 414351918, 277457416, 691655079, 19749544, 514923249, 853022799, 28421378, 743744211, 216746387, 530455579, 604647888, 968230516, 812059746, 280398541, 450326125, 997515625, 38187680, 860075686, 798490237, 573855826, 909004489, 795965017, 92672900, 748059561, 809609676, 48689739, 672524606, 564119980, 108453996, 418006412, 450724276, 40330154, 436501271, 389000967, 373478579, 88841076, 755739607, 819459288, 902913483, 113373395, 662459604, 915574506, 75507248, 292384579, 283376087, 757651446, 753681131, 618874345, 486788659, 39565227, 88489282, 897496655, 790011166, 163342846, 136085384, 703279666, 203958469, 447381723, 492508228, 57926236, 821403679, 691171615, 616700588, 968656521, 982016538, 376723780, 847043599, 664005239, 192635347, 52776465, 247493059, 665903753, 742931430, 943059412, 670712571, 13598144, 8217306, 227917131, 65604644, 31374687, 881574637, 285048735, 974393217, 343714759, 775028978, 527276896, 193962226, 256040320, 199187634, 829899111, 475820546, 862592353, 301449265, 833950401, 199710728, 746116482, 446113244, 162017984, 129615795, 933751984, 11710373, 62765247, 268679094, 99536874, 795865484, 136888643, 947914449, 972727350, 860211856, 552368746, 768734683, 729557231, 72064449, 375163558, 147095859, 487777602, 881870701, 125409092, 867021157, 280637408, 253432639, 459285908, 745774645, 39716963, 535710978, 7209648, 289269703, 558376831, 16106495, 272494196, 944920830, 803985197, 101507307, 889720027, 944197228, 315528280, 317487307, 419584353, 280993115, 432280189, 873545048, 329153215, 962173490, 48841565, 495571623, 378990849, 994341021, 660783344, 214313849, 234571679, 362441526, 110995240, 477512643, 738083018, 357572846, 294262074, 718797708, 182209179, 689358608, 551662994, 571938960, 190652147, 545316838, 490025218, 462350500, 101468617, 676340777, 726179527, 607502904, 844000668, 298965525, 590469843, 226155806, 116953820, 116998942, 104122097, 104487899, 65426904, 443051248, 92003332, 68858403, 433582222, 810854467, 50686718, 571737246, 721249322, 921239269, 596430550, 476056155, 982860858, 613212695, 529134997, 505772630, 207285061, 862842968, 486152896, 511646494, 738739230, 13285452, 871331129, 935574581, 804310633, 446656762, 328134742, 299952704, 186526901, 348194917, 133185747, 923294750, 701943823, 855577123, 926918506, 296065438, 413810540, 156194099, 200004471, 803620627, 866255008, 808726777, 415956949, 35572301, 68781066, 985957330, 571580939, 225161957, 925637195, 418495702, 390877191, 573315063, 42792955, 19345702, 166663377, 201138625, 899595907, 102406553, 944624200, 165121507, 180230275, 768230028, 422667792, 408083076, 266942880, 746436764, 335205169, 620804698, 376732397, 707132576, 605264459, 160915341, 364004752, 13413279, 863501822, 84906095, 803838719, 488749085, 208406273, 323722456, 788741897, 878438642, 967153257, 194837067, 526427675, 314262130, 870756031, 512407368, 902616892, 210378769, 54341349, 978695069, 409673816, 551287398, 165554073, 114728939, 645923842, 577877974, 349378738, 73432834, 687380456, 849503538, 553137830, 826515250, 904517968, 364518623, 550871816, 323363347, 41835029, 86624316, 576608778, 79071063, 382485476, 326977285, 187447063, 832459670, 460361731, 426489102, 825638219, 986860155, 907450625, 275778231, 861849673, 482280182, 614614761, 812157048, 410286797, 60533055, 391276014, 50248856, 317996432, 687132674, 748915709, 627169549, 83896975, 673067725, 517702363, 515333953, 3415098, 342455338, 721668145, 799350668, 291778073, 380846052, 850879184, 984229944, 39158197, 664439624, 738520892, 487095366, 972832628, 838126220, 939605256, 963566373, 503360784, 350618864, 526543544, 14644830, 776405763, 756090577, 5621829, 240332637, 463377888, 689375299, 20990444, 100466109, 693520768, 233823440, 769739277, 629215634, 333669999, 320390374, 175653607, 756667350, 31753226, 181549233, 884441976, 892331084, 204481552, 830191988, 518607254, 120525434, 166385263, 544085312, 305125716, 679323232, 537378885, 349752565, 560535169, 988846448, 313857752, 198846908, 346387960, 814657444, 773440278, 562432389, 212772637, 825787427, 979233845, 154018625, 744934448, 341697190, 481708096, 339513709, 504359540, 954733057, 605941971, 305727819, 141315095, 528589138, 594146400, 481660900, 844303256, 876098588, 263045463, 622580836, 987543881, 835027350, 439265193, 964311387, 325700901, 338165073, 350682937, 444994187, 71526298, 74838903, 72988556, 258285919, 106695270, 541692490, 584706032, 430460632, 133375097, 92132590, 60740798, 699253824, 665384925, 231639982, 476571547, 928210072, 283428460, 519482620, 858548699, 687776, 629706538, 54539233, 698310010, 638417603, 351626256, 142324083, 306555781, 448066908, 14419330, 465119255, 955939266, 668222500, 939209854, 416698882, 451295375, 795513769, 242017417, 84828103, 250275598, 269514339, 55045455, 162050485, 432149934, 821864212, 290597998, 694870012, 700735484, 377198510, 204538040, 167977427, 982743118, 578243366, 692949521, 590881254, 97386928, 121343798, 591459487, 579025782, 947828893, 624926048, 584766018, 191554785, 777216386, 980056986, 245863015, 241656510, 429601207, 500903056, 145652227, 162526691, 617892768, 211960034, 129168150, 52231692, 901978433, 584987032, 127825300, 434285309, 755788407, 158430426, 567944956, 192855315, 309858535, 94046680, 492074159, 308580880, 104962590, 974216651, 510491431, 693235649, 35921107, 851661572, 450609080, 423366133, 193784020, 118949063, 427497670, 572715320, 358553594, 539060928, 508342549, 653903459, 867209718, 100012091, 172873070, 87436492, 641043785, 885700856, 144077930, 713416564, 291638948, 263671285, 104814716, 645267868, 31623645, 618227076, 285614954, 445305784, 345112342, 425302521, 315253993, 367560504, 616391687, 93385879, 18106302, 579863032, 76923769, 908311834, 932592222, 367916585, 590030877, 889689025, 51649381, 890262591, 307802705, 803776177, 396774968, 932914272, 308475537, 577215575, 937132313, 893282439, 991031329, 806264143, 295042344, 540523909, 99881343, 434583570, 948086478, 570448833, 831704018, 97330343, 701001346, 765686930, 557016004, 3276074, 112436319, 314572622, 303484619, 792991341, 209755836, 650199331, 475490512, 423327307, 935879083, 241887104, 164765541, 814076486, 789699463, 66928152, 860872568, 849063055, 569772716, 669157053, 574060129, 144219531, 687913062, 716246678, 404115736, 470215592, 298862383, 657194579, 627492385, 302717903, 997852738, 39535240, 303368956, 8476049, 115773266, 509007738, 545538945, 258792745, 183993183, 26841641, 70266556, 387283134, 105600046, 812107995, 201892616, 975675352, 431857244, 615363017, 676548161, 289592291, 291982496, 358763158, 983083883, 591835330, 362386750, 692005681, 195764808, 489456007, 138363188, 855406699, 639455966, 421268944, 673739089, 191376074, 821171149, 536994162, 27242880, 290648097, 399148814, 288148654, 949401053, 560752144, 467367408, 854556514, 898984771, 150141309, 62663322, 627124092, 831073106, 173522410, 604073329, 660919046, 713083857, 962228989, 768885864, 596689567, 84491191, 841034162, 484861819, 543104168, 144159786, 717826243, 463710954, 946455624, 770882640, 513425276, 814912788, 428817912, 67333524, 125460719, 823251164, 668467137, 711556055, 122743415, 719560407, 660337464, 668446244, 558120018, 643249869, 784961237, 961153503, 414920490, 815917631, 381176201, 22002379, 177624486, 328090936, 755290535, 493853820, 296607680, 852855650, 181141453, 257171346, 123083607, 950154918, 733558557, 315859492, 191731695, 713104267, 581517878, 588763379, 407710247, 771345120, 800307399, 737244346, 605976130, 789853668, 540427777, 350566360, 198288959, 167438958, 152433315, 343397166, 452360979, 275421035, 988075415, 376048232, 14553453, 360339468, 11599522, 188918343, 863546404, 723423076, 827012152, 885774126, 798920062, 739356455, 368573783, 181945884, 429724467, 535135683, 702200116, 934603456, 718147890, 480908518, 963600778, 636873648, 432387080, 965122543, 479118773, 543707694, 879506194, 529734768, 182870164, 981558962, 974716137, 513145214, 473918010, 377908440, 784216833, 276285981, 639075369, 530006545, 529408522, 310934743, 651213133, 674572005, 14972950, 489647254, 993577943, 816174305, 577837752, 647243740, 901596664, 337821325, 907284103, 476727089, 121267579, 542318914, 64674771, 844361878, 678625640, 900760316, 777645772, 107081946, 214912322, 190333680, 151576365, 433841038, 41852337, 527356397, 451020079, 298449236, 986508754, 244350520, 75965330, 370610805, 340298059, 804157386, 747113251, 420571981, 766048584, 335922955, 586493714, 467765347, 209914802, 992643952, 194336239, 989062843, 151540952, 703374264, 33436243, 998645728, 933472618, 204181077, 203294559, 958243292, 158454184, 112704627, 162360865, 144858168, 11219716, 611733797, 360812352, 638695871, 748344527, 176606185, 127995846, 711644136, 970790848, 880290, 520737080, 14802214, 328958747, 317367000, 976199007, 439308538, 257083836, 571073631, 170563752, 220696746, 401872378, 155183129, 619948406, 949869706, 309690127, 904243040, 786730226, 119581966, 632592864, 455622088, 619701081, 82270130, 3403280, 635503783, 695987152, 502835031, 343255074, 172864627, 436044040, 825329721, 211093919, 471177523, 747749888, 43211207, 582010423, 188938312, 989339017, 780204515, 940256803, 113212106, 249278578, 281939580, 937152915, 105203407, 629106519, 281828653, 857852801, 199326797, 412402076, 319816897, 719987646, 916952792, 911515639, 896648127, 496630128, 428814725, 100043089, 287543423, 84224179, 73277487, 997407970, 658750817, 701808187, 61274987, 223061343, 290857724, 682073121, 159830738, 724225067, 923392344, 920112685, 749788284, 999517624, 573337638, 555615988, 712072226, 710351580, 160292078, 459349735, 970161399, 207647289, 852648271, 133769707, 691813122, 324791152, 805394002, 267730315, 690013652, 341296316, 848022938, 122496863, 622921341, 618838133, 601809359, 479002298, 17629014, 687212373, 589217013, 68734406, 211169552, 461442185, 756252882, 585311497, 205932086, 222191955, 366310258, 766315767, 989212677, 184949386, 492117076, 185891713, 589520010, 573318345, 347130224, 982181496, 430127483, 303605556, 727280725, 327531525, 151309364, 916418990, 32127305, 373239495, 938005147, 914548942, 293633809, 96855583, 738178797, 646612965, 970662166, 929587951, 560945317, 745776108, 507395116, 105364299, 350333938, 163874432, 309695545, 687991734, 164221759, 50418195, 609248183, 970856871, 624766204, 592256165, 775567664, 245029287, 775941178, 713743658, 20985339, 984884495, 678143259, 960151501, 828387416, 667591587, 671791532, 227746225, 664660056, 264242677, 940783206, 985582228, 187415692, 381627586, 969654789, 903657937, 154869844, 775802543, 774696001, 895525340, 775961002, 731481897, 791440612, 199304961, 858544212, 928098004, 742330249, 620297642, 394661439, 226765385, 365488298, 519039365, 71650774, 611817535, 36919638, 155336296, 292583160, 943150044, 608100326, 984552676, 125428844, 637362066, 639605163, 609464468, 561583133, 870501455, 8054203, 892852442, 654428045, 880482, 814614041, 359769163, 367229115, 607298987, 156801509, 387937093, 979171469, 812966511, 49777957, 406581355, 673560235, 455355089, 710883921, 796325574, 588101685, 701954394, 621205082, 527526420, 762320782, 420756512, 848809205, 968800016, 972278784, 979670915, 674277165, 743415345, 34180043, 446249159, 593909056, 229651433, 671008697, 233820763, 797634701, 733622626, 298341290, 971151496, 656921347, 549064750, 415738707, 399261211, 8715673, 91546605, 787853477, 465999631, 618626307, 79701527, 869266430, 117548369, 82831802, 965172263, 224277235, 35770553, 696353095, 972276108, 175553069, 882318924, 444598737, 531813455, 268980197, 192951565, 239993441, 634087129, 751689896, 822473190, 489395906, 722741069, 63252259, 753726456, 438893336, 914587427, 578225212, 194920978, 289058669, 267151437, 228556647, 904249191, 771636604, 387686416, 729470508, 378916561, 930707196, 443823180, 574973802, 714346625, 277537854, 300180056, 656705636, 730862008, 125853451, 588095764, 920119971, 484214781, 811910574, 757282318, 787335449, 985225903, 529899016, 993271311, 969842032, 390910994, 148976571, 385906962, 839649736, 790809346, 341607322, 293005025, 415151521, 776289020, 919275485, 537902612, 240911117, 262995596, 67480147, 985555335, 921214980, 268958446, 546352035, 50820626, 162413440, 89149474, 795729405, 703625104, 735075479, 42047801, 715615895, 517798495, 41231495, 509001569, 103025441, 170065624, 792095650, 551001852, 884400366, 871421926, 244738280, 904986275, 657130700, 74755928, 844038355, 473077699, 587607565, 63658005, 567557782, 561655606, 232421260, 783645792, 818042541, 47841624, 890494230, 213533201, 337091468, 620507479, 288253178, 484862019, 929066068, 801406447, 965656822, 334810684, 411075839, 995739987, 745368892, 143264184, 200007309, 815246710, 283080260, 78565033, 520098573, 512423934, 804698036, 251324438, 397505231, 62007505, 161309578, 529067927, 982737111, 63413751, 632695702, 170242015, 263419908, 512021064, 525530786, 82570014, 858295157, 884883541, 539114298, 196681928, 406743233, 66964976, 667592480, 78660121, 917946661, 296628182, 989193271, 667325549, 463148849, 820632014, 873549891, 485837326, 697864224, 584087944, 895853629, 423008773, 668495721, 621720503, 170232037, 280788912, 484298334, 192723152, 20640839, 778015589, 786642863, 912874145, 753823122, 938234615, 307523470, 430084898, 394383456, 501743941, 126757665, 815064833, 998285807, 699446347, 295454762, 823848881, 119352567, 895070361, 451833165, 110604359, 883757456, 165432111, 982718510, 677479740, 162447568, 566551955, 512152210, 937615536, 768850697, 562083818, 64865331, 738910941, 989247257, 308200587, 635692634, 35672539, 979966732, 582697918, 224828336, 858634417, 329602688, 953250619, 172662899, 427374187, 594415152, 746527781, 616704998, 753455480, 526309979, 361685041, 998927585, 305315492, 295049433, 374913294, 391371245, 371871074, 91709520, 411272772, 591255394, 573129020, 174085894, 587765856, 738877600, 217747592, 249633190, 772814249, 777933029, 188828614, 287932191, 794337982, 239683449, 22106593, 465274385, 928336546, 159126827, 465148166, 132336925, 810993250, 515187143, 175367011, 279204864, 922245546, 585442406, 456983930, 682814062, 688763681, 923038350, 126592455, 403103929, 673879706, 421360996, 738083155, 808654652, 111173035, 804050219, 351710327, 6650114, 772483288, 791627820, 619800876, 846962011, 988422880, 691147461, 897305234, 475188837, 222690495, 587506865, 182226103, 438517990, 744158205, 725436137, 643978441, 22462736, 349297234, 716989413, 936028930, 293225798, 619035848, 486470501, 265054812, 722400087, 719657702, 561243826, 632890028, 728482494, 592614527, 694838744, 241795547, 287453287, 467956706, 147266668, 51606369, 467762157, 192100089, 397457409, 89383013, 952264019, 505825508, 512787132, 486925989, 11852191, 881322981, 996616140, 642498995, 367283192, 378309710, 493000337, 833416308, 132176480, 96347124, 907140763, 630373160, 583438791, 933937365, 134459317, 756083569, 69682323, 435409358, 952622876, 584798221, 264929198, 741529253, 844639525, 803511406, 76562215, 674561633, 932016794, 653867987, 978027719, 617395733, 182770712, 648063459, 68716849, 163962141, 839387089, 41717636, 983099574, 339512166, 675718378, 46239149, 833945047, 939936995, 103188854, 911034054, 848277452, 756367677, 881883725, 291958951, 185515072, 465508298, 565809603, 641193509, 669251157, 831093785, 472395653, 578964166, 87245804, 599435128, 87892882, 822648652, 747048899, 752906253, 844680639, 662005529, 280932634, 31656978, 669401540, 111504030, 730232174, 849340436, 415840331, 312066634, 539415368, 291117172, 185601161, 640370494, 820077441, 297799327, 766896620, 991611185, 791067222, 750287474, 365817783, 93366515, 611800072, 327972303, 565936771, 966230219, 343149061, 976195696, 788067228, 841363342, 514724669, 942722108, 291822952, 443683170, 772729065, 518308624, 745407718, 730814848, 543236336, 600934459, 743334024, 155310076, 810000986, 141915146, 630946041, 141910466, 261910966, 994225799, 473130729, 897894094, 985107831, 502557044, 47889593, 408780404, 679172150, 654046547, 84834330, 265388432, 700570984, 368269004, 994268687, 103496715, 103752752, 27765388, 448521384, 896917140, 412648771, 92830922, 991836019, 752765323, 655219085, 150841473, 139142450, 719633743, 73663777, 872140779, 989060922, 308246754, 361163372, 463375164, 36869068, 497734837, 918279385, 966663343, 400190947, 829939329, 410325756, 510042500, 816360557, 523865982, 214201112, 910712884, 648528192, 863623847, 540470249, 139764597, 729108395, 908335106, 542500820, 184858420, 785178867, 80774172, 97988850, 573527913, 797247265, 703891684, 214613635, 26241811, 908422276, 661895730, 914490792, 764149451, 205072192, 163364341, 480401747, 742605543, 456630320, 864675966, 262035135, 339874929, 152105747, 679792434, 879308424, 867832566, 833346862, 43680313, 211813497, 535855142, 665541460, 202750346, 570077765, 529209562, 646493598, 180016312, 81332123, 822339905, 66386160, 630457309, 522863168, 989217971, 690480371, 138613851, 963392165, 745645412, 122026458, 907883042, 130643538, 678539411, 907734277, 828140541, 150614908, 917722135, 927284102, 216160246, 911765241, 938623977, 557007236, 680246392, 465121822, 984379431, 826163238, 651398034, 828057408, 137533965, 867141882, 234458103, 585292046, 297811700, 553205963, 943740380, 66806084, 795623175, 783171704, 658336483, 825879862, 885166675, 107956989, 853394189, 672116110, 310078773, 148910275, 472014403, 125306352, 847686569, 165688801, 814418028, 363102171, 923443946, 565984560, 841426564, 75842904, 910322810, 172382651, 645740023, 702458635, 913987062, 308033109, 955162441, 347287800, 498454021, 331159224, 492142815, 727318556, 198003685, 52641178, 631663931, 339830307, 321917869, 135882209, 525394405, 889154983, 165136223, 518201575, 395040447, 792788527, 989232247, 110884291, 360347893, 305362482, 400425846, 462197560, 475832418, 618949391, 420406777, 171728123, 514754411, 565942818, 252186378, 864243663, 739103650, 668629628, 884600870, 756970637, 44679581, 489514805, 741822758, 274976077, 562209816, 843362382, 939723823, 440994318, 127931341, 87746840, 862969363, 615787653, 186484142, 597387329, 848434330, 803796983, 975117807, 802927869, 180624217, 894986548, 605079336, 955044247, 816631921, 216094178, 729568914, 939979623, 137337798, 8327164, 462845226, 727145345, 709232617, 297554595, 459232799, 346565155, 316085533, 322121627, 76430431, 808934278, 143247719, 241274008, 299978880, 778275665, 342367482, 976025990, 530849868, 421220401, 847773028, 885935807, 578923463, 936697619, 185817342, 418749201, 119149074, 229143491, 975947398, 819853562, 770194242, 745467516, 854211176, 137864901, 828102534, 921170012, 823869361, 348286015, 159257234, 991489646, 17382860, 785087485, 101123299, 727510197, 366534301, 124921766, 598480980, 334913704, 501133245, 600478007, 763920920, 428045662, 474787286, 383150894, 181143009, 788443943, 46616819, 883227871, 853531864, 114403766, 920460168, 313145473, 938209699, 838538158, 460379823, 829985017, 70073780, 290491377, 774333906, 274785999, 943429616, 574109157, 755511452, 901126176, 137160821, 686386353, 938845252, 883861836, 15190593, 473097016, 301852620, 570496027, 570283302, 187548266, 460267414, 29933182, 647460922, 28821394, 360778722, 819672810, 543525111, 910676721, 443813933, 642996959, 204408585, 886151017, 41451313, 324137796, 231278608, 876864481, 624433521, 66293080, 80511917, 566656297, 839373954, 954304751, 671611172, 549738572, 360306729, 540311893, 639259678, 592443276, 788283957, 814836960, 725547846, 765495963, 975700394, 596368917, 43709601, 124655947, 801094676, 682497302, 35189000, 11153274, 296277298, 918809572, 257354952, 381932697, 299553461, 672177621, 808590741, 937190246, 335592232, 270645083, 135677221, 489004021, 820050804, 65425260, 118077164, 159418700, 768478013, 342236789, 309345838, 596626076, 874943133, 882704165, 670010458, 182706626, 480269861, 850692173, 818189756, 23464531, 854718813, 460039879, 412190936, 472392873, 972589311, 444438162, 500338579, 476555835, 238876072, 425314402, 207260205, 643555040, 108931990, 216716758, 452598594, 570291371, 508531017, 642040951, 888816903, 523004509, 315845464, 864123976, 18404426, 946314163, 510494920, 526563622, 202108526, 655004836, 660800208, 848478215, 64149194, 309443931, 316175249, 551032056, 916500380, 101962175, 905383886, 118560752, 781347868, 369400534, 68346830, 70867211, 611848558, 880254642, 345715219, 586138729, 85457883, 613969176, 790498883, 335036360, 6894546, 797947581, 862895005, 787839107, 630029172, 567139842, 905470726, 437061701, 909646124, 210948163, 114490249, 366494921, 540051544, 806886078, 295369099, 587591573, 558260585, 290444833, 327926970, 298281030, 765906211, 133916402, 549275314, 589341553, 480875174, 577625053, 819726796, 328500754, 572321177, 813895947, 634094376, 334198472, 238715780, 648165722, 33906048, 82458079, 528591457, 243025744, 378317845, 727577661, 784612248, 382577287, 139804178, 537823007, 967535759, 531561470, 816356271, 581404099, 741464621, 738854903, 439811749, 929351230, 107845579, 563369619, 993449214, 47159361, 407789726, 897746161, 905484730, 261319298, 715053097, 826649347, 568668220, 369457222, 369041502, 749481970, 516683697, 497557503, 193437954, 469248010, 179977283, 247560999, 718390080, 963495894, 658361398, 406108768, 165275618, 76532795, 95818225, 488993099, 811242196, 893982460, 780534030, 96141828, 924561312, 50242261, 184739086, 657603844, 435428199, 860409633, 649213634, 499563045, 174033612, 7491711, 532074672, 34702728, 294100318, 632856128, 347794924, 471411287, 519734622, 952060175, 539637480, 993612578, 190406846, 511177791, 266897534, 145766803, 464885210, 977827425, 308566292, 427600152, 864260002, 797683379, 47502557, 131529711, 827229417, 638380864, 888400362, 23274326, 92603492, 233692987, 645392766, 593117815, 589699825, 62808513, 127038842, 350541901, 378046962, 839506064, 562431634, 164922012, 463419844, 146937336, 693654966, 441833486, 549814391, 528404387, 596257193, 758688029, 110896696, 938456135, 502428404, 915075257, 425620493, 621462350, 434334727, 35243281, 452168455, 953120157, 70923908, 782120189, 85535493, 530186181, 389098157, 179344431, 966997194, 960601909, 86333721, 128574828, 554147840, 436754621, 867951473, 580201550, 360255979, 965468005, 56218697, 106116502, 582437523, 810060481, 182639617, 339844828, 555211350, 410092935, 542665280, 621154374, 204120086, 195324365, 995572939, 698813167, 257638199, 668651409, 872047043, 341256534, 973473467, 294804034, 329037452, 286860449, 336962753, 811468376, 901581251, 579255890, 509230790, 682270434, 628468941, 61495011, 34050000, 414428041, 139160866, 302785678, 571825081, 326321390, 482212678, 960348540, 455190000, 294418410, 518297338, 247697470, 294206896, 800896173, 302677183, 644100037, 876875215, 939844649, 502495183, 872841926, 202083686, 294313489, 156807668, 280513485, 901244875, 760909276, 725124902, 813314027, 715850259, 74006837, 361972084, 520609105, 359820979, 824493829, 328445918, 584177761, 159012921, 352305060, 896478086, 475633475, 304493335, 913758601, 446117899, 494945142, 895343205, 82516896, 932260257, 942105422, 873611446, 27524600, 122670318, 716760417, 464187166, 370268984, 289931405, 28756516, 270174466, 238387513, 924938806, 436744366, 342135581, 28879383, 870907274, 859641509, 808715491, 35106193, 186153294, 956784444, 995914013, 765569618, 455772490, 700143713, 947208672, 257265899, 849701208, 312566113, 164205858, 114091718, 684997944, 70533514, 531028204, 961136534, 728970987, 890206207, 129293936, 95389808, 781693367, 454883952, 710223544, 518373966, 480229769, 267240229, 362614175, 446299409, 568065573, 95346595, 528178264, 1291923, 592009060, 59179195, 646051156, 545331734, 494673899, 160274249, 85498709, 118240780, 269871016, 653903771, 523622215, 367531664, 519416545, 843364152, 504638884, 738526629, 100695194, 496826964, 982089755, 76340216, 131973353, 516274186, 779337428, 853143868, 670032112, 864305971, 385364479, 274930716, 633947620, 978104979, 118922662, 306332493, 393807213, 187636415, 623213878, 868468009, 482143947, 850367139, 522853201, 280284654, 101634180, 527120129, 4549461, 890272424, 788562723, 739735212, 684611011, 840079918, 355588443, 643719263, 396745068, 968265504, 618285051, 876135499, 664300116, 342449443, 534301989, 247963724, 539371908, 714530057, 359688391, 902594931, 133325284, 936223312, 156802711, 715059021, 960178024, 705084398, 543084579, 162965667, 874072824, 407978063, 11561802, 440682471, 38812654, 520388324, 474048715, 580286378, 812139788, 952532178, 525550971, 384931581, 986271088, 328380257, 999738381, 31005236, 736671541, 262278191, 405540851, 340696013, 186731802, 979158159, 872088368, 104964325, 895153383, 121269370, 741922740, 30597026, 910799658, 107817022, 910408277, 253615044, 886396186, 361283176, 85763046, 358306517, 26758423, 111886455, 804527739, 206840417, 47770196, 891751599, 356871209, 232121380, 869919914, 330066129, 797259525, 651693899, 20283492, 434294301, 163018732, 550870589, 991826608, 580703453, 111792206, 661498669, 280981097, 391178121, 347293096, 646933117, 95999707, 891715552, 99417314, 91837477, 252989986, 73453236, 87943888, 265557858, 192235163, 277336567, 913082133, 276450995, 786058331, 549033843, 951395768, 533513865, 977038250, 793918457, 892952653, 956854730, 316873565, 934824343, 110076010, 596612890, 787477170, 469830019, 757773729, 228202979, 999674341, 945847093, 317083521, 763054293, 476843021, 565136204, 752725513, 131442259, 55841256, 952791017, 526120402, 534963409, 66968883, 129812730, 816463381, 565316871, 550258841, 383980447, 531404709, 724180743, 704521640, 426794250, 675820837, 749213218, 69224414, 450245997, 550091741, 941610659, 63283199, 525332926, 739961514, 54033010, 322675714, 963285467, 949633690, 49849559, 758504280, 221457807, 768055841, 78952, 609148656, 813664607, 596483587, 404810798, 720290289, 786235618, 813286999, 402708411, 169632774, 280267258, 963002291, 243244597, 705622014, 429751051, 387334942, 757309543, 605403867, 60477197, 458001665, 307322027, 169317163, 559122424, 186393211, 735574934, 733024988, 797914662, 293680054, 146491107, 3156954, 979803348, 443844508, 170276183, 179872928, 388180496, 838305013, 814090296, 673701302, 782172380, 523627105, 718077964, 747359532, 647577715, 179178052, 868358682, 21863375, 458355337, 342948189, 441237832, 522641077, 976301435, 821710967, 284233557, 825792020, 826397844, 702130772, 644801759, 413485033, 263898504, 755641895, 408786017, 929870018, 869295526, 548647377, 141252014, 45212434, 649733110, 9643896, 337970446, 209219154, 67100797, 917206877, 477223611, 331651686, 774729915, 145958493, 442833209, 640098219, 506734095, 379345531, 78935328, 682940272, 830469704, 820696369, 538923430, 573502341, 351156261, 652141593, 165990857, 549928150, 482843596, 275750927, 351359463, 966972212, 945939711, 726554882, 752820529, 793776758, 434865670, 337547563, 958184665, 364455570, 23256196, 463383230, 609220234, 495886183, 573396425, 461668855, 593440880, 652510688, 594251265, 264318456, 780878971, 625987392, 715177281, 164000967, 969564025, 649339803, 273925492, 764359901, 183532143, 101698513, 734990030, 575570737, 971285903, 216066517, 961124793, 243237637, 186644931, 886376324, 391046321, 581271089, 522450345, 968352867, 957501179, 550453339, 886037438, 521817146, 677705816, 192436438, 785386488, 732137319, 378913442, 916520908, 295983308, 807728818, 995899585, 130889560, 541583091, 25219977, 934367369, 261653931, 355246489, 361969281, 738660955, 811445277, 380148554, 491220723, 582781742, 104347943, 819130118, 91299224, 181361348, 389337060, 752482331, 144402387, 687967566, 838838892, 710430613, 773916894, 614535992, 960028876, 992899086, 724343501, 832208894, 338823417, 995269928, 541904159, 428197668, 477033774, 548275635, 7439478, 464309657, 485953955, 977315311, 341922314, 617938889, 173176336, 523247851, 304456520, 611142784, 340540475, 76092957, 648459887, 350747816, 568087380, 150947528, 405733, 736947022, 959679520, 26680780, 659505662, 694615749, 22929321, 836791276, 157345328, 692597716, 243515892, 778269055, 770173486, 518205661, 442182740, 110761531, 428691890, 699360044, 177175689, 360665345, 417591978, 913244089, 479478136, 432035697, 454028437, 789446331, 516282680, 837731046, 455657900, 806839282, 735151314, 57364557, 872428843, 778690997, 899501946, 557230097, 744002539, 5867574, 250669153, 456613856, 6110401, 581799263, 905113646, 213879014, 843053643, 651360350, 574142214, 862710936, 860504897, 194852126, 311844477, 587623097, 463801901, 95753776, 989328550, 435184109, 149061279, 107461418, 792202885, 927566802, 271430090, 874882875, 45170985, 73542215, 600380059, 362925966, 989644723, 291326752, 720975539, 555817799, 847285083, 648954953, 476681068, 50124769, 240124557, 431629633, 140425708, 66703104, 314120290, 870139671, 420096557, 610075888, 834619643, 736543219, 737809294, 779024669, 85877610, 880658665, 737526783, 8812646, 782592746, 906445909, 997218352, 760664729, 560541542, 300191672, 852037978, 943721857, 463619515, 940624222, 811639972, 595486652, 820527349, 759431790, 890396910, 162869292, 62501089, 248526420, 199900456, 865254089, 812745885, 207413809, 618960887, 814413065, 241457268, 662675420, 629295760, 933264523, 567363940, 924216294, 848360804, 634221806, 956184686, 421516853, 232841040, 706290070, 66051373, 961043539, 950072155, 915747569, 670972694, 91138629, 190322772, 893817265, 178479473, 649244290, 140388340, 350404694, 288335401, 661102973, 670940349, 854707119, 568241982, 246871872, 286674141, 839843314, 652119020, 764563149, 927811448, 15469822, 204742171, 474614927, 682070774, 84614990, 80044928, 104325347, 24033290, 783768589, 174258296, 444066918, 960598056, 57760858, 702547674, 256972327, 666099918, 824075749, 4736060, 134358536, 284372830, 159659395, 582802654, 647490747, 462858399, 35181096, 502169647, 932614492, 888937592, 494179709, 230380784, 37733002, 745113520, 664095590, 451099985, 843509169, 120543471, 458237819, 448189759, 911310046, 794719253, 424905628, 827495185, 996873791, 890650456, 789860743, 111642020, 555870249, 919276131, 22252396, 512343597, 421690023, 375897119, 828736809, 566530464, 202684677, 88222714, 250011967, 391643778, 991330792, 41408746, 305238594, 150493233, 247866585, 673860357, 79823370, 245432005, 881832008, 850883458, 830983785, 850983797, 57234042, 297918921, 44940715, 252349328, 945636395, 827975081, 763264697, 776395186, 385758015, 272273129, 39750122, 303479494, 552649155, 809890423, 363609102, 618368568, 35381079, 44046245, 12986845, 954994209, 763646831, 257602798, 259317827, 350683338, 640090562, 136292912, 192874530, 920689007, 21367914, 453798042, 493041794, 386333896, 291276733, 526330320, 357542923, 169972274, 620812953, 746913722, 91479411, 266669734, 673070267, 572382954, 541736757, 28104800, 557714243, 352090361, 944250291, 352260227, 528087494, 963763490, 78921712, 820492392, 42548081, 801765177, 47123079, 595366727, 410398705, 945981823, 205114741, 55112944, 877618137, 817984893, 461331834, 523410302, 993951198, 116004076, 653394205, 816783643, 362185641, 889768011, 331590658, 542784338, 532759646, 323955177, 501281526, 902728159, 51814549, 90442028, 214853916, 473330212, 225845861, 920628175, 848971753, 602442257, 908615141, 498827137, 235210900, 833706874, 192725867, 26286119, 866722050, 500156731, 311678026, 223761813, 471351416, 400771762, 12017270, 973258072, 327318740, 426779662, 659952482, 103359803, 792674661, 600073613, 862227844, 820576790, 126753371, 885387378, 122391957, 269327767, 136773745, 160491014, 298705187, 299179167, 120012048, 931916058, 20416707, 579782570, 656913063, 91740508, 622684038, 702537400, 703805374, 210640811, 322409481, 295676105, 678377098, 362530208, 592052759, 662558224, 80563500, 436574251, 611567365, 162273698, 539992018, 210599797, 496489148, 830134736, 949964983, 420100294, 680040757, 150620889, 398279347, 370523034, 48300745, 426155623, 424898623, 89068123, 756675008, 16965951, 930378997, 285606283, 921225575, 718841310, 661772146, 921707085, 976661523, 534234329, 149399647, 656368820, 423616308, 274458341, 197734111, 570771768, 963190265, 69496940, 745476119, 909130001, 666000796, 804705344, 287504765, 503045462, 338322422, 121844196, 726784995, 138268587, 700774149, 758819304, 105516379, 816914990, 974109827, 898876342, 630428917, 764271763, 716783593, 969279276, 708243559, 651495878, 518815144, 299105731, 802193778, 441717553, 38379260, 583130611, 340820762, 509549677, 936352113, 522625567, 89928886, 596337906, 938366507, 463192380, 437738163, 621503976, 664446711, 252531301, 130632882, 383121227, 709724063, 194184674, 850908440, 309636512, 801914853, 737814835, 574693004, 730659104, 200917505, 562080860, 500715478, 967573449, 845013539, 672605952, 510785426, 652314550, 683743942, 830004647, 524972261, 856871615, 504340201, 63979382, 233620794, 430161289, 94358732, 459612919, 383366346, 394288718, 495561747, 772623828, 805527817, 758147088, 567895718, 634874546, 982071924, 641869806, 623278354, 617180334, 52361714, 126974831, 196159188, 669814914, 333244598, 771370686, 177201473, 336292905, 561791701, 831813049, 63899716, 859173132, 213230547, 148459037, 380215895, 703525855, 249865967, 259113041, 289968118, 90373186, 438446592, 657090042, 670455848, 246500124, 445530645, 844869571, 733171539, 307705387, 220174719, 335066228, 370277409, 289702154, 729625141, 17704736, 661340902, 695904849, 557805875, 157098501, 884312164, 341619623, 371998503, 613554165, 384857845, 287637594, 659403241, 74864472, 577165101, 565464909, 327365984, 339839445, 610038390, 143955677, 90377764, 644731247, 364811224, 943718358, 235833005, 118712852, 243023652, 410371069, 635654576, 358569837, 943947399, 214301860, 57253984, 34350982, 777276178, 386876655, 849063287, 923783364, 270737117, 915310840, 58911434, 475000010, 644462533, 892699146, 508090359, 896206002, 713087186, 13664997, 725473707, 50909854, 436134936, 117566580, 197312727, 178627643, 393704984, 134512176, 961805790, 867803606, 702836183, 801437255, 989427222, 875558822, 534712567, 253165713, 207107955, 880567951, 44179710, 72056699, 964600290, 522780145, 420036283, 890292800, 595586233, 750375987, 288600442, 284029005, 493857100, 605995932, 654059368, 297719006, 374733586, 187429082, 760692473, 712443961, 176104858, 202348886, 32352723, 134858890, 906341325, 930467263, 411161275, 10195870, 775881437, 566463267, 361044867, 425881910, 988991761, 287154304, 819979413, 582126486, 316136298, 137096140, 936922780, 218876650, 109980738, 985052385, 607452587, 734165749, 752733246, 398522967, 786273727, 69397306, 72812288, 895252706, 515424095, 882036375, 573022750, 334908288, 75981620, 628420888, 248007484, 7174919, 867721212, 514137039, 155993929, 971821444, 396133596, 123819302, 163015600, 990209396, 323232656, 982358663, 685899015, 895415395, 197408460, 414358947, 169004403, 34014811, 462324393, 599038198, 890668595, 367113772, 974766450, 568461276, 796454245, 586943216, 367103516, 626319661, 614729138, 147753299, 238145955, 889097953, 854453623, 778154426, 786767251, 773471596, 551647712, 141590655, 159127527, 60797777, 37451973, 192709904, 573336817, 589289795, 706999463, 106282598, 706002060, 91056070, 901574420, 568572092, 601411645, 837255289, 90887852, 177676670, 526030518, 73691212, 751999060, 48568338, 420706590, 212637118, 805571164, 897701516, 830836202, 469837698, 425995960, 782482940, 645975186, 651066400, 161527345, 500452280, 951653093, 940658873, 415165722, 817354777, 224449310, 808255707, 593819367, 443134796, 742497025, 410929604, 376355492, 75837200, 555443363, 540367299, 977831791, 526286419, 334791932, 556384876, 27536657, 92655717, 657023306, 252147017, 740226187, 514918463, 816373328, 839565735, 784335017, 172108662, 136187710, 517512236, 435488945, 694461186, 958002764, 244885579, 435106604, 935373804, 881363415, 559695653, 470567921, 81461616, 798192404, 546235972, 315626141, 21976282, 691455156, 486495442, 942928553, 310400930, 5653271, 844160567, 488235273, 733991435, 821405638, 956544390, 385184366, 100757524, 319753327, 469356818, 313196048, 302299854, 350752150, 90530624, 896495737, 150470130, 282921633, 712424094, 27482817, 651715430, 747784774, 898213951, 107769372, 768651942, 867557953, 514277345, 913752651, 625580715, 221676775, 358663140, 842659425, 135192309, 764965914, 145672262, 521534759, 602542169, 356093075, 730057977, 803419164, 417896436, 199373010, 477373350, 826430633, 756502840, 250813115, 290998356, 5417690, 565182164, 604403927, 868805386, 199274916, 181911438, 820944427, 162719958, 848841587, 561054964, 24339551, 290502108, 297901471, 481454262, 45212521, 825112537, 593781811, 523544215, 142749794, 552717622, 256843677, 621417660, 557858185, 890144461, 659661127, 125152198, 542622920, 255238115, 681695151, 481546742, 616978502, 453298950, 946542255, 107204059, 356781849, 855734935, 959459351, 514898411, 862198954, 871495762, 84020246, 359489789, 484857832, 608184852, 692288913, 89798918, 377305743, 339366523, 330794462, 318195301, 849228059, 674111526, 211368866, 232999618, 834308456, 455897882, 597852114, 128369200, 164423058, 597123795, 392536287, 257420267, 989981255, 976824726, 16183407, 779525840, 33974220, 533381181, 630212105, 678568426, 535894892, 555224135, 426711387, 702580863, 976683782, 96079480, 806251719, 102204861, 266098146, 430245989, 617405607, 862245500, 84203150, 547136277, 965699617, 219049808, 121807159, 648067593, 386097415, 601226862, 368195000, 358344766, 437837874, 921630662, 796519651, 205314078, 353994865, 222716205, 219089891, 109132944, 922004157, 454599427, 357489621, 130002999, 896427584, 714933375, 56324321, 400451506, 909319734, 290800887, 431675653, 638061876, 57772072, 533044713, 55323636, 842123102, 352674403, 430186949, 21524824, 890779416, 401787381, 606393126, 823174271, 557396635, 61483451, 411624100, 954483194, 576402176, 912702140, 734174710, 987912638, 214581402, 758274325, 45648672, 74801233, 412702785, 663358751, 251597224, 426832476, 798081489, 33494873, 576713184, 172101800, 164578158, 563216298, 571317114, 961363299, 430588028, 318196230, 683145173, 129770808, 295154498, 87347697, 244159504, 812917048, 342162769, 429463796, 358713897, 181295656, 921798722, 450248331, 995972022, 141351063, 340845404, 280830113, 584530589, 330916510, 718113352, 929157555, 181207992, 122822851, 47742326, 77943556, 387028879, 373329656, 517338077, 537623440, 511276751, 117775461, 337927495, 78888945, 215990677, 99483279, 883430627, 158705361, 740969484, 327343218, 877896124, 799511104, 862636883, 595282210, 110466900, 626463624, 512353718, 195753305, 712507618, 996663971, 646665, 779508573, 351728046, 869447169, 422052491, 472707603, 95228722, 551605759, 955939010, 157730458, 680206093, 842654804, 826393720, 426408693, 636308385, 852033002, 235678009, 45259380, 640687129, 178637043, 924014191, 807625131, 426712716, 364753700, 579809411, 976138248, 891657834, 921137055, 130576800, 903123982, 650036293, 903507605, 596068733, 474865278, 128516336, 740309843, 539757434, 789005829, 377587157, 553317040, 75112155, 943968968, 119479100, 612475954, 567897383, 309050712, 291973921, 936845672, 303959925, 225565079, 925005464, 854528097, 217689340, 146877116, 49442970, 837847733, 296987327, 904147245, 153062488, 764010658, 663692797, 276196316, 529240166, 851548850, 920497040, 641526591, 379624661, 546003581, 497634655, 163689269, 405279586, 197584682, 939204331, 151720985, 546256737, 94413475, 290585074, 569424962, 957028704, 997568876, 589983691, 584105286, 753127018, 605533577, 950445818, 834572685, 431675047, 970478675, 687746629, 507327511, 18452557, 536366664, 754118544, 237267900, 654978478, 13838835, 244578048, 884471055, 203015558, 271372858, 673543212, 178286511, 306572909, 459538475, 413204668, 737958562, 319967514, 999021712, 224650187, 35003195, 966571389, 554005951, 468429379, 970960400, 682156084, 385474279, 137372066, 839092589, 99126975, 963018112, 180957208, 189900947, 412274457, 451783090, 553975046, 859524523, 953896118, 900143271, 917848007, 287532891, 784289763, 958363870, 664608062, 118374848, 317152495, 351740393, 827395237, 700792542, 446907307, 299723018, 873437960, 516131021, 389614130, 139563966, 917804150, 584804658, 350889800, 905482036, 620458616, 606657331, 387729882, 455721617, 347835505, 278313017, 503979436, 542061033, 578298115, 792304247, 826786737, 305332589, 460929376, 772739780, 512281994, 835407134, 714460566, 482462322, 399422027, 545359767, 635674519, 446355187, 103492366, 712428184, 438804156, 377829727, 739177451, 579704901, 424833658, 657598936, 468121624, 904967184, 897201222, 543927510, 104846010, 274867483, 898591215, 701316124, 908544450, 265598042, 579787761, 83830880, 264355224, 684501860, 842775392, 49687298, 266313904, 189295820, 198074920, 55458857, 6166828, 942787199, 305152900, 991057298, 101575342, 124518065, 539838956, 445099317, 841519927, 239838023, 292987505, 109134639, 119754068, 785504633, 537394773, 578215282, 147109340, 757602719, 619200634, 809601210, 827890893, 51736323, 501706680, 595433338, 134448616, 285542324, 901582795, 754597379, 276323983, 619176329, 721710648, 504217527, 266140030, 16219642, 859286805, 461379043, 638570672, 62008281, 911107517, 746820714, 487309294, 238770406, 551908901, 428615685, 505179165, 740402887, 260325760, 4877352, 411197156, 809923075, 388666218, 773837478, 203595774, 820423431, 457272944, 772466114, 740451151, 668119569, 25373409, 279327102, 96221137, 428085903, 912487524, 409737668, 899156150, 427904672, 205607956, 347231892, 386910263, 122340623, 590439989, 159304955, 18744610, 73338089, 707797567, 864713326, 324832556, 560795180, 182649391, 439546282, 42394625, 410453139, 917138890, 607680131, 673929602, 67925577, 533824907, 509102790, 569032296, 594789918, 431282772, 44344020, 691479111, 58460153, 586039077, 479700811, 712635638, 689588036, 113918559, 675107950, 51799869, 753040919, 694994237, 991209080, 33182102, 553269350, 40698320, 861019683, 852150717, 91594167, 152068570, 536288683, 250048507, 54206960, 235010014, 343087511, 384029973, 158841523, 494901156, 950570137, 923302532, 101245139, 143960381, 15598882, 112151081, 893401773, 991374791, 236611884, 100734158, 202215955, 71701359, 717220900, 801273540, 979771466, 784826808, 328632536, 172008993, 294232753, 505571704, 435447562, 15281404, 267032859, 408068448, 898827230, 245671572, 537192365, 238789435, 315841205, 667589770, 463592931, 216399183, 733480692, 912573870, 87494950, 782895604, 34782290, 766088252, 99884336, 460698144, 237957906, 942535021, 555331690, 650077551, 108163106, 679307559, 92197630, 52939010, 893334394, 457047155, 729106809, 349333725, 41666833, 977942323, 23281731, 119624745, 383948542, 486852263, 698308260, 721857298, 691205029, 737609265, 735298475, 528914158, 146590079, 898229952, 596721058, 462583789, 562755105, 185938975, 74974779, 761024378, 484938884, 690029858, 200583897, 129536652, 400412666, 17548175, 82962620, 652453255, 386510575, 635018105, 472983562, 262607671, 437670038, 488834164, 430202673, 796709652, 320756950, 539353024, 481616754, 295149392, 898001944, 556781367, 977038956, 971204406, 971819521, 228156155, 304984587, 562772758, 561751097, 579030652, 886333110, 135960962, 457818916, 946067384, 802217912, 901775033, 870436702, 944755397, 911497471, 872006660, 977849795, 211853165, 759389394, 826362376, 564702334, 997346680, 28091461, 896490626, 721637032, 727686400, 597596027, 106575071, 227353954, 436807996, 216883506, 16602193, 107594004, 717085470, 401943385, 521045022, 329755603, 478400453, 900777445, 408567351, 461645448, 736741871, 688094870, 392445212, 15818091, 693485761, 457199866, 525852815, 663446086, 350230710, 564614568, 365258695, 899570096, 115268466, 23373446, 626889257, 201029688, 593809151, 209296821, 683546724, 441806798, 582735427, 165503059, 349432491, 608113963, 89155276, 257223972, 755937619, 468146834, 891130879, 559848680, 955256365, 150212743, 21154654, 216393473, 869870712, 966971649, 396036872, 438882199, 893253880, 482080474, 76599947, 101981691, 659819252, 344288228, 721577009, 346141186, 440718144, 407091806, 72045011, 140794953, 880697540, 256101396, 642662248, 158194623, 20612763, 698149151, 546523393, 874622556, 635222706, 103282462, 687419952, 882110875, 806343064, 612266978, 710727961, 770874736, 368495772, 519432461, 86654972, 46785081, 439118124, 920832414, 766086435, 447461948, 530187780, 74909762, 308043233, 849135533, 796908853, 6323464, 559074788, 691184827, 293058240, 342539438, 515392013, 488280208, 623640736, 758577556, 416272876, 283474230, 910095262, 929491934, 184520088, 208161803, 204629480, 165987074, 674268174, 621189703, 683606313, 763604799, 226362846, 340851572, 376571778, 908678652, 369595320, 900325672, 705661273, 938912948, 118356004, 929837725, 758953876, 66278946, 840143475, 210952242, 857135585, 699442904, 808165584, 938504473, 136747162, 267249571, 706924604, 296687760, 233265805, 981964657, 148543900, 381375761, 230715307, 410841166, 377216305, 999789369, 217273654, 716495945, 340219124, 230141735, 512629758, 32357747, 262593821, 975059713, 180030216, 405249407, 513771015, 937175650, 703168319, 998890301, 378410994, 857719646, 750016659, 538146897, 225215924, 194754525, 26258728, 245447389, 116796966, 898987005, 958010284, 884606825, 507535540, 489999347, 828935709, 960147880, 958648865, 464544031, 406621312, 465527401, 485198896, 782633052, 93087183, 109289781, 955500397, 999755483, 833005358, 667716067, 448922765, 44764417, 203607173, 857845112, 793446701, 358337580, 240182411, 782819757, 343979028, 893708724, 697901240, 246029911, 260383119, 379189923, 818384565, 415951250, 55403024, 236642534, 54823685, 155390452, 550484091, 624952657, 712330874, 584798868, 228583555, 117443477, 300636603, 348890374, 416788883, 912690717, 182564016, 85290950, 873050419, 398819276, 413087506, 242535092, 441270677, 386370044, 696486353, 720359720, 669547559, 963768256, 966240073, 393329426, 247596250, 973814410, 885969580, 828819050, 567825625, 410886077, 112813902, 251799792, 951988654, 429995443, 238623691, 157714089, 31447113, 207379949, 649002330, 88228111, 887378173, 607379317, 947511678, 708498959, 909253999, 373000307, 395690593, 45845243, 401259589, 728897942, 551430643, 441158562, 9200341, 846711300, 56291451, 316791712, 487255503, 641642951, 889293416, 785675596, 622042303, 86822783, 917440762, 197325066, 66827378, 270834818, 745991675, 859533063, 30763454, 62095, 529704270, 105941722, 472299220, 323609475, 193229246, 427082773, 283848347, 191256301, 679648175, 438679558, 770732853, 640230364, 876454231, 235456366, 255315707, 904319221, 488003281, 67858703, 259321435, 735359273, 289682554, 888188298, 584688986, 225851567, 602224235, 929910643, 586679626, 928061902, 539488199, 283326031, 965546997, 263566560, 676866109, 412755728, 758880039, 613923282, 934063939, 263430447, 834612593, 969959186, 742476002, 615589416, 383558844, 880925460, 882383516, 59925124, 104205219, 775225428, 416746997, 735277108, 271619777, 674436142, 592381611, 71330641, 792241845, 689292205, 620379965, 33345764, 252546858, 183450512, 752029187, 241280944, 851116215, 717641063, 114026138, 485029718, 779096649, 94350877, 787837955, 95255325, 725020300, 178165834, 214319446, 803159344, 214107983, 715747044, 131816814, 285216684, 900495267, 24146378, 371296669, 643959343, 421926689, 235956539, 206748906, 745614880, 33369137, 617632536, 546254540, 359629228, 326927098, 485812582, 788106513, 997798432, 301945763, 966225600, 585200655, 822980154, 377425965, 844613217, 200437936, 382608522, 64996884, 937548873, 552215435, 702498824, 157354919, 838534248, 697868072, 385948967, 930892893, 219853330, 867057840, 613945514, 30684315, 305725687, 422059725, 242321075, 465075024, 999846841, 664555292, 648502311, 53801982, 748490547, 514024335, 904117450, 966725932, 717682132, 920183672, 161417118, 64951783, 623727051, 350962176, 281206876, 700523985, 657587940, 809920521, 910058814, 369952417, 281894198, 160930676, 318255747, 387022658, 316020674, 47698111, 701168524, 129971438, 499036590, 235173190, 170072747, 900430765, 513824524, 955685567, 827608323, 803930273, 898514272, 165374691, 704495323, 332452861, 893407664, 109994983, 700665836, 404632990, 434093997, 268922436, 716968998, 225760907, 574731298, 236437720, 551306349, 333994987, 75231339, 744773600, 492240838, 972873335, 650604530, 703250652, 931900925, 639443122, 409561380, 154419999, 239388733, 671766555, 495136487, 313110632, 299644464, 319704396, 110312044, 655257342, 133645615, 717539208, 719562077, 530138119, 541581302, 686277406, 419101257, 27192544, 75219108, 126666812, 483749558, 614572950, 256885492, 647552043, 31953040, 806821914, 795371207, 773720373, 519204654, 208295383, 232053453, 179266930, 291159475, 1692648, 120940289, 406684235, 373589220, 220873466, 803259944, 173102726, 723993964, 154138308, 833383727, 331872652, 253864520, 739342787, 775884151, 697804700, 115995439, 238461779, 574508344, 710591968, 720053064, 984402190, 347958933, 797697551, 244040434, 743202586, 166918567, 165684811, 658016510, 635938617, 728416749, 278083697, 939414487, 12410475, 191366012, 637410174, 30664317, 460326699, 543464412, 617676770, 17542140, 599099050, 713005699, 836410631, 448261483, 795916402, 851446413, 187678090, 658072931, 773079533, 634222151, 549714565, 464087779, 655718638, 597771257, 211013503, 67872839, 82683107, 631703458, 633090374, 922087227, 155431254, 803057021, 314596889, 972120046, 160849291, 43357648, 550953896, 143316724, 719164637, 307415758, 962052442, 425392197, 922982103, 299317591, 916494766, 763856390, 537581112, 409957935, 609764084, 385722402, 610886830, 648545742, 411794441, 496844057, 950873497, 667534712, 641059086, 593752429, 974347123, 830380815, 204560854, 374047035, 679415838, 815527036, 15336556, 575172026, 256650838, 468521610, 26055675, 317862191, 520540280, 989733402, 65022744, 517333209, 522858586, 891649758, 513142454, 475123766, 950038060, 618431176, 44715453, 83829218, 516223285, 200205989, 963050243, 566841397, 641897798, 628665520, 767544387, 172104378, 859946822, 564686917, 323988932, 331536323, 733221379, 395999586, 581130820, 221029982, 655767073, 890102587, 822176048, 915437319, 344106572, 481191541, 372578728, 872415923, 469372593, 174486980, 654346028, 200321683, 387589304, 344966838, 442130433, 750520706, 61542431, 629024922, 43463561, 448371604, 556330151, 640488789, 189752209, 73077828, 426876297, 883199036, 790775492, 441519415, 730841631, 694058224, 674283096, 750935748, 217802381, 591224987, 490696085, 288973041, 258546546, 848715341, 416033936, 919722015, 931409048, 976716584, 911371611, 58722938, 686627026, 57248062, 88108634, 516732748, 667916519, 149973289, 745774228, 814717454, 992468330, 810643050, 355293669, 585834112, 933761951, 254151353, 58626535, 853468283, 480806736, 599452980, 504283627, 497132052, 450181060, 429343416, 959800936, 115074486, 731340970, 147539206, 671140106, 3579920, 412211975, 524179735, 149050942, 967912822, 587434346, 45502510, 321571909, 836375713, 336576350, 947153073, 762120545, 561946021, 606225029, 865269172, 13572188, 604090007, 753055517, 997074457, 927258655, 650720152, 117761432, 717872117, 731427333, 526465025, 530706388, 168487432, 324584999, 110113554, 993149498, 398105155, 256297114, 803873755, 138895684, 174237741, 468459672, 458197248, 233318214, 860275559, 703840288, 575648561, 121744148, 968123441, 113370124, 654182074, 894153984, 232782718, 722843512, 236421956, 811351095, 328007227, 767538793, 866303945, 386373317, 685976054, 701461779, 200610029, 816076555, 313401987, 992776561, 679670435, 620811197, 434383360, 236427882, 809840983, 821604181, 343007114, 79683863, 77360677, 9417313, 371653034, 135754952, 816031403, 398742213, 636091564, 153249215, 654439706, 440557636, 471074308, 469435745, 573047962, 695494754, 98062090, 534702710, 685861803, 538492159, 286616112, 967377684, 125720783, 505637711, 4189636, 801838010, 622189972, 64430917, 495686629, 806962020, 258067307, 135069631, 702078365, 705627127, 153685378, 921430929, 708969565, 676140594, 771508337, 395865558, 17153163, 453018645, 373041399, 285694459, 959135294, 207026808, 820588975, 467130073, 174658116, 816099811, 56918065, 98139646, 916932702, 253527475, 109683117, 931962739, 532553637, 578692952, 160698230, 368682505, 96500474, 271013035, 274113327, 974106520, 861844629, 868588307, 337910338, 192153163, 565161861, 378493147, 962274264, 656877339, 887589400, 706841777, 129479380, 770927237, 831317622, 674365707, 635199899, 66520542, 109453957, 97630857, 262767827, 208724382, 641279325, 708616758, 350037685, 239275380, 877005511, 704610428, 233183813, 500044933, 770621889, 648374796, 22949999, 43817935, 534112747, 231913445, 488693030, 651900253, 539608263, 440593482, 565437180, 338060031, 69961620, 141896677, 497520855, 819540680, 166438367, 234031241, 527890799, 853792205, 977489352, 225386389, 778621472, 289520837, 952397119, 204437004, 972445826, 207235713, 98730942, 915302330, 561663022, 263169963, 662306352, 649461554, 968580523, 735319566, 183792245, 938703755, 508404935, 712810860, 17240024, 500398758, 260654606, 650953887, 392231749, 502472239, 776804904, 610878197, 310689526, 889300335, 239796608, 996147124, 677118810, 648533616, 934934612, 700858567, 230360420, 536190535, 540461799, 647501096, 790172405, 749037446, 273365364, 769392053, 947035231, 15258676, 219168744, 591731226, 746365420, 109387714, 531312918, 473346250, 549051940, 391239002, 535585969, 677627414, 540227089, 957627867, 81544190, 198139649, 254397269, 500759896, 86091857, 988794317, 331311386, 18712762, 345854343, 583211265, 18674817, 987470967, 909005805, 602325150, 188383650, 853378261, 250659557, 158267854, 405281886, 137057779, 426274412, 290160925, 152121706, 83325232, 667397852, 756481758, 881653300, 278293473, 895104896, 956781280, 428918470, 681247062, 543592015, 527045761, 744947217, 813027334, 618064994, 377272247, 706939059, 322089985, 626761856, 886448004, 518801073, 327734808, 509002975, 463189187, 962194325, 935876052, 523439995, 883707263, 619978402, 530941065, 865515471, 565558713, 44528288, 878382331, 609302675, 659245985, 248512611, 303060574, 832374357, 493339116, 776545208, 599302237, 851972266, 366653286, 732055116, 923127856, 514762514, 421272976, 46259688, 5971891, 356184326, 151297681, 42494016, 399594761, 691716841, 372532371, 784260333, 918023377, 268951604, 906728219, 732765533, 33715132, 786474585, 530858448, 786094510, 324385200, 243714534, 668213384, 951625517, 7469208, 964078202, 788041512, 862112658, 482585685, 241357746, 905205014, 242778590, 354853451, 722305741, 148833018, 413046805, 653368127, 300297849, 971141211, 662726642, 795724875, 602488320, 375285210, 389818047, 648239831, 596990398, 376997372, 110030349, 556399159, 855488777, 741383927, 985980045, 350631334, 839075452, 127035987, 224368831, 759195304, 302354110, 372371559, 282852952, 933577217, 727046708, 180122577, 461801389, 540763511, 538578138, 428076243, 71304943, 670810664, 191367817, 142205264, 621282975, 957872066, 510721870, 942389498, 800123614, 500082777, 209834040, 345440183, 357701824, 848202898, 860422791, 842779062, 404821037, 697045673, 288289487, 576257013, 633198233, 311102851, 628275741, 528783127, 834908304, 974116201, 660711394, 475125963, 662664033, 157659562, 501711622, 252776639, 452795601, 387435643, 98896023, 612854265, 463249899, 125435003, 207197821, 279592894, 89971837, 848851227, 492658342, 488939485, 260817995, 619949716, 111314198, 912171377, 543104942, 917983970, 544821383, 571904067, 540207970, 809030595, 529090872, 744968234, 793948049, 202224123, 20479893, 384574462, 631409163, 288291323, 383617955, 370741778, 620783159, 556298213, 359733329, 850889547, 19121848, 634898686, 182926309, 115026212, 200785991, 90628692, 532433327, 522033535, 446180928, 340552189, 972123546, 951082014, 465467490, 49759961, 796559427, 302414561, 227298764, 30274749, 227383396, 928937774, 634466972, 389534178, 215530561, 876888491, 574246721, 386861180, 773229541, 171753013, 147310807, 415644859, 336477666, 742095065, 173095393, 953979282, 83662953, 214168741, 234140442, 225845230, 101587422, 934143088, 910552674, 335332223, 444573705, 376788358, 348440989, 350983473, 325551916, 18528910, 961397023, 810752889, 611869686, 22692405, 540104699, 626007032, 643915014, 124664529, 882452283, 624604139, 455107539, 381239040, 86093749, 875513307, 658611396, 455723003, 440406983, 114298646, 297233398, 640765378, 962181399, 723277796, 735069752, 418619503, 642119337, 271920087, 325617558, 127353897, 442197530, 929618904, 746747656, 248601335, 291794247, 161682519, 581775848, 207697382, 867620358, 399120855, 18392124, 572596927, 419123995, 818361590, 731870144, 928540672, 550680616, 604374663, 745814746, 807899937, 603273736, 180054063, 194744393, 559257805, 771344026, 27263041, 5773085, 522943085, 853456879, 569171383, 168520787, 414562080, 302782640, 547155770, 830781194, 232454301, 703281297, 517082985, 782549374, 754020502, 109338120, 681305825, 603977415, 911276663, 998260453, 415154419, 215503609, 353575512, 373119659, 953551245, 717356849, 247073511, 166573609, 754833061, 787813237, 621801680, 704068639, 423640993, 898662789, 837015173, 842459055, 675768423, 700343294, 441381634, 272156625, 65459161, 524598035, 809484348, 746326835, 570668336, 497806006, 953313438, 747586439, 15554519, 759621927, 378206494, 954192775, 710099212, 109498701, 48959136, 804427273, 637273584, 985870848, 94242207, 544325700, 385525126, 33870598, 939214498, 295621434, 141782875, 174161623, 106780598, 750518573, 700687137, 990351827, 423288251, 995698866, 252862781, 349809396, 412128982, 518174056, 984696853, 410672713, 95851600, 166603153, 896648726, 169992710, 635025781, 580556995, 733947381, 226280283, 392881887, 132221739, 228150172, 781731782, 100177147, 520626725, 521333157, 308020906, 505296103, 439032392, 664765555, 635729393, 815479284, 84689203, 895370601, 261795972, 773207412, 127653735, 150382680, 571102031, 350445442, 146538607, 718603611, 405804779, 519686112, 496917137, 284467255, 536752858, 623864512, 684754769, 765250762, 484620465, 379590549, 225867450, 502128249, 936230196, 437853023, 14759566, 50739716, 869099994, 426120738, 853948796, 909199045, 132775064, 598868505, 33935724, 45135363, 448848337, 518547061, 155532172, 339436574, 673846453, 372055225, 115961942, 67795545, 859804038, 2914397, 262458794, 8973124, 467428257, 218887364, 87402064, 281536757, 922973777, 390695456, 55196852, 989974059, 884452438, 467661184, 62180044, 821620126, 643605427, 39505577, 120889682, 389329796, 893898777, 504633791, 256975800, 571351530, 486504077, 434409955, 602802740, 104481316, 634857970, 982912457, 296446887, 790943898, 520031479, 874993258, 748877550, 108360437, 960622292, 877263744, 458536926, 216927312, 920388565, 84939992, 660600171, 673714661, 590050480, 167999957, 840620036, 242100545, 200075493, 324874815, 25750015, 321182967, 680684322, 955682927, 843541486, 182028144, 107922181, 47636715, 341796080, 45513841, 302815099, 36355394, 712713822, 701370719, 352807009, 700774041, 905233453, 638487824, 911532897, 517971230, 872953480, 921308437, 982982005, 776531143, 474190503, 43088286, 412551959, 368802629, 36309682, 229710761, 144702026, 938658384, 628633524, 920383389, 865066326, 532203240, 606137057, 894960906, 919246588, 867745108, 923879770, 242319513, 770458751, 13180868, 292337249, 176659055, 520084501, 76610005, 713261948, 839526049, 155514881, 508563360, 312207938, 162018983, 855183560, 569254126, 754755923, 354401235, 838116346, 11501774, 82845720, 40569320, 259185330, 115393513, 976989495, 688663259, 547896661, 517806175, 25612725, 151623069, 206702501, 631016, 583331897, 580997277, 583173649, 439601751, 750444084, 985129243, 905412926, 269250267, 207357336, 328274416, 139838429, 813709667, 459760314, 433753820, 55753139, 86528692, 213024625, 293626615, 315727764, 853229985, 399742699, 661376915, 149067483, 444882796, 197645904, 205763874, 203911555, 99564610, 83596434, 166535327, 767600534, 754522977, 106179120, 581856404, 772218117, 604580000, 940405361, 612527871, 315820625, 121579855, 667994718, 773533533, 934519832, 470573856, 809185095, 727197751, 664200109, 667966126, 568241638, 366402761, 969205614, 611560848, 674932435, 939552967, 154635533, 739018796, 587145042, 387213538, 623870031, 540600619, 480883870, 472239564, 119512886, 485751113, 465729060, 875799613, 367429445, 618743126, 823526045, 851578745, 24966279, 336537667, 706587535, 100644124, 511687580, 55041864, 739147731, 511900004, 456560007, 476119288, 171682812, 538788085, 812092111, 890059270, 487165849, 519653348, 404251738, 991993024, 298163231, 13381497, 720080969, 650325040, 262952176, 666754434, 382435637, 754939427, 859797501, 3450986, 584323664, 93691916, 698351039, 768349891, 307321675, 677943478, 706077039, 724232087, 927738731, 16772987, 279273725, 754684805, 182606160, 764848843, 122908480, 499211730, 40802466, 107681886, 741904672, 882371397, 514803378, 797344380, 933811856, 26564668, 104651175, 242030014, 83236770, 784424919, 575237972, 930578857, 631767396, 848374782, 921659778, 972315784, 570781652, 577633569, 462384024, 794851088, 128977030, 190581483, 474880931, 424281842, 823813948, 298952555, 990725665, 974467651, 765595382, 440134671, 185983177, 446427361, 27309508, 42427575, 721696355, 806267032, 555999621, 882005557, 66739149, 167435114, 291548833, 708426064, 50254113, 495410126, 864452271, 374188824, 423252593, 13478630, 708240897, 400557475, 957431740, 980121116, 298823992, 12715754, 520059113, 465973954, 163236735, 697502498, 558408507, 974758733, 48775437, 727192403, 645678840, 385235003, 4207951, 201844575, 410265264, 38808145, 230631070, 418263404, 734327458, 274573464, 507337140, 59195812, 560444355, 530405907, 150827639, 974122573, 800590913, 916647077, 915043882, 743159744, 255592274, 754635453, 805630051, 604867086, 824290005, 848504624, 507036928, 295335816, 13075464, 442877113, 860859376, 87571464, 614756201, 654874955, 296647730, 330317428, 447546391, 240841940, 917561813, 39173819, 440759722, 244996468, 717476243, 466941991, 403374278, 125721828, 940646782, 2771267, 430724200, 376718918, 978286458, 805966613, 57854630, 38049479, 692375930, 923782673, 338706161, 118681139, 766826348, 128473087, 508762173, 851605686, 685537798, 147998978, 729549970, 743430466, 811639675, 38343962, 554472294, 22726004, 767828242, 864193394, 719256143, 630941042, 959712740, 689829629, 663169753, 976055049, 6411981, 815423823, 204891470, 237672109, 624638824, 49599420, 720906516, 586385591, 254910559, 243134646, 675505606, 224133211, 201074824, 583450300, 293973251, 634072549, 909213594, 31834846, 721084624, 279255115, 795854177, 408689307, 712224642, 301988796, 646828644, 273980587, 549302337, 181452251, 84209088, 393820370, 169258757, 303406629, 16455162, 189793827, 962956719, 99809898, 399686869, 682760888, 959456584, 376595096, 386259147, 818977689, 571880706, 967509919, 9656617, 619565636, 723549684, 296643362, 27420352, 477568054, 27089344, 888877766, 771513514, 270130629, 631841879, 821827763, 185624126, 789911967, 235495389, 675842016, 962561540, 594122326, 190983724, 272786504, 359522956, 544568369, 723653844, 301123489, 3391902, 896822165, 101298718, 536834852, 549503250, 414864350, 915714483, 583152181, 844846010, 945325538, 54586128, 644373993, 252721698, 895257018, 929928528, 734049291, 775646771, 772024615, 962299940, 568833414, 429493199, 777363727, 318995115, 991833778, 692953825, 78976349, 83414683, 737220922, 313088063, 839929174, 486229181, 964817985, 997726848, 221343479, 613378555, 959857978, 450609772, 397908156, 235967714, 92472577, 854739016, 258304980, 616745838, 25880466, 875469948, 330189502, 28826591, 859265685, 790738357, 224374315, 739738218, 337179730, 288180678, 893340118, 811428308, 622431730, 117824652, 946880788, 382804382, 606376827, 497608754, 956924002, 838066047, 480642566, 714152561, 472277862, 739425943, 252447467, 273352581, 392550586, 58224376, 609684060, 500159907, 323085437, 810700438, 616341896, 708982533, 205952805, 83331062, 70657948, 616037293, 680140947, 398473356, 910187729, 798032546, 600491311, 325653815, 508399479, 467867142, 912958895, 444034426, 849132265, 479952766, 396496915, 438210139, 417497003, 741157365, 803810323, 903206702, 226830699, 149982726, 228117709, 194449452, 578703014, 429991377, 485166070, 174825868, 448943614, 978208148, 794867083, 312466526, 437486891, 28311458, 390678496, 48228664, 369564977, 378345374, 852652404, 795472694, 254888659, 144819470, 34369323, 404746155, 339194706, 100927851, 225232967, 236658409, 423613386, 535929319, 192879895, 729641595, 330148967, 559264888, 55894912, 375104288, 781557637, 462469551, 860493165, 812339574, 127895771, 155940613, 513655291, 393318504, 690107453, 261634364, 592713255, 711861878, 160649260, 813977975, 175912468, 723070330, 557493855, 188881327, 233128558, 125474533, 500415080, 557308629, 319609604, 474177763, 837350110, 172979708, 398082668, 404351745, 468023855, 490711822, 38343454, 988659137, 566835158, 731272, 766695012, 267424833, 762279229, 813718573, 330249710, 561310467, 876571540, 937307434, 414524789, 786974281, 411760156, 220189502, 136789914, 503155886, 832960191, 224983246, 958693440, 524599075, 309303236, 240817695, 231485602, 632759283, 286375247, 136402647, 868245926, 598949857, 703764031, 204466344, 916492378, 619647369, 862452972, 454371519, 949140036, 123440022, 907203233, 668227278, 38983703, 705378483, 969951223, 602388147, 526519302, 908212021, 795427138, 817980840, 463443714, 505818963, 462090219, 248850929, 741133280, 675775151, 149202457, 143239349, 598905135, 484996092, 740012040, 551099100, 107303203, 924725390, 810133601, 848001608, 78133944, 26322065, 53991450, 529780998, 667905129, 970039245, 93523710, 379535003, 5876898, 406189218, 449203011, 320950531, 929103054, 183627995, 99769333, 934800582, 334700784, 27471546, 77938819, 46535936, 825122086, 614377828, 186141636, 47534246, 273403255, 44218599, 681423515, 264789443, 3064615, 43830200, 56605810, 883604893, 131664995, 716623405, 368475922, 5426467, 400352212, 626530554, 68962489, 229510199, 839559131, 206964191, 752374097, 88281032, 470273306, 45439378, 182381244, 720825652, 224102665, 656018600, 635636013, 578962224, 894529710, 602951739, 109524293, 349288325, 852820523, 42428779, 174895477, 51374278, 34355106, 348302841, 307363202, 654565237, 381071563, 700253349, 900131394, 967442270, 414913975, 771950568, 895919754, 980653220, 243051796, 463054314, 665953075, 36246411, 571635471, 558201816, 820580371, 667760903, 154641347, 526496824, 967199048, 104632726, 248428786, 595088034, 792745355, 694207644, 703683847, 906222321, 507814418, 906595848, 387999273, 900571310, 803409716, 773880246, 184011301, 836264779, 499955776, 985576274, 333107565, 676084677, 674135091, 772570395, 408374905, 275508793, 305617304, 861522963, 702055899, 722378068, 611976171, 491343584, 260121637, 474428243, 330105481, 521422361, 742142579, 823516794, 652353637, 869626328, 208789711, 847438720, 447051327, 813521769, 852418908, 513542334, 264143133, 193238074, 54654192, 680243099, 373716007, 423450202, 559944961, 803894440, 675219104, 391606617, 472662037, 663224946, 375640733, 430261901, 211320864, 467385581, 176353451, 37423859, 312932050, 987211136, 9157107, 319594892, 674284823, 555420943, 406085594, 479147402, 640319199, 33877880, 104869875, 151503512, 261511789, 332227328, 971575061, 755867218, 740897546, 695329503, 777686686, 51403991, 809547864, 97295649, 922906706, 84355001, 551331579, 119367586, 414026994, 787110250, 912869903, 864544987, 939928507, 752371653, 198028251, 644566825, 771980719, 209927646, 214403972, 517618356, 262455691, 153109485, 58296204, 29445130, 431334037, 261819495, 483817487, 997821726, 439288691, 739163690, 785153624, 14822718, 673419645, 132858461, 62453309, 968089536, 446973541, 648389267, 175909639, 288611205, 489214345, 519431658, 145900904, 374422233, 882880598, 314097660, 416664690, 250325906, 528125713, 166326716, 851937978, 160603319, 558648765, 863350058, 770420257, 172039634, 823129588, 710007646, 470684721, 152706641, 817940668, 816097882, 987110869, 838770813, 755248205, 871129880, 18820740, 978468898, 726645574, 642349358, 851997630, 408686983, 512159673, 893350340, 649812065, 16024266, 383152854, 807366359, 615218061, 913352489, 805378678, 487877416, 560814107, 640082931, 495431516, 445169104, 392176732, 617801549, 754301660, 298315708, 172047688, 823503324, 835314555, 884088720, 421367188, 951083413, 593052397, 834511216, 365550764, 178160990, 327371451, 746837717, 856397456, 327246272, 835236442, 535517058, 914121780, 75173977, 274263202, 84613571, 511593408, 935763643, 107428494, 922521935, 164816618, 606101327, 292192137, 227792576, 763966161, 194303471, 503521334, 499261841, 835066359, 194148119, 862497261, 455093970, 758535475, 902221198, 552988804, 478399231, 53309053, 516943296, 703259378, 919232382, 211991799, 874545470, 865731441, 53074040, 634301707, 991730556, 457003668, 177174071, 508231093, 167709623, 473486979, 717121079, 314431483, 406524119, 221427728, 774097775, 289135519, 928981930, 354959726, 629111898, 6549975, 473661063, 773357804, 883128488, 293526028, 156073374, 742634066, 983374633, 866414214, 247307807, 363218232, 983918068, 204355314, 498170262, 443934632, 803511404, 861832078, 537542732, 813371190, 407788028, 237420215, 727783100, 154825308, 582335448, 506653594, 889995134, 167880264, 725100292, 965562894, 801498579, 118072072, 264496833, 373635698, 696095649, 629043988, 574156958, 391868374, 512988166, 45915440, 221142488, 523862530, 605313700, 517825558, 675943229, 152274550, 685911566, 933178661, 419672491, 722648236, 184989042, 457574862, 153653922, 143132572, 991387932, 522726436, 910413066, 542313842, 520190702, 152985418, 915469167, 142297084, 781820943, 924797930, 758663857, 875196332, 609083412, 388189497, 810194585, 717768058, 693534644, 618207629, 724093256, 901536385, 40979282, 140476513, 127632923, 272606120, 135841948, 226103164, 719158742, 173894328, 233706243, 685700586, 520467486, 344460919, 556782103, 814457290, 313871123, 888550392, 52972389, 685289306, 106077904, 872063740, 391285557, 155098026, 708210851, 668643249, 944337699, 568694869, 733432898, 844835456, 17995809, 640933571, 969134202, 669304948, 721517771, 433167790, 551005980, 575815134, 249691602, 134721295, 386798245, 809900613, 614797499, 241966765, 189792897, 557355666, 806532323, 607821845, 387343922, 930269446, 852458235, 661581917, 603463451, 879896500, 166329090, 275729413, 294197253, 542229112, 658673704, 221093689, 888333459, 562398850, 5451401, 241151352, 492792559, 147736873, 764614603, 119525946, 468113895, 466184936, 640156584, 802076899, 847694056, 662503555, 776085372, 891421757, 372911721, 296047394, 507004215, 805904603, 583634042, 625091600, 583522877, 615330592, 217832278, 519222541, 562188134, 531444810, 236218943, 639260940, 657924790, 468625106, 764589559, 226184259, 164177544, 720009731, 536177125, 969396005, 717167361, 992092704, 765032020, 802389634, 222658996, 589045842, 691298071, 391385768, 436852464, 872342688, 907218667, 921827908, 360506443, 279240396, 949374180, 537743143, 846254666, 400936289, 253957913, 343501212, 237303948, 82089102, 421009645, 917219255, 120067291, 364826286, 950252697, 475636923, 721048051, 170832861, 893920528, 495438126, 506358244, 55589003, 103359522, 653659436, 968345975, 865895845, 353500729, 386580519, 875529667, 810183697, 560880374, 600971835, 897786723, 477687077, 529660234, 808528715, 453087890, 272891436, 658118778, 513559751, 293633124, 740208614, 571481302, 702794359, 886162107, 972473326, 165195313, 58493315, 990966743, 624659366, 149711529, 486634870, 481572836, 863962881, 138675525, 823547020, 249720633, 153443669, 220923211, 184504025, 87263341, 756713992, 983476516, 575203042, 952463354, 572172373, 131339992, 573050262, 373424239, 710370975, 114375477, 451617721, 388768300, 726440950, 908654551, 662815480, 572944434, 211492224, 822237838, 392554576, 340334946, 679452258, 73462167, 942143327, 414839314, 131224886, 945424518, 779766171, 403760238, 2214362, 813944075, 850576058, 12507756, 408081119, 554685939, 301281716, 134239486, 330801678, 574739707, 161107119, 573143265, 864176582, 458549617, 882978541, 123950067, 381059128, 49570501, 575807917, 17055734, 376506640, 828496312, 949231089, 290649114, 467018781, 519978158, 422231000, 497059672, 785045186, 390625348, 233711533, 579038522, 567094679, 406861317, 655480287, 452412403, 561057296, 814437886, 557867252, 600731889, 233011908, 706697881, 714332380, 39349059, 870883921, 725706493, 279810377, 754665531, 217953784, 10541414, 615705449, 234319913, 933661788, 185156819, 167324028, 20635379, 595632650, 495464884, 670353875, 690355235, 459327104, 909111005, 235496122, 932183553, 803242997, 323263639, 30001235, 125261239, 83672877, 349723341, 952995996, 551057720, 356357924, 285272045, 869182211, 7465746, 417652268, 540926088, 349034040, 54512142, 290864543, 313356144, 500041373, 429308799, 350079905, 921176892, 926557438, 235471797, 387446772, 2648570, 314983629, 164148259, 776371215, 977150873, 1030862, 226145358, 255932901, 699556602, 988071018, 128995796, 620732011, 682275013, 486297118, 31946855, 846237275, 365229878, 100281530, 953375758, 810884725, 878352241, 461038433, 959155394, 611147623, 558023822, 866871160, 914114780, 677263116, 463947179, 737662093, 488152025, 263814168, 683396794, 587770410, 930074291, 398214959, 902949011, 166363681, 557761866, 83846570, 840919204, 92867890, 685773184, 580463657, 354526631, 972054683, 875757982, 878888169, 550395596, 316986065, 719817097, 986833114, 605110575, 490634088, 836276639, 902960667, 264851516, 599572082, 760961260, 799599764, 444266472, 153609009, 769432782, 287080547, 490106168, 290526795, 283030118, 994071285, 153000607, 803456951, 651164157, 838983627, 356822746, 421449130, 200491667, 653282079, 874001000, 407646262, 35581162, 575793348, 100595303, 111727961, 523070604, 583577187, 646147114, 231232692, 668271826, 416813341, 442288808, 185694120, 855968201, 468732441, 765493459, 400226183, 728669770, 700487471, 432299704, 875207926, 919179912, 939234185, 256522497, 59995355, 71639188, 39053533, 705523318, 604930838, 664027023, 157359387, 588663870, 634006349, 545486437, 183778137, 297371343, 494011502, 529138908, 313717789, 362619608, 360566710, 908202470, 499255329, 102241499, 122089882, 513590344, 381348023, 703065747, 951559121, 32815574, 819531192, 951697386, 232032233, 893243559, 219016734, 532013202, 476721528, 667304609, 611290020, 136488407, 627520922, 196609868, 269029408, 530132081, 159851947, 13340766, 331967331, 176489577, 462517845, 500276202, 657845482, 784333986, 333257364, 370515898, 952508089, 232366841, 354453767, 268412933, 582769746, 257721448, 567493382, 176110931, 839295192, 454717413, 983489137, 986549876, 280186698, 9959805, 88500864, 97549703, 409132066, 935989479, 255889591, 30694673, 247786677, 661875363, 57452946, 361557531, 690435069, 36758805, 682990854, 338595068, 997088689, 724279216, 755610582, 360727203, 961063451, 335208127, 953183773, 992103621, 465786495, 28658946, 202068086, 487384017, 330430138, 866166914, 962060973, 161899848, 820582720, 991537534, 818302904, 965400843, 134909247, 387549460, 780558894, 818477519, 495884687, 609311032, 926643028, 443739688, 640805269, 361990098, 990942805, 57621359, 674470850, 875535602, 792388177, 151690439, 858824872, 808259021, 573875328, 945644136, 873447580, 325881202, 579071608, 277642919, 16749947, 679209259, 326283542, 273341900, 690695009, 78432125, 24777153, 566542593, 706305131, 542034302, 59827022, 696590866, 573980724, 300561509, 604702157, 250747894, 993982733, 311490687, 850953648, 987950135, 953683821, 210061811, 900963678, 114854407, 598632130, 822514178, 745077812, 998229246, 978112508, 345336580, 115200508, 667938798, 306036219, 628753262, 312778972, 994899683, 697806457, 48311313, 286688615, 33928900, 783459381, 334505751, 723583974, 411611505, 740590376, 387709424, 768565345, 61497762, 138984998, 327953993, 74587524, 614680168, 328114243, 602108550, 839915595, 167976053, 815034407, 51305363, 652044383, 968080, 238403305, 486937439, 707026101, 336431182, 650809445, 38706346, 500087773, 365441979, 384891192, 710812062, 505124909, 195149635, 210746393, 510476947, 503380180, 653665168, 791933809, 925511358, 4409648, 794661675, 832332459, 478041795, 88409110, 345812730, 701018628, 104666105, 702443110, 196034842, 842449953, 709536820, 728652040, 630903226, 953673320, 982127639, 228444992, 736460362, 932077647, 368029051, 578474098, 386854193, 642649806, 204408806, 231954501, 309155292, 835526868, 695787326, 458736527, 65432707, 552805039, 289046351, 85702152, 275336156, 153988012, 892342259, 597568718, 195414197, 961307133, 304763557, 412828809, 827471189, 305623995, 412640240, 870733799, 141608933, 966115170, 723308220, 8000293, 551131485, 49894856, 232685045, 253966556, 600282775, 645965895, 194679256, 881914870, 662391198, 915805796, 583242296, 844476861, 342755642, 421052635, 961944389, 713862950, 34888655, 496726973, 86543671, 475730759, 445266056, 400912607, 255154522, 972714233, 650641803, 776697037, 32999490, 262027481, 771537048, 901933662, 699915045, 978317170, 452711187, 600608528, 549396078, 277656402, 497078618, 157417103, 283367290, 283323902, 911366354, 274210543, 337341758, 459863222, 533216687, 923401370, 81361870, 24244346, 73404128, 678368116, 686498559, 728470171, 552727994, 366364796, 860148539, 351918939, 134536243, 540860198, 178322080, 8528098, 548873273, 424224954, 243715711, 244216592, 244859802, 979686560, 782168261, 571599549, 15499972, 283486909, 882989248, 554937301, 189412456, 13792086, 606128896, 11438316, 200202283, 902788470, 660188382, 973960192, 632503797, 397735328, 877404459, 135569933, 342127742, 72465329, 291158767, 586963052, 773583858, 620188661, 124823334, 980923337, 23313582, 34213660, 462179334, 893985868, 398703282, 88112739, 32044915, 308785434, 443918175, 632899813, 393325940, 362578749, 312193838, 955504824, 581291307, 359276306, 334963072, 68949621, 516632930, 202272995, 57479208, 614385586, 321105169, 319981771, 249038849, 104395925, 557845514, 825205583, 46060764, 239209568, 624157787, 864470114, 674587036, 381839143, 180811385, 967011777, 832427545, 140069119, 594781825, 860778296, 269975645, 903329965, 8383153, 225941174, 266978268, 360153424, 909367099, 133274754, 425784018, 855207186, 715822532, 92773578, 232035342, 425236714, 528550245, 979653023, 791539205, 120961318, 277689991, 521911374, 279444469, 17329292, 284050131, 952641624, 778960096, 443921325, 176526263, 406927788, 185685945, 904159366, 23511148, 261294316, 568701907, 164934037, 977654524, 113229493, 321415384, 385665803, 598013211, 235204400, 497657989, 709347396, 50932509, 621433781, 335535429, 802052073, 747893520, 515734590, 849275330, 862549780, 977226341, 644646922, 465284311, 921765943, 503240160, 838554450, 284965289, 915447327, 112535653, 337285578, 334425990, 422855962, 190395298, 740831526, 207095455, 431415117, 347706906, 152726169, 259460300, 186981754, 698316682, 911225091, 839675804, 842930210, 149676427, 619211398, 349705117, 701615924, 598936444, 910959735, 409719743, 166341916, 515239436, 83471587, 159988624, 130067718, 958327704, 916167792, 536000015, 160878486, 546335419, 748509618, 988339450, 358953489, 970491344, 230239602, 697367324, 613570475, 297005053, 438754589, 504449520, 45881122, 965887716, 17812571, 10706314, 807961253, 8286610, 679455907, 795172933, 880181515, 228730271, 690211173, 69395992, 825985543, 426447820, 617951567, 54864998, 294953601, 802359876, 964711221, 48935380, 163591073, 814156923, 430270980, 535208434, 319448247, 703444347, 203003034, 598944671, 732243238, 790991413, 110577466, 216654716, 615713306, 130379961, 441240031, 968401670, 901474630, 989263582, 472424633, 855126524, 115779634, 833429284, 578545293, 669735696, 196214608, 344463742, 713152402, 141653639, 540263699, 49847288, 225356677, 517038768, 265272253, 485826901, 385698441, 78637012, 435881804, 702624894, 979740406, 733794509, 934777284, 972637845, 436987089, 950248234, 411297759, 196212791, 17600405, 206974420, 382835321, 985273426, 894998916, 410039289, 234515662, 543900947, 730578523, 525320086, 25140190, 114647366, 465384886, 189219632, 987876400, 574067046, 635994968, 235334265, 779810947, 801243602, 513249549, 329824085, 56620550, 137498635, 579771423, 917493833, 618147880, 38889122, 963450198, 909449791, 135717368, 35481530, 207625770, 624038195, 278210574, 133453635, 384780352, 321958214, 858518622, 271100031, 799452076, 52812273, 324024919, 397548046, 90868016, 905654210, 417914904, 580314610, 152805121, 804977457, 276400221, 986405760, 495284860, 329672825, 500427594, 533910443, 310510580, 954581228, 22128268, 899111605, 135886386, 584272180, 342427714, 438270630, 834972006, 996449356, 957783813, 319785483, 548033334, 822946061, 149635550, 435988658, 745005825, 153493788, 832982345, 102829414, 721904344, 187075493, 422623963, 319594692, 62523796, 180719275, 760473522, 337574757, 614929869, 247428188, 566076695, 140247443, 145048758, 505717505, 61509100, 821301261, 97268299, 500352343, 492861070, 304003787, 880642306, 623874031, 695842424, 961882378, 477549544, 34112772, 183445328, 668032203, 745335278, 924289709, 256113529, 199957678, 642698737, 813485959, 107702994, 903956160, 998695776, 961384526, 163595137, 405757197, 661150918, 344456037, 833053150, 396163013, 657909911, 808566769, 848554338, 249874226, 784060979, 608425694, 668774080, 984648974, 881861112, 239526650, 896291614, 520636148, 805118615, 657449113, 691588145, 694112366, 199531486, 761811006, 778417660, 211198332, 974113545, 347810442, 111139871, 95576649, 464491743, 558415785, 180291961, 825672554, 669697102, 228690044, 905894303, 219063669, 55986663, 25056559, 958103247, 303144658, 838836553, 642974475, 748491900, 172211012, 142338022, 444921512, 804350519, 425437841, 238438580, 617339678, 797012611, 629465460, 323067475, 199762682, 816683353, 100588119, 234112303, 76194057, 698308860, 859391015, 224501511, 618707225, 233736768, 194603656, 102627571, 232157042, 878682709, 564235135, 878015826, 526805527, 521261939, 68523114, 75187929, 911497469, 645165869, 415148533, 128549321, 305951590, 51960225, 427311013, 361054583, 63719395, 633645407, 239047431, 882818539, 56349768, 994297723, 745974703, 399801578, 293370896, 676108159, 465190966, 596886834, 713181157, 10395088, 218116302, 841684185, 990154913, 808931109, 362646549, 74181222, 10486737, 302103287, 542520988, 880575713, 711364535, 470873291, 38823005, 854676487, 285101141, 165021760, 742309552, 494214063, 225523525, 725572862, 934243362, 303982918, 394321745, 229629745, 593065075, 604021244, 895997221, 974691693, 523928606, 131257618, 717861064, 468941329, 792625911, 562719431, 799837028, 76047663, 156999155, 762634132, 219114901, 130900501, 584640271, 221527585, 932627862, 957582695, 330362288, 399045144, 11410231, 785946263, 942657737, 111245722, 458782212, 853014896, 375210043, 687172676, 541574732, 171982653, 596966812, 492934654, 151476685, 741560109, 713236878, 462118438, 501365730, 485062799, 876316145, 193373623, 959302945, 34419436, 221784316, 882463650, 935811919, 312118591, 277339683, 250402383, 195713482, 764111815, 971537525, 844977232, 229106098, 914708288, 21722029, 197327848, 993117276, 452556780, 666012928, 160383720, 300596649, 626560321, 785483409, 551575543, 895297505, 979944822, 266306122, 741910753, 494625463, 882223645, 6334225, 585917760, 710628264, 484465402, 810450866, 731210768, 506336176, 994599693, 291989536, 307566304, 605198243, 256973501, 853240483, 744536030, 416528551, 233978809, 368761079, 275686806, 265928218, 934007455, 144843056, 596278464, 394677271, 739986182, 622087892, 232153455, 187232014, 934347149, 661801406, 388989284, 362740420, 538143881, 209566708, 105736727, 207797216, 545344397, 902236203, 746977415, 748829974, 812120589, 600900344, 719117857, 778830922, 46662220, 393343939, 35157046, 943955093, 246201254, 248657021, 984484067, 188951666, 614027966, 562224433, 357425511, 675077503, 923073807, 408053788, 753418993, 632177733, 573954431, 903812453, 394580153, 60000673, 617323845, 176190192, 992106337, 284698325, 598400070, 573791993, 312934765, 274016175, 852406066, 706844490, 195703995, 211847647, 861419532, 852538857, 397093815, 220838630, 83917530, 476581938, 969164155, 856222143, 695231926, 594688964, 989821485, 501506403, 613120528, 184914477, 838614813, 580972552, 816048153, 168984349, 756310519, 792810181, 118611702, 350314077, 131009130, 763116935, 165367774, 82917328, 735574968, 808157566, 931132809, 243761308, 494434060, 653726975, 359579715, 213963492, 708855687, 269185013, 210217674, 870503657, 997368043, 618407816, 746739468, 482316078, 391552713, 739135513, 34919476, 311576394, 958711120, 779875245, 531523660, 994460714, 449243350, 230105703, 806790501, 284878102, 414780661, 57912935, 956052504, 976670751, 765212443, 783596418, 687476952, 184686391, 476460323, 939840591, 17725973, 833462842, 568880404, 471850675, 978752209, 65146703, 452583444, 789300455, 112612724, 302167051, 785136199, 475714001, 487125226, 517419337, 462969636, 106039490, 727366029, 503144944, 596550547, 374061174, 228824137, 329481263, 66791757, 324949860, 977387877, 771218402, 659499517, 957598236, 687356448, 245115882, 484488978, 781381531, 999443037, 350003572, 423313815, 518943780, 15223719, 909807276, 789481539, 828477831, 4748916, 172347842, 552759429, 881118873, 688619723, 299942928, 398178620, 140943694, 937783259, 331005843, 16065655, 476036155, 130518490, 717744652, 307632277, 518218459, 779426351, 443655244, 354922574, 712444897, 868620869, 395797088, 804495381, 401484944, 617508474, 321532339, 849073481, 445906662, 557438792, 767583311, 328428414, 597408754, 964439692, 52287406, 578667147, 784546224, 532297729, 711732566, 614508172, 976555236, 95100367, 497919928, 445795784, 246541574, 412713706, 258177891, 425696915, 619037118, 335074837, 119704927, 930657694, 48683797, 788501798, 209402888, 729326548, 925636142, 775323283, 561443535, 583534607, 998020233, 463067092, 174501860, 774078649, 198866986, 293304753, 921084612, 416045979, 56597888, 351477300, 638245241, 529249899, 68092518, 277381178, 676580854, 430481301, 189049489, 149722221, 188751050, 661652534, 744678413, 136230450, 852320474, 71682476, 277948733, 454107672, 627575627, 755780721, 372243032, 464697561, 993140020, 351065297, 340884434, 867408818, 97428623, 541239666, 969215205, 695917151, 579113610, 463504276, 140542219, 603349209, 416874143, 966801842, 8430680, 146336652, 972654598, 166718980, 758533914, 413227647, 173562643, 149613571, 116490176, 652074682, 172285975, 114701189, 598706066, 841981011, 789341049, 446779092, 39873109, 111814207, 292417075, 989340416, 751179686, 36751795, 691397239, 770885227, 394900078, 820751137, 384235177, 211112556, 232777005, 698014151, 811716171, 310244959, 181875351, 754255583, 571560044, 358691320, 512749239, 42132198, 675239621, 684509557, 902882538, 721390037, 33385425, 876135741, 813089673, 782765150, 540148873, 422345268, 893691658, 576869865, 972252608, 500510126, 671598983, 139123889, 785838650, 379374873, 716035110, 872044039, 484066807, 989612403, 461694203, 775602517, 218838353, 875792058, 33867579, 933397012, 522608098, 216309358, 329121625, 177106220, 637802175, 350247683, 844547807, 940709000, 346048746, 290250106, 968866774, 161597607, 768195103, 58505166, 32900023, 338375820, 556421718, 76248023, 41995721, 549987599, 244399892, 849274142, 595939651, 945344988, 598166365, 36333655, 639618451, 291657944, 648687969, 665108397, 533410149, 358540868, 953573587, 23654932, 385598096, 511558822, 635878929, 92669199, 338239109, 1968200, 324219589, 460225572, 83797323, 399477579, 767484235, 72943413, 817172043, 622088648, 297014300, 559777741, 400733495, 567381573, 316822394, 670337563, 440849889, 424316492, 928735702, 11135142, 736166633, 226935708, 511299781, 869028841, 76386821, 185044397, 203840501, 849568548, 929061039, 397506720, 917668881, 707705820, 94020547, 720205535, 116343383, 760546644, 840650871, 269058338, 676549444, 305519727, 81283930, 44599886, 982109252, 218523367, 509773021, 17601199, 61019207, 521169580, 881984673, 252756814, 843069783, 413969701, 392919285, 569085672, 543023698, 437063203, 749546438, 165615908, 303223088, 450476051, 833393957, 540585510, 61751110, 523868793, 101540208, 309965550, 260885279, 690068322, 339324520, 2536007, 836162524, 286481832, 756299103, 985098606, 838212743, 86172744, 460877868, 838240924, 151361892, 155831196, 339316299, 40126174, 808510734, 967054151, 169759797, 425259750, 483503932, 110076694, 726671125, 11128247, 939467108, 676770720, 477989613, 108746709, 409692825, 161429, 704745446, 576604155, 396723152, 740711235, 208780959, 189806806, 781194653, 357590757, 245664726, 663954754, 884178372, 673536581, 439474818, 241494156, 590440258, 730820555, 849377991, 610274520, 739842370, 188662207, 21633954, 21204918, 792809071, 597384884, 838003, 692051821, 598490309, 47527231, 451166172, 938191459, 217038708, 251302718, 481610465, 329366318, 653318915, 796758862, 849401800, 686450842, 746104860, 316156443, 663285112, 887850459, 726480935, 304684884, 5431285, 816906899, 944450200, 670917006, 840235495, 802749470, 243580012, 611425416, 297842755, 556869656, 540460344, 709202410, 825864194, 675565996, 359272856, 123476329, 957035200, 693068246, 488097970, 903303823, 301254466, 314710569, 116813979, 143217173, 272431774, 546425016, 235212170, 237041589, 540300276, 857060981, 244519809, 594112364, 135694081, 624672397, 671242586, 946244503, 217417588, 394206325, 738586342, 483831314, 538678920, 761561436, 829886077, 318196543, 28441258, 22892725, 398618330, 488330509, 543754945, 469429541, 183368373, 600609335, 533858352, 750778344, 454506388, 186053028, 105116508, 575705807, 316543052, 866457144, 550971673, 41457573, 613620789, 130218873, 42906999, 910509219, 193371286, 278807470, 767361157, 544724367, 808389784, 223473475, 617692315, 127298107, 505910144, 119555942, 396017718, 241902149, 452030589, 664170511, 835375636, 5513541, 985440470, 110319101, 839615958, 780039662, 561723168, 406757456, 350268473, 402673390, 391760299, 697270641, 958172723, 691445766, 591664754, 222846774, 393388776, 386115599, 845012735, 590631887, 347372265, 403591897, 438651539, 718809759, 408020433, 228864277, 220005566, 755297583, 79600550, 366284596, 891886485, 155579750, 669716449, 44149417, 769506558, 507560498, 958712381, 464654755, 750087831, 305855646, 470848065, 195552106, 984948683, 801677714, 260747014, 573689729, 709479699, 85813213, 550855284, 456965149, 952099731, 86512186, 909783871, 305367600, 83653855, 492305481, 220339986, 152701830, 86356333, 355688045, 283283105, 767971336, 533444553, 64357990, 223762203, 810452328, 856772692, 486580291, 234022364, 692126549, 284846416, 800407084, 391491354, 110493132, 143435814, 144206113, 737927826, 177289470, 964069418, 807199258, 991796851, 405130181, 521394977, 10153029, 758766711, 103840827, 269458708, 907505774, 748754080, 987909135, 769253050, 992326250, 60170532, 460228997, 660674584, 176256356, 746301633, 176785920, 901243639, 591262580, 238791964, 313854438, 646426821, 61372709, 271183673, 730764324, 667940242, 522893698, 306922666, 963518601, 719497701, 511238053, 792973596, 38210846, 145681222, 769285009, 41849444, 282654708, 324751362, 753566434, 461756671, 128695995, 658178219, 918668475, 636977227, 579322440, 251035289, 445169223, 653629397, 295710135, 718166829, 158844007, 202285422, 363560152, 336454054, 985228260, 903149831, 896421200, 175351704, 647920389, 173554806, 395527419, 648818802, 212496850, 717363718, 950166182, 652157268, 790567656, 664001483, 250664163, 178536092, 948246884, 76465393, 270358411, 169216917, 264446665, 472146468, 245619858, 663044974, 399884931, 145578331, 323066841, 858890369, 389188108, 688795905, 739539972, 749979885, 337257199, 546083777, 808484811, 569201883, 93622214, 158285096, 69122606, 311875739, 521644779, 281459825, 864180541, 351157347, 894274176, 316359926, 940220938, 596129597, 297379819, 691929601, 760956157, 676716511, 182710837, 68190275, 918780188, 659917632, 199005252, 240220232, 322435645, 60073264, 693518408, 876301890, 682197288, 26525702, 597810795, 249008103, 799015662, 212174721, 613600983, 982652756, 74473581, 913959080, 417073566, 412100768, 794764587, 968414110, 882387680, 965950416, 434210465, 502366922, 400518604, 46008956, 605045419, 749202416, 779167829, 623461333, 647555982, 866099850, 203150209, 226388730, 553301101, 836619408, 354950105, 72680904, 564618992, 114834847, 889854944, 461902631, 751635132, 218525725, 199142206, 468790235, 503333934, 386376855, 473897059, 22606278, 462696638, 37664680, 539687111, 68636709, 421314319, 606814536, 527095215, 48625252, 108377523, 774100460, 495874260, 170541178, 606459928, 138271019, 606178096, 415725001, 42289999, 323923355, 246465601, 463433760, 43349936, 98175745, 428112775, 973600722, 54320678, 443004986, 912001059, 432491375, 500500034, 610850228, 782112554, 489838406, 473916214, 564607483, 651542132, 743811456, 510511297, 542074405, 827372614, 275679375, 714174721, 666667057, 243794048, 194083408, 453344713, 3186481, 191456297, 114111910, 8901436, 902632552, 97360990, 355433466, 321409741, 334218642, 34768162, 874679563, 599562432, 327839199, 561162956, 982319509, 906074583, 502930966, 639065454, 66663035, 369531303, 745264257, 286417380, 856383917, 844245914, 167700358, 686897263, 582914288, 959409042, 102406331, 670852921, 475068010, 90124231, 822852182, 388649993, 593832152, 978151987, 760788562, 657416548, 509857307, 546382285, 894172760, 156584440, 989943503, 851726772, 355572809, 800343926, 736372943, 328615724, 113805508, 767260877, 29632189, 987799753, 841442124, 961461708, 873364018, 870206544, 507765516, 240113662, 278797723, 168568221, 929135436, 436994410, 339597166, 683260107, 423436730, 715493918, 29801064, 813279110, 194229730, 768976552, 635954105, 187889545, 649005278, 819470720, 782283413, 136367365, 846819819, 822523417, 676850861, 605927240, 425342768, 693387962, 215659489, 91308991, 326614122, 35993236, 653025994, 39294006, 681029639, 643265784, 141946960, 274299338, 374683627, 655964129, 53438925, 43216486, 96469738, 935152243, 640430379, 202171881, 564622714, 53391157, 583468612, 564276090, 867590036, 470349095, 696328919, 871808684, 822474465, 10247420, 983933554, 12137987, 993119653, 745849596, 205495845, 348075851, 501848456, 579259063, 39662520, 158352555, 785474152, 27696700, 332332066, 398529123, 350801354, 375228051, 438337853, 379875833, 74833051, 826022928, 830062858, 250082452, 366130797, 333360242, 904880266, 314254371, 93324061, 180094465, 881972601, 667110101, 865823739, 618712528, 908519795, 152878769, 54073080, 820372262, 166947144, 425674162, 704792001, 596270524, 134581294, 519749734, 381556435, 322555407, 639679156, 630392817, 251095722, 809173544, 911111797, 527533502, 197735671, 97364901, 6143952, 378847016, 598383936, 826734937, 61404480, 736842472, 188253236, 261007009, 712428649, 221046394, 933276184, 65311264, 270984916, 144918227, 953597411, 715522938, 944071606, 207503820, 355282974, 203552759, 699820562, 436965322, 766789006, 214318436, 418128416, 729096956, 552561546, 38929059, 845580904, 583709418, 250384331, 683849708, 62348429, 798590697, 4670685, 591916337, 67155108, 555407878, 694019357, 907006372, 844231432, 33213593, 826535175, 823021636, 519560095, 951073944, 739013562, 184042498, 113875005, 255626099, 267520754, 318529875, 462363525, 558653472, 139137281, 966249478, 480578571, 395269159, 454410974, 411777165, 232625548, 150053061, 700459784, 216743798, 956446203, 58589393, 729939378, 907810110, 182352455, 474873731, 292261258, 627610774, 870998040, 68993090, 812373918, 208252523, 1462802, 886272994, 578445219, 445142556, 356133043, 721200673, 696651197, 478465676, 100157201, 192267884, 730178374, 157043646, 518610253, 710262822, 310566485, 58218031, 517133682, 620081754, 379987514, 921332226, 885964726, 426470265, 305758900, 953921383, 672159126, 629466289, 907582591, 491056826, 872032101, 390539114, 776851092, 474722564, 982071829, 873176795, 643172955, 465546526, 213552732, 512597633, 927367174, 155500029, 989512396, 595709292, 403012782, 182461896, 535383087, 101330504, 40560197, 71413773, 84286873, 886863395, 719306966, 835555835, 607672717, 111020325, 173075978, 917615181, 85777874, 366661477, 390183771, 730090322, 803114421, 697194701, 134660112, 405808910, 168181595, 250941569, 166335089, 664542136, 136683298, 970811053, 520909604, 854109579, 197117053, 838977026, 813323178, 285216868, 592390147, 396839261, 468768647, 335633385, 815932334, 771959530, 911012089, 855090098, 237361326, 906984036, 890747369, 862860007, 385000335, 749551593, 144128209, 693424168, 343418343, 947736626, 757132713, 795766995, 240207773, 770537517, 336061826, 28843243, 498408247, 312723364, 73094130, 826671366, 990680311, 148679413, 343989786, 548239600, 101227779, 768800513, 288373497, 644575924, 162101554, 690766879, 336415725, 193261721, 608855925, 212105816, 539787258, 117260041, 823498865, 308298318, 842853951, 932270762, 434073915, 11806936, 800538444, 397541198, 235101348, 586987999, 300648795, 931643204, 940019881, 736295324, 803492521, 13444041, 118760167, 296549620, 832491841, 925796429, 995655514, 79153792, 91576135, 453639024, 751367548, 929530299, 696923392, 258691256, 650482476, 450970111, 506893987, 407063922, 886320217, 462254032, 425601504, 765670266, 739054002, 415210863, 84618837, 994132003, 392498747, 924277851, 368659679, 892345370, 844697374, 501570416, 82230036, 122450583, 695284737, 642298762, 496384781, 658667253, 248123296, 377339701, 766232423, 268426645, 651376096, 250682373, 143050214, 96814932, 857737218, 974274506, 797516365, 484011918, 259721501, 267384060, 501104478, 201105573, 484971205, 671204930, 25631703, 865434490, 738334545, 673098877, 883269559, 575235436, 439186722, 325136987, 625333751, 716290796, 192576972, 562520268, 104334510, 126041472, 814745627, 883553365, 778006804, 845837255, 847775280, 398674356, 576000096, 280477878, 539015963, 456166735, 99386071, 705359096, 784806774, 996771230, 302418112, 596607932, 450537959, 802945012, 496112740, 193698235, 178509021, 926661593, 404145477, 794128852, 426552958, 943003584, 441213367, 508991477, 183153542, 798429200, 547707004, 291871557, 146229116, 339500331, 870409554, 44825864, 782737645, 992115859, 983853501, 378366774, 126060004, 502530551, 410584054, 736167388, 878335839, 140190021, 599630565, 958589494, 176081815, 233543648, 703427482, 851077133, 533270426, 572709956, 369964648, 747354837, 733856411, 161111097, 645478535, 841761031, 572422458, 896429025, 673317578, 117459974, 487071495, 892723364, 672910687, 995895271, 810130950, 767425784, 939308310, 762908395, 126537753, 829215166, 424102144, 471153582, 608370445, 703104229, 206132265, 545780814, 2796834, 187130270, 667673201, 367411375, 792999065, 951187149, 970861953, 565922876, 957834689, 722980043, 60161992, 845510673, 201245573, 89012483, 555372967, 166682261, 271818650, 966875233, 871801498, 431872389, 632149895, 241655358, 735589394, 318387988, 434979895, 333559128, 873751675, 235319292, 709128644, 382387768, 970494639, 151466850, 390402311, 74811321, 302859390, 918968723, 542509286, 408269165, 432576277, 299348486, 965340232, 945063776, 776904042, 314814357, 917537217, 445226053, 361690019, 377854611, 806438813, 874356011, 953408592, 88758728, 629721394, 394560786, 467327936, 978591162, 625189536, 84483516, 625765117, 320081860, 55459587, 481004160, 182883637, 697078908, 455207330, 297193843, 908466859, 180042859, 891381601, 474646235, 822804297, 902589720, 430815497, 764848479, 26075048, 517571004, 857293532, 950364011, 543570376, 497956348, 287840258, 46407443, 323241241, 167499937, 626120819, 275790081, 283275808, 990213455, 509150790, 950317751, 582775954, 623727075, 243781058, 935120728, 319461014, 845484719, 943580950, 136505467, 140991699, 863177744, 385813298, 952788056, 365289916, 752343863, 531845344, 379702328, 884056060, 23981423, 999573993, 28561136, 617221273, 678371576, 368125140, 734782184, 549020851, 187150746, 839029028, 225603459, 868042164, 935844717, 599650410, 647290056, 324236734, 817906739, 141316591, 88764454, 101591548, 40209308, 666924417, 910129813, 812234058, 345891800, 130302855, 654126196, 693355571, 778968941, 872322011, 449346707, 227619445, 116339776, 536960818, 825573405, 141979913, 793990758, 73629194, 425304557, 755327124, 880296659, 462748754, 164926548, 9361391, 846731182, 634305279, 195342500, 653982201, 152399071, 725829319, 102725646, 779809543, 569692954, 753792875, 749250577, 140447952, 484077933, 971334335, 108026300, 568415611, 825623100, 175344578, 512518839, 613395639, 125910018, 444380637, 772803195, 574240869, 440931800, 778183222, 316832677, 546355408, 572386009, 120387577, 332579685, 314434990, 771095260, 691989790, 166788753, 618493741, 94787043, 535294483, 134014637, 63135069, 573694892, 993253034, 756149954, 890921510, 747382767, 220740219, 70331102, 448492709, 128317721, 656152344, 274077342, 188473908, 871453827, 945610115, 789688342, 609795213, 283398208, 980704757, 232881411, 615546559, 441828414, 858067773, 905437065, 949516905, 814364405, 64920716, 189705642, 30473638, 277876935, 319332043, 908735102, 22304275, 35414842, 588613415, 468919456, 701931309, 361552819, 116587596, 804355479, 644629337, 458577604, 409287006, 317347166, 107964507, 748673668, 503393422, 799914420, 457321105, 11964948, 819876582, 516938402, 155329154, 153523346, 320507364, 512086134, 647534999, 870225804, 953312735, 792736853, 585450092, 573324524, 504264838, 944363572, 791335959, 980812765, 653508220, 19780945, 601844626, 51810991, 454887031, 156216758, 158578915, 164507871, 455462420, 868225095, 525263462, 857664008, 536319681, 937116595, 607766166, 555805768, 741721519, 432722554, 76416192, 459042702, 268869898, 368859267, 518800977, 803028566, 946183403, 664274029, 986174087, 378015499, 563181951, 314884474, 16704275, 234822475, 122640601, 435492063, 217836461, 392364179, 477934791, 286509734, 699541673, 143435145, 574740945, 632999480, 599243982, 539537864, 285584280, 241321950, 850680887, 99822252, 997008170, 340053751, 44841560, 120445549, 747390411, 612142224, 306863536, 271866773, 4279523, 786506700, 104778935, 550809450, 259291966, 771566343, 794959554, 834502131, 141352047, 659784828, 683953636, 518986060, 511554741, 493606043, 163779078, 773261369, 343282959, 23040400, 340085981, 839972836, 297381677, 536951838, 353572825, 416762909, 393487177, 795382144, 759241069, 649753264, 435041754, 816641707, 460444709, 747996722, 680123046, 543020478, 949293494, 686692738, 692848656, 152511843, 851367726, 834837008, 148696234, 703227859, 446736724, 285327443, 311612749, 770022775, 92171284, 468972874, 614757249, 965618081, 442273032, 779796203, 725221300, 829474811, 822329157, 638885601, 249094144, 866393753, 501542622, 544326778, 833374080, 558102947, 806000249, 155187883, 628860967, 672321290, 460096696, 73698378, 7609235, 398681639, 650129125, 559125644, 429643918, 946654182, 297389479, 162982966, 545386539, 320066077, 607903064, 800667396, 433348977, 975444296, 894944829, 641544745, 264327659, 829688217, 449088405, 525696858, 881923008, 682682314, 772670330, 632257526, 544151439, 680748951, 314168151, 218980153, 250359, 725506909, 330060892, 365560805, 7570396, 113793202, 700329762, 640334633, 177002449, 340193573, 245509781, 831988077, 226270173, 100113585, 973495055, 452955372, 719750472, 596764799, 286080670, 132975382, 848017770, 763241118, 106167406, 80069461, 275409312, 138227937, 127959675, 52489594, 77425962, 359147853, 490272267, 692741955, 260222264, 976469822, 154336131, 730617779, 111351429, 813190014, 3818031, 22270227, 921464503, 601288662, 477458257, 12055801, 306931187, 331144732, 906559065, 90984380, 975003679, 369678981, 11489379, 859964362, 625071750, 249614149, 915046031, 348954827, 363727948, 579779793, 493581796, 948567040, 265371504, 154729605, 387808411, 828796810, 581718364, 327614067, 710508897, 782332160, 155538252, 976389310, 928893857, 34746898, 293679122, 448638550, 829414294, 794870870, 549938955, 589479191, 740374868, 376448556, 81879798, 326071974, 963294609, 637429938, 847038364, 69703514, 853193074, 278658240, 713777245, 344786130, 600289795, 69302356, 649051643, 918713653, 674426680, 571187767, 506003956, 383455497, 92965884, 793227045, 728442281, 762841203, 818406435, 746501933, 653090944, 789798178, 449664138, 916927573, 732498028, 824414298, 199492636, 798758454, 294594632, 431349221, 102168853, 513516416, 191476263, 210400567, 256052903, 816165162, 853409622, 928799826, 994918325, 932553146, 555309709, 752418717, 349456191, 824199850, 217706720, 763624030, 565002191, 75969580, 574427774, 978865287, 567191805, 408960864, 482004040, 110685283, 432271847, 557668078, 824224432, 18648175, 10364359, 964873152, 186303998, 855902190, 180753696, 557619158, 218770707, 110855367, 215938652, 315449814, 330333255, 610724021, 736004060, 644963692, 455765239, 479242282, 132436626, 834518337, 560627114, 181236259, 725732205, 822876330, 202481807, 945303569, 637213095, 968758262, 624037207, 996252948, 814471981, 993950132, 848328985, 88621655, 674533178, 509213230, 408182794, 489403380, 855274501, 433822427, 316910125, 834253047, 783788744, 983682609, 562627094, 664776664, 29300829, 298515518, 94249560, 861406458, 765718952, 460741726, 38478667, 789221932, 499806861, 187072569, 50533955, 218763282, 242244907, 447699842, 247651345, 455887629, 81445289, 69440507, 345050016, 661703186, 420269540, 28486810, 899255912, 964521444, 753835929, 785643732, 676846047, 792056985, 547386165, 764590656, 906296127, 186742188, 766974237, 451266309, 153295625, 143052523, 330870232, 308403090, 219314918, 797942132, 177333740, 798291908, 687113329, 986363035, 106003676, 91292166, 478132781, 59185106, 665272528, 382825735, 815080387, 42614377, 670164987, 26673845, 254627834, 126189754, 638141412, 497019130, 314237757, 289495368, 715947466, 371238411, 7712945, 117291204, 799004181, 491068825, 571243388, 78395140, 245840863, 975682698, 783797669, 874671231, 60644705, 383135238, 245307795, 599721489, 768368921, 427804442, 977707058, 721684026, 501471154, 452073492, 526721976, 434178626, 954201161, 858516051, 557698322, 672754934, 787250561, 54294394, 323760529, 973072222, 874481693, 617919028, 25619748, 257854483, 716977858, 975390957, 648611819, 792912088, 84268966, 99675491, 395744592, 324574014, 705929169, 730770477, 456168081, 239013564, 112971413, 408453987, 528737752, 986748237, 783830279, 444790318, 189958744, 640940618, 98089799, 248482809, 490543308, 94547776, 428055548, 988840089, 566655153, 691098228, 680052681, 374524429, 351439019, 280642707, 45258087, 925672261, 883517522, 730956688, 406335493, 428668327, 328122645, 440108814, 833232513, 347965985, 951214961, 246576132, 487135476, 897335554, 145826579, 4153090, 120348453, 520506407, 515789724, 239270928, 766863208, 433573730, 735781430, 663190755, 687435807, 281340660, 307350535, 22807841, 998543632, 27678536, 400573950, 139758604, 841031690, 72083718, 355204718, 731558862, 80232386, 764216166, 378226759, 6590466, 122577154, 520707179, 675228003, 853419648, 906300791, 206639514, 251667329, 872665542, 251023013, 81222771, 694960433, 863374689, 802359235, 367993107, 640518336, 73138984, 246668022, 450527982, 705011681, 220937348, 591834622, 672487494, 189477688, 399071972, 922982397, 72039682, 720248062, 822781804, 383709297, 910025432, 529839663, 488370958, 662172394, 751075197, 593328987, 517816533, 248879161, 838734853, 628645670, 730786537, 905632059, 398310529, 957844463, 722680819, 123468267, 196576455, 801306672, 227115055, 813551158, 570937279, 632863735, 617777033, 594655585, 500783104, 928642093, 266920967, 822959292, 16929881, 821819524, 510255305, 38417798, 606281844, 943236692, 824901300, 154313914, 597999642, 172015391, 413900566, 324883491, 208807703, 926319416, 148127959, 483561730, 258127069, 425788563, 954949545, 565596283, 159900286, 593150465, 80157665, 435073345, 617655458, 400406327, 150047010, 895166013, 979817919, 16229942, 25267872, 605644018, 250097234, 466404922, 723175020, 243833686, 635163298, 418155738, 936195886, 682870098, 613331213, 44855373, 225442293, 935853134, 765005793, 616399381, 138150741, 168602641, 311468523, 160425349, 585114807, 314999581, 615413171, 699315554, 273595672, 782374020, 731329388, 27571834, 263501243, 235809533, 18319048, 84337407, 646403120, 70853526, 152629256, 395829989, 126637532, 95852831, 613452484, 366311003, 556033697, 161818222, 500297330, 323632654, 38791842, 163857061, 307890520, 795238172, 408691296, 908105130, 390436065, 273367170, 149080851, 832557043, 490600497, 888851427, 814516515, 486774766, 526423285, 17648515, 428683307, 219929549, 176261595, 712330270, 101128825, 17395307, 616476515, 105186333, 822195301, 633190682, 97825498, 297906695, 41255667, 863388094, 485453900, 705880444, 517933085, 9496792, 606366884, 21264073, 342317826, 894785865, 70646775, 894789376, 602136402, 623393174, 737339635, 237810328, 798572845, 661346178, 619571380, 782295742, 534169457, 814768557, 976459095, 938042590, 637575226, 998561150, 38733597, 603446004, 128048862, 102691584, 88186388, 607725678, 601645764, 627183143, 809918753, 9019218, 30700310, 79866920, 272325602, 410772466, 621411835, 591638797, 974633922, 93713353, 939400650, 443690755, 63675484, 472567819, 521139099, 152419538, 524715632, 191438956, 890859059, 6776185, 410514620, 634064515, 461037548, 153177353, 71715029, 596828341, 299799933, 351940389, 485048407, 73381106, 399962708, 533549030, 486255852, 234047647, 177904353, 733534195, 902062469, 51387293, 338709975, 55086399, 429933177, 42008961, 718442739, 710363516, 701401527, 870290139, 230927094, 218726850, 267847101, 542710036, 619333613, 520163519, 596540243, 95910354, 227987541, 246514176, 342616342, 414536786, 174731113, 13166335, 595463336, 474574065, 741628842, 853984814, 191427497, 355033646, 832172400, 485220046, 582881830, 189251335, 155405597, 197624559, 219672220, 357672047, 477103121, 30599531, 193885334, 621544420, 888666534, 460978028, 611775697, 522227088, 221600539, 447657224, 327741726, 4681497, 864291818, 792345197, 370889184, 3088514, 184696579, 205959930, 265559999, 577302387, 807543710, 391756066, 576828242, 72987057, 989920511, 314386016, 152062047, 594009914, 115608194, 456930663, 154582844, 119404200, 113371582, 724063568, 91833821, 258794394, 732793783, 779727530, 458586870, 910348859, 315750027, 220339839, 633017744, 724304452, 69037982, 583033272, 543073665, 468716946, 81589049, 573295824, 236836322, 507657707, 337665054, 118688975, 829969275, 753055263, 498802642, 199171788, 549863309, 254384291, 153530620, 418789160, 927313984, 238331378, 424935219, 902316678, 495222809, 229471851, 378026205, 464217119, 801581009, 130479389, 767157009, 774403995, 637281114, 493257789, 204871255, 301915766, 677889777, 748407210, 811275181, 70395693, 670233365, 36237643, 43601191, 735804133, 544535916, 844762402, 986068938, 139938271, 133994273, 70957955, 87815522, 944270058, 65628194, 602793543, 411346059, 477739472, 262570885, 149034197, 768689248, 477286635, 246924545, 758606531, 614265782, 172834893, 203902236, 530807736, 710516721, 614376769, 513669671, 564838564, 948384349, 576197673, 756807006, 203467953, 482131019, 410651561, 8075234, 542435180, 861894166, 354921318, 849911051, 374965441, 656504971, 673398195, 321603851, 508559559, 666425310, 139473879, 725260578, 646527600, 71559376, 485798556, 494517224, 70570882, 881080110, 145830712, 45584510, 760141449, 58086270, 989161278, 91913872, 455414313, 607947484, 443697201, 473253286, 190792892, 539988137, 272312561, 120213283, 667039206, 252227644, 454622880, 230093467, 670861284, 335977983, 606867754, 942341353, 119138127, 275792218, 872423222, 256767769, 688869188, 412830432, 666061505, 34056885, 486508402, 304245646, 520425309, 297965032, 902342160, 279750017, 414268144, 373504707, 352536494, 897795358, 421593790, 497149101, 457245073, 311106536, 209627416, 974667934, 857451410, 518944075, 704347711, 686308345, 452117020, 630884991, 697920509, 889413515, 86325168, 311152926, 12944262, 903718354, 373581411, 907056144, 224419446, 571503820, 416816088, 500105118, 524915246, 860498701, 637806023, 842035640, 150885990, 845814940, 133191617, 975576855, 140279040, 82681598, 55666894, 899066753, 84925764, 813390881, 653654736, 383555701, 243973356, 785888732, 898368549, 676698366, 409545517, 127776642, 170942373, 110613328, 907575394, 57725516, 578796935, 898879104, 719387965, 848199954, 810694395, 485586935, 194697880, 103261032, 388608624, 212448228, 758319212, 320238790, 207418497, 116782895, 712535663, 608991064, 785525144, 640712525, 290880051, 204774784, 745379105, 946507383, 897881131, 95134397, 839869677, 199605242, 831197201, 952372187, 758287260, 164261043, 462119008, 917235640, 801565288, 479658551, 291295002, 841441181, 77370219, 80451679, 820806338, 928390924, 605768067, 956162233, 472247286, 88726465, 113520311, 584596704, 285164432, 158223781, 371161392, 583068369, 96203622, 344386584, 493822891, 980160473, 207899488, 676897580, 981979477, 110359846, 354663452, 795504923, 583125272, 581970434, 148533286, 988869933, 430275343, 924061921, 79353698, 708120443, 34428812, 40783187, 758991760, 873834321, 824270967, 435256467, 115677896, 89558488, 917227465, 993511910, 654309058, 682174716, 594488997, 131607160, 950561348, 527327559, 149032197, 2722355, 512817369, 897582713, 536888657, 768280450, 736861636, 851400453, 668458582, 742990947, 450713365, 690386373, 560704577, 761497608, 98764977, 967549766, 691733464, 11369445, 956105927, 633021371, 842789701, 615377050, 337044466, 10340756, 951254477, 446625120, 534348725, 244816494, 589392264, 778821682, 47972684, 936991886, 131451834, 959074307, 897009421, 636348630, 45787785, 796612757, 420498906, 621931126, 939646302, 945877640, 704013299, 836059618, 157902250, 12137207, 917175178, 645928709, 689195401, 749082265, 830288681, 210856714, 21876957, 773711408, 2160241, 582583932, 576772702, 312088390, 717371973, 250569050, 87009367, 415718718, 689396212, 78261207, 586827105, 691946546, 460254495, 969657205, 827075437, 523426374, 830150103, 677574592, 746880962, 133790703, 500979678, 243682379, 68807879, 276258182, 282271171, 145450917, 461967913, 410782807, 9997560, 759041342, 451813440, 418333589, 329220693, 370380393, 665109197, 457808869, 828104299, 974490211, 29049982, 329288650, 395289146, 392539004, 174502709, 577613442, 895109517, 75277104, 297907604, 130809399, 340628735, 437101900, 619523178, 712921322, 815166196, 321130095, 668107469, 216326609, 857094090, 575685758, 747966894, 539800968, 70190863, 511042315, 147078166, 455830025, 27134580, 907253912, 764659204, 571286601, 318663285, 315301684, 171722844, 398651801, 260985793, 434898432, 916090203, 909161211, 594754113, 620026481, 241919805, 622058598, 671332560, 360924856, 328204549, 840070920, 862153014, 970563959, 858278262, 873267813, 718861951, 417000171, 887921966, 456637430, 948217321, 734977215, 525207712, 244170579, 396813836, 34742954, 500523373, 847983383, 85164499, 940979703, 584348100, 822897974, 707251941, 704031467, 974411837, 44515729, 445208519, 422971647, 338291197, 809369816, 942266851, 771209737, 111984565, 773787912, 67870169, 58724598, 691861919, 235108551, 772555639, 138875457, 230002801, 925306119, 309320776, 402847394, 176931448, 403379594, 999075680, 514530717, 528489616, 763515118, 297519964, 476860890, 267976428, 973237854, 671161092, 120302790, 128300636, 162891793, 873091755, 553782187, 32923232, 365872215, 435257964, 504098887, 945516462, 190992407, 296729058, 350414400, 303132348, 932166574, 53207399, 969965802, 382237064, 244346859, 359648425, 41797209, 934790097, 261443606, 484209773, 771447287, 989781717, 726556473, 999104715, 438710144, 321829015, 406220601, 648721877, 254237969, 65014417, 7415832, 939850242, 613061069, 907366704, 616698690, 600726324, 844645737, 886477842, 863229716, 254598129, 99040456, 723959456, 922624637, 147799631, 484665906, 356550204, 983563017, 758122872, 866198363, 375809858, 556139810, 834491346, 410248745, 931403479, 490467639, 554659450, 897856179, 739214920, 161500438, 283151294, 892067565, 131783173, 604190423, 891836579, 650389206, 349474614, 359297948, 467261265, 839275372, 951096686, 3618722, 978909775, 700723532, 892681586, 340320558, 365491991, 220058940, 666772318, 39511707, 750257253, 668850299, 32913987, 975794017, 922629816, 349520006, 701146330, 315372714, 118661482, 907868479, 747236776, 47913721, 747499008, 425394755, 924349351, 973040113, 412260701, 312818803, 158073712, 208107491, 328555737, 325407118, 836910890, 895921453, 549993768, 373119081, 726802565, 490589828, 758064638, 779431824, 850848033, 446942668, 202185650, 334450820, 745591594, 167343711, 114800147, 792606757, 408362842, 8275247, 753731054, 422438491, 381891911, 400984128, 524481208, 57773056, 683163894, 571479950, 235112092, 152127344, 97092228, 439909624, 333760915, 977902177, 861867260, 666752643, 942837155, 738359525, 523645912, 391600118, 444799705, 445698445, 634914783, 220027628, 708584818, 160975257, 484872522, 321462316, 433918545, 773258017, 964607727, 174660043, 570120687, 653935897, 244346789, 355714095, 783655287, 110402401, 743463181, 783110991, 102109035, 803604025, 55598292, 252075884, 387655319, 431384653, 795830605, 18371316, 561401438, 721974197, 114951709, 307683925, 272091573, 923769490, 473232910, 529901166, 962744357, 208041383, 772820073, 38924308, 416999242, 317930293, 368798422, 661204508, 71615221, 440506677, 28658788, 582591679, 295708085, 79872400, 453580063, 674704917, 752482745, 936620702, 763009656, 150904461, 316884143, 65003366, 17757695, 883204543, 870548686, 210816309, 68159514, 941087745, 943784067, 508947193, 822170877, 95224195, 473499561, 763563129, 123621955, 691346549, 147905724, 750579535, 326704800, 108508276, 598368341, 159872989, 819389483, 582005783, 365930006, 231482203, 774918057, 188782617, 972744542, 542985121, 980578995, 106753758, 230408583, 450315597, 734005159, 824775738, 664240161, 919813251, 870439061, 131546678, 717594900, 393935891, 323152376, 951206089, 342153812, 564440003, 305242461, 681717990, 508319647, 43248030, 357762160, 392296333, 658524714, 310008709, 899819862, 759846170, 174734585, 945980858, 614667479, 692441556, 492486077, 741100596, 87423365, 920010658, 191932439, 319112111, 744253714, 233566239, 371466185, 833059978, 837786401, 213001560, 890978300, 602925497, 537077284, 318169276, 703638730, 113388369, 327031614, 109616158, 518763281, 996938235, 541672322, 892108842, 530623004, 287427600, 91136705, 322843887, 932443835, 896854247, 553968266, 574014113, 200506112, 31368682, 203384892, 914462254, 461288372, 661680098, 557388811, 331052462, 195184116, 604472224, 292709557, 256938315, 331300418, 544890368, 887095271, 439087278, 568073466, 973742352, 126514013, 591989927, 295182847, 246378620, 824495449, 384896537, 282204798, 711054013, 815652987, 182740342, 537606479, 204652739, 109295182, 685626696, 428968117, 314993047, 997881891, 935030561, 441057273, 4353999, 986116423, 436237489, 994008535, 765275720, 152583328, 973121224, 861895335, 679716567, 267568710, 826367153, 498133032, 104824745, 809900454, 604052174, 647251685, 469978089, 343636177, 993938230, 277103936, 755134612, 194765050, 522870822, 9525929, 453305080, 705532921, 788485133, 654223745, 240893473, 433368860, 396151139, 876287545, 942016004, 394400976, 183139770, 753439935, 16482884, 74153928, 105673088, 131274640, 931694829, 536944066, 531676448, 525433121, 538687978, 302733709, 385252157, 655585847, 349116304, 640856465, 714351334, 180059136, 229734664, 875477147, 469158939, 334520211, 706095306, 576960779, 612414569, 706412438, 782438352, 893949503, 49116056, 550270449, 167631187, 697446117, 559953143, 724260299, 206241044, 465177151, 570167383, 315518577, 996344793, 520403556, 557066833, 98848892, 321195504, 971639911, 934958853, 393689587, 387592688, 956746161, 734055765, 449070542, 406847364, 422924355, 39836533, 388598133, 293266517, 335387816, 728694242, 47830415, 452991846, 638177062, 886640939, 202323072, 489195779, 472310824, 47825640, 408019857, 211507981, 889089313, 892640149, 624189735, 437064264, 352937136, 853713602, 6067973, 785197831, 773881007, 867265480, 4956879, 596633406, 780207028, 748228620, 898302151, 460979363, 228769532, 90321207, 37352606, 8960766, 176494791, 213376174, 23814436, 229889863, 512672198, 437684568, 252998119, 113051724, 122697921, 897395992, 261421594, 357358272, 508851149, 388019548, 752197510, 927176796, 147305254, 504013831, 299110426, 855718982, 174679512, 948426736, 308682504, 758088227, 388759491, 39233858, 870257119, 631716892, 875762971, 961337489, 275336469, 567491037, 70837343, 423185407, 808657161, 283442286, 188018029, 531029166, 616706714, 19525019, 901426336, 650671043, 159072103, 578395691, 913972117, 713326385, 424410997, 442579801, 444632696, 612580972, 547212086, 935533347, 708473952, 227550807, 185371338, 390550725, 885709273, 162554710, 236329027, 737727317, 292515306, 754737813, 576986482, 368191796, 674146645, 629861908, 221241874, 419138508, 865992131, 470210619, 388968498, 117441066, 663599400, 440054224, 317997809, 847999017, 60996199, 872942093, 758308133, 939793521, 841522295, 975926622, 357940627, 142623708, 596234994, 18583713, 463502293, 356463841, 432022553, 662876960, 499701618, 842266814, 77325287, 976888172, 35662175, 384624082, 54677330, 896748893, 812531415, 304982948, 299773502, 180910260, 84737821, 266748056, 351269052, 258959313, 269077203, 516661597, 675065566, 941948350, 845239224, 706257059, 389346998, 373900824, 143552267, 916697086, 965307886, 514298947, 672208212, 644662089, 556539008, 974107352, 213882084, 19516788, 104788722, 935197979, 655462594, 861656211, 46853438, 462526007, 40434493, 187907463, 792235940, 268196122, 221134340, 303619783, 107932346, 562464196, 394815099, 962935155, 487984872, 640006630, 378786662, 304058729, 987348000, 380627871, 173849265, 878860841, 771259305, 908390158, 994368444, 356609090, 808012215, 805162786, 244571652, 574003351, 471362130, 770732387, 851832213, 492118381, 396068109, 645269811, 953974643, 433427989, 403252528, 363297296, 144538220, 573166509, 772899924, 318677830, 562559350, 28648918, 924578676, 570448645, 192628492, 489192013, 709865314, 331441340, 131879515, 25536171, 713295258, 659947021, 615369000, 554292120, 18751696, 472882353, 271534333, 265268256, 58458586, 105392515, 694419840, 832379790, 903173330, 272584733, 121136076, 971535805, 608776376, 631015627, 738969536, 151669569, 481186921, 974608718, 536103525, 113424074, 352035245, 572293276, 622977803, 612798337, 913667652, 896074838, 900986348, 10057748, 425048234, 831569974, 164931289, 869332833, 390461801, 119287882, 948612153, 835054941, 64873963, 687448147, 624228437, 644532673, 402947762, 906052358, 346258454, 243148458, 793263317, 841958256, 116453136, 121191887, 140556429, 4369793, 886273109, 354040573, 568974011, 189182379, 159605555, 703511977, 9931825, 292307826, 813415209, 568236278, 873330311, 414456726, 898411775, 320026589, 655576635, 330224625, 379642089, 124549144, 566740044, 424176299, 451978714, 899312974, 147693843, 11293260, 903161519, 54329462, 97761597, 910290025, 488269707, 974943903, 654561394, 66789580, 185836296, 671685132, 202424624, 98712859, 656528823, 349734464, 616762264, 348232843, 113961305, 699801092, 176099971, 963153669, 287175030, 624479822, 989632914, 77246486, 660526733, 400321950, 440471877, 118187333, 17093199, 358701044, 305134918, 482666284, 656700235, 257202705, 61749441, 684565902, 853324820, 952924805, 759079919, 447728929, 704796880, 138347922, 128442580, 848513077, 181842935, 936335087, 134225379, 304807785, 802256003, 604343865, 968659146, 801616700, 787992113, 425994249, 933219240, 830613508, 384577294, 219398608, 663274838, 367959059, 751585434, 374451877, 711650619, 380979143, 796039877, 261936184, 849421496, 561652520, 146515690, 18966445, 898417520, 953464208, 378947621, 202188167, 888873533, 504328276, 843880531, 795814922, 494802316, 524341068, 870423704, 432494876, 842614832, 443855379, 306557581, 528800162, 732194326, 887304987, 332627822, 233189462, 504981122, 51043141, 370655737, 760647539, 654183225, 543312427, 436562325, 678034729, 490818356, 304272740, 594795867, 952458368, 463662700, 410880627, 844398133, 891532866, 149505404, 819410272, 280422395, 119417016, 786445639, 409925014, 814498446, 506342168, 896590252, 156561716, 718291297, 768622089, 474118039, 731459452, 843034720, 290700353, 629020904, 613879173, 710953464, 256823005, 388590875, 559425222, 582365718, 622038039, 508872286, 790380106, 539376522, 234445354, 355752633, 574341270, 792483628, 74469735, 969077063, 802599764, 565480416, 272038720, 438083990, 669040030, 380589503, 41209055, 886071850, 432083638, 22727062, 845724656, 643704692, 844898512, 384220220, 285447924, 4581843, 737871565, 646129020, 383525703, 96912955, 860501922, 504658773, 72470098, 73121062, 907485123, 537352080, 136447333, 45796825, 377346461, 496868167, 339949169, 616379205, 973383965, 292405637, 252247048, 374986262, 514647041, 399905614, 358416417, 765942818, 943953522, 4498282, 741498589, 747136108, 786765548, 111312900, 954793679, 185355380, 370175835, 587557473, 978160583, 888214355, 991614966, 121732191, 557029992, 976594545, 658421606, 207983658, 159822950, 734973550, 370256822, 628924226, 157495767, 828427629, 745894413, 671258756, 75945124, 695212356, 533366192, 869140298, 826855139, 378475419, 238501410, 478038807, 4994280, 53132738, 284723855, 726357016, 32025022, 424450753, 749368249, 275261145, 62201615, 319919194, 400241431, 670589381, 663528021, 978605192, 847423944, 231328792, 487460855, 116972207, 216081711, 560612657, 750648123, 511879252, 478800767, 245837621, 443807583, 558051246, 403293063, 677078556, 568598802, 795677368, 250736866, 767634841, 844340540, 516489996, 657385413, 904593322, 572775206, 317272459, 525961366, 384875101, 26942995, 380425300, 926918615, 260054523, 29307227, 902738656, 677701701, 495538256, 456393878, 882205921, 762758406, 33086750, 600257622, 160741517, 267120963, 452037721, 961995150, 490012313, 231610223, 662918837, 388870725, 539804678, 838374663, 102637032, 178519889, 304645570, 304811942, 718473640, 936119820, 402905607, 772924031, 92172179, 965284760, 289628208, 360104078, 580074665, 29769301, 831118407, 825456384, 506597333, 862822554, 622079035, 478571775, 739483512, 720483455, 388219479, 177790139, 579345556, 382665303, 551567275, 89669640, 162407259, 384436686, 462628460, 486745427, 369067462, 563926906, 501939065, 960127551, 444901733, 403088373, 678464889, 319988631, 569898486, 913165351, 478794965, 262898915, 774209864, 480797472, 914837248, 65985007, 45334999, 843201860, 28801187, 287147857, 957408941, 682861006, 584734396, 403167998, 984362890, 500257721, 856594256, 528244865, 707771667, 980330473, 895780067, 259593816, 838878176, 370105724, 288103794, 191702596, 494661117, 20984306, 568021285, 965006156, 181689451, 935848212, 132594204, 922827728, 69205709, 288507984, 513473106, 486202606, 454899819, 26712989, 453310031, 581797927, 411141410, 846737280, 116186094, 326106936, 809216551, 7904790, 979453540, 623208614, 276850322, 601119332, 906540098, 326844237, 753465612, 552654419, 986772339, 19625893, 706199313, 415911701, 788213185, 308397603, 988533951, 431347944, 412465514, 782755244, 603663614, 476126821, 61695130, 981233142, 77947254, 274331433, 52418929, 904936134, 501957264, 681624643, 235282521, 804211255, 917569771, 404213800, 87393984, 499260173, 151875047, 725077696, 597278976, 361567274, 803133059, 805938421, 34131400, 980010717, 658453079, 921693223, 757242902, 124392504, 887449541, 997215094, 503504879, 712282694, 167788940, 385176814, 148560816, 460435999, 17770685, 638683699, 894985418, 202167138, 166771798, 90833795, 324801899, 135810230, 534063419, 528883442, 5418578, 297833925, 866775619, 40397360, 960978892, 592548338, 847356886, 1555518, 870467780, 568670938, 21484019, 767019123, 831880808, 419743778, 401709780, 585321209, 602328741, 239667686, 678774414, 871766697, 982157094, 723025623, 185987815, 16794967, 231875470, 19535012, 29551196, 78683048, 952378376, 650248590, 340006463, 561579805, 725312193, 609386139, 330947161, 353651511, 988732394, 634512269, 766168487, 928516329, 301920883, 638821212, 869863, 253725908, 550236729, 536538077, 666068409, 162734673, 479617393, 894192806, 857434344, 225065026, 805479574, 280448059, 249020295, 985982865, 242963396, 629803986, 801767321, 548320256, 869596227, 796054547, 42785693, 299133898, 119564049, 918500916, 785582245, 876392600, 513419541, 629987577, 251957943, 4203079, 103642626, 567342608, 207104062, 433467317, 647245271, 556792645, 135781044, 518632861, 915596580, 151352267, 326013750, 908295636, 582827035, 843619929, 675474129, 98637462, 807432072, 662029376, 864930166, 896162238, 506280992, 710334662, 942790440, 517929066, 565707417, 351745282, 73574527, 895905491, 60747584, 445719563, 627423167, 121106616, 601970108, 336438994, 511046097, 108210676, 481577641, 668988150, 683466633, 100891880, 166829156, 869555218, 633687078, 535882477, 548901998, 189831315, 190574456, 321445186, 33051332, 774725834, 40336098, 77230220, 902162081, 23629649, 715456076, 225491767, 99325036, 515950352, 182539137, 200681118, 863600358, 755525690, 843693099, 180067637, 880038208, 57447722, 807816398, 559277845, 651917444, 831644488, 461353630, 384181062, 790869964, 994573122, 388242985, 547327588, 708897084, 837304021, 180783056, 949935527, 368448583, 890780377, 199950205, 110880794, 585301377, 955743462, 574937080, 118264911, 821939593, 507112373, 997364290, 39638195, 205248970, 119094607, 965322868, 914759182, 785746383, 345804065, 226535253, 41039728, 527762043, 935716369, 358605920, 815122306, 445216435, 46016383, 693444718, 350551322, 674944064, 75971740, 696828850, 157531252, 482801380, 54318649, 771995061, 823650335, 46647383, 205195520, 221932471, 901025882, 940460722, 600110429, 213010087, 901901108, 476422036, 933212644, 851278444, 622715957, 885498355, 404570115, 888745486, 302993661, 693954869, 798918378, 684022814, 142681512, 559204485, 361172828, 807713438, 209664299, 2220957, 164515215, 500243067, 35655138, 606010734, 816529147, 966521020, 803582292, 812792643, 612269348, 474274598, 684501887, 153880867, 508936069, 979811141, 91312745, 456661887, 229087949, 551412728, 875847185, 797468147, 29696038, 558668121, 569479686, 370353401, 128187570, 141789601, 149733650, 424739900, 312920971, 670690512, 332142418, 499326763, 646697894, 60861033, 982017679, 481800619, 988726053, 260520863, 971024431, 706534019, 383334347, 810679944, 959556974, 322151962, 819022877, 240738690, 928425654, 542829222, 614484421, 643827079, 557200418, 195448446, 635076710, 504563405, 526122381, 643244062, 157672403, 397865906, 84674857, 874310539, 254605353, 520116039, 22104821, 767281997, 56964284, 369095497, 910326852, 345225785, 469516968, 891377978, 218069747, 705638496, 45893085, 434754547, 50072380, 533734857, 466624144, 772134005, 977712198, 791441087, 135977581, 491244891, 8905165, 758285706, 119017272, 205403768, 191656029, 264763799, 403788431, 818893659, 877463444, 220681599, 244201127, 695916762, 254991858, 18767492, 305147005, 282369903, 35790819, 460788517, 142379579, 3826478, 772600802, 576688051, 641427286, 6336143, 86567583, 267091593, 883827807, 446248101, 565610354, 489409297, 399570192, 145536236, 68273487, 350674863, 416738430, 269015064, 973484181, 486412585, 55745012, 656413820, 855935579, 50768655, 954650468, 581700177, 81142000, 393261609, 221313720, 105172558, 955082278, 656814704, 796936512, 569119682, 916465700, 73138269, 575994604, 122670924, 283769295, 91672758, 8836646, 798111447, 869494472, 10081545, 345971998, 151558007, 546384561, 765998603, 148259907, 294175221, 764537384, 252651829, 164921696, 475761936, 704962543, 881172678, 510046750, 825081809, 255386896, 883413581, 11672981, 293249102, 436663516, 590747811, 655144299, 465414875, 350872517, 413849935, 256617155, 854609058, 473208340, 904741096, 24451213, 664705897, 641804971, 200816220, 101955852, 809460348, 527040452, 995378424, 226976910, 625670396, 226604231, 963101593, 598659826, 757800005, 960267270, 142736970, 764276006, 379279245, 931291005, 355575411, 573230158, 355203734, 911354696, 152193850, 908930328, 77490475, 927651905, 840557449, 335142359, 855089445, 663067987, 349630148, 681992294, 841778835, 36024968, 127827073, 851181847, 510956210, 484277277, 726570974, 440210209, 770811001, 701819816, 708415798, 329029125, 438184284, 903222420, 488018929, 173058245, 617109011, 703946029, 650965030, 675170337, 124587861, 100500242, 713504201, 660553188, 866130313, 602835135, 565348498, 240021297, 249358644, 803466080, 702118784, 12021438, 386867951, 607232630, 892617854, 188452174, 361914106, 239468732, 327533253, 725785123, 916708655, 954664314, 658029174, 490099756, 753004095, 940112358, 856083429, 875991579, 879918272, 992188119, 744571559, 480591859, 49930022, 696933384, 415570059, 791113918, 345605749, 887494816, 762419054, 247297058, 435047355, 984149638, 647748008, 654051106, 891730422, 641073991, 995232890, 968340265, 644412013, 869206568, 824157175, 876280817, 666470387, 617236728, 912974728, 631732778, 752985481, 408914752, 891439896, 812401283, 372237824, 765251210, 748114865, 923757928, 641958286, 118300761, 28837725, 826808481, 391011768, 697837032, 877585709, 96669488, 351930878, 62124924, 427660118, 772318449, 150639371, 614075926, 211204966, 164635391, 524322634, 252354623, 268204551, 168781852, 351338206, 297818516, 956860163, 160103377, 115005732, 95228405, 334320417, 346889324, 705711797, 763131388, 456788898, 930866840, 522097137, 407628698, 549416929, 38568009, 675177355, 288034371, 186614316, 672863454, 752020138, 422470234, 568048671, 404023313, 385804581, 442624771, 156266992, 442190102, 979874130, 219938693, 570328058, 797170644, 685194615, 222490790, 746301825, 28561130, 329441498, 677422605, 715577752, 330925442, 787517815, 486689726, 62935579, 301088322, 297559764, 75424756, 963793789, 343693807, 116125458, 811117538, 255108074, 270916867, 870987276, 180345171, 178160203, 547330966, 740457929, 327878842, 804810298, 12592611, 731203452, 892071263, 679176462, 818076080, 183120509, 507627471, 54114337, 657757100, 109506958, 956106753, 701585778, 642588361, 250484878, 444395188, 135862881, 862571231, 140536973, 534381602, 375466866, 734282985, 670800566, 378072047, 469692493, 931514100, 683560260, 605630788, 878768880, 581089872, 671711794, 683158797, 700315545, 792433778, 237732782, 630164771, 70483599, 140802674, 405384279, 542288502, 748884049, 751357403, 141954625, 450863021, 252657036, 353740427, 752926802, 442322355, 579535335, 406263693, 898475977, 891832837, 592252750, 190545028, 801566452, 687397329, 215894673, 507575640, 288485930, 640107226, 613186569, 924047538, 66624226, 878186500, 709112790, 622122539, 331384401, 12058216, 485463591, 462932653, 325484648, 621809756, 471872639, 540096343, 958473580, 544997776, 114173477, 316433802, 8662414, 845831467, 264377298, 14470438, 846556828, 671698635, 579468539, 639320030, 240982578, 842355844, 454172488, 552580382, 283083808, 668981564, 293101323, 895602262, 4813355, 207530083, 301431738, 780889889, 408393307, 120228756, 668954804, 986865104, 629747081, 606321137, 402791225, 283955189, 35564436, 602484554, 338622121, 784204193, 148597861, 227406318, 440055844, 566311735, 128167847, 829151432, 689542755, 607337137, 733302732, 221522665, 258835184, 596316179, 624973760, 637511818, 303314679, 169162819, 429147635, 826788001, 672694596, 578680350, 490432063, 935521734, 91428443, 882227790, 862736242, 452919606, 451043172, 251386733, 961442264, 518224035, 801237848, 536428097, 248262660, 663057929, 433065248, 634870000, 662810663, 399879591, 61079136, 512116799, 609803265, 313724657, 217891194, 482282523, 669683161, 199096124, 22817740, 499329399, 579604923, 936700695, 769107124, 165509763, 790219959, 912946570, 319361873, 452192714, 754148004, 204308276, 888335813, 559691923, 492914699, 931770357, 709677162, 365854508, 66616040, 694790830, 657173073, 619949657, 395264561, 413561727, 100024944, 218651029, 469423616, 755610858, 106747916, 950301288, 690779466, 315074253, 206665365, 283341926, 927871722, 724015964, 959182210, 521556122, 984460220, 157790948, 448595300, 864121929, 987274867, 256252463, 314734973, 805174901, 727619569, 930393156, 200695991, 231998820, 20910271, 461177505, 116744704, 337765102, 622035637, 267798070, 549051367, 2388137, 955477512, 856183238, 898569242, 449087121, 530866563, 998444564, 535322698, 46444835, 801824231, 757389454, 168017261, 450622813, 219555821, 914476766, 339943366, 342413253, 231281861, 481661674, 580671010, 492172316, 690231827, 264792898, 15584009, 738881519, 773870215, 971683733, 931390049, 237667396, 705422211, 373417233, 165140694, 369189177, 826372183, 231605954, 363748446, 639717562, 409049362, 713980947, 280334434, 981392349, 399777582, 755829009, 641109007, 533134352, 569535481, 21682908, 844939003, 685828737, 158258779, 906105379, 885163131, 817629887, 390664337, 559736932, 857407745, 895791430, 61644251, 652252369, 306368789, 26658764, 152487549, 269956414, 961769444, 32508691, 6334457, 964158821, 981002465, 62818981, 154012940, 127527378, 511067661, 785266628, 707148671, 151393746, 469660087, 106140478, 24355594, 773163319, 870355633, 3747128, 407481579, 664920250, 203026174, 75490644, 744377430, 888083312, 427003259, 848105885, 779205612, 760196905, 91655303, 253306598, 670802617, 798512115, 488690673, 912651182, 33806091, 443556127, 408657410, 693626500, 603396463, 968067468, 856171867, 438156029, 465668780, 543736088, 58210182, 507845865, 543139986, 288282290, 547218313, 657330476, 314357582, 172465593, 131861636, 120498931, 831030663, 706244999, 784450012, 405247240, 905901697, 988475100, 592772849, 152048730, 496571747, 10729427, 479220090, 886749715, 236584527, 302307453, 857547289, 790314590, 662877952, 928773332, 563923659, 444695288, 953546734, 440431494, 666250429, 525167525, 499158668, 804968843, 788445114, 859279639, 620293519, 273538467, 768978503, 119658213, 384082735, 380183391, 474086152, 148778391, 413767607, 331208031, 686466174, 288280417, 887150731, 261089601, 128966417, 335234238, 739921472, 755510742, 851145826, 846854168, 970589759, 210592544, 863516323, 511389397, 498676806, 485632885, 310488689, 496308739, 446766243, 313392030, 683165700, 458634852, 985195469, 571160578, 634717501, 927139864, 660572169, 846223365, 447562542, 197594910, 86064939, 548028712, 867946698, 658662840, 184888848, 512950751, 196554925, 415719629, 152853144, 712516794, 858566445, 700068655, 138560952, 854295280, 587268778, 423111961, 505813685, 782671381, 813274411, 896266162, 634457289, 610099420, 391868110, 812312549, 385523785, 200203568, 352125688, 636215684, 773739372, 501155314, 851827232, 571918818, 25742386, 675469179, 563816638, 163858581, 100057886, 243000712, 354690779, 248578498, 100645915, 78989658, 83071524, 109218658, 760013953, 946950680, 944023293, 258156395, 92495178, 743732570, 988132844, 926826307, 638980712, 38521659, 547286674, 571530061, 972452170, 766209055, 628531330, 790825436, 732898574, 740988095, 640600812, 172711939, 702643911, 507923808, 468802022, 172421986, 319890421, 867851747, 173861881, 262384081, 886671671, 610973456, 667355424, 974054228, 375074980, 564122415, 231128793, 72554370, 535459111, 474381993, 182981706, 517319067, 509513506, 494611742, 4897063, 699491899, 129399804, 999313432, 962822023, 200754663, 899941705, 901370838, 722703112, 637560343, 990874954, 456490914, 449768343, 879869079, 163189837, 909356788, 239378938, 698804488, 901814188, 214164624, 371313036, 959244468, 878798600, 838638448, 117832645, 753168762, 677002913, 380091873, 674844527, 727246001, 274227621, 150490961, 990518587, 974003486, 266181675, 282301597, 972167040, 235131399, 303099385, 496369837, 156910344, 446693346, 169837278, 278740440, 120476105, 883493641, 255982150, 876774726, 931733168, 895299922, 111869257, 265661307, 526368643, 908827021, 768010066, 961656742, 345715707, 996053311, 940050577, 451100326, 199538628, 422028476, 54620178, 446049680, 24224780, 212456562, 839562968, 807229590, 799398765, 857819575, 799093093, 158422129, 108036875, 188881270, 942431236, 897907739, 527430463, 288042614, 507451625, 195292203, 182034877, 283705774, 941855340, 852650717, 146287004, 546829202, 736949755, 848882374, 237263872, 237531841, 457759661, 562460584, 205827234, 660216366, 5876517, 509207609, 616995849, 614927607, 463436470, 597962170, 45410610, 995574661, 290368112, 552981521, 461600589, 124387933, 269481951, 772732477, 564704342, 507493304, 253602786, 79019496, 281895622, 193900081, 53028975, 967930747, 589330673, 131089561, 904854366, 591395509, 519102039, 157978136, 704842741, 660831025, 242312781, 995605429, 808039878, 7599648, 208419789, 895122834, 777804599, 675799176, 4969659, 466556598, 547403399, 6800609, 336795970, 56611159, 796274480, 462472734, 942953663, 775263954, 984364692, 737444285, 977402653, 789013026, 775065362, 421780275, 980222510, 682764376, 150018198, 686630403, 875195119, 492340963, 265431490, 868035037, 835675657, 895631763, 352488077, 149537863, 12955227, 970294698, 535870627, 231497858, 612751675, 188746129, 919206881, 80513552, 570775999, 409410748, 667027650, 981402501, 372954447, 571672319, 85518137, 470088602, 10641316, 368628823, 16200275, 856510839, 931277696, 60248852, 572844943, 561732605, 936488166, 762174959, 283482872, 142568518, 343420712, 79899936, 700895578, 454618924, 618947151, 810135880, 26145878, 290952596, 317714509, 10358530, 517443353, 928069211, 243237140, 756109419, 630771020, 792204435, 600129567, 933392418, 309929763, 718681869, 209558404, 414346032, 845235605, 451688597, 590039639, 225364932, 868822505, 562043201, 117553030, 453207679, 881484264, 236598664, 893583022, 606421640, 778785360, 544451503, 235240939, 710694655, 353205797, 107913432, 543774486, 582138670, 635583512, 506917698, 203028967, 501643484, 710028233, 363656922, 73848638, 941450014, 836594971, 541953461, 985120451, 81792045, 614885093, 31190508, 661388997, 378063153, 222362426, 440922778, 583458319, 778989574, 389675147, 272327624, 357584148, 376691650, 129559305, 256007202, 111472662, 256685519, 159057007, 971637971, 51025795, 561444464, 84015802, 654993487, 182015179, 704791697, 23809205, 61515549, 475187587, 268766005, 383431515, 675516060, 505566653, 607547089, 998153221, 354921480, 129837825, 767458434, 220768027, 825317094, 416034834, 317386751, 134699936, 652542258, 903775459, 991987514, 409484773, 60380519, 774316886, 611776551, 168009533, 295245211, 173485485, 618512776, 173822021, 261306222, 322432117, 516745068, 841487040, 608726123, 750719132, 281848606, 879065244, 463836917, 10884985, 764728353, 639450782, 131494384, 653909997, 328840753, 779949934, 49481494, 677930328, 733172154, 560094917, 365333213, 663572332, 914132032, 182281371, 731327710, 865935225, 364083380, 709981690, 292386635, 34426291, 757838178, 581828752, 206598244, 7610163, 17503622, 199029497, 271253890, 774298741, 672332343, 281576999, 139250078, 373206626, 127152059, 540760969, 786049200, 1519567, 262843266, 254311643, 893976612, 325888497, 388257927, 381866694, 44616252, 533342122, 126616385, 428290997, 656348225, 839706703, 140225250, 776414387, 5585369, 603872922, 930943271, 88745964, 803208724, 186303258, 48742589, 576898900, 571841658, 786517719, 108212747, 81457808, 876632901, 860384833, 941688372, 569021731, 149715112, 352671952, 712511884, 326807220, 347586542, 533738626, 448380399, 74427558, 808796802, 22239895, 564733321, 86765650, 707340043, 280205772, 363644332, 385105936, 975914745, 154890956, 917663344, 135706182, 512211962, 492333532, 711583469, 306230660, 231745094, 242927153, 400571572, 479157853, 12493947, 961848809, 631521147, 260077021, 972167508, 668303273, 590741108, 927320855, 707316102, 290285216, 562117649, 711678647, 204317108, 108119281, 926449912, 29062264, 725932470, 949659538, 877569940, 375181432, 463267263, 363056520, 679759736, 121435625, 246799508, 669340566, 538810977, 306554737, 253144594, 795522177, 50372655, 223768231, 949512332, 821304193, 966460199, 578516795, 796621954, 972661636, 765349915, 676762072, 103816652, 139450104, 486619174, 191472832, 60890087, 679830563, 575164020, 837976493, 195758697, 472046089, 774991289, 341631016, 212017104, 511732970, 329859088, 656930908, 160117272, 98495046, 626501224, 316013620, 893977108, 333934960, 367819380, 938350109, 995501121, 719857176, 430151380, 45686052, 53428336, 360812305, 505127177, 21533336, 723497633, 41336295, 517331646, 110666859, 735805309, 637549244, 576008193, 171012526, 995521287, 678471898, 433300543, 456993412, 45333492, 338074584, 108454846, 946637457, 566655824, 444851619, 770004731, 590527992, 329831278, 899215721, 691744857, 342323767, 583334479, 217839633, 680572771, 583806058, 426854024, 991463760, 315530042, 3913938, 204852870, 668207150, 164975995, 761618770, 640584119, 378462827, 171753637, 299727009, 852209928, 452870623, 942682863, 433191544, 473571336, 874051939, 765282733, 143881903, 417777563, 844866587, 492141878, 416800245, 25078759, 749181968, 748966612, 666550937, 438249682, 355995823, 773179235, 311334761, 928691412, 100708785, 884135793, 338266591, 467122858, 822645419, 813247111, 14879782, 188413542, 268442580, 547104173, 490328337, 989052803, 52096881, 370681143, 429705426, 9189120, 229223464, 529264284, 608626725, 808120390, 636226430, 429778900, 746587764, 27175542, 912310102, 717423387, 26237452, 996066465, 956174421, 184705179, 770960734, 971790063, 254812302, 240721654, 907655248, 729368194, 669295083, 869490044, 919283892, 100158327, 789158938, 975674178, 636734872, 472727144, 436118720, 687369217, 633730754, 84978723, 828216160, 792530015, 225778297, 188408595, 777436975, 341272909, 13092671, 994044427, 20974526, 426672291, 140293702, 712891415, 597637840, 421813799, 881848724, 993694452, 922937813, 152886100, 481906564, 747244962, 145770989, 412516565, 105969233, 784024866, 162250925, 418015540, 125547103, 236337926, 454160683, 102945238, 453180564, 589035943, 93796238, 474812029, 278924856, 114572044, 862793713, 551889684, 820843540, 105897919, 863191679, 817608931, 841528657, 395233466, 157437476, 132945006, 399927719, 654966331, 344893043, 875455676, 647293190, 76325574, 25411520, 186928820, 972607494, 385236299, 542052728, 793891288, 731067874, 808320406, 407087831, 19105987, 15495524, 595083548, 744036445, 246674508, 924340504, 534757679, 576097441, 525974073, 548817096, 708350740, 553508699, 87044237, 279100717, 906030297, 350063466, 614204558, 19246739, 11831662, 154849782, 187043054, 495334305, 95048459, 793512123, 510578650, 350798022, 856099026, 798468381, 455649803, 602533760, 610936216, 303585791, 589834693, 761905071, 903904692, 742279999, 170696339, 279424629, 476060064, 888095491, 192050070, 84142635, 626464706, 279077548, 58065529, 113702357, 656242511, 171440259, 668939809, 899947794, 804575974, 531464659, 866396337, 647867480, 922614254, 193061292, 647090655, 442994985, 812864332, 380915517, 733016226, 683244276, 699047713, 198840581, 725077937, 366031371, 639053940, 817938660, 378455836, 852902849, 60225041, 703806579, 170749223, 696647746, 875129828, 885222977, 683439174, 291447198, 287525287, 959434763, 996872855, 169441342, 614467745, 356962909, 244063030, 557343149, 355857953, 150661551, 948851345, 29698306, 326028964, 708336687, 107652271, 177546313, 684799865, 638406306, 196419888, 911746604, 340874785, 612900208, 855609897, 451903372, 881462907, 206127427, 229998355, 346917126, 694068970, 121633114, 741354165, 152935159, 484166457, 196531653, 619894567, 390712194, 344821207, 772250157, 263491712, 146287106, 865193633, 47371164, 556335327, 605213454, 168079108, 23060429, 704603889, 85177015, 366719725, 818907135, 122378211, 703798682, 328411040, 683158068, 489665260, 172915715, 71684679, 945383699, 920030102, 279977272, 54163555, 457756518, 118075789, 348803324, 601528285, 711650619, 119420506, 191899130, 438716898, 639527244, 645136884, 265075376, 922176578, 891006050, 567473580, 102061155, 840235902, 811145259, 636089505, 386029975, 998869729, 162873773, 348991673, 49637179, 225570860, 890937767, 88084600, 542833900, 458339028, 162587544, 773809302, 899579923, 332929066, 770136031, 418730503, 952830489, 221680398, 653805852, 697760781, 998075532, 571869827, 299590545, 501941095, 230437750, 515858494, 436251217, 431323955, 354149405, 480160156, 341410161, 249105471, 304620439, 147698371, 719292790, 477126636, 422108517, 330676475, 887316971, 490033984, 606919780, 373801273, 345174033, 784228086, 152396876, 648223286, 928411220, 261481730, 996228585, 553865360, 983667404, 943354259, 766121054, 60920616, 570291250, 562832031, 711643057, 646741085, 429179648, 845405466, 868932865, 213685978, 618782673, 46147872, 680347298, 768671587, 474118820, 871570096, 850207349, 890225268, 21975411, 468205185, 532370177, 322398059, 979427189, 368408284, 897357146, 712619859, 264062891, 513628272, 244637469, 338908968, 384576389, 958562677, 707789508, 253830005, 119623732, 580636375, 450138362, 951049246, 864552823, 526905486, 346056815, 227505520, 739579256, 328655604, 694647750, 93035742, 970956280, 599110152, 489614687, 253220215, 483834753, 853541464, 64819895, 491025962, 375846015, 608810189, 541845267, 574836617, 840495010, 57416689, 775700255, 213932135, 495092677, 572863042, 365019412, 887230762, 803744113, 363346409, 338361299, 624100128, 105844903, 140346667, 442584969, 242989970, 888763991, 282869829, 545002258, 625728729, 640623548, 368207580, 384401734, 456201992, 79964077, 178673941, 967345882, 714112795, 368958080, 872096350, 584264646, 233800405, 359281307, 405256054, 803315590, 929565069, 263415255, 947985265, 753204637, 575904934, 270590247, 293818423, 460675624, 153083546, 706102978, 536810763, 921519181, 115542993, 117972319, 430165879, 905026567, 889033577, 627894745, 999162063, 289151607, 575993992, 602044487, 575739554, 374800074, 853742089, 17696438, 856456879, 923021309, 944446022, 915564768, 414802849, 691675604, 283675551, 727557613, 548790640, 648014782, 483713699, 563747119, 73642924, 935760491, 16529363, 925453877, 238426343, 447760382, 613530313, 311695550, 959379696, 530605434, 934929149, 253603769, 427331977, 143714389, 620506994, 122306381, 855613096, 237628629, 893428467, 733217943, 687111275, 475490308, 786949123, 292310842, 470784713, 970667122, 613657461, 550068946, 329927758, 621581424, 964197548, 961755402, 138518147, 720468683, 364322468, 513699901, 953053497, 483097399, 252575178, 715262115, 924198454, 14202756, 323151032, 307740192, 679128964, 417424863, 418254686, 150089771, 731232550, 57915470, 289389066, 849051578, 288758271, 750622140, 906262607, 598845872, 419157074, 910958545, 437307376, 796859359, 910689645, 124121895, 977625773, 161859296, 868931214, 524749267, 191495816, 22828034, 693241399, 846412502, 720800051, 38345478, 22239635, 596445876, 993233257, 575146571, 292935050, 951756400, 207342876, 756816907, 890147733, 962438281, 88635936, 461112149, 288541210, 356713615, 18030775, 300585354, 404921150, 298756368, 643454680, 604509324, 280353550, 343382812, 644824944, 628528571, 796898361, 705625502, 348241584, 522971638, 940272105, 670030665, 622504408, 209633423, 829446576, 733724305, 14894230, 332404192, 764183346, 697936798, 836996598, 193429817, 805321524, 129774688, 152867419, 117270009, 116270730, 117139643, 515643885, 134167237, 899429301, 743846486, 744600807, 347219890, 307537067, 917631171, 85981471, 618737441, 202423707, 710405065, 827939943, 432067578, 539495006, 262131951, 252496944, 345784693, 236447727, 262682314, 353176975, 295532328, 592943438, 840152109, 844629580, 787669253, 760329907, 875736812, 30610988, 715521017, 890962779, 502154232, 651168504, 101205061, 500047281, 462411760, 847338160, 850378956, 552866732, 628781920, 591983596, 61596028, 75629339, 291843338, 899688657, 563158737, 368618987, 465314095, 211096072, 999967088, 957607158, 624558566, 393099126, 923712184, 538722309, 209291051, 833820368, 187648852, 588007414, 93789131, 134491654, 896624597, 278302996, 352212860, 222887368, 407041294, 395364959, 473592941, 919154164, 766873386, 887733147, 891045623, 466627342, 476636199, 555705674, 221525483, 167430190, 205397526, 338453757, 457177682, 984120762, 507269785, 714309866, 826892208, 955298543, 609340947, 208419625, 357825463, 153123096, 24550810, 237104917, 298945784, 300065436, 134875197, 206048146, 977579488, 248048864, 178230290, 325419049, 636194574, 200233705, 884312428, 469853719, 521244654, 43757586, 477800356, 131815190, 9614230, 125623341, 160204613, 723487045, 393429860, 506138861, 748050087, 216505622, 428745880, 439246633, 105122793, 360152691, 739398116, 703421232, 762710670, 4417631, 875725545, 671919113, 646075898, 417051068, 152729620, 827152007, 419992279, 274906062, 368805966, 578243597, 431701844, 540996826, 368503054, 100223834, 6925639, 743141532, 996743454, 695902999, 799972435, 646077527, 367027618, 684275681, 28111611, 707790299, 685875956, 188913153, 549609958, 490388077, 945957236, 447950510, 291655772, 198834480, 240207540, 56375478, 135863869, 943149081, 539646972, 686309760, 836040569, 355733037, 399272693, 665414869, 274836968, 430053169, 153002161, 310363854, 300394656, 316177227, 959585470, 329656715, 937787755, 501519571, 69604089, 770752234, 604575731, 203220648, 605030278, 17100666, 103316888, 116278407, 848868553, 466895933, 452479604, 658014087, 518548113, 785697004, 623718719, 911844408, 119916554, 289109913, 387393605, 366826161, 612856139, 387454134, 824823204, 148377151, 24454695, 796794540, 406969543, 478181644, 877997627, 537965862, 450502005, 530769405, 680094712, 626391642, 190621038, 572693169, 550322291, 752392934, 115769903, 474236550, 604659760, 596891387, 915964502, 168088390, 896487687, 345711288, 400778763, 201531907, 416556819, 704691152, 715057004, 350379569, 70462847, 360366358, 187692237, 236998184, 224780120, 515382569, 82313641, 100610642, 396804862, 687587314, 674809803, 240515064, 74628245, 88090338, 505331229, 772477834, 834663801, 612434551, 451217973, 288657377, 218544844, 338188426, 304417961, 14231615, 712809294, 116516621, 285351867, 403395180, 944326705, 480253888, 886586784, 982679369, 535862762, 40617365, 104969351, 659375448, 278843628, 412242163, 974950668, 980115132, 292049327, 713052852, 598654269, 37795526, 243754245, 454807965, 865082013, 53568663, 69480470, 776517001, 484528574, 760849623, 709451648, 720441103, 645073903, 998112091, 283866198, 276871890, 30472217, 177787664, 470895394, 273713889, 274537717, 822413671, 595361545, 875765540, 273220472, 302089729, 719203317, 882176885, 896698022, 389471897, 879478738, 454212763, 498852814, 512452185, 975874049, 605125368, 613225374, 88811777, 682164229, 830174441, 95002362, 172035520, 315347889, 742060259, 901871503, 756086464, 706816978, 470646800, 681319058, 771198083, 707991185, 411575008, 522778711, 327198309, 364574818, 191718788, 314794667, 199694872, 523278837, 546412798, 395561336, 709139341, 452919949, 658822136, 437771336, 531041388, 42059354, 8966291, 395966803, 479978634, 833893460, 686105890, 224391836, 245260614, 707588954, 835406969, 471787119, 882050607, 417622769, 676472317, 115764444, 836397728, 53542297, 209530097, 717525985, 431066043, 178074630, 232456629, 386025608, 504415119, 141338774, 11308283, 466394067, 476076898, 268996803, 675230337, 528518865, 882346773, 347150411, 620038422, 615700966, 723825835, 457876233, 240737583, 132520789, 758848344, 77480890, 730223721, 818431876, 934199694, 568462489, 383630762, 267382721, 440104400, 509058973, 213298495, 830591832, 8673465, 888904400, 443925390, 870436582, 257096409, 253168124, 766300920, 423864735, 504415878, 800982396, 812945447, 742935086, 45178428, 77734096, 97738023, 364205718, 407314964, 847551504, 8980554, 628278645, 330588329, 986449728, 801358523, 624719726, 411037102, 140038296, 895068811, 804559670, 146313160, 303095213, 460826122, 576921814, 311197466, 207374544, 248569001, 52157434, 927953772, 550175162, 675567409, 37348313, 731537513, 979344443, 960294174, 663062959, 233653184, 693110223, 786970374, 532676734, 432022803, 641741557, 78151892, 564600076, 55153456, 257591747, 551371472, 120313963, 293354834, 920725037, 150941070, 864036605, 573980884, 619103892, 856749562, 85259387, 530877923, 241261792, 785121900, 898138969, 322424163, 759848624, 593778985, 618276939, 798935905, 520431106, 531081413, 559271011, 860646386, 165011865, 18040411, 527898715, 401028363, 705033639, 14357341, 99621530, 314388062, 81154556, 14199232, 563950509, 915675389, 173279429, 164393154, 571044218, 190204400, 425623852, 39549865, 732465608, 947073689, 893338641, 730553450, 596832284, 445017087, 992392956, 231226530, 442944278, 91993129, 352906011, 326648056, 544059966, 80275355, 796725303, 642459031, 922661968, 687487945, 548496859, 414286702, 120422141, 907592129, 151890326, 527715000, 485023908, 312782587, 121882739, 48259811, 142917657, 125258417, 387547439, 830654674, 7906821, 68129701, 653786243, 920396749, 992131615, 504293479, 533122480, 414552247, 852183165, 597882506, 19017762, 869644325, 914867533, 895179236, 819862134, 759918382, 915056947, 764824188, 939575621, 9021934, 486261658, 34127357, 158351237, 692256744, 681337104, 315574000, 78430500, 649459949, 541498056, 444345595, 850318596, 512078329, 392579089, 782868596, 865985679, 775931581, 626825322, 827585091, 412854542, 568566405, 3760406, 978977859, 762282953, 964455121, 396621288, 801266022, 944712296, 357705644, 551074925, 588911935, 926663973, 933895611, 829075990, 673324443, 170930382, 866778608, 977554413, 979923613, 166023299, 221516978, 49053165, 82877238, 225548548, 33666987, 987429038, 740265531, 458903688, 675422526, 425067214, 727816943, 648307173, 148258107, 48400, 95223184, 105871026, 870775999, 478699666, 803407822, 26022537, 443670024, 127275273, 531827413, 169704872, 749400111, 110199891, 266498310, 445269394, 163316132, 590995942, 976168330, 665783772, 611597545, 808822897, 317716251, 469318947, 835554344, 513012861, 540231700, 18317706, 102724476, 764592422, 407910930, 757683153, 146452200, 333801784, 835565509, 660435288, 921298627, 455512014, 212870121, 632144396, 366796654, 678109705, 169496727, 947561338, 366176995, 562441215, 327949150, 326507344, 327955717, 389079708, 495530490, 698082131, 994671478, 580633221, 486066916, 650254138, 895903517, 763998096, 919122789, 427240691, 356559227, 432804726, 908458900, 313584380, 534315348, 319059156, 559202609, 390533968, 634070809, 308586957, 656609052, 551997733, 991473410, 440786043, 598987432, 262856529, 504159824, 817726381, 277132136, 166587124, 397475745, 437477406, 739469250, 406689907, 442635406, 757542888, 939534755, 450973882, 894137527, 278747042, 621515163, 683958993, 820913491, 244282983, 756765444, 850854402, 10152935, 674217446, 498047606, 473920692, 473419681, 922730254, 527029587, 639807468, 644993823, 609811911, 566064561, 57047204, 201838967, 20146402, 910299168, 290537006, 467908135, 988162920, 343247051, 864198045, 532086584, 959250751, 953248675, 461774256, 804313758, 611213934, 814460400, 481252712, 837786346, 729785151, 43962093, 807677606, 430946372, 251009254, 790632542, 951838745, 292877528, 422631983, 807595668, 700997182, 127479338, 533590459, 24922288, 527041774, 10611498, 838448041, 72090628, 332663451, 661253717, 547709072, 777824794, 308068607, 417540022, 955802071, 585092165, 507286437, 895235525, 225856351, 330403750, 629901368, 647371895, 671931348, 740872536, 777212935, 968691031, 814013576, 992264008, 737775010, 846882027, 614915285, 270035675, 878447019, 6143829, 123506274, 389857252, 537839807, 691191997, 155045607, 598508067, 587847661, 147517094, 414495345, 220569067, 806820188, 835278251, 762571284, 545958867, 895070529, 942357838, 735640985, 481480980, 816070281, 13119778, 817160526, 92320522, 804124111, 455020820, 224306786, 859276749, 259623313, 446685209, 891733262, 411791924, 999165936, 335930808, 425484389, 206406021, 294046158, 49798698, 550877047, 237161166, 941009332, 458676934, 786951242, 639240677, 629364901, 414565089, 486539256, 364632231, 668062795, 722730455, 391373243, 352881751, 121798368, 995061107, 591032185, 150615892, 442584044, 745641376, 662987025, 227016895, 359839681, 697830852, 620886765, 766129041, 736726878, 284996443, 890025582, 177695790, 745023471, 251472510, 182922970, 508974360, 279141860, 923709787, 456277138, 638049116, 116521120, 382262159, 669255320, 830796365, 824479453, 794693634, 681948553, 894373502, 328747678, 864485513, 838625639, 98959710, 698385626, 719121740, 563268221, 126075350, 256878478, 267930928, 643837003, 396531760, 288420261, 575623270, 954867513, 76288095, 300820423, 137293858, 504123554, 225955642, 687427144, 833368834, 347759034, 41113314, 640143859, 81854420, 610780925, 478379480, 129367061, 360294445, 571359139, 427089785, 587252686, 637044626, 744555971, 724875231, 861307602, 936703235, 567941550, 705457068, 301139008, 846545798, 218353739, 806631147, 90042853, 965649597, 762712263, 488958661, 889905523, 622154837, 13170042, 923906316, 440139429, 334704619, 94565509, 503337427, 940514073, 74647368, 565769922, 348625004, 797237524, 202871051, 10687597, 680781042, 367319681, 649045910, 757948988, 388824208, 515936490, 442408645, 298597613, 911540058, 199910139, 5970166, 973675571, 733591705, 154666287, 536389760, 455738994, 934454788, 714077695, 650008814, 114989652, 542402951, 812961660, 443572409, 297485486, 692134086, 282277901, 643831506, 684280302, 910718671, 6046757, 911202254, 999958596, 599351672, 16895306, 695246968, 335467544, 312861148, 914152376, 740602364, 418903541, 783782627, 263968089, 861673978, 87536547, 908828136, 627635372, 938905415, 353971814, 128659112, 533074038, 684485059, 950684951, 246840247, 889537067, 116399463, 104663759, 592237175, 144550341, 502678268, 128968695, 999236791, 548150972, 267088905, 505882298, 543917403, 640665773, 714468921, 924116603, 454716059, 890843806, 45994820, 316981011, 635481476, 775362750, 930803004, 150552571, 846304960, 153611133, 326999337, 296852548, 37237401, 732931956, 480244143, 566518230, 859380869, 816985397, 47042691, 983932457, 212844320, 806847046, 975408547, 636672977, 924373197, 935508099, 79806626, 760988245, 423696738, 149942084, 791787743, 209963025, 552633484, 292901172, 821758315, 224076172, 535221954, 223853398, 999582611, 945129968, 49812709, 177590203, 758987378, 960848979, 833116934, 51027106, 424579263, 699734263, 102644325, 962878294, 453243740, 606885333, 754856338, 866934442, 404667100, 489763824, 547323945, 162982510, 152931732, 276574423, 182050969, 374287071, 262628343, 979523447, 589354171, 123294786, 414697229, 592712394, 478226358, 146943273, 704291884, 981139613, 596805868, 685777285, 174235915, 744126673, 382667107, 412392724, 249716142, 650814920, 212669066, 878650706, 320983569, 345098538, 812796189, 425592653, 570747770, 155074130, 379089732, 354442062, 626909837, 16901904, 253294429, 542515372, 414194026, 693046379, 264754498, 273001819, 383541456, 648370199, 207662666, 364995095, 656572820, 484008022, 631128552, 941464516, 377767295, 927844834, 395125563, 622926796, 180442649, 325800157, 708731403, 412764162, 996964429, 784760998, 608087087, 87808976, 878283239, 178419143, 704813323, 148297349, 621229496, 779090208, 827050870, 404238830, 183015273, 138453150, 834588759, 557135585, 585089811, 644437177, 993243931, 449611380, 384192443, 683602224, 452042881, 156675609, 427401731, 6380658, 916341775, 410312734, 187457312, 532844424, 242971034, 780598650, 573209722, 648251402, 133918559, 206798296, 263308005, 763114301, 52584, 600252984, 850995828, 374245446, 814423717, 412821632, 129275757, 558065168, 679041488, 985564503, 675565808, 188992036, 683949114, 184580956, 683010189, 711885849, 593297161, 24127831, 279947354, 811963258, 663041177, 631985183, 464578151, 118280454, 148809173, 234803329, 921105604, 552622660, 237321859, 264673620, 568813722, 552564886, 939780465, 849121531, 449834980, 456548297, 409219868, 263603677, 102620956, 231263633, 384729003, 222614374, 68469514, 598864564, 988996689, 13946001, 337731884, 535888197, 501071619, 996626537, 922211125, 217100405, 660828775, 70235628, 826954083, 709453408, 212490331, 533692059, 97407291, 702626770, 351010468, 858840274, 875061410, 788058667, 407703510, 652351048, 211344532, 500786749, 159317529, 583119935, 391936626, 680468775, 553713350, 429802987, 564423502, 933088134, 336646493, 938636606, 217829921, 900406752, 593831058, 767391294, 271748548, 822950156, 227219979, 64605813, 947573570, 183296840, 940509960, 948107718, 768271879, 250146981, 129716266, 904412852, 588395391, 815149788, 528099452, 150016703, 813220612, 914577629, 290976184, 753181743, 21281645, 674174799, 503403287, 780695392, 718582122, 264188816, 716167129, 30517959, 73982598, 826335924, 357765273, 963867596, 649803322, 462992156, 582745762, 455351967, 689342044, 370709269, 816593034, 640429942, 668771264, 778997875, 333393671, 411482311, 608579424, 446681207, 410371876, 768093514, 330294780, 495084100, 910279208, 997137327, 238906383, 578555612, 1029079, 538152030, 750437212, 913195992, 657978350, 412211985, 677632167, 345362827, 756289171, 488583858, 177004470, 348821051, 454241609, 791951005, 348887259, 543130138, 664574726, 135383846, 5584222, 194432454, 601083661, 756182290, 897314650, 360886136, 815749240, 81709728, 603740120, 340579047, 885781871, 873799520, 578298498, 729096664, 765460390, 967671850, 898604103, 939878592, 861921995, 73786669, 962592447, 706753593, 220393321, 710539908, 454445001, 622348557, 84237956, 434991323, 491554004, 717626383, 782342803, 14719726, 689183368, 233372998, 323913118, 582498076, 179009198, 263297456, 657722521, 260440516, 72244391, 183737589, 441287707, 101258909, 495706214, 900115512, 477765295, 688619540, 602259372, 700836527, 147971017, 437744088, 961399039, 298626588, 386716142, 352064192, 971860471, 430097276, 159314583, 413364675, 615227276, 589224107, 611514724, 1749386, 864251574, 2622094, 792715873, 992555172, 276562566, 562349686, 835424155, 117069395, 427040066, 417183303, 81231531, 773745198, 894680142, 99980293, 108622086, 789780093, 575881254, 476559007, 521012790, 187597816, 75576626, 937188733, 3263277, 677100482, 617387746, 565779997, 992741604, 34580155, 272962036, 737444924, 286654409, 292251364, 164487979, 178868613, 839174363, 250469679, 963790825, 122470609, 443480610, 247798534, 621797607, 238590922, 330662362, 614736096, 621029827, 16597716, 148397080, 222638023, 489994244, 245587915, 360145784, 230520939, 947464863, 920922846, 191227198, 818313940, 783395239, 657676398, 409494398, 903216709, 12431143, 334123739, 141556947, 428631934, 657629690, 409104360, 789077997, 984825556, 657492905, 972487456, 957655175, 995187421, 626869515, 21651676, 333341035, 775273287, 243967810, 688040499, 51897725, 130064304, 510081095, 492695411, 375239975, 890146884, 542568786, 163479187, 770113442, 920708329, 497159816, 490019422, 295222630, 850070042, 537599594, 626973130, 210422729, 651999357, 608546472, 380378171, 386778681, 975481131, 799353288, 109069647, 242370997, 50802631, 149462687, 526685557, 567106193, 19126507, 186975213, 210294469, 312520538, 423548066, 400598869, 738834499, 836256750, 950713632, 453939156, 748152535, 416868278, 210376251, 870178445, 539751958, 666238609, 452324448, 167891190, 421320542, 139172522, 838600774, 971494377, 237626210, 529866300, 867461824, 538970439, 690276716, 91202303, 863134329, 420572234, 565585163, 520494980, 15552642, 349663655, 66779176, 814713617, 593286239, 61908672, 757838985, 476496362, 253703257, 851797305, 360471958, 177494138, 162474121, 816525649, 681443077, 838702697, 547058950, 449890373, 684005683, 128563422, 40669734, 560570704, 498292407, 212399549, 906021364, 884940784, 492443529, 964991069, 91738021, 420237397, 330690904, 548180932, 507152081, 161143526, 874984092, 425563178, 438659084, 917142825, 630820212, 347875881, 888530107, 27302338, 653427566, 17010420, 103206963, 923673915, 806873087, 472492983, 936278116, 175989199, 612770188, 305013586, 764165513, 579323647, 597188681, 421196188, 10351270, 174811512, 661410711, 444223204, 892308936, 714638616, 214045485, 244803794, 63347878, 232484557, 625625351, 516074314, 161495284, 284403797, 721862710, 236070795, 45045473, 819762680, 933263924, 467149005, 521232829, 235860463, 302266719, 890156281, 977064322, 785565922, 2699785, 854444781, 154559333, 619567108, 509171112, 479428286, 82511479, 547067716, 850018361, 885272771, 610574071, 394571382, 54774362, 758523993, 9685369, 236288847, 676011886, 442796185, 763584235, 860378606, 730483800, 77810020, 648680343, 262213181, 184233203, 818188209, 580853128, 249401709, 573749398, 203529869, 95703428, 412437341, 830475419, 861733328, 324544574, 713705898, 895200743, 815971892, 304170217, 925518890, 999432485, 430773541, 912087903, 899178438, 701133194, 656559694, 764502132, 777104687, 449749601, 938139078, 52704369, 168631253, 546957116, 676778833, 425047115, 231118081, 299668358, 531622240, 800569465, 543138473, 351093289, 318092949, 85633899, 48927015, 9386, 808345347, 6506291, 275644013, 72595825, 856459083, 347368048, 72601957, 521324052, 804555550, 783601344, 351304823, 843621859, 439528836, 923776967, 672533642, 409345738, 188675582, 66626254, 233776742, 60426751, 83845930, 184759396, 87353864, 710282049, 795657628, 170310358, 995919337, 535480956, 380223183, 966464940, 975350672, 436909863, 318785911, 185287582, 567160256, 311347019, 877575241, 727359010, 154008765, 716017157, 619763331, 225356571, 955671123, 964523037, 892361196, 630607928, 205992123, 975942397, 587866958, 295628805, 993885084, 705196272, 151797521, 293762346, 546538681, 854768371, 177162023, 400776645, 67110226, 74162669, 792575153, 422010531, 180858590, 527488238, 478127225, 319341355, 741773621, 278361549, 759553550, 981574239, 93059066, 665667665, 29674932, 617666309, 456368401, 412505023, 146191635, 37248584, 129551176, 119098605, 116537905, 423985019, 960967156, 173118705, 166708789, 152346463, 366155269, 954010383, 250865473, 159761164, 641634808, 345542217, 750168517, 762481303, 393810957, 514589969, 236837506, 950294301, 113804528, 905884523, 614693722, 702750785, 159214789, 4183336, 271446975, 184221641, 220521111, 699949129, 434119007, 98951430, 511080258, 949616155, 501618580, 454205, 818212007, 200136492, 262067591, 654047254, 735759937, 933481115, 481798487, 192665089, 655984129, 716281152, 912588041, 348430245, 644574839, 17152011, 583887522, 486972618, 929845275, 485562404, 500601904, 550049053, 220027565, 928175067, 146570897, 641005747, 111351196, 427097719, 465573341, 990278147, 562203109, 960481325, 284301345, 92919018, 870907868, 417026272, 404726953, 138369165, 412553422, 615792589, 6590279, 597298465, 514553976, 442278474, 943765408, 399623748, 659683189, 577448622, 560015110, 974203732, 594130544, 626993077, 378384483, 202403614, 999415583, 191842503, 110284832, 924046838, 740088176, 317075291, 458592686, 413030060, 197516929, 912950899, 3381547, 911192444, 974082196, 556516170, 656207756, 726166636, 82477490, 808541369, 307664337, 27286737, 212321281, 802215508, 911372117, 294524810, 625037215, 169420358, 490918314, 391123197, 401855021, 570192539, 540467354, 241826140, 215001976, 384632450, 629660897, 497546998, 367769637, 226945926, 915460275, 12895030, 711444924, 12603750, 304150925, 784508077, 598105361, 689888138, 781782316, 645582531, 231762739, 485456153, 301006249, 631395212, 88328698, 626855473, 78474935, 953038004, 220791330, 147455827, 729800214, 608048181, 264439328, 19382750, 193575665, 879133499, 588840388, 334491760, 950062741, 931437957, 929289885, 540994044, 576394560, 762770056, 200781985, 453885333, 761631019, 66557506, 216393037, 338673320, 725062223, 81955080, 771059941, 403548130, 775536104, 634185613, 589541121, 746431719, 10317430, 314324711, 869847053, 847176438, 551687470, 640269676, 565272761, 587268088, 42271445, 913308827, 475405227, 322685705, 319753566, 320150279, 769575142, 581704457, 164623981, 114095409, 962283107, 509682157, 971286224, 547676267, 71718632, 532906223, 803686342, 188267015, 955842795, 249023321, 499621278, 547658021, 877820003, 846193429, 890772310, 389226292, 146468334, 414646320, 789405999, 577951761, 761692941, 791579429, 805800297, 132303701, 849588356, 997210945, 138616662, 141764092, 192012809, 247641122, 337854262, 544020860, 417801760, 605498212, 172601219, 856352900, 320086795, 482161752, 473554377, 471052385, 870342513, 890973546, 458163780, 476111798, 217658584, 937700543, 724493485, 259769261, 345019985, 707191349, 521839000, 332284353, 113607790, 248581010, 956223673, 853803867, 661492625, 415499961, 351450992, 72810808, 492750971, 343654037, 386701600, 163090083, 933892156, 358525100, 117815177, 973284243, 397679224, 188936796, 26315336, 134392689, 686773810, 10007163, 184573631, 577501941, 577182257, 635685863, 743295786, 223581928, 387280373, 474422497, 134673494, 548971680, 816552680, 770947336, 762954504, 489581292, 846966708, 822915629, 504626010, 313555772, 386409606, 924459614, 8711410, 903029174, 593514513, 159801793, 568214572, 302246488, 399153636, 576301473, 342546836, 762657423, 738043402, 146986851, 167669530, 607048554, 727410353, 978873334, 518241451, 500690524, 960965324, 749357832, 8657608, 500827035, 686038037, 340253114, 730715442, 688366357, 514173576, 311830586, 460972543, 612870767, 641953057, 8426768, 36199896, 943228534, 113532233, 629284069, 61482207, 305247873, 705461987, 933705807, 5150676, 398822914, 290372884, 129418006, 197045422, 143751681, 885606956, 748864761, 766416878, 637763950, 127476586, 519356979, 253083242, 521076517, 732325762, 969790226, 429473671, 571932583, 772715114, 199694748, 366911495, 705389596, 188722396, 535263218, 280926958, 535456401, 395159182, 252865916, 849248807, 208473480, 259911586, 918017196, 284363373, 106097923, 566965441, 576577972, 555176605, 835795698, 239186410, 692641488, 597740841, 848980741, 613136138, 716851116, 545133222, 382691653, 42705004, 508274380, 563020701, 340256894, 985647396, 386458544, 448302055, 590128900, 252310619, 935164636, 488651132, 357883355, 142808530, 280359688, 630063882, 325238637, 312048682, 897941133, 592049755, 959044588, 422991282, 80397567, 418221439, 864178651, 862507275, 324402983, 370514269, 171695377, 883603801, 993478750, 892329317, 658010808, 948066574, 624917813, 623271738, 839679608, 218001687, 870279148, 137121359, 761155176, 33643354, 908286393, 947566974, 725398669, 607675997, 478376810, 931109087, 893451557, 621602227, 649455366, 969016750, 813268638, 15620283, 463771504, 460062575, 868486248, 69460260, 915932223, 150875904, 926827013, 700896282, 84576471, 283100109, 793285847, 248613801, 964337021, 149804717, 174858436, 922506921, 866093282, 929899688, 993017102, 594371844, 355188813, 499182596, 394865342, 381142891, 37342369, 57440099, 27852524, 800638700, 859732169, 323328312, 297879488, 83271607, 300536209, 657086494, 832678735, 781515266, 197979233, 839955921, 668699627, 297551522, 252319375, 589233114, 897839839, 377339424, 701599422, 975302032, 359662343, 885136235, 334176095, 316209996, 340466966, 213824721, 107123455, 449458420, 411220237, 507867035, 986145723, 242727588, 339833855, 251916932, 991398011, 367197349, 397710634, 350853135, 558653765, 706495407, 905544704, 554287438, 225927814, 337792630, 21557249, 876963578, 557266983, 598622765, 513144480, 582066903, 595406895, 555408282, 704251407, 551445675, 815135034, 804254835, 475054968, 947505929, 581011258, 446587580, 888424093, 622241243, 170902235, 776986169, 583416425, 290628978, 394817621, 682303907, 204082623, 226658283, 400619232, 133964511, 155404524, 885872580, 649072924, 438148928, 106496308, 800716092, 615673839, 247799052, 87419517, 96406492, 632327768, 735356546, 888174479, 801745470, 908992553, 902686302, 569087256, 523865593, 734459208, 586007695, 986163693, 730280350, 444014979, 833852555, 530325312, 249082171, 529816604, 354191443, 426749226, 548885293, 987041121, 42460755, 997368616, 787130725, 739157963, 246428028, 294018789, 460021994, 979475731, 999439113, 912799385, 731475172, 148413701, 716343147, 393203298, 918113337, 300670368, 337375907, 355951288, 80797459, 364506279, 524771590, 322896716, 81623858, 582469632, 429962570, 465401608, 429523426, 338898069, 228816992, 764910263, 470744493, 275444885, 808163604, 175182102, 280904963, 417318779, 962944015, 903813670, 925780802, 848395568, 469448459, 927941783, 391592418, 288197896, 777214732, 225431925, 636633997, 529099999, 557277774, 509426363, 572834112, 581457277, 956997180, 41299115, 647967972, 695387926, 288884303, 426967824, 851497140, 912734607, 831388435, 329545197, 239029960, 827965556, 247423221, 918519026, 166606417, 187770408, 563074624, 928172608, 883578815, 924733899, 881323138, 3229861, 958815508, 840104184, 156221349, 97354273, 388289570, 306285712, 247740926, 622956133, 671017117, 58527743, 636033194, 722298518, 334576284, 145875078, 466397008, 563411732, 620282185, 356184565, 482700155, 933987561, 991879254, 509466632, 121321018, 768784756, 958514006, 271921724, 703850529, 13011801, 644328450, 279076711, 325568836, 538383116, 656915080, 196990032, 657867505, 51183392, 581529272, 668468129, 959187622, 39720125, 207377348, 357212793, 75746425, 732421617, 722385227, 148914281, 797948173, 289998138, 331585547, 230117676, 417650578, 219333676, 404720802, 258300267, 937639501, 705031390, 372436715, 509469557, 219896258, 625016998, 332621350, 346013590, 441128769, 818081599, 731097083, 754340198, 439093930, 58753445, 187692720, 493805860, 362049599, 589015914, 769982165, 185507227, 771735978, 140678370, 593851678, 449693266, 516090507, 27140571, 839645578, 342150861, 259361806, 323598245, 175787642, 24232975, 491435599, 274638754, 620487103, 59529520, 146501509, 119825704, 608983596, 658983579, 203850815, 425503271, 483716517, 204694046, 915511790, 572720117, 250379940, 148711341, 1372358, 889874164, 587127722, 428653894, 934402351, 686988933, 274621598, 325092206, 577223425, 805666669, 573200046, 893035667, 382672352, 349539797, 27085997, 117231921, 755383126, 166500593, 471601692, 675315352, 46464007, 89231492, 11573562, 896539293, 226475324, 263930525, 283211442, 465373503, 262185281, 248795052, 416511284, 748804216, 290537719, 554893865, 619975645, 309526347, 560668904, 58323349, 681268819, 209452359, 898473036, 865332760, 623338180, 21616943, 457993979, 594725406, 27922920, 264277514, 370093882, 79938127, 361156308, 906155121, 333225799, 4221997, 539554232, 150886081, 180920924, 554379432, 179097337, 556914044, 707205176, 101193584, 509426953, 384504620, 680228264, 938175281, 300555337, 735002633, 942318179, 773404290, 772153431, 233729323, 903893, 481263995, 314949467, 300438565, 506848498, 653419194, 955734197, 690799762, 617937947, 758477355, 248617754, 767305073, 756694765, 170898429, 289062188, 549584902, 691627679, 996054102, 171037463, 937784064, 624768337, 500635287, 775538659, 908423889, 507493292, 870075232, 249881153, 623391594, 762107006, 700684426, 44836538, 969608968, 620251239, 670534097, 701402059, 7446170, 6355609, 299827955, 414077752, 529092127, 715011607, 685668266, 30691379, 84981811, 456470279, 938959914, 832579667, 710149014, 695120985, 237535455, 97243940, 728868186, 990579948, 214705724, 674262589, 111706221, 566479310, 143416720, 815914759, 902882295, 100696224, 506888675, 559307932, 936043683, 269933655, 804601230, 31494426, 398537744, 286644421, 937704969, 173919202, 717402796, 133195587, 565684884, 553335052, 911690226, 405015827, 225749207, 826155734, 11034605, 397718024, 635946701, 450634783, 642328528, 442535458, 43894157, 613249290, 274014224, 595270424, 745585415, 242390683, 184719463, 835371057, 495763451, 72426064, 481709566, 666550074, 828813655, 133129806, 784545106, 571077920, 537785761, 962556963, 142436922, 284952774, 609741923, 742494673, 970358205, 552459562, 352561593, 46786297, 352723810, 648910768, 428459772, 163816700, 729157065, 988788663, 755932693, 907673682, 719923538, 883351668, 458997903, 534816162, 476492195, 882813452, 266985881, 566210348, 957902194, 271281226, 925447962, 516305502, 198371266, 696822824, 481643345, 666998721, 582817150, 74055689, 861604060, 240081894, 920287233, 81026130, 352872767, 923788265, 439613677, 239495893, 504642288, 199105662, 746579608, 52382105, 457654374, 238857314, 530986034, 578654764, 784489546, 453494681, 677038747, 742178080, 692138269, 67015647, 764583405, 386086478, 218146882, 270429837, 857575049, 895514755, 252665507, 531192778, 14154590, 853722785, 406452596, 443597350, 78026875, 18470934, 65908013, 929471774, 375551947, 75741706, 974266166, 457023717, 56079480, 530607312, 924002864, 136039180, 174381951, 53140245, 369504019, 408222308, 938051527, 872687747, 662325306, 888047338, 292865844, 60544170, 320014590, 493786046, 533109332, 369517190, 381498714, 96933710, 272441340, 644725907, 845161365, 135249944, 2191989, 257991813, 417008643, 425021177, 181706881, 85482846, 28705329, 727543086, 480196119, 413055196, 783912062, 29111850, 361260801, 75161862, 753857446, 408116675, 74986058, 95036027, 317169629, 668486442, 503955482, 5279347, 221784877, 28078184, 837063538, 191849259, 153213623, 584974029, 463178723, 527900564, 201307356, 250182478, 953423773, 89593762, 670443203, 739895968, 989290991, 141178588, 341335688, 7544513, 835779901, 229793964, 325794278, 791242519, 350275551, 817671843, 91670840, 251046176, 161768782, 695880370, 564530976, 642608495, 218312895, 719424956, 754053714, 81693232, 279710936, 431237832, 108070367, 331682049, 176569018, 828329106, 246186735, 181904931, 970499812, 268379951, 676558664, 537419713, 629208690, 131684407, 725680511, 838141865, 305643816, 88711396, 853722620, 849607654, 792845554, 92000564, 876429515, 825960780, 536444185, 255204030, 739952405, 485805306, 790926571, 400106410, 933211998, 291118999, 954763575, 472948130, 654090399, 908442145, 218624589, 869010267, 443869949, 648488543, 446553508, 519199407, 132744069, 210897795, 403627685, 556842444, 354211983, 846949772, 246453247, 995313883, 501910847, 407730086, 59876778, 153103549, 568707033, 309487491, 133692383, 68445747, 564127677, 229444851, 612939141, 105563056, 465352073, 664685516, 327016694, 535538899, 883131370, 247246387, 148825558, 766858351, 627593632, 180044227, 983741685, 538885812, 135476250, 614012399, 750199833, 972349882, 2855582, 403730735, 361454824, 580875726, 204364679, 253144924, 961094877, 603196799, 96497418, 569447050, 781182508, 200513413, 782876306, 705976479, 42861570, 797668746, 714689887, 825665712, 608506997, 733141129, 459889774, 498316981, 367562952, 758919828, 590312770, 90596658, 203869037, 703287365, 884175355, 582498741, 317268171, 111497473, 945056846, 73430444, 950358748, 612297414, 508098754, 889615770, 818469973, 22813555, 402666122, 227585890, 401847004, 556012445, 309055905, 8185055, 702769430, 240841533, 433866517, 357722566, 919833706, 566279772, 270040696, 746553767, 271471663, 510841330, 472814625, 175490060, 380555459, 61952033, 106375245, 531812494, 87785137, 195845768, 94010417, 182823711, 257823918, 150760858, 155211498, 303095827, 718846492, 671927542, 158467410, 114344208, 329149557, 384444114, 214657241, 987756410, 852852386, 523394541, 271678419, 587725996, 726185820, 832413682, 651436076, 211305157, 485974890, 362723098, 548876520, 120009679, 463804511, 129901646, 681195189, 247637320, 535564879, 237108890, 958579428, 906387096, 708397421, 88568825, 183243547, 129531850, 299699670, 104279768, 804604769, 531517535, 711288021, 527194824, 463913521, 157972838, 345950016, 758085846, 290731718, 829824514, 439277102, 665561866, 369671390, 868159376, 213414747, 208539030, 305408214, 198061691, 156104144, 784298168, 23381502, 589593334, 384437321, 687803019, 807531532, 593608385, 872356367, 75480640, 98420683, 802834282, 777799173, 824369555, 46892096, 180280853, 668459779, 712435708, 705659613, 286799034, 22445518, 877859309, 432319269, 503759211, 161251195, 718227284, 345699729, 977574586, 379105912, 304322361, 815543524, 711478035, 756959959, 268616941, 272714092, 538238242, 567876646, 673860600, 783065042, 329065250, 604936167, 322308350, 119208442, 591293564, 160698169, 229594080, 955515054, 711030305, 715575597, 658965845, 159907997, 359957510, 432611886, 696438040, 822171098, 325170550, 751882249, 314275667, 347497811, 754350820, 887827678, 572818261, 832743490, 110725246, 482118375, 33622281, 445596389, 337651337, 928797691, 91639312, 92364892, 774093082, 557542226, 845455920, 980223516, 268988407, 835026441, 65801842, 407742640, 77739318, 700830462, 81955126, 423689688, 324353048, 492752740, 97865270, 288492880, 190432270, 798144340, 213774556, 965567760, 285770192, 503333878, 597560358, 988998059, 743757431, 527463462, 347546114, 107564202, 819297178, 564142693, 887361400, 96405857, 426970599, 734468312, 288289985, 619823110, 155507484, 209692253, 390457477, 214301941, 1837416, 95205946, 429260591, 432695267, 174862726, 772303928, 481626398, 783134511, 677900711, 957065857, 37057583, 948871917, 641739934, 911511760, 352618639, 144144884, 642550638, 797834095, 463006664, 464388113, 728985125, 106574706, 844551739, 532767458, 707715667, 851689093, 110184963, 611739256, 513682935, 856429092, 326777561, 744972921, 877791939, 132978690, 135803803, 926136772, 968590174, 567882723, 694782523, 861682127, 152256335, 790725824, 596916483, 367571719, 627420629, 136173879, 198044353, 511070611, 442455017, 834116714, 701693337, 992900302, 771747360, 617784839, 522960141, 346429435, 169500046, 6071737, 316867778, 277787152, 188993407, 990685361, 312029437, 96117817, 687289715, 720968293, 900389433, 927588466, 639758844, 162513219, 710391516, 774529200, 562823075, 765712224, 266138608, 193301190, 214860502, 569621103, 488870689, 399252209, 673757438, 375409390, 445687655, 733416580, 531558204, 948227586, 946302828, 636845835, 162843359, 535088652, 704196763, 433614275, 976185238, 638199673, 18575114, 760098967, 714132944, 73926617, 969084096, 205996466, 925332702, 269773141, 662659411, 827610981, 351513379, 169478736, 340121492, 692665906, 709329717, 647919030, 490994344, 949825790, 520026019, 384548813, 696151191, 765437277, 148263379, 873730131, 940605067, 533176151, 846086907, 527762075, 715335656, 301820554, 230461124, 841050218, 630261373, 744228791, 143619525, 223674426, 240328857, 946432016, 374537753, 755909513, 472304041, 228392771, 951318893, 777143591, 597909051, 612832640, 978572924, 372443016, 712332806, 463371403, 983093144, 267849842, 530278126, 875006043, 375265125, 696106962, 338964489, 916735522, 265029251, 818473463, 448638713, 757806898, 574340535, 179918040, 431791600, 920277555, 385162752, 471660133, 87158064, 993161900, 99534653, 531834173, 937548633, 243645459, 271691341, 533753312, 443292544, 562033813, 798339860, 174427780, 691762520, 746633641, 594698411, 747607868, 289948115, 873140690, 408948715, 457545238, 790088344, 609910000, 92359424, 502459453, 993681303, 170578854, 933143308, 847159630, 902660503, 202816025, 961378094, 586870797, 6597422, 715009393, 544352161, 442388790, 442351555, 413270310, 364829953, 709908780, 948316405, 355401700, 832550571, 741420053, 415584444, 427590056, 579496827, 101833951, 649060577, 132455349, 150302460, 793979921, 268856371, 64571225, 594205180, 742588338, 613143851, 925893458, 573604747, 314432722, 784578329, 120615346, 945634791, 816299875, 720827422, 257689098, 497213787, 618589955, 830126427, 287617909, 435479642, 308682117, 393551572, 158192768, 24162952, 453280450, 798940506, 721966326, 706730633, 951474354, 94194893, 174866621, 632614063, 702367567, 761763812, 324931167, 948598417, 541163292, 384196586, 179582683, 374962133, 682696873, 277922584, 352332351, 541560896, 34363151, 225452952, 660202266, 266195117, 469381641, 124704964, 252546926, 925602092, 420243494, 3721371, 151605106, 860251977, 590861630, 468721681, 547860123, 883652779, 959746031, 823374824, 972573207, 551047867, 680876209, 308132831, 187365545, 925546248, 718306121, 308304633, 756443336, 974590100, 324709392, 269103071, 528559879, 52077121, 457190533, 605555588, 64636890, 728812749, 656837376, 303206439, 756724558, 768541929, 619719857, 140133572, 20037392, 699549844, 200105788, 725966424, 52626940, 642719923, 902223160, 607417710, 611363645, 765676583, 144467559, 272759488, 232056684, 431514201, 561775599, 762774971, 765368743, 678927833, 504996642, 589808713, 725956198, 102598644, 24343121, 168446691, 158488841, 523060401, 313024510, 663699005, 676252294, 389492895, 127110452, 467574029, 531376319, 319752410, 220004095, 181299782, 901194408, 301958470, 877086216, 419799505, 181678283, 766476610, 524326144, 120523468, 906199801, 967103129, 541178054, 667606643, 593245416, 700184361, 862588623, 7729757, 255547371, 513649039, 705794691, 893024843, 555620833, 148745345, 235838290, 571859499, 760890356, 789225584, 620181679, 189159665, 516468687, 237916185, 6004873, 695858848, 355834694, 941682223, 665572248, 640879378, 206170582, 11620037, 598830471, 718853325, 333750561, 46022443, 713162272, 76052352, 458407071, 52642838, 942629118, 875017777, 824776439, 117808409, 210172271, 953278262, 475103977, 370650413, 83556775, 490097345, 216216753, 524648284, 703888970, 594140357, 164389401, 580821229, 639006993, 825313107, 959324446, 105279256, 768637528, 887154661, 713643119, 345563531, 241851440, 468053686, 304233619, 186648232, 635051997, 586210266, 109505328, 543061133, 795294900, 304925672, 64032801, 71700010, 523834741, 372045097, 902849209, 53393516, 328998138, 505957716, 727289606, 759344172, 476853046, 206395041, 412369212, 749583277, 884036910, 298591982, 544587976, 774996158, 78912228, 653275598, 588015491, 441401240, 517533620, 554788326, 515174318, 758298812, 865157144, 566552194, 35566884, 376432292, 913158433, 231021695, 682098243, 850106823, 572657477, 225178574, 301975599, 135216956, 81019875, 893119116, 816214254, 386273176, 200711396, 274749711, 553604322, 701931559, 337684414, 416505804, 900364702, 335306857, 141138437, 875508655, 750682435, 745315101, 421238668, 290499948, 713431952, 729330812, 783533455, 214620898, 537035183, 359697066, 424848105, 592308769, 922974206, 434587250, 781063254, 677359730, 578801518, 254112420, 546264638, 564625919, 288547106, 631717369, 962440683, 871576618, 732235820, 592430330, 191097560, 422577898, 27697112, 445790749, 613609811, 990495869, 528011278, 779882921, 669181639, 556441757, 242540064, 739535102, 238134499, 691702551, 284781491, 115148353, 147823259, 996910195, 329053336, 389570946, 691655128, 934532143, 299871032, 94296310, 661577161, 540491979, 659669849, 757820564, 850815194, 950209198, 209397377, 351955066, 646454981, 556199745, 713339169, 542619132, 702196035, 873883018, 114994320, 357740473, 324418361, 360128258, 30464796, 58763251, 180065047, 671787939, 606458741, 349206976, 961121451, 90979793, 201074021, 916739971, 973003515, 287889421, 689706873, 459856621, 132147537, 544152005, 879220327, 273059892, 571553118, 447972901, 78821172, 142483696, 864224754, 443448749, 511758471, 323581968, 477472237, 698951631, 921073785, 990476246, 861510331, 220186279, 340893201, 205058867, 951293810, 417823605, 169771655, 428368501, 728476319, 580186758, 899237290, 360889787, 411219803, 212245330, 878023329, 658509296, 620441037, 60359273, 296932527, 304472254, 391439193, 281759930, 244250835, 609545569, 775036642, 729201978, 471997336, 224293731, 648455905, 50760899, 123102135, 557496190, 118739950, 530301232, 245052612, 949584331, 662163325, 986528797, 486420052, 68016361, 302564668, 996915993, 824477472, 211419341, 694961215, 577281722, 418543701, 399334933, 501687616, 148512259, 420841448, 265859905, 828017219, 485472177, 62352006, 419263994, 565988475, 213284769, 699240977, 182297367, 921150811, 444071126, 519477715, 971905873, 965035184, 795226346, 178181105, 659684665, 191147930, 374522357, 48537247, 915553762, 833959323, 118854226, 209388529, 875315216, 743121202, 969738172, 688821495, 237677656, 668608086, 353535346, 436943807, 931827111, 13503687, 722169690, 68444323, 503181611, 826818028, 995992149, 922222753, 210270003, 870576713, 514794567, 957653473, 495115268, 274657332, 922497304, 379247044, 635569057, 240726314, 673412017, 705796677, 445980716, 247373963, 94125378, 30247298, 816122174, 834461642, 567408153, 302923798, 583586149, 32447768, 658966431, 39407641, 7671863, 574471819, 86121522, 703427546, 226942506, 172649419, 57290023, 435941924, 350516776, 315117095, 286531744, 993637784, 609526200, 342846696, 906215450, 177373487, 687616539, 934662845, 629650622, 107119201, 183274200, 701577867, 415983954, 124794816, 946255079, 396414986, 34034727, 703347277, 357163123, 67486690, 718039272, 998500287, 867069353, 63893679, 963517227, 981435537, 973410024, 50754474, 267295059, 727538218, 906227859, 899621102, 508184803, 56308256, 923068016, 645073164, 310377034, 61443477, 502079563, 566378219, 193610590, 524805908, 608627088, 195375010, 368338363, 10929718, 838857713, 759101260, 572085386, 438659309, 784537779, 91058934, 793385541, 505974032, 608101361, 852173722, 646111756, 414443317, 709872298, 755996920, 830199153, 501580885, 862535224, 835854845, 330571542, 39633931, 609454405, 631021917, 387184689, 245562093, 387604622, 25168812, 556845426, 19579083, 403115686, 625651623, 755874140, 166524606, 916721667, 283048133, 755772163, 670640056, 565950606, 589677042, 324086291, 312096382, 942677747, 353799980, 743414976, 480961541, 536265664, 438796872, 697476460, 164728333, 835634807, 707669997, 378089303, 597368773, 120655130, 978502159, 492654119, 467903183, 693283459, 386157185, 356892496, 804733882, 837902475, 600352099, 128943683, 53305159, 671520581, 957197359, 931362385, 325461456, 973066711, 587377016, 855673712, 466338386, 61091770, 67884920, 898720486, 169644205, 327975638, 288115824, 9650375, 960890627, 72148407, 471320877, 65405941, 588830578, 835981486, 277507716, 49653032, 808460942, 655723378, 836923916, 539313390, 768074464, 56562190, 665069539, 60061611, 406337925, 811232481, 453739276, 336602049, 239822259, 714397807, 394172243, 896454209, 718668637, 637446587, 10157207, 116263952, 542727050, 792122066, 760726432, 539163229, 638559849, 66301722, 53964505, 210002256, 984708115, 176065099, 774969561, 542681340, 640534091, 882076218, 577385590, 551297534, 747708869, 527615229, 746958489, 554531109, 38464602, 759603821, 171537249, 984029685, 644162022, 200801530, 788810160, 325555831, 473095762, 600034027, 450997974, 929045494, 336232052, 803600611, 433462131, 822703240, 419152890, 945447715, 660516099, 494353410, 69066313, 229328465, 624611059, 621137952, 591053781, 336255491, 128599203, 509047229, 611449157, 310199588, 602030934, 633054802, 737089094, 287447701, 565479189, 906617033, 998565251, 897335508, 462393286, 752152053, 114164270, 148588125, 200661487, 553206077, 744160790, 443352794, 525120666, 750962165, 329609388, 751236684, 620422628, 401901470, 986868068, 872858194, 331530843, 251515082, 315758016, 468379702, 317849272, 985308785, 524711632, 615624295, 498613974, 372457527, 467245914, 206783621, 267031170, 350528769, 387682853, 467543613, 589260936, 593121586, 731302053, 289218299, 826793843, 61563721, 269697783, 861494287, 485860917, 19509170, 670351443, 209578257, 465554469, 173255496, 979086261, 418344147, 854735999, 849003048, 476319668, 952060848, 535566379, 839584243, 497286976, 4121450, 204739308, 62350977, 555170562, 616435200, 976875222, 245218901, 692865614, 293105488, 279433569, 48022497, 952527955, 805313788, 378969765, 690708821, 837732599, 44859351, 457696053, 246923589, 608234187, 717179588, 372382662, 981977575, 983841518, 927011095, 340018541, 560292672, 36039156, 491381937, 771438641, 784984059, 658564772, 874485223, 383442586, 22770931, 816173380, 889324366, 519927195, 101593243, 781667610, 288316929, 761922944, 43639547, 522883774, 783604736, 738904298, 339430769, 578270028, 151726500, 781920009, 389135055, 58124181, 736913445, 99196910, 544855652, 547226239, 458805062, 350190667, 404565785, 564263886, 864511847, 106791622, 363443022, 502919362, 277911572, 907489740, 889052600, 601440638, 834788068, 461972904, 695962531, 415957013, 3200457, 633707260, 428186609, 494793189, 570777221, 528595721, 950465415, 559056275, 668327127, 496098791, 28777923, 648247238, 87160076, 211540937, 274722171, 487284682, 987322090, 859845533, 668057019, 493274470, 609548008, 746515405, 645830083, 448487679, 823467490, 879524609, 687385904, 72315572, 276275689, 502916707, 883761496, 639716784, 769157644, 298078120, 818924293, 983140590, 319435898, 645646458, 812131028, 325311880, 712937634, 491417652, 333554799, 915714931, 882402681, 541204188, 40957590, 656850440, 356421761, 676317532, 5622936, 659572450, 866357556, 212850957, 212638323, 216429618, 598241205, 423964009, 660582645, 66768945, 85361888, 517089143, 357397416, 779658213, 334398169, 45344920, 101672354, 874885702, 719088961, 318005085, 834518260, 385274389, 988188052, 641549666, 327415664, 864290668, 171866290, 211578323, 356201329, 76647487, 258977595, 729684744, 484363673, 416865365, 277170750, 339625323, 277504064, 411873853, 295048653, 382248060, 605817012, 337893607, 178296901, 472917286, 137937258, 997993585, 305625211, 535857787, 357156436, 630600836, 448232069, 94269910, 648737761, 745558338, 394381066, 34134522, 86492788, 383259062, 650939869, 455961379, 201365368, 351719784, 888270213, 995063186, 554564634, 356848291, 150722161, 325551399, 679783145, 269409756, 920866741, 264348307, 466050933, 794769058, 691251159, 683764477, 483802812, 773212158, 120591452, 178153591, 961556439, 752369053, 205822320, 902705331, 352459958, 151630344, 971585578, 988614948, 372860828, 714814893, 742980320, 299996082, 716603946, 784819410, 163319723, 145556174, 402908003, 844749505, 938811841, 468061323, 514528083, 744013414, 590443249, 104254797, 275568862, 824035155, 387929096, 688830919, 719012036, 822337082, 366700867, 380252723, 721884996, 145389558, 678351481, 13524306, 219726969, 574213679, 284650660, 404750202, 987130780, 540111236, 105010989, 901486662, 405435963, 386168566, 14260086, 88240121, 426750443, 113659236, 344966040, 817143679, 666206999, 479214505, 500639280, 10072596, 668084788, 252172925, 514175439, 989751676, 843738987, 52420190, 146327201, 645114564, 566693437, 917662986, 197322948, 129956511, 102616595, 763856407, 662828821, 776754286, 19405554, 510541809, 335713783, 567517224, 261026794, 432539522, 212967252, 99166365, 446253563, 142722813, 104824695, 60595603, 244139769, 755035094, 681726466, 125173240, 9578851, 619529435, 636415912, 876202954, 78469011, 717871799, 82900499, 878527333, 820002426, 518551060, 47490290, 101806443, 389234853, 386551227, 277328592, 737604086, 132185282, 669034485, 969435585, 598100955, 715811776, 636504784, 856744429, 65590208, 898833611, 55518828, 939547371, 701227139, 99840370, 281535449, 71566599, 75896634, 27526300, 114765775, 784727425, 929364147, 327420087, 138185847, 9772389, 13166049, 310284843, 840314958, 155692526, 281999868, 538436225, 461005202, 107068321, 295215952, 462345389, 106901092, 485209488, 184976943, 393386691, 209708309, 191612465, 751478592, 38400941, 669583145, 614108024, 640074950, 131850921, 224195497, 918701737, 214072355, 728940370, 853807440, 904862675, 440153458, 739254614, 820984788, 899613793, 967296548, 95722450, 453022010, 933979785, 386684850, 538790156, 639525323, 762890702, 684661339, 774632435, 378089322, 225886548, 540219173, 774451779, 485166257, 67113848, 916253033, 699535512, 774795262, 809291986, 763849599, 105766401, 796439230, 347886791, 591223154, 643944645, 585946760, 853220638, 745467455, 843961391, 533033587, 648456993, 669100164, 130348532, 937840327, 126110711, 874305014, 821819998, 886853806, 917189549, 477262712, 4191601, 564864806, 797294662, 718628210, 325044849, 695231254, 228514290, 595127536, 347062987, 501331700, 562518091, 847419589, 307899781, 539024531, 116965848, 221822793, 866296887, 334685650, 323707837, 748457326, 732555907, 970997331, 304449202, 228940288, 252590977, 769624648, 392426317, 114951730, 403636625, 65941958, 602535988, 941290997, 268778904, 936087319, 818876600, 92608052, 994049900, 529071482, 235847346, 156533418, 832863780, 940457909, 228726355, 745384272, 453710879, 438555133, 61481725, 213525205, 424468067, 915967002, 208399975, 749434019, 145356082, 436083801, 630053680, 23170609, 29615523, 14776093, 660036083, 284320398, 784924981, 103301722, 277334674, 689769090, 222833413, 463497468, 581990211, 794407154, 598563157, 642264712, 214883292, 57145794, 611740147, 316064632, 183121636, 529488030, 713886317, 237420240, 269498457, 564536197, 18387356, 20515055, 132931990, 746087756, 622754828, 859605228, 270612887, 479963670, 599736739, 331999666, 968333759, 478220276, 578730886, 312123930, 194810515, 70304493, 752818835, 593587012, 217597220, 148384072, 306543279, 645496960, 389563472, 689716124, 709441316, 886503896, 111926986, 254986711, 299853548, 615680955, 532067658, 779871424, 347203465, 424083656, 593446231, 186417032, 121671462, 848516170, 980413883, 714077280, 274122656, 322170780, 135680177, 308493679, 265979305, 980182866, 763411515, 115135797, 779671590, 707046748, 966022020, 746961000, 492381879, 83665402, 779728695, 705854087, 744869949, 268069690, 687432118, 409025612, 891709245, 798766316, 472170991, 696814503, 67387522, 482822510, 589276708, 13996119, 724767823, 522404097, 795688697, 446833231, 468352728, 130350914, 92120063, 303002245, 705712736, 504931677, 467983834, 288931058, 217954806, 547314205, 9688871, 170344406, 449686054, 435050745, 482666621, 396553003, 487586433, 406995978, 859004499, 945200437, 445103856, 424650261, 437296786, 160091128, 364137204, 280646892, 937287854, 835902905, 734961520, 749091580, 426027322, 27549675, 222097820, 492696140, 544895652, 129658139, 851718998, 763152507, 415766999, 473936583, 782901222, 770764330, 153603879, 366306397, 422894072, 876218872, 726960789, 229086088, 242631193, 136685804, 657884309, 427359214, 364185871, 265918942, 384184510, 912530420, 622103381, 266207244, 239390389, 48521135, 441753237, 256977240, 133849630, 579369454, 154046249, 937204148, 784363338, 653420708, 678159901, 682224900, 907542747, 961958137, 662702044, 38787740, 695943210, 264935143, 887146647, 128269367, 674976090, 504857095, 405195138, 374226705, 952865939, 10363092, 926672936, 827263440, 992988245, 542119717, 547928198, 934926247, 292266020, 816717854, 767206041, 11767068, 761747754, 395951348, 698644151, 139855839, 93023263, 627447273, 682484168, 703158195, 841969922, 218162894, 766202511, 900361386, 94153238, 277274942, 740955526, 645846502, 222084099, 400928018, 807356852, 378685388, 934495764, 412321665, 904995946, 783396093, 842581450, 373874962, 442737980, 466880851, 5500653, 177066758, 297564931, 793161302, 302530136, 511943523, 617396687, 13243465, 816544425, 484808777, 625168317, 307375821, 215338712, 73090113, 221790043, 735275174, 621241982, 576869490, 177097903, 434065749, 355235213, 21696126, 656547690, 245072611, 207228542, 477178537, 905475705, 791774666, 370147878, 465023810, 296552025, 810219913, 246356315, 161281101, 258682040, 453800214, 980282937, 768980182, 172560379, 480722808, 881673460, 795982666, 677874875, 376907516, 403667377, 426089990, 931432601, 986043866, 449798831, 965755201, 877047537, 552357535, 323997857, 778521883, 299140642, 694928323, 236517854, 301514239, 469970109, 844657739, 905273260, 68677008, 752546875, 555750605, 965368118, 346975839, 320153753, 890657328, 370759910, 326300523, 361204642, 672027973, 659475632, 164943876, 735627829, 800036331, 607321884, 22618501, 945064190, 232359073, 624917983, 416495664, 191484105, 96210571, 861164540, 229889095, 170611314, 309756653, 453517442, 360101524, 40182056, 419254962, 379702688, 419383449, 661599392, 902465566, 977344788, 238169649, 837886834, 644510375, 822034485, 436404118, 60474682, 641397071, 732215680, 704588629, 418744616, 22555554, 883253333, 577516294, 740680184, 800712521, 763568243, 166867832, 694561312, 453698769, 929071274, 45961852, 646357776, 906369822, 960003418, 642978768, 923153983, 462462807, 441469159, 975511785, 818796375, 13061984, 62807383, 423307990, 108770293, 491245407, 909311400, 113230781, 863799141, 840899936, 715723312, 340691716, 269392014, 87609348, 251466970, 81962387, 945915473, 434257719, 817959186, 752419559, 15050906, 882887739, 798317778, 920301376, 879375758, 772235330, 219862805, 289765137, 79593065, 364509034, 94670309, 328986851, 450436797, 681695769, 802874598, 302965611, 548803735, 687447386, 626421274, 241528057, 424686671, 538909106, 635748415, 515532156, 220470682, 242771826, 687883842, 392176335, 809852262, 716273639, 565507424, 568072226, 745103990, 861024694, 281179502, 33366513, 611091211, 292540781, 194384412, 754195424, 243323030, 641384874, 171612861, 878609865, 877327621, 705584869, 655638886, 172984699, 154382270, 716072668, 126067057, 648936876, 710354490, 412172833, 840869771, 557471778, 742965422, 330860498, 406927212, 712326474, 341406263, 575138360, 184943817, 970545121, 175223031, 924085225, 449434884, 187782126, 171495851, 768716569, 250438686, 922630070, 162808845, 758506048, 339594056, 115935389, 458536273, 722928047, 433213069, 674559140, 567855165, 572531446, 437261993, 547528772, 130106890, 205713873, 385407712, 234127341, 830808653, 63572650, 666126259, 675342225, 553621919, 887286253, 895260311, 481417750, 537748229, 359858118, 722668094, 598676490, 955709578, 765577359, 588114826, 481328606, 522449454, 248178882, 532371387, 186764161, 659672264, 531104660, 305713282, 633200585, 765944549, 340343028, 624440808, 253124973, 538529624, 780472834, 119884814, 953334605, 648179362, 315301370, 513034440, 899751775, 563170447, 209134507, 207876425, 277128030, 467461719, 906953487, 619448050, 417895547, 883512713, 169343662, 326137338, 517832160, 212076261, 77387326, 282951065, 447337531, 796110121, 775635205, 793998942, 866076785, 995438122, 397852697, 933460567, 274195894, 383650474, 248465290, 637875565, 498627614, 538034034, 407412895, 931413394, 155069591, 760975128, 500490863, 526207464, 119660256, 402810652, 6231759, 302646793, 849076769, 915937596, 77737716, 353382057, 182391240, 325360133, 576519638, 122006239, 426056871, 322903985, 44115428, 291663041, 38447964, 379328175, 659239434, 915342114, 773113809, 435127599, 584488661, 20802633, 789128521, 459996626, 609458500, 108403145, 177731317, 730017426, 288795724, 880636878, 510499157, 874650585, 954313362, 600561506, 890411103, 995850330, 980219082, 936724713, 972874604, 113154008, 925756228, 659319594, 661884619, 539469994, 951910645, 318045208, 208142063, 153345529, 58146804, 863132300, 640074959, 101663102, 449710593, 345123077, 841774926, 837277424, 5609682, 776193072, 178677051, 67774698, 202024586, 432083536, 212887641, 180981525, 943067197, 930902281, 529790005, 527758074, 528234749, 453186210, 254305097, 440074139, 719738724, 231409609, 50180430, 463983102, 394538670, 964772704, 113710452, 199771185, 947126055, 832581440, 465302771, 677298093, 626033222, 65934604, 557141594, 618103185, 747799953, 220793886, 715573827, 226562041, 474372890, 876699056, 545810662, 278524051, 647717170, 880425476, 337993606, 143543197, 674454263, 30485978, 542023106, 635391340, 368258062, 858414428, 459895136, 81810869, 623263942, 71904775, 733017653, 3257160, 955987163, 769459492, 595041258, 399610049, 203570730, 462720055, 351620132, 257584146, 409966220, 242155586, 997447042, 808322717, 528225311, 615509000, 349291065, 601610163, 791569879, 255372151, 747433608, 656462710, 616176789, 556386116, 64207688, 404090963, 664057896, 882426521, 958745976, 249529132, 383519410, 529924640, 190837427, 936334133, 664419976, 393828040, 16597383, 391222621, 181660758, 289552083, 338747754, 311289003, 761525166, 579924860, 855938530, 482400316, 730137797, 644535388, 429716853, 37243795, 356236813, 992169613, 100393310, 403105964, 190169326, 252997337, 536578567, 283308741, 853054080, 18300158, 626827610, 971270932, 36523668, 558316526, 489248464, 733024290, 664208599, 731290035, 980332699, 331545266, 447503228, 66830286, 290871090, 122686563, 915048074, 882203672, 243761311, 494570981, 944839692, 160834566, 892935812, 153464185, 406320990, 413058083, 391470840, 504507293, 965990565, 463889105, 522796302, 977376607, 454750928, 154805856, 904285332, 809854230, 827245688, 499467946, 115954994, 678044105, 632769508, 681773826, 300257514, 216253335, 119170222, 862633951, 706805233, 789668490, 157612607, 200587281, 863222346, 415729787, 637165729, 210580216, 550288003, 847379034, 83088159, 900091703, 482024976, 672626924, 665126656, 343313975, 356205451, 369781540, 527125643, 518008528, 957570556, 530911825, 933611234, 12747404, 178404863, 62523615, 873925844, 915008100, 146147319, 971644491, 843012296, 395991207, 560918319, 594647970, 44328989, 246434640, 916047667, 992173867, 597490090, 56673897, 538831137, 512112861, 818787386, 795383469, 494724133, 688865476, 325490330, 911232429, 350172270, 533515525, 31555297, 838764031, 869955248, 576906911, 281131117, 965347857, 431551523, 802792199, 77927702, 635417966, 926080849, 463008189, 316224621, 150617510, 562825207, 813048585, 100519896, 665633741, 925711847, 549060675, 478456209, 860035967, 867693921, 271984538, 532414663, 32830327, 578892237, 542165116, 206820898, 249746087, 809842400, 134302359, 910567754, 45795305, 511978532, 632056752, 942070394, 340309735, 990758987, 685914211, 887914694, 792795099, 838292628, 376689743, 310084120, 404424468, 774442839, 937361296, 353124649, 757197016, 919206247, 10665028, 482648276, 396529581, 924112819, 708863313, 28392373, 209356915, 549237609, 147546935, 901347273, 659321078, 503645415, 456912870, 951049796, 2141147, 488128069, 904467583, 977729171, 90373205, 853954707, 93509668, 533184971, 946524347, 698968854, 220935105, 396081351, 448552309, 177823368, 219665004, 575489025, 754994258, 956609650, 544387882, 803989465, 239498439, 779290903, 183061653, 652093164, 372158138, 151869953, 224009123, 630717653, 861156535, 779457977, 162951920, 304605136, 26317500, 673826759, 790239519, 69537735, 529302750, 74362454, 376259388, 142120771, 756440227, 225639916, 586674529, 416563484, 699628267, 32473396, 409358154, 236509130, 384068184, 789626037, 148769239, 790004861, 882999002, 113693636, 893683402, 927872522, 522972675, 545535202, 875035079, 238746861, 630565261, 457201226, 713909678, 342619950, 339170711, 389583848, 162934521, 367012027, 101516838, 596992239, 689744793, 452631902, 698890992, 769239504, 793020655, 267032966, 613644452, 97474368, 731125100, 38082803, 402037323, 873077076, 822377458, 546623749, 199358731, 116808391, 293077137, 482828536, 999096398, 979284899, 880737302, 452137555, 872626904, 581801254, 981899168, 802735827, 173681252, 639354195, 651943636, 245669476, 89675195, 345729503, 79414217, 253769581, 186443125, 119824387, 274198495, 940922572, 94896809, 692462972, 771844935, 888398937, 496908603, 253319301, 511682790, 990988682, 336310952, 235091552, 431583247, 721125759, 807655269, 2732200, 949424943, 757132666, 260136852, 284922698, 203016354, 517744582, 305204070, 175043218, 653424595, 119393673, 828478635, 701332925, 753615336, 862288383, 1654968, 562677046, 439147265, 489698815, 948849696, 603243149, 985398491, 508423322, 708554003, 220809129, 474558040, 78312231, 198134566, 207086586, 231636819, 771698792, 581173667, 331916938, 512117726, 131009430, 457838937, 54057143, 960759199, 487509864, 152416886, 435108788, 940715163, 748860228, 609715419, 550583848, 954413228, 220733916, 848071823, 593329324, 247918724, 676448622, 576904137, 589079622, 892152760, 720611345, 566284189, 314187655, 396394533, 905505800, 30399423, 479718980, 748773353, 36008622, 455202271, 261003477, 362460814, 10144663, 985477176, 707491204, 711699519, 185855993, 437644953, 939417540, 695784442, 249556486, 431968459, 968428575, 185462068, 819282691, 377281464, 5768789, 216221404, 436877215, 842773505, 447018746, 742866466, 751009777, 700449983, 699271081, 668253553, 971023312, 438447893, 927037672, 714835184, 446744308, 597447925, 836359213, 771461963, 987784048, 401152464, 410415443, 514570654, 951041605, 198337406, 809832693, 685090811, 688118514, 323749820, 323352213, 821964083, 126539084, 784070552, 676960100, 463516716, 565382006, 163314280, 80229122, 607028734, 571248930, 536040511, 108255601, 750237653, 871483690, 312398094, 22712474, 455569795, 758338504, 436193212, 392025604, 250386181, 967527628, 458918577, 523083475, 965873848, 940505515, 358838427, 743670923, 782955769, 751783755, 557191108, 457917092, 253890200, 829315231, 82258222, 101128386, 560837958, 387088578, 686431672, 68604824, 659827184, 170944772, 951782976, 558872016, 568323900, 489947227, 373258871, 709517022, 823486453, 953074954, 172229998, 713346615, 39620682, 874907717, 304642991, 741484849, 341462453, 846639744, 326855200, 144318082, 690136804, 298243596, 933674299, 101670732, 587548471, 622218298, 521303407, 820734323, 807029723, 217515259, 623335757, 541644438, 866271312, 49370470, 671292519, 119712551, 409226982, 634833192, 496427743, 62270180, 978224323, 796567098, 627048541, 409292865, 515327270, 912781910, 105543769, 574686388, 611150849, 541036321, 560452092, 797447338, 859250066, 731443509, 779408531, 808675248, 292627884, 724029081, 167455501, 667739603, 682149342, 92918258, 499484230, 653748889, 810288126, 132653316, 453021536, 445836074, 8081469, 993148462, 722230609, 828947796, 254718635, 970373796, 301112477, 450220074, 744130892, 972573335, 375056718, 697175261, 303016157, 866121895, 795533664, 552003185, 833793605, 762325167, 891995743, 345256790, 717097645, 436940331, 106278844, 27754746, 379554207, 286755141, 369110163, 607145102, 655009341, 571835204, 47862801, 352550562, 222785719, 532879327, 159316850, 197480575, 754125851, 191110, 83467704, 56720530, 252204408, 678152626, 254395688, 212999878, 973416851, 161183273, 766741437, 156510363, 790591476, 260293080, 36139309, 443711906, 944764373, 745513065, 878715680, 587442381, 925959446, 467406376, 699593498, 436986679, 472003764, 571681218, 573189543, 301463730, 91248982, 149014672, 297958210, 599611288, 710981358, 781972278, 413272483, 986862277, 15594348, 980697792, 163524222, 278137754, 226656901, 271273962, 931136580, 401764852, 144459773, 50817760, 792741695, 878926919, 242382442, 84874653, 998103613, 749287106, 273846270, 920868875, 356147066, 372452972, 929863673, 70897077, 858049244, 136815880, 649360402, 37347506, 378659202, 695173373, 821725981, 362914096, 187868377, 467379441, 566055677, 334231649, 511436287, 52846067, 654418359, 321027058, 359874542, 355946773, 148969692, 815223919, 675157406, 286813647, 336631942, 944759774, 18737877, 70291224, 238121572, 338158151, 83941744, 884547400, 111284910, 993700963, 200783779, 811072935, 21408585, 147830732, 988656088, 576098186, 600538869, 853492825, 165670177, 570781688, 481646771, 69693534, 650728418, 688057818, 732146488, 360409809, 112951612, 58245412, 525826840, 955257922, 271507710, 985230075, 386035708, 992377878, 301700151, 454416880, 329296798, 616150455, 44215072, 730432258, 834324438, 284748082, 597962490, 954197790, 640432076, 776638870, 131011479, 952222292, 637468025, 56551706, 94968433, 843076063, 129506822, 977113980, 667927827, 444109128, 521262209, 534792971, 330232528, 519513376, 350734269, 413700549, 950458591, 53511096, 244229852, 283898023, 424175978, 587836618, 370345453, 883710455, 503023245, 105502666, 422906353, 205316474, 610333478, 967159939, 740365028, 981589637, 99051327, 961005126, 448441775, 579297767, 783630248, 894282873, 196592762, 356286781, 198120281, 893390942, 712743141, 283253492, 265694962, 442804457, 577959835, 674858151, 703296695, 190429874, 155591215, 690809778, 838141920, 346499602, 392040890, 255376212, 435541270, 739293618, 360344406, 183814564, 509338256, 320013256, 885041868, 455750625, 399526024, 628496865, 494219611, 265829064, 655626921, 414489838, 733489019, 186299079, 678746345, 385746299, 86174475, 321405377, 636849670, 832591081, 494096747, 584971536, 339294606, 723066776, 88177011, 102454268, 242953706, 744612204, 271091184, 343654145, 186323516, 133619441, 161334339, 94148197, 820445624, 449400585, 638939726, 681038749, 458087092, 523993155, 940245700, 759399604, 791113066, 681216247, 264218754, 935070793, 497939615, 472017383, 563584451, 96283537, 136393106, 632803692, 67812024, 626524907, 130340981, 663121947, 527873691, 58976995, 160554817, 681328210, 73288516, 848826591, 418824905, 633423409, 225626614, 545129803, 343643609, 319227015, 381011201, 578717739, 683077646, 834317071, 885582234, 457160624, 614251152, 566305412, 359653416, 919983865, 677669170, 775729744, 588452752, 412152068, 263713774, 449561728, 251321697, 758798994, 472364333, 13452989, 215499485, 427455875, 733265560, 555351713, 897521972, 52992027, 425460241, 312316635, 430226152, 866681943, 562973788, 51141434, 22586068, 718763708, 798113515, 693452496, 163201424, 97209878, 638739852, 32835305, 928145863, 940060345, 122709889, 279817012, 23460670, 628214938, 795302735, 153842139, 969270970, 284181126, 475764923, 260121030, 352214804, 559132247, 565888408, 36050659, 429968280, 999257738, 197155659, 399904050, 814553767, 719290554, 128621594, 271892338, 897883593, 937609771, 496891826, 727461131, 963364146, 423241183, 536922299, 388453961, 544863644, 623247080, 438052955, 820474308, 975952727, 919596825, 167981981, 128402831, 847726830, 708162115, 247311948, 700348516, 418905225, 26204255, 412216841, 14823379, 426653713, 805260024, 189898378, 564069453, 875582163, 872461792, 534948783, 708516364, 397684043, 318986601, 636137976, 131421585, 393853462, 367034150, 331647615, 126832238, 810093983, 480966333, 608481935, 498576789, 883251989, 894714261, 634473406, 651831769, 331001046, 264640449, 286088627, 53638573, 540749534, 353803612, 112698294, 37927009, 116622311, 253565735, 445929891, 651779003, 918247054, 943270007, 206463198, 746145035, 823311941, 27887729, 843266329, 425426981, 807981526, 735104779, 808459088, 895079936, 161255772, 740666384, 83689724, 666621557, 709255072, 499290939, 304249710, 547946489, 93840578, 867086643, 22936005, 777065980, 659413981, 733504919, 15049961, 237574092, 68324446, 603627490, 805137383, 222935431, 519390195, 7118712, 945817983, 260363723, 825197777, 456671713, 158760543, 520121107, 810462777, 780487155, 723840669, 120584278, 888337605, 749902088, 483148487, 365070031, 302702417, 962285121, 912311523, 101210012, 712874489, 6324937, 841064360, 696401089, 633808849, 405141792, 692764923, 484449917, 195463638, 459037831, 389160930, 776686969, 747230108, 770355808, 685488287, 326933302, 851378511, 193929573, 673874117, 9519405, 581765200, 990847043, 467718633, 53851304, 332656955, 814517741, 11065289, 171692410, 123260937, 941837143, 32961787, 986783707, 931922060, 250391047, 86826734, 198607871, 488015331, 158990313, 35723714, 864642783, 789712130, 30003762, 233758901, 169882036, 845200979, 522776078, 948998960, 531343661, 354000394, 863002749, 946494988, 531130104, 941852249, 497566688, 570003048, 46420337, 134639585, 950357205, 981611551, 942156310, 923305067, 889237050, 544512149, 183591358, 190962207, 892170683, 77990322, 124178804, 712406116, 868519128, 297078627, 56836479, 874607904, 717348152, 214733837, 205035843, 587822176, 591793609, 153553773, 167593446, 429184338, 513366945, 709500553, 983398506, 143951412, 199507927, 815223909, 891406672, 810415370, 613681838, 733233642, 115155989, 184104680, 383616310, 281012764, 294875557, 991192749, 979583317, 919920136, 352379087, 781250166, 539769949, 149072925, 576985566, 484517220, 961853207, 356783813, 382417288, 54546077, 805792283, 153943757, 156692571, 436546841, 503314538, 352254353, 28686316, 339505691, 656690436, 994336148, 886971752, 846884743, 810938448, 155548086, 859236161, 614638421, 839054117, 413400623, 636908983, 510179700, 652438597, 228224693, 337616254, 972475804, 468067223, 968868273, 482644907, 575828404, 704245297, 778682992, 597497646, 77535714, 408124920, 209431341, 48683825, 455999282, 126956166, 857951286, 6524747, 565807558, 353761516, 156745983, 312330803, 45603373, 955454260, 163387438, 149610768, 131585998, 921061309, 502581024, 330609141, 911244183, 415359109, 843140805, 664440439, 754426389, 491502182, 846619257, 618601937, 247926835, 186211970, 718454076, 116698947, 767612136, 695270275, 218795089, 758679389, 896118312, 979242672, 429143165, 21727548, 469373834, 326238888, 684999469, 881243905, 675699993, 66792724, 917796605, 354361922, 606553921, 826254125, 587716494, 227243322, 278341394, 149888410, 408792462, 855915930, 294138396, 500038320, 552444853, 958896390, 629279231, 473921955, 353164465, 750683228, 413283190, 559083674, 973084895, 350327728, 324049830, 819448147, 72359988, 311378114, 957890571, 262787833, 761614414, 110706464, 373073998, 978790282, 243098711, 208171896, 677151781, 309510800, 376272764, 886711380, 926135931, 603275077, 837220302, 389591541, 378060633, 436215490, 21553817, 595305410, 663724925, 360353976, 333622753, 22542545, 485068714, 519826385, 523531926, 358129826, 390304613, 830433583, 206071137, 724386796, 290146857, 535198282, 8380227, 47696422, 218497491, 56404889, 267231426, 69247514, 357216743, 243565965, 362912984, 302097974, 436866614, 575477912, 861256252, 512504058, 956661775, 250667384, 829839441, 867117698, 759428727, 45299178, 950461676, 760133624, 306570459, 307558692, 290739306, 435385951, 795293771, 966661941, 616868071, 24302014, 147800457, 449910800, 493631355, 106917275, 69319818, 744873396, 51679898, 414107677, 859356072, 467790182, 344749775, 382774478, 933107076, 604932539, 869464051, 712410701, 498246990, 515914345, 978269073, 394680608, 440184752, 482056547, 249987166, 250057797, 875225271, 132674862, 365141148, 49175762, 7221927, 612189608, 136923525, 142563764, 328509157, 98042181, 377397726, 921055577, 264079780, 226574179, 588023400, 935505634, 322673301, 722627840, 560165330, 659129168, 880016627, 645627214, 820577270, 560667581, 267483681, 820764801, 748046895, 630408123, 71614722, 578358257, 321657976, 504076977, 180449652, 158526096, 710459176, 610318115, 343457530, 817036635, 478829613, 349641233, 967451815, 989383848, 632907539, 679611628, 3338194, 57803935, 954452660, 372653539, 797030045, 955635644, 441137630, 965961460, 709443093, 288706950, 962942616, 79950283, 341912091, 680949768, 805490642, 272381045, 89937128, 564716647, 864523334, 863805192, 972096452, 678411219, 66700733, 607362203, 228937879, 180424789, 311759649, 783908559, 353669394, 974243195, 605926888, 167478142, 561509326, 158672140, 565852180, 543181455, 259775499, 518917978, 92076061, 453404582, 22868202, 678276012, 559889638, 479069929, 464079299, 871916070, 256306432, 471642455, 226515558, 769749762, 538992818, 103320420, 593766215, 906398784, 697985055, 931366105, 260798596, 765143089, 961598039, 663855021, 991893818, 205290608, 151591441, 547396930, 661706823, 532857877, 800640210, 201889559, 929291626, 857862514, 942492710, 555984106, 598315703, 765180319, 174207982, 54275227, 503319496, 566826387, 732979842, 31922859, 25145329, 999226186, 447509733, 390038315, 123022592, 632407090, 876605201, 778160774, 86840969, 340259980, 523294054, 266388962, 499941941, 448975754, 651064339, 587772257, 185725032, 305084357, 85250685, 484949577, 964245830, 787789559, 928053917, 242053520, 388249720, 102628387, 347878240, 982166799, 330734777, 292715402, 691526137, 720503407, 159918307, 4407442, 778116019, 736579081, 788307779, 278349816, 299268242, 157574211, 683883859, 404259787, 364893645, 9262794, 558861477, 366413488, 294968259, 546567397, 568316916, 752955466, 855589734, 885622077, 840188739, 576149977, 280373544, 527814903, 886747847, 443911945, 12591466, 979237229, 257895713, 120115109, 611773736, 476983738, 829713323, 437582839, 700679911, 518547936, 718827144, 537229440, 393638791, 819224799, 650292954, 105780307, 850882155, 144012597, 988196512, 951068196, 124493438, 155828004, 223784170, 534685032, 335006116, 119938264, 894275994, 590348912, 34028063, 68771942, 281446282, 750644859, 859898946, 471600008, 92139735, 755329289, 487562531, 331165104, 691224782, 94181281, 574549795, 446513034, 856151505, 172785387, 709643754, 806729602, 471942916, 926914984, 773707072, 67647299, 819961677, 510633383, 647192410, 306849447, 72017865, 345582441, 914334787, 319630859, 19611860, 862620217, 445542396, 99610393, 9584732, 367397851, 747629700, 912645785, 782699626, 326694003, 660728684, 319415528, 17961446, 678383108, 61117671, 349815823, 183473684, 661239726, 765695347, 512036986, 392073687, 936652365, 10258403, 913414994, 140857443, 640638148, 411681631, 569475030, 212125992, 316498943, 318434193, 523393740, 584520776, 998261838, 275215604, 610681382, 720355946, 219803192, 413630367, 798351669, 741201366, 777010579, 499729238, 383014402, 420256483, 291190137, 322709428, 576523215, 338330540, 969112457, 187570124, 70624011, 68754182, 672642514, 175462387, 114130517, 460481977, 538155182, 892476757, 418942814, 872162277, 213338544, 337612432, 904111113, 519436940, 342138634, 118928233, 123211100, 90401757, 617911172, 562391218, 889318354, 124529263, 495787172, 638348305, 886817805, 569199910, 485634095, 848778720, 109676494, 920904932, 629403753, 113659237, 116009117, 654948905, 645376055, 414065528, 461555242, 527755856, 920228357, 330126005, 172218060, 483888817, 90933081, 375189159, 310669680, 792975986, 870455538, 251296201, 188117655, 633906507, 80854410, 562817629, 595648184, 416280287, 533990561, 868919398, 316506709, 532026510, 298172470, 625711757, 611015370, 138512091, 12922031, 668284073, 913973564, 929482649, 103126621, 239042365, 986127464, 97603766, 884777015, 496925023, 581246321, 337819543, 215377505, 120046570, 825822370, 832541694, 693701382, 94341939, 935011056, 689904122, 235637587, 406755694, 81205847, 328232013, 153801359, 427246432, 304310472, 38374749, 850938412, 776822150, 720803158, 217620076, 276514970, 150283306, 770847527, 81722556, 154630249, 931381766, 925022950, 413339339, 716346794, 472543677, 533092116, 644316733, 734058919, 656550714, 563990490, 787322078, 913116296, 77197605, 587827661, 784822554, 623366377, 939706739, 245066760, 980124616, 257233308, 689684639, 667833759, 367443466, 579661218, 406536593, 560577092, 773313222, 800070907, 799646415, 154722619, 356956677, 582613933, 14382394, 331759619, 875798556, 966140758, 931952982, 164483357, 769483928, 282788883, 645847897, 379792202, 518539476, 215392706, 740769641, 76679710, 282623998, 363459544, 850964692, 686278613, 283820867, 554381667, 287546368, 381719729, 373129007, 590348881, 669047227, 792415111, 135177134, 683494911, 2136992, 972783594, 682411018, 95346748, 844301845, 693796617, 723292386, 199963606, 16526311, 410100231, 246296903, 942164630, 950362620, 18712061, 952120107, 418433108, 406189598, 338650425, 207546422, 427740052, 195818393, 511955507, 862151364, 571863570, 880263403, 681251699, 996909766, 712916363, 651284464, 381988296, 505753320, 79823272, 256222931, 290160337, 661435591, 292126572, 496017691, 402809231, 571584390, 678369638, 607833062, 643773284, 100761655, 56163405, 94522504, 839203721, 81034118, 732983868, 176955481, 216150313, 657456685, 80589685, 864318871, 812199476, 486604001, 906545355, 450774593, 467401755, 205830621, 775207394, 458626206, 723722515, 143041049, 35114061, 580456074, 298070358, 628798255, 466478016, 130891594, 179776469, 873259073, 186697368, 481652319, 153287709, 762914721, 657292678, 110375727, 115164071, 303502894, 57287155, 235298525, 553820179, 99256638, 862305549, 59180551, 652546607, 541082436, 697271936, 205243477, 425669452, 525726997, 596910157, 55611534, 467420068, 484651436, 253721921, 114035116, 492457754, 108493904, 7305627, 24106459, 718958412, 888307390, 482954269, 739442668, 723820783, 972076104, 453116420, 527243006, 672329138, 261219588, 988187082, 692172139, 683243361, 359994922, 446341409, 34730512, 513051257, 549004992, 875407441, 339475888, 801978917, 341913072, 352032824, 73045462, 788143941, 486806907, 941207758, 704466288, 961300646, 615117414, 457455664, 307748117, 662071893, 681399497, 884371865, 811984687, 490101097, 639878390, 776156711, 30933800, 734355766, 49832018, 21553567, 494787326, 518872501, 588652671, 983971993, 557308620, 772727782, 172776052, 436625251, 792626344, 812399963, 436225778, 545922646, 288019242, 909659552, 683990603, 181957621, 71708368, 701403686, 39788369, 354644587, 239947505, 850151930, 559408927, 208751774, 267518467, 130976581, 528258771, 630843052, 224250644, 80358985, 930100659, 812714860, 878438919, 764846926, 902537298, 791516676, 921897788, 966461607, 980354211, 14741077, 582690108, 762726440, 802931766, 632907183, 28469309, 167463751, 738558818, 41149020, 99348568, 866093586, 614408536, 24104620, 338348521, 48427151, 262170212, 551573846, 886543808, 984129027, 563658956, 739251594, 863604404, 487838126, 248838626, 779830378, 682961964, 916562779, 955560284, 900325568, 664607494, 482503806, 263463112, 289806901, 582499696, 798157342, 659860507, 620710361, 936303085, 662932607, 188614683, 891858757, 165614760, 366850729, 984664468, 267661679, 141881376, 922523934, 682894967, 473632549, 904459684, 872326084, 183075629, 423123883, 877288855, 172003090, 440448080, 950794820, 387857036, 278163054, 472637823, 901824589, 726975016, 720036600, 166240653, 923302162, 319580533, 596306679, 228036778, 640870425, 441026158, 907699090, 394462675, 449037853, 247866276, 674405405, 893516684, 299087375, 87721130, 38054049, 904233468, 131186639, 123857708, 370170186, 344537991, 935149775, 955633829, 21999150, 544822001, 336098034, 791968, 222850775, 664573907, 671406800, 650644822, 624821321, 938638689, 317501504, 93437412, 756288866, 278335803, 909598407, 39975067, 258994972, 933841135, 674873967, 465081292, 174638121, 646906895, 505547010, 668563309, 558420199, 995225341, 20985172, 41349614, 496798587, 584219798, 335521128, 605527342, 663245372, 125415394, 168619762, 997267443, 490625272, 855214493, 998394747, 597156032, 777221429, 541754532, 225342305, 881154796, 637091365, 509500954, 679382043, 412009765, 646899645, 276283736, 881671311, 264922912, 763488988, 668927793, 69172732, 85477745, 873580884, 258604031, 106906998, 192681507, 902446708, 357272778, 146919579, 185735589, 950058535, 653675656, 78499060, 287665972, 466592532, 321113820, 14918203, 900492232, 366803924, 858496276, 199454832, 416508219, 674941272, 502177710, 565107217, 776372522, 937637961, 426627269, 286083577, 910453801, 879458000, 980962192, 752531195, 148885466, 808249430, 268302465, 882028305, 116246489, 235335348, 535188395, 245014809, 519385307, 943717922, 171225450, 364427323, 610312247, 236720240, 826629251, 669292792, 986093700, 669216263, 862269858, 400897320, 812023189, 746811695, 107960223, 232285054, 835761991, 691140534, 582225403, 330780571, 519658877, 996344573, 938573311, 223953098, 68659660, 741740498, 84523998, 76473253, 618535018, 461634778, 224291426, 5940777, 2209975, 175691483, 935735634, 184413706, 227320909, 651173203, 675093616, 906126877, 123463684, 927812281, 183640699, 621695948, 41260416, 243988536, 308119346, 545672418, 274719937, 649943810, 938471446, 165015341, 759269150, 786324433, 806537412, 287536065, 679695153, 27677199, 350332333, 993613511, 341942147, 404930292, 453985639, 410537098, 414719146, 767107114, 604078145, 271194973, 122155184, 354368128, 328086493, 566273160, 154937574, 312551762, 824867586, 256511252, 537055020, 224670644, 545790786, 887824585, 325840333, 822797125, 415543330, 798702452, 263860454, 137411294, 654572426, 805271771, 789788500, 853249358, 490343154, 174580068, 263277734, 91792123, 536858743, 305934676, 614536272, 21735800, 159046937, 219952759, 755245887, 81582599, 39474638, 605073366, 430231552, 4537200, 133287322, 342412261, 819069700, 946843442, 769630791, 824921732, 942693538, 929994947, 709505547, 99946370, 280394621, 636055305, 83426434, 73386901, 43974340, 301229731, 348032866, 683283990, 792067975, 660035720, 301439973, 882417521, 263532712, 252582246, 415834826, 814869679, 444470364, 192660594, 200194773, 155917154, 614048777, 611072455, 510328931, 928285363, 155911966, 181789298, 835248707, 843602935, 111209509, 91012326, 229683503, 874416991, 994623076, 970498645, 82404829, 857781682, 279764694, 668911290, 741130356, 771839362, 410927327, 475595896, 412909510, 415407331, 131879523, 232845576, 784004936, 895206179, 428529337, 605485852, 98737270, 233281582, 741576458, 250221547, 893690403, 481079345, 674263597, 610176110, 446606868, 343164094, 780632186, 489557069, 202248000, 608914861, 210384338, 881333593, 820608649, 451193413, 988795643, 844576626, 198234264, 358468755, 436796374, 498152287, 255467900, 195734649, 954184502, 78596582, 18369038, 675796871, 457729788, 527331512, 340265355, 640161110, 213741627, 347376402, 851426855, 528827279, 425849713, 932705314, 977065711, 925446077, 748008011, 467472080, 291514379, 737341205, 610389146, 684435964, 820693111, 805908942, 892710075, 860163435, 663339260, 694001210, 354596550, 711023656, 386261855, 82972429, 174108457, 498352664, 102485967, 721835688, 704424385, 559135913, 483849819, 277956217, 191278523, 106466567, 143695536, 177164952, 315304036, 495156183, 138215018, 159543646, 960663106, 493036428, 379780158, 711547258, 156599965, 66294435, 778763249, 832138239, 483022276, 725965812, 743351035, 873347963, 562634883, 976641104, 383669663, 32339698, 784727473, 37742842, 660689000, 715929919, 399474929, 104312692, 813353169, 749138248, 285400362, 743295569, 498606573, 786916566, 295437818, 441338104, 947674071, 109442851, 405626092, 18345461, 56061814, 779214307, 486140549, 649668556, 4098618, 375331443, 172899058, 921789840, 24348643, 790324683, 263383076, 190155165, 390979112, 668922470, 183526475, 425830776, 249650602, 660949413, 329674226, 271581477, 368724504, 156218924, 768246373, 894281129, 818389753, 803078932, 63488081, 109713907, 540595626, 313142350, 217560277, 808537809, 956409480, 52070499, 594825299, 940581562, 217446044, 663847115, 142919138, 508143660, 629432383, 306190261, 554267278, 90312904, 762193559, 303827283, 482080459, 762736262, 519214376, 13009024, 663398399, 369416678, 288577945, 506003829, 672454760, 304269823, 603849592, 454130773, 890929387, 741085335, 410580120, 305084350, 244753041, 42711220, 7180416, 699907821, 126631605, 631008989, 497252930, 912400023, 285043421, 364097786, 909741435, 537788243, 625141971, 46705573, 509880524, 395860786, 291662337, 754546015, 702284439, 349096291, 164382881, 569660269, 330392023, 82898695, 921738751, 52697231, 301372899, 362059644, 97827412, 894383914, 854812602, 531556924, 895887297, 217497972, 347757694, 207613017, 45761566, 287340801, 656976937, 782474080, 217718072, 767168402, 125217402, 867480189, 502474358, 745404887, 312222704, 857847846, 626480596, 201816938, 91037811, 771020367, 271153286, 910336763, 717802864, 300075436, 92816318, 745890115, 32765160, 606166679, 933971761, 714994807, 227242726, 978364673, 975922931, 695243832, 872804502, 652947256, 585880832, 292584863, 195257712, 108132747, 396424928, 338151174, 140230878, 466974954, 638582661, 261435776, 734339394, 810738994, 45000950, 45307592, 901926567, 754377514, 896860320, 730316268, 415807449, 419263561, 38073310, 931794880, 231021484, 747950505, 28637925, 149658248, 44504199, 469290750, 452206199, 445931457, 678906679, 713681286, 468098897, 112475442, 39155998, 806968017, 576981052, 242279728, 807633665, 502239145, 369417052, 59447436, 544823193, 932016280, 318020529, 24749070, 724509429, 441323437, 145190319, 516268817, 925048926, 234575422, 888009392, 938944141, 590550581, 417878389, 272305549, 596720572, 395521184, 43028012, 240122162, 96683962, 424729184, 718756805, 3199235, 71333802, 2260850, 434482574, 692469904, 632674521, 215445342, 826830245, 392400827, 937920059, 671816256, 702556936, 905195859, 395085192, 975138548, 768604555, 243014118, 377155345, 217013998, 337803726, 351553252, 122578293, 189822324, 434298345, 945214574, 285777998, 692416920, 815933536, 303518868, 227537214, 85577558, 831528138, 970515065, 887628555, 151712495, 809708486, 842457630, 291881262, 638671516, 699902701, 727472306, 151606175, 770032454, 226963869, 458415542, 463517127, 369568533, 734316179, 891115443, 312898364, 129217343, 380255813, 695790256, 319627995, 806049511, 662099051, 466183258, 699991422, 405141323, 796070035, 349543269, 924321829, 620059119, 356657026, 968587533, 949762128, 818762840, 6337730, 972788532, 440447728, 187753349, 939005264, 899381828, 835587516, 853138994, 312120574, 645085673, 685620175, 512218446, 881241152, 943583188, 102073392, 210669929, 454192886, 546470127, 370061341, 623489716, 190356855, 414713596, 754664957, 205268792, 379961779, 788323627, 930202542, 67338965, 116156519, 922392616, 435853776, 447243127, 732688405, 822428704, 517631230, 529133453, 72395627, 760620745, 707719754, 838562303, 779656155, 906075480, 242779061, 444448208, 350000379, 485386296, 895807793, 563220969, 252416092, 523830907, 802784124, 739680610, 347218594, 520027605, 74656724, 575392727, 933534838, 981293874, 854708059, 180389356, 322974446, 669573715, 861156718, 462012091, 519456752, 147118465, 259546974, 748128945, 601184336, 463518309, 742007655, 272266179, 10667670, 282988511, 660415545, 817636130, 199180281, 62077546, 63663864, 346528765, 196749137, 831786705, 61192478, 58554971, 954367555, 747105718, 864316913, 847807520, 690616096, 580347474, 31288564, 162861713, 902201923, 319830556, 837629279, 909537135, 231080615, 791933549, 170394153, 810627676, 140600862, 975194198, 29913354, 191004549, 937110092, 446563737, 43630185, 38050114, 727844671, 723189475, 355664237, 853758097, 760708051, 217174157, 865927248, 441220085, 315691446, 654690387, 685062010, 443482590, 231756653, 115465725, 426955492, 734511978, 415049251, 201590340, 636530431, 252051877, 517528500, 29837650, 49783845, 121238094, 760011423, 295618020, 533822196, 103292796, 903714411, 106145255, 30367295, 1364772, 149273709, 538774480, 219400184, 237644840, 738187261, 987837103, 810873676, 849949322, 132557319, 838074879, 136929604, 263490973, 549700068, 540089613, 754181559, 875555594, 144183097, 980019417, 845657666, 300979606, 618766607, 98416556, 215958832, 118402300, 390606945, 269796657, 709330396, 429680974, 540503080, 212202315, 168278309, 492224747, 26553863, 395495556, 90167681, 841319733, 478550428, 24242652, 336549942, 208047428, 531085360, 30697369, 686982744, 757998699, 986923831, 699766215, 807483054, 141019169, 90368320, 234683498, 351464962, 939459187, 52856887, 858573721, 295763424, 151223445, 340693047, 683997022, 905644219, 762139432, 666885723, 183895807, 376828800, 584124808, 769312216, 724698119, 429038989, 90018145, 89098985, 746118195, 762461323, 669816796, 808929527, 821214703, 271671230, 163840837, 138354672, 980331144, 467927936, 198769649, 532486122, 49122062, 805533869, 106478519, 445992957, 555837008, 832519260, 751287523, 188174366, 235900164, 730436717, 354043538, 611759744, 457926378, 476021725, 808848434, 237722595, 511618308, 430785860, 245224980, 437741919, 614376753, 384953685, 709729527, 811122008, 505425023, 408164069, 753800608, 470906530, 851338320, 645504337, 599706892, 343713536, 132686920, 415065369, 740126906, 497194201, 549479651, 863266238, 203106604, 541960676, 725983545, 410464722, 895396356, 744558290, 438552731, 768176778, 841523385, 328735457, 631045672, 996711193, 282922097, 157547040, 160772732, 27950908, 839951487, 655769260, 307052633, 330023700, 362701812, 539310933, 605132407, 414288056, 666395258, 32623038, 135894179, 956840338, 129816640, 97400853, 639169803, 205282943, 557646660, 729148300, 306940629, 459876123, 744028783, 158410455, 957540698, 843177929, 160066314, 103031222, 797773137, 770923959, 794551091, 402319613, 131232606, 275298909, 818545054, 644228326, 629899279, 535409524, 300910105, 188447951, 73496615, 312009879, 47765845, 958621762, 734392011, 188304467, 183341252, 577659863, 696826295, 357402089, 228770942, 536625337, 624338675, 863372747, 749915500, 964970660, 827542431, 219439383, 142986799, 269744924, 252843828, 952376114, 17855101, 14540396, 620995798, 206599715, 484202845, 514309373, 860197007, 209769738, 404520364, 89149500, 318770122, 831859011, 319625507, 907709834, 929304466, 172289047, 933000907, 48088197, 295190770, 151750399, 698442032, 54179648, 907425796, 629912977, 764963258, 402963478, 125723896, 320669803, 308212996, 98806838, 183768739, 850529323, 912065397, 833576654, 609702843, 482255166, 703250283, 867825057, 598425463, 677346492, 124961507, 565848670, 445337482, 770393256, 931579153, 11610833, 467405358, 414485199, 876448045, 897080713, 771216500, 920775009, 819484460, 955077101, 694091063, 210805042, 729813229, 317290635, 562162239, 275812975, 957532434, 88348850, 300391336, 778587056, 68681967, 263627047, 194029181, 957921776, 376032848, 165222388, 673472835, 925358023, 783151335, 469760361, 741455933, 78073347, 331001193, 166190253, 239505676, 540621646, 780685540, 661411823, 62429992, 321639543, 941227315, 838225736, 308686485, 194115382, 492979850, 440127445, 268848647, 685371525, 350174059, 569350211, 147073260, 475617558, 577885054, 746703285, 606107851, 468736170, 345594965, 334166237, 721121062, 180308884, 168254578, 85490032, 586891010, 245153679, 501848714, 355485128, 129706123, 966700628, 755289411, 477792573, 51883673, 424960540, 910889461, 9695931, 989026658, 13759332, 398503737, 145731744, 356830852, 288727112, 106591525, 544777651, 830974685, 958081454, 92846971, 307716505, 1122365, 506198036, 222702619, 848566638, 704315534, 998119593, 375340888, 339529846, 469598872, 950299856, 297638170, 810432399, 396501749, 762651007, 251975889, 840855859, 602269450, 406064833, 258437677, 299089393, 98992356, 800427056, 113362473, 269931961, 87130824, 271746729, 43141142, 489233675, 462961641, 848803761, 431772135, 192484789, 289752689, 67362721, 464363464, 557660852, 50823445, 891575924, 546325975, 735431282, 390508346, 500717824, 839723784, 636085180, 427197642, 154411479, 875470076, 931215830, 63994856, 16899506, 997012016, 232689928, 897179920, 513793771, 311425315, 887003569, 679187508, 464242903, 52119742, 852496977, 102997921, 21956903, 811297887, 845808774, 835970030, 929595715, 625691394, 739437142, 901567416, 580172705, 35910292, 443428090, 66937583, 141754336, 387760784, 125820298, 762487296, 851797159, 268636259, 190732944, 152837131, 824281655, 883186091, 518705697, 40895700, 346123043, 225327740, 382318548, 507661992, 46307416, 210032917, 226375511, 318140275, 392574064, 200838021, 273466996, 109160709, 37303990, 19170283, 804642947, 34224680, 842518778, 379185682, 974288172, 522391639, 933345877, 742200908, 817227156, 680735934, 261457825, 72340153, 998228265, 440471203, 302386338, 606448452, 797470722, 138163875, 925201326, 267177551, 229744423, 812099836, 989741941, 171814608, 580356940, 537711440, 659448335, 927897073, 958512978, 201236064, 147553147, 77022046, 326823972, 829529292, 944457989, 717636033, 455738859, 380750578, 581606584, 390344570, 147964209, 336930463, 232195618, 696704609, 586970284, 445591096, 232615249, 670650903, 652245077, 919744701, 94779404, 408657952, 677980170, 450611637, 708318360, 951896001, 791125802, 190241256, 594946089, 573411353, 28281389, 891573419, 499017337, 779769593, 143818247, 210535452, 46597977, 75081417, 238287161, 764954573, 608978862, 866644590, 693742498, 880760441, 279565411, 301143691, 77417693, 827002622, 663146963, 346542562, 305129228, 842674699, 968860650, 569364830, 842324123, 672564954, 248526309, 235883487, 494366532, 736548032, 609558639, 183669090, 420768787, 517101427, 491494086, 862168791, 917819711, 95976372, 354177508, 267773922, 764338908, 614699510, 149336788, 845697621, 176409562, 621121373, 607335077, 395908920, 765421529, 310200836, 668501080, 945690112, 832374729, 950134304, 315767630, 137846269, 229036203, 571093119, 882236442, 417892739, 207182376, 348345362, 125791757, 347900298, 219511455, 649456346, 383288225, 581730659, 833016385, 667137693, 887539256, 558607846, 568329572, 467837252, 637772766, 70959129, 857560501, 475377314, 504640992, 765168677, 315428815, 812297758, 530935670, 583651825, 104216283, 304840761, 699441770, 453046142, 561839844, 690160073, 857750195, 493196532, 883742649, 683942490, 683977010, 131618398, 357117004, 106480792, 77372076, 326919194, 549861423, 834618987, 905821494, 353637235, 518163439, 187349396, 907580690, 402278904, 298189980, 93522494, 375607004, 186778280, 817451454, 61469590, 218089315, 221933657, 625433088, 103228171, 79394522, 203543741, 149899246, 678978840, 931771201, 720204355, 147526291, 870538013, 623792465, 908449376, 410412112, 389430817, 506263684, 544015517, 592988747, 305887041, 585706960, 15375188, 808478634, 430780510, 50020144, 654673863, 225516586, 238308610, 521417147, 24132553, 51477345, 878332896, 531133291, 419675209, 938460383, 697449252, 484488907, 771916424, 172638034, 86248041, 952090243, 7331047, 240898572, 355486707, 579380063, 327393828, 21649059, 840250798, 160490193, 9534382, 176724635, 220038298, 716012288, 360771567, 258603305, 453681382, 202258182, 751217713, 861587917, 878714956, 967653405, 385456855, 319205917, 130179888, 183291346, 188871693, 794921068, 177896855, 910931488, 233122524, 57036327, 919308611, 831518991, 70800999, 674140457, 454005360, 839196108, 348756059, 77410248, 144781812, 496822173, 742340833, 410547755, 432295600, 340696016, 383137870, 656652402, 366479878, 593777147, 799262747, 165752850, 373680804, 134879441, 909195480, 481487733, 870628466, 136289853, 622086716, 593855566, 44947374, 745125257, 701563402, 810394404, 191315688, 872059089, 9727702, 11357346, 654960664, 342918908, 144119586, 958133617, 847678102, 899058957, 908101698, 128144042, 790019702, 649700441, 898836906, 832403948, 264982871, 150473044, 165141087, 735105803, 525359968, 422953172, 231666363, 636695002, 616901869, 886705447, 828547271, 90687584, 992927470, 996542641, 225889349, 222587693, 698307677, 26140986, 784250216, 267233503, 60936214, 410743698, 449066409, 903325856, 322827976, 792800245, 881096689, 918297828, 542550835, 698614673, 451396308, 368997572, 979158492, 589721370, 440079381, 939945862, 293388177, 476175676, 989150567, 543950449, 769356492, 121842361, 538697859, 995490307, 427815317, 626509600, 275806743, 434144640, 262728736, 32190587, 854499567, 472762127, 963005240, 914738084, 287317604, 573638192, 421131499, 381157205, 230431737, 275458860, 150187491, 204953565, 304577882, 631267136, 187877068, 945933055, 477662364, 134988972, 907446580, 592200622, 311569364, 357738776, 998623491, 983082280, 968903061, 611072664, 205347207, 580654246, 835532914, 589687497, 909449096, 20935542, 457217198, 491698089, 202644816, 81077389, 846973073, 273357079, 207721218, 257001127, 958703733, 106043656, 538495542, 511145655, 962692982, 352127529, 93580435, 692376431, 668737940, 183941612, 49837630, 731315857, 197168843, 352144845, 506513021, 503970341, 224321945, 46322820, 963806490, 536977711, 612105759, 537965413, 38847259, 113237891, 512058976, 547417325, 743719640, 929095934, 131732406, 847518246, 937086742, 973674223, 601243405, 810918792, 813304598, 739884018, 49147964, 54945803, 125374840, 583267566, 764334094, 962367191, 708121561, 916580948, 247330993, 640680661, 94566748, 96817957, 233780747, 410653224, 864494569, 364301213, 83012652, 517205672, 426144724, 212009812, 718984621, 573491999, 864288807, 774435881, 418043501, 287830170, 122813150, 399080832, 561893134, 810433325, 624437637, 43683655, 920990410, 761588457, 5929915, 501999378, 837240346, 116915600, 470698717, 885786007, 749873332, 696670459, 197112293, 704696980, 428337317, 688353983, 181536967, 924343916, 18148356, 974079903, 981877249, 143865689, 254451039, 905101152, 743353007, 662270743, 54184521, 71484722, 686192837, 400502772, 431527031, 647327973, 903585676, 752160660, 303737394, 545602734, 978829849, 243036636, 921334221, 982753833, 452962424, 793957994, 130125913, 553293190, 114555372, 624677572, 810816862, 198197982, 474192133, 798324399, 237709423, 349588652, 279645383, 913382256, 71293937, 440776795, 992449482, 681254016, 247035043, 621853349, 237982138, 370190824, 565326974, 816124993, 991280932, 247745035, 389207750, 973675204, 142201632, 596953568, 409235322, 786971959, 567248154, 797398862, 748126685, 492029607, 869849088, 103832552, 982925401, 388236036, 700802252, 462722249, 295764793, 432156440, 87252336, 978404917, 279644149, 52128006, 233727008, 116818673, 21323443, 335148942, 340493116, 755880468, 236384079, 363304394, 159830449, 458480617, 483437198, 795262405, 261379825, 321947057, 659316571, 924108959, 207112692, 580339413, 685070536, 904497780, 817661563, 942928916, 518970302, 610943286, 388326967, 248039767, 606645385, 405797780, 218260718, 569245356, 838890325, 862448791, 420055193, 889929622, 312556153, 715530133, 157093240, 211748696, 870394365, 278754193, 57780127, 867919930, 725175898, 446198986, 482739813, 224731710, 326021778, 712239752, 874418387, 819849946, 349634452, 371363868, 15068087, 292631152, 46655874, 884191712, 808233795, 882686212, 880101290, 948485162, 436484433, 344867116, 919340761, 45964043, 494048203, 242916101, 898185085, 990289696, 895636314, 335728325, 639764796, 178451461, 387738245, 939112765, 405638860, 260160649, 334422926, 787792314, 734060715, 716446050, 387822203, 352728343, 707267841, 472565511, 646748158, 408502436, 402524172, 909809065, 337739192, 149433203, 629518512, 364350079, 906067810, 301316119, 22519887, 609076862, 329318412, 222903723, 192319192, 561612654, 657010639, 872713229, 259792888, 368383239, 469139659, 770838847, 527292355, 546492521, 249814918, 412359095, 418304604, 145124018, 184897588, 759362067, 424173623, 803811158, 438884343, 793227300, 911562664, 128773676, 88075407, 256080858, 337733147, 405375826, 952302343, 465453117, 637453413, 59522115, 953710956, 178223073, 509201999, 384796276, 340827312, 724033228, 648398647, 764749989, 7691524, 268883614, 726200738, 790363458, 163234576, 980932739, 485347221, 9501766, 884406147, 679921443, 246739651, 864324046, 601842621, 612545934, 744645769, 668811877, 687625126, 306131768, 649445217, 121694244, 466249364, 564974407, 865997, 638040307, 559768020, 306105440, 291987153, 978801326, 342907459, 372230598, 348626476, 294771142, 89609539, 410134279, 236854449, 384997951, 157190076, 54676408, 543322515, 379564305, 206424112, 218880549, 657175320, 90879541, 631032936, 868144783, 415867004, 577701991, 897638201, 861996781, 424167318, 246924552, 269515001, 339967367, 817477559, 195962604, 61088570, 459617793, 555383826, 161591582, 914620268, 719753943, 299952796, 721756184, 663735613, 767545275, 497076058, 995891990, 940544546, 642951002, 19187792, 539846558, 747738362, 304318150, 109603633, 328643822, 6334334, 454304234, 620333433, 958482083, 829335015, 543987775, 942221641, 65395104, 809243864, 32171646, 848375333, 52937571, 561600628, 713140960, 104705326, 840947407, 77380374, 421187709, 257725900, 630497594, 109155437, 13496256, 7027641, 847261075, 469542354, 482691327, 541271750, 643965167, 212614188, 740096501, 724492318, 951706084, 255081134, 997385736, 170225504, 195701050, 826798081, 897334106, 924983957, 531672707, 500622748, 193127076, 923378497, 489452936, 190324202, 885820526, 123951688, 572354792, 230851608, 454458933, 103945799, 19742192, 225004856, 754154749, 668052526, 447030515, 458330384, 204481567, 742389942, 475271841, 799303958, 967803038, 123797891, 937499720, 598346441, 934679920, 492158691, 560166987, 484065126, 251261078, 861848615, 927437178, 58879008, 365326610, 239587810, 969217903, 208273084, 889677732, 327784389, 476776332, 743915838, 893909537, 579898947, 436375113, 163303483, 351473046, 858210984, 975315604, 918199619, 322451666, 401522381, 328592514, 569206933, 681160030, 517443431, 647701337, 126973372, 365607183, 275640930, 603949359, 272137161, 137510109, 134932725, 729714695, 303929323, 714754886, 797200648, 773618260, 749945903, 346065709, 916592688, 848750809, 858966919, 746524649, 220689568, 379391878, 209067542, 586271650, 646667800, 674592007, 164279989, 925683817, 664992378, 587397964, 556434936, 984841000, 950674472, 817766443, 127469420, 170271031, 445905382, 24857217, 58497020, 858941753, 21622432, 739312450, 866449283, 696756995, 957443137, 359831477, 39971710, 276757105, 721984151, 805619895, 692758397, 703520476, 502005674, 830858704, 568269083, 240705675, 26528451, 562047714, 762514850, 224407111, 625974702, 57551794, 851179568, 442769118, 828423142, 126792011, 65476375, 737862463, 452679994, 804524025, 97871468, 772627534, 143168647, 681467550, 753035439, 178165489, 37360048, 141895120, 69731650, 387557439, 953699554, 365006433, 4503937, 117605657, 128785937, 764486238, 373121517, 366856764, 266018339, 12016910, 57727480, 949875823, 60109248, 937049558, 356253387, 655275280, 148809862, 770690965, 599682049, 959473274, 640470859, 96853455, 343031827, 938464324, 184510900, 396137157, 85852136, 818576117, 18251312, 745146817, 797642866, 959556096, 64472827, 295270067, 400169634, 610269567, 935059624, 178623337, 788406711, 779053261, 887261374, 842013365, 167741105, 186406966, 315749591, 666111826, 788478927, 544039460, 271477857, 780662713, 155344262, 758375995, 699862908, 581282717, 147218367, 716305014, 959760997, 926389988, 929140846, 392260406, 68564114, 15825844, 551604500, 264952869, 776423136, 727025160, 75302401, 298275570, 725561276, 111046068, 158784883, 455990605, 832648632, 192202949, 828447853, 126706611, 218106264, 872605949, 981107668, 788355609, 781408364, 215710836, 931500942, 777902065, 944123306, 761466686, 769152492, 625340031, 352697681, 146353908, 779967552, 555346655, 501672712, 700310870, 888767711, 304734439, 978808424, 839072937, 413472761, 821354395, 433881588, 557823424, 466618555, 628216666, 505991582, 304676025, 778786881, 606553737, 435243067, 230748972, 975558835, 274478523, 273993377, 381162478, 906447076, 874876543, 449969735, 975508495, 221438406, 678510554, 457659814, 348078205, 961096661, 386484980, 661822316, 849950842, 92610978, 988451749, 119981822, 442173268, 107755934, 664577333, 315719330, 584239568, 712964785, 100526588, 702342986, 536630276, 485135363, 426830120, 618965641, 243833435, 903227304, 680776349, 660440213, 592199426, 161167338, 882776716, 877711831, 217127295, 431054338, 322253183, 542353710, 788729975, 259116528, 414216552, 67096084, 803873586, 102400143, 844823147, 894421320, 514914512, 750703452, 355734805, 849089321, 206337560, 285208440, 980480103, 29617520, 720066038, 381188055, 494950789, 921521495, 773068380, 750932270, 260692880, 700345056, 621474986, 782054060, 218288008, 461612318, 406649063, 747050581, 183844806, 324438875, 487052918, 353976719, 532415919, 442308979, 623743307, 867511372, 114428454, 249870323, 978869848, 734637023, 821028611, 953570227, 403176789, 660798578, 659155050, 23398762, 458817254, 778699758, 533556307, 784276353, 104105705, 101949013, 62024764, 144794709, 57260185, 135650117, 306616028, 502850188, 920929728, 129182216, 531306083, 66315988, 508927804, 618669674, 995812656, 174302636, 44606659, 564933554, 712279812, 870487766, 468889845, 477207091, 374364754, 917457041, 193305922, 482477177, 460046275, 958480065, 924161715, 53591722, 686803660, 592435648, 334938437, 848928216, 860114560, 895465398, 388239620, 424655699, 405496470, 848272851, 59905340, 199838852, 306193026, 919210633, 43961359, 611583473, 885169439, 88403258, 650286809, 307424617, 286341211, 195467346, 696715099, 341904601, 936452287, 256546332, 621395517, 617004720, 156668623, 180086627, 617438043, 975296934, 203993633, 447743213, 954330356, 675295980, 151960512, 213292344, 862418574, 338012598, 499325895, 312526834, 128071257, 821086891, 840542934, 418114893, 385213295, 622400142, 506309419, 959054169, 941816955, 621327568, 225500220, 637699723, 191162819, 668110916, 820889868, 732556544, 159051300, 136828892, 112537982, 1049591, 226275921, 569103682, 631937958, 221578466, 792940384, 511107925, 94485838, 595070749, 4051397, 600148491, 974500342, 217343604, 742708990, 21287671, 718505937, 186820208, 844995109, 347071681, 967262711, 962649898, 880825407, 414576718, 402377796, 785932603, 871309443, 954355569, 984224236, 620816823, 60617627, 309980989, 466180849, 784383663, 824074745, 433464929, 762322753, 132380813, 293653208, 779334338, 380711669, 736277422, 520751184, 778899273, 435323494, 374886812, 802486854, 537043093, 198905466, 21874450, 299538696, 884026010, 730893542, 549421630, 911845655, 21152504, 668061596, 98145981, 456789519, 537043877, 384027312, 669336959, 155717032, 520203384, 811119976, 185775413, 707556582, 799094231, 79431578, 974708331, 260917224, 743201808, 574780871, 5437542, 237597653, 276254756, 289631444, 371812601, 103331403, 803140243, 381018792, 607726771, 224139194, 731267007, 637708238, 497652408, 658315640, 51634200, 130593890, 664242238, 602060321, 630844718, 353864997, 579353069, 100958297, 677081430, 279274768, 273432432, 778443025, 604093941, 241580638, 123730917, 464271532, 181067248, 604121535, 22599994, 754842329, 931573915, 218416559, 803372107, 859774763, 193105272, 764926510, 185821439, 891598028, 268046324, 875369656, 776429459, 613845821, 537186713, 724752047, 314656705, 493388312, 8905743, 602833968, 317692811, 747473099, 955896338, 294146083, 403868251, 915107609, 973038955, 362418666, 415354546, 815690291, 880179391, 186539843, 459769167, 247473741, 610701359, 831437228, 301347713, 191768750, 110338729, 909369128, 755811465, 264836516, 161390554, 667072699, 25813167, 94636033, 153191439, 138894764, 290790843, 944438890, 178643569, 733867365, 722419305, 540404350, 625423067, 220047260, 597117590, 210317285, 218923363, 596091985, 495879607, 838793463, 931495532, 150388087, 80243195, 567796458, 233306825, 836982172, 390360891, 509155105, 189817312, 648698670, 107729866, 688106166, 177214180, 816403263, 289510864, 483807502, 797552663, 615971149, 849654771, 366485819, 116456478, 558071273, 288813945, 276976725, 386736390, 606527089, 164856560, 632808075, 188015630, 464508152, 332711203, 887227350, 18839165, 535439306, 251897815, 989127341, 511527393, 666874554, 528822371, 923493584, 812481270, 888467761, 349320130, 641253874, 225338867, 669170361, 101434501, 835231909, 542424022, 582407262, 24999951, 649075563, 774735650, 398377246, 12444859, 254060160, 248832777, 799973175, 880318784, 121940336, 899314435, 996693628, 344609321, 450585720, 334158157, 914454248, 553638021, 175336613, 169342321, 406594046, 754739644, 719640390, 686926181, 12653286, 443331116, 951328723, 682068013, 344763484, 91563703, 132505775, 588088306, 39910723, 642605663, 336668320, 671166180, 194126121, 545792429, 427178670, 113603170, 788452941, 846221591, 366830206, 823282557, 416713030, 794552248, 655075304, 762714669, 664025349, 648690244, 447010650, 480311427, 814404251, 551314622, 652970459, 160818817, 602778793, 810757979, 981892289, 585355713, 291223659, 512020549, 783357923, 997942154, 428297153, 719113687, 354020740, 799818940, 711319465, 769221102, 333389329, 988537082, 535653376, 692061719, 916965284, 926271918, 455134176, 346554337, 150825737, 642110139, 813968234, 990079920, 309972914, 525666570, 597789529, 555873158, 361477517, 84750527, 53958534, 97004562, 129194641, 407863504, 421317610, 882816221, 311060780, 377498439, 528887312, 154987413, 728801668, 879930164, 152261073, 696851005, 797224722, 485830967, 206899034, 11096761, 544671870, 679066320, 728305965, 897208518, 61373589, 687793406, 342303329, 505587565, 465939166, 364388972, 994693045, 348979502, 317656066, 441605598, 691909307, 555700080, 589685958, 613943657, 121529867, 460592831, 773356650, 934048964, 448827760, 60533702, 424619305, 863919174, 566484608, 284281721, 516926078, 156977383, 612086608, 326466502, 861994200, 197325612, 307643621, 672737134, 721959868, 986586649, 51345927, 13845429, 813200704, 283897605, 641764882, 74808605, 636557748, 132251089, 999452299, 693022041, 828291602, 165397557, 643720680, 196265477, 710651969, 578424128, 705982219, 775725723, 113934936, 448194891, 317404991, 902347115, 355602135, 441996159, 117784421, 608223092, 42907799, 583903579, 98987109, 196196859, 688686805, 203778743, 617713405, 416882988, 690269196, 863160343, 489851548, 572206025, 751735062, 642024234, 831564942, 849060480, 143571670, 182367099, 686044101, 250974424, 997578209, 49936750, 701899265, 748501921, 663697102, 424516478, 253173287, 380219773, 874829943, 328857099, 8285295, 645860944, 601054489, 535816651, 490966589, 837717487, 739348292, 780090507, 741211562, 838968349, 490779681, 213074648, 534309005, 602571237, 680364669, 74048724, 652852467, 156110737, 396305226, 120520332, 573322189, 553152379, 460866485, 997855802, 915198829, 906335111, 972661162, 606172666, 103219447, 193012432, 566448223, 705351327, 579582611, 279387768, 956908241, 548837386, 960540956, 457195820, 61880891, 129822773, 890541033, 729212946, 40754628, 498962213, 518054458, 187940764, 974939618, 40003675, 379003324, 669598291, 828413076, 735721619, 68303580, 161112975, 962782957, 805641333, 761336413, 597615160, 246918620, 672546122, 541026720, 300682168, 282160339, 504023092, 819141190, 803916780, 185897413, 234570134, 586760222, 973680801, 891627255, 977399625, 701474008, 80010761, 223723702, 276498347, 427904166, 384264781, 435998967, 429361665, 189364543, 105078895, 968728656, 222634353, 568562898, 548943639, 780498355, 717133325, 415809469, 100938973, 362222048, 57846075, 343860192, 929811642, 715435242, 867758175, 317219671, 963108024, 930237044, 722607469, 646486903, 623859000, 923185547, 610007757, 237695957, 568169033, 686443366, 331100054, 482667617, 902446397, 471781358, 420369246, 63074917, 803586196, 276458524, 96401471, 613183697, 75405555, 816679253, 34033402, 823839212, 431906199, 976388635, 732890855, 984399007, 917231263, 870395574, 310782198, 31255985, 568809609, 659279120, 992192259, 570259363, 821312516, 446391583, 765023793, 440540219, 614113763, 797605388, 955129382, 771128241, 251331255, 459215269, 571153529, 845407564, 668809571, 391894495, 939989868, 794605374, 298588192, 342844815, 136471262, 611057424, 10567368, 853074887, 661334513, 361997341, 76642646, 326278249, 424623068, 310946525, 872621620, 345678837, 840443269, 251072177, 998820581, 74761154, 376172352, 165438335, 205372471, 947599248, 594933599, 323892786, 110732312, 934107551, 755117712, 684497106, 332373521, 966460779, 959572111, 376923176, 168339182, 157030501, 692569008, 356101832, 444559752, 701815442, 999471023, 83565487, 552090671, 231321574, 973431675, 106109794, 389400557, 978698842, 575607457, 333737342, 518132327, 421729486, 489038833, 800984012, 851467040, 289850681, 2682046, 768423857, 879851517, 378041509, 327844750, 371449108, 182527083, 535692937, 170519470, 213085981, 438011762, 146947965, 832195994, 757421902, 294421857, 146126972, 665235827, 332067741, 608291245, 71328629, 104646507, 908591538, 240888983, 449158073, 721236605, 213422194, 264741975, 12517408, 742671332, 45335208, 152731904, 541058897, 309049783, 31396934, 308027326, 446545631, 287434876, 894977433, 879788724, 134719042, 924012622, 183152278, 479093175, 142163347, 697879092, 226906144, 893587031, 182236184, 691837785, 646137529, 585729178, 655647302, 217892129, 372930950, 978137315, 34075700, 899703080, 388196861, 315124381, 326639639, 876783181, 736765908, 934713990, 56939417, 723242578, 664513107, 167427437, 715163748, 510395040, 363679724, 326906178, 403370801, 644422044, 796901191, 446619533, 891551502, 355243781, 639385994, 593289507, 216185604, 951084061, 845477582, 221726010, 542406670, 484382801, 352547884, 369977233, 978332185, 67723407, 181749415, 715553377, 369563763, 364179984, 62953923, 149875435, 729696288, 461254477, 142360306, 995619786, 128180158, 45633921, 711421157, 12087500, 38438450, 953855183, 269043835, 989531959, 197820113, 581648986, 580094700, 279163473, 20699517, 319853982, 170047027, 766433520, 600661870, 342345627, 555334845, 907320281, 612455656, 222629662, 324093245, 793628597, 401682571, 452110779, 839989854, 925348758, 612137187, 907251748, 945027389, 457695133, 698431960, 454882839, 920749327, 121987979, 145731689, 742812067, 901273200, 377318696, 445308584, 654769159, 971819270, 950650498, 841968317, 198460939, 907641004, 118688991, 663503198, 336998394, 906547676, 927912941, 104319635, 322877796, 701957861, 285566221, 296144828, 205096694, 769888362, 666307110, 821293422, 111440834, 572393343, 697502000, 49292291, 56557194, 421528945, 23557997, 790716518, 862547671, 12061898, 935935100, 165797170, 529281400, 389258416, 924981975, 134850389, 264415526, 780895323, 380762735, 414566725, 120808470, 250028124, 878314481, 280482046, 604790169, 35510675, 215776754, 87741477, 187611631, 531541918, 190986471, 244058796, 531056196, 931320782, 5046418, 435237574, 198775258, 493050179, 255357929, 8254578, 586374550, 64450647, 798861546, 30605413, 961788412, 452796185, 438925542, 797651112, 517067610, 375573359, 903626820, 332024983, 598418413, 721557877, 134648850, 142294315, 409380821, 71077676, 687771565, 238727977, 205906346, 251878111, 693286740, 477311361, 642216487, 204328101, 378809136, 135698332, 501293958, 999858669, 756195399, 951795192, 659802489, 573216290, 154277792, 378515086, 45234371, 986077772, 928260284, 286327693, 247705055, 972436019, 933803126, 225839632, 672394262, 59244389, 538566909, 342152601, 360604800, 244575393, 309412647, 58016929, 155510656, 904633120, 885103746, 636008381, 682853015, 131878307, 574863962, 381327427, 783937115, 3073240, 753915855, 120174123, 11183460, 448523721, 223318412, 696229110, 391337329, 879133223, 886459375, 43334606, 603398800, 169378545, 321119632, 563650026, 359960607, 478190633, 967812347, 670734819, 965697399, 322269337, 935879025, 309937574, 835476159, 140304554, 508818759, 235889315, 290880868, 424595930, 669385053, 606199577, 946151756, 486633141, 542869934, 194733517, 678230302, 590327166, 180338630, 967753599, 364867250, 653265840, 626306663, 653821258, 790569169, 370028191, 58053464, 623810120, 310582804, 812919829, 340760981, 929809532, 156593119, 775965862, 450304838, 940328811, 540297388, 566030216, 875008671, 424442756, 366130564, 215030325, 781192051, 470671711, 341480079, 832986314, 271651497, 971387220, 223225512, 109541483, 98779104, 750713318, 92378757, 6859113, 182333567, 611641187, 606452042, 649260738, 857763970, 670092824, 114256277, 397999546, 270182640, 696925856, 627795690, 612858430, 382057972, 141019923, 221673621, 943511467, 897913880, 799902534, 853670517, 276015049, 941057534, 323786935, 565205033, 73897872, 690051821, 272795635, 181133081, 761146177, 998152620, 894449856, 55662529, 680673704, 418409816, 282446005, 320970167, 828432036, 544727516, 656296779, 897085684, 415644642, 410794140, 683325877, 348548182, 606019032, 214287859, 956395855, 779859894, 950888846, 446009650, 578512862, 772122554, 155458250, 48323652, 48904626, 300741321, 941615327, 816132500, 97988138, 386453479, 971074259, 34129137, 74856043, 556175303, 183767995, 953938141, 140218999, 773623377, 705437697, 553277748, 304511793, 464777142, 307453946, 965946081, 628458057, 444393825, 83204046, 554215230, 495225563, 673740304, 343313388, 822283656, 382551260, 842139987, 154741685, 998692997, 431490745, 666332010, 70840739, 344435595, 503814180, 361648899, 69673624, 396106029, 919287027, 237443506, 129028322, 649632673, 643091982, 863778016, 714495174, 294974369, 369205787, 774236615, 959847610, 313259742, 328775789, 83149703, 677475830, 48346173, 303705428, 428390714, 852899250, 181280105, 275088947, 364313094, 170219768, 985825791, 609582807, 836674014, 331615886, 608846876, 487840278, 332385535, 982096843, 833680889, 167818654, 149659478, 395058685, 720131343, 891595156, 181078893, 710531531, 528985133, 541603490, 295430049, 793269684, 435422980, 192649970, 389608300, 332764541, 670598120, 375747337, 919545420, 120339623, 857125658, 366371305, 488435609, 745524541, 500710969, 372503141, 555409562, 416611128, 824166430, 5366239, 812407106, 389726338, 132835448, 657796922, 487766040, 301891684, 674541748, 907499268, 20493847, 512509414, 434051534, 97328622, 648713540, 748361958, 312096046, 460977171, 520157474, 823534440, 118902406, 352196258, 545719025, 685397487, 611547958, 579246881, 623986621, 801137817, 514798694, 870554525, 765031680, 887626602, 830417326, 327602502, 375943900, 391392680, 97070941, 924099829, 856027264, 466058750, 242723160, 958977794, 772178302, 578882834, 537868354, 11175285, 265160163, 216901078, 864082709, 411321312, 175156176, 916917424, 658900903, 983235257, 34835407, 636893629, 280803227, 721419129, 272461144, 302856333, 403501096, 288669606, 166571990, 916131185, 46162351, 430006993, 114653498, 288799765, 899578561, 275549129, 569652145, 324701836, 1875303, 482716120, 610301647, 627794615, 487597851, 717844277, 697810555, 788719125, 116402961, 738975643, 973484900, 536322670, 557256334, 908277164, 685673762, 906592163, 218820863, 826513311, 274694662, 315775122, 61354141, 35465867, 889797638, 750329664, 247359149, 532503412, 502564790, 350479125, 896668487, 414950330, 66456487, 911033631, 260714817, 181897186, 202561872, 659860146, 852560796, 214582526, 368642735, 298786189, 238348637, 114491395, 199581978, 919899234, 717936090, 357843640, 42839688, 616869572, 761002970, 249999570, 889837565, 41815749, 65547404, 866345401, 432242203, 387014628, 497578246, 224908865, 181826966, 995061775, 620398167, 560954585, 51454265, 415167881, 708656130, 787798616, 98440804, 8858604, 357618466, 79457452, 111361879, 970301626, 216452259, 629158998, 671704115, 171998451, 16400126, 182899640, 800823797, 126179484, 945175625, 752939346, 486262078, 579207771, 60233303, 934324250, 477164241, 704773734, 968726247, 231838489, 199168586, 371867382, 415458101, 950943820, 410206779, 407288493, 582075807, 721761189, 830502828, 399803303, 955096460, 152924116, 20220866, 161722301, 388201078, 411807067, 859342636, 987323727, 53031590, 805034595, 330356368, 575723296, 536743629, 543626306, 521729886, 206765919, 785991466, 580096849, 521515133, 434562047, 556307588, 939322682, 817297046, 794833872, 384556647, 4313793, 458235044, 455404722, 925745644, 628283037, 662188194, 507617991, 774944185, 828570107, 529834394, 42713807, 69430001, 716764644, 230940883, 236469759, 666626314, 664376059, 699738623, 547776724, 489613746, 974181104, 774946431, 682416961, 265235444, 797621309, 877510381, 772980288, 821331446, 669985597, 227736732, 707456213, 387789135, 921484511, 851853396, 192041143, 161882318, 303050777, 784432021, 322640723, 939681766, 429009550, 955890862, 468996983, 41882248, 897001964, 618987720, 918771425, 437932275, 959996704, 171013700, 543958350, 768017712, 648073123, 426704184, 292680221, 657338124, 53855757, 732369515, 823824844, 936723658, 243365791, 734170736, 268921794, 238745686, 718077499, 340336555, 193048826, 939051858, 401680815, 776495511, 37811560, 161162867, 71891779, 932714216, 484671645, 125311421, 366648980, 967835435, 594226713, 452726897, 397078953, 459942300, 645922101, 370982862, 178327433, 740961494, 247235985, 489273009, 640398526, 448972260, 300308494, 92979829, 730202887, 715176701, 442607006, 976015976, 21512421, 936079806, 557395777, 213111955, 154457733, 343863899, 369675646, 560377946, 821362058, 198441120, 34506, 219156442, 834328434, 413242828, 133264799, 782538136, 528807922, 262796359, 243445268, 752862591, 913668985, 723762954, 782149407, 105155413, 547863054, 597081252, 117111390, 48996982, 381258190, 240176444, 870447696, 71297629, 80494637, 337682441, 299450100, 641691928, 855818562, 580974128, 692534427, 258924276, 121369905, 645227762, 412094442, 652612758, 5609803, 683296288, 9128385, 228792651, 955482721, 732616446, 26817283, 578985578, 94866638, 634428239, 865265271, 934888072, 41188567, 889006559, 408000921, 130754530, 665767456, 99602089, 19951446, 615721558, 518219227, 628630694, 556925096, 903825149, 32830901, 295429912, 164155610, 85515511, 329495171, 653717766, 867037956, 868811889, 503736078, 143056487, 815541232, 580572643, 851302550, 167949182, 706801509, 978664598, 974272189, 59904777, 192789922, 222206199, 22694988, 224897925, 808194159, 597868072, 978640002, 153235535, 433571529, 919356097, 217312416, 797795321, 846811650, 291409879, 247848910, 824317636, 559318742, 841447317, 211146269, 969170505, 868378846, 774870779, 745335720, 464643032, 819072204, 605020134, 151522012, 18157212, 602221834, 981629953, 856875383, 902025912, 893420676, 774686948, 20074112, 996679551, 756325216, 266057955, 35550994, 413361283, 868158324, 516666393, 638902791, 574967182, 497235205, 607280129, 559452937, 484464601, 753525929, 195090415, 860429825, 760935235, 279313873, 98758199, 184961688, 966458707, 786786025, 638471228, 255114608, 401817915, 677990793, 38968704, 576806925, 717117419, 714212758, 625281086, 994805658, 362286692, 545667352, 897088601, 281752189, 700771217, 190549203, 7709977, 364917112, 61467411, 508754408, 665606228, 734674823, 459278667, 41869865, 536351162, 126761771, 640637941, 790410062, 132693434, 559226521, 355658466, 383098232, 648955790, 210894114, 221663872, 204857886, 519399668, 574824314, 748532394, 933844992, 628084076, 82310208, 166091775, 876796838, 796421679, 267193022, 338431147, 502521184, 685215617, 981566971, 131052398, 752685943, 12151326, 91367253, 282218295, 886922080, 642362925, 482556015, 588730177, 638788591, 126886894, 51055613, 916571218, 997565145, 171128135, 22776854, 855461297, 425920701, 488000072, 697492469, 157943966, 150884971, 625030658, 282464407, 230756062, 657468927, 544656639, 880543587, 117783684, 199314509, 460609045, 200266911, 652160962, 326050354, 863783819, 355880856, 475342627, 510934703, 272076972, 266881173, 892110553, 953125345, 189666092, 718093968, 441402075, 800280757, 47727750, 129587245, 603995551, 883782484, 603853440, 877371209, 374237467, 76189334, 211029409, 9961218, 171974100, 569244796, 776646544, 323590865, 935751798, 367183785, 918666532, 998371396, 109672162, 597171037, 837895739, 242141100, 997673183, 965715293, 530946749, 162122103, 597710444, 406211400, 546903222, 47482574, 39854599, 99056203, 659394165, 825356380, 655099454, 537486204, 984678319, 229129836, 314970894, 379519867, 376500377, 2734131, 878291775, 102364497, 263014209, 488443588, 899838615, 791732369, 645638, 496098463, 889467075, 379407716, 104010431, 391792954, 215478045, 687761543, 85469326, 712878761, 585737540, 974802858, 54681702, 256988701, 65391111, 29581851, 397966530, 419820542, 365301768, 144512771, 31330663, 118580966, 431017042, 519379876, 25468884, 887632435, 942010027, 360869422, 712750589, 942730832, 914935629, 584981030, 342202287, 908759822, 631383359, 598502981, 445720045, 872305194, 125975331, 740894874, 334000455, 545945098, 498712720, 874886883, 689524010, 101384559, 495440000, 295956827, 285220180, 379111771, 609119657, 485366008, 913694104, 6432647, 240833940, 906361622, 125676768, 541222654, 190913386, 446198045, 276352106, 213930628, 661712241, 500850579, 454283711, 218360594, 845910646, 990919068, 958509152, 977598256, 899741200, 380851268, 332875603, 862190244, 332127660, 228506317, 824721350, 869994422, 38469217, 619595089, 231146114, 846278251, 651334560, 61745902, 56293196, 991703862, 610698607, 881959700, 152650584, 167470984, 857517335, 863802000, 208389484, 918737362, 401613108, 96543939, 881675548, 662898596, 35887940, 536427009, 366700501, 560039213, 346010475, 534359799, 74814220, 136016333, 268982872, 95334056, 626238233, 49234339, 836191625, 85270267, 825533730, 925050071, 749139021, 464862952, 270579900, 162481514, 892564544, 352538413, 299769746, 995493562, 982483625, 763203857, 489391816, 977136474, 855206923, 351333533, 457457881, 796144834, 844933990, 406817045, 896154628, 291828623, 124626303, 704072722, 599689686, 734986801, 759298696, 855274637, 415553743, 352432042, 427832384, 204482402, 842370057, 488266181, 886074269, 331485916, 610402842, 8421782, 71550749, 569732184, 35676466, 613015975, 520021951, 36176070, 426375791, 747246671, 111335976, 235226998, 582869707, 453629810, 896572081, 558690138, 942263581, 740790959, 818087652, 168892693, 538441898, 958126894, 788138033, 38021837, 441176021, 880699442, 761410910, 936187203, 772309929, 513914449, 513480770, 721530727, 610093628, 242397651, 817941805, 182630312, 888991455, 248107655, 663223443, 712124787, 513013991, 624095893, 815061418, 73159208, 7706082, 458674921, 500371387, 91210508, 910997570, 105670515, 412184099, 724827775, 40120972, 493126822, 203011614, 206582178, 654042240, 705567112, 150357478, 715583359, 765707640, 552964791, 701221243, 915881294, 541505490, 807417232, 591418788, 579270824, 337013027, 613955636, 814770055, 924822373, 909985974, 453455575, 646477281, 226216681, 486050987, 422293017, 2249929, 129700608, 820773188, 636288786, 793032226, 401804190, 463272559, 284209808, 174349244, 485476502, 647638917, 445659117, 39294662, 62982554, 546329507, 196545713, 820684327, 415666712, 12249220, 898148911, 629233639, 997687652, 461568211, 646654681, 998438709, 977879928, 37310730, 273179882, 399953671, 237759036, 244963347, 854280601, 787136656, 980394210, 23062030, 886804023, 864803764, 349111759, 519202482, 549464397, 56722991, 453402899, 125513623, 716910249, 117439089, 270029520, 122788977, 94455493, 163429700, 154922960, 864303749, 293158627, 768681042, 233764689, 183718324, 795839253, 459690398, 275094600, 440051788, 568962983, 120363596, 89404401, 187287076, 88369214, 328044304, 502859655, 267418462, 240136666, 782909165, 149409029, 282180906, 530898266, 868359677, 709223248, 808410597, 774348475, 450494921, 927491094, 411277643, 602833832, 217165643, 303926428, 304662933, 549316418, 822047953, 346794017, 520120478, 76006874, 905245409, 770998174, 605183283, 792757634, 252390568, 309752560, 965092876, 856878629, 614044968, 107255787, 578932079, 571331886, 605442081, 128133446, 986102879, 941024347, 737840706, 355266618, 98982465, 94443997, 591165911, 896903334, 874782891, 192301980, 465197894, 794089596, 575000556, 715467954, 136376098, 377554186, 437570472, 421285140, 614055916, 954097559, 88385723, 477946493, 85359008, 896532414, 952143562, 913743321, 273051884, 953117319, 919127750, 918338193, 346368672, 261637799, 12596175, 170457798, 489629174, 528571099, 284337232, 681775278, 220942216, 211048164, 805863378, 186661080, 797773280, 318386637, 590491752, 490544201, 311863015, 85111644, 295091475, 563474663, 620007717, 123619539, 540403427, 292892020, 59767959, 941823564, 898534721, 74972849, 515111087, 816363688, 600576606, 847267705, 453583633, 829859999, 780557216, 216727741, 991680065, 918096425, 924070845, 833442320, 266973080, 887494457, 767028792, 466673730, 568004457, 511541280, 985467994, 817292247, 204892736, 575542004, 634750167, 331309678, 484660623, 722752126, 391890763, 922823327, 898025275, 298680979, 416516937, 288331737, 748340664, 509638944, 296185364, 29219003, 723934617, 541857361, 203566719, 862937809, 696788190, 49247855, 126150316, 60983205, 440754328, 742981627, 989933843, 27821279, 308529813, 22914275, 258302594, 18178707, 46853544, 1181600, 768387399, 438212715, 774310024, 444080274, 646124814, 395132897, 100417574, 962192128, 131728146, 627940101, 100366944, 713129566, 944764075, 200464964, 739103068, 344038735, 610047213, 701287369, 903568819, 313323950, 535662853, 279796379, 218517822, 949794360, 64927840, 463231251, 120137716, 288956921, 237661404, 89242909, 970629087, 842440273, 605066822, 499578419, 61069518, 313895898, 659824381, 164728630, 873955089, 311709085, 515420883, 906278198, 82099986, 967713274, 96205998, 239512011, 879725606, 809077756, 489521574, 846049429, 363473544, 777174350, 246160151, 487499869, 259953945, 172500635, 225959881, 450616805, 510264962, 207179545, 612838384, 663371547, 148192277, 211154407, 518692749, 124545033, 394652816, 721547392, 641818392, 990393905, 111377185, 304108744, 45567288, 514587986, 400166681, 165707015, 820190354, 181085374, 959845105, 111795513, 55678706, 618398555, 497253187, 45605536, 364338780, 369678872, 893684258, 975705028, 970586365, 602606639, 372671867, 207379626, 952709935, 599063284, 420356329, 714415327, 341353508, 831055033, 490265677, 79577520, 300133658, 937419701, 678745740, 258711607, 775393918, 432615263, 667803563, 256225563, 177407930, 849159109, 624943823, 37472777, 270044765, 724591624, 726191123, 849506690, 935924777, 406132317, 986681876, 176621041, 932324674, 583610771, 267871840, 608945874, 186939818, 220488045, 410620497, 221505836, 556039966, 490254916, 672246921, 769135886, 187750095, 664164235, 943931876, 158434042, 461413139, 562886231, 807362089, 802883597, 197797504, 754795957, 681166908, 884331161, 497297232, 514101013, 19322175, 618283278, 558780138, 667202655, 65377942, 849399315, 40393723, 489340549, 693415998, 562519129, 161726220, 773776585, 701416678, 739674570, 64561871, 91123456, 852167389, 932450825, 297818200, 234475595, 821273069, 483728185, 884861754, 866964731, 436244389, 872705141, 820325921, 970490340, 881285243, 337883382, 89925735, 235514996, 325386555, 770610348, 368011347, 803772330, 248352060, 693070213, 472077851, 444392557, 991054122, 486047932, 303724307, 537152416, 259943100, 141803930, 819595337, 689813006, 778198819, 763911657, 247551929, 690613519, 101664425, 131360888, 453607478, 735828635, 662575524, 688398363, 90559166, 340150542, 423196080, 540467296, 537374017, 892928785, 835033107, 552876757, 286926525, 986107223, 752993896, 958448042, 327233717, 359112570, 385653584, 842972739, 776501979, 18104642, 160385060, 707684580, 633479551, 67647524, 547488471, 589035811, 419848852, 478759389, 369346904, 561922552, 698500351, 524461787, 459046739, 910468843, 126400015, 565659092, 82037722, 915088525, 297880940, 206209059, 908484388, 604230379, 829556181, 542662522, 898987860, 40191259, 875142109, 503522286, 254296255, 241146149, 325665955, 763910334, 695862180, 968203137, 234479287, 330483900, 575071469, 374891109, 784108199, 192597152, 242290024, 601888980, 525169690, 726352551, 201179018, 870462828, 936907288, 848868950, 830854190, 463397249, 581121361, 141406375, 732944368, 490901336, 594182774, 802922057, 384112211, 781662447, 119997329, 793669815, 691726768, 607969807, 677060760, 576438860, 611011946, 110471899, 149864250, 913709964, 486517694, 649017642, 358235726, 296900258, 58532591, 941723000, 965696822, 577728411, 401414047, 598575634, 647856539, 663140925, 449481097, 674923258, 137271464, 775919799, 258411214, 68203322, 282347964, 850585522, 903101584, 24959103, 443352448, 354729085, 832648433, 49374045, 392330518, 728211710, 182413330, 391995757, 607346067, 909800732, 478672832, 434573454, 719637033, 411108495, 820428871, 260350919, 182098678, 228610241, 351157864, 403841297, 908651127, 882803715, 374526239, 118672016, 165760893, 789651238, 382962814, 562232793, 961628604, 272915418, 689530712, 920570127, 842264975, 841065907, 860757110, 128034092, 850669852, 110794576, 665084646, 509703692, 610034547, 360972453, 553445413, 930918931, 159171900, 990901982, 78771224, 59472441, 635811739, 790071984, 397940865, 876092650, 423444629, 732311259, 549091488, 108137908, 202921774, 218700159, 832642487, 43269794, 989270889, 718241021, 127615937, 139926887, 935896405, 758234537, 475788598, 169263000, 49125704, 822146801, 573644950, 442597256, 996214571, 481894304, 374077415, 623323621, 362558940, 401759374, 418054881, 587485421, 230255758, 660706953, 810336583, 667831603, 931978600, 839607241, 161679446, 240035108, 467731865, 154486255, 723315568, 839235424, 256785806, 760536420, 33803110, 192506274, 223852875, 529360529, 206869251, 350132520, 903639860, 63806530, 409749151, 688602556, 479620684, 938268852, 381587169, 507117108, 463262022, 502838094, 644466975, 40696189, 694765527, 809916929, 760161269, 887322913, 593890842, 653153090, 412592034, 871467547, 264486814, 733605727, 141949967, 337464542, 645501081, 7469689, 214384560, 14857835, 791017096, 712899065, 361363806, 485761894, 286782314, 746609125, 191219081, 690667356, 997138745, 220786241, 144322973, 260185340, 637952964, 605025724, 309778930, 13612529, 786919891, 959154690, 211367212, 603927587, 925642117, 655734357, 379418304, 140705590, 239318807, 896725833, 105895411, 719657099, 817538231, 917510260, 404297148, 342052778, 99664271, 822021542, 782911485, 829578635, 422622994, 578844163, 307718594, 653604290, 166447569, 480186123, 974800839, 409370970, 177258110, 928780280, 825678675, 120704749, 216253185, 30491126, 55686430, 479215743, 556126272, 738595021, 392320548, 997526018, 641049948, 855362851, 402165421, 462633546, 810801052, 154113816, 204693370, 254084657, 355234513, 48936676, 771162480, 815287425, 897224087, 242009197, 264266675, 266762272, 884191042, 809316125, 977005006, 319113355, 254841611, 101670946, 713132421, 21246347, 232202734, 70743067, 982900630, 734903269, 22044505, 118370918, 712458797, 775278861, 287891339, 656435065, 248856919, 945780412, 242980157, 653925562, 85295515, 947724693, 151862345, 339381788, 823930155, 45928557, 158809012, 261864433, 362868655, 739157771, 842202781, 719264690, 389711557, 714680331, 575180873, 970681591, 296536976, 946873692, 439135465, 535258906, 830036044, 529299606, 179030099, 676325812, 442233167, 816326706, 227571041, 508588381, 425677642, 272859900, 584090990, 823425104, 108251378, 35393044, 735722675, 569572330, 739034846, 95104518, 105118590, 437624092, 204320639, 367619462, 944055750, 412014079, 468590898, 642203243, 47685103, 544226928, 247611971, 827425988, 39325017, 47129994, 181201063, 994586033, 678618108, 18784887, 725061901, 585550591, 396029350, 828659323, 786058547, 392560770, 957717608, 235435921, 748618747, 189711292, 338101916, 100719775, 657928019, 475025317, 805615630, 365767506, 341040255, 986081292, 795686026, 68277830, 395511826, 987690332, 78908092, 487531130, 625279746, 610700210, 423266215, 799687667, 341748849, 936751914, 290839247, 622046678, 464751879, 599515445, 495133455, 798346341, 757045399, 859131350, 993345629, 240725577, 780633092, 968090404, 860885912, 19009871, 391226710, 670973103, 455031558, 656217305, 48738498, 72880752, 642260823, 548860366, 287783201, 566879307, 543191896, 384897831, 417313809, 258715830, 640126796, 127346623, 353599786, 938831811, 567460640, 681661720, 98197160, 623462160, 48437687, 471022373, 199813687, 232987646, 916538808, 531204109, 935396801, 580113697, 482815540, 692068381, 642488182, 69405993, 750708940, 842755980, 845214576, 873852497, 168757503, 860251831, 522563157, 382948208, 415713204, 706469291, 316985248, 984415103, 523964364, 405108730, 773419332, 424291106, 966122190, 73107447, 506033893, 183709106, 727847417, 47276338, 959965002, 19965223, 720702698, 771834989, 254639884, 595399353, 852876697, 771143866, 623947516, 136997554, 586911350, 851776564, 122321397, 763743599, 418844540, 297680258, 845502205, 107682133, 529169112, 639274253, 746587956, 348641702, 251128694, 547209084, 764967630, 444478026, 803548347, 23627958, 856688354, 754096726, 543161213, 823216755, 670381491, 370449452, 803622136, 45059433, 32145521, 717768310, 58022780, 451709279, 981572435, 601655762, 891376419, 94312122, 23912700, 95353728, 763806128, 952495681, 156244243, 756914609, 784411323, 202556518, 930716174, 599549141, 60218300, 826104829, 567497533, 934877174, 81722768, 755972125, 115555925, 648536099, 152070397, 244363421, 486061823, 230120970, 127886833, 365350643, 549997145, 735738218, 255680375, 897335901, 183403863, 470446547, 252325426, 314332986, 347184720, 664566840, 893330177, 606302725, 753082855, 218215186, 639747578, 817303649, 499015416, 147330720, 745274416, 642375564, 837273276, 122690822, 930972614, 602319664, 469276322, 577570739, 411801223, 967935435, 146393507, 878916051, 349593077, 793158028, 324923405, 211115344, 151534611, 430924690, 856988523, 258076135, 937598403, 990156049, 916673953, 483518424, 572121392, 894334823, 286799694, 523577995, 359688573, 215536287, 686118986, 743266133, 886877951, 366292601, 139208573, 775558351, 92126077, 986434048, 891985650, 59739281, 969829945, 214449121, 514230747, 511348609, 440592635, 911754332, 774118431, 122004988, 370262905, 368187860, 864426303, 901595776, 668153402, 989047088, 81246797, 32911116, 373469823, 706784043, 249110056, 201298110, 703710721, 530330347, 840358924, 958024002, 980752409, 490099940, 666811916, 565845466, 200254654, 125832463, 935820946, 438399248, 91439031, 186188725, 191319221, 976606608, 410408730, 942747938, 454473085, 430072132, 662135949, 617869325, 651217295, 933156436, 658762357, 917232243, 927062377, 680088339, 757343473, 365886413, 548201019, 127801987, 568122934, 540983911, 804933115, 384455726, 17338388, 691014662, 214552631, 610110290, 69501234, 451976583, 380976407, 35939840, 250989993, 103049635, 389515567, 462267674, 753288958, 826252515, 105362110, 575316855, 109794507, 604229891, 757746884, 598508197, 697259255, 955333566, 330353071, 692393726, 106123547, 276740439, 167003472, 441232952, 792650645, 780924630, 672708920, 839513530, 650685767, 130983002, 681975328, 438720531, 290197336, 474530415, 737942224, 597568975, 870904524, 507667504, 144116508, 238581339, 709628106, 361077135, 218375510, 990008569, 302542060, 954910460, 434734411, 988861394, 827841299, 753323071, 677753895, 384890391, 970249243, 5684819, 708639748, 337604621, 125925772, 396670209, 449015229, 132038103, 947309122, 744990831, 64637697, 598832879, 989374093, 20413771, 604756376, 384773853, 386810965, 671114203, 634961462, 925857820, 705282643, 367295840, 145048421, 922701027, 773769150, 782971635, 394815901, 989225040, 433751793, 569908864, 538455747, 193148691, 927572728, 957743304, 108240065, 557297364, 360043940, 249106095, 642362712, 214312667, 191487936, 38547548, 360282552, 17429904, 310057773, 605860315, 726410925, 695098802, 616775376, 543232182, 377137399, 141226165, 53260744, 780338309, 578842027, 713326978, 77467968, 960283102, 876528311, 441552188, 741525263, 769981392, 889301557, 812228436, 690823698, 282610301, 254694533, 782885110, 388383827, 309471821, 99753629, 284247671, 494463472, 224883599, 802500841, 887938160, 490928788, 499969063, 190236327, 596161321, 417001798, 142815922, 199300343, 586735204, 870638977, 970706279, 887457098, 111295247, 607983706, 291753137, 944817366, 773720300, 874265397, 103225335, 128827561, 400185926, 866960681, 44854643, 211403946, 807234475, 873716485, 477614456, 264899306, 440517955, 48261538, 589417879, 800553288, 831181592, 367165316, 29623233, 406643420, 669231402, 405149396, 652412997, 585769236, 752757523, 360882866, 845555393, 186870187, 280271358, 397698736, 128266231, 586244705, 325048709, 957490036, 122290529, 450522778, 896021616, 275148968, 685886191, 505704380, 632326401, 252493045, 945058381, 413983162, 471961021, 357644870, 498938314, 910493505, 886575651, 564352957, 234898223, 409310563, 818932703, 282785851, 922365628, 737463988, 303161415, 994451345, 701615247, 219467063, 437452354, 719199569, 362864980, 412183023, 596851534, 677895891, 226651995, 789764509, 99841359, 475282377, 715041439, 101858926, 451723557, 492845000, 2166975, 813278644, 693973776, 521258661, 979428849, 934799725, 916892106, 851988654, 167492310, 569646609, 868960030, 41739645, 357973448, 295853823, 140714904, 194119932, 337048597, 702603568, 847346661, 190601064, 895948384, 224754313, 418518109, 981323382, 294133830, 823055632, 397991890, 473378307, 141285948, 662992452, 776754892, 491509130, 305737653, 194880251, 121002434, 522628237, 153352241, 720358249, 997079372, 254823732, 650841617, 99254067, 459373534, 772873472, 133016237, 219850174, 578290976, 492649613, 326644546, 962777530, 67243532, 85986572, 87432079, 726596102, 785075685, 458522359, 514131633, 375719348, 314487505, 707919398, 27580423, 737831494, 326487232, 525522642, 330489361, 908216916, 469829244, 481168589, 705523539, 256955957, 309656987, 545627025, 272688538, 752133894, 950370264, 45274638, 451098207, 231840706, 306491635, 231113409, 662935757, 640416520, 237535951, 174785989, 758206336, 347644252, 679446179, 264929886, 642501607, 481506808, 23628327, 291058712, 965651629, 381486673, 537097824, 653853466, 451198902, 230377753, 668301496, 484356968, 792015416, 111012448, 408169278, 63596556, 107102101, 627592637, 255924270, 511224702, 782691457, 695259502, 570538058, 732283482, 376559037, 439100794, 244754188, 366143769, 273609987, 808720975, 546582334, 171726757, 938391125, 510178963, 633535554, 112063058, 747936247, 842498857, 317974426, 510561752, 602927847, 101710097, 98103696, 896871344, 626853136, 126861317, 260231362, 447838536, 159020861, 913919612, 987123586, 635289087, 295129770, 305075231, 26034737, 720721231, 599981870, 221055431, 979274326, 79333886, 869096114, 64033632, 672899128, 599528099, 340536125, 689804090, 460497644, 735875311, 576947850, 943540289, 752972354, 236827714, 218216776, 244219430, 705902770, 571093803, 938062929, 382707828, 820036499, 92782111, 497537599, 894225719, 303397587, 558605160, 369869866, 765610672, 443709139, 857158018, 947508188, 291686865, 467030699, 31015130, 794279782, 405061695, 480931716, 297701664, 163692644, 342985892, 300296577, 848125193, 654382843, 808441574, 136289184, 610873916, 230813514, 785289089, 744103329, 885736185, 28725594, 452032754, 848604758, 102073606, 70721971, 19915687, 687136575, 342804379, 42543961, 31286285, 223555178, 420747102, 379786045, 920855836, 313202611, 18377964, 73684697, 356929887, 372468589, 406254831, 454869336, 338069504, 839453092, 154374131, 382595668, 615277528, 449200167, 172179251, 932394564, 486737149, 910995648, 760406051, 317613840, 378756404, 879091127, 471459472, 748085312, 643842048, 523306433, 176188907, 650354849, 558328308, 737466983, 791329084, 204695618, 104505729, 403184523, 903389597, 648730985, 887060191, 432332860, 558280435, 69016767, 585454077, 724802053, 82251088, 45176456, 116675008, 571452786, 799486636, 606786982, 693218173, 440841410, 316674092, 559993008, 41949608, 674400728, 576134381, 404055, 948208242, 708003350, 733379843, 144527083, 888027410, 36573046, 921658007, 337334541, 704716332, 712934801, 2522857, 523664660, 90014517, 268020981, 104525049, 893929243, 275187217, 742868157, 607907918, 637418360, 384163361, 317845440, 602252030, 459836554, 854416392, 851359783, 823238506, 549419303, 853269269, 149040665, 639799639, 105424291, 793340468, 282070837, 572988240, 206921319, 154715583, 497347343, 999519643, 900382675, 311851245, 245450255, 292151001, 351679806, 799603146, 628787348, 709419854, 533389507, 802467313, 504470345, 913870765, 647938342, 45169572, 895849819, 674715257, 290710924, 325258085, 419963892, 897159023, 10990781, 82876539, 339382711, 818856883, 429953787, 169996708, 72080095, 435899831, 741103484, 227356989, 156202729, 17183776, 34979049, 172124953, 340397706, 680204742, 49946617, 8011724, 708845945, 933467452, 301594747, 440212655, 40817878, 632116323, 683301047, 807548900, 864483003, 748489626, 805723851, 656106740, 99752686, 856007981, 755996147, 141830441, 830530808, 624438628, 772907788, 325117489, 389619189, 705284174, 612187903, 584236953, 508007121, 796435536, 705397227, 708594272, 325652721, 662764479, 246032990, 862301868, 301042074, 243158307, 867032762, 450888990, 964791661, 754951159, 277626968, 615687604, 80862322, 245823757, 343602704, 603127999, 630115357, 717417695, 256170944, 123071375, 406490467, 230272589, 232198310, 859698761, 138602054, 783991443, 875267231, 83026773, 270787831, 75774537, 875224130, 373515860, 77222769, 493121215, 847973589, 11209392, 784349637, 767457874, 78833256, 813808043, 561213476, 429116535, 740704613, 408742240, 299997149, 435832160, 49384177, 687243078, 4384091, 438529485, 828095959, 329871776, 607950099, 695544568, 992808469, 251001709, 708236617, 492251900, 442925319, 644358982, 44148031, 247979419, 92484033, 681928931, 680886851, 415912796, 44055720, 833119044, 158747245, 25480472, 469224755, 497240394, 551187804, 273751205, 643077600, 543929101, 623380891, 780030365, 974048774, 928823495, 308448423, 689618012, 621367339, 70637342, 270603778, 392547249, 671685485, 207647401, 21607672, 291069924, 438543253, 797111052, 499539165, 261036675, 250200038, 838071762, 529331969, 972122144, 580033986, 908436991, 797121198, 238163852, 110591097, 121967193, 376116549, 274971006, 391727812, 252651749, 60434757, 185486505, 50860680, 663436575, 41102657, 458105948, 799080781, 382589208, 314091254, 121719478, 628975036, 790768771, 826037713, 876229467, 445292083, 210887206, 356495831, 631293250, 46123180, 609420104, 278475717, 504092265, 727510433, 176355198, 705659826, 802013595, 820197990, 404654358, 642786776, 162184238, 777786288, 905294343, 775672267, 879239397, 373149308, 315734589, 104440724, 701606228, 582270552, 608110397, 173634336, 960255415, 327433118, 370732942, 762722271, 427647859, 569472466, 283807003, 930488838, 559390974, 967663392, 737811157, 539408866, 776459186, 376239893, 551813004, 609345322, 985179427, 907303663, 84166670, 736138237, 889898749, 48903588, 584294251, 885111789, 134578711, 589806123, 864300999, 672111861, 37308795, 264749797, 155553334, 789890106, 206464786, 498824406, 45292882, 543586362, 23111975, 97589842, 671828284, 938782300, 955081193, 340822410, 693885699, 142028179, 920221727, 254968262, 918789436, 739012902, 349521477, 53748016, 591340856, 239340983, 667141767, 429528615, 738297419, 917484744, 531408885, 818776919, 960876273, 396194713, 849702589, 174839824, 744548742, 313861534, 395539227, 609715350, 653206975, 504542977, 283496079, 491969452, 887004486, 105081723, 597144148, 562285567, 480877337, 207117735, 662493644, 649091684, 682121569, 659149336, 175503568, 41013771, 52129876, 52348975, 363812286, 267015946, 681184317, 758879628, 325183387, 227435647, 857471701, 362852366, 161955169, 283617403, 490768186, 967845661, 285971419, 820054818, 503172439, 113698268, 208907799, 810313643, 847456117, 862867730, 37075664, 818157003, 806746852, 175512043, 666730756, 833627386, 904404394, 611248305, 745947057, 85015202, 502214058, 861204689, 485797971, 834782231, 768966580, 609810874, 521080950, 880403609, 384313664, 843387991, 612910822, 533588344, 105825443, 863463124, 765289790, 408785591, 346042897, 12358587, 461183998, 753506697, 887134747, 496348893, 498091137, 571721651, 117701818, 49844886, 325786316, 145227287, 185152998, 444377333, 743387319, 23598812, 184089140, 745582081, 135118766, 154437566, 774611889, 184306226, 726179989, 341936528, 248011673, 221682549, 877462276, 597284376, 478931799, 43369296, 902576186, 611271323, 957563795, 213364790, 53368366, 97174409, 320263551, 260229394, 836680380, 241621445, 217522716, 394501857, 381363812, 283000415, 143737778, 330648288, 654933135, 257305515, 693656634, 917881343, 784413065, 588672967, 905381306, 775407169, 739193188, 322905563, 618964454, 877178564, 621695931, 897858011, 127839387, 482784945, 16572907, 487919072, 777134208, 552619539, 382175892, 19493128, 522767261, 960881694, 967742380, 539028190, 870548520, 598435939, 54351692, 990777000, 437952549, 840796778, 694904142, 216145925, 553071997, 842695799, 97768516, 589094987, 853502363, 100667121, 938606349, 759768539, 387799415, 97214460, 24248698, 790215702, 153996352, 119252649, 612799535, 824420911, 513107973, 725245478, 546892775, 584522909, 92497998, 715783402, 417474019, 353699900, 766825378, 945920282, 632619099, 675471469, 940857695, 230261485, 378528472, 383348566, 305446729, 297386747, 196498616, 608691503, 585723253, 482947574, 525017957, 691080297, 670794190, 858145109, 809279246, 484650754, 591387379, 892477640, 356032981, 866433982, 235328601, 737335130, 219381516, 718682830, 60103923, 889128318, 145973358, 887686949, 704106232, 878622576, 680562966, 79516404, 593254471, 326900718, 189082138, 658639198, 601255862, 608809690, 448800764, 11724012, 837092363, 432437012, 374273318, 688903639, 525804373, 283961805, 843875344, 782400563, 864008783, 301629771, 607454029, 282986136, 45920261, 899546986, 297032154, 6912796, 979167533, 475097465, 937451797, 125713876, 538119832, 873128806, 452588330, 370825489, 149611359, 314756633, 8398491, 254868235, 572775570, 996349238, 569608058, 706318843, 543769463, 850233190, 162350709, 674481942, 759459431, 174462100, 557087410, 58512597, 174296901, 54515225, 71556271, 258734859, 548717131, 381100319, 493977755, 207356410, 81500998, 919509850, 212114777, 913109189, 126278254, 759002256, 275842805, 213320237, 107813161, 506024041, 851933931, 725398313, 704168038, 805668407, 599805192, 351463481, 804510709, 941345439, 790166216, 493731917, 459213772, 391189370, 843376511, 629473754, 841854732, 286761104, 559612250, 212418184, 957758202, 156658017, 268317902, 124163347, 698289395, 436078967, 851879484, 447556999, 83259312, 281933639, 31187891, 235910184, 172690310, 847791196, 691379664, 92800505, 53016921, 29746960, 338443780, 22456268, 421817763, 809478877, 535165823, 487346864, 779321078, 505854227, 349759444, 433616276, 181253312, 803370010, 169153989, 282601956, 141257391, 892158977, 429989619, 825147758, 971553040, 282134473, 453021392, 885037209, 134912014, 692429766, 113410785, 473233928, 464675207, 47534149, 70734482, 737662291, 481124844, 551217445, 616008506, 100122990, 721769405, 691284265, 853772779, 975778472, 214649634, 593818420, 554092464, 210950919, 698997899, 115928686, 160390065, 71596716, 652323235, 513339192, 172958392, 464459299, 185842488, 142177054, 478842331, 110858208, 134647629, 272510105, 556276982, 146085149, 526679189, 235719701, 226847887, 194058178, 746849360, 721898324, 60811440, 40615298, 612443947, 233708202, 213680704, 346288400, 747039320, 319044145, 604332110, 732021534, 861550211, 462472984, 543828202, 278247713, 621501754, 278090641, 685390911, 800473795, 830144128, 721821478, 494313462, 391976390, 7173523, 110824724, 948590544, 324212058, 387626925, 861391644, 754081804, 345419736, 162289342, 86109943, 258164023, 996354442, 199276435, 862338377, 524616182, 599218991, 88938028, 743517149, 672866298, 270272014, 326471893, 813535241, 934142546, 297697304, 409689507, 937017538, 569737856, 355780668, 879902397, 765660723, 348383864, 516463855, 247914318, 333844480, 269729178, 564675546, 627631600, 133791894, 60755664, 611697056, 290133135, 573445125, 589946443, 872673521, 219916579, 456854681, 789039330, 429092439, 646434057, 668518001, 10937245, 160405731, 180012470, 598619325, 519581691, 363523769, 158109056, 207494427, 985665834, 834243623, 983202443, 808338842, 598913887, 976431821, 885255663, 108691957, 980828211, 74185735, 848795170, 565924072, 629648361, 70783224, 674110258, 74358952, 152233492, 179170933, 808400529, 578025834, 943260480, 579442288, 351330544, 425311539, 179808968, 896771630, 762254134, 495737215, 398492531, 499477743, 525513910, 810516833, 737171599, 74752115, 842623089, 307885224, 428729611, 545888221, 77407565, 69415259, 557294058, 868551885, 993067860, 896415517, 57972040, 561797372, 200333210, 904190495, 549302048, 119126849, 427629364, 471664697, 497156612, 24296570, 75946211, 849677520, 860810589, 908428168, 525029521, 735625041, 578978267, 811771023, 579917607, 954080424, 412813823, 737680765, 527177891, 914445723, 643388250, 159299791, 679345276, 791997022, 730614808, 485627880, 325502018, 573062178, 672150235, 376304105, 584128985, 917570636, 261546228, 408480084, 46358528, 115117350, 187535659, 715739839, 332078783, 593342800, 252353648, 531097239, 414186668, 891161331, 558373908, 561855611, 845295532, 6316040, 291701316, 901379703, 828582306, 720209545, 79107397, 296088096, 483194275, 180508274, 406952080, 639018830, 733113234, 904228276, 691355328, 673339898, 914527569, 695166827, 3816349, 770694018, 734759094, 163994995, 192337995, 721681280, 483913311, 250856529, 418847552, 212162196, 87237301, 195837122, 328571029, 773433530, 428522240, 616141613, 734316023, 105072750, 680745019, 265871652, 631658452, 686417134, 177682363, 685488967, 531113859, 922995144, 965181673, 608170056, 869024884, 824419652, 392282305, 940686188, 526587485, 235458504, 160933232, 51580412, 35575758, 490303896, 254355096, 525773066, 921048315, 712832360, 334505179, 329620100, 432072335, 383099690, 473847573, 578158208, 469070344, 631393928, 864174709, 906315813, 10788287, 159121436, 371849297, 464341150, 625241053, 563540180, 523243802, 857899935, 100026964, 252847571, 945230609, 120158396, 447042312, 436983733, 950158974, 634513264, 291473157, 243881935, 416064983, 121663128, 736369686, 3769328, 687586243, 525070099, 227811750, 336887800, 262663057, 450912147, 762569664, 688448558, 4628367, 696715116, 349188994, 110007614, 996748738, 743210552, 638017310, 439018035, 497239409, 851871343, 444237036, 501523212, 707242605, 624789503, 834255844, 7126632, 257598434, 246850940, 612162437, 747043433, 448390861, 113539348, 600172262, 625390642, 281631168, 199356398, 642524835, 258019146, 227300853, 984274217, 782006858, 942203118, 579736194, 129984026, 837598262, 404425172, 909031864, 191497961, 827510193, 858455992, 189768090, 742322120, 386641069, 329005621, 420617220, 702790111, 118872101, 406727902, 222088077, 473307130, 55406329, 27691310, 82325313, 157791701, 249943865, 992337343, 863081199, 492886357, 681918016, 911670858, 809263489, 487751862, 534878067, 288067650, 346972149, 175265425, 808196067, 42406932, 695460002, 440056295, 431953962, 38183121, 65190340, 287765315, 30604626, 392675824, 932846531, 399433170, 407322180, 666298966, 32554354, 168641863, 632656270, 159791528, 477666050, 962457243, 759126769, 119939630, 44351372, 210597155, 128494651, 931275808, 121953080, 766076752, 155982247, 907365777, 491198093, 525365194, 916254510, 335054252, 138365367, 937945497, 274596570, 425558746, 347836456, 638307245, 533885578, 972625099, 39685450, 530667808, 911001381, 271052482, 968352361, 598019645, 43642255, 521135435, 707298977, 859993637, 265514260, 847463229, 231925467, 772786586, 623502738, 466408526, 774990036, 129296767, 833968434, 537432659, 102464075, 564823078, 680012123, 779981351, 203723073, 943839262, 519370468, 613992695, 405592179, 116340051, 574863179, 546257975, 63468759, 423652964, 163329819, 753971185, 650731504, 996396173, 939121029, 770222730, 112591318, 713432706, 342859609, 636683328, 842457100, 14021592, 352968369, 932864533, 892766190, 299335490, 702155493, 82841521, 183204872, 440273288, 335901725, 470051453, 948267758, 318616954, 725885801, 76859135, 101628880, 765710033, 684868829, 712449424, 667242817, 94552586, 795766640, 91940227, 54418542, 273931469, 309723452, 375754328, 799170023, 501698542, 315015633, 537801538, 757189963, 853881968, 897017669, 196615295, 534861318, 106389736, 718998581, 611714365, 904041700, 799661019, 966348098, 401292971, 980888482, 175824291, 223479260, 962118327, 392203957, 127417118, 288418232, 546401622, 996868301, 562300226, 991402546, 742009768, 36767249, 821612983, 265739884, 384696154, 48891940, 455962226, 443783802, 728867599, 10095249, 507334214, 509801023, 705132618, 236300162, 864028460, 476059183, 848428949, 35982421, 965861402, 878279488, 70596602, 86815460, 238541983, 46961426, 100464921, 976866629, 642506529, 279616350, 998903194, 305244051, 630784654, 867524799, 170526416, 977407347, 749463560, 38084527, 518773580, 460612607, 817786109, 936319767, 673220449, 609221992, 865079470, 171433892, 669191800, 211603867, 663116654, 999273639, 929672093, 131762178, 613401666, 789800358, 401908722, 54255536, 34560471, 119263689, 425874436, 945081261, 35873952, 909941608, 347228688, 230612028, 638076120, 515295819, 327409888, 736437763, 549098880, 445747192, 418807447, 257794257, 878523094, 541287191, 967352308, 255283358, 358801617, 522151781, 565274623, 290902875, 372709602, 493298875, 109385233, 952913731, 603831637, 670380995, 806800607, 68571489, 780770785, 726329432, 516401002, 165849277, 233391426, 292840490, 381311395, 353369564, 675521631, 599616297, 736689682, 365519267, 898799691, 760250760, 795851446, 833871245, 752277787, 959186820, 775860367, 475752568, 302459576, 117045483, 416102140, 824591904, 867775236, 52956427, 373884037, 423242200, 567321419, 313328000, 934580930, 654867007, 436632476, 92021094, 164642298, 102014581, 933203769, 754429367, 372544102, 466696789, 702291404, 155863081, 836886447, 644106600, 333633272, 761598659, 720050467, 550244460, 216885869, 624578872, 343263773, 168854767, 772260600, 597504336, 403080340, 459368466, 461901929, 794572037, 983664865, 4057379, 989966079, 254261077, 82690265, 563001546, 28911735, 199144539, 40869398, 981004148, 446682628, 724413502, 352958680, 744784922, 454043969, 191599319, 175768726, 765264539, 3925237, 615634561, 193424375, 771935061, 711892240, 939792186, 243813944, 527931236, 657285341, 932333263, 314742552, 578521227, 352974173, 18085082, 233802439, 518708161, 979646476, 530290526, 83041982, 833192602, 137576951, 935136871, 873372417, 551159602, 122463484, 4341497, 996303693, 372572415, 656004490, 119537687, 41641065, 350292260, 493115049, 361511341, 765412789, 911050708, 264839251, 690587174, 103565736, 968380703, 331428429, 174991259, 949310699, 932753337, 605669478, 594219539, 319260426, 740255418, 81950411, 890824304, 113386023, 576529450, 489047925, 691489322, 863987909, 707723378, 27112281, 628814540, 104842599, 500526791, 307309053, 922123657, 810636226, 229061119, 526746442, 415478649, 80239290, 863923379, 194457923, 217517579, 619061424, 868634092, 577626927, 45265084, 794267698, 502287183, 176733243, 502438758, 159516694, 548608509, 196788244, 415897541, 708433212, 162018527, 464819957, 174098056, 955301889, 935664650, 199746973, 769963647, 525502545, 398668584, 9218509, 971535488, 99584261, 256746459, 508305833, 438750502, 603948309, 919807388, 128912291, 498288687, 968342968, 121035762, 745286926, 710935477, 79679422, 524293774, 123729832, 422697631, 261276848, 253841041, 309135623, 452919499, 41811494, 233219624, 20223165, 629006202, 745583557, 884368054, 291918081, 601814462, 460803541, 978441030, 170503193, 295351330, 422635781, 260494030, 417525062, 60536903, 371299284, 340480496, 781466813, 76510776, 46546742, 733733670, 262087025, 349847603, 590423206, 414545176, 890745434, 527411748, 337041644, 898262451, 495130089, 359121069, 353015554, 296493571, 230557031, 449034758, 648215754, 204156957, 264311014, 296334123, 847585896, 629171037, 358034349, 203821851, 482016470, 194381078, 493403776, 125554173, 46390993, 512628804, 228256397, 607004923, 80226066, 221278746, 750748668, 85924285, 283377316, 37473446, 327817747, 106674531, 135077686, 63217376, 239891855, 823356139, 347600299, 369126735, 975209004, 171433685, 319517514, 923486442, 767064477, 718291992, 454233021, 636164746, 345177170, 815435047, 731494040, 843694769, 640106843, 41591141, 983924130, 447662779, 27092306, 67169282, 265760011, 835798179, 743041835, 611637272, 887016696, 641405148, 35675823, 237744407, 745074730, 200463973, 833581229, 355728542, 39123526, 149028641, 234875319, 387173352, 895749604, 814788523, 210355037, 363947989, 443761360, 472370666, 478564141, 730384361, 647356637, 989903326, 582094538, 498649877, 71875237, 782901929, 733383197, 530275334, 775835115, 311515935, 245093653, 842035022, 204239763, 22174473, 566834824, 844939493, 605035353, 537761315, 778659614, 537743220, 390063554, 944670870, 878565892, 99687812, 927863435, 752816451, 452823621, 915038714, 446512533, 842310454, 903096919, 466425477, 250047936, 688456200, 532347039, 652660436, 603941862, 812722475, 549727771, 15786745, 272127664, 979370792, 682891972, 728105840, 854125001, 600129051, 10331715, 59409923, 581429288, 583611725, 371748517, 568553927, 908487984, 355324523, 68072551, 299195705, 380879615, 679315317, 883627137, 89553953, 599384066, 776575181, 370513333, 505107996, 20572507, 396093717, 613166162, 905031008, 315625874, 899734776, 454418845, 58321121, 602211995, 766923736, 758492467, 368044209, 268718515, 307360163, 192143484, 440675214, 467852455, 960094046, 351890143, 507040312, 303892592, 642468909, 142724388, 779263327, 269813598, 203864842, 443259033, 719928829, 13070916, 887803280, 648738928, 38442351, 18056085, 764507855, 454941657, 96811258, 898079213, 313473354, 960991979, 419250202, 585542821, 586881150, 958985189, 394191870, 149438499, 772006898, 427370268, 345149571, 870643900, 930332589, 756891947, 28754927, 621135895, 484508477, 541327780, 519580603, 499914409, 610274982, 950030942, 602536822, 706440685, 426090942, 540497362, 531869112, 996069874, 425960553, 281740021, 83899295, 247815322, 946921608, 97687138, 386780143, 118160523, 529125516, 908160725, 348588266, 676490661, 511431867, 303305348, 382356143, 483470661, 895681368, 123080045, 351918674, 684011347, 505847104, 697153811, 225602918, 240470423, 476046247, 153492705, 296387589, 404097720, 292121792, 977170833, 526660637, 765201409, 654554711, 138249835, 423578070, 514731049, 431047176, 704734380, 187558851, 370287949, 491750490, 411644500, 490129719, 925859723, 271063943, 709424567, 866970026, 711217242, 371158443, 237795603, 730524316, 906031427, 163106605, 464466243, 256440722, 196886769, 629532448, 504293455, 165248371, 856149194, 584390319, 736127201, 350761782, 473042740, 913280883, 210578495, 991425615, 187676304, 525233913, 646656085, 468156220, 376445566, 112932796, 748497917, 379974251, 937076985, 4909653, 488227465, 861647274, 929670095, 990652178, 86856787, 670081706, 229112668, 517041026, 339607981, 622604955, 254841916, 198378661, 958630846, 492411426, 550996027, 231154955, 587066293, 172908103, 875132441, 557888164, 906106935, 845758800, 404111692, 289637106, 300101932, 947019926, 135390204, 436256302, 658033357, 942491646, 712555021, 532242765, 884985685, 875174960, 758825030, 628441476, 925241405, 613786864, 122628256, 610761646, 664430542, 439971509, 392482598, 144951317, 571374301, 314573796, 579931864, 851789455, 411634616, 908982533, 461200419, 240643835, 808903357, 837787827, 539853611, 42616001, 353988703, 283499217, 918626521, 126728980, 769292482, 786911002, 93828073, 403281233, 718442793, 692156526, 237941648, 138093772, 460749549, 567213650, 496536933, 324658137, 864444015, 209165697, 571892881, 187865917, 371452938, 547233437, 493686688, 154238910, 918918592, 735947319, 245785118, 640259933, 79363770, 709530353, 989827623, 464519247, 943242857, 835442140, 81453145, 441102770, 94699523, 303346450, 242274604, 759385008, 904910085, 872540679, 552453620, 286702537, 941611597, 75060412, 265995329, 266227753, 158374793, 269048152, 489974795, 513575009, 999713968, 490336385, 876123465, 579632558, 83323967, 203559439, 184217297, 641710810, 878387641, 543202786, 455913687, 301318527, 968166193, 300382113, 333762290, 906201380, 456250921, 603509149, 791465289, 918456404, 766985092, 294139690, 599088715, 577573713, 514527630, 656664860, 956190436, 208569033, 942715845, 200706399, 722445973, 923585583, 368645890, 803063028, 111967099, 75695510, 889255487, 168514512, 383866556, 155471769, 237670055, 165318783, 688524379, 204519362, 222908245, 971948400, 373727407, 673308319, 134604770, 823224812, 161822869, 200663478, 105316173, 171870471, 852045416, 884258310, 266593738, 226725818, 743709552, 631774544, 921562720, 538231753, 768962330, 207496912, 373077754, 880228867, 873050330, 466433961, 438553245, 915841866, 760552962, 225281074, 27529020, 693312850, 839109679, 958350342, 342487233, 548088560, 610954913, 359520741, 87075868, 570831510, 340574184, 856276264, 746866729, 67933913, 497739002, 26335037, 506016657, 548380973, 471437599, 908631907, 175742945, 280255865, 785941865, 327621547, 667603184, 87452398, 214409986, 484637179, 505606777, 727410232, 636294309, 634157847, 617886388, 784277442, 85466339, 622372471, 603272619, 798410605, 989975983, 360754011, 347407408, 873569660, 43634003, 345404360, 604268245, 76702331, 700733022, 150541702, 203513139, 970632124, 351592609, 290900536, 349718430, 880311251, 872916816, 816335848, 668930997, 763988493, 871107171, 563064741, 517166814, 661039857, 119171380, 265480037, 378625288, 638866540, 184207684, 573346540, 546671655, 56031535, 514043381, 840941612, 892438260, 755622598, 182139956, 783306183, 492284061, 63274319, 7926962, 809231560, 801334235, 488947670, 450278218, 978722699, 922671516, 984745152, 514026765, 181012354, 225410175, 732818274, 69722472, 828295833, 634286590, 65872778, 873369673, 48129716, 104908707, 840578058, 169548563, 492731162, 45141742, 212797839, 249037453, 841494862, 734323085, 388947744, 926247227, 672230083, 202253312, 734512334, 937839148, 44998267, 967918328, 559897216, 997177046, 843623712, 399070130, 599433687, 826381085, 336608287, 629036902, 31099415, 933513378, 4934745, 790571729, 894115248, 677697394, 427808533, 516959296, 233397560, 278949672, 138215745, 133224401, 339557464, 392851981, 958545895, 188127147, 883823816, 229863256, 23053409, 714437179, 330021152, 712380201, 287968403, 814912800, 386802800, 897491745, 660077647, 951663377, 879571817, 439781095, 921210178, 886119612, 67164456, 784011224, 212766174, 37201767, 537563014, 440204513, 986053838, 266379086, 867431146, 460798750, 350539260, 570044678, 528864368, 191756566, 630191530, 340752075, 252622474, 272078954, 237254537, 612324001, 225048548, 96977464, 210580168, 515005199, 431228832, 91923590, 971589655, 706427483, 722659013, 453836675, 412376649, 445524448, 972290945, 327567124, 990097132, 37691263, 100401635, 936512, 636715025, 250671703, 454832179, 102252214, 495009359, 262527606, 686127808, 806945143, 918281428, 1937382, 217673237, 695892254, 22644504, 336304466, 112128314, 728563748, 26135337, 138614967, 563519808, 631776298, 360925592, 424696571, 817761203, 46630863, 155149446, 245206972, 20950501, 89489060, 702380621, 847616536, 229039039, 800550766, 78883343, 792038578, 973953566, 440233285, 692143966, 383258972, 433511746, 395440755, 614642547, 643363425, 725085226, 198670356, 902937414, 59026491, 607011128, 482232497, 269972303, 70396363, 591704886, 21148294, 22298632, 848503446, 925818257, 118195236, 685415597, 86405832, 614748586, 332890885, 113252253, 923809363, 435867370, 856670932, 644304096, 136421262, 102952008, 727731544, 368072995, 387323524, 278365288, 600373243, 159935401, 845077073, 408449083, 541726886, 562242409, 199132305, 455811323, 25301183, 741157721, 678896684, 762751791, 581888883, 795479019, 441530627, 201583834, 73429213, 631784532, 284747476, 907867960, 975473785, 674248957, 594621978, 710664221, 871301114, 618294828, 823602214, 896759037, 455548845, 127296308, 564446903, 425337669, 678243336, 237252642, 140082609, 54139153, 546568938, 862658423, 692954268, 586106678, 347089342, 684119481, 882293096, 727622415, 584225511, 837872151, 927812401, 891020394, 459098313, 524229988, 400618593, 144233708, 126665186, 363617713, 714757815, 234359306, 90483192, 35696734, 748412828, 976610672, 920023435, 334790411, 415613634, 157769988, 801962517, 342275829, 775080169, 141978694, 347443114, 496900560, 404302005, 402702646, 343813894, 387209951, 228924156, 86075543, 906861978, 876974887, 469502628, 340179167, 154015765, 229157248, 521977653, 875389899, 831090087, 239030902, 258473485, 587239921, 334458327, 223893230, 97450404, 56998536, 764507851, 860064895, 834148940, 165676687, 301660165, 457546086, 53832583, 483941609, 459130099, 750333246, 949324772, 629360906, 884290308, 40405607, 868914170, 905159240, 804155778, 176128048, 383352783, 562393403, 121624317, 437718967, 95844153, 326500952, 651919745, 121327219, 884634167, 413839324, 302678474, 635755824, 922535625, 397520240, 423569913, 809083146, 916931293, 223671042, 2794666, 397755994, 409982219, 259104695, 37760881, 587011035, 145232683, 51604967, 414047939, 49542484, 313082584, 905333331, 884527093, 131031450, 928697422, 591308967, 827004998, 400057520, 43890898, 376902173, 301771275, 529224486, 695228203, 897721803, 898696058, 644890253, 497317092, 345730700, 454564480, 281742474, 894500055, 92175688, 43045005, 662881108, 508640736, 425205834, 90452847, 74616279, 877738613, 587899024, 428739640, 215350779, 635264513, 173775820, 500378634, 542058542, 228168117, 643034785, 892880631, 496078095, 914164796, 546195608, 651878884, 648464723, 782956563, 676768581, 881479866, 164176703, 923044456, 71948078, 448759692, 844253965, 479054454, 474753258, 850058609, 24095156, 202596846, 957576989, 347226699, 346930691, 599649689, 920132705, 109781658, 40769138, 551160772, 820516839, 437063445, 808349729, 402696401, 730630132, 487661126, 231124935, 446348675, 142082403, 730588311, 475029523, 833398491, 99590595, 979378615, 645768777, 646557073, 900367743, 315090817, 845582723, 517748882, 281730889, 641806300, 983547271, 109829654, 699123544, 815225780, 720042682, 405125323, 596324522, 279499534, 667442300, 107332738, 117010288, 536656135, 682270372, 34714294, 15742184, 876395419, 142010477, 38560363, 387042106, 926796126, 94593624, 570446864, 623955457, 202120514, 126330987, 156757609, 103806189, 354899247, 218660243, 665763216, 78760319, 386445739, 719773885, 43793660, 747518209, 450503706, 972821426, 539259066, 681996465, 754771468, 334841423, 567434863, 456320627, 545910245, 584109691, 694096215, 620682995, 232964030, 738544627, 111419497, 17906087, 765004868, 232917506, 830993728, 558021573, 492769428, 863702439, 454066520, 757348476, 199072255, 339192021, 718136422, 437434207, 918245104, 405788820, 394301058, 307939839, 191730197, 625294713, 933474132, 421750618, 424620957, 338532255, 193804647, 843036624, 573038740, 901675969, 989224916, 233216035, 53438174, 221059372, 541921148, 503920213, 471125637, 941962632, 705247663, 875854223, 513504807, 767781266, 876613442, 772908801, 135351830, 291849992, 954992564, 723576619, 709831262, 259739509, 546879126, 397241756, 207788674, 834729661, 269076168, 593795400, 933289167, 418196570, 597971877, 628384165, 251737696, 788124250, 2335914, 264477564, 222370379, 335071141, 802601388, 867104769, 799030972, 781989467, 208396929, 768867985, 636528999, 727357960, 346945477, 194701687, 394560219, 484201767, 804853772, 492666546, 204365868, 592213147, 356026062, 394301059, 733623693, 722229719, 974946426, 494005262, 368846711, 547047810, 879104872, 523996169, 106500022, 303914597, 522424651, 508719380, 762412219, 564392489, 721800195, 907297204, 695285600, 374191002, 902713892, 512611751, 49675175, 306705382, 252032090, 684724536, 677716117, 294025346, 997967009, 30234313, 382293882, 826323950, 988528049, 625041847, 53895882, 175104222, 133514554, 526997743, 524755768, 722169337, 37207707, 937626844, 456099622, 770216424, 284876396, 670644090, 634900580, 584552344, 451665824, 368398947, 740074413, 413343590, 526968585, 450318381, 277139380, 20941984, 770816362, 255343869, 373165782, 145818863, 275104646, 428606131, 795721881, 586733817, 553053855, 968270805, 756357406, 222591940, 26828780, 967161859, 742206025, 888148994, 201919302, 254509846, 782091762, 775852971, 617524911, 738387033, 144328247, 310344336, 376249511, 439064374, 365510027, 240779857, 493885253, 338385792, 90885509, 213704418, 562619320, 345059960, 39363953, 337464602, 137736661, 62294997, 796338349, 783259487, 268172090, 290734960, 143651321, 291506499, 119930614, 425298874, 405783720, 827397006, 280952798, 365035644, 537840609, 311960932, 938824288, 841547782, 859014334, 761384436, 703197146, 221802491, 377957155, 66091001, 778816542, 919671958, 752073260, 980728796, 598718777, 362565611, 964268049, 876951153, 688235140, 302875359, 121267261, 103640614, 324005035, 880662808, 696756323, 975840643, 681498581, 718557961, 235742343, 17836141, 530417653, 48023601, 573004009, 182996295, 676654268, 938998913, 853271609, 240328543, 154068467, 625325511, 982037638, 528407320, 794644800, 932133309, 818251209, 922570652, 110122252, 506729464, 422418736, 887075016, 541789378, 19598471, 28360264, 709482803, 746686321, 892286685, 696173058, 500027068, 950457256, 587589132, 681444394, 404526178, 719010178, 984311833, 642038848, 101706727, 525973741, 632787463, 944979537, 178196185, 572131630, 863073323, 738251877, 115457634, 55035144, 105635409, 633812981, 656649089, 15936499, 11764072, 812418475, 981306642, 127142534, 665847441, 919675024, 688816819, 683099687, 432479604, 322494186, 225519854, 67031268, 917579847, 37125386, 101332221, 397665918, 909446297, 755406689, 681879361, 245934828, 634684099, 718610527, 561914191, 932093150, 18252049, 450053499, 878075419, 736573702, 533681523, 88186267, 934301659, 782777655, 886082942, 318556859, 725255679, 559021758, 44254996, 443968864, 675378593, 119447476, 21778450, 291854800, 882426567, 64731038, 375988624, 888352300, 871509704, 133846522, 146970922, 634663994, 822806115, 158227124, 375187455, 984859529, 774463145, 588537622, 526454312, 950248876, 227531909, 816263788, 827840468, 264432596, 429123826, 224415281, 838920005, 299288453, 429522787, 130794148, 953593532, 559551852, 55504780, 260286399, 59695547, 958332469, 543475979, 619470908, 837122160, 432665505, 456330220, 3993715, 624013139, 921429973, 51941239, 805297163, 927463953, 98110645, 280038537, 43664565, 461653845, 543300141, 535644895, 920949048, 503023840, 53889871, 697771441, 506746123, 657516508, 367443102, 360288383, 113581120, 570458998, 341916474, 539998638, 951965255, 846205799, 513162712, 960786918, 1403718, 373625420, 537150204, 111953309, 429163815, 276846758, 341840341, 172741054, 161961803, 61499338, 559615058, 314125942, 969107135, 351351396, 553010481, 778222437, 936929235, 566995818, 427594028, 169947163, 141980999, 872033571, 597607478, 196238449, 816878194, 117884101, 608223089, 771070624, 926273280, 347851497, 31606965, 481687037, 628154135, 154581106, 458551971, 574450600, 542158409, 813656444, 619470733, 624828617, 274549618, 455065242, 571417540, 756752086, 975910662, 621143958, 935287245, 977888139, 680735467, 323187071, 773962868, 133170808, 292443269, 165920123, 314820551, 526721682, 490561586, 520207019, 667753385, 678032735, 596898214, 679881912, 870065454, 446203249, 42705698, 898997407, 206214847, 111091594, 655186413, 281007908, 437535178, 826093615, 52997574, 44753042, 269524530, 96831467, 926656379, 959875347, 444704887, 619955520, 762123407, 687606069, 301661627, 798550580, 206199633, 879519311, 975551740, 345925943, 378011151, 960631807, 729061636, 786870405, 730285790, 330266753, 546651459, 206271894, 781844774, 326229517, 894446699, 325275959, 847402202, 221423494, 821124326, 944018947, 904667253, 908009565, 669396625, 63718657, 975087820, 574112412, 962912827, 70440558, 644829217, 460548471, 193209974, 948558255, 721635220, 97274013, 975075433, 608971439, 435196126, 888753099, 541563251, 969093351, 282374456, 204746408, 842005405, 116795232, 20728703, 456840653, 522456381, 406362678, 885578300, 41364683, 320079166, 733875620, 806517175, 190002189, 562996823, 764198564, 740627659, 725571110, 992623962, 192364969, 278218030, 59010330, 943960310, 512629039, 523078483, 56668074, 58483753, 101624464, 507757720, 847039159, 31629425, 746497240, 774106000, 555615961, 955513388, 453532928, 293122993, 277206415, 493598825, 368637474, 231922950, 675055480, 579136062, 370489035, 41252706, 450128966, 953246486, 732683653, 314292831, 988546792, 596553883, 254601372, 981380413, 571542903, 851463642, 32588950, 422610867, 28900343, 192069687, 303938463, 831602207, 539658790, 353305377, 473853215, 913985564, 152380552, 308130873, 25307299, 693998345, 366464099, 391695752, 532557572, 138713648, 556152737, 790656973, 710109186, 364206053, 674664849, 822085163, 382676409, 620595709, 354861218, 694864931, 280550408, 847900532, 132213121, 745258609, 350385438, 519316917, 11207901, 38665677, 553023093, 980560883, 635096069, 32652272, 549077206, 644370442, 973749829, 630676841, 397353578, 452826387, 750803558, 178315979, 731116338, 969079800, 760809597, 162631423, 272998632, 351723328, 554435729, 380201621, 580246504, 265069862, 237464448, 767698644, 991809432, 986810904, 705889622, 676138971, 770453089, 878494727, 285526528, 879134073, 26844358, 502906871, 227958094, 599530430, 342729222, 1331210, 785978522, 725397184, 729377907, 62870078, 937824146, 42177836, 548132593, 342281685, 619025827, 243601145, 560672769, 163318959, 202526914, 744882865, 412687510, 679597089, 138071491, 300486552, 717060274, 527903140, 683505309, 875152429, 135349404, 980359751, 10764836, 302530764, 274424746, 358042616, 7293391, 163499866, 203507096, 893560302, 952807544, 138736629, 307249060, 460324047, 85297672, 614373042, 766424692, 300939999, 931252605, 151424387, 721749125, 150107678, 561558039, 94383397, 376066659, 290740002, 375309819, 719495852, 64430097, 976164716, 192040469, 380268252, 217496060, 602853755, 411456413, 424656659, 980866341, 450088564, 177080510, 39913537, 747905845, 414597906, 431001830, 250894405, 762407990, 658392023, 262748159, 187028280, 862872761, 154713341, 178868356, 447279610, 437015346, 575585668, 616888469, 378849188, 972151645, 814854290, 863361925, 884834938, 619058476, 874175566, 316359697, 189340701, 79429848, 628710918, 942687912, 959026995, 236155325, 32261839, 70351732, 275236179, 200130268, 608452639, 48140540, 955177646, 594714241, 828778590, 143395881, 630497932, 38034605, 671710954, 591161145, 620196814, 312407522, 135112729, 387887703, 917017720, 325522148, 876489808, 892065727, 31931663, 500115556, 671689192, 757949402, 635320799, 818434240, 338554270, 136445494, 529300820, 493636264, 194571197, 77574346, 852667500, 463745852, 596610104, 359689795, 685103173, 425629062, 842294993, 213404120, 363998377, 367110603, 376787982, 128951841, 221555919, 823925525, 652505270, 311526634, 53439800, 918930317, 679622561, 160457634, 313131314, 104929658, 203048410, 350416130, 291389832, 39314958, 357843861, 32475101, 40760805, 9114052, 989629343, 331292260, 596245605, 885684945, 856323273, 68888479, 786044261, 577132694, 175492809, 9190415, 482209332, 768039876, 510690393, 177395593, 153271046, 203850294, 442038972, 549059995, 325971958, 33221652, 72002094, 412827029, 110571958, 611116511, 238937824, 125000537, 837439677, 510064091, 849609686, 805532487, 493598111, 738264553, 854650429, 806187252, 194171996, 162355734, 983731200, 348139876, 296439424, 54691845, 639286972, 773617997, 617451677, 501364298, 239206148, 526672487, 913741564, 13661078, 448669564, 265590526, 209532980, 724468535, 623550305, 11456371, 166595170, 916498573, 612259237, 226085256, 846326284, 492308761, 145670232, 942833361, 784931315, 805146468, 982177258, 458580572, 844087713, 215705970, 329874481, 317393683, 569117494, 292774450, 504905400, 489034651, 870438461, 341233178, 756776259, 890714239, 635798174, 293943166, 445108862, 639271101, 259129509, 811971984, 410854247, 57558628, 525543198, 895724654, 736974353, 991554719, 131537395, 839041936, 266080741, 323055163, 648292107, 19835942, 471843236, 899129201, 387154054, 430963850, 255614407, 207285686, 525991128, 720880469, 5755070, 832320767, 442130168, 869265201, 989526893, 145681832, 398425167, 657523205, 90468986, 584770244, 200566804, 444218837, 117440460, 764741195, 923571355, 859106784, 550797060, 537569840, 763957570, 798785661, 875557531, 523057936, 767892022, 12510667, 235737205, 317790836, 961897387, 385903487, 665443383, 928840881, 693698995, 682597699, 332093071, 69424227, 790937271, 545830751, 740062508, 767219273, 859254406, 380776773, 444356230, 212606924, 630650416, 653615410, 795481104, 216245689, 969083417, 236557419, 787823275, 455266847, 518638494, 237879276, 582183748, 323813566, 829556308, 185432622, 391749307, 8494490, 807947065, 312003091, 191504753, 886256525, 841449737, 271015340, 882766982, 6016832, 750461297, 21075006, 330677506, 769126951, 982208810, 645876853, 551666298, 56617834, 709725139, 300323861, 741753725, 565539537, 660007432, 326069037, 37406902, 572264048, 72457260, 517135655, 549420464, 959565146, 250764349, 437633677, 449719675, 992955715, 968493444, 771783168, 471273173, 596987836, 234394459, 955233047, 294933140, 650240681, 490974386, 936256865, 40639542, 745838573, 696924259, 509709455, 747907476, 901701693, 25190909, 769742531, 341526885, 641353551, 915002418, 664866205, 541571435, 372334404, 800343824, 806350977, 235463427, 883246636, 959089569, 510531193, 661557615, 195505493, 510815654, 6931602, 382229828, 828359070, 410028929, 449400336, 754132846, 794275389, 62208513, 378748331, 442332539, 83382752, 770642560, 636326372, 57151321, 748816715, 458215020, 277869413, 949729754, 701934019, 673931114, 801055665, 816717809, 920715471, 975696806, 162453901, 826359837, 950538006, 93396432, 129024383, 228429347, 285530655, 512822878, 626295117, 874468415, 556306598, 523730653, 632381055, 471596721, 807821919, 465560209, 625644232, 691263911, 228854930, 486186164, 607980870, 753319057, 926959747, 481723048, 762441505, 917209440, 312838662, 846552557, 209192922, 585569400, 209602178, 640083532, 471719787, 12001475, 595600927, 216850256, 831162544, 638170749, 368010937, 351725728, 220373495, 63396881, 659281384, 826620756, 988682899, 653984385, 236906744, 503850487, 993637358, 640680566, 456866706, 997507472, 299546546, 273045731, 94384440, 362505537, 457372005, 843513037, 715167218, 226550042, 601209048, 951632041, 535063143, 943218653, 525567787, 595571228, 69341515, 709483356, 144255579, 254732918, 247053850, 392590176, 127075455, 931296749, 900678770, 194899005, 531323099, 50307831, 23634310, 465415133, 829154383, 339131156, 300575496, 61162017, 801427742, 344630990, 13557891, 973089209, 101629618, 888750663, 58085587, 116782218, 716181553, 939780727, 649461580, 308389597, 4933099, 299085811, 9564074, 388777525, 132075868, 657627856, 762011191, 190398922, 705164102, 192321813, 581898708, 345810169, 358371737, 332036016, 717564014, 663723752, 821373348, 106277409, 377469631, 654213575, 162162117, 274951884, 269441718, 590787898, 840145087, 885971846, 981175321, 765724574, 962091479, 2926838, 964228116, 697971092, 769795264, 789798141, 337748721, 722101172, 316696131, 287190511, 9657420, 669782911, 298056695, 154898579, 557988367, 457459161, 204394618, 145922351, 85609095, 57270204, 870389433, 144879668, 820343035, 732506250, 718844806, 55889531, 81076946, 406722911, 252035790, 919961902, 601372189, 75792693, 86342765, 547789571, 378077465, 79419696, 685833681, 394099694, 790959774, 295703209, 253796131, 33905460, 931759836, 463913795, 860418500, 947537861, 210646051, 77423826, 396128593, 63595598, 121573738, 104364120, 548861259, 238530871, 438687344, 264140165, 820088402, 952206536, 489220665, 951299503, 249585320, 912272682, 43809245, 348755040, 901784271, 83027637, 599872188, 938097569, 316343587, 10663436, 462989964, 201300935, 831654470, 130561234, 462653233, 594871167, 656489735, 557723944, 356071108, 577664894, 936278815, 434700472, 212590415, 487704781, 926501764, 595745712, 221985048, 709680943, 599508377, 71602008, 821354004, 54137871, 66992083, 856885348, 396797865, 213593436, 7318581, 633589678, 487426685, 977346328, 106767859, 840217505, 3819382, 722913028, 117306121, 9623568, 465888315, 199696802, 582418095, 700809146, 94444910, 85784839, 694420973, 438472155, 190720793, 216113195, 812132654, 410977303, 67132049, 380466500, 651185435, 61535614, 663833479, 383020995, 768111364, 932435842, 634162960, 147788773, 883752425, 891440455, 804045825, 858454359, 801470478, 684837502, 908252695, 557340514, 717883608, 694799281, 869518363, 643272988, 569381614, 366610539, 700623600, 280547313, 184712473, 312195745, 170103548, 86597476, 824245371, 927740837, 88891186, 430723154, 412434106, 860972048, 89367642, 987707294, 819148004, 190506112, 967788421, 180809811, 959878067, 2495558, 794028163, 53231938, 673289386, 142502791, 219462293, 435810100, 579922109, 314040705, 271285339, 357101831, 298910469, 761598806, 477406413, 714416882, 212685498, 798143269, 608813964, 347181212, 50036615, 492005512, 656915369, 994949753, 194319928, 325324864, 123131929, 79362801, 633452640, 569586780, 328807555, 55439112, 756128013, 766312061, 296743114, 187143403, 961210711, 396353587, 894140635, 790359733, 51476334, 986089924, 993387296, 272018898, 684042114, 808408255, 768885670, 476914318, 557037411, 497117004, 994401794, 667766629, 544620503, 705028659, 21850876, 315593519, 38764888, 935518999, 62505126, 148433881, 461176239, 402734365, 123880746, 864161677, 976234724, 331404898, 408941322, 692656988, 193601003, 41231402, 616706722, 458215974, 48781654, 843797673, 331741171, 728814270, 614000399, 181083054, 207685577, 156695349, 620308392, 415749270, 870217429, 517235109, 576118953, 673952869, 728758397, 111678328, 81811103, 707157196, 99730760, 435524581, 364302095, 363830596, 86328278, 746491393, 326362956, 268570487, 473881382, 573144625, 34130654, 241798756, 221661593, 475246372, 784822852, 437797480, 84314389, 433217058, 578999791, 360049769, 678695736, 618427950, 178921363, 831600485, 992685185, 850431218, 326844148, 324378422, 588142463, 385075182, 374361984, 861688495, 338989471, 340300409, 266340440, 200376782, 215854548, 923212486, 447039698, 521543991, 197941775, 723306015, 248035199, 48968472, 353182723, 214526061, 923638638, 270000532, 191765947, 294671668, 815883876, 176667164, 760766010, 201132563, 519619182, 608026474, 632637447, 819887564, 832421049, 608478723, 213858397, 99815688, 596458441, 348003355, 821729361, 403431358, 291995623, 427626035, 111439364, 622568046, 121426529, 204697071, 180654299, 580007845, 78140541, 892333457, 438912170, 844281487, 9569218, 76452938, 952437978, 412465190, 859254583, 904080960, 368045761, 718848389, 686136312, 121085622, 642551652, 177989288, 392997188, 857933904, 78612369, 346474640, 243734658, 256908736, 610242980, 39534363, 985346903, 699118842, 204081148, 52305213, 861204063, 467541940, 606105274, 80143464, 973606614, 261621002, 712036920, 731494073, 312475884, 767114240, 178012715, 531406995, 165480138, 97034107, 894212927, 199334380, 886546003, 697569618, 759359164, 925169314, 785057459, 354443423, 107401290, 463912333, 492540291, 341386658, 300144514, 41073984, 110328927, 876310698, 12530762, 792625971, 3377345, 60376372, 994349223, 790446815, 339814954, 176758533, 233113483, 466290040, 329155198, 159645620, 276206717, 538529399, 453687921, 880444855, 596720783, 400630306, 91614717, 2698100, 276968269, 212555952, 274222418, 554605638, 38917567, 34674526, 877892446, 720205762, 462900957, 250964918, 187203113, 827461746, 203307741, 646872016, 193171356, 212990842, 194381791, 440719117, 633490741, 619274957, 334015810, 485895810, 448924279, 736325457, 619779259, 716876130, 661176747, 940573289, 673519855, 708218056, 37970778, 980082109, 361434683, 567562403, 44563632, 920722999, 623658797, 594542993, 205307277, 741431463, 215207115, 173477543, 889496849, 607677061, 845816492, 284324480, 490248829, 847723799, 853148036, 285534543, 60938848, 976707202, 430127735, 703638250, 409268647, 187152032, 98281134, 272984837, 290434098, 26573434, 574310971, 122248679, 459450009, 154559768, 204607588, 788103938, 187627623, 79944406, 885934071, 959382838, 940122218, 528358235, 228316724, 467092844, 484371158, 4950922, 87838508, 607736080, 10948794, 805754219, 192905155, 793436240, 856998271, 494325045, 873857406, 66378025, 408730227, 189136518, 61493142, 929865721, 924709062, 743826095, 292891888, 805145517, 608448845, 201081812, 410822293, 317680141, 409492553, 888217678, 817416635, 392584648, 265285951, 669933113, 146184809, 796302251, 990079881, 487528828, 634922829, 996457980, 987002037, 332373475, 937191257, 837249583, 292118065, 826732897, 962754365, 273708121, 160204849, 882374686, 619478519, 501291017, 885807650, 35186851, 704007458, 759698792, 937845943, 591955123, 881279695, 732448380, 561301852, 132093927, 912342902, 506290512, 491145499, 614108050, 68626318, 208320892, 493350256, 281264389, 497177563, 360219348, 867045044, 756087413, 733199184, 624606739, 559523432, 270658258, 576794223, 8512397, 891493619, 443840661, 709456857, 262451529, 906025488, 835086971, 466380620, 908543219, 971174960, 828805926, 158396998, 573081832, 762607064, 245536485, 648781260, 221701573, 837223625, 598044595, 628893951, 529198698, 28454686, 836720295, 836628124, 959603692, 582306205, 114764129, 200515729, 756776571, 779857292, 127663976, 190599776, 36469572, 336752272, 411032856, 872264163, 923234662, 659036040, 643857528, 246368093, 18137011, 816512956, 519940543, 279599931, 670786097, 989900993, 582937112, 668246420, 156945432, 60353298, 257355633, 567076580, 928328104, 514239587, 934864954, 798196655, 939236756, 314243232, 238411913, 9287335, 596118744, 748396732, 351026979, 945582044, 710706374, 725609356, 89392976, 158719897, 1719803, 58077915, 269921199, 737852793, 799809615, 146111126, 386627523, 502440911, 484917069, 779027186, 475171165, 574276446, 14420177, 898443122, 565778871, 902794659, 663058127, 981357155, 998484935, 347698453, 396158218, 490011772, 485041657, 872975470, 974663183, 842956850, 378570108, 492204456, 363821193, 815855650, 796858844, 907458902, 78175615, 889623870, 390630408, 727112262, 826117130, 266173806, 665541866, 588113805, 616057664, 432731895, 701912525, 639663835, 242847366, 987831771, 561193457, 700557636, 854934645, 190302811, 943958551, 593635819, 808696176, 691017846, 894209724, 331686985, 761700313, 502027826, 503084945, 611218506, 273842539, 138086485, 475072455, 147768322, 208905080, 424139493, 548312572, 113292786, 934275775, 751997337, 848352959, 82727738, 525076001, 781644640, 811709986, 137074694, 860147050, 135940196, 318064359, 112403588, 395039925, 946136782, 178740872, 990144448, 912031403, 996491461, 852414841, 175096578, 455544189, 892679300, 90028423, 386884146, 551686888, 586054066, 835209094, 309857504, 968112445, 388146850, 658544444, 973038311, 409895236, 510431261, 200753244, 795376580, 634070554, 887877422, 395845053, 125316571, 254112105, 261774283, 198665671, 273259230, 613334230, 374756448, 135132193, 224069552, 457287145, 882407321, 912548733, 320776803, 841827413, 87607810, 247906864, 90060945, 563561653, 370399895, 429776901, 701941272, 591184107, 42242654, 132493494, 623937008, 232848164, 420070816, 826156332, 533892158, 777683866, 937023748, 729327040, 213087697, 579487088, 276626641, 865654665, 831953060, 949939339, 147613666, 402584685, 189908267, 422415770, 537069623, 439248837, 714734960, 924459570, 462569961, 767069690, 496375779, 30983173, 242228375, 637609222, 99414579, 667027794, 996022751, 501271139, 160579950, 474179509, 826536234, 702001658, 754425239, 43530450, 384459162, 417332265, 961106733, 611395100, 758469889, 327478685, 444283296, 828687856, 837106191, 840559285, 762456109, 590754626, 557836673, 236079597, 784853669, 598703855, 573818038, 161509795, 878731108, 203047502, 412457755, 980618319, 648620912, 242752064, 798872539, 68439678, 616531509, 260000359, 209196613, 739766364, 181192032, 861799412, 691331907, 858850117, 819547223, 1150464, 503072638, 961385950, 234470327, 126327052, 811458251, 461907182, 454336128, 194399485, 282859479, 944696443, 827108904, 760747834, 621889337, 826282238, 72173167, 364977054, 404378526, 364248110, 38541217, 752707598, 201297259, 295617150, 200318749, 623021770, 654374411, 401060688, 640659106, 703665912, 23099631, 475593337, 167637597, 354796952, 880881516, 54493414, 871391453, 592035174, 205802088, 369588094, 80609983, 961084515, 402358170, 325639527, 384444135, 402355164, 185265007, 974501033, 748024788, 28348466, 969189465, 737011519, 883277840, 670006494, 854378237, 13595348, 464469788, 326785162, 994951862, 662870853, 798183391, 937457385, 586815286, 256572563, 325381142, 201415253, 808627115, 811335213, 164030385, 74985402, 490691587, 256398830, 297709763, 731018714, 218325505, 515957781, 341129316, 18483616, 506904406, 419634062, 753715202, 278439828, 664414157, 512736228, 904388898, 582163053, 264864284, 202448480, 343435197, 623349965, 139734047, 786675232, 306427434, 115004998, 128815247, 478725100, 726561050, 564876212, 865340235, 256330592, 906938975, 207257099, 909474104, 427725038, 876397589, 461778263, 398272123, 519708990, 820787611, 169591777, 411206678, 830491677, 384832047, 750619726, 84921906, 989580692, 136211437, 944475446, 463577202, 812696165, 365126295, 320148460, 75442925, 320211549, 605994281, 21121370, 18455898, 541907606, 473556068, 818271436, 71392326, 339929728, 209146888, 899531083, 540187946, 164553653, 110563327, 399400884, 929664856, 984801855, 326932244, 407317520, 863233774, 881097195, 547952339, 555476900, 120429515, 930589563, 941207173, 331007092, 682892182, 864487690, 914593391, 380469773, 446403517, 475796453, 140684554, 925969229, 529341059, 133984475, 974499274, 544670559, 717405384, 815624352, 830973477, 153406905, 961617048, 541025477, 682536729, 249398452, 287454500, 915446546, 605701521, 491038151, 977198156, 361453718, 909373408, 627258541, 121942134, 959862407, 221844451, 451702838, 389276718, 454782350, 764209895, 738649481, 317549110, 828065931, 929048218, 247641522, 729417194, 991649535, 230773381, 140341084, 450917085, 312555269, 445150842, 879541685, 907620015, 995211279, 283997856, 553074165, 447928676, 703373344, 761263441, 74556710, 875141401, 170631529, 124702563, 720760139, 873060984, 905856839, 626942643, 328096154, 578565260, 847247395, 40064030, 776948629, 991408394, 131159218, 321789864, 710114948, 745128436, 985090031, 424388426, 887945089, 417485025, 454791575, 500564606, 827187127, 581207589, 367126440, 692209013, 408178531, 894936016, 945998614, 604312759, 788265136, 73501957, 135835043, 279457641, 194912394, 725057256, 990923061, 262809143, 301364168, 906377207, 523454826, 984175409, 249908287, 629779263, 75396703, 256934153, 516947537, 469729236, 552998754, 85178820, 124032170, 302668082, 666225148, 572281347, 689848055, 170408227, 811081317, 135824530, 842477307, 152921565, 273113096, 600221913, 414407528, 721570262, 503595930, 705159982, 869752973, 171416692, 691371308, 812178743, 624326102, 874690508, 600426913, 636927211, 856147295, 825935870, 73228144, 517478151, 819771796, 267042650, 340553411, 175756278, 108785274, 545158226, 126060584, 331208625, 804860822, 862384582, 29715076, 447480380, 489160954, 446055858, 924403529, 414733762, 224535012, 318489280, 688959557, 241000029, 590815791, 97627841, 275623132, 692095564, 936954806, 157825252, 424749232, 937376723, 65064405, 297063734, 513089529, 201978937, 155395404, 597019352, 451288900, 308835371, 785137110, 154537272, 24620718, 604489017, 620018880, 228170582, 262687193, 732820010, 475623308, 913033906, 203605132, 960821337, 255787579, 10324819, 772676424, 151372633, 191613175, 727199129, 851180641, 698102224, 277480386, 795379362, 516011658, 395866303, 214820297, 802230932, 790519922, 41919061, 980060671, 119679994, 764228445, 174144078, 716413604, 209054142, 896831530, 204341498, 421457619, 744750697, 943620883, 99187646, 195977921, 195948876, 757868233, 562041684, 890548077, 733605630, 215650371, 110632204, 140655374, 145866191, 518895193, 459736305, 5929870, 875521827, 346984959, 939473614, 469661700, 511213033, 371211082, 100241111, 425428675, 553402119, 771791394, 621055817, 75915210, 730749612, 682954708, 440164260, 219380166, 224257133, 700177965, 786350904, 252902183, 229506582, 701591093, 260396561, 437980844, 336575059, 778994146, 203670354, 423483327, 376572797, 442557469, 694762130, 680425984, 687246810, 13005729, 712135452, 180417531, 838409874, 845728988, 199235178, 59485630, 307998968, 330570690, 980963434, 912604296, 814143911, 911613969, 800234982, 301288706, 971092076, 957030074, 994674869, 625804951, 449040462, 666128341, 724769778, 171335809, 880630599, 159203076, 888980883, 610317538, 260070264, 940756685, 580393587, 112725065, 166607433, 337176444, 915866806, 941286898, 438446140, 923211262, 473290563, 25878594, 53726486, 423247441, 937022638, 876552170, 737494062, 984339467, 105775429, 73065143, 73420661, 254951229, 386406945, 73040070, 665091333, 214177010, 140429170, 234396864, 383495955, 613561973, 838984843, 409504019, 815517891, 849147413, 662259145, 337904637, 816384562, 325863910, 426019015, 276961187, 990303403, 534560241, 82909948, 392594836, 966339906, 948108675, 163415919, 149939167, 168505784, 147295257, 664315696, 711045969, 962614784, 7620934, 980502662, 496169581, 967042967, 955855276, 241571387, 361589807, 94705725, 731916655, 788350004, 390079877, 804896091, 809261850, 307265441, 593303548, 647100827, 54558400, 317997854, 791028838, 201732727, 450907070, 866554185, 279483418, 788014264, 57823610, 376130992, 208252442, 708564937, 990357966, 288046223, 424832959, 189686605, 815280648, 632141298, 608439751, 262236797, 356814321, 109838100, 620269543, 292281029, 442360584, 723347572, 722048276, 592692246, 175093639, 808220122, 364550114, 597556582, 15749580, 529256512, 187046352, 121362450, 388786701, 979671005, 465697245, 313541667, 806946897, 263095189, 290486403, 166407225, 935160232, 846239735, 41563869, 178010614, 719583817, 544833681, 820855128, 596813480, 704959710, 948970464, 70177618, 511348315, 472238188, 781825253, 484699019, 952680148, 530380815, 784195274, 764174682, 798600043, 592204235, 75434209, 8166141, 279553787, 168628972, 496394971, 527994783, 517543395, 252321046, 70654741, 758024840, 397794498, 118477889, 262790772, 550909888, 460915142, 986420838, 663747166, 191816127, 628796262, 182271625, 105275084, 83062125, 163369005, 595655502, 293026738, 98762035, 238460353, 511446978, 78013361, 121149664, 8624808, 777372166, 937094406, 265154926, 776401982, 505051390, 960470907, 928631876, 482919208, 673057777, 301472925, 353044291, 959448843, 812560663, 419169589, 354268800, 36225700, 183682663, 879233542, 123242291, 342271862, 736094280, 474662938, 886804353, 811514801, 779942955, 936492211, 968011092, 975341777, 533159823, 11028927, 957016887, 364152833, 410120908, 484859671, 248309442, 863679106, 995848376, 474790902, 636567171, 689255752, 70197333, 793206309, 312390730, 438710270, 721807456, 930970811, 340750026, 445169718, 313214919, 672530893, 994447906, 381761552, 978406474, 384426562, 991634751, 523333505, 958039852, 287727146, 536021526, 810550187, 925739515, 694527843, 423750730, 909442920, 36198203, 253146788, 937894034, 242635101, 831967116, 329453632, 745371161, 524915006, 72759092, 693926200, 150259532, 347939158, 231996580, 160477260, 941243793, 380627186, 271955842, 575370896, 987636384, 426629340, 25879733, 320035163, 382972405, 641084022, 521031142, 265572986, 371500459, 686098916, 355059274, 987999867, 238843928, 935805799, 171002473, 378353913, 69554730, 193661460, 121276124, 610209803, 34706888, 909089001, 852307480, 693845268, 737174719, 198369388, 531191200, 509544861, 399304458, 222551477, 482766165, 285540185, 163983640, 685645614, 783581675, 94192008, 555585878, 609125050, 890861612, 454582197, 202351129, 144357638, 453101193, 82015663, 112237510, 940237360, 936627570, 647766505, 179382300, 565573395, 276235559, 369477425, 11536170, 289133646, 53179888, 555867705, 621685090, 132678771, 659014200, 597154346, 209887307, 267466858, 725189737, 534192288, 126028606, 41825736, 866780785, 170612318, 750987079, 811912981, 744446211, 70989612, 436351830, 44790994, 801518956, 417772089, 525498542, 494526693, 396278405, 119827726, 974008868, 591534822, 891443299, 882518835, 42400532, 104092878, 337630936, 338417657, 270461677, 844429103, 225297400, 591598172, 952575799, 733240170, 724937523, 657274519, 123901276, 646950796, 735679546, 839961026, 700312898, 653860830, 585583792, 328157176, 283396066, 986514154, 693439811, 999215414, 167472749, 854274588, 949957342, 415336511, 819001566, 908394123, 417651874, 309194216, 129186881, 969656294, 728384208, 911266969, 503679563, 123602829, 265023951, 660044170, 4397939, 964412931, 341631254, 307752164, 443994280, 901595004, 864338333, 97957216, 668228879, 997528186, 615954398, 215185205, 569197319, 848686284, 442808693, 186829782, 209639441, 790584676, 825938374, 879787114, 774035953, 212980350, 42543816, 552198307, 585331367, 502947143, 752342796, 650644375, 957027723, 973149231, 749777072, 175852964, 639509670, 379598690, 394973536, 93626233, 408760948, 179667960, 686757982, 705691062, 989903145, 764254713, 274635998, 121131501, 356921592, 305388958, 162559039, 372312087, 709988602, 112668206, 490591262, 794105981, 518899912, 331042842, 970758861, 197297252, 390364636, 85166700, 349411492, 698540766, 413061136, 993272933, 786381318, 343894922, 20917284, 4162469, 818986811, 788392271, 343864149, 49813590, 854778573, 577329127, 212290533, 582017931, 181499940, 718292918, 976197912, 653388167, 607129045, 7339064, 225240018, 485774889, 86942900, 328392154, 479547052, 772380189, 475228221, 847088734, 14313225, 575692530, 90328446, 763361740, 171004488, 709335576, 400612011, 99914507, 51609070, 62520579, 319803593, 714094857, 123215178, 477615656, 16209250, 199351999, 538780836, 561036744, 107923232, 523998792, 166330927, 853896866, 381803422, 531229335, 728074918, 689573684, 907573007, 590581884, 916711217, 95609844, 129410712, 56584327, 959503064, 957056750, 174215174, 744459038, 628985450, 544700981, 256370856, 274085016, 569969065, 80965709, 570140769, 278915121, 384090535, 908985961, 495909709, 899372711, 798393288, 634366113, 367735202, 222448367, 351845737, 954035471, 983250113, 820438584, 42704652, 653660836, 812552967, 657742693, 792480327, 753678477, 263812641, 154229201, 496536597, 999420510, 299597162, 364773715, 211490008, 21104206, 310972890, 186942321, 757251207, 812453231, 663833786, 922407489, 59946741, 564704393, 126756380, 685616429, 893601589, 736990521, 400966741, 116627896, 112251287, 358147473, 656532732, 341659779, 781811635, 496072654, 84594744, 834210672, 774323215, 286979415, 236179242, 497487631, 986294165, 606264334, 581344411, 604436841, 89367990, 183301355, 735670029, 428543862, 505296770, 785706692, 234715939, 277162883, 32222492, 18460317, 271996127, 799991118, 760150530, 269722520, 146813081, 926958666, 951859911, 503574939, 195066606, 804553622, 215936770, 918069808, 378537540, 798837642, 425180116, 165197802, 499316498, 22168589, 185500076, 508722878, 889723976, 908263988, 139195262, 606246954, 657755291, 315325647, 228660461, 927778893, 773886452, 439856948, 162230151, 879081064, 101925670, 524899845, 354342522, 133025868, 108866469, 121189181, 270276064, 969560216, 722147931, 313498007, 719133170, 624863408, 938930036, 536249581, 425190927, 272648950, 434021221, 387834573, 292316946, 274994692, 507311664, 570350651, 195366142, 485475398, 442659745, 471245125, 706289563, 654688224, 271869745, 209340773, 706623957, 567840485, 616912489, 167930641, 303686752, 367962771, 350789032, 80236200, 488932009, 964321600, 927976838, 81006556, 774412764, 160244233, 471356767, 991797103, 666297061, 416998448, 934599153, 595460050, 776591390, 257742904, 808988958, 693050843, 103653544, 128413832, 354563702, 462954621, 195328082, 359138347, 441836915, 957489681, 796564917, 846676910, 540525398, 513848662, 997378051, 228900217, 171561307, 884494259, 721353654, 167291613, 123767666, 215668879, 729854390, 397159915, 5679327, 91757280, 460993580, 758892395, 63364111, 208641496, 970003687, 634189428, 430341582, 744490912, 968857586, 949030417, 553839150, 216345426, 782160216, 792328776, 395705944, 866853155, 286856891, 52236982, 297869558, 201704212, 642231314, 334898280, 455213838, 232079102, 352590943, 178636650, 535975629, 82298428, 646038502, 502890869, 706507039, 474355858, 378367492, 535213711, 116407579, 319484256, 720767517, 246535744, 149382399, 917995160, 670775554, 681126581, 954512373, 797491622, 604082172, 729862161, 511091348, 100672983, 385805541, 762425255, 256157537, 931194850, 560295789, 722837799, 328350201, 354399213, 92596021, 587112390, 810973259, 938371616, 329036152, 46203198, 11616611, 21259407, 692061430, 750532131, 105217242, 726942756, 514312248, 941080895, 335716006, 907162999, 246758021, 552082575, 75297184, 709313219, 695892239, 580985617, 426368424, 824466468, 170874326, 903685463, 174693086, 947539186, 37396746, 101157192, 662256145, 260992070, 622977927, 968943493, 901178788, 862455773, 76973103, 433756078, 68125774, 825843489, 329407402, 955478178, 600573316, 479181475, 453581187, 595941271, 433304677, 56378151, 633487342, 494755687, 493647493, 702660394, 836942765, 920512286, 969629067, 708496326, 976141398, 673631482, 481578887, 745001298, 228865290, 492279631, 902358953, 665644545, 357636002, 407896753, 399474653, 957377649, 720649709, 312245988, 726258976, 655544170, 656631691, 923978810, 525496169, 583172968, 278704317, 266763811, 868822416, 289935922, 413678974, 742915793, 625366611, 417987874, 154357619, 378033914, 586283498, 821889053, 545559974, 299862341, 386532046, 239241952, 856158621, 887565736, 934086935, 495469834, 804782016, 300335237, 253522125, 516950612, 191703017, 690509366, 389966439, 774017734, 305822339, 43597842, 28146425, 840223154, 40448111, 762009308, 964358276, 776198924, 676125809, 405387575, 889967028, 958667358, 239935066, 89479564, 685958360, 367961757, 811350539, 630777525, 568511668, 374273340, 283463622, 781474126, 211086524, 390712317, 40869657, 253756557, 626884512, 113319930, 428770206, 516517849, 182327581, 258051145, 751062164, 453021476, 209763508, 935194281, 20060535, 60414480, 177719930, 884271211, 109869739, 209653092, 708260, 385501635, 886535262, 867463132, 978581191, 598943712, 805049182, 260627808, 163405322, 286408763, 743219258, 128122552, 534875474, 54629670, 649512062, 279312123, 402845103, 359140116, 372800395, 539408118, 137486651, 66594538, 648677736, 249037799, 352003761, 805983648, 855661793, 838101977, 966584215, 254313752, 707375407, 179607649, 200880027, 143531642, 715758635, 114842541, 777971516, 533948872, 853579446, 237192132, 399153048, 253078883, 786767054, 621974218, 661204384, 384911236, 186524396, 694187772, 41970709, 919169660, 864282142, 239421868, 339161732, 516488567, 519958019, 528531659, 61409824, 173364939, 182203345, 98940850, 349373260, 856604823, 916497458, 674392523, 282236000, 713833160, 462506977, 708401279, 694659673, 579465778, 13682218, 535394141, 727635635, 54414410, 80052747, 921974647, 988265240, 641338878, 857810302, 877310557, 543762279, 680159043, 828170042, 248374536, 996825065, 914358257, 483572020, 872306412, 102228516, 363830363, 199715027, 483424229, 681246862, 358050989, 739865461, 729474664, 687499309, 83883873, 619888911, 63919509, 89580931, 986969515, 880180653, 782124246, 772211624, 926728556, 750498195, 960907109, 468747481, 582459775, 194419538, 593745981, 107572772, 453139383, 858102731, 73196554, 642796804, 739325068, 736678254, 424960581, 80889136, 943870697, 117909597, 964629010, 540697635, 854314233, 136923569, 923459171, 964763093, 139833097, 808367725, 824353455, 188538504, 507976604, 887012128, 455119635, 284572309, 583753838, 378567908, 40274501, 271766003, 709663162, 350727677, 415386190, 456743571, 367387199, 80759919, 259383170, 547971560, 325695832, 428876929, 722090305, 492455680, 369959056, 663461364, 180943918, 927920824, 958017640, 57607853, 569509347, 116227148, 579311918, 864362565, 369474601, 615265190, 10288847, 251052525, 876303943, 193318381, 393265834, 780360005, 854401549, 889920065, 814928908, 892193817, 935735418, 878590351, 746315093, 664023130, 929215657, 712351016, 139546212, 205397901, 458050712, 724796747, 9881699, 36003408, 517835809, 381185336, 436786129, 533180198, 542553241, 471298520, 848299852, 941739321, 115719311, 914530382, 795361160, 988057911, 530273205, 511801399, 938922843, 716481221, 896904800, 542110113, 400475008, 772598967, 962724510, 778504679, 895860878, 715570724, 657062446, 557913851, 332375012, 710161345, 437115597, 778865076, 891746056, 301495540, 968423949, 982231830, 509654458, 420687400, 520397609, 592358099, 345820764, 883737198, 684728911, 196012538, 929423939, 266041472, 203595711, 303278580, 536587286, 186641062, 689276880, 711843897, 69385283, 786573587, 151243040, 940899730, 154270385, 507704474, 655133128, 546175456, 790601309, 484502229, 342591236, 115725530, 675141648, 933513489, 195412461, 33284616, 559571005, 330088016, 681807694, 215489036, 276630185, 318633981, 473747201, 5890801, 367430025, 990203628, 482638487, 880277518, 757334763, 835918336, 463648647, 573354787, 310731880, 542362672, 609456683, 624315036, 30367523, 561258876, 976008579, 451264498, 637525413, 654094145, 859258865, 330674929, 949234116, 911831688, 396631776, 305845421, 875418685, 660443533, 170079267, 197271500, 896952110, 218035953, 373722107, 176882676, 179875131, 792713209, 907300979, 351836111, 665322090, 426080727, 557077245, 122952213, 834475237, 630623172, 188734328, 35610417, 283155016, 649073326, 135972305, 202028472, 528968016, 318104437, 779481509, 34235204, 500529349, 385362030, 928509185, 184816722, 476677263, 921949041, 658523635, 439872785, 645597630, 210965006, 937870322, 283047652, 334222466, 15757041, 744118288, 377465833, 12445159, 58467670, 972894210, 548857504, 451306700, 216926386, 473106473, 121624855, 520660155, 232353639, 300385241, 818452051, 721507323, 257346264, 933631541, 437734302, 433006708, 115722054, 309992116, 683901974, 530969488, 575938556, 71796861, 432986593, 133094722, 975020293, 666387762, 221730377, 799402032, 438180688, 310390850, 244770169, 371527436, 444463680, 912982892, 670785103, 65732576, 990656124, 659263839, 58192336, 247116856, 944799334, 58685830, 461556911, 809867551, 736153959, 941822068, 196906842, 398447758, 146111551, 681271638, 711745479, 903672505, 612893310, 893406661, 442568961, 868135642, 204264014, 270742220, 693535504, 272463798, 419541703, 990125512, 47649036, 995664098, 424885982, 126875588, 102094765, 485836019, 684175303, 204043001, 653456205, 248596608, 451351765, 79730793, 761383720, 309108407, 989012460, 188000877, 772836066, 45027618, 68760502, 757395029, 46885137, 437613817, 336367813, 813885235, 901206600, 886136046, 229779095, 891209406, 204971276, 136003383, 113707337, 367269602, 56234599, 428472518, 481084472, 340172985, 931208691, 795779068, 859420339, 122621829, 703661822, 234375734, 799563149, 833391187, 567767346, 20891410, 533372525, 165931429, 960668568, 488410580, 758431447, 374747576, 299825383, 560616134, 381575079, 371450078, 960444484, 318488581, 126541428, 388556068, 902565104, 708149762, 602082201, 668915994, 184030685, 607343436, 588063337, 278810564, 570227758, 203403527, 663861439, 204924938, 364449939, 514403442, 367144138, 434299640, 971931913, 737842781, 107971338, 462669375, 946145057, 543401997, 543657975, 726106279, 672368443, 250340852, 123303840, 369581598, 621165906, 845401109, 509261301, 525379199, 349790107, 473201407, 588311524, 556034306, 278655301, 124368382, 605176024, 509218708, 101147878, 515068372, 147246394, 371116300, 843912590, 752657612, 778569830, 817957199, 979453570, 465411058, 213807931, 487681542, 304816351, 595871843, 378417567, 821739500, 436357133, 332040925, 699082862, 723101268, 357818742, 385027562, 72448155, 9426366, 53449665, 377338294, 983906464, 900128180, 665928022, 449572779, 122009240, 362529297, 756596544, 475888523, 141972648, 259820516, 447433920, 99879154, 788710288, 875698851, 745695174, 48899240, 20189679, 605540793, 132615570, 430511160, 363742760, 998270835, 140199943, 588168152, 826739812, 562511712, 485204670, 624524396, 502472205, 557134465, 190451554, 889046148, 792943058, 624804443, 967528804, 31491341, 540156648, 823581440, 532008436, 840033593, 745764517, 832299653, 76079889, 702740912, 226594493, 536192981, 706575619, 608206918, 216668130, 506786228, 997880007, 438376534, 742050043, 148943874, 264888049, 601719026, 268447298, 933806462, 998123340, 808283301, 331836330, 222421613, 913500248, 170019784, 687155346, 778733630, 97940580, 517088522, 190242075, 887682906, 747710093, 499042930, 745041228, 885044095, 111822895, 456592942, 858849654, 821323179, 519900669, 196055786, 92576367, 687135986, 177719954, 430330440, 141348772, 114567453, 518703000, 54540544, 152125693, 82548652, 35697320, 132459448, 595227510, 503568801, 907755, 939470459, 742360673, 804854641, 250892542, 257764185, 988638727, 305560289, 830750018, 267997696, 480470986, 816447015, 35613210, 973655637, 262829702, 680757480, 970823635, 486587761, 21146520, 118649308, 99749580, 259699796, 90679265, 291503336, 15469292, 745348150, 982044677, 1177114, 64484920, 959690296, 928130942, 421395413, 931730894, 677520010, 685550958, 125092725, 950249646, 380302096, 79533380, 599098826, 178350661, 924822628, 177408891, 544799990, 595540777, 491914245, 674571438, 635853884, 955868785, 980759056, 803184353, 515510975, 758508810, 338169920, 272293457, 1544045, 219251485, 604376101, 865324164, 659828884, 889483907, 742772053, 986149420, 532204187, 66164191, 712175026, 248054315, 846579805, 79137520, 145656303, 454769853, 66760724, 350810002, 602616804, 874720011, 843459401, 500102309, 621818043, 671679008, 435778088, 974184418, 537710360, 397806782, 601295491, 406823846, 102123720, 874137648, 964315143, 425878915, 380601196, 757014150, 468062964, 449809805, 61475284, 437151921, 892333200, 295853524, 755784950, 473502580, 582447599, 178527685, 621225413, 909699458, 982036677, 851382779, 608001085, 986290945, 147654185, 982722044, 615506010, 468228796, 110852254, 51576746, 469871799, 691423098, 790177557, 469584804, 450787906, 291737697, 150723020, 899374535, 131539979, 123670081, 682224816, 254438757, 811637070, 355446783, 733924224, 2310157, 662000513, 584713932, 107049950, 804894839, 953102208, 539143966, 614823394, 753356414, 388564083, 491029560, 314942459, 836879766, 234519757, 822674687, 676750325, 451393208, 559789790, 226696490, 156859937, 61268552, 665437415, 217324070, 382844115, 719644950, 863935623, 832174860, 66265682, 408913511, 301624803, 108698918, 796408132, 555773377, 498877490, 283746741, 176624017, 17317757, 337157761, 674230233, 255924396, 85037055, 764462217, 364221237, 700756109, 317029786, 804325112, 382428615, 543678781, 628212109, 172279690, 616412781, 184740260, 445454218, 35748665, 308373504, 403806371, 910772887, 508289327, 948315401, 614407265, 442443691, 602745783, 718564968, 983511598, 576086311, 245665947, 948595855, 888629378, 736701290, 483104740, 540699597, 131022426, 909681416, 106257394, 7507747, 883529380, 286254270, 862316551, 810144884, 817312181, 953535949, 214848160, 174474070, 349394021, 188614549, 199324084, 968395396, 363748716, 814272093, 426447544, 461185348, 392279401, 525341782, 708597489, 512289730, 874064448, 198576013, 551070237, 327980630, 369253736, 494732228, 763006062, 655231210, 766990531, 624407768, 260087797, 149428995, 442793232, 830096897, 453224997, 75979337, 825169843, 52572231, 189526942, 32248548, 605044421, 163746587, 250276278, 750637380, 30050616, 449928117, 695446487, 960640988, 400470825, 996049280, 719355502, 332729485, 977345417, 541831822, 227456297, 97872329, 296082599, 70911513, 242531336, 899255100, 299665544, 123152539, 800780041, 300499151, 17234694, 93545057, 633951216, 841615832, 635428601, 359133739, 421571058, 310398552, 723044270, 170045986, 761472497, 680837441, 843623585, 413035879, 912501955, 291934777, 496011478, 544872418, 995799807, 916513660, 689643591, 974460670, 711978457, 784288472, 17520541, 602259454, 996784306, 126554430, 495475184, 546386102, 918184064, 935243398, 746585929, 605860071, 218346665, 111093999, 104928935, 726464760, 295795629, 351894703, 941236363, 626689993, 144232765, 232425296, 146929936, 927322090, 483251745, 960669780, 737704027, 701495845, 312475057, 1615781, 966282581, 256638242, 475057140, 507374803, 840142422, 968105862, 663868801, 745882387, 606275217, 559958078, 96984052, 57142272, 815702652, 40182356, 994718218, 779643195, 365351960, 743400523, 194215994, 138294111, 637952740, 951594365, 534604750, 552643304, 739114338, 953857779, 288801960, 658487189, 334144414, 571355966, 280361034, 64693972, 90548086, 955624619, 387515384, 357584602, 523815377, 876577485, 684941544, 194853520, 519636506, 737645295, 349387639, 125932529, 246699010, 237641122, 649975687, 511421175, 328139546, 56178882, 659980645, 962704899, 443272199, 846861677, 141693182, 796615676, 253461330, 62162780, 396032488, 615736785, 268053776, 654970531, 54534761, 180999714, 520446347, 427954409, 331431219, 711641493, 603072311, 149107918, 979334989, 705115334, 530612748, 88143785, 28843252, 792888842, 137589101, 623787781, 375477319, 221209197, 267341032, 667950012, 611625448, 67885028, 339195132, 687261245, 1599387, 659374924, 827645797, 940881963, 654819982, 403024857, 650924657, 777222728, 394361903, 491267974, 152961708, 502304869, 14387873, 111690445, 625069964, 950849925, 616223560, 746312872, 327605933, 48211900, 149407121, 598665792, 319636868, 417858298, 143800720, 437245342, 326508948, 685265451, 88935845, 856740257, 633517489, 138494265, 562284320, 496281201, 903192654, 469464658, 529721006, 899977730, 495530646, 751799467, 961640740, 889483112, 169705660, 529072383, 437476570, 65110952, 736887177, 336872129, 223229677, 950220161, 567781903, 108876178, 801907681, 189860094, 93820508, 11261840, 333924624, 88853935, 187595603, 358401350, 348342871, 493375571, 730688088, 111408861, 220493930, 930821006, 352551214, 769173970, 363356766, 949293492, 663290646, 430434241, 934442424, 516018724, 718334738, 16080964, 552545294, 586648411, 35369517, 45955824, 546503811, 178095178, 53518691, 270289508, 405036189, 275699776, 166491856, 798071196, 656778448, 362953862, 43616866, 71709781, 412708908, 638948052, 331237108, 383432163, 286023412, 133963484, 469796059, 511908793, 946537192, 900780057, 595888679, 416159579, 119543155, 177162293, 867265305, 645171813, 946316992, 909059283, 914814032, 743216292, 316736819, 159355148, 663508686, 783030256, 946899545, 821213414, 420267383, 393470923, 280888559, 990871878, 241350123, 311665373, 243345662, 116137987, 749380753, 945377675, 173854494, 634448983, 847664974, 863686262, 748649297, 712073281, 969066110, 17656665, 718746022, 686700678, 84223914, 875149189, 357691471, 742860807, 717165597, 965221004, 308788878, 836628298, 872063664, 326622608, 713991127, 467097591, 389244605, 576329451, 384984457, 627058696, 282044112, 358348316, 119903774, 678076172, 875892281, 292988619, 471145855, 874635784, 690831021, 536011185, 61842282, 55984841, 255313910, 21633367, 294610215, 935221413, 498238262, 585405783, 237765412, 899986986, 695876464, 415392126, 273430946, 53773510, 26149799, 650082571, 927078726, 19228640, 451381423, 560289483, 940529082, 428501190, 340315082, 507923841, 498032659, 836050854, 815920962, 571059817, 424987106, 185547053, 381849835, 570526863, 180955112, 850806883, 845442115, 689614330, 195444339, 307495168, 226230219, 879041419, 436892018, 629323820, 429571247, 2005431, 623088843, 440468740, 973852281, 765827108, 696926861, 432442461, 99227490, 677254696, 977152834, 254338962, 749229, 50141898, 601955169, 348035003, 907927559, 842497506, 45669545, 403972998, 382345180, 862320111, 71458826, 499357965, 368848352, 383206665, 400750628, 904964744, 458211660, 35208087, 41514642, 806921399, 956918911, 74517698, 775151423, 195708998, 464305048, 586319253, 695990456, 272191302, 934759869, 838841552, 886860995, 953088139, 981036412, 643019348, 644187430, 475176369, 709522978, 435562650, 393905129, 115301629, 42461115, 995806369, 393742457, 233957003, 634294668, 671256724, 581855273, 197487355, 378455300, 268445185, 612965455, 601983783, 250847145, 407427879, 47661763, 807203944, 187607103, 133019848, 322902794, 687613475, 781621001, 264447509, 679595511, 557202808, 725016213, 421550471, 46086906, 973832923, 131872133, 48262013, 81154059, 931388246, 2488276, 681210857, 707861157, 789428928, 746159608, 685680822, 267915538, 404486747, 338854071, 613194767, 876993837, 987763822, 149341488, 940652119, 536766406, 252688994, 638579902, 359114209, 77828797, 543814004, 198429455, 965602927, 866585787, 535373446, 85523636, 667471333, 803469703, 357999071, 465318218, 620582637, 599432336, 129743687, 960762026, 856207448, 32984659, 176281546, 779461689, 768350350, 50367821, 89564945, 366021990, 164097647, 459402427, 139250993, 593196199, 965957450, 751415505, 535381840, 419969016, 194880719, 576035025, 167649765, 67748459, 779983033, 128373536, 570744043, 549446195, 143228318, 541980313, 464333185, 243137620, 110154564, 179875796, 164202130, 97802556, 823758519, 432651005, 196302407, 66565107, 196458440, 3201610, 446658, 535286357, 746070465, 10814587, 108414447, 722166439, 970021076, 253809874, 310574235, 5822878, 600347458, 554357879, 834416065, 935189980, 963486683, 485321472, 98042754, 651700002, 453339055, 347938737, 173925671, 468474463, 809232005, 191643914, 566399626, 162758840, 670276583, 827265964, 174004048, 433062554, 808524482, 222513836, 532167290, 360564496, 769928691, 797620197, 824155065, 388777, 71007442, 506883838, 563291030, 352031059, 824803229, 539282210, 193164515, 189512352, 837262768, 210246031, 17678486, 519941500, 811001622, 142452300, 248610074, 174527128, 217949010, 796613211, 887308530, 377110042, 241206706, 273387813, 838818424, 657687027, 224802816, 24896262, 852620075, 939196582, 285549434, 890029624, 53042820, 779957626, 101248220, 732155084, 896906221, 695790986, 665447874, 572694482, 480813741, 784242740, 301161205, 300810236, 28243374, 111453978, 445469049, 336530590, 855976067, 895346461, 288524683, 661445371, 276611686, 687649606, 923840952, 6698953, 96276914, 197355023, 209849241, 330677273, 856768813, 362695948, 893284970, 444728750, 726145181, 244881883, 281009951, 529018553, 935827323, 363059764, 825464094, 82061511, 70054430, 811640504, 640852654, 964360175, 626407045, 75449007, 958103008, 114716958, 867395283, 325845736, 191897746, 498556300, 747992850, 670180491, 511570331, 167025985, 4385650, 281023033, 78938448, 732289270, 994676831, 460178875, 585075749, 659640600, 473123211, 384011986, 494854497, 259455661, 70597317, 458415606, 863102639, 178635756, 134953631, 924014673, 715871521, 429243165, 693546101, 146417511, 837923242, 719275835, 216959381, 216732424, 707086543, 262559105, 752130810, 303886466, 529916472, 938437581, 165746988, 576115151, 193914653, 217564832, 547535259, 169776360, 401674725, 422530721, 180491859, 938144888, 40035954, 279832950, 662235723, 716073403, 359986749, 859131963, 121745326, 461257090, 609718101, 414827292, 86103216, 2681433, 149307394, 806800296, 993341736, 938747282, 641504171, 757851639, 473947441, 685471928, 235973887, 277425662, 514714668, 653746228, 505796036, 170522441, 748720104, 214176378, 862963405, 253934875, 372259462, 496271067, 149208016, 255990068, 35620838, 408441115, 304505441, 862918157, 433751626, 261059379, 215878209, 669305764, 763825600, 529695460, 174476643, 143751394, 912127531, 722647815, 649758036, 653654754, 140650120, 555947591, 427106504, 838007690, 377297397, 284327015, 722050673, 283098430, 854243356, 488305417, 74461752, 15010803, 725149420, 614445485, 959550012, 76873762, 742883454, 43823524, 809713026, 234643734, 69028747, 26033435, 285046044, 400500155, 456863249, 316304521, 523267711, 711962542, 996479151, 947249260, 2216268, 111570039, 906586131, 876437542, 84906249, 432807043, 846820701, 515498573, 952787021, 63638955, 714526015, 863238254, 155796602, 16522862, 602024414, 6332892, 219382169, 924639934, 238682351, 950453473, 535559040, 52429990, 199399202, 482815644, 697929640, 117656527, 133150630, 770878826, 787131145, 576732310, 135378759, 588414052, 752207234, 50392475, 767022377, 594001584, 997585870, 346599472, 610548899, 983784705, 343144743, 492481682, 758491243, 778390804, 262456915, 855390828, 88043154, 592118165, 276571930, 824870295, 972054120, 682425755, 570866261, 239094726, 886034404, 593868826, 885582334, 934465191, 672727839, 600989338, 491151662, 238242567, 821520239, 705578188, 474024065, 253038307, 286323487, 215983593, 877677357, 49295443, 119657665, 682163618, 377923045, 677334500, 721064768, 135248077, 326163360, 788156832, 319761500, 796904155, 143353188, 603461863, 409152673, 736490702, 973555810, 753649814, 43547228, 170430754, 598836839, 670437507, 250924187, 293012218, 609078557, 352479657, 386028718, 411826614, 696411471, 269150518, 712451467, 987828344, 516659756, 420115960, 584779015, 687929523, 497758719, 215033438, 654319988, 679851583, 939875904, 306599669, 775585536, 92505780, 584977696, 668331137, 248952992, 531604760, 35985106, 123965089, 9470483, 482485115, 561383165, 573724953, 92681107, 545913429, 66804044, 315875511, 700968797, 829397608, 549648691, 323356577, 941649790, 371983855, 111122625, 570714476, 44331211, 54554824, 679996420, 634520679, 672318168, 741719323, 190954241, 915024030, 951948173, 109417503, 64965207, 725050789, 860977465, 38444411, 327028150, 682829078, 85029570, 356109546, 662412516, 546218886, 495527633, 159425444, 396824883, 787336129, 837697965, 228290379, 444542543, 63733047, 614025845, 738964111, 81474850, 957654637, 630111012, 248201054, 484882594, 912847904, 188791526, 995403366, 100481323, 173468099, 564385354, 421106755, 288796411, 52197514, 583899222, 963013876, 976506220, 300338080, 606268824, 172169165, 670422827, 325918558, 289245738, 461929082, 975983339, 929240235, 651476200, 868260105, 274781169, 119251766, 971397026, 173902595, 495699857, 552992311, 674064163, 815212002, 812927258, 785977279, 82448657, 275482542, 139194238, 273897708, 220177990, 903120102, 545055358, 786863883, 618417053, 418900585, 979721531, 626913285, 58050742, 806349324, 985735515, 439829172, 485513827, 300930458, 444166664, 954433827, 178599027, 596160530, 397893721, 907701552, 826671380, 165906512, 955862217, 881910640, 865128420, 572795532, 565103470, 509704708, 212909438, 864117140, 963886601, 673381742, 317764852, 451412512, 489623601, 801502227, 309719431, 267295633, 385583903, 531563988, 835819410, 795829143, 960071238, 575655498, 508730252, 526663767, 789443226, 221193743, 902525043, 195640753, 125712797, 990467904, 507683374, 850882115, 964995216, 550324955, 248286543, 779951988, 220389794, 767268915, 611625991, 772918214, 650068458, 406270936, 602323631, 855189994, 693997687, 50673117, 834282228, 8753233, 283100408, 78029415, 898128398, 304633674, 358473901, 57671675, 749067650, 910397244, 448649256, 525099093, 139507871, 923022332, 529483924, 67074431, 130802898, 65349084, 302670392, 327039423, 978233221, 147007938, 817929485, 516899116, 728003903, 300930476, 216333745, 864173842, 205616293, 139125181, 710710067, 838627828, 516540334, 503517745, 372343184, 172057950, 149035861, 587931537, 164109657, 242511342, 412462730, 86622825, 283744303, 692370883, 289422107, 613269068, 514398255, 155067362, 604172565, 917274572, 818422869, 993423004, 763699999, 757748318, 101029667, 856217183, 213630193, 469392143, 571518168, 265022416, 900028283, 732078412, 70567897, 194271437, 897569702, 537905845, 129538105, 363834821, 776695001, 359440608, 179731329, 677420254, 45235722, 471542153, 395771141, 847744685, 162347048, 903629513, 644645020, 622104177, 774417672, 396141822, 610075265, 939968385, 121637040, 833545718, 919029984, 77610459, 964490234, 721924959, 32319928, 120229011, 490902809, 35517493, 640177779, 15121853, 954000294, 308599485, 406475164, 74840343, 870300643, 160422124, 186036411, 965436221, 697753632, 810078601, 302595334, 352013999, 971605423, 338971933, 950021383, 74876201, 959943537, 743915562, 793390837, 648922537, 551448333, 37088447, 113499323, 668322968, 426594033, 387066623, 180772673, 475630157, 338238578, 692314349, 845103411, 375885404, 250092144, 566026469, 341773124, 869501419, 630825638, 24110724, 615982710, 540370913, 598589888, 682972503, 403228289, 826871596, 265852877, 330266945, 893639800, 835257865, 304282458, 185741033, 38504583, 750995036, 687124971, 328210072, 234899376, 956070838, 582697103, 587748946, 127391936, 682869259, 19715392, 373409659, 586664469, 905797514, 401841322, 56334065, 938861306, 768419381, 934563527, 611490014, 506837974, 451529935, 50300541, 990993227, 768793350, 532157092, 196197824, 352337641, 423946703, 416925199, 585833590, 368833582, 881713229, 292992520, 662877758, 59080594, 25746956, 845002585, 924958928, 317144121, 176969397, 247228579, 173168645, 791111055, 189408174, 661765805, 105345267, 410741195, 545984664, 256921855, 655544555, 295381500, 742983089, 336911528, 154187345, 912819488, 349368157, 97690182, 96285936, 74464974, 145489168, 260159897, 690891866, 463940099, 950826241, 804035758, 789185726, 583067834, 511545513, 173198802, 886685794, 681522156, 213770927, 193877128, 647528509, 255150220, 421034243, 970894556, 461104050, 854672675, 373231146, 350908572, 771058363, 551682333, 277530860, 705279888, 952861901, 1211247, 470239554, 277858274, 943974561, 914261766, 931077601, 927309949, 849511488, 207458701, 776004679, 257440861, 962418285, 907641543, 245571629, 135753935, 529259158, 421663170, 71919489, 614027682, 348106639, 630803740, 432913598, 160097566, 219457023, 776508056, 291697076, 259424745, 768623679, 216655972, 708859358, 530682078, 987316804, 404289670, 595771990, 273249854, 149508777, 71203155, 713398475, 456081375, 303563851, 568499333, 512672065, 126334413, 526460970, 107472442, 282244778, 286699057, 493932218, 638782210, 581816903, 85489105, 586774856, 61015758, 175092101, 610242223, 747420776, 433804131, 704111182, 877148573, 828413359, 878855602, 236053006, 528097269, 549830212, 40446500, 968171859, 520288333, 364535660, 670637272, 942580850, 921544501, 933220856, 81463433, 43185921, 598808143, 991247398, 675616963, 121981235, 544714909, 139811264, 41023675, 761625127, 68785290, 807462665, 197550272, 912354198, 336234010, 417973084, 235963409, 218269206, 482510992, 463526224, 566497699, 760142121, 354976953, 310435389, 426613866, 263680237, 593937351, 651363402, 262293544, 630005736, 786703585, 106299577, 795230207, 194539670, 685159617, 401609024, 181881831, 352555717, 922716031, 570858267, 806242878, 812129441, 222107408, 360697000, 558054193, 21436340, 948919304, 697060931, 989922595, 681676498, 348869101, 441978495, 334004427, 520438573, 785080058, 426714772, 998594121, 801715878, 972879838, 499765065, 532975907, 195758070, 524827730, 54312099, 916014577, 283165590, 632632405, 387395759, 324287623, 54824509, 573536864, 57353798, 209875643, 426084184, 925087136, 42692571, 6650096, 306463962, 34446374, 767565696, 178681459, 333265872, 91522023, 216598488, 472146999, 582102230, 598610788, 182048444, 508068765, 145737535, 704528729, 870495174, 934776368, 329614827, 23012401, 965551426, 897220575, 374105702, 320263014, 274295201, 230639616, 188839359, 890154924, 313160252, 636826981, 131228866, 885295815, 664327081, 550235625, 375648927, 815746154, 464965031, 429421500, 539186954, 439885812, 511454366, 504433086, 555198486, 755623548, 393278516, 759572176, 607833230, 513895677, 877521004, 681219745, 343635221, 386343738, 977102889, 325262577, 17993467, 606414710, 839532889, 911345769, 71756176, 214775276, 730531370, 54906386, 630000297, 618227693, 813516432, 363456354, 308104732, 321109476, 509652459, 73006029, 663643709, 258951009, 339882378, 773251714, 21449291, 628476369, 273267766, 580747328, 332830190, 94694005, 42625129, 695810238, 982658846, 452169270, 771035190, 80348571, 970848545, 943937097, 172033751, 404147378, 598904764, 700531095, 498868754, 990973349, 920066862, 697683496, 684534059, 423812465, 902806807, 119737717, 317774775, 806637443, 278977696, 656114106, 238512840, 972942001, 207219752, 334304093, 455306696, 610295863, 727306850, 808936321, 570495328, 673996006, 461035961, 35419530, 666694411, 8915842, 247010638, 462682664, 185861822, 518878490, 561311016, 677364809, 602499003, 267734192, 295464341, 932361458, 432406011, 152050684, 810656616, 906665410, 373706812, 706021905, 472200363, 551936608, 738440243, 718917302, 879742445, 145664089, 302646953, 678778845, 669414652, 128470741, 810504842, 836406042, 275671104, 677222252, 476771535, 75605489, 456514787, 659976885, 897186774, 159830068, 252165668, 661463448, 833738531, 748408836, 967689765, 160996808, 258894979, 134902748, 141406993, 999549179, 295680690, 37364322, 461802718, 613307824, 25915497, 807742944, 969000624, 598802119, 955333451, 401378382, 996925028, 625023668, 63687356, 143548413, 123022123, 939817474, 120579160, 995315922, 825854458, 40040733, 177297158, 359523621, 930324004, 311243667, 273253182, 500240862, 415359577, 343957461, 229955628, 741653321, 14852651, 966344628, 271824675, 469693809, 5149787, 364877273, 301276125, 333402205, 193756479, 419268118, 831962580, 306005446, 623331456, 833451008, 999753943, 783636348, 502851451, 599279850, 157673463, 841647244, 390116362, 597113055, 820433541, 577626231, 478294830, 862025047, 880576630, 712888600, 956629282, 560666556, 488399244, 630842028, 416202879, 514763102, 346993185, 860569085, 15159589, 251576652, 512544842, 91277033, 452746644, 144055838, 796549630, 792218317, 921367904, 22283631, 83511829, 460262265, 92890194, 407751621, 926248355, 656973959, 224305582, 708462908, 54249591, 141249158, 542920927, 372844671, 726343485, 120182961, 253579215, 835188894, 804982035, 852554602, 297387066, 431489385, 940123946, 77480950, 150153886, 422171524, 860915944, 326571987, 944674406, 538880698, 843894316, 839228755, 179771471, 296114554, 790843952, 192161924, 31965220, 549902800, 960419534, 631810756, 150561352, 932490722, 19333608, 542801445, 567997712, 453003730, 637026843, 941564233, 937717388, 939985904, 489597812, 205505017, 102309919, 27295311, 273362, 272563062, 484149234, 818311710, 223959504, 809354207, 804119995, 246172532, 265869025, 99133031, 374921714, 163207745, 489591905, 810750399, 607156417, 849954472, 973654990, 948819596, 625398874, 662690282, 402685107, 235415646, 418858014, 138180681, 936895810, 570176381, 26083764, 203925185, 538110543, 876355868, 883587553, 134908497, 719379389, 667022154, 486425006, 335408331, 788308144, 894059036, 51527537, 498602301, 528500128, 57744710, 942133279, 647808629, 695337403, 935506697, 948444733, 608644392, 251504617, 657959214, 185749779, 478559906, 578700841, 528393427, 448473148, 438443714, 602311556, 322057259, 102347929, 708417538, 349451108, 254554389, 468121385, 759261194, 412764398, 96601336, 420736120, 403617916, 401094440, 102315181, 796367858, 623311337, 896211180, 625301335, 502546306, 130095747, 317807298, 94427687, 186827229, 413048933, 32955665, 737693023, 331576603, 52689892, 229298106, 961912845, 885781864, 736043641, 738400410, 236849640, 562291464, 935310324, 239501664, 804348972, 652386669, 963293609, 356835413, 388392649, 634534617, 472083001, 196854789, 858389750, 550345022, 351825780, 304032438, 682846558, 906068384, 724834434, 78777153, 632056677, 165576795, 484112060, 147354515, 109496742, 687073201, 359890602, 556864513, 280188803, 56653780, 446300063, 104382015, 237456354, 541009387, 713838788, 559202635, 263469117, 789593477, 2095614, 423359851, 950453795, 762299530, 140963918, 32780864, 679550611, 352996115, 635271416, 58865372, 418570133, 406790259, 775629350, 13259964, 474536354, 175188052, 298393001, 639074935, 886018249, 261709592, 433616958, 552521566, 87752439, 514838568, 444150628, 969129265, 887186703, 660814723, 395727927, 495380359, 281401758, 787853229, 685333935, 5961968, 157858285, 970260075, 792614898, 798099129, 394082473, 124930359, 224121619, 167368066, 59148776, 258492924, 828587897, 474657976, 805104696, 489979878, 625572930, 661453802, 458330439, 747234705, 909365899, 426254228, 191340513, 358761486, 622740553, 42717430, 13921711, 169843959, 182714393, 955482942, 119006396, 716859585, 988115266, 667505526, 886169039, 296305317, 981409067, 101433410, 811649487, 609937209, 414418039, 680080242, 350372501, 638963062, 195937516, 493895941, 370051303, 994620595, 582866158, 67403394, 773626884, 238950242, 87658721, 788673616, 262801302, 753992616, 186330807, 429591360, 586447961, 448015769, 820093601, 871257915, 867708937, 416456599, 115399936, 922531855, 887574762, 63219024, 267634563, 184444772, 219282774, 883528963, 306104732, 79757304, 723269864, 297381020, 120949259, 941404265, 203394324, 860655544, 346146867, 496518746, 58467521, 66174328, 997249750, 782614143, 816383203, 38962891, 158981961, 461683704, 604977094, 243240696, 27632052, 905949848, 180433771, 118575662, 712509222, 668803908, 356018628, 908780317, 415938424, 894253181, 522824388, 80097598, 889932597, 203372524, 188097818, 758252500, 454998072, 373499714, 835841273, 744212856, 533426439, 66467752, 193233673, 27000985, 632311651, 789177693, 486667041, 623283304, 20224792, 625800385, 292137521, 992011589, 516102356, 540288283, 349869252, 444212112, 942848737, 451648307, 801508809, 23958115, 562266820, 218460485, 892535071, 68588872, 516346239, 814389511, 363423269, 857324123, 872051618, 514039322, 714514153, 982754707, 256289202, 537596373, 698379334, 661911286, 943035873, 551689034, 840274948, 777004458, 686891791, 12294014, 25159363, 149301485, 181418948, 780010779, 240298898, 113084395, 119881372, 444567148, 837021901, 19233892, 146205200, 117441236, 502237451, 78226946, 227008585, 657617521, 963621185, 598565971, 942338263, 827492389, 331979260, 491224743, 381476224, 701307700, 685708526, 43686461, 869066266, 659059766, 225705045, 766069548, 595366506, 436958688, 726299501, 484768942, 392641774, 88385794, 121972007, 809398722, 166682363, 533760973, 136463117, 686012076, 78386700, 499915456, 65539718, 98193575, 288475792, 157783755, 123089510, 352585259, 566137124, 471321494, 915397211, 723292632, 742384780, 100172555, 2170546, 789949857, 231001010, 883483282, 147021419, 129163034, 955615962, 387446532, 275400542, 439929978, 498287771, 18013327, 99611627, 653282021, 191820948, 443190813, 905014679, 312684136, 691477968, 683742433, 544089261, 240820413, 858192038, 117341222, 769483562, 774823388, 713978978, 545639566, 1771860, 21811138, 938109714, 560636146, 89203414, 124310202, 107345839, 472314257, 963502926, 427625322, 85182965, 158548081, 274380448, 587819665, 481303508, 388112487, 898234900, 673045889, 172810915, 228946981, 375786282, 903074792, 170911985, 172980656, 87433783, 710485478, 483790135, 702623127, 625288684, 546255041, 736791130, 118382762, 456580340, 365918582, 904730345, 660301045, 619201000, 729474348, 420097430, 217085295, 850196933, 813856130, 830907803, 736863591, 979885141, 173441798, 624426868, 545662404, 660854329, 175739727, 491157904, 169381707, 82970671, 365028521, 366743118, 842638748, 264784950, 523184378, 974746210, 326158570, 569710445, 755728649, 337104683, 227400241, 150898954, 295795680, 355157612, 385401396, 111310571, 912497574, 452183070, 903040968, 217699069, 526987891, 806717032, 931053772, 248863603, 682794052, 171256474, 378549178, 615562593, 809762140, 805466618, 141825038, 526979985, 338416207, 360993164, 318430138, 66272017, 2766514, 999584573, 307485011, 853915777, 786610238, 951423816, 41149376, 455652602, 598588375, 36637626, 33805783, 286873857, 991912968, 249809541, 940893357, 419563656, 453104978, 629634667, 73726548, 689144132, 3998450, 987314851, 9662926, 91566174, 974443021, 251138294, 896671208, 829679653, 85905223, 790364296, 124254188, 738359941, 68919431, 295849133, 612580467, 141292897, 148015843, 77690465, 856183035, 647834414, 378746687, 446316372, 521083937, 111799567, 231818269, 772968068, 89902031, 702771150, 795982028, 721747455, 194195464, 707332576, 554480021, 209039795, 394631398, 878770138, 381916241, 499866439, 125480542, 802558199, 76703296, 98271946, 588347834, 231969734, 158962589, 388564173, 693812259, 172021812, 362975332, 187541013, 462933580, 896520962, 223083416, 673750726, 767872906, 235938610, 284939400, 968742952, 862992390, 863078473, 771316761, 90415195, 700643622, 194982208, 471712911, 127719718, 387325985, 109371523, 57078602, 495800335, 450892203, 65269250, 601824139, 981634218, 510886063, 122832505, 183225102, 330212607, 480805120, 644392610, 912032142, 996556912, 206657277, 687397090, 158278423, 693207487, 223352443, 507203382, 854214325, 100540844, 782739174, 302605993, 340127369, 938203229, 670839825, 443451717, 829138699, 259071, 709583895, 862050272, 930741611, 897273166, 75348557, 278248563, 928270259, 288247062, 280968733, 805342105, 309665265, 427246159, 4289700, 333239587, 703297452, 994589968, 249506791, 552727355, 87251505, 55599758, 881733228, 424056630, 560526125, 843870099, 594057085, 123566753, 499728536, 452326098, 373616585, 62833286, 323731511, 392520425, 651302492, 530391026, 543037763, 316036568, 287761227, 844675711, 540947202, 995114280, 628645434, 859758183, 465224867, 636030202, 1539441, 451491317, 227645732, 977024284, 759619546, 887551781, 464547107, 216822526, 404841888, 807658172, 558543551, 763924652, 63368742, 451222588, 611067056, 79540602, 655033263, 190443181, 288792060, 109838701, 396903152, 308162276, 270040632, 169578101, 737074394, 831780773, 240135821, 748388385, 167134710, 124064962, 228498825, 730392983, 816226864, 543878744, 963384194, 312536100, 741071998, 566621292, 820609066, 397815264, 425175324, 440811132, 995865224, 91678454, 216227569, 816004889, 829346862, 461100891, 720403097, 752741609, 257261186, 838934528, 557669742, 636588899, 690688240, 58809903, 841926599, 60418296, 404377303, 237087484, 660556860, 955232865, 612999528, 840103916, 156360668, 526373298, 160659228, 123318377, 949239724, 113341615, 827014106, 583009273, 202083140, 753956451, 353813457, 57595737, 389930087, 593790434, 691756113, 26630498, 439977053, 188394177, 553812535, 444789586, 131422042, 969035371, 583201273, 340878488, 700666180, 130789595, 350828448, 572366636, 631159150, 190433613, 503048782, 996551535, 647647110, 110879795, 612564742, 309859062, 411994558, 621321861, 230578455, 291249717, 108024663, 749181218, 528028734, 579667194, 208520026, 811710912, 124030938, 607506859, 362418936, 272726275, 865058886, 55555063, 668738689, 591363306, 776113029, 311918818, 181004298, 265645169, 979953227, 29142851, 716379920, 827603008, 190220883, 788025372, 396731733, 920209311, 689912336, 327584574, 309071470, 418687926, 152079856, 843816642, 240250397, 309806922, 662548623, 60869125, 94867079, 776922816, 414863324, 730990381, 149896807, 883511927, 436077063, 85710604, 249531086, 168200317, 205196849, 209846358, 911819191, 169821830, 140879863, 475783566, 514693215, 624120236, 695661517, 463147869, 258489213, 970384113, 80592558, 863185756, 338505938, 581081640, 560234890, 752068360, 794523358, 345585813, 799888553, 149712738, 656066943, 138607213, 832146481, 649289753, 88131706, 111498012, 99092792, 92153476, 226618152, 872827188, 605299938, 533288758, 195124375, 903617409, 720441389, 619921301, 653087829, 660384155, 808472452, 535093885, 61743370, 915598481, 677953198, 66708794, 907598526, 623010390, 259769456, 438109705, 935980436, 170690977, 113311683, 622077484, 461341263, 903452258, 903826930, 135166704, 361994604, 740321788, 697224732, 350080183, 627266168, 368807326, 549284997, 438268425, 917175813, 602660850, 996366802, 620550639, 785128439, 74574882, 422882265, 378646700, 513869969, 283937334, 613939238, 74065474, 142948436, 407366968, 431648652, 881294781, 797191104, 674591305, 900878810, 401130590, 766864304, 481897276, 198217441, 852136474, 481178773, 662399245, 837059521, 671171774, 641898469, 868847127, 695988179, 152971851, 505204311, 903862744, 887208251, 452303861, 255501246, 829599685, 743646673, 795763532, 933986916, 276961909, 460311086, 724342224, 60155044, 346446918, 95818779, 488116996, 503258131, 700308788, 250198895, 605871008, 293394331, 31788838, 914273586, 48992704, 746276682, 830494687, 950994197, 549651480, 169209092, 614357427, 623217976, 206909789, 660294311, 800761960, 803595244, 563212220, 877414205, 334824088, 129612967, 31319702, 517277614, 971450625, 40549884, 418302764, 975921886, 494110414, 428501681, 100458862, 297970288, 796975028, 931840328, 710854942, 943725745, 355498282, 437876873, 595898068, 590738419, 628468209, 413713772, 294104914, 608617142, 17330788, 501590819, 970269472, 812135352, 47996991, 791325981, 50813179, 480143653, 665919450, 542089691, 422259713, 20469006, 810631489, 816177254, 272800407, 196065156, 9864814, 347187840, 412773939, 752665877, 167342234, 711837372, 10372310, 913919197, 199000834, 52010775, 21149421, 404997467, 532338011, 368067294, 189821398, 626822515, 936094756, 72456398, 998090956, 846860488, 670190959, 732966308, 762177563, 984326850, 127068431, 861398365, 898026869, 456728101, 161028580, 609993830, 814329303, 721015200, 691288967, 400622132, 636913793, 5418253, 878347907, 75256556, 339631562, 128047869, 219939217, 856722242, 392341701, 198573721, 128296963, 946968941, 640177087, 572642068, 63010919, 361497801, 288897874, 191300965, 410933620, 630686982, 766283577, 289111996, 437001075, 984351013, 657759562, 38076518, 32386262, 198655624, 945199294, 264818333, 642138350, 858301119, 532791158, 114552945, 215469982, 975998634, 633206488, 211990855, 107059507, 353654794, 155786842, 815948486, 415376950, 476463705, 960592603, 867756672, 305946890, 739448470, 739530858, 706232997, 619705099, 677677380, 285712183, 903068449, 760852172, 792383952, 161195864, 184276951, 266531901, 949155693, 731257509, 631310392, 817272334, 346860929, 480940439, 512365216, 859283350, 151116933, 104391363, 185703611, 774436183, 179987559, 727207807, 62375412, 632745460, 610592494, 353952291, 708143009, 548785222, 741529982, 8126400, 53457455, 365889985, 33220315, 108885474, 192072112, 567479726, 446156043, 736307692, 551945514, 757136940, 193701970, 524017529, 272770802, 847563540, 137893944, 164772817, 73311874, 463184305, 605561995, 72460209, 299477051, 309359622, 67660247, 752632625, 406350412, 641578674, 380601277, 279381620, 222136007, 567401191, 102775792, 839912879, 817307586, 524336918, 203710404, 733260492, 309216013, 979709197, 839340849, 924511647, 731218291, 483077581, 652732288, 662441820, 135562132, 719477130, 967508955, 11081394, 79140850, 379680911, 545517760, 655357313, 541191762, 237786502, 551052556, 272953852, 303775637, 170764772, 553341236, 648308294, 368813375, 943813144, 942749452, 726434784, 368486001, 114342567, 891309178, 511066998, 816861374, 87881401, 277168568, 132347043, 779102686, 326733124, 318240520, 694561747, 819143510, 454555783, 456963001, 231010281, 671456290, 413680218, 55004740, 124299147, 763765718, 655623497, 30513945, 760016232, 776035128, 687033325, 639705659, 239878248, 209222146, 189347140, 761781249, 552031923, 35143196, 815872965, 429074409, 890259595, 712309485, 933780447, 948030009, 765830083, 489377762, 977210883, 228169112, 245726169, 78289682, 998239478, 43225300, 821924168, 117078931, 630627631, 695649483, 672114695, 818700928, 16605382, 435583074, 97567064, 30905827, 710450012, 401194320, 825686399, 707599091, 162068943, 88240498, 403348990, 402717876, 35577349, 52282356, 186402623, 496401056, 843877507, 94657396, 497655354, 97535851, 776779690, 789429817, 492947846, 652496805, 627858703, 164622770, 111093910, 796445609, 801664942, 704403607, 156835611, 366332183, 174390670, 161540643, 83571668, 238365638, 323406626, 974883043, 336159096, 532893127, 614079202, 137859971, 715910366, 43709408, 501887149, 741713207, 821882784, 315964741, 697600687, 232799126, 877210255, 429470291, 510677121, 223583435, 749593789, 649686131, 724585654, 478878889, 221702698, 754240087, 578353168, 351094952, 8947826, 305636452, 759739584, 644093734, 89857020, 951056098, 275115697, 332185559, 513376910, 992967798, 906221426, 788703245, 209969047, 222807489, 113338578, 41873753, 263367409, 91902892, 529577237, 657212092, 966339895, 777659357, 361452870, 220157222, 495100976, 58435367, 359263756, 903336137, 588770160, 945083277, 604725980, 330253763, 688294281, 418997820, 16746734, 102090671, 51718713, 125735780, 218541398, 908647834, 423141054, 553267784, 883171904, 856969963, 549224047, 757662839, 211670728, 553604472, 686555071, 490142339, 948371243, 977280039, 406374265, 422489130, 635153204, 799067464, 958923809, 263648636, 986388315, 341184045, 839384672, 754699667, 197895152, 613291260, 180145033, 882365979, 535607248, 298318195, 212058628, 721497066, 722051660, 220330170, 247858939, 742508154, 64571907, 581520866, 303972505, 543529071, 103478606, 945415427, 203174953, 290396436, 572046687, 715536963, 646509874, 159562010, 749890118, 847150617, 745380773, 874536993, 740888242, 582672159, 572525206, 223006034, 837007827, 933090002, 911627279, 502652088, 799430881, 627487933, 677280310, 175562453, 445714182, 221862512, 960820176, 613527486, 931489259, 466566184, 134319200, 466523228, 70940554, 565504657, 385480621, 291171862, 891220796, 353872983, 6472955, 381455450, 13374229, 635540518, 470105967, 232900844, 196707179, 719790938, 549061269, 793882793, 883460563, 635932393, 495007780, 886089547, 845503936, 431310449, 363660363, 973133937, 384868068, 550732572, 355239404, 163417121, 327193713, 223214408, 718091879, 881870883, 384689677, 101074665, 813385507, 659645981, 361465422, 657346814, 52882712, 207857782, 119633633, 397764051, 969311866, 415835287, 549409625, 927964416, 662168518, 670872118, 613048140, 682589623, 514378573, 327231281, 978860422, 321461298, 88208944, 31854494, 550849653, 454157907, 547896687, 469127023, 763372642, 596340589, 962881315, 858202250, 241885188, 592685193, 483497617, 268565483, 921386708, 381385138, 993970140, 147976534, 552230865, 352844518, 950516472, 347669413, 688088616, 810273864, 46075398, 848099773, 331613322, 551938035, 922406835, 777768177, 882798274, 486335911, 909292973, 256831147, 644994126, 150547995, 288370795, 323795663, 108742265, 453149073, 912532352, 15582072, 542098727, 800502675, 544882890, 26501794, 349426998, 49633702, 568923524, 491756306, 104857663, 462931562, 286692666, 477256230, 514175190, 787063840, 221154006, 261952541, 660711329, 397456899, 981818417, 530128147, 528257350, 963119957, 380377420, 686809808, 132144647, 528985910, 822294053, 616751510, 342510535, 542964752, 953736559, 313493164, 606887229, 911292, 661263553, 317923504, 150918173, 953725773, 362959048, 728509806, 653017803, 557664301, 394839285, 564024321, 704009062, 582571207, 210773563, 934715457, 217651160, 146271867, 175351431, 734103732, 619211915, 788609505, 966641330, 664196629, 88484452, 4375848, 264242203, 283978763, 83505158, 129465938, 995387596, 673405066, 911938491, 848086590, 312531131, 231829372, 534010781, 208109621, 934747745, 59758280, 861199006, 292364283, 422301545, 170556456, 982043871, 461717221, 923602512, 439408812, 554739754, 322796482, 602385737, 606130602, 803857160, 184414665, 331495691, 115086127, 473735814, 720760173, 865176005, 911883067, 739298005, 710288379, 824096197, 208072427, 882631896, 909755613, 158794979, 561655918, 239980500, 294709389, 859781803, 386790038, 236223300, 117115216, 133665300, 627007489, 862633710, 949048873, 305030016, 491724165, 27711678, 663042318, 856215328, 322408442, 240477405, 571620355, 570994377, 519959176, 222186849, 586598305, 196850282, 89750964, 256459655, 742976209, 26407404, 238815112, 726482896, 26355249, 310573384, 196809673, 532263838, 19124291, 794786340, 769165130, 41163052, 913648000, 799429256, 123697854, 897390823, 97875423, 185273922, 141443839, 219477736, 469243930, 995093812, 579215653, 65184158, 21448310, 193287709, 746956323, 24277780, 919064137, 910732439, 561660236, 830485783, 126349456, 434520385, 301911573, 536666991, 176665085, 400954491, 978235065, 371380724, 348013368, 259798936, 327489424, 111043722, 314249202, 222824710, 728307409, 270371251, 75183573, 154614057, 510711750, 782148192, 635853480, 301575301, 530572053, 345524638, 437031322, 752844285, 988264720, 305379142, 891520954, 768977588, 358878989, 389180951, 861964780, 798867116, 393911788, 21750507, 2233747, 531158231, 541881482, 442255072, 575213953, 828578790, 67894413, 256710500, 785265036, 403538256, 59202696, 989532536, 394166965, 837938694, 576886567, 617846895, 410323912, 807527372, 895741629, 386416813, 449271395, 373633647, 727394498, 347734284, 12223382, 287148315, 67155248, 669491060, 912542072, 888119566, 55675429, 17359237, 29359169, 778123732, 669850475, 784249755, 898534023, 747242469, 975754501, 355261389, 98103520, 38885553, 888991824, 567438991, 539767105, 741520318, 217905171, 938406910, 960444514, 991012863, 887743765, 935872850, 123954930, 277260410, 757880475, 622227102, 748936696, 119120740, 296073344, 890727352, 510793528, 72710488, 518483154, 388362322, 875867656, 934948443, 149838834, 473598381, 52607866, 197134941, 900372787, 918542323, 959804948, 887071515, 396721017, 126255377, 910945082, 75320725, 757075137, 738945772, 477074789, 73043753, 277156626, 242124511, 353796082, 405966230, 907579650, 559454138, 401850903, 289320501, 580367026, 956423402, 383334128, 158486392, 217962084, 100351542, 627266404, 30158315, 852741828, 38685779, 359487251, 177384403, 744300229, 648044924, 757211372, 608618902, 709949274, 774431650, 50030624, 882837771, 845662011, 884149917, 886509289, 828776883, 349835217, 304493295, 280532931, 937781840, 653830358, 761388380, 79857414, 466954147, 791394412, 161927485, 883185226, 637460453, 368855267, 895727304, 414455204, 511026749, 41992615, 751131197, 865454175, 915612067, 95439329, 956801634, 564580135, 493670196, 243576528, 592912467, 965327208, 722836392, 669703383, 808506599, 397074674, 776575936, 673595131, 260697013, 401493934, 965560807, 788173731, 921330088, 60084730, 420687211, 798036709, 210645326, 306179972, 134004315, 518908306, 34104910, 800684544, 784291119, 59398704, 917164084, 792699705, 301163631, 776747883, 757977528, 121460391, 473587570, 430795729, 965445788, 841403811, 258923773, 232207692, 573968501, 149786305, 29281179, 363984292, 869045797, 826023315, 741425895, 636061738, 546546035, 133785744, 859079739, 764042548, 802354412, 7432871, 924757157, 787578336, 130791650, 380832386, 824853418, 527345636, 702825644, 19195472, 311714088, 999987183, 386352721, 453561610, 101405884, 217794774, 554227798, 386223742, 741247177, 184234488, 773042155, 746730418, 201656162, 512238163, 860004682, 621676168, 612563329, 188960352, 561690139, 795381960, 580975369, 994515448, 651406105, 806319080, 393287282, 661901674, 222246555, 390430152, 173701513, 916012551, 691757183, 325832846, 127859073, 77872131, 415439568, 950209196, 107539137, 292216862, 159134497, 262734923, 842321712, 810558124, 123338743, 228572778, 73877527, 725207314, 449781771, 126136370, 493209802, 122191830, 461055221, 927307682, 942103589, 836864296, 812494051, 480006228, 574368423, 147487189, 200368795, 397629089, 749894799, 847407093, 526401691, 825137320, 343542092, 630964770, 149337816, 487677948, 323312911, 605057304, 49685560, 658159751, 135388919, 269778034, 335019398, 915906471, 615455978, 908037049, 370613706, 292456318, 95153823, 936746655, 664101642, 134551675, 786283958, 397480237, 489957991, 883429052, 58148192, 163724705, 556646778, 487127893, 873950753, 240118459, 76709311, 488294905, 857245484, 470151377, 457636272, 460342131, 18970678, 52579061, 365270712, 30121069, 69510073, 63464735, 675868929, 519290240, 372968085, 810208216, 35902803, 354531635, 718478917, 739384972, 895309457, 122291699, 149801531, 623433839, 109100382, 913795799, 579443123, 145554883, 67064978, 454360307, 761766713, 767821127, 245084073, 639831264, 633911214, 684592466, 662829613, 168689615, 514097300, 864575192, 127492807, 569210589, 200969789, 672989948, 157298037, 260121378, 372535162, 740500173, 614399997, 209756398, 437751939, 70216461, 919377953, 636868159, 611647266, 739038802, 669791722, 634968912, 523782817, 246466077, 781550689, 857862514, 631765108, 934618139, 134911091, 499986181, 332933853, 2388202, 904314823, 101576934, 268142918, 714357650, 500498285, 789553540, 869948508, 15119601, 349671566, 460592097, 731229268, 460440625, 504433141, 410121050, 206614040, 784817524, 280328026, 990661188, 71293396, 546741534, 916159385, 467920599, 479239690, 855221442, 734003225, 900522521, 448119365, 15952230, 884236467, 720282520, 95559146, 709555077, 38023111, 425258929, 667852763, 150857760, 543192919, 216650584, 996932464, 563404211, 387183590, 376064719, 675186704, 925467917, 518477309, 25254100, 87610164, 339483852, 950492746, 687035064, 95929345, 336516408, 552108397, 872071614, 287025798, 573827221, 349418062, 861236277, 610803084, 93914624, 807727386, 511962918, 118127131, 750516545, 504773742, 698088723, 254015423, 439580051, 865594893, 369591351, 505457839, 909161793, 125802968, 648238587, 620163057, 752240302, 208371000, 554672907, 908923113, 691208646, 680150642, 982569843, 272565607, 220474013, 289257773, 831036036, 478234772, 904839538, 883351484, 243935493, 435045332, 67885304, 599614988, 567628384, 692715970, 488119562, 195687829, 477744439, 89767695, 81160738, 541503588, 742909032, 532260643, 870210219, 994344898, 236901382, 400503978, 600668952, 960241804, 340633329, 107635009, 374601728, 19393327, 862434018, 119863094, 182997012, 837858699, 717506034, 413492772, 472221080, 194991705, 744556528, 144613995, 310138987, 565571184, 858022536, 943444627, 962158673, 595049979, 179220585, 704070887, 160237233, 477085377, 255927738, 150442171, 931070496, 597470447, 671667023, 168901479, 253160229, 570515721, 192871455, 284090318, 284265096, 549682217, 388105147, 656460894, 152054205, 983987071, 703815544, 660506749, 49522211, 721887506, 552806081, 789884098, 34727658, 389788065, 145263477, 34771746, 424316757, 429357439, 150740702, 245535506, 36428018, 458168723, 71055236, 997807635, 566315912, 988530862, 336961919, 358210582, 18710980, 922935910, 902878721, 617340446, 606578348, 484678172, 582865234, 352322852, 905830887, 491155124, 823949539, 614484020, 172925175, 838013959, 381286844, 498417285, 168637181, 887345322, 735240299, 582345698, 457925687, 868846067, 656646167, 142243954, 985856185, 36975115, 888408217, 289834120, 532180922, 201476790, 944240429, 697726890, 295191773, 227467691, 415246335, 297638632, 327213240, 460072257, 804704640, 472593394, 5825417, 335831791, 127094751, 428711710, 733865156, 665863183, 56962079, 486933019, 193477510, 260518214, 693371689, 359803458, 134240304, 779384689, 291819979, 555571219, 724491118, 581141362, 261844385, 84211219, 167317494, 38122087, 101820907, 527924199, 301706713, 485473338, 448804674, 866178514, 52851903, 201837489, 654858746, 338347881, 306030046, 193840302, 825206474, 816946438, 500184743, 783368635, 372282411, 759742073, 155954716, 246143493, 378156549, 645784700, 13130991, 627619075, 699521635, 831047652, 65852125, 771587822, 178952090, 667403659, 652980654, 453771103, 240094761, 742890135, 109387330, 222371791, 313122406, 646966903, 20906564, 716551824, 712746309, 430062404, 152985948, 281788563, 695030216, 467669674, 387625563, 996126282, 978729982, 452665999, 374883679, 472541987, 375163245, 450497146, 771431170, 141092259, 96379674, 467256840, 819347245, 861041536, 859687117, 700033481, 305807697, 272812389, 172375657, 737841018, 828387192, 255937049, 421873875, 896636096, 293298864, 351918724, 823009369, 55953731, 307992016, 560729600, 539316305, 178666582, 668618692, 98646235, 610126421, 180834089, 185732298, 628776400, 924030424, 838338208, 446179012, 776193139, 821389435, 930602686, 144030460, 215201776, 664099881, 416431864, 928219177, 162510839, 136836401, 285640077, 935767895, 324206298, 656075340, 105279057, 683178869, 594496694, 450830646, 390254356, 801278184, 751808522, 580262205, 230113826, 392279339, 468242630, 480415006, 250318474, 738328138, 133753276, 346787716, 311879760, 24608894, 957240224, 781887175, 446467482, 782342386, 636650002, 644789936, 203726165, 108914381, 945758806, 317018560, 652714399, 995639220, 556220212, 880645629, 728502911, 403173639, 898360330, 56535034, 977967672, 499834858, 72542345, 778317801, 124366767, 904716141, 268348120, 370777691, 196437409, 936929688, 114016085, 843899887, 59661756, 651590314, 220929887, 792559410, 851879828, 297591720, 356730489, 233982235, 786917250, 983595690, 105738170, 788904746, 945664792, 759281859, 996372862, 143414335, 918592811, 927251733, 301828457, 63832378, 942603838, 609820644, 641729645, 877658216, 308085303, 43050301, 989325505, 15934819, 193301295, 66937268, 10406700, 514701720, 697842162, 356037918, 770808883, 340000141, 135311152, 678476857, 621616277, 226187690, 584302387, 536275848, 26418234, 204105489, 52330170, 330072895, 757760144, 898340451, 465752402, 629717625, 267542437, 445510822, 218998901, 766472016, 142066030, 316962063, 770436254, 263121718, 273736303, 163356070, 905515281, 753343710, 375442443, 437077521, 496495687, 87545072, 988067686, 600908676, 214159275, 772083458, 392151623, 973480317, 174531099, 710167308, 307951561, 757743388, 470663190, 410846582, 788292846, 271745627, 18002451, 928439910, 668691736, 780072316, 971495577, 256400373, 176247816, 651359766, 683660846, 365925120, 178875674, 194658943, 995341230, 295527486, 826522741, 498912872, 375389259, 639513611, 951567016, 685452215, 7501372, 75516535, 412257324, 31071168, 577971849, 878056383, 117854684, 367777950, 768034361, 598135814, 242688966, 456085242, 402388950, 308967038, 440046966, 321870905, 577593041, 967025720, 618747494, 619891341, 312420017, 664054596, 868750614, 57854413, 95137461, 657263347, 262349609, 650300679, 109499647, 33022647, 530333413, 957413526, 485218136, 756583954, 461718628, 616234889, 589232521, 581795370, 901894202, 461965874, 831945404, 248305563, 370366146, 678715281, 676560097, 198375040, 726530850, 613156570, 657545512, 782013588, 433818643, 936307406, 206033208, 302670108, 592493566, 969417247, 224102638, 727992868, 511428770, 572711193, 577397067, 560429238, 230104301, 234128646, 251547439, 569232598, 797971996, 996454163, 17960039, 546436037, 266654814, 813071035, 918906513, 227917633, 164724075, 444941941, 486159419, 635296456, 394137620, 12748994, 575516436, 607037501, 179863956, 410644517, 258591978, 270515835, 407157429, 7383863, 965814940, 277073772, 868191176, 689697204, 396432714, 881213179, 782935872, 977666711, 534372662, 965101574, 698052880, 438766759, 692131586, 102298656, 902724614, 64260801, 179414425, 524887537, 934106762, 288058991, 515555007, 765891082, 681756677, 565498025, 958245480, 541111469, 10117908, 154463138, 500847302, 972364, 736757617, 259041070, 116335075, 440548069, 974112818, 728313003, 421926481, 160443765, 754814050, 568410958, 173201281, 512704946, 415315751, 74236558, 623015143, 188685048, 843035726, 238928128, 935375730, 350815928, 249602418, 377139337, 571527393, 878097337, 699794163, 939215234, 810302683, 867077880, 990366976, 34807494, 307856365, 566668604, 874199905, 153461405, 201656169, 131604790, 270179035, 340429448, 676511917, 872175211, 603280808, 288881522, 187476224, 974729139, 705501975, 53210750, 624682801, 598638862, 285769585, 916760939, 895448258, 559085289, 164795977, 810468188, 821712525, 797971200, 712276098, 14319315, 684362510, 510110255, 962549472, 870909151, 775812764, 649067005, 482978253, 641987026, 178051169, 946384181, 959691768, 256284477, 64294052, 70010655, 654071670, 555612518, 284420876, 611584860, 737256549, 682138336, 291778961, 447682923, 933038065, 584879617, 252676725, 220330386, 245438584, 312526589, 242559145, 733882255, 641792782, 948371526, 38372856, 175792530, 201276868, 765661535, 321604222, 859456329, 38448978, 58579696, 526744205, 137658291, 813631234, 391090646, 765596167, 240397108, 158882040, 687158248, 717161640, 269235096, 324046669, 434245208, 369474155, 525735041, 302841995, 418208960, 843231139, 307067664, 100711599, 679899728, 824404738, 602712641, 818037532, 76958739, 367922392, 637698158, 628898164, 503061710, 788455055, 319173801, 966191683, 806209192, 510490940, 667810117, 585807097, 816347595, 134832850, 789521893, 738410717, 478206829, 202198861, 776934115, 391851233, 945990646, 610241700, 526017195, 553111094, 458614957, 159999453, 197503075, 598454310, 268982470, 13396792, 76210763, 391811495, 59331291, 961069305, 291000519, 79797649, 379321932, 458409315, 586498475, 32237156, 253544517, 604644784, 352698893, 33466460, 128397866, 84591632, 610152661, 972917197, 685982841, 407047398, 363909724, 656792838, 810787801, 934844627, 414070322, 718318649, 575142248, 555199158, 22072846, 717413314, 786622069, 719560903, 752319422, 683977399, 789890958, 475394769, 12494347, 485631847, 299655377, 35778753, 716348505, 789926672, 527126937, 837134094, 193978135, 996551003, 570101275, 7841138, 494342942, 763539421, 525314304, 464604430, 7060903, 378451175, 220324036, 569221357, 978704384, 366355658, 270561088, 702743363, 623613256, 957692098, 793947793, 721914109, 82396540, 111300969, 70598115, 649545626, 60749743, 435791196, 234664822, 730946115, 117342043, 308965253, 973235974, 407705733, 943670816, 523753183, 30871659, 41351032, 142604362, 478085188, 938149430, 127520854, 186204953, 595193115, 39680129, 538968189, 289341308, 144766491, 102017032, 640463513, 666025780, 610991562, 8130091, 400660134, 754127841, 354415124, 404291690, 527047499, 49301586, 590101458, 972449123, 279635986, 291194383, 546493927, 939066593, 429487725, 872399237, 379111725, 93384623, 226825408, 397427851, 9596322, 298212332, 912730393, 127391045, 874617259, 100923266, 685445631, 347587579, 608929452, 216192910, 233165478, 109866122, 751247412, 23215909, 586222348, 205117872, 212442112, 253421247, 194483130, 28291936, 610676862, 77107076, 774261385, 999969534, 261230857, 347196699, 704840995, 42395833, 421532537, 961732049, 680426653, 774070243, 12386817, 736377291, 41017364, 323032148, 86378664, 512043129, 903586490, 610159057, 884027401, 51947878, 345033125, 720862599, 132352106, 231416941, 663360067, 279609073, 881358442, 37603902, 136930909, 169278725, 466701515, 274388184, 586038843, 620946077, 123349186, 497883839, 192980670, 795804368, 447642062, 564248023, 562623424, 870091907, 341325877, 891860700, 285200391, 188066336, 257831411, 195896642, 770488127, 146911855, 27352784, 190301928, 857403456, 373323595, 219028788, 27517442, 666561401, 950958246, 748225693, 780552380, 458273811, 358439601, 569625165, 738609774, 922625485, 958581705, 240168183, 737837597, 322724599, 800793027, 271158434, 728745190, 779002898, 243195892, 861811306, 571460005, 355245528, 651116615, 835324683, 414041801, 344852190, 886700336, 210587788, 999140936, 624231241, 110957245, 189745894, 711900592, 712590705, 686913959, 197156072, 405180266, 782182395, 779742160, 901805061, 188068627, 880971248, 51891339, 949468190, 485129883, 536192571, 656637463, 388133304, 925709740, 581303741, 218502684, 306765802, 69438499, 956069316, 506741836, 874728415, 485669893, 492784528, 479320785, 512064430, 21181732, 844800469, 778196692, 71155907, 814985890, 112133683, 863887248, 580161477, 187355586, 801113862, 590430279, 587005539, 25017876, 722036450, 777931451, 26265377, 487508416, 141029643, 484448533, 633759770, 677199394, 528916331, 603627912, 135710241, 572969117, 164856741, 262070882, 587535607, 266156223, 136275256, 973313797, 601214211, 955160138, 944591574, 134765261, 712073531, 888054435, 629141366, 291948342, 3472831, 529505077, 990092347, 258153046, 880594210, 554422360, 609017993, 441823940, 730361783, 638082907, 22982479, 388808421, 190075276, 623194197, 476647879, 51977957, 801917972, 259294178, 635975932, 225994177, 812751613, 73511054, 10384748, 321215716, 882737611, 9462059, 882961369, 609820269, 774763331, 595347323, 366791043, 167472883, 613015495, 603881869, 610339813, 147615465, 44589835, 730040366, 63074094, 470020303, 130902770, 402810439, 592346839, 504327990, 497705397, 879838371, 784745953, 405040745, 28531228, 625884273, 202403950, 35373710, 740178684, 477180456, 968802961, 364043969, 516847113, 85592324, 707527799, 706751410, 901481868, 72522841, 639974341, 788906206, 615794925, 8880624, 833961207, 946452682, 323621443, 703860596, 741598891, 155987152, 383232499, 291692448, 334527017, 311657264, 928134642, 538465429, 146179557, 505546368, 450125862, 933122707, 640359806, 204099097, 233820497, 24862116, 181687639, 45355096, 950419730, 405629676, 170976257, 588899275, 883529247, 22344905, 996820236, 283906693, 492578350, 164042544, 905730439, 462138497, 937745914, 126694129, 189191329, 661929751, 914972532, 478786998, 722778654, 125466743, 569487467, 529646018, 270815378, 983264373, 209995394, 459672602, 254581458, 829478238, 725500828, 356886710, 383225336, 403567727, 791770486, 107430562, 820507011, 599524720, 363368664, 486972586, 212797959, 243584123, 297182616, 347268338, 369623847, 308809369, 269612079, 320750987, 502543402, 43953442, 249941011, 949751701, 348695351, 906451067, 473153203, 776299366, 963824407, 896678266, 163165562, 961786505, 191899485, 63842725, 353798124, 860138338, 70813271, 649126846, 718135785, 531173832, 376551, 375388868, 439609514, 338387113, 575352627, 901901833, 853967432, 688025479, 132711550, 215189888, 800185032, 567106499, 779909380, 123924753, 676455212, 176304453, 870512254, 583193978, 76466762, 888295234, 382442413, 716162238, 8610800, 477368696, 286768668, 437527221, 265420282, 811616477, 324637747, 137264749, 893145168, 496074256, 420940472, 849301008, 136286701, 813834949, 503816593, 755016220, 539673923, 885909682, 85932578, 639096227, 214355545, 994187065, 241608691, 471646715, 887931715, 470408284, 185697376, 374616998, 718492062, 473510154, 578272650, 999834361, 896719494, 856168819, 45061071, 247323494, 248897060, 211924520, 183071433, 987944833, 844477146, 84739747, 574423453, 271687006, 809815658, 402583453, 633161532, 563706336, 615353141, 828261862, 550571968, 758189436, 227886391, 275193455, 100157889, 778234003, 748322611, 724434762, 458540265, 798725580, 592345040, 910984644, 619572359, 367413960, 330597467, 986866851, 871559106, 907416455, 762622571, 822177498, 631798314, 874668925, 839735475, 820983193, 751873995, 269478987, 322073278, 349271861, 270339518, 325293065, 602274046, 395997911, 407865489, 262424590, 215529374, 390488705, 806019090, 741628096, 782694749, 222749744, 369122762, 475119304, 807637095, 137338104, 418509382, 109721406, 839161715, 245503790, 913316106, 529696445, 160987381, 755174540, 664403805, 506677552, 921650837, 323108565, 417411536, 647363506, 274143311, 750056862, 790001962, 968486564, 605237584, 102201993, 809713536, 164437053, 687417500, 849557812, 545948846, 678674703, 278932401, 6918092, 579005667, 349352875, 565838776, 377763224, 606559358, 78437169, 457921675, 248888513, 386936840, 983443110, 4063754, 727850861, 278372235, 912638489, 551743408, 20090741, 966613824, 855539993, 614145159, 876488463, 824553596, 656569962, 66120889, 733870574, 973782071, 691101542, 559761376, 596296428, 579553544, 867700646, 862196586, 217016089, 815891058, 158523224, 937155725, 794887485, 364154557, 692352489, 396378187, 835099487, 838454049, 735284630, 496770360, 649907842, 31320500, 612841464, 675910987, 50205885, 73821948, 878630162, 532091273, 787743725, 471166935, 390643971, 536918634, 411733067, 635778281, 881441675, 222902532, 617000848, 23490124, 776065500, 538150313, 496212149, 698435592, 358665540, 960913113, 673925250, 603544474, 4959572, 366065473, 657489679, 626026794, 359296739, 462539298, 195345863, 355189878, 361875357, 804099352, 759320339, 792900014, 553507191, 352819975, 880938990, 725076051, 488976734, 27918088, 197614676, 33200102, 763176346, 363935980, 753448034, 594262111, 60828043, 728062780, 438258859, 346510882, 359708307, 915349300, 790814739, 587160083, 512078790, 537513663, 144979537, 865505725, 878259433, 819173934, 306040556, 551699463, 110634356, 935907812, 476626573, 728135428, 153018477, 859851371, 444175863, 456520545, 731372377, 100667793, 764970082, 847779225, 39232627, 916386408, 142170074, 752433909, 946888749, 589967451, 380629639, 262068888, 562366262, 899134921, 734854276, 47203343, 33235758, 701033083, 583692261, 518738374, 821771661, 170917934, 475545632, 10827000, 83903728, 827000744, 388224923, 378881512, 260075729, 312407158, 850791856, 356982719, 926314462, 682546344, 594933921, 183432962, 542634264, 293182604, 520623716, 661155513, 847860552, 60064434, 129648037, 883095294, 840151409, 717185097, 438085026, 640716462, 338701108, 724760554, 221236683, 49975012, 209980906, 964320310, 537281855, 300657539, 705599867, 576214468, 858008059, 684837178, 431890950, 266242056, 791077066, 86139474, 968547166, 93929277, 73903026, 873247058, 211237509, 948933633, 97313275, 156471471, 156195812, 533065676, 879025855, 765442455, 75263811, 14917530, 598880435, 309578866, 876875368, 518086493, 360445225, 372725387, 355995964, 167308009, 816380100, 410226415, 545975741, 11596662, 754688063, 982339790, 413870145, 122185786, 210618131, 917576896, 403537201, 342406270, 344037789, 947027171, 139222145, 399928314, 567933579, 372937876, 491944441, 350754469, 861838337, 505698952, 974688904, 507321266, 469916161, 710960626, 377437695, 997601050, 458217160, 467505678, 548080703, 652264870, 709472447, 240570054, 555730989, 716700229, 456345140, 558160065, 54225921, 560393536, 266233377, 844953830, 657944231, 566473576, 786832050, 465773208, 347584768, 814899933, 270184789, 159854693, 70924549, 964037299, 788370007, 825939974, 891372560, 848075490, 719105910, 691158970, 273157599, 915184192, 395831323, 213871679, 515297307, 815337133, 22951905, 107496558, 222208598, 510848518, 539467548, 291158711, 736664142, 314038330, 653072699, 996495000, 391521727, 327934919, 702709827, 571828044, 277946990, 84960961, 896648388, 931974867, 863797388, 12210923, 812497240, 105032477, 89985007, 78564304, 556762055, 138510167, 139536656, 923741819, 221615960, 707365849, 626596303, 846641, 210064003, 627169362, 911970605, 216570752, 693902578, 416042938, 209751607, 269737997, 852295719, 412749144, 275090529, 859435303, 38991556, 991294061, 492852639, 389595239, 366278485, 797300397, 561854198, 67966987, 456971379, 752703864, 890746112, 584609144, 807186312, 745104189, 617969324, 872052726, 253997476, 813919479, 868790462, 689886206, 572389277, 208755844, 994011150, 727636506, 278499944, 851347836, 167044299, 293734898, 956825263, 714523021, 783585574, 655831720, 106212024, 974754339, 308900102, 532350812, 526602021, 213984817, 921553945, 532106960, 599972247, 700016153, 308885342, 468173839, 812912256, 59583811, 334290120, 350684217, 196983789, 748707075, 912255904, 15443246, 937971092, 822428490, 859810106, 978565902, 770573356, 722999925, 971196807, 116314098, 31802479, 283006767, 96699880, 673863742, 698642333, 339733510, 131739668, 341748502, 545782183, 276600793, 959694456, 139212043, 649379470, 971902479, 580700004, 440517362, 47768160, 227695320, 853452964, 113510686, 38563739, 216683081, 643929684, 285518142, 562912655, 703139411, 366601261, 901936887, 703303693, 995603991, 45710680, 171039452, 838501261, 469514072, 486468899, 676101921, 280213057, 348567783, 4079998, 434969673, 305152566, 639148785, 486603449, 792126552, 382195620, 7319566, 74267223, 896452444, 251361974, 141089098, 696671065, 855680031, 976196970, 666842442, 638533162, 851484296, 869838328, 331217719, 959112626, 249799191, 673230230, 207203896, 63412688, 48607119, 410801296, 785609729, 912671797, 129782268, 25720480, 598056530, 806446463, 709797179, 886839954, 804920990, 2754095, 620221783, 292448301, 100767824, 33747730, 666182562, 700799054, 685715281, 606431223, 519931824, 826834483, 285052414, 92740613, 821755514, 808526209, 649777757, 84364030, 714919204, 965136805, 744753136, 122848413, 68524566, 299937457, 196650818, 515513830, 291937389, 586091769, 762410349, 668542901, 711877741, 699478732, 612076786, 786759108, 993783726, 740834952, 519112668, 184107406, 320294546, 257250095, 878952113, 105865000, 921152926, 825990301, 373452043, 284667329, 660768553, 96347146, 242580370, 892736978, 854049911, 55832872, 738805178, 999131027, 478464729, 973247015, 409303979, 537477462, 94133910, 26199849, 411598243, 855131236, 470280769, 394937156, 12704950, 63556812, 351581766, 769921056, 539880776, 636907560, 4821151, 311090772, 725817535, 481778787, 469580583, 544360258, 132466360, 331305815, 115080132, 188270412, 113721961, 163864476, 757926961, 331231551, 439128171, 425916308, 435549166, 529618696, 320059222, 851648305, 403737998, 877563729, 507895691, 152774399, 714367909, 182875281, 400263381, 946294726, 140818999, 170170842, 50269688, 719131833, 663913074, 68338545, 435462774, 618023833, 402581508, 505603739, 251836078, 923265683, 999822786, 348717869, 917555223, 372614190, 481756372, 637037413, 387095292, 97913949, 38491465, 407883443, 398674811, 403136150, 577739117, 225819343, 635279345, 353400944, 78091574, 29184080, 756238123, 518780154, 811104105, 562117039, 869133267, 533011326, 604439510, 273988040, 697134195, 886752860, 782226300, 661864060, 876678632, 842626109, 201623563, 512682538, 376472913, 666048515, 682763874, 812947994, 878374994, 754693877, 337492642, 934159197, 666191250, 113664860, 337489437, 763011534, 776088717, 276878739, 33999622, 174516056, 323119595, 101920265, 223904764, 67770313, 346483968, 207216866, 87467065, 605507897, 377369155, 787536791, 950155217, 315901113, 437346158, 644312127, 312022347, 445472361, 252822649, 417335901, 214344964, 425563225, 511401058, 839864888, 492066899, 110832418, 569941128, 423699003, 505674320, 479989995, 15448009, 751831208, 442146097, 46305793, 282361372, 605560672, 992619680, 8790253, 235156179, 75887068, 742199433, 918454676, 326772474, 613706758, 883650319, 646959262, 787036225, 844989357, 960303767, 133626961, 220205778, 371372871, 172835284, 677532641, 105538284, 387972456, 976171180, 988442753, 159883071, 933210879, 51913104, 875456011, 885254378, 116717762, 311929673, 598736631, 714071059, 394792736, 189835722, 859946094, 955517484, 567430702, 603976507, 474477093, 88981945, 982643699, 4672762, 995784080, 222286788, 766744098, 119597245, 256842706, 862253875, 670399767, 873633816, 545033465, 31779959, 529352301, 359192945, 688651050, 759655278, 362679416, 487365671, 317909358, 961086252, 235550135, 295182377, 863276550, 71541398, 385840959, 306965088, 63317983, 551548694, 595576502, 929511297, 143513523, 560374794, 840040880, 184002173, 56128326, 327737922, 446348909, 849995709, 665794467, 394549856, 666121013, 117260902, 329659928, 563985786, 138080886, 824943509, 304845476, 660901139, 811478520, 176757366, 618032086, 292708041, 521156851, 969131643, 783019939, 96005987, 226011296, 9155534, 419584844, 438076874, 153038377, 736575732, 160157331, 582305655, 764187908, 559595917, 733263173, 147469999, 534729470, 175870344, 581706332, 31407639, 737149590, 812950356, 63705689, 498732263, 942213672, 138613776, 147425592, 329046423, 379507102, 746623477, 205755272, 684775241, 340387201, 770549575, 767423163, 565950324, 389093325, 993408069, 612414817, 318815464, 208818707, 876666783, 648950819, 182086737, 89575221, 125786028, 800627706, 54182401, 767363951, 184995281, 24293548, 448913715, 399640729, 108656654, 526127648, 556845867, 11282769, 493970231, 365810476, 308677129, 993497328, 944383658, 942011531, 864234230, 404866642, 210767025, 225072958, 991022563, 788316711, 562421437, 831689009, 253084075, 4555766, 523353082, 253695448, 267349651, 330492246, 914810366, 71209315, 872565141, 328750605, 553752543, 976380244, 526991670, 143092931, 251014484, 342518217, 125295154, 654427442, 511119600, 460453245, 82717411, 896619656, 213626802, 764362914, 710743680, 961615757, 464785104, 132433702, 794579890, 188135697, 168316432, 757736042, 738555150, 131164039, 693056475, 306641329, 643558023, 987291572, 138042905, 590497194, 677132863, 230789332, 206940626, 768479144, 937111229, 306931555, 330765231, 59976762, 317688534, 278877002, 673178186, 455359187, 590397471, 150252162, 7831118, 605225676, 334803871, 876946581, 450021354, 219501320, 554359138, 717448378, 328813999, 848316579, 676187984, 756501199, 719563236, 194517457, 293069158, 23650785, 973241055, 914665615, 255127063, 411662607, 333547431, 157515123, 67399595, 229641175, 287475249, 461357938, 960672790, 218088253, 212957257, 599881906, 823041642, 242687108, 330692695, 863338848, 780464024, 984105034, 503286716, 333698825, 214924562, 702018166, 158502303, 517975303, 418858238, 369000869, 668223521, 595306717, 226405167, 970234187, 142200758, 741811193, 422011562, 338962407, 735909941, 704704395, 151248053, 911812613, 498805001, 273010992, 367883707, 255612294, 364299286, 423538754, 974484870, 318963887, 858815964, 311808432, 295657925, 301439654, 655760000, 641118082, 231997553, 115785071, 784720052, 176189388, 662558970, 672451012, 437556258, 885818501, 274060624, 501912870, 548700662, 844231988, 383046448, 995838821, 516901425, 765314321, 45937700, 717459685, 418688507, 825923604, 797795246, 107378783, 900147599, 79585847, 613115569, 461171792, 381465177, 395491030, 630588457, 997637140, 281968763, 175187083, 626511030, 196070666, 686529269, 205678675, 32323479, 567954883, 561326924, 528996461, 874427185, 652637279, 79254490, 188500783, 860014879, 958962076, 68934893, 229244688, 826580198, 15592540, 881521586, 8984295, 445299760, 282220266, 559544769, 518601731, 521945886, 426079554, 927764364, 152795834, 668371735, 119508006, 83788470, 132317993, 478725017, 85094505, 953046411, 746644289, 482623018, 676652072, 705761975, 497207426, 597473768, 711570428, 658596893, 708307213, 836999630, 705563100, 243746263, 147766240, 792684972, 813524214, 953063157, 269270260, 795455942, 772757748, 48641015, 516115979, 847600803, 377477207, 717718098, 671350818, 122534310, 962812318, 369744883, 852982630, 363168652, 393859648, 5509414, 725940647, 790909575, 803157461, 37103540, 226146560, 486889733, 125323459, 741022252, 516509770, 174354246, 381145783, 673679021, 314491062, 369255021, 530632681, 745303096, 839163887, 225083963, 53845047, 333873981, 819806364, 312804930, 231399892, 897145085, 547473991, 388301132, 531496549, 799346566, 63230990, 428493445, 729306163, 884595612, 172287890, 298753505, 722859934, 778637079, 704585127, 501200133, 490096595, 639537497, 733981400, 715610865, 226270154, 693600825, 280207702, 21665100, 726135415, 864704909, 280622911, 573189685, 829750085, 526950147, 133758849, 103398289, 446526685, 320659958, 923417287, 910416745, 2774804, 214833185, 113515060, 27439599, 475423287, 113886584, 198228096, 419352523, 416904595, 895166959, 351677316, 524620439, 695429652, 379472910, 269032851, 702773717, 97926391, 425053419, 746179303, 587005599, 255079370, 944325227, 540726867, 693744002, 909987355, 411048237, 254180465, 694051622, 728147556, 823185264, 41181497, 705102416, 632432010, 143628768, 685486548, 122401526, 992271099, 112074300, 781454918, 350411293, 83652950, 443107100, 121603557, 699383372, 525300958, 312297366, 953085848, 863494528, 943118806, 320720579, 973764389, 188778446, 619870529, 549441636, 55016496, 997034462, 482472114, 146304099, 92677793, 496147315, 837438660, 484172099, 185446036, 810324844, 892431164, 503308430, 588161243, 548847707, 948720549, 229380850, 885513530, 633252580, 590869059, 430577066, 593597268, 363606311, 480784146, 709537735, 410119907, 952851057, 575369061, 481863844, 374404189, 600603335, 89258047, 550601314, 850169213, 33427637, 600336493, 783563755, 474814473, 239919447, 896811562, 567159407, 180058166, 926318362, 592581549, 130423912, 682929618, 383921878, 75302368, 175875569, 266775133, 871889617, 248320773, 61672667, 295366164, 369760337, 588746476, 257409150, 57774210, 310566013, 189513619, 639648425, 268855558, 658392890, 384694261, 608496104, 38307741, 379073787, 194800450, 570148627, 44073480, 326775284, 300019584, 417684464, 439353244, 994363867, 293323217, 545047441, 223765773, 737970641, 26364581, 523601477, 775676507, 284465174, 999937562, 226470458, 122130382, 623834719, 386469727, 140106320, 997437587, 44470756, 235159326, 387806051, 91999373, 111967406, 892882023, 891038089, 194082042, 248162319, 738202678, 803449095, 300275580, 917334514, 318571309, 11067579, 273973771, 7778693, 769233552, 409819160, 228530372, 757269050, 465749000, 194394583, 442974036, 379176647, 553362305, 28679814, 368616016, 990357690, 347882475, 226945833, 364456847, 371848476, 317920082, 782856875, 476543678, 915949156, 986584200, 542947392, 965004340, 803644522, 919783055, 993403048, 73762196, 776790852, 926328899, 830597370, 774367212, 94152712, 9210042, 433814831, 40225957, 968165812, 487336188, 907840883, 885931161, 354400999, 985212614, 418199566, 900265838, 642149262, 103555583, 46497210, 599421683, 714105323, 796500339, 446980473, 855552989, 641246639, 173180807, 370208248, 387666465, 802396743, 302139536, 513221846, 15630988, 863620847, 545356493, 44525988, 746475254, 106229667, 420828135, 757123985, 857492182, 952496679, 161880718, 573795078, 182241927, 695441287, 990924944, 169366860, 663397280, 137679160, 316519941, 518766992, 270932403, 90378789, 678670794, 727684729, 396749272, 181113184, 118323329, 697233815, 737613471, 81058359, 462575088, 452628347, 503638720, 310806586, 436967111, 876207731, 844723443, 390152911, 807419853, 405883143, 411663147, 721270814, 430493514, 24343714, 865536840, 64555215, 860650888, 945164870, 2720959, 312828090, 568559199, 732559882, 20822479, 63927261, 847120586, 472941584, 981659648, 211074673, 315578500, 784307682, 834869734, 815164525, 913993554, 583533488, 556398271, 260150506, 892584147, 957997106, 222943457, 11927161, 977429913, 395939333, 436635312, 20917574, 123386309, 490167761, 863623792, 882755007, 130194285, 202288306, 178207677, 686525689, 822607927, 8133674, 572039493, 545101473, 61615512, 761416750, 271328616, 467981999, 864850589, 33208149, 306799482, 507788622, 234233829, 757243321, 91088181, 129180632, 725627143, 826049384, 334064371, 64712360, 578046951, 844640913, 648374111, 59780041, 529305139, 60073777, 259042929, 149311122, 655864759, 934306261, 356024558, 319674157, 186081142, 415493718, 21585018, 400487257, 70941995, 557854522, 266552932, 94722602, 779316998, 628986838, 39166078, 926118563, 220048867, 530888157, 225465931, 352817318, 652169191, 82368958, 24013479, 84412998, 561097752, 507389500, 991984981, 775765505, 458048028, 948326856, 727891682, 452164448, 410431161, 601306250, 498425941, 406824516, 287136374, 4065486, 570336637, 783153553, 653059435, 144767272, 117348323, 912284837, 966672962, 112749333, 810463283, 88986145, 647233700, 751092668, 675686255, 737325229, 763491790, 410563701, 653769647, 756650826, 869417631, 533570246, 621024307, 101221913, 798629465, 800304543, 27129210, 325982142, 734358841, 123458221, 505387384, 47962002, 954900617, 829706439, 267656728, 761471545, 126962153, 276504903, 73206328, 480752117, 734057964, 682511314, 707691086, 513851640, 622848554, 808690529, 861718802, 839917220, 969856363, 993146342, 496105875, 252355034, 993502530, 737227128, 15143444, 606579614, 534860138, 454023870, 595947392, 829000635, 843686017, 731599880, 88939077, 467654711, 127630988, 350312755, 601967802, 97393114, 400571239, 352616975, 542370201, 703446718, 300478932, 572733627, 934880095, 120000520, 502527056, 645539731, 624211535, 636190024, 805318227, 430637917, 875816828, 701226902, 278391620, 193622805, 414594389, 480921965, 155969988, 948307018, 833802462, 37656550, 534776976, 113653705, 295229486, 776339318, 395418750, 882886808, 729980775, 703778930, 13724585, 680660998, 931610295, 71021575, 250809298, 217483323, 248262216, 551356857, 536861130, 55267817, 537827318, 570911128, 286745233, 282624739, 905620052, 709416881, 935233287, 473906786, 367790645, 695255321, 383493659, 834440891, 89625448, 102878443, 582777883, 49304641, 490999497, 392351778, 11894370, 980408328, 165553224, 182842134, 961840826, 140146407, 120313054, 848017614, 687923003, 422023464, 878209942, 2769943, 1766028, 249718926, 990130836, 69207214, 539273022, 820091329, 834654324, 330710744, 677029111, 326468388, 512832726, 346895817, 215884219, 237033546, 972684946, 37761498, 258081861, 37740117, 47794371, 613678551, 177930103, 652522955, 134819081, 225079899, 4809048, 308957511, 101526192, 32818356, 581638000, 409519726, 855120794, 934507490, 242228346, 614609769, 483639142, 455392501, 176074851, 725759663, 666170013, 98785587, 967379221, 784122314, 445637175, 683825852, 666734503, 850985281, 801067138, 39211581, 462803606, 65591743, 874419627, 808507425, 521587806, 946096027, 565968967, 680333938, 6864633, 120325066, 137247593, 499908282, 397385449, 285396434, 485746337, 487845712, 778342604, 334400494, 784464098, 758433617, 458518671, 805424884, 159941429, 970222267, 836169701, 464169997, 952753586, 763231971, 653475660, 766366420, 951832681, 919453263, 493210280, 606992708, 447972254, 305969600, 675638147, 721740410, 873908893, 695967912, 308354116, 767390005, 392502069, 473155221, 965413583, 687277870, 23038315, 534999093, 542567275, 799659087, 231163995, 205093127, 30018822, 550186300, 23366389, 463379960, 81716872, 455290643, 137946304, 761949869, 769087415, 165389343, 738695224, 263003108, 947588561, 880834637, 153285946, 527180086, 112708418, 775511096, 813008890, 699266831, 167206283, 621315757, 990049771, 922098298, 164595706, 737957403, 331051488, 31969303, 638341940, 696489443, 370796197, 268865905, 902080576, 731074380, 54991287, 697144386, 851286387, 447120651, 231516007, 347836430, 919873569, 335339419, 92199506, 495109374, 101529686, 420869469, 88288954, 750004624, 231606357, 272473238, 853684780, 19661124, 414738889, 300326238, 405962189, 134746369, 875575150, 10660060, 880998108, 75555714, 958365924, 506485484, 274943549, 839091815, 255948682, 213140836, 79382250, 254623797, 368427476, 8974237, 799414820, 769659576, 895541091, 45041762, 221683177, 855644499, 459513751, 169087417, 373790404, 91401149, 600146641, 357858955, 525786182, 716297094, 615704037, 822923297, 420304957, 547849722, 204783207, 389779180, 484219472, 675110924, 121831266, 379494838, 420758530, 18881439, 592334727, 419393073, 864175089, 530131608, 922039031, 24280458, 848566342, 747700528, 911330309, 742872243, 520411171, 164667407, 434203253, 215401177, 759496974, 376656847, 584455901, 551480564, 205341919, 120530247, 814037550, 149730787, 944836678, 863452867, 742648620, 505717176, 596522339, 66088190, 963093300, 447284858, 432425327, 143398237, 606475325, 104109108, 969142509, 414536400, 324898646, 851411514, 497311198, 259629141, 780627408, 1909915, 662230901, 696407787, 220603254, 479622739, 891463842, 847297007, 395090129, 75903537, 651958547, 922414329, 321668793, 686813549, 280564504, 352024707, 440549924, 516904474, 724857036, 170957567, 476651191, 508398817, 576688146, 943523273, 11746091, 513710746, 359188318, 217503521, 523726063, 894701604, 749593543, 488040162, 282699727, 330211631, 438623529, 167982367, 87651605, 851357296, 546612581, 693775777, 474861418, 187935321, 907700928, 308895804, 642401441, 674420043, 983114993, 471544237, 640279443, 680421308, 589839286, 707010122, 765218124, 826237095, 524057781, 896350341, 162149681, 882749381, 73864903, 195801114, 110615316, 897264328, 745067112, 657537392, 560852266, 634337794, 337560761, 893579611, 368188036, 300182832, 641421337, 697016721, 941767281, 241220988, 515766449, 247070679, 329698837, 592286686, 104348197, 546227361, 634155051, 190116580, 813943111, 639902950, 868531112, 178021378, 2448280, 354904906, 804782883, 863690283, 343318360, 381654563, 504082070, 91902746, 123148687, 540951000, 630424881, 298663486, 591749666, 227645676, 690211186, 675834125, 877462241, 618069862, 161378001, 116296658, 543019483, 848816987, 424345466, 874893247, 379509284, 603480898, 802238757, 601823565, 752595555, 550713120, 637674732, 843784323, 742176862, 712179511, 283406199, 47948563, 674533945, 641600929, 772053066, 380257605, 284019266, 831604921, 456904246, 784735856, 571475525, 824173751, 792991498, 190537707, 272635303, 973320650, 283472404, 388861769, 370326799, 934049608, 301148831, 566105445, 351830806, 800391609, 310274634, 338338236, 23844802, 79990543, 52698991, 196927988, 702995024, 507010711, 693143364, 502752195, 836814330, 56696225, 400550063, 637616091, 179544174, 817741074, 759434773, 580666903, 293174662, 407469608, 51310453, 648846915, 659313551, 135017288, 267882643, 393484292, 857911933, 776428996, 299407667, 60948276, 924612038, 41804827, 670287755, 344388249, 505838339, 551803989, 826211050, 908755949, 448515952, 903953241, 756564178, 902949296, 883806580, 687260726, 213650934, 849181416, 604526745, 591191644, 572852655, 293025530, 136346898, 713776235, 154384447, 284548878, 843940035, 366946564, 415403598, 958827073, 997052400, 989794300, 773225865, 852768823, 595164725, 19152157, 889512700, 166163264, 25512221, 223515806, 169621595, 537337393, 313305329, 145114193, 328910071, 334699929, 798455684, 642150574, 413642078, 442604319, 990795298, 239023427, 425729731, 685718686, 272439018, 423771334, 377768400, 396497290, 446360628, 427756252, 790204582, 746511141, 936361879, 265236016, 116412745, 649124670, 710948965, 721631433, 490255544, 777872555, 898019819, 402859363, 500387538, 958123638, 463980439, 871487053, 136092929, 517622780, 304855921, 300593628, 708381587, 994671704, 988234501, 167138683, 1179255, 20854996, 232888751, 375657682, 542158955, 238145782, 817363739, 391328612, 823445815, 663406329, 955990594, 742481676, 457670654, 484902679, 501951815, 744344745, 397590930, 626509452, 417428563, 527257343, 552592557, 303621882, 6076450, 583849499, 457693551, 610819310, 580913565, 824468582, 550177748, 357623750, 317382870, 467366992, 777992700, 329539640, 287954426, 833292636, 127870171, 495122481, 740468222, 155146511, 676781797, 781706134, 204942367, 478370581, 280420376, 379932078, 890316968, 927421962, 906620313, 944940125, 293721997, 355603907, 942436763, 626144028, 19847359, 977880193, 880713753, 15647815, 999209718, 582115954, 173069346, 195006436, 244431226, 477109681, 72544408, 305296504, 952529038, 939462317, 101868540, 345069048, 660429392, 127425877, 248557860, 137213817, 641789160, 763061731, 865107577, 89387784, 878983574, 847286802, 893106399, 437437034, 650821692, 498106134, 31245637, 551489736, 992758659, 212139721, 230306804, 31960949, 622465855, 500503388, 352210238, 133051508, 324555984, 890136870, 508273031, 408930764, 477200699, 984043459, 323331882, 328685538, 198514383, 765127071, 968994572, 725917927, 467404717, 406549776, 310646654, 839249931, 85875958, 937590786, 520682692, 733644112, 479673111, 770290703, 185211688, 991789307, 466328798, 89522200, 768258648, 628337631, 881746144, 14306613, 690076360, 341729436, 94453669, 867485922, 615769893, 821430188, 385952105, 441002266, 651360109, 814401444, 317273371, 564932610, 9904579, 636164812, 25615686, 875653400, 580902448, 935284196, 572466500, 47999693, 528401066, 855324784, 431626156, 817202204, 514095597, 910827885, 918314679, 823170751, 694234807, 720910491, 249560667, 522303565, 561817999, 960685595, 855252438, 678052111, 860917951, 502261189, 238390129, 155704571, 454279051, 119093341, 864614103, 97222966, 571846938, 810556604, 279402942, 912171467, 230509960, 526208012, 369913871, 125045390, 760793005, 137086787, 571818670, 806974348, 385397841, 503521973, 387083047, 381272921, 938512996, 409128060, 854959831, 876940771, 593513045, 233599865, 854815404, 435059498, 813650105, 971638861, 901723598, 118541747, 77437649, 371805533, 679297158, 638122463, 648723168, 995745103, 560056710, 182170648, 557442012, 934884204, 724264539, 970467346, 468130245, 835854841, 865719074, 260951243, 509544356, 590600546, 733332866, 548285835, 910736513, 84776589, 62358096, 306530121, 628467337, 239605295, 687483537, 610703735, 786586042, 525290048, 294182103, 942080977, 840571418, 139439877, 33688697, 870049565, 206001236, 198189030, 961484305, 367564080, 12835874, 288475999, 793451322, 995502312, 264237994, 625376527, 227858208, 993168449, 449983177, 826104910, 710164359, 707669920, 518085462, 884336555, 638129314, 397826958, 594658354, 928662744, 618383946, 150541168, 26962846, 510537985, 16069100, 62301131, 514036619, 476465911, 943096391, 764722841, 798453292, 548829542, 68109785, 143301770, 731801154, 762742634, 735940665, 642042090, 597783996, 647814934, 752296191, 834262498, 877308013, 761342004, 368675859, 291536391, 494832052, 628768304, 727852766, 162663591, 654764636, 69873666, 78662978, 878252023, 51636135, 441401046, 361282855, 738983715, 895988464, 687045536, 381985180, 567957065, 759777637, 29023851, 439002304, 499762587, 34467163, 220579639, 763651762, 297286693, 942102078, 502445897, 156628071, 259537400, 524949388, 552082426, 732484205, 96568926, 926150953, 771014713, 709877763, 268834444, 50622949, 105528737, 602645414, 270026629, 363070916, 184885664, 196947132, 995422201, 409555980, 563326400, 615250596, 884349866, 55273276, 570114204, 708639151, 301617528, 361919408, 877761999, 485488199, 842780476, 354098388, 608327575, 7948085, 46905170, 552859770, 603940406, 245542218, 861058514, 815998066, 739445600, 335174988, 773725473, 627671940, 715983866, 677643406, 357027295, 996134379, 988529640, 778127967, 303111444, 997480693, 568034243, 818862023, 716296176, 8981061, 338899256, 768929532, 196985722, 256017845, 52211725, 295206094, 547165570, 566040167, 503803421, 38772505, 746121643, 368874696, 228927971, 683395165, 397329475, 872180635, 352460027, 52034686, 45070067, 862285100, 115395310, 634246436, 944832606, 712814127, 733833066, 470578886, 126987865, 238794888, 561922379, 407957982, 709695573, 194249951, 558831115, 919319431, 711876868, 895947690, 600835116, 5322988, 771669746, 108946135, 768789529, 934811615, 224434828, 675015152, 695905477, 158667252, 851556294, 727562378, 357200808, 779272218, 48693648, 833159280, 955183319, 260133758, 962127052, 245634628, 65063354, 715524785, 535640058, 365946214, 511763100, 789635766, 955254848, 270795199, 279525540, 34671354, 317180112, 463498051, 956222368, 126848066, 890613616, 746896027, 74709088, 889609898, 213811320, 921153176, 829892199, 25774578, 845016611, 755418628, 774366573, 897439926, 999428903, 599669258, 533488962, 134638949, 72295042, 846672132, 990439904, 277414610, 41841888, 882698041, 593502213, 887537486, 808125854, 295701474, 133020999, 48934516, 550210917, 741983553, 832064355, 128786693, 309774374, 475631480, 702556187, 82363731, 930160411, 464675278, 180458193, 669718794, 841857873, 854568131, 311504245, 46352171, 960994082, 912301090, 933537118, 36766416, 559374834, 291144027, 527290442, 756746865, 885803846, 65420366, 396986543, 893570454, 390077065, 607007079, 65611102, 342751071, 743106660, 845318831, 943040030, 538457020, 638291882, 325448626, 77277750, 984708381, 932058524, 720262387, 290178811, 121196777, 753441669, 199200141, 102188144, 201013307, 661347561, 854964016, 450620788, 449753326, 667452744, 100396848, 562249432, 646785167, 656846402, 945635932, 755476019, 595518649, 196766672, 704706081, 403232144, 728070619, 417534391, 604362616, 621011318, 298129831, 514768341, 324504756, 334204456, 908382228, 345896243, 681892937, 96725372, 28288478, 342786790, 100397862, 162655675, 641416292, 562959825, 825509928, 119556579, 372127030, 603959717, 996001552, 899812761, 254851180, 948148529, 641895253, 859743947, 198958135, 80355490, 605245603, 240513236, 561444151, 843384186, 279483816, 253933672, 78246128, 93711938, 838578905, 454021772, 66762912, 375577217, 630141134, 762731116, 204519107, 397220208, 331094898, 133518572, 292311009, 484583812, 826186558, 488721327, 661286417, 415474043, 63303186, 522908785, 69186072, 682719510, 998059750, 635525962, 511348349, 879627507, 236199437, 333331490, 348610128, 149110213, 684697173, 672248348, 146213189, 219857943, 530518287, 195171667, 948094442, 700656302, 170718530, 871470955, 688340224, 807928588, 617491667, 417113343, 746350863, 264813895, 758717987, 673937914, 894092010, 541353395, 58143360, 56557908, 697381065, 784953818, 583885161, 930338439, 752341986, 601298064, 39040913, 951768657, 938184116, 916150756, 720518849, 674392398, 39202618, 498614716, 837685014, 196882292, 937030580, 477486626, 848752837, 981723699, 795491108, 607295469, 556932478, 763713445, 340015113, 388586161, 958938279, 535430207, 254613699, 525829856, 496723323, 646256470, 91393119, 419285612, 794970929, 751057707, 145509369, 929210836, 360169722, 767901502, 68402804, 250243135, 327150889, 784370983, 955474392, 27652690, 587923691, 927009113, 352205253, 803056685, 422280206, 407348044, 956338869, 897536983, 327030657, 406725055, 103338775, 761523793, 648057883, 386379252, 920414609, 362055411, 840484549, 655893508, 761232802, 139633001, 685604954, 453668255, 211407301, 795084832, 833724703, 980624027, 929768624, 773211528, 821933096, 735034689, 938664953, 437342674, 505114605, 676900479, 545316816, 971720771, 376925451, 546493700, 822166138, 231335860, 997324937, 51089353, 710787365, 783290858, 29102606, 553151824, 326590362, 131082025, 434247805, 832141224, 579070929, 496767291, 330470199, 465321529, 656587313, 468108608, 76973069, 141069439, 944758752, 903978155, 284655185, 134626155, 149696455, 792546914, 350358812, 653737542, 832978923, 765561552, 516765659, 497824315, 980436814, 749914558, 92336473, 24135831, 240263779, 52445887, 761691225, 202495279, 263226630, 435657016, 985971715, 569184380, 10670315, 301504587, 953486251, 967877969, 580582297, 110492525, 700102901, 167067531, 120231867, 643977376, 838702292, 704747757, 839695866, 518982644, 853638102, 852584109, 515578729, 801176792, 662175091, 694233299, 138830241, 642920291, 3771778, 514875037, 225409844, 89165750, 254124568, 702050596, 168609599, 723336007, 943656729, 257717500, 715507424, 430273826, 963618412, 420328760, 251431713, 241402727, 87126518, 887171075, 914194041, 624022299, 697716124, 543370037, 426588274, 861937974, 291875948, 814449627, 119075357, 554537271, 609175964, 587437976, 66897890, 148011409, 127543800, 334028084, 839105441, 67216654, 961130750, 985685449, 348007111, 439755050, 605672068, 190596560, 559795213, 690630247, 898964185, 79085646, 304379390, 477499208, 798992675, 282557495, 832113545, 471861974, 304901143, 184258606, 975086745, 566155308, 728010165, 527325732, 669719618, 407921089, 389241315, 551104161, 539813563, 6506798, 258400318, 831877216, 246566730, 377031551, 243914036, 524770674, 696716466, 275284050, 3744158, 305972490, 348569725, 655733622, 226255609, 936640317, 305582424, 532352249, 538780239, 396963705, 746079824, 800621510, 985028541, 634956467, 999438714, 313214019, 210715275, 504734596, 522272488, 276193898, 339333252, 316159507, 827777538, 404511, 373412213, 624844419, 103363583, 622908077, 179301439, 549012827, 392506821, 665545683, 515207001, 62563746, 60927088, 974624914, 62539899, 602493548, 883975212, 321338858, 710470967, 218365254, 189244642, 702018159, 875354499, 825180266, 779666231, 988308612, 381075183, 892719287, 279942287, 556511052, 228622161, 315652142, 954219659, 742018849, 241680472, 529618305, 8933814, 794915293, 207702274, 595275272, 885422280, 254850412, 185504896, 915300609, 193917588, 160356309, 921692641, 40357060, 567892738, 232232689, 159263923, 245108324, 911791358, 465616485, 8296737, 725076321, 633415659, 695497019, 850750237, 703425692, 711323824, 391576335, 836214082, 186215638, 472505205, 881968389, 509828434, 150578706, 94533780, 465573745, 334367690, 328966707, 22061494, 86178716, 420770704, 115609362, 267060927, 83802503, 524101728, 40612967, 24520086, 4101101, 442973024, 178160811, 372755093, 228225013, 486192871, 620791447, 969813012, 853986445, 843592080, 627298019, 205054981, 508425718, 535200878, 766114139, 62776973, 869533654, 243704004, 841811692, 136867411, 73010518, 433487268, 165198298, 802559780, 986455328, 435742092, 110608922, 436189129, 397527781, 440574820, 849837114, 759026467, 440979039, 487904246, 848926378, 72013264, 629446951, 287486633, 564469920, 342319085, 941301495, 184170969, 11274716, 677361774, 295397427, 805672604, 752698059, 836435251, 926657751, 104413984, 24090721, 810595632, 218340693, 259296732, 265896322, 518604846, 938415160, 829356750, 277346667, 741957993, 567181608, 641411451, 467905144, 903309100, 275680565, 508752404, 144899734, 471454438, 36451896, 349865293, 13239527, 42962529, 946739010, 198783189, 790291755, 491176344, 390682005, 750465729, 971760660, 857225958, 229775687, 317718567, 329317953, 368233939, 111339297, 259308738, 971368358, 558059011, 622438081, 186337388, 899558844, 201742131, 236841628, 863128123, 441150365, 99257840, 853272183, 847355108, 633079057, 164862179, 844962371, 917628073, 200462954, 797936691, 282567297, 290539069, 869049780, 456795485, 420568615, 434560790, 876300997, 795065136, 437349548, 605178698, 256901016, 853964140, 490905702, 66295656, 439444905, 177198442, 898364849, 291518030, 28515732, 199503407, 229599556, 252539721, 106219886, 403868944, 881965300, 873168713, 72815588, 143999370, 2826093, 277280192, 561480991, 788991056, 442705751, 854922784, 529192545, 569536905, 289710788, 745306595, 136139293, 835603732, 126811268, 168564423, 937564167, 101090314, 951226330, 96135821, 816007059, 358609069, 778065673, 645462422, 500331020, 145082796, 714915509, 364177462, 332549510, 583144072, 922874642, 641312519, 515459533, 608030244, 144940595, 836424354, 907649413, 337251610, 875563838, 960302720, 53540678, 597334451, 281236972, 601827522, 218815975, 456579359, 99924523, 274332457, 798607558, 393024863, 155876937, 880212564, 515285757, 972515866, 240662088, 480314629, 638119683, 980236267, 277495537, 921179933, 165028445, 612591477, 641627511, 802763530, 789299235, 334409767, 467200516, 680248848, 362326768, 237048199, 820936738, 344498019, 502552077, 474588289, 755876997, 261309370, 718377667, 391489767, 528788049, 712477560, 671316714, 67575332, 370151912, 199200305, 712744074, 777806943, 974599348, 365620272, 874629263, 489240177, 9909076, 195817063, 138756879, 498032485, 914975855, 861837770, 932270905, 849957738, 280115650, 830347169, 419465764, 890683419, 852339798, 908768764, 105688457, 683319820, 556534531, 109332587, 400718170, 155910708, 47274964, 506130433, 205852542, 932773618, 160871180, 579686907, 744649635, 336196184, 514630580, 315864478, 227684599, 330868371, 837387613, 192528527, 414254607, 305676725, 74946339, 709967307, 702276239, 20913925, 73139724, 552283874, 280904536, 179369719, 788024167, 949693725, 840237145, 511620589, 426443482, 831940320, 297506106, 706304974, 968238058, 810547796, 212555071, 833120839, 57037685, 88788643, 469975793, 177567093, 251815856, 488609105, 637536492, 747421048, 86043301, 104907235, 259304280, 305332132, 800504653, 827505212, 235947912, 157035786, 762680689, 501627794, 641421845, 214520658, 330911620, 112348813, 486168408, 80908449, 146357047, 588603774, 922618833, 790777531, 328027076, 373440832, 876372212, 336677425, 442182997, 158577086, 872721279, 941490172, 192651100, 950121949, 920798984, 130388246, 863589845, 19446199, 327015466, 840746181, 431984306, 179483013, 755393712, 713851509, 48893701, 746018419, 883765073, 504331758, 772146176, 492272017, 820357695, 96557021, 181776954, 810717424, 849210412, 539462837, 143897315, 656963115, 718944886, 503637592, 848011186, 639542206, 91839929, 163567111, 766979571, 929706502, 530631158, 984312871, 323518456, 360147516, 652364881, 82667630, 701437760, 561343444, 884628159, 800309479, 114709057, 996311855, 191561700, 835505038, 785966849, 195355266, 335323656, 677539884, 813447989, 642591856, 440732280, 243592343, 539772141, 448568103, 368439, 926285248, 407496359, 465644514, 374977968, 654827506, 608940051, 696145267, 229953602, 671488569, 401866260, 955620428, 379557012, 178148842, 846984594, 661771272, 29992296, 795765512, 819535483, 401510753, 666044510, 107998653, 294570892, 236077416, 841667007, 450022919, 163798017, 226820088, 254389907, 62878284, 462315333, 316403723, 834036694, 982580324, 526159765, 443185818, 660846445, 655471346, 656236737, 388712220, 527999410, 503115688, 436033529, 386566699, 284855684, 411923746, 291591914, 976780907, 655086673, 415214020, 134176614, 344742464, 274113781, 764521887, 448455857, 338619148, 287736785, 162069939, 117767146, 275269128, 807980183, 677592470, 8904466, 745460311, 396784442, 658191692, 749474761, 708722704, 249625503, 825965333, 608221270, 638051186, 815263493, 133260362, 144562719, 19128252, 157197069, 54085982, 814875594, 918774832, 74595292, 254206875, 428777065, 197076641, 398703085, 754236479, 483148150, 297604206, 576962887, 268988626, 11444175, 788397289, 89084187, 46440800, 899715607, 353773910, 123897304, 177489192, 569151664, 446858813, 179152220, 647193939, 827142314, 542051267, 980309899, 361641513, 761723933, 376737494, 32352898, 920581336, 888733704, 754344285, 420471035, 242320418, 111758437, 156354479, 547979653, 925270587, 753842520, 836883444, 723807311, 323218780, 802348382, 397097667, 799371886, 494599852, 497658110, 160882593, 159581809, 925697188, 334721938, 778808286, 983803792, 776609535, 346172535, 918514437, 342048235, 32592503, 959538230, 195752510, 744200025, 394958806, 307067966, 353056174, 33357541, 938719452, 452487831, 953736525, 91538788, 835321933, 14662852, 443620109, 14095416, 144582334, 994428952, 221370093, 103816330, 98298082, 112446481, 600099800, 711657368, 795741820, 633351938, 726944813, 878378807, 816659384, 893894872, 170387843, 101248467, 780188561, 232870519, 100191210, 701316031, 934916654, 381443339, 271151078, 16061899, 555248202, 384163349, 243688415, 186707724, 181546269, 982881862, 793197865, 157356563, 294952851, 712296288, 512313225, 524785900, 509117492, 580503429, 54443948, 471755345, 231945366, 898195979, 577138597, 665437838, 542329524, 636620541, 800157571, 442215366, 763596409, 753082067, 547805195, 28688727, 805401858, 247541501, 994492692, 793923218, 237178686, 23781941, 892887311, 987643794, 512890155, 563210268, 711766615, 179719485, 212756355, 73742432, 382040913, 774234845, 205608438, 854970604, 164895028, 685227628, 372574990, 925276444, 625419536, 924633282, 760830483, 193763574, 322690107, 110547838, 390319102, 9764992, 666607406, 596902685, 704233813, 860078670, 276497234, 539034905, 496237162, 842637053, 419044945, 855505890, 433189403, 566312060, 757874013, 292867504, 505535174, 579310212, 629836768, 519980530, 740237456, 785080121, 182857255, 193003601, 306125131, 760482231, 221069619, 23281586, 50951787, 627041767, 394223034, 345040045, 522402810, 559968319, 967357821, 722768843, 308243634, 356074991, 138330983, 206517606, 504999298, 316690866, 781787854, 730038089, 443241546, 827104287, 887527553, 994389013, 123938452, 826720655, 875655865, 40096583, 35868985, 70578375, 413040676, 734511721, 595441334, 217820515, 488429076, 701007791, 373237357, 959452237, 823054378, 446916771, 794794712, 45757616, 324422755, 893130620, 929906956, 152967620, 319906422, 968499608, 242568569, 136420576, 519451491, 855656183, 209941780, 915420147, 659835020, 258855951, 614218773, 390749259, 809895336, 69838226, 978080798, 4451337, 229525206, 378006841, 235753620, 581779628, 599071430, 634992492, 237514092, 572161015, 861061659, 507824284, 288165143, 544004313, 267451446, 912100705, 94788648, 183437500, 753406036, 12432273, 684497887, 213046242, 264929465, 87924610, 400802719, 714474667, 383870118, 953745055, 773467227, 751995346, 835241369, 803242010, 75760351, 706632759, 914426041, 849689741, 626645148, 387408606, 522871455, 503465847, 1729239, 204875998, 724580790, 548482794, 855194613, 677692557, 382042476, 136310466, 100902360, 394146739, 559463761, 41107191, 619307704, 451782019, 722842261, 149202340, 527929095, 343327334, 920041714, 219151741, 317773804, 458774067, 685976648, 633156451, 777288513, 659875617, 620734796, 8115781, 558904445, 330699046, 297100803, 554252897, 339945449, 476136590, 882302308, 195207157, 752030133, 272891517, 328986697, 251616238, 664269252, 196420510, 805880467, 854818014, 210756638, 249295726, 428617938, 625638643, 730338466, 665259552, 913610988, 922224435, 935479998, 860773135, 995955771, 24363542, 344616096, 947868060, 480512930, 152612131, 622120017, 124009538, 502111162, 592556549, 131060674, 857640290, 874666726, 597017294, 215423175, 556002744, 335166160, 904169195, 903512268, 642377639, 212574978, 744202703, 934083146, 680193481, 861236406, 38755038, 625549379, 251133749, 522494355, 983260803, 307833018, 951707517, 7343783, 879548077, 326575680, 13266689, 618129471, 367182622, 761849392, 298946502, 74787955, 276543890, 128396197, 513046135, 680524730, 734006661, 792220202, 450212445, 893453299, 403043622, 403904202, 219848345, 157546738, 143047633, 520125776, 127098725, 862051562, 134306797, 259182772, 952689403, 756217931, 849226779, 861479970, 407907674, 278948920, 846587045, 967091984, 268524589, 640266995, 933732723, 534333384, 63235519, 373127757, 569866842, 536893168, 618479535, 529273212, 774455488, 418720659, 344864787, 639182936, 893706288, 370166368, 828943588, 183280054, 280052755, 143907082, 831798117, 51252617, 866280316, 29391423, 894713479, 47363760, 709241223, 178544838, 171614155, 836965301, 580863284, 692624323, 662495888, 175860559, 593046462, 312427681, 440879106, 160234840, 759852789, 475589953, 67835563, 223830146, 36253693, 857787674, 743318455, 842785511, 595012565, 537718550, 247268777, 688942075, 50901933, 408962850, 79257096, 903182629, 493630287, 82240673, 666667994, 515728885, 143243634, 124009221, 348078864, 900397983, 713628455, 752490658, 767118452, 120968954, 376516280, 362803549, 567928938, 131544933, 615274934, 189237423, 752629039, 779423227, 937898757, 431610733, 888481298, 777958954, 3772096, 997084290, 251486732, 267646194, 886407238, 400149833, 675847101, 289977692, 586440003, 965753275, 190138075, 473771493, 741250386, 853379567, 546504436, 385408901, 905068910, 514152059, 357123269, 766383861, 171671325, 731494758, 863186618, 800420383, 195468904, 707940452, 634343068, 184648244, 920607596, 180660510, 540353755, 524174021, 987969893, 660594493, 502504720, 239235074, 317492939, 600247330, 542988347, 993254229, 177307708, 679297616, 787255843, 368037692, 403728984, 862267268, 728021653, 436335289, 561946925, 294414990, 120604902, 216268433, 558629722, 308355883, 688752881, 742786498, 465575636, 455544983, 780087046, 319661645, 431726641, 405090230, 852955131, 493880700, 74595975, 170584942, 299050742, 518414702, 605125202, 935908407, 909598635, 81898604, 928657277, 685835291, 901735937, 412609179, 950570473, 738222487, 491394226, 304634203, 404540954, 228423653, 538899781, 267848758, 769219690, 696890279, 495687599, 698531125, 54264632, 67548286, 650572968, 985402864, 760108730, 593032848, 555231717, 949425112, 747102551, 494610245, 887570291, 691230408, 833036030, 115079861, 424798710, 125968155, 374783846, 151915334, 359222259, 845575540, 405534026, 670244493, 519851063, 951660848, 945236610, 54872024, 741906152, 44655901, 352336743, 586772229, 990520565, 966938820, 593727091, 889281087, 581663579, 169510, 747328881, 400448899, 479154834, 686325590, 459304478, 722066541, 335417196, 98275071, 361367558, 326683862, 173569818, 836694299, 219038141, 91650008, 953673022, 598888866, 364291302, 45150675, 690194250, 841648058, 520655873, 761978087, 789020790, 84838839, 155741394, 452635457, 187666921, 802402775, 975660920, 909167547, 769476319, 436769058, 669150326, 767354272, 475024577, 1240102, 667815512, 39408234, 377346150, 798680526, 926737793, 14628095, 691460568, 66239560, 885116470, 220468129, 946508311, 524054958, 811121729, 68017249, 938921694, 513449358, 330071777, 950474895, 953684618, 848714612, 957459069, 500039640, 128637637, 97127304, 100095193, 524635402, 850509084, 291688432, 660856444, 921667524, 248997293, 123121241, 510057096, 224626672, 521573178, 273462494, 452256140, 4055520, 390275419, 921264594, 422278561, 102047182, 20554424, 51293195, 245093644, 407149180, 925690102, 520245031, 919073486, 751701716, 135206552, 789303604, 87105066, 373680962, 789135409, 454036279, 627942981, 924865253, 312139381, 152771610, 49407893, 488882074, 587008901, 465960235, 265116692, 155758580, 30509290, 273337605, 189109861, 142854504, 49035427, 674270223, 349238696, 681997226, 6203812, 236039496, 4241982, 448518696, 181043515, 337989413, 469422763, 8746846, 404507295, 572142400, 521897837, 572711705, 52706405, 41200275, 829782735, 798684437, 153476329, 77204318, 384520567, 243417784, 765459794, 323189912, 748247311, 440456663, 955883508, 182914326, 744610157, 841448884, 376612938, 760561700, 652218625, 845134273, 54936426, 206011691, 370738980, 570651447, 746960097, 694717876, 279158420, 478964424, 692136995, 222525178, 819192097, 458784290, 367166537, 240148067, 583025415, 876173110, 905946779, 756825527, 760735350, 489436035, 670991439, 515957368, 365398856, 708070110, 713445500, 777624352, 897561217, 91129301, 728049700, 782302035, 998276014, 630413315, 683950393, 181443365, 796518034, 127543039, 806821145, 552317928, 423164292, 48893362, 212925868, 568109701, 479181840, 226400581, 358922000, 708316350, 963868441, 162647428, 345951633, 403125558, 253569382, 806938814, 274682382, 146101202, 876863834, 370207321, 538965902, 248123947, 150724922, 277452362, 169740630, 930282512, 391436449, 239357919, 308727784, 170868534, 747340543, 733369172, 229884628, 476981602, 243879274, 468470738, 780243521, 294536240, 902801220, 933012609, 908906117, 646633730, 917488309, 225841513, 854494839, 192084228, 231109777, 660040991, 522476308, 950017555, 390620771, 278533750, 992481517, 698504522, 509835189, 129087413, 633710917, 16933368, 753910721, 539931663, 20346082, 590571682, 294645497, 726375855, 216212909, 414015886, 32597803, 28668272, 446679320, 422154640, 270059626, 991070652, 730206614, 424632321, 882637673, 473703010, 649015504, 889191062, 347572214, 921661337, 651477777, 182399655, 317500126, 766906332, 668128116, 663392617, 957301072, 746148302, 852604785, 180017638, 731166389, 353106492, 908401599, 413236400, 812515656, 22411953, 766521031, 564514165, 722241718, 191764041, 115647844, 444433391, 32239772, 710675047, 169017470, 155364053, 902210281, 546095837, 917184986, 601233657, 27182138, 238360458, 964160462, 959276609, 771590866, 996640454, 905369934, 610244021, 699393057, 513606210, 883829028, 244178150, 519040379, 723129320, 470753376, 473528252, 879745059, 596595560, 397897423, 467492083, 921099332, 880769847, 271291500, 657414872, 454981422, 532480930, 314577755, 940795090, 765646340, 274724207, 314077446, 876069884, 751563425, 926995865, 257714606, 944861989, 113599099, 150005398, 971439806, 830793982, 39120374, 396450381, 378057811, 996148710, 611278782, 518656498, 649374468, 973899284, 977336521, 481414473, 366341789, 661000026, 194207183, 627034979, 96981609, 895049463, 334305899, 744419888, 455142153, 446588904, 679797473, 873160251, 653843571, 769966969, 832290286, 32902901, 868343108, 770515251, 230276019, 205951235, 195454041, 546286386, 204371028, 589218473, 895920105, 850783613, 761761197, 345638863, 318342676, 927633712, 753193876, 886211002, 510963519, 124885556, 884570341, 157638712, 590178653, 98945377, 179808775, 536235030, 937568974, 288712975, 948274886, 331881550, 634353857, 757393355, 673292867, 516125830, 31016642, 414063610, 744566339, 119299730, 257348501, 662277552, 677976210, 632514767, 714022595, 356463512, 445835172, 81112790, 60822693, 263284653, 279148857, 408619834, 365426834, 613869908, 518460288, 856929592, 835542313, 743906765, 689328836, 348966221, 178233141, 946484780, 83300550, 617207220, 424121271, 775408201, 948766486, 572270908, 665503795, 420516896, 568600027, 496372718, 59805556, 159753333, 439754766, 774779166, 665732821, 513252321, 165813046, 427552777, 501248545, 986746273, 614019304, 662789410, 433093032, 514183858, 595142926, 267506055, 743242572, 668053761, 122006443, 242475971, 260320454, 486761238, 696471514, 741174514, 208470595, 709524602, 745688379, 721395404, 905013656, 488037690, 961898348, 393301049, 957946703, 318273541, 356614873, 683240152, 86339491, 252242303, 94772817, 686975064, 218819388, 222598502, 793847592, 942507782, 379082810, 87699605, 90765238, 505825969, 574261670, 430246184, 111393731, 138889203, 553104504, 362692526, 262002398, 198327426, 355650958, 614774966, 75930059, 37748405, 869753293, 720137860, 290784528, 658712397, 154138801, 75545878, 282424477, 437472567, 583073375, 883778440, 120452853, 905154520, 389495379, 364552523, 671337402, 62006873, 559141277, 723930066, 294170345, 441937041, 695763151, 789022551, 873471553, 727356072, 943602610, 869219821, 546139355, 333760421, 490314792, 404718155, 530598927, 10561213, 1655766, 660561122, 957123195, 102888535, 523370502, 19913423, 340470814, 614001199, 894493343, 643584745, 724740996, 347205444, 868462978, 934462456, 71233720, 192820269, 341894863, 483575442, 363793392, 615703899, 41530426, 610643618, 711175407, 315383461, 470124807, 549500251, 387619570, 39353463, 74161946, 257432427, 598957091, 79122299, 515605309, 171144850, 222467704, 876312958, 869008144, 906359354, 991046768, 887358959, 2998062, 42244682, 606802457, 820435030, 945278257, 348174532, 197265660, 856048928, 137005063, 200412656, 219275767, 655118783, 379829483, 82033627, 823449813, 433771475, 35616642, 803939391, 778527095, 384390971, 993844785, 613163457, 145936581, 69209030, 645028096, 793305241, 149351846, 182304576, 12578038, 745135666, 479011947, 937781590, 573695512, 172145588, 753876254, 159388559, 901067010, 212489162, 46282452, 789315904, 549845880, 297953397, 296966148, 245394344, 915256516, 105541877, 616629881, 752031544, 859862792, 774746839, 720778857, 449118578, 176251278, 713918570, 650596473, 681705411, 840538642, 337062281, 363127289, 74395005, 72504180, 793721771, 752608346, 87047545, 851317275, 611117093, 284968102, 465771374, 63277870, 547255317, 800604665, 447471624, 692163811, 947039758, 244037322, 817926984, 837787465, 156086647, 38022451, 812879600, 585916860, 966561067, 112852263, 961926386, 587938845, 725168147, 506505927, 581105151, 816047833, 8301876, 154807495, 962733270, 88957551, 649268502, 833104028, 574493744, 321080055, 947734638, 680301625, 404047114, 182546184, 885050286, 286814353, 2185749, 403312728, 656366850, 127723420, 986602305, 25265407, 467338417, 766081880, 206507203, 548629610, 755640445, 943757217, 955201728, 793809133, 678977614, 785091445, 224179967, 574428045, 187276613, 212216011, 476993387, 330661161, 947227302, 783505883, 330122322, 872326336, 639332590, 867007043, 536251238, 574261285, 93741686, 377476997, 656432266, 87986425, 681180316, 341937178, 597909811, 261930500, 945645394, 856226259, 103829619, 706837737, 525494369, 487643794, 299100051, 673781646, 488944536, 831900591, 823626397, 874546888, 582111677, 312106010, 961333147, 341349702, 576227641, 345038902, 820709580, 95910474, 742330081, 236433005, 863855223, 955053645, 18955068, 765990187, 604595588, 90773005, 579390670, 804286690, 424355703, 392307454, 509890995, 944483786, 503989989, 72616422, 373958548, 685627523, 368543567, 649617295, 473788300, 802095688, 365984053, 589279509, 267911886, 83021921, 402997984, 163397157, 752367138, 63736686, 245444917, 502356088, 722780469, 671373429, 951560541, 431510277, 728323178, 316091121, 643170117, 466419457, 196685183, 123538430, 133895657, 749004938, 873324928, 33141694, 861230019, 724775758, 691914652, 940196512, 500792776, 116815233, 594381666, 177571067, 621827302, 333167191, 24518101, 41413284, 985835482, 253500590, 131041651, 47425430, 283229398, 526393103, 426116867, 804368179, 967914538, 125995, 513875641, 131545703, 714140748, 263719060, 434528109, 723135746, 277656880, 924060868, 999414453, 571799130, 771451146, 82088849, 23304534, 746797883, 222291299, 48003783, 650928365, 282129789, 792408087, 867699649, 672170461, 637690370, 587971474, 751450500, 240910046, 859915261, 476689021, 515299494, 268851858, 162318380, 757549326, 432181018, 395410942, 648953140, 372661969, 299889815, 597419089, 574247071, 446836127, 321471354, 251867548, 750304051, 98016586, 952207722, 191611246, 939564147, 642666568, 250773804, 644257420, 100685236, 745432999, 807123894, 476509621, 783167225, 673158218, 576445771, 222794393, 162270810, 122510261, 531129174, 805902143, 410790143, 713749862, 796224386, 28950555, 530345152, 447456316, 989753525, 578911610, 158583159, 446332158, 545476761, 848704269, 727022531, 320462380, 891327663, 586601136, 314131798, 392740852, 898516130, 252751982, 312667117, 363303407, 541386308, 865143620, 182257351, 580193362, 802275639, 824759852, 525439636, 388098228, 203398436, 752045221, 369779165, 386862766, 576989726, 652408367, 382023340, 801511857, 203692190, 48505396, 665792738, 628258887, 970107321, 456581835, 637089456, 479399978, 762098105, 949752544, 247484042, 665546735, 53578362, 72409449, 207886600, 272963010, 852085119, 349199065, 997446837, 132110651, 483227889, 841775473, 904714774, 637153119, 461450708, 866296057, 869699720, 871945485, 252634706, 165916156, 25419359, 727507135, 306169115, 719111750, 569152385, 211911820, 593314160, 635763587, 612017494, 249834684, 791446420, 969597938, 792215812, 486059857, 418816021, 854883057, 741272462, 307090607, 545227223, 616807784, 695520764, 157825147, 55509894, 54710947, 401051742, 473681414, 944705836, 921281938, 827728454, 303228186, 54022369, 583885208, 663372368, 314649148, 18330942, 277414561, 379063829, 374890745, 647224851, 218624519, 413977447, 192128488, 709650413, 797742594, 188326760, 499040377, 290456690, 868918357, 750120637, 92502220, 908241898, 293404537, 19540918, 735762928, 116535022, 796352966, 934971322, 549772703, 386513135, 329675703, 906195310, 344580588, 655507149, 261342670, 691907379, 621894058, 625898307, 967726115, 9506399, 13894509, 642691464, 843466097, 913057040, 304446047, 657632942, 733974725, 679099910, 118478591, 62437861, 371440432, 740846538, 314904295, 251969414, 981295152, 937476158, 67969020, 56926822, 446274134, 197867013, 750491124, 724167695, 618650134, 91124791, 795024561, 782726988, 610955009, 73229578, 908259936, 861284216, 42684369, 565533247, 313307291, 908117302, 351066919, 33239469, 368494655, 349932206, 326267105, 777069220, 949141388, 646619187, 652104188, 659108573, 613979572, 519970523, 896761232, 581141366, 507251213, 614134550, 281389976, 762692361, 800521517, 614476007, 84739727, 417597618, 473244106, 392515412, 842326800, 76899402, 179857924, 135067205, 159035886, 891228001, 545556682, 753058673, 713208623, 299539686, 693010361, 964493849, 28068328, 926702974, 162495044, 110731502, 827530711, 219214657, 437739407, 265925030, 741645973, 291552034, 961403175, 268381107, 123526437, 345563092, 375371427, 671887685, 529128824, 403941709, 829345245, 680157649, 271988229, 822422384, 744333955, 583108432, 851826443, 775330832, 70470292, 123379714, 369449503, 846994471, 384764634, 138473055, 99875115, 137296701, 961097037, 654124429, 881782127, 817704544, 236943234, 65069868, 850201763, 687215016, 72518897, 827718835, 855601984, 331061912, 995218631, 344980723, 485754731, 692377712, 265864576, 176031367, 874185570, 829201611, 498816735, 729062668, 230573439, 832506515, 344535764, 918813240, 358594145, 461637754, 4074483, 376639845, 640937829, 257651751, 255618037, 701840512, 291789657, 645080074, 846832358, 295880587, 570776882, 763833156, 757574934, 571754010, 470087913, 397175663, 261004695, 267569676, 96886704, 365446329, 334423528, 122846927, 219803984, 288277520, 30005991, 423214481, 706769011, 886131332, 428671501, 701919854, 917312345, 819274147, 232048440, 532663351, 26612983, 648436633, 89617310, 744258122, 540694038, 71300066, 469029651, 115578805, 818513700, 176350856, 485844976, 26542856, 51908940, 92134759, 372112087, 257659731, 711577965, 424012070, 638424167, 185205609, 299932715, 135648636, 770150606, 992311672, 384359187, 6314245, 435080047, 919662150, 733393941, 976395414, 439370250, 763603894, 701495011, 719402320, 293600071, 391596044, 36937169, 985246774, 918964476, 295079198, 726364368, 955987565, 745590535, 60071943, 448622840, 16355419, 803631002, 348023011, 258913618, 40210488, 67483000, 795675437, 129354431, 198172990, 736735054, 916407434, 92381533, 717064368, 957434693, 158049568, 4026733, 596285400, 31160033, 401877756, 896552089, 161288612, 284432964, 77730185, 71374632, 147745860, 149376058, 558478618, 125708246, 582813515, 283714928, 939386391, 786369308, 48007517, 496577379, 865930736, 265086092, 545035943, 398122240, 838068375, 91843685, 662420646, 665214562, 151213794, 324608622, 797196930, 135862821, 653056181, 12054646, 817436559, 556914381, 613263381, 735121997, 310657433, 903410263, 610863497, 694311387, 597459204, 122168567, 409246243, 126030708, 476919633, 781551419, 38237327, 466755438, 172987115, 948450172, 950565806, 919799338, 811451726, 892843954, 121019450, 971918178, 366472010, 880539528, 926002533, 841147378, 629584804, 425321941, 44427657, 474185481, 782303056, 605971090, 279027766, 182544206, 323951367, 885627018, 643868531, 26036143, 794586594, 313312796, 644735878, 370759302, 303716918, 645740256, 947883099, 804812889, 820590077, 918489339, 721503268, 365478558, 299305986, 209907412, 730608442, 206613969, 453180033, 660718401, 712985456, 792820281, 440369194, 588452859, 525355316, 447586143, 755416500, 184099262, 601680342, 936501763, 168354080, 351198187, 270615434, 118281395, 487197805, 606971477, 422710473, 869408144, 58362397, 398455366, 921993621, 302548509, 940916216, 595126323, 351550489, 813117855, 197350801, 505510241, 652647209, 676400268, 873083195, 254842234, 737119113, 981538986, 216184867, 38984402, 603641084, 356706006, 832542210, 701629353, 38966880, 934486007, 222648011, 524034106, 679401823, 42995380, 960887587, 322968955, 837481611, 505458966, 837205523, 310958291, 834218518, 188087320, 882530642, 339309318, 5548886, 774186365, 55126581, 153329408, 921843297, 962838481, 37318557, 316558658, 405898964, 302179009, 895008428, 704980201, 115692980, 616289619, 30105671, 422470965, 372147688, 408975359, 834374490, 128690535, 238091114, 300107469, 653235283, 258696689, 723754292, 799250810, 421436297, 426875724, 627379467, 316862194, 212861259, 292567870, 72587094, 107057928, 625158626, 354465924, 889605769, 535516522, 122320974, 780222492, 155762412, 78838290, 542993075, 783741614, 114846801, 191170335, 618906683, 833549087, 978333073, 325730972, 973008, 554376578, 185567868, 631064278, 504426122, 703966597, 879759001, 668378942, 267525919, 373125639, 800582130, 554317752, 453395563, 253144815, 871047699, 440162809, 762511470, 246795969, 3579179, 198432037, 729627349, 183011607, 81956275, 177823323, 969874865, 289999843, 768770324, 308152815, 951109195, 587550959, 787866073, 971240919, 455934360, 105520866, 154224933, 488503671, 467933927, 803585114, 287435763, 520722140, 166885373, 8939219, 793981255, 990581313, 584048593, 894308833, 175327895, 268133876, 783004518, 374119071, 509002841, 342607118, 610283614, 202107234, 832545698, 787162571, 380143043, 658455643, 642195185, 421062846, 687232705, 542563480, 413958315, 13354060, 561120305, 191377378, 148778803, 879879478, 345584778, 265107426, 473617101, 733407333, 245029493, 727291088, 351145573, 221766210, 297243697, 589953149, 122058881, 793146176, 871389499, 23008782, 103066808, 54969358, 337834797, 796335826, 380660881, 592741120, 290920908, 110097776, 273945345, 870191289, 199250902, 191897106, 929821734, 726201181, 336579445, 281945530, 779486459, 834732610, 296483037, 115386994, 801314465, 90005670, 242641004, 498780797, 650934937, 829729989, 6250055, 101062684, 510419173, 935009964, 469728953, 864435170, 297382689, 641711338, 792558054, 569088398, 632214889, 19529133, 673514825, 570700647, 372659095, 995517719, 504625940, 680827544, 545368950, 139757300, 330475496, 822195600, 608280164, 836918854, 257080794, 547138487, 128477153, 49950962, 260424626, 949002067, 539697789, 234867684, 932434259, 617144487, 214506720, 310608065, 487426512, 938616751, 694102541, 882031404, 801767510, 330399357, 882424482, 619783792, 957319597, 36837235, 126289994, 857124975, 167158044, 42202751, 207618356, 60578422, 210951858, 807769611, 622706717, 43516881, 699573099, 69431193, 433951490, 807351713, 188505355, 930082086, 739657821, 575015213, 648746156, 388392514, 783664814, 146620680, 393808379, 676070677, 800329032, 443080813, 121171833, 582628487, 822863124, 766830521, 417848240, 880487242, 496710183, 345637463, 335913816, 334488710, 539291505, 846870684, 573024946, 614748148, 278225405, 197956896, 415867284, 474940220, 228240667, 401282812, 145136335, 850879366, 860862769, 674030433, 898699841, 967407218, 662617711, 260188718, 932013762, 626485223, 710311892, 919647569, 884764728, 239049497, 934246996, 307796244, 279059173, 863502994, 842756157, 270302447, 56130784, 486427142, 760955528, 666183411, 497727643, 752235514, 659196962, 236376464, 691304709, 488308301, 689772466, 752922075, 896850820, 432766454, 900536164, 420451421, 142067254, 888162318, 202914887, 520189869, 252528423, 896148461, 43309874, 428623004, 797848884, 284223150, 970300636, 276153878, 648219937, 806889623, 215699788, 414960170, 647343680, 238556322, 66819800, 253863080, 990816576, 423965666, 283460600, 295864556, 246515325, 334535465, 185680846, 578869785, 643925029, 537303246, 140796824, 689568371, 736265660, 846745205, 606636577, 262227356, 402192667, 748165969, 278305242, 216308487, 274764669, 208516067, 732852660, 139190700, 722946743, 615041488, 113938777, 739573071, 76085666, 846167554, 624831917, 885508544, 553645561, 757273194, 72797776, 61337061, 710864480, 888834643, 430217005, 596819200, 595973776, 47590668, 792272784, 601856027, 9053409, 480606165, 976467583, 93304345, 673009343, 326872034, 894337989, 32740638, 369059188, 607650689, 325167476, 852837395, 760362711, 463437657, 222280471, 836898076, 390258311, 458812261, 630259595, 669545286, 83700780, 652489418, 783383001, 664659386, 999119745, 606554486, 646490719, 549950799, 890518905, 634425247, 303549941, 828537048, 297274988, 744411503, 162456648, 844079218, 697602220, 738468053, 702546518, 664229719, 298094871, 408468596, 358906145, 175057725, 428280163, 123494983, 391145240, 174527561, 919408225, 425567432, 425694693, 352398821, 651850835, 116615953, 850325737, 20890832, 300926530, 486196326, 576737184, 84930926, 544794690, 373186036, 914998246, 552748274, 270597679, 715147765, 52825746, 45715533, 293806876, 164867075, 304794208, 312531638, 208561339, 461238696, 635338474, 286591171, 895830041, 6137051, 254160041, 431842319, 62217269, 959100097, 585989663, 455950, 428199474, 168396950, 442832694, 423898529, 157721403, 795525827, 530459192, 437695038, 442886733, 678463458, 841337099, 942179102, 538435426, 273866141, 83783746, 527033168, 373121825, 206212702, 737022124, 989889910, 320877500, 683326707, 741004540, 573971213, 635449523, 303483178, 10873287, 805273541, 810169506, 786856008, 448378925, 207321386, 776403854, 70347931, 489768159, 493131075, 573773683, 123215004, 898359890, 233290576, 241393386, 464880394, 996090898, 827974790, 418846058, 300129056, 775253067, 770333095, 670684669, 666460806, 504656866, 390695524, 806826378, 277468755, 519047091, 848144932, 823833906, 525597093, 525167158, 51213398, 993312138, 144617802, 851807999, 333071486, 561132867, 618989000, 342119032, 583203138, 484486484, 719142326, 245076259, 752838697, 127840864, 582856190, 337220623, 906600189, 363494024, 761332774, 558074157, 900177875, 66174970, 71387723, 41694087, 228065795, 82339314, 814630477, 678892835, 555568471, 466379686, 997421352, 133772779, 27582946, 661670372, 51989283, 198252047, 997003270, 320012117, 320160541, 907069135, 83866473, 822572240, 382316892, 944129569, 657109212, 433291076, 565217204, 938290874, 72537938, 659884132, 626493285, 739705769, 580969423, 835569731, 302617243, 107264369, 25905280, 715361231, 187268133, 253749628, 691551820, 651518567, 795458124, 241637971, 11004841, 134621212, 553167367, 42264991, 784860869, 688180260, 747787763, 180715356, 731896671, 599916432, 133942594, 936275730, 681218923, 745671286, 996671653, 42166412, 667810006, 455941547, 139318322, 565118063, 941224400, 36186815, 166873507, 520262570, 262884483, 731472898, 197882711, 611595984, 958089760, 576734356, 995293320, 701309870, 774629810, 977683103, 471192241, 230746500, 308941602, 782582665, 746981066, 503189902, 242622443, 144004851, 219764093, 69797326, 135369879, 195206200, 987949131, 3870140, 121464369, 177226595, 40680502, 331614277, 433641582, 544475723, 337862367, 464517350, 481273221, 797106375, 443013777, 517783312, 162363610, 136048610, 10331468, 230640476, 898641863, 78431535, 120253436, 110905862, 947648743, 117209500, 226352874, 213526536, 166660411, 254702766, 256979993, 169681677, 513398699, 603487934, 528729207, 493408158, 793660306, 713179061, 157920112, 110350264, 353286349, 17160461, 304475789, 806254612, 413475701, 961069815, 84559904, 118309233, 247192970, 45474104, 425187152, 838209941, 477007512, 8990173, 306531001, 632855156, 854961784, 699122457, 160588927, 264533675, 392528414, 202018487, 378289105, 610141226, 919733698, 694704368, 60013571, 532393389, 413464420, 473309961, 606084597, 406778092, 640898159, 41202673, 101345986, 840042152, 476760631, 390638864, 334163680, 899650388, 885486445, 473717097, 804422523, 648008086, 807189965, 723491503, 207840045, 538981609, 582396408, 114215828, 844727100, 922630662, 291679374, 338914322, 376098108, 57897581, 481570858, 108397800, 922935329, 512265827, 614349604, 657014519, 232392826, 744165618, 127877604, 554874390, 482611437, 396163312, 494597577, 723821942, 808097407, 228931748, 131045972, 417616255, 529455811, 800380252, 222927595, 547627559, 668678048, 122623875, 48217216, 71771606, 821386186, 313591805, 234362888, 94352308, 907659883, 655154433, 980029655, 516776520, 507607316, 34627093, 473574378, 519698183, 303983128, 939777357, 856787029, 566513300, 167999905, 561584603, 328209034, 533300436, 909778408, 582422596, 992752219, 3101106, 443293817, 370930737, 513420998, 193544401, 712644811, 771750719, 534986335, 952324215, 276149214, 92988547, 814940868, 287954444, 590889408, 927997816, 747043433, 667415701, 228666482, 480251360, 944581131, 34364736, 419540631, 503614028, 335130541, 539341966, 246487934, 364897467, 566386334, 931030570, 189582676, 269255351, 736094644, 170996985, 803257254, 470517878, 395534033, 481914480, 859394623, 340493694, 238686631, 734960758, 398047727, 851459636, 425012231, 875225830, 281042766, 122924977, 350294244, 694879136, 929177003, 882533016, 194055301, 132616923, 637435856, 658629935, 834346978, 775387232, 817744912, 564893145, 593492894, 106499434, 120449649, 524096663, 672830173, 952071694, 836062317, 588341541, 369804997, 821947046, 964796894, 819020498, 221659397, 851026132, 573570475, 162720721, 836047305, 203980725, 589021348, 250586791, 595644069, 252308421, 555426215, 9392027, 125363374, 352869545, 160428056, 494852331, 231172421, 421694949, 968705062, 701656916, 193926293, 771513449, 642516064, 70911214, 107252883, 87774313, 928345081, 52030812, 799208385, 136177634, 593750270, 907050324, 434465533, 695257862, 493157108, 215306481, 522363120, 589390081, 202008631, 169374678, 756676193, 251932506, 139074378, 509851262, 263188214, 671881181, 328504690, 783929195, 171522176, 383513435, 2777667, 869116635, 90251721, 282960186, 48782880, 729969927, 100519706, 306127832, 77754925, 470914455, 441260190, 978239297, 203970673, 582749883, 150681491, 573463688, 33745117, 211324023, 479554379, 50635577, 614898890, 704719461, 217361929, 558489662, 418947951, 676893400, 97083721, 403314690, 827942904, 926400335, 486095572, 16141615, 885806248, 464367906, 739293432, 325010252, 561962572, 807291394, 330704, 519951221, 811603146, 741667347, 213820291, 183956594, 115243636, 517460253, 80459800, 974764954, 329869027, 513146719, 136684251, 121011713, 903212516, 358236421, 720789357, 508044234, 680048256, 267357321, 963428002, 214734498, 599181797, 50709771, 997750222, 969043820, 969823708, 490106795, 948323714, 32289800, 242273588, 82324271, 224813376, 743461698, 346689277, 501334939, 672602906, 66201247, 497725540, 22752167, 247515037, 533425896, 264256264, 950938559, 850965741, 424444785, 804181611, 771100082, 996074903, 227641568, 311464636, 216923410, 865960092, 532312448, 948279160, 49352712, 522596178, 514285219, 817128974, 755799048, 70343335, 721096699, 998175798, 126249651, 205638226, 721646921, 946055273, 930118782, 192231803, 300891973, 746994542, 398376072, 780361093, 630953896, 814966852, 888350171, 859073574, 669322181, 267241156, 674037936, 89863996, 774167547, 130810508, 616908159, 66096496, 424919156, 798725648, 289751495, 540417256, 338799816, 453302887, 243381228, 236085733, 446675695, 747127108, 305901311, 760555700, 272607418, 597362525, 600674534, 782690684, 14916341, 377705767, 19063088, 89387533, 674306310, 987982578, 932356474, 631657642, 435419869, 899017235, 758755887, 579699998, 395320118, 708399980, 835370561, 439754716, 939462302, 350459944, 517725528, 804810408, 113385838, 98406128, 174855935, 928696125, 731762720, 654225607, 100052236, 64408049, 120530295, 790069288, 22134590, 483156939, 858978773, 874504322, 903196873, 217932252, 516399470, 819260534, 570471615, 854423933, 618269242, 435159126, 170686550, 288737416, 377540974, 345658058, 314894651, 113676492, 869390768, 273396262, 55827869, 836107106, 946815955, 498782507, 695610239, 701622297, 678939785, 189238024, 601108780, 213816644, 186311623, 517948066, 718418547, 436590872, 491031125, 856955476, 296953659, 822881092, 334001165, 177396726, 499359575, 902773462, 636891393, 369600827, 147828319, 112450704, 152801680, 764010838, 510215554, 39623003, 429453048, 464397393, 56970157, 431634592, 527568394, 25703109, 445265957, 412632830, 442873261, 117227423, 958691532, 770715034, 970440436, 844876549, 864045968, 184027287, 877504316, 473763041, 229466341, 353091342, 193493867, 405958297, 435290451, 447993242, 106654511, 437308416, 705178227, 226148938, 850928718, 443147341, 626992751, 395978982, 156996170, 680395962, 884777418, 99240146, 174918682, 645840767, 492002300, 580694642, 367029226, 193964962, 575352928, 709991068, 113854089, 237017456, 236860974, 959965499, 836486714, 526074955, 577471237, 181277210, 490923725, 141715614, 828299637, 133169519, 234436085, 508198910, 517559010, 37367122, 56779657, 172097489, 516242959, 877302854, 449749377, 524707248, 906329957, 895764505, 630425208, 844426251, 819822674, 541632868, 159948083, 246345807, 321571806, 25267560, 700918849, 683224486, 795648861, 76462539, 899594597, 332401300, 348697406, 598476214, 408895968, 915994450, 468057035, 734480450, 544576266, 828767837, 719245068, 105376487, 512530837, 736357373, 470029422, 660995524, 665949143, 201029424, 100825024, 208118172, 763985837, 128866186, 802411714, 108950350, 936263513, 191876840, 106480177, 870323442, 128554853, 535613055, 938288848, 387714375, 848392728, 803940225, 265432885, 203140155, 790304246, 433539038, 408457921, 948152094, 141824979, 982435665, 324219741, 753133290, 458391443, 721247726, 568041240, 160924340, 763856950, 279534873, 481832772, 141031113, 176357664, 361022591, 986982324, 875032717, 658909914, 692023725, 947179049, 605808674, 633449604, 422936094, 305482330, 822728574, 10895023, 75447714, 782956246, 704436797, 245244161, 587688740, 786549415, 640337190, 904238849, 403310678, 467763852, 424853267, 610892635, 546796590, 270577947, 53554367, 759958163, 565924493, 22084820, 164252653, 739880900, 758403993, 52736641, 458276327, 982495188, 51748705, 913851651, 437155599, 45455267, 85456269, 826097735, 118969605, 318220327, 145152346, 616152076, 542785603, 411298896, 925548533, 154033799, 483943513, 602941344, 133606669, 55432757, 241267595, 94753598, 22481877, 444786315, 18464431, 166650880, 691834475, 886718522, 738297621, 945172959, 168607266, 758956128, 22507687, 23264575, 859180732, 973210276, 304454966, 546246027, 797561254, 922748030, 535938286, 360553437, 491275361, 686043795, 330572196, 228192418, 969523825, 757780798, 483586911, 181902362, 387775415, 100144486, 218254581, 163142316, 268531503, 76425536, 634018710, 722133363, 35276485, 653841233, 517599248, 983559777, 593495618, 759767903, 55171640, 944214799, 384376213, 628886141, 124033625, 47557029, 243022096, 164935379, 962245635, 557957704, 63487017, 346745386, 597612954, 964079123, 114195556, 803102658, 683016521, 164215993, 589758934, 188479167, 434217061, 375327054, 526647965, 590190113, 398578451, 897578561, 383336179, 187164323, 628805846, 103664372, 801453041, 109088096, 338550179, 595978760, 988977793, 972786183, 652487521, 311417796, 13494677, 552090872, 439620742, 131201903, 933723398, 963441317, 498082480, 782142143, 414393704, 665941895, 45267719, 391950894, 269477493, 949683996, 369957860, 86331679, 374218026, 659060582, 417624002, 359591954, 406935939, 905136558, 464801202, 60319458, 694953231, 568985282, 75846834, 12757687, 980277126, 242487512, 746027333, 730909819, 689930531, 453520688, 365264313, 863362203, 249768326, 998058686, 305151432, 686110597, 412139067, 354383491, 73173879, 701124021, 319475809, 355053807, 423226660, 431088863, 3968521, 58806315, 724550645, 625102509, 873045003, 182369178, 975152844, 882318168, 205337366, 747894383, 795373949, 959324482, 466179706, 671192835, 296119457, 20887552, 817306446, 561043872, 801622732, 468992429, 540056893, 158672635, 522004624, 152831397, 136357698, 159629567, 496143794, 112781763, 804620003, 437734073, 713949189, 586803209, 442039507, 110868786, 370678943, 552776350, 127081646, 684911584, 404762682, 662081750, 590069207, 670562384, 556761480, 887581285, 943625888, 133925321, 811772114, 304072841, 635051606, 454629118, 880897490, 758281412, 975821370, 874391548, 386038885, 120194155, 32414755, 420150999, 767664218, 785269898, 534218786, 758464127, 958824347, 70200623, 366418597, 540975881, 368782227, 963300128, 285880543, 491875588, 848544143, 919975909, 593619509, 971138451, 35171927, 15175132, 653325183, 684799220, 673514657, 554883329, 593776474, 11059524, 617216675, 381366493, 396245123, 253785303, 909522420, 202200462, 298600726, 65777148, 460925778, 756412397, 801108563, 373810765, 498447671, 160669202, 847573471, 158122871, 75201414, 417998506, 141954811, 195116597, 276869240, 442173540, 668344306, 183975582, 330082827, 568829616, 644112976, 418689402, 911443436, 110344385, 552062929, 436641193, 239910844, 866726437, 184140449, 323716542, 495749731, 760389256, 406180284, 249026740, 294016138, 828836363, 195362334, 759516388, 741771722, 785147910, 885218887, 1679353, 339359657, 265588881, 462472680, 752483389, 959064885, 444221756, 268764853, 356994815, 145580533, 649266599, 585128781, 38599736, 640127158, 831748762, 243249419, 632918016, 514812479, 98807222, 920195122, 147374017, 839344442, 736420862, 434600500, 202988225, 454806259, 45883402, 25345484, 805508471, 435542131, 842020710, 676517758, 532394653, 110012169, 743069378, 357226793, 613789973, 735885235, 443296925, 96723567, 302219805, 492968554, 372618122, 186520336, 111499166, 544318983, 844080542, 115024831, 178569238, 838187958, 565226292, 115345479, 922042100, 53376678, 704179820, 587972479, 733508398, 606033786, 906492753, 134309683, 764465879, 386279427, 41169647, 752449935, 59559387, 252485668, 275351672, 220390277, 339356362, 31085638, 809975614, 501851237, 792867239, 693345919, 593182051, 244788174, 277999196, 311381054, 612076090, 523860896, 454564057, 613060003, 221180519, 664227040, 419863033, 712196238, 65352736, 807186853, 685814296, 95681689, 461398767, 946658321, 550064671, 919120123, 869619187, 614491472, 247656062, 124489782, 806105951, 655924603, 426276271, 960765173, 728297405, 382376486, 138342820, 89489277, 54448349, 192523871, 541722136, 496201089, 537578973, 659433110, 902986365, 47077093, 691301082, 227473274, 108708973, 634025669, 526455029, 942150210, 371335313, 77850306, 233738682, 984174085, 829989344, 784371285, 976958016, 408449072, 7506161, 660001308, 425336430, 191243127, 684563888, 667088918, 943203951, 158535153, 697081657, 882700604, 688011691, 694117041, 699320916, 759577175, 541365024, 414035033, 826068686, 462743779, 420858056, 236398813, 319891519, 403523834, 549535060, 651465241, 6078706, 367830616, 244982509, 528757946, 632251300, 227529379, 874664259, 461255188, 213320984, 842204782, 779815524, 517861701, 645112975, 425154924, 218489961, 79601626, 405599819, 49301906, 682637864, 697152823, 229778766, 208156385, 635839900, 612567942, 544461113, 583564905, 914054862, 915239820, 585439564, 148040893, 707082960, 279958374, 694971238, 800181452, 883667769, 121862348, 354805326, 142860724, 414407127, 971392137, 741733087, 346175915, 39840042, 94033230, 465746709, 957131649, 289352256, 772516136, 768530786, 297669695, 287351794, 721132709, 683745276, 841348575, 287419659, 669131090, 93347107, 717494971, 6748285, 758724481, 979824905, 719682823, 318424447, 895716429, 919659927, 33974269, 557792415, 73695803, 939435842, 545349018, 83613737, 365700098, 512537134, 64206043, 361582960, 677440602, 530079947, 181667456, 724014847, 582498038, 251589953, 839088867, 609610029, 25942044, 659618166, 819229457, 32115255, 931192897, 340210225, 396019590, 253109678, 411527247, 926745993, 628651830, 514951650, 288535413, 241555458, 851658644, 307303454, 682453862, 651672862, 894742979, 873522485, 609957, 674853346, 841548967, 655294526, 674397416, 891057897, 667085076, 392682630, 978088088, 363310448, 978938719, 442947679, 50484962, 336657003, 569892791, 673245068, 285681694, 756518535, 276718096, 619429742, 663530356, 860640050, 169716042, 490409387, 166871689, 270604710, 126126704, 916449433, 628409951, 248638832, 729699303, 890759411, 851578122, 902955173, 943890156, 696280954, 984197281, 675316328, 860540386, 660306758, 119052463, 458645604, 828645436, 838954059, 846187700, 246754733, 853509640, 309813792, 516977011, 630791251, 873880699, 145300761, 776238929, 275945908, 35086913, 518254034, 565264375, 63621401, 402875587, 757995165, 381647061, 366122522, 816877873, 158287209, 92320160, 108822059, 426565218, 655433255, 433364079, 848763201, 816614490, 631410767, 689624828, 300778620, 323548196, 258647249, 217476789, 327363211, 389706387, 339519910, 44921059, 690554089, 396972066, 32072104, 516860388, 198893765, 93991562, 277539169, 485683075, 418721614, 790159340, 264362452, 242900202, 183604672, 343783346, 91947083, 354167995, 927258683, 576553070, 969196132, 75783279, 11763728, 658258314, 933371557, 57829509, 992536766, 810872833, 856567394, 368696853, 326160895, 68353280, 746766341, 797570314, 134545228, 188741043, 634015855, 1287069, 135636159, 490132201, 839366475, 564146898, 116494062, 322682385, 628791864, 806434943, 557837080, 517975082, 410770981, 567151712, 177992827, 110511634, 107497691, 745077426, 761141655, 452263614, 296664826, 798141485, 932601926, 470648280, 108125929, 608993437, 818957373, 550055266, 61318359, 944685830, 949969820, 404986889, 734490389, 435881178, 362494467, 908656439, 804783971, 616639411, 311369153, 409534202, 468918367, 155606185, 202705731, 440801047, 575688835, 561745001, 367868934, 210047820, 731025955, 432033919, 532272029, 927890293, 577433055, 65171686, 703933643, 289326539, 807401980, 406881205, 750458209, 842589504, 505597012, 958032450, 503807165, 973434566, 219576813, 791930534, 22712269, 576822280, 895594428, 92287916, 844133046, 628234613, 123186743, 931454399, 770680545, 735349529, 569844802, 561996408, 742842237, 802452246, 646215986, 282087765, 351664312, 774521636, 965047152, 844625054, 586497174, 515894843, 864643973, 258762859, 804186638, 816960404, 839487400, 234020012, 906275010, 807751787, 295905850, 519727895, 814729871, 903111344, 267951764, 833167707, 404604085, 208900562, 307216750, 262901150, 198140608, 701626993, 294367174, 323830547, 558467784, 753619932, 290678986, 764763173, 656556773, 5197474, 237000633, 622359352, 444671443, 99445531, 729480226, 960778920, 639019535, 222293153, 86631947, 262893688, 717913786, 550286513, 654494988, 952737486, 403258127, 870947956, 770029586, 166320676, 225210382, 638829448, 908661809, 928243991, 344876810, 255777676, 638541545, 318894066, 513137099, 513724046, 264807406, 141002439, 778137832, 99989638, 409005627, 524247909, 145796714, 567422700, 887565141, 238894704, 601065579, 341497785, 941907501, 955761700, 926325792, 862432294, 653837675, 996318167, 800681407, 967851912, 298376754, 350285971, 240968011, 854944433, 838088931, 674788386, 639762070, 588018397, 637185559, 784289352, 218737034, 745792225, 161948278, 473735404, 377096796, 241927206, 978702146, 922305917, 545541129, 53708641, 619538668, 116750773, 759304082, 375205310, 718145487, 125624733, 166189958, 844858003, 201482375, 861441157, 105530315, 83077940, 682398423, 869222439, 155563492, 739490095, 450664443, 678626165, 72904421, 299490679, 514461326, 241537194, 910120779, 820327925, 340810342, 964390700, 565392002, 245533431, 647915238, 30903616, 984067315, 817422333, 892980758, 129799946, 263236783, 569414386, 526860219, 748969735, 729135628, 966428665, 74091809, 773182346, 382408050, 154277798, 610927249, 691418618, 117268965, 436609513, 258854018, 529223767, 679531241, 207615725, 497797412, 591312292, 728357706, 142734872, 908901357, 740008264, 845691626, 611774689, 13331356, 535269054, 234544761, 660445056, 75660461, 170561295, 981848724, 654281494, 62557045, 523526992, 936764672, 849518505, 189717736, 381932409, 310366126, 561069302, 702336258, 181430032, 313436204, 218232211, 159238758, 64873734, 146432957, 316591666, 182768580, 37714513, 762895041, 169602630, 606807783, 24786880, 713710318, 56604785, 986563383, 604746251, 453900889, 637023674, 268759114, 742594823, 893492358, 149638286, 149237186, 674686758, 623038028, 695924934, 779090091, 146393930, 532571331, 454045906, 256858757, 928494482, 668063194, 52046201, 88011734, 423369226, 891448562, 884166406, 809759541, 725585837, 267745013, 65523721, 109477898, 784815041, 478103469, 310756036, 501812366, 441519354, 893520644, 284372665, 638581049, 848384476, 679232653, 678082385, 589995396, 138561513, 214214976, 948809760, 456341659, 876839638, 653463585, 979748844, 81774405, 588097114, 323245335, 767303716, 304740580, 789693868, 63043016, 226586014, 91491228, 822692401, 52909426, 122045336, 870069983, 645313937, 316001456, 459437388, 291254059, 392280831, 536314188, 102252477, 719090502, 396116399, 357320554, 15213000, 947756231, 252536375, 503990747, 766809778, 397154679, 942997308, 638865088, 794786729, 868906557, 160370175, 192453123, 345163833, 271329233, 122612197, 983553187, 405676564, 563615621, 359024059, 524505722, 670846317, 206592317, 874220881, 736207497, 15695691, 209161442, 491804610, 140533489, 58444072, 434357879, 234506227, 916057639, 964621256, 55125690, 313935274, 528344643, 219810570, 356818363, 137352996, 330587198, 943102086, 829139549, 382570071, 827733146, 502397096, 941785447, 161369519, 261661626, 198787635, 396899715, 654835419, 289594352, 621954787, 737225983, 410156304, 206674918, 526050196, 601669439, 580677468, 584701248, 893146491, 703512118, 690383212, 977901393, 427800277, 636511868, 350415137, 733904199, 310675930, 519007843, 395539985, 162706588, 216793910, 27330846, 246713928, 974477308, 234199402, 534240016, 913765481, 645377928, 862284585, 950313419, 349100021, 746150881, 928689086, 352221203, 318534335, 327819385, 128166957, 795680681, 49522040, 98228521, 494438721, 661083359, 264237874, 542410965, 264702059, 422547239, 843876342, 255782789, 821434552, 20669131, 896808437, 595998827, 152969534, 118072978, 44214096, 217306396, 516792566, 12410960, 60096592, 460195566, 230453467, 613935441, 327097050, 353622316, 87120515, 351761061, 501978697, 905687054, 268809395, 429807530, 761353126, 660416826, 561285682, 383640289, 574057467, 670933968, 394151232, 775220183, 581911950, 439931152, 840246612, 525023760, 455099827, 623973170, 449932122, 825574515, 476141207, 771111624, 706906016, 560006959, 816351049, 892504672, 513404768, 883814869, 896059895, 856108355, 311088619, 491189447, 371226431, 599756054, 699417402, 697492366, 541401658, 980688253, 966499333, 126110174, 697775211, 864120440, 723570426, 347362771, 197132785, 172083468, 219677901, 103236264, 927906802, 388048833, 393368216, 55899811, 82487217, 118550680, 496942882, 287596364, 883503672, 705048473, 157803686, 298689905, 851629435, 108198443, 806510345, 779889684, 610410670, 605740646, 895592570, 22526370, 415805228, 901014572, 179146843, 267852062, 742548489, 65040418, 193533165, 614401627, 296342572, 129756023, 841254155, 339188648, 884386662, 157489248, 531478552, 984465119, 69125036, 863545888, 712897792, 221087186, 788982332, 625922261, 615984261, 429277985, 272828441, 347824178, 549875547, 440982949, 769757793, 266846506, 720554367, 627191137, 280244071, 95803677, 763100037, 747504863, 391889765, 114144084, 948080646, 155128559, 459241362, 245343784, 359547891, 818990634, 609920328, 870677606, 304337373, 139037079, 762582851, 36732433, 695066533, 169842807, 912293536, 297312850, 57350720, 104452713, 425229843, 13993171, 866235970, 241916413, 394521418, 912920091, 106427807, 898040999, 924746568, 714237685, 267825105, 521173187, 528653390, 872655583, 634653984, 731723439, 226742389, 674939408, 639984506, 759496145, 284649066, 226934614, 956889115, 787715533, 827364582, 511069549, 649618112, 412019067, 10862271, 280001154, 286262573, 863926508, 609178082, 76509537, 948018077, 675140175, 653611, 464172437, 800975970, 923617332, 23398063, 539229173, 423305418, 510716991, 318112171, 920190860, 916363827, 396111056, 421387655, 309533114, 543013810, 145308431, 14436163, 460176615, 441407963, 528552863, 304959582, 602614523, 554702189, 573800842, 971544359, 338143732, 461381036, 853679764, 411673702, 136245486, 160269604, 997210633, 549579955, 780901235, 502847891, 55427249, 348780960, 576281923, 460624932, 156198079, 27866589, 899887003, 291715193, 629370156, 948011931, 455478272, 413515546, 250554687, 508333503, 471040699, 517484832, 682286776, 191882175, 972998149, 298096193, 445976013, 190154320, 337772891, 296439080, 395341597, 182155082, 759385359, 398477477, 23115128, 984549834, 512878981, 238626078, 639839103, 454049327, 428076390, 702244570, 577783040, 590160550, 146447651, 15227703, 501241732, 177560206, 608803340, 858658026, 693083133, 22254998, 670700343, 883511272, 954166099, 417333086, 571798843, 238703835, 474096575, 386707653, 724103151, 952501658, 702630162, 773418065, 772580476, 648682643, 530918826, 72751038, 416255332, 295484970, 549336702, 646084330, 634137735, 219138887, 918762135, 579232108, 357669985, 759336451, 204783165, 708927169, 216536427, 645196198, 815947713, 672214520, 630988755, 807618594, 743487673, 753418401, 610503299, 36790980, 522110314, 502417715, 352725096, 674473374, 687333539, 452346763, 832631190, 12206912, 698811410, 873654684, 841225327, 914929896, 446963960, 377311649, 958137085, 534486851, 857003773, 39911639, 136679209, 456651795, 542215703, 887074303, 246892301, 890595339, 28893668, 723009018, 696054530, 495284476, 590461350, 854275493, 74351868, 663788056, 645292201, 513029362, 285274037, 361258038, 445998673, 58761719, 961999751, 848543725, 242248457, 931261860, 492004977, 459897886, 357750024, 729368743, 979819880, 263415187, 590895832, 499717792, 106446023, 646732628, 84623820, 468184580, 452122066, 167132020, 689591556, 354025198, 180584345, 471193744, 525766737, 132632012, 498025844, 542670355, 666271908, 950197465, 1239359, 989646570, 942990395, 995818348, 465900873, 624677107, 555301738, 932592467, 820565659, 243223213, 40231385, 373712163, 308507731, 931379214, 274491833, 623207005, 632033366, 612517165, 639647835, 602478571, 409050195, 730127417, 863234611, 458212747, 670975029, 957842597, 123039459, 308285258, 833353392, 290961223, 62704722, 943455699, 226324803, 675555893, 14795939, 202124916, 539217405, 704728462, 656621339, 324677437, 161850658, 884805946, 507761951, 958449816, 557852930, 479259886, 783186117, 221505567, 40878645, 162962109, 15306407, 769606424, 112972594, 184894061, 320563194, 742472086, 974007397, 374887660, 19862034, 519555741, 760006889, 836968978, 600388171, 510867892, 234720582, 446759165, 24473136, 322292560, 502221422, 956200135, 924595314, 370183340, 924262673, 160985339, 341778774, 74115099, 967597498, 879635193, 719475068, 351529071, 217212282, 366374626, 154793464, 737238861, 359168476, 290529348, 751126638, 887020782, 596696658, 188243621, 454741670, 506799748, 932234581, 638925894, 733652519, 475813778, 328790927, 790663703, 652284730, 297039215, 212715365, 66936647, 70410728, 287300801, 620856857, 317982831, 475579654, 944304792, 804492380, 640703057, 637316587, 127272227, 964916891, 668680581, 543794207, 551318410, 453335400, 53935623, 255713615, 657534372, 285007138, 688097223, 905813094, 861663713, 382423868, 981908153, 861707685, 634276112, 44730652, 799958705, 292438646, 59290699, 449397346, 670939732, 117602468, 999564244, 871896971, 155772115, 470636841, 937260486, 855503429, 28023345, 996168255, 193274095, 90033179, 163050350, 770498357, 679081650, 794601403, 468517156, 668989845, 122717418, 166203395, 774178214, 936290870, 631468045, 244786089, 100083871, 436819765, 556273426, 641957264, 217324167, 39105395, 24006890, 959467359, 508733002, 456794833, 192479020, 782368409, 946941774, 508225725, 845151666, 757021787, 11852953, 426839572, 952076607, 263498955, 35248595, 416565801, 967901679, 148023460, 473855923, 741063813, 346800241, 789574735, 926858564, 805828814, 71877992, 602911943, 969732358, 697353691, 504236400, 858943267, 462708483, 732445350, 774210978, 550116759, 593523449, 152329914, 17003552, 512496348, 682986914, 151844832, 878060054, 639156802, 416262935, 343861767, 466598722, 441823423, 847407662, 444059217, 598541444, 206145786, 905678286, 39900405, 881030847, 578689908, 520885120, 203515444, 839606289, 834972735, 685762610, 15535481, 459518283, 182044078, 972304645, 574831946, 597440129, 367695378, 13481047, 104576215, 895763058, 302747884, 295148202, 606022765, 488195282, 873885990, 80979412, 142031327, 44713183, 967350900, 930770971, 935975028, 109521301, 621616715, 294545885, 767917393, 173596790, 803692455, 254027543, 231844491, 50925047, 296840164, 555182750, 481209745, 129544882, 201760309, 65427737, 920778328, 126415808, 344671253, 115903192, 297974741, 730451028, 656191981, 962671712, 451741635, 397830946, 290804307, 995859886, 96304453, 758636649, 93226984, 562264628, 234075960, 935354869, 993147690, 72199716, 821104845, 902019363, 408486333, 29806843, 854188846, 173677282, 433677588, 601909526, 607373696, 411902280, 903674072, 533310710, 719996428, 123798261, 853901207, 784712047, 580814967, 422343341, 184458258, 331036863, 719089129, 56687009, 727305623, 10505150, 554666726, 687917431, 422969386, 452309646, 483143539, 684233345, 18422156, 947475923, 197111345, 923274635, 429634573, 702013672, 590539663, 743981111, 369604007, 502656441, 359234698, 451750187, 668240729, 73095826, 808063249, 924208236, 78358005, 858333327, 226378829, 518630657, 325070435, 295724232, 404441959, 453763775, 176533752, 731791310, 655599972, 814201578, 635711576, 506243121, 890581558, 341178872, 30730907, 844139187, 663658331, 813819081, 276778941, 621043020, 816802569, 801239729, 343690782, 491261780, 792003677, 113754301, 993944373, 994774191, 132323212, 929089437, 492907353, 45972438, 299909396, 476267367, 277750585, 728249004, 775561144, 43677178, 751638316, 94252671, 630440710, 280254059, 741737508, 62042212, 736373674, 887044237, 194168735, 192147276, 358141209, 203609442, 966838986, 316814460, 146639862, 33023784, 35633445, 677055162, 139593229, 834937259, 467877931, 108454529, 578864060, 817023534, 955042861, 212189492, 293552922, 320335134, 397081992, 710146963, 268801388, 12254519, 409405312, 367354747, 437019283, 527099222, 313325765, 341275642, 559281989, 517311276, 510208979, 387435500, 57760131, 525272792, 311055374, 716279565, 509932816, 699481115, 4518172, 831812160, 100156023, 765154519, 853284968, 736902460, 438062931, 920323927, 948921445, 949525947, 576596800, 533680172, 609843398, 892567487, 610335839, 720364430, 577758994, 42116222, 185673628, 410312022, 307329717, 225713657, 76175319, 53383780, 778350931, 850252696, 455734239, 610781624, 124630875, 704913301, 566480413, 692226216, 421612326, 854048636, 214665148, 696939401, 245168864, 839122852, 807699489, 687573007, 979535160, 105568231, 751741029, 842243625, 457441155, 481220919, 290556609, 350722664, 837611607, 317287777, 273196923, 458510682, 317535448, 64328696, 175771246, 979504270, 600673554, 874142064, 531414084, 856848107, 618151222, 130645002, 35674494, 451820005, 146854450, 482989768, 682814913, 860836769, 557419123, 709258586, 930747946, 69989421, 985592585, 439104631, 808893313, 518194884, 724915252, 70193356, 226870070, 179856913, 651293752, 462282575, 907462923, 53619567, 59113825, 713899706, 303757577, 217091576, 806157979, 7629132, 752417608, 25134135, 230668707, 25491256, 120733976, 345134978, 706511419, 506161004, 27961297, 394087167, 917876255, 424193232, 112168588, 328315026, 525803170, 352291403, 437956888, 200939293, 607400817, 335785243, 539339506, 250592051, 395018560, 289859738, 933351600, 436062217, 762180759, 203018383, 193935830, 174697567, 631989541, 330938543, 97398701, 42062082, 671037790, 913744665, 397347567, 533566166, 680579952, 410762153, 605738870, 544268183, 148777629, 613775172, 390660648, 209749730, 674386898, 133946564, 573888832, 220468714, 608770505, 266225724, 525838830, 821543506, 760695755, 834674815, 852234541, 496349497, 16580828, 788375701, 722788328, 587414480, 764950425, 677619079, 229538080, 262833492, 965241024, 959335483, 844395882, 94831131, 677186099, 908922190, 286807296, 715829792, 86681542, 418755552, 681214582, 240002809, 666843173, 844668228, 681221441, 853618471, 44264483, 113267847, 975151776, 673568256, 363360749, 494774531, 500391532, 718826516, 823774419, 793974162, 45937234, 415352723, 218951283, 683103946, 930256343, 846413605, 312415291, 486438396, 878619430, 332691447, 928441966, 235681941, 877843786, 476907306, 756951270, 905234732, 893140207, 681005111, 980599887, 340756284, 574163268, 391289180, 694874731, 376263165, 507996342, 227407153, 321650006, 379974232, 677850097, 650084971, 41580068, 914071771, 955939789, 157095553, 316751986, 563529368, 834530988, 936983896, 149054899, 348708444, 613940856, 378560900, 530189900, 722593705, 475114403, 858101911, 802178788, 898692142, 988425221, 565402778, 133298659, 891917148, 61742607, 648422796, 628277187, 838345023, 683435106, 826691308, 347176437, 368689884, 784070742, 235114105, 819284720, 734455185, 895782308, 246180643, 646609892, 258185080, 844853751, 619766469, 5241087, 833101197, 172480987, 811529343, 217304843, 992659187, 708551240, 352108675, 960478452, 923086838, 75836578, 543760106, 674812932, 533457866, 498924903, 192940064, 889427563, 675202708, 667040170, 547446115, 393186707, 739030743, 98567681, 421997733, 512521823, 140810054, 522691281, 922266145, 243130627, 70281443, 83041501, 897627171, 426413991, 4500255, 844950065, 420218935, 791861539, 521426799, 560950022, 632773253, 528873936, 97325327, 260764153, 197765823, 972550080, 976524480, 207668912, 707436055, 47550474, 232206124, 50815648, 636139773, 660579400, 656783677, 195910028, 10734120, 508851321, 29183177, 550885614, 453080374, 611969121, 810062019, 963801027, 178448514, 193889350, 52382659, 286000418, 323883250, 303928879, 468118652, 73327722, 454601640, 992958374, 309161105, 701030972, 732866595, 378198202, 646677613, 769451424, 652277369, 784046748, 923975282, 649164388, 836022753, 619468275, 651711884, 48427200, 657794789, 171574199, 30781222, 464779355, 442486624, 591400900, 74817215, 282468589, 881544300, 287432058, 206635809, 325315665, 279849705, 344426700, 568243898, 733128775, 801546642, 640898795, 991051624, 203915171, 578538736, 20266722, 651673429, 247590288, 357508818, 552701476, 440071757, 401557259, 911578672, 283262758, 984815008, 72209635, 251252450, 642933132, 349260490, 903198902, 451861685, 429520743, 404139691, 114686837, 530338035, 29951033, 650335710, 674564378, 823917080, 601825991, 388602660, 720149357, 227250638, 694669871, 94426948, 47253924, 527639684, 509840425, 48000295, 535162897, 620863911, 208121147, 391155956, 637059679, 893215098, 484930157, 350943451, 56143212, 344829811, 529801577, 160630482, 212264158, 774379344, 351505060, 635315566, 998927541, 157464482, 233684201, 188220607, 204982739, 940886275, 216320300, 597628899, 685407172, 252649972, 756859966, 128245763, 344983008, 57374439, 131464170, 615635414, 237424800, 482317509, 868780551, 492298067, 75941773, 109925184, 408395553, 880232169, 757447268, 687153089, 56397958, 344179982, 691219827, 56281370, 868607418, 966428978, 455688564, 761819773, 321663709, 157261220, 149537586, 195503800, 812747816, 800858322, 487147941, 554424950, 246724296, 736952532, 150133067, 879688858, 511633520, 108547571, 48733488, 886065812, 519474799, 753594171, 578989355, 48168912, 504826003, 653944510, 968256524, 192960339, 845355083, 638757619, 816845325, 776464153, 284592586, 885790772, 235179996, 559308317, 377567749, 242328361, 674866507, 759954347, 969560540, 295999446, 797323221, 882482086, 764617035, 35002677, 69172354, 105551761, 496944497, 468364054, 562193207, 760690711, 34815681, 366619790, 396338313, 409434044, 838576360, 439243295, 879091893, 764116122, 403070129, 162206649, 688410978, 995391129, 241271573, 201172885, 129622951, 916143520, 89510248, 777325620, 526386474, 605493718, 923411604, 784785629, 451558183, 922551580, 452203976, 614799899, 536097825, 43766968, 402465100, 821738636, 766332340, 673754929, 329464259, 401288202, 544948171, 161296876, 221901174, 721972832, 265249440, 196852938, 221651406, 344004670, 11261071, 883866161, 858037513, 999739220, 707406269, 647917352, 572872470, 825830605, 991352818, 508273313, 811870564, 752893475, 935822791, 910177921, 629811832, 87145884, 930258390, 29537611, 890802706, 551047464, 343035641, 997703795, 471351161, 938606874, 745456757, 268083428, 901714215, 927772416, 765960790, 24508903, 916619048, 265458301, 796704377, 634720762, 627147733, 802272475, 776984150, 996485655, 548157013, 142110843, 716392152, 864808446, 808754718, 764392405, 675088725, 358101778, 999510791, 485929314, 52835048, 160209249, 152802818, 672744681, 976607981, 697056654, 651167306, 493973947, 637983741, 849191636, 311531414, 52931943, 142611574, 742288255, 495923299, 692605819, 368900034, 360772910, 716177323, 740867530, 444316590, 736505207, 942980380, 514754361, 829534286, 460117505, 168592952, 879380748, 811743581, 445408105, 598755970, 634541771, 726545831, 778898068, 134859486, 307663066, 731631239, 511315214, 171437141, 414355920, 992900837, 989238289, 432809009, 673503506, 611065310, 801149231, 932669225, 604782682, 300969971, 61753328, 69784726, 764892843, 856688647, 265234965, 916929828, 598362768, 937664444, 672381810, 509414539, 402587159, 305023485, 715387335, 635676618, 746647237, 69345528, 434436134, 993123577, 793635137, 995139457, 876563527, 986730714, 565982769, 136629143, 998911247, 42984641, 565395143, 245660276, 303055731, 21235930, 924083843, 865572097, 9590985, 731868945, 68699531, 305276478, 630622297, 225132652, 115959947, 600340953, 392134549, 321163476, 52381326, 401886510, 67160112, 26556850, 388625186, 882072412, 579658284, 853990097, 365837276, 401462505, 878945031, 587483102, 686409621, 905768823, 377983047, 71089629, 72813572, 513654167, 355403463, 808042275, 675303681, 255570242, 16142284, 186952507, 258784944, 809161833, 976905609, 735063787, 401533489, 209152590, 670576063, 395718926, 134136681, 848581273, 324188301, 940416774, 3654149, 880803961, 111627822, 333242350, 484398331, 821496495, 653788181, 94551982, 332625209, 109485981, 405309324, 967278837, 779898013, 162155505, 817289648, 214179507, 911562593, 104057462, 981676340, 362394984, 292762382, 523970729, 122087581, 52929677, 77580388, 740660794, 409165718, 432087289, 90518256, 396568912, 62730687, 494126732, 530822156, 444160081, 269372410, 13544963, 238024512, 889058075, 311508940, 388286696, 297291369, 989009812, 922751761, 36957370, 559481480, 68283427, 337576586, 929624300, 663562937, 709580219, 423932956, 368919144, 634553916, 217318479, 903860449, 42555110, 869486039, 300383653, 617838464, 165613951, 938608046, 952763726, 229689389, 514481480, 662590224, 318254559, 177847862, 603701410, 953093723, 678552383, 524361638, 518621982, 83524316, 298381417, 481688608, 488430590, 723431923, 869764527, 161002847, 349599614, 179815660, 582868051, 597633518, 811388361, 812368800, 916842283, 98799713, 15888143, 533305176, 322575546, 146696457, 776704479, 800484601, 403989946, 786064931, 379681009, 536176554, 394135659, 904228305, 770721983, 321892804, 353383813, 707622662, 164386384, 643475333, 103612459, 873923411, 419819702, 656697625, 616632211, 32981178, 90592628, 11268692, 271740308, 123208160, 401084923, 806102458, 616814390, 105018622, 29725533, 107842426, 535466463, 259068045, 812045590, 488230438, 311469982, 59870257, 248692410, 216310648, 949945793, 571392323, 112896397, 132246696, 331578634, 677452537, 254982251, 617415555, 103051260, 127883316, 300217651, 270899255, 243834588, 325323257, 511760204, 654590460, 280151316, 623275330, 15429939, 687341326, 926955745, 326957373, 484412951, 543107233, 874717104, 165528270, 369128639, 703535519, 279764353, 107903664, 896067598, 533788873, 568714974, 605711581, 297401308, 966500872, 869354117, 196170273, 835285782, 430911187, 303794005, 375870326, 276387423, 923975170, 178953028, 261023706, 189311877, 274299531, 796745701, 478067124, 50441558, 161403949, 866885738, 810981592, 773366553, 580785342, 37903099, 209862609, 649476435, 302347862, 549425945, 842272730, 835948578, 680952477, 271147694, 270961407, 763143034, 632412168, 865217851, 923550785, 206079725, 420586269, 799701054, 114994376, 416385747, 830944790, 337607035, 715665117, 800633857, 976965746, 173027967, 846548442, 436422307, 75730865, 462235105, 179401832, 221378691, 944407173, 160127530, 345153656, 543692161, 483702958, 92057840, 971506228, 279937154, 477293598, 77548566, 331391489, 852722776, 765339827, 718713237, 222818622, 894450660, 551544118, 936430017, 16168034, 491793612, 902399490, 809919345, 477794887, 895174489, 287393876, 491434744, 450293316, 426530152, 558999004, 696945012, 384049721, 410261235, 97933182, 200680637, 185349638, 766153575, 87929963, 307892758, 321059538, 890233666, 309611078, 670647726, 551732814, 145310871, 313627502, 245966363, 824533718, 377453223, 171339762, 858064970, 341523746, 402713469, 40873556, 253225403, 81290980, 733417629, 37758374, 25114969, 784141317, 899825618, 812205427, 736853177, 723536791, 80400721, 816209210, 953489114, 491588768, 773647691, 521293359, 702766242, 199430356, 793155978, 801187870, 600216723, 389956443, 469128753, 882010142, 268305050, 530116497, 597406520, 577408066, 915735486, 947091940, 376026355, 605337957, 55095498, 119085681, 304606837, 491020121, 381644720, 8759261, 200755830, 889074611, 629777262, 906681287, 692314422, 936650445, 766468853, 335572390, 101919549, 739729337, 500388678, 912201004, 172874399, 482307649, 4095673, 395998648, 708404726, 832118048, 973014190, 218026184, 701267271, 542820428, 460126794, 488819498, 221205037, 670641271, 317555577, 498454373, 70163853, 68833048, 390535526, 168158476, 347551838, 464211638, 518506743, 915334316, 493577721, 417266195, 225221304, 785865460, 154790355, 227397125, 149306691, 722667819, 531408060, 509922263, 145728031, 399444814, 995947710, 537708929, 990326565, 879870733, 662469984, 186757688, 142371740, 367187412, 444561814, 172932415, 607696874, 293125151, 477097829, 198004047, 658592660, 885565462, 735812337, 203387210, 802997509, 14720734, 761951290, 120766677, 728501286, 497299105, 202066779, 990099218, 978158440, 671146272, 447770334, 193802216, 252660930, 505582646, 822267798, 407634040, 20405485, 414420025, 677709080, 685829119, 3358990, 833392572, 785780720, 17255269, 392153236, 372462024, 347644795, 150796706, 731726650, 420347065, 590196723, 441866825, 304300753, 538409041, 801873276, 190701861, 241562168, 176428676, 144648867, 364592967, 926186201, 256888551, 151970011, 724208570, 405651423, 699414150, 944332303, 975615975, 807767907, 907839519, 866178192, 620153433, 870796990, 667255944, 636640938, 661902467, 197602057, 177912062, 401597122, 639989973, 618826656, 306891431, 393213341, 179716395, 218872865, 645320644, 458659307, 435398080, 499702679, 210992247, 591809588, 946748785, 52693828, 942033706, 364168263, 948793106, 531055027, 381088744, 147989894, 614379709, 97447387, 864062105, 261816467, 829674983, 651113979, 598024344, 631642380, 878672990, 396566849, 86435122, 956323221, 566225960, 214237259, 322392165, 603391567, 755797413, 141925056, 886296702, 631007649, 270700915, 511209009, 944111816, 246229654, 593627539, 495584646, 964177676, 626856074, 420586797, 292246522, 702975773, 395861055, 429546334, 979717573, 633551830, 463561159, 42089758, 153886383, 663600476, 593835618, 643602361, 279708686, 611773378, 652395358, 665832971, 566503289, 940759769, 829919345, 84911913, 33848036, 218077142, 805816201, 257315906, 287290311, 512378183, 124295045, 537101359, 869865632, 60169310, 949896725, 895200317, 745772369, 918116608, 929957653, 308354420, 466171888, 826190947, 676980663, 762208763, 490716418, 765189435, 243171423, 719624691, 671376257, 256041224, 650609602, 500423092, 171620436, 104022575, 803273831, 170408275, 380146168, 439029363, 92966740, 190727326, 371082725, 520103943, 861152372, 373302844, 586626657, 18855617, 667959685, 349778558, 859177732, 625998006, 988548264, 615111162, 307766823, 835458789, 61524304, 580918193, 490303308, 561014985, 384218539, 894108139, 213124033, 594918271, 325819490, 93988505, 68530576, 870566218, 992034269, 28497569, 765795488, 810466544, 698914910, 903245931, 399362109, 52461938, 513569711, 704842936, 5740928, 133930666, 614786644, 812574471, 27873113, 75961449, 772005911, 734312701, 98165838, 484025330, 663201194, 730948457, 510345543, 213245720, 367915571, 564045725, 204204197, 932759820, 685406721, 727127191, 899213229, 404998382, 623483368, 638187727, 279218558, 363304743, 817550756, 331586479, 367285814, 628969182, 162834044, 665620180, 42879863, 295895973, 845433367, 116737024, 681567555, 241742271, 965822757, 476558217, 601139452, 728337800, 77383824, 181931848, 286188985, 495793646, 17211381, 661760786, 935863207, 168621316, 87385813, 837648601, 787820526, 378983903, 933476077, 774830545, 44172938, 227254170, 339957832, 934667268, 369760544, 503349334, 1300610, 30194697, 294492957, 860230577, 431277771, 260933439, 249530981, 404844917, 715524925, 519110372, 149482339, 475687065, 20809637, 187081805, 303630298, 142098294, 42488725, 225275226, 273293966, 146793419, 521067909, 557259613, 538114914, 288022823, 505188527, 950451136, 542197132, 510285571, 83615108, 203572573, 721186910, 105606839, 381999636, 773650688, 26888501, 198575715, 66580867, 661393874, 782163377, 2980831, 358473041, 563989103, 909593567, 137669380, 557820305, 113095562, 877368595, 674966579, 265562610, 166961905, 617447197, 887834030, 333722460, 55345974, 474261352, 134399905, 317291596, 752893094, 173797853, 771515640, 692149519, 931631417, 770987563, 980954737, 904734549, 378032296, 735405168, 470399345, 5223343, 479821075, 76741115, 989581048, 464714214, 518851647, 360828038, 996151474, 937390374, 315420064, 483668734, 99505404, 532161887, 914494410, 304192285, 306356634, 443542747, 953369482, 133673137, 460118104, 382475159, 405243685, 643954148, 464970023, 635694851, 71988540, 727815720, 822761199, 49783590, 777292906, 162800216, 613035651, 107737561, 962462769, 260957505, 742174756, 377778448, 669589216, 618683022, 36928359, 424362506, 650509454, 616116159, 690227938, 883519558, 987357226, 601689899, 586888860, 387493489, 709735608, 349887464, 112413828, 503103568, 984401736, 94569181, 784431985, 669806977, 46385063, 34683728, 432687935, 474018040, 508406096, 134374082, 918667499, 860575247, 36241328, 482182020, 714755365, 727326641, 561704795, 882354829, 433727391, 284082888, 738656970, 427655948, 143183496, 732865635, 209324256, 976744265, 402560415, 199682761, 939326070, 30651731, 34853947, 37232901, 283006825, 141780434, 906944728, 123067972, 223535420, 11646228, 403349389, 602609961, 675930780, 868075260, 856394108, 341033628, 515327198, 811887611, 969170618, 516571935, 391924100, 644876227, 933096835, 22807274, 340117802, 415408026, 5547985, 164367545, 614670634, 637294122, 790715161, 124399409, 877926096, 584343287, 783307204, 845652875, 920175812, 724031081, 489205272, 592999870, 715141348, 754870919, 514258025, 145055453, 799580773, 403282483, 754151279, 314529142, 36159509, 101472995, 317613485, 107658630, 329403626, 533254384, 29295663, 598671291, 153123433, 626774160, 308699528, 272929534, 126169446, 263447992, 730373908, 262446590, 333664842, 415809542, 198620989, 452989877, 389561813, 687843731, 52109923, 278127158, 91979809, 948713106, 898536543, 796061726, 605610151, 937133816, 576883685, 727289597, 916072755, 887294680, 443985901, 642358078, 408546035, 711619805, 75179366, 865307648, 95893680, 471951979, 756167927, 80786122, 793402127, 78649037, 240779539, 589819856, 958978138, 611637511, 946140423, 893636953, 667516950, 7997866, 604300711, 632010541, 873972503, 631131752, 549429524, 717165010, 348746027, 95238619, 614079314, 698819380, 635627559, 500328634, 199532546, 18140766, 207832216, 401266034, 399116655, 893465913, 500526205, 290600605, 654806666, 366671446, 780674128, 756105026, 501537079, 17361520, 883149953, 680443420, 737835255, 635831786, 826421406, 288748375, 681072556, 775310554, 338083331, 865969486, 188530625, 20776679, 130876610, 406458393, 530090550, 478642156, 196946221, 519055383, 114044597, 139128559, 651847167, 982954587, 844965804, 878040956, 62353954, 935332505, 911616025, 580841829, 221197616, 65887153, 542219308, 226157176, 727189362, 675105093, 323328133, 747370259, 948034449, 414247081, 41121413, 790356886, 476499712, 690407099, 664284945, 775383681, 64722277, 210048143, 834351139, 545551393, 2065049, 952287959, 859679162, 856780670, 809782698, 534142021, 13818955, 431105379, 965385027, 134013072, 202865071, 559431478, 119995433, 37243472, 525476124, 344541499, 440109904, 429565742, 311027744, 783965953, 590536079, 17718156, 307700604, 605653776, 251940451, 693813795, 211942185, 743592536, 70614638, 790805599, 285983908, 491135616, 457646547, 627959560, 570273199, 591317731, 44243485, 33746176, 244127549, 422090531, 244946346, 967603413, 416626923, 282646633, 964419821, 380866430, 627776442, 559651164, 463994093, 977318358, 515991572, 763009233, 787458121, 322099709, 348955125, 175060411, 316941046, 13911777, 389624641, 839172413, 274729974, 360181348, 384597437, 609078213, 264891881, 804755286, 838545014, 542241111, 432206422, 691180874, 113212351, 149244, 709435707, 138407849, 569975309, 653693334, 908486710, 317715783, 221669859, 106238201, 580602141, 888237594, 988596343, 273631392, 758478236, 856043730, 837593374, 943782842, 587388081, 579239540, 767832296, 145461827, 633741245, 840645273, 790580105, 751185222, 624579060, 499518580, 944733832, 29189123, 511597592, 501337168, 641839541, 832500105, 431750222, 786917378, 44826211, 3405666, 283642148, 335756434, 44637757, 429007724, 237649594, 671466264, 301070852, 302251977, 607814738, 492529865, 509896469, 791993432, 826509974, 950141501, 434587278, 200132451, 854674080, 101581156, 809117738, 268145027, 348019255, 27395412, 19531824, 969859497, 828856096, 820915727, 119326883, 207944489, 876788413, 42142078, 744276091, 714331903, 756560325, 226653914, 560498752, 316200008, 497959067, 111220722, 553904348, 990930074, 911056068, 399903610, 165537350, 847470491, 475305663, 602259888, 453937300, 711716400, 332076848, 851950329, 392114634, 210226938, 920594397, 740785008, 587498666, 84276948, 714357099, 861039409, 179911107, 305184440, 546728516, 460749209, 124255529, 13724877, 332991489, 857079878, 662112331, 35198647, 138814131, 811798651, 820686481, 364239785, 65157433, 865982492, 407152012, 362253435, 194228283, 94568838, 62603026, 554652288, 805727087, 257283869, 951021506, 85336919, 341832420, 335479861, 33308057, 751013954, 503888405, 233697326, 488187490, 887275206, 594985441, 832119941, 278565759, 483406838, 524416197, 451058774, 773605442, 628357800, 363680392, 644243528, 210154545, 190314289, 95687297, 778815637, 128938813, 506146360, 232999281, 266284961, 419294959, 985416909, 703417941, 97783891, 140897055, 151847103, 437746353, 203578261, 5235900, 577935268, 912142210, 381629486, 594909629, 949483737, 485072739, 175357182, 779405757, 683491560, 296307771, 331398983, 883035212, 825581906, 837140667, 136333511, 764480513, 518771940, 728267529, 352401977, 974242580, 700400823, 398912481, 665811547, 635594746, 158890307, 326859558, 963490747, 727664775, 375686757, 523904398, 500949844, 464362759, 945478182, 674196808, 405880446, 870271372, 915563184, 523951441, 401847204, 630792705, 496451116, 729942382, 672189552, 484997535, 346279844, 385461435, 996251719, 677938035, 46115834, 270389257, 381981623, 551464765, 56306901, 228034957, 247089304, 619155934, 866152714, 785712927, 60872817, 973888678, 499777525, 424198094, 677149722, 362012181, 602750277, 659408573, 889094210, 537660321, 288456718, 668935626, 169189110, 339691399, 662578177, 288925095, 122879108, 849291049, 308756399, 946664131, 153805056, 483308704, 830016259, 129149136, 502773036, 312312265, 406770600, 956504364, 541059915, 229949428, 270460903, 215657186, 643914165, 248497792, 379704920, 867435729, 99696621, 667917511, 715800801, 947119808, 69433937, 533244994, 413531763, 161759822, 215872503, 128752139, 421768383, 365299332, 815570092, 24612329, 689597831, 839368775, 276694060, 410711452, 231143688, 87526177, 209798370, 386981896, 222540169, 720153433, 334156940, 988335516, 498610949, 641095040, 758997416, 471503543, 405840403, 823635913, 963453175, 389796456, 134859727, 565116944, 655520432, 976908689, 15287562, 173525579, 923126328, 933599959, 18493022, 200433164, 603841862, 233771115, 370386054, 702857570, 524950935, 637328214, 522723476, 857904248, 786967061, 738057317, 791959135, 515404818, 945316587, 720358916, 910725708, 51557301, 367994574, 562738792, 375569226, 969021927, 821834900, 29926609, 580948448, 990141943, 28424974, 106428668, 614678002, 333748456, 895198697, 891104825, 799381086, 676839139, 378809804, 506584328, 668313895, 623790011, 14674258, 985329033, 253905361, 697167280, 112970772, 469464594, 10172235, 392402507, 139262805, 750985758, 598295396, 579497607, 508501945, 396627389, 904655150, 388534310, 987470296, 797971728, 446547116, 304515496, 76658662, 122258339, 257216575, 195438056, 450292681, 970089567, 160364075, 686947112, 910488359, 176509791, 247282195, 206222640, 302276991, 551188671, 629709073, 733254839, 748140098, 371973235, 980188554, 374662086, 628994312, 498311052, 31013667, 89920248, 861692325, 356496556, 422467305, 571544054, 704478905, 685990050, 821278486, 307978767, 240423978, 924000390, 38156173, 81895509, 578235901, 788105824, 25358510, 952500594, 918380037, 673558825, 905628695, 98010129, 989403320, 169645377, 308727183, 343031258, 340942787, 608648268, 148750279, 872756742, 206041206, 865128663, 278226368, 266060436, 985401900, 350884407, 204170892, 404204690, 160341059, 327037641, 430975292, 526070821, 71413476, 783800571, 877632212, 725895674, 62814042, 380445468, 644707242, 705240648, 176597001, 92831030, 107733959, 611326362, 657432952, 69687031, 996677701, 230915540, 323515128, 450739387, 881471900, 584368573, 679560111, 922620212, 820677725, 637916690, 675204495, 973606389, 332763526, 122347876, 731389898, 526871944, 729605012, 986577427, 903387313, 137725640, 62367128, 453651040, 395423870, 823473407, 251466037, 760601029, 852658862, 980365940, 716653084, 771278816, 188877850, 776196840, 206657149, 781784163, 239355293, 663726884, 188657155, 230612681, 342053061, 594167311, 174632924, 639150676, 119326651, 789829862, 717536391, 567052071, 740326314, 732131640, 699610568, 621604968, 247029495, 928990834, 349274655, 20522836, 875859808, 720157605, 951589978, 322161884, 235621855, 409473782, 609007302, 556648580, 8390490, 601490123, 138401717, 144589149, 694018422, 371603226, 524340811, 585499715, 714942877, 207892975, 655023551, 321231063, 45945753, 409961359, 464138239, 973525267, 891328563, 97999747, 439946096, 182411808, 993372456, 228796976, 497178451, 563830627, 888167231, 736495565, 335655228, 536437602, 962269709, 721474015, 305638542, 681842616, 497594033, 732272442, 335687413, 747341891, 178883501, 543111759, 48162938, 773279464, 223141816, 795215725, 641593351, 498912657, 314375697, 772709820, 627400168, 414710102, 926088306, 987657227, 190854327, 77137767, 562484173, 266298378, 581166336, 745653072, 969536419, 543219474, 143769678, 178676485, 860504313, 317563372, 259406622, 717258975, 622870643, 156857528, 251775974, 628169314, 388574373, 895269620, 372024608, 808026632, 27714937, 425062738, 698360762, 77582372, 775160790, 718978129, 566287854, 599362395, 72122246, 54816022, 647279688, 492401984, 514011443, 228822841, 894760401, 432844100, 214438828, 301284660, 681848557, 148795090, 241149751, 845301932, 658582114, 768280041, 947867508, 702901328, 905941552, 174980326, 166357962, 933128731, 204091370, 428325874, 315578609, 426630691, 501437731, 263083171, 313289102, 378024982, 811163074, 896605437, 315420805, 253353560, 143079134, 744444932, 145754841, 238048654, 320305749, 789409073, 551478604, 187070592, 80323794, 835582219, 163086436, 340370945, 516563283, 878013578, 182387742, 880832226, 912233766, 770659639, 804913180, 673597384, 237817484, 670469668, 948439259, 914969076, 876883565, 89633973, 630977507, 428839562, 912197272, 983113983, 565096697, 685793387, 331565895, 533814312, 625979895, 483785559, 864997348, 437620001, 307834843, 181748831, 900521518, 423360488, 188001069, 130035767, 150317880, 594002074, 737216307, 957171552, 109978028, 198143309, 966900500, 856062976, 303577280, 697525840, 137336397, 543672041, 784204026, 211380076, 325559882, 63801235, 501829366, 951165833, 519903387, 47802369, 41407174, 348614142, 773779652, 724084450, 604561140, 16764475, 381926008, 663968842, 335278421, 570428434, 41859330, 609202142, 427128913, 844714942, 945291393, 337730901, 501477967, 630750258, 286423732, 974621563, 623881546, 559317712, 405179056, 705962120, 496168946, 901286323, 980178638, 713832492, 989740250, 336259995, 213632017, 380347256, 876831772, 427075652, 998613200, 709267859, 965569922, 41037362, 639543265, 389779466, 444948947, 187437238, 907115341, 738161343, 486912589, 922324875, 125514310, 787003433, 300033978, 490101878, 606096007, 39746711, 196431154, 319239330, 957651710, 287029057, 932724963, 891922484, 399632361, 749794095, 427710809, 881703527, 846511386, 489290705, 879900606, 8646401, 119999740, 406954807, 856909016, 277756403, 517076984, 684896561, 558258782, 804572941, 10782320, 656251647, 689100239, 825230437, 197063603, 29355297, 525896150, 552354982, 245945992, 716590226, 435211993, 215670339, 581877531, 49533339, 889657698, 820871438, 175082498, 33833647, 509779831, 523238406, 920160333, 605220052, 971853347, 356338937, 714475918, 437068095, 883251094, 414745864, 281048399, 400205615, 75008093, 201050530, 599930129, 887752971, 206052048, 255208993, 515885823, 859465453, 61522625, 53653198, 248587976, 998377410, 292514883, 670336885, 542566520, 484741680, 363322089, 428025067, 843128984, 608770057, 484694981, 353867676, 713740051, 145546920, 76632583, 462978899, 277190053, 405095494, 651425185, 2382353, 263770364, 86277363, 452278581, 508865559, 521364427, 347277539, 551370929, 478459301, 970196761, 334959179, 496894344, 845482053, 400294502, 61097412, 867906140, 51232511, 561804829, 56493562, 743579313, 875454964, 936730013, 887763707, 592096434, 229083337, 731371594, 536002704, 359472383, 408541095, 734879479, 508901650, 747347318, 51232778, 895476482, 188565043, 706729304, 139901244, 926927420, 548754632, 141389560, 539649339, 158092537, 853986578, 654482596, 350057482, 913000620, 377565459, 307005708, 572393240, 852651005, 202774458, 429029628, 538388583, 43243475, 614756376, 51612641, 806492929, 316664749, 119722652, 438856731, 339203041, 302246810, 310809883, 885372574, 938960106, 365961503, 661174049, 609350538, 892229590, 503760913, 440869156, 514731486, 862133031, 384774904, 605564512, 63342572, 619062769, 252318734, 850972184, 230502227, 839170044, 228638321, 321910896, 723598918, 310871881, 973470739, 929234324, 672118224, 59832857, 672553980, 473573851, 812341883, 390256933, 831384735, 193583011, 768624917, 101233160, 274250373, 526688062, 40426463, 689997032, 626300471, 984080254, 599299291, 361085179, 973969617, 136845671, 161245930, 10071770, 361925808, 849684956, 372327818, 666148904, 387759756, 167894470, 737125008, 784171134, 351376990, 353005609, 528023496, 994243522, 145214693, 619775288, 995717305, 403556058, 919508318, 373903425, 607868194, 617217521, 40505437, 549781282, 261528354, 468079334, 450096082, 919937528, 954336956, 812408577, 727430643, 397690443, 213042333, 550606512, 858584873, 877844939, 202600987, 891399474, 947584164, 352292550, 149160727, 374169070, 18300689, 603437300, 374339317, 35282235, 112180510, 878994637, 36465305, 726866071, 820658012, 251430562, 416786392, 683150830, 831793699, 139859659, 402598883, 94378261, 39194310, 300461467, 127708158, 352056217, 794473357, 622442097, 382830924, 666482877, 262129358, 18133550, 990016424, 360934944, 979679534, 732899546, 840296224, 953045787, 15373, 997276116, 770433192, 3767936, 452540333, 164983106, 703532049, 139954857, 996501759, 487375711, 279816681, 27915572, 376620567, 844620044, 787507840, 316212934, 525987674, 565802056, 426030674, 978918641, 19201250, 944959094, 870126572, 478617760, 114741511, 451185078, 467321599, 78735171, 971713009, 198766436, 40990175, 700312784, 549261220, 565126202, 360233081, 658669736, 458919164, 583924950, 469097072, 746725301, 512512323, 498510671, 355155210, 628905275, 900264324, 984077594, 815017604, 394046757, 390673621, 586457485, 574770808, 317048357, 920220949, 30930886, 456697945, 500132973, 484411951, 450951288, 46588628, 467211643, 803489767, 729288942, 642342948, 269468742, 609784032, 983602674, 496366014, 980735884, 391164265, 750244820, 983199393, 14534793, 86476794, 755273961, 469047061, 839464113, 341600711, 835890878, 449647058, 732659769, 896136688, 297447478, 430114134, 297298388, 735034405, 696491188, 582165853, 160080174, 230225608, 801097214, 463371504, 730572047, 511669560, 851303472, 736127240, 449536227, 962730017, 645368139, 406802233, 402436153, 389650282, 98550855, 756967866, 58232260, 212733957, 610967177, 879316604, 61078811, 378127748, 144198419, 575051398, 320426193, 175610390, 120126405, 509335018, 6981649, 301776696, 395893113, 159983082, 334565426, 222906151, 808501696, 182794663, 961727838, 241712984, 616507619, 895479993, 295669833, 432000326, 613402744, 554238745, 811907672, 567682361, 176439617, 481239439, 688703675, 573780415, 201007674, 785359569, 314725441, 788191419, 829737775, 682144896, 380655130, 513392046, 858810819, 881642267, 174994365, 108327454, 498226452, 361670275, 37956596, 209715234, 535805938, 682438159, 688437803, 953138512, 951169768, 616929900, 689590842, 271963035, 606223204, 419207728, 302205192, 438554755, 54546966, 284660638, 218128197, 550210681, 843253862, 220634105, 410861308, 349174655, 272621424, 352222459, 736508794, 588771734, 779370090, 857480902, 745677570, 693618527, 735862941, 291877913, 531950257, 720670626, 49812239, 357449331, 395235959, 746868290, 44791195, 808625255, 189323893, 855330218, 746778175, 87995227, 77312615, 456430459, 853075529, 101585697, 276859281, 43518050, 722471123, 722042764, 326599861, 968788127, 146630605, 250602068, 102659130, 729014644, 275090663, 482445211, 598774619, 510029883, 58120426, 499112705, 719152897, 677976947, 598822977, 474334335, 658214181, 628543567, 198895256, 720727644, 864823889, 224673013, 188577003, 854536343, 541768863, 576922483, 377733930, 574384508, 784470426, 421210855, 486498132, 696605683, 539927073, 913820694, 636841536, 863096350, 151370672, 256859243, 132566970, 211124277, 369184892, 723244961, 959044623, 595290980, 493680576, 922202350, 694442637, 609620081, 518921681, 164764484, 762391857, 156113384, 507359211, 790101723, 660159745, 232201150, 163795322, 55435734, 978677744, 633035787, 71508471, 827918514, 887484062, 243535150, 708503351, 294089871, 260805695, 174907109, 84168836, 344019606, 977977540, 896617804, 693162593, 585029938, 917405736, 771611389, 979099181, 566254971, 793501372, 404234249, 800615917, 122862319, 78710425, 577044214, 762930623, 894340720, 129593303, 425182056, 23199828, 590275301, 399912770, 648190306, 83038023, 604004991, 100509851, 269816559, 398677867, 747522278, 685777269, 927006982, 875059926, 88443430, 598888934, 147807703, 949519026, 936384185, 887799770, 186171577, 8059881, 721670213, 182003147, 639103104, 695737162, 589925957, 672603871, 882623802, 999712032, 599173840, 398962414, 171808060, 733820300, 346838708, 308205730, 526788208, 534291804, 310573422, 457045868, 489540142, 331000898, 939538987, 976217559, 711582303, 892978643, 967180419, 53721378, 561689789, 108654321, 655043893, 427740996, 17492617, 570256158, 854377660, 112234644, 709219699, 856186789, 380316988, 662367450, 767795126, 73630187, 426956061, 474693065, 86603869, 911968255, 790864362, 751647647, 993277827, 360358821, 703587670, 146868131, 17728860, 595136778, 132116878, 709047013, 216041957, 249025134, 433801233, 609398788, 620998759, 592373554, 48930352, 947068547, 94276598, 704898842, 964321413, 660060113, 419244928, 158403352, 853027779, 524017971, 359123313, 649782863, 180686177, 169871864, 392286647, 543618265, 36395324, 882984626, 847584966, 528682648, 768470106, 550441400, 108742834, 24858159, 397686273, 229789564, 270236369, 754705661, 544346930, 511718913, 129781482, 850548701, 19515091, 360512585, 244238204, 760696462, 521997713, 835451249, 194050124, 50626355, 660986784, 571454222, 496473620, 417900158, 504954919, 327639000, 368523957, 543753455, 60778331, 892473911, 584418233, 620057786, 612393155, 620364848, 530701726, 593568870, 732499260, 360410387, 386081400, 153718913, 400703436, 52867793, 769688712, 464179773, 607771841, 841338427, 868322901, 49905572, 631960808, 856455674, 337570224, 125180096, 798665259, 800421995, 740986502, 220866814, 414431716, 636022647, 49459486, 554740424, 38853209, 120471779, 480649060, 640098475, 384093864, 798791246, 48595479, 110996841, 265266820, 545079580, 238761053, 457349771, 409315974, 755455249, 558224387, 728623114, 639065995, 246199180, 9114078, 225012306, 724747213, 727230867, 264380695, 677643822, 312193883, 781420614, 117169346, 665402836, 657919421, 527488860, 689166624, 124603220, 548287749, 360722402, 656652841, 467540246, 670564529, 4216198, 900130653, 555635685, 496703242, 463601738, 304296113, 559035322, 295297828, 311010352, 509385968, 853958649, 784173712, 127573317, 122812045, 217934172, 625465655, 668321558, 983136553, 708122049, 894654344, 844427637, 650748072, 646530810, 687389193, 101128355, 441318268, 376413187, 221763508, 125779457, 69419746, 49203201, 522350807, 625363647, 678678430, 217213394, 603742665, 515749745, 217860539, 582919085, 401084996, 818886876, 328131760, 455008496, 499830688, 722679797, 76509633, 103593814, 818669023, 775740326, 184516199, 7685695, 558716120, 541938693, 642081704, 777680129, 96498325, 655924387, 975970872, 595610703, 77272960, 546596516, 954811927, 595600993, 880808499, 164450087, 735070806, 597118196, 702728380, 731908101, 466569011, 680759384, 764213866, 802780483, 289947056, 61424476, 116058213, 88099621, 971943955, 319991548, 611829200, 963434479, 474668649, 566116429, 505412101, 908789874, 726738654, 369894120, 82620437, 548842377, 232947416, 52327729, 433352283, 414563553, 693512357, 294309348, 596714856, 547113472, 909135606, 347117444, 118662652, 257474198, 480740368, 987000901, 179681175, 880234580, 379159384, 924645285, 796847248, 865753083, 254250388, 290257676, 231170861, 449799767, 698418766, 399766491, 515217698, 765650061, 249587906, 407499750, 93781907, 183610469, 2321929, 615503215, 468784357, 443023406, 88882383, 971803587, 663868099, 59567724, 277565921, 778679221, 71912546, 873227631, 619627840, 778290872, 796854045, 787733744, 439908832, 964615367, 256087313, 534069083, 790431276, 867170327, 901210900, 627783728, 950502565, 807463437, 396981484, 334428065, 14534556, 451158362, 922971190, 453607452, 220884446, 670716684, 247940206, 143047490, 383737193, 181861444, 542367583, 310434015, 250798893, 174685305, 995068011, 900251870, 353883668, 853653357, 483140462, 985454337, 621289480, 483584815, 950985017, 382756065, 564581712, 518789229, 544800656, 163828514, 142985431, 401822910, 103977366, 56329138, 625005290, 975360590, 676281869, 438116056, 401056922, 601614231, 459420890, 346869162, 114812322, 106592353, 42944056, 113258009, 755353747, 500629524, 910954403, 156626096, 676652497, 349118279, 484505817, 501268425, 685217038, 944994198, 24507502, 639641940, 393107567, 703965362, 244781623, 446205114, 824513506, 850329452, 246317929, 27785941, 401609303, 466415365, 535892486, 749608913, 763876056, 38141897, 791780693, 692083459, 957841976, 277456469, 750326627, 386692199, 679331812, 228882113, 29635733, 170783247, 369543560, 940071191, 601840153, 515510752, 626213877, 518077651, 532601014, 889644807, 620490798, 44568272, 55578066, 494086100, 536336366, 42629548, 123971002, 7935435, 561372961, 143788903, 90224380, 850892602, 417749652, 730270646, 836291528, 423611354, 233523814, 498643877, 631188437, 151869452, 400161007, 172309753, 616087847, 444488735, 102987453, 502975554, 810303193, 602557418, 124428976, 505653401, 729059244, 304146295, 90982286, 263588047, 748320961, 388284560, 664777602, 603583560, 717972597, 61087417, 215618977, 840211902, 891379273, 83131294, 161503198, 486562364, 622704586, 264877427, 666348830, 123933071, 669873358, 401703381, 302886540, 597130375, 801044244, 220568814, 459924332, 165190378, 912555972, 184653153, 346049620, 238047377, 812981350, 33648885, 84954214, 38703894, 525908831, 14565868, 274058857, 703513094, 622840516, 506409213, 293150435, 641685287, 508149921, 193569247, 40793630, 908387030, 296289771, 845780867, 94275982, 758613689, 240524383, 725682845, 287220371, 366142532, 567451863, 779259196, 475881056, 327331242, 59228070, 689863636, 915381308, 393764477, 596140071, 96647024, 743679878, 356649233, 514293000, 984239473, 815011605, 87723271, 91180473, 931847415, 376424748, 230608455, 335634883, 568098719, 308553847, 321548022, 170341896, 14470360, 469237965, 828855931, 402919391, 567168715, 317828487, 904022270, 475572924, 979555330, 319664614, 88052342, 126282152, 855178124, 175674539, 830291876, 911100696, 142230218, 643807268, 133170174, 13147186, 34002344, 701157829, 778475383, 901710444, 688532048, 637183689, 46413801, 145050406, 687976624, 976768437, 859986624, 804626066, 533614941, 327073018, 179354321, 493644793, 616544455, 61409701, 561199849, 890304712, 816163611, 423643973, 747483890, 257689900, 165072457, 25381974, 633160565, 815971508, 126806903, 184864224, 415002742, 205366569, 840893602, 241360343, 85499418, 829397184, 587999281, 10329229, 926115830, 210350886, 25504080, 476581111, 123254679, 606895449, 76583042, 192547656, 492773730, 185605358, 400853624, 585033999, 708031336, 412180256, 825964821, 781905042, 622024551, 952983723, 222583759, 616879966, 298725360, 715680135, 349396085, 285729589, 752108659, 801734993, 360171809, 325686472, 116279272, 826125520, 61956937, 764306757, 847006607, 917684861, 700554904, 959829390, 268151651, 904969097, 266054488, 606001497, 999305338, 672369290, 827937986, 374284153, 909965535, 463461955, 181329734, 368463070, 153607173, 889338775, 662155889, 483393033, 963015571, 717181138, 147936010, 784561804, 430248572, 324102226, 880202079, 123233620, 917802285, 144293405, 453677049, 711421792, 106583886, 119046641, 986711377, 63108601, 116054090, 628716319, 513183494, 80261572, 316751255, 800363700, 342616005, 726740720, 252612276, 717991781, 866481209, 917938335, 732476485, 764422159, 269722012, 743800690, 284409016, 727989235, 874444652, 966744323, 878355701, 650660334, 935607095, 980770148, 60988098, 647349136, 888235232, 528353866, 685939846, 465084367, 985222410, 286804540, 875623754, 859757307, 690845559, 202910366, 807788388, 430169902, 449222965, 764440433, 712820280, 308683313, 530594120, 762690091, 765921735, 417113171, 28657474, 771790122, 710730219, 716324025, 788337348, 800552416, 277705688, 675792678, 520222859, 19101338, 115476223, 574633083, 413051437, 619524949, 378328913, 505468651, 786725263, 709756403, 321326995, 310941073, 621895323, 621230616, 645842220, 12042243, 470841862, 488443792, 358687185, 646523599, 432254545, 772964663, 726214518, 395501656, 460770024, 482294903, 401612651, 941205432, 56311955, 170972877, 95942260, 762227625, 139512858, 42862214, 676597626, 399276082, 629808305, 265909890, 289731895, 478466102, 522204670, 697572365, 799059260, 991358480, 254968398, 792878964, 548993540, 356779601, 633899380, 440095962, 816989624, 451952360, 896608073, 782136977, 481902314, 131662046, 648075590, 843461974, 600545643, 384565027, 940618194, 340121157, 132455962, 282109091, 401143692, 173730048, 43386970, 915624202, 449233431, 290531651, 164608350, 288911136, 306149316, 397014374, 341870390, 374222400, 653219180, 650258368, 985113901, 29587607, 378210148, 382362307, 462951324, 632160640, 323798219, 59930075, 665862878, 131615396, 805553808, 123685153, 546460986, 535762293, 547351310, 464311112, 634134582, 942546823, 680826928, 688756691, 323417483, 430368764, 966171665, 900326677, 297695148, 592525187, 233277586, 283751243, 326987011, 727699483, 620667137, 24576546, 551583990, 874888429, 414096503, 239700718, 268682217, 695415821, 539902199, 759940925, 552778296, 133226163, 711262134, 888809295, 879849362, 469534637, 870673379, 390399328, 635493568, 111265962, 963789334, 986027263, 56643179, 370605889, 66783933, 494742526, 989615807, 840579315, 413811219, 184203386, 838344520, 832011031, 497062359, 98591176, 308978043, 577580567, 160029493, 665381845, 826199376, 561995896, 356634123, 790660380, 93745487, 656605956, 464783673, 30450065, 420742524, 958001553, 5066574, 466794373, 334290425, 884049434, 532640488, 930303573, 95485959, 452405146, 680352248, 882338363, 851608258, 962028073, 91511461, 26848662, 529411339, 631241906, 803963521, 725450791, 571362014, 337521211, 643825877, 299214342, 549112875, 272056497, 292506176, 258851704, 915108080, 205002673, 37469240, 307954400, 162981946, 19237505, 130781279, 295820354, 167495545, 813258373, 938910888, 859610879, 20842671, 939634900, 121819605, 873045113, 88077986, 697976440, 686493734, 143527769, 974984554, 503739341, 843827083, 892207544, 663354004, 271984781, 504866821, 977702108, 937851518, 283546791, 322114948, 70832123, 127091208, 510663017, 289142859, 959486148, 552138056, 307445015, 726230854, 436760654, 358753429, 133970647, 422607847, 998997500, 846388725, 143892011, 733904539, 620447460, 62229636, 604687395, 697609618, 68176943, 810921443, 341008612, 865563678, 580718837, 405600568, 573155666, 117804850, 957052050, 283958261, 170023882, 768716815, 492256949, 671047038, 7037610, 81522487, 382768011, 667590847, 328951339, 18108822, 904821365, 26946969, 614947723, 341847785, 965917237, 969793156, 602466359, 352581442, 493181037, 567733381, 363667521, 737022209, 32522294, 51065796, 840474078, 454421787, 422273149, 520635536, 57349295, 630738832, 139695705, 591664026, 381004410, 194387693, 934143076, 814209073, 944644236, 89899746, 548184505, 470600647, 176914388, 13202620, 318156580, 457067238, 708692155, 353869759, 550637306, 607004220, 25466895, 979246133, 126018376, 752791373, 877391112, 176801976, 613360760, 692924574, 229677017, 298432239, 393536252, 770960240, 280620434, 300024702, 179602568, 316994063, 446887606, 777808638, 549669447, 611901941, 598935025, 892727733, 55189679, 965052188, 847264126, 321059344, 920165790, 172392689, 861613910, 468551360, 105538994, 735864845, 806799887, 272438802, 274905712, 979443091, 45196455, 43620675, 167615190, 729688143, 676398661, 219210922, 539776453, 907760758, 970531033, 794966680, 872331510, 458741028, 270163883, 933396280, 21038276, 207417919, 599326826, 96220945, 913681184, 788967346, 996348225, 418987639, 838566818, 518070026, 59903215, 981014708, 609860417, 274408060, 396225486, 693228197, 595626986, 204693377, 956645615, 338740107, 60906927, 904343169, 75636732, 478556284, 579754269, 21910851, 238722453, 420951830, 531920503, 383986213, 520548427, 256757951, 124066665, 93461619, 2077471, 403361689, 263728569, 396418090, 365963283, 388231696, 147555407, 476723696, 660297848, 329265544, 797609924, 125905467, 770051127, 59682270, 321822848, 828470157, 916552944, 981426371, 503182462, 455726695, 662124546, 938681627, 419822102, 320226586, 278407800, 319219811, 443769549, 500607983, 883242140, 55348389, 794943858, 331574166, 80245592, 922781789, 209669301, 76199789, 374766480, 158534931, 424243523, 291928807, 457646388, 465821111, 958614286, 837656168, 454092804, 936673035, 380006796, 800441899, 250424783, 515974584, 489699893, 852629576, 604531406, 735370858, 976217974, 458401711, 969732960, 420923194, 406725141, 146051040, 105148925, 516786300, 474023258, 81744693, 275892953, 304688504, 321007350, 162972813, 454460104, 810250044, 207187824, 197563107, 526130816, 761671795, 512030194, 193501971, 149760218, 960173034, 808022810, 745491715, 425530249, 446238038, 562646828, 594030391, 341305742, 738164146, 221953282, 149764579, 640162616, 380067085, 110487770, 364161281, 285118635, 914460090, 238821985, 406473184, 655866498, 924441417, 392848593, 874884845, 249319609, 164835701, 646521440, 967148280, 663937897, 493286202, 992799841, 469168988, 303768833, 828335552, 338290811, 814590628, 666655474, 539781291, 818671891, 327273687, 512171554, 812221636, 89715562, 704234186, 702824149, 313368568, 174895299, 459333224, 574382525, 218996366, 471967931, 37355429, 350687392, 275785144, 489194688, 176254151, 117425351, 442976155, 570636686, 422603672, 756332842, 366800796, 720148055, 188035949, 616049030, 82346053, 799707975, 588691934, 148741776, 132012691, 760304543, 910455751, 896791542, 272164613, 637096497, 693794431, 855435616, 199081630, 442512721, 996731748, 625027741, 70201623, 777520694, 261167516, 69993196, 413088058, 211153187, 966625242, 911079091, 61772631, 942012637, 670449573, 258117252, 379571741, 658373481, 704859575, 534607666, 647079088, 804739664, 103082964, 555109767, 359531571, 771451622, 515015872, 573851672, 999059756, 67279214, 840749794, 358645896, 949476093, 194086593, 446166006, 621237569, 789931885, 186999590, 717206998, 150946432, 45341937, 827381217, 595253894, 246563769, 215325708, 49630993, 130300765, 176543430, 55713747, 983896306, 407115720, 181204509, 732727194, 679633794, 734771012, 868078040, 354564356, 721095009, 794042428, 405820909, 341619155, 231134934, 795032268, 547702012, 386321351, 186008722, 316177138, 686831179, 441491496, 391411187, 696237308, 718510918, 32851549, 253702508, 277336195, 993069436, 93588495, 118973092, 734735787, 63379536, 787685202, 314134397, 299946236, 410558146, 382377017, 907669839, 4068775, 917289804, 224071405, 428152196, 286969670, 515048121, 492159903, 511290562, 278961288, 880054445, 831317239, 940331249, 385114363, 146083032, 340774736, 18544656, 111024787, 272178417, 849199812, 452132842, 496506274, 100970238, 477082340, 639863760, 377886134, 503387824, 669964179, 530342106, 249623415, 781517846, 108091132, 325254883, 851920935, 671379292, 332815304, 608829034, 831494306, 73322231, 244068394, 705025045, 596553667, 861735176, 978269278, 521172544, 785135806, 43876492, 824550781, 594961532, 883502739, 909117020, 601358578, 198037636, 869092343, 107979509, 753709083, 818672202, 887234380, 141881904, 80774801, 818445643, 173779165, 503200000, 701596790, 857795353, 241634972, 187310145, 799968850, 958241101, 863466828, 506703572, 778660690, 136355920, 634188820, 868371483, 256702527, 529908493, 239499193, 901921589, 722604454, 103491651, 21959183, 823982275, 521410600, 570335356, 283901869, 68028593, 312038477, 9636032, 563303200, 160826339, 698697404, 60384525, 239794542, 694360541, 38123004, 591904572, 205038578, 636347009, 536871551, 279802577, 935130183, 92011676, 855330343, 38070037, 867080438, 311630004, 462829192, 864030532, 2031480, 249465063, 788256180, 982279957, 483122707, 782928298, 596768985, 525268382, 875173742, 434816551, 987374634, 367638315, 963534789, 302031868, 399790672, 460905248, 186507161, 389349470, 99622518, 814344562, 351759144, 731126077, 621583958, 251344005, 899499703, 121214452, 207709177, 456566818, 304961539, 865736049, 273981035, 203257476, 761473298, 746825427, 487010960, 863750888, 77708677, 18797616, 746082554, 543614103, 60791106, 904717111, 673900183, 480077192, 140634465, 162245764, 422737487, 892887811, 812643216, 329725747, 985959404, 564524347, 273585890, 33748269, 95723001, 564240115, 932567744, 320183015, 953187309, 877949666, 148959155, 729219902, 441906790, 404996254, 455176671, 727777919, 246597346, 701322262, 452657245, 353871491, 49650551, 13290531, 510246283, 284504615, 973499235, 547076630, 354279041, 858549411, 148291107, 75448038, 3714252, 445462049, 277831922, 379826809, 964087014, 506342279, 306644483, 790067319, 506203203, 780877102, 359328450, 381334446, 94027836, 616704239, 898163616, 712360543, 912045942, 152845202, 821905938, 704925378, 674755564, 1912123, 706892973, 426019148, 800498727, 796157223, 196639938, 77493597, 708486906, 140700465, 834922833, 258288024, 672069010, 439249249, 622953139, 757037634, 378667398, 837978446, 503328271, 60117306, 826268451, 217922656, 1167241, 858709853, 834462474, 930430791, 987946223, 539831445, 709300168, 396376154, 873706965, 171835183, 769784355, 682779692, 787105458, 358668849, 622391437, 682083095, 152543235, 658063092, 960371469, 786475797, 679026011, 75143712, 755987025, 70645268, 453395683, 211752856, 175883161, 321329054, 713292016, 596411351, 164743070, 345440332, 620846154, 956978509, 821724284, 791427977, 174787211, 748766253, 667067738, 613104463, 442627046, 313116099, 969218269, 305325948, 188622344, 72675863, 811428819, 944406265, 34844779, 904588164, 511247173, 391665744, 304161057, 258218462, 494235262, 937705055, 234270790, 100009622, 513055261, 665673529, 361572033, 26323754, 546823550, 697951549, 48533195, 160916410, 156130833, 912538829, 733963007, 534123568, 856642689, 441639916, 506606064, 872022728, 235205416, 52612288, 579678001, 384089714, 358010354, 752398556, 612087609, 904031466, 640716094, 795822362, 363527425, 76353174, 699252062, 907004634, 809750934, 166089748, 861840194, 719465934, 416062009, 544544785, 72112566, 314471950, 889845441, 730054736, 878038632, 974142038, 516842567, 740905556, 274842010, 755941223, 81711499, 386117995, 166514748, 121498832, 965639164, 533259987, 876525631, 533368258, 959801474, 364558976, 803144808, 661669693, 358136176, 809915641, 7805900, 173708053, 872128942, 432502200, 451768679, 479369443, 131130648, 232762235, 530140803, 335029945, 211748079, 204435083, 678474078, 642632168, 461037944, 642932677, 906730420, 520108262, 640349579, 923198814, 572796081, 626457163, 105573278, 413278503, 763991904, 551271705, 250733420, 491464178, 434600715, 503710868, 530541083, 445802035, 829253665, 6697631, 123697930, 401644458, 295323871, 448462139, 516841863, 132881364, 986817394, 129782443, 642184512, 709668083, 605689586, 571992304, 969501554, 78396395, 292328559, 640235053, 984296826, 511685478, 633871284, 44482619, 919686221, 487176028, 722603268, 632140546, 52247053, 544341528, 487644427, 367842787, 463922372, 480104163, 427543686, 635180691, 773466080, 873034167, 73332972, 944704559, 447020080, 24205260, 851725038, 418330208, 596002648, 843329795, 190991872, 479705907, 486340812, 279899230, 436917941, 90645798, 199067624, 489966543, 875175199, 459071647, 623005735, 105266204, 657052233, 973718944, 583138098, 308312065, 631115848, 851469780, 136664422, 971272127, 422335512, 714787819, 77710874, 324540949, 974026443, 299972970, 642151850, 756049538, 204493423, 575055484, 191861888, 329092854, 49673860, 576611981, 474562800, 193976402, 454543341, 86172305, 178084658, 248754004, 226245882, 969960550, 870385476, 942682956, 587351636, 9213622, 471800105, 71527620, 535599317, 388384228, 523342480, 11029451, 164995209, 701041169, 878966574, 613284628, 140572358, 556827188, 234633761, 621480175, 696315631, 642905201, 686052188, 997542404, 477634659, 775170402, 769417795, 121623540, 984533954, 909432703, 62952571, 202232970, 434379071, 377511225, 441228192, 896733101, 389309971, 219721187, 833498718, 546738472, 722200655, 500878869, 872513390, 863957062, 552470138, 50154606, 878006761, 21426953, 466177901, 182515221, 734652813, 224969834, 892408388, 625652223, 731470862, 204780013, 921654404, 544022066, 559152087, 785375746, 515279195, 592377129, 543155790, 617061539, 301873010, 533357193, 498774404, 798673812, 920329664, 542055992, 185324053, 397085491, 947402319, 664620792, 288328673, 545108432, 176793274, 676306204, 545011161, 6244899, 68593778, 51536804, 572526118, 981860509, 20948430, 908704682, 696576913, 958051428, 424303348, 327876939, 372987861, 919513860, 267357957, 193077076, 49543054, 323281840, 445583903, 244876839, 287094760, 638393395, 941755598, 743832611, 461476856, 830685995, 351675570, 193604238, 310114842, 667126317, 91354329, 121185775, 559698441, 619093018, 2760423, 623499997, 934586703, 798518497, 817401859, 386004017, 46405852, 428072597, 99921003, 88426343, 952403222, 541801469, 747926058, 338185892, 305353107, 610991679, 50545766, 773370035, 511542170, 259601543, 973835687, 678476124, 395814187, 144939659, 331167672, 363376650, 518141917, 476833352, 64055072, 290099821, 256826906, 74279031, 178023485, 842814605, 769474672, 60285517, 594727669, 711140474, 971902956, 635819439, 275819585, 557856110, 561071097, 673388705, 375846992, 631631174, 752011259, 381008463, 415423490, 402211702, 611877408, 787061461, 930862077, 904716263, 479910347, 615443106, 661847086, 21258081, 379170980, 810197696, 953120583, 998670497, 435453059, 523290526, 948773787, 483315387, 544885551, 580560417, 696619559, 588021771, 294350698, 999396857, 10314674, 839729817, 367752394, 646337948, 215194833, 349479463, 109065328, 790902589, 194108706, 791072713, 406673403, 14700335, 315997996, 646316681, 591253980, 829615992, 730598653, 352006534, 590184972, 468793448, 363649000, 797163073, 94236777, 387604177, 693097722, 411646602, 597427991, 295092711, 771405730, 405900071, 343635381, 814062215, 818011055, 916027072, 717420854, 594922886, 81413458, 683828747, 43014823, 25548432, 282136107, 701296436, 361833256, 505840731, 953439814, 915508386, 14324568, 555195477, 67415115, 811310727, 316206652, 809867955, 326805707, 831306732, 121577373, 363995019, 596710541, 840383425, 318101884, 19807496, 43632145, 779935421, 485079257, 125951824, 117569620, 636877055, 238670297, 292037696, 777276177, 477813665, 577276847, 458012323, 162436820, 649215751, 735244061, 786206294, 361224032, 367831509, 240259472, 689668860, 276630449, 517316803, 67897630, 777976673, 755218340, 48113229, 788241387, 334394453, 190793524, 14783472, 84961013, 960488704, 369506132, 352401963, 388315224, 163483319, 877917891, 153035398, 45289032, 186072565, 457420974, 828473050, 17779292, 263164993, 783015670, 27985221, 136592420, 862152917, 580708018, 535126971, 486864364, 943734939, 843779833, 17990853, 566537137, 859969907, 934195574, 206710768, 812997784, 44993076, 394542348, 427901643, 629355902, 349098129, 526833314, 1371962, 520203580, 643515057, 20489563, 482625921, 950790440, 781490638, 754543890, 95038737, 577805291, 915861961, 685921442, 939158518, 444806204, 679226159, 733782406, 206609950, 892298629, 831382033, 445688021, 399943457, 145377803, 971732616, 209264648, 596298205, 184601216, 568259821, 165960128, 914493442, 144372062, 917335626, 670219593, 434007154, 930325249, 706531451, 893167050, 290588405, 467888706, 824240672, 346675873, 31573065, 288200855, 104120717, 219850851, 765485075, 207921152, 327319107, 781977225, 278459163, 585409807, 632890500, 768522072, 729862284, 778729878, 41987748, 666142333, 66604899, 10072284, 484002074, 684090423, 796467066, 991007187, 768224816, 922214160, 300103570, 792817421, 534968642, 483185580, 445561941, 591016632, 915305977, 647991372, 258254867, 404373757, 347331094, 333225793, 716852582, 474031264, 318337416, 771389052, 873757014, 711865861, 57604619, 135148358, 771144064, 262424664, 613076790, 67697442, 630388525, 552479623, 77264008, 191423057, 402764854, 525063868, 542557057, 844350630, 478261647, 447905211, 549833431, 952466742, 441236953, 692462827, 789130022, 321084766, 416194919, 460084569, 713946309, 17214264, 356414415, 52358882, 933434406, 933525798, 499872349, 634494060, 627340585, 738324608, 725220816, 455747134, 428821863, 421586069, 735432533, 925266874, 884586904, 512164418, 937087124, 19672522, 75657819, 212953591, 101714357, 914069683, 513183597, 345170035, 735120560, 655807122, 718929141, 855586350, 606741644, 973888756, 25880203, 127259597, 462797431, 355111029, 911758296, 908510409, 989414571, 341480865, 554310244, 298901539, 969420535, 707063751, 831115454, 986715233, 742853620, 446668836, 6735176, 430807403, 309701380, 555723761, 824473396, 528610662, 848644223, 890990179, 68844567, 762988727, 416990675, 775502813, 214055791, 106049075, 723566367, 382549923, 224042942, 795626520, 168814105, 375324907, 765653454, 597302838, 851461829, 147982554, 817915394, 670388519, 97641071, 173923127, 994833882, 140311825, 521561148, 485169470, 56979435, 317037941, 760966471, 32637660, 64557727, 480831442, 178525550, 775939214, 287545435, 50260053, 384801470, 865035171, 232858115, 567617341, 756907194, 574475848, 83581047, 332044164, 120975071, 857538410, 893064690, 355383553, 169577325, 293712211, 711503844, 947948450, 333771027, 448271425, 532567101, 120621051, 284811001, 765060601, 216568205, 177693083, 803414212, 69052602, 632983847, 930918077, 208531481, 919505815, 962910810, 321341476, 969661764, 518754443, 753859476, 597641111, 587964969, 195360556, 691438793, 474918657, 289536132, 280937392, 654544893, 242187956, 680087225, 66241315, 935471324, 337557653, 775573724, 294783971, 8065320, 412128399, 368333746, 927379733, 834977966, 769755422, 840228289, 442284814, 496657769, 143728120, 560571501, 505642215, 40039811, 840443686, 814920206, 108272533, 545505544, 514523829, 827869817, 2441896, 654928768, 343621618, 583177521, 28667891, 812839186, 314466186, 198017458, 322557524, 204083361, 280894502, 919973847, 404154866, 985207545, 812743451, 503353533, 639975055, 449421214, 396390867, 560429791, 428162692, 882808281, 772189854, 779466004, 132425414, 279252789, 101776047, 997775306, 75626453, 834304992, 57478785, 400296791, 888870667, 324876814, 323548005, 15118500, 523705039, 102894672, 293271106, 351942509, 285229991, 743076323, 728611339, 177633988, 207379125, 211155318, 596395294, 330635692, 859050995, 370212493, 606116405, 468180948, 848909443, 877900943, 394573666, 807756930, 760299833, 728099102, 283496623, 540899260, 570933634, 47905545, 946700045, 190423395, 272990692, 212020409, 127257208, 521338802, 378572869, 612412603, 309684398, 949819973, 28351414, 366115473, 66783981, 251332428, 423387050, 491267932, 215162664, 440646022, 73700711, 859707243, 944103710, 363185331, 920288938, 200598740, 569785452, 484623067, 512284489, 939441074, 347005916, 316403992, 174018292, 209475290, 797260944, 152205300, 507508555, 450693898, 507206062, 697366663, 874455400, 527897190, 781661244, 997179766, 807547477, 152855430, 682013714, 23877192, 721676360, 304911417, 338907720, 642906752, 433635207, 925232818, 304902205, 385035337, 149989101, 800673989, 666106307, 443412220, 321715997, 480618341, 127300837, 422258606, 105830976, 616460513, 217596986, 993985795, 787114800, 630331547, 295502996, 741173459, 901186440, 214647289, 370431005, 974876500, 336392099, 217187666, 909281484, 940867194, 971550172, 721523195, 649465855, 973129428, 548407475, 917522633, 919803297, 442829498, 17117185, 562862061, 711630385, 223388895, 902302938, 902825950, 112809835, 776695649, 519183600, 677618459, 842172629, 17007959, 430391477, 471216066, 484726222, 782975094, 376933492, 951623573, 645252542, 31890893, 239507426, 492638308, 591339859, 797975494, 275221423, 411923998, 521298363, 548454533, 636352029, 7407149, 325657114, 17764532, 662158314, 983899258, 62204899, 257827720, 513542996, 461639494, 893148503, 278178466, 325657556, 30680110, 42330126, 3137846, 229355035, 625300960, 143405126, 990999118, 681540797, 482815508, 580828215, 259409717, 270545606, 331436884, 172994971, 18794637, 613674155, 588176421, 189292824, 96324596, 146665692, 899767655, 263348512, 228024674, 503706243, 215699355, 778489491, 173880146, 860237933, 533637207, 407837395, 891977777, 148339793, 39023837, 897801408, 854280827, 879972356, 235405738, 457044945, 265134991, 76893415, 775500283, 105263681, 484250092, 918836350, 739003373, 144782385, 925321221, 776653665, 520994929, 901516302, 996486476, 780076420, 647737189, 884375586, 551832245, 625893209, 843294161, 968555190, 591913123, 577477507, 345714475, 216052753, 812162831, 303903334, 659361814, 749423526, 780095367, 864141506, 946007090, 35482584, 278033273, 27716594, 226440075, 553518442, 212466037, 470158131, 8251636, 104401475, 906492151, 941749716, 967765245, 467895849, 152857011, 126603748, 3278740, 378313325, 191982188, 310383143, 701833350, 681480423, 483109071, 103598102, 712948811, 90922847, 563260129, 262860854, 909394003, 166288486, 38691469, 190307756, 13203742, 772669437, 409976920, 38570600, 315725952, 5567783, 99837513, 429064162, 608597176, 782086760, 967542179, 457868402, 657381540, 484359959, 273467215, 814629525, 771053655, 484396846, 549727464, 773068760, 523072490, 300779742, 44937467, 609627092, 287416062, 770020896, 632492958, 375137547, 44864216, 832781348, 120114558, 327048369, 634459417, 489591103, 341860905, 598093130, 701370662, 788093473, 435778803, 697440796, 88549602, 785122924, 742946850, 723922768, 419036125, 649598866, 844813283, 900009949, 203988276, 371191510, 612833082, 772319562, 620020512, 338169579, 544060422, 16266423, 592091759, 1025175, 199433419, 383479529, 504586886, 195293709, 266672934, 140166996, 198792875, 58438932, 67514518, 294151583, 297088239, 768867012, 809347034, 784160001, 97615493, 357524073, 117498359, 118414851, 213438665, 244319264, 319453548, 307364692, 732237589, 309265821, 660277744, 45338051, 180179910, 367875312, 333703609, 827947986, 152311939, 899413517, 702447384, 550499560, 363251679, 513792449, 157443546, 604480277, 85750987, 794428288, 356127000, 659385501, 672317385, 747587806, 519982134, 257928658, 363720532, 95724194, 199574939, 344545324, 485768648, 210723051, 909735716, 765078136, 82613088, 545323255, 516319127, 954343044, 580658840, 92928570, 648073011, 509938883, 940400257, 23128244, 909000930, 392555062, 801049554, 85909880, 797674267, 302379338, 705691033, 488986141, 239093260, 102557482, 356699949, 278917153, 329516446, 274239437, 233382875, 123574374, 508426029, 182949729, 179729698, 553734942, 741801734, 561952462, 47391152, 19863986, 97306960, 733783954, 959782724, 703407976, 716303114, 316418219, 620163017, 57037848, 486822419, 257673221, 915981752, 658415727, 203130506, 134314615, 800229624, 714260474, 400933635, 839953715, 682302196, 927782539, 897153614, 992317192, 890106386, 334136281, 880480441, 629964799, 893583473, 825641591, 33084216, 264643283, 257479805, 375813094, 823274964, 849796443, 953699688, 370699454, 627543223, 561818772, 743934926, 591918331, 879607652, 397307123, 450238291, 419068976, 539012139, 771073153, 579756364, 398319242, 628223095, 969464342, 890486122, 281882583, 628610058, 807788677, 117302902, 138934073, 552017770, 36487019, 453025991, 196234890, 946660148, 818512605, 906665527, 452294978, 649579018, 217853998, 658637832, 611654580, 811742356, 641463870, 310118861, 206380599, 154671437, 744995622, 522148225, 256580545, 949998179, 322034949, 543721994, 896334555, 758361328, 770052268, 143460361, 50071657, 851247045, 61609561, 886712037, 666666727, 824975136, 253061983, 532149434, 754071213, 61941055, 737331302, 910706031, 281516688, 794176726, 945438182, 554254074, 406048857, 963618539, 371609476, 213798983, 83712611, 186792523, 696939605, 30888672, 966094694, 590381463, 129034753, 399946960, 160250204, 690834700, 903153771, 751097029, 71044949, 314951143, 228423877, 78993464, 29203494, 306777683, 619318660, 958310676, 887961896, 265479404, 305124458, 668995421, 543145125, 622964125, 804004891, 619995093, 172405371, 334206079, 824476711, 722853462, 935876301, 724470980, 816569431, 767596340, 671130622, 502200340, 600383110, 59241655, 532115235, 696180192, 855163213, 18515251, 220608527, 183422539, 349997421, 18156135, 780043290, 905065325, 605728590, 35137863, 10653427, 870447187, 12646052, 766705755, 728775653, 888896621, 91745587, 296206341, 410675576, 251028693, 215077340, 48408999, 279121072, 125868576, 681096562, 511588301, 432664707, 803445596, 594289845, 688320863, 393865966, 174880215, 840879551, 644954703, 513082804, 597208735, 84136547, 486091013, 290448377, 207966875, 239898245, 454442223, 860071203, 526811529, 908949998, 815255630, 668564275, 566636087, 691101607, 424084675, 669101675, 777503855, 59108927, 43014561, 182020868, 541306873, 680681859, 894394278, 323132606, 615527423, 287224932, 80322721, 154990319, 660726689, 341439205, 683799921, 578068809, 396850320, 812036742, 913738031, 576672523, 302709455, 913460855, 72258922, 779620609, 584739665, 773291183, 739046691, 431266873, 558195594, 456289500, 298737995, 265531664, 604881129, 110588404, 182476258, 37952813, 123733035, 747630729, 668941955, 400125357, 114774978, 729727825, 170802297, 277135312, 7900997, 962236454, 218716661, 915751880, 672516493, 681316106, 141797240, 184759999, 480499181, 856054942, 460099146, 993012267, 135805789, 279332667, 147192654, 151743041, 640047134, 701745686, 914155071, 93410265, 285626962, 953742805, 500742447, 865714980, 430793794, 66494081, 13225744, 697366075, 834903759, 741934048, 271641932, 70967851, 951272120, 681827096, 888442794, 299409406, 932730950, 310320640, 458544522, 792557712, 897885559, 727042110, 691917942, 607310210, 609181843, 422926550, 112491675, 129215895, 470688900, 739552025, 644524817, 718600214, 414202350, 528169542, 713266662, 333822966, 8313102, 857948229, 893329819, 260248145, 19453001, 382979850, 143441466, 672703823, 802222576, 73881846, 72823741, 316930079, 15079771, 784397128, 55539999, 177043390, 566233721, 736855206, 41324810, 409078018, 673274831, 181565532, 349169716, 406876746, 344235628, 307807966, 501969119, 831800056, 439836590, 772695645, 264222198, 926893387, 781978491, 97171708, 615394385, 635202743, 595164994, 943474068, 706237509, 701452471, 931951660, 130830996, 594428363, 103903763, 535510083, 432502978, 92698085, 598225646, 826330408, 811947439, 327199743, 765427150, 540118361, 409604442, 509559312, 649987285, 147102835, 769136235, 970970520, 220334052, 992858439, 550331126, 345134368, 689307995, 169675560, 612734079, 452259244, 81107559, 633192037, 630071262, 234112943, 520951691, 171774268, 86921864, 745438065, 678098619, 579520204, 652993409, 10810262, 262406589, 641724637, 105474379, 465213442, 909713039, 453510871, 24293876, 793583278, 722431057, 421398324, 570455366, 167517850, 164000648, 504631849, 831663621, 444090821, 589221061, 464157966, 448078714, 103034698, 743401970, 795356892, 566803340, 673772485, 54476883, 249025921, 468364279, 906106404, 809961806, 24805522, 958679406, 869329093, 980641732, 88651849, 856482055, 183284720, 249783177, 214709044, 333126796, 499694256, 330284780, 805450373, 592813741, 689241086, 5532583, 996291179, 89972801, 86090703, 372019639, 922975371, 418477210, 766793516, 111797484, 520750989, 231458291, 251788946, 657285751, 600424228, 382344803, 332311427, 552968012, 796829524, 245146552, 980528220, 556421809, 874861590, 68307169, 44236136, 637100210, 544490394, 823069629, 339929836, 977238599, 184647842, 173065800, 800494910, 514245492, 821909643, 259667622, 406233696, 858905107, 101987015, 261045555, 340910010, 372570607, 925918861, 959313876, 396174984, 620329578, 331023946, 117551153, 868703892, 333645074, 850860628, 33552615, 233441364, 46015346, 868326351, 270368623, 183976174, 338732774, 572726764, 789992269, 895093501, 870213910, 252776941, 361372228, 680352246, 256114355, 299425952, 896039406, 833828456, 147152639, 82533441, 380125505, 763755139, 712690708, 865834725, 237187282, 332266954, 813920126, 438266677, 858397088, 44362541, 231399850, 817925402, 863463333, 374478849, 407385598, 901305383, 711112167, 990398067, 684187527, 397918017, 178119547, 674380325, 546829908, 898156893, 648929545, 925894958, 474594270, 242082597, 602103594, 670873268, 857192878, 771501019, 200182144, 640668621, 990344856, 853983771, 782491231, 93239133, 462291482, 265228543, 273321469, 617908953, 573696573, 718087201, 196162311, 553598980, 90191096, 582963321, 630493578, 766323405, 787758612, 897881768, 696508717, 599740978, 348374745, 281374585, 392314678, 995002931, 792968740, 572273241, 596579610, 177655664, 424706575, 155937702, 20449492, 617436514, 481923031, 279517592, 294853656, 116962471, 276412754, 970621326, 677359760, 835957314, 812020904, 203059433, 307448842, 969016064, 777333419, 177661320, 216827043, 885439178, 350697932, 664172170, 190938103, 53028187, 968595375, 571692323, 692495147, 551678598, 336425978, 415520038, 958360104, 709312087, 782155944, 742966876, 302264515, 336784132, 720388834, 235097695, 225805740, 337334057, 770092337, 393183628, 209380170, 227788484, 735912113, 637373153, 629945416, 798411682, 898075137, 76903557, 780656464, 648310721, 397832646, 87807165, 711947521, 988513320, 762966579, 548733821, 278179159, 46965314, 633687703, 997362929, 960408512, 882577795, 880841391, 279664912, 326390113, 743153531, 385293286, 61293601, 107850032, 432519106, 655464953, 572885386, 921564602, 666679172, 533433272, 503096669, 161886235, 204346875, 50346607, 688272252, 659552454, 830018578, 426657936, 331913173, 250152044, 438596841, 207687791, 35309318, 153336049, 370965602, 359415956, 61395443, 635925433, 445691691, 764265441, 846175918, 736363710, 389720865, 797151107, 324876648, 11584001, 82572586, 233942374, 39299065, 846954196, 374907553, 506551492, 961492245, 711601930, 262762289, 940503780, 320785591, 647612132, 50720267, 552107857, 699772988, 67741057, 873405287, 288978634, 862980183, 738569512, 23592868, 614004674, 215527839, 473537508, 217026406, 613031935, 635988087, 608744935, 55981542, 278767474, 436251533, 734928518, 424340788, 546157049, 596965756, 931339782, 359475005, 431284453, 92057662, 83254349, 557792268, 555344673, 678496308, 423922253, 641914617, 887563407, 191273157, 343981319, 735544289, 489666897, 327974487, 682326381, 832264300, 95114022, 233542303, 931192206, 582186658, 542366922, 827121581, 294836761, 767928698, 125635237, 449382065, 783012181, 533399248, 736192578, 452312486, 643648291, 469034827, 6204926, 754257081, 869244517, 367407644, 657601245, 537396099, 565375586, 677270381, 712065339, 211680190, 403286844, 141402610, 209607012, 299815018, 17228696, 307908329, 978265360, 476288944, 353400249, 243818803, 794332905, 866412578, 580043944, 744794364, 345478196, 706871081, 781049708, 368262270, 5231706, 511813186, 404471494, 703436199, 522868382, 857149446, 597128818, 755689692, 152846262, 415311908, 326838723, 846308891, 512532192, 967901947, 297820237, 247524090, 787121497, 756418262, 549437181, 467222565, 66029545, 179822211, 232140203, 448364917, 126983258, 253704282, 946102930, 887203620, 54732275, 168264917, 325840214, 895440810, 275347949, 824024386, 289592370, 602890503, 710589612, 604276664, 100719403, 436385434, 669008948, 348847752, 791238325, 949005477, 394242895, 949348793, 691465108, 843682099, 981564174, 722655015, 177881338, 452971593, 436225945, 179981671, 470970595, 160499069, 534474977, 195779269, 856317214, 45512742, 793990805, 523988651, 346634950, 746159064, 39685873, 262465044, 150531394, 126854, 186893167, 139852826, 675061566, 701937155, 636393247, 966116173, 872614376, 116686052, 586443298, 592593499, 25899325, 434840546, 890515910, 173323433, 445662697, 439074530, 863222244, 840794720, 657147441, 167781920, 898650871, 638983906, 333627167, 189418421, 647387401, 319461659, 201930557, 748937497, 213170241, 623759838, 681768315, 859715318, 234524985, 899475709, 819458753, 391246263, 43585670, 56580453, 979462645, 521108289, 396309723, 918937602, 707998929, 773906437, 802221709, 568579366, 598197898, 869357968, 379934272, 755926019, 723097128, 208754005, 997545849, 114648230, 36296582, 361894229, 320410478, 394050838, 421630402, 536589743, 189022211, 915393826, 87084765, 957883529, 670702169, 985125754, 899722147, 380400264, 728575324, 620968665, 330647830, 278751019, 249947021, 7360780, 597484258, 120908304, 74990485, 129389943, 382572677, 203399844, 506285710, 729207013, 753569951, 306711581, 987268946, 39343654, 726190948, 111351091, 924269849, 179163326, 842172983, 67679321, 239584418, 133933449, 579788457, 167158467, 27968337, 399186949, 872031325, 753335193, 749495877, 381261761, 401011365, 464126386, 72457786, 10993310, 573663498, 865338788, 87016459, 589729420, 954597557, 388090973, 593265638, 580545314, 89553574, 77283084, 8093222, 354201119, 938294004, 828323546, 324760215, 742935641, 326727956, 295475873, 649108281, 295622208, 327927634, 940518039, 616238708, 375179917, 750723048, 849346305, 309936393, 854299193, 17577868, 54669318, 861377827, 599534642, 881965595, 569679876, 909229443, 9852285, 895581181, 655469763, 83239350, 96862980, 390125277, 361038908, 54127803, 128972066, 380114324, 663874180, 478999394, 106718060, 109053646, 990166455, 227218885, 544050174, 438389702, 927943481, 630293097, 455219888, 636425912, 890707506, 199137241, 832511739, 134203080, 890865964, 31848860, 679903522, 138765091, 205472408, 106859535, 103519329, 67620415, 806616492, 533361425, 746816059, 12794213, 824948540, 315133282, 114375704, 228479189, 913021788, 614053333, 722820424, 237648039, 223610489, 809214945, 508821219, 544774050, 364893091, 391563224, 769093088, 39996233, 821486731, 290256661, 210843811, 83118414, 890639898, 850623759, 567026127, 92862841, 862585118, 325549171, 652011435, 829214386, 9197913, 92097637, 599938675, 860161725, 789790810, 114930349, 319132057, 417850815, 628402589, 136360209, 762692456, 342393096, 526087009, 393629444, 629868628, 686858562, 104658300, 527515158, 74651188, 745327960, 909854546, 494982534, 331349128, 981956439, 37011301, 328374715, 985013826, 380624156, 597149871, 250802984, 531482049, 686924493, 289558185, 186502997, 942527315, 817604640, 398077232, 824851797, 682782580, 124626759, 941294909, 784212013, 774563923, 736174786, 666745836, 655052853, 562747268, 149447716, 16503869, 607712208, 931872885, 447372646, 651930387, 906155795, 23679707, 11996242, 586370839, 951332479, 817558876, 403611649, 376177512, 697556626, 773070913, 846687651, 192838283, 279950315, 664201597, 428582870, 880168416, 154480026, 161261533, 194293863, 43951905, 906131239, 624501380, 128565738, 992846738, 581110517, 115117308, 693620009, 398906485, 202794562, 838881166, 131643464, 964997889, 642828625, 175208101, 13245987, 418453758, 811943079, 829497331, 400578160, 864159731, 475596762, 784856925, 480758466, 903984087, 988877441, 404145605, 106124254, 729207058, 643822793, 565500912, 801197902, 964978921, 270914836, 709795277, 30128267, 350699448, 904395004, 755426811, 445206657, 52225560, 566942786, 16054723, 881964798, 438290032, 147106121, 161503322, 901005583, 163243444, 691589064, 380213619, 493814330, 72493195, 374585490, 945781817, 79201153, 355912771, 374996587, 232489441, 247269738, 492227623, 411752993, 996145130, 403766735, 196647917, 367538234, 323282302, 217016475, 131416656, 455163501, 493312558, 541876024, 191070772, 809596869, 975891460, 497980027, 424732450, 673350738, 137116530, 557943586, 311468602, 248836195, 248604512, 352954119, 304303389, 238581999, 29345972, 212733348, 206902791, 656075067, 955461138, 724836212, 599814222, 311076919, 978453480, 868833300, 509787573, 865922063, 437076792, 958367222, 187626325, 660789146, 216379248, 38724155, 643244917, 541487869, 269323843, 690230646, 945122871, 167119804, 524508603, 910340204, 970754290, 120343763, 459501332, 137232691, 337077193, 553971139, 224506458, 36639622, 851059113, 655202974, 790859533, 840638526, 482769777, 133630440, 365634125, 549394842, 754874644, 99768369, 357906796, 264076061, 580644696, 549626685, 446815895, 765298369, 86484160, 548429950, 822272018, 239623382, 866459196, 835771182, 564619829, 757376608, 740107748, 120038679, 461298913, 719291039, 656047437, 753730678, 280420767, 768294503, 293041369, 298507095, 380137196, 763193361, 178427494, 922631372, 38165253, 172615517, 482901537, 193268319, 198377078, 739535072, 111052171, 610986205, 783589025, 437414494, 869709413, 843634840, 673323716, 281774174, 389164731, 965439711, 220005684, 538481726, 42821645, 818602915, 770598049, 621357888, 475055954, 700946289, 821912664, 152639316, 427060750, 239681621, 257235163, 850605041, 162862604, 896309726, 210377975, 495527854, 914133875, 642372123, 109870596, 668408661, 874984725, 59701083, 613461866, 723377726, 921734041, 709629478, 322951192, 186901879, 859354638, 150225148, 22644308, 350749265, 96172786, 429809040, 103345570, 554767944, 151641306, 532359496, 388507019, 950989098, 403755146, 617534076, 952313148, 243258507, 86295946, 811264215, 768300150, 627467916, 833435537, 471107381, 224049133, 112756754, 201658210, 366173018, 613038441, 869919565, 13120561, 642504534, 211832919, 96640486, 629885687, 640186970, 705614467, 375377034, 128923806, 670090135, 802376991, 314756189, 612840166, 358864786, 12259502, 561423893, 330902338, 164781720, 902587382, 766731177, 721472083, 37001363, 116937224, 608701268, 610776136, 404183406, 2371995, 401237414, 170571097, 135007500, 710519576, 473083735, 943425607, 732545211, 886650042, 110085359, 929853865, 785631854, 236940136, 176337995, 18427767, 854222312, 752773786, 167789188, 612697440, 699104676, 576860182, 934032164, 155157890, 741821530, 851964842, 872286759, 398487582, 29674029, 287804536, 231676619, 695110720, 710239285, 716195287, 268399564, 376725101, 443867949, 868349017, 316722094, 358069776, 88688482, 382837341, 252933372, 962648640, 961299523, 816623529, 47205851, 141977256, 712179829, 119837270, 92877946, 915382336, 249059418, 798566071, 36291707, 345612939, 662389659, 818621515, 457752981, 575388590, 341091078, 429901611, 11486227, 17061445, 112101347, 244150311, 283202258, 94430915, 119930487, 205710495, 648454000, 244894022, 821964036, 985328257, 651316242, 852313718, 729718833, 386141481, 105913125, 909670874, 653661586, 733185677, 843405356, 690950133, 361207029, 426492956, 810271931, 23437450, 84705382, 749416742, 88354973, 612860362, 291379837, 631052503, 568447116, 120284594, 301516277, 814324521, 148560346, 149771148, 184150469, 153642615, 260759414, 134819815, 365153102, 462161011, 729507752, 564994690, 736417890, 822067646, 370479929, 173991683, 905046435, 275967171, 480909412, 19929268, 13636105, 744118095, 790899397, 962417269, 962736324, 117920917, 304940897, 649172913, 365028214, 175698154, 302612507, 87149223, 817989534, 916974010, 845281080, 527867770, 380882596, 98676163, 536179231, 687580882, 399092491, 745706264, 86921972, 832473835, 161159847, 347417136, 659996134, 602227457, 321959737, 747163971, 198633364, 247052691, 214495177, 241688667, 64797477, 380075408, 745550176, 958285057, 420878074, 344750773, 759622859, 372162504, 45047112, 688611583, 475597560, 255074566, 317642722, 526745083, 665427398, 829001207, 694104109, 681757978, 597900709, 830278953, 990278581, 27728369, 546518115, 885763723, 212155069, 489134492, 89596263, 660395311, 90964954, 883183734, 272639564, 273703568, 945723266, 534587424, 980344613, 799679624, 647531081, 128157031, 561084192, 596265751, 896694725, 718726313, 65020233, 162149912, 978131445, 800540467, 260589946, 716541007, 182114653, 513415862, 277804606, 528871959, 751464651, 310098868, 980415555, 384287213, 522380257, 23202895, 777018368, 135023159, 857500520, 796306458, 820217959, 345921797, 709864427, 481990589, 935853275, 490707815, 717951653, 663760457, 943964041, 447762398, 665385599, 533377719, 794737361, 942328921, 647652228, 148870131, 758506687, 457895546, 155104764, 455809557, 457368859, 184046322, 721602660, 694125902, 522436670, 312914426, 679325936, 882225464, 518646130, 965055124, 774862241, 504582947, 615113554, 71686339, 300635987, 93053363, 73058288, 121311780, 668647374, 552343117, 953281570, 567622809, 495423823, 898089588, 561397124, 674155817, 220523465, 421281929, 453880160, 186802771, 383635411, 746468438, 349633588, 944027903, 519739429, 345261735, 360093165, 796473363, 36369763, 26301434, 214920149, 247312705, 626980272, 334658482, 568741695, 4485299, 690023999, 966895098, 399989306, 959636373, 571946610, 332122198, 723826407, 840674263, 876140214, 30858705, 926011395, 620646699, 276609234, 310303871, 885610934, 567336328, 73720505, 318781766, 565101611, 901481340, 700912709, 442566779, 179267790, 352748348, 194998300, 637377460, 62296358, 254440858, 439151803, 379320151, 820757653, 636042888, 881842181, 467991477, 69384126, 781821096, 522145551, 219895776, 704765846, 685982905, 456209821, 853681210, 790333083, 229450375, 105912003, 184549653, 886475980, 362453804, 163750976, 835524238, 213942877, 753113015, 756405923, 987498101, 750599179, 382095182, 37558319, 997484480, 525137165, 175943634, 687181801, 161007043, 999958215, 940877945, 280760197, 672205629, 465727753, 987696458, 831841142, 198325195, 304884560, 24459121, 850685706, 451532639, 853795862, 537144182, 735181950, 392783308, 103313915, 811792022, 236709831, 992695806, 50781643, 606507366, 337589797, 107509154, 664201577, 389159456, 614081109, 322073195, 224358632, 976450953, 502596082, 139829339, 568321745, 291343240, 639165083, 28786770, 735514500, 545058759, 163943563, 982005661, 956652487, 648323546, 983588048, 752311091, 631251547, 186783412, 769393515, 483299492, 75387747, 898462290, 630485973, 253213917, 143598161, 153303405, 105299037, 248902353, 851548394, 13135959, 833529120, 305471441, 6217980, 219569514, 628102281, 414235097, 858732557, 354452550, 303936043, 76292410, 490622349, 913848809, 438340299, 757866421, 108265730, 310042929, 953701866, 95357220, 306411531, 799761106, 186110473, 51093024, 769938395, 571095868, 220207378, 391614156, 385322781, 196550766, 360989876, 600936955, 819318953, 952281691, 370575557, 480066652, 213328923, 178632844, 786980008, 659059262, 12227517, 593370218, 755377894, 623593369, 151724770, 998191686, 157654842, 55000129, 599865415, 920791311, 308768569, 960695368, 572334194, 431652556, 556249318, 783917095, 651927966, 481388343, 812841789, 105491406, 11437269, 763027261, 459280177, 271033609, 966218099, 764938535, 696145393, 767957240, 828669846, 474045453, 794932989, 735558317, 693408014, 241350273, 130333545, 248554991, 690280909, 995689906, 397910055, 175629901, 571517146, 990203022, 281347693, 667140, 939668721, 27662806, 617176635, 996234410, 736917270, 173217736, 55954124, 598265619, 650469593, 685483296, 335149384, 934815242, 677371310, 716648422, 380163979, 225250866, 710222816, 606385331, 739420632, 14084009, 901592322, 672531767, 523723950, 151824987, 238992528, 348739888, 163768174, 823204503, 780747393, 733954334, 633072617, 367378195, 314254345, 382968856, 624468732, 178046497, 286371348, 168569422, 657009523, 380141889, 193924380, 239691012, 161829284, 636651783, 99673716, 342854453, 576408858, 598831665, 531836396, 858625362, 112512317, 841622599, 495775855, 668898378, 653029038, 957702649, 684691750, 830350591, 982513342, 918739949, 180338176, 906361314, 626666048, 822262984, 223554106, 610059780, 393221027, 845548423, 397964241, 450514409, 237553046, 916001576, 315965408, 609647319, 404880975, 901810787, 24463953, 606190287, 712148710, 862966420, 700874999, 588454837, 67227931, 538804851, 700846661, 172162986, 82205084, 222113937, 607607230, 966438685, 480105178, 855234177, 671352957, 984046573, 322456597, 788383453, 550116364, 262801243, 985335107, 87627748, 273253974, 598466861, 940725935, 55799647, 390469286, 265514226, 996753499, 536135173, 38920035, 326363314, 260148059, 988500444, 859826519, 601823738, 412565349, 109709782, 311687984, 206911220, 141507397, 317667145, 903413526, 19705390, 720882025, 537390606, 944367045, 598750562, 591230202, 8853405, 829025645, 509554745, 57614777, 673021578, 813917871, 662835612, 140199937, 215028406, 744364700, 58273074, 612410786, 912969076, 332648087, 289611530, 259874055, 298498923, 932914319, 791202378, 206172633, 724285543, 597914265, 3286249, 777943270, 677994693, 18307633, 754410377, 682295054, 17300153, 991400593, 624006451, 18555047, 401960518, 206101641, 911750504, 867219383, 51702163, 777011323, 98575065, 376926819, 971284916, 369709437, 751709601, 682885422, 261990935, 114238708, 337241269, 197149968, 63846134, 999310944, 741843331, 499167938, 595437222, 523245528, 985466563, 607422674, 794147676, 597727722, 598928179, 430722475, 695470872, 235130074, 413519690, 105504287, 154072793, 129274816, 135054588, 195572758, 353939178, 424536469, 827765541, 769139142, 115601493, 204856241, 283906635, 575589733, 361766574, 426321431, 454702860, 304321712, 661562188, 7663736, 750468914, 703210298, 704159631, 254285180, 718719539, 473772802, 300999484, 660903661, 228380370, 23332607, 937547643, 308448558, 808694827, 278402879, 108422915, 654796028, 356765387, 171453695, 933571548, 95850420, 643668921, 4182777, 212592997, 664429005, 410166513, 433605742, 787760699, 735425230, 133875442, 188855539, 27393510, 423707690, 953128397, 679553693, 170347395, 245076842, 642097414, 929593218, 42071058, 35104748, 675891581, 526797784, 951284655, 838784228, 680645442, 485224672, 110193101, 227331633, 858542054, 551775611, 88076041, 944704115, 149320513, 364703160, 502599171, 891967187, 683974911, 479237915, 139935891, 574811542, 474359458, 639071436, 736830265, 133590604, 986430985, 223025412, 985812336, 624067866, 355077770, 377245137, 679344163, 781091359, 230027947, 22300197, 140821423, 675472944, 564070052, 730124423, 150821779, 39963102, 172300096, 611242831, 356836814, 323226171, 490630975, 394582947, 68930618, 797462554, 346961806, 829859808, 22475483, 283991327, 662181099, 511452677, 855770275, 958232050, 224405243, 762800174, 606147673, 200551704, 938967662, 346985600, 153300168, 279764391, 634447378, 68774207, 972406328, 40592430, 232248815, 409238569, 113851853, 615514057, 236357303, 766449082, 916414201, 63090703, 939220890, 527286879, 144094034, 724647889, 495017665, 648191564, 497574785, 267761337, 251819459, 470451219, 447976486, 782682894, 344833827, 108576841, 127088452, 665604434, 295958265, 165210595, 325356401, 430718599, 373473026, 404687892, 603699946, 331526390, 642193994, 647548679, 923958911, 201947430, 999637401, 364671939, 920728022, 364866363, 486186925, 170938904, 399427944, 180529832, 779483062, 596778060, 344499670, 690923583, 497271858, 93319236, 319167027, 424728637, 585924296, 211207559, 384420365, 186533790, 96132367, 415397138, 198127980, 456342037, 977677992, 199568859, 838061427, 98365136, 98782195, 364340070, 594548449, 1529512, 283731492, 307156495, 621641065, 23581712, 607641284, 678188956, 645283439, 115771923, 966354407, 641924970, 332190940, 625028540, 235660333, 540507808, 839241001, 87824699, 981633958, 736532063, 99394345, 545457269, 439977928, 818626907, 882245070, 45173246, 184296627, 223055876, 35868165, 570644225, 629010291, 243148661, 935857249, 588399755, 704807787, 414610262, 361978138, 252757307, 42963698, 694712915, 214565828, 952614694, 635146214, 809099130, 942469426, 982695480, 660087157, 815285801, 333737944, 81685683, 776639768, 939218595, 319864853, 88895232, 235399331, 88664419, 366779592, 503985975, 828720441, 904443082, 57517986, 412889294, 331848505, 624889212, 276543133, 9615342, 177729890, 700954417, 704076570, 803306488, 913664315, 793087822, 892616934, 867721704, 532680584, 265929828, 832413359, 668474079, 929704378, 295608471, 826676033, 835181920, 854399001, 25327441, 33914472, 314236031, 875140461, 226422656, 619759165, 234365392, 332078725, 727633621, 673445898, 213613424, 89544798, 734463096, 321283442, 226325249, 747881366, 3339780, 690155949, 183313009, 388020314, 293947088, 266907420, 898659854, 536732017, 373183931, 417407304, 254023199, 213298873, 545283083, 52212215, 664404240, 125511204, 80290581, 274078222, 519901555, 766670097, 647701189, 802503828, 631512179, 315818593, 691984443, 830329082, 899067600, 542015042, 778308693, 198457144, 376108970, 289213167, 527682033, 722442949, 506891582, 889163052, 923986625, 524261250, 705512823, 798912302, 873222002, 647621742, 197470620, 600576817, 720029311, 744503646, 30514387, 176361078, 593230667, 11890591, 913188881, 127435449, 827642293, 681936623, 70509540, 72536170, 378611668, 748147288, 922037096, 982654552, 731396052, 63395032, 753721296, 736757255, 375421698, 211379539, 143146878, 732145127, 303974915, 437836712, 820394274, 750621525, 217416908, 795186582, 189709038, 219866724, 480105200, 413112017, 743651662, 705282807, 145122632, 286975201, 893722621, 545701082, 518571992, 263547201, 346658753, 371888016, 68518168, 601626551, 744322839, 227987561, 58912383, 178660721, 902376830, 51191471, 440517503, 624126677, 782991576, 201439836, 714823104, 741882755, 808832032, 812444608, 264782750, 944187973, 854043047, 501587157, 603721385, 793870326, 470793706, 149943082, 553352716, 96403710, 851791189, 13906923, 798525012, 942729228, 802825782, 107229472, 485951855, 516128471, 393861141, 397399465, 363846566, 454688309, 639315794, 83829769, 505912711, 472992959, 138983417, 766846734, 161918030, 453647940, 223302967, 693703550, 386187943, 610232959, 936628734, 392570463, 169144501, 846916998, 695639295, 795373451, 217276095, 989379072, 789607985, 191152460, 913685441, 352124966, 543799634, 810593491, 8679394, 78486976, 384616886, 345901117, 607599922, 630879855, 569817192, 328156856, 770689625, 321233893, 796314629, 911345686, 379839302, 825503108, 861476431, 701590885, 100403590, 249268554, 657178765, 953308960, 515181111, 653825577, 691212488, 817307658, 821996660, 425789190, 264682662, 127309839, 42492830, 650272373, 353940087, 716689628, 83446527, 611087093, 952192610, 834350795, 617644925, 37275826, 285808101, 544487511, 505602898, 280339426, 58508911, 728219192, 239077278, 190952376, 564648807, 741232314, 847876752, 940160677, 797912598, 214762465, 324548159, 329592292, 827495836, 623861375, 801652245, 173761351, 20104467, 341993201, 232337787, 90219720, 595179861, 239360431, 191307012, 382351974, 33035099, 911944809, 820247947, 996480038, 464626253, 656972329, 78443055, 752052045, 258267793, 559094408, 239073724, 105590191, 217866452, 956507105, 663922377, 46851689, 538400837, 324701367, 644289761, 736786761, 499615204, 376538623, 711605958, 572335414, 150057687, 677067731, 332975367, 926801169, 616081723, 19920906, 531013925, 34993572, 490436318, 847445552, 266906782, 936024890, 195580391, 842354960, 450460136, 20274533, 196935008, 787076882, 826876637, 535858307, 549196391, 316694226, 806457026, 629855583, 863563625, 914782258, 974337181, 429270802, 527580517, 523984922, 113923869, 811334285, 461177181, 279838070, 111371453, 79325065, 821308376, 335975412, 243614919, 825116895, 498921789, 608259139, 663712586, 260285682, 603137638, 341980141, 384018171, 509691463, 695611009, 113874875, 212904751, 329528120, 69629163, 736770738, 104112326, 878670767, 200481908, 324880961, 678558404, 41705414, 344538260, 811878596, 386608956, 651042838, 68809391, 959914659, 573143699, 824284712, 117104861, 804721453, 68366055, 505713284, 564813240, 864825402, 507917575, 72404696, 114643110, 736371162, 542693521, 775065300, 57471692, 555330998, 699717203, 403007909, 39747400, 464456209, 652633954, 648838526, 27955212, 982143794, 387229126, 167560864, 626502628, 403550914, 218635638, 910443796, 159714175, 474059427, 991798825, 461150043, 527330827, 384317469, 304014388, 531923195, 588547891, 865684766, 525170127, 652469653, 663572806, 417494105, 554646594, 482195551, 54358640, 362798315, 399634207, 923919656, 732987842, 115935917, 781792802, 806244354, 788292135, 451120963, 419331499, 582492068, 101314541, 436812063, 219922194, 911224222, 342336123, 364436942, 493607033, 758820934, 313627861, 657925277, 261732439, 409327934, 941235741, 764469578, 490417435, 842883714, 272655629, 668345270, 23994738, 684580160, 206950606, 564839051, 898243515, 977553981, 470738801, 351139037, 247829949, 242499671, 944468524, 865833616, 364906727, 577440734, 585949211, 198912881, 297976919, 479609938, 79623690, 345088450, 152688310, 6928812, 502042670, 350671845, 255058155, 333735506, 428852390, 174012951, 666373578, 489844732, 990841498, 253261763, 464338389, 551451327, 252396818, 242626363, 192628882, 67435135, 419689041, 840807245, 626923238, 258577165, 174288150, 330548645, 950657713, 645411103, 186120612, 12548360, 494514941, 142115189, 307837993, 5672794, 419375020, 496047231, 23306173, 401131181, 180806754, 10841706, 636878491, 701774697, 940767462, 590542913, 627164450, 851111003, 806757352, 410487523, 889234094, 543491184, 438624596, 151064368, 406430719, 662682323, 772996330, 300028365, 702722761, 964468824, 411238301, 34152881, 229213150, 184969961, 362866047, 575894075, 217117676, 396484574, 712088915, 112099943, 831912231, 84575519, 889709903, 158658384, 901137082, 885898440, 471871195, 234666561, 746125444, 436925692, 799608256, 215948997, 162248527, 803926016, 357660628, 357903927, 91050517, 647777867, 592456305, 504752952, 121202909, 686225442, 59851481, 715855152, 527852437, 197909196, 723955262, 902619717, 10240796, 45195209, 887661510, 586417099, 803771514, 509661368, 23293765, 366184883, 701516360, 661054294, 939369955, 621085820, 42533461, 914796942, 947071001, 219724556, 485391570, 607797679, 355948474, 734984097, 39895987, 89270221, 41963839, 389615516, 890345716, 722032821, 289929855, 104192519, 863277431, 601011809, 666816156, 425776232, 552572868, 603196837, 761691433, 964441909, 530215261, 692613830, 75181782, 801501873, 803781597, 137480281, 430721656, 29164832, 250078954, 869810726, 460735226, 366989677, 700797177, 872564590, 280464315, 796475551, 190340450, 318664915, 611606052, 688279360, 895506157, 768505255, 935260854, 790044583, 379009447, 649436334, 798030340, 432931265, 811723352, 667470689, 706457820, 634329976, 523246816, 697935190, 758925470, 306809461, 66444414, 645609263, 447913746, 536244283, 877976605, 623324286, 506948816, 854872946, 834000679, 543899806, 555073738, 246751817, 787511655, 208642866, 131730358, 531890992, 467685252, 93810624, 77363003, 509253025, 791259303, 394624206, 996746690, 78003241, 799911069, 497833389, 37214648, 962440973, 728374351, 177191466, 6022373, 249413015, 417466720, 368637271, 365602281, 567240438, 742567697, 847592437, 979187930, 428437406, 970511686, 166106526, 908324762, 654161597, 301887420, 803257610, 912367048, 415820808, 345721574, 585118128, 877682611, 664788664, 599523175, 993347196, 993209569, 491088496, 694423663, 448472737, 536665768, 456276033, 848754438, 691604521, 876381226, 159298711, 1392236, 79444164, 251313597, 152095737, 55642184, 221072545, 145939186, 598170474, 477061060, 856020402, 715134874, 459115723, 629165645, 194001774, 527630907, 770186591, 836883786, 866907974, 934349434, 20727810, 473058042, 428586201, 951791314, 134107174, 323557463, 88816619, 551277022, 802548534, 164773722, 89768218, 514704084, 324403849, 833945114, 662782611, 774818841, 616313535, 743316120, 955732435, 329267195, 659738459, 145028402, 24050941, 62387118, 295795031, 106791464, 518711208, 244907206, 192382855, 874967944, 626304545, 394076065, 738304328, 107983559, 301670283, 467292527, 145045456, 912454342, 516736552, 962069434, 726620194, 537457560, 92605700, 258570388, 684316319, 368288455, 885614440, 590887797, 599892554, 919714654, 532090593, 652828379, 595255944, 642708187, 781590068, 183541722, 298892077, 412222122, 925699114, 843119482, 962256275, 321379137, 807527899, 300212293, 418360534, 302653219, 871656850, 224692383, 595716132, 34475580, 142366243, 900581057, 458326226, 491680710, 882410308, 91824052, 604173344, 8243158, 342800527, 15832332, 422699437, 363719339, 855364040, 488142413, 510309158, 147005435, 603117729, 100494043, 565346673, 495770219, 138886980, 133863144, 912561016, 121290531, 630589352, 960968687, 744821247, 772313662, 959848675, 82867073, 976432944, 22958071, 504213538, 60635680, 90032846, 67586123, 101347399, 593217305, 787981693, 595570611, 596553011, 280729940, 216016943, 722222300, 99587131, 994241671, 927294049, 191839561, 916924338, 313989722, 401126964, 360706287, 662557456, 395614500, 715922449, 13683792, 272006607, 46788981, 982362538, 234391132, 672430718, 680872203, 325372883, 671573985, 68142470, 624164526, 990101020, 728517163, 148293796, 959871252, 731802306, 296567609, 737880167, 632145843, 226449080, 114389104, 23444169, 263869011, 40541501, 36875729, 289460743, 761454949, 401394396, 655044459, 102831369, 610405320, 510646248, 700817461, 799868189, 164103077, 106359726, 313285253, 942343836, 843919441, 631765544, 843525590, 271108409, 372082996, 178988939, 264447788, 101713373, 857549554, 575687567, 497065221, 198158773, 977440912, 449533621, 10472630, 666628896, 795156383, 576242523, 42695742, 770202928, 763049156, 285801186, 771145851, 342499390, 817732574, 389688821, 149847848, 70094705, 297193609, 755110323, 949278440, 452660711, 476538738, 610985624, 346287829, 666771185, 30325169, 395638855, 463334879, 641436379, 546288372, 222678400, 966459843, 656006616, 432587971, 107313057, 33598233, 74006833, 830428300, 809671128, 539129559, 241523757, 80900075, 949329782, 172901739, 154444972, 685128679, 375726798, 430739811, 187985898, 742686925, 865421896, 259373377, 838502623, 284877244, 232780387, 902119473, 490596614, 470197491, 372720825, 320926319, 735063149, 96449942, 943281582, 964237513, 569243779, 615071851, 314865438, 654882057, 103306734, 718749349, 627274308, 246437976, 147004156, 978873386, 579422059, 817095532, 389751057, 150957440, 857218084, 191793711, 738442551, 548577788, 808640760, 65381483, 390494313, 409839716, 307097076, 165408469, 969701262, 852626791, 891944604, 991687789, 58915100, 627247615, 732136465, 302150023, 712566397, 463614236, 527952951, 828610458, 404025651, 818474030, 914934132, 824416847, 986451119, 200115021, 65788795, 483231932, 360861091, 735873450, 184919016, 125838113, 717802601, 585046392, 579286789, 313697798, 561915847, 430913594, 297248954, 302865941, 321507762, 915106260, 736680043, 761214008, 888633455, 317127670, 190936174, 692251634, 177827389, 918999021, 220190044, 396117996, 628568199, 26102509, 811530328, 923947717, 55252740, 337419520, 658507034, 378036244, 472052417, 654313257, 406058743, 390867131, 500382591, 462743950, 665671557, 549734307, 79290003, 93693914, 868961708, 709073649, 80337270, 775502165, 627004436, 556640777, 83868075, 883650303, 75657958, 855372773, 968686496, 470643161, 15838115, 789341076, 400641052, 35676652, 583143325, 508108660, 925853850, 516864895, 562537011, 353492917, 772695372, 142927657, 45429278, 45380915, 748304418, 68479614, 248260876, 691503410, 89406788, 647535039, 792620439, 249301599, 650267021, 541524575, 216976940, 807800317, 759057249, 690015472, 552021336, 123912751, 224084687, 941139650, 875177595, 638850000, 410405227, 554011643, 494879351, 573191697, 578791208, 705110949, 847819699, 981601703, 274873117, 720298603, 734189142, 106244833, 776060474, 626983047, 945204613, 751745477, 997150170, 809320498, 226538738, 321458542, 276648172, 574697698, 334109839, 294079551, 181227799, 958053552, 472212119, 407929550, 547877066, 183747013, 475879629, 94617612, 807354696, 882763026, 211275900, 251153000, 915438415, 400942514, 328605606, 222212519, 355541176, 260904719, 281440774, 974502972, 817783723, 195916587, 444584990, 709547448, 872146924, 194181959, 631049771, 14899912, 123647157, 854433845, 723424984, 688810013, 517421940, 208580394, 422609214, 412091115, 886023169, 804043640, 822396152, 542087888, 127977360, 870144285, 922830129, 190043447, 677979576, 750585734, 414489475, 314336584, 621462920, 876822167, 880942582, 364207708, 492976938, 526377216, 363216832, 903376249, 76263958, 581860800, 982265310, 371172748, 599028596, 860373684, 562774468, 192933502, 898259535, 606759995, 685881501, 3304270, 17128575, 214411944, 682426811, 895521289, 622157762, 962164202, 253533197, 668402319, 657285663, 481112295, 860517038, 580393168, 920520959, 534689745, 772032587, 354958887, 824582013, 478505481, 339520553, 809556239, 443720496, 589395538, 955066590, 411197764, 426434677, 293373165, 192393410, 252702486, 321342551, 163599000, 85518746, 769364541, 834326234, 264827941, 602189183, 66422511, 836263847, 557169782, 965768511, 943890145, 138567198, 290280797, 55998339, 176758673, 255990268, 405067889, 485223819, 326257453, 41801771, 300599161, 522937048, 964868733, 374590487, 348642396, 330600259, 187951714, 239643314, 486568268, 727204814, 896103362, 506719830, 454646956, 309343592, 164780752, 500543213, 411930770, 145405078, 361636234, 187007084, 62487178, 917692236, 907148403, 909747942, 849463219, 73857482, 345576566, 487249414, 946054614, 155802869, 156310762, 957263165, 49484130, 524727501, 33013087, 510244451, 954617469, 627963369, 728146927, 624377773, 79157397, 152638049, 341743619, 656712582, 893597881, 516477517, 692572811, 917468953, 920250588, 589748417, 1459643, 379441942, 37252933, 145462292, 850537523, 735230746, 450259308, 761951708, 893359126, 282490095, 68844790, 667017304, 270176650, 142458820, 304210311, 354256325, 47478055, 586368181, 628082731, 186058217, 734446717, 150743162, 840405274, 184298476, 204959115, 576991599, 478395010, 692552546, 737191691, 738757298, 349891731, 498507673, 159269388, 215203440, 262287754, 868412497, 328792006, 714488932, 231218075, 33845727, 948073700, 326188080, 278790909, 815469350, 953540117, 514045769, 235860140, 987998610, 535847292, 186157940, 696076926, 724017363, 121824867, 299806509, 421938928, 291774915, 51841205, 287236072, 572228415, 558164570, 950003344, 879907506, 473493552, 774818248, 845708259, 898794869, 56459255, 796772042, 375337054, 971083401, 423636847, 750800330, 399865749, 327665303, 4057308, 763531927, 558029241, 340062576, 133913325, 199574414, 734184755, 562649442, 144129551, 911597463, 22111520, 85690535, 239939987, 198285546, 401680775, 615417291, 15772515, 377386206, 759462991, 495538757, 743870183, 332244917, 80916598, 7316464, 843126102, 258278425, 10908732, 679838691, 236447324, 538451172, 40272839, 46541250, 549919017, 289254695, 718358200, 702643347, 83461821, 923335595, 38165615, 168705185, 783973190, 99039569, 982305823, 913040739, 700919409, 551888822, 904959024, 464166169, 83558929, 391125636, 969110020, 337226464, 621047524, 651657489, 300195180, 972137042, 266192816, 843558426, 560722978, 991612801, 685097958, 875618415, 679679037, 308691009, 262552480, 860540393, 813784008, 52762035, 640980592, 881614443, 932487147, 244043388, 494279567, 557995408, 689483528, 666241328, 370031497, 229554457, 386956473, 153326136, 572943214, 221139611, 202201457, 871451742, 731872617, 712632919, 37332798, 871399459, 706288238, 364737882, 682673855, 484173961, 549893021, 127130365, 785643772, 866996577, 123091874, 812973037, 550042819, 321785676, 669647155, 863871826, 348654971, 518630139, 285618580, 616583471, 713331193, 276825038, 599387857, 897758426, 754347176, 880233544, 518001800, 576050561, 855178569, 701480061, 95097274, 851528633, 791075357, 704411492, 771832795, 464116037, 184630816, 711143696, 676133120, 638071142, 64227033, 223855760, 222200440, 359317764, 946448122, 271021522, 476408498, 431147530, 411110763, 837304898, 762763683, 875457018, 253349234, 679779727, 95021319, 87047538, 897306997, 289897045, 29247771, 863680675, 813187840, 701133485, 102948951, 152087573, 272646939, 469157771, 193061072, 748320388, 729204526, 372192280, 918089936, 348290013, 5841329, 589221720, 363342557, 492556170, 955046549, 766755730, 119189065, 65925707, 823983681, 279723170, 256188704, 850596249, 949676256, 690558807, 8571939, 69563223, 558637985, 175450762, 620823722, 236799703, 581891535, 24666490, 640207019, 283325270, 376635181, 745356996, 274819358, 988602924, 148426670, 593710906, 4253844, 484426851, 89884046, 882358398, 861796240, 79661506, 974991808, 947216100, 506012485, 436807644, 684178305, 906853429, 290762531, 315715801, 623901066, 301930359, 763820190, 464359479, 200255563, 859121848, 267496949, 57338545, 845509189, 933751956, 34738299, 568696737, 763222085, 982812509, 594430870, 787673875, 961156889, 494196706, 472970221, 914426847, 690571330, 914108021, 292925210, 156385753, 66073144, 105464259, 780480772, 592287881, 690930628, 925420495, 565354784, 298175124, 349854442, 101164164, 899375561, 170157910, 102136019, 834066817, 989836492, 184631096, 833660445, 786795713, 713548051, 641807104, 229436970, 201641921, 560489227, 854446085, 472888205, 970664813, 639920280, 785409829, 787022726, 462865012, 569980048, 275540748, 165970557, 1889237, 622791781, 202623801, 834940307, 310580857, 606943347, 238628170, 444302883, 641240201, 471363401, 658770635, 402794814, 609214127, 255238900, 469254801, 438759034, 578260393, 166715951, 611248244, 355601301, 444040301, 428635391, 279665981, 790131150, 783273484, 470544525, 691546789, 603243096, 285138606, 747440044, 318420356, 761681839, 624056935, 719769107, 658952971, 788782061, 181814573, 291765530, 585776625, 838099622, 900835297, 777669605, 590717020, 702310962, 48622839, 705321197, 821883491, 470804252, 192981831, 110991328, 87318376, 11035542, 80507137, 575813607, 289450600, 606318493, 851005888, 919056892, 66927271, 97633852, 485004287, 249687202, 908360427, 180230041, 269962016, 645424671, 815178330, 532381442, 245038780, 974597428, 578223705, 492597859, 766153947, 995538923, 363527278, 755826725, 647139554, 445861555, 742064401, 45576451, 287981263, 676583068, 60224936, 951626087, 214370574, 911393025, 366365897, 891514259, 590746314, 543768753, 132823666, 689047470, 916268612, 412228698, 173165566, 534395165, 940767503, 388998263, 3311077, 897255656, 370536348, 832064183, 53007332, 311139942, 972431835, 806418483, 356227161, 808760045, 410384782, 772792393, 888565380, 487993003, 518738494, 12543900, 512509125, 848109644, 661441535, 19311007, 513450976, 777226606, 335686202, 897163267, 268198822, 355187107, 633489672, 425695944, 88920662, 873263778, 60081997, 265595702, 922398162, 819771642, 295538480, 268322103, 382290093, 447066923, 796385116, 22509996, 757520500, 194593219, 496081844, 645697965, 849971315, 479363534, 79955001, 545447227, 236456471, 448153505, 974571188, 261972926, 118913323, 274618938, 325415895, 759662046, 962833753, 664638114, 130231034, 83408531, 396955253, 121964459, 375415413, 176709293, 78846037, 393887789, 833554893, 38750607, 263524531, 111467789, 92755662, 924718513, 995316765, 824668497, 440299253, 688168066, 781626671, 54889791, 640600323, 524736289, 829811852, 501192637, 121631957, 473979383, 427405895, 848345648, 559148660, 288250753, 769474111, 979870253, 168692512, 248815449, 642823960, 478841080, 517622890, 598833801, 882863752, 603758796, 69734848, 898723534, 323080384, 911083089, 272374179, 842879823, 689287350, 638809065, 282921243, 246585127, 773971446, 997675743, 962777757, 578769687, 568950323, 770342723, 892549939, 155050579, 947220893, 994003655, 518024991, 137148477, 983625903, 309813507, 745947622, 482986386, 809444763, 289738684, 86120610, 235178057, 219580863, 521663607, 193776216, 248165902, 9777455, 681340188, 599753489, 437977659, 220769375, 917995945, 192874960, 647970962, 21760017, 522617830, 117659063, 356863362, 1537485, 311081766, 5643082, 732970033, 831832659, 357456080, 262615073, 81887119, 213552633, 300555990, 656608097, 30024117, 915730063, 405132249, 144978145, 389168214, 158433451, 157809979, 813028329, 718378620, 257863918, 632145867, 447761027, 69196905, 64254285, 645774933, 909333345, 265991464, 562292561, 752175378, 335757526, 5996023, 447158574, 278298595, 789920372, 292426121, 964652152, 701689144, 859990105, 200836041, 89596709, 682374246, 673878239, 367068047, 265044014, 680988505, 768750393, 785717116, 511672667, 664923158, 616481353, 238197061, 475767569, 265875563, 692191376, 634715795, 2570390, 657129653, 887799140, 360376721, 292086076, 575023302, 571223522, 485523464, 184784202, 855678585, 342374655, 801561844, 819650222, 140468740, 869689580, 396003197, 188082502, 789595271, 593725877, 607463026, 542749857, 375243167, 883235674, 903442563, 221887034, 132872532, 225300691, 836708641, 127345829, 888761853, 401953400, 143753469, 353977350, 734449771, 734486225, 517973893, 742108050, 293536010, 124278545, 31071536, 818315015, 980865758, 166905416, 539073384, 780302059, 247341847, 788176900, 818780650, 9014734, 485211281, 662075747, 446943574, 296298323, 701139013, 384233463, 726307754, 63327783, 162224639, 272659834, 114210948, 176275056, 322225550, 494750750, 435669923, 420248974, 986923079, 807935496, 399245868, 240568485, 489415215, 779556156, 427862330, 715874501, 998890082, 312816648, 404230372, 138879977, 640035370, 658236913, 536133749, 189409930, 985378651, 943408375, 244475569, 342436343, 217071200, 312520183, 921967322, 599949387, 715139783, 479602169, 787520539, 320852034, 582400795, 646764451, 584141842, 272599159, 146246103, 705519308, 908469826, 149776052, 267306117, 892535958, 485679048, 24664527, 667251401, 363245894, 483856980, 118587216, 138497368, 375310717, 770031900, 559257920, 79138722, 18520294, 16236625, 247841769, 810183668, 555624201, 89682385, 543556387, 184227865, 29159080, 631463993, 578841998, 719125332, 718134409, 560105243, 695783366, 495795269, 877322068, 742774246, 136519799, 322297293, 190953648, 642965942, 651148009, 825793291, 848366880, 262203117, 788454627, 848185147, 469585955, 515526063, 849242782, 899876173, 757247669, 518912586, 657080028, 907242368, 626542912, 205780432, 357717717, 343906484, 973891627, 906484860, 675047429, 962312160, 432320801, 484360702, 776761958, 969031601, 23632000, 968420513, 706607924, 554882741, 372447081, 694701826, 873771783, 169534173, 841623676, 460981187, 655401077, 366849104, 431681920, 679935562, 37828438, 208182645, 995530820, 422509247, 100772786, 201215358, 862588899, 44779329, 567671325, 328576529, 740653190, 176051277, 690320401, 288966913, 635154108, 339500686, 270641061, 669593275, 20704746, 207555787, 531607726, 803159973, 745736972, 637261987, 440599680, 54199868, 39427439, 534290375, 548593029, 215936349, 412117230, 578238884, 62270160, 945719965, 360064481, 116054742, 27711553, 492381786, 94087964, 692769097, 856830651, 10079110, 197390042, 570833308, 398103844, 271414016, 876763582, 179067241, 856907644, 299473961, 85168672, 227913635, 182646106, 7953039, 30008040, 23481539, 988007091, 494318636, 418666553, 301209462, 954936837, 852261784, 598763136, 363752446, 879770656, 281885262, 339547946, 524769731, 113533882, 62688088, 944701683, 540569955, 805914594, 174318444, 636478775, 288935996, 846163118, 6933279, 948143655, 798966516, 992546518, 283749336, 293638126, 682628756, 675381425, 734493757, 892734725, 867766886, 648926284, 656234375, 12291511, 43332683, 226275343, 274810104, 940339915, 535725641, 771829090, 494952143, 676321148, 816658558, 414217821, 223925295, 129870265, 163676703, 87841183, 493811269, 219736597, 583384202, 605405151, 122010915, 783240518, 994873462, 321881180, 902070369, 633129504, 29566631, 666010803, 249878860, 11703525, 634872961, 814565278, 322674240, 3768196, 972212568, 721173578, 200544544, 482460777, 518450026, 435331927, 605349521, 770413209, 823119462, 161788846, 7964471, 100637231, 970084812, 783421997, 201097047, 266752500, 30207067, 202412961, 728531581, 728895609, 614426019, 398499830, 100953717, 992215407, 43445998, 851684325, 30958392, 432309097, 902032955, 472530145, 14599818, 162022319, 116446857, 926123886, 285615768, 951329543, 237593170, 541738879, 941894822, 468388868, 900937349, 897808791, 634620723, 19733648, 365834960, 383353347, 12077503, 285630379, 410400835, 518977870, 728374378, 499105059, 687241336, 187509732, 91777862, 66436514, 581040299, 544511686, 848330775, 506948508, 852295134, 352117921, 480048443, 711425558, 637081445, 886315932, 715137752, 737870362, 848108942, 456443354, 275901370, 779773386, 910145766, 182551234, 772530601, 823633058, 175198429, 697646565, 384318624, 698533227, 774534675, 574986922, 287286845, 740509082, 502078495, 774719793, 191152899, 459082349, 608549553, 630243867, 62822387, 673101955, 206264350, 821934609, 339317585, 607765385, 731603762, 815542012, 32158127, 208254331, 545489321, 878167018, 373401899, 705359126, 911210908, 751099254, 611170386, 180678505, 481032847, 561489024, 437540447, 714743416, 623470341, 867032431, 426103035, 187394170, 972770300, 767087515, 370523297, 7674861, 944474792, 541986061, 771598434, 6405700, 269233814, 763686761, 793758062, 148403583, 484421578, 376346017, 143978985, 292651974, 743217116, 430172240, 440608717, 119850863, 710330150, 849584841, 756419165, 395218534, 313735374, 512449608, 670639704, 916004494, 787945132, 225528918, 164386336, 23553749, 565626363, 314337475, 580280503, 400323809, 240870136, 229370031, 570539938, 465347228, 803211533, 418703449, 366085891, 496577607, 490830370, 297997277, 46899797, 271291375, 248755674, 146620732, 175431417, 633134805, 873301314, 16602139, 293661599, 868370986, 970316555, 187997377, 14275234, 2613735, 148424093, 791606209, 305710533, 219634156, 414055225, 388621152, 322172629, 725317450, 14720368, 361220672, 437032596, 17088960, 55031101, 297321695, 247089060, 537445195, 95681841, 712900488, 853380491, 246115213, 151639446, 507220727, 748643990, 930648537, 683730996, 306229334, 81132001, 224289122, 221413952, 621881907, 404886702, 96250993, 147214863, 517846881, 557469333, 705789570, 983977196, 906031793, 615414840, 208665310, 665994138, 166290313, 770492812, 587575497, 856096171, 264023389, 620179413, 207522876, 907709904, 375005922, 104128842, 82975774, 124811182, 570750565, 260358335, 439367887, 899060034, 462396692, 477197115, 325902845, 795333818, 624307681, 809459085, 834097495, 768979319, 487622626, 902648985, 907877770, 608843222, 384953349, 300421778, 614268213, 563653071, 599946935, 352328657, 69706539, 112815841, 954522432, 171267047, 778253987, 678850347, 711712870, 963490133, 668004367, 565825914, 908233023, 161933692, 780093430, 410403042, 28676842, 443060720, 15654405, 797981880, 657989737, 264500421, 227477741, 278194421, 268619871, 391240962, 554883853, 398259327, 955276782, 77023455, 807043527, 348045056, 530579812, 956206885, 277944499, 459009114, 729758297, 54720464, 562765471, 887005134, 995119959, 635904012, 766614885, 74550887, 775927403, 355919579, 194565851, 793881314, 483814251, 821939531, 299968251, 96397305, 68367844, 36778963, 593055904, 575361304, 606073908, 216646301, 453644587, 712408878, 392318206, 50981118, 177052714, 657434125, 960675992, 847481327, 954944360, 346653587, 505365047, 732879667, 918375961, 740854295, 292598772, 428908485, 874597924, 626967042, 745127237, 923196868, 279939851, 908018437, 891117962, 9457006, 279962571, 121617314, 537158128, 746000627, 206195021, 297568541, 201952039, 964233700, 100030331, 983303194, 686878277, 384705376, 892102859, 631990587, 550767535, 536243148, 765761453, 542057054, 511529530, 861252225, 867880081, 690241597, 176630702, 121533156, 91551525, 466095630, 782198730, 491182019, 201842032, 729885951, 654740909, 635006939, 78937086, 319666468, 284013814, 189447754, 873284036, 645647297, 953162432, 769582145, 507482857, 397839417, 655285864, 44571021, 134977231, 329870814, 895435441, 943625697, 907812037, 243048152, 945751497, 806184324, 844674374, 600500313, 546949394, 337333299, 443243254, 13259500, 694782541, 654273724, 742602848, 581240864, 860995157, 33393512, 584606166, 371294819, 81472055, 271353026, 864024293, 791658761, 670830023, 745238340, 95603171, 139791326, 176245360, 308197955, 168479805, 33573126, 282387854, 5773279, 401902226, 536576121, 91296643, 70488132, 711630875, 505703933, 895318099, 861664820, 353371275, 973753725, 230530512, 631599588, 546183701, 679194142, 465575779, 200112264, 97997718, 920333062, 534207337, 733306045, 477572757, 185524323, 281403524, 728503414, 842742708, 118889571, 820422996, 859682059, 29060121, 442559572, 888773115, 909469310, 479629637, 740414019, 479315594, 128990933, 111596984, 79051459, 114805631, 213196446, 937716199, 754661403, 837441596, 383411396, 553541389, 95366387, 800489383, 56360624, 213546130, 364546796, 903795617, 854198358, 730577364, 615718556, 634878447, 911799848, 421772836, 288963920, 315600360, 236630537, 248321485, 857815513, 782330384, 225812404, 616463730, 666464852, 650983840, 56379411, 275302893, 547891617, 957230532, 404519336, 454329224, 859367103, 853098622, 219230306, 117117027, 368051407, 112091008, 672701203, 605479038, 670687296, 578141485, 45683294, 202405911, 834524469, 993575878, 536962551, 717730959, 543926600, 781563949, 163824685, 157458705, 846706589, 789086580, 550250943, 537380764, 581454505, 758331964, 688797485, 11543057, 51162869, 916678590, 490409915, 19612841, 456182322, 745003424, 35953862, 276883104, 257423427, 955836491, 819276005, 904024572, 378186331, 506952712, 65106136, 145015496, 536134437, 346157928, 524731574, 689623730, 954998003, 546593694, 79039056, 409754782, 213421330, 613314748, 25933167, 835472967, 1646365, 783481497, 598975102, 561393480, 378091033, 671047478, 457264909, 70212475, 622152907, 12732708, 346656640, 446946300, 806619391, 468225671, 542168892, 538696662, 300526318, 895280124, 916902533, 537842911, 983333846, 136622672, 24933862, 802469667, 69905931, 421700350, 835816807, 526502451, 269528634, 908138868, 105372984, 304469792, 597262227, 886492997, 469536119, 451209998, 343057163, 105093077, 557735336, 442058029, 897693743, 689215100, 963313567, 483462176, 518278936, 800410207, 13228855, 290540737, 146220506, 53905759, 818981368, 819539353, 948737548, 83332120, 464410520, 924051903, 767837073, 652796828, 302944747, 530953290, 542009593, 724996057, 890889249, 376452260, 822441448, 62236054, 443564856, 762021694, 888128620, 750785556, 615046021, 850651124, 684427967, 763045363, 409767145, 573716577, 16242486, 910907536, 682514732, 771662550, 382551027, 562185876, 561099510, 154473060, 956227622, 310881752, 24885738, 122724740, 705865887, 579444701, 350632134, 812647317, 109046085, 740326830, 641476421, 597608474, 572733277, 477175718, 49176658, 509912961, 64381912, 959912721, 488347562, 386208528, 231515089, 40376279, 241145272, 87997934, 932544449, 723485947, 484388170, 550696959, 374739313, 298557956, 856479869, 919892510, 610309496, 154978481, 445316117, 875339274, 374028593, 513139270, 85166735, 327758896, 472996630, 822842317, 365646201, 823264141, 883709398, 369599735, 735372989, 739143376, 807625713, 183512181, 271826617, 882449681, 503156378, 168640499, 165591767, 77824710, 295158483, 527180708, 805858786, 694526654, 592001157, 883072702, 390573122, 884634676, 340847402, 439862584, 254121992, 685836198, 446591464, 340154785, 98959457, 454035207, 102613333, 552120046, 198003336, 814577658, 365436522, 640562003, 117249241, 993818233, 870412405, 2282143, 147254648, 594791355, 328548056, 89111233, 920260078, 362907827, 265226889, 644929606, 390969639, 288767299, 915217856, 430961380, 945276360, 595497295, 942638564, 123248722, 739589557, 450516390, 866479818, 339626728, 558993589, 363608529, 839366024, 473939996, 293538212, 512822186, 656228361, 51898543, 66845216, 930625070, 723807565, 626250469, 33788579, 590071493, 239769018, 496623753, 588900196, 758019906, 628553545, 169943210, 854083597, 702508216, 649825579, 47710310, 420623734, 865222646, 34755128, 693550148, 239003571, 918254884, 210003819, 530595180, 678775264, 639460732, 940944330, 630570197, 733087774, 428101833, 71844828, 312722250, 665573923, 177173264, 481026137, 135562158, 116550547, 200927417, 997961521, 242026757, 951270566, 193464133, 797201026, 580980008, 946350988, 879659449, 63196024, 527046539, 990712408, 716520871, 891622739, 99827641, 320422, 816255759, 480469749, 628515100, 789663457, 140538673, 864967151, 736756204, 144233709, 239102183, 420918027, 195562331, 844239525, 67998405, 534747550, 243026788, 844902190, 706778400, 918729605, 512888025, 417920306, 362290991, 331739204, 981648114, 246335728, 147773591, 877180640, 327754867, 899266030, 639872255, 660366740, 75054143, 229171949, 17214651, 820663589, 306544354, 764802269, 438109478, 128396429, 223909258, 515199998, 504346286, 368932477, 235067399, 995766686, 640434261, 812307191, 148754014, 100822101, 499777226, 133598491, 335154260, 764540345, 574574946, 934351844, 441112801, 94074073, 698248824, 428913539, 739127693, 225142797, 662006326, 138881162, 396135311, 694608632, 346332638, 280483294, 394878560, 531886777, 241360672, 707094479, 397068974, 212655443, 988113671, 744961217, 871190317, 679211348, 373968552, 36437364, 725192369, 208073080, 951447821, 596434345, 41851886, 215450484, 7529701, 977243234, 211070765, 392620846, 158683689, 235353800, 204069917, 744834659, 986008113, 965070638, 949972036, 375428641, 34800993, 227721263, 696172084, 687277739, 117695665, 562933603, 688172945, 226035889, 674509272, 212740824, 413651329, 638506580, 916752809, 343785640, 107684402, 538791351, 967986475, 32029322, 57964298, 520258549, 573049828, 33769934, 72359330, 610883651, 758730345, 880239839, 651639765, 498452124, 545198207, 515965087, 29044934, 888505474, 370002530, 663103197, 456079650, 10114849, 1230956, 691740715, 16371824, 128566645, 372741257, 840108845, 623196700, 935501956, 399540057, 108190420, 47506429, 918824986, 905941637, 723385873, 279224471, 763552502, 307288794, 165732605, 525152639, 122121504, 350449014, 267668893, 913316992, 985893468, 74460985, 128069743, 639707735, 306044134, 117051413, 399139638, 721213237, 775858993, 924155671, 565387108, 174666874, 802716534, 196179737, 949203619, 236448417, 633551621, 659021787, 966179447, 675559866, 145145376, 765979016, 672404352, 871845773, 508803703, 633093970, 188144917, 554513289, 809026801, 586683293, 554576994, 768495736, 164096027, 576167186, 96539800, 134106467, 207202361, 458923633, 315490763, 156729882, 277297948, 782044030, 398475314, 983622482, 808479778, 756395371, 581429421, 477390208, 895770603, 603064840, 761213791, 208097644, 521456340, 674183376, 376963439, 26879528, 872688136, 906960320, 935336940, 93954497, 683597379, 139202780, 376388069, 68348299, 331323606, 493373994, 532553878, 280935067, 180508704, 893046296, 864220488, 418579698, 323254110, 565203037, 749159191, 925441298, 36351469, 859500533, 499027018, 930626787, 548222194, 863636918, 698743279, 252848134, 741857389, 107139244, 797742196, 962890625, 712467654, 771971417, 361267511, 418667603, 33151542, 661958709, 987168804, 199716945, 822814867, 847654879, 472516781, 370134415, 341672960, 643113914, 763391559, 827670926, 693402939, 342102894, 190682981, 830696690, 67772051, 89586108, 929978994, 64224599, 686485618, 123665810, 366908934, 401933522, 134750897, 942160784, 636383959, 522110042, 33282928, 168925512, 550111026, 525756927, 616179447, 771691906, 551466930, 372571206, 124792243, 697946290, 962915433, 752389788, 627754902, 481878115, 799653211, 341180752, 226964223, 511451791, 906604785, 657575207, 989915472, 598018166, 432854237, 59090613, 583209615, 438108042, 921428921, 348232111, 48787627, 604412040, 967226912, 810281039, 544434213, 903290324, 287509705, 783986962, 789976497, 441181864, 659781267, 878361662, 820093335, 808801763, 426539298, 435184059, 12226377, 676676217, 849140987, 724963631, 496209489, 8325207, 466404251, 574380929, 752754067, 312224012, 285903765, 174841468, 746056271, 539635064, 212800852, 786335636, 347397682, 387785792, 658226722, 245734428, 278687424, 889165245, 944451964, 75934319, 266079533, 240891135, 85416194, 277796425, 366997447, 508581532, 930329759, 49331561, 149647163, 39373778, 141609852, 144560473, 560215924, 237829388, 173820854, 795519705, 388009395, 250622078, 888390110, 551509238, 109554083, 723709286, 907051275, 294195647, 397397743, 564504330, 193830488, 196425724, 991545401, 91749100, 599249205, 717915375, 845104619, 622991295, 51074084, 101475535, 670207001, 12448108, 681269774, 151619883, 923053854, 639432028, 470095265, 574019403, 377633861, 186462382, 646110058, 437944495, 177604296, 797866069, 379669388, 526101627, 742336150, 63092175, 155469945, 19174041, 173015852, 568849173, 103486721, 574891816, 250045036, 546850377, 727806215, 583013326, 549999877, 454689926, 860098791, 318790173, 942747679, 881932356, 514445243, 169371246, 350929779, 939560757, 261853115, 865950642, 787133091, 537537210, 982852945, 581752928, 100262439, 508808777, 734314104, 526309812, 912050137, 218770320, 676610204, 662480723, 850983427, 889476384, 615169657, 346829421, 10175472, 887861029, 961658978, 258016791, 734028276, 359430923, 335493480, 523736938, 967757691, 258964030, 48962224, 282491898, 137444961, 67422077, 155764079, 405947510, 160957298, 986248126, 139166970, 612301449, 475282361, 693674473, 639696443, 89847926, 657534925, 283689333, 452011972, 447978195, 224726879, 327522442, 196268760, 50705101, 458071437, 125636823, 474740824, 836779619, 275146272, 262097736, 397330671, 438349278, 854116894, 754885020, 20972617, 906381922, 556988836, 69246340, 750931437, 230803960, 874582026, 452961059, 514841468, 478651030, 502749599, 331392841, 676179085, 955783494, 263347970, 523891783, 702796169, 394927073, 318939704, 341205353, 752761330, 240564481, 731874628, 900448853, 773469961, 3084504, 169731473, 814502764, 272511570, 498598738, 220918974, 919129517, 949987460, 974341707, 193801190, 232042183, 669504788, 970336096, 770217174, 230112784, 462331927, 32610244, 968808852, 471086245, 473923514, 485368507, 17362174, 762758088, 809504638, 901079008, 406197455, 878415548, 853008590, 130112796, 322316748, 301061661, 478813290, 613847385, 206025968, 146928245, 992133837, 405576087, 401351861, 376252801, 730339055, 863088594, 197048727, 516420441, 525435387, 359543704, 23831317, 510063841, 167318910, 151799833, 623836293, 456559158, 295036904, 521029492, 276407420, 816170515, 72692762, 499681414, 439487526, 363737936, 706893350, 243725415, 369291299, 389251100, 774452866, 855155600, 460149714, 933832611, 210186237, 507839328, 132509535, 146364591, 326259758, 279487861, 588784007, 870238555, 6871473, 376439119, 19333574, 164675758, 276015700, 671065884, 595317232, 917440768, 498753185, 874598108, 473458834, 678621186, 898421600, 340202317, 557378795, 293201942, 118907454, 954343315, 391506043, 336805137, 332222605, 563485190, 223571042, 495930910, 899911996, 733296626, 167927514, 553795602, 994546198, 773691315, 928041898, 39688888, 850636319, 722022188, 812938367, 152730768, 529003251, 277670665, 271145036, 237231940, 313876342, 346536357, 860978673, 988042129, 512656679, 435696133, 28601086, 271873979, 896683795, 278083274, 748844812, 799457661, 349216713, 80371511, 11450357, 147283588, 249722693, 234482109, 187520236, 535315470, 77686736, 273104279, 187635600, 869885835, 382883006, 652471052, 348241787, 649403534, 855287122, 696701927, 881420789, 610741191, 383456178, 450525592, 945872729, 76495630, 147041429, 419275208, 915871800, 677534717, 90324698, 912862622, 942382519, 965402926, 709557982, 635939533, 522989948, 710529737, 36719634, 326490283, 394753549, 572235170, 918536872, 142590965, 656075536, 642331747, 275856025, 923155034, 926358143, 128126498, 528267812, 728159353, 703969841, 319648609, 530257436, 512325754, 950070584, 182131103, 288846625, 132804988, 396085702, 198175598, 318849815, 295036951, 186966742, 467653437, 924076961, 211148945, 780934710, 351351432, 240881848, 173384085, 722565007, 984634779, 750387064, 599494951, 432531563, 585068781, 28871339, 241046897, 327900897, 12247691, 23813751, 917131240, 491323108, 33763780, 378049595, 561652757, 743273597, 203357598, 10093880, 797780147, 37919061, 197182606, 889549114, 322152281, 355868054, 869251941, 830999567, 237269681, 949676043, 204672167, 501001272, 564194428, 954105130, 716230425, 437943494, 807878394, 681918306, 372059981, 26635778, 871140949, 682119215, 655111198, 896766262, 223017060, 483851617, 882729622, 449438850, 209078136, 223698833, 797351119, 943450085, 660300108, 195929723, 337650360, 103431817, 650185574, 873215570, 901561, 180269663, 101265262, 463726481, 922501997, 473603907, 680552591, 877641564, 684965996, 377458468, 440471720, 984476606, 955870604, 756802941, 340368249, 223963841, 651054392, 994210546, 554179954, 234983402, 617744133, 494160397, 335217882, 328731621, 335620825, 900541336, 754304869, 460084825, 782846447, 781181348, 913354721, 414339241, 577868722, 868970432, 286227852, 133221445, 3559841, 844327829, 502321556, 960255340, 359349618, 544595545, 560778758, 237177696, 994712134, 495930003, 791210102, 975091647, 231953671, 883540346, 366773729, 706251568, 591739732, 200637803, 153067217, 723491663, 494064032, 820802705, 258359209, 200358169, 338687431, 307469646, 464877405, 177910444, 575749366, 640580689, 190991751, 14683228, 314100133, 410455204, 415553343, 964613586, 634237752, 605057370, 428739706, 360552801, 760556575, 686102542, 992861121, 602074738, 5709910, 735003101, 203403810, 738494376, 411796598, 788271953, 953628577, 893073130, 200801575, 123543805, 372835656, 929385688, 221971916, 404220073, 118082508, 8969653, 899950307, 132608856, 139354167, 363469787, 396066056, 143654194, 649231384, 892145741, 746529597, 123452388, 902121851, 822471220, 156284957, 218599996, 753911234, 4395684, 350863143, 853626483, 37531701, 893316450, 6980520, 69772638, 760636498, 662302623, 320620668, 377782217, 124567135, 869257916, 166856231, 658229899, 327132662, 105110269, 403647970, 817527109, 850175818, 352705952, 910509593, 761567403, 200960635, 876112537, 808609736, 293706415, 317955241, 276588039, 925570755, 345777668, 385005827, 809353637, 170178613, 496768710, 181985233, 315318387, 440208469, 936308569, 57583115, 20618925, 286209645, 890862016, 651966032, 341042140, 964664140, 29616439, 958918109, 49485705, 640544536, 91699968, 662805271, 71048922, 408185415, 891584267, 424421700, 929399251, 707902318, 594316014, 360480411, 496363200, 488455501, 970541246, 387018072, 729502464, 200183080, 878948850, 916680114, 662996141, 208307530, 364748362, 935812413, 133160846, 940563662, 310855802, 632492126, 154716647, 33596857, 744202470, 256999061, 756872550, 971246277, 93976455, 221329065, 290989946, 579204201, 497279546, 945477337, 638652052, 93619016, 481315889, 671437185, 345593739, 632810701, 288317494, 394016544, 2684089, 187665070, 56229132, 918267759, 208544814, 965508393, 72475716, 285800850, 900058927, 964734527, 405866963, 452204718, 990015662, 325669650, 867781006, 998926494, 517865061, 439758271, 975695557, 775306986, 641909567, 696757002, 11378786, 579776699, 406190883, 563015184, 459421516, 187157818, 710135030, 773739178, 419278729, 890374827, 623327864, 190341956, 407258148, 159527729, 430923261, 842629533, 897506555, 236258058, 563992629, 435967022, 350512722, 272051307, 628193606, 228504053, 398608995, 416866242, 804525809, 499084891, 7908875, 484248874, 101759945, 853848738, 834253099, 309142804, 976047413, 730724304, 356373280, 125999636, 586586877, 63220682, 865422487, 654824852, 520026057, 813143195, 55971195, 395310788, 62513204, 887830365, 81640209, 308275328, 504641661, 366937017, 856349932, 218356630, 80571094, 648800083, 786893486, 447259175, 724360928, 20443411, 510430168, 262237899, 246786391, 221418350, 254478843, 337249062, 94706717, 457085804, 550661231, 478762714, 646173108, 812818603, 471547338, 95145840, 667381656, 662568098, 757106818, 466167276, 549403309, 639847164, 865332068, 880902900, 211667403, 328460179, 276865579, 111515760, 970431794, 199415213, 305524276, 10796812, 53962766, 315568277, 746510794, 67093862, 484016721, 430784087, 338900103, 377096180, 597096624, 69128589, 716902117, 362214180, 192933894, 519667534, 776377767, 359033150, 777054348, 800962659, 564315218, 235767424, 988895548, 874198576, 971175702, 272577654, 257171005, 503145301, 943417365, 97341019, 194850163, 37697402, 336156213, 99905577, 31586699, 97873377, 95425991, 365334477, 873112258, 986914418, 629984151, 950857386, 264107472, 444392057, 713862392, 199445772, 773386823, 686471340, 653485585, 358709576, 30329780, 631204920, 831415355, 180830404, 652169807, 895778407, 744735601, 530951869, 625253984, 197941560, 332041981, 388597197, 394380769, 348151309, 46126096, 970088141, 247767842, 394953774, 583319765, 799398853, 296042244, 60817222, 153988770, 99882215, 757020869, 690923729, 434444578, 638614352, 48968908, 148503327, 346453101, 59545608, 198217339, 2111613, 179134867, 231415702, 923236313, 780225101, 690367714, 360675066, 161451115, 647611033, 292714863, 120984596, 205840350, 851816937, 823694137, 199304189, 329828839, 743636565, 697885987, 109257996, 864899676, 563718601, 408318781, 15702437, 813814795, 253925202, 258730713, 272658650, 948800413, 855983021, 879202152, 516215667, 657615301, 600292149, 748230114, 974846888, 244370897, 222245287, 491619152, 802565880, 799899533, 652678405, 403880734, 666626244, 844271458, 196779942, 217535716, 195928799, 448183342, 435143720, 193784454, 952215119, 228281294, 239634377, 509417572, 697232623, 327642850, 398711545, 374612687, 649791496, 126968874, 898760200, 103174691, 199428996, 833225965, 488762612, 600991116, 66984308, 711872644, 614342625, 317891904, 567857834, 643634353, 168358534, 95423274, 675599450, 76203872, 169470366, 692617011, 818729485, 84863162, 975497351, 136876859, 951817379, 666347568, 379341062, 394269910, 896046145, 286649062, 514749592, 221200329, 534413225, 541475039, 376383915, 677267436, 352685758, 27114154, 125255734, 234012043, 657053715, 857726298, 141430769, 547429248, 394230879, 453095759, 883148772, 394464412, 783143215, 536369570, 499010265, 351384809, 143851716, 961922902, 164564944, 380225974, 13927014, 130863054, 940236666, 452460023, 656426353, 538726256, 823944972, 975334874, 482120758, 448529509, 285654538, 77368476, 354113728, 565344598, 980218064, 949305017, 799248860, 275977262, 357038655, 275594232, 844870009, 70316529, 700544279, 649656981, 30566796, 218945512, 591642401, 384779112, 986340585, 904317397, 449199680, 326764768, 28295960, 18687880, 395588489, 204603301, 565837237, 47044178, 815977777, 470538900, 62865242, 11285158, 599010878, 178176676, 988500331, 112138860, 428100508, 999263666, 250135920, 859132051, 740924632, 478357802, 632275507, 94100885, 701802098, 157125951, 121865638, 291677535, 774005337, 517016321, 407086779, 956872590, 653170921, 946551418, 769247390, 7601513, 678737394, 146095366, 516041045, 156981291, 284869639, 772072193, 617988144, 17977168, 756386060, 715855822, 680448852, 404424520, 453690261, 536075808, 494121306, 771593660, 932670678, 561731510, 410414541, 243111190, 380345716, 481316186, 306280998, 955613745, 539597092, 729236395, 685118116, 999900263, 304049140, 749364982, 819775452, 95637006, 97588146, 973155547, 909821488, 583805501, 383554102, 3476532, 997429234, 395656307, 412444801, 773379846, 869023532, 974126247, 851489904, 220784315, 578502085, 680252276, 453433623, 302648926, 683791853, 992061640, 831902357, 68478182, 128638502, 416682263, 908872477, 26317165, 228583607, 721094204, 549518889, 496153249, 998337047, 731508363, 593096933, 16826479, 996455880, 326040482, 685807611, 66124801, 804459434, 182462857, 67557405, 681034984, 640393212, 696684415, 821359477, 505046006, 58775578, 307770096, 752499660, 820497891, 72564925, 331580702, 626682928, 102943046, 687914428, 771976779, 14381387, 700526973, 298382503, 665739561, 951371644, 584147618, 519514425, 397287854, 150504079, 429017327, 550833497, 16257117, 852781514, 370152649, 136780506, 463550098, 287339788, 168504688, 128284781, 290363756, 258433917, 243086372, 921499580, 965114965, 762952507, 616287461, 369850859, 186683564, 105096028, 107987617, 840252679, 316672029, 238846883, 218205842, 811785991, 249157020, 997859095, 549163546, 835591008, 404995179, 566513065, 441760534, 136630135, 203332319, 565543864, 886636509, 960738521, 293742507, 765785150, 307411496, 686990785, 426668685, 537450880, 958364493, 869356216, 199613330, 818278301, 80912993, 813099894, 751400263, 883043472, 980328226, 676141026, 252680776, 363464083, 603978277, 922352863, 378444823, 167754199, 612550973, 573125742, 885630493, 158916773, 832998220, 811370455, 492715233, 964276412, 414167042, 410262095, 742764815, 316656246, 185277190, 497965903, 198747333, 929057251, 128595177, 747216745, 75185247, 17991255, 456757236, 325938600, 759115741, 866490843, 523493457, 644121724, 353402828, 803599932, 432016032, 87650965, 750177719, 596344606, 515348319, 576037649, 36575015, 891076206, 443090227, 311555463, 563097239, 201201862, 19915210, 197126047, 876132967, 375722834, 674518728, 36833123, 128343321, 610073745, 613475254, 473159679, 595363563, 566974359, 280563017, 209320496, 958684408, 661509945, 627710215, 107850182, 959637394, 631934638, 140135108, 918716482, 815223540, 778524397, 162265314, 739211967, 708381537, 64978508, 231130882, 353187023, 552712332, 421768691, 753927055, 928393480, 144051213, 101436411, 923874028, 679387602, 731106721, 59036250, 651701385, 75956938, 122331053, 577210916, 730294310, 479869706, 614499100, 223697546, 750990127, 442605518, 603406270, 509093818, 659443266, 127912665, 288370849, 298776220, 22917408, 624557624, 167355019, 826817509, 152585720, 531743955, 352120846, 900930421, 641222739, 562936849, 110456648, 128892316, 178619682, 590549527, 463955469, 425339725, 138545705, 553990656, 941450093, 225341252, 908703385, 894680134, 202479269, 718378828, 968657244, 916962207, 360808500, 581004815, 164290529, 388924378, 797835151, 207489061, 179067132, 113049599, 175929109, 769452790, 715049140, 581362025, 467537986, 841338858, 475102365, 666987836, 846685501, 957633472, 429837032, 868914894, 898954929, 140329368, 854770883, 359328377, 329197511, 77190726, 386540761, 61747241, 386414653, 543056521, 215071618, 710372319, 660823707, 924048963, 526217166, 145668579, 845269113, 198643144, 36313107, 794661827, 72002673, 78784862, 49406796, 443067454, 90545449, 213390135, 688036866, 149023615, 775892849, 954196635, 633220424, 840164875, 285791832, 343947462, 432975411, 125535048, 187766324, 366827312, 981829916, 686088914, 816691836, 847877530, 541565109, 443255529, 145854383, 770376840, 955040752, 833200146, 388880112, 796592472, 635361003, 169086291, 199230933, 411517043, 902813132, 381925417, 753631470, 95065849, 376552251, 566234891, 757207489, 108282609, 197220604, 156944614, 525144477, 911499830, 758282013, 636369688, 41793616, 846177916, 476676339, 773860245, 111370900, 525186000, 597412929, 430069519, 448210023, 819714405, 249920831, 929468050, 7883370, 793097820, 465914513, 236725096, 728709146, 351144633, 187348293, 485269670, 103065161, 859441895, 503670112, 478588610, 902441825, 664088782, 457493671, 566173392, 72771833, 24950574, 236677637, 746403132, 89514671, 799814537, 346026221, 294357516, 243378069, 834909301, 931105012, 181589080, 964914276, 809461643, 126398601, 246257896, 475948446, 268042789, 384578621, 231750172, 980459362, 534667724, 54995671, 662642039, 674408372, 981677841, 281974352, 187477744, 688072457, 388904634, 10615180, 445577085, 257093576, 100146795, 307698350, 487241862, 150814935, 878486034, 672361623, 471363005, 63196505, 462636986, 838603787, 890509439, 541243138, 5418093, 447277640, 152056240, 750074071, 748798102, 848676451, 175220187, 623565273, 731562734, 594011748, 14613092, 802667770, 870902794, 663011518, 693075356, 635019790, 949915511, 948166876, 162383430, 534165084, 905657694, 372920162, 313752881, 884460071, 110891399, 48183338, 513145401, 61344807, 281610686, 231024092, 361121443, 97502696, 444101001, 656696163, 961336942, 894102596, 937606624, 848909847, 108262245, 518683417, 773278519, 803338819, 368560249, 917151059, 86913188, 277009462, 366394324, 792664371, 832225137, 931927773, 89959328, 629643131, 244339385, 762104955, 230438783, 853802266, 813612646, 801346459, 334773905, 500291012, 800020000, 713689156, 47516179, 154680905, 51796706, 865612821, 324322253, 857175006, 352201490, 792172719, 109942428, 645786811, 985718823, 762296307, 300829949, 433821620, 261873828, 467878378, 576831372, 3741803, 607988906, 389142562, 38006933, 576854256, 442012465, 710555532, 819021591, 492765852, 776975923, 739131577, 412128575, 963773552, 823234329, 240820233, 987093623, 426974220, 124908151, 205666419, 563124912, 864146282, 128770356, 733853593, 977286840, 61770222, 660254401, 290807349, 366733884, 912848128, 143448859, 950462745, 904578284, 858275927, 558105820, 226139507, 369737749, 776330210, 753858873, 977524726, 858320892, 825085437, 884821992, 74881360, 314623715, 533698463, 229249292, 925118387, 400298977, 688097450, 336982129, 904128892, 904543589, 194717749, 891410237, 75647801, 26176917, 748224154, 520158404, 620223105, 140669681, 698896058, 741666875, 598802022, 401794095, 872434527, 827666, 123047174, 346113366, 886280828, 97219402, 694793891, 177967118, 258129911, 159091689, 712238728, 918400855, 514117056, 694326131, 570614232, 167509519, 94646414, 402631068, 123092153, 487963842, 45666383, 617391014, 655785946, 21894444, 798074558, 793891328, 872082901, 987293260, 806520426, 910267068, 387725368, 91500798, 84987168, 133465092, 106667126, 98971270, 83016183, 565696517, 495400084, 473846713, 707286794, 901857477, 296104704, 115512704, 125632882, 947885136, 318393543, 717387350, 188752311, 16597375, 999707709, 991035931, 205952423, 809328496, 227945042, 950622104, 228506651, 915939097, 154813956, 723848140, 398002546, 810343884, 567214624, 966148508, 44424230, 41320551, 396853125, 405655315, 539941311, 713713608, 550144480, 313539162, 530358945, 634007306, 310902549, 513946029, 996734270, 18258783, 695161736, 229532516, 500659459, 808735771, 218672801, 986524218, 358642710, 962462017, 635699077, 159504878, 996734648, 542465076, 963258008, 638407540, 664091282, 373427303, 881860103, 975996688, 885806540, 722329594, 324854828, 255461627, 422357885, 882940023, 309003263, 585059504, 492566623, 861837440, 21306595, 803861330, 71836216, 455276657, 31497591, 856406370, 811665913, 269219192, 629021615, 986171277, 21199970, 158084493, 205787422, 359940157, 855477157, 469671847, 144922723, 765989004, 174884902, 668351476, 986489329, 938469469, 586459529, 550569470, 246442132, 725474290, 160311824, 730878590, 94269599, 445647542, 886494621, 923496734, 703034493, 843729283, 609622772, 815075813, 671582917, 241266722, 361206893, 37230979, 741992429, 498941236, 875543224, 341469609, 797445646, 820351805, 18648391, 523610190, 942577664, 272468680, 213515734, 293767787, 569633839, 183014214, 947353868, 148636272, 338673779, 347952784, 992494763, 514534244, 631915974, 508029088, 956900411, 347339628, 751333800, 218969697, 4524734, 188425992, 264244673, 626838124, 362937276, 437431772, 708107779, 465494802, 547359416, 330587972, 48177900, 530873603, 755550985, 367179621, 62704524, 656226839, 368362571, 154304899, 511787239, 527829580, 411322490, 42329848, 537307188, 595913015, 615460255, 985720108, 309084845, 573056073, 105596506, 343282402, 529653803, 320273626, 279663090, 848107195, 239100461, 938638683, 731225176, 678266555, 428131676, 105346141, 143519612, 670331253, 74892075, 286019741, 951655653, 456592110, 335688181, 949844091, 8269580, 110725314, 97931729, 788076237, 608957166, 694668387, 190499033, 609260102, 691473652, 351690438, 687835638, 901928667, 974487478, 416040660, 5427384, 645534912, 98000664, 952111488, 593653677, 153504530, 998654572, 832183438, 714550604, 350169353, 887891959, 531966002, 960104929, 619203691, 369786335, 341328640, 208017715, 416596122, 880233714, 155402055, 752941938, 149996609, 736810490, 762744924, 310357908, 833752017, 319087892, 188508175, 899907862, 496906921, 805983152, 31741161, 505838153, 861629764, 503421391, 511160822, 584928733, 874620009, 312497073, 915290533, 257291992, 185848566, 347026771, 661184333, 265134961, 584981491, 485099171, 528433337, 94491781, 250490934, 298653820, 857120154, 907277466, 341399480, 129194815, 293203131, 431960142, 966237773, 301396890, 856338688, 116492543, 12430031, 22808747, 310428991, 202838390, 666279295, 751817037, 448319007, 501845705, 489733300, 551562710, 185820249, 914105738, 39851981, 379589722, 56875165, 981233063, 314754824, 508014413, 745212386, 657375062, 419665, 508783753, 988323960, 471414494, 966849060, 460693588, 444040385, 562092294, 243531410, 710041749, 451268355, 467058681, 289853258, 535277494, 900470353, 973501120, 69098664, 8127649, 484916501, 101088655, 418568020, 584713224, 593273335, 614459196, 680618615, 534553909, 688781836, 299951847, 691390075, 723263808, 154167238, 864512787, 743354110, 567750116, 262345348, 126661557, 418351999, 28529531, 684260482, 183420305, 23856276, 833303558, 906335712, 70731824, 393820115, 483820421, 770334925, 540329791, 376966774, 338582704, 58773395, 954479833, 319299361, 131772965, 93015980, 741941683, 904592935, 274601848, 798842046, 430763329, 28441783, 96211403, 918834219, 808692629, 645897861, 920654590, 680000669, 958987024, 208899228, 675266579, 931789662, 217781253, 511629689, 909438733, 778010357, 281543585, 996126666, 937979199, 689912384, 47225492, 997687159, 185946204, 609847778, 228493713, 657728575, 302849916, 362859208, 225895567, 940383938, 654732754, 470498391, 986998546, 896576201, 681727949, 175595719, 117436496, 441285832, 225245142, 159994574, 680070740, 34495583, 397666979, 295569857, 474820580, 732945277, 844343121, 218338911, 336813783, 276339140, 632344425, 88288988, 993871965, 381200673, 923625459, 156349142, 957999232, 350991453, 133307887, 484122927, 152498388, 914608996, 474952065, 431699899, 407539239, 375152953, 333557375, 137764137, 857072022, 602727984, 150099467, 779189692, 685675802, 447007829, 577659643, 545478125, 681770104, 247543368, 103482410, 475101309, 844694689, 252664481, 736396207, 723180470, 986912227, 89091391, 700870217, 14805349, 303812349, 944914112, 604766683, 816221230, 581408510, 374436471, 691054992, 527059170, 48758421, 327390156, 760447124, 874371438, 168991479, 936056771, 612435976, 176964718, 211348682, 258628623, 982809811, 345026788, 802414958, 184223985, 377660735, 417996664, 749264138, 212889682, 283907468, 781482414, 882893240, 956084162, 646397275, 881385824, 221670946, 686290619, 219332938, 616126005, 251975416, 457306012, 506102857, 242885264, 284214614, 627769064, 230693506, 21319166, 684930291, 976953267, 492797496, 793551474, 358127325, 103791251, 287222229, 651488472, 947349571, 253053425, 119161217, 543917246, 584297716, 144498180, 193430150, 902826262, 642330345, 711448756, 609612005, 688074427, 374390183, 855110380, 93535335, 70612888, 501142405, 532151590, 367703865, 246165953, 856179679, 294109842, 471455853, 822550416, 394906595, 743543765, 38106170, 162675666, 784039368, 650670158, 406001896, 154578659, 582684240, 704624951, 112883046, 997288652, 279812013, 825891822, 809747393, 242971212, 978281970, 162283308, 737714988, 674497177, 310472730, 896676095, 7014847, 84288054, 242712482, 289575458, 809263598, 856858864, 529960910, 49800761, 430849902, 338619728, 412162393, 674279558, 228829704, 493598293, 72408916, 618719366, 500864299, 651135284, 422713954, 842431228, 484659457, 797099814, 276056919, 121083174, 26261956, 310824857, 625839443, 322904738, 246308821, 745061655, 70333486, 86747571, 949597652, 802571351, 521347897, 513292585, 823793860, 595588217, 601404706, 763544760, 75517740, 35171890, 442417424, 550190239, 88139565, 508089107, 135246017, 8669901, 154816022, 965208461, 843930617, 38240959, 976655499, 107604343, 363576848, 370450938, 46296990, 263039039, 873866788, 649841250, 303172124, 933283070, 401538634, 728577577, 370581325, 438223102, 585688888, 882584477, 219307550, 595553855, 156729914, 386563509, 812112954, 294769598, 222055607, 908649422, 531667197, 380928491, 413871009, 828003922, 685588394, 277949631, 741088474, 700026515, 379288058, 62753302, 291661447, 487637545, 500450573, 808861577, 950787047, 167466493, 454939006, 529040611, 36437670, 237877932, 597303436, 253171749, 271506145, 9462921, 99214672, 533281904, 991514583, 455006025, 375286368, 557187405, 76740385, 431599489, 526337206, 244060653, 904162986, 310593933, 869812043, 583712192, 942814157, 763344151, 771083384, 920495054, 934546350, 447530953, 876483509, 813661041, 4322520, 45295225, 186298891, 682021284, 179949076, 118305553, 363009517, 159856008, 167351084, 756518514, 951064217, 897559130, 95406662, 801960729, 994421723, 240705608, 115273383, 746856118, 248240600, 839038610, 931846789, 253231287, 128720813, 263250487, 544343094, 315256787, 570496601, 730063806, 227803308, 182068972, 419708845, 901868692, 493705064, 739836789, 375243407, 148658385, 68639694, 304712096, 17281405, 519374683, 890805010, 35849691, 567544666, 78821061, 52994419, 115766810, 993050807, 51351414, 599945846, 341297247, 345535360, 418544574, 895369467, 308666287, 383319598, 794627223, 875970425, 651247049, 18595899, 474247629, 892656054, 40761243, 529697181, 325772547, 80325121, 18409740, 240171036, 766037219, 772740007, 364868837, 182965165, 384302698, 561388080, 265511311, 898161321, 246291103, 754354636, 379973430, 329613305, 818589453, 236720955, 23553091, 9932253, 378252552, 254912861, 579450974, 780684963, 907539454, 501097386, 845921484, 532139572, 170628203, 714796676, 705109182, 281893189, 548687121, 461660068, 65737470, 377239209, 980536221, 618531872, 695127763, 691766223, 884060013, 255549143, 406203411, 249753022, 40920662, 855103417, 18953347, 200818061, 847457867, 958835881, 754560685, 936657253, 616015628, 526060227, 915387399, 239983539, 318330396, 373679982, 9444841, 460737962, 779512252, 485142341, 255348988, 732680329, 30973579, 551367238, 533322903, 110482007, 350598013, 626922855, 484885412, 412361243, 367080323, 314044747, 952309294, 467865531, 514165196, 772207120, 955467035, 276276402, 872408959, 721317036, 804319148, 454722900, 674706632, 668470409, 526353728, 827215660, 954324353, 703228518, 221117986, 461162999, 926663717, 706946012, 464108493, 578531316, 428472899, 242422497, 315155060, 928812189, 640640276, 47645752, 978579306, 419832680, 99929831, 824138784, 690279631, 234513328, 249380918, 519360121, 657310192, 532907584, 536914837, 778734322, 760762060, 481241166, 811321578, 185611578, 554963751, 513017647, 786776222, 333400141, 767642860, 934303279, 570232287, 408538582, 145216419, 486247977, 330840061, 569989828, 424057, 692401837, 159877397, 562959494, 270120103, 587437844, 440659102, 205863936, 118740550, 710761476, 957217951, 531377337, 681242760, 985913128, 888584122, 931988877, 566039769, 807380073, 64366178, 83248670, 156862502, 493045996, 298161406, 806340857, 46848173, 861646606, 178129798, 741790981, 114395896, 754880599, 842698824, 409820963, 87907167, 610057743, 135801220, 333665406, 33473000, 631451773, 752932483, 790736056, 757349968, 652166184, 146817114, 158321695, 598066579, 196701356, 982264735, 599202081, 909898156, 813594639, 775235249, 34841629, 424259706, 960353604, 760953256, 242449360, 741085064, 158680777, 842737124, 403283210, 126505414, 122506227, 76093783, 559832666, 865171127, 72605369, 786799391, 162364900, 199360419, 659513050, 342036383, 173925043, 36196354, 651461436, 701522084, 852487301, 297603991, 183477447, 938205146, 72168195, 177416866, 551844881, 139171404, 669801849, 655742386, 201229147, 406276652, 791976016, 520428621, 160607335, 163773414, 362314275, 208623764, 715113825, 874858116, 145702456, 862941546, 517438344, 926624109, 281439624, 434708480, 85739815, 983307157, 896190340, 45538313, 1112283, 950417477, 399621420, 43017426, 318124950, 473264489, 294139005, 71955413, 721961085, 807882748, 804101990, 778615669, 737868279, 962721449, 915666144, 637163029, 348939732, 626537220, 185217384, 526371273, 243982703, 428722948, 621680292, 157006153, 388187046, 748100406, 289201400, 445979358, 849864270, 542913999, 719550391, 274936038, 987972446, 120241828, 360547065, 677699961, 284434244, 154679809, 278159965, 910877490, 483419828, 423110961, 963586421, 470228642, 321591509, 208365460, 441155137, 917845819, 862802388, 536636759, 7551770, 33951591, 308995971, 583693854, 446791978, 251257935, 202245619, 887805673, 975942625, 435554413, 719521468, 242628865, 778151157, 122435315, 442096814, 251712495, 9530670, 80415506, 353140795, 257723090, 593831007, 704597499, 56261553, 940260192, 927729137, 16366877, 461846148, 317039188, 244313787, 667996239, 562378934, 231415353, 818822583, 583153471, 149684859, 810348054, 824825037, 44359382, 491355565, 470575784, 227565090, 229355790, 961912974, 983862211, 738749786, 38627710, 404353964, 352192861, 409204281, 844056339, 897316985, 268188697, 269423565, 193463230, 323422523, 296754900, 357941336, 675414827, 128426050, 226698094, 299356455, 669140252, 274377839, 74070800, 458498010, 153108571, 432900129, 730400920, 159087248, 238215822, 234803160, 35033238, 905989403, 974459499, 621098963, 926127705, 214507535, 771929957, 948186250, 283336522, 252122627, 320234647, 71608032, 133946123, 443917029, 33769953, 968093437, 215210889, 159255697, 814967151, 184130555, 220011713, 536171265, 328411621, 616356417, 56667039, 583897930, 717435641, 95740772, 808460829, 88171114, 685347574, 514506689, 988092848, 479986810, 40536411, 849668630, 939343183, 895169473, 532158639, 355038138, 466417320, 106557820, 942660427, 458454605, 209798628, 726455887, 355860083, 121802461, 60192827, 703491165, 655844672, 188194921, 305620615, 646465031, 740582378, 914455503, 24824306, 52469972, 142000487, 305845048, 534649247, 829911126, 101051375, 921899676, 410876562, 818114745, 735180172, 876696325, 187728751, 104805607, 843756101, 164481807, 929522104, 914883040, 517628466, 414437627, 374101556, 205065143, 822114862, 73106046, 789590032, 930071565, 948515562, 764742223, 445590247, 881254618, 405741805, 673496269, 912001339, 934004146, 767933137, 327828000, 434731625, 823479643, 688660420, 738084020, 774633477, 164325947, 246433467, 333603668, 936232837, 876267833, 798595808, 936968425, 902061235, 954873129, 597732305, 806409226, 94671672, 837211208, 728209283, 955334309, 920178977, 744558705, 534014270, 998130972, 435147928, 193930914, 322153093, 740942865, 705922779, 381777014, 950670937, 744583549, 251579496, 549364646, 317598139, 71417875, 856287515, 643939251, 280563986, 151384423, 823878938, 178042031, 614105112, 185815204, 30889561, 214602558, 703479549, 827119949, 462598351, 264362965, 18710098, 311756894, 887293002, 850997785, 956368221, 624194679, 115383106, 987794536, 956596708, 81360378, 584582246, 403541567, 534419263, 558113207, 126549395, 859073546, 576185303, 648116925, 562317695, 975981229, 901737647, 235125303, 779675974, 785625036, 135729012, 529464219, 186307351, 342264233, 847775556, 775832855, 83637432, 459198402, 603625459, 258971535, 630761552, 970187734, 527321746, 365494020, 733918007, 308258117, 734009071, 778429431, 12014057, 186514062, 725583125, 394943884, 217867877, 474452676, 263469773, 250529960, 292674429, 289687249, 679738115, 150613461, 368625358, 33003442, 735574277, 492849305, 454162183, 48136844, 4371965, 544373150, 716003200, 592434294, 63183668, 782378661, 725414139, 567652120, 232115047, 740148084, 403487557, 619676888, 730615864, 939285587, 197530959, 587042003, 838262736, 151800086, 14289903, 642463302, 463530836, 950221869, 145570441, 996360113, 328677931, 172397903, 928826428, 91587137, 297979301, 277607278, 753521859, 342383631, 938626557, 588628886, 101916003, 298733952, 68282356, 884058173, 485817497, 367986843, 739959333, 277126169, 888787363, 174333752, 34925415, 974236736, 76794443, 918920470, 709897863, 304182886, 68483033, 630101073, 809812377, 940734685, 860414016, 77694641, 378625376, 355881721, 265605966, 64749486, 337004580, 524362235, 625564337, 164346675, 515106828, 803993118, 197934412, 54995419, 683022256, 206880437, 835041626, 454029682, 506949697, 598457262, 976086854, 921621835, 96179571, 813874872, 577365678, 431277249, 685715191, 744997087, 350098437, 172845013, 47544411, 317611190, 5974481, 552147395, 11037920, 132029516, 466933954, 530725215, 488935504, 261884161, 704168525, 60335007, 617654229, 732349363, 568456682, 432175192, 995705108, 564072966, 212025999, 604679939, 384760633, 997688772, 148434460, 293091947, 593524792, 143536251, 239241407, 152661494, 614020038, 856863374, 829881544, 736535867, 783899201, 955855237, 702207271, 655825049, 520753353, 926574090, 280176440, 531859350, 286086230, 654475584, 108925227, 792545370, 637727042, 317626178, 156502094, 714038015, 65342031, 66841191, 273500717, 576685875, 720596377, 477820895, 829323791, 603374008, 280208250, 465470224, 148589809, 108101495, 458151974, 519594273, 395878909, 118099045, 403587185, 204743178, 486927114, 763652130, 885711955, 519770509, 560208862, 351411642, 197465968, 157133609, 774875748, 933544766, 560407189, 801458710, 567058611, 675270159, 383847808, 956854241, 259521614, 406870158, 240032454, 901915509, 186855231, 742415207, 242274657, 959096046, 163319765, 358314433, 666326910, 513017411, 902996236, 118670838, 868541127, 718845814, 746672526, 403102022, 953462348, 839495960, 484887845, 306432870, 33458487, 946875292, 767426018, 651187853, 343150103, 592775930, 668539598, 262499423, 675594229, 821618088, 718521791, 643885619, 979494966, 384834948, 37280488, 517518897, 678364595, 696510042, 567204766, 414636007, 95971199, 640314474, 163909760, 75157691, 819647921, 898139358, 166219609, 622435208, 745280484, 317724165, 940799410, 347193677, 970358612, 769580086, 236303693, 224150731, 655036487, 44546009, 906787027, 451671130, 59892617, 48158270, 641682973, 241697565, 230772827, 809411568, 344115059, 954647591, 712101651, 551684118, 484885139, 764602580, 273009365, 333154511, 895316888, 180479542, 907642959, 399382357, 14264731, 522972253, 323163690, 92836881, 112272943, 657092203, 37078900, 979732006, 772893034, 435270512, 305727027, 669889646, 244180559, 339480992, 458488757, 706890040, 378271219, 802857428, 373504048, 131667616, 248811784, 776539383, 155707458, 369297467, 102353910, 12623269, 93128455, 89277859, 719668570, 913208813, 715763139, 426726923, 93486747, 48746567, 420487773, 765083915, 224119101, 283081311, 429332490, 809151562, 281898991, 880144185, 924612960, 952121065, 74726899, 829716652, 778789659, 793964093, 171254422, 774102855, 577393938, 682956436, 799027767, 603598892, 177573240, 758988736, 521325569, 54389, 849558279, 197449240, 420979185, 165887442, 849243037, 237527000, 859656082, 910089065, 863794942, 896759802, 760187456, 654011007, 993779456, 598059163, 26507790, 644795228, 667628621, 311549812, 816461782, 352403635, 710193047, 497685921, 574177560, 597396727, 105352830, 416185177, 795305062, 532046064, 16386591, 308970338, 661315607, 869855683, 22679204, 783243325, 665726836, 531705740, 736616353, 703975601, 317780795, 577479503, 784640010, 820417412, 996619129, 882199668, 251582170, 562087017, 453168166, 721519090, 723145880, 108237235, 304425717, 191395458, 640004573, 279147704, 466600315, 521032995, 398900302, 713554274, 455031274, 776855083, 678663518, 290694425, 114628984, 849134681, 336675328, 223460308, 49041376, 197460514, 878894743, 332404458, 339203584, 525211902, 763597666, 875054302, 959423203, 65934989, 523206660, 141845340, 867678832, 498673377, 725942255, 836515788, 115916062, 382131722, 644446532, 632876276, 203766625, 962935389, 962220236, 966688176, 593527404, 390819871, 108088800, 496743056, 750822144, 221279839, 894481869, 35249478, 494028126, 553646521, 725808068, 920354045, 260775837, 40238087, 762364230, 823626928, 695093754, 257111848, 754302072, 903092103, 278847282, 261492149, 706305034, 64384447, 415599890, 489964780, 385578820, 502077636, 544454439, 188489711, 658064644, 925508908, 706734840, 702066896, 887652087, 759567181, 817073872, 333890654, 480372521, 560184335, 241038563, 505828954, 665410274, 65529703, 161240881, 266653379, 372967977, 875431530, 595388306, 377651150, 447866565, 739281355, 633080886, 342804302, 986351030, 942688445, 127442542, 400166688, 585304084, 680599574, 486762938, 391667817, 321583307, 483352859, 571439884, 584241766, 649268287, 429395153, 51794678, 542265211, 945413832, 904902134, 281462172, 484890554, 38395377, 364748628, 561334742, 408200372, 889195374, 709098769, 294450139, 358975487, 275056697, 971891006, 353310462, 124671601, 112814546, 456140527, 104303308, 425739669, 147135047, 477139169, 593925044, 242194032, 983539952, 486946373, 356899443, 769752231, 976414479, 910771061, 632830691, 473491463, 269780976, 976289778, 200893426, 683282992, 672589064, 223950925, 11640087, 492382120, 148314825, 607531069, 350657654, 153432165, 267094113, 562344199, 885440473, 276166685, 126421445, 261580745, 666655002, 591541935, 684107303, 643257950, 945082773, 933104692, 933371791, 720614531, 882262297, 206407461, 104484630, 979786002, 919310367, 511896064, 11748098, 81936213, 605635070, 747186390, 364945334, 469524071, 864482894, 315495222, 176562020, 930093507, 161325039, 206217924, 377675417, 470109905, 818798706, 104336754, 638882454, 656493156, 667900349, 25687976, 201224361, 79418487, 836143931, 508498048, 146246699, 584391717, 460967377, 124469255, 427630465, 816269711, 186593358, 246566863, 559486303, 76786236, 166829702, 946884055, 696079233, 34696455, 52132422, 70039888, 773753381, 49172643, 604762053, 253220718, 397475039, 827744120, 455108587, 855366273, 605804893, 916330276, 142935781, 952232776, 560329555, 150035019, 293113109, 886287915, 449949540, 925839963, 574000328, 632815240, 306829756, 489688347, 452002413, 743736095, 627621371, 195036209, 217037922, 499005168, 139305178, 357104653, 183192303, 371641002, 628039937, 295047460, 571351545, 990523662, 919858907, 964294919, 206288094, 66730432, 122647978, 500170464, 624977153, 282736544, 664983934, 286502504, 590334478, 278516021, 888109985, 96098053, 304400121, 136102395, 610488707, 453688400, 251444462, 566704393, 908359008, 506946819, 2257787, 700900168, 711989335, 719425519, 7931397, 459513159, 638369910, 241114997, 262075203, 885677533, 950965070, 329746411, 385962925, 954944053, 151182322, 384229648, 152818565, 57180014, 319773718, 954271419, 591295161, 564157843, 594541013, 554206642, 259994354, 911430988, 493183618, 782573227, 945209374, 477351983, 704177193, 250665392, 10559713, 306067112, 396035650, 701249776, 464281307, 149125797, 383507771, 863010023, 573291608, 786823945, 507371182, 622780976, 596507826, 950845201, 227578766, 219624222, 623862138, 742875465, 715080795, 325694419, 586663229, 873275077, 384253511, 51157628, 996224726, 156218192, 229264136, 927319871, 657320965, 947939591, 490983977, 75750410, 304226475, 447947763, 922115514, 205533897, 598818174, 387486209, 371532163, 10124250, 390433225, 387338278, 720179459, 15836137, 130445295, 730876362, 65982530, 84435624, 54590680, 193018195, 460313454, 106319035, 625228784, 964584018, 541630423, 613455411, 141847256, 218261746, 661431768, 660772375, 862777623, 399315836, 189780167, 548942527, 226970113, 171399455, 966947634, 91324846, 122473943, 781250239, 989269353, 218815265, 96070738, 936728380, 314779960, 223138827, 307584021, 637614595, 981865017, 331794996, 678018954, 295641257, 670632465, 738610102, 174574169, 689102608, 838296460, 813592969, 118159801, 872793884, 282987461, 319291009, 21502469, 575329341, 656790991, 560046448, 865771890, 389123451, 422414767, 908643669, 23465659, 732729752, 578628561, 187328349, 93293274, 20053715, 574948704, 516088591, 793043384, 174481858, 18138981, 411228430, 524286646, 126504775, 583971725, 905342870, 377521892, 731749259, 679715554, 563491876, 239516606, 286725474, 615856637, 535912757, 714708979, 247655396, 212612476, 567867789, 985710546, 112606043, 836339500, 997514108, 266323259, 74230628, 446751451, 388982212, 346822128, 770660671, 982483230, 139853014, 632674196, 60650318, 367871422, 879497744, 379374174, 382546892, 594819486, 435228617, 51537503, 439396286, 57256020, 89008227, 843515744, 318363193, 474492435, 131896424, 912131855, 747749147, 945906737, 118656015, 989575573, 997179946, 180468931, 955970975, 903056864, 722842822, 498700250, 214365046, 834690300, 971494045, 496538688, 364733654, 530372604, 776485011, 134644576, 533615789, 114758393, 999528264, 155735946, 213956323, 474869444, 379296547, 65529981, 830178955, 59923825, 91997235, 265115601, 881758341, 69423903, 229762867, 757860486, 600216247, 213650636, 400131606, 512941130, 805837567, 81718552, 880623625, 274694697, 282920001, 655538855, 71265667, 845777843, 892854262, 624819346, 477302298, 230694951, 969350493, 827270904, 276205153, 802411083, 991085412, 456646734, 324982879, 456189714, 317206809, 466288847, 400268751, 212253577, 343050869, 400932195, 705398329, 976319441, 791264660, 168262714, 192946904, 109616695, 632719563, 200706110, 99138534, 406998799, 171441699, 765191009, 486225529, 407462874, 217980801, 711128178, 503245453, 469165098, 144272784, 996487543, 729822420, 667486770, 148512858, 789622617, 455835192, 657137393, 734991280, 185701017, 705941069, 187830970, 180360398, 598354745, 451064261, 700783119, 361092623, 972895709, 997965812, 341682934, 367973170, 905859374, 243297516, 68690510, 944472193, 822783796, 53010150, 835431925, 486253801, 258733706, 713775306, 777991129, 238075331, 524759581, 302340492, 249336486, 893120949, 403329136, 546164352, 732347992, 647596174, 592691310, 682648666, 342978898, 389156178, 607327435, 964077807, 926942930, 299637281, 817641302, 451076456, 895881308, 552120364, 28886126, 978340406, 359030012, 981661011, 989898029, 972726182, 669074279, 154717489, 247358209, 1567095, 251198378, 670223341, 574941481, 587502321, 886343299, 91921573, 481174315, 470266789, 663662311, 968070692, 827371440, 696292628, 568309077, 75518081, 642404272, 436796959, 295805696, 92972978, 56714605, 660230133, 179324666, 996220499, 326722997, 350211631, 534500170, 110616770, 912320728, 160411527, 607991298, 24008878, 526905479, 778446400, 257996331, 408182380, 774175664, 129523174, 376770415, 340672401, 712849537, 725536276, 121066388, 423463461, 200964968, 260361605, 142261876, 377293696, 890954226, 339059984, 677080094, 726193229, 562734158, 736296318, 217662854, 852106637, 294273590, 629621607, 336352812, 836221174, 49353368, 928330660, 307674657, 342224512, 210979586, 639758196, 660725273, 363905666, 343532459, 532315034, 51468143, 947329737, 759470262, 122220562, 684312995, 425586645, 818749186, 318425101, 151887771, 82597482, 481367594, 180100183, 984139992, 476048124, 465774624, 311756521, 558460356, 571615523, 958471807, 920825316, 316367361, 870491944, 404793783, 134382417, 511229688, 558259997, 104014142, 290706140, 683649089, 68881791, 506410612, 475965870, 821249181, 490171788, 157720730, 188382793, 232289062, 941557039, 346983142, 188022483, 387241926, 305204029, 720996758, 792412612, 983709300, 213242014, 94889974, 163994387, 945325905, 642133418, 540175008, 303387835, 559224204, 268953632, 509234275, 270120043, 221635381, 438847358, 678932527, 838126012, 243506258, 43794464, 776269579, 266166422, 693811795, 378978879, 172645472, 169408809, 762929332, 771094798, 770866182, 986875297, 48933129, 855145245, 192563917, 852071237, 449620950, 550674318, 29758676, 986586796, 247717821, 5004583, 18086875, 835016681, 758011422, 513892748, 813296557, 671217022, 509817786, 382662034, 494828704, 721623705, 557036560, 715238622, 804173106, 532884614, 433303867, 37247159, 260098694, 720822637, 4392390, 405191129, 888177745, 381609400, 890698274, 152653467, 354137624, 850007133, 315993039, 754312586, 123516728, 415902041, 317092309, 123751014, 931638019, 973027623, 35425412, 421975578, 339647515, 333060999, 921437701, 454370103, 514224288, 620277896, 614708320, 264099489, 74559083, 58403566, 278336398, 805984663, 878337100, 222064315, 898014792, 71873259, 486926150, 394120279, 646943052, 822638107, 608911308, 321259759, 585105111, 108912146, 863250184, 34423217, 663775007, 880247622, 576577422, 71725923, 654879997, 444425178, 916336627, 523429723, 807323311, 317693028, 438821251, 236113337, 595507065, 538543853, 951227371, 909323957, 732788597, 249394477, 665420894, 555338614, 811380444, 668757089, 739278856, 274659300, 928878152, 844793511, 924048993, 591031272, 601890462, 336450193, 172469526, 809872767, 414479515, 116984280, 536484107, 412777791, 63443203, 143720746, 657918773, 434733980, 173582554, 833727106, 170311413, 423568308, 353902282, 368627321, 887295564, 168747502, 27597089, 949621007, 114308930, 364341486, 267931581, 238332638, 301369045, 210848559, 7204561, 426336978, 900702606, 463895372, 874456767, 1808154, 92128493, 153907722, 414643146, 993886985, 336218089, 622622149, 574944274, 476831135, 225553314, 636064631, 901478671, 932441965, 148513322, 276693944, 695842581, 331181188, 82804097, 846359493, 359842833, 964803664, 302289167, 463125434, 695428621, 475675462, 856901458, 268107925, 533634498, 496919658, 68756071, 607987817, 404532247, 428803354, 340891206, 597541204, 973460477, 435707904, 606207778, 62354152, 700574856, 994984486, 91119732, 337579548, 853811862, 194664538, 800822703, 837873409, 418191555, 308524054, 805641382, 649971975, 56058547, 994712455, 459967619, 408162655, 292282372, 524406554, 194093632, 138796626, 698005554, 54701274, 225626011, 805665144, 643020417, 996616831, 711271331, 833694280, 532682775, 820254764, 764309148, 734160205, 76739998, 144180889, 17061684, 552608786, 973876721, 691855726, 285838342, 210278856, 881594848, 808420601, 390147594, 318434390, 549425437, 786521963, 387332901, 617804340, 90556746, 16934989, 328635464, 288087360, 395497637, 115291885, 79644554, 177180205, 824063133, 776348546, 142966529, 57266687, 565862316, 98388696, 877453169, 316748887, 853832365, 562253547, 787985848, 988333849, 38611611, 719457005, 313440781, 246830379, 90410612, 867751382, 471449881, 197129739, 750390218, 573880508, 141955116, 468044047, 408756299, 939862562, 71042185, 982229035, 195632441, 647978488, 367100677, 565759614, 12149647, 972360395, 489315973, 460562189, 205338945, 236080501, 991768978, 388835129, 533452914, 175421574, 322620195, 670192688, 887466050, 675881634, 964272413, 139769490, 877619271, 918030149, 775752121, 727606156, 680489212, 334526212, 773386569, 163194271, 198453696, 831207914, 238036346, 458986615, 530758581, 40051236, 83802839, 759692055, 605274772, 779922898, 14816567, 239526214, 939153265, 123386377, 405302514, 48450935, 844585211, 496707034, 982354970, 645656689, 727163077, 957368776, 184273411, 855663945, 73759488, 972262008, 56399106, 666744847, 551528024, 773203407, 645536635, 976305586, 787466797, 198329086, 366458506, 912369721, 648748175, 810162237, 20770936, 857362559, 563333405, 635838840, 731464859, 127798218, 988776058, 278764253, 164853061, 794792429, 934410560, 858112786, 106344815, 12944883, 96970870, 844053229, 540290924, 654049225, 782655379, 68491279, 387132817, 678604063, 611069337, 419226644, 989075591, 900735416, 998007687, 213847245, 402137097, 482779016, 366724404, 422207436, 97362978, 805150462, 418630771, 422002970, 242366780, 213393403, 632461599, 811679276, 485947882, 163030813, 708161842, 404702953, 137359656, 538905387, 505013529, 556529353, 564792178, 163191280, 637630282, 104817617, 340622339, 807825892, 454025716, 572386899, 55533747, 15135584, 233438761, 702365210, 585062790, 408183380, 429712654, 501034318, 714456212, 37818011, 668438498, 729839940, 458483728, 676450485, 370197555, 779711623, 873381189, 249647304, 882525905, 87404187, 363591103, 547492629, 869718678, 230480690, 84370016, 889494105, 588548273, 335867460, 950675514, 186509953, 782419800, 830070978, 645422701, 381870221, 486413809, 241520057, 196715836, 946472728, 132343659, 808283780, 461310013, 58423391, 672398716, 228677875, 874841154, 222926594, 204812213, 470191151, 822482699, 466938122, 386662605, 719403737, 10019658, 811593303, 319290272, 175884145, 342302352, 497154088, 746825338, 545416993, 313202223, 495119654, 109031387, 715115255, 771770331, 700564287, 374454631, 216957814, 883318291, 137409098, 302176011, 262200195, 700602625, 177619610, 434798980, 829807714, 651703459, 680415371, 945931808, 444679827, 245568533, 737310817, 96798350, 198423492, 297448676, 785013481, 423594203, 460398744, 169220257, 232670425, 212057835, 640331314, 71155197, 829977434, 146082212, 663540970, 41530322, 965092379, 871364842, 954677707, 86025994, 184454184, 483913926, 61217277, 120802877, 323790721, 746861262, 538386074, 802896098, 50477979, 859908790, 452493309, 432006792, 183813844, 717833918, 937032458, 492071352, 638524265, 162567983, 518015488, 992163021, 476110775, 182320197, 198041722, 467858964, 307665964, 224214954, 479314979, 714378843, 189926771, 356355999, 939210931, 436985088, 988689696, 798467438, 140424887, 723285233, 57430619, 443918776, 413259592, 850802215, 401109379, 401966101, 210746460, 744051858, 468908025, 909130898, 269361972, 524330934, 239392636, 222601765, 594274990, 978154143, 463937512, 902748928, 568345797, 986269911, 759551437, 862872179, 921014787, 391001153, 244295444, 60054154, 57536832, 761477879, 999950259, 861366959, 975177410, 530573948, 903617857, 166680933, 82458450, 415247299, 566883257, 165801, 584193133, 610343579, 322956872, 183953895, 866578174, 966239445, 294854283, 431928608, 130814367, 581324267, 630346170, 157311480, 674185636, 536948984, 233675564, 850191416, 887907459, 598702181, 333865741, 145950979, 327227660, 154980713, 750401422, 285814142, 281660377, 240736940, 516058103, 368535165, 287268639, 207662910, 957106969, 363864838, 32743033, 422766766, 907095953, 722295275, 317800741, 415315369, 951050076, 446422553, 316338188, 530843702, 937367661, 306940406, 13605024, 859731505, 79517406, 160262395, 38966296, 248378390, 977379237, 661750454, 62270266, 826663391, 746922682, 715720637, 428163407, 676925386, 349496208, 514822916, 871328685, 579445949, 351352009, 62870808, 935849362, 577271074, 726479865, 875948936, 429930801, 900077986, 687584396, 237184088, 899405602, 553126069, 289344494, 82372007, 672401865, 52499822, 458191831, 631281497, 533631641, 60903350, 280805548, 291629434, 330719837, 291666842, 685611336, 47720339, 215148617, 539476427, 62866834, 73368946, 323304464, 574095154, 272689952, 790158135, 692139774, 112268124, 306323259, 271301793, 526967500, 271379567, 247999442, 4310199, 602436379, 485283794, 321051955, 712579788, 568946043, 352965662, 184457963, 510721099, 112387897, 386142754, 121268352, 993478869, 581434590, 557215616, 889566030, 369440148, 743045533, 830107369, 490319283, 804840910, 6419180, 959945396, 190614911, 444278912, 424589218, 977907001, 854525719, 610694612, 681362815, 368200300, 684828514, 450942926, 514029875, 913849655, 851306301, 673317426, 559407571, 638727600, 385822892, 104721048, 475832743, 405816550, 803070000, 603927207, 635092947, 343478431, 665162793, 756201078, 54799913, 998138231, 743075914, 730375930, 814393170, 728232261, 62044653, 749501841, 415427038, 513028142, 249417179, 407489793, 8834419, 763455232, 575579214, 336172053, 664149160, 552764934, 368989298, 869381235, 245760504, 559601798, 459411092, 128521566, 105948064, 822503862, 28182710, 425804549, 296216902, 783985669, 738287529, 245216367, 205671521, 219292492, 417375923, 88060995, 221789467, 103643152, 97007674, 946405, 547224805, 375118476, 106191758, 19985374, 728029622, 798077597, 598195072, 932201935, 741122904, 387694757, 677287916, 195375494, 874040994, 454154459, 32085124, 349686963, 164908756, 814292456, 592063801, 788139179, 537873054, 827359417, 801913924, 597757325, 48010650, 837545334, 819126990, 855957844, 85007013, 572464285, 548926678, 725367000, 116115369, 512413926, 342314126, 968581504, 52547535, 772240546, 383799947, 585911059, 282867863, 700287741, 549921260, 532655537, 138258764, 432791725, 357752860, 940644567, 704421017, 168261924, 605897316, 432426039, 374132771, 610045010, 447019469, 243162073, 975979616, 97008845, 719608588, 353366225, 787500224, 593440073, 47629185, 434626138, 512744854, 251118508, 623122670, 11094260, 169645830, 528048638, 566621041, 381884160, 773486573, 94360158, 82760880, 463204505, 422480116, 167581376, 783857268, 661271465, 909522961, 659253075, 326023500, 371004541, 262730988, 680953610, 432595175, 231244248, 546215018, 84259289, 504556555, 219654290, 195501912, 307052632, 418356154, 329362376, 669865795, 439812306, 860016622, 74360913, 332152235, 807622082, 443082613, 508234766, 528623685, 402633623, 740506255, 852911932, 867133523, 163157266, 736508791, 708896062, 803882785, 272961421, 643298792, 748868096, 319073360, 454788453, 682479981, 957887577, 596018191, 905769375, 434845080, 962708802, 377896464, 63166324, 331744668, 109860589, 779815618, 372429780, 910941329, 945187623, 53099201, 41645261, 579844663, 248498587, 35411060, 771965983, 250289077, 425512707, 931649263, 890365559, 782715791, 10368292, 380281668, 586461314, 880299475, 246702094, 378895698, 441890601, 615160867, 785072999, 167198517, 681651389, 502261139, 30492505, 524230436, 913121407, 772694165, 657502740, 940222153, 698531638, 46485602, 252280180, 324826643, 931927926, 78078388, 70692540, 143551684, 525801083, 954362043, 359272479, 744807174, 641495624, 876453513, 543179161, 153134709, 12259712, 968845964, 597240007, 31447396, 409096573, 944256961, 877583951, 550958411, 722863008, 851332097, 224362744, 252506815, 403259766, 652995660, 435785420, 259996738, 31630275, 243228613, 806375772, 558952114, 972753138, 231295310, 113272882, 604453865, 98227579, 674278659, 813750494, 413117764, 859130011, 3094164, 700511972, 918203760, 254260806, 225253062, 388047763, 603269028, 990381164, 877610281, 509735984, 430443935, 431244873, 590767225, 713929682, 422487228, 491005288, 566600838, 833917760, 247484487, 532852586, 108413801, 796282761, 895608902, 178139895, 332713512, 396607835, 479071664, 737810377, 230357708, 860724198, 374069142, 683885075, 736271585, 742340049, 765103134, 490733760, 107248094, 752467299, 182445563, 283010196, 11062589, 506855704, 590475623, 290446001, 823104265, 751959050, 311126747, 702020617, 681859438, 30558111, 105667063, 927741330, 111720908, 818645528, 134266315, 384625240, 677050185, 189406663, 201602163, 105957159, 986615719, 154010121, 302506315, 307468237, 812304523, 336152959, 601709125, 369094842, 96879803, 830015342, 106907980, 848035832, 295227574, 347856849, 77376250, 561500158, 931648827, 246873453, 291259566, 428365077, 324972831, 285458643, 50159839, 191645091, 143728999, 778599734, 588716423, 443187210, 599923028, 992771172, 349106695, 404138926, 368557161, 688753223, 26034686, 701430935, 862852355, 972599532, 422698371, 192374540, 573769308, 325972876, 813485907, 851640889, 635276925, 502404213, 96179126, 456985364, 551501026, 601050839, 69426017, 667030460, 89824047, 667102356, 120093951, 870892374, 726981505, 108139288, 136729659, 889892456, 244753859, 987401415, 853379828, 974191889, 800906583, 134679303, 421788470, 867918010, 143563227, 964397993, 565126020, 226026569, 62692353, 104691804, 805197861, 173075132, 97404202, 829426454, 50324380, 918363521, 310504710, 509605502, 350244463, 951401051, 376989234, 518184902, 303172756, 495588178, 361007044, 24635485, 294855537, 639718699, 967944739, 976231398, 628763772, 213951682, 67461587, 649856532, 799086632, 716188892, 606553555, 235114409, 867987903, 264412700, 550362495, 510639510, 863680262, 233822549, 388386883, 420317888, 787391491, 928913176, 514811533, 654051267, 413908611, 527521048, 252867047, 861700693, 35599428, 988081535, 756954055, 611533857, 353887235, 564100042, 485056490, 591079944, 7488448, 858550074, 772857673, 241404324, 576037379, 671266486, 261450768, 380180467, 707952724, 44254078, 568914479, 982957896, 274160953, 925263072, 90424024, 562462113, 600363674, 59281989, 149189899, 113649739, 114946011, 887845366, 942669589, 312934106, 541110202, 456583701, 379685084, 160441356, 237412712, 180052990, 991433915, 252223453, 770942710, 953963047, 444569309, 394568426, 56514351, 344954175, 499818526, 147024029, 188856377, 565284449, 433806778, 676122119, 872126020, 483218092, 206931404, 357612144, 239681416, 782030071, 582677173, 782489823, 799898864, 200420270, 191167074, 302929200, 13508807, 536523068, 896911056, 479245690, 299601953, 110864590, 678443411, 728343594, 213045007, 340473408, 298365386, 135715419, 223447964, 282418027, 704213012, 218754678, 811914173, 651968236, 867149977, 78036033, 959634982, 375879259, 681801680, 699468176, 349579714, 283253986, 497982948, 292378715, 380733629, 536251555, 828774089, 41097237, 111292987, 559373928, 70406845, 158131274, 524111767, 31941572, 174423976, 274804747, 151276996, 395139115, 869010220, 151647672, 189547143, 480510360, 867878088, 962238125, 29103961, 658988924, 178611180, 360128378, 444676885, 148703598, 300236085, 957832620, 412576911, 626520094, 797871906, 405118863, 453891060, 488281388, 498404409, 743210762, 459379063, 21916561, 483794779, 233305318, 678633939, 971440356, 984905924, 690037836, 69224950, 351413268, 604690700, 398599242, 106068461, 482059240, 579282034, 807349159, 7362140, 679296297, 901627025, 66161952, 500198323, 582569585, 851237895, 666396035, 871355894, 248644389, 100185132, 283526771, 832099900, 424143063, 230260260, 724009961, 976142116, 274933527, 954529713, 521582576, 595681626, 79439440, 585208603, 394282014, 26915106, 283855753, 387608944, 52402357, 483491500, 518832740, 686299637, 610949725, 91868083, 489845622, 111425070, 516378689, 303075289, 199102939, 12716760, 947414396, 890441873, 491342929, 718441104, 13613602, 268558954, 223343842, 594275398, 275874225, 560524867, 682620926, 304430968, 321573489, 127376203, 95283016, 543026665, 394584916, 978809985, 631421061, 744216506, 975696451, 848393873, 969476195, 430417725, 600848444, 297716251, 871415526, 568144481, 544544993, 130774489, 169340200, 27784490, 94244094, 887330586, 256467142, 793709155, 615068257, 518484366, 195164923, 187728695, 538328592, 386249009, 632218824, 154085776, 696731548, 446853727, 157284584, 59664445, 456769260, 33467294, 8134763, 579133049, 771838356, 999125855, 33180418, 567762676, 415230602, 534411830, 329789307, 323840712, 439776468, 36135493, 924663349, 40237295, 651759500, 186686129, 5859494, 841522649, 486869804, 330183205, 252128448, 219337107, 650205142, 155080169, 449912497, 605410196, 183023867, 266334854, 754687107, 617556850, 503699120, 573580158, 448547684, 167200757, 795629199, 383040004, 165807453, 322767276, 426624352, 309741672, 915632670, 653962559, 309835615, 625860991, 261881652, 685311721, 670236104, 422976723, 970224587, 665776583, 378479495, 283769222, 526648452, 304356747, 95099547, 735483291, 481510622, 225044746, 22449856, 639091996, 324694637, 986616893, 401462979, 794686388, 504208634, 128313269, 234617362, 512561470, 262606860, 699238481, 589454310, 654586686, 711344197, 604766517, 515605241, 913431003, 467625107, 721522378, 854529151, 452467351, 695810422, 92826777, 888559728, 391763995, 679312867, 738018492, 652047638, 494374661, 566200043, 983753820, 748295216, 926959528, 527881778, 662185194, 504953369, 927031371, 679263469, 67822409, 923337735, 770184721, 466522329, 955269672, 448142536, 530382572, 595726765, 646767702, 381910356, 301590949, 788378854, 200689880, 798988118, 604078480, 499238874, 79103449, 74586534, 38260451, 447934820, 964733949, 503133409, 155259969, 431236182, 73670836, 235958999, 300958992, 325503025, 90694630, 47754827, 276215982, 65496606, 14738333, 570963709, 124708353, 599634703, 493573360, 256037880, 939230502, 488578050, 151313999, 880379235, 919441769, 3910909, 970598464, 442881139, 121056434, 446195333, 962045360, 169610698, 676329764, 67675944, 503986522, 258149920, 941413137, 832453943, 181903759, 991119510, 351916838, 253260870, 208551606, 732327269, 218828594, 249363392, 547597227, 557113148, 980508161, 267275594, 916714265, 137356924, 627119829, 137458419, 472368566, 160199259, 759742708, 247822677, 945952695, 327604062, 82137680, 705136950, 755533808, 646485035, 389527410, 946900939, 450870082, 403031267, 317564199, 445860142, 434063437, 447922794, 388057478, 318665589, 641170231, 75425619, 918536352, 248323417, 587065077, 941526476, 618107024, 537306087, 878909894, 514382603, 261058736, 152633683, 565655159, 383019115, 403529583, 319349417, 231704298, 569401610, 483841004, 589404682, 923000532, 747243516, 242683865, 272718847, 334320714, 616497255, 922421868, 662758242, 474953226, 401788580, 176989543, 836627602, 855800690, 412280930, 667716402, 952230068, 501357166, 339610696, 576477753, 220462838, 875406870, 713634432, 38025135, 155186518, 107005045, 447178699, 820697383, 875844343, 995582121, 673836818, 821133860, 390911629, 218390267, 187598631, 509515014, 900717977, 928611831, 868490977, 466379996, 337163581, 843362162, 435637787, 472794434, 283116222, 613086290, 651054712, 701348621, 861604014, 734512669, 282061580, 577444592, 293503211, 468482893, 364729149, 392662118, 623948258, 46455521, 651182072, 991867625, 682062868, 876781970, 273658458, 45448422, 824761474, 643057457, 608444358, 743625706, 386514843, 720593676, 441037089, 152548801, 364608114, 869691, 247386823, 286796381, 541902242, 558160211, 898582961, 847306280, 489382302, 714606110, 853433458, 877617333, 988949306, 663594240, 480214018, 713648496, 620813608, 459155124, 742118271, 103832884, 376061463, 4915750, 665612771, 97207552, 417886128, 134338274, 475428382, 73608071, 735521452, 241663428, 462161644, 103177277, 566354564, 451900567, 87749221, 105981094, 702345569, 141824179, 175115134, 931320465, 611912525, 88789578, 165234443, 768738451, 905989656, 111456350, 777538523, 309730680, 308330795, 379026751, 932578725, 910335919, 625817232, 598606493, 71788901, 464978102, 711022637, 534482620, 635806559, 705584519, 823449810, 588846434, 69565655, 274281303, 17768884, 698588528, 190263584, 823300283, 235142147, 378820305, 858139810, 940065141, 486405933, 268668095, 973646968, 146312986, 620440452, 25709842, 256542819, 903786187, 956748457, 433417515, 747024625, 532157355, 886561729, 550287627, 884423739, 468564473, 40824135, 654600518, 30354327, 32264664, 299463565, 420349838, 584390039, 926058296, 483315897, 359292871, 88737691, 820885183, 399326998, 609104707, 281668450, 509585438, 896475554, 46825493, 468175916, 93146429, 75149704, 663945520, 844992600, 747199150, 381976042, 567887089, 790146181, 499682098, 188354601, 368394039, 461814082, 618525622, 208568799, 634902128, 842504461, 631065971, 328232174, 787092377, 762373467, 738156109, 610773471, 847517091, 823071944, 812936080, 985907183, 874637884, 409199912, 6778537, 639827695, 15414877, 490871172, 440502471, 459501128, 703075592, 951217217, 435403924, 680905235, 52572693, 811611071, 384472809, 552480571, 419707062, 864430119, 267693063, 33125960, 23424146, 79183057, 971115026, 67647480, 428309109, 846555598, 889238181, 338857109, 988031387, 726461916, 575892930, 550148611, 156133494, 686994614, 959336912, 265870310, 471241316, 766481714, 738318595, 489724425, 558965445, 406224990, 675731134, 584984429, 532072331, 456677628, 543944643, 207642517, 481843579, 766686819, 62673231, 684746266, 296614473, 987936672, 19519947, 157030240, 305477145, 690719276, 650432460, 999877674, 449013119, 711616514, 738457598, 582792279, 161408407, 921045761, 700203709, 113771659, 912181014, 660629709, 180668993, 34831689, 733854275, 220090215, 379314949, 529604791, 454984012, 380711321, 273495668, 853109795, 458562207, 444750756, 581879175, 151301155, 403012540, 936429416, 859800328, 517159323, 969294440, 748569252, 46502979, 655932216, 400917819, 247759804, 585079863, 885366759, 325462567, 629681970, 537328364, 862317211, 708162533, 873574985, 600419684, 568432517, 816089667, 855717697, 756100362, 382269211, 415798304, 505172088, 678463704, 826181259, 168654032, 283228072, 678106381, 978914852, 230076371, 505058053, 434198823, 492078513, 824859141, 499215027, 557034704, 855729777, 592654519, 963416576, 866329149, 781467615, 198456441, 297385850, 572084703, 578073592, 545800232, 763320005, 728353116, 647863503, 485365707, 565388682, 837752668, 904290666, 291597032, 506093193, 929407324, 412268093, 669021757, 728326381, 369543892, 659123072, 794111656, 550725265, 145324131, 895969177, 666036436, 137411881, 960174420, 489544997, 499370634, 332541091, 446995581, 586162909, 943801876, 612369162, 675278068, 947459680, 730978686, 823701539, 860368525, 624502675, 285808357, 194205621, 263041954, 34235256, 66196927, 300211725, 145089385, 150906829, 381059146, 318695029, 137424165, 784538743, 98258913, 739126686, 986631644, 473616305, 837142890, 779861176, 904128869, 324858944, 765990009, 753193367, 234404703, 2018552, 891090340, 49318523, 719988975, 14791816, 951676131, 599780206, 222436151, 266653993, 641223270, 320173432, 584031640, 444357784, 298383769, 780372614, 342652106, 555327977, 131851970, 175194347, 741304901, 251582985, 342156324, 345796243, 605906087, 352421040, 230253366, 993235257, 1969693, 281474188, 111016296, 824690716, 894944977, 482038080, 636320156, 790578990, 502396837, 523840788, 349748619, 972128524, 701054830, 337786421, 875171484, 822916241, 286921120, 561846284, 613580799, 484573305, 993610851, 872196940, 333242067, 349937096, 849906783, 49908089, 743533372, 658266306, 386639072, 586011970, 842935939, 342371414, 393986007, 575207498, 168604948, 214304006, 907795244, 248420370, 363625364, 827514166, 221096498, 966836689, 971929622, 418585743, 706739447, 425853724, 900128790, 900733193, 30543942, 734187883, 394415880, 544856894, 569566671, 103290435, 70580858, 59711808, 710032977, 249851645, 337334402, 461705316, 92329528, 366911765, 334796049, 567192930, 791923255, 720232864, 343679461, 262185886, 554970574, 254142664, 913079752, 814761387, 888735188, 520983618, 455389107, 431755676, 798174929, 259893423, 64405313, 7243084, 925615955, 842598743, 902785203, 846361742, 122749378, 180632462, 708810233, 812366622, 233173292, 131033349, 112196428, 304306776, 645307287, 570759260, 60834827, 116662236, 899219934, 757525569, 766719924, 588649303, 570844993, 51002503, 604170753, 591132281, 378547274, 146049476, 183819447, 913955497, 550078327, 559529384, 24905873, 647073766, 198415512, 719343295, 508295435, 400409892, 760265724, 94184038, 539214553, 991847031, 485747217, 399102641, 664971753, 991477592, 108275119, 561147043, 562040342, 621779645, 785938050, 739144722, 615225248, 994805428, 394487930, 894037259, 923682240, 43004805, 369479471, 919077148, 639980054, 626703243, 454692327, 976087245, 707307036, 400626082, 124955200, 851810788, 669003450, 810519571, 883995293, 213845740, 236095867, 179602456, 855296527, 455118220, 510528471, 35108972, 843937697, 329008005, 971054715, 737705562, 348582493, 693737258, 603275003, 902089194, 103543926, 777539873, 153241748, 956580036, 761807478, 539430966, 480418983, 65363229, 460487854, 40743548, 454671158, 972206433, 908974449, 322315503, 110268610, 686926985, 177133879, 335037877, 161075744, 474092329, 754030143, 801772724, 817148787, 674611573, 758240652, 461913824, 821388309, 787212142, 118920323, 698116007, 704100039, 136795407, 366183003, 985541015, 497120673, 343162110, 58858634, 328193124, 59333140, 505457807, 370925360, 887102724, 590207630, 995904364, 978227184, 128533219, 361116492, 927416478, 287046958, 334598404, 826567560, 766380956, 387399293, 610040213, 67889025, 500279753, 221039914, 761947924, 290590030, 357294274, 762258931, 463085570, 104944345, 53891189, 816753000, 652028847, 76693454, 807361377, 774642291, 386368608, 429808163, 305491914, 612238657, 860079063, 157182675, 766764369, 164551872, 798878302, 7676265, 427862487, 418784890, 696961656, 986449456, 628464644, 606692017, 863966009, 213796025, 350494043, 754629315, 457740603, 465408182, 155366244, 434162926, 166266940, 544697861, 455817159, 745621596, 116214986, 407037763, 37510297, 659103718, 947206768, 380146779, 178441882, 588810473, 910702477, 742100513, 506398900, 78948914, 148915085, 586726661, 94511150, 89416212, 669066166, 176452143, 814622632, 610142321, 143581589, 806938583, 106132945, 575441670, 810768819, 940699304, 279715288, 210603555, 655719558, 623234413, 531189354, 679465713, 962245112, 117956501, 42536699, 10175078, 441359588, 260534326, 73271918, 9934085, 726983284, 493505781, 694158561, 39742021, 404208445, 778428736, 197940120, 568628378, 127094494, 117983659, 159874068, 796861743, 186406357, 463133716, 413252565, 65007814, 676083694, 356659794, 551966221, 15387105, 567542672, 477316217, 520316086, 964023870, 331846008, 960616796, 994028705, 656053807, 143840958, 710032805, 859406265, 266078336, 87538504, 713379627, 851373517, 12465574, 578822303, 534153334, 743297876, 678474482, 574120829, 351800460, 306688009, 840029909, 325463859, 795813923, 766224438, 453029252, 784640243, 102097305, 667580443, 964021748, 703999087, 846300429, 800326353, 450701585, 234612325, 138453683, 528583114, 410123543, 435580382, 20901999, 167906042, 282080030, 474304373, 247547544, 115326016, 26372501, 651823049, 414152575, 808294514, 839236603, 51990413, 947148583, 268282871, 172462538, 715353239, 87015120, 623803143, 398092712, 768985006, 63174591, 598850834, 920479944, 390740505, 476732193, 168503448, 76253371, 434259097, 308079295, 380666113, 671126536, 120376766, 778453294, 758731887, 719045564, 802583270, 171667173, 91649316, 112540254, 921161700, 419910330, 965984748, 703849834, 402194578, 319564218, 833790073, 862772637, 13973749, 295506953, 560192226, 241845300, 459016554, 284424176, 495322860, 908548077, 453250224, 549830587, 101519816, 316306680, 4297274, 477591933, 929962688, 687356969, 704176315, 570802613, 192540473, 876244597, 2352570, 161476919, 849719649, 326532826, 914425547, 304260255, 705752182, 191928536, 818243490, 48026838, 751112307, 727240325, 14192232, 305402925, 698844691, 499796875, 761261339, 92939287, 322481627, 393009167, 554761352, 363499340, 938467278, 213523609, 408615979, 969704197, 999792740, 871268387, 960925764, 965551046, 744832839, 489557826, 597085985, 474378523, 880102871, 909535741, 599457438, 692812284, 346285099, 623217380, 501353328, 56899865, 636911947, 738219084, 70134573, 527461049, 106559068, 810111463, 208249045, 924396426, 561698898, 684186001, 462551659, 626727259, 601653983, 961752476, 194549712, 404788333, 383369236, 741701702, 123955592, 179934961, 273323873, 262253410, 370068399, 589383282, 118500823, 225341612, 114207638, 324748608, 353578569, 400723274, 485376116, 155237963, 416915063, 801437726, 926540916, 873433287, 980821313, 32012835, 409561044, 126219618, 130251090, 231497075, 775502207, 48683846, 676215637, 20165694, 109965397, 983224952, 930484600, 736322146, 908251788, 933599195, 357570996, 193187040, 981127519, 279774120, 24542801, 418039497, 599573216, 281940477, 445646172, 288693840, 98193540, 599139456, 37471004, 644669251, 807518813, 63138917, 582451650, 767067766, 783088986, 33248852, 244162103, 774330124, 995667619, 578111063, 345500715, 184658013, 566535159, 999106421, 746817361, 289654502, 950468044, 439475067, 746402749, 298074927, 590414146, 190468335, 541570670, 847385340, 590407191, 670118320, 434966136, 430797375, 764314557, 569495540, 139367547, 116201815, 626245134, 309618198, 130055973, 100416415, 573457213, 678091931, 244142167, 324520935, 755759385, 641620088, 548111354, 789034994, 288527047, 695926502, 739586343, 820328226, 933287844, 20797880, 335199579, 380319210, 435632491, 944033827, 564667116, 460531104, 44054348, 527896444, 7651123, 65919309, 813049872, 516541406, 741169518, 387004322, 565924865, 680072669, 399151257, 716301105, 166297630, 954483141, 755689683, 880992351, 830736318, 582944143, 830408622, 349102087, 938381719, 305397575, 579727518, 75458779, 601566722, 969806471, 468843697, 959576032, 362248172, 937378584, 7807180, 732124825, 729049850, 220189016, 559158857, 139651929, 1463412, 63171720, 285623426, 604091081, 56228109, 916158069, 315683725, 431421794, 381203992, 695736713, 423822025, 179242122, 814611460, 32896558, 509381281, 485614243, 834665169, 404153196, 117447196, 280830851, 84815114, 155386312, 1329059, 367109128, 866577119, 136010953, 843735615, 649702963, 636104388, 790151515, 513602221, 39418187, 907639117, 943447839, 931904679, 459274839, 597337805, 362097618, 525459536, 95379158, 312513417, 321117234, 767943294, 253133714, 667804728, 700176654, 324244555, 70142379, 228916152, 887835813, 895075926, 482060838, 398579272, 991435210, 637972955, 546930296, 92598921, 367636733, 899317402, 139931578, 191792528, 622050078, 472161889, 12990656, 782876033, 867037140, 64108588, 788425697, 284655044, 339114067, 973071478, 841539100, 363056050, 70597670, 359364937, 494640469, 546357925, 579039900, 240903677, 93629298, 640438653, 441368826, 901699704, 600858681, 808182921, 556126971, 823332898, 407742352, 495276847, 336011469, 814144096, 489300362, 994186836, 123258915, 754640406, 673725403, 536401347, 392476048, 492359725, 842458229, 428737161, 403418619, 134564446, 747843565, 774234013, 905143115, 509512978, 27540945, 402786805, 699152761, 189284580, 280401553, 613188750, 746867896, 751684378, 588480054, 199861508, 256800902, 595750656, 749939986, 35376617, 309394126, 299074763, 112880695, 120490986, 21072336, 679537329, 950081033, 379636076, 187372636, 412874225, 637481275, 717934761, 322908379, 531009794, 241289814, 621709486, 624372339, 571733658, 482766056, 310218859, 23866849, 76783484, 324268685, 644079303, 354946735, 678367543, 559769159, 978098509, 658309176, 736161886, 399717784, 370905484, 166566210, 858575674, 148885655, 737161300, 902104899, 61635611, 917081504, 436469173, 585869534, 719837919, 549464893, 829727570, 995533162, 541997907, 262144445, 547275155, 886195719, 957193337, 293479774, 479676865, 696098435, 959507792, 848520788, 440126476, 24473989, 120738889, 944157022, 285504747, 377028055, 194837927, 198891834, 872631411, 827040694, 14375858, 942532076, 659457233, 224378233, 499869537, 177114504, 978257617, 401684550, 429446992, 169546692, 269008166, 70767055, 470591578, 900298047, 135460987, 896423477, 284015191, 273262409, 517269787, 908210616, 940902190, 881078390, 85810042, 152864765, 314285346, 535486758, 733577043, 911357131, 358407621, 470238691, 624161928, 867739423, 701486904, 660337017, 418806455, 567425082, 529003838, 380512038, 693293983, 925608375, 512643488, 777674221, 950965174, 872827677, 243168775, 170114437, 734220766, 234947022, 260363344, 186253978, 282406891, 138494753, 811380047, 341470523, 344712208, 575150361, 882071547, 696314909, 960055551, 954436743, 614902137, 770152008, 906808679, 376065057, 477866428, 164279933, 339858387, 27691811, 90944574, 581132438, 304106063, 468235382, 240100618, 769105562, 981533962, 447615421, 88733927, 672034535, 116989791, 971859441, 808556584, 53640331, 574280584, 755610974, 840111086, 200862065, 678605080, 265399357, 938896489, 125408770, 667150480, 531751640, 135611975, 865790609, 484354978, 969106335, 762215342, 257085675, 11285334, 997304190, 576683819, 345234604, 615205268, 413720835, 808213612, 254999251, 521958774, 568185130, 92450161, 896903685, 372989939, 314453410, 128946272, 682811172, 927013764, 535038161, 743948205, 315857009, 23522915, 495408157, 382101413, 229315293, 667522338, 431301704, 907099926, 750818505, 907662608, 563437251, 606436150, 106906060, 268092662, 513804138, 193586474, 868146365, 680632439, 606411606, 394903405, 29973001, 332338915, 841426986, 141387984, 285691568, 811860049, 806602229, 578777525, 95815635, 161227109, 781428350, 854231576, 23801469, 864543917, 660887189, 451422782, 447030518, 910119326, 917932506, 475366017, 935026767, 913608001, 914595264, 449377033, 335530279, 341705115, 780979229, 350318685, 607278383, 698400202, 183352745, 146902547, 209548942, 610663784, 79801766, 538978216, 653239336, 107219187, 545020881, 224076956, 695982056, 87742618, 94365928, 634077828, 320742547, 550941190, 469387268, 434859837, 940940804, 678957866, 292955728, 329439289, 94333042, 278345457, 858243016, 74726194, 707721520, 460110807, 217500722, 697201353, 795924739, 135379576, 792132830, 53506081, 706117293, 751706013, 13821647, 268379239, 773264196, 572233715, 345962374, 716098664, 72810058, 115219508, 179713996, 690826061, 126084203, 382374368, 882749945, 37956358, 564365236, 614338288, 613764357, 870679107, 12376425, 168434382, 794883417, 488056334, 862867100, 483242104, 798763634, 721936784, 652827822, 511234568, 991313962, 79140652, 163227445, 689075505, 917194787, 117585392, 375780557, 420134621, 995608505, 798731199, 680162805, 614884880, 350354175, 181150062, 163607923, 917382585, 176456828, 89327578, 521373805, 549586811, 216272104, 135100940, 947323154, 867350206, 41188893, 573046386, 946791505, 737285722, 851727591, 689375699, 534315589, 611844035, 446036068, 452111465, 521643701, 65655139, 182732508, 608619692, 884164679, 897328400, 939740721, 640284550, 129663799, 346629938, 161006562, 123514654, 73507542, 249804843, 579365570, 509414053, 479731659, 382623671, 549406959, 690637795, 936974505, 518249911, 702440353, 241327875, 94487395, 659213063, 364141193, 243045103, 578343799, 90598353, 693862614, 983711303, 879863798, 390540956, 776748405, 674755168, 874775359, 22358214, 383571817, 834573462, 202108645, 81895939, 415855937, 761978991, 357768787, 332015400, 133849785, 785665519, 915741652, 675535506, 679326274, 643261894, 799176595, 358801654, 254640771, 283314552, 138850237, 471569068, 366538759, 985425824, 768587513, 610910698, 199488999, 353683990, 333592392, 290093053, 347299647, 469809681, 289830084, 162542430, 722732867, 628682119, 775480858, 349673218, 737763604, 831456733, 120341430, 215910959, 437991797, 485179003, 189904315, 993488642, 36042255, 812412062, 687118595, 8529421, 768249810, 93681710, 450102893, 220249566, 561932576, 169299630, 947933781, 335971708, 580505579, 550004833, 888462212, 359737857, 64376312, 469536041, 384547572, 107557034, 42644741, 297017776, 413152195, 78478474, 952214320, 477744252, 813747780, 132255987, 161829348, 51395914, 901969386, 192423700, 735070215, 314285496, 698468829, 465062496, 861228192, 338475080, 855228061, 7736550, 934883368, 508063109, 58713890, 191762703, 874026144, 670369127, 949152258, 100652616, 70548221, 310182480, 157702151, 999901689, 548105805, 859470440, 579517283, 358825649, 405116740, 626337972, 757382508, 144011680, 165795269, 802556541, 340161889, 348015914, 682784533, 828490878, 428968986, 418113468, 637393553, 725411757, 13548659, 362002690, 429139847, 348425250, 636322451, 582945143, 897321660, 529631104, 336098411, 496137528, 164900465, 423320754, 477961501, 44668908, 907418977, 728521159, 770626710, 920403638, 464417063, 508792848, 949424450, 99488635, 512629612, 240454553, 138726665, 226789679, 800938679, 488849372, 842984090, 44553005, 810902200, 732552831, 418376353, 436075160, 551854637, 503048867, 781633304, 993667788, 780584657, 784130396, 971831539, 35883327, 838669367, 951033573, 425174345, 203787818, 272580377, 835152899, 659034237, 36823633, 641793367, 632956764, 823884054, 746580290, 998096688, 911347749, 180845138, 200892512, 698676843, 260582752, 781079496, 590866381, 847850621, 196339713, 235713193, 757107442, 37552046, 167733476, 611061364, 994160845, 114415537, 84032915, 510959365, 280434308, 708916667, 161522109, 626460847, 85718917, 488828165, 808300872, 689398226, 410369573, 533763623, 170665233, 189016958, 729258720, 601032042, 750293129, 61096412, 917156571, 605066142, 85245862, 319848822, 321989965, 398103189, 162872728, 809066465, 757736168, 747591753, 389342377, 731672491, 578597716, 822517095, 549043907, 921753308, 443769688, 974365820, 390535126, 926832445, 120005023, 198612333, 525325127, 21124145, 345706697, 9949073, 402937373, 766685574, 388561793, 205766771, 447559887, 713710589, 84994391, 228434413, 253076567, 791207126, 552949391, 470286388, 239810609, 195885326, 197262441, 360996238, 803692993, 309023825, 693184435, 514528489, 827644232, 521273537, 157062220, 296252043, 822305091, 93250131, 403128828, 68675526, 769506427, 430238302, 794917917, 865151044, 953878432, 829424565, 806377546, 587299019, 966406670, 825700067, 264091256, 669930195, 398745721, 953747710, 157996010, 636403663, 838793796, 413445528, 687120921, 347176692, 792674522, 497887644, 556105482, 693861498, 513225677, 528589901, 860579475, 818839821, 487675286, 641146471, 158289303, 299790514, 393753590, 360355601, 466599199, 189591000, 535342059, 257048285, 159358611, 303460437, 367009393, 107551280, 421802038, 297118767, 152328438, 256688902, 914518734, 293475987, 869694362, 925004238, 766442796, 965016738, 848633193, 81050153, 300223426, 723891521, 322205414, 30423389, 758738292, 736517899, 452398732, 928965970, 858472706, 196618652, 247368082, 503402430, 698541649, 531774140, 938504533, 258381977, 587161825, 651529965, 206866593, 276307788, 870862953, 601650796, 568705991, 959896655, 982318309, 751186916, 20394769, 552104856, 49397896, 681478899, 115561957, 351365976, 30071065, 139587736, 715132944, 59899336, 350346619, 629660394, 680783567, 214138596, 788304478, 633150380, 469816614, 457406363, 625545515, 903216180, 665051278, 642997589, 963713795, 855939978, 74276671, 533230858, 178066839, 873459340, 561979550, 13331900, 634708693, 407080402, 323626175, 109595601, 188416641, 624172863, 663529773, 357165096, 538752918, 784784445, 594702965, 408656949, 176619623, 655379714, 453094052, 547583652, 185417500, 726595904, 543910805, 852072328, 968804941, 643541495, 923068653, 452598273, 829456043, 428641607, 850563715, 597047854, 482823291, 1986615, 101204923, 378072579, 634574291, 637365552, 847106000, 493365606, 631533530, 111286574, 892647978, 238382878, 820756891, 501273955, 247702653, 382115093, 420056588, 327563650, 774521635, 515066110, 226885318, 194380511, 984328133, 101462064, 60518522, 246131197, 507711586, 244974205, 777347035, 338072534, 242046448, 79045400, 318533274, 156356531, 261624662, 259403816, 661948138, 713106738, 341719040, 224307127, 207270668, 157940434, 281630398, 754900757, 188795228, 769040774, 25210163, 1866727, 419429022, 730155411, 85808304, 403759992, 556554461, 363182733, 694802732, 127461591, 405909971, 220415838, 643861437, 643684255, 49551252, 955604605, 589191119, 877864876, 841940222, 331290771, 339286015, 547248592, 680542299, 576764655, 337413066, 407647185, 691349584, 643035896, 439645541, 396047842, 549822685, 60081770, 4885345, 50686509, 179634422, 454774638, 35230731, 11058983, 857288037, 690275019, 335615786, 712340163, 436006593, 786515029, 639614649, 397311159, 972303772, 955031943, 442870665, 827744871, 7385499, 730258113, 654128782, 318070324, 770494456, 769241501, 256060216, 981842064, 698911814, 625627534, 760379056, 500499598, 967728579, 875587635, 484546148, 389717277, 807986249, 61768244, 937259428, 595592663, 608010707, 572194041, 606739403, 100542012, 52159143, 842341025, 638608345, 313796167, 470528491, 424848364, 461290502, 570020439, 626638211, 540488914, 350767983, 637427765, 626931714, 55361867, 905746813, 485376282, 224138883, 131484680, 650338724, 881099674, 26557555, 756219949, 333921261, 854779915, 652001474, 255775201, 861991627, 809320052, 203069067, 716077623, 905649538, 64678528, 959847429, 826314670, 449237136, 120389110, 192995523, 57281810, 204247889, 774800231, 473626491, 940608, 224857472, 13348333, 731593203, 772223976, 291449826, 119440279, 633537740, 309441463, 245992735, 388501055, 294202968, 735861114, 874938575, 742759489, 817000849, 454395691, 83264021, 197552580, 553167034, 427793695, 73394659, 351279521, 573711696, 183277880, 625796567, 682528352, 316545931, 76174860, 428676574, 188341959, 595079274, 464627925, 528659317, 364936675, 735352767, 326908931, 588436185, 901951792, 855485568, 319534836, 977956492, 859048557, 420977603, 53582065, 756846398, 279916768, 381674156, 381413761, 415864789, 936478592, 104412598, 309355501, 357919716, 40964196, 21584807, 601728699, 745147675, 204856002, 92635426, 761962462, 1942547, 820774103, 14861187, 269583266, 164156948, 724729398, 373786991, 326181959, 816273998, 549198235, 38279490, 870364591, 299709420, 549500468, 834220798, 349876246, 91445236, 518195064, 13434468, 337562150, 41805838, 126527149, 51050452, 964491228, 575567480, 134262383, 310993420, 317131613, 848908283, 223914060, 240451185, 498214996, 317790406, 866305505, 908477731, 652923035, 248051645, 703255713, 507823328, 537735965, 890737910, 103279416, 328446033, 985433585, 632440012, 519269640, 478605651, 942314833, 806787724, 709677464, 784521440, 502252073, 727135012, 687648214, 442299062, 615531491, 989502491, 390163500, 425447090, 287631688, 432235208, 735938202, 696264953, 636590969, 249569588, 286774297, 760009888, 436827026, 723194067, 480007887, 681399783, 202740575, 899688664, 556058674, 891898584, 748123783, 405465272, 407741421, 466621124, 172309120, 774403291, 961944585, 592405473, 467298547, 853383847, 941978152, 893300255, 620687369, 30839037, 352770182, 323976612, 520835469, 706003761, 574409077, 169133868, 945874789, 434698843, 405803923, 521639085, 73707186, 99240304, 967522279, 825059784, 222954018, 196779355, 184824774, 99522019, 326451190, 293519204, 671855378, 28764564, 153668719, 654665941, 381945801, 116621366, 183713898, 664863552, 107002452, 667375954, 417029343, 697735377, 216936739, 591451202, 869520514, 645231415, 258130042, 925293341, 381249108, 740694206, 206869671, 545012688, 299161892, 617746985, 480850909, 463773429, 205654231, 496659825, 984231702, 822439359, 838260886, 76822065, 866733944, 314972206, 448823460, 351830395, 881465901, 756325779, 965114158, 335362984, 29834908, 466593162, 59164478, 183879299, 238863544, 41605134, 813603804, 878653717, 610770413, 184228362, 216341402, 375448108, 636458846, 770577601, 644626290, 404446022, 101018315, 552553220, 30105501, 17394695, 462532140, 651548338, 510483511, 421638119, 662435694, 42502735, 756582540, 257586193, 1120856, 299442172, 846095275, 884920547, 52191460, 815226793, 86101301, 22703951, 806685882, 860505256, 400668135, 190554048, 355990246, 238986754, 731767318, 183358634, 420481201, 272673260, 647645097, 215410417, 797356287, 651070455, 244978850, 714449227, 182150862, 714744241, 837805117, 453238590, 952955294, 415591901, 67705919, 567062673, 614226777, 28324755, 391773113, 358402249, 199528943, 621010078, 204821371, 158010766, 995981778, 824814812, 573821004, 987384412, 697117950, 21810646, 157263348, 602181950, 42212843, 780492129, 677076333, 567631483, 951928214, 678632466, 745187481, 944049415, 722570609, 31692486, 748365174, 70597322, 360698118, 999477667, 999623181, 765129745, 81984627, 799846627, 6052048, 468346676, 413093862, 438955516, 935250007, 854924495, 196020289, 345402354, 559528841, 646906903, 897692032, 166948615, 255819755, 124726623, 898212259, 625751524, 954171620, 923731864, 348854930, 245872142, 235150186, 161440713, 744723326, 683903602, 447172834, 268223520, 476030877, 604620590, 324388620, 78732012, 941526750, 7493642, 170215645, 549190057, 618558139, 790407029, 825905118, 139316406, 21430402, 955531943, 193384917, 247030879, 815397728, 439635568, 422197954, 348005127, 185400353, 696873564, 518322974, 902133451, 116211698, 349127787, 340508421, 915965026, 487662374, 884233003, 823298880, 17512240, 84406226, 890615591, 865267167, 604283314, 254801352, 805296851, 298910890, 911728361, 918359488, 418680928, 596406212, 241470439, 571501938, 269776317, 859794168, 817962378, 482400590, 870646933, 725326923, 64827121, 837655454, 74307807, 494278614, 453054338, 307221158, 807983520, 979804374, 958278003, 712582424, 77659347, 202008235, 360233855, 902976981, 443300704, 32601444, 683298649, 277301826, 400389898, 647484184, 316379672, 105884113, 849961529, 794697910, 996518209, 181467390, 905116426, 635563891, 124493246, 223739341, 778040499, 589924308, 88203762, 861723630, 139852258, 799117365, 593646089, 286390349, 668617052, 641880867, 852910779, 704487390, 410436273, 170828481, 300519316, 164830587, 550310190, 785571164, 515854907, 169529477, 94657699, 626232561, 616493450, 662799039, 535079643, 479967197, 282492320, 591402845, 295153195, 356681586, 355540432, 459626601, 133188119, 396482749, 178283259, 552832654, 449983996, 217460395, 746851968, 257124923, 495687830, 405330539, 943979909, 569314072, 348741175, 445790424, 426425461, 812415823, 373113859, 648625232, 323649560, 717971412, 508128002, 684143970, 684894619, 943251705, 353026981, 934003226, 963917732, 845494080, 187195396, 67510256, 749102773, 983731203, 793982308, 565363347, 661434929, 285118853, 530731415, 595942855, 566621540, 207724688, 63778788, 368453951, 666504136, 402971260, 261100035, 982027923, 142821207, 730819813, 802334156, 239515079, 654215244, 488790154, 872739367, 848804878, 214573678, 420060371, 370133908, 636281155, 707747597, 350758953, 629642806, 490543288, 870981091, 993781203, 678003313, 213295192, 386317842, 764992044, 99068162, 911615970, 56288790, 723673829, 118175837, 66203249, 872679598, 221827199, 705666830, 759131658, 461146682, 535628211, 177757143, 614537836, 206340788, 914621301, 251295314, 65201599, 595527269, 948960412, 258392481, 420867790, 141651288, 884833983, 25376583, 641429607, 447336962, 226608234, 672745827, 299559484, 365884605, 437242125, 863893737, 437601286, 154345172, 681864582, 41077535, 493008373, 331338726, 533888521, 359072508, 66647170, 697300059, 780522963, 410854724, 535420603, 403088422, 452040112, 238050015, 563056444, 84422239, 312439908, 659293756, 474660926, 731297508, 296456749, 601753030, 38097459, 75449987, 89081386, 309459657, 793655534, 834882344, 770027384, 993982708, 731462191, 542155109, 955301608, 100736504, 725832879, 811787170, 708506823, 82290325, 516609376, 167515743, 795620762, 892909073, 460790121, 930327207, 929740875, 586030266, 569297038, 728696756, 786978436, 386346956, 935499785, 119598238, 546795687, 388091327, 468041255, 305051712, 201926418, 258335880, 791379428, 937858705, 119576645, 850751491, 170073556, 87811692, 853232848, 859171186, 950999820, 988599284, 916675203, 107047129, 373167657, 715060300, 874895022, 546471259, 251447810, 773293686, 740245499, 294668424, 189622522, 777450492, 565953524, 93868385, 398804669, 253188147, 222557214, 649358746, 908108667, 912255850, 615921829, 201474062, 192987479, 362394321, 58441155, 88223718, 874483960, 628014592, 962289441, 163385815, 708857398, 809191891, 866445040, 397903745, 983473644, 402241624, 828792145, 486596400, 559587476, 118370443, 348603309, 966883568, 18832078, 882909634, 299623094, 201001266, 549855166, 446064608, 927454286, 721649964, 263384516, 489301635, 490149406, 407361119, 294828795, 805228392, 357399330, 865570098, 615893508, 402982092, 237427321, 427169299, 629400991, 158704132, 668050172, 334475571, 33044653, 338937952, 993744503, 130325132, 814317635, 610759951, 264649186, 748838775, 223878670, 392482284, 635614465, 737961407, 529358376, 40569051, 687273491, 104821368, 970442312, 511678973, 687201125, 647451501, 81545610, 577143112, 21352551, 289136454, 932192977, 862009622, 513073827, 324994475, 997768798, 384931040, 612362579, 935970488, 969580199, 564009628, 449684679, 508115807, 995217219, 137926574, 875838, 746776608, 845361793, 264431007, 65771898, 111094216, 376216731, 887107839, 348982427, 643239556, 558353955, 914246203, 364842510, 231662968, 614826001, 334097430, 249464628, 435587383, 703981914, 249150630, 673502830, 450434060, 75242863, 431832606, 779735110, 66525468, 418286519, 687317763, 529225040, 816243581, 960509130, 499660210, 33841660, 991925104, 889416294, 533442087, 663175676, 718665176, 708847948, 614539213, 234965634, 112852141, 351482105, 832271554, 544950470, 959164750, 164797156, 466443387, 64837782, 530635696, 881416619, 881953601, 298341641, 710538, 210957201, 542877794, 728265041, 192582118, 405769326, 782441828, 680232586, 137265680, 234058360, 269340739, 378189525, 50760879, 940926474, 811087380, 352693930, 365609301, 633493528, 581002602, 54807765, 509955028, 9717398, 521024770, 71555321, 308381735, 452347982, 807264948, 743143340, 624227361, 905902175, 307338869, 266317631, 269951747, 187089974, 165207846, 345022355, 429425690, 312036865, 435928981, 502335405, 283890247, 287137777, 57517898, 599517561, 375655146, 863017980, 476518045, 242146776, 968092120, 547030188, 944465553, 131255512, 24416377, 254044389, 27746910, 666994139, 897738149, 372079735, 477768531, 607598911, 756223245, 577641394, 476449419, 292125690, 995512346, 478436449, 732357130, 181795980, 822786917, 721908181, 11638156, 57110056, 92301093, 849998922, 987470243, 761282106, 781743430, 83240174, 372913455, 500034957, 829088729, 81412915, 676930845, 190676278, 90268180, 272121322, 386362265, 573545795, 672064573, 346582784, 648847965, 833543399, 895147244, 697062775, 745934085, 211258423, 87874342, 198966368, 485916659, 837616954, 802264239, 817153251, 20066946, 674628906, 457594135, 476108039, 790843552, 221717758, 93183170, 515191374, 641067873, 977920322, 861993442, 39954598, 90302687, 92950441, 22716925, 896355875, 286603447, 222348982, 452913621, 786497472, 663687048, 661058210, 352169058, 927399381, 883684554, 536411055, 314569678, 264898228, 997748824, 566238113, 400382602, 822568438, 787125147, 422038355, 113326691, 718140328, 268292764, 783032651, 517884825, 35479189, 944057781, 63163324, 150928674, 223537025, 915418679, 478282252, 812868516, 179652820, 156745736, 842559433, 890400142, 835460258, 102642454, 336437874, 374840362, 241590919, 138497942, 871296897, 494769491, 969111084, 331841604, 331281274, 479256783, 359044995, 123894304, 728943460, 21169780, 416441296, 310762961, 266626659, 578540207, 792745873, 283886915, 709856079, 355357976, 884750802, 292463515, 318123905, 610712921, 493840386, 333691994, 671148244, 146589535, 869892464, 191850076, 579549964, 43475329, 432200920, 24292317, 558339244, 731656332, 994386812, 599595585, 73153628, 23808289, 193257072, 463418980, 950658287, 843689224, 55726030, 189286443, 104900285, 321100852, 416779643, 420983660, 432560635, 424511022, 102631877, 142954956, 622379660, 477373132, 83126060, 619590981, 310435279, 329029244, 545463241, 263895751, 745227508, 548394391, 273287013, 211182312, 523893355, 342134792, 60323578, 787960930, 957963285, 415894351, 480474271, 39937509, 575189254, 669374958, 968094784, 547552992, 858847361, 667452881, 281871376, 163826094, 510884493, 954650183, 947669366, 50296031, 620295390, 676469969, 491971703, 799707091, 577189390, 533890926, 289047434, 160130012, 135880570, 47611469, 205903845, 374156995, 175352630, 786663697, 811184709, 669071438, 120812354, 592516269, 464179584, 496219092, 819482897, 149826, 834561728, 360348495, 415898783, 874589754, 272300199, 577836254, 733936039, 185619139, 258588542, 336550260, 330050257, 993850159, 895112162, 122655187, 638121265, 446489750, 217034251, 14000894, 471375648, 264013044, 633207826, 475102954, 731243149, 538400443, 674447007, 519714318, 132424151, 451262994, 581274178, 132132220, 868504934, 773056353, 292831174, 109554198, 218795782, 133977113, 764110893, 437633544, 753765546, 960749520, 492705857, 475089306, 125296608, 874795965, 910174584, 433585047, 683077291, 793491455, 480475855, 838906714, 315895210, 587750029, 624683692, 458105748, 368045077, 631559501, 55626372, 119613622, 518392998, 107077433, 580050306, 157010649, 452346915, 290972855, 797180856, 642803651, 78861598, 410299541, 676339401, 609428236, 529899442, 107930697, 896460612, 643692798, 685310721, 78143919, 305661872, 567281944, 355533221, 601633797, 731257558, 904482032, 621752597, 281613384, 975054439, 595804854, 133558746, 662307231, 408399836, 335443417, 292310620, 790240786, 923007248, 963960720, 143459535, 373738661, 770154283, 681835186, 685061352, 905923434, 364877070, 557307237, 64918172, 928395802, 417383317, 597488685, 501882731, 191843314, 669660295, 694188187, 488382343, 958488595, 570151466, 627306890, 843506122, 652692384, 951788617, 227108822, 270705232, 116927678, 214282671, 660713160, 737415375, 649443440, 105518385, 887892388, 121290394, 744091652, 202059305, 629066638, 15248679, 80635262, 10129406, 471937663, 675663164, 941214445, 568850960, 391948828, 974991748, 388887006, 591474058, 868642298, 760461398, 612635114, 410281975, 468319238, 242571514, 293037455, 901659583, 177673801, 157032141, 570494763, 951081458, 791488299, 607269806, 196521820, 13028193, 786192772, 666243968, 669056077, 134871770, 357027376, 270541314, 706978469, 191091842, 394562, 642474268, 433505198, 700652574, 15354129, 698273743, 762674082, 90624117, 562501204, 494702268, 654764373, 930310624, 688592943, 468379023, 436049988, 939204784, 6530753, 514825246, 487790274, 198797955, 553933198, 528620934, 773430805, 837755737, 391007660, 632532295, 761891675, 150092795, 381368940, 318991230, 171025072, 845562953, 730725629, 484730114, 603293301, 315529891, 563655244, 759901611, 874116945, 57938538, 114771320, 765461586, 626932627, 710921135, 644784826, 86042666, 137278669, 83361654, 995964643, 926456340, 909280831, 928452094, 154656350, 21134999, 438211404, 704898417, 877415759, 127540641, 250620110, 804887431, 287654435, 770356823, 135561708, 970622941, 715418108, 436001010, 404439384, 285331260, 763985492, 358583576, 81914602, 810188066, 850445794, 971868069, 807230530, 463848052, 864504373, 562647675, 663400509, 185958221, 729360437, 367263221, 683916250, 965886033, 482807872, 831468009, 277306046, 798406773, 923997682, 901009575, 129268485, 842744251, 854262137, 397322924, 572531462, 553275116, 178952502, 425000487, 30656773, 716222745, 782806760, 223738316, 307156465, 546301665, 34747332, 983207427, 446760138, 19063006, 251226809, 339004060, 578091948, 738293391, 188562820, 218720029, 493013997, 236525971, 471837947, 896092249, 541262630, 657866345, 412641154, 877499764, 676687754, 20946553, 725506496, 179760451, 677960508, 767526241, 272464941, 723208292, 418785985, 645692978, 772527166, 64512562, 701943177, 735147988, 464201129, 672096903, 523978270, 302739430, 702352268, 956226739, 853744807, 601800954, 429775483, 302195939, 403098076, 946103790, 647765396, 958815717, 724798259, 313844636, 334318383, 360680037, 2061090, 798117832, 300817477, 353877021, 871744128, 988669104, 792651874, 86512063, 379759269, 774950713, 323678935, 430910761, 254592656, 317173052, 927947213, 712193956, 291985166, 338105252, 71800003, 50341887, 716403861, 670889109, 987200169, 684733263, 741264568, 751010811, 454250587, 137178579, 624078895, 438595107, 759615112, 754699154, 431710698, 576281792, 750443356, 41483759, 270981464, 319460153, 826811633, 273976076, 83341164, 854777148, 436448978, 575354680, 974115490, 569844915, 766294145, 378962412, 361616819, 440680357, 64187451, 337382004, 833062494, 441846476, 157484985, 552415012, 515661682, 626058226, 693849619, 374053100, 640756661, 139050982, 257178186, 274742761, 562122980, 805007554, 487931242, 958571550, 628889036, 718537940, 980204217, 418184612, 40399852, 416859409, 157870920, 765425759, 551526252, 617064916, 995107430, 286895937, 457565676, 657249525, 491344066, 649811719, 821511820, 416599311, 669512085, 554766925, 956593690, 983458172, 90990257, 333150211, 64283379, 24469475, 433292533, 778359767, 899080160, 905192624, 817510956, 401406437, 529411953, 214099599, 166660819, 265658323, 26813526, 977312081, 70889095, 235613772, 813073025, 5618071, 228643598, 833240330, 607812331, 164983524, 214399518, 928440313, 868067104, 315385065, 554387895, 157948515, 606775793, 760770743, 769162754, 877587914, 7774152, 7435486, 662408372, 348924930, 258591288, 975976107, 47897164, 210586480, 232349428, 845800257, 432247724, 933767689, 154733781, 480545675, 679863681, 656975482, 499633189, 984350878, 228601524, 29922699, 637836072, 770639004, 381478937, 92169866, 807321359, 867416585, 701645679, 240185285, 562359027, 370303786, 176836115, 300201500, 59522069, 111006542, 944176246, 691163989, 412196690, 754263748, 443437086, 961809391, 947745991, 427954887, 749270821, 704944212, 597971956, 884659575, 389240365, 704854353, 928655728, 690567056, 272675145, 552333625, 197195349, 251867375, 443389522, 698191959, 305568431, 576399440, 261128024, 728895785, 823396379, 509847676, 976331384, 963180665, 48525314, 309623821, 923180047, 77199751, 582866991, 710144196, 50500759, 52743915, 982099393, 195620625, 405815325, 868401873, 336709152, 709687310, 665566146, 301508781, 579356845, 555495768, 898419305, 856607270, 458608773, 475966907, 303602865, 860265298, 648514527, 246234031, 838773220, 223639309, 18549294, 947052788, 643107995, 312196267, 825188550, 164820723, 270995346, 820904731, 723942066, 808953407, 599764702, 626516253, 318850163, 506742940, 180558837, 983897664, 264391, 682261908, 528161276, 553996973, 672358721, 859184329, 671139888, 132256043, 418878605, 180884989, 255762396, 108799393, 216622377, 639362489, 320679022, 620301200, 817862365, 73539363, 309126805, 267246959, 228729277, 56015486, 735242545, 937683125, 514479349, 978730922, 426539184, 238391222, 568436311, 626427868, 685853562, 738031463, 983684284, 89130836, 728076735, 516368709, 120827997, 548325659, 324866115, 522712735, 62470303, 537559197, 557300356, 934414758, 387716446, 759645631, 770673358, 303655540, 75097143, 265709865, 159903686, 392966307, 829498418, 745647466, 749254045, 646495089, 763707743, 164367566, 680657696, 412854443, 564543987, 90637367, 476159695, 376359552, 656116363, 228436955, 308256470, 502213541, 381142232, 214743447, 924201669, 78770513, 35192569, 587451154, 129014820, 239733475, 85276129, 329932595, 282263208, 499168227, 230673733, 768055604, 695690661, 630475731, 220345679, 520850288, 355730165, 822751393, 119315243, 637584096, 804635523, 125723704, 993338767, 534706595, 626227568, 129394665, 933096485, 675614175, 528012254, 528829764, 440356699, 861620640, 800570790, 474536658, 572553330, 456018997, 770426851, 257097265, 120855013, 613808747, 186425409, 193379232, 777107268, 87760798, 172447934, 632791583, 794504621, 775507241, 568513299, 85889541, 94645910, 381612925, 339421605, 788197974, 87242643, 749224336, 702341321, 932525404, 692065248, 905364761, 469232743, 901631336, 157028677, 654336264, 754060682, 31378041, 433981990, 134806524, 450429820, 332507924, 965868757, 704973519, 578736630, 121175574, 217441261, 357802894, 416718303, 651287470, 271826232, 361013289, 515375746, 550840777, 575142297, 79452488, 194833805, 378537188, 478810809, 393993587, 352460233, 294921782, 235215229, 853171295, 241866480, 831768803, 172136107, 33457120, 474905737, 129031101, 567950290, 153504067, 338823888, 319798907, 170467449, 19961707, 628457446, 188999691, 72299454, 511911967, 741613504, 920446432, 305785003, 754075144, 88848820, 68653229, 850025767, 447973432, 509195717, 384195112, 350775823, 400191910, 189368300, 738340611, 29238337, 120990980, 739495296, 783067611, 506751270, 789944625, 499363333, 774686812, 568852585, 207383033, 146185968, 678750209, 84831626, 560681006, 66076541, 499746387, 588246736, 166190490, 277755270, 363383669, 699064161, 662034583, 578325095, 812931644, 739647188, 164794106, 443969266, 215550455, 981166585, 330453478, 724789723, 615488304, 453463376, 2070371, 932412374, 59326196, 830444363, 447671647, 88240155, 382165641, 123782909, 793603213, 394214310, 809516842, 746342753, 365953881, 715766783, 980297287, 945668379, 802367388, 620607905, 874994999, 334489774, 679090361, 526259593, 238380034, 631112746, 818755364, 817148816, 485987029, 211499843, 63848296, 828794563, 155693687, 655730978, 156583225, 30968629, 69539646, 541665059, 331063865, 820811078, 865160957, 787270456, 333354266, 253557198, 190838252, 725001830, 240579638, 258011269, 964012313, 702574204, 378989479, 189374945, 145372992, 131641654, 841867535, 658488353, 779330400, 544694757, 114583305, 866204967, 827068725, 100770317, 710033869, 768708024, 701958239, 746547016, 323144478, 882972776, 414994744, 514812430, 731318627, 40617318, 74997752, 850396485, 782670477, 405241392, 524078426, 526938691, 617624754, 797753001, 408285259, 764596161, 598974966, 205542371, 276590592, 125503640, 143306851, 727055448, 389701112, 713180217, 48576593, 91709946, 56250850, 944810540, 242415272, 919659701, 822059745, 743090178, 762423598, 380285506, 523838421, 853246105, 340517917, 740144783, 37582462, 9229653, 817668189, 516410136, 525423270, 652885243, 365469500, 108282810, 50796708, 772605448, 477267927, 304509581, 472399243, 390492548, 734730768, 834399943, 400571697, 795142052, 807807303, 797922871, 260619428, 454133868, 145035139, 356117145, 847036660, 853778140, 303013438, 611694832, 652947404, 552372237, 135955387, 294188084, 696199456, 211608499, 166693975, 720450779, 607763608, 283202868, 951750590, 613964580, 207703526, 388212826, 348259036, 890213780, 246383242, 757050714, 830807191, 740006335, 613084832, 794458747, 818208460, 447915125, 473442687, 384057193, 910066830, 998487408, 69560391, 56847170, 643190245, 747077656, 332447026, 94075813, 561271042, 765222756, 330595912, 241283819, 750696172, 833877887, 341347216, 589373837, 447747922, 466719938, 286501838, 415157405, 654323175, 339406409, 694699051, 740171585, 340701794, 341947345, 500777718, 267610730, 919930709, 436667296, 24737943, 167094743, 640102068, 246259531, 573000117, 315299327, 536261878, 813573916, 65177949, 950279972, 820455868, 11599820, 435261814, 716812237, 956836295, 323568640, 241366397, 963495805, 127701176, 762541479, 615028171, 752788501, 823037906, 535372959, 385635106, 941936765, 318492717, 906391237, 785422647, 518134527, 787851504, 409102412, 39661327, 893090327, 493629644, 393201140, 618250836, 674692266, 388949077, 357859741, 673349140, 130821281, 552431869, 682941580, 776818990, 830456594, 571540892, 557365895, 271083551, 569902777, 295687509, 421540897, 412008793, 838523779, 390644604, 326196112, 922133105, 768081750, 891832047, 479048029, 663935615, 227745053, 220025048, 269045687, 353428895, 631663339, 114347252, 916950203, 264040959, 30253368, 346399737, 548830616, 496868496, 552711987, 116460721, 418887541, 344223934, 153831484, 710695126, 71384069, 180529339, 461483144, 940538449, 973861150, 255801366, 59765487, 864272275, 740423831, 42050439, 951967505, 504112793, 47731860, 176674232, 991339871, 266543875, 339820313, 731818878, 594834983, 4232530, 542317995, 359657200, 898200644, 636109328, 968503921, 875234670, 192146770, 442374890, 648519369, 755991595, 293296620, 895802621, 224497175, 917251986, 82018717, 793558114, 178713476, 578505896, 944636983, 72635932, 558066699, 691552885, 114797461, 206504307, 469539168, 541946627, 173464713, 432691088, 706226817, 142594280, 415117581, 804383853, 277002786, 496767343, 49241848, 738120105, 660826332, 489747157, 619556203, 693661936, 982104718, 301246684, 67291404, 145435718, 347119917, 75356399, 826771875, 736754953, 909241257, 482099288, 302243390, 514153785, 930001605, 452239107, 740712008, 696123907, 688364320, 622207635, 224353619, 185647226, 320094234, 871637084, 836218802, 592431428, 976226949, 254769093, 840691108, 939013398, 757170812, 49920838, 461621542, 473655048, 946427983, 945983065, 190769907, 501401760, 798174723, 601062662, 718030365, 197453090, 121162742, 737954930, 8834615, 66246298, 960354104, 669008526, 277585720, 84372118, 268150528, 736902085, 627948284, 949265932, 692552235, 443631945, 426175261, 406093711, 227739831, 569276031, 603168124, 847264773, 46771623, 440960572, 146935725, 47566620, 974152036, 116642530, 482593735, 392417265, 882243715, 615450320, 414988271, 2683349, 206210938, 252986277, 971556828, 450765916, 94338953, 783564849, 45777331, 314889374, 993437809, 444149648, 863650596, 259688741, 54993000, 511577082, 641380806, 485724663, 844553945, 35047955, 161530303, 197715767, 701642456, 361862667, 275478806, 411810330, 373094668, 197505874, 76494714, 394072504, 775781758, 718173692, 691782715, 97774777, 503721370, 635471307, 800040117, 125790047, 441886482, 439997603, 362781875, 560173444, 226771493, 357597773, 158841958, 775624462, 850108805, 138028998, 872086520, 411647263, 189855650, 921366847, 125794398, 979671301, 568808402, 514003137, 503436421, 763545728, 487985427, 121016482, 971008275, 998457882, 463098070, 797622187, 388014247, 120092830, 13125268, 742198069, 900895696, 567201212, 802758118, 36535572, 264848536, 229680934, 903770651, 934678501, 787889262, 922721447, 696521730, 471723727, 580540076, 98095217, 12510537, 734070487, 946148440, 971816548, 263447197, 403698583, 855959995, 622098730, 70828604, 61663901, 213068000, 778597684, 724305004, 372135378, 354375894, 132322774, 902552158, 644293518, 961820461, 199356169, 698057494, 71784317, 837261961, 345091016, 140572634, 619753287, 532818259, 334113120, 529006482, 726758966, 4930115, 370581302, 476595119, 184647591, 454973618, 699367749, 729145937, 153796152, 620393255, 587707207, 583575290, 386277986, 486557842, 427519961, 240978444, 802993269, 250205064, 483008330, 597950406, 747600557, 325363856, 714091827, 659075588, 976147334, 285391461, 598305690, 714577857, 319803889, 254409672, 167272662, 384718163, 266435481, 677935561, 607185653, 728451121, 865092691, 656317974, 745906660, 926807883, 90386292, 187512202, 524904460, 673427954, 368868331, 943167273, 210785892, 16896793, 658987006, 994453986, 760808677, 173299866, 931638751, 965249567, 39605288, 564994334, 368975951, 267391626, 403789301, 866065923, 263576992, 945671397, 177687995, 800503228, 210543073, 498365183, 279793182, 475207258, 632634543, 725194197, 357223271, 731568704, 143836833, 576631554, 689795641, 919662204, 183655, 316612381, 46825941, 322355614, 34488804, 482706850, 90341229, 809681891, 600647741, 53069606, 145608798, 44125849, 313787926, 615459747, 779761832, 281126837, 98615617, 448752259, 664304567, 463324195, 859643897, 98720709, 977529450, 571637553, 573658838, 948372675, 417078080, 879461418, 191514336, 447941796, 975539007, 169235073, 487596182, 36637418, 332545134, 298746872, 402930566, 994736910, 283072560, 400730249, 761438065, 644786584, 29655238, 617835034, 397623969, 754305774, 273669566, 276170216, 269366314, 525406669, 174868278, 344346251, 44290543, 499417720, 273840589, 195390389, 771829551, 853074494, 834188073, 318726513, 890754068, 819911938, 507856531, 394697742, 253473821, 840456037, 682395194, 109257200, 201434541, 675903596, 132318071, 569238123, 401514312, 237857056, 47899593, 530329021, 66587919, 607980289, 943743783, 660647622, 125240556, 833033359, 20879481, 316011758, 282379425, 733202365, 956598237, 223601523, 987388331, 478723707, 198120656, 134684419, 54608638, 837211336, 616688894, 60492843, 622942063, 494984705, 419285621, 120903664, 814639775, 367083861, 705417247, 517335123, 812935726, 86328936, 854663334, 719744044, 977314129, 534515935, 334044293, 904008788, 636513550, 684535717, 987146489, 790770855, 183697750, 60642934, 473029999, 925098145, 942727397, 830620864, 628535409, 365495442, 23579478, 938238478, 37037127, 482169318, 812731234, 750484607, 424072242, 587798654, 497045282, 436932020, 596448266, 397906922, 467677202, 94204822, 157598642, 509154619, 754158848, 533615797, 411708975, 970909222, 404118645, 90424160, 53802023, 407497094, 193588183, 264813407, 905535223, 142837909, 702969027, 302159885, 71492777, 121249047, 171403688, 738635662, 91550264, 114041934, 380660620, 453137966, 854282160, 616102928, 828721970, 82620218, 79293304, 667289657, 160763354, 242836965, 664396273, 645312548, 664565492, 25299864, 838788602, 769948258, 522503714, 241285854, 709512925, 562834801, 408634499, 219600070, 640090758, 719672645, 925737998, 603961365, 306362643, 998369759, 76984956, 180112670, 711717936, 506822425, 644197780, 26695985, 736398046, 13136100, 871344448, 78055788, 858357727, 309141568, 773209331, 214395283, 335746968, 632114367, 276424147, 584174063, 350709, 520808353, 255093840, 540916492, 32953454, 989696566, 305986684, 307110152, 75617259, 999326356, 924394448, 698083305, 58151588, 313331750, 262090258, 346811462, 493143959, 258087748, 86988624, 543913712, 511797185, 478061604, 790614686, 958231295, 304918581, 506503807, 810240101, 328398092, 751508354, 364786931, 875842830, 166792095, 797655638, 366956300, 15539360, 85122050, 901107652, 822247340, 43025268, 929034529, 821695403, 308031946, 383380379, 660085896, 824968768, 171764404, 254548074, 204692456, 895247031, 873779609, 636622724, 343888054, 126004981, 106935807, 722520912, 176677929, 133935323, 989702312, 482032411, 671433588, 682530274, 135313599, 236700108, 169560702, 123823956, 270070055, 276472440, 596874386, 470835763, 717099065, 832199412, 953909678, 168447365, 55892528, 8845059, 407620328, 17936881, 633218755, 708821998, 254034632, 528085081, 935365319, 667738721, 944139384, 488145296, 935738349, 738989535, 753761734, 403003964, 91286555, 385358154, 38749192, 712210471, 387212941, 403579589, 356141729, 45881281, 171984323, 423765853, 768586751, 805192543, 673377760, 112401658, 808373577, 393081051, 122283982, 608559886, 509505249, 717361317, 189959413, 441695428, 931245005, 236317038, 645179480, 262664709, 459901875, 91090898, 972824469, 699220199, 777212786, 326820901, 171464291, 478966832, 918927359, 786456261, 77971979, 958948872, 594163724, 924473700, 70660433, 146364205, 226797256, 832094353, 341955006, 626646471, 577369989, 93326990, 843001495, 705656119, 960002666, 4356773, 142809875, 514159560, 889593985, 923753210, 802897926, 241764091, 262905339, 131674907, 224035980, 830177297, 146305020, 477767685, 719967443, 747045233, 65666992, 768195689, 101148134, 891421381, 851717209, 469088910, 463941425, 144432347, 474336389, 676615632, 390917048, 605723383, 736168898, 533814977, 4794081, 531811175, 925364631, 311467691, 603357470, 608856729, 40693242, 246151749, 237233762, 525268648, 124349391, 522733058, 666762623, 188553158, 851878623, 90073999, 132710109, 587906991, 677829666, 273051604, 92364039, 693148997, 134060127, 244953437, 638068087, 958503460, 922497660, 655065820, 406629054, 865140342, 840974530, 702276776, 965557832, 928280891, 973110827, 33447554, 452905811, 244362347, 901501694, 103453403, 201970632, 798508057, 627789079, 51871658, 533425628, 649202399, 797043496, 207882677, 403358293, 197260099, 970025602, 711565081, 461638717, 832407164, 777578330, 386163809, 116738539, 798073860, 863808317, 195663879, 126580199, 561751114, 854953612, 366993396, 765702162, 808450406, 759572885, 866339587, 317298913, 675289622, 692647873, 813044271, 687063064, 920108553, 715129660, 209941279, 761292060, 320233262, 459045570, 802653486, 280565996, 276945184, 56896188, 167244773, 725350932, 406158200, 296397794, 380666997, 439687820, 800992687, 476737244, 880157971, 533060156, 290349059, 548966754, 781801049, 838142882, 207005401, 630918026, 112355534, 519450726, 367473778, 66613053, 116230427, 566184635, 531975831, 88654218, 853222831, 4396776, 726565057, 357806781, 422148525, 306591792, 940264374, 592055167, 191720836, 779923854, 286151146, 711343862, 868508382, 62748734, 128986615, 817885888, 147384863, 83944398, 217487609, 892110200, 765627041, 524950352, 893703810, 337177738, 912328193, 747537195, 71405405, 18453709, 195780796, 653911058, 201681830, 758887299, 888212776, 175779142, 296353428, 575424861, 631417042, 555263824, 677847692, 698120073, 498265003, 887937440, 430544801, 251662914, 817557584, 559165194, 363749127, 299846644, 664399656, 336631637, 142555285, 965530742, 905167468, 952188964, 180611355, 417498642, 455031791, 61971192, 728565565, 586993971, 510700007, 618589664, 285241967, 97291780, 632816648, 618311458, 657632391, 116599784, 5886959, 917146117, 714831549, 755982023, 67413985, 63826797, 657879185, 267171024, 207887739, 415794080, 565934381, 866043552, 137471223, 427503863, 884002504, 249689425, 909848372, 141956628, 404575354, 559918570, 332641892, 440201103, 66028444, 273313981, 284013482, 510839458, 658268332, 615341922, 894046904, 141014936, 871817922, 281786552, 444243681, 844840386, 889945049, 257157160, 228010294, 136163350, 874200220, 506571701, 777117411, 737180102, 96122604, 662876096, 593652964, 979885136, 184589576, 202746214, 161682401, 255958520, 527477664, 241528992, 915915394, 335020572, 442397426, 328583980, 216931542, 22998540, 358662633, 301314580, 640964851, 218625097, 745960127, 580122997, 757515914, 261046391, 846235486, 430115019, 813461000, 820463463, 1929040, 843145538, 663116857, 843096378, 824694590, 970130625, 942720485, 350046942, 141846927, 328799506, 217513224, 86446562, 364170264, 345974801, 33842698, 120880123, 138611725, 548355287, 558381316, 919355445, 981247239, 312592235, 221909417, 693788186, 149252587, 910924303, 225485747, 574624352, 878627345, 594284807, 871200859, 104810785, 122788955, 946440856, 543083580, 676691983, 886900657, 223278693, 268268923, 293530436, 561399405, 891024856, 474285982, 764383440, 925449240, 702031161, 567167411, 591441162, 455813745, 196450732, 13926343, 646321674, 663825397, 306364896, 127689541, 378151221, 67498553, 405065211, 997107842, 865901382, 168009018, 125521549, 363443057, 649037047, 192904063, 436171489, 783865448, 874487710, 806586006, 362022091, 477481399, 220411427, 758943254, 204097643, 501293845, 941281494, 280366944, 708077402, 430490432, 349050704, 762252662, 936373141, 60953542, 695036784, 425258089, 688105496, 706092706, 278381003, 968195893, 169161628, 647738606, 622415018, 860527044, 689307198, 557912272, 82363822, 684651647, 922045945, 3862342, 886320864, 521905316, 192004635, 353312548, 413878723, 373106662, 796255747, 233625552, 717664035, 869043114, 188544811, 162106928, 667043603, 20382320, 644230476, 460580417, 7100485, 624656868, 709442995, 871850262, 146332367, 789725442, 454983443, 711706781, 627361186, 859000991, 538990216, 775780173, 31338284, 153640275, 441116054, 943769232, 277869641, 797112129, 933275628, 855948279, 42060805, 689069488, 629900443, 717193998, 436560729, 448343139, 10312445, 864818015, 95866923, 832918554, 736146622, 880846200, 277176931, 163201971, 857946602, 747288259, 855504302, 670845777, 928539720, 570843428, 665374297, 111809093, 415956067, 163814542, 118258118, 111308151, 160314365, 752782619, 686460220, 175198008, 312550097, 679103015, 186852356, 435196326, 46354963, 388856336, 964103187, 861256268, 50518654, 86269283, 115626389, 806785080, 301047035, 383844971, 125947306, 899279409, 945307423, 5739043, 883488201, 534802403, 775215354, 63966579, 599192849, 788857250, 360694362, 794794544, 136291099, 976592327, 691148717, 728791559, 202117875, 682638723, 856174395, 841618967, 35160986, 848298868, 430247350, 208521078, 548246469, 129406116, 39217090, 746090086, 725115926, 103270647, 8883840, 292323072, 692076177, 615438959, 624303420, 663273315, 619933595, 408635662, 916075117, 748977808, 260208738, 229202452, 415068590, 407693135, 824212119, 803779068, 662483015, 929718523, 43933125, 71579431, 691487081, 105926572, 137977399, 743229996, 856506178, 44452046, 710948240, 84072192, 798186365, 561456417, 61039087, 66028835, 419922872, 99459129, 96646445, 425212477, 230446082, 859032424, 289708293, 667894012, 935884271, 959190179, 647428446, 403882521, 477780539, 597692972, 232011832, 447977636, 431938210, 4958356, 518590152, 531601520, 707691184, 581006853, 890391386, 4494027, 821736478, 644106809, 778226675, 747937442, 674199528, 490845203, 148826883, 60878299, 340576886, 344476046, 755287265, 61609844, 308388196, 53430227, 897523250, 453373177, 347813467, 946351202, 52808567, 526427973, 829903057, 287693934, 605368989, 291086852, 169364425, 697700082, 687482886, 728527912, 855164673, 330022318, 357869124, 979284614, 17575106, 376222728, 627951343, 910844342, 844891587, 173732075, 720061065, 272081137, 604139347, 856671027, 482750862, 858270082, 691357368, 734033286, 147862489, 657680671, 551592220, 143938066, 56783701, 425904374, 727944137, 45130029, 463603522, 771993089, 335763483, 262988327, 830278861, 589300751, 49276646, 787053440, 916767116, 556477467, 279398732, 86106663, 444731550, 709853534, 526350328, 760982524, 882767931, 142955184, 450971935, 297860941, 501021150, 382902277, 646358976, 63758878, 73489725, 590401350, 826114915, 366459765, 931467601, 269945193, 861598786, 441548036, 365765743, 426482712, 907637041, 651891592, 35490857, 537273575, 405614374, 958181812, 138170890, 632810746, 233756611, 242083586, 733708323, 85435870, 720161523, 643205444, 713995532, 216158931, 674590589, 186430075, 234132939, 596572670, 437186989, 782376520, 454214096, 133505657, 135974528, 346277054, 886451042, 311146420, 701984220, 186825127, 599600934, 831773668, 649086984, 979636405, 619789976, 541792645, 476908925, 684555496, 183562750, 615882355, 168452967, 759690577, 7991467, 341650327, 280190439, 487628685, 795164864, 926196782, 725221598, 260580409, 806543758, 801519240, 949594482, 667694532, 537728488, 794869729, 294187800, 356856465, 96027443, 448514102, 869065914, 749458286, 938647296, 506385419, 169338293, 482241812, 337030162, 285224469, 210119780, 134560753, 966639002, 981903970, 138059038, 988035462, 449989412, 487097365, 770393411, 642576096, 351195061, 701573450, 128792137, 154216014, 776644076, 938029814, 263539278, 276786699, 829249536, 658936107, 689190427, 746552781, 583530974, 897984363, 939604499, 423592163, 422900769, 377777003, 675775183, 476157744, 823204076, 26893839, 866486839, 965882697, 518822777, 885230319, 451770514, 819720997, 208068722, 223562612, 929464246, 601004610, 902819339, 340679469, 730596827, 992290738, 62510301, 51232315, 710615508, 278866796, 529201122, 168855124, 864944885, 194161584, 938126921, 999633763, 671971196, 451027494, 477593154, 792830210, 973983806, 419323807, 208614149, 777264013, 891876302, 302133663, 198676737, 94880876, 413663187, 743564204, 280855802, 102105646, 366572302, 170953999, 706679798, 592197822, 129944119, 30213796, 850917955, 440431362, 116711619, 405628182, 809253424, 173544021, 989172822, 393185488, 778704432, 279666133, 943663774, 365594819, 92373414, 904010169, 165769963, 56277366, 474942257, 959990012, 938236627, 977037415, 497845467, 433487125, 651572792, 973982568, 296452287, 228844685, 131477654, 357424564, 730354800, 630195333, 754360083, 16227591, 948081521, 669733316, 912363872, 371536323, 529616051, 567860314, 630773073, 42020941, 51331575, 661883160, 405689644, 757104276, 936191619, 174639181, 349379697, 180326118, 171704107, 317250396, 922453293, 760434220, 475922086, 519988152, 295686379, 31840779, 831298263, 521700720, 521797454, 426961375, 854470982, 174593506, 836973878, 312393307, 148785753, 79419581, 19007546, 85226210, 219957737, 489842246, 469513111, 721906484, 49527374, 357363208, 956734774, 110052547, 150959932, 189994078, 609039572, 599003192, 989958109, 30925686, 800802157, 185859775, 321213562, 602033559, 389868903, 431075169, 537173725, 449838380, 170442817, 796979111, 356179943, 611627587, 153371652, 520944237, 332861073, 561736410, 817316416, 951051472, 791384198, 261432782, 44076330, 96816940, 986417000, 813922097, 20961109, 617167673, 607105342, 461653930, 170343661, 257252153, 670629417, 886951042, 12917248, 818205444, 156063133, 406238560, 320867415, 71357299, 127187924, 609181387, 104849144, 81351081, 822164287, 904314075, 26015789, 544027523, 600749801, 920984606, 883705090, 596416338, 513963497, 669582659, 700403188, 724491114, 901919277, 309716827, 449433155, 120280168, 467306612, 544882858, 652327775, 144824046, 406886819, 205802625, 979579082, 382194864, 999753055, 920521563, 846699203, 451548810, 990163744, 387166495, 439669122, 616544434, 956717071, 149689664, 555995616, 274816282, 434706588, 1924594, 855314471, 931822042, 61686979, 608468214, 768879056, 513829875, 818900641, 184992235, 323772776, 130705760, 93546202, 955335407, 417823390, 423260360, 24782857, 626618467, 9481036, 37301703, 45976603, 283588902, 485829787, 371404534, 540414045, 644500988, 30438653, 669998808, 844037117, 285191057, 772038769, 395379111, 191604087, 906340478, 794151717, 133324820, 414015116, 67516248, 84078088, 156993471, 41073301, 297957752, 395996177, 64195968, 992538422, 998904557, 502632869, 726863076, 889769404, 495778311, 561587012, 186141106, 532307425, 514673080, 950183413, 914704028, 85189078, 818016864, 876499127, 225703133, 222535040, 116629799, 641344937, 692079169, 902419141, 905395273, 309769426, 255570681, 734878586, 578485887, 551792849, 500391943, 576745940, 26767566, 686612305, 905608791, 171154379, 695487816, 501020275, 901867102, 107836585, 123326863, 372518962, 825875876, 268224608, 669062310, 53668623, 243026546, 586658149, 812725612, 162686727, 479697440, 497400754, 807608597, 432008500, 483846438, 473357194, 937755014, 260105609, 33350561, 179203012, 73729957, 212780648, 781095053, 777963203, 834635959, 494391036, 493720201, 407855562, 800451918, 649187896, 412115489, 495522090, 110403133, 787901656, 433678553, 981499613, 386016252, 837357010, 797119729, 557126491, 917643367, 492481659, 233081207, 478678828, 444774571, 661169354, 151809840, 11481167, 739448672, 932542223, 959838404, 298527082, 64014903, 747676461, 165701950, 385562095, 202473446, 334403949, 48553453, 189169951, 159834683, 134786209, 308356525, 595759928, 548242528, 551613783, 949871152, 174313239, 688364113, 925854149, 247796986, 530331679, 809182353, 718277860, 292661810, 554631667, 497799991, 268375708, 478591593, 827049698, 629913496, 424812248, 272810406, 956038971, 929745609, 68608368, 260691378, 294640610, 127404513, 70529183, 588961419, 198393731, 156527987, 951833719, 112340978, 309797205, 583838670, 678991122, 391726602, 799964357, 457044742, 361572151, 849508906, 931097422, 855871296, 248907772, 639137612, 89471532, 988442296, 248998454, 763452733, 374730264, 571923166, 157102687, 777175198, 447922102, 717456192, 277400508, 879039323, 452341032, 699247581, 489088179, 421035324, 17005101, 388046553, 25604850, 265164331, 401849145, 827138871, 834271654, 936073639, 480002944, 995703263, 8504080, 264129903, 633760524, 537390725, 797156220, 632996269, 436701757, 358128439, 3336327, 247841830, 825774156, 996158263, 406534736, 896789696, 861888927, 910781247, 228147041, 188755023, 170858474, 575890612, 876924726, 635569952, 371594568, 453828190, 195873903, 456658132, 114108647, 777723991, 458093745, 972589093, 32443540, 203519365, 468080374, 236739055, 157275081, 49441879, 812330322, 185596365, 778185102, 848631548, 194239016, 469350758, 109717324, 313025770, 325758907, 994315040, 580628816, 393257624, 156495859, 342723483, 368531795, 360467181, 86728322, 252402366, 168236836, 374297013, 363296806, 290448397, 186042173, 476450658, 937634492, 647193210, 781710475, 60810568, 259687788, 505673796, 668268833, 472533482, 89608398, 921551218, 756448396, 790064506, 580689620, 675872520, 31432472, 849400480, 335006311, 501224443, 221646518, 201418938, 868098219, 811115218, 27571990, 815866342, 598338998, 666597462, 786214986, 291885590, 715493094, 323456648, 8254352, 341235214, 93236893, 480577866, 586865123, 278484670, 24469285, 408982217, 690814524, 748461779, 254358555, 858934605, 849429481, 296566366, 814107112, 202515008, 558588562, 54538395, 461430460, 538694509, 795677044, 536131557, 539962161, 323907420, 649389490, 57450621, 247697237, 291236662, 818621915, 195676541, 401171861, 762449176, 96353306, 439936771, 972210535, 846754802, 707560993, 146696799, 744256508, 218435506, 655103999, 447134057, 5616733, 251014568, 396335859, 31388980, 948209543, 235355131, 100961605, 822740043, 401247194, 667866867, 386510435, 892882870, 345305018, 852891129, 632538359, 173259021, 487306676, 614856744, 555684926, 757261435, 601854766, 193904732, 965949720, 387458727, 754827659, 611589519, 420410326, 231888335, 611743091, 902493750, 346334470, 177261935, 159417873, 349652055, 638066598, 622879749, 490662967, 208779426, 419620167, 306412423, 90735735, 243752085, 397676505, 165691738, 434262156, 163200640, 86481356, 431590688, 64693798, 926465645, 739406510, 725697397, 73468804, 379476313, 148613993, 398334749, 898539090, 470336658, 721463758, 840913860, 68908954, 417575153, 687334748, 877362470, 700250120, 554016101, 578495879, 553696399, 843604342, 794195738, 30842153, 588374935, 738872270, 667307269, 784486568, 173386641, 72527260, 370614996, 277600446, 208045213, 405952359, 485479526, 852221974, 780315249, 404510283, 766775967, 438422825, 2365062, 459879918, 282654263, 157683186, 740913400, 124078446, 323872637, 425664895, 812446063, 117542318, 799332912, 630474073, 173204533, 533086719, 253930303, 86569696, 630480803, 70383093, 323666621, 575563281, 260001160, 710760995, 734475403, 368004315, 759378295, 89279208, 459003404, 891807133, 267918696, 655087854, 261306290, 853280523, 480544723, 374896896, 135246298, 342316704, 413391827, 628153912, 476315109, 786915659, 25313174, 229859414, 652276106, 119977372, 305292978, 257733158, 323241548, 354359230, 905718995, 36696034, 320452589, 214737142, 723813129, 835765397, 311161856, 393181904, 133342379, 75270716, 757946703, 459515609, 391871860, 760447350, 16189455, 898708933, 122572472, 496198641, 458305011, 838443468, 357311736, 749741379, 928394688, 750330296, 623411919, 607752334, 296084682, 160996197, 626820453, 551867962, 964074023, 849487731, 738233725, 54482006, 727864924, 909193462, 504453630, 679839480, 828674858, 875509731, 658590320, 851878237, 758673077, 519331475, 93082583, 791699654, 83691918, 253100146, 636608370, 428376683, 337782236, 614515663, 672403031, 109297967, 664463221, 194865697, 856550541, 731942663, 558457824, 11830971, 236850022, 773793235, 133280664, 107849999, 569615448, 791977698, 718085871, 302430232, 161820627, 27333912, 271820109, 919442657, 520578049, 299263574, 4801556, 39101015, 56110438, 51780648, 97448798, 147135118, 339259448, 276745309, 368567496, 794736270, 352388292, 943852324, 747754412, 931233430, 651599690, 524659056, 722253733, 543186350, 598793922, 8490559, 729423802, 665858987, 319183663, 393747593, 465307462, 919617379, 601263789, 480631625, 110221039, 252058252, 307882698, 853372378, 748904471, 93308923, 221782720, 917781589, 376008529, 203307819, 986592510, 600223457, 190185980, 799013245, 59494647, 669563232, 448129144, 993321297, 51582990, 721198065, 246669399, 747568553, 604147123, 110046095, 915993007, 314947945, 861603552, 314707380, 496671780, 425386397, 611147879, 852897556, 889005988, 858344277, 562569159, 552799456, 660550061, 29313576, 711296561, 890932504, 91466822, 379031077, 83253269, 230746154, 584557418, 13176714, 455441041, 239966369, 429460142, 995070743, 22437574, 688178934, 903567531, 907273557, 90604471, 912768902, 722745151, 253712351, 53427968, 357074994, 802672909, 933713351, 802383404, 493912461, 945108850, 129058817, 611485277, 169588239, 266972681, 255851257, 965679762, 983966906, 572600402, 528634368, 761532145, 420431195, 883570296, 666729528, 114854646, 536571179, 450842242, 941093580, 844053229, 971568520, 139419926, 549066863, 663300476, 402748502, 124629627, 343982686, 567646713, 731847475, 861758921, 383389892, 562266145, 15173795, 282042183, 230061430, 723117763, 363592744, 96856562, 411423161, 617301715, 153403644, 15231246, 683415115, 109789710, 666935794, 215240187, 730564107, 964863935, 839908261, 803930750, 964805854, 58042719, 914599265, 167435821, 111536110, 838949971, 167381372, 686119133, 378989517, 417711977, 884545714, 367003724, 328449824, 240640549, 361861935, 506572917, 293773783, 347765439, 329107036, 115582443, 109804752, 115171005, 33720278, 142622766, 694002808, 874608597, 394593297, 301154944, 529313752, 993714937, 648830024, 332611827, 182800107, 722186551, 435138590, 764124312, 447147075, 79607127, 412468713, 212696415, 122929866, 679997285, 720706618, 374997461, 378005901, 557795638, 504318385, 849399175, 184125608, 282666859, 471666248, 962619182, 477238697, 760618348, 323127896, 756643916, 102728692, 737327550, 810404463, 657937982, 319602728, 116602518, 948219808, 729972538, 982931107, 566016684, 340926439, 667746868, 990885525, 253186854, 157774077, 931261376, 782648584, 262853232, 334468537, 350539912, 534281651, 627121030, 220191225, 41687950, 104711697, 488746840, 498095407, 905070111, 904326056, 393297086, 245254104, 246244793, 519066514, 630917652, 373369441, 93169445, 60362580, 973529823, 441711045, 159636073, 638456206, 586092699, 575367628, 249793959, 965615194, 853066739, 632321343, 289924109, 633987907, 818877835, 83665914, 760260918, 306574444, 63882364, 211418905, 489154740, 826197635, 418233471, 476500642, 935229877, 143266509, 405910611, 276064312, 978903931, 217312482, 436365527, 79266812, 165988795, 979829371, 654266058, 42749456, 304075964, 556582024, 482185495, 996898690, 569635832, 570723803, 361749979, 686019855, 801568169, 424046104, 69907726, 735984366, 692220419, 755393179, 386925081, 38523033, 659261357, 472482945, 115185045, 90958023, 813265491, 581099216, 639385341, 298244941, 572061272, 198896360, 354616368, 220480893, 814905826, 86578118, 4856655, 952062387, 999679249, 765175844, 17177664, 152652282, 92874975, 172966527, 533659557, 196464533, 666813208, 907863360, 574853804, 424152949, 275718304, 574177751, 953510205, 413690639, 989791011, 322130896, 496959492, 337917088, 894090511, 47923190, 424259943, 747643809, 324500706, 325942642, 757363208, 546422640, 63290649, 173755257, 559881377, 244840797, 30604778, 825859046, 362943682, 388766975, 420245226, 657436367, 364418116, 480311315, 254422730, 912758732, 199294939, 391938490, 109957960, 331749764, 840578261, 279462113, 598821039, 619248248, 767469030, 241033965, 967464977, 41579992, 975250264, 583448915, 23202633, 449395286, 160902450, 974314752, 846711778, 248558489, 226487850, 337047108, 215184850, 659421640, 401446837, 146768080, 534833697, 549587699, 997838975, 578861344, 197858289, 480727753, 995551763, 322650977, 971741014, 755001023, 201458934, 328806615, 631831501, 664451073, 672748934, 232830225, 128771853, 851944187, 485157521, 967744679, 40430741, 639291521, 630443091, 177724000, 277761929, 191722318, 505147193, 198946729, 141402472, 832398633, 527178616, 92380440, 613108822, 662421624, 790637212, 227485101, 295907866, 713931772, 552270281, 811566946, 284378539, 142854970, 507546074, 284240786, 550281467, 694706565, 868546458, 528567853, 874582535, 28677643, 340486485, 722950566, 643434399, 151200704, 834123096, 810561891, 114920098, 864710911, 162657436, 164566062, 797576586, 281785639, 747264524, 585112173, 354890963, 63487789, 666912142, 684735160, 835655543, 221565647, 945081758, 537583104, 58467591, 533393285, 373937724, 106072202, 875676168, 690387905, 811376241, 777190141, 659364489, 412134714, 793074028, 374157065, 210752890, 570999413, 495150125, 424319408, 781064738, 76833071, 702409455, 154325053, 233193189, 71192768, 790492665, 279226868, 836380957, 5143184, 835996497, 476789215, 237092719, 742682985, 394198343, 120369276, 335413082, 179016836, 965999255, 678108625, 109735336, 900174654, 167614707, 365268944, 390655378, 571300807, 790518145, 398116329, 793151366, 136837804, 2539670, 147341650, 416562993, 44864510, 131744850, 267558041, 674367660, 898168501, 157494938, 581623540, 249079800, 273858269, 417273889, 625227462, 353089, 857770395, 726937797, 216741989, 238832234, 436968130, 407604164, 122463840, 482116536, 483602711, 404656743, 323952971, 481005288, 496385340, 979183065, 861894618, 995458091, 970649044, 275662331, 983886550, 41320826, 342811871, 427044739, 577265462, 410945687, 532312653, 770968055, 490244567, 794443441, 826358894, 345609561, 635292190, 713870317, 499001760, 579501478, 638104456, 341564774, 633034598, 752855151, 85678095, 529588502, 10100856, 309648888, 725387929, 336870946, 94914952, 304249472, 211889663, 560024652, 454470939, 745570773, 534534199, 945861577, 187721572, 257954248, 165249373, 195168303, 606995773, 575495870, 814430519, 273645864, 516094514, 525442448, 701695942, 498009464, 405380689, 999063644, 877400182, 140525674, 6116395, 410137941, 926971301, 510607761, 531659697, 149457004, 826394210, 264927657, 604135198, 161267176, 683083843, 603701197, 907249112, 920610534, 306211601, 325474087, 678061948, 483330124, 613940116, 357458639, 985490872, 647893622, 513796557, 987888572, 477563751, 392956387, 864785345, 110883112, 494320592, 327601745, 33436060, 760757415, 36183590, 461786416, 11824510, 897802472, 911992973, 228262802, 478354186, 48744581, 501092903, 57546371, 878976262, 199405253, 262487868, 806299246, 485919334, 748092042, 245997320, 638973030, 981681293, 816162859, 561979040, 223198165, 723279015, 996147735, 200535839, 645811325, 881492637, 205874295, 732100467, 608737003, 127922269, 933548219, 527307475, 222015059, 454609427, 535657962, 142679965, 454466340, 739343317, 795715177, 872398393, 356088380, 368303084, 696883524, 911196989, 520359986, 566307915, 586804794, 706497836, 874759310, 194658946, 210324286, 938463865, 418483162, 850381310, 293764716, 135066259, 899007020, 985807408, 269025459, 937837609, 762588544, 81379959, 756439941, 263900159, 25354017, 878839173, 976323072, 559111453, 803064739, 413216585, 197622124, 484867221, 137564193, 52563777, 901359495, 462455561, 971517174, 335661816, 828351707, 804670910, 714673714, 505229740, 241061348, 465895190, 374455211, 440322140, 585459569, 193811358, 423168760, 616930952, 29633798, 337470654, 469838703, 600181295, 157268165, 902319721, 364327090, 571596292, 729321032, 137182769, 940349493, 312124088, 717873887, 759584487, 174928910, 459751429, 284836863, 660153341, 402502185, 718989633, 304090911, 388129052, 553952937, 987503338, 117236730, 192051963, 256595971, 918154677, 608611011, 347168386, 955704595, 824710280, 276670098, 476282714, 660446618, 494853790, 327045619, 235541121, 490738199, 576876767, 97793294, 33138323, 866595552, 273824802, 895058905, 716463359, 862169038, 985758238, 312354863, 747915281, 91788771, 933204631, 17231173, 753994836, 288591600, 247807724, 511578078, 224093151, 903932302, 142576964, 907250457, 790494300, 569351541, 210649965, 174955459, 841344060, 342196597, 498596929, 469907766, 333100332, 765755906, 39944125, 501541950, 242082036, 631996322, 721872045, 602511069, 807489048, 932539475, 658007438, 842895932, 144365086, 641654969, 814353546, 493788602, 69524031, 43692549, 602613862, 251333769, 416630186, 401530146, 494413731, 632246965, 778168788, 563663822, 536143137, 232964164, 40704988, 577588069, 574158631, 355056844, 658465557, 866873042, 544064421, 156834494, 432510854, 211764753, 697423177, 221304505, 249870172, 487919191, 306717309, 352776278, 286854543, 112222299, 7678598, 962738115, 763662429, 592517888, 744245611, 927649239, 949403202, 914001446, 958261884, 667800976, 143443008, 843388369, 513656859, 699608003, 806214488, 98923696, 662724546, 700463092, 452472977, 36915907, 244942945, 554941631, 103236428, 939879187, 858696270, 347292830, 940043604, 585234113, 696979934, 5028311, 569948107, 155267758, 529287685, 338440333, 924120993, 167535435, 922211684, 288998382, 836954318, 797236629, 188948750, 766600862, 737750890, 624708519, 92443897, 969216546, 48858999, 949185252, 901755060, 721072478, 435306888, 307731289, 225062143, 312258464, 459195177, 38939143, 313806817, 209034837, 819052713, 784890227, 141083609, 678630054, 954448092, 73234506, 887917544, 597204429, 478052826, 273287481, 101191426, 364897194, 183627390, 110499547, 787366545, 60270623, 215616221, 288587541, 69755785, 591889681, 721710022, 474308352, 671655590, 576798588, 234762207, 96625968, 340445625, 630413609, 162212395, 703744310, 416201914, 715820575, 586037474, 261936697, 600386023, 815367015, 20243328, 481933621, 708889533, 515033833, 487788901, 277751327, 191888497, 339866473, 762888236, 895312917, 802821383, 224401700, 394955007, 475106538, 230040019, 416061000, 927990313, 201367556, 179189955, 538699097, 658186008, 454890854, 260467976, 60625401, 116745592, 17997513, 950099718, 417547913, 437758919, 492965688, 560065527, 806777321, 435825907, 916345026, 239518910, 894430644, 523734298, 869617410, 187234156, 129793708, 691746626, 562938162, 645709093, 452641932, 840341683, 666906824, 702964060, 759976506, 177978132, 983387243, 820661967, 239886706, 689033607, 928818317, 511201727, 203160376, 474274569, 228160881, 831176496, 931932301, 345935567, 378177276, 13174572, 218757031, 233842305, 706313317, 977540191, 801899578, 150980316, 856493202, 633536251, 661130236, 616993517, 553355039, 924548554, 411061749, 510990859, 694808223, 39385891, 940517284, 620438054, 282950474, 858920540, 497910454, 550393908, 319960062, 980797171, 381359553, 136069775, 179414143, 480821233, 392796781, 636368406, 942564317, 539943987, 44099157, 243761740, 424812652, 151864445, 927134333, 271921299, 968340300, 454296805, 121666590, 496124853, 420442184, 77065870, 658623634, 271385210, 858709383, 180223597, 285229390, 129081555, 514001627, 88921492, 177260463, 27211200, 806007861, 981988127, 719913879, 810402582, 32292516, 852386845, 684707854, 760457669, 905112294, 776673992, 338539687, 759580947, 745798909, 289126224, 268362470, 930223510, 584991974, 664511688, 664596757, 723722168, 739522285, 128422668, 404198898, 591480380, 2880542, 119425937, 323628766, 445596392, 337461989, 355477886, 487660129, 839656705, 285008179, 557856358, 767310535, 851729006, 141128288, 809353827, 781131834, 537360544, 244268598, 856795748, 319278387, 978893083, 61029908, 224189090, 109978629, 307991966, 104220720, 739006549, 621869907, 588814043, 810126001, 35628041, 493641954, 133127634, 671678650, 536373032, 184428139, 173928902, 252037154, 339153114, 896957731, 615249212, 726699021, 587583945, 117743722, 746897794, 146246663, 160056113, 276634470, 851717117, 618851, 98652353, 77493932, 516504581, 94112448, 677966037, 978442920, 917221487, 228593946, 386184340, 118443591, 375593961, 957961311, 1437858, 740036311, 583476035, 50699495, 230387452, 12515103, 24706690, 396537374, 303411603, 716178286, 349925975, 456919213, 99111026, 960903580, 443505518, 185957043, 991773047, 310477902, 907271083, 15505633, 372369036, 838405592, 862919932, 186225874, 46331009, 897513637, 568915175, 325776551, 858724419, 535905283, 773447142, 37705172, 287977969, 751000538, 567983078, 487950801, 422159659, 424650368, 640043773, 538881721, 269721246, 261224664, 677888488, 491855487, 412243291, 270202924, 558039042, 864475926, 784879337, 993215045, 913884277, 836038613, 707237122, 925524276, 186799349, 47619720, 366946396, 291401517, 684287779, 725367828, 731742623, 82243475, 205424073, 359622053, 148553983, 936464576, 1098689, 380716709, 378033389, 584600222, 396683529, 985411268, 854102224, 641087499, 36635607, 669942704, 117497428, 443843639, 699630270, 20303357, 605384525, 936333738, 319613328, 216796463, 71243985, 59200569, 325823903, 244079104, 94208773, 130883823, 805617115, 53964385, 368589820, 651526398, 610501991, 681619336, 181734832, 416436383, 915878567, 874044478, 729702324, 787210389, 511660626, 466465683, 113886202, 397586408, 797531776, 648208849, 728774458, 374298099, 85852925, 638734278, 750819466, 200121723, 807606499, 238006541, 749238872, 136182526, 763232831, 267391200, 270134859, 340087546, 565118491, 884455051, 833739397, 100418947, 817002980, 474533047, 676434764, 267917440, 703437346, 703467485, 308875632, 132849841, 637936875, 14181357, 29987693, 180663210, 608355256, 237449539, 83531966, 298073011, 525757374, 604600660, 476953818, 147204796, 309967479, 826587509, 9086469, 984511323, 721871330, 906842313, 809650448, 609996470, 36990439, 803739209, 512837785, 415887381, 900783914, 358684257, 514751889, 183209872, 21234562, 385660424, 480144446, 558064465, 510778989, 174792593, 264334668, 856458220, 935049673, 443915509, 951866318, 664583058, 744511156, 847910721, 824484073, 330715796, 923758850, 55828758, 108607391, 839835935, 925367290, 411251887, 55210749, 440041103, 989524270, 888501194, 625274090, 316082839, 46972852, 434252517, 898248640, 700684603, 885228564, 368694975, 121045111, 777125535, 898111360, 692743907, 448928843, 768007627, 348005504, 887334858, 936415761, 339272225, 535158982, 956689663, 780509769, 808034045, 499737629, 892827683, 488180082, 555374544, 496153914, 654375306, 48295924, 156417973, 455910670, 530273261, 590002094, 875016621, 927281809, 517893901, 601780039, 296517546, 768006117, 748775812, 875267429, 896470491, 93185076, 722494489, 653128012, 340280627, 705861341, 977478912, 512912195, 726075690, 571018123, 645744775, 350822496, 749410761, 610472518, 851631353, 138631445, 333581651, 850443766, 198372728, 344790137, 604446814, 65710161, 417134049, 750033273, 37139437, 44176111, 981815447, 302324743, 220372398, 875964815, 582566028, 966643287, 373080434, 939211651, 736334842, 40949669, 302487963, 624056101, 404109380, 539118036, 855270666, 341220053, 411211944, 634489140, 723842173, 727441754, 313747582, 857389241, 313742185, 105577620, 267064832, 907743407, 565542217, 522338688, 990157842, 949504855, 401282858, 68463666, 355543899, 649978993, 256137682, 825723459, 803158935, 912416932, 863092670, 789926902, 225427715, 501547264, 468644318, 165539390, 217358812, 824820456, 944572216, 212174546, 89493573, 462367199, 491164930, 301848559, 787231084, 650722612, 46049897, 352007546, 852788767, 340276454, 943637168, 864666873, 556910286, 956013133, 217531078, 980394246, 166473930, 281393931, 945519808, 885157041, 11861436, 134575889, 626526530, 778240402, 775207440, 328132011, 829723298, 23066448, 205253267, 698082411, 492404285, 160369868, 354817921, 814598522, 381584360, 465639554, 289902284, 744489193, 338181246, 719767604, 573314583, 337021764, 463563487, 90784936, 895513103, 58409912, 469135882, 323784003, 542359488, 971972260, 218262155, 564512939, 752878007, 143002295, 960071148, 860418237, 349016289, 4388370, 162147717, 684784604, 489860987, 102599577, 437727979, 457568935, 955121200, 588419436, 259141549, 332716, 492587822, 747979184, 318665488, 228987526, 105236998, 197231672, 351617291, 959259748, 741403502, 176502269, 952156011, 406554277, 252476480, 944904677, 101267021, 786336679, 674562742, 242784304, 495116047, 361367816, 220689501, 218253452, 246101813, 749345920, 722397722, 160811903, 57292793, 961934566, 882084260, 663082460, 390016552, 520002104, 102410022, 41742954, 696768254, 910099074, 874563218, 840237424, 131929166, 905105487, 331480514, 558121571, 768482517, 873071426, 682799516, 534008870, 827714146, 778494456, 386017605, 551372532, 869503131, 857592387, 435976563, 191474826, 325193834, 727787966, 107651600, 125561084, 410777474, 352104142, 155392630, 649671596, 307278536, 391888965, 177006913, 641932381, 869943628, 711973151, 430627776, 404986977, 953659476, 970691398, 178723365, 192311034, 273563836, 208253301, 292329925, 489761656, 278992191, 654909761, 579258214, 174499229, 163210971, 593375104, 190773194, 517849999, 99289257, 99554951, 789211939, 596446657, 411365930, 810029279, 893545475, 642714048, 562240688, 46094743, 444755263, 670176910, 413725557, 463480103, 675096037, 23503169, 397331272, 685443593, 959348099, 749922846, 676184779, 60719168, 749776462, 438640896, 842372063, 59780326, 216878392, 559099556, 57686034, 579811283, 871270469, 153792519, 728608349, 847838722, 90384765, 137080005, 909918201, 751077056, 463733752, 578966937, 585238055, 577733505, 544320334, 361305552, 694017685, 133370459, 63628776, 872376524, 199436454, 374551570, 995038692, 721458493, 97167871, 860484640, 65875618, 179314841, 735934376, 700590851, 748312149, 350381457, 547964540, 928059089, 663485746, 322264125, 655780519, 530546490, 676706629, 415900114, 978103944, 894413333, 754129870, 630545791, 137277236, 224575865, 939767623, 146259623, 770831093, 124553480, 250846928, 168498993, 289498760, 808858396, 525490268, 667423982, 540916603, 878556124, 272992855, 399306120, 780183434, 564400665, 635207512, 457397568, 825185501, 336044533, 24094228, 142907410, 495139219, 356888061, 762350606, 477917408, 287806547, 603146684, 134421804, 519386883, 865023624, 599093449, 485941259, 937602395, 639963617, 407313449, 526201982, 905458846, 714280305, 382910159, 701535498, 235518093, 262234797, 205882687, 408110777, 994079112, 268592694, 922248037, 152484289, 718986420, 662557311, 113842057, 708094944, 408296353, 713453993, 931022751, 299418649, 475853067, 599215234, 39094516, 907485430, 964850332, 531148951, 107476550, 713948, 324605075, 575937511, 351999867, 214887437, 66804314, 747910483, 77242871, 652108904, 293267893, 34246068, 524538259, 336737201, 324679467, 712557086, 289843069, 249106249, 143409680, 160223741, 554086317, 352030842, 298888363, 30968832, 541330494, 884073790, 190008059, 71057448, 318224772, 68901930, 889425019, 449147331, 901243108, 330166455, 872589082, 229424621, 82421970, 359634740, 67604175, 974159378, 718461121, 713542274, 910459307, 481834314, 218763014, 380436427, 745582726, 198306429, 823161367, 14000382, 988303330, 408122013, 706349653, 693156952, 540730052, 330255645, 645321969, 27150520, 364044782, 639327587, 726268997, 937275097, 241349772, 92200588, 478846801, 468988235, 461762776, 496769421, 449163284, 142632762, 487237244, 651858511, 940515597, 824962912, 346141149, 226917770, 713714141, 481004676, 987922215, 959343724, 993680820, 810986829, 168275603, 34399705, 231433982, 184479858, 440253733, 54476505, 986559477, 392936445, 875455030, 439209845, 828368642, 461734359, 442892213, 568602268, 524108624, 811642473, 350689815, 847266071, 730289534, 870925457, 410586674, 33199834, 967726298, 829979267, 887232351, 118027885, 762829429, 723512770, 538296655, 88253348, 335879847, 2904090, 163633211, 898306117, 716694484, 237441244, 46939906, 19002488, 767676875, 894352157, 726064836, 845561095, 739253713, 521959008, 964127762, 30037020, 960205677, 121961735, 831593954, 274453232, 501778405, 417797251, 59176691, 551219661, 393084728, 329899986, 591596330, 839363476, 480377495, 984783759, 409181085, 923753053, 820210959, 624500746, 931096459, 767275910, 13900732, 615821497, 891118019, 125870491, 338627450, 586916442, 292703732, 177864296, 574733295, 224925888, 408706746, 946450900, 30302846, 683231539, 546480227, 83410541, 681778989, 955482500, 9949245, 620565845, 790120007, 264818989, 357524417, 351392217, 475927471, 175949331, 641148282, 149275188, 61408659, 461881854, 837951554, 833974139, 756855876, 109414169, 540622198, 319549229, 530860266, 586462305, 706067535, 921964648, 940788567, 456125081, 972250045, 109740609, 933157941, 888055385, 267279281, 116395324, 478657743, 504110404, 870196436, 711470277, 871972143, 932163534, 125115940, 751204948, 286963619, 975953504, 72550255, 363331558, 973500155, 330419827, 941886585, 168342153, 692384075, 465908886, 534005141, 531557978, 135795459, 834935616, 852657115, 570093057, 945000636, 964041726, 86957005, 215333323, 502949469, 278809539, 483753449, 191775788, 174024362, 803642703, 556352449, 706224631, 687745682, 647471363, 135165561, 10300062, 637784478, 405218651, 88629630, 540991074, 100530980, 153195331, 181675261, 435553101, 58872767, 729092778, 125103468, 353681232, 676080438, 932831209, 90416428, 553061406, 37226913, 610905049, 571867088, 602383310, 376483950, 300925946, 608111340, 883827204, 67846577, 61989463, 389922849, 58292967, 50785801, 447899096, 407449350, 395843881, 200964428, 253932131, 616563449, 106496432, 336243655, 993373574, 720142491, 178236831, 957784024, 932538121, 101107948, 747299417, 421576476, 471781264, 304187784, 580184990, 288751535, 573724510, 911887168, 267041855, 767926434, 250851337, 405205435, 742957197, 391701462, 402483860, 462692538, 452388646, 312373999, 347046570, 863315058, 142110637, 235438954, 405151476, 831334205, 212159633, 983880992, 353832172, 431554988, 993957909, 347861913, 654506818, 336083146, 113742922, 965094514, 263867673, 463436495, 511167182, 609526674, 941119117, 958864833, 340167656, 750867109, 974219699, 785418281, 225935008, 18172388, 550556558, 188053919, 475572540, 426371017, 965656491, 902347847, 576445396, 358080328, 774920485, 417680488, 555672160, 368092074, 366610396, 331668181, 805133077, 191427328, 957453885, 320686945, 995201927, 900098043, 367240786, 923485763, 430449133, 419823767, 164938893, 355234076, 108593712, 342205853, 302838566, 886662788, 149914307, 838689790, 6899306, 851014611, 49205671, 483660648, 173669724, 430043838, 93501684, 744091571, 402832286, 560567723, 792191645, 704538967, 501874340, 581374908, 728695650, 637749076, 775088276, 315371698, 63971611, 299287553, 307149752, 971765536, 469903501, 346391566, 692022360, 244730485, 87149859, 625233445, 690585636, 469853641, 263166006, 459947842, 130628479, 146429460, 550122791, 530608340, 789611608, 117052679, 171107747, 460212768, 763920950, 102954561, 373837879, 869959149, 692467097, 130818409, 261313152, 270886613, 824403371, 418505102, 859730620, 376441024, 30257350, 436252459, 358258915, 629362375, 36932783, 917038458, 483479565, 556484004, 652638016, 71921896, 113608835, 378526933, 405698028, 930125746, 390241864, 553178507, 920726356, 872872366, 106752417, 848516696, 299734955, 217130551, 442452874, 49691590, 968175512, 730262413, 732039187, 318911413, 653642455, 783363403, 415268734, 615422435, 740586116, 724762423, 691071301, 205120761, 534659341, 304312622, 66276133, 641902157, 557406376, 808832859, 622939599, 936532125, 154870070, 327649878, 369793333, 682350487, 642897774, 512279602, 285961092, 445114343, 619383768, 610714514, 993079477, 204526851, 824765407, 695517898, 645463052, 354616501, 770438849, 236149706, 916366240, 111777913, 434882424, 838251761, 687492370, 216625131, 730287997, 92069042, 363606817, 676695197, 617227839, 840521104, 977833451, 541879416, 94667487, 923403815, 95115045, 816604230, 921843085, 222012565, 367746625, 859798472, 953618058, 127948713, 915646585, 539083065, 553232558, 209406499, 692954101, 876193409, 12702356, 333191596, 921084609, 350520341, 643157091, 614128065, 381820500, 347552043, 32844668, 301794311, 903403585, 984188097, 766973235, 938947910, 48330723, 791034474, 519321054, 304666504, 290021274, 697834580, 871666023, 52038838, 935928833, 481315149, 437846568, 269532320, 932265961, 115832901, 452960498, 143333103, 980419399, 319023901, 481512157, 472534023, 642370669, 135073111, 36986179, 444704594, 859586185, 103737554, 360338761, 973833557, 299246165, 36182655, 55550106, 682305996, 390655950, 9346371, 761993235, 760784308, 666058985, 593787872, 947944942, 642890446, 326862692, 135459953, 255358261, 743987019, 592825969, 165143041, 380732297, 897121981, 193511364, 914042875, 113303771, 707876468, 611999702, 747503991, 315020105, 718190068, 559368988, 394054521, 887972607, 294122383, 280878529, 719831019, 818528577, 119676512, 300293568, 834117428, 471323286, 72243326, 573539621, 232962336, 496398255, 419895290, 608304925, 103904243, 656411364, 254897755, 246933793, 483720377, 784422670, 142155089, 149656113, 391069583, 376169958, 152100808, 694805519, 334346360, 854314170, 155012609, 719519820, 515298325, 627127627, 505886089, 338407543, 30325757, 950190995, 509305783, 796110423, 746972285, 609249120, 91942846, 95470451, 821395913, 508743746, 980516336, 884723944, 999592596, 280045901, 475045621, 27782304, 285162738, 99843273, 91798488, 994791734, 522648305, 2091167, 288416071, 212747442, 348353112, 960004467, 723209777, 282519702, 196159760, 975425382, 223626142, 720525367, 471983063, 512977026, 230023446, 992480709, 513456072, 496617754, 875333342, 525927045, 723163386, 487201443, 531737172, 649154727, 396311326, 903871828, 347392116, 8779206, 496748095, 278273546, 585448909, 103331224, 64390248, 618856147, 944554705, 288260705, 797042585, 634923394, 629311785, 746780830, 332922245, 89164883, 342246264, 152138281, 220241908, 69306352, 441285871, 583782110, 664583895, 132544023, 402828425, 384069007, 822418413, 447790230, 647632152, 674888133, 383487471, 683273470, 382263639, 118452292, 583584334, 46995171, 79923725, 119114783, 480764150, 166523257, 679815895, 759519630, 66650446, 574630944, 475038918, 830659756, 214906641, 947721513, 875895129, 776702842, 198625247, 890461317, 986592550, 595987024, 819564196, 84029497, 855139209, 192219946, 566168710, 343155858, 247884967, 157402139, 114261532, 75269476, 177317304, 661191748, 838053628, 362043788, 254087181, 266697393, 683386967, 563801051, 445172833, 507277809, 631959431, 7832234, 437494326, 41699744, 8429419, 775159428, 853798499, 95240338, 936590705, 932603036, 840289958, 109081437, 66990917, 158206518, 862673170, 811571724, 766373911, 210439510, 161187506, 546809864, 968493540, 300490507, 411385066, 482189639, 130536611, 469841880, 736816813, 674234620, 227959297, 737118462, 223640052, 740242495, 285141256, 225903761, 415126490, 202609566, 162951567, 370947887, 408428060, 558693280, 462733663, 721559283, 707420434, 376916167, 522655906, 637303809, 981038803, 877096772, 117209946, 191212390, 190233199, 965322968, 832996349, 264605963, 320960512, 261980192, 76721305, 282926215, 762913098, 59024430, 675712067, 292530078, 639448741, 780461154, 17799743, 478769669, 332785694, 474152255, 312867677, 755954873, 904072508, 307677182, 879413159, 691077253, 700688768, 847137441, 603362041, 920121916, 441249037, 258454613, 59719194, 665319296, 175276771, 314848168, 418676214, 398298773, 722256430, 354395239, 507880640, 884321085, 104468848, 102755235, 38886682, 417693225, 895789464, 474622134, 48418158, 815870536, 17850671, 570616522, 953636294, 374986785, 902856132, 883668784, 255039593, 219007321, 270192034, 471651372, 875303409, 812689410, 403991984, 71836709, 992410402, 563518033, 156428456, 51828467, 941702580, 207006561, 529209102, 542008523, 991799747, 643664599, 43846765, 96603475, 83983597, 896220491, 572160064, 680915426, 604365054, 466758993, 593530461, 478428327, 433245446, 36462308, 993296111, 775109977, 929577560, 40806593, 90816121, 455915738, 465019986, 394100358, 371546494, 815092541, 168098707, 942733065, 694450779, 355310759, 162903280, 504057120, 244996046, 475819319, 816147936, 239275918, 917935884, 897366406, 702681770, 974726920, 774647791, 452763862, 210540693, 656700675, 108871711, 214335262, 88596601, 588986433, 645047084, 82476340, 199242641, 124134192, 944813384, 482170399, 554977641, 357213889, 45250230, 253805984, 133961647, 3034497, 746553702, 264774880, 439194209, 292890505, 566855757, 748626057, 273679971, 31761046, 821841090, 369178731, 441590356, 567752315, 921394127, 705155434, 81370654, 25097067, 975726055, 129424508, 275622690, 531167879, 863524506, 873537340, 482550244, 526785941, 450879609, 477726313, 965710424, 286335041, 806291988, 761430415, 149500683, 252617849, 337002327, 601367881, 413360246, 759615826, 53513790, 936115918, 198048168, 485858352, 857172444, 538796204, 749765900, 861126019, 479889684, 484936453, 196284165, 145158828, 995453133, 793956647, 444598597, 645060430, 717554538, 455617892, 697882760, 315963126, 74398452, 504534005, 870538633, 16426812, 335868820, 833093242, 999610523, 687251161, 495879176, 3802598, 970914516, 799349234, 253498109, 673753576, 267407538, 390799013, 116595422, 896550287, 600516894, 982473562, 95430406, 162939278, 933664124, 499649089, 18035050, 165263999, 538359076, 749971678, 216302378, 808656252, 411146853, 616873238, 296615860, 303505033, 64527878, 710114099, 782045538, 915972561, 874433623, 687054739, 260817048, 948139455, 785771201, 932549940, 81630851, 116702704, 234913324, 654454209, 760727327, 609738986, 392807850, 45532224, 725150352, 315128517, 869198295, 846768992, 313431114, 803824950, 997125135, 908412004, 361516038, 998350524, 121126451, 689628403, 934308129, 935864778, 286719589, 477154288, 831226268, 922908419, 976645133, 461654187, 434048188, 366633001, 528582759, 877679486, 83810237, 643112827, 90999081, 930528959, 653095466, 784667694, 978419973, 922633477, 455591955, 450215356, 70449071, 138793900, 826565005, 723857787, 327281216, 652222150, 753091372, 166014330, 292484429, 16141882, 125757988, 314660292, 8194055, 459520505, 316517810, 203781853, 809922118, 146631601, 105299794, 851779018, 147038075, 343910194, 651006378, 577143252, 352627678, 857392747, 709842604, 934337802, 275549844, 314845906, 295703726, 995401899, 673591732, 103411560, 236004872, 994802740, 528963750, 593573531, 932612912, 876042722, 55003605, 796963851, 372993958, 782722757, 343243319, 810442165, 276141994, 323605465, 162699557, 289469366, 481069769, 834781892, 882141650, 189684550, 993125996, 798052985, 44361245, 528732646, 775095424, 496071609, 416444069, 398338605, 376566226, 760345224, 390666561, 935016739, 654743570, 439949849, 367020355, 757884498, 298478949, 511663656, 25463811, 642230924, 456434174, 948309208, 786631161, 711608471, 904969979, 499185390, 535765291, 552890614, 860756772, 425952074, 543816741, 363319716, 705489176, 584368481, 620176873, 388081449, 722885536, 263095528, 389438457, 332164422, 710152719, 976576766, 350595210, 380901378, 197024537, 714741598, 273213370, 562564828, 849955523, 858639924, 95420942, 557135877, 878229437, 942979103, 247269029, 925659590, 974306787, 39547588, 279560832, 896677376, 6200505, 760350285, 715280178, 578755324, 734130842, 298139533, 979831526, 352317493, 416091835, 304769074, 613373698, 719589737, 607513253, 524531724, 74108970, 266978399, 842987730, 235207216, 186365861, 375162204, 505561304, 993821990, 443287488, 546019767, 76544673, 3694195, 991002912, 97952223, 988933148, 431408943, 949514676, 428417391, 917360943, 92154208, 584167529, 200365270, 90564009, 822547865, 571445673, 242407744, 499787483, 554436502, 952364195, 842911495, 75618905, 341510251, 491556807, 721417574, 384820700, 196756367, 156808749, 587223283, 696995226, 758605056, 433902813, 975732458, 56853317, 626317733, 417675097, 916754614, 998449585, 193141822, 643489308, 667136896, 338942872, 69766673, 5930427, 524322138, 414696991, 540112988, 564299726, 586921007, 588438167, 868452404, 678829619, 337915554, 469187062, 714295457, 276308105, 769155547, 99177763, 767168097, 552406844, 269131541, 178983653, 538004409, 337703358, 955673018, 600194391, 249179066, 521782063, 573013201, 222850241, 584145008, 306182660, 981157380, 940733861, 378151650, 634382909, 768050276, 312246053, 759165582, 37022343, 645804949, 592537776, 822940513, 467941774, 208154530, 974223573, 160318130, 361467995, 433208664, 154165101, 52286020, 779095963, 857356402, 581689499, 810852308, 202511234, 622589413, 186979287, 92424521, 977650565, 102442640, 2886749, 78857208, 686677422, 785764223, 623387940, 695683396, 41120054, 822140092, 495657403, 625194029, 463546285, 273534112, 508002633, 706695015, 591811777, 210827397, 155645507, 143475711, 974496796, 654136417, 592524815, 472457812, 972769287, 180138585, 382823988, 169792633, 696903231, 804812814, 819875911, 997841631, 175584679, 465107020, 125666612, 835714854, 958151761, 276752114, 776566811, 783180384, 441050856, 872921800, 231487404, 938773255, 440066634, 930810015, 514413360, 366867759, 270231125, 368513276, 174078729, 436525318, 402508891, 919147709, 944289463, 929475235, 396227789, 795062890, 576668621, 393878710, 584076187, 482757608, 607893961, 641555654, 841066936, 986182872, 813285026, 857724688, 834126817, 520433564, 119293857, 727581763, 279192420, 199882868, 518696469, 662879347, 593242050, 452080726, 394023073, 526647760, 388429795, 426047373, 665685254, 55115900, 817046145, 109119925, 558242467, 176101769, 368352878, 250541365, 417763402, 537570305, 955685886, 355392052, 385790335, 962129471, 770302513, 560720023, 609577227, 983848094, 531409550, 41047623, 946345407, 572553063, 132122834, 292158894, 118754653, 4149870, 412846221, 258836547, 126039366, 383203930, 6796577, 939906175, 997996295, 645686358, 232971909, 891865285, 4034339, 430213362, 747881183, 113286110, 350716338, 609796395, 586742502, 287815818, 4230182, 688022162, 296075562, 921011252, 34240152, 374178260, 8159874, 109570151, 865084368, 181994972, 975375220, 955613322, 889958973, 623347780, 195904897, 14958398, 574931204, 156982050, 489423194, 129557622, 991458202, 732585446, 251043815, 771270974, 681895933, 857811983, 676567238, 3097996, 91719800, 329753993, 522333227, 310464743, 877366026, 410984325, 14595964, 334049467, 49195689, 522313091, 428838379, 17854638, 610753584, 514181307, 312944670, 269085135, 54194558, 627781753, 321532652, 528426487, 46942454, 250203079, 259140570, 663289153, 914643032, 225859315, 894276027, 915380332, 982242293, 591776122, 271018639, 611743802, 171878840, 364998299, 177724413, 90732649, 81281864, 477856251, 454072288, 537719066, 744384180, 606092642, 513417077, 871418600, 304004310, 325036021, 602982270, 307224431, 707822043, 254091028, 501944059, 135684519, 875645439, 476992242, 817898318, 467021057, 59804257, 532060640, 665084356, 215396346, 455276267, 417703908, 695958537, 685067522, 157585765, 684630870, 414036208, 440196852, 779248519, 481027446, 816408870, 952937215, 232048546, 787046555, 168582340, 479631032, 125696569, 630188299, 708387614, 31239594, 974726978, 274527663, 198260181, 785556377, 735140954, 507452817, 543327024, 313279441, 712708378, 457320815, 677021166, 284594478, 879657188, 959675606, 751972215, 569374606, 384846190, 76542388, 962456713, 556621671, 868532328, 452389609, 647956086, 271881012, 134921627, 656468079, 274694889, 796767691, 296837005, 740150965, 255270180, 899253388, 939426781, 838133211, 823837149, 268223936, 339227977, 905710482, 286823478, 303538370, 603772768, 262913356, 418019920, 453415220, 822835319, 3124317, 770707526, 479553401, 430946514, 190583300, 456602747, 938619278, 301198120, 566936031, 685517372, 943801760, 109923305, 605949025, 325505201, 376757144, 765649422, 957759072, 847519727, 809848877, 639961918, 630644733, 587286892, 528101067, 625081015, 412337436, 180386843, 918440275, 226849931, 439182886, 961940848, 312525222, 190889187, 172381468, 389894064, 621497906, 821232248, 510514463, 890341854, 548036570, 644790666, 875365567, 731241980, 829780934, 713211388, 526859586, 778123021, 259277784, 96741518, 933012102, 236099662, 721606256, 339157051, 350584452, 968523318, 61049860, 832186208, 892821331, 204689146, 331272480, 933104969, 281112254, 274196262, 754339362, 756871442, 482552290, 41097325, 628258476, 465348374, 739764845, 988677796, 381408145, 75782622, 700892704, 932856464, 349808123, 223758003, 210252644, 566212004, 28438325, 31834613, 660506197, 797004573, 635430673, 11119677, 700534104, 897086419, 724736505, 37271464, 599776769, 148621065, 958373480, 961993036, 18146025, 54519258, 498293652, 408057042, 819200077, 932331585, 786967943, 491975159, 497226350, 343441994, 590230083, 26177683, 666154709, 913358944, 262101701, 351134477, 804009871, 333520286, 103285173, 153110533, 637242361, 206055802, 42645631, 248322065, 975678213, 931101188, 251057161, 324717763, 607954785, 820377363, 518013815, 451900852, 527048120, 631158748, 275165154, 764042842, 278891031, 526592508, 543897975, 111037400, 261342810, 47037143, 442725126, 199331953, 660472028, 690516812, 368615179, 806291129, 481710353, 684540763, 953953277, 205173399, 624069672, 522193341, 619594068, 173921214, 223759628, 294306357, 636714903, 98017507, 774680646, 723016996, 258602386, 259711945, 433552239, 37612808, 22042910, 475984449, 748576708, 221701566, 670896994, 23837075, 382557702, 889384298, 4937259, 135223808, 612801996, 865249086, 74439681, 865204625, 56129472, 611696858, 209228491, 751161708, 519027054, 389010329, 134883328, 598204163, 431386320, 493512629, 46131676, 872507324, 746028154, 801065926, 769825996, 847646184, 171521083, 707487003, 447058003, 935097913, 395727947, 961335683, 366349083, 526139715, 736457475, 339409975, 919630097, 403438583, 688599823, 134335244, 204901187, 30294971, 200942475, 310021193, 28650179, 518463220, 11641775, 983890781, 659294422, 474058710, 295039554, 937283176, 688622304, 152835959, 687195814, 618571664, 230153374, 744996130, 107115298, 244308641, 516782696, 706459691, 540704208, 744474601, 881019507, 180140830, 417837567, 990784838, 597290370, 506981205, 319513496, 34557189, 90120658, 420999518, 137586474, 780238388, 83697066, 195344546, 603929915, 748804351, 36448383, 205318022, 680356832, 187533905, 666656159, 566871037, 234245445, 186969545, 527845487, 115955, 605854765, 181203442, 800869228, 494849913, 941335441, 735501857, 440742807, 80398541, 388107936, 503133297, 3197515, 977173090, 948197281, 866149030, 890336241, 737596275, 239635358, 763128793, 464260133, 34597222, 964315349, 966698994, 550837991, 975100395, 482333357, 670852629, 606619048, 136457243, 257228789, 673786956, 719476553, 255045898, 434789793, 444366287, 33716053, 677384030, 531727370, 799307461, 766726992, 868268592, 805286845, 72495250, 760160131, 22466245, 614423273, 642394171, 450064837, 993072964, 602744724, 751187501, 254919657, 596080075, 725099497, 187626331, 289529676, 686447514, 59030443, 617579753, 95757627, 255926332, 430369520, 421793393, 153845646, 691709934, 816021786, 610895947, 140851285, 939394708, 28437159, 145476209, 958148237, 559758662, 848249845, 921372382, 702243153, 555134166, 656801764, 897738223, 203000159, 390106757, 818710121, 685271237, 820221118, 348154174, 769008365, 756086965, 711073105, 960711921, 251585986, 539029627, 942889107, 479045202, 797403137, 354064939, 18609673, 360608350, 221907315, 860590850, 485044445, 160630607, 282451344, 972023571, 595221899, 324405145, 768928757, 308246831, 537466560, 457078115, 341280099, 732827119, 827209551, 365284460, 957146180, 534142839, 682828334, 775037956, 666998442, 502363463, 485545469, 279132970, 336070178, 949728800, 323652840, 755751018, 681927740, 183035896, 704675063, 600718620, 283792085, 914050916, 669799915, 639358090, 965856421, 250151927, 8772769, 214268657, 616964115, 594064258, 688802527, 458847668, 446003312, 570378651, 797270856, 300864262, 253232240, 659497774, 868774917, 549100110, 524496549, 732181914, 173500988, 670667595, 869665063, 603547692, 926926, 914429430, 272748408, 268355759, 597576430, 718987854, 936361271, 391375997, 499825952, 973019958, 181675125, 738481588, 205268467, 291872837, 739022275, 149926094, 263717232, 168178914, 712859476, 762894829, 21112388, 771540142, 913718864, 35967132, 990282591, 235895331, 80891970, 45765177, 867665261, 676387447, 110434464, 668459812, 915840473, 974456395, 955804968, 530308455, 421293578, 338752716, 179945203, 407873933, 230148297, 372248231, 390495586, 268984781, 22278233, 642690544, 916079713, 836434955, 305638684, 62126415, 912864197, 179848353, 489565849, 386010553, 743838764, 754482035, 129036507, 2498307, 78943861, 829277865, 892418677, 813082127, 414516241, 610465301, 409230647, 120925686, 827143102, 686232368, 38546949, 939685019, 511868195, 136316668, 774637573, 143850388, 73013809, 213445303, 765917163, 757061965, 474802205, 753082880, 264023107, 473227731, 929298070, 833859926, 263036402, 768522445, 609588007, 664900084, 369443341, 283111630, 20417587, 840901619, 54231653, 859992222, 615364247, 720624878, 187583154, 582608511, 565906775, 44883342, 727169413, 819523610, 60260068, 768389783, 132575818, 782820229, 482896706, 882701726, 981861980, 873495995, 168773289, 510531831, 774687808, 205086306, 237147367, 233084474, 487412049, 231693497, 35063592, 598909418, 937999060, 958267583, 978295086, 716854435, 229929979, 25331989, 779100581, 991205270, 486940401, 597366968, 155856079, 729535814, 220501769, 923414583, 294466901, 559693808, 208462182, 516415494, 235193270, 578101207, 956864089, 329917509, 19053583, 685764829, 780838801, 249194407, 169210087, 67464814, 382394634, 11756297, 258526064, 203778532, 987427343, 960488911, 566353928, 688009974, 873146774, 799138281, 367264497, 993571830, 363443535, 83238653, 726862939, 923750727, 480371563, 174296309, 753164267, 323409712, 95686228, 169305287, 129361246, 414172278, 452318191, 793485050, 294885095, 152712538, 149484478, 255793961, 681610053, 946620266, 446601418, 134245316, 369299767, 232496389, 296763292, 702230830, 670344619, 124485348, 173508040, 734216183, 942535356, 87383407, 706164124, 372861955, 793927526, 561482241, 715708749, 620079710, 981762816, 465547587, 11018605, 19767265, 220855265, 111168400, 257996380, 309097972, 406161058, 636806751, 972498898, 306759091, 978872603, 944467315, 12661573, 278338376, 320268298, 909105388, 72624790, 290007253, 934232102, 837831850, 303663759, 474769279, 697532180, 584422801, 861530836, 223507490, 427366996, 964080498, 327638807, 827986187, 979939560, 902855506, 704120104, 560066393, 147271314, 675214855, 691992468, 681900825, 834186625, 365361207, 364497972, 667189316, 682860146, 432159145, 132386673, 554485194, 240482790, 664008582, 458369883, 989281128, 179226460, 431624525, 91645563, 152686868, 758925700, 567602475, 449287093, 414186515, 727135078, 932148828, 290999326, 551556274, 116532166, 455769405, 545681621, 498217646, 488087820, 41031618, 604286578, 780370464, 154619658, 198231676, 383279611, 486181060, 881980584, 228616345, 932123600, 324912088, 528081057, 186660967, 890806377, 19188082, 373949309, 869949676, 878927671, 723754130, 532192038, 731046105, 559709999, 946873598, 556211195, 495324452, 440309506, 436174680, 785162269, 231370732, 701815684, 343032512, 386287194, 631927650, 978095954, 622122780, 855426535, 275014465, 825824457, 937368088, 358875310, 65969834, 510507901, 484539030, 725045636, 25686682, 267525123, 716564742, 39573811, 833200653, 283186200, 426512798, 912293816, 559483085, 456625205, 568874573, 35359450, 183765097, 123674607, 87069097, 85763087, 662360684, 326160611, 624473049, 13569885, 828763412, 258898445, 164740308, 289527924, 858492882, 834398355, 146955650, 168187128, 823840138, 504833323, 859411286, 259357026, 412422633, 9147708, 412560843, 302327744, 76984845, 526036869, 56513271, 906859970, 509858699, 552911684, 781866379, 55407333, 693439682, 246276549, 235415042, 652515306, 946406977, 330987937, 651551277, 116597111, 298285907, 97164926, 493463647, 953102838, 406718547, 491507539, 159239270, 562860256, 388941907, 292138986, 787690527, 468267704, 470288309, 75073453, 437842129, 832258914, 184816169, 432407364, 86244669, 140571080, 829751935, 619408107, 611561131, 210981242, 743430369, 792628340, 607392285, 856655501, 85832159, 164852741, 681570229, 639025476, 119131938, 548766570, 316351484, 149383612, 417289650, 356524025, 739236545, 959878008, 724932776, 697290933, 949081786, 25817246, 265607051, 329252196, 795222990, 713599530, 660142994, 278230173, 120397406, 965534996, 520962850, 885014371, 74912593, 972619866, 717357351, 108494954, 959140949, 512463327, 593155902, 221144115, 783578143, 411253076, 84856884, 492123461, 622314257, 667293418, 225178426, 784815321, 917497793, 257668865, 627928571, 936122338, 954161688, 908198224, 542376519, 64835017, 509819907, 59918286, 837037758, 646564554, 610161322, 39725718, 5920405, 90981425, 118778082, 166764935, 281025610, 864576952, 169264401, 80661029, 959548482, 84561787, 430204757, 406161961, 182442904, 524166664, 250907368, 734209044, 450184782, 664998723, 900872658, 212775663, 156810902, 445136947, 53888129, 593724904, 940952365, 961676430, 654921262, 212433632, 123598427, 914919615, 776561755, 574880577, 329770150, 235454763, 956516639, 238069495, 837950049, 387790443, 582575429, 784546926, 843336310, 323158530, 978927673, 274849627, 693213033, 276444121, 695634700, 553419910, 352344236, 115123159, 561286001, 450849699, 764258746, 688900337, 919694336, 93831335, 7871929, 446252570, 265539885, 663999910, 769666319, 412493231, 10275649, 185928089, 574447495, 746936443, 655387690, 225621260, 33626325, 537046001, 461141994, 211694884, 36147225, 961358753, 646629930, 941907998, 80903034, 227738374, 942820193, 382080750, 460359487, 495374877, 93447711, 384645003, 689172601, 186717547, 367563199, 836020663, 565502006, 369499083, 917111870, 127629536, 432796675, 211863243, 470057627, 694288694, 68193476, 529978529, 678985771, 399488719, 783649245, 212378386, 10387746, 768076633, 100232004, 773439854, 126917990, 115998412, 387479229, 49107686, 271021538, 636228886, 702710050, 712029214, 739195587, 594501397, 675502851, 469411023, 283507488, 273526398, 769055306, 244556051, 823989136, 407381796, 33036596, 355954559, 468952495, 101297912, 881399567, 549557262, 101573349, 541712929, 685921078, 204701566, 436728694, 759817136, 47202490, 365296404, 533527126, 242574687, 894711498, 924049819, 142093212, 328176832, 593796832, 124040798, 602654682, 699984559, 412880968, 534776659, 341864782, 707944727, 359392061, 374098408, 486575505, 994993113, 932557553, 417725805, 336306419, 545689959, 717391394, 5705780, 265765397, 988265621, 148287949, 62442428, 892605647, 613745851, 991785191, 893459725, 172459006, 386532532, 321047614, 6517013, 763915066, 328865461, 931618436, 745183281, 580651289, 438015163, 873222862, 153689432, 206243193, 371274775, 13017962, 726042315, 472846824, 322966085, 510494186, 902876859, 254754455, 989285734, 23483477, 268887377, 593211259, 659933490, 49642522, 81939300, 544224714, 291051668, 543219767, 644223891, 557542236, 869657383, 940850797, 234589148, 556539940, 295197135, 299266676, 577686735, 747831278, 519598055, 229059773, 887253905, 939814024, 493700319, 421549615, 435954622, 48167750, 5952188, 887799848, 951265088, 327200808, 575622586, 615518021, 622005824, 119059442, 496765334, 979002929, 943120749, 836865184, 227278378, 175379652, 399069461, 397890881, 944097169, 664147870, 642565020, 377836838, 885048100, 212073339, 303999642, 200755308, 218517362, 472163525, 915622075, 91964324, 497502683, 849685724, 214264421, 175058029, 729010692, 138789040, 990012706, 433491235, 479732408, 712153728, 785782718, 932351375, 204165321, 655861192, 904175587, 291404946, 706845618, 169987847, 515890838, 227988628, 751864658, 898249038, 375479886, 716138752, 889965976, 590641898, 138984012, 862451486, 504252900, 977406538, 777840490, 568923699, 502211323, 5550779, 510745557, 212082544, 776654790, 512686930, 639636802, 862788235, 318813593, 572440710, 644831119, 556576240, 844625550, 15662194, 481579661, 506396828, 448987712, 266421942, 452336934, 961477447, 44102481, 140273548, 241238346, 534969733, 673666200, 203528849, 128559262, 401816342, 588784901, 752332485, 872611583, 932530246, 598749703, 581320532, 68732116, 63677622, 50462933, 46806666, 715359964, 510680941, 921229751, 832510269, 658621337, 520673825, 638016323, 67912424, 99547707, 607043762, 682447997, 333651622, 982779610, 914062605, 351302057, 729706237, 765288893, 495528358, 788465749, 882930574, 695809664, 413949152, 653296740, 352827969, 99552102, 895885315, 380502346, 354390084, 996868665, 950106346, 426025635, 832873877, 766631445, 4453745, 312322491, 905463216, 893378510, 284228791, 58489502, 359291975, 905447857, 624922154, 773689566, 149009423, 168666334, 978327568, 645790579, 529625544, 88185820, 40737156, 3003036, 111849464, 919428477, 509357675, 718158179, 919703100, 22982600, 296339876, 584292476, 237319205, 881355437, 431765876, 548508856, 793408317, 944615471, 467971902, 754611636, 157710013, 480065675, 295707019, 225090712, 800872156, 248109913, 930750674, 100040376, 869150602, 59008290, 732862698, 255954333, 574024659, 807951584, 281664871, 297439574, 971410429, 305393269, 931683700, 473304327, 893586888, 107551136, 300170552, 480861732, 735518053, 479924427, 183083170, 393314671, 990541996, 953811123, 73999066, 157098641, 624145443, 246599345, 735724238, 808076080, 897850144, 137843217, 228500680, 721391227, 442033784, 958742400, 203803262, 325610604, 727158796, 418595061, 502820325, 444780191, 643992188, 111921352, 180815322, 690015439, 541674973, 625855711, 4431222, 593354606, 695629644, 755795480, 948716964, 515854804, 136048729, 872376767, 57165617, 928579393, 631886469, 791528858, 786331026, 118881650, 460505116, 79735947, 318517981, 970235017, 859577385, 849326222, 761997296, 407218062, 940053427, 424028639, 4334474, 123696761, 350723574, 834277957, 138178517, 744068153, 174699396, 675641095, 308471254, 157178105, 644114959, 4879829, 601424266, 839728221, 569478504, 28503202, 115698645, 922494475, 553910558, 656487342, 66292765, 64015684, 70840226, 998292320, 844094342, 552851024, 433879996, 731281676, 368025205, 876582833, 7764751, 278689124, 525468401, 875517236, 818300624, 218578725, 297658962, 859833697, 37451953, 341849396, 688582269, 119491177, 680297318, 289498012, 565708780, 361104633, 833086445, 904588969, 522692179, 251930191, 707914813, 219138410, 632801950, 80243463, 257131548, 382679769, 812228450, 771083905, 427562878, 130317278, 44431534, 266440573, 618361621, 68481604, 621314695, 47568868, 667312411, 466842055, 461159596, 524482792, 438293462, 252493161, 547379658, 541894260, 732181840, 526932855, 216141216, 558725237, 578084620, 457520135, 192563358, 365758860, 729898262, 464635341, 323912290, 793526714, 356283194, 806809822, 164597654, 385396619, 735975399, 791573496, 883936525, 942901881, 910291268, 316961366, 497183215, 879154980, 18123103, 732431816, 69869305, 916910881, 254865372, 939878303, 627814787, 348490126, 713405971, 639419729, 837276173, 899022105, 169843100, 124833444, 526928727, 363709837, 226559697, 584416400, 350880701, 886061118, 238487357, 881677073, 454706952, 519423653, 493531449, 590008280, 424528930, 93485529, 673526337, 332017718, 177311403, 413680485, 610537350, 276038599, 411706943, 873517334, 266952368, 222988376, 840864888, 825793803, 888270982, 618458696, 222772848, 266301442, 443123172, 650172208, 905908030, 320618589, 349242455, 370304269, 81079933, 458349642, 830833476, 986868896, 650877118, 283634297, 882186640, 937139985, 630821074, 213586555, 78288765, 405040616, 975711864, 275940919, 804000556, 243169391, 924988637, 83943360, 55263861, 679702325, 55884361, 776000754, 430230621, 895456092, 204448518, 527639705, 461148089, 246009583, 110011444, 819284534, 341436217, 542702463, 368430591, 20837376, 717550134, 202356060, 540629826, 128341783, 434358202, 99782926, 313984572, 977445012, 418870559, 48886291, 224413689, 683413990, 725742420, 46369693, 161795291, 63119264, 909134264, 505959229, 834657553, 502816339, 636378955, 62013618, 740703946, 132495418, 78026618, 676512806, 827413136, 359951465, 747793075, 536867316, 462799169, 820263374, 578238114, 256377788, 763910767, 819541349, 268899364, 959345974, 646877159, 414631065, 65341594, 155277273, 813492765, 694379162, 935639748, 288969264, 656741331, 460923572, 167975035, 737702017, 900891546, 772397047, 472009695, 900779964, 220419076, 403222106, 947621345, 186420067, 473233131, 925288141, 91057645, 810519380, 396002722, 214352706, 299671683, 7151931, 928830411, 122224679, 965059840, 686154804, 342905383, 975726646, 56415548, 41620279, 937919246, 213560412, 62185083, 999677490, 494979843, 413960258, 115756135, 492553224, 524240568, 631621415, 277391545, 459940418, 689170329, 284166238, 625687690, 296033942, 57296896, 162603034, 414660566, 61979657, 252095261, 987081390, 85160619, 821688080, 706806111, 164273089, 913025027, 73016406, 633905749, 104647238, 822584948, 609932786, 399211256, 467796275, 280885218, 51444380, 958315367, 482996521, 171852395, 271535765, 139329910, 600210534, 330036565, 369325150, 374288494, 181009456, 998950153, 341712313, 901914490, 754282166, 798955196, 691167751, 710692043, 210153888, 683300487, 463372175, 953898013, 923787318, 168894396, 917691148, 364137082, 216204484, 397976522, 215182485, 66782943, 926439009, 863320620, 930326372, 204745116, 111529907, 652903570, 235600891, 529315701, 735351269, 440280318, 856129194, 346240756, 461142265, 954885576, 252212516, 494859564, 18252394, 697048861, 604038253, 700585924, 111464052, 772003503, 508764573, 744461014, 498194730, 192607077, 59014459, 252726994, 444875440, 895561989, 364765282, 122763089, 296380657, 708431098, 70029521, 784406828, 965752415, 393463064, 448634990, 62529564, 179442073, 697680816, 280770236, 588425868, 459949243, 609401396, 405381024, 108676586, 251651928, 71854382, 540292012, 406745450, 494548588, 480473512, 490311952, 156849868, 56851966, 876192476, 583636209, 31580401, 723786044, 420421459, 249267948, 373183846, 500132820, 650928808, 370649206, 4957740, 817081885, 499890236, 938184233, 353246393, 795521059, 781798177, 76004630, 665927282, 116385909, 777035354, 975828901, 333639193, 710839127, 861608113, 691188115, 449093713, 198955798, 331442777, 23341620, 425004840, 418908931, 369054877, 778624723, 121621090, 196836658, 189717906, 80004680, 382851612, 518327869, 376811770, 429464571, 753600420, 467779552, 158772213, 773311050, 643621064, 450224496, 571537341, 313607706, 171265985, 332946220, 40192530, 280359633, 590010725, 433196885, 768913760, 514731011, 491723065, 476451660, 892432132, 115423475, 463917545, 722189036, 385693403, 743437116, 510331629, 14200148, 586808507, 369926119, 442381074, 665205813, 852036598, 362580290, 301624232, 344146079, 240517067, 506850346, 726396608, 749746203, 585210702, 164581525, 553353225, 636655656, 856476935, 182963029, 874282120, 605443271, 70079119, 595545509, 535256983, 284379026, 194278783, 155954826, 79156837, 207733775, 257226120, 306109780, 114930835, 993927157, 445113153, 916699238, 408571174, 692104553, 890472899, 287977210, 492923516, 313351616, 574931743, 123828145, 126038280, 952942697, 154926875, 215392862, 962636104, 792592391, 867420576, 772566430, 343796377, 944327292, 917631669, 941743080, 580458101, 626767564, 60667043, 303696728, 163173580, 105376459, 223085301, 134147597, 805526319, 597678708, 508275676, 550971728, 741485076, 630288688, 999959099, 644135653, 306694135, 650089660, 481531597, 879447963, 29798766, 668869840, 716640393, 195611051, 548790237, 201467479, 324083474, 750434048, 466752138, 266737461, 244413667, 895685670, 832398579, 959158647, 315484542, 321277731, 153834493, 484278430, 516506539, 756272074, 307437792, 680894127, 873232577, 348409375, 365924454, 230497815, 870640109, 246289828, 377816704, 50401191, 96489057, 352049463, 816668093, 10241209, 759982080, 283198305, 341623527, 786239615, 976339601, 251209009, 201502676, 836623043, 477105240, 573567639, 823734383, 902433386, 360646602, 617810974, 69894342, 839965842, 41526833, 350967152, 836619174, 404723997, 939156721, 972018230, 285599318, 947371776, 465399025, 60749986, 183940662, 216537699, 534120469, 122598516, 495470097, 709028289, 216717789, 70268480, 990936982, 777553074, 787344075, 184022448, 32194494, 570215090, 952124515, 496548787, 67827971, 750286453, 331416370, 914571613, 443220164, 345585511, 275183237, 548164867, 618671830, 448006778, 26922112, 638465674, 658372151, 218162064, 71861337, 418494918, 373580448, 441538182, 25197456, 428617719, 327359659, 786141098, 199357039, 291628709, 724531365, 175653246, 200219524, 190346582, 713644324, 250472405, 126779823, 976930012, 161327001, 445870296, 68395385, 921090469, 543120269, 564029886, 332899960, 929636136, 840174534, 849142793, 554057826, 561070101, 839105154, 897524003, 945926415, 552268877, 399520367, 631118031, 972303672, 398719234, 65094440, 770591899, 681985616, 504722760, 134546445, 323833377, 922028817, 986696610, 872840424, 109029801, 859591417, 86959283, 495334232, 538905226, 567910125, 959404125, 957973903, 292951378, 438216158, 490267170, 875511373, 835958362, 768222525, 137793698, 367350187, 524460436, 20607206, 526642120, 467437025, 562688367, 161899453, 731786549, 976607553, 605494158, 381433095, 574132709, 469278264, 982482335, 142876152, 895230683, 943225518, 189338498, 965772079, 152606469, 296363955, 724670356, 912314485, 260603793, 983075145, 108785951, 508067371, 974104727, 757033131, 47173310, 664152821, 232774320, 257816407, 906639417, 218027397, 40484081, 139745142, 328568553, 848017594, 719196784, 656156307, 186502247, 346514626, 326492481, 320073786, 560144498, 140248345, 858550219, 973599894, 219249921, 21044390, 670577263, 413784229, 629671095, 682135776, 474711026, 6005323, 765436990, 885721272, 738549208, 420151591, 602566315, 658609692, 919528692, 853127508, 317258812, 485580638, 727757853, 718091994, 399410229, 34652787, 322379807, 700819777, 909073242, 331975559, 664268994, 931553147, 653395789, 769020407, 780900410, 11025660, 227818113, 484139613, 432959142, 88997020, 543221710, 321408644, 801196849, 728574470, 402490877, 918246521, 691370613, 214028968, 959647728, 464842213, 663373800, 274559847, 757987769, 983186324, 501975515, 927224479, 231005399, 586677353, 45782049, 296829649, 678856162, 95858032, 635221956, 551199915, 841555778, 449289242, 608138582, 72660505, 798077801, 224205948, 480472978, 460628756, 443412624, 357975082, 429510570, 293607334, 855470494, 968254758, 261952854, 182981974, 314777143, 240740675, 362126319, 824482246, 687609476, 337694804, 817412346, 969979718, 270606990, 655352311, 500315719, 648058595, 972127231, 155445550, 525365118, 928728931, 497758841, 134605705, 561755786, 834677085, 200384731, 589593068, 499259289, 541812393, 775551519, 202487900, 222519852, 439129086, 797079090, 100051539, 886645741, 433763923, 312743293, 955210161, 684615865, 369875521, 256393581, 675913695, 282625300, 768934543, 4417206, 163763541, 756102252, 637937470, 417967485, 791796288, 961180390, 186606235, 935960413, 682638268, 50924304, 3933807, 256092067, 1366342, 464017715, 334171124, 645178173, 426345309, 801174697, 232188148, 197147039, 616305550, 721874668, 652739245, 874618374, 651628291, 791203369, 534887119, 875802619, 431491374, 141165871, 749324203, 51196948, 841530975, 446225699, 689143256, 863641109, 793692858, 984994617, 953639216, 146526507, 434889113, 255992444, 599190496, 342791457, 111341359, 794594069, 783834095, 460721056, 206877888, 652932992, 434812772, 562546831, 965269982, 389936314, 232534079, 359743296, 949731858, 575462856, 79244676, 722087397, 588769984, 84449803, 151369284, 475800445, 236644539, 312581742, 568136381, 465892994, 667320419, 489544218, 332188376, 531164474, 695283343, 351614460, 922207162, 390237027, 152348348, 266270570, 982775041, 684318822, 788235919, 775907819, 484576791, 506562958, 206543270, 358542787, 538415426, 945693360, 121434455, 200818592, 194753870, 10520769, 628607690, 285205795, 643296214, 936346845, 685268856, 812895569, 142342149, 80798203, 151301972, 728027806, 78155076, 890317439, 458796325, 734671262, 503973961, 899634035, 581928668, 920317014, 19070499, 912396186, 817753676, 895895365, 291904051, 11751454, 673372922, 309154079, 16844291, 266583100, 366343257, 997329675, 557494192, 601448346, 22511813, 384017767, 814119384, 397443100, 956954416, 357421734, 180949593, 730321001, 736214400, 283578618, 785673587, 482342682, 896703341, 594723969, 767724024, 626839595, 15107764, 150208408, 245615218, 943700230, 128933319, 661429486, 485396310, 166989113, 799703074, 672875441, 588684495, 879352949, 805347612, 848074654, 701595869, 678273878, 415168061, 636289299, 770514626, 873856739, 452061571, 19493776, 648876986, 29585257, 964838142, 490308806, 519898295, 664345035, 90966790, 270310110, 162228522, 587995622, 290733306, 14584422, 20758521, 279102929, 755033255, 745216, 822224178, 38602452, 313638057, 497860940, 910789932, 858545326, 599629104, 986773090, 70566495, 654513257, 9090310, 24851194, 847415795, 81074957, 495909556, 452057592, 674304556, 291720689, 493730442, 83631688, 323093331, 951201546, 832843092, 16449382, 489301078, 630671871, 381475960, 883033149, 602870578, 747509890, 692345830, 874799323, 905922865, 798861771, 256224501, 30942935, 652884405, 288178489, 632838431, 495575275, 478641872, 58556155, 568021944, 986904513, 463850961, 770470942, 2326362, 375980481, 948623405, 907456838, 614333368, 790158070, 903469461, 191497204, 918905991, 969339255, 212828402, 152336227, 70570967, 279490161, 574443642, 334323107, 59455531, 352579544, 107569391, 856342642, 552729520, 289272886, 597136898, 355445342, 519459776, 215040700, 866093004, 895544993, 682682822, 166793107, 859943628, 202998679, 347803721, 456269304, 447675345, 563398777, 432870151, 719846469, 267480088, 901105877, 981178328, 875907128, 759821478, 398979763, 430449941, 749448655, 141853137, 365919660, 453043675, 655490084, 829066270, 476333844, 655776598, 991324506, 220109239, 853649590, 692526508, 887634313, 741171437, 399884955, 54594303, 776356237, 208197577, 526444339, 120758200, 540818605, 810037417, 704105542, 814069257, 355709088, 386294256, 623696136, 787053297, 473910994, 350501450, 185226395, 915584265, 698732034, 379422619, 995399067, 132458880, 440713975, 943276396, 206473781, 828887956, 856715140, 439552026, 641805196, 880255083, 787108519, 461551515, 763649557, 282797221, 560748040, 466311501, 298630537, 387865656, 452477152, 118231865, 324202402, 256469861, 496314313, 696304588, 596026258, 174715864, 639004751, 243009454, 666630087, 520403727, 267033748, 348057792, 684973082, 507619261, 914749136, 379371808, 538169520, 145498560, 336700401, 585359835, 354424664, 195997239, 171819890, 637011823, 230041494, 232064374, 496844790, 83775907, 330850834, 826199752, 775186436, 788221721, 728907966, 809123422, 438890988, 281574878, 339314727, 424619606, 644923795, 565065506, 517990277, 54848275, 343874973, 723338410, 713049027, 766985311, 932473378, 578696185, 689350884, 352272734, 440409016, 858117263, 113789611, 671021911, 312751005, 217866827, 660207492, 282054823, 862756473, 477128923, 348654750, 982862467, 993589270, 100088473, 614342573, 367547699, 924825284, 306685823, 290002644, 451994141, 554454797, 260616847, 382132816, 456829770, 257982752, 252652600, 806931226, 14460290, 27044588, 254201711, 621468797, 120911975, 25974614, 735618204, 819183427, 393716266, 778148217, 761992460, 269301138, 239332957, 862448948, 153746569, 985806327, 739288094, 437389534, 506602262, 641220760, 86775938, 703675679, 296318354, 25576991, 777575852, 303064074, 15143586, 829980917, 237447739, 554589218, 604371189, 234331940, 832498931, 91973940, 211484865, 161172571, 852053011, 382453869, 984189448, 94480683, 868761452, 965479009, 591664967, 181967024, 451090090, 942505492, 893319038, 319364456, 870461452, 694507177, 342084890, 165249536, 572205981, 618246587, 960284116, 356594950, 681944367, 545386101, 148672141, 948262533, 493205113, 642025803, 719929652, 259833886, 296829777, 668993367, 979474244, 663309934, 915875025, 717555741, 176772730, 466964330, 972916374, 824655995, 612222356, 716184918, 234690425, 667093229, 679182069, 180829615, 717232235, 619374456, 665344420, 160475692, 937173092, 451290265, 698847830, 895656770, 285784355, 112904809, 742141419, 409486875, 54165492, 756609185, 790767975, 293671891, 133640718, 98137931, 687153752, 910153839, 644113458, 308922925, 754291746, 80024014, 993188150, 918545260, 349731602, 810253861, 745418011, 532093722, 747670870, 67994161, 220139902, 288024810, 442889032, 35745642, 780208764, 907437674, 526965944, 830445472, 141102296, 909407529, 370468571, 288428484, 425262669, 835500738, 340947250, 617106209, 453766252, 147290103, 309208524, 332519526, 217380476, 456094364, 961476614, 785146497, 433104183, 810500946, 697196408, 222016721, 147735923, 779356685, 688949090, 465142709, 220915609, 685394997, 161586723, 141735279, 408633910, 619062152, 149043031, 806042480, 660808891, 582091844, 646261242, 618410, 740620670, 962921007, 829708339, 177198287, 139185645, 154934116, 332869410, 183514809, 526354280, 274846633, 478956333, 575369483, 412617216, 762659844, 722807424, 244498257, 983662712, 222669348, 330300989, 960741756, 116892145, 45668480, 100495268, 847769746, 494018865, 381441083, 817391339, 433829954, 712234932, 761222177, 502561548, 912690545, 674823643, 523130346, 104734318, 756094088, 966291985, 347489277, 338249913, 512446119, 504165240, 725451021, 375782135, 532188835, 597791956, 524551474, 794084051, 130320774, 114096078, 104709907, 622904041, 805547514, 324740492, 113123319, 412448521, 985929814, 599419106, 54523901, 392607608, 334282936, 114951791, 319570576, 114194945, 973841894, 110652161, 550742457, 47101653, 31963195, 628611906, 589911586, 62634234, 850782871, 708904817, 150921320, 652258459, 873572484, 110807640, 79152626, 911367464, 83094153, 591488090, 423908202, 568049872, 198075196, 406291820, 393725215, 76936961, 852595018, 275384059, 834837226, 125331771, 262797990, 385918415, 338816150, 575452759, 474690548, 362504677, 781861903, 542905832, 385993371, 489248163, 509536466, 507287103, 186735314, 145215553, 605739580, 728758128, 709374407, 836589511, 211580448, 122272610, 114297439, 678603469, 941159335, 697220322, 585440651, 161749105, 585554105, 363462453, 699715191, 447758073, 636499310, 703033249, 228473291, 609798502, 34543524, 520590068, 632522248, 225318501, 81713709, 939956662, 109626249, 159321616, 220515110, 35495444, 704569366, 66063165, 994434197, 735686974, 30716684, 32954171, 986472967, 198804786, 859626549, 481893714, 311966788, 770108148, 451832145, 312435714, 878224469, 402594670, 516480149, 340812188, 577849333, 335531648, 790139766, 575501144, 20074617, 693724053, 293167754, 994919211, 562869025, 129507452, 191508034, 870140753, 56047313, 551527979, 61811968, 285584627, 33328593, 462143193, 901711239, 3839049, 962126371, 259631790, 405445156, 297490662, 392481940, 411257565, 187185138, 996829915, 492290409, 669966383, 333203453, 459724269, 482575491, 582581997, 371432063, 199729181, 686069763, 346314071, 123050611, 824480188, 124499439, 52650978, 865353273, 368261485, 24881613, 701073088, 319396489, 691586765, 475223909, 74390366, 536846112, 53188786, 644836271, 102647120, 709925049, 356548252, 451394681, 360599504, 951361826, 245839023, 942496219, 483222776, 706656261, 820791317, 449952553, 499595817, 753182741, 347880611, 356634204, 10947438, 208774870, 58285304, 951951122, 400037059, 448747179, 876799362, 147248073, 141085814, 464599129, 742551144, 836909331, 637893993, 101913891, 65191905, 849792775, 291880390, 460106495, 304559476, 118000142, 611710666, 924371587, 366362349, 443323059, 914115465, 425005507, 981649320, 372635212, 994298926, 539047597, 262107893, 922385333, 949858349, 887666526, 498908797, 605729185, 784240505, 636668015, 462637665, 234550184, 769406235, 424127482, 117337155, 522245458, 371562589, 758980106, 553980108, 654971621, 158352645, 652259175, 216475488, 140669367, 511115279, 979731055, 621833914, 216514877, 384527840, 803977341, 773637396, 850852054, 133961208, 747442541, 898880329, 252813859, 454621418, 274597410, 814783839, 549559897, 631866532, 947147293, 948674252, 777472383, 387054676, 350660752, 761702649, 567338215, 800109996, 501383763, 811565590, 604491446, 847086148, 373961812, 303856435, 421941343, 121961547, 121435845, 410907267, 509785496, 129476736, 360258087, 997029164, 977136416, 993394682, 772195655, 995805856, 210091480, 882440865, 869958583, 646418209, 794445433, 658889317, 60588184, 418328386, 173168950, 441713771, 290736346, 531750748, 583633900, 933808685, 859091239, 567272467, 759986416, 785408863, 524678137, 107332495, 30422453, 728573456, 816993795, 764397388, 308564842, 876089984, 233551342, 272116690, 930299041, 298330392, 123869734, 741467716, 429249455, 984033974, 464817166, 791891684, 191861567, 869014641, 483754025, 311166741, 706556279, 540518185, 695648979, 206751882, 396165815, 233497442, 683437999, 333662510, 616775865, 55940155, 798395972, 930678403, 395181145, 672225788, 626992343, 436889747, 763923595, 212775405, 566686494, 730397262, 564022261, 178705456, 657438131, 87501909, 792957293, 836034789, 361846090, 904333724, 522625684, 559783354, 869207131, 788538582, 213619928, 609395192, 186450494, 26706188, 679586871, 83492727, 163871449, 710423073, 664433227, 69205703, 522681821, 700923645, 387703912, 419031468, 29219236, 23209141, 324244938, 37099744, 973228873, 634520576, 447333475, 234800459, 239398804, 144794143, 637869225, 515844524, 434016146, 511187955, 333423311, 526530832, 625279823, 14912588, 646542549, 717481168, 629496324, 766403512, 780831286, 840217857, 89465628, 707233106, 918416363, 494617348, 446573192, 713470002, 350904868, 347316307, 57765669, 384351095, 315880156, 974218818, 124665201, 992529014, 249590592, 534815596, 652290538, 181244168, 61922092, 220008911, 142026713, 671092873, 264498505, 370482242, 90771651, 243723750, 162431447, 945747403, 94796884, 768018322, 299081104, 96473894, 763302232, 971543940, 673869773, 559952396, 789325112, 95166449, 434535304, 438372342, 363201109, 334251004, 485947993, 878883605, 133526893, 528450084, 99168212, 744589478, 741568127, 449792404, 354164562, 40375492, 12209993, 580102196, 666777832, 602474072, 647948735, 3737829, 147751414, 773040052, 182635, 108778522, 568915043, 787584675, 427221534, 967662863, 859404736, 230266631, 658903434, 945692375, 255661535, 496239450, 691548400, 501213035, 813750059, 242880991, 165912636, 790181666, 880996728, 212017848, 908340205, 547639609, 263463691, 779849829, 640234328, 824049284, 586197647, 471645518, 47731671, 258785732, 710305963, 737106960, 648514728, 89873066, 955517360, 484847967, 136349155, 671550111, 580228564, 395546022, 570672797, 34634363, 138563209, 719364670, 640889735, 116493170, 330553164, 717593690, 355072441, 646996537, 736409429, 304536937, 875603171, 77805015, 504975955, 683775571, 692648974, 477580255, 366324434, 511575072, 36026935, 809105316, 817485841, 234840687, 645176348, 853771063, 889540726, 847587287, 567830097, 990398070, 815594002, 352345377, 634786219, 845537276, 659902974, 359850463, 166696237, 475113038, 597847681, 774721580, 30447849, 175151725, 386305283, 105842088, 353309986, 95389262, 171545547, 51207066, 191166182, 787880404, 455287580, 267619981, 282034206, 269376442, 221163451, 208675253, 663939410, 769908950, 834433364, 157200475, 94759224, 382417222, 364239941, 680674440, 754315499, 607778236, 713645524, 650672991, 510334190, 786557448, 364273855, 726680164, 909368723, 295084039, 618114773, 439717409, 633683677, 779824559, 311910934, 794023712, 307373674, 975777204, 926957112, 252941124, 50785573, 804610625, 936024143, 705328323, 991314868, 528547958, 343660251, 57593422, 505592441, 522268011, 547220080, 712567970, 739742375, 442367986, 703320003, 749052, 862516731, 697482480, 129123574, 590728461, 192436162, 244354341, 828083514, 505729759, 904177423, 345528039, 843301940, 413327598, 932714483, 669800361, 955133641, 489903817, 817074185, 358601003, 483195784, 923673205, 391658391, 283769408, 209311898, 856254367, 242619884, 90972439, 412945641, 552117048, 651886848, 49875272, 31570335, 877251409, 286999934, 161043476, 802271788, 326931455, 273539194, 660160574, 220970713, 674741825, 387720355, 432281800, 387052952, 797462016, 49722665, 436339396, 222114119, 982585945, 360430469, 934968789, 588763803, 882675316, 775036124, 762141334, 933932690, 576682023, 390897809, 631623102, 421385443, 434248004, 448125977, 717347107, 780680535, 313021007, 387921582, 868018649, 598269016, 490296397, 321265565, 371399758, 158087230, 525243790, 750147076, 601180268, 309118558, 784521765, 731221411, 664426633, 340178558, 393941174, 259335550, 76125688, 587457648, 674636782, 123412327, 399726106, 921994469, 828178616, 572432397, 193730690, 330983783, 713409071, 513426450, 159876201, 279435206, 351228360, 19275485, 4304357, 998772866, 838943729, 856735371, 435789540, 516057022, 675194557, 897705543, 699456612, 205806469, 471189932, 141309408, 403507488, 670074850, 805910406, 689293018, 823221446, 505447323, 529813038, 429023104, 920854026, 306871270, 108533993, 999305227, 106501390, 938604520, 965434359, 61692357, 502421129, 302512105, 331560305, 714479111, 50864708, 729153386, 253918335, 924697082, 618477059, 495415637, 829388280, 135160856, 402771852, 363253716, 711462222, 342755251, 708128827, 423711621, 616603415, 802258255, 503073010, 591805583, 38656846, 661322254, 487132366, 445721197, 151427089, 285076788, 972628857, 213289251, 255591922, 721641107, 318923207, 76595837, 718208841, 954871546, 791534258, 365799610, 848691661, 247126248, 461966489, 859010425, 811370238, 472755146, 996242458, 513906148, 711807449, 54620974, 298083624, 420486212, 489082405, 282057687, 781017210, 604954060, 489102895, 430605036, 836465866, 679404718, 615443582, 203079310, 332917684, 51245717, 204650604, 88067932, 742769054, 123904803, 419039294, 830941069, 353198418, 763346293, 197230926, 98376231, 313123934, 245553527, 410841865, 803079104, 526696748, 839866137, 796758677, 287063695, 949846236, 280518386, 50892702, 790234746, 766085814, 835642842, 860820074, 239626025, 893266648, 899558582, 228369429, 951904893, 286558101, 4441901, 706962712, 23363669, 917928297, 239808199, 521156244, 303337947, 710896143, 458430964, 819070982, 569208530, 973490399, 358571557, 514845948, 998041851, 429880334, 151579152, 583697355, 443392308, 200974585, 907679799, 324840308, 799222916, 749782910, 278974195, 116185700, 831724553, 892030259, 155043237, 711052789, 756509318, 154838684, 313367043, 467877714, 690160886, 264195313, 245570771, 987956253, 663900608, 621674438, 657099925, 973484081, 272279171, 424127481, 200940882, 527963458, 134374478, 48090944, 758994160, 54006683, 348725734, 754989485, 732886245, 539068323, 4999465, 804015582, 262085601, 912819551, 401164581, 549972408, 259711981, 156918579, 67819713, 2860541, 544413692, 268687525, 459777126, 278608561, 50958690, 21809282, 936296463, 811239089, 199973616, 761078770, 722316254, 500115719, 679162896, 381163849, 675512751, 299986512, 536323751, 427433484, 561497111, 103699433, 348339397, 217002553, 534934967, 497958696, 379682404, 872329413, 179176950, 548855106, 35799405, 930860742, 315749807, 834344525, 37550344, 208769757, 536872294, 33748932, 37439942, 593306682, 67684710, 196206784, 115351515, 991139841, 114072939, 818240233, 565625601, 625095802, 977022434, 604099737, 565218999, 473646299, 439320491, 816015938, 631013132, 626334419, 186400599, 882151420, 981399434, 66803220, 393353039, 829144641, 462542281, 640433211, 503009605, 606908914, 825420360, 295650246, 342304395, 789033465, 215086700, 855420574, 131296247, 993657577, 87514843, 382009611, 688253913, 221869744, 128733517, 776687996, 735520176, 271400720, 345321372, 539682369, 787331048, 529096126, 148141681, 690262202, 218789225, 372898988, 508926927, 862576544, 624765648, 260694345, 41125454, 754571273, 977829907, 876247028, 525039308, 130712689, 946705074, 399322890, 171775821, 973250829, 17890508, 289475912, 952751767, 359690128, 161935639, 999393894, 465129521, 158354601, 724105866, 215680689, 355851980, 942773758, 98935929, 144803849, 284606955, 414896528, 433503558, 108557301, 42143237, 578031597, 342057903, 201923442, 246782288, 900603515, 383319619, 516229516, 787525200, 758462287, 439931268, 279821553, 573032536, 154025070, 464142181, 998431397, 308974470, 786892252, 126168762, 379370937, 896648525, 909465483, 374834653, 370002361, 47532589, 996819098, 591585621, 973864421, 607526706, 702396132, 196838322, 744929630, 863794782, 902315058, 615206820, 434310129, 528075950, 518089603, 617336853, 36094186, 183245483, 16930329, 745132718, 93601774, 14713868, 845506957, 296106643, 915699119, 927276459, 659101344, 887402252, 659580542, 170726278, 556771164, 337259837, 192352288, 43020394, 162901129, 84417560, 408718049, 65679967, 375209297, 309098306, 779129644, 822837520, 265512127, 328259286, 27935292, 545806242, 514797660, 736882815, 553306784, 387120956, 407207802, 255363472, 819180375, 407385551, 722700999, 38411898, 592379784, 586382632, 271642784, 159017557, 296528475, 491687592, 201786728, 280676076, 678794601, 852635187, 162451953, 414863116, 721311708, 436516355, 1178999, 861766954, 561986646, 629639024, 442286279, 243731837, 929665254, 418386178, 781560318, 541822797, 697817058, 231220914, 891615077, 918384524, 711184425, 939184450, 107310140, 122742854, 832094229, 121529173, 340919545, 945921201, 430030908, 431462707, 942632119, 523166618, 778467777, 786254017, 691364177, 909300008, 766191707, 641488982, 907281837, 727723414, 739436467, 693970169, 44074125, 911030741, 106078522, 878561881, 137711288, 584518700, 159024972, 177096819, 287016287, 516715443, 836844846, 371185033, 16379239, 665482751, 337738038, 772545413, 718816596, 376927706, 648830282, 963097343, 327736411, 762318164, 946543417, 34576269, 560686002, 580268397, 548484296, 427902751, 302815133, 199877298, 966115458, 523889527, 366679991, 170583288, 504438383, 458389772, 873804234, 163457852, 677036288, 522010530, 648962186, 653475565, 353069803, 193472444, 343264989, 884524028, 284690004, 571688077, 925462329, 773892153, 999270592, 143942920, 799256578, 920592757, 115366565, 875458771, 762236727, 860865666, 956443185, 855217228, 356322323, 750283209, 343698327, 904836744, 872445976, 802391322, 849413614, 439316870, 499446666, 382870006, 654701659, 902438931, 301712444, 568513323, 103257806, 794959294, 468969021, 510938210, 309391607, 546747152, 637031744, 57779852, 836056124, 524847918, 288018440, 297107209, 953801745, 836933201, 564579217, 200245564, 761848211, 201661058, 535616489, 434305232, 587552991, 131621621, 285704237, 555418568, 438427205, 305140579, 345026500, 414052839, 377017381, 347437553, 534454741, 633516975, 297241387, 992759648, 273227074, 258396668, 124635619, 771665356, 483459032, 3986571, 448173848, 627286407, 101162590, 656977643, 988789740, 705587064, 712439783, 282580216, 269527473, 174719818, 192450692, 81665048, 827602920, 901957157, 253867285, 971444006, 963946458, 183404941, 808894722, 148512446, 467989853, 860333484, 287576423, 859896385, 576535000, 58275570, 454720632, 482560810, 676131790, 741969582, 856837271, 148273919, 412043906, 589386678, 660034506, 100442320, 211084914, 741722691, 501608998, 905136359, 473674000, 261378343, 308260669, 737252421, 513343871, 303420822, 377680622, 297816455, 192703364, 86180594, 262976151, 470593807, 766221573, 523425597, 18369709, 582586594, 15431546, 238417944, 298878487, 578107427, 286902568, 407691347, 120100474, 919717905, 403173524, 259709695, 563377762, 954103173, 554013203, 740661171, 866702194, 255372010, 290701040, 813319484, 944760258, 62161000, 575581408, 661467622, 681748516, 230522971, 152343446, 186785174, 91074868, 462099824, 847274327, 970169865, 37771633, 133096866, 59317043, 79387510, 373048438, 40350819, 135772408, 221143684, 814993850, 257059509, 710605563, 725466403, 633980993, 796634065, 158064301, 233958291, 805891383, 979293416, 580329628, 787262059, 633314621, 231394192, 675461348, 938708222, 539123600, 813498459, 199103236, 720033974, 842461065, 54453788, 609939687, 846846107, 649699540, 528539586, 256630112, 664780586, 777273222, 480716841, 468197890, 381953298, 819932316, 459032856, 954516687, 61716714, 577057795, 265102803, 43249939, 992221166, 569672702, 230453523, 940752640, 820142267, 149279043, 75276911, 797608117, 259355897, 409225133, 753187712, 48702654, 336722569, 927771529, 123890469, 922897682, 994569163, 589527140, 601278052, 260573311, 720357870, 166711485, 998362029, 450033896, 127827220, 175364305, 680385590, 570143290, 934914880, 594057741, 205405305, 632662725, 916002706, 493909818, 977316382, 999347937, 65938021, 427623801, 43442589, 117081811, 342754821, 419143568, 287965578, 693153874, 781041860, 627247954, 680444978, 812797036, 175025447, 907627796, 996432068, 461847571, 751628028, 915010356, 343108941, 611005078, 183083677, 485926380, 272269316, 293063156, 204409997, 697182210, 529853431, 435410879, 661652009, 785829438, 6341402, 994915770, 359720844, 122316828, 696732072, 348164111, 960123101, 281562239, 636471962, 582329770, 151690646, 236261123, 918408542, 447320894, 75511995, 698871483, 435983619, 390437172, 139390533, 175228271, 562068292, 340638344, 265134365, 871007437, 181889623, 656654194, 588182074, 446073177, 385224938, 317508879, 492002253, 22288029, 716595596, 888505663, 290594241, 472521198, 202468977, 472285703, 675321705, 494308648, 238449968, 518373963, 597435559, 438590785, 899202183, 56119171, 439461682, 315768373, 612818890, 371080469, 547282098, 300606201, 143981703, 199248484, 513787731, 299664997, 223805213, 679201302, 294714474, 647997571, 443401398, 346999732, 395000392, 684692188, 264152919, 256858049, 175948175, 386779384, 352346967, 689434064, 960392355, 818854588, 97428839, 910509047, 88596066, 868588526, 476981223, 53258353, 240257037, 812334135, 980616644, 56043227, 606734079, 443226259, 583138829, 687694044, 137689876, 291439036, 818336807, 704806894, 424891919, 266463815, 719299113, 744006376, 814785471, 135633887, 733177496, 78247204, 751650402, 306450375, 673381582, 562259544, 706266178, 520540233, 889153174, 170644056, 494694193, 424345456, 820916712, 587748270, 922466298, 829471579, 106646698, 573779763, 947124293, 471129852, 286420668, 706139608, 605334642, 341523445, 444439456, 314294864, 794722471, 840709590, 896741938, 6175913, 464950780, 492717917, 601196120, 73460084, 83486540, 393934239, 228808247, 814285361, 641290622, 763575786, 418426888, 991665717, 910234248, 879095686, 216033299, 693452585, 487920739, 991478126, 731776621, 836124411, 983511689, 970119350, 565952492, 260660180, 466379629, 408585797, 150122453, 624533772, 28375586, 86769922, 207964322, 929931104, 83079980, 521791406, 909693144, 964092031, 254630924, 237638256, 151413174, 488120809, 150378657, 51487877, 947028469, 315685109, 715652862, 980635361, 523588016, 44824741, 730017625, 591434610, 701113798, 730103128, 415707599, 101409332, 353876396, 198850418, 665632711, 482693909, 516084758, 162103090, 695144079, 665979495, 590955810, 923775223, 721169338, 883529679, 740595304, 892709399, 950614139, 75297248, 282862842, 564393186, 275473664, 894550957, 825765083, 352110602, 66099804, 153476348, 45403193, 488438243, 556943640, 760339085, 742048164, 297199625, 714328309, 61781913, 627797587, 56510512, 817810275, 713808866, 580908476, 562488369, 487994518, 79825604, 917080314, 955746867, 828527122, 100088772, 451872031, 154726852, 952081214, 846983775, 309451426, 868496750, 606893344, 143942251, 533862662, 246123437, 379830087, 905397028, 638857002, 487279854, 921290830, 655604205, 955731528, 922131916, 335767429, 575939744, 165216627, 856969380, 299267618, 96940553, 329230750, 374215668, 564289494, 710375848, 632804864, 287261323, 240101972, 281434172, 755471750, 969789791, 521449268, 475047117, 418723320, 334261201, 666269923, 117665135, 830418001, 153786364, 881510295, 776763567, 593413455, 23321095, 936216165, 208823522, 334526556, 535057523, 472955044, 965896881, 835426941, 265338622, 654860335, 212658718, 156227112, 225830579, 920841862, 97642954, 279322827, 597071867, 841172676, 422931805, 232809159, 505316937, 967089300, 483484504, 103309439, 122191885, 411098523, 987459320, 540692627, 344270089, 923890182, 756264174, 429282675, 710638310, 260500221, 452307232, 190790846, 703351558, 826353309, 932245433, 458718348, 440869037, 95711352, 961050530, 612430014, 714095832, 838654919, 833686122, 959015882, 617132287, 591759707, 906999256, 933221441, 414681774, 157358069, 346768796, 873559092, 275311548, 901399133, 491666736, 61002846, 311519348, 540064519, 870150750, 981897249, 906716551, 235862751, 229640853, 830463082, 397286167, 692133278, 957481549, 549653033, 440077558, 788977986, 584865906, 287106195, 475247429, 239163926, 26780037, 424774902, 763680185, 798166802, 525596468, 329936229, 464958632, 552335185, 800783620, 863015384, 693588186, 806811423, 164402765, 485026128, 584302578, 339284276, 234443784, 899814044, 62801894, 122047038, 14061882, 192416967, 716937743, 264754244, 804417461, 157549301, 631406999, 499038610, 238484492, 687822551, 443460025, 249466858, 760372310, 141706574, 708815330, 285793087, 886740026, 503870195, 388580988, 315699850, 784007050, 908872184, 826480710, 291748471, 350112169, 934068180, 982291152, 523056729, 868858960, 534263673, 49796801, 506577900, 776837321, 303474624, 594791881, 369776795, 690084556, 48404682, 967451709, 117744449, 745203079, 401720533, 184846091, 435815392, 533235548, 683698742, 61429920, 109751208, 61993444, 594544909, 215582376, 614222383, 39079321, 769042729, 938925663, 701472031, 473374767, 500778991, 615698461, 583252897, 562398639, 59244887, 299947642, 551763428, 168075786, 116343891, 532351958, 762391314, 859096579, 873760453, 87831091, 172714012, 718044495, 65589027, 745796636, 508992133, 344301778, 571924505, 650814952, 687683002, 854407911, 633236124, 58273804, 15004485, 376501697, 536860891, 32201389, 527873894, 872541416, 645762421, 130530668, 773235388, 218130846, 640163770, 125554671, 700800870, 937442264, 280623626, 596093742, 33235938, 487866024, 401145028, 441355449, 965234949, 834844497, 374988036, 674694939, 427550041, 821741851, 121483976, 692554721, 622309477, 202812072, 970361005, 394407121, 499186524, 449148526, 773619312, 870774967, 460168166, 915796113, 614369025, 103288862, 755144645, 577684255, 363840181, 738655687, 195474754, 548639807, 585390587, 672922798, 438204778, 355929949, 736839939, 474433349, 479866518, 676532518, 705156272, 171220251, 79393072, 143835631, 380050591, 138963098, 696201416, 736719187, 750288917, 690561354, 105766936, 763322654, 762652220, 713379299, 191503992, 397094154, 840692497, 648409904, 7792449, 989269389, 277374296, 554530580, 128419401, 682746611, 918027351, 370681349, 217935349, 534943883, 84590635, 842316012, 200860060, 776868523, 571609507, 547755948, 498478911, 139292891, 542338304, 420395549, 92549880, 534257067, 22898025, 455377957, 174717204, 164140555, 849989774, 123620176, 644576441, 414066722, 729138040, 824572432, 947834622, 180464031, 710890653, 472271017, 613674905, 593016128, 871038411, 399191, 190398952, 777478367, 479111441, 248375976, 937647836, 203604353, 489502750, 473073985, 933424578, 702303676, 248754071, 720356513, 745699978, 631072955, 895742857, 779744951, 755545125, 246730262, 280100439, 815866078, 732049361, 329434046, 274732383, 132580788, 320488189, 35518717, 617905349, 559340992, 956823223, 555161611, 632843321, 734661996, 12015986, 778193767, 83346726, 120626162, 245615184, 621589550, 369104929, 738232059, 43491660, 536420941, 978467733, 615686312, 544896973, 738750059, 804556770, 796618719, 287304998, 286273513, 473665279, 748073826, 371210278, 262526552, 182828122, 816957295, 154390876, 801790290, 813098697, 794577011, 80515197, 470278221, 506059236, 436189703, 966918479, 626572719, 245863160, 292184347, 911921762, 773952225, 219100443, 305614933, 740449676, 973335512, 868851964, 576700937, 854547821, 408855037, 578352824, 374199105, 364339430, 415329736, 706182885, 216151965, 654681024, 738362851, 723023314, 385546647, 797520396, 368285767, 907073547, 378686891, 746058190, 469574038, 226396615, 343991409, 855212674, 37069095, 136037335, 512681461, 181537820, 628788994, 154831616, 454888241, 674796279, 997708893, 323160762, 614452030, 886986660, 214366572, 250248939, 838397244, 830171495, 496872500, 470276641, 367104959, 370239443, 459262182, 147657407, 561343399, 613019485, 770594008, 481902937, 839536177, 700971153, 577567232, 498919850, 152535211, 936202494, 217615955, 662842516, 737595672, 418881311, 492201555, 760533546, 592786185, 374367012, 800635234, 552962428, 910501877, 601250324, 221993220, 173553811, 504954057, 163235665, 526210927, 917425152, 94916067, 946711251, 316396976, 642635578, 706873873, 604515209, 105376410, 401438596, 829951653, 933144992, 675313252, 924657052, 588707748, 235916715, 991979999, 562613924, 929048842, 641934737, 312790544, 894788696, 895646083, 482784340, 90672080, 342929734, 548608281, 572932609, 547998283, 558911653, 27209108, 876357712, 462839669, 726714504, 102651069, 327120614, 49479217, 728506248, 382596010, 457480722, 769893166, 764179563, 700251204, 435379075, 636429166, 905778713, 43770334, 679374076, 323322269, 687494366, 998107963, 271564500, 990515627, 308231711, 628837893, 896128917, 843320208, 382870887, 264714357, 85139429, 140348119, 578631147, 354538822, 4048335, 210195764, 629062578, 387641628, 221676559, 347311946, 298561879, 409653590, 106542022, 405292117, 986894746, 747645365, 640572775, 365361789, 839032085, 346573067, 230133271, 850199492, 685088021, 255108698, 201707868, 652329975, 340873078, 579521357, 939530378, 797875742, 173243649, 518461988, 773598598, 167654640, 891350609, 420109056, 241438267, 965409057, 846322747, 255442642, 293168890, 477309059, 214401933, 151575989, 999686802, 671438292, 403217671, 279827496, 773686537, 624924847, 864109687, 498835900, 526181526, 424562823, 370132077, 958021142, 619361621, 689926739, 914945229, 275722006, 451459162, 505418695, 786306709, 788057705, 399418096, 327174521, 995846504, 848399330, 366626143, 892714067, 784665677, 796982979, 963692215, 838644547, 250909301, 215607524, 209425645, 33637024, 487570401, 944090701, 236637806, 261742033, 961465464, 20203639, 943989676, 404364187, 21084007, 937641771, 988076060, 23371151, 544545664, 77781758, 754681749, 67622818, 635418340, 866612061, 140485141, 191154401, 636846662, 190714451, 2452550, 65681144, 196385762, 285441348, 616432652, 105624619, 656991385, 633956222, 430353799, 80240626, 934954835, 80890200, 198959226, 635493068, 819089308, 605896178, 485714928, 241218845, 722625242, 371366260, 792131562, 655871913, 791038563, 190839385, 864979334, 430678910, 847052480, 802288291, 773241783, 993873579, 57439035, 343400372, 368124417, 754096227, 371522658, 975032317, 449630689, 909454111, 690107781, 814417687, 144781229, 115784844, 285248427, 198444196, 789288102, 668831166, 309150763, 443360455, 109485013, 680025273, 62376392, 311141990, 743072586, 667526187, 30578159, 994643860, 74715494, 212887928, 148237342, 760203288, 745330428, 196606693, 987754525, 437758794, 404891190, 937507260, 613065375, 102070911, 15229914, 151328645, 838102532, 236232220, 191519346, 429042201, 478285367, 772631417, 20458334, 940311693, 276518589, 477835738, 246283514, 97074812, 88734161, 92759848, 991820124, 102495961, 314093431, 661353111, 971206438, 812007547, 414036725, 482045967, 154771634, 811610519, 952305795, 801942713, 198903183, 399949626, 353840075, 584403139, 466768740, 947602240, 127701071, 252170247, 211629586, 347497091, 752980204, 558608593, 234034966, 680793786, 434144943, 57958290, 606329832, 353435816, 9006563, 894976813, 295976637, 334004455, 267514398, 656565280, 364751667, 59398178, 455763576, 44453277, 863027875, 477682748, 839601955, 141301828, 711649616, 754187159, 77493080, 766826490, 168228087, 307978046, 621514422, 7206479, 623736142, 597169952, 955865176, 32435835, 34354190, 633256567, 979190122, 788668453, 957222349, 950409696, 864639486, 745587234, 45990883, 553811285, 230963018, 648629578, 615339344, 594159037, 113687207, 482272232, 119558572, 21751453, 742704770, 199786164, 734535653, 605823319, 731709787, 74619403, 538943114, 409357894, 649600862, 253730538, 562013278, 274455824, 517429287, 783469245, 711357188, 749042768, 883933280, 173351592, 686265159, 975352470, 156354564, 485077778, 807096668, 966395511, 782080199, 854068023, 96785181, 745293616, 851404128, 544373979, 680728077, 447380400, 820657423, 267073584, 266317815, 928059589, 637387117, 803875836, 840953589, 175337463, 725246466, 595325250, 7932068, 319641824, 358185802, 444374662, 522445087, 883315649, 438792029, 822661433, 363196247, 109490145, 353379694, 932549278, 911392589, 890158943, 400901370, 278910050, 934345056, 288086163, 447397669, 529673002, 303391581, 642684909, 510436052, 2452068, 783500104, 213898837, 163176819, 935512293, 110894216, 387421793, 689705100, 716631432, 641549776, 216267831, 919877366, 372224659, 873288035, 583939456, 38472254, 904887784, 127864388, 645092081, 822067636, 63285009, 356798095, 459607521, 838805039, 632339124, 1468712, 345603638, 297307149, 894899100, 409565086, 312052073, 351531128, 967631542, 862708378, 4221787, 489024187, 460792097, 425122296, 701036372, 169239436, 494768730, 703596537, 67385173, 25248935, 240309742, 976449435, 715850128, 546273897, 398650009, 604461635, 892550973, 880573467, 357826380, 267726812, 119458518, 130031115, 479147030, 259399620, 713683481, 612300755, 160183579, 40526590, 347305188, 912364449, 974932502, 350439057, 883625829, 56311945, 737304420, 809564853, 159316934, 227438176, 20647206, 736826475, 295440742, 329147913, 96605533, 335614883, 809573801, 192244507, 13358584, 860718084, 770359743, 820901900, 592243826, 452370547, 508411417, 797887629, 50959861, 164955685, 970419576, 464568409, 94330999, 136983671, 414676345, 9144979, 94703430, 483891575, 616654624, 83233019, 545654569, 737001285, 912502644, 80498787, 799357849, 526498057, 506040441, 994825342, 457032474, 707597693, 454376690, 149429459, 565710807, 897185101, 879503398, 481909735, 804884057, 785716323, 217013060, 509816336, 314556963, 861767112, 193288261, 629364344, 491583266, 168127655, 254813330, 780232306, 426954772, 842167237, 274682856, 166632736, 499420123, 839558997, 424382775, 975315411, 938344038, 841052896, 652860952, 900218636, 520999118, 963747491, 643594968, 553093268, 112618230, 735427407, 443546203, 719741168, 258681933, 741408560, 610184494, 81265557, 401012702, 282621574, 143498856, 126869200, 657407790, 24582852, 520490498, 937823245, 852778650, 254141537, 422310951, 477771511, 246330956, 510450387, 162542121, 717534495, 656062648, 139109222, 382246983, 504158742, 756828196, 992001664, 422351855, 40593011, 912911695, 788733754, 568072556, 798263339, 468221402, 604627699, 745571081, 54329265, 224379249, 16978652, 158477961, 866341527, 754286691, 571870407, 61292560, 580928799, 809666583, 653411711, 711680418, 739784545, 461402203, 962552564, 700932188, 755151248, 872691290, 271840409, 144059653, 580569000, 934252118, 947047882, 821841106, 867633537, 57681533, 411543269, 249593245, 151495692, 376176671, 937687912, 400555785, 177861240, 144494917, 268959441, 173539479, 447521749, 191842288, 580573710, 546342650, 134134906, 244680700, 283203045, 498510458, 140316864, 81467865, 873366708, 919734154, 612221827, 119355976, 856832903, 722595998, 512198518, 199039326, 640300177, 516620263, 417863209, 480229147, 956452607, 839727306, 285531294, 36604378, 860114927, 318377287, 418197852, 993840005, 566446195, 975488721, 341189208, 627622333, 73667105, 464333402, 193258587, 166718377, 70390886, 174373372, 838006823, 765809563, 665977461, 187569982, 30626304, 494538736, 949703767, 778590642, 949922871, 946869598, 915027418, 314072286, 624427031, 942500740, 359490187, 81239799, 759086484, 367325823, 161645554, 785936762, 51373534, 326110723, 374272050, 391202444, 876225223, 935860883, 231896403, 671607089, 110891714, 373375991, 445458918, 528993496, 561880223, 450846125, 925988030, 138344035, 997994271, 65031049, 96349637, 660572156, 555040750, 590393181, 322762122, 415009817, 148320367, 158407900, 952772042, 902890867, 551586489, 940862323, 843626195, 962771051, 603844712, 666644326, 374393081, 225191373, 21278118, 57386114, 15140219, 925951430, 46335618, 843157187, 141149602, 64428558, 702979676, 885069899, 529192389, 483243507, 117237608, 714026187, 145750521, 852396971, 37046850, 94767189, 895445330, 799740360, 812901332, 958582623, 184907230, 922115856, 590526681, 703230716, 395789462, 441477394, 759258463, 440258385, 787725935, 291746238, 613189069, 702923233, 377404410, 139677013, 365998506, 961256380, 435969706, 483317906, 158209065, 546566001, 358204651, 853426092, 30055646, 457226199, 358745433, 724856586, 768422809, 330854873, 641213220, 153942009, 324250109, 668924536, 680109154, 93539740, 748750542, 473539826, 622399647, 334242246, 992224325, 200315414, 259639188, 989705347, 402103029, 804780574, 636010559, 708225532, 669232369, 314089962, 507265996, 600357636, 316063262, 116158340, 429456680, 444212202, 438217929, 63128353, 614818178, 692242563, 687965372, 228819513, 510121221, 75637643, 665214406, 397996304, 500153638, 897529117, 915367161, 240130894, 22520695, 276334604, 926866979, 833784214, 835016554, 476286293, 628585804, 410231549, 576603884, 249007509, 839417781, 294019159, 916456143, 175813045, 760308398, 404844998, 68542135, 840809673, 172275336, 103261200, 23025111, 538492775, 513109566, 241547863, 674047362, 679548637, 265080891, 633168424, 126774711, 734752569, 170848240, 497095257, 96371763, 738029873, 758523862, 271415853, 544068378, 154316107, 794368872, 303347802, 635748311, 962265781, 887943502, 516515780, 239200770, 971160216, 773593886, 928853698, 535568036, 492062707, 220549273, 498493675, 701574495, 161915236, 637896528, 313891535, 581291887, 556719290, 382376434, 823465065, 831466080, 500852666, 842344037, 790340698, 21438197, 656656513, 750827842, 377921990, 528448648, 141186589, 728260145, 670905000, 715038227, 342286047, 966812948, 144222298, 381418312, 68520645, 563380281, 415273682, 15968827, 161719865, 879505908, 873922562, 877273358, 580569983, 848449682, 2933244, 749962741, 460763502, 311975615, 439897065, 764334511, 683861148, 8292504, 107872849, 826696138, 692316819, 121112593, 975731494, 335653947, 815347480, 660142649, 43470078, 205605, 282176925, 359873050, 164584845, 884131957, 432446292, 901674386, 651654039, 749098753, 342301452, 706262918, 608352415, 886486860, 491619783, 809670994, 872524327, 104816938, 130964085, 813355555, 329442769, 524781751, 219965172, 927595292, 532647614, 564947160, 998086084, 18937753, 763726301, 683175891, 858516715, 995702899, 745889716, 100792706, 153506115, 76372012, 521483360, 283086731, 89611203, 31617480, 55198557, 57549565, 563808949, 510553989, 391500258, 768943379, 368518150, 221290077, 376202603, 93375738, 750648536, 284354217, 696136947, 906544910, 96760498, 569201202, 259008825, 918587463, 20558580, 499952315, 753891858, 541627501, 487667754, 38885217, 262145767, 278674949, 756776636, 319106163, 923211243, 530026639, 677064147, 565683731, 947684540, 266200076, 663528978, 573292238, 382006151, 335140847, 793845484, 545746510, 187456754, 467016637, 600234337, 187123381, 160403629, 934170495, 912361201, 366042499, 189110624, 33666388, 416863358, 801158790, 829543675, 592334777, 375418405, 683880490, 654654841, 118432309, 521899517, 726161014, 229011746, 297748395, 897545731, 382840394, 629694251, 443021378, 567238633, 288873026, 560698793, 327517991, 886367713, 378003544, 383172707, 896538270, 9976827, 115073944, 661040601, 1376214, 430212374, 439554922, 770063953, 781526973, 350187526, 316400295, 933378979, 173428392, 262426035, 814450884, 488592999, 802921356, 221797502, 880801229, 603392271, 670842584, 65877096, 340617684, 923083754, 600896996, 500098312, 426140053, 393785614, 257907088, 828850091, 818442606, 963762160, 410929983, 811570332, 508120875, 405539468, 100437182, 744662122, 153380559, 864870412, 58466468, 337220478, 738511746, 437008022, 956113934, 348852466, 312113653, 486834025, 128203511, 779770707, 524093989, 905862155, 348270395, 124027670, 915430171, 869326758, 533964402, 384214658, 12824386, 857541496, 893583526, 533843669, 712768911, 585056314, 170458971, 347630829, 365297078, 245687659, 725292124, 570426642, 502767304, 312821347, 684515905, 897139355, 331215829, 456806754, 979563309, 267837444, 32074166, 953439926, 179433136, 337659, 258923251, 751468537, 49261334, 213184347, 149833786, 963697446, 417230731, 382390474, 764915020, 530971612, 121578345, 366107679, 455485684, 232745, 442778923, 860910116, 279080880, 813505583, 264563813, 665952988, 717083102, 882762138, 510974399, 104640958, 952493644, 799244598, 330081359, 805585320, 791298005, 952554773, 481269664, 923096590, 83426659, 693545303, 800841792, 971740416, 908456240, 67985876, 384318581, 260427096, 237090946, 496763022, 573031847, 412631414, 418431934, 51781292, 161496048, 449227243, 496618823, 355104383, 174734589, 238432978, 285620255, 866037537, 291950751, 757735661, 159768, 721945339, 521974809, 207984283, 653131249, 431783819, 9723667, 680998321, 823036050, 900965529, 110295829, 830246963, 855896506, 218850696, 494427170, 972685249, 837918661, 53344095, 689279273, 224556043, 473558953, 862935210, 674853974, 910603311, 538269987, 399910239, 18796429, 431634118, 91449448, 921583915, 794506749, 653538576, 117651110, 418552700, 85476135, 147755682, 281669879, 670747565, 823145331, 308077421, 511523823, 598235260, 412239799, 88131960, 884781840, 186110047, 375904515, 849310765, 868341235, 130290395, 315113507, 892225624, 534644521, 343073463, 451976860, 497962034, 408165227, 441903747, 573040987, 86977914, 123956782, 396610856, 931558273, 688119548, 790976508, 245573275, 291601581, 656248525, 298008695, 786772492, 613390146, 847099822, 974568212, 321246068, 240564386, 647928424, 847602720, 949016252, 338878002, 75634749, 492525584, 103141922, 998253559, 746996486, 169054144, 339763405, 642506066, 354178723, 522517737, 787172146, 733198521, 457606147, 777309176, 516452955, 234821649, 889419759, 601982684, 608441910, 738804935, 614207646, 716471846, 348406862, 200592107, 707019708, 624100061, 840281521, 458414150, 998086575, 227248965, 852880251, 821086190, 48595945, 399426074, 7927466, 538210883, 990327560, 490188897, 50689428, 940800745, 106269393, 895311027, 637955384, 961963731, 583068745, 351290155, 518841721, 124895063, 94346160, 118250393, 123751013, 567095575, 182110409, 222365465, 543598211, 511953088, 787948569, 310687219, 812023653, 606039563, 502728488, 222671322, 156224459, 154937941, 861139292, 782655294, 232746794, 821776358, 191623848, 34339665, 882976489, 772287636, 544615473, 597248991, 347417269, 260472775, 720535127, 498067533, 473599533, 819712165, 803123921, 114629441, 446524563, 407595221, 899654148, 155165141, 182572343, 582476810, 803824913, 96917304, 608705695, 32018385, 566127628, 29114836, 708600493, 260536221, 281263548, 537873888, 386393177, 681078981, 220181334, 787690871, 207665827, 267407734, 549721932, 531030630, 692173619, 984961476, 977468830, 351793322, 588199816, 479107548, 238954636, 896858407, 596981637, 903434525, 858801302, 821848353, 617487598, 132090093, 817975598, 772685445, 480303585, 488252276, 864278074, 869660804, 18446466, 410190665, 705905443, 816452212, 722333019, 114718899, 248433458, 621374398, 822690501, 344557981, 880791743, 782215487, 935446963, 189469762, 231860929, 68074409, 274422827, 291380196, 201378492, 311604057, 636679097, 674422385, 718934794, 80968584, 782344741, 386682386, 541978459, 600129945, 26473624, 356799255, 49310159, 549277166, 502769990, 735659307, 479328110, 147247989, 923591939, 408962240, 895378714, 458770547, 154366063, 595643079, 47154528, 649872477, 890566476, 870492616, 119349121, 349463332, 566058561, 392226432, 789726112, 444290190, 207795358, 365104680, 389859919, 483121886, 486461764, 612641460, 98575684, 250052760, 423985518, 228653970, 499410570, 854026828, 40881674, 452029559, 712098956, 620405309, 653515278, 98265128, 379052215, 408101064, 429179679, 565599961, 770055062, 546746128, 615313917, 286206970, 885340228, 924356842, 834804395, 535306426, 13996192, 595784505, 311460842, 812547195, 396454669, 347068147, 538898290, 30666219, 310822470, 552167945, 693377729, 648777736, 606809643, 416950238, 39116275, 994647640, 743743800, 547157237, 827393521, 970255773, 196340923, 912530028, 452604715, 269458809, 239757323, 229221335, 719808894, 846619707, 430449199, 371588858, 981649651, 687224424, 417070380, 5217890, 380904699, 229346395, 783590248, 105866654, 44850498, 797492877, 219508540, 326675470, 466150584, 465179336, 839443964, 586047361, 491757433, 440637715, 739189904, 609185153, 820658353, 297669685, 654572171, 678048029, 692327674, 773062573, 841516965, 454282739, 276275203, 589208831, 710851411, 220379156, 354647533, 366380643, 122998295, 812479826, 549098577, 604215178, 209814372, 914072055, 701935750, 875611418, 983205652, 596758087, 995053382, 948625690, 927681121, 465623278, 688864536, 226910793, 255175729, 34430623, 525424258, 393908664, 212282245, 64943964, 586190407, 266612941, 562803300, 689504719, 331042656, 410729346, 192705866, 885904105, 496045229, 78066311, 117923444, 642202124, 381229161, 823133535, 126034898, 914586881, 186561395, 565832678, 991932322, 499218579, 681919284, 491977898, 907078347, 283751704, 985884895, 967599307, 982855881, 22200354, 356593169, 645895361, 806316211, 482048817, 189490694, 550868249, 627232091, 738506602, 277389714, 900356220, 965465105, 642320204, 362466666, 906987727, 363216965, 742610788, 23875957, 533460242, 14477543, 336332778, 878604456, 485569359, 751912859, 538209978, 365935489, 769198444, 998031693, 328513096, 84148461, 319795204, 919112878, 261810429, 49989421, 188097625, 288377556, 165184798, 421486265, 436824984, 633858855, 267779772, 562760533, 16550226, 549205106, 276460750, 319480434, 855854126, 250497334, 813668944, 69405367, 953129364, 16664304, 691032420, 471297948, 339437920, 13902324, 605685687, 513155004, 830612912, 883389377, 876208357, 510861580, 893923786, 557222757, 983249811, 692201327, 270621964, 556158895, 315328540, 396380967, 580366028, 468223727, 63813728, 509272947, 566063995, 730371153, 775496743, 382960841, 235493609, 646046593, 948954801, 92908437, 291004803, 28454485, 913463518, 790740450, 182435888, 487147985, 421501634, 878007683, 460419315, 372962212, 624329582, 420504403, 150682114, 511386944, 629711016, 187031405, 350582580, 206440111, 227579959, 428276338, 727425908, 216702924, 968952334, 519584624, 50209217, 117928222, 996291318, 960158891, 521653959, 223107533, 143139910, 541790350, 407657678, 367068437, 559272817, 872192817, 397274366, 52845081, 199452570, 653984040, 227275544, 612505797, 491445531, 807283331, 110195359, 291393495, 681101683, 129576104, 492923964, 634780850, 192970498, 795300869, 287208728, 763265829, 852166970, 335304293, 179947098, 695272343, 120160302, 410302888, 831918772, 634181891, 170175529, 836062086, 199106104, 790204538, 899386796, 2306211, 260657160, 6944574, 192340118, 964882408, 104726379, 531278451, 788548997, 287376619, 463520714, 834258352, 963361740, 792281980, 621104506, 409176018, 286814982, 124381367, 450924531, 840362209, 918152482, 941738740, 696163934, 357543841, 375179419, 879236908, 838815128, 707150851, 13000434, 657219812, 896184373, 410799321, 254041464, 61276274, 963239117, 50420946, 156965280, 601428529, 52929091, 716428147, 609200529, 554011147, 543502765, 493577659, 78280222, 490380279, 950352396, 326849010, 777647061, 414951598, 976933357, 177811822, 642568524, 618400882, 4046329, 954193571, 959123384, 349154524, 454878775, 521535202, 685079986, 472853312, 440566840, 320525820, 490590934, 429953333, 370578556, 222823637, 125591633, 518683019, 122210378, 277250220, 308348652, 357575120, 58058720, 371840425, 519156901, 741623454, 484389517, 999979426, 149825589, 513275019, 517963637, 455117064, 60023032, 108110138, 282583854, 100625418, 609922080, 602279293, 361227197, 337780166, 258463150, 237433997, 755541788, 440633712, 667829898, 520871625, 549991751, 52837102, 698200506, 800480307, 349216414, 749890541, 368355506, 217943087, 800718553, 2959189, 98495595, 624570480, 205793900, 306543657, 260482010, 429241576, 468202902, 640322090, 821502635, 190223082, 969660404, 956313794, 90029744, 776516312, 663207192, 877721263, 486162291, 642871749, 756548011, 397231330, 211235169, 491834110, 737338451, 111630968, 734494753, 100247775, 601271560, 424252792, 993874956, 246735618, 235016229, 780959680, 49920453, 81242087, 336197488, 46739559, 72173474, 30937988, 798252414, 280870873, 485953609, 706493530, 937364318, 299429452, 150415622, 461289952, 120932482, 206184422, 974467711, 906681768, 543315717, 367055390, 32193065, 157168728, 696680991, 945470820, 692998586, 729070143, 91810378, 41430493, 113979681, 554239482, 652653691, 708044816, 150752809, 856798119, 874327728, 514300169, 936081418, 188121884, 577406915, 124387665, 778249932, 620911393, 486629438, 768917722, 482081260, 146096353, 919824841, 869903632, 830890695, 635695974, 379445396, 633588634, 419540921, 941021315, 145821830, 156137233, 773844429, 842913593, 90163063, 841202107, 782564079, 217967540, 517341231, 352290740, 367604639, 561116435, 821248015, 244148842, 576010686, 327592162, 127943208, 20653178, 238770147, 116403344, 829611187, 873785751, 211788006, 397387810, 207096443, 501899762, 568760900, 542299211, 204828811, 755485223, 500927972, 406403126, 684999797, 104293639, 856314901, 283623929, 205300533, 587623482, 87558509, 788022713, 981110289, 377877650, 108804551, 140527476, 717063482, 323899426, 309930879, 103673047, 711000425, 768468621, 217684134, 948727042, 493584095, 763833645, 126237106, 187402847, 941111956, 510630299, 551222355, 971187624, 420174995, 55728558, 992689907, 536040511, 775829268, 393938242, 784381350, 512360303, 184531923, 338013727, 541871789, 715223202, 414736566, 848369308, 157690982, 439723507, 137212142, 821296177, 457326783, 177535554, 880235950, 702560221, 131772177, 897632616, 238071357, 865954645, 136661367, 868425002, 595364595, 364492853, 410748516, 23620486, 797154329, 38195027, 968988967, 977640090, 370894268, 107037074, 503337843, 827141652, 960963541, 481726630, 812294031, 618584284, 835403834, 806332040, 226422629, 269497427, 362761982, 756455644, 429275808, 718851443, 784165307, 88137399, 376338729, 449027318, 865176641, 58615597, 314146516, 233097736, 682800090, 985435713, 475772500, 710905425, 833395336, 33326755, 760752639, 219055682, 752944299, 926227329, 881770688, 379003430, 384903948, 438428386, 793477160, 488580922, 312295223, 594381371, 425851400, 657273500, 753014353, 701724814, 134368644, 218524169, 461564927, 412531485, 274445407, 529874449, 887024990, 615402004, 50282401, 294769152, 339441127, 746274339, 879518605, 618824549, 298441905, 312499555, 387648213, 520818137, 739253936, 626874234, 585033942, 135919525, 543838987, 263582901, 250769586, 560248378, 596039331, 779558128, 835975183, 704525381, 149609245, 981553345, 993072674, 570082286, 259470053, 603658908, 723244229, 151138275, 442681794, 306171003, 663818984, 586159628, 613983326, 280783242, 191987933, 973623946, 680793175, 234107382, 940472371, 326049458, 627193409, 113913392, 629223251, 47777033, 245043, 996830701, 614955710, 520566934, 842689609, 924052163, 276899044, 830570275, 19011674, 502291744, 36707905, 117617134, 161175155, 496087486, 483057730, 525034182, 20761697, 956747859, 816767526, 385901577, 913839340, 22024799, 421698842, 164188514, 843744414, 662160687, 817584121, 295442071, 882058102, 868964577, 275036126, 214212771, 739542573, 625384606, 128643268, 907698340, 427305156, 422101613, 329923711, 424855536, 354741513, 848435351, 704151706, 451179717, 233934086, 405443156, 16694297, 855400196, 783515507, 498318655, 964655296, 299303565, 397261968, 520069747, 689576291, 756774446, 878208779, 662366957, 37210364, 333917203, 361791519, 730491638, 181980761, 549043086, 788984727, 843335630, 557771649, 157452611, 721320900, 118322989, 954694851, 164676287, 221062004, 658619923, 598283288, 784313299, 833988250, 208065737, 764816021, 180327382, 265572096, 761658654, 863214027, 106279028, 158709020, 25477440, 941675929, 808414128, 436055768, 999507170, 92544296, 85024576, 385409467, 26177231, 190508335, 711449051, 544085237, 773092606, 946031057, 9147137, 901986310, 492508593, 24430040, 719007675, 156331773, 681066184, 259135457, 466115244, 914616588, 179668747, 135106304, 444578854, 329289695, 543380255, 832512051, 830300638, 742532305, 693178321, 362654818, 454325430, 85179909, 771373308, 768347313, 283718289, 781332990, 842520425, 294971944, 628138743, 48418347, 714271802, 993018547, 290133045, 760392693, 380855177, 77328480, 541276022, 643860528, 24887083, 856069018, 995174002, 557056572, 412190044, 621050154, 850705083, 325890950, 913981241, 161619560, 307647676, 377472342, 348847820, 715659266, 563717105, 213179093, 219841309, 864014093, 619960943, 779025081, 669197022, 105200758, 1712610, 578611124, 585892920, 240968257, 617956629, 971660499, 145551811, 919453138, 841663618, 318176871, 280447817, 480586488, 811756392, 901940040, 306589835, 36245769, 268212776, 648047806, 122321765, 553401625, 973126334, 819217528, 460265058, 509159510, 982124813, 545814618, 136038933, 973778858, 876289699, 718127074, 432149555, 114446610, 819026475, 856134517, 173862503, 819184307, 383449933, 564466685, 167659921, 42228039, 380884469, 644201406, 845860713, 13746872, 248902909, 405704880, 491774951, 308841684, 247135843, 760455084, 684061597, 659647924, 906381871, 686900054, 944946583, 265007391, 697489446, 850929243, 650703236, 170322349, 826356374, 490477120, 877136493, 629198072, 170969520, 601766041, 108306511, 308526160, 610300013, 956025657, 674914614, 989371530, 724152922, 406752407, 561621282, 957401359, 608038888, 779638689, 579405511, 830226719, 1361716, 155339681, 791116098, 661990103, 942179664, 378703473, 294198979, 197619733, 460723542, 650115072, 541792500, 19439547, 989458207, 270591328, 82642802, 320491878, 15944256, 572741035, 938614036, 533658593, 120880260, 389804785, 302677665, 833314604, 174531212, 739888957, 246146934, 223348808, 290614989, 533264548, 332310647, 249203043, 596895552, 185285905, 917742306, 101416699, 773274855, 125834445, 970722613, 864933252, 299901189, 744450222, 380608088, 965652699, 756424801, 307174582, 746136002, 233676301, 855479540, 128403306, 286563154, 544287400, 338212098, 994233201, 98702645, 852780946, 491953787, 939544884, 536476775, 55977326, 946477867, 272803237, 51009976, 596296269, 800007909, 846179116, 751715832, 867682762, 500240735, 734219971, 367690914, 634525297, 916585004, 625334193, 474705578, 591768934, 730284315, 977266647, 454416091, 209679072, 943607119, 161045671, 589979405, 452858721, 478161800, 164998904, 361540760, 876419452, 926533639, 960718316, 145132051, 679832182, 323074592, 126211130, 785965463, 901605177, 423569508, 543209649, 340975508, 687924899, 366904522, 289934338, 440559661, 746890450, 329842498, 649834424, 246537112, 337877716, 637221436, 333924343, 670371206, 769618090, 658259270, 769424175, 705753403, 42053232, 848244068, 821735380, 198954534, 714751261, 714175317, 938863051, 411775358, 560041747, 750770452, 251886139, 404673499, 872686658, 937234361, 188846632, 460904175, 586901741, 986646915, 19227211, 565389539, 389129850, 616904688, 253188719, 91158905, 796557200, 578165454, 310326402, 621071443, 631273376, 430117655, 23839794, 868764425, 763736286, 592750275, 756813327, 917766214, 634322729, 8189203, 411926204, 928296127, 74638292, 48275083, 795782438, 964837334, 523828969, 350204143, 847261555, 145939545, 361811987, 591602819, 413204936, 595383384, 503824436, 356590613, 44735604, 213627169, 439524404, 192624446, 961544489, 213949769, 411950078, 769314014, 635639724, 733779946, 141894335, 153130877, 218877740, 812514690, 299348373, 318174564, 672150864, 842185365, 366482461, 489119415, 856227392, 79127334, 448142449, 331040612, 601460194, 199163389, 329351572, 379080992, 931492957, 885448222, 414607879, 9865567, 441840607, 543632852, 993953541, 551355779, 557116200, 548554295, 164515601, 339348860, 697664406, 940935064, 963633352, 131440812, 697837125, 466779188, 980445145, 953032009, 509245392, 306677059, 880499684, 65365690, 322524642, 830131893, 45941680, 616660823, 998493429, 672409648, 646310056, 434597813, 492119412, 715597754, 136208747, 979973665, 825355440, 12636845, 448719488, 123177503, 340723982, 661721726, 16979030, 362566039, 526578106, 591268603, 772909969, 864933823, 687225308, 989726966, 936782861, 86862427, 79493654, 739307914, 867459947, 114315652, 665227881, 277039228, 325101302, 610736783, 386422037, 799900399, 343517507, 162765339, 744348348, 731899517, 521479840, 222343874, 549465030, 487944090, 726596325, 208489028, 968636465, 429354682, 704680156, 785126779, 592441634, 28213188, 131056651, 309993619, 187007152, 504679453, 750708112, 932982076, 164207432, 426942136, 635420477, 406843445, 101269158, 643304709, 441221306, 426391481, 655107293, 959736794, 760035059, 312166929, 456623159, 624148732, 159385433, 986596260, 953777007, 557448155, 188859353, 816258821, 749671646, 505459063, 123363884, 572735513, 96965693, 337133156, 43384706, 924855384, 77008918, 654640105, 263460298, 798903626, 858095101, 74233749, 745723065, 398989212, 937575734, 520579152, 319590705, 722949888, 438546210, 549296243, 48860621, 51197155, 875513367, 954957279, 146383933, 103146233, 785585212, 815508657, 216863371, 840307540, 922870734, 867343285, 579770621, 450250038, 490164571, 991389703, 641703796, 407265229, 921228637, 551625845, 523428615, 796169792, 147130299, 360140334, 785603002, 970625185, 267182551, 364112366, 993391772, 530670478, 65901199, 360230933, 406505087, 608658428, 104822226, 448937658, 930715535, 698528166, 244292348, 441451548, 947154800, 701064371, 658946533, 609794881, 909422781, 559408081, 989998809, 295505073, 760871442, 175400483, 820622616, 738488630, 276147133, 20488681, 891039647, 629475424, 251632146, 263505424, 242423762, 368640091, 223205437, 470907878, 884550018, 340978535, 352285015, 671974514, 277374711, 868506412, 705019112, 900040069, 940660371, 504054398, 772706266, 662283657, 712929266, 163869271, 227327409, 324866533, 132639465, 747834951, 187004990, 882372377, 556791382, 937859710, 314456839, 425305753, 948288934, 851804917, 576973905, 205802083, 279450197, 30416676, 715932020, 696186556, 942011903, 252031837, 918987810, 394695440, 898698400, 300689394, 673951568, 98226237, 230600709, 424006781, 436268414, 114047805, 838517157, 434354992, 450448581, 855931897, 477926696, 884544112, 305135953, 361354704, 242539185, 726194826, 60219042, 980171883, 555408966, 30370764, 156736082, 907711360, 380709729, 901022114, 926595680, 355880106, 559098416, 486834314, 570385782, 636313766, 800078883, 541015939, 675825003, 390227193, 111226425, 909952193, 796977256, 557949376, 755834216, 615545335, 872811530, 939644280, 574345566, 912914538, 719202877, 982849568, 34756910, 820404397, 526747196, 775449939, 339607073, 461570893, 462102393, 358172719, 711115398, 379053612, 419672390, 974558320, 948550169, 427081534, 998301320, 91150345, 797911924, 108013225, 761621193, 305673826, 171959362, 610391906, 646042937, 180881983, 656952004, 47181714, 511917547, 461362063, 570420510, 108669174, 788448614, 207527329, 507481344, 302304025, 195545006, 82520388, 794214073, 753653964, 792126992, 110174412, 660801647, 719371486, 521703890, 909061821, 50038249, 842772780, 154140893, 152299512, 258872363, 593028043, 600764414, 613346181, 673152124, 927938011, 767329378, 629405821, 269327467, 796527314, 652295758, 699864342, 634738628, 983842475, 126081053, 651491916, 699642801, 748464326, 957903030, 775421332, 982620126, 435130275, 635980195, 41160443, 909353153, 615823951, 692774949, 344163480, 519625243, 300195901, 512064480, 826868890, 54974031, 613490168, 848575837, 686507571, 922736368, 744816277, 276079266, 296079636, 442189600, 189346955, 590520268, 621794822, 944089615, 891680113, 513565007, 832811717, 617561768, 156693609, 467613533, 558492596, 104578300, 553813186, 34518498, 201190063, 468360317, 376544087, 746833394, 816112070, 499988634, 190037094, 470342488, 849528371, 497721043, 940868929, 860706981, 230913132, 979773257, 422037593, 145853987, 561107608, 381983232, 571480783, 712399158, 932757900, 495440318, 28402301, 138853759, 22651967, 808111315, 429361799, 961025254, 782688443, 221524571, 172358431, 294422605, 217493096, 172678090, 992936808, 173799229, 259245794, 256805505, 615177219, 814190202, 806180639, 979024670, 132060056, 20556529, 117784372, 233642894, 545939742, 115096281, 209682224, 583594200, 255424880, 59717067, 274549927, 131666471, 633151990, 139467571, 983486044, 212068536, 407702327, 406662561, 314170473, 609057381, 204806350, 380489188, 959983080, 98731331, 28572301, 954227442, 474221509, 444602218, 579053013, 164651006, 961369079, 660210294, 181310201, 497708860, 972787285, 853777818, 367213993, 104217037, 899288873, 372341999, 596478806, 6876653, 388067470, 429736422, 106844395, 362595910, 262696474, 802106511, 524369152, 117469657, 351611813, 814708269, 277636878, 325567566, 696721191, 675842861, 592085245, 754151818, 138074933, 588351872, 260247399, 393927098, 20455095, 352664708, 778597162, 143996345, 15491096, 864241300, 711934825, 205387306, 796390747, 175736912, 213977265, 72411407, 843348613, 709882970, 549465453, 515621888, 189591920, 759774136, 535241566, 803932232, 947444688, 964271771, 889230443, 230319887, 184270474, 315665633, 826674530, 834906030, 954634405, 446545369, 944039496, 122453816, 643895199, 760516931, 142662424, 202068401, 243294111, 723160711, 731647249, 847666020, 902006440, 287034562, 415893500, 364947651, 461710160, 930878122, 107338839, 43291915, 472926475, 744616403, 144869463, 31761987, 891705275, 771266725, 434000439, 200214025, 563782106, 693324886, 991874726, 926265523, 891130057, 305592562, 301308076, 182212263, 968207952, 629700422, 279005368, 445227561, 839448745, 664567249, 453822222, 364909984, 748102661, 807240643, 180402129, 213194540, 239965833, 222183498, 936944942, 776206955, 554128876, 661858630, 457861821, 28167338, 369608636, 416303540, 483894168, 518428140, 549690892, 995100323, 476926984, 899627863, 608069000, 669675651, 547840593, 520804536, 599919776, 415877640, 222262397, 807375798, 958965408, 182328057, 101760711, 638006756, 395734780, 907810865, 485855980, 672239160, 165784139, 884678747, 342706651, 645021880, 961669568, 549194915, 419657253, 630710378, 261300033, 980465445, 959726180, 88558392, 881224540, 930280702, 300540117, 746905972, 954847387, 608502263, 372403145, 35289151, 723330398, 756035326, 368928464, 214197040, 247319518, 581888560, 620896055, 144445075, 38609320, 525102325, 586259224, 182875124, 42800660, 630811607, 218705081, 987364233, 807310512, 399591623, 200987322, 464006531, 551321492, 743570043, 76648754, 785780462, 427986642, 516233167, 267484932, 676309418, 628475898, 998835512, 380313020, 824066439, 599943429, 362322164, 824883466, 805212089, 434294925, 601587028, 788326671, 458821388, 413887434, 743745737, 837917638, 159394787, 329235459, 357331175, 321043898, 794117050, 317808246, 139649744, 981486398, 879106055, 609280062, 515104245, 505762842, 556022671, 160931189, 489195583, 140240800, 183607619, 98905870, 556334596, 863614356, 226175834, 707859522, 295191893, 38646451, 68354487, 296224209, 627787628, 374931585, 413149707, 437723717, 966711601, 323592472, 671690963, 273987660, 791754087, 309814027, 853663379, 81566561, 552819121, 149702555, 368301927, 862604187, 402838623, 349284169, 747205580, 484053083, 71822118, 695198028, 375917943, 106664549, 605851767, 487555504, 970836060, 478542705, 799525831, 136831595, 510820288, 903503748, 812869855, 286582540, 611016794, 91110357, 797152280, 2938279, 47757710, 23104934, 575552013, 694761277, 744456229, 687306414, 321265239, 716796402, 155116265, 189880509, 307435632, 403284599, 917690937, 38193593, 861462088, 811415080, 772051082, 590342491, 720430355, 710521098, 694622684, 273921236, 172884934, 715260063, 347314263, 874898591, 21324035, 895832717, 332386506, 594343913, 790550403, 693002375, 77932346, 205045702, 444905923, 152536119, 174660388, 933795101, 384520548, 591200622, 378629516, 87521165, 125641881, 787625626, 310431981, 849752910, 217591906, 92841760, 450952130, 703448128, 233180580, 343539270, 88577582, 743180295, 447999661, 544877296, 2395745, 693529895, 712162349, 704388082, 418185385, 709589780, 381228772, 909714420, 463839344, 875533097, 71732290, 624235240, 234328455, 849131331, 620029542, 20744961, 39425396, 651298430, 728366276, 340304243, 654092523, 341137214, 576926536, 166850192, 767342380, 927285204, 886982387, 856028395, 868826684, 349744492, 731817101, 155717045, 217098133, 421409116, 241204741, 379033908, 104109596, 557413457, 854816434, 848170611, 767150303, 169283972, 65693602, 542915213, 618194088, 754400888, 899211639, 736481990, 663909863, 52967659, 839603181, 811539937, 658428501, 848013867, 478006369, 637470612, 909331631, 610103968, 12784129, 574661650, 84886174, 801660168, 134928101, 672340358, 589576309, 862590747, 795265671, 293562901, 806276142, 17435055, 468195676, 32829469, 23259558, 152186930, 331510298, 303994497, 954716255, 489713692, 993799788, 149762880, 929889707, 625384897, 295633632, 28999372, 972435607, 811121924, 492650125, 475237521, 929433721, 20696408, 81608107, 727687020, 906564263, 359576693, 314985550, 676528890, 540594949, 398734549, 431913760, 783648331, 621672656, 670597001, 292909422, 477931563, 23977796, 489983524, 364506731, 649088787, 122893686, 449147509, 975830640, 960687309, 44034244, 43989281, 383926375, 386379940, 559437593, 322418379, 956229266, 14597367, 186957848, 76807179, 967210433, 807246467, 871361327, 269375564, 976004845, 519056403, 451583444, 748328502, 754692349, 864027745, 358508997, 247804975, 272215318, 2949372, 542772065, 556821547, 679288007, 526296936, 903773010, 831617071, 120430601, 286042570, 563012674, 569160163, 755157617, 217152111, 419280484, 666439282, 179625075, 532497264, 349355241, 984017703, 344036363, 582920899, 372188908, 18413440, 552541710, 732836734, 805555667, 330716090, 615031046, 144718861, 892064309, 627203728, 78036906, 230708085, 137578195, 905229731, 986895209, 86896474, 388949455, 772135168, 673503886, 632985467, 765631833, 421880375, 885007297, 839099759, 123686965, 772645858, 32367062, 376382608, 500710485, 325497209, 496539180, 310554115, 511574991, 661626656, 834671442, 63380510, 188906442, 804579401, 266149788, 160857338, 97152706, 709421166, 923246661, 455559695, 665538924, 260625800, 42814107, 407074280, 406817579, 151990798, 598866318, 918725392, 502753028, 606221713, 473905485, 351242321, 550196055, 123714281, 443750308, 226831297, 348247174, 251706539, 789196729, 883204548, 934796182, 260116666, 869094784, 781845297, 900261430, 959656266, 595222161, 950826166, 753410604, 569311779, 437721562, 732633234, 453250445, 750692612, 725533101, 385305998, 881471255, 841346732, 720748827, 448519264, 489730810, 663281417, 936270698, 761968532, 662960019, 518934522, 433996149, 486169707, 919089634, 207976247, 78111422, 540142208, 572193855, 23104356, 554123773, 877099912, 764626475, 61456369, 527532467, 955766234, 779672878, 886198689, 307317019, 696354706, 923472889, 462076432, 613506898, 378354713, 783073866, 41087837, 676355157, 353123302, 531897793, 417537047, 988693717, 7275835, 77328185, 293573892, 993252209, 116996457, 373086841, 308178701, 733331568, 992591110, 242779561, 203509859, 476261734, 999597008, 273797533, 822634593, 552598053, 994659564, 359155586, 747471188, 514021673, 587098634, 892796682, 513032552, 644489503, 339320090, 690270924, 484083341, 925719610, 33963532, 775484531, 574721029, 847191628, 470495603, 51266344, 544804399, 182828263, 222246885, 372521960, 381780972, 886950140, 214623751, 822949870, 357654972, 630625377, 781440297, 89704126, 365115655, 685712049, 327579995, 889093459, 97781325, 4350643, 329573955, 910578974, 833884836, 90226186, 659939025, 110795371, 41955382, 928225307, 865047566, 368563131, 54801868, 579569341, 66500442, 879297527, 957499760, 744032981, 440361632, 286074104, 132728526, 70931152, 388753483, 159255226, 209954369, 998598349, 600097199, 246707640, 730218136, 889332451, 775007140, 564750240, 932499271, 627956961, 672570011, 645056753, 423274049, 221948232, 548545387, 98837430, 304995353, 58146606, 766560950, 8941493, 88146726, 120376263, 676594427, 262392681, 751613579, 111449261, 180271061, 312305143, 631526433, 683494606, 337406597, 907142075, 373333560, 381068233, 452972607, 907384064, 556575606, 170850405, 368852565, 883419250, 727892126, 782368977, 381696399, 110122627, 746043533, 965037006, 718073062, 468125278, 950138947, 780626085, 453798943, 149239858, 578492203, 355228552, 874960073, 798965884, 975757270, 898046008, 660904098, 302499909, 148566166, 236066354, 537626618, 18032354, 288207573, 763536434, 181189101, 45031057, 123701508, 325381776, 928705267, 469482652, 735677431, 700460614, 316567525, 192510307, 915814044, 557778604, 56283675, 275895756, 882763240, 82996600, 664713092, 397330704, 839655699, 578466419, 635568203, 912146694, 37006807, 479340476, 684007731, 987790770, 206965980, 718612929, 49362501, 924078935, 379271501, 422410370, 601018013, 504186323, 118120816, 815677643, 933710931, 193416441, 564765061, 501425477, 717020093, 401603461, 370633918, 848644617, 274299680, 530731761, 395283410, 646428403, 751502020, 620124685, 812072995, 683975384, 315919855, 227323123, 423755272, 650350608, 339138875, 920388511, 387436177, 358644487, 641873496, 878806278, 4571152, 87468319, 415431482, 28029816, 951459671, 209620232, 291311561, 235485249, 690129781, 248488813, 359982685, 259879562, 689220446, 641952545, 132135912, 358814514, 894359978, 361626126, 608162399, 557865951, 95857732, 376407364, 894693541, 760415825, 800394874, 70210330, 380597843, 792608353, 291236798, 947363608, 466262826, 328650754, 301778238, 979436324, 728153712, 411211209, 906659540, 346544208, 91162010, 842409192, 965270253, 586918572, 476418934, 22828546, 816899457, 50439608, 324279020, 617892336, 311740134, 334899416, 560869137, 430869790, 369305518, 732323064, 28855133, 253375156, 888398706, 804182035, 728223411, 177820769, 441317726, 587271697, 880008679, 384472, 888586781, 200136805, 525764481, 190751604, 361703007, 22721373, 675758072, 433047965, 794283010, 624773645, 3806286, 200017127, 672189469, 36508867, 349181022, 654244279, 316739431, 244364429, 93619580, 583136384, 400245676, 12423710, 107970957, 303616706, 46166688, 46485109, 734617682, 220448949, 841429511, 961325660, 810116091, 576085948, 943364242, 308478978, 451193276, 969234222, 16640770, 777435164, 377862537, 214974910, 805174549, 914564121, 822570929, 765841277, 431198616, 929778772, 744053564, 979622870, 864515900, 961048882, 738217526, 891277504, 71873995, 444342293, 616040571, 327210289, 756465816, 73969090, 598338825, 307606301, 872871064, 80698802, 97129899, 353265466, 609224168, 200783850, 181088931, 386746361, 978104227, 214030950, 350650102, 384588073, 786557699, 767960205, 517390756, 71652652, 831486597, 512439277, 751262587, 80099103, 350802933, 512080884, 317200351, 609528981, 739089895, 818199847, 792384858, 669065025, 566508843, 507062129, 732548473, 186123421, 335427207, 486319936, 427614127, 604384832])," 98660 (continuousSubarrays [545474762, 953787709, 674751628, 547108892, 139086321, 913984794, 455213752, 457371038, 837804203, 321301980, 622340159, 762005224, 508473801, 816102502, 114924508, 46789407, 657987508, 379771108, 196416467, 719296810, 495054479, 643462943, 12654004, 326443663, 440676053, 994855948, 95788762, 100456096, 270977958, 713933605, 740874937, 707881191, 521361591, 856258740, 718514932, 170403000, 175385464, 277230308, 624255322, 273359290, 953643451, 417501937, 798361803, 70944199, 962379022, 801126488, 109005986, 412779329, 318426048, 349405407, 598302991, 660867031, 1287363, 498039388, 655636954, 694997519, 513650074, 537106096, 30938447, 50239758, 504254037, 187552256, 870317830, 151919568, 869264851, 469086257, 222105663, 223490643, 893523557, 882450539, 549267987, 529469954, 823331810, 705347339, 65639947, 153171028, 265941837, 960051315, 292768994, 146881323, 628344033, 765468117, 857907900, 501562920, 787517433, 704861639, 11308443, 62725156, 607283388, 129346720, 348144468, 851306922, 344199521, 964292328, 128065732, 117805474, 467572364, 259778214, 319062270, 88533611, 126196412, 506345806, 441891684, 624403986, 870190098, 966167749, 858664638, 259225645, 985568593, 240806542, 796991554, 651969579, 924176268, 939796052, 377908036, 255806797, 181631657, 583668594, 429223101, 874833713, 412446693, 587837591, 958218101, 640627901, 177088445, 292216349, 193286102, 650633109, 853390624, 923312715, 362299943, 658210714, 804686394, 515526266, 451181064, 662930694, 626753689, 783555897, 12400310, 651814387, 938473743, 921168035, 391708552, 990604624, 979125847, 390093813, 825136930, 336454227, 376681215, 295643059, 419679702, 466493923, 73261819, 810794197, 487436405, 647687668, 233793725, 421738676, 898054550, 954533970, 103780920, 258582691, 866068063, 769182044, 998691651, 216046946, 570575460, 722218063, 359388980, 671059253, 883861116, 599293317, 30980739, 148289732, 358975391, 392969658, 746363205, 135600987, 710084864, 763429926, 323673486, 482258903, 499559815, 867845406, 483136077, 607104626, 16356966, 292267078, 422213889, 760807147, 567904255, 188239674, 673159479, 948735836, 882373507, 465742361, 506189533, 780640488, 752952151, 558539784, 486650725, 925079399, 291818571, 280039695, 314645165, 827470841, 73409681, 371218556, 216918091, 255693008, 667729327, 157759, 84608120, 127134321, 619916149, 327789042, 29728282, 876431758, 885622384, 482327881, 339660627, 352158148, 589081320, 396738219, 42795378, 803488061, 611767376, 960250059, 684476138, 197317093, 950355897, 406931811, 24349873, 970957800, 768442025, 754695890, 945932300, 136657174, 741180125, 807693202, 787725639, 360386485, 206012637, 519172129, 443867048, 81643105, 299588156, 218403345, 21451125, 616192657, 846590558, 443337316, 869802114, 421812875, 185371674, 257591463, 625879557, 78544716, 480628532, 627635990, 802455816, 921237920, 487488040, 561862634, 230240853, 773074864, 390584721, 232335660, 652529420, 448011690, 8324566, 335030889, 806053899, 940893509, 619360012, 723933263, 972239726, 714735400, 402518771, 742677165, 71418875, 296399566, 502505589, 827333130, 921605726, 143917835, 854959077, 895195342, 46950801, 675823938, 793162894, 446665270, 69742208, 418936131, 335363404, 614036870, 478481976, 971486173, 535186782, 838381379, 554100015, 598992997, 696657391, 870254447, 711831205, 176323343, 417694819, 151955415, 167281484, 448398683, 486830952, 593857530, 34967712, 824252004, 711386403, 402415956, 308979473, 623988414, 297692250, 684000792, 801637230, 25551290, 47406041, 339996352, 578815397, 997125839, 346630568, 445549892, 536888157, 712676461, 893316267, 811898762, 232287079, 341088297, 772011188, 693856715, 506001495, 856328082, 847418912, 575406390, 596785758, 774764468, 889530908, 966351783, 882592495, 340930891, 553807837, 123214609, 654854481, 978491472, 773065653, 776036754, 434109022, 219322095, 716182903, 628698585, 585623443, 125470931, 896459871, 730677023, 486053605, 365888700, 828118172, 896692557, 241894416, 63500807, 721254487, 117459765, 800286276, 329169937, 139984775, 456143947, 224908111, 600061356, 619292656, 58115536, 820843928, 685023287, 906494665, 480558257, 17825086, 621866055, 279233987, 655043510, 803392170, 251772159, 759906701, 444886526, 703414433, 85614203, 449268379, 293106900, 620959312, 845176523, 389202392, 788358775, 593593095, 922865226, 225037727, 183064595, 289253763, 118446192, 657233912, 364740200, 980925159, 693694199, 889243693, 403977707, 849606682, 872903781, 665011827, 343570614, 694238753, 115686435, 386119859, 540127512, 92791100, 810369430, 73933972, 311821610, 477772414, 927807719, 897029559, 742243851, 677803148, 98629375, 660516032, 342403461, 680146081, 867895850, 684963515, 77257011, 828987793, 478516366, 806952055, 870457563, 159392578, 939188936, 736487428, 437405433, 178709496, 841991515, 974735087, 130253428, 878145233, 526259799, 900845676, 374434377, 975849426, 757178258, 966787063, 302266026, 566020965, 61328760, 485590426, 238707687, 541324004, 998654768, 5456994, 117168740, 943595809, 926590565, 483231730, 535417750, 113506112, 938549495, 660732544, 274494701, 226314107, 625050478, 408899361, 635160847, 473933508, 383932427, 269667017, 998850970, 671265289, 44704132, 631168982, 904297704, 654040943, 649082038, 704955159, 23179026, 219543654, 886638783, 490363439, 708727854, 341920967, 171857227, 566349222, 326658879, 351134898, 878098244, 163527856, 444522521, 636185358, 165360294, 883016603, 307589084, 1127876, 297094573, 2266870, 773320646, 449377654, 411159915, 991928672, 865085084, 823684697, 526299204, 189163363, 450936725, 400494331, 984643951, 904036482, 633380680, 269002587, 145582883, 990288863, 818395328, 591997773, 653587918, 283333259, 657517832, 121590451, 406976514, 86341578, 295248803, 842841358, 318955430, 866162711, 369675805, 140687209, 304949464, 451470721, 831427057, 924145515, 933203451, 896902519, 188560232, 721521820, 108724259, 884227111, 610251465, 98122207, 990137877, 136448228, 271610438, 396784217, 391952157, 365569312, 517400730, 543789050, 248576794, 686942509, 91683708, 161802583, 678197563, 792922455, 883944849, 240477286, 909619908, 899484842, 31218726, 489212141, 128414243, 434785859, 301813582, 510916403, 606770772, 560480638, 924010217, 29758439, 573495626, 306790691, 656871980, 188519384, 591351428, 434265823, 319057051, 616827891, 618236668, 795953631, 401636033, 108600394, 765687252, 192922795, 47122622, 149055472, 312022541, 919094598, 968937120, 273189234, 588170831, 674991522, 995665825, 163566593, 631901094, 676082689, 245491590, 170263264, 313268266, 398558884, 654178111, 586145685, 55545839, 62681921, 652472126, 661456537, 943362938, 648407692, 874675248, 400391181, 617985661, 600650899, 500102731, 742685142, 431436545, 515024357, 894852168, 95010406, 393126650, 718767077, 143355012, 287816003, 445061639, 687716793, 986302907, 46160337, 328768315, 363690151, 442972337, 868444648, 981732261, 873563843, 973373342, 441344806, 440848829, 541238310, 385022583, 151948139, 663589540, 59689588, 717520943, 453600351, 509327393, 344240072, 775178739, 562700376, 258352741, 319843064, 472851438, 51278135, 146737094, 220689807, 700320382, 837332102, 762385525, 399959971, 340391529, 506350075, 309244592, 922326445, 308581072, 693856672, 435122256, 549415026, 943761953, 878234910, 38686776, 341990619, 332794128, 163334525, 436719687, 57646657, 917462331, 850315480, 380669479, 537835446, 204877363, 699662373, 39358988, 410026675, 94768102, 329948058, 721550840, 825553659, 304712541, 196325200, 607009647, 945395785, 967956293, 388320607, 133243535, 640342851, 445277384, 240854060, 469239245, 221896301, 325377114, 171457041, 925879675, 607293320, 53067765, 740263642, 898186869, 169410240, 948730095, 941019494, 294476646, 178250682, 305501864, 413087864, 924901626, 458315450, 958314557, 590331576, 75593805, 97061820, 145043190, 162473687, 951836985, 962466400, 167018333, 341206137, 134960982, 838815629, 382897871, 599308775, 101595843, 493804524, 230089706, 14722163, 350127480, 403371683, 613235294, 915894561, 834618526, 475187293, 27401342, 25363743, 932209539, 493936940, 524781045, 341384337, 885707986, 931029183, 988701420, 283148480, 935006656, 137668991, 874762225, 269100666, 90798739, 260988534, 126779018, 590532967, 97365741, 140736498, 714123802, 145722215, 722460160, 490322286, 811290287, 67742715, 713677709, 39743735, 332639627, 218125803, 713378338, 824495521, 802155217, 464190961, 508591532, 782584768, 62270081, 473801997, 780246306, 492962814, 596922368, 830159474, 982171716, 485473444, 748662054, 641029558, 211481352, 142625254, 754603067, 189617175, 441925744, 147899125, 860281759, 721251483, 864773403, 872633785, 33285556, 512721503, 163153735, 923076165, 499134592, 305679331, 52448476, 304471733, 904986224, 180173469, 873491106, 54145038, 850413878, 907977403, 729927922, 811633977, 904950176, 967333052, 873826354, 201838752, 805215738, 401471602, 198851990, 100308971, 820767311, 271177128, 626224830, 878636669, 766515865, 698046510, 94262611, 91220413, 34511572, 369678587, 136416738, 135295118, 835665387, 837010861, 1778766, 188983056, 520636238, 67932808, 842490299, 537076134, 257837150, 254214487, 640539077, 163653725, 365902396, 360638622, 747990900, 366004316, 518292904, 316433552, 864242416, 553070922, 855359306, 274710491, 30862493, 371214965, 74018785, 860725025, 23212647, 773378365, 244988883, 23911823, 995715530, 619254393, 873229435, 906485693, 802772084, 109348094, 337709190, 360376560, 620412528, 748806078, 96927764, 645692670, 515921770, 829497017, 319535006, 410349879, 365477827, 825984480, 420095159, 907728075, 453525347, 599004529, 524492831, 573007531, 588571259, 845043093, 659303990, 897664755, 689141490, 553464385, 612402452, 373088932, 290561218, 547062193, 182482668, 552490321, 631921117, 410498709, 897645415, 334252520, 853354392, 481839029, 499111479, 448327286, 758790177, 942150784, 810550498, 325945856, 864779657, 911600156, 737246429, 721670995, 370483014, 306381760, 582988068, 606736194, 528288688, 684396087, 981207893, 889223032, 452556604, 545934929, 432351484, 76192129, 24442032, 559427512, 118522351, 324985000, 602642254, 479431557, 820891887, 169957371, 692922048, 418135756, 575759197, 409144974, 546524375, 212836422, 869372143, 739934065, 103096338, 71683468, 166537114, 274182811, 152109497, 595401186, 943372376, 769966230, 376541867, 755512473, 826110380, 675752392, 767459616, 896331002, 624758059, 740305558, 560126549, 658826649, 539109044, 816910325, 566750152, 471067553, 688551621, 741199527, 52483806, 953002908, 730160068, 995900903, 331283408, 968015001, 4126543, 976093594, 862752300, 398483383, 659408192, 237199285, 348457285, 772972019, 480622739, 406044796, 751533503, 863596949, 571567136, 352641320, 668049650, 826962409, 690997860, 910314042, 713494248, 600901841, 688516875, 214834897, 177692862, 531026235, 990390602, 43541428, 617020987, 570722474, 162450513, 635827725, 63288761, 415548905, 286793206, 714088196, 940059162, 893899441, 749707054, 54067503, 27553999, 265237786, 264657154, 918428214, 542011994, 973059413, 979487296, 445331640, 21967865, 890594067, 768968716, 635514547, 575301384, 855634337, 367200514, 675846346, 642148298, 484407741, 221163342, 533925647, 843020373, 625603149, 916232486, 873072403, 779163460, 454060507, 75836, 7985462, 736721012, 383345697, 742346767, 660760312, 879114550, 29098064, 960655198, 426890371, 931812190, 428746353, 461046966, 494984288, 141134427, 811563191, 78726270, 588642920, 393699714, 142913769, 518877134, 604838140, 556676182, 152929184, 602798185, 910403651, 898625854, 626487224, 266034437, 725262406, 889614366, 597343152, 570666408, 218575288, 434917749, 516664, 944606220, 308338510, 871383776, 734925803, 297242798, 23889061, 627743907, 801456652, 575033010, 368240050, 672023672, 416777299, 789532761, 715855021, 70299680, 243983876, 33760751, 793001861, 750079838, 917145769, 643627426, 135779765, 721092021, 349580710, 937386887, 885945353, 528411233, 381325889, 774124795, 555778758, 377724189, 948995789, 430383986, 977767872, 411335735, 142426216, 80314555, 960647770, 840694797, 793202061, 329255107, 140086498, 532839916, 176196362, 57914219, 508464092, 992844662, 436809653, 212757427, 65689962, 366513380, 889148347, 837903010, 239554660, 779049456, 519381998, 395974210, 966870175, 474141784, 857071524, 688749281, 823683661, 256223060, 45021479, 70949872, 894833262, 211212585, 538535431, 414150849, 715635319, 586877556, 82270020, 556856608, 413749079, 681255945, 245554097, 408996897, 798777881, 964027279, 363846487, 290313722, 545523710, 991273368, 765412282, 617077811, 861215115, 26299008, 862797793, 59596791, 301896640, 761869449, 639849999, 800538240, 866748390, 993625200, 338906345, 470425459, 548423176, 536041050, 10782658, 382980242, 929027491, 738060623, 813836313, 658393818, 311258651, 960649848, 157822478, 514337768, 303480104, 84584675, 522762408, 473132591, 862805502, 349693312, 685105050, 200084935, 183456708, 337091315, 311170111, 601955385, 306355864, 36355775, 566661078, 901658014, 239156691, 24297902, 729470068, 52099623, 861296757, 87538180, 223653700, 558360570, 800466924, 964342519, 28164274, 97396457, 142583731, 37955214, 598490362, 65710058, 796478107, 319102805, 805443945, 128652129, 829657375, 744635191, 573704173, 423364048, 337376628, 912558285, 817468003, 818742040, 527484292, 745921998, 891911812, 457218573, 829125159, 566269154, 840080035, 612959021, 203165549, 19604136, 8674653, 402126667, 42695166, 189514194, 899650021, 348613324, 544024948, 462169960, 756134466, 508658848, 416201885, 77415861, 689685712, 940375657, 387694047, 184410804, 451594042, 677737450, 700266841, 790998449, 983438722, 706328626, 250762882, 647220267, 596114504, 522573431, 368335835, 116968162, 265467938, 433197341, 410593071, 689722571, 100882194, 250517565, 267394198, 654885954, 791220086, 385387395, 512629463, 427780382, 170956603, 560612281, 772076965, 720564842, 488615934, 496487939, 938725656, 344192520, 688755731, 110702180, 922350327, 273458122, 737158042, 781943315, 303792122, 340675387, 864307143, 806616164, 521146724, 388790616, 690256761, 60107634, 286219868, 596962067, 401129328, 3889485, 847924455, 979435561, 636654269, 910632239, 75718267, 430645998, 883062573, 78731248, 458560935, 210409424, 822159050, 391028691, 479458762, 807759689, 805467099, 391472631, 999061610, 863224004, 688267509, 179558502, 308937627, 171612608, 196507573, 8226690, 35218013, 651260077, 917416729, 283822888, 729020905, 489577865, 925303596, 246169850, 447609486, 305785839, 138918250, 535618005, 395080705, 840329533, 642433981, 923222229, 97518185, 943216342, 863719630, 837664589, 177492642, 613251889, 883509110, 864465797, 844094073, 421112860, 102956809, 553334773, 33367108, 400740021, 203737987, 316599432, 236017967, 410849848, 635198107, 771254195, 251259615, 459544712, 540355720, 484074381, 120134184, 780456768, 485597522, 617441391, 620328097, 781190683, 426842509, 693597921, 595298352, 178975374, 656798243, 151445934, 811132838, 235866953, 877793433, 786950615, 22681856, 920348392, 452775298, 986977771, 56345757, 766117314, 119243437, 510109445, 148064871, 103002707, 531949818, 966192244, 617095082, 639927510, 358547925, 2883468, 323176740, 33976940, 887381028, 639641104, 444391049, 825848115, 401579326, 49924231, 774504372, 878084802, 438736343, 280764838, 477861458, 305398000, 365919126, 117014660, 90530276, 223286082, 291332275, 194474090, 894003353, 565760011, 375913198, 153404764, 341017814, 313645146, 358356814, 552393957, 479675974, 64236486, 988652945, 940311595, 573275015, 588685691, 739444804, 715734849, 92919073, 95753635, 536207137, 946370747, 839488653, 498323784, 476451053, 72413659, 933210640, 457112560, 458752884, 180856524, 983236538, 557099459, 529995835, 926253994, 742849187, 342913171, 604768245, 838018587, 803865502, 200652393, 169706181, 614344516, 674422514, 308979502, 765984833, 348054262, 126912774, 707577036, 472653114, 423888161, 456193180, 66461691, 285685093, 540995782, 214301182, 22299842, 539000136, 11718239, 13206791, 91466661, 63830789, 844963994, 589466276, 226811295, 167471765, 853430338, 108591090, 51827920, 869173817, 301480866, 935946965, 919250600, 154795190, 425361886, 171870810, 316299095, 215697575, 155462995, 664565769, 609527593, 350858889, 766351396, 708760825, 144720506, 5326842, 351968601, 795875700, 633752781, 144309113, 269426973, 514590742, 478952952, 397068883, 483210, 903556971, 384232999, 384525706, 317350321, 673491018, 102183212, 367097956, 868164933, 999030445, 736378698, 217439879, 283982012, 438397539, 575564836, 753967089, 175708960, 412930649, 884483303, 923631348, 944453572, 37184601, 942236403, 616279693, 320226682, 762709977, 245927662, 479470077, 778597054, 765306649, 904549370, 727876269, 872620103, 170886370, 888444142, 855990907, 746741327, 623543118, 616767394, 274015708, 371264586, 938363172, 602136544, 5121907, 816193356, 278008691, 120457940, 292909843, 134407516, 266855193, 582265333, 487428920, 33903388, 883944844, 996644083, 144719175, 39689161, 424289042, 553754672, 117371262, 182849470, 573768345, 15512358, 438205647, 709504272, 245854884, 758552849, 911166829, 179552501, 933420287, 170398995, 750671721, 558518772, 739363661, 174590890, 988584173, 597670431, 988919279, 380917937, 235322464, 916511528, 964987293, 912235250, 460751322, 481062140, 517178602, 433118684, 884187269, 813047920, 260108521, 771891610, 67180856, 67692516, 946607800, 748465252, 807227704, 605986010, 639569963, 823459529, 774631666, 779371270, 391824543, 334621050, 425194741, 490986952, 405423883, 294658403, 855035557, 268810322, 908627670, 850662293, 544492775, 787998170, 836929703, 305979856, 207950875, 66843008, 916238441, 572189328, 966287456, 144131350, 889967423, 771031945, 394270857, 224536928, 695808640, 388137927, 771022337, 625631027, 303754181, 653353920, 964589853, 938425465, 755683021, 323880830, 750963488, 337444540, 47795552, 504231403, 362678177, 711224267, 239181312, 352082927, 844697922, 608690808, 567108619, 820648549, 831470735, 131819488, 452875939, 236504294, 812755420, 448395358, 127429881, 895215665, 136500513, 680103027, 709741933, 83237379, 31186693, 85280038, 225015595, 990263321, 17403044, 702768466, 371625217, 689428379, 926411632, 208823805, 937725433, 687037143, 254938728, 813469932, 87663854, 742699924, 357511406, 704424156, 273193473, 335307671, 452555265, 760105171, 286664170, 999193583, 311599503, 465829552, 675180690, 326904371, 85410941, 709871833, 624283060, 314883674, 700936741, 986713996, 294309855, 230899320, 383249980, 94270733, 837273005, 707287632, 567074790, 114619612, 31292085, 718908009, 810426882, 152494066, 832704914, 945591132, 126567325, 388012698, 501494863, 718251516, 420292959, 169090612, 816089214, 486041868, 408081394, 653652506, 624130979, 980270500, 499322388, 51461772, 20518627, 959149107, 946721170, 30358281, 153193848, 402188570, 382703386, 97311690, 943934004, 267493692, 676485361, 271088763, 189392, 849949014, 368141519, 364426571, 929718969, 411807418, 526643452, 47842799, 162637920, 512298819, 624946145, 288148069, 730546282, 223375135, 279669518, 342929454, 346568452, 626325245, 203796627, 337747070, 546891917, 193446517, 88258816, 355206206, 168611927, 378242113, 633047195, 968530242, 220672359, 642613345, 77669205, 680408968, 348361636, 756117845, 487840395, 614614203, 290965357, 61735792, 775505792, 744913573, 74812209, 472870216, 498746395, 978216286, 992911656, 493492912, 416336926, 92777874, 378133612, 766773580, 503914590, 964014124, 816870855, 332837871, 549028976, 243723848, 611509005, 622776867, 701613586, 927530077, 29286350, 599358839, 272131387, 103586743, 650687795, 311131803, 72046091, 68131563, 459227920, 218545147, 402032457, 317222954, 981607464, 420560723, 834304223, 877986590, 617532088, 501035956, 959751365, 360466345, 929031678, 416090738, 486185860, 706203269, 387536723, 239108411, 531218988, 513951010, 507598745, 616765115, 821162559, 928774996, 273176472, 467459755, 290104105, 192278967, 748449422, 654293301, 386210412, 327961863, 638157305, 151392660, 779705436, 942335051, 487000033, 148619671, 901344202, 666388055, 393066941, 54726027, 191645409, 684468687, 980175064, 464987474, 833480336, 695936859, 464097615, 402828229, 295634363, 853727004, 1661910, 958138899, 33754215, 431244903, 559227878, 183171949, 244173362, 428954133, 584028446, 583152145, 447569574, 556165918, 89814802, 978740599, 965800971, 618787714, 162891221, 284079827, 121087786, 136778506, 366529974, 66624914, 677243573, 620811433, 793088703, 335350530, 308776003, 510778331, 560004445, 548539507, 944485252, 929068866, 422083797, 259531117, 616175949, 338886401, 560067580, 56068534, 403938305, 244133026, 14701152, 872463625, 963999547, 480723683, 97051622, 817860493, 8632649, 587901920, 105791497, 503119781, 544039641, 468694243, 249831778, 410203092, 862064688, 179676223, 784850455, 217885201, 629649222, 262463805, 865377180, 597277248, 604703598, 556928608, 945023813, 622907090, 415827563, 39885883, 744104712, 416657176, 525432884, 140724163, 223387080, 641317504, 626482675, 675861094, 79295850, 724357963, 762270059, 474202963, 252982983, 309335964, 852023575, 18761755, 212480871, 291500510, 474320530, 985554089, 933603379, 738044811, 563917627, 903925207, 387100824, 427841910, 45834372, 92553571, 98102425, 446235023, 25095098, 89786949, 512483814, 492330064, 136816605, 30099403, 857366777, 104934903, 579573961, 660556988, 601268415, 26240169, 705633420, 819961837, 272848665, 950592612, 900366993, 985378679, 916037221, 171375585, 949992542, 299967623, 283407342, 586902371, 480730687, 4088114, 380394370, 846518041, 867835508, 381493660, 706952084, 349131763, 750459987, 214077262, 437482647, 213515026, 579824327, 498340209, 498202749, 625073265, 988972259, 177523029, 784369756, 411918352, 680773690, 57695851, 172042152, 523892175, 43706140, 582641462, 584292083, 688261450, 590012175, 575450050, 364291531, 695107845, 148741851, 583468807, 474626062, 258562553, 566000705, 212770026, 734185142, 267619855, 841904976, 796960237, 949019366, 500928349, 273616844, 601858185, 115202506, 254433683, 823657759, 925761178, 390652234, 20905617, 60797389, 376248729, 886385098, 117979069, 679843273, 381652609, 103936454, 786941909, 91286776, 761794271, 826854270, 113928621, 49796393, 403052800, 202560184, 849612874, 862639786, 954851896, 946197829, 347013707, 136982428, 952003383, 287436486, 238181924, 537279327, 28579892, 676414413, 160655288, 83043560, 667895652, 536182301, 685278090, 567135300, 27400168, 812549357, 725852630, 465160349, 921396435, 902934209, 727315626, 271807750, 234055703, 347941992, 217346896, 935937011, 989386614, 146767874, 870930333, 678406583, 186581172, 214804318, 792178530, 273792025, 191345509, 365145778, 301612373, 360215683, 379102492, 268158014, 956724493, 670556196, 506120037, 567746164, 113041681, 264033478, 601202897, 957627338, 840088178, 86824413, 445340116, 181509034, 416619273, 659185210, 870122037, 969490674, 350761605, 234399748, 536636448, 900739384, 974382167, 44417973, 102839031, 76166966, 278503326, 31102458, 943072102, 831756119, 960378827, 556842802, 306024335, 231584378, 503839857, 261105150, 129403563, 38240617, 566476727, 25028064, 65465971, 181578371, 837045496, 861095475, 732392588, 16785361, 261830968, 287649773, 192973925, 361958570, 875160560, 752728547, 218428289, 863595469, 295557775, 726614606, 922582021, 402740625, 307713163, 135184696, 526938641, 825723154, 473161125, 622463123, 415279809, 618053891, 981487310, 680772766, 206049248, 311165464, 456151871, 931405637, 876272495, 482680006, 530479461, 318895592, 253914388, 600544174, 434429887, 718953453, 821302784, 31339654, 502185703, 787212430, 786958035, 717125604, 89926190, 378926973, 260457654, 258326884, 333508196, 920081823, 888386730, 109721355, 317288849, 284888377, 871748095, 92999752, 129853916, 860626543, 961375327, 217319026, 767591300, 679515786, 861694653, 391141160, 88724233, 898719585, 193332111, 799380521, 160104301, 720185093, 812746383, 257409242, 913721848, 752988567, 972404785, 453738053, 143024510, 151131826, 171577136, 755425529, 648956078, 475703195, 193490964, 155830244, 401693373, 501547323, 149233723, 501253165, 796094513, 560557365, 674880158, 425847412, 789234724, 934522982, 235543747, 640964113, 868599905, 506939895, 26688794, 235455597, 119204086, 885724989, 418558546, 243624597, 979976483, 913358438, 654359926, 135937620, 569321168, 211509609, 307349745, 384998829, 563177493, 510387494, 322418416, 382155418, 179873810, 85818298, 40487879, 286977883, 264650851, 239246502, 433008, 795409932, 161143395, 851066705, 522577922, 51969475, 303097170, 525446882, 1260937, 813518302, 621876167, 768213354, 889225166, 564564166, 64079567, 855391565, 558931146, 818035247, 99770910, 278994908, 43228303, 281022961, 74639090, 36669996, 332255545, 409997028, 29504392, 515492845, 403369011, 594607407, 472078682, 319344991, 746437824, 611353666, 858373052, 617373639, 471994843, 763925526, 141853143, 369516300, 495755351, 133929659, 304278447, 340412102, 182609802, 194427504, 260506160, 912804989, 136246535, 19131913, 770883893, 222764940, 622729176, 999390488, 27942475, 292693708, 323781574, 480939154, 267234098, 44354366, 238789023, 756340601, 913622507, 810880044, 767373666, 952476974, 218531847, 337345311, 269719503, 124549413, 332859772, 913039131, 825371411, 550775739, 743858124, 250821189, 677756223, 65370794, 347351633, 85301263, 155371960, 758492635, 306945004, 507009987, 806625865, 587306687, 94151435, 445273913, 464176579, 594574641, 396701891, 68229526, 347861958, 49736786, 156968774, 486977742, 908771719, 387923681, 545191516, 589794745, 570976491, 983061156, 99594946, 863327089, 478535740, 173801790, 505716536, 980059937, 823448352, 310516801, 236536245, 596843812, 793446145, 509000348, 279449893, 371168424, 740725742, 220318780, 804525331, 148531381, 591440983, 787936188, 172089621, 839330789, 155362486, 176904476, 179920846, 462273540, 949684681, 116941022, 298917022, 963045832, 148226950, 313079294, 297045981, 272514387, 19472100, 787574941, 917085852, 685356712, 899339069, 452791686, 463182021, 63056345, 44241627, 536478890, 151523778, 395522268, 367864926, 838841020, 285726507, 554669659, 184905634, 742433109, 249409261, 781280163, 684857004, 460892738, 245052214, 312672979, 644463614, 44150004, 824160443, 195874280, 855248962, 169104717, 597163617, 103510010, 751954822, 374287915, 769316563, 113759039, 665659317, 661241451, 802341914, 11181895, 851763213, 135346535, 825844045, 638189759, 172707220, 188567925, 699433552, 790140084, 710954284, 5020665, 790507422, 909813702, 799202767, 789744445, 44956269, 988941546, 662253141, 471931895, 863889811, 858315485, 643220129, 609553047, 788851957, 813822809, 800287507, 293922598, 183525156, 870331995, 486472005, 722356426, 1426155, 466071882, 37128501, 21550214, 159863360, 904448010, 535656596, 134020476, 495084181, 155440139, 976719629, 767544431, 228240157, 726004533, 321958094, 385010040, 527642363, 336883841, 393828409, 552663231, 238746592, 874641217, 238295470, 490506067, 890256380, 313887046, 954571558, 625347754, 137036504, 299137324, 187974073, 984118908, 17567153, 677307178, 671898072, 593636359, 409297401, 470938340, 195383404, 663287121, 774337040, 168454574, 234914258, 591403157, 85601696, 120836858, 504575553, 301142091, 893963887, 762067181, 95759418, 200289891, 478819458, 582943946, 21537448, 996425170, 727074791, 239265113, 366577079, 635968060, 209879763, 384305484, 913054350, 347477148, 251727432, 461658224, 464731534, 979080068, 992882432, 565021945, 581353310, 66165450, 346489985, 462560156, 828518484, 389122463, 423075823, 619297788, 137971880, 747645232, 920305068, 377438381, 404712970, 655316265, 746386685, 862736878, 91442617, 877556098, 369810960, 504277209, 823766413, 507818138, 68788864, 159468632, 136847349, 348839851, 835510406, 159459664, 404903009, 401552292, 459435207, 628383693, 7539421, 515146380, 262182013, 659089754, 440013090, 300924598, 173328361, 803604029, 250969610, 191677037, 556387584, 472610737, 909624019, 629047472, 168708979, 769301010, 533755719, 319195838, 860266461, 298559175, 287451096, 309594172, 459704419, 829247412, 639996372, 41301244, 930750077, 249425630, 629210538, 14532017, 946954128, 982886385, 9672197, 262585052, 664742393, 749692050, 592716590, 626932772, 747161998, 482916310, 343875324, 274023813, 273160949, 423904105, 90029175, 874020739, 347848841, 219446851, 80505871, 917793532, 135853995, 631608006, 731641895, 526321382, 587101429, 890249558, 51830958, 766713682, 241537294, 620012991, 714012879, 958934633, 918409416, 309089925, 472080943, 246336413, 189852268, 396966351, 794652402, 677436245, 492197810, 438966600, 265407286, 970767471, 747527271, 415635650, 673595508, 109319236, 249603864, 698188341, 998080299, 10579186, 458689641, 333071021, 397600865, 837531047, 865092630, 207637421, 710313196, 485252187, 717954835, 94011131, 817893332, 922481624, 418417011, 547825706, 987001149, 467716181, 189803599, 933009911, 450364499, 366419009, 507471621, 297013854, 611625157, 913848205, 816940710, 363241574, 480376004, 632511988, 349268017, 99510975, 896800618, 20957257, 667136626, 682967420, 784432860, 936889935, 795903918, 709771676, 389322139, 709051292, 427393296, 565935890, 697876732, 299955216, 37364267, 939049548, 940010077, 831345644, 769648045, 7767575, 240758134, 871547295, 684371172, 340981263, 123073219, 654636490, 150638263, 906037085, 268941026, 825993582, 375449959, 888633615, 727905021, 434615509, 637455730, 875646512, 980782540, 115616482, 437050826, 625133362, 272940390, 53279330, 623642143, 650342096, 800562138, 373612502, 803727922, 134013241, 722570984, 925052253, 681045189, 595119700, 403399826, 793811892, 380288517, 452016335, 298884778, 418798496, 559519837, 446947295, 522268675, 746812883, 847977696, 440670840, 967253108, 883729101, 813625414, 470472376, 497893062, 565421185, 514770449, 37886862, 422107130, 877888262, 805448769, 317842972, 106716364, 457077222, 487386776, 619884017, 701647167, 323450706, 924675576, 610525255, 842585852, 652421730, 613903086, 677038111, 150424496, 659692947, 719704394, 916209547, 121672094, 529693614, 54797798, 355035678, 600808582, 367375414, 294615020, 543142894, 163510762, 20182205, 749075965, 401998900, 798941538, 766101146, 554427678, 116285338, 690396432, 953594662, 30152042, 265342790, 624927895, 406342314, 504305670, 144546567, 842780975, 215600692, 383314323, 601198807, 274737470, 838130097, 266973847, 320987561, 435707079, 860112419, 359254473, 497999205, 55304625, 805638418, 130798849, 690412174, 830031540, 407276482, 329203935, 553667410, 953334599, 145087607, 752962719, 263446847, 65441300, 546519690, 615474310, 110000670, 113613743, 794313965, 384112437, 979174410, 13444838, 286743230, 960285697, 540069925, 307282004, 148409652, 818464889, 883057580, 33644699, 436034836, 140356312, 2184607, 761906890, 884268489, 943341822, 420814233, 572487785, 292664984, 987956843, 717597808, 509417288, 767309817, 559812155, 695660327, 395390504, 534562117, 391757712, 7292167, 122059701, 957559000, 315275253, 778089919, 701002690, 181426825, 43522511, 874544364, 419889381, 184640792, 257743383, 169919953, 162725719, 530746589, 21806025, 476313762, 636951355, 800361405, 199108840, 382194066, 171850, 182032140, 882473899, 419825710, 230011401, 326551197, 538153943, 279350642, 975678077, 292781118, 229768421, 205974333, 228565731, 815782915, 517567123, 413415691, 754329842, 366819372, 491593618, 71984570, 779202181, 259947311, 585952820, 162426984, 952918457, 269362805, 337253256, 510218295, 649671982, 178624419, 94501319, 439764255, 113656980, 749911571, 87429388, 852778470, 526001577, 540223890, 631124558, 311330614, 497745293, 54532352, 771725480, 330326274, 953422291, 771513107, 447191508, 895359470, 584675952, 909682893, 842294783, 539964461, 543466915, 32259542, 429130140, 244716802, 588018096, 186919973, 13737814, 611496091, 614893652, 498994654, 352651128, 801803828, 919197043, 485607819, 108949943, 291446205, 972551903, 516407308, 413126928, 919424637, 896930886, 307862015, 814033447, 318545669, 808337199, 552441836, 142526986, 482161945, 333884475, 227902651, 375325318, 39716905, 761194257, 562130061, 199071171, 131669099, 834118162, 374503943, 518128121, 631198166, 684089095, 833168999, 299036033, 936907476, 480713720, 326609459, 696062255, 539999792, 341634517, 713933165, 60170184, 969838470, 98234515, 143644328, 447199661, 567459071, 173421784, 474477103, 591538911, 157378742, 970931835, 885372590, 593190162, 943680189, 843782140, 856553820, 961005059, 335999118, 132469133, 866426887, 39003681, 938035445, 64233449, 560301601, 659620340, 67489220, 854908012, 499436233, 396299190, 857356731, 420885009, 753668604, 579383007, 494250532, 754370691, 807814911, 393671176, 350419980, 763643068, 91942721, 298664625, 513244281, 8797265, 470654720, 617081822, 963548162, 234261667, 829281497, 314920608, 852863458, 490662676, 868882072, 628079678, 891799838, 1812998, 873499912, 38691623, 841533297, 167964955, 605066796, 924624422, 691771372, 439664955, 942670008, 654484888, 170748298, 747733646, 260786379, 842420800, 181424110, 815489453, 475734791, 700185636, 608358158, 226858118, 681415459, 96736907, 381944746, 827521318, 703542235, 155532871, 407634914, 372097683, 672932118, 612165085, 806007121, 613165029, 728944103, 729386837, 573812128, 98208085, 38742914, 660565653, 443433587, 942478662, 966984816, 252301134, 295644383, 508400964, 83194518, 726833898, 196571294, 330906682, 727945202, 291177859, 357257567, 876350021, 359804581, 882466846, 795423888, 933717538, 304795984, 818845402, 821064879, 710432881, 740586928, 111851235, 468896735, 250315980, 192487966, 953249374, 989150763, 755387932, 752385659, 724609614, 883040840, 826568048, 482726987, 421891126, 316418313, 658814755, 882765721, 433597764, 729608548, 349705465, 457684921, 770037177, 41844118, 914173109, 872405637, 623957606, 792914047, 970234671, 907160801, 313272429, 201980284, 4415540, 102294948, 463235521, 533767982, 858366441, 124631524, 854720101, 224014115, 179269573, 372916320, 367664179, 345584137, 440079604, 365731905, 906576589, 230396316, 696038073, 909298470, 820759515, 310697347, 394387811, 615547298, 277554074, 242064995, 186607097, 385874757, 366635781, 993019754, 551073392, 613802945, 351339310, 723933323, 216823676, 465630420, 808511690, 114580355, 607233196, 86344405, 902961958, 337238707, 670457623, 569227451, 473232309, 396057735, 489295628, 904032665, 96034423, 628704359, 187767876, 244720697, 96169740, 247451818, 157888538, 938261622, 532502908, 974541108, 16598964, 166183417, 32806768, 782528087, 581059701, 429308404, 487507376, 604568531, 502854853, 526553809, 149028214, 787161712, 721618473, 520562451, 429163690, 363157162, 220253999, 695225224, 982322828, 791164750, 337571118, 972845412, 582638093, 229689491, 970221085, 746856183, 920073521, 442360272, 933867718, 406917372, 820222333, 395566927, 74262648, 175459690, 348950108, 539590845, 521928331, 904073434, 479738473, 437525738, 593836748, 392311990, 985410115, 836419060, 567219940, 564571095, 322015210, 755193180, 675048605, 51872729, 997335598, 421763411, 224809678, 596705858, 494207959, 292840255, 384390431, 979223483, 423783352, 671024248, 291182996, 174291134, 113857815, 476449231, 598988087, 607520564, 241186112, 22518697, 287485696, 690042956, 597861321, 176692171, 363583340, 500981474, 529131136, 908673974, 226738800, 418333793, 382108029, 893220378, 425323068, 381068680, 791606499, 552518635, 814214360, 249422074, 971167094, 791650734, 972366174, 26095831, 952305754, 529716826, 87264678, 935598819, 139411762, 501010245, 820960210, 873972570, 381154881, 990483134, 305807054, 42694275, 332779388, 497658913, 826675642, 232820606, 186101300, 6452380, 131556289, 838356187, 242900912, 850609692, 390292465, 660518595, 625249774, 846890585, 167185603, 336847158, 104004260, 154733079, 85737883, 103773178, 527223041, 133049136, 480461050, 83233235, 432387866, 999455285, 562474336, 697237048, 564983857, 600563691, 755456968, 44454508, 601539069, 114678988, 467756875, 810206800, 367692613, 650823323, 832450066, 745362761, 440796599, 880985113, 263314425, 687540443, 131547277, 780405485, 608983333, 848629795, 121713727, 362244363, 20802011, 910794057, 657942580, 886873606, 749572972, 307550848, 991001286, 489857597, 451765092, 24809275, 401834863, 170047998, 669445711, 504031158, 707824005, 999635609, 378201136, 378164139, 867185612, 314606663, 754170687, 998551922, 35869012, 186699720, 411247520, 172236003, 366586508, 144939596, 866778617, 984875454, 454853169, 701985486, 636092747, 81700805, 153247666, 662888841, 505645766, 636735750, 96800926, 202773384, 121592492, 322859856, 602275330, 239591873, 75336373, 559535464, 750299632, 454604499, 309692294, 796412677, 492429571, 113770007, 93921921, 783255432, 158894702, 75289566, 38253721, 595188931, 225206247, 132825687, 83053018, 595960892, 84200213, 699640525, 173035739, 279346495, 840446828, 516415193, 476285079, 385936308, 381429656, 993492287, 777499323, 594569139, 19299769, 211946536, 323193473, 824004564, 28577311, 94173679, 95509250, 820897906, 669474889, 334962809, 229030035, 562798363, 194378149, 246339042, 280893132, 300305786, 951277337, 847652131, 32535455, 65399122, 881898648, 261940645, 443902890, 846479912, 449779450, 183159146, 400912971, 337079300, 20824019, 225133778, 276749314, 207861772, 90215278, 299106632, 505867044, 643516985, 526646587, 36706942, 738687372, 759633761, 253849571, 603903906, 804589932, 455301181, 463014322, 903006479, 562828633, 995624047, 745903908, 678991733, 489876267, 138401171, 848635772, 888164204, 739694927, 333582014, 248367592, 10721427, 357446407, 475434206, 320664224, 852006760, 678803159, 409826055, 717744813, 403299367, 963934599, 188580419, 209368084, 556102879, 109670284, 951323069, 984693169, 687725676, 545295012, 397147671, 372368649, 31046366, 779217099, 653421129, 203037957, 507225572, 457427594, 579724166, 42025757, 856843065, 139552008, 516148088, 516134979, 627741342, 630564797, 517878981, 707225372, 876224637, 472062017, 840849039, 692335505, 854080264, 975812067, 766960862, 455687168, 638096007, 404799545, 500240821, 615244280, 168298481, 889187427, 302653187, 325541097, 298196988, 702370838, 154390320, 548368091, 893741826, 456499954, 422473015, 377587600, 880675987, 972887979, 92848960, 439985665, 904178321, 518756855, 163439077, 501601045, 363576494, 107548285, 11079074, 346919542, 739876470, 35332562, 549592668, 13245524, 143062310, 650389392, 310000901, 137273781, 564696340, 17657246, 581107704, 662224915, 301333325, 844074554, 531132302, 667724130, 536413906, 27187851, 850600294, 321326826, 807319693, 256619042, 103256708, 755779642, 683467922, 646673062, 806091318, 818584041, 982805134, 622763658, 86972367, 204299098, 695723166, 238374877, 313058903, 599409902, 757769385, 935094903, 685387304, 551967586, 626401837, 27026799, 77264148, 958142238, 7021931, 902537294, 348505552, 156417532, 301182818, 380969143, 153256999, 432625203, 833405002, 983108878, 547444435, 624703926, 610310131, 301214259, 188384275, 413424852, 186605343, 928205672, 235866055, 91155011, 944142278, 844056060, 921357311, 547530392, 621366421, 868379621, 101890134, 744294122, 108400965, 585535431, 941223236, 202413414, 707964873, 954375981, 655806805, 148469318, 69933221, 481973396, 355094075, 291842012, 28583510, 520303777, 931691932, 373652373, 715224878, 340120109, 923074984, 656566333, 394603976, 193378397, 519399779, 242009600, 16249142, 205159838, 593127618, 133643239, 700501613, 507148355, 95810671, 518804081, 555480872, 838952366, 2722467, 232199376, 504242239, 992972387, 578617371, 175243675, 834856251, 84288631, 510090496, 527454853, 774153742, 451205376, 978473956, 672055800, 106895170, 658257324, 287447496, 703310011, 44245185, 281613759, 985117004, 806731670, 472746043, 131297326, 261766978, 93496296, 999631754, 930502436, 723861751, 447817714, 411571551, 580752396, 865672175, 460794428, 654252143, 705162682, 687675245, 522234030, 820100348, 398260854, 674209868, 1073287, 753762350, 125031358, 310295870, 726360835, 451312891, 569659846, 81852236, 648305201, 776455795, 937816883, 591725649, 958549189, 216967266, 982968757, 390179751, 208660960, 889006537, 756009824, 982146223, 554521392, 311129475, 500014701, 157545041, 20332501, 776257409, 948679308, 911461378, 278846990, 26078764, 567884673, 906617361, 999429812, 611685361, 291493954, 608793488, 900727214, 853224874, 66347913, 761303311, 965239635, 270941528, 137700479, 618612918, 65240759, 94973333, 434948543, 170983368, 353121657, 603331236, 494893572, 997580715, 401807424, 54371163, 794762770, 779150306, 407431856, 550733040, 650085067, 947941945, 984061253, 140142363, 248444734, 805084822, 278075736, 171120616, 191257921, 885867795, 382869907, 503122447, 343798655, 384161000, 514737082, 624615692, 707356725, 808810963, 226929570, 657378152, 495090263, 606067931, 852630001, 170937035, 712454612, 853122997, 42120808, 727284869, 341096867, 22916188, 747518081, 342960800, 541434116, 259919570, 349127, 993343309, 626957752, 294428033, 737854833, 708209238, 309401533, 89247876, 338569055, 218861075, 751517369, 605433330, 132254374, 306074196, 512702090, 752793226, 767048599, 504130315, 491045674, 341924584, 910608849, 637168597, 981983350, 522503466, 634761242, 842141589, 568824613, 330413190, 76174864, 151965562, 494736532, 745191988, 61228323, 410754245, 300684995, 901179527, 299612696, 795948597, 984356687, 315227548, 325340712, 720374318, 675427002, 106754704, 157232235, 273125698, 80246967, 154867932, 945585378, 532734615, 509582186, 296879847, 504462953, 965241506, 731614057, 43159677, 597928482, 330501085, 201375012, 293116718, 789470025, 412051075, 123429227, 975239366, 959980500, 355217012, 676088395, 860350698, 644343162, 42805924, 850842927, 617621396, 399950486, 579897164, 827421169, 938043968, 16870023, 369030755, 643319719, 49010457, 847888143, 392955385, 861540428, 521128128, 338350848, 821243982, 175778591, 116316082, 441043590, 498558857, 67113237, 365510371, 865564135, 895616843, 743361912, 755817912, 274680224, 667702203, 331649606, 296293474, 265490951, 797897015, 427017048, 513697670, 276335268, 797377010, 316447667, 59199545, 91552432, 251685847, 755105758, 533615198, 280849262, 571184940, 477250279, 692446598, 598228469, 216265570, 897172815, 512751725, 459802963, 47556047, 824621973, 801694655, 576844448, 71019235, 782710850, 540470220, 439892195, 305117831, 227232427, 471042743, 712756973, 123412983, 180832466, 675348514, 52408662, 175893445, 196900351, 256446609, 175193596, 726046383, 82372866, 983564175, 866158019, 471862971, 884272346, 390602269, 436928712, 614660183, 644288691, 422304872, 41869798, 181764762, 261535194, 426929939, 923357917, 87827360, 60596586, 247347948, 769012480, 479205598, 931963956, 967720718, 290070190, 247361720, 62988197, 230649759, 987472641, 196923581, 3020652, 265541235, 950332780, 218729854, 595953973, 585980485, 1049341, 472378275, 915531017, 966696050, 328274778, 332339825, 100782021, 669862095, 634015965, 431928420, 876412218, 471742221, 341240474, 26411080, 811219030, 954564390, 662428408, 637180214, 683937983, 991082328, 872685635, 274240436, 614234364, 84066481, 292074727, 269987752, 730504483, 59299152, 76097898, 33234435, 4707415, 321995643, 291177990, 219800510, 336158875, 306987359, 213596888, 804688165, 76352290, 866148290, 268983350, 515389464, 350744158, 232213927, 229038912, 411478417, 91276077, 76120473, 239865962, 72768319, 674391680, 293279925, 658195814, 145271473, 718192601, 442842733, 141455265, 411955230, 787858555, 341936714, 14896526, 108465692, 907801107, 363027072, 567540935, 749349823, 874020240, 335409888, 364388497, 81386145, 353465126, 28677775, 271651389, 109786821, 210181167, 810454502, 4119885, 471715295, 392262679, 272102105, 795880843, 341811774, 608510591, 154952936, 645254885, 756387854, 309306425, 182736007, 80538287, 671847088, 839015619, 109286328, 927619921, 465487020, 322896298, 762295577, 243062349, 927160927, 478436486, 981151512, 627651722, 297385933, 129442147, 764156526, 605525100, 582633598, 136131263, 274738902, 846923848, 966792777, 308713592, 719511657, 29870503, 948788382, 857738320, 489596091, 948565876, 88212201, 963598575, 218263680, 888716879, 863492698, 313352910, 224431206, 488039853, 746572565, 960599248, 807108758, 77343710, 165977337, 314360776, 860285583, 845450648, 331869266, 231444848, 485783936, 124786773, 692279043, 735881960, 86716194, 533038415, 395733870, 481907322, 79901425, 395413660, 636175044, 7972257, 667917360, 963383598, 190773384, 795533673, 885491635, 43106956, 309843017, 219121805, 609611326, 525457480, 455795613, 323573405, 20775239, 634898447, 392909801, 619959599, 4364973, 245444266, 311852750, 398931584, 836918116, 830431729, 6179725, 365396715, 236529057, 410446320, 986781053, 759817341, 412089055, 683781065, 220035735, 753353454, 839021563, 769140388, 27883023, 972739683, 78818518, 185360838, 623684733, 143053054, 638283146, 636167349, 349866027, 107063186, 878962912, 813174934, 758421025, 701540056, 85176722, 640681566, 78692219, 246051071, 172531813, 463400958, 688910160, 624785059, 48315934, 750709744, 303766313, 856783449, 931617088, 414135145, 702151870, 377205554, 671135489, 29653348, 49511929, 477881760, 436209714, 135628027, 802668726, 366100099, 403868931, 124967851, 32168004, 214985704, 978536328, 490086959, 460321464, 149576320, 97265789, 976450769, 438008389, 339072412, 656209103, 119614048, 418919804, 209521705, 914807537, 177205340, 581579776, 831491660, 359286813, 799422869, 738211743, 483675752, 764491357, 255929965, 185567232, 910323464, 712603003, 360588102, 308422388, 944043506, 630448956, 719358714, 369788555, 930512707, 797651110, 146319052, 268063276, 109011404, 801815204, 194773774, 598527292, 686878087, 953818032, 350190002, 132463614, 946165673, 914386438, 929622586, 31011207, 168685941, 37629321, 295071029, 453958026, 68973279, 274654257, 880904438, 911937400, 954331410, 491575905, 662685110, 33125488, 830650132, 250206619, 137772541, 164874543, 517084669, 781965160, 49569870, 281108956, 559037099, 987558578, 559638001, 225719175, 807159003, 440466585, 221791771, 893810416, 273962374, 591738945, 136459156, 111930935, 357113791, 77250565, 920201686, 27652921, 168061656, 509320230, 516236067, 228649175, 774019665, 303946537, 912568273, 763982616, 814731048, 771947795, 334699555, 628612266, 596320429, 359215528, 682801891, 610310506, 93248248, 546367917, 716583227, 509610741, 125797324, 202732687, 272679576, 1566601, 599410264, 579158307, 986106133, 226082651, 9196670, 452031023, 377595955, 367211206, 945739883, 934168080, 411854489, 541875469, 85079543, 643238705, 803234091, 930067972, 61248417, 932082998, 48275023, 699265683, 48090667, 40563186, 410666315, 310785172, 954924700, 64499823, 576291359, 803790065, 763516453, 319717553, 631613305, 134729877, 309260974, 570730339, 298896114, 624164835, 68189626, 201075232, 930238317, 832210948, 387221131, 379234378, 581078136, 163310224, 626566813, 651528636, 314905808, 13715252, 647461562, 425520697, 782160862, 13790874, 318687662, 626706735, 873305154, 222712864, 819672815, 276759749, 443233133, 827780705, 794394959, 133790435, 241515, 19590787, 54039318, 415013753, 147581836, 46625924, 92889757, 508140979, 155224236, 8908223, 725387605, 779871287, 909809433, 847217386, 244412946, 494377820, 91464815, 722049408, 854090353, 838274522, 292201407, 175902588, 405074835, 879817110, 278636758, 990291673, 501230063, 771141450, 466565035, 20134486, 998308196, 435346588, 583540864, 336495482, 516189271, 727287876, 121376351, 759083153, 130222151, 989673181, 312390828, 213376807, 251154842, 72828133, 347163791, 573150579, 44801007, 758426463, 771117180, 598612227, 466033922, 983961311, 836608657, 691703808, 462537714, 117702848, 142700122, 39927497, 400286121, 343350224, 448272113, 457717101, 660334804, 661323424, 800828097, 649898204, 238974644, 621253816, 237644022, 21394704, 18123825, 724149981, 302630605, 328909429, 541812005, 269743978, 902189488, 733845154, 379746703, 125592107, 356348040, 898544769, 742083643, 638662725, 861458055, 300704556, 57960267, 594348857, 273938190, 582957275, 45761410, 490665613, 374629510, 294037919, 904040790, 175524620, 823512783, 185239212, 542256019, 634630394, 762726173, 111593753, 392390659, 507474845, 614478438, 509120492, 967479295, 570781248, 204366439, 43729486, 305249271, 379815559, 326375174, 598175359, 77027376, 222130061, 689566924, 127085324, 841837324, 493629956, 308368220, 815004732, 94011610, 934500887, 532192852, 52085408, 101605081, 573464966, 902797262, 511750870, 533480792, 975644147, 838130212, 44067041, 775639688, 717380387, 677544053, 879614676, 849979561, 488806939, 292690755, 569430596, 399265537, 273423626, 451424875, 283165157, 51614068, 719900712, 251749337, 477550408, 729368883, 712658770, 442348107, 500498376, 533765664, 429132549, 869559432, 28391562, 565553705, 47536227, 105120973, 659717322, 211334714, 675586740, 672214740, 520625067, 59518038, 363774808, 412520611, 168758003, 125511572, 274552628, 998319631, 819850490, 127700024, 345733417, 866491539, 260958064, 747458265, 756555289, 467356946, 49025781, 888989615, 18955356, 943318907, 223375917, 472322509, 839264788, 962731500, 18373763, 674186799, 483691233, 287699619, 394382480, 249063594, 177133931, 509862015, 300434737, 517869700, 162903855, 887831408, 17081290, 832372463, 193902147, 618744624, 949572142, 400018469, 365338013, 993611400, 322078411, 14412190, 316317087, 461222651, 724835889, 216746160, 422324153, 758037318, 523416651, 25971966, 397736414, 947742921, 602889233, 253001174, 366678080, 335732288, 330947431, 606806497, 365220294, 1462533, 493351584, 15010989, 399621255, 599092291, 841883837, 19304563, 456186135, 449885657, 841039626, 177284185, 111779506, 147872243, 179645108, 956344328, 115186766, 812040138, 762983109, 772874994, 307718072, 264128625, 131825355, 220738025, 560712238, 426321346, 926309996, 694145216, 721149714, 974693059, 965643779, 822697210, 277136118, 738418906, 822884858, 469382809, 244975983, 72422893, 825364137, 780016878, 706408504, 769934716, 687462176, 722060755, 10435324, 566990662, 532170938, 383736607, 99254347, 575147745, 997568637, 720203232, 943868770, 436527114, 415693868, 259218282, 722085351, 518246840, 789285592, 898287526, 449102767, 793181179, 806927494, 859547188, 438742317, 940060614, 292255655, 958912907, 371037362, 201573712, 981341186, 288688140, 430325864, 320442932, 780183623, 577630137, 713001794, 303340728, 611301852, 428218252, 186955055, 278908837, 270473175, 183226485, 178703264, 771768930, 720853870, 88148198, 378287345, 339613481, 348088268, 245394542, 836716854, 759825472, 908951770, 237515786, 735892832, 211334542, 231098168, 216322645, 218098514, 631449621, 687141486, 265281288, 278197432, 69428162, 108040680, 328544366, 800536756, 970680472, 699575151, 898791987, 78968650, 16307726, 622702406, 448488082, 367967619, 577500600, 487433747, 350902033, 207444368, 6486453, 997194843, 91199240, 781881569, 565525725, 524532906, 950308773, 520693729, 734788432, 242228010, 818281151, 629790800, 648718418, 904644692, 121402358, 474885458, 980084251, 615086010, 463128921, 344573756, 525003540, 723318395, 976922538, 317083106, 283296013, 862407203, 167985345, 840442640, 350835330, 409934654, 849550879, 323058386, 772099836, 607885987, 699209238, 346998251, 52642402, 391352374, 780698389, 317688305, 655360324, 170564486, 991941413, 825350213, 279660862, 437709892, 460395511, 522703863, 282638873, 798741780, 303949678, 21507056, 440826544, 935580456, 566382606, 310315614, 816346169, 768483402, 621481847, 423729807, 792883632, 304454996, 114261947, 293553660, 99659489, 448387087, 199109541, 952110272, 836308647, 797452788, 192339000, 549022692, 871819452, 164626996, 378127861, 539590116, 358073785, 367549194, 840830866, 660700424, 427730165, 54297020, 356442819, 290476152, 220104825, 459576902, 999402942, 896686287, 445426452, 643790002, 513075886, 82525027, 169543716, 698723951, 759581233, 699779422, 683931787, 794687063, 829398661, 516972090, 602261659, 308926345, 677469924, 670347735, 945214899, 825680089, 8241522, 182300987, 402365909, 952625971, 476530458, 300288408, 345324021, 357096280, 710901085, 367581301, 394396551, 425243208, 344131463, 924836572, 285854297, 71337918, 105265701, 715685044, 516631475, 366651059, 657335452, 345644403, 948985305, 919964644, 635711434, 528617184, 11366851, 534289110, 675785459, 534705671, 76126783, 816006469, 995607326, 384685882, 199831315, 612393616, 528644132, 957754555, 209018611, 934033111, 978354087, 894623191, 418261699, 697116900, 44726549, 778752118, 766178863, 216824018, 703269954, 35429709, 542796113, 239394651, 582379406, 233127181, 406048947, 558900170, 204179245, 417179470, 771912667, 482475141, 422713235, 243589721, 466910617, 315029013, 519291465, 333177672, 70010498, 592445348, 751078960, 779163065, 277967051, 84403913, 534077, 394046359, 288873084, 981985836, 977690679, 873750047, 551270972, 164832864, 145061495, 416200494, 974295365, 344822591, 566522641, 394473699, 859961900, 446188157, 468269894, 334770446, 434540463, 525282703, 518008808, 138474383, 25529740, 182237390, 151235695, 26344826, 33531072, 445908646, 66380264, 595050779, 210308128, 602383865, 841614987, 759122598, 936076986, 977793448, 33324623, 789627345, 327289047, 311287224, 591140580, 516757792, 61023073, 341015749, 403758670, 447860175, 584666818, 670864171, 632952801, 416670365, 318826498, 496678871, 76700048, 402700754, 684300700, 531450029, 816085483, 665673479, 808178120, 412534582, 994907815, 96165668, 791820198, 32425513, 414852364, 894644088, 875719614, 20165962, 129529423, 309917181, 586839102, 252804809, 272937772, 405548376, 747082929, 918847590, 892213693, 448849161, 287943630, 560520722, 41099651, 344069311, 858964086, 769684170, 703576234, 391544911, 92824821, 615926077, 769602053, 916677045, 102206603, 318539689, 74144617, 703594238, 691287905, 942643365, 618831238, 933114262, 176965299, 383399242, 850203575, 33759475, 650444141, 375407612, 857817471, 778523635, 221032336, 777163111, 200514448, 703357632, 165062472, 554418890, 281181784, 21261289, 864941665, 576299760, 913282810, 802828768, 90390955, 895759223, 743317362, 917647131, 374328911, 755006595, 78037841, 203981221, 141915330, 123334474, 544662014, 894688957, 3129072, 954368147, 141821580, 247950886, 697919323, 73395494, 808137480, 767182913, 469678548, 595572320, 740725689, 337268045, 53922488, 414351769, 788250364, 451288814, 660008309, 277769666, 370460378, 202117331, 166543654, 909647841, 667049197, 133447098, 538465467, 750734303, 975797291, 781114222, 696021313, 864547752, 303517401, 416907372, 688001548, 420072397, 236845950, 699674629, 277380358, 676434434, 949337122, 138406650, 265935489, 286705836, 189162265, 285574170, 995700635, 598584002, 768369647, 43546280, 713026718, 927855402, 645725818, 261903090, 916533087, 624912356, 879589763, 206625452, 555431775, 955024790, 624556438, 936743494, 31358075, 838955981, 688128976, 999217717, 627490669, 996100033, 725827911, 580876210, 330838545, 66631684, 538614394, 489633817, 521347772, 434313671, 414628404, 910033903, 167448328, 315242897, 964579390, 457698856, 393133320, 912362879, 422170362, 625976039, 426071329, 395426705, 24146330, 402982785, 584732950, 951238810, 668978060, 896681061, 399958118, 372286825, 906345022, 361242009, 642826278, 602671653, 59921087, 470883790, 6171240, 221901154, 80530451, 940572475, 369272976, 159050404, 626040046, 789581909, 849195667, 961184889, 919727631, 983864478, 357121036, 827878426, 811879156, 171836076, 250128627, 933243951, 30589691, 225427713, 882202893, 566548791, 938475743, 127341287, 915741228, 766555079, 1587683, 116582782, 931155138, 574312519, 310839147, 314016824, 401561679, 428044190, 497317200, 872400778, 417863236, 954613895, 489975298, 597460299, 954001842, 207119449, 239738147, 371129008, 707484338, 954659810, 922336765, 542583172, 670247651, 636164531, 205599344, 62718669, 460037520, 196880465, 739780648, 212633100, 27012885, 736275764, 631100032, 10051694, 747146176, 746685209, 906101682, 638654241, 3665865, 451057269, 973533707, 273054449, 550430595, 6111708, 564292081, 58941981, 778661486, 670828682, 659013828, 309910666, 259254310, 158950106, 370078691, 863150754, 46272462, 397948660, 173077842, 846997377, 42851308, 95765996, 763537080, 703396496, 673249894, 691860202, 551891619, 837976032, 884398172, 73793849, 905707761, 317074207, 164652720, 470142916, 562619110, 512753340, 986492838, 642777847, 6354271, 359970889, 801994792, 845070482, 785934339, 360976462, 334116721, 992059265, 362900116, 245354145, 676033522, 505767025, 140117135, 233586667, 66056534, 278047158, 993172274, 509972581, 223966186, 972589452, 330989404, 254798936, 723919868, 592922515, 187272287, 187999862, 793225844, 312073504, 833592618, 106063724, 287152445, 692831144, 558874070, 136455, 734432171, 253967746, 277617807, 576753285, 359764178, 551347414, 693962746, 19094212, 67450498, 445978811, 37677300, 449619456, 145710235, 609178657, 355428884, 834651818, 801628964, 96016193, 564767128, 378598268, 203346166, 976963112, 381938699, 886140668, 778394259, 359673223, 377476822, 143427020, 934353337, 979958483, 635584437, 319117582, 178804381, 234172140, 851191527, 957856759, 819713313, 48368099, 313379989, 265141668, 27578257, 421889592, 873158703, 914122338, 523946218, 880484083, 707135768, 208939077, 318179490, 967159963, 629485146, 386213878, 801049463, 722273795, 991523032, 250267709, 126537048, 81496523, 640515931, 198373371, 624406397, 690392596, 136691034, 555056998, 555406152, 884538362, 123571657, 749630188, 800979894, 244587021, 83303463, 370619012, 619518176, 157275768, 11497896, 622720070, 671269785, 523282528, 804156335, 662596981, 194858145, 29610450, 476781315, 764794912, 854829465, 203694909, 815136602, 656488244, 90577211, 656491398, 601229421, 383190077, 62103533, 360943589, 538290737, 526682119, 670442866, 769246126, 227917602, 557877997, 274962456, 939530476, 872630531, 968579987, 266390249, 237029062, 407334818, 349939367, 369895639, 371741323, 824838518, 131948779, 285637578, 280763227, 354878016, 547578866, 689476647, 727212434, 824487586, 194384146, 98863431, 621469240, 926253645, 747369952, 212688618, 939484429, 120734020, 566618824, 614910812, 179381690, 171084273, 826779925, 942069745, 345361741, 280173662, 360116255, 697606655, 419345688, 537275267, 661058480, 47022952, 47462942, 509742274, 58329263, 773025156, 400566257, 745855834, 30907139, 506000243, 779257994, 246513674, 355884307, 166800364, 834782723, 396558241, 948565471, 577477205, 304789289, 11407914, 971190835, 381684561, 905575601, 909173908, 648280308, 485640651, 58122435, 384028336, 290523459, 696595799, 847206463, 214293134, 973786974, 25808633, 943138330, 689613278, 354657283, 918895405, 109585189, 492224537, 305621500, 844449536, 1981115, 810973767, 851395130, 719637352, 274906634, 877142623, 562281547, 167072742, 837587774, 444480348, 753273110, 494400930, 793335570, 495633575, 635973932, 177437975, 170486243, 255364801, 331484739, 465741292, 186863186, 171779898, 114244391, 725082975, 210555636, 743904882, 597860982, 253161427, 161114031, 634119906, 550759000, 836848822, 21689123, 369446673, 588286219, 55398026, 230573389, 731041143, 945731857, 220233530, 483267707, 967827554, 942676206, 98628368, 754374776, 114941647, 81140203, 416223918, 676441875, 675455920, 132599917, 426846667, 73361693, 185033784, 750489822, 39651952, 405973134, 465673550, 509036968, 818463127, 265241464, 917527218, 188951446, 504349793, 32883883, 848637096, 53285478, 547199763, 558653589, 128690823, 704496015, 622874009, 323620467, 564213773, 111470097, 589725659, 165858007, 502967771, 667204064, 571311880, 331891928, 18241935, 472560382, 172068734, 583812279, 794158111, 354478823, 257078024, 751880093, 593443902, 651965532, 75093005, 208425507, 156636638, 524092256, 183167082, 495736626, 794473942, 492658390, 166195496, 768407698, 768950583, 437172722, 35665201, 817233433, 80438376, 907797398, 749557771, 898026295, 683045057, 151519936, 827194715, 764204640, 217458895, 133776319, 144599035, 411921019, 704204086, 611453839, 374162114, 824891507, 164122143, 836589849, 605615611, 217859112, 902662874, 394831311, 637607254, 575169282, 800030381, 497002710, 650997486, 362524743, 747174634, 655357890, 305956891, 925098283, 523114204, 387867506, 889697959, 688435396, 165792841, 768286970, 389520063, 387448565, 118633801, 787226464, 650070003, 429046251, 163609428, 34668457, 45521116, 507464393, 393924576, 389093615, 372333314, 360527568, 965853717, 266071460, 660485360, 191997465, 916152290, 651805856, 598368600, 237711689, 38559696, 428570160, 974216749, 133675820, 6280369, 168162907, 569527871, 878645378, 156226192, 350193805, 331679186, 300322035, 482208536, 321889727, 24446613, 941566190, 908115494, 731258454, 161618923, 998974512, 326543059, 961746990, 74503316, 308675290, 469927472, 494480207, 936011220, 464596640, 624191746, 456928972, 739597217, 343796821, 478940258, 659655766, 596736287, 406440355, 807422328, 734603455, 973533709, 175194365, 6802303, 286586552, 448621027, 534532358, 96179426, 292135459, 407754378, 652593551, 631127561, 412208706, 408544449, 420583980, 583759519, 761581033, 319115566, 62674934, 279907075, 138681886, 421503296, 102404411, 295022457, 63742111, 187607382, 895411841, 680644612, 23632721, 540849616, 330412243, 150963154, 76280870, 501598607, 123651771, 952848533, 117513319, 97193703, 487513383, 386282671, 958151797, 289889111, 485698810, 104645018, 780481315, 38401948, 670669890, 639501121, 938114816, 219689111, 520213635, 262283309, 901302393, 145396696, 308235606, 724188792, 781008513, 719237187, 889455717, 591210483, 225588961, 27177056, 668694747, 815247160, 948883962, 580962229, 679734409, 469728341, 323015353, 221388750, 661419368, 389042475, 718632833, 77164446, 482039392, 337108227, 636911021, 182274850, 630942894, 140126897, 887542240, 472317092, 321141246, 814471726, 117989669, 54600151, 473343111, 700815318, 465520622, 20765598, 836280753, 216748760, 763550341, 127731477, 255967670, 259660875, 647270634, 477714936, 283381924, 52246746, 230281456, 984787639, 829501764, 972165415, 906448818, 969318173, 462507029, 92552300, 863123364, 765538974, 437440798, 756256034, 923776637, 32056350, 24811060, 886981298, 602058500, 264335022, 746931616, 411491479, 837213410, 820041357, 693066443, 611621254, 746392781, 855064473, 292305280, 388639735, 233304939, 966715940, 41113925, 403423047, 708150866, 568135508, 776887607, 374190086, 924389812, 714248582, 904221726, 152741436, 879016637, 864085822, 59878782, 339091149, 818546947, 988330764, 97271430, 441932814, 691402693, 225305253, 78986220, 316841370, 313930023, 141049949, 839597275, 244201107, 443706712, 96415466, 105961813, 840280439, 188656385, 211266547, 227850165, 924837827, 239145553, 526357369, 126252816, 374500394, 682798911, 493768817, 639718544, 106228260, 117340982, 649501511, 96618806, 162317011, 874923341, 549469094, 282734706, 815314049, 361274868, 512377781, 911884384, 131613660, 663684499, 419153345, 249152862, 322501649, 188572320, 498036905, 878038981, 593843880, 169870020, 616140121, 770874675, 100848267, 55104098, 329740501, 394034196, 572975122, 894579573, 998198764, 106549152, 227666644, 2836009, 765729681, 623818589, 927027639, 176660416, 513200766, 225882058, 857449297, 644087563, 881121435, 595379135, 507260066, 413532575, 716775216, 221341108, 36370262, 506327199, 415802787, 924595018, 654820986, 330125572, 262200142, 184486541, 510103948, 830605770, 134837001, 94269470, 478558788, 235182575, 60056264, 805417912, 88630908, 563426627, 218106157, 565231815, 419109602, 206642620, 918525837, 62112315, 422005459, 16639142, 312842017, 182910673, 76826371, 846928365, 356232375, 484898203, 337821222, 465872814, 944088378, 15087559, 128258020, 778049658, 284849438, 784457504, 46880140, 505785892, 746956277, 508179008, 447883665, 919324739, 608501290, 830995999, 485924863, 465375762, 482114104, 340130703, 17093569, 811399868, 70430942, 458342214, 210155644, 40316310, 329950439, 287198863, 534650769, 114407704, 130577434, 732230435, 499066347, 74131918, 550179784, 898442144, 764086520, 358950083, 766651477, 725557112, 473666552, 228164578, 436371007, 81359423, 530979699, 190238962, 447048702, 530559015, 560197666, 33071433, 728001303, 63608677, 93676469, 596005987, 848681828, 749544233, 717900358, 872554931, 856171127, 428183314, 303951902, 452565174, 107475052, 299238894, 645010815, 414789583, 773897863, 343830692, 376562730, 660394972, 486295161, 124868762, 669751826, 751470236, 634277053, 156396053, 498138641, 292729184, 573010447, 100913693, 369560033, 182003488, 511811917, 736236010, 437125361, 949374004, 490046333, 963246738, 259620333, 62521003, 774297932, 955152851, 349796873, 96644811, 684452761, 225123239, 495654107, 665507123, 644826919, 898484919, 221611021, 985274848, 131251482, 311112178, 70136389, 181540010, 734200283, 913073446, 464769328, 177172138, 5261052, 827149502, 474126408, 565820391, 219211892, 909448638, 241715063, 308749550, 14472089, 569050805, 343535526, 930181590, 833644264, 893491197, 271090975, 513530281, 940042284, 192547564, 402588308, 682207499, 41912788, 400557369, 256361116, 636869369, 23739839, 614110853, 604785610, 462690687, 74326839, 895282858, 887949286, 760621772, 334884756, 513525968, 156437406, 29951050, 397526164, 112040868, 833070821, 295693385, 132005261, 255298664, 92467741, 631210150, 759483409, 36629504, 898419620, 972486626, 191051388, 774826495, 913095695, 413846008, 616358602, 338284152, 166215278, 172269282, 212904639, 458350559, 545964413, 97697848, 755076026, 338637972, 49234415, 36442070, 329728118, 563346499, 532091694, 685054867, 604027800, 14829640, 182546154, 176340308, 5970052, 1529375, 962178547, 634141329, 465778999, 516715593, 853361205, 431091494, 501136499, 347458881, 572265056, 710173427, 45770766, 220881277, 676748598, 745303721, 558894565, 57210969, 643780362, 412898655, 478867975, 152215999, 569997057, 267873507, 249443369, 235410360, 428703886, 181261863, 241561832, 511995468, 68413166, 811839632, 303936858, 812875274, 654739770, 834689175, 951191218, 688404255, 204284885, 196593660, 64841274, 45386093, 673865389, 529302137, 220409501, 379534571, 813213470, 560408080, 547992729, 44453022, 331186382, 475814994, 64313694, 814578431, 514007812, 16672094, 802306469, 972459441, 1405550, 384064935, 595300303, 578709177, 434360356, 18570009, 492655091, 743778801, 676181087, 103725683, 480492340, 563294075, 617802667, 679123288, 785004296, 337531899, 780442449, 933421412, 266253070, 834571921, 532186986, 633963417, 893331951, 802755188, 596103921, 13785244, 4098596, 229324060, 345622909, 976191160, 204998233, 655690564, 255276044, 379248461, 397004064, 254245716, 184762418, 94922417, 992515947, 256114901, 422046468, 51468799, 52340223, 688582806, 687906851, 572036359, 819276210, 538339145, 553178285, 626307946, 732707498, 815952838, 687854363, 606507813, 748085220, 324390051, 167219874, 686451017, 15435942, 234405244, 259246610, 678499730, 689580899, 663503503, 353470968, 869455633, 690144856, 43720259, 957047650, 781346303, 489283000, 961001681, 768259120, 563994147, 298249992, 765666580, 586816110, 669859053, 164042926, 36223189, 366936781, 388461061, 385332579, 781593369, 872854379, 679735822, 309149234, 165421338, 118607777, 986229295, 548718956, 183337636, 437938332, 841444483, 110634513, 848880614, 308441849, 974393552, 874895908, 891697552, 534909088, 885995416, 230606857, 67928181, 969245224, 311475631, 88682426, 803392596, 628456979, 741452262, 666455945, 914324247, 126435115, 582512021, 519272548, 451281495, 445846504, 9340113, 857461169, 66787062, 759500984, 968040814, 142876765, 580470482, 423852676, 602328049, 139337477, 11517719, 703464644, 978035012, 146970103, 127319194, 936176880, 606045078, 242073569, 332581814, 948270084, 794393449, 421769255, 93068290, 935215521, 292073598, 321062439, 483426274, 780692179, 419041235, 64015594, 66295981, 676436652, 581821969, 960822588, 73672453, 579836988, 82330549, 516742276, 221577086, 425104969, 976741976, 236762320, 332853018, 545053451, 373746288, 717925409, 62024803, 100391442, 233542162, 130767988, 875196115, 665249421, 159270098, 626072642, 658319413, 751338394, 146901992, 207350173, 788318092, 101182383, 241154502, 971649735, 409785466, 698181415, 203642481, 812299850, 324022699, 962931526, 62539015, 688597261, 282811166, 663467257, 482006783, 187847878, 354765320, 134338525, 531267570, 877718625, 789444174, 744543442, 935859526, 904182496, 610004400, 515797688, 317200449, 591291342, 685184438, 118667186, 768625404, 219201766, 469258478, 403895575, 294611592, 876292847, 777345433, 379809622, 51052012, 292041340, 492392263, 767892361, 615218279, 999298346, 779972011, 900891841, 571241560, 307078275, 998736286, 642246553, 959601829, 320119988, 382511917, 662441686, 178480874, 247654954, 929544249, 344463283, 477424845, 451202124, 189567238, 400523867, 975841121, 392592330, 11305005, 792514394, 350777665, 221506667, 649603846, 903428383, 868488500, 992010851, 244213724, 522071303, 399331904, 752846266, 717446057, 784245358, 464632713, 713090267, 629901542, 5979383, 161049790, 707976485, 410108815, 555842951, 772616111, 220238375, 741365887, 799413046, 176572416, 851316727, 926962134, 223149574, 13540494, 378737186, 992998791, 590823221, 672504243, 761070300, 555175928, 500008875, 853134766, 866974787, 405924346, 540839602, 285927771, 824890779, 431436321, 484183082, 443026111, 896769395, 38004515, 665761414, 610806104, 873335971, 436742526, 797176470, 247162340, 143293563, 352355954, 590806481, 637428822, 706361473, 406562930, 888393574, 711896362, 57238668, 215002429, 866296990, 804173396, 144375390, 211537060, 534865171, 137994320, 177022526, 273808417, 552052594, 345234863, 33078003, 748187637, 603670321, 107893423, 904905425, 425626013, 501838856, 546161906, 734164157, 529104215, 792152139, 355093769, 761995153, 140357303, 83384383, 514916641, 174771544, 21125058, 624900121, 266162051, 605272175, 653629142, 681851646, 568736596, 132540582, 767448160, 799996207, 135942914, 655733352, 366303819, 793280790, 611307483, 916268811, 178812712, 840116499, 338407692, 682996055, 894778566, 167853599, 731381734, 916442293, 546891301, 667358817, 219974891, 505135635, 426043596, 810986119, 655034577, 257103093, 661292476, 185861926, 307767284, 153894013, 506821987, 508980076, 66632587, 571228972, 660551259, 246533494, 19579730, 576449067, 554374940, 153977045, 628969390, 226017798, 246351962, 388977965, 53900891, 354115890, 498658072, 756071954, 850359907, 93994583, 436697835, 720723736, 515721514, 613434902, 106865457, 505947037, 638403860, 808295164, 729253157, 880018396, 81162229, 711371909, 938192712, 945251039, 859134601, 261770885, 709373395, 553953846, 345946735, 272986839, 225462337, 595387169, 98283278, 462863000, 164134955, 227957351, 557935994, 367290060, 234615338, 383629127, 400474607, 423925389, 842745965, 32078394, 24310237, 634158729, 89400319, 591082560, 903585444, 776117466, 109950290, 684585224, 364465125, 804623536, 412109860, 711942302, 18311294, 245897873, 453014637, 55152324, 865389273, 149518297, 377974439, 833211359, 333945366, 769963559, 75356638, 645490890, 681127287, 391679875, 390282160, 371660941, 257553030, 52615770, 798331209, 887546323, 836556725, 152532505, 873006083, 126803876, 835365876, 109134314, 242953122, 129750628, 761392837, 779969953, 153392061, 476714365, 507910267, 764927499, 633279638, 669276538, 609436605, 725832898, 598418539, 370711033, 696251734, 232928331, 630167100, 257926743, 197299157, 101098435, 11895779, 389301816, 801476641, 70887541, 852310241, 309380863, 225539641, 679665913, 461241915, 553035879, 639447514, 200877404, 517417934, 164014871, 744383796, 54007431, 224962933, 738387277, 722292966, 156298937, 249747051, 984485339, 295141878, 901871191, 640921448, 942569742, 815469543, 656219174, 900546188, 632180714, 369072909, 162001296, 20760452, 564674219, 835753474, 10856907, 887290682, 43029118, 923480493, 860275255, 87039872, 776583885, 797943828, 720684466, 958498647, 984037133, 477909959, 321340543, 891179127, 220707342, 89717912, 383691709, 946552488, 69462298, 550589688, 799931487, 469893510, 268830432, 894299794, 305961871, 981052648, 572534218, 181346385, 105499890, 250194, 872667217, 956700602, 315409740, 802200404, 752690264, 121410575, 334993662, 196414735, 832492768, 10430822, 867400784, 356046982, 960588787, 359461879, 271850193, 979439225, 31497354, 866349260, 833557393, 658854508, 706833655, 708388751, 248058960, 142610128, 930394695, 799924094, 835865530, 229237829, 701905081, 412365567, 707752529, 357127092, 810034856, 846761987, 656934889, 783737450, 211880334, 569314146, 836198760, 741944298, 259229372, 840911744, 472239924, 788209950, 423830439, 489493141, 197526530, 115721397, 633897245, 768787423, 94659410, 281777707, 568557542, 719512776, 961443319, 971386178, 73647506, 47079709, 102893908, 384097448, 332681764, 36731856, 392588047, 764509957, 988628050, 690175947, 664984852, 985672183, 883168283, 531806955, 493968347, 877150840, 209032568, 271336061, 454810027, 475272578, 832406769, 62139852, 615806882, 212908758, 760462569, 288876513, 89154227, 730533561, 79779648, 603794215, 913442975, 44766524, 373544249, 531817658, 528441954, 486228888, 556657020, 269613074, 193296809, 764389271, 635160535, 190641955, 377186741, 108495269, 513151972, 589046392, 8602755, 50594510, 176129120, 873052628, 811199530, 647077247, 173554404, 53112316, 956513949, 478752432, 20470136, 125904903, 158014537, 716075221, 235589274, 482410508, 866212216, 790702026, 82815604, 77029717, 913465628, 222536605, 85054611, 306337598, 993575545, 977995019, 481851437, 920812533, 868626338, 782528655, 160180081, 18077935, 461059224, 560186127, 850018463, 424182941, 654163302, 222488716, 10256981, 847556410, 403050898, 508968671, 746240266, 333294953, 262243502, 118428282, 21564048, 15181469, 811054867, 992703648, 91839244, 147793301, 87850505, 500497479, 229523453, 870672814, 657004922, 217029909, 969353578, 116920950, 620054016, 842810726, 500984010, 677489002, 679168369, 41564173, 315250962, 868043614, 204039227, 565683346, 831533692, 806000751, 326332420, 391191059, 305020645, 941826191, 17186278, 824892410, 134307296, 788432171, 291957981, 878976367, 172348229, 213818755, 703021027, 303508303, 555336737, 358800521, 184889011, 830421811, 659712179, 306044163, 248837509, 457761546, 611085549, 267850848, 632506504, 296497750, 836215576, 189855820, 140032771, 146409046, 411628952, 749274722, 386590667, 459005739, 645936650, 401483197, 485950202, 516442988, 768244910, 961052450, 692361752, 793501724, 330883650, 143138272, 252531601, 512221284, 999049882, 315272965, 311766223, 417656279, 360721642, 714067250, 510577557, 10837148, 563844378, 347380557, 936695487, 696974712, 300025871, 81438137, 443964501, 510470680, 988913231, 404580211, 659377072, 694064696, 989397113, 662322212, 941588695, 89194804, 453469784, 920489560, 305552781, 741781491, 68173110, 362242289, 156518930, 316399963, 301533072, 126304930, 830853669, 961339731, 635118737, 675024543, 62491937, 799161690, 729766092, 560468978, 798423685, 702084912, 507047615, 951047110, 106712354, 426041823, 626350523, 582533119, 898470229, 752921218, 945176809, 629906760, 398341733, 456065360, 903773315, 987252827, 915091595, 263008477, 355972536, 977503906, 982438077, 74890398, 491482432, 42528573, 727628212, 514691220, 258058808, 540751102, 180193999, 889888881, 570583758, 418461411, 724001852, 559951606, 764716344, 998592253, 675745745, 441215420, 98157543, 896273590, 973382377, 778867677, 945485768, 582834337, 67171212, 331328640, 944809020, 482413825, 214790203, 514397300, 159079388, 830102444, 589394925, 124173729, 775617282, 970606297, 132275341, 991229881, 62712924, 107616951, 681252251, 904448150, 428671037, 651794328, 189459514, 605123256, 445978191, 22441708, 176819952, 413159888, 134087111, 855664427, 695622054, 330995284, 285858328, 686630429, 594779598, 622233660, 611350147, 718272547, 114704604, 927518455, 857911838, 603121300, 404478076, 625916027, 462289930, 997011482, 741125465, 730947637, 169307885, 655708396, 711616632, 735386893, 658579149, 569288636, 477798521, 681322620, 5804326, 995985714, 393474749, 853792403, 603601887, 78699766, 852329616, 24118142, 423357650, 385227354, 858799805, 690901980, 607122000, 149343097, 411395371, 394632816, 340423309, 733513440, 544661042, 87555993, 329665262, 59354086, 922980016, 557638742, 914737796, 620348434, 896429734, 547228135, 834738687, 660734821, 137167733, 830240000, 511622912, 807254286, 970536620, 641764585, 794529024, 192210347, 121389060, 497099197, 99361069, 227586650, 610153541, 866567829, 443762790, 95507701, 506147194, 654789716, 991266106, 571491373, 872338392, 768088112, 874278444, 971201339, 718587376, 348082345, 566757563, 443335132, 776132422, 778122976, 985347431, 190390745, 38541135, 674262698, 785024726, 27716429, 803143706, 433979900, 64636589, 238339954, 53235219, 210466020, 158379120, 875308463, 367740048, 372293868, 753720663, 399499405, 667224273, 971410951, 342962787, 933527037, 476132832, 125948861, 536317697, 48137010, 466080253, 197824550, 245035368, 341261197, 543233450, 55811546, 726681132, 964224160, 201779490, 893369030, 541353218, 725169368, 541133225, 159165321, 133885138, 698453426, 629988985, 551982076, 517004587, 254234687, 27790039, 383908732, 123069613, 131850383, 434176995, 531244357, 484850168, 498131765, 138598196, 113482497, 778416353, 94721209, 451190893, 159977821, 679427274, 995045116, 958321411, 434125642, 839961475, 478284216, 400450716, 246398862, 318671510, 642812879, 296582343, 950765967, 343118991, 91617403, 34576811, 923387482, 104329739, 39591161, 939073127, 63331887, 369188738, 20937291, 738295824, 257668192, 212518459, 215489932, 837601823, 67748386, 791453284, 486952502, 715655198, 228463830, 468638996, 872824691, 843251702, 538860972, 458216988, 920442338, 388365947, 10710475, 790052207, 22685895, 48412841, 35769442, 840260647, 169985529, 774933836, 423843688, 794733691, 618923052, 91571890, 878459848, 757822313, 322226255, 39230241, 511287672, 658309944, 548350442, 921103811, 520057964, 954295128, 169154439, 895254070, 137947369, 856039908, 610063352, 419194340, 191295383, 671742276, 890759003, 31053884, 540093289, 288155521, 446998247, 22620470, 351238993, 359958736, 690081398, 790214115, 305016075, 755215457, 12413933, 750311770, 939459555, 356723874, 810124083, 132591586, 698691709, 830210807, 598819465, 816740495, 298199236, 830979661, 581507527, 391735400, 127304331, 75969691, 425515929, 342000804, 837441500, 332714662, 487720495, 24021979, 271855128, 78172424, 797867928, 522686773, 899805025, 661130702, 104571001, 419588984, 402903791, 58225627, 945046951, 101827033, 76568176, 655312802, 339041752, 671884788, 937845125, 931238443, 78333452, 447946157, 53761225, 423078245, 739714513, 777798790, 750441296, 490786544, 250031627, 799261251, 695794988, 184906180, 500915905, 508933387, 680351870, 381061039, 439598959, 818993431, 74136503, 564349790, 296262842, 753937425, 690659817, 323597246, 796627366, 916447180, 528099324, 241346275, 492671062, 776968066, 599434574, 561767688, 959305266, 820244174, 896178473, 186492272, 434097897, 610770889, 282407166, 56902412, 118539099, 978003618, 659781461, 814234193, 711073211, 61894401, 846772277, 712450100, 485559319, 78523152, 420006520, 326529767, 374181464, 276626240, 681159684, 666046977, 849747130, 616598512, 333301045, 308968164, 37964435, 232947768, 221194741, 546430939, 954285163, 858869600, 686407358, 84622181, 344901455, 713907413, 389337144, 170607235, 621009310, 276654532, 175147120, 967940140, 249695378, 664559704, 736332312, 595607931, 697693134, 139094083, 307850955, 514541928, 383319958, 512110189, 258201574, 180723426, 91283469, 776554823, 184461148, 152517742, 980754664, 814319114, 662960156, 135636750, 253349385, 914580536, 724260895, 847118082, 893455798, 272683104, 795679817, 77221982, 442434877, 904692654, 632170992, 390703469, 204548856, 114993422, 691713169, 970452573, 873381791, 731143822, 922390374, 266599055, 838091957, 411062003, 604946661, 395202229, 236354630, 387045968, 780577325, 895974026, 987945395, 836125888, 391008272, 844164664, 195174595, 393744887, 136945234, 54058178, 685479689, 635656129, 588076011, 252630357, 680260544, 942668653, 576110681, 777784089, 400781048, 245151032, 599232983, 84605484, 376887935, 121879419, 548715822, 345814081, 945644841, 485115293, 733881951, 752498760, 123389173, 232798848, 606373153, 113144452, 825117190, 567523029, 828576190, 813279580, 647146307, 739524209, 757189893, 397229670, 977069384, 950657485, 351320591, 130511889, 969949796, 738285013, 942037191, 875674110, 990920465, 178910903, 150396007, 746898792, 356619246, 604170936, 742016544, 659500443, 358723473, 918281950, 896686420, 486006974, 293226973, 885358870, 103912401, 678932909, 770540150, 752128377, 675427074, 218740804, 204676430, 878227929, 995476366, 365592894, 199139734, 457604265, 76667367, 819385630, 636752133, 878506038, 737924420, 505560433, 116616396, 886626226, 313100396, 738912311, 184483883, 468340890, 175883540, 794292570, 121003624, 245504150, 409232597, 40486441, 840794260, 692448813, 511791252, 37874766, 514797059, 98359065, 636704286, 245313215, 908413906, 72225890, 198323405, 39130633, 452962301, 884138289, 249682604, 159919409, 216258396, 910688073, 469365220, 165186311, 788377882, 104248960, 474582802, 533077530, 349328721, 857262789, 364013446, 524293651, 812231331, 524801617, 136305717, 17262271, 833773371, 721741197, 796148446, 602845184, 536649611, 291707711, 930904869, 70381828, 470314283, 73741257, 105529821, 349537322, 41064579, 468986213, 13763716, 599047005, 76558911, 703427325, 975542232, 428966361, 65060644, 487485419, 843671971, 883628755, 638431181, 137595656, 767726132, 805244547, 626040445, 277370339, 565040317, 513850686, 261838657, 831264510, 96673899, 740814444, 632617390, 86038280, 835594485, 864228041, 213421548, 479094851, 291672568, 324190766, 322607217, 756529342, 840013612, 222968851, 954419095, 44175791, 777372623, 958988742, 160111145, 918780081, 509692894, 688206109, 899516405, 639400611, 659253409, 462586043, 728862471, 913486396, 909533112, 491905235, 530233669, 227911147, 698079473, 642851035, 78270570, 962022206, 596634037, 561163032, 260374947, 562540462, 985603099, 953968456, 847792980, 70625987, 791302155, 125568504, 301636553, 369625600, 10425614, 275779033, 762998874, 628768729, 930645909, 220475640, 306891181, 55253351, 973129249, 792543879, 439238002, 811524680, 507059579, 113022388, 725015106, 236371790, 772239300, 673758906, 251968381, 413749943, 409805687, 807267484, 460352962, 722778854, 223214669, 728823763, 615193826, 846639355, 946990330, 480619851, 81363707, 552242031, 107563147, 109057790, 993388625, 115610893, 624487351, 176474746, 815921015, 594808797, 114786312, 80144548, 951299457, 690934479, 958376920, 389759589, 999375660, 525894305, 723379227, 384112854, 415911529, 416451835, 136281654, 481276140, 733234650, 940359425, 862549002, 492155145, 590675586, 589368728, 748097317, 160851843, 732048379, 498063564, 964202493, 77999382, 854189027, 676813302, 562742030, 280188245, 888862876, 495100362, 261987036, 779813355, 264210001, 835294108, 197780764, 698252090, 817678929, 618917446, 564406902, 794777063, 385755569, 383039558, 273381028, 922152621, 268937618, 459910870, 238659074, 854781572, 327930904, 571238748, 103176967, 541115587, 508063707, 753635986, 540015383, 765165746, 505325940, 284579730, 305201001, 526308963, 297748097, 835265863, 637660592, 726792545, 491267142, 724531727, 479701701, 588358525, 504698732, 970020241, 772359792, 253570033, 37174916, 989968559, 678073022, 175782714, 348784243, 624914929, 813559065, 985301021, 489417008, 513227093, 46490565, 481289013, 731593200, 369824927, 858469495, 386360515, 384591650, 937733599, 279436260, 777763556, 925588680, 578157666, 926875682, 816877368, 830767316, 454967698, 699084137, 674783843, 54297999, 516129544, 836647065, 531295315, 546573346, 581317790, 853546781, 233455533, 604996028, 121109988, 721547583, 406080100, 706575243, 104596024, 907727441, 43392153, 300571075, 996728702, 852935969, 153658428, 6020672, 964941858, 25330383, 7866633, 344604267, 605213275, 178962401, 658212918, 271350544, 796897681, 429494524, 857864275, 974011975, 847872830, 775452450, 917225963, 109704557, 759506073, 831268874, 709883312, 38156034, 426348921, 869451254, 516442066, 76822665, 561177932, 864126808, 329882082, 271915229, 780381076, 771990193, 344153953, 850304097, 73052788, 15645850, 591022595, 703279888, 900736001, 126744175, 378365229, 604124390, 27487247, 874166292, 400173912, 511972980, 232217527, 495900806, 444196777, 759297535, 427204918, 444059020, 346903239, 3706344, 341040705, 539999428, 79185860, 71402853, 983851198, 600741494, 967706226, 129618235, 583187251, 843982144, 402034026, 736106487, 917181610, 661340524, 494527078, 233587837, 714831415, 723927379, 970173533, 88679741, 367899452, 40291140, 365954133, 121937660, 927210387, 531463348, 856873794, 535483815, 995502624, 820475571, 8993749, 620387526, 340660275, 456994156, 917527818, 574901170, 642880421, 114578242, 562881026, 501926433, 433018142, 655642449, 697780052, 664541924, 917355694, 299157800, 438645775, 958636280, 481877609, 700794867, 373887882, 730375075, 877371935, 936361566, 850279352, 524208145, 530669607, 757143840, 32109574, 521158400, 184831432, 899240264, 978932422, 189977470, 378080502, 447654, 522229206, 667148648, 901379921, 818699043, 521353419, 579170895, 305833511, 714568984, 656859123, 269665733, 566510367, 779431071, 320743651, 735483746, 775246984, 367781555, 843564786, 795043394, 285100527, 36246539, 207672564, 792862831, 337773666, 555698000, 341951371, 211106043, 971891172, 813144345, 786892549, 642215271, 56275173, 25338503, 729116423, 522676185, 795104372, 250174828, 858523887, 402032232, 649223526, 492611022, 476678411, 270291390, 15693461, 672482803, 414314904, 113593155, 16115990, 622735087, 798727072, 861355370, 490952186, 8413949, 398544633, 628323359, 512039870, 552574363, 550662316, 208591101, 36753241, 848315029, 585663894, 468917252, 264968041, 704560704, 444299723, 546141831, 335277318, 640659626, 752836734, 563139250, 469444984, 71087694, 684798095, 893464596, 576942019, 203924055, 820987409, 382415822, 679626818, 123985216, 88842557, 984175499, 414240522, 732967526, 774299612, 64232060, 406174935, 640098922, 240871602, 447066864, 702859506, 117374246, 627585030, 374732317, 963760316, 939466614, 544495906, 942340731, 613896666, 672115868, 293949932, 109168853, 228950000, 770564756, 507479639, 288009478, 368366821, 471066995, 742716230, 961648285, 739340962, 318705611, 51574483, 656497976, 703326415, 108218364, 194387320, 515963350, 448983811, 873569309, 646329706, 69593243, 920851821, 787677764, 913395298, 152130889, 821603723, 244041570, 121231151, 188478095, 868235379, 375543426, 592133057, 372714463, 400824957, 57714193, 751268044, 99332294, 639686713, 422560312, 290959192, 803486254, 120660798, 531198814, 468750334, 32314678, 998140098, 347475324, 96834955, 1355991, 606514038, 124294382, 709629342, 774777764, 939828501, 297803189, 929638475, 906243058, 282594119, 350183550, 444309239, 628139669, 135459612, 377382812, 961033459, 961147012, 218225179, 753858026, 47005387, 119268526, 84187319, 149147072, 889766736, 439108087, 840341551, 200212946, 836886434, 162179730, 260584946, 610323917, 508423210, 244615926, 357414516, 492326865, 161181687, 656183108, 288716694, 168351909, 770528902, 340418744, 117013911, 89074442, 807487104, 312441700, 186127758, 881409039, 289270704, 562759620, 157910656, 648771508, 217531951, 247706235, 510437717, 129763352, 950643033, 393563050, 337508032, 184660720, 875604818, 37905675, 210586726, 894292444, 350572261, 296073379, 688821974, 712063269, 10707447, 462546220, 772016108, 672672538, 804848961, 626378254, 56430630, 472284107, 580146152, 647229450, 256993129, 421621665, 671633012, 357073952, 964560756, 550883350, 444993969, 726248018, 427488178, 37555316, 147931183, 328863065, 855233192, 333584136, 259139624, 984720745, 541092362, 883128670, 176712093, 423342239, 771745231, 952348026, 582606195, 979451475, 670799243, 898649324, 848616293, 517365451, 58951977, 80909402, 192456033, 692871465, 310615392, 362082929, 768489982, 508684398, 151130194, 179103852, 984094223, 416665955, 3197287, 918505550, 470774392, 643055155, 961563237, 979616074, 183428144, 420670013, 996860754, 926047222, 77749779, 725228770, 163571365, 679153547, 541163985, 602977917, 398706665, 85734279, 480544008, 810751466, 45349027, 850717862, 278169551, 869270176, 51115166, 476095885, 382361110, 837251245, 957497082, 768993455, 184202269, 859950077, 509661320, 971405485, 236407553, 717640283, 853550856, 793401649, 632972843, 909682658, 862226290, 959357316, 204436647, 713995378, 536736742, 952991548, 680334804, 22851052, 19145618, 678117439, 307482116, 153205811, 766718687, 964924565, 461596038, 481898140, 807796086, 990743908, 309385038, 727862002, 690606822, 950315718, 939868946, 63072112, 373508041, 861087344, 283231653, 449783268, 826878613, 433561003, 745114644, 70792788, 941063268, 356245450, 597886681, 204204780, 577502657, 544004511, 739441349, 98430762, 109752920, 208720855, 751485650, 914816975, 202411389, 266740231, 889015861, 987968259, 793166087, 78291027, 436159791, 332827393, 945512881, 65873306, 215284504, 57062284, 926085448, 760926427, 826577551, 772216329, 505294290, 473704696, 473151561, 147413381, 73369974, 949287387, 373881244, 612176119, 555728566, 927731917, 891271868, 787874652, 811073755, 838624392, 827101728, 509631850, 783542116, 341999480, 331539832, 363976023, 11996466, 512118695, 754620592, 842433211, 723049155, 856901404, 467782503, 897382377, 871467267, 676835195, 779592808, 986030577, 950229067, 98856627, 39375374, 159381073, 804862932, 390091585, 313225029, 727030804, 237476435, 453155171, 54426713, 492816759, 297170383, 537963635, 352520704, 54148086, 219346969, 354260240, 231351122, 249185216, 698105901, 598186034, 882011708, 432936549, 51836104, 568586834, 126105841, 643224403, 840261875, 327780360, 758291799, 375032871, 597336859, 113493458, 566912634, 337555697, 527783271, 10041133, 265710726, 35698635, 610896758, 388514613, 981708100, 53607401, 459547942, 785979286, 623660961, 46231950, 126242943, 608356225, 763083892, 258566332, 608102914, 671356779, 1397073, 44191096, 142254083, 866826771, 374252863, 16311417, 245930015, 581904393, 35558652, 121691544, 299716204, 814414923, 187124662, 288638620, 768488458, 428907855, 620995281, 744470338, 922079879, 186815401, 452622815, 38418783, 790229019, 706586689, 774431088, 2069856, 989006064, 450477107, 851108427, 255326152, 694294806, 401630562, 463616380, 398575521, 703756461, 179716294, 505088941, 424974143, 981095788, 740110498, 524447931, 102550570, 132739284, 658235109, 504478075, 95818748, 722157035, 106449379, 208006394, 242222035, 381660331, 652366567, 347344272, 761002608, 171867326, 690343006, 936520495, 477014191, 68009875, 93501928, 675051693, 268276315, 672046771, 916233613, 128932755, 467200544, 472422948, 564987816, 102387602, 227526395, 246452909, 151828591, 606312585, 307058761, 557411488, 370424569, 89032340, 506960839, 276131785, 848436679, 698668327, 961654345, 991721365, 132064428, 378328657, 683910826, 144557409, 618959648, 71813783, 399218924, 212678075, 886061735, 2865853, 766195974, 617495153, 697270645, 155607141, 228414512, 405718991, 104985402, 909071179, 719606221, 59130199, 759881300, 819173588, 93768081, 179763928, 604625699, 200324591, 602849796, 134118583, 810082477, 172906198, 217610567, 755400621, 833493826, 127980123, 658450854, 533645031, 811217479, 677904482, 222588886, 994369236, 843399486, 682037897, 578574720, 12013653, 204027465, 335097035, 315111732, 327393925, 680248885, 684764707, 835874158, 267406330, 900481942, 235399952, 622706490, 67379273, 963645507, 152676412, 198743202, 788596366, 406237611, 398350904, 949576582, 339671528, 598893206, 354394093, 264843762, 495498317, 527089257, 350701406, 406388206, 927787491, 560024453, 351971093, 828163658, 431925229, 619757138, 478880167, 984592905, 349558988, 829534587, 528434776, 892058663, 713357141, 9248783, 664665037, 276164259, 169251560, 348585926, 593578992, 903340803, 795678795, 221497027, 502817542, 35618342, 400979603, 731499642, 979800271, 407196332, 564669933, 558074686, 395019049, 721535665, 282429539, 488573943, 933250501, 330225075, 253714937, 220211138, 786525006, 549734019, 436704871, 870829055, 427930525, 16053851, 381249136, 643992099, 718942760, 989322368, 811637293, 415185126, 610698231, 888423265, 969287506, 438838916, 138366119, 541166038, 725740666, 377786643, 999629503, 928821251, 717858768, 724920075, 534206307, 403189912, 25814084, 163157447, 995852111, 456392162, 329619306, 146068402, 774622685, 701958401, 334776578, 103309811, 859077450, 714206041, 261603469, 928108725, 233161654, 721712205, 418691156, 337794258, 33350305, 32783709, 478671630, 703418069, 483633424, 208876915, 8253054, 69344720, 267629391, 233035771, 900936142, 401854283, 898207822, 938679267, 171548771, 520574583, 680414306, 661398315, 671060407, 540265907, 375392893, 949280303, 170503459, 973796604, 394443654, 723412337, 621965119, 445066719, 739992977, 615769781, 628803367, 103976854, 732059094, 53872183, 653308759, 870478476, 759168560, 488233659, 695874565, 214916468, 412998035, 54685521, 767262040, 985575391, 828526876, 644118554, 332975218, 595312810, 186973604, 723321804, 428754024, 685089186, 564145918, 683210362, 499556515, 985674106, 478200070, 810247136, 743043645, 222372063, 577944618, 204891389, 984715786, 181978068, 107580593, 85864710, 898820447, 43260270, 670238221, 523819029, 935258583, 203004434, 209822519, 569184245, 124547344, 512467178, 612585270, 20558147, 787665538, 791659683, 556592210, 175416882, 726236651, 141701563, 93505999, 147888385, 667890873, 583212894, 190991870, 479980260, 22535723, 391387840, 787298780, 93058124, 936101750, 72668451, 785386012, 863717228, 253671867, 897394463, 659190734, 443333954, 990431285, 551591929, 403586515, 928965751, 589375983, 856589090, 157775197, 133642436, 25570232, 84428508, 950526822, 96988529, 328323095, 185367719, 706542042, 899842850, 636769822, 595295984, 940233645, 912091359, 781780697, 548878355, 320442790, 903909822, 744817791, 82712857, 311292230, 528478722, 851195908, 88996398, 594975340, 128749510, 630439515, 968357652, 362584692, 67868513, 271687586, 982282774, 342213665, 293425061, 753340052, 781288379, 862326112, 32287425, 810465226, 416192521, 356568718, 331897101, 62073572, 871994250, 976281386, 875031394, 885045984, 891552481, 769781381, 234451312, 250316431, 180768713, 787968012, 594817040, 270355675, 818937229, 498224599, 548928140, 427747260, 455196161, 748358340, 989509379, 170256002, 430399540, 931039665, 424937285, 534925473, 182359323, 804800300, 556090902, 978574296, 307760437, 128743253, 19546286, 372591902, 56476460, 378807165, 418131012, 1975259, 74266083, 366893828, 806572141, 898914921, 435551793, 447745191, 637469510, 608667604, 859775638, 780048638, 840703647, 96076104, 805801425, 132911822, 488434004, 888419383, 281461303, 741352674, 86883512, 179436460, 46739856, 449486812, 295611204, 373376670, 304706096, 621317838, 246601956, 782971335, 449932427, 602735723, 311972605, 678783495, 700605458, 659477371, 834391526, 18601016, 586362587, 490901537, 344509051, 465330652, 822594525, 97787032, 518638460, 180567077, 492342946, 681502684, 643288678, 839995143, 176684776, 774700403, 717789181, 219892753, 13451939, 622769565, 214378849, 959834404, 629321624, 685871848, 270452748, 564631983, 197332506, 899040303, 936217383, 219078467, 799154720, 88904390, 287259286, 724011468, 623998029, 838375649, 588760377, 45305176, 552776349, 761997798, 55251434, 370982493, 898693169, 875922357, 63984151, 95311674, 158500231, 88260203, 679039867, 588203913, 280985864, 81170408, 972732838, 569329138, 842422945, 964144042, 363884329, 442476882, 368325060, 849410477, 537395044, 42361596, 595752614, 386799936, 861032400, 519226592, 903921042, 941903541, 135654896, 13797163, 840139671, 855123775, 74421517, 85370095, 768702473, 999196352, 632409162, 456928651, 436943563, 536125058, 546473689, 27950220, 930611099, 376511084, 47344533, 391484562, 767764361, 158027473, 97344415, 913776575, 540078356, 425024917, 268116720, 383946210, 537071657, 960942985, 507482066, 162694725, 424479755, 780117668, 304404971, 596834114, 236152774, 390399303, 886920705, 819108898, 952953584, 637321964, 81231003, 908684549, 654429049, 222808824, 277516384, 360020886, 835492480, 542845951, 603571519, 757607617, 407803519, 711632309, 57237206, 464905454, 895667046, 50129213, 442237421, 986386359, 130602164, 454051425, 773866938, 793084241, 803832603, 491968114, 866966614, 250499328, 794209961, 626075246, 101205818, 246357195, 662030951, 82010131, 241383109, 382198310, 259458039, 915082633, 48449379, 258497781, 70924140, 490670183, 567025680, 140902695, 214370801, 52701903, 785270407, 212566968, 903054791, 557618184, 322043053, 521113507, 393021503, 223842012, 828266814, 19073475, 986148657, 189896, 852137807, 237369761, 540867931, 493461115, 830710061, 371944433, 157096, 822696117, 926792831, 790552149, 149542742, 875475311, 263341162, 498567280, 865771817, 24426181, 298509079, 808869834, 60115568, 421693840, 443106293, 697913829, 681516370, 72028738, 936920298, 580795652, 145193033, 536126271, 340120488, 641962635, 273390515, 818178222, 510376730, 621271252, 178700516, 511604306, 767984464, 232563748, 79360784, 551516419, 660450387, 732246157, 323532631, 57972064, 881156697, 811348802, 41610134, 496502972, 622635559, 552281061, 734722058, 906618907, 281873751, 167399539, 775040853, 424515249, 825651876, 387902414, 390643739, 178000583, 988311404, 286655957, 907679819, 889296929, 433097819, 186677888, 395362472, 202990718, 450677767, 466487998, 37563874, 222743976, 700041750, 395380169, 226730616, 349241250, 548353668, 906907064, 874858547, 273183590, 797519621, 710421006, 110305504, 879227816, 505676552, 430588341, 479981994, 407018250, 37158322, 898679763, 942668050, 451810890, 511803525, 243131301, 972617195, 380871258, 149724080, 730113767, 223250783, 377018910, 271593149, 30632044, 18737223, 721131972, 190646947, 906341616, 256470953, 555225760, 69210624, 20546185, 705457561, 870946224, 695044231, 75740133, 293277839, 548073334, 610948149, 454581225, 313542709, 596797497, 655644050, 711059264, 595940252, 55838734, 39068253, 985403689, 926243481, 889556477, 131371845, 431477747, 441250707, 650754096, 233464077, 357225275, 115575861, 485408887, 963342752, 887874952, 43276035, 37390807, 542295634, 630093221, 404363740, 202309720, 127617483, 508871205, 449013208, 479992365, 804967991, 407398113, 299535925, 366254929, 453815648, 313676804, 728230043, 825584643, 716636324, 821827781, 945839036, 66685331, 893280498, 358831257, 402324804, 350438085, 426811002, 238818649, 25087526, 186407362, 931153878, 691307129, 288532815, 976321592, 62431988, 312790221, 794085718, 77162742, 877485907, 436135753, 62927067, 773204109, 271403128, 778502611, 635084361, 509625953, 817339061, 513811268, 429634492, 846645891, 852697777, 215171906, 724880841, 956919279, 911273573, 549131361, 152048388, 429869467, 396017593, 851184803, 74572545, 768051318, 213400658, 99603573, 105343804, 190686520, 392185027, 522664017, 694120303, 209527911, 56675523, 444316040, 421651776, 395963385, 217347075, 44466288, 357871492, 489889351, 802920669, 649770023, 753739643, 859978225, 963409793, 429888298, 929571323, 470971619, 77745345, 426748370, 465020468, 332979674, 928220097, 958216976, 140939215, 97953022, 964696223, 141742684, 186289647, 658221883, 743049830, 429540660, 190093878, 323126355, 966801305, 521050710, 114677373, 601526094, 389507121, 885475379, 723904403, 318678456, 451276075, 429671970, 822529231, 103978968, 726439384, 25641118, 340592854, 730764981, 799798571, 420460023, 625664709, 558214991, 15631605, 336516352, 861268312, 455274745, 209034241, 971331903, 774974557, 966352428, 216278807, 568372964, 4569074, 146293084, 870601162, 26488570, 631552141, 475812731, 539529561, 421429405, 4085915, 115785344, 434786155, 787127920, 531612351, 145761904, 635394026, 542695510, 685791596, 400409757, 95598981, 620987461, 109737118, 782904117, 778061290, 187891702, 898535816, 852828980, 951849420, 383518035, 218442078, 698118555, 936670962, 438514166, 66122021, 361703311, 901427499, 301374907, 36870310, 524381545, 613442444, 273133321, 797574704, 130399509, 678199395, 620938578, 244314952, 442263189, 233744104, 661134990, 567701746, 52987426, 76320970, 528256173, 712897589, 996996707, 616682992, 361454069, 827876724, 271154061, 545750337, 867888301, 839348783, 335601096, 335855314, 731990300, 866615154, 671714353, 643745593, 663922261, 952182175, 820776176, 152327301, 220619567, 986342041, 902617828, 433696951, 791976096, 306493266, 398684713, 224889980, 557181767, 154964988, 964249440, 894263612, 771386961, 947657092, 896633415, 624113664, 776666912, 417002763, 822867570, 149912584, 923107944, 666877107, 419257748, 343808078, 890427121, 346737030, 387331302, 547738850, 617546179, 960355266, 323726074, 973348960, 914470856, 866866224, 197156719, 797468348, 3267625, 989009795, 676956016, 834391531, 784750313, 880272968, 896889303, 830233481, 312381255, 457981414, 416013086, 195418406, 481022794, 207621588, 948305360, 471476670, 596569751, 474149764, 625188397, 81569052, 204058906, 102913203, 523005083, 99850534, 887007649, 477325732, 366729538, 840650275, 422894148, 465628435, 48262607, 174151921, 328389529, 166418086, 93467312, 516314761, 303535388, 949576958, 699467047, 997393033, 664969059, 86020279, 644127831, 703951918, 745376176, 878340881, 695942934, 649286400, 890759179, 981187135, 180114670, 790882294, 931942407, 830764316, 880340001, 915748914, 854165826, 317736121, 537023024, 130450130, 908434251, 7172493, 899790325, 68355339, 374052090, 144214997, 512034747, 103225200, 194124971, 846739948, 960116612, 296730949, 60842416, 678976229, 671845545, 992328304, 496572428, 647666162, 258418641, 121980297, 694237378, 886711412, 153525843, 393624156, 784457684, 597772341, 52022688, 205455739, 407642958, 93272043, 301441897, 598827738, 397026192, 316739104, 630368699, 971845475, 802873170, 803214281, 754923550, 486089789, 369609056, 243515302, 432530790, 613983396, 217378905, 39099621, 94389371, 201601503, 859581589, 931603699, 585622738, 319566610, 706698384, 375586861, 29074246, 169999605, 124052168, 913609096, 794849736, 975370580, 551421987, 188565714, 74367152, 672260689, 950520037, 37223827, 986290506, 944017242, 159120925, 575833797, 246064892, 611927969, 302489586, 602165802, 143054344, 831451768, 758933894, 300654811, 979087327, 952680909, 397757719, 858700629, 493934399, 920534327, 424986968, 240148414, 507099643, 899011212, 279066076, 386758501, 209072178, 848492765, 936128695, 905905592, 665233712, 236227807, 130783677, 417564679, 529737034, 99817490, 989140438, 666177881, 879230083, 144481928, 141912285, 8551477, 700193690, 925038285, 537242138, 845656106, 592789320, 931127923, 883376641, 729433588, 123955691, 174758427, 56284211, 413297504, 502743670, 257750454, 196336751, 718983617, 383687403, 543053546, 628346681, 405366919, 574412387, 76867974, 789684161, 746044209, 174898702, 458109634, 441597067, 515979202, 709610505, 876838107, 463503401, 354026459, 415382132, 401391014, 806111107, 871499976, 185174559, 747903655, 646489773, 271836832, 397704293, 339286886, 333876780, 577625159, 943969644, 53072141, 750308594, 148331955, 465046877, 978487670, 950872562, 696143409, 421299664, 375324150, 432374317, 461812277, 644974279, 466393054, 801217303, 845410388, 462231472, 454202013, 714955848, 824678581, 803244917, 455337797, 345140497, 554091497, 310096135, 300761894, 25443080, 348213179, 935681192, 133544100, 124198249, 85653258, 847374360, 908877894, 588409206, 210349801, 182566729, 835820478, 819771514, 85504066, 154143941, 475066395, 126233919, 631941065, 397379307, 620768664, 237985565, 673261203, 650481886, 518073721, 153623019, 669650529, 374961475, 762626756, 98399667, 702230290, 153946466, 357600788, 452992422, 931713352, 763111978, 616545532, 877104525, 183783920, 198757960, 358711595, 130841201, 836724041, 262024974, 708067862, 968660340, 683219404, 67575654, 811713870, 8862311, 86214801, 223527303, 35863281, 193031781, 496361694, 577168638, 906284547, 124255417, 878833948, 616170392, 494293918, 528274238, 883630817, 352875295, 245143320, 538580646, 83679469, 523327031, 620220447, 162115359, 377937527, 240999938, 965235727, 935522536, 167343746, 895926522, 659802315, 770217285, 305263702, 468810669, 468352939, 905911531, 687810712, 574413858, 895818500, 344889040, 628292587, 977919306, 758369766, 455651981, 270946665, 817481968, 746340844, 321224011, 938683223, 977328259, 134089138, 640686426, 576977307, 378625114, 610877673, 195115064, 842666858, 541614679, 333880272, 244739958, 486761093, 679384644, 779951154, 235817065, 457338609, 427817159, 25503136, 664534121, 449587881, 675572262, 600210017, 12332011, 143235386, 56408211, 360272817, 455860456, 316503537, 532725032, 788569264, 981670581, 275310502, 715084069, 405855563, 629409485, 303657626, 604173340, 590435879, 166406610, 247083914, 311401810, 880589270, 120877495, 245743357, 268189366, 642956415, 34837734, 480352137, 302177736, 165045449, 922836688, 378566734, 760144548, 500231788, 451846440, 877809350, 914949319, 859416058, 151251459, 723247753, 69710364, 393962480, 275259098, 777318661, 606217229, 985555004, 62271450, 301500625, 388571345, 696523335, 20691345, 931201204, 521135709, 717376752, 590117762, 261667524, 492841088, 8206807, 98336501, 94692887, 455607120, 103271578, 492074748, 631915211, 844546782, 104884390, 168717512, 480939094, 978160398, 551677547, 520839364, 474977305, 735735412, 481225596, 361305453, 853673880, 184266164, 347198214, 194367044, 382632056, 998120094, 889539941, 89896848, 940871449, 642714453, 909002408, 971916430, 639295512, 124506374, 333949290, 656112456, 653231751, 838159632, 998186450, 952464663, 18170408, 51701563, 480872433, 713256671, 131472933, 435159083, 177524615, 255932662, 277319763, 358317304, 117590125, 382915062, 131036743, 323978274, 895745338, 833222874, 198382548, 818592512, 901728822, 355827384, 687656790, 411612913, 121155545, 236366847, 931634936, 132112060, 681141110, 242877421, 516094046, 491728967, 971842229, 787666781, 535880120, 763377167, 249254839, 969925391, 912922667, 720910551, 162657613, 666194006, 164180464, 693840185, 757338061, 895773073, 763336921, 988522379, 258295858, 833027114, 6403203, 605758479, 63573951, 771396359, 347111244, 824674386, 523653114, 546034112, 333953339, 708426511, 266891200, 630581970, 548103865, 909326326, 322663623, 653352504, 247816487, 934606289, 127627474, 112549027, 692600215, 166003825, 394871285, 999491229, 606963133, 337694030, 807310763, 860955343, 334518454, 605680958, 837331049, 306688006, 632545144, 30475479, 196093323, 777731741, 655209821, 506947041, 481020167, 854261200, 683864432, 303043470, 149597052, 567436446, 464378690, 774980032, 65716692, 269458797, 230794664, 25088439, 762867218, 536896527, 635404668, 122170865, 577709862, 917340976, 442551885, 448486142, 394597748, 202681413, 123792473, 407394101, 63954609, 363602778, 291454403, 800593900, 616245226, 80808730, 197986289, 88438162, 212358022, 676821469, 874576822, 844659928, 293432961, 228493470, 876943534, 831131595, 119546784, 587528815, 897412555, 669594425, 735303586, 454576372, 229844988, 399186351, 591257481, 3635458, 202260702, 602430835, 672797228, 972090572, 535196849, 627665501, 888190613, 320877873, 957325960, 768455100, 77583922, 57078780, 646648646, 156558123, 49710376, 812183747, 26376823, 950379041, 111340245, 774812180, 910350180, 172575394, 158892348, 535189598, 582872526, 419269502, 214555432, 328741641, 244941109, 542792685, 859890817, 331743555, 883957277, 656642733, 706309251, 760955856, 875406863, 992953360, 615774604, 159053692, 615180401, 86584893, 911159292, 315755788, 351819632, 102327562, 136458115, 408286650, 252789920, 423789731, 352509379, 769324300, 608829335, 389000939, 737073095, 938672679, 124025588, 512860975, 28619717, 251181966, 816406882, 506801475, 497780356, 115450205, 92141442, 447302057, 958341375, 147412508, 866595554, 19238659, 858724790, 432361759, 862943535, 62388817, 957918199, 862043617, 645823553, 860316607, 415853229, 138566999, 394895850, 795757439, 860962168, 676836652, 244785627, 701839426, 679823751, 923030299, 565354358, 740944252, 732580696, 554455007, 270126718, 139193759, 314492018, 839306545, 131882802, 119622971, 162994388, 662487349, 815589397, 392141096, 99367577, 6863519, 819442323, 986545811, 670556883, 280000122, 364510580, 732892077, 530807088, 37220044, 742870454, 727718438, 799255158, 855561094, 323372319, 452403154, 781841979, 861721310, 599738336, 140374579, 281626469, 960822539, 160336447, 93379420, 62102201, 819601216, 523626718, 295912375, 361046143, 59498997, 67138898, 369187726, 530694281, 47590362, 334616449, 844134905, 880141965, 340138943, 132046757, 816681821, 576717677, 172834626, 539574546, 548857878, 667149265, 112274813, 654174721, 140155485, 418802485, 30269822, 183492361, 71611519, 747320948, 690781933, 25046233, 402285177, 237346569, 380007724, 382996502, 87271021, 366615862, 232004847, 767572741, 806410431, 415592365, 364284482, 610179989, 677530099, 858700220, 139499154, 426044378, 886793242, 410999684, 379013686, 92501427, 628544541, 560913372, 812633423, 411717004, 61034440, 550023485, 87208890, 986187310, 667583945, 32887041, 951218692, 701091218, 170989837, 230056055, 11945872, 263037157, 163894622, 64400091, 716450329, 147355439, 172133386, 375783064, 325367355, 148149083, 566110201, 359217946, 495948764, 50846998, 490436049, 177481086, 41221509, 91259239, 388445297, 875446973, 616948565, 404441215, 500089600, 707047661, 500100541, 739400761, 506789718, 68124844, 701676847, 974537636, 71308628, 588959908, 622535497, 844660758, 173386876, 982818324, 861052538, 691757538, 859138998, 238777665, 339128579, 340194003, 846046097, 941663918, 829904307, 792663177, 281156043, 38022908, 548353773, 322782951, 469301841, 1868017, 240604061, 968125871, 831728464, 682270179, 777824579, 759561213, 949151979, 584290495, 661040715, 481769970, 827666004, 293839865, 44270795, 715915491, 980810928, 208176105, 743565001, 499807929, 721979270, 262845130, 87086722, 228776687, 110003514, 347758729, 251473841, 630352369, 61023499, 846111161, 266703498, 877153035, 955436647, 603176123, 808799003, 489626185, 880333910, 493141409, 426364417, 429618644, 728298515, 654795564, 305693260, 197052847, 915897489, 991252892, 445438275, 575465255, 965958985, 298782500, 291305069, 601594039, 542155896, 510810483, 557994645, 164188386, 63307973, 305812083, 470060441, 821526849, 992665935, 573804767, 411431772, 583529116, 648323161, 709580889, 572790702, 127004784, 235270674, 195696201, 913495328, 798862487, 133626985, 992646813, 71236054, 303295183, 417084418, 812907536, 725614822, 219874180, 601252008, 988328213, 649769809, 241513713, 519619499, 722826587, 504741107, 272943773, 480843246, 377377407, 572152038, 74246285, 566826206, 641333999, 476080636, 724830179, 830267324, 188510376, 388135272, 33675684, 6805221, 372208585, 826318532, 953410185, 715467996, 229670335, 897011920, 533523057, 861728575, 671135258, 288010080, 529004866, 435605620, 176206570, 899805749, 898061098, 540539632, 643133450, 452819121, 956553113, 906563866, 762469316, 894940359, 928127539, 960090293, 72891308, 317170354, 671989700, 413607935, 30561838, 910377257, 680233539, 670383504, 867061631, 433498516, 132144601, 800027174, 917931929, 517486945, 533692281, 121710005, 888745005, 855313892, 321711999, 191329372, 753097384, 668330269, 569240503, 284410320, 222047787, 105297614, 924738276, 466596987, 729781257, 911254799, 589625186, 891583740, 957090586, 616365552, 465840479, 65769771, 155323903, 844412463, 145439305, 318599493, 299092913, 596701607, 595440667, 211557055, 131925545, 852370497, 511247209, 976999240, 993825405, 502493297, 307821281, 894547366, 936024736, 40347232, 968438875, 224069518, 450433756, 798170970, 705995740, 795027569, 944369414, 260638421, 658679499, 981220190, 652340394, 701757498, 652876821, 376756194, 422185324, 213350036, 139503993, 623050408, 951689315, 195132408, 637593238, 132946891, 843192205, 256549951, 665663327, 880693471, 779492030, 22597984, 451409639, 853635317, 856430828, 166721174, 742914789, 576404518, 39397410, 462820744, 922178288, 708595921, 749185389, 648117715, 803634820, 85677732, 129519971, 822441511, 143613092, 107000764, 552824102, 722677742, 426995267, 142222971, 897431130, 448246337, 216532336, 746068825, 480339528, 28824685, 529587725, 70042980, 140893597, 473492639, 208576540, 627836549, 272655760, 993866097, 329196533, 340061684, 845084727, 183073494, 74322949, 576056931, 477373849, 315945708, 132203296, 1988593, 316791540, 24727042, 241100089, 59770117, 581686126, 377583931, 403487698, 302920385, 11196269, 804951842, 436319362, 806761309, 654836227, 834621231, 827845481, 317356352, 829062099, 160582745, 509806947, 335974201, 939554395, 279869100, 530891580, 179170526, 86062501, 261435641, 72473543, 227360039, 119096548, 234199550, 881027465, 154514328, 668235364, 848355101, 594276087, 848620389, 388129540, 304086043, 972587408, 824851270, 398883587, 121063308, 419523984, 122068416, 28495849, 391126811, 492579149, 334193456, 806005413, 277822329, 465256010, 16619499, 240333162, 647012846, 356000203, 988542129, 923002354, 702124075, 703461577, 226801569, 647247437, 372914616, 405823446, 439681526, 89178200, 599619453, 558778393, 940976267, 892627605, 361208398, 7486588, 811847798, 823723351, 107410531, 373544949, 564602348, 894435475, 422855397, 894296711, 193106563, 681431761, 312704412, 263008006, 811472676, 821346747, 759358423, 582184145, 80172253, 359757433, 843449966, 711935626, 438869852, 321102563, 704738076, 681898942, 941673654, 139113920, 761850660, 307662071, 597154566, 185620719, 779949426, 857020722, 660373529, 239667906, 332962794, 263561138, 164341798, 975619968, 842355894, 413484624, 79888577, 942247986, 962596891, 377731314, 462245359, 710821169, 759356426, 357992308, 721216663, 639630982, 531981641, 695916905, 464600767, 85265588, 304337794, 755584584, 182537415, 505017514, 757670149, 500927795, 191428826, 195139108, 50151371, 788719937, 561542082, 713007529, 425744272, 58039201, 238380675, 818650657, 764658622, 430051988, 108009748, 262738720, 940328552, 447227115, 628889130, 974455437, 412512029, 607414731, 747061952, 530595242, 641304692, 918300061, 479853846, 967147885, 146015429, 326353886, 42356452, 923582377, 185084397, 835944168, 627119031, 138615994, 486644713, 834485263, 871280457, 576670443, 112943167, 794206983, 558886950, 951952993, 92946971, 447951969, 630630272, 614396050, 650400148, 927415739, 389391219, 687707293, 924650327, 546755737, 377122392, 543623301, 518970615, 506014870, 969106752, 360428600, 333811234, 166971155, 891171388, 608546288, 148504328, 515718407, 136068624, 652090808, 532611126, 159051587, 639183609, 738241278, 697507722, 719299294, 396866933, 680856395, 496860452, 155970988, 601615384, 661454668, 229704258, 271000593, 314535908, 524845863, 44998905, 119189605, 444949863, 985251979, 680108622, 84230405, 810902569, 255933787, 200476009, 752288961, 695059403, 67978655, 30242110, 353789875, 508940545, 91309485, 605042824, 923577415, 596418244, 750521312, 389374489, 744553191, 609242549, 607743233, 191137580, 135833343, 13073271, 527146897, 791157349, 433699238, 200802090, 851865797, 924696749, 257191611, 842823614, 319225941, 709065594, 739205069, 483496856, 102670928, 502136087, 98705484, 532060658, 824752949, 978339321, 433124485, 97424338, 687866179, 98276026, 180513309, 274214252, 195189279, 244795967, 575786981, 1577268, 636285498, 318958583, 18736864, 356866219, 46298457, 242327033, 339481388, 97079284, 884903772, 546106518, 71980937, 517496092, 553206025, 353811494, 122834016, 415750004, 627559746, 748516255, 879481292, 37440133, 651582880, 992754685, 311713790, 744416198, 48292844, 761306491, 111762821, 189455534, 945249289, 65999483, 996053008, 777456557, 201762235, 365249220, 636373872, 681989472, 141608111, 78327039, 348854450, 164296494, 904275247, 520526858, 300742977, 431784206, 51588997, 59775797, 256135133, 834083987, 846045291, 55456038, 767325529, 708124280, 674919805, 136609383, 849255299, 920565049, 303452642, 317846268, 407118907, 103250462, 911646403, 136313190, 848897264, 267437167, 419574113, 211590680, 882769870, 253142275, 144919612, 253536666, 494175242, 343271565, 292164935, 479649210, 33864692, 393580285, 558034976, 260536714, 491666068, 153801954, 750502764, 556702038, 66932332, 498864989, 852621867, 539087913, 367153628, 45343652, 408286103, 74684167, 942080072, 496383611, 534716398, 414669393, 759093035, 200250748, 1550302, 979084743, 987087896, 335884304, 714448099, 860263707, 981010905, 167012941, 847787624, 633272925, 909963810, 713756179, 308020512, 815818532, 349724152, 5033611, 115184463, 546931713, 256563669, 111667287, 268995115, 303164771, 668426057, 328231656, 768988437, 137766465, 737080294, 16815702, 354202559, 341250368, 119578306, 43256918, 402522162, 631740459, 589773807, 773753314, 469742304, 505547235, 19124297, 650496595, 948699960, 248833532, 405521419, 888068116, 516494479, 132446111, 106932482, 945134520, 204314297, 98839245, 157741809, 311733833, 21042016, 582460549, 821235526, 88109167, 15840914, 456270867, 37777556, 963242650, 199511556, 687556787, 409832711, 979966162, 63427975, 161781285, 558357123, 352838560, 933706420, 319792054, 368055059, 895302354, 323947737, 353262610, 754654344, 898544547, 97254215, 581986472, 324636936, 215149827, 856172685, 199477821, 777835276, 212763359, 398498026, 493405779, 22086502, 248835005, 539429380, 111394479, 156546990, 798000022, 146971903, 11390249, 87054109, 778070922, 190157018, 51136291, 525601755, 652047249, 204625207, 955159361, 153410514, 77754178, 578045378, 90419937, 354592215, 724995567, 83197751, 768115793, 577831645, 24737215, 510265454, 764545007, 480266985, 222822371, 714149155, 798193307, 134503919, 193074903, 482123874, 16457049, 878364758, 994804865, 332738510, 316025805, 718749653, 245192692, 289169038, 534226813, 927527514, 788927813, 230746642, 628745875, 614092811, 203107889, 156825165, 381472907, 692772781, 714488608, 597073130, 987152426, 719930677, 802541267, 358738013, 164864849, 192148772, 131605610, 192749041, 250401277, 397271465, 423642600, 655619736, 848257999, 901451388, 65436397, 206105301, 958575920, 571538926, 24701775, 17962576, 509692501, 805112341, 568841302, 290132699, 671548356, 982872667, 45056966, 541020424, 274232922, 515732512, 982938806, 199797073, 704973236, 808514528, 968614006, 594080042, 648200428, 589255760, 920472535, 434896204, 4304874, 443912623, 31922821, 777777789, 827839349, 541052020, 360128270, 944044001, 967147216, 688928370, 794148966, 786070749, 478236244, 849456718, 291245794, 58217521, 75487451, 832621046, 304283844, 329927521, 213330079, 831140089, 991403027, 776860196, 742073915, 628803896, 452212807, 658804914, 436592135, 243224242, 414666725, 119478253, 131797461, 314129827, 45008622, 173116790, 321146173, 329929055, 437919231, 3646200, 999616106, 10781786, 584079677, 226459115, 741601457, 936953151, 953406278, 970595727, 419259228, 207446373, 279473056, 50821601, 129113294, 835513465, 997420875, 685289325, 319876517, 178742371, 572029261, 254851662, 473230960, 880422133, 252851152, 402476488, 610765521, 333560271, 558194300, 968554450, 655058466, 544077036, 863273645, 318705546, 440957446, 981128530, 709482383, 24463754, 521742059, 449395023, 915189408, 846764899, 788389432, 255266077, 824709844, 349911943, 29945912, 841456407, 763847605, 331832469, 8398434, 680818809, 710586193, 903194242, 81760546, 187329992, 19784040, 920652537, 308388270, 792059234, 469435596, 861449726, 770793487, 192577058, 457643168, 82360719, 135399871, 609457327, 1752737, 430928874, 310793350, 467162861, 192483992, 279685945, 752592560, 900600202, 484670056, 588701991, 738742570, 777389449, 563168630, 113708200, 383759595, 911848849, 335714400, 28267264, 730787981, 834781496, 842945479, 479244125, 659655039, 578894822, 193832490, 781388051, 393705446, 832619959, 376903937, 231980942, 502732709, 690908120, 207462847, 724076646, 524329743, 585109301, 57681674, 484064030, 415016276, 54505502, 144403467, 107920929, 360340461, 655587202, 461581159, 491641330, 766232967, 676716847, 633901904, 369473028, 755974217, 974466582, 484402024, 296044179, 700708664, 466365136, 987194237, 612915937, 116435910, 500661858, 627553617, 354523773, 503041941, 858219083, 200516963, 386026422, 124671132, 334611823, 451325605, 626313165, 243249951, 299335144, 704926394, 759626079, 86036522, 66664252, 161638289, 415474954, 927435131, 355785912, 576969037, 971669753, 174155856, 901858172, 976888269, 207367867, 600771198, 722248571, 93353650, 151314442, 414568150, 420565646, 178600338, 594698451, 728188325, 283961875, 780401341, 511250669, 541197084, 638837311, 513456433, 18577091, 344624800, 399201053, 521104846, 802652480, 266239342, 683824967, 640547356, 594150260, 870869426, 988681916, 268630517, 604490397, 378551991, 434675155, 920147380, 134608800, 862249909, 779632688, 90778386, 769508527, 742854726, 143390675, 57396524, 763244977, 747628520, 764002325, 887758855, 162085215, 923212761, 114239926, 230890772, 423909687, 649194657, 765870954, 212275025, 392112741, 92423765, 277052286, 752494153, 764595499, 343743126, 210923371, 820807604, 737734329, 411485797, 719096496, 995109706, 796190578, 108561363, 496746234, 834046321, 47425955, 451452167, 303983848, 933742837, 899921688, 694520631, 21122058, 890020507, 49823675, 109810756, 110944151, 496958229, 804392161, 631096307, 280413982, 580332092, 401727422, 822802848, 588154227, 977931296, 377144113, 335497071, 898885096, 484506554, 705804241, 207203296, 45869977, 651527074, 942638861, 338672249, 807275741, 459282255, 636951664, 324176288, 400125759, 653665868, 174103992, 996141561, 189149341, 58115081, 514895786, 692391307, 220652756, 118758545, 431737501, 736225798, 318716430, 167999269, 486463414, 930832008, 580472087, 859782625, 258894038, 646078961, 771131169, 112418058, 820860466, 98087706, 524500928, 563842016, 176996341, 676586883, 937386578, 704181139, 250761532, 874872121, 84479636, 452439385, 683225741, 71844415, 522592444, 215217177, 600487601, 506406133, 188192311, 202080610, 670969061, 405582990, 515638372, 227150808, 583002316, 100446865, 837574866, 370835474, 457849426, 757920592, 989922665, 289967708, 255324014, 123046160, 109948120, 843478379, 623943657, 931291732, 333342881, 528899844, 808983261, 406022715, 878206066, 50640690, 275428052, 539540546, 648907500, 681332297, 276405651, 576874225, 968626564, 950580175, 738538059, 195275628, 594606501, 595903491, 997375122, 957970945, 351079492, 481830021, 288666747, 645865143, 902007277, 202003745, 906982912, 821346419, 161913173, 249643097, 802307, 442535491, 876948542, 11368638, 251923406, 234564178, 247386464, 291096139, 820441192, 492632070, 515493460, 742543168, 273981926, 65783362, 295065328, 128392291, 702991167, 630540445, 486428493, 365400465, 50694642, 975155054, 802446544, 682258533, 914645128, 934338432, 639876503, 633266644, 499698974, 410855143, 451384478, 513962155, 688163376, 330117475, 816112741, 817328564, 269570531, 936039999, 580167299, 979167584, 449477199, 288133256, 430495857, 248378103, 154139308, 742054773, 965639655, 691763570, 457079261, 760613539, 526869229, 886546044, 102176759, 802602768, 910674082, 745201095, 590299345, 807090953, 674071738, 977600702, 369858403, 886903746, 180277721, 137447412, 48231698, 865071282, 87986513, 305950335, 298679079, 362082477, 105306931, 141251133, 262506976, 227715541, 9233687, 690570587, 865468096, 26332373, 464041304, 115266067, 640312839, 901504018, 400250031, 741498923, 664829986, 53110056, 640448114, 961826468, 842065975, 152778500, 151130227, 465718966, 824691780, 613082040, 690702683, 625059759, 3153555, 421095110, 238175138, 99674246, 243659028, 202598282, 822169783, 824535872, 412360563, 529148755, 485129469, 809608557, 843150241, 330867270, 673583455, 7520683, 589538619, 276653122, 503117922, 217912531, 931369631, 39501957, 467044641, 759232885, 632780278, 200785511, 249426731, 206566917, 133104128, 712230975, 936356675, 360663247, 210606916, 410434668, 528798370, 650001544, 319747674, 980070720, 168891630, 609032442, 103614938, 356749046, 885562068, 661674055, 133306546, 766824182, 962619998, 855643951, 525049061, 96338557, 498116240, 230359116, 148571596, 859161869, 918024410, 46429460, 887106154, 930154232, 39102759, 623397038, 961756214, 238264502, 154584908, 881758400, 793750541, 543888522, 479266067, 560453807, 178958019, 211204906, 628088234, 791009617, 302224087, 628237856, 967531329, 242045563, 58773004, 579116240, 521989584, 635396328, 963558492, 178926362, 462232090, 177794976, 512545607, 551398491, 820275990, 960386524, 143402705, 553028203, 598012734, 352741380, 449430293, 332223037, 788354416, 421201794, 883173821, 180609100, 541752282, 362523525, 70887403, 495674867, 878133259, 213094863, 384735465, 230719289, 91371944, 259692044, 965136237, 626937066, 105577493, 164483923, 939332245, 297863375, 746178940, 513900075, 506939528, 319378455, 228685413, 126760135, 409150513, 183866682, 110724344, 4464528, 626555379, 947944230, 791539410, 964267784, 396791558, 998758162, 768418885, 368599415, 897246651, 49168485, 364460862, 418198122, 865588825, 966395405, 616117672, 277026233, 384976735, 256165830, 822770663, 872225043, 655369134, 867164436, 281505351, 793059163, 598453204, 331899461, 99447372, 916684939, 10115978, 354402636, 524833285, 456981676, 216936, 633970386, 190643328, 268624703, 467320757, 404553457, 948007396, 742221146, 610195120, 364728249, 539083438, 960339597, 327957468, 731321707, 957539585, 93463143, 359958971, 833221526, 467527444, 649466433, 583310080, 685521438, 608921569, 551755268, 156276483, 620554269, 60286114, 105447483, 56288202, 494293604, 18482813, 316804290, 592190736, 943794166, 306579605, 713787468, 968303931, 8848973, 12996002, 178202364, 519541108, 358638379, 501739965, 548985079, 918011409, 568585680, 691899278, 762941907, 171175549, 89746373, 233210965, 10419835, 937302150, 634444967, 41245968, 558049249, 689685664, 841885138, 266742919, 166218952, 473483252, 868246228, 647678332, 914252977, 360658938, 585705565, 445367541, 489897541, 358156429, 189202323, 963941103, 703488722, 486443698, 793096444, 622169287, 431522462, 724226447, 529932431, 417677105, 775586110, 648971993, 84886554, 687882736, 143703384, 840350955, 10564955, 587140305, 919400478, 969746000, 28602753, 154527604, 595499512, 120266279, 808593953, 739675851, 522321155, 621111997, 511728552, 215987071, 250433540, 289169876, 197424996, 229937375, 275123839, 613206902, 449685670, 839250151, 516325077, 695900273, 9927709, 128014309, 399562974, 500525207, 657530197, 80971902, 517770948, 172868744, 92292288, 943480383, 146177280, 209410685, 931810237, 172300983, 453712199, 418219615, 753294636, 858099302, 446906020, 50315625, 348729961, 486819153, 528031568, 877824924, 741587688, 378343115, 459659318, 358599572, 272207617, 660945885, 812281098, 486369593, 98308485, 22879204, 488819487, 693239822, 613034070, 956845, 609081075, 328660295, 607155939, 592323552, 100292785, 561397589, 571877420, 374731747, 714807601, 898061356, 332039338, 661687063, 266003162, 648918002, 499138939, 197832888, 767995636, 903803470, 56946529, 243841580, 91483127, 868312644, 389727973, 483763606, 894466263, 807589259, 851407558, 401992025, 696449202, 792703448, 670670584, 551297457, 949161329, 578931252, 592202875, 85849288, 106589736, 981022427, 828490766, 291562890, 722400170, 957915970, 797047978, 175527056, 988123353, 462280656, 524285460, 32119028, 632894937, 219091465, 190343289, 719577249, 197518061, 393396223, 711339173, 976930437, 420064469, 389494978, 763681758, 898968509, 368176693, 781004969, 79885963, 877108206, 930457059, 929309220, 431113373, 106645450, 522490268, 204950432, 297601498, 840822041, 42788992, 388426951, 618862091, 539035746, 200139228, 478108437, 85392403, 143447220, 587402793, 572129795, 646047777, 363432306, 859087230, 211561185, 355554209, 759063641, 851023938, 8536451, 47160110, 295743470, 659771860, 389348670, 471230723, 548257914, 909125326, 829623391, 814571234, 335073079, 101675816, 723709165, 430141623, 805547969, 21863389, 107914405, 469422398, 488903643, 214629869, 591974321, 845608001, 446338459, 740025665, 408272753, 969816042, 82059823, 469895949, 250727455, 309363578, 512402038, 720863057, 119203804, 867359102, 233353581, 73376918, 603345589, 129774511, 254449326, 835622928, 631319821, 726760775, 299783245, 213806278, 495017295, 359697125, 881529974, 502704479, 109959829, 397074777, 399449153, 883863409, 537222306, 674710448, 206202196, 256048775, 420134229, 703938717, 317395221, 386415346, 151698906, 893405749, 118684636, 929158986, 962140323, 30481205, 840604534, 750289628, 338501479, 288351152, 45957503, 490989597, 258993666, 458087361, 187495842, 229449633, 277591623, 55787124, 40212025, 555632084, 355125899, 707221426, 260905319, 103455974, 921779247, 564104820, 453975120, 28679267, 844987910, 917870946, 833394997, 537405604, 42483903, 923673112, 408018313, 307594874, 52966144, 802768416, 646715969, 160285267, 399944068, 704555591, 33736132, 761441442, 281500261, 901208504, 408462618, 120251939, 801109245, 275921388, 36935760, 198031419, 89456626, 522493103, 190345008, 769564320, 851479813, 645527587, 467498864, 718419245, 961340978, 114644291, 847061787, 700514578, 752471444, 875686582, 630901708, 945659145, 784117504, 100780691, 961514782, 193475399, 40055170, 987634031, 711318467, 574050818, 269050476, 643172404, 740824366, 660517615, 239774490, 738629527, 441294003, 91274394, 804761591, 968238677, 676471901, 715307333, 255477761, 231056004, 151032983, 908668210, 665261491, 465689829, 199827911, 173293871, 502621403, 644193744, 457176626, 95586449, 559212922, 812907464, 306364125, 93932351, 504953662, 650904938, 262428421, 79736987, 405245927, 629617697, 473782892, 267633277, 804485252, 40750576, 718373238, 802284567, 899508943, 33391337, 161750596, 571097983, 144467481, 39243147, 142051540, 992504159, 61327913, 237758732, 975398246, 533614675, 821282541, 803778465, 666053596, 482474688, 287343026, 402110709, 361467820, 660682459, 766863962, 940971332, 133443376, 299322317, 403289380, 91773147, 578740420, 178337753, 626487223, 3329078, 133029916, 3445303, 180192376, 348345874, 382546435, 166253188, 762642188, 407937250, 357625136, 577200245, 379724244, 19232721, 345288519, 722704102, 223235722, 598922463, 881090280, 630053391, 718604012, 141511726, 273913253, 102354794, 476017907, 422540672, 695048655, 265734182, 240752030, 72436120, 74561677, 369765754, 986102028, 271213492, 144489834, 932666818, 473117188, 947829933, 341732375, 416832921, 206474181, 188913129, 998511470, 73646354, 299332842, 270671030, 77491204, 199382630, 620056299, 593621476, 205712819, 370899908, 27972373, 247878908, 471032089, 602821904, 36654639, 472210204, 1506888, 675608009, 188051949, 1167041, 532098903, 476252659, 669257691, 559553425, 715122734, 20547462, 536253493, 64166682, 494508143, 856419984, 546429105, 401304239, 483683742, 561236488, 925680184, 97940018, 739642396, 215456008, 179172199, 457743168, 454303229, 40214746, 666384953, 570926099, 317619550, 675864306, 585532696, 579862672, 529502563, 740576505, 385691413, 560222402, 93681395, 542474751, 950202120, 878048451, 808731428, 463878722, 831849211, 690138855, 104977773, 644018655, 81525857, 621911831, 722700955, 885090699, 165054401, 214052164, 53318648, 531691184, 780786743, 759193573, 810047374, 385843571, 636137416, 699791663, 918197910, 917669687, 604733759, 128077557, 282018282, 818485977, 404253604, 224796331, 830717554, 736892077, 237971203, 686952929, 832352844, 939385224, 864533054, 558246504, 332102058, 181428997, 170905489, 965822013, 311167709, 424290155, 324675837, 744974423, 923753558, 215435880, 661537145, 98598118, 401814655, 585513086, 500782111, 982056643, 280836371, 777948762, 62053892, 989591926, 558089027, 150308517, 102494307, 761855398, 491719540, 313833799, 787853830, 680999807, 285474868, 823831355, 487419754, 775390507, 774844102, 674678210, 107334650, 651914174, 731087618, 424443194, 779124300, 311082994, 66146814, 574712978, 195648032, 47340149, 740048564, 774440625, 912386616, 106712487, 990929093, 479657623, 579562917, 979925905, 896835207, 588948714, 924994467, 641703137, 103851144, 181744391, 903478053, 173534727, 835429479, 779727670, 518445180, 797801167, 84688954, 271757591, 243561365, 383869750, 12503155, 733977353, 328482802, 220455684, 325796704, 701277435, 225703491, 371908522, 315305513, 943278837, 417213490, 476407708, 204101784, 924105650, 956566869, 187723133, 674794433, 330150559, 145352675, 764384131, 523608159, 522652896, 240079428, 588212077, 826744362, 678228374, 713681319, 323625951, 626134311, 576030436, 172499205, 527153247, 849978068, 538483200, 307960863, 288873086, 708805257, 929145923, 796650440, 755467254, 516490791, 566444533, 179811163, 368151876, 375227087, 962418280, 844732958, 660975984, 864078849, 767284855, 110599079, 414761854, 814506949, 640661821, 753940276, 211161007, 122619936, 855029226, 846373552, 124254601, 976515689, 702139420, 289323689, 800855803, 895860146, 52670232, 236408258, 337587658, 20052478, 107643886, 821932709, 47777713, 424699248, 787285352, 11511992, 435779428, 37640569, 105997829, 555901379, 256164510, 394017575, 138177804, 72280161, 269242166, 705900441, 507045556, 875410672, 600076836, 366396719, 742936519, 826096577, 268159050, 108434341, 498995760, 52964357, 33585445, 163960723, 928550671, 367423573, 24222656, 574303907, 909532602, 579341391, 380140407, 166386321, 230546300, 520910726, 851814753, 454958295, 285031541, 117589106, 93524253, 433786619, 758377794, 119826477, 843242724, 573561994, 185503411, 711162233, 7833516, 897992628, 791063982, 842376379, 286786970, 28894124, 373799675, 731072534, 133306498, 518557782, 207121887, 133229360, 681637585, 454196646, 664997512, 643888558, 473008641, 79626084, 300700803, 191904399, 294943269, 650725754, 678191650, 369444142, 542419740, 995746712, 100493269, 213208444, 395996385, 153421443, 958461258, 45564257, 969273327, 259908894, 810923083, 98927862, 520543653, 195700116, 369892009, 767633128, 902866211, 310665207, 819037660, 8972278, 297942802, 31459453, 95988447, 563361072, 86692933, 81124319, 867978444, 383316498, 487051984, 62934898, 239833867, 552196833, 53955629, 172657428, 606474412, 335557460, 145557222, 644823371, 48857577, 45270372, 725657204, 897239268, 97006795, 99455912, 860385715, 618984039, 672552024, 323090996, 1130878, 971983578, 854323538, 550120983, 493765136, 512540169, 561639076, 510345063, 581009977, 50474279, 935374775, 789252348, 580877485, 254793747, 247650635, 171603249, 542555979, 388928136, 601735654, 990325645, 416595669, 485334449, 213389490, 725840032, 6462992, 408051361, 870301011, 888597507, 609682693, 940986890, 996838573, 449783687, 84467663, 110434429, 324095380, 493339444, 184782661, 316722012, 100792193, 828304402, 756504878, 83966780, 823557645, 546126079, 577093129, 543374338, 849555733, 910871853, 93692770, 563883649, 120131515, 480773657, 824738829, 772663671, 410735421, 356807837, 570974460, 668574348, 327972049, 370234855, 595632569, 681193488, 238224832, 583114028, 768501086, 385460389, 66838389, 646221508, 318319593, 928936405, 417756186, 363878096, 169957149, 469388416, 206113929, 688953663, 998234811, 312908002, 577528725, 863737144, 502698131, 678088765, 572716338, 49506241, 950917746, 985064567, 578032951, 775046937, 653979252, 28855707, 907658180, 103380183, 128592879, 402168262, 830451830, 552320941, 947382580, 405287281, 338298324, 874171231, 598853720, 312738333, 659912057, 83552159, 97149317, 885450385, 608808659, 307443193, 809488793, 334444846, 13540615, 764069004, 989411837, 989992867, 494376208, 185304716, 933025516, 515558383, 959573915, 108841997, 337676042, 894760342, 791444274, 421313607, 337925556, 770226917, 802806322, 362827296, 336345887, 552663403, 766035273, 152846983, 70085777, 525289153, 862330203, 281677461, 512692600, 394750755, 353567578, 252486796, 945051323, 545368762, 617985398, 661085622, 679889865, 203348884, 45884218, 597036160, 740552638, 974927841, 874985946, 941776850, 286236561, 967628725, 600622103, 260412816, 704410679, 368354222, 797512010, 109104239, 549187430, 383658072, 698882757, 981908961, 859206008, 745484739, 57199793, 972706842, 593761504, 942002813, 898482953, 476560035, 475965690, 693678800, 683701966, 333391163, 576355713, 810265280, 272429292, 558257999, 109464290, 179138554, 41466949, 176540931, 189861841, 981234983, 424636343, 124258832, 800922188, 418732796, 380582968, 905507432, 506342546, 808914618, 757178351, 587270257, 760521781, 911011621, 354844574, 124637577, 866964211, 76936541, 995624618, 449681445, 528960601, 296202055, 7345553, 222383668, 185814912, 119281004, 596424749, 518415262, 785769749, 638400725, 391979220, 345960069, 869376035, 807042212, 549559674, 526259562, 795429429, 881280355, 429003935, 995613209, 569463349, 877093595, 419656156, 835479133, 66941963, 259274570, 825432626, 454765865, 819550971, 560993317, 324416025, 602721331, 310489512, 263994145, 154753998, 745457465, 296265200, 605405662, 250004664, 726772805, 989003967, 908444294, 2920588, 582688591, 251601325, 443210894, 675453202, 540306057, 732456118, 395282948, 835086136, 852001992, 83764786, 40667549, 951979223, 808652033, 869454031, 905453644, 325720543, 996372842, 579542889, 619916537, 693010352, 489068235, 927058352, 610405815, 339728522, 235234812, 878570623, 852372411, 781151027, 553607427, 15363387, 717303588, 698589801, 597745275, 789292153, 880270263, 342877813, 688838394, 284787111, 619088937, 215590940, 694355700, 293942294, 383390671, 935896784, 275503424, 196619482, 893285648, 996765693, 522322373, 146765950, 456733515, 551795855, 77949424, 852104082, 111825070, 633615404, 239413760, 233191069, 574380711, 487199587, 900723693, 412684785, 279283213, 370635070, 736314697, 612268011, 622205130, 95438309, 752687355, 211208420, 919014092, 357355447, 919683657, 364605565, 695480980, 989316742, 344130607, 466273897, 842499131, 11997156, 951942443, 99086312, 185365541, 719618851, 223250053, 531648148, 524358945, 647562599, 761151530, 852435953, 700025611, 916514242, 781097730, 18965179, 73094835, 67009942, 868623138, 985274163, 905813142, 766811906, 326396497, 596910842, 378542348, 584198061, 261217027, 32571459, 531749954, 841916611, 480237711, 602064862, 684835787, 538121019, 802965947, 433618520, 589885902, 626474801, 674154450, 741087985, 531854984, 447766527, 866780667, 42336726, 914565176, 822599924, 176281041, 391936955, 433183131, 667990938, 83095976, 36239261, 597891560, 616093281, 5539284, 606304917, 577141687, 674393153, 313714352, 217655441, 561559108, 976206234, 137262940, 646906336, 716624919, 751223980, 618658735, 676580770, 406712107, 13866377, 619258417, 740252049, 78799433, 49195247, 30060546, 573665494, 968860567, 579977314, 411406301, 908988429, 717483905, 30487385, 409674069, 348889880, 536894554, 175243472, 672001272, 279723668, 225105401, 317982189, 61453406, 487580996, 596486437, 414801014, 120156595, 721921242, 485615087, 517512313, 998563768, 385496905, 447209845, 655020908, 489858077, 674990726, 239787862, 347298343, 245618144, 766957722, 869189848, 429135495, 334140348, 710850674, 64730003, 698676127, 961141339, 984087171, 733228099, 594763978, 103019364, 768957906, 418147016, 330657156, 356151898, 224529032, 396734064, 376763479, 527936717, 770677401, 228374783, 126384213, 934714492, 749662421, 708250738, 792394347, 603523181, 785978433, 609748589, 421821890, 19173848, 654740655, 255291638, 499622185, 978968167, 255392627, 488518263, 333984564, 49304163, 825206766, 346315378, 521189558, 688279418, 987150806, 846638527, 464217069, 776784899, 135981291, 105135949, 208289723, 646554056, 332293053, 442736141, 188226460, 215789208, 138174560, 592218878, 653613996, 900037555, 447860103, 717227196, 448725582, 60123482, 769184604, 323146137, 64756097, 782767668, 337782619, 445617802, 81836694, 144328560, 564462110, 685333335, 192038120, 191947512, 453391184, 598445831, 258686250, 987489337, 586958329, 329345726, 931328536, 355611485, 678166421, 342687338, 383412041, 795546264, 865592850, 874327994, 381911315, 694050430, 745616572, 23713184, 660564632, 77866698, 632123422, 639450650, 903327210, 241009825, 679477476, 712084634, 467313823, 544925538, 291840575, 892290046, 963064003, 838258507, 392722392, 59191994, 457691534, 569468050, 77122561, 387385228, 930025991, 235190867, 371859794, 441674240, 968833855, 925115259, 777264344, 645589091, 104939955, 815752445, 150235142, 627460803, 706095376, 177407119, 20126085, 537612254, 733398470, 800830806, 41806905, 332874224, 51656492, 378935836, 251743565, 510654415, 464392944, 544260210, 833754051, 195234792, 299761392, 925978906, 457196399, 503698712, 107707281, 62499352, 415364722, 495618004, 280067077, 61714292, 794471720, 118721274, 791617134, 234264639, 775707710, 613740901, 402118540, 770764445, 531948657, 764812423, 817709672, 775516771, 376800145, 724976445, 428222566, 275687964, 812158735, 800529615, 67720569, 112275127, 93017313, 569091474, 948224004, 73020223, 364028206, 478051176, 261123233, 727577865, 379562349, 721761824, 284636392, 899996212, 475008901, 51094687, 598945856, 163034792, 101270354, 158545962, 704249237, 570341606, 208632339, 215763178, 939746840, 789746151, 347981524, 130810868, 105559948, 10052307, 40379749, 956485618, 356426423, 904734098, 384562504, 35979345, 421313463, 798181183, 672386287, 33975308, 977917089, 106553803, 385127774, 658603049, 387971061, 574294014, 692442714, 888359348, 719902819, 271637867, 875949580, 87146486, 302234534, 84557591, 143298125, 233406675, 91604257, 478245644, 965849536, 909314012, 784622758, 710485916, 720180937, 28865996, 582629024, 191242812, 944239809, 256594268, 881543462, 66373940, 255145095, 203116237, 396237979, 548633450, 583695071, 845576177, 768835118, 96160897, 854420863, 906996306, 517320948, 278109403, 511594676, 599701949, 347104608, 928057125, 123672135, 31464331, 548156883, 520598517, 306098618, 840025741, 799153722, 125594930, 59734421, 30718316, 238449178, 479463034, 190922872, 58678430, 457338028, 385691409, 476574662, 872872802, 225080512, 538137607, 897838317, 1096368, 200768967, 333134346, 973724191, 203031742, 441405017, 524561663, 621331211, 516869709, 184389030, 422546122, 464233037, 136705980, 728662413, 425709861, 543848460, 498969960, 891941, 909292884, 94260512, 983060790, 64985685, 692128896, 901518431, 129847054, 645336449, 494020862, 217111084, 739727651, 380346460, 661926068, 805264711, 250873211, 80296717, 273596715, 463941095, 596253695, 377498853, 374529413, 236192566, 448450710, 458304190, 445586817, 934671396, 951316172, 548906586, 48612385, 494798144, 690156394, 858024161, 778858270, 660386928, 65816071, 366584952, 421337068, 439222200, 204512149, 580575632, 72295461, 562336296, 171532892, 881913285, 129273202, 542090702, 984487562, 512134183, 361973477, 858383931, 355291940, 598286070, 464495931, 270923827, 392311474, 811923288, 773431731, 551966809, 694703171, 470623217, 36222177, 912363586, 721144439, 863705054, 895346502, 360101391, 1057773, 575551143, 813757489, 706957740, 596941446, 575159600, 518894511, 765191701, 739083127, 352162624, 593879374, 280186941, 731538545, 837932608, 209341449, 963450938, 578636770, 294408018, 108209852, 945901723, 269907064, 879576225, 151916759, 913786088, 952755826, 596039178, 994857167, 725261826, 36947395, 254329752, 854505153, 192186150, 954581668, 576104495, 608243712, 601501019, 392219914, 473516887, 50140872, 709237172, 798846123, 305902072, 617175670, 246496903, 889324875, 83607783, 421443076, 442176836, 912117055, 775505045, 689776441, 44730679, 39233036, 514710124, 569352791, 504798947, 760396259, 868129724, 674686656, 504417300, 796832350, 808558254, 735009920, 753806670, 557188081, 994307511, 23191543, 265882485, 924350299, 806633003, 712490242, 769257315, 956159, 669864698, 949392879, 236238962, 245569993, 400163315, 388532812, 577888101, 829222178, 203324357, 305805743, 385401783, 993477192, 891434964, 827551902, 407493111, 925487433, 482724964, 716187107, 152801963, 545689470, 286012981, 978430321, 16081423, 30642163, 183667106, 787139011, 665215469, 198592326, 498814191, 991941883, 406301543, 765569060, 436089039, 747939681, 647402864, 104276176, 842308704, 756533946, 37176631, 850632460, 134480337, 909465770, 173660234, 74405402, 919140794, 392847545, 285164145, 914677522, 965238724, 420212580, 98840815, 140777567, 815689564, 888734912, 833014795, 491716891, 125392756, 607040999, 90588475, 121140212, 635219047, 312245967, 717883664, 185966426, 666195054, 14080036, 872948143, 705531232, 369122767, 868971826, 309278071, 475433933, 724133766, 164548688, 816199014, 176875097, 504746864, 518670801, 942612381, 169412591, 377165881, 856203854, 426555451, 186590900, 166310227, 537728486, 147583599, 524028789, 682046360, 944341933, 100803683, 388030076, 817072505, 854048073, 244827002, 124655865, 884032618, 777108077, 857548484, 966689005, 599074938, 953398496, 487915955, 737029682, 382288226, 999641713, 24479245, 319214931, 658969325, 321149409, 482207657, 855578624, 382738297, 152084148, 19030066, 718750031, 395013854, 813692538, 225278515, 753356335, 625314949, 10319456, 905975164, 230514397, 737558968, 142554687, 210791436, 762434637, 53139455, 744208977, 691429168, 613877584, 821442870, 864055646, 165922588, 538949985, 991324442, 482026728, 450337745, 229019450, 910098049, 267783092, 646311994, 148686709, 481769535, 427711825, 351537411, 361963638, 76367774, 561727633, 823939092, 227835647, 219570532, 154377598, 495577211, 941387373, 484088613, 153483587, 985464731, 649427575, 95217182, 825311755, 974559273, 332217377, 691775307, 713787960, 807643916, 601437997, 307189733, 416870973, 505366341, 964015118, 312477955, 150779455, 327779974, 612366315, 312802901, 897113267, 150021216, 863527594, 814008839, 96206996, 551437073, 908795568, 827087052, 565179602, 394682559, 989272027, 830830010, 778158965, 519323043, 423096842, 62728625, 542381516, 885963135, 849547406, 229136652, 80411291, 782355719, 486454622, 737646881, 468022605, 295615214, 283560683, 770553835, 642961277, 885635970, 92120198, 235210300, 198996690, 639808751, 488727741, 915804120, 765761331, 548415038, 269419593, 506733660, 712537102, 965867619, 547437437, 239738778, 24894528, 413013737, 413204118, 821439529, 310151141, 478066513, 354170399, 458009425, 589551259, 411229704, 488435910, 386217589, 703020251, 634337427, 409791403, 857652589, 823087444, 10792859, 463459162, 748195775, 924891440, 356567825, 173987539, 162069100, 555479034, 34299114, 494138058, 724171555, 751968496, 152756761, 725754099, 486412795, 978065974, 382914491, 652867614, 912106190, 644373146, 821119819, 401186403, 780239272, 703259082, 592129930, 839956086, 392517048, 302862578, 4202958, 556354926, 172331154, 675063187, 617894432, 305707039, 774371595, 366194315, 160964317, 944104077, 522814859, 345784715, 316498835, 840926624, 419799563, 200863888, 750027352, 579984398, 992818181, 105099840, 172760698, 288353491, 955534366, 961616277, 628029535, 779977522, 259273089, 302383727, 262292676, 469187699, 929106117, 301416520, 331216857, 263041463, 889593151, 663782352, 32703198, 607645779, 482073648, 949454102, 319437571, 760121969, 683532612, 764813576, 170396156, 840453955, 758879192, 382128093, 650812380, 443403703, 222043830, 701784268, 96959012, 380856183, 645482181, 879070201, 984212185, 987547942, 774950044, 744571855, 254067752, 626742781, 888725629, 992934995, 703628848, 800195717, 118063612, 61323368, 462780462, 79832285, 172941180, 770438425, 821383642, 504708824, 45866009, 139945967, 648178858, 774944009, 2290854, 340145240, 496835341, 251311895, 4014940, 309682075, 800264397, 311941786, 234759805, 292156367, 214581976, 608156970, 242092270, 462537137, 370547655, 47281654, 762044681, 45318250, 385415010, 31550598, 489056461, 942892597, 829627325, 41459462, 800223916, 645563231, 952797762, 253844153, 710725627, 234445175, 779468191, 612540609, 339936418, 886274682, 240578707, 607810886, 715797778, 366767916, 979914873, 384483358, 583381405, 871574190, 704787475, 240543561, 905094240, 580734156, 541428837, 806061442, 839176985, 630501646, 178266037, 236255770, 185563239, 611098694, 570594373, 71862607, 210015956, 950884496, 829796502, 543703918, 286896994, 633677691, 886551291, 979404013, 738728258, 253794042, 663212785, 559174449, 448424582, 517090892, 888834207, 574254484, 961863299, 323295496, 622936573, 46472058, 78287807, 875107966, 638163377, 346684215, 9263104, 990165992, 902284234, 274481740, 805695809, 672458663, 908783286, 65531672, 371304841, 161792504, 434364980, 900440081, 198855761, 373248848, 373189256, 708531671, 910812985, 196695467, 543097289, 318239319, 236489539, 403037290, 587760445, 215544422, 934976222, 443128086, 123995112, 343201889, 504000477, 637841283, 551200698, 8605913, 661152182, 414745296, 305983792, 747008903, 231495028, 43813556, 864259207, 906999308, 484276672, 262011104, 935806150, 398347619, 749145212, 238575016, 236182071, 496052592, 2918395, 260098390, 285763408, 345047467, 567945432, 285877496, 864165175, 452898767, 5472849, 32750441, 292911209, 132761940, 999180238, 76183694, 653606882, 913651064, 487942053, 181642367, 589656211, 74525157, 78893726, 419882564, 263985937, 328959797, 2801214, 58238074, 39594491, 274488803, 518930514, 36730028, 787140732, 536430970, 639005662, 155288663, 632162451, 729349495, 875644555, 375688525, 674221558, 904964211, 533957836, 935798560, 698532664, 624025322, 703240082, 181145974, 105270235, 485374538, 122103499, 166419326, 816440940, 372592950, 912678253, 375303042, 633313274, 875613607, 625266161, 644383146, 907260653, 630509859, 3664695, 15699693, 46927008, 160508324, 229490826, 509622211, 732768383, 80563664, 165670370, 787259783, 961702618, 3508396, 662581834, 983578185, 22454607, 957011870, 195051467, 703248341, 136180554, 143672365, 179935572, 194313556, 386575814, 539455002, 802371123, 551225485, 180646044, 2177733, 858205206, 805957222, 743872156, 115686623, 760536714, 273499229, 302794538, 943051520, 559934214, 234118829, 745304381, 703007443, 495552792, 595729163, 880004630, 444028443, 319238243, 736047233, 941899102, 735156551, 377419897, 281974908, 966269672, 283449197, 839911740, 5410528, 577639038, 684502268, 896760679, 264506405, 695278823, 888036793, 679552914, 960500501, 276878567, 451645825, 885172410, 749714322, 467023469, 547222190, 641309850, 941535577, 789917136, 33850681, 185017280, 636861250, 506973336, 979911627, 669689041, 548482880, 52911909, 15056346, 196242148, 497034770, 745463938, 83166201, 835827469, 55863867, 195282951, 46378517, 352105645, 562135566, 698594760, 988722550, 973020080, 168018070, 822949041, 894176898, 947057705, 256683109, 305580341, 963279900, 948349906, 320234188, 255821449, 318018386, 644687810, 110365825, 402496030, 333519274, 129364220, 11092815, 723257320, 495592184, 631309027, 880009188, 849935547, 464092293, 440137835, 229583781, 325272160, 252460281, 7925450, 286615879, 548063519, 681698591, 370939767, 787090109, 373501847, 784901333, 976655400, 969037023, 338817382, 557984004, 442955928, 224523477, 308233289, 385031063, 71538400, 751797223, 689076423, 355424952, 56645481, 16824821, 213266757, 974129263, 772637772, 638101616, 383289282, 690997561, 331296571, 400654523, 313556603, 76082353, 302591278, 564232560, 89510929, 491886698, 444877553, 157395646, 419934865, 484474219, 161649464, 281093131, 742786218, 524618137, 94122679, 852629817, 981980698, 26210962, 704089464, 587348353, 208623213, 151948789, 652687506, 743350743, 642809474, 697639577, 268715581, 223013805, 966616324, 165457371, 627085482, 688674127, 315330012, 611127023, 124560589, 646856942, 916705789, 926165619, 484359471, 947748845, 794631145, 111514400, 706294725, 217852618, 419051075, 493788174, 746392430, 241477982, 244284285, 412131589, 405906463, 161229615, 580308167, 983749128, 971703368, 901982613, 577986259, 623547041, 528053240, 307472792, 593443833, 320205639, 104252841, 625999972, 713641035, 145675459, 456392610, 392343285, 912837682, 710155571, 254531757, 257380464, 227833241, 874421715, 106425676, 892365521, 399628090, 454123833, 974115307, 361042589, 828960161, 13430404, 340220601, 584469476, 625275881, 663798829, 39170935, 718249402, 733511936, 18312224, 769849964, 182334389, 843432929, 998712293, 818439373, 139670982, 311856588, 585214175, 703946616, 708719769, 51518287, 202565097, 727864816, 351823905, 197407686, 305328983, 36991302, 712144578, 564967582, 386061421, 32379911, 404875066, 440537546, 208533688, 600445948, 658577900, 553932626, 751286527, 98360460, 521741871, 666432125, 239988898, 582319553, 556217651, 680458107, 48681980, 751208022, 113181054, 930278266, 142706301, 568930612, 558929952, 713586163, 255194722, 869472682, 452475170, 38394135, 978464772, 325897535, 641851056, 721468079, 756682349, 316689518, 733177541, 48039703, 835282705, 349026805, 921752074, 795032872, 950852447, 222812251, 83669459, 382256160, 236538630, 698285846, 426127580, 270837526, 701335351, 128538599, 268271576, 26653481, 739145792, 501421001, 575880540, 588656604, 292285650, 100809162, 516520849, 734841734, 620221489, 578229682, 1886363, 868418521, 229529468, 674556119, 487368543, 274908119, 565317382, 503490895, 498763871, 434118058, 202048033, 550274104, 115773412, 360794999, 573571486, 935446615, 830590025, 896045066, 695247867, 238199062, 262066940, 750665452, 833909504, 587559778, 163030207, 186329379, 868715944, 789451672, 448541550, 230624480, 963853823, 2883947, 513375703, 55707019, 366628270, 921499379, 802365401, 635490551, 807643846, 216166570, 987978292, 595407820, 118232324, 954152806, 89799231, 461173284, 693154341, 441026061, 542000805, 417419489, 925798481, 371773309, 241341162, 930871954, 616652399, 247440302, 378428018, 60539432, 210658390, 53017839, 629073753, 985364126, 970947909, 132100442, 819577283, 391218636, 47199857, 554195841, 157149007, 198581106, 567185780, 269960119, 379297520, 901221768, 279635365, 152152232, 702782438, 314760288, 669308942, 98808748, 557592456, 37997652, 911356891, 321844133, 927186779, 754187692, 826990335, 842530531, 307881668, 864903165, 745566228, 350033964, 37176350, 120937580, 504800822, 970914555, 468064942, 884894754, 827432623, 655268842, 824149707, 267137233, 376444107, 697669367, 497023341, 265964585, 274059656, 736142643, 39542051, 773066275, 601962983, 886489539, 464975908, 793927728, 358282689, 789163369, 687324285, 313744897, 57945227, 378476031, 989054139, 406230184, 132193368, 108120160, 162681552, 743575282, 869639420, 251197205, 640098922, 222981173, 713239299, 18329730, 861268598, 628377437, 978738018, 931013793, 226653929, 133213637, 614559577, 741040391, 828242595, 590112216, 230744959, 942282188, 16458030, 887832589, 770572104, 643716456, 507062062, 366395368, 177229063, 714555951, 280963750, 213312227, 769796387, 757334198, 955171085, 378260320, 727721109, 479198299, 720944930, 796909874, 783746303, 191248554, 343524679, 45961365, 423649900, 385409730, 771587366, 741333307, 23383200, 369866197, 965530449, 6180350, 904918337, 831387764, 118478783, 978099999, 956299431, 391384763, 412018417, 64414726, 779761465, 997691195, 735902755, 830762283, 98320621, 225795420, 913446888, 67698858, 762525780, 926177590, 715107954, 865225988, 144532007, 715735358, 429350917, 245767548, 494038144, 545271365, 298845170, 211391420, 758048017, 456376700, 705763254, 808926765, 224449051, 185244447, 649976475, 108640919, 185789919, 878400809, 764309454, 431918308, 977015446, 64999447, 995001287, 894858066, 510658032, 752139930, 451684991, 213749847, 555065171, 862859318, 241716797, 328905236, 397905208, 326501072, 858066532, 720888376, 591630177, 332871064, 493837579, 238523462, 315481760, 447580571, 308574787, 614195816, 379323307, 973614001, 644359838, 416913285, 665750735, 359860876, 57199542, 915647249, 595725390, 109639037, 745605518, 58716967, 542603627, 307988290, 677655425, 7792142, 33831841, 543312931, 292129146, 707967456, 644718710, 205511192, 763410504, 556755574, 957485705, 489288045, 553785613, 136958546, 940600193, 289276966, 71268704, 383329987, 404350687, 261848214, 514544828, 296481298, 651338752, 57817451, 311183765, 116832483, 739571022, 174991927, 240862125, 241667508, 665368089, 595301314, 799953201, 875687855, 143889597, 375140184, 380317752, 689116055, 955823867, 546702571, 255295869, 376718417, 23813433, 331443797, 328231276, 655193535, 874600009, 164072750, 355916405, 527279188, 267177353, 532445434, 368447684, 564608820, 580407020, 972805360, 205049401, 707340332, 872592723, 410856949, 45248952, 562122189, 501426967, 98884309, 872213852, 70760075, 856796943, 38925597, 141248556, 980789836, 345363490, 232037688, 388627111, 795662592, 529655799, 97223928, 907341273, 799069028, 540305609, 166026148, 72155212, 863518487, 984141170, 485215135, 858492811, 225707349, 34929090, 465589469, 402531366, 880555894, 445820754, 313118787, 765120794, 535619358, 968515105, 248490934, 561652734, 726796323, 298566871, 595550978, 289455360, 108896537, 338101408, 165160348, 330080735, 47415330, 784799001, 595243863, 207513278, 495981097, 88021848, 314283019, 804137627, 562605730, 776712272, 181405166, 632256513, 120833930, 590357072, 820985686, 268354169, 395166956, 49645517, 208638132, 214271934, 855229675, 228830826, 743368693, 247132575, 704081398, 562465429, 845937946, 410978599, 971062880, 510110685, 98205372, 462903466, 407285528, 584542020, 414531529, 318178836, 358579919, 929228046, 896276149, 64958837, 982803128, 996906056, 170928101, 417565216, 11404472, 660032101, 832912325, 130047737, 974522250, 706302133, 323342718, 474326956, 258803911, 91638016, 292544724, 954898686, 95963228, 422404987, 375219399, 785495108, 375221197, 754869574, 105172765, 635963052, 357588926, 209590306, 595602035, 170488820, 113594018, 151715544, 386151307, 120657271, 258288852, 192284020, 433201047, 322603664, 979920964, 193581294, 257456800, 931770146, 392765141, 157670266, 939958365, 350382357, 987259651, 405712574, 427642126, 636547836, 879382788, 697152615, 128634252, 437120957, 274374261, 339486994, 964997494, 733828623, 969091245, 92695216, 193571359, 1532690, 821798443, 636329728, 692774353, 976234995, 370233917, 943698691, 743487430, 528178055, 187812710, 507821419, 935014076, 605690001, 177125102, 298838724, 32052365, 833119048, 766145479, 508073842, 97028898, 842212037, 175815045, 544196273, 152967360, 442493635, 528143676, 221288243, 945079578, 431813259, 868796240, 64459937, 916512574, 939042485, 127532820, 714451101, 386839469, 552479123, 248987036, 337025316, 867697291, 847904381, 183940303, 49207826, 503372852, 319315531, 975686991, 703652120, 572419564, 884986310, 387566551, 231708921, 799099056, 402199547, 616568683, 588999110, 417483702, 807267918, 141925927, 262686484, 375698299, 323208772, 577354654, 542470092, 909922382, 376802368, 714502293, 386258217, 481459634, 927626285, 107678598, 554157798, 7934308, 848212950, 80996129, 392899332, 759239073, 582900183, 287054859, 802305193, 529155551, 442020888, 465099659, 186336261, 44954624, 694044427, 127806856, 640409227, 803728220, 946471200, 602198919, 450685535, 581564574, 482852732, 254064594, 373957508, 986117530, 442622365, 554471361, 359173776, 841254633, 195738361, 75886032, 788396695, 20428037, 93651515, 72358372, 136464916, 651723632, 563127125, 25490727, 173599858, 997501153, 987166235, 613192305, 435826972, 482466771, 205116129, 838999426, 200607887, 614489182, 264713778, 783627647, 990062426, 130910673, 607718694, 610377309, 573971785, 44762487, 835681954, 901110225, 810635240, 907611164, 18990065, 891266584, 443709899, 856361936, 333544319, 449821086, 391819344, 492571820, 569201419, 43290455, 715139587, 977360249, 911158090, 208880862, 120246831, 325012151, 933168271, 59056896, 452251614, 42677113, 329291183, 507672703, 828848904, 805074800, 927800487, 112119792, 671013909, 280205230, 304046225, 233620113, 82697693, 603202922, 431708257, 924598392, 771690178, 162826872, 556646653, 754736670, 691737621, 893738106, 828481698, 847417499, 711097283, 335748196, 648357347, 253025199, 401170055, 175724403, 176989383, 329081393, 821902026, 668264335, 931168239, 31404023, 264373266, 209633728, 281695773, 900023297, 304588401, 112910078, 535724287, 512675127, 211323872, 424940210, 940956705, 852411436, 720955844, 276896509, 775331342, 843433286, 93024939, 126634849, 237184412, 942062873, 791406974, 124699996, 579130417, 725044404, 366851505, 528133958, 337290560, 932310854, 734525480, 223812483, 834958217, 674476081, 818888091, 63761621, 254695498, 805113726, 840952636, 570419319, 487364464, 726128723, 796227572, 794725038, 950841452, 394301434, 791909502, 544663440, 399423788, 854629610, 723654707, 106580963, 952996021, 783544010, 533572122, 323567763, 219718785, 144002928, 348711, 268688938, 811586929, 599960972, 225211524, 527867956, 336262974, 92080553, 737311714, 196860926, 598253403, 190309270, 565120269, 465452917, 731607347, 272736106, 503430147, 212730386, 904925581, 720277894, 260795263, 210596187, 694790634, 624776087, 671663944, 847511013, 683925203, 636072522, 702102668, 447575011, 851687143, 883015212, 439516260, 16750807, 485427525, 888327453, 221465665, 909695686, 780635295, 932254232, 203119849, 320378411, 668426417, 763693420, 471444790, 241684027, 982953794, 960328452, 997520736, 913929868, 924579815, 777271518, 205492851, 221105073, 417782751, 117922847, 446445473, 501688424, 569325831, 353735051, 100947722, 552928046, 550517992, 409502063, 956136319, 35561079, 319349605, 285689093, 340466719, 699578802, 316307848, 485863505, 884645562, 228275908, 892506654, 31171149, 806590153, 796510306, 200902063, 738864517, 226777850, 111505909, 387592741, 865027458, 513133876, 910770118, 692239882, 659768857, 407995501, 132054630, 414570827, 767478608, 767363709, 237939981, 167125796, 457778291, 436383327, 247025420, 427653923, 687809316, 542568515, 258138862, 429591349, 831078643, 691563804, 6076712, 32832048, 651801971, 832436927, 383723073, 516565758, 663885240, 634741769, 156052531, 386969098, 896948673, 62889360, 806506987, 989947807, 959873038, 561568856, 907200468, 336886056, 399053830, 293312423, 883103631, 269935595, 847651833, 79170664, 547333795, 376080999, 593947268, 187421151, 264310614, 657721321, 621107862, 493669992, 764718750, 232810153, 752127194, 342901750, 357453511, 698109784, 859753082, 489914655, 955400174, 519959228, 246128707, 402468393, 685729119, 69856467, 367165748, 138369385, 562354182, 262904273, 10199255, 477488697, 132021531, 739029924, 779281102, 63612578, 626669690, 897048978, 419058738, 601638816, 744011098, 576599564, 812800558, 561703165, 39063056, 479380867, 929458705, 451396871, 307851439, 13291917, 491960891, 720528393, 408003208, 948856978, 216061878, 45363753, 431877031, 631572742, 486743468, 754614879, 938257294, 263274600, 103073283, 624897259, 634425191, 772325148, 827981337, 239509894, 408247025, 451882216, 474576441, 35104984, 293481671, 932372206, 416207244, 423187228, 886949683, 424331940, 448827726, 338304841, 675688993, 682176060, 474347768, 874258027, 680756980, 872130223, 109959412, 229729139, 354010016, 205799359, 438538723, 110254676, 371094555, 291120096, 450255246, 641644943, 850492225, 298814161, 988770042, 304274002, 716843243, 866866936, 974204375, 806858506, 826482270, 794173391, 878088530, 856980379, 908736049, 487913784, 142531387, 358480247, 727393711, 609738411, 426290335, 112548255, 211014775, 209912135, 41133458, 35264820, 743422796, 164235339, 13758379, 953981087, 196733812, 701044552, 712119106, 871012964, 380621390, 426359759, 218396581, 696874394, 704436303, 441930125, 222108652, 317952760, 961443205, 630423306, 258285433, 562451173, 982711292, 810991713, 683327677, 493663435, 314871021, 716089855, 758511951, 406227696, 67761985, 651785462, 185683564, 263942043, 266487354, 877115452, 279581012, 564191654, 188659276, 565082849, 412460785, 644728891, 155611384, 947081884, 126227509, 300457549, 909107582, 734620264, 516285455, 475335700, 516547497, 22021010, 371484309, 13475656, 271775417, 240483396, 493507914, 251423575, 342383990, 495373032, 5646399, 559212030, 430495522, 746456282, 354419228, 308384321, 350513233, 537447859, 500997406, 112435378, 667185557, 358906711, 900407852, 325662938, 203365486, 287355104, 370227382, 948358472, 987413314, 632990611, 657630885, 985825811, 629071056, 392255905, 469519912, 152864550, 116324934, 896431336, 691886714, 220560258, 425470610, 126003363, 84407098, 192485033, 932678841, 225344184, 93908835, 921156465, 124830866, 997347540, 761390909, 182793301, 454895537, 551960614, 893629668, 763497900, 535489631, 901662949, 954715266, 655343788, 677661529, 695166119, 560716517, 603966178, 145107468, 621524376, 814733835, 621754418, 253617223, 326101572, 315225228, 682773281, 160514706, 363140981, 374193828, 222509896, 750780404, 673939334, 44143854, 94775450, 600235672, 68006694, 595204676, 543329678, 81916148, 500736663, 129304543, 59061803, 499771112, 184890948, 190205673, 386598581, 295062338, 420816574, 37465154, 663297757, 464682612, 424405978, 758902354, 474916087, 933979147, 818096702, 225532561, 194927230, 314379252, 348071739, 87576268, 404194126, 267546512, 414736173, 617817923, 523619556, 478369149, 839782358, 359701547, 290668765, 703427987, 355012053, 859392856, 687592704, 176163227, 966835656, 612730629, 850873501, 190900846, 1891782, 524348898, 843974712, 211926064, 711720847, 633514798, 651269086, 410030874, 561395294, 146011348, 942009467, 416449875, 442660810, 181053991, 275742831, 652219209, 587357577, 150583521, 175388851, 345735968, 870165551, 389517571, 417320093, 646833144, 39564564, 769306564, 847798749, 970327769, 148952539, 609517647, 78626713, 602969360, 912406833, 35184725, 407763477, 669360706, 513627859, 509484005, 814053844, 638591226, 239576871, 464961419, 859658791, 651839026, 871909042, 703465773, 830668544, 625480185, 54495912, 788286887, 286583073, 976295257, 225449454, 948681774, 443799554, 408335956, 623171282, 415363920, 467324352, 637361797, 41845785, 118858588, 905230900, 564201581, 478525902, 642649869, 809525144, 243304164, 370453202, 646373885, 791607163, 353127986, 87017951, 734063559, 411032701, 510185216, 60574322, 785080230, 927780460, 754693760, 272295819, 723996102, 398311808, 989380209, 600664571, 88397500, 625587845, 757337620, 600716059, 599453541, 48968802, 717154486, 160413947, 891968562, 233147788, 397846850, 851156951, 566889001, 100689184, 936478328, 797168865, 112635655, 988527615, 899075102, 794410288, 946657162, 550117697, 16711288, 745502969, 54751684, 208385516, 496782678, 6378482, 127938444, 803582092, 150282643, 472657363, 733417184, 759187749, 771343629, 453959644, 430864872, 882857389, 61117358, 187677199, 196620473, 924991771, 49630299, 79319450, 58320803, 811931935, 225293095, 961932961, 993014260, 146275865, 211750788, 141385755, 770732726, 65941134, 706252289, 43959019, 160326808, 763935726, 537542646, 455346968, 461727655, 184611323, 527313282, 396804095, 738275751, 847313622, 948534327, 470864984, 25156089, 81392770, 819635414, 433728046, 144133770, 920310188, 738824642, 866233095, 921653029, 901746821, 976566935, 563071924, 120697329, 583292608, 933985142, 142641853, 707653767, 489574686, 915653857, 543162187, 617929391, 839854517, 973096839, 901497380, 741758313, 477510583, 915075561, 997372955, 508054407, 841129465, 630539801, 314899931, 561387300, 265990603, 14274272, 157883278, 364268551, 261234686, 394755980, 541905605, 389962084, 742985486, 355539146, 636431347, 673422000, 192057606, 985241812, 831606645, 323375306, 268007203, 905243081, 52617681, 573858557, 752330170, 657868708, 293933037, 223594690, 490177861, 612473742, 148821926, 58392760, 825680570, 175510101, 519072272, 904529413, 523252638, 622737136, 33796199, 981217879, 331716646, 370274270, 125522874, 297759193, 900818297, 188037002, 431699080, 843119457, 541810826, 270548794, 973680675, 96626912, 56282126, 381033187, 725758999, 511556944, 444079168, 778786714, 497731571, 666381886, 115999073, 687550808, 425091007, 38990048, 459250090, 113048245, 305012308, 470004084, 544426322, 521937044, 626223896, 339654645, 35654721, 669625512, 679733418, 512857064, 599635822, 774362890, 747016601, 939787033, 304356189, 61159262, 205499617, 42001673, 360718450, 719619452, 281089549, 911484458, 533004272, 72386455, 178136088, 642393312, 681808155, 723069963, 887977296, 163133222, 380089394, 148275063, 877008944, 824766232, 714021273, 516302020, 793928247, 481327365, 334567959, 423445627, 806623044, 953655596, 14065101, 371252093, 386139764, 898270893, 517755493, 249149395, 655755150, 519952720, 491777117, 796647443, 404478568, 851005565, 349242215, 973522156, 699618675, 164158207, 134038287, 686754625, 562714158, 79731415, 460347518, 534499456, 743767373, 774702764, 295045999, 455165743, 99120201, 344979336, 944351340, 121307847, 700239121, 371106627, 802510563, 850749961, 214288743, 160938373, 861653320, 451705561, 947571976, 220909594, 425801429, 747743094, 72356034, 265926179, 19199909, 275908414, 749001187, 967114232, 661614699, 334248838, 600158563, 326656177, 967108898, 344242533, 289540119, 902119423, 288790031, 726253927, 783854038, 397864115, 334226459, 611851006, 410117386, 73297332, 652302941, 978439712, 899070495, 143873593, 916563119, 912036141, 551666623, 23809432, 49873486, 322957604, 447387940, 968328567, 693172442, 710939025, 59387796, 406074838, 574527647, 649444778, 967610412, 387340105, 265175917, 558285840, 358861257, 689552937, 635803044, 348262385, 180328739, 946917215, 786487668, 582308299, 633229103, 214061194, 155209472, 381314344, 673018610, 967006291, 963991669, 759351162, 663025199, 672682769, 527509032, 603306862, 159648545, 404879826, 815401195, 698039461, 439353284, 667496857, 59980597, 934601845, 647355926, 194635046, 520329193, 234858707, 696394106, 447099840, 236084788, 741940097, 66071739, 333905813, 311346847, 644537586, 497092124, 347530796, 546018082, 798852350, 573216603, 726528025, 176023366, 404222370, 602390702, 819439551, 912128174, 266327760, 845241323, 591440729, 452414445, 729829912, 265636544, 966213428, 675912053, 44336523, 764380926, 634801842, 321842824, 25799519, 732972498, 463836137, 802604609, 645393705, 622224703, 50769918, 978921986, 952469435, 144685679, 639931826, 363846651, 238431255, 251477467, 800311621, 354068641, 563795406, 766744495, 786539066, 759229923, 862359618, 937907376, 846531304, 281321793, 158533597, 641852703, 956115567, 180758139, 370286763, 641534736, 330244002, 364769202, 189250198, 344523794, 50425702, 888177386, 4144815, 39263721, 767176840, 65062159, 448424742, 816460173, 371906214, 672564225, 491452664, 583906590, 742790472, 317756115, 959378306, 687183102, 93799278, 712677415, 47230610, 870730357, 641841558, 985181744, 207766310, 473377581, 953867832, 873534481, 424054657, 218357420, 489960398, 46376143, 656381227, 491006218, 940258407, 882218991, 639613783, 806211473, 11272344, 511214862, 719160497, 122553512, 343684464, 229783308, 245131914, 922431825, 456315985, 931899094, 987633945, 21981495, 296999037, 226376658, 574518781, 678681355, 949456264, 111447694, 37810589, 773801808, 371488005, 663554740, 198082193, 201913472, 853177769, 526291953, 471622984, 568351086, 114604701, 990067011, 957948439, 185602036, 285814266, 380477347, 450486296, 357716969, 770704096, 527524998, 272263555, 192386529, 668941030, 582376850, 807533510, 232698175, 208225109, 528093328, 380327528, 875957400, 856721425, 567320092, 140167172, 111312331, 882274370, 325844268, 417562397, 691817927, 589295667, 704660467, 692990959, 847093212, 382085392, 133209757, 974308956, 515651534, 53452380, 782181343, 651130190, 481400685, 457202460, 57774375, 200795668, 205520849, 401002981, 135119115, 423036096, 392371803, 745604673, 178348777, 965654400, 471250961, 705076072, 226545755, 131675127, 89118592, 561530346, 111420977, 788480146, 360600984, 880526132, 116720867, 924356194, 852977914, 520401761, 29987231, 654613487, 85333479, 689407513, 848048785, 495212763, 47112295, 764244987, 800364611, 204057160, 715329745, 981606051, 708777512, 961194380, 781562061, 840221360, 349290197, 893482026, 278177817, 511770756, 239578576, 460817467, 295023894, 90130210, 734325785, 738261950, 484410745, 591139251, 207429271, 529137997, 33379445, 696281680, 834729647, 393927454, 366366315, 417485863, 454455727, 926928521, 337967342, 733596178, 646060709, 121941044, 891438943, 162957710, 769451022, 21714015, 463324960, 778643247, 694601077, 517434273, 753491974, 440368241, 291097727, 754324982, 932644380, 945720753, 504573513, 413019921, 490841710, 721854867, 857985960, 439408572, 706554284, 56874718, 784163326, 709811136, 502901492, 322414340, 589037580, 220077169, 770378102, 339387201, 151258623, 489906356, 674983662, 53785518, 687724056, 139509225, 694509727, 573036610, 878352757, 745423666, 484011725, 543265643, 639858284, 973594854, 950219043, 649109976, 505333301, 303045276, 369846903, 490593262, 338808024, 606841703, 576000177, 507407788, 863577833, 594235814, 883340541, 397357863, 665045157, 679057623, 967068678, 153176947, 851949599, 674683131, 70063117, 633892267, 182222343, 380971579, 700754812, 595637943, 643172489, 618581184, 952496533, 24414398, 329468785, 180998970, 217466443, 620173167, 541787068, 972237781, 358904055, 527053260, 999067793, 503568617, 998601816, 763802925, 386345379, 578974443, 933429597, 936742647, 79354351, 281460937, 769146704, 875531807, 309444046, 420210685, 761813642, 787037967, 79337549, 420222635, 827083818, 645862952, 529851802, 916278843, 423443727, 864250716, 241841336, 361692275, 499590268, 547507923, 980789910, 218142558, 506880171, 638398651, 956614798, 317298138, 264511288, 624520946, 355301476, 427990870, 213492919, 407596281, 588052435, 511812170, 733017120, 731074092, 612809753, 163406548, 287945191, 914645414, 233439113, 733240348, 317366568, 690817672, 434229962, 784851770, 488158715, 329812462, 816034479, 235464015, 480986860, 746730495, 326587445, 407587130, 868241354, 999681351, 59638102, 195814973, 634363797, 574665349, 166091056, 825221483, 78310006, 183126816, 476745249, 245740804, 139233000, 522295560, 711498495, 333215572, 341769974, 438648640, 373376152, 412650513, 756060417, 857613200, 846701223, 525834583, 461505844, 595856986, 801443328, 309951105, 434397408, 623691225, 349592507, 566475983, 795818425, 402118701, 5657466, 67644717, 158688772, 22887247, 508006197, 528712867, 224941202, 719170196, 271700379, 622258884, 363608887, 525161922, 852193174, 668876605, 902115121, 805295698, 55310320, 729060417, 788740098, 502207389, 750893446, 856809665, 706138306, 662478671, 306177051, 640975971, 249335681, 854040659, 829705226, 808892414, 922183589, 295534604, 619568649, 854450401, 42383252, 94691042, 800708868, 64452472, 453991593, 698668561, 445605713, 952640987, 331161356, 911367067, 384077272, 618919896, 160460273, 466688497, 414351918, 277457416, 691655079, 19749544, 514923249, 853022799, 28421378, 743744211, 216746387, 530455579, 604647888, 968230516, 812059746, 280398541, 450326125, 997515625, 38187680, 860075686, 798490237, 573855826, 909004489, 795965017, 92672900, 748059561, 809609676, 48689739, 672524606, 564119980, 108453996, 418006412, 450724276, 40330154, 436501271, 389000967, 373478579, 88841076, 755739607, 819459288, 902913483, 113373395, 662459604, 915574506, 75507248, 292384579, 283376087, 757651446, 753681131, 618874345, 486788659, 39565227, 88489282, 897496655, 790011166, 163342846, 136085384, 703279666, 203958469, 447381723, 492508228, 57926236, 821403679, 691171615, 616700588, 968656521, 982016538, 376723780, 847043599, 664005239, 192635347, 52776465, 247493059, 665903753, 742931430, 943059412, 670712571, 13598144, 8217306, 227917131, 65604644, 31374687, 881574637, 285048735, 974393217, 343714759, 775028978, 527276896, 193962226, 256040320, 199187634, 829899111, 475820546, 862592353, 301449265, 833950401, 199710728, 746116482, 446113244, 162017984, 129615795, 933751984, 11710373, 62765247, 268679094, 99536874, 795865484, 136888643, 947914449, 972727350, 860211856, 552368746, 768734683, 729557231, 72064449, 375163558, 147095859, 487777602, 881870701, 125409092, 867021157, 280637408, 253432639, 459285908, 745774645, 39716963, 535710978, 7209648, 289269703, 558376831, 16106495, 272494196, 944920830, 803985197, 101507307, 889720027, 944197228, 315528280, 317487307, 419584353, 280993115, 432280189, 873545048, 329153215, 962173490, 48841565, 495571623, 378990849, 994341021, 660783344, 214313849, 234571679, 362441526, 110995240, 477512643, 738083018, 357572846, 294262074, 718797708, 182209179, 689358608, 551662994, 571938960, 190652147, 545316838, 490025218, 462350500, 101468617, 676340777, 726179527, 607502904, 844000668, 298965525, 590469843, 226155806, 116953820, 116998942, 104122097, 104487899, 65426904, 443051248, 92003332, 68858403, 433582222, 810854467, 50686718, 571737246, 721249322, 921239269, 596430550, 476056155, 982860858, 613212695, 529134997, 505772630, 207285061, 862842968, 486152896, 511646494, 738739230, 13285452, 871331129, 935574581, 804310633, 446656762, 328134742, 299952704, 186526901, 348194917, 133185747, 923294750, 701943823, 855577123, 926918506, 296065438, 413810540, 156194099, 200004471, 803620627, 866255008, 808726777, 415956949, 35572301, 68781066, 985957330, 571580939, 225161957, 925637195, 418495702, 390877191, 573315063, 42792955, 19345702, 166663377, 201138625, 899595907, 102406553, 944624200, 165121507, 180230275, 768230028, 422667792, 408083076, 266942880, 746436764, 335205169, 620804698, 376732397, 707132576, 605264459, 160915341, 364004752, 13413279, 863501822, 84906095, 803838719, 488749085, 208406273, 323722456, 788741897, 878438642, 967153257, 194837067, 526427675, 314262130, 870756031, 512407368, 902616892, 210378769, 54341349, 978695069, 409673816, 551287398, 165554073, 114728939, 645923842, 577877974, 349378738, 73432834, 687380456, 849503538, 553137830, 826515250, 904517968, 364518623, 550871816, 323363347, 41835029, 86624316, 576608778, 79071063, 382485476, 326977285, 187447063, 832459670, 460361731, 426489102, 825638219, 986860155, 907450625, 275778231, 861849673, 482280182, 614614761, 812157048, 410286797, 60533055, 391276014, 50248856, 317996432, 687132674, 748915709, 627169549, 83896975, 673067725, 517702363, 515333953, 3415098, 342455338, 721668145, 799350668, 291778073, 380846052, 850879184, 984229944, 39158197, 664439624, 738520892, 487095366, 972832628, 838126220, 939605256, 963566373, 503360784, 350618864, 526543544, 14644830, 776405763, 756090577, 5621829, 240332637, 463377888, 689375299, 20990444, 100466109, 693520768, 233823440, 769739277, 629215634, 333669999, 320390374, 175653607, 756667350, 31753226, 181549233, 884441976, 892331084, 204481552, 830191988, 518607254, 120525434, 166385263, 544085312, 305125716, 679323232, 537378885, 349752565, 560535169, 988846448, 313857752, 198846908, 346387960, 814657444, 773440278, 562432389, 212772637, 825787427, 979233845, 154018625, 744934448, 341697190, 481708096, 339513709, 504359540, 954733057, 605941971, 305727819, 141315095, 528589138, 594146400, 481660900, 844303256, 876098588, 263045463, 622580836, 987543881, 835027350, 439265193, 964311387, 325700901, 338165073, 350682937, 444994187, 71526298, 74838903, 72988556, 258285919, 106695270, 541692490, 584706032, 430460632, 133375097, 92132590, 60740798, 699253824, 665384925, 231639982, 476571547, 928210072, 283428460, 519482620, 858548699, 687776, 629706538, 54539233, 698310010, 638417603, 351626256, 142324083, 306555781, 448066908, 14419330, 465119255, 955939266, 668222500, 939209854, 416698882, 451295375, 795513769, 242017417, 84828103, 250275598, 269514339, 55045455, 162050485, 432149934, 821864212, 290597998, 694870012, 700735484, 377198510, 204538040, 167977427, 982743118, 578243366, 692949521, 590881254, 97386928, 121343798, 591459487, 579025782, 947828893, 624926048, 584766018, 191554785, 777216386, 980056986, 245863015, 241656510, 429601207, 500903056, 145652227, 162526691, 617892768, 211960034, 129168150, 52231692, 901978433, 584987032, 127825300, 434285309, 755788407, 158430426, 567944956, 192855315, 309858535, 94046680, 492074159, 308580880, 104962590, 974216651, 510491431, 693235649, 35921107, 851661572, 450609080, 423366133, 193784020, 118949063, 427497670, 572715320, 358553594, 539060928, 508342549, 653903459, 867209718, 100012091, 172873070, 87436492, 641043785, 885700856, 144077930, 713416564, 291638948, 263671285, 104814716, 645267868, 31623645, 618227076, 285614954, 445305784, 345112342, 425302521, 315253993, 367560504, 616391687, 93385879, 18106302, 579863032, 76923769, 908311834, 932592222, 367916585, 590030877, 889689025, 51649381, 890262591, 307802705, 803776177, 396774968, 932914272, 308475537, 577215575, 937132313, 893282439, 991031329, 806264143, 295042344, 540523909, 99881343, 434583570, 948086478, 570448833, 831704018, 97330343, 701001346, 765686930, 557016004, 3276074, 112436319, 314572622, 303484619, 792991341, 209755836, 650199331, 475490512, 423327307, 935879083, 241887104, 164765541, 814076486, 789699463, 66928152, 860872568, 849063055, 569772716, 669157053, 574060129, 144219531, 687913062, 716246678, 404115736, 470215592, 298862383, 657194579, 627492385, 302717903, 997852738, 39535240, 303368956, 8476049, 115773266, 509007738, 545538945, 258792745, 183993183, 26841641, 70266556, 387283134, 105600046, 812107995, 201892616, 975675352, 431857244, 615363017, 676548161, 289592291, 291982496, 358763158, 983083883, 591835330, 362386750, 692005681, 195764808, 489456007, 138363188, 855406699, 639455966, 421268944, 673739089, 191376074, 821171149, 536994162, 27242880, 290648097, 399148814, 288148654, 949401053, 560752144, 467367408, 854556514, 898984771, 150141309, 62663322, 627124092, 831073106, 173522410, 604073329, 660919046, 713083857, 962228989, 768885864, 596689567, 84491191, 841034162, 484861819, 543104168, 144159786, 717826243, 463710954, 946455624, 770882640, 513425276, 814912788, 428817912, 67333524, 125460719, 823251164, 668467137, 711556055, 122743415, 719560407, 660337464, 668446244, 558120018, 643249869, 784961237, 961153503, 414920490, 815917631, 381176201, 22002379, 177624486, 328090936, 755290535, 493853820, 296607680, 852855650, 181141453, 257171346, 123083607, 950154918, 733558557, 315859492, 191731695, 713104267, 581517878, 588763379, 407710247, 771345120, 800307399, 737244346, 605976130, 789853668, 540427777, 350566360, 198288959, 167438958, 152433315, 343397166, 452360979, 275421035, 988075415, 376048232, 14553453, 360339468, 11599522, 188918343, 863546404, 723423076, 827012152, 885774126, 798920062, 739356455, 368573783, 181945884, 429724467, 535135683, 702200116, 934603456, 718147890, 480908518, 963600778, 636873648, 432387080, 965122543, 479118773, 543707694, 879506194, 529734768, 182870164, 981558962, 974716137, 513145214, 473918010, 377908440, 784216833, 276285981, 639075369, 530006545, 529408522, 310934743, 651213133, 674572005, 14972950, 489647254, 993577943, 816174305, 577837752, 647243740, 901596664, 337821325, 907284103, 476727089, 121267579, 542318914, 64674771, 844361878, 678625640, 900760316, 777645772, 107081946, 214912322, 190333680, 151576365, 433841038, 41852337, 527356397, 451020079, 298449236, 986508754, 244350520, 75965330, 370610805, 340298059, 804157386, 747113251, 420571981, 766048584, 335922955, 586493714, 467765347, 209914802, 992643952, 194336239, 989062843, 151540952, 703374264, 33436243, 998645728, 933472618, 204181077, 203294559, 958243292, 158454184, 112704627, 162360865, 144858168, 11219716, 611733797, 360812352, 638695871, 748344527, 176606185, 127995846, 711644136, 970790848, 880290, 520737080, 14802214, 328958747, 317367000, 976199007, 439308538, 257083836, 571073631, 170563752, 220696746, 401872378, 155183129, 619948406, 949869706, 309690127, 904243040, 786730226, 119581966, 632592864, 455622088, 619701081, 82270130, 3403280, 635503783, 695987152, 502835031, 343255074, 172864627, 436044040, 825329721, 211093919, 471177523, 747749888, 43211207, 582010423, 188938312, 989339017, 780204515, 940256803, 113212106, 249278578, 281939580, 937152915, 105203407, 629106519, 281828653, 857852801, 199326797, 412402076, 319816897, 719987646, 916952792, 911515639, 896648127, 496630128, 428814725, 100043089, 287543423, 84224179, 73277487, 997407970, 658750817, 701808187, 61274987, 223061343, 290857724, 682073121, 159830738, 724225067, 923392344, 920112685, 749788284, 999517624, 573337638, 555615988, 712072226, 710351580, 160292078, 459349735, 970161399, 207647289, 852648271, 133769707, 691813122, 324791152, 805394002, 267730315, 690013652, 341296316, 848022938, 122496863, 622921341, 618838133, 601809359, 479002298, 17629014, 687212373, 589217013, 68734406, 211169552, 461442185, 756252882, 585311497, 205932086, 222191955, 366310258, 766315767, 989212677, 184949386, 492117076, 185891713, 589520010, 573318345, 347130224, 982181496, 430127483, 303605556, 727280725, 327531525, 151309364, 916418990, 32127305, 373239495, 938005147, 914548942, 293633809, 96855583, 738178797, 646612965, 970662166, 929587951, 560945317, 745776108, 507395116, 105364299, 350333938, 163874432, 309695545, 687991734, 164221759, 50418195, 609248183, 970856871, 624766204, 592256165, 775567664, 245029287, 775941178, 713743658, 20985339, 984884495, 678143259, 960151501, 828387416, 667591587, 671791532, 227746225, 664660056, 264242677, 940783206, 985582228, 187415692, 381627586, 969654789, 903657937, 154869844, 775802543, 774696001, 895525340, 775961002, 731481897, 791440612, 199304961, 858544212, 928098004, 742330249, 620297642, 394661439, 226765385, 365488298, 519039365, 71650774, 611817535, 36919638, 155336296, 292583160, 943150044, 608100326, 984552676, 125428844, 637362066, 639605163, 609464468, 561583133, 870501455, 8054203, 892852442, 654428045, 880482, 814614041, 359769163, 367229115, 607298987, 156801509, 387937093, 979171469, 812966511, 49777957, 406581355, 673560235, 455355089, 710883921, 796325574, 588101685, 701954394, 621205082, 527526420, 762320782, 420756512, 848809205, 968800016, 972278784, 979670915, 674277165, 743415345, 34180043, 446249159, 593909056, 229651433, 671008697, 233820763, 797634701, 733622626, 298341290, 971151496, 656921347, 549064750, 415738707, 399261211, 8715673, 91546605, 787853477, 465999631, 618626307, 79701527, 869266430, 117548369, 82831802, 965172263, 224277235, 35770553, 696353095, 972276108, 175553069, 882318924, 444598737, 531813455, 268980197, 192951565, 239993441, 634087129, 751689896, 822473190, 489395906, 722741069, 63252259, 753726456, 438893336, 914587427, 578225212, 194920978, 289058669, 267151437, 228556647, 904249191, 771636604, 387686416, 729470508, 378916561, 930707196, 443823180, 574973802, 714346625, 277537854, 300180056, 656705636, 730862008, 125853451, 588095764, 920119971, 484214781, 811910574, 757282318, 787335449, 985225903, 529899016, 993271311, 969842032, 390910994, 148976571, 385906962, 839649736, 790809346, 341607322, 293005025, 415151521, 776289020, 919275485, 537902612, 240911117, 262995596, 67480147, 985555335, 921214980, 268958446, 546352035, 50820626, 162413440, 89149474, 795729405, 703625104, 735075479, 42047801, 715615895, 517798495, 41231495, 509001569, 103025441, 170065624, 792095650, 551001852, 884400366, 871421926, 244738280, 904986275, 657130700, 74755928, 844038355, 473077699, 587607565, 63658005, 567557782, 561655606, 232421260, 783645792, 818042541, 47841624, 890494230, 213533201, 337091468, 620507479, 288253178, 484862019, 929066068, 801406447, 965656822, 334810684, 411075839, 995739987, 745368892, 143264184, 200007309, 815246710, 283080260, 78565033, 520098573, 512423934, 804698036, 251324438, 397505231, 62007505, 161309578, 529067927, 982737111, 63413751, 632695702, 170242015, 263419908, 512021064, 525530786, 82570014, 858295157, 884883541, 539114298, 196681928, 406743233, 66964976, 667592480, 78660121, 917946661, 296628182, 989193271, 667325549, 463148849, 820632014, 873549891, 485837326, 697864224, 584087944, 895853629, 423008773, 668495721, 621720503, 170232037, 280788912, 484298334, 192723152, 20640839, 778015589, 786642863, 912874145, 753823122, 938234615, 307523470, 430084898, 394383456, 501743941, 126757665, 815064833, 998285807, 699446347, 295454762, 823848881, 119352567, 895070361, 451833165, 110604359, 883757456, 165432111, 982718510, 677479740, 162447568, 566551955, 512152210, 937615536, 768850697, 562083818, 64865331, 738910941, 989247257, 308200587, 635692634, 35672539, 979966732, 582697918, 224828336, 858634417, 329602688, 953250619, 172662899, 427374187, 594415152, 746527781, 616704998, 753455480, 526309979, 361685041, 998927585, 305315492, 295049433, 374913294, 391371245, 371871074, 91709520, 411272772, 591255394, 573129020, 174085894, 587765856, 738877600, 217747592, 249633190, 772814249, 777933029, 188828614, 287932191, 794337982, 239683449, 22106593, 465274385, 928336546, 159126827, 465148166, 132336925, 810993250, 515187143, 175367011, 279204864, 922245546, 585442406, 456983930, 682814062, 688763681, 923038350, 126592455, 403103929, 673879706, 421360996, 738083155, 808654652, 111173035, 804050219, 351710327, 6650114, 772483288, 791627820, 619800876, 846962011, 988422880, 691147461, 897305234, 475188837, 222690495, 587506865, 182226103, 438517990, 744158205, 725436137, 643978441, 22462736, 349297234, 716989413, 936028930, 293225798, 619035848, 486470501, 265054812, 722400087, 719657702, 561243826, 632890028, 728482494, 592614527, 694838744, 241795547, 287453287, 467956706, 147266668, 51606369, 467762157, 192100089, 397457409, 89383013, 952264019, 505825508, 512787132, 486925989, 11852191, 881322981, 996616140, 642498995, 367283192, 378309710, 493000337, 833416308, 132176480, 96347124, 907140763, 630373160, 583438791, 933937365, 134459317, 756083569, 69682323, 435409358, 952622876, 584798221, 264929198, 741529253, 844639525, 803511406, 76562215, 674561633, 932016794, 653867987, 978027719, 617395733, 182770712, 648063459, 68716849, 163962141, 839387089, 41717636, 983099574, 339512166, 675718378, 46239149, 833945047, 939936995, 103188854, 911034054, 848277452, 756367677, 881883725, 291958951, 185515072, 465508298, 565809603, 641193509, 669251157, 831093785, 472395653, 578964166, 87245804, 599435128, 87892882, 822648652, 747048899, 752906253, 844680639, 662005529, 280932634, 31656978, 669401540, 111504030, 730232174, 849340436, 415840331, 312066634, 539415368, 291117172, 185601161, 640370494, 820077441, 297799327, 766896620, 991611185, 791067222, 750287474, 365817783, 93366515, 611800072, 327972303, 565936771, 966230219, 343149061, 976195696, 788067228, 841363342, 514724669, 942722108, 291822952, 443683170, 772729065, 518308624, 745407718, 730814848, 543236336, 600934459, 743334024, 155310076, 810000986, 141915146, 630946041, 141910466, 261910966, 994225799, 473130729, 897894094, 985107831, 502557044, 47889593, 408780404, 679172150, 654046547, 84834330, 265388432, 700570984, 368269004, 994268687, 103496715, 103752752, 27765388, 448521384, 896917140, 412648771, 92830922, 991836019, 752765323, 655219085, 150841473, 139142450, 719633743, 73663777, 872140779, 989060922, 308246754, 361163372, 463375164, 36869068, 497734837, 918279385, 966663343, 400190947, 829939329, 410325756, 510042500, 816360557, 523865982, 214201112, 910712884, 648528192, 863623847, 540470249, 139764597, 729108395, 908335106, 542500820, 184858420, 785178867, 80774172, 97988850, 573527913, 797247265, 703891684, 214613635, 26241811, 908422276, 661895730, 914490792, 764149451, 205072192, 163364341, 480401747, 742605543, 456630320, 864675966, 262035135, 339874929, 152105747, 679792434, 879308424, 867832566, 833346862, 43680313, 211813497, 535855142, 665541460, 202750346, 570077765, 529209562, 646493598, 180016312, 81332123, 822339905, 66386160, 630457309, 522863168, 989217971, 690480371, 138613851, 963392165, 745645412, 122026458, 907883042, 130643538, 678539411, 907734277, 828140541, 150614908, 917722135, 927284102, 216160246, 911765241, 938623977, 557007236, 680246392, 465121822, 984379431, 826163238, 651398034, 828057408, 137533965, 867141882, 234458103, 585292046, 297811700, 553205963, 943740380, 66806084, 795623175, 783171704, 658336483, 825879862, 885166675, 107956989, 853394189, 672116110, 310078773, 148910275, 472014403, 125306352, 847686569, 165688801, 814418028, 363102171, 923443946, 565984560, 841426564, 75842904, 910322810, 172382651, 645740023, 702458635, 913987062, 308033109, 955162441, 347287800, 498454021, 331159224, 492142815, 727318556, 198003685, 52641178, 631663931, 339830307, 321917869, 135882209, 525394405, 889154983, 165136223, 518201575, 395040447, 792788527, 989232247, 110884291, 360347893, 305362482, 400425846, 462197560, 475832418, 618949391, 420406777, 171728123, 514754411, 565942818, 252186378, 864243663, 739103650, 668629628, 884600870, 756970637, 44679581, 489514805, 741822758, 274976077, 562209816, 843362382, 939723823, 440994318, 127931341, 87746840, 862969363, 615787653, 186484142, 597387329, 848434330, 803796983, 975117807, 802927869, 180624217, 894986548, 605079336, 955044247, 816631921, 216094178, 729568914, 939979623, 137337798, 8327164, 462845226, 727145345, 709232617, 297554595, 459232799, 346565155, 316085533, 322121627, 76430431, 808934278, 143247719, 241274008, 299978880, 778275665, 342367482, 976025990, 530849868, 421220401, 847773028, 885935807, 578923463, 936697619, 185817342, 418749201, 119149074, 229143491, 975947398, 819853562, 770194242, 745467516, 854211176, 137864901, 828102534, 921170012, 823869361, 348286015, 159257234, 991489646, 17382860, 785087485, 101123299, 727510197, 366534301, 124921766, 598480980, 334913704, 501133245, 600478007, 763920920, 428045662, 474787286, 383150894, 181143009, 788443943, 46616819, 883227871, 853531864, 114403766, 920460168, 313145473, 938209699, 838538158, 460379823, 829985017, 70073780, 290491377, 774333906, 274785999, 943429616, 574109157, 755511452, 901126176, 137160821, 686386353, 938845252, 883861836, 15190593, 473097016, 301852620, 570496027, 570283302, 187548266, 460267414, 29933182, 647460922, 28821394, 360778722, 819672810, 543525111, 910676721, 443813933, 642996959, 204408585, 886151017, 41451313, 324137796, 231278608, 876864481, 624433521, 66293080, 80511917, 566656297, 839373954, 954304751, 671611172, 549738572, 360306729, 540311893, 639259678, 592443276, 788283957, 814836960, 725547846, 765495963, 975700394, 596368917, 43709601, 124655947, 801094676, 682497302, 35189000, 11153274, 296277298, 918809572, 257354952, 381932697, 299553461, 672177621, 808590741, 937190246, 335592232, 270645083, 135677221, 489004021, 820050804, 65425260, 118077164, 159418700, 768478013, 342236789, 309345838, 596626076, 874943133, 882704165, 670010458, 182706626, 480269861, 850692173, 818189756, 23464531, 854718813, 460039879, 412190936, 472392873, 972589311, 444438162, 500338579, 476555835, 238876072, 425314402, 207260205, 643555040, 108931990, 216716758, 452598594, 570291371, 508531017, 642040951, 888816903, 523004509, 315845464, 864123976, 18404426, 946314163, 510494920, 526563622, 202108526, 655004836, 660800208, 848478215, 64149194, 309443931, 316175249, 551032056, 916500380, 101962175, 905383886, 118560752, 781347868, 369400534, 68346830, 70867211, 611848558, 880254642, 345715219, 586138729, 85457883, 613969176, 790498883, 335036360, 6894546, 797947581, 862895005, 787839107, 630029172, 567139842, 905470726, 437061701, 909646124, 210948163, 114490249, 366494921, 540051544, 806886078, 295369099, 587591573, 558260585, 290444833, 327926970, 298281030, 765906211, 133916402, 549275314, 589341553, 480875174, 577625053, 819726796, 328500754, 572321177, 813895947, 634094376, 334198472, 238715780, 648165722, 33906048, 82458079, 528591457, 243025744, 378317845, 727577661, 784612248, 382577287, 139804178, 537823007, 967535759, 531561470, 816356271, 581404099, 741464621, 738854903, 439811749, 929351230, 107845579, 563369619, 993449214, 47159361, 407789726, 897746161, 905484730, 261319298, 715053097, 826649347, 568668220, 369457222, 369041502, 749481970, 516683697, 497557503, 193437954, 469248010, 179977283, 247560999, 718390080, 963495894, 658361398, 406108768, 165275618, 76532795, 95818225, 488993099, 811242196, 893982460, 780534030, 96141828, 924561312, 50242261, 184739086, 657603844, 435428199, 860409633, 649213634, 499563045, 174033612, 7491711, 532074672, 34702728, 294100318, 632856128, 347794924, 471411287, 519734622, 952060175, 539637480, 993612578, 190406846, 511177791, 266897534, 145766803, 464885210, 977827425, 308566292, 427600152, 864260002, 797683379, 47502557, 131529711, 827229417, 638380864, 888400362, 23274326, 92603492, 233692987, 645392766, 593117815, 589699825, 62808513, 127038842, 350541901, 378046962, 839506064, 562431634, 164922012, 463419844, 146937336, 693654966, 441833486, 549814391, 528404387, 596257193, 758688029, 110896696, 938456135, 502428404, 915075257, 425620493, 621462350, 434334727, 35243281, 452168455, 953120157, 70923908, 782120189, 85535493, 530186181, 389098157, 179344431, 966997194, 960601909, 86333721, 128574828, 554147840, 436754621, 867951473, 580201550, 360255979, 965468005, 56218697, 106116502, 582437523, 810060481, 182639617, 339844828, 555211350, 410092935, 542665280, 621154374, 204120086, 195324365, 995572939, 698813167, 257638199, 668651409, 872047043, 341256534, 973473467, 294804034, 329037452, 286860449, 336962753, 811468376, 901581251, 579255890, 509230790, 682270434, 628468941, 61495011, 34050000, 414428041, 139160866, 302785678, 571825081, 326321390, 482212678, 960348540, 455190000, 294418410, 518297338, 247697470, 294206896, 800896173, 302677183, 644100037, 876875215, 939844649, 502495183, 872841926, 202083686, 294313489, 156807668, 280513485, 901244875, 760909276, 725124902, 813314027, 715850259, 74006837, 361972084, 520609105, 359820979, 824493829, 328445918, 584177761, 159012921, 352305060, 896478086, 475633475, 304493335, 913758601, 446117899, 494945142, 895343205, 82516896, 932260257, 942105422, 873611446, 27524600, 122670318, 716760417, 464187166, 370268984, 289931405, 28756516, 270174466, 238387513, 924938806, 436744366, 342135581, 28879383, 870907274, 859641509, 808715491, 35106193, 186153294, 956784444, 995914013, 765569618, 455772490, 700143713, 947208672, 257265899, 849701208, 312566113, 164205858, 114091718, 684997944, 70533514, 531028204, 961136534, 728970987, 890206207, 129293936, 95389808, 781693367, 454883952, 710223544, 518373966, 480229769, 267240229, 362614175, 446299409, 568065573, 95346595, 528178264, 1291923, 592009060, 59179195, 646051156, 545331734, 494673899, 160274249, 85498709, 118240780, 269871016, 653903771, 523622215, 367531664, 519416545, 843364152, 504638884, 738526629, 100695194, 496826964, 982089755, 76340216, 131973353, 516274186, 779337428, 853143868, 670032112, 864305971, 385364479, 274930716, 633947620, 978104979, 118922662, 306332493, 393807213, 187636415, 623213878, 868468009, 482143947, 850367139, 522853201, 280284654, 101634180, 527120129, 4549461, 890272424, 788562723, 739735212, 684611011, 840079918, 355588443, 643719263, 396745068, 968265504, 618285051, 876135499, 664300116, 342449443, 534301989, 247963724, 539371908, 714530057, 359688391, 902594931, 133325284, 936223312, 156802711, 715059021, 960178024, 705084398, 543084579, 162965667, 874072824, 407978063, 11561802, 440682471, 38812654, 520388324, 474048715, 580286378, 812139788, 952532178, 525550971, 384931581, 986271088, 328380257, 999738381, 31005236, 736671541, 262278191, 405540851, 340696013, 186731802, 979158159, 872088368, 104964325, 895153383, 121269370, 741922740, 30597026, 910799658, 107817022, 910408277, 253615044, 886396186, 361283176, 85763046, 358306517, 26758423, 111886455, 804527739, 206840417, 47770196, 891751599, 356871209, 232121380, 869919914, 330066129, 797259525, 651693899, 20283492, 434294301, 163018732, 550870589, 991826608, 580703453, 111792206, 661498669, 280981097, 391178121, 347293096, 646933117, 95999707, 891715552, 99417314, 91837477, 252989986, 73453236, 87943888, 265557858, 192235163, 277336567, 913082133, 276450995, 786058331, 549033843, 951395768, 533513865, 977038250, 793918457, 892952653, 956854730, 316873565, 934824343, 110076010, 596612890, 787477170, 469830019, 757773729, 228202979, 999674341, 945847093, 317083521, 763054293, 476843021, 565136204, 752725513, 131442259, 55841256, 952791017, 526120402, 534963409, 66968883, 129812730, 816463381, 565316871, 550258841, 383980447, 531404709, 724180743, 704521640, 426794250, 675820837, 749213218, 69224414, 450245997, 550091741, 941610659, 63283199, 525332926, 739961514, 54033010, 322675714, 963285467, 949633690, 49849559, 758504280, 221457807, 768055841, 78952, 609148656, 813664607, 596483587, 404810798, 720290289, 786235618, 813286999, 402708411, 169632774, 280267258, 963002291, 243244597, 705622014, 429751051, 387334942, 757309543, 605403867, 60477197, 458001665, 307322027, 169317163, 559122424, 186393211, 735574934, 733024988, 797914662, 293680054, 146491107, 3156954, 979803348, 443844508, 170276183, 179872928, 388180496, 838305013, 814090296, 673701302, 782172380, 523627105, 718077964, 747359532, 647577715, 179178052, 868358682, 21863375, 458355337, 342948189, 441237832, 522641077, 976301435, 821710967, 284233557, 825792020, 826397844, 702130772, 644801759, 413485033, 263898504, 755641895, 408786017, 929870018, 869295526, 548647377, 141252014, 45212434, 649733110, 9643896, 337970446, 209219154, 67100797, 917206877, 477223611, 331651686, 774729915, 145958493, 442833209, 640098219, 506734095, 379345531, 78935328, 682940272, 830469704, 820696369, 538923430, 573502341, 351156261, 652141593, 165990857, 549928150, 482843596, 275750927, 351359463, 966972212, 945939711, 726554882, 752820529, 793776758, 434865670, 337547563, 958184665, 364455570, 23256196, 463383230, 609220234, 495886183, 573396425, 461668855, 593440880, 652510688, 594251265, 264318456, 780878971, 625987392, 715177281, 164000967, 969564025, 649339803, 273925492, 764359901, 183532143, 101698513, 734990030, 575570737, 971285903, 216066517, 961124793, 243237637, 186644931, 886376324, 391046321, 581271089, 522450345, 968352867, 957501179, 550453339, 886037438, 521817146, 677705816, 192436438, 785386488, 732137319, 378913442, 916520908, 295983308, 807728818, 995899585, 130889560, 541583091, 25219977, 934367369, 261653931, 355246489, 361969281, 738660955, 811445277, 380148554, 491220723, 582781742, 104347943, 819130118, 91299224, 181361348, 389337060, 752482331, 144402387, 687967566, 838838892, 710430613, 773916894, 614535992, 960028876, 992899086, 724343501, 832208894, 338823417, 995269928, 541904159, 428197668, 477033774, 548275635, 7439478, 464309657, 485953955, 977315311, 341922314, 617938889, 173176336, 523247851, 304456520, 611142784, 340540475, 76092957, 648459887, 350747816, 568087380, 150947528, 405733, 736947022, 959679520, 26680780, 659505662, 694615749, 22929321, 836791276, 157345328, 692597716, 243515892, 778269055, 770173486, 518205661, 442182740, 110761531, 428691890, 699360044, 177175689, 360665345, 417591978, 913244089, 479478136, 432035697, 454028437, 789446331, 516282680, 837731046, 455657900, 806839282, 735151314, 57364557, 872428843, 778690997, 899501946, 557230097, 744002539, 5867574, 250669153, 456613856, 6110401, 581799263, 905113646, 213879014, 843053643, 651360350, 574142214, 862710936, 860504897, 194852126, 311844477, 587623097, 463801901, 95753776, 989328550, 435184109, 149061279, 107461418, 792202885, 927566802, 271430090, 874882875, 45170985, 73542215, 600380059, 362925966, 989644723, 291326752, 720975539, 555817799, 847285083, 648954953, 476681068, 50124769, 240124557, 431629633, 140425708, 66703104, 314120290, 870139671, 420096557, 610075888, 834619643, 736543219, 737809294, 779024669, 85877610, 880658665, 737526783, 8812646, 782592746, 906445909, 997218352, 760664729, 560541542, 300191672, 852037978, 943721857, 463619515, 940624222, 811639972, 595486652, 820527349, 759431790, 890396910, 162869292, 62501089, 248526420, 199900456, 865254089, 812745885, 207413809, 618960887, 814413065, 241457268, 662675420, 629295760, 933264523, 567363940, 924216294, 848360804, 634221806, 956184686, 421516853, 232841040, 706290070, 66051373, 961043539, 950072155, 915747569, 670972694, 91138629, 190322772, 893817265, 178479473, 649244290, 140388340, 350404694, 288335401, 661102973, 670940349, 854707119, 568241982, 246871872, 286674141, 839843314, 652119020, 764563149, 927811448, 15469822, 204742171, 474614927, 682070774, 84614990, 80044928, 104325347, 24033290, 783768589, 174258296, 444066918, 960598056, 57760858, 702547674, 256972327, 666099918, 824075749, 4736060, 134358536, 284372830, 159659395, 582802654, 647490747, 462858399, 35181096, 502169647, 932614492, 888937592, 494179709, 230380784, 37733002, 745113520, 664095590, 451099985, 843509169, 120543471, 458237819, 448189759, 911310046, 794719253, 424905628, 827495185, 996873791, 890650456, 789860743, 111642020, 555870249, 919276131, 22252396, 512343597, 421690023, 375897119, 828736809, 566530464, 202684677, 88222714, 250011967, 391643778, 991330792, 41408746, 305238594, 150493233, 247866585, 673860357, 79823370, 245432005, 881832008, 850883458, 830983785, 850983797, 57234042, 297918921, 44940715, 252349328, 945636395, 827975081, 763264697, 776395186, 385758015, 272273129, 39750122, 303479494, 552649155, 809890423, 363609102, 618368568, 35381079, 44046245, 12986845, 954994209, 763646831, 257602798, 259317827, 350683338, 640090562, 136292912, 192874530, 920689007, 21367914, 453798042, 493041794, 386333896, 291276733, 526330320, 357542923, 169972274, 620812953, 746913722, 91479411, 266669734, 673070267, 572382954, 541736757, 28104800, 557714243, 352090361, 944250291, 352260227, 528087494, 963763490, 78921712, 820492392, 42548081, 801765177, 47123079, 595366727, 410398705, 945981823, 205114741, 55112944, 877618137, 817984893, 461331834, 523410302, 993951198, 116004076, 653394205, 816783643, 362185641, 889768011, 331590658, 542784338, 532759646, 323955177, 501281526, 902728159, 51814549, 90442028, 214853916, 473330212, 225845861, 920628175, 848971753, 602442257, 908615141, 498827137, 235210900, 833706874, 192725867, 26286119, 866722050, 500156731, 311678026, 223761813, 471351416, 400771762, 12017270, 973258072, 327318740, 426779662, 659952482, 103359803, 792674661, 600073613, 862227844, 820576790, 126753371, 885387378, 122391957, 269327767, 136773745, 160491014, 298705187, 299179167, 120012048, 931916058, 20416707, 579782570, 656913063, 91740508, 622684038, 702537400, 703805374, 210640811, 322409481, 295676105, 678377098, 362530208, 592052759, 662558224, 80563500, 436574251, 611567365, 162273698, 539992018, 210599797, 496489148, 830134736, 949964983, 420100294, 680040757, 150620889, 398279347, 370523034, 48300745, 426155623, 424898623, 89068123, 756675008, 16965951, 930378997, 285606283, 921225575, 718841310, 661772146, 921707085, 976661523, 534234329, 149399647, 656368820, 423616308, 274458341, 197734111, 570771768, 963190265, 69496940, 745476119, 909130001, 666000796, 804705344, 287504765, 503045462, 338322422, 121844196, 726784995, 138268587, 700774149, 758819304, 105516379, 816914990, 974109827, 898876342, 630428917, 764271763, 716783593, 969279276, 708243559, 651495878, 518815144, 299105731, 802193778, 441717553, 38379260, 583130611, 340820762, 509549677, 936352113, 522625567, 89928886, 596337906, 938366507, 463192380, 437738163, 621503976, 664446711, 252531301, 130632882, 383121227, 709724063, 194184674, 850908440, 309636512, 801914853, 737814835, 574693004, 730659104, 200917505, 562080860, 500715478, 967573449, 845013539, 672605952, 510785426, 652314550, 683743942, 830004647, 524972261, 856871615, 504340201, 63979382, 233620794, 430161289, 94358732, 459612919, 383366346, 394288718, 495561747, 772623828, 805527817, 758147088, 567895718, 634874546, 982071924, 641869806, 623278354, 617180334, 52361714, 126974831, 196159188, 669814914, 333244598, 771370686, 177201473, 336292905, 561791701, 831813049, 63899716, 859173132, 213230547, 148459037, 380215895, 703525855, 249865967, 259113041, 289968118, 90373186, 438446592, 657090042, 670455848, 246500124, 445530645, 844869571, 733171539, 307705387, 220174719, 335066228, 370277409, 289702154, 729625141, 17704736, 661340902, 695904849, 557805875, 157098501, 884312164, 341619623, 371998503, 613554165, 384857845, 287637594, 659403241, 74864472, 577165101, 565464909, 327365984, 339839445, 610038390, 143955677, 90377764, 644731247, 364811224, 943718358, 235833005, 118712852, 243023652, 410371069, 635654576, 358569837, 943947399, 214301860, 57253984, 34350982, 777276178, 386876655, 849063287, 923783364, 270737117, 915310840, 58911434, 475000010, 644462533, 892699146, 508090359, 896206002, 713087186, 13664997, 725473707, 50909854, 436134936, 117566580, 197312727, 178627643, 393704984, 134512176, 961805790, 867803606, 702836183, 801437255, 989427222, 875558822, 534712567, 253165713, 207107955, 880567951, 44179710, 72056699, 964600290, 522780145, 420036283, 890292800, 595586233, 750375987, 288600442, 284029005, 493857100, 605995932, 654059368, 297719006, 374733586, 187429082, 760692473, 712443961, 176104858, 202348886, 32352723, 134858890, 906341325, 930467263, 411161275, 10195870, 775881437, 566463267, 361044867, 425881910, 988991761, 287154304, 819979413, 582126486, 316136298, 137096140, 936922780, 218876650, 109980738, 985052385, 607452587, 734165749, 752733246, 398522967, 786273727, 69397306, 72812288, 895252706, 515424095, 882036375, 573022750, 334908288, 75981620, 628420888, 248007484, 7174919, 867721212, 514137039, 155993929, 971821444, 396133596, 123819302, 163015600, 990209396, 323232656, 982358663, 685899015, 895415395, 197408460, 414358947, 169004403, 34014811, 462324393, 599038198, 890668595, 367113772, 974766450, 568461276, 796454245, 586943216, 367103516, 626319661, 614729138, 147753299, 238145955, 889097953, 854453623, 778154426, 786767251, 773471596, 551647712, 141590655, 159127527, 60797777, 37451973, 192709904, 573336817, 589289795, 706999463, 106282598, 706002060, 91056070, 901574420, 568572092, 601411645, 837255289, 90887852, 177676670, 526030518, 73691212, 751999060, 48568338, 420706590, 212637118, 805571164, 897701516, 830836202, 469837698, 425995960, 782482940, 645975186, 651066400, 161527345, 500452280, 951653093, 940658873, 415165722, 817354777, 224449310, 808255707, 593819367, 443134796, 742497025, 410929604, 376355492, 75837200, 555443363, 540367299, 977831791, 526286419, 334791932, 556384876, 27536657, 92655717, 657023306, 252147017, 740226187, 514918463, 816373328, 839565735, 784335017, 172108662, 136187710, 517512236, 435488945, 694461186, 958002764, 244885579, 435106604, 935373804, 881363415, 559695653, 470567921, 81461616, 798192404, 546235972, 315626141, 21976282, 691455156, 486495442, 942928553, 310400930, 5653271, 844160567, 488235273, 733991435, 821405638, 956544390, 385184366, 100757524, 319753327, 469356818, 313196048, 302299854, 350752150, 90530624, 896495737, 150470130, 282921633, 712424094, 27482817, 651715430, 747784774, 898213951, 107769372, 768651942, 867557953, 514277345, 913752651, 625580715, 221676775, 358663140, 842659425, 135192309, 764965914, 145672262, 521534759, 602542169, 356093075, 730057977, 803419164, 417896436, 199373010, 477373350, 826430633, 756502840, 250813115, 290998356, 5417690, 565182164, 604403927, 868805386, 199274916, 181911438, 820944427, 162719958, 848841587, 561054964, 24339551, 290502108, 297901471, 481454262, 45212521, 825112537, 593781811, 523544215, 142749794, 552717622, 256843677, 621417660, 557858185, 890144461, 659661127, 125152198, 542622920, 255238115, 681695151, 481546742, 616978502, 453298950, 946542255, 107204059, 356781849, 855734935, 959459351, 514898411, 862198954, 871495762, 84020246, 359489789, 484857832, 608184852, 692288913, 89798918, 377305743, 339366523, 330794462, 318195301, 849228059, 674111526, 211368866, 232999618, 834308456, 455897882, 597852114, 128369200, 164423058, 597123795, 392536287, 257420267, 989981255, 976824726, 16183407, 779525840, 33974220, 533381181, 630212105, 678568426, 535894892, 555224135, 426711387, 702580863, 976683782, 96079480, 806251719, 102204861, 266098146, 430245989, 617405607, 862245500, 84203150, 547136277, 965699617, 219049808, 121807159, 648067593, 386097415, 601226862, 368195000, 358344766, 437837874, 921630662, 796519651, 205314078, 353994865, 222716205, 219089891, 109132944, 922004157, 454599427, 357489621, 130002999, 896427584, 714933375, 56324321, 400451506, 909319734, 290800887, 431675653, 638061876, 57772072, 533044713, 55323636, 842123102, 352674403, 430186949, 21524824, 890779416, 401787381, 606393126, 823174271, 557396635, 61483451, 411624100, 954483194, 576402176, 912702140, 734174710, 987912638, 214581402, 758274325, 45648672, 74801233, 412702785, 663358751, 251597224, 426832476, 798081489, 33494873, 576713184, 172101800, 164578158, 563216298, 571317114, 961363299, 430588028, 318196230, 683145173, 129770808, 295154498, 87347697, 244159504, 812917048, 342162769, 429463796, 358713897, 181295656, 921798722, 450248331, 995972022, 141351063, 340845404, 280830113, 584530589, 330916510, 718113352, 929157555, 181207992, 122822851, 47742326, 77943556, 387028879, 373329656, 517338077, 537623440, 511276751, 117775461, 337927495, 78888945, 215990677, 99483279, 883430627, 158705361, 740969484, 327343218, 877896124, 799511104, 862636883, 595282210, 110466900, 626463624, 512353718, 195753305, 712507618, 996663971, 646665, 779508573, 351728046, 869447169, 422052491, 472707603, 95228722, 551605759, 955939010, 157730458, 680206093, 842654804, 826393720, 426408693, 636308385, 852033002, 235678009, 45259380, 640687129, 178637043, 924014191, 807625131, 426712716, 364753700, 579809411, 976138248, 891657834, 921137055, 130576800, 903123982, 650036293, 903507605, 596068733, 474865278, 128516336, 740309843, 539757434, 789005829, 377587157, 553317040, 75112155, 943968968, 119479100, 612475954, 567897383, 309050712, 291973921, 936845672, 303959925, 225565079, 925005464, 854528097, 217689340, 146877116, 49442970, 837847733, 296987327, 904147245, 153062488, 764010658, 663692797, 276196316, 529240166, 851548850, 920497040, 641526591, 379624661, 546003581, 497634655, 163689269, 405279586, 197584682, 939204331, 151720985, 546256737, 94413475, 290585074, 569424962, 957028704, 997568876, 589983691, 584105286, 753127018, 605533577, 950445818, 834572685, 431675047, 970478675, 687746629, 507327511, 18452557, 536366664, 754118544, 237267900, 654978478, 13838835, 244578048, 884471055, 203015558, 271372858, 673543212, 178286511, 306572909, 459538475, 413204668, 737958562, 319967514, 999021712, 224650187, 35003195, 966571389, 554005951, 468429379, 970960400, 682156084, 385474279, 137372066, 839092589, 99126975, 963018112, 180957208, 189900947, 412274457, 451783090, 553975046, 859524523, 953896118, 900143271, 917848007, 287532891, 784289763, 958363870, 664608062, 118374848, 317152495, 351740393, 827395237, 700792542, 446907307, 299723018, 873437960, 516131021, 389614130, 139563966, 917804150, 584804658, 350889800, 905482036, 620458616, 606657331, 387729882, 455721617, 347835505, 278313017, 503979436, 542061033, 578298115, 792304247, 826786737, 305332589, 460929376, 772739780, 512281994, 835407134, 714460566, 482462322, 399422027, 545359767, 635674519, 446355187, 103492366, 712428184, 438804156, 377829727, 739177451, 579704901, 424833658, 657598936, 468121624, 904967184, 897201222, 543927510, 104846010, 274867483, 898591215, 701316124, 908544450, 265598042, 579787761, 83830880, 264355224, 684501860, 842775392, 49687298, 266313904, 189295820, 198074920, 55458857, 6166828, 942787199, 305152900, 991057298, 101575342, 124518065, 539838956, 445099317, 841519927, 239838023, 292987505, 109134639, 119754068, 785504633, 537394773, 578215282, 147109340, 757602719, 619200634, 809601210, 827890893, 51736323, 501706680, 595433338, 134448616, 285542324, 901582795, 754597379, 276323983, 619176329, 721710648, 504217527, 266140030, 16219642, 859286805, 461379043, 638570672, 62008281, 911107517, 746820714, 487309294, 238770406, 551908901, 428615685, 505179165, 740402887, 260325760, 4877352, 411197156, 809923075, 388666218, 773837478, 203595774, 820423431, 457272944, 772466114, 740451151, 668119569, 25373409, 279327102, 96221137, 428085903, 912487524, 409737668, 899156150, 427904672, 205607956, 347231892, 386910263, 122340623, 590439989, 159304955, 18744610, 73338089, 707797567, 864713326, 324832556, 560795180, 182649391, 439546282, 42394625, 410453139, 917138890, 607680131, 673929602, 67925577, 533824907, 509102790, 569032296, 594789918, 431282772, 44344020, 691479111, 58460153, 586039077, 479700811, 712635638, 689588036, 113918559, 675107950, 51799869, 753040919, 694994237, 991209080, 33182102, 553269350, 40698320, 861019683, 852150717, 91594167, 152068570, 536288683, 250048507, 54206960, 235010014, 343087511, 384029973, 158841523, 494901156, 950570137, 923302532, 101245139, 143960381, 15598882, 112151081, 893401773, 991374791, 236611884, 100734158, 202215955, 71701359, 717220900, 801273540, 979771466, 784826808, 328632536, 172008993, 294232753, 505571704, 435447562, 15281404, 267032859, 408068448, 898827230, 245671572, 537192365, 238789435, 315841205, 667589770, 463592931, 216399183, 733480692, 912573870, 87494950, 782895604, 34782290, 766088252, 99884336, 460698144, 237957906, 942535021, 555331690, 650077551, 108163106, 679307559, 92197630, 52939010, 893334394, 457047155, 729106809, 349333725, 41666833, 977942323, 23281731, 119624745, 383948542, 486852263, 698308260, 721857298, 691205029, 737609265, 735298475, 528914158, 146590079, 898229952, 596721058, 462583789, 562755105, 185938975, 74974779, 761024378, 484938884, 690029858, 200583897, 129536652, 400412666, 17548175, 82962620, 652453255, 386510575, 635018105, 472983562, 262607671, 437670038, 488834164, 430202673, 796709652, 320756950, 539353024, 481616754, 295149392, 898001944, 556781367, 977038956, 971204406, 971819521, 228156155, 304984587, 562772758, 561751097, 579030652, 886333110, 135960962, 457818916, 946067384, 802217912, 901775033, 870436702, 944755397, 911497471, 872006660, 977849795, 211853165, 759389394, 826362376, 564702334, 997346680, 28091461, 896490626, 721637032, 727686400, 597596027, 106575071, 227353954, 436807996, 216883506, 16602193, 107594004, 717085470, 401943385, 521045022, 329755603, 478400453, 900777445, 408567351, 461645448, 736741871, 688094870, 392445212, 15818091, 693485761, 457199866, 525852815, 663446086, 350230710, 564614568, 365258695, 899570096, 115268466, 23373446, 626889257, 201029688, 593809151, 209296821, 683546724, 441806798, 582735427, 165503059, 349432491, 608113963, 89155276, 257223972, 755937619, 468146834, 891130879, 559848680, 955256365, 150212743, 21154654, 216393473, 869870712, 966971649, 396036872, 438882199, 893253880, 482080474, 76599947, 101981691, 659819252, 344288228, 721577009, 346141186, 440718144, 407091806, 72045011, 140794953, 880697540, 256101396, 642662248, 158194623, 20612763, 698149151, 546523393, 874622556, 635222706, 103282462, 687419952, 882110875, 806343064, 612266978, 710727961, 770874736, 368495772, 519432461, 86654972, 46785081, 439118124, 920832414, 766086435, 447461948, 530187780, 74909762, 308043233, 849135533, 796908853, 6323464, 559074788, 691184827, 293058240, 342539438, 515392013, 488280208, 623640736, 758577556, 416272876, 283474230, 910095262, 929491934, 184520088, 208161803, 204629480, 165987074, 674268174, 621189703, 683606313, 763604799, 226362846, 340851572, 376571778, 908678652, 369595320, 900325672, 705661273, 938912948, 118356004, 929837725, 758953876, 66278946, 840143475, 210952242, 857135585, 699442904, 808165584, 938504473, 136747162, 267249571, 706924604, 296687760, 233265805, 981964657, 148543900, 381375761, 230715307, 410841166, 377216305, 999789369, 217273654, 716495945, 340219124, 230141735, 512629758, 32357747, 262593821, 975059713, 180030216, 405249407, 513771015, 937175650, 703168319, 998890301, 378410994, 857719646, 750016659, 538146897, 225215924, 194754525, 26258728, 245447389, 116796966, 898987005, 958010284, 884606825, 507535540, 489999347, 828935709, 960147880, 958648865, 464544031, 406621312, 465527401, 485198896, 782633052, 93087183, 109289781, 955500397, 999755483, 833005358, 667716067, 448922765, 44764417, 203607173, 857845112, 793446701, 358337580, 240182411, 782819757, 343979028, 893708724, 697901240, 246029911, 260383119, 379189923, 818384565, 415951250, 55403024, 236642534, 54823685, 155390452, 550484091, 624952657, 712330874, 584798868, 228583555, 117443477, 300636603, 348890374, 416788883, 912690717, 182564016, 85290950, 873050419, 398819276, 413087506, 242535092, 441270677, 386370044, 696486353, 720359720, 669547559, 963768256, 966240073, 393329426, 247596250, 973814410, 885969580, 828819050, 567825625, 410886077, 112813902, 251799792, 951988654, 429995443, 238623691, 157714089, 31447113, 207379949, 649002330, 88228111, 887378173, 607379317, 947511678, 708498959, 909253999, 373000307, 395690593, 45845243, 401259589, 728897942, 551430643, 441158562, 9200341, 846711300, 56291451, 316791712, 487255503, 641642951, 889293416, 785675596, 622042303, 86822783, 917440762, 197325066, 66827378, 270834818, 745991675, 859533063, 30763454, 62095, 529704270, 105941722, 472299220, 323609475, 193229246, 427082773, 283848347, 191256301, 679648175, 438679558, 770732853, 640230364, 876454231, 235456366, 255315707, 904319221, 488003281, 67858703, 259321435, 735359273, 289682554, 888188298, 584688986, 225851567, 602224235, 929910643, 586679626, 928061902, 539488199, 283326031, 965546997, 263566560, 676866109, 412755728, 758880039, 613923282, 934063939, 263430447, 834612593, 969959186, 742476002, 615589416, 383558844, 880925460, 882383516, 59925124, 104205219, 775225428, 416746997, 735277108, 271619777, 674436142, 592381611, 71330641, 792241845, 689292205, 620379965, 33345764, 252546858, 183450512, 752029187, 241280944, 851116215, 717641063, 114026138, 485029718, 779096649, 94350877, 787837955, 95255325, 725020300, 178165834, 214319446, 803159344, 214107983, 715747044, 131816814, 285216684, 900495267, 24146378, 371296669, 643959343, 421926689, 235956539, 206748906, 745614880, 33369137, 617632536, 546254540, 359629228, 326927098, 485812582, 788106513, 997798432, 301945763, 966225600, 585200655, 822980154, 377425965, 844613217, 200437936, 382608522, 64996884, 937548873, 552215435, 702498824, 157354919, 838534248, 697868072, 385948967, 930892893, 219853330, 867057840, 613945514, 30684315, 305725687, 422059725, 242321075, 465075024, 999846841, 664555292, 648502311, 53801982, 748490547, 514024335, 904117450, 966725932, 717682132, 920183672, 161417118, 64951783, 623727051, 350962176, 281206876, 700523985, 657587940, 809920521, 910058814, 369952417, 281894198, 160930676, 318255747, 387022658, 316020674, 47698111, 701168524, 129971438, 499036590, 235173190, 170072747, 900430765, 513824524, 955685567, 827608323, 803930273, 898514272, 165374691, 704495323, 332452861, 893407664, 109994983, 700665836, 404632990, 434093997, 268922436, 716968998, 225760907, 574731298, 236437720, 551306349, 333994987, 75231339, 744773600, 492240838, 972873335, 650604530, 703250652, 931900925, 639443122, 409561380, 154419999, 239388733, 671766555, 495136487, 313110632, 299644464, 319704396, 110312044, 655257342, 133645615, 717539208, 719562077, 530138119, 541581302, 686277406, 419101257, 27192544, 75219108, 126666812, 483749558, 614572950, 256885492, 647552043, 31953040, 806821914, 795371207, 773720373, 519204654, 208295383, 232053453, 179266930, 291159475, 1692648, 120940289, 406684235, 373589220, 220873466, 803259944, 173102726, 723993964, 154138308, 833383727, 331872652, 253864520, 739342787, 775884151, 697804700, 115995439, 238461779, 574508344, 710591968, 720053064, 984402190, 347958933, 797697551, 244040434, 743202586, 166918567, 165684811, 658016510, 635938617, 728416749, 278083697, 939414487, 12410475, 191366012, 637410174, 30664317, 460326699, 543464412, 617676770, 17542140, 599099050, 713005699, 836410631, 448261483, 795916402, 851446413, 187678090, 658072931, 773079533, 634222151, 549714565, 464087779, 655718638, 597771257, 211013503, 67872839, 82683107, 631703458, 633090374, 922087227, 155431254, 803057021, 314596889, 972120046, 160849291, 43357648, 550953896, 143316724, 719164637, 307415758, 962052442, 425392197, 922982103, 299317591, 916494766, 763856390, 537581112, 409957935, 609764084, 385722402, 610886830, 648545742, 411794441, 496844057, 950873497, 667534712, 641059086, 593752429, 974347123, 830380815, 204560854, 374047035, 679415838, 815527036, 15336556, 575172026, 256650838, 468521610, 26055675, 317862191, 520540280, 989733402, 65022744, 517333209, 522858586, 891649758, 513142454, 475123766, 950038060, 618431176, 44715453, 83829218, 516223285, 200205989, 963050243, 566841397, 641897798, 628665520, 767544387, 172104378, 859946822, 564686917, 323988932, 331536323, 733221379, 395999586, 581130820, 221029982, 655767073, 890102587, 822176048, 915437319, 344106572, 481191541, 372578728, 872415923, 469372593, 174486980, 654346028, 200321683, 387589304, 344966838, 442130433, 750520706, 61542431, 629024922, 43463561, 448371604, 556330151, 640488789, 189752209, 73077828, 426876297, 883199036, 790775492, 441519415, 730841631, 694058224, 674283096, 750935748, 217802381, 591224987, 490696085, 288973041, 258546546, 848715341, 416033936, 919722015, 931409048, 976716584, 911371611, 58722938, 686627026, 57248062, 88108634, 516732748, 667916519, 149973289, 745774228, 814717454, 992468330, 810643050, 355293669, 585834112, 933761951, 254151353, 58626535, 853468283, 480806736, 599452980, 504283627, 497132052, 450181060, 429343416, 959800936, 115074486, 731340970, 147539206, 671140106, 3579920, 412211975, 524179735, 149050942, 967912822, 587434346, 45502510, 321571909, 836375713, 336576350, 947153073, 762120545, 561946021, 606225029, 865269172, 13572188, 604090007, 753055517, 997074457, 927258655, 650720152, 117761432, 717872117, 731427333, 526465025, 530706388, 168487432, 324584999, 110113554, 993149498, 398105155, 256297114, 803873755, 138895684, 174237741, 468459672, 458197248, 233318214, 860275559, 703840288, 575648561, 121744148, 968123441, 113370124, 654182074, 894153984, 232782718, 722843512, 236421956, 811351095, 328007227, 767538793, 866303945, 386373317, 685976054, 701461779, 200610029, 816076555, 313401987, 992776561, 679670435, 620811197, 434383360, 236427882, 809840983, 821604181, 343007114, 79683863, 77360677, 9417313, 371653034, 135754952, 816031403, 398742213, 636091564, 153249215, 654439706, 440557636, 471074308, 469435745, 573047962, 695494754, 98062090, 534702710, 685861803, 538492159, 286616112, 967377684, 125720783, 505637711, 4189636, 801838010, 622189972, 64430917, 495686629, 806962020, 258067307, 135069631, 702078365, 705627127, 153685378, 921430929, 708969565, 676140594, 771508337, 395865558, 17153163, 453018645, 373041399, 285694459, 959135294, 207026808, 820588975, 467130073, 174658116, 816099811, 56918065, 98139646, 916932702, 253527475, 109683117, 931962739, 532553637, 578692952, 160698230, 368682505, 96500474, 271013035, 274113327, 974106520, 861844629, 868588307, 337910338, 192153163, 565161861, 378493147, 962274264, 656877339, 887589400, 706841777, 129479380, 770927237, 831317622, 674365707, 635199899, 66520542, 109453957, 97630857, 262767827, 208724382, 641279325, 708616758, 350037685, 239275380, 877005511, 704610428, 233183813, 500044933, 770621889, 648374796, 22949999, 43817935, 534112747, 231913445, 488693030, 651900253, 539608263, 440593482, 565437180, 338060031, 69961620, 141896677, 497520855, 819540680, 166438367, 234031241, 527890799, 853792205, 977489352, 225386389, 778621472, 289520837, 952397119, 204437004, 972445826, 207235713, 98730942, 915302330, 561663022, 263169963, 662306352, 649461554, 968580523, 735319566, 183792245, 938703755, 508404935, 712810860, 17240024, 500398758, 260654606, 650953887, 392231749, 502472239, 776804904, 610878197, 310689526, 889300335, 239796608, 996147124, 677118810, 648533616, 934934612, 700858567, 230360420, 536190535, 540461799, 647501096, 790172405, 749037446, 273365364, 769392053, 947035231, 15258676, 219168744, 591731226, 746365420, 109387714, 531312918, 473346250, 549051940, 391239002, 535585969, 677627414, 540227089, 957627867, 81544190, 198139649, 254397269, 500759896, 86091857, 988794317, 331311386, 18712762, 345854343, 583211265, 18674817, 987470967, 909005805, 602325150, 188383650, 853378261, 250659557, 158267854, 405281886, 137057779, 426274412, 290160925, 152121706, 83325232, 667397852, 756481758, 881653300, 278293473, 895104896, 956781280, 428918470, 681247062, 543592015, 527045761, 744947217, 813027334, 618064994, 377272247, 706939059, 322089985, 626761856, 886448004, 518801073, 327734808, 509002975, 463189187, 962194325, 935876052, 523439995, 883707263, 619978402, 530941065, 865515471, 565558713, 44528288, 878382331, 609302675, 659245985, 248512611, 303060574, 832374357, 493339116, 776545208, 599302237, 851972266, 366653286, 732055116, 923127856, 514762514, 421272976, 46259688, 5971891, 356184326, 151297681, 42494016, 399594761, 691716841, 372532371, 784260333, 918023377, 268951604, 906728219, 732765533, 33715132, 786474585, 530858448, 786094510, 324385200, 243714534, 668213384, 951625517, 7469208, 964078202, 788041512, 862112658, 482585685, 241357746, 905205014, 242778590, 354853451, 722305741, 148833018, 413046805, 653368127, 300297849, 971141211, 662726642, 795724875, 602488320, 375285210, 389818047, 648239831, 596990398, 376997372, 110030349, 556399159, 855488777, 741383927, 985980045, 350631334, 839075452, 127035987, 224368831, 759195304, 302354110, 372371559, 282852952, 933577217, 727046708, 180122577, 461801389, 540763511, 538578138, 428076243, 71304943, 670810664, 191367817, 142205264, 621282975, 957872066, 510721870, 942389498, 800123614, 500082777, 209834040, 345440183, 357701824, 848202898, 860422791, 842779062, 404821037, 697045673, 288289487, 576257013, 633198233, 311102851, 628275741, 528783127, 834908304, 974116201, 660711394, 475125963, 662664033, 157659562, 501711622, 252776639, 452795601, 387435643, 98896023, 612854265, 463249899, 125435003, 207197821, 279592894, 89971837, 848851227, 492658342, 488939485, 260817995, 619949716, 111314198, 912171377, 543104942, 917983970, 544821383, 571904067, 540207970, 809030595, 529090872, 744968234, 793948049, 202224123, 20479893, 384574462, 631409163, 288291323, 383617955, 370741778, 620783159, 556298213, 359733329, 850889547, 19121848, 634898686, 182926309, 115026212, 200785991, 90628692, 532433327, 522033535, 446180928, 340552189, 972123546, 951082014, 465467490, 49759961, 796559427, 302414561, 227298764, 30274749, 227383396, 928937774, 634466972, 389534178, 215530561, 876888491, 574246721, 386861180, 773229541, 171753013, 147310807, 415644859, 336477666, 742095065, 173095393, 953979282, 83662953, 214168741, 234140442, 225845230, 101587422, 934143088, 910552674, 335332223, 444573705, 376788358, 348440989, 350983473, 325551916, 18528910, 961397023, 810752889, 611869686, 22692405, 540104699, 626007032, 643915014, 124664529, 882452283, 624604139, 455107539, 381239040, 86093749, 875513307, 658611396, 455723003, 440406983, 114298646, 297233398, 640765378, 962181399, 723277796, 735069752, 418619503, 642119337, 271920087, 325617558, 127353897, 442197530, 929618904, 746747656, 248601335, 291794247, 161682519, 581775848, 207697382, 867620358, 399120855, 18392124, 572596927, 419123995, 818361590, 731870144, 928540672, 550680616, 604374663, 745814746, 807899937, 603273736, 180054063, 194744393, 559257805, 771344026, 27263041, 5773085, 522943085, 853456879, 569171383, 168520787, 414562080, 302782640, 547155770, 830781194, 232454301, 703281297, 517082985, 782549374, 754020502, 109338120, 681305825, 603977415, 911276663, 998260453, 415154419, 215503609, 353575512, 373119659, 953551245, 717356849, 247073511, 166573609, 754833061, 787813237, 621801680, 704068639, 423640993, 898662789, 837015173, 842459055, 675768423, 700343294, 441381634, 272156625, 65459161, 524598035, 809484348, 746326835, 570668336, 497806006, 953313438, 747586439, 15554519, 759621927, 378206494, 954192775, 710099212, 109498701, 48959136, 804427273, 637273584, 985870848, 94242207, 544325700, 385525126, 33870598, 939214498, 295621434, 141782875, 174161623, 106780598, 750518573, 700687137, 990351827, 423288251, 995698866, 252862781, 349809396, 412128982, 518174056, 984696853, 410672713, 95851600, 166603153, 896648726, 169992710, 635025781, 580556995, 733947381, 226280283, 392881887, 132221739, 228150172, 781731782, 100177147, 520626725, 521333157, 308020906, 505296103, 439032392, 664765555, 635729393, 815479284, 84689203, 895370601, 261795972, 773207412, 127653735, 150382680, 571102031, 350445442, 146538607, 718603611, 405804779, 519686112, 496917137, 284467255, 536752858, 623864512, 684754769, 765250762, 484620465, 379590549, 225867450, 502128249, 936230196, 437853023, 14759566, 50739716, 869099994, 426120738, 853948796, 909199045, 132775064, 598868505, 33935724, 45135363, 448848337, 518547061, 155532172, 339436574, 673846453, 372055225, 115961942, 67795545, 859804038, 2914397, 262458794, 8973124, 467428257, 218887364, 87402064, 281536757, 922973777, 390695456, 55196852, 989974059, 884452438, 467661184, 62180044, 821620126, 643605427, 39505577, 120889682, 389329796, 893898777, 504633791, 256975800, 571351530, 486504077, 434409955, 602802740, 104481316, 634857970, 982912457, 296446887, 790943898, 520031479, 874993258, 748877550, 108360437, 960622292, 877263744, 458536926, 216927312, 920388565, 84939992, 660600171, 673714661, 590050480, 167999957, 840620036, 242100545, 200075493, 324874815, 25750015, 321182967, 680684322, 955682927, 843541486, 182028144, 107922181, 47636715, 341796080, 45513841, 302815099, 36355394, 712713822, 701370719, 352807009, 700774041, 905233453, 638487824, 911532897, 517971230, 872953480, 921308437, 982982005, 776531143, 474190503, 43088286, 412551959, 368802629, 36309682, 229710761, 144702026, 938658384, 628633524, 920383389, 865066326, 532203240, 606137057, 894960906, 919246588, 867745108, 923879770, 242319513, 770458751, 13180868, 292337249, 176659055, 520084501, 76610005, 713261948, 839526049, 155514881, 508563360, 312207938, 162018983, 855183560, 569254126, 754755923, 354401235, 838116346, 11501774, 82845720, 40569320, 259185330, 115393513, 976989495, 688663259, 547896661, 517806175, 25612725, 151623069, 206702501, 631016, 583331897, 580997277, 583173649, 439601751, 750444084, 985129243, 905412926, 269250267, 207357336, 328274416, 139838429, 813709667, 459760314, 433753820, 55753139, 86528692, 213024625, 293626615, 315727764, 853229985, 399742699, 661376915, 149067483, 444882796, 197645904, 205763874, 203911555, 99564610, 83596434, 166535327, 767600534, 754522977, 106179120, 581856404, 772218117, 604580000, 940405361, 612527871, 315820625, 121579855, 667994718, 773533533, 934519832, 470573856, 809185095, 727197751, 664200109, 667966126, 568241638, 366402761, 969205614, 611560848, 674932435, 939552967, 154635533, 739018796, 587145042, 387213538, 623870031, 540600619, 480883870, 472239564, 119512886, 485751113, 465729060, 875799613, 367429445, 618743126, 823526045, 851578745, 24966279, 336537667, 706587535, 100644124, 511687580, 55041864, 739147731, 511900004, 456560007, 476119288, 171682812, 538788085, 812092111, 890059270, 487165849, 519653348, 404251738, 991993024, 298163231, 13381497, 720080969, 650325040, 262952176, 666754434, 382435637, 754939427, 859797501, 3450986, 584323664, 93691916, 698351039, 768349891, 307321675, 677943478, 706077039, 724232087, 927738731, 16772987, 279273725, 754684805, 182606160, 764848843, 122908480, 499211730, 40802466, 107681886, 741904672, 882371397, 514803378, 797344380, 933811856, 26564668, 104651175, 242030014, 83236770, 784424919, 575237972, 930578857, 631767396, 848374782, 921659778, 972315784, 570781652, 577633569, 462384024, 794851088, 128977030, 190581483, 474880931, 424281842, 823813948, 298952555, 990725665, 974467651, 765595382, 440134671, 185983177, 446427361, 27309508, 42427575, 721696355, 806267032, 555999621, 882005557, 66739149, 167435114, 291548833, 708426064, 50254113, 495410126, 864452271, 374188824, 423252593, 13478630, 708240897, 400557475, 957431740, 980121116, 298823992, 12715754, 520059113, 465973954, 163236735, 697502498, 558408507, 974758733, 48775437, 727192403, 645678840, 385235003, 4207951, 201844575, 410265264, 38808145, 230631070, 418263404, 734327458, 274573464, 507337140, 59195812, 560444355, 530405907, 150827639, 974122573, 800590913, 916647077, 915043882, 743159744, 255592274, 754635453, 805630051, 604867086, 824290005, 848504624, 507036928, 295335816, 13075464, 442877113, 860859376, 87571464, 614756201, 654874955, 296647730, 330317428, 447546391, 240841940, 917561813, 39173819, 440759722, 244996468, 717476243, 466941991, 403374278, 125721828, 940646782, 2771267, 430724200, 376718918, 978286458, 805966613, 57854630, 38049479, 692375930, 923782673, 338706161, 118681139, 766826348, 128473087, 508762173, 851605686, 685537798, 147998978, 729549970, 743430466, 811639675, 38343962, 554472294, 22726004, 767828242, 864193394, 719256143, 630941042, 959712740, 689829629, 663169753, 976055049, 6411981, 815423823, 204891470, 237672109, 624638824, 49599420, 720906516, 586385591, 254910559, 243134646, 675505606, 224133211, 201074824, 583450300, 293973251, 634072549, 909213594, 31834846, 721084624, 279255115, 795854177, 408689307, 712224642, 301988796, 646828644, 273980587, 549302337, 181452251, 84209088, 393820370, 169258757, 303406629, 16455162, 189793827, 962956719, 99809898, 399686869, 682760888, 959456584, 376595096, 386259147, 818977689, 571880706, 967509919, 9656617, 619565636, 723549684, 296643362, 27420352, 477568054, 27089344, 888877766, 771513514, 270130629, 631841879, 821827763, 185624126, 789911967, 235495389, 675842016, 962561540, 594122326, 190983724, 272786504, 359522956, 544568369, 723653844, 301123489, 3391902, 896822165, 101298718, 536834852, 549503250, 414864350, 915714483, 583152181, 844846010, 945325538, 54586128, 644373993, 252721698, 895257018, 929928528, 734049291, 775646771, 772024615, 962299940, 568833414, 429493199, 777363727, 318995115, 991833778, 692953825, 78976349, 83414683, 737220922, 313088063, 839929174, 486229181, 964817985, 997726848, 221343479, 613378555, 959857978, 450609772, 397908156, 235967714, 92472577, 854739016, 258304980, 616745838, 25880466, 875469948, 330189502, 28826591, 859265685, 790738357, 224374315, 739738218, 337179730, 288180678, 893340118, 811428308, 622431730, 117824652, 946880788, 382804382, 606376827, 497608754, 956924002, 838066047, 480642566, 714152561, 472277862, 739425943, 252447467, 273352581, 392550586, 58224376, 609684060, 500159907, 323085437, 810700438, 616341896, 708982533, 205952805, 83331062, 70657948, 616037293, 680140947, 398473356, 910187729, 798032546, 600491311, 325653815, 508399479, 467867142, 912958895, 444034426, 849132265, 479952766, 396496915, 438210139, 417497003, 741157365, 803810323, 903206702, 226830699, 149982726, 228117709, 194449452, 578703014, 429991377, 485166070, 174825868, 448943614, 978208148, 794867083, 312466526, 437486891, 28311458, 390678496, 48228664, 369564977, 378345374, 852652404, 795472694, 254888659, 144819470, 34369323, 404746155, 339194706, 100927851, 225232967, 236658409, 423613386, 535929319, 192879895, 729641595, 330148967, 559264888, 55894912, 375104288, 781557637, 462469551, 860493165, 812339574, 127895771, 155940613, 513655291, 393318504, 690107453, 261634364, 592713255, 711861878, 160649260, 813977975, 175912468, 723070330, 557493855, 188881327, 233128558, 125474533, 500415080, 557308629, 319609604, 474177763, 837350110, 172979708, 398082668, 404351745, 468023855, 490711822, 38343454, 988659137, 566835158, 731272, 766695012, 267424833, 762279229, 813718573, 330249710, 561310467, 876571540, 937307434, 414524789, 786974281, 411760156, 220189502, 136789914, 503155886, 832960191, 224983246, 958693440, 524599075, 309303236, 240817695, 231485602, 632759283, 286375247, 136402647, 868245926, 598949857, 703764031, 204466344, 916492378, 619647369, 862452972, 454371519, 949140036, 123440022, 907203233, 668227278, 38983703, 705378483, 969951223, 602388147, 526519302, 908212021, 795427138, 817980840, 463443714, 505818963, 462090219, 248850929, 741133280, 675775151, 149202457, 143239349, 598905135, 484996092, 740012040, 551099100, 107303203, 924725390, 810133601, 848001608, 78133944, 26322065, 53991450, 529780998, 667905129, 970039245, 93523710, 379535003, 5876898, 406189218, 449203011, 320950531, 929103054, 183627995, 99769333, 934800582, 334700784, 27471546, 77938819, 46535936, 825122086, 614377828, 186141636, 47534246, 273403255, 44218599, 681423515, 264789443, 3064615, 43830200, 56605810, 883604893, 131664995, 716623405, 368475922, 5426467, 400352212, 626530554, 68962489, 229510199, 839559131, 206964191, 752374097, 88281032, 470273306, 45439378, 182381244, 720825652, 224102665, 656018600, 635636013, 578962224, 894529710, 602951739, 109524293, 349288325, 852820523, 42428779, 174895477, 51374278, 34355106, 348302841, 307363202, 654565237, 381071563, 700253349, 900131394, 967442270, 414913975, 771950568, 895919754, 980653220, 243051796, 463054314, 665953075, 36246411, 571635471, 558201816, 820580371, 667760903, 154641347, 526496824, 967199048, 104632726, 248428786, 595088034, 792745355, 694207644, 703683847, 906222321, 507814418, 906595848, 387999273, 900571310, 803409716, 773880246, 184011301, 836264779, 499955776, 985576274, 333107565, 676084677, 674135091, 772570395, 408374905, 275508793, 305617304, 861522963, 702055899, 722378068, 611976171, 491343584, 260121637, 474428243, 330105481, 521422361, 742142579, 823516794, 652353637, 869626328, 208789711, 847438720, 447051327, 813521769, 852418908, 513542334, 264143133, 193238074, 54654192, 680243099, 373716007, 423450202, 559944961, 803894440, 675219104, 391606617, 472662037, 663224946, 375640733, 430261901, 211320864, 467385581, 176353451, 37423859, 312932050, 987211136, 9157107, 319594892, 674284823, 555420943, 406085594, 479147402, 640319199, 33877880, 104869875, 151503512, 261511789, 332227328, 971575061, 755867218, 740897546, 695329503, 777686686, 51403991, 809547864, 97295649, 922906706, 84355001, 551331579, 119367586, 414026994, 787110250, 912869903, 864544987, 939928507, 752371653, 198028251, 644566825, 771980719, 209927646, 214403972, 517618356, 262455691, 153109485, 58296204, 29445130, 431334037, 261819495, 483817487, 997821726, 439288691, 739163690, 785153624, 14822718, 673419645, 132858461, 62453309, 968089536, 446973541, 648389267, 175909639, 288611205, 489214345, 519431658, 145900904, 374422233, 882880598, 314097660, 416664690, 250325906, 528125713, 166326716, 851937978, 160603319, 558648765, 863350058, 770420257, 172039634, 823129588, 710007646, 470684721, 152706641, 817940668, 816097882, 987110869, 838770813, 755248205, 871129880, 18820740, 978468898, 726645574, 642349358, 851997630, 408686983, 512159673, 893350340, 649812065, 16024266, 383152854, 807366359, 615218061, 913352489, 805378678, 487877416, 560814107, 640082931, 495431516, 445169104, 392176732, 617801549, 754301660, 298315708, 172047688, 823503324, 835314555, 884088720, 421367188, 951083413, 593052397, 834511216, 365550764, 178160990, 327371451, 746837717, 856397456, 327246272, 835236442, 535517058, 914121780, 75173977, 274263202, 84613571, 511593408, 935763643, 107428494, 922521935, 164816618, 606101327, 292192137, 227792576, 763966161, 194303471, 503521334, 499261841, 835066359, 194148119, 862497261, 455093970, 758535475, 902221198, 552988804, 478399231, 53309053, 516943296, 703259378, 919232382, 211991799, 874545470, 865731441, 53074040, 634301707, 991730556, 457003668, 177174071, 508231093, 167709623, 473486979, 717121079, 314431483, 406524119, 221427728, 774097775, 289135519, 928981930, 354959726, 629111898, 6549975, 473661063, 773357804, 883128488, 293526028, 156073374, 742634066, 983374633, 866414214, 247307807, 363218232, 983918068, 204355314, 498170262, 443934632, 803511404, 861832078, 537542732, 813371190, 407788028, 237420215, 727783100, 154825308, 582335448, 506653594, 889995134, 167880264, 725100292, 965562894, 801498579, 118072072, 264496833, 373635698, 696095649, 629043988, 574156958, 391868374, 512988166, 45915440, 221142488, 523862530, 605313700, 517825558, 675943229, 152274550, 685911566, 933178661, 419672491, 722648236, 184989042, 457574862, 153653922, 143132572, 991387932, 522726436, 910413066, 542313842, 520190702, 152985418, 915469167, 142297084, 781820943, 924797930, 758663857, 875196332, 609083412, 388189497, 810194585, 717768058, 693534644, 618207629, 724093256, 901536385, 40979282, 140476513, 127632923, 272606120, 135841948, 226103164, 719158742, 173894328, 233706243, 685700586, 520467486, 344460919, 556782103, 814457290, 313871123, 888550392, 52972389, 685289306, 106077904, 872063740, 391285557, 155098026, 708210851, 668643249, 944337699, 568694869, 733432898, 844835456, 17995809, 640933571, 969134202, 669304948, 721517771, 433167790, 551005980, 575815134, 249691602, 134721295, 386798245, 809900613, 614797499, 241966765, 189792897, 557355666, 806532323, 607821845, 387343922, 930269446, 852458235, 661581917, 603463451, 879896500, 166329090, 275729413, 294197253, 542229112, 658673704, 221093689, 888333459, 562398850, 5451401, 241151352, 492792559, 147736873, 764614603, 119525946, 468113895, 466184936, 640156584, 802076899, 847694056, 662503555, 776085372, 891421757, 372911721, 296047394, 507004215, 805904603, 583634042, 625091600, 583522877, 615330592, 217832278, 519222541, 562188134, 531444810, 236218943, 639260940, 657924790, 468625106, 764589559, 226184259, 164177544, 720009731, 536177125, 969396005, 717167361, 992092704, 765032020, 802389634, 222658996, 589045842, 691298071, 391385768, 436852464, 872342688, 907218667, 921827908, 360506443, 279240396, 949374180, 537743143, 846254666, 400936289, 253957913, 343501212, 237303948, 82089102, 421009645, 917219255, 120067291, 364826286, 950252697, 475636923, 721048051, 170832861, 893920528, 495438126, 506358244, 55589003, 103359522, 653659436, 968345975, 865895845, 353500729, 386580519, 875529667, 810183697, 560880374, 600971835, 897786723, 477687077, 529660234, 808528715, 453087890, 272891436, 658118778, 513559751, 293633124, 740208614, 571481302, 702794359, 886162107, 972473326, 165195313, 58493315, 990966743, 624659366, 149711529, 486634870, 481572836, 863962881, 138675525, 823547020, 249720633, 153443669, 220923211, 184504025, 87263341, 756713992, 983476516, 575203042, 952463354, 572172373, 131339992, 573050262, 373424239, 710370975, 114375477, 451617721, 388768300, 726440950, 908654551, 662815480, 572944434, 211492224, 822237838, 392554576, 340334946, 679452258, 73462167, 942143327, 414839314, 131224886, 945424518, 779766171, 403760238, 2214362, 813944075, 850576058, 12507756, 408081119, 554685939, 301281716, 134239486, 330801678, 574739707, 161107119, 573143265, 864176582, 458549617, 882978541, 123950067, 381059128, 49570501, 575807917, 17055734, 376506640, 828496312, 949231089, 290649114, 467018781, 519978158, 422231000, 497059672, 785045186, 390625348, 233711533, 579038522, 567094679, 406861317, 655480287, 452412403, 561057296, 814437886, 557867252, 600731889, 233011908, 706697881, 714332380, 39349059, 870883921, 725706493, 279810377, 754665531, 217953784, 10541414, 615705449, 234319913, 933661788, 185156819, 167324028, 20635379, 595632650, 495464884, 670353875, 690355235, 459327104, 909111005, 235496122, 932183553, 803242997, 323263639, 30001235, 125261239, 83672877, 349723341, 952995996, 551057720, 356357924, 285272045, 869182211, 7465746, 417652268, 540926088, 349034040, 54512142, 290864543, 313356144, 500041373, 429308799, 350079905, 921176892, 926557438, 235471797, 387446772, 2648570, 314983629, 164148259, 776371215, 977150873, 1030862, 226145358, 255932901, 699556602, 988071018, 128995796, 620732011, 682275013, 486297118, 31946855, 846237275, 365229878, 100281530, 953375758, 810884725, 878352241, 461038433, 959155394, 611147623, 558023822, 866871160, 914114780, 677263116, 463947179, 737662093, 488152025, 263814168, 683396794, 587770410, 930074291, 398214959, 902949011, 166363681, 557761866, 83846570, 840919204, 92867890, 685773184, 580463657, 354526631, 972054683, 875757982, 878888169, 550395596, 316986065, 719817097, 986833114, 605110575, 490634088, 836276639, 902960667, 264851516, 599572082, 760961260, 799599764, 444266472, 153609009, 769432782, 287080547, 490106168, 290526795, 283030118, 994071285, 153000607, 803456951, 651164157, 838983627, 356822746, 421449130, 200491667, 653282079, 874001000, 407646262, 35581162, 575793348, 100595303, 111727961, 523070604, 583577187, 646147114, 231232692, 668271826, 416813341, 442288808, 185694120, 855968201, 468732441, 765493459, 400226183, 728669770, 700487471, 432299704, 875207926, 919179912, 939234185, 256522497, 59995355, 71639188, 39053533, 705523318, 604930838, 664027023, 157359387, 588663870, 634006349, 545486437, 183778137, 297371343, 494011502, 529138908, 313717789, 362619608, 360566710, 908202470, 499255329, 102241499, 122089882, 513590344, 381348023, 703065747, 951559121, 32815574, 819531192, 951697386, 232032233, 893243559, 219016734, 532013202, 476721528, 667304609, 611290020, 136488407, 627520922, 196609868, 269029408, 530132081, 159851947, 13340766, 331967331, 176489577, 462517845, 500276202, 657845482, 784333986, 333257364, 370515898, 952508089, 232366841, 354453767, 268412933, 582769746, 257721448, 567493382, 176110931, 839295192, 454717413, 983489137, 986549876, 280186698, 9959805, 88500864, 97549703, 409132066, 935989479, 255889591, 30694673, 247786677, 661875363, 57452946, 361557531, 690435069, 36758805, 682990854, 338595068, 997088689, 724279216, 755610582, 360727203, 961063451, 335208127, 953183773, 992103621, 465786495, 28658946, 202068086, 487384017, 330430138, 866166914, 962060973, 161899848, 820582720, 991537534, 818302904, 965400843, 134909247, 387549460, 780558894, 818477519, 495884687, 609311032, 926643028, 443739688, 640805269, 361990098, 990942805, 57621359, 674470850, 875535602, 792388177, 151690439, 858824872, 808259021, 573875328, 945644136, 873447580, 325881202, 579071608, 277642919, 16749947, 679209259, 326283542, 273341900, 690695009, 78432125, 24777153, 566542593, 706305131, 542034302, 59827022, 696590866, 573980724, 300561509, 604702157, 250747894, 993982733, 311490687, 850953648, 987950135, 953683821, 210061811, 900963678, 114854407, 598632130, 822514178, 745077812, 998229246, 978112508, 345336580, 115200508, 667938798, 306036219, 628753262, 312778972, 994899683, 697806457, 48311313, 286688615, 33928900, 783459381, 334505751, 723583974, 411611505, 740590376, 387709424, 768565345, 61497762, 138984998, 327953993, 74587524, 614680168, 328114243, 602108550, 839915595, 167976053, 815034407, 51305363, 652044383, 968080, 238403305, 486937439, 707026101, 336431182, 650809445, 38706346, 500087773, 365441979, 384891192, 710812062, 505124909, 195149635, 210746393, 510476947, 503380180, 653665168, 791933809, 925511358, 4409648, 794661675, 832332459, 478041795, 88409110, 345812730, 701018628, 104666105, 702443110, 196034842, 842449953, 709536820, 728652040, 630903226, 953673320, 982127639, 228444992, 736460362, 932077647, 368029051, 578474098, 386854193, 642649806, 204408806, 231954501, 309155292, 835526868, 695787326, 458736527, 65432707, 552805039, 289046351, 85702152, 275336156, 153988012, 892342259, 597568718, 195414197, 961307133, 304763557, 412828809, 827471189, 305623995, 412640240, 870733799, 141608933, 966115170, 723308220, 8000293, 551131485, 49894856, 232685045, 253966556, 600282775, 645965895, 194679256, 881914870, 662391198, 915805796, 583242296, 844476861, 342755642, 421052635, 961944389, 713862950, 34888655, 496726973, 86543671, 475730759, 445266056, 400912607, 255154522, 972714233, 650641803, 776697037, 32999490, 262027481, 771537048, 901933662, 699915045, 978317170, 452711187, 600608528, 549396078, 277656402, 497078618, 157417103, 283367290, 283323902, 911366354, 274210543, 337341758, 459863222, 533216687, 923401370, 81361870, 24244346, 73404128, 678368116, 686498559, 728470171, 552727994, 366364796, 860148539, 351918939, 134536243, 540860198, 178322080, 8528098, 548873273, 424224954, 243715711, 244216592, 244859802, 979686560, 782168261, 571599549, 15499972, 283486909, 882989248, 554937301, 189412456, 13792086, 606128896, 11438316, 200202283, 902788470, 660188382, 973960192, 632503797, 397735328, 877404459, 135569933, 342127742, 72465329, 291158767, 586963052, 773583858, 620188661, 124823334, 980923337, 23313582, 34213660, 462179334, 893985868, 398703282, 88112739, 32044915, 308785434, 443918175, 632899813, 393325940, 362578749, 312193838, 955504824, 581291307, 359276306, 334963072, 68949621, 516632930, 202272995, 57479208, 614385586, 321105169, 319981771, 249038849, 104395925, 557845514, 825205583, 46060764, 239209568, 624157787, 864470114, 674587036, 381839143, 180811385, 967011777, 832427545, 140069119, 594781825, 860778296, 269975645, 903329965, 8383153, 225941174, 266978268, 360153424, 909367099, 133274754, 425784018, 855207186, 715822532, 92773578, 232035342, 425236714, 528550245, 979653023, 791539205, 120961318, 277689991, 521911374, 279444469, 17329292, 284050131, 952641624, 778960096, 443921325, 176526263, 406927788, 185685945, 904159366, 23511148, 261294316, 568701907, 164934037, 977654524, 113229493, 321415384, 385665803, 598013211, 235204400, 497657989, 709347396, 50932509, 621433781, 335535429, 802052073, 747893520, 515734590, 849275330, 862549780, 977226341, 644646922, 465284311, 921765943, 503240160, 838554450, 284965289, 915447327, 112535653, 337285578, 334425990, 422855962, 190395298, 740831526, 207095455, 431415117, 347706906, 152726169, 259460300, 186981754, 698316682, 911225091, 839675804, 842930210, 149676427, 619211398, 349705117, 701615924, 598936444, 910959735, 409719743, 166341916, 515239436, 83471587, 159988624, 130067718, 958327704, 916167792, 536000015, 160878486, 546335419, 748509618, 988339450, 358953489, 970491344, 230239602, 697367324, 613570475, 297005053, 438754589, 504449520, 45881122, 965887716, 17812571, 10706314, 807961253, 8286610, 679455907, 795172933, 880181515, 228730271, 690211173, 69395992, 825985543, 426447820, 617951567, 54864998, 294953601, 802359876, 964711221, 48935380, 163591073, 814156923, 430270980, 535208434, 319448247, 703444347, 203003034, 598944671, 732243238, 790991413, 110577466, 216654716, 615713306, 130379961, 441240031, 968401670, 901474630, 989263582, 472424633, 855126524, 115779634, 833429284, 578545293, 669735696, 196214608, 344463742, 713152402, 141653639, 540263699, 49847288, 225356677, 517038768, 265272253, 485826901, 385698441, 78637012, 435881804, 702624894, 979740406, 733794509, 934777284, 972637845, 436987089, 950248234, 411297759, 196212791, 17600405, 206974420, 382835321, 985273426, 894998916, 410039289, 234515662, 543900947, 730578523, 525320086, 25140190, 114647366, 465384886, 189219632, 987876400, 574067046, 635994968, 235334265, 779810947, 801243602, 513249549, 329824085, 56620550, 137498635, 579771423, 917493833, 618147880, 38889122, 963450198, 909449791, 135717368, 35481530, 207625770, 624038195, 278210574, 133453635, 384780352, 321958214, 858518622, 271100031, 799452076, 52812273, 324024919, 397548046, 90868016, 905654210, 417914904, 580314610, 152805121, 804977457, 276400221, 986405760, 495284860, 329672825, 500427594, 533910443, 310510580, 954581228, 22128268, 899111605, 135886386, 584272180, 342427714, 438270630, 834972006, 996449356, 957783813, 319785483, 548033334, 822946061, 149635550, 435988658, 745005825, 153493788, 832982345, 102829414, 721904344, 187075493, 422623963, 319594692, 62523796, 180719275, 760473522, 337574757, 614929869, 247428188, 566076695, 140247443, 145048758, 505717505, 61509100, 821301261, 97268299, 500352343, 492861070, 304003787, 880642306, 623874031, 695842424, 961882378, 477549544, 34112772, 183445328, 668032203, 745335278, 924289709, 256113529, 199957678, 642698737, 813485959, 107702994, 903956160, 998695776, 961384526, 163595137, 405757197, 661150918, 344456037, 833053150, 396163013, 657909911, 808566769, 848554338, 249874226, 784060979, 608425694, 668774080, 984648974, 881861112, 239526650, 896291614, 520636148, 805118615, 657449113, 691588145, 694112366, 199531486, 761811006, 778417660, 211198332, 974113545, 347810442, 111139871, 95576649, 464491743, 558415785, 180291961, 825672554, 669697102, 228690044, 905894303, 219063669, 55986663, 25056559, 958103247, 303144658, 838836553, 642974475, 748491900, 172211012, 142338022, 444921512, 804350519, 425437841, 238438580, 617339678, 797012611, 629465460, 323067475, 199762682, 816683353, 100588119, 234112303, 76194057, 698308860, 859391015, 224501511, 618707225, 233736768, 194603656, 102627571, 232157042, 878682709, 564235135, 878015826, 526805527, 521261939, 68523114, 75187929, 911497469, 645165869, 415148533, 128549321, 305951590, 51960225, 427311013, 361054583, 63719395, 633645407, 239047431, 882818539, 56349768, 994297723, 745974703, 399801578, 293370896, 676108159, 465190966, 596886834, 713181157, 10395088, 218116302, 841684185, 990154913, 808931109, 362646549, 74181222, 10486737, 302103287, 542520988, 880575713, 711364535, 470873291, 38823005, 854676487, 285101141, 165021760, 742309552, 494214063, 225523525, 725572862, 934243362, 303982918, 394321745, 229629745, 593065075, 604021244, 895997221, 974691693, 523928606, 131257618, 717861064, 468941329, 792625911, 562719431, 799837028, 76047663, 156999155, 762634132, 219114901, 130900501, 584640271, 221527585, 932627862, 957582695, 330362288, 399045144, 11410231, 785946263, 942657737, 111245722, 458782212, 853014896, 375210043, 687172676, 541574732, 171982653, 596966812, 492934654, 151476685, 741560109, 713236878, 462118438, 501365730, 485062799, 876316145, 193373623, 959302945, 34419436, 221784316, 882463650, 935811919, 312118591, 277339683, 250402383, 195713482, 764111815, 971537525, 844977232, 229106098, 914708288, 21722029, 197327848, 993117276, 452556780, 666012928, 160383720, 300596649, 626560321, 785483409, 551575543, 895297505, 979944822, 266306122, 741910753, 494625463, 882223645, 6334225, 585917760, 710628264, 484465402, 810450866, 731210768, 506336176, 994599693, 291989536, 307566304, 605198243, 256973501, 853240483, 744536030, 416528551, 233978809, 368761079, 275686806, 265928218, 934007455, 144843056, 596278464, 394677271, 739986182, 622087892, 232153455, 187232014, 934347149, 661801406, 388989284, 362740420, 538143881, 209566708, 105736727, 207797216, 545344397, 902236203, 746977415, 748829974, 812120589, 600900344, 719117857, 778830922, 46662220, 393343939, 35157046, 943955093, 246201254, 248657021, 984484067, 188951666, 614027966, 562224433, 357425511, 675077503, 923073807, 408053788, 753418993, 632177733, 573954431, 903812453, 394580153, 60000673, 617323845, 176190192, 992106337, 284698325, 598400070, 573791993, 312934765, 274016175, 852406066, 706844490, 195703995, 211847647, 861419532, 852538857, 397093815, 220838630, 83917530, 476581938, 969164155, 856222143, 695231926, 594688964, 989821485, 501506403, 613120528, 184914477, 838614813, 580972552, 816048153, 168984349, 756310519, 792810181, 118611702, 350314077, 131009130, 763116935, 165367774, 82917328, 735574968, 808157566, 931132809, 243761308, 494434060, 653726975, 359579715, 213963492, 708855687, 269185013, 210217674, 870503657, 997368043, 618407816, 746739468, 482316078, 391552713, 739135513, 34919476, 311576394, 958711120, 779875245, 531523660, 994460714, 449243350, 230105703, 806790501, 284878102, 414780661, 57912935, 956052504, 976670751, 765212443, 783596418, 687476952, 184686391, 476460323, 939840591, 17725973, 833462842, 568880404, 471850675, 978752209, 65146703, 452583444, 789300455, 112612724, 302167051, 785136199, 475714001, 487125226, 517419337, 462969636, 106039490, 727366029, 503144944, 596550547, 374061174, 228824137, 329481263, 66791757, 324949860, 977387877, 771218402, 659499517, 957598236, 687356448, 245115882, 484488978, 781381531, 999443037, 350003572, 423313815, 518943780, 15223719, 909807276, 789481539, 828477831, 4748916, 172347842, 552759429, 881118873, 688619723, 299942928, 398178620, 140943694, 937783259, 331005843, 16065655, 476036155, 130518490, 717744652, 307632277, 518218459, 779426351, 443655244, 354922574, 712444897, 868620869, 395797088, 804495381, 401484944, 617508474, 321532339, 849073481, 445906662, 557438792, 767583311, 328428414, 597408754, 964439692, 52287406, 578667147, 784546224, 532297729, 711732566, 614508172, 976555236, 95100367, 497919928, 445795784, 246541574, 412713706, 258177891, 425696915, 619037118, 335074837, 119704927, 930657694, 48683797, 788501798, 209402888, 729326548, 925636142, 775323283, 561443535, 583534607, 998020233, 463067092, 174501860, 774078649, 198866986, 293304753, 921084612, 416045979, 56597888, 351477300, 638245241, 529249899, 68092518, 277381178, 676580854, 430481301, 189049489, 149722221, 188751050, 661652534, 744678413, 136230450, 852320474, 71682476, 277948733, 454107672, 627575627, 755780721, 372243032, 464697561, 993140020, 351065297, 340884434, 867408818, 97428623, 541239666, 969215205, 695917151, 579113610, 463504276, 140542219, 603349209, 416874143, 966801842, 8430680, 146336652, 972654598, 166718980, 758533914, 413227647, 173562643, 149613571, 116490176, 652074682, 172285975, 114701189, 598706066, 841981011, 789341049, 446779092, 39873109, 111814207, 292417075, 989340416, 751179686, 36751795, 691397239, 770885227, 394900078, 820751137, 384235177, 211112556, 232777005, 698014151, 811716171, 310244959, 181875351, 754255583, 571560044, 358691320, 512749239, 42132198, 675239621, 684509557, 902882538, 721390037, 33385425, 876135741, 813089673, 782765150, 540148873, 422345268, 893691658, 576869865, 972252608, 500510126, 671598983, 139123889, 785838650, 379374873, 716035110, 872044039, 484066807, 989612403, 461694203, 775602517, 218838353, 875792058, 33867579, 933397012, 522608098, 216309358, 329121625, 177106220, 637802175, 350247683, 844547807, 940709000, 346048746, 290250106, 968866774, 161597607, 768195103, 58505166, 32900023, 338375820, 556421718, 76248023, 41995721, 549987599, 244399892, 849274142, 595939651, 945344988, 598166365, 36333655, 639618451, 291657944, 648687969, 665108397, 533410149, 358540868, 953573587, 23654932, 385598096, 511558822, 635878929, 92669199, 338239109, 1968200, 324219589, 460225572, 83797323, 399477579, 767484235, 72943413, 817172043, 622088648, 297014300, 559777741, 400733495, 567381573, 316822394, 670337563, 440849889, 424316492, 928735702, 11135142, 736166633, 226935708, 511299781, 869028841, 76386821, 185044397, 203840501, 849568548, 929061039, 397506720, 917668881, 707705820, 94020547, 720205535, 116343383, 760546644, 840650871, 269058338, 676549444, 305519727, 81283930, 44599886, 982109252, 218523367, 509773021, 17601199, 61019207, 521169580, 881984673, 252756814, 843069783, 413969701, 392919285, 569085672, 543023698, 437063203, 749546438, 165615908, 303223088, 450476051, 833393957, 540585510, 61751110, 523868793, 101540208, 309965550, 260885279, 690068322, 339324520, 2536007, 836162524, 286481832, 756299103, 985098606, 838212743, 86172744, 460877868, 838240924, 151361892, 155831196, 339316299, 40126174, 808510734, 967054151, 169759797, 425259750, 483503932, 110076694, 726671125, 11128247, 939467108, 676770720, 477989613, 108746709, 409692825, 161429, 704745446, 576604155, 396723152, 740711235, 208780959, 189806806, 781194653, 357590757, 245664726, 663954754, 884178372, 673536581, 439474818, 241494156, 590440258, 730820555, 849377991, 610274520, 739842370, 188662207, 21633954, 21204918, 792809071, 597384884, 838003, 692051821, 598490309, 47527231, 451166172, 938191459, 217038708, 251302718, 481610465, 329366318, 653318915, 796758862, 849401800, 686450842, 746104860, 316156443, 663285112, 887850459, 726480935, 304684884, 5431285, 816906899, 944450200, 670917006, 840235495, 802749470, 243580012, 611425416, 297842755, 556869656, 540460344, 709202410, 825864194, 675565996, 359272856, 123476329, 957035200, 693068246, 488097970, 903303823, 301254466, 314710569, 116813979, 143217173, 272431774, 546425016, 235212170, 237041589, 540300276, 857060981, 244519809, 594112364, 135694081, 624672397, 671242586, 946244503, 217417588, 394206325, 738586342, 483831314, 538678920, 761561436, 829886077, 318196543, 28441258, 22892725, 398618330, 488330509, 543754945, 469429541, 183368373, 600609335, 533858352, 750778344, 454506388, 186053028, 105116508, 575705807, 316543052, 866457144, 550971673, 41457573, 613620789, 130218873, 42906999, 910509219, 193371286, 278807470, 767361157, 544724367, 808389784, 223473475, 617692315, 127298107, 505910144, 119555942, 396017718, 241902149, 452030589, 664170511, 835375636, 5513541, 985440470, 110319101, 839615958, 780039662, 561723168, 406757456, 350268473, 402673390, 391760299, 697270641, 958172723, 691445766, 591664754, 222846774, 393388776, 386115599, 845012735, 590631887, 347372265, 403591897, 438651539, 718809759, 408020433, 228864277, 220005566, 755297583, 79600550, 366284596, 891886485, 155579750, 669716449, 44149417, 769506558, 507560498, 958712381, 464654755, 750087831, 305855646, 470848065, 195552106, 984948683, 801677714, 260747014, 573689729, 709479699, 85813213, 550855284, 456965149, 952099731, 86512186, 909783871, 305367600, 83653855, 492305481, 220339986, 152701830, 86356333, 355688045, 283283105, 767971336, 533444553, 64357990, 223762203, 810452328, 856772692, 486580291, 234022364, 692126549, 284846416, 800407084, 391491354, 110493132, 143435814, 144206113, 737927826, 177289470, 964069418, 807199258, 991796851, 405130181, 521394977, 10153029, 758766711, 103840827, 269458708, 907505774, 748754080, 987909135, 769253050, 992326250, 60170532, 460228997, 660674584, 176256356, 746301633, 176785920, 901243639, 591262580, 238791964, 313854438, 646426821, 61372709, 271183673, 730764324, 667940242, 522893698, 306922666, 963518601, 719497701, 511238053, 792973596, 38210846, 145681222, 769285009, 41849444, 282654708, 324751362, 753566434, 461756671, 128695995, 658178219, 918668475, 636977227, 579322440, 251035289, 445169223, 653629397, 295710135, 718166829, 158844007, 202285422, 363560152, 336454054, 985228260, 903149831, 896421200, 175351704, 647920389, 173554806, 395527419, 648818802, 212496850, 717363718, 950166182, 652157268, 790567656, 664001483, 250664163, 178536092, 948246884, 76465393, 270358411, 169216917, 264446665, 472146468, 245619858, 663044974, 399884931, 145578331, 323066841, 858890369, 389188108, 688795905, 739539972, 749979885, 337257199, 546083777, 808484811, 569201883, 93622214, 158285096, 69122606, 311875739, 521644779, 281459825, 864180541, 351157347, 894274176, 316359926, 940220938, 596129597, 297379819, 691929601, 760956157, 676716511, 182710837, 68190275, 918780188, 659917632, 199005252, 240220232, 322435645, 60073264, 693518408, 876301890, 682197288, 26525702, 597810795, 249008103, 799015662, 212174721, 613600983, 982652756, 74473581, 913959080, 417073566, 412100768, 794764587, 968414110, 882387680, 965950416, 434210465, 502366922, 400518604, 46008956, 605045419, 749202416, 779167829, 623461333, 647555982, 866099850, 203150209, 226388730, 553301101, 836619408, 354950105, 72680904, 564618992, 114834847, 889854944, 461902631, 751635132, 218525725, 199142206, 468790235, 503333934, 386376855, 473897059, 22606278, 462696638, 37664680, 539687111, 68636709, 421314319, 606814536, 527095215, 48625252, 108377523, 774100460, 495874260, 170541178, 606459928, 138271019, 606178096, 415725001, 42289999, 323923355, 246465601, 463433760, 43349936, 98175745, 428112775, 973600722, 54320678, 443004986, 912001059, 432491375, 500500034, 610850228, 782112554, 489838406, 473916214, 564607483, 651542132, 743811456, 510511297, 542074405, 827372614, 275679375, 714174721, 666667057, 243794048, 194083408, 453344713, 3186481, 191456297, 114111910, 8901436, 902632552, 97360990, 355433466, 321409741, 334218642, 34768162, 874679563, 599562432, 327839199, 561162956, 982319509, 906074583, 502930966, 639065454, 66663035, 369531303, 745264257, 286417380, 856383917, 844245914, 167700358, 686897263, 582914288, 959409042, 102406331, 670852921, 475068010, 90124231, 822852182, 388649993, 593832152, 978151987, 760788562, 657416548, 509857307, 546382285, 894172760, 156584440, 989943503, 851726772, 355572809, 800343926, 736372943, 328615724, 113805508, 767260877, 29632189, 987799753, 841442124, 961461708, 873364018, 870206544, 507765516, 240113662, 278797723, 168568221, 929135436, 436994410, 339597166, 683260107, 423436730, 715493918, 29801064, 813279110, 194229730, 768976552, 635954105, 187889545, 649005278, 819470720, 782283413, 136367365, 846819819, 822523417, 676850861, 605927240, 425342768, 693387962, 215659489, 91308991, 326614122, 35993236, 653025994, 39294006, 681029639, 643265784, 141946960, 274299338, 374683627, 655964129, 53438925, 43216486, 96469738, 935152243, 640430379, 202171881, 564622714, 53391157, 583468612, 564276090, 867590036, 470349095, 696328919, 871808684, 822474465, 10247420, 983933554, 12137987, 993119653, 745849596, 205495845, 348075851, 501848456, 579259063, 39662520, 158352555, 785474152, 27696700, 332332066, 398529123, 350801354, 375228051, 438337853, 379875833, 74833051, 826022928, 830062858, 250082452, 366130797, 333360242, 904880266, 314254371, 93324061, 180094465, 881972601, 667110101, 865823739, 618712528, 908519795, 152878769, 54073080, 820372262, 166947144, 425674162, 704792001, 596270524, 134581294, 519749734, 381556435, 322555407, 639679156, 630392817, 251095722, 809173544, 911111797, 527533502, 197735671, 97364901, 6143952, 378847016, 598383936, 826734937, 61404480, 736842472, 188253236, 261007009, 712428649, 221046394, 933276184, 65311264, 270984916, 144918227, 953597411, 715522938, 944071606, 207503820, 355282974, 203552759, 699820562, 436965322, 766789006, 214318436, 418128416, 729096956, 552561546, 38929059, 845580904, 583709418, 250384331, 683849708, 62348429, 798590697, 4670685, 591916337, 67155108, 555407878, 694019357, 907006372, 844231432, 33213593, 826535175, 823021636, 519560095, 951073944, 739013562, 184042498, 113875005, 255626099, 267520754, 318529875, 462363525, 558653472, 139137281, 966249478, 480578571, 395269159, 454410974, 411777165, 232625548, 150053061, 700459784, 216743798, 956446203, 58589393, 729939378, 907810110, 182352455, 474873731, 292261258, 627610774, 870998040, 68993090, 812373918, 208252523, 1462802, 886272994, 578445219, 445142556, 356133043, 721200673, 696651197, 478465676, 100157201, 192267884, 730178374, 157043646, 518610253, 710262822, 310566485, 58218031, 517133682, 620081754, 379987514, 921332226, 885964726, 426470265, 305758900, 953921383, 672159126, 629466289, 907582591, 491056826, 872032101, 390539114, 776851092, 474722564, 982071829, 873176795, 643172955, 465546526, 213552732, 512597633, 927367174, 155500029, 989512396, 595709292, 403012782, 182461896, 535383087, 101330504, 40560197, 71413773, 84286873, 886863395, 719306966, 835555835, 607672717, 111020325, 173075978, 917615181, 85777874, 366661477, 390183771, 730090322, 803114421, 697194701, 134660112, 405808910, 168181595, 250941569, 166335089, 664542136, 136683298, 970811053, 520909604, 854109579, 197117053, 838977026, 813323178, 285216868, 592390147, 396839261, 468768647, 335633385, 815932334, 771959530, 911012089, 855090098, 237361326, 906984036, 890747369, 862860007, 385000335, 749551593, 144128209, 693424168, 343418343, 947736626, 757132713, 795766995, 240207773, 770537517, 336061826, 28843243, 498408247, 312723364, 73094130, 826671366, 990680311, 148679413, 343989786, 548239600, 101227779, 768800513, 288373497, 644575924, 162101554, 690766879, 336415725, 193261721, 608855925, 212105816, 539787258, 117260041, 823498865, 308298318, 842853951, 932270762, 434073915, 11806936, 800538444, 397541198, 235101348, 586987999, 300648795, 931643204, 940019881, 736295324, 803492521, 13444041, 118760167, 296549620, 832491841, 925796429, 995655514, 79153792, 91576135, 453639024, 751367548, 929530299, 696923392, 258691256, 650482476, 450970111, 506893987, 407063922, 886320217, 462254032, 425601504, 765670266, 739054002, 415210863, 84618837, 994132003, 392498747, 924277851, 368659679, 892345370, 844697374, 501570416, 82230036, 122450583, 695284737, 642298762, 496384781, 658667253, 248123296, 377339701, 766232423, 268426645, 651376096, 250682373, 143050214, 96814932, 857737218, 974274506, 797516365, 484011918, 259721501, 267384060, 501104478, 201105573, 484971205, 671204930, 25631703, 865434490, 738334545, 673098877, 883269559, 575235436, 439186722, 325136987, 625333751, 716290796, 192576972, 562520268, 104334510, 126041472, 814745627, 883553365, 778006804, 845837255, 847775280, 398674356, 576000096, 280477878, 539015963, 456166735, 99386071, 705359096, 784806774, 996771230, 302418112, 596607932, 450537959, 802945012, 496112740, 193698235, 178509021, 926661593, 404145477, 794128852, 426552958, 943003584, 441213367, 508991477, 183153542, 798429200, 547707004, 291871557, 146229116, 339500331, 870409554, 44825864, 782737645, 992115859, 983853501, 378366774, 126060004, 502530551, 410584054, 736167388, 878335839, 140190021, 599630565, 958589494, 176081815, 233543648, 703427482, 851077133, 533270426, 572709956, 369964648, 747354837, 733856411, 161111097, 645478535, 841761031, 572422458, 896429025, 673317578, 117459974, 487071495, 892723364, 672910687, 995895271, 810130950, 767425784, 939308310, 762908395, 126537753, 829215166, 424102144, 471153582, 608370445, 703104229, 206132265, 545780814, 2796834, 187130270, 667673201, 367411375, 792999065, 951187149, 970861953, 565922876, 957834689, 722980043, 60161992, 845510673, 201245573, 89012483, 555372967, 166682261, 271818650, 966875233, 871801498, 431872389, 632149895, 241655358, 735589394, 318387988, 434979895, 333559128, 873751675, 235319292, 709128644, 382387768, 970494639, 151466850, 390402311, 74811321, 302859390, 918968723, 542509286, 408269165, 432576277, 299348486, 965340232, 945063776, 776904042, 314814357, 917537217, 445226053, 361690019, 377854611, 806438813, 874356011, 953408592, 88758728, 629721394, 394560786, 467327936, 978591162, 625189536, 84483516, 625765117, 320081860, 55459587, 481004160, 182883637, 697078908, 455207330, 297193843, 908466859, 180042859, 891381601, 474646235, 822804297, 902589720, 430815497, 764848479, 26075048, 517571004, 857293532, 950364011, 543570376, 497956348, 287840258, 46407443, 323241241, 167499937, 626120819, 275790081, 283275808, 990213455, 509150790, 950317751, 582775954, 623727075, 243781058, 935120728, 319461014, 845484719, 943580950, 136505467, 140991699, 863177744, 385813298, 952788056, 365289916, 752343863, 531845344, 379702328, 884056060, 23981423, 999573993, 28561136, 617221273, 678371576, 368125140, 734782184, 549020851, 187150746, 839029028, 225603459, 868042164, 935844717, 599650410, 647290056, 324236734, 817906739, 141316591, 88764454, 101591548, 40209308, 666924417, 910129813, 812234058, 345891800, 130302855, 654126196, 693355571, 778968941, 872322011, 449346707, 227619445, 116339776, 536960818, 825573405, 141979913, 793990758, 73629194, 425304557, 755327124, 880296659, 462748754, 164926548, 9361391, 846731182, 634305279, 195342500, 653982201, 152399071, 725829319, 102725646, 779809543, 569692954, 753792875, 749250577, 140447952, 484077933, 971334335, 108026300, 568415611, 825623100, 175344578, 512518839, 613395639, 125910018, 444380637, 772803195, 574240869, 440931800, 778183222, 316832677, 546355408, 572386009, 120387577, 332579685, 314434990, 771095260, 691989790, 166788753, 618493741, 94787043, 535294483, 134014637, 63135069, 573694892, 993253034, 756149954, 890921510, 747382767, 220740219, 70331102, 448492709, 128317721, 656152344, 274077342, 188473908, 871453827, 945610115, 789688342, 609795213, 283398208, 980704757, 232881411, 615546559, 441828414, 858067773, 905437065, 949516905, 814364405, 64920716, 189705642, 30473638, 277876935, 319332043, 908735102, 22304275, 35414842, 588613415, 468919456, 701931309, 361552819, 116587596, 804355479, 644629337, 458577604, 409287006, 317347166, 107964507, 748673668, 503393422, 799914420, 457321105, 11964948, 819876582, 516938402, 155329154, 153523346, 320507364, 512086134, 647534999, 870225804, 953312735, 792736853, 585450092, 573324524, 504264838, 944363572, 791335959, 980812765, 653508220, 19780945, 601844626, 51810991, 454887031, 156216758, 158578915, 164507871, 455462420, 868225095, 525263462, 857664008, 536319681, 937116595, 607766166, 555805768, 741721519, 432722554, 76416192, 459042702, 268869898, 368859267, 518800977, 803028566, 946183403, 664274029, 986174087, 378015499, 563181951, 314884474, 16704275, 234822475, 122640601, 435492063, 217836461, 392364179, 477934791, 286509734, 699541673, 143435145, 574740945, 632999480, 599243982, 539537864, 285584280, 241321950, 850680887, 99822252, 997008170, 340053751, 44841560, 120445549, 747390411, 612142224, 306863536, 271866773, 4279523, 786506700, 104778935, 550809450, 259291966, 771566343, 794959554, 834502131, 141352047, 659784828, 683953636, 518986060, 511554741, 493606043, 163779078, 773261369, 343282959, 23040400, 340085981, 839972836, 297381677, 536951838, 353572825, 416762909, 393487177, 795382144, 759241069, 649753264, 435041754, 816641707, 460444709, 747996722, 680123046, 543020478, 949293494, 686692738, 692848656, 152511843, 851367726, 834837008, 148696234, 703227859, 446736724, 285327443, 311612749, 770022775, 92171284, 468972874, 614757249, 965618081, 442273032, 779796203, 725221300, 829474811, 822329157, 638885601, 249094144, 866393753, 501542622, 544326778, 833374080, 558102947, 806000249, 155187883, 628860967, 672321290, 460096696, 73698378, 7609235, 398681639, 650129125, 559125644, 429643918, 946654182, 297389479, 162982966, 545386539, 320066077, 607903064, 800667396, 433348977, 975444296, 894944829, 641544745, 264327659, 829688217, 449088405, 525696858, 881923008, 682682314, 772670330, 632257526, 544151439, 680748951, 314168151, 218980153, 250359, 725506909, 330060892, 365560805, 7570396, 113793202, 700329762, 640334633, 177002449, 340193573, 245509781, 831988077, 226270173, 100113585, 973495055, 452955372, 719750472, 596764799, 286080670, 132975382, 848017770, 763241118, 106167406, 80069461, 275409312, 138227937, 127959675, 52489594, 77425962, 359147853, 490272267, 692741955, 260222264, 976469822, 154336131, 730617779, 111351429, 813190014, 3818031, 22270227, 921464503, 601288662, 477458257, 12055801, 306931187, 331144732, 906559065, 90984380, 975003679, 369678981, 11489379, 859964362, 625071750, 249614149, 915046031, 348954827, 363727948, 579779793, 493581796, 948567040, 265371504, 154729605, 387808411, 828796810, 581718364, 327614067, 710508897, 782332160, 155538252, 976389310, 928893857, 34746898, 293679122, 448638550, 829414294, 794870870, 549938955, 589479191, 740374868, 376448556, 81879798, 326071974, 963294609, 637429938, 847038364, 69703514, 853193074, 278658240, 713777245, 344786130, 600289795, 69302356, 649051643, 918713653, 674426680, 571187767, 506003956, 383455497, 92965884, 793227045, 728442281, 762841203, 818406435, 746501933, 653090944, 789798178, 449664138, 916927573, 732498028, 824414298, 199492636, 798758454, 294594632, 431349221, 102168853, 513516416, 191476263, 210400567, 256052903, 816165162, 853409622, 928799826, 994918325, 932553146, 555309709, 752418717, 349456191, 824199850, 217706720, 763624030, 565002191, 75969580, 574427774, 978865287, 567191805, 408960864, 482004040, 110685283, 432271847, 557668078, 824224432, 18648175, 10364359, 964873152, 186303998, 855902190, 180753696, 557619158, 218770707, 110855367, 215938652, 315449814, 330333255, 610724021, 736004060, 644963692, 455765239, 479242282, 132436626, 834518337, 560627114, 181236259, 725732205, 822876330, 202481807, 945303569, 637213095, 968758262, 624037207, 996252948, 814471981, 993950132, 848328985, 88621655, 674533178, 509213230, 408182794, 489403380, 855274501, 433822427, 316910125, 834253047, 783788744, 983682609, 562627094, 664776664, 29300829, 298515518, 94249560, 861406458, 765718952, 460741726, 38478667, 789221932, 499806861, 187072569, 50533955, 218763282, 242244907, 447699842, 247651345, 455887629, 81445289, 69440507, 345050016, 661703186, 420269540, 28486810, 899255912, 964521444, 753835929, 785643732, 676846047, 792056985, 547386165, 764590656, 906296127, 186742188, 766974237, 451266309, 153295625, 143052523, 330870232, 308403090, 219314918, 797942132, 177333740, 798291908, 687113329, 986363035, 106003676, 91292166, 478132781, 59185106, 665272528, 382825735, 815080387, 42614377, 670164987, 26673845, 254627834, 126189754, 638141412, 497019130, 314237757, 289495368, 715947466, 371238411, 7712945, 117291204, 799004181, 491068825, 571243388, 78395140, 245840863, 975682698, 783797669, 874671231, 60644705, 383135238, 245307795, 599721489, 768368921, 427804442, 977707058, 721684026, 501471154, 452073492, 526721976, 434178626, 954201161, 858516051, 557698322, 672754934, 787250561, 54294394, 323760529, 973072222, 874481693, 617919028, 25619748, 257854483, 716977858, 975390957, 648611819, 792912088, 84268966, 99675491, 395744592, 324574014, 705929169, 730770477, 456168081, 239013564, 112971413, 408453987, 528737752, 986748237, 783830279, 444790318, 189958744, 640940618, 98089799, 248482809, 490543308, 94547776, 428055548, 988840089, 566655153, 691098228, 680052681, 374524429, 351439019, 280642707, 45258087, 925672261, 883517522, 730956688, 406335493, 428668327, 328122645, 440108814, 833232513, 347965985, 951214961, 246576132, 487135476, 897335554, 145826579, 4153090, 120348453, 520506407, 515789724, 239270928, 766863208, 433573730, 735781430, 663190755, 687435807, 281340660, 307350535, 22807841, 998543632, 27678536, 400573950, 139758604, 841031690, 72083718, 355204718, 731558862, 80232386, 764216166, 378226759, 6590466, 122577154, 520707179, 675228003, 853419648, 906300791, 206639514, 251667329, 872665542, 251023013, 81222771, 694960433, 863374689, 802359235, 367993107, 640518336, 73138984, 246668022, 450527982, 705011681, 220937348, 591834622, 672487494, 189477688, 399071972, 922982397, 72039682, 720248062, 822781804, 383709297, 910025432, 529839663, 488370958, 662172394, 751075197, 593328987, 517816533, 248879161, 838734853, 628645670, 730786537, 905632059, 398310529, 957844463, 722680819, 123468267, 196576455, 801306672, 227115055, 813551158, 570937279, 632863735, 617777033, 594655585, 500783104, 928642093, 266920967, 822959292, 16929881, 821819524, 510255305, 38417798, 606281844, 943236692, 824901300, 154313914, 597999642, 172015391, 413900566, 324883491, 208807703, 926319416, 148127959, 483561730, 258127069, 425788563, 954949545, 565596283, 159900286, 593150465, 80157665, 435073345, 617655458, 400406327, 150047010, 895166013, 979817919, 16229942, 25267872, 605644018, 250097234, 466404922, 723175020, 243833686, 635163298, 418155738, 936195886, 682870098, 613331213, 44855373, 225442293, 935853134, 765005793, 616399381, 138150741, 168602641, 311468523, 160425349, 585114807, 314999581, 615413171, 699315554, 273595672, 782374020, 731329388, 27571834, 263501243, 235809533, 18319048, 84337407, 646403120, 70853526, 152629256, 395829989, 126637532, 95852831, 613452484, 366311003, 556033697, 161818222, 500297330, 323632654, 38791842, 163857061, 307890520, 795238172, 408691296, 908105130, 390436065, 273367170, 149080851, 832557043, 490600497, 888851427, 814516515, 486774766, 526423285, 17648515, 428683307, 219929549, 176261595, 712330270, 101128825, 17395307, 616476515, 105186333, 822195301, 633190682, 97825498, 297906695, 41255667, 863388094, 485453900, 705880444, 517933085, 9496792, 606366884, 21264073, 342317826, 894785865, 70646775, 894789376, 602136402, 623393174, 737339635, 237810328, 798572845, 661346178, 619571380, 782295742, 534169457, 814768557, 976459095, 938042590, 637575226, 998561150, 38733597, 603446004, 128048862, 102691584, 88186388, 607725678, 601645764, 627183143, 809918753, 9019218, 30700310, 79866920, 272325602, 410772466, 621411835, 591638797, 974633922, 93713353, 939400650, 443690755, 63675484, 472567819, 521139099, 152419538, 524715632, 191438956, 890859059, 6776185, 410514620, 634064515, 461037548, 153177353, 71715029, 596828341, 299799933, 351940389, 485048407, 73381106, 399962708, 533549030, 486255852, 234047647, 177904353, 733534195, 902062469, 51387293, 338709975, 55086399, 429933177, 42008961, 718442739, 710363516, 701401527, 870290139, 230927094, 218726850, 267847101, 542710036, 619333613, 520163519, 596540243, 95910354, 227987541, 246514176, 342616342, 414536786, 174731113, 13166335, 595463336, 474574065, 741628842, 853984814, 191427497, 355033646, 832172400, 485220046, 582881830, 189251335, 155405597, 197624559, 219672220, 357672047, 477103121, 30599531, 193885334, 621544420, 888666534, 460978028, 611775697, 522227088, 221600539, 447657224, 327741726, 4681497, 864291818, 792345197, 370889184, 3088514, 184696579, 205959930, 265559999, 577302387, 807543710, 391756066, 576828242, 72987057, 989920511, 314386016, 152062047, 594009914, 115608194, 456930663, 154582844, 119404200, 113371582, 724063568, 91833821, 258794394, 732793783, 779727530, 458586870, 910348859, 315750027, 220339839, 633017744, 724304452, 69037982, 583033272, 543073665, 468716946, 81589049, 573295824, 236836322, 507657707, 337665054, 118688975, 829969275, 753055263, 498802642, 199171788, 549863309, 254384291, 153530620, 418789160, 927313984, 238331378, 424935219, 902316678, 495222809, 229471851, 378026205, 464217119, 801581009, 130479389, 767157009, 774403995, 637281114, 493257789, 204871255, 301915766, 677889777, 748407210, 811275181, 70395693, 670233365, 36237643, 43601191, 735804133, 544535916, 844762402, 986068938, 139938271, 133994273, 70957955, 87815522, 944270058, 65628194, 602793543, 411346059, 477739472, 262570885, 149034197, 768689248, 477286635, 246924545, 758606531, 614265782, 172834893, 203902236, 530807736, 710516721, 614376769, 513669671, 564838564, 948384349, 576197673, 756807006, 203467953, 482131019, 410651561, 8075234, 542435180, 861894166, 354921318, 849911051, 374965441, 656504971, 673398195, 321603851, 508559559, 666425310, 139473879, 725260578, 646527600, 71559376, 485798556, 494517224, 70570882, 881080110, 145830712, 45584510, 760141449, 58086270, 989161278, 91913872, 455414313, 607947484, 443697201, 473253286, 190792892, 539988137, 272312561, 120213283, 667039206, 252227644, 454622880, 230093467, 670861284, 335977983, 606867754, 942341353, 119138127, 275792218, 872423222, 256767769, 688869188, 412830432, 666061505, 34056885, 486508402, 304245646, 520425309, 297965032, 902342160, 279750017, 414268144, 373504707, 352536494, 897795358, 421593790, 497149101, 457245073, 311106536, 209627416, 974667934, 857451410, 518944075, 704347711, 686308345, 452117020, 630884991, 697920509, 889413515, 86325168, 311152926, 12944262, 903718354, 373581411, 907056144, 224419446, 571503820, 416816088, 500105118, 524915246, 860498701, 637806023, 842035640, 150885990, 845814940, 133191617, 975576855, 140279040, 82681598, 55666894, 899066753, 84925764, 813390881, 653654736, 383555701, 243973356, 785888732, 898368549, 676698366, 409545517, 127776642, 170942373, 110613328, 907575394, 57725516, 578796935, 898879104, 719387965, 848199954, 810694395, 485586935, 194697880, 103261032, 388608624, 212448228, 758319212, 320238790, 207418497, 116782895, 712535663, 608991064, 785525144, 640712525, 290880051, 204774784, 745379105, 946507383, 897881131, 95134397, 839869677, 199605242, 831197201, 952372187, 758287260, 164261043, 462119008, 917235640, 801565288, 479658551, 291295002, 841441181, 77370219, 80451679, 820806338, 928390924, 605768067, 956162233, 472247286, 88726465, 113520311, 584596704, 285164432, 158223781, 371161392, 583068369, 96203622, 344386584, 493822891, 980160473, 207899488, 676897580, 981979477, 110359846, 354663452, 795504923, 583125272, 581970434, 148533286, 988869933, 430275343, 924061921, 79353698, 708120443, 34428812, 40783187, 758991760, 873834321, 824270967, 435256467, 115677896, 89558488, 917227465, 993511910, 654309058, 682174716, 594488997, 131607160, 950561348, 527327559, 149032197, 2722355, 512817369, 897582713, 536888657, 768280450, 736861636, 851400453, 668458582, 742990947, 450713365, 690386373, 560704577, 761497608, 98764977, 967549766, 691733464, 11369445, 956105927, 633021371, 842789701, 615377050, 337044466, 10340756, 951254477, 446625120, 534348725, 244816494, 589392264, 778821682, 47972684, 936991886, 131451834, 959074307, 897009421, 636348630, 45787785, 796612757, 420498906, 621931126, 939646302, 945877640, 704013299, 836059618, 157902250, 12137207, 917175178, 645928709, 689195401, 749082265, 830288681, 210856714, 21876957, 773711408, 2160241, 582583932, 576772702, 312088390, 717371973, 250569050, 87009367, 415718718, 689396212, 78261207, 586827105, 691946546, 460254495, 969657205, 827075437, 523426374, 830150103, 677574592, 746880962, 133790703, 500979678, 243682379, 68807879, 276258182, 282271171, 145450917, 461967913, 410782807, 9997560, 759041342, 451813440, 418333589, 329220693, 370380393, 665109197, 457808869, 828104299, 974490211, 29049982, 329288650, 395289146, 392539004, 174502709, 577613442, 895109517, 75277104, 297907604, 130809399, 340628735, 437101900, 619523178, 712921322, 815166196, 321130095, 668107469, 216326609, 857094090, 575685758, 747966894, 539800968, 70190863, 511042315, 147078166, 455830025, 27134580, 907253912, 764659204, 571286601, 318663285, 315301684, 171722844, 398651801, 260985793, 434898432, 916090203, 909161211, 594754113, 620026481, 241919805, 622058598, 671332560, 360924856, 328204549, 840070920, 862153014, 970563959, 858278262, 873267813, 718861951, 417000171, 887921966, 456637430, 948217321, 734977215, 525207712, 244170579, 396813836, 34742954, 500523373, 847983383, 85164499, 940979703, 584348100, 822897974, 707251941, 704031467, 974411837, 44515729, 445208519, 422971647, 338291197, 809369816, 942266851, 771209737, 111984565, 773787912, 67870169, 58724598, 691861919, 235108551, 772555639, 138875457, 230002801, 925306119, 309320776, 402847394, 176931448, 403379594, 999075680, 514530717, 528489616, 763515118, 297519964, 476860890, 267976428, 973237854, 671161092, 120302790, 128300636, 162891793, 873091755, 553782187, 32923232, 365872215, 435257964, 504098887, 945516462, 190992407, 296729058, 350414400, 303132348, 932166574, 53207399, 969965802, 382237064, 244346859, 359648425, 41797209, 934790097, 261443606, 484209773, 771447287, 989781717, 726556473, 999104715, 438710144, 321829015, 406220601, 648721877, 254237969, 65014417, 7415832, 939850242, 613061069, 907366704, 616698690, 600726324, 844645737, 886477842, 863229716, 254598129, 99040456, 723959456, 922624637, 147799631, 484665906, 356550204, 983563017, 758122872, 866198363, 375809858, 556139810, 834491346, 410248745, 931403479, 490467639, 554659450, 897856179, 739214920, 161500438, 283151294, 892067565, 131783173, 604190423, 891836579, 650389206, 349474614, 359297948, 467261265, 839275372, 951096686, 3618722, 978909775, 700723532, 892681586, 340320558, 365491991, 220058940, 666772318, 39511707, 750257253, 668850299, 32913987, 975794017, 922629816, 349520006, 701146330, 315372714, 118661482, 907868479, 747236776, 47913721, 747499008, 425394755, 924349351, 973040113, 412260701, 312818803, 158073712, 208107491, 328555737, 325407118, 836910890, 895921453, 549993768, 373119081, 726802565, 490589828, 758064638, 779431824, 850848033, 446942668, 202185650, 334450820, 745591594, 167343711, 114800147, 792606757, 408362842, 8275247, 753731054, 422438491, 381891911, 400984128, 524481208, 57773056, 683163894, 571479950, 235112092, 152127344, 97092228, 439909624, 333760915, 977902177, 861867260, 666752643, 942837155, 738359525, 523645912, 391600118, 444799705, 445698445, 634914783, 220027628, 708584818, 160975257, 484872522, 321462316, 433918545, 773258017, 964607727, 174660043, 570120687, 653935897, 244346789, 355714095, 783655287, 110402401, 743463181, 783110991, 102109035, 803604025, 55598292, 252075884, 387655319, 431384653, 795830605, 18371316, 561401438, 721974197, 114951709, 307683925, 272091573, 923769490, 473232910, 529901166, 962744357, 208041383, 772820073, 38924308, 416999242, 317930293, 368798422, 661204508, 71615221, 440506677, 28658788, 582591679, 295708085, 79872400, 453580063, 674704917, 752482745, 936620702, 763009656, 150904461, 316884143, 65003366, 17757695, 883204543, 870548686, 210816309, 68159514, 941087745, 943784067, 508947193, 822170877, 95224195, 473499561, 763563129, 123621955, 691346549, 147905724, 750579535, 326704800, 108508276, 598368341, 159872989, 819389483, 582005783, 365930006, 231482203, 774918057, 188782617, 972744542, 542985121, 980578995, 106753758, 230408583, 450315597, 734005159, 824775738, 664240161, 919813251, 870439061, 131546678, 717594900, 393935891, 323152376, 951206089, 342153812, 564440003, 305242461, 681717990, 508319647, 43248030, 357762160, 392296333, 658524714, 310008709, 899819862, 759846170, 174734585, 945980858, 614667479, 692441556, 492486077, 741100596, 87423365, 920010658, 191932439, 319112111, 744253714, 233566239, 371466185, 833059978, 837786401, 213001560, 890978300, 602925497, 537077284, 318169276, 703638730, 113388369, 327031614, 109616158, 518763281, 996938235, 541672322, 892108842, 530623004, 287427600, 91136705, 322843887, 932443835, 896854247, 553968266, 574014113, 200506112, 31368682, 203384892, 914462254, 461288372, 661680098, 557388811, 331052462, 195184116, 604472224, 292709557, 256938315, 331300418, 544890368, 887095271, 439087278, 568073466, 973742352, 126514013, 591989927, 295182847, 246378620, 824495449, 384896537, 282204798, 711054013, 815652987, 182740342, 537606479, 204652739, 109295182, 685626696, 428968117, 314993047, 997881891, 935030561, 441057273, 4353999, 986116423, 436237489, 994008535, 765275720, 152583328, 973121224, 861895335, 679716567, 267568710, 826367153, 498133032, 104824745, 809900454, 604052174, 647251685, 469978089, 343636177, 993938230, 277103936, 755134612, 194765050, 522870822, 9525929, 453305080, 705532921, 788485133, 654223745, 240893473, 433368860, 396151139, 876287545, 942016004, 394400976, 183139770, 753439935, 16482884, 74153928, 105673088, 131274640, 931694829, 536944066, 531676448, 525433121, 538687978, 302733709, 385252157, 655585847, 349116304, 640856465, 714351334, 180059136, 229734664, 875477147, 469158939, 334520211, 706095306, 576960779, 612414569, 706412438, 782438352, 893949503, 49116056, 550270449, 167631187, 697446117, 559953143, 724260299, 206241044, 465177151, 570167383, 315518577, 996344793, 520403556, 557066833, 98848892, 321195504, 971639911, 934958853, 393689587, 387592688, 956746161, 734055765, 449070542, 406847364, 422924355, 39836533, 388598133, 293266517, 335387816, 728694242, 47830415, 452991846, 638177062, 886640939, 202323072, 489195779, 472310824, 47825640, 408019857, 211507981, 889089313, 892640149, 624189735, 437064264, 352937136, 853713602, 6067973, 785197831, 773881007, 867265480, 4956879, 596633406, 780207028, 748228620, 898302151, 460979363, 228769532, 90321207, 37352606, 8960766, 176494791, 213376174, 23814436, 229889863, 512672198, 437684568, 252998119, 113051724, 122697921, 897395992, 261421594, 357358272, 508851149, 388019548, 752197510, 927176796, 147305254, 504013831, 299110426, 855718982, 174679512, 948426736, 308682504, 758088227, 388759491, 39233858, 870257119, 631716892, 875762971, 961337489, 275336469, 567491037, 70837343, 423185407, 808657161, 283442286, 188018029, 531029166, 616706714, 19525019, 901426336, 650671043, 159072103, 578395691, 913972117, 713326385, 424410997, 442579801, 444632696, 612580972, 547212086, 935533347, 708473952, 227550807, 185371338, 390550725, 885709273, 162554710, 236329027, 737727317, 292515306, 754737813, 576986482, 368191796, 674146645, 629861908, 221241874, 419138508, 865992131, 470210619, 388968498, 117441066, 663599400, 440054224, 317997809, 847999017, 60996199, 872942093, 758308133, 939793521, 841522295, 975926622, 357940627, 142623708, 596234994, 18583713, 463502293, 356463841, 432022553, 662876960, 499701618, 842266814, 77325287, 976888172, 35662175, 384624082, 54677330, 896748893, 812531415, 304982948, 299773502, 180910260, 84737821, 266748056, 351269052, 258959313, 269077203, 516661597, 675065566, 941948350, 845239224, 706257059, 389346998, 373900824, 143552267, 916697086, 965307886, 514298947, 672208212, 644662089, 556539008, 974107352, 213882084, 19516788, 104788722, 935197979, 655462594, 861656211, 46853438, 462526007, 40434493, 187907463, 792235940, 268196122, 221134340, 303619783, 107932346, 562464196, 394815099, 962935155, 487984872, 640006630, 378786662, 304058729, 987348000, 380627871, 173849265, 878860841, 771259305, 908390158, 994368444, 356609090, 808012215, 805162786, 244571652, 574003351, 471362130, 770732387, 851832213, 492118381, 396068109, 645269811, 953974643, 433427989, 403252528, 363297296, 144538220, 573166509, 772899924, 318677830, 562559350, 28648918, 924578676, 570448645, 192628492, 489192013, 709865314, 331441340, 131879515, 25536171, 713295258, 659947021, 615369000, 554292120, 18751696, 472882353, 271534333, 265268256, 58458586, 105392515, 694419840, 832379790, 903173330, 272584733, 121136076, 971535805, 608776376, 631015627, 738969536, 151669569, 481186921, 974608718, 536103525, 113424074, 352035245, 572293276, 622977803, 612798337, 913667652, 896074838, 900986348, 10057748, 425048234, 831569974, 164931289, 869332833, 390461801, 119287882, 948612153, 835054941, 64873963, 687448147, 624228437, 644532673, 402947762, 906052358, 346258454, 243148458, 793263317, 841958256, 116453136, 121191887, 140556429, 4369793, 886273109, 354040573, 568974011, 189182379, 159605555, 703511977, 9931825, 292307826, 813415209, 568236278, 873330311, 414456726, 898411775, 320026589, 655576635, 330224625, 379642089, 124549144, 566740044, 424176299, 451978714, 899312974, 147693843, 11293260, 903161519, 54329462, 97761597, 910290025, 488269707, 974943903, 654561394, 66789580, 185836296, 671685132, 202424624, 98712859, 656528823, 349734464, 616762264, 348232843, 113961305, 699801092, 176099971, 963153669, 287175030, 624479822, 989632914, 77246486, 660526733, 400321950, 440471877, 118187333, 17093199, 358701044, 305134918, 482666284, 656700235, 257202705, 61749441, 684565902, 853324820, 952924805, 759079919, 447728929, 704796880, 138347922, 128442580, 848513077, 181842935, 936335087, 134225379, 304807785, 802256003, 604343865, 968659146, 801616700, 787992113, 425994249, 933219240, 830613508, 384577294, 219398608, 663274838, 367959059, 751585434, 374451877, 711650619, 380979143, 796039877, 261936184, 849421496, 561652520, 146515690, 18966445, 898417520, 953464208, 378947621, 202188167, 888873533, 504328276, 843880531, 795814922, 494802316, 524341068, 870423704, 432494876, 842614832, 443855379, 306557581, 528800162, 732194326, 887304987, 332627822, 233189462, 504981122, 51043141, 370655737, 760647539, 654183225, 543312427, 436562325, 678034729, 490818356, 304272740, 594795867, 952458368, 463662700, 410880627, 844398133, 891532866, 149505404, 819410272, 280422395, 119417016, 786445639, 409925014, 814498446, 506342168, 896590252, 156561716, 718291297, 768622089, 474118039, 731459452, 843034720, 290700353, 629020904, 613879173, 710953464, 256823005, 388590875, 559425222, 582365718, 622038039, 508872286, 790380106, 539376522, 234445354, 355752633, 574341270, 792483628, 74469735, 969077063, 802599764, 565480416, 272038720, 438083990, 669040030, 380589503, 41209055, 886071850, 432083638, 22727062, 845724656, 643704692, 844898512, 384220220, 285447924, 4581843, 737871565, 646129020, 383525703, 96912955, 860501922, 504658773, 72470098, 73121062, 907485123, 537352080, 136447333, 45796825, 377346461, 496868167, 339949169, 616379205, 973383965, 292405637, 252247048, 374986262, 514647041, 399905614, 358416417, 765942818, 943953522, 4498282, 741498589, 747136108, 786765548, 111312900, 954793679, 185355380, 370175835, 587557473, 978160583, 888214355, 991614966, 121732191, 557029992, 976594545, 658421606, 207983658, 159822950, 734973550, 370256822, 628924226, 157495767, 828427629, 745894413, 671258756, 75945124, 695212356, 533366192, 869140298, 826855139, 378475419, 238501410, 478038807, 4994280, 53132738, 284723855, 726357016, 32025022, 424450753, 749368249, 275261145, 62201615, 319919194, 400241431, 670589381, 663528021, 978605192, 847423944, 231328792, 487460855, 116972207, 216081711, 560612657, 750648123, 511879252, 478800767, 245837621, 443807583, 558051246, 403293063, 677078556, 568598802, 795677368, 250736866, 767634841, 844340540, 516489996, 657385413, 904593322, 572775206, 317272459, 525961366, 384875101, 26942995, 380425300, 926918615, 260054523, 29307227, 902738656, 677701701, 495538256, 456393878, 882205921, 762758406, 33086750, 600257622, 160741517, 267120963, 452037721, 961995150, 490012313, 231610223, 662918837, 388870725, 539804678, 838374663, 102637032, 178519889, 304645570, 304811942, 718473640, 936119820, 402905607, 772924031, 92172179, 965284760, 289628208, 360104078, 580074665, 29769301, 831118407, 825456384, 506597333, 862822554, 622079035, 478571775, 739483512, 720483455, 388219479, 177790139, 579345556, 382665303, 551567275, 89669640, 162407259, 384436686, 462628460, 486745427, 369067462, 563926906, 501939065, 960127551, 444901733, 403088373, 678464889, 319988631, 569898486, 913165351, 478794965, 262898915, 774209864, 480797472, 914837248, 65985007, 45334999, 843201860, 28801187, 287147857, 957408941, 682861006, 584734396, 403167998, 984362890, 500257721, 856594256, 528244865, 707771667, 980330473, 895780067, 259593816, 838878176, 370105724, 288103794, 191702596, 494661117, 20984306, 568021285, 965006156, 181689451, 935848212, 132594204, 922827728, 69205709, 288507984, 513473106, 486202606, 454899819, 26712989, 453310031, 581797927, 411141410, 846737280, 116186094, 326106936, 809216551, 7904790, 979453540, 623208614, 276850322, 601119332, 906540098, 326844237, 753465612, 552654419, 986772339, 19625893, 706199313, 415911701, 788213185, 308397603, 988533951, 431347944, 412465514, 782755244, 603663614, 476126821, 61695130, 981233142, 77947254, 274331433, 52418929, 904936134, 501957264, 681624643, 235282521, 804211255, 917569771, 404213800, 87393984, 499260173, 151875047, 725077696, 597278976, 361567274, 803133059, 805938421, 34131400, 980010717, 658453079, 921693223, 757242902, 124392504, 887449541, 997215094, 503504879, 712282694, 167788940, 385176814, 148560816, 460435999, 17770685, 638683699, 894985418, 202167138, 166771798, 90833795, 324801899, 135810230, 534063419, 528883442, 5418578, 297833925, 866775619, 40397360, 960978892, 592548338, 847356886, 1555518, 870467780, 568670938, 21484019, 767019123, 831880808, 419743778, 401709780, 585321209, 602328741, 239667686, 678774414, 871766697, 982157094, 723025623, 185987815, 16794967, 231875470, 19535012, 29551196, 78683048, 952378376, 650248590, 340006463, 561579805, 725312193, 609386139, 330947161, 353651511, 988732394, 634512269, 766168487, 928516329, 301920883, 638821212, 869863, 253725908, 550236729, 536538077, 666068409, 162734673, 479617393, 894192806, 857434344, 225065026, 805479574, 280448059, 249020295, 985982865, 242963396, 629803986, 801767321, 548320256, 869596227, 796054547, 42785693, 299133898, 119564049, 918500916, 785582245, 876392600, 513419541, 629987577, 251957943, 4203079, 103642626, 567342608, 207104062, 433467317, 647245271, 556792645, 135781044, 518632861, 915596580, 151352267, 326013750, 908295636, 582827035, 843619929, 675474129, 98637462, 807432072, 662029376, 864930166, 896162238, 506280992, 710334662, 942790440, 517929066, 565707417, 351745282, 73574527, 895905491, 60747584, 445719563, 627423167, 121106616, 601970108, 336438994, 511046097, 108210676, 481577641, 668988150, 683466633, 100891880, 166829156, 869555218, 633687078, 535882477, 548901998, 189831315, 190574456, 321445186, 33051332, 774725834, 40336098, 77230220, 902162081, 23629649, 715456076, 225491767, 99325036, 515950352, 182539137, 200681118, 863600358, 755525690, 843693099, 180067637, 880038208, 57447722, 807816398, 559277845, 651917444, 831644488, 461353630, 384181062, 790869964, 994573122, 388242985, 547327588, 708897084, 837304021, 180783056, 949935527, 368448583, 890780377, 199950205, 110880794, 585301377, 955743462, 574937080, 118264911, 821939593, 507112373, 997364290, 39638195, 205248970, 119094607, 965322868, 914759182, 785746383, 345804065, 226535253, 41039728, 527762043, 935716369, 358605920, 815122306, 445216435, 46016383, 693444718, 350551322, 674944064, 75971740, 696828850, 157531252, 482801380, 54318649, 771995061, 823650335, 46647383, 205195520, 221932471, 901025882, 940460722, 600110429, 213010087, 901901108, 476422036, 933212644, 851278444, 622715957, 885498355, 404570115, 888745486, 302993661, 693954869, 798918378, 684022814, 142681512, 559204485, 361172828, 807713438, 209664299, 2220957, 164515215, 500243067, 35655138, 606010734, 816529147, 966521020, 803582292, 812792643, 612269348, 474274598, 684501887, 153880867, 508936069, 979811141, 91312745, 456661887, 229087949, 551412728, 875847185, 797468147, 29696038, 558668121, 569479686, 370353401, 128187570, 141789601, 149733650, 424739900, 312920971, 670690512, 332142418, 499326763, 646697894, 60861033, 982017679, 481800619, 988726053, 260520863, 971024431, 706534019, 383334347, 810679944, 959556974, 322151962, 819022877, 240738690, 928425654, 542829222, 614484421, 643827079, 557200418, 195448446, 635076710, 504563405, 526122381, 643244062, 157672403, 397865906, 84674857, 874310539, 254605353, 520116039, 22104821, 767281997, 56964284, 369095497, 910326852, 345225785, 469516968, 891377978, 218069747, 705638496, 45893085, 434754547, 50072380, 533734857, 466624144, 772134005, 977712198, 791441087, 135977581, 491244891, 8905165, 758285706, 119017272, 205403768, 191656029, 264763799, 403788431, 818893659, 877463444, 220681599, 244201127, 695916762, 254991858, 18767492, 305147005, 282369903, 35790819, 460788517, 142379579, 3826478, 772600802, 576688051, 641427286, 6336143, 86567583, 267091593, 883827807, 446248101, 565610354, 489409297, 399570192, 145536236, 68273487, 350674863, 416738430, 269015064, 973484181, 486412585, 55745012, 656413820, 855935579, 50768655, 954650468, 581700177, 81142000, 393261609, 221313720, 105172558, 955082278, 656814704, 796936512, 569119682, 916465700, 73138269, 575994604, 122670924, 283769295, 91672758, 8836646, 798111447, 869494472, 10081545, 345971998, 151558007, 546384561, 765998603, 148259907, 294175221, 764537384, 252651829, 164921696, 475761936, 704962543, 881172678, 510046750, 825081809, 255386896, 883413581, 11672981, 293249102, 436663516, 590747811, 655144299, 465414875, 350872517, 413849935, 256617155, 854609058, 473208340, 904741096, 24451213, 664705897, 641804971, 200816220, 101955852, 809460348, 527040452, 995378424, 226976910, 625670396, 226604231, 963101593, 598659826, 757800005, 960267270, 142736970, 764276006, 379279245, 931291005, 355575411, 573230158, 355203734, 911354696, 152193850, 908930328, 77490475, 927651905, 840557449, 335142359, 855089445, 663067987, 349630148, 681992294, 841778835, 36024968, 127827073, 851181847, 510956210, 484277277, 726570974, 440210209, 770811001, 701819816, 708415798, 329029125, 438184284, 903222420, 488018929, 173058245, 617109011, 703946029, 650965030, 675170337, 124587861, 100500242, 713504201, 660553188, 866130313, 602835135, 565348498, 240021297, 249358644, 803466080, 702118784, 12021438, 386867951, 607232630, 892617854, 188452174, 361914106, 239468732, 327533253, 725785123, 916708655, 954664314, 658029174, 490099756, 753004095, 940112358, 856083429, 875991579, 879918272, 992188119, 744571559, 480591859, 49930022, 696933384, 415570059, 791113918, 345605749, 887494816, 762419054, 247297058, 435047355, 984149638, 647748008, 654051106, 891730422, 641073991, 995232890, 968340265, 644412013, 869206568, 824157175, 876280817, 666470387, 617236728, 912974728, 631732778, 752985481, 408914752, 891439896, 812401283, 372237824, 765251210, 748114865, 923757928, 641958286, 118300761, 28837725, 826808481, 391011768, 697837032, 877585709, 96669488, 351930878, 62124924, 427660118, 772318449, 150639371, 614075926, 211204966, 164635391, 524322634, 252354623, 268204551, 168781852, 351338206, 297818516, 956860163, 160103377, 115005732, 95228405, 334320417, 346889324, 705711797, 763131388, 456788898, 930866840, 522097137, 407628698, 549416929, 38568009, 675177355, 288034371, 186614316, 672863454, 752020138, 422470234, 568048671, 404023313, 385804581, 442624771, 156266992, 442190102, 979874130, 219938693, 570328058, 797170644, 685194615, 222490790, 746301825, 28561130, 329441498, 677422605, 715577752, 330925442, 787517815, 486689726, 62935579, 301088322, 297559764, 75424756, 963793789, 343693807, 116125458, 811117538, 255108074, 270916867, 870987276, 180345171, 178160203, 547330966, 740457929, 327878842, 804810298, 12592611, 731203452, 892071263, 679176462, 818076080, 183120509, 507627471, 54114337, 657757100, 109506958, 956106753, 701585778, 642588361, 250484878, 444395188, 135862881, 862571231, 140536973, 534381602, 375466866, 734282985, 670800566, 378072047, 469692493, 931514100, 683560260, 605630788, 878768880, 581089872, 671711794, 683158797, 700315545, 792433778, 237732782, 630164771, 70483599, 140802674, 405384279, 542288502, 748884049, 751357403, 141954625, 450863021, 252657036, 353740427, 752926802, 442322355, 579535335, 406263693, 898475977, 891832837, 592252750, 190545028, 801566452, 687397329, 215894673, 507575640, 288485930, 640107226, 613186569, 924047538, 66624226, 878186500, 709112790, 622122539, 331384401, 12058216, 485463591, 462932653, 325484648, 621809756, 471872639, 540096343, 958473580, 544997776, 114173477, 316433802, 8662414, 845831467, 264377298, 14470438, 846556828, 671698635, 579468539, 639320030, 240982578, 842355844, 454172488, 552580382, 283083808, 668981564, 293101323, 895602262, 4813355, 207530083, 301431738, 780889889, 408393307, 120228756, 668954804, 986865104, 629747081, 606321137, 402791225, 283955189, 35564436, 602484554, 338622121, 784204193, 148597861, 227406318, 440055844, 566311735, 128167847, 829151432, 689542755, 607337137, 733302732, 221522665, 258835184, 596316179, 624973760, 637511818, 303314679, 169162819, 429147635, 826788001, 672694596, 578680350, 490432063, 935521734, 91428443, 882227790, 862736242, 452919606, 451043172, 251386733, 961442264, 518224035, 801237848, 536428097, 248262660, 663057929, 433065248, 634870000, 662810663, 399879591, 61079136, 512116799, 609803265, 313724657, 217891194, 482282523, 669683161, 199096124, 22817740, 499329399, 579604923, 936700695, 769107124, 165509763, 790219959, 912946570, 319361873, 452192714, 754148004, 204308276, 888335813, 559691923, 492914699, 931770357, 709677162, 365854508, 66616040, 694790830, 657173073, 619949657, 395264561, 413561727, 100024944, 218651029, 469423616, 755610858, 106747916, 950301288, 690779466, 315074253, 206665365, 283341926, 927871722, 724015964, 959182210, 521556122, 984460220, 157790948, 448595300, 864121929, 987274867, 256252463, 314734973, 805174901, 727619569, 930393156, 200695991, 231998820, 20910271, 461177505, 116744704, 337765102, 622035637, 267798070, 549051367, 2388137, 955477512, 856183238, 898569242, 449087121, 530866563, 998444564, 535322698, 46444835, 801824231, 757389454, 168017261, 450622813, 219555821, 914476766, 339943366, 342413253, 231281861, 481661674, 580671010, 492172316, 690231827, 264792898, 15584009, 738881519, 773870215, 971683733, 931390049, 237667396, 705422211, 373417233, 165140694, 369189177, 826372183, 231605954, 363748446, 639717562, 409049362, 713980947, 280334434, 981392349, 399777582, 755829009, 641109007, 533134352, 569535481, 21682908, 844939003, 685828737, 158258779, 906105379, 885163131, 817629887, 390664337, 559736932, 857407745, 895791430, 61644251, 652252369, 306368789, 26658764, 152487549, 269956414, 961769444, 32508691, 6334457, 964158821, 981002465, 62818981, 154012940, 127527378, 511067661, 785266628, 707148671, 151393746, 469660087, 106140478, 24355594, 773163319, 870355633, 3747128, 407481579, 664920250, 203026174, 75490644, 744377430, 888083312, 427003259, 848105885, 779205612, 760196905, 91655303, 253306598, 670802617, 798512115, 488690673, 912651182, 33806091, 443556127, 408657410, 693626500, 603396463, 968067468, 856171867, 438156029, 465668780, 543736088, 58210182, 507845865, 543139986, 288282290, 547218313, 657330476, 314357582, 172465593, 131861636, 120498931, 831030663, 706244999, 784450012, 405247240, 905901697, 988475100, 592772849, 152048730, 496571747, 10729427, 479220090, 886749715, 236584527, 302307453, 857547289, 790314590, 662877952, 928773332, 563923659, 444695288, 953546734, 440431494, 666250429, 525167525, 499158668, 804968843, 788445114, 859279639, 620293519, 273538467, 768978503, 119658213, 384082735, 380183391, 474086152, 148778391, 413767607, 331208031, 686466174, 288280417, 887150731, 261089601, 128966417, 335234238, 739921472, 755510742, 851145826, 846854168, 970589759, 210592544, 863516323, 511389397, 498676806, 485632885, 310488689, 496308739, 446766243, 313392030, 683165700, 458634852, 985195469, 571160578, 634717501, 927139864, 660572169, 846223365, 447562542, 197594910, 86064939, 548028712, 867946698, 658662840, 184888848, 512950751, 196554925, 415719629, 152853144, 712516794, 858566445, 700068655, 138560952, 854295280, 587268778, 423111961, 505813685, 782671381, 813274411, 896266162, 634457289, 610099420, 391868110, 812312549, 385523785, 200203568, 352125688, 636215684, 773739372, 501155314, 851827232, 571918818, 25742386, 675469179, 563816638, 163858581, 100057886, 243000712, 354690779, 248578498, 100645915, 78989658, 83071524, 109218658, 760013953, 946950680, 944023293, 258156395, 92495178, 743732570, 988132844, 926826307, 638980712, 38521659, 547286674, 571530061, 972452170, 766209055, 628531330, 790825436, 732898574, 740988095, 640600812, 172711939, 702643911, 507923808, 468802022, 172421986, 319890421, 867851747, 173861881, 262384081, 886671671, 610973456, 667355424, 974054228, 375074980, 564122415, 231128793, 72554370, 535459111, 474381993, 182981706, 517319067, 509513506, 494611742, 4897063, 699491899, 129399804, 999313432, 962822023, 200754663, 899941705, 901370838, 722703112, 637560343, 990874954, 456490914, 449768343, 879869079, 163189837, 909356788, 239378938, 698804488, 901814188, 214164624, 371313036, 959244468, 878798600, 838638448, 117832645, 753168762, 677002913, 380091873, 674844527, 727246001, 274227621, 150490961, 990518587, 974003486, 266181675, 282301597, 972167040, 235131399, 303099385, 496369837, 156910344, 446693346, 169837278, 278740440, 120476105, 883493641, 255982150, 876774726, 931733168, 895299922, 111869257, 265661307, 526368643, 908827021, 768010066, 961656742, 345715707, 996053311, 940050577, 451100326, 199538628, 422028476, 54620178, 446049680, 24224780, 212456562, 839562968, 807229590, 799398765, 857819575, 799093093, 158422129, 108036875, 188881270, 942431236, 897907739, 527430463, 288042614, 507451625, 195292203, 182034877, 283705774, 941855340, 852650717, 146287004, 546829202, 736949755, 848882374, 237263872, 237531841, 457759661, 562460584, 205827234, 660216366, 5876517, 509207609, 616995849, 614927607, 463436470, 597962170, 45410610, 995574661, 290368112, 552981521, 461600589, 124387933, 269481951, 772732477, 564704342, 507493304, 253602786, 79019496, 281895622, 193900081, 53028975, 967930747, 589330673, 131089561, 904854366, 591395509, 519102039, 157978136, 704842741, 660831025, 242312781, 995605429, 808039878, 7599648, 208419789, 895122834, 777804599, 675799176, 4969659, 466556598, 547403399, 6800609, 336795970, 56611159, 796274480, 462472734, 942953663, 775263954, 984364692, 737444285, 977402653, 789013026, 775065362, 421780275, 980222510, 682764376, 150018198, 686630403, 875195119, 492340963, 265431490, 868035037, 835675657, 895631763, 352488077, 149537863, 12955227, 970294698, 535870627, 231497858, 612751675, 188746129, 919206881, 80513552, 570775999, 409410748, 667027650, 981402501, 372954447, 571672319, 85518137, 470088602, 10641316, 368628823, 16200275, 856510839, 931277696, 60248852, 572844943, 561732605, 936488166, 762174959, 283482872, 142568518, 343420712, 79899936, 700895578, 454618924, 618947151, 810135880, 26145878, 290952596, 317714509, 10358530, 517443353, 928069211, 243237140, 756109419, 630771020, 792204435, 600129567, 933392418, 309929763, 718681869, 209558404, 414346032, 845235605, 451688597, 590039639, 225364932, 868822505, 562043201, 117553030, 453207679, 881484264, 236598664, 893583022, 606421640, 778785360, 544451503, 235240939, 710694655, 353205797, 107913432, 543774486, 582138670, 635583512, 506917698, 203028967, 501643484, 710028233, 363656922, 73848638, 941450014, 836594971, 541953461, 985120451, 81792045, 614885093, 31190508, 661388997, 378063153, 222362426, 440922778, 583458319, 778989574, 389675147, 272327624, 357584148, 376691650, 129559305, 256007202, 111472662, 256685519, 159057007, 971637971, 51025795, 561444464, 84015802, 654993487, 182015179, 704791697, 23809205, 61515549, 475187587, 268766005, 383431515, 675516060, 505566653, 607547089, 998153221, 354921480, 129837825, 767458434, 220768027, 825317094, 416034834, 317386751, 134699936, 652542258, 903775459, 991987514, 409484773, 60380519, 774316886, 611776551, 168009533, 295245211, 173485485, 618512776, 173822021, 261306222, 322432117, 516745068, 841487040, 608726123, 750719132, 281848606, 879065244, 463836917, 10884985, 764728353, 639450782, 131494384, 653909997, 328840753, 779949934, 49481494, 677930328, 733172154, 560094917, 365333213, 663572332, 914132032, 182281371, 731327710, 865935225, 364083380, 709981690, 292386635, 34426291, 757838178, 581828752, 206598244, 7610163, 17503622, 199029497, 271253890, 774298741, 672332343, 281576999, 139250078, 373206626, 127152059, 540760969, 786049200, 1519567, 262843266, 254311643, 893976612, 325888497, 388257927, 381866694, 44616252, 533342122, 126616385, 428290997, 656348225, 839706703, 140225250, 776414387, 5585369, 603872922, 930943271, 88745964, 803208724, 186303258, 48742589, 576898900, 571841658, 786517719, 108212747, 81457808, 876632901, 860384833, 941688372, 569021731, 149715112, 352671952, 712511884, 326807220, 347586542, 533738626, 448380399, 74427558, 808796802, 22239895, 564733321, 86765650, 707340043, 280205772, 363644332, 385105936, 975914745, 154890956, 917663344, 135706182, 512211962, 492333532, 711583469, 306230660, 231745094, 242927153, 400571572, 479157853, 12493947, 961848809, 631521147, 260077021, 972167508, 668303273, 590741108, 927320855, 707316102, 290285216, 562117649, 711678647, 204317108, 108119281, 926449912, 29062264, 725932470, 949659538, 877569940, 375181432, 463267263, 363056520, 679759736, 121435625, 246799508, 669340566, 538810977, 306554737, 253144594, 795522177, 50372655, 223768231, 949512332, 821304193, 966460199, 578516795, 796621954, 972661636, 765349915, 676762072, 103816652, 139450104, 486619174, 191472832, 60890087, 679830563, 575164020, 837976493, 195758697, 472046089, 774991289, 341631016, 212017104, 511732970, 329859088, 656930908, 160117272, 98495046, 626501224, 316013620, 893977108, 333934960, 367819380, 938350109, 995501121, 719857176, 430151380, 45686052, 53428336, 360812305, 505127177, 21533336, 723497633, 41336295, 517331646, 110666859, 735805309, 637549244, 576008193, 171012526, 995521287, 678471898, 433300543, 456993412, 45333492, 338074584, 108454846, 946637457, 566655824, 444851619, 770004731, 590527992, 329831278, 899215721, 691744857, 342323767, 583334479, 217839633, 680572771, 583806058, 426854024, 991463760, 315530042, 3913938, 204852870, 668207150, 164975995, 761618770, 640584119, 378462827, 171753637, 299727009, 852209928, 452870623, 942682863, 433191544, 473571336, 874051939, 765282733, 143881903, 417777563, 844866587, 492141878, 416800245, 25078759, 749181968, 748966612, 666550937, 438249682, 355995823, 773179235, 311334761, 928691412, 100708785, 884135793, 338266591, 467122858, 822645419, 813247111, 14879782, 188413542, 268442580, 547104173, 490328337, 989052803, 52096881, 370681143, 429705426, 9189120, 229223464, 529264284, 608626725, 808120390, 636226430, 429778900, 746587764, 27175542, 912310102, 717423387, 26237452, 996066465, 956174421, 184705179, 770960734, 971790063, 254812302, 240721654, 907655248, 729368194, 669295083, 869490044, 919283892, 100158327, 789158938, 975674178, 636734872, 472727144, 436118720, 687369217, 633730754, 84978723, 828216160, 792530015, 225778297, 188408595, 777436975, 341272909, 13092671, 994044427, 20974526, 426672291, 140293702, 712891415, 597637840, 421813799, 881848724, 993694452, 922937813, 152886100, 481906564, 747244962, 145770989, 412516565, 105969233, 784024866, 162250925, 418015540, 125547103, 236337926, 454160683, 102945238, 453180564, 589035943, 93796238, 474812029, 278924856, 114572044, 862793713, 551889684, 820843540, 105897919, 863191679, 817608931, 841528657, 395233466, 157437476, 132945006, 399927719, 654966331, 344893043, 875455676, 647293190, 76325574, 25411520, 186928820, 972607494, 385236299, 542052728, 793891288, 731067874, 808320406, 407087831, 19105987, 15495524, 595083548, 744036445, 246674508, 924340504, 534757679, 576097441, 525974073, 548817096, 708350740, 553508699, 87044237, 279100717, 906030297, 350063466, 614204558, 19246739, 11831662, 154849782, 187043054, 495334305, 95048459, 793512123, 510578650, 350798022, 856099026, 798468381, 455649803, 602533760, 610936216, 303585791, 589834693, 761905071, 903904692, 742279999, 170696339, 279424629, 476060064, 888095491, 192050070, 84142635, 626464706, 279077548, 58065529, 113702357, 656242511, 171440259, 668939809, 899947794, 804575974, 531464659, 866396337, 647867480, 922614254, 193061292, 647090655, 442994985, 812864332, 380915517, 733016226, 683244276, 699047713, 198840581, 725077937, 366031371, 639053940, 817938660, 378455836, 852902849, 60225041, 703806579, 170749223, 696647746, 875129828, 885222977, 683439174, 291447198, 287525287, 959434763, 996872855, 169441342, 614467745, 356962909, 244063030, 557343149, 355857953, 150661551, 948851345, 29698306, 326028964, 708336687, 107652271, 177546313, 684799865, 638406306, 196419888, 911746604, 340874785, 612900208, 855609897, 451903372, 881462907, 206127427, 229998355, 346917126, 694068970, 121633114, 741354165, 152935159, 484166457, 196531653, 619894567, 390712194, 344821207, 772250157, 263491712, 146287106, 865193633, 47371164, 556335327, 605213454, 168079108, 23060429, 704603889, 85177015, 366719725, 818907135, 122378211, 703798682, 328411040, 683158068, 489665260, 172915715, 71684679, 945383699, 920030102, 279977272, 54163555, 457756518, 118075789, 348803324, 601528285, 711650619, 119420506, 191899130, 438716898, 639527244, 645136884, 265075376, 922176578, 891006050, 567473580, 102061155, 840235902, 811145259, 636089505, 386029975, 998869729, 162873773, 348991673, 49637179, 225570860, 890937767, 88084600, 542833900, 458339028, 162587544, 773809302, 899579923, 332929066, 770136031, 418730503, 952830489, 221680398, 653805852, 697760781, 998075532, 571869827, 299590545, 501941095, 230437750, 515858494, 436251217, 431323955, 354149405, 480160156, 341410161, 249105471, 304620439, 147698371, 719292790, 477126636, 422108517, 330676475, 887316971, 490033984, 606919780, 373801273, 345174033, 784228086, 152396876, 648223286, 928411220, 261481730, 996228585, 553865360, 983667404, 943354259, 766121054, 60920616, 570291250, 562832031, 711643057, 646741085, 429179648, 845405466, 868932865, 213685978, 618782673, 46147872, 680347298, 768671587, 474118820, 871570096, 850207349, 890225268, 21975411, 468205185, 532370177, 322398059, 979427189, 368408284, 897357146, 712619859, 264062891, 513628272, 244637469, 338908968, 384576389, 958562677, 707789508, 253830005, 119623732, 580636375, 450138362, 951049246, 864552823, 526905486, 346056815, 227505520, 739579256, 328655604, 694647750, 93035742, 970956280, 599110152, 489614687, 253220215, 483834753, 853541464, 64819895, 491025962, 375846015, 608810189, 541845267, 574836617, 840495010, 57416689, 775700255, 213932135, 495092677, 572863042, 365019412, 887230762, 803744113, 363346409, 338361299, 624100128, 105844903, 140346667, 442584969, 242989970, 888763991, 282869829, 545002258, 625728729, 640623548, 368207580, 384401734, 456201992, 79964077, 178673941, 967345882, 714112795, 368958080, 872096350, 584264646, 233800405, 359281307, 405256054, 803315590, 929565069, 263415255, 947985265, 753204637, 575904934, 270590247, 293818423, 460675624, 153083546, 706102978, 536810763, 921519181, 115542993, 117972319, 430165879, 905026567, 889033577, 627894745, 999162063, 289151607, 575993992, 602044487, 575739554, 374800074, 853742089, 17696438, 856456879, 923021309, 944446022, 915564768, 414802849, 691675604, 283675551, 727557613, 548790640, 648014782, 483713699, 563747119, 73642924, 935760491, 16529363, 925453877, 238426343, 447760382, 613530313, 311695550, 959379696, 530605434, 934929149, 253603769, 427331977, 143714389, 620506994, 122306381, 855613096, 237628629, 893428467, 733217943, 687111275, 475490308, 786949123, 292310842, 470784713, 970667122, 613657461, 550068946, 329927758, 621581424, 964197548, 961755402, 138518147, 720468683, 364322468, 513699901, 953053497, 483097399, 252575178, 715262115, 924198454, 14202756, 323151032, 307740192, 679128964, 417424863, 418254686, 150089771, 731232550, 57915470, 289389066, 849051578, 288758271, 750622140, 906262607, 598845872, 419157074, 910958545, 437307376, 796859359, 910689645, 124121895, 977625773, 161859296, 868931214, 524749267, 191495816, 22828034, 693241399, 846412502, 720800051, 38345478, 22239635, 596445876, 993233257, 575146571, 292935050, 951756400, 207342876, 756816907, 890147733, 962438281, 88635936, 461112149, 288541210, 356713615, 18030775, 300585354, 404921150, 298756368, 643454680, 604509324, 280353550, 343382812, 644824944, 628528571, 796898361, 705625502, 348241584, 522971638, 940272105, 670030665, 622504408, 209633423, 829446576, 733724305, 14894230, 332404192, 764183346, 697936798, 836996598, 193429817, 805321524, 129774688, 152867419, 117270009, 116270730, 117139643, 515643885, 134167237, 899429301, 743846486, 744600807, 347219890, 307537067, 917631171, 85981471, 618737441, 202423707, 710405065, 827939943, 432067578, 539495006, 262131951, 252496944, 345784693, 236447727, 262682314, 353176975, 295532328, 592943438, 840152109, 844629580, 787669253, 760329907, 875736812, 30610988, 715521017, 890962779, 502154232, 651168504, 101205061, 500047281, 462411760, 847338160, 850378956, 552866732, 628781920, 591983596, 61596028, 75629339, 291843338, 899688657, 563158737, 368618987, 465314095, 211096072, 999967088, 957607158, 624558566, 393099126, 923712184, 538722309, 209291051, 833820368, 187648852, 588007414, 93789131, 134491654, 896624597, 278302996, 352212860, 222887368, 407041294, 395364959, 473592941, 919154164, 766873386, 887733147, 891045623, 466627342, 476636199, 555705674, 221525483, 167430190, 205397526, 338453757, 457177682, 984120762, 507269785, 714309866, 826892208, 955298543, 609340947, 208419625, 357825463, 153123096, 24550810, 237104917, 298945784, 300065436, 134875197, 206048146, 977579488, 248048864, 178230290, 325419049, 636194574, 200233705, 884312428, 469853719, 521244654, 43757586, 477800356, 131815190, 9614230, 125623341, 160204613, 723487045, 393429860, 506138861, 748050087, 216505622, 428745880, 439246633, 105122793, 360152691, 739398116, 703421232, 762710670, 4417631, 875725545, 671919113, 646075898, 417051068, 152729620, 827152007, 419992279, 274906062, 368805966, 578243597, 431701844, 540996826, 368503054, 100223834, 6925639, 743141532, 996743454, 695902999, 799972435, 646077527, 367027618, 684275681, 28111611, 707790299, 685875956, 188913153, 549609958, 490388077, 945957236, 447950510, 291655772, 198834480, 240207540, 56375478, 135863869, 943149081, 539646972, 686309760, 836040569, 355733037, 399272693, 665414869, 274836968, 430053169, 153002161, 310363854, 300394656, 316177227, 959585470, 329656715, 937787755, 501519571, 69604089, 770752234, 604575731, 203220648, 605030278, 17100666, 103316888, 116278407, 848868553, 466895933, 452479604, 658014087, 518548113, 785697004, 623718719, 911844408, 119916554, 289109913, 387393605, 366826161, 612856139, 387454134, 824823204, 148377151, 24454695, 796794540, 406969543, 478181644, 877997627, 537965862, 450502005, 530769405, 680094712, 626391642, 190621038, 572693169, 550322291, 752392934, 115769903, 474236550, 604659760, 596891387, 915964502, 168088390, 896487687, 345711288, 400778763, 201531907, 416556819, 704691152, 715057004, 350379569, 70462847, 360366358, 187692237, 236998184, 224780120, 515382569, 82313641, 100610642, 396804862, 687587314, 674809803, 240515064, 74628245, 88090338, 505331229, 772477834, 834663801, 612434551, 451217973, 288657377, 218544844, 338188426, 304417961, 14231615, 712809294, 116516621, 285351867, 403395180, 944326705, 480253888, 886586784, 982679369, 535862762, 40617365, 104969351, 659375448, 278843628, 412242163, 974950668, 980115132, 292049327, 713052852, 598654269, 37795526, 243754245, 454807965, 865082013, 53568663, 69480470, 776517001, 484528574, 760849623, 709451648, 720441103, 645073903, 998112091, 283866198, 276871890, 30472217, 177787664, 470895394, 273713889, 274537717, 822413671, 595361545, 875765540, 273220472, 302089729, 719203317, 882176885, 896698022, 389471897, 879478738, 454212763, 498852814, 512452185, 975874049, 605125368, 613225374, 88811777, 682164229, 830174441, 95002362, 172035520, 315347889, 742060259, 901871503, 756086464, 706816978, 470646800, 681319058, 771198083, 707991185, 411575008, 522778711, 327198309, 364574818, 191718788, 314794667, 199694872, 523278837, 546412798, 395561336, 709139341, 452919949, 658822136, 437771336, 531041388, 42059354, 8966291, 395966803, 479978634, 833893460, 686105890, 224391836, 245260614, 707588954, 835406969, 471787119, 882050607, 417622769, 676472317, 115764444, 836397728, 53542297, 209530097, 717525985, 431066043, 178074630, 232456629, 386025608, 504415119, 141338774, 11308283, 466394067, 476076898, 268996803, 675230337, 528518865, 882346773, 347150411, 620038422, 615700966, 723825835, 457876233, 240737583, 132520789, 758848344, 77480890, 730223721, 818431876, 934199694, 568462489, 383630762, 267382721, 440104400, 509058973, 213298495, 830591832, 8673465, 888904400, 443925390, 870436582, 257096409, 253168124, 766300920, 423864735, 504415878, 800982396, 812945447, 742935086, 45178428, 77734096, 97738023, 364205718, 407314964, 847551504, 8980554, 628278645, 330588329, 986449728, 801358523, 624719726, 411037102, 140038296, 895068811, 804559670, 146313160, 303095213, 460826122, 576921814, 311197466, 207374544, 248569001, 52157434, 927953772, 550175162, 675567409, 37348313, 731537513, 979344443, 960294174, 663062959, 233653184, 693110223, 786970374, 532676734, 432022803, 641741557, 78151892, 564600076, 55153456, 257591747, 551371472, 120313963, 293354834, 920725037, 150941070, 864036605, 573980884, 619103892, 856749562, 85259387, 530877923, 241261792, 785121900, 898138969, 322424163, 759848624, 593778985, 618276939, 798935905, 520431106, 531081413, 559271011, 860646386, 165011865, 18040411, 527898715, 401028363, 705033639, 14357341, 99621530, 314388062, 81154556, 14199232, 563950509, 915675389, 173279429, 164393154, 571044218, 190204400, 425623852, 39549865, 732465608, 947073689, 893338641, 730553450, 596832284, 445017087, 992392956, 231226530, 442944278, 91993129, 352906011, 326648056, 544059966, 80275355, 796725303, 642459031, 922661968, 687487945, 548496859, 414286702, 120422141, 907592129, 151890326, 527715000, 485023908, 312782587, 121882739, 48259811, 142917657, 125258417, 387547439, 830654674, 7906821, 68129701, 653786243, 920396749, 992131615, 504293479, 533122480, 414552247, 852183165, 597882506, 19017762, 869644325, 914867533, 895179236, 819862134, 759918382, 915056947, 764824188, 939575621, 9021934, 486261658, 34127357, 158351237, 692256744, 681337104, 315574000, 78430500, 649459949, 541498056, 444345595, 850318596, 512078329, 392579089, 782868596, 865985679, 775931581, 626825322, 827585091, 412854542, 568566405, 3760406, 978977859, 762282953, 964455121, 396621288, 801266022, 944712296, 357705644, 551074925, 588911935, 926663973, 933895611, 829075990, 673324443, 170930382, 866778608, 977554413, 979923613, 166023299, 221516978, 49053165, 82877238, 225548548, 33666987, 987429038, 740265531, 458903688, 675422526, 425067214, 727816943, 648307173, 148258107, 48400, 95223184, 105871026, 870775999, 478699666, 803407822, 26022537, 443670024, 127275273, 531827413, 169704872, 749400111, 110199891, 266498310, 445269394, 163316132, 590995942, 976168330, 665783772, 611597545, 808822897, 317716251, 469318947, 835554344, 513012861, 540231700, 18317706, 102724476, 764592422, 407910930, 757683153, 146452200, 333801784, 835565509, 660435288, 921298627, 455512014, 212870121, 632144396, 366796654, 678109705, 169496727, 947561338, 366176995, 562441215, 327949150, 326507344, 327955717, 389079708, 495530490, 698082131, 994671478, 580633221, 486066916, 650254138, 895903517, 763998096, 919122789, 427240691, 356559227, 432804726, 908458900, 313584380, 534315348, 319059156, 559202609, 390533968, 634070809, 308586957, 656609052, 551997733, 991473410, 440786043, 598987432, 262856529, 504159824, 817726381, 277132136, 166587124, 397475745, 437477406, 739469250, 406689907, 442635406, 757542888, 939534755, 450973882, 894137527, 278747042, 621515163, 683958993, 820913491, 244282983, 756765444, 850854402, 10152935, 674217446, 498047606, 473920692, 473419681, 922730254, 527029587, 639807468, 644993823, 609811911, 566064561, 57047204, 201838967, 20146402, 910299168, 290537006, 467908135, 988162920, 343247051, 864198045, 532086584, 959250751, 953248675, 461774256, 804313758, 611213934, 814460400, 481252712, 837786346, 729785151, 43962093, 807677606, 430946372, 251009254, 790632542, 951838745, 292877528, 422631983, 807595668, 700997182, 127479338, 533590459, 24922288, 527041774, 10611498, 838448041, 72090628, 332663451, 661253717, 547709072, 777824794, 308068607, 417540022, 955802071, 585092165, 507286437, 895235525, 225856351, 330403750, 629901368, 647371895, 671931348, 740872536, 777212935, 968691031, 814013576, 992264008, 737775010, 846882027, 614915285, 270035675, 878447019, 6143829, 123506274, 389857252, 537839807, 691191997, 155045607, 598508067, 587847661, 147517094, 414495345, 220569067, 806820188, 835278251, 762571284, 545958867, 895070529, 942357838, 735640985, 481480980, 816070281, 13119778, 817160526, 92320522, 804124111, 455020820, 224306786, 859276749, 259623313, 446685209, 891733262, 411791924, 999165936, 335930808, 425484389, 206406021, 294046158, 49798698, 550877047, 237161166, 941009332, 458676934, 786951242, 639240677, 629364901, 414565089, 486539256, 364632231, 668062795, 722730455, 391373243, 352881751, 121798368, 995061107, 591032185, 150615892, 442584044, 745641376, 662987025, 227016895, 359839681, 697830852, 620886765, 766129041, 736726878, 284996443, 890025582, 177695790, 745023471, 251472510, 182922970, 508974360, 279141860, 923709787, 456277138, 638049116, 116521120, 382262159, 669255320, 830796365, 824479453, 794693634, 681948553, 894373502, 328747678, 864485513, 838625639, 98959710, 698385626, 719121740, 563268221, 126075350, 256878478, 267930928, 643837003, 396531760, 288420261, 575623270, 954867513, 76288095, 300820423, 137293858, 504123554, 225955642, 687427144, 833368834, 347759034, 41113314, 640143859, 81854420, 610780925, 478379480, 129367061, 360294445, 571359139, 427089785, 587252686, 637044626, 744555971, 724875231, 861307602, 936703235, 567941550, 705457068, 301139008, 846545798, 218353739, 806631147, 90042853, 965649597, 762712263, 488958661, 889905523, 622154837, 13170042, 923906316, 440139429, 334704619, 94565509, 503337427, 940514073, 74647368, 565769922, 348625004, 797237524, 202871051, 10687597, 680781042, 367319681, 649045910, 757948988, 388824208, 515936490, 442408645, 298597613, 911540058, 199910139, 5970166, 973675571, 733591705, 154666287, 536389760, 455738994, 934454788, 714077695, 650008814, 114989652, 542402951, 812961660, 443572409, 297485486, 692134086, 282277901, 643831506, 684280302, 910718671, 6046757, 911202254, 999958596, 599351672, 16895306, 695246968, 335467544, 312861148, 914152376, 740602364, 418903541, 783782627, 263968089, 861673978, 87536547, 908828136, 627635372, 938905415, 353971814, 128659112, 533074038, 684485059, 950684951, 246840247, 889537067, 116399463, 104663759, 592237175, 144550341, 502678268, 128968695, 999236791, 548150972, 267088905, 505882298, 543917403, 640665773, 714468921, 924116603, 454716059, 890843806, 45994820, 316981011, 635481476, 775362750, 930803004, 150552571, 846304960, 153611133, 326999337, 296852548, 37237401, 732931956, 480244143, 566518230, 859380869, 816985397, 47042691, 983932457, 212844320, 806847046, 975408547, 636672977, 924373197, 935508099, 79806626, 760988245, 423696738, 149942084, 791787743, 209963025, 552633484, 292901172, 821758315, 224076172, 535221954, 223853398, 999582611, 945129968, 49812709, 177590203, 758987378, 960848979, 833116934, 51027106, 424579263, 699734263, 102644325, 962878294, 453243740, 606885333, 754856338, 866934442, 404667100, 489763824, 547323945, 162982510, 152931732, 276574423, 182050969, 374287071, 262628343, 979523447, 589354171, 123294786, 414697229, 592712394, 478226358, 146943273, 704291884, 981139613, 596805868, 685777285, 174235915, 744126673, 382667107, 412392724, 249716142, 650814920, 212669066, 878650706, 320983569, 345098538, 812796189, 425592653, 570747770, 155074130, 379089732, 354442062, 626909837, 16901904, 253294429, 542515372, 414194026, 693046379, 264754498, 273001819, 383541456, 648370199, 207662666, 364995095, 656572820, 484008022, 631128552, 941464516, 377767295, 927844834, 395125563, 622926796, 180442649, 325800157, 708731403, 412764162, 996964429, 784760998, 608087087, 87808976, 878283239, 178419143, 704813323, 148297349, 621229496, 779090208, 827050870, 404238830, 183015273, 138453150, 834588759, 557135585, 585089811, 644437177, 993243931, 449611380, 384192443, 683602224, 452042881, 156675609, 427401731, 6380658, 916341775, 410312734, 187457312, 532844424, 242971034, 780598650, 573209722, 648251402, 133918559, 206798296, 263308005, 763114301, 52584, 600252984, 850995828, 374245446, 814423717, 412821632, 129275757, 558065168, 679041488, 985564503, 675565808, 188992036, 683949114, 184580956, 683010189, 711885849, 593297161, 24127831, 279947354, 811963258, 663041177, 631985183, 464578151, 118280454, 148809173, 234803329, 921105604, 552622660, 237321859, 264673620, 568813722, 552564886, 939780465, 849121531, 449834980, 456548297, 409219868, 263603677, 102620956, 231263633, 384729003, 222614374, 68469514, 598864564, 988996689, 13946001, 337731884, 535888197, 501071619, 996626537, 922211125, 217100405, 660828775, 70235628, 826954083, 709453408, 212490331, 533692059, 97407291, 702626770, 351010468, 858840274, 875061410, 788058667, 407703510, 652351048, 211344532, 500786749, 159317529, 583119935, 391936626, 680468775, 553713350, 429802987, 564423502, 933088134, 336646493, 938636606, 217829921, 900406752, 593831058, 767391294, 271748548, 822950156, 227219979, 64605813, 947573570, 183296840, 940509960, 948107718, 768271879, 250146981, 129716266, 904412852, 588395391, 815149788, 528099452, 150016703, 813220612, 914577629, 290976184, 753181743, 21281645, 674174799, 503403287, 780695392, 718582122, 264188816, 716167129, 30517959, 73982598, 826335924, 357765273, 963867596, 649803322, 462992156, 582745762, 455351967, 689342044, 370709269, 816593034, 640429942, 668771264, 778997875, 333393671, 411482311, 608579424, 446681207, 410371876, 768093514, 330294780, 495084100, 910279208, 997137327, 238906383, 578555612, 1029079, 538152030, 750437212, 913195992, 657978350, 412211985, 677632167, 345362827, 756289171, 488583858, 177004470, 348821051, 454241609, 791951005, 348887259, 543130138, 664574726, 135383846, 5584222, 194432454, 601083661, 756182290, 897314650, 360886136, 815749240, 81709728, 603740120, 340579047, 885781871, 873799520, 578298498, 729096664, 765460390, 967671850, 898604103, 939878592, 861921995, 73786669, 962592447, 706753593, 220393321, 710539908, 454445001, 622348557, 84237956, 434991323, 491554004, 717626383, 782342803, 14719726, 689183368, 233372998, 323913118, 582498076, 179009198, 263297456, 657722521, 260440516, 72244391, 183737589, 441287707, 101258909, 495706214, 900115512, 477765295, 688619540, 602259372, 700836527, 147971017, 437744088, 961399039, 298626588, 386716142, 352064192, 971860471, 430097276, 159314583, 413364675, 615227276, 589224107, 611514724, 1749386, 864251574, 2622094, 792715873, 992555172, 276562566, 562349686, 835424155, 117069395, 427040066, 417183303, 81231531, 773745198, 894680142, 99980293, 108622086, 789780093, 575881254, 476559007, 521012790, 187597816, 75576626, 937188733, 3263277, 677100482, 617387746, 565779997, 992741604, 34580155, 272962036, 737444924, 286654409, 292251364, 164487979, 178868613, 839174363, 250469679, 963790825, 122470609, 443480610, 247798534, 621797607, 238590922, 330662362, 614736096, 621029827, 16597716, 148397080, 222638023, 489994244, 245587915, 360145784, 230520939, 947464863, 920922846, 191227198, 818313940, 783395239, 657676398, 409494398, 903216709, 12431143, 334123739, 141556947, 428631934, 657629690, 409104360, 789077997, 984825556, 657492905, 972487456, 957655175, 995187421, 626869515, 21651676, 333341035, 775273287, 243967810, 688040499, 51897725, 130064304, 510081095, 492695411, 375239975, 890146884, 542568786, 163479187, 770113442, 920708329, 497159816, 490019422, 295222630, 850070042, 537599594, 626973130, 210422729, 651999357, 608546472, 380378171, 386778681, 975481131, 799353288, 109069647, 242370997, 50802631, 149462687, 526685557, 567106193, 19126507, 186975213, 210294469, 312520538, 423548066, 400598869, 738834499, 836256750, 950713632, 453939156, 748152535, 416868278, 210376251, 870178445, 539751958, 666238609, 452324448, 167891190, 421320542, 139172522, 838600774, 971494377, 237626210, 529866300, 867461824, 538970439, 690276716, 91202303, 863134329, 420572234, 565585163, 520494980, 15552642, 349663655, 66779176, 814713617, 593286239, 61908672, 757838985, 476496362, 253703257, 851797305, 360471958, 177494138, 162474121, 816525649, 681443077, 838702697, 547058950, 449890373, 684005683, 128563422, 40669734, 560570704, 498292407, 212399549, 906021364, 884940784, 492443529, 964991069, 91738021, 420237397, 330690904, 548180932, 507152081, 161143526, 874984092, 425563178, 438659084, 917142825, 630820212, 347875881, 888530107, 27302338, 653427566, 17010420, 103206963, 923673915, 806873087, 472492983, 936278116, 175989199, 612770188, 305013586, 764165513, 579323647, 597188681, 421196188, 10351270, 174811512, 661410711, 444223204, 892308936, 714638616, 214045485, 244803794, 63347878, 232484557, 625625351, 516074314, 161495284, 284403797, 721862710, 236070795, 45045473, 819762680, 933263924, 467149005, 521232829, 235860463, 302266719, 890156281, 977064322, 785565922, 2699785, 854444781, 154559333, 619567108, 509171112, 479428286, 82511479, 547067716, 850018361, 885272771, 610574071, 394571382, 54774362, 758523993, 9685369, 236288847, 676011886, 442796185, 763584235, 860378606, 730483800, 77810020, 648680343, 262213181, 184233203, 818188209, 580853128, 249401709, 573749398, 203529869, 95703428, 412437341, 830475419, 861733328, 324544574, 713705898, 895200743, 815971892, 304170217, 925518890, 999432485, 430773541, 912087903, 899178438, 701133194, 656559694, 764502132, 777104687, 449749601, 938139078, 52704369, 168631253, 546957116, 676778833, 425047115, 231118081, 299668358, 531622240, 800569465, 543138473, 351093289, 318092949, 85633899, 48927015, 9386, 808345347, 6506291, 275644013, 72595825, 856459083, 347368048, 72601957, 521324052, 804555550, 783601344, 351304823, 843621859, 439528836, 923776967, 672533642, 409345738, 188675582, 66626254, 233776742, 60426751, 83845930, 184759396, 87353864, 710282049, 795657628, 170310358, 995919337, 535480956, 380223183, 966464940, 975350672, 436909863, 318785911, 185287582, 567160256, 311347019, 877575241, 727359010, 154008765, 716017157, 619763331, 225356571, 955671123, 964523037, 892361196, 630607928, 205992123, 975942397, 587866958, 295628805, 993885084, 705196272, 151797521, 293762346, 546538681, 854768371, 177162023, 400776645, 67110226, 74162669, 792575153, 422010531, 180858590, 527488238, 478127225, 319341355, 741773621, 278361549, 759553550, 981574239, 93059066, 665667665, 29674932, 617666309, 456368401, 412505023, 146191635, 37248584, 129551176, 119098605, 116537905, 423985019, 960967156, 173118705, 166708789, 152346463, 366155269, 954010383, 250865473, 159761164, 641634808, 345542217, 750168517, 762481303, 393810957, 514589969, 236837506, 950294301, 113804528, 905884523, 614693722, 702750785, 159214789, 4183336, 271446975, 184221641, 220521111, 699949129, 434119007, 98951430, 511080258, 949616155, 501618580, 454205, 818212007, 200136492, 262067591, 654047254, 735759937, 933481115, 481798487, 192665089, 655984129, 716281152, 912588041, 348430245, 644574839, 17152011, 583887522, 486972618, 929845275, 485562404, 500601904, 550049053, 220027565, 928175067, 146570897, 641005747, 111351196, 427097719, 465573341, 990278147, 562203109, 960481325, 284301345, 92919018, 870907868, 417026272, 404726953, 138369165, 412553422, 615792589, 6590279, 597298465, 514553976, 442278474, 943765408, 399623748, 659683189, 577448622, 560015110, 974203732, 594130544, 626993077, 378384483, 202403614, 999415583, 191842503, 110284832, 924046838, 740088176, 317075291, 458592686, 413030060, 197516929, 912950899, 3381547, 911192444, 974082196, 556516170, 656207756, 726166636, 82477490, 808541369, 307664337, 27286737, 212321281, 802215508, 911372117, 294524810, 625037215, 169420358, 490918314, 391123197, 401855021, 570192539, 540467354, 241826140, 215001976, 384632450, 629660897, 497546998, 367769637, 226945926, 915460275, 12895030, 711444924, 12603750, 304150925, 784508077, 598105361, 689888138, 781782316, 645582531, 231762739, 485456153, 301006249, 631395212, 88328698, 626855473, 78474935, 953038004, 220791330, 147455827, 729800214, 608048181, 264439328, 19382750, 193575665, 879133499, 588840388, 334491760, 950062741, 931437957, 929289885, 540994044, 576394560, 762770056, 200781985, 453885333, 761631019, 66557506, 216393037, 338673320, 725062223, 81955080, 771059941, 403548130, 775536104, 634185613, 589541121, 746431719, 10317430, 314324711, 869847053, 847176438, 551687470, 640269676, 565272761, 587268088, 42271445, 913308827, 475405227, 322685705, 319753566, 320150279, 769575142, 581704457, 164623981, 114095409, 962283107, 509682157, 971286224, 547676267, 71718632, 532906223, 803686342, 188267015, 955842795, 249023321, 499621278, 547658021, 877820003, 846193429, 890772310, 389226292, 146468334, 414646320, 789405999, 577951761, 761692941, 791579429, 805800297, 132303701, 849588356, 997210945, 138616662, 141764092, 192012809, 247641122, 337854262, 544020860, 417801760, 605498212, 172601219, 856352900, 320086795, 482161752, 473554377, 471052385, 870342513, 890973546, 458163780, 476111798, 217658584, 937700543, 724493485, 259769261, 345019985, 707191349, 521839000, 332284353, 113607790, 248581010, 956223673, 853803867, 661492625, 415499961, 351450992, 72810808, 492750971, 343654037, 386701600, 163090083, 933892156, 358525100, 117815177, 973284243, 397679224, 188936796, 26315336, 134392689, 686773810, 10007163, 184573631, 577501941, 577182257, 635685863, 743295786, 223581928, 387280373, 474422497, 134673494, 548971680, 816552680, 770947336, 762954504, 489581292, 846966708, 822915629, 504626010, 313555772, 386409606, 924459614, 8711410, 903029174, 593514513, 159801793, 568214572, 302246488, 399153636, 576301473, 342546836, 762657423, 738043402, 146986851, 167669530, 607048554, 727410353, 978873334, 518241451, 500690524, 960965324, 749357832, 8657608, 500827035, 686038037, 340253114, 730715442, 688366357, 514173576, 311830586, 460972543, 612870767, 641953057, 8426768, 36199896, 943228534, 113532233, 629284069, 61482207, 305247873, 705461987, 933705807, 5150676, 398822914, 290372884, 129418006, 197045422, 143751681, 885606956, 748864761, 766416878, 637763950, 127476586, 519356979, 253083242, 521076517, 732325762, 969790226, 429473671, 571932583, 772715114, 199694748, 366911495, 705389596, 188722396, 535263218, 280926958, 535456401, 395159182, 252865916, 849248807, 208473480, 259911586, 918017196, 284363373, 106097923, 566965441, 576577972, 555176605, 835795698, 239186410, 692641488, 597740841, 848980741, 613136138, 716851116, 545133222, 382691653, 42705004, 508274380, 563020701, 340256894, 985647396, 386458544, 448302055, 590128900, 252310619, 935164636, 488651132, 357883355, 142808530, 280359688, 630063882, 325238637, 312048682, 897941133, 592049755, 959044588, 422991282, 80397567, 418221439, 864178651, 862507275, 324402983, 370514269, 171695377, 883603801, 993478750, 892329317, 658010808, 948066574, 624917813, 623271738, 839679608, 218001687, 870279148, 137121359, 761155176, 33643354, 908286393, 947566974, 725398669, 607675997, 478376810, 931109087, 893451557, 621602227, 649455366, 969016750, 813268638, 15620283, 463771504, 460062575, 868486248, 69460260, 915932223, 150875904, 926827013, 700896282, 84576471, 283100109, 793285847, 248613801, 964337021, 149804717, 174858436, 922506921, 866093282, 929899688, 993017102, 594371844, 355188813, 499182596, 394865342, 381142891, 37342369, 57440099, 27852524, 800638700, 859732169, 323328312, 297879488, 83271607, 300536209, 657086494, 832678735, 781515266, 197979233, 839955921, 668699627, 297551522, 252319375, 589233114, 897839839, 377339424, 701599422, 975302032, 359662343, 885136235, 334176095, 316209996, 340466966, 213824721, 107123455, 449458420, 411220237, 507867035, 986145723, 242727588, 339833855, 251916932, 991398011, 367197349, 397710634, 350853135, 558653765, 706495407, 905544704, 554287438, 225927814, 337792630, 21557249, 876963578, 557266983, 598622765, 513144480, 582066903, 595406895, 555408282, 704251407, 551445675, 815135034, 804254835, 475054968, 947505929, 581011258, 446587580, 888424093, 622241243, 170902235, 776986169, 583416425, 290628978, 394817621, 682303907, 204082623, 226658283, 400619232, 133964511, 155404524, 885872580, 649072924, 438148928, 106496308, 800716092, 615673839, 247799052, 87419517, 96406492, 632327768, 735356546, 888174479, 801745470, 908992553, 902686302, 569087256, 523865593, 734459208, 586007695, 986163693, 730280350, 444014979, 833852555, 530325312, 249082171, 529816604, 354191443, 426749226, 548885293, 987041121, 42460755, 997368616, 787130725, 739157963, 246428028, 294018789, 460021994, 979475731, 999439113, 912799385, 731475172, 148413701, 716343147, 393203298, 918113337, 300670368, 337375907, 355951288, 80797459, 364506279, 524771590, 322896716, 81623858, 582469632, 429962570, 465401608, 429523426, 338898069, 228816992, 764910263, 470744493, 275444885, 808163604, 175182102, 280904963, 417318779, 962944015, 903813670, 925780802, 848395568, 469448459, 927941783, 391592418, 288197896, 777214732, 225431925, 636633997, 529099999, 557277774, 509426363, 572834112, 581457277, 956997180, 41299115, 647967972, 695387926, 288884303, 426967824, 851497140, 912734607, 831388435, 329545197, 239029960, 827965556, 247423221, 918519026, 166606417, 187770408, 563074624, 928172608, 883578815, 924733899, 881323138, 3229861, 958815508, 840104184, 156221349, 97354273, 388289570, 306285712, 247740926, 622956133, 671017117, 58527743, 636033194, 722298518, 334576284, 145875078, 466397008, 563411732, 620282185, 356184565, 482700155, 933987561, 991879254, 509466632, 121321018, 768784756, 958514006, 271921724, 703850529, 13011801, 644328450, 279076711, 325568836, 538383116, 656915080, 196990032, 657867505, 51183392, 581529272, 668468129, 959187622, 39720125, 207377348, 357212793, 75746425, 732421617, 722385227, 148914281, 797948173, 289998138, 331585547, 230117676, 417650578, 219333676, 404720802, 258300267, 937639501, 705031390, 372436715, 509469557, 219896258, 625016998, 332621350, 346013590, 441128769, 818081599, 731097083, 754340198, 439093930, 58753445, 187692720, 493805860, 362049599, 589015914, 769982165, 185507227, 771735978, 140678370, 593851678, 449693266, 516090507, 27140571, 839645578, 342150861, 259361806, 323598245, 175787642, 24232975, 491435599, 274638754, 620487103, 59529520, 146501509, 119825704, 608983596, 658983579, 203850815, 425503271, 483716517, 204694046, 915511790, 572720117, 250379940, 148711341, 1372358, 889874164, 587127722, 428653894, 934402351, 686988933, 274621598, 325092206, 577223425, 805666669, 573200046, 893035667, 382672352, 349539797, 27085997, 117231921, 755383126, 166500593, 471601692, 675315352, 46464007, 89231492, 11573562, 896539293, 226475324, 263930525, 283211442, 465373503, 262185281, 248795052, 416511284, 748804216, 290537719, 554893865, 619975645, 309526347, 560668904, 58323349, 681268819, 209452359, 898473036, 865332760, 623338180, 21616943, 457993979, 594725406, 27922920, 264277514, 370093882, 79938127, 361156308, 906155121, 333225799, 4221997, 539554232, 150886081, 180920924, 554379432, 179097337, 556914044, 707205176, 101193584, 509426953, 384504620, 680228264, 938175281, 300555337, 735002633, 942318179, 773404290, 772153431, 233729323, 903893, 481263995, 314949467, 300438565, 506848498, 653419194, 955734197, 690799762, 617937947, 758477355, 248617754, 767305073, 756694765, 170898429, 289062188, 549584902, 691627679, 996054102, 171037463, 937784064, 624768337, 500635287, 775538659, 908423889, 507493292, 870075232, 249881153, 623391594, 762107006, 700684426, 44836538, 969608968, 620251239, 670534097, 701402059, 7446170, 6355609, 299827955, 414077752, 529092127, 715011607, 685668266, 30691379, 84981811, 456470279, 938959914, 832579667, 710149014, 695120985, 237535455, 97243940, 728868186, 990579948, 214705724, 674262589, 111706221, 566479310, 143416720, 815914759, 902882295, 100696224, 506888675, 559307932, 936043683, 269933655, 804601230, 31494426, 398537744, 286644421, 937704969, 173919202, 717402796, 133195587, 565684884, 553335052, 911690226, 405015827, 225749207, 826155734, 11034605, 397718024, 635946701, 450634783, 642328528, 442535458, 43894157, 613249290, 274014224, 595270424, 745585415, 242390683, 184719463, 835371057, 495763451, 72426064, 481709566, 666550074, 828813655, 133129806, 784545106, 571077920, 537785761, 962556963, 142436922, 284952774, 609741923, 742494673, 970358205, 552459562, 352561593, 46786297, 352723810, 648910768, 428459772, 163816700, 729157065, 988788663, 755932693, 907673682, 719923538, 883351668, 458997903, 534816162, 476492195, 882813452, 266985881, 566210348, 957902194, 271281226, 925447962, 516305502, 198371266, 696822824, 481643345, 666998721, 582817150, 74055689, 861604060, 240081894, 920287233, 81026130, 352872767, 923788265, 439613677, 239495893, 504642288, 199105662, 746579608, 52382105, 457654374, 238857314, 530986034, 578654764, 784489546, 453494681, 677038747, 742178080, 692138269, 67015647, 764583405, 386086478, 218146882, 270429837, 857575049, 895514755, 252665507, 531192778, 14154590, 853722785, 406452596, 443597350, 78026875, 18470934, 65908013, 929471774, 375551947, 75741706, 974266166, 457023717, 56079480, 530607312, 924002864, 136039180, 174381951, 53140245, 369504019, 408222308, 938051527, 872687747, 662325306, 888047338, 292865844, 60544170, 320014590, 493786046, 533109332, 369517190, 381498714, 96933710, 272441340, 644725907, 845161365, 135249944, 2191989, 257991813, 417008643, 425021177, 181706881, 85482846, 28705329, 727543086, 480196119, 413055196, 783912062, 29111850, 361260801, 75161862, 753857446, 408116675, 74986058, 95036027, 317169629, 668486442, 503955482, 5279347, 221784877, 28078184, 837063538, 191849259, 153213623, 584974029, 463178723, 527900564, 201307356, 250182478, 953423773, 89593762, 670443203, 739895968, 989290991, 141178588, 341335688, 7544513, 835779901, 229793964, 325794278, 791242519, 350275551, 817671843, 91670840, 251046176, 161768782, 695880370, 564530976, 642608495, 218312895, 719424956, 754053714, 81693232, 279710936, 431237832, 108070367, 331682049, 176569018, 828329106, 246186735, 181904931, 970499812, 268379951, 676558664, 537419713, 629208690, 131684407, 725680511, 838141865, 305643816, 88711396, 853722620, 849607654, 792845554, 92000564, 876429515, 825960780, 536444185, 255204030, 739952405, 485805306, 790926571, 400106410, 933211998, 291118999, 954763575, 472948130, 654090399, 908442145, 218624589, 869010267, 443869949, 648488543, 446553508, 519199407, 132744069, 210897795, 403627685, 556842444, 354211983, 846949772, 246453247, 995313883, 501910847, 407730086, 59876778, 153103549, 568707033, 309487491, 133692383, 68445747, 564127677, 229444851, 612939141, 105563056, 465352073, 664685516, 327016694, 535538899, 883131370, 247246387, 148825558, 766858351, 627593632, 180044227, 983741685, 538885812, 135476250, 614012399, 750199833, 972349882, 2855582, 403730735, 361454824, 580875726, 204364679, 253144924, 961094877, 603196799, 96497418, 569447050, 781182508, 200513413, 782876306, 705976479, 42861570, 797668746, 714689887, 825665712, 608506997, 733141129, 459889774, 498316981, 367562952, 758919828, 590312770, 90596658, 203869037, 703287365, 884175355, 582498741, 317268171, 111497473, 945056846, 73430444, 950358748, 612297414, 508098754, 889615770, 818469973, 22813555, 402666122, 227585890, 401847004, 556012445, 309055905, 8185055, 702769430, 240841533, 433866517, 357722566, 919833706, 566279772, 270040696, 746553767, 271471663, 510841330, 472814625, 175490060, 380555459, 61952033, 106375245, 531812494, 87785137, 195845768, 94010417, 182823711, 257823918, 150760858, 155211498, 303095827, 718846492, 671927542, 158467410, 114344208, 329149557, 384444114, 214657241, 987756410, 852852386, 523394541, 271678419, 587725996, 726185820, 832413682, 651436076, 211305157, 485974890, 362723098, 548876520, 120009679, 463804511, 129901646, 681195189, 247637320, 535564879, 237108890, 958579428, 906387096, 708397421, 88568825, 183243547, 129531850, 299699670, 104279768, 804604769, 531517535, 711288021, 527194824, 463913521, 157972838, 345950016, 758085846, 290731718, 829824514, 439277102, 665561866, 369671390, 868159376, 213414747, 208539030, 305408214, 198061691, 156104144, 784298168, 23381502, 589593334, 384437321, 687803019, 807531532, 593608385, 872356367, 75480640, 98420683, 802834282, 777799173, 824369555, 46892096, 180280853, 668459779, 712435708, 705659613, 286799034, 22445518, 877859309, 432319269, 503759211, 161251195, 718227284, 345699729, 977574586, 379105912, 304322361, 815543524, 711478035, 756959959, 268616941, 272714092, 538238242, 567876646, 673860600, 783065042, 329065250, 604936167, 322308350, 119208442, 591293564, 160698169, 229594080, 955515054, 711030305, 715575597, 658965845, 159907997, 359957510, 432611886, 696438040, 822171098, 325170550, 751882249, 314275667, 347497811, 754350820, 887827678, 572818261, 832743490, 110725246, 482118375, 33622281, 445596389, 337651337, 928797691, 91639312, 92364892, 774093082, 557542226, 845455920, 980223516, 268988407, 835026441, 65801842, 407742640, 77739318, 700830462, 81955126, 423689688, 324353048, 492752740, 97865270, 288492880, 190432270, 798144340, 213774556, 965567760, 285770192, 503333878, 597560358, 988998059, 743757431, 527463462, 347546114, 107564202, 819297178, 564142693, 887361400, 96405857, 426970599, 734468312, 288289985, 619823110, 155507484, 209692253, 390457477, 214301941, 1837416, 95205946, 429260591, 432695267, 174862726, 772303928, 481626398, 783134511, 677900711, 957065857, 37057583, 948871917, 641739934, 911511760, 352618639, 144144884, 642550638, 797834095, 463006664, 464388113, 728985125, 106574706, 844551739, 532767458, 707715667, 851689093, 110184963, 611739256, 513682935, 856429092, 326777561, 744972921, 877791939, 132978690, 135803803, 926136772, 968590174, 567882723, 694782523, 861682127, 152256335, 790725824, 596916483, 367571719, 627420629, 136173879, 198044353, 511070611, 442455017, 834116714, 701693337, 992900302, 771747360, 617784839, 522960141, 346429435, 169500046, 6071737, 316867778, 277787152, 188993407, 990685361, 312029437, 96117817, 687289715, 720968293, 900389433, 927588466, 639758844, 162513219, 710391516, 774529200, 562823075, 765712224, 266138608, 193301190, 214860502, 569621103, 488870689, 399252209, 673757438, 375409390, 445687655, 733416580, 531558204, 948227586, 946302828, 636845835, 162843359, 535088652, 704196763, 433614275, 976185238, 638199673, 18575114, 760098967, 714132944, 73926617, 969084096, 205996466, 925332702, 269773141, 662659411, 827610981, 351513379, 169478736, 340121492, 692665906, 709329717, 647919030, 490994344, 949825790, 520026019, 384548813, 696151191, 765437277, 148263379, 873730131, 940605067, 533176151, 846086907, 527762075, 715335656, 301820554, 230461124, 841050218, 630261373, 744228791, 143619525, 223674426, 240328857, 946432016, 374537753, 755909513, 472304041, 228392771, 951318893, 777143591, 597909051, 612832640, 978572924, 372443016, 712332806, 463371403, 983093144, 267849842, 530278126, 875006043, 375265125, 696106962, 338964489, 916735522, 265029251, 818473463, 448638713, 757806898, 574340535, 179918040, 431791600, 920277555, 385162752, 471660133, 87158064, 993161900, 99534653, 531834173, 937548633, 243645459, 271691341, 533753312, 443292544, 562033813, 798339860, 174427780, 691762520, 746633641, 594698411, 747607868, 289948115, 873140690, 408948715, 457545238, 790088344, 609910000, 92359424, 502459453, 993681303, 170578854, 933143308, 847159630, 902660503, 202816025, 961378094, 586870797, 6597422, 715009393, 544352161, 442388790, 442351555, 413270310, 364829953, 709908780, 948316405, 355401700, 832550571, 741420053, 415584444, 427590056, 579496827, 101833951, 649060577, 132455349, 150302460, 793979921, 268856371, 64571225, 594205180, 742588338, 613143851, 925893458, 573604747, 314432722, 784578329, 120615346, 945634791, 816299875, 720827422, 257689098, 497213787, 618589955, 830126427, 287617909, 435479642, 308682117, 393551572, 158192768, 24162952, 453280450, 798940506, 721966326, 706730633, 951474354, 94194893, 174866621, 632614063, 702367567, 761763812, 324931167, 948598417, 541163292, 384196586, 179582683, 374962133, 682696873, 277922584, 352332351, 541560896, 34363151, 225452952, 660202266, 266195117, 469381641, 124704964, 252546926, 925602092, 420243494, 3721371, 151605106, 860251977, 590861630, 468721681, 547860123, 883652779, 959746031, 823374824, 972573207, 551047867, 680876209, 308132831, 187365545, 925546248, 718306121, 308304633, 756443336, 974590100, 324709392, 269103071, 528559879, 52077121, 457190533, 605555588, 64636890, 728812749, 656837376, 303206439, 756724558, 768541929, 619719857, 140133572, 20037392, 699549844, 200105788, 725966424, 52626940, 642719923, 902223160, 607417710, 611363645, 765676583, 144467559, 272759488, 232056684, 431514201, 561775599, 762774971, 765368743, 678927833, 504996642, 589808713, 725956198, 102598644, 24343121, 168446691, 158488841, 523060401, 313024510, 663699005, 676252294, 389492895, 127110452, 467574029, 531376319, 319752410, 220004095, 181299782, 901194408, 301958470, 877086216, 419799505, 181678283, 766476610, 524326144, 120523468, 906199801, 967103129, 541178054, 667606643, 593245416, 700184361, 862588623, 7729757, 255547371, 513649039, 705794691, 893024843, 555620833, 148745345, 235838290, 571859499, 760890356, 789225584, 620181679, 189159665, 516468687, 237916185, 6004873, 695858848, 355834694, 941682223, 665572248, 640879378, 206170582, 11620037, 598830471, 718853325, 333750561, 46022443, 713162272, 76052352, 458407071, 52642838, 942629118, 875017777, 824776439, 117808409, 210172271, 953278262, 475103977, 370650413, 83556775, 490097345, 216216753, 524648284, 703888970, 594140357, 164389401, 580821229, 639006993, 825313107, 959324446, 105279256, 768637528, 887154661, 713643119, 345563531, 241851440, 468053686, 304233619, 186648232, 635051997, 586210266, 109505328, 543061133, 795294900, 304925672, 64032801, 71700010, 523834741, 372045097, 902849209, 53393516, 328998138, 505957716, 727289606, 759344172, 476853046, 206395041, 412369212, 749583277, 884036910, 298591982, 544587976, 774996158, 78912228, 653275598, 588015491, 441401240, 517533620, 554788326, 515174318, 758298812, 865157144, 566552194, 35566884, 376432292, 913158433, 231021695, 682098243, 850106823, 572657477, 225178574, 301975599, 135216956, 81019875, 893119116, 816214254, 386273176, 200711396, 274749711, 553604322, 701931559, 337684414, 416505804, 900364702, 335306857, 141138437, 875508655, 750682435, 745315101, 421238668, 290499948, 713431952, 729330812, 783533455, 214620898, 537035183, 359697066, 424848105, 592308769, 922974206, 434587250, 781063254, 677359730, 578801518, 254112420, 546264638, 564625919, 288547106, 631717369, 962440683, 871576618, 732235820, 592430330, 191097560, 422577898, 27697112, 445790749, 613609811, 990495869, 528011278, 779882921, 669181639, 556441757, 242540064, 739535102, 238134499, 691702551, 284781491, 115148353, 147823259, 996910195, 329053336, 389570946, 691655128, 934532143, 299871032, 94296310, 661577161, 540491979, 659669849, 757820564, 850815194, 950209198, 209397377, 351955066, 646454981, 556199745, 713339169, 542619132, 702196035, 873883018, 114994320, 357740473, 324418361, 360128258, 30464796, 58763251, 180065047, 671787939, 606458741, 349206976, 961121451, 90979793, 201074021, 916739971, 973003515, 287889421, 689706873, 459856621, 132147537, 544152005, 879220327, 273059892, 571553118, 447972901, 78821172, 142483696, 864224754, 443448749, 511758471, 323581968, 477472237, 698951631, 921073785, 990476246, 861510331, 220186279, 340893201, 205058867, 951293810, 417823605, 169771655, 428368501, 728476319, 580186758, 899237290, 360889787, 411219803, 212245330, 878023329, 658509296, 620441037, 60359273, 296932527, 304472254, 391439193, 281759930, 244250835, 609545569, 775036642, 729201978, 471997336, 224293731, 648455905, 50760899, 123102135, 557496190, 118739950, 530301232, 245052612, 949584331, 662163325, 986528797, 486420052, 68016361, 302564668, 996915993, 824477472, 211419341, 694961215, 577281722, 418543701, 399334933, 501687616, 148512259, 420841448, 265859905, 828017219, 485472177, 62352006, 419263994, 565988475, 213284769, 699240977, 182297367, 921150811, 444071126, 519477715, 971905873, 965035184, 795226346, 178181105, 659684665, 191147930, 374522357, 48537247, 915553762, 833959323, 118854226, 209388529, 875315216, 743121202, 969738172, 688821495, 237677656, 668608086, 353535346, 436943807, 931827111, 13503687, 722169690, 68444323, 503181611, 826818028, 995992149, 922222753, 210270003, 870576713, 514794567, 957653473, 495115268, 274657332, 922497304, 379247044, 635569057, 240726314, 673412017, 705796677, 445980716, 247373963, 94125378, 30247298, 816122174, 834461642, 567408153, 302923798, 583586149, 32447768, 658966431, 39407641, 7671863, 574471819, 86121522, 703427546, 226942506, 172649419, 57290023, 435941924, 350516776, 315117095, 286531744, 993637784, 609526200, 342846696, 906215450, 177373487, 687616539, 934662845, 629650622, 107119201, 183274200, 701577867, 415983954, 124794816, 946255079, 396414986, 34034727, 703347277, 357163123, 67486690, 718039272, 998500287, 867069353, 63893679, 963517227, 981435537, 973410024, 50754474, 267295059, 727538218, 906227859, 899621102, 508184803, 56308256, 923068016, 645073164, 310377034, 61443477, 502079563, 566378219, 193610590, 524805908, 608627088, 195375010, 368338363, 10929718, 838857713, 759101260, 572085386, 438659309, 784537779, 91058934, 793385541, 505974032, 608101361, 852173722, 646111756, 414443317, 709872298, 755996920, 830199153, 501580885, 862535224, 835854845, 330571542, 39633931, 609454405, 631021917, 387184689, 245562093, 387604622, 25168812, 556845426, 19579083, 403115686, 625651623, 755874140, 166524606, 916721667, 283048133, 755772163, 670640056, 565950606, 589677042, 324086291, 312096382, 942677747, 353799980, 743414976, 480961541, 536265664, 438796872, 697476460, 164728333, 835634807, 707669997, 378089303, 597368773, 120655130, 978502159, 492654119, 467903183, 693283459, 386157185, 356892496, 804733882, 837902475, 600352099, 128943683, 53305159, 671520581, 957197359, 931362385, 325461456, 973066711, 587377016, 855673712, 466338386, 61091770, 67884920, 898720486, 169644205, 327975638, 288115824, 9650375, 960890627, 72148407, 471320877, 65405941, 588830578, 835981486, 277507716, 49653032, 808460942, 655723378, 836923916, 539313390, 768074464, 56562190, 665069539, 60061611, 406337925, 811232481, 453739276, 336602049, 239822259, 714397807, 394172243, 896454209, 718668637, 637446587, 10157207, 116263952, 542727050, 792122066, 760726432, 539163229, 638559849, 66301722, 53964505, 210002256, 984708115, 176065099, 774969561, 542681340, 640534091, 882076218, 577385590, 551297534, 747708869, 527615229, 746958489, 554531109, 38464602, 759603821, 171537249, 984029685, 644162022, 200801530, 788810160, 325555831, 473095762, 600034027, 450997974, 929045494, 336232052, 803600611, 433462131, 822703240, 419152890, 945447715, 660516099, 494353410, 69066313, 229328465, 624611059, 621137952, 591053781, 336255491, 128599203, 509047229, 611449157, 310199588, 602030934, 633054802, 737089094, 287447701, 565479189, 906617033, 998565251, 897335508, 462393286, 752152053, 114164270, 148588125, 200661487, 553206077, 744160790, 443352794, 525120666, 750962165, 329609388, 751236684, 620422628, 401901470, 986868068, 872858194, 331530843, 251515082, 315758016, 468379702, 317849272, 985308785, 524711632, 615624295, 498613974, 372457527, 467245914, 206783621, 267031170, 350528769, 387682853, 467543613, 589260936, 593121586, 731302053, 289218299, 826793843, 61563721, 269697783, 861494287, 485860917, 19509170, 670351443, 209578257, 465554469, 173255496, 979086261, 418344147, 854735999, 849003048, 476319668, 952060848, 535566379, 839584243, 497286976, 4121450, 204739308, 62350977, 555170562, 616435200, 976875222, 245218901, 692865614, 293105488, 279433569, 48022497, 952527955, 805313788, 378969765, 690708821, 837732599, 44859351, 457696053, 246923589, 608234187, 717179588, 372382662, 981977575, 983841518, 927011095, 340018541, 560292672, 36039156, 491381937, 771438641, 784984059, 658564772, 874485223, 383442586, 22770931, 816173380, 889324366, 519927195, 101593243, 781667610, 288316929, 761922944, 43639547, 522883774, 783604736, 738904298, 339430769, 578270028, 151726500, 781920009, 389135055, 58124181, 736913445, 99196910, 544855652, 547226239, 458805062, 350190667, 404565785, 564263886, 864511847, 106791622, 363443022, 502919362, 277911572, 907489740, 889052600, 601440638, 834788068, 461972904, 695962531, 415957013, 3200457, 633707260, 428186609, 494793189, 570777221, 528595721, 950465415, 559056275, 668327127, 496098791, 28777923, 648247238, 87160076, 211540937, 274722171, 487284682, 987322090, 859845533, 668057019, 493274470, 609548008, 746515405, 645830083, 448487679, 823467490, 879524609, 687385904, 72315572, 276275689, 502916707, 883761496, 639716784, 769157644, 298078120, 818924293, 983140590, 319435898, 645646458, 812131028, 325311880, 712937634, 491417652, 333554799, 915714931, 882402681, 541204188, 40957590, 656850440, 356421761, 676317532, 5622936, 659572450, 866357556, 212850957, 212638323, 216429618, 598241205, 423964009, 660582645, 66768945, 85361888, 517089143, 357397416, 779658213, 334398169, 45344920, 101672354, 874885702, 719088961, 318005085, 834518260, 385274389, 988188052, 641549666, 327415664, 864290668, 171866290, 211578323, 356201329, 76647487, 258977595, 729684744, 484363673, 416865365, 277170750, 339625323, 277504064, 411873853, 295048653, 382248060, 605817012, 337893607, 178296901, 472917286, 137937258, 997993585, 305625211, 535857787, 357156436, 630600836, 448232069, 94269910, 648737761, 745558338, 394381066, 34134522, 86492788, 383259062, 650939869, 455961379, 201365368, 351719784, 888270213, 995063186, 554564634, 356848291, 150722161, 325551399, 679783145, 269409756, 920866741, 264348307, 466050933, 794769058, 691251159, 683764477, 483802812, 773212158, 120591452, 178153591, 961556439, 752369053, 205822320, 902705331, 352459958, 151630344, 971585578, 988614948, 372860828, 714814893, 742980320, 299996082, 716603946, 784819410, 163319723, 145556174, 402908003, 844749505, 938811841, 468061323, 514528083, 744013414, 590443249, 104254797, 275568862, 824035155, 387929096, 688830919, 719012036, 822337082, 366700867, 380252723, 721884996, 145389558, 678351481, 13524306, 219726969, 574213679, 284650660, 404750202, 987130780, 540111236, 105010989, 901486662, 405435963, 386168566, 14260086, 88240121, 426750443, 113659236, 344966040, 817143679, 666206999, 479214505, 500639280, 10072596, 668084788, 252172925, 514175439, 989751676, 843738987, 52420190, 146327201, 645114564, 566693437, 917662986, 197322948, 129956511, 102616595, 763856407, 662828821, 776754286, 19405554, 510541809, 335713783, 567517224, 261026794, 432539522, 212967252, 99166365, 446253563, 142722813, 104824695, 60595603, 244139769, 755035094, 681726466, 125173240, 9578851, 619529435, 636415912, 876202954, 78469011, 717871799, 82900499, 878527333, 820002426, 518551060, 47490290, 101806443, 389234853, 386551227, 277328592, 737604086, 132185282, 669034485, 969435585, 598100955, 715811776, 636504784, 856744429, 65590208, 898833611, 55518828, 939547371, 701227139, 99840370, 281535449, 71566599, 75896634, 27526300, 114765775, 784727425, 929364147, 327420087, 138185847, 9772389, 13166049, 310284843, 840314958, 155692526, 281999868, 538436225, 461005202, 107068321, 295215952, 462345389, 106901092, 485209488, 184976943, 393386691, 209708309, 191612465, 751478592, 38400941, 669583145, 614108024, 640074950, 131850921, 224195497, 918701737, 214072355, 728940370, 853807440, 904862675, 440153458, 739254614, 820984788, 899613793, 967296548, 95722450, 453022010, 933979785, 386684850, 538790156, 639525323, 762890702, 684661339, 774632435, 378089322, 225886548, 540219173, 774451779, 485166257, 67113848, 916253033, 699535512, 774795262, 809291986, 763849599, 105766401, 796439230, 347886791, 591223154, 643944645, 585946760, 853220638, 745467455, 843961391, 533033587, 648456993, 669100164, 130348532, 937840327, 126110711, 874305014, 821819998, 886853806, 917189549, 477262712, 4191601, 564864806, 797294662, 718628210, 325044849, 695231254, 228514290, 595127536, 347062987, 501331700, 562518091, 847419589, 307899781, 539024531, 116965848, 221822793, 866296887, 334685650, 323707837, 748457326, 732555907, 970997331, 304449202, 228940288, 252590977, 769624648, 392426317, 114951730, 403636625, 65941958, 602535988, 941290997, 268778904, 936087319, 818876600, 92608052, 994049900, 529071482, 235847346, 156533418, 832863780, 940457909, 228726355, 745384272, 453710879, 438555133, 61481725, 213525205, 424468067, 915967002, 208399975, 749434019, 145356082, 436083801, 630053680, 23170609, 29615523, 14776093, 660036083, 284320398, 784924981, 103301722, 277334674, 689769090, 222833413, 463497468, 581990211, 794407154, 598563157, 642264712, 214883292, 57145794, 611740147, 316064632, 183121636, 529488030, 713886317, 237420240, 269498457, 564536197, 18387356, 20515055, 132931990, 746087756, 622754828, 859605228, 270612887, 479963670, 599736739, 331999666, 968333759, 478220276, 578730886, 312123930, 194810515, 70304493, 752818835, 593587012, 217597220, 148384072, 306543279, 645496960, 389563472, 689716124, 709441316, 886503896, 111926986, 254986711, 299853548, 615680955, 532067658, 779871424, 347203465, 424083656, 593446231, 186417032, 121671462, 848516170, 980413883, 714077280, 274122656, 322170780, 135680177, 308493679, 265979305, 980182866, 763411515, 115135797, 779671590, 707046748, 966022020, 746961000, 492381879, 83665402, 779728695, 705854087, 744869949, 268069690, 687432118, 409025612, 891709245, 798766316, 472170991, 696814503, 67387522, 482822510, 589276708, 13996119, 724767823, 522404097, 795688697, 446833231, 468352728, 130350914, 92120063, 303002245, 705712736, 504931677, 467983834, 288931058, 217954806, 547314205, 9688871, 170344406, 449686054, 435050745, 482666621, 396553003, 487586433, 406995978, 859004499, 945200437, 445103856, 424650261, 437296786, 160091128, 364137204, 280646892, 937287854, 835902905, 734961520, 749091580, 426027322, 27549675, 222097820, 492696140, 544895652, 129658139, 851718998, 763152507, 415766999, 473936583, 782901222, 770764330, 153603879, 366306397, 422894072, 876218872, 726960789, 229086088, 242631193, 136685804, 657884309, 427359214, 364185871, 265918942, 384184510, 912530420, 622103381, 266207244, 239390389, 48521135, 441753237, 256977240, 133849630, 579369454, 154046249, 937204148, 784363338, 653420708, 678159901, 682224900, 907542747, 961958137, 662702044, 38787740, 695943210, 264935143, 887146647, 128269367, 674976090, 504857095, 405195138, 374226705, 952865939, 10363092, 926672936, 827263440, 992988245, 542119717, 547928198, 934926247, 292266020, 816717854, 767206041, 11767068, 761747754, 395951348, 698644151, 139855839, 93023263, 627447273, 682484168, 703158195, 841969922, 218162894, 766202511, 900361386, 94153238, 277274942, 740955526, 645846502, 222084099, 400928018, 807356852, 378685388, 934495764, 412321665, 904995946, 783396093, 842581450, 373874962, 442737980, 466880851, 5500653, 177066758, 297564931, 793161302, 302530136, 511943523, 617396687, 13243465, 816544425, 484808777, 625168317, 307375821, 215338712, 73090113, 221790043, 735275174, 621241982, 576869490, 177097903, 434065749, 355235213, 21696126, 656547690, 245072611, 207228542, 477178537, 905475705, 791774666, 370147878, 465023810, 296552025, 810219913, 246356315, 161281101, 258682040, 453800214, 980282937, 768980182, 172560379, 480722808, 881673460, 795982666, 677874875, 376907516, 403667377, 426089990, 931432601, 986043866, 449798831, 965755201, 877047537, 552357535, 323997857, 778521883, 299140642, 694928323, 236517854, 301514239, 469970109, 844657739, 905273260, 68677008, 752546875, 555750605, 965368118, 346975839, 320153753, 890657328, 370759910, 326300523, 361204642, 672027973, 659475632, 164943876, 735627829, 800036331, 607321884, 22618501, 945064190, 232359073, 624917983, 416495664, 191484105, 96210571, 861164540, 229889095, 170611314, 309756653, 453517442, 360101524, 40182056, 419254962, 379702688, 419383449, 661599392, 902465566, 977344788, 238169649, 837886834, 644510375, 822034485, 436404118, 60474682, 641397071, 732215680, 704588629, 418744616, 22555554, 883253333, 577516294, 740680184, 800712521, 763568243, 166867832, 694561312, 453698769, 929071274, 45961852, 646357776, 906369822, 960003418, 642978768, 923153983, 462462807, 441469159, 975511785, 818796375, 13061984, 62807383, 423307990, 108770293, 491245407, 909311400, 113230781, 863799141, 840899936, 715723312, 340691716, 269392014, 87609348, 251466970, 81962387, 945915473, 434257719, 817959186, 752419559, 15050906, 882887739, 798317778, 920301376, 879375758, 772235330, 219862805, 289765137, 79593065, 364509034, 94670309, 328986851, 450436797, 681695769, 802874598, 302965611, 548803735, 687447386, 626421274, 241528057, 424686671, 538909106, 635748415, 515532156, 220470682, 242771826, 687883842, 392176335, 809852262, 716273639, 565507424, 568072226, 745103990, 861024694, 281179502, 33366513, 611091211, 292540781, 194384412, 754195424, 243323030, 641384874, 171612861, 878609865, 877327621, 705584869, 655638886, 172984699, 154382270, 716072668, 126067057, 648936876, 710354490, 412172833, 840869771, 557471778, 742965422, 330860498, 406927212, 712326474, 341406263, 575138360, 184943817, 970545121, 175223031, 924085225, 449434884, 187782126, 171495851, 768716569, 250438686, 922630070, 162808845, 758506048, 339594056, 115935389, 458536273, 722928047, 433213069, 674559140, 567855165, 572531446, 437261993, 547528772, 130106890, 205713873, 385407712, 234127341, 830808653, 63572650, 666126259, 675342225, 553621919, 887286253, 895260311, 481417750, 537748229, 359858118, 722668094, 598676490, 955709578, 765577359, 588114826, 481328606, 522449454, 248178882, 532371387, 186764161, 659672264, 531104660, 305713282, 633200585, 765944549, 340343028, 624440808, 253124973, 538529624, 780472834, 119884814, 953334605, 648179362, 315301370, 513034440, 899751775, 563170447, 209134507, 207876425, 277128030, 467461719, 906953487, 619448050, 417895547, 883512713, 169343662, 326137338, 517832160, 212076261, 77387326, 282951065, 447337531, 796110121, 775635205, 793998942, 866076785, 995438122, 397852697, 933460567, 274195894, 383650474, 248465290, 637875565, 498627614, 538034034, 407412895, 931413394, 155069591, 760975128, 500490863, 526207464, 119660256, 402810652, 6231759, 302646793, 849076769, 915937596, 77737716, 353382057, 182391240, 325360133, 576519638, 122006239, 426056871, 322903985, 44115428, 291663041, 38447964, 379328175, 659239434, 915342114, 773113809, 435127599, 584488661, 20802633, 789128521, 459996626, 609458500, 108403145, 177731317, 730017426, 288795724, 880636878, 510499157, 874650585, 954313362, 600561506, 890411103, 995850330, 980219082, 936724713, 972874604, 113154008, 925756228, 659319594, 661884619, 539469994, 951910645, 318045208, 208142063, 153345529, 58146804, 863132300, 640074959, 101663102, 449710593, 345123077, 841774926, 837277424, 5609682, 776193072, 178677051, 67774698, 202024586, 432083536, 212887641, 180981525, 943067197, 930902281, 529790005, 527758074, 528234749, 453186210, 254305097, 440074139, 719738724, 231409609, 50180430, 463983102, 394538670, 964772704, 113710452, 199771185, 947126055, 832581440, 465302771, 677298093, 626033222, 65934604, 557141594, 618103185, 747799953, 220793886, 715573827, 226562041, 474372890, 876699056, 545810662, 278524051, 647717170, 880425476, 337993606, 143543197, 674454263, 30485978, 542023106, 635391340, 368258062, 858414428, 459895136, 81810869, 623263942, 71904775, 733017653, 3257160, 955987163, 769459492, 595041258, 399610049, 203570730, 462720055, 351620132, 257584146, 409966220, 242155586, 997447042, 808322717, 528225311, 615509000, 349291065, 601610163, 791569879, 255372151, 747433608, 656462710, 616176789, 556386116, 64207688, 404090963, 664057896, 882426521, 958745976, 249529132, 383519410, 529924640, 190837427, 936334133, 664419976, 393828040, 16597383, 391222621, 181660758, 289552083, 338747754, 311289003, 761525166, 579924860, 855938530, 482400316, 730137797, 644535388, 429716853, 37243795, 356236813, 992169613, 100393310, 403105964, 190169326, 252997337, 536578567, 283308741, 853054080, 18300158, 626827610, 971270932, 36523668, 558316526, 489248464, 733024290, 664208599, 731290035, 980332699, 331545266, 447503228, 66830286, 290871090, 122686563, 915048074, 882203672, 243761311, 494570981, 944839692, 160834566, 892935812, 153464185, 406320990, 413058083, 391470840, 504507293, 965990565, 463889105, 522796302, 977376607, 454750928, 154805856, 904285332, 809854230, 827245688, 499467946, 115954994, 678044105, 632769508, 681773826, 300257514, 216253335, 119170222, 862633951, 706805233, 789668490, 157612607, 200587281, 863222346, 415729787, 637165729, 210580216, 550288003, 847379034, 83088159, 900091703, 482024976, 672626924, 665126656, 343313975, 356205451, 369781540, 527125643, 518008528, 957570556, 530911825, 933611234, 12747404, 178404863, 62523615, 873925844, 915008100, 146147319, 971644491, 843012296, 395991207, 560918319, 594647970, 44328989, 246434640, 916047667, 992173867, 597490090, 56673897, 538831137, 512112861, 818787386, 795383469, 494724133, 688865476, 325490330, 911232429, 350172270, 533515525, 31555297, 838764031, 869955248, 576906911, 281131117, 965347857, 431551523, 802792199, 77927702, 635417966, 926080849, 463008189, 316224621, 150617510, 562825207, 813048585, 100519896, 665633741, 925711847, 549060675, 478456209, 860035967, 867693921, 271984538, 532414663, 32830327, 578892237, 542165116, 206820898, 249746087, 809842400, 134302359, 910567754, 45795305, 511978532, 632056752, 942070394, 340309735, 990758987, 685914211, 887914694, 792795099, 838292628, 376689743, 310084120, 404424468, 774442839, 937361296, 353124649, 757197016, 919206247, 10665028, 482648276, 396529581, 924112819, 708863313, 28392373, 209356915, 549237609, 147546935, 901347273, 659321078, 503645415, 456912870, 951049796, 2141147, 488128069, 904467583, 977729171, 90373205, 853954707, 93509668, 533184971, 946524347, 698968854, 220935105, 396081351, 448552309, 177823368, 219665004, 575489025, 754994258, 956609650, 544387882, 803989465, 239498439, 779290903, 183061653, 652093164, 372158138, 151869953, 224009123, 630717653, 861156535, 779457977, 162951920, 304605136, 26317500, 673826759, 790239519, 69537735, 529302750, 74362454, 376259388, 142120771, 756440227, 225639916, 586674529, 416563484, 699628267, 32473396, 409358154, 236509130, 384068184, 789626037, 148769239, 790004861, 882999002, 113693636, 893683402, 927872522, 522972675, 545535202, 875035079, 238746861, 630565261, 457201226, 713909678, 342619950, 339170711, 389583848, 162934521, 367012027, 101516838, 596992239, 689744793, 452631902, 698890992, 769239504, 793020655, 267032966, 613644452, 97474368, 731125100, 38082803, 402037323, 873077076, 822377458, 546623749, 199358731, 116808391, 293077137, 482828536, 999096398, 979284899, 880737302, 452137555, 872626904, 581801254, 981899168, 802735827, 173681252, 639354195, 651943636, 245669476, 89675195, 345729503, 79414217, 253769581, 186443125, 119824387, 274198495, 940922572, 94896809, 692462972, 771844935, 888398937, 496908603, 253319301, 511682790, 990988682, 336310952, 235091552, 431583247, 721125759, 807655269, 2732200, 949424943, 757132666, 260136852, 284922698, 203016354, 517744582, 305204070, 175043218, 653424595, 119393673, 828478635, 701332925, 753615336, 862288383, 1654968, 562677046, 439147265, 489698815, 948849696, 603243149, 985398491, 508423322, 708554003, 220809129, 474558040, 78312231, 198134566, 207086586, 231636819, 771698792, 581173667, 331916938, 512117726, 131009430, 457838937, 54057143, 960759199, 487509864, 152416886, 435108788, 940715163, 748860228, 609715419, 550583848, 954413228, 220733916, 848071823, 593329324, 247918724, 676448622, 576904137, 589079622, 892152760, 720611345, 566284189, 314187655, 396394533, 905505800, 30399423, 479718980, 748773353, 36008622, 455202271, 261003477, 362460814, 10144663, 985477176, 707491204, 711699519, 185855993, 437644953, 939417540, 695784442, 249556486, 431968459, 968428575, 185462068, 819282691, 377281464, 5768789, 216221404, 436877215, 842773505, 447018746, 742866466, 751009777, 700449983, 699271081, 668253553, 971023312, 438447893, 927037672, 714835184, 446744308, 597447925, 836359213, 771461963, 987784048, 401152464, 410415443, 514570654, 951041605, 198337406, 809832693, 685090811, 688118514, 323749820, 323352213, 821964083, 126539084, 784070552, 676960100, 463516716, 565382006, 163314280, 80229122, 607028734, 571248930, 536040511, 108255601, 750237653, 871483690, 312398094, 22712474, 455569795, 758338504, 436193212, 392025604, 250386181, 967527628, 458918577, 523083475, 965873848, 940505515, 358838427, 743670923, 782955769, 751783755, 557191108, 457917092, 253890200, 829315231, 82258222, 101128386, 560837958, 387088578, 686431672, 68604824, 659827184, 170944772, 951782976, 558872016, 568323900, 489947227, 373258871, 709517022, 823486453, 953074954, 172229998, 713346615, 39620682, 874907717, 304642991, 741484849, 341462453, 846639744, 326855200, 144318082, 690136804, 298243596, 933674299, 101670732, 587548471, 622218298, 521303407, 820734323, 807029723, 217515259, 623335757, 541644438, 866271312, 49370470, 671292519, 119712551, 409226982, 634833192, 496427743, 62270180, 978224323, 796567098, 627048541, 409292865, 515327270, 912781910, 105543769, 574686388, 611150849, 541036321, 560452092, 797447338, 859250066, 731443509, 779408531, 808675248, 292627884, 724029081, 167455501, 667739603, 682149342, 92918258, 499484230, 653748889, 810288126, 132653316, 453021536, 445836074, 8081469, 993148462, 722230609, 828947796, 254718635, 970373796, 301112477, 450220074, 744130892, 972573335, 375056718, 697175261, 303016157, 866121895, 795533664, 552003185, 833793605, 762325167, 891995743, 345256790, 717097645, 436940331, 106278844, 27754746, 379554207, 286755141, 369110163, 607145102, 655009341, 571835204, 47862801, 352550562, 222785719, 532879327, 159316850, 197480575, 754125851, 191110, 83467704, 56720530, 252204408, 678152626, 254395688, 212999878, 973416851, 161183273, 766741437, 156510363, 790591476, 260293080, 36139309, 443711906, 944764373, 745513065, 878715680, 587442381, 925959446, 467406376, 699593498, 436986679, 472003764, 571681218, 573189543, 301463730, 91248982, 149014672, 297958210, 599611288, 710981358, 781972278, 413272483, 986862277, 15594348, 980697792, 163524222, 278137754, 226656901, 271273962, 931136580, 401764852, 144459773, 50817760, 792741695, 878926919, 242382442, 84874653, 998103613, 749287106, 273846270, 920868875, 356147066, 372452972, 929863673, 70897077, 858049244, 136815880, 649360402, 37347506, 378659202, 695173373, 821725981, 362914096, 187868377, 467379441, 566055677, 334231649, 511436287, 52846067, 654418359, 321027058, 359874542, 355946773, 148969692, 815223919, 675157406, 286813647, 336631942, 944759774, 18737877, 70291224, 238121572, 338158151, 83941744, 884547400, 111284910, 993700963, 200783779, 811072935, 21408585, 147830732, 988656088, 576098186, 600538869, 853492825, 165670177, 570781688, 481646771, 69693534, 650728418, 688057818, 732146488, 360409809, 112951612, 58245412, 525826840, 955257922, 271507710, 985230075, 386035708, 992377878, 301700151, 454416880, 329296798, 616150455, 44215072, 730432258, 834324438, 284748082, 597962490, 954197790, 640432076, 776638870, 131011479, 952222292, 637468025, 56551706, 94968433, 843076063, 129506822, 977113980, 667927827, 444109128, 521262209, 534792971, 330232528, 519513376, 350734269, 413700549, 950458591, 53511096, 244229852, 283898023, 424175978, 587836618, 370345453, 883710455, 503023245, 105502666, 422906353, 205316474, 610333478, 967159939, 740365028, 981589637, 99051327, 961005126, 448441775, 579297767, 783630248, 894282873, 196592762, 356286781, 198120281, 893390942, 712743141, 283253492, 265694962, 442804457, 577959835, 674858151, 703296695, 190429874, 155591215, 690809778, 838141920, 346499602, 392040890, 255376212, 435541270, 739293618, 360344406, 183814564, 509338256, 320013256, 885041868, 455750625, 399526024, 628496865, 494219611, 265829064, 655626921, 414489838, 733489019, 186299079, 678746345, 385746299, 86174475, 321405377, 636849670, 832591081, 494096747, 584971536, 339294606, 723066776, 88177011, 102454268, 242953706, 744612204, 271091184, 343654145, 186323516, 133619441, 161334339, 94148197, 820445624, 449400585, 638939726, 681038749, 458087092, 523993155, 940245700, 759399604, 791113066, 681216247, 264218754, 935070793, 497939615, 472017383, 563584451, 96283537, 136393106, 632803692, 67812024, 626524907, 130340981, 663121947, 527873691, 58976995, 160554817, 681328210, 73288516, 848826591, 418824905, 633423409, 225626614, 545129803, 343643609, 319227015, 381011201, 578717739, 683077646, 834317071, 885582234, 457160624, 614251152, 566305412, 359653416, 919983865, 677669170, 775729744, 588452752, 412152068, 263713774, 449561728, 251321697, 758798994, 472364333, 13452989, 215499485, 427455875, 733265560, 555351713, 897521972, 52992027, 425460241, 312316635, 430226152, 866681943, 562973788, 51141434, 22586068, 718763708, 798113515, 693452496, 163201424, 97209878, 638739852, 32835305, 928145863, 940060345, 122709889, 279817012, 23460670, 628214938, 795302735, 153842139, 969270970, 284181126, 475764923, 260121030, 352214804, 559132247, 565888408, 36050659, 429968280, 999257738, 197155659, 399904050, 814553767, 719290554, 128621594, 271892338, 897883593, 937609771, 496891826, 727461131, 963364146, 423241183, 536922299, 388453961, 544863644, 623247080, 438052955, 820474308, 975952727, 919596825, 167981981, 128402831, 847726830, 708162115, 247311948, 700348516, 418905225, 26204255, 412216841, 14823379, 426653713, 805260024, 189898378, 564069453, 875582163, 872461792, 534948783, 708516364, 397684043, 318986601, 636137976, 131421585, 393853462, 367034150, 331647615, 126832238, 810093983, 480966333, 608481935, 498576789, 883251989, 894714261, 634473406, 651831769, 331001046, 264640449, 286088627, 53638573, 540749534, 353803612, 112698294, 37927009, 116622311, 253565735, 445929891, 651779003, 918247054, 943270007, 206463198, 746145035, 823311941, 27887729, 843266329, 425426981, 807981526, 735104779, 808459088, 895079936, 161255772, 740666384, 83689724, 666621557, 709255072, 499290939, 304249710, 547946489, 93840578, 867086643, 22936005, 777065980, 659413981, 733504919, 15049961, 237574092, 68324446, 603627490, 805137383, 222935431, 519390195, 7118712, 945817983, 260363723, 825197777, 456671713, 158760543, 520121107, 810462777, 780487155, 723840669, 120584278, 888337605, 749902088, 483148487, 365070031, 302702417, 962285121, 912311523, 101210012, 712874489, 6324937, 841064360, 696401089, 633808849, 405141792, 692764923, 484449917, 195463638, 459037831, 389160930, 776686969, 747230108, 770355808, 685488287, 326933302, 851378511, 193929573, 673874117, 9519405, 581765200, 990847043, 467718633, 53851304, 332656955, 814517741, 11065289, 171692410, 123260937, 941837143, 32961787, 986783707, 931922060, 250391047, 86826734, 198607871, 488015331, 158990313, 35723714, 864642783, 789712130, 30003762, 233758901, 169882036, 845200979, 522776078, 948998960, 531343661, 354000394, 863002749, 946494988, 531130104, 941852249, 497566688, 570003048, 46420337, 134639585, 950357205, 981611551, 942156310, 923305067, 889237050, 544512149, 183591358, 190962207, 892170683, 77990322, 124178804, 712406116, 868519128, 297078627, 56836479, 874607904, 717348152, 214733837, 205035843, 587822176, 591793609, 153553773, 167593446, 429184338, 513366945, 709500553, 983398506, 143951412, 199507927, 815223909, 891406672, 810415370, 613681838, 733233642, 115155989, 184104680, 383616310, 281012764, 294875557, 991192749, 979583317, 919920136, 352379087, 781250166, 539769949, 149072925, 576985566, 484517220, 961853207, 356783813, 382417288, 54546077, 805792283, 153943757, 156692571, 436546841, 503314538, 352254353, 28686316, 339505691, 656690436, 994336148, 886971752, 846884743, 810938448, 155548086, 859236161, 614638421, 839054117, 413400623, 636908983, 510179700, 652438597, 228224693, 337616254, 972475804, 468067223, 968868273, 482644907, 575828404, 704245297, 778682992, 597497646, 77535714, 408124920, 209431341, 48683825, 455999282, 126956166, 857951286, 6524747, 565807558, 353761516, 156745983, 312330803, 45603373, 955454260, 163387438, 149610768, 131585998, 921061309, 502581024, 330609141, 911244183, 415359109, 843140805, 664440439, 754426389, 491502182, 846619257, 618601937, 247926835, 186211970, 718454076, 116698947, 767612136, 695270275, 218795089, 758679389, 896118312, 979242672, 429143165, 21727548, 469373834, 326238888, 684999469, 881243905, 675699993, 66792724, 917796605, 354361922, 606553921, 826254125, 587716494, 227243322, 278341394, 149888410, 408792462, 855915930, 294138396, 500038320, 552444853, 958896390, 629279231, 473921955, 353164465, 750683228, 413283190, 559083674, 973084895, 350327728, 324049830, 819448147, 72359988, 311378114, 957890571, 262787833, 761614414, 110706464, 373073998, 978790282, 243098711, 208171896, 677151781, 309510800, 376272764, 886711380, 926135931, 603275077, 837220302, 389591541, 378060633, 436215490, 21553817, 595305410, 663724925, 360353976, 333622753, 22542545, 485068714, 519826385, 523531926, 358129826, 390304613, 830433583, 206071137, 724386796, 290146857, 535198282, 8380227, 47696422, 218497491, 56404889, 267231426, 69247514, 357216743, 243565965, 362912984, 302097974, 436866614, 575477912, 861256252, 512504058, 956661775, 250667384, 829839441, 867117698, 759428727, 45299178, 950461676, 760133624, 306570459, 307558692, 290739306, 435385951, 795293771, 966661941, 616868071, 24302014, 147800457, 449910800, 493631355, 106917275, 69319818, 744873396, 51679898, 414107677, 859356072, 467790182, 344749775, 382774478, 933107076, 604932539, 869464051, 712410701, 498246990, 515914345, 978269073, 394680608, 440184752, 482056547, 249987166, 250057797, 875225271, 132674862, 365141148, 49175762, 7221927, 612189608, 136923525, 142563764, 328509157, 98042181, 377397726, 921055577, 264079780, 226574179, 588023400, 935505634, 322673301, 722627840, 560165330, 659129168, 880016627, 645627214, 820577270, 560667581, 267483681, 820764801, 748046895, 630408123, 71614722, 578358257, 321657976, 504076977, 180449652, 158526096, 710459176, 610318115, 343457530, 817036635, 478829613, 349641233, 967451815, 989383848, 632907539, 679611628, 3338194, 57803935, 954452660, 372653539, 797030045, 955635644, 441137630, 965961460, 709443093, 288706950, 962942616, 79950283, 341912091, 680949768, 805490642, 272381045, 89937128, 564716647, 864523334, 863805192, 972096452, 678411219, 66700733, 607362203, 228937879, 180424789, 311759649, 783908559, 353669394, 974243195, 605926888, 167478142, 561509326, 158672140, 565852180, 543181455, 259775499, 518917978, 92076061, 453404582, 22868202, 678276012, 559889638, 479069929, 464079299, 871916070, 256306432, 471642455, 226515558, 769749762, 538992818, 103320420, 593766215, 906398784, 697985055, 931366105, 260798596, 765143089, 961598039, 663855021, 991893818, 205290608, 151591441, 547396930, 661706823, 532857877, 800640210, 201889559, 929291626, 857862514, 942492710, 555984106, 598315703, 765180319, 174207982, 54275227, 503319496, 566826387, 732979842, 31922859, 25145329, 999226186, 447509733, 390038315, 123022592, 632407090, 876605201, 778160774, 86840969, 340259980, 523294054, 266388962, 499941941, 448975754, 651064339, 587772257, 185725032, 305084357, 85250685, 484949577, 964245830, 787789559, 928053917, 242053520, 388249720, 102628387, 347878240, 982166799, 330734777, 292715402, 691526137, 720503407, 159918307, 4407442, 778116019, 736579081, 788307779, 278349816, 299268242, 157574211, 683883859, 404259787, 364893645, 9262794, 558861477, 366413488, 294968259, 546567397, 568316916, 752955466, 855589734, 885622077, 840188739, 576149977, 280373544, 527814903, 886747847, 443911945, 12591466, 979237229, 257895713, 120115109, 611773736, 476983738, 829713323, 437582839, 700679911, 518547936, 718827144, 537229440, 393638791, 819224799, 650292954, 105780307, 850882155, 144012597, 988196512, 951068196, 124493438, 155828004, 223784170, 534685032, 335006116, 119938264, 894275994, 590348912, 34028063, 68771942, 281446282, 750644859, 859898946, 471600008, 92139735, 755329289, 487562531, 331165104, 691224782, 94181281, 574549795, 446513034, 856151505, 172785387, 709643754, 806729602, 471942916, 926914984, 773707072, 67647299, 819961677, 510633383, 647192410, 306849447, 72017865, 345582441, 914334787, 319630859, 19611860, 862620217, 445542396, 99610393, 9584732, 367397851, 747629700, 912645785, 782699626, 326694003, 660728684, 319415528, 17961446, 678383108, 61117671, 349815823, 183473684, 661239726, 765695347, 512036986, 392073687, 936652365, 10258403, 913414994, 140857443, 640638148, 411681631, 569475030, 212125992, 316498943, 318434193, 523393740, 584520776, 998261838, 275215604, 610681382, 720355946, 219803192, 413630367, 798351669, 741201366, 777010579, 499729238, 383014402, 420256483, 291190137, 322709428, 576523215, 338330540, 969112457, 187570124, 70624011, 68754182, 672642514, 175462387, 114130517, 460481977, 538155182, 892476757, 418942814, 872162277, 213338544, 337612432, 904111113, 519436940, 342138634, 118928233, 123211100, 90401757, 617911172, 562391218, 889318354, 124529263, 495787172, 638348305, 886817805, 569199910, 485634095, 848778720, 109676494, 920904932, 629403753, 113659237, 116009117, 654948905, 645376055, 414065528, 461555242, 527755856, 920228357, 330126005, 172218060, 483888817, 90933081, 375189159, 310669680, 792975986, 870455538, 251296201, 188117655, 633906507, 80854410, 562817629, 595648184, 416280287, 533990561, 868919398, 316506709, 532026510, 298172470, 625711757, 611015370, 138512091, 12922031, 668284073, 913973564, 929482649, 103126621, 239042365, 986127464, 97603766, 884777015, 496925023, 581246321, 337819543, 215377505, 120046570, 825822370, 832541694, 693701382, 94341939, 935011056, 689904122, 235637587, 406755694, 81205847, 328232013, 153801359, 427246432, 304310472, 38374749, 850938412, 776822150, 720803158, 217620076, 276514970, 150283306, 770847527, 81722556, 154630249, 931381766, 925022950, 413339339, 716346794, 472543677, 533092116, 644316733, 734058919, 656550714, 563990490, 787322078, 913116296, 77197605, 587827661, 784822554, 623366377, 939706739, 245066760, 980124616, 257233308, 689684639, 667833759, 367443466, 579661218, 406536593, 560577092, 773313222, 800070907, 799646415, 154722619, 356956677, 582613933, 14382394, 331759619, 875798556, 966140758, 931952982, 164483357, 769483928, 282788883, 645847897, 379792202, 518539476, 215392706, 740769641, 76679710, 282623998, 363459544, 850964692, 686278613, 283820867, 554381667, 287546368, 381719729, 373129007, 590348881, 669047227, 792415111, 135177134, 683494911, 2136992, 972783594, 682411018, 95346748, 844301845, 693796617, 723292386, 199963606, 16526311, 410100231, 246296903, 942164630, 950362620, 18712061, 952120107, 418433108, 406189598, 338650425, 207546422, 427740052, 195818393, 511955507, 862151364, 571863570, 880263403, 681251699, 996909766, 712916363, 651284464, 381988296, 505753320, 79823272, 256222931, 290160337, 661435591, 292126572, 496017691, 402809231, 571584390, 678369638, 607833062, 643773284, 100761655, 56163405, 94522504, 839203721, 81034118, 732983868, 176955481, 216150313, 657456685, 80589685, 864318871, 812199476, 486604001, 906545355, 450774593, 467401755, 205830621, 775207394, 458626206, 723722515, 143041049, 35114061, 580456074, 298070358, 628798255, 466478016, 130891594, 179776469, 873259073, 186697368, 481652319, 153287709, 762914721, 657292678, 110375727, 115164071, 303502894, 57287155, 235298525, 553820179, 99256638, 862305549, 59180551, 652546607, 541082436, 697271936, 205243477, 425669452, 525726997, 596910157, 55611534, 467420068, 484651436, 253721921, 114035116, 492457754, 108493904, 7305627, 24106459, 718958412, 888307390, 482954269, 739442668, 723820783, 972076104, 453116420, 527243006, 672329138, 261219588, 988187082, 692172139, 683243361, 359994922, 446341409, 34730512, 513051257, 549004992, 875407441, 339475888, 801978917, 341913072, 352032824, 73045462, 788143941, 486806907, 941207758, 704466288, 961300646, 615117414, 457455664, 307748117, 662071893, 681399497, 884371865, 811984687, 490101097, 639878390, 776156711, 30933800, 734355766, 49832018, 21553567, 494787326, 518872501, 588652671, 983971993, 557308620, 772727782, 172776052, 436625251, 792626344, 812399963, 436225778, 545922646, 288019242, 909659552, 683990603, 181957621, 71708368, 701403686, 39788369, 354644587, 239947505, 850151930, 559408927, 208751774, 267518467, 130976581, 528258771, 630843052, 224250644, 80358985, 930100659, 812714860, 878438919, 764846926, 902537298, 791516676, 921897788, 966461607, 980354211, 14741077, 582690108, 762726440, 802931766, 632907183, 28469309, 167463751, 738558818, 41149020, 99348568, 866093586, 614408536, 24104620, 338348521, 48427151, 262170212, 551573846, 886543808, 984129027, 563658956, 739251594, 863604404, 487838126, 248838626, 779830378, 682961964, 916562779, 955560284, 900325568, 664607494, 482503806, 263463112, 289806901, 582499696, 798157342, 659860507, 620710361, 936303085, 662932607, 188614683, 891858757, 165614760, 366850729, 984664468, 267661679, 141881376, 922523934, 682894967, 473632549, 904459684, 872326084, 183075629, 423123883, 877288855, 172003090, 440448080, 950794820, 387857036, 278163054, 472637823, 901824589, 726975016, 720036600, 166240653, 923302162, 319580533, 596306679, 228036778, 640870425, 441026158, 907699090, 394462675, 449037853, 247866276, 674405405, 893516684, 299087375, 87721130, 38054049, 904233468, 131186639, 123857708, 370170186, 344537991, 935149775, 955633829, 21999150, 544822001, 336098034, 791968, 222850775, 664573907, 671406800, 650644822, 624821321, 938638689, 317501504, 93437412, 756288866, 278335803, 909598407, 39975067, 258994972, 933841135, 674873967, 465081292, 174638121, 646906895, 505547010, 668563309, 558420199, 995225341, 20985172, 41349614, 496798587, 584219798, 335521128, 605527342, 663245372, 125415394, 168619762, 997267443, 490625272, 855214493, 998394747, 597156032, 777221429, 541754532, 225342305, 881154796, 637091365, 509500954, 679382043, 412009765, 646899645, 276283736, 881671311, 264922912, 763488988, 668927793, 69172732, 85477745, 873580884, 258604031, 106906998, 192681507, 902446708, 357272778, 146919579, 185735589, 950058535, 653675656, 78499060, 287665972, 466592532, 321113820, 14918203, 900492232, 366803924, 858496276, 199454832, 416508219, 674941272, 502177710, 565107217, 776372522, 937637961, 426627269, 286083577, 910453801, 879458000, 980962192, 752531195, 148885466, 808249430, 268302465, 882028305, 116246489, 235335348, 535188395, 245014809, 519385307, 943717922, 171225450, 364427323, 610312247, 236720240, 826629251, 669292792, 986093700, 669216263, 862269858, 400897320, 812023189, 746811695, 107960223, 232285054, 835761991, 691140534, 582225403, 330780571, 519658877, 996344573, 938573311, 223953098, 68659660, 741740498, 84523998, 76473253, 618535018, 461634778, 224291426, 5940777, 2209975, 175691483, 935735634, 184413706, 227320909, 651173203, 675093616, 906126877, 123463684, 927812281, 183640699, 621695948, 41260416, 243988536, 308119346, 545672418, 274719937, 649943810, 938471446, 165015341, 759269150, 786324433, 806537412, 287536065, 679695153, 27677199, 350332333, 993613511, 341942147, 404930292, 453985639, 410537098, 414719146, 767107114, 604078145, 271194973, 122155184, 354368128, 328086493, 566273160, 154937574, 312551762, 824867586, 256511252, 537055020, 224670644, 545790786, 887824585, 325840333, 822797125, 415543330, 798702452, 263860454, 137411294, 654572426, 805271771, 789788500, 853249358, 490343154, 174580068, 263277734, 91792123, 536858743, 305934676, 614536272, 21735800, 159046937, 219952759, 755245887, 81582599, 39474638, 605073366, 430231552, 4537200, 133287322, 342412261, 819069700, 946843442, 769630791, 824921732, 942693538, 929994947, 709505547, 99946370, 280394621, 636055305, 83426434, 73386901, 43974340, 301229731, 348032866, 683283990, 792067975, 660035720, 301439973, 882417521, 263532712, 252582246, 415834826, 814869679, 444470364, 192660594, 200194773, 155917154, 614048777, 611072455, 510328931, 928285363, 155911966, 181789298, 835248707, 843602935, 111209509, 91012326, 229683503, 874416991, 994623076, 970498645, 82404829, 857781682, 279764694, 668911290, 741130356, 771839362, 410927327, 475595896, 412909510, 415407331, 131879523, 232845576, 784004936, 895206179, 428529337, 605485852, 98737270, 233281582, 741576458, 250221547, 893690403, 481079345, 674263597, 610176110, 446606868, 343164094, 780632186, 489557069, 202248000, 608914861, 210384338, 881333593, 820608649, 451193413, 988795643, 844576626, 198234264, 358468755, 436796374, 498152287, 255467900, 195734649, 954184502, 78596582, 18369038, 675796871, 457729788, 527331512, 340265355, 640161110, 213741627, 347376402, 851426855, 528827279, 425849713, 932705314, 977065711, 925446077, 748008011, 467472080, 291514379, 737341205, 610389146, 684435964, 820693111, 805908942, 892710075, 860163435, 663339260, 694001210, 354596550, 711023656, 386261855, 82972429, 174108457, 498352664, 102485967, 721835688, 704424385, 559135913, 483849819, 277956217, 191278523, 106466567, 143695536, 177164952, 315304036, 495156183, 138215018, 159543646, 960663106, 493036428, 379780158, 711547258, 156599965, 66294435, 778763249, 832138239, 483022276, 725965812, 743351035, 873347963, 562634883, 976641104, 383669663, 32339698, 784727473, 37742842, 660689000, 715929919, 399474929, 104312692, 813353169, 749138248, 285400362, 743295569, 498606573, 786916566, 295437818, 441338104, 947674071, 109442851, 405626092, 18345461, 56061814, 779214307, 486140549, 649668556, 4098618, 375331443, 172899058, 921789840, 24348643, 790324683, 263383076, 190155165, 390979112, 668922470, 183526475, 425830776, 249650602, 660949413, 329674226, 271581477, 368724504, 156218924, 768246373, 894281129, 818389753, 803078932, 63488081, 109713907, 540595626, 313142350, 217560277, 808537809, 956409480, 52070499, 594825299, 940581562, 217446044, 663847115, 142919138, 508143660, 629432383, 306190261, 554267278, 90312904, 762193559, 303827283, 482080459, 762736262, 519214376, 13009024, 663398399, 369416678, 288577945, 506003829, 672454760, 304269823, 603849592, 454130773, 890929387, 741085335, 410580120, 305084350, 244753041, 42711220, 7180416, 699907821, 126631605, 631008989, 497252930, 912400023, 285043421, 364097786, 909741435, 537788243, 625141971, 46705573, 509880524, 395860786, 291662337, 754546015, 702284439, 349096291, 164382881, 569660269, 330392023, 82898695, 921738751, 52697231, 301372899, 362059644, 97827412, 894383914, 854812602, 531556924, 895887297, 217497972, 347757694, 207613017, 45761566, 287340801, 656976937, 782474080, 217718072, 767168402, 125217402, 867480189, 502474358, 745404887, 312222704, 857847846, 626480596, 201816938, 91037811, 771020367, 271153286, 910336763, 717802864, 300075436, 92816318, 745890115, 32765160, 606166679, 933971761, 714994807, 227242726, 978364673, 975922931, 695243832, 872804502, 652947256, 585880832, 292584863, 195257712, 108132747, 396424928, 338151174, 140230878, 466974954, 638582661, 261435776, 734339394, 810738994, 45000950, 45307592, 901926567, 754377514, 896860320, 730316268, 415807449, 419263561, 38073310, 931794880, 231021484, 747950505, 28637925, 149658248, 44504199, 469290750, 452206199, 445931457, 678906679, 713681286, 468098897, 112475442, 39155998, 806968017, 576981052, 242279728, 807633665, 502239145, 369417052, 59447436, 544823193, 932016280, 318020529, 24749070, 724509429, 441323437, 145190319, 516268817, 925048926, 234575422, 888009392, 938944141, 590550581, 417878389, 272305549, 596720572, 395521184, 43028012, 240122162, 96683962, 424729184, 718756805, 3199235, 71333802, 2260850, 434482574, 692469904, 632674521, 215445342, 826830245, 392400827, 937920059, 671816256, 702556936, 905195859, 395085192, 975138548, 768604555, 243014118, 377155345, 217013998, 337803726, 351553252, 122578293, 189822324, 434298345, 945214574, 285777998, 692416920, 815933536, 303518868, 227537214, 85577558, 831528138, 970515065, 887628555, 151712495, 809708486, 842457630, 291881262, 638671516, 699902701, 727472306, 151606175, 770032454, 226963869, 458415542, 463517127, 369568533, 734316179, 891115443, 312898364, 129217343, 380255813, 695790256, 319627995, 806049511, 662099051, 466183258, 699991422, 405141323, 796070035, 349543269, 924321829, 620059119, 356657026, 968587533, 949762128, 818762840, 6337730, 972788532, 440447728, 187753349, 939005264, 899381828, 835587516, 853138994, 312120574, 645085673, 685620175, 512218446, 881241152, 943583188, 102073392, 210669929, 454192886, 546470127, 370061341, 623489716, 190356855, 414713596, 754664957, 205268792, 379961779, 788323627, 930202542, 67338965, 116156519, 922392616, 435853776, 447243127, 732688405, 822428704, 517631230, 529133453, 72395627, 760620745, 707719754, 838562303, 779656155, 906075480, 242779061, 444448208, 350000379, 485386296, 895807793, 563220969, 252416092, 523830907, 802784124, 739680610, 347218594, 520027605, 74656724, 575392727, 933534838, 981293874, 854708059, 180389356, 322974446, 669573715, 861156718, 462012091, 519456752, 147118465, 259546974, 748128945, 601184336, 463518309, 742007655, 272266179, 10667670, 282988511, 660415545, 817636130, 199180281, 62077546, 63663864, 346528765, 196749137, 831786705, 61192478, 58554971, 954367555, 747105718, 864316913, 847807520, 690616096, 580347474, 31288564, 162861713, 902201923, 319830556, 837629279, 909537135, 231080615, 791933549, 170394153, 810627676, 140600862, 975194198, 29913354, 191004549, 937110092, 446563737, 43630185, 38050114, 727844671, 723189475, 355664237, 853758097, 760708051, 217174157, 865927248, 441220085, 315691446, 654690387, 685062010, 443482590, 231756653, 115465725, 426955492, 734511978, 415049251, 201590340, 636530431, 252051877, 517528500, 29837650, 49783845, 121238094, 760011423, 295618020, 533822196, 103292796, 903714411, 106145255, 30367295, 1364772, 149273709, 538774480, 219400184, 237644840, 738187261, 987837103, 810873676, 849949322, 132557319, 838074879, 136929604, 263490973, 549700068, 540089613, 754181559, 875555594, 144183097, 980019417, 845657666, 300979606, 618766607, 98416556, 215958832, 118402300, 390606945, 269796657, 709330396, 429680974, 540503080, 212202315, 168278309, 492224747, 26553863, 395495556, 90167681, 841319733, 478550428, 24242652, 336549942, 208047428, 531085360, 30697369, 686982744, 757998699, 986923831, 699766215, 807483054, 141019169, 90368320, 234683498, 351464962, 939459187, 52856887, 858573721, 295763424, 151223445, 340693047, 683997022, 905644219, 762139432, 666885723, 183895807, 376828800, 584124808, 769312216, 724698119, 429038989, 90018145, 89098985, 746118195, 762461323, 669816796, 808929527, 821214703, 271671230, 163840837, 138354672, 980331144, 467927936, 198769649, 532486122, 49122062, 805533869, 106478519, 445992957, 555837008, 832519260, 751287523, 188174366, 235900164, 730436717, 354043538, 611759744, 457926378, 476021725, 808848434, 237722595, 511618308, 430785860, 245224980, 437741919, 614376753, 384953685, 709729527, 811122008, 505425023, 408164069, 753800608, 470906530, 851338320, 645504337, 599706892, 343713536, 132686920, 415065369, 740126906, 497194201, 549479651, 863266238, 203106604, 541960676, 725983545, 410464722, 895396356, 744558290, 438552731, 768176778, 841523385, 328735457, 631045672, 996711193, 282922097, 157547040, 160772732, 27950908, 839951487, 655769260, 307052633, 330023700, 362701812, 539310933, 605132407, 414288056, 666395258, 32623038, 135894179, 956840338, 129816640, 97400853, 639169803, 205282943, 557646660, 729148300, 306940629, 459876123, 744028783, 158410455, 957540698, 843177929, 160066314, 103031222, 797773137, 770923959, 794551091, 402319613, 131232606, 275298909, 818545054, 644228326, 629899279, 535409524, 300910105, 188447951, 73496615, 312009879, 47765845, 958621762, 734392011, 188304467, 183341252, 577659863, 696826295, 357402089, 228770942, 536625337, 624338675, 863372747, 749915500, 964970660, 827542431, 219439383, 142986799, 269744924, 252843828, 952376114, 17855101, 14540396, 620995798, 206599715, 484202845, 514309373, 860197007, 209769738, 404520364, 89149500, 318770122, 831859011, 319625507, 907709834, 929304466, 172289047, 933000907, 48088197, 295190770, 151750399, 698442032, 54179648, 907425796, 629912977, 764963258, 402963478, 125723896, 320669803, 308212996, 98806838, 183768739, 850529323, 912065397, 833576654, 609702843, 482255166, 703250283, 867825057, 598425463, 677346492, 124961507, 565848670, 445337482, 770393256, 931579153, 11610833, 467405358, 414485199, 876448045, 897080713, 771216500, 920775009, 819484460, 955077101, 694091063, 210805042, 729813229, 317290635, 562162239, 275812975, 957532434, 88348850, 300391336, 778587056, 68681967, 263627047, 194029181, 957921776, 376032848, 165222388, 673472835, 925358023, 783151335, 469760361, 741455933, 78073347, 331001193, 166190253, 239505676, 540621646, 780685540, 661411823, 62429992, 321639543, 941227315, 838225736, 308686485, 194115382, 492979850, 440127445, 268848647, 685371525, 350174059, 569350211, 147073260, 475617558, 577885054, 746703285, 606107851, 468736170, 345594965, 334166237, 721121062, 180308884, 168254578, 85490032, 586891010, 245153679, 501848714, 355485128, 129706123, 966700628, 755289411, 477792573, 51883673, 424960540, 910889461, 9695931, 989026658, 13759332, 398503737, 145731744, 356830852, 288727112, 106591525, 544777651, 830974685, 958081454, 92846971, 307716505, 1122365, 506198036, 222702619, 848566638, 704315534, 998119593, 375340888, 339529846, 469598872, 950299856, 297638170, 810432399, 396501749, 762651007, 251975889, 840855859, 602269450, 406064833, 258437677, 299089393, 98992356, 800427056, 113362473, 269931961, 87130824, 271746729, 43141142, 489233675, 462961641, 848803761, 431772135, 192484789, 289752689, 67362721, 464363464, 557660852, 50823445, 891575924, 546325975, 735431282, 390508346, 500717824, 839723784, 636085180, 427197642, 154411479, 875470076, 931215830, 63994856, 16899506, 997012016, 232689928, 897179920, 513793771, 311425315, 887003569, 679187508, 464242903, 52119742, 852496977, 102997921, 21956903, 811297887, 845808774, 835970030, 929595715, 625691394, 739437142, 901567416, 580172705, 35910292, 443428090, 66937583, 141754336, 387760784, 125820298, 762487296, 851797159, 268636259, 190732944, 152837131, 824281655, 883186091, 518705697, 40895700, 346123043, 225327740, 382318548, 507661992, 46307416, 210032917, 226375511, 318140275, 392574064, 200838021, 273466996, 109160709, 37303990, 19170283, 804642947, 34224680, 842518778, 379185682, 974288172, 522391639, 933345877, 742200908, 817227156, 680735934, 261457825, 72340153, 998228265, 440471203, 302386338, 606448452, 797470722, 138163875, 925201326, 267177551, 229744423, 812099836, 989741941, 171814608, 580356940, 537711440, 659448335, 927897073, 958512978, 201236064, 147553147, 77022046, 326823972, 829529292, 944457989, 717636033, 455738859, 380750578, 581606584, 390344570, 147964209, 336930463, 232195618, 696704609, 586970284, 445591096, 232615249, 670650903, 652245077, 919744701, 94779404, 408657952, 677980170, 450611637, 708318360, 951896001, 791125802, 190241256, 594946089, 573411353, 28281389, 891573419, 499017337, 779769593, 143818247, 210535452, 46597977, 75081417, 238287161, 764954573, 608978862, 866644590, 693742498, 880760441, 279565411, 301143691, 77417693, 827002622, 663146963, 346542562, 305129228, 842674699, 968860650, 569364830, 842324123, 672564954, 248526309, 235883487, 494366532, 736548032, 609558639, 183669090, 420768787, 517101427, 491494086, 862168791, 917819711, 95976372, 354177508, 267773922, 764338908, 614699510, 149336788, 845697621, 176409562, 621121373, 607335077, 395908920, 765421529, 310200836, 668501080, 945690112, 832374729, 950134304, 315767630, 137846269, 229036203, 571093119, 882236442, 417892739, 207182376, 348345362, 125791757, 347900298, 219511455, 649456346, 383288225, 581730659, 833016385, 667137693, 887539256, 558607846, 568329572, 467837252, 637772766, 70959129, 857560501, 475377314, 504640992, 765168677, 315428815, 812297758, 530935670, 583651825, 104216283, 304840761, 699441770, 453046142, 561839844, 690160073, 857750195, 493196532, 883742649, 683942490, 683977010, 131618398, 357117004, 106480792, 77372076, 326919194, 549861423, 834618987, 905821494, 353637235, 518163439, 187349396, 907580690, 402278904, 298189980, 93522494, 375607004, 186778280, 817451454, 61469590, 218089315, 221933657, 625433088, 103228171, 79394522, 203543741, 149899246, 678978840, 931771201, 720204355, 147526291, 870538013, 623792465, 908449376, 410412112, 389430817, 506263684, 544015517, 592988747, 305887041, 585706960, 15375188, 808478634, 430780510, 50020144, 654673863, 225516586, 238308610, 521417147, 24132553, 51477345, 878332896, 531133291, 419675209, 938460383, 697449252, 484488907, 771916424, 172638034, 86248041, 952090243, 7331047, 240898572, 355486707, 579380063, 327393828, 21649059, 840250798, 160490193, 9534382, 176724635, 220038298, 716012288, 360771567, 258603305, 453681382, 202258182, 751217713, 861587917, 878714956, 967653405, 385456855, 319205917, 130179888, 183291346, 188871693, 794921068, 177896855, 910931488, 233122524, 57036327, 919308611, 831518991, 70800999, 674140457, 454005360, 839196108, 348756059, 77410248, 144781812, 496822173, 742340833, 410547755, 432295600, 340696016, 383137870, 656652402, 366479878, 593777147, 799262747, 165752850, 373680804, 134879441, 909195480, 481487733, 870628466, 136289853, 622086716, 593855566, 44947374, 745125257, 701563402, 810394404, 191315688, 872059089, 9727702, 11357346, 654960664, 342918908, 144119586, 958133617, 847678102, 899058957, 908101698, 128144042, 790019702, 649700441, 898836906, 832403948, 264982871, 150473044, 165141087, 735105803, 525359968, 422953172, 231666363, 636695002, 616901869, 886705447, 828547271, 90687584, 992927470, 996542641, 225889349, 222587693, 698307677, 26140986, 784250216, 267233503, 60936214, 410743698, 449066409, 903325856, 322827976, 792800245, 881096689, 918297828, 542550835, 698614673, 451396308, 368997572, 979158492, 589721370, 440079381, 939945862, 293388177, 476175676, 989150567, 543950449, 769356492, 121842361, 538697859, 995490307, 427815317, 626509600, 275806743, 434144640, 262728736, 32190587, 854499567, 472762127, 963005240, 914738084, 287317604, 573638192, 421131499, 381157205, 230431737, 275458860, 150187491, 204953565, 304577882, 631267136, 187877068, 945933055, 477662364, 134988972, 907446580, 592200622, 311569364, 357738776, 998623491, 983082280, 968903061, 611072664, 205347207, 580654246, 835532914, 589687497, 909449096, 20935542, 457217198, 491698089, 202644816, 81077389, 846973073, 273357079, 207721218, 257001127, 958703733, 106043656, 538495542, 511145655, 962692982, 352127529, 93580435, 692376431, 668737940, 183941612, 49837630, 731315857, 197168843, 352144845, 506513021, 503970341, 224321945, 46322820, 963806490, 536977711, 612105759, 537965413, 38847259, 113237891, 512058976, 547417325, 743719640, 929095934, 131732406, 847518246, 937086742, 973674223, 601243405, 810918792, 813304598, 739884018, 49147964, 54945803, 125374840, 583267566, 764334094, 962367191, 708121561, 916580948, 247330993, 640680661, 94566748, 96817957, 233780747, 410653224, 864494569, 364301213, 83012652, 517205672, 426144724, 212009812, 718984621, 573491999, 864288807, 774435881, 418043501, 287830170, 122813150, 399080832, 561893134, 810433325, 624437637, 43683655, 920990410, 761588457, 5929915, 501999378, 837240346, 116915600, 470698717, 885786007, 749873332, 696670459, 197112293, 704696980, 428337317, 688353983, 181536967, 924343916, 18148356, 974079903, 981877249, 143865689, 254451039, 905101152, 743353007, 662270743, 54184521, 71484722, 686192837, 400502772, 431527031, 647327973, 903585676, 752160660, 303737394, 545602734, 978829849, 243036636, 921334221, 982753833, 452962424, 793957994, 130125913, 553293190, 114555372, 624677572, 810816862, 198197982, 474192133, 798324399, 237709423, 349588652, 279645383, 913382256, 71293937, 440776795, 992449482, 681254016, 247035043, 621853349, 237982138, 370190824, 565326974, 816124993, 991280932, 247745035, 389207750, 973675204, 142201632, 596953568, 409235322, 786971959, 567248154, 797398862, 748126685, 492029607, 869849088, 103832552, 982925401, 388236036, 700802252, 462722249, 295764793, 432156440, 87252336, 978404917, 279644149, 52128006, 233727008, 116818673, 21323443, 335148942, 340493116, 755880468, 236384079, 363304394, 159830449, 458480617, 483437198, 795262405, 261379825, 321947057, 659316571, 924108959, 207112692, 580339413, 685070536, 904497780, 817661563, 942928916, 518970302, 610943286, 388326967, 248039767, 606645385, 405797780, 218260718, 569245356, 838890325, 862448791, 420055193, 889929622, 312556153, 715530133, 157093240, 211748696, 870394365, 278754193, 57780127, 867919930, 725175898, 446198986, 482739813, 224731710, 326021778, 712239752, 874418387, 819849946, 349634452, 371363868, 15068087, 292631152, 46655874, 884191712, 808233795, 882686212, 880101290, 948485162, 436484433, 344867116, 919340761, 45964043, 494048203, 242916101, 898185085, 990289696, 895636314, 335728325, 639764796, 178451461, 387738245, 939112765, 405638860, 260160649, 334422926, 787792314, 734060715, 716446050, 387822203, 352728343, 707267841, 472565511, 646748158, 408502436, 402524172, 909809065, 337739192, 149433203, 629518512, 364350079, 906067810, 301316119, 22519887, 609076862, 329318412, 222903723, 192319192, 561612654, 657010639, 872713229, 259792888, 368383239, 469139659, 770838847, 527292355, 546492521, 249814918, 412359095, 418304604, 145124018, 184897588, 759362067, 424173623, 803811158, 438884343, 793227300, 911562664, 128773676, 88075407, 256080858, 337733147, 405375826, 952302343, 465453117, 637453413, 59522115, 953710956, 178223073, 509201999, 384796276, 340827312, 724033228, 648398647, 764749989, 7691524, 268883614, 726200738, 790363458, 163234576, 980932739, 485347221, 9501766, 884406147, 679921443, 246739651, 864324046, 601842621, 612545934, 744645769, 668811877, 687625126, 306131768, 649445217, 121694244, 466249364, 564974407, 865997, 638040307, 559768020, 306105440, 291987153, 978801326, 342907459, 372230598, 348626476, 294771142, 89609539, 410134279, 236854449, 384997951, 157190076, 54676408, 543322515, 379564305, 206424112, 218880549, 657175320, 90879541, 631032936, 868144783, 415867004, 577701991, 897638201, 861996781, 424167318, 246924552, 269515001, 339967367, 817477559, 195962604, 61088570, 459617793, 555383826, 161591582, 914620268, 719753943, 299952796, 721756184, 663735613, 767545275, 497076058, 995891990, 940544546, 642951002, 19187792, 539846558, 747738362, 304318150, 109603633, 328643822, 6334334, 454304234, 620333433, 958482083, 829335015, 543987775, 942221641, 65395104, 809243864, 32171646, 848375333, 52937571, 561600628, 713140960, 104705326, 840947407, 77380374, 421187709, 257725900, 630497594, 109155437, 13496256, 7027641, 847261075, 469542354, 482691327, 541271750, 643965167, 212614188, 740096501, 724492318, 951706084, 255081134, 997385736, 170225504, 195701050, 826798081, 897334106, 924983957, 531672707, 500622748, 193127076, 923378497, 489452936, 190324202, 885820526, 123951688, 572354792, 230851608, 454458933, 103945799, 19742192, 225004856, 754154749, 668052526, 447030515, 458330384, 204481567, 742389942, 475271841, 799303958, 967803038, 123797891, 937499720, 598346441, 934679920, 492158691, 560166987, 484065126, 251261078, 861848615, 927437178, 58879008, 365326610, 239587810, 969217903, 208273084, 889677732, 327784389, 476776332, 743915838, 893909537, 579898947, 436375113, 163303483, 351473046, 858210984, 975315604, 918199619, 322451666, 401522381, 328592514, 569206933, 681160030, 517443431, 647701337, 126973372, 365607183, 275640930, 603949359, 272137161, 137510109, 134932725, 729714695, 303929323, 714754886, 797200648, 773618260, 749945903, 346065709, 916592688, 848750809, 858966919, 746524649, 220689568, 379391878, 209067542, 586271650, 646667800, 674592007, 164279989, 925683817, 664992378, 587397964, 556434936, 984841000, 950674472, 817766443, 127469420, 170271031, 445905382, 24857217, 58497020, 858941753, 21622432, 739312450, 866449283, 696756995, 957443137, 359831477, 39971710, 276757105, 721984151, 805619895, 692758397, 703520476, 502005674, 830858704, 568269083, 240705675, 26528451, 562047714, 762514850, 224407111, 625974702, 57551794, 851179568, 442769118, 828423142, 126792011, 65476375, 737862463, 452679994, 804524025, 97871468, 772627534, 143168647, 681467550, 753035439, 178165489, 37360048, 141895120, 69731650, 387557439, 953699554, 365006433, 4503937, 117605657, 128785937, 764486238, 373121517, 366856764, 266018339, 12016910, 57727480, 949875823, 60109248, 937049558, 356253387, 655275280, 148809862, 770690965, 599682049, 959473274, 640470859, 96853455, 343031827, 938464324, 184510900, 396137157, 85852136, 818576117, 18251312, 745146817, 797642866, 959556096, 64472827, 295270067, 400169634, 610269567, 935059624, 178623337, 788406711, 779053261, 887261374, 842013365, 167741105, 186406966, 315749591, 666111826, 788478927, 544039460, 271477857, 780662713, 155344262, 758375995, 699862908, 581282717, 147218367, 716305014, 959760997, 926389988, 929140846, 392260406, 68564114, 15825844, 551604500, 264952869, 776423136, 727025160, 75302401, 298275570, 725561276, 111046068, 158784883, 455990605, 832648632, 192202949, 828447853, 126706611, 218106264, 872605949, 981107668, 788355609, 781408364, 215710836, 931500942, 777902065, 944123306, 761466686, 769152492, 625340031, 352697681, 146353908, 779967552, 555346655, 501672712, 700310870, 888767711, 304734439, 978808424, 839072937, 413472761, 821354395, 433881588, 557823424, 466618555, 628216666, 505991582, 304676025, 778786881, 606553737, 435243067, 230748972, 975558835, 274478523, 273993377, 381162478, 906447076, 874876543, 449969735, 975508495, 221438406, 678510554, 457659814, 348078205, 961096661, 386484980, 661822316, 849950842, 92610978, 988451749, 119981822, 442173268, 107755934, 664577333, 315719330, 584239568, 712964785, 100526588, 702342986, 536630276, 485135363, 426830120, 618965641, 243833435, 903227304, 680776349, 660440213, 592199426, 161167338, 882776716, 877711831, 217127295, 431054338, 322253183, 542353710, 788729975, 259116528, 414216552, 67096084, 803873586, 102400143, 844823147, 894421320, 514914512, 750703452, 355734805, 849089321, 206337560, 285208440, 980480103, 29617520, 720066038, 381188055, 494950789, 921521495, 773068380, 750932270, 260692880, 700345056, 621474986, 782054060, 218288008, 461612318, 406649063, 747050581, 183844806, 324438875, 487052918, 353976719, 532415919, 442308979, 623743307, 867511372, 114428454, 249870323, 978869848, 734637023, 821028611, 953570227, 403176789, 660798578, 659155050, 23398762, 458817254, 778699758, 533556307, 784276353, 104105705, 101949013, 62024764, 144794709, 57260185, 135650117, 306616028, 502850188, 920929728, 129182216, 531306083, 66315988, 508927804, 618669674, 995812656, 174302636, 44606659, 564933554, 712279812, 870487766, 468889845, 477207091, 374364754, 917457041, 193305922, 482477177, 460046275, 958480065, 924161715, 53591722, 686803660, 592435648, 334938437, 848928216, 860114560, 895465398, 388239620, 424655699, 405496470, 848272851, 59905340, 199838852, 306193026, 919210633, 43961359, 611583473, 885169439, 88403258, 650286809, 307424617, 286341211, 195467346, 696715099, 341904601, 936452287, 256546332, 621395517, 617004720, 156668623, 180086627, 617438043, 975296934, 203993633, 447743213, 954330356, 675295980, 151960512, 213292344, 862418574, 338012598, 499325895, 312526834, 128071257, 821086891, 840542934, 418114893, 385213295, 622400142, 506309419, 959054169, 941816955, 621327568, 225500220, 637699723, 191162819, 668110916, 820889868, 732556544, 159051300, 136828892, 112537982, 1049591, 226275921, 569103682, 631937958, 221578466, 792940384, 511107925, 94485838, 595070749, 4051397, 600148491, 974500342, 217343604, 742708990, 21287671, 718505937, 186820208, 844995109, 347071681, 967262711, 962649898, 880825407, 414576718, 402377796, 785932603, 871309443, 954355569, 984224236, 620816823, 60617627, 309980989, 466180849, 784383663, 824074745, 433464929, 762322753, 132380813, 293653208, 779334338, 380711669, 736277422, 520751184, 778899273, 435323494, 374886812, 802486854, 537043093, 198905466, 21874450, 299538696, 884026010, 730893542, 549421630, 911845655, 21152504, 668061596, 98145981, 456789519, 537043877, 384027312, 669336959, 155717032, 520203384, 811119976, 185775413, 707556582, 799094231, 79431578, 974708331, 260917224, 743201808, 574780871, 5437542, 237597653, 276254756, 289631444, 371812601, 103331403, 803140243, 381018792, 607726771, 224139194, 731267007, 637708238, 497652408, 658315640, 51634200, 130593890, 664242238, 602060321, 630844718, 353864997, 579353069, 100958297, 677081430, 279274768, 273432432, 778443025, 604093941, 241580638, 123730917, 464271532, 181067248, 604121535, 22599994, 754842329, 931573915, 218416559, 803372107, 859774763, 193105272, 764926510, 185821439, 891598028, 268046324, 875369656, 776429459, 613845821, 537186713, 724752047, 314656705, 493388312, 8905743, 602833968, 317692811, 747473099, 955896338, 294146083, 403868251, 915107609, 973038955, 362418666, 415354546, 815690291, 880179391, 186539843, 459769167, 247473741, 610701359, 831437228, 301347713, 191768750, 110338729, 909369128, 755811465, 264836516, 161390554, 667072699, 25813167, 94636033, 153191439, 138894764, 290790843, 944438890, 178643569, 733867365, 722419305, 540404350, 625423067, 220047260, 597117590, 210317285, 218923363, 596091985, 495879607, 838793463, 931495532, 150388087, 80243195, 567796458, 233306825, 836982172, 390360891, 509155105, 189817312, 648698670, 107729866, 688106166, 177214180, 816403263, 289510864, 483807502, 797552663, 615971149, 849654771, 366485819, 116456478, 558071273, 288813945, 276976725, 386736390, 606527089, 164856560, 632808075, 188015630, 464508152, 332711203, 887227350, 18839165, 535439306, 251897815, 989127341, 511527393, 666874554, 528822371, 923493584, 812481270, 888467761, 349320130, 641253874, 225338867, 669170361, 101434501, 835231909, 542424022, 582407262, 24999951, 649075563, 774735650, 398377246, 12444859, 254060160, 248832777, 799973175, 880318784, 121940336, 899314435, 996693628, 344609321, 450585720, 334158157, 914454248, 553638021, 175336613, 169342321, 406594046, 754739644, 719640390, 686926181, 12653286, 443331116, 951328723, 682068013, 344763484, 91563703, 132505775, 588088306, 39910723, 642605663, 336668320, 671166180, 194126121, 545792429, 427178670, 113603170, 788452941, 846221591, 366830206, 823282557, 416713030, 794552248, 655075304, 762714669, 664025349, 648690244, 447010650, 480311427, 814404251, 551314622, 652970459, 160818817, 602778793, 810757979, 981892289, 585355713, 291223659, 512020549, 783357923, 997942154, 428297153, 719113687, 354020740, 799818940, 711319465, 769221102, 333389329, 988537082, 535653376, 692061719, 916965284, 926271918, 455134176, 346554337, 150825737, 642110139, 813968234, 990079920, 309972914, 525666570, 597789529, 555873158, 361477517, 84750527, 53958534, 97004562, 129194641, 407863504, 421317610, 882816221, 311060780, 377498439, 528887312, 154987413, 728801668, 879930164, 152261073, 696851005, 797224722, 485830967, 206899034, 11096761, 544671870, 679066320, 728305965, 897208518, 61373589, 687793406, 342303329, 505587565, 465939166, 364388972, 994693045, 348979502, 317656066, 441605598, 691909307, 555700080, 589685958, 613943657, 121529867, 460592831, 773356650, 934048964, 448827760, 60533702, 424619305, 863919174, 566484608, 284281721, 516926078, 156977383, 612086608, 326466502, 861994200, 197325612, 307643621, 672737134, 721959868, 986586649, 51345927, 13845429, 813200704, 283897605, 641764882, 74808605, 636557748, 132251089, 999452299, 693022041, 828291602, 165397557, 643720680, 196265477, 710651969, 578424128, 705982219, 775725723, 113934936, 448194891, 317404991, 902347115, 355602135, 441996159, 117784421, 608223092, 42907799, 583903579, 98987109, 196196859, 688686805, 203778743, 617713405, 416882988, 690269196, 863160343, 489851548, 572206025, 751735062, 642024234, 831564942, 849060480, 143571670, 182367099, 686044101, 250974424, 997578209, 49936750, 701899265, 748501921, 663697102, 424516478, 253173287, 380219773, 874829943, 328857099, 8285295, 645860944, 601054489, 535816651, 490966589, 837717487, 739348292, 780090507, 741211562, 838968349, 490779681, 213074648, 534309005, 602571237, 680364669, 74048724, 652852467, 156110737, 396305226, 120520332, 573322189, 553152379, 460866485, 997855802, 915198829, 906335111, 972661162, 606172666, 103219447, 193012432, 566448223, 705351327, 579582611, 279387768, 956908241, 548837386, 960540956, 457195820, 61880891, 129822773, 890541033, 729212946, 40754628, 498962213, 518054458, 187940764, 974939618, 40003675, 379003324, 669598291, 828413076, 735721619, 68303580, 161112975, 962782957, 805641333, 761336413, 597615160, 246918620, 672546122, 541026720, 300682168, 282160339, 504023092, 819141190, 803916780, 185897413, 234570134, 586760222, 973680801, 891627255, 977399625, 701474008, 80010761, 223723702, 276498347, 427904166, 384264781, 435998967, 429361665, 189364543, 105078895, 968728656, 222634353, 568562898, 548943639, 780498355, 717133325, 415809469, 100938973, 362222048, 57846075, 343860192, 929811642, 715435242, 867758175, 317219671, 963108024, 930237044, 722607469, 646486903, 623859000, 923185547, 610007757, 237695957, 568169033, 686443366, 331100054, 482667617, 902446397, 471781358, 420369246, 63074917, 803586196, 276458524, 96401471, 613183697, 75405555, 816679253, 34033402, 823839212, 431906199, 976388635, 732890855, 984399007, 917231263, 870395574, 310782198, 31255985, 568809609, 659279120, 992192259, 570259363, 821312516, 446391583, 765023793, 440540219, 614113763, 797605388, 955129382, 771128241, 251331255, 459215269, 571153529, 845407564, 668809571, 391894495, 939989868, 794605374, 298588192, 342844815, 136471262, 611057424, 10567368, 853074887, 661334513, 361997341, 76642646, 326278249, 424623068, 310946525, 872621620, 345678837, 840443269, 251072177, 998820581, 74761154, 376172352, 165438335, 205372471, 947599248, 594933599, 323892786, 110732312, 934107551, 755117712, 684497106, 332373521, 966460779, 959572111, 376923176, 168339182, 157030501, 692569008, 356101832, 444559752, 701815442, 999471023, 83565487, 552090671, 231321574, 973431675, 106109794, 389400557, 978698842, 575607457, 333737342, 518132327, 421729486, 489038833, 800984012, 851467040, 289850681, 2682046, 768423857, 879851517, 378041509, 327844750, 371449108, 182527083, 535692937, 170519470, 213085981, 438011762, 146947965, 832195994, 757421902, 294421857, 146126972, 665235827, 332067741, 608291245, 71328629, 104646507, 908591538, 240888983, 449158073, 721236605, 213422194, 264741975, 12517408, 742671332, 45335208, 152731904, 541058897, 309049783, 31396934, 308027326, 446545631, 287434876, 894977433, 879788724, 134719042, 924012622, 183152278, 479093175, 142163347, 697879092, 226906144, 893587031, 182236184, 691837785, 646137529, 585729178, 655647302, 217892129, 372930950, 978137315, 34075700, 899703080, 388196861, 315124381, 326639639, 876783181, 736765908, 934713990, 56939417, 723242578, 664513107, 167427437, 715163748, 510395040, 363679724, 326906178, 403370801, 644422044, 796901191, 446619533, 891551502, 355243781, 639385994, 593289507, 216185604, 951084061, 845477582, 221726010, 542406670, 484382801, 352547884, 369977233, 978332185, 67723407, 181749415, 715553377, 369563763, 364179984, 62953923, 149875435, 729696288, 461254477, 142360306, 995619786, 128180158, 45633921, 711421157, 12087500, 38438450, 953855183, 269043835, 989531959, 197820113, 581648986, 580094700, 279163473, 20699517, 319853982, 170047027, 766433520, 600661870, 342345627, 555334845, 907320281, 612455656, 222629662, 324093245, 793628597, 401682571, 452110779, 839989854, 925348758, 612137187, 907251748, 945027389, 457695133, 698431960, 454882839, 920749327, 121987979, 145731689, 742812067, 901273200, 377318696, 445308584, 654769159, 971819270, 950650498, 841968317, 198460939, 907641004, 118688991, 663503198, 336998394, 906547676, 927912941, 104319635, 322877796, 701957861, 285566221, 296144828, 205096694, 769888362, 666307110, 821293422, 111440834, 572393343, 697502000, 49292291, 56557194, 421528945, 23557997, 790716518, 862547671, 12061898, 935935100, 165797170, 529281400, 389258416, 924981975, 134850389, 264415526, 780895323, 380762735, 414566725, 120808470, 250028124, 878314481, 280482046, 604790169, 35510675, 215776754, 87741477, 187611631, 531541918, 190986471, 244058796, 531056196, 931320782, 5046418, 435237574, 198775258, 493050179, 255357929, 8254578, 586374550, 64450647, 798861546, 30605413, 961788412, 452796185, 438925542, 797651112, 517067610, 375573359, 903626820, 332024983, 598418413, 721557877, 134648850, 142294315, 409380821, 71077676, 687771565, 238727977, 205906346, 251878111, 693286740, 477311361, 642216487, 204328101, 378809136, 135698332, 501293958, 999858669, 756195399, 951795192, 659802489, 573216290, 154277792, 378515086, 45234371, 986077772, 928260284, 286327693, 247705055, 972436019, 933803126, 225839632, 672394262, 59244389, 538566909, 342152601, 360604800, 244575393, 309412647, 58016929, 155510656, 904633120, 885103746, 636008381, 682853015, 131878307, 574863962, 381327427, 783937115, 3073240, 753915855, 120174123, 11183460, 448523721, 223318412, 696229110, 391337329, 879133223, 886459375, 43334606, 603398800, 169378545, 321119632, 563650026, 359960607, 478190633, 967812347, 670734819, 965697399, 322269337, 935879025, 309937574, 835476159, 140304554, 508818759, 235889315, 290880868, 424595930, 669385053, 606199577, 946151756, 486633141, 542869934, 194733517, 678230302, 590327166, 180338630, 967753599, 364867250, 653265840, 626306663, 653821258, 790569169, 370028191, 58053464, 623810120, 310582804, 812919829, 340760981, 929809532, 156593119, 775965862, 450304838, 940328811, 540297388, 566030216, 875008671, 424442756, 366130564, 215030325, 781192051, 470671711, 341480079, 832986314, 271651497, 971387220, 223225512, 109541483, 98779104, 750713318, 92378757, 6859113, 182333567, 611641187, 606452042, 649260738, 857763970, 670092824, 114256277, 397999546, 270182640, 696925856, 627795690, 612858430, 382057972, 141019923, 221673621, 943511467, 897913880, 799902534, 853670517, 276015049, 941057534, 323786935, 565205033, 73897872, 690051821, 272795635, 181133081, 761146177, 998152620, 894449856, 55662529, 680673704, 418409816, 282446005, 320970167, 828432036, 544727516, 656296779, 897085684, 415644642, 410794140, 683325877, 348548182, 606019032, 214287859, 956395855, 779859894, 950888846, 446009650, 578512862, 772122554, 155458250, 48323652, 48904626, 300741321, 941615327, 816132500, 97988138, 386453479, 971074259, 34129137, 74856043, 556175303, 183767995, 953938141, 140218999, 773623377, 705437697, 553277748, 304511793, 464777142, 307453946, 965946081, 628458057, 444393825, 83204046, 554215230, 495225563, 673740304, 343313388, 822283656, 382551260, 842139987, 154741685, 998692997, 431490745, 666332010, 70840739, 344435595, 503814180, 361648899, 69673624, 396106029, 919287027, 237443506, 129028322, 649632673, 643091982, 863778016, 714495174, 294974369, 369205787, 774236615, 959847610, 313259742, 328775789, 83149703, 677475830, 48346173, 303705428, 428390714, 852899250, 181280105, 275088947, 364313094, 170219768, 985825791, 609582807, 836674014, 331615886, 608846876, 487840278, 332385535, 982096843, 833680889, 167818654, 149659478, 395058685, 720131343, 891595156, 181078893, 710531531, 528985133, 541603490, 295430049, 793269684, 435422980, 192649970, 389608300, 332764541, 670598120, 375747337, 919545420, 120339623, 857125658, 366371305, 488435609, 745524541, 500710969, 372503141, 555409562, 416611128, 824166430, 5366239, 812407106, 389726338, 132835448, 657796922, 487766040, 301891684, 674541748, 907499268, 20493847, 512509414, 434051534, 97328622, 648713540, 748361958, 312096046, 460977171, 520157474, 823534440, 118902406, 352196258, 545719025, 685397487, 611547958, 579246881, 623986621, 801137817, 514798694, 870554525, 765031680, 887626602, 830417326, 327602502, 375943900, 391392680, 97070941, 924099829, 856027264, 466058750, 242723160, 958977794, 772178302, 578882834, 537868354, 11175285, 265160163, 216901078, 864082709, 411321312, 175156176, 916917424, 658900903, 983235257, 34835407, 636893629, 280803227, 721419129, 272461144, 302856333, 403501096, 288669606, 166571990, 916131185, 46162351, 430006993, 114653498, 288799765, 899578561, 275549129, 569652145, 324701836, 1875303, 482716120, 610301647, 627794615, 487597851, 717844277, 697810555, 788719125, 116402961, 738975643, 973484900, 536322670, 557256334, 908277164, 685673762, 906592163, 218820863, 826513311, 274694662, 315775122, 61354141, 35465867, 889797638, 750329664, 247359149, 532503412, 502564790, 350479125, 896668487, 414950330, 66456487, 911033631, 260714817, 181897186, 202561872, 659860146, 852560796, 214582526, 368642735, 298786189, 238348637, 114491395, 199581978, 919899234, 717936090, 357843640, 42839688, 616869572, 761002970, 249999570, 889837565, 41815749, 65547404, 866345401, 432242203, 387014628, 497578246, 224908865, 181826966, 995061775, 620398167, 560954585, 51454265, 415167881, 708656130, 787798616, 98440804, 8858604, 357618466, 79457452, 111361879, 970301626, 216452259, 629158998, 671704115, 171998451, 16400126, 182899640, 800823797, 126179484, 945175625, 752939346, 486262078, 579207771, 60233303, 934324250, 477164241, 704773734, 968726247, 231838489, 199168586, 371867382, 415458101, 950943820, 410206779, 407288493, 582075807, 721761189, 830502828, 399803303, 955096460, 152924116, 20220866, 161722301, 388201078, 411807067, 859342636, 987323727, 53031590, 805034595, 330356368, 575723296, 536743629, 543626306, 521729886, 206765919, 785991466, 580096849, 521515133, 434562047, 556307588, 939322682, 817297046, 794833872, 384556647, 4313793, 458235044, 455404722, 925745644, 628283037, 662188194, 507617991, 774944185, 828570107, 529834394, 42713807, 69430001, 716764644, 230940883, 236469759, 666626314, 664376059, 699738623, 547776724, 489613746, 974181104, 774946431, 682416961, 265235444, 797621309, 877510381, 772980288, 821331446, 669985597, 227736732, 707456213, 387789135, 921484511, 851853396, 192041143, 161882318, 303050777, 784432021, 322640723, 939681766, 429009550, 955890862, 468996983, 41882248, 897001964, 618987720, 918771425, 437932275, 959996704, 171013700, 543958350, 768017712, 648073123, 426704184, 292680221, 657338124, 53855757, 732369515, 823824844, 936723658, 243365791, 734170736, 268921794, 238745686, 718077499, 340336555, 193048826, 939051858, 401680815, 776495511, 37811560, 161162867, 71891779, 932714216, 484671645, 125311421, 366648980, 967835435, 594226713, 452726897, 397078953, 459942300, 645922101, 370982862, 178327433, 740961494, 247235985, 489273009, 640398526, 448972260, 300308494, 92979829, 730202887, 715176701, 442607006, 976015976, 21512421, 936079806, 557395777, 213111955, 154457733, 343863899, 369675646, 560377946, 821362058, 198441120, 34506, 219156442, 834328434, 413242828, 133264799, 782538136, 528807922, 262796359, 243445268, 752862591, 913668985, 723762954, 782149407, 105155413, 547863054, 597081252, 117111390, 48996982, 381258190, 240176444, 870447696, 71297629, 80494637, 337682441, 299450100, 641691928, 855818562, 580974128, 692534427, 258924276, 121369905, 645227762, 412094442, 652612758, 5609803, 683296288, 9128385, 228792651, 955482721, 732616446, 26817283, 578985578, 94866638, 634428239, 865265271, 934888072, 41188567, 889006559, 408000921, 130754530, 665767456, 99602089, 19951446, 615721558, 518219227, 628630694, 556925096, 903825149, 32830901, 295429912, 164155610, 85515511, 329495171, 653717766, 867037956, 868811889, 503736078, 143056487, 815541232, 580572643, 851302550, 167949182, 706801509, 978664598, 974272189, 59904777, 192789922, 222206199, 22694988, 224897925, 808194159, 597868072, 978640002, 153235535, 433571529, 919356097, 217312416, 797795321, 846811650, 291409879, 247848910, 824317636, 559318742, 841447317, 211146269, 969170505, 868378846, 774870779, 745335720, 464643032, 819072204, 605020134, 151522012, 18157212, 602221834, 981629953, 856875383, 902025912, 893420676, 774686948, 20074112, 996679551, 756325216, 266057955, 35550994, 413361283, 868158324, 516666393, 638902791, 574967182, 497235205, 607280129, 559452937, 484464601, 753525929, 195090415, 860429825, 760935235, 279313873, 98758199, 184961688, 966458707, 786786025, 638471228, 255114608, 401817915, 677990793, 38968704, 576806925, 717117419, 714212758, 625281086, 994805658, 362286692, 545667352, 897088601, 281752189, 700771217, 190549203, 7709977, 364917112, 61467411, 508754408, 665606228, 734674823, 459278667, 41869865, 536351162, 126761771, 640637941, 790410062, 132693434, 559226521, 355658466, 383098232, 648955790, 210894114, 221663872, 204857886, 519399668, 574824314, 748532394, 933844992, 628084076, 82310208, 166091775, 876796838, 796421679, 267193022, 338431147, 502521184, 685215617, 981566971, 131052398, 752685943, 12151326, 91367253, 282218295, 886922080, 642362925, 482556015, 588730177, 638788591, 126886894, 51055613, 916571218, 997565145, 171128135, 22776854, 855461297, 425920701, 488000072, 697492469, 157943966, 150884971, 625030658, 282464407, 230756062, 657468927, 544656639, 880543587, 117783684, 199314509, 460609045, 200266911, 652160962, 326050354, 863783819, 355880856, 475342627, 510934703, 272076972, 266881173, 892110553, 953125345, 189666092, 718093968, 441402075, 800280757, 47727750, 129587245, 603995551, 883782484, 603853440, 877371209, 374237467, 76189334, 211029409, 9961218, 171974100, 569244796, 776646544, 323590865, 935751798, 367183785, 918666532, 998371396, 109672162, 597171037, 837895739, 242141100, 997673183, 965715293, 530946749, 162122103, 597710444, 406211400, 546903222, 47482574, 39854599, 99056203, 659394165, 825356380, 655099454, 537486204, 984678319, 229129836, 314970894, 379519867, 376500377, 2734131, 878291775, 102364497, 263014209, 488443588, 899838615, 791732369, 645638, 496098463, 889467075, 379407716, 104010431, 391792954, 215478045, 687761543, 85469326, 712878761, 585737540, 974802858, 54681702, 256988701, 65391111, 29581851, 397966530, 419820542, 365301768, 144512771, 31330663, 118580966, 431017042, 519379876, 25468884, 887632435, 942010027, 360869422, 712750589, 942730832, 914935629, 584981030, 342202287, 908759822, 631383359, 598502981, 445720045, 872305194, 125975331, 740894874, 334000455, 545945098, 498712720, 874886883, 689524010, 101384559, 495440000, 295956827, 285220180, 379111771, 609119657, 485366008, 913694104, 6432647, 240833940, 906361622, 125676768, 541222654, 190913386, 446198045, 276352106, 213930628, 661712241, 500850579, 454283711, 218360594, 845910646, 990919068, 958509152, 977598256, 899741200, 380851268, 332875603, 862190244, 332127660, 228506317, 824721350, 869994422, 38469217, 619595089, 231146114, 846278251, 651334560, 61745902, 56293196, 991703862, 610698607, 881959700, 152650584, 167470984, 857517335, 863802000, 208389484, 918737362, 401613108, 96543939, 881675548, 662898596, 35887940, 536427009, 366700501, 560039213, 346010475, 534359799, 74814220, 136016333, 268982872, 95334056, 626238233, 49234339, 836191625, 85270267, 825533730, 925050071, 749139021, 464862952, 270579900, 162481514, 892564544, 352538413, 299769746, 995493562, 982483625, 763203857, 489391816, 977136474, 855206923, 351333533, 457457881, 796144834, 844933990, 406817045, 896154628, 291828623, 124626303, 704072722, 599689686, 734986801, 759298696, 855274637, 415553743, 352432042, 427832384, 204482402, 842370057, 488266181, 886074269, 331485916, 610402842, 8421782, 71550749, 569732184, 35676466, 613015975, 520021951, 36176070, 426375791, 747246671, 111335976, 235226998, 582869707, 453629810, 896572081, 558690138, 942263581, 740790959, 818087652, 168892693, 538441898, 958126894, 788138033, 38021837, 441176021, 880699442, 761410910, 936187203, 772309929, 513914449, 513480770, 721530727, 610093628, 242397651, 817941805, 182630312, 888991455, 248107655, 663223443, 712124787, 513013991, 624095893, 815061418, 73159208, 7706082, 458674921, 500371387, 91210508, 910997570, 105670515, 412184099, 724827775, 40120972, 493126822, 203011614, 206582178, 654042240, 705567112, 150357478, 715583359, 765707640, 552964791, 701221243, 915881294, 541505490, 807417232, 591418788, 579270824, 337013027, 613955636, 814770055, 924822373, 909985974, 453455575, 646477281, 226216681, 486050987, 422293017, 2249929, 129700608, 820773188, 636288786, 793032226, 401804190, 463272559, 284209808, 174349244, 485476502, 647638917, 445659117, 39294662, 62982554, 546329507, 196545713, 820684327, 415666712, 12249220, 898148911, 629233639, 997687652, 461568211, 646654681, 998438709, 977879928, 37310730, 273179882, 399953671, 237759036, 244963347, 854280601, 787136656, 980394210, 23062030, 886804023, 864803764, 349111759, 519202482, 549464397, 56722991, 453402899, 125513623, 716910249, 117439089, 270029520, 122788977, 94455493, 163429700, 154922960, 864303749, 293158627, 768681042, 233764689, 183718324, 795839253, 459690398, 275094600, 440051788, 568962983, 120363596, 89404401, 187287076, 88369214, 328044304, 502859655, 267418462, 240136666, 782909165, 149409029, 282180906, 530898266, 868359677, 709223248, 808410597, 774348475, 450494921, 927491094, 411277643, 602833832, 217165643, 303926428, 304662933, 549316418, 822047953, 346794017, 520120478, 76006874, 905245409, 770998174, 605183283, 792757634, 252390568, 309752560, 965092876, 856878629, 614044968, 107255787, 578932079, 571331886, 605442081, 128133446, 986102879, 941024347, 737840706, 355266618, 98982465, 94443997, 591165911, 896903334, 874782891, 192301980, 465197894, 794089596, 575000556, 715467954, 136376098, 377554186, 437570472, 421285140, 614055916, 954097559, 88385723, 477946493, 85359008, 896532414, 952143562, 913743321, 273051884, 953117319, 919127750, 918338193, 346368672, 261637799, 12596175, 170457798, 489629174, 528571099, 284337232, 681775278, 220942216, 211048164, 805863378, 186661080, 797773280, 318386637, 590491752, 490544201, 311863015, 85111644, 295091475, 563474663, 620007717, 123619539, 540403427, 292892020, 59767959, 941823564, 898534721, 74972849, 515111087, 816363688, 600576606, 847267705, 453583633, 829859999, 780557216, 216727741, 991680065, 918096425, 924070845, 833442320, 266973080, 887494457, 767028792, 466673730, 568004457, 511541280, 985467994, 817292247, 204892736, 575542004, 634750167, 331309678, 484660623, 722752126, 391890763, 922823327, 898025275, 298680979, 416516937, 288331737, 748340664, 509638944, 296185364, 29219003, 723934617, 541857361, 203566719, 862937809, 696788190, 49247855, 126150316, 60983205, 440754328, 742981627, 989933843, 27821279, 308529813, 22914275, 258302594, 18178707, 46853544, 1181600, 768387399, 438212715, 774310024, 444080274, 646124814, 395132897, 100417574, 962192128, 131728146, 627940101, 100366944, 713129566, 944764075, 200464964, 739103068, 344038735, 610047213, 701287369, 903568819, 313323950, 535662853, 279796379, 218517822, 949794360, 64927840, 463231251, 120137716, 288956921, 237661404, 89242909, 970629087, 842440273, 605066822, 499578419, 61069518, 313895898, 659824381, 164728630, 873955089, 311709085, 515420883, 906278198, 82099986, 967713274, 96205998, 239512011, 879725606, 809077756, 489521574, 846049429, 363473544, 777174350, 246160151, 487499869, 259953945, 172500635, 225959881, 450616805, 510264962, 207179545, 612838384, 663371547, 148192277, 211154407, 518692749, 124545033, 394652816, 721547392, 641818392, 990393905, 111377185, 304108744, 45567288, 514587986, 400166681, 165707015, 820190354, 181085374, 959845105, 111795513, 55678706, 618398555, 497253187, 45605536, 364338780, 369678872, 893684258, 975705028, 970586365, 602606639, 372671867, 207379626, 952709935, 599063284, 420356329, 714415327, 341353508, 831055033, 490265677, 79577520, 300133658, 937419701, 678745740, 258711607, 775393918, 432615263, 667803563, 256225563, 177407930, 849159109, 624943823, 37472777, 270044765, 724591624, 726191123, 849506690, 935924777, 406132317, 986681876, 176621041, 932324674, 583610771, 267871840, 608945874, 186939818, 220488045, 410620497, 221505836, 556039966, 490254916, 672246921, 769135886, 187750095, 664164235, 943931876, 158434042, 461413139, 562886231, 807362089, 802883597, 197797504, 754795957, 681166908, 884331161, 497297232, 514101013, 19322175, 618283278, 558780138, 667202655, 65377942, 849399315, 40393723, 489340549, 693415998, 562519129, 161726220, 773776585, 701416678, 739674570, 64561871, 91123456, 852167389, 932450825, 297818200, 234475595, 821273069, 483728185, 884861754, 866964731, 436244389, 872705141, 820325921, 970490340, 881285243, 337883382, 89925735, 235514996, 325386555, 770610348, 368011347, 803772330, 248352060, 693070213, 472077851, 444392557, 991054122, 486047932, 303724307, 537152416, 259943100, 141803930, 819595337, 689813006, 778198819, 763911657, 247551929, 690613519, 101664425, 131360888, 453607478, 735828635, 662575524, 688398363, 90559166, 340150542, 423196080, 540467296, 537374017, 892928785, 835033107, 552876757, 286926525, 986107223, 752993896, 958448042, 327233717, 359112570, 385653584, 842972739, 776501979, 18104642, 160385060, 707684580, 633479551, 67647524, 547488471, 589035811, 419848852, 478759389, 369346904, 561922552, 698500351, 524461787, 459046739, 910468843, 126400015, 565659092, 82037722, 915088525, 297880940, 206209059, 908484388, 604230379, 829556181, 542662522, 898987860, 40191259, 875142109, 503522286, 254296255, 241146149, 325665955, 763910334, 695862180, 968203137, 234479287, 330483900, 575071469, 374891109, 784108199, 192597152, 242290024, 601888980, 525169690, 726352551, 201179018, 870462828, 936907288, 848868950, 830854190, 463397249, 581121361, 141406375, 732944368, 490901336, 594182774, 802922057, 384112211, 781662447, 119997329, 793669815, 691726768, 607969807, 677060760, 576438860, 611011946, 110471899, 149864250, 913709964, 486517694, 649017642, 358235726, 296900258, 58532591, 941723000, 965696822, 577728411, 401414047, 598575634, 647856539, 663140925, 449481097, 674923258, 137271464, 775919799, 258411214, 68203322, 282347964, 850585522, 903101584, 24959103, 443352448, 354729085, 832648433, 49374045, 392330518, 728211710, 182413330, 391995757, 607346067, 909800732, 478672832, 434573454, 719637033, 411108495, 820428871, 260350919, 182098678, 228610241, 351157864, 403841297, 908651127, 882803715, 374526239, 118672016, 165760893, 789651238, 382962814, 562232793, 961628604, 272915418, 689530712, 920570127, 842264975, 841065907, 860757110, 128034092, 850669852, 110794576, 665084646, 509703692, 610034547, 360972453, 553445413, 930918931, 159171900, 990901982, 78771224, 59472441, 635811739, 790071984, 397940865, 876092650, 423444629, 732311259, 549091488, 108137908, 202921774, 218700159, 832642487, 43269794, 989270889, 718241021, 127615937, 139926887, 935896405, 758234537, 475788598, 169263000, 49125704, 822146801, 573644950, 442597256, 996214571, 481894304, 374077415, 623323621, 362558940, 401759374, 418054881, 587485421, 230255758, 660706953, 810336583, 667831603, 931978600, 839607241, 161679446, 240035108, 467731865, 154486255, 723315568, 839235424, 256785806, 760536420, 33803110, 192506274, 223852875, 529360529, 206869251, 350132520, 903639860, 63806530, 409749151, 688602556, 479620684, 938268852, 381587169, 507117108, 463262022, 502838094, 644466975, 40696189, 694765527, 809916929, 760161269, 887322913, 593890842, 653153090, 412592034, 871467547, 264486814, 733605727, 141949967, 337464542, 645501081, 7469689, 214384560, 14857835, 791017096, 712899065, 361363806, 485761894, 286782314, 746609125, 191219081, 690667356, 997138745, 220786241, 144322973, 260185340, 637952964, 605025724, 309778930, 13612529, 786919891, 959154690, 211367212, 603927587, 925642117, 655734357, 379418304, 140705590, 239318807, 896725833, 105895411, 719657099, 817538231, 917510260, 404297148, 342052778, 99664271, 822021542, 782911485, 829578635, 422622994, 578844163, 307718594, 653604290, 166447569, 480186123, 974800839, 409370970, 177258110, 928780280, 825678675, 120704749, 216253185, 30491126, 55686430, 479215743, 556126272, 738595021, 392320548, 997526018, 641049948, 855362851, 402165421, 462633546, 810801052, 154113816, 204693370, 254084657, 355234513, 48936676, 771162480, 815287425, 897224087, 242009197, 264266675, 266762272, 884191042, 809316125, 977005006, 319113355, 254841611, 101670946, 713132421, 21246347, 232202734, 70743067, 982900630, 734903269, 22044505, 118370918, 712458797, 775278861, 287891339, 656435065, 248856919, 945780412, 242980157, 653925562, 85295515, 947724693, 151862345, 339381788, 823930155, 45928557, 158809012, 261864433, 362868655, 739157771, 842202781, 719264690, 389711557, 714680331, 575180873, 970681591, 296536976, 946873692, 439135465, 535258906, 830036044, 529299606, 179030099, 676325812, 442233167, 816326706, 227571041, 508588381, 425677642, 272859900, 584090990, 823425104, 108251378, 35393044, 735722675, 569572330, 739034846, 95104518, 105118590, 437624092, 204320639, 367619462, 944055750, 412014079, 468590898, 642203243, 47685103, 544226928, 247611971, 827425988, 39325017, 47129994, 181201063, 994586033, 678618108, 18784887, 725061901, 585550591, 396029350, 828659323, 786058547, 392560770, 957717608, 235435921, 748618747, 189711292, 338101916, 100719775, 657928019, 475025317, 805615630, 365767506, 341040255, 986081292, 795686026, 68277830, 395511826, 987690332, 78908092, 487531130, 625279746, 610700210, 423266215, 799687667, 341748849, 936751914, 290839247, 622046678, 464751879, 599515445, 495133455, 798346341, 757045399, 859131350, 993345629, 240725577, 780633092, 968090404, 860885912, 19009871, 391226710, 670973103, 455031558, 656217305, 48738498, 72880752, 642260823, 548860366, 287783201, 566879307, 543191896, 384897831, 417313809, 258715830, 640126796, 127346623, 353599786, 938831811, 567460640, 681661720, 98197160, 623462160, 48437687, 471022373, 199813687, 232987646, 916538808, 531204109, 935396801, 580113697, 482815540, 692068381, 642488182, 69405993, 750708940, 842755980, 845214576, 873852497, 168757503, 860251831, 522563157, 382948208, 415713204, 706469291, 316985248, 984415103, 523964364, 405108730, 773419332, 424291106, 966122190, 73107447, 506033893, 183709106, 727847417, 47276338, 959965002, 19965223, 720702698, 771834989, 254639884, 595399353, 852876697, 771143866, 623947516, 136997554, 586911350, 851776564, 122321397, 763743599, 418844540, 297680258, 845502205, 107682133, 529169112, 639274253, 746587956, 348641702, 251128694, 547209084, 764967630, 444478026, 803548347, 23627958, 856688354, 754096726, 543161213, 823216755, 670381491, 370449452, 803622136, 45059433, 32145521, 717768310, 58022780, 451709279, 981572435, 601655762, 891376419, 94312122, 23912700, 95353728, 763806128, 952495681, 156244243, 756914609, 784411323, 202556518, 930716174, 599549141, 60218300, 826104829, 567497533, 934877174, 81722768, 755972125, 115555925, 648536099, 152070397, 244363421, 486061823, 230120970, 127886833, 365350643, 549997145, 735738218, 255680375, 897335901, 183403863, 470446547, 252325426, 314332986, 347184720, 664566840, 893330177, 606302725, 753082855, 218215186, 639747578, 817303649, 499015416, 147330720, 745274416, 642375564, 837273276, 122690822, 930972614, 602319664, 469276322, 577570739, 411801223, 967935435, 146393507, 878916051, 349593077, 793158028, 324923405, 211115344, 151534611, 430924690, 856988523, 258076135, 937598403, 990156049, 916673953, 483518424, 572121392, 894334823, 286799694, 523577995, 359688573, 215536287, 686118986, 743266133, 886877951, 366292601, 139208573, 775558351, 92126077, 986434048, 891985650, 59739281, 969829945, 214449121, 514230747, 511348609, 440592635, 911754332, 774118431, 122004988, 370262905, 368187860, 864426303, 901595776, 668153402, 989047088, 81246797, 32911116, 373469823, 706784043, 249110056, 201298110, 703710721, 530330347, 840358924, 958024002, 980752409, 490099940, 666811916, 565845466, 200254654, 125832463, 935820946, 438399248, 91439031, 186188725, 191319221, 976606608, 410408730, 942747938, 454473085, 430072132, 662135949, 617869325, 651217295, 933156436, 658762357, 917232243, 927062377, 680088339, 757343473, 365886413, 548201019, 127801987, 568122934, 540983911, 804933115, 384455726, 17338388, 691014662, 214552631, 610110290, 69501234, 451976583, 380976407, 35939840, 250989993, 103049635, 389515567, 462267674, 753288958, 826252515, 105362110, 575316855, 109794507, 604229891, 757746884, 598508197, 697259255, 955333566, 330353071, 692393726, 106123547, 276740439, 167003472, 441232952, 792650645, 780924630, 672708920, 839513530, 650685767, 130983002, 681975328, 438720531, 290197336, 474530415, 737942224, 597568975, 870904524, 507667504, 144116508, 238581339, 709628106, 361077135, 218375510, 990008569, 302542060, 954910460, 434734411, 988861394, 827841299, 753323071, 677753895, 384890391, 970249243, 5684819, 708639748, 337604621, 125925772, 396670209, 449015229, 132038103, 947309122, 744990831, 64637697, 598832879, 989374093, 20413771, 604756376, 384773853, 386810965, 671114203, 634961462, 925857820, 705282643, 367295840, 145048421, 922701027, 773769150, 782971635, 394815901, 989225040, 433751793, 569908864, 538455747, 193148691, 927572728, 957743304, 108240065, 557297364, 360043940, 249106095, 642362712, 214312667, 191487936, 38547548, 360282552, 17429904, 310057773, 605860315, 726410925, 695098802, 616775376, 543232182, 377137399, 141226165, 53260744, 780338309, 578842027, 713326978, 77467968, 960283102, 876528311, 441552188, 741525263, 769981392, 889301557, 812228436, 690823698, 282610301, 254694533, 782885110, 388383827, 309471821, 99753629, 284247671, 494463472, 224883599, 802500841, 887938160, 490928788, 499969063, 190236327, 596161321, 417001798, 142815922, 199300343, 586735204, 870638977, 970706279, 887457098, 111295247, 607983706, 291753137, 944817366, 773720300, 874265397, 103225335, 128827561, 400185926, 866960681, 44854643, 211403946, 807234475, 873716485, 477614456, 264899306, 440517955, 48261538, 589417879, 800553288, 831181592, 367165316, 29623233, 406643420, 669231402, 405149396, 652412997, 585769236, 752757523, 360882866, 845555393, 186870187, 280271358, 397698736, 128266231, 586244705, 325048709, 957490036, 122290529, 450522778, 896021616, 275148968, 685886191, 505704380, 632326401, 252493045, 945058381, 413983162, 471961021, 357644870, 498938314, 910493505, 886575651, 564352957, 234898223, 409310563, 818932703, 282785851, 922365628, 737463988, 303161415, 994451345, 701615247, 219467063, 437452354, 719199569, 362864980, 412183023, 596851534, 677895891, 226651995, 789764509, 99841359, 475282377, 715041439, 101858926, 451723557, 492845000, 2166975, 813278644, 693973776, 521258661, 979428849, 934799725, 916892106, 851988654, 167492310, 569646609, 868960030, 41739645, 357973448, 295853823, 140714904, 194119932, 337048597, 702603568, 847346661, 190601064, 895948384, 224754313, 418518109, 981323382, 294133830, 823055632, 397991890, 473378307, 141285948, 662992452, 776754892, 491509130, 305737653, 194880251, 121002434, 522628237, 153352241, 720358249, 997079372, 254823732, 650841617, 99254067, 459373534, 772873472, 133016237, 219850174, 578290976, 492649613, 326644546, 962777530, 67243532, 85986572, 87432079, 726596102, 785075685, 458522359, 514131633, 375719348, 314487505, 707919398, 27580423, 737831494, 326487232, 525522642, 330489361, 908216916, 469829244, 481168589, 705523539, 256955957, 309656987, 545627025, 272688538, 752133894, 950370264, 45274638, 451098207, 231840706, 306491635, 231113409, 662935757, 640416520, 237535951, 174785989, 758206336, 347644252, 679446179, 264929886, 642501607, 481506808, 23628327, 291058712, 965651629, 381486673, 537097824, 653853466, 451198902, 230377753, 668301496, 484356968, 792015416, 111012448, 408169278, 63596556, 107102101, 627592637, 255924270, 511224702, 782691457, 695259502, 570538058, 732283482, 376559037, 439100794, 244754188, 366143769, 273609987, 808720975, 546582334, 171726757, 938391125, 510178963, 633535554, 112063058, 747936247, 842498857, 317974426, 510561752, 602927847, 101710097, 98103696, 896871344, 626853136, 126861317, 260231362, 447838536, 159020861, 913919612, 987123586, 635289087, 295129770, 305075231, 26034737, 720721231, 599981870, 221055431, 979274326, 79333886, 869096114, 64033632, 672899128, 599528099, 340536125, 689804090, 460497644, 735875311, 576947850, 943540289, 752972354, 236827714, 218216776, 244219430, 705902770, 571093803, 938062929, 382707828, 820036499, 92782111, 497537599, 894225719, 303397587, 558605160, 369869866, 765610672, 443709139, 857158018, 947508188, 291686865, 467030699, 31015130, 794279782, 405061695, 480931716, 297701664, 163692644, 342985892, 300296577, 848125193, 654382843, 808441574, 136289184, 610873916, 230813514, 785289089, 744103329, 885736185, 28725594, 452032754, 848604758, 102073606, 70721971, 19915687, 687136575, 342804379, 42543961, 31286285, 223555178, 420747102, 379786045, 920855836, 313202611, 18377964, 73684697, 356929887, 372468589, 406254831, 454869336, 338069504, 839453092, 154374131, 382595668, 615277528, 449200167, 172179251, 932394564, 486737149, 910995648, 760406051, 317613840, 378756404, 879091127, 471459472, 748085312, 643842048, 523306433, 176188907, 650354849, 558328308, 737466983, 791329084, 204695618, 104505729, 403184523, 903389597, 648730985, 887060191, 432332860, 558280435, 69016767, 585454077, 724802053, 82251088, 45176456, 116675008, 571452786, 799486636, 606786982, 693218173, 440841410, 316674092, 559993008, 41949608, 674400728, 576134381, 404055, 948208242, 708003350, 733379843, 144527083, 888027410, 36573046, 921658007, 337334541, 704716332, 712934801, 2522857, 523664660, 90014517, 268020981, 104525049, 893929243, 275187217, 742868157, 607907918, 637418360, 384163361, 317845440, 602252030, 459836554, 854416392, 851359783, 823238506, 549419303, 853269269, 149040665, 639799639, 105424291, 793340468, 282070837, 572988240, 206921319, 154715583, 497347343, 999519643, 900382675, 311851245, 245450255, 292151001, 351679806, 799603146, 628787348, 709419854, 533389507, 802467313, 504470345, 913870765, 647938342, 45169572, 895849819, 674715257, 290710924, 325258085, 419963892, 897159023, 10990781, 82876539, 339382711, 818856883, 429953787, 169996708, 72080095, 435899831, 741103484, 227356989, 156202729, 17183776, 34979049, 172124953, 340397706, 680204742, 49946617, 8011724, 708845945, 933467452, 301594747, 440212655, 40817878, 632116323, 683301047, 807548900, 864483003, 748489626, 805723851, 656106740, 99752686, 856007981, 755996147, 141830441, 830530808, 624438628, 772907788, 325117489, 389619189, 705284174, 612187903, 584236953, 508007121, 796435536, 705397227, 708594272, 325652721, 662764479, 246032990, 862301868, 301042074, 243158307, 867032762, 450888990, 964791661, 754951159, 277626968, 615687604, 80862322, 245823757, 343602704, 603127999, 630115357, 717417695, 256170944, 123071375, 406490467, 230272589, 232198310, 859698761, 138602054, 783991443, 875267231, 83026773, 270787831, 75774537, 875224130, 373515860, 77222769, 493121215, 847973589, 11209392, 784349637, 767457874, 78833256, 813808043, 561213476, 429116535, 740704613, 408742240, 299997149, 435832160, 49384177, 687243078, 4384091, 438529485, 828095959, 329871776, 607950099, 695544568, 992808469, 251001709, 708236617, 492251900, 442925319, 644358982, 44148031, 247979419, 92484033, 681928931, 680886851, 415912796, 44055720, 833119044, 158747245, 25480472, 469224755, 497240394, 551187804, 273751205, 643077600, 543929101, 623380891, 780030365, 974048774, 928823495, 308448423, 689618012, 621367339, 70637342, 270603778, 392547249, 671685485, 207647401, 21607672, 291069924, 438543253, 797111052, 499539165, 261036675, 250200038, 838071762, 529331969, 972122144, 580033986, 908436991, 797121198, 238163852, 110591097, 121967193, 376116549, 274971006, 391727812, 252651749, 60434757, 185486505, 50860680, 663436575, 41102657, 458105948, 799080781, 382589208, 314091254, 121719478, 628975036, 790768771, 826037713, 876229467, 445292083, 210887206, 356495831, 631293250, 46123180, 609420104, 278475717, 504092265, 727510433, 176355198, 705659826, 802013595, 820197990, 404654358, 642786776, 162184238, 777786288, 905294343, 775672267, 879239397, 373149308, 315734589, 104440724, 701606228, 582270552, 608110397, 173634336, 960255415, 327433118, 370732942, 762722271, 427647859, 569472466, 283807003, 930488838, 559390974, 967663392, 737811157, 539408866, 776459186, 376239893, 551813004, 609345322, 985179427, 907303663, 84166670, 736138237, 889898749, 48903588, 584294251, 885111789, 134578711, 589806123, 864300999, 672111861, 37308795, 264749797, 155553334, 789890106, 206464786, 498824406, 45292882, 543586362, 23111975, 97589842, 671828284, 938782300, 955081193, 340822410, 693885699, 142028179, 920221727, 254968262, 918789436, 739012902, 349521477, 53748016, 591340856, 239340983, 667141767, 429528615, 738297419, 917484744, 531408885, 818776919, 960876273, 396194713, 849702589, 174839824, 744548742, 313861534, 395539227, 609715350, 653206975, 504542977, 283496079, 491969452, 887004486, 105081723, 597144148, 562285567, 480877337, 207117735, 662493644, 649091684, 682121569, 659149336, 175503568, 41013771, 52129876, 52348975, 363812286, 267015946, 681184317, 758879628, 325183387, 227435647, 857471701, 362852366, 161955169, 283617403, 490768186, 967845661, 285971419, 820054818, 503172439, 113698268, 208907799, 810313643, 847456117, 862867730, 37075664, 818157003, 806746852, 175512043, 666730756, 833627386, 904404394, 611248305, 745947057, 85015202, 502214058, 861204689, 485797971, 834782231, 768966580, 609810874, 521080950, 880403609, 384313664, 843387991, 612910822, 533588344, 105825443, 863463124, 765289790, 408785591, 346042897, 12358587, 461183998, 753506697, 887134747, 496348893, 498091137, 571721651, 117701818, 49844886, 325786316, 145227287, 185152998, 444377333, 743387319, 23598812, 184089140, 745582081, 135118766, 154437566, 774611889, 184306226, 726179989, 341936528, 248011673, 221682549, 877462276, 597284376, 478931799, 43369296, 902576186, 611271323, 957563795, 213364790, 53368366, 97174409, 320263551, 260229394, 836680380, 241621445, 217522716, 394501857, 381363812, 283000415, 143737778, 330648288, 654933135, 257305515, 693656634, 917881343, 784413065, 588672967, 905381306, 775407169, 739193188, 322905563, 618964454, 877178564, 621695931, 897858011, 127839387, 482784945, 16572907, 487919072, 777134208, 552619539, 382175892, 19493128, 522767261, 960881694, 967742380, 539028190, 870548520, 598435939, 54351692, 990777000, 437952549, 840796778, 694904142, 216145925, 553071997, 842695799, 97768516, 589094987, 853502363, 100667121, 938606349, 759768539, 387799415, 97214460, 24248698, 790215702, 153996352, 119252649, 612799535, 824420911, 513107973, 725245478, 546892775, 584522909, 92497998, 715783402, 417474019, 353699900, 766825378, 945920282, 632619099, 675471469, 940857695, 230261485, 378528472, 383348566, 305446729, 297386747, 196498616, 608691503, 585723253, 482947574, 525017957, 691080297, 670794190, 858145109, 809279246, 484650754, 591387379, 892477640, 356032981, 866433982, 235328601, 737335130, 219381516, 718682830, 60103923, 889128318, 145973358, 887686949, 704106232, 878622576, 680562966, 79516404, 593254471, 326900718, 189082138, 658639198, 601255862, 608809690, 448800764, 11724012, 837092363, 432437012, 374273318, 688903639, 525804373, 283961805, 843875344, 782400563, 864008783, 301629771, 607454029, 282986136, 45920261, 899546986, 297032154, 6912796, 979167533, 475097465, 937451797, 125713876, 538119832, 873128806, 452588330, 370825489, 149611359, 314756633, 8398491, 254868235, 572775570, 996349238, 569608058, 706318843, 543769463, 850233190, 162350709, 674481942, 759459431, 174462100, 557087410, 58512597, 174296901, 54515225, 71556271, 258734859, 548717131, 381100319, 493977755, 207356410, 81500998, 919509850, 212114777, 913109189, 126278254, 759002256, 275842805, 213320237, 107813161, 506024041, 851933931, 725398313, 704168038, 805668407, 599805192, 351463481, 804510709, 941345439, 790166216, 493731917, 459213772, 391189370, 843376511, 629473754, 841854732, 286761104, 559612250, 212418184, 957758202, 156658017, 268317902, 124163347, 698289395, 436078967, 851879484, 447556999, 83259312, 281933639, 31187891, 235910184, 172690310, 847791196, 691379664, 92800505, 53016921, 29746960, 338443780, 22456268, 421817763, 809478877, 535165823, 487346864, 779321078, 505854227, 349759444, 433616276, 181253312, 803370010, 169153989, 282601956, 141257391, 892158977, 429989619, 825147758, 971553040, 282134473, 453021392, 885037209, 134912014, 692429766, 113410785, 473233928, 464675207, 47534149, 70734482, 737662291, 481124844, 551217445, 616008506, 100122990, 721769405, 691284265, 853772779, 975778472, 214649634, 593818420, 554092464, 210950919, 698997899, 115928686, 160390065, 71596716, 652323235, 513339192, 172958392, 464459299, 185842488, 142177054, 478842331, 110858208, 134647629, 272510105, 556276982, 146085149, 526679189, 235719701, 226847887, 194058178, 746849360, 721898324, 60811440, 40615298, 612443947, 233708202, 213680704, 346288400, 747039320, 319044145, 604332110, 732021534, 861550211, 462472984, 543828202, 278247713, 621501754, 278090641, 685390911, 800473795, 830144128, 721821478, 494313462, 391976390, 7173523, 110824724, 948590544, 324212058, 387626925, 861391644, 754081804, 345419736, 162289342, 86109943, 258164023, 996354442, 199276435, 862338377, 524616182, 599218991, 88938028, 743517149, 672866298, 270272014, 326471893, 813535241, 934142546, 297697304, 409689507, 937017538, 569737856, 355780668, 879902397, 765660723, 348383864, 516463855, 247914318, 333844480, 269729178, 564675546, 627631600, 133791894, 60755664, 611697056, 290133135, 573445125, 589946443, 872673521, 219916579, 456854681, 789039330, 429092439, 646434057, 668518001, 10937245, 160405731, 180012470, 598619325, 519581691, 363523769, 158109056, 207494427, 985665834, 834243623, 983202443, 808338842, 598913887, 976431821, 885255663, 108691957, 980828211, 74185735, 848795170, 565924072, 629648361, 70783224, 674110258, 74358952, 152233492, 179170933, 808400529, 578025834, 943260480, 579442288, 351330544, 425311539, 179808968, 896771630, 762254134, 495737215, 398492531, 499477743, 525513910, 810516833, 737171599, 74752115, 842623089, 307885224, 428729611, 545888221, 77407565, 69415259, 557294058, 868551885, 993067860, 896415517, 57972040, 561797372, 200333210, 904190495, 549302048, 119126849, 427629364, 471664697, 497156612, 24296570, 75946211, 849677520, 860810589, 908428168, 525029521, 735625041, 578978267, 811771023, 579917607, 954080424, 412813823, 737680765, 527177891, 914445723, 643388250, 159299791, 679345276, 791997022, 730614808, 485627880, 325502018, 573062178, 672150235, 376304105, 584128985, 917570636, 261546228, 408480084, 46358528, 115117350, 187535659, 715739839, 332078783, 593342800, 252353648, 531097239, 414186668, 891161331, 558373908, 561855611, 845295532, 6316040, 291701316, 901379703, 828582306, 720209545, 79107397, 296088096, 483194275, 180508274, 406952080, 639018830, 733113234, 904228276, 691355328, 673339898, 914527569, 695166827, 3816349, 770694018, 734759094, 163994995, 192337995, 721681280, 483913311, 250856529, 418847552, 212162196, 87237301, 195837122, 328571029, 773433530, 428522240, 616141613, 734316023, 105072750, 680745019, 265871652, 631658452, 686417134, 177682363, 685488967, 531113859, 922995144, 965181673, 608170056, 869024884, 824419652, 392282305, 940686188, 526587485, 235458504, 160933232, 51580412, 35575758, 490303896, 254355096, 525773066, 921048315, 712832360, 334505179, 329620100, 432072335, 383099690, 473847573, 578158208, 469070344, 631393928, 864174709, 906315813, 10788287, 159121436, 371849297, 464341150, 625241053, 563540180, 523243802, 857899935, 100026964, 252847571, 945230609, 120158396, 447042312, 436983733, 950158974, 634513264, 291473157, 243881935, 416064983, 121663128, 736369686, 3769328, 687586243, 525070099, 227811750, 336887800, 262663057, 450912147, 762569664, 688448558, 4628367, 696715116, 349188994, 110007614, 996748738, 743210552, 638017310, 439018035, 497239409, 851871343, 444237036, 501523212, 707242605, 624789503, 834255844, 7126632, 257598434, 246850940, 612162437, 747043433, 448390861, 113539348, 600172262, 625390642, 281631168, 199356398, 642524835, 258019146, 227300853, 984274217, 782006858, 942203118, 579736194, 129984026, 837598262, 404425172, 909031864, 191497961, 827510193, 858455992, 189768090, 742322120, 386641069, 329005621, 420617220, 702790111, 118872101, 406727902, 222088077, 473307130, 55406329, 27691310, 82325313, 157791701, 249943865, 992337343, 863081199, 492886357, 681918016, 911670858, 809263489, 487751862, 534878067, 288067650, 346972149, 175265425, 808196067, 42406932, 695460002, 440056295, 431953962, 38183121, 65190340, 287765315, 30604626, 392675824, 932846531, 399433170, 407322180, 666298966, 32554354, 168641863, 632656270, 159791528, 477666050, 962457243, 759126769, 119939630, 44351372, 210597155, 128494651, 931275808, 121953080, 766076752, 155982247, 907365777, 491198093, 525365194, 916254510, 335054252, 138365367, 937945497, 274596570, 425558746, 347836456, 638307245, 533885578, 972625099, 39685450, 530667808, 911001381, 271052482, 968352361, 598019645, 43642255, 521135435, 707298977, 859993637, 265514260, 847463229, 231925467, 772786586, 623502738, 466408526, 774990036, 129296767, 833968434, 537432659, 102464075, 564823078, 680012123, 779981351, 203723073, 943839262, 519370468, 613992695, 405592179, 116340051, 574863179, 546257975, 63468759, 423652964, 163329819, 753971185, 650731504, 996396173, 939121029, 770222730, 112591318, 713432706, 342859609, 636683328, 842457100, 14021592, 352968369, 932864533, 892766190, 299335490, 702155493, 82841521, 183204872, 440273288, 335901725, 470051453, 948267758, 318616954, 725885801, 76859135, 101628880, 765710033, 684868829, 712449424, 667242817, 94552586, 795766640, 91940227, 54418542, 273931469, 309723452, 375754328, 799170023, 501698542, 315015633, 537801538, 757189963, 853881968, 897017669, 196615295, 534861318, 106389736, 718998581, 611714365, 904041700, 799661019, 966348098, 401292971, 980888482, 175824291, 223479260, 962118327, 392203957, 127417118, 288418232, 546401622, 996868301, 562300226, 991402546, 742009768, 36767249, 821612983, 265739884, 384696154, 48891940, 455962226, 443783802, 728867599, 10095249, 507334214, 509801023, 705132618, 236300162, 864028460, 476059183, 848428949, 35982421, 965861402, 878279488, 70596602, 86815460, 238541983, 46961426, 100464921, 976866629, 642506529, 279616350, 998903194, 305244051, 630784654, 867524799, 170526416, 977407347, 749463560, 38084527, 518773580, 460612607, 817786109, 936319767, 673220449, 609221992, 865079470, 171433892, 669191800, 211603867, 663116654, 999273639, 929672093, 131762178, 613401666, 789800358, 401908722, 54255536, 34560471, 119263689, 425874436, 945081261, 35873952, 909941608, 347228688, 230612028, 638076120, 515295819, 327409888, 736437763, 549098880, 445747192, 418807447, 257794257, 878523094, 541287191, 967352308, 255283358, 358801617, 522151781, 565274623, 290902875, 372709602, 493298875, 109385233, 952913731, 603831637, 670380995, 806800607, 68571489, 780770785, 726329432, 516401002, 165849277, 233391426, 292840490, 381311395, 353369564, 675521631, 599616297, 736689682, 365519267, 898799691, 760250760, 795851446, 833871245, 752277787, 959186820, 775860367, 475752568, 302459576, 117045483, 416102140, 824591904, 867775236, 52956427, 373884037, 423242200, 567321419, 313328000, 934580930, 654867007, 436632476, 92021094, 164642298, 102014581, 933203769, 754429367, 372544102, 466696789, 702291404, 155863081, 836886447, 644106600, 333633272, 761598659, 720050467, 550244460, 216885869, 624578872, 343263773, 168854767, 772260600, 597504336, 403080340, 459368466, 461901929, 794572037, 983664865, 4057379, 989966079, 254261077, 82690265, 563001546, 28911735, 199144539, 40869398, 981004148, 446682628, 724413502, 352958680, 744784922, 454043969, 191599319, 175768726, 765264539, 3925237, 615634561, 193424375, 771935061, 711892240, 939792186, 243813944, 527931236, 657285341, 932333263, 314742552, 578521227, 352974173, 18085082, 233802439, 518708161, 979646476, 530290526, 83041982, 833192602, 137576951, 935136871, 873372417, 551159602, 122463484, 4341497, 996303693, 372572415, 656004490, 119537687, 41641065, 350292260, 493115049, 361511341, 765412789, 911050708, 264839251, 690587174, 103565736, 968380703, 331428429, 174991259, 949310699, 932753337, 605669478, 594219539, 319260426, 740255418, 81950411, 890824304, 113386023, 576529450, 489047925, 691489322, 863987909, 707723378, 27112281, 628814540, 104842599, 500526791, 307309053, 922123657, 810636226, 229061119, 526746442, 415478649, 80239290, 863923379, 194457923, 217517579, 619061424, 868634092, 577626927, 45265084, 794267698, 502287183, 176733243, 502438758, 159516694, 548608509, 196788244, 415897541, 708433212, 162018527, 464819957, 174098056, 955301889, 935664650, 199746973, 769963647, 525502545, 398668584, 9218509, 971535488, 99584261, 256746459, 508305833, 438750502, 603948309, 919807388, 128912291, 498288687, 968342968, 121035762, 745286926, 710935477, 79679422, 524293774, 123729832, 422697631, 261276848, 253841041, 309135623, 452919499, 41811494, 233219624, 20223165, 629006202, 745583557, 884368054, 291918081, 601814462, 460803541, 978441030, 170503193, 295351330, 422635781, 260494030, 417525062, 60536903, 371299284, 340480496, 781466813, 76510776, 46546742, 733733670, 262087025, 349847603, 590423206, 414545176, 890745434, 527411748, 337041644, 898262451, 495130089, 359121069, 353015554, 296493571, 230557031, 449034758, 648215754, 204156957, 264311014, 296334123, 847585896, 629171037, 358034349, 203821851, 482016470, 194381078, 493403776, 125554173, 46390993, 512628804, 228256397, 607004923, 80226066, 221278746, 750748668, 85924285, 283377316, 37473446, 327817747, 106674531, 135077686, 63217376, 239891855, 823356139, 347600299, 369126735, 975209004, 171433685, 319517514, 923486442, 767064477, 718291992, 454233021, 636164746, 345177170, 815435047, 731494040, 843694769, 640106843, 41591141, 983924130, 447662779, 27092306, 67169282, 265760011, 835798179, 743041835, 611637272, 887016696, 641405148, 35675823, 237744407, 745074730, 200463973, 833581229, 355728542, 39123526, 149028641, 234875319, 387173352, 895749604, 814788523, 210355037, 363947989, 443761360, 472370666, 478564141, 730384361, 647356637, 989903326, 582094538, 498649877, 71875237, 782901929, 733383197, 530275334, 775835115, 311515935, 245093653, 842035022, 204239763, 22174473, 566834824, 844939493, 605035353, 537761315, 778659614, 537743220, 390063554, 944670870, 878565892, 99687812, 927863435, 752816451, 452823621, 915038714, 446512533, 842310454, 903096919, 466425477, 250047936, 688456200, 532347039, 652660436, 603941862, 812722475, 549727771, 15786745, 272127664, 979370792, 682891972, 728105840, 854125001, 600129051, 10331715, 59409923, 581429288, 583611725, 371748517, 568553927, 908487984, 355324523, 68072551, 299195705, 380879615, 679315317, 883627137, 89553953, 599384066, 776575181, 370513333, 505107996, 20572507, 396093717, 613166162, 905031008, 315625874, 899734776, 454418845, 58321121, 602211995, 766923736, 758492467, 368044209, 268718515, 307360163, 192143484, 440675214, 467852455, 960094046, 351890143, 507040312, 303892592, 642468909, 142724388, 779263327, 269813598, 203864842, 443259033, 719928829, 13070916, 887803280, 648738928, 38442351, 18056085, 764507855, 454941657, 96811258, 898079213, 313473354, 960991979, 419250202, 585542821, 586881150, 958985189, 394191870, 149438499, 772006898, 427370268, 345149571, 870643900, 930332589, 756891947, 28754927, 621135895, 484508477, 541327780, 519580603, 499914409, 610274982, 950030942, 602536822, 706440685, 426090942, 540497362, 531869112, 996069874, 425960553, 281740021, 83899295, 247815322, 946921608, 97687138, 386780143, 118160523, 529125516, 908160725, 348588266, 676490661, 511431867, 303305348, 382356143, 483470661, 895681368, 123080045, 351918674, 684011347, 505847104, 697153811, 225602918, 240470423, 476046247, 153492705, 296387589, 404097720, 292121792, 977170833, 526660637, 765201409, 654554711, 138249835, 423578070, 514731049, 431047176, 704734380, 187558851, 370287949, 491750490, 411644500, 490129719, 925859723, 271063943, 709424567, 866970026, 711217242, 371158443, 237795603, 730524316, 906031427, 163106605, 464466243, 256440722, 196886769, 629532448, 504293455, 165248371, 856149194, 584390319, 736127201, 350761782, 473042740, 913280883, 210578495, 991425615, 187676304, 525233913, 646656085, 468156220, 376445566, 112932796, 748497917, 379974251, 937076985, 4909653, 488227465, 861647274, 929670095, 990652178, 86856787, 670081706, 229112668, 517041026, 339607981, 622604955, 254841916, 198378661, 958630846, 492411426, 550996027, 231154955, 587066293, 172908103, 875132441, 557888164, 906106935, 845758800, 404111692, 289637106, 300101932, 947019926, 135390204, 436256302, 658033357, 942491646, 712555021, 532242765, 884985685, 875174960, 758825030, 628441476, 925241405, 613786864, 122628256, 610761646, 664430542, 439971509, 392482598, 144951317, 571374301, 314573796, 579931864, 851789455, 411634616, 908982533, 461200419, 240643835, 808903357, 837787827, 539853611, 42616001, 353988703, 283499217, 918626521, 126728980, 769292482, 786911002, 93828073, 403281233, 718442793, 692156526, 237941648, 138093772, 460749549, 567213650, 496536933, 324658137, 864444015, 209165697, 571892881, 187865917, 371452938, 547233437, 493686688, 154238910, 918918592, 735947319, 245785118, 640259933, 79363770, 709530353, 989827623, 464519247, 943242857, 835442140, 81453145, 441102770, 94699523, 303346450, 242274604, 759385008, 904910085, 872540679, 552453620, 286702537, 941611597, 75060412, 265995329, 266227753, 158374793, 269048152, 489974795, 513575009, 999713968, 490336385, 876123465, 579632558, 83323967, 203559439, 184217297, 641710810, 878387641, 543202786, 455913687, 301318527, 968166193, 300382113, 333762290, 906201380, 456250921, 603509149, 791465289, 918456404, 766985092, 294139690, 599088715, 577573713, 514527630, 656664860, 956190436, 208569033, 942715845, 200706399, 722445973, 923585583, 368645890, 803063028, 111967099, 75695510, 889255487, 168514512, 383866556, 155471769, 237670055, 165318783, 688524379, 204519362, 222908245, 971948400, 373727407, 673308319, 134604770, 823224812, 161822869, 200663478, 105316173, 171870471, 852045416, 884258310, 266593738, 226725818, 743709552, 631774544, 921562720, 538231753, 768962330, 207496912, 373077754, 880228867, 873050330, 466433961, 438553245, 915841866, 760552962, 225281074, 27529020, 693312850, 839109679, 958350342, 342487233, 548088560, 610954913, 359520741, 87075868, 570831510, 340574184, 856276264, 746866729, 67933913, 497739002, 26335037, 506016657, 548380973, 471437599, 908631907, 175742945, 280255865, 785941865, 327621547, 667603184, 87452398, 214409986, 484637179, 505606777, 727410232, 636294309, 634157847, 617886388, 784277442, 85466339, 622372471, 603272619, 798410605, 989975983, 360754011, 347407408, 873569660, 43634003, 345404360, 604268245, 76702331, 700733022, 150541702, 203513139, 970632124, 351592609, 290900536, 349718430, 880311251, 872916816, 816335848, 668930997, 763988493, 871107171, 563064741, 517166814, 661039857, 119171380, 265480037, 378625288, 638866540, 184207684, 573346540, 546671655, 56031535, 514043381, 840941612, 892438260, 755622598, 182139956, 783306183, 492284061, 63274319, 7926962, 809231560, 801334235, 488947670, 450278218, 978722699, 922671516, 984745152, 514026765, 181012354, 225410175, 732818274, 69722472, 828295833, 634286590, 65872778, 873369673, 48129716, 104908707, 840578058, 169548563, 492731162, 45141742, 212797839, 249037453, 841494862, 734323085, 388947744, 926247227, 672230083, 202253312, 734512334, 937839148, 44998267, 967918328, 559897216, 997177046, 843623712, 399070130, 599433687, 826381085, 336608287, 629036902, 31099415, 933513378, 4934745, 790571729, 894115248, 677697394, 427808533, 516959296, 233397560, 278949672, 138215745, 133224401, 339557464, 392851981, 958545895, 188127147, 883823816, 229863256, 23053409, 714437179, 330021152, 712380201, 287968403, 814912800, 386802800, 897491745, 660077647, 951663377, 879571817, 439781095, 921210178, 886119612, 67164456, 784011224, 212766174, 37201767, 537563014, 440204513, 986053838, 266379086, 867431146, 460798750, 350539260, 570044678, 528864368, 191756566, 630191530, 340752075, 252622474, 272078954, 237254537, 612324001, 225048548, 96977464, 210580168, 515005199, 431228832, 91923590, 971589655, 706427483, 722659013, 453836675, 412376649, 445524448, 972290945, 327567124, 990097132, 37691263, 100401635, 936512, 636715025, 250671703, 454832179, 102252214, 495009359, 262527606, 686127808, 806945143, 918281428, 1937382, 217673237, 695892254, 22644504, 336304466, 112128314, 728563748, 26135337, 138614967, 563519808, 631776298, 360925592, 424696571, 817761203, 46630863, 155149446, 245206972, 20950501, 89489060, 702380621, 847616536, 229039039, 800550766, 78883343, 792038578, 973953566, 440233285, 692143966, 383258972, 433511746, 395440755, 614642547, 643363425, 725085226, 198670356, 902937414, 59026491, 607011128, 482232497, 269972303, 70396363, 591704886, 21148294, 22298632, 848503446, 925818257, 118195236, 685415597, 86405832, 614748586, 332890885, 113252253, 923809363, 435867370, 856670932, 644304096, 136421262, 102952008, 727731544, 368072995, 387323524, 278365288, 600373243, 159935401, 845077073, 408449083, 541726886, 562242409, 199132305, 455811323, 25301183, 741157721, 678896684, 762751791, 581888883, 795479019, 441530627, 201583834, 73429213, 631784532, 284747476, 907867960, 975473785, 674248957, 594621978, 710664221, 871301114, 618294828, 823602214, 896759037, 455548845, 127296308, 564446903, 425337669, 678243336, 237252642, 140082609, 54139153, 546568938, 862658423, 692954268, 586106678, 347089342, 684119481, 882293096, 727622415, 584225511, 837872151, 927812401, 891020394, 459098313, 524229988, 400618593, 144233708, 126665186, 363617713, 714757815, 234359306, 90483192, 35696734, 748412828, 976610672, 920023435, 334790411, 415613634, 157769988, 801962517, 342275829, 775080169, 141978694, 347443114, 496900560, 404302005, 402702646, 343813894, 387209951, 228924156, 86075543, 906861978, 876974887, 469502628, 340179167, 154015765, 229157248, 521977653, 875389899, 831090087, 239030902, 258473485, 587239921, 334458327, 223893230, 97450404, 56998536, 764507851, 860064895, 834148940, 165676687, 301660165, 457546086, 53832583, 483941609, 459130099, 750333246, 949324772, 629360906, 884290308, 40405607, 868914170, 905159240, 804155778, 176128048, 383352783, 562393403, 121624317, 437718967, 95844153, 326500952, 651919745, 121327219, 884634167, 413839324, 302678474, 635755824, 922535625, 397520240, 423569913, 809083146, 916931293, 223671042, 2794666, 397755994, 409982219, 259104695, 37760881, 587011035, 145232683, 51604967, 414047939, 49542484, 313082584, 905333331, 884527093, 131031450, 928697422, 591308967, 827004998, 400057520, 43890898, 376902173, 301771275, 529224486, 695228203, 897721803, 898696058, 644890253, 497317092, 345730700, 454564480, 281742474, 894500055, 92175688, 43045005, 662881108, 508640736, 425205834, 90452847, 74616279, 877738613, 587899024, 428739640, 215350779, 635264513, 173775820, 500378634, 542058542, 228168117, 643034785, 892880631, 496078095, 914164796, 546195608, 651878884, 648464723, 782956563, 676768581, 881479866, 164176703, 923044456, 71948078, 448759692, 844253965, 479054454, 474753258, 850058609, 24095156, 202596846, 957576989, 347226699, 346930691, 599649689, 920132705, 109781658, 40769138, 551160772, 820516839, 437063445, 808349729, 402696401, 730630132, 487661126, 231124935, 446348675, 142082403, 730588311, 475029523, 833398491, 99590595, 979378615, 645768777, 646557073, 900367743, 315090817, 845582723, 517748882, 281730889, 641806300, 983547271, 109829654, 699123544, 815225780, 720042682, 405125323, 596324522, 279499534, 667442300, 107332738, 117010288, 536656135, 682270372, 34714294, 15742184, 876395419, 142010477, 38560363, 387042106, 926796126, 94593624, 570446864, 623955457, 202120514, 126330987, 156757609, 103806189, 354899247, 218660243, 665763216, 78760319, 386445739, 719773885, 43793660, 747518209, 450503706, 972821426, 539259066, 681996465, 754771468, 334841423, 567434863, 456320627, 545910245, 584109691, 694096215, 620682995, 232964030, 738544627, 111419497, 17906087, 765004868, 232917506, 830993728, 558021573, 492769428, 863702439, 454066520, 757348476, 199072255, 339192021, 718136422, 437434207, 918245104, 405788820, 394301058, 307939839, 191730197, 625294713, 933474132, 421750618, 424620957, 338532255, 193804647, 843036624, 573038740, 901675969, 989224916, 233216035, 53438174, 221059372, 541921148, 503920213, 471125637, 941962632, 705247663, 875854223, 513504807, 767781266, 876613442, 772908801, 135351830, 291849992, 954992564, 723576619, 709831262, 259739509, 546879126, 397241756, 207788674, 834729661, 269076168, 593795400, 933289167, 418196570, 597971877, 628384165, 251737696, 788124250, 2335914, 264477564, 222370379, 335071141, 802601388, 867104769, 799030972, 781989467, 208396929, 768867985, 636528999, 727357960, 346945477, 194701687, 394560219, 484201767, 804853772, 492666546, 204365868, 592213147, 356026062, 394301059, 733623693, 722229719, 974946426, 494005262, 368846711, 547047810, 879104872, 523996169, 106500022, 303914597, 522424651, 508719380, 762412219, 564392489, 721800195, 907297204, 695285600, 374191002, 902713892, 512611751, 49675175, 306705382, 252032090, 684724536, 677716117, 294025346, 997967009, 30234313, 382293882, 826323950, 988528049, 625041847, 53895882, 175104222, 133514554, 526997743, 524755768, 722169337, 37207707, 937626844, 456099622, 770216424, 284876396, 670644090, 634900580, 584552344, 451665824, 368398947, 740074413, 413343590, 526968585, 450318381, 277139380, 20941984, 770816362, 255343869, 373165782, 145818863, 275104646, 428606131, 795721881, 586733817, 553053855, 968270805, 756357406, 222591940, 26828780, 967161859, 742206025, 888148994, 201919302, 254509846, 782091762, 775852971, 617524911, 738387033, 144328247, 310344336, 376249511, 439064374, 365510027, 240779857, 493885253, 338385792, 90885509, 213704418, 562619320, 345059960, 39363953, 337464602, 137736661, 62294997, 796338349, 783259487, 268172090, 290734960, 143651321, 291506499, 119930614, 425298874, 405783720, 827397006, 280952798, 365035644, 537840609, 311960932, 938824288, 841547782, 859014334, 761384436, 703197146, 221802491, 377957155, 66091001, 778816542, 919671958, 752073260, 980728796, 598718777, 362565611, 964268049, 876951153, 688235140, 302875359, 121267261, 103640614, 324005035, 880662808, 696756323, 975840643, 681498581, 718557961, 235742343, 17836141, 530417653, 48023601, 573004009, 182996295, 676654268, 938998913, 853271609, 240328543, 154068467, 625325511, 982037638, 528407320, 794644800, 932133309, 818251209, 922570652, 110122252, 506729464, 422418736, 887075016, 541789378, 19598471, 28360264, 709482803, 746686321, 892286685, 696173058, 500027068, 950457256, 587589132, 681444394, 404526178, 719010178, 984311833, 642038848, 101706727, 525973741, 632787463, 944979537, 178196185, 572131630, 863073323, 738251877, 115457634, 55035144, 105635409, 633812981, 656649089, 15936499, 11764072, 812418475, 981306642, 127142534, 665847441, 919675024, 688816819, 683099687, 432479604, 322494186, 225519854, 67031268, 917579847, 37125386, 101332221, 397665918, 909446297, 755406689, 681879361, 245934828, 634684099, 718610527, 561914191, 932093150, 18252049, 450053499, 878075419, 736573702, 533681523, 88186267, 934301659, 782777655, 886082942, 318556859, 725255679, 559021758, 44254996, 443968864, 675378593, 119447476, 21778450, 291854800, 882426567, 64731038, 375988624, 888352300, 871509704, 133846522, 146970922, 634663994, 822806115, 158227124, 375187455, 984859529, 774463145, 588537622, 526454312, 950248876, 227531909, 816263788, 827840468, 264432596, 429123826, 224415281, 838920005, 299288453, 429522787, 130794148, 953593532, 559551852, 55504780, 260286399, 59695547, 958332469, 543475979, 619470908, 837122160, 432665505, 456330220, 3993715, 624013139, 921429973, 51941239, 805297163, 927463953, 98110645, 280038537, 43664565, 461653845, 543300141, 535644895, 920949048, 503023840, 53889871, 697771441, 506746123, 657516508, 367443102, 360288383, 113581120, 570458998, 341916474, 539998638, 951965255, 846205799, 513162712, 960786918, 1403718, 373625420, 537150204, 111953309, 429163815, 276846758, 341840341, 172741054, 161961803, 61499338, 559615058, 314125942, 969107135, 351351396, 553010481, 778222437, 936929235, 566995818, 427594028, 169947163, 141980999, 872033571, 597607478, 196238449, 816878194, 117884101, 608223089, 771070624, 926273280, 347851497, 31606965, 481687037, 628154135, 154581106, 458551971, 574450600, 542158409, 813656444, 619470733, 624828617, 274549618, 455065242, 571417540, 756752086, 975910662, 621143958, 935287245, 977888139, 680735467, 323187071, 773962868, 133170808, 292443269, 165920123, 314820551, 526721682, 490561586, 520207019, 667753385, 678032735, 596898214, 679881912, 870065454, 446203249, 42705698, 898997407, 206214847, 111091594, 655186413, 281007908, 437535178, 826093615, 52997574, 44753042, 269524530, 96831467, 926656379, 959875347, 444704887, 619955520, 762123407, 687606069, 301661627, 798550580, 206199633, 879519311, 975551740, 345925943, 378011151, 960631807, 729061636, 786870405, 730285790, 330266753, 546651459, 206271894, 781844774, 326229517, 894446699, 325275959, 847402202, 221423494, 821124326, 944018947, 904667253, 908009565, 669396625, 63718657, 975087820, 574112412, 962912827, 70440558, 644829217, 460548471, 193209974, 948558255, 721635220, 97274013, 975075433, 608971439, 435196126, 888753099, 541563251, 969093351, 282374456, 204746408, 842005405, 116795232, 20728703, 456840653, 522456381, 406362678, 885578300, 41364683, 320079166, 733875620, 806517175, 190002189, 562996823, 764198564, 740627659, 725571110, 992623962, 192364969, 278218030, 59010330, 943960310, 512629039, 523078483, 56668074, 58483753, 101624464, 507757720, 847039159, 31629425, 746497240, 774106000, 555615961, 955513388, 453532928, 293122993, 277206415, 493598825, 368637474, 231922950, 675055480, 579136062, 370489035, 41252706, 450128966, 953246486, 732683653, 314292831, 988546792, 596553883, 254601372, 981380413, 571542903, 851463642, 32588950, 422610867, 28900343, 192069687, 303938463, 831602207, 539658790, 353305377, 473853215, 913985564, 152380552, 308130873, 25307299, 693998345, 366464099, 391695752, 532557572, 138713648, 556152737, 790656973, 710109186, 364206053, 674664849, 822085163, 382676409, 620595709, 354861218, 694864931, 280550408, 847900532, 132213121, 745258609, 350385438, 519316917, 11207901, 38665677, 553023093, 980560883, 635096069, 32652272, 549077206, 644370442, 973749829, 630676841, 397353578, 452826387, 750803558, 178315979, 731116338, 969079800, 760809597, 162631423, 272998632, 351723328, 554435729, 380201621, 580246504, 265069862, 237464448, 767698644, 991809432, 986810904, 705889622, 676138971, 770453089, 878494727, 285526528, 879134073, 26844358, 502906871, 227958094, 599530430, 342729222, 1331210, 785978522, 725397184, 729377907, 62870078, 937824146, 42177836, 548132593, 342281685, 619025827, 243601145, 560672769, 163318959, 202526914, 744882865, 412687510, 679597089, 138071491, 300486552, 717060274, 527903140, 683505309, 875152429, 135349404, 980359751, 10764836, 302530764, 274424746, 358042616, 7293391, 163499866, 203507096, 893560302, 952807544, 138736629, 307249060, 460324047, 85297672, 614373042, 766424692, 300939999, 931252605, 151424387, 721749125, 150107678, 561558039, 94383397, 376066659, 290740002, 375309819, 719495852, 64430097, 976164716, 192040469, 380268252, 217496060, 602853755, 411456413, 424656659, 980866341, 450088564, 177080510, 39913537, 747905845, 414597906, 431001830, 250894405, 762407990, 658392023, 262748159, 187028280, 862872761, 154713341, 178868356, 447279610, 437015346, 575585668, 616888469, 378849188, 972151645, 814854290, 863361925, 884834938, 619058476, 874175566, 316359697, 189340701, 79429848, 628710918, 942687912, 959026995, 236155325, 32261839, 70351732, 275236179, 200130268, 608452639, 48140540, 955177646, 594714241, 828778590, 143395881, 630497932, 38034605, 671710954, 591161145, 620196814, 312407522, 135112729, 387887703, 917017720, 325522148, 876489808, 892065727, 31931663, 500115556, 671689192, 757949402, 635320799, 818434240, 338554270, 136445494, 529300820, 493636264, 194571197, 77574346, 852667500, 463745852, 596610104, 359689795, 685103173, 425629062, 842294993, 213404120, 363998377, 367110603, 376787982, 128951841, 221555919, 823925525, 652505270, 311526634, 53439800, 918930317, 679622561, 160457634, 313131314, 104929658, 203048410, 350416130, 291389832, 39314958, 357843861, 32475101, 40760805, 9114052, 989629343, 331292260, 596245605, 885684945, 856323273, 68888479, 786044261, 577132694, 175492809, 9190415, 482209332, 768039876, 510690393, 177395593, 153271046, 203850294, 442038972, 549059995, 325971958, 33221652, 72002094, 412827029, 110571958, 611116511, 238937824, 125000537, 837439677, 510064091, 849609686, 805532487, 493598111, 738264553, 854650429, 806187252, 194171996, 162355734, 983731200, 348139876, 296439424, 54691845, 639286972, 773617997, 617451677, 501364298, 239206148, 526672487, 913741564, 13661078, 448669564, 265590526, 209532980, 724468535, 623550305, 11456371, 166595170, 916498573, 612259237, 226085256, 846326284, 492308761, 145670232, 942833361, 784931315, 805146468, 982177258, 458580572, 844087713, 215705970, 329874481, 317393683, 569117494, 292774450, 504905400, 489034651, 870438461, 341233178, 756776259, 890714239, 635798174, 293943166, 445108862, 639271101, 259129509, 811971984, 410854247, 57558628, 525543198, 895724654, 736974353, 991554719, 131537395, 839041936, 266080741, 323055163, 648292107, 19835942, 471843236, 899129201, 387154054, 430963850, 255614407, 207285686, 525991128, 720880469, 5755070, 832320767, 442130168, 869265201, 989526893, 145681832, 398425167, 657523205, 90468986, 584770244, 200566804, 444218837, 117440460, 764741195, 923571355, 859106784, 550797060, 537569840, 763957570, 798785661, 875557531, 523057936, 767892022, 12510667, 235737205, 317790836, 961897387, 385903487, 665443383, 928840881, 693698995, 682597699, 332093071, 69424227, 790937271, 545830751, 740062508, 767219273, 859254406, 380776773, 444356230, 212606924, 630650416, 653615410, 795481104, 216245689, 969083417, 236557419, 787823275, 455266847, 518638494, 237879276, 582183748, 323813566, 829556308, 185432622, 391749307, 8494490, 807947065, 312003091, 191504753, 886256525, 841449737, 271015340, 882766982, 6016832, 750461297, 21075006, 330677506, 769126951, 982208810, 645876853, 551666298, 56617834, 709725139, 300323861, 741753725, 565539537, 660007432, 326069037, 37406902, 572264048, 72457260, 517135655, 549420464, 959565146, 250764349, 437633677, 449719675, 992955715, 968493444, 771783168, 471273173, 596987836, 234394459, 955233047, 294933140, 650240681, 490974386, 936256865, 40639542, 745838573, 696924259, 509709455, 747907476, 901701693, 25190909, 769742531, 341526885, 641353551, 915002418, 664866205, 541571435, 372334404, 800343824, 806350977, 235463427, 883246636, 959089569, 510531193, 661557615, 195505493, 510815654, 6931602, 382229828, 828359070, 410028929, 449400336, 754132846, 794275389, 62208513, 378748331, 442332539, 83382752, 770642560, 636326372, 57151321, 748816715, 458215020, 277869413, 949729754, 701934019, 673931114, 801055665, 816717809, 920715471, 975696806, 162453901, 826359837, 950538006, 93396432, 129024383, 228429347, 285530655, 512822878, 626295117, 874468415, 556306598, 523730653, 632381055, 471596721, 807821919, 465560209, 625644232, 691263911, 228854930, 486186164, 607980870, 753319057, 926959747, 481723048, 762441505, 917209440, 312838662, 846552557, 209192922, 585569400, 209602178, 640083532, 471719787, 12001475, 595600927, 216850256, 831162544, 638170749, 368010937, 351725728, 220373495, 63396881, 659281384, 826620756, 988682899, 653984385, 236906744, 503850487, 993637358, 640680566, 456866706, 997507472, 299546546, 273045731, 94384440, 362505537, 457372005, 843513037, 715167218, 226550042, 601209048, 951632041, 535063143, 943218653, 525567787, 595571228, 69341515, 709483356, 144255579, 254732918, 247053850, 392590176, 127075455, 931296749, 900678770, 194899005, 531323099, 50307831, 23634310, 465415133, 829154383, 339131156, 300575496, 61162017, 801427742, 344630990, 13557891, 973089209, 101629618, 888750663, 58085587, 116782218, 716181553, 939780727, 649461580, 308389597, 4933099, 299085811, 9564074, 388777525, 132075868, 657627856, 762011191, 190398922, 705164102, 192321813, 581898708, 345810169, 358371737, 332036016, 717564014, 663723752, 821373348, 106277409, 377469631, 654213575, 162162117, 274951884, 269441718, 590787898, 840145087, 885971846, 981175321, 765724574, 962091479, 2926838, 964228116, 697971092, 769795264, 789798141, 337748721, 722101172, 316696131, 287190511, 9657420, 669782911, 298056695, 154898579, 557988367, 457459161, 204394618, 145922351, 85609095, 57270204, 870389433, 144879668, 820343035, 732506250, 718844806, 55889531, 81076946, 406722911, 252035790, 919961902, 601372189, 75792693, 86342765, 547789571, 378077465, 79419696, 685833681, 394099694, 790959774, 295703209, 253796131, 33905460, 931759836, 463913795, 860418500, 947537861, 210646051, 77423826, 396128593, 63595598, 121573738, 104364120, 548861259, 238530871, 438687344, 264140165, 820088402, 952206536, 489220665, 951299503, 249585320, 912272682, 43809245, 348755040, 901784271, 83027637, 599872188, 938097569, 316343587, 10663436, 462989964, 201300935, 831654470, 130561234, 462653233, 594871167, 656489735, 557723944, 356071108, 577664894, 936278815, 434700472, 212590415, 487704781, 926501764, 595745712, 221985048, 709680943, 599508377, 71602008, 821354004, 54137871, 66992083, 856885348, 396797865, 213593436, 7318581, 633589678, 487426685, 977346328, 106767859, 840217505, 3819382, 722913028, 117306121, 9623568, 465888315, 199696802, 582418095, 700809146, 94444910, 85784839, 694420973, 438472155, 190720793, 216113195, 812132654, 410977303, 67132049, 380466500, 651185435, 61535614, 663833479, 383020995, 768111364, 932435842, 634162960, 147788773, 883752425, 891440455, 804045825, 858454359, 801470478, 684837502, 908252695, 557340514, 717883608, 694799281, 869518363, 643272988, 569381614, 366610539, 700623600, 280547313, 184712473, 312195745, 170103548, 86597476, 824245371, 927740837, 88891186, 430723154, 412434106, 860972048, 89367642, 987707294, 819148004, 190506112, 967788421, 180809811, 959878067, 2495558, 794028163, 53231938, 673289386, 142502791, 219462293, 435810100, 579922109, 314040705, 271285339, 357101831, 298910469, 761598806, 477406413, 714416882, 212685498, 798143269, 608813964, 347181212, 50036615, 492005512, 656915369, 994949753, 194319928, 325324864, 123131929, 79362801, 633452640, 569586780, 328807555, 55439112, 756128013, 766312061, 296743114, 187143403, 961210711, 396353587, 894140635, 790359733, 51476334, 986089924, 993387296, 272018898, 684042114, 808408255, 768885670, 476914318, 557037411, 497117004, 994401794, 667766629, 544620503, 705028659, 21850876, 315593519, 38764888, 935518999, 62505126, 148433881, 461176239, 402734365, 123880746, 864161677, 976234724, 331404898, 408941322, 692656988, 193601003, 41231402, 616706722, 458215974, 48781654, 843797673, 331741171, 728814270, 614000399, 181083054, 207685577, 156695349, 620308392, 415749270, 870217429, 517235109, 576118953, 673952869, 728758397, 111678328, 81811103, 707157196, 99730760, 435524581, 364302095, 363830596, 86328278, 746491393, 326362956, 268570487, 473881382, 573144625, 34130654, 241798756, 221661593, 475246372, 784822852, 437797480, 84314389, 433217058, 578999791, 360049769, 678695736, 618427950, 178921363, 831600485, 992685185, 850431218, 326844148, 324378422, 588142463, 385075182, 374361984, 861688495, 338989471, 340300409, 266340440, 200376782, 215854548, 923212486, 447039698, 521543991, 197941775, 723306015, 248035199, 48968472, 353182723, 214526061, 923638638, 270000532, 191765947, 294671668, 815883876, 176667164, 760766010, 201132563, 519619182, 608026474, 632637447, 819887564, 832421049, 608478723, 213858397, 99815688, 596458441, 348003355, 821729361, 403431358, 291995623, 427626035, 111439364, 622568046, 121426529, 204697071, 180654299, 580007845, 78140541, 892333457, 438912170, 844281487, 9569218, 76452938, 952437978, 412465190, 859254583, 904080960, 368045761, 718848389, 686136312, 121085622, 642551652, 177989288, 392997188, 857933904, 78612369, 346474640, 243734658, 256908736, 610242980, 39534363, 985346903, 699118842, 204081148, 52305213, 861204063, 467541940, 606105274, 80143464, 973606614, 261621002, 712036920, 731494073, 312475884, 767114240, 178012715, 531406995, 165480138, 97034107, 894212927, 199334380, 886546003, 697569618, 759359164, 925169314, 785057459, 354443423, 107401290, 463912333, 492540291, 341386658, 300144514, 41073984, 110328927, 876310698, 12530762, 792625971, 3377345, 60376372, 994349223, 790446815, 339814954, 176758533, 233113483, 466290040, 329155198, 159645620, 276206717, 538529399, 453687921, 880444855, 596720783, 400630306, 91614717, 2698100, 276968269, 212555952, 274222418, 554605638, 38917567, 34674526, 877892446, 720205762, 462900957, 250964918, 187203113, 827461746, 203307741, 646872016, 193171356, 212990842, 194381791, 440719117, 633490741, 619274957, 334015810, 485895810, 448924279, 736325457, 619779259, 716876130, 661176747, 940573289, 673519855, 708218056, 37970778, 980082109, 361434683, 567562403, 44563632, 920722999, 623658797, 594542993, 205307277, 741431463, 215207115, 173477543, 889496849, 607677061, 845816492, 284324480, 490248829, 847723799, 853148036, 285534543, 60938848, 976707202, 430127735, 703638250, 409268647, 187152032, 98281134, 272984837, 290434098, 26573434, 574310971, 122248679, 459450009, 154559768, 204607588, 788103938, 187627623, 79944406, 885934071, 959382838, 940122218, 528358235, 228316724, 467092844, 484371158, 4950922, 87838508, 607736080, 10948794, 805754219, 192905155, 793436240, 856998271, 494325045, 873857406, 66378025, 408730227, 189136518, 61493142, 929865721, 924709062, 743826095, 292891888, 805145517, 608448845, 201081812, 410822293, 317680141, 409492553, 888217678, 817416635, 392584648, 265285951, 669933113, 146184809, 796302251, 990079881, 487528828, 634922829, 996457980, 987002037, 332373475, 937191257, 837249583, 292118065, 826732897, 962754365, 273708121, 160204849, 882374686, 619478519, 501291017, 885807650, 35186851, 704007458, 759698792, 937845943, 591955123, 881279695, 732448380, 561301852, 132093927, 912342902, 506290512, 491145499, 614108050, 68626318, 208320892, 493350256, 281264389, 497177563, 360219348, 867045044, 756087413, 733199184, 624606739, 559523432, 270658258, 576794223, 8512397, 891493619, 443840661, 709456857, 262451529, 906025488, 835086971, 466380620, 908543219, 971174960, 828805926, 158396998, 573081832, 762607064, 245536485, 648781260, 221701573, 837223625, 598044595, 628893951, 529198698, 28454686, 836720295, 836628124, 959603692, 582306205, 114764129, 200515729, 756776571, 779857292, 127663976, 190599776, 36469572, 336752272, 411032856, 872264163, 923234662, 659036040, 643857528, 246368093, 18137011, 816512956, 519940543, 279599931, 670786097, 989900993, 582937112, 668246420, 156945432, 60353298, 257355633, 567076580, 928328104, 514239587, 934864954, 798196655, 939236756, 314243232, 238411913, 9287335, 596118744, 748396732, 351026979, 945582044, 710706374, 725609356, 89392976, 158719897, 1719803, 58077915, 269921199, 737852793, 799809615, 146111126, 386627523, 502440911, 484917069, 779027186, 475171165, 574276446, 14420177, 898443122, 565778871, 902794659, 663058127, 981357155, 998484935, 347698453, 396158218, 490011772, 485041657, 872975470, 974663183, 842956850, 378570108, 492204456, 363821193, 815855650, 796858844, 907458902, 78175615, 889623870, 390630408, 727112262, 826117130, 266173806, 665541866, 588113805, 616057664, 432731895, 701912525, 639663835, 242847366, 987831771, 561193457, 700557636, 854934645, 190302811, 943958551, 593635819, 808696176, 691017846, 894209724, 331686985, 761700313, 502027826, 503084945, 611218506, 273842539, 138086485, 475072455, 147768322, 208905080, 424139493, 548312572, 113292786, 934275775, 751997337, 848352959, 82727738, 525076001, 781644640, 811709986, 137074694, 860147050, 135940196, 318064359, 112403588, 395039925, 946136782, 178740872, 990144448, 912031403, 996491461, 852414841, 175096578, 455544189, 892679300, 90028423, 386884146, 551686888, 586054066, 835209094, 309857504, 968112445, 388146850, 658544444, 973038311, 409895236, 510431261, 200753244, 795376580, 634070554, 887877422, 395845053, 125316571, 254112105, 261774283, 198665671, 273259230, 613334230, 374756448, 135132193, 224069552, 457287145, 882407321, 912548733, 320776803, 841827413, 87607810, 247906864, 90060945, 563561653, 370399895, 429776901, 701941272, 591184107, 42242654, 132493494, 623937008, 232848164, 420070816, 826156332, 533892158, 777683866, 937023748, 729327040, 213087697, 579487088, 276626641, 865654665, 831953060, 949939339, 147613666, 402584685, 189908267, 422415770, 537069623, 439248837, 714734960, 924459570, 462569961, 767069690, 496375779, 30983173, 242228375, 637609222, 99414579, 667027794, 996022751, 501271139, 160579950, 474179509, 826536234, 702001658, 754425239, 43530450, 384459162, 417332265, 961106733, 611395100, 758469889, 327478685, 444283296, 828687856, 837106191, 840559285, 762456109, 590754626, 557836673, 236079597, 784853669, 598703855, 573818038, 161509795, 878731108, 203047502, 412457755, 980618319, 648620912, 242752064, 798872539, 68439678, 616531509, 260000359, 209196613, 739766364, 181192032, 861799412, 691331907, 858850117, 819547223, 1150464, 503072638, 961385950, 234470327, 126327052, 811458251, 461907182, 454336128, 194399485, 282859479, 944696443, 827108904, 760747834, 621889337, 826282238, 72173167, 364977054, 404378526, 364248110, 38541217, 752707598, 201297259, 295617150, 200318749, 623021770, 654374411, 401060688, 640659106, 703665912, 23099631, 475593337, 167637597, 354796952, 880881516, 54493414, 871391453, 592035174, 205802088, 369588094, 80609983, 961084515, 402358170, 325639527, 384444135, 402355164, 185265007, 974501033, 748024788, 28348466, 969189465, 737011519, 883277840, 670006494, 854378237, 13595348, 464469788, 326785162, 994951862, 662870853, 798183391, 937457385, 586815286, 256572563, 325381142, 201415253, 808627115, 811335213, 164030385, 74985402, 490691587, 256398830, 297709763, 731018714, 218325505, 515957781, 341129316, 18483616, 506904406, 419634062, 753715202, 278439828, 664414157, 512736228, 904388898, 582163053, 264864284, 202448480, 343435197, 623349965, 139734047, 786675232, 306427434, 115004998, 128815247, 478725100, 726561050, 564876212, 865340235, 256330592, 906938975, 207257099, 909474104, 427725038, 876397589, 461778263, 398272123, 519708990, 820787611, 169591777, 411206678, 830491677, 384832047, 750619726, 84921906, 989580692, 136211437, 944475446, 463577202, 812696165, 365126295, 320148460, 75442925, 320211549, 605994281, 21121370, 18455898, 541907606, 473556068, 818271436, 71392326, 339929728, 209146888, 899531083, 540187946, 164553653, 110563327, 399400884, 929664856, 984801855, 326932244, 407317520, 863233774, 881097195, 547952339, 555476900, 120429515, 930589563, 941207173, 331007092, 682892182, 864487690, 914593391, 380469773, 446403517, 475796453, 140684554, 925969229, 529341059, 133984475, 974499274, 544670559, 717405384, 815624352, 830973477, 153406905, 961617048, 541025477, 682536729, 249398452, 287454500, 915446546, 605701521, 491038151, 977198156, 361453718, 909373408, 627258541, 121942134, 959862407, 221844451, 451702838, 389276718, 454782350, 764209895, 738649481, 317549110, 828065931, 929048218, 247641522, 729417194, 991649535, 230773381, 140341084, 450917085, 312555269, 445150842, 879541685, 907620015, 995211279, 283997856, 553074165, 447928676, 703373344, 761263441, 74556710, 875141401, 170631529, 124702563, 720760139, 873060984, 905856839, 626942643, 328096154, 578565260, 847247395, 40064030, 776948629, 991408394, 131159218, 321789864, 710114948, 745128436, 985090031, 424388426, 887945089, 417485025, 454791575, 500564606, 827187127, 581207589, 367126440, 692209013, 408178531, 894936016, 945998614, 604312759, 788265136, 73501957, 135835043, 279457641, 194912394, 725057256, 990923061, 262809143, 301364168, 906377207, 523454826, 984175409, 249908287, 629779263, 75396703, 256934153, 516947537, 469729236, 552998754, 85178820, 124032170, 302668082, 666225148, 572281347, 689848055, 170408227, 811081317, 135824530, 842477307, 152921565, 273113096, 600221913, 414407528, 721570262, 503595930, 705159982, 869752973, 171416692, 691371308, 812178743, 624326102, 874690508, 600426913, 636927211, 856147295, 825935870, 73228144, 517478151, 819771796, 267042650, 340553411, 175756278, 108785274, 545158226, 126060584, 331208625, 804860822, 862384582, 29715076, 447480380, 489160954, 446055858, 924403529, 414733762, 224535012, 318489280, 688959557, 241000029, 590815791, 97627841, 275623132, 692095564, 936954806, 157825252, 424749232, 937376723, 65064405, 297063734, 513089529, 201978937, 155395404, 597019352, 451288900, 308835371, 785137110, 154537272, 24620718, 604489017, 620018880, 228170582, 262687193, 732820010, 475623308, 913033906, 203605132, 960821337, 255787579, 10324819, 772676424, 151372633, 191613175, 727199129, 851180641, 698102224, 277480386, 795379362, 516011658, 395866303, 214820297, 802230932, 790519922, 41919061, 980060671, 119679994, 764228445, 174144078, 716413604, 209054142, 896831530, 204341498, 421457619, 744750697, 943620883, 99187646, 195977921, 195948876, 757868233, 562041684, 890548077, 733605630, 215650371, 110632204, 140655374, 145866191, 518895193, 459736305, 5929870, 875521827, 346984959, 939473614, 469661700, 511213033, 371211082, 100241111, 425428675, 553402119, 771791394, 621055817, 75915210, 730749612, 682954708, 440164260, 219380166, 224257133, 700177965, 786350904, 252902183, 229506582, 701591093, 260396561, 437980844, 336575059, 778994146, 203670354, 423483327, 376572797, 442557469, 694762130, 680425984, 687246810, 13005729, 712135452, 180417531, 838409874, 845728988, 199235178, 59485630, 307998968, 330570690, 980963434, 912604296, 814143911, 911613969, 800234982, 301288706, 971092076, 957030074, 994674869, 625804951, 449040462, 666128341, 724769778, 171335809, 880630599, 159203076, 888980883, 610317538, 260070264, 940756685, 580393587, 112725065, 166607433, 337176444, 915866806, 941286898, 438446140, 923211262, 473290563, 25878594, 53726486, 423247441, 937022638, 876552170, 737494062, 984339467, 105775429, 73065143, 73420661, 254951229, 386406945, 73040070, 665091333, 214177010, 140429170, 234396864, 383495955, 613561973, 838984843, 409504019, 815517891, 849147413, 662259145, 337904637, 816384562, 325863910, 426019015, 276961187, 990303403, 534560241, 82909948, 392594836, 966339906, 948108675, 163415919, 149939167, 168505784, 147295257, 664315696, 711045969, 962614784, 7620934, 980502662, 496169581, 967042967, 955855276, 241571387, 361589807, 94705725, 731916655, 788350004, 390079877, 804896091, 809261850, 307265441, 593303548, 647100827, 54558400, 317997854, 791028838, 201732727, 450907070, 866554185, 279483418, 788014264, 57823610, 376130992, 208252442, 708564937, 990357966, 288046223, 424832959, 189686605, 815280648, 632141298, 608439751, 262236797, 356814321, 109838100, 620269543, 292281029, 442360584, 723347572, 722048276, 592692246, 175093639, 808220122, 364550114, 597556582, 15749580, 529256512, 187046352, 121362450, 388786701, 979671005, 465697245, 313541667, 806946897, 263095189, 290486403, 166407225, 935160232, 846239735, 41563869, 178010614, 719583817, 544833681, 820855128, 596813480, 704959710, 948970464, 70177618, 511348315, 472238188, 781825253, 484699019, 952680148, 530380815, 784195274, 764174682, 798600043, 592204235, 75434209, 8166141, 279553787, 168628972, 496394971, 527994783, 517543395, 252321046, 70654741, 758024840, 397794498, 118477889, 262790772, 550909888, 460915142, 986420838, 663747166, 191816127, 628796262, 182271625, 105275084, 83062125, 163369005, 595655502, 293026738, 98762035, 238460353, 511446978, 78013361, 121149664, 8624808, 777372166, 937094406, 265154926, 776401982, 505051390, 960470907, 928631876, 482919208, 673057777, 301472925, 353044291, 959448843, 812560663, 419169589, 354268800, 36225700, 183682663, 879233542, 123242291, 342271862, 736094280, 474662938, 886804353, 811514801, 779942955, 936492211, 968011092, 975341777, 533159823, 11028927, 957016887, 364152833, 410120908, 484859671, 248309442, 863679106, 995848376, 474790902, 636567171, 689255752, 70197333, 793206309, 312390730, 438710270, 721807456, 930970811, 340750026, 445169718, 313214919, 672530893, 994447906, 381761552, 978406474, 384426562, 991634751, 523333505, 958039852, 287727146, 536021526, 810550187, 925739515, 694527843, 423750730, 909442920, 36198203, 253146788, 937894034, 242635101, 831967116, 329453632, 745371161, 524915006, 72759092, 693926200, 150259532, 347939158, 231996580, 160477260, 941243793, 380627186, 271955842, 575370896, 987636384, 426629340, 25879733, 320035163, 382972405, 641084022, 521031142, 265572986, 371500459, 686098916, 355059274, 987999867, 238843928, 935805799, 171002473, 378353913, 69554730, 193661460, 121276124, 610209803, 34706888, 909089001, 852307480, 693845268, 737174719, 198369388, 531191200, 509544861, 399304458, 222551477, 482766165, 285540185, 163983640, 685645614, 783581675, 94192008, 555585878, 609125050, 890861612, 454582197, 202351129, 144357638, 453101193, 82015663, 112237510, 940237360, 936627570, 647766505, 179382300, 565573395, 276235559, 369477425, 11536170, 289133646, 53179888, 555867705, 621685090, 132678771, 659014200, 597154346, 209887307, 267466858, 725189737, 534192288, 126028606, 41825736, 866780785, 170612318, 750987079, 811912981, 744446211, 70989612, 436351830, 44790994, 801518956, 417772089, 525498542, 494526693, 396278405, 119827726, 974008868, 591534822, 891443299, 882518835, 42400532, 104092878, 337630936, 338417657, 270461677, 844429103, 225297400, 591598172, 952575799, 733240170, 724937523, 657274519, 123901276, 646950796, 735679546, 839961026, 700312898, 653860830, 585583792, 328157176, 283396066, 986514154, 693439811, 999215414, 167472749, 854274588, 949957342, 415336511, 819001566, 908394123, 417651874, 309194216, 129186881, 969656294, 728384208, 911266969, 503679563, 123602829, 265023951, 660044170, 4397939, 964412931, 341631254, 307752164, 443994280, 901595004, 864338333, 97957216, 668228879, 997528186, 615954398, 215185205, 569197319, 848686284, 442808693, 186829782, 209639441, 790584676, 825938374, 879787114, 774035953, 212980350, 42543816, 552198307, 585331367, 502947143, 752342796, 650644375, 957027723, 973149231, 749777072, 175852964, 639509670, 379598690, 394973536, 93626233, 408760948, 179667960, 686757982, 705691062, 989903145, 764254713, 274635998, 121131501, 356921592, 305388958, 162559039, 372312087, 709988602, 112668206, 490591262, 794105981, 518899912, 331042842, 970758861, 197297252, 390364636, 85166700, 349411492, 698540766, 413061136, 993272933, 786381318, 343894922, 20917284, 4162469, 818986811, 788392271, 343864149, 49813590, 854778573, 577329127, 212290533, 582017931, 181499940, 718292918, 976197912, 653388167, 607129045, 7339064, 225240018, 485774889, 86942900, 328392154, 479547052, 772380189, 475228221, 847088734, 14313225, 575692530, 90328446, 763361740, 171004488, 709335576, 400612011, 99914507, 51609070, 62520579, 319803593, 714094857, 123215178, 477615656, 16209250, 199351999, 538780836, 561036744, 107923232, 523998792, 166330927, 853896866, 381803422, 531229335, 728074918, 689573684, 907573007, 590581884, 916711217, 95609844, 129410712, 56584327, 959503064, 957056750, 174215174, 744459038, 628985450, 544700981, 256370856, 274085016, 569969065, 80965709, 570140769, 278915121, 384090535, 908985961, 495909709, 899372711, 798393288, 634366113, 367735202, 222448367, 351845737, 954035471, 983250113, 820438584, 42704652, 653660836, 812552967, 657742693, 792480327, 753678477, 263812641, 154229201, 496536597, 999420510, 299597162, 364773715, 211490008, 21104206, 310972890, 186942321, 757251207, 812453231, 663833786, 922407489, 59946741, 564704393, 126756380, 685616429, 893601589, 736990521, 400966741, 116627896, 112251287, 358147473, 656532732, 341659779, 781811635, 496072654, 84594744, 834210672, 774323215, 286979415, 236179242, 497487631, 986294165, 606264334, 581344411, 604436841, 89367990, 183301355, 735670029, 428543862, 505296770, 785706692, 234715939, 277162883, 32222492, 18460317, 271996127, 799991118, 760150530, 269722520, 146813081, 926958666, 951859911, 503574939, 195066606, 804553622, 215936770, 918069808, 378537540, 798837642, 425180116, 165197802, 499316498, 22168589, 185500076, 508722878, 889723976, 908263988, 139195262, 606246954, 657755291, 315325647, 228660461, 927778893, 773886452, 439856948, 162230151, 879081064, 101925670, 524899845, 354342522, 133025868, 108866469, 121189181, 270276064, 969560216, 722147931, 313498007, 719133170, 624863408, 938930036, 536249581, 425190927, 272648950, 434021221, 387834573, 292316946, 274994692, 507311664, 570350651, 195366142, 485475398, 442659745, 471245125, 706289563, 654688224, 271869745, 209340773, 706623957, 567840485, 616912489, 167930641, 303686752, 367962771, 350789032, 80236200, 488932009, 964321600, 927976838, 81006556, 774412764, 160244233, 471356767, 991797103, 666297061, 416998448, 934599153, 595460050, 776591390, 257742904, 808988958, 693050843, 103653544, 128413832, 354563702, 462954621, 195328082, 359138347, 441836915, 957489681, 796564917, 846676910, 540525398, 513848662, 997378051, 228900217, 171561307, 884494259, 721353654, 167291613, 123767666, 215668879, 729854390, 397159915, 5679327, 91757280, 460993580, 758892395, 63364111, 208641496, 970003687, 634189428, 430341582, 744490912, 968857586, 949030417, 553839150, 216345426, 782160216, 792328776, 395705944, 866853155, 286856891, 52236982, 297869558, 201704212, 642231314, 334898280, 455213838, 232079102, 352590943, 178636650, 535975629, 82298428, 646038502, 502890869, 706507039, 474355858, 378367492, 535213711, 116407579, 319484256, 720767517, 246535744, 149382399, 917995160, 670775554, 681126581, 954512373, 797491622, 604082172, 729862161, 511091348, 100672983, 385805541, 762425255, 256157537, 931194850, 560295789, 722837799, 328350201, 354399213, 92596021, 587112390, 810973259, 938371616, 329036152, 46203198, 11616611, 21259407, 692061430, 750532131, 105217242, 726942756, 514312248, 941080895, 335716006, 907162999, 246758021, 552082575, 75297184, 709313219, 695892239, 580985617, 426368424, 824466468, 170874326, 903685463, 174693086, 947539186, 37396746, 101157192, 662256145, 260992070, 622977927, 968943493, 901178788, 862455773, 76973103, 433756078, 68125774, 825843489, 329407402, 955478178, 600573316, 479181475, 453581187, 595941271, 433304677, 56378151, 633487342, 494755687, 493647493, 702660394, 836942765, 920512286, 969629067, 708496326, 976141398, 673631482, 481578887, 745001298, 228865290, 492279631, 902358953, 665644545, 357636002, 407896753, 399474653, 957377649, 720649709, 312245988, 726258976, 655544170, 656631691, 923978810, 525496169, 583172968, 278704317, 266763811, 868822416, 289935922, 413678974, 742915793, 625366611, 417987874, 154357619, 378033914, 586283498, 821889053, 545559974, 299862341, 386532046, 239241952, 856158621, 887565736, 934086935, 495469834, 804782016, 300335237, 253522125, 516950612, 191703017, 690509366, 389966439, 774017734, 305822339, 43597842, 28146425, 840223154, 40448111, 762009308, 964358276, 776198924, 676125809, 405387575, 889967028, 958667358, 239935066, 89479564, 685958360, 367961757, 811350539, 630777525, 568511668, 374273340, 283463622, 781474126, 211086524, 390712317, 40869657, 253756557, 626884512, 113319930, 428770206, 516517849, 182327581, 258051145, 751062164, 453021476, 209763508, 935194281, 20060535, 60414480, 177719930, 884271211, 109869739, 209653092, 708260, 385501635, 886535262, 867463132, 978581191, 598943712, 805049182, 260627808, 163405322, 286408763, 743219258, 128122552, 534875474, 54629670, 649512062, 279312123, 402845103, 359140116, 372800395, 539408118, 137486651, 66594538, 648677736, 249037799, 352003761, 805983648, 855661793, 838101977, 966584215, 254313752, 707375407, 179607649, 200880027, 143531642, 715758635, 114842541, 777971516, 533948872, 853579446, 237192132, 399153048, 253078883, 786767054, 621974218, 661204384, 384911236, 186524396, 694187772, 41970709, 919169660, 864282142, 239421868, 339161732, 516488567, 519958019, 528531659, 61409824, 173364939, 182203345, 98940850, 349373260, 856604823, 916497458, 674392523, 282236000, 713833160, 462506977, 708401279, 694659673, 579465778, 13682218, 535394141, 727635635, 54414410, 80052747, 921974647, 988265240, 641338878, 857810302, 877310557, 543762279, 680159043, 828170042, 248374536, 996825065, 914358257, 483572020, 872306412, 102228516, 363830363, 199715027, 483424229, 681246862, 358050989, 739865461, 729474664, 687499309, 83883873, 619888911, 63919509, 89580931, 986969515, 880180653, 782124246, 772211624, 926728556, 750498195, 960907109, 468747481, 582459775, 194419538, 593745981, 107572772, 453139383, 858102731, 73196554, 642796804, 739325068, 736678254, 424960581, 80889136, 943870697, 117909597, 964629010, 540697635, 854314233, 136923569, 923459171, 964763093, 139833097, 808367725, 824353455, 188538504, 507976604, 887012128, 455119635, 284572309, 583753838, 378567908, 40274501, 271766003, 709663162, 350727677, 415386190, 456743571, 367387199, 80759919, 259383170, 547971560, 325695832, 428876929, 722090305, 492455680, 369959056, 663461364, 180943918, 927920824, 958017640, 57607853, 569509347, 116227148, 579311918, 864362565, 369474601, 615265190, 10288847, 251052525, 876303943, 193318381, 393265834, 780360005, 854401549, 889920065, 814928908, 892193817, 935735418, 878590351, 746315093, 664023130, 929215657, 712351016, 139546212, 205397901, 458050712, 724796747, 9881699, 36003408, 517835809, 381185336, 436786129, 533180198, 542553241, 471298520, 848299852, 941739321, 115719311, 914530382, 795361160, 988057911, 530273205, 511801399, 938922843, 716481221, 896904800, 542110113, 400475008, 772598967, 962724510, 778504679, 895860878, 715570724, 657062446, 557913851, 332375012, 710161345, 437115597, 778865076, 891746056, 301495540, 968423949, 982231830, 509654458, 420687400, 520397609, 592358099, 345820764, 883737198, 684728911, 196012538, 929423939, 266041472, 203595711, 303278580, 536587286, 186641062, 689276880, 711843897, 69385283, 786573587, 151243040, 940899730, 154270385, 507704474, 655133128, 546175456, 790601309, 484502229, 342591236, 115725530, 675141648, 933513489, 195412461, 33284616, 559571005, 330088016, 681807694, 215489036, 276630185, 318633981, 473747201, 5890801, 367430025, 990203628, 482638487, 880277518, 757334763, 835918336, 463648647, 573354787, 310731880, 542362672, 609456683, 624315036, 30367523, 561258876, 976008579, 451264498, 637525413, 654094145, 859258865, 330674929, 949234116, 911831688, 396631776, 305845421, 875418685, 660443533, 170079267, 197271500, 896952110, 218035953, 373722107, 176882676, 179875131, 792713209, 907300979, 351836111, 665322090, 426080727, 557077245, 122952213, 834475237, 630623172, 188734328, 35610417, 283155016, 649073326, 135972305, 202028472, 528968016, 318104437, 779481509, 34235204, 500529349, 385362030, 928509185, 184816722, 476677263, 921949041, 658523635, 439872785, 645597630, 210965006, 937870322, 283047652, 334222466, 15757041, 744118288, 377465833, 12445159, 58467670, 972894210, 548857504, 451306700, 216926386, 473106473, 121624855, 520660155, 232353639, 300385241, 818452051, 721507323, 257346264, 933631541, 437734302, 433006708, 115722054, 309992116, 683901974, 530969488, 575938556, 71796861, 432986593, 133094722, 975020293, 666387762, 221730377, 799402032, 438180688, 310390850, 244770169, 371527436, 444463680, 912982892, 670785103, 65732576, 990656124, 659263839, 58192336, 247116856, 944799334, 58685830, 461556911, 809867551, 736153959, 941822068, 196906842, 398447758, 146111551, 681271638, 711745479, 903672505, 612893310, 893406661, 442568961, 868135642, 204264014, 270742220, 693535504, 272463798, 419541703, 990125512, 47649036, 995664098, 424885982, 126875588, 102094765, 485836019, 684175303, 204043001, 653456205, 248596608, 451351765, 79730793, 761383720, 309108407, 989012460, 188000877, 772836066, 45027618, 68760502, 757395029, 46885137, 437613817, 336367813, 813885235, 901206600, 886136046, 229779095, 891209406, 204971276, 136003383, 113707337, 367269602, 56234599, 428472518, 481084472, 340172985, 931208691, 795779068, 859420339, 122621829, 703661822, 234375734, 799563149, 833391187, 567767346, 20891410, 533372525, 165931429, 960668568, 488410580, 758431447, 374747576, 299825383, 560616134, 381575079, 371450078, 960444484, 318488581, 126541428, 388556068, 902565104, 708149762, 602082201, 668915994, 184030685, 607343436, 588063337, 278810564, 570227758, 203403527, 663861439, 204924938, 364449939, 514403442, 367144138, 434299640, 971931913, 737842781, 107971338, 462669375, 946145057, 543401997, 543657975, 726106279, 672368443, 250340852, 123303840, 369581598, 621165906, 845401109, 509261301, 525379199, 349790107, 473201407, 588311524, 556034306, 278655301, 124368382, 605176024, 509218708, 101147878, 515068372, 147246394, 371116300, 843912590, 752657612, 778569830, 817957199, 979453570, 465411058, 213807931, 487681542, 304816351, 595871843, 378417567, 821739500, 436357133, 332040925, 699082862, 723101268, 357818742, 385027562, 72448155, 9426366, 53449665, 377338294, 983906464, 900128180, 665928022, 449572779, 122009240, 362529297, 756596544, 475888523, 141972648, 259820516, 447433920, 99879154, 788710288, 875698851, 745695174, 48899240, 20189679, 605540793, 132615570, 430511160, 363742760, 998270835, 140199943, 588168152, 826739812, 562511712, 485204670, 624524396, 502472205, 557134465, 190451554, 889046148, 792943058, 624804443, 967528804, 31491341, 540156648, 823581440, 532008436, 840033593, 745764517, 832299653, 76079889, 702740912, 226594493, 536192981, 706575619, 608206918, 216668130, 506786228, 997880007, 438376534, 742050043, 148943874, 264888049, 601719026, 268447298, 933806462, 998123340, 808283301, 331836330, 222421613, 913500248, 170019784, 687155346, 778733630, 97940580, 517088522, 190242075, 887682906, 747710093, 499042930, 745041228, 885044095, 111822895, 456592942, 858849654, 821323179, 519900669, 196055786, 92576367, 687135986, 177719954, 430330440, 141348772, 114567453, 518703000, 54540544, 152125693, 82548652, 35697320, 132459448, 595227510, 503568801, 907755, 939470459, 742360673, 804854641, 250892542, 257764185, 988638727, 305560289, 830750018, 267997696, 480470986, 816447015, 35613210, 973655637, 262829702, 680757480, 970823635, 486587761, 21146520, 118649308, 99749580, 259699796, 90679265, 291503336, 15469292, 745348150, 982044677, 1177114, 64484920, 959690296, 928130942, 421395413, 931730894, 677520010, 685550958, 125092725, 950249646, 380302096, 79533380, 599098826, 178350661, 924822628, 177408891, 544799990, 595540777, 491914245, 674571438, 635853884, 955868785, 980759056, 803184353, 515510975, 758508810, 338169920, 272293457, 1544045, 219251485, 604376101, 865324164, 659828884, 889483907, 742772053, 986149420, 532204187, 66164191, 712175026, 248054315, 846579805, 79137520, 145656303, 454769853, 66760724, 350810002, 602616804, 874720011, 843459401, 500102309, 621818043, 671679008, 435778088, 974184418, 537710360, 397806782, 601295491, 406823846, 102123720, 874137648, 964315143, 425878915, 380601196, 757014150, 468062964, 449809805, 61475284, 437151921, 892333200, 295853524, 755784950, 473502580, 582447599, 178527685, 621225413, 909699458, 982036677, 851382779, 608001085, 986290945, 147654185, 982722044, 615506010, 468228796, 110852254, 51576746, 469871799, 691423098, 790177557, 469584804, 450787906, 291737697, 150723020, 899374535, 131539979, 123670081, 682224816, 254438757, 811637070, 355446783, 733924224, 2310157, 662000513, 584713932, 107049950, 804894839, 953102208, 539143966, 614823394, 753356414, 388564083, 491029560, 314942459, 836879766, 234519757, 822674687, 676750325, 451393208, 559789790, 226696490, 156859937, 61268552, 665437415, 217324070, 382844115, 719644950, 863935623, 832174860, 66265682, 408913511, 301624803, 108698918, 796408132, 555773377, 498877490, 283746741, 176624017, 17317757, 337157761, 674230233, 255924396, 85037055, 764462217, 364221237, 700756109, 317029786, 804325112, 382428615, 543678781, 628212109, 172279690, 616412781, 184740260, 445454218, 35748665, 308373504, 403806371, 910772887, 508289327, 948315401, 614407265, 442443691, 602745783, 718564968, 983511598, 576086311, 245665947, 948595855, 888629378, 736701290, 483104740, 540699597, 131022426, 909681416, 106257394, 7507747, 883529380, 286254270, 862316551, 810144884, 817312181, 953535949, 214848160, 174474070, 349394021, 188614549, 199324084, 968395396, 363748716, 814272093, 426447544, 461185348, 392279401, 525341782, 708597489, 512289730, 874064448, 198576013, 551070237, 327980630, 369253736, 494732228, 763006062, 655231210, 766990531, 624407768, 260087797, 149428995, 442793232, 830096897, 453224997, 75979337, 825169843, 52572231, 189526942, 32248548, 605044421, 163746587, 250276278, 750637380, 30050616, 449928117, 695446487, 960640988, 400470825, 996049280, 719355502, 332729485, 977345417, 541831822, 227456297, 97872329, 296082599, 70911513, 242531336, 899255100, 299665544, 123152539, 800780041, 300499151, 17234694, 93545057, 633951216, 841615832, 635428601, 359133739, 421571058, 310398552, 723044270, 170045986, 761472497, 680837441, 843623585, 413035879, 912501955, 291934777, 496011478, 544872418, 995799807, 916513660, 689643591, 974460670, 711978457, 784288472, 17520541, 602259454, 996784306, 126554430, 495475184, 546386102, 918184064, 935243398, 746585929, 605860071, 218346665, 111093999, 104928935, 726464760, 295795629, 351894703, 941236363, 626689993, 144232765, 232425296, 146929936, 927322090, 483251745, 960669780, 737704027, 701495845, 312475057, 1615781, 966282581, 256638242, 475057140, 507374803, 840142422, 968105862, 663868801, 745882387, 606275217, 559958078, 96984052, 57142272, 815702652, 40182356, 994718218, 779643195, 365351960, 743400523, 194215994, 138294111, 637952740, 951594365, 534604750, 552643304, 739114338, 953857779, 288801960, 658487189, 334144414, 571355966, 280361034, 64693972, 90548086, 955624619, 387515384, 357584602, 523815377, 876577485, 684941544, 194853520, 519636506, 737645295, 349387639, 125932529, 246699010, 237641122, 649975687, 511421175, 328139546, 56178882, 659980645, 962704899, 443272199, 846861677, 141693182, 796615676, 253461330, 62162780, 396032488, 615736785, 268053776, 654970531, 54534761, 180999714, 520446347, 427954409, 331431219, 711641493, 603072311, 149107918, 979334989, 705115334, 530612748, 88143785, 28843252, 792888842, 137589101, 623787781, 375477319, 221209197, 267341032, 667950012, 611625448, 67885028, 339195132, 687261245, 1599387, 659374924, 827645797, 940881963, 654819982, 403024857, 650924657, 777222728, 394361903, 491267974, 152961708, 502304869, 14387873, 111690445, 625069964, 950849925, 616223560, 746312872, 327605933, 48211900, 149407121, 598665792, 319636868, 417858298, 143800720, 437245342, 326508948, 685265451, 88935845, 856740257, 633517489, 138494265, 562284320, 496281201, 903192654, 469464658, 529721006, 899977730, 495530646, 751799467, 961640740, 889483112, 169705660, 529072383, 437476570, 65110952, 736887177, 336872129, 223229677, 950220161, 567781903, 108876178, 801907681, 189860094, 93820508, 11261840, 333924624, 88853935, 187595603, 358401350, 348342871, 493375571, 730688088, 111408861, 220493930, 930821006, 352551214, 769173970, 363356766, 949293492, 663290646, 430434241, 934442424, 516018724, 718334738, 16080964, 552545294, 586648411, 35369517, 45955824, 546503811, 178095178, 53518691, 270289508, 405036189, 275699776, 166491856, 798071196, 656778448, 362953862, 43616866, 71709781, 412708908, 638948052, 331237108, 383432163, 286023412, 133963484, 469796059, 511908793, 946537192, 900780057, 595888679, 416159579, 119543155, 177162293, 867265305, 645171813, 946316992, 909059283, 914814032, 743216292, 316736819, 159355148, 663508686, 783030256, 946899545, 821213414, 420267383, 393470923, 280888559, 990871878, 241350123, 311665373, 243345662, 116137987, 749380753, 945377675, 173854494, 634448983, 847664974, 863686262, 748649297, 712073281, 969066110, 17656665, 718746022, 686700678, 84223914, 875149189, 357691471, 742860807, 717165597, 965221004, 308788878, 836628298, 872063664, 326622608, 713991127, 467097591, 389244605, 576329451, 384984457, 627058696, 282044112, 358348316, 119903774, 678076172, 875892281, 292988619, 471145855, 874635784, 690831021, 536011185, 61842282, 55984841, 255313910, 21633367, 294610215, 935221413, 498238262, 585405783, 237765412, 899986986, 695876464, 415392126, 273430946, 53773510, 26149799, 650082571, 927078726, 19228640, 451381423, 560289483, 940529082, 428501190, 340315082, 507923841, 498032659, 836050854, 815920962, 571059817, 424987106, 185547053, 381849835, 570526863, 180955112, 850806883, 845442115, 689614330, 195444339, 307495168, 226230219, 879041419, 436892018, 629323820, 429571247, 2005431, 623088843, 440468740, 973852281, 765827108, 696926861, 432442461, 99227490, 677254696, 977152834, 254338962, 749229, 50141898, 601955169, 348035003, 907927559, 842497506, 45669545, 403972998, 382345180, 862320111, 71458826, 499357965, 368848352, 383206665, 400750628, 904964744, 458211660, 35208087, 41514642, 806921399, 956918911, 74517698, 775151423, 195708998, 464305048, 586319253, 695990456, 272191302, 934759869, 838841552, 886860995, 953088139, 981036412, 643019348, 644187430, 475176369, 709522978, 435562650, 393905129, 115301629, 42461115, 995806369, 393742457, 233957003, 634294668, 671256724, 581855273, 197487355, 378455300, 268445185, 612965455, 601983783, 250847145, 407427879, 47661763, 807203944, 187607103, 133019848, 322902794, 687613475, 781621001, 264447509, 679595511, 557202808, 725016213, 421550471, 46086906, 973832923, 131872133, 48262013, 81154059, 931388246, 2488276, 681210857, 707861157, 789428928, 746159608, 685680822, 267915538, 404486747, 338854071, 613194767, 876993837, 987763822, 149341488, 940652119, 536766406, 252688994, 638579902, 359114209, 77828797, 543814004, 198429455, 965602927, 866585787, 535373446, 85523636, 667471333, 803469703, 357999071, 465318218, 620582637, 599432336, 129743687, 960762026, 856207448, 32984659, 176281546, 779461689, 768350350, 50367821, 89564945, 366021990, 164097647, 459402427, 139250993, 593196199, 965957450, 751415505, 535381840, 419969016, 194880719, 576035025, 167649765, 67748459, 779983033, 128373536, 570744043, 549446195, 143228318, 541980313, 464333185, 243137620, 110154564, 179875796, 164202130, 97802556, 823758519, 432651005, 196302407, 66565107, 196458440, 3201610, 446658, 535286357, 746070465, 10814587, 108414447, 722166439, 970021076, 253809874, 310574235, 5822878, 600347458, 554357879, 834416065, 935189980, 963486683, 485321472, 98042754, 651700002, 453339055, 347938737, 173925671, 468474463, 809232005, 191643914, 566399626, 162758840, 670276583, 827265964, 174004048, 433062554, 808524482, 222513836, 532167290, 360564496, 769928691, 797620197, 824155065, 388777, 71007442, 506883838, 563291030, 352031059, 824803229, 539282210, 193164515, 189512352, 837262768, 210246031, 17678486, 519941500, 811001622, 142452300, 248610074, 174527128, 217949010, 796613211, 887308530, 377110042, 241206706, 273387813, 838818424, 657687027, 224802816, 24896262, 852620075, 939196582, 285549434, 890029624, 53042820, 779957626, 101248220, 732155084, 896906221, 695790986, 665447874, 572694482, 480813741, 784242740, 301161205, 300810236, 28243374, 111453978, 445469049, 336530590, 855976067, 895346461, 288524683, 661445371, 276611686, 687649606, 923840952, 6698953, 96276914, 197355023, 209849241, 330677273, 856768813, 362695948, 893284970, 444728750, 726145181, 244881883, 281009951, 529018553, 935827323, 363059764, 825464094, 82061511, 70054430, 811640504, 640852654, 964360175, 626407045, 75449007, 958103008, 114716958, 867395283, 325845736, 191897746, 498556300, 747992850, 670180491, 511570331, 167025985, 4385650, 281023033, 78938448, 732289270, 994676831, 460178875, 585075749, 659640600, 473123211, 384011986, 494854497, 259455661, 70597317, 458415606, 863102639, 178635756, 134953631, 924014673, 715871521, 429243165, 693546101, 146417511, 837923242, 719275835, 216959381, 216732424, 707086543, 262559105, 752130810, 303886466, 529916472, 938437581, 165746988, 576115151, 193914653, 217564832, 547535259, 169776360, 401674725, 422530721, 180491859, 938144888, 40035954, 279832950, 662235723, 716073403, 359986749, 859131963, 121745326, 461257090, 609718101, 414827292, 86103216, 2681433, 149307394, 806800296, 993341736, 938747282, 641504171, 757851639, 473947441, 685471928, 235973887, 277425662, 514714668, 653746228, 505796036, 170522441, 748720104, 214176378, 862963405, 253934875, 372259462, 496271067, 149208016, 255990068, 35620838, 408441115, 304505441, 862918157, 433751626, 261059379, 215878209, 669305764, 763825600, 529695460, 174476643, 143751394, 912127531, 722647815, 649758036, 653654754, 140650120, 555947591, 427106504, 838007690, 377297397, 284327015, 722050673, 283098430, 854243356, 488305417, 74461752, 15010803, 725149420, 614445485, 959550012, 76873762, 742883454, 43823524, 809713026, 234643734, 69028747, 26033435, 285046044, 400500155, 456863249, 316304521, 523267711, 711962542, 996479151, 947249260, 2216268, 111570039, 906586131, 876437542, 84906249, 432807043, 846820701, 515498573, 952787021, 63638955, 714526015, 863238254, 155796602, 16522862, 602024414, 6332892, 219382169, 924639934, 238682351, 950453473, 535559040, 52429990, 199399202, 482815644, 697929640, 117656527, 133150630, 770878826, 787131145, 576732310, 135378759, 588414052, 752207234, 50392475, 767022377, 594001584, 997585870, 346599472, 610548899, 983784705, 343144743, 492481682, 758491243, 778390804, 262456915, 855390828, 88043154, 592118165, 276571930, 824870295, 972054120, 682425755, 570866261, 239094726, 886034404, 593868826, 885582334, 934465191, 672727839, 600989338, 491151662, 238242567, 821520239, 705578188, 474024065, 253038307, 286323487, 215983593, 877677357, 49295443, 119657665, 682163618, 377923045, 677334500, 721064768, 135248077, 326163360, 788156832, 319761500, 796904155, 143353188, 603461863, 409152673, 736490702, 973555810, 753649814, 43547228, 170430754, 598836839, 670437507, 250924187, 293012218, 609078557, 352479657, 386028718, 411826614, 696411471, 269150518, 712451467, 987828344, 516659756, 420115960, 584779015, 687929523, 497758719, 215033438, 654319988, 679851583, 939875904, 306599669, 775585536, 92505780, 584977696, 668331137, 248952992, 531604760, 35985106, 123965089, 9470483, 482485115, 561383165, 573724953, 92681107, 545913429, 66804044, 315875511, 700968797, 829397608, 549648691, 323356577, 941649790, 371983855, 111122625, 570714476, 44331211, 54554824, 679996420, 634520679, 672318168, 741719323, 190954241, 915024030, 951948173, 109417503, 64965207, 725050789, 860977465, 38444411, 327028150, 682829078, 85029570, 356109546, 662412516, 546218886, 495527633, 159425444, 396824883, 787336129, 837697965, 228290379, 444542543, 63733047, 614025845, 738964111, 81474850, 957654637, 630111012, 248201054, 484882594, 912847904, 188791526, 995403366, 100481323, 173468099, 564385354, 421106755, 288796411, 52197514, 583899222, 963013876, 976506220, 300338080, 606268824, 172169165, 670422827, 325918558, 289245738, 461929082, 975983339, 929240235, 651476200, 868260105, 274781169, 119251766, 971397026, 173902595, 495699857, 552992311, 674064163, 815212002, 812927258, 785977279, 82448657, 275482542, 139194238, 273897708, 220177990, 903120102, 545055358, 786863883, 618417053, 418900585, 979721531, 626913285, 58050742, 806349324, 985735515, 439829172, 485513827, 300930458, 444166664, 954433827, 178599027, 596160530, 397893721, 907701552, 826671380, 165906512, 955862217, 881910640, 865128420, 572795532, 565103470, 509704708, 212909438, 864117140, 963886601, 673381742, 317764852, 451412512, 489623601, 801502227, 309719431, 267295633, 385583903, 531563988, 835819410, 795829143, 960071238, 575655498, 508730252, 526663767, 789443226, 221193743, 902525043, 195640753, 125712797, 990467904, 507683374, 850882115, 964995216, 550324955, 248286543, 779951988, 220389794, 767268915, 611625991, 772918214, 650068458, 406270936, 602323631, 855189994, 693997687, 50673117, 834282228, 8753233, 283100408, 78029415, 898128398, 304633674, 358473901, 57671675, 749067650, 910397244, 448649256, 525099093, 139507871, 923022332, 529483924, 67074431, 130802898, 65349084, 302670392, 327039423, 978233221, 147007938, 817929485, 516899116, 728003903, 300930476, 216333745, 864173842, 205616293, 139125181, 710710067, 838627828, 516540334, 503517745, 372343184, 172057950, 149035861, 587931537, 164109657, 242511342, 412462730, 86622825, 283744303, 692370883, 289422107, 613269068, 514398255, 155067362, 604172565, 917274572, 818422869, 993423004, 763699999, 757748318, 101029667, 856217183, 213630193, 469392143, 571518168, 265022416, 900028283, 732078412, 70567897, 194271437, 897569702, 537905845, 129538105, 363834821, 776695001, 359440608, 179731329, 677420254, 45235722, 471542153, 395771141, 847744685, 162347048, 903629513, 644645020, 622104177, 774417672, 396141822, 610075265, 939968385, 121637040, 833545718, 919029984, 77610459, 964490234, 721924959, 32319928, 120229011, 490902809, 35517493, 640177779, 15121853, 954000294, 308599485, 406475164, 74840343, 870300643, 160422124, 186036411, 965436221, 697753632, 810078601, 302595334, 352013999, 971605423, 338971933, 950021383, 74876201, 959943537, 743915562, 793390837, 648922537, 551448333, 37088447, 113499323, 668322968, 426594033, 387066623, 180772673, 475630157, 338238578, 692314349, 845103411, 375885404, 250092144, 566026469, 341773124, 869501419, 630825638, 24110724, 615982710, 540370913, 598589888, 682972503, 403228289, 826871596, 265852877, 330266945, 893639800, 835257865, 304282458, 185741033, 38504583, 750995036, 687124971, 328210072, 234899376, 956070838, 582697103, 587748946, 127391936, 682869259, 19715392, 373409659, 586664469, 905797514, 401841322, 56334065, 938861306, 768419381, 934563527, 611490014, 506837974, 451529935, 50300541, 990993227, 768793350, 532157092, 196197824, 352337641, 423946703, 416925199, 585833590, 368833582, 881713229, 292992520, 662877758, 59080594, 25746956, 845002585, 924958928, 317144121, 176969397, 247228579, 173168645, 791111055, 189408174, 661765805, 105345267, 410741195, 545984664, 256921855, 655544555, 295381500, 742983089, 336911528, 154187345, 912819488, 349368157, 97690182, 96285936, 74464974, 145489168, 260159897, 690891866, 463940099, 950826241, 804035758, 789185726, 583067834, 511545513, 173198802, 886685794, 681522156, 213770927, 193877128, 647528509, 255150220, 421034243, 970894556, 461104050, 854672675, 373231146, 350908572, 771058363, 551682333, 277530860, 705279888, 952861901, 1211247, 470239554, 277858274, 943974561, 914261766, 931077601, 927309949, 849511488, 207458701, 776004679, 257440861, 962418285, 907641543, 245571629, 135753935, 529259158, 421663170, 71919489, 614027682, 348106639, 630803740, 432913598, 160097566, 219457023, 776508056, 291697076, 259424745, 768623679, 216655972, 708859358, 530682078, 987316804, 404289670, 595771990, 273249854, 149508777, 71203155, 713398475, 456081375, 303563851, 568499333, 512672065, 126334413, 526460970, 107472442, 282244778, 286699057, 493932218, 638782210, 581816903, 85489105, 586774856, 61015758, 175092101, 610242223, 747420776, 433804131, 704111182, 877148573, 828413359, 878855602, 236053006, 528097269, 549830212, 40446500, 968171859, 520288333, 364535660, 670637272, 942580850, 921544501, 933220856, 81463433, 43185921, 598808143, 991247398, 675616963, 121981235, 544714909, 139811264, 41023675, 761625127, 68785290, 807462665, 197550272, 912354198, 336234010, 417973084, 235963409, 218269206, 482510992, 463526224, 566497699, 760142121, 354976953, 310435389, 426613866, 263680237, 593937351, 651363402, 262293544, 630005736, 786703585, 106299577, 795230207, 194539670, 685159617, 401609024, 181881831, 352555717, 922716031, 570858267, 806242878, 812129441, 222107408, 360697000, 558054193, 21436340, 948919304, 697060931, 989922595, 681676498, 348869101, 441978495, 334004427, 520438573, 785080058, 426714772, 998594121, 801715878, 972879838, 499765065, 532975907, 195758070, 524827730, 54312099, 916014577, 283165590, 632632405, 387395759, 324287623, 54824509, 573536864, 57353798, 209875643, 426084184, 925087136, 42692571, 6650096, 306463962, 34446374, 767565696, 178681459, 333265872, 91522023, 216598488, 472146999, 582102230, 598610788, 182048444, 508068765, 145737535, 704528729, 870495174, 934776368, 329614827, 23012401, 965551426, 897220575, 374105702, 320263014, 274295201, 230639616, 188839359, 890154924, 313160252, 636826981, 131228866, 885295815, 664327081, 550235625, 375648927, 815746154, 464965031, 429421500, 539186954, 439885812, 511454366, 504433086, 555198486, 755623548, 393278516, 759572176, 607833230, 513895677, 877521004, 681219745, 343635221, 386343738, 977102889, 325262577, 17993467, 606414710, 839532889, 911345769, 71756176, 214775276, 730531370, 54906386, 630000297, 618227693, 813516432, 363456354, 308104732, 321109476, 509652459, 73006029, 663643709, 258951009, 339882378, 773251714, 21449291, 628476369, 273267766, 580747328, 332830190, 94694005, 42625129, 695810238, 982658846, 452169270, 771035190, 80348571, 970848545, 943937097, 172033751, 404147378, 598904764, 700531095, 498868754, 990973349, 920066862, 697683496, 684534059, 423812465, 902806807, 119737717, 317774775, 806637443, 278977696, 656114106, 238512840, 972942001, 207219752, 334304093, 455306696, 610295863, 727306850, 808936321, 570495328, 673996006, 461035961, 35419530, 666694411, 8915842, 247010638, 462682664, 185861822, 518878490, 561311016, 677364809, 602499003, 267734192, 295464341, 932361458, 432406011, 152050684, 810656616, 906665410, 373706812, 706021905, 472200363, 551936608, 738440243, 718917302, 879742445, 145664089, 302646953, 678778845, 669414652, 128470741, 810504842, 836406042, 275671104, 677222252, 476771535, 75605489, 456514787, 659976885, 897186774, 159830068, 252165668, 661463448, 833738531, 748408836, 967689765, 160996808, 258894979, 134902748, 141406993, 999549179, 295680690, 37364322, 461802718, 613307824, 25915497, 807742944, 969000624, 598802119, 955333451, 401378382, 996925028, 625023668, 63687356, 143548413, 123022123, 939817474, 120579160, 995315922, 825854458, 40040733, 177297158, 359523621, 930324004, 311243667, 273253182, 500240862, 415359577, 343957461, 229955628, 741653321, 14852651, 966344628, 271824675, 469693809, 5149787, 364877273, 301276125, 333402205, 193756479, 419268118, 831962580, 306005446, 623331456, 833451008, 999753943, 783636348, 502851451, 599279850, 157673463, 841647244, 390116362, 597113055, 820433541, 577626231, 478294830, 862025047, 880576630, 712888600, 956629282, 560666556, 488399244, 630842028, 416202879, 514763102, 346993185, 860569085, 15159589, 251576652, 512544842, 91277033, 452746644, 144055838, 796549630, 792218317, 921367904, 22283631, 83511829, 460262265, 92890194, 407751621, 926248355, 656973959, 224305582, 708462908, 54249591, 141249158, 542920927, 372844671, 726343485, 120182961, 253579215, 835188894, 804982035, 852554602, 297387066, 431489385, 940123946, 77480950, 150153886, 422171524, 860915944, 326571987, 944674406, 538880698, 843894316, 839228755, 179771471, 296114554, 790843952, 192161924, 31965220, 549902800, 960419534, 631810756, 150561352, 932490722, 19333608, 542801445, 567997712, 453003730, 637026843, 941564233, 937717388, 939985904, 489597812, 205505017, 102309919, 27295311, 273362, 272563062, 484149234, 818311710, 223959504, 809354207, 804119995, 246172532, 265869025, 99133031, 374921714, 163207745, 489591905, 810750399, 607156417, 849954472, 973654990, 948819596, 625398874, 662690282, 402685107, 235415646, 418858014, 138180681, 936895810, 570176381, 26083764, 203925185, 538110543, 876355868, 883587553, 134908497, 719379389, 667022154, 486425006, 335408331, 788308144, 894059036, 51527537, 498602301, 528500128, 57744710, 942133279, 647808629, 695337403, 935506697, 948444733, 608644392, 251504617, 657959214, 185749779, 478559906, 578700841, 528393427, 448473148, 438443714, 602311556, 322057259, 102347929, 708417538, 349451108, 254554389, 468121385, 759261194, 412764398, 96601336, 420736120, 403617916, 401094440, 102315181, 796367858, 623311337, 896211180, 625301335, 502546306, 130095747, 317807298, 94427687, 186827229, 413048933, 32955665, 737693023, 331576603, 52689892, 229298106, 961912845, 885781864, 736043641, 738400410, 236849640, 562291464, 935310324, 239501664, 804348972, 652386669, 963293609, 356835413, 388392649, 634534617, 472083001, 196854789, 858389750, 550345022, 351825780, 304032438, 682846558, 906068384, 724834434, 78777153, 632056677, 165576795, 484112060, 147354515, 109496742, 687073201, 359890602, 556864513, 280188803, 56653780, 446300063, 104382015, 237456354, 541009387, 713838788, 559202635, 263469117, 789593477, 2095614, 423359851, 950453795, 762299530, 140963918, 32780864, 679550611, 352996115, 635271416, 58865372, 418570133, 406790259, 775629350, 13259964, 474536354, 175188052, 298393001, 639074935, 886018249, 261709592, 433616958, 552521566, 87752439, 514838568, 444150628, 969129265, 887186703, 660814723, 395727927, 495380359, 281401758, 787853229, 685333935, 5961968, 157858285, 970260075, 792614898, 798099129, 394082473, 124930359, 224121619, 167368066, 59148776, 258492924, 828587897, 474657976, 805104696, 489979878, 625572930, 661453802, 458330439, 747234705, 909365899, 426254228, 191340513, 358761486, 622740553, 42717430, 13921711, 169843959, 182714393, 955482942, 119006396, 716859585, 988115266, 667505526, 886169039, 296305317, 981409067, 101433410, 811649487, 609937209, 414418039, 680080242, 350372501, 638963062, 195937516, 493895941, 370051303, 994620595, 582866158, 67403394, 773626884, 238950242, 87658721, 788673616, 262801302, 753992616, 186330807, 429591360, 586447961, 448015769, 820093601, 871257915, 867708937, 416456599, 115399936, 922531855, 887574762, 63219024, 267634563, 184444772, 219282774, 883528963, 306104732, 79757304, 723269864, 297381020, 120949259, 941404265, 203394324, 860655544, 346146867, 496518746, 58467521, 66174328, 997249750, 782614143, 816383203, 38962891, 158981961, 461683704, 604977094, 243240696, 27632052, 905949848, 180433771, 118575662, 712509222, 668803908, 356018628, 908780317, 415938424, 894253181, 522824388, 80097598, 889932597, 203372524, 188097818, 758252500, 454998072, 373499714, 835841273, 744212856, 533426439, 66467752, 193233673, 27000985, 632311651, 789177693, 486667041, 623283304, 20224792, 625800385, 292137521, 992011589, 516102356, 540288283, 349869252, 444212112, 942848737, 451648307, 801508809, 23958115, 562266820, 218460485, 892535071, 68588872, 516346239, 814389511, 363423269, 857324123, 872051618, 514039322, 714514153, 982754707, 256289202, 537596373, 698379334, 661911286, 943035873, 551689034, 840274948, 777004458, 686891791, 12294014, 25159363, 149301485, 181418948, 780010779, 240298898, 113084395, 119881372, 444567148, 837021901, 19233892, 146205200, 117441236, 502237451, 78226946, 227008585, 657617521, 963621185, 598565971, 942338263, 827492389, 331979260, 491224743, 381476224, 701307700, 685708526, 43686461, 869066266, 659059766, 225705045, 766069548, 595366506, 436958688, 726299501, 484768942, 392641774, 88385794, 121972007, 809398722, 166682363, 533760973, 136463117, 686012076, 78386700, 499915456, 65539718, 98193575, 288475792, 157783755, 123089510, 352585259, 566137124, 471321494, 915397211, 723292632, 742384780, 100172555, 2170546, 789949857, 231001010, 883483282, 147021419, 129163034, 955615962, 387446532, 275400542, 439929978, 498287771, 18013327, 99611627, 653282021, 191820948, 443190813, 905014679, 312684136, 691477968, 683742433, 544089261, 240820413, 858192038, 117341222, 769483562, 774823388, 713978978, 545639566, 1771860, 21811138, 938109714, 560636146, 89203414, 124310202, 107345839, 472314257, 963502926, 427625322, 85182965, 158548081, 274380448, 587819665, 481303508, 388112487, 898234900, 673045889, 172810915, 228946981, 375786282, 903074792, 170911985, 172980656, 87433783, 710485478, 483790135, 702623127, 625288684, 546255041, 736791130, 118382762, 456580340, 365918582, 904730345, 660301045, 619201000, 729474348, 420097430, 217085295, 850196933, 813856130, 830907803, 736863591, 979885141, 173441798, 624426868, 545662404, 660854329, 175739727, 491157904, 169381707, 82970671, 365028521, 366743118, 842638748, 264784950, 523184378, 974746210, 326158570, 569710445, 755728649, 337104683, 227400241, 150898954, 295795680, 355157612, 385401396, 111310571, 912497574, 452183070, 903040968, 217699069, 526987891, 806717032, 931053772, 248863603, 682794052, 171256474, 378549178, 615562593, 809762140, 805466618, 141825038, 526979985, 338416207, 360993164, 318430138, 66272017, 2766514, 999584573, 307485011, 853915777, 786610238, 951423816, 41149376, 455652602, 598588375, 36637626, 33805783, 286873857, 991912968, 249809541, 940893357, 419563656, 453104978, 629634667, 73726548, 689144132, 3998450, 987314851, 9662926, 91566174, 974443021, 251138294, 896671208, 829679653, 85905223, 790364296, 124254188, 738359941, 68919431, 295849133, 612580467, 141292897, 148015843, 77690465, 856183035, 647834414, 378746687, 446316372, 521083937, 111799567, 231818269, 772968068, 89902031, 702771150, 795982028, 721747455, 194195464, 707332576, 554480021, 209039795, 394631398, 878770138, 381916241, 499866439, 125480542, 802558199, 76703296, 98271946, 588347834, 231969734, 158962589, 388564173, 693812259, 172021812, 362975332, 187541013, 462933580, 896520962, 223083416, 673750726, 767872906, 235938610, 284939400, 968742952, 862992390, 863078473, 771316761, 90415195, 700643622, 194982208, 471712911, 127719718, 387325985, 109371523, 57078602, 495800335, 450892203, 65269250, 601824139, 981634218, 510886063, 122832505, 183225102, 330212607, 480805120, 644392610, 912032142, 996556912, 206657277, 687397090, 158278423, 693207487, 223352443, 507203382, 854214325, 100540844, 782739174, 302605993, 340127369, 938203229, 670839825, 443451717, 829138699, 259071, 709583895, 862050272, 930741611, 897273166, 75348557, 278248563, 928270259, 288247062, 280968733, 805342105, 309665265, 427246159, 4289700, 333239587, 703297452, 994589968, 249506791, 552727355, 87251505, 55599758, 881733228, 424056630, 560526125, 843870099, 594057085, 123566753, 499728536, 452326098, 373616585, 62833286, 323731511, 392520425, 651302492, 530391026, 543037763, 316036568, 287761227, 844675711, 540947202, 995114280, 628645434, 859758183, 465224867, 636030202, 1539441, 451491317, 227645732, 977024284, 759619546, 887551781, 464547107, 216822526, 404841888, 807658172, 558543551, 763924652, 63368742, 451222588, 611067056, 79540602, 655033263, 190443181, 288792060, 109838701, 396903152, 308162276, 270040632, 169578101, 737074394, 831780773, 240135821, 748388385, 167134710, 124064962, 228498825, 730392983, 816226864, 543878744, 963384194, 312536100, 741071998, 566621292, 820609066, 397815264, 425175324, 440811132, 995865224, 91678454, 216227569, 816004889, 829346862, 461100891, 720403097, 752741609, 257261186, 838934528, 557669742, 636588899, 690688240, 58809903, 841926599, 60418296, 404377303, 237087484, 660556860, 955232865, 612999528, 840103916, 156360668, 526373298, 160659228, 123318377, 949239724, 113341615, 827014106, 583009273, 202083140, 753956451, 353813457, 57595737, 389930087, 593790434, 691756113, 26630498, 439977053, 188394177, 553812535, 444789586, 131422042, 969035371, 583201273, 340878488, 700666180, 130789595, 350828448, 572366636, 631159150, 190433613, 503048782, 996551535, 647647110, 110879795, 612564742, 309859062, 411994558, 621321861, 230578455, 291249717, 108024663, 749181218, 528028734, 579667194, 208520026, 811710912, 124030938, 607506859, 362418936, 272726275, 865058886, 55555063, 668738689, 591363306, 776113029, 311918818, 181004298, 265645169, 979953227, 29142851, 716379920, 827603008, 190220883, 788025372, 396731733, 920209311, 689912336, 327584574, 309071470, 418687926, 152079856, 843816642, 240250397, 309806922, 662548623, 60869125, 94867079, 776922816, 414863324, 730990381, 149896807, 883511927, 436077063, 85710604, 249531086, 168200317, 205196849, 209846358, 911819191, 169821830, 140879863, 475783566, 514693215, 624120236, 695661517, 463147869, 258489213, 970384113, 80592558, 863185756, 338505938, 581081640, 560234890, 752068360, 794523358, 345585813, 799888553, 149712738, 656066943, 138607213, 832146481, 649289753, 88131706, 111498012, 99092792, 92153476, 226618152, 872827188, 605299938, 533288758, 195124375, 903617409, 720441389, 619921301, 653087829, 660384155, 808472452, 535093885, 61743370, 915598481, 677953198, 66708794, 907598526, 623010390, 259769456, 438109705, 935980436, 170690977, 113311683, 622077484, 461341263, 903452258, 903826930, 135166704, 361994604, 740321788, 697224732, 350080183, 627266168, 368807326, 549284997, 438268425, 917175813, 602660850, 996366802, 620550639, 785128439, 74574882, 422882265, 378646700, 513869969, 283937334, 613939238, 74065474, 142948436, 407366968, 431648652, 881294781, 797191104, 674591305, 900878810, 401130590, 766864304, 481897276, 198217441, 852136474, 481178773, 662399245, 837059521, 671171774, 641898469, 868847127, 695988179, 152971851, 505204311, 903862744, 887208251, 452303861, 255501246, 829599685, 743646673, 795763532, 933986916, 276961909, 460311086, 724342224, 60155044, 346446918, 95818779, 488116996, 503258131, 700308788, 250198895, 605871008, 293394331, 31788838, 914273586, 48992704, 746276682, 830494687, 950994197, 549651480, 169209092, 614357427, 623217976, 206909789, 660294311, 800761960, 803595244, 563212220, 877414205, 334824088, 129612967, 31319702, 517277614, 971450625, 40549884, 418302764, 975921886, 494110414, 428501681, 100458862, 297970288, 796975028, 931840328, 710854942, 943725745, 355498282, 437876873, 595898068, 590738419, 628468209, 413713772, 294104914, 608617142, 17330788, 501590819, 970269472, 812135352, 47996991, 791325981, 50813179, 480143653, 665919450, 542089691, 422259713, 20469006, 810631489, 816177254, 272800407, 196065156, 9864814, 347187840, 412773939, 752665877, 167342234, 711837372, 10372310, 913919197, 199000834, 52010775, 21149421, 404997467, 532338011, 368067294, 189821398, 626822515, 936094756, 72456398, 998090956, 846860488, 670190959, 732966308, 762177563, 984326850, 127068431, 861398365, 898026869, 456728101, 161028580, 609993830, 814329303, 721015200, 691288967, 400622132, 636913793, 5418253, 878347907, 75256556, 339631562, 128047869, 219939217, 856722242, 392341701, 198573721, 128296963, 946968941, 640177087, 572642068, 63010919, 361497801, 288897874, 191300965, 410933620, 630686982, 766283577, 289111996, 437001075, 984351013, 657759562, 38076518, 32386262, 198655624, 945199294, 264818333, 642138350, 858301119, 532791158, 114552945, 215469982, 975998634, 633206488, 211990855, 107059507, 353654794, 155786842, 815948486, 415376950, 476463705, 960592603, 867756672, 305946890, 739448470, 739530858, 706232997, 619705099, 677677380, 285712183, 903068449, 760852172, 792383952, 161195864, 184276951, 266531901, 949155693, 731257509, 631310392, 817272334, 346860929, 480940439, 512365216, 859283350, 151116933, 104391363, 185703611, 774436183, 179987559, 727207807, 62375412, 632745460, 610592494, 353952291, 708143009, 548785222, 741529982, 8126400, 53457455, 365889985, 33220315, 108885474, 192072112, 567479726, 446156043, 736307692, 551945514, 757136940, 193701970, 524017529, 272770802, 847563540, 137893944, 164772817, 73311874, 463184305, 605561995, 72460209, 299477051, 309359622, 67660247, 752632625, 406350412, 641578674, 380601277, 279381620, 222136007, 567401191, 102775792, 839912879, 817307586, 524336918, 203710404, 733260492, 309216013, 979709197, 839340849, 924511647, 731218291, 483077581, 652732288, 662441820, 135562132, 719477130, 967508955, 11081394, 79140850, 379680911, 545517760, 655357313, 541191762, 237786502, 551052556, 272953852, 303775637, 170764772, 553341236, 648308294, 368813375, 943813144, 942749452, 726434784, 368486001, 114342567, 891309178, 511066998, 816861374, 87881401, 277168568, 132347043, 779102686, 326733124, 318240520, 694561747, 819143510, 454555783, 456963001, 231010281, 671456290, 413680218, 55004740, 124299147, 763765718, 655623497, 30513945, 760016232, 776035128, 687033325, 639705659, 239878248, 209222146, 189347140, 761781249, 552031923, 35143196, 815872965, 429074409, 890259595, 712309485, 933780447, 948030009, 765830083, 489377762, 977210883, 228169112, 245726169, 78289682, 998239478, 43225300, 821924168, 117078931, 630627631, 695649483, 672114695, 818700928, 16605382, 435583074, 97567064, 30905827, 710450012, 401194320, 825686399, 707599091, 162068943, 88240498, 403348990, 402717876, 35577349, 52282356, 186402623, 496401056, 843877507, 94657396, 497655354, 97535851, 776779690, 789429817, 492947846, 652496805, 627858703, 164622770, 111093910, 796445609, 801664942, 704403607, 156835611, 366332183, 174390670, 161540643, 83571668, 238365638, 323406626, 974883043, 336159096, 532893127, 614079202, 137859971, 715910366, 43709408, 501887149, 741713207, 821882784, 315964741, 697600687, 232799126, 877210255, 429470291, 510677121, 223583435, 749593789, 649686131, 724585654, 478878889, 221702698, 754240087, 578353168, 351094952, 8947826, 305636452, 759739584, 644093734, 89857020, 951056098, 275115697, 332185559, 513376910, 992967798, 906221426, 788703245, 209969047, 222807489, 113338578, 41873753, 263367409, 91902892, 529577237, 657212092, 966339895, 777659357, 361452870, 220157222, 495100976, 58435367, 359263756, 903336137, 588770160, 945083277, 604725980, 330253763, 688294281, 418997820, 16746734, 102090671, 51718713, 125735780, 218541398, 908647834, 423141054, 553267784, 883171904, 856969963, 549224047, 757662839, 211670728, 553604472, 686555071, 490142339, 948371243, 977280039, 406374265, 422489130, 635153204, 799067464, 958923809, 263648636, 986388315, 341184045, 839384672, 754699667, 197895152, 613291260, 180145033, 882365979, 535607248, 298318195, 212058628, 721497066, 722051660, 220330170, 247858939, 742508154, 64571907, 581520866, 303972505, 543529071, 103478606, 945415427, 203174953, 290396436, 572046687, 715536963, 646509874, 159562010, 749890118, 847150617, 745380773, 874536993, 740888242, 582672159, 572525206, 223006034, 837007827, 933090002, 911627279, 502652088, 799430881, 627487933, 677280310, 175562453, 445714182, 221862512, 960820176, 613527486, 931489259, 466566184, 134319200, 466523228, 70940554, 565504657, 385480621, 291171862, 891220796, 353872983, 6472955, 381455450, 13374229, 635540518, 470105967, 232900844, 196707179, 719790938, 549061269, 793882793, 883460563, 635932393, 495007780, 886089547, 845503936, 431310449, 363660363, 973133937, 384868068, 550732572, 355239404, 163417121, 327193713, 223214408, 718091879, 881870883, 384689677, 101074665, 813385507, 659645981, 361465422, 657346814, 52882712, 207857782, 119633633, 397764051, 969311866, 415835287, 549409625, 927964416, 662168518, 670872118, 613048140, 682589623, 514378573, 327231281, 978860422, 321461298, 88208944, 31854494, 550849653, 454157907, 547896687, 469127023, 763372642, 596340589, 962881315, 858202250, 241885188, 592685193, 483497617, 268565483, 921386708, 381385138, 993970140, 147976534, 552230865, 352844518, 950516472, 347669413, 688088616, 810273864, 46075398, 848099773, 331613322, 551938035, 922406835, 777768177, 882798274, 486335911, 909292973, 256831147, 644994126, 150547995, 288370795, 323795663, 108742265, 453149073, 912532352, 15582072, 542098727, 800502675, 544882890, 26501794, 349426998, 49633702, 568923524, 491756306, 104857663, 462931562, 286692666, 477256230, 514175190, 787063840, 221154006, 261952541, 660711329, 397456899, 981818417, 530128147, 528257350, 963119957, 380377420, 686809808, 132144647, 528985910, 822294053, 616751510, 342510535, 542964752, 953736559, 313493164, 606887229, 911292, 661263553, 317923504, 150918173, 953725773, 362959048, 728509806, 653017803, 557664301, 394839285, 564024321, 704009062, 582571207, 210773563, 934715457, 217651160, 146271867, 175351431, 734103732, 619211915, 788609505, 966641330, 664196629, 88484452, 4375848, 264242203, 283978763, 83505158, 129465938, 995387596, 673405066, 911938491, 848086590, 312531131, 231829372, 534010781, 208109621, 934747745, 59758280, 861199006, 292364283, 422301545, 170556456, 982043871, 461717221, 923602512, 439408812, 554739754, 322796482, 602385737, 606130602, 803857160, 184414665, 331495691, 115086127, 473735814, 720760173, 865176005, 911883067, 739298005, 710288379, 824096197, 208072427, 882631896, 909755613, 158794979, 561655918, 239980500, 294709389, 859781803, 386790038, 236223300, 117115216, 133665300, 627007489, 862633710, 949048873, 305030016, 491724165, 27711678, 663042318, 856215328, 322408442, 240477405, 571620355, 570994377, 519959176, 222186849, 586598305, 196850282, 89750964, 256459655, 742976209, 26407404, 238815112, 726482896, 26355249, 310573384, 196809673, 532263838, 19124291, 794786340, 769165130, 41163052, 913648000, 799429256, 123697854, 897390823, 97875423, 185273922, 141443839, 219477736, 469243930, 995093812, 579215653, 65184158, 21448310, 193287709, 746956323, 24277780, 919064137, 910732439, 561660236, 830485783, 126349456, 434520385, 301911573, 536666991, 176665085, 400954491, 978235065, 371380724, 348013368, 259798936, 327489424, 111043722, 314249202, 222824710, 728307409, 270371251, 75183573, 154614057, 510711750, 782148192, 635853480, 301575301, 530572053, 345524638, 437031322, 752844285, 988264720, 305379142, 891520954, 768977588, 358878989, 389180951, 861964780, 798867116, 393911788, 21750507, 2233747, 531158231, 541881482, 442255072, 575213953, 828578790, 67894413, 256710500, 785265036, 403538256, 59202696, 989532536, 394166965, 837938694, 576886567, 617846895, 410323912, 807527372, 895741629, 386416813, 449271395, 373633647, 727394498, 347734284, 12223382, 287148315, 67155248, 669491060, 912542072, 888119566, 55675429, 17359237, 29359169, 778123732, 669850475, 784249755, 898534023, 747242469, 975754501, 355261389, 98103520, 38885553, 888991824, 567438991, 539767105, 741520318, 217905171, 938406910, 960444514, 991012863, 887743765, 935872850, 123954930, 277260410, 757880475, 622227102, 748936696, 119120740, 296073344, 890727352, 510793528, 72710488, 518483154, 388362322, 875867656, 934948443, 149838834, 473598381, 52607866, 197134941, 900372787, 918542323, 959804948, 887071515, 396721017, 126255377, 910945082, 75320725, 757075137, 738945772, 477074789, 73043753, 277156626, 242124511, 353796082, 405966230, 907579650, 559454138, 401850903, 289320501, 580367026, 956423402, 383334128, 158486392, 217962084, 100351542, 627266404, 30158315, 852741828, 38685779, 359487251, 177384403, 744300229, 648044924, 757211372, 608618902, 709949274, 774431650, 50030624, 882837771, 845662011, 884149917, 886509289, 828776883, 349835217, 304493295, 280532931, 937781840, 653830358, 761388380, 79857414, 466954147, 791394412, 161927485, 883185226, 637460453, 368855267, 895727304, 414455204, 511026749, 41992615, 751131197, 865454175, 915612067, 95439329, 956801634, 564580135, 493670196, 243576528, 592912467, 965327208, 722836392, 669703383, 808506599, 397074674, 776575936, 673595131, 260697013, 401493934, 965560807, 788173731, 921330088, 60084730, 420687211, 798036709, 210645326, 306179972, 134004315, 518908306, 34104910, 800684544, 784291119, 59398704, 917164084, 792699705, 301163631, 776747883, 757977528, 121460391, 473587570, 430795729, 965445788, 841403811, 258923773, 232207692, 573968501, 149786305, 29281179, 363984292, 869045797, 826023315, 741425895, 636061738, 546546035, 133785744, 859079739, 764042548, 802354412, 7432871, 924757157, 787578336, 130791650, 380832386, 824853418, 527345636, 702825644, 19195472, 311714088, 999987183, 386352721, 453561610, 101405884, 217794774, 554227798, 386223742, 741247177, 184234488, 773042155, 746730418, 201656162, 512238163, 860004682, 621676168, 612563329, 188960352, 561690139, 795381960, 580975369, 994515448, 651406105, 806319080, 393287282, 661901674, 222246555, 390430152, 173701513, 916012551, 691757183, 325832846, 127859073, 77872131, 415439568, 950209196, 107539137, 292216862, 159134497, 262734923, 842321712, 810558124, 123338743, 228572778, 73877527, 725207314, 449781771, 126136370, 493209802, 122191830, 461055221, 927307682, 942103589, 836864296, 812494051, 480006228, 574368423, 147487189, 200368795, 397629089, 749894799, 847407093, 526401691, 825137320, 343542092, 630964770, 149337816, 487677948, 323312911, 605057304, 49685560, 658159751, 135388919, 269778034, 335019398, 915906471, 615455978, 908037049, 370613706, 292456318, 95153823, 936746655, 664101642, 134551675, 786283958, 397480237, 489957991, 883429052, 58148192, 163724705, 556646778, 487127893, 873950753, 240118459, 76709311, 488294905, 857245484, 470151377, 457636272, 460342131, 18970678, 52579061, 365270712, 30121069, 69510073, 63464735, 675868929, 519290240, 372968085, 810208216, 35902803, 354531635, 718478917, 739384972, 895309457, 122291699, 149801531, 623433839, 109100382, 913795799, 579443123, 145554883, 67064978, 454360307, 761766713, 767821127, 245084073, 639831264, 633911214, 684592466, 662829613, 168689615, 514097300, 864575192, 127492807, 569210589, 200969789, 672989948, 157298037, 260121378, 372535162, 740500173, 614399997, 209756398, 437751939, 70216461, 919377953, 636868159, 611647266, 739038802, 669791722, 634968912, 523782817, 246466077, 781550689, 857862514, 631765108, 934618139, 134911091, 499986181, 332933853, 2388202, 904314823, 101576934, 268142918, 714357650, 500498285, 789553540, 869948508, 15119601, 349671566, 460592097, 731229268, 460440625, 504433141, 410121050, 206614040, 784817524, 280328026, 990661188, 71293396, 546741534, 916159385, 467920599, 479239690, 855221442, 734003225, 900522521, 448119365, 15952230, 884236467, 720282520, 95559146, 709555077, 38023111, 425258929, 667852763, 150857760, 543192919, 216650584, 996932464, 563404211, 387183590, 376064719, 675186704, 925467917, 518477309, 25254100, 87610164, 339483852, 950492746, 687035064, 95929345, 336516408, 552108397, 872071614, 287025798, 573827221, 349418062, 861236277, 610803084, 93914624, 807727386, 511962918, 118127131, 750516545, 504773742, 698088723, 254015423, 439580051, 865594893, 369591351, 505457839, 909161793, 125802968, 648238587, 620163057, 752240302, 208371000, 554672907, 908923113, 691208646, 680150642, 982569843, 272565607, 220474013, 289257773, 831036036, 478234772, 904839538, 883351484, 243935493, 435045332, 67885304, 599614988, 567628384, 692715970, 488119562, 195687829, 477744439, 89767695, 81160738, 541503588, 742909032, 532260643, 870210219, 994344898, 236901382, 400503978, 600668952, 960241804, 340633329, 107635009, 374601728, 19393327, 862434018, 119863094, 182997012, 837858699, 717506034, 413492772, 472221080, 194991705, 744556528, 144613995, 310138987, 565571184, 858022536, 943444627, 962158673, 595049979, 179220585, 704070887, 160237233, 477085377, 255927738, 150442171, 931070496, 597470447, 671667023, 168901479, 253160229, 570515721, 192871455, 284090318, 284265096, 549682217, 388105147, 656460894, 152054205, 983987071, 703815544, 660506749, 49522211, 721887506, 552806081, 789884098, 34727658, 389788065, 145263477, 34771746, 424316757, 429357439, 150740702, 245535506, 36428018, 458168723, 71055236, 997807635, 566315912, 988530862, 336961919, 358210582, 18710980, 922935910, 902878721, 617340446, 606578348, 484678172, 582865234, 352322852, 905830887, 491155124, 823949539, 614484020, 172925175, 838013959, 381286844, 498417285, 168637181, 887345322, 735240299, 582345698, 457925687, 868846067, 656646167, 142243954, 985856185, 36975115, 888408217, 289834120, 532180922, 201476790, 944240429, 697726890, 295191773, 227467691, 415246335, 297638632, 327213240, 460072257, 804704640, 472593394, 5825417, 335831791, 127094751, 428711710, 733865156, 665863183, 56962079, 486933019, 193477510, 260518214, 693371689, 359803458, 134240304, 779384689, 291819979, 555571219, 724491118, 581141362, 261844385, 84211219, 167317494, 38122087, 101820907, 527924199, 301706713, 485473338, 448804674, 866178514, 52851903, 201837489, 654858746, 338347881, 306030046, 193840302, 825206474, 816946438, 500184743, 783368635, 372282411, 759742073, 155954716, 246143493, 378156549, 645784700, 13130991, 627619075, 699521635, 831047652, 65852125, 771587822, 178952090, 667403659, 652980654, 453771103, 240094761, 742890135, 109387330, 222371791, 313122406, 646966903, 20906564, 716551824, 712746309, 430062404, 152985948, 281788563, 695030216, 467669674, 387625563, 996126282, 978729982, 452665999, 374883679, 472541987, 375163245, 450497146, 771431170, 141092259, 96379674, 467256840, 819347245, 861041536, 859687117, 700033481, 305807697, 272812389, 172375657, 737841018, 828387192, 255937049, 421873875, 896636096, 293298864, 351918724, 823009369, 55953731, 307992016, 560729600, 539316305, 178666582, 668618692, 98646235, 610126421, 180834089, 185732298, 628776400, 924030424, 838338208, 446179012, 776193139, 821389435, 930602686, 144030460, 215201776, 664099881, 416431864, 928219177, 162510839, 136836401, 285640077, 935767895, 324206298, 656075340, 105279057, 683178869, 594496694, 450830646, 390254356, 801278184, 751808522, 580262205, 230113826, 392279339, 468242630, 480415006, 250318474, 738328138, 133753276, 346787716, 311879760, 24608894, 957240224, 781887175, 446467482, 782342386, 636650002, 644789936, 203726165, 108914381, 945758806, 317018560, 652714399, 995639220, 556220212, 880645629, 728502911, 403173639, 898360330, 56535034, 977967672, 499834858, 72542345, 778317801, 124366767, 904716141, 268348120, 370777691, 196437409, 936929688, 114016085, 843899887, 59661756, 651590314, 220929887, 792559410, 851879828, 297591720, 356730489, 233982235, 786917250, 983595690, 105738170, 788904746, 945664792, 759281859, 996372862, 143414335, 918592811, 927251733, 301828457, 63832378, 942603838, 609820644, 641729645, 877658216, 308085303, 43050301, 989325505, 15934819, 193301295, 66937268, 10406700, 514701720, 697842162, 356037918, 770808883, 340000141, 135311152, 678476857, 621616277, 226187690, 584302387, 536275848, 26418234, 204105489, 52330170, 330072895, 757760144, 898340451, 465752402, 629717625, 267542437, 445510822, 218998901, 766472016, 142066030, 316962063, 770436254, 263121718, 273736303, 163356070, 905515281, 753343710, 375442443, 437077521, 496495687, 87545072, 988067686, 600908676, 214159275, 772083458, 392151623, 973480317, 174531099, 710167308, 307951561, 757743388, 470663190, 410846582, 788292846, 271745627, 18002451, 928439910, 668691736, 780072316, 971495577, 256400373, 176247816, 651359766, 683660846, 365925120, 178875674, 194658943, 995341230, 295527486, 826522741, 498912872, 375389259, 639513611, 951567016, 685452215, 7501372, 75516535, 412257324, 31071168, 577971849, 878056383, 117854684, 367777950, 768034361, 598135814, 242688966, 456085242, 402388950, 308967038, 440046966, 321870905, 577593041, 967025720, 618747494, 619891341, 312420017, 664054596, 868750614, 57854413, 95137461, 657263347, 262349609, 650300679, 109499647, 33022647, 530333413, 957413526, 485218136, 756583954, 461718628, 616234889, 589232521, 581795370, 901894202, 461965874, 831945404, 248305563, 370366146, 678715281, 676560097, 198375040, 726530850, 613156570, 657545512, 782013588, 433818643, 936307406, 206033208, 302670108, 592493566, 969417247, 224102638, 727992868, 511428770, 572711193, 577397067, 560429238, 230104301, 234128646, 251547439, 569232598, 797971996, 996454163, 17960039, 546436037, 266654814, 813071035, 918906513, 227917633, 164724075, 444941941, 486159419, 635296456, 394137620, 12748994, 575516436, 607037501, 179863956, 410644517, 258591978, 270515835, 407157429, 7383863, 965814940, 277073772, 868191176, 689697204, 396432714, 881213179, 782935872, 977666711, 534372662, 965101574, 698052880, 438766759, 692131586, 102298656, 902724614, 64260801, 179414425, 524887537, 934106762, 288058991, 515555007, 765891082, 681756677, 565498025, 958245480, 541111469, 10117908, 154463138, 500847302, 972364, 736757617, 259041070, 116335075, 440548069, 974112818, 728313003, 421926481, 160443765, 754814050, 568410958, 173201281, 512704946, 415315751, 74236558, 623015143, 188685048, 843035726, 238928128, 935375730, 350815928, 249602418, 377139337, 571527393, 878097337, 699794163, 939215234, 810302683, 867077880, 990366976, 34807494, 307856365, 566668604, 874199905, 153461405, 201656169, 131604790, 270179035, 340429448, 676511917, 872175211, 603280808, 288881522, 187476224, 974729139, 705501975, 53210750, 624682801, 598638862, 285769585, 916760939, 895448258, 559085289, 164795977, 810468188, 821712525, 797971200, 712276098, 14319315, 684362510, 510110255, 962549472, 870909151, 775812764, 649067005, 482978253, 641987026, 178051169, 946384181, 959691768, 256284477, 64294052, 70010655, 654071670, 555612518, 284420876, 611584860, 737256549, 682138336, 291778961, 447682923, 933038065, 584879617, 252676725, 220330386, 245438584, 312526589, 242559145, 733882255, 641792782, 948371526, 38372856, 175792530, 201276868, 765661535, 321604222, 859456329, 38448978, 58579696, 526744205, 137658291, 813631234, 391090646, 765596167, 240397108, 158882040, 687158248, 717161640, 269235096, 324046669, 434245208, 369474155, 525735041, 302841995, 418208960, 843231139, 307067664, 100711599, 679899728, 824404738, 602712641, 818037532, 76958739, 367922392, 637698158, 628898164, 503061710, 788455055, 319173801, 966191683, 806209192, 510490940, 667810117, 585807097, 816347595, 134832850, 789521893, 738410717, 478206829, 202198861, 776934115, 391851233, 945990646, 610241700, 526017195, 553111094, 458614957, 159999453, 197503075, 598454310, 268982470, 13396792, 76210763, 391811495, 59331291, 961069305, 291000519, 79797649, 379321932, 458409315, 586498475, 32237156, 253544517, 604644784, 352698893, 33466460, 128397866, 84591632, 610152661, 972917197, 685982841, 407047398, 363909724, 656792838, 810787801, 934844627, 414070322, 718318649, 575142248, 555199158, 22072846, 717413314, 786622069, 719560903, 752319422, 683977399, 789890958, 475394769, 12494347, 485631847, 299655377, 35778753, 716348505, 789926672, 527126937, 837134094, 193978135, 996551003, 570101275, 7841138, 494342942, 763539421, 525314304, 464604430, 7060903, 378451175, 220324036, 569221357, 978704384, 366355658, 270561088, 702743363, 623613256, 957692098, 793947793, 721914109, 82396540, 111300969, 70598115, 649545626, 60749743, 435791196, 234664822, 730946115, 117342043, 308965253, 973235974, 407705733, 943670816, 523753183, 30871659, 41351032, 142604362, 478085188, 938149430, 127520854, 186204953, 595193115, 39680129, 538968189, 289341308, 144766491, 102017032, 640463513, 666025780, 610991562, 8130091, 400660134, 754127841, 354415124, 404291690, 527047499, 49301586, 590101458, 972449123, 279635986, 291194383, 546493927, 939066593, 429487725, 872399237, 379111725, 93384623, 226825408, 397427851, 9596322, 298212332, 912730393, 127391045, 874617259, 100923266, 685445631, 347587579, 608929452, 216192910, 233165478, 109866122, 751247412, 23215909, 586222348, 205117872, 212442112, 253421247, 194483130, 28291936, 610676862, 77107076, 774261385, 999969534, 261230857, 347196699, 704840995, 42395833, 421532537, 961732049, 680426653, 774070243, 12386817, 736377291, 41017364, 323032148, 86378664, 512043129, 903586490, 610159057, 884027401, 51947878, 345033125, 720862599, 132352106, 231416941, 663360067, 279609073, 881358442, 37603902, 136930909, 169278725, 466701515, 274388184, 586038843, 620946077, 123349186, 497883839, 192980670, 795804368, 447642062, 564248023, 562623424, 870091907, 341325877, 891860700, 285200391, 188066336, 257831411, 195896642, 770488127, 146911855, 27352784, 190301928, 857403456, 373323595, 219028788, 27517442, 666561401, 950958246, 748225693, 780552380, 458273811, 358439601, 569625165, 738609774, 922625485, 958581705, 240168183, 737837597, 322724599, 800793027, 271158434, 728745190, 779002898, 243195892, 861811306, 571460005, 355245528, 651116615, 835324683, 414041801, 344852190, 886700336, 210587788, 999140936, 624231241, 110957245, 189745894, 711900592, 712590705, 686913959, 197156072, 405180266, 782182395, 779742160, 901805061, 188068627, 880971248, 51891339, 949468190, 485129883, 536192571, 656637463, 388133304, 925709740, 581303741, 218502684, 306765802, 69438499, 956069316, 506741836, 874728415, 485669893, 492784528, 479320785, 512064430, 21181732, 844800469, 778196692, 71155907, 814985890, 112133683, 863887248, 580161477, 187355586, 801113862, 590430279, 587005539, 25017876, 722036450, 777931451, 26265377, 487508416, 141029643, 484448533, 633759770, 677199394, 528916331, 603627912, 135710241, 572969117, 164856741, 262070882, 587535607, 266156223, 136275256, 973313797, 601214211, 955160138, 944591574, 134765261, 712073531, 888054435, 629141366, 291948342, 3472831, 529505077, 990092347, 258153046, 880594210, 554422360, 609017993, 441823940, 730361783, 638082907, 22982479, 388808421, 190075276, 623194197, 476647879, 51977957, 801917972, 259294178, 635975932, 225994177, 812751613, 73511054, 10384748, 321215716, 882737611, 9462059, 882961369, 609820269, 774763331, 595347323, 366791043, 167472883, 613015495, 603881869, 610339813, 147615465, 44589835, 730040366, 63074094, 470020303, 130902770, 402810439, 592346839, 504327990, 497705397, 879838371, 784745953, 405040745, 28531228, 625884273, 202403950, 35373710, 740178684, 477180456, 968802961, 364043969, 516847113, 85592324, 707527799, 706751410, 901481868, 72522841, 639974341, 788906206, 615794925, 8880624, 833961207, 946452682, 323621443, 703860596, 741598891, 155987152, 383232499, 291692448, 334527017, 311657264, 928134642, 538465429, 146179557, 505546368, 450125862, 933122707, 640359806, 204099097, 233820497, 24862116, 181687639, 45355096, 950419730, 405629676, 170976257, 588899275, 883529247, 22344905, 996820236, 283906693, 492578350, 164042544, 905730439, 462138497, 937745914, 126694129, 189191329, 661929751, 914972532, 478786998, 722778654, 125466743, 569487467, 529646018, 270815378, 983264373, 209995394, 459672602, 254581458, 829478238, 725500828, 356886710, 383225336, 403567727, 791770486, 107430562, 820507011, 599524720, 363368664, 486972586, 212797959, 243584123, 297182616, 347268338, 369623847, 308809369, 269612079, 320750987, 502543402, 43953442, 249941011, 949751701, 348695351, 906451067, 473153203, 776299366, 963824407, 896678266, 163165562, 961786505, 191899485, 63842725, 353798124, 860138338, 70813271, 649126846, 718135785, 531173832, 376551, 375388868, 439609514, 338387113, 575352627, 901901833, 853967432, 688025479, 132711550, 215189888, 800185032, 567106499, 779909380, 123924753, 676455212, 176304453, 870512254, 583193978, 76466762, 888295234, 382442413, 716162238, 8610800, 477368696, 286768668, 437527221, 265420282, 811616477, 324637747, 137264749, 893145168, 496074256, 420940472, 849301008, 136286701, 813834949, 503816593, 755016220, 539673923, 885909682, 85932578, 639096227, 214355545, 994187065, 241608691, 471646715, 887931715, 470408284, 185697376, 374616998, 718492062, 473510154, 578272650, 999834361, 896719494, 856168819, 45061071, 247323494, 248897060, 211924520, 183071433, 987944833, 844477146, 84739747, 574423453, 271687006, 809815658, 402583453, 633161532, 563706336, 615353141, 828261862, 550571968, 758189436, 227886391, 275193455, 100157889, 778234003, 748322611, 724434762, 458540265, 798725580, 592345040, 910984644, 619572359, 367413960, 330597467, 986866851, 871559106, 907416455, 762622571, 822177498, 631798314, 874668925, 839735475, 820983193, 751873995, 269478987, 322073278, 349271861, 270339518, 325293065, 602274046, 395997911, 407865489, 262424590, 215529374, 390488705, 806019090, 741628096, 782694749, 222749744, 369122762, 475119304, 807637095, 137338104, 418509382, 109721406, 839161715, 245503790, 913316106, 529696445, 160987381, 755174540, 664403805, 506677552, 921650837, 323108565, 417411536, 647363506, 274143311, 750056862, 790001962, 968486564, 605237584, 102201993, 809713536, 164437053, 687417500, 849557812, 545948846, 678674703, 278932401, 6918092, 579005667, 349352875, 565838776, 377763224, 606559358, 78437169, 457921675, 248888513, 386936840, 983443110, 4063754, 727850861, 278372235, 912638489, 551743408, 20090741, 966613824, 855539993, 614145159, 876488463, 824553596, 656569962, 66120889, 733870574, 973782071, 691101542, 559761376, 596296428, 579553544, 867700646, 862196586, 217016089, 815891058, 158523224, 937155725, 794887485, 364154557, 692352489, 396378187, 835099487, 838454049, 735284630, 496770360, 649907842, 31320500, 612841464, 675910987, 50205885, 73821948, 878630162, 532091273, 787743725, 471166935, 390643971, 536918634, 411733067, 635778281, 881441675, 222902532, 617000848, 23490124, 776065500, 538150313, 496212149, 698435592, 358665540, 960913113, 673925250, 603544474, 4959572, 366065473, 657489679, 626026794, 359296739, 462539298, 195345863, 355189878, 361875357, 804099352, 759320339, 792900014, 553507191, 352819975, 880938990, 725076051, 488976734, 27918088, 197614676, 33200102, 763176346, 363935980, 753448034, 594262111, 60828043, 728062780, 438258859, 346510882, 359708307, 915349300, 790814739, 587160083, 512078790, 537513663, 144979537, 865505725, 878259433, 819173934, 306040556, 551699463, 110634356, 935907812, 476626573, 728135428, 153018477, 859851371, 444175863, 456520545, 731372377, 100667793, 764970082, 847779225, 39232627, 916386408, 142170074, 752433909, 946888749, 589967451, 380629639, 262068888, 562366262, 899134921, 734854276, 47203343, 33235758, 701033083, 583692261, 518738374, 821771661, 170917934, 475545632, 10827000, 83903728, 827000744, 388224923, 378881512, 260075729, 312407158, 850791856, 356982719, 926314462, 682546344, 594933921, 183432962, 542634264, 293182604, 520623716, 661155513, 847860552, 60064434, 129648037, 883095294, 840151409, 717185097, 438085026, 640716462, 338701108, 724760554, 221236683, 49975012, 209980906, 964320310, 537281855, 300657539, 705599867, 576214468, 858008059, 684837178, 431890950, 266242056, 791077066, 86139474, 968547166, 93929277, 73903026, 873247058, 211237509, 948933633, 97313275, 156471471, 156195812, 533065676, 879025855, 765442455, 75263811, 14917530, 598880435, 309578866, 876875368, 518086493, 360445225, 372725387, 355995964, 167308009, 816380100, 410226415, 545975741, 11596662, 754688063, 982339790, 413870145, 122185786, 210618131, 917576896, 403537201, 342406270, 344037789, 947027171, 139222145, 399928314, 567933579, 372937876, 491944441, 350754469, 861838337, 505698952, 974688904, 507321266, 469916161, 710960626, 377437695, 997601050, 458217160, 467505678, 548080703, 652264870, 709472447, 240570054, 555730989, 716700229, 456345140, 558160065, 54225921, 560393536, 266233377, 844953830, 657944231, 566473576, 786832050, 465773208, 347584768, 814899933, 270184789, 159854693, 70924549, 964037299, 788370007, 825939974, 891372560, 848075490, 719105910, 691158970, 273157599, 915184192, 395831323, 213871679, 515297307, 815337133, 22951905, 107496558, 222208598, 510848518, 539467548, 291158711, 736664142, 314038330, 653072699, 996495000, 391521727, 327934919, 702709827, 571828044, 277946990, 84960961, 896648388, 931974867, 863797388, 12210923, 812497240, 105032477, 89985007, 78564304, 556762055, 138510167, 139536656, 923741819, 221615960, 707365849, 626596303, 846641, 210064003, 627169362, 911970605, 216570752, 693902578, 416042938, 209751607, 269737997, 852295719, 412749144, 275090529, 859435303, 38991556, 991294061, 492852639, 389595239, 366278485, 797300397, 561854198, 67966987, 456971379, 752703864, 890746112, 584609144, 807186312, 745104189, 617969324, 872052726, 253997476, 813919479, 868790462, 689886206, 572389277, 208755844, 994011150, 727636506, 278499944, 851347836, 167044299, 293734898, 956825263, 714523021, 783585574, 655831720, 106212024, 974754339, 308900102, 532350812, 526602021, 213984817, 921553945, 532106960, 599972247, 700016153, 308885342, 468173839, 812912256, 59583811, 334290120, 350684217, 196983789, 748707075, 912255904, 15443246, 937971092, 822428490, 859810106, 978565902, 770573356, 722999925, 971196807, 116314098, 31802479, 283006767, 96699880, 673863742, 698642333, 339733510, 131739668, 341748502, 545782183, 276600793, 959694456, 139212043, 649379470, 971902479, 580700004, 440517362, 47768160, 227695320, 853452964, 113510686, 38563739, 216683081, 643929684, 285518142, 562912655, 703139411, 366601261, 901936887, 703303693, 995603991, 45710680, 171039452, 838501261, 469514072, 486468899, 676101921, 280213057, 348567783, 4079998, 434969673, 305152566, 639148785, 486603449, 792126552, 382195620, 7319566, 74267223, 896452444, 251361974, 141089098, 696671065, 855680031, 976196970, 666842442, 638533162, 851484296, 869838328, 331217719, 959112626, 249799191, 673230230, 207203896, 63412688, 48607119, 410801296, 785609729, 912671797, 129782268, 25720480, 598056530, 806446463, 709797179, 886839954, 804920990, 2754095, 620221783, 292448301, 100767824, 33747730, 666182562, 700799054, 685715281, 606431223, 519931824, 826834483, 285052414, 92740613, 821755514, 808526209, 649777757, 84364030, 714919204, 965136805, 744753136, 122848413, 68524566, 299937457, 196650818, 515513830, 291937389, 586091769, 762410349, 668542901, 711877741, 699478732, 612076786, 786759108, 993783726, 740834952, 519112668, 184107406, 320294546, 257250095, 878952113, 105865000, 921152926, 825990301, 373452043, 284667329, 660768553, 96347146, 242580370, 892736978, 854049911, 55832872, 738805178, 999131027, 478464729, 973247015, 409303979, 537477462, 94133910, 26199849, 411598243, 855131236, 470280769, 394937156, 12704950, 63556812, 351581766, 769921056, 539880776, 636907560, 4821151, 311090772, 725817535, 481778787, 469580583, 544360258, 132466360, 331305815, 115080132, 188270412, 113721961, 163864476, 757926961, 331231551, 439128171, 425916308, 435549166, 529618696, 320059222, 851648305, 403737998, 877563729, 507895691, 152774399, 714367909, 182875281, 400263381, 946294726, 140818999, 170170842, 50269688, 719131833, 663913074, 68338545, 435462774, 618023833, 402581508, 505603739, 251836078, 923265683, 999822786, 348717869, 917555223, 372614190, 481756372, 637037413, 387095292, 97913949, 38491465, 407883443, 398674811, 403136150, 577739117, 225819343, 635279345, 353400944, 78091574, 29184080, 756238123, 518780154, 811104105, 562117039, 869133267, 533011326, 604439510, 273988040, 697134195, 886752860, 782226300, 661864060, 876678632, 842626109, 201623563, 512682538, 376472913, 666048515, 682763874, 812947994, 878374994, 754693877, 337492642, 934159197, 666191250, 113664860, 337489437, 763011534, 776088717, 276878739, 33999622, 174516056, 323119595, 101920265, 223904764, 67770313, 346483968, 207216866, 87467065, 605507897, 377369155, 787536791, 950155217, 315901113, 437346158, 644312127, 312022347, 445472361, 252822649, 417335901, 214344964, 425563225, 511401058, 839864888, 492066899, 110832418, 569941128, 423699003, 505674320, 479989995, 15448009, 751831208, 442146097, 46305793, 282361372, 605560672, 992619680, 8790253, 235156179, 75887068, 742199433, 918454676, 326772474, 613706758, 883650319, 646959262, 787036225, 844989357, 960303767, 133626961, 220205778, 371372871, 172835284, 677532641, 105538284, 387972456, 976171180, 988442753, 159883071, 933210879, 51913104, 875456011, 885254378, 116717762, 311929673, 598736631, 714071059, 394792736, 189835722, 859946094, 955517484, 567430702, 603976507, 474477093, 88981945, 982643699, 4672762, 995784080, 222286788, 766744098, 119597245, 256842706, 862253875, 670399767, 873633816, 545033465, 31779959, 529352301, 359192945, 688651050, 759655278, 362679416, 487365671, 317909358, 961086252, 235550135, 295182377, 863276550, 71541398, 385840959, 306965088, 63317983, 551548694, 595576502, 929511297, 143513523, 560374794, 840040880, 184002173, 56128326, 327737922, 446348909, 849995709, 665794467, 394549856, 666121013, 117260902, 329659928, 563985786, 138080886, 824943509, 304845476, 660901139, 811478520, 176757366, 618032086, 292708041, 521156851, 969131643, 783019939, 96005987, 226011296, 9155534, 419584844, 438076874, 153038377, 736575732, 160157331, 582305655, 764187908, 559595917, 733263173, 147469999, 534729470, 175870344, 581706332, 31407639, 737149590, 812950356, 63705689, 498732263, 942213672, 138613776, 147425592, 329046423, 379507102, 746623477, 205755272, 684775241, 340387201, 770549575, 767423163, 565950324, 389093325, 993408069, 612414817, 318815464, 208818707, 876666783, 648950819, 182086737, 89575221, 125786028, 800627706, 54182401, 767363951, 184995281, 24293548, 448913715, 399640729, 108656654, 526127648, 556845867, 11282769, 493970231, 365810476, 308677129, 993497328, 944383658, 942011531, 864234230, 404866642, 210767025, 225072958, 991022563, 788316711, 562421437, 831689009, 253084075, 4555766, 523353082, 253695448, 267349651, 330492246, 914810366, 71209315, 872565141, 328750605, 553752543, 976380244, 526991670, 143092931, 251014484, 342518217, 125295154, 654427442, 511119600, 460453245, 82717411, 896619656, 213626802, 764362914, 710743680, 961615757, 464785104, 132433702, 794579890, 188135697, 168316432, 757736042, 738555150, 131164039, 693056475, 306641329, 643558023, 987291572, 138042905, 590497194, 677132863, 230789332, 206940626, 768479144, 937111229, 306931555, 330765231, 59976762, 317688534, 278877002, 673178186, 455359187, 590397471, 150252162, 7831118, 605225676, 334803871, 876946581, 450021354, 219501320, 554359138, 717448378, 328813999, 848316579, 676187984, 756501199, 719563236, 194517457, 293069158, 23650785, 973241055, 914665615, 255127063, 411662607, 333547431, 157515123, 67399595, 229641175, 287475249, 461357938, 960672790, 218088253, 212957257, 599881906, 823041642, 242687108, 330692695, 863338848, 780464024, 984105034, 503286716, 333698825, 214924562, 702018166, 158502303, 517975303, 418858238, 369000869, 668223521, 595306717, 226405167, 970234187, 142200758, 741811193, 422011562, 338962407, 735909941, 704704395, 151248053, 911812613, 498805001, 273010992, 367883707, 255612294, 364299286, 423538754, 974484870, 318963887, 858815964, 311808432, 295657925, 301439654, 655760000, 641118082, 231997553, 115785071, 784720052, 176189388, 662558970, 672451012, 437556258, 885818501, 274060624, 501912870, 548700662, 844231988, 383046448, 995838821, 516901425, 765314321, 45937700, 717459685, 418688507, 825923604, 797795246, 107378783, 900147599, 79585847, 613115569, 461171792, 381465177, 395491030, 630588457, 997637140, 281968763, 175187083, 626511030, 196070666, 686529269, 205678675, 32323479, 567954883, 561326924, 528996461, 874427185, 652637279, 79254490, 188500783, 860014879, 958962076, 68934893, 229244688, 826580198, 15592540, 881521586, 8984295, 445299760, 282220266, 559544769, 518601731, 521945886, 426079554, 927764364, 152795834, 668371735, 119508006, 83788470, 132317993, 478725017, 85094505, 953046411, 746644289, 482623018, 676652072, 705761975, 497207426, 597473768, 711570428, 658596893, 708307213, 836999630, 705563100, 243746263, 147766240, 792684972, 813524214, 953063157, 269270260, 795455942, 772757748, 48641015, 516115979, 847600803, 377477207, 717718098, 671350818, 122534310, 962812318, 369744883, 852982630, 363168652, 393859648, 5509414, 725940647, 790909575, 803157461, 37103540, 226146560, 486889733, 125323459, 741022252, 516509770, 174354246, 381145783, 673679021, 314491062, 369255021, 530632681, 745303096, 839163887, 225083963, 53845047, 333873981, 819806364, 312804930, 231399892, 897145085, 547473991, 388301132, 531496549, 799346566, 63230990, 428493445, 729306163, 884595612, 172287890, 298753505, 722859934, 778637079, 704585127, 501200133, 490096595, 639537497, 733981400, 715610865, 226270154, 693600825, 280207702, 21665100, 726135415, 864704909, 280622911, 573189685, 829750085, 526950147, 133758849, 103398289, 446526685, 320659958, 923417287, 910416745, 2774804, 214833185, 113515060, 27439599, 475423287, 113886584, 198228096, 419352523, 416904595, 895166959, 351677316, 524620439, 695429652, 379472910, 269032851, 702773717, 97926391, 425053419, 746179303, 587005599, 255079370, 944325227, 540726867, 693744002, 909987355, 411048237, 254180465, 694051622, 728147556, 823185264, 41181497, 705102416, 632432010, 143628768, 685486548, 122401526, 992271099, 112074300, 781454918, 350411293, 83652950, 443107100, 121603557, 699383372, 525300958, 312297366, 953085848, 863494528, 943118806, 320720579, 973764389, 188778446, 619870529, 549441636, 55016496, 997034462, 482472114, 146304099, 92677793, 496147315, 837438660, 484172099, 185446036, 810324844, 892431164, 503308430, 588161243, 548847707, 948720549, 229380850, 885513530, 633252580, 590869059, 430577066, 593597268, 363606311, 480784146, 709537735, 410119907, 952851057, 575369061, 481863844, 374404189, 600603335, 89258047, 550601314, 850169213, 33427637, 600336493, 783563755, 474814473, 239919447, 896811562, 567159407, 180058166, 926318362, 592581549, 130423912, 682929618, 383921878, 75302368, 175875569, 266775133, 871889617, 248320773, 61672667, 295366164, 369760337, 588746476, 257409150, 57774210, 310566013, 189513619, 639648425, 268855558, 658392890, 384694261, 608496104, 38307741, 379073787, 194800450, 570148627, 44073480, 326775284, 300019584, 417684464, 439353244, 994363867, 293323217, 545047441, 223765773, 737970641, 26364581, 523601477, 775676507, 284465174, 999937562, 226470458, 122130382, 623834719, 386469727, 140106320, 997437587, 44470756, 235159326, 387806051, 91999373, 111967406, 892882023, 891038089, 194082042, 248162319, 738202678, 803449095, 300275580, 917334514, 318571309, 11067579, 273973771, 7778693, 769233552, 409819160, 228530372, 757269050, 465749000, 194394583, 442974036, 379176647, 553362305, 28679814, 368616016, 990357690, 347882475, 226945833, 364456847, 371848476, 317920082, 782856875, 476543678, 915949156, 986584200, 542947392, 965004340, 803644522, 919783055, 993403048, 73762196, 776790852, 926328899, 830597370, 774367212, 94152712, 9210042, 433814831, 40225957, 968165812, 487336188, 907840883, 885931161, 354400999, 985212614, 418199566, 900265838, 642149262, 103555583, 46497210, 599421683, 714105323, 796500339, 446980473, 855552989, 641246639, 173180807, 370208248, 387666465, 802396743, 302139536, 513221846, 15630988, 863620847, 545356493, 44525988, 746475254, 106229667, 420828135, 757123985, 857492182, 952496679, 161880718, 573795078, 182241927, 695441287, 990924944, 169366860, 663397280, 137679160, 316519941, 518766992, 270932403, 90378789, 678670794, 727684729, 396749272, 181113184, 118323329, 697233815, 737613471, 81058359, 462575088, 452628347, 503638720, 310806586, 436967111, 876207731, 844723443, 390152911, 807419853, 405883143, 411663147, 721270814, 430493514, 24343714, 865536840, 64555215, 860650888, 945164870, 2720959, 312828090, 568559199, 732559882, 20822479, 63927261, 847120586, 472941584, 981659648, 211074673, 315578500, 784307682, 834869734, 815164525, 913993554, 583533488, 556398271, 260150506, 892584147, 957997106, 222943457, 11927161, 977429913, 395939333, 436635312, 20917574, 123386309, 490167761, 863623792, 882755007, 130194285, 202288306, 178207677, 686525689, 822607927, 8133674, 572039493, 545101473, 61615512, 761416750, 271328616, 467981999, 864850589, 33208149, 306799482, 507788622, 234233829, 757243321, 91088181, 129180632, 725627143, 826049384, 334064371, 64712360, 578046951, 844640913, 648374111, 59780041, 529305139, 60073777, 259042929, 149311122, 655864759, 934306261, 356024558, 319674157, 186081142, 415493718, 21585018, 400487257, 70941995, 557854522, 266552932, 94722602, 779316998, 628986838, 39166078, 926118563, 220048867, 530888157, 225465931, 352817318, 652169191, 82368958, 24013479, 84412998, 561097752, 507389500, 991984981, 775765505, 458048028, 948326856, 727891682, 452164448, 410431161, 601306250, 498425941, 406824516, 287136374, 4065486, 570336637, 783153553, 653059435, 144767272, 117348323, 912284837, 966672962, 112749333, 810463283, 88986145, 647233700, 751092668, 675686255, 737325229, 763491790, 410563701, 653769647, 756650826, 869417631, 533570246, 621024307, 101221913, 798629465, 800304543, 27129210, 325982142, 734358841, 123458221, 505387384, 47962002, 954900617, 829706439, 267656728, 761471545, 126962153, 276504903, 73206328, 480752117, 734057964, 682511314, 707691086, 513851640, 622848554, 808690529, 861718802, 839917220, 969856363, 993146342, 496105875, 252355034, 993502530, 737227128, 15143444, 606579614, 534860138, 454023870, 595947392, 829000635, 843686017, 731599880, 88939077, 467654711, 127630988, 350312755, 601967802, 97393114, 400571239, 352616975, 542370201, 703446718, 300478932, 572733627, 934880095, 120000520, 502527056, 645539731, 624211535, 636190024, 805318227, 430637917, 875816828, 701226902, 278391620, 193622805, 414594389, 480921965, 155969988, 948307018, 833802462, 37656550, 534776976, 113653705, 295229486, 776339318, 395418750, 882886808, 729980775, 703778930, 13724585, 680660998, 931610295, 71021575, 250809298, 217483323, 248262216, 551356857, 536861130, 55267817, 537827318, 570911128, 286745233, 282624739, 905620052, 709416881, 935233287, 473906786, 367790645, 695255321, 383493659, 834440891, 89625448, 102878443, 582777883, 49304641, 490999497, 392351778, 11894370, 980408328, 165553224, 182842134, 961840826, 140146407, 120313054, 848017614, 687923003, 422023464, 878209942, 2769943, 1766028, 249718926, 990130836, 69207214, 539273022, 820091329, 834654324, 330710744, 677029111, 326468388, 512832726, 346895817, 215884219, 237033546, 972684946, 37761498, 258081861, 37740117, 47794371, 613678551, 177930103, 652522955, 134819081, 225079899, 4809048, 308957511, 101526192, 32818356, 581638000, 409519726, 855120794, 934507490, 242228346, 614609769, 483639142, 455392501, 176074851, 725759663, 666170013, 98785587, 967379221, 784122314, 445637175, 683825852, 666734503, 850985281, 801067138, 39211581, 462803606, 65591743, 874419627, 808507425, 521587806, 946096027, 565968967, 680333938, 6864633, 120325066, 137247593, 499908282, 397385449, 285396434, 485746337, 487845712, 778342604, 334400494, 784464098, 758433617, 458518671, 805424884, 159941429, 970222267, 836169701, 464169997, 952753586, 763231971, 653475660, 766366420, 951832681, 919453263, 493210280, 606992708, 447972254, 305969600, 675638147, 721740410, 873908893, 695967912, 308354116, 767390005, 392502069, 473155221, 965413583, 687277870, 23038315, 534999093, 542567275, 799659087, 231163995, 205093127, 30018822, 550186300, 23366389, 463379960, 81716872, 455290643, 137946304, 761949869, 769087415, 165389343, 738695224, 263003108, 947588561, 880834637, 153285946, 527180086, 112708418, 775511096, 813008890, 699266831, 167206283, 621315757, 990049771, 922098298, 164595706, 737957403, 331051488, 31969303, 638341940, 696489443, 370796197, 268865905, 902080576, 731074380, 54991287, 697144386, 851286387, 447120651, 231516007, 347836430, 919873569, 335339419, 92199506, 495109374, 101529686, 420869469, 88288954, 750004624, 231606357, 272473238, 853684780, 19661124, 414738889, 300326238, 405962189, 134746369, 875575150, 10660060, 880998108, 75555714, 958365924, 506485484, 274943549, 839091815, 255948682, 213140836, 79382250, 254623797, 368427476, 8974237, 799414820, 769659576, 895541091, 45041762, 221683177, 855644499, 459513751, 169087417, 373790404, 91401149, 600146641, 357858955, 525786182, 716297094, 615704037, 822923297, 420304957, 547849722, 204783207, 389779180, 484219472, 675110924, 121831266, 379494838, 420758530, 18881439, 592334727, 419393073, 864175089, 530131608, 922039031, 24280458, 848566342, 747700528, 911330309, 742872243, 520411171, 164667407, 434203253, 215401177, 759496974, 376656847, 584455901, 551480564, 205341919, 120530247, 814037550, 149730787, 944836678, 863452867, 742648620, 505717176, 596522339, 66088190, 963093300, 447284858, 432425327, 143398237, 606475325, 104109108, 969142509, 414536400, 324898646, 851411514, 497311198, 259629141, 780627408, 1909915, 662230901, 696407787, 220603254, 479622739, 891463842, 847297007, 395090129, 75903537, 651958547, 922414329, 321668793, 686813549, 280564504, 352024707, 440549924, 516904474, 724857036, 170957567, 476651191, 508398817, 576688146, 943523273, 11746091, 513710746, 359188318, 217503521, 523726063, 894701604, 749593543, 488040162, 282699727, 330211631, 438623529, 167982367, 87651605, 851357296, 546612581, 693775777, 474861418, 187935321, 907700928, 308895804, 642401441, 674420043, 983114993, 471544237, 640279443, 680421308, 589839286, 707010122, 765218124, 826237095, 524057781, 896350341, 162149681, 882749381, 73864903, 195801114, 110615316, 897264328, 745067112, 657537392, 560852266, 634337794, 337560761, 893579611, 368188036, 300182832, 641421337, 697016721, 941767281, 241220988, 515766449, 247070679, 329698837, 592286686, 104348197, 546227361, 634155051, 190116580, 813943111, 639902950, 868531112, 178021378, 2448280, 354904906, 804782883, 863690283, 343318360, 381654563, 504082070, 91902746, 123148687, 540951000, 630424881, 298663486, 591749666, 227645676, 690211186, 675834125, 877462241, 618069862, 161378001, 116296658, 543019483, 848816987, 424345466, 874893247, 379509284, 603480898, 802238757, 601823565, 752595555, 550713120, 637674732, 843784323, 742176862, 712179511, 283406199, 47948563, 674533945, 641600929, 772053066, 380257605, 284019266, 831604921, 456904246, 784735856, 571475525, 824173751, 792991498, 190537707, 272635303, 973320650, 283472404, 388861769, 370326799, 934049608, 301148831, 566105445, 351830806, 800391609, 310274634, 338338236, 23844802, 79990543, 52698991, 196927988, 702995024, 507010711, 693143364, 502752195, 836814330, 56696225, 400550063, 637616091, 179544174, 817741074, 759434773, 580666903, 293174662, 407469608, 51310453, 648846915, 659313551, 135017288, 267882643, 393484292, 857911933, 776428996, 299407667, 60948276, 924612038, 41804827, 670287755, 344388249, 505838339, 551803989, 826211050, 908755949, 448515952, 903953241, 756564178, 902949296, 883806580, 687260726, 213650934, 849181416, 604526745, 591191644, 572852655, 293025530, 136346898, 713776235, 154384447, 284548878, 843940035, 366946564, 415403598, 958827073, 997052400, 989794300, 773225865, 852768823, 595164725, 19152157, 889512700, 166163264, 25512221, 223515806, 169621595, 537337393, 313305329, 145114193, 328910071, 334699929, 798455684, 642150574, 413642078, 442604319, 990795298, 239023427, 425729731, 685718686, 272439018, 423771334, 377768400, 396497290, 446360628, 427756252, 790204582, 746511141, 936361879, 265236016, 116412745, 649124670, 710948965, 721631433, 490255544, 777872555, 898019819, 402859363, 500387538, 958123638, 463980439, 871487053, 136092929, 517622780, 304855921, 300593628, 708381587, 994671704, 988234501, 167138683, 1179255, 20854996, 232888751, 375657682, 542158955, 238145782, 817363739, 391328612, 823445815, 663406329, 955990594, 742481676, 457670654, 484902679, 501951815, 744344745, 397590930, 626509452, 417428563, 527257343, 552592557, 303621882, 6076450, 583849499, 457693551, 610819310, 580913565, 824468582, 550177748, 357623750, 317382870, 467366992, 777992700, 329539640, 287954426, 833292636, 127870171, 495122481, 740468222, 155146511, 676781797, 781706134, 204942367, 478370581, 280420376, 379932078, 890316968, 927421962, 906620313, 944940125, 293721997, 355603907, 942436763, 626144028, 19847359, 977880193, 880713753, 15647815, 999209718, 582115954, 173069346, 195006436, 244431226, 477109681, 72544408, 305296504, 952529038, 939462317, 101868540, 345069048, 660429392, 127425877, 248557860, 137213817, 641789160, 763061731, 865107577, 89387784, 878983574, 847286802, 893106399, 437437034, 650821692, 498106134, 31245637, 551489736, 992758659, 212139721, 230306804, 31960949, 622465855, 500503388, 352210238, 133051508, 324555984, 890136870, 508273031, 408930764, 477200699, 984043459, 323331882, 328685538, 198514383, 765127071, 968994572, 725917927, 467404717, 406549776, 310646654, 839249931, 85875958, 937590786, 520682692, 733644112, 479673111, 770290703, 185211688, 991789307, 466328798, 89522200, 768258648, 628337631, 881746144, 14306613, 690076360, 341729436, 94453669, 867485922, 615769893, 821430188, 385952105, 441002266, 651360109, 814401444, 317273371, 564932610, 9904579, 636164812, 25615686, 875653400, 580902448, 935284196, 572466500, 47999693, 528401066, 855324784, 431626156, 817202204, 514095597, 910827885, 918314679, 823170751, 694234807, 720910491, 249560667, 522303565, 561817999, 960685595, 855252438, 678052111, 860917951, 502261189, 238390129, 155704571, 454279051, 119093341, 864614103, 97222966, 571846938, 810556604, 279402942, 912171467, 230509960, 526208012, 369913871, 125045390, 760793005, 137086787, 571818670, 806974348, 385397841, 503521973, 387083047, 381272921, 938512996, 409128060, 854959831, 876940771, 593513045, 233599865, 854815404, 435059498, 813650105, 971638861, 901723598, 118541747, 77437649, 371805533, 679297158, 638122463, 648723168, 995745103, 560056710, 182170648, 557442012, 934884204, 724264539, 970467346, 468130245, 835854841, 865719074, 260951243, 509544356, 590600546, 733332866, 548285835, 910736513, 84776589, 62358096, 306530121, 628467337, 239605295, 687483537, 610703735, 786586042, 525290048, 294182103, 942080977, 840571418, 139439877, 33688697, 870049565, 206001236, 198189030, 961484305, 367564080, 12835874, 288475999, 793451322, 995502312, 264237994, 625376527, 227858208, 993168449, 449983177, 826104910, 710164359, 707669920, 518085462, 884336555, 638129314, 397826958, 594658354, 928662744, 618383946, 150541168, 26962846, 510537985, 16069100, 62301131, 514036619, 476465911, 943096391, 764722841, 798453292, 548829542, 68109785, 143301770, 731801154, 762742634, 735940665, 642042090, 597783996, 647814934, 752296191, 834262498, 877308013, 761342004, 368675859, 291536391, 494832052, 628768304, 727852766, 162663591, 654764636, 69873666, 78662978, 878252023, 51636135, 441401046, 361282855, 738983715, 895988464, 687045536, 381985180, 567957065, 759777637, 29023851, 439002304, 499762587, 34467163, 220579639, 763651762, 297286693, 942102078, 502445897, 156628071, 259537400, 524949388, 552082426, 732484205, 96568926, 926150953, 771014713, 709877763, 268834444, 50622949, 105528737, 602645414, 270026629, 363070916, 184885664, 196947132, 995422201, 409555980, 563326400, 615250596, 884349866, 55273276, 570114204, 708639151, 301617528, 361919408, 877761999, 485488199, 842780476, 354098388, 608327575, 7948085, 46905170, 552859770, 603940406, 245542218, 861058514, 815998066, 739445600, 335174988, 773725473, 627671940, 715983866, 677643406, 357027295, 996134379, 988529640, 778127967, 303111444, 997480693, 568034243, 818862023, 716296176, 8981061, 338899256, 768929532, 196985722, 256017845, 52211725, 295206094, 547165570, 566040167, 503803421, 38772505, 746121643, 368874696, 228927971, 683395165, 397329475, 872180635, 352460027, 52034686, 45070067, 862285100, 115395310, 634246436, 944832606, 712814127, 733833066, 470578886, 126987865, 238794888, 561922379, 407957982, 709695573, 194249951, 558831115, 919319431, 711876868, 895947690, 600835116, 5322988, 771669746, 108946135, 768789529, 934811615, 224434828, 675015152, 695905477, 158667252, 851556294, 727562378, 357200808, 779272218, 48693648, 833159280, 955183319, 260133758, 962127052, 245634628, 65063354, 715524785, 535640058, 365946214, 511763100, 789635766, 955254848, 270795199, 279525540, 34671354, 317180112, 463498051, 956222368, 126848066, 890613616, 746896027, 74709088, 889609898, 213811320, 921153176, 829892199, 25774578, 845016611, 755418628, 774366573, 897439926, 999428903, 599669258, 533488962, 134638949, 72295042, 846672132, 990439904, 277414610, 41841888, 882698041, 593502213, 887537486, 808125854, 295701474, 133020999, 48934516, 550210917, 741983553, 832064355, 128786693, 309774374, 475631480, 702556187, 82363731, 930160411, 464675278, 180458193, 669718794, 841857873, 854568131, 311504245, 46352171, 960994082, 912301090, 933537118, 36766416, 559374834, 291144027, 527290442, 756746865, 885803846, 65420366, 396986543, 893570454, 390077065, 607007079, 65611102, 342751071, 743106660, 845318831, 943040030, 538457020, 638291882, 325448626, 77277750, 984708381, 932058524, 720262387, 290178811, 121196777, 753441669, 199200141, 102188144, 201013307, 661347561, 854964016, 450620788, 449753326, 667452744, 100396848, 562249432, 646785167, 656846402, 945635932, 755476019, 595518649, 196766672, 704706081, 403232144, 728070619, 417534391, 604362616, 621011318, 298129831, 514768341, 324504756, 334204456, 908382228, 345896243, 681892937, 96725372, 28288478, 342786790, 100397862, 162655675, 641416292, 562959825, 825509928, 119556579, 372127030, 603959717, 996001552, 899812761, 254851180, 948148529, 641895253, 859743947, 198958135, 80355490, 605245603, 240513236, 561444151, 843384186, 279483816, 253933672, 78246128, 93711938, 838578905, 454021772, 66762912, 375577217, 630141134, 762731116, 204519107, 397220208, 331094898, 133518572, 292311009, 484583812, 826186558, 488721327, 661286417, 415474043, 63303186, 522908785, 69186072, 682719510, 998059750, 635525962, 511348349, 879627507, 236199437, 333331490, 348610128, 149110213, 684697173, 672248348, 146213189, 219857943, 530518287, 195171667, 948094442, 700656302, 170718530, 871470955, 688340224, 807928588, 617491667, 417113343, 746350863, 264813895, 758717987, 673937914, 894092010, 541353395, 58143360, 56557908, 697381065, 784953818, 583885161, 930338439, 752341986, 601298064, 39040913, 951768657, 938184116, 916150756, 720518849, 674392398, 39202618, 498614716, 837685014, 196882292, 937030580, 477486626, 848752837, 981723699, 795491108, 607295469, 556932478, 763713445, 340015113, 388586161, 958938279, 535430207, 254613699, 525829856, 496723323, 646256470, 91393119, 419285612, 794970929, 751057707, 145509369, 929210836, 360169722, 767901502, 68402804, 250243135, 327150889, 784370983, 955474392, 27652690, 587923691, 927009113, 352205253, 803056685, 422280206, 407348044, 956338869, 897536983, 327030657, 406725055, 103338775, 761523793, 648057883, 386379252, 920414609, 362055411, 840484549, 655893508, 761232802, 139633001, 685604954, 453668255, 211407301, 795084832, 833724703, 980624027, 929768624, 773211528, 821933096, 735034689, 938664953, 437342674, 505114605, 676900479, 545316816, 971720771, 376925451, 546493700, 822166138, 231335860, 997324937, 51089353, 710787365, 783290858, 29102606, 553151824, 326590362, 131082025, 434247805, 832141224, 579070929, 496767291, 330470199, 465321529, 656587313, 468108608, 76973069, 141069439, 944758752, 903978155, 284655185, 134626155, 149696455, 792546914, 350358812, 653737542, 832978923, 765561552, 516765659, 497824315, 980436814, 749914558, 92336473, 24135831, 240263779, 52445887, 761691225, 202495279, 263226630, 435657016, 985971715, 569184380, 10670315, 301504587, 953486251, 967877969, 580582297, 110492525, 700102901, 167067531, 120231867, 643977376, 838702292, 704747757, 839695866, 518982644, 853638102, 852584109, 515578729, 801176792, 662175091, 694233299, 138830241, 642920291, 3771778, 514875037, 225409844, 89165750, 254124568, 702050596, 168609599, 723336007, 943656729, 257717500, 715507424, 430273826, 963618412, 420328760, 251431713, 241402727, 87126518, 887171075, 914194041, 624022299, 697716124, 543370037, 426588274, 861937974, 291875948, 814449627, 119075357, 554537271, 609175964, 587437976, 66897890, 148011409, 127543800, 334028084, 839105441, 67216654, 961130750, 985685449, 348007111, 439755050, 605672068, 190596560, 559795213, 690630247, 898964185, 79085646, 304379390, 477499208, 798992675, 282557495, 832113545, 471861974, 304901143, 184258606, 975086745, 566155308, 728010165, 527325732, 669719618, 407921089, 389241315, 551104161, 539813563, 6506798, 258400318, 831877216, 246566730, 377031551, 243914036, 524770674, 696716466, 275284050, 3744158, 305972490, 348569725, 655733622, 226255609, 936640317, 305582424, 532352249, 538780239, 396963705, 746079824, 800621510, 985028541, 634956467, 999438714, 313214019, 210715275, 504734596, 522272488, 276193898, 339333252, 316159507, 827777538, 404511, 373412213, 624844419, 103363583, 622908077, 179301439, 549012827, 392506821, 665545683, 515207001, 62563746, 60927088, 974624914, 62539899, 602493548, 883975212, 321338858, 710470967, 218365254, 189244642, 702018159, 875354499, 825180266, 779666231, 988308612, 381075183, 892719287, 279942287, 556511052, 228622161, 315652142, 954219659, 742018849, 241680472, 529618305, 8933814, 794915293, 207702274, 595275272, 885422280, 254850412, 185504896, 915300609, 193917588, 160356309, 921692641, 40357060, 567892738, 232232689, 159263923, 245108324, 911791358, 465616485, 8296737, 725076321, 633415659, 695497019, 850750237, 703425692, 711323824, 391576335, 836214082, 186215638, 472505205, 881968389, 509828434, 150578706, 94533780, 465573745, 334367690, 328966707, 22061494, 86178716, 420770704, 115609362, 267060927, 83802503, 524101728, 40612967, 24520086, 4101101, 442973024, 178160811, 372755093, 228225013, 486192871, 620791447, 969813012, 853986445, 843592080, 627298019, 205054981, 508425718, 535200878, 766114139, 62776973, 869533654, 243704004, 841811692, 136867411, 73010518, 433487268, 165198298, 802559780, 986455328, 435742092, 110608922, 436189129, 397527781, 440574820, 849837114, 759026467, 440979039, 487904246, 848926378, 72013264, 629446951, 287486633, 564469920, 342319085, 941301495, 184170969, 11274716, 677361774, 295397427, 805672604, 752698059, 836435251, 926657751, 104413984, 24090721, 810595632, 218340693, 259296732, 265896322, 518604846, 938415160, 829356750, 277346667, 741957993, 567181608, 641411451, 467905144, 903309100, 275680565, 508752404, 144899734, 471454438, 36451896, 349865293, 13239527, 42962529, 946739010, 198783189, 790291755, 491176344, 390682005, 750465729, 971760660, 857225958, 229775687, 317718567, 329317953, 368233939, 111339297, 259308738, 971368358, 558059011, 622438081, 186337388, 899558844, 201742131, 236841628, 863128123, 441150365, 99257840, 853272183, 847355108, 633079057, 164862179, 844962371, 917628073, 200462954, 797936691, 282567297, 290539069, 869049780, 456795485, 420568615, 434560790, 876300997, 795065136, 437349548, 605178698, 256901016, 853964140, 490905702, 66295656, 439444905, 177198442, 898364849, 291518030, 28515732, 199503407, 229599556, 252539721, 106219886, 403868944, 881965300, 873168713, 72815588, 143999370, 2826093, 277280192, 561480991, 788991056, 442705751, 854922784, 529192545, 569536905, 289710788, 745306595, 136139293, 835603732, 126811268, 168564423, 937564167, 101090314, 951226330, 96135821, 816007059, 358609069, 778065673, 645462422, 500331020, 145082796, 714915509, 364177462, 332549510, 583144072, 922874642, 641312519, 515459533, 608030244, 144940595, 836424354, 907649413, 337251610, 875563838, 960302720, 53540678, 597334451, 281236972, 601827522, 218815975, 456579359, 99924523, 274332457, 798607558, 393024863, 155876937, 880212564, 515285757, 972515866, 240662088, 480314629, 638119683, 980236267, 277495537, 921179933, 165028445, 612591477, 641627511, 802763530, 789299235, 334409767, 467200516, 680248848, 362326768, 237048199, 820936738, 344498019, 502552077, 474588289, 755876997, 261309370, 718377667, 391489767, 528788049, 712477560, 671316714, 67575332, 370151912, 199200305, 712744074, 777806943, 974599348, 365620272, 874629263, 489240177, 9909076, 195817063, 138756879, 498032485, 914975855, 861837770, 932270905, 849957738, 280115650, 830347169, 419465764, 890683419, 852339798, 908768764, 105688457, 683319820, 556534531, 109332587, 400718170, 155910708, 47274964, 506130433, 205852542, 932773618, 160871180, 579686907, 744649635, 336196184, 514630580, 315864478, 227684599, 330868371, 837387613, 192528527, 414254607, 305676725, 74946339, 709967307, 702276239, 20913925, 73139724, 552283874, 280904536, 179369719, 788024167, 949693725, 840237145, 511620589, 426443482, 831940320, 297506106, 706304974, 968238058, 810547796, 212555071, 833120839, 57037685, 88788643, 469975793, 177567093, 251815856, 488609105, 637536492, 747421048, 86043301, 104907235, 259304280, 305332132, 800504653, 827505212, 235947912, 157035786, 762680689, 501627794, 641421845, 214520658, 330911620, 112348813, 486168408, 80908449, 146357047, 588603774, 922618833, 790777531, 328027076, 373440832, 876372212, 336677425, 442182997, 158577086, 872721279, 941490172, 192651100, 950121949, 920798984, 130388246, 863589845, 19446199, 327015466, 840746181, 431984306, 179483013, 755393712, 713851509, 48893701, 746018419, 883765073, 504331758, 772146176, 492272017, 820357695, 96557021, 181776954, 810717424, 849210412, 539462837, 143897315, 656963115, 718944886, 503637592, 848011186, 639542206, 91839929, 163567111, 766979571, 929706502, 530631158, 984312871, 323518456, 360147516, 652364881, 82667630, 701437760, 561343444, 884628159, 800309479, 114709057, 996311855, 191561700, 835505038, 785966849, 195355266, 335323656, 677539884, 813447989, 642591856, 440732280, 243592343, 539772141, 448568103, 368439, 926285248, 407496359, 465644514, 374977968, 654827506, 608940051, 696145267, 229953602, 671488569, 401866260, 955620428, 379557012, 178148842, 846984594, 661771272, 29992296, 795765512, 819535483, 401510753, 666044510, 107998653, 294570892, 236077416, 841667007, 450022919, 163798017, 226820088, 254389907, 62878284, 462315333, 316403723, 834036694, 982580324, 526159765, 443185818, 660846445, 655471346, 656236737, 388712220, 527999410, 503115688, 436033529, 386566699, 284855684, 411923746, 291591914, 976780907, 655086673, 415214020, 134176614, 344742464, 274113781, 764521887, 448455857, 338619148, 287736785, 162069939, 117767146, 275269128, 807980183, 677592470, 8904466, 745460311, 396784442, 658191692, 749474761, 708722704, 249625503, 825965333, 608221270, 638051186, 815263493, 133260362, 144562719, 19128252, 157197069, 54085982, 814875594, 918774832, 74595292, 254206875, 428777065, 197076641, 398703085, 754236479, 483148150, 297604206, 576962887, 268988626, 11444175, 788397289, 89084187, 46440800, 899715607, 353773910, 123897304, 177489192, 569151664, 446858813, 179152220, 647193939, 827142314, 542051267, 980309899, 361641513, 761723933, 376737494, 32352898, 920581336, 888733704, 754344285, 420471035, 242320418, 111758437, 156354479, 547979653, 925270587, 753842520, 836883444, 723807311, 323218780, 802348382, 397097667, 799371886, 494599852, 497658110, 160882593, 159581809, 925697188, 334721938, 778808286, 983803792, 776609535, 346172535, 918514437, 342048235, 32592503, 959538230, 195752510, 744200025, 394958806, 307067966, 353056174, 33357541, 938719452, 452487831, 953736525, 91538788, 835321933, 14662852, 443620109, 14095416, 144582334, 994428952, 221370093, 103816330, 98298082, 112446481, 600099800, 711657368, 795741820, 633351938, 726944813, 878378807, 816659384, 893894872, 170387843, 101248467, 780188561, 232870519, 100191210, 701316031, 934916654, 381443339, 271151078, 16061899, 555248202, 384163349, 243688415, 186707724, 181546269, 982881862, 793197865, 157356563, 294952851, 712296288, 512313225, 524785900, 509117492, 580503429, 54443948, 471755345, 231945366, 898195979, 577138597, 665437838, 542329524, 636620541, 800157571, 442215366, 763596409, 753082067, 547805195, 28688727, 805401858, 247541501, 994492692, 793923218, 237178686, 23781941, 892887311, 987643794, 512890155, 563210268, 711766615, 179719485, 212756355, 73742432, 382040913, 774234845, 205608438, 854970604, 164895028, 685227628, 372574990, 925276444, 625419536, 924633282, 760830483, 193763574, 322690107, 110547838, 390319102, 9764992, 666607406, 596902685, 704233813, 860078670, 276497234, 539034905, 496237162, 842637053, 419044945, 855505890, 433189403, 566312060, 757874013, 292867504, 505535174, 579310212, 629836768, 519980530, 740237456, 785080121, 182857255, 193003601, 306125131, 760482231, 221069619, 23281586, 50951787, 627041767, 394223034, 345040045, 522402810, 559968319, 967357821, 722768843, 308243634, 356074991, 138330983, 206517606, 504999298, 316690866, 781787854, 730038089, 443241546, 827104287, 887527553, 994389013, 123938452, 826720655, 875655865, 40096583, 35868985, 70578375, 413040676, 734511721, 595441334, 217820515, 488429076, 701007791, 373237357, 959452237, 823054378, 446916771, 794794712, 45757616, 324422755, 893130620, 929906956, 152967620, 319906422, 968499608, 242568569, 136420576, 519451491, 855656183, 209941780, 915420147, 659835020, 258855951, 614218773, 390749259, 809895336, 69838226, 978080798, 4451337, 229525206, 378006841, 235753620, 581779628, 599071430, 634992492, 237514092, 572161015, 861061659, 507824284, 288165143, 544004313, 267451446, 912100705, 94788648, 183437500, 753406036, 12432273, 684497887, 213046242, 264929465, 87924610, 400802719, 714474667, 383870118, 953745055, 773467227, 751995346, 835241369, 803242010, 75760351, 706632759, 914426041, 849689741, 626645148, 387408606, 522871455, 503465847, 1729239, 204875998, 724580790, 548482794, 855194613, 677692557, 382042476, 136310466, 100902360, 394146739, 559463761, 41107191, 619307704, 451782019, 722842261, 149202340, 527929095, 343327334, 920041714, 219151741, 317773804, 458774067, 685976648, 633156451, 777288513, 659875617, 620734796, 8115781, 558904445, 330699046, 297100803, 554252897, 339945449, 476136590, 882302308, 195207157, 752030133, 272891517, 328986697, 251616238, 664269252, 196420510, 805880467, 854818014, 210756638, 249295726, 428617938, 625638643, 730338466, 665259552, 913610988, 922224435, 935479998, 860773135, 995955771, 24363542, 344616096, 947868060, 480512930, 152612131, 622120017, 124009538, 502111162, 592556549, 131060674, 857640290, 874666726, 597017294, 215423175, 556002744, 335166160, 904169195, 903512268, 642377639, 212574978, 744202703, 934083146, 680193481, 861236406, 38755038, 625549379, 251133749, 522494355, 983260803, 307833018, 951707517, 7343783, 879548077, 326575680, 13266689, 618129471, 367182622, 761849392, 298946502, 74787955, 276543890, 128396197, 513046135, 680524730, 734006661, 792220202, 450212445, 893453299, 403043622, 403904202, 219848345, 157546738, 143047633, 520125776, 127098725, 862051562, 134306797, 259182772, 952689403, 756217931, 849226779, 861479970, 407907674, 278948920, 846587045, 967091984, 268524589, 640266995, 933732723, 534333384, 63235519, 373127757, 569866842, 536893168, 618479535, 529273212, 774455488, 418720659, 344864787, 639182936, 893706288, 370166368, 828943588, 183280054, 280052755, 143907082, 831798117, 51252617, 866280316, 29391423, 894713479, 47363760, 709241223, 178544838, 171614155, 836965301, 580863284, 692624323, 662495888, 175860559, 593046462, 312427681, 440879106, 160234840, 759852789, 475589953, 67835563, 223830146, 36253693, 857787674, 743318455, 842785511, 595012565, 537718550, 247268777, 688942075, 50901933, 408962850, 79257096, 903182629, 493630287, 82240673, 666667994, 515728885, 143243634, 124009221, 348078864, 900397983, 713628455, 752490658, 767118452, 120968954, 376516280, 362803549, 567928938, 131544933, 615274934, 189237423, 752629039, 779423227, 937898757, 431610733, 888481298, 777958954, 3772096, 997084290, 251486732, 267646194, 886407238, 400149833, 675847101, 289977692, 586440003, 965753275, 190138075, 473771493, 741250386, 853379567, 546504436, 385408901, 905068910, 514152059, 357123269, 766383861, 171671325, 731494758, 863186618, 800420383, 195468904, 707940452, 634343068, 184648244, 920607596, 180660510, 540353755, 524174021, 987969893, 660594493, 502504720, 239235074, 317492939, 600247330, 542988347, 993254229, 177307708, 679297616, 787255843, 368037692, 403728984, 862267268, 728021653, 436335289, 561946925, 294414990, 120604902, 216268433, 558629722, 308355883, 688752881, 742786498, 465575636, 455544983, 780087046, 319661645, 431726641, 405090230, 852955131, 493880700, 74595975, 170584942, 299050742, 518414702, 605125202, 935908407, 909598635, 81898604, 928657277, 685835291, 901735937, 412609179, 950570473, 738222487, 491394226, 304634203, 404540954, 228423653, 538899781, 267848758, 769219690, 696890279, 495687599, 698531125, 54264632, 67548286, 650572968, 985402864, 760108730, 593032848, 555231717, 949425112, 747102551, 494610245, 887570291, 691230408, 833036030, 115079861, 424798710, 125968155, 374783846, 151915334, 359222259, 845575540, 405534026, 670244493, 519851063, 951660848, 945236610, 54872024, 741906152, 44655901, 352336743, 586772229, 990520565, 966938820, 593727091, 889281087, 581663579, 169510, 747328881, 400448899, 479154834, 686325590, 459304478, 722066541, 335417196, 98275071, 361367558, 326683862, 173569818, 836694299, 219038141, 91650008, 953673022, 598888866, 364291302, 45150675, 690194250, 841648058, 520655873, 761978087, 789020790, 84838839, 155741394, 452635457, 187666921, 802402775, 975660920, 909167547, 769476319, 436769058, 669150326, 767354272, 475024577, 1240102, 667815512, 39408234, 377346150, 798680526, 926737793, 14628095, 691460568, 66239560, 885116470, 220468129, 946508311, 524054958, 811121729, 68017249, 938921694, 513449358, 330071777, 950474895, 953684618, 848714612, 957459069, 500039640, 128637637, 97127304, 100095193, 524635402, 850509084, 291688432, 660856444, 921667524, 248997293, 123121241, 510057096, 224626672, 521573178, 273462494, 452256140, 4055520, 390275419, 921264594, 422278561, 102047182, 20554424, 51293195, 245093644, 407149180, 925690102, 520245031, 919073486, 751701716, 135206552, 789303604, 87105066, 373680962, 789135409, 454036279, 627942981, 924865253, 312139381, 152771610, 49407893, 488882074, 587008901, 465960235, 265116692, 155758580, 30509290, 273337605, 189109861, 142854504, 49035427, 674270223, 349238696, 681997226, 6203812, 236039496, 4241982, 448518696, 181043515, 337989413, 469422763, 8746846, 404507295, 572142400, 521897837, 572711705, 52706405, 41200275, 829782735, 798684437, 153476329, 77204318, 384520567, 243417784, 765459794, 323189912, 748247311, 440456663, 955883508, 182914326, 744610157, 841448884, 376612938, 760561700, 652218625, 845134273, 54936426, 206011691, 370738980, 570651447, 746960097, 694717876, 279158420, 478964424, 692136995, 222525178, 819192097, 458784290, 367166537, 240148067, 583025415, 876173110, 905946779, 756825527, 760735350, 489436035, 670991439, 515957368, 365398856, 708070110, 713445500, 777624352, 897561217, 91129301, 728049700, 782302035, 998276014, 630413315, 683950393, 181443365, 796518034, 127543039, 806821145, 552317928, 423164292, 48893362, 212925868, 568109701, 479181840, 226400581, 358922000, 708316350, 963868441, 162647428, 345951633, 403125558, 253569382, 806938814, 274682382, 146101202, 876863834, 370207321, 538965902, 248123947, 150724922, 277452362, 169740630, 930282512, 391436449, 239357919, 308727784, 170868534, 747340543, 733369172, 229884628, 476981602, 243879274, 468470738, 780243521, 294536240, 902801220, 933012609, 908906117, 646633730, 917488309, 225841513, 854494839, 192084228, 231109777, 660040991, 522476308, 950017555, 390620771, 278533750, 992481517, 698504522, 509835189, 129087413, 633710917, 16933368, 753910721, 539931663, 20346082, 590571682, 294645497, 726375855, 216212909, 414015886, 32597803, 28668272, 446679320, 422154640, 270059626, 991070652, 730206614, 424632321, 882637673, 473703010, 649015504, 889191062, 347572214, 921661337, 651477777, 182399655, 317500126, 766906332, 668128116, 663392617, 957301072, 746148302, 852604785, 180017638, 731166389, 353106492, 908401599, 413236400, 812515656, 22411953, 766521031, 564514165, 722241718, 191764041, 115647844, 444433391, 32239772, 710675047, 169017470, 155364053, 902210281, 546095837, 917184986, 601233657, 27182138, 238360458, 964160462, 959276609, 771590866, 996640454, 905369934, 610244021, 699393057, 513606210, 883829028, 244178150, 519040379, 723129320, 470753376, 473528252, 879745059, 596595560, 397897423, 467492083, 921099332, 880769847, 271291500, 657414872, 454981422, 532480930, 314577755, 940795090, 765646340, 274724207, 314077446, 876069884, 751563425, 926995865, 257714606, 944861989, 113599099, 150005398, 971439806, 830793982, 39120374, 396450381, 378057811, 996148710, 611278782, 518656498, 649374468, 973899284, 977336521, 481414473, 366341789, 661000026, 194207183, 627034979, 96981609, 895049463, 334305899, 744419888, 455142153, 446588904, 679797473, 873160251, 653843571, 769966969, 832290286, 32902901, 868343108, 770515251, 230276019, 205951235, 195454041, 546286386, 204371028, 589218473, 895920105, 850783613, 761761197, 345638863, 318342676, 927633712, 753193876, 886211002, 510963519, 124885556, 884570341, 157638712, 590178653, 98945377, 179808775, 536235030, 937568974, 288712975, 948274886, 331881550, 634353857, 757393355, 673292867, 516125830, 31016642, 414063610, 744566339, 119299730, 257348501, 662277552, 677976210, 632514767, 714022595, 356463512, 445835172, 81112790, 60822693, 263284653, 279148857, 408619834, 365426834, 613869908, 518460288, 856929592, 835542313, 743906765, 689328836, 348966221, 178233141, 946484780, 83300550, 617207220, 424121271, 775408201, 948766486, 572270908, 665503795, 420516896, 568600027, 496372718, 59805556, 159753333, 439754766, 774779166, 665732821, 513252321, 165813046, 427552777, 501248545, 986746273, 614019304, 662789410, 433093032, 514183858, 595142926, 267506055, 743242572, 668053761, 122006443, 242475971, 260320454, 486761238, 696471514, 741174514, 208470595, 709524602, 745688379, 721395404, 905013656, 488037690, 961898348, 393301049, 957946703, 318273541, 356614873, 683240152, 86339491, 252242303, 94772817, 686975064, 218819388, 222598502, 793847592, 942507782, 379082810, 87699605, 90765238, 505825969, 574261670, 430246184, 111393731, 138889203, 553104504, 362692526, 262002398, 198327426, 355650958, 614774966, 75930059, 37748405, 869753293, 720137860, 290784528, 658712397, 154138801, 75545878, 282424477, 437472567, 583073375, 883778440, 120452853, 905154520, 389495379, 364552523, 671337402, 62006873, 559141277, 723930066, 294170345, 441937041, 695763151, 789022551, 873471553, 727356072, 943602610, 869219821, 546139355, 333760421, 490314792, 404718155, 530598927, 10561213, 1655766, 660561122, 957123195, 102888535, 523370502, 19913423, 340470814, 614001199, 894493343, 643584745, 724740996, 347205444, 868462978, 934462456, 71233720, 192820269, 341894863, 483575442, 363793392, 615703899, 41530426, 610643618, 711175407, 315383461, 470124807, 549500251, 387619570, 39353463, 74161946, 257432427, 598957091, 79122299, 515605309, 171144850, 222467704, 876312958, 869008144, 906359354, 991046768, 887358959, 2998062, 42244682, 606802457, 820435030, 945278257, 348174532, 197265660, 856048928, 137005063, 200412656, 219275767, 655118783, 379829483, 82033627, 823449813, 433771475, 35616642, 803939391, 778527095, 384390971, 993844785, 613163457, 145936581, 69209030, 645028096, 793305241, 149351846, 182304576, 12578038, 745135666, 479011947, 937781590, 573695512, 172145588, 753876254, 159388559, 901067010, 212489162, 46282452, 789315904, 549845880, 297953397, 296966148, 245394344, 915256516, 105541877, 616629881, 752031544, 859862792, 774746839, 720778857, 449118578, 176251278, 713918570, 650596473, 681705411, 840538642, 337062281, 363127289, 74395005, 72504180, 793721771, 752608346, 87047545, 851317275, 611117093, 284968102, 465771374, 63277870, 547255317, 800604665, 447471624, 692163811, 947039758, 244037322, 817926984, 837787465, 156086647, 38022451, 812879600, 585916860, 966561067, 112852263, 961926386, 587938845, 725168147, 506505927, 581105151, 816047833, 8301876, 154807495, 962733270, 88957551, 649268502, 833104028, 574493744, 321080055, 947734638, 680301625, 404047114, 182546184, 885050286, 286814353, 2185749, 403312728, 656366850, 127723420, 986602305, 25265407, 467338417, 766081880, 206507203, 548629610, 755640445, 943757217, 955201728, 793809133, 678977614, 785091445, 224179967, 574428045, 187276613, 212216011, 476993387, 330661161, 947227302, 783505883, 330122322, 872326336, 639332590, 867007043, 536251238, 574261285, 93741686, 377476997, 656432266, 87986425, 681180316, 341937178, 597909811, 261930500, 945645394, 856226259, 103829619, 706837737, 525494369, 487643794, 299100051, 673781646, 488944536, 831900591, 823626397, 874546888, 582111677, 312106010, 961333147, 341349702, 576227641, 345038902, 820709580, 95910474, 742330081, 236433005, 863855223, 955053645, 18955068, 765990187, 604595588, 90773005, 579390670, 804286690, 424355703, 392307454, 509890995, 944483786, 503989989, 72616422, 373958548, 685627523, 368543567, 649617295, 473788300, 802095688, 365984053, 589279509, 267911886, 83021921, 402997984, 163397157, 752367138, 63736686, 245444917, 502356088, 722780469, 671373429, 951560541, 431510277, 728323178, 316091121, 643170117, 466419457, 196685183, 123538430, 133895657, 749004938, 873324928, 33141694, 861230019, 724775758, 691914652, 940196512, 500792776, 116815233, 594381666, 177571067, 621827302, 333167191, 24518101, 41413284, 985835482, 253500590, 131041651, 47425430, 283229398, 526393103, 426116867, 804368179, 967914538, 125995, 513875641, 131545703, 714140748, 263719060, 434528109, 723135746, 277656880, 924060868, 999414453, 571799130, 771451146, 82088849, 23304534, 746797883, 222291299, 48003783, 650928365, 282129789, 792408087, 867699649, 672170461, 637690370, 587971474, 751450500, 240910046, 859915261, 476689021, 515299494, 268851858, 162318380, 757549326, 432181018, 395410942, 648953140, 372661969, 299889815, 597419089, 574247071, 446836127, 321471354, 251867548, 750304051, 98016586, 952207722, 191611246, 939564147, 642666568, 250773804, 644257420, 100685236, 745432999, 807123894, 476509621, 783167225, 673158218, 576445771, 222794393, 162270810, 122510261, 531129174, 805902143, 410790143, 713749862, 796224386, 28950555, 530345152, 447456316, 989753525, 578911610, 158583159, 446332158, 545476761, 848704269, 727022531, 320462380, 891327663, 586601136, 314131798, 392740852, 898516130, 252751982, 312667117, 363303407, 541386308, 865143620, 182257351, 580193362, 802275639, 824759852, 525439636, 388098228, 203398436, 752045221, 369779165, 386862766, 576989726, 652408367, 382023340, 801511857, 203692190, 48505396, 665792738, 628258887, 970107321, 456581835, 637089456, 479399978, 762098105, 949752544, 247484042, 665546735, 53578362, 72409449, 207886600, 272963010, 852085119, 349199065, 997446837, 132110651, 483227889, 841775473, 904714774, 637153119, 461450708, 866296057, 869699720, 871945485, 252634706, 165916156, 25419359, 727507135, 306169115, 719111750, 569152385, 211911820, 593314160, 635763587, 612017494, 249834684, 791446420, 969597938, 792215812, 486059857, 418816021, 854883057, 741272462, 307090607, 545227223, 616807784, 695520764, 157825147, 55509894, 54710947, 401051742, 473681414, 944705836, 921281938, 827728454, 303228186, 54022369, 583885208, 663372368, 314649148, 18330942, 277414561, 379063829, 374890745, 647224851, 218624519, 413977447, 192128488, 709650413, 797742594, 188326760, 499040377, 290456690, 868918357, 750120637, 92502220, 908241898, 293404537, 19540918, 735762928, 116535022, 796352966, 934971322, 549772703, 386513135, 329675703, 906195310, 344580588, 655507149, 261342670, 691907379, 621894058, 625898307, 967726115, 9506399, 13894509, 642691464, 843466097, 913057040, 304446047, 657632942, 733974725, 679099910, 118478591, 62437861, 371440432, 740846538, 314904295, 251969414, 981295152, 937476158, 67969020, 56926822, 446274134, 197867013, 750491124, 724167695, 618650134, 91124791, 795024561, 782726988, 610955009, 73229578, 908259936, 861284216, 42684369, 565533247, 313307291, 908117302, 351066919, 33239469, 368494655, 349932206, 326267105, 777069220, 949141388, 646619187, 652104188, 659108573, 613979572, 519970523, 896761232, 581141366, 507251213, 614134550, 281389976, 762692361, 800521517, 614476007, 84739727, 417597618, 473244106, 392515412, 842326800, 76899402, 179857924, 135067205, 159035886, 891228001, 545556682, 753058673, 713208623, 299539686, 693010361, 964493849, 28068328, 926702974, 162495044, 110731502, 827530711, 219214657, 437739407, 265925030, 741645973, 291552034, 961403175, 268381107, 123526437, 345563092, 375371427, 671887685, 529128824, 403941709, 829345245, 680157649, 271988229, 822422384, 744333955, 583108432, 851826443, 775330832, 70470292, 123379714, 369449503, 846994471, 384764634, 138473055, 99875115, 137296701, 961097037, 654124429, 881782127, 817704544, 236943234, 65069868, 850201763, 687215016, 72518897, 827718835, 855601984, 331061912, 995218631, 344980723, 485754731, 692377712, 265864576, 176031367, 874185570, 829201611, 498816735, 729062668, 230573439, 832506515, 344535764, 918813240, 358594145, 461637754, 4074483, 376639845, 640937829, 257651751, 255618037, 701840512, 291789657, 645080074, 846832358, 295880587, 570776882, 763833156, 757574934, 571754010, 470087913, 397175663, 261004695, 267569676, 96886704, 365446329, 334423528, 122846927, 219803984, 288277520, 30005991, 423214481, 706769011, 886131332, 428671501, 701919854, 917312345, 819274147, 232048440, 532663351, 26612983, 648436633, 89617310, 744258122, 540694038, 71300066, 469029651, 115578805, 818513700, 176350856, 485844976, 26542856, 51908940, 92134759, 372112087, 257659731, 711577965, 424012070, 638424167, 185205609, 299932715, 135648636, 770150606, 992311672, 384359187, 6314245, 435080047, 919662150, 733393941, 976395414, 439370250, 763603894, 701495011, 719402320, 293600071, 391596044, 36937169, 985246774, 918964476, 295079198, 726364368, 955987565, 745590535, 60071943, 448622840, 16355419, 803631002, 348023011, 258913618, 40210488, 67483000, 795675437, 129354431, 198172990, 736735054, 916407434, 92381533, 717064368, 957434693, 158049568, 4026733, 596285400, 31160033, 401877756, 896552089, 161288612, 284432964, 77730185, 71374632, 147745860, 149376058, 558478618, 125708246, 582813515, 283714928, 939386391, 786369308, 48007517, 496577379, 865930736, 265086092, 545035943, 398122240, 838068375, 91843685, 662420646, 665214562, 151213794, 324608622, 797196930, 135862821, 653056181, 12054646, 817436559, 556914381, 613263381, 735121997, 310657433, 903410263, 610863497, 694311387, 597459204, 122168567, 409246243, 126030708, 476919633, 781551419, 38237327, 466755438, 172987115, 948450172, 950565806, 919799338, 811451726, 892843954, 121019450, 971918178, 366472010, 880539528, 926002533, 841147378, 629584804, 425321941, 44427657, 474185481, 782303056, 605971090, 279027766, 182544206, 323951367, 885627018, 643868531, 26036143, 794586594, 313312796, 644735878, 370759302, 303716918, 645740256, 947883099, 804812889, 820590077, 918489339, 721503268, 365478558, 299305986, 209907412, 730608442, 206613969, 453180033, 660718401, 712985456, 792820281, 440369194, 588452859, 525355316, 447586143, 755416500, 184099262, 601680342, 936501763, 168354080, 351198187, 270615434, 118281395, 487197805, 606971477, 422710473, 869408144, 58362397, 398455366, 921993621, 302548509, 940916216, 595126323, 351550489, 813117855, 197350801, 505510241, 652647209, 676400268, 873083195, 254842234, 737119113, 981538986, 216184867, 38984402, 603641084, 356706006, 832542210, 701629353, 38966880, 934486007, 222648011, 524034106, 679401823, 42995380, 960887587, 322968955, 837481611, 505458966, 837205523, 310958291, 834218518, 188087320, 882530642, 339309318, 5548886, 774186365, 55126581, 153329408, 921843297, 962838481, 37318557, 316558658, 405898964, 302179009, 895008428, 704980201, 115692980, 616289619, 30105671, 422470965, 372147688, 408975359, 834374490, 128690535, 238091114, 300107469, 653235283, 258696689, 723754292, 799250810, 421436297, 426875724, 627379467, 316862194, 212861259, 292567870, 72587094, 107057928, 625158626, 354465924, 889605769, 535516522, 122320974, 780222492, 155762412, 78838290, 542993075, 783741614, 114846801, 191170335, 618906683, 833549087, 978333073, 325730972, 973008, 554376578, 185567868, 631064278, 504426122, 703966597, 879759001, 668378942, 267525919, 373125639, 800582130, 554317752, 453395563, 253144815, 871047699, 440162809, 762511470, 246795969, 3579179, 198432037, 729627349, 183011607, 81956275, 177823323, 969874865, 289999843, 768770324, 308152815, 951109195, 587550959, 787866073, 971240919, 455934360, 105520866, 154224933, 488503671, 467933927, 803585114, 287435763, 520722140, 166885373, 8939219, 793981255, 990581313, 584048593, 894308833, 175327895, 268133876, 783004518, 374119071, 509002841, 342607118, 610283614, 202107234, 832545698, 787162571, 380143043, 658455643, 642195185, 421062846, 687232705, 542563480, 413958315, 13354060, 561120305, 191377378, 148778803, 879879478, 345584778, 265107426, 473617101, 733407333, 245029493, 727291088, 351145573, 221766210, 297243697, 589953149, 122058881, 793146176, 871389499, 23008782, 103066808, 54969358, 337834797, 796335826, 380660881, 592741120, 290920908, 110097776, 273945345, 870191289, 199250902, 191897106, 929821734, 726201181, 336579445, 281945530, 779486459, 834732610, 296483037, 115386994, 801314465, 90005670, 242641004, 498780797, 650934937, 829729989, 6250055, 101062684, 510419173, 935009964, 469728953, 864435170, 297382689, 641711338, 792558054, 569088398, 632214889, 19529133, 673514825, 570700647, 372659095, 995517719, 504625940, 680827544, 545368950, 139757300, 330475496, 822195600, 608280164, 836918854, 257080794, 547138487, 128477153, 49950962, 260424626, 949002067, 539697789, 234867684, 932434259, 617144487, 214506720, 310608065, 487426512, 938616751, 694102541, 882031404, 801767510, 330399357, 882424482, 619783792, 957319597, 36837235, 126289994, 857124975, 167158044, 42202751, 207618356, 60578422, 210951858, 807769611, 622706717, 43516881, 699573099, 69431193, 433951490, 807351713, 188505355, 930082086, 739657821, 575015213, 648746156, 388392514, 783664814, 146620680, 393808379, 676070677, 800329032, 443080813, 121171833, 582628487, 822863124, 766830521, 417848240, 880487242, 496710183, 345637463, 335913816, 334488710, 539291505, 846870684, 573024946, 614748148, 278225405, 197956896, 415867284, 474940220, 228240667, 401282812, 145136335, 850879366, 860862769, 674030433, 898699841, 967407218, 662617711, 260188718, 932013762, 626485223, 710311892, 919647569, 884764728, 239049497, 934246996, 307796244, 279059173, 863502994, 842756157, 270302447, 56130784, 486427142, 760955528, 666183411, 497727643, 752235514, 659196962, 236376464, 691304709, 488308301, 689772466, 752922075, 896850820, 432766454, 900536164, 420451421, 142067254, 888162318, 202914887, 520189869, 252528423, 896148461, 43309874, 428623004, 797848884, 284223150, 970300636, 276153878, 648219937, 806889623, 215699788, 414960170, 647343680, 238556322, 66819800, 253863080, 990816576, 423965666, 283460600, 295864556, 246515325, 334535465, 185680846, 578869785, 643925029, 537303246, 140796824, 689568371, 736265660, 846745205, 606636577, 262227356, 402192667, 748165969, 278305242, 216308487, 274764669, 208516067, 732852660, 139190700, 722946743, 615041488, 113938777, 739573071, 76085666, 846167554, 624831917, 885508544, 553645561, 757273194, 72797776, 61337061, 710864480, 888834643, 430217005, 596819200, 595973776, 47590668, 792272784, 601856027, 9053409, 480606165, 976467583, 93304345, 673009343, 326872034, 894337989, 32740638, 369059188, 607650689, 325167476, 852837395, 760362711, 463437657, 222280471, 836898076, 390258311, 458812261, 630259595, 669545286, 83700780, 652489418, 783383001, 664659386, 999119745, 606554486, 646490719, 549950799, 890518905, 634425247, 303549941, 828537048, 297274988, 744411503, 162456648, 844079218, 697602220, 738468053, 702546518, 664229719, 298094871, 408468596, 358906145, 175057725, 428280163, 123494983, 391145240, 174527561, 919408225, 425567432, 425694693, 352398821, 651850835, 116615953, 850325737, 20890832, 300926530, 486196326, 576737184, 84930926, 544794690, 373186036, 914998246, 552748274, 270597679, 715147765, 52825746, 45715533, 293806876, 164867075, 304794208, 312531638, 208561339, 461238696, 635338474, 286591171, 895830041, 6137051, 254160041, 431842319, 62217269, 959100097, 585989663, 455950, 428199474, 168396950, 442832694, 423898529, 157721403, 795525827, 530459192, 437695038, 442886733, 678463458, 841337099, 942179102, 538435426, 273866141, 83783746, 527033168, 373121825, 206212702, 737022124, 989889910, 320877500, 683326707, 741004540, 573971213, 635449523, 303483178, 10873287, 805273541, 810169506, 786856008, 448378925, 207321386, 776403854, 70347931, 489768159, 493131075, 573773683, 123215004, 898359890, 233290576, 241393386, 464880394, 996090898, 827974790, 418846058, 300129056, 775253067, 770333095, 670684669, 666460806, 504656866, 390695524, 806826378, 277468755, 519047091, 848144932, 823833906, 525597093, 525167158, 51213398, 993312138, 144617802, 851807999, 333071486, 561132867, 618989000, 342119032, 583203138, 484486484, 719142326, 245076259, 752838697, 127840864, 582856190, 337220623, 906600189, 363494024, 761332774, 558074157, 900177875, 66174970, 71387723, 41694087, 228065795, 82339314, 814630477, 678892835, 555568471, 466379686, 997421352, 133772779, 27582946, 661670372, 51989283, 198252047, 997003270, 320012117, 320160541, 907069135, 83866473, 822572240, 382316892, 944129569, 657109212, 433291076, 565217204, 938290874, 72537938, 659884132, 626493285, 739705769, 580969423, 835569731, 302617243, 107264369, 25905280, 715361231, 187268133, 253749628, 691551820, 651518567, 795458124, 241637971, 11004841, 134621212, 553167367, 42264991, 784860869, 688180260, 747787763, 180715356, 731896671, 599916432, 133942594, 936275730, 681218923, 745671286, 996671653, 42166412, 667810006, 455941547, 139318322, 565118063, 941224400, 36186815, 166873507, 520262570, 262884483, 731472898, 197882711, 611595984, 958089760, 576734356, 995293320, 701309870, 774629810, 977683103, 471192241, 230746500, 308941602, 782582665, 746981066, 503189902, 242622443, 144004851, 219764093, 69797326, 135369879, 195206200, 987949131, 3870140, 121464369, 177226595, 40680502, 331614277, 433641582, 544475723, 337862367, 464517350, 481273221, 797106375, 443013777, 517783312, 162363610, 136048610, 10331468, 230640476, 898641863, 78431535, 120253436, 110905862, 947648743, 117209500, 226352874, 213526536, 166660411, 254702766, 256979993, 169681677, 513398699, 603487934, 528729207, 493408158, 793660306, 713179061, 157920112, 110350264, 353286349, 17160461, 304475789, 806254612, 413475701, 961069815, 84559904, 118309233, 247192970, 45474104, 425187152, 838209941, 477007512, 8990173, 306531001, 632855156, 854961784, 699122457, 160588927, 264533675, 392528414, 202018487, 378289105, 610141226, 919733698, 694704368, 60013571, 532393389, 413464420, 473309961, 606084597, 406778092, 640898159, 41202673, 101345986, 840042152, 476760631, 390638864, 334163680, 899650388, 885486445, 473717097, 804422523, 648008086, 807189965, 723491503, 207840045, 538981609, 582396408, 114215828, 844727100, 922630662, 291679374, 338914322, 376098108, 57897581, 481570858, 108397800, 922935329, 512265827, 614349604, 657014519, 232392826, 744165618, 127877604, 554874390, 482611437, 396163312, 494597577, 723821942, 808097407, 228931748, 131045972, 417616255, 529455811, 800380252, 222927595, 547627559, 668678048, 122623875, 48217216, 71771606, 821386186, 313591805, 234362888, 94352308, 907659883, 655154433, 980029655, 516776520, 507607316, 34627093, 473574378, 519698183, 303983128, 939777357, 856787029, 566513300, 167999905, 561584603, 328209034, 533300436, 909778408, 582422596, 992752219, 3101106, 443293817, 370930737, 513420998, 193544401, 712644811, 771750719, 534986335, 952324215, 276149214, 92988547, 814940868, 287954444, 590889408, 927997816, 747043433, 667415701, 228666482, 480251360, 944581131, 34364736, 419540631, 503614028, 335130541, 539341966, 246487934, 364897467, 566386334, 931030570, 189582676, 269255351, 736094644, 170996985, 803257254, 470517878, 395534033, 481914480, 859394623, 340493694, 238686631, 734960758, 398047727, 851459636, 425012231, 875225830, 281042766, 122924977, 350294244, 694879136, 929177003, 882533016, 194055301, 132616923, 637435856, 658629935, 834346978, 775387232, 817744912, 564893145, 593492894, 106499434, 120449649, 524096663, 672830173, 952071694, 836062317, 588341541, 369804997, 821947046, 964796894, 819020498, 221659397, 851026132, 573570475, 162720721, 836047305, 203980725, 589021348, 250586791, 595644069, 252308421, 555426215, 9392027, 125363374, 352869545, 160428056, 494852331, 231172421, 421694949, 968705062, 701656916, 193926293, 771513449, 642516064, 70911214, 107252883, 87774313, 928345081, 52030812, 799208385, 136177634, 593750270, 907050324, 434465533, 695257862, 493157108, 215306481, 522363120, 589390081, 202008631, 169374678, 756676193, 251932506, 139074378, 509851262, 263188214, 671881181, 328504690, 783929195, 171522176, 383513435, 2777667, 869116635, 90251721, 282960186, 48782880, 729969927, 100519706, 306127832, 77754925, 470914455, 441260190, 978239297, 203970673, 582749883, 150681491, 573463688, 33745117, 211324023, 479554379, 50635577, 614898890, 704719461, 217361929, 558489662, 418947951, 676893400, 97083721, 403314690, 827942904, 926400335, 486095572, 16141615, 885806248, 464367906, 739293432, 325010252, 561962572, 807291394, 330704, 519951221, 811603146, 741667347, 213820291, 183956594, 115243636, 517460253, 80459800, 974764954, 329869027, 513146719, 136684251, 121011713, 903212516, 358236421, 720789357, 508044234, 680048256, 267357321, 963428002, 214734498, 599181797, 50709771, 997750222, 969043820, 969823708, 490106795, 948323714, 32289800, 242273588, 82324271, 224813376, 743461698, 346689277, 501334939, 672602906, 66201247, 497725540, 22752167, 247515037, 533425896, 264256264, 950938559, 850965741, 424444785, 804181611, 771100082, 996074903, 227641568, 311464636, 216923410, 865960092, 532312448, 948279160, 49352712, 522596178, 514285219, 817128974, 755799048, 70343335, 721096699, 998175798, 126249651, 205638226, 721646921, 946055273, 930118782, 192231803, 300891973, 746994542, 398376072, 780361093, 630953896, 814966852, 888350171, 859073574, 669322181, 267241156, 674037936, 89863996, 774167547, 130810508, 616908159, 66096496, 424919156, 798725648, 289751495, 540417256, 338799816, 453302887, 243381228, 236085733, 446675695, 747127108, 305901311, 760555700, 272607418, 597362525, 600674534, 782690684, 14916341, 377705767, 19063088, 89387533, 674306310, 987982578, 932356474, 631657642, 435419869, 899017235, 758755887, 579699998, 395320118, 708399980, 835370561, 439754716, 939462302, 350459944, 517725528, 804810408, 113385838, 98406128, 174855935, 928696125, 731762720, 654225607, 100052236, 64408049, 120530295, 790069288, 22134590, 483156939, 858978773, 874504322, 903196873, 217932252, 516399470, 819260534, 570471615, 854423933, 618269242, 435159126, 170686550, 288737416, 377540974, 345658058, 314894651, 113676492, 869390768, 273396262, 55827869, 836107106, 946815955, 498782507, 695610239, 701622297, 678939785, 189238024, 601108780, 213816644, 186311623, 517948066, 718418547, 436590872, 491031125, 856955476, 296953659, 822881092, 334001165, 177396726, 499359575, 902773462, 636891393, 369600827, 147828319, 112450704, 152801680, 764010838, 510215554, 39623003, 429453048, 464397393, 56970157, 431634592, 527568394, 25703109, 445265957, 412632830, 442873261, 117227423, 958691532, 770715034, 970440436, 844876549, 864045968, 184027287, 877504316, 473763041, 229466341, 353091342, 193493867, 405958297, 435290451, 447993242, 106654511, 437308416, 705178227, 226148938, 850928718, 443147341, 626992751, 395978982, 156996170, 680395962, 884777418, 99240146, 174918682, 645840767, 492002300, 580694642, 367029226, 193964962, 575352928, 709991068, 113854089, 237017456, 236860974, 959965499, 836486714, 526074955, 577471237, 181277210, 490923725, 141715614, 828299637, 133169519, 234436085, 508198910, 517559010, 37367122, 56779657, 172097489, 516242959, 877302854, 449749377, 524707248, 906329957, 895764505, 630425208, 844426251, 819822674, 541632868, 159948083, 246345807, 321571806, 25267560, 700918849, 683224486, 795648861, 76462539, 899594597, 332401300, 348697406, 598476214, 408895968, 915994450, 468057035, 734480450, 544576266, 828767837, 719245068, 105376487, 512530837, 736357373, 470029422, 660995524, 665949143, 201029424, 100825024, 208118172, 763985837, 128866186, 802411714, 108950350, 936263513, 191876840, 106480177, 870323442, 128554853, 535613055, 938288848, 387714375, 848392728, 803940225, 265432885, 203140155, 790304246, 433539038, 408457921, 948152094, 141824979, 982435665, 324219741, 753133290, 458391443, 721247726, 568041240, 160924340, 763856950, 279534873, 481832772, 141031113, 176357664, 361022591, 986982324, 875032717, 658909914, 692023725, 947179049, 605808674, 633449604, 422936094, 305482330, 822728574, 10895023, 75447714, 782956246, 704436797, 245244161, 587688740, 786549415, 640337190, 904238849, 403310678, 467763852, 424853267, 610892635, 546796590, 270577947, 53554367, 759958163, 565924493, 22084820, 164252653, 739880900, 758403993, 52736641, 458276327, 982495188, 51748705, 913851651, 437155599, 45455267, 85456269, 826097735, 118969605, 318220327, 145152346, 616152076, 542785603, 411298896, 925548533, 154033799, 483943513, 602941344, 133606669, 55432757, 241267595, 94753598, 22481877, 444786315, 18464431, 166650880, 691834475, 886718522, 738297621, 945172959, 168607266, 758956128, 22507687, 23264575, 859180732, 973210276, 304454966, 546246027, 797561254, 922748030, 535938286, 360553437, 491275361, 686043795, 330572196, 228192418, 969523825, 757780798, 483586911, 181902362, 387775415, 100144486, 218254581, 163142316, 268531503, 76425536, 634018710, 722133363, 35276485, 653841233, 517599248, 983559777, 593495618, 759767903, 55171640, 944214799, 384376213, 628886141, 124033625, 47557029, 243022096, 164935379, 962245635, 557957704, 63487017, 346745386, 597612954, 964079123, 114195556, 803102658, 683016521, 164215993, 589758934, 188479167, 434217061, 375327054, 526647965, 590190113, 398578451, 897578561, 383336179, 187164323, 628805846, 103664372, 801453041, 109088096, 338550179, 595978760, 988977793, 972786183, 652487521, 311417796, 13494677, 552090872, 439620742, 131201903, 933723398, 963441317, 498082480, 782142143, 414393704, 665941895, 45267719, 391950894, 269477493, 949683996, 369957860, 86331679, 374218026, 659060582, 417624002, 359591954, 406935939, 905136558, 464801202, 60319458, 694953231, 568985282, 75846834, 12757687, 980277126, 242487512, 746027333, 730909819, 689930531, 453520688, 365264313, 863362203, 249768326, 998058686, 305151432, 686110597, 412139067, 354383491, 73173879, 701124021, 319475809, 355053807, 423226660, 431088863, 3968521, 58806315, 724550645, 625102509, 873045003, 182369178, 975152844, 882318168, 205337366, 747894383, 795373949, 959324482, 466179706, 671192835, 296119457, 20887552, 817306446, 561043872, 801622732, 468992429, 540056893, 158672635, 522004624, 152831397, 136357698, 159629567, 496143794, 112781763, 804620003, 437734073, 713949189, 586803209, 442039507, 110868786, 370678943, 552776350, 127081646, 684911584, 404762682, 662081750, 590069207, 670562384, 556761480, 887581285, 943625888, 133925321, 811772114, 304072841, 635051606, 454629118, 880897490, 758281412, 975821370, 874391548, 386038885, 120194155, 32414755, 420150999, 767664218, 785269898, 534218786, 758464127, 958824347, 70200623, 366418597, 540975881, 368782227, 963300128, 285880543, 491875588, 848544143, 919975909, 593619509, 971138451, 35171927, 15175132, 653325183, 684799220, 673514657, 554883329, 593776474, 11059524, 617216675, 381366493, 396245123, 253785303, 909522420, 202200462, 298600726, 65777148, 460925778, 756412397, 801108563, 373810765, 498447671, 160669202, 847573471, 158122871, 75201414, 417998506, 141954811, 195116597, 276869240, 442173540, 668344306, 183975582, 330082827, 568829616, 644112976, 418689402, 911443436, 110344385, 552062929, 436641193, 239910844, 866726437, 184140449, 323716542, 495749731, 760389256, 406180284, 249026740, 294016138, 828836363, 195362334, 759516388, 741771722, 785147910, 885218887, 1679353, 339359657, 265588881, 462472680, 752483389, 959064885, 444221756, 268764853, 356994815, 145580533, 649266599, 585128781, 38599736, 640127158, 831748762, 243249419, 632918016, 514812479, 98807222, 920195122, 147374017, 839344442, 736420862, 434600500, 202988225, 454806259, 45883402, 25345484, 805508471, 435542131, 842020710, 676517758, 532394653, 110012169, 743069378, 357226793, 613789973, 735885235, 443296925, 96723567, 302219805, 492968554, 372618122, 186520336, 111499166, 544318983, 844080542, 115024831, 178569238, 838187958, 565226292, 115345479, 922042100, 53376678, 704179820, 587972479, 733508398, 606033786, 906492753, 134309683, 764465879, 386279427, 41169647, 752449935, 59559387, 252485668, 275351672, 220390277, 339356362, 31085638, 809975614, 501851237, 792867239, 693345919, 593182051, 244788174, 277999196, 311381054, 612076090, 523860896, 454564057, 613060003, 221180519, 664227040, 419863033, 712196238, 65352736, 807186853, 685814296, 95681689, 461398767, 946658321, 550064671, 919120123, 869619187, 614491472, 247656062, 124489782, 806105951, 655924603, 426276271, 960765173, 728297405, 382376486, 138342820, 89489277, 54448349, 192523871, 541722136, 496201089, 537578973, 659433110, 902986365, 47077093, 691301082, 227473274, 108708973, 634025669, 526455029, 942150210, 371335313, 77850306, 233738682, 984174085, 829989344, 784371285, 976958016, 408449072, 7506161, 660001308, 425336430, 191243127, 684563888, 667088918, 943203951, 158535153, 697081657, 882700604, 688011691, 694117041, 699320916, 759577175, 541365024, 414035033, 826068686, 462743779, 420858056, 236398813, 319891519, 403523834, 549535060, 651465241, 6078706, 367830616, 244982509, 528757946, 632251300, 227529379, 874664259, 461255188, 213320984, 842204782, 779815524, 517861701, 645112975, 425154924, 218489961, 79601626, 405599819, 49301906, 682637864, 697152823, 229778766, 208156385, 635839900, 612567942, 544461113, 583564905, 914054862, 915239820, 585439564, 148040893, 707082960, 279958374, 694971238, 800181452, 883667769, 121862348, 354805326, 142860724, 414407127, 971392137, 741733087, 346175915, 39840042, 94033230, 465746709, 957131649, 289352256, 772516136, 768530786, 297669695, 287351794, 721132709, 683745276, 841348575, 287419659, 669131090, 93347107, 717494971, 6748285, 758724481, 979824905, 719682823, 318424447, 895716429, 919659927, 33974269, 557792415, 73695803, 939435842, 545349018, 83613737, 365700098, 512537134, 64206043, 361582960, 677440602, 530079947, 181667456, 724014847, 582498038, 251589953, 839088867, 609610029, 25942044, 659618166, 819229457, 32115255, 931192897, 340210225, 396019590, 253109678, 411527247, 926745993, 628651830, 514951650, 288535413, 241555458, 851658644, 307303454, 682453862, 651672862, 894742979, 873522485, 609957, 674853346, 841548967, 655294526, 674397416, 891057897, 667085076, 392682630, 978088088, 363310448, 978938719, 442947679, 50484962, 336657003, 569892791, 673245068, 285681694, 756518535, 276718096, 619429742, 663530356, 860640050, 169716042, 490409387, 166871689, 270604710, 126126704, 916449433, 628409951, 248638832, 729699303, 890759411, 851578122, 902955173, 943890156, 696280954, 984197281, 675316328, 860540386, 660306758, 119052463, 458645604, 828645436, 838954059, 846187700, 246754733, 853509640, 309813792, 516977011, 630791251, 873880699, 145300761, 776238929, 275945908, 35086913, 518254034, 565264375, 63621401, 402875587, 757995165, 381647061, 366122522, 816877873, 158287209, 92320160, 108822059, 426565218, 655433255, 433364079, 848763201, 816614490, 631410767, 689624828, 300778620, 323548196, 258647249, 217476789, 327363211, 389706387, 339519910, 44921059, 690554089, 396972066, 32072104, 516860388, 198893765, 93991562, 277539169, 485683075, 418721614, 790159340, 264362452, 242900202, 183604672, 343783346, 91947083, 354167995, 927258683, 576553070, 969196132, 75783279, 11763728, 658258314, 933371557, 57829509, 992536766, 810872833, 856567394, 368696853, 326160895, 68353280, 746766341, 797570314, 134545228, 188741043, 634015855, 1287069, 135636159, 490132201, 839366475, 564146898, 116494062, 322682385, 628791864, 806434943, 557837080, 517975082, 410770981, 567151712, 177992827, 110511634, 107497691, 745077426, 761141655, 452263614, 296664826, 798141485, 932601926, 470648280, 108125929, 608993437, 818957373, 550055266, 61318359, 944685830, 949969820, 404986889, 734490389, 435881178, 362494467, 908656439, 804783971, 616639411, 311369153, 409534202, 468918367, 155606185, 202705731, 440801047, 575688835, 561745001, 367868934, 210047820, 731025955, 432033919, 532272029, 927890293, 577433055, 65171686, 703933643, 289326539, 807401980, 406881205, 750458209, 842589504, 505597012, 958032450, 503807165, 973434566, 219576813, 791930534, 22712269, 576822280, 895594428, 92287916, 844133046, 628234613, 123186743, 931454399, 770680545, 735349529, 569844802, 561996408, 742842237, 802452246, 646215986, 282087765, 351664312, 774521636, 965047152, 844625054, 586497174, 515894843, 864643973, 258762859, 804186638, 816960404, 839487400, 234020012, 906275010, 807751787, 295905850, 519727895, 814729871, 903111344, 267951764, 833167707, 404604085, 208900562, 307216750, 262901150, 198140608, 701626993, 294367174, 323830547, 558467784, 753619932, 290678986, 764763173, 656556773, 5197474, 237000633, 622359352, 444671443, 99445531, 729480226, 960778920, 639019535, 222293153, 86631947, 262893688, 717913786, 550286513, 654494988, 952737486, 403258127, 870947956, 770029586, 166320676, 225210382, 638829448, 908661809, 928243991, 344876810, 255777676, 638541545, 318894066, 513137099, 513724046, 264807406, 141002439, 778137832, 99989638, 409005627, 524247909, 145796714, 567422700, 887565141, 238894704, 601065579, 341497785, 941907501, 955761700, 926325792, 862432294, 653837675, 996318167, 800681407, 967851912, 298376754, 350285971, 240968011, 854944433, 838088931, 674788386, 639762070, 588018397, 637185559, 784289352, 218737034, 745792225, 161948278, 473735404, 377096796, 241927206, 978702146, 922305917, 545541129, 53708641, 619538668, 116750773, 759304082, 375205310, 718145487, 125624733, 166189958, 844858003, 201482375, 861441157, 105530315, 83077940, 682398423, 869222439, 155563492, 739490095, 450664443, 678626165, 72904421, 299490679, 514461326, 241537194, 910120779, 820327925, 340810342, 964390700, 565392002, 245533431, 647915238, 30903616, 984067315, 817422333, 892980758, 129799946, 263236783, 569414386, 526860219, 748969735, 729135628, 966428665, 74091809, 773182346, 382408050, 154277798, 610927249, 691418618, 117268965, 436609513, 258854018, 529223767, 679531241, 207615725, 497797412, 591312292, 728357706, 142734872, 908901357, 740008264, 845691626, 611774689, 13331356, 535269054, 234544761, 660445056, 75660461, 170561295, 981848724, 654281494, 62557045, 523526992, 936764672, 849518505, 189717736, 381932409, 310366126, 561069302, 702336258, 181430032, 313436204, 218232211, 159238758, 64873734, 146432957, 316591666, 182768580, 37714513, 762895041, 169602630, 606807783, 24786880, 713710318, 56604785, 986563383, 604746251, 453900889, 637023674, 268759114, 742594823, 893492358, 149638286, 149237186, 674686758, 623038028, 695924934, 779090091, 146393930, 532571331, 454045906, 256858757, 928494482, 668063194, 52046201, 88011734, 423369226, 891448562, 884166406, 809759541, 725585837, 267745013, 65523721, 109477898, 784815041, 478103469, 310756036, 501812366, 441519354, 893520644, 284372665, 638581049, 848384476, 679232653, 678082385, 589995396, 138561513, 214214976, 948809760, 456341659, 876839638, 653463585, 979748844, 81774405, 588097114, 323245335, 767303716, 304740580, 789693868, 63043016, 226586014, 91491228, 822692401, 52909426, 122045336, 870069983, 645313937, 316001456, 459437388, 291254059, 392280831, 536314188, 102252477, 719090502, 396116399, 357320554, 15213000, 947756231, 252536375, 503990747, 766809778, 397154679, 942997308, 638865088, 794786729, 868906557, 160370175, 192453123, 345163833, 271329233, 122612197, 983553187, 405676564, 563615621, 359024059, 524505722, 670846317, 206592317, 874220881, 736207497, 15695691, 209161442, 491804610, 140533489, 58444072, 434357879, 234506227, 916057639, 964621256, 55125690, 313935274, 528344643, 219810570, 356818363, 137352996, 330587198, 943102086, 829139549, 382570071, 827733146, 502397096, 941785447, 161369519, 261661626, 198787635, 396899715, 654835419, 289594352, 621954787, 737225983, 410156304, 206674918, 526050196, 601669439, 580677468, 584701248, 893146491, 703512118, 690383212, 977901393, 427800277, 636511868, 350415137, 733904199, 310675930, 519007843, 395539985, 162706588, 216793910, 27330846, 246713928, 974477308, 234199402, 534240016, 913765481, 645377928, 862284585, 950313419, 349100021, 746150881, 928689086, 352221203, 318534335, 327819385, 128166957, 795680681, 49522040, 98228521, 494438721, 661083359, 264237874, 542410965, 264702059, 422547239, 843876342, 255782789, 821434552, 20669131, 896808437, 595998827, 152969534, 118072978, 44214096, 217306396, 516792566, 12410960, 60096592, 460195566, 230453467, 613935441, 327097050, 353622316, 87120515, 351761061, 501978697, 905687054, 268809395, 429807530, 761353126, 660416826, 561285682, 383640289, 574057467, 670933968, 394151232, 775220183, 581911950, 439931152, 840246612, 525023760, 455099827, 623973170, 449932122, 825574515, 476141207, 771111624, 706906016, 560006959, 816351049, 892504672, 513404768, 883814869, 896059895, 856108355, 311088619, 491189447, 371226431, 599756054, 699417402, 697492366, 541401658, 980688253, 966499333, 126110174, 697775211, 864120440, 723570426, 347362771, 197132785, 172083468, 219677901, 103236264, 927906802, 388048833, 393368216, 55899811, 82487217, 118550680, 496942882, 287596364, 883503672, 705048473, 157803686, 298689905, 851629435, 108198443, 806510345, 779889684, 610410670, 605740646, 895592570, 22526370, 415805228, 901014572, 179146843, 267852062, 742548489, 65040418, 193533165, 614401627, 296342572, 129756023, 841254155, 339188648, 884386662, 157489248, 531478552, 984465119, 69125036, 863545888, 712897792, 221087186, 788982332, 625922261, 615984261, 429277985, 272828441, 347824178, 549875547, 440982949, 769757793, 266846506, 720554367, 627191137, 280244071, 95803677, 763100037, 747504863, 391889765, 114144084, 948080646, 155128559, 459241362, 245343784, 359547891, 818990634, 609920328, 870677606, 304337373, 139037079, 762582851, 36732433, 695066533, 169842807, 912293536, 297312850, 57350720, 104452713, 425229843, 13993171, 866235970, 241916413, 394521418, 912920091, 106427807, 898040999, 924746568, 714237685, 267825105, 521173187, 528653390, 872655583, 634653984, 731723439, 226742389, 674939408, 639984506, 759496145, 284649066, 226934614, 956889115, 787715533, 827364582, 511069549, 649618112, 412019067, 10862271, 280001154, 286262573, 863926508, 609178082, 76509537, 948018077, 675140175, 653611, 464172437, 800975970, 923617332, 23398063, 539229173, 423305418, 510716991, 318112171, 920190860, 916363827, 396111056, 421387655, 309533114, 543013810, 145308431, 14436163, 460176615, 441407963, 528552863, 304959582, 602614523, 554702189, 573800842, 971544359, 338143732, 461381036, 853679764, 411673702, 136245486, 160269604, 997210633, 549579955, 780901235, 502847891, 55427249, 348780960, 576281923, 460624932, 156198079, 27866589, 899887003, 291715193, 629370156, 948011931, 455478272, 413515546, 250554687, 508333503, 471040699, 517484832, 682286776, 191882175, 972998149, 298096193, 445976013, 190154320, 337772891, 296439080, 395341597, 182155082, 759385359, 398477477, 23115128, 984549834, 512878981, 238626078, 639839103, 454049327, 428076390, 702244570, 577783040, 590160550, 146447651, 15227703, 501241732, 177560206, 608803340, 858658026, 693083133, 22254998, 670700343, 883511272, 954166099, 417333086, 571798843, 238703835, 474096575, 386707653, 724103151, 952501658, 702630162, 773418065, 772580476, 648682643, 530918826, 72751038, 416255332, 295484970, 549336702, 646084330, 634137735, 219138887, 918762135, 579232108, 357669985, 759336451, 204783165, 708927169, 216536427, 645196198, 815947713, 672214520, 630988755, 807618594, 743487673, 753418401, 610503299, 36790980, 522110314, 502417715, 352725096, 674473374, 687333539, 452346763, 832631190, 12206912, 698811410, 873654684, 841225327, 914929896, 446963960, 377311649, 958137085, 534486851, 857003773, 39911639, 136679209, 456651795, 542215703, 887074303, 246892301, 890595339, 28893668, 723009018, 696054530, 495284476, 590461350, 854275493, 74351868, 663788056, 645292201, 513029362, 285274037, 361258038, 445998673, 58761719, 961999751, 848543725, 242248457, 931261860, 492004977, 459897886, 357750024, 729368743, 979819880, 263415187, 590895832, 499717792, 106446023, 646732628, 84623820, 468184580, 452122066, 167132020, 689591556, 354025198, 180584345, 471193744, 525766737, 132632012, 498025844, 542670355, 666271908, 950197465, 1239359, 989646570, 942990395, 995818348, 465900873, 624677107, 555301738, 932592467, 820565659, 243223213, 40231385, 373712163, 308507731, 931379214, 274491833, 623207005, 632033366, 612517165, 639647835, 602478571, 409050195, 730127417, 863234611, 458212747, 670975029, 957842597, 123039459, 308285258, 833353392, 290961223, 62704722, 943455699, 226324803, 675555893, 14795939, 202124916, 539217405, 704728462, 656621339, 324677437, 161850658, 884805946, 507761951, 958449816, 557852930, 479259886, 783186117, 221505567, 40878645, 162962109, 15306407, 769606424, 112972594, 184894061, 320563194, 742472086, 974007397, 374887660, 19862034, 519555741, 760006889, 836968978, 600388171, 510867892, 234720582, 446759165, 24473136, 322292560, 502221422, 956200135, 924595314, 370183340, 924262673, 160985339, 341778774, 74115099, 967597498, 879635193, 719475068, 351529071, 217212282, 366374626, 154793464, 737238861, 359168476, 290529348, 751126638, 887020782, 596696658, 188243621, 454741670, 506799748, 932234581, 638925894, 733652519, 475813778, 328790927, 790663703, 652284730, 297039215, 212715365, 66936647, 70410728, 287300801, 620856857, 317982831, 475579654, 944304792, 804492380, 640703057, 637316587, 127272227, 964916891, 668680581, 543794207, 551318410, 453335400, 53935623, 255713615, 657534372, 285007138, 688097223, 905813094, 861663713, 382423868, 981908153, 861707685, 634276112, 44730652, 799958705, 292438646, 59290699, 449397346, 670939732, 117602468, 999564244, 871896971, 155772115, 470636841, 937260486, 855503429, 28023345, 996168255, 193274095, 90033179, 163050350, 770498357, 679081650, 794601403, 468517156, 668989845, 122717418, 166203395, 774178214, 936290870, 631468045, 244786089, 100083871, 436819765, 556273426, 641957264, 217324167, 39105395, 24006890, 959467359, 508733002, 456794833, 192479020, 782368409, 946941774, 508225725, 845151666, 757021787, 11852953, 426839572, 952076607, 263498955, 35248595, 416565801, 967901679, 148023460, 473855923, 741063813, 346800241, 789574735, 926858564, 805828814, 71877992, 602911943, 969732358, 697353691, 504236400, 858943267, 462708483, 732445350, 774210978, 550116759, 593523449, 152329914, 17003552, 512496348, 682986914, 151844832, 878060054, 639156802, 416262935, 343861767, 466598722, 441823423, 847407662, 444059217, 598541444, 206145786, 905678286, 39900405, 881030847, 578689908, 520885120, 203515444, 839606289, 834972735, 685762610, 15535481, 459518283, 182044078, 972304645, 574831946, 597440129, 367695378, 13481047, 104576215, 895763058, 302747884, 295148202, 606022765, 488195282, 873885990, 80979412, 142031327, 44713183, 967350900, 930770971, 935975028, 109521301, 621616715, 294545885, 767917393, 173596790, 803692455, 254027543, 231844491, 50925047, 296840164, 555182750, 481209745, 129544882, 201760309, 65427737, 920778328, 126415808, 344671253, 115903192, 297974741, 730451028, 656191981, 962671712, 451741635, 397830946, 290804307, 995859886, 96304453, 758636649, 93226984, 562264628, 234075960, 935354869, 993147690, 72199716, 821104845, 902019363, 408486333, 29806843, 854188846, 173677282, 433677588, 601909526, 607373696, 411902280, 903674072, 533310710, 719996428, 123798261, 853901207, 784712047, 580814967, 422343341, 184458258, 331036863, 719089129, 56687009, 727305623, 10505150, 554666726, 687917431, 422969386, 452309646, 483143539, 684233345, 18422156, 947475923, 197111345, 923274635, 429634573, 702013672, 590539663, 743981111, 369604007, 502656441, 359234698, 451750187, 668240729, 73095826, 808063249, 924208236, 78358005, 858333327, 226378829, 518630657, 325070435, 295724232, 404441959, 453763775, 176533752, 731791310, 655599972, 814201578, 635711576, 506243121, 890581558, 341178872, 30730907, 844139187, 663658331, 813819081, 276778941, 621043020, 816802569, 801239729, 343690782, 491261780, 792003677, 113754301, 993944373, 994774191, 132323212, 929089437, 492907353, 45972438, 299909396, 476267367, 277750585, 728249004, 775561144, 43677178, 751638316, 94252671, 630440710, 280254059, 741737508, 62042212, 736373674, 887044237, 194168735, 192147276, 358141209, 203609442, 966838986, 316814460, 146639862, 33023784, 35633445, 677055162, 139593229, 834937259, 467877931, 108454529, 578864060, 817023534, 955042861, 212189492, 293552922, 320335134, 397081992, 710146963, 268801388, 12254519, 409405312, 367354747, 437019283, 527099222, 313325765, 341275642, 559281989, 517311276, 510208979, 387435500, 57760131, 525272792, 311055374, 716279565, 509932816, 699481115, 4518172, 831812160, 100156023, 765154519, 853284968, 736902460, 438062931, 920323927, 948921445, 949525947, 576596800, 533680172, 609843398, 892567487, 610335839, 720364430, 577758994, 42116222, 185673628, 410312022, 307329717, 225713657, 76175319, 53383780, 778350931, 850252696, 455734239, 610781624, 124630875, 704913301, 566480413, 692226216, 421612326, 854048636, 214665148, 696939401, 245168864, 839122852, 807699489, 687573007, 979535160, 105568231, 751741029, 842243625, 457441155, 481220919, 290556609, 350722664, 837611607, 317287777, 273196923, 458510682, 317535448, 64328696, 175771246, 979504270, 600673554, 874142064, 531414084, 856848107, 618151222, 130645002, 35674494, 451820005, 146854450, 482989768, 682814913, 860836769, 557419123, 709258586, 930747946, 69989421, 985592585, 439104631, 808893313, 518194884, 724915252, 70193356, 226870070, 179856913, 651293752, 462282575, 907462923, 53619567, 59113825, 713899706, 303757577, 217091576, 806157979, 7629132, 752417608, 25134135, 230668707, 25491256, 120733976, 345134978, 706511419, 506161004, 27961297, 394087167, 917876255, 424193232, 112168588, 328315026, 525803170, 352291403, 437956888, 200939293, 607400817, 335785243, 539339506, 250592051, 395018560, 289859738, 933351600, 436062217, 762180759, 203018383, 193935830, 174697567, 631989541, 330938543, 97398701, 42062082, 671037790, 913744665, 397347567, 533566166, 680579952, 410762153, 605738870, 544268183, 148777629, 613775172, 390660648, 209749730, 674386898, 133946564, 573888832, 220468714, 608770505, 266225724, 525838830, 821543506, 760695755, 834674815, 852234541, 496349497, 16580828, 788375701, 722788328, 587414480, 764950425, 677619079, 229538080, 262833492, 965241024, 959335483, 844395882, 94831131, 677186099, 908922190, 286807296, 715829792, 86681542, 418755552, 681214582, 240002809, 666843173, 844668228, 681221441, 853618471, 44264483, 113267847, 975151776, 673568256, 363360749, 494774531, 500391532, 718826516, 823774419, 793974162, 45937234, 415352723, 218951283, 683103946, 930256343, 846413605, 312415291, 486438396, 878619430, 332691447, 928441966, 235681941, 877843786, 476907306, 756951270, 905234732, 893140207, 681005111, 980599887, 340756284, 574163268, 391289180, 694874731, 376263165, 507996342, 227407153, 321650006, 379974232, 677850097, 650084971, 41580068, 914071771, 955939789, 157095553, 316751986, 563529368, 834530988, 936983896, 149054899, 348708444, 613940856, 378560900, 530189900, 722593705, 475114403, 858101911, 802178788, 898692142, 988425221, 565402778, 133298659, 891917148, 61742607, 648422796, 628277187, 838345023, 683435106, 826691308, 347176437, 368689884, 784070742, 235114105, 819284720, 734455185, 895782308, 246180643, 646609892, 258185080, 844853751, 619766469, 5241087, 833101197, 172480987, 811529343, 217304843, 992659187, 708551240, 352108675, 960478452, 923086838, 75836578, 543760106, 674812932, 533457866, 498924903, 192940064, 889427563, 675202708, 667040170, 547446115, 393186707, 739030743, 98567681, 421997733, 512521823, 140810054, 522691281, 922266145, 243130627, 70281443, 83041501, 897627171, 426413991, 4500255, 844950065, 420218935, 791861539, 521426799, 560950022, 632773253, 528873936, 97325327, 260764153, 197765823, 972550080, 976524480, 207668912, 707436055, 47550474, 232206124, 50815648, 636139773, 660579400, 656783677, 195910028, 10734120, 508851321, 29183177, 550885614, 453080374, 611969121, 810062019, 963801027, 178448514, 193889350, 52382659, 286000418, 323883250, 303928879, 468118652, 73327722, 454601640, 992958374, 309161105, 701030972, 732866595, 378198202, 646677613, 769451424, 652277369, 784046748, 923975282, 649164388, 836022753, 619468275, 651711884, 48427200, 657794789, 171574199, 30781222, 464779355, 442486624, 591400900, 74817215, 282468589, 881544300, 287432058, 206635809, 325315665, 279849705, 344426700, 568243898, 733128775, 801546642, 640898795, 991051624, 203915171, 578538736, 20266722, 651673429, 247590288, 357508818, 552701476, 440071757, 401557259, 911578672, 283262758, 984815008, 72209635, 251252450, 642933132, 349260490, 903198902, 451861685, 429520743, 404139691, 114686837, 530338035, 29951033, 650335710, 674564378, 823917080, 601825991, 388602660, 720149357, 227250638, 694669871, 94426948, 47253924, 527639684, 509840425, 48000295, 535162897, 620863911, 208121147, 391155956, 637059679, 893215098, 484930157, 350943451, 56143212, 344829811, 529801577, 160630482, 212264158, 774379344, 351505060, 635315566, 998927541, 157464482, 233684201, 188220607, 204982739, 940886275, 216320300, 597628899, 685407172, 252649972, 756859966, 128245763, 344983008, 57374439, 131464170, 615635414, 237424800, 482317509, 868780551, 492298067, 75941773, 109925184, 408395553, 880232169, 757447268, 687153089, 56397958, 344179982, 691219827, 56281370, 868607418, 966428978, 455688564, 761819773, 321663709, 157261220, 149537586, 195503800, 812747816, 800858322, 487147941, 554424950, 246724296, 736952532, 150133067, 879688858, 511633520, 108547571, 48733488, 886065812, 519474799, 753594171, 578989355, 48168912, 504826003, 653944510, 968256524, 192960339, 845355083, 638757619, 816845325, 776464153, 284592586, 885790772, 235179996, 559308317, 377567749, 242328361, 674866507, 759954347, 969560540, 295999446, 797323221, 882482086, 764617035, 35002677, 69172354, 105551761, 496944497, 468364054, 562193207, 760690711, 34815681, 366619790, 396338313, 409434044, 838576360, 439243295, 879091893, 764116122, 403070129, 162206649, 688410978, 995391129, 241271573, 201172885, 129622951, 916143520, 89510248, 777325620, 526386474, 605493718, 923411604, 784785629, 451558183, 922551580, 452203976, 614799899, 536097825, 43766968, 402465100, 821738636, 766332340, 673754929, 329464259, 401288202, 544948171, 161296876, 221901174, 721972832, 265249440, 196852938, 221651406, 344004670, 11261071, 883866161, 858037513, 999739220, 707406269, 647917352, 572872470, 825830605, 991352818, 508273313, 811870564, 752893475, 935822791, 910177921, 629811832, 87145884, 930258390, 29537611, 890802706, 551047464, 343035641, 997703795, 471351161, 938606874, 745456757, 268083428, 901714215, 927772416, 765960790, 24508903, 916619048, 265458301, 796704377, 634720762, 627147733, 802272475, 776984150, 996485655, 548157013, 142110843, 716392152, 864808446, 808754718, 764392405, 675088725, 358101778, 999510791, 485929314, 52835048, 160209249, 152802818, 672744681, 976607981, 697056654, 651167306, 493973947, 637983741, 849191636, 311531414, 52931943, 142611574, 742288255, 495923299, 692605819, 368900034, 360772910, 716177323, 740867530, 444316590, 736505207, 942980380, 514754361, 829534286, 460117505, 168592952, 879380748, 811743581, 445408105, 598755970, 634541771, 726545831, 778898068, 134859486, 307663066, 731631239, 511315214, 171437141, 414355920, 992900837, 989238289, 432809009, 673503506, 611065310, 801149231, 932669225, 604782682, 300969971, 61753328, 69784726, 764892843, 856688647, 265234965, 916929828, 598362768, 937664444, 672381810, 509414539, 402587159, 305023485, 715387335, 635676618, 746647237, 69345528, 434436134, 993123577, 793635137, 995139457, 876563527, 986730714, 565982769, 136629143, 998911247, 42984641, 565395143, 245660276, 303055731, 21235930, 924083843, 865572097, 9590985, 731868945, 68699531, 305276478, 630622297, 225132652, 115959947, 600340953, 392134549, 321163476, 52381326, 401886510, 67160112, 26556850, 388625186, 882072412, 579658284, 853990097, 365837276, 401462505, 878945031, 587483102, 686409621, 905768823, 377983047, 71089629, 72813572, 513654167, 355403463, 808042275, 675303681, 255570242, 16142284, 186952507, 258784944, 809161833, 976905609, 735063787, 401533489, 209152590, 670576063, 395718926, 134136681, 848581273, 324188301, 940416774, 3654149, 880803961, 111627822, 333242350, 484398331, 821496495, 653788181, 94551982, 332625209, 109485981, 405309324, 967278837, 779898013, 162155505, 817289648, 214179507, 911562593, 104057462, 981676340, 362394984, 292762382, 523970729, 122087581, 52929677, 77580388, 740660794, 409165718, 432087289, 90518256, 396568912, 62730687, 494126732, 530822156, 444160081, 269372410, 13544963, 238024512, 889058075, 311508940, 388286696, 297291369, 989009812, 922751761, 36957370, 559481480, 68283427, 337576586, 929624300, 663562937, 709580219, 423932956, 368919144, 634553916, 217318479, 903860449, 42555110, 869486039, 300383653, 617838464, 165613951, 938608046, 952763726, 229689389, 514481480, 662590224, 318254559, 177847862, 603701410, 953093723, 678552383, 524361638, 518621982, 83524316, 298381417, 481688608, 488430590, 723431923, 869764527, 161002847, 349599614, 179815660, 582868051, 597633518, 811388361, 812368800, 916842283, 98799713, 15888143, 533305176, 322575546, 146696457, 776704479, 800484601, 403989946, 786064931, 379681009, 536176554, 394135659, 904228305, 770721983, 321892804, 353383813, 707622662, 164386384, 643475333, 103612459, 873923411, 419819702, 656697625, 616632211, 32981178, 90592628, 11268692, 271740308, 123208160, 401084923, 806102458, 616814390, 105018622, 29725533, 107842426, 535466463, 259068045, 812045590, 488230438, 311469982, 59870257, 248692410, 216310648, 949945793, 571392323, 112896397, 132246696, 331578634, 677452537, 254982251, 617415555, 103051260, 127883316, 300217651, 270899255, 243834588, 325323257, 511760204, 654590460, 280151316, 623275330, 15429939, 687341326, 926955745, 326957373, 484412951, 543107233, 874717104, 165528270, 369128639, 703535519, 279764353, 107903664, 896067598, 533788873, 568714974, 605711581, 297401308, 966500872, 869354117, 196170273, 835285782, 430911187, 303794005, 375870326, 276387423, 923975170, 178953028, 261023706, 189311877, 274299531, 796745701, 478067124, 50441558, 161403949, 866885738, 810981592, 773366553, 580785342, 37903099, 209862609, 649476435, 302347862, 549425945, 842272730, 835948578, 680952477, 271147694, 270961407, 763143034, 632412168, 865217851, 923550785, 206079725, 420586269, 799701054, 114994376, 416385747, 830944790, 337607035, 715665117, 800633857, 976965746, 173027967, 846548442, 436422307, 75730865, 462235105, 179401832, 221378691, 944407173, 160127530, 345153656, 543692161, 483702958, 92057840, 971506228, 279937154, 477293598, 77548566, 331391489, 852722776, 765339827, 718713237, 222818622, 894450660, 551544118, 936430017, 16168034, 491793612, 902399490, 809919345, 477794887, 895174489, 287393876, 491434744, 450293316, 426530152, 558999004, 696945012, 384049721, 410261235, 97933182, 200680637, 185349638, 766153575, 87929963, 307892758, 321059538, 890233666, 309611078, 670647726, 551732814, 145310871, 313627502, 245966363, 824533718, 377453223, 171339762, 858064970, 341523746, 402713469, 40873556, 253225403, 81290980, 733417629, 37758374, 25114969, 784141317, 899825618, 812205427, 736853177, 723536791, 80400721, 816209210, 953489114, 491588768, 773647691, 521293359, 702766242, 199430356, 793155978, 801187870, 600216723, 389956443, 469128753, 882010142, 268305050, 530116497, 597406520, 577408066, 915735486, 947091940, 376026355, 605337957, 55095498, 119085681, 304606837, 491020121, 381644720, 8759261, 200755830, 889074611, 629777262, 906681287, 692314422, 936650445, 766468853, 335572390, 101919549, 739729337, 500388678, 912201004, 172874399, 482307649, 4095673, 395998648, 708404726, 832118048, 973014190, 218026184, 701267271, 542820428, 460126794, 488819498, 221205037, 670641271, 317555577, 498454373, 70163853, 68833048, 390535526, 168158476, 347551838, 464211638, 518506743, 915334316, 493577721, 417266195, 225221304, 785865460, 154790355, 227397125, 149306691, 722667819, 531408060, 509922263, 145728031, 399444814, 995947710, 537708929, 990326565, 879870733, 662469984, 186757688, 142371740, 367187412, 444561814, 172932415, 607696874, 293125151, 477097829, 198004047, 658592660, 885565462, 735812337, 203387210, 802997509, 14720734, 761951290, 120766677, 728501286, 497299105, 202066779, 990099218, 978158440, 671146272, 447770334, 193802216, 252660930, 505582646, 822267798, 407634040, 20405485, 414420025, 677709080, 685829119, 3358990, 833392572, 785780720, 17255269, 392153236, 372462024, 347644795, 150796706, 731726650, 420347065, 590196723, 441866825, 304300753, 538409041, 801873276, 190701861, 241562168, 176428676, 144648867, 364592967, 926186201, 256888551, 151970011, 724208570, 405651423, 699414150, 944332303, 975615975, 807767907, 907839519, 866178192, 620153433, 870796990, 667255944, 636640938, 661902467, 197602057, 177912062, 401597122, 639989973, 618826656, 306891431, 393213341, 179716395, 218872865, 645320644, 458659307, 435398080, 499702679, 210992247, 591809588, 946748785, 52693828, 942033706, 364168263, 948793106, 531055027, 381088744, 147989894, 614379709, 97447387, 864062105, 261816467, 829674983, 651113979, 598024344, 631642380, 878672990, 396566849, 86435122, 956323221, 566225960, 214237259, 322392165, 603391567, 755797413, 141925056, 886296702, 631007649, 270700915, 511209009, 944111816, 246229654, 593627539, 495584646, 964177676, 626856074, 420586797, 292246522, 702975773, 395861055, 429546334, 979717573, 633551830, 463561159, 42089758, 153886383, 663600476, 593835618, 643602361, 279708686, 611773378, 652395358, 665832971, 566503289, 940759769, 829919345, 84911913, 33848036, 218077142, 805816201, 257315906, 287290311, 512378183, 124295045, 537101359, 869865632, 60169310, 949896725, 895200317, 745772369, 918116608, 929957653, 308354420, 466171888, 826190947, 676980663, 762208763, 490716418, 765189435, 243171423, 719624691, 671376257, 256041224, 650609602, 500423092, 171620436, 104022575, 803273831, 170408275, 380146168, 439029363, 92966740, 190727326, 371082725, 520103943, 861152372, 373302844, 586626657, 18855617, 667959685, 349778558, 859177732, 625998006, 988548264, 615111162, 307766823, 835458789, 61524304, 580918193, 490303308, 561014985, 384218539, 894108139, 213124033, 594918271, 325819490, 93988505, 68530576, 870566218, 992034269, 28497569, 765795488, 810466544, 698914910, 903245931, 399362109, 52461938, 513569711, 704842936, 5740928, 133930666, 614786644, 812574471, 27873113, 75961449, 772005911, 734312701, 98165838, 484025330, 663201194, 730948457, 510345543, 213245720, 367915571, 564045725, 204204197, 932759820, 685406721, 727127191, 899213229, 404998382, 623483368, 638187727, 279218558, 363304743, 817550756, 331586479, 367285814, 628969182, 162834044, 665620180, 42879863, 295895973, 845433367, 116737024, 681567555, 241742271, 965822757, 476558217, 601139452, 728337800, 77383824, 181931848, 286188985, 495793646, 17211381, 661760786, 935863207, 168621316, 87385813, 837648601, 787820526, 378983903, 933476077, 774830545, 44172938, 227254170, 339957832, 934667268, 369760544, 503349334, 1300610, 30194697, 294492957, 860230577, 431277771, 260933439, 249530981, 404844917, 715524925, 519110372, 149482339, 475687065, 20809637, 187081805, 303630298, 142098294, 42488725, 225275226, 273293966, 146793419, 521067909, 557259613, 538114914, 288022823, 505188527, 950451136, 542197132, 510285571, 83615108, 203572573, 721186910, 105606839, 381999636, 773650688, 26888501, 198575715, 66580867, 661393874, 782163377, 2980831, 358473041, 563989103, 909593567, 137669380, 557820305, 113095562, 877368595, 674966579, 265562610, 166961905, 617447197, 887834030, 333722460, 55345974, 474261352, 134399905, 317291596, 752893094, 173797853, 771515640, 692149519, 931631417, 770987563, 980954737, 904734549, 378032296, 735405168, 470399345, 5223343, 479821075, 76741115, 989581048, 464714214, 518851647, 360828038, 996151474, 937390374, 315420064, 483668734, 99505404, 532161887, 914494410, 304192285, 306356634, 443542747, 953369482, 133673137, 460118104, 382475159, 405243685, 643954148, 464970023, 635694851, 71988540, 727815720, 822761199, 49783590, 777292906, 162800216, 613035651, 107737561, 962462769, 260957505, 742174756, 377778448, 669589216, 618683022, 36928359, 424362506, 650509454, 616116159, 690227938, 883519558, 987357226, 601689899, 586888860, 387493489, 709735608, 349887464, 112413828, 503103568, 984401736, 94569181, 784431985, 669806977, 46385063, 34683728, 432687935, 474018040, 508406096, 134374082, 918667499, 860575247, 36241328, 482182020, 714755365, 727326641, 561704795, 882354829, 433727391, 284082888, 738656970, 427655948, 143183496, 732865635, 209324256, 976744265, 402560415, 199682761, 939326070, 30651731, 34853947, 37232901, 283006825, 141780434, 906944728, 123067972, 223535420, 11646228, 403349389, 602609961, 675930780, 868075260, 856394108, 341033628, 515327198, 811887611, 969170618, 516571935, 391924100, 644876227, 933096835, 22807274, 340117802, 415408026, 5547985, 164367545, 614670634, 637294122, 790715161, 124399409, 877926096, 584343287, 783307204, 845652875, 920175812, 724031081, 489205272, 592999870, 715141348, 754870919, 514258025, 145055453, 799580773, 403282483, 754151279, 314529142, 36159509, 101472995, 317613485, 107658630, 329403626, 533254384, 29295663, 598671291, 153123433, 626774160, 308699528, 272929534, 126169446, 263447992, 730373908, 262446590, 333664842, 415809542, 198620989, 452989877, 389561813, 687843731, 52109923, 278127158, 91979809, 948713106, 898536543, 796061726, 605610151, 937133816, 576883685, 727289597, 916072755, 887294680, 443985901, 642358078, 408546035, 711619805, 75179366, 865307648, 95893680, 471951979, 756167927, 80786122, 793402127, 78649037, 240779539, 589819856, 958978138, 611637511, 946140423, 893636953, 667516950, 7997866, 604300711, 632010541, 873972503, 631131752, 549429524, 717165010, 348746027, 95238619, 614079314, 698819380, 635627559, 500328634, 199532546, 18140766, 207832216, 401266034, 399116655, 893465913, 500526205, 290600605, 654806666, 366671446, 780674128, 756105026, 501537079, 17361520, 883149953, 680443420, 737835255, 635831786, 826421406, 288748375, 681072556, 775310554, 338083331, 865969486, 188530625, 20776679, 130876610, 406458393, 530090550, 478642156, 196946221, 519055383, 114044597, 139128559, 651847167, 982954587, 844965804, 878040956, 62353954, 935332505, 911616025, 580841829, 221197616, 65887153, 542219308, 226157176, 727189362, 675105093, 323328133, 747370259, 948034449, 414247081, 41121413, 790356886, 476499712, 690407099, 664284945, 775383681, 64722277, 210048143, 834351139, 545551393, 2065049, 952287959, 859679162, 856780670, 809782698, 534142021, 13818955, 431105379, 965385027, 134013072, 202865071, 559431478, 119995433, 37243472, 525476124, 344541499, 440109904, 429565742, 311027744, 783965953, 590536079, 17718156, 307700604, 605653776, 251940451, 693813795, 211942185, 743592536, 70614638, 790805599, 285983908, 491135616, 457646547, 627959560, 570273199, 591317731, 44243485, 33746176, 244127549, 422090531, 244946346, 967603413, 416626923, 282646633, 964419821, 380866430, 627776442, 559651164, 463994093, 977318358, 515991572, 763009233, 787458121, 322099709, 348955125, 175060411, 316941046, 13911777, 389624641, 839172413, 274729974, 360181348, 384597437, 609078213, 264891881, 804755286, 838545014, 542241111, 432206422, 691180874, 113212351, 149244, 709435707, 138407849, 569975309, 653693334, 908486710, 317715783, 221669859, 106238201, 580602141, 888237594, 988596343, 273631392, 758478236, 856043730, 837593374, 943782842, 587388081, 579239540, 767832296, 145461827, 633741245, 840645273, 790580105, 751185222, 624579060, 499518580, 944733832, 29189123, 511597592, 501337168, 641839541, 832500105, 431750222, 786917378, 44826211, 3405666, 283642148, 335756434, 44637757, 429007724, 237649594, 671466264, 301070852, 302251977, 607814738, 492529865, 509896469, 791993432, 826509974, 950141501, 434587278, 200132451, 854674080, 101581156, 809117738, 268145027, 348019255, 27395412, 19531824, 969859497, 828856096, 820915727, 119326883, 207944489, 876788413, 42142078, 744276091, 714331903, 756560325, 226653914, 560498752, 316200008, 497959067, 111220722, 553904348, 990930074, 911056068, 399903610, 165537350, 847470491, 475305663, 602259888, 453937300, 711716400, 332076848, 851950329, 392114634, 210226938, 920594397, 740785008, 587498666, 84276948, 714357099, 861039409, 179911107, 305184440, 546728516, 460749209, 124255529, 13724877, 332991489, 857079878, 662112331, 35198647, 138814131, 811798651, 820686481, 364239785, 65157433, 865982492, 407152012, 362253435, 194228283, 94568838, 62603026, 554652288, 805727087, 257283869, 951021506, 85336919, 341832420, 335479861, 33308057, 751013954, 503888405, 233697326, 488187490, 887275206, 594985441, 832119941, 278565759, 483406838, 524416197, 451058774, 773605442, 628357800, 363680392, 644243528, 210154545, 190314289, 95687297, 778815637, 128938813, 506146360, 232999281, 266284961, 419294959, 985416909, 703417941, 97783891, 140897055, 151847103, 437746353, 203578261, 5235900, 577935268, 912142210, 381629486, 594909629, 949483737, 485072739, 175357182, 779405757, 683491560, 296307771, 331398983, 883035212, 825581906, 837140667, 136333511, 764480513, 518771940, 728267529, 352401977, 974242580, 700400823, 398912481, 665811547, 635594746, 158890307, 326859558, 963490747, 727664775, 375686757, 523904398, 500949844, 464362759, 945478182, 674196808, 405880446, 870271372, 915563184, 523951441, 401847204, 630792705, 496451116, 729942382, 672189552, 484997535, 346279844, 385461435, 996251719, 677938035, 46115834, 270389257, 381981623, 551464765, 56306901, 228034957, 247089304, 619155934, 866152714, 785712927, 60872817, 973888678, 499777525, 424198094, 677149722, 362012181, 602750277, 659408573, 889094210, 537660321, 288456718, 668935626, 169189110, 339691399, 662578177, 288925095, 122879108, 849291049, 308756399, 946664131, 153805056, 483308704, 830016259, 129149136, 502773036, 312312265, 406770600, 956504364, 541059915, 229949428, 270460903, 215657186, 643914165, 248497792, 379704920, 867435729, 99696621, 667917511, 715800801, 947119808, 69433937, 533244994, 413531763, 161759822, 215872503, 128752139, 421768383, 365299332, 815570092, 24612329, 689597831, 839368775, 276694060, 410711452, 231143688, 87526177, 209798370, 386981896, 222540169, 720153433, 334156940, 988335516, 498610949, 641095040, 758997416, 471503543, 405840403, 823635913, 963453175, 389796456, 134859727, 565116944, 655520432, 976908689, 15287562, 173525579, 923126328, 933599959, 18493022, 200433164, 603841862, 233771115, 370386054, 702857570, 524950935, 637328214, 522723476, 857904248, 786967061, 738057317, 791959135, 515404818, 945316587, 720358916, 910725708, 51557301, 367994574, 562738792, 375569226, 969021927, 821834900, 29926609, 580948448, 990141943, 28424974, 106428668, 614678002, 333748456, 895198697, 891104825, 799381086, 676839139, 378809804, 506584328, 668313895, 623790011, 14674258, 985329033, 253905361, 697167280, 112970772, 469464594, 10172235, 392402507, 139262805, 750985758, 598295396, 579497607, 508501945, 396627389, 904655150, 388534310, 987470296, 797971728, 446547116, 304515496, 76658662, 122258339, 257216575, 195438056, 450292681, 970089567, 160364075, 686947112, 910488359, 176509791, 247282195, 206222640, 302276991, 551188671, 629709073, 733254839, 748140098, 371973235, 980188554, 374662086, 628994312, 498311052, 31013667, 89920248, 861692325, 356496556, 422467305, 571544054, 704478905, 685990050, 821278486, 307978767, 240423978, 924000390, 38156173, 81895509, 578235901, 788105824, 25358510, 952500594, 918380037, 673558825, 905628695, 98010129, 989403320, 169645377, 308727183, 343031258, 340942787, 608648268, 148750279, 872756742, 206041206, 865128663, 278226368, 266060436, 985401900, 350884407, 204170892, 404204690, 160341059, 327037641, 430975292, 526070821, 71413476, 783800571, 877632212, 725895674, 62814042, 380445468, 644707242, 705240648, 176597001, 92831030, 107733959, 611326362, 657432952, 69687031, 996677701, 230915540, 323515128, 450739387, 881471900, 584368573, 679560111, 922620212, 820677725, 637916690, 675204495, 973606389, 332763526, 122347876, 731389898, 526871944, 729605012, 986577427, 903387313, 137725640, 62367128, 453651040, 395423870, 823473407, 251466037, 760601029, 852658862, 980365940, 716653084, 771278816, 188877850, 776196840, 206657149, 781784163, 239355293, 663726884, 188657155, 230612681, 342053061, 594167311, 174632924, 639150676, 119326651, 789829862, 717536391, 567052071, 740326314, 732131640, 699610568, 621604968, 247029495, 928990834, 349274655, 20522836, 875859808, 720157605, 951589978, 322161884, 235621855, 409473782, 609007302, 556648580, 8390490, 601490123, 138401717, 144589149, 694018422, 371603226, 524340811, 585499715, 714942877, 207892975, 655023551, 321231063, 45945753, 409961359, 464138239, 973525267, 891328563, 97999747, 439946096, 182411808, 993372456, 228796976, 497178451, 563830627, 888167231, 736495565, 335655228, 536437602, 962269709, 721474015, 305638542, 681842616, 497594033, 732272442, 335687413, 747341891, 178883501, 543111759, 48162938, 773279464, 223141816, 795215725, 641593351, 498912657, 314375697, 772709820, 627400168, 414710102, 926088306, 987657227, 190854327, 77137767, 562484173, 266298378, 581166336, 745653072, 969536419, 543219474, 143769678, 178676485, 860504313, 317563372, 259406622, 717258975, 622870643, 156857528, 251775974, 628169314, 388574373, 895269620, 372024608, 808026632, 27714937, 425062738, 698360762, 77582372, 775160790, 718978129, 566287854, 599362395, 72122246, 54816022, 647279688, 492401984, 514011443, 228822841, 894760401, 432844100, 214438828, 301284660, 681848557, 148795090, 241149751, 845301932, 658582114, 768280041, 947867508, 702901328, 905941552, 174980326, 166357962, 933128731, 204091370, 428325874, 315578609, 426630691, 501437731, 263083171, 313289102, 378024982, 811163074, 896605437, 315420805, 253353560, 143079134, 744444932, 145754841, 238048654, 320305749, 789409073, 551478604, 187070592, 80323794, 835582219, 163086436, 340370945, 516563283, 878013578, 182387742, 880832226, 912233766, 770659639, 804913180, 673597384, 237817484, 670469668, 948439259, 914969076, 876883565, 89633973, 630977507, 428839562, 912197272, 983113983, 565096697, 685793387, 331565895, 533814312, 625979895, 483785559, 864997348, 437620001, 307834843, 181748831, 900521518, 423360488, 188001069, 130035767, 150317880, 594002074, 737216307, 957171552, 109978028, 198143309, 966900500, 856062976, 303577280, 697525840, 137336397, 543672041, 784204026, 211380076, 325559882, 63801235, 501829366, 951165833, 519903387, 47802369, 41407174, 348614142, 773779652, 724084450, 604561140, 16764475, 381926008, 663968842, 335278421, 570428434, 41859330, 609202142, 427128913, 844714942, 945291393, 337730901, 501477967, 630750258, 286423732, 974621563, 623881546, 559317712, 405179056, 705962120, 496168946, 901286323, 980178638, 713832492, 989740250, 336259995, 213632017, 380347256, 876831772, 427075652, 998613200, 709267859, 965569922, 41037362, 639543265, 389779466, 444948947, 187437238, 907115341, 738161343, 486912589, 922324875, 125514310, 787003433, 300033978, 490101878, 606096007, 39746711, 196431154, 319239330, 957651710, 287029057, 932724963, 891922484, 399632361, 749794095, 427710809, 881703527, 846511386, 489290705, 879900606, 8646401, 119999740, 406954807, 856909016, 277756403, 517076984, 684896561, 558258782, 804572941, 10782320, 656251647, 689100239, 825230437, 197063603, 29355297, 525896150, 552354982, 245945992, 716590226, 435211993, 215670339, 581877531, 49533339, 889657698, 820871438, 175082498, 33833647, 509779831, 523238406, 920160333, 605220052, 971853347, 356338937, 714475918, 437068095, 883251094, 414745864, 281048399, 400205615, 75008093, 201050530, 599930129, 887752971, 206052048, 255208993, 515885823, 859465453, 61522625, 53653198, 248587976, 998377410, 292514883, 670336885, 542566520, 484741680, 363322089, 428025067, 843128984, 608770057, 484694981, 353867676, 713740051, 145546920, 76632583, 462978899, 277190053, 405095494, 651425185, 2382353, 263770364, 86277363, 452278581, 508865559, 521364427, 347277539, 551370929, 478459301, 970196761, 334959179, 496894344, 845482053, 400294502, 61097412, 867906140, 51232511, 561804829, 56493562, 743579313, 875454964, 936730013, 887763707, 592096434, 229083337, 731371594, 536002704, 359472383, 408541095, 734879479, 508901650, 747347318, 51232778, 895476482, 188565043, 706729304, 139901244, 926927420, 548754632, 141389560, 539649339, 158092537, 853986578, 654482596, 350057482, 913000620, 377565459, 307005708, 572393240, 852651005, 202774458, 429029628, 538388583, 43243475, 614756376, 51612641, 806492929, 316664749, 119722652, 438856731, 339203041, 302246810, 310809883, 885372574, 938960106, 365961503, 661174049, 609350538, 892229590, 503760913, 440869156, 514731486, 862133031, 384774904, 605564512, 63342572, 619062769, 252318734, 850972184, 230502227, 839170044, 228638321, 321910896, 723598918, 310871881, 973470739, 929234324, 672118224, 59832857, 672553980, 473573851, 812341883, 390256933, 831384735, 193583011, 768624917, 101233160, 274250373, 526688062, 40426463, 689997032, 626300471, 984080254, 599299291, 361085179, 973969617, 136845671, 161245930, 10071770, 361925808, 849684956, 372327818, 666148904, 387759756, 167894470, 737125008, 784171134, 351376990, 353005609, 528023496, 994243522, 145214693, 619775288, 995717305, 403556058, 919508318, 373903425, 607868194, 617217521, 40505437, 549781282, 261528354, 468079334, 450096082, 919937528, 954336956, 812408577, 727430643, 397690443, 213042333, 550606512, 858584873, 877844939, 202600987, 891399474, 947584164, 352292550, 149160727, 374169070, 18300689, 603437300, 374339317, 35282235, 112180510, 878994637, 36465305, 726866071, 820658012, 251430562, 416786392, 683150830, 831793699, 139859659, 402598883, 94378261, 39194310, 300461467, 127708158, 352056217, 794473357, 622442097, 382830924, 666482877, 262129358, 18133550, 990016424, 360934944, 979679534, 732899546, 840296224, 953045787, 15373, 997276116, 770433192, 3767936, 452540333, 164983106, 703532049, 139954857, 996501759, 487375711, 279816681, 27915572, 376620567, 844620044, 787507840, 316212934, 525987674, 565802056, 426030674, 978918641, 19201250, 944959094, 870126572, 478617760, 114741511, 451185078, 467321599, 78735171, 971713009, 198766436, 40990175, 700312784, 549261220, 565126202, 360233081, 658669736, 458919164, 583924950, 469097072, 746725301, 512512323, 498510671, 355155210, 628905275, 900264324, 984077594, 815017604, 394046757, 390673621, 586457485, 574770808, 317048357, 920220949, 30930886, 456697945, 500132973, 484411951, 450951288, 46588628, 467211643, 803489767, 729288942, 642342948, 269468742, 609784032, 983602674, 496366014, 980735884, 391164265, 750244820, 983199393, 14534793, 86476794, 755273961, 469047061, 839464113, 341600711, 835890878, 449647058, 732659769, 896136688, 297447478, 430114134, 297298388, 735034405, 696491188, 582165853, 160080174, 230225608, 801097214, 463371504, 730572047, 511669560, 851303472, 736127240, 449536227, 962730017, 645368139, 406802233, 402436153, 389650282, 98550855, 756967866, 58232260, 212733957, 610967177, 879316604, 61078811, 378127748, 144198419, 575051398, 320426193, 175610390, 120126405, 509335018, 6981649, 301776696, 395893113, 159983082, 334565426, 222906151, 808501696, 182794663, 961727838, 241712984, 616507619, 895479993, 295669833, 432000326, 613402744, 554238745, 811907672, 567682361, 176439617, 481239439, 688703675, 573780415, 201007674, 785359569, 314725441, 788191419, 829737775, 682144896, 380655130, 513392046, 858810819, 881642267, 174994365, 108327454, 498226452, 361670275, 37956596, 209715234, 535805938, 682438159, 688437803, 953138512, 951169768, 616929900, 689590842, 271963035, 606223204, 419207728, 302205192, 438554755, 54546966, 284660638, 218128197, 550210681, 843253862, 220634105, 410861308, 349174655, 272621424, 352222459, 736508794, 588771734, 779370090, 857480902, 745677570, 693618527, 735862941, 291877913, 531950257, 720670626, 49812239, 357449331, 395235959, 746868290, 44791195, 808625255, 189323893, 855330218, 746778175, 87995227, 77312615, 456430459, 853075529, 101585697, 276859281, 43518050, 722471123, 722042764, 326599861, 968788127, 146630605, 250602068, 102659130, 729014644, 275090663, 482445211, 598774619, 510029883, 58120426, 499112705, 719152897, 677976947, 598822977, 474334335, 658214181, 628543567, 198895256, 720727644, 864823889, 224673013, 188577003, 854536343, 541768863, 576922483, 377733930, 574384508, 784470426, 421210855, 486498132, 696605683, 539927073, 913820694, 636841536, 863096350, 151370672, 256859243, 132566970, 211124277, 369184892, 723244961, 959044623, 595290980, 493680576, 922202350, 694442637, 609620081, 518921681, 164764484, 762391857, 156113384, 507359211, 790101723, 660159745, 232201150, 163795322, 55435734, 978677744, 633035787, 71508471, 827918514, 887484062, 243535150, 708503351, 294089871, 260805695, 174907109, 84168836, 344019606, 977977540, 896617804, 693162593, 585029938, 917405736, 771611389, 979099181, 566254971, 793501372, 404234249, 800615917, 122862319, 78710425, 577044214, 762930623, 894340720, 129593303, 425182056, 23199828, 590275301, 399912770, 648190306, 83038023, 604004991, 100509851, 269816559, 398677867, 747522278, 685777269, 927006982, 875059926, 88443430, 598888934, 147807703, 949519026, 936384185, 887799770, 186171577, 8059881, 721670213, 182003147, 639103104, 695737162, 589925957, 672603871, 882623802, 999712032, 599173840, 398962414, 171808060, 733820300, 346838708, 308205730, 526788208, 534291804, 310573422, 457045868, 489540142, 331000898, 939538987, 976217559, 711582303, 892978643, 967180419, 53721378, 561689789, 108654321, 655043893, 427740996, 17492617, 570256158, 854377660, 112234644, 709219699, 856186789, 380316988, 662367450, 767795126, 73630187, 426956061, 474693065, 86603869, 911968255, 790864362, 751647647, 993277827, 360358821, 703587670, 146868131, 17728860, 595136778, 132116878, 709047013, 216041957, 249025134, 433801233, 609398788, 620998759, 592373554, 48930352, 947068547, 94276598, 704898842, 964321413, 660060113, 419244928, 158403352, 853027779, 524017971, 359123313, 649782863, 180686177, 169871864, 392286647, 543618265, 36395324, 882984626, 847584966, 528682648, 768470106, 550441400, 108742834, 24858159, 397686273, 229789564, 270236369, 754705661, 544346930, 511718913, 129781482, 850548701, 19515091, 360512585, 244238204, 760696462, 521997713, 835451249, 194050124, 50626355, 660986784, 571454222, 496473620, 417900158, 504954919, 327639000, 368523957, 543753455, 60778331, 892473911, 584418233, 620057786, 612393155, 620364848, 530701726, 593568870, 732499260, 360410387, 386081400, 153718913, 400703436, 52867793, 769688712, 464179773, 607771841, 841338427, 868322901, 49905572, 631960808, 856455674, 337570224, 125180096, 798665259, 800421995, 740986502, 220866814, 414431716, 636022647, 49459486, 554740424, 38853209, 120471779, 480649060, 640098475, 384093864, 798791246, 48595479, 110996841, 265266820, 545079580, 238761053, 457349771, 409315974, 755455249, 558224387, 728623114, 639065995, 246199180, 9114078, 225012306, 724747213, 727230867, 264380695, 677643822, 312193883, 781420614, 117169346, 665402836, 657919421, 527488860, 689166624, 124603220, 548287749, 360722402, 656652841, 467540246, 670564529, 4216198, 900130653, 555635685, 496703242, 463601738, 304296113, 559035322, 295297828, 311010352, 509385968, 853958649, 784173712, 127573317, 122812045, 217934172, 625465655, 668321558, 983136553, 708122049, 894654344, 844427637, 650748072, 646530810, 687389193, 101128355, 441318268, 376413187, 221763508, 125779457, 69419746, 49203201, 522350807, 625363647, 678678430, 217213394, 603742665, 515749745, 217860539, 582919085, 401084996, 818886876, 328131760, 455008496, 499830688, 722679797, 76509633, 103593814, 818669023, 775740326, 184516199, 7685695, 558716120, 541938693, 642081704, 777680129, 96498325, 655924387, 975970872, 595610703, 77272960, 546596516, 954811927, 595600993, 880808499, 164450087, 735070806, 597118196, 702728380, 731908101, 466569011, 680759384, 764213866, 802780483, 289947056, 61424476, 116058213, 88099621, 971943955, 319991548, 611829200, 963434479, 474668649, 566116429, 505412101, 908789874, 726738654, 369894120, 82620437, 548842377, 232947416, 52327729, 433352283, 414563553, 693512357, 294309348, 596714856, 547113472, 909135606, 347117444, 118662652, 257474198, 480740368, 987000901, 179681175, 880234580, 379159384, 924645285, 796847248, 865753083, 254250388, 290257676, 231170861, 449799767, 698418766, 399766491, 515217698, 765650061, 249587906, 407499750, 93781907, 183610469, 2321929, 615503215, 468784357, 443023406, 88882383, 971803587, 663868099, 59567724, 277565921, 778679221, 71912546, 873227631, 619627840, 778290872, 796854045, 787733744, 439908832, 964615367, 256087313, 534069083, 790431276, 867170327, 901210900, 627783728, 950502565, 807463437, 396981484, 334428065, 14534556, 451158362, 922971190, 453607452, 220884446, 670716684, 247940206, 143047490, 383737193, 181861444, 542367583, 310434015, 250798893, 174685305, 995068011, 900251870, 353883668, 853653357, 483140462, 985454337, 621289480, 483584815, 950985017, 382756065, 564581712, 518789229, 544800656, 163828514, 142985431, 401822910, 103977366, 56329138, 625005290, 975360590, 676281869, 438116056, 401056922, 601614231, 459420890, 346869162, 114812322, 106592353, 42944056, 113258009, 755353747, 500629524, 910954403, 156626096, 676652497, 349118279, 484505817, 501268425, 685217038, 944994198, 24507502, 639641940, 393107567, 703965362, 244781623, 446205114, 824513506, 850329452, 246317929, 27785941, 401609303, 466415365, 535892486, 749608913, 763876056, 38141897, 791780693, 692083459, 957841976, 277456469, 750326627, 386692199, 679331812, 228882113, 29635733, 170783247, 369543560, 940071191, 601840153, 515510752, 626213877, 518077651, 532601014, 889644807, 620490798, 44568272, 55578066, 494086100, 536336366, 42629548, 123971002, 7935435, 561372961, 143788903, 90224380, 850892602, 417749652, 730270646, 836291528, 423611354, 233523814, 498643877, 631188437, 151869452, 400161007, 172309753, 616087847, 444488735, 102987453, 502975554, 810303193, 602557418, 124428976, 505653401, 729059244, 304146295, 90982286, 263588047, 748320961, 388284560, 664777602, 603583560, 717972597, 61087417, 215618977, 840211902, 891379273, 83131294, 161503198, 486562364, 622704586, 264877427, 666348830, 123933071, 669873358, 401703381, 302886540, 597130375, 801044244, 220568814, 459924332, 165190378, 912555972, 184653153, 346049620, 238047377, 812981350, 33648885, 84954214, 38703894, 525908831, 14565868, 274058857, 703513094, 622840516, 506409213, 293150435, 641685287, 508149921, 193569247, 40793630, 908387030, 296289771, 845780867, 94275982, 758613689, 240524383, 725682845, 287220371, 366142532, 567451863, 779259196, 475881056, 327331242, 59228070, 689863636, 915381308, 393764477, 596140071, 96647024, 743679878, 356649233, 514293000, 984239473, 815011605, 87723271, 91180473, 931847415, 376424748, 230608455, 335634883, 568098719, 308553847, 321548022, 170341896, 14470360, 469237965, 828855931, 402919391, 567168715, 317828487, 904022270, 475572924, 979555330, 319664614, 88052342, 126282152, 855178124, 175674539, 830291876, 911100696, 142230218, 643807268, 133170174, 13147186, 34002344, 701157829, 778475383, 901710444, 688532048, 637183689, 46413801, 145050406, 687976624, 976768437, 859986624, 804626066, 533614941, 327073018, 179354321, 493644793, 616544455, 61409701, 561199849, 890304712, 816163611, 423643973, 747483890, 257689900, 165072457, 25381974, 633160565, 815971508, 126806903, 184864224, 415002742, 205366569, 840893602, 241360343, 85499418, 829397184, 587999281, 10329229, 926115830, 210350886, 25504080, 476581111, 123254679, 606895449, 76583042, 192547656, 492773730, 185605358, 400853624, 585033999, 708031336, 412180256, 825964821, 781905042, 622024551, 952983723, 222583759, 616879966, 298725360, 715680135, 349396085, 285729589, 752108659, 801734993, 360171809, 325686472, 116279272, 826125520, 61956937, 764306757, 847006607, 917684861, 700554904, 959829390, 268151651, 904969097, 266054488, 606001497, 999305338, 672369290, 827937986, 374284153, 909965535, 463461955, 181329734, 368463070, 153607173, 889338775, 662155889, 483393033, 963015571, 717181138, 147936010, 784561804, 430248572, 324102226, 880202079, 123233620, 917802285, 144293405, 453677049, 711421792, 106583886, 119046641, 986711377, 63108601, 116054090, 628716319, 513183494, 80261572, 316751255, 800363700, 342616005, 726740720, 252612276, 717991781, 866481209, 917938335, 732476485, 764422159, 269722012, 743800690, 284409016, 727989235, 874444652, 966744323, 878355701, 650660334, 935607095, 980770148, 60988098, 647349136, 888235232, 528353866, 685939846, 465084367, 985222410, 286804540, 875623754, 859757307, 690845559, 202910366, 807788388, 430169902, 449222965, 764440433, 712820280, 308683313, 530594120, 762690091, 765921735, 417113171, 28657474, 771790122, 710730219, 716324025, 788337348, 800552416, 277705688, 675792678, 520222859, 19101338, 115476223, 574633083, 413051437, 619524949, 378328913, 505468651, 786725263, 709756403, 321326995, 310941073, 621895323, 621230616, 645842220, 12042243, 470841862, 488443792, 358687185, 646523599, 432254545, 772964663, 726214518, 395501656, 460770024, 482294903, 401612651, 941205432, 56311955, 170972877, 95942260, 762227625, 139512858, 42862214, 676597626, 399276082, 629808305, 265909890, 289731895, 478466102, 522204670, 697572365, 799059260, 991358480, 254968398, 792878964, 548993540, 356779601, 633899380, 440095962, 816989624, 451952360, 896608073, 782136977, 481902314, 131662046, 648075590, 843461974, 600545643, 384565027, 940618194, 340121157, 132455962, 282109091, 401143692, 173730048, 43386970, 915624202, 449233431, 290531651, 164608350, 288911136, 306149316, 397014374, 341870390, 374222400, 653219180, 650258368, 985113901, 29587607, 378210148, 382362307, 462951324, 632160640, 323798219, 59930075, 665862878, 131615396, 805553808, 123685153, 546460986, 535762293, 547351310, 464311112, 634134582, 942546823, 680826928, 688756691, 323417483, 430368764, 966171665, 900326677, 297695148, 592525187, 233277586, 283751243, 326987011, 727699483, 620667137, 24576546, 551583990, 874888429, 414096503, 239700718, 268682217, 695415821, 539902199, 759940925, 552778296, 133226163, 711262134, 888809295, 879849362, 469534637, 870673379, 390399328, 635493568, 111265962, 963789334, 986027263, 56643179, 370605889, 66783933, 494742526, 989615807, 840579315, 413811219, 184203386, 838344520, 832011031, 497062359, 98591176, 308978043, 577580567, 160029493, 665381845, 826199376, 561995896, 356634123, 790660380, 93745487, 656605956, 464783673, 30450065, 420742524, 958001553, 5066574, 466794373, 334290425, 884049434, 532640488, 930303573, 95485959, 452405146, 680352248, 882338363, 851608258, 962028073, 91511461, 26848662, 529411339, 631241906, 803963521, 725450791, 571362014, 337521211, 643825877, 299214342, 549112875, 272056497, 292506176, 258851704, 915108080, 205002673, 37469240, 307954400, 162981946, 19237505, 130781279, 295820354, 167495545, 813258373, 938910888, 859610879, 20842671, 939634900, 121819605, 873045113, 88077986, 697976440, 686493734, 143527769, 974984554, 503739341, 843827083, 892207544, 663354004, 271984781, 504866821, 977702108, 937851518, 283546791, 322114948, 70832123, 127091208, 510663017, 289142859, 959486148, 552138056, 307445015, 726230854, 436760654, 358753429, 133970647, 422607847, 998997500, 846388725, 143892011, 733904539, 620447460, 62229636, 604687395, 697609618, 68176943, 810921443, 341008612, 865563678, 580718837, 405600568, 573155666, 117804850, 957052050, 283958261, 170023882, 768716815, 492256949, 671047038, 7037610, 81522487, 382768011, 667590847, 328951339, 18108822, 904821365, 26946969, 614947723, 341847785, 965917237, 969793156, 602466359, 352581442, 493181037, 567733381, 363667521, 737022209, 32522294, 51065796, 840474078, 454421787, 422273149, 520635536, 57349295, 630738832, 139695705, 591664026, 381004410, 194387693, 934143076, 814209073, 944644236, 89899746, 548184505, 470600647, 176914388, 13202620, 318156580, 457067238, 708692155, 353869759, 550637306, 607004220, 25466895, 979246133, 126018376, 752791373, 877391112, 176801976, 613360760, 692924574, 229677017, 298432239, 393536252, 770960240, 280620434, 300024702, 179602568, 316994063, 446887606, 777808638, 549669447, 611901941, 598935025, 892727733, 55189679, 965052188, 847264126, 321059344, 920165790, 172392689, 861613910, 468551360, 105538994, 735864845, 806799887, 272438802, 274905712, 979443091, 45196455, 43620675, 167615190, 729688143, 676398661, 219210922, 539776453, 907760758, 970531033, 794966680, 872331510, 458741028, 270163883, 933396280, 21038276, 207417919, 599326826, 96220945, 913681184, 788967346, 996348225, 418987639, 838566818, 518070026, 59903215, 981014708, 609860417, 274408060, 396225486, 693228197, 595626986, 204693377, 956645615, 338740107, 60906927, 904343169, 75636732, 478556284, 579754269, 21910851, 238722453, 420951830, 531920503, 383986213, 520548427, 256757951, 124066665, 93461619, 2077471, 403361689, 263728569, 396418090, 365963283, 388231696, 147555407, 476723696, 660297848, 329265544, 797609924, 125905467, 770051127, 59682270, 321822848, 828470157, 916552944, 981426371, 503182462, 455726695, 662124546, 938681627, 419822102, 320226586, 278407800, 319219811, 443769549, 500607983, 883242140, 55348389, 794943858, 331574166, 80245592, 922781789, 209669301, 76199789, 374766480, 158534931, 424243523, 291928807, 457646388, 465821111, 958614286, 837656168, 454092804, 936673035, 380006796, 800441899, 250424783, 515974584, 489699893, 852629576, 604531406, 735370858, 976217974, 458401711, 969732960, 420923194, 406725141, 146051040, 105148925, 516786300, 474023258, 81744693, 275892953, 304688504, 321007350, 162972813, 454460104, 810250044, 207187824, 197563107, 526130816, 761671795, 512030194, 193501971, 149760218, 960173034, 808022810, 745491715, 425530249, 446238038, 562646828, 594030391, 341305742, 738164146, 221953282, 149764579, 640162616, 380067085, 110487770, 364161281, 285118635, 914460090, 238821985, 406473184, 655866498, 924441417, 392848593, 874884845, 249319609, 164835701, 646521440, 967148280, 663937897, 493286202, 992799841, 469168988, 303768833, 828335552, 338290811, 814590628, 666655474, 539781291, 818671891, 327273687, 512171554, 812221636, 89715562, 704234186, 702824149, 313368568, 174895299, 459333224, 574382525, 218996366, 471967931, 37355429, 350687392, 275785144, 489194688, 176254151, 117425351, 442976155, 570636686, 422603672, 756332842, 366800796, 720148055, 188035949, 616049030, 82346053, 799707975, 588691934, 148741776, 132012691, 760304543, 910455751, 896791542, 272164613, 637096497, 693794431, 855435616, 199081630, 442512721, 996731748, 625027741, 70201623, 777520694, 261167516, 69993196, 413088058, 211153187, 966625242, 911079091, 61772631, 942012637, 670449573, 258117252, 379571741, 658373481, 704859575, 534607666, 647079088, 804739664, 103082964, 555109767, 359531571, 771451622, 515015872, 573851672, 999059756, 67279214, 840749794, 358645896, 949476093, 194086593, 446166006, 621237569, 789931885, 186999590, 717206998, 150946432, 45341937, 827381217, 595253894, 246563769, 215325708, 49630993, 130300765, 176543430, 55713747, 983896306, 407115720, 181204509, 732727194, 679633794, 734771012, 868078040, 354564356, 721095009, 794042428, 405820909, 341619155, 231134934, 795032268, 547702012, 386321351, 186008722, 316177138, 686831179, 441491496, 391411187, 696237308, 718510918, 32851549, 253702508, 277336195, 993069436, 93588495, 118973092, 734735787, 63379536, 787685202, 314134397, 299946236, 410558146, 382377017, 907669839, 4068775, 917289804, 224071405, 428152196, 286969670, 515048121, 492159903, 511290562, 278961288, 880054445, 831317239, 940331249, 385114363, 146083032, 340774736, 18544656, 111024787, 272178417, 849199812, 452132842, 496506274, 100970238, 477082340, 639863760, 377886134, 503387824, 669964179, 530342106, 249623415, 781517846, 108091132, 325254883, 851920935, 671379292, 332815304, 608829034, 831494306, 73322231, 244068394, 705025045, 596553667, 861735176, 978269278, 521172544, 785135806, 43876492, 824550781, 594961532, 883502739, 909117020, 601358578, 198037636, 869092343, 107979509, 753709083, 818672202, 887234380, 141881904, 80774801, 818445643, 173779165, 503200000, 701596790, 857795353, 241634972, 187310145, 799968850, 958241101, 863466828, 506703572, 778660690, 136355920, 634188820, 868371483, 256702527, 529908493, 239499193, 901921589, 722604454, 103491651, 21959183, 823982275, 521410600, 570335356, 283901869, 68028593, 312038477, 9636032, 563303200, 160826339, 698697404, 60384525, 239794542, 694360541, 38123004, 591904572, 205038578, 636347009, 536871551, 279802577, 935130183, 92011676, 855330343, 38070037, 867080438, 311630004, 462829192, 864030532, 2031480, 249465063, 788256180, 982279957, 483122707, 782928298, 596768985, 525268382, 875173742, 434816551, 987374634, 367638315, 963534789, 302031868, 399790672, 460905248, 186507161, 389349470, 99622518, 814344562, 351759144, 731126077, 621583958, 251344005, 899499703, 121214452, 207709177, 456566818, 304961539, 865736049, 273981035, 203257476, 761473298, 746825427, 487010960, 863750888, 77708677, 18797616, 746082554, 543614103, 60791106, 904717111, 673900183, 480077192, 140634465, 162245764, 422737487, 892887811, 812643216, 329725747, 985959404, 564524347, 273585890, 33748269, 95723001, 564240115, 932567744, 320183015, 953187309, 877949666, 148959155, 729219902, 441906790, 404996254, 455176671, 727777919, 246597346, 701322262, 452657245, 353871491, 49650551, 13290531, 510246283, 284504615, 973499235, 547076630, 354279041, 858549411, 148291107, 75448038, 3714252, 445462049, 277831922, 379826809, 964087014, 506342279, 306644483, 790067319, 506203203, 780877102, 359328450, 381334446, 94027836, 616704239, 898163616, 712360543, 912045942, 152845202, 821905938, 704925378, 674755564, 1912123, 706892973, 426019148, 800498727, 796157223, 196639938, 77493597, 708486906, 140700465, 834922833, 258288024, 672069010, 439249249, 622953139, 757037634, 378667398, 837978446, 503328271, 60117306, 826268451, 217922656, 1167241, 858709853, 834462474, 930430791, 987946223, 539831445, 709300168, 396376154, 873706965, 171835183, 769784355, 682779692, 787105458, 358668849, 622391437, 682083095, 152543235, 658063092, 960371469, 786475797, 679026011, 75143712, 755987025, 70645268, 453395683, 211752856, 175883161, 321329054, 713292016, 596411351, 164743070, 345440332, 620846154, 956978509, 821724284, 791427977, 174787211, 748766253, 667067738, 613104463, 442627046, 313116099, 969218269, 305325948, 188622344, 72675863, 811428819, 944406265, 34844779, 904588164, 511247173, 391665744, 304161057, 258218462, 494235262, 937705055, 234270790, 100009622, 513055261, 665673529, 361572033, 26323754, 546823550, 697951549, 48533195, 160916410, 156130833, 912538829, 733963007, 534123568, 856642689, 441639916, 506606064, 872022728, 235205416, 52612288, 579678001, 384089714, 358010354, 752398556, 612087609, 904031466, 640716094, 795822362, 363527425, 76353174, 699252062, 907004634, 809750934, 166089748, 861840194, 719465934, 416062009, 544544785, 72112566, 314471950, 889845441, 730054736, 878038632, 974142038, 516842567, 740905556, 274842010, 755941223, 81711499, 386117995, 166514748, 121498832, 965639164, 533259987, 876525631, 533368258, 959801474, 364558976, 803144808, 661669693, 358136176, 809915641, 7805900, 173708053, 872128942, 432502200, 451768679, 479369443, 131130648, 232762235, 530140803, 335029945, 211748079, 204435083, 678474078, 642632168, 461037944, 642932677, 906730420, 520108262, 640349579, 923198814, 572796081, 626457163, 105573278, 413278503, 763991904, 551271705, 250733420, 491464178, 434600715, 503710868, 530541083, 445802035, 829253665, 6697631, 123697930, 401644458, 295323871, 448462139, 516841863, 132881364, 986817394, 129782443, 642184512, 709668083, 605689586, 571992304, 969501554, 78396395, 292328559, 640235053, 984296826, 511685478, 633871284, 44482619, 919686221, 487176028, 722603268, 632140546, 52247053, 544341528, 487644427, 367842787, 463922372, 480104163, 427543686, 635180691, 773466080, 873034167, 73332972, 944704559, 447020080, 24205260, 851725038, 418330208, 596002648, 843329795, 190991872, 479705907, 486340812, 279899230, 436917941, 90645798, 199067624, 489966543, 875175199, 459071647, 623005735, 105266204, 657052233, 973718944, 583138098, 308312065, 631115848, 851469780, 136664422, 971272127, 422335512, 714787819, 77710874, 324540949, 974026443, 299972970, 642151850, 756049538, 204493423, 575055484, 191861888, 329092854, 49673860, 576611981, 474562800, 193976402, 454543341, 86172305, 178084658, 248754004, 226245882, 969960550, 870385476, 942682956, 587351636, 9213622, 471800105, 71527620, 535599317, 388384228, 523342480, 11029451, 164995209, 701041169, 878966574, 613284628, 140572358, 556827188, 234633761, 621480175, 696315631, 642905201, 686052188, 997542404, 477634659, 775170402, 769417795, 121623540, 984533954, 909432703, 62952571, 202232970, 434379071, 377511225, 441228192, 896733101, 389309971, 219721187, 833498718, 546738472, 722200655, 500878869, 872513390, 863957062, 552470138, 50154606, 878006761, 21426953, 466177901, 182515221, 734652813, 224969834, 892408388, 625652223, 731470862, 204780013, 921654404, 544022066, 559152087, 785375746, 515279195, 592377129, 543155790, 617061539, 301873010, 533357193, 498774404, 798673812, 920329664, 542055992, 185324053, 397085491, 947402319, 664620792, 288328673, 545108432, 176793274, 676306204, 545011161, 6244899, 68593778, 51536804, 572526118, 981860509, 20948430, 908704682, 696576913, 958051428, 424303348, 327876939, 372987861, 919513860, 267357957, 193077076, 49543054, 323281840, 445583903, 244876839, 287094760, 638393395, 941755598, 743832611, 461476856, 830685995, 351675570, 193604238, 310114842, 667126317, 91354329, 121185775, 559698441, 619093018, 2760423, 623499997, 934586703, 798518497, 817401859, 386004017, 46405852, 428072597, 99921003, 88426343, 952403222, 541801469, 747926058, 338185892, 305353107, 610991679, 50545766, 773370035, 511542170, 259601543, 973835687, 678476124, 395814187, 144939659, 331167672, 363376650, 518141917, 476833352, 64055072, 290099821, 256826906, 74279031, 178023485, 842814605, 769474672, 60285517, 594727669, 711140474, 971902956, 635819439, 275819585, 557856110, 561071097, 673388705, 375846992, 631631174, 752011259, 381008463, 415423490, 402211702, 611877408, 787061461, 930862077, 904716263, 479910347, 615443106, 661847086, 21258081, 379170980, 810197696, 953120583, 998670497, 435453059, 523290526, 948773787, 483315387, 544885551, 580560417, 696619559, 588021771, 294350698, 999396857, 10314674, 839729817, 367752394, 646337948, 215194833, 349479463, 109065328, 790902589, 194108706, 791072713, 406673403, 14700335, 315997996, 646316681, 591253980, 829615992, 730598653, 352006534, 590184972, 468793448, 363649000, 797163073, 94236777, 387604177, 693097722, 411646602, 597427991, 295092711, 771405730, 405900071, 343635381, 814062215, 818011055, 916027072, 717420854, 594922886, 81413458, 683828747, 43014823, 25548432, 282136107, 701296436, 361833256, 505840731, 953439814, 915508386, 14324568, 555195477, 67415115, 811310727, 316206652, 809867955, 326805707, 831306732, 121577373, 363995019, 596710541, 840383425, 318101884, 19807496, 43632145, 779935421, 485079257, 125951824, 117569620, 636877055, 238670297, 292037696, 777276177, 477813665, 577276847, 458012323, 162436820, 649215751, 735244061, 786206294, 361224032, 367831509, 240259472, 689668860, 276630449, 517316803, 67897630, 777976673, 755218340, 48113229, 788241387, 334394453, 190793524, 14783472, 84961013, 960488704, 369506132, 352401963, 388315224, 163483319, 877917891, 153035398, 45289032, 186072565, 457420974, 828473050, 17779292, 263164993, 783015670, 27985221, 136592420, 862152917, 580708018, 535126971, 486864364, 943734939, 843779833, 17990853, 566537137, 859969907, 934195574, 206710768, 812997784, 44993076, 394542348, 427901643, 629355902, 349098129, 526833314, 1371962, 520203580, 643515057, 20489563, 482625921, 950790440, 781490638, 754543890, 95038737, 577805291, 915861961, 685921442, 939158518, 444806204, 679226159, 733782406, 206609950, 892298629, 831382033, 445688021, 399943457, 145377803, 971732616, 209264648, 596298205, 184601216, 568259821, 165960128, 914493442, 144372062, 917335626, 670219593, 434007154, 930325249, 706531451, 893167050, 290588405, 467888706, 824240672, 346675873, 31573065, 288200855, 104120717, 219850851, 765485075, 207921152, 327319107, 781977225, 278459163, 585409807, 632890500, 768522072, 729862284, 778729878, 41987748, 666142333, 66604899, 10072284, 484002074, 684090423, 796467066, 991007187, 768224816, 922214160, 300103570, 792817421, 534968642, 483185580, 445561941, 591016632, 915305977, 647991372, 258254867, 404373757, 347331094, 333225793, 716852582, 474031264, 318337416, 771389052, 873757014, 711865861, 57604619, 135148358, 771144064, 262424664, 613076790, 67697442, 630388525, 552479623, 77264008, 191423057, 402764854, 525063868, 542557057, 844350630, 478261647, 447905211, 549833431, 952466742, 441236953, 692462827, 789130022, 321084766, 416194919, 460084569, 713946309, 17214264, 356414415, 52358882, 933434406, 933525798, 499872349, 634494060, 627340585, 738324608, 725220816, 455747134, 428821863, 421586069, 735432533, 925266874, 884586904, 512164418, 937087124, 19672522, 75657819, 212953591, 101714357, 914069683, 513183597, 345170035, 735120560, 655807122, 718929141, 855586350, 606741644, 973888756, 25880203, 127259597, 462797431, 355111029, 911758296, 908510409, 989414571, 341480865, 554310244, 298901539, 969420535, 707063751, 831115454, 986715233, 742853620, 446668836, 6735176, 430807403, 309701380, 555723761, 824473396, 528610662, 848644223, 890990179, 68844567, 762988727, 416990675, 775502813, 214055791, 106049075, 723566367, 382549923, 224042942, 795626520, 168814105, 375324907, 765653454, 597302838, 851461829, 147982554, 817915394, 670388519, 97641071, 173923127, 994833882, 140311825, 521561148, 485169470, 56979435, 317037941, 760966471, 32637660, 64557727, 480831442, 178525550, 775939214, 287545435, 50260053, 384801470, 865035171, 232858115, 567617341, 756907194, 574475848, 83581047, 332044164, 120975071, 857538410, 893064690, 355383553, 169577325, 293712211, 711503844, 947948450, 333771027, 448271425, 532567101, 120621051, 284811001, 765060601, 216568205, 177693083, 803414212, 69052602, 632983847, 930918077, 208531481, 919505815, 962910810, 321341476, 969661764, 518754443, 753859476, 597641111, 587964969, 195360556, 691438793, 474918657, 289536132, 280937392, 654544893, 242187956, 680087225, 66241315, 935471324, 337557653, 775573724, 294783971, 8065320, 412128399, 368333746, 927379733, 834977966, 769755422, 840228289, 442284814, 496657769, 143728120, 560571501, 505642215, 40039811, 840443686, 814920206, 108272533, 545505544, 514523829, 827869817, 2441896, 654928768, 343621618, 583177521, 28667891, 812839186, 314466186, 198017458, 322557524, 204083361, 280894502, 919973847, 404154866, 985207545, 812743451, 503353533, 639975055, 449421214, 396390867, 560429791, 428162692, 882808281, 772189854, 779466004, 132425414, 279252789, 101776047, 997775306, 75626453, 834304992, 57478785, 400296791, 888870667, 324876814, 323548005, 15118500, 523705039, 102894672, 293271106, 351942509, 285229991, 743076323, 728611339, 177633988, 207379125, 211155318, 596395294, 330635692, 859050995, 370212493, 606116405, 468180948, 848909443, 877900943, 394573666, 807756930, 760299833, 728099102, 283496623, 540899260, 570933634, 47905545, 946700045, 190423395, 272990692, 212020409, 127257208, 521338802, 378572869, 612412603, 309684398, 949819973, 28351414, 366115473, 66783981, 251332428, 423387050, 491267932, 215162664, 440646022, 73700711, 859707243, 944103710, 363185331, 920288938, 200598740, 569785452, 484623067, 512284489, 939441074, 347005916, 316403992, 174018292, 209475290, 797260944, 152205300, 507508555, 450693898, 507206062, 697366663, 874455400, 527897190, 781661244, 997179766, 807547477, 152855430, 682013714, 23877192, 721676360, 304911417, 338907720, 642906752, 433635207, 925232818, 304902205, 385035337, 149989101, 800673989, 666106307, 443412220, 321715997, 480618341, 127300837, 422258606, 105830976, 616460513, 217596986, 993985795, 787114800, 630331547, 295502996, 741173459, 901186440, 214647289, 370431005, 974876500, 336392099, 217187666, 909281484, 940867194, 971550172, 721523195, 649465855, 973129428, 548407475, 917522633, 919803297, 442829498, 17117185, 562862061, 711630385, 223388895, 902302938, 902825950, 112809835, 776695649, 519183600, 677618459, 842172629, 17007959, 430391477, 471216066, 484726222, 782975094, 376933492, 951623573, 645252542, 31890893, 239507426, 492638308, 591339859, 797975494, 275221423, 411923998, 521298363, 548454533, 636352029, 7407149, 325657114, 17764532, 662158314, 983899258, 62204899, 257827720, 513542996, 461639494, 893148503, 278178466, 325657556, 30680110, 42330126, 3137846, 229355035, 625300960, 143405126, 990999118, 681540797, 482815508, 580828215, 259409717, 270545606, 331436884, 172994971, 18794637, 613674155, 588176421, 189292824, 96324596, 146665692, 899767655, 263348512, 228024674, 503706243, 215699355, 778489491, 173880146, 860237933, 533637207, 407837395, 891977777, 148339793, 39023837, 897801408, 854280827, 879972356, 235405738, 457044945, 265134991, 76893415, 775500283, 105263681, 484250092, 918836350, 739003373, 144782385, 925321221, 776653665, 520994929, 901516302, 996486476, 780076420, 647737189, 884375586, 551832245, 625893209, 843294161, 968555190, 591913123, 577477507, 345714475, 216052753, 812162831, 303903334, 659361814, 749423526, 780095367, 864141506, 946007090, 35482584, 278033273, 27716594, 226440075, 553518442, 212466037, 470158131, 8251636, 104401475, 906492151, 941749716, 967765245, 467895849, 152857011, 126603748, 3278740, 378313325, 191982188, 310383143, 701833350, 681480423, 483109071, 103598102, 712948811, 90922847, 563260129, 262860854, 909394003, 166288486, 38691469, 190307756, 13203742, 772669437, 409976920, 38570600, 315725952, 5567783, 99837513, 429064162, 608597176, 782086760, 967542179, 457868402, 657381540, 484359959, 273467215, 814629525, 771053655, 484396846, 549727464, 773068760, 523072490, 300779742, 44937467, 609627092, 287416062, 770020896, 632492958, 375137547, 44864216, 832781348, 120114558, 327048369, 634459417, 489591103, 341860905, 598093130, 701370662, 788093473, 435778803, 697440796, 88549602, 785122924, 742946850, 723922768, 419036125, 649598866, 844813283, 900009949, 203988276, 371191510, 612833082, 772319562, 620020512, 338169579, 544060422, 16266423, 592091759, 1025175, 199433419, 383479529, 504586886, 195293709, 266672934, 140166996, 198792875, 58438932, 67514518, 294151583, 297088239, 768867012, 809347034, 784160001, 97615493, 357524073, 117498359, 118414851, 213438665, 244319264, 319453548, 307364692, 732237589, 309265821, 660277744, 45338051, 180179910, 367875312, 333703609, 827947986, 152311939, 899413517, 702447384, 550499560, 363251679, 513792449, 157443546, 604480277, 85750987, 794428288, 356127000, 659385501, 672317385, 747587806, 519982134, 257928658, 363720532, 95724194, 199574939, 344545324, 485768648, 210723051, 909735716, 765078136, 82613088, 545323255, 516319127, 954343044, 580658840, 92928570, 648073011, 509938883, 940400257, 23128244, 909000930, 392555062, 801049554, 85909880, 797674267, 302379338, 705691033, 488986141, 239093260, 102557482, 356699949, 278917153, 329516446, 274239437, 233382875, 123574374, 508426029, 182949729, 179729698, 553734942, 741801734, 561952462, 47391152, 19863986, 97306960, 733783954, 959782724, 703407976, 716303114, 316418219, 620163017, 57037848, 486822419, 257673221, 915981752, 658415727, 203130506, 134314615, 800229624, 714260474, 400933635, 839953715, 682302196, 927782539, 897153614, 992317192, 890106386, 334136281, 880480441, 629964799, 893583473, 825641591, 33084216, 264643283, 257479805, 375813094, 823274964, 849796443, 953699688, 370699454, 627543223, 561818772, 743934926, 591918331, 879607652, 397307123, 450238291, 419068976, 539012139, 771073153, 579756364, 398319242, 628223095, 969464342, 890486122, 281882583, 628610058, 807788677, 117302902, 138934073, 552017770, 36487019, 453025991, 196234890, 946660148, 818512605, 906665527, 452294978, 649579018, 217853998, 658637832, 611654580, 811742356, 641463870, 310118861, 206380599, 154671437, 744995622, 522148225, 256580545, 949998179, 322034949, 543721994, 896334555, 758361328, 770052268, 143460361, 50071657, 851247045, 61609561, 886712037, 666666727, 824975136, 253061983, 532149434, 754071213, 61941055, 737331302, 910706031, 281516688, 794176726, 945438182, 554254074, 406048857, 963618539, 371609476, 213798983, 83712611, 186792523, 696939605, 30888672, 966094694, 590381463, 129034753, 399946960, 160250204, 690834700, 903153771, 751097029, 71044949, 314951143, 228423877, 78993464, 29203494, 306777683, 619318660, 958310676, 887961896, 265479404, 305124458, 668995421, 543145125, 622964125, 804004891, 619995093, 172405371, 334206079, 824476711, 722853462, 935876301, 724470980, 816569431, 767596340, 671130622, 502200340, 600383110, 59241655, 532115235, 696180192, 855163213, 18515251, 220608527, 183422539, 349997421, 18156135, 780043290, 905065325, 605728590, 35137863, 10653427, 870447187, 12646052, 766705755, 728775653, 888896621, 91745587, 296206341, 410675576, 251028693, 215077340, 48408999, 279121072, 125868576, 681096562, 511588301, 432664707, 803445596, 594289845, 688320863, 393865966, 174880215, 840879551, 644954703, 513082804, 597208735, 84136547, 486091013, 290448377, 207966875, 239898245, 454442223, 860071203, 526811529, 908949998, 815255630, 668564275, 566636087, 691101607, 424084675, 669101675, 777503855, 59108927, 43014561, 182020868, 541306873, 680681859, 894394278, 323132606, 615527423, 287224932, 80322721, 154990319, 660726689, 341439205, 683799921, 578068809, 396850320, 812036742, 913738031, 576672523, 302709455, 913460855, 72258922, 779620609, 584739665, 773291183, 739046691, 431266873, 558195594, 456289500, 298737995, 265531664, 604881129, 110588404, 182476258, 37952813, 123733035, 747630729, 668941955, 400125357, 114774978, 729727825, 170802297, 277135312, 7900997, 962236454, 218716661, 915751880, 672516493, 681316106, 141797240, 184759999, 480499181, 856054942, 460099146, 993012267, 135805789, 279332667, 147192654, 151743041, 640047134, 701745686, 914155071, 93410265, 285626962, 953742805, 500742447, 865714980, 430793794, 66494081, 13225744, 697366075, 834903759, 741934048, 271641932, 70967851, 951272120, 681827096, 888442794, 299409406, 932730950, 310320640, 458544522, 792557712, 897885559, 727042110, 691917942, 607310210, 609181843, 422926550, 112491675, 129215895, 470688900, 739552025, 644524817, 718600214, 414202350, 528169542, 713266662, 333822966, 8313102, 857948229, 893329819, 260248145, 19453001, 382979850, 143441466, 672703823, 802222576, 73881846, 72823741, 316930079, 15079771, 784397128, 55539999, 177043390, 566233721, 736855206, 41324810, 409078018, 673274831, 181565532, 349169716, 406876746, 344235628, 307807966, 501969119, 831800056, 439836590, 772695645, 264222198, 926893387, 781978491, 97171708, 615394385, 635202743, 595164994, 943474068, 706237509, 701452471, 931951660, 130830996, 594428363, 103903763, 535510083, 432502978, 92698085, 598225646, 826330408, 811947439, 327199743, 765427150, 540118361, 409604442, 509559312, 649987285, 147102835, 769136235, 970970520, 220334052, 992858439, 550331126, 345134368, 689307995, 169675560, 612734079, 452259244, 81107559, 633192037, 630071262, 234112943, 520951691, 171774268, 86921864, 745438065, 678098619, 579520204, 652993409, 10810262, 262406589, 641724637, 105474379, 465213442, 909713039, 453510871, 24293876, 793583278, 722431057, 421398324, 570455366, 167517850, 164000648, 504631849, 831663621, 444090821, 589221061, 464157966, 448078714, 103034698, 743401970, 795356892, 566803340, 673772485, 54476883, 249025921, 468364279, 906106404, 809961806, 24805522, 958679406, 869329093, 980641732, 88651849, 856482055, 183284720, 249783177, 214709044, 333126796, 499694256, 330284780, 805450373, 592813741, 689241086, 5532583, 996291179, 89972801, 86090703, 372019639, 922975371, 418477210, 766793516, 111797484, 520750989, 231458291, 251788946, 657285751, 600424228, 382344803, 332311427, 552968012, 796829524, 245146552, 980528220, 556421809, 874861590, 68307169, 44236136, 637100210, 544490394, 823069629, 339929836, 977238599, 184647842, 173065800, 800494910, 514245492, 821909643, 259667622, 406233696, 858905107, 101987015, 261045555, 340910010, 372570607, 925918861, 959313876, 396174984, 620329578, 331023946, 117551153, 868703892, 333645074, 850860628, 33552615, 233441364, 46015346, 868326351, 270368623, 183976174, 338732774, 572726764, 789992269, 895093501, 870213910, 252776941, 361372228, 680352246, 256114355, 299425952, 896039406, 833828456, 147152639, 82533441, 380125505, 763755139, 712690708, 865834725, 237187282, 332266954, 813920126, 438266677, 858397088, 44362541, 231399850, 817925402, 863463333, 374478849, 407385598, 901305383, 711112167, 990398067, 684187527, 397918017, 178119547, 674380325, 546829908, 898156893, 648929545, 925894958, 474594270, 242082597, 602103594, 670873268, 857192878, 771501019, 200182144, 640668621, 990344856, 853983771, 782491231, 93239133, 462291482, 265228543, 273321469, 617908953, 573696573, 718087201, 196162311, 553598980, 90191096, 582963321, 630493578, 766323405, 787758612, 897881768, 696508717, 599740978, 348374745, 281374585, 392314678, 995002931, 792968740, 572273241, 596579610, 177655664, 424706575, 155937702, 20449492, 617436514, 481923031, 279517592, 294853656, 116962471, 276412754, 970621326, 677359760, 835957314, 812020904, 203059433, 307448842, 969016064, 777333419, 177661320, 216827043, 885439178, 350697932, 664172170, 190938103, 53028187, 968595375, 571692323, 692495147, 551678598, 336425978, 415520038, 958360104, 709312087, 782155944, 742966876, 302264515, 336784132, 720388834, 235097695, 225805740, 337334057, 770092337, 393183628, 209380170, 227788484, 735912113, 637373153, 629945416, 798411682, 898075137, 76903557, 780656464, 648310721, 397832646, 87807165, 711947521, 988513320, 762966579, 548733821, 278179159, 46965314, 633687703, 997362929, 960408512, 882577795, 880841391, 279664912, 326390113, 743153531, 385293286, 61293601, 107850032, 432519106, 655464953, 572885386, 921564602, 666679172, 533433272, 503096669, 161886235, 204346875, 50346607, 688272252, 659552454, 830018578, 426657936, 331913173, 250152044, 438596841, 207687791, 35309318, 153336049, 370965602, 359415956, 61395443, 635925433, 445691691, 764265441, 846175918, 736363710, 389720865, 797151107, 324876648, 11584001, 82572586, 233942374, 39299065, 846954196, 374907553, 506551492, 961492245, 711601930, 262762289, 940503780, 320785591, 647612132, 50720267, 552107857, 699772988, 67741057, 873405287, 288978634, 862980183, 738569512, 23592868, 614004674, 215527839, 473537508, 217026406, 613031935, 635988087, 608744935, 55981542, 278767474, 436251533, 734928518, 424340788, 546157049, 596965756, 931339782, 359475005, 431284453, 92057662, 83254349, 557792268, 555344673, 678496308, 423922253, 641914617, 887563407, 191273157, 343981319, 735544289, 489666897, 327974487, 682326381, 832264300, 95114022, 233542303, 931192206, 582186658, 542366922, 827121581, 294836761, 767928698, 125635237, 449382065, 783012181, 533399248, 736192578, 452312486, 643648291, 469034827, 6204926, 754257081, 869244517, 367407644, 657601245, 537396099, 565375586, 677270381, 712065339, 211680190, 403286844, 141402610, 209607012, 299815018, 17228696, 307908329, 978265360, 476288944, 353400249, 243818803, 794332905, 866412578, 580043944, 744794364, 345478196, 706871081, 781049708, 368262270, 5231706, 511813186, 404471494, 703436199, 522868382, 857149446, 597128818, 755689692, 152846262, 415311908, 326838723, 846308891, 512532192, 967901947, 297820237, 247524090, 787121497, 756418262, 549437181, 467222565, 66029545, 179822211, 232140203, 448364917, 126983258, 253704282, 946102930, 887203620, 54732275, 168264917, 325840214, 895440810, 275347949, 824024386, 289592370, 602890503, 710589612, 604276664, 100719403, 436385434, 669008948, 348847752, 791238325, 949005477, 394242895, 949348793, 691465108, 843682099, 981564174, 722655015, 177881338, 452971593, 436225945, 179981671, 470970595, 160499069, 534474977, 195779269, 856317214, 45512742, 793990805, 523988651, 346634950, 746159064, 39685873, 262465044, 150531394, 126854, 186893167, 139852826, 675061566, 701937155, 636393247, 966116173, 872614376, 116686052, 586443298, 592593499, 25899325, 434840546, 890515910, 173323433, 445662697, 439074530, 863222244, 840794720, 657147441, 167781920, 898650871, 638983906, 333627167, 189418421, 647387401, 319461659, 201930557, 748937497, 213170241, 623759838, 681768315, 859715318, 234524985, 899475709, 819458753, 391246263, 43585670, 56580453, 979462645, 521108289, 396309723, 918937602, 707998929, 773906437, 802221709, 568579366, 598197898, 869357968, 379934272, 755926019, 723097128, 208754005, 997545849, 114648230, 36296582, 361894229, 320410478, 394050838, 421630402, 536589743, 189022211, 915393826, 87084765, 957883529, 670702169, 985125754, 899722147, 380400264, 728575324, 620968665, 330647830, 278751019, 249947021, 7360780, 597484258, 120908304, 74990485, 129389943, 382572677, 203399844, 506285710, 729207013, 753569951, 306711581, 987268946, 39343654, 726190948, 111351091, 924269849, 179163326, 842172983, 67679321, 239584418, 133933449, 579788457, 167158467, 27968337, 399186949, 872031325, 753335193, 749495877, 381261761, 401011365, 464126386, 72457786, 10993310, 573663498, 865338788, 87016459, 589729420, 954597557, 388090973, 593265638, 580545314, 89553574, 77283084, 8093222, 354201119, 938294004, 828323546, 324760215, 742935641, 326727956, 295475873, 649108281, 295622208, 327927634, 940518039, 616238708, 375179917, 750723048, 849346305, 309936393, 854299193, 17577868, 54669318, 861377827, 599534642, 881965595, 569679876, 909229443, 9852285, 895581181, 655469763, 83239350, 96862980, 390125277, 361038908, 54127803, 128972066, 380114324, 663874180, 478999394, 106718060, 109053646, 990166455, 227218885, 544050174, 438389702, 927943481, 630293097, 455219888, 636425912, 890707506, 199137241, 832511739, 134203080, 890865964, 31848860, 679903522, 138765091, 205472408, 106859535, 103519329, 67620415, 806616492, 533361425, 746816059, 12794213, 824948540, 315133282, 114375704, 228479189, 913021788, 614053333, 722820424, 237648039, 223610489, 809214945, 508821219, 544774050, 364893091, 391563224, 769093088, 39996233, 821486731, 290256661, 210843811, 83118414, 890639898, 850623759, 567026127, 92862841, 862585118, 325549171, 652011435, 829214386, 9197913, 92097637, 599938675, 860161725, 789790810, 114930349, 319132057, 417850815, 628402589, 136360209, 762692456, 342393096, 526087009, 393629444, 629868628, 686858562, 104658300, 527515158, 74651188, 745327960, 909854546, 494982534, 331349128, 981956439, 37011301, 328374715, 985013826, 380624156, 597149871, 250802984, 531482049, 686924493, 289558185, 186502997, 942527315, 817604640, 398077232, 824851797, 682782580, 124626759, 941294909, 784212013, 774563923, 736174786, 666745836, 655052853, 562747268, 149447716, 16503869, 607712208, 931872885, 447372646, 651930387, 906155795, 23679707, 11996242, 586370839, 951332479, 817558876, 403611649, 376177512, 697556626, 773070913, 846687651, 192838283, 279950315, 664201597, 428582870, 880168416, 154480026, 161261533, 194293863, 43951905, 906131239, 624501380, 128565738, 992846738, 581110517, 115117308, 693620009, 398906485, 202794562, 838881166, 131643464, 964997889, 642828625, 175208101, 13245987, 418453758, 811943079, 829497331, 400578160, 864159731, 475596762, 784856925, 480758466, 903984087, 988877441, 404145605, 106124254, 729207058, 643822793, 565500912, 801197902, 964978921, 270914836, 709795277, 30128267, 350699448, 904395004, 755426811, 445206657, 52225560, 566942786, 16054723, 881964798, 438290032, 147106121, 161503322, 901005583, 163243444, 691589064, 380213619, 493814330, 72493195, 374585490, 945781817, 79201153, 355912771, 374996587, 232489441, 247269738, 492227623, 411752993, 996145130, 403766735, 196647917, 367538234, 323282302, 217016475, 131416656, 455163501, 493312558, 541876024, 191070772, 809596869, 975891460, 497980027, 424732450, 673350738, 137116530, 557943586, 311468602, 248836195, 248604512, 352954119, 304303389, 238581999, 29345972, 212733348, 206902791, 656075067, 955461138, 724836212, 599814222, 311076919, 978453480, 868833300, 509787573, 865922063, 437076792, 958367222, 187626325, 660789146, 216379248, 38724155, 643244917, 541487869, 269323843, 690230646, 945122871, 167119804, 524508603, 910340204, 970754290, 120343763, 459501332, 137232691, 337077193, 553971139, 224506458, 36639622, 851059113, 655202974, 790859533, 840638526, 482769777, 133630440, 365634125, 549394842, 754874644, 99768369, 357906796, 264076061, 580644696, 549626685, 446815895, 765298369, 86484160, 548429950, 822272018, 239623382, 866459196, 835771182, 564619829, 757376608, 740107748, 120038679, 461298913, 719291039, 656047437, 753730678, 280420767, 768294503, 293041369, 298507095, 380137196, 763193361, 178427494, 922631372, 38165253, 172615517, 482901537, 193268319, 198377078, 739535072, 111052171, 610986205, 783589025, 437414494, 869709413, 843634840, 673323716, 281774174, 389164731, 965439711, 220005684, 538481726, 42821645, 818602915, 770598049, 621357888, 475055954, 700946289, 821912664, 152639316, 427060750, 239681621, 257235163, 850605041, 162862604, 896309726, 210377975, 495527854, 914133875, 642372123, 109870596, 668408661, 874984725, 59701083, 613461866, 723377726, 921734041, 709629478, 322951192, 186901879, 859354638, 150225148, 22644308, 350749265, 96172786, 429809040, 103345570, 554767944, 151641306, 532359496, 388507019, 950989098, 403755146, 617534076, 952313148, 243258507, 86295946, 811264215, 768300150, 627467916, 833435537, 471107381, 224049133, 112756754, 201658210, 366173018, 613038441, 869919565, 13120561, 642504534, 211832919, 96640486, 629885687, 640186970, 705614467, 375377034, 128923806, 670090135, 802376991, 314756189, 612840166, 358864786, 12259502, 561423893, 330902338, 164781720, 902587382, 766731177, 721472083, 37001363, 116937224, 608701268, 610776136, 404183406, 2371995, 401237414, 170571097, 135007500, 710519576, 473083735, 943425607, 732545211, 886650042, 110085359, 929853865, 785631854, 236940136, 176337995, 18427767, 854222312, 752773786, 167789188, 612697440, 699104676, 576860182, 934032164, 155157890, 741821530, 851964842, 872286759, 398487582, 29674029, 287804536, 231676619, 695110720, 710239285, 716195287, 268399564, 376725101, 443867949, 868349017, 316722094, 358069776, 88688482, 382837341, 252933372, 962648640, 961299523, 816623529, 47205851, 141977256, 712179829, 119837270, 92877946, 915382336, 249059418, 798566071, 36291707, 345612939, 662389659, 818621515, 457752981, 575388590, 341091078, 429901611, 11486227, 17061445, 112101347, 244150311, 283202258, 94430915, 119930487, 205710495, 648454000, 244894022, 821964036, 985328257, 651316242, 852313718, 729718833, 386141481, 105913125, 909670874, 653661586, 733185677, 843405356, 690950133, 361207029, 426492956, 810271931, 23437450, 84705382, 749416742, 88354973, 612860362, 291379837, 631052503, 568447116, 120284594, 301516277, 814324521, 148560346, 149771148, 184150469, 153642615, 260759414, 134819815, 365153102, 462161011, 729507752, 564994690, 736417890, 822067646, 370479929, 173991683, 905046435, 275967171, 480909412, 19929268, 13636105, 744118095, 790899397, 962417269, 962736324, 117920917, 304940897, 649172913, 365028214, 175698154, 302612507, 87149223, 817989534, 916974010, 845281080, 527867770, 380882596, 98676163, 536179231, 687580882, 399092491, 745706264, 86921972, 832473835, 161159847, 347417136, 659996134, 602227457, 321959737, 747163971, 198633364, 247052691, 214495177, 241688667, 64797477, 380075408, 745550176, 958285057, 420878074, 344750773, 759622859, 372162504, 45047112, 688611583, 475597560, 255074566, 317642722, 526745083, 665427398, 829001207, 694104109, 681757978, 597900709, 830278953, 990278581, 27728369, 546518115, 885763723, 212155069, 489134492, 89596263, 660395311, 90964954, 883183734, 272639564, 273703568, 945723266, 534587424, 980344613, 799679624, 647531081, 128157031, 561084192, 596265751, 896694725, 718726313, 65020233, 162149912, 978131445, 800540467, 260589946, 716541007, 182114653, 513415862, 277804606, 528871959, 751464651, 310098868, 980415555, 384287213, 522380257, 23202895, 777018368, 135023159, 857500520, 796306458, 820217959, 345921797, 709864427, 481990589, 935853275, 490707815, 717951653, 663760457, 943964041, 447762398, 665385599, 533377719, 794737361, 942328921, 647652228, 148870131, 758506687, 457895546, 155104764, 455809557, 457368859, 184046322, 721602660, 694125902, 522436670, 312914426, 679325936, 882225464, 518646130, 965055124, 774862241, 504582947, 615113554, 71686339, 300635987, 93053363, 73058288, 121311780, 668647374, 552343117, 953281570, 567622809, 495423823, 898089588, 561397124, 674155817, 220523465, 421281929, 453880160, 186802771, 383635411, 746468438, 349633588, 944027903, 519739429, 345261735, 360093165, 796473363, 36369763, 26301434, 214920149, 247312705, 626980272, 334658482, 568741695, 4485299, 690023999, 966895098, 399989306, 959636373, 571946610, 332122198, 723826407, 840674263, 876140214, 30858705, 926011395, 620646699, 276609234, 310303871, 885610934, 567336328, 73720505, 318781766, 565101611, 901481340, 700912709, 442566779, 179267790, 352748348, 194998300, 637377460, 62296358, 254440858, 439151803, 379320151, 820757653, 636042888, 881842181, 467991477, 69384126, 781821096, 522145551, 219895776, 704765846, 685982905, 456209821, 853681210, 790333083, 229450375, 105912003, 184549653, 886475980, 362453804, 163750976, 835524238, 213942877, 753113015, 756405923, 987498101, 750599179, 382095182, 37558319, 997484480, 525137165, 175943634, 687181801, 161007043, 999958215, 940877945, 280760197, 672205629, 465727753, 987696458, 831841142, 198325195, 304884560, 24459121, 850685706, 451532639, 853795862, 537144182, 735181950, 392783308, 103313915, 811792022, 236709831, 992695806, 50781643, 606507366, 337589797, 107509154, 664201577, 389159456, 614081109, 322073195, 224358632, 976450953, 502596082, 139829339, 568321745, 291343240, 639165083, 28786770, 735514500, 545058759, 163943563, 982005661, 956652487, 648323546, 983588048, 752311091, 631251547, 186783412, 769393515, 483299492, 75387747, 898462290, 630485973, 253213917, 143598161, 153303405, 105299037, 248902353, 851548394, 13135959, 833529120, 305471441, 6217980, 219569514, 628102281, 414235097, 858732557, 354452550, 303936043, 76292410, 490622349, 913848809, 438340299, 757866421, 108265730, 310042929, 953701866, 95357220, 306411531, 799761106, 186110473, 51093024, 769938395, 571095868, 220207378, 391614156, 385322781, 196550766, 360989876, 600936955, 819318953, 952281691, 370575557, 480066652, 213328923, 178632844, 786980008, 659059262, 12227517, 593370218, 755377894, 623593369, 151724770, 998191686, 157654842, 55000129, 599865415, 920791311, 308768569, 960695368, 572334194, 431652556, 556249318, 783917095, 651927966, 481388343, 812841789, 105491406, 11437269, 763027261, 459280177, 271033609, 966218099, 764938535, 696145393, 767957240, 828669846, 474045453, 794932989, 735558317, 693408014, 241350273, 130333545, 248554991, 690280909, 995689906, 397910055, 175629901, 571517146, 990203022, 281347693, 667140, 939668721, 27662806, 617176635, 996234410, 736917270, 173217736, 55954124, 598265619, 650469593, 685483296, 335149384, 934815242, 677371310, 716648422, 380163979, 225250866, 710222816, 606385331, 739420632, 14084009, 901592322, 672531767, 523723950, 151824987, 238992528, 348739888, 163768174, 823204503, 780747393, 733954334, 633072617, 367378195, 314254345, 382968856, 624468732, 178046497, 286371348, 168569422, 657009523, 380141889, 193924380, 239691012, 161829284, 636651783, 99673716, 342854453, 576408858, 598831665, 531836396, 858625362, 112512317, 841622599, 495775855, 668898378, 653029038, 957702649, 684691750, 830350591, 982513342, 918739949, 180338176, 906361314, 626666048, 822262984, 223554106, 610059780, 393221027, 845548423, 397964241, 450514409, 237553046, 916001576, 315965408, 609647319, 404880975, 901810787, 24463953, 606190287, 712148710, 862966420, 700874999, 588454837, 67227931, 538804851, 700846661, 172162986, 82205084, 222113937, 607607230, 966438685, 480105178, 855234177, 671352957, 984046573, 322456597, 788383453, 550116364, 262801243, 985335107, 87627748, 273253974, 598466861, 940725935, 55799647, 390469286, 265514226, 996753499, 536135173, 38920035, 326363314, 260148059, 988500444, 859826519, 601823738, 412565349, 109709782, 311687984, 206911220, 141507397, 317667145, 903413526, 19705390, 720882025, 537390606, 944367045, 598750562, 591230202, 8853405, 829025645, 509554745, 57614777, 673021578, 813917871, 662835612, 140199937, 215028406, 744364700, 58273074, 612410786, 912969076, 332648087, 289611530, 259874055, 298498923, 932914319, 791202378, 206172633, 724285543, 597914265, 3286249, 777943270, 677994693, 18307633, 754410377, 682295054, 17300153, 991400593, 624006451, 18555047, 401960518, 206101641, 911750504, 867219383, 51702163, 777011323, 98575065, 376926819, 971284916, 369709437, 751709601, 682885422, 261990935, 114238708, 337241269, 197149968, 63846134, 999310944, 741843331, 499167938, 595437222, 523245528, 985466563, 607422674, 794147676, 597727722, 598928179, 430722475, 695470872, 235130074, 413519690, 105504287, 154072793, 129274816, 135054588, 195572758, 353939178, 424536469, 827765541, 769139142, 115601493, 204856241, 283906635, 575589733, 361766574, 426321431, 454702860, 304321712, 661562188, 7663736, 750468914, 703210298, 704159631, 254285180, 718719539, 473772802, 300999484, 660903661, 228380370, 23332607, 937547643, 308448558, 808694827, 278402879, 108422915, 654796028, 356765387, 171453695, 933571548, 95850420, 643668921, 4182777, 212592997, 664429005, 410166513, 433605742, 787760699, 735425230, 133875442, 188855539, 27393510, 423707690, 953128397, 679553693, 170347395, 245076842, 642097414, 929593218, 42071058, 35104748, 675891581, 526797784, 951284655, 838784228, 680645442, 485224672, 110193101, 227331633, 858542054, 551775611, 88076041, 944704115, 149320513, 364703160, 502599171, 891967187, 683974911, 479237915, 139935891, 574811542, 474359458, 639071436, 736830265, 133590604, 986430985, 223025412, 985812336, 624067866, 355077770, 377245137, 679344163, 781091359, 230027947, 22300197, 140821423, 675472944, 564070052, 730124423, 150821779, 39963102, 172300096, 611242831, 356836814, 323226171, 490630975, 394582947, 68930618, 797462554, 346961806, 829859808, 22475483, 283991327, 662181099, 511452677, 855770275, 958232050, 224405243, 762800174, 606147673, 200551704, 938967662, 346985600, 153300168, 279764391, 634447378, 68774207, 972406328, 40592430, 232248815, 409238569, 113851853, 615514057, 236357303, 766449082, 916414201, 63090703, 939220890, 527286879, 144094034, 724647889, 495017665, 648191564, 497574785, 267761337, 251819459, 470451219, 447976486, 782682894, 344833827, 108576841, 127088452, 665604434, 295958265, 165210595, 325356401, 430718599, 373473026, 404687892, 603699946, 331526390, 642193994, 647548679, 923958911, 201947430, 999637401, 364671939, 920728022, 364866363, 486186925, 170938904, 399427944, 180529832, 779483062, 596778060, 344499670, 690923583, 497271858, 93319236, 319167027, 424728637, 585924296, 211207559, 384420365, 186533790, 96132367, 415397138, 198127980, 456342037, 977677992, 199568859, 838061427, 98365136, 98782195, 364340070, 594548449, 1529512, 283731492, 307156495, 621641065, 23581712, 607641284, 678188956, 645283439, 115771923, 966354407, 641924970, 332190940, 625028540, 235660333, 540507808, 839241001, 87824699, 981633958, 736532063, 99394345, 545457269, 439977928, 818626907, 882245070, 45173246, 184296627, 223055876, 35868165, 570644225, 629010291, 243148661, 935857249, 588399755, 704807787, 414610262, 361978138, 252757307, 42963698, 694712915, 214565828, 952614694, 635146214, 809099130, 942469426, 982695480, 660087157, 815285801, 333737944, 81685683, 776639768, 939218595, 319864853, 88895232, 235399331, 88664419, 366779592, 503985975, 828720441, 904443082, 57517986, 412889294, 331848505, 624889212, 276543133, 9615342, 177729890, 700954417, 704076570, 803306488, 913664315, 793087822, 892616934, 867721704, 532680584, 265929828, 832413359, 668474079, 929704378, 295608471, 826676033, 835181920, 854399001, 25327441, 33914472, 314236031, 875140461, 226422656, 619759165, 234365392, 332078725, 727633621, 673445898, 213613424, 89544798, 734463096, 321283442, 226325249, 747881366, 3339780, 690155949, 183313009, 388020314, 293947088, 266907420, 898659854, 536732017, 373183931, 417407304, 254023199, 213298873, 545283083, 52212215, 664404240, 125511204, 80290581, 274078222, 519901555, 766670097, 647701189, 802503828, 631512179, 315818593, 691984443, 830329082, 899067600, 542015042, 778308693, 198457144, 376108970, 289213167, 527682033, 722442949, 506891582, 889163052, 923986625, 524261250, 705512823, 798912302, 873222002, 647621742, 197470620, 600576817, 720029311, 744503646, 30514387, 176361078, 593230667, 11890591, 913188881, 127435449, 827642293, 681936623, 70509540, 72536170, 378611668, 748147288, 922037096, 982654552, 731396052, 63395032, 753721296, 736757255, 375421698, 211379539, 143146878, 732145127, 303974915, 437836712, 820394274, 750621525, 217416908, 795186582, 189709038, 219866724, 480105200, 413112017, 743651662, 705282807, 145122632, 286975201, 893722621, 545701082, 518571992, 263547201, 346658753, 371888016, 68518168, 601626551, 744322839, 227987561, 58912383, 178660721, 902376830, 51191471, 440517503, 624126677, 782991576, 201439836, 714823104, 741882755, 808832032, 812444608, 264782750, 944187973, 854043047, 501587157, 603721385, 793870326, 470793706, 149943082, 553352716, 96403710, 851791189, 13906923, 798525012, 942729228, 802825782, 107229472, 485951855, 516128471, 393861141, 397399465, 363846566, 454688309, 639315794, 83829769, 505912711, 472992959, 138983417, 766846734, 161918030, 453647940, 223302967, 693703550, 386187943, 610232959, 936628734, 392570463, 169144501, 846916998, 695639295, 795373451, 217276095, 989379072, 789607985, 191152460, 913685441, 352124966, 543799634, 810593491, 8679394, 78486976, 384616886, 345901117, 607599922, 630879855, 569817192, 328156856, 770689625, 321233893, 796314629, 911345686, 379839302, 825503108, 861476431, 701590885, 100403590, 249268554, 657178765, 953308960, 515181111, 653825577, 691212488, 817307658, 821996660, 425789190, 264682662, 127309839, 42492830, 650272373, 353940087, 716689628, 83446527, 611087093, 952192610, 834350795, 617644925, 37275826, 285808101, 544487511, 505602898, 280339426, 58508911, 728219192, 239077278, 190952376, 564648807, 741232314, 847876752, 940160677, 797912598, 214762465, 324548159, 329592292, 827495836, 623861375, 801652245, 173761351, 20104467, 341993201, 232337787, 90219720, 595179861, 239360431, 191307012, 382351974, 33035099, 911944809, 820247947, 996480038, 464626253, 656972329, 78443055, 752052045, 258267793, 559094408, 239073724, 105590191, 217866452, 956507105, 663922377, 46851689, 538400837, 324701367, 644289761, 736786761, 499615204, 376538623, 711605958, 572335414, 150057687, 677067731, 332975367, 926801169, 616081723, 19920906, 531013925, 34993572, 490436318, 847445552, 266906782, 936024890, 195580391, 842354960, 450460136, 20274533, 196935008, 787076882, 826876637, 535858307, 549196391, 316694226, 806457026, 629855583, 863563625, 914782258, 974337181, 429270802, 527580517, 523984922, 113923869, 811334285, 461177181, 279838070, 111371453, 79325065, 821308376, 335975412, 243614919, 825116895, 498921789, 608259139, 663712586, 260285682, 603137638, 341980141, 384018171, 509691463, 695611009, 113874875, 212904751, 329528120, 69629163, 736770738, 104112326, 878670767, 200481908, 324880961, 678558404, 41705414, 344538260, 811878596, 386608956, 651042838, 68809391, 959914659, 573143699, 824284712, 117104861, 804721453, 68366055, 505713284, 564813240, 864825402, 507917575, 72404696, 114643110, 736371162, 542693521, 775065300, 57471692, 555330998, 699717203, 403007909, 39747400, 464456209, 652633954, 648838526, 27955212, 982143794, 387229126, 167560864, 626502628, 403550914, 218635638, 910443796, 159714175, 474059427, 991798825, 461150043, 527330827, 384317469, 304014388, 531923195, 588547891, 865684766, 525170127, 652469653, 663572806, 417494105, 554646594, 482195551, 54358640, 362798315, 399634207, 923919656, 732987842, 115935917, 781792802, 806244354, 788292135, 451120963, 419331499, 582492068, 101314541, 436812063, 219922194, 911224222, 342336123, 364436942, 493607033, 758820934, 313627861, 657925277, 261732439, 409327934, 941235741, 764469578, 490417435, 842883714, 272655629, 668345270, 23994738, 684580160, 206950606, 564839051, 898243515, 977553981, 470738801, 351139037, 247829949, 242499671, 944468524, 865833616, 364906727, 577440734, 585949211, 198912881, 297976919, 479609938, 79623690, 345088450, 152688310, 6928812, 502042670, 350671845, 255058155, 333735506, 428852390, 174012951, 666373578, 489844732, 990841498, 253261763, 464338389, 551451327, 252396818, 242626363, 192628882, 67435135, 419689041, 840807245, 626923238, 258577165, 174288150, 330548645, 950657713, 645411103, 186120612, 12548360, 494514941, 142115189, 307837993, 5672794, 419375020, 496047231, 23306173, 401131181, 180806754, 10841706, 636878491, 701774697, 940767462, 590542913, 627164450, 851111003, 806757352, 410487523, 889234094, 543491184, 438624596, 151064368, 406430719, 662682323, 772996330, 300028365, 702722761, 964468824, 411238301, 34152881, 229213150, 184969961, 362866047, 575894075, 217117676, 396484574, 712088915, 112099943, 831912231, 84575519, 889709903, 158658384, 901137082, 885898440, 471871195, 234666561, 746125444, 436925692, 799608256, 215948997, 162248527, 803926016, 357660628, 357903927, 91050517, 647777867, 592456305, 504752952, 121202909, 686225442, 59851481, 715855152, 527852437, 197909196, 723955262, 902619717, 10240796, 45195209, 887661510, 586417099, 803771514, 509661368, 23293765, 366184883, 701516360, 661054294, 939369955, 621085820, 42533461, 914796942, 947071001, 219724556, 485391570, 607797679, 355948474, 734984097, 39895987, 89270221, 41963839, 389615516, 890345716, 722032821, 289929855, 104192519, 863277431, 601011809, 666816156, 425776232, 552572868, 603196837, 761691433, 964441909, 530215261, 692613830, 75181782, 801501873, 803781597, 137480281, 430721656, 29164832, 250078954, 869810726, 460735226, 366989677, 700797177, 872564590, 280464315, 796475551, 190340450, 318664915, 611606052, 688279360, 895506157, 768505255, 935260854, 790044583, 379009447, 649436334, 798030340, 432931265, 811723352, 667470689, 706457820, 634329976, 523246816, 697935190, 758925470, 306809461, 66444414, 645609263, 447913746, 536244283, 877976605, 623324286, 506948816, 854872946, 834000679, 543899806, 555073738, 246751817, 787511655, 208642866, 131730358, 531890992, 467685252, 93810624, 77363003, 509253025, 791259303, 394624206, 996746690, 78003241, 799911069, 497833389, 37214648, 962440973, 728374351, 177191466, 6022373, 249413015, 417466720, 368637271, 365602281, 567240438, 742567697, 847592437, 979187930, 428437406, 970511686, 166106526, 908324762, 654161597, 301887420, 803257610, 912367048, 415820808, 345721574, 585118128, 877682611, 664788664, 599523175, 993347196, 993209569, 491088496, 694423663, 448472737, 536665768, 456276033, 848754438, 691604521, 876381226, 159298711, 1392236, 79444164, 251313597, 152095737, 55642184, 221072545, 145939186, 598170474, 477061060, 856020402, 715134874, 459115723, 629165645, 194001774, 527630907, 770186591, 836883786, 866907974, 934349434, 20727810, 473058042, 428586201, 951791314, 134107174, 323557463, 88816619, 551277022, 802548534, 164773722, 89768218, 514704084, 324403849, 833945114, 662782611, 774818841, 616313535, 743316120, 955732435, 329267195, 659738459, 145028402, 24050941, 62387118, 295795031, 106791464, 518711208, 244907206, 192382855, 874967944, 626304545, 394076065, 738304328, 107983559, 301670283, 467292527, 145045456, 912454342, 516736552, 962069434, 726620194, 537457560, 92605700, 258570388, 684316319, 368288455, 885614440, 590887797, 599892554, 919714654, 532090593, 652828379, 595255944, 642708187, 781590068, 183541722, 298892077, 412222122, 925699114, 843119482, 962256275, 321379137, 807527899, 300212293, 418360534, 302653219, 871656850, 224692383, 595716132, 34475580, 142366243, 900581057, 458326226, 491680710, 882410308, 91824052, 604173344, 8243158, 342800527, 15832332, 422699437, 363719339, 855364040, 488142413, 510309158, 147005435, 603117729, 100494043, 565346673, 495770219, 138886980, 133863144, 912561016, 121290531, 630589352, 960968687, 744821247, 772313662, 959848675, 82867073, 976432944, 22958071, 504213538, 60635680, 90032846, 67586123, 101347399, 593217305, 787981693, 595570611, 596553011, 280729940, 216016943, 722222300, 99587131, 994241671, 927294049, 191839561, 916924338, 313989722, 401126964, 360706287, 662557456, 395614500, 715922449, 13683792, 272006607, 46788981, 982362538, 234391132, 672430718, 680872203, 325372883, 671573985, 68142470, 624164526, 990101020, 728517163, 148293796, 959871252, 731802306, 296567609, 737880167, 632145843, 226449080, 114389104, 23444169, 263869011, 40541501, 36875729, 289460743, 761454949, 401394396, 655044459, 102831369, 610405320, 510646248, 700817461, 799868189, 164103077, 106359726, 313285253, 942343836, 843919441, 631765544, 843525590, 271108409, 372082996, 178988939, 264447788, 101713373, 857549554, 575687567, 497065221, 198158773, 977440912, 449533621, 10472630, 666628896, 795156383, 576242523, 42695742, 770202928, 763049156, 285801186, 771145851, 342499390, 817732574, 389688821, 149847848, 70094705, 297193609, 755110323, 949278440, 452660711, 476538738, 610985624, 346287829, 666771185, 30325169, 395638855, 463334879, 641436379, 546288372, 222678400, 966459843, 656006616, 432587971, 107313057, 33598233, 74006833, 830428300, 809671128, 539129559, 241523757, 80900075, 949329782, 172901739, 154444972, 685128679, 375726798, 430739811, 187985898, 742686925, 865421896, 259373377, 838502623, 284877244, 232780387, 902119473, 490596614, 470197491, 372720825, 320926319, 735063149, 96449942, 943281582, 964237513, 569243779, 615071851, 314865438, 654882057, 103306734, 718749349, 627274308, 246437976, 147004156, 978873386, 579422059, 817095532, 389751057, 150957440, 857218084, 191793711, 738442551, 548577788, 808640760, 65381483, 390494313, 409839716, 307097076, 165408469, 969701262, 852626791, 891944604, 991687789, 58915100, 627247615, 732136465, 302150023, 712566397, 463614236, 527952951, 828610458, 404025651, 818474030, 914934132, 824416847, 986451119, 200115021, 65788795, 483231932, 360861091, 735873450, 184919016, 125838113, 717802601, 585046392, 579286789, 313697798, 561915847, 430913594, 297248954, 302865941, 321507762, 915106260, 736680043, 761214008, 888633455, 317127670, 190936174, 692251634, 177827389, 918999021, 220190044, 396117996, 628568199, 26102509, 811530328, 923947717, 55252740, 337419520, 658507034, 378036244, 472052417, 654313257, 406058743, 390867131, 500382591, 462743950, 665671557, 549734307, 79290003, 93693914, 868961708, 709073649, 80337270, 775502165, 627004436, 556640777, 83868075, 883650303, 75657958, 855372773, 968686496, 470643161, 15838115, 789341076, 400641052, 35676652, 583143325, 508108660, 925853850, 516864895, 562537011, 353492917, 772695372, 142927657, 45429278, 45380915, 748304418, 68479614, 248260876, 691503410, 89406788, 647535039, 792620439, 249301599, 650267021, 541524575, 216976940, 807800317, 759057249, 690015472, 552021336, 123912751, 224084687, 941139650, 875177595, 638850000, 410405227, 554011643, 494879351, 573191697, 578791208, 705110949, 847819699, 981601703, 274873117, 720298603, 734189142, 106244833, 776060474, 626983047, 945204613, 751745477, 997150170, 809320498, 226538738, 321458542, 276648172, 574697698, 334109839, 294079551, 181227799, 958053552, 472212119, 407929550, 547877066, 183747013, 475879629, 94617612, 807354696, 882763026, 211275900, 251153000, 915438415, 400942514, 328605606, 222212519, 355541176, 260904719, 281440774, 974502972, 817783723, 195916587, 444584990, 709547448, 872146924, 194181959, 631049771, 14899912, 123647157, 854433845, 723424984, 688810013, 517421940, 208580394, 422609214, 412091115, 886023169, 804043640, 822396152, 542087888, 127977360, 870144285, 922830129, 190043447, 677979576, 750585734, 414489475, 314336584, 621462920, 876822167, 880942582, 364207708, 492976938, 526377216, 363216832, 903376249, 76263958, 581860800, 982265310, 371172748, 599028596, 860373684, 562774468, 192933502, 898259535, 606759995, 685881501, 3304270, 17128575, 214411944, 682426811, 895521289, 622157762, 962164202, 253533197, 668402319, 657285663, 481112295, 860517038, 580393168, 920520959, 534689745, 772032587, 354958887, 824582013, 478505481, 339520553, 809556239, 443720496, 589395538, 955066590, 411197764, 426434677, 293373165, 192393410, 252702486, 321342551, 163599000, 85518746, 769364541, 834326234, 264827941, 602189183, 66422511, 836263847, 557169782, 965768511, 943890145, 138567198, 290280797, 55998339, 176758673, 255990268, 405067889, 485223819, 326257453, 41801771, 300599161, 522937048, 964868733, 374590487, 348642396, 330600259, 187951714, 239643314, 486568268, 727204814, 896103362, 506719830, 454646956, 309343592, 164780752, 500543213, 411930770, 145405078, 361636234, 187007084, 62487178, 917692236, 907148403, 909747942, 849463219, 73857482, 345576566, 487249414, 946054614, 155802869, 156310762, 957263165, 49484130, 524727501, 33013087, 510244451, 954617469, 627963369, 728146927, 624377773, 79157397, 152638049, 341743619, 656712582, 893597881, 516477517, 692572811, 917468953, 920250588, 589748417, 1459643, 379441942, 37252933, 145462292, 850537523, 735230746, 450259308, 761951708, 893359126, 282490095, 68844790, 667017304, 270176650, 142458820, 304210311, 354256325, 47478055, 586368181, 628082731, 186058217, 734446717, 150743162, 840405274, 184298476, 204959115, 576991599, 478395010, 692552546, 737191691, 738757298, 349891731, 498507673, 159269388, 215203440, 262287754, 868412497, 328792006, 714488932, 231218075, 33845727, 948073700, 326188080, 278790909, 815469350, 953540117, 514045769, 235860140, 987998610, 535847292, 186157940, 696076926, 724017363, 121824867, 299806509, 421938928, 291774915, 51841205, 287236072, 572228415, 558164570, 950003344, 879907506, 473493552, 774818248, 845708259, 898794869, 56459255, 796772042, 375337054, 971083401, 423636847, 750800330, 399865749, 327665303, 4057308, 763531927, 558029241, 340062576, 133913325, 199574414, 734184755, 562649442, 144129551, 911597463, 22111520, 85690535, 239939987, 198285546, 401680775, 615417291, 15772515, 377386206, 759462991, 495538757, 743870183, 332244917, 80916598, 7316464, 843126102, 258278425, 10908732, 679838691, 236447324, 538451172, 40272839, 46541250, 549919017, 289254695, 718358200, 702643347, 83461821, 923335595, 38165615, 168705185, 783973190, 99039569, 982305823, 913040739, 700919409, 551888822, 904959024, 464166169, 83558929, 391125636, 969110020, 337226464, 621047524, 651657489, 300195180, 972137042, 266192816, 843558426, 560722978, 991612801, 685097958, 875618415, 679679037, 308691009, 262552480, 860540393, 813784008, 52762035, 640980592, 881614443, 932487147, 244043388, 494279567, 557995408, 689483528, 666241328, 370031497, 229554457, 386956473, 153326136, 572943214, 221139611, 202201457, 871451742, 731872617, 712632919, 37332798, 871399459, 706288238, 364737882, 682673855, 484173961, 549893021, 127130365, 785643772, 866996577, 123091874, 812973037, 550042819, 321785676, 669647155, 863871826, 348654971, 518630139, 285618580, 616583471, 713331193, 276825038, 599387857, 897758426, 754347176, 880233544, 518001800, 576050561, 855178569, 701480061, 95097274, 851528633, 791075357, 704411492, 771832795, 464116037, 184630816, 711143696, 676133120, 638071142, 64227033, 223855760, 222200440, 359317764, 946448122, 271021522, 476408498, 431147530, 411110763, 837304898, 762763683, 875457018, 253349234, 679779727, 95021319, 87047538, 897306997, 289897045, 29247771, 863680675, 813187840, 701133485, 102948951, 152087573, 272646939, 469157771, 193061072, 748320388, 729204526, 372192280, 918089936, 348290013, 5841329, 589221720, 363342557, 492556170, 955046549, 766755730, 119189065, 65925707, 823983681, 279723170, 256188704, 850596249, 949676256, 690558807, 8571939, 69563223, 558637985, 175450762, 620823722, 236799703, 581891535, 24666490, 640207019, 283325270, 376635181, 745356996, 274819358, 988602924, 148426670, 593710906, 4253844, 484426851, 89884046, 882358398, 861796240, 79661506, 974991808, 947216100, 506012485, 436807644, 684178305, 906853429, 290762531, 315715801, 623901066, 301930359, 763820190, 464359479, 200255563, 859121848, 267496949, 57338545, 845509189, 933751956, 34738299, 568696737, 763222085, 982812509, 594430870, 787673875, 961156889, 494196706, 472970221, 914426847, 690571330, 914108021, 292925210, 156385753, 66073144, 105464259, 780480772, 592287881, 690930628, 925420495, 565354784, 298175124, 349854442, 101164164, 899375561, 170157910, 102136019, 834066817, 989836492, 184631096, 833660445, 786795713, 713548051, 641807104, 229436970, 201641921, 560489227, 854446085, 472888205, 970664813, 639920280, 785409829, 787022726, 462865012, 569980048, 275540748, 165970557, 1889237, 622791781, 202623801, 834940307, 310580857, 606943347, 238628170, 444302883, 641240201, 471363401, 658770635, 402794814, 609214127, 255238900, 469254801, 438759034, 578260393, 166715951, 611248244, 355601301, 444040301, 428635391, 279665981, 790131150, 783273484, 470544525, 691546789, 603243096, 285138606, 747440044, 318420356, 761681839, 624056935, 719769107, 658952971, 788782061, 181814573, 291765530, 585776625, 838099622, 900835297, 777669605, 590717020, 702310962, 48622839, 705321197, 821883491, 470804252, 192981831, 110991328, 87318376, 11035542, 80507137, 575813607, 289450600, 606318493, 851005888, 919056892, 66927271, 97633852, 485004287, 249687202, 908360427, 180230041, 269962016, 645424671, 815178330, 532381442, 245038780, 974597428, 578223705, 492597859, 766153947, 995538923, 363527278, 755826725, 647139554, 445861555, 742064401, 45576451, 287981263, 676583068, 60224936, 951626087, 214370574, 911393025, 366365897, 891514259, 590746314, 543768753, 132823666, 689047470, 916268612, 412228698, 173165566, 534395165, 940767503, 388998263, 3311077, 897255656, 370536348, 832064183, 53007332, 311139942, 972431835, 806418483, 356227161, 808760045, 410384782, 772792393, 888565380, 487993003, 518738494, 12543900, 512509125, 848109644, 661441535, 19311007, 513450976, 777226606, 335686202, 897163267, 268198822, 355187107, 633489672, 425695944, 88920662, 873263778, 60081997, 265595702, 922398162, 819771642, 295538480, 268322103, 382290093, 447066923, 796385116, 22509996, 757520500, 194593219, 496081844, 645697965, 849971315, 479363534, 79955001, 545447227, 236456471, 448153505, 974571188, 261972926, 118913323, 274618938, 325415895, 759662046, 962833753, 664638114, 130231034, 83408531, 396955253, 121964459, 375415413, 176709293, 78846037, 393887789, 833554893, 38750607, 263524531, 111467789, 92755662, 924718513, 995316765, 824668497, 440299253, 688168066, 781626671, 54889791, 640600323, 524736289, 829811852, 501192637, 121631957, 473979383, 427405895, 848345648, 559148660, 288250753, 769474111, 979870253, 168692512, 248815449, 642823960, 478841080, 517622890, 598833801, 882863752, 603758796, 69734848, 898723534, 323080384, 911083089, 272374179, 842879823, 689287350, 638809065, 282921243, 246585127, 773971446, 997675743, 962777757, 578769687, 568950323, 770342723, 892549939, 155050579, 947220893, 994003655, 518024991, 137148477, 983625903, 309813507, 745947622, 482986386, 809444763, 289738684, 86120610, 235178057, 219580863, 521663607, 193776216, 248165902, 9777455, 681340188, 599753489, 437977659, 220769375, 917995945, 192874960, 647970962, 21760017, 522617830, 117659063, 356863362, 1537485, 311081766, 5643082, 732970033, 831832659, 357456080, 262615073, 81887119, 213552633, 300555990, 656608097, 30024117, 915730063, 405132249, 144978145, 389168214, 158433451, 157809979, 813028329, 718378620, 257863918, 632145867, 447761027, 69196905, 64254285, 645774933, 909333345, 265991464, 562292561, 752175378, 335757526, 5996023, 447158574, 278298595, 789920372, 292426121, 964652152, 701689144, 859990105, 200836041, 89596709, 682374246, 673878239, 367068047, 265044014, 680988505, 768750393, 785717116, 511672667, 664923158, 616481353, 238197061, 475767569, 265875563, 692191376, 634715795, 2570390, 657129653, 887799140, 360376721, 292086076, 575023302, 571223522, 485523464, 184784202, 855678585, 342374655, 801561844, 819650222, 140468740, 869689580, 396003197, 188082502, 789595271, 593725877, 607463026, 542749857, 375243167, 883235674, 903442563, 221887034, 132872532, 225300691, 836708641, 127345829, 888761853, 401953400, 143753469, 353977350, 734449771, 734486225, 517973893, 742108050, 293536010, 124278545, 31071536, 818315015, 980865758, 166905416, 539073384, 780302059, 247341847, 788176900, 818780650, 9014734, 485211281, 662075747, 446943574, 296298323, 701139013, 384233463, 726307754, 63327783, 162224639, 272659834, 114210948, 176275056, 322225550, 494750750, 435669923, 420248974, 986923079, 807935496, 399245868, 240568485, 489415215, 779556156, 427862330, 715874501, 998890082, 312816648, 404230372, 138879977, 640035370, 658236913, 536133749, 189409930, 985378651, 943408375, 244475569, 342436343, 217071200, 312520183, 921967322, 599949387, 715139783, 479602169, 787520539, 320852034, 582400795, 646764451, 584141842, 272599159, 146246103, 705519308, 908469826, 149776052, 267306117, 892535958, 485679048, 24664527, 667251401, 363245894, 483856980, 118587216, 138497368, 375310717, 770031900, 559257920, 79138722, 18520294, 16236625, 247841769, 810183668, 555624201, 89682385, 543556387, 184227865, 29159080, 631463993, 578841998, 719125332, 718134409, 560105243, 695783366, 495795269, 877322068, 742774246, 136519799, 322297293, 190953648, 642965942, 651148009, 825793291, 848366880, 262203117, 788454627, 848185147, 469585955, 515526063, 849242782, 899876173, 757247669, 518912586, 657080028, 907242368, 626542912, 205780432, 357717717, 343906484, 973891627, 906484860, 675047429, 962312160, 432320801, 484360702, 776761958, 969031601, 23632000, 968420513, 706607924, 554882741, 372447081, 694701826, 873771783, 169534173, 841623676, 460981187, 655401077, 366849104, 431681920, 679935562, 37828438, 208182645, 995530820, 422509247, 100772786, 201215358, 862588899, 44779329, 567671325, 328576529, 740653190, 176051277, 690320401, 288966913, 635154108, 339500686, 270641061, 669593275, 20704746, 207555787, 531607726, 803159973, 745736972, 637261987, 440599680, 54199868, 39427439, 534290375, 548593029, 215936349, 412117230, 578238884, 62270160, 945719965, 360064481, 116054742, 27711553, 492381786, 94087964, 692769097, 856830651, 10079110, 197390042, 570833308, 398103844, 271414016, 876763582, 179067241, 856907644, 299473961, 85168672, 227913635, 182646106, 7953039, 30008040, 23481539, 988007091, 494318636, 418666553, 301209462, 954936837, 852261784, 598763136, 363752446, 879770656, 281885262, 339547946, 524769731, 113533882, 62688088, 944701683, 540569955, 805914594, 174318444, 636478775, 288935996, 846163118, 6933279, 948143655, 798966516, 992546518, 283749336, 293638126, 682628756, 675381425, 734493757, 892734725, 867766886, 648926284, 656234375, 12291511, 43332683, 226275343, 274810104, 940339915, 535725641, 771829090, 494952143, 676321148, 816658558, 414217821, 223925295, 129870265, 163676703, 87841183, 493811269, 219736597, 583384202, 605405151, 122010915, 783240518, 994873462, 321881180, 902070369, 633129504, 29566631, 666010803, 249878860, 11703525, 634872961, 814565278, 322674240, 3768196, 972212568, 721173578, 200544544, 482460777, 518450026, 435331927, 605349521, 770413209, 823119462, 161788846, 7964471, 100637231, 970084812, 783421997, 201097047, 266752500, 30207067, 202412961, 728531581, 728895609, 614426019, 398499830, 100953717, 992215407, 43445998, 851684325, 30958392, 432309097, 902032955, 472530145, 14599818, 162022319, 116446857, 926123886, 285615768, 951329543, 237593170, 541738879, 941894822, 468388868, 900937349, 897808791, 634620723, 19733648, 365834960, 383353347, 12077503, 285630379, 410400835, 518977870, 728374378, 499105059, 687241336, 187509732, 91777862, 66436514, 581040299, 544511686, 848330775, 506948508, 852295134, 352117921, 480048443, 711425558, 637081445, 886315932, 715137752, 737870362, 848108942, 456443354, 275901370, 779773386, 910145766, 182551234, 772530601, 823633058, 175198429, 697646565, 384318624, 698533227, 774534675, 574986922, 287286845, 740509082, 502078495, 774719793, 191152899, 459082349, 608549553, 630243867, 62822387, 673101955, 206264350, 821934609, 339317585, 607765385, 731603762, 815542012, 32158127, 208254331, 545489321, 878167018, 373401899, 705359126, 911210908, 751099254, 611170386, 180678505, 481032847, 561489024, 437540447, 714743416, 623470341, 867032431, 426103035, 187394170, 972770300, 767087515, 370523297, 7674861, 944474792, 541986061, 771598434, 6405700, 269233814, 763686761, 793758062, 148403583, 484421578, 376346017, 143978985, 292651974, 743217116, 430172240, 440608717, 119850863, 710330150, 849584841, 756419165, 395218534, 313735374, 512449608, 670639704, 916004494, 787945132, 225528918, 164386336, 23553749, 565626363, 314337475, 580280503, 400323809, 240870136, 229370031, 570539938, 465347228, 803211533, 418703449, 366085891, 496577607, 490830370, 297997277, 46899797, 271291375, 248755674, 146620732, 175431417, 633134805, 873301314, 16602139, 293661599, 868370986, 970316555, 187997377, 14275234, 2613735, 148424093, 791606209, 305710533, 219634156, 414055225, 388621152, 322172629, 725317450, 14720368, 361220672, 437032596, 17088960, 55031101, 297321695, 247089060, 537445195, 95681841, 712900488, 853380491, 246115213, 151639446, 507220727, 748643990, 930648537, 683730996, 306229334, 81132001, 224289122, 221413952, 621881907, 404886702, 96250993, 147214863, 517846881, 557469333, 705789570, 983977196, 906031793, 615414840, 208665310, 665994138, 166290313, 770492812, 587575497, 856096171, 264023389, 620179413, 207522876, 907709904, 375005922, 104128842, 82975774, 124811182, 570750565, 260358335, 439367887, 899060034, 462396692, 477197115, 325902845, 795333818, 624307681, 809459085, 834097495, 768979319, 487622626, 902648985, 907877770, 608843222, 384953349, 300421778, 614268213, 563653071, 599946935, 352328657, 69706539, 112815841, 954522432, 171267047, 778253987, 678850347, 711712870, 963490133, 668004367, 565825914, 908233023, 161933692, 780093430, 410403042, 28676842, 443060720, 15654405, 797981880, 657989737, 264500421, 227477741, 278194421, 268619871, 391240962, 554883853, 398259327, 955276782, 77023455, 807043527, 348045056, 530579812, 956206885, 277944499, 459009114, 729758297, 54720464, 562765471, 887005134, 995119959, 635904012, 766614885, 74550887, 775927403, 355919579, 194565851, 793881314, 483814251, 821939531, 299968251, 96397305, 68367844, 36778963, 593055904, 575361304, 606073908, 216646301, 453644587, 712408878, 392318206, 50981118, 177052714, 657434125, 960675992, 847481327, 954944360, 346653587, 505365047, 732879667, 918375961, 740854295, 292598772, 428908485, 874597924, 626967042, 745127237, 923196868, 279939851, 908018437, 891117962, 9457006, 279962571, 121617314, 537158128, 746000627, 206195021, 297568541, 201952039, 964233700, 100030331, 983303194, 686878277, 384705376, 892102859, 631990587, 550767535, 536243148, 765761453, 542057054, 511529530, 861252225, 867880081, 690241597, 176630702, 121533156, 91551525, 466095630, 782198730, 491182019, 201842032, 729885951, 654740909, 635006939, 78937086, 319666468, 284013814, 189447754, 873284036, 645647297, 953162432, 769582145, 507482857, 397839417, 655285864, 44571021, 134977231, 329870814, 895435441, 943625697, 907812037, 243048152, 945751497, 806184324, 844674374, 600500313, 546949394, 337333299, 443243254, 13259500, 694782541, 654273724, 742602848, 581240864, 860995157, 33393512, 584606166, 371294819, 81472055, 271353026, 864024293, 791658761, 670830023, 745238340, 95603171, 139791326, 176245360, 308197955, 168479805, 33573126, 282387854, 5773279, 401902226, 536576121, 91296643, 70488132, 711630875, 505703933, 895318099, 861664820, 353371275, 973753725, 230530512, 631599588, 546183701, 679194142, 465575779, 200112264, 97997718, 920333062, 534207337, 733306045, 477572757, 185524323, 281403524, 728503414, 842742708, 118889571, 820422996, 859682059, 29060121, 442559572, 888773115, 909469310, 479629637, 740414019, 479315594, 128990933, 111596984, 79051459, 114805631, 213196446, 937716199, 754661403, 837441596, 383411396, 553541389, 95366387, 800489383, 56360624, 213546130, 364546796, 903795617, 854198358, 730577364, 615718556, 634878447, 911799848, 421772836, 288963920, 315600360, 236630537, 248321485, 857815513, 782330384, 225812404, 616463730, 666464852, 650983840, 56379411, 275302893, 547891617, 957230532, 404519336, 454329224, 859367103, 853098622, 219230306, 117117027, 368051407, 112091008, 672701203, 605479038, 670687296, 578141485, 45683294, 202405911, 834524469, 993575878, 536962551, 717730959, 543926600, 781563949, 163824685, 157458705, 846706589, 789086580, 550250943, 537380764, 581454505, 758331964, 688797485, 11543057, 51162869, 916678590, 490409915, 19612841, 456182322, 745003424, 35953862, 276883104, 257423427, 955836491, 819276005, 904024572, 378186331, 506952712, 65106136, 145015496, 536134437, 346157928, 524731574, 689623730, 954998003, 546593694, 79039056, 409754782, 213421330, 613314748, 25933167, 835472967, 1646365, 783481497, 598975102, 561393480, 378091033, 671047478, 457264909, 70212475, 622152907, 12732708, 346656640, 446946300, 806619391, 468225671, 542168892, 538696662, 300526318, 895280124, 916902533, 537842911, 983333846, 136622672, 24933862, 802469667, 69905931, 421700350, 835816807, 526502451, 269528634, 908138868, 105372984, 304469792, 597262227, 886492997, 469536119, 451209998, 343057163, 105093077, 557735336, 442058029, 897693743, 689215100, 963313567, 483462176, 518278936, 800410207, 13228855, 290540737, 146220506, 53905759, 818981368, 819539353, 948737548, 83332120, 464410520, 924051903, 767837073, 652796828, 302944747, 530953290, 542009593, 724996057, 890889249, 376452260, 822441448, 62236054, 443564856, 762021694, 888128620, 750785556, 615046021, 850651124, 684427967, 763045363, 409767145, 573716577, 16242486, 910907536, 682514732, 771662550, 382551027, 562185876, 561099510, 154473060, 956227622, 310881752, 24885738, 122724740, 705865887, 579444701, 350632134, 812647317, 109046085, 740326830, 641476421, 597608474, 572733277, 477175718, 49176658, 509912961, 64381912, 959912721, 488347562, 386208528, 231515089, 40376279, 241145272, 87997934, 932544449, 723485947, 484388170, 550696959, 374739313, 298557956, 856479869, 919892510, 610309496, 154978481, 445316117, 875339274, 374028593, 513139270, 85166735, 327758896, 472996630, 822842317, 365646201, 823264141, 883709398, 369599735, 735372989, 739143376, 807625713, 183512181, 271826617, 882449681, 503156378, 168640499, 165591767, 77824710, 295158483, 527180708, 805858786, 694526654, 592001157, 883072702, 390573122, 884634676, 340847402, 439862584, 254121992, 685836198, 446591464, 340154785, 98959457, 454035207, 102613333, 552120046, 198003336, 814577658, 365436522, 640562003, 117249241, 993818233, 870412405, 2282143, 147254648, 594791355, 328548056, 89111233, 920260078, 362907827, 265226889, 644929606, 390969639, 288767299, 915217856, 430961380, 945276360, 595497295, 942638564, 123248722, 739589557, 450516390, 866479818, 339626728, 558993589, 363608529, 839366024, 473939996, 293538212, 512822186, 656228361, 51898543, 66845216, 930625070, 723807565, 626250469, 33788579, 590071493, 239769018, 496623753, 588900196, 758019906, 628553545, 169943210, 854083597, 702508216, 649825579, 47710310, 420623734, 865222646, 34755128, 693550148, 239003571, 918254884, 210003819, 530595180, 678775264, 639460732, 940944330, 630570197, 733087774, 428101833, 71844828, 312722250, 665573923, 177173264, 481026137, 135562158, 116550547, 200927417, 997961521, 242026757, 951270566, 193464133, 797201026, 580980008, 946350988, 879659449, 63196024, 527046539, 990712408, 716520871, 891622739, 99827641, 320422, 816255759, 480469749, 628515100, 789663457, 140538673, 864967151, 736756204, 144233709, 239102183, 420918027, 195562331, 844239525, 67998405, 534747550, 243026788, 844902190, 706778400, 918729605, 512888025, 417920306, 362290991, 331739204, 981648114, 246335728, 147773591, 877180640, 327754867, 899266030, 639872255, 660366740, 75054143, 229171949, 17214651, 820663589, 306544354, 764802269, 438109478, 128396429, 223909258, 515199998, 504346286, 368932477, 235067399, 995766686, 640434261, 812307191, 148754014, 100822101, 499777226, 133598491, 335154260, 764540345, 574574946, 934351844, 441112801, 94074073, 698248824, 428913539, 739127693, 225142797, 662006326, 138881162, 396135311, 694608632, 346332638, 280483294, 394878560, 531886777, 241360672, 707094479, 397068974, 212655443, 988113671, 744961217, 871190317, 679211348, 373968552, 36437364, 725192369, 208073080, 951447821, 596434345, 41851886, 215450484, 7529701, 977243234, 211070765, 392620846, 158683689, 235353800, 204069917, 744834659, 986008113, 965070638, 949972036, 375428641, 34800993, 227721263, 696172084, 687277739, 117695665, 562933603, 688172945, 226035889, 674509272, 212740824, 413651329, 638506580, 916752809, 343785640, 107684402, 538791351, 967986475, 32029322, 57964298, 520258549, 573049828, 33769934, 72359330, 610883651, 758730345, 880239839, 651639765, 498452124, 545198207, 515965087, 29044934, 888505474, 370002530, 663103197, 456079650, 10114849, 1230956, 691740715, 16371824, 128566645, 372741257, 840108845, 623196700, 935501956, 399540057, 108190420, 47506429, 918824986, 905941637, 723385873, 279224471, 763552502, 307288794, 165732605, 525152639, 122121504, 350449014, 267668893, 913316992, 985893468, 74460985, 128069743, 639707735, 306044134, 117051413, 399139638, 721213237, 775858993, 924155671, 565387108, 174666874, 802716534, 196179737, 949203619, 236448417, 633551621, 659021787, 966179447, 675559866, 145145376, 765979016, 672404352, 871845773, 508803703, 633093970, 188144917, 554513289, 809026801, 586683293, 554576994, 768495736, 164096027, 576167186, 96539800, 134106467, 207202361, 458923633, 315490763, 156729882, 277297948, 782044030, 398475314, 983622482, 808479778, 756395371, 581429421, 477390208, 895770603, 603064840, 761213791, 208097644, 521456340, 674183376, 376963439, 26879528, 872688136, 906960320, 935336940, 93954497, 683597379, 139202780, 376388069, 68348299, 331323606, 493373994, 532553878, 280935067, 180508704, 893046296, 864220488, 418579698, 323254110, 565203037, 749159191, 925441298, 36351469, 859500533, 499027018, 930626787, 548222194, 863636918, 698743279, 252848134, 741857389, 107139244, 797742196, 962890625, 712467654, 771971417, 361267511, 418667603, 33151542, 661958709, 987168804, 199716945, 822814867, 847654879, 472516781, 370134415, 341672960, 643113914, 763391559, 827670926, 693402939, 342102894, 190682981, 830696690, 67772051, 89586108, 929978994, 64224599, 686485618, 123665810, 366908934, 401933522, 134750897, 942160784, 636383959, 522110042, 33282928, 168925512, 550111026, 525756927, 616179447, 771691906, 551466930, 372571206, 124792243, 697946290, 962915433, 752389788, 627754902, 481878115, 799653211, 341180752, 226964223, 511451791, 906604785, 657575207, 989915472, 598018166, 432854237, 59090613, 583209615, 438108042, 921428921, 348232111, 48787627, 604412040, 967226912, 810281039, 544434213, 903290324, 287509705, 783986962, 789976497, 441181864, 659781267, 878361662, 820093335, 808801763, 426539298, 435184059, 12226377, 676676217, 849140987, 724963631, 496209489, 8325207, 466404251, 574380929, 752754067, 312224012, 285903765, 174841468, 746056271, 539635064, 212800852, 786335636, 347397682, 387785792, 658226722, 245734428, 278687424, 889165245, 944451964, 75934319, 266079533, 240891135, 85416194, 277796425, 366997447, 508581532, 930329759, 49331561, 149647163, 39373778, 141609852, 144560473, 560215924, 237829388, 173820854, 795519705, 388009395, 250622078, 888390110, 551509238, 109554083, 723709286, 907051275, 294195647, 397397743, 564504330, 193830488, 196425724, 991545401, 91749100, 599249205, 717915375, 845104619, 622991295, 51074084, 101475535, 670207001, 12448108, 681269774, 151619883, 923053854, 639432028, 470095265, 574019403, 377633861, 186462382, 646110058, 437944495, 177604296, 797866069, 379669388, 526101627, 742336150, 63092175, 155469945, 19174041, 173015852, 568849173, 103486721, 574891816, 250045036, 546850377, 727806215, 583013326, 549999877, 454689926, 860098791, 318790173, 942747679, 881932356, 514445243, 169371246, 350929779, 939560757, 261853115, 865950642, 787133091, 537537210, 982852945, 581752928, 100262439, 508808777, 734314104, 526309812, 912050137, 218770320, 676610204, 662480723, 850983427, 889476384, 615169657, 346829421, 10175472, 887861029, 961658978, 258016791, 734028276, 359430923, 335493480, 523736938, 967757691, 258964030, 48962224, 282491898, 137444961, 67422077, 155764079, 405947510, 160957298, 986248126, 139166970, 612301449, 475282361, 693674473, 639696443, 89847926, 657534925, 283689333, 452011972, 447978195, 224726879, 327522442, 196268760, 50705101, 458071437, 125636823, 474740824, 836779619, 275146272, 262097736, 397330671, 438349278, 854116894, 754885020, 20972617, 906381922, 556988836, 69246340, 750931437, 230803960, 874582026, 452961059, 514841468, 478651030, 502749599, 331392841, 676179085, 955783494, 263347970, 523891783, 702796169, 394927073, 318939704, 341205353, 752761330, 240564481, 731874628, 900448853, 773469961, 3084504, 169731473, 814502764, 272511570, 498598738, 220918974, 919129517, 949987460, 974341707, 193801190, 232042183, 669504788, 970336096, 770217174, 230112784, 462331927, 32610244, 968808852, 471086245, 473923514, 485368507, 17362174, 762758088, 809504638, 901079008, 406197455, 878415548, 853008590, 130112796, 322316748, 301061661, 478813290, 613847385, 206025968, 146928245, 992133837, 405576087, 401351861, 376252801, 730339055, 863088594, 197048727, 516420441, 525435387, 359543704, 23831317, 510063841, 167318910, 151799833, 623836293, 456559158, 295036904, 521029492, 276407420, 816170515, 72692762, 499681414, 439487526, 363737936, 706893350, 243725415, 369291299, 389251100, 774452866, 855155600, 460149714, 933832611, 210186237, 507839328, 132509535, 146364591, 326259758, 279487861, 588784007, 870238555, 6871473, 376439119, 19333574, 164675758, 276015700, 671065884, 595317232, 917440768, 498753185, 874598108, 473458834, 678621186, 898421600, 340202317, 557378795, 293201942, 118907454, 954343315, 391506043, 336805137, 332222605, 563485190, 223571042, 495930910, 899911996, 733296626, 167927514, 553795602, 994546198, 773691315, 928041898, 39688888, 850636319, 722022188, 812938367, 152730768, 529003251, 277670665, 271145036, 237231940, 313876342, 346536357, 860978673, 988042129, 512656679, 435696133, 28601086, 271873979, 896683795, 278083274, 748844812, 799457661, 349216713, 80371511, 11450357, 147283588, 249722693, 234482109, 187520236, 535315470, 77686736, 273104279, 187635600, 869885835, 382883006, 652471052, 348241787, 649403534, 855287122, 696701927, 881420789, 610741191, 383456178, 450525592, 945872729, 76495630, 147041429, 419275208, 915871800, 677534717, 90324698, 912862622, 942382519, 965402926, 709557982, 635939533, 522989948, 710529737, 36719634, 326490283, 394753549, 572235170, 918536872, 142590965, 656075536, 642331747, 275856025, 923155034, 926358143, 128126498, 528267812, 728159353, 703969841, 319648609, 530257436, 512325754, 950070584, 182131103, 288846625, 132804988, 396085702, 198175598, 318849815, 295036951, 186966742, 467653437, 924076961, 211148945, 780934710, 351351432, 240881848, 173384085, 722565007, 984634779, 750387064, 599494951, 432531563, 585068781, 28871339, 241046897, 327900897, 12247691, 23813751, 917131240, 491323108, 33763780, 378049595, 561652757, 743273597, 203357598, 10093880, 797780147, 37919061, 197182606, 889549114, 322152281, 355868054, 869251941, 830999567, 237269681, 949676043, 204672167, 501001272, 564194428, 954105130, 716230425, 437943494, 807878394, 681918306, 372059981, 26635778, 871140949, 682119215, 655111198, 896766262, 223017060, 483851617, 882729622, 449438850, 209078136, 223698833, 797351119, 943450085, 660300108, 195929723, 337650360, 103431817, 650185574, 873215570, 901561, 180269663, 101265262, 463726481, 922501997, 473603907, 680552591, 877641564, 684965996, 377458468, 440471720, 984476606, 955870604, 756802941, 340368249, 223963841, 651054392, 994210546, 554179954, 234983402, 617744133, 494160397, 335217882, 328731621, 335620825, 900541336, 754304869, 460084825, 782846447, 781181348, 913354721, 414339241, 577868722, 868970432, 286227852, 133221445, 3559841, 844327829, 502321556, 960255340, 359349618, 544595545, 560778758, 237177696, 994712134, 495930003, 791210102, 975091647, 231953671, 883540346, 366773729, 706251568, 591739732, 200637803, 153067217, 723491663, 494064032, 820802705, 258359209, 200358169, 338687431, 307469646, 464877405, 177910444, 575749366, 640580689, 190991751, 14683228, 314100133, 410455204, 415553343, 964613586, 634237752, 605057370, 428739706, 360552801, 760556575, 686102542, 992861121, 602074738, 5709910, 735003101, 203403810, 738494376, 411796598, 788271953, 953628577, 893073130, 200801575, 123543805, 372835656, 929385688, 221971916, 404220073, 118082508, 8969653, 899950307, 132608856, 139354167, 363469787, 396066056, 143654194, 649231384, 892145741, 746529597, 123452388, 902121851, 822471220, 156284957, 218599996, 753911234, 4395684, 350863143, 853626483, 37531701, 893316450, 6980520, 69772638, 760636498, 662302623, 320620668, 377782217, 124567135, 869257916, 166856231, 658229899, 327132662, 105110269, 403647970, 817527109, 850175818, 352705952, 910509593, 761567403, 200960635, 876112537, 808609736, 293706415, 317955241, 276588039, 925570755, 345777668, 385005827, 809353637, 170178613, 496768710, 181985233, 315318387, 440208469, 936308569, 57583115, 20618925, 286209645, 890862016, 651966032, 341042140, 964664140, 29616439, 958918109, 49485705, 640544536, 91699968, 662805271, 71048922, 408185415, 891584267, 424421700, 929399251, 707902318, 594316014, 360480411, 496363200, 488455501, 970541246, 387018072, 729502464, 200183080, 878948850, 916680114, 662996141, 208307530, 364748362, 935812413, 133160846, 940563662, 310855802, 632492126, 154716647, 33596857, 744202470, 256999061, 756872550, 971246277, 93976455, 221329065, 290989946, 579204201, 497279546, 945477337, 638652052, 93619016, 481315889, 671437185, 345593739, 632810701, 288317494, 394016544, 2684089, 187665070, 56229132, 918267759, 208544814, 965508393, 72475716, 285800850, 900058927, 964734527, 405866963, 452204718, 990015662, 325669650, 867781006, 998926494, 517865061, 439758271, 975695557, 775306986, 641909567, 696757002, 11378786, 579776699, 406190883, 563015184, 459421516, 187157818, 710135030, 773739178, 419278729, 890374827, 623327864, 190341956, 407258148, 159527729, 430923261, 842629533, 897506555, 236258058, 563992629, 435967022, 350512722, 272051307, 628193606, 228504053, 398608995, 416866242, 804525809, 499084891, 7908875, 484248874, 101759945, 853848738, 834253099, 309142804, 976047413, 730724304, 356373280, 125999636, 586586877, 63220682, 865422487, 654824852, 520026057, 813143195, 55971195, 395310788, 62513204, 887830365, 81640209, 308275328, 504641661, 366937017, 856349932, 218356630, 80571094, 648800083, 786893486, 447259175, 724360928, 20443411, 510430168, 262237899, 246786391, 221418350, 254478843, 337249062, 94706717, 457085804, 550661231, 478762714, 646173108, 812818603, 471547338, 95145840, 667381656, 662568098, 757106818, 466167276, 549403309, 639847164, 865332068, 880902900, 211667403, 328460179, 276865579, 111515760, 970431794, 199415213, 305524276, 10796812, 53962766, 315568277, 746510794, 67093862, 484016721, 430784087, 338900103, 377096180, 597096624, 69128589, 716902117, 362214180, 192933894, 519667534, 776377767, 359033150, 777054348, 800962659, 564315218, 235767424, 988895548, 874198576, 971175702, 272577654, 257171005, 503145301, 943417365, 97341019, 194850163, 37697402, 336156213, 99905577, 31586699, 97873377, 95425991, 365334477, 873112258, 986914418, 629984151, 950857386, 264107472, 444392057, 713862392, 199445772, 773386823, 686471340, 653485585, 358709576, 30329780, 631204920, 831415355, 180830404, 652169807, 895778407, 744735601, 530951869, 625253984, 197941560, 332041981, 388597197, 394380769, 348151309, 46126096, 970088141, 247767842, 394953774, 583319765, 799398853, 296042244, 60817222, 153988770, 99882215, 757020869, 690923729, 434444578, 638614352, 48968908, 148503327, 346453101, 59545608, 198217339, 2111613, 179134867, 231415702, 923236313, 780225101, 690367714, 360675066, 161451115, 647611033, 292714863, 120984596, 205840350, 851816937, 823694137, 199304189, 329828839, 743636565, 697885987, 109257996, 864899676, 563718601, 408318781, 15702437, 813814795, 253925202, 258730713, 272658650, 948800413, 855983021, 879202152, 516215667, 657615301, 600292149, 748230114, 974846888, 244370897, 222245287, 491619152, 802565880, 799899533, 652678405, 403880734, 666626244, 844271458, 196779942, 217535716, 195928799, 448183342, 435143720, 193784454, 952215119, 228281294, 239634377, 509417572, 697232623, 327642850, 398711545, 374612687, 649791496, 126968874, 898760200, 103174691, 199428996, 833225965, 488762612, 600991116, 66984308, 711872644, 614342625, 317891904, 567857834, 643634353, 168358534, 95423274, 675599450, 76203872, 169470366, 692617011, 818729485, 84863162, 975497351, 136876859, 951817379, 666347568, 379341062, 394269910, 896046145, 286649062, 514749592, 221200329, 534413225, 541475039, 376383915, 677267436, 352685758, 27114154, 125255734, 234012043, 657053715, 857726298, 141430769, 547429248, 394230879, 453095759, 883148772, 394464412, 783143215, 536369570, 499010265, 351384809, 143851716, 961922902, 164564944, 380225974, 13927014, 130863054, 940236666, 452460023, 656426353, 538726256, 823944972, 975334874, 482120758, 448529509, 285654538, 77368476, 354113728, 565344598, 980218064, 949305017, 799248860, 275977262, 357038655, 275594232, 844870009, 70316529, 700544279, 649656981, 30566796, 218945512, 591642401, 384779112, 986340585, 904317397, 449199680, 326764768, 28295960, 18687880, 395588489, 204603301, 565837237, 47044178, 815977777, 470538900, 62865242, 11285158, 599010878, 178176676, 988500331, 112138860, 428100508, 999263666, 250135920, 859132051, 740924632, 478357802, 632275507, 94100885, 701802098, 157125951, 121865638, 291677535, 774005337, 517016321, 407086779, 956872590, 653170921, 946551418, 769247390, 7601513, 678737394, 146095366, 516041045, 156981291, 284869639, 772072193, 617988144, 17977168, 756386060, 715855822, 680448852, 404424520, 453690261, 536075808, 494121306, 771593660, 932670678, 561731510, 410414541, 243111190, 380345716, 481316186, 306280998, 955613745, 539597092, 729236395, 685118116, 999900263, 304049140, 749364982, 819775452, 95637006, 97588146, 973155547, 909821488, 583805501, 383554102, 3476532, 997429234, 395656307, 412444801, 773379846, 869023532, 974126247, 851489904, 220784315, 578502085, 680252276, 453433623, 302648926, 683791853, 992061640, 831902357, 68478182, 128638502, 416682263, 908872477, 26317165, 228583607, 721094204, 549518889, 496153249, 998337047, 731508363, 593096933, 16826479, 996455880, 326040482, 685807611, 66124801, 804459434, 182462857, 67557405, 681034984, 640393212, 696684415, 821359477, 505046006, 58775578, 307770096, 752499660, 820497891, 72564925, 331580702, 626682928, 102943046, 687914428, 771976779, 14381387, 700526973, 298382503, 665739561, 951371644, 584147618, 519514425, 397287854, 150504079, 429017327, 550833497, 16257117, 852781514, 370152649, 136780506, 463550098, 287339788, 168504688, 128284781, 290363756, 258433917, 243086372, 921499580, 965114965, 762952507, 616287461, 369850859, 186683564, 105096028, 107987617, 840252679, 316672029, 238846883, 218205842, 811785991, 249157020, 997859095, 549163546, 835591008, 404995179, 566513065, 441760534, 136630135, 203332319, 565543864, 886636509, 960738521, 293742507, 765785150, 307411496, 686990785, 426668685, 537450880, 958364493, 869356216, 199613330, 818278301, 80912993, 813099894, 751400263, 883043472, 980328226, 676141026, 252680776, 363464083, 603978277, 922352863, 378444823, 167754199, 612550973, 573125742, 885630493, 158916773, 832998220, 811370455, 492715233, 964276412, 414167042, 410262095, 742764815, 316656246, 185277190, 497965903, 198747333, 929057251, 128595177, 747216745, 75185247, 17991255, 456757236, 325938600, 759115741, 866490843, 523493457, 644121724, 353402828, 803599932, 432016032, 87650965, 750177719, 596344606, 515348319, 576037649, 36575015, 891076206, 443090227, 311555463, 563097239, 201201862, 19915210, 197126047, 876132967, 375722834, 674518728, 36833123, 128343321, 610073745, 613475254, 473159679, 595363563, 566974359, 280563017, 209320496, 958684408, 661509945, 627710215, 107850182, 959637394, 631934638, 140135108, 918716482, 815223540, 778524397, 162265314, 739211967, 708381537, 64978508, 231130882, 353187023, 552712332, 421768691, 753927055, 928393480, 144051213, 101436411, 923874028, 679387602, 731106721, 59036250, 651701385, 75956938, 122331053, 577210916, 730294310, 479869706, 614499100, 223697546, 750990127, 442605518, 603406270, 509093818, 659443266, 127912665, 288370849, 298776220, 22917408, 624557624, 167355019, 826817509, 152585720, 531743955, 352120846, 900930421, 641222739, 562936849, 110456648, 128892316, 178619682, 590549527, 463955469, 425339725, 138545705, 553990656, 941450093, 225341252, 908703385, 894680134, 202479269, 718378828, 968657244, 916962207, 360808500, 581004815, 164290529, 388924378, 797835151, 207489061, 179067132, 113049599, 175929109, 769452790, 715049140, 581362025, 467537986, 841338858, 475102365, 666987836, 846685501, 957633472, 429837032, 868914894, 898954929, 140329368, 854770883, 359328377, 329197511, 77190726, 386540761, 61747241, 386414653, 543056521, 215071618, 710372319, 660823707, 924048963, 526217166, 145668579, 845269113, 198643144, 36313107, 794661827, 72002673, 78784862, 49406796, 443067454, 90545449, 213390135, 688036866, 149023615, 775892849, 954196635, 633220424, 840164875, 285791832, 343947462, 432975411, 125535048, 187766324, 366827312, 981829916, 686088914, 816691836, 847877530, 541565109, 443255529, 145854383, 770376840, 955040752, 833200146, 388880112, 796592472, 635361003, 169086291, 199230933, 411517043, 902813132, 381925417, 753631470, 95065849, 376552251, 566234891, 757207489, 108282609, 197220604, 156944614, 525144477, 911499830, 758282013, 636369688, 41793616, 846177916, 476676339, 773860245, 111370900, 525186000, 597412929, 430069519, 448210023, 819714405, 249920831, 929468050, 7883370, 793097820, 465914513, 236725096, 728709146, 351144633, 187348293, 485269670, 103065161, 859441895, 503670112, 478588610, 902441825, 664088782, 457493671, 566173392, 72771833, 24950574, 236677637, 746403132, 89514671, 799814537, 346026221, 294357516, 243378069, 834909301, 931105012, 181589080, 964914276, 809461643, 126398601, 246257896, 475948446, 268042789, 384578621, 231750172, 980459362, 534667724, 54995671, 662642039, 674408372, 981677841, 281974352, 187477744, 688072457, 388904634, 10615180, 445577085, 257093576, 100146795, 307698350, 487241862, 150814935, 878486034, 672361623, 471363005, 63196505, 462636986, 838603787, 890509439, 541243138, 5418093, 447277640, 152056240, 750074071, 748798102, 848676451, 175220187, 623565273, 731562734, 594011748, 14613092, 802667770, 870902794, 663011518, 693075356, 635019790, 949915511, 948166876, 162383430, 534165084, 905657694, 372920162, 313752881, 884460071, 110891399, 48183338, 513145401, 61344807, 281610686, 231024092, 361121443, 97502696, 444101001, 656696163, 961336942, 894102596, 937606624, 848909847, 108262245, 518683417, 773278519, 803338819, 368560249, 917151059, 86913188, 277009462, 366394324, 792664371, 832225137, 931927773, 89959328, 629643131, 244339385, 762104955, 230438783, 853802266, 813612646, 801346459, 334773905, 500291012, 800020000, 713689156, 47516179, 154680905, 51796706, 865612821, 324322253, 857175006, 352201490, 792172719, 109942428, 645786811, 985718823, 762296307, 300829949, 433821620, 261873828, 467878378, 576831372, 3741803, 607988906, 389142562, 38006933, 576854256, 442012465, 710555532, 819021591, 492765852, 776975923, 739131577, 412128575, 963773552, 823234329, 240820233, 987093623, 426974220, 124908151, 205666419, 563124912, 864146282, 128770356, 733853593, 977286840, 61770222, 660254401, 290807349, 366733884, 912848128, 143448859, 950462745, 904578284, 858275927, 558105820, 226139507, 369737749, 776330210, 753858873, 977524726, 858320892, 825085437, 884821992, 74881360, 314623715, 533698463, 229249292, 925118387, 400298977, 688097450, 336982129, 904128892, 904543589, 194717749, 891410237, 75647801, 26176917, 748224154, 520158404, 620223105, 140669681, 698896058, 741666875, 598802022, 401794095, 872434527, 827666, 123047174, 346113366, 886280828, 97219402, 694793891, 177967118, 258129911, 159091689, 712238728, 918400855, 514117056, 694326131, 570614232, 167509519, 94646414, 402631068, 123092153, 487963842, 45666383, 617391014, 655785946, 21894444, 798074558, 793891328, 872082901, 987293260, 806520426, 910267068, 387725368, 91500798, 84987168, 133465092, 106667126, 98971270, 83016183, 565696517, 495400084, 473846713, 707286794, 901857477, 296104704, 115512704, 125632882, 947885136, 318393543, 717387350, 188752311, 16597375, 999707709, 991035931, 205952423, 809328496, 227945042, 950622104, 228506651, 915939097, 154813956, 723848140, 398002546, 810343884, 567214624, 966148508, 44424230, 41320551, 396853125, 405655315, 539941311, 713713608, 550144480, 313539162, 530358945, 634007306, 310902549, 513946029, 996734270, 18258783, 695161736, 229532516, 500659459, 808735771, 218672801, 986524218, 358642710, 962462017, 635699077, 159504878, 996734648, 542465076, 963258008, 638407540, 664091282, 373427303, 881860103, 975996688, 885806540, 722329594, 324854828, 255461627, 422357885, 882940023, 309003263, 585059504, 492566623, 861837440, 21306595, 803861330, 71836216, 455276657, 31497591, 856406370, 811665913, 269219192, 629021615, 986171277, 21199970, 158084493, 205787422, 359940157, 855477157, 469671847, 144922723, 765989004, 174884902, 668351476, 986489329, 938469469, 586459529, 550569470, 246442132, 725474290, 160311824, 730878590, 94269599, 445647542, 886494621, 923496734, 703034493, 843729283, 609622772, 815075813, 671582917, 241266722, 361206893, 37230979, 741992429, 498941236, 875543224, 341469609, 797445646, 820351805, 18648391, 523610190, 942577664, 272468680, 213515734, 293767787, 569633839, 183014214, 947353868, 148636272, 338673779, 347952784, 992494763, 514534244, 631915974, 508029088, 956900411, 347339628, 751333800, 218969697, 4524734, 188425992, 264244673, 626838124, 362937276, 437431772, 708107779, 465494802, 547359416, 330587972, 48177900, 530873603, 755550985, 367179621, 62704524, 656226839, 368362571, 154304899, 511787239, 527829580, 411322490, 42329848, 537307188, 595913015, 615460255, 985720108, 309084845, 573056073, 105596506, 343282402, 529653803, 320273626, 279663090, 848107195, 239100461, 938638683, 731225176, 678266555, 428131676, 105346141, 143519612, 670331253, 74892075, 286019741, 951655653, 456592110, 335688181, 949844091, 8269580, 110725314, 97931729, 788076237, 608957166, 694668387, 190499033, 609260102, 691473652, 351690438, 687835638, 901928667, 974487478, 416040660, 5427384, 645534912, 98000664, 952111488, 593653677, 153504530, 998654572, 832183438, 714550604, 350169353, 887891959, 531966002, 960104929, 619203691, 369786335, 341328640, 208017715, 416596122, 880233714, 155402055, 752941938, 149996609, 736810490, 762744924, 310357908, 833752017, 319087892, 188508175, 899907862, 496906921, 805983152, 31741161, 505838153, 861629764, 503421391, 511160822, 584928733, 874620009, 312497073, 915290533, 257291992, 185848566, 347026771, 661184333, 265134961, 584981491, 485099171, 528433337, 94491781, 250490934, 298653820, 857120154, 907277466, 341399480, 129194815, 293203131, 431960142, 966237773, 301396890, 856338688, 116492543, 12430031, 22808747, 310428991, 202838390, 666279295, 751817037, 448319007, 501845705, 489733300, 551562710, 185820249, 914105738, 39851981, 379589722, 56875165, 981233063, 314754824, 508014413, 745212386, 657375062, 419665, 508783753, 988323960, 471414494, 966849060, 460693588, 444040385, 562092294, 243531410, 710041749, 451268355, 467058681, 289853258, 535277494, 900470353, 973501120, 69098664, 8127649, 484916501, 101088655, 418568020, 584713224, 593273335, 614459196, 680618615, 534553909, 688781836, 299951847, 691390075, 723263808, 154167238, 864512787, 743354110, 567750116, 262345348, 126661557, 418351999, 28529531, 684260482, 183420305, 23856276, 833303558, 906335712, 70731824, 393820115, 483820421, 770334925, 540329791, 376966774, 338582704, 58773395, 954479833, 319299361, 131772965, 93015980, 741941683, 904592935, 274601848, 798842046, 430763329, 28441783, 96211403, 918834219, 808692629, 645897861, 920654590, 680000669, 958987024, 208899228, 675266579, 931789662, 217781253, 511629689, 909438733, 778010357, 281543585, 996126666, 937979199, 689912384, 47225492, 997687159, 185946204, 609847778, 228493713, 657728575, 302849916, 362859208, 225895567, 940383938, 654732754, 470498391, 986998546, 896576201, 681727949, 175595719, 117436496, 441285832, 225245142, 159994574, 680070740, 34495583, 397666979, 295569857, 474820580, 732945277, 844343121, 218338911, 336813783, 276339140, 632344425, 88288988, 993871965, 381200673, 923625459, 156349142, 957999232, 350991453, 133307887, 484122927, 152498388, 914608996, 474952065, 431699899, 407539239, 375152953, 333557375, 137764137, 857072022, 602727984, 150099467, 779189692, 685675802, 447007829, 577659643, 545478125, 681770104, 247543368, 103482410, 475101309, 844694689, 252664481, 736396207, 723180470, 986912227, 89091391, 700870217, 14805349, 303812349, 944914112, 604766683, 816221230, 581408510, 374436471, 691054992, 527059170, 48758421, 327390156, 760447124, 874371438, 168991479, 936056771, 612435976, 176964718, 211348682, 258628623, 982809811, 345026788, 802414958, 184223985, 377660735, 417996664, 749264138, 212889682, 283907468, 781482414, 882893240, 956084162, 646397275, 881385824, 221670946, 686290619, 219332938, 616126005, 251975416, 457306012, 506102857, 242885264, 284214614, 627769064, 230693506, 21319166, 684930291, 976953267, 492797496, 793551474, 358127325, 103791251, 287222229, 651488472, 947349571, 253053425, 119161217, 543917246, 584297716, 144498180, 193430150, 902826262, 642330345, 711448756, 609612005, 688074427, 374390183, 855110380, 93535335, 70612888, 501142405, 532151590, 367703865, 246165953, 856179679, 294109842, 471455853, 822550416, 394906595, 743543765, 38106170, 162675666, 784039368, 650670158, 406001896, 154578659, 582684240, 704624951, 112883046, 997288652, 279812013, 825891822, 809747393, 242971212, 978281970, 162283308, 737714988, 674497177, 310472730, 896676095, 7014847, 84288054, 242712482, 289575458, 809263598, 856858864, 529960910, 49800761, 430849902, 338619728, 412162393, 674279558, 228829704, 493598293, 72408916, 618719366, 500864299, 651135284, 422713954, 842431228, 484659457, 797099814, 276056919, 121083174, 26261956, 310824857, 625839443, 322904738, 246308821, 745061655, 70333486, 86747571, 949597652, 802571351, 521347897, 513292585, 823793860, 595588217, 601404706, 763544760, 75517740, 35171890, 442417424, 550190239, 88139565, 508089107, 135246017, 8669901, 154816022, 965208461, 843930617, 38240959, 976655499, 107604343, 363576848, 370450938, 46296990, 263039039, 873866788, 649841250, 303172124, 933283070, 401538634, 728577577, 370581325, 438223102, 585688888, 882584477, 219307550, 595553855, 156729914, 386563509, 812112954, 294769598, 222055607, 908649422, 531667197, 380928491, 413871009, 828003922, 685588394, 277949631, 741088474, 700026515, 379288058, 62753302, 291661447, 487637545, 500450573, 808861577, 950787047, 167466493, 454939006, 529040611, 36437670, 237877932, 597303436, 253171749, 271506145, 9462921, 99214672, 533281904, 991514583, 455006025, 375286368, 557187405, 76740385, 431599489, 526337206, 244060653, 904162986, 310593933, 869812043, 583712192, 942814157, 763344151, 771083384, 920495054, 934546350, 447530953, 876483509, 813661041, 4322520, 45295225, 186298891, 682021284, 179949076, 118305553, 363009517, 159856008, 167351084, 756518514, 951064217, 897559130, 95406662, 801960729, 994421723, 240705608, 115273383, 746856118, 248240600, 839038610, 931846789, 253231287, 128720813, 263250487, 544343094, 315256787, 570496601, 730063806, 227803308, 182068972, 419708845, 901868692, 493705064, 739836789, 375243407, 148658385, 68639694, 304712096, 17281405, 519374683, 890805010, 35849691, 567544666, 78821061, 52994419, 115766810, 993050807, 51351414, 599945846, 341297247, 345535360, 418544574, 895369467, 308666287, 383319598, 794627223, 875970425, 651247049, 18595899, 474247629, 892656054, 40761243, 529697181, 325772547, 80325121, 18409740, 240171036, 766037219, 772740007, 364868837, 182965165, 384302698, 561388080, 265511311, 898161321, 246291103, 754354636, 379973430, 329613305, 818589453, 236720955, 23553091, 9932253, 378252552, 254912861, 579450974, 780684963, 907539454, 501097386, 845921484, 532139572, 170628203, 714796676, 705109182, 281893189, 548687121, 461660068, 65737470, 377239209, 980536221, 618531872, 695127763, 691766223, 884060013, 255549143, 406203411, 249753022, 40920662, 855103417, 18953347, 200818061, 847457867, 958835881, 754560685, 936657253, 616015628, 526060227, 915387399, 239983539, 318330396, 373679982, 9444841, 460737962, 779512252, 485142341, 255348988, 732680329, 30973579, 551367238, 533322903, 110482007, 350598013, 626922855, 484885412, 412361243, 367080323, 314044747, 952309294, 467865531, 514165196, 772207120, 955467035, 276276402, 872408959, 721317036, 804319148, 454722900, 674706632, 668470409, 526353728, 827215660, 954324353, 703228518, 221117986, 461162999, 926663717, 706946012, 464108493, 578531316, 428472899, 242422497, 315155060, 928812189, 640640276, 47645752, 978579306, 419832680, 99929831, 824138784, 690279631, 234513328, 249380918, 519360121, 657310192, 532907584, 536914837, 778734322, 760762060, 481241166, 811321578, 185611578, 554963751, 513017647, 786776222, 333400141, 767642860, 934303279, 570232287, 408538582, 145216419, 486247977, 330840061, 569989828, 424057, 692401837, 159877397, 562959494, 270120103, 587437844, 440659102, 205863936, 118740550, 710761476, 957217951, 531377337, 681242760, 985913128, 888584122, 931988877, 566039769, 807380073, 64366178, 83248670, 156862502, 493045996, 298161406, 806340857, 46848173, 861646606, 178129798, 741790981, 114395896, 754880599, 842698824, 409820963, 87907167, 610057743, 135801220, 333665406, 33473000, 631451773, 752932483, 790736056, 757349968, 652166184, 146817114, 158321695, 598066579, 196701356, 982264735, 599202081, 909898156, 813594639, 775235249, 34841629, 424259706, 960353604, 760953256, 242449360, 741085064, 158680777, 842737124, 403283210, 126505414, 122506227, 76093783, 559832666, 865171127, 72605369, 786799391, 162364900, 199360419, 659513050, 342036383, 173925043, 36196354, 651461436, 701522084, 852487301, 297603991, 183477447, 938205146, 72168195, 177416866, 551844881, 139171404, 669801849, 655742386, 201229147, 406276652, 791976016, 520428621, 160607335, 163773414, 362314275, 208623764, 715113825, 874858116, 145702456, 862941546, 517438344, 926624109, 281439624, 434708480, 85739815, 983307157, 896190340, 45538313, 1112283, 950417477, 399621420, 43017426, 318124950, 473264489, 294139005, 71955413, 721961085, 807882748, 804101990, 778615669, 737868279, 962721449, 915666144, 637163029, 348939732, 626537220, 185217384, 526371273, 243982703, 428722948, 621680292, 157006153, 388187046, 748100406, 289201400, 445979358, 849864270, 542913999, 719550391, 274936038, 987972446, 120241828, 360547065, 677699961, 284434244, 154679809, 278159965, 910877490, 483419828, 423110961, 963586421, 470228642, 321591509, 208365460, 441155137, 917845819, 862802388, 536636759, 7551770, 33951591, 308995971, 583693854, 446791978, 251257935, 202245619, 887805673, 975942625, 435554413, 719521468, 242628865, 778151157, 122435315, 442096814, 251712495, 9530670, 80415506, 353140795, 257723090, 593831007, 704597499, 56261553, 940260192, 927729137, 16366877, 461846148, 317039188, 244313787, 667996239, 562378934, 231415353, 818822583, 583153471, 149684859, 810348054, 824825037, 44359382, 491355565, 470575784, 227565090, 229355790, 961912974, 983862211, 738749786, 38627710, 404353964, 352192861, 409204281, 844056339, 897316985, 268188697, 269423565, 193463230, 323422523, 296754900, 357941336, 675414827, 128426050, 226698094, 299356455, 669140252, 274377839, 74070800, 458498010, 153108571, 432900129, 730400920, 159087248, 238215822, 234803160, 35033238, 905989403, 974459499, 621098963, 926127705, 214507535, 771929957, 948186250, 283336522, 252122627, 320234647, 71608032, 133946123, 443917029, 33769953, 968093437, 215210889, 159255697, 814967151, 184130555, 220011713, 536171265, 328411621, 616356417, 56667039, 583897930, 717435641, 95740772, 808460829, 88171114, 685347574, 514506689, 988092848, 479986810, 40536411, 849668630, 939343183, 895169473, 532158639, 355038138, 466417320, 106557820, 942660427, 458454605, 209798628, 726455887, 355860083, 121802461, 60192827, 703491165, 655844672, 188194921, 305620615, 646465031, 740582378, 914455503, 24824306, 52469972, 142000487, 305845048, 534649247, 829911126, 101051375, 921899676, 410876562, 818114745, 735180172, 876696325, 187728751, 104805607, 843756101, 164481807, 929522104, 914883040, 517628466, 414437627, 374101556, 205065143, 822114862, 73106046, 789590032, 930071565, 948515562, 764742223, 445590247, 881254618, 405741805, 673496269, 912001339, 934004146, 767933137, 327828000, 434731625, 823479643, 688660420, 738084020, 774633477, 164325947, 246433467, 333603668, 936232837, 876267833, 798595808, 936968425, 902061235, 954873129, 597732305, 806409226, 94671672, 837211208, 728209283, 955334309, 920178977, 744558705, 534014270, 998130972, 435147928, 193930914, 322153093, 740942865, 705922779, 381777014, 950670937, 744583549, 251579496, 549364646, 317598139, 71417875, 856287515, 643939251, 280563986, 151384423, 823878938, 178042031, 614105112, 185815204, 30889561, 214602558, 703479549, 827119949, 462598351, 264362965, 18710098, 311756894, 887293002, 850997785, 956368221, 624194679, 115383106, 987794536, 956596708, 81360378, 584582246, 403541567, 534419263, 558113207, 126549395, 859073546, 576185303, 648116925, 562317695, 975981229, 901737647, 235125303, 779675974, 785625036, 135729012, 529464219, 186307351, 342264233, 847775556, 775832855, 83637432, 459198402, 603625459, 258971535, 630761552, 970187734, 527321746, 365494020, 733918007, 308258117, 734009071, 778429431, 12014057, 186514062, 725583125, 394943884, 217867877, 474452676, 263469773, 250529960, 292674429, 289687249, 679738115, 150613461, 368625358, 33003442, 735574277, 492849305, 454162183, 48136844, 4371965, 544373150, 716003200, 592434294, 63183668, 782378661, 725414139, 567652120, 232115047, 740148084, 403487557, 619676888, 730615864, 939285587, 197530959, 587042003, 838262736, 151800086, 14289903, 642463302, 463530836, 950221869, 145570441, 996360113, 328677931, 172397903, 928826428, 91587137, 297979301, 277607278, 753521859, 342383631, 938626557, 588628886, 101916003, 298733952, 68282356, 884058173, 485817497, 367986843, 739959333, 277126169, 888787363, 174333752, 34925415, 974236736, 76794443, 918920470, 709897863, 304182886, 68483033, 630101073, 809812377, 940734685, 860414016, 77694641, 378625376, 355881721, 265605966, 64749486, 337004580, 524362235, 625564337, 164346675, 515106828, 803993118, 197934412, 54995419, 683022256, 206880437, 835041626, 454029682, 506949697, 598457262, 976086854, 921621835, 96179571, 813874872, 577365678, 431277249, 685715191, 744997087, 350098437, 172845013, 47544411, 317611190, 5974481, 552147395, 11037920, 132029516, 466933954, 530725215, 488935504, 261884161, 704168525, 60335007, 617654229, 732349363, 568456682, 432175192, 995705108, 564072966, 212025999, 604679939, 384760633, 997688772, 148434460, 293091947, 593524792, 143536251, 239241407, 152661494, 614020038, 856863374, 829881544, 736535867, 783899201, 955855237, 702207271, 655825049, 520753353, 926574090, 280176440, 531859350, 286086230, 654475584, 108925227, 792545370, 637727042, 317626178, 156502094, 714038015, 65342031, 66841191, 273500717, 576685875, 720596377, 477820895, 829323791, 603374008, 280208250, 465470224, 148589809, 108101495, 458151974, 519594273, 395878909, 118099045, 403587185, 204743178, 486927114, 763652130, 885711955, 519770509, 560208862, 351411642, 197465968, 157133609, 774875748, 933544766, 560407189, 801458710, 567058611, 675270159, 383847808, 956854241, 259521614, 406870158, 240032454, 901915509, 186855231, 742415207, 242274657, 959096046, 163319765, 358314433, 666326910, 513017411, 902996236, 118670838, 868541127, 718845814, 746672526, 403102022, 953462348, 839495960, 484887845, 306432870, 33458487, 946875292, 767426018, 651187853, 343150103, 592775930, 668539598, 262499423, 675594229, 821618088, 718521791, 643885619, 979494966, 384834948, 37280488, 517518897, 678364595, 696510042, 567204766, 414636007, 95971199, 640314474, 163909760, 75157691, 819647921, 898139358, 166219609, 622435208, 745280484, 317724165, 940799410, 347193677, 970358612, 769580086, 236303693, 224150731, 655036487, 44546009, 906787027, 451671130, 59892617, 48158270, 641682973, 241697565, 230772827, 809411568, 344115059, 954647591, 712101651, 551684118, 484885139, 764602580, 273009365, 333154511, 895316888, 180479542, 907642959, 399382357, 14264731, 522972253, 323163690, 92836881, 112272943, 657092203, 37078900, 979732006, 772893034, 435270512, 305727027, 669889646, 244180559, 339480992, 458488757, 706890040, 378271219, 802857428, 373504048, 131667616, 248811784, 776539383, 155707458, 369297467, 102353910, 12623269, 93128455, 89277859, 719668570, 913208813, 715763139, 426726923, 93486747, 48746567, 420487773, 765083915, 224119101, 283081311, 429332490, 809151562, 281898991, 880144185, 924612960, 952121065, 74726899, 829716652, 778789659, 793964093, 171254422, 774102855, 577393938, 682956436, 799027767, 603598892, 177573240, 758988736, 521325569, 54389, 849558279, 197449240, 420979185, 165887442, 849243037, 237527000, 859656082, 910089065, 863794942, 896759802, 760187456, 654011007, 993779456, 598059163, 26507790, 644795228, 667628621, 311549812, 816461782, 352403635, 710193047, 497685921, 574177560, 597396727, 105352830, 416185177, 795305062, 532046064, 16386591, 308970338, 661315607, 869855683, 22679204, 783243325, 665726836, 531705740, 736616353, 703975601, 317780795, 577479503, 784640010, 820417412, 996619129, 882199668, 251582170, 562087017, 453168166, 721519090, 723145880, 108237235, 304425717, 191395458, 640004573, 279147704, 466600315, 521032995, 398900302, 713554274, 455031274, 776855083, 678663518, 290694425, 114628984, 849134681, 336675328, 223460308, 49041376, 197460514, 878894743, 332404458, 339203584, 525211902, 763597666, 875054302, 959423203, 65934989, 523206660, 141845340, 867678832, 498673377, 725942255, 836515788, 115916062, 382131722, 644446532, 632876276, 203766625, 962935389, 962220236, 966688176, 593527404, 390819871, 108088800, 496743056, 750822144, 221279839, 894481869, 35249478, 494028126, 553646521, 725808068, 920354045, 260775837, 40238087, 762364230, 823626928, 695093754, 257111848, 754302072, 903092103, 278847282, 261492149, 706305034, 64384447, 415599890, 489964780, 385578820, 502077636, 544454439, 188489711, 658064644, 925508908, 706734840, 702066896, 887652087, 759567181, 817073872, 333890654, 480372521, 560184335, 241038563, 505828954, 665410274, 65529703, 161240881, 266653379, 372967977, 875431530, 595388306, 377651150, 447866565, 739281355, 633080886, 342804302, 986351030, 942688445, 127442542, 400166688, 585304084, 680599574, 486762938, 391667817, 321583307, 483352859, 571439884, 584241766, 649268287, 429395153, 51794678, 542265211, 945413832, 904902134, 281462172, 484890554, 38395377, 364748628, 561334742, 408200372, 889195374, 709098769, 294450139, 358975487, 275056697, 971891006, 353310462, 124671601, 112814546, 456140527, 104303308, 425739669, 147135047, 477139169, 593925044, 242194032, 983539952, 486946373, 356899443, 769752231, 976414479, 910771061, 632830691, 473491463, 269780976, 976289778, 200893426, 683282992, 672589064, 223950925, 11640087, 492382120, 148314825, 607531069, 350657654, 153432165, 267094113, 562344199, 885440473, 276166685, 126421445, 261580745, 666655002, 591541935, 684107303, 643257950, 945082773, 933104692, 933371791, 720614531, 882262297, 206407461, 104484630, 979786002, 919310367, 511896064, 11748098, 81936213, 605635070, 747186390, 364945334, 469524071, 864482894, 315495222, 176562020, 930093507, 161325039, 206217924, 377675417, 470109905, 818798706, 104336754, 638882454, 656493156, 667900349, 25687976, 201224361, 79418487, 836143931, 508498048, 146246699, 584391717, 460967377, 124469255, 427630465, 816269711, 186593358, 246566863, 559486303, 76786236, 166829702, 946884055, 696079233, 34696455, 52132422, 70039888, 773753381, 49172643, 604762053, 253220718, 397475039, 827744120, 455108587, 855366273, 605804893, 916330276, 142935781, 952232776, 560329555, 150035019, 293113109, 886287915, 449949540, 925839963, 574000328, 632815240, 306829756, 489688347, 452002413, 743736095, 627621371, 195036209, 217037922, 499005168, 139305178, 357104653, 183192303, 371641002, 628039937, 295047460, 571351545, 990523662, 919858907, 964294919, 206288094, 66730432, 122647978, 500170464, 624977153, 282736544, 664983934, 286502504, 590334478, 278516021, 888109985, 96098053, 304400121, 136102395, 610488707, 453688400, 251444462, 566704393, 908359008, 506946819, 2257787, 700900168, 711989335, 719425519, 7931397, 459513159, 638369910, 241114997, 262075203, 885677533, 950965070, 329746411, 385962925, 954944053, 151182322, 384229648, 152818565, 57180014, 319773718, 954271419, 591295161, 564157843, 594541013, 554206642, 259994354, 911430988, 493183618, 782573227, 945209374, 477351983, 704177193, 250665392, 10559713, 306067112, 396035650, 701249776, 464281307, 149125797, 383507771, 863010023, 573291608, 786823945, 507371182, 622780976, 596507826, 950845201, 227578766, 219624222, 623862138, 742875465, 715080795, 325694419, 586663229, 873275077, 384253511, 51157628, 996224726, 156218192, 229264136, 927319871, 657320965, 947939591, 490983977, 75750410, 304226475, 447947763, 922115514, 205533897, 598818174, 387486209, 371532163, 10124250, 390433225, 387338278, 720179459, 15836137, 130445295, 730876362, 65982530, 84435624, 54590680, 193018195, 460313454, 106319035, 625228784, 964584018, 541630423, 613455411, 141847256, 218261746, 661431768, 660772375, 862777623, 399315836, 189780167, 548942527, 226970113, 171399455, 966947634, 91324846, 122473943, 781250239, 989269353, 218815265, 96070738, 936728380, 314779960, 223138827, 307584021, 637614595, 981865017, 331794996, 678018954, 295641257, 670632465, 738610102, 174574169, 689102608, 838296460, 813592969, 118159801, 872793884, 282987461, 319291009, 21502469, 575329341, 656790991, 560046448, 865771890, 389123451, 422414767, 908643669, 23465659, 732729752, 578628561, 187328349, 93293274, 20053715, 574948704, 516088591, 793043384, 174481858, 18138981, 411228430, 524286646, 126504775, 583971725, 905342870, 377521892, 731749259, 679715554, 563491876, 239516606, 286725474, 615856637, 535912757, 714708979, 247655396, 212612476, 567867789, 985710546, 112606043, 836339500, 997514108, 266323259, 74230628, 446751451, 388982212, 346822128, 770660671, 982483230, 139853014, 632674196, 60650318, 367871422, 879497744, 379374174, 382546892, 594819486, 435228617, 51537503, 439396286, 57256020, 89008227, 843515744, 318363193, 474492435, 131896424, 912131855, 747749147, 945906737, 118656015, 989575573, 997179946, 180468931, 955970975, 903056864, 722842822, 498700250, 214365046, 834690300, 971494045, 496538688, 364733654, 530372604, 776485011, 134644576, 533615789, 114758393, 999528264, 155735946, 213956323, 474869444, 379296547, 65529981, 830178955, 59923825, 91997235, 265115601, 881758341, 69423903, 229762867, 757860486, 600216247, 213650636, 400131606, 512941130, 805837567, 81718552, 880623625, 274694697, 282920001, 655538855, 71265667, 845777843, 892854262, 624819346, 477302298, 230694951, 969350493, 827270904, 276205153, 802411083, 991085412, 456646734, 324982879, 456189714, 317206809, 466288847, 400268751, 212253577, 343050869, 400932195, 705398329, 976319441, 791264660, 168262714, 192946904, 109616695, 632719563, 200706110, 99138534, 406998799, 171441699, 765191009, 486225529, 407462874, 217980801, 711128178, 503245453, 469165098, 144272784, 996487543, 729822420, 667486770, 148512858, 789622617, 455835192, 657137393, 734991280, 185701017, 705941069, 187830970, 180360398, 598354745, 451064261, 700783119, 361092623, 972895709, 997965812, 341682934, 367973170, 905859374, 243297516, 68690510, 944472193, 822783796, 53010150, 835431925, 486253801, 258733706, 713775306, 777991129, 238075331, 524759581, 302340492, 249336486, 893120949, 403329136, 546164352, 732347992, 647596174, 592691310, 682648666, 342978898, 389156178, 607327435, 964077807, 926942930, 299637281, 817641302, 451076456, 895881308, 552120364, 28886126, 978340406, 359030012, 981661011, 989898029, 972726182, 669074279, 154717489, 247358209, 1567095, 251198378, 670223341, 574941481, 587502321, 886343299, 91921573, 481174315, 470266789, 663662311, 968070692, 827371440, 696292628, 568309077, 75518081, 642404272, 436796959, 295805696, 92972978, 56714605, 660230133, 179324666, 996220499, 326722997, 350211631, 534500170, 110616770, 912320728, 160411527, 607991298, 24008878, 526905479, 778446400, 257996331, 408182380, 774175664, 129523174, 376770415, 340672401, 712849537, 725536276, 121066388, 423463461, 200964968, 260361605, 142261876, 377293696, 890954226, 339059984, 677080094, 726193229, 562734158, 736296318, 217662854, 852106637, 294273590, 629621607, 336352812, 836221174, 49353368, 928330660, 307674657, 342224512, 210979586, 639758196, 660725273, 363905666, 343532459, 532315034, 51468143, 947329737, 759470262, 122220562, 684312995, 425586645, 818749186, 318425101, 151887771, 82597482, 481367594, 180100183, 984139992, 476048124, 465774624, 311756521, 558460356, 571615523, 958471807, 920825316, 316367361, 870491944, 404793783, 134382417, 511229688, 558259997, 104014142, 290706140, 683649089, 68881791, 506410612, 475965870, 821249181, 490171788, 157720730, 188382793, 232289062, 941557039, 346983142, 188022483, 387241926, 305204029, 720996758, 792412612, 983709300, 213242014, 94889974, 163994387, 945325905, 642133418, 540175008, 303387835, 559224204, 268953632, 509234275, 270120043, 221635381, 438847358, 678932527, 838126012, 243506258, 43794464, 776269579, 266166422, 693811795, 378978879, 172645472, 169408809, 762929332, 771094798, 770866182, 986875297, 48933129, 855145245, 192563917, 852071237, 449620950, 550674318, 29758676, 986586796, 247717821, 5004583, 18086875, 835016681, 758011422, 513892748, 813296557, 671217022, 509817786, 382662034, 494828704, 721623705, 557036560, 715238622, 804173106, 532884614, 433303867, 37247159, 260098694, 720822637, 4392390, 405191129, 888177745, 381609400, 890698274, 152653467, 354137624, 850007133, 315993039, 754312586, 123516728, 415902041, 317092309, 123751014, 931638019, 973027623, 35425412, 421975578, 339647515, 333060999, 921437701, 454370103, 514224288, 620277896, 614708320, 264099489, 74559083, 58403566, 278336398, 805984663, 878337100, 222064315, 898014792, 71873259, 486926150, 394120279, 646943052, 822638107, 608911308, 321259759, 585105111, 108912146, 863250184, 34423217, 663775007, 880247622, 576577422, 71725923, 654879997, 444425178, 916336627, 523429723, 807323311, 317693028, 438821251, 236113337, 595507065, 538543853, 951227371, 909323957, 732788597, 249394477, 665420894, 555338614, 811380444, 668757089, 739278856, 274659300, 928878152, 844793511, 924048993, 591031272, 601890462, 336450193, 172469526, 809872767, 414479515, 116984280, 536484107, 412777791, 63443203, 143720746, 657918773, 434733980, 173582554, 833727106, 170311413, 423568308, 353902282, 368627321, 887295564, 168747502, 27597089, 949621007, 114308930, 364341486, 267931581, 238332638, 301369045, 210848559, 7204561, 426336978, 900702606, 463895372, 874456767, 1808154, 92128493, 153907722, 414643146, 993886985, 336218089, 622622149, 574944274, 476831135, 225553314, 636064631, 901478671, 932441965, 148513322, 276693944, 695842581, 331181188, 82804097, 846359493, 359842833, 964803664, 302289167, 463125434, 695428621, 475675462, 856901458, 268107925, 533634498, 496919658, 68756071, 607987817, 404532247, 428803354, 340891206, 597541204, 973460477, 435707904, 606207778, 62354152, 700574856, 994984486, 91119732, 337579548, 853811862, 194664538, 800822703, 837873409, 418191555, 308524054, 805641382, 649971975, 56058547, 994712455, 459967619, 408162655, 292282372, 524406554, 194093632, 138796626, 698005554, 54701274, 225626011, 805665144, 643020417, 996616831, 711271331, 833694280, 532682775, 820254764, 764309148, 734160205, 76739998, 144180889, 17061684, 552608786, 973876721, 691855726, 285838342, 210278856, 881594848, 808420601, 390147594, 318434390, 549425437, 786521963, 387332901, 617804340, 90556746, 16934989, 328635464, 288087360, 395497637, 115291885, 79644554, 177180205, 824063133, 776348546, 142966529, 57266687, 565862316, 98388696, 877453169, 316748887, 853832365, 562253547, 787985848, 988333849, 38611611, 719457005, 313440781, 246830379, 90410612, 867751382, 471449881, 197129739, 750390218, 573880508, 141955116, 468044047, 408756299, 939862562, 71042185, 982229035, 195632441, 647978488, 367100677, 565759614, 12149647, 972360395, 489315973, 460562189, 205338945, 236080501, 991768978, 388835129, 533452914, 175421574, 322620195, 670192688, 887466050, 675881634, 964272413, 139769490, 877619271, 918030149, 775752121, 727606156, 680489212, 334526212, 773386569, 163194271, 198453696, 831207914, 238036346, 458986615, 530758581, 40051236, 83802839, 759692055, 605274772, 779922898, 14816567, 239526214, 939153265, 123386377, 405302514, 48450935, 844585211, 496707034, 982354970, 645656689, 727163077, 957368776, 184273411, 855663945, 73759488, 972262008, 56399106, 666744847, 551528024, 773203407, 645536635, 976305586, 787466797, 198329086, 366458506, 912369721, 648748175, 810162237, 20770936, 857362559, 563333405, 635838840, 731464859, 127798218, 988776058, 278764253, 164853061, 794792429, 934410560, 858112786, 106344815, 12944883, 96970870, 844053229, 540290924, 654049225, 782655379, 68491279, 387132817, 678604063, 611069337, 419226644, 989075591, 900735416, 998007687, 213847245, 402137097, 482779016, 366724404, 422207436, 97362978, 805150462, 418630771, 422002970, 242366780, 213393403, 632461599, 811679276, 485947882, 163030813, 708161842, 404702953, 137359656, 538905387, 505013529, 556529353, 564792178, 163191280, 637630282, 104817617, 340622339, 807825892, 454025716, 572386899, 55533747, 15135584, 233438761, 702365210, 585062790, 408183380, 429712654, 501034318, 714456212, 37818011, 668438498, 729839940, 458483728, 676450485, 370197555, 779711623, 873381189, 249647304, 882525905, 87404187, 363591103, 547492629, 869718678, 230480690, 84370016, 889494105, 588548273, 335867460, 950675514, 186509953, 782419800, 830070978, 645422701, 381870221, 486413809, 241520057, 196715836, 946472728, 132343659, 808283780, 461310013, 58423391, 672398716, 228677875, 874841154, 222926594, 204812213, 470191151, 822482699, 466938122, 386662605, 719403737, 10019658, 811593303, 319290272, 175884145, 342302352, 497154088, 746825338, 545416993, 313202223, 495119654, 109031387, 715115255, 771770331, 700564287, 374454631, 216957814, 883318291, 137409098, 302176011, 262200195, 700602625, 177619610, 434798980, 829807714, 651703459, 680415371, 945931808, 444679827, 245568533, 737310817, 96798350, 198423492, 297448676, 785013481, 423594203, 460398744, 169220257, 232670425, 212057835, 640331314, 71155197, 829977434, 146082212, 663540970, 41530322, 965092379, 871364842, 954677707, 86025994, 184454184, 483913926, 61217277, 120802877, 323790721, 746861262, 538386074, 802896098, 50477979, 859908790, 452493309, 432006792, 183813844, 717833918, 937032458, 492071352, 638524265, 162567983, 518015488, 992163021, 476110775, 182320197, 198041722, 467858964, 307665964, 224214954, 479314979, 714378843, 189926771, 356355999, 939210931, 436985088, 988689696, 798467438, 140424887, 723285233, 57430619, 443918776, 413259592, 850802215, 401109379, 401966101, 210746460, 744051858, 468908025, 909130898, 269361972, 524330934, 239392636, 222601765, 594274990, 978154143, 463937512, 902748928, 568345797, 986269911, 759551437, 862872179, 921014787, 391001153, 244295444, 60054154, 57536832, 761477879, 999950259, 861366959, 975177410, 530573948, 903617857, 166680933, 82458450, 415247299, 566883257, 165801, 584193133, 610343579, 322956872, 183953895, 866578174, 966239445, 294854283, 431928608, 130814367, 581324267, 630346170, 157311480, 674185636, 536948984, 233675564, 850191416, 887907459, 598702181, 333865741, 145950979, 327227660, 154980713, 750401422, 285814142, 281660377, 240736940, 516058103, 368535165, 287268639, 207662910, 957106969, 363864838, 32743033, 422766766, 907095953, 722295275, 317800741, 415315369, 951050076, 446422553, 316338188, 530843702, 937367661, 306940406, 13605024, 859731505, 79517406, 160262395, 38966296, 248378390, 977379237, 661750454, 62270266, 826663391, 746922682, 715720637, 428163407, 676925386, 349496208, 514822916, 871328685, 579445949, 351352009, 62870808, 935849362, 577271074, 726479865, 875948936, 429930801, 900077986, 687584396, 237184088, 899405602, 553126069, 289344494, 82372007, 672401865, 52499822, 458191831, 631281497, 533631641, 60903350, 280805548, 291629434, 330719837, 291666842, 685611336, 47720339, 215148617, 539476427, 62866834, 73368946, 323304464, 574095154, 272689952, 790158135, 692139774, 112268124, 306323259, 271301793, 526967500, 271379567, 247999442, 4310199, 602436379, 485283794, 321051955, 712579788, 568946043, 352965662, 184457963, 510721099, 112387897, 386142754, 121268352, 993478869, 581434590, 557215616, 889566030, 369440148, 743045533, 830107369, 490319283, 804840910, 6419180, 959945396, 190614911, 444278912, 424589218, 977907001, 854525719, 610694612, 681362815, 368200300, 684828514, 450942926, 514029875, 913849655, 851306301, 673317426, 559407571, 638727600, 385822892, 104721048, 475832743, 405816550, 803070000, 603927207, 635092947, 343478431, 665162793, 756201078, 54799913, 998138231, 743075914, 730375930, 814393170, 728232261, 62044653, 749501841, 415427038, 513028142, 249417179, 407489793, 8834419, 763455232, 575579214, 336172053, 664149160, 552764934, 368989298, 869381235, 245760504, 559601798, 459411092, 128521566, 105948064, 822503862, 28182710, 425804549, 296216902, 783985669, 738287529, 245216367, 205671521, 219292492, 417375923, 88060995, 221789467, 103643152, 97007674, 946405, 547224805, 375118476, 106191758, 19985374, 728029622, 798077597, 598195072, 932201935, 741122904, 387694757, 677287916, 195375494, 874040994, 454154459, 32085124, 349686963, 164908756, 814292456, 592063801, 788139179, 537873054, 827359417, 801913924, 597757325, 48010650, 837545334, 819126990, 855957844, 85007013, 572464285, 548926678, 725367000, 116115369, 512413926, 342314126, 968581504, 52547535, 772240546, 383799947, 585911059, 282867863, 700287741, 549921260, 532655537, 138258764, 432791725, 357752860, 940644567, 704421017, 168261924, 605897316, 432426039, 374132771, 610045010, 447019469, 243162073, 975979616, 97008845, 719608588, 353366225, 787500224, 593440073, 47629185, 434626138, 512744854, 251118508, 623122670, 11094260, 169645830, 528048638, 566621041, 381884160, 773486573, 94360158, 82760880, 463204505, 422480116, 167581376, 783857268, 661271465, 909522961, 659253075, 326023500, 371004541, 262730988, 680953610, 432595175, 231244248, 546215018, 84259289, 504556555, 219654290, 195501912, 307052632, 418356154, 329362376, 669865795, 439812306, 860016622, 74360913, 332152235, 807622082, 443082613, 508234766, 528623685, 402633623, 740506255, 852911932, 867133523, 163157266, 736508791, 708896062, 803882785, 272961421, 643298792, 748868096, 319073360, 454788453, 682479981, 957887577, 596018191, 905769375, 434845080, 962708802, 377896464, 63166324, 331744668, 109860589, 779815618, 372429780, 910941329, 945187623, 53099201, 41645261, 579844663, 248498587, 35411060, 771965983, 250289077, 425512707, 931649263, 890365559, 782715791, 10368292, 380281668, 586461314, 880299475, 246702094, 378895698, 441890601, 615160867, 785072999, 167198517, 681651389, 502261139, 30492505, 524230436, 913121407, 772694165, 657502740, 940222153, 698531638, 46485602, 252280180, 324826643, 931927926, 78078388, 70692540, 143551684, 525801083, 954362043, 359272479, 744807174, 641495624, 876453513, 543179161, 153134709, 12259712, 968845964, 597240007, 31447396, 409096573, 944256961, 877583951, 550958411, 722863008, 851332097, 224362744, 252506815, 403259766, 652995660, 435785420, 259996738, 31630275, 243228613, 806375772, 558952114, 972753138, 231295310, 113272882, 604453865, 98227579, 674278659, 813750494, 413117764, 859130011, 3094164, 700511972, 918203760, 254260806, 225253062, 388047763, 603269028, 990381164, 877610281, 509735984, 430443935, 431244873, 590767225, 713929682, 422487228, 491005288, 566600838, 833917760, 247484487, 532852586, 108413801, 796282761, 895608902, 178139895, 332713512, 396607835, 479071664, 737810377, 230357708, 860724198, 374069142, 683885075, 736271585, 742340049, 765103134, 490733760, 107248094, 752467299, 182445563, 283010196, 11062589, 506855704, 590475623, 290446001, 823104265, 751959050, 311126747, 702020617, 681859438, 30558111, 105667063, 927741330, 111720908, 818645528, 134266315, 384625240, 677050185, 189406663, 201602163, 105957159, 986615719, 154010121, 302506315, 307468237, 812304523, 336152959, 601709125, 369094842, 96879803, 830015342, 106907980, 848035832, 295227574, 347856849, 77376250, 561500158, 931648827, 246873453, 291259566, 428365077, 324972831, 285458643, 50159839, 191645091, 143728999, 778599734, 588716423, 443187210, 599923028, 992771172, 349106695, 404138926, 368557161, 688753223, 26034686, 701430935, 862852355, 972599532, 422698371, 192374540, 573769308, 325972876, 813485907, 851640889, 635276925, 502404213, 96179126, 456985364, 551501026, 601050839, 69426017, 667030460, 89824047, 667102356, 120093951, 870892374, 726981505, 108139288, 136729659, 889892456, 244753859, 987401415, 853379828, 974191889, 800906583, 134679303, 421788470, 867918010, 143563227, 964397993, 565126020, 226026569, 62692353, 104691804, 805197861, 173075132, 97404202, 829426454, 50324380, 918363521, 310504710, 509605502, 350244463, 951401051, 376989234, 518184902, 303172756, 495588178, 361007044, 24635485, 294855537, 639718699, 967944739, 976231398, 628763772, 213951682, 67461587, 649856532, 799086632, 716188892, 606553555, 235114409, 867987903, 264412700, 550362495, 510639510, 863680262, 233822549, 388386883, 420317888, 787391491, 928913176, 514811533, 654051267, 413908611, 527521048, 252867047, 861700693, 35599428, 988081535, 756954055, 611533857, 353887235, 564100042, 485056490, 591079944, 7488448, 858550074, 772857673, 241404324, 576037379, 671266486, 261450768, 380180467, 707952724, 44254078, 568914479, 982957896, 274160953, 925263072, 90424024, 562462113, 600363674, 59281989, 149189899, 113649739, 114946011, 887845366, 942669589, 312934106, 541110202, 456583701, 379685084, 160441356, 237412712, 180052990, 991433915, 252223453, 770942710, 953963047, 444569309, 394568426, 56514351, 344954175, 499818526, 147024029, 188856377, 565284449, 433806778, 676122119, 872126020, 483218092, 206931404, 357612144, 239681416, 782030071, 582677173, 782489823, 799898864, 200420270, 191167074, 302929200, 13508807, 536523068, 896911056, 479245690, 299601953, 110864590, 678443411, 728343594, 213045007, 340473408, 298365386, 135715419, 223447964, 282418027, 704213012, 218754678, 811914173, 651968236, 867149977, 78036033, 959634982, 375879259, 681801680, 699468176, 349579714, 283253986, 497982948, 292378715, 380733629, 536251555, 828774089, 41097237, 111292987, 559373928, 70406845, 158131274, 524111767, 31941572, 174423976, 274804747, 151276996, 395139115, 869010220, 151647672, 189547143, 480510360, 867878088, 962238125, 29103961, 658988924, 178611180, 360128378, 444676885, 148703598, 300236085, 957832620, 412576911, 626520094, 797871906, 405118863, 453891060, 488281388, 498404409, 743210762, 459379063, 21916561, 483794779, 233305318, 678633939, 971440356, 984905924, 690037836, 69224950, 351413268, 604690700, 398599242, 106068461, 482059240, 579282034, 807349159, 7362140, 679296297, 901627025, 66161952, 500198323, 582569585, 851237895, 666396035, 871355894, 248644389, 100185132, 283526771, 832099900, 424143063, 230260260, 724009961, 976142116, 274933527, 954529713, 521582576, 595681626, 79439440, 585208603, 394282014, 26915106, 283855753, 387608944, 52402357, 483491500, 518832740, 686299637, 610949725, 91868083, 489845622, 111425070, 516378689, 303075289, 199102939, 12716760, 947414396, 890441873, 491342929, 718441104, 13613602, 268558954, 223343842, 594275398, 275874225, 560524867, 682620926, 304430968, 321573489, 127376203, 95283016, 543026665, 394584916, 978809985, 631421061, 744216506, 975696451, 848393873, 969476195, 430417725, 600848444, 297716251, 871415526, 568144481, 544544993, 130774489, 169340200, 27784490, 94244094, 887330586, 256467142, 793709155, 615068257, 518484366, 195164923, 187728695, 538328592, 386249009, 632218824, 154085776, 696731548, 446853727, 157284584, 59664445, 456769260, 33467294, 8134763, 579133049, 771838356, 999125855, 33180418, 567762676, 415230602, 534411830, 329789307, 323840712, 439776468, 36135493, 924663349, 40237295, 651759500, 186686129, 5859494, 841522649, 486869804, 330183205, 252128448, 219337107, 650205142, 155080169, 449912497, 605410196, 183023867, 266334854, 754687107, 617556850, 503699120, 573580158, 448547684, 167200757, 795629199, 383040004, 165807453, 322767276, 426624352, 309741672, 915632670, 653962559, 309835615, 625860991, 261881652, 685311721, 670236104, 422976723, 970224587, 665776583, 378479495, 283769222, 526648452, 304356747, 95099547, 735483291, 481510622, 225044746, 22449856, 639091996, 324694637, 986616893, 401462979, 794686388, 504208634, 128313269, 234617362, 512561470, 262606860, 699238481, 589454310, 654586686, 711344197, 604766517, 515605241, 913431003, 467625107, 721522378, 854529151, 452467351, 695810422, 92826777, 888559728, 391763995, 679312867, 738018492, 652047638, 494374661, 566200043, 983753820, 748295216, 926959528, 527881778, 662185194, 504953369, 927031371, 679263469, 67822409, 923337735, 770184721, 466522329, 955269672, 448142536, 530382572, 595726765, 646767702, 381910356, 301590949, 788378854, 200689880, 798988118, 604078480, 499238874, 79103449, 74586534, 38260451, 447934820, 964733949, 503133409, 155259969, 431236182, 73670836, 235958999, 300958992, 325503025, 90694630, 47754827, 276215982, 65496606, 14738333, 570963709, 124708353, 599634703, 493573360, 256037880, 939230502, 488578050, 151313999, 880379235, 919441769, 3910909, 970598464, 442881139, 121056434, 446195333, 962045360, 169610698, 676329764, 67675944, 503986522, 258149920, 941413137, 832453943, 181903759, 991119510, 351916838, 253260870, 208551606, 732327269, 218828594, 249363392, 547597227, 557113148, 980508161, 267275594, 916714265, 137356924, 627119829, 137458419, 472368566, 160199259, 759742708, 247822677, 945952695, 327604062, 82137680, 705136950, 755533808, 646485035, 389527410, 946900939, 450870082, 403031267, 317564199, 445860142, 434063437, 447922794, 388057478, 318665589, 641170231, 75425619, 918536352, 248323417, 587065077, 941526476, 618107024, 537306087, 878909894, 514382603, 261058736, 152633683, 565655159, 383019115, 403529583, 319349417, 231704298, 569401610, 483841004, 589404682, 923000532, 747243516, 242683865, 272718847, 334320714, 616497255, 922421868, 662758242, 474953226, 401788580, 176989543, 836627602, 855800690, 412280930, 667716402, 952230068, 501357166, 339610696, 576477753, 220462838, 875406870, 713634432, 38025135, 155186518, 107005045, 447178699, 820697383, 875844343, 995582121, 673836818, 821133860, 390911629, 218390267, 187598631, 509515014, 900717977, 928611831, 868490977, 466379996, 337163581, 843362162, 435637787, 472794434, 283116222, 613086290, 651054712, 701348621, 861604014, 734512669, 282061580, 577444592, 293503211, 468482893, 364729149, 392662118, 623948258, 46455521, 651182072, 991867625, 682062868, 876781970, 273658458, 45448422, 824761474, 643057457, 608444358, 743625706, 386514843, 720593676, 441037089, 152548801, 364608114, 869691, 247386823, 286796381, 541902242, 558160211, 898582961, 847306280, 489382302, 714606110, 853433458, 877617333, 988949306, 663594240, 480214018, 713648496, 620813608, 459155124, 742118271, 103832884, 376061463, 4915750, 665612771, 97207552, 417886128, 134338274, 475428382, 73608071, 735521452, 241663428, 462161644, 103177277, 566354564, 451900567, 87749221, 105981094, 702345569, 141824179, 175115134, 931320465, 611912525, 88789578, 165234443, 768738451, 905989656, 111456350, 777538523, 309730680, 308330795, 379026751, 932578725, 910335919, 625817232, 598606493, 71788901, 464978102, 711022637, 534482620, 635806559, 705584519, 823449810, 588846434, 69565655, 274281303, 17768884, 698588528, 190263584, 823300283, 235142147, 378820305, 858139810, 940065141, 486405933, 268668095, 973646968, 146312986, 620440452, 25709842, 256542819, 903786187, 956748457, 433417515, 747024625, 532157355, 886561729, 550287627, 884423739, 468564473, 40824135, 654600518, 30354327, 32264664, 299463565, 420349838, 584390039, 926058296, 483315897, 359292871, 88737691, 820885183, 399326998, 609104707, 281668450, 509585438, 896475554, 46825493, 468175916, 93146429, 75149704, 663945520, 844992600, 747199150, 381976042, 567887089, 790146181, 499682098, 188354601, 368394039, 461814082, 618525622, 208568799, 634902128, 842504461, 631065971, 328232174, 787092377, 762373467, 738156109, 610773471, 847517091, 823071944, 812936080, 985907183, 874637884, 409199912, 6778537, 639827695, 15414877, 490871172, 440502471, 459501128, 703075592, 951217217, 435403924, 680905235, 52572693, 811611071, 384472809, 552480571, 419707062, 864430119, 267693063, 33125960, 23424146, 79183057, 971115026, 67647480, 428309109, 846555598, 889238181, 338857109, 988031387, 726461916, 575892930, 550148611, 156133494, 686994614, 959336912, 265870310, 471241316, 766481714, 738318595, 489724425, 558965445, 406224990, 675731134, 584984429, 532072331, 456677628, 543944643, 207642517, 481843579, 766686819, 62673231, 684746266, 296614473, 987936672, 19519947, 157030240, 305477145, 690719276, 650432460, 999877674, 449013119, 711616514, 738457598, 582792279, 161408407, 921045761, 700203709, 113771659, 912181014, 660629709, 180668993, 34831689, 733854275, 220090215, 379314949, 529604791, 454984012, 380711321, 273495668, 853109795, 458562207, 444750756, 581879175, 151301155, 403012540, 936429416, 859800328, 517159323, 969294440, 748569252, 46502979, 655932216, 400917819, 247759804, 585079863, 885366759, 325462567, 629681970, 537328364, 862317211, 708162533, 873574985, 600419684, 568432517, 816089667, 855717697, 756100362, 382269211, 415798304, 505172088, 678463704, 826181259, 168654032, 283228072, 678106381, 978914852, 230076371, 505058053, 434198823, 492078513, 824859141, 499215027, 557034704, 855729777, 592654519, 963416576, 866329149, 781467615, 198456441, 297385850, 572084703, 578073592, 545800232, 763320005, 728353116, 647863503, 485365707, 565388682, 837752668, 904290666, 291597032, 506093193, 929407324, 412268093, 669021757, 728326381, 369543892, 659123072, 794111656, 550725265, 145324131, 895969177, 666036436, 137411881, 960174420, 489544997, 499370634, 332541091, 446995581, 586162909, 943801876, 612369162, 675278068, 947459680, 730978686, 823701539, 860368525, 624502675, 285808357, 194205621, 263041954, 34235256, 66196927, 300211725, 145089385, 150906829, 381059146, 318695029, 137424165, 784538743, 98258913, 739126686, 986631644, 473616305, 837142890, 779861176, 904128869, 324858944, 765990009, 753193367, 234404703, 2018552, 891090340, 49318523, 719988975, 14791816, 951676131, 599780206, 222436151, 266653993, 641223270, 320173432, 584031640, 444357784, 298383769, 780372614, 342652106, 555327977, 131851970, 175194347, 741304901, 251582985, 342156324, 345796243, 605906087, 352421040, 230253366, 993235257, 1969693, 281474188, 111016296, 824690716, 894944977, 482038080, 636320156, 790578990, 502396837, 523840788, 349748619, 972128524, 701054830, 337786421, 875171484, 822916241, 286921120, 561846284, 613580799, 484573305, 993610851, 872196940, 333242067, 349937096, 849906783, 49908089, 743533372, 658266306, 386639072, 586011970, 842935939, 342371414, 393986007, 575207498, 168604948, 214304006, 907795244, 248420370, 363625364, 827514166, 221096498, 966836689, 971929622, 418585743, 706739447, 425853724, 900128790, 900733193, 30543942, 734187883, 394415880, 544856894, 569566671, 103290435, 70580858, 59711808, 710032977, 249851645, 337334402, 461705316, 92329528, 366911765, 334796049, 567192930, 791923255, 720232864, 343679461, 262185886, 554970574, 254142664, 913079752, 814761387, 888735188, 520983618, 455389107, 431755676, 798174929, 259893423, 64405313, 7243084, 925615955, 842598743, 902785203, 846361742, 122749378, 180632462, 708810233, 812366622, 233173292, 131033349, 112196428, 304306776, 645307287, 570759260, 60834827, 116662236, 899219934, 757525569, 766719924, 588649303, 570844993, 51002503, 604170753, 591132281, 378547274, 146049476, 183819447, 913955497, 550078327, 559529384, 24905873, 647073766, 198415512, 719343295, 508295435, 400409892, 760265724, 94184038, 539214553, 991847031, 485747217, 399102641, 664971753, 991477592, 108275119, 561147043, 562040342, 621779645, 785938050, 739144722, 615225248, 994805428, 394487930, 894037259, 923682240, 43004805, 369479471, 919077148, 639980054, 626703243, 454692327, 976087245, 707307036, 400626082, 124955200, 851810788, 669003450, 810519571, 883995293, 213845740, 236095867, 179602456, 855296527, 455118220, 510528471, 35108972, 843937697, 329008005, 971054715, 737705562, 348582493, 693737258, 603275003, 902089194, 103543926, 777539873, 153241748, 956580036, 761807478, 539430966, 480418983, 65363229, 460487854, 40743548, 454671158, 972206433, 908974449, 322315503, 110268610, 686926985, 177133879, 335037877, 161075744, 474092329, 754030143, 801772724, 817148787, 674611573, 758240652, 461913824, 821388309, 787212142, 118920323, 698116007, 704100039, 136795407, 366183003, 985541015, 497120673, 343162110, 58858634, 328193124, 59333140, 505457807, 370925360, 887102724, 590207630, 995904364, 978227184, 128533219, 361116492, 927416478, 287046958, 334598404, 826567560, 766380956, 387399293, 610040213, 67889025, 500279753, 221039914, 761947924, 290590030, 357294274, 762258931, 463085570, 104944345, 53891189, 816753000, 652028847, 76693454, 807361377, 774642291, 386368608, 429808163, 305491914, 612238657, 860079063, 157182675, 766764369, 164551872, 798878302, 7676265, 427862487, 418784890, 696961656, 986449456, 628464644, 606692017, 863966009, 213796025, 350494043, 754629315, 457740603, 465408182, 155366244, 434162926, 166266940, 544697861, 455817159, 745621596, 116214986, 407037763, 37510297, 659103718, 947206768, 380146779, 178441882, 588810473, 910702477, 742100513, 506398900, 78948914, 148915085, 586726661, 94511150, 89416212, 669066166, 176452143, 814622632, 610142321, 143581589, 806938583, 106132945, 575441670, 810768819, 940699304, 279715288, 210603555, 655719558, 623234413, 531189354, 679465713, 962245112, 117956501, 42536699, 10175078, 441359588, 260534326, 73271918, 9934085, 726983284, 493505781, 694158561, 39742021, 404208445, 778428736, 197940120, 568628378, 127094494, 117983659, 159874068, 796861743, 186406357, 463133716, 413252565, 65007814, 676083694, 356659794, 551966221, 15387105, 567542672, 477316217, 520316086, 964023870, 331846008, 960616796, 994028705, 656053807, 143840958, 710032805, 859406265, 266078336, 87538504, 713379627, 851373517, 12465574, 578822303, 534153334, 743297876, 678474482, 574120829, 351800460, 306688009, 840029909, 325463859, 795813923, 766224438, 453029252, 784640243, 102097305, 667580443, 964021748, 703999087, 846300429, 800326353, 450701585, 234612325, 138453683, 528583114, 410123543, 435580382, 20901999, 167906042, 282080030, 474304373, 247547544, 115326016, 26372501, 651823049, 414152575, 808294514, 839236603, 51990413, 947148583, 268282871, 172462538, 715353239, 87015120, 623803143, 398092712, 768985006, 63174591, 598850834, 920479944, 390740505, 476732193, 168503448, 76253371, 434259097, 308079295, 380666113, 671126536, 120376766, 778453294, 758731887, 719045564, 802583270, 171667173, 91649316, 112540254, 921161700, 419910330, 965984748, 703849834, 402194578, 319564218, 833790073, 862772637, 13973749, 295506953, 560192226, 241845300, 459016554, 284424176, 495322860, 908548077, 453250224, 549830587, 101519816, 316306680, 4297274, 477591933, 929962688, 687356969, 704176315, 570802613, 192540473, 876244597, 2352570, 161476919, 849719649, 326532826, 914425547, 304260255, 705752182, 191928536, 818243490, 48026838, 751112307, 727240325, 14192232, 305402925, 698844691, 499796875, 761261339, 92939287, 322481627, 393009167, 554761352, 363499340, 938467278, 213523609, 408615979, 969704197, 999792740, 871268387, 960925764, 965551046, 744832839, 489557826, 597085985, 474378523, 880102871, 909535741, 599457438, 692812284, 346285099, 623217380, 501353328, 56899865, 636911947, 738219084, 70134573, 527461049, 106559068, 810111463, 208249045, 924396426, 561698898, 684186001, 462551659, 626727259, 601653983, 961752476, 194549712, 404788333, 383369236, 741701702, 123955592, 179934961, 273323873, 262253410, 370068399, 589383282, 118500823, 225341612, 114207638, 324748608, 353578569, 400723274, 485376116, 155237963, 416915063, 801437726, 926540916, 873433287, 980821313, 32012835, 409561044, 126219618, 130251090, 231497075, 775502207, 48683846, 676215637, 20165694, 109965397, 983224952, 930484600, 736322146, 908251788, 933599195, 357570996, 193187040, 981127519, 279774120, 24542801, 418039497, 599573216, 281940477, 445646172, 288693840, 98193540, 599139456, 37471004, 644669251, 807518813, 63138917, 582451650, 767067766, 783088986, 33248852, 244162103, 774330124, 995667619, 578111063, 345500715, 184658013, 566535159, 999106421, 746817361, 289654502, 950468044, 439475067, 746402749, 298074927, 590414146, 190468335, 541570670, 847385340, 590407191, 670118320, 434966136, 430797375, 764314557, 569495540, 139367547, 116201815, 626245134, 309618198, 130055973, 100416415, 573457213, 678091931, 244142167, 324520935, 755759385, 641620088, 548111354, 789034994, 288527047, 695926502, 739586343, 820328226, 933287844, 20797880, 335199579, 380319210, 435632491, 944033827, 564667116, 460531104, 44054348, 527896444, 7651123, 65919309, 813049872, 516541406, 741169518, 387004322, 565924865, 680072669, 399151257, 716301105, 166297630, 954483141, 755689683, 880992351, 830736318, 582944143, 830408622, 349102087, 938381719, 305397575, 579727518, 75458779, 601566722, 969806471, 468843697, 959576032, 362248172, 937378584, 7807180, 732124825, 729049850, 220189016, 559158857, 139651929, 1463412, 63171720, 285623426, 604091081, 56228109, 916158069, 315683725, 431421794, 381203992, 695736713, 423822025, 179242122, 814611460, 32896558, 509381281, 485614243, 834665169, 404153196, 117447196, 280830851, 84815114, 155386312, 1329059, 367109128, 866577119, 136010953, 843735615, 649702963, 636104388, 790151515, 513602221, 39418187, 907639117, 943447839, 931904679, 459274839, 597337805, 362097618, 525459536, 95379158, 312513417, 321117234, 767943294, 253133714, 667804728, 700176654, 324244555, 70142379, 228916152, 887835813, 895075926, 482060838, 398579272, 991435210, 637972955, 546930296, 92598921, 367636733, 899317402, 139931578, 191792528, 622050078, 472161889, 12990656, 782876033, 867037140, 64108588, 788425697, 284655044, 339114067, 973071478, 841539100, 363056050, 70597670, 359364937, 494640469, 546357925, 579039900, 240903677, 93629298, 640438653, 441368826, 901699704, 600858681, 808182921, 556126971, 823332898, 407742352, 495276847, 336011469, 814144096, 489300362, 994186836, 123258915, 754640406, 673725403, 536401347, 392476048, 492359725, 842458229, 428737161, 403418619, 134564446, 747843565, 774234013, 905143115, 509512978, 27540945, 402786805, 699152761, 189284580, 280401553, 613188750, 746867896, 751684378, 588480054, 199861508, 256800902, 595750656, 749939986, 35376617, 309394126, 299074763, 112880695, 120490986, 21072336, 679537329, 950081033, 379636076, 187372636, 412874225, 637481275, 717934761, 322908379, 531009794, 241289814, 621709486, 624372339, 571733658, 482766056, 310218859, 23866849, 76783484, 324268685, 644079303, 354946735, 678367543, 559769159, 978098509, 658309176, 736161886, 399717784, 370905484, 166566210, 858575674, 148885655, 737161300, 902104899, 61635611, 917081504, 436469173, 585869534, 719837919, 549464893, 829727570, 995533162, 541997907, 262144445, 547275155, 886195719, 957193337, 293479774, 479676865, 696098435, 959507792, 848520788, 440126476, 24473989, 120738889, 944157022, 285504747, 377028055, 194837927, 198891834, 872631411, 827040694, 14375858, 942532076, 659457233, 224378233, 499869537, 177114504, 978257617, 401684550, 429446992, 169546692, 269008166, 70767055, 470591578, 900298047, 135460987, 896423477, 284015191, 273262409, 517269787, 908210616, 940902190, 881078390, 85810042, 152864765, 314285346, 535486758, 733577043, 911357131, 358407621, 470238691, 624161928, 867739423, 701486904, 660337017, 418806455, 567425082, 529003838, 380512038, 693293983, 925608375, 512643488, 777674221, 950965174, 872827677, 243168775, 170114437, 734220766, 234947022, 260363344, 186253978, 282406891, 138494753, 811380047, 341470523, 344712208, 575150361, 882071547, 696314909, 960055551, 954436743, 614902137, 770152008, 906808679, 376065057, 477866428, 164279933, 339858387, 27691811, 90944574, 581132438, 304106063, 468235382, 240100618, 769105562, 981533962, 447615421, 88733927, 672034535, 116989791, 971859441, 808556584, 53640331, 574280584, 755610974, 840111086, 200862065, 678605080, 265399357, 938896489, 125408770, 667150480, 531751640, 135611975, 865790609, 484354978, 969106335, 762215342, 257085675, 11285334, 997304190, 576683819, 345234604, 615205268, 413720835, 808213612, 254999251, 521958774, 568185130, 92450161, 896903685, 372989939, 314453410, 128946272, 682811172, 927013764, 535038161, 743948205, 315857009, 23522915, 495408157, 382101413, 229315293, 667522338, 431301704, 907099926, 750818505, 907662608, 563437251, 606436150, 106906060, 268092662, 513804138, 193586474, 868146365, 680632439, 606411606, 394903405, 29973001, 332338915, 841426986, 141387984, 285691568, 811860049, 806602229, 578777525, 95815635, 161227109, 781428350, 854231576, 23801469, 864543917, 660887189, 451422782, 447030518, 910119326, 917932506, 475366017, 935026767, 913608001, 914595264, 449377033, 335530279, 341705115, 780979229, 350318685, 607278383, 698400202, 183352745, 146902547, 209548942, 610663784, 79801766, 538978216, 653239336, 107219187, 545020881, 224076956, 695982056, 87742618, 94365928, 634077828, 320742547, 550941190, 469387268, 434859837, 940940804, 678957866, 292955728, 329439289, 94333042, 278345457, 858243016, 74726194, 707721520, 460110807, 217500722, 697201353, 795924739, 135379576, 792132830, 53506081, 706117293, 751706013, 13821647, 268379239, 773264196, 572233715, 345962374, 716098664, 72810058, 115219508, 179713996, 690826061, 126084203, 382374368, 882749945, 37956358, 564365236, 614338288, 613764357, 870679107, 12376425, 168434382, 794883417, 488056334, 862867100, 483242104, 798763634, 721936784, 652827822, 511234568, 991313962, 79140652, 163227445, 689075505, 917194787, 117585392, 375780557, 420134621, 995608505, 798731199, 680162805, 614884880, 350354175, 181150062, 163607923, 917382585, 176456828, 89327578, 521373805, 549586811, 216272104, 135100940, 947323154, 867350206, 41188893, 573046386, 946791505, 737285722, 851727591, 689375699, 534315589, 611844035, 446036068, 452111465, 521643701, 65655139, 182732508, 608619692, 884164679, 897328400, 939740721, 640284550, 129663799, 346629938, 161006562, 123514654, 73507542, 249804843, 579365570, 509414053, 479731659, 382623671, 549406959, 690637795, 936974505, 518249911, 702440353, 241327875, 94487395, 659213063, 364141193, 243045103, 578343799, 90598353, 693862614, 983711303, 879863798, 390540956, 776748405, 674755168, 874775359, 22358214, 383571817, 834573462, 202108645, 81895939, 415855937, 761978991, 357768787, 332015400, 133849785, 785665519, 915741652, 675535506, 679326274, 643261894, 799176595, 358801654, 254640771, 283314552, 138850237, 471569068, 366538759, 985425824, 768587513, 610910698, 199488999, 353683990, 333592392, 290093053, 347299647, 469809681, 289830084, 162542430, 722732867, 628682119, 775480858, 349673218, 737763604, 831456733, 120341430, 215910959, 437991797, 485179003, 189904315, 993488642, 36042255, 812412062, 687118595, 8529421, 768249810, 93681710, 450102893, 220249566, 561932576, 169299630, 947933781, 335971708, 580505579, 550004833, 888462212, 359737857, 64376312, 469536041, 384547572, 107557034, 42644741, 297017776, 413152195, 78478474, 952214320, 477744252, 813747780, 132255987, 161829348, 51395914, 901969386, 192423700, 735070215, 314285496, 698468829, 465062496, 861228192, 338475080, 855228061, 7736550, 934883368, 508063109, 58713890, 191762703, 874026144, 670369127, 949152258, 100652616, 70548221, 310182480, 157702151, 999901689, 548105805, 859470440, 579517283, 358825649, 405116740, 626337972, 757382508, 144011680, 165795269, 802556541, 340161889, 348015914, 682784533, 828490878, 428968986, 418113468, 637393553, 725411757, 13548659, 362002690, 429139847, 348425250, 636322451, 582945143, 897321660, 529631104, 336098411, 496137528, 164900465, 423320754, 477961501, 44668908, 907418977, 728521159, 770626710, 920403638, 464417063, 508792848, 949424450, 99488635, 512629612, 240454553, 138726665, 226789679, 800938679, 488849372, 842984090, 44553005, 810902200, 732552831, 418376353, 436075160, 551854637, 503048867, 781633304, 993667788, 780584657, 784130396, 971831539, 35883327, 838669367, 951033573, 425174345, 203787818, 272580377, 835152899, 659034237, 36823633, 641793367, 632956764, 823884054, 746580290, 998096688, 911347749, 180845138, 200892512, 698676843, 260582752, 781079496, 590866381, 847850621, 196339713, 235713193, 757107442, 37552046, 167733476, 611061364, 994160845, 114415537, 84032915, 510959365, 280434308, 708916667, 161522109, 626460847, 85718917, 488828165, 808300872, 689398226, 410369573, 533763623, 170665233, 189016958, 729258720, 601032042, 750293129, 61096412, 917156571, 605066142, 85245862, 319848822, 321989965, 398103189, 162872728, 809066465, 757736168, 747591753, 389342377, 731672491, 578597716, 822517095, 549043907, 921753308, 443769688, 974365820, 390535126, 926832445, 120005023, 198612333, 525325127, 21124145, 345706697, 9949073, 402937373, 766685574, 388561793, 205766771, 447559887, 713710589, 84994391, 228434413, 253076567, 791207126, 552949391, 470286388, 239810609, 195885326, 197262441, 360996238, 803692993, 309023825, 693184435, 514528489, 827644232, 521273537, 157062220, 296252043, 822305091, 93250131, 403128828, 68675526, 769506427, 430238302, 794917917, 865151044, 953878432, 829424565, 806377546, 587299019, 966406670, 825700067, 264091256, 669930195, 398745721, 953747710, 157996010, 636403663, 838793796, 413445528, 687120921, 347176692, 792674522, 497887644, 556105482, 693861498, 513225677, 528589901, 860579475, 818839821, 487675286, 641146471, 158289303, 299790514, 393753590, 360355601, 466599199, 189591000, 535342059, 257048285, 159358611, 303460437, 367009393, 107551280, 421802038, 297118767, 152328438, 256688902, 914518734, 293475987, 869694362, 925004238, 766442796, 965016738, 848633193, 81050153, 300223426, 723891521, 322205414, 30423389, 758738292, 736517899, 452398732, 928965970, 858472706, 196618652, 247368082, 503402430, 698541649, 531774140, 938504533, 258381977, 587161825, 651529965, 206866593, 276307788, 870862953, 601650796, 568705991, 959896655, 982318309, 751186916, 20394769, 552104856, 49397896, 681478899, 115561957, 351365976, 30071065, 139587736, 715132944, 59899336, 350346619, 629660394, 680783567, 214138596, 788304478, 633150380, 469816614, 457406363, 625545515, 903216180, 665051278, 642997589, 963713795, 855939978, 74276671, 533230858, 178066839, 873459340, 561979550, 13331900, 634708693, 407080402, 323626175, 109595601, 188416641, 624172863, 663529773, 357165096, 538752918, 784784445, 594702965, 408656949, 176619623, 655379714, 453094052, 547583652, 185417500, 726595904, 543910805, 852072328, 968804941, 643541495, 923068653, 452598273, 829456043, 428641607, 850563715, 597047854, 482823291, 1986615, 101204923, 378072579, 634574291, 637365552, 847106000, 493365606, 631533530, 111286574, 892647978, 238382878, 820756891, 501273955, 247702653, 382115093, 420056588, 327563650, 774521635, 515066110, 226885318, 194380511, 984328133, 101462064, 60518522, 246131197, 507711586, 244974205, 777347035, 338072534, 242046448, 79045400, 318533274, 156356531, 261624662, 259403816, 661948138, 713106738, 341719040, 224307127, 207270668, 157940434, 281630398, 754900757, 188795228, 769040774, 25210163, 1866727, 419429022, 730155411, 85808304, 403759992, 556554461, 363182733, 694802732, 127461591, 405909971, 220415838, 643861437, 643684255, 49551252, 955604605, 589191119, 877864876, 841940222, 331290771, 339286015, 547248592, 680542299, 576764655, 337413066, 407647185, 691349584, 643035896, 439645541, 396047842, 549822685, 60081770, 4885345, 50686509, 179634422, 454774638, 35230731, 11058983, 857288037, 690275019, 335615786, 712340163, 436006593, 786515029, 639614649, 397311159, 972303772, 955031943, 442870665, 827744871, 7385499, 730258113, 654128782, 318070324, 770494456, 769241501, 256060216, 981842064, 698911814, 625627534, 760379056, 500499598, 967728579, 875587635, 484546148, 389717277, 807986249, 61768244, 937259428, 595592663, 608010707, 572194041, 606739403, 100542012, 52159143, 842341025, 638608345, 313796167, 470528491, 424848364, 461290502, 570020439, 626638211, 540488914, 350767983, 637427765, 626931714, 55361867, 905746813, 485376282, 224138883, 131484680, 650338724, 881099674, 26557555, 756219949, 333921261, 854779915, 652001474, 255775201, 861991627, 809320052, 203069067, 716077623, 905649538, 64678528, 959847429, 826314670, 449237136, 120389110, 192995523, 57281810, 204247889, 774800231, 473626491, 940608, 224857472, 13348333, 731593203, 772223976, 291449826, 119440279, 633537740, 309441463, 245992735, 388501055, 294202968, 735861114, 874938575, 742759489, 817000849, 454395691, 83264021, 197552580, 553167034, 427793695, 73394659, 351279521, 573711696, 183277880, 625796567, 682528352, 316545931, 76174860, 428676574, 188341959, 595079274, 464627925, 528659317, 364936675, 735352767, 326908931, 588436185, 901951792, 855485568, 319534836, 977956492, 859048557, 420977603, 53582065, 756846398, 279916768, 381674156, 381413761, 415864789, 936478592, 104412598, 309355501, 357919716, 40964196, 21584807, 601728699, 745147675, 204856002, 92635426, 761962462, 1942547, 820774103, 14861187, 269583266, 164156948, 724729398, 373786991, 326181959, 816273998, 549198235, 38279490, 870364591, 299709420, 549500468, 834220798, 349876246, 91445236, 518195064, 13434468, 337562150, 41805838, 126527149, 51050452, 964491228, 575567480, 134262383, 310993420, 317131613, 848908283, 223914060, 240451185, 498214996, 317790406, 866305505, 908477731, 652923035, 248051645, 703255713, 507823328, 537735965, 890737910, 103279416, 328446033, 985433585, 632440012, 519269640, 478605651, 942314833, 806787724, 709677464, 784521440, 502252073, 727135012, 687648214, 442299062, 615531491, 989502491, 390163500, 425447090, 287631688, 432235208, 735938202, 696264953, 636590969, 249569588, 286774297, 760009888, 436827026, 723194067, 480007887, 681399783, 202740575, 899688664, 556058674, 891898584, 748123783, 405465272, 407741421, 466621124, 172309120, 774403291, 961944585, 592405473, 467298547, 853383847, 941978152, 893300255, 620687369, 30839037, 352770182, 323976612, 520835469, 706003761, 574409077, 169133868, 945874789, 434698843, 405803923, 521639085, 73707186, 99240304, 967522279, 825059784, 222954018, 196779355, 184824774, 99522019, 326451190, 293519204, 671855378, 28764564, 153668719, 654665941, 381945801, 116621366, 183713898, 664863552, 107002452, 667375954, 417029343, 697735377, 216936739, 591451202, 869520514, 645231415, 258130042, 925293341, 381249108, 740694206, 206869671, 545012688, 299161892, 617746985, 480850909, 463773429, 205654231, 496659825, 984231702, 822439359, 838260886, 76822065, 866733944, 314972206, 448823460, 351830395, 881465901, 756325779, 965114158, 335362984, 29834908, 466593162, 59164478, 183879299, 238863544, 41605134, 813603804, 878653717, 610770413, 184228362, 216341402, 375448108, 636458846, 770577601, 644626290, 404446022, 101018315, 552553220, 30105501, 17394695, 462532140, 651548338, 510483511, 421638119, 662435694, 42502735, 756582540, 257586193, 1120856, 299442172, 846095275, 884920547, 52191460, 815226793, 86101301, 22703951, 806685882, 860505256, 400668135, 190554048, 355990246, 238986754, 731767318, 183358634, 420481201, 272673260, 647645097, 215410417, 797356287, 651070455, 244978850, 714449227, 182150862, 714744241, 837805117, 453238590, 952955294, 415591901, 67705919, 567062673, 614226777, 28324755, 391773113, 358402249, 199528943, 621010078, 204821371, 158010766, 995981778, 824814812, 573821004, 987384412, 697117950, 21810646, 157263348, 602181950, 42212843, 780492129, 677076333, 567631483, 951928214, 678632466, 745187481, 944049415, 722570609, 31692486, 748365174, 70597322, 360698118, 999477667, 999623181, 765129745, 81984627, 799846627, 6052048, 468346676, 413093862, 438955516, 935250007, 854924495, 196020289, 345402354, 559528841, 646906903, 897692032, 166948615, 255819755, 124726623, 898212259, 625751524, 954171620, 923731864, 348854930, 245872142, 235150186, 161440713, 744723326, 683903602, 447172834, 268223520, 476030877, 604620590, 324388620, 78732012, 941526750, 7493642, 170215645, 549190057, 618558139, 790407029, 825905118, 139316406, 21430402, 955531943, 193384917, 247030879, 815397728, 439635568, 422197954, 348005127, 185400353, 696873564, 518322974, 902133451, 116211698, 349127787, 340508421, 915965026, 487662374, 884233003, 823298880, 17512240, 84406226, 890615591, 865267167, 604283314, 254801352, 805296851, 298910890, 911728361, 918359488, 418680928, 596406212, 241470439, 571501938, 269776317, 859794168, 817962378, 482400590, 870646933, 725326923, 64827121, 837655454, 74307807, 494278614, 453054338, 307221158, 807983520, 979804374, 958278003, 712582424, 77659347, 202008235, 360233855, 902976981, 443300704, 32601444, 683298649, 277301826, 400389898, 647484184, 316379672, 105884113, 849961529, 794697910, 996518209, 181467390, 905116426, 635563891, 124493246, 223739341, 778040499, 589924308, 88203762, 861723630, 139852258, 799117365, 593646089, 286390349, 668617052, 641880867, 852910779, 704487390, 410436273, 170828481, 300519316, 164830587, 550310190, 785571164, 515854907, 169529477, 94657699, 626232561, 616493450, 662799039, 535079643, 479967197, 282492320, 591402845, 295153195, 356681586, 355540432, 459626601, 133188119, 396482749, 178283259, 552832654, 449983996, 217460395, 746851968, 257124923, 495687830, 405330539, 943979909, 569314072, 348741175, 445790424, 426425461, 812415823, 373113859, 648625232, 323649560, 717971412, 508128002, 684143970, 684894619, 943251705, 353026981, 934003226, 963917732, 845494080, 187195396, 67510256, 749102773, 983731203, 793982308, 565363347, 661434929, 285118853, 530731415, 595942855, 566621540, 207724688, 63778788, 368453951, 666504136, 402971260, 261100035, 982027923, 142821207, 730819813, 802334156, 239515079, 654215244, 488790154, 872739367, 848804878, 214573678, 420060371, 370133908, 636281155, 707747597, 350758953, 629642806, 490543288, 870981091, 993781203, 678003313, 213295192, 386317842, 764992044, 99068162, 911615970, 56288790, 723673829, 118175837, 66203249, 872679598, 221827199, 705666830, 759131658, 461146682, 535628211, 177757143, 614537836, 206340788, 914621301, 251295314, 65201599, 595527269, 948960412, 258392481, 420867790, 141651288, 884833983, 25376583, 641429607, 447336962, 226608234, 672745827, 299559484, 365884605, 437242125, 863893737, 437601286, 154345172, 681864582, 41077535, 493008373, 331338726, 533888521, 359072508, 66647170, 697300059, 780522963, 410854724, 535420603, 403088422, 452040112, 238050015, 563056444, 84422239, 312439908, 659293756, 474660926, 731297508, 296456749, 601753030, 38097459, 75449987, 89081386, 309459657, 793655534, 834882344, 770027384, 993982708, 731462191, 542155109, 955301608, 100736504, 725832879, 811787170, 708506823, 82290325, 516609376, 167515743, 795620762, 892909073, 460790121, 930327207, 929740875, 586030266, 569297038, 728696756, 786978436, 386346956, 935499785, 119598238, 546795687, 388091327, 468041255, 305051712, 201926418, 258335880, 791379428, 937858705, 119576645, 850751491, 170073556, 87811692, 853232848, 859171186, 950999820, 988599284, 916675203, 107047129, 373167657, 715060300, 874895022, 546471259, 251447810, 773293686, 740245499, 294668424, 189622522, 777450492, 565953524, 93868385, 398804669, 253188147, 222557214, 649358746, 908108667, 912255850, 615921829, 201474062, 192987479, 362394321, 58441155, 88223718, 874483960, 628014592, 962289441, 163385815, 708857398, 809191891, 866445040, 397903745, 983473644, 402241624, 828792145, 486596400, 559587476, 118370443, 348603309, 966883568, 18832078, 882909634, 299623094, 201001266, 549855166, 446064608, 927454286, 721649964, 263384516, 489301635, 490149406, 407361119, 294828795, 805228392, 357399330, 865570098, 615893508, 402982092, 237427321, 427169299, 629400991, 158704132, 668050172, 334475571, 33044653, 338937952, 993744503, 130325132, 814317635, 610759951, 264649186, 748838775, 223878670, 392482284, 635614465, 737961407, 529358376, 40569051, 687273491, 104821368, 970442312, 511678973, 687201125, 647451501, 81545610, 577143112, 21352551, 289136454, 932192977, 862009622, 513073827, 324994475, 997768798, 384931040, 612362579, 935970488, 969580199, 564009628, 449684679, 508115807, 995217219, 137926574, 875838, 746776608, 845361793, 264431007, 65771898, 111094216, 376216731, 887107839, 348982427, 643239556, 558353955, 914246203, 364842510, 231662968, 614826001, 334097430, 249464628, 435587383, 703981914, 249150630, 673502830, 450434060, 75242863, 431832606, 779735110, 66525468, 418286519, 687317763, 529225040, 816243581, 960509130, 499660210, 33841660, 991925104, 889416294, 533442087, 663175676, 718665176, 708847948, 614539213, 234965634, 112852141, 351482105, 832271554, 544950470, 959164750, 164797156, 466443387, 64837782, 530635696, 881416619, 881953601, 298341641, 710538, 210957201, 542877794, 728265041, 192582118, 405769326, 782441828, 680232586, 137265680, 234058360, 269340739, 378189525, 50760879, 940926474, 811087380, 352693930, 365609301, 633493528, 581002602, 54807765, 509955028, 9717398, 521024770, 71555321, 308381735, 452347982, 807264948, 743143340, 624227361, 905902175, 307338869, 266317631, 269951747, 187089974, 165207846, 345022355, 429425690, 312036865, 435928981, 502335405, 283890247, 287137777, 57517898, 599517561, 375655146, 863017980, 476518045, 242146776, 968092120, 547030188, 944465553, 131255512, 24416377, 254044389, 27746910, 666994139, 897738149, 372079735, 477768531, 607598911, 756223245, 577641394, 476449419, 292125690, 995512346, 478436449, 732357130, 181795980, 822786917, 721908181, 11638156, 57110056, 92301093, 849998922, 987470243, 761282106, 781743430, 83240174, 372913455, 500034957, 829088729, 81412915, 676930845, 190676278, 90268180, 272121322, 386362265, 573545795, 672064573, 346582784, 648847965, 833543399, 895147244, 697062775, 745934085, 211258423, 87874342, 198966368, 485916659, 837616954, 802264239, 817153251, 20066946, 674628906, 457594135, 476108039, 790843552, 221717758, 93183170, 515191374, 641067873, 977920322, 861993442, 39954598, 90302687, 92950441, 22716925, 896355875, 286603447, 222348982, 452913621, 786497472, 663687048, 661058210, 352169058, 927399381, 883684554, 536411055, 314569678, 264898228, 997748824, 566238113, 400382602, 822568438, 787125147, 422038355, 113326691, 718140328, 268292764, 783032651, 517884825, 35479189, 944057781, 63163324, 150928674, 223537025, 915418679, 478282252, 812868516, 179652820, 156745736, 842559433, 890400142, 835460258, 102642454, 336437874, 374840362, 241590919, 138497942, 871296897, 494769491, 969111084, 331841604, 331281274, 479256783, 359044995, 123894304, 728943460, 21169780, 416441296, 310762961, 266626659, 578540207, 792745873, 283886915, 709856079, 355357976, 884750802, 292463515, 318123905, 610712921, 493840386, 333691994, 671148244, 146589535, 869892464, 191850076, 579549964, 43475329, 432200920, 24292317, 558339244, 731656332, 994386812, 599595585, 73153628, 23808289, 193257072, 463418980, 950658287, 843689224, 55726030, 189286443, 104900285, 321100852, 416779643, 420983660, 432560635, 424511022, 102631877, 142954956, 622379660, 477373132, 83126060, 619590981, 310435279, 329029244, 545463241, 263895751, 745227508, 548394391, 273287013, 211182312, 523893355, 342134792, 60323578, 787960930, 957963285, 415894351, 480474271, 39937509, 575189254, 669374958, 968094784, 547552992, 858847361, 667452881, 281871376, 163826094, 510884493, 954650183, 947669366, 50296031, 620295390, 676469969, 491971703, 799707091, 577189390, 533890926, 289047434, 160130012, 135880570, 47611469, 205903845, 374156995, 175352630, 786663697, 811184709, 669071438, 120812354, 592516269, 464179584, 496219092, 819482897, 149826, 834561728, 360348495, 415898783, 874589754, 272300199, 577836254, 733936039, 185619139, 258588542, 336550260, 330050257, 993850159, 895112162, 122655187, 638121265, 446489750, 217034251, 14000894, 471375648, 264013044, 633207826, 475102954, 731243149, 538400443, 674447007, 519714318, 132424151, 451262994, 581274178, 132132220, 868504934, 773056353, 292831174, 109554198, 218795782, 133977113, 764110893, 437633544, 753765546, 960749520, 492705857, 475089306, 125296608, 874795965, 910174584, 433585047, 683077291, 793491455, 480475855, 838906714, 315895210, 587750029, 624683692, 458105748, 368045077, 631559501, 55626372, 119613622, 518392998, 107077433, 580050306, 157010649, 452346915, 290972855, 797180856, 642803651, 78861598, 410299541, 676339401, 609428236, 529899442, 107930697, 896460612, 643692798, 685310721, 78143919, 305661872, 567281944, 355533221, 601633797, 731257558, 904482032, 621752597, 281613384, 975054439, 595804854, 133558746, 662307231, 408399836, 335443417, 292310620, 790240786, 923007248, 963960720, 143459535, 373738661, 770154283, 681835186, 685061352, 905923434, 364877070, 557307237, 64918172, 928395802, 417383317, 597488685, 501882731, 191843314, 669660295, 694188187, 488382343, 958488595, 570151466, 627306890, 843506122, 652692384, 951788617, 227108822, 270705232, 116927678, 214282671, 660713160, 737415375, 649443440, 105518385, 887892388, 121290394, 744091652, 202059305, 629066638, 15248679, 80635262, 10129406, 471937663, 675663164, 941214445, 568850960, 391948828, 974991748, 388887006, 591474058, 868642298, 760461398, 612635114, 410281975, 468319238, 242571514, 293037455, 901659583, 177673801, 157032141, 570494763, 951081458, 791488299, 607269806, 196521820, 13028193, 786192772, 666243968, 669056077, 134871770, 357027376, 270541314, 706978469, 191091842, 394562, 642474268, 433505198, 700652574, 15354129, 698273743, 762674082, 90624117, 562501204, 494702268, 654764373, 930310624, 688592943, 468379023, 436049988, 939204784, 6530753, 514825246, 487790274, 198797955, 553933198, 528620934, 773430805, 837755737, 391007660, 632532295, 761891675, 150092795, 381368940, 318991230, 171025072, 845562953, 730725629, 484730114, 603293301, 315529891, 563655244, 759901611, 874116945, 57938538, 114771320, 765461586, 626932627, 710921135, 644784826, 86042666, 137278669, 83361654, 995964643, 926456340, 909280831, 928452094, 154656350, 21134999, 438211404, 704898417, 877415759, 127540641, 250620110, 804887431, 287654435, 770356823, 135561708, 970622941, 715418108, 436001010, 404439384, 285331260, 763985492, 358583576, 81914602, 810188066, 850445794, 971868069, 807230530, 463848052, 864504373, 562647675, 663400509, 185958221, 729360437, 367263221, 683916250, 965886033, 482807872, 831468009, 277306046, 798406773, 923997682, 901009575, 129268485, 842744251, 854262137, 397322924, 572531462, 553275116, 178952502, 425000487, 30656773, 716222745, 782806760, 223738316, 307156465, 546301665, 34747332, 983207427, 446760138, 19063006, 251226809, 339004060, 578091948, 738293391, 188562820, 218720029, 493013997, 236525971, 471837947, 896092249, 541262630, 657866345, 412641154, 877499764, 676687754, 20946553, 725506496, 179760451, 677960508, 767526241, 272464941, 723208292, 418785985, 645692978, 772527166, 64512562, 701943177, 735147988, 464201129, 672096903, 523978270, 302739430, 702352268, 956226739, 853744807, 601800954, 429775483, 302195939, 403098076, 946103790, 647765396, 958815717, 724798259, 313844636, 334318383, 360680037, 2061090, 798117832, 300817477, 353877021, 871744128, 988669104, 792651874, 86512063, 379759269, 774950713, 323678935, 430910761, 254592656, 317173052, 927947213, 712193956, 291985166, 338105252, 71800003, 50341887, 716403861, 670889109, 987200169, 684733263, 741264568, 751010811, 454250587, 137178579, 624078895, 438595107, 759615112, 754699154, 431710698, 576281792, 750443356, 41483759, 270981464, 319460153, 826811633, 273976076, 83341164, 854777148, 436448978, 575354680, 974115490, 569844915, 766294145, 378962412, 361616819, 440680357, 64187451, 337382004, 833062494, 441846476, 157484985, 552415012, 515661682, 626058226, 693849619, 374053100, 640756661, 139050982, 257178186, 274742761, 562122980, 805007554, 487931242, 958571550, 628889036, 718537940, 980204217, 418184612, 40399852, 416859409, 157870920, 765425759, 551526252, 617064916, 995107430, 286895937, 457565676, 657249525, 491344066, 649811719, 821511820, 416599311, 669512085, 554766925, 956593690, 983458172, 90990257, 333150211, 64283379, 24469475, 433292533, 778359767, 899080160, 905192624, 817510956, 401406437, 529411953, 214099599, 166660819, 265658323, 26813526, 977312081, 70889095, 235613772, 813073025, 5618071, 228643598, 833240330, 607812331, 164983524, 214399518, 928440313, 868067104, 315385065, 554387895, 157948515, 606775793, 760770743, 769162754, 877587914, 7774152, 7435486, 662408372, 348924930, 258591288, 975976107, 47897164, 210586480, 232349428, 845800257, 432247724, 933767689, 154733781, 480545675, 679863681, 656975482, 499633189, 984350878, 228601524, 29922699, 637836072, 770639004, 381478937, 92169866, 807321359, 867416585, 701645679, 240185285, 562359027, 370303786, 176836115, 300201500, 59522069, 111006542, 944176246, 691163989, 412196690, 754263748, 443437086, 961809391, 947745991, 427954887, 749270821, 704944212, 597971956, 884659575, 389240365, 704854353, 928655728, 690567056, 272675145, 552333625, 197195349, 251867375, 443389522, 698191959, 305568431, 576399440, 261128024, 728895785, 823396379, 509847676, 976331384, 963180665, 48525314, 309623821, 923180047, 77199751, 582866991, 710144196, 50500759, 52743915, 982099393, 195620625, 405815325, 868401873, 336709152, 709687310, 665566146, 301508781, 579356845, 555495768, 898419305, 856607270, 458608773, 475966907, 303602865, 860265298, 648514527, 246234031, 838773220, 223639309, 18549294, 947052788, 643107995, 312196267, 825188550, 164820723, 270995346, 820904731, 723942066, 808953407, 599764702, 626516253, 318850163, 506742940, 180558837, 983897664, 264391, 682261908, 528161276, 553996973, 672358721, 859184329, 671139888, 132256043, 418878605, 180884989, 255762396, 108799393, 216622377, 639362489, 320679022, 620301200, 817862365, 73539363, 309126805, 267246959, 228729277, 56015486, 735242545, 937683125, 514479349, 978730922, 426539184, 238391222, 568436311, 626427868, 685853562, 738031463, 983684284, 89130836, 728076735, 516368709, 120827997, 548325659, 324866115, 522712735, 62470303, 537559197, 557300356, 934414758, 387716446, 759645631, 770673358, 303655540, 75097143, 265709865, 159903686, 392966307, 829498418, 745647466, 749254045, 646495089, 763707743, 164367566, 680657696, 412854443, 564543987, 90637367, 476159695, 376359552, 656116363, 228436955, 308256470, 502213541, 381142232, 214743447, 924201669, 78770513, 35192569, 587451154, 129014820, 239733475, 85276129, 329932595, 282263208, 499168227, 230673733, 768055604, 695690661, 630475731, 220345679, 520850288, 355730165, 822751393, 119315243, 637584096, 804635523, 125723704, 993338767, 534706595, 626227568, 129394665, 933096485, 675614175, 528012254, 528829764, 440356699, 861620640, 800570790, 474536658, 572553330, 456018997, 770426851, 257097265, 120855013, 613808747, 186425409, 193379232, 777107268, 87760798, 172447934, 632791583, 794504621, 775507241, 568513299, 85889541, 94645910, 381612925, 339421605, 788197974, 87242643, 749224336, 702341321, 932525404, 692065248, 905364761, 469232743, 901631336, 157028677, 654336264, 754060682, 31378041, 433981990, 134806524, 450429820, 332507924, 965868757, 704973519, 578736630, 121175574, 217441261, 357802894, 416718303, 651287470, 271826232, 361013289, 515375746, 550840777, 575142297, 79452488, 194833805, 378537188, 478810809, 393993587, 352460233, 294921782, 235215229, 853171295, 241866480, 831768803, 172136107, 33457120, 474905737, 129031101, 567950290, 153504067, 338823888, 319798907, 170467449, 19961707, 628457446, 188999691, 72299454, 511911967, 741613504, 920446432, 305785003, 754075144, 88848820, 68653229, 850025767, 447973432, 509195717, 384195112, 350775823, 400191910, 189368300, 738340611, 29238337, 120990980, 739495296, 783067611, 506751270, 789944625, 499363333, 774686812, 568852585, 207383033, 146185968, 678750209, 84831626, 560681006, 66076541, 499746387, 588246736, 166190490, 277755270, 363383669, 699064161, 662034583, 578325095, 812931644, 739647188, 164794106, 443969266, 215550455, 981166585, 330453478, 724789723, 615488304, 453463376, 2070371, 932412374, 59326196, 830444363, 447671647, 88240155, 382165641, 123782909, 793603213, 394214310, 809516842, 746342753, 365953881, 715766783, 980297287, 945668379, 802367388, 620607905, 874994999, 334489774, 679090361, 526259593, 238380034, 631112746, 818755364, 817148816, 485987029, 211499843, 63848296, 828794563, 155693687, 655730978, 156583225, 30968629, 69539646, 541665059, 331063865, 820811078, 865160957, 787270456, 333354266, 253557198, 190838252, 725001830, 240579638, 258011269, 964012313, 702574204, 378989479, 189374945, 145372992, 131641654, 841867535, 658488353, 779330400, 544694757, 114583305, 866204967, 827068725, 100770317, 710033869, 768708024, 701958239, 746547016, 323144478, 882972776, 414994744, 514812430, 731318627, 40617318, 74997752, 850396485, 782670477, 405241392, 524078426, 526938691, 617624754, 797753001, 408285259, 764596161, 598974966, 205542371, 276590592, 125503640, 143306851, 727055448, 389701112, 713180217, 48576593, 91709946, 56250850, 944810540, 242415272, 919659701, 822059745, 743090178, 762423598, 380285506, 523838421, 853246105, 340517917, 740144783, 37582462, 9229653, 817668189, 516410136, 525423270, 652885243, 365469500, 108282810, 50796708, 772605448, 477267927, 304509581, 472399243, 390492548, 734730768, 834399943, 400571697, 795142052, 807807303, 797922871, 260619428, 454133868, 145035139, 356117145, 847036660, 853778140, 303013438, 611694832, 652947404, 552372237, 135955387, 294188084, 696199456, 211608499, 166693975, 720450779, 607763608, 283202868, 951750590, 613964580, 207703526, 388212826, 348259036, 890213780, 246383242, 757050714, 830807191, 740006335, 613084832, 794458747, 818208460, 447915125, 473442687, 384057193, 910066830, 998487408, 69560391, 56847170, 643190245, 747077656, 332447026, 94075813, 561271042, 765222756, 330595912, 241283819, 750696172, 833877887, 341347216, 589373837, 447747922, 466719938, 286501838, 415157405, 654323175, 339406409, 694699051, 740171585, 340701794, 341947345, 500777718, 267610730, 919930709, 436667296, 24737943, 167094743, 640102068, 246259531, 573000117, 315299327, 536261878, 813573916, 65177949, 950279972, 820455868, 11599820, 435261814, 716812237, 956836295, 323568640, 241366397, 963495805, 127701176, 762541479, 615028171, 752788501, 823037906, 535372959, 385635106, 941936765, 318492717, 906391237, 785422647, 518134527, 787851504, 409102412, 39661327, 893090327, 493629644, 393201140, 618250836, 674692266, 388949077, 357859741, 673349140, 130821281, 552431869, 682941580, 776818990, 830456594, 571540892, 557365895, 271083551, 569902777, 295687509, 421540897, 412008793, 838523779, 390644604, 326196112, 922133105, 768081750, 891832047, 479048029, 663935615, 227745053, 220025048, 269045687, 353428895, 631663339, 114347252, 916950203, 264040959, 30253368, 346399737, 548830616, 496868496, 552711987, 116460721, 418887541, 344223934, 153831484, 710695126, 71384069, 180529339, 461483144, 940538449, 973861150, 255801366, 59765487, 864272275, 740423831, 42050439, 951967505, 504112793, 47731860, 176674232, 991339871, 266543875, 339820313, 731818878, 594834983, 4232530, 542317995, 359657200, 898200644, 636109328, 968503921, 875234670, 192146770, 442374890, 648519369, 755991595, 293296620, 895802621, 224497175, 917251986, 82018717, 793558114, 178713476, 578505896, 944636983, 72635932, 558066699, 691552885, 114797461, 206504307, 469539168, 541946627, 173464713, 432691088, 706226817, 142594280, 415117581, 804383853, 277002786, 496767343, 49241848, 738120105, 660826332, 489747157, 619556203, 693661936, 982104718, 301246684, 67291404, 145435718, 347119917, 75356399, 826771875, 736754953, 909241257, 482099288, 302243390, 514153785, 930001605, 452239107, 740712008, 696123907, 688364320, 622207635, 224353619, 185647226, 320094234, 871637084, 836218802, 592431428, 976226949, 254769093, 840691108, 939013398, 757170812, 49920838, 461621542, 473655048, 946427983, 945983065, 190769907, 501401760, 798174723, 601062662, 718030365, 197453090, 121162742, 737954930, 8834615, 66246298, 960354104, 669008526, 277585720, 84372118, 268150528, 736902085, 627948284, 949265932, 692552235, 443631945, 426175261, 406093711, 227739831, 569276031, 603168124, 847264773, 46771623, 440960572, 146935725, 47566620, 974152036, 116642530, 482593735, 392417265, 882243715, 615450320, 414988271, 2683349, 206210938, 252986277, 971556828, 450765916, 94338953, 783564849, 45777331, 314889374, 993437809, 444149648, 863650596, 259688741, 54993000, 511577082, 641380806, 485724663, 844553945, 35047955, 161530303, 197715767, 701642456, 361862667, 275478806, 411810330, 373094668, 197505874, 76494714, 394072504, 775781758, 718173692, 691782715, 97774777, 503721370, 635471307, 800040117, 125790047, 441886482, 439997603, 362781875, 560173444, 226771493, 357597773, 158841958, 775624462, 850108805, 138028998, 872086520, 411647263, 189855650, 921366847, 125794398, 979671301, 568808402, 514003137, 503436421, 763545728, 487985427, 121016482, 971008275, 998457882, 463098070, 797622187, 388014247, 120092830, 13125268, 742198069, 900895696, 567201212, 802758118, 36535572, 264848536, 229680934, 903770651, 934678501, 787889262, 922721447, 696521730, 471723727, 580540076, 98095217, 12510537, 734070487, 946148440, 971816548, 263447197, 403698583, 855959995, 622098730, 70828604, 61663901, 213068000, 778597684, 724305004, 372135378, 354375894, 132322774, 902552158, 644293518, 961820461, 199356169, 698057494, 71784317, 837261961, 345091016, 140572634, 619753287, 532818259, 334113120, 529006482, 726758966, 4930115, 370581302, 476595119, 184647591, 454973618, 699367749, 729145937, 153796152, 620393255, 587707207, 583575290, 386277986, 486557842, 427519961, 240978444, 802993269, 250205064, 483008330, 597950406, 747600557, 325363856, 714091827, 659075588, 976147334, 285391461, 598305690, 714577857, 319803889, 254409672, 167272662, 384718163, 266435481, 677935561, 607185653, 728451121, 865092691, 656317974, 745906660, 926807883, 90386292, 187512202, 524904460, 673427954, 368868331, 943167273, 210785892, 16896793, 658987006, 994453986, 760808677, 173299866, 931638751, 965249567, 39605288, 564994334, 368975951, 267391626, 403789301, 866065923, 263576992, 945671397, 177687995, 800503228, 210543073, 498365183, 279793182, 475207258, 632634543, 725194197, 357223271, 731568704, 143836833, 576631554, 689795641, 919662204, 183655, 316612381, 46825941, 322355614, 34488804, 482706850, 90341229, 809681891, 600647741, 53069606, 145608798, 44125849, 313787926, 615459747, 779761832, 281126837, 98615617, 448752259, 664304567, 463324195, 859643897, 98720709, 977529450, 571637553, 573658838, 948372675, 417078080, 879461418, 191514336, 447941796, 975539007, 169235073, 487596182, 36637418, 332545134, 298746872, 402930566, 994736910, 283072560, 400730249, 761438065, 644786584, 29655238, 617835034, 397623969, 754305774, 273669566, 276170216, 269366314, 525406669, 174868278, 344346251, 44290543, 499417720, 273840589, 195390389, 771829551, 853074494, 834188073, 318726513, 890754068, 819911938, 507856531, 394697742, 253473821, 840456037, 682395194, 109257200, 201434541, 675903596, 132318071, 569238123, 401514312, 237857056, 47899593, 530329021, 66587919, 607980289, 943743783, 660647622, 125240556, 833033359, 20879481, 316011758, 282379425, 733202365, 956598237, 223601523, 987388331, 478723707, 198120656, 134684419, 54608638, 837211336, 616688894, 60492843, 622942063, 494984705, 419285621, 120903664, 814639775, 367083861, 705417247, 517335123, 812935726, 86328936, 854663334, 719744044, 977314129, 534515935, 334044293, 904008788, 636513550, 684535717, 987146489, 790770855, 183697750, 60642934, 473029999, 925098145, 942727397, 830620864, 628535409, 365495442, 23579478, 938238478, 37037127, 482169318, 812731234, 750484607, 424072242, 587798654, 497045282, 436932020, 596448266, 397906922, 467677202, 94204822, 157598642, 509154619, 754158848, 533615797, 411708975, 970909222, 404118645, 90424160, 53802023, 407497094, 193588183, 264813407, 905535223, 142837909, 702969027, 302159885, 71492777, 121249047, 171403688, 738635662, 91550264, 114041934, 380660620, 453137966, 854282160, 616102928, 828721970, 82620218, 79293304, 667289657, 160763354, 242836965, 664396273, 645312548, 664565492, 25299864, 838788602, 769948258, 522503714, 241285854, 709512925, 562834801, 408634499, 219600070, 640090758, 719672645, 925737998, 603961365, 306362643, 998369759, 76984956, 180112670, 711717936, 506822425, 644197780, 26695985, 736398046, 13136100, 871344448, 78055788, 858357727, 309141568, 773209331, 214395283, 335746968, 632114367, 276424147, 584174063, 350709, 520808353, 255093840, 540916492, 32953454, 989696566, 305986684, 307110152, 75617259, 999326356, 924394448, 698083305, 58151588, 313331750, 262090258, 346811462, 493143959, 258087748, 86988624, 543913712, 511797185, 478061604, 790614686, 958231295, 304918581, 506503807, 810240101, 328398092, 751508354, 364786931, 875842830, 166792095, 797655638, 366956300, 15539360, 85122050, 901107652, 822247340, 43025268, 929034529, 821695403, 308031946, 383380379, 660085896, 824968768, 171764404, 254548074, 204692456, 895247031, 873779609, 636622724, 343888054, 126004981, 106935807, 722520912, 176677929, 133935323, 989702312, 482032411, 671433588, 682530274, 135313599, 236700108, 169560702, 123823956, 270070055, 276472440, 596874386, 470835763, 717099065, 832199412, 953909678, 168447365, 55892528, 8845059, 407620328, 17936881, 633218755, 708821998, 254034632, 528085081, 935365319, 667738721, 944139384, 488145296, 935738349, 738989535, 753761734, 403003964, 91286555, 385358154, 38749192, 712210471, 387212941, 403579589, 356141729, 45881281, 171984323, 423765853, 768586751, 805192543, 673377760, 112401658, 808373577, 393081051, 122283982, 608559886, 509505249, 717361317, 189959413, 441695428, 931245005, 236317038, 645179480, 262664709, 459901875, 91090898, 972824469, 699220199, 777212786, 326820901, 171464291, 478966832, 918927359, 786456261, 77971979, 958948872, 594163724, 924473700, 70660433, 146364205, 226797256, 832094353, 341955006, 626646471, 577369989, 93326990, 843001495, 705656119, 960002666, 4356773, 142809875, 514159560, 889593985, 923753210, 802897926, 241764091, 262905339, 131674907, 224035980, 830177297, 146305020, 477767685, 719967443, 747045233, 65666992, 768195689, 101148134, 891421381, 851717209, 469088910, 463941425, 144432347, 474336389, 676615632, 390917048, 605723383, 736168898, 533814977, 4794081, 531811175, 925364631, 311467691, 603357470, 608856729, 40693242, 246151749, 237233762, 525268648, 124349391, 522733058, 666762623, 188553158, 851878623, 90073999, 132710109, 587906991, 677829666, 273051604, 92364039, 693148997, 134060127, 244953437, 638068087, 958503460, 922497660, 655065820, 406629054, 865140342, 840974530, 702276776, 965557832, 928280891, 973110827, 33447554, 452905811, 244362347, 901501694, 103453403, 201970632, 798508057, 627789079, 51871658, 533425628, 649202399, 797043496, 207882677, 403358293, 197260099, 970025602, 711565081, 461638717, 832407164, 777578330, 386163809, 116738539, 798073860, 863808317, 195663879, 126580199, 561751114, 854953612, 366993396, 765702162, 808450406, 759572885, 866339587, 317298913, 675289622, 692647873, 813044271, 687063064, 920108553, 715129660, 209941279, 761292060, 320233262, 459045570, 802653486, 280565996, 276945184, 56896188, 167244773, 725350932, 406158200, 296397794, 380666997, 439687820, 800992687, 476737244, 880157971, 533060156, 290349059, 548966754, 781801049, 838142882, 207005401, 630918026, 112355534, 519450726, 367473778, 66613053, 116230427, 566184635, 531975831, 88654218, 853222831, 4396776, 726565057, 357806781, 422148525, 306591792, 940264374, 592055167, 191720836, 779923854, 286151146, 711343862, 868508382, 62748734, 128986615, 817885888, 147384863, 83944398, 217487609, 892110200, 765627041, 524950352, 893703810, 337177738, 912328193, 747537195, 71405405, 18453709, 195780796, 653911058, 201681830, 758887299, 888212776, 175779142, 296353428, 575424861, 631417042, 555263824, 677847692, 698120073, 498265003, 887937440, 430544801, 251662914, 817557584, 559165194, 363749127, 299846644, 664399656, 336631637, 142555285, 965530742, 905167468, 952188964, 180611355, 417498642, 455031791, 61971192, 728565565, 586993971, 510700007, 618589664, 285241967, 97291780, 632816648, 618311458, 657632391, 116599784, 5886959, 917146117, 714831549, 755982023, 67413985, 63826797, 657879185, 267171024, 207887739, 415794080, 565934381, 866043552, 137471223, 427503863, 884002504, 249689425, 909848372, 141956628, 404575354, 559918570, 332641892, 440201103, 66028444, 273313981, 284013482, 510839458, 658268332, 615341922, 894046904, 141014936, 871817922, 281786552, 444243681, 844840386, 889945049, 257157160, 228010294, 136163350, 874200220, 506571701, 777117411, 737180102, 96122604, 662876096, 593652964, 979885136, 184589576, 202746214, 161682401, 255958520, 527477664, 241528992, 915915394, 335020572, 442397426, 328583980, 216931542, 22998540, 358662633, 301314580, 640964851, 218625097, 745960127, 580122997, 757515914, 261046391, 846235486, 430115019, 813461000, 820463463, 1929040, 843145538, 663116857, 843096378, 824694590, 970130625, 942720485, 350046942, 141846927, 328799506, 217513224, 86446562, 364170264, 345974801, 33842698, 120880123, 138611725, 548355287, 558381316, 919355445, 981247239, 312592235, 221909417, 693788186, 149252587, 910924303, 225485747, 574624352, 878627345, 594284807, 871200859, 104810785, 122788955, 946440856, 543083580, 676691983, 886900657, 223278693, 268268923, 293530436, 561399405, 891024856, 474285982, 764383440, 925449240, 702031161, 567167411, 591441162, 455813745, 196450732, 13926343, 646321674, 663825397, 306364896, 127689541, 378151221, 67498553, 405065211, 997107842, 865901382, 168009018, 125521549, 363443057, 649037047, 192904063, 436171489, 783865448, 874487710, 806586006, 362022091, 477481399, 220411427, 758943254, 204097643, 501293845, 941281494, 280366944, 708077402, 430490432, 349050704, 762252662, 936373141, 60953542, 695036784, 425258089, 688105496, 706092706, 278381003, 968195893, 169161628, 647738606, 622415018, 860527044, 689307198, 557912272, 82363822, 684651647, 922045945, 3862342, 886320864, 521905316, 192004635, 353312548, 413878723, 373106662, 796255747, 233625552, 717664035, 869043114, 188544811, 162106928, 667043603, 20382320, 644230476, 460580417, 7100485, 624656868, 709442995, 871850262, 146332367, 789725442, 454983443, 711706781, 627361186, 859000991, 538990216, 775780173, 31338284, 153640275, 441116054, 943769232, 277869641, 797112129, 933275628, 855948279, 42060805, 689069488, 629900443, 717193998, 436560729, 448343139, 10312445, 864818015, 95866923, 832918554, 736146622, 880846200, 277176931, 163201971, 857946602, 747288259, 855504302, 670845777, 928539720, 570843428, 665374297, 111809093, 415956067, 163814542, 118258118, 111308151, 160314365, 752782619, 686460220, 175198008, 312550097, 679103015, 186852356, 435196326, 46354963, 388856336, 964103187, 861256268, 50518654, 86269283, 115626389, 806785080, 301047035, 383844971, 125947306, 899279409, 945307423, 5739043, 883488201, 534802403, 775215354, 63966579, 599192849, 788857250, 360694362, 794794544, 136291099, 976592327, 691148717, 728791559, 202117875, 682638723, 856174395, 841618967, 35160986, 848298868, 430247350, 208521078, 548246469, 129406116, 39217090, 746090086, 725115926, 103270647, 8883840, 292323072, 692076177, 615438959, 624303420, 663273315, 619933595, 408635662, 916075117, 748977808, 260208738, 229202452, 415068590, 407693135, 824212119, 803779068, 662483015, 929718523, 43933125, 71579431, 691487081, 105926572, 137977399, 743229996, 856506178, 44452046, 710948240, 84072192, 798186365, 561456417, 61039087, 66028835, 419922872, 99459129, 96646445, 425212477, 230446082, 859032424, 289708293, 667894012, 935884271, 959190179, 647428446, 403882521, 477780539, 597692972, 232011832, 447977636, 431938210, 4958356, 518590152, 531601520, 707691184, 581006853, 890391386, 4494027, 821736478, 644106809, 778226675, 747937442, 674199528, 490845203, 148826883, 60878299, 340576886, 344476046, 755287265, 61609844, 308388196, 53430227, 897523250, 453373177, 347813467, 946351202, 52808567, 526427973, 829903057, 287693934, 605368989, 291086852, 169364425, 697700082, 687482886, 728527912, 855164673, 330022318, 357869124, 979284614, 17575106, 376222728, 627951343, 910844342, 844891587, 173732075, 720061065, 272081137, 604139347, 856671027, 482750862, 858270082, 691357368, 734033286, 147862489, 657680671, 551592220, 143938066, 56783701, 425904374, 727944137, 45130029, 463603522, 771993089, 335763483, 262988327, 830278861, 589300751, 49276646, 787053440, 916767116, 556477467, 279398732, 86106663, 444731550, 709853534, 526350328, 760982524, 882767931, 142955184, 450971935, 297860941, 501021150, 382902277, 646358976, 63758878, 73489725, 590401350, 826114915, 366459765, 931467601, 269945193, 861598786, 441548036, 365765743, 426482712, 907637041, 651891592, 35490857, 537273575, 405614374, 958181812, 138170890, 632810746, 233756611, 242083586, 733708323, 85435870, 720161523, 643205444, 713995532, 216158931, 674590589, 186430075, 234132939, 596572670, 437186989, 782376520, 454214096, 133505657, 135974528, 346277054, 886451042, 311146420, 701984220, 186825127, 599600934, 831773668, 649086984, 979636405, 619789976, 541792645, 476908925, 684555496, 183562750, 615882355, 168452967, 759690577, 7991467, 341650327, 280190439, 487628685, 795164864, 926196782, 725221598, 260580409, 806543758, 801519240, 949594482, 667694532, 537728488, 794869729, 294187800, 356856465, 96027443, 448514102, 869065914, 749458286, 938647296, 506385419, 169338293, 482241812, 337030162, 285224469, 210119780, 134560753, 966639002, 981903970, 138059038, 988035462, 449989412, 487097365, 770393411, 642576096, 351195061, 701573450, 128792137, 154216014, 776644076, 938029814, 263539278, 276786699, 829249536, 658936107, 689190427, 746552781, 583530974, 897984363, 939604499, 423592163, 422900769, 377777003, 675775183, 476157744, 823204076, 26893839, 866486839, 965882697, 518822777, 885230319, 451770514, 819720997, 208068722, 223562612, 929464246, 601004610, 902819339, 340679469, 730596827, 992290738, 62510301, 51232315, 710615508, 278866796, 529201122, 168855124, 864944885, 194161584, 938126921, 999633763, 671971196, 451027494, 477593154, 792830210, 973983806, 419323807, 208614149, 777264013, 891876302, 302133663, 198676737, 94880876, 413663187, 743564204, 280855802, 102105646, 366572302, 170953999, 706679798, 592197822, 129944119, 30213796, 850917955, 440431362, 116711619, 405628182, 809253424, 173544021, 989172822, 393185488, 778704432, 279666133, 943663774, 365594819, 92373414, 904010169, 165769963, 56277366, 474942257, 959990012, 938236627, 977037415, 497845467, 433487125, 651572792, 973982568, 296452287, 228844685, 131477654, 357424564, 730354800, 630195333, 754360083, 16227591, 948081521, 669733316, 912363872, 371536323, 529616051, 567860314, 630773073, 42020941, 51331575, 661883160, 405689644, 757104276, 936191619, 174639181, 349379697, 180326118, 171704107, 317250396, 922453293, 760434220, 475922086, 519988152, 295686379, 31840779, 831298263, 521700720, 521797454, 426961375, 854470982, 174593506, 836973878, 312393307, 148785753, 79419581, 19007546, 85226210, 219957737, 489842246, 469513111, 721906484, 49527374, 357363208, 956734774, 110052547, 150959932, 189994078, 609039572, 599003192, 989958109, 30925686, 800802157, 185859775, 321213562, 602033559, 389868903, 431075169, 537173725, 449838380, 170442817, 796979111, 356179943, 611627587, 153371652, 520944237, 332861073, 561736410, 817316416, 951051472, 791384198, 261432782, 44076330, 96816940, 986417000, 813922097, 20961109, 617167673, 607105342, 461653930, 170343661, 257252153, 670629417, 886951042, 12917248, 818205444, 156063133, 406238560, 320867415, 71357299, 127187924, 609181387, 104849144, 81351081, 822164287, 904314075, 26015789, 544027523, 600749801, 920984606, 883705090, 596416338, 513963497, 669582659, 700403188, 724491114, 901919277, 309716827, 449433155, 120280168, 467306612, 544882858, 652327775, 144824046, 406886819, 205802625, 979579082, 382194864, 999753055, 920521563, 846699203, 451548810, 990163744, 387166495, 439669122, 616544434, 956717071, 149689664, 555995616, 274816282, 434706588, 1924594, 855314471, 931822042, 61686979, 608468214, 768879056, 513829875, 818900641, 184992235, 323772776, 130705760, 93546202, 955335407, 417823390, 423260360, 24782857, 626618467, 9481036, 37301703, 45976603, 283588902, 485829787, 371404534, 540414045, 644500988, 30438653, 669998808, 844037117, 285191057, 772038769, 395379111, 191604087, 906340478, 794151717, 133324820, 414015116, 67516248, 84078088, 156993471, 41073301, 297957752, 395996177, 64195968, 992538422, 998904557, 502632869, 726863076, 889769404, 495778311, 561587012, 186141106, 532307425, 514673080, 950183413, 914704028, 85189078, 818016864, 876499127, 225703133, 222535040, 116629799, 641344937, 692079169, 902419141, 905395273, 309769426, 255570681, 734878586, 578485887, 551792849, 500391943, 576745940, 26767566, 686612305, 905608791, 171154379, 695487816, 501020275, 901867102, 107836585, 123326863, 372518962, 825875876, 268224608, 669062310, 53668623, 243026546, 586658149, 812725612, 162686727, 479697440, 497400754, 807608597, 432008500, 483846438, 473357194, 937755014, 260105609, 33350561, 179203012, 73729957, 212780648, 781095053, 777963203, 834635959, 494391036, 493720201, 407855562, 800451918, 649187896, 412115489, 495522090, 110403133, 787901656, 433678553, 981499613, 386016252, 837357010, 797119729, 557126491, 917643367, 492481659, 233081207, 478678828, 444774571, 661169354, 151809840, 11481167, 739448672, 932542223, 959838404, 298527082, 64014903, 747676461, 165701950, 385562095, 202473446, 334403949, 48553453, 189169951, 159834683, 134786209, 308356525, 595759928, 548242528, 551613783, 949871152, 174313239, 688364113, 925854149, 247796986, 530331679, 809182353, 718277860, 292661810, 554631667, 497799991, 268375708, 478591593, 827049698, 629913496, 424812248, 272810406, 956038971, 929745609, 68608368, 260691378, 294640610, 127404513, 70529183, 588961419, 198393731, 156527987, 951833719, 112340978, 309797205, 583838670, 678991122, 391726602, 799964357, 457044742, 361572151, 849508906, 931097422, 855871296, 248907772, 639137612, 89471532, 988442296, 248998454, 763452733, 374730264, 571923166, 157102687, 777175198, 447922102, 717456192, 277400508, 879039323, 452341032, 699247581, 489088179, 421035324, 17005101, 388046553, 25604850, 265164331, 401849145, 827138871, 834271654, 936073639, 480002944, 995703263, 8504080, 264129903, 633760524, 537390725, 797156220, 632996269, 436701757, 358128439, 3336327, 247841830, 825774156, 996158263, 406534736, 896789696, 861888927, 910781247, 228147041, 188755023, 170858474, 575890612, 876924726, 635569952, 371594568, 453828190, 195873903, 456658132, 114108647, 777723991, 458093745, 972589093, 32443540, 203519365, 468080374, 236739055, 157275081, 49441879, 812330322, 185596365, 778185102, 848631548, 194239016, 469350758, 109717324, 313025770, 325758907, 994315040, 580628816, 393257624, 156495859, 342723483, 368531795, 360467181, 86728322, 252402366, 168236836, 374297013, 363296806, 290448397, 186042173, 476450658, 937634492, 647193210, 781710475, 60810568, 259687788, 505673796, 668268833, 472533482, 89608398, 921551218, 756448396, 790064506, 580689620, 675872520, 31432472, 849400480, 335006311, 501224443, 221646518, 201418938, 868098219, 811115218, 27571990, 815866342, 598338998, 666597462, 786214986, 291885590, 715493094, 323456648, 8254352, 341235214, 93236893, 480577866, 586865123, 278484670, 24469285, 408982217, 690814524, 748461779, 254358555, 858934605, 849429481, 296566366, 814107112, 202515008, 558588562, 54538395, 461430460, 538694509, 795677044, 536131557, 539962161, 323907420, 649389490, 57450621, 247697237, 291236662, 818621915, 195676541, 401171861, 762449176, 96353306, 439936771, 972210535, 846754802, 707560993, 146696799, 744256508, 218435506, 655103999, 447134057, 5616733, 251014568, 396335859, 31388980, 948209543, 235355131, 100961605, 822740043, 401247194, 667866867, 386510435, 892882870, 345305018, 852891129, 632538359, 173259021, 487306676, 614856744, 555684926, 757261435, 601854766, 193904732, 965949720, 387458727, 754827659, 611589519, 420410326, 231888335, 611743091, 902493750, 346334470, 177261935, 159417873, 349652055, 638066598, 622879749, 490662967, 208779426, 419620167, 306412423, 90735735, 243752085, 397676505, 165691738, 434262156, 163200640, 86481356, 431590688, 64693798, 926465645, 739406510, 725697397, 73468804, 379476313, 148613993, 398334749, 898539090, 470336658, 721463758, 840913860, 68908954, 417575153, 687334748, 877362470, 700250120, 554016101, 578495879, 553696399, 843604342, 794195738, 30842153, 588374935, 738872270, 667307269, 784486568, 173386641, 72527260, 370614996, 277600446, 208045213, 405952359, 485479526, 852221974, 780315249, 404510283, 766775967, 438422825, 2365062, 459879918, 282654263, 157683186, 740913400, 124078446, 323872637, 425664895, 812446063, 117542318, 799332912, 630474073, 173204533, 533086719, 253930303, 86569696, 630480803, 70383093, 323666621, 575563281, 260001160, 710760995, 734475403, 368004315, 759378295, 89279208, 459003404, 891807133, 267918696, 655087854, 261306290, 853280523, 480544723, 374896896, 135246298, 342316704, 413391827, 628153912, 476315109, 786915659, 25313174, 229859414, 652276106, 119977372, 305292978, 257733158, 323241548, 354359230, 905718995, 36696034, 320452589, 214737142, 723813129, 835765397, 311161856, 393181904, 133342379, 75270716, 757946703, 459515609, 391871860, 760447350, 16189455, 898708933, 122572472, 496198641, 458305011, 838443468, 357311736, 749741379, 928394688, 750330296, 623411919, 607752334, 296084682, 160996197, 626820453, 551867962, 964074023, 849487731, 738233725, 54482006, 727864924, 909193462, 504453630, 679839480, 828674858, 875509731, 658590320, 851878237, 758673077, 519331475, 93082583, 791699654, 83691918, 253100146, 636608370, 428376683, 337782236, 614515663, 672403031, 109297967, 664463221, 194865697, 856550541, 731942663, 558457824, 11830971, 236850022, 773793235, 133280664, 107849999, 569615448, 791977698, 718085871, 302430232, 161820627, 27333912, 271820109, 919442657, 520578049, 299263574, 4801556, 39101015, 56110438, 51780648, 97448798, 147135118, 339259448, 276745309, 368567496, 794736270, 352388292, 943852324, 747754412, 931233430, 651599690, 524659056, 722253733, 543186350, 598793922, 8490559, 729423802, 665858987, 319183663, 393747593, 465307462, 919617379, 601263789, 480631625, 110221039, 252058252, 307882698, 853372378, 748904471, 93308923, 221782720, 917781589, 376008529, 203307819, 986592510, 600223457, 190185980, 799013245, 59494647, 669563232, 448129144, 993321297, 51582990, 721198065, 246669399, 747568553, 604147123, 110046095, 915993007, 314947945, 861603552, 314707380, 496671780, 425386397, 611147879, 852897556, 889005988, 858344277, 562569159, 552799456, 660550061, 29313576, 711296561, 890932504, 91466822, 379031077, 83253269, 230746154, 584557418, 13176714, 455441041, 239966369, 429460142, 995070743, 22437574, 688178934, 903567531, 907273557, 90604471, 912768902, 722745151, 253712351, 53427968, 357074994, 802672909, 933713351, 802383404, 493912461, 945108850, 129058817, 611485277, 169588239, 266972681, 255851257, 965679762, 983966906, 572600402, 528634368, 761532145, 420431195, 883570296, 666729528, 114854646, 536571179, 450842242, 941093580, 844053229, 971568520, 139419926, 549066863, 663300476, 402748502, 124629627, 343982686, 567646713, 731847475, 861758921, 383389892, 562266145, 15173795, 282042183, 230061430, 723117763, 363592744, 96856562, 411423161, 617301715, 153403644, 15231246, 683415115, 109789710, 666935794, 215240187, 730564107, 964863935, 839908261, 803930750, 964805854, 58042719, 914599265, 167435821, 111536110, 838949971, 167381372, 686119133, 378989517, 417711977, 884545714, 367003724, 328449824, 240640549, 361861935, 506572917, 293773783, 347765439, 329107036, 115582443, 109804752, 115171005, 33720278, 142622766, 694002808, 874608597, 394593297, 301154944, 529313752, 993714937, 648830024, 332611827, 182800107, 722186551, 435138590, 764124312, 447147075, 79607127, 412468713, 212696415, 122929866, 679997285, 720706618, 374997461, 378005901, 557795638, 504318385, 849399175, 184125608, 282666859, 471666248, 962619182, 477238697, 760618348, 323127896, 756643916, 102728692, 737327550, 810404463, 657937982, 319602728, 116602518, 948219808, 729972538, 982931107, 566016684, 340926439, 667746868, 990885525, 253186854, 157774077, 931261376, 782648584, 262853232, 334468537, 350539912, 534281651, 627121030, 220191225, 41687950, 104711697, 488746840, 498095407, 905070111, 904326056, 393297086, 245254104, 246244793, 519066514, 630917652, 373369441, 93169445, 60362580, 973529823, 441711045, 159636073, 638456206, 586092699, 575367628, 249793959, 965615194, 853066739, 632321343, 289924109, 633987907, 818877835, 83665914, 760260918, 306574444, 63882364, 211418905, 489154740, 826197635, 418233471, 476500642, 935229877, 143266509, 405910611, 276064312, 978903931, 217312482, 436365527, 79266812, 165988795, 979829371, 654266058, 42749456, 304075964, 556582024, 482185495, 996898690, 569635832, 570723803, 361749979, 686019855, 801568169, 424046104, 69907726, 735984366, 692220419, 755393179, 386925081, 38523033, 659261357, 472482945, 115185045, 90958023, 813265491, 581099216, 639385341, 298244941, 572061272, 198896360, 354616368, 220480893, 814905826, 86578118, 4856655, 952062387, 999679249, 765175844, 17177664, 152652282, 92874975, 172966527, 533659557, 196464533, 666813208, 907863360, 574853804, 424152949, 275718304, 574177751, 953510205, 413690639, 989791011, 322130896, 496959492, 337917088, 894090511, 47923190, 424259943, 747643809, 324500706, 325942642, 757363208, 546422640, 63290649, 173755257, 559881377, 244840797, 30604778, 825859046, 362943682, 388766975, 420245226, 657436367, 364418116, 480311315, 254422730, 912758732, 199294939, 391938490, 109957960, 331749764, 840578261, 279462113, 598821039, 619248248, 767469030, 241033965, 967464977, 41579992, 975250264, 583448915, 23202633, 449395286, 160902450, 974314752, 846711778, 248558489, 226487850, 337047108, 215184850, 659421640, 401446837, 146768080, 534833697, 549587699, 997838975, 578861344, 197858289, 480727753, 995551763, 322650977, 971741014, 755001023, 201458934, 328806615, 631831501, 664451073, 672748934, 232830225, 128771853, 851944187, 485157521, 967744679, 40430741, 639291521, 630443091, 177724000, 277761929, 191722318, 505147193, 198946729, 141402472, 832398633, 527178616, 92380440, 613108822, 662421624, 790637212, 227485101, 295907866, 713931772, 552270281, 811566946, 284378539, 142854970, 507546074, 284240786, 550281467, 694706565, 868546458, 528567853, 874582535, 28677643, 340486485, 722950566, 643434399, 151200704, 834123096, 810561891, 114920098, 864710911, 162657436, 164566062, 797576586, 281785639, 747264524, 585112173, 354890963, 63487789, 666912142, 684735160, 835655543, 221565647, 945081758, 537583104, 58467591, 533393285, 373937724, 106072202, 875676168, 690387905, 811376241, 777190141, 659364489, 412134714, 793074028, 374157065, 210752890, 570999413, 495150125, 424319408, 781064738, 76833071, 702409455, 154325053, 233193189, 71192768, 790492665, 279226868, 836380957, 5143184, 835996497, 476789215, 237092719, 742682985, 394198343, 120369276, 335413082, 179016836, 965999255, 678108625, 109735336, 900174654, 167614707, 365268944, 390655378, 571300807, 790518145, 398116329, 793151366, 136837804, 2539670, 147341650, 416562993, 44864510, 131744850, 267558041, 674367660, 898168501, 157494938, 581623540, 249079800, 273858269, 417273889, 625227462, 353089, 857770395, 726937797, 216741989, 238832234, 436968130, 407604164, 122463840, 482116536, 483602711, 404656743, 323952971, 481005288, 496385340, 979183065, 861894618, 995458091, 970649044, 275662331, 983886550, 41320826, 342811871, 427044739, 577265462, 410945687, 532312653, 770968055, 490244567, 794443441, 826358894, 345609561, 635292190, 713870317, 499001760, 579501478, 638104456, 341564774, 633034598, 752855151, 85678095, 529588502, 10100856, 309648888, 725387929, 336870946, 94914952, 304249472, 211889663, 560024652, 454470939, 745570773, 534534199, 945861577, 187721572, 257954248, 165249373, 195168303, 606995773, 575495870, 814430519, 273645864, 516094514, 525442448, 701695942, 498009464, 405380689, 999063644, 877400182, 140525674, 6116395, 410137941, 926971301, 510607761, 531659697, 149457004, 826394210, 264927657, 604135198, 161267176, 683083843, 603701197, 907249112, 920610534, 306211601, 325474087, 678061948, 483330124, 613940116, 357458639, 985490872, 647893622, 513796557, 987888572, 477563751, 392956387, 864785345, 110883112, 494320592, 327601745, 33436060, 760757415, 36183590, 461786416, 11824510, 897802472, 911992973, 228262802, 478354186, 48744581, 501092903, 57546371, 878976262, 199405253, 262487868, 806299246, 485919334, 748092042, 245997320, 638973030, 981681293, 816162859, 561979040, 223198165, 723279015, 996147735, 200535839, 645811325, 881492637, 205874295, 732100467, 608737003, 127922269, 933548219, 527307475, 222015059, 454609427, 535657962, 142679965, 454466340, 739343317, 795715177, 872398393, 356088380, 368303084, 696883524, 911196989, 520359986, 566307915, 586804794, 706497836, 874759310, 194658946, 210324286, 938463865, 418483162, 850381310, 293764716, 135066259, 899007020, 985807408, 269025459, 937837609, 762588544, 81379959, 756439941, 263900159, 25354017, 878839173, 976323072, 559111453, 803064739, 413216585, 197622124, 484867221, 137564193, 52563777, 901359495, 462455561, 971517174, 335661816, 828351707, 804670910, 714673714, 505229740, 241061348, 465895190, 374455211, 440322140, 585459569, 193811358, 423168760, 616930952, 29633798, 337470654, 469838703, 600181295, 157268165, 902319721, 364327090, 571596292, 729321032, 137182769, 940349493, 312124088, 717873887, 759584487, 174928910, 459751429, 284836863, 660153341, 402502185, 718989633, 304090911, 388129052, 553952937, 987503338, 117236730, 192051963, 256595971, 918154677, 608611011, 347168386, 955704595, 824710280, 276670098, 476282714, 660446618, 494853790, 327045619, 235541121, 490738199, 576876767, 97793294, 33138323, 866595552, 273824802, 895058905, 716463359, 862169038, 985758238, 312354863, 747915281, 91788771, 933204631, 17231173, 753994836, 288591600, 247807724, 511578078, 224093151, 903932302, 142576964, 907250457, 790494300, 569351541, 210649965, 174955459, 841344060, 342196597, 498596929, 469907766, 333100332, 765755906, 39944125, 501541950, 242082036, 631996322, 721872045, 602511069, 807489048, 932539475, 658007438, 842895932, 144365086, 641654969, 814353546, 493788602, 69524031, 43692549, 602613862, 251333769, 416630186, 401530146, 494413731, 632246965, 778168788, 563663822, 536143137, 232964164, 40704988, 577588069, 574158631, 355056844, 658465557, 866873042, 544064421, 156834494, 432510854, 211764753, 697423177, 221304505, 249870172, 487919191, 306717309, 352776278, 286854543, 112222299, 7678598, 962738115, 763662429, 592517888, 744245611, 927649239, 949403202, 914001446, 958261884, 667800976, 143443008, 843388369, 513656859, 699608003, 806214488, 98923696, 662724546, 700463092, 452472977, 36915907, 244942945, 554941631, 103236428, 939879187, 858696270, 347292830, 940043604, 585234113, 696979934, 5028311, 569948107, 155267758, 529287685, 338440333, 924120993, 167535435, 922211684, 288998382, 836954318, 797236629, 188948750, 766600862, 737750890, 624708519, 92443897, 969216546, 48858999, 949185252, 901755060, 721072478, 435306888, 307731289, 225062143, 312258464, 459195177, 38939143, 313806817, 209034837, 819052713, 784890227, 141083609, 678630054, 954448092, 73234506, 887917544, 597204429, 478052826, 273287481, 101191426, 364897194, 183627390, 110499547, 787366545, 60270623, 215616221, 288587541, 69755785, 591889681, 721710022, 474308352, 671655590, 576798588, 234762207, 96625968, 340445625, 630413609, 162212395, 703744310, 416201914, 715820575, 586037474, 261936697, 600386023, 815367015, 20243328, 481933621, 708889533, 515033833, 487788901, 277751327, 191888497, 339866473, 762888236, 895312917, 802821383, 224401700, 394955007, 475106538, 230040019, 416061000, 927990313, 201367556, 179189955, 538699097, 658186008, 454890854, 260467976, 60625401, 116745592, 17997513, 950099718, 417547913, 437758919, 492965688, 560065527, 806777321, 435825907, 916345026, 239518910, 894430644, 523734298, 869617410, 187234156, 129793708, 691746626, 562938162, 645709093, 452641932, 840341683, 666906824, 702964060, 759976506, 177978132, 983387243, 820661967, 239886706, 689033607, 928818317, 511201727, 203160376, 474274569, 228160881, 831176496, 931932301, 345935567, 378177276, 13174572, 218757031, 233842305, 706313317, 977540191, 801899578, 150980316, 856493202, 633536251, 661130236, 616993517, 553355039, 924548554, 411061749, 510990859, 694808223, 39385891, 940517284, 620438054, 282950474, 858920540, 497910454, 550393908, 319960062, 980797171, 381359553, 136069775, 179414143, 480821233, 392796781, 636368406, 942564317, 539943987, 44099157, 243761740, 424812652, 151864445, 927134333, 271921299, 968340300, 454296805, 121666590, 496124853, 420442184, 77065870, 658623634, 271385210, 858709383, 180223597, 285229390, 129081555, 514001627, 88921492, 177260463, 27211200, 806007861, 981988127, 719913879, 810402582, 32292516, 852386845, 684707854, 760457669, 905112294, 776673992, 338539687, 759580947, 745798909, 289126224, 268362470, 930223510, 584991974, 664511688, 664596757, 723722168, 739522285, 128422668, 404198898, 591480380, 2880542, 119425937, 323628766, 445596392, 337461989, 355477886, 487660129, 839656705, 285008179, 557856358, 767310535, 851729006, 141128288, 809353827, 781131834, 537360544, 244268598, 856795748, 319278387, 978893083, 61029908, 224189090, 109978629, 307991966, 104220720, 739006549, 621869907, 588814043, 810126001, 35628041, 493641954, 133127634, 671678650, 536373032, 184428139, 173928902, 252037154, 339153114, 896957731, 615249212, 726699021, 587583945, 117743722, 746897794, 146246663, 160056113, 276634470, 851717117, 618851, 98652353, 77493932, 516504581, 94112448, 677966037, 978442920, 917221487, 228593946, 386184340, 118443591, 375593961, 957961311, 1437858, 740036311, 583476035, 50699495, 230387452, 12515103, 24706690, 396537374, 303411603, 716178286, 349925975, 456919213, 99111026, 960903580, 443505518, 185957043, 991773047, 310477902, 907271083, 15505633, 372369036, 838405592, 862919932, 186225874, 46331009, 897513637, 568915175, 325776551, 858724419, 535905283, 773447142, 37705172, 287977969, 751000538, 567983078, 487950801, 422159659, 424650368, 640043773, 538881721, 269721246, 261224664, 677888488, 491855487, 412243291, 270202924, 558039042, 864475926, 784879337, 993215045, 913884277, 836038613, 707237122, 925524276, 186799349, 47619720, 366946396, 291401517, 684287779, 725367828, 731742623, 82243475, 205424073, 359622053, 148553983, 936464576, 1098689, 380716709, 378033389, 584600222, 396683529, 985411268, 854102224, 641087499, 36635607, 669942704, 117497428, 443843639, 699630270, 20303357, 605384525, 936333738, 319613328, 216796463, 71243985, 59200569, 325823903, 244079104, 94208773, 130883823, 805617115, 53964385, 368589820, 651526398, 610501991, 681619336, 181734832, 416436383, 915878567, 874044478, 729702324, 787210389, 511660626, 466465683, 113886202, 397586408, 797531776, 648208849, 728774458, 374298099, 85852925, 638734278, 750819466, 200121723, 807606499, 238006541, 749238872, 136182526, 763232831, 267391200, 270134859, 340087546, 565118491, 884455051, 833739397, 100418947, 817002980, 474533047, 676434764, 267917440, 703437346, 703467485, 308875632, 132849841, 637936875, 14181357, 29987693, 180663210, 608355256, 237449539, 83531966, 298073011, 525757374, 604600660, 476953818, 147204796, 309967479, 826587509, 9086469, 984511323, 721871330, 906842313, 809650448, 609996470, 36990439, 803739209, 512837785, 415887381, 900783914, 358684257, 514751889, 183209872, 21234562, 385660424, 480144446, 558064465, 510778989, 174792593, 264334668, 856458220, 935049673, 443915509, 951866318, 664583058, 744511156, 847910721, 824484073, 330715796, 923758850, 55828758, 108607391, 839835935, 925367290, 411251887, 55210749, 440041103, 989524270, 888501194, 625274090, 316082839, 46972852, 434252517, 898248640, 700684603, 885228564, 368694975, 121045111, 777125535, 898111360, 692743907, 448928843, 768007627, 348005504, 887334858, 936415761, 339272225, 535158982, 956689663, 780509769, 808034045, 499737629, 892827683, 488180082, 555374544, 496153914, 654375306, 48295924, 156417973, 455910670, 530273261, 590002094, 875016621, 927281809, 517893901, 601780039, 296517546, 768006117, 748775812, 875267429, 896470491, 93185076, 722494489, 653128012, 340280627, 705861341, 977478912, 512912195, 726075690, 571018123, 645744775, 350822496, 749410761, 610472518, 851631353, 138631445, 333581651, 850443766, 198372728, 344790137, 604446814, 65710161, 417134049, 750033273, 37139437, 44176111, 981815447, 302324743, 220372398, 875964815, 582566028, 966643287, 373080434, 939211651, 736334842, 40949669, 302487963, 624056101, 404109380, 539118036, 855270666, 341220053, 411211944, 634489140, 723842173, 727441754, 313747582, 857389241, 313742185, 105577620, 267064832, 907743407, 565542217, 522338688, 990157842, 949504855, 401282858, 68463666, 355543899, 649978993, 256137682, 825723459, 803158935, 912416932, 863092670, 789926902, 225427715, 501547264, 468644318, 165539390, 217358812, 824820456, 944572216, 212174546, 89493573, 462367199, 491164930, 301848559, 787231084, 650722612, 46049897, 352007546, 852788767, 340276454, 943637168, 864666873, 556910286, 956013133, 217531078, 980394246, 166473930, 281393931, 945519808, 885157041, 11861436, 134575889, 626526530, 778240402, 775207440, 328132011, 829723298, 23066448, 205253267, 698082411, 492404285, 160369868, 354817921, 814598522, 381584360, 465639554, 289902284, 744489193, 338181246, 719767604, 573314583, 337021764, 463563487, 90784936, 895513103, 58409912, 469135882, 323784003, 542359488, 971972260, 218262155, 564512939, 752878007, 143002295, 960071148, 860418237, 349016289, 4388370, 162147717, 684784604, 489860987, 102599577, 437727979, 457568935, 955121200, 588419436, 259141549, 332716, 492587822, 747979184, 318665488, 228987526, 105236998, 197231672, 351617291, 959259748, 741403502, 176502269, 952156011, 406554277, 252476480, 944904677, 101267021, 786336679, 674562742, 242784304, 495116047, 361367816, 220689501, 218253452, 246101813, 749345920, 722397722, 160811903, 57292793, 961934566, 882084260, 663082460, 390016552, 520002104, 102410022, 41742954, 696768254, 910099074, 874563218, 840237424, 131929166, 905105487, 331480514, 558121571, 768482517, 873071426, 682799516, 534008870, 827714146, 778494456, 386017605, 551372532, 869503131, 857592387, 435976563, 191474826, 325193834, 727787966, 107651600, 125561084, 410777474, 352104142, 155392630, 649671596, 307278536, 391888965, 177006913, 641932381, 869943628, 711973151, 430627776, 404986977, 953659476, 970691398, 178723365, 192311034, 273563836, 208253301, 292329925, 489761656, 278992191, 654909761, 579258214, 174499229, 163210971, 593375104, 190773194, 517849999, 99289257, 99554951, 789211939, 596446657, 411365930, 810029279, 893545475, 642714048, 562240688, 46094743, 444755263, 670176910, 413725557, 463480103, 675096037, 23503169, 397331272, 685443593, 959348099, 749922846, 676184779, 60719168, 749776462, 438640896, 842372063, 59780326, 216878392, 559099556, 57686034, 579811283, 871270469, 153792519, 728608349, 847838722, 90384765, 137080005, 909918201, 751077056, 463733752, 578966937, 585238055, 577733505, 544320334, 361305552, 694017685, 133370459, 63628776, 872376524, 199436454, 374551570, 995038692, 721458493, 97167871, 860484640, 65875618, 179314841, 735934376, 700590851, 748312149, 350381457, 547964540, 928059089, 663485746, 322264125, 655780519, 530546490, 676706629, 415900114, 978103944, 894413333, 754129870, 630545791, 137277236, 224575865, 939767623, 146259623, 770831093, 124553480, 250846928, 168498993, 289498760, 808858396, 525490268, 667423982, 540916603, 878556124, 272992855, 399306120, 780183434, 564400665, 635207512, 457397568, 825185501, 336044533, 24094228, 142907410, 495139219, 356888061, 762350606, 477917408, 287806547, 603146684, 134421804, 519386883, 865023624, 599093449, 485941259, 937602395, 639963617, 407313449, 526201982, 905458846, 714280305, 382910159, 701535498, 235518093, 262234797, 205882687, 408110777, 994079112, 268592694, 922248037, 152484289, 718986420, 662557311, 113842057, 708094944, 408296353, 713453993, 931022751, 299418649, 475853067, 599215234, 39094516, 907485430, 964850332, 531148951, 107476550, 713948, 324605075, 575937511, 351999867, 214887437, 66804314, 747910483, 77242871, 652108904, 293267893, 34246068, 524538259, 336737201, 324679467, 712557086, 289843069, 249106249, 143409680, 160223741, 554086317, 352030842, 298888363, 30968832, 541330494, 884073790, 190008059, 71057448, 318224772, 68901930, 889425019, 449147331, 901243108, 330166455, 872589082, 229424621, 82421970, 359634740, 67604175, 974159378, 718461121, 713542274, 910459307, 481834314, 218763014, 380436427, 745582726, 198306429, 823161367, 14000382, 988303330, 408122013, 706349653, 693156952, 540730052, 330255645, 645321969, 27150520, 364044782, 639327587, 726268997, 937275097, 241349772, 92200588, 478846801, 468988235, 461762776, 496769421, 449163284, 142632762, 487237244, 651858511, 940515597, 824962912, 346141149, 226917770, 713714141, 481004676, 987922215, 959343724, 993680820, 810986829, 168275603, 34399705, 231433982, 184479858, 440253733, 54476505, 986559477, 392936445, 875455030, 439209845, 828368642, 461734359, 442892213, 568602268, 524108624, 811642473, 350689815, 847266071, 730289534, 870925457, 410586674, 33199834, 967726298, 829979267, 887232351, 118027885, 762829429, 723512770, 538296655, 88253348, 335879847, 2904090, 163633211, 898306117, 716694484, 237441244, 46939906, 19002488, 767676875, 894352157, 726064836, 845561095, 739253713, 521959008, 964127762, 30037020, 960205677, 121961735, 831593954, 274453232, 501778405, 417797251, 59176691, 551219661, 393084728, 329899986, 591596330, 839363476, 480377495, 984783759, 409181085, 923753053, 820210959, 624500746, 931096459, 767275910, 13900732, 615821497, 891118019, 125870491, 338627450, 586916442, 292703732, 177864296, 574733295, 224925888, 408706746, 946450900, 30302846, 683231539, 546480227, 83410541, 681778989, 955482500, 9949245, 620565845, 790120007, 264818989, 357524417, 351392217, 475927471, 175949331, 641148282, 149275188, 61408659, 461881854, 837951554, 833974139, 756855876, 109414169, 540622198, 319549229, 530860266, 586462305, 706067535, 921964648, 940788567, 456125081, 972250045, 109740609, 933157941, 888055385, 267279281, 116395324, 478657743, 504110404, 870196436, 711470277, 871972143, 932163534, 125115940, 751204948, 286963619, 975953504, 72550255, 363331558, 973500155, 330419827, 941886585, 168342153, 692384075, 465908886, 534005141, 531557978, 135795459, 834935616, 852657115, 570093057, 945000636, 964041726, 86957005, 215333323, 502949469, 278809539, 483753449, 191775788, 174024362, 803642703, 556352449, 706224631, 687745682, 647471363, 135165561, 10300062, 637784478, 405218651, 88629630, 540991074, 100530980, 153195331, 181675261, 435553101, 58872767, 729092778, 125103468, 353681232, 676080438, 932831209, 90416428, 553061406, 37226913, 610905049, 571867088, 602383310, 376483950, 300925946, 608111340, 883827204, 67846577, 61989463, 389922849, 58292967, 50785801, 447899096, 407449350, 395843881, 200964428, 253932131, 616563449, 106496432, 336243655, 993373574, 720142491, 178236831, 957784024, 932538121, 101107948, 747299417, 421576476, 471781264, 304187784, 580184990, 288751535, 573724510, 911887168, 267041855, 767926434, 250851337, 405205435, 742957197, 391701462, 402483860, 462692538, 452388646, 312373999, 347046570, 863315058, 142110637, 235438954, 405151476, 831334205, 212159633, 983880992, 353832172, 431554988, 993957909, 347861913, 654506818, 336083146, 113742922, 965094514, 263867673, 463436495, 511167182, 609526674, 941119117, 958864833, 340167656, 750867109, 974219699, 785418281, 225935008, 18172388, 550556558, 188053919, 475572540, 426371017, 965656491, 902347847, 576445396, 358080328, 774920485, 417680488, 555672160, 368092074, 366610396, 331668181, 805133077, 191427328, 957453885, 320686945, 995201927, 900098043, 367240786, 923485763, 430449133, 419823767, 164938893, 355234076, 108593712, 342205853, 302838566, 886662788, 149914307, 838689790, 6899306, 851014611, 49205671, 483660648, 173669724, 430043838, 93501684, 744091571, 402832286, 560567723, 792191645, 704538967, 501874340, 581374908, 728695650, 637749076, 775088276, 315371698, 63971611, 299287553, 307149752, 971765536, 469903501, 346391566, 692022360, 244730485, 87149859, 625233445, 690585636, 469853641, 263166006, 459947842, 130628479, 146429460, 550122791, 530608340, 789611608, 117052679, 171107747, 460212768, 763920950, 102954561, 373837879, 869959149, 692467097, 130818409, 261313152, 270886613, 824403371, 418505102, 859730620, 376441024, 30257350, 436252459, 358258915, 629362375, 36932783, 917038458, 483479565, 556484004, 652638016, 71921896, 113608835, 378526933, 405698028, 930125746, 390241864, 553178507, 920726356, 872872366, 106752417, 848516696, 299734955, 217130551, 442452874, 49691590, 968175512, 730262413, 732039187, 318911413, 653642455, 783363403, 415268734, 615422435, 740586116, 724762423, 691071301, 205120761, 534659341, 304312622, 66276133, 641902157, 557406376, 808832859, 622939599, 936532125, 154870070, 327649878, 369793333, 682350487, 642897774, 512279602, 285961092, 445114343, 619383768, 610714514, 993079477, 204526851, 824765407, 695517898, 645463052, 354616501, 770438849, 236149706, 916366240, 111777913, 434882424, 838251761, 687492370, 216625131, 730287997, 92069042, 363606817, 676695197, 617227839, 840521104, 977833451, 541879416, 94667487, 923403815, 95115045, 816604230, 921843085, 222012565, 367746625, 859798472, 953618058, 127948713, 915646585, 539083065, 553232558, 209406499, 692954101, 876193409, 12702356, 333191596, 921084609, 350520341, 643157091, 614128065, 381820500, 347552043, 32844668, 301794311, 903403585, 984188097, 766973235, 938947910, 48330723, 791034474, 519321054, 304666504, 290021274, 697834580, 871666023, 52038838, 935928833, 481315149, 437846568, 269532320, 932265961, 115832901, 452960498, 143333103, 980419399, 319023901, 481512157, 472534023, 642370669, 135073111, 36986179, 444704594, 859586185, 103737554, 360338761, 973833557, 299246165, 36182655, 55550106, 682305996, 390655950, 9346371, 761993235, 760784308, 666058985, 593787872, 947944942, 642890446, 326862692, 135459953, 255358261, 743987019, 592825969, 165143041, 380732297, 897121981, 193511364, 914042875, 113303771, 707876468, 611999702, 747503991, 315020105, 718190068, 559368988, 394054521, 887972607, 294122383, 280878529, 719831019, 818528577, 119676512, 300293568, 834117428, 471323286, 72243326, 573539621, 232962336, 496398255, 419895290, 608304925, 103904243, 656411364, 254897755, 246933793, 483720377, 784422670, 142155089, 149656113, 391069583, 376169958, 152100808, 694805519, 334346360, 854314170, 155012609, 719519820, 515298325, 627127627, 505886089, 338407543, 30325757, 950190995, 509305783, 796110423, 746972285, 609249120, 91942846, 95470451, 821395913, 508743746, 980516336, 884723944, 999592596, 280045901, 475045621, 27782304, 285162738, 99843273, 91798488, 994791734, 522648305, 2091167, 288416071, 212747442, 348353112, 960004467, 723209777, 282519702, 196159760, 975425382, 223626142, 720525367, 471983063, 512977026, 230023446, 992480709, 513456072, 496617754, 875333342, 525927045, 723163386, 487201443, 531737172, 649154727, 396311326, 903871828, 347392116, 8779206, 496748095, 278273546, 585448909, 103331224, 64390248, 618856147, 944554705, 288260705, 797042585, 634923394, 629311785, 746780830, 332922245, 89164883, 342246264, 152138281, 220241908, 69306352, 441285871, 583782110, 664583895, 132544023, 402828425, 384069007, 822418413, 447790230, 647632152, 674888133, 383487471, 683273470, 382263639, 118452292, 583584334, 46995171, 79923725, 119114783, 480764150, 166523257, 679815895, 759519630, 66650446, 574630944, 475038918, 830659756, 214906641, 947721513, 875895129, 776702842, 198625247, 890461317, 986592550, 595987024, 819564196, 84029497, 855139209, 192219946, 566168710, 343155858, 247884967, 157402139, 114261532, 75269476, 177317304, 661191748, 838053628, 362043788, 254087181, 266697393, 683386967, 563801051, 445172833, 507277809, 631959431, 7832234, 437494326, 41699744, 8429419, 775159428, 853798499, 95240338, 936590705, 932603036, 840289958, 109081437, 66990917, 158206518, 862673170, 811571724, 766373911, 210439510, 161187506, 546809864, 968493540, 300490507, 411385066, 482189639, 130536611, 469841880, 736816813, 674234620, 227959297, 737118462, 223640052, 740242495, 285141256, 225903761, 415126490, 202609566, 162951567, 370947887, 408428060, 558693280, 462733663, 721559283, 707420434, 376916167, 522655906, 637303809, 981038803, 877096772, 117209946, 191212390, 190233199, 965322968, 832996349, 264605963, 320960512, 261980192, 76721305, 282926215, 762913098, 59024430, 675712067, 292530078, 639448741, 780461154, 17799743, 478769669, 332785694, 474152255, 312867677, 755954873, 904072508, 307677182, 879413159, 691077253, 700688768, 847137441, 603362041, 920121916, 441249037, 258454613, 59719194, 665319296, 175276771, 314848168, 418676214, 398298773, 722256430, 354395239, 507880640, 884321085, 104468848, 102755235, 38886682, 417693225, 895789464, 474622134, 48418158, 815870536, 17850671, 570616522, 953636294, 374986785, 902856132, 883668784, 255039593, 219007321, 270192034, 471651372, 875303409, 812689410, 403991984, 71836709, 992410402, 563518033, 156428456, 51828467, 941702580, 207006561, 529209102, 542008523, 991799747, 643664599, 43846765, 96603475, 83983597, 896220491, 572160064, 680915426, 604365054, 466758993, 593530461, 478428327, 433245446, 36462308, 993296111, 775109977, 929577560, 40806593, 90816121, 455915738, 465019986, 394100358, 371546494, 815092541, 168098707, 942733065, 694450779, 355310759, 162903280, 504057120, 244996046, 475819319, 816147936, 239275918, 917935884, 897366406, 702681770, 974726920, 774647791, 452763862, 210540693, 656700675, 108871711, 214335262, 88596601, 588986433, 645047084, 82476340, 199242641, 124134192, 944813384, 482170399, 554977641, 357213889, 45250230, 253805984, 133961647, 3034497, 746553702, 264774880, 439194209, 292890505, 566855757, 748626057, 273679971, 31761046, 821841090, 369178731, 441590356, 567752315, 921394127, 705155434, 81370654, 25097067, 975726055, 129424508, 275622690, 531167879, 863524506, 873537340, 482550244, 526785941, 450879609, 477726313, 965710424, 286335041, 806291988, 761430415, 149500683, 252617849, 337002327, 601367881, 413360246, 759615826, 53513790, 936115918, 198048168, 485858352, 857172444, 538796204, 749765900, 861126019, 479889684, 484936453, 196284165, 145158828, 995453133, 793956647, 444598597, 645060430, 717554538, 455617892, 697882760, 315963126, 74398452, 504534005, 870538633, 16426812, 335868820, 833093242, 999610523, 687251161, 495879176, 3802598, 970914516, 799349234, 253498109, 673753576, 267407538, 390799013, 116595422, 896550287, 600516894, 982473562, 95430406, 162939278, 933664124, 499649089, 18035050, 165263999, 538359076, 749971678, 216302378, 808656252, 411146853, 616873238, 296615860, 303505033, 64527878, 710114099, 782045538, 915972561, 874433623, 687054739, 260817048, 948139455, 785771201, 932549940, 81630851, 116702704, 234913324, 654454209, 760727327, 609738986, 392807850, 45532224, 725150352, 315128517, 869198295, 846768992, 313431114, 803824950, 997125135, 908412004, 361516038, 998350524, 121126451, 689628403, 934308129, 935864778, 286719589, 477154288, 831226268, 922908419, 976645133, 461654187, 434048188, 366633001, 528582759, 877679486, 83810237, 643112827, 90999081, 930528959, 653095466, 784667694, 978419973, 922633477, 455591955, 450215356, 70449071, 138793900, 826565005, 723857787, 327281216, 652222150, 753091372, 166014330, 292484429, 16141882, 125757988, 314660292, 8194055, 459520505, 316517810, 203781853, 809922118, 146631601, 105299794, 851779018, 147038075, 343910194, 651006378, 577143252, 352627678, 857392747, 709842604, 934337802, 275549844, 314845906, 295703726, 995401899, 673591732, 103411560, 236004872, 994802740, 528963750, 593573531, 932612912, 876042722, 55003605, 796963851, 372993958, 782722757, 343243319, 810442165, 276141994, 323605465, 162699557, 289469366, 481069769, 834781892, 882141650, 189684550, 993125996, 798052985, 44361245, 528732646, 775095424, 496071609, 416444069, 398338605, 376566226, 760345224, 390666561, 935016739, 654743570, 439949849, 367020355, 757884498, 298478949, 511663656, 25463811, 642230924, 456434174, 948309208, 786631161, 711608471, 904969979, 499185390, 535765291, 552890614, 860756772, 425952074, 543816741, 363319716, 705489176, 584368481, 620176873, 388081449, 722885536, 263095528, 389438457, 332164422, 710152719, 976576766, 350595210, 380901378, 197024537, 714741598, 273213370, 562564828, 849955523, 858639924, 95420942, 557135877, 878229437, 942979103, 247269029, 925659590, 974306787, 39547588, 279560832, 896677376, 6200505, 760350285, 715280178, 578755324, 734130842, 298139533, 979831526, 352317493, 416091835, 304769074, 613373698, 719589737, 607513253, 524531724, 74108970, 266978399, 842987730, 235207216, 186365861, 375162204, 505561304, 993821990, 443287488, 546019767, 76544673, 3694195, 991002912, 97952223, 988933148, 431408943, 949514676, 428417391, 917360943, 92154208, 584167529, 200365270, 90564009, 822547865, 571445673, 242407744, 499787483, 554436502, 952364195, 842911495, 75618905, 341510251, 491556807, 721417574, 384820700, 196756367, 156808749, 587223283, 696995226, 758605056, 433902813, 975732458, 56853317, 626317733, 417675097, 916754614, 998449585, 193141822, 643489308, 667136896, 338942872, 69766673, 5930427, 524322138, 414696991, 540112988, 564299726, 586921007, 588438167, 868452404, 678829619, 337915554, 469187062, 714295457, 276308105, 769155547, 99177763, 767168097, 552406844, 269131541, 178983653, 538004409, 337703358, 955673018, 600194391, 249179066, 521782063, 573013201, 222850241, 584145008, 306182660, 981157380, 940733861, 378151650, 634382909, 768050276, 312246053, 759165582, 37022343, 645804949, 592537776, 822940513, 467941774, 208154530, 974223573, 160318130, 361467995, 433208664, 154165101, 52286020, 779095963, 857356402, 581689499, 810852308, 202511234, 622589413, 186979287, 92424521, 977650565, 102442640, 2886749, 78857208, 686677422, 785764223, 623387940, 695683396, 41120054, 822140092, 495657403, 625194029, 463546285, 273534112, 508002633, 706695015, 591811777, 210827397, 155645507, 143475711, 974496796, 654136417, 592524815, 472457812, 972769287, 180138585, 382823988, 169792633, 696903231, 804812814, 819875911, 997841631, 175584679, 465107020, 125666612, 835714854, 958151761, 276752114, 776566811, 783180384, 441050856, 872921800, 231487404, 938773255, 440066634, 930810015, 514413360, 366867759, 270231125, 368513276, 174078729, 436525318, 402508891, 919147709, 944289463, 929475235, 396227789, 795062890, 576668621, 393878710, 584076187, 482757608, 607893961, 641555654, 841066936, 986182872, 813285026, 857724688, 834126817, 520433564, 119293857, 727581763, 279192420, 199882868, 518696469, 662879347, 593242050, 452080726, 394023073, 526647760, 388429795, 426047373, 665685254, 55115900, 817046145, 109119925, 558242467, 176101769, 368352878, 250541365, 417763402, 537570305, 955685886, 355392052, 385790335, 962129471, 770302513, 560720023, 609577227, 983848094, 531409550, 41047623, 946345407, 572553063, 132122834, 292158894, 118754653, 4149870, 412846221, 258836547, 126039366, 383203930, 6796577, 939906175, 997996295, 645686358, 232971909, 891865285, 4034339, 430213362, 747881183, 113286110, 350716338, 609796395, 586742502, 287815818, 4230182, 688022162, 296075562, 921011252, 34240152, 374178260, 8159874, 109570151, 865084368, 181994972, 975375220, 955613322, 889958973, 623347780, 195904897, 14958398, 574931204, 156982050, 489423194, 129557622, 991458202, 732585446, 251043815, 771270974, 681895933, 857811983, 676567238, 3097996, 91719800, 329753993, 522333227, 310464743, 877366026, 410984325, 14595964, 334049467, 49195689, 522313091, 428838379, 17854638, 610753584, 514181307, 312944670, 269085135, 54194558, 627781753, 321532652, 528426487, 46942454, 250203079, 259140570, 663289153, 914643032, 225859315, 894276027, 915380332, 982242293, 591776122, 271018639, 611743802, 171878840, 364998299, 177724413, 90732649, 81281864, 477856251, 454072288, 537719066, 744384180, 606092642, 513417077, 871418600, 304004310, 325036021, 602982270, 307224431, 707822043, 254091028, 501944059, 135684519, 875645439, 476992242, 817898318, 467021057, 59804257, 532060640, 665084356, 215396346, 455276267, 417703908, 695958537, 685067522, 157585765, 684630870, 414036208, 440196852, 779248519, 481027446, 816408870, 952937215, 232048546, 787046555, 168582340, 479631032, 125696569, 630188299, 708387614, 31239594, 974726978, 274527663, 198260181, 785556377, 735140954, 507452817, 543327024, 313279441, 712708378, 457320815, 677021166, 284594478, 879657188, 959675606, 751972215, 569374606, 384846190, 76542388, 962456713, 556621671, 868532328, 452389609, 647956086, 271881012, 134921627, 656468079, 274694889, 796767691, 296837005, 740150965, 255270180, 899253388, 939426781, 838133211, 823837149, 268223936, 339227977, 905710482, 286823478, 303538370, 603772768, 262913356, 418019920, 453415220, 822835319, 3124317, 770707526, 479553401, 430946514, 190583300, 456602747, 938619278, 301198120, 566936031, 685517372, 943801760, 109923305, 605949025, 325505201, 376757144, 765649422, 957759072, 847519727, 809848877, 639961918, 630644733, 587286892, 528101067, 625081015, 412337436, 180386843, 918440275, 226849931, 439182886, 961940848, 312525222, 190889187, 172381468, 389894064, 621497906, 821232248, 510514463, 890341854, 548036570, 644790666, 875365567, 731241980, 829780934, 713211388, 526859586, 778123021, 259277784, 96741518, 933012102, 236099662, 721606256, 339157051, 350584452, 968523318, 61049860, 832186208, 892821331, 204689146, 331272480, 933104969, 281112254, 274196262, 754339362, 756871442, 482552290, 41097325, 628258476, 465348374, 739764845, 988677796, 381408145, 75782622, 700892704, 932856464, 349808123, 223758003, 210252644, 566212004, 28438325, 31834613, 660506197, 797004573, 635430673, 11119677, 700534104, 897086419, 724736505, 37271464, 599776769, 148621065, 958373480, 961993036, 18146025, 54519258, 498293652, 408057042, 819200077, 932331585, 786967943, 491975159, 497226350, 343441994, 590230083, 26177683, 666154709, 913358944, 262101701, 351134477, 804009871, 333520286, 103285173, 153110533, 637242361, 206055802, 42645631, 248322065, 975678213, 931101188, 251057161, 324717763, 607954785, 820377363, 518013815, 451900852, 527048120, 631158748, 275165154, 764042842, 278891031, 526592508, 543897975, 111037400, 261342810, 47037143, 442725126, 199331953, 660472028, 690516812, 368615179, 806291129, 481710353, 684540763, 953953277, 205173399, 624069672, 522193341, 619594068, 173921214, 223759628, 294306357, 636714903, 98017507, 774680646, 723016996, 258602386, 259711945, 433552239, 37612808, 22042910, 475984449, 748576708, 221701566, 670896994, 23837075, 382557702, 889384298, 4937259, 135223808, 612801996, 865249086, 74439681, 865204625, 56129472, 611696858, 209228491, 751161708, 519027054, 389010329, 134883328, 598204163, 431386320, 493512629, 46131676, 872507324, 746028154, 801065926, 769825996, 847646184, 171521083, 707487003, 447058003, 935097913, 395727947, 961335683, 366349083, 526139715, 736457475, 339409975, 919630097, 403438583, 688599823, 134335244, 204901187, 30294971, 200942475, 310021193, 28650179, 518463220, 11641775, 983890781, 659294422, 474058710, 295039554, 937283176, 688622304, 152835959, 687195814, 618571664, 230153374, 744996130, 107115298, 244308641, 516782696, 706459691, 540704208, 744474601, 881019507, 180140830, 417837567, 990784838, 597290370, 506981205, 319513496, 34557189, 90120658, 420999518, 137586474, 780238388, 83697066, 195344546, 603929915, 748804351, 36448383, 205318022, 680356832, 187533905, 666656159, 566871037, 234245445, 186969545, 527845487, 115955, 605854765, 181203442, 800869228, 494849913, 941335441, 735501857, 440742807, 80398541, 388107936, 503133297, 3197515, 977173090, 948197281, 866149030, 890336241, 737596275, 239635358, 763128793, 464260133, 34597222, 964315349, 966698994, 550837991, 975100395, 482333357, 670852629, 606619048, 136457243, 257228789, 673786956, 719476553, 255045898, 434789793, 444366287, 33716053, 677384030, 531727370, 799307461, 766726992, 868268592, 805286845, 72495250, 760160131, 22466245, 614423273, 642394171, 450064837, 993072964, 602744724, 751187501, 254919657, 596080075, 725099497, 187626331, 289529676, 686447514, 59030443, 617579753, 95757627, 255926332, 430369520, 421793393, 153845646, 691709934, 816021786, 610895947, 140851285, 939394708, 28437159, 145476209, 958148237, 559758662, 848249845, 921372382, 702243153, 555134166, 656801764, 897738223, 203000159, 390106757, 818710121, 685271237, 820221118, 348154174, 769008365, 756086965, 711073105, 960711921, 251585986, 539029627, 942889107, 479045202, 797403137, 354064939, 18609673, 360608350, 221907315, 860590850, 485044445, 160630607, 282451344, 972023571, 595221899, 324405145, 768928757, 308246831, 537466560, 457078115, 341280099, 732827119, 827209551, 365284460, 957146180, 534142839, 682828334, 775037956, 666998442, 502363463, 485545469, 279132970, 336070178, 949728800, 323652840, 755751018, 681927740, 183035896, 704675063, 600718620, 283792085, 914050916, 669799915, 639358090, 965856421, 250151927, 8772769, 214268657, 616964115, 594064258, 688802527, 458847668, 446003312, 570378651, 797270856, 300864262, 253232240, 659497774, 868774917, 549100110, 524496549, 732181914, 173500988, 670667595, 869665063, 603547692, 926926, 914429430, 272748408, 268355759, 597576430, 718987854, 936361271, 391375997, 499825952, 973019958, 181675125, 738481588, 205268467, 291872837, 739022275, 149926094, 263717232, 168178914, 712859476, 762894829, 21112388, 771540142, 913718864, 35967132, 990282591, 235895331, 80891970, 45765177, 867665261, 676387447, 110434464, 668459812, 915840473, 974456395, 955804968, 530308455, 421293578, 338752716, 179945203, 407873933, 230148297, 372248231, 390495586, 268984781, 22278233, 642690544, 916079713, 836434955, 305638684, 62126415, 912864197, 179848353, 489565849, 386010553, 743838764, 754482035, 129036507, 2498307, 78943861, 829277865, 892418677, 813082127, 414516241, 610465301, 409230647, 120925686, 827143102, 686232368, 38546949, 939685019, 511868195, 136316668, 774637573, 143850388, 73013809, 213445303, 765917163, 757061965, 474802205, 753082880, 264023107, 473227731, 929298070, 833859926, 263036402, 768522445, 609588007, 664900084, 369443341, 283111630, 20417587, 840901619, 54231653, 859992222, 615364247, 720624878, 187583154, 582608511, 565906775, 44883342, 727169413, 819523610, 60260068, 768389783, 132575818, 782820229, 482896706, 882701726, 981861980, 873495995, 168773289, 510531831, 774687808, 205086306, 237147367, 233084474, 487412049, 231693497, 35063592, 598909418, 937999060, 958267583, 978295086, 716854435, 229929979, 25331989, 779100581, 991205270, 486940401, 597366968, 155856079, 729535814, 220501769, 923414583, 294466901, 559693808, 208462182, 516415494, 235193270, 578101207, 956864089, 329917509, 19053583, 685764829, 780838801, 249194407, 169210087, 67464814, 382394634, 11756297, 258526064, 203778532, 987427343, 960488911, 566353928, 688009974, 873146774, 799138281, 367264497, 993571830, 363443535, 83238653, 726862939, 923750727, 480371563, 174296309, 753164267, 323409712, 95686228, 169305287, 129361246, 414172278, 452318191, 793485050, 294885095, 152712538, 149484478, 255793961, 681610053, 946620266, 446601418, 134245316, 369299767, 232496389, 296763292, 702230830, 670344619, 124485348, 173508040, 734216183, 942535356, 87383407, 706164124, 372861955, 793927526, 561482241, 715708749, 620079710, 981762816, 465547587, 11018605, 19767265, 220855265, 111168400, 257996380, 309097972, 406161058, 636806751, 972498898, 306759091, 978872603, 944467315, 12661573, 278338376, 320268298, 909105388, 72624790, 290007253, 934232102, 837831850, 303663759, 474769279, 697532180, 584422801, 861530836, 223507490, 427366996, 964080498, 327638807, 827986187, 979939560, 902855506, 704120104, 560066393, 147271314, 675214855, 691992468, 681900825, 834186625, 365361207, 364497972, 667189316, 682860146, 432159145, 132386673, 554485194, 240482790, 664008582, 458369883, 989281128, 179226460, 431624525, 91645563, 152686868, 758925700, 567602475, 449287093, 414186515, 727135078, 932148828, 290999326, 551556274, 116532166, 455769405, 545681621, 498217646, 488087820, 41031618, 604286578, 780370464, 154619658, 198231676, 383279611, 486181060, 881980584, 228616345, 932123600, 324912088, 528081057, 186660967, 890806377, 19188082, 373949309, 869949676, 878927671, 723754130, 532192038, 731046105, 559709999, 946873598, 556211195, 495324452, 440309506, 436174680, 785162269, 231370732, 701815684, 343032512, 386287194, 631927650, 978095954, 622122780, 855426535, 275014465, 825824457, 937368088, 358875310, 65969834, 510507901, 484539030, 725045636, 25686682, 267525123, 716564742, 39573811, 833200653, 283186200, 426512798, 912293816, 559483085, 456625205, 568874573, 35359450, 183765097, 123674607, 87069097, 85763087, 662360684, 326160611, 624473049, 13569885, 828763412, 258898445, 164740308, 289527924, 858492882, 834398355, 146955650, 168187128, 823840138, 504833323, 859411286, 259357026, 412422633, 9147708, 412560843, 302327744, 76984845, 526036869, 56513271, 906859970, 509858699, 552911684, 781866379, 55407333, 693439682, 246276549, 235415042, 652515306, 946406977, 330987937, 651551277, 116597111, 298285907, 97164926, 493463647, 953102838, 406718547, 491507539, 159239270, 562860256, 388941907, 292138986, 787690527, 468267704, 470288309, 75073453, 437842129, 832258914, 184816169, 432407364, 86244669, 140571080, 829751935, 619408107, 611561131, 210981242, 743430369, 792628340, 607392285, 856655501, 85832159, 164852741, 681570229, 639025476, 119131938, 548766570, 316351484, 149383612, 417289650, 356524025, 739236545, 959878008, 724932776, 697290933, 949081786, 25817246, 265607051, 329252196, 795222990, 713599530, 660142994, 278230173, 120397406, 965534996, 520962850, 885014371, 74912593, 972619866, 717357351, 108494954, 959140949, 512463327, 593155902, 221144115, 783578143, 411253076, 84856884, 492123461, 622314257, 667293418, 225178426, 784815321, 917497793, 257668865, 627928571, 936122338, 954161688, 908198224, 542376519, 64835017, 509819907, 59918286, 837037758, 646564554, 610161322, 39725718, 5920405, 90981425, 118778082, 166764935, 281025610, 864576952, 169264401, 80661029, 959548482, 84561787, 430204757, 406161961, 182442904, 524166664, 250907368, 734209044, 450184782, 664998723, 900872658, 212775663, 156810902, 445136947, 53888129, 593724904, 940952365, 961676430, 654921262, 212433632, 123598427, 914919615, 776561755, 574880577, 329770150, 235454763, 956516639, 238069495, 837950049, 387790443, 582575429, 784546926, 843336310, 323158530, 978927673, 274849627, 693213033, 276444121, 695634700, 553419910, 352344236, 115123159, 561286001, 450849699, 764258746, 688900337, 919694336, 93831335, 7871929, 446252570, 265539885, 663999910, 769666319, 412493231, 10275649, 185928089, 574447495, 746936443, 655387690, 225621260, 33626325, 537046001, 461141994, 211694884, 36147225, 961358753, 646629930, 941907998, 80903034, 227738374, 942820193, 382080750, 460359487, 495374877, 93447711, 384645003, 689172601, 186717547, 367563199, 836020663, 565502006, 369499083, 917111870, 127629536, 432796675, 211863243, 470057627, 694288694, 68193476, 529978529, 678985771, 399488719, 783649245, 212378386, 10387746, 768076633, 100232004, 773439854, 126917990, 115998412, 387479229, 49107686, 271021538, 636228886, 702710050, 712029214, 739195587, 594501397, 675502851, 469411023, 283507488, 273526398, 769055306, 244556051, 823989136, 407381796, 33036596, 355954559, 468952495, 101297912, 881399567, 549557262, 101573349, 541712929, 685921078, 204701566, 436728694, 759817136, 47202490, 365296404, 533527126, 242574687, 894711498, 924049819, 142093212, 328176832, 593796832, 124040798, 602654682, 699984559, 412880968, 534776659, 341864782, 707944727, 359392061, 374098408, 486575505, 994993113, 932557553, 417725805, 336306419, 545689959, 717391394, 5705780, 265765397, 988265621, 148287949, 62442428, 892605647, 613745851, 991785191, 893459725, 172459006, 386532532, 321047614, 6517013, 763915066, 328865461, 931618436, 745183281, 580651289, 438015163, 873222862, 153689432, 206243193, 371274775, 13017962, 726042315, 472846824, 322966085, 510494186, 902876859, 254754455, 989285734, 23483477, 268887377, 593211259, 659933490, 49642522, 81939300, 544224714, 291051668, 543219767, 644223891, 557542236, 869657383, 940850797, 234589148, 556539940, 295197135, 299266676, 577686735, 747831278, 519598055, 229059773, 887253905, 939814024, 493700319, 421549615, 435954622, 48167750, 5952188, 887799848, 951265088, 327200808, 575622586, 615518021, 622005824, 119059442, 496765334, 979002929, 943120749, 836865184, 227278378, 175379652, 399069461, 397890881, 944097169, 664147870, 642565020, 377836838, 885048100, 212073339, 303999642, 200755308, 218517362, 472163525, 915622075, 91964324, 497502683, 849685724, 214264421, 175058029, 729010692, 138789040, 990012706, 433491235, 479732408, 712153728, 785782718, 932351375, 204165321, 655861192, 904175587, 291404946, 706845618, 169987847, 515890838, 227988628, 751864658, 898249038, 375479886, 716138752, 889965976, 590641898, 138984012, 862451486, 504252900, 977406538, 777840490, 568923699, 502211323, 5550779, 510745557, 212082544, 776654790, 512686930, 639636802, 862788235, 318813593, 572440710, 644831119, 556576240, 844625550, 15662194, 481579661, 506396828, 448987712, 266421942, 452336934, 961477447, 44102481, 140273548, 241238346, 534969733, 673666200, 203528849, 128559262, 401816342, 588784901, 752332485, 872611583, 932530246, 598749703, 581320532, 68732116, 63677622, 50462933, 46806666, 715359964, 510680941, 921229751, 832510269, 658621337, 520673825, 638016323, 67912424, 99547707, 607043762, 682447997, 333651622, 982779610, 914062605, 351302057, 729706237, 765288893, 495528358, 788465749, 882930574, 695809664, 413949152, 653296740, 352827969, 99552102, 895885315, 380502346, 354390084, 996868665, 950106346, 426025635, 832873877, 766631445, 4453745, 312322491, 905463216, 893378510, 284228791, 58489502, 359291975, 905447857, 624922154, 773689566, 149009423, 168666334, 978327568, 645790579, 529625544, 88185820, 40737156, 3003036, 111849464, 919428477, 509357675, 718158179, 919703100, 22982600, 296339876, 584292476, 237319205, 881355437, 431765876, 548508856, 793408317, 944615471, 467971902, 754611636, 157710013, 480065675, 295707019, 225090712, 800872156, 248109913, 930750674, 100040376, 869150602, 59008290, 732862698, 255954333, 574024659, 807951584, 281664871, 297439574, 971410429, 305393269, 931683700, 473304327, 893586888, 107551136, 300170552, 480861732, 735518053, 479924427, 183083170, 393314671, 990541996, 953811123, 73999066, 157098641, 624145443, 246599345, 735724238, 808076080, 897850144, 137843217, 228500680, 721391227, 442033784, 958742400, 203803262, 325610604, 727158796, 418595061, 502820325, 444780191, 643992188, 111921352, 180815322, 690015439, 541674973, 625855711, 4431222, 593354606, 695629644, 755795480, 948716964, 515854804, 136048729, 872376767, 57165617, 928579393, 631886469, 791528858, 786331026, 118881650, 460505116, 79735947, 318517981, 970235017, 859577385, 849326222, 761997296, 407218062, 940053427, 424028639, 4334474, 123696761, 350723574, 834277957, 138178517, 744068153, 174699396, 675641095, 308471254, 157178105, 644114959, 4879829, 601424266, 839728221, 569478504, 28503202, 115698645, 922494475, 553910558, 656487342, 66292765, 64015684, 70840226, 998292320, 844094342, 552851024, 433879996, 731281676, 368025205, 876582833, 7764751, 278689124, 525468401, 875517236, 818300624, 218578725, 297658962, 859833697, 37451953, 341849396, 688582269, 119491177, 680297318, 289498012, 565708780, 361104633, 833086445, 904588969, 522692179, 251930191, 707914813, 219138410, 632801950, 80243463, 257131548, 382679769, 812228450, 771083905, 427562878, 130317278, 44431534, 266440573, 618361621, 68481604, 621314695, 47568868, 667312411, 466842055, 461159596, 524482792, 438293462, 252493161, 547379658, 541894260, 732181840, 526932855, 216141216, 558725237, 578084620, 457520135, 192563358, 365758860, 729898262, 464635341, 323912290, 793526714, 356283194, 806809822, 164597654, 385396619, 735975399, 791573496, 883936525, 942901881, 910291268, 316961366, 497183215, 879154980, 18123103, 732431816, 69869305, 916910881, 254865372, 939878303, 627814787, 348490126, 713405971, 639419729, 837276173, 899022105, 169843100, 124833444, 526928727, 363709837, 226559697, 584416400, 350880701, 886061118, 238487357, 881677073, 454706952, 519423653, 493531449, 590008280, 424528930, 93485529, 673526337, 332017718, 177311403, 413680485, 610537350, 276038599, 411706943, 873517334, 266952368, 222988376, 840864888, 825793803, 888270982, 618458696, 222772848, 266301442, 443123172, 650172208, 905908030, 320618589, 349242455, 370304269, 81079933, 458349642, 830833476, 986868896, 650877118, 283634297, 882186640, 937139985, 630821074, 213586555, 78288765, 405040616, 975711864, 275940919, 804000556, 243169391, 924988637, 83943360, 55263861, 679702325, 55884361, 776000754, 430230621, 895456092, 204448518, 527639705, 461148089, 246009583, 110011444, 819284534, 341436217, 542702463, 368430591, 20837376, 717550134, 202356060, 540629826, 128341783, 434358202, 99782926, 313984572, 977445012, 418870559, 48886291, 224413689, 683413990, 725742420, 46369693, 161795291, 63119264, 909134264, 505959229, 834657553, 502816339, 636378955, 62013618, 740703946, 132495418, 78026618, 676512806, 827413136, 359951465, 747793075, 536867316, 462799169, 820263374, 578238114, 256377788, 763910767, 819541349, 268899364, 959345974, 646877159, 414631065, 65341594, 155277273, 813492765, 694379162, 935639748, 288969264, 656741331, 460923572, 167975035, 737702017, 900891546, 772397047, 472009695, 900779964, 220419076, 403222106, 947621345, 186420067, 473233131, 925288141, 91057645, 810519380, 396002722, 214352706, 299671683, 7151931, 928830411, 122224679, 965059840, 686154804, 342905383, 975726646, 56415548, 41620279, 937919246, 213560412, 62185083, 999677490, 494979843, 413960258, 115756135, 492553224, 524240568, 631621415, 277391545, 459940418, 689170329, 284166238, 625687690, 296033942, 57296896, 162603034, 414660566, 61979657, 252095261, 987081390, 85160619, 821688080, 706806111, 164273089, 913025027, 73016406, 633905749, 104647238, 822584948, 609932786, 399211256, 467796275, 280885218, 51444380, 958315367, 482996521, 171852395, 271535765, 139329910, 600210534, 330036565, 369325150, 374288494, 181009456, 998950153, 341712313, 901914490, 754282166, 798955196, 691167751, 710692043, 210153888, 683300487, 463372175, 953898013, 923787318, 168894396, 917691148, 364137082, 216204484, 397976522, 215182485, 66782943, 926439009, 863320620, 930326372, 204745116, 111529907, 652903570, 235600891, 529315701, 735351269, 440280318, 856129194, 346240756, 461142265, 954885576, 252212516, 494859564, 18252394, 697048861, 604038253, 700585924, 111464052, 772003503, 508764573, 744461014, 498194730, 192607077, 59014459, 252726994, 444875440, 895561989, 364765282, 122763089, 296380657, 708431098, 70029521, 784406828, 965752415, 393463064, 448634990, 62529564, 179442073, 697680816, 280770236, 588425868, 459949243, 609401396, 405381024, 108676586, 251651928, 71854382, 540292012, 406745450, 494548588, 480473512, 490311952, 156849868, 56851966, 876192476, 583636209, 31580401, 723786044, 420421459, 249267948, 373183846, 500132820, 650928808, 370649206, 4957740, 817081885, 499890236, 938184233, 353246393, 795521059, 781798177, 76004630, 665927282, 116385909, 777035354, 975828901, 333639193, 710839127, 861608113, 691188115, 449093713, 198955798, 331442777, 23341620, 425004840, 418908931, 369054877, 778624723, 121621090, 196836658, 189717906, 80004680, 382851612, 518327869, 376811770, 429464571, 753600420, 467779552, 158772213, 773311050, 643621064, 450224496, 571537341, 313607706, 171265985, 332946220, 40192530, 280359633, 590010725, 433196885, 768913760, 514731011, 491723065, 476451660, 892432132, 115423475, 463917545, 722189036, 385693403, 743437116, 510331629, 14200148, 586808507, 369926119, 442381074, 665205813, 852036598, 362580290, 301624232, 344146079, 240517067, 506850346, 726396608, 749746203, 585210702, 164581525, 553353225, 636655656, 856476935, 182963029, 874282120, 605443271, 70079119, 595545509, 535256983, 284379026, 194278783, 155954826, 79156837, 207733775, 257226120, 306109780, 114930835, 993927157, 445113153, 916699238, 408571174, 692104553, 890472899, 287977210, 492923516, 313351616, 574931743, 123828145, 126038280, 952942697, 154926875, 215392862, 962636104, 792592391, 867420576, 772566430, 343796377, 944327292, 917631669, 941743080, 580458101, 626767564, 60667043, 303696728, 163173580, 105376459, 223085301, 134147597, 805526319, 597678708, 508275676, 550971728, 741485076, 630288688, 999959099, 644135653, 306694135, 650089660, 481531597, 879447963, 29798766, 668869840, 716640393, 195611051, 548790237, 201467479, 324083474, 750434048, 466752138, 266737461, 244413667, 895685670, 832398579, 959158647, 315484542, 321277731, 153834493, 484278430, 516506539, 756272074, 307437792, 680894127, 873232577, 348409375, 365924454, 230497815, 870640109, 246289828, 377816704, 50401191, 96489057, 352049463, 816668093, 10241209, 759982080, 283198305, 341623527, 786239615, 976339601, 251209009, 201502676, 836623043, 477105240, 573567639, 823734383, 902433386, 360646602, 617810974, 69894342, 839965842, 41526833, 350967152, 836619174, 404723997, 939156721, 972018230, 285599318, 947371776, 465399025, 60749986, 183940662, 216537699, 534120469, 122598516, 495470097, 709028289, 216717789, 70268480, 990936982, 777553074, 787344075, 184022448, 32194494, 570215090, 952124515, 496548787, 67827971, 750286453, 331416370, 914571613, 443220164, 345585511, 275183237, 548164867, 618671830, 448006778, 26922112, 638465674, 658372151, 218162064, 71861337, 418494918, 373580448, 441538182, 25197456, 428617719, 327359659, 786141098, 199357039, 291628709, 724531365, 175653246, 200219524, 190346582, 713644324, 250472405, 126779823, 976930012, 161327001, 445870296, 68395385, 921090469, 543120269, 564029886, 332899960, 929636136, 840174534, 849142793, 554057826, 561070101, 839105154, 897524003, 945926415, 552268877, 399520367, 631118031, 972303672, 398719234, 65094440, 770591899, 681985616, 504722760, 134546445, 323833377, 922028817, 986696610, 872840424, 109029801, 859591417, 86959283, 495334232, 538905226, 567910125, 959404125, 957973903, 292951378, 438216158, 490267170, 875511373, 835958362, 768222525, 137793698, 367350187, 524460436, 20607206, 526642120, 467437025, 562688367, 161899453, 731786549, 976607553, 605494158, 381433095, 574132709, 469278264, 982482335, 142876152, 895230683, 943225518, 189338498, 965772079, 152606469, 296363955, 724670356, 912314485, 260603793, 983075145, 108785951, 508067371, 974104727, 757033131, 47173310, 664152821, 232774320, 257816407, 906639417, 218027397, 40484081, 139745142, 328568553, 848017594, 719196784, 656156307, 186502247, 346514626, 326492481, 320073786, 560144498, 140248345, 858550219, 973599894, 219249921, 21044390, 670577263, 413784229, 629671095, 682135776, 474711026, 6005323, 765436990, 885721272, 738549208, 420151591, 602566315, 658609692, 919528692, 853127508, 317258812, 485580638, 727757853, 718091994, 399410229, 34652787, 322379807, 700819777, 909073242, 331975559, 664268994, 931553147, 653395789, 769020407, 780900410, 11025660, 227818113, 484139613, 432959142, 88997020, 543221710, 321408644, 801196849, 728574470, 402490877, 918246521, 691370613, 214028968, 959647728, 464842213, 663373800, 274559847, 757987769, 983186324, 501975515, 927224479, 231005399, 586677353, 45782049, 296829649, 678856162, 95858032, 635221956, 551199915, 841555778, 449289242, 608138582, 72660505, 798077801, 224205948, 480472978, 460628756, 443412624, 357975082, 429510570, 293607334, 855470494, 968254758, 261952854, 182981974, 314777143, 240740675, 362126319, 824482246, 687609476, 337694804, 817412346, 969979718, 270606990, 655352311, 500315719, 648058595, 972127231, 155445550, 525365118, 928728931, 497758841, 134605705, 561755786, 834677085, 200384731, 589593068, 499259289, 541812393, 775551519, 202487900, 222519852, 439129086, 797079090, 100051539, 886645741, 433763923, 312743293, 955210161, 684615865, 369875521, 256393581, 675913695, 282625300, 768934543, 4417206, 163763541, 756102252, 637937470, 417967485, 791796288, 961180390, 186606235, 935960413, 682638268, 50924304, 3933807, 256092067, 1366342, 464017715, 334171124, 645178173, 426345309, 801174697, 232188148, 197147039, 616305550, 721874668, 652739245, 874618374, 651628291, 791203369, 534887119, 875802619, 431491374, 141165871, 749324203, 51196948, 841530975, 446225699, 689143256, 863641109, 793692858, 984994617, 953639216, 146526507, 434889113, 255992444, 599190496, 342791457, 111341359, 794594069, 783834095, 460721056, 206877888, 652932992, 434812772, 562546831, 965269982, 389936314, 232534079, 359743296, 949731858, 575462856, 79244676, 722087397, 588769984, 84449803, 151369284, 475800445, 236644539, 312581742, 568136381, 465892994, 667320419, 489544218, 332188376, 531164474, 695283343, 351614460, 922207162, 390237027, 152348348, 266270570, 982775041, 684318822, 788235919, 775907819, 484576791, 506562958, 206543270, 358542787, 538415426, 945693360, 121434455, 200818592, 194753870, 10520769, 628607690, 285205795, 643296214, 936346845, 685268856, 812895569, 142342149, 80798203, 151301972, 728027806, 78155076, 890317439, 458796325, 734671262, 503973961, 899634035, 581928668, 920317014, 19070499, 912396186, 817753676, 895895365, 291904051, 11751454, 673372922, 309154079, 16844291, 266583100, 366343257, 997329675, 557494192, 601448346, 22511813, 384017767, 814119384, 397443100, 956954416, 357421734, 180949593, 730321001, 736214400, 283578618, 785673587, 482342682, 896703341, 594723969, 767724024, 626839595, 15107764, 150208408, 245615218, 943700230, 128933319, 661429486, 485396310, 166989113, 799703074, 672875441, 588684495, 879352949, 805347612, 848074654, 701595869, 678273878, 415168061, 636289299, 770514626, 873856739, 452061571, 19493776, 648876986, 29585257, 964838142, 490308806, 519898295, 664345035, 90966790, 270310110, 162228522, 587995622, 290733306, 14584422, 20758521, 279102929, 755033255, 745216, 822224178, 38602452, 313638057, 497860940, 910789932, 858545326, 599629104, 986773090, 70566495, 654513257, 9090310, 24851194, 847415795, 81074957, 495909556, 452057592, 674304556, 291720689, 493730442, 83631688, 323093331, 951201546, 832843092, 16449382, 489301078, 630671871, 381475960, 883033149, 602870578, 747509890, 692345830, 874799323, 905922865, 798861771, 256224501, 30942935, 652884405, 288178489, 632838431, 495575275, 478641872, 58556155, 568021944, 986904513, 463850961, 770470942, 2326362, 375980481, 948623405, 907456838, 614333368, 790158070, 903469461, 191497204, 918905991, 969339255, 212828402, 152336227, 70570967, 279490161, 574443642, 334323107, 59455531, 352579544, 107569391, 856342642, 552729520, 289272886, 597136898, 355445342, 519459776, 215040700, 866093004, 895544993, 682682822, 166793107, 859943628, 202998679, 347803721, 456269304, 447675345, 563398777, 432870151, 719846469, 267480088, 901105877, 981178328, 875907128, 759821478, 398979763, 430449941, 749448655, 141853137, 365919660, 453043675, 655490084, 829066270, 476333844, 655776598, 991324506, 220109239, 853649590, 692526508, 887634313, 741171437, 399884955, 54594303, 776356237, 208197577, 526444339, 120758200, 540818605, 810037417, 704105542, 814069257, 355709088, 386294256, 623696136, 787053297, 473910994, 350501450, 185226395, 915584265, 698732034, 379422619, 995399067, 132458880, 440713975, 943276396, 206473781, 828887956, 856715140, 439552026, 641805196, 880255083, 787108519, 461551515, 763649557, 282797221, 560748040, 466311501, 298630537, 387865656, 452477152, 118231865, 324202402, 256469861, 496314313, 696304588, 596026258, 174715864, 639004751, 243009454, 666630087, 520403727, 267033748, 348057792, 684973082, 507619261, 914749136, 379371808, 538169520, 145498560, 336700401, 585359835, 354424664, 195997239, 171819890, 637011823, 230041494, 232064374, 496844790, 83775907, 330850834, 826199752, 775186436, 788221721, 728907966, 809123422, 438890988, 281574878, 339314727, 424619606, 644923795, 565065506, 517990277, 54848275, 343874973, 723338410, 713049027, 766985311, 932473378, 578696185, 689350884, 352272734, 440409016, 858117263, 113789611, 671021911, 312751005, 217866827, 660207492, 282054823, 862756473, 477128923, 348654750, 982862467, 993589270, 100088473, 614342573, 367547699, 924825284, 306685823, 290002644, 451994141, 554454797, 260616847, 382132816, 456829770, 257982752, 252652600, 806931226, 14460290, 27044588, 254201711, 621468797, 120911975, 25974614, 735618204, 819183427, 393716266, 778148217, 761992460, 269301138, 239332957, 862448948, 153746569, 985806327, 739288094, 437389534, 506602262, 641220760, 86775938, 703675679, 296318354, 25576991, 777575852, 303064074, 15143586, 829980917, 237447739, 554589218, 604371189, 234331940, 832498931, 91973940, 211484865, 161172571, 852053011, 382453869, 984189448, 94480683, 868761452, 965479009, 591664967, 181967024, 451090090, 942505492, 893319038, 319364456, 870461452, 694507177, 342084890, 165249536, 572205981, 618246587, 960284116, 356594950, 681944367, 545386101, 148672141, 948262533, 493205113, 642025803, 719929652, 259833886, 296829777, 668993367, 979474244, 663309934, 915875025, 717555741, 176772730, 466964330, 972916374, 824655995, 612222356, 716184918, 234690425, 667093229, 679182069, 180829615, 717232235, 619374456, 665344420, 160475692, 937173092, 451290265, 698847830, 895656770, 285784355, 112904809, 742141419, 409486875, 54165492, 756609185, 790767975, 293671891, 133640718, 98137931, 687153752, 910153839, 644113458, 308922925, 754291746, 80024014, 993188150, 918545260, 349731602, 810253861, 745418011, 532093722, 747670870, 67994161, 220139902, 288024810, 442889032, 35745642, 780208764, 907437674, 526965944, 830445472, 141102296, 909407529, 370468571, 288428484, 425262669, 835500738, 340947250, 617106209, 453766252, 147290103, 309208524, 332519526, 217380476, 456094364, 961476614, 785146497, 433104183, 810500946, 697196408, 222016721, 147735923, 779356685, 688949090, 465142709, 220915609, 685394997, 161586723, 141735279, 408633910, 619062152, 149043031, 806042480, 660808891, 582091844, 646261242, 618410, 740620670, 962921007, 829708339, 177198287, 139185645, 154934116, 332869410, 183514809, 526354280, 274846633, 478956333, 575369483, 412617216, 762659844, 722807424, 244498257, 983662712, 222669348, 330300989, 960741756, 116892145, 45668480, 100495268, 847769746, 494018865, 381441083, 817391339, 433829954, 712234932, 761222177, 502561548, 912690545, 674823643, 523130346, 104734318, 756094088, 966291985, 347489277, 338249913, 512446119, 504165240, 725451021, 375782135, 532188835, 597791956, 524551474, 794084051, 130320774, 114096078, 104709907, 622904041, 805547514, 324740492, 113123319, 412448521, 985929814, 599419106, 54523901, 392607608, 334282936, 114951791, 319570576, 114194945, 973841894, 110652161, 550742457, 47101653, 31963195, 628611906, 589911586, 62634234, 850782871, 708904817, 150921320, 652258459, 873572484, 110807640, 79152626, 911367464, 83094153, 591488090, 423908202, 568049872, 198075196, 406291820, 393725215, 76936961, 852595018, 275384059, 834837226, 125331771, 262797990, 385918415, 338816150, 575452759, 474690548, 362504677, 781861903, 542905832, 385993371, 489248163, 509536466, 507287103, 186735314, 145215553, 605739580, 728758128, 709374407, 836589511, 211580448, 122272610, 114297439, 678603469, 941159335, 697220322, 585440651, 161749105, 585554105, 363462453, 699715191, 447758073, 636499310, 703033249, 228473291, 609798502, 34543524, 520590068, 632522248, 225318501, 81713709, 939956662, 109626249, 159321616, 220515110, 35495444, 704569366, 66063165, 994434197, 735686974, 30716684, 32954171, 986472967, 198804786, 859626549, 481893714, 311966788, 770108148, 451832145, 312435714, 878224469, 402594670, 516480149, 340812188, 577849333, 335531648, 790139766, 575501144, 20074617, 693724053, 293167754, 994919211, 562869025, 129507452, 191508034, 870140753, 56047313, 551527979, 61811968, 285584627, 33328593, 462143193, 901711239, 3839049, 962126371, 259631790, 405445156, 297490662, 392481940, 411257565, 187185138, 996829915, 492290409, 669966383, 333203453, 459724269, 482575491, 582581997, 371432063, 199729181, 686069763, 346314071, 123050611, 824480188, 124499439, 52650978, 865353273, 368261485, 24881613, 701073088, 319396489, 691586765, 475223909, 74390366, 536846112, 53188786, 644836271, 102647120, 709925049, 356548252, 451394681, 360599504, 951361826, 245839023, 942496219, 483222776, 706656261, 820791317, 449952553, 499595817, 753182741, 347880611, 356634204, 10947438, 208774870, 58285304, 951951122, 400037059, 448747179, 876799362, 147248073, 141085814, 464599129, 742551144, 836909331, 637893993, 101913891, 65191905, 849792775, 291880390, 460106495, 304559476, 118000142, 611710666, 924371587, 366362349, 443323059, 914115465, 425005507, 981649320, 372635212, 994298926, 539047597, 262107893, 922385333, 949858349, 887666526, 498908797, 605729185, 784240505, 636668015, 462637665, 234550184, 769406235, 424127482, 117337155, 522245458, 371562589, 758980106, 553980108, 654971621, 158352645, 652259175, 216475488, 140669367, 511115279, 979731055, 621833914, 216514877, 384527840, 803977341, 773637396, 850852054, 133961208, 747442541, 898880329, 252813859, 454621418, 274597410, 814783839, 549559897, 631866532, 947147293, 948674252, 777472383, 387054676, 350660752, 761702649, 567338215, 800109996, 501383763, 811565590, 604491446, 847086148, 373961812, 303856435, 421941343, 121961547, 121435845, 410907267, 509785496, 129476736, 360258087, 997029164, 977136416, 993394682, 772195655, 995805856, 210091480, 882440865, 869958583, 646418209, 794445433, 658889317, 60588184, 418328386, 173168950, 441713771, 290736346, 531750748, 583633900, 933808685, 859091239, 567272467, 759986416, 785408863, 524678137, 107332495, 30422453, 728573456, 816993795, 764397388, 308564842, 876089984, 233551342, 272116690, 930299041, 298330392, 123869734, 741467716, 429249455, 984033974, 464817166, 791891684, 191861567, 869014641, 483754025, 311166741, 706556279, 540518185, 695648979, 206751882, 396165815, 233497442, 683437999, 333662510, 616775865, 55940155, 798395972, 930678403, 395181145, 672225788, 626992343, 436889747, 763923595, 212775405, 566686494, 730397262, 564022261, 178705456, 657438131, 87501909, 792957293, 836034789, 361846090, 904333724, 522625684, 559783354, 869207131, 788538582, 213619928, 609395192, 186450494, 26706188, 679586871, 83492727, 163871449, 710423073, 664433227, 69205703, 522681821, 700923645, 387703912, 419031468, 29219236, 23209141, 324244938, 37099744, 973228873, 634520576, 447333475, 234800459, 239398804, 144794143, 637869225, 515844524, 434016146, 511187955, 333423311, 526530832, 625279823, 14912588, 646542549, 717481168, 629496324, 766403512, 780831286, 840217857, 89465628, 707233106, 918416363, 494617348, 446573192, 713470002, 350904868, 347316307, 57765669, 384351095, 315880156, 974218818, 124665201, 992529014, 249590592, 534815596, 652290538, 181244168, 61922092, 220008911, 142026713, 671092873, 264498505, 370482242, 90771651, 243723750, 162431447, 945747403, 94796884, 768018322, 299081104, 96473894, 763302232, 971543940, 673869773, 559952396, 789325112, 95166449, 434535304, 438372342, 363201109, 334251004, 485947993, 878883605, 133526893, 528450084, 99168212, 744589478, 741568127, 449792404, 354164562, 40375492, 12209993, 580102196, 666777832, 602474072, 647948735, 3737829, 147751414, 773040052, 182635, 108778522, 568915043, 787584675, 427221534, 967662863, 859404736, 230266631, 658903434, 945692375, 255661535, 496239450, 691548400, 501213035, 813750059, 242880991, 165912636, 790181666, 880996728, 212017848, 908340205, 547639609, 263463691, 779849829, 640234328, 824049284, 586197647, 471645518, 47731671, 258785732, 710305963, 737106960, 648514728, 89873066, 955517360, 484847967, 136349155, 671550111, 580228564, 395546022, 570672797, 34634363, 138563209, 719364670, 640889735, 116493170, 330553164, 717593690, 355072441, 646996537, 736409429, 304536937, 875603171, 77805015, 504975955, 683775571, 692648974, 477580255, 366324434, 511575072, 36026935, 809105316, 817485841, 234840687, 645176348, 853771063, 889540726, 847587287, 567830097, 990398070, 815594002, 352345377, 634786219, 845537276, 659902974, 359850463, 166696237, 475113038, 597847681, 774721580, 30447849, 175151725, 386305283, 105842088, 353309986, 95389262, 171545547, 51207066, 191166182, 787880404, 455287580, 267619981, 282034206, 269376442, 221163451, 208675253, 663939410, 769908950, 834433364, 157200475, 94759224, 382417222, 364239941, 680674440, 754315499, 607778236, 713645524, 650672991, 510334190, 786557448, 364273855, 726680164, 909368723, 295084039, 618114773, 439717409, 633683677, 779824559, 311910934, 794023712, 307373674, 975777204, 926957112, 252941124, 50785573, 804610625, 936024143, 705328323, 991314868, 528547958, 343660251, 57593422, 505592441, 522268011, 547220080, 712567970, 739742375, 442367986, 703320003, 749052, 862516731, 697482480, 129123574, 590728461, 192436162, 244354341, 828083514, 505729759, 904177423, 345528039, 843301940, 413327598, 932714483, 669800361, 955133641, 489903817, 817074185, 358601003, 483195784, 923673205, 391658391, 283769408, 209311898, 856254367, 242619884, 90972439, 412945641, 552117048, 651886848, 49875272, 31570335, 877251409, 286999934, 161043476, 802271788, 326931455, 273539194, 660160574, 220970713, 674741825, 387720355, 432281800, 387052952, 797462016, 49722665, 436339396, 222114119, 982585945, 360430469, 934968789, 588763803, 882675316, 775036124, 762141334, 933932690, 576682023, 390897809, 631623102, 421385443, 434248004, 448125977, 717347107, 780680535, 313021007, 387921582, 868018649, 598269016, 490296397, 321265565, 371399758, 158087230, 525243790, 750147076, 601180268, 309118558, 784521765, 731221411, 664426633, 340178558, 393941174, 259335550, 76125688, 587457648, 674636782, 123412327, 399726106, 921994469, 828178616, 572432397, 193730690, 330983783, 713409071, 513426450, 159876201, 279435206, 351228360, 19275485, 4304357, 998772866, 838943729, 856735371, 435789540, 516057022, 675194557, 897705543, 699456612, 205806469, 471189932, 141309408, 403507488, 670074850, 805910406, 689293018, 823221446, 505447323, 529813038, 429023104, 920854026, 306871270, 108533993, 999305227, 106501390, 938604520, 965434359, 61692357, 502421129, 302512105, 331560305, 714479111, 50864708, 729153386, 253918335, 924697082, 618477059, 495415637, 829388280, 135160856, 402771852, 363253716, 711462222, 342755251, 708128827, 423711621, 616603415, 802258255, 503073010, 591805583, 38656846, 661322254, 487132366, 445721197, 151427089, 285076788, 972628857, 213289251, 255591922, 721641107, 318923207, 76595837, 718208841, 954871546, 791534258, 365799610, 848691661, 247126248, 461966489, 859010425, 811370238, 472755146, 996242458, 513906148, 711807449, 54620974, 298083624, 420486212, 489082405, 282057687, 781017210, 604954060, 489102895, 430605036, 836465866, 679404718, 615443582, 203079310, 332917684, 51245717, 204650604, 88067932, 742769054, 123904803, 419039294, 830941069, 353198418, 763346293, 197230926, 98376231, 313123934, 245553527, 410841865, 803079104, 526696748, 839866137, 796758677, 287063695, 949846236, 280518386, 50892702, 790234746, 766085814, 835642842, 860820074, 239626025, 893266648, 899558582, 228369429, 951904893, 286558101, 4441901, 706962712, 23363669, 917928297, 239808199, 521156244, 303337947, 710896143, 458430964, 819070982, 569208530, 973490399, 358571557, 514845948, 998041851, 429880334, 151579152, 583697355, 443392308, 200974585, 907679799, 324840308, 799222916, 749782910, 278974195, 116185700, 831724553, 892030259, 155043237, 711052789, 756509318, 154838684, 313367043, 467877714, 690160886, 264195313, 245570771, 987956253, 663900608, 621674438, 657099925, 973484081, 272279171, 424127481, 200940882, 527963458, 134374478, 48090944, 758994160, 54006683, 348725734, 754989485, 732886245, 539068323, 4999465, 804015582, 262085601, 912819551, 401164581, 549972408, 259711981, 156918579, 67819713, 2860541, 544413692, 268687525, 459777126, 278608561, 50958690, 21809282, 936296463, 811239089, 199973616, 761078770, 722316254, 500115719, 679162896, 381163849, 675512751, 299986512, 536323751, 427433484, 561497111, 103699433, 348339397, 217002553, 534934967, 497958696, 379682404, 872329413, 179176950, 548855106, 35799405, 930860742, 315749807, 834344525, 37550344, 208769757, 536872294, 33748932, 37439942, 593306682, 67684710, 196206784, 115351515, 991139841, 114072939, 818240233, 565625601, 625095802, 977022434, 604099737, 565218999, 473646299, 439320491, 816015938, 631013132, 626334419, 186400599, 882151420, 981399434, 66803220, 393353039, 829144641, 462542281, 640433211, 503009605, 606908914, 825420360, 295650246, 342304395, 789033465, 215086700, 855420574, 131296247, 993657577, 87514843, 382009611, 688253913, 221869744, 128733517, 776687996, 735520176, 271400720, 345321372, 539682369, 787331048, 529096126, 148141681, 690262202, 218789225, 372898988, 508926927, 862576544, 624765648, 260694345, 41125454, 754571273, 977829907, 876247028, 525039308, 130712689, 946705074, 399322890, 171775821, 973250829, 17890508, 289475912, 952751767, 359690128, 161935639, 999393894, 465129521, 158354601, 724105866, 215680689, 355851980, 942773758, 98935929, 144803849, 284606955, 414896528, 433503558, 108557301, 42143237, 578031597, 342057903, 201923442, 246782288, 900603515, 383319619, 516229516, 787525200, 758462287, 439931268, 279821553, 573032536, 154025070, 464142181, 998431397, 308974470, 786892252, 126168762, 379370937, 896648525, 909465483, 374834653, 370002361, 47532589, 996819098, 591585621, 973864421, 607526706, 702396132, 196838322, 744929630, 863794782, 902315058, 615206820, 434310129, 528075950, 518089603, 617336853, 36094186, 183245483, 16930329, 745132718, 93601774, 14713868, 845506957, 296106643, 915699119, 927276459, 659101344, 887402252, 659580542, 170726278, 556771164, 337259837, 192352288, 43020394, 162901129, 84417560, 408718049, 65679967, 375209297, 309098306, 779129644, 822837520, 265512127, 328259286, 27935292, 545806242, 514797660, 736882815, 553306784, 387120956, 407207802, 255363472, 819180375, 407385551, 722700999, 38411898, 592379784, 586382632, 271642784, 159017557, 296528475, 491687592, 201786728, 280676076, 678794601, 852635187, 162451953, 414863116, 721311708, 436516355, 1178999, 861766954, 561986646, 629639024, 442286279, 243731837, 929665254, 418386178, 781560318, 541822797, 697817058, 231220914, 891615077, 918384524, 711184425, 939184450, 107310140, 122742854, 832094229, 121529173, 340919545, 945921201, 430030908, 431462707, 942632119, 523166618, 778467777, 786254017, 691364177, 909300008, 766191707, 641488982, 907281837, 727723414, 739436467, 693970169, 44074125, 911030741, 106078522, 878561881, 137711288, 584518700, 159024972, 177096819, 287016287, 516715443, 836844846, 371185033, 16379239, 665482751, 337738038, 772545413, 718816596, 376927706, 648830282, 963097343, 327736411, 762318164, 946543417, 34576269, 560686002, 580268397, 548484296, 427902751, 302815133, 199877298, 966115458, 523889527, 366679991, 170583288, 504438383, 458389772, 873804234, 163457852, 677036288, 522010530, 648962186, 653475565, 353069803, 193472444, 343264989, 884524028, 284690004, 571688077, 925462329, 773892153, 999270592, 143942920, 799256578, 920592757, 115366565, 875458771, 762236727, 860865666, 956443185, 855217228, 356322323, 750283209, 343698327, 904836744, 872445976, 802391322, 849413614, 439316870, 499446666, 382870006, 654701659, 902438931, 301712444, 568513323, 103257806, 794959294, 468969021, 510938210, 309391607, 546747152, 637031744, 57779852, 836056124, 524847918, 288018440, 297107209, 953801745, 836933201, 564579217, 200245564, 761848211, 201661058, 535616489, 434305232, 587552991, 131621621, 285704237, 555418568, 438427205, 305140579, 345026500, 414052839, 377017381, 347437553, 534454741, 633516975, 297241387, 992759648, 273227074, 258396668, 124635619, 771665356, 483459032, 3986571, 448173848, 627286407, 101162590, 656977643, 988789740, 705587064, 712439783, 282580216, 269527473, 174719818, 192450692, 81665048, 827602920, 901957157, 253867285, 971444006, 963946458, 183404941, 808894722, 148512446, 467989853, 860333484, 287576423, 859896385, 576535000, 58275570, 454720632, 482560810, 676131790, 741969582, 856837271, 148273919, 412043906, 589386678, 660034506, 100442320, 211084914, 741722691, 501608998, 905136359, 473674000, 261378343, 308260669, 737252421, 513343871, 303420822, 377680622, 297816455, 192703364, 86180594, 262976151, 470593807, 766221573, 523425597, 18369709, 582586594, 15431546, 238417944, 298878487, 578107427, 286902568, 407691347, 120100474, 919717905, 403173524, 259709695, 563377762, 954103173, 554013203, 740661171, 866702194, 255372010, 290701040, 813319484, 944760258, 62161000, 575581408, 661467622, 681748516, 230522971, 152343446, 186785174, 91074868, 462099824, 847274327, 970169865, 37771633, 133096866, 59317043, 79387510, 373048438, 40350819, 135772408, 221143684, 814993850, 257059509, 710605563, 725466403, 633980993, 796634065, 158064301, 233958291, 805891383, 979293416, 580329628, 787262059, 633314621, 231394192, 675461348, 938708222, 539123600, 813498459, 199103236, 720033974, 842461065, 54453788, 609939687, 846846107, 649699540, 528539586, 256630112, 664780586, 777273222, 480716841, 468197890, 381953298, 819932316, 459032856, 954516687, 61716714, 577057795, 265102803, 43249939, 992221166, 569672702, 230453523, 940752640, 820142267, 149279043, 75276911, 797608117, 259355897, 409225133, 753187712, 48702654, 336722569, 927771529, 123890469, 922897682, 994569163, 589527140, 601278052, 260573311, 720357870, 166711485, 998362029, 450033896, 127827220, 175364305, 680385590, 570143290, 934914880, 594057741, 205405305, 632662725, 916002706, 493909818, 977316382, 999347937, 65938021, 427623801, 43442589, 117081811, 342754821, 419143568, 287965578, 693153874, 781041860, 627247954, 680444978, 812797036, 175025447, 907627796, 996432068, 461847571, 751628028, 915010356, 343108941, 611005078, 183083677, 485926380, 272269316, 293063156, 204409997, 697182210, 529853431, 435410879, 661652009, 785829438, 6341402, 994915770, 359720844, 122316828, 696732072, 348164111, 960123101, 281562239, 636471962, 582329770, 151690646, 236261123, 918408542, 447320894, 75511995, 698871483, 435983619, 390437172, 139390533, 175228271, 562068292, 340638344, 265134365, 871007437, 181889623, 656654194, 588182074, 446073177, 385224938, 317508879, 492002253, 22288029, 716595596, 888505663, 290594241, 472521198, 202468977, 472285703, 675321705, 494308648, 238449968, 518373963, 597435559, 438590785, 899202183, 56119171, 439461682, 315768373, 612818890, 371080469, 547282098, 300606201, 143981703, 199248484, 513787731, 299664997, 223805213, 679201302, 294714474, 647997571, 443401398, 346999732, 395000392, 684692188, 264152919, 256858049, 175948175, 386779384, 352346967, 689434064, 960392355, 818854588, 97428839, 910509047, 88596066, 868588526, 476981223, 53258353, 240257037, 812334135, 980616644, 56043227, 606734079, 443226259, 583138829, 687694044, 137689876, 291439036, 818336807, 704806894, 424891919, 266463815, 719299113, 744006376, 814785471, 135633887, 733177496, 78247204, 751650402, 306450375, 673381582, 562259544, 706266178, 520540233, 889153174, 170644056, 494694193, 424345456, 820916712, 587748270, 922466298, 829471579, 106646698, 573779763, 947124293, 471129852, 286420668, 706139608, 605334642, 341523445, 444439456, 314294864, 794722471, 840709590, 896741938, 6175913, 464950780, 492717917, 601196120, 73460084, 83486540, 393934239, 228808247, 814285361, 641290622, 763575786, 418426888, 991665717, 910234248, 879095686, 216033299, 693452585, 487920739, 991478126, 731776621, 836124411, 983511689, 970119350, 565952492, 260660180, 466379629, 408585797, 150122453, 624533772, 28375586, 86769922, 207964322, 929931104, 83079980, 521791406, 909693144, 964092031, 254630924, 237638256, 151413174, 488120809, 150378657, 51487877, 947028469, 315685109, 715652862, 980635361, 523588016, 44824741, 730017625, 591434610, 701113798, 730103128, 415707599, 101409332, 353876396, 198850418, 665632711, 482693909, 516084758, 162103090, 695144079, 665979495, 590955810, 923775223, 721169338, 883529679, 740595304, 892709399, 950614139, 75297248, 282862842, 564393186, 275473664, 894550957, 825765083, 352110602, 66099804, 153476348, 45403193, 488438243, 556943640, 760339085, 742048164, 297199625, 714328309, 61781913, 627797587, 56510512, 817810275, 713808866, 580908476, 562488369, 487994518, 79825604, 917080314, 955746867, 828527122, 100088772, 451872031, 154726852, 952081214, 846983775, 309451426, 868496750, 606893344, 143942251, 533862662, 246123437, 379830087, 905397028, 638857002, 487279854, 921290830, 655604205, 955731528, 922131916, 335767429, 575939744, 165216627, 856969380, 299267618, 96940553, 329230750, 374215668, 564289494, 710375848, 632804864, 287261323, 240101972, 281434172, 755471750, 969789791, 521449268, 475047117, 418723320, 334261201, 666269923, 117665135, 830418001, 153786364, 881510295, 776763567, 593413455, 23321095, 936216165, 208823522, 334526556, 535057523, 472955044, 965896881, 835426941, 265338622, 654860335, 212658718, 156227112, 225830579, 920841862, 97642954, 279322827, 597071867, 841172676, 422931805, 232809159, 505316937, 967089300, 483484504, 103309439, 122191885, 411098523, 987459320, 540692627, 344270089, 923890182, 756264174, 429282675, 710638310, 260500221, 452307232, 190790846, 703351558, 826353309, 932245433, 458718348, 440869037, 95711352, 961050530, 612430014, 714095832, 838654919, 833686122, 959015882, 617132287, 591759707, 906999256, 933221441, 414681774, 157358069, 346768796, 873559092, 275311548, 901399133, 491666736, 61002846, 311519348, 540064519, 870150750, 981897249, 906716551, 235862751, 229640853, 830463082, 397286167, 692133278, 957481549, 549653033, 440077558, 788977986, 584865906, 287106195, 475247429, 239163926, 26780037, 424774902, 763680185, 798166802, 525596468, 329936229, 464958632, 552335185, 800783620, 863015384, 693588186, 806811423, 164402765, 485026128, 584302578, 339284276, 234443784, 899814044, 62801894, 122047038, 14061882, 192416967, 716937743, 264754244, 804417461, 157549301, 631406999, 499038610, 238484492, 687822551, 443460025, 249466858, 760372310, 141706574, 708815330, 285793087, 886740026, 503870195, 388580988, 315699850, 784007050, 908872184, 826480710, 291748471, 350112169, 934068180, 982291152, 523056729, 868858960, 534263673, 49796801, 506577900, 776837321, 303474624, 594791881, 369776795, 690084556, 48404682, 967451709, 117744449, 745203079, 401720533, 184846091, 435815392, 533235548, 683698742, 61429920, 109751208, 61993444, 594544909, 215582376, 614222383, 39079321, 769042729, 938925663, 701472031, 473374767, 500778991, 615698461, 583252897, 562398639, 59244887, 299947642, 551763428, 168075786, 116343891, 532351958, 762391314, 859096579, 873760453, 87831091, 172714012, 718044495, 65589027, 745796636, 508992133, 344301778, 571924505, 650814952, 687683002, 854407911, 633236124, 58273804, 15004485, 376501697, 536860891, 32201389, 527873894, 872541416, 645762421, 130530668, 773235388, 218130846, 640163770, 125554671, 700800870, 937442264, 280623626, 596093742, 33235938, 487866024, 401145028, 441355449, 965234949, 834844497, 374988036, 674694939, 427550041, 821741851, 121483976, 692554721, 622309477, 202812072, 970361005, 394407121, 499186524, 449148526, 773619312, 870774967, 460168166, 915796113, 614369025, 103288862, 755144645, 577684255, 363840181, 738655687, 195474754, 548639807, 585390587, 672922798, 438204778, 355929949, 736839939, 474433349, 479866518, 676532518, 705156272, 171220251, 79393072, 143835631, 380050591, 138963098, 696201416, 736719187, 750288917, 690561354, 105766936, 763322654, 762652220, 713379299, 191503992, 397094154, 840692497, 648409904, 7792449, 989269389, 277374296, 554530580, 128419401, 682746611, 918027351, 370681349, 217935349, 534943883, 84590635, 842316012, 200860060, 776868523, 571609507, 547755948, 498478911, 139292891, 542338304, 420395549, 92549880, 534257067, 22898025, 455377957, 174717204, 164140555, 849989774, 123620176, 644576441, 414066722, 729138040, 824572432, 947834622, 180464031, 710890653, 472271017, 613674905, 593016128, 871038411, 399191, 190398952, 777478367, 479111441, 248375976, 937647836, 203604353, 489502750, 473073985, 933424578, 702303676, 248754071, 720356513, 745699978, 631072955, 895742857, 779744951, 755545125, 246730262, 280100439, 815866078, 732049361, 329434046, 274732383, 132580788, 320488189, 35518717, 617905349, 559340992, 956823223, 555161611, 632843321, 734661996, 12015986, 778193767, 83346726, 120626162, 245615184, 621589550, 369104929, 738232059, 43491660, 536420941, 978467733, 615686312, 544896973, 738750059, 804556770, 796618719, 287304998, 286273513, 473665279, 748073826, 371210278, 262526552, 182828122, 816957295, 154390876, 801790290, 813098697, 794577011, 80515197, 470278221, 506059236, 436189703, 966918479, 626572719, 245863160, 292184347, 911921762, 773952225, 219100443, 305614933, 740449676, 973335512, 868851964, 576700937, 854547821, 408855037, 578352824, 374199105, 364339430, 415329736, 706182885, 216151965, 654681024, 738362851, 723023314, 385546647, 797520396, 368285767, 907073547, 378686891, 746058190, 469574038, 226396615, 343991409, 855212674, 37069095, 136037335, 512681461, 181537820, 628788994, 154831616, 454888241, 674796279, 997708893, 323160762, 614452030, 886986660, 214366572, 250248939, 838397244, 830171495, 496872500, 470276641, 367104959, 370239443, 459262182, 147657407, 561343399, 613019485, 770594008, 481902937, 839536177, 700971153, 577567232, 498919850, 152535211, 936202494, 217615955, 662842516, 737595672, 418881311, 492201555, 760533546, 592786185, 374367012, 800635234, 552962428, 910501877, 601250324, 221993220, 173553811, 504954057, 163235665, 526210927, 917425152, 94916067, 946711251, 316396976, 642635578, 706873873, 604515209, 105376410, 401438596, 829951653, 933144992, 675313252, 924657052, 588707748, 235916715, 991979999, 562613924, 929048842, 641934737, 312790544, 894788696, 895646083, 482784340, 90672080, 342929734, 548608281, 572932609, 547998283, 558911653, 27209108, 876357712, 462839669, 726714504, 102651069, 327120614, 49479217, 728506248, 382596010, 457480722, 769893166, 764179563, 700251204, 435379075, 636429166, 905778713, 43770334, 679374076, 323322269, 687494366, 998107963, 271564500, 990515627, 308231711, 628837893, 896128917, 843320208, 382870887, 264714357, 85139429, 140348119, 578631147, 354538822, 4048335, 210195764, 629062578, 387641628, 221676559, 347311946, 298561879, 409653590, 106542022, 405292117, 986894746, 747645365, 640572775, 365361789, 839032085, 346573067, 230133271, 850199492, 685088021, 255108698, 201707868, 652329975, 340873078, 579521357, 939530378, 797875742, 173243649, 518461988, 773598598, 167654640, 891350609, 420109056, 241438267, 965409057, 846322747, 255442642, 293168890, 477309059, 214401933, 151575989, 999686802, 671438292, 403217671, 279827496, 773686537, 624924847, 864109687, 498835900, 526181526, 424562823, 370132077, 958021142, 619361621, 689926739, 914945229, 275722006, 451459162, 505418695, 786306709, 788057705, 399418096, 327174521, 995846504, 848399330, 366626143, 892714067, 784665677, 796982979, 963692215, 838644547, 250909301, 215607524, 209425645, 33637024, 487570401, 944090701, 236637806, 261742033, 961465464, 20203639, 943989676, 404364187, 21084007, 937641771, 988076060, 23371151, 544545664, 77781758, 754681749, 67622818, 635418340, 866612061, 140485141, 191154401, 636846662, 190714451, 2452550, 65681144, 196385762, 285441348, 616432652, 105624619, 656991385, 633956222, 430353799, 80240626, 934954835, 80890200, 198959226, 635493068, 819089308, 605896178, 485714928, 241218845, 722625242, 371366260, 792131562, 655871913, 791038563, 190839385, 864979334, 430678910, 847052480, 802288291, 773241783, 993873579, 57439035, 343400372, 368124417, 754096227, 371522658, 975032317, 449630689, 909454111, 690107781, 814417687, 144781229, 115784844, 285248427, 198444196, 789288102, 668831166, 309150763, 443360455, 109485013, 680025273, 62376392, 311141990, 743072586, 667526187, 30578159, 994643860, 74715494, 212887928, 148237342, 760203288, 745330428, 196606693, 987754525, 437758794, 404891190, 937507260, 613065375, 102070911, 15229914, 151328645, 838102532, 236232220, 191519346, 429042201, 478285367, 772631417, 20458334, 940311693, 276518589, 477835738, 246283514, 97074812, 88734161, 92759848, 991820124, 102495961, 314093431, 661353111, 971206438, 812007547, 414036725, 482045967, 154771634, 811610519, 952305795, 801942713, 198903183, 399949626, 353840075, 584403139, 466768740, 947602240, 127701071, 252170247, 211629586, 347497091, 752980204, 558608593, 234034966, 680793786, 434144943, 57958290, 606329832, 353435816, 9006563, 894976813, 295976637, 334004455, 267514398, 656565280, 364751667, 59398178, 455763576, 44453277, 863027875, 477682748, 839601955, 141301828, 711649616, 754187159, 77493080, 766826490, 168228087, 307978046, 621514422, 7206479, 623736142, 597169952, 955865176, 32435835, 34354190, 633256567, 979190122, 788668453, 957222349, 950409696, 864639486, 745587234, 45990883, 553811285, 230963018, 648629578, 615339344, 594159037, 113687207, 482272232, 119558572, 21751453, 742704770, 199786164, 734535653, 605823319, 731709787, 74619403, 538943114, 409357894, 649600862, 253730538, 562013278, 274455824, 517429287, 783469245, 711357188, 749042768, 883933280, 173351592, 686265159, 975352470, 156354564, 485077778, 807096668, 966395511, 782080199, 854068023, 96785181, 745293616, 851404128, 544373979, 680728077, 447380400, 820657423, 267073584, 266317815, 928059589, 637387117, 803875836, 840953589, 175337463, 725246466, 595325250, 7932068, 319641824, 358185802, 444374662, 522445087, 883315649, 438792029, 822661433, 363196247, 109490145, 353379694, 932549278, 911392589, 890158943, 400901370, 278910050, 934345056, 288086163, 447397669, 529673002, 303391581, 642684909, 510436052, 2452068, 783500104, 213898837, 163176819, 935512293, 110894216, 387421793, 689705100, 716631432, 641549776, 216267831, 919877366, 372224659, 873288035, 583939456, 38472254, 904887784, 127864388, 645092081, 822067636, 63285009, 356798095, 459607521, 838805039, 632339124, 1468712, 345603638, 297307149, 894899100, 409565086, 312052073, 351531128, 967631542, 862708378, 4221787, 489024187, 460792097, 425122296, 701036372, 169239436, 494768730, 703596537, 67385173, 25248935, 240309742, 976449435, 715850128, 546273897, 398650009, 604461635, 892550973, 880573467, 357826380, 267726812, 119458518, 130031115, 479147030, 259399620, 713683481, 612300755, 160183579, 40526590, 347305188, 912364449, 974932502, 350439057, 883625829, 56311945, 737304420, 809564853, 159316934, 227438176, 20647206, 736826475, 295440742, 329147913, 96605533, 335614883, 809573801, 192244507, 13358584, 860718084, 770359743, 820901900, 592243826, 452370547, 508411417, 797887629, 50959861, 164955685, 970419576, 464568409, 94330999, 136983671, 414676345, 9144979, 94703430, 483891575, 616654624, 83233019, 545654569, 737001285, 912502644, 80498787, 799357849, 526498057, 506040441, 994825342, 457032474, 707597693, 454376690, 149429459, 565710807, 897185101, 879503398, 481909735, 804884057, 785716323, 217013060, 509816336, 314556963, 861767112, 193288261, 629364344, 491583266, 168127655, 254813330, 780232306, 426954772, 842167237, 274682856, 166632736, 499420123, 839558997, 424382775, 975315411, 938344038, 841052896, 652860952, 900218636, 520999118, 963747491, 643594968, 553093268, 112618230, 735427407, 443546203, 719741168, 258681933, 741408560, 610184494, 81265557, 401012702, 282621574, 143498856, 126869200, 657407790, 24582852, 520490498, 937823245, 852778650, 254141537, 422310951, 477771511, 246330956, 510450387, 162542121, 717534495, 656062648, 139109222, 382246983, 504158742, 756828196, 992001664, 422351855, 40593011, 912911695, 788733754, 568072556, 798263339, 468221402, 604627699, 745571081, 54329265, 224379249, 16978652, 158477961, 866341527, 754286691, 571870407, 61292560, 580928799, 809666583, 653411711, 711680418, 739784545, 461402203, 962552564, 700932188, 755151248, 872691290, 271840409, 144059653, 580569000, 934252118, 947047882, 821841106, 867633537, 57681533, 411543269, 249593245, 151495692, 376176671, 937687912, 400555785, 177861240, 144494917, 268959441, 173539479, 447521749, 191842288, 580573710, 546342650, 134134906, 244680700, 283203045, 498510458, 140316864, 81467865, 873366708, 919734154, 612221827, 119355976, 856832903, 722595998, 512198518, 199039326, 640300177, 516620263, 417863209, 480229147, 956452607, 839727306, 285531294, 36604378, 860114927, 318377287, 418197852, 993840005, 566446195, 975488721, 341189208, 627622333, 73667105, 464333402, 193258587, 166718377, 70390886, 174373372, 838006823, 765809563, 665977461, 187569982, 30626304, 494538736, 949703767, 778590642, 949922871, 946869598, 915027418, 314072286, 624427031, 942500740, 359490187, 81239799, 759086484, 367325823, 161645554, 785936762, 51373534, 326110723, 374272050, 391202444, 876225223, 935860883, 231896403, 671607089, 110891714, 373375991, 445458918, 528993496, 561880223, 450846125, 925988030, 138344035, 997994271, 65031049, 96349637, 660572156, 555040750, 590393181, 322762122, 415009817, 148320367, 158407900, 952772042, 902890867, 551586489, 940862323, 843626195, 962771051, 603844712, 666644326, 374393081, 225191373, 21278118, 57386114, 15140219, 925951430, 46335618, 843157187, 141149602, 64428558, 702979676, 885069899, 529192389, 483243507, 117237608, 714026187, 145750521, 852396971, 37046850, 94767189, 895445330, 799740360, 812901332, 958582623, 184907230, 922115856, 590526681, 703230716, 395789462, 441477394, 759258463, 440258385, 787725935, 291746238, 613189069, 702923233, 377404410, 139677013, 365998506, 961256380, 435969706, 483317906, 158209065, 546566001, 358204651, 853426092, 30055646, 457226199, 358745433, 724856586, 768422809, 330854873, 641213220, 153942009, 324250109, 668924536, 680109154, 93539740, 748750542, 473539826, 622399647, 334242246, 992224325, 200315414, 259639188, 989705347, 402103029, 804780574, 636010559, 708225532, 669232369, 314089962, 507265996, 600357636, 316063262, 116158340, 429456680, 444212202, 438217929, 63128353, 614818178, 692242563, 687965372, 228819513, 510121221, 75637643, 665214406, 397996304, 500153638, 897529117, 915367161, 240130894, 22520695, 276334604, 926866979, 833784214, 835016554, 476286293, 628585804, 410231549, 576603884, 249007509, 839417781, 294019159, 916456143, 175813045, 760308398, 404844998, 68542135, 840809673, 172275336, 103261200, 23025111, 538492775, 513109566, 241547863, 674047362, 679548637, 265080891, 633168424, 126774711, 734752569, 170848240, 497095257, 96371763, 738029873, 758523862, 271415853, 544068378, 154316107, 794368872, 303347802, 635748311, 962265781, 887943502, 516515780, 239200770, 971160216, 773593886, 928853698, 535568036, 492062707, 220549273, 498493675, 701574495, 161915236, 637896528, 313891535, 581291887, 556719290, 382376434, 823465065, 831466080, 500852666, 842344037, 790340698, 21438197, 656656513, 750827842, 377921990, 528448648, 141186589, 728260145, 670905000, 715038227, 342286047, 966812948, 144222298, 381418312, 68520645, 563380281, 415273682, 15968827, 161719865, 879505908, 873922562, 877273358, 580569983, 848449682, 2933244, 749962741, 460763502, 311975615, 439897065, 764334511, 683861148, 8292504, 107872849, 826696138, 692316819, 121112593, 975731494, 335653947, 815347480, 660142649, 43470078, 205605, 282176925, 359873050, 164584845, 884131957, 432446292, 901674386, 651654039, 749098753, 342301452, 706262918, 608352415, 886486860, 491619783, 809670994, 872524327, 104816938, 130964085, 813355555, 329442769, 524781751, 219965172, 927595292, 532647614, 564947160, 998086084, 18937753, 763726301, 683175891, 858516715, 995702899, 745889716, 100792706, 153506115, 76372012, 521483360, 283086731, 89611203, 31617480, 55198557, 57549565, 563808949, 510553989, 391500258, 768943379, 368518150, 221290077, 376202603, 93375738, 750648536, 284354217, 696136947, 906544910, 96760498, 569201202, 259008825, 918587463, 20558580, 499952315, 753891858, 541627501, 487667754, 38885217, 262145767, 278674949, 756776636, 319106163, 923211243, 530026639, 677064147, 565683731, 947684540, 266200076, 663528978, 573292238, 382006151, 335140847, 793845484, 545746510, 187456754, 467016637, 600234337, 187123381, 160403629, 934170495, 912361201, 366042499, 189110624, 33666388, 416863358, 801158790, 829543675, 592334777, 375418405, 683880490, 654654841, 118432309, 521899517, 726161014, 229011746, 297748395, 897545731, 382840394, 629694251, 443021378, 567238633, 288873026, 560698793, 327517991, 886367713, 378003544, 383172707, 896538270, 9976827, 115073944, 661040601, 1376214, 430212374, 439554922, 770063953, 781526973, 350187526, 316400295, 933378979, 173428392, 262426035, 814450884, 488592999, 802921356, 221797502, 880801229, 603392271, 670842584, 65877096, 340617684, 923083754, 600896996, 500098312, 426140053, 393785614, 257907088, 828850091, 818442606, 963762160, 410929983, 811570332, 508120875, 405539468, 100437182, 744662122, 153380559, 864870412, 58466468, 337220478, 738511746, 437008022, 956113934, 348852466, 312113653, 486834025, 128203511, 779770707, 524093989, 905862155, 348270395, 124027670, 915430171, 869326758, 533964402, 384214658, 12824386, 857541496, 893583526, 533843669, 712768911, 585056314, 170458971, 347630829, 365297078, 245687659, 725292124, 570426642, 502767304, 312821347, 684515905, 897139355, 331215829, 456806754, 979563309, 267837444, 32074166, 953439926, 179433136, 337659, 258923251, 751468537, 49261334, 213184347, 149833786, 963697446, 417230731, 382390474, 764915020, 530971612, 121578345, 366107679, 455485684, 232745, 442778923, 860910116, 279080880, 813505583, 264563813, 665952988, 717083102, 882762138, 510974399, 104640958, 952493644, 799244598, 330081359, 805585320, 791298005, 952554773, 481269664, 923096590, 83426659, 693545303, 800841792, 971740416, 908456240, 67985876, 384318581, 260427096, 237090946, 496763022, 573031847, 412631414, 418431934, 51781292, 161496048, 449227243, 496618823, 355104383, 174734589, 238432978, 285620255, 866037537, 291950751, 757735661, 159768, 721945339, 521974809, 207984283, 653131249, 431783819, 9723667, 680998321, 823036050, 900965529, 110295829, 830246963, 855896506, 218850696, 494427170, 972685249, 837918661, 53344095, 689279273, 224556043, 473558953, 862935210, 674853974, 910603311, 538269987, 399910239, 18796429, 431634118, 91449448, 921583915, 794506749, 653538576, 117651110, 418552700, 85476135, 147755682, 281669879, 670747565, 823145331, 308077421, 511523823, 598235260, 412239799, 88131960, 884781840, 186110047, 375904515, 849310765, 868341235, 130290395, 315113507, 892225624, 534644521, 343073463, 451976860, 497962034, 408165227, 441903747, 573040987, 86977914, 123956782, 396610856, 931558273, 688119548, 790976508, 245573275, 291601581, 656248525, 298008695, 786772492, 613390146, 847099822, 974568212, 321246068, 240564386, 647928424, 847602720, 949016252, 338878002, 75634749, 492525584, 103141922, 998253559, 746996486, 169054144, 339763405, 642506066, 354178723, 522517737, 787172146, 733198521, 457606147, 777309176, 516452955, 234821649, 889419759, 601982684, 608441910, 738804935, 614207646, 716471846, 348406862, 200592107, 707019708, 624100061, 840281521, 458414150, 998086575, 227248965, 852880251, 821086190, 48595945, 399426074, 7927466, 538210883, 990327560, 490188897, 50689428, 940800745, 106269393, 895311027, 637955384, 961963731, 583068745, 351290155, 518841721, 124895063, 94346160, 118250393, 123751013, 567095575, 182110409, 222365465, 543598211, 511953088, 787948569, 310687219, 812023653, 606039563, 502728488, 222671322, 156224459, 154937941, 861139292, 782655294, 232746794, 821776358, 191623848, 34339665, 882976489, 772287636, 544615473, 597248991, 347417269, 260472775, 720535127, 498067533, 473599533, 819712165, 803123921, 114629441, 446524563, 407595221, 899654148, 155165141, 182572343, 582476810, 803824913, 96917304, 608705695, 32018385, 566127628, 29114836, 708600493, 260536221, 281263548, 537873888, 386393177, 681078981, 220181334, 787690871, 207665827, 267407734, 549721932, 531030630, 692173619, 984961476, 977468830, 351793322, 588199816, 479107548, 238954636, 896858407, 596981637, 903434525, 858801302, 821848353, 617487598, 132090093, 817975598, 772685445, 480303585, 488252276, 864278074, 869660804, 18446466, 410190665, 705905443, 816452212, 722333019, 114718899, 248433458, 621374398, 822690501, 344557981, 880791743, 782215487, 935446963, 189469762, 231860929, 68074409, 274422827, 291380196, 201378492, 311604057, 636679097, 674422385, 718934794, 80968584, 782344741, 386682386, 541978459, 600129945, 26473624, 356799255, 49310159, 549277166, 502769990, 735659307, 479328110, 147247989, 923591939, 408962240, 895378714, 458770547, 154366063, 595643079, 47154528, 649872477, 890566476, 870492616, 119349121, 349463332, 566058561, 392226432, 789726112, 444290190, 207795358, 365104680, 389859919, 483121886, 486461764, 612641460, 98575684, 250052760, 423985518, 228653970, 499410570, 854026828, 40881674, 452029559, 712098956, 620405309, 653515278, 98265128, 379052215, 408101064, 429179679, 565599961, 770055062, 546746128, 615313917, 286206970, 885340228, 924356842, 834804395, 535306426, 13996192, 595784505, 311460842, 812547195, 396454669, 347068147, 538898290, 30666219, 310822470, 552167945, 693377729, 648777736, 606809643, 416950238, 39116275, 994647640, 743743800, 547157237, 827393521, 970255773, 196340923, 912530028, 452604715, 269458809, 239757323, 229221335, 719808894, 846619707, 430449199, 371588858, 981649651, 687224424, 417070380, 5217890, 380904699, 229346395, 783590248, 105866654, 44850498, 797492877, 219508540, 326675470, 466150584, 465179336, 839443964, 586047361, 491757433, 440637715, 739189904, 609185153, 820658353, 297669685, 654572171, 678048029, 692327674, 773062573, 841516965, 454282739, 276275203, 589208831, 710851411, 220379156, 354647533, 366380643, 122998295, 812479826, 549098577, 604215178, 209814372, 914072055, 701935750, 875611418, 983205652, 596758087, 995053382, 948625690, 927681121, 465623278, 688864536, 226910793, 255175729, 34430623, 525424258, 393908664, 212282245, 64943964, 586190407, 266612941, 562803300, 689504719, 331042656, 410729346, 192705866, 885904105, 496045229, 78066311, 117923444, 642202124, 381229161, 823133535, 126034898, 914586881, 186561395, 565832678, 991932322, 499218579, 681919284, 491977898, 907078347, 283751704, 985884895, 967599307, 982855881, 22200354, 356593169, 645895361, 806316211, 482048817, 189490694, 550868249, 627232091, 738506602, 277389714, 900356220, 965465105, 642320204, 362466666, 906987727, 363216965, 742610788, 23875957, 533460242, 14477543, 336332778, 878604456, 485569359, 751912859, 538209978, 365935489, 769198444, 998031693, 328513096, 84148461, 319795204, 919112878, 261810429, 49989421, 188097625, 288377556, 165184798, 421486265, 436824984, 633858855, 267779772, 562760533, 16550226, 549205106, 276460750, 319480434, 855854126, 250497334, 813668944, 69405367, 953129364, 16664304, 691032420, 471297948, 339437920, 13902324, 605685687, 513155004, 830612912, 883389377, 876208357, 510861580, 893923786, 557222757, 983249811, 692201327, 270621964, 556158895, 315328540, 396380967, 580366028, 468223727, 63813728, 509272947, 566063995, 730371153, 775496743, 382960841, 235493609, 646046593, 948954801, 92908437, 291004803, 28454485, 913463518, 790740450, 182435888, 487147985, 421501634, 878007683, 460419315, 372962212, 624329582, 420504403, 150682114, 511386944, 629711016, 187031405, 350582580, 206440111, 227579959, 428276338, 727425908, 216702924, 968952334, 519584624, 50209217, 117928222, 996291318, 960158891, 521653959, 223107533, 143139910, 541790350, 407657678, 367068437, 559272817, 872192817, 397274366, 52845081, 199452570, 653984040, 227275544, 612505797, 491445531, 807283331, 110195359, 291393495, 681101683, 129576104, 492923964, 634780850, 192970498, 795300869, 287208728, 763265829, 852166970, 335304293, 179947098, 695272343, 120160302, 410302888, 831918772, 634181891, 170175529, 836062086, 199106104, 790204538, 899386796, 2306211, 260657160, 6944574, 192340118, 964882408, 104726379, 531278451, 788548997, 287376619, 463520714, 834258352, 963361740, 792281980, 621104506, 409176018, 286814982, 124381367, 450924531, 840362209, 918152482, 941738740, 696163934, 357543841, 375179419, 879236908, 838815128, 707150851, 13000434, 657219812, 896184373, 410799321, 254041464, 61276274, 963239117, 50420946, 156965280, 601428529, 52929091, 716428147, 609200529, 554011147, 543502765, 493577659, 78280222, 490380279, 950352396, 326849010, 777647061, 414951598, 976933357, 177811822, 642568524, 618400882, 4046329, 954193571, 959123384, 349154524, 454878775, 521535202, 685079986, 472853312, 440566840, 320525820, 490590934, 429953333, 370578556, 222823637, 125591633, 518683019, 122210378, 277250220, 308348652, 357575120, 58058720, 371840425, 519156901, 741623454, 484389517, 999979426, 149825589, 513275019, 517963637, 455117064, 60023032, 108110138, 282583854, 100625418, 609922080, 602279293, 361227197, 337780166, 258463150, 237433997, 755541788, 440633712, 667829898, 520871625, 549991751, 52837102, 698200506, 800480307, 349216414, 749890541, 368355506, 217943087, 800718553, 2959189, 98495595, 624570480, 205793900, 306543657, 260482010, 429241576, 468202902, 640322090, 821502635, 190223082, 969660404, 956313794, 90029744, 776516312, 663207192, 877721263, 486162291, 642871749, 756548011, 397231330, 211235169, 491834110, 737338451, 111630968, 734494753, 100247775, 601271560, 424252792, 993874956, 246735618, 235016229, 780959680, 49920453, 81242087, 336197488, 46739559, 72173474, 30937988, 798252414, 280870873, 485953609, 706493530, 937364318, 299429452, 150415622, 461289952, 120932482, 206184422, 974467711, 906681768, 543315717, 367055390, 32193065, 157168728, 696680991, 945470820, 692998586, 729070143, 91810378, 41430493, 113979681, 554239482, 652653691, 708044816, 150752809, 856798119, 874327728, 514300169, 936081418, 188121884, 577406915, 124387665, 778249932, 620911393, 486629438, 768917722, 482081260, 146096353, 919824841, 869903632, 830890695, 635695974, 379445396, 633588634, 419540921, 941021315, 145821830, 156137233, 773844429, 842913593, 90163063, 841202107, 782564079, 217967540, 517341231, 352290740, 367604639, 561116435, 821248015, 244148842, 576010686, 327592162, 127943208, 20653178, 238770147, 116403344, 829611187, 873785751, 211788006, 397387810, 207096443, 501899762, 568760900, 542299211, 204828811, 755485223, 500927972, 406403126, 684999797, 104293639, 856314901, 283623929, 205300533, 587623482, 87558509, 788022713, 981110289, 377877650, 108804551, 140527476, 717063482, 323899426, 309930879, 103673047, 711000425, 768468621, 217684134, 948727042, 493584095, 763833645, 126237106, 187402847, 941111956, 510630299, 551222355, 971187624, 420174995, 55728558, 992689907, 536040511, 775829268, 393938242, 784381350, 512360303, 184531923, 338013727, 541871789, 715223202, 414736566, 848369308, 157690982, 439723507, 137212142, 821296177, 457326783, 177535554, 880235950, 702560221, 131772177, 897632616, 238071357, 865954645, 136661367, 868425002, 595364595, 364492853, 410748516, 23620486, 797154329, 38195027, 968988967, 977640090, 370894268, 107037074, 503337843, 827141652, 960963541, 481726630, 812294031, 618584284, 835403834, 806332040, 226422629, 269497427, 362761982, 756455644, 429275808, 718851443, 784165307, 88137399, 376338729, 449027318, 865176641, 58615597, 314146516, 233097736, 682800090, 985435713, 475772500, 710905425, 833395336, 33326755, 760752639, 219055682, 752944299, 926227329, 881770688, 379003430, 384903948, 438428386, 793477160, 488580922, 312295223, 594381371, 425851400, 657273500, 753014353, 701724814, 134368644, 218524169, 461564927, 412531485, 274445407, 529874449, 887024990, 615402004, 50282401, 294769152, 339441127, 746274339, 879518605, 618824549, 298441905, 312499555, 387648213, 520818137, 739253936, 626874234, 585033942, 135919525, 543838987, 263582901, 250769586, 560248378, 596039331, 779558128, 835975183, 704525381, 149609245, 981553345, 993072674, 570082286, 259470053, 603658908, 723244229, 151138275, 442681794, 306171003, 663818984, 586159628, 613983326, 280783242, 191987933, 973623946, 680793175, 234107382, 940472371, 326049458, 627193409, 113913392, 629223251, 47777033, 245043, 996830701, 614955710, 520566934, 842689609, 924052163, 276899044, 830570275, 19011674, 502291744, 36707905, 117617134, 161175155, 496087486, 483057730, 525034182, 20761697, 956747859, 816767526, 385901577, 913839340, 22024799, 421698842, 164188514, 843744414, 662160687, 817584121, 295442071, 882058102, 868964577, 275036126, 214212771, 739542573, 625384606, 128643268, 907698340, 427305156, 422101613, 329923711, 424855536, 354741513, 848435351, 704151706, 451179717, 233934086, 405443156, 16694297, 855400196, 783515507, 498318655, 964655296, 299303565, 397261968, 520069747, 689576291, 756774446, 878208779, 662366957, 37210364, 333917203, 361791519, 730491638, 181980761, 549043086, 788984727, 843335630, 557771649, 157452611, 721320900, 118322989, 954694851, 164676287, 221062004, 658619923, 598283288, 784313299, 833988250, 208065737, 764816021, 180327382, 265572096, 761658654, 863214027, 106279028, 158709020, 25477440, 941675929, 808414128, 436055768, 999507170, 92544296, 85024576, 385409467, 26177231, 190508335, 711449051, 544085237, 773092606, 946031057, 9147137, 901986310, 492508593, 24430040, 719007675, 156331773, 681066184, 259135457, 466115244, 914616588, 179668747, 135106304, 444578854, 329289695, 543380255, 832512051, 830300638, 742532305, 693178321, 362654818, 454325430, 85179909, 771373308, 768347313, 283718289, 781332990, 842520425, 294971944, 628138743, 48418347, 714271802, 993018547, 290133045, 760392693, 380855177, 77328480, 541276022, 643860528, 24887083, 856069018, 995174002, 557056572, 412190044, 621050154, 850705083, 325890950, 913981241, 161619560, 307647676, 377472342, 348847820, 715659266, 563717105, 213179093, 219841309, 864014093, 619960943, 779025081, 669197022, 105200758, 1712610, 578611124, 585892920, 240968257, 617956629, 971660499, 145551811, 919453138, 841663618, 318176871, 280447817, 480586488, 811756392, 901940040, 306589835, 36245769, 268212776, 648047806, 122321765, 553401625, 973126334, 819217528, 460265058, 509159510, 982124813, 545814618, 136038933, 973778858, 876289699, 718127074, 432149555, 114446610, 819026475, 856134517, 173862503, 819184307, 383449933, 564466685, 167659921, 42228039, 380884469, 644201406, 845860713, 13746872, 248902909, 405704880, 491774951, 308841684, 247135843, 760455084, 684061597, 659647924, 906381871, 686900054, 944946583, 265007391, 697489446, 850929243, 650703236, 170322349, 826356374, 490477120, 877136493, 629198072, 170969520, 601766041, 108306511, 308526160, 610300013, 956025657, 674914614, 989371530, 724152922, 406752407, 561621282, 957401359, 608038888, 779638689, 579405511, 830226719, 1361716, 155339681, 791116098, 661990103, 942179664, 378703473, 294198979, 197619733, 460723542, 650115072, 541792500, 19439547, 989458207, 270591328, 82642802, 320491878, 15944256, 572741035, 938614036, 533658593, 120880260, 389804785, 302677665, 833314604, 174531212, 739888957, 246146934, 223348808, 290614989, 533264548, 332310647, 249203043, 596895552, 185285905, 917742306, 101416699, 773274855, 125834445, 970722613, 864933252, 299901189, 744450222, 380608088, 965652699, 756424801, 307174582, 746136002, 233676301, 855479540, 128403306, 286563154, 544287400, 338212098, 994233201, 98702645, 852780946, 491953787, 939544884, 536476775, 55977326, 946477867, 272803237, 51009976, 596296269, 800007909, 846179116, 751715832, 867682762, 500240735, 734219971, 367690914, 634525297, 916585004, 625334193, 474705578, 591768934, 730284315, 977266647, 454416091, 209679072, 943607119, 161045671, 589979405, 452858721, 478161800, 164998904, 361540760, 876419452, 926533639, 960718316, 145132051, 679832182, 323074592, 126211130, 785965463, 901605177, 423569508, 543209649, 340975508, 687924899, 366904522, 289934338, 440559661, 746890450, 329842498, 649834424, 246537112, 337877716, 637221436, 333924343, 670371206, 769618090, 658259270, 769424175, 705753403, 42053232, 848244068, 821735380, 198954534, 714751261, 714175317, 938863051, 411775358, 560041747, 750770452, 251886139, 404673499, 872686658, 937234361, 188846632, 460904175, 586901741, 986646915, 19227211, 565389539, 389129850, 616904688, 253188719, 91158905, 796557200, 578165454, 310326402, 621071443, 631273376, 430117655, 23839794, 868764425, 763736286, 592750275, 756813327, 917766214, 634322729, 8189203, 411926204, 928296127, 74638292, 48275083, 795782438, 964837334, 523828969, 350204143, 847261555, 145939545, 361811987, 591602819, 413204936, 595383384, 503824436, 356590613, 44735604, 213627169, 439524404, 192624446, 961544489, 213949769, 411950078, 769314014, 635639724, 733779946, 141894335, 153130877, 218877740, 812514690, 299348373, 318174564, 672150864, 842185365, 366482461, 489119415, 856227392, 79127334, 448142449, 331040612, 601460194, 199163389, 329351572, 379080992, 931492957, 885448222, 414607879, 9865567, 441840607, 543632852, 993953541, 551355779, 557116200, 548554295, 164515601, 339348860, 697664406, 940935064, 963633352, 131440812, 697837125, 466779188, 980445145, 953032009, 509245392, 306677059, 880499684, 65365690, 322524642, 830131893, 45941680, 616660823, 998493429, 672409648, 646310056, 434597813, 492119412, 715597754, 136208747, 979973665, 825355440, 12636845, 448719488, 123177503, 340723982, 661721726, 16979030, 362566039, 526578106, 591268603, 772909969, 864933823, 687225308, 989726966, 936782861, 86862427, 79493654, 739307914, 867459947, 114315652, 665227881, 277039228, 325101302, 610736783, 386422037, 799900399, 343517507, 162765339, 744348348, 731899517, 521479840, 222343874, 549465030, 487944090, 726596325, 208489028, 968636465, 429354682, 704680156, 785126779, 592441634, 28213188, 131056651, 309993619, 187007152, 504679453, 750708112, 932982076, 164207432, 426942136, 635420477, 406843445, 101269158, 643304709, 441221306, 426391481, 655107293, 959736794, 760035059, 312166929, 456623159, 624148732, 159385433, 986596260, 953777007, 557448155, 188859353, 816258821, 749671646, 505459063, 123363884, 572735513, 96965693, 337133156, 43384706, 924855384, 77008918, 654640105, 263460298, 798903626, 858095101, 74233749, 745723065, 398989212, 937575734, 520579152, 319590705, 722949888, 438546210, 549296243, 48860621, 51197155, 875513367, 954957279, 146383933, 103146233, 785585212, 815508657, 216863371, 840307540, 922870734, 867343285, 579770621, 450250038, 490164571, 991389703, 641703796, 407265229, 921228637, 551625845, 523428615, 796169792, 147130299, 360140334, 785603002, 970625185, 267182551, 364112366, 993391772, 530670478, 65901199, 360230933, 406505087, 608658428, 104822226, 448937658, 930715535, 698528166, 244292348, 441451548, 947154800, 701064371, 658946533, 609794881, 909422781, 559408081, 989998809, 295505073, 760871442, 175400483, 820622616, 738488630, 276147133, 20488681, 891039647, 629475424, 251632146, 263505424, 242423762, 368640091, 223205437, 470907878, 884550018, 340978535, 352285015, 671974514, 277374711, 868506412, 705019112, 900040069, 940660371, 504054398, 772706266, 662283657, 712929266, 163869271, 227327409, 324866533, 132639465, 747834951, 187004990, 882372377, 556791382, 937859710, 314456839, 425305753, 948288934, 851804917, 576973905, 205802083, 279450197, 30416676, 715932020, 696186556, 942011903, 252031837, 918987810, 394695440, 898698400, 300689394, 673951568, 98226237, 230600709, 424006781, 436268414, 114047805, 838517157, 434354992, 450448581, 855931897, 477926696, 884544112, 305135953, 361354704, 242539185, 726194826, 60219042, 980171883, 555408966, 30370764, 156736082, 907711360, 380709729, 901022114, 926595680, 355880106, 559098416, 486834314, 570385782, 636313766, 800078883, 541015939, 675825003, 390227193, 111226425, 909952193, 796977256, 557949376, 755834216, 615545335, 872811530, 939644280, 574345566, 912914538, 719202877, 982849568, 34756910, 820404397, 526747196, 775449939, 339607073, 461570893, 462102393, 358172719, 711115398, 379053612, 419672390, 974558320, 948550169, 427081534, 998301320, 91150345, 797911924, 108013225, 761621193, 305673826, 171959362, 610391906, 646042937, 180881983, 656952004, 47181714, 511917547, 461362063, 570420510, 108669174, 788448614, 207527329, 507481344, 302304025, 195545006, 82520388, 794214073, 753653964, 792126992, 110174412, 660801647, 719371486, 521703890, 909061821, 50038249, 842772780, 154140893, 152299512, 258872363, 593028043, 600764414, 613346181, 673152124, 927938011, 767329378, 629405821, 269327467, 796527314, 652295758, 699864342, 634738628, 983842475, 126081053, 651491916, 699642801, 748464326, 957903030, 775421332, 982620126, 435130275, 635980195, 41160443, 909353153, 615823951, 692774949, 344163480, 519625243, 300195901, 512064480, 826868890, 54974031, 613490168, 848575837, 686507571, 922736368, 744816277, 276079266, 296079636, 442189600, 189346955, 590520268, 621794822, 944089615, 891680113, 513565007, 832811717, 617561768, 156693609, 467613533, 558492596, 104578300, 553813186, 34518498, 201190063, 468360317, 376544087, 746833394, 816112070, 499988634, 190037094, 470342488, 849528371, 497721043, 940868929, 860706981, 230913132, 979773257, 422037593, 145853987, 561107608, 381983232, 571480783, 712399158, 932757900, 495440318, 28402301, 138853759, 22651967, 808111315, 429361799, 961025254, 782688443, 221524571, 172358431, 294422605, 217493096, 172678090, 992936808, 173799229, 259245794, 256805505, 615177219, 814190202, 806180639, 979024670, 132060056, 20556529, 117784372, 233642894, 545939742, 115096281, 209682224, 583594200, 255424880, 59717067, 274549927, 131666471, 633151990, 139467571, 983486044, 212068536, 407702327, 406662561, 314170473, 609057381, 204806350, 380489188, 959983080, 98731331, 28572301, 954227442, 474221509, 444602218, 579053013, 164651006, 961369079, 660210294, 181310201, 497708860, 972787285, 853777818, 367213993, 104217037, 899288873, 372341999, 596478806, 6876653, 388067470, 429736422, 106844395, 362595910, 262696474, 802106511, 524369152, 117469657, 351611813, 814708269, 277636878, 325567566, 696721191, 675842861, 592085245, 754151818, 138074933, 588351872, 260247399, 393927098, 20455095, 352664708, 778597162, 143996345, 15491096, 864241300, 711934825, 205387306, 796390747, 175736912, 213977265, 72411407, 843348613, 709882970, 549465453, 515621888, 189591920, 759774136, 535241566, 803932232, 947444688, 964271771, 889230443, 230319887, 184270474, 315665633, 826674530, 834906030, 954634405, 446545369, 944039496, 122453816, 643895199, 760516931, 142662424, 202068401, 243294111, 723160711, 731647249, 847666020, 902006440, 287034562, 415893500, 364947651, 461710160, 930878122, 107338839, 43291915, 472926475, 744616403, 144869463, 31761987, 891705275, 771266725, 434000439, 200214025, 563782106, 693324886, 991874726, 926265523, 891130057, 305592562, 301308076, 182212263, 968207952, 629700422, 279005368, 445227561, 839448745, 664567249, 453822222, 364909984, 748102661, 807240643, 180402129, 213194540, 239965833, 222183498, 936944942, 776206955, 554128876, 661858630, 457861821, 28167338, 369608636, 416303540, 483894168, 518428140, 549690892, 995100323, 476926984, 899627863, 608069000, 669675651, 547840593, 520804536, 599919776, 415877640, 222262397, 807375798, 958965408, 182328057, 101760711, 638006756, 395734780, 907810865, 485855980, 672239160, 165784139, 884678747, 342706651, 645021880, 961669568, 549194915, 419657253, 630710378, 261300033, 980465445, 959726180, 88558392, 881224540, 930280702, 300540117, 746905972, 954847387, 608502263, 372403145, 35289151, 723330398, 756035326, 368928464, 214197040, 247319518, 581888560, 620896055, 144445075, 38609320, 525102325, 586259224, 182875124, 42800660, 630811607, 218705081, 987364233, 807310512, 399591623, 200987322, 464006531, 551321492, 743570043, 76648754, 785780462, 427986642, 516233167, 267484932, 676309418, 628475898, 998835512, 380313020, 824066439, 599943429, 362322164, 824883466, 805212089, 434294925, 601587028, 788326671, 458821388, 413887434, 743745737, 837917638, 159394787, 329235459, 357331175, 321043898, 794117050, 317808246, 139649744, 981486398, 879106055, 609280062, 515104245, 505762842, 556022671, 160931189, 489195583, 140240800, 183607619, 98905870, 556334596, 863614356, 226175834, 707859522, 295191893, 38646451, 68354487, 296224209, 627787628, 374931585, 413149707, 437723717, 966711601, 323592472, 671690963, 273987660, 791754087, 309814027, 853663379, 81566561, 552819121, 149702555, 368301927, 862604187, 402838623, 349284169, 747205580, 484053083, 71822118, 695198028, 375917943, 106664549, 605851767, 487555504, 970836060, 478542705, 799525831, 136831595, 510820288, 903503748, 812869855, 286582540, 611016794, 91110357, 797152280, 2938279, 47757710, 23104934, 575552013, 694761277, 744456229, 687306414, 321265239, 716796402, 155116265, 189880509, 307435632, 403284599, 917690937, 38193593, 861462088, 811415080, 772051082, 590342491, 720430355, 710521098, 694622684, 273921236, 172884934, 715260063, 347314263, 874898591, 21324035, 895832717, 332386506, 594343913, 790550403, 693002375, 77932346, 205045702, 444905923, 152536119, 174660388, 933795101, 384520548, 591200622, 378629516, 87521165, 125641881, 787625626, 310431981, 849752910, 217591906, 92841760, 450952130, 703448128, 233180580, 343539270, 88577582, 743180295, 447999661, 544877296, 2395745, 693529895, 712162349, 704388082, 418185385, 709589780, 381228772, 909714420, 463839344, 875533097, 71732290, 624235240, 234328455, 849131331, 620029542, 20744961, 39425396, 651298430, 728366276, 340304243, 654092523, 341137214, 576926536, 166850192, 767342380, 927285204, 886982387, 856028395, 868826684, 349744492, 731817101, 155717045, 217098133, 421409116, 241204741, 379033908, 104109596, 557413457, 854816434, 848170611, 767150303, 169283972, 65693602, 542915213, 618194088, 754400888, 899211639, 736481990, 663909863, 52967659, 839603181, 811539937, 658428501, 848013867, 478006369, 637470612, 909331631, 610103968, 12784129, 574661650, 84886174, 801660168, 134928101, 672340358, 589576309, 862590747, 795265671, 293562901, 806276142, 17435055, 468195676, 32829469, 23259558, 152186930, 331510298, 303994497, 954716255, 489713692, 993799788, 149762880, 929889707, 625384897, 295633632, 28999372, 972435607, 811121924, 492650125, 475237521, 929433721, 20696408, 81608107, 727687020, 906564263, 359576693, 314985550, 676528890, 540594949, 398734549, 431913760, 783648331, 621672656, 670597001, 292909422, 477931563, 23977796, 489983524, 364506731, 649088787, 122893686, 449147509, 975830640, 960687309, 44034244, 43989281, 383926375, 386379940, 559437593, 322418379, 956229266, 14597367, 186957848, 76807179, 967210433, 807246467, 871361327, 269375564, 976004845, 519056403, 451583444, 748328502, 754692349, 864027745, 358508997, 247804975, 272215318, 2949372, 542772065, 556821547, 679288007, 526296936, 903773010, 831617071, 120430601, 286042570, 563012674, 569160163, 755157617, 217152111, 419280484, 666439282, 179625075, 532497264, 349355241, 984017703, 344036363, 582920899, 372188908, 18413440, 552541710, 732836734, 805555667, 330716090, 615031046, 144718861, 892064309, 627203728, 78036906, 230708085, 137578195, 905229731, 986895209, 86896474, 388949455, 772135168, 673503886, 632985467, 765631833, 421880375, 885007297, 839099759, 123686965, 772645858, 32367062, 376382608, 500710485, 325497209, 496539180, 310554115, 511574991, 661626656, 834671442, 63380510, 188906442, 804579401, 266149788, 160857338, 97152706, 709421166, 923246661, 455559695, 665538924, 260625800, 42814107, 407074280, 406817579, 151990798, 598866318, 918725392, 502753028, 606221713, 473905485, 351242321, 550196055, 123714281, 443750308, 226831297, 348247174, 251706539, 789196729, 883204548, 934796182, 260116666, 869094784, 781845297, 900261430, 959656266, 595222161, 950826166, 753410604, 569311779, 437721562, 732633234, 453250445, 750692612, 725533101, 385305998, 881471255, 841346732, 720748827, 448519264, 489730810, 663281417, 936270698, 761968532, 662960019, 518934522, 433996149, 486169707, 919089634, 207976247, 78111422, 540142208, 572193855, 23104356, 554123773, 877099912, 764626475, 61456369, 527532467, 955766234, 779672878, 886198689, 307317019, 696354706, 923472889, 462076432, 613506898, 378354713, 783073866, 41087837, 676355157, 353123302, 531897793, 417537047, 988693717, 7275835, 77328185, 293573892, 993252209, 116996457, 373086841, 308178701, 733331568, 992591110, 242779561, 203509859, 476261734, 999597008, 273797533, 822634593, 552598053, 994659564, 359155586, 747471188, 514021673, 587098634, 892796682, 513032552, 644489503, 339320090, 690270924, 484083341, 925719610, 33963532, 775484531, 574721029, 847191628, 470495603, 51266344, 544804399, 182828263, 222246885, 372521960, 381780972, 886950140, 214623751, 822949870, 357654972, 630625377, 781440297, 89704126, 365115655, 685712049, 327579995, 889093459, 97781325, 4350643, 329573955, 910578974, 833884836, 90226186, 659939025, 110795371, 41955382, 928225307, 865047566, 368563131, 54801868, 579569341, 66500442, 879297527, 957499760, 744032981, 440361632, 286074104, 132728526, 70931152, 388753483, 159255226, 209954369, 998598349, 600097199, 246707640, 730218136, 889332451, 775007140, 564750240, 932499271, 627956961, 672570011, 645056753, 423274049, 221948232, 548545387, 98837430, 304995353, 58146606, 766560950, 8941493, 88146726, 120376263, 676594427, 262392681, 751613579, 111449261, 180271061, 312305143, 631526433, 683494606, 337406597, 907142075, 373333560, 381068233, 452972607, 907384064, 556575606, 170850405, 368852565, 883419250, 727892126, 782368977, 381696399, 110122627, 746043533, 965037006, 718073062, 468125278, 950138947, 780626085, 453798943, 149239858, 578492203, 355228552, 874960073, 798965884, 975757270, 898046008, 660904098, 302499909, 148566166, 236066354, 537626618, 18032354, 288207573, 763536434, 181189101, 45031057, 123701508, 325381776, 928705267, 469482652, 735677431, 700460614, 316567525, 192510307, 915814044, 557778604, 56283675, 275895756, 882763240, 82996600, 664713092, 397330704, 839655699, 578466419, 635568203, 912146694, 37006807, 479340476, 684007731, 987790770, 206965980, 718612929, 49362501, 924078935, 379271501, 422410370, 601018013, 504186323, 118120816, 815677643, 933710931, 193416441, 564765061, 501425477, 717020093, 401603461, 370633918, 848644617, 274299680, 530731761, 395283410, 646428403, 751502020, 620124685, 812072995, 683975384, 315919855, 227323123, 423755272, 650350608, 339138875, 920388511, 387436177, 358644487, 641873496, 878806278, 4571152, 87468319, 415431482, 28029816, 951459671, 209620232, 291311561, 235485249, 690129781, 248488813, 359982685, 259879562, 689220446, 641952545, 132135912, 358814514, 894359978, 361626126, 608162399, 557865951, 95857732, 376407364, 894693541, 760415825, 800394874, 70210330, 380597843, 792608353, 291236798, 947363608, 466262826, 328650754, 301778238, 979436324, 728153712, 411211209, 906659540, 346544208, 91162010, 842409192, 965270253, 586918572, 476418934, 22828546, 816899457, 50439608, 324279020, 617892336, 311740134, 334899416, 560869137, 430869790, 369305518, 732323064, 28855133, 253375156, 888398706, 804182035, 728223411, 177820769, 441317726, 587271697, 880008679, 384472, 888586781, 200136805, 525764481, 190751604, 361703007, 22721373, 675758072, 433047965, 794283010, 624773645, 3806286, 200017127, 672189469, 36508867, 349181022, 654244279, 316739431, 244364429, 93619580, 583136384, 400245676, 12423710, 107970957, 303616706, 46166688, 46485109, 734617682, 220448949, 841429511, 961325660, 810116091, 576085948, 943364242, 308478978, 451193276, 969234222, 16640770, 777435164, 377862537, 214974910, 805174549, 914564121, 822570929, 765841277, 431198616, 929778772, 744053564, 979622870, 864515900, 961048882, 738217526, 891277504, 71873995, 444342293, 616040571, 327210289, 756465816, 73969090, 598338825, 307606301, 872871064, 80698802, 97129899, 353265466, 609224168, 200783850, 181088931, 386746361, 978104227, 214030950, 350650102, 384588073, 786557699, 767960205, 517390756, 71652652, 831486597, 512439277, 751262587, 80099103, 350802933, 512080884, 317200351, 609528981, 739089895, 818199847, 792384858, 669065025, 566508843, 507062129, 732548473, 186123421, 335427207, 486319936, 427614127, 604384832]))
+
+test6 :: Test
+test6 = TestCase (assertEqual "for (continuousSubarrays [986576039, 601518733, 744798894, 581260814, 819551063, 25280437, 912790185, 566200129, 512449764, 813324259, 935779477, 75523677, 110564640, 996917008, 24329099, 81044379, 639852709, 485230276, 868577009, 991579590, 173179412, 153444229, 696412320, 668285025, 665305513, 374760041, 395657366, 431207308, 723415171, 78217974, 231578479, 44787201, 520128365, 190886570, 99544457, 834752183, 839840220, 23156798, 568958840, 828175027, 573601719, 646397626, 359922464, 610592950, 761436656, 991866724, 975548126, 596278074, 51352469, 709760089, 137138347, 35412739, 740326384, 428595150, 561686033, 826522352, 528512395, 166766340, 903971986, 930175620, 291876450, 325746465, 226954604, 342184919, 786100937, 33431144, 559960353, 228435020, 981753250, 477182859, 853319621, 531074058, 293762369, 756977260, 982115626, 109505171, 97662291, 597546699, 25539355, 514871975, 21469506, 866882384, 749542329, 187314233, 668059077, 880111727, 802394008, 684226238, 295590795, 933475698, 603784570, 805706585, 106664159, 706632391, 920925278, 534703454, 809799056, 533469791, 699009564, 574769508, 286021995, 580299338, 927136527, 182061139, 50256606, 963343548, 2079973, 759980720, 239896735, 944973942, 715128164, 958534922, 284255197, 962076026, 543624223, 280308022, 922047898, 608663068, 462272761, 947562676, 27146468, 341833914, 373203844, 406807671, 587150376, 428133803, 347613221, 515250274, 825463982, 900359800, 907386894, 758524660, 920655262, 270154021, 958873500, 110226802, 114234297, 326643960, 5861654, 49217327, 698710492, 81052676, 486338667, 421658147, 698878003, 522872439, 376629510, 608900195, 61788074, 690780333, 11942994, 539935304, 292087332, 12152539, 317686301, 915961372, 150374730, 869266096, 1003629, 142908381, 204197001, 394544263, 969450770, 171841363, 370991241, 650184990, 292091080, 505109506, 592028441, 596806545, 834483109, 673378639, 767537232, 201264498, 585809426, 849412291, 631715774, 259388106, 462631908, 473311307, 585798379, 905873551, 750313742, 391002361, 68500749, 679610590, 82384498, 896993563, 234936883, 75315577, 354955786, 941817712, 104302093, 713662616, 936482013, 43657259, 745642043, 405663793, 895477621, 69916754, 662157906, 108643574, 133515441, 947816601, 42991330, 35801373, 846689945, 783572043, 615345014, 800773933, 436105384, 559804754, 325938750, 603283553, 389448681, 445037108, 787491667, 185306896, 634916738, 477037552, 787317467, 959074084, 555832639, 203512770, 942124651, 552642935, 946815932, 511046362, 791528968, 910331118, 417421115, 171635618, 60882630, 695292693, 979469165, 954647745, 664340639, 608490206, 175615746, 788066583, 210609215, 662081854, 502078228, 552639148, 408995863, 928867883, 788865214, 78446845, 390010046, 956279858, 273414686, 456561571, 177779246, 215293145, 144082790, 620526520, 398982331, 234873517, 527385946, 613566832, 477765282, 278465563, 989951319, 385737853, 481073764, 240056230, 749226389, 667689555, 935319591, 540379075, 897989401, 613685104, 385113713, 338480692, 257208208, 875552232, 739900834, 742532026, 42254847, 502853370, 396247091, 481159225, 557415631, 914083869, 281797106, 292457360, 112959996, 351547590, 265676736, 923147125, 266464434, 687374493, 580794148, 716602199, 338798401, 913791489, 677172734, 738912761, 152982023, 525315575, 430182817, 354623499, 937500825, 376724848, 757581895, 876521213, 551782406, 151721898, 789720210, 342190487, 319203609, 966485054, 958968137, 513122548, 975613889, 866247534, 281738095, 917981986, 531829981, 359842995, 6622721, 904674242, 974976449, 748258437, 567842348, 638743706, 61494949, 303462355, 445161378, 749225931, 787139081, 668259182, 234981552, 462258435, 726625304, 341510016, 577058185, 992554850, 749445478, 582595339, 780481917, 750180751, 262124589, 106535883, 367687558, 971214612, 61319084, 965726400, 657516977, 883701697, 862522904, 64115696, 513783295, 999052937, 486700811, 796573702, 280239976, 234185826, 461204650, 758125925, 126775922, 838175995, 806801831, 700071822, 989267637, 910282003, 878022355, 244255278, 225338144, 881659572, 538074143, 865267119, 764307133, 253726616, 4475863, 87932273, 729809419, 268502433, 65681120, 535102289, 173483085, 798364418, 968369339, 396296576, 73922307, 899252389, 412462346, 964316305, 761282647, 255990326, 949404058, 812590373, 34026036, 97939548, 322224015, 510940653, 506559314, 503977550, 774514848, 36247643, 437658632, 479381, 51878343, 337682815, 597869299, 870247035, 663466909, 420381212, 288653041, 58094622, 9581960, 423701880, 571611425, 593983811, 982942712, 615198986, 370820134, 665231038, 466181876, 543638295, 78012277, 808025712, 110429581, 481671110, 198451122, 555980045, 252794221, 789193201, 299465441, 145553688, 174638070, 110315978, 181179796, 552120081, 995670736, 455857983, 158953526, 789054048, 936324288, 712896109, 176108370, 623745811, 385669462, 386367438, 216076496, 852262157, 392113704, 800367361, 35297933, 382493560, 153843060, 691569272, 206751308, 496810232, 948567947, 909942776, 22548182, 269168821, 784279534, 404708186, 642552253, 157290956, 844643546, 749012594, 319158474, 309157145, 449213107, 253681659, 306003941, 528681663, 947286174, 13134287, 868446224, 362358182, 264069010, 580630077, 322123947, 773675502, 415357338, 756222969, 259106790, 105858528, 30623735, 167775546, 197595956, 450054857, 724671100, 682749838, 558106911, 883549230, 269667837, 756991009, 252082110, 787111586, 56626871, 790643061, 566304803, 587813314, 77961425, 273087539, 830963409, 133834852, 587489818, 989427376, 498572580, 639829475, 751779327, 41302627, 222532052, 697417077, 52806010, 982963393, 149885608, 395105597, 645764472, 191141038, 845031106, 312109458, 729512844, 176127964, 809793848, 664968995, 704916862, 875673216, 141833510, 182051317, 992183445, 297792113, 355574825, 606046037, 194300931, 632720241, 610881837, 186754220, 720832108, 146071000, 243419454, 828709151, 43639123, 666855247, 163869981, 268559201, 361847381, 104957194, 190591744, 634468624, 321594174, 862283064, 205152266, 177397962, 556311619, 863894633, 373831766, 942279545, 653006149, 160951075, 236801325, 493232814, 339583131, 484320386, 21025914, 256711360, 849624193, 401395721, 496381864, 332735864, 217338016, 331625978, 57067206, 524966047, 567366924, 118409006, 770385788, 603521587, 306874647, 230486584, 917544600, 410833394, 488486675, 88688023, 501855718, 308799624, 198553054, 293888196, 109345877, 584831299, 935375323, 319691116, 790173522, 433793231, 350306105, 656922791, 254787836, 648834473, 69769848, 79680095, 577271913, 577615598, 83426119, 167136032, 716304509, 840447832, 554251141, 917904548, 611101123, 78487475, 472387413, 187390057, 831236707, 74874951, 451113402, 934949752, 252310862, 79253725, 903689754, 269740554, 752807142, 982768130, 5205489, 201734494, 538149812, 306360124, 504690456, 216678578, 141422302, 142708240, 334420714, 789870378, 332615884, 644067726, 846846492, 889176620, 421265897, 962675830, 944303527, 217209454, 293583694, 823750001, 492538867, 305676053, 309983666, 902029229, 854985728, 144425088, 642729776, 526520803, 366059436, 172215933, 976733788, 909084484, 124595472, 453968460, 99113563, 173436747, 636604497, 866277760, 505575047, 520608862, 46301245, 868493326, 269333051, 940295888, 595054344, 809152297, 540724164, 154224803, 873893058, 733259375, 536533553, 617692870, 733884839, 460666106, 274602303, 950741840, 468289936, 544801847, 496872794, 188022530, 308361846, 473824480, 644807993, 410054596, 482314084, 372411277, 28145300, 517628091, 494398440, 108336654, 231230366, 455525638, 785967900, 909775888, 663148606, 947641873, 547442634, 327586571, 368743086, 812934032, 242359806, 900501040, 481701585, 625197976, 906163166, 572389826, 749804175, 770180626, 423149784, 690990313, 764392216, 779926189, 145452549, 395972668, 642625619, 450047676, 140155889, 654897705, 340834937, 596247349, 253367486, 772441625, 397178326, 516751524, 656974341, 141116671, 773481839, 180473357, 636719804, 936547609, 336092653, 191634486, 258920566, 953378934, 161483711, 733252003, 212620250, 72639104, 920522471, 376147673, 351072337, 750975083, 474000170, 431964154, 604802291, 936933417, 536723843, 325972811, 81511779, 183576561, 394027356, 865906962, 408834402, 520074229, 245029833, 415970722, 487181359, 525147700, 955420289, 419546405, 35534058, 244737094, 351570728, 393362930, 864420719, 987440502, 914151300, 732024790, 517887877, 940220056, 474807908, 54332016, 450628737, 248165962, 708385943, 277002523, 540665248, 729421264, 372474544, 173854046, 848679620, 591958283, 387139566, 366709532, 490529618, 733230433, 555310779, 212871363, 634593613, 789815897, 344012663, 192291081, 754686060, 693344777, 852397477, 482465668, 402928302, 976386953, 185141768, 215267652, 159292854, 640962388, 156621561, 706192644, 946595396, 641923802, 848690811, 729896504, 199608705, 447301337, 736791970, 878841552, 30301284, 468198364, 332347314, 764408034, 62518773, 893624383, 511404789, 216219825, 459444145, 9837850, 851832373, 396526624, 408886323, 260246028, 272648477, 662543268, 884571944, 504589438, 735466421, 943634437, 987392460, 174198798, 985001154, 628559284, 274251988, 739793275, 768341410, 880418500, 364542649, 393945987, 247599498, 851319424, 345604729, 455254550, 913063364, 598539995, 386146064, 695090808, 156259258, 73962034, 588884334, 800086874, 740188025, 59302474, 181600767, 66082533, 510776571, 36633108, 728512690, 635382302, 393939959, 767127464, 687207892, 323448714, 903413875, 784772324, 769847240, 385363892, 277499606, 552770739, 198009999, 865700508, 6122709, 998815288, 639486594, 737034697, 426771340, 995923120, 843073558, 674510925, 171483616, 950272084, 473017770, 276155357, 946732144, 77878333, 326866906, 284809603, 11916753, 76483263, 491178725, 195357618, 32928657, 360264741, 368002046, 797667558, 479883567, 3806652, 100053441, 49764335, 233827150, 966165851, 299691293, 191059346, 424648450, 937697832, 891631170, 810474530, 141424072, 494037220, 426259722, 105210394, 673567320, 480246657, 395288408, 530636929, 499914791, 304213778, 715201314, 901449164, 381721199, 913862153, 179346872, 148469490, 223565496, 79303151, 994169369, 470918881, 86267931, 501375786, 404137902, 788330108, 296937007, 253346788, 845839600, 728150937, 44676193, 957357770, 152888575, 835705180, 196081889, 90926363, 504445250, 806072267, 53423666, 459045713, 761478620, 748173243, 377592615, 794069247, 46074891, 618733588, 613480327, 807958893, 738744322, 177399515, 489924779, 737922419, 339764223, 784456098, 666610787, 123385633, 200519390, 916326464, 524138634, 459359318, 432076898, 92551987, 126605305, 647923175, 151676410, 748276775, 952524998, 610607034, 535093358, 69335779, 651055828, 968479865, 851695058, 219941076, 587985205, 933745954, 259887416, 56597410, 389914717, 402822378, 904001354, 527432726, 961502247, 470139454, 745115869, 524821435, 720089395, 497674929, 538781692, 126687566, 849812508, 510357606, 700626030, 641862225, 900942001, 700885907, 735519805, 584910579, 994399994, 771534636, 311788676, 305841072, 124840659, 426699010, 925815049, 828691029, 568176087, 358396156, 770402906, 616542608, 502606997, 33565309, 756280776, 490494482, 865071710, 124254311, 505042767, 507835801, 149903760, 541774159, 680101366, 515097761, 910887206, 200928602, 25018206, 137263416, 471738493, 300829837, 772014793, 477042531, 668810692, 449670700, 274442516, 617516315, 216702299, 582885872, 630457303, 455678745, 112646971, 716419192, 820618514, 854269641, 742875822, 682600898, 27486674, 648247165, 325734409, 149726892, 996802993, 860986715, 222003754, 856662976, 18652603, 202240329, 387477952, 270113319, 679287443, 974880243, 49504286, 895388288, 22300516, 13751064, 976411258, 958640931, 221159301, 327380748, 955221902, 9425450, 181415223, 854854441, 989110191, 329839749, 733713179, 6866679, 187093683, 723886631, 294524679, 726149748, 135382460, 935085411, 495085316, 497704213, 99324041, 511778957, 543128576, 996621738, 744290255, 301798288, 527774475, 2283682, 459737942, 731435429, 349076351, 375330492, 381836982, 524367832, 997958386, 606338879, 365247869, 989070681, 423330089, 430331870, 430450084, 674033136, 699278942, 982132569, 673877576, 478823225, 588011223, 572520597, 52590548, 658849578, 109285107, 498488460, 534344859, 484576872, 557655008, 900053888, 922972287, 559122206, 484335605, 419515969, 964121136, 498330080, 183983701, 166898608, 728609354, 683295908, 951496687, 913234493, 228643392, 122451236, 326248725, 381025726, 553549307, 175233471, 787119947, 346584126, 807008210, 564651643, 744271522, 514794366, 924364324, 545214668, 658854025, 880745050, 241643207, 548526374, 998536424, 975604461, 478134892, 829968428, 612135198, 438573255, 687846362, 224800446, 678060653, 957344959, 492412450, 36273190, 113782707, 865842852, 704565173, 406187724, 973340673, 301125429, 478044041, 314361811, 180597293, 744883721, 628700550, 604143322, 451008067, 480834434, 183988201, 859180156, 375001260, 889386689, 451787242, 652102751, 167156824, 413155326, 519672357, 319886201, 300779618, 58124313, 830567026, 250707961, 513720380, 610627934, 112843799, 191436616, 747163762, 115774537, 151884727, 266636220, 657665974, 920606028, 164187109, 862474737, 917705845, 82584871, 511206272, 107922931, 103875332, 542355762, 297863866, 700687804, 412327941, 263152644, 319526495, 387630768, 650176479, 651400390, 522673786, 50844782, 887565269, 395477533, 706752245, 508399207, 413363997, 445076369, 169200104, 130908062, 768044002, 347537954, 697579513, 796408345, 132850467, 597617278, 602475506, 945958255, 23823331, 970944437, 537329692, 103848475, 47006196, 525250853, 323465378, 345220343, 647712376, 620256803, 561723687, 306535944, 147888705, 759909856, 313402006, 525375313, 871856491, 301130834, 137546158, 499821461, 714292167, 580737118, 84985910, 468713941, 728211737, 464327518, 280414810, 846609010, 5789267, 711396078, 721326933, 838225532, 889825409, 296774397, 573675103, 296627806, 694496114, 228034366, 312583229, 413396179, 650706030, 810763132, 656748092, 326338824, 367130339, 963050464, 612700577, 38078765, 369620097, 402721352, 612846892, 719511018, 887400356, 780477034, 405419444, 639851418, 636069705, 807024698, 324792234, 448441139, 556194397, 962751237, 397277287, 250853382, 117616066, 333782066, 56221931, 346456768, 668230224, 205064744, 674434480, 152685602, 333711527, 833552139, 946801018, 134996218, 396930307, 704721069, 586389265, 127493541, 293380144, 315930416, 876779591, 415510520, 595467505, 186618457, 571640009, 210841865, 115248499, 697830266, 785552679, 691774331, 531882328, 320296450, 319948371, 948942538, 781146654, 125631270, 753976436, 933707675, 286978444, 721564824, 110497466, 360327851, 220193725, 969813144, 133861104, 86184704, 645801405, 412238564, 524205942, 669156985, 725418297, 572124885, 235305580, 620443728, 378158887, 992849496, 944447407, 289657433, 972558855, 760792668, 939409858, 113833843, 121870897, 989112181, 968319028, 461233291, 313896944, 166320624, 978652417, 828343576, 285392956, 930176169, 479437221, 909866334, 327089606, 741593535, 695211265, 653341008, 493140645, 943135234, 892369361, 391458871, 372977658, 663522758, 70745703, 296573451, 987563405, 930230329, 818530969, 468783218, 284551398, 785158843, 422830132, 866042448, 539399871, 172742336, 953610433, 735901718, 755671210, 24687842, 918059021, 891693651, 773627646, 262804676, 845835876, 104771818, 330078383, 673195378, 199614261, 715142396, 570957848, 195133203, 659682907, 551511513, 597871569, 389806908, 728219943, 912136988, 922329718, 980340515, 786933442, 555838838, 348248307, 995182610, 553338903, 634432486, 238909929, 505060720, 60007623, 332681811, 229138999, 750056366, 135608661, 867659239, 517673397, 214592814, 329258851, 110379871, 536266069, 831653225, 156869239, 57866175, 372771662, 198587103, 232800264, 582995445, 619477519, 145249641, 994266095, 883176178, 627987925, 673311512, 359530039, 223425877, 668057290, 320699950, 712859313, 576683225, 752391878, 967753571, 992482062, 38524512, 810422231, 190495740, 990497174, 682326920, 783553180, 586085802, 913440283, 245612384, 86481359, 507195397, 692434313, 24230073, 867891023, 985253645, 249976897, 211546544, 132271048, 68067628, 862357524, 158078750, 758267781, 114455258, 712586056, 546994934, 808326761, 838981173, 966368905, 864995256, 934999680, 276125059, 979540976, 399015349, 329343570, 623837261, 904989746, 995350662, 974746624, 20126639, 256669532, 644585916, 906817904, 622607804, 680167615, 64433292, 487201484, 627663049, 356459009, 993489733, 491229920, 295500541, 198780092, 331908340, 842045201, 880406211, 340937757, 325862857, 243407439, 658087317, 956308756, 644062108, 873353301, 183457389, 378005760, 409772395, 581053569, 751042001, 993256723, 324826774, 608797529, 815824680, 242532832, 880535373, 317717750, 672372272, 371416030, 431423441, 103602024, 67109546, 329893263, 988786735, 224973953, 724462393, 427459818, 327145347, 277712776, 394072537, 584870600, 266303282, 836513660, 300418431, 2665482, 215218726, 273713571, 651405723, 571305561, 834307748, 29659598, 137383013, 292524, 901038717, 461619099, 41101029, 971364034, 679805575, 244587278, 384179079, 318209343, 620799662, 118743259, 168203256, 435370432, 317463526, 972645750, 344845525, 280522222, 329343261, 763470329, 253303267, 43401087, 633539460, 904801161, 152589864, 129198178, 698207955, 688597268, 759347235, 216463268, 119184452, 230246787, 483164029, 90684422, 484813684, 995044366, 647524100, 250111736, 31109154, 760403936, 355380622, 220397008, 877296750, 576011695, 526398022, 977541168, 909186901, 358538309, 369908689, 976733050, 395469033, 618950160, 148817624, 96391011, 841554406, 886450972, 628474861, 168667519, 693433495, 976034748, 584654523, 972189615, 696216855, 473742137, 586122783, 334414483, 418400651, 102585734, 198955796, 383351846, 89621709, 186397325, 901228819, 206592579, 442678482, 646847024, 215762963, 705052374, 166308595, 236009260, 308007156, 733144348, 911714719, 576867231, 350502547, 517696144, 10419386, 373477478, 500895193, 682732667, 352496488, 337175771, 732797690, 425202741, 189448651, 861389089, 125820957, 475905145, 390855792, 122541166, 589138727, 703690873, 488638808, 765217488, 245796100, 327336741, 409359149, 940996252, 150631338, 471300375, 986460604, 894064038, 1271202, 434271359, 546018019, 476511333, 16274396, 595108601, 380198879, 559298182, 384680037, 110631233, 189454993, 371278246, 438550068, 408497749, 234126240, 585862047, 71382324, 197836158, 841610406, 358700792, 38659181, 120561653, 237770088, 636994454, 61088040, 437579765, 976439946, 676199075, 319278431, 680302593, 631122874, 899726990, 125230482, 437347682, 503862589, 909489156, 370869300, 572185459, 436662762, 66527855, 575593536, 134605578, 833703074, 927607631, 219336839, 6906079, 490219673, 622744038, 994220801, 327163518, 887086762, 676735112, 347495993, 876531703, 55373820, 819152967, 356113070, 232027931, 189446369, 162238011, 344681371, 394444617, 299084855, 927274627, 925424622, 472383396, 107913977, 555582312, 598634062, 451341034, 832988297, 711016734, 555276702, 892173115, 190973611, 697102582, 840375991, 123038610, 212299011, 491374175, 772594350, 584439670, 277605241, 928636891, 804987172, 445970535, 355038974, 617029532, 589983294, 682217758, 89625762, 803571486, 593180573, 484509209, 947433617, 86872088, 285874384, 960332023, 434347604, 622491942, 350191556, 843130289, 341556911, 507105248, 239449109, 912622725, 581724026, 722136006, 691139400, 703803324, 935445408, 555548639, 914421790, 116080079, 9294548, 848156274, 499314704, 7342392, 814923956, 92860087, 220102440, 634212351, 679221602, 920296890, 388852010, 642053629, 807079836, 922941714, 820219917, 185082979, 235055663, 403019282, 297803197, 930570216, 855126672, 914359065, 287327286, 877444406, 432392221, 398392751, 851638454, 514697828, 218853487, 730052752, 775191292, 725225009, 634512699, 350910894, 890116956, 308432895, 708563535, 804739795, 751841678, 152162816, 677584120, 837057032, 444390754, 589864873, 645654364, 66226096, 73229082, 377199914, 839959549, 952209899, 769216269, 133837249, 674305692, 13606016, 76489727, 625780525, 665901670, 671489906, 547958357, 20365291, 910977788, 416499743, 72598511, 762595046, 616621649, 425171642, 114440826, 640871155, 750138018, 335887902, 210052080, 124424056, 421611272, 547746156, 621604874, 811503057, 972326559, 909589502, 50174297, 142719028, 368497648, 840597435, 87540760, 640825534, 953150151, 197124631, 283419391, 241154464, 563244807, 829610363, 55522671, 746971220, 861129400, 535995036, 4215625, 933231512, 342380750, 520767203, 679638508, 210050792, 558489503, 576267227, 177348452, 580515022, 383894600, 283750129, 766520363, 506062684, 446629186, 279138609, 284978643, 859734483, 305991557, 315187158, 974921157, 117576867, 169089999, 925761418, 764373041, 405651415, 647875816, 53415649, 491300306, 723776343, 221852702, 372818911, 743061445, 429331787, 232384, 128746533, 489187589, 126689009, 184608888, 25045905, 184934206, 955719495, 517276052, 83447309, 367792505, 274706927, 345760393, 920153104, 854530779, 956425369, 986933640, 900088347, 234028316, 189010951, 834443404, 332383957, 720470590, 493349935, 623682564, 771936958, 629287634, 230042467, 120160190, 128074868, 972127117, 428933190, 31688257, 831349278, 717314750, 526708673, 966963183, 157001778, 526208230, 442311495, 50603303, 752250239, 949894597, 603541187, 6269166, 922597839, 755528875, 300932105, 954591827, 810255418, 777227661, 707459169, 100480160, 502639112, 343216866, 939581098, 68653891, 115840262, 122262261, 952432533, 918594966, 699504172, 437275013, 647702839, 736325185, 597375337, 900388168, 218015160, 93655587, 88257692, 162604800, 20672805, 571083319, 328362800, 326033993, 871864315, 704539602, 693795848, 268722689, 575146902, 544684235, 223700567, 789120757, 994333602, 795505390, 763615908, 238029391, 640693473, 184815452, 630113412, 72071330, 295628311, 430088647, 241075639, 278667254, 749705384, 664147718, 125130661, 993682714, 544763375, 903367057, 542017263, 726764966, 220151078, 229955686, 5212841, 440922845, 297316977, 858145969, 92622074, 141001854, 960320811, 764211441, 729251622, 774205031, 522150538, 781133985, 744754267, 362391736, 469529585, 751349436, 953868544, 59811003, 614778948, 894074215, 949287753, 793052735, 236202071, 255051005, 180439030, 383519238, 265909058, 807498554, 509766146, 886416122, 50880873, 458742912, 429742515, 823121209, 409883806, 62630351, 225481646, 525314727, 360855493, 926715425, 558581733, 96074629, 56471696, 604239828, 662595248, 235077164, 250607577, 462515565, 452300935, 628372017, 426346660, 653144897, 521868355, 955790793, 355374280, 618179015, 260855274, 35277335, 377535052, 517302416, 127035430, 586928688, 320411861, 654938124, 629723419, 167412238, 912487835, 510492008, 815020417, 31788417, 33529360, 65186782, 759977513, 960720405, 818056734, 868804836, 766835333, 776352926, 63367556, 735909085, 889872994, 49765661, 174063293, 245237911, 449418849, 682970022, 839172805, 463939462, 100736418, 380402157, 9061407, 548163824, 368840454, 84615631, 257757918, 182127386, 376794701, 65856158, 601753845, 670936689, 317886345, 341748076, 806444113, 3737778, 721181926, 32647468, 4736468, 10918975, 423801524, 560284523, 650483626, 289657048, 698364862, 58927298, 598768927, 804287668, 920878181, 77898939, 72452829, 783763756, 249048354, 573063387, 631533880, 202741975, 643453093, 617659082, 33643917, 483505542, 948412732, 846131071, 743930, 711856856, 296980839, 483010592, 436519969, 11190890, 708922535, 148094106, 579583246, 577829389, 746848688, 632920240, 616367274, 375545667, 793456996, 741810189, 394206866, 434039440, 959454100, 849854952, 319106341, 883123155, 654999752, 132785683, 195809817, 616816108, 592308316, 130639031, 801536267, 448027297, 456391331, 415067985, 320675141, 95346307, 72945622, 64121938, 405322477, 388802816, 389599993, 799007370, 645482210, 326781402, 67604548, 721508019, 549669015, 6934247, 851855876, 603204343, 559726058, 432817983, 516100652, 667962146, 501070070, 42266921, 841233220, 977458990, 318723580, 246398453, 654783477, 825836134, 162559306, 143289014, 323071962, 633247251, 43039917, 268058280, 754633280, 845133748, 191928692, 887548131, 128541, 13948703, 803610402, 806522931, 851623468, 520461919, 929480302, 259414838, 531434782, 60281330, 886313490, 200667907, 787773947, 617771333, 260405048, 817086321, 805698257, 71375144, 756957149, 13486796, 717612617, 686063691, 15213485, 277778354, 490540748, 7007016, 452304510, 91141491, 839657227, 53907887, 475468234, 453265091, 923008830, 570124892, 64231546, 397691429, 188072356, 591490965, 933097387, 817134155, 432785777, 775343623, 302451124, 227795582, 228841479, 98800598, 704272462, 654840714, 640935261, 813973555, 654728203, 448787508, 911383314, 210486298, 655880496, 672453622, 437321762, 729855343, 352752534, 236291785, 341980717, 915027601, 689301897, 278836475, 942793486, 578152146, 472508049, 136121057, 416755895, 493246860, 488641408, 973216434, 459385216, 136088924, 579924464, 388400813, 13195159, 775011893, 17663574, 465973123, 131356934, 569769804, 984198730, 953264250, 252183195, 532346146, 754390766, 626612734, 594561146, 942816846, 116112412, 965321568, 980368854, 418148218, 630254272, 180102482, 778418086, 801146575, 23520247, 597264595, 582591953, 848193494, 242049540, 587081940, 55372911, 163529373, 6597606, 710057761, 265927480, 183631325, 581225743, 362932861, 49004629, 460152851, 529438055, 822430771, 798950224, 495435605, 148360068, 549387665, 86923119, 511997226, 748201368, 911514329, 340058083, 916915838, 989430614, 716587270, 793730435, 603430274, 702680784, 140199876, 289341908, 847530806, 716934163, 635505378, 806661448, 840708180, 383437566, 335990415, 611797694, 762895183, 292734082, 362255094, 467994684, 584189206, 548896020, 395742238, 26365817, 465620147, 368052838, 834434978, 477330746, 624248485, 396403443, 465779826, 740952398, 93001567, 275138027, 564041897, 839787464, 567082944, 477432405, 236387712, 230458838, 371799818, 991120726, 342076033, 954237051, 553643873, 608140350, 278259543, 952913556, 669117032, 162463966, 581386365, 292386153, 312967626, 557488077, 722001828, 123129121, 682186795, 831279410, 448654567, 658821312, 116391311, 541782326, 763980852, 184938202, 318982151, 651407791, 351365424, 520278092, 890359285, 876675294, 182822782, 18748040, 916571707, 750587716, 278555242, 8009990, 126607627, 8323219, 605058452, 969321900, 176712248, 485398843, 227545829, 55758292, 52880424, 497547351, 686894369, 119244350, 637578478, 807175975, 646890547, 621748480, 898435345, 968654831, 918716337, 47190041, 974512999, 270441707, 679237163, 830257507, 652152960, 681011783, 843800897, 735032661, 145424971, 620328333, 139930119, 818019690, 991851758, 446815153, 767831439, 924813682, 510081042, 851256241, 186811769, 891451206, 446773688, 196164199, 214643654, 910341835, 637520024, 172065480, 887573010, 700997131, 531733496, 656672082, 36075340, 664335614, 108372306, 495177697, 841693596, 619225803, 393083816, 48262744, 442105323, 37990760, 923595516, 773580990, 742932707, 874130362, 86535282, 254622390, 46386604, 800219045, 627094331, 570881064, 417315119, 878168401, 471621287, 965360993, 346737256, 772113295, 571678353, 102222720, 356769943, 801308721, 414093192, 7274657, 297140410, 900476622, 26545369, 330836775, 781778198, 189015037, 301927085, 737704355, 755271210, 451584653, 743869747, 952811301, 204992213, 846888761, 389810920, 790341554, 374273343, 649743534, 944740304, 126553505, 448897970, 787676728, 36720535, 685601135, 546688979, 758263620, 766166623, 831630231, 328622466, 914611096, 405631388, 296847439, 389358530, 605879232, 557670692, 27170848, 978622976, 276222900, 556902984, 832945328, 816863085, 523227373, 124927231, 546915054, 938785584, 927487954, 101424099, 399756993, 681275342, 89120137, 992215643, 684064376, 466859536, 935208624, 401920582, 263219327, 280287859, 605028222, 233931078, 244555238, 9454390, 592914144, 904953631, 21541492, 133371738, 798172242, 759785395, 125284326, 173327525, 435343047, 865305356, 605619062, 947865034, 804190994, 749830301, 719047130, 446471442, 431901713, 593538832, 792773282, 108359957, 401824407, 581195461, 371443516, 779789087, 769205262, 824721709, 601456405, 485616383, 185544580, 95385672, 297682149, 442739750, 85022014, 480946068, 232546994, 437720966, 197141447, 452344290, 475346394, 448968866, 556880073, 235260629, 741357253, 969813968, 68715074, 657033311, 836737364, 655196179, 403647660, 916100633, 805881321, 467378822, 816937888, 790551592, 390806718, 314687318, 54278481, 402885488, 862114635, 392390476, 98850108, 162298090, 876541434, 326488770, 204919626, 461286844, 195632246, 868570469, 137157266, 450948928, 526416205, 555660735, 216343143, 35886438, 525808681, 959312986, 679788284, 772376614, 940967231, 474988741, 167486380, 219420893, 944251785, 66285368, 616133153, 997395884, 899104230, 768787298, 385221046, 685913055, 892972249, 932064476, 785378186, 659973230, 848832618, 968344528, 505944211, 507114713, 235289417, 918163896, 692505315, 834927456, 756195638, 37427989, 341549252, 943622643, 194055173, 461959777, 970392575, 99217183, 914418247, 934314709, 948122650, 357117528, 460256407, 57147611, 648063189, 897179811, 733995206, 530782294, 133743367, 103618827, 299293793, 713124880, 179358768, 249518162, 302670054, 290429864, 554726363, 819151452, 730553853, 514463096, 370877976, 255852831, 651401778, 606842639, 60721709, 220761774, 444053767, 884453197, 504646309, 921344230, 529398215, 943939959, 43454959, 795249684, 515658780, 818350977, 314270107, 726271232, 843665591, 67458445, 320394839, 637780031, 169937442, 787160719, 200208585, 204768851, 305296710, 386984798, 105196401, 408298448, 610609537, 22592327, 999077140, 321915257, 346366718, 292441921, 744917334, 605218192, 427501465, 901289145, 869043943, 276640175, 354058877, 352450856, 518532572, 538221075, 567350761, 149051501, 702656305, 141233430, 240610869, 550509442, 520758643, 160914009, 647178859, 76449582, 779024598, 250046377, 378744548, 513531663, 878425057, 617538842, 298370855, 699488348, 228206810, 722830496, 453503962, 436791122, 177593047, 356773497, 548572252, 640434155, 166473740, 971968542, 479297232, 96198247, 380111658, 608803298, 75052686, 759147855, 617721202, 143741817, 661602088, 880098795, 604182246, 125336277, 49877053, 34548867, 570896299, 888150380, 72907235, 459960666, 870237203, 172094126, 141538958, 895282074, 355111110, 848265364, 6704928, 522419913, 968827293, 823328680, 270896549, 706719677, 149619187, 287429763, 754377052, 507202626, 992743343, 990757015, 214437200, 209904640, 642019325, 746459080, 599636726, 488022744, 953893170, 153409683, 657933071, 370525149, 351468672, 194576011, 842767546, 33057, 225090164, 757950439, 368141655, 552226479, 31359432, 743706892, 442623670, 646948925, 838333757, 814760907, 480914407, 862033625, 706789671, 713642893, 46287214, 88831530, 961140999, 445781649, 300458461, 560143054, 784986980, 660938773, 663212491, 482549052, 605333289, 967370204, 218206398, 849976133, 901176090, 743863425, 114642946, 202590218, 651005392, 216645793, 799057299, 364767266, 619375310, 778945782, 848890405, 381488849, 845815373, 520448078, 597026690, 203342712, 103184205, 398891166, 521442381, 372682677, 135134729, 206367196, 332376787, 462103570, 210200967, 768681256, 382192136, 362401990, 374954224, 668284735, 110094511, 52476413, 219511306, 12637816, 177198682, 486433255, 171661952, 730556114, 38820146, 722637309, 557980333, 461208812, 152235679, 816228319, 453300754, 223532473, 520790128, 946809769, 637886279, 84171018, 712702015, 291973126, 993493794, 551298327, 217660394, 610901649, 904379303, 256879979, 980553146, 207079755, 289881296, 461453215, 741148609, 769133734, 244262326, 447055210, 550402450, 274057369, 436419980, 709930607, 487361319, 161597939, 615414142, 940420157, 165156501, 561417111, 229040581, 578885580, 368835808, 760980160, 452734404, 337934681, 3315128, 55233429, 619285614, 442318876, 573260694, 66271070, 703974984, 369485891, 311073703, 508785052, 676163350, 585732715, 815869603, 692430286, 359447110, 950855123, 659053977, 815807927, 860378567, 70223700, 511820699, 196837545, 784728013, 131672076, 42892773, 376068736, 911982463, 80798098, 515712249, 221974133, 148383753, 797663870, 908814999, 581344672, 549012261, 72985707, 372284951, 184119969, 460135231, 615914409, 668543305, 776191559, 119414179, 649559894, 428507884, 514984443, 194695522, 103878983, 250811486, 362369938, 882373766, 443020108, 602484135, 40281377, 772412226, 452973083, 305600188, 938049828, 483542563, 718497324, 187128782, 294634681, 145774537, 999840436, 868096855, 690784224, 451136972, 890490038, 676442403, 219850051, 337947119, 35556822, 217588532, 467499312, 327054616, 206119070, 532785811, 360204811, 451828340, 652759019, 23275788, 256866858, 945300335, 890975666, 601563775, 187551252, 374284843, 437182482, 227680064, 472966274, 790310295, 709547557, 425227694, 693988265, 904046356, 640487227, 594988499, 571741202, 630165059, 557312568, 500463297, 605221758, 647986367, 13100109, 947479680, 365662029, 321825758, 104495209, 257268029, 819419290, 923593954, 679503020, 110391213, 973494463, 321013779, 796313290, 19891823, 112360900, 325156860, 557562806, 133392328, 182512378, 578233468, 513223587, 143464387, 668904644, 508763604, 420416416, 347022086, 464746581, 217997224, 965033078, 840805883, 392585432, 378114188, 502312553, 706204727, 240852805, 554731655, 555855622, 969074772, 878541689, 291079659, 234461704, 265735317, 578628270, 630066211, 617611411, 614756556, 432680618, 506644774, 273705391, 853518284, 944757304, 134688505, 425190142, 786155015, 447927499, 281438999, 265643492, 775608158, 644842792, 176291337, 556294405, 614429562, 653312303, 77264730, 209766134, 545702931, 409037798, 812067719, 703858040, 875190548, 667146978, 713926731, 945888913, 940819321, 386664157, 365583076, 715116161, 43477113, 550741628, 532103657, 665685383, 791505484, 681837388, 946733680, 832599074, 349570595, 15480007, 120784291, 837278084, 779863437, 965608893, 551180002, 41886636, 578383287, 454924643, 999028303, 648966755, 741336997, 593536591, 65740948, 362020726, 518218849, 640495427, 483418543, 622575356, 155418034, 110226931, 216657821, 666656955, 584606375, 491448759, 956087708, 159214277, 910034857, 315946950, 355773330, 588527314, 712570910, 612529133, 662935433, 531876812, 842860336, 409244660, 504363670, 598338775, 448117849, 254479755, 757551275, 240890696, 779738256, 291245509, 731586472, 654721303, 888990568, 98322842, 594921965, 284895538, 648922231, 754067479, 726228569, 342340223, 236259683, 472211605, 186167998, 829894773, 444927358, 782119357, 693600488, 436851297, 103064180, 222115546, 444526840, 605578599, 176587866, 736973798, 473086610, 74101891, 762745807, 854794122, 541897801, 187198378, 632407095, 536862994, 120703424, 604573334, 464315876, 729453392, 781448295, 782320759, 948980113, 357587823, 150233004, 291149587, 731564774, 413682917, 610311931, 683360474, 675247150, 323802092, 496184625, 743022134, 34196944, 259929883, 976034591, 484787059, 940794516, 602842406, 128087058, 204552993, 329963919, 595147756, 373203080, 342962348, 889378250, 129697687, 370872758, 789493700, 782375648, 913505252, 582185331, 847391977, 374901328, 787135007, 722567593, 444681766, 185442461, 940246385, 246532151, 460032693, 320527969, 669436954, 876930300, 214562744, 713522966, 276045913, 520408452, 24480611, 514346684, 400147134, 972418751, 131374302, 415982421, 860286275, 493929934, 334621196, 436875290, 715716170, 592387495, 527723524, 728780028, 506605524, 688973166, 671888141, 905386111, 520383626, 862925921, 830575591, 403104684, 106425503, 331808456, 188089443, 10815219, 565642939, 358094969, 867175074, 29066438, 924721666, 544286766, 949220361, 830356434, 322186438, 797193948, 999088195, 944168751, 17296315, 890667968, 228600007, 689463800, 549461114, 407062945, 992741540, 644421095, 256227231, 449048778, 511541812, 433690742, 471926479, 298416439, 922848226, 463237372, 696399197, 990165276, 126746212, 929465355, 171829000, 688944091, 386745327, 30684224, 583176818, 535162625, 57037215, 902111214, 610620379, 779236177, 721063716, 907064426, 194030915, 275393172, 627252200, 464694205, 543426838, 302281508, 598425543, 154663581, 968630936, 70174958, 772688641, 460094785, 845398822, 923687205, 119662297, 12986991, 329973646, 229840711, 888382852, 929917485, 180103723, 363932208, 965428031, 705458355, 294353381, 532132948, 900202384, 47863497, 43684819, 290522645, 453193026, 389886117, 871853160, 65327774, 592273774, 791906761, 303073314, 825127167, 7861424, 652106810, 707997475, 853473899, 288078750, 296366579, 753958320, 92979083, 880497856, 580041700, 336240302, 943001247, 558273475, 666893107, 232852259, 910943303, 734718839, 992576534, 972667864, 934536176, 122186083, 798138702, 878165482, 987682975, 415555455, 638826798, 973746721, 748252865, 605406427, 395229697, 916495069, 808527122, 764273058, 504442542, 942513426, 53045046, 998103045, 402982620, 610150125, 78643856, 370691006, 606947766, 699127215, 581310088, 520189570, 731093766, 200942881, 410997201, 506764123, 270889434, 3214019, 67917091, 192861192, 118168651, 872261890, 614385714, 253792561, 29201571, 974773766, 191634218, 549402052, 932941723, 453093668, 222666012, 971800714, 90668489, 736496201, 973834698, 323221978, 181780500, 370769177, 601972012, 464746187, 820205139, 5631204, 225121752, 999690739, 218099399, 914055263, 468644838, 27536217, 437735413, 82202453, 336712227, 957416531, 609854370, 91358152, 685143970, 607945368, 323506158, 499834623, 900243029, 17405950, 155272930, 299324309, 501638246, 188885176, 950085620, 957576258, 795527746, 808378867, 974679676, 346445754, 663524805, 410945110, 194188112, 481769462, 719420608, 451804077, 549610158, 349558025, 679008651, 189047350, 613770535, 564426911, 999313000, 379723930, 829627532, 68213419, 406843175, 765938588, 982766631, 109028515, 508739701, 937509627, 241297356, 547559258, 570983840, 996991456, 715856085, 901737485, 935048656, 354467528, 49428885, 578632410, 611433240, 631619443, 751726794, 612270331, 373695102, 545065749, 744959829, 371470059, 739772678, 913550211, 167484129, 66634279, 868468519, 560011929, 570066733, 978652222, 278915183, 497105318, 501406252, 505469007, 44424902, 861468706, 655961020, 967413462, 269595980, 961337940, 61978990, 721043629, 259634431, 836576635, 885521519, 546441422, 190080486, 806491576, 416577696, 911560487, 555314857, 827301887, 65700299, 95583493, 989384574, 932878488, 843009525, 901915327, 175894974, 346037861, 281003195, 883692425, 419706572, 470318984, 70227489, 207090707, 941495333, 918758130, 662850211, 101330114, 583187243, 953062301, 384887919, 108018284, 450598564, 326501138, 930485101, 300867470, 267614698, 447740996, 881038602, 368237118, 413718958, 505675570, 88786161, 892089332, 839845015, 745241488, 285892382, 209713032, 911931071, 676073164, 759319822, 781061092, 190291952, 742717837, 81117746, 904929968, 892834302, 987145938, 529683689, 471349853, 885797666, 743496573, 906527721, 886027926, 905291228, 103945278, 315591141, 91061696, 753720009, 26178002, 217917690, 951492207, 951406264, 369770442, 441621808, 621470889, 667286255, 596259589, 422938507, 939320694, 535141947, 57332918, 877994421, 188347799, 338590617, 13682392, 83040141, 664788894, 776147858, 891525260, 302886385, 903522802, 217885392, 597132833, 920161087, 960156739, 409495545, 998535992, 8917970, 176154406, 38453571, 668158421, 52500275, 274086399, 296723018, 997397688, 16213568, 724741923, 624178400, 705804348, 778000057, 647593158, 314325022, 227594710, 564258072, 368451036, 437069493, 108946197, 118469114, 38843632, 399539341, 294386849, 622196728, 270713816, 753365648, 701083767, 174267094, 554640305, 191358519, 16899022, 140901269, 394250193, 746041002, 637316636, 224800036, 702358732, 723810604, 755404900, 410025473, 393850672, 196035405, 409421379, 573665010, 883218846, 664923003, 662585796, 405014269, 778258328, 758945783, 31098884, 470593804, 835918086, 654029947, 299107080, 630252741, 784651504, 824280924, 531336009, 729832690, 19250974, 832861208, 493183055, 898480941, 459502292, 588482201, 111557187, 993019915, 641188960, 640672998, 189700268, 819705047, 385076358, 104696782, 771313886, 534769807, 156143141, 550616193, 832417358, 244086153, 943943389, 367451730, 828534121, 886694721, 836510198, 67701662, 564481459, 602836040, 410216558, 106992468, 792801219, 549645882, 759241084, 399824233, 209316885, 522901372, 149102861, 762357531, 235701969, 68577912, 901337136, 473930717, 893053762, 750922847, 144041187, 186174561, 887627528, 205426865, 589009819, 87107494, 920196240, 983140536, 102121639, 783686011, 97734112, 425404216, 982190774, 387782503, 869494970, 992593396, 565442077, 469391335, 226832602, 197033040, 911039500, 457228487, 432352132, 77077779, 120261726, 470304300, 322034176, 370805045, 291436924, 332229928, 395352732, 41563722, 845389930, 381878511, 325863614, 397889250, 695119672, 752493429, 92762301, 473841878, 495959726, 727357277, 231784134, 950186296, 961684510, 821247368, 983495697, 345894586, 898191128, 246316098, 580022122, 294050132, 974283293, 169991162, 94307333, 696229949, 715721934, 62870355, 493757314, 69302701, 571791870, 123982466, 548294631, 409693909, 220827204, 421438557, 34618256, 547935185, 965860576, 322835389, 521530010, 955908493, 868139673, 979753097, 513067041, 842606279, 732476154, 111138436, 1657182, 870130807, 423931151, 559675266, 953707177, 553313698, 819382176, 364562663, 303699218, 516464167, 363487640, 307656948, 8760029, 758736431, 129262889, 672525553, 26049884, 278808835, 255337588, 120612924, 818270566, 713988212, 790347750, 19099710, 92695610, 376725301, 404270887, 716722565, 582533559, 889958979, 102641439, 501914051, 926757613, 14633289, 653476358, 736415081, 970267289, 650287860, 670710925, 855085978, 891046183, 655795636, 431892716, 679211064, 248380657, 837610515, 676163700, 153629147, 459229857, 671573062, 830281455, 596057407, 936670166, 287013197, 192164446, 980990740, 390816208, 934542498, 631076711, 970641919, 467451663, 356901889, 920627624, 843378964, 898524355, 761808047, 663799447, 590479885, 430072083, 57564303, 369798365, 696972611, 452525695, 765701606, 226838962, 539619984, 896814690, 397521927, 695447533, 81296124, 787929606, 439955988, 983224675, 161635573, 854381594, 177129388, 185547037, 887624794, 221931249, 600816462, 733073665, 910370145, 114686897, 437485077, 863341806, 501838021, 9053931, 759546133, 312968900, 254634339, 709225937, 300649094, 995732236, 743435725, 888926342, 962819185, 700389830, 853288255, 822977590, 607231344, 603294436, 254202060, 956995867, 785615133, 483367706, 538049782, 833595097, 118652448, 53600746, 565477479, 875515443, 320488266, 555304249, 622984510, 725781097, 740660225, 915004905, 125795075, 231831629, 320973517, 971375215, 416413727, 19369321, 818811537, 638517355, 732642423, 404738070, 883768603, 221945452, 628630828, 447463835, 213374755, 793083226, 535617260, 697307058, 891073176, 49462967, 915659272, 406236695, 4172174, 967581898, 589077504, 463557772, 587011878, 25681370, 667278613, 824751350, 138415654, 818998509, 244348375, 566289087, 505379178, 719960320, 425268390, 833923057, 107288952, 232791640, 903518268, 819430027, 635068909, 204151962, 203995830, 621749655, 120617360, 141692446, 796948433, 859910161, 307679122, 458190182, 301631516, 408047460, 827044205, 945829145, 438580256, 535655861, 654752002, 820438095, 552227983, 65279650, 245565220, 457305011, 539439573, 461009708, 729321239, 954511080, 194765059, 708304314, 446710905, 621024607, 337774371, 800347618, 971344589, 250340891, 971065072, 525152759, 235402812, 259290305, 539441840, 242781598, 246111995, 26879317, 589926868, 436576020, 980390610, 937813048, 634376378, 587584248, 777873570, 836464431, 372479223, 368949362, 293443707, 242779055, 810758409, 610296916, 717914911, 571331642, 75452382, 375425906, 281149284, 423107974, 150049876, 869311390, 902039205, 413717965, 41118469, 461367202, 916379846, 258965117, 700325562, 303092891, 86800329, 49310758, 952473190, 538870766, 49466714, 735035154, 524113292, 164599405, 877290077, 446531628, 654727039, 565450812, 494589836, 357049151, 97030971, 677413473, 69086640, 982706192, 819680197, 953099202, 647453216, 758805489, 690820344, 390630169, 754051408, 155446519, 10603184, 369554723, 350714089, 373607463, 104246760, 678068028, 886424273, 101591392, 854029229, 899238578, 609541379, 943451378, 677655517, 365804023, 517987198, 316097811, 630337763, 118921212, 20608702, 853172095, 529234628, 414138542, 434625299, 410545284, 764998678, 960152790, 580552277, 596193119, 581276702, 665324394, 457100260, 133019534, 873634210, 53255530, 497985717, 669282348, 571546133, 241494652, 489182388, 810737001, 774501013, 680226697, 200465027, 693491541, 113783516, 596327367, 676374254, 120806007, 496607189, 262120651, 278992181, 75721762, 854949310, 462051187, 655531299, 221589171, 687083955, 292734943, 314006533, 946191589, 562736332, 946955199, 570265764, 733648586, 677492119, 444434066, 875130968, 88914647, 553988425, 610849011, 189275568, 512186308, 64714314, 892718001, 928762219, 668824200, 191816319, 994183189, 695340557, 511358681, 956444470, 891323066, 686607568, 990877883, 208053993, 953333254, 101824103, 240541336, 361420109, 902559492, 76109821, 773081586, 408338839, 154495692, 784722256, 189603220, 830282775, 861839574, 216865899, 172486948, 723052708, 796607840, 602166123, 654981828, 646781070, 486580438, 373212519, 874561697, 554070373, 167441550, 750171145, 118223373, 300683884, 981300789, 432653897, 766230010, 106833584, 964693921, 386664714, 626962744, 11473185, 314015696, 2672577, 312071384, 275603243, 694392504, 166444513, 587020837, 86475791, 294231551, 215741055, 699764571, 116139525, 586501687, 177722947, 564474623, 652038712, 511882547, 471977172, 815783462, 531546739, 152910342, 16711971, 425667472, 37533101, 600003268, 914653573, 402056459, 433868203, 229126770, 769215350, 375429561, 807734105, 75324370, 752198179, 601127580, 771601530, 620581496, 373249689, 530186652, 957848364, 853378087, 487710824, 997238512, 867921136, 542672403, 705186705, 54122350, 559808962, 493820787, 142427631, 12509719, 522143765, 110733668, 516362496, 840929793, 771843860, 979094839, 67840472, 885942071, 51138090, 760613808, 226511243, 186517046, 181640884, 565507634, 574424189, 297063504, 323851881, 103760229, 241454390, 658225333, 26368553, 178506139, 637315973, 539727341, 750232099, 143616984, 68083813, 20134678, 499571753, 770007381, 712585131, 744480811, 706305647, 441987970, 619279583, 336872586, 210455073, 75966377, 871530093, 134922569, 166714264, 17639355, 578345769, 145635, 332270560, 283219630, 625282943, 84102072, 269936478, 950431044, 783972134, 525673851, 402641490, 354256278, 265235451, 702634934, 865872523, 739354480, 466181327, 512846015, 27833641, 292351458, 44133307, 899987661, 329438586, 751599880, 588113901, 907508690, 561087799, 95427431, 436519310, 159846905, 139508027, 642572586, 211911196, 784693506, 808923493, 367118805, 660581143, 157778860, 678716255, 735781260, 463543857, 901630623, 929926592, 432638269, 313909667, 334644815, 94732082, 472254851, 41725816, 813657249, 831659891, 862483890, 760375856, 165957802, 138950716, 548867407, 788856493, 190796801, 312834157, 782140171, 120039234, 767506325, 581444432, 995401619, 360786105, 416813730, 49064924, 78119635, 638015791, 855921776, 311067115, 254350764, 499887089, 749059205, 976457171, 31214816, 748181237, 836496917, 250619827, 630893932, 349732314, 899372695, 670644530, 118036884, 749881420, 760297040, 597812342, 888852281, 617446105, 834637373, 404888581, 433887930, 252575530, 962884275, 277900486, 554245737, 319506045, 258954451, 370921394, 782675613, 761624438, 978806362, 51065618, 995089471, 185815913, 937819890, 321820508, 65378678, 776461611, 154775569, 770159843, 869523911, 235135585, 749248182, 370507750, 337676952, 211749682, 324910470, 402202464, 691789883, 978287174, 377541733, 586508972, 921078682, 341660957, 80867431, 664669371, 791577960, 142420963, 40655853, 253334589, 378452395, 261206111, 849667451, 345437009, 763928719, 345129243, 628523175, 86382500, 428696581, 408207142, 49910328, 559786467, 248794057, 6676487, 201370850, 12648471, 267054088, 839719785, 362638702, 975517714, 596639507, 230421708, 362762923, 57787446, 743004975, 633616035, 298801715, 464893346, 415110350, 696591795, 298937150, 765366805, 843120015, 669037895, 13487239, 960168215, 862606920, 968644335, 329802181, 863102717, 839104638, 976203464, 598119310, 843551558, 995177134, 69168761, 649247976, 711017717, 254636619, 136728592, 607723295, 882064751, 511429583, 559246940, 684821565, 255356174, 524354061, 562206129, 823586022, 134995736, 717068194, 545773852, 267980342, 651986664, 915101771, 538431240, 902228229, 542480907, 180960353, 901305213, 808553644, 302801958, 835952470, 887023268, 807365582, 863312452, 891841, 827027403, 788340107, 199522754, 70827764, 841959434, 258994338, 591132244, 279437053, 616385878, 203635184, 128824370, 970082409, 627212132, 901849047, 119777219, 610000608, 295999813, 695061694, 861311570, 486737863, 58456488, 374900942, 319131727, 865393319, 953430586, 919040101, 584692873, 731531993, 998563224, 502694191, 848160792, 194895064, 549824870, 821187886, 676343041, 322966670, 154202671, 842338863, 296181701, 430133676, 439629268, 702652307, 216386072, 389741675, 185817946, 440387328, 894537922, 336722056, 973924095, 478261103, 992907905, 364378103, 352038298, 164151351, 161125679, 779096237, 635760530, 8088846, 960330672, 563516561, 803763353, 623728659, 463829494, 800826562, 48280692, 89564913, 157720853, 75506721, 199288195, 266824590, 22431626, 983518810, 611747341, 702683777, 95454039, 527747369, 146117868, 611998825, 298655910, 994808582, 476774076, 747444674, 402995445, 603051398, 221373106, 454514409, 555724143, 878115456, 842958132, 800243495, 112083217, 526598869, 113934522, 327129830, 421966678, 869831096, 885780597, 674522806, 269282212, 706389509, 705681255, 38702430, 404985527, 249996177, 623868707, 293286923, 438744192, 442519584, 861374360, 477487083, 349748852, 865333113, 440769555, 536533373, 187442392, 784096282, 26932394, 241589254, 55175047, 538862299, 160902027, 737579369, 85103511, 409643639, 483318631, 543183304, 620725431, 468217457, 224757657, 978536901, 791871715, 710605863, 33312080, 753469505, 906728486, 209298248, 399896029, 625752086, 286975498, 693872612, 430959972, 109166424, 800032686, 840371529, 613495193, 822426667, 165521172, 771762221, 612143940, 805452791, 73584331, 820997608, 350094672, 299617181, 781675916, 291073487, 412860254, 510915688, 704899772, 863034099, 315875887, 106086302, 301712802, 791203342, 167196613, 778633799, 174989425, 18286133, 647826669, 513168041, 590231295, 575815779, 949480769, 294281935, 809644322, 625869164, 969686783, 719992388, 633544746, 739388324, 69248318, 896692519, 442685441, 583561100, 789766844, 356052239, 140149248, 412173036, 274380692, 734888340, 375918521, 884867598, 413208837, 495902991, 165572488, 581953179, 963544308, 201208195, 638228065, 730158902, 946020246, 420116986, 97300496, 94579099, 396413086, 919275372, 275620808, 739431286, 330792837, 331811130, 683633297, 983400538, 273919185, 41527513, 639414538, 747065240, 212116645, 881968589, 107885185, 300078257, 886969463, 669995077, 448816021, 899806604, 30000900, 893603686, 486668473, 929726267, 444341559, 80741964, 128118760, 687442595, 258945335, 729366318, 182120644, 389861525, 290115649, 264665261, 386219993, 310644253, 519266580, 400353444, 30983579, 655025070, 910821985, 727158963, 904171034, 840231768, 56347682, 299367596, 974453300, 835834637, 954753125, 654116376, 689251059, 938156675, 427009525, 913353246, 154901290, 673642788, 796176844, 864864014, 893580269, 338726382, 31892362, 43263181, 941985369, 261983580, 261556368, 85995705, 729063824, 398764625, 739091344, 149542575, 182245285, 450378773, 947518607, 679578960, 566394058, 574925612, 15751191, 746112028, 277174192, 309954594, 316786900, 634284768, 21746509, 570478224, 429581392, 585301103, 784214977, 497577212, 394136466, 898482550, 307675926, 9537559, 821626235, 310476691, 806951780, 988109586, 156038206, 73195493, 884297747, 82754242, 822937850, 915908519, 588564381, 434427486, 502479448, 84314377, 760195689, 875107757, 547265520, 971203689, 226020219, 331910469, 966153157, 965730160, 387092392, 311717364, 882214270, 309760050, 150034346, 950966700, 474236987, 637672854, 674590620, 353389932, 789294112, 418842060, 462039398, 346011415, 186883243, 783371307, 321195572, 763131578, 707931162, 761293684, 857275067, 450688967, 365297895, 826722743, 867620367, 751092466, 542966857, 651936638, 520549115, 860538705, 562477681, 180730138, 701323489, 643078766, 996183122, 475096869, 810662781, 17540252, 362995215, 869884826, 404930008, 300005920, 698863623, 208365879, 103827198, 442837073, 8668328, 974687216, 132832980, 655452843, 260181735, 559457259, 787374062, 445289976, 246924038, 620039171, 662954386, 626280296, 697968998, 571940671, 571402991, 170638761, 988154874, 850655062, 653603513, 618953959, 155732817, 217036651, 630602896, 628387385, 722246879, 995233160, 754228094, 598346886, 117608204, 550053513, 131820839, 950285522, 839445244, 646084628, 700314276, 737370241, 255640417, 153189076, 994981342, 286059797, 711656309, 345438216, 35926743, 678771606, 890297202, 281235431, 240784899, 399917064, 509325438, 763077172, 779389632, 799932195, 338383869, 116872261, 689923738, 203550735, 319193010, 441439073, 738704912, 669585777, 730641692, 266021944, 189893970, 774543085, 351706363, 113651295, 734740611, 918495446, 265461548, 659659326, 391900267, 596252484, 365201030, 598274221, 370826911, 244510029, 689141182, 119410676, 10343580, 439287889, 499146090, 331794920, 666567614, 281992529, 502770083, 305091160, 201666550, 728994232, 204202710, 722555787, 22464031, 172876159, 827372965, 429315435, 371820638, 452214155, 39696828, 969206450, 705760693, 812279939, 95307565, 4111065, 617655, 851741487, 107999871, 15354719, 396442631, 735278380, 131876443, 921585112, 741527016, 484966030, 830165491, 372460408, 972897367, 465580542, 853402983, 526251621, 162979560, 88253680, 639921709, 223661240, 233702433, 834760908, 381341548, 534289448, 583711114, 617362645, 414329819, 73021259, 91277810, 149139162, 436606813, 156866303, 109296135, 643616911, 693398491, 346259067, 455421565, 677197809, 893005993, 213208475, 550686918, 676116780, 751275722, 94085680, 357096623, 327463044, 910670295, 786183306, 475353918, 881517271, 973964242, 687919547, 298898408, 224958673, 410052733, 780675438, 752229324, 938636524, 128854994, 985251938, 154589371, 317368160, 175436951, 670763097, 134708138, 92525470, 445876349, 9870277, 823279039, 832025292, 601866834, 657593542, 562114049, 667899343, 259256387, 449730514, 90049481, 232889706, 302857085, 158602748, 379555203, 177568239, 313187993, 158365268, 681219686, 390645789, 19342663, 427583740, 895051127, 725934247, 76089452, 378303528, 382297831, 949516414, 704001063, 226980081, 561009316, 434623712, 215981203, 193900780, 48503257, 867947979, 50525230, 187521487, 160687268, 158211534, 122218198, 41112553, 918600876, 850075240, 798956125, 416523471, 641669096, 570315789, 940699243, 243224063, 468155632, 926801555, 694412756, 126304776, 983508325, 96026416, 680153341, 709498101, 91442717, 992558391, 419997461, 196021007, 645369311, 826927240, 494233052, 193566425, 583102363, 225153408, 322613966, 674582672, 44611739, 640701898, 8581508, 375550018, 652309558, 773872686, 915241885, 591860033, 490857049, 115041257, 920666949, 356913049, 859505755, 16679878, 731155980, 734651919, 194382589, 722172786, 597359734, 907093853, 265924588, 324885586, 259480601, 243852158, 800676484, 648674980, 734824566, 274026659, 569733284, 303489513, 950644676, 625403037, 165031728, 472276861, 412850980, 709723947, 15367513, 538220726, 589380627, 669108141, 513956987, 523361134, 173567461, 268745890, 674414148, 803506583, 519645396, 983132447, 237961585, 218250916, 623856322, 331580081, 499916733, 788439496, 867129642, 556198816, 652043849, 64417408, 372258142, 602375596, 399859994, 248075779, 564989100, 319476826, 19329350, 626952412, 845826669, 719685576, 451805181, 891062739, 666376296, 952883424, 921822635, 469565716, 687551490, 906916656, 960004330, 188624276, 82723782, 275366813, 953368885, 814065722, 162099127, 794357798, 508063434, 551654224, 394171122, 497924298, 963612472, 47335286, 209101940, 876856523, 81206168, 647375608, 867035131, 594211198, 314479061, 532062269, 730503093, 25382420, 632167989, 908275038, 832089108, 859392397, 745438659, 783398541, 594869050, 777814513, 403902555, 749908626, 976879765, 322519990, 487264781, 451080455, 768566840, 963689504, 956909630, 379760871, 214794607, 138260268, 248705930, 865181611, 690514283, 119052845, 308179111, 534857366, 363487890, 456694794, 68423438, 709889323, 490492453, 726347823, 285193503, 726936701, 224472328, 955710675, 994204844, 575981905, 202346463, 318950289, 864103813, 899140796, 857176467, 864910678, 688999432, 668873811, 613386244, 360945398, 838928068, 937954184, 833571945, 961740823, 614495158, 838626033, 547620253, 261583236, 686236176, 195364830, 314636411, 835726227, 74522664, 611565480, 858520189, 720298177, 217538070, 46481923, 493923236, 478135761, 916479343, 607810678, 297391607, 677904747, 773654039, 558357951, 555652643, 617572874, 124694055, 882443707, 906941998, 355394326, 112964691, 100472106, 36881425, 709494465, 693717979, 561017375, 133961901, 971863953, 481571089, 324289225, 843451368, 278959473, 399226812, 285579945, 78482752, 417278379, 428924163, 775015819, 913043980, 388307991, 714962673, 460884407, 265627241, 30023227, 181732789, 937017994, 563602271, 668869547, 743843327, 602918341, 96439516, 334038585, 176299133, 787008171, 937862774, 487375385, 409903689, 29132219, 964945257, 241356155, 649303935, 358294921, 397325414, 220586918, 851883989, 557898870, 747959571, 1156663, 10480960, 271586610, 53620157, 860978931, 652996630, 794127643, 933697420, 674632487, 88067458, 403708304, 35256285, 43914945, 255850543, 234732819, 206817332, 94023423, 222849008, 67875524, 852019111, 488458783, 590622193, 19301788, 378079574, 375463915, 149529648, 787005579, 790633926, 281263642, 686351790, 934450906, 471731947, 295900320, 972080183, 292897916, 620832144, 235275649, 117411466, 622645231, 701293943, 681053313, 581386546, 226124776, 915370984, 383103454, 901736473, 535980730, 424008117, 554220558, 625554190, 841458974, 304356743, 144978538, 792142906, 759017383, 323808241, 139897770, 681340962, 267494673, 561628911, 932328241, 861512346, 184630696, 866136153, 241088282, 58676422, 334864133, 641431435, 453564203, 420333321, 107821497, 469861846, 953120914, 603508891, 783813592, 297462390, 779763938, 905266075, 616096518, 788619104, 707675929, 630130931, 670169489, 892612188, 266190309, 562573589, 684540397, 701936636, 387117407, 417406534, 326834057, 133110960, 526988889, 520532681, 740095320, 133375094, 180346519, 299335942, 243801356, 620944196, 735791181, 408196243, 153998233, 900096231, 820092296, 769411869, 896530768, 147048906, 753000275, 17746593, 768119246, 614921133, 592559349, 899387616, 440376725, 527994247, 68704492, 497622519, 61287001, 621093931, 258088115, 471988152, 774106770, 710689144, 356125804, 902896641, 718302370, 744993559, 330500311, 573449279, 234058350, 21373459, 217780589, 504008949, 697327891, 836937429, 467088609, 537891470, 270280412, 434344271, 803960467, 84444777, 347503651, 599884060, 777709014, 778884240, 181962406, 43030662, 533763747, 708954442, 93029678, 627304698, 940082859, 53459599, 583094296, 537429716, 462352188, 113027941, 521464874, 549910627, 316053539, 53902286, 838853294, 726530849, 379139509, 373985941, 648801534, 423892201, 736178419, 8451307, 776163973, 389451609, 500402603, 550454654, 973473754, 324431379, 878704036, 534455398, 901780046, 350129121, 685953906, 909412156, 713328606, 429443220, 543783702, 521191758, 979198648, 353724462, 879663608, 993799631, 484844452, 24848104, 955427905, 141942568, 590771295, 552453013, 736274028, 116067877, 88925904, 48414268, 191487445, 558316821, 183999024, 573345138, 797299896, 981515883, 493258351, 686263625, 39929343, 890564813, 875874168, 659485263, 852719729, 257534565, 211274719, 945830860, 377340725, 352421164, 184800603, 106936992, 51969625, 644343678, 222517051, 475164643, 295179641, 680088666, 539195866, 221932867, 784881018, 255498536, 264594958, 49927463, 722288873, 221146538, 785135560, 99582529, 128756142, 59352238, 291264479, 811676475, 630926012, 947380867, 214126329, 975880579, 283613796, 126042478, 372870386, 711488531, 272122269, 831466360, 685211001, 125346271, 466799008, 315452855, 364880166, 49007027, 984657751, 9164978, 804217705, 2049449, 263581761, 344230816, 623166199, 242279521, 397344468, 583577504, 936579884, 28380236, 218643714, 95064749, 19977315, 922579290, 371968273, 523121972, 67246632, 769156572, 647150692, 229397126, 530149022, 236543736, 175240155, 364330900, 939420927, 744129181, 139243439, 387086470, 891163341, 968153719, 520565693, 484789336, 723605279, 610639127, 608005870, 490360624, 573757589, 54053021, 63732927, 244172885, 715329966, 44847971, 418999532, 438198856, 657732023, 757688222, 504152852, 914632687, 186725859, 791873050, 234933455, 738160319, 478151913, 786484263, 252377528, 135932468, 478995225, 363202526, 212509401, 320391497, 534839415, 466030517, 759954544, 623134661, 542232528, 667133635, 337593371, 732873748, 788773058, 490014758, 793155137, 800604579, 285728211, 651189402, 284974861, 84334217, 41475237, 256334745, 565545805, 370262567, 756355197, 366819468, 49918500, 163111163, 478601917, 778853449, 106486145, 284149223, 662441035, 110796247, 683839526, 483178694, 551874305, 398796274, 699577285, 118742729, 367599290, 602239483, 630388583, 144621073, 992187706, 746649662, 617926710, 750120746, 153336042, 76037972, 82169988, 879708995, 988146344, 347829385, 699095545, 833610981, 695445138, 308891230, 485223142, 106200028, 803773752, 847263200, 829808875, 148939117, 925174048, 856652746, 769624111, 748778060, 622611248, 439189205, 999562693, 353776032, 986849973, 818696263, 206059914, 592999423, 267166713, 120320461, 879492521, 319451236, 977949469, 467055967, 9325256, 506195155, 113696033, 314428178, 110264589, 918713707, 218702989, 747279103, 63550672, 637886578, 412359030, 194763760, 362527211, 718662614, 455439376, 145586915, 250152678, 449743695, 244685004, 770872414, 317640769, 81013618, 737532282, 515590961, 541374555, 628868034, 421757720, 837653538, 886781920, 891521400, 250498725, 729143583, 36219749, 52471322, 774066491, 759637083, 881255802, 761308218, 566902011, 413489429, 973843296, 270912492, 244159089, 437504135, 406389056, 459326396, 439253318, 515621856, 287381241, 701790927, 924293223, 774479979, 908409961, 96875283, 385572489, 815651137, 284859709, 948122728, 772397431, 417289356, 128887741, 811764897, 65415832, 214814416, 729420550, 244351556, 914997482, 86873257, 17947347, 211607219, 55422350, 869138566, 98839823, 488760678, 629313263, 599145477, 576604485, 749302865, 44447713, 666422499, 913621468, 41286968, 263640051, 8430690, 226742403, 858080467, 413309803, 465617442, 862685254, 269636798, 885344144, 597792513, 279832370, 733396309, 780285949, 364920942, 561388916, 236123094, 57277316, 395967465, 866739189, 923506524, 676921919, 741366127, 983787889, 33316734, 300720930, 349739964, 243982600, 228498962, 371615839, 377044750, 402756128, 366266447, 794831306, 729184717, 317210475, 519724850, 995576522, 862408208, 729612085, 454968405, 77004022, 535249291, 429590455, 810539863, 89488124, 149068650, 352139401, 874487477, 370030145, 577191338, 797907638, 837272794, 386502608, 636777727, 393006584, 462939091, 476730583, 628345902, 463764081, 38829272, 776658229, 201287732, 227713219, 863415766, 325934344, 888290701, 716696955, 416599106, 202094387, 456096032, 103524342, 230451257, 998635276, 342970028, 918080754, 22831863, 221915146, 390624461, 437206479, 394398030, 243000000, 670721054, 912445961, 74864262, 476547875, 801255080, 729739227, 729221810, 624002653, 648269782, 128130116, 843043130, 63665483, 316499054, 231346872, 881481429, 79174268, 51306796, 789268367, 198806327, 636807586, 111801567, 941913818, 485453654, 769935806, 231757606, 477760008, 744305469, 23629295, 203837574, 217151623, 67965759, 8190394, 446948106, 876481005, 313672514, 934273856, 532699571, 848731664, 846624933, 517222488, 841083327, 200760308, 549628088, 460859838, 814780401, 843189296, 846812980, 859058037, 291660257, 201539829, 109029071, 494825648, 880472371, 598258397, 766585137, 873375955, 507762524, 205978125, 633289121, 734034923, 289580785, 363046386, 651070685, 318899903, 145202317, 73908216, 3142068, 846707767, 7113165, 858063193, 644999694, 808856820, 993748726, 221051976, 15598435, 420003338, 902969444, 694745684, 828167871, 810904867, 317734049, 191083092, 808201616, 986075462, 551687290, 715309706, 332578268, 301789762, 381606632, 843232612, 339239828, 984499952, 336255863, 360770146, 496901229, 911604616, 91818915, 768240702, 318069251, 432109927, 419764356, 247799605, 102817127, 791848549, 140468460, 12045087, 302047297, 193839744, 150573720, 705935135, 403407650, 564932267, 740460372, 757688892, 482784982, 913791137, 363485331, 345569238, 950359899, 93062422, 629685502, 847513776, 925100076, 718142463, 986372300, 919229573, 404923887, 471528720, 704229689, 745418910, 283346025, 626718914, 702953297, 676166469, 453608470, 730754799, 902331172, 329668504, 553498284, 90026620, 946094141, 924677701, 115634849, 243796448, 478829336, 552531469, 777486156, 602013014, 199524112, 579007450, 48587912, 8358767, 681495410, 796860332, 114434910, 648172113, 738184908, 317997965, 23349328, 42484611, 644990308, 814706888, 820503307, 718176532, 233861260, 58672922, 98283572, 295881315, 843116494, 243359375, 911674214, 316653367, 563060777, 560165272, 231632551, 967808205, 273204379, 704473631, 627151166, 652375849, 268348197, 673816725, 325816970, 180343180, 966174754, 585075566, 446336585, 547582773, 224067922, 204952166, 338737959, 591493604, 896926445, 125206887, 753547725, 296537993, 269487239, 210098904, 415865744, 566450721, 326377800, 434989884, 29970038, 177151577, 537179916, 837105710, 676897480, 765071744, 337712511, 730605054, 678657310, 162712899, 73558948, 630873262, 941409157, 904956337, 340627376, 335451498, 584489298, 252793995, 811590417, 162560194, 937965402, 463608421, 351697922, 299953999, 77028390, 699881357, 739619696, 523972260, 732276412, 74782845, 877026950, 155305330, 491180858, 471141939, 509000990, 159701444, 444053003, 60028990, 815655870, 948952958, 97932922, 302771436, 488966978, 39943696, 696874510, 239288884, 846085380, 285276767, 246297884, 965050473, 269465290, 501472407, 94469383, 965106662, 974278269, 687454157, 740899227, 760903207, 534875943, 920322773, 726930556, 905597667, 134777919, 423669592, 362289628, 718879036, 684409563, 226265314, 143266892, 121585634, 473663893, 505957348, 617015910, 545810339, 42416038, 841217058, 254594564, 699268568, 543532012, 776506428, 210495869, 879550592, 457153931, 605571461, 185263474, 478420582, 440214267, 764221488, 998464340, 999019585, 348346806, 819345373, 770270118, 328424697, 475579213, 780403117, 102381261, 882208094, 89997765, 807012804, 458750682, 64519435, 728954279, 203218941, 769231203, 500397655, 517554281, 577070807, 402720915, 714218465, 966165376, 974814347, 320917521, 862995438, 938731897, 286185221, 534561390, 603199838, 279734903, 258680720, 372393945, 701287795, 288179654, 74648268, 117163070, 952179512, 346482194, 259050326, 790389825, 578954253, 661943953, 71558136, 706157438, 695220544, 22553693, 952684967, 86500704, 215999817, 65908789, 303018315, 398722670, 397497342, 805904607, 684178989, 432307133, 272727537, 925110602, 70159148, 205435585, 21906141, 871478165, 530943217, 600367208, 883731665, 278231993, 434103141, 845572613, 331282809, 890758999, 483086733, 414585638, 556984683, 438581130, 398892726, 705728767, 277712531, 595503689, 32482125, 82003183, 279535338, 405146322, 905003159, 487248654, 296781320, 226065754, 22795241, 31944465, 228149790, 894909981, 124005246, 514598000, 216688263, 207450543, 723845751, 790105238, 271695677, 72903010, 591802009, 166198351, 966747001, 921850414, 847697476, 639173146, 672985428, 654360672, 38930364, 615929832, 983633030, 8835968, 770034920, 334184725, 163424463, 373994706, 761900776, 306316197, 433002814, 242273226, 311241275, 778784712, 987947715, 638426621, 626496423, 395284020, 533118818, 423574416, 733483485, 730727351, 591641676, 702168136, 530162517, 226803345, 849265858, 348815240, 973507787, 717119120, 931609226, 748068158, 443584370, 504224731, 283973261, 29294275, 955948979, 11258704, 564938254, 339774751, 744071891, 907835982, 92397457, 524038045, 382560811, 172080338, 129515527, 928886176, 327726128, 517668380, 41343112, 945869231, 458576682, 193244051, 475253942, 320259643, 136311721, 776099463, 456006334, 245804384, 675576800, 359978700, 357493669, 913521369, 901534771, 593630558, 744408305, 170260732, 144936252, 506827243, 427410807, 986218071, 172000910, 709127117, 619688646, 889963575, 18840956, 543711174, 808206974, 857169470, 50886794, 87275099, 650881351, 460537741, 879646050, 810488007, 671665385, 707286958, 64200578, 655026126, 553719640, 91233365, 323320711, 856932891, 746826921, 19157953, 95135123, 104014495, 702146261, 472994556, 578185033, 898070864, 699657337, 850016666, 724087635, 72376413, 421168232, 631426931, 296714136, 297479180, 957599232, 497847475, 355432644, 877041442, 805016511, 673194497, 31097010, 237191936, 958691346, 184806223, 707349700, 24622857, 891101226, 850485744, 563985859, 185372338, 348282877, 382013156, 529347546, 768969458, 903769492, 596434605, 609058558, 709613104, 757032974, 875248778, 536290552, 571805823, 774476841, 333359946, 189873424, 533195333, 531257363, 33553140, 96354606, 997826886, 443542786, 580129941, 501283751, 849492301, 29179980, 360739097, 184705719, 550518477, 174498708, 370793071, 435537138, 183035156, 546190171, 727800269, 323669353, 81971452, 715927126, 635042852, 379228559, 162319545, 913154790, 736839744, 690367065, 284561553, 408592547, 386431306, 502076370, 776332442, 935900269, 432106808, 717775049, 716946335, 664418038, 711420724, 195840896, 11585560, 404386916, 513054013, 868824830, 920076748, 175238985, 833208655, 531183662, 698433053, 937329688, 433580610, 895604239, 261140546, 516815089, 569654986, 512663801, 581619329, 431389095, 872988301, 971435274, 862526288, 226627610, 319272207, 205210774, 622117200, 923217463, 150625902, 647398667, 472282282, 419121646, 294631655, 576092446, 586418990, 242408655, 258670650, 831065741, 232982921, 463827966, 536404483, 957114841, 943615484, 345288404, 261464510, 530384155, 101601990, 836944071, 79641783, 704575063, 821510669, 915433760, 864410950, 927505142, 206104110, 222516796, 687944239, 931241837, 9243085, 281234265, 600381204, 16895487, 693140415, 642052399, 64501088, 972541029, 518111532, 266036664, 846392743, 993923893, 716347145, 141146981, 946226726, 477001904, 793987103, 140071203, 33204314, 585478901, 363591863, 998890976, 497501213, 557255484, 970405444, 28227915, 655328291, 885990146, 170531223, 605501230, 334129286, 295496697, 181637058, 939276393, 543684612, 360874346, 647045756, 433906655, 759840919, 380079816, 324936924, 867252024, 699384748, 984998296, 28204191, 29373904, 153769521, 957897651, 274895551, 76556346, 51069235, 968402492, 450484417, 962816948, 935018419, 770040062, 590216630, 560679166, 734426274, 346188120, 612894029, 666496828, 824212602, 387313157, 134981767, 572658141, 770379071, 430267150, 650520413, 349007077, 523284190, 35880412, 500495379, 524147664, 48745947, 15233558, 19489814, 668036224, 216990515, 636656515, 227150935, 833821348, 873782787, 454448846, 155161264, 139859645, 612862153, 873871450, 752479549, 542665885, 594496792, 643937142, 986144816, 957816041, 883772613, 477225144, 558224944, 510631804, 557594918, 943588438, 763159942, 634978373, 883757948, 638236268, 940482311, 616150143, 244927255, 456974788, 714735556, 892428236, 732314555, 886301374, 453015702, 988653086, 914816734, 10519312, 795554260, 146071247, 364327336, 698018543, 938121404, 872106307, 183891481, 160239925, 380273607, 970726066, 671797814, 792214836, 79527292, 158057141, 378849799, 830938767, 453424408, 946481827, 208641561, 29817330, 404701453, 20240999, 240941391, 205506889, 820011060, 13572413, 476682267, 232325224, 245500566, 984881183, 629285054, 76919553, 976633877, 803773721, 699622345, 930462214, 222126497, 473871246, 538145309, 461799840, 708874837, 924860910, 387352601, 755795283, 921577676, 685085156, 890896196, 790499022, 477799837, 52142507, 914931803, 263145336, 827355181, 440261269, 239159666, 589009658, 975581463, 575399382, 423694655, 300925534, 693845629, 505751867, 588254858, 706460411, 956683067, 962324950, 19204232, 170036417, 214514882, 541201696, 498136510, 374826368, 608268625, 885967937, 720542104, 104227274, 827998256, 84554812, 72458141, 791249573, 425097027, 807003161, 982002914, 994732675, 468127261, 671358602, 782369960, 317799042, 145384939, 242133778, 778355345, 477138187, 656981445, 942544258, 981265209, 320189147, 67853561, 951889867, 228964884, 814019672, 705739715, 585127128, 225467595, 769830596, 608704377, 907681319, 315170825, 849866770, 493344217, 958059185, 45919048, 381264700, 55646738, 870686738, 282420712, 495126066, 372819491, 547544083, 138644298, 264562177, 813878855, 406658793, 810944312, 97367274, 483631052, 296983907, 800789954, 191192528, 796689767, 39147558, 97681407, 118982634, 715402925, 669600832, 156384380, 287790075, 773714053, 216878800, 229688724, 91730127, 149996630, 691284980, 400108935, 367324551, 96640800, 504237405, 217678714, 74055471, 66491526, 707653825, 542853192, 428127996, 216704955, 543728001, 354600118, 188393247, 64068703, 899323411, 429272645, 886283685, 728239886, 823235610, 290963866, 771048478, 84556843, 364594694, 404242004, 667466130, 573765757, 12372859, 446331684, 529432113, 265792451, 500603186, 875066766, 176489562, 513698152, 95174117, 802303091, 63690658, 684579233, 184036102, 244479655, 769051503, 351910673, 167611055, 595634616, 108646009, 410616622, 731904193, 543672294, 793146628, 971218977, 435061682, 330468673, 567101916, 339681007, 417309905, 106522137, 662457098, 380584950, 841259532, 417296723, 414640133, 86146840, 691431511, 24958705, 151409647, 544984737, 745016960, 297916835, 884833141, 632257310, 837155737, 285790629, 719791707, 172960546, 318403324, 627769689, 715669799, 958640570, 610713626, 826450499, 809778506, 965677433, 598622562, 343244646, 844195297, 18036010, 668029946, 836398434, 145925486, 854004060, 70763827, 34861353, 143402246, 144524644, 989783120, 769336667, 851201145, 372687590, 78477705, 526419789, 969126988, 357895011, 59387627, 388917625, 864175196, 651520698, 876988379, 968384986, 261834486, 874835013, 74602801, 379609499, 543906942, 61554716, 186356578, 629970048, 846910324, 329468652, 50503345, 326231778, 543850408, 124553398, 38851850, 803625465, 215582731, 624638484, 696489744, 828639507, 84616754, 302638473, 422705117, 916694750, 305055940, 218648246, 992283505, 552722442, 33930849, 70107543, 240240361, 412295933, 336015128, 618647554, 837385498, 861134480, 969488578, 406710011, 268577735, 846138148, 949450669, 859825702, 33858967, 931848339, 900810978, 477557084, 265467053, 82661930, 962523347, 143421667, 950951991, 192221293, 971110430, 859367614, 435098013, 519617528, 476027942, 112468806, 424056327, 42097006, 786810272, 792876291, 826034255, 291637928, 38295626, 926469602, 135976947, 45565748, 861469891, 828314052, 393669869, 170864220, 112908162, 256658066, 63758852, 797088366, 166129785, 776785360, 211080611, 441271392, 259311545, 135637411, 528759008, 402891449, 879143227, 606879316, 661886261, 190417934, 741968692, 151131335, 656281264, 944011088, 301258972, 162526355, 224577933, 233121901, 513644260, 186916431, 826138007, 799999207, 758904719, 974840222, 356750522, 741213101, 28197275, 295032380, 704341215, 47263181, 609800198, 698950786, 317795865, 550177711, 351931304, 94470693, 895827688, 209057933, 835870878, 769973034, 968895808, 966798841, 422840629, 406988244, 979618393, 180104053, 91242857, 779830079, 951849963, 397869634, 845328085, 79297522, 532545797, 246709541, 363080326, 67254292, 77083263, 487909674, 919920000, 207277677, 124092212, 372687464, 913149281, 620545734, 738527769, 195124821, 445517334, 56466180, 476391591, 515823874, 782140203, 632954178, 675954149, 24850130, 240602312, 250631988, 654881467, 877791219, 851193367, 477820710, 660753598, 158719491, 750489604, 680454504, 195149741, 543409457, 825095896, 446263310, 96229602, 245104600, 724872414, 314060623, 897589964, 881596546, 250350783, 396926474, 705314383, 330558523, 980062111, 796149493, 674811586, 791891020, 121387826, 692350987, 462307449, 943848788, 737692950, 123161210, 551508752, 656398699, 901705389, 443181639, 754693639, 604277805, 306125925, 756960630, 813606399, 230666577, 100981563, 351083580, 129208490, 501072656, 74316675, 85472309, 318432614, 189032535, 656028550, 184111103, 254939971, 889999737, 855183396, 93388353, 113155590, 297056668, 732128387, 444800251, 215299851, 505709642, 737512155, 543542831, 236225077, 436272057, 32929106, 371616796, 938394400, 950717276, 623385347, 357129800, 906249759, 616113587, 227465443, 383349018, 898784165, 701377559, 340684249, 106114586, 730912767, 827326728, 871998015, 843269938, 841751999, 463662346, 843803120, 888385884, 438315550, 516443924, 376845132, 154291675, 543792931, 327504933, 479954589, 600075003, 21651795, 159596432, 333872405, 596598213, 812608731, 444225341, 801041848, 343629743, 13896159, 876266495, 70004632, 12571559, 229135159, 643856259, 346634405, 391802517, 942118661, 276158429, 520247069, 358694284, 457303457, 425018064, 556832282, 833308084, 775575864, 514707862, 466315055, 209007311, 330598670, 354367393, 809394048, 736275145, 219521949, 990584169, 99278815, 774556327, 134408240, 230284410, 390862998, 751124590, 899405624, 272934271, 574844632, 678640376, 362199681, 921892032, 750244632, 583756931, 571497070, 443326612, 389084281, 527775626, 43912368, 306501497, 591009230, 569758158, 980328582, 126692175, 43071447, 87013294, 602335496, 346576933, 74807718, 627414249, 9978230, 287416714, 948445893, 242171497, 721724914, 911932075, 284112217, 850601881, 313735895, 358112566, 194971182, 117153032, 605233136, 937046399, 749530021, 878891557, 551703667, 617422420, 980979054, 452827952, 391411758, 899921381, 504975528, 799522321, 884156255, 60618558, 816653900, 368569935, 350184073, 889851978, 790920355, 205692030, 712789485, 590358025, 108793766, 61060083, 174825221, 764475126, 468864015, 157674953, 999681726, 697921083, 834878552, 970171640, 204277399, 92311844, 968513919, 909752366, 676618781, 477056366, 590899132, 46491492, 482236456, 163873115, 713624163, 697250127, 336036136, 161659227, 625538375, 161861964, 539792550, 308481311, 771785108, 181461731, 761112947, 636869415, 462699868, 204277542, 356281836, 12285448, 147677896, 441078147, 187060773, 113907391, 267117339, 337126916, 224005462, 666604566, 306036264, 887672464, 627236084, 850252019, 156045892, 925442707, 508670816, 696350876, 557394507, 331063236, 640002895, 35407870, 234641076, 151790369, 607943472, 292655944, 289601652, 72730343, 418167231, 924729281, 287209651, 380899109, 671595932, 553701793, 141302697, 314902010, 831951339, 832439276, 339974816, 275660018, 614385315, 544359201, 448107167, 486880255, 859366778, 5465148, 370813241, 87633658, 409000395, 690884025, 136116370, 546268230, 96022786, 795950870, 778050868, 54889553, 913805309, 992338269, 267730003, 251714190, 372078835, 760298368, 909611236, 953522692, 813802805, 973118189, 615951557, 485192314, 239609232, 578058948, 982557728, 434841529, 870854141, 269926672, 211103787, 559590877, 132632102, 733784718, 22405694, 63787653, 535200627, 202750729, 651955880, 417649088, 233855484, 867104841, 358253286, 436799116, 800008590, 110155457, 240458095, 334625669, 679318025, 709930986, 619346389, 669840902, 973904384, 779738945, 759561330, 424780055, 967467612, 560268945, 949477666, 338572125, 859656993, 685343587, 937227731, 705140853, 48344109, 18951735, 556771290, 260027411, 722026190, 933987230, 799512919, 120297053, 812503725, 38224828, 89816636, 513285347, 53423485, 170977100, 872130779, 785727821, 744249599, 806779766, 7668171, 270649102, 21750586, 504846251, 358627443, 411029566, 349082514, 241652977, 450269385, 461591700, 931882124, 23265187, 692078122, 802953520, 290184719, 508902087, 658880174, 148803298, 947245377, 203297454, 160961216, 208404700, 201246478, 641906347, 29764624, 671179072, 269891554, 684419768, 483838031, 22539352, 668620852, 86558175, 347902793, 891482597, 246995302, 611116868, 904824780, 107083874, 582098679, 733503064, 580846735, 891352095, 430468568, 768002790, 324650218, 607307530, 393421892, 784929440, 223550593, 503070351, 558872695, 955994170, 954905525, 613151598, 192688303, 510635010, 923542833, 512252745, 997890823, 522204813, 997399672, 816585452, 794941905, 603995751, 927938364, 444395994, 884967614, 602822812, 29059190, 762821261, 988786263, 9099927, 715979502, 34374309, 481536701, 940979333, 747258875, 5673684, 646752137, 962112032, 10136576, 576983697, 376369791, 430300296, 349945589, 473702758, 240642140, 647939317, 527903497, 742740935, 348430629, 297540506, 743219192, 36294792, 879362823, 395366220, 119809385, 909921622, 187472659, 118805683, 266118030, 702795323, 131712592, 841972304, 152492742, 935494351, 808917460, 412002585, 59210531, 87775266, 906877557, 916289822, 122119195, 405081817, 16574665, 207672203, 637238136, 478801407, 820982703, 448900929, 605882035, 464649343, 97647335, 317829887, 647171225, 710270612, 632781032, 110461794, 613525651, 74449948, 403440931, 387585029, 561604231, 622050143, 840804994, 96296864, 246391522, 699538215, 627150052, 779901295, 209279994, 440130458, 312788613, 510369858, 297086189, 390739295, 884708305, 229858971, 578272510, 915835891, 484256672, 955298663, 333008241, 411630624, 508077021, 663885661, 469600236, 376980240, 200673522, 574419448, 292668495, 358192098, 944146252, 891325880, 695543809, 211331729, 163504525, 587295260, 97648747, 276421622, 941863258, 151673871, 578382767, 246576195, 598063131, 746880727, 843117422, 486710546, 185463097, 286520803, 140748354, 296090531, 581473274, 32032301, 963900725, 666739002, 162152382, 115292942, 47792170, 175716485, 578283676, 766277538, 480872606, 278113172, 819305991, 842885678, 346160156, 661157710, 444157048, 29181397, 516238414, 142926449, 715409874, 806094053, 143612014, 694417955, 788174086, 880736416, 143857191, 415549819, 92387957, 120416653, 43174815, 449401706, 127811276, 408075702, 977533795, 580986024, 696636278, 323670792, 566352355, 311507901, 240754479, 513012377, 184827528, 398532777, 894617761, 90082434, 699137063, 130822160, 366426365, 119811345, 529859520, 226894169, 889460584, 166873267, 16333668, 22612992, 95322665, 633358374, 302690951, 715934458, 123651182, 466082148, 657903002, 595802193, 5799723, 395789706, 883902071, 642114024, 428308441, 979701351, 777720115, 876709179, 332538889, 232925409, 544161267, 335583320, 598889867, 896556408, 753727113, 586628175, 988287113, 721151323, 902306399, 460346444, 146973138, 160605781, 257603123, 39790478, 765899337, 169386609, 982556892, 209540248, 578699075, 745551659, 378793816, 108142294, 1799315, 805647775, 833917799, 312720743, 685791641, 452681219, 914293464, 15240643, 523776806, 726085577, 987473956, 971254459, 283831715, 638431362, 225634583, 777112030, 586443550, 316908482, 35971162, 249314171, 742617540, 493427233, 996142536, 41528691, 12171165, 382006435, 813615288, 942850098, 735863001, 717711678, 219776004, 335776818, 535388077, 274196478, 706710747, 380813783, 400863923, 251875489, 96961365, 144273571, 755103290, 621983174, 535303188, 386033466, 600650184, 73296030, 962882627, 404324016, 241293051, 147525610, 255437320, 765439751, 54051675, 282136741, 561381177, 952700846, 426402967, 179311373, 774263254, 361984363, 547994636, 138393261, 331543729, 332770812, 707555296, 987220383, 345930078, 359021247, 311971885, 905755812, 489866397, 428933345, 170994206, 386391723, 145103068, 85662060, 667516336, 197283554, 470113870, 797482288, 330714922, 303272531, 131805153, 582690722, 292265383, 103200303, 567875857, 905241537, 636193136, 609807477, 114093752, 172287790, 933713386, 172175836, 557087258, 709231264, 946313347, 170056426, 713803018, 10641456, 719064472, 653919069, 104000967, 158802678, 986867814, 502986035, 8056914, 994499126, 785354446, 252442040, 969753736, 486338665, 21362896, 321999925, 618323000, 223022683, 389125175, 643570581, 679765310, 873250597, 20472660, 271068353, 417111976, 635861730, 960302840, 320422954, 955543385, 613237997, 314479779, 702301691, 789819905, 563242998, 727709933, 104970003, 352210988, 389340740, 689229277, 505317493, 914590859, 97261561, 156429978, 329256582, 986320092, 955343167, 608418357, 211358446, 390046792, 995166773, 727507, 772905268, 317553089, 131393370, 924021144, 543361104, 692701319, 889461118, 60087007, 794936747, 245274985, 117554833, 974712488, 306110196, 250651028, 462659695, 691227912, 700557242, 543191576, 808307571, 298502357, 877877241, 598887971, 475345532, 428858717, 623613046, 853142602, 5940176, 823049685, 406930559, 39729568, 817569660, 696402804, 491990040, 124353060, 130967204, 938743547, 69706916, 35663534, 570483983, 248998169, 143209424, 793674611, 48378595, 416039885, 514212401, 140645815, 38310434, 718830216, 566671271, 671308358, 40742041, 878579039, 221255041, 896595133, 658870554, 751443022, 648238062, 700122099, 362811096, 841846185, 769707091, 889526992, 735930794, 273344514, 486397214, 108150417, 213170575, 803989989, 975422103, 461003364, 673731947, 982852612, 989183174, 945744090, 931291636, 54927288, 446520509, 208576632, 667880767, 234614270, 825609432, 819343549, 433181697, 304018187, 812894315, 16419547, 821836858, 210746602, 62786045, 77460897, 467742801, 40918231, 837459602, 908678895, 896171482, 614977721, 329667359, 840929756, 599411284, 63521810, 261988607, 740109007, 283732559, 561984544, 773027594, 815563296, 501926230, 797644293, 705873791, 165169491, 66353534, 809018851, 673131136, 391860501, 359634532, 421925888, 749135510, 566972576, 210135147, 65050849, 772896666, 825212811, 601483129, 452806235, 105738409, 295455317, 677189026, 380662220, 769112673, 34444817, 190653494, 820714897, 425807465, 756009917, 224548719, 442160213, 455281408, 667987684, 394740208, 575666021, 799631588, 203320519, 193622798, 853746866, 667901992, 596872864, 621067049, 629124989, 893419701, 821047595, 990571468, 306225910, 716741857, 222173136, 755581271, 128678196, 586552101, 234314461, 796204519, 790789301, 500189527, 819200240, 236524150, 416980345, 552695720, 867632708, 57153096, 818045233, 450722181, 306573263, 444415550, 395552971, 601982849, 800849517, 520857953, 457813291, 248176424, 354445568, 529515278, 123791706, 984965617, 385588410, 283811546, 719693960, 988997421, 859294728, 9141725, 803468339, 279879917, 543445385, 587640023, 302571940, 366879167, 501608887, 468240942, 996247885, 58932320, 18275384, 231121155, 708630370, 578367479, 927676837, 747379621, 646297107, 690093097, 989451226, 404928327, 714181980, 279694755, 820097880, 433444076, 139771498, 582678772, 538714249, 775123331, 831829355, 507222582, 107163489, 994438286, 898672757, 919744423, 637808815, 704595917, 702224731, 455455906, 698796936, 285339550, 872182579, 562716676, 201234731, 862375074, 541435378, 238366036, 746236984, 784249985, 133420147, 239976697, 624929763, 798106185, 199524593, 138882332, 750652375, 928821489, 289671838, 406888460, 626180032, 456528523, 616472734, 817440624, 44941298, 536509370, 68007678, 440206578, 145109004, 947340191, 860939768, 549028357, 631910835, 193738558, 172320586, 20242775, 985414839, 186330740, 670301703, 49515218, 271590540, 887515888, 511508667, 999924627, 928691585, 198025574, 278455234, 575496364, 839949669, 847315041, 291280566, 563862026, 163310631, 157347865, 330392463, 453667138, 790734550, 24860928, 262861120, 696814680, 305792398, 178803813, 131057582, 579216520, 320678795, 90093940, 815997813, 67829503, 863933969, 751119236, 87506135, 792477305, 103356236, 454766194, 872003249, 936036183, 47715692, 421770460, 290278314, 798802021, 699280073, 325064405, 787414279, 943909903, 900421774, 479452237, 221903334, 280934808, 2736175, 342472468, 687536791, 529260484, 174376041, 741418220, 263755756, 626301334, 317760797, 260758519, 713423500, 415308849, 561195454, 217963749, 499109725, 955662922, 429191987, 71531800, 501799089, 188865312, 718305927, 416529161, 728632616, 462779994, 580205595, 889915334, 361097692, 391732092, 462879482, 11364672, 575670546, 99617937, 935126145, 419265807, 841678250, 742645081, 72143468, 243304447, 878295163, 377553258, 89568242, 239166601, 983951484, 231851425, 444598786, 583752810, 175799177, 645828225, 658034160, 114492453, 323378716, 395362181, 685635342, 62242603, 445512116, 179031261, 47354534, 258468962, 75834826, 464096676, 60569516, 1148157, 410765643, 259353187, 529430046, 451655396, 808653204, 917216242, 683007357, 83778593, 10510338, 749528061, 347168377, 956892923, 694940513, 383375539, 928286032, 114063832, 865061420, 203654685, 557863440, 798918046, 765009768, 787347140, 545208566, 680970669, 25503588, 356426285, 927261766, 732017521, 892266263, 488194652, 566953646, 839051699, 670576110, 213878972, 980796052, 280444148, 315564087, 195528852, 102148936, 839991225, 151916071, 954368873, 120979623, 665793011, 64461344, 495475814, 963340978, 380042803, 764784660, 436133482, 831515997, 796739668, 204735844, 173566806, 439421739, 782421097, 551660635, 402612653, 68476461, 885811354, 721572294, 197535973, 184562215, 192924504, 769761267, 958412091, 419701188, 361859137, 876181907, 552603913, 286715402, 318579774, 357111442, 940767138, 617494323, 708712391, 129628486, 212770791, 811488605, 174877559, 399316331, 564281582, 909138907, 508364778, 891567784, 30000961, 497316489, 856141933, 537564185, 43314122, 283648923, 444005104, 894947996, 276975825, 193211468, 580842508, 852394302, 768080764, 210037348, 549881157, 55948298, 217070899, 166819403, 290380122, 908578792, 294146588, 108257057, 138657736, 570163454, 833899572, 592698651, 490708240, 744928205, 464827271, 218198747, 383797216, 673700066, 102349891, 510260196, 850688535, 529607188, 689292466, 636410462, 484969774, 883262169, 208321824, 250463828, 31754939, 942951640, 610437894, 732582410, 772822246, 123112012, 664706812, 82702259, 146700234, 328387320, 355522575, 865808334, 344293037, 381048705, 492268882, 193422256, 140058299, 908733860, 960953598, 726363950, 394154879, 985720116, 443530815, 260505478, 382900745, 703630264, 983890944, 378831388, 847165580, 808103374, 924421768, 304302718, 425533912, 935592011, 402664723, 967453713, 335913276, 727657788, 447573773, 827399158, 227658645, 857199118, 433737299, 426205454, 14961062, 330727284, 632180593, 389169865, 301534664, 144669735, 195818667, 589641655, 605429417, 849624055, 962063010, 705612189, 369680507, 491760566, 130151390, 371799820, 7649828, 926066955, 298864892, 459686713, 75951519, 141838199, 2022073, 360672400, 995271440, 681950314, 213838349, 343135082, 421279119, 151527135, 914982551, 704371665, 981141003, 836481399, 383219543, 964806747, 834862181, 636100822, 373832751, 929524975, 707820065, 826891122, 998710104, 600751741, 43702923, 611758807, 540734737, 32752670, 944724561, 720739690, 879135789, 295470074, 589144283, 719229156, 30548842, 498604947, 563135053, 604009750, 898737668, 966546640, 639590869, 672183606, 280548435, 13116591, 187443183, 807474103, 169415203, 193152060, 959693494, 158277431, 828566722, 41702011, 574313919, 219111828, 112227251, 892461874, 483473527, 264471151, 183102642, 618965012, 533985337, 143569397, 955502465, 53292424, 653969017, 153790661, 877190932, 345791657, 902137131, 135679105, 738745208, 236266754, 604272926, 972420370, 160523008, 262031829, 953343331, 197973309, 65234771, 211834110, 820242087, 654435690, 117876544, 506401914, 750150116, 338898516, 621950475, 16181949, 798702387, 106709232, 13826661, 876658973, 104000590, 202808154, 690299095, 595729816, 643301397, 323877730, 297777216, 13989614, 922377895, 350753160, 694509508, 277991035, 720459748, 683041462, 413539143, 360359316, 813834407, 779101948, 401160568, 685066243, 376869643, 357491228, 158851430, 644682358, 100373933, 859603509, 500747334, 888082707, 282754342, 457757341, 532652380, 2948609, 16254612, 342719626, 420249853, 211636898, 330220770, 36017210, 2339268, 728825485, 112276790, 408147851, 211773355, 426309864, 66082527, 921836670, 931349837, 775731733, 43722937, 657197034, 293178567, 677072967, 552429256, 640143864, 808474358, 685854045, 423951761, 714533840, 213164972, 592565922, 642101617, 350689379, 34913472, 239291636, 473733831, 927055318, 117297053, 144804740, 587701686, 356162278, 649139353, 701320825, 811986856, 824902778, 426697658, 443853039, 659536867, 613765802, 136110943, 206939411, 854362971, 838228240, 584048129, 419497266, 159166509, 987001882, 142020333, 998980575, 939656032, 56190079, 837614335, 90471104, 853695092, 124686073, 810635338, 777250927, 613764389, 418207056, 827824649, 577049578, 54607483, 459155841, 317477662, 559419056, 773195697, 97938056, 581863346, 46297487, 113584296, 898438388, 618322733, 203423728, 559022547, 938766389, 119809374, 276902935, 319493308, 156551190, 901631681, 312317724, 130907035, 108056408, 736234348, 585324415, 197181451, 478687086, 606661636, 380050833, 6459561, 394848214, 12464262, 621070195, 793327019, 252027645, 231793375, 354018755, 5219119, 219707631, 262859774, 282768978, 462561195, 365499126, 773863438, 583983783, 98151134, 28633751, 272515221, 614070035, 586763884, 723738649, 283243923, 920976043, 316664167, 887831195, 440843759, 243689065, 63472663, 741815318, 992463042, 775464448, 947777879, 527274021, 946072478, 100457046, 169509822, 13467830, 584068663, 392235932, 239454510, 403679684, 435641965, 461584752, 909469567, 775582869, 196885681, 629866707, 388550171, 172670362, 318140544, 380268617, 782499826, 696466947, 816213879, 902896323, 20079659, 29342698, 613436978, 20693325, 250735405, 310745242, 3353893, 694337601, 717407246, 880944813, 599799369, 669383452, 304066699, 604577967, 326740607, 404944348, 697721834, 440808658, 581584746, 397365361, 47579241, 309414350, 833812143, 302636640, 172390188, 872112511, 575914710, 831162131, 698051312, 22949753, 785587486, 31643859, 616660562, 582810953, 71821263, 581620677, 270273767, 852455731, 49273196, 724038376, 546665635, 847356882, 854426633, 624709050, 227519058, 606704103, 403561023, 636719235, 397884546, 130117130, 754396729, 899834678, 298242858, 362705477, 51144826, 735112731, 477609910, 907479131, 22467798, 250814610, 836553146, 105528222, 129350994, 245670049, 938445283, 896188584, 684758741, 170672606, 590654267, 852909970, 346782112, 697669411, 695451293, 212187734, 687975078, 277418562, 460452066, 478244391, 883377172, 735570549, 609327750, 721911133, 991518215, 390836158, 96713729, 207163383, 356941033, 901919528, 994154952, 340860253, 780269912, 604155342, 997899915, 806661683, 247368833, 246795439, 784924589, 879727963, 565763387, 448005580, 608691458, 658653970, 297312642, 561583232, 505625346, 484440771, 719883044, 29634863, 707412625, 281275386, 888872051, 624549590, 351800435, 183259790, 688889972, 466942713, 384460091, 452390939, 227110060, 689623803, 473900608, 250131661, 521918815, 616319148, 249419342, 356534311, 564640176, 676779585, 704963942, 418231242, 549553595, 299006552, 923863198, 193852416, 686250583, 221535266, 268430507, 357301115, 665362416, 146473269, 759852153, 172162872, 736018386, 838449085, 66004204, 891192167, 786307698, 769648622, 999588054, 412821103, 968362234, 98515912, 191726332, 223329202, 389410572, 192966055, 205597169, 527358375, 8262336, 669884635, 143098815, 832234999, 1483786, 777225002, 74277934, 1558641, 790373364, 271940266, 781824791, 460438690, 504001533, 910759765, 910660415, 661940815, 747366719, 892351003, 150901558, 149270089, 490770176, 122933572, 372867313, 628761306, 207037212, 3822517, 893890365, 334482285, 443779427, 683644816, 548362365, 222587541, 848754849, 227912924, 916709666, 407619599, 99515491, 990190472, 646046786, 640471507, 273327980, 313578681, 117056870, 582819445, 904218356, 225798770, 788351660, 622056127, 639558709, 13539901, 844858969, 357533386, 292020044, 493980712, 788755128, 197794208, 527738252, 380522422, 224969111, 302977041, 977977822, 332180242, 934432170, 167827132, 500492891, 249366552, 96410552, 746587089, 922414610, 911235137, 448278667, 784348332, 57416331, 593225491, 856399779, 842528640, 156186871, 620749373, 78785451, 774461370, 835217147, 421929220, 853129529, 319045001, 874370765, 344391903, 754294934, 201782612, 711098510, 392989540, 788634882, 707891680, 269800052, 326586889, 882435831, 242132414, 782071493, 157141033, 85776491, 417833560, 622130429, 66317624, 750682056, 854176874, 746567924, 696792547, 622793065, 227247326, 459887907, 936852761, 527729311, 368401290, 449300595, 203917648, 888173730, 555666812, 905370142, 587405853, 380815101, 53750786, 354060332, 487885518, 502120738, 107318466, 966452551, 899120774, 301147836, 158627599, 746668193, 449161010, 479922398, 26275448, 883714027, 188311446, 718268148, 693427355, 632497217, 380360804, 209656722, 610878926, 869291919, 136667829, 944516826, 548406991, 866707717, 687291201, 453965074, 730477913, 45752540, 70875801, 123969685, 529674065, 585797004, 567750099, 680991802, 846544733, 596044458, 825970617, 267836369, 393413684, 593324893, 468606398, 91117135, 972097509, 142542523, 103045253, 547657907, 790643050, 545913651, 30133631, 232411941, 513916303, 45300323, 519493285, 32579373, 237394487, 655995674, 331505993, 77683927, 542430814, 688616639, 936806911, 866477245, 251284127, 907902991, 689741382, 839654389, 537678996, 972862283, 796085401, 809960278, 417979261, 529429803, 383877936, 450792801, 282781426, 436432544, 303352449, 623330065, 299438017, 609738655, 808528303, 623407049, 577826572, 11327463, 458159990, 414771553, 525483863, 617747750, 201491013, 169519321, 248537923, 947381861, 652402786, 67911911, 351620329, 667810578, 10473782, 197214014, 106177589, 117048964, 586628712, 121257459, 182426924, 249930667, 21002122, 364082117, 108199469, 544209976, 174292284, 773121479, 42352401, 697424933, 279410098, 166232318, 656552762, 142353021, 189898692, 949611774, 306848993, 664630216, 168506352, 897855258, 833590386, 87559798, 521149754, 852612556, 909296165, 657375660, 495186784, 254689948, 644209034, 763387436, 355181267, 19320616, 979422779, 300292233, 344068642, 980375218, 105525376, 88253358, 939778701, 838942120, 610612867, 994816045, 105514711, 394207258, 326991288, 335869922, 85998738, 595242027, 303023149, 634528197, 89394285, 779515048, 208949946, 267055870, 938697586, 854614051, 185245003, 699594787, 598775692, 658825337, 679386898, 351877405, 731354577, 146834343, 99128962, 747507300, 318548288, 70151273, 913204432, 47405517, 505080720, 850017889, 681182903, 218124883, 42198316, 725729666, 221391719, 909433719, 514442062, 705164428, 424204630, 719454258, 216298730, 927457804, 376009698, 364690013, 794126718, 803333581, 212028580, 831608656, 553407929, 925766485, 100257577, 472292202, 245251761, 131666035, 603218638, 148273479, 12971044, 92621709, 354362202, 32081930, 62704975, 347653043, 317177199, 513447489, 886430424, 77043977, 119526735, 770366026, 346296225, 290572064, 938141588, 345477243, 45847431, 523057056, 17476776, 791543877, 344922729, 634486369, 304090301, 531291351, 988985927, 782371749, 575011352, 538911930, 799699871, 585997607, 206240830, 533809113, 360676008, 206118078, 560300272, 79479823, 611675573, 270958999, 523627039, 194816654, 916732536, 680149003, 473984670, 400921278, 939229953, 895007407, 935686466, 187452479, 850869117, 335870360, 291764299, 117118395, 478835661, 200575876, 200861258, 286759594, 610723415, 283682825, 410195261, 511572762, 693844702, 274037870, 215279426, 622633969, 939746069, 993145192, 895586520, 525124491, 985982765, 469141388, 389532774, 236671135, 818686599, 85547650, 25068300, 685334392, 133989866, 802813270, 144153439, 877668158, 693764835, 315430606, 482374564, 751180018, 533972397, 636480274, 859495173, 851384603, 671688909, 257677172, 748744846, 589301644, 573849378, 262631040, 593637835, 944376894, 368842327, 682616025, 393233711, 111713127, 254886180, 499556320, 827927588, 731808489, 242897958, 744384361, 113335117, 917552939, 471044691, 522236704, 599627797, 150692741, 456155692, 412722797, 549442671, 347107335, 390292152, 412919466, 438367551, 151425188, 92414080, 181599403, 656433497, 237913972, 56665766, 916704590, 878773471, 906306801, 721847904, 683297165, 528143122, 56348014, 370806584, 395779454, 238276771, 225917520, 443698934, 322257537, 133005297, 733083416, 352030484, 416417987, 31046177, 789610154, 143078289, 972144169, 519585422, 713773983, 743953909, 789468052, 579673103, 793077905, 561509525, 547511691, 593908937, 426791970, 304949014, 92605386, 311836787, 351572040, 416125165, 15472407, 735831411, 737020969, 498659090, 960977342, 285434549, 170962514, 594956944, 309926421, 674016021, 916315119, 29939701, 688865608, 426322789, 905395416, 397284131, 471742146, 296394215, 387697167, 505295992, 345166291, 477731925, 769333391, 96180846, 460853583, 234052321, 798098319, 849346879, 731258574, 429623658, 401958066, 71962849, 935393286, 935306780, 809304567, 507944616, 859484908, 286095697, 662967281, 85859510, 296579683, 993281324, 422814357, 33626861, 611097269, 572518423, 161063952, 160650037, 297723925, 250327663, 471902634, 926101990, 154045072, 780099016, 552910104, 804265347, 673658970, 778480557, 187521644, 870275979, 878530300, 777726947, 453108825, 961072409, 578291182, 36501843, 216442318, 821779412, 12635942, 349467917, 373418970, 925297933, 942637689, 365317250, 367852686, 49791316, 419923008, 811268382, 305959333, 936228679, 317854878, 743876490, 333509752, 935519233, 722300783, 32138366, 236289356, 411396024, 866498365, 25533157, 31403714, 921008884, 249715479, 221580585, 259604756, 785352734, 473300458, 211225496, 245946816, 878165324, 114587802, 894937202, 852051504, 653135057, 864154595, 293382658, 140584367, 214829093, 541484804, 636368738, 275908913, 630990221, 52287870, 135102029, 157684645, 551869617, 256866758, 867163657, 313571664, 230201671, 264659636, 365218866, 838051052, 361977820, 506668830, 958067380, 94215046, 394261684, 290131835, 201232719, 906987965, 490955060, 828745297, 325680669, 792873507, 491884312, 309420133, 368844860, 360275305, 82615682, 169824353, 438015288, 720404055, 22496448, 974401044, 399085001, 548353350, 764889531, 169949759, 573087189, 527679337, 536934990, 184154604, 947085119, 306214358, 835979189, 395101060, 672311951, 638748746, 346214892, 145910820, 419220379, 633452007, 82074997, 569742361, 843233207, 468175601, 836581049, 433826698, 238339172, 962079774, 172080233, 606581687, 452831506, 225247041, 696785545, 132485734, 335275890, 596403077, 235472522, 7311951, 51374839, 488429779, 345241863, 415525054, 80860917, 323782201, 944627672, 731920277, 554379450, 531284688, 835425170, 932370287, 740648950, 733268791, 878758718, 295272248, 430588860, 962686527, 765421094, 336808317, 806559711, 300462122, 169516450, 572985532, 928559132, 704134186, 138111481, 20596399, 2397533, 892867010, 971069636, 971323697, 391576882, 15306792, 866272869, 182721887, 460134764, 619704157, 732255009, 769073573, 172078313, 890065983, 446203991, 963161522, 435109120, 225052066, 56883933, 661502941, 805074765, 250239271, 585018648, 487906196, 881558834, 135670766, 337529928, 433594809, 398879773, 548362613, 285300625, 98432571, 158374060, 537034894, 805816233, 49044300, 124122579, 543925542, 585773748, 980897343, 898348949, 457553989, 922350488, 752938305, 708119865, 172528328, 471951795, 609034098, 989630209, 841727420, 271862097, 351706597, 256718269, 232614165, 670509500, 903185872, 982459788, 363350187, 970600865, 814171627, 357990800, 808504596, 531122928, 572208398, 518022365, 122547055, 124470049, 481557735, 769396486, 3495307, 103349173, 491768391, 104537750, 195536897, 602217169, 734622399, 106565302, 868728965, 341247443, 235533602, 383986358, 684989650, 851734868, 371465755, 672574893, 74163486, 504501605, 784942139, 736621646, 154109523, 508281373, 745708661, 803155514, 211936417, 713077183, 771442077, 685768328, 314937687, 794244951, 323349738, 283603904, 599564081, 525123408, 756461336, 162522900, 642476502, 28277410, 760492107, 380921533, 848381540, 573222682, 155204004, 871905629, 349765603, 229753852, 435579468, 942475017, 537401518, 664892757, 49097599, 979515817, 733596390, 291916738, 924533445, 5237515, 835901177, 198385216, 515236823, 192555486, 112070315, 632609485, 965585751, 28355587, 961248183, 16759605, 590769780, 713999165, 844686638, 560919609, 955981811, 826128466, 31136076, 763754777, 973511878, 314183718, 297409165, 434118760, 974092364, 834781362, 183120393, 733824595, 665460098, 80130820, 616392854, 611382187, 940138038, 826243756, 275228295, 665025095, 84795116, 142488551, 768655555, 619278626, 376307873, 770001805, 258571358, 967199493, 477627567, 604871755, 770956248, 346331922, 991286173, 514976182, 830629451, 956044352, 248850561, 440387509, 482276865, 602783791, 533059261, 221837307, 243283294, 798792589, 220381983, 305796150, 659097514, 857179223, 160169776, 562384655, 524380909, 29593579, 192403950, 458152320, 710712925, 544206001, 2189089, 843515265, 931146764, 468134614, 420807519, 854981143, 37322675, 601121046, 450634292, 621607298, 164396962, 662130050, 918427797, 767222412, 93498564, 286046994, 960351024, 445349969, 472744730, 567226357, 926401017, 130218543, 252744011, 142674459, 441669541, 22203417, 415433244, 807555956, 569271461, 319221987, 954967958, 749377940, 35584261, 31350250, 159355915, 388002186, 199182605, 724492140, 42898601, 377948317, 839718206, 780466903, 551324929, 378592251, 510179683, 141872831, 696800866, 637044321, 138831305, 724838741, 50681291, 641321803, 668999329, 83888322, 730985912, 402647325, 343110130, 187938311, 645739752, 642275207, 551049599, 36141837, 32033551, 131636805, 342801278, 192051462, 204043333, 302454997, 468686439, 421545508, 221590818, 975016376, 700155211, 15183851, 847118995, 673173803, 282824164, 973115914, 443666189, 987340313, 533526077, 125472168, 694143633, 161173970, 426497860, 715045458, 875176998, 218430033, 326657225, 644865309, 23933391, 167071016, 398223623, 449389961, 725517176, 128904936, 241319892, 49696880, 605030102, 32042374, 124249240, 692645923, 853223384, 162263594, 940540236, 909835584, 945664999, 46034178, 446675554, 514360176, 261262499, 165505131, 995566070, 836768339, 203852759, 324415270, 310159539, 694458590, 154373895, 212255971, 336434345, 303908698, 399332118, 135701511, 701081927, 428262038, 416121134, 2218658, 603925156, 122414996, 872572839, 713113718, 187728101, 163765542, 753641172, 885075064, 927388705, 288985921, 848642816, 443951843, 729206188, 882945987, 652814722, 976909454, 923538500, 695773511, 718966519, 954757456, 446476119, 760573933, 970398455, 941429085, 410347056, 364893492, 447306283, 179404217, 864039695, 519300250, 451583160, 760150404, 252545589, 427959888, 903556055, 5060832, 758978429, 13078736, 894393961, 886413421, 624665766, 529331765, 145441798, 423309500, 5701368, 494734368, 381487959, 926821008, 166128837, 157119093, 650945805, 262320858, 720653639, 13919612, 193906056, 141383686, 812764885, 134504427, 153452702, 779744098, 803848399, 371249709, 468612421, 909276166, 764916539, 460693708, 435203406, 969071140, 18112654, 576341769, 611312664, 721846682, 684390252, 993611079, 166118612, 690657594, 622002333, 100754341, 990659253, 25186307, 838338647, 262217242, 874525662, 366571802, 82199410, 268389854, 701461894, 124803758, 619268577, 695615062, 973053757, 984550390, 300512020, 792906532, 725021225, 213221716, 865494131, 164528207, 626659692, 710289451, 412492345, 799777047, 845554355, 383097634, 460923821, 78219324, 816697679, 442330272, 468101124, 719353050, 446670631, 661555455, 17933926, 490089616, 935480244, 92820514, 467853163, 317070516, 562951588, 777125215, 601329505, 466104218, 333510011, 891970822, 175348915, 48044660, 904657631, 830131672, 616396728, 650764363, 652412519, 501147544, 484521989, 619607066, 874257758, 14142788, 258778420, 134421995, 684650543, 995525689, 675726598, 699149849, 562090912, 256886552, 993136461, 209995554, 187900142, 359667358, 469366773, 928610905, 776757799, 880269748, 358732575, 793762438, 672760617, 346914643, 249295820, 698077454, 315429962, 194822823, 270560, 32065196, 193479561, 732149753, 968817337, 761883097, 830753, 946073030, 730397015, 831964041, 354793996, 959087495, 236418845, 568660035, 76201685, 564918274, 386928675, 349150986, 116505627, 457554331, 692203413, 291365098, 22519046, 15472805, 223507623, 100146284, 300694563, 829247071, 672021530, 945078586, 234683603, 26442681, 57268515, 492648311, 267817732, 762499214, 307340057, 266286106, 22789079, 105564697, 628267543, 380802673, 840694527, 383421605, 789351305, 742661675, 63982133, 250232067, 677301124, 963376201, 629571313, 581368651, 540139265, 315352492, 995731916, 652243234, 85860182, 911952530, 617270275, 457447134, 971435619, 375843644, 666288526, 121460229, 600592140, 143952232, 898468791, 923614341, 901705394, 220682387, 25238581, 652077558, 893364186, 721335697, 832488786, 299929164, 7048817, 808122349, 493831213, 770353336, 609455737, 81316157, 47707244, 201351344, 389040217, 317102773, 681938890, 173342253, 34405110, 648830192, 981323980, 515698953, 6372545, 665048853, 617199746, 478730093, 355610841, 298273073, 741419122, 709908993, 571790679, 355661072, 924843415, 586160294, 53228001, 147647409, 494488994, 31549834, 550954735, 264318373, 536313245, 401322785, 508119563, 615122054, 214915475, 531666473, 566996142, 515377467, 916359065, 522304736, 787386686, 909564698, 228765854, 116695588, 478852948, 473005300, 481356062, 348717616, 984063960, 14317413, 286773810, 366615, 19707164, 688542535, 321262801, 591153012, 918875252, 223927970, 59190891, 746177690, 527915232, 96171570, 590439468, 936420473, 520674289, 131791792, 899601970, 395891923, 654404096, 789444026, 604373936, 543551305, 844121449, 921104358, 731741792, 17253410, 999882469, 450934822, 239207533, 674360674, 563015352, 841757334, 189041483, 953373394, 722807309, 652680376, 496732536, 784995206, 137132942, 407272146, 831711854, 310245725, 732028082, 166962027, 125070710, 561094953, 728309579, 907767201, 151323696, 638055342, 129840896, 503873311, 414105261, 84435840, 331336178, 84108599, 304682092, 139621389, 468742216, 450355345, 842946636, 79244312, 94293806, 825039370, 804822231, 621202289, 198367794, 883859363, 572222452, 842336546, 761156656, 652938617, 527694132, 224785750, 970398563, 938226703, 326090918, 741104246, 174270617, 14628012, 163615293, 258692877, 813007055, 236982895, 206444232, 125737839, 145214723, 148140948, 567708674, 559262431, 598938337, 176656210, 346089052, 38517754, 246935917, 996714514, 716373486, 373631941, 109296952, 277380732, 9867536, 573803764, 994084059, 996296344, 444276926, 808475779, 613073958, 650153119, 380426480, 674645832, 641407710, 599796556, 579061117, 618187912, 921512391, 978205515, 765527425, 450412050, 918965883, 683879666, 91092704, 2060337, 973165258, 260370625, 970268658, 607779034, 921604218, 354228084, 255790563, 600977888, 543505576, 162761113, 659621584, 862427805, 48395682, 659608724, 515051598, 321131197, 795616390, 412024338, 182602409, 113725272, 577317006, 806389805, 706419690, 768788117, 716617876, 555245957, 626962554, 609898936, 585042482, 572481961, 662775524, 26152675, 775583272, 284551047, 805608448, 46601761, 435877133, 642608809, 225014936, 947351526, 674191420, 94210197, 661630841, 501895977, 589819651, 56061857, 591920205, 306335498, 235720179, 187996397, 109076676, 212258037, 18806379, 704921619, 29065513, 312245014, 460852442, 113347196, 348777197, 296894075, 954047397, 166816684, 976451957, 786001657, 382433029, 103159197, 999300705, 600062232, 767324743, 852658857, 27955141, 946093509, 571307419, 478419613, 69422873, 32791318, 504900661, 631976273, 458459298, 556288675, 830436046, 409469613, 633680916, 694853189, 234377872, 831941578, 307692878, 93417879, 437991293, 738566875, 29071738, 967752955, 345228424, 799466808, 486908939, 247079283, 332321175, 359442027, 818467117, 782532663, 985861204, 950448050, 942953796, 870979853, 168593535, 873019271, 943022554, 843553954, 450166857, 387015546, 563474530, 753992524, 496994008, 973012857, 330964207, 216826113, 808514236, 160913572, 563985531, 484514245, 181387609, 126392208, 658680021, 220474408, 247048587, 404744375, 125869550, 794243357, 330379701, 789365091, 937270256, 488452043, 178860235, 112572671, 770123010, 689369859, 494579646, 934655351, 654444005, 299942220, 354339838, 864670265, 869616167, 288397811, 879076025, 958726295, 920247464, 438009021, 377635852, 457329646, 180891798, 551936712, 754547525, 38700280, 424439215, 64218147, 773993782, 122170188, 156293912, 112753837, 108442117, 191980910, 124773611, 322228571, 417582531, 148906922, 593528441, 504597850, 442460132, 321169789, 10186217, 498967481, 132185195, 869232253, 55220946, 343517944, 100150656, 874898699, 818718240, 492391063, 937478415, 797735750, 981531107, 360110763, 997496965, 164700734, 437422135, 435714044, 555713332, 423260531, 523466755, 296687039, 901003093, 585359029, 996656965, 963849710, 185492948, 151472620, 858181987, 230733479, 593391210, 686680786, 592667522, 125666884, 530561946, 378864710, 725252877, 557674108, 467491194, 630581906, 685866809, 971681825, 703236088, 38175141, 13354206, 879630360, 500469866, 662703637, 6505129, 160694368, 707358224, 476605899, 274298675, 42032014, 968437477, 427251980, 369246364, 97233556, 509739248, 281690967, 535537297, 137596508, 756828402, 785510168, 489688367, 290147236, 616328296, 261951265, 29550469, 17164306, 294223944, 421680359, 482058167, 248984997, 515860609, 749347651, 863347129, 524198958, 284379674, 270125988, 315262257, 30308059, 335552859, 348041033, 147266523, 370007756, 922331939, 359728108, 829072467, 700259779, 472753930, 647117325, 597886929, 631911847, 751884093, 211146129, 246130219, 280370701, 220406260, 23599735, 688389490, 54601535, 869184516, 123853969, 891353789, 729129868, 455114276, 331417358, 107235494, 616292797, 202567167, 722053683, 17026864, 921951687, 379550553, 652214052, 784716637, 865145873, 555924123, 99729399, 547450891, 141630236, 265366331, 913621332, 740596852, 802453918, 293227861, 777061220, 275644209, 53013662, 659243083, 370686554, 550178825, 674325902, 746585199, 891043801, 229634964, 718833785, 531554473, 562018886, 650003074, 389516143, 723981737, 306577384, 797138857, 843159529, 60495958, 276007533, 274747970, 934860618, 297264474, 148423922, 410503489, 409776418, 288385786, 735392563, 847514490, 561809620, 795834628, 858394720, 540503720, 801566515, 420477314, 58582833, 384586716, 722603957, 990693488, 181655902, 608918611, 628265379, 741717925, 275043332, 915487751, 750538532, 446629638, 311708560, 903285376, 499891289, 376591808, 395533892, 49006501, 600765095, 427077902, 741301863, 332126846, 7895827, 894881512, 614524168, 15353313, 912826176, 568593747, 42297770, 644000572, 391335302, 880313573, 790265985, 533221853, 388419280, 744998837, 376307201, 343379415, 563973690, 235881475, 160385904, 799045291, 583921334, 717081597, 267094819, 996746242, 748753038, 38913665, 904533540, 905791671, 679199170, 543778983, 614208087, 553788239, 905011652, 525286002, 19772510, 441615032, 894373481, 951361320, 897959878, 344113971, 623528071, 469835084, 446104348, 543630107, 884827011, 829092398, 822504001, 782524695, 661238212, 906555986, 695220599, 402525621, 605874754, 833459458, 858710397, 628579473, 62693522, 574975796, 663299575, 900923391, 424744909, 517809985, 972417857, 161187141, 42458426, 168473300, 842844706, 799715602, 70935144, 373215513, 277453353, 846343474, 75503954, 613618491, 34807420, 713323123, 149515617, 26598624, 840877756, 626474967, 125714371, 515929801, 202908734, 314326717, 465234945, 295602001, 431272976, 93391274, 424645419, 455274020, 739989340, 516717877, 787740422, 475999874, 382872511, 464735890, 926129047, 355207206, 369760677, 558002190, 262163298, 430086295, 203554272, 520983080, 306518520, 726329248, 99640741, 285492629, 349943304, 775752325, 992866188, 97207011, 57299242, 998598988, 635711271, 763416184, 44656149, 163390108, 797855174, 695305361, 560243809, 179157315, 900190017, 953845994, 744799255, 649814180, 858592642, 249476167, 960317777, 349253487, 853003288, 243172703, 70458743, 807023161, 275930756, 368443496, 373115789, 407970033, 913083795, 789317019, 286122178, 441322471, 326415897, 405486483, 203995852, 600903593, 77100505, 786147360, 459903034, 474584720, 249084960, 3804547, 647981135, 74503689, 892895756, 749760613, 595012395, 256318116, 499032197, 968098591, 770320295, 760007083, 26849484, 770409054, 788684182, 880440369, 280706893, 461016767, 564237910, 973392124, 385659270, 652583441, 633931532, 189626842, 35337614, 608785619, 860278743, 30178449, 160783387, 603302242, 263556644, 568107144, 376562178, 964303469, 843004581, 77276115, 41244275, 929694283, 768122525, 402469877, 100600554, 951630171, 749427392, 977723268, 961905471, 125181640, 683234812, 876978079, 319051103, 314216376, 765210395, 99409402, 977335358, 228643244, 334470828, 881027766, 973854217, 518503526, 56526401, 376315483, 332477269, 590949227, 953996370, 728062481, 84764756, 336207609, 802005322, 605535537, 209438327, 857802365, 929955439, 478441381, 543475903, 207241610, 175088292, 130028661, 207546687, 241634137, 68260727, 355639175, 638650472, 328898557, 519092642, 37286917, 979764824, 745882537, 587966150, 697758397, 137629763, 212066470, 817832666, 639717282, 6357857, 94212857, 660052466, 171796015, 669714215, 210660829, 2044437, 869069584, 478139369, 321066807, 880154338, 834061329, 759616479, 23548247, 5172068, 599614816, 869266597, 269394785, 173262487, 334417599, 977517366, 630838251, 5192410, 793264665, 195534386, 567101510, 425764506, 728736936, 305960951, 796725237, 113248809, 649262628, 658287778, 135328977, 322625805, 552922573, 615922778, 923744383, 778221586, 725033066, 521285726, 884105989, 161535762, 753093267, 10312256, 426179691, 394872112, 259252858, 132563719, 146785274, 538561016, 135912688, 166948319, 872183439, 377116162, 637038155, 722504267, 421955892, 54261878, 374690273, 721221665, 848806401, 542707589, 27636530, 439232121, 54998719, 762110098, 131228296, 74606423, 722656332, 394330531, 35968402, 756010928, 797987807, 937013339, 732045205, 627435054, 968848943, 262942701, 866797727, 231936715, 115142366, 485794677, 341469061, 926416479, 626966140, 372881042, 108259309, 820940027, 599236400, 518091081, 355753007, 669431518, 71225844, 448389289, 183560522, 112806999, 914329366, 114699008, 848940086, 761392156, 360583348, 303794666, 15735626, 913144113, 847340076, 643982419, 350417398, 614673409, 702316442, 633023007, 264069491, 488132171, 101981640, 614999199, 998504717, 697650534, 32951143, 815591968, 983040712, 487424124, 827379026, 974278602, 347211296, 241092780, 66276998, 635873871, 718247728, 838659880, 117371352, 150349874, 22729099, 999265435, 961592630, 141434750, 959745671, 913412261, 725444217, 725871614, 970988777, 357966697, 413996919, 933504419, 535578924, 702360068, 775608700, 798756577, 932210019, 631181645, 42123917, 580341945, 459090480, 545096447, 500471616, 742301239, 500676739, 918250701, 861937408, 8280869, 639926834, 656185952, 561163726, 736323876, 507277165, 651666706, 281074016, 437181713, 948189449, 629982350, 186579761, 182453591, 772837696, 21585112, 18662620, 85708314, 863213229, 942777407, 289582393, 275613653, 73153973, 199050554, 778575806, 100848257, 299267636, 138664184, 58380279, 156407473, 811008534, 738864498, 565535313, 847979462, 243990363, 462176763, 47470630, 714911269, 518052990, 739199340, 811462171, 892763361, 926994665, 830055654, 749458370, 384326141, 167063871, 486970881, 528990087, 582449234, 720493175, 69040626, 199769815, 376541564, 570737090, 709910928, 781655745, 129254432, 435152478, 879133647, 748862042, 292922549, 754049270, 374622468, 937140144, 641874572, 540582450, 106467705, 464423930, 144197909, 619269359, 272323162, 65440667, 630113736, 877130843, 100224033, 472705006, 574935651, 441585831, 673440368, 720406916, 86182358, 707790620, 973604957, 871929702, 687504409, 277667190, 248413966, 81196684, 20036225, 435832959, 235781349, 319143872, 712403026, 182482729, 178597127, 917657598, 798732108, 930724816, 675858490, 285556424, 16284690, 860555597, 266862304, 855365897, 519634996, 227539515, 79958251, 221064119, 548463771, 162313483, 789262911, 880028850, 829245666, 960773735, 85178354, 749243297, 954810539, 983111419, 885457784, 323032775, 380164502, 546223482, 405159918, 696325217, 922387410, 279357074, 67387491, 126580273, 240803894, 638710421, 59490484, 283585228, 838799954, 241862971, 994659720, 323502749, 699300057, 366918356, 494727339, 1024681, 388277619, 747484210, 83616577, 769593534, 907067909, 62760932, 543825333, 880901277, 563001392, 100460915, 414154226, 282745336, 565682060, 635321750, 118299597, 597759801, 19889596, 43042958, 252100829, 311404069, 372771824, 758661218, 485544760, 663996948, 362440128, 444026297, 136780373, 376442843, 687414262, 664594787, 680420599, 117875129, 392569481, 332488239, 757949615, 681925457, 905492653, 280609200, 344219740, 157434544, 391064327, 418611297, 15755941, 822219247, 549602928, 641015850, 693095160, 257923416, 907260118, 523343607, 658059729, 350444051, 845394114, 69644221, 919554829, 538461120, 784523405, 993460647, 643365807, 619933079, 904180143, 792262657, 763969016, 445235545, 172714017, 203987133, 835494425, 6943654, 418420601, 516283366, 286437902, 775230428, 429955581, 359414909, 604317007, 44971019, 203911818, 463184002, 681839771, 243684114, 927102705, 268090772, 882401972, 477165818, 162004921, 401340496, 937816774, 244556256, 27431235, 752251367, 240273721, 71801001, 622439643, 895958220, 547884921, 692117173, 655351950, 382446893, 713967805, 956142661, 12597096, 726864219, 152098110, 649297589, 477932358, 366418538, 364509162, 454629907, 638384414, 705524845, 265642660, 291184178, 384856795, 398303390, 597833102, 640466525, 231011273, 838529434, 35418702, 844765019, 72763678, 422894784, 903584718, 427507133, 347922855, 656495467, 766618509, 361805703, 475545353, 488531214, 599609589, 305472999, 297064377, 593161933, 733619287, 167749290, 656300912, 527812076, 729427239, 651175038, 856840668, 886077269, 596789076, 602186572, 353774743, 175596176, 32898709, 550250194, 163051871, 548082146, 975803247, 704015217, 763413709, 476166265, 361463272, 935941909, 782410867, 164197608, 415075040, 746644402, 912222943, 884033559, 335395033, 129817968, 883803328, 261814408, 181745608, 173942592, 794380828, 958514213, 472041161, 533027824, 610650000, 80838522, 107805476, 513203870, 197600551, 838247769, 214463082, 330068127, 178707351, 875667251, 676601934, 539638424, 405589312, 579013248, 336277012, 890338651, 334536953, 759052267, 241601832, 133324125, 84521621, 586378603, 245442140, 820529434, 589738323, 666336143, 659548438, 549182076, 702940427, 906532988, 877542615, 336775413, 139824534, 774367420, 743734441, 643112670, 378428506, 911484539, 257865298, 28523855, 90563137, 732487786, 812154152, 885681848, 277288064, 735080496, 819510677, 599552368, 565844761, 197516557, 964974571, 206761206, 254786802, 111656708, 688082166, 127106272, 520682500, 10998749, 922304211, 318772816, 891103200, 7250144, 316276777, 953357416, 731365014, 115373675, 888961496, 269780044, 62009377, 54525210, 423956543, 764845318, 377753156, 709944970, 757549368, 371389093, 112542248, 802309757, 354180689, 910308264, 898861658, 104164436, 332310998, 879768239, 148384358, 869276119, 476857480, 423609118, 323130891, 816150689, 48948387, 586158466, 627028051, 270823037, 64202148, 130775948, 951650694, 860515850, 63724305, 567198025, 952893157, 5652813, 816611892, 772709698, 99850417, 737131893, 482048764, 718108736, 488065568, 763943650, 442413271, 405528809, 903687726, 532356596, 286199778, 359784070, 169860390, 897382605, 703431116, 560576068, 474289376, 66383975, 391618092, 819853316, 962693745, 731148239, 700566784, 113234750, 600906768, 11152377, 151966172, 997445506, 878214815, 943385219, 430025849, 534811567, 640539163, 617098204, 518944618, 574755527, 762810663, 385058712, 901167239, 859972170, 446978605, 935839343, 951326371, 716241883, 763576893, 282408570, 734330358, 852471763, 131141618, 621043402, 775298012, 609688584, 45033053, 774534917, 708269490, 398003900, 856421876, 537959975, 856394681, 512548399, 254383052, 688604107, 848932266, 844529508, 770908770, 221347721, 547104787, 814451709, 424062741, 430361380, 322808354, 629665142, 495331185, 638295734, 473054492, 3759407, 893173367, 604273846, 544750922, 262007758, 678585628, 612576231, 855981471, 904367380, 432074886, 326565578, 146318194, 129786947, 977241798, 352057925, 243776739, 183196659, 87982829, 733597206, 386320971, 995770082, 815630532, 856413075, 479942212, 291367612, 172526851, 359013372, 288363442, 41506582, 208740122, 842104349, 847089179, 312925971, 884773571, 327643864, 232034733, 609119837, 276284523, 164823052, 895983932, 130289088, 727145030, 55119274, 402362369, 61689409, 514512153, 526171655, 236329542, 99150039, 308034637, 32575637, 123102176, 770539916, 780399635, 838864777, 827309366, 238902699, 932737103, 441688292, 275118677, 220889654, 12262326, 518057800, 384044823, 945771671, 504151470, 303785273, 542678951, 161018490, 432971574, 762193646, 562971521, 707460493, 163133188, 517197231, 974382823, 648389296, 726138962, 683280263, 828474126, 537440692, 182201047, 550027420, 398410329, 639210330, 998791579, 790501947, 162938885, 344814228, 248730821, 680270246, 209266398, 978135715, 628616202, 155861357, 63346321, 573211563, 991520229, 719240673, 854074538, 44543058, 19838979, 198338550, 608332081, 617909526, 521968666, 975122232, 405806427, 850595463, 676397369, 201244222, 740138564, 34425404, 251516993, 355289598, 75929233, 395319685, 238423626, 612112850, 968175998, 994268020, 545132249, 880453590, 897492165, 541999679, 863220635, 281629870, 673757460, 248446919, 416769731, 814507328, 576033008, 139385176, 364848634, 509828150, 954731831, 19765277, 814222992, 579854984, 901438171, 691516188, 671461595, 756926586, 906590703, 882675528, 349252897, 563938360, 746242133, 960739993, 951927094, 248613442, 547359002, 951771783, 381561694, 415192127, 637439611, 754588237, 394282302, 496255210, 5698622, 994933195, 907694035, 973594873, 132972243, 484428358, 341754567, 401969810, 389891654, 692401913, 398749165, 642201226, 788787815, 693469651, 213818224, 848703806, 669865526, 817002932, 620790802, 621178361, 79921241, 292246655, 531276409, 63851981, 831544678, 31724463, 769271241, 140019214, 114444306, 270719928, 888284663, 658139657, 84674633, 910290933, 184906694, 621144015, 375356783, 250200207, 903142899, 486742375, 815664840, 924860499, 249473133, 447126146, 402262263, 158494528, 951075723, 402369309, 935739360, 302252169, 264303032, 306264765, 713195216, 909511516, 51542163, 764134472, 658880907, 91794972, 428410328, 616090065, 410124957, 853888549, 434113112, 655926463, 660971813, 61671738, 997962962, 661765829, 406879449, 440719067, 886385138, 928355130, 671344844, 285424056, 802308116, 617030581, 528752009, 55390350, 918529354, 618733972, 326398092, 28284861, 547675417, 214074341, 432170719, 390952069, 351741090, 26296748, 2673052, 694014516, 939907871, 820004542, 377476295, 871721159, 109601510, 662308225, 97020374, 883996416, 32878892, 603636652, 864672861, 543631259, 854845307, 913986810, 467607544, 270468442, 307683874, 631017134, 476188572, 946463352, 36678345, 965360754, 979835110, 257071893, 307998109, 512251967, 7396003, 477526692, 719334699, 258741376, 297284301, 190384272, 442954713, 986939577, 433662670, 637571738, 235354050, 920397333, 940004735, 925164120, 525665397, 540082402, 619069831, 693072720, 269134391, 883068466, 375159674, 235250888, 474537248, 492380181, 64810575, 960200631, 555035412, 639077177, 902359660, 228427736, 861917607, 933816759, 246992974, 117868675, 953526831, 832727574, 176791330, 94166204, 774586698, 863252000, 808846802, 210002673, 447770042, 695469409, 911321593, 160602700, 327364465, 936455648, 159184321, 288475381, 962645859, 266574850, 655494890, 535703975, 144299369, 266023458, 789976809, 503890316, 680203671, 139364015, 191721686, 136303482, 167890963, 385733298, 396973093, 715545432, 283419581, 403820989, 449881610, 508224619, 75042411, 115470705, 453024555, 84064004, 20904844, 529457355, 963783020, 703886942, 124543796, 201389325, 508971003, 89681260, 686259307, 510661876, 55966729, 98563160, 245938590, 359653537, 340866589, 29932285, 425929960, 657145626, 925923682, 202314685, 40196349, 438556220, 329178285, 336514401, 80331344, 112037042, 591593770, 723325844, 150521601, 268748844, 941604590, 685319323, 730969331, 191662397, 747874072, 584712626, 592284998, 811073002, 309901800, 487784316, 495397557, 342549, 517391480, 678012624, 700053136, 633299300, 575102495, 753113048, 490321246, 864922955, 234006069, 206424571, 166370377, 764339191, 963833550, 328197093, 527726385, 297481306, 632912262, 844063002, 489659517, 233332323, 745716264, 120465693, 64599939, 565186717, 49558498, 573250773, 551152778, 974350265, 493266784, 531183327, 706993856, 814713783, 180823112, 535218055, 158783478, 550771994, 863674501, 295922182, 812045430, 707996573, 508054161, 566243350, 191383862, 653252955, 646602194, 949034611, 694323867, 417958632, 504639167, 842839832, 880120414, 97196651, 29172659, 572560814, 362298722, 649535528, 968085477, 490451093, 486885312, 181035975, 976337549, 547139982, 337117495, 503150031, 447207361, 936428878, 451994772, 582801903, 266214091, 635636018, 790944012, 345248270, 12741962, 214919800, 53820100, 41039801, 422758675, 763194779, 438899082, 464178890, 418685789, 692307465, 109754932, 928211947, 842319900, 457713325, 407058802, 650592661, 81577063, 904111687, 107733459, 316226209, 467642459, 700214466, 359875716, 526383549, 885657892, 739879786, 533693685, 225702804, 56684377, 335648978, 834115450, 675173390, 323355127, 213027756, 342213032, 317303413, 599508382, 490635002, 214571991, 343461440, 248270546, 93225317, 840541484, 310288733, 258696141, 282684485, 301374384, 536414270, 379543679, 424287452, 891365780, 693093025, 875567783, 287458839, 808369820, 518837599, 779129224, 43555002, 464957442, 483246176, 176236615, 116493180, 677096772, 645590529, 788249982, 276112575, 591886897, 354554060, 337452726, 594553656, 353544897, 93095187, 643456065, 448008944, 668074971, 16469741, 566566119, 325510620, 887961604, 513855572, 665116931, 183537138, 354347506, 422683566, 475405138, 810563012, 332120407, 113846153, 355063817, 322886194, 89633227, 476510004, 229552630, 37330339, 89840177, 778656572, 397002822, 94849392, 485367025, 694110556, 992617187, 12224487, 238333290, 992811266, 91532536, 483736226, 180596510, 739263100, 27173345, 408703627, 125911928, 861707658, 909933249, 640871073, 718649191, 982093080, 695650104, 364255963, 587972631, 614725630, 659113614, 581891460, 167484911, 292827660, 701153967, 318799084, 655692538, 52505362, 972450197, 298359317, 968899185, 495797557, 461394395, 655070372, 38019002, 186209351, 123226904, 569655959, 839698507, 426793526, 120001674, 848351916, 405821506, 480391566, 56108455, 903297189, 761871428, 620921666, 53086403, 961706806, 697013924, 802968544, 86403102, 872084265, 396286794, 575144149, 273949336, 193530295, 496525995, 874955996, 773897489, 675185385, 721082033, 895630773, 894417600, 220925803, 427868089, 64837301, 485192178, 793988748, 449254835, 358706485, 486580399, 424217172, 635706223, 4477775, 577906432, 555689671, 435079780, 436649269, 253352805, 57146299, 911139477, 256958133, 574888866, 525536903, 530507181, 669548584, 832034351, 451992574, 846941128, 494354805, 617309410, 878072023, 369302250, 673969187, 227944978, 698974770, 564197780, 451460533, 35891183, 357138925, 894039299, 687040721, 739011001, 109340960, 204171232, 24470041, 375461076, 97196682, 689623442, 444955514, 612766067, 795003545, 219236470, 207306131, 608629542, 711786568, 692172424, 450940279, 943399972, 733098474, 108305534, 638927472, 2853788, 629484912, 631183135, 881045895, 264521970, 476875628, 315664685, 927815305, 840244324, 820409515, 220111397, 452781068, 566725857, 9046532, 77053593, 417307747, 60528746, 47980282, 969094810, 734039453, 686588444, 712645152, 579084236, 301852231, 84284376, 992391295, 173936729, 358698817, 559465136, 563989175, 839834779, 249276436, 285357626, 552524333, 55245200, 594761723, 377939522, 853274016, 630083652, 279059869, 511031468, 714894163, 906414892, 203828130, 383852761, 254628245, 606424538, 729864405, 459009821, 394219795, 914954096, 777334307, 292424255, 635270225, 400426787, 912680940, 868550215, 975694236, 225345746, 770787257, 429666221, 414083488, 976120147, 461114148, 518664708, 83378344, 321100666, 752176027, 84185176, 417829537, 616685422, 142298837, 376507489, 231831349, 256389089, 750251114, 497344155, 99737296, 785409928, 445599030, 391378411, 463709831, 943547204, 350424060, 98078702, 648220229, 977739439, 410295980, 21905264, 270807761, 155101687, 486650107, 414508567, 682891156, 491444743, 450438301, 396565874, 469387518, 942364311, 135027469, 297085866, 426610199, 4997814, 387654759, 386297650, 868341221, 97460259, 924991977, 443923791, 475943090, 437277219, 835412428, 180220632, 602503582, 679935369, 737289131, 581301413, 893319970, 990060056, 528583181, 283520577, 227653409, 788528774, 914711846, 534984893, 305561072, 258743325, 208881225, 763111794, 837963897, 795400588, 912682564, 711440561, 579732930, 738611475, 158395684, 188367775, 339899200, 271377262, 292146360, 710453664, 427125480, 24925201, 923055269, 520910261, 297253032, 769302660, 27265467, 357231129, 307238005, 515072349, 458156592, 339329086, 867209461, 507438067, 286882719, 512847335, 584614770, 51757485, 803903573, 153341653, 795780297, 384747884, 366442700, 686951938, 624505316, 936611077, 285544303, 483214906, 600606463, 891373053, 958598456, 305785506, 773577830, 14563262, 111792130, 655999038, 451356757, 491839318, 592122939, 699094223, 333286970, 651477571, 681952502, 435889236, 570648901, 921546237, 430392845, 686303269, 881101750, 977404297, 107414835, 864528906, 775178265, 692808137, 6729171, 916698534, 323378979, 124995529, 47455253, 265320042, 647731329, 782944569, 415726785, 598981059, 952068364, 45645819, 300773919, 445493956, 311457993, 352758057, 648111110, 955593906, 722863280, 360562123, 39504466, 69827274, 628550576, 282895426, 753905090, 566140057, 331269055, 122772696, 756422518, 129123994, 242031048, 793216161, 80180942, 47557061, 879173845, 711187195, 208458674, 998156779, 560146678, 502187485, 636399733, 557657361, 430011865, 844270555, 119557967, 480599326, 754138367, 132542186, 561072095, 583659347, 356367004, 901689683, 235139568, 805532957, 369317902, 315674688, 539263987, 552598102, 727227132, 681758860, 268387118, 740922567, 29655649, 447875151, 523405226, 426879137, 629213569, 225404966, 973957145, 3131649, 424747468, 792110986, 776632439, 158725263, 632443299, 321052689, 172977442, 383928916, 597021478, 605674309, 842521879, 109270910, 237990125, 283103895, 51478354, 516567175, 675950121, 474644165, 110706931, 101161479, 814855041, 328136184, 953984427, 460678248, 821486824, 521578752, 20893078, 842445597, 233110662, 536073882, 6070899, 491169338, 541791987, 953268955, 403568703, 166272985, 995507144, 245669355, 131836584, 143237404, 914783361, 428490420, 359013388, 763076357, 934794404, 851894616, 400615478, 575199947, 252570298, 143840147, 998842679, 129003058, 802300757, 953665068, 490687576, 30981485, 400652107, 320686927, 206088528, 135699127, 535210934, 789090753, 192722360, 123819993, 745904578, 950065808, 216337554, 863177543, 287556830, 179610429, 339373019, 900506148, 575211468, 906496551, 469928213, 912749664, 274044086, 222048557, 933476943, 121795040, 892948567, 306476338, 542454291, 165673214, 292313701, 618990545, 518742811, 780617024, 475490939, 388777352, 29664402, 211933264, 113782837, 86598788, 956608325, 769782407, 742819970, 413804262, 258996019, 655892344, 50889250, 423199319, 885818710, 469473075, 57288920, 464987397, 220016741, 429883616, 895420125, 791719362, 336119839, 953363924, 324661290, 961383344, 29302452, 316003978, 14502851, 691389979, 552753299, 255318302, 742906325, 13188593, 239626465, 500563830, 154979491, 622228645, 88528475, 883732367, 102230432, 371225343, 437314221, 322777771, 310265925, 575705030, 425779276, 37407570, 320350349, 675592983, 120139100, 336073721, 967362227, 479389477, 373576464, 214528105, 684809621, 73117252, 401728246, 628585838, 429562946, 691400077, 239461651, 33079510, 416929522, 307990346, 148355062, 385836862, 21993270, 323707395, 54230867, 412596911, 372979886, 43546425, 436452551, 598217416, 824073001, 771656973, 165006636, 197586302, 667042834, 334057196, 54960185, 985573913, 352255773, 366381544, 828736491, 315964124, 731340225, 597816192, 54173456, 307242489, 981869607, 529477538, 333543779, 678681776, 431986446, 957594935, 274522642, 715105238, 28794427, 65138256, 690066824, 453782254, 136173311, 804749072, 454073130, 118473747, 46643202, 224010865, 500031641, 698378436, 895636803, 715504516, 862777219, 270643697, 592770910, 528177380, 766582830, 701729619, 968109788, 682287803, 853035954, 840258912, 144811203, 150456104, 882087137, 768645428, 514332188, 235985524, 216547968, 866450876, 613073758, 405670890, 642175890, 675622064, 112551797, 764218449, 773474216, 106901256, 688242996, 651886495, 163678301, 202741736, 104273190, 553399159, 239455240, 677757781, 836169968, 899580888, 534633893, 455484195, 984037262, 860915549, 776324347, 314179479, 729847769, 895319746, 388116565, 607396109, 706585658, 210933250, 721296475, 938988935, 675925150, 27411417, 400129426, 175543931, 565538225, 411349380, 729076358, 205395768, 970043045, 216538015, 874914611, 159232198, 637960750, 92343346, 6125275, 339556520, 867185775, 903669597, 240849465, 378518641, 716811641, 137140376, 500286929, 116509627, 102396404, 953789441, 478043492, 349468572, 827078719, 650132045, 548386065, 249657928, 784289350, 883176065, 875473866, 511087971, 992808904, 902602910, 348186688, 489586165, 122216078, 217022904, 146886775, 535364013, 71667259, 936965629, 708139634, 773297905, 633253408, 597442270, 425404862, 737423214, 384278300, 487473963, 899086993, 982531550, 592740256, 737262357, 781015909, 290271428, 828133234, 211626672, 534344250, 306805002, 202048988, 567932300, 516249494, 460312738, 757281124, 588771802, 251938826, 496167204, 618220052, 433565981, 340154910, 75232983, 758184412, 495618854, 369834492, 627827911, 376876642, 593123918, 474041096, 401725121, 275413500, 451563092, 902170997, 240339154, 616834680, 443588292, 799057588, 536191819, 34009148, 613775575, 746886681, 722240601, 37772184, 765972055, 663959844, 696896982, 61379729, 276675257, 88233785, 292402912, 257465946, 239862616, 440377402, 63715394, 52404902, 294408353, 215618341, 183054356, 106784806, 837400649, 419876786, 99286146, 142745404, 382490913, 139390062, 354892006, 70651506, 246121556, 737308093, 239813908, 711253785, 666311777, 560776350, 212928408, 866454660, 696044611, 2386397, 823465128, 406493874, 737551456, 616100517, 27470896, 348397400, 328766985, 184823742, 93775102, 821164234, 942485202, 811473457, 244526795, 385315166, 172633639, 676495075, 688818973, 388784085, 461061939, 938448529, 655258841, 174208457, 436332946, 657400240, 54981356, 404583854, 412748284, 663464818, 732871469, 736298901, 219193599, 46259103, 289557552, 344594570, 404578656, 647824033, 790049869, 463404340, 764765397, 674085352, 105217376, 855703786, 11855461, 923245036, 644644321, 410518287, 621845606, 340544974, 95062463, 52787153, 780594757, 712241366, 427619624, 893032986, 682149446, 503870964, 406004068, 294550100, 934346071, 296310678, 362825530, 802791621, 418533905, 178001762, 913224370, 922326605, 175378482, 262134665, 682530977, 207979752, 996973816, 472767408, 998976339, 16861024, 987024620, 673834692, 399439172, 596692085, 652521442, 949657179, 33973541, 251392289, 188212130, 667242453, 421549362, 382898279, 569733545, 727561473, 397487683, 762806463, 711435264, 753501845, 746076791, 69601812, 510257390, 514519719, 180051536, 317091452, 213608677, 319291496, 181898947, 459640392, 1260826, 570243308, 670106523, 610077765, 361557740, 493450938, 809397559, 207329482, 502743920, 329817438, 211796127, 864415077, 850825798, 575765688, 225054518, 57236854, 444015186, 318381382, 318163333, 22866781, 58976866, 165719121, 371582920, 748308460, 272761519, 399649738, 338158841, 31759462, 514974992, 682757308, 801164990, 31712403, 786330217, 882478234, 343215355, 847390703, 106478433, 696097831, 137781359, 215306131, 536035612, 70301654, 28418496, 98422251, 177477857, 763525829, 724399276, 524161107, 945439952, 718285180, 904590532, 367484346, 178862069, 210981193, 133272729, 782829828, 779975948, 214082941, 905906800, 196735092, 97629186, 401998992, 1309135, 384495691, 87164178, 381524951, 747908229, 258613503, 857775094, 511528684, 529155034, 3892900, 236892050, 442061365, 734521449, 78687372, 354125273, 526388541, 41692542, 984642719, 774581516, 494317064, 547350126, 19123710, 28668667, 919392617, 415768241, 795092014, 221859952, 318476194, 767763050, 383711792, 248053793, 767953111, 678776616, 444295899, 238604791, 426653852, 635305334, 786463072, 969406340, 892890754, 419254193, 142386276, 742571975, 788142112, 144421321, 512684191, 292666379, 301968560, 470532311, 278627357, 807983453, 475754364, 632766953, 647670689, 4491528, 656977701, 47496963, 255040743, 977271273, 111199846, 677455132, 442130607, 139437520, 424242510, 181046351, 728666858, 122133193, 910629415, 183141283, 279640298, 608172145, 841857944, 686973783, 88067233, 519167458, 910920633, 57897382, 140788536, 382010048, 853053477, 929943141, 80619984, 553643205, 383716227, 897167410, 92838210, 89523673, 858121327, 806189957, 581510164, 918692397, 727764920, 141192989, 103057354, 416615187, 181052914, 386754223, 117283255, 116744352, 107876835, 142217033, 841565775, 693752787, 551172192, 338495693, 185057378, 720011062, 693028111, 813814167, 581516104, 838672758, 664026559, 361226798, 836210323, 149544411, 634203948, 903143800, 701236869, 874021604, 652868437, 419964383, 450438185, 306189946, 465132877, 256845149, 185496894, 247655037, 648621801, 785943410, 110058370, 607686725, 302930475, 242951700, 648814829, 466775753, 172626561, 522230370, 823959636, 669065160, 776533785, 610247571, 155600806, 610874345, 874257109, 490741397, 819928806, 294609210, 339870442, 712324637, 305617798, 298968660, 781174243, 478103255, 948648115, 666365048, 179723839, 979665869, 256856553, 162606996, 48696894, 321788711, 432609218, 727176980, 675769685, 764931003, 943587527, 159659281, 6454602, 51230891, 535837892, 762613317, 66616438, 459459743, 147258921, 80120588, 971179724, 990614681, 933426694, 169378120, 940226552, 171662375, 49009516, 667032069, 141368688, 211686499, 32338413, 715784474, 299696283, 164933582, 93188307, 577469153, 103301458, 664955202, 51871111, 933823576, 119570170, 730086066, 157270753, 518089592, 228469577, 677154030, 865893788, 418393504, 879193400, 609921150, 775778897, 70396072, 213992875, 670280246, 932929790, 867339999, 503231391, 723483926, 165778155, 885655461, 356115307, 711207330, 587949339, 107402201, 909424595, 621838503, 997099283, 806773023, 289567862, 773249799, 909858779, 945189338, 559637767, 28583803, 783455910, 939817811, 762386439, 986390722, 733684702, 83043709, 877762503, 767189930, 511853626, 206911864, 443358833, 310138825, 456865381, 358404987, 245365537, 857941315, 572549750, 377633627, 603974410, 179880331, 795842328, 389034700, 470890310, 897879736, 867420234, 179354450, 500695422, 919361384, 99066697, 783558979, 295688465, 50731484, 958099435, 603766474, 142873585, 561093144, 10847208, 24423881, 467551725, 866590130, 697376306, 157560541, 419727876, 599885327, 733899739, 820557908, 260973644, 492330736, 859575691, 153551715, 672540411, 905551537, 616352711, 44419232, 659751428, 386978154, 187257512, 817121937, 781910388, 321646635, 285721287, 524715662, 40607574, 511738450, 212605281, 527291341, 753557294, 417986221, 684551848, 572470467, 629213296, 392737450, 912038352, 78662453, 59768261, 452888036, 71881063, 235813254, 532081040, 303672179, 527081417, 566635268, 746077098, 411337006, 663455731, 234637655, 779011486, 647559656, 736685740, 307997276, 449164027, 876323182, 631850864, 211076751, 153459373, 727685260, 307532588, 127690912, 617386044, 109688540, 537460267, 266102822, 533340937, 171820835, 490430214, 391764478, 415224691, 335340431, 671662228, 346779629, 574377111, 291803367, 453652095, 714827064, 492617163, 500061606, 304313558, 140499516, 577419863, 31043163, 206933980, 828573784, 91846181, 983826216, 584191473, 803202312, 322601827, 167424048, 2096042, 667603483, 142146891, 328858242, 930779362, 304680931, 646749882, 637496618, 311705001, 244842714, 166433418, 894084424, 802708097, 590216807, 529963479, 232937427, 146764839, 860838922, 510905658, 874995555, 777591464, 356987957, 544699671, 403058554, 749148375, 227495545, 637849595, 896792696, 34423927, 227535910, 634224327, 982475882, 936318119, 626781025, 869759675, 303679757, 439774921, 88618577, 657113042, 238500436, 458566512, 172026435, 179615605, 617215193, 817952791, 310221542, 701897958, 386945664, 582446504, 544587236, 865957872, 693523376, 923629577, 749660376, 516430742, 110952710, 644496080, 44033681, 524499247, 228851361, 564774126, 410492701, 227772752, 280532345, 466869511, 701791839, 732060456, 427291437, 907642905, 239593063, 890225918, 65181351, 44790496, 498194442, 350420866, 565654900, 849339592, 115159004, 717812548, 849377671, 252442328, 682376521, 382530524, 62265902, 349581205, 242212392, 240025836, 620622866, 13011704, 673341543, 817784290, 99075486, 642668028, 813621723, 61884683, 613222565, 79836216, 860177088, 146641573, 484890808, 999595687, 907801570, 288948229, 206156742, 617044769, 950855812, 467721976, 764845221, 559345475, 350859832, 110492303, 292925234, 916811388, 970394913, 362409869, 703445858, 682368394, 254501015, 523796438, 326124648, 139073736, 440772350, 819098536, 656758845, 59740017, 59847804, 586103165, 190070548, 202460049, 422646247, 249542629, 689077318, 176916304, 773005945, 503739032, 211756959, 728282725, 903439614, 607993261, 996750646, 772747365, 318535162, 492718728, 821535469, 617315545, 970611660, 703314809, 278777079, 297654956, 405565379, 625892970, 517268242, 689253698, 954378328, 15500598, 534655258, 725198877, 317564931, 879592133, 395446070, 971703996, 145360328, 197639188, 95623455, 837029629, 197663461, 855103374, 850479560, 793249129, 912762378, 364650022, 174891476, 601233451, 262147166, 744097767, 138596866, 464278862, 863368134, 763382991, 926945942, 287059201, 38515433, 156211935, 299091210, 155618237, 961465663, 86877695, 101401229, 684628237, 960689870, 555511931, 224811864, 235119294, 394484931, 424030543, 486238472, 776983866, 487879294, 755999894, 358292525, 651724387, 586863005, 974925485, 328509708, 445730880, 575704914, 458864055, 819880377, 621208158, 770241378, 225739453, 929544022, 856074862, 255756381, 236576569, 347205385, 939852378, 719992411, 750365886, 656326352, 523852223, 739762587, 854833590, 231386604, 190599098, 100946815, 647535549, 783710939, 822113161, 963658082, 686559963, 544274683, 379595556, 331318565, 298261636, 419844821, 632229373, 186353687, 61969555, 35700984, 709192372, 443645976, 212005854, 435666616, 71371467, 597090820, 599043761, 365701165, 76614725, 529624623, 875546428, 633204518, 463785493, 235100547, 913535437, 121157369, 326249435, 457378619, 392009333, 881405508, 512033222, 541573674, 411389172, 111033103, 568033648, 135546543, 753494875, 362346880, 631372537, 383990903, 245792664, 556673021, 922450312, 792117178, 790231865, 493114913, 31718604, 85651179, 268759748, 239648044, 593030616, 830298563, 244754426, 631109101, 397216063, 64896776, 48760959, 239550911, 643525498, 47292571, 930386446, 656640743, 354112885, 99828003, 507327249, 831865333, 635655477, 585960508, 869365432, 15849435, 90255234, 399888327, 568108342, 549770633, 883937874, 478770524, 876586561, 213237848, 334869304, 525773424, 255227041, 375049744, 671586028, 100362885, 185916136, 994476550, 339595626, 700899131, 859804284, 524343004, 822349663, 759213601, 756901794, 111607908, 180801163, 355165655, 750314930, 557828276, 797896272, 369808155, 799170337, 902912131, 507294577, 279242753, 217696097, 439048676, 210351560, 640993739, 108409280, 884751268, 259241787, 497082039, 847427574, 488622848, 799326223, 774746729, 286907382, 839194872, 893523556, 68558333, 268040503, 345398771, 661143812, 481983019, 397598357, 14851905, 355984460, 777245739, 921121591, 577985740, 974383236, 881441670, 152720249, 708083188, 309248100, 313666447, 440322367, 465889527, 775512782, 169075792, 876180540, 820320285, 865008556, 924929810, 772013783, 649715678, 751577405, 155944303, 811114353, 320459190, 859098203, 267342918, 507370346, 419189773, 613287463, 501035965, 505344582, 530308775, 742656727, 287777102, 666375511, 347382105, 23619795, 368373197, 993802733, 826018715, 65570875, 985727416, 179391926, 599350221, 661732144, 674899949, 255738289, 134326644, 28233386, 383140068, 763428948, 523436104, 290337172, 331859719, 242761924, 815327029, 990712420, 288536865, 735168877, 724562935, 643366053, 613424758, 109468700, 205273889, 145547491, 41237257, 856039006, 698145743, 644570717, 162276548, 199244642, 280736094, 967846460, 64058055, 682364453, 950919946, 20757921, 760790909, 113613254, 569449431, 76500970, 675782708, 869827284, 812687712, 732203422, 759129752, 880702106, 877050919, 719465408, 712559585, 962860767, 423196149, 176520506, 810830294, 49355261, 77433615, 410630304, 465037790, 847434130, 147591492, 560644303, 370395701, 16763986, 819517872, 817295352, 953311248, 43939517, 649277166, 702455863, 76761818, 878595367, 716395107, 573124123, 503493125, 550559855, 60181377, 857416448, 573166242, 918201524, 447325883, 442424120, 858040618, 824822617, 736709316, 378247792, 331247023, 249333895, 348961621, 682840569, 34126502, 315700532, 72856849, 652810624, 662695314, 947654119, 892420703, 402734321, 973481297, 262645085, 901670079, 541369833, 781524862, 26287986, 847488235, 198506932, 756542168, 370540646, 90866626, 483428311, 755044935, 108660534, 670581529, 926586535, 253461644, 619838354, 722221975, 809142114, 710226723, 47801838, 48921733, 90289542, 585359222, 320841126, 959678946, 939928422, 415260132, 337139462, 778884017, 224999621, 5828161, 900130472, 747171630, 794726081, 378447249, 294773686, 512867789, 9273730, 450387647, 763864885, 80587959, 667725713, 822014127, 427072318, 863768187, 993261796, 679157876, 558856011, 224816823, 243350180, 412828452, 455492471, 806431699, 462747535, 38591367, 587570040, 825428805, 465856749, 459827856, 727915347, 87354187, 809716835, 25101241, 544602493, 318224914, 185851343, 882216779, 695197120, 388711205, 75664101, 677307818, 717934588, 542040860, 694102242, 825588608, 610350976, 167892085, 534065796, 408024754, 658132654, 369180727, 990904808, 334322104, 393648665, 774536392, 365547423, 662911796, 373977922, 238428683, 547340419, 787522244, 381847907, 148828060, 239365182, 900599044, 577241780, 666355672, 643514845, 104932402, 965227386, 627858291, 635100599, 710388632, 247094330, 144999007, 496165340, 75509098, 393807454, 489425162, 492335193, 373906443, 849679382, 978272287, 82736088, 697330226, 533745636, 624676015, 268060357, 259953855, 438424658, 21794482, 33054202, 861855384, 746464529, 396787019, 277967004, 827301024, 468583961, 817621180, 304518586, 584453155, 337661710, 70782571, 995277741, 844042172, 749043641, 177584711, 275638128, 820097884, 263141088, 963282371, 223003411, 460135221, 530262740, 729843152, 277998800, 441076884, 434746678, 627754166, 31746587, 355810291, 272881078, 238088808, 434244785, 440114008, 474891191, 278651577, 632522426, 90966191, 567574506, 835345810, 634067863, 89013316, 841054204, 300284974, 12610450, 54347857, 335295604, 955177984, 60477382, 738094173, 8511592, 267861202, 568977949, 782555886, 813391362, 622612687, 34989910, 900373451, 930477132, 744325536, 27312717, 110180198, 452631930, 625506622, 884880932, 669532860, 991636922, 864843772, 865989710, 302575388, 819427561, 39471331, 171181881, 963774660, 958808352, 559166975, 809704743, 406297510, 48113105, 10709460, 37010998, 808202679, 372122308, 18479159, 47009610, 414332774, 51326073, 484734100, 416589416, 805591882, 692526210, 813031245, 789646275, 892042591, 938671398, 732169101, 465388741, 543745275, 65133168, 62591848, 887854502, 965040958, 213207638, 659192885, 815769308, 643823515, 889420891, 138071985, 941365128, 176788381, 946379950, 16047902, 646476826, 379397383, 170442602, 771977719, 815374649, 323978153, 486775828, 760120380, 969888376, 771351304, 200034070, 975946002, 414607430, 696603478, 736815330, 631270672, 491285422, 672845324, 690727359, 575962458, 841257354, 938029154, 502302573, 47232312, 849863841, 97838212, 503280957, 836163247, 336434150, 670244886, 231896633, 930160990, 811628524, 455847351, 298023294, 310603334, 396591345, 114964124, 433665735, 191230677, 734323251, 825390858, 842163168, 635309758, 210995664, 171587067, 687015715, 111284748, 145450521, 395142051, 621308774, 934282032, 394444932, 947714979, 566851314, 331922541, 192902103, 35791284, 942480562, 722420988, 189556766, 132076627, 460104497, 774001110, 798699792, 346116223, 500916115, 475288466, 911097845, 406483956, 398658213, 940532410, 369806543, 607122474, 863056409, 776579987, 668633247, 173951958, 746416023, 852179098, 884037426, 41365597, 875984112, 981283089, 394440043, 110774421, 653138996, 915960716, 171668305, 29963977, 778895672, 869732510, 83802934, 457788176, 943793413, 278652132, 22547710, 632846888, 327104047, 61550435, 240639486, 809010043, 515833625, 219418196, 230817224, 661068976, 837693310, 105593796, 682402239, 252588509, 606700140, 450173431, 468254417, 478214465, 161762799, 333110613, 876218307, 640643801, 968597920, 492197706, 735661350, 960366346, 613691437, 228251188, 831508878, 117916025, 93533982, 890022696, 248091678, 488794655, 240425219, 229377606, 787858458, 337893355, 579380439, 135783476, 124602981, 378632906, 554130256, 306768669, 53783203, 248977175, 25765309, 273199936, 769878755, 381228679, 82585866, 13617401, 48870250, 623873106, 172152084, 794071683, 906878694, 596748018, 340145711, 51965141, 748805967, 29156173, 156147080, 466790759, 326076328, 750454984, 628749592, 805109512, 128600432, 87966224, 556839365, 714403006, 476090948, 325629474, 874923740, 754402904, 330451074, 840238478, 230906879, 121475924, 22965396, 318075684, 139188312, 134264620, 962145037, 810889333, 999664717, 495080238, 380901160, 14873888, 844091738, 12862184, 176619219, 358981385, 202898398, 314402497, 280053892, 918573112, 937847769, 146223422, 905932530, 254275309, 465507241, 583122162, 412243882, 535897676, 979382090, 188178283, 546805327, 980214939, 677814102, 805712305, 251127143, 873380065, 425051550, 929577324, 449732242, 414215658, 115044560, 209876386, 983409653, 157379717, 415835435, 182908938, 419398139, 171712634, 639996498, 779694343, 413640533, 719274956, 435572318, 916374460, 592004688, 746016066, 985593665, 183631920, 459183159, 684687028, 865211783, 363600925, 341962094, 437916009, 295570993, 926107576, 702417742, 332416185, 853882631, 696826478, 635460395, 919071685, 288646534, 579354045, 493160563, 703312815, 563978530, 362378436, 455059566, 302123239, 551908220, 581667454, 121575625, 677534337, 369133681, 97595996, 768201903, 400981769, 932529968, 677293794, 992633022, 650370266, 265148569, 859426669, 839354843, 307627803, 383460864, 195024268, 75746305, 788604383, 434760907, 209011696, 154469806, 288755805, 429675873, 590961118, 976458141, 517323041, 992718700, 252229161, 480217481, 22125964, 328789567, 611381297, 511464002, 450070164, 102743149, 84752319, 102244397, 909310761, 70008260, 726386628, 8930065, 809871151, 415585470, 934913727, 191958874, 323248104, 250978464, 828021491, 955543966, 806336125, 782671787, 814955936, 224400113, 740951951, 893960378, 963295724, 478265924, 187061102, 640161733, 516404532, 541058852, 107848943, 88114010, 903817202, 776233101, 99840255, 15608283, 823116246, 727334144, 776890412, 414235309, 284441588, 827200010, 8132541, 1889149, 313667458, 663189209, 731617268, 868620554, 553235324, 278789546, 104092994, 189171485, 992326918, 295901567, 979438423, 575050379, 253063158, 815363083, 123344178, 594457935, 914614830, 628643890, 968033151, 429977686, 575629983, 237016481, 420699111, 90897153, 989112663, 622833562, 497179019, 643348292, 802549704, 453581788, 189754165, 349378299, 571022588, 367795146, 599289419, 686045601, 580445975, 231810700, 67499522, 595151602, 833188096, 849750938, 298555496, 215346700, 761609014, 823593509, 705517136, 323903516, 527240214, 535306500, 580828105, 531704427, 168741436, 850727776, 331341569, 585529251, 170366334, 86885736, 673818317, 168381788, 652711355, 204457981, 520665726, 270132391, 766426995, 971752155, 507965075, 298505121, 690588185, 44893863, 932180021, 653891284, 369714035, 572055565, 345046505, 813294993, 788544867, 620600064, 733164805, 139100851, 966658376, 293486511, 525889037, 935850133, 299837452, 133328064, 38129194, 478473373, 35718017, 948656518, 650546962, 510618201, 440715660, 884081662, 315634878, 460559751, 366779061, 704891858, 794507884, 309268955, 509785984, 839508331, 348283666, 293135542, 604514839, 817973677, 714137296, 960947804, 46896418, 22815135, 614007247, 295215873, 6553938, 517592421, 542961791, 317706935, 845829861, 619555212, 464621881, 402428848, 69976301, 202046623, 564333294, 332875760, 14349164, 908217652, 114482922, 50644432, 218468915, 791072235, 448936181, 584102390, 174907776, 436932146, 194480567, 917050378, 134572969, 367556337, 244807059, 909384604, 368422838, 841274505, 702549276, 761429137, 215890965, 411155465, 721025600, 735862980, 770999425, 754033919, 870893538, 556338620, 278482083, 752619169, 444164650, 854908003, 598160708, 667743708, 729061515, 989516901, 825014768, 921826819, 799516822, 812762698, 214852986, 620461900, 869971667, 662550409, 577601286, 336553383, 839485361, 617432516, 827842993, 633417342, 354043727, 670684396, 63399594, 661221843, 175229187, 83227990, 650533811, 295058707, 796178499, 154628718, 873940848, 889669929, 772156321, 897849045, 31072958, 878202628, 350649092, 27219624, 181442155, 848564823, 489020160, 218236804, 883255437, 800860271, 525491312, 599127262, 902281259, 405505168, 42440692, 340349524, 601324565, 395325789, 68807301, 229902452, 872821805, 341466201, 16782445, 49039866, 960849375, 62863235, 591622128, 795029532, 739343348, 63929144, 276857275, 997366843, 83691421, 88778132, 941994078, 361866967, 423881130, 237844290, 678136033, 957956017, 611920934, 918376654, 904777732, 20643010, 701319938, 242547366, 614777907, 559886872, 381989125, 683007201, 54931969, 993550747, 625221727, 812857531, 83404540, 706248888, 760983237, 974612160, 500892444, 723762396, 393866907, 337348882, 955323514, 999887525, 140610140, 420939709, 801493926, 136797408, 547288414, 734862798, 985868293, 886074080, 86804592, 410548738, 792420786, 114031742, 719713081, 757688703, 475701821, 368000951, 581600583, 76427658, 955542578, 505260987, 572679556, 1880081, 955556056, 625376097, 357894472, 100083258, 361606809, 281049806, 385207071, 473386094, 485047466, 155065676, 458386627, 295315776, 230675754, 949889955, 76786339, 714091557, 851411350, 157778460, 246714929, 190238933, 705872446, 678418043, 875475253, 948466698, 841658047, 993921990, 143555326, 389150691, 332877812, 18852856, 412433860, 967299083, 44750778, 441158818, 682124971, 323863273, 411541626, 597871306, 149789263, 56592961, 457347271, 361838030, 597095221, 911072886, 943395909, 595285032, 15750916, 208770221, 379118132, 137618471, 326374187, 997899394, 247680269, 269959485, 787599564, 562933582, 959437074, 570072262, 716316951, 582905787, 260564454, 356738771, 233006062, 443432538, 555501732, 316270890, 458239566, 703141615, 352860678, 531494454, 694035889, 688264144, 707904865, 971067318, 506658965, 140225879, 563967039, 382010243, 27977662, 42080293, 46642449, 143270409, 494175467, 93526500, 662947735, 912026465, 807241989, 347369665, 642981916, 989785125, 652421633, 775846074, 865164585, 500349694, 104237840, 91353990, 36012196, 147126290, 65277588, 655913818, 350265093, 311685281, 585786496, 414146170, 963762506, 686782687, 870675617, 774684683, 217113329, 668055898, 567630772, 917569731, 93711244, 640135174, 978819037, 408094212, 426149422, 967013731, 740091464, 269010180, 938934236, 800711052, 315738085, 895349402, 575618809, 202123651, 810145307, 312032375, 613818651, 343931181, 399766007, 956253314, 187301877, 784577875, 570297697, 294458739, 188845270, 645898151, 741508067, 994600469, 21782098, 580005946, 980804918, 643865319, 801837394, 564809058, 81157706, 585254458, 459675257, 223000974, 742580424, 765034978, 744955354, 951826943, 749408749, 813941756, 191975918, 488962071, 8575810, 567578883, 678698983, 147537963, 145693312, 71319377, 100585756, 126139422, 150491861, 868090359, 281864217, 746107900, 704423641, 650130288, 721724918, 498108211, 259540353, 528022336, 22497318, 37906951, 778244897, 303663049, 898906997, 249538581, 563920856, 121627774, 476030136, 50148918, 618722700, 574042139, 389349113, 71006430, 116703301, 568998388, 884217382, 278715399, 932335224, 275233138, 852181515, 583431310, 602060669, 166493373, 277012698, 805021754, 721232478, 555316115, 813125580, 402050049, 217839946, 906029111, 415074046, 446585827, 586970903, 573219164, 661332828, 66525060, 687233014, 932110565, 438159, 572057460, 157768071, 715950248, 507845526, 627453463, 883032957, 504393184, 197050393, 891718758, 194165892, 432186948, 733280707, 404068614, 1709172, 860764399, 5148366, 724848856, 734607491, 677215036, 322677671, 143301455, 90068959, 641733304, 807403052, 398857762, 624219676, 796029024, 208134324, 582333135, 590090010, 896222722, 994323405, 275101997, 868055698, 199216492, 152714980, 944940648, 752500951, 176024901, 261127988, 361100049, 176721081, 344531376, 72866967, 59296316, 988325511, 91347430, 433535541, 869624796, 497005482, 62165488, 213090133, 127742951, 527632049, 50538673, 910700888, 649340341, 945618343, 525949178, 919305152, 551879330, 492339898, 368291375, 113453513, 629845817, 258737092, 72015780, 813048674, 384847827, 23396161, 985045371, 846730716, 377279147, 262696200, 290861828, 602716889, 604686755, 736329737, 717607998, 973522918, 281881968, 716734203, 105866459, 839198353, 81672533, 570282821, 805430656, 325037959, 14187227, 636356941, 939909676, 295049569, 438595025, 199027317, 126128725, 510159863, 312386971, 257783723, 33732381, 805850386, 573626254, 203776569, 909440655, 973242220, 870969879, 280282376, 576880465, 376119086, 607126586, 54262542, 785085271, 671710792, 308168229, 699380014, 626675748, 996569460, 893021990, 973709731, 493491601, 159451285, 162121314, 143065036, 464106217, 259770187, 959788837, 679426080, 788593101, 521865319, 462017685, 639349137, 644025213, 10841013, 925722184, 395650458, 107482552, 205016125, 973498906, 781451695, 165640182, 324843967, 924438777, 183684052, 587627572, 246648644, 576881121, 79248821, 192340389, 779505505, 737282734, 960934187, 181418593, 832800321, 391633124, 596178494, 309331068, 246865783, 932125576, 927623955, 667262585, 1935841, 456825319, 192409714, 110998672, 245940518, 443528644, 681480540, 598964852, 370996190, 272786700, 58925569, 688634194, 812216049, 532014023, 942529502, 240922132, 137107567, 173879911, 690740091, 145897827, 987647783, 435726355, 132149188, 804474410, 419656634, 898808858, 320209035, 821279425, 240594847, 444091537, 159295033, 350917217, 723692159, 918636128, 690419236, 353652549, 519620739, 807114831, 757392663, 196080064, 544606576, 126515777, 465990018, 304474011, 388560024, 553316265, 78027007, 459795656, 252604593, 569992563, 465238944, 853333860, 193158107, 212910653, 885692515, 504832220, 106743877, 889581021, 364480740, 3996190, 458682497, 376144421, 807686633, 469566097, 632641717, 590175602, 324135810, 121245160, 918570161, 229411798, 577782715, 983851497, 755405130, 630252776, 12762252, 390752330, 168384363, 812946448, 558129043, 622407966, 148773249, 69918728, 524456702, 146833132, 819322093, 170734357, 311386339, 390524893, 678097498, 859895242, 149416892, 36353569, 398487397, 636028455, 461815336, 784322596, 613049692, 727065957, 62155657, 871366035, 580729855, 221007468, 376468400, 828508807, 30924235, 251558176, 731288469, 694781288, 73575474, 193301905, 598982886, 565993529, 318918372, 486052832, 135326268, 633413403, 814663261, 230272333, 920355688, 460187934, 185961359, 321577692, 21440156, 111500140, 37925321, 781545171, 576631925, 109973668, 536320995, 22991234, 777735744, 503260722, 362489484, 129486993, 438981907, 493588937, 628752524, 243774361, 62233331, 957934411, 178400013, 997910131, 924233089, 6483827, 387132442, 706170500, 296965348, 941686106, 774729626, 505767628, 672896118, 537684855, 512534858, 258578604, 538505609, 906187124, 218675954, 575185832, 756832772, 671679194, 285244713, 416762208, 742588745, 707485219, 410995085, 16294995, 639014325, 709768977, 987952736, 30573038, 691502938, 232605205, 648337369, 128192503, 929754459, 74437226, 316256119, 252282840, 659007314, 752308051, 941171282, 253174528, 464557180, 274505891, 345749670, 290786504, 651057404, 651129293, 84456330, 606604760, 44245741, 83004648, 149714901, 212252324, 23778305, 431830116, 91657540, 946206470, 954467713, 873042990, 715112730, 759646576, 841550970, 809286308, 228681604, 275804629, 478733442, 735192797, 657912376, 319694632, 225719301, 792653703, 638504206, 14297761, 793634122, 999856267, 7295995, 806441945, 752093076, 336579929, 688390144, 418641422, 722039112, 801301997, 971963094, 414506591, 521653166, 184661365, 154274462, 143616134, 116437389, 649754795, 355110959, 2336542, 512729787, 530223661, 536755995, 773648073, 463228243, 626516806, 717320137, 787020568, 389407301, 444480506, 814241993, 987824013, 854698579, 760319849, 831379428, 515023388, 426910952, 277410256, 386639791, 61762587, 861858869, 980406759, 807273305, 694295377, 744678716, 636884098, 684485816, 578253501, 161734734, 237612955, 256495268, 310007263, 762669279, 31158012, 974624785, 20335412, 526839655, 73937357, 177108889, 287756333, 793705499, 597664209, 691673205, 197594617, 462833046, 320413248, 340360621, 230961078, 464616329, 766510947, 769414221, 569201388, 736161203, 900139588, 958139010, 888177993, 525240454, 229181186, 592276588, 363943864, 316162159, 683931078, 346002519, 370905085, 199950519, 944452918, 786885740, 415684506, 145763796, 191112048, 676409251, 337693099, 283690484, 16860168, 608170365, 985843515, 485053591, 148815573, 644965945, 512367112, 620707801, 593330275, 146627513, 134444288, 686678858, 62044510, 666205908, 958236429, 41813797, 492003065, 424357713, 906671434, 746858007, 55437609, 445560292, 709702398, 74662063, 191868486, 889088930, 545752488, 506046187, 669999823, 202678655, 57770031, 730789328, 723877858, 237151232, 537466581, 14890076, 913492945, 526567672, 978781191, 28731026, 256739534, 832077002, 706988456, 654643834, 124196213, 617960730, 783859637, 925202917, 259631387, 866529567, 736091111, 185807404, 485144014, 58240898, 521997172, 96345976, 875687815, 452905811, 692339728, 1771392, 306519447, 273341419, 874438585, 471810764, 537304038, 266473462, 585984650, 613506419, 512757869, 241809614, 421696409, 324906227, 587524199, 141781920, 160374296, 160160619, 308425831, 26382883, 602287959, 235907456, 868698634, 127562550, 168180296, 390659128, 155719244, 225084612, 543438055, 767575402, 604074972, 216167916, 942169591, 174410045, 61258936, 687834747, 303028272, 671719175, 281520829, 535122722, 418069513, 467795411, 836074608, 932508796, 614831178, 638773558, 895154567, 298796357, 622102451, 88026062, 64351753, 571786206, 368723945, 749972366, 804193204, 33913062, 513492667, 653923765, 793019029, 680271540, 84130108, 187814673, 345529235, 486224776, 68731105, 534140844, 93253577, 350076926, 837609825, 594168797, 355100458, 330673214, 568533015, 297150888, 908244979, 285042117, 848918537, 190453671, 350886286, 136752253, 727367905, 848029823, 634862148, 892317080, 464019027, 500164973, 834681333, 732794144, 763293064, 722790909, 59178612, 165797595, 408452116, 130127591, 200712973, 642207046, 872838913, 494083354, 776866346, 181431839, 617175622, 400063647, 968376480, 509540086, 83677139, 458022179, 484906370, 653969303, 914071878, 133779426, 908347670, 157763730, 336848052, 118493809, 769251885, 712149232, 730857150, 390060997, 414844005, 897182622, 509721337, 378800592, 500861772, 438177011, 46143200, 925185854, 649832118, 248885133, 159952500, 737986818, 594191365, 505426825, 898318960, 536327995, 789402176, 581792550, 332124362, 613778045, 266511109, 412227397, 601296740, 589656655, 219824325, 240955817, 991811079, 566556091, 448157401, 254373426, 959457873, 524632311, 325831673, 346989868, 488127763, 976362851, 441426880, 373684292, 517657835, 697642739, 376149252, 664769264, 213623883, 883137710, 552871739, 586310270, 565728301, 805888194, 538524453, 888855094, 788923625, 250342251, 15554433, 465127779, 871284977, 480705394, 842158178, 671177222, 516751731, 373904364, 311402506, 780863322, 458951854, 971987421, 453400163, 146258295, 254512205, 370801995, 755632722, 755268142, 774311182, 566118035, 519831301, 822280599, 75265589, 845306049, 255676800, 556185937, 612223842, 588132955, 690155632, 150153575, 27365200, 315501983, 725494863, 59688761, 600731531, 692738880, 802134567, 391695295, 172204672, 475920284, 827798885, 409626969, 715158804, 149377727, 331701974, 597707005, 5247636, 702756760, 519366914, 668375974, 182611525, 948871606, 976018906, 967624984, 689576711, 457036964, 89951903, 823169773, 132151349, 743808207, 191836130, 532602795, 90224748, 599485015, 124676649, 278875244, 599353127, 870196732, 908953516, 202409704, 312286198, 420904776, 359559687, 205815286, 444560053, 549239063, 147397210, 17841422, 218889978, 842416015, 497001114, 723684238, 95982422, 8354017, 514857908, 636479688, 612469165, 692897717, 365339805, 360766864, 267620755, 734619844, 735559411, 410579136, 249729923, 175592664, 889901648, 472999620, 851916723, 721417037, 389429806, 54701227, 829194423, 742634766, 612228605, 298022503, 634934126, 582026413, 234059157, 49143156, 454945832, 382010785, 429387857, 230909354, 655987640, 327249246, 540871731, 985921911, 253140794, 920993632, 613281847, 576507344, 352689696, 160461992, 889968354, 487757697, 612247143, 390425795, 641629984, 600053079, 673930306, 410703647, 788728718, 524537597, 247649967, 707337496, 174862991, 263042568, 877392734, 921069759, 529346212, 798915350, 905481733, 332237332, 41367280, 734154323, 788562583, 416605508, 589307751, 661464935, 890557166, 4511581, 182285219, 411477560, 464238404, 375885763, 710261732, 438379274, 213379163, 840697802, 298464897, 583244265, 856923728, 607586512, 203371691, 63326311, 314013626, 868707774, 952768120, 381495488, 227485859, 753066815, 877136745, 24527367, 310793455, 156643423, 81496687, 771116326, 492208002, 513928635, 364780306, 798371846, 366701245, 539502986, 324952141, 194318502, 810024194, 394688006, 862002165, 791724752, 488094998, 4829209, 887703245, 134001726, 213105485, 304472952, 365448652, 821397809, 243153278, 890320934, 719790091, 295124973, 348698912, 97616234, 830926388, 870288045, 601695075, 944298204, 2838524, 58908133, 306986918, 996958935, 265965394, 835917535, 87053197, 360689714, 873550770, 98244563, 981073979, 701178289, 775269899, 461170862, 776601819, 836875644, 84501465, 719309232, 332997101, 611187862, 137713876, 206373938, 850807769, 178821812, 264356103, 98756345, 131557329, 433256711, 312645399, 80722125, 279563077, 576283301, 618776306, 648932114, 183614756, 571400002, 322743438, 402602329, 502626556, 86139102, 16161485, 133570512, 855547929, 631143158, 725692022, 212656733, 739997988, 875671298, 961845591, 906236791, 97475956, 519962358, 221492850, 39077844, 119927089, 484980968, 880102060, 526694905, 127415747, 897990930, 501479682, 27108898, 207915205, 282188993, 846864650, 445028351, 377473055, 891656144, 468587632, 817853499, 964649186, 83106895, 610305391, 71153501, 922296616, 631101094, 651190324, 190683674, 995320864, 739628743, 705201714, 379940709, 92103366, 360756610, 417820404, 516340298, 812084621, 450320941, 958094100, 426293261, 989640267, 518635420, 344699896, 217447693, 364745159, 823806256, 514192650, 599952515, 179181541, 839878930, 189673100, 10138778, 464349919, 238118280, 544098974, 161076383, 608530744, 988766717, 787230487, 187568018, 788824346, 592357387, 870697567, 326890649, 203257174, 840256502, 420949778, 65366324, 18726784, 538326910, 127679756, 121538426, 676906267, 152545856, 730434149, 673412366, 229439742, 340784897, 836369040, 444345334, 414677870, 561864495, 750548128, 45609383, 41785322, 937259288, 844234060, 55150590, 334392896, 730783083, 295413139, 102335884, 207855526, 264925758, 649663928, 479669231, 518615215, 176023566, 402360127, 548716438, 419252197, 127926036, 725260335, 860197855, 382857026, 19639238, 875856319, 930779118, 556414216, 294932608, 767699470, 715449833, 947883629, 779601017, 980240690, 655549797, 204653543, 584282038, 100641757, 173763809, 715456322, 397364756, 184826948, 285014919, 193382889, 857400879, 403905887, 652621619, 933204725, 497984193, 375444510, 773673722, 571061782, 639583485, 81699934, 95135494, 535660654, 867799407, 899579264, 277731882, 891329600, 932191948, 78492934, 845151810, 155779450, 196877912, 724512259, 832356582, 738508195, 277214997, 64245370, 183583929, 33876711, 587429397, 821827741, 459688744, 536406323, 281989382, 26579463, 902706730, 767072482, 163220933, 366291606, 77350376, 371376936, 684407032, 92393654, 882910882, 959733119, 964108314, 129151454, 120526849, 864344647, 597559025, 2325089, 528440978, 405090366, 698506819, 508913741, 880615144, 560685357, 447772076, 841567562, 528725059, 865560795, 359553110, 56021873, 225357088, 140291257, 66847947, 582490779, 63002829, 271735944, 514623948, 519994549, 894584907, 231692245, 518207131, 889452865, 148612524, 856397488, 556795537, 973110387, 270452570, 27763201, 918759212, 485407663, 537493362, 920441521, 927490951, 371545223, 840692055, 492771006, 803319982, 161983317, 571360634, 673468603, 736500827, 19252079, 99448104, 855213456, 684564928, 208908833, 169054256, 309713554, 936524882, 936306717, 173402544, 802764769, 684710843, 55940702, 990981232, 14743186, 23804486, 499858268, 57658474, 333827928, 557042438, 957177321, 765709101, 64625784, 847048000, 816237086, 302287655, 885824095, 896512056, 323788104, 36801912, 365999286, 745809261, 295286055, 371469877, 655138859, 181136929, 410408326, 754072177, 892759739, 9258495, 507025679, 729219919, 238162985, 974515700, 636349799, 36516011, 35342115, 500263894, 461161449, 139617791, 998678857, 337309190, 337207014, 8936616, 251149063, 442499058, 441474055, 85232778, 820300485, 729749047, 94376453, 125392103, 425927842, 93901954, 176269209, 415651264, 250430247, 122995152, 327453157, 252353904, 717465821, 627284531, 878329112, 83803592, 94168037, 938606031, 353051810, 543473928, 725664113, 205119137, 461206966, 456061460, 375712170, 670920333, 403768884, 608547114, 467454605, 113911885, 647829358, 69553203, 399929076, 977306098, 879676986, 29663927, 880786007, 713338776, 129252590, 2343793, 138156540, 521683851, 489163101, 894693981, 535880491, 429176001, 864551759, 559788534, 256521528, 972789700, 981526272, 667176545, 499093633, 130483252, 610365345, 666603083, 884360963, 673800212, 653891098, 435858848, 214693735, 249857604, 41880834, 854961773, 425792374, 263744462, 69883056, 864997978, 235915575, 874596987, 549091674, 73304342, 480723689, 934868056, 700955024, 842975461, 656222499, 489448846, 651538463, 610823701, 111129487, 930800426, 690327670, 471745287, 787206015, 171428460, 276035870, 823029622, 309923914, 910562892, 214198661, 194327125, 395743316, 294379922, 520906223, 41032589, 98218936, 183741072, 692202828, 404112154, 361639487, 919320628, 402439405, 440721501, 903573892, 998817898, 931605854, 583214122, 235966550, 703982598, 692249827, 451466118, 19361831, 423975098, 244150373, 898341039, 225080841, 443372008, 5717787, 39866530, 805269137, 445693501, 379876676, 919449617, 992499986, 173441897, 903387139, 839815970, 714931906, 928994965, 72628924, 640827115, 402479941, 260679674, 45393352, 724852247, 373421945, 895245659, 668790237, 476946160, 576595537, 618347943, 51402887, 223027424, 821775490, 618786999, 39343872, 388046565, 587697251, 82791816, 226139118, 710467798, 720339492, 72871237, 256676182, 923763350, 970788003, 593769184, 619722326, 85928439, 986679131, 343631991, 523991643, 282431765, 491777352, 856026124, 689182188, 712075240, 909245841, 407715189, 543192090, 195174081, 358921289, 256344001, 848282376, 704523246, 839970445, 435693776, 131523028, 47099300, 377334804, 13188979, 374952454, 696557433, 660665833, 810875565, 706024573, 125603141, 260320524, 456905514, 649860205, 63730584, 499317530, 579584292, 310610305, 675344924, 29875350, 518513977, 489775140, 343736924, 398112995, 417612318, 670960891, 352924219, 536346597, 723176813, 581803731, 95290714, 443898974, 932443991, 606593824, 589070057, 12883098, 9997912, 969976834, 591834126, 539952778, 635371460, 552595130, 938250591, 157858650, 877926464, 704961236, 600713088, 249359122, 347269494, 357328560, 630070548, 585674060, 93181009, 305052703, 480386090, 312226164, 150983080, 213256738, 663406884, 13250122, 748409109, 223313651, 835224313, 509733495, 533432454, 904453904, 287208613, 652021505, 127689201, 902488867, 796208028, 901661034, 451022754, 640528916, 869093012, 677023367, 376311315, 289612822, 699644561, 587632458, 880794543, 570372608, 842345585, 433269712, 75391473, 154370509, 977954268, 259749715, 329605221, 54975581, 979949685, 962681629, 722931629, 698990709, 659803294, 410876451, 236991610, 286108964, 988015968, 579263550, 600198469, 352233925, 619791351, 809497313, 723268530, 667205986, 505574561, 422395968, 473678343, 2618772, 111496407, 898333899, 938645154, 722728083, 88617753, 358866608, 174356375, 523359374, 682314968, 812736650, 382136656, 835251463, 372185700, 227853714, 193053339, 515934976, 69732367, 301617296, 572385545, 401575989, 2294265, 737486292, 484491830, 521036527, 675304381, 194831501, 789263412, 980776379, 543505264, 45653299, 43221231, 883169955, 257091989, 437069085, 199850079, 299883122, 797538256, 467792138, 784867678, 147675644, 785384443, 464295015, 199682165, 633667362, 343256494, 614996900, 280929975, 15374265, 234180959, 25826286, 931991764, 167762382, 125432545, 11774318, 28678928, 499801697, 696729529, 488378104, 377646822, 920229100, 493676124, 145930727, 59744823, 25680677, 589888452, 941909058, 702354002, 751192963, 333310023, 182429621, 628187958, 859119678, 505230968, 846124106, 353936886, 491249947, 957435506, 588876526, 667459739, 591531018, 267981804, 343333736, 165479920, 407877715, 186522456, 71424610, 91082199, 523475223, 53552718, 987493791, 963597440, 272883182, 596316037, 492564680, 377361455, 414810695, 120499637, 368428653, 274628184, 903046512, 939827633, 480244893, 485553539, 226059972, 856839041, 898484587, 417769184, 403015253, 639510471, 929781597, 279343597, 454239802, 34193364, 656888393, 747013666, 616862193, 437037838, 890894003, 532525378, 664154629, 577923877, 419814478, 460412966, 50482910, 788237267, 623021749, 947030299, 647476819, 631529780, 998457045, 408196886, 268030138, 361271589, 493554433, 614985282, 523526624, 462388192, 129378932, 474571093, 857194926, 491031489, 88463643, 265098533, 398063521, 820656776, 656929649, 934100143, 368835966, 76954013, 33172832, 551620180, 964383603, 37702960, 841047411, 369298375, 540732811, 740530804, 115727540, 12327410, 299629090, 773659246, 565366036, 472233273, 91439131, 398255646, 43896713, 610213457, 408336739, 729630941, 870984049, 225483882, 54879221, 990417587, 418900776, 509723392, 874825167, 255673019, 699923303, 272163674, 137291683, 349913071, 401314692, 918689511, 117584311, 774644802, 52151368, 149929074, 836382182, 773104296, 359290595, 154807351, 853818189, 818155449, 725696057, 806808547, 85945075, 875941350, 158961379, 514890991, 895525926, 370265061, 176998479, 544075736, 111063243, 539296455, 847064143, 88924344, 903309550, 983886064, 195376541, 870208097, 507882215, 316430623, 289903141, 360920837, 99702958, 917989972, 732627418, 45131458, 948231811, 5975589, 173553600, 863841788, 110706355, 738997573, 841172935, 646643952, 592630171, 674650275, 707426910, 85498765, 328506812, 118948212, 302273152, 183490299, 131892184, 709081640, 419045924, 517387527, 378972783, 554795530, 777033878, 754143677, 900681105, 878510993, 914745977, 631747687, 293558810, 643135792, 357053313, 437417920, 841448495, 176404081, 782623794, 435765034, 864437660, 393195282, 777840052, 409701319, 352483832, 191536007, 928607057, 722899634, 967398698, 389661321, 322474973, 572496365, 825155445, 393953075, 443164399, 305530363, 24116117, 531897807, 764128421, 112995744, 406325075, 366697522, 656883410, 222505706, 12746672, 811279362, 107789942, 919028444, 921356861, 820556442, 331299560, 912525664, 397625803, 266038982, 788212719, 615873799, 895263325, 822569978, 358086679, 13411423, 130502809, 27457381, 39097756, 319480702, 369667693, 877074578, 643764663, 382810554, 992698853, 165459882, 539555009, 53617565, 144150991, 132360266, 408902805, 161698726, 452353756, 954747322, 744617304, 415137447, 967001135, 802788613, 585703216, 456015463, 632028539, 723677219, 387568939, 698159824, 532824282, 549871874, 863561420, 975780517, 710295000, 991273443, 263575879, 438662587, 982524373, 489304339, 164614518, 846473896, 828987125, 958767933, 311895492, 947383090, 755311456, 913901135, 537617157, 878926387, 579189548, 638890658, 678458501, 475778263, 819525620, 139408182, 631024563, 743452645, 741731520, 836189391, 970134383, 638896719, 904460586, 483340371, 141999462, 579040050, 380253728, 994590094, 572999102, 968908980, 843589653, 314704300, 338509050, 970247105, 181392165, 178208966, 65969920, 672350878, 819581416, 970697566, 33322247, 987200701, 845302361, 427035892, 850160640, 438216972, 640602603, 469087482, 949489800, 701264781, 627859430, 981034739, 492623530, 267133738, 827046430, 694562924, 512154082, 307020553, 572792806, 815181985, 737203185, 75970187, 76010293, 197304969, 209683904, 229395786, 938843866, 76795716, 332628395, 672580662, 943962119, 307747611, 648862489, 780140679, 546482706, 672114176, 906295356, 438197194, 449173706, 321801242, 874026543, 390491358, 837540119, 342558211, 268449283, 507042684, 202693938, 9066281, 423770205, 630239056, 515651442, 539679236, 74677779, 807455026, 133847856, 883759264, 378729053, 376956352, 232514674, 403657262, 667288456, 695631944, 833839000, 386125524, 851991705, 971733644, 373235409, 824815027, 21059224, 794462101, 763016785, 873863147, 89004160, 212134658, 727190646, 428467583, 537491449, 151071070, 721769905, 912434426, 674706931, 5692172, 890289559, 878762416, 957871034, 772379641, 205635005, 115562386, 283557485, 711504519, 89278997, 839968171, 154147873, 371418567, 663380923, 728219480, 681110338, 166071219, 443162123, 846684542, 719713404, 868930306, 181321494, 87333910, 993023640, 689177814, 164849761, 229447487, 553040685, 565469089, 503250571, 128317815, 767962413, 258010480, 974352974, 154778476, 135951485, 816950094, 678714207, 351835075, 520953896, 624087702, 657801304, 912974940, 251339188, 986631943, 812158992, 13740311, 657019699, 618360959, 867356827, 601661946, 793594330, 178428992, 161998299, 216406065, 694923333, 49438865, 990291935, 509148138, 115844003, 630127421, 532492345, 846714384, 447651101, 496811116, 478033995, 949151567, 250091934, 540915063, 719603462, 606028696, 773167810, 413016499, 131067940, 906662044, 784437211, 165972551, 126498026, 730138771, 8261135, 76089380, 486299236, 354532166, 16037735, 697192029, 816757803, 960099152, 29901659, 575118012, 253060884, 919012580, 594436573, 829251935, 469035056, 161293866, 657450636, 430913806, 314293731, 150289542, 795576845, 758006778, 68003623, 917745020, 256918708, 563424214, 231468468, 469380715, 716292121, 357221791, 646402652, 994121168, 518546581, 221475260, 562775621, 32522520, 291304291, 996021564, 799234554, 268958415, 724125817, 900231164, 419941101, 587466772, 207863204, 4128356, 105052830, 234036726, 857751928, 330046185, 46756661, 497660006, 564196851, 433798804, 111388607, 110001759, 131505138, 241189800, 792076622, 118264502, 474528676, 968444727, 796218661, 442775428, 367799575, 400414636, 738256013, 399032936, 95880832, 58834186, 786452165, 740152682, 620169133, 524667053, 692584535, 981692229, 552088608, 888414738, 581395061, 466449417, 514611425, 687208699, 286283603, 596207508, 916187857, 408926108, 919261489, 315351705, 378855918, 410222324, 830369205, 323173341, 95585561, 855297490, 87701193, 765842198, 442402948, 621082904, 277240910, 711792064, 3947785, 133423134, 891366793, 133213052, 363043444, 93640413, 246125464, 723251303, 779008026, 245419594, 669433851, 917670855, 917469074, 672277988, 657711858, 384787816, 45660429, 17553455, 744956052, 957045787, 466676967, 683205679, 721947801, 683828822, 291840346, 612378543, 933404052, 345402397, 888145868, 714861998, 257118267, 275470006, 587584486, 190470237, 223642626, 900717637, 564767362, 494575592, 131163760, 925601722, 413268683, 292586476, 56394416, 833073186, 305069260, 468404833, 141427710, 275945289, 307696055, 710659153, 997408465, 487050908, 629294772, 795656416, 481782322, 430654987, 141327789, 198114839, 315952264, 376806055, 198364674, 87510827, 844247625, 999893816, 693858280, 266405016, 685056097, 476398661, 8403550, 792612318, 328854920, 50520483, 605401824, 333059196, 331690885, 468653162, 275396323, 353499338, 987339763, 786571483, 804576794, 518915749, 731370244, 92333643, 73645554, 196114684, 190498456, 11152309, 223563610, 964940860, 359892050, 249351704, 540021460, 164120359, 541535035, 202506563, 503025927, 230913366, 161234535, 698676317, 898735814, 128898853, 945146739, 296937014, 136930700, 516316283, 750501850, 739440115, 92385198, 816790890, 37359368, 57357961, 560142102, 682311707, 71767951, 770786303, 131478374, 666312391, 197399420, 508129834, 265021213, 265929477, 158476067, 965848737, 852982880, 24346489, 83835622, 702431000, 140731154, 728583433, 848122024, 42822975, 236412835, 127589923, 986462906, 871669998, 512076163, 420378621, 19318063, 776338151, 42932228, 561058723, 458785974, 892617809, 940989152, 159518319, 55441098, 728881507, 609897929, 601220660, 801604467, 980120705, 187654980, 409735043, 895327450, 362473826, 144610335, 191151840, 542034392, 281475527, 443127209, 25313581, 403591852, 4998600, 814473319, 474361403, 279186513, 246058333, 414366938, 761160369, 296333322, 247678578, 899908528, 68397979, 672693834, 525211449, 972832784, 73369804, 199525754, 192903441, 943880814, 3032743, 467352031, 746959959, 982237962, 163736345, 337743714, 1575345, 401865441, 798692489, 585210627, 981885409, 13703448, 483040832, 380022861, 930648367, 933247249, 811697070, 769366818, 925095141, 850881699, 33998833, 812504313, 434515516, 525952801, 61162688, 441886866, 848854240, 509380772, 918428943, 796673875, 184843378, 96189754, 857034956, 812366312, 702078460, 541579421, 61493883, 768560206, 822813381, 980900947, 115721082, 718863257, 684632622, 713181074, 588602398, 766105878, 700167421, 452809580, 868953833, 169029859, 836457760, 504111812, 95872149, 128434321, 63817115, 545521463, 718927862, 806622202, 277268344, 241415758, 252780424, 48142844, 936865670, 724512127, 291572774, 162145195, 273765227, 841889579, 185560948, 440113137, 230616149, 841264995, 288075310, 578013418, 758441329, 519454302, 436987240, 844836295, 264832209, 812985390, 846292806, 394518142, 348973247, 360104409, 669536055, 876096774, 932465938, 74700793, 134930439, 577139781, 988588106, 241622432, 506697348, 969164017, 28924576, 917701625, 919509033, 174785391, 207975062, 966774708, 49451431, 533874769, 336018906, 63335597, 220692475, 10277779, 137704696, 841398327, 812332744, 2538307, 139396617, 66321398, 432815322, 213707353, 77348425, 368421590, 283531904, 352111639, 647111252, 298558675, 16597579, 624534301, 62344657, 530099869, 308384456, 680761246, 98552510, 394338147, 460740897, 897714941, 225337029, 587035696, 560083095, 850421309, 945666927, 859244528, 94749904, 885934563, 529561981, 819095083, 37138274, 329751971, 970915640, 877093036, 229827899, 29349447, 865461062, 5562048, 870847215, 267797325, 655465315, 163008749, 731796265, 146444274, 89321290, 366922142, 316578891, 252251936, 788410748, 667729832, 200799669, 305178243, 489280635, 223020463, 555711042, 725620931, 630678766, 194952975, 371882761, 325822875, 164835306, 321365624, 4696613, 47055443, 553843452, 322696408, 798886301, 982848001, 230399098, 869603347, 938614479, 766435168, 783909785, 299014480, 147432547, 958890122, 667353842, 520093357, 844795961, 478730112, 881366995, 213029755, 362071249, 940396157, 659528386, 49537646, 750106248, 379073144, 551518420, 838561140, 780696686, 201860695, 498573007, 886171087, 89882792, 669439041, 889852666, 340082834, 561315536, 100307817, 863181298, 707025911, 673846944, 168309030, 771453180, 9133166, 978142315, 683981551, 874483875, 441721334, 479337942, 571889810, 693971431, 491142174, 84523777, 995195076, 893856479, 742879722, 945974800, 335422033, 516359552, 570553441, 934136296, 709754778, 534888962, 981468002, 324695348, 547216780, 87385342, 269323421, 516482251, 247996726, 747341886, 647086344, 756219876, 674793002, 567216641, 488524473, 999455875, 664626322, 481454134, 253835163, 347484149, 980783510, 431595097, 44241714, 159681053, 369801472, 63065345, 547143090, 392152911, 245741074, 464638167, 652936042, 469475983, 153851556, 788437707, 26183251, 738119285, 829186848, 362396552, 807606498, 408332541, 104717376, 10126100, 371423684, 114925605, 737142129, 681808245, 547890635, 748982901, 829944870, 60685221, 766388111, 289945203, 4905966, 912738308, 678008996, 98598288, 82083476, 535092435, 845483854, 439507678, 566148456, 112834742, 430087177, 471268101, 383543732, 290781562, 889258925, 846628335, 547651327, 396046703, 485092737, 634687725, 671497720, 849587886, 121640019, 102890954, 974236192, 27817075, 862694814, 79852123, 385794647, 333432372, 135888585, 879056425, 566937903, 355939601, 784838386, 515733474, 619274434, 248135564, 280614798, 888286016, 409042012, 740765221, 946255696, 831015025, 942790425, 4620438, 129804195, 697878431, 698101266, 415004912, 124512864, 648271875, 290321858, 494280647, 269916465, 186523315, 692153961, 866044259, 456565545, 867703162, 903711912, 693683649, 887798699, 374794141, 961439707, 987572024, 324103, 469579076, 208694146, 699096753, 475012066, 928100761, 440834117, 834654794, 269716503, 639695861, 796648501, 532009533, 278773625, 372722949, 129440253, 856487985, 1904118, 19499975, 50849331, 200602327, 914201026, 843431277, 4422622, 627598265, 885563942, 630305235, 319966781, 311584711, 293493198, 345009835, 928911903, 243394949, 195544504, 536169822, 593715124, 57769865, 970039359, 871459038, 220620954, 844684604, 137858476, 184583026, 71890200, 268671105, 443022747, 786649143, 90751148, 915044461, 520736457, 596810973, 103321764, 777446607, 267764825, 165915815, 972010221, 587145602, 679254225, 687126563, 935117418, 631456730, 592466370, 671178158, 156493515, 826803522, 664970071, 995696784, 645118596, 375029570, 52841348, 277758920, 984226480, 125674742, 732163821, 680701020, 918195239, 33051804, 361506341, 580325942, 557075056, 269628418, 707226206, 616211791, 77735845, 219921236, 247037390, 453772529, 255134613, 104632581, 674872186, 259492533, 674000299, 7063990, 101256548, 435865749, 896524302, 550873563, 50026765, 746590892, 571272371, 134361171, 731122020, 506824308, 160421953, 290547488, 491553619, 446368077, 541515801, 664744807, 959286155, 673516598, 376088256, 656047823, 486260335, 381963470, 830401065, 577180301, 770581081, 21677998, 274390091, 943037993, 433444622, 152644915, 78778498, 263270046, 711652546, 814903530, 815193959, 631145673, 489286607, 758402103, 162194413, 996080405, 44179469, 863623448, 778649769, 947265028, 773903368, 326770950, 648170896, 692720037, 412530596, 889138348, 961340348, 74072619, 78201465, 133734761, 151339974, 799578501, 681139946, 529721677, 845926684, 884311353, 973259070, 357603567, 366256590, 555471590, 684565719, 836737538, 929858618, 537530198, 353542685, 330278017, 79967226, 565347351, 918332528, 988720613, 176507082, 395429302, 287483779, 495252357, 608236651, 727604882, 294500618, 699659325, 855392600, 577649118, 612447287, 476219667, 991373902, 812162823, 453589620, 239419779, 897971518, 483495950, 938617313, 485461633, 205797988, 102827077, 709944140, 97960623, 673633091, 266070189, 547962296, 568435826, 443094678, 184669243, 125913964, 464358971, 352923333, 902505092, 941206942, 869051165, 246348126, 372691047, 802470916, 325585291, 701296239, 352652075, 236245547, 903302297, 31989297, 45749676, 720269239, 637031435, 145373404, 217215200, 723787358, 244199174, 260335747, 740128985, 879242821, 70294168, 821334495, 479230240, 930383370, 70817972, 200546940, 619930199, 489087810, 54349688, 139088378, 563247699, 263066024, 743094435, 370932430, 447504066, 153844238, 638488801, 601985491, 453636076, 499313842, 34760929, 9485195, 243162735, 778652543, 715967737, 714965281, 489122109, 188559721, 637660068, 238628709, 271235655, 942971853, 947652994, 999410192, 540414868, 626107828, 226048171, 182367621, 104517092, 611980698, 709709167, 684769299, 954232006, 653948574, 486955208, 681747572, 496570812, 659043641, 825267398, 83372392, 371922306, 79585534, 861097570, 70930214, 523036654, 14823773, 792703220, 509376247, 453620331, 911252367, 655600430, 893445629, 599287572, 659818844, 204428856, 843758251, 473863005, 735866181, 636465606, 933822225, 811334133, 27901594, 66485855, 977481244, 652946394, 730819628, 935053353, 199370286, 293573328, 459524247, 482492634, 291551448, 402902043, 948297237, 349971513, 782899633, 701584495, 327068310, 786716092, 289467382, 526340015, 914305513, 894130414, 268685684, 135873222, 854887437, 354118229, 990617597, 674850424, 592523892, 158508561, 705495007, 521342146, 673270692, 211190367, 870459775, 440193048, 99972808, 508863118, 206205938, 378875840, 310029102, 986611476, 656467878, 354980920, 889649754, 983443023, 651067233, 619042050, 13242676, 178356902, 661629994, 825710339, 139529742, 959638333, 85354561, 321537511, 767570911, 804976772, 672881542, 889104338, 595656976, 401613620, 390669817, 881343300, 382620817, 699897178, 562805837, 983615912, 879676898, 706659868, 375778604, 324491915, 715017660, 122427005, 625820835, 236527259, 660194331, 38856314, 996199754, 743886795, 407452556, 996510941, 109479318, 785138777, 245336509, 526305054, 523556764, 52747388, 928147564, 36156849, 280019977, 506076456, 876409002, 214872899, 841307054, 389393672, 307670226, 374083815, 483879524, 942380015, 360287770, 411166558, 552532444, 20362631, 763842364, 629270137, 642602782, 628232986, 687042667, 182317496, 500976760, 588810855, 721686709, 941437960, 280577135, 508451954, 409772085, 548620504, 291083189, 740035663, 912091655, 936515601, 162048973, 83015523, 408447938, 576831116, 889297826, 220772000, 675569001, 502102036, 479374478, 202654480, 187374782, 513094434, 203368758, 895059619, 768584939, 628030998, 933676235, 47381206, 487083888, 378386982, 495332950, 640577408, 630137005, 689021145, 325689118, 237560173, 671836236, 265247132, 90181613, 33484661, 574700895, 313854348, 660264463, 209792787, 333717051, 812928064, 934427838, 618482205, 577300073, 522770707, 438756281, 171711171, 351665106, 525416930, 97107745, 47097081, 618515390, 186604942, 109941126, 374819782, 205754748, 613970699, 573023482, 701288562, 86111714, 235752642, 82506274, 46217516, 428263566, 613565717, 192238089, 153619499, 637049695, 127309069, 720976269, 546728774, 62890546, 474843172, 679456166, 240624002, 113682884, 63931679, 133203869, 338525581, 7615614, 958139544, 753357455, 99931652, 605335603, 721440483, 328484290, 664157575, 774127958, 108342084, 422677449, 392124925, 794889428, 158650533, 503446483, 508683553, 963497342, 26558303, 168135536, 29484000, 76939759, 908451157, 238847561, 770599539, 28977670, 528043483, 456786532, 241847401, 629990996, 260246871, 221874582, 497671631, 250025917, 114007840, 370290898, 652842334, 886995709, 624983670, 653614605, 65200106, 5726389, 707626096, 147647527, 568770130, 276441894, 683979691, 753328558, 896269060, 86312901, 533710485, 306798283, 843905846, 525855472, 477404927, 180988372, 168638268, 595099235, 269852184, 825172693, 125045031, 806892293, 685502283, 177114102, 264825941, 484888652, 618335741, 765412424, 842665153, 318094454, 766082442, 127033181, 325845334, 319369632, 187577220, 163831444, 443773665, 24772454, 710353326, 752981125, 808402389, 809661972, 528881574, 945420558, 239635094, 192678854, 435382136, 31206453, 178433992, 50409089, 312497856, 653544561, 370507032, 712664094, 187057659, 373560224, 837692852, 227654693, 925838144, 325824874, 633089236, 214642040, 50773784, 770647372, 765067748, 586793305, 213673073, 510654749, 537130068, 151618294, 536948683, 417625595, 6668351, 231864618, 765570071, 423646274, 260353763, 702258501, 511117411, 637025251, 933900151, 14257946, 428882242, 563610598, 215689215, 525076951, 723939898, 357152512, 67639477, 133322456, 343167214, 306685626, 549873695, 757095556, 774656522, 86054106, 51371040, 878879588, 241943292, 831133542, 265940589, 435898247, 978697468, 149987882, 883988926, 681563322, 896541571, 102707236, 776278973, 717700952, 838445720, 584417945, 806331456, 428231910, 115177245, 462036209, 857219544, 118524332, 857008204, 774548365, 755632978, 666855244, 274715876, 414452278, 43689051, 739316877, 809608195, 637278213, 322399029, 168753214, 785234172, 888313027, 503295764, 289295722, 68192958, 704521501, 489356131, 512859860, 815194307, 963807323, 475839098, 259729792, 200073511, 740678317, 702387174, 957703704, 734975559, 795062619, 747651610, 251198478, 146416112, 792891051, 113907425, 634647452, 638614028, 519305424, 5347193, 269175041, 769396972, 18633872, 328228960, 324249051, 639584650, 194262913, 365580245, 58675816, 777933203, 106195375, 905603572, 74583354, 489229336, 332773212, 41026033, 815540976, 316976500, 995861551, 465452503, 704399048, 860459309, 701295233, 768289746, 702787946, 317107676, 128507029, 845662511, 264594787, 936795572, 105416006, 603821817, 411904995, 680534808, 20844794, 391683293, 902451025, 479221704, 751864121, 32067785, 590846770, 412550280, 686389294, 979586319, 567781757, 125435511, 334589965, 818387069, 274365856, 818335600, 688388211, 995735525, 397678180, 475936837, 930646328, 59314877, 911653594, 303419082, 826485027, 227600587, 489399108, 183170796, 873825702, 338318533, 69772286, 260125053, 409150425, 385980619, 187450750, 883459971, 547869531, 966562583, 105331657, 849724494, 353682615, 830000048, 385904783, 305355730, 153652834, 30975478, 617977000, 920676101, 863552030, 864582615, 550486779, 767263383, 572489480, 647875999, 363383985, 687913224, 944341654, 163537293, 716825758, 629235568, 889898943, 995999775, 324188567, 187194520, 63353177, 574119970, 919220142, 356257980, 280451809, 595949319, 400426142, 641482758, 262031, 521586065, 69543994, 398250529, 342254279, 80679661, 645748250, 854888531, 997296650, 754489902, 707492135, 164100814, 79763541, 784973948, 451324267, 542168073, 238606515, 76917255, 779595350, 708271785, 665050774, 359801426, 997013986, 87465508, 105306260, 237670398, 668148548, 681552733, 42805663, 294205161, 712202382, 151268837, 475041200, 464370666, 740936305, 262047680, 201617776, 197632205, 804121146, 984446865, 681009902, 522144762, 388662524, 86529350, 415205538, 111742467, 51407974, 553573153, 397976056, 657043924, 76668010, 509892480, 864115412, 893568252, 868452415, 945431449, 396820033, 569165452, 813741397, 421953957, 216408679, 225479506, 357777648, 96450575, 478594017, 342907012, 311835031, 520906139, 733385171, 991949201, 936291492, 242647665, 530531462, 62340474, 794373860, 246521862, 199545098, 606433912, 731336344, 737943073, 772098615, 112747362, 259707167, 67197268, 264073453, 776437029, 69315328, 279980333, 935520695, 599409565, 355052057, 976635953, 16870860, 247878215, 183742255, 885231733, 910850248, 381268519, 510287517, 704491140, 895310915, 243018923, 693314473, 808734189, 420582935, 666339221, 466947493, 590471918, 998806089, 396645822, 148402610, 347013090, 372464149, 179564886, 131732198, 998378343, 508776184, 861649268, 571612191, 558061666, 905568948, 559365812, 390762998, 575667928, 451848386, 125591147, 440797383, 193865619, 834437307, 939217988, 826191316, 301045527, 62180104, 845602327, 231443918, 322378828, 500759974, 778720117, 896705337, 660411899, 689998085, 763302598, 929403168, 691488234, 618145269, 74887455, 586898694, 927914231, 19484441, 608688259, 844197614, 356028569, 132898986, 773543499, 328372784, 586903971, 634528859, 682944971, 766528593, 878004588, 843321638, 26949301, 257700974, 966429459, 484949070, 74815500, 155398003, 385874365, 821937046, 357441254, 413444585, 921949471, 89897908, 671958443, 536733515, 952751465, 334240292, 686954004, 440027909, 527745906, 233688192, 175236064, 210060665, 891756295, 135516646, 321653460, 590170812, 45055701, 267949970, 458955011, 430754872, 32128400, 792918191, 594208917, 847267281, 301886299, 343908788, 753734009, 587678547, 986080445, 921758297, 877649659, 447170495, 432734057, 53223820, 276711947, 494185667, 684434482, 886802071, 827086348, 378368415, 43018833, 852497642, 958137291, 972202068, 116851059, 813146452, 53318843, 781560549, 550571684, 373596523, 882485218, 74675785, 957797542, 658508716, 465058349, 431786414, 300420339, 738837764, 893350276, 537117670, 404513286, 63677786, 937789110, 947885788, 492881309, 92719951, 796005878, 392609066, 453664195, 967243268, 612474073, 678241553, 130178835, 609214553, 1305806, 149337632, 508470077, 921204896, 61103850, 514056611, 742660901, 287766351, 687880854, 990805186, 714958436, 416369453, 105932139, 192122533, 44756720, 272582589, 673783678, 278849352, 406312918, 529974894, 993649076, 335104139, 976413146, 74343139, 624660408, 269677090, 840659346, 547893220, 491007719, 972796683, 692362985, 127386173, 439428799, 141862439, 523521601, 262146584, 795139615, 270403405, 255438845, 609877796, 17888765, 165597639, 120489448, 944496425, 479394385, 763287987, 616577993, 518162895, 814809512, 474248913, 599185834, 793460718, 825522328, 249456531, 16870550, 971347951, 53847782, 18260255, 62705940, 729336887, 501011516, 440324012, 710701542, 566583831, 718196163, 480129055, 767731532, 411905637, 911332325, 704023100, 707667681, 930015387, 876976606, 422919440, 636278719, 350988981, 719258582, 178436818, 69923632, 230996323, 706269687, 291386979, 344613475, 390925772, 833913242, 793089953, 56340542, 192806762, 197781666, 702675174, 497172389, 106921258, 181799608, 660326219, 307738063, 803948747, 153099730, 333080704, 976367107, 953011714, 691787785, 359365340, 197036160, 935319918, 369393637, 207874328, 364074460, 302313238, 694742050, 683160629, 850365307, 343914383, 845223416, 893232210, 805639371, 950029311, 462055761, 826002218, 224753888, 227550905, 630768686, 164634439, 354049027, 853769624, 968214308, 692529434, 410469603, 251274117, 498121192, 315075127, 874038098, 642476222, 587909665, 835115101, 997643519, 734258281, 990964437, 616753490, 491924719, 292281717, 693524515, 320317955, 903943386, 247266094, 696177267, 797158741, 854566367, 941294044, 485826406, 515425501, 852027979, 946420811, 128429715, 593206699, 730478595, 196841116, 259066570, 94271953, 673946163, 559061031, 442529961, 806699411, 728873788, 486578960, 704603435, 251037277, 425769312, 208139852, 394715076, 622929056, 618638106, 773425178, 656221297, 539781856, 136472352, 713597070, 576588395, 891296403, 133844083, 809672218, 466771256, 921876309, 158461473, 567350, 332360788, 166187547, 879954080, 626629140, 664316986, 130723156, 372661398, 942900733, 248219023, 854569281, 229007931, 291214564, 305039383, 192257504, 785108566, 803998527, 354833821, 492933753, 197782910, 118579285, 281708278, 208909522, 132687259, 304869656, 476034378, 45941304, 875614275, 447883271, 743262934, 82405230, 435658132, 428264370, 406384717, 797556277, 889866648, 620247745, 964990606, 239491738, 879217103, 287694830, 975908032, 853819746, 876628667, 854271443, 998557940, 187234556, 302226831, 2902488, 219095297, 542239379, 127705548, 959032859, 628345596, 205686923, 994028705, 959368127, 169199021, 648340519, 909345064, 587304783, 189399373, 404859250, 67466457, 216961082, 439532522, 420711641, 11263556, 17509430, 216598977, 89871708, 940625639, 77743552, 391491256, 458920870, 863442257, 437160316, 787237706, 863226851, 397981589, 717239917, 962894518, 549050125, 67105413, 51827120, 788850010, 909220432, 648921583, 374536160, 513884469, 793335416, 933608023, 608828980, 747223556, 762749882, 438335570, 65856652, 289138440, 235336459, 845326940, 969557163, 719972486, 910655501, 481328718, 728053348, 519121420, 813716244, 876639527, 739519862, 660845855, 525983157, 881559087, 115240987, 990966506, 590054870, 800522951, 459745791, 969880680, 787543290, 747656646, 282068057, 557326328, 591157504, 806831914, 225249875, 57419579, 876798190, 352140707, 480262810, 327916441, 760565285, 493079242, 592394839, 186778434, 529621984, 290546429, 917484691, 513860089, 549081078, 41734746, 732435642, 403728253, 208117794, 459109314, 57718925, 992892497, 112643818, 427117139, 484606428, 381372000, 696953083, 386690980, 792058267, 478257086, 210653464, 363981393, 656239726, 463007182, 30962799, 259433288, 618191299, 250669930, 276098218, 156249354, 158409915, 506368306, 752435603, 50869059, 696143338, 433086568, 86113180, 955727652, 646840649, 23442257, 33065215, 40869542, 440168586, 526339973, 794868534, 115160226, 985977591, 514406652, 562971566, 604551408, 183976065, 874109619, 922351428, 254056511, 959037989, 358865248, 37966714, 78598190, 835742455, 7744740, 627028633, 993432281, 480942448, 104552939, 965648615, 414513071, 335256350, 544587719, 371601386, 265117608, 562087191, 189167579, 150680386, 121281830, 438470999, 308406480, 341424613, 948218840, 551827609, 796337299, 159047020, 695475657, 190102914, 341837347, 862894752, 960827247, 181088493, 942564442, 306895916, 292450843, 998919837, 634714320, 76801660, 111538059, 779195007, 298224506, 753874503, 248183040, 943290200, 260924196, 496612522, 105881817, 630176445, 392051922, 65795996, 924871045, 91631944, 16048059, 622213309, 929120551, 875307039, 158848706, 178258000, 720267734, 803150570, 43977412, 607521218, 939186539, 719491271, 55119685, 39746932, 328096722, 898037476, 195705478, 787978661, 898462337, 168342264, 100443278, 185297139, 555016709, 274225048, 494561083, 484073414, 246274620, 409884976, 519272222, 669449352, 950286242, 228650837, 887025485, 819630022, 109450038, 852982313, 157908449, 397843853, 918475513, 432162258, 687588256, 453905806, 641484222, 815809312, 120857234, 607252232, 484575934, 530159635, 21382794, 104168201, 610716825, 578984581, 921729477, 553913482, 438482353, 967290581, 147444329, 195364868, 738662059, 618827435, 622813305, 839258693, 27342041, 76879443, 502349206, 149495581, 45461032, 434870940, 709750128, 284152119, 862171761, 901030955, 92507875, 130812759, 331672837, 862417776, 755560399, 219504742, 951149314, 229138593, 401730412, 493215355, 619140001, 858064982, 884762034, 422120232, 808709288, 330215643, 72524013, 494644279, 750825763, 737327934, 706422304, 547261355, 384776986, 403826170, 798655218, 419514880, 960600763, 196914195, 734583320, 217668605, 134665126, 403865335, 121979869, 195197362, 301739304, 862875222, 182146598, 711957234, 233136951, 958742539, 552412762, 594663695, 430177018, 975002700, 859130431, 690678487, 600049483, 996320679, 312499380, 83480915, 475473144, 988387081, 928926977, 780648876, 300775473, 943269480, 564997101, 349733680, 686929026, 858642198, 605101591, 89270591, 205678734, 178450033, 886301092, 838077867, 991221060, 212973450, 612284585, 975173970, 437294836, 849767679, 773989194, 674340421, 144717426, 163023702, 722399141, 598263875, 314792583, 688568932, 453908602, 152766327, 164730460, 611331558, 467396745, 471606670, 870027816, 483422264, 520243821, 429442583, 849813640, 607618141, 962919378, 827896118, 178331625, 888695600, 265901630, 15922874, 396110082, 649583331, 830937207, 60621105, 791261112, 168079422, 489711756, 748588854, 985385522, 71854332, 512933896, 767950191, 12472926, 599941054, 633018199, 441889182, 375446904, 221801218, 88875514, 826809639, 288746131, 870118992, 66981866, 167272987, 859234189, 252902211, 701727075, 716785485, 317599513, 17668797, 331599353, 661178357, 205624727, 564440045, 708425384, 278657540, 491896240, 233079622, 985807386, 781097074, 344725593, 542798355, 488881882, 267350075, 467876317, 142883074, 418962000, 788276614, 76705362, 999255864, 633931376, 174543134, 78982088, 696706947, 260370293, 209117804, 180704309, 104383854, 513967897, 316656700, 309469336, 573888252, 350956031, 698066393, 410901630, 332169164, 422227012, 489899553, 812646942, 349789835, 389741635, 729513398, 691650590, 260783078, 119002497, 278300817, 803673102, 632625138, 141954481, 916681464, 154749626, 481826196, 892669084, 11328018, 282917752, 555253217, 764747364, 7047083, 499818407, 706139669, 927768961, 989313270, 93416806, 686421545, 772008104, 217397902, 622410727, 271788893, 897977827, 410952489, 345032165, 940699678, 871718162, 305459686, 104060220, 608261895, 719476719, 1580942, 181653723, 717006503, 498192533, 813646946, 548968882, 975870219, 385552187, 452539906, 598141428, 890396898, 976840593, 181777756, 484721904, 750110707, 265496406, 502539170, 168163827, 53600807, 606529708, 366786374, 39817358, 921448385, 801412758, 981917979, 523446702, 191281933, 17468610, 200048198, 235118916, 366897640, 93955655, 604900441, 256845572, 624182164, 460175348, 281753381, 41437322, 3091712, 694634548, 494959177, 21048538, 800735037, 927578002, 297539160, 846641985, 235139177, 487774514, 811225483, 901537277, 797603105, 238190523, 606904417, 428343688, 975774712, 409764451, 582378893, 224769862, 647137391, 502320582, 694681031, 510682148, 708630317, 793459579, 170048160, 109306056, 285540087, 184492501, 268858158, 503054278, 633155670, 682058837, 349442137, 70360344, 947677536, 872229653, 131556495, 145085854, 260610960, 338909152, 228431826, 27423133, 693868374, 426010515, 723807249, 437430295, 403482664, 119263545, 991723177, 519651238, 658726118, 581134376, 828217253, 39641908, 775971897, 788233197, 412311879, 507870045, 609638015, 250311410, 278937276, 320844316, 873647532, 263655498, 222321788, 330443052, 53329843, 525207350, 174348371, 616923785, 863188325, 386439453, 581850155, 608281404, 19282529, 993685590, 986096343, 228455017, 55176102, 623254139, 857462164, 402579076, 54999617, 411301568, 925816859, 68443292, 293931098, 899640030, 426543657, 597451213, 96866387, 695982124, 707254452, 690480319, 808896644, 989067061, 843900016, 103513320, 218978948, 66846784, 912571692, 625802799, 300340752, 56588521, 341255768, 714333365, 544625842, 950124284, 31014761, 77937596, 129528551, 42346485, 696959188, 421274885, 512670630, 572902335, 437311640, 430207549, 239686357, 70011857, 158245009, 829324646, 425196056, 295892674, 768366860, 958699042, 670571366, 332081891, 958771420, 376104656, 434408074, 172514630, 87476998, 934423611, 344444557, 265054586, 741003158, 543575231, 704772756, 420654765, 626084629, 880741702, 372740698, 205737829, 327161919, 672210592, 560183980, 264072993, 411684732, 983473927, 796746688, 905938996, 840942870, 951691109, 666030037, 1974398, 54932731, 661793718, 925695603, 240903629, 874843463, 151530852, 383035114, 565695958, 274670473, 203291624, 287863301, 221421425, 993291508, 753191798, 870520814, 22233997, 434745071, 795625145, 217479910, 974432612, 44338847, 169745036, 238805134, 177018899, 505689108, 53708709, 695304759, 769154442, 675655371, 610124599, 101761809, 143824267, 696490600, 633734497, 250224506, 408848496, 823112795, 229093963, 112150830, 493498714, 260898733, 360062261, 298620752, 685175970, 496144125, 359232227, 527708838, 159034608, 166075364, 794734684, 896279086, 851714082, 703539420, 645927097, 742642621, 494964519, 847934072, 250597160, 354729236, 821215862, 553183991, 935604317, 521908995, 859168974, 63054176, 306659948, 495565416, 745039384, 227455252, 97415741, 451278784, 529339811, 462458825, 99068292, 578964231, 275939435, 670079070, 931737412, 604754229, 802391719, 804796879, 546683742, 830057059, 370476774, 944144879, 818288455, 7196, 874266759, 417727968, 528968353, 235911857, 809237044, 413028434, 208933505, 23920190, 577983127, 788854247, 456961621, 747846754, 599741848, 137286922, 346929368, 130497715, 543596088, 289136723, 519440605, 355642872, 804114103, 208317896, 216013318, 403945583, 526333082, 593224258, 912533254, 139571803, 428510389, 656843177, 356530126, 939795738, 824890527, 437165737, 547345537, 188863319, 685250695, 16245761, 206538377, 634288720, 777404702, 804239641, 728767415, 598568307, 335738634, 425645535, 305376840, 399516873, 286699755, 20848175, 875316404, 595800091, 270815159, 394243920, 637225255, 245835536, 468940523, 275337854, 755995489, 264580468, 65634440, 754207693, 616182640, 85591113, 392838428, 726114283, 417795761, 386120651, 603927949, 747122369, 552413820, 928808280, 685156935, 613220170, 612277255, 613744794, 788707229, 984919085, 45985546, 340063915, 904067092, 362974624, 183963321, 463360543, 621507787, 809566801, 878592420, 847477429, 9312053, 566904911, 246359439, 705889100, 745329604, 216356718, 344324700, 477698712, 46049720, 488163638, 67690668, 833175293, 508766244, 913013917, 67302659, 67503105, 716617961, 398106561, 638516600, 148553382, 509966402, 961424263, 271521527, 536979787, 45797631, 252419760, 829484401, 416467636, 176082825, 647524889, 799073312, 127362270, 639764824, 24206710, 523259473, 351442261, 628065873, 998357563, 349654283, 515184617, 170520173, 137926365, 485039151, 463474319, 423577173, 132358962, 804070230, 378997149, 949338724, 405512305, 425988943, 467186165, 683550150, 984772932, 215427713, 134109790, 656717834, 564967803, 693477258, 483100920, 651047885, 238777496, 912457661, 415143532, 396287110, 160147761, 718929943, 106375850, 65622385, 598097835, 308311596, 891108016, 514778905, 15946287, 480651066, 808253737, 986027556, 388267911, 975779962, 44287553, 974193343, 293394641, 654337403, 918881815, 387335016, 379115267, 242854779, 90384282, 787134346, 119265416, 817483155, 984853017, 851579346, 217573137, 953173807, 499729564, 996433457, 66971678, 153669459, 780993894, 141433204, 470912662, 852651051, 622846245, 89036864, 737043062, 880627555, 619165256, 123258613, 920796837, 533351098, 154349285, 439080158, 839276664, 139779643, 458283270, 655211931, 193847628, 310793748, 310188487, 393678623, 843041345, 651595877, 372785867, 729223920, 4765085, 579323054, 830092628, 713835191, 975629161, 26524044, 264271559, 221461445, 188891559, 98992006, 708493699, 565041516, 501136240, 559183024, 326403294, 485857982, 336542293, 244491964, 578563678, 176401693, 312083906, 560379734, 949455924, 571326283, 191324448, 270072833, 596023184, 361693704, 303766377, 171278565, 9864715, 672024780, 741817466, 742085160, 544560521, 333187334, 687217695, 852443714, 447513700, 489965305, 380979537, 610605157, 691727379, 818691899, 646002588, 530894894, 81589735, 283939528, 471146216, 487541794, 404206278, 971712188, 504578842, 525375418, 163047530, 441588565, 16234968, 51907052, 842199873, 214195050, 85625379, 728100337, 869171499, 376845369, 173509981, 443939752, 447973640, 755229208, 506065651, 184914068, 676382266, 758785995, 420435728, 524661868, 188278911, 933339454, 211515220, 398092380, 833143349, 612067307, 569304021, 635592056, 916053081, 207844324, 388585929, 668131598, 227059319, 854859413, 294983001, 525606372, 896047825, 561300045, 819382210, 749974134, 687777625, 241748260, 764393351, 14793187, 140150895, 318036687, 236113923, 119426377, 571954821, 287720154, 678401350, 752580438, 567180715, 123346652, 225918193, 104113279, 728122516, 4486949, 564627264, 742777576, 470263349, 108983572, 271687232, 318628834, 865482019, 679478084, 622465012, 544095152, 468277887, 82806120, 724568267, 726523946, 352724289, 247678618, 979013452, 874085356, 751556744, 754515765, 673625090, 997139504, 686064025, 430836516, 496886260, 874152899, 998611739, 448836022, 798399781, 696409683, 516398137, 975353670, 654072845, 304963721, 19777615, 730350765, 729067047, 872865711, 80507283, 725832865, 276833634, 884516462, 259299579, 275245845, 608662407, 101596240, 574729702, 677085082, 161742063, 540890369, 29906642, 192535530, 776576289, 602121652, 198079457, 10034163, 872662919, 546031730, 66236638, 816269810, 742456985, 92889924, 791399182, 409289038, 285010621, 342799112, 571139781, 553250887, 486692820, 581256897, 184741886, 847257436, 259186717, 548989947, 856030573, 275785965, 5783073, 690579079, 301298757, 205766067, 991372743, 205702938, 993912149, 478160342, 226148106, 942488839, 281380788, 739574366, 734319006, 228945744, 889023744, 876074559, 482941241, 449715207, 576607053, 416382965, 769020271, 888368040, 962489132, 423180122, 269788131, 589768664, 6464419, 290252173, 817288615, 670029577, 939895919, 518957863, 199379513, 569578959, 483122331, 651991350, 807708770, 934531134, 345037977, 507473429, 261239439, 130045997, 620839083, 211913187, 821461332, 558346195, 244289773, 429096824, 603403955, 608196214, 906057704, 91992812, 914513104, 778536544, 830748556, 974418872, 881313021, 373755243, 890982173, 147254449, 803254551, 561626428, 219578361, 234121168, 966084005, 401546095, 334568025, 728950471, 184140047, 80538845, 719217159, 126024177, 540450816, 762567820, 67873783, 204351991, 132418225, 994575368, 977635252, 146167505, 112114251, 360056644, 797901546, 847273587, 411038862, 271337288, 123065693, 270435828, 506274631, 238010520, 225756681, 97946928, 495501962, 111525375, 722475322, 663363243, 151869791, 685437592, 925456897, 831830913, 50512571, 927526404, 585726813, 377890302, 525720503, 972917563, 302012072, 331179630, 981732085, 198830732, 483646123, 186276329, 592573890, 116680555, 811721884, 442744461, 139843102, 243067975, 935831581, 254185367, 370015195, 407260454, 815719404, 314117126, 441478219, 4358188, 244521162, 151654969, 907982826, 667608335, 533012464, 342510068, 874608661, 689525775, 453013324, 158666512, 100403301, 754523088, 936831733, 237076593, 232789926, 269299400, 221205828, 512791005, 11709004, 275837375, 683476268, 576766308, 103573825, 706574807, 193738172, 702658307, 820938763, 772521311, 714902584, 790222121, 616929377, 771463749, 152495121, 784347014, 165833030, 462108089, 911545890, 118838785, 960234221, 805798154, 987896837, 613623585, 77261426, 120187584, 784543552, 652393259, 815707642, 80771725, 90942185, 194140359, 702357073, 968971822, 678016206, 810228791, 691680709, 335407068, 725804688, 509462002, 327630901, 418504775, 909692446, 874002136, 591224518, 770943390, 396494497, 225840592, 474712679, 568610270, 918606523, 818252144, 557611375, 966540368, 137517604, 915666622, 734597970, 606978393, 376295287, 515279572, 266352319, 858342482, 259638812, 219121278, 84450301, 917500465, 276283695, 484133131, 881074642, 878901645, 770461034, 848947235, 353513303, 324926938, 101109856, 888264873, 642157001, 45078000, 96989775, 210254483, 63196183, 688356023, 894956645, 861220884, 587962395, 668213598, 119665681, 398251433, 675694966, 999086120, 683198212, 273468838, 238095961, 148713097, 394188228, 253242693, 795647009, 136897182, 119844594, 808719709, 50032544, 407808876, 738584225, 95300045, 12503292, 997466558, 806285702, 629346955, 746204626, 645326050, 842746471, 190624676, 187544715, 252949750, 18605000, 631589951, 534486810, 921409422, 162744658, 385358203, 376954784, 297332583, 596576466, 72840012, 596407994, 715724818, 880885655, 350465645, 394812025, 864465702, 952609032, 187669261, 678667463, 937379334, 655349578, 41813829, 473174119, 750600260, 979345131, 406062982, 884754603, 800616963, 598215418, 672358486, 477694185, 86179939, 526961051, 541989700, 223941133, 359250937, 392125427, 181619185, 870503861, 685565454, 431301204, 334514534, 268456038, 98248982, 451875485, 290492944, 499607938, 854674740, 648606263, 598740156, 477211256, 155020682, 302868056, 207140483, 138633125, 658929923, 631884921, 311758821, 460928872, 131791182, 53335310, 559540138, 994819424, 475745322, 393181644, 829606487, 239769124, 662905965, 585113031, 978814053, 641962504, 464405049, 628921583, 101745000, 874207344, 371388886, 453252949, 456029037, 873458325, 892537860, 603411979, 855613838, 502920570, 838346438, 15437696, 753073362, 644365174, 322463141, 141346544, 14527871, 276469594, 666840280, 759650337, 620631333, 287496652, 852123074, 125920564, 557324973, 677418029, 656191506, 798998440, 209455835, 913064304, 465497406, 895911052, 391951881, 860321034, 646783113, 66189039, 555804336, 343227258, 800171546, 849684073, 430996071, 318349993, 483188840, 587509292, 767872198, 341375158, 541950523, 767793476, 274386856, 100254917, 104727740, 395302263, 449899356, 390843379, 863329313, 842638414, 109103335, 441915923, 990730438, 554759896, 268200411, 839125055, 513600857, 945434841, 251388263, 307273628, 295898667, 945817410, 90936555, 373432336, 108214309, 926053611, 564988946, 669829542, 123543438, 756066419, 260631543, 955870155, 190715, 724104638, 585775255, 213300477, 283216266, 419709842, 975664882, 448612339, 71274640, 27598387, 94291987, 689564862, 548846689, 175983219, 240276252, 290199229, 394538687, 256121787, 143009432, 367438287, 394442563, 717471595, 209714222, 360434935, 759874372, 765051980, 573432365, 810746581, 715663005, 710010712, 2763857, 481831936, 661443686, 95870374, 132516411, 880559774, 768503402, 399817133, 540463548, 844118813, 294850596, 782850195, 689819606, 726316030, 929551008, 544916256, 441345499, 337263069, 942843636, 961349906, 810245984, 409859617, 403634314, 197070363, 636858187, 219616804, 364343620, 272326701, 709793631, 555674260, 596338922, 93668999, 678707424, 105172622, 738240378, 184169336, 7871361, 773418172, 144385151, 559938344, 342624945, 903250965, 980799402, 664392122, 9975315, 117967570, 876600930, 518678823, 887314055, 924462563, 740080433, 347010148, 907877187, 990812087, 876308627, 763008000, 736172163, 122521294, 806475115, 831140680, 274879792, 39869967, 779150239, 232861936, 387763827, 630654987, 884427889, 488325117, 427315126, 694880138, 739844175, 452514992, 956608783, 74956031, 619535825, 487361279, 219641237, 499595949, 299466294, 49004948, 290132491, 171375203, 928768348, 68229757, 288890792, 988466136, 583057039, 984146186, 799107945, 928032089, 894103602, 871292270, 328090417, 211144895, 348212316, 693270394, 977787775, 359111950, 546279142, 332189024, 22152623, 322392025, 175957409, 689972732, 916707147, 735297369, 174035272, 638381075, 447329618, 38039822, 362833245, 778764691, 743706250, 934681343, 191923322, 141578303, 259270111, 566616804, 815187344, 241029196, 154055420, 327307145, 174591000, 727167689, 404140967, 792025457, 829077588, 671289435, 312569320, 835069383, 5447096, 256222080, 416942274, 331572399, 918874728, 987799633, 491290092, 992672333, 939429871, 336987329, 599798227, 751748057, 48623364, 660906491, 483298529, 790604907, 931970346, 384818392, 500389663, 682648397, 687212261, 931635093, 63561014, 647646529, 66429847, 111976858, 604910209, 506679375, 555515669, 123847693, 44492632, 178847708, 946204343, 845354283, 427846975, 690556757, 914308617, 189403235, 36675450, 542238247, 794804663, 577442071, 517924905, 795204990, 501340080, 613354260, 854322902, 571260895, 510260438, 414373757, 959194226, 105045310, 477394368, 72800755, 445731641, 103854338, 841523771, 957791852, 191532511, 961580297, 388877143, 102309775, 428357400, 830081461, 563818151, 866259007, 485835690, 30082297, 948589886, 562392830, 499109369, 58433073, 733283579, 36428328, 742298882, 982643403, 593203780, 144755224, 578059814, 254472399, 22301867, 789998879, 735889165, 918792549, 557462809, 552573722, 576530981, 680153828, 916392479, 646974858, 34567001, 994679482, 9460630, 972487263, 300018493, 640747865, 657751837, 627670811, 587663859, 814605409, 776005740, 344540768, 914442808, 323409866, 565987127, 539745133, 675037315, 450123788, 413095721, 54159360, 368457255, 171562353, 621533236, 59200583, 982705473, 142943196, 24181977, 786801377, 843283079, 40385945, 194742271, 75718708, 644665269, 829591822, 640312514, 509973082, 836543579, 306452012, 813042080, 944898820, 550143784, 62021861, 992978935, 196696601, 710776674, 757759648, 788128770, 508886684, 407131667, 523136459, 620527910, 480558764, 915736219, 812216291, 91417414, 520775627, 949658687, 84409460, 816577062, 384304457, 930699848, 511428540, 836975433, 968245972, 453251047, 921779564, 216048536, 494252696, 254735994, 205744844, 981264789, 990061028, 985782286, 822067443, 316563393, 763292217, 708024504, 693075248, 99141092, 956296872, 55694579, 52732834, 308486669, 557081203, 58042609, 935091786, 601181323, 938701215, 779116109, 989803820, 873890548, 589353904, 723945581, 876703675, 211910418, 896307042, 762777210, 278865821, 110798924, 437579393, 628929110, 829831404, 526410075, 619011952, 978008449, 65222966, 849172173, 144839480, 782970345, 398869366, 641298141, 698001818, 170673426, 345647972, 659858130, 112495963, 432970454, 7230343, 585967399, 715821978, 40623996, 971749782, 842350030, 580042921, 989912562, 166642836, 973760291, 161765884, 782228883, 527819807, 138626752, 850353393, 333606921, 648705625, 47313075, 266982238, 201833381, 308526839, 68814931, 927686741, 262022530, 535614874, 863188936, 616955547, 104202132, 171104622, 331238109, 251912037, 286572272, 573456646, 949203657, 53043725, 806243760, 203265019, 876486006, 948937495, 567449238, 415256129, 988070406, 968023790, 17019473, 248737963, 120681248, 583983950, 153993219, 201935152, 136164457, 829871955, 626291047, 394802246, 260007922, 607931843, 24306224, 28575069, 225321218, 908829358, 169220022, 936512506, 665776761, 704549784, 698417525, 255461139, 163951408, 261229082, 220008280, 348623912, 807148420, 371106186, 366690995, 544609152, 213870993, 408196963, 754669215, 399795747, 559323631, 485832609, 350352952, 721747050, 21631935, 355573914, 206023787, 964425951, 691307920, 159549218, 671420169, 951126219, 634927534, 643582950, 274406843, 632962879, 760518512, 229811483, 390881175, 924757771, 38194303, 293272202, 173491328, 486019127, 734258251, 387215108, 437262928, 728554527, 275024192, 248976244, 343245733, 701258706, 170540138, 465617442, 858198203, 574360296, 946008040, 664094170, 517178634, 693040995, 799594735, 255316661, 449678209, 87199479, 511287441, 125791016, 282384294, 785396986, 457604138, 287610759, 723403051, 10837888, 746035325, 640711757, 995757787, 2202152, 917093046, 577936335, 648767243, 785286990, 635011419, 695112654, 374068143, 14921666, 440382233, 660237890, 526475247, 957351727, 252635667, 812396571, 412310376, 326907154, 30634198, 706007029, 970271608, 580512741, 972748916, 201325968, 314261339, 716665373, 962091777, 486226702, 273466370, 840975366, 599150520, 164993432, 484979571, 418559139, 363203519, 162207943, 208330032, 473511398, 794841071, 171891390, 336414769, 600986238, 936969299, 859143400, 350403043, 292803417, 958133236, 937969576, 384765730, 741217260, 719124565, 511975130, 529929688, 872979520, 413094461, 630884202, 651374826, 857264663, 228977297, 822943843, 77199492, 710743715, 932154071, 658944343, 426960928, 905863513, 849222023, 315065974, 933274562, 40403835, 803059944, 407747168, 714968487, 955036691, 961766212, 307500705, 475154160, 623864479, 399106155, 274460576, 874887932, 936834756, 339899692, 94033093, 512791616, 159687579, 734508020, 867806917, 575669353, 479473359, 574347008, 79762627, 134124861, 471750395, 165249715, 875142716, 792987970, 24874855, 280763719, 405529976, 351781845, 254659557, 344786449, 430895550, 933134790, 249828212, 490208485, 678075790, 434169584, 949903024, 747154630, 302454525, 893883097, 226358666, 752566952, 839129014, 742747936, 33190139, 395772530, 458036737, 292028714, 192074274, 74568408, 403968414, 748157558, 257293201, 281945344, 653838435, 6418166, 891108797, 915633643, 346851287, 238668024, 519068579, 990641799, 785190834, 689000043, 617317650, 214079151, 651673204, 509008143, 739303645, 839388246, 925063421, 921156601, 846270348, 23338925, 77029027, 980991821, 827897533, 469982935, 53943776, 846861414, 697151374, 165612553, 633591435, 796789686, 94826135, 191030409, 643245772, 130417543, 247948564, 119420540, 580850845, 676206991, 72685894, 636684603, 927693599, 49440245, 847822314, 682549684, 556752146, 961680458, 169120186, 531127546, 728504491, 155076752, 472477553, 26185430, 314397086, 593668662, 434302073, 803071656, 166722904, 728113321, 419246569, 823603977, 150361255, 524260741, 503555043, 714625615, 899435873, 935657071, 874663104, 400776830, 362487258, 525738000, 760317843, 548463811, 885266979, 839427412, 433041928, 412050312, 612894997, 821381333, 652561053, 229504992, 846168965, 640505243, 931920981, 276540988, 449906316, 911718584, 415403493, 558731555, 210481417, 997112380, 677146064, 356596017, 440393803, 795920226, 536832024, 380483176, 750339439, 586263421, 998945515, 742636966, 19095687, 544759610, 601077107, 910875650, 945314815, 63859444, 662491110, 300032016, 403559725, 419986460, 776754797, 628474677, 467268624, 829082135, 908578842, 585907583, 789607167, 744806186, 183096567, 761609482, 249420887, 836197476, 253923842, 308179723, 450254095, 243805445, 266396839, 346532591, 905313627, 551598215, 702201115, 726758130, 687676614, 236631803, 640582483, 423115271, 686022811, 633283961, 827195312, 15568263, 353725033, 784509879, 492037019, 149962977, 442760370, 802224471, 84215802, 419503084, 192316496, 71993407, 898152326, 526961975, 549858601, 420927066, 647960203, 952264125, 611390294, 881248879, 420701208, 60215625, 141109577, 140160557, 666087815, 899711095, 497256422, 239930430, 321162812, 247695959, 381869073, 479077357, 90739426, 900726892, 976853294, 956843221, 967708363, 216888022, 867880771, 358897449, 13482112, 922833301, 106553674, 364182536, 125102074, 136642006, 688150639, 908680559, 829094436, 783161410, 568528323, 465539993, 312580456, 995303187, 981020101, 163170974, 610314979, 514265265, 891956656, 534089572, 612165061, 474487037, 420431481, 81497077, 710994339, 499216688, 424426240, 487816844, 567122801, 892902782, 26150520, 808970139, 588523652, 958430586, 105232988, 52316094, 34727794, 987544946, 87835266, 680533528, 263981250, 834389173, 899284767, 953714733, 713657205, 540007592, 214744952, 937463253, 217212870, 326849700, 348041291, 65211132, 267468726, 437899834, 547960261, 634687043, 392830359, 329034061, 362074703, 328208783, 422784216, 932991516, 547859838, 705978615, 566715229, 113056206, 595149478, 241510837, 687025596, 152375504, 236767204, 922545066, 426562337, 764458519, 378479846, 490049868, 837941031, 791007688, 249012139, 383285845, 45636102, 911597607, 203463101, 989067196, 692922359, 203195107, 451818278, 508067011, 342071527, 910130955, 137533350, 352096990, 738630796, 869751449, 86932798, 340287770, 188560444, 307565626, 401961661, 224216713, 621863829, 842680673, 571616418, 735386469, 2994442, 554920496, 363702774, 583077970, 171947489, 823150020, 823902366, 111183003, 398388622, 522257152, 566670610, 788013440, 590697365, 640831838, 39024039, 912499884, 8811370, 62327191, 687633831, 304313578, 981335386, 482320016, 206110601, 332061080, 718366693, 329269658, 164039620, 390897235, 57110029, 241165783, 701173195, 435585244, 587926996, 578277565, 506059373, 823881904, 588590690, 840384877, 75079957, 338120657, 579233837, 539072223, 792473388, 668530066, 291709434, 495383836, 823482821, 358797138, 975488661, 758708968, 925414921, 360134510, 741241064, 37619542, 682589918, 48862538, 570095291, 763958119, 621446693, 354067065, 940041555, 342589058, 638973134, 749428019, 399463367, 889464314, 664903991, 720245045, 306576824, 230806347, 880052144, 629948087, 913718898, 476414358, 697858195, 61381550, 61461081, 859594576, 587650728, 998124639, 306126281, 653894853, 307950863, 14633817, 284023905, 590365765, 545910454, 819049149, 573339380, 646451912, 641630250, 724397922, 708891862, 635458180, 129075787, 767080136, 123487615, 882529405, 675313439, 703226753, 739187981, 853046248, 948038338, 643249244, 768863064, 701097138, 75531109, 102341767, 633534452, 24761866, 736101180, 901665193, 778152980, 460992832, 464506199, 203942172, 559441245, 327089644, 46981070, 890113926, 75116040, 972911787, 675457626, 551810784, 861759921, 656744224, 150777945, 234041263, 870554880, 48222598, 274714785, 922810899, 77014428, 475706068, 136451449, 515841741, 932306844, 653963566, 648096103, 127387380, 324983733, 264651335, 553422746, 527078004, 555777622, 760112411, 813247311, 771462213, 877911242, 904042902, 217633781, 173158697, 584727329, 706707, 610046718, 40515473, 571061819, 293189931, 721063574, 684877919, 593336402, 518410949, 673907818, 514645308, 856952067, 317852271, 563922201, 629861151, 336665376, 506707673, 833158059, 918759307, 728126286, 600815654, 746718612, 530026694, 73916388, 113380899, 485324156, 819072449, 60419600, 317004428, 673267345, 115082905, 650069318, 692402405, 370925640, 260504939, 968442637, 690558453, 719518542, 845572865, 44393154, 656342609, 706521349, 675521812, 920522813, 74338647, 506450328, 303648011, 414981551, 990147473, 903752679, 656120861, 373969947, 460605808, 218197943, 343657869, 801041350, 365256237, 186579864, 363974994, 33095639, 248969511, 596486751, 976626114, 175936801, 398791517, 706523353, 305891304, 324467721, 605883243, 102235086, 670445618, 421578110, 937202171, 861036786, 629395370, 902333728, 851475660, 848159169, 604164741, 546868877, 481435383, 819203296, 92821429, 532217465, 782357409, 639142220, 466790988, 516584104, 61030522, 112368078, 37749876, 701033099, 104647262, 858917270, 999384912, 71321166, 476244126, 830106372, 544502078, 420715197, 460469625, 584895085, 148621123, 385574952, 705794784, 476184414, 22499926, 661112901, 689485482, 740713953, 496915368, 773467369, 659268335, 852433556, 733186459, 679050719, 950680433, 463354019, 838588445, 632758605, 380703242, 443091731, 863618103, 856823436, 715628120, 877256093, 615311867, 183404594, 831364448, 670076213, 283444682, 536917618, 946639188, 474329183, 132762094, 377620255, 20938794, 630938362, 728185366, 654971181, 659659924, 474502329, 399361003, 831846199, 866451000, 528151476, 698318225, 21578227, 13484903, 386393512, 932173833, 159886041, 611743992, 481581898, 821427954, 476051379, 229569326, 40498099, 722860691, 580949579, 188563007, 361986406, 164323131, 855539550, 472627050, 196008803, 448757672, 60147938, 380236897, 342414189, 992665181, 854067633, 537199697, 815002180, 949668564, 995420461, 252792146, 506939191, 588591261, 465239896, 923936433, 459213428, 790016887, 953428129, 198562045, 134433120, 390731329, 237861089, 352207466, 198838063, 650966007, 907524701, 973836631, 194280773, 313362887, 841713715, 741555664, 289571749, 182026438, 676853213, 338403868, 971741892, 599536672, 447400313, 453102960, 388256185, 540775774, 135006146, 832590058, 856498157, 513902142, 748409569, 437107926, 150070716, 197283110, 89733469, 981088839, 287384371, 890684329, 503581152, 112951890, 386935, 223185113, 820225465, 180025191, 261169410, 498382002, 882687321, 406839741, 902823003, 224733556, 624419782, 921001849, 924363120, 371344149, 384057924, 107488408, 817392123, 560377711, 150550232, 727251767, 484686273, 795929620, 97335536, 690323329, 399346394, 651586337, 100114919, 189352689, 403674965, 778330339, 955315906, 458162032, 88324999, 914924605, 543829871, 640807812, 422743119, 724498518, 64719281, 858268302, 422233699, 462267402, 988865491, 687690797, 113871494, 423064530, 972072447, 43486560, 278071456, 984831690, 818741308, 82364960, 502040092, 729686853, 617882051, 628893994, 233796161, 558171484, 443469250, 915910912, 872876582, 206772666, 966593565, 306375982, 989755171, 176775937, 225837963, 77474066, 948191818, 117085995, 173420583, 476397306, 912878478, 521710220, 132154911, 577540016, 747417741, 748470411, 103087652, 775127361, 622349710, 851280213, 310066490, 674759422, 166691120, 652824521, 449089140, 468357719, 969748336, 380534571, 807099450, 296158404, 220916255, 823203704, 944496576, 521983178, 956426189, 998398177, 617619846, 156418679, 93712391, 362638936, 753430600, 26038008, 466165272, 328264083, 384970500, 819703612, 373541233, 722749887, 584543402, 411704180, 165278640, 306712970, 481492020, 14792935, 994039037, 778079817, 10797187, 299941497, 135937569, 23554048, 624234941, 44403889, 594511540, 778366993, 341523603, 505308650, 439021223, 403041835, 672153445, 758973978, 449806207, 496684321, 645325154, 351693378, 596645329, 313193861, 664630058, 714591689, 600853143, 815744859, 113013761, 919272573, 801116015, 665991004, 517341576, 985084526, 809821486, 282384491, 58315628, 330791718, 428356156, 814152980, 868066649, 531323996, 23821439, 675287952, 273833187, 389878180, 946274035, 291083151, 333883021, 186152604, 573417850, 808374986, 775059355, 799597656, 819308879, 996826153, 806820696, 54120541, 635740259, 357873666, 545269632, 605499640, 671166872, 461812857, 114856031, 133484564, 206773696, 836706678, 342845268, 414529581, 897124006, 816038766, 646947121, 945231149, 816991153, 892650799, 47249382, 162285210, 95957867, 767761183, 993420812, 635432003, 323889691, 450636372, 388490735, 62915124, 203797467, 614608242, 619663878, 968085565, 995891825, 490866337, 15929608, 122271888, 795415673, 356177681, 784433321, 570130425, 702662225, 122958230, 819513736, 35730060, 894722321, 975275319, 763543796, 850828039, 334775150, 492257525, 959334232, 237013909, 305682828, 156520940, 35991473, 66198886, 281137634, 969016320, 782453162, 343968108, 243713420, 374114407, 516562255, 352288841, 666834571, 85608581, 803140843, 242398302, 31688794, 804221635, 361036875, 249129344, 993671805, 609750962, 446212271, 485951259, 985671232, 577935586, 862199000, 632148540, 279508034, 721746014, 237200564, 652212722, 87685516, 25143314, 398122225, 66972651, 491896791, 220593876, 539336501, 663497910, 526153292, 269715156, 495593716, 42621373, 855786274, 90687105, 780527801, 27806373, 438172694, 301675144, 208317744, 817116931, 752722689, 429310674, 258181958, 768977567, 283628015, 351072331, 544837875, 760515204, 331136661, 938022905, 429787769, 48229663, 438247536, 589444452, 904963613, 822375608, 920165216, 510679307, 129785810, 628752487, 304822709, 647592754, 54721439, 970901985, 654793480, 677833424, 928274087, 187702904, 564833637, 753722930, 537256772, 914386439, 564632792, 806678587, 218615742, 712809008, 18456551, 606560007, 652254524, 362382103, 225610908, 45108532, 149382676, 311793692, 449915414, 460217855, 404116920, 979543882, 158669251, 874690777, 844661936, 365098734, 684341563, 849928485, 221425130, 759669828, 361040617, 762331829, 657807221, 960325681, 988574631, 90801365, 177369198, 847767572, 246623445, 838601621, 930521264, 119407793, 593388444, 489313410, 448574489, 349496338, 476886260, 204618925, 798812712, 948800524, 982903132, 817607822, 122145922, 939011800, 761150305, 768746374, 904255629, 377328698, 861067152, 565840120, 814080805, 846197143, 100070009, 115121747, 4794494, 437869142, 125923431, 909143679, 215445248, 996053455, 714906352, 113136051, 344378635, 897365626, 112980894, 912468444, 512974104, 790273993, 820982727, 149344919, 860445130, 603826364, 17524662, 71617417, 668881656, 691324148, 317772586, 989487738, 761531163, 573906794, 283745905, 843418579, 855624374, 80911880, 579115416, 723709971, 761375577, 227640224, 806909587, 198799948, 429370687, 416547153, 704520613, 522049522, 388032450, 878629882, 405575040, 389638498, 435374108, 95257077, 232218936, 186557331, 384518599, 722751421, 451478752, 987891555, 411215134, 319701476, 626044609, 929851570, 696956615, 593719023, 165631373, 31113609, 277772666, 384098694, 681146999, 60579862, 27969567, 199669819, 945161475, 463130709, 536779528, 9918650, 452184757, 343552320, 328368690, 172775376, 534360189, 518240281, 222148990, 168915281, 22111349, 54850381, 268094778, 721281870, 373897306, 674275086, 231091274, 985059674, 708807550, 465793647, 252820800, 995408259, 144243848, 787001796, 142889231, 920236296, 541023273, 827037954, 725236611, 702586499, 458556832, 214444598, 177376678, 688758570, 889195801, 325250553, 494992, 335245354, 663800100, 553846389, 713664205, 40795768, 713040466, 352133193, 257962983, 435161560, 540558180, 148467171, 824899859, 591623284, 287770878, 844592551, 597840141, 756672696, 125161684, 77625643, 727733629, 677401932, 977002146, 475075822, 547839372, 487390404, 359103874, 820885348, 573672410, 959547848, 964485433, 755110607, 391081756, 414992551, 225702950, 87427772, 754353808, 549197043, 810235068, 994782119, 700626406, 727978273, 728394893, 66314870, 678146814, 864057926, 319734341, 972070207, 114557696, 30985117, 643142626, 697571160, 404360373, 999781036, 451921543, 196494961, 121389722, 583451070, 361961662, 550465955, 499291816, 763327108, 400808047, 242921605, 872574074, 228589764, 438866545, 753842, 226530700, 286017299, 956966107, 569283358, 952846502, 9105751, 368453422, 299372519, 261041244, 878080173, 773411448, 314011997, 852671694, 657067561, 401471727, 704111140, 645487496, 996917309, 851595852, 114532715, 940287214, 5412057, 176538797, 182618370, 354439696, 170946495, 210228363, 789932920, 724540540, 875873137, 991543791, 59365427, 957541799, 595436325, 595178129, 646449991, 999135056, 755600978, 466862105, 521342747, 622443129, 963403392, 332147557, 629948104, 287601044, 472243910, 751373365, 589991470, 770609168, 255927480, 242694466, 705231654, 926559103, 417379338, 745872627, 985551716, 587685809, 309817047, 574440066, 955196538, 684384664, 535745911, 3869235, 65638140, 766068824, 127804175, 998406814, 416767052, 623676990, 802239553, 623707060, 854335206, 755612068, 314706117, 430011066, 80602555, 667295792, 39906305, 654638183, 860533618, 461805653, 570673212, 97563302, 144850872, 712722693, 654225117, 395554701, 110128394, 143624490, 592734389, 985680928, 297547688, 940039435, 140966669, 837116361, 123340973, 905986838, 512456135, 49845206, 938100224, 83103860, 755892854, 683031408, 482697864, 883298326, 223001629, 334618454, 723478739, 226763291, 810665668, 664403323, 61829583, 602190449, 298713246, 927340639, 253523770, 653593048, 18338981, 671532829, 810477206, 51578726, 366403504, 635890108, 586673215, 883907689, 446026920, 82860574, 858344365, 617077824, 281208964, 146278779, 703798050, 436195336, 917055911, 773032465, 40973761, 233941271, 176759421, 977889077, 803613325, 622223644, 729276593, 985427806, 538269071, 854683567, 946551100, 656628143, 686292560, 907040331, 829731296, 437748484, 973992568, 141824555, 794335140, 827409377, 294099587, 386553357, 232856843, 950893595, 882814603, 143094950, 196402292, 195292356, 154475156, 415621172, 337788857, 757532708, 836286159, 327559762, 398027270, 93946094, 592488156, 933427054, 376944623, 214478089, 814816713, 651659755, 540363005, 735017108, 630485858, 743448954, 518071660, 308072573, 384779151, 270179497, 368075025, 777609333, 259367444, 192071033, 852146396, 527426831, 686352, 910339518, 768960781, 458014174, 873725932, 821371367, 961874001, 323862525, 599315539, 976190282, 244224318, 562162857, 390681672, 903476493, 973667245, 747892227, 344239338, 598342065, 181720354, 660719179, 853341242, 721247596, 817576524, 646629034, 369969766, 275490552, 542983348, 391694266, 312587840, 577918652, 483013297, 222577962, 246050625, 550021767, 631983411, 124676445, 403831237, 30431663, 202772267, 383986644, 418308562, 537984796, 639572477, 981804859, 122946880, 661104476, 795495545, 153912772, 531381974, 718905464, 268540152, 562579601, 702517233, 236615789, 593694061, 842220953, 284363147, 445436719, 189572020, 130567489, 134639331, 345543873, 973394064, 165956637, 278797541, 384444102, 217315862, 83807333, 326981675, 484164694, 80165886, 511387076, 750879124, 622351447, 57149934, 572776425, 851344389, 492686069, 764158670, 100337843, 811227648, 367243272, 849258581, 402510371, 4923888, 214958230, 981713433, 833733153, 199881005, 141725982, 930995332, 60004419, 858554703, 787094236, 781794052, 237227928, 225466738, 427926591, 482129408, 443739531, 43355532, 337453283, 804945489, 2491058, 249849165, 398913822, 467791624, 400509065, 459581367, 962990925, 690989829, 364169054, 895165168, 532778156, 662061056, 198905049, 304037144, 462461953, 579239787, 826514406, 298104478, 400743947, 996545477, 389017394, 156585037, 231349437, 894406530, 699143037, 281860178, 240625350, 658017814, 183144767, 37835281, 982306868, 823892625, 538353285, 22085152, 540260334, 122756032, 939637118, 661357847, 152499782, 652415242, 711829352, 160895697, 833299055, 380043790, 61047311, 455280624, 427003562, 127377627, 263371423, 352265402, 555370632, 3342546, 546515490, 915170071, 320970482, 309331195, 866003123, 445329210, 239760193, 270145790, 262699349, 109063579, 293605958, 28028742, 43108044, 714531802, 292831882, 5258158, 960578706, 174313495, 50686647, 38306937, 263794623, 34698030, 545961364, 417771782, 432359561, 595953435, 385752188, 548660554, 285702298, 673161030, 608012755, 205230966, 498956144, 368135075, 216958840, 446938231, 568591358, 331547128, 559376318, 68611527, 665301170, 34844435, 516892973, 845043683, 240248260, 401307982, 567153471, 960405747, 153609039, 857419861, 118309051, 547682379, 648148426, 991952539, 882545773, 184061399, 999070781, 765982521, 267411076, 419502384, 124165446, 224058051, 857998522, 14496073, 264213459, 986820692, 570282129, 211753213, 245597268, 930143204, 774551498, 514652876, 925073693, 921086628, 640773887, 73060225, 529715420, 40958571, 366734118, 683946677, 432313285, 992760200, 784693488, 930677383, 619151604, 805284759, 457772432, 592456091, 485100032, 955898868, 391900453, 219676832, 562759638, 430856434, 967077015, 421103699, 992963917, 110482359, 777569921, 470580703, 460032189, 233271275, 82572015, 650552543, 189372307, 550063160, 647746980, 236384115, 179347295, 402139142, 159629222, 273418934, 139601570, 639676421, 652064016, 84453428, 465043456, 114055612, 584001438, 882590566, 676394963, 483216179, 745966194, 825327985, 985623490, 306947409, 409524159, 138263163, 64619898, 417338433, 406408681, 176380047, 442151325, 151506186, 149746198, 474173500, 102746034, 226566556, 996627825, 966584070, 365471770, 849933266, 413800255, 598244754, 126970922, 185758186, 706461626, 401986302, 678089530, 630918032, 620166883, 400240225, 221398836, 433075871, 195422184, 666716900, 602329513, 751455164, 227663599, 121331035, 46276718, 596554704, 50099848, 554281974, 271420442, 500849468, 661363368, 634675694, 460763583, 913662985, 991783536, 333018579, 731640294, 559230455, 999669244, 758691851, 593952435, 511148631, 493139256, 94739801, 638739681, 281785165, 660608903, 886479304, 978275634, 683136324, 434348291, 724037738, 886238552, 683542926, 3901775, 770688715, 985889474, 744394045, 687499632, 112022925, 709757837, 808444152, 388990657, 414047616, 771749579, 40009897, 498367058, 958240729, 510152993, 969036435, 944212125, 311926042, 395130471, 761896151, 180718861, 980058142, 562067677, 69013272, 789419877, 169030287, 934204461, 315969032, 819974762, 550314188, 144251778, 822839592, 632707453, 420496940, 348080391, 772142856, 290303779, 943238844, 849751516, 485101918, 860570586, 469092857, 46109389, 874054586, 699654764, 761626656, 568016869, 600632192, 355393880, 762871144, 90723412, 421396573, 821959691, 688529170, 1176013, 636078683, 112883067, 320579043, 381618296, 65758063, 25110816, 490864813, 386913272, 267005790, 562375298, 289107207, 762698447, 434785338, 856447011, 259157584, 270443820, 38413935, 900862060, 219634624, 624575829, 287227775, 972836461, 345965740, 122320627, 994577485, 892542517, 410959298, 971836054, 585178827, 117477242, 84885627, 212011083, 294328681, 180829844, 579330251, 12516062, 70827964, 248185109, 531725514, 74432849, 906905354, 514687983, 780610483, 153238624, 849709297, 946298535, 53595615, 745693607, 804622002, 54756627, 43445771, 681610311, 38927291, 250831651, 92816901, 208539633, 621293214, 38923469, 40014046, 94843065, 835306181, 420634293, 34189616, 137708148, 520134747, 933145517, 831535807, 123049281, 651596986, 290989476, 517207984, 479116597, 81926487, 304904974, 813467686, 898725379, 136962177, 297897895, 269825097, 250849752, 841034435, 52275124, 410518997, 430127781, 228071649, 857447845, 538068858, 870164542, 486173353, 408732220, 508445817, 690253051, 460612092, 861451465, 825936684, 792543852, 33860420, 246938348, 74650582, 274397244, 779003226, 47608585, 373548413, 729452187, 450947645, 64419561, 570761831, 893669977, 512129496, 560247894, 157216026, 460511522, 286346537, 125211998, 68607530, 453266903, 322374612, 609662657, 941008795, 447510415, 622127857, 232525273, 271107278, 146650050, 798543450, 199014443, 378559878, 2556259, 485621987, 525607726, 982004596, 891950318, 691909166, 986595406, 477928614, 879722556, 343044273, 843756926, 934192441, 734762611, 451061712, 218968049, 164305574, 360301957, 346527467, 3541627, 831749710, 554744489, 863022260, 469664021, 195610995, 716813815, 468569610, 505213642, 891866880, 497163608, 516967543, 663054584, 17592232, 266839037, 75364631, 640890895, 42432106, 400458258, 50573085, 635496654, 987670980, 54635066, 106795671, 287172203, 407075415, 987319132, 14555118, 364617675, 762036431, 130174471, 746255821, 523371353, 192952137, 917919583, 592421069, 260621830, 727676083, 718418651, 478613439, 341651556, 32387074, 33993304, 670410400, 778137207, 816385576, 779768161, 348218763, 558107106, 377331256, 348076380, 463754910, 968312238, 623691316, 843438135, 192144111, 263062791, 8396254, 188375947, 268693563, 655663148, 980204049, 662748233, 886987069, 500848743, 127991937, 90328199, 655925105, 802214454, 551894196, 338525449, 272553358, 89074570, 403690229, 750680529, 963767653, 348220040, 992991157, 481705836, 368971410, 520848735, 487146815, 200981416, 473334755, 102479729, 150311732, 733699420, 994750700, 701747533, 176834944, 953437533, 290193853, 770726758, 323588193, 875700073, 247099866, 94618591, 244764061, 295905921, 730670025, 438770849, 646314144, 167970305, 672538052, 707512052, 247123584, 608636102, 66828623, 932791585, 697725469, 739802925, 417783928, 530322736, 689774871, 936311568, 241103937, 3521906, 943169413, 818582953, 441718464, 736967953, 32964558, 876680770, 571792946, 877812978, 298006531, 946872519, 818601383, 397880826, 306917487, 974441601, 417490162, 596268138, 550148939, 728347200, 525715189, 252588339, 159300732, 908036027, 485683162, 319262407, 650688839, 444978653, 675148744, 663825138, 595867279, 601918782, 509387871, 387643530, 252143331, 175342659, 369316536, 955448187, 468611249, 827371036, 106674969, 792723706, 921717691, 261315152, 438355800, 536649863, 118600045, 580022577, 837980446, 915027864, 488953072, 166942234, 121702104, 282827493, 33811094, 264601835, 697395753, 758331025, 460562419, 661776659, 603126663, 135508693, 18070721, 816161078, 43800422, 745569448, 297127530, 252617221, 409557014, 504670446, 880394325, 819534188, 449546171, 669337584, 820619341, 184891006, 809311187, 159490172, 934081215, 471144905, 917871470, 383249098, 767639231, 501804806, 867699982, 97482663, 991894058, 502902913, 457924233, 235772728, 120059640, 471404572, 418640164, 796749337, 884715396, 373490539, 315204547, 875694208, 882820176, 571585124, 795112399, 899878622, 950346063, 734371932, 435264627, 823235001, 764596698, 944984736, 724990926, 518324522, 208374588, 143958253, 295957868, 997607882, 622113846, 89409853, 324426646, 526812725, 887937857, 9242879, 868877127, 391738492, 565950121, 291059769, 922024566, 415464520, 551954645, 807666712, 413521823, 228025840, 526452536, 562960385, 906565819, 803103892, 666267790, 929723599, 976953569, 111074976, 429420284, 837161900, 312739976, 12447175, 74041168, 687543860, 633979864, 846578667, 450391738, 107315174, 233237385, 80426975, 311773273, 590603851, 162972060, 912706750, 517798952, 720431751, 591764198, 798839458, 370700607, 636758625, 651751707, 725876751, 831139589, 202094277, 352227371, 743385763, 493988052, 891721329, 313094736, 198719551, 84095382, 208912988, 157142055, 466731154, 963034302, 665968701, 316810614, 199275182, 934727791, 797407116, 257650561, 416314489, 631506157, 614898732, 691145005, 586859638, 836139692, 409334067, 887604882, 531412748, 431268935, 722847932, 870789722, 625150397, 767377140, 784795644, 342128836, 241530187, 112350823, 769080106, 353760448, 53585152, 319520015, 642906548, 3268567, 616176553, 565160808, 238703460, 945973409, 193817389, 652493598, 388666686, 122337561, 530505008, 556664850, 451765895, 612451766, 564998699, 980721121, 670499449, 486266383, 685585232, 983390550, 515573142, 723486808, 429971424, 186489493, 900915107, 446162002, 44195415, 721458526, 419382420, 38472364, 833236265, 742693020, 152289252, 788193186, 158534880, 709857716, 749692283, 838669423, 246931602, 432779306, 452892037, 379150706, 932674412, 834895791, 63823237, 971883606, 19950235, 125686603, 184080153, 771784856, 931889805, 910272493, 91086825, 672174521, 129873723, 120628653, 153232096, 421582024, 134854291, 857585432, 791909848, 886973026, 684807308, 522339755, 27019515, 120986756, 93938277, 394714582, 137916484, 545632001, 416067371, 955901998, 737197454, 276881529, 200880494, 200210786, 201382939, 88603172, 968466280, 946719592, 852109140, 170208850, 618661849, 808755398, 93699019, 472965026, 666049850, 864672953, 202150658, 146219364, 529903725, 694968427, 774710888, 695690527, 975561063, 543791842, 712420773, 339634466, 412937220, 445125911, 816632838, 180353024, 794988472, 272128307, 558280784, 685474672, 794226082, 308420646, 161604439, 664740149, 57270111, 671706433, 403836511, 690809050, 639963225, 257216895, 967186256, 877003452, 33371717, 678943845, 205349068, 204266438, 113014077, 311831096, 271180892, 230863634, 834664394, 189741775, 225454859, 701649003, 28558475, 46024313, 129103814, 927831952, 336871941, 268368470, 534710260, 98266561, 860456173, 58303246, 713763110, 545122597, 304308805, 377925326, 967056249, 24270457, 492144901, 963185690, 575042937, 676016448, 572412148, 127449999, 942812609, 464498389, 686975585, 634310698, 726970388, 223304640, 392076644, 37436532, 999577952, 433596510, 450893746, 41594508, 938064667, 162362543, 180567918, 330826407, 831883855, 872498659, 905374879, 234314456, 1690028, 932882230, 813821405, 897120941, 610312780, 153021946, 394075752, 564315820, 217724865, 645556053, 201955868, 432667550, 625254382, 100396400, 407275555, 159267747, 266617410, 505037638, 187305277, 421879283, 329845624, 845971555, 932712123, 794330869, 280222316, 993534372, 15709157, 410064240, 45223373, 130810233, 181848167, 972495506, 855473340, 184899409, 276596449, 361359373, 197311659, 929170490, 154515025, 612426231, 706645594, 716582270, 212234101, 949264455, 246580819, 472303767, 387761508, 438163293, 373034005, 752732522, 676156721, 770717256, 282166512, 414653065, 239175977, 947929162, 31315205, 632910563, 918021486, 449701935, 732284512, 705089200, 410280868, 567651668, 499123066, 623183068, 648501761, 7725981, 697760836, 680474976, 267185913, 86724888, 595682747, 326720240, 338784224, 643186769, 894638394, 779067952, 518106609, 652334385, 45367437, 306138260, 754313117, 882783693, 856647229, 996142913, 928719098, 582462674, 770351642, 48025526, 268455896, 901856644, 987586738, 311824759, 868528826, 43557545, 243134916, 901640220, 29174898, 495498466, 364574572, 124758335, 7676108, 588380837, 686922015, 732555383, 474906951, 983070077, 559261369, 377986296, 225211041, 525653320, 220795793, 39190849, 938714152, 100850287, 532570449, 184165016, 274486516, 606523033, 39713904, 618708245, 472665290, 62905052, 922767035, 649502393, 125297053, 88722436, 316629164, 16682629, 263267114, 276770014, 295062126, 379134026, 560665854, 690349664, 489001678, 67937508, 314009954, 463869681, 769704707, 312100972, 543248859, 148302438, 686338912, 217231154, 109690457, 357692698, 480765785, 779119801, 613561320, 451754302, 228132163, 221412586, 121589493, 847573833, 866828181, 556242893, 712003522, 474446048, 70029459, 165874727, 774201826, 245574651, 809070706, 13008546, 695215898, 683067125, 763593209, 764710607, 489313451, 796268962, 196597499, 251558476, 51341986, 740910897, 873204250, 249131287, 667507174, 786856346, 604474983, 942253712, 837743906, 713990862, 668204701, 705857922, 899556484, 481658146, 954306340, 462799196, 408862387, 314726495, 429050331, 807263256, 468763545, 204361148, 508259725, 671412127, 615761930, 877899480, 970615258, 227853658, 753566040, 610081705, 645749538, 462300112, 681249544, 275807651, 479644612, 48748794, 24844886, 895940714, 433970387, 687222785, 124592386, 565405950, 456695031, 626509407, 18150260, 284511170, 37810205, 934391563, 423893106, 960097671, 584923487, 188729211, 950909944, 837558087, 327692653, 858304808, 400231520, 475217469, 677530166, 155821128, 942491270, 16444835, 479988130, 558363586, 189198735, 751679344, 858475479, 902405036, 217947462, 465251689, 761568755, 747427843, 460037280, 183235588, 318795864, 362667376, 572179478, 744213751, 978238392, 940658530, 403486194, 109213485, 829453427, 20394071, 901216926, 681821836, 953926582, 13300776, 10681424, 755248434, 242720529, 686708382, 382546355, 636177389, 728025130, 862204907, 846166989, 976762670, 682555094, 815289826, 908553720, 827180134, 582985652, 494652516, 723567369, 630844740, 430517347, 751647587, 440188199, 777122922, 571440430, 838592354, 653873765, 136228969, 203934228, 635274763, 63272117, 969045804, 812242788, 314170822, 861884924, 893357962, 727143427, 336358730, 318791986, 617264357, 386186885, 102880216, 140639030, 897868620, 890232980, 209394415, 230074373, 505083221, 238948881, 208252468, 975355388, 98368664, 95480383, 611957140, 755038565, 112340234, 107372298, 282964981, 59454795, 881044741, 467207094, 409453124, 56606141, 651896222, 718951682, 326917272, 146368147, 482080110, 885369886, 471896742, 925897479, 686605303, 735037199, 559209066, 332676394, 229659200, 400785554, 552179900, 821141865, 448169209, 570112747, 339462652, 188532255, 561273645, 744969872, 380669713, 672318286, 146690548, 91741325, 380885031, 977518244, 825548322, 616080575, 559251848, 586438587, 775199138, 435295099, 319868821, 613649805, 849405103, 114212011, 355672673, 964248912, 620258708, 471262175, 954996483, 960138710, 688094520, 775210168, 696492812, 57686194, 110404064, 442305718, 83428432, 502177232, 935689106, 581167159, 78504597, 624937500, 730342428, 755428666, 100159332, 604288964, 968216276, 385884642, 868759727, 383356248, 345206870, 36814550, 277183278, 583804276, 616420055, 775059128, 847835043, 139488823, 580987814, 652493418, 696486925, 478440735, 360700735, 595793307, 181137332, 563852413, 267774103, 825120992, 214720247, 5318311, 524436263, 461688175, 913288165, 980742124, 147904858, 561681453, 401165469, 355073056, 125008541, 321218820, 15908594, 423015611, 659907261, 740488558, 196570463, 380714533, 22107340, 205233727, 479035013, 278836630, 536593570, 267994686, 368908909, 396765180, 711518235, 857313996, 59356538, 731472739, 519640328, 959942868, 408844447, 254480486, 968014610, 484256446, 545374673, 136703931, 30669465, 5655597, 303716087, 819891267, 319826206, 439503712, 447309052, 433973195, 197247272, 226285280, 178649181, 682763048, 702168261, 592791496, 69055537, 879816207, 422873596, 64957935, 606980159, 720596994, 782342545, 14625896, 607151750, 602873833, 539892258, 950208134, 835865482, 4447765, 423035275, 775139035, 151728578, 315317838, 16898165, 844024823, 372920263, 905799025, 273008680, 874673976, 176402825, 163833626, 544752903, 357546787, 806690655, 478831369, 158403968, 470499899, 762579643, 745619967, 533962789, 987236412, 645546035, 646352823, 289185650, 651287169, 766274199, 643506546, 611287705, 59352029, 944461980, 309643678, 734119328, 347146702, 590550647, 60749610, 158714924, 580457711, 333714420, 856518404, 464755333, 895477869, 663289463, 895396732, 501001558, 85266375, 379875325, 298463576, 755399790, 244318525, 580187875, 7199134, 183290209, 962292727, 992089208, 134538998, 200683816, 645861912, 865923905, 78535994, 281937871, 173574170, 398454248, 860958422, 637437768, 624320127, 20126064, 658493639, 765097934, 57137425, 683783651, 679414790, 297471854, 341076940, 956229375, 629961940, 847381884, 399607287, 599601074, 43833924, 42150779, 208563553, 610307813, 98659168, 933330881, 898833570, 997420634, 389224083, 884233642, 872788184, 238451280, 470201872, 770043293, 371300959, 295112562, 891370563, 728976045, 995191024, 320882776, 194398767, 292269689, 117112992, 678423562, 487333118, 95765960, 190009770, 348993691, 260041689, 699134365, 471678793, 342999415, 122737384, 894844054, 653383246, 337290883, 3065964, 237673342, 157268126, 708047007, 773257874, 562216848, 683285690, 986336100, 535889424, 26985864, 872837416, 272284351, 460016280, 185858984, 429584916, 585603286, 581305222, 133472310, 681119877, 246471283, 403621953, 846844353, 781549352, 187546341, 879255202, 452058691, 569854191, 27063255, 487457855, 641487822, 9225698, 449451784, 307541033, 708160509, 745471212, 861208075, 768232471, 167953326, 233360853, 175217320, 437741600, 99932833, 330317052, 90319782, 20707655, 372037950, 176977836, 585825723, 196646106, 137246156, 112941997, 740407981, 790528804, 522747088, 291174166, 390972587, 615610314, 484877548, 217550936, 897262751, 191692754, 760104027, 257288794, 509702830, 507258890, 132814310, 196376917, 663851522, 852213852, 419901023, 949985895, 22477927, 231685824, 567728211, 214503116, 194357603, 790071354, 792416044, 749560886, 210263952, 660997683, 840210728, 793519616, 354485711, 198716207, 194504322, 454804011, 77875936, 344367387, 225936631, 69006046, 610655039, 878431516, 721522978, 393191837, 873482784, 316248801, 993193659, 712431810, 558637298, 863284362, 355851112, 99164405, 672089354, 838002714, 239147862, 418511889, 329898526, 683759881, 128348574, 531006072, 721437774, 565902759, 111930463, 902260402, 386917368, 197682330, 334218947, 923375749, 638396654, 202030766, 802341545, 260902797, 743865100, 900054634, 537211025, 629316524, 85982149, 436084541, 687383101, 352705514, 593182780, 335298662, 15149435, 892675868, 706853099, 818082592, 834324972, 222456075, 168148103, 249865195, 855199946, 654598886, 304808561, 483756325, 575073647, 424156165, 923837106, 423847277, 333883018, 702480469, 960381536, 832561886, 374187823, 361017231, 790998837, 285740862, 139184071, 860486939, 853034367, 945175819, 62072175, 300620109, 744503867, 89484259, 503897498, 392232511, 232649891, 713272552, 279424593, 531796026, 217130314, 157248173, 712937081, 488342488, 37423682, 343881772, 536638416, 377484952, 858221762, 849246978, 487246932, 660743520, 18719792, 556132483, 801771864, 719160610, 662869582, 97364353, 807212759, 256972176, 26517698, 494417720, 424395535, 128579660, 221917257, 544474030, 282443565, 92252792, 986956661, 337155475, 858532998, 80484372, 528893305, 801294870, 60291982, 952617324, 996827571, 998796880, 944318572, 544525289, 578532461, 534988074, 875565775, 53838220, 140211625, 107183450, 816591767, 603876683, 23032991, 295109360, 301241956, 301107275, 550180524, 154912203, 387673283, 696800161, 131789624, 254069311, 550567955, 276436431, 174419605, 451616086, 950905114, 320452390, 683127737, 502708025, 54655819, 501388054, 62097464, 997857814, 696144975, 601832532, 674328002, 848908953, 530998785, 220440588, 872179573, 223939703, 920777017, 98883482, 199656749, 30792653, 731069901, 30580567, 864687202, 558637068, 710655356, 445225062, 521512996, 272215571, 339211861, 424528489, 295805899, 787292624, 282381961, 31005678, 570001074, 790144579, 306735478, 794192860, 752403826, 318150678, 386197008, 44299858, 529050008, 378611591, 8127356, 314513246, 825567852, 701950378, 959176235, 745827370, 991532702, 703676246, 31449349, 440613326, 569650908, 421253867, 401404122, 677135028, 353940298, 286282797, 385144711, 113314322, 107693898, 663756440, 162887284, 796379634, 505838938, 887422847, 551430538, 654300439, 991944488, 348259568, 395360717, 120445308, 599324553, 714793921, 77976707, 82491505, 144466254, 278543027, 124850295, 424510953, 777841441, 234539617, 341744986, 260977580, 195489659, 548757014, 723300495, 808871041, 643772040, 759943485, 893363058, 676270748, 926949219, 351295457, 766188765, 865150097, 347551611, 592112698, 558051016, 613151238, 95014958, 105832930, 769922352, 563460614, 756803588, 505083261, 925562586, 270967336, 832275163, 232597928, 241968392, 389513882, 81294937, 415376924, 935884559, 755640816, 504224487, 230526568, 200155956, 389380601, 611716464, 44801050, 146401806, 691000590, 887692342, 151711747, 99583145, 151089993, 761019296, 954702920, 702524054, 974558440, 556367325, 909849264, 345500154, 819320046, 266417474, 59530039, 373581039, 191485717, 820612413, 667427691, 224616580, 12840638, 264796352, 696256056, 253655424, 675863721, 103722785, 671047034, 319653155, 768223028, 642636814, 614637776, 106856282, 354474186, 886530582, 308449101, 513516428, 174577269, 740770924, 727773892, 192088924, 827403631, 924325387, 251267394, 627566030, 939882816, 835337507, 173526786, 953499757, 917390368, 950240045, 272723423, 843924938, 51552042, 825388908, 779707273, 352288039, 934433876, 418755913, 967180594, 953770786, 210859924, 349186812, 458179482, 100305747, 101547526, 775531664, 253793745, 564356228, 285230071, 593983199, 983301497, 499052724, 627185405, 986198050, 857412383, 992512664, 393174002, 543514663, 837798460, 248081279, 519176381, 371406007, 328927014, 840728318, 123081289, 274976193, 423840560, 2225477, 668820258, 305842183, 695351429, 112293993, 499483595, 428203836, 186037180, 290944764, 415356981, 94398010, 689781729, 770573549, 287419102, 405682794, 243540918, 472328033, 70035397, 780358734, 718273097, 598779918, 16043589, 973632690, 619250067, 833240826, 552237187, 93137254, 602291945, 787007210, 302663075, 154667191, 537908167, 198757782, 58587313, 735833574, 128224406, 112673785, 478561052, 266070427, 877026739, 542489264, 204227384, 821471097, 207778079, 997498763, 151231557, 927081060, 920473677, 365094269, 159532403, 434861685, 858054751, 323886309, 394434268, 49901571, 86001227, 74483994, 957369807, 188220023, 22459593, 216251751, 6658931, 862942417, 850172338, 291662443, 782326732, 834271756, 967533368, 601019018, 879880125, 637821937, 690373524, 221616164, 877063910, 781008972, 881229426, 917225031, 929404585, 96064546, 488648881, 671720685, 670741475, 462408108, 60817248, 257836222, 262358412, 591677625, 338222755, 161975451, 140110473, 263721016, 750588170, 333791301, 180150838, 586775840, 339779166, 418113408, 955375821, 410677758, 616030933, 967511492, 587070885, 648306063, 339107222, 926805547, 891284989, 799854258, 106780076, 582094959, 713936385, 655903800, 903964777, 51968587, 142320192, 71501772, 25805228, 23056306, 574052113, 143440083, 497745452, 998843550, 79828138, 26412418, 58230957, 690619599, 297032095, 51729757, 661753912, 648827504, 336390232, 230257090, 400036906, 947862198, 876258686, 135133770, 590618895, 119987411, 864626764, 107612666, 978515591, 754766987, 672225591, 94639628, 170910703, 244342265, 414447081, 210003734, 643354269, 582992249, 390505883, 251252369, 620310440, 273701060, 164898093, 714983766, 743954156, 278750153, 855718465, 519085776, 735107401, 471562590, 712753569, 560107498, 707971694, 336113812, 298157748, 301584153, 427069770, 44953005, 652364548, 658951932, 357659605, 721413358, 32108926, 115618048, 574373670, 920897616, 220954639, 31942913, 189336255, 774069051, 252050459, 339989221, 236572258, 663541465, 859364263, 633690439, 381782640, 748898259, 173726746, 412451028, 192222001, 326106306, 722802391, 102167411, 781395059, 550993423, 553777713, 363608429, 281876836, 43467319, 778748756, 725914308, 776129343, 755860080, 678279456, 976874720, 565872094, 141999997, 250519009, 441586558, 500983751, 749803394, 63556107, 22738804, 309858397, 15358229, 358981331, 633657724, 440726909, 28431541, 657422571, 592330081, 572637125, 482291682, 9360301, 872346107, 743341423, 87379793, 322839812, 668409060, 236584975, 907718373, 711291879, 481224321, 958172333, 197220472, 695947102, 52791705, 730262568, 254185580, 386864563, 653577178, 113670251, 295759287, 488828824, 716955596, 243210998, 346501369, 821076608, 132757075, 573747037, 823473820, 927897562, 869547288, 712990389, 448900886, 342956013, 62946866, 470700815, 778713867, 591184071, 874254021, 850048762, 862801087, 906022336, 381745405, 888489701, 72579896, 674193275, 523047089, 57562013, 488742855, 723796291, 502818880, 70231012, 194873222, 248436665, 881011336, 493388234, 986871195, 266001859, 805574107, 324129304, 291286451, 939365850, 614937137, 799592506, 124645474, 591165664, 264480988, 43946154, 365319517, 254900857, 395105462, 661158006, 623284071, 56606772, 438868503, 899964353, 610261048, 592220551, 262264227, 113867784, 193973750, 40568260, 790754049, 266615786, 417989549, 444677017, 728938005, 420210665, 231476103, 651387430, 372132429, 733363133, 643252984, 545154801, 584039189, 315191527, 729476622, 347283407, 706782604, 836868755, 369557298, 722335612, 596740966, 993239046, 705077042, 522757734, 169234038, 722358125, 312995249, 31523089, 947857746, 845743937, 579326153, 442766549, 29389217, 905422346, 409334484, 269631386, 233631683, 225724529, 923951812, 889956534, 203715968, 829383665, 62973801, 386543036, 526031756, 297744561, 345911153, 273523115, 759380623, 248452136, 29734461, 319129446, 730199171, 754935454, 364320935, 659271948, 955157818, 651552939, 70070951, 426377554, 158188832, 737182146, 482712249, 627256339, 423009123, 10595346, 208226972, 725354163, 891720318, 285833075, 742188228, 739170820, 829286826, 500004038, 176466978, 34633101, 491439998, 47563491, 895379997, 72325094, 979727784, 525918634, 597037233, 1253490, 438491495, 383927229, 348915987, 270213822, 659637193, 121572526, 439308598, 956950675, 182997059, 543564241, 416640645, 963245065, 120805278, 602403709, 751118608, 232868269, 967076615, 303760989, 963744205, 483762681, 714566879, 249844387, 967301203, 121533022, 173534810, 924948108, 23115684, 204503280, 689877536, 577238466, 291860468, 364110721, 894053981, 535662030, 687738242, 351387870, 239733208, 919563012, 351181369, 854385366, 527299716, 380170568, 154063459, 16250013, 385313238, 620445227, 347477450, 294600438, 149666332, 934544422, 530343938, 229559987, 320684072, 471431174, 771536056, 467021111, 474014384, 383660108, 117813690, 206262236, 588464004, 834122700, 869784968, 520256984, 797257253, 62929844, 312485086, 60133028, 573082857, 961228181, 281469050, 628843197, 429330412, 162744004, 646175539, 1119615, 459335628, 629751548, 844476576, 212719391, 118526553, 69086729, 7888637, 258349798, 182878265, 97088305, 736633711, 229899339, 657544631, 716401531, 28103941, 822945063, 781537595, 477796317, 751840789, 264327691, 554124683, 693636310, 815951077, 737246147, 486654437, 14564934, 508572660, 427849, 93341145, 109271727, 191201461, 964702303, 596816148, 443996292, 136131341, 487972056, 91204483, 265979813, 502920362, 810652210, 478113065, 810938198, 951164190, 967510479, 788860727, 650928434, 79677902, 545421232, 181472052, 14673997, 914766164, 13900403, 224019226, 67467365, 60795978, 518290825, 717627223, 975622168, 950805529, 800048952, 781975241, 435302116, 920976938, 222344303, 92228384, 357481763, 763469708, 551757242, 529802867, 127801267, 873137987, 57456621, 439295858, 861592037, 584621490, 558554354, 817920676, 681672740, 453879759, 305645955, 891782738, 216672678, 942240725, 705006341, 99312050, 266519177, 186216016, 564809469, 736787018, 509886679, 869468409, 267862731, 365288612, 940687816, 190167702, 803221656, 294247907, 816607721, 360314708, 816463969, 242280715, 103002439, 647240311, 723793354, 708057443, 918857346, 872745297, 737529797, 213492298, 401841981, 197781877, 18314148, 561996337, 596215117, 269788807, 915492200, 629275831, 438737245, 641655389, 129473076, 547024393, 289350393, 284817603, 480810091, 344470024, 967164418, 155882593, 240184933, 463033732, 792336817, 672727114, 741774492, 936871003, 799531606, 577861735, 988296746, 569271364, 107811251, 706334064, 700896456, 856812505, 483560612, 741885122, 842665023, 805590109, 680494655, 190087409, 22835001, 408769441, 785450835, 655472403, 157232143, 424900489, 1428815, 883888354, 232631142, 163571550, 827219382, 805423309, 400736232, 471821397, 678960641, 14946273, 297619210, 753401614, 696104761, 973608492, 618241016, 916517496, 246092140, 986113339, 449436269, 796051684, 523098985, 650155079, 968339192, 397789538, 747677460, 360278724, 232528717, 859384884, 780813321, 284468717, 59629660, 272186618, 47149208, 86189919, 489326197, 142622130, 528676838, 889214301, 124532962, 73805032, 268027056, 564189199, 643179526, 346409773, 704099365, 703682192, 883495791, 638565274, 506041885, 904792883, 950423991, 25595872, 296701822, 160345722, 799298124, 820023780, 64056660, 523187286, 839651709, 635754596, 377451821, 933403465, 124438534, 647769566, 894993535, 255206134, 509238907, 801489120, 502358555, 893148781, 340278576, 253716224, 884287930, 430536841, 56703288, 134109891, 611372364, 606526574, 514880499, 281196454, 39118238, 496620646, 73564383, 2045781, 845082077, 267046152, 366291041, 277249272, 644064829, 648372340, 24754877, 422260005, 72568596, 830676766, 673380800, 448823683, 340912770, 336532722, 35338522, 842824103, 901938081, 509822792, 579791271, 709427380, 868948900, 997416744, 380050961, 789382894, 537263910, 281279593, 519139875, 356376464, 47450668, 802137427, 584325278, 391760856, 631574623, 163631814, 111067538, 395021283, 839469472, 826685366, 875327254, 221831810, 173890589, 569934909, 492428303, 108646901, 776875922, 972082680, 162499885, 307668300, 67677843, 785210953, 13668041, 946792292, 654377006, 232857064, 601398917, 574414818, 48402038, 634501201, 278974905, 811584033, 182486049, 280613626, 474327105, 695373979, 410639160, 71958394, 697710470, 361348190, 65335366, 444062089, 283877944, 458743115, 771705543, 889517223, 730069642, 221797191, 825303326, 391107255, 806963926, 449451927, 56089637, 909463275, 651971216, 353644255, 94916656, 714005232, 364392261, 547519371, 983798782, 483362481, 199700172, 359032329, 550141309, 975703808, 666386277, 737548896, 584729075, 574642655, 860877794, 429374975, 173541631, 214964176, 935835921, 722077452, 718178829, 359127597, 515885040, 296305929, 751014390, 114983681, 896003398, 347907595, 395202565, 624300244, 475798849, 172054989, 405255293, 534357038, 146301815, 817211577, 796278904, 62082228, 532529227, 437232494, 153775651, 531052977, 897452785, 477712354, 240784643, 470012081, 910541507, 567847581, 118037769, 22060264, 699421501, 712455587, 993185775, 402240159, 857590714, 307532047, 853741297, 381254894, 88270740, 407461014, 94254701, 701052201, 123255635, 325947910, 732068367, 126017248, 556424519, 645579305, 377571373, 774828982, 328673431, 355901675, 268234906, 854625516, 304196401, 116349503, 870905463, 473340326, 636759474, 850205857, 787689375, 874006619, 782105927, 758929485, 904557879, 539197176, 80517907, 600289406, 366794950, 516315995, 350075455, 59845417, 325469171, 507518298, 295261308, 186598941, 348053987, 706289713, 808114633, 317197685, 493548718, 644216752, 979690156, 135155851, 290996686, 245488300, 75736133, 196225048, 588907915, 63930052, 294235470, 296867975, 545539171, 839390727, 48633409, 538805545, 454578993, 708262224, 666406987, 581105933, 952684106, 915659543, 837928462, 866632693, 148752556, 877170998, 185555570, 187368999, 691548607, 844878054, 841017640, 63452495, 793588850, 545058075, 302068802, 174602921, 424715309, 722757680, 591693806, 209407808, 740141027, 652418247, 21205979, 195824769, 442702605, 872376274, 77017008, 323605836, 631443149, 623278404, 227262090, 43130591, 913592143, 217789247, 279647811, 938394328, 527793598, 595053355, 724938793, 217326614, 403445015, 25532656, 592239841, 927309624, 570210233, 826108064, 722287683, 324254064, 317202445, 131103538, 896663107, 590619181, 98501759, 435957877, 407867899, 785324371, 826888191, 373490561, 928187274, 65121529, 768450279, 662175583, 972732993, 689754817, 733883467, 572433702, 999865442, 457517042, 408951853, 997820839, 818342470, 198420266, 50481007, 102547840, 81100718, 201101185, 776008358, 827774931, 94774976, 537896954, 361166401, 645808838, 972739634, 529808788, 584756322, 93751597, 337896177, 35927701, 843934946, 534021463, 782345690, 268485641, 312800497, 956899137, 595545090, 378742831, 150299769, 604479316, 6111559, 242140679, 986658238, 857028141, 470103712, 521246039, 1206572, 170978346, 692057147, 450947426, 911033537, 445478876, 394709266, 532247027, 280375281, 820487896, 105207321, 937025196, 927519840, 830234939, 788048149, 875723770, 99053303, 978528135, 850350575, 691196852, 900166361, 360710102, 268331617, 516468232, 238024446, 723010707, 717719779, 800802601, 385452281, 892466786, 796627760, 462173604, 469222129, 596482971, 815980398, 448828491, 374170018, 579274025, 585309314, 529025641, 21484839, 754656326, 598517323, 765241878, 668590316, 150197314, 847436458, 347942147, 474974548, 882735152, 536163114, 869089128, 767671456, 803171036, 421485242, 59612141, 538673456, 964244387, 93996827, 222825415, 665001341, 798897502, 663990172, 650350901, 53664039, 516894341, 257510729, 247765140, 589927162, 503307224, 534305866, 951876540, 315923406, 492888505, 410295720, 561554848, 797688707, 837240079, 168327000, 107309626, 22353151, 786902000, 898255547, 296648999, 560934694, 694211945, 96477912, 3669769, 473702283, 356673289, 957604259, 799464580, 836732947, 835214815, 718137918, 19374895, 635815665, 555800761, 597287525, 899222272, 189391537, 475193476, 616732875, 37621319, 121489398, 867910102, 20855178, 142429321, 745269930, 621897377, 650559613, 463225670, 950836285, 578835712, 535313730, 307526338, 47527675, 3533005, 632764154, 893819029, 66578746, 770487183, 47130177, 120271116, 938492701, 483647907, 956885313, 383716011, 941866472, 192931995, 787960595, 923447369, 382616089, 861500718, 281158144, 661084841, 349218552, 188361441, 75102744, 324498333, 846920045, 28845621, 224005854, 958707590, 912793218, 785835703, 725639442, 184237717, 774244317, 548255498, 693332044, 628808591, 959636655, 958311127, 939146175, 708886525, 513165677, 313436627, 494736671, 526812940, 678015008, 460257599, 836010513, 154357106, 625912439, 421229738, 55951323, 573392089, 57061417, 389255502, 686906384, 498788030, 814180755, 252948531, 939804987, 752303815, 53909635, 775868636, 830440088, 232400900, 338868567, 676319977, 282397759, 521012445, 152163299, 506001548, 607371717, 378989209, 432250053, 36286821, 769296018, 504260135, 543742730, 129934092, 367419982, 789960940, 229222175, 42189780, 456385978, 504365754, 624204216, 714073216, 536217608, 671368979, 547946196, 323745992, 985082505, 912950206, 258641034, 507608191, 646352877, 58521971, 283732034, 212896505, 71680601, 24625836, 809686630, 843588491, 483107929, 775095540, 482836543, 315858264, 164119128, 258079306, 842883635, 52923925, 746395361, 993155668, 907931041, 238917278, 943025427, 681671456, 596418830, 743289852, 809012756, 24571235, 631716840, 764151947, 433462061, 880706492, 357441226, 413850113, 138736616, 500693300, 697393163, 821093756, 626242223, 787819966, 381064479, 509586938, 228579830, 821679743, 730894938, 555761402, 770421453, 716434546, 918122412, 334242765, 401664382, 623323548, 465254441, 162447404, 932815885, 965382344, 891555791, 255082036, 375969108, 950636069, 983189641, 378173311, 52573390, 650142418, 982256994, 443682143, 247643659, 679756860, 410616901, 68319351, 107362669, 523594593, 388593708, 708757452, 373955785, 969164217, 72812237, 249985093, 87168275, 401718756, 475620170, 189564414, 19574942, 56060636, 557088232, 123852003, 101680522, 512327747, 470773045, 804028110, 905074534, 817847144, 78907144, 287001307, 523101522, 596144520, 940176675, 451492945, 729231384, 168334691, 378996733, 697557519, 897990902, 57479189, 980603873, 830969557, 56643110, 653899069, 973536564, 65548762, 687267076, 999555960, 140811332, 96759756, 990085874, 536829929, 530427414, 301363726, 550814368, 211031293, 514040843, 668255735, 464715234, 914374478, 568594562, 547697425, 142381245, 664095624, 542034533, 599260227, 208787039, 430478178, 1901043, 957133817, 619144063, 667293697, 152737069, 558835375, 998240327, 20919229, 278293823, 941888758, 849707178, 547130287, 12315257, 564719416, 5808845, 346715048, 589804000, 831878458, 11837854, 989265559, 356432357, 247832014, 763731429, 617252076, 115836420, 608405494, 647909382, 119666521, 103124803, 374421701, 503951735, 59475368, 972498929, 468596447, 90810908, 55216537, 362317252, 156541955, 373968315, 559509132, 765496655, 903105387, 165225030, 446305479, 448484195, 990066521, 923117455, 153204165, 129088537, 470425245, 434417803, 624855229, 303074898, 511174627, 305991001, 733317651, 234554084, 43796977, 973811833, 26466208, 611419446, 111760345, 893573557, 806935792, 948601341, 47468969, 554075070, 181127368, 470669046, 64051768, 921808246, 263802239, 994506385, 793176606, 18532048, 817381537, 16329382, 448615304, 680720897, 45121596, 318284576, 584030794, 399563773, 291830076, 312555357, 713522538, 408590852, 225124363, 854616821, 981945637, 309600402, 606889734, 5637693, 18304272, 168819764, 66093062, 170405242, 992278358, 687257285, 695591104, 224631768, 741114099, 934834771, 444657592, 265715821, 163809508, 268613978, 232883504, 425960621, 880840291, 414662471, 544746236, 971863892, 468782179, 923624547, 87241799, 859167687, 374387972, 405822268, 482789304, 877175890, 528020272, 95717776, 515066666, 5661940, 728640439, 754690237, 92923743, 539575692, 310493127, 814579501, 124055270, 315368293, 864703032, 629068724, 380745558, 365623199, 5827209, 427110588, 241200957, 540910306, 116043043, 269590632, 749484381, 376140340, 978885863, 417716400, 828586745, 425629647, 464560992, 562002956, 91299940, 805193554, 497298607, 39772937, 552867122, 290224033, 210945804, 550028335, 81171184, 728936463, 754067963, 437610537, 590497958, 223035169, 45404270, 148791411, 394387547, 143604048, 86414520, 815029160, 667768656, 616656901, 208352710, 711498025, 770850644, 54747174, 762624405, 676068853, 341217678, 701455687, 624789989, 811229164, 554900350, 267872379, 553483722, 893703499, 136444788, 732527786, 859762273, 618750479, 841084963, 893545502, 90176780, 973442234, 178366420, 256522328, 893417992, 216331323, 305403837, 932555406, 803103063, 932578986, 541075978, 781680725, 38275944, 803971252, 866787178, 380875875, 32981102, 105014563, 931474280, 417744106, 188954433, 903124332, 455674192, 498990554, 394592099, 66627341, 6180776, 980577504, 278297854, 988303797, 403442988, 806614674, 225413154, 929659053, 595084761, 522213835, 253603207, 120083210, 690667857, 101368480, 968445519, 116441793, 638573728, 413233316, 121160630, 425559558, 732023072, 208854584, 517394750, 727760999, 218542663, 45665071, 641469519, 915925611, 23508259, 897908457, 687378138, 696391798, 628519267, 278306633, 707034941, 598544185, 467482528, 273382676, 213726009, 226608443, 510107210, 491994627, 29441924, 295410470, 305374166, 595180995, 641685156, 644145150, 699091218, 940532453, 766590666, 895365139, 518178338, 23299416, 106405403, 571381207, 582292521, 380052160, 856572264, 322131608, 819296652, 849386644, 904120492, 442231527, 663290319, 783364802, 334971974, 916515126, 880400578, 420519342, 354143891, 825610063, 96228593, 782778425, 36057410, 807755811, 612015380, 168865563, 538670235, 75791290, 34835301, 278086492, 458908914, 780371304, 226840985, 509261940, 747294759, 895321485, 893521884, 199714389, 776500141, 180498837, 575770756, 455149403, 99963456, 305037795, 600945257, 740223827, 362646136, 331932108, 892767685, 944982135, 621489854, 456312081, 938661908, 808181523, 302408532, 53948291, 918699047, 705208452, 118328474, 584609922, 3855995, 659137873, 767971462, 303070052, 170198304, 943754754, 819368007, 988419637, 57256373, 740101435, 145357089, 355409283, 507552156, 932349910, 731760110, 921676800, 137195679, 936303874, 625954583, 968999469, 790034376, 957452455, 313446667, 590817412, 852159993, 699214507, 224273411, 109146919, 801889664, 495244906, 134854579, 268016249, 707928762, 819793825, 475929011, 863787009, 130389973, 209095520, 871139387, 459356463, 994895502, 284440683, 86090192, 814313986, 98739619, 862607429, 409458903, 865901953, 779129574, 829740389, 184898970, 565261835, 522306288, 103760875, 800628288, 448238440, 37138864, 23593016, 190762927, 15701713, 464027619, 455132617, 604907393, 970608805, 61293634, 53928008, 431394516, 310196710, 933826028, 467232135, 667350424, 335035604, 515855097, 697867277, 54984315, 391983482, 328395586, 251145225, 863794634, 97565404, 971729905, 763563013, 354048014, 757198833, 765214887, 885890351, 648595090, 690199291, 107214863, 163217862, 529383258, 811417026, 819210766, 659196905, 369331536, 108977903, 349553862, 790414061, 396697274, 363325450, 327305319, 559471324, 871221532, 477785782, 354161149, 990217719, 348837620, 309611724, 862242079, 397962406, 142961948, 244509781, 624851695, 996861382, 875256683, 545148143, 225646399, 740060257, 353713758, 640618767, 260624143, 754822791, 98652192, 694525354, 121614204, 11612764, 870386523, 86642858, 832780632, 304804871, 357382015, 794524990, 969326746, 516213812, 607155279, 182283448, 318970225, 939755489, 874532114, 999697860, 997309426, 472557058, 443187259, 713469498, 425777103, 95177149, 998924688, 626812254, 397060259, 919898708, 521501046, 129626112, 156186722, 574295788, 250002624, 340666707, 749206106, 495414499, 78020226, 772290034, 787707334, 653473077, 797286807, 251895784, 770264888, 855920456, 710132820, 500385234, 629100460, 265559566, 972580306, 933347892, 606484099, 45443317, 85089213, 892085992, 884950211, 24938107, 993149547, 556390451, 325459652, 801558409, 178116387, 565294918, 454566099, 814792580, 315151493, 783637850, 396020517, 773893710, 239568126, 235693699, 442755467, 240987976, 468477054, 994358940, 235162395, 976184102, 632357929, 519509068, 435334498, 873652813, 728316272, 855715466, 928639210, 427797531, 73789579, 659752264, 49023225, 164149389, 176635802, 154364457, 825568255, 809479909, 149718931, 320071960, 855633415, 210674953, 484127433, 805383942, 233877307, 448852045, 733049424, 187782139, 356271770, 565597010, 876775324, 907545382, 90001322, 667967532, 475011002, 806197273, 338646026, 608724463, 987540658, 42466771, 553000296, 72381452, 737305182, 332861429, 160462848, 847383672, 576302693, 47861800, 162601912, 322811093, 215950220, 65428160, 752861773, 682082974, 710425236, 602859585, 438822725, 393232565, 682956926, 747500370, 994673642, 617979877, 271339811, 247224764, 752096724, 876430953, 11899254, 465454672, 866059624, 968398668, 579665242, 27146612, 749763940, 865545682, 711405086, 450848881, 579977880, 487633244, 106813059, 697545030, 518372418, 911343857, 757714474, 250814709, 950415578, 310473690, 651018128, 673967075, 742411343, 628973523, 898336676, 612025879, 719256045, 656208550, 916494597, 854256865, 372208696, 612403430, 349840234, 881576298, 110930348, 89378906, 38080217, 619104723, 152243846, 824406728, 673649884, 654093757, 883207414, 183072448, 493003196, 122022724, 641997183, 134169783, 734773893, 926013012, 351364105, 731673433, 279192243, 148658601, 545178716, 427747991, 906492413, 977043108, 356972133, 107563071, 261037535, 359183435, 591148574, 345368609, 820043677, 931106836, 872035820, 102484111, 581070439, 643260451, 126106997, 879966982, 811595632, 256410725, 90947920, 750895360, 77322771, 638969439, 841730416, 163294853, 956912894, 587097955, 116166183, 8845222, 440387449, 803739267, 676661658, 237026484, 482237103, 593147314, 721400219, 729100504, 141805034, 91438899, 412904983, 928556719, 504019727, 408586119, 369980598, 679073549, 617381323, 725530303, 424363395, 428562168, 820393061, 739888336, 35670799, 602047458, 319945731, 449257369, 462481716, 497233695, 41456287, 723103253, 135241060, 165572223, 773659773, 934536318, 949499478, 567455091, 927169223, 285706177, 607604309, 369397231, 197192979, 95065252, 427894496, 933402591, 99439073, 622663082, 265423967, 738336812, 713870421, 770580313, 164850171, 227809813, 59684670, 965559985, 62469515, 833373235, 591870749, 460458609, 948232831, 445681207, 364622836, 966319561, 925440557, 592067802, 310096430, 812746709, 533933634, 308459228, 431276641, 170159199, 148512880, 590766228, 903525579, 981163176, 899634160, 583807110, 842685873, 563290202, 444401100, 872117754, 524134995, 204376238, 560771833, 956956078, 534218966, 437867466, 191144989, 736283146, 541608636, 424814238, 460842328, 728795300, 902746668, 360152615, 120264116, 386646222, 64865594, 252625082, 779729158, 887621412, 646379539, 195156464, 570302675, 614773064, 580517378, 120330820, 228415631, 168082007, 403320616, 944311666, 496559196, 810202606, 744561256, 204373272, 237210500, 297606078, 240111274, 274250, 268460726, 546111470, 556372357, 427031701, 764565458, 630182628, 573463013, 839694916, 533925831, 138355152, 97742583, 786035307, 869666321, 90990689, 619823506, 561301354, 716913445, 483539151, 305094395, 645209915, 632477715, 733031609, 725623304, 528253606, 813830704, 16768231, 522858685, 381749510, 97177616, 924251166, 773983254, 429403313, 588027334, 713054238, 503776138, 209445811, 593460990, 248284608, 351372515, 383774208, 244384301, 799863342, 29943714, 74552905, 442262534, 59691909, 487342671, 368484759, 980432440, 306936262, 166047338, 770029420, 244363679, 805007873, 674466862, 727761333, 766449047, 507831964, 274375128, 640245116, 980616243, 465923433, 777151878, 655725993, 655471391, 437059324, 230382405, 61325531, 466983513, 955440324, 661701336, 712604877, 442908169, 940248174, 568802928, 439746442, 791693494, 676169829, 276783621, 715847073, 893666447, 737403414, 313460699, 555075596, 69913114, 616707631, 501219349, 807284493, 355431425, 904562860, 814317461, 639973534, 798508943, 889541065, 95241704, 17294787, 908332215, 235138517, 221730952, 720249237, 122031642, 652243151, 909065723, 208847459, 75316948, 551095230, 326971053, 973445060, 11420993, 664214616, 779976382, 675577048, 900308200, 420837649, 319648840, 125576596, 998699406, 9798110, 244589798, 358273953, 116893548, 673021657, 462822565, 87016896, 342194587, 602890161, 682388546, 769619208, 95230424, 394778262, 111849353, 202211103, 769467527, 310554035, 565768153, 520405489, 185143915, 403350515, 411310737, 38190128, 219194604, 487625023, 247453768, 684373216, 318016633, 610994322, 664290343, 859866901, 351328936, 196507651, 189360664, 953111028, 149776873, 217424809, 775799505, 210286088, 875544883, 469213261, 82973865, 623156242, 841984025, 992049850, 348107512, 306443657, 623812872, 10623407, 779260107, 325434507, 663258218, 284015252, 549239098, 560984020, 654938147, 899382267, 888436538, 19305141, 74940696, 148363523, 807447417, 973558635, 476532136, 865487040, 272407631, 655630501, 52061733, 795625494, 513146800, 374959316, 810153941, 975591313, 480182889, 898378300, 166782095, 148644558, 974607307, 323486395, 854429988, 190236779, 599218310, 893598001, 845383157, 214414484, 445990978, 382139423, 806863152, 495051380, 884115121, 407334821, 766286808, 405103311, 411703362, 370973434, 611024242, 33210016, 496927953, 593192723, 933782305, 893206985, 870062899, 34228923, 335732358, 267334020, 829588831, 366730218, 499012303, 828413860, 389631637, 855865996, 441944288, 694260849, 9180457, 133293314, 530796362, 994451356, 811035272, 87596036, 228239287, 66121526, 76999727, 975853232, 661592784, 7157673, 754303622, 642612073, 857950145, 158426810, 171571850, 66366491, 361225197, 729127412, 194358394, 348624339, 47520307, 394691079, 580799653, 812312702, 175124540, 950829891, 826579517, 359195428, 730778419, 108575628, 427459159, 111268217, 483725758, 265700593, 630927720, 58191940, 364551355, 374740417, 261047376, 516868920, 302031156, 975663522, 528730608, 964206454, 698225241, 53863366, 28561846, 127681440, 321266752, 192787526, 358300595, 904984245, 463892416, 639329024, 174737038, 84936967, 389410408, 580238546, 26479574, 451503345, 315852356, 514982652, 334695497, 470942614, 771942501, 693428024, 577652741, 453932381, 876546717, 223202380, 211300658, 587177273, 26273627, 945425172, 323120808, 49182317, 673038725, 662343241, 58758502, 468497766, 404767326, 975931226, 789879238, 937961440, 433052760, 227779378, 854779405, 945841174, 885989513, 268143286, 254945316, 856766229, 689107275, 433854672, 69822338, 602346551, 230945224, 618184599, 832598984, 451112799, 424790354, 487632330, 582629664, 952196338, 197506451, 131475977, 993122146, 625633681, 68373577, 846339868, 756508912, 297098605, 220073018, 276928389, 107184998, 969172180, 202769283, 170878744, 140103125, 64413140, 719202931, 283927707, 976564097, 559368709, 215549418, 892477546, 240986347, 826672270, 726825377, 526767845, 426055934, 914350974, 33342675, 991080260, 80139223, 212122515, 539480169, 211517330, 649681681, 673933201, 804130678, 538082172, 719925797, 240423191, 659825404, 183897574, 662232042, 504064396, 587381503, 743541302, 981660877, 363267644, 78876861, 369112785, 337625744, 804111731, 561043876, 581497287, 699330723, 595662853, 291864412, 430704250, 775023669, 744870078, 992671369, 813968163, 293509551, 878280305, 880513372, 647872909, 573117395, 395240038, 766261535, 961532976, 941591900, 401203607, 712549829, 249369013, 873792874, 801483222, 329398569, 65174936, 659771060, 692707195, 846411902, 312976913, 224085188, 505354458, 701948221, 742026269, 432627585, 577936443, 463347295, 961595081, 637712385, 595582740, 195291006, 124569602, 626435158, 950685648, 725371946, 502356972, 227215932, 282530161, 613603139, 830382434, 945729511, 856444413, 159320705, 651969654, 962061199, 403645629, 476790246, 348714860, 719965958, 762314695, 498534288, 110256931, 801717234, 255055712, 461639814, 226102296, 179450993, 55316122, 557999971, 933291484, 356779828, 450488582, 180199575, 166409116, 703691314, 787965127, 573472191, 991889950, 710490872, 261889876, 203158524, 723839812, 393684365, 76843307, 877287641, 530174659, 921573337, 771784570, 357938435, 270958405, 832015711, 697545459, 955252552, 657570840, 275434815, 884994725, 609012138, 689543558, 245758129, 702420967, 837070213, 362055582, 14159338, 734897836, 662102462, 33082345, 811971998, 793587768, 984595443, 841202834, 810316703, 100859587, 393351803, 128488539, 635757568, 494933873, 661214914, 634600896, 581836243, 687121779, 281685145, 551289616, 892917001, 973541694, 609710351, 263849791, 663630335, 321850502, 517992051, 755626652, 176453367, 850323963, 145827465, 777307227, 727876468, 856642971, 73181940, 551625965, 827294043, 264471380, 929238631, 404367107, 607926156, 718043112, 290001864, 330278560, 533562017, 154162929, 4110593, 6018653, 383713095, 989679532, 47469540, 862771313, 969167162, 620068356, 830536761, 936047463, 943659483, 954566180, 566788898, 334322320, 227302308, 814518089, 211631757, 892691351, 321579696, 891497258, 986059241, 73004084, 375225753, 665495412, 41523120, 560564313, 61311013, 397725207, 876194170, 192604656, 296519260, 602629913, 460759326, 241280322, 134692821, 575624863, 382686863, 626687363, 65052012, 211056330, 746314798, 672057706, 172250570, 667873757, 190050810, 394971825, 33908734, 228474483, 364899295, 888880283, 603979224, 908489409, 709707775, 361674213, 918789844, 475457209, 458233649, 141163886, 141369088, 50798026, 63900555, 463178127, 476389833, 362003658, 275724540, 327453508, 632456207, 170221614, 287395486, 17817613, 628356326, 394643194, 645648841, 31312362, 127783830, 502361927, 256149444, 62089184, 871693780, 169421995, 207668740, 700306959, 734222937, 797251613, 213076186, 863501582, 350855761, 38421872, 510736669, 817707483, 381277079, 872128627, 65206971, 161189445, 15431851, 498573302, 358857210, 323228059, 669487198, 682032776, 858634776, 392272879, 501685419, 986109947, 374558482, 804011978, 269230248, 962692090, 45842300, 141551052, 871764785, 652398618, 32393840, 634371060, 349374746, 147060487, 453166990, 762703224, 824393718, 776318219, 648417761, 988554891, 939775431, 361529110, 933740706, 289373728, 227234039, 536528355, 41339786, 764442127, 233604481, 257266699, 381149365, 729158449, 522486578, 546019307, 146287852, 930694116, 90008755, 424330431, 487445174, 572648134, 962840614, 494019937, 321825151, 355020886, 138633544, 275109357, 436280664, 592915588, 939632589, 912578005, 442127724, 72526311, 411577835, 395949900, 529004299, 447942720, 885525703, 937358782, 718151020, 9208171, 274479847, 439889477, 538973743, 949210202, 94432148, 156071740, 942306036, 759100257, 591148742, 230735595, 278776122, 725413435, 409225743, 476050567, 658824088, 442298973, 816794040, 743565699, 919839227, 788376774, 103745504, 318415091, 749420093, 275600838, 369300363, 163374543, 643770620, 907192686, 78989546, 41118799, 874561775, 48435351, 213572892, 780166819, 363991396, 144137356, 248528083, 236491112, 356743157, 845660075, 991256474, 318146952, 96593683, 103060001, 942914845, 123067998, 597920777, 769162210, 838221314, 104016786, 835219687, 350548880, 207584677, 964063259, 481716124, 261928649, 622664897, 291628851, 4070510, 126696335, 667869101, 23733622, 298421648, 993439682, 888172374, 806469111, 112276310, 750306965, 763977681, 700701189, 775420167, 568977404, 725713149, 334700146, 294821454, 740134296, 12467748, 527484894, 299892101, 34453278, 922337396, 551417214, 474082976, 894650308, 629637355, 527301238, 51987057, 634869252, 119642258, 538143231, 396625006, 479612167, 284813651, 308045758, 760574246, 321851894, 69874748, 981626676, 241441187, 395157513, 123725985, 456561299, 819607006, 488597475, 963084577, 626599924, 416875721, 920503144, 806638202, 44185495, 694641742, 426040986, 576822688, 587890609, 874085990, 245492986, 990588699, 902324428, 478166465, 630163117, 652322655, 691774702, 726041102, 997210045, 887434515, 925781915, 395284642, 467986985, 653984645, 160684134, 115042867, 984616555, 224037035, 235668566, 604594754, 301123944, 109995806, 803007829, 476109644, 960607613, 641402975, 496486832, 636084305, 234102648, 883875240, 156582557, 757602118, 712936604, 101899289, 898613904, 57455409, 398264593, 194457379, 3075162, 81109220, 89948470, 32539664, 603742698, 677356359, 542612475, 698202203, 319679279, 32178710, 124184170, 556471759, 415989399, 134821426, 654456179, 81524781, 472360352, 641340755, 337575578, 303948539, 227446907, 313849217, 659440278, 712740755, 156592784, 706675632, 652694438, 451049965, 560523017, 656146355, 601360187, 420886154, 411525674, 283151623, 118145294, 325909968, 168681856, 344136304, 777063399, 19395518, 942487837, 222120838, 148330985, 1537594, 990387959, 874543287, 118046944, 603772537, 483090057, 922081316, 130916018, 703568136, 941237073, 720371686, 425033383, 111652452, 768436390, 225904196, 262856765, 270263702, 933939341, 63977023, 678541383, 493201842, 65591572, 622650188, 626153602, 485340516, 768268355, 842940195, 286532127, 847767297, 679552179, 615095193, 108427237, 131794833, 424098449, 102032942, 178461411, 398451121, 250970009, 157981278, 890426906, 530615092, 778917995, 976838595, 32801313, 87015558, 524272063, 468666664, 629438017, 360710690, 484051057, 589142096, 621550759, 746941543, 65226776, 699283267, 845541591, 232467648, 340703355, 485821337, 966641417, 617579938, 911785189, 668269633, 601857977, 587109096, 157208720, 727643271, 376030472, 850263867, 759904130, 781907744, 656734045, 43406179, 543601073, 874228208, 83335087, 857667271, 634595907, 755801743, 991328532, 770772534, 51335257, 67987993, 569243021, 405090906, 811952624, 465160579, 313196346, 40954909, 267349697, 854908705, 84213508, 549029513, 593732381, 887617779, 318010086, 868207622, 546019321, 804252734, 839408917, 764936156, 366013232, 642739538, 206744394, 779517242, 196445227, 935776326, 596600096, 113749095, 449377795, 821590621, 234282385, 155750006, 3210504, 931484805, 265654853, 488383667, 408803783, 183277731, 66120858, 441697997, 716228403, 912055686, 953478742, 770747172, 618371798, 543004634, 216042791, 536738115, 292180719, 181669924, 147336032, 761055082, 708788867, 701926947, 604166552, 605781890, 305262933, 830270420, 840949796, 468953786, 305079982, 211407008, 183837544, 558340987, 244744720, 673333037, 32073969, 253008061, 153676706, 50024921, 868109893, 687985138, 800445637, 235856596, 843153286, 954207371, 372855950, 197660071, 17138960, 378403391, 714168818, 721730386, 860169708, 909692379, 312884099, 699313230, 523406877, 224698123, 522394758, 805721804, 399535228, 79351898, 793558593, 317956623, 469377347, 915767636, 322265569, 113567841, 882165768, 375418991, 375787698, 406264355, 754374381, 65736069, 513294537, 13915602, 311895837, 174364363, 551314634, 230115406, 17509191, 731640718, 184750965, 240936982, 608459212, 759556139, 386427072, 939941306, 1084596, 944622295, 888105818, 683429213, 467941196, 167555162, 800811412, 943520634, 685245164, 365344722, 625947429, 590033489, 288294686, 426303363, 760000717, 686610972, 983654797, 30223327, 172279920, 963468190, 988195975, 930101545, 447318843, 107940831, 279717184, 768256643, 359825952, 124638361, 313620877, 715856057, 918988234, 558561981, 989231476, 21003731, 747581316, 476059631, 513294160, 366960105, 522654444, 92677193, 306088597, 841367108, 139531625, 787389549, 799651660, 550269972, 88698557, 593197782, 232982813, 689678434, 986844354, 761831103, 126982039, 33465291, 460509975, 368177552, 937219458, 235033911, 720237139, 825279117, 190825576, 233886638, 71204959, 332110214, 589417586, 245733294, 898966545, 434155050, 894429496, 585259268, 316509982, 178786252, 624388191, 660786840, 767113303, 764543690, 788631982, 167750499, 742082530, 531415963, 213174695, 616996716, 334574013, 580504278, 199717139, 850009152, 841537564, 196654876, 80266104, 116741407, 667361367, 981984716, 976840858, 460754639, 937996385, 838440728, 214294784, 879479458, 809817791, 445464182, 150596300, 823856223, 448103373, 773219400, 974944955, 502792891, 352686926, 525624070, 619956052, 473238333, 253580407, 687413772, 818788556, 56760352, 209812276, 33792159, 333566025, 39078170, 898679936, 291796560, 888947360, 329867394, 755413328, 47219272, 658943141, 237915059, 615934050, 503022788, 956240610, 80616816, 962431806, 19549209, 460822167, 319645836, 362350400, 710827991, 86264545, 674413469, 295518697, 651762883, 910589985, 605286588, 973310188, 449044243, 519204052, 622339434, 655855127, 568395026, 972546951, 917275994, 740527326, 263374100, 520628329, 184557159, 258614287, 816946929, 447570458, 508861, 275081474, 291974591, 730087353, 851185258, 710364590, 311354896, 631130942, 961147529, 82739541, 961145646, 984697287, 718206659, 21764960, 54510538, 24519650, 721515678, 958759189, 957430601, 746631037, 609729141, 93658442, 360745944, 987356916, 292121280, 497821393, 824333194, 74286612, 313399709, 917396775, 295822238, 607511685, 889658547, 549139919, 708774626, 362549790, 973150238, 292092011, 947383079, 852676077, 160314994, 865491006, 671889161, 489158857, 605942765, 108322917, 18795017, 317117032, 428474051, 339761377, 691469075, 396274082, 309970246, 513596893, 857381369, 901433946, 176869187, 441183761, 209526799, 786822940, 859679505, 651239734, 790121296, 509212792, 438472130, 174189969, 903043816, 270602641, 354054956, 284536458, 429755216, 876290380, 206661418, 866409550, 64084268, 986880876, 953794047, 189532375, 542905201, 646572213, 427516189, 25482982, 883203732, 764534192, 347676473, 562783816, 845541065, 196815944, 588370287, 185936183, 348688018, 34943815, 165931412, 89741939, 76699180, 864208276, 2404070, 332217312, 945088076, 878169220, 524468853, 587817646, 972565213, 426902669, 25971855, 413641425, 560821069, 822281268, 44567671, 153763262, 356458470, 690319201, 415999535, 881209647, 48305157, 975762445, 920708188, 905282401, 577243441, 201592697, 684366277, 904052808, 896596240, 354975142, 131960987, 893244763, 83723961, 342350361, 196034410, 112495163, 948597001, 278089646, 105570022, 649957672, 481107234, 977707439, 895273007, 818563848, 509038466, 359768011, 63504892, 372846840, 527375253, 707243422, 689616871, 102383695, 698207106, 123651426, 948438160, 535497711, 131534098, 16658316, 403169530, 643566501, 161522635, 183850167, 352800487, 947019580, 299185716, 405296286, 867141854, 350771533, 870507931, 27009692, 973925489, 309578891, 494835714, 298561821, 160872588, 6862296, 113446258, 152857019, 956147144, 989695262, 336468124, 892508321, 174059518, 262175966, 662392475, 20747370, 397147732, 178690478, 431528937, 374329264, 963338409, 573516642, 352864060, 483298332, 401691709, 442975669, 461591058, 887727334, 185041345, 661306440, 863201774, 246063444, 329089016, 786956189, 117517976, 961495315, 286759501, 419145665, 913321646, 204035774, 19380998, 565439199, 490761667, 856236244, 13195176, 599609243, 441845076, 611677230, 933405833, 381525746, 822746530, 194403901, 667143271, 793103110, 468159389, 277666996, 997633658, 419910676, 546587783, 340123275, 88942993, 911635474, 306830386, 597275106, 216726959, 639616019, 892079684, 388053367, 729962713, 147117206, 716948108, 589977770, 55940031, 200666733, 748524309, 443198776, 347528534, 407249340, 499066939, 172348639, 457514235, 962178581, 470101229, 198321865, 922990170, 624953146, 552401725, 524837661, 864305256, 282422892, 255562397, 414153710, 721844924, 246288528, 129984255, 588884486, 679412175, 246368085, 653829215, 842883845, 120580762, 178617481, 861788961, 251478023, 449666290, 580073675, 700044777, 938011894, 163991800, 592823833, 71376831, 704025309, 695426386, 391098840, 807107018, 577911888, 50383105, 88784452, 494774456, 520254808, 25103493, 562961574, 69353142, 469096372, 718612190, 512938717, 675473213, 221263375, 800602198, 347838878, 635033361, 310918017, 396346634, 165230804, 310983013, 549187643, 417158682, 202973967, 13352410, 858661706, 651956804, 217227360, 416323479, 942154520, 79712880, 405875331, 456145960, 143486723, 289391373, 381298204, 902258301, 288874258, 148340326, 688795004, 325162635, 640047735, 156613373, 197560165, 737694642, 436223750, 33628984, 734415543, 189299067, 728080996, 391513459, 361945171, 351827650, 222919459, 139184834, 586243457, 986168753, 531487947, 644321099, 432079745, 868371871, 279178176, 39005609, 70001961, 478138480, 342461408, 873352067, 252095936, 231398461, 341674849, 826221847, 22720563, 539680857, 883796549, 115691161, 916712734, 790238066, 460243813, 171187443, 932370625, 183196236, 677091601, 595281894, 647352007, 469898729, 970737815, 574693367, 596676918, 593589709, 490349561, 349443365, 305312163, 548364821, 103120937, 868984703, 125904814, 661716466, 559368625, 40960031, 479119670, 496828400, 597814141, 41281820, 770235948, 742927443, 846757222, 37518979, 339517917, 389103789, 442350892, 645847346, 534448774, 747233460, 177065154, 72186333, 548098688, 854027439, 425984264, 542699688, 602164789, 110406150, 48678539, 991060483, 738079760, 556553247, 124463927, 6024661, 354933786, 168241782, 705693286, 965254357, 864471863, 65635684, 865820111, 102583220, 230197041, 977914964, 694617178, 407424471, 9918295, 773169689, 189595968, 947766535, 574952795, 898693372, 512832757, 130715656, 269481036, 199067150, 86794194, 758819874, 786516855, 434603480, 813137386, 603134710, 184066083, 154548272, 332658552, 781428919, 98298478, 387036520, 124746509, 705276545, 251671563, 93305257, 96479509, 388404506, 508915714, 543479223, 192878197, 618531230, 636837678, 812512015, 708963024, 656659626, 236414500, 883671081, 253852993, 741945285, 905822784, 418918585, 883790402, 794789015, 278860852, 258177663, 111724771, 294270156, 70041412, 979531849, 692908281, 322837068, 659929806, 477939119, 668735400, 893669091, 53667357, 640574557, 114428629, 247205984, 564261738, 325492575, 184244529, 616829362, 799041771, 598895557, 543350205, 7308893, 874277818, 518837647, 539298296, 118357996, 272239214, 75005465, 51690737, 129643894, 479833642, 809478979, 7275918, 648278177, 453347504, 736870103, 818284380, 828669043, 955200610, 847389936, 664743906, 309029792, 483925235, 975891916, 267380949, 775640858, 836256493, 663624264, 305412531, 112949625, 928585716, 339686382, 766743636, 997271816, 424953165, 207370178, 447236056, 479228237, 605803283, 883591327, 994592584, 473559264, 691825390, 59026281, 917978763, 46972958, 425183058, 16064290, 1839961, 303342030, 656684479, 609323398, 433475501, 985528226, 101388875, 136302585, 591960578, 91508745, 184542045, 809719350, 22428967, 902867101, 638182620, 626640464, 793625058, 446718846, 318363922, 420538361, 642814064, 409262984, 383302368, 115376576, 474868455, 705817310, 670369963, 542155010, 430439664, 625850429, 111647532, 313083692, 283134903, 126900746, 467748257, 394877761, 552775839, 915791764, 613204921, 870150479, 214240138, 709655150, 442856918, 170094840, 773014055, 562719901, 509492555, 907295643, 714342542, 767339475, 707888996, 460529712, 474737587, 74092315, 187948792, 195903948, 298823132, 14508169, 516251583, 640486235, 510535706, 341073976, 110725252, 244465724, 720416993, 123562227, 560385561, 984851360, 227622481, 295240153, 7468945, 158115048, 100392990, 161449362, 752302130, 796605070, 463713576, 313737765, 266787460, 55065998, 884326617, 371613208, 790683251, 245621505, 540302462, 493947350, 146045611, 953972417, 850269168, 921316959, 782715586, 51088433, 814291941, 191519440, 766857391, 303594649, 418905653, 117909535, 600535368, 638574670, 860152644, 722121204, 531142523, 624268601, 519013605, 264059325, 182407573, 693056269, 80285468, 1737389, 546519070, 567843451, 780277723, 661325243, 888114650, 901522208, 804051424, 631855074, 781359457, 253006678, 207782284, 864062314, 130778504, 328706482, 914627015, 582085819, 412437047, 31803047, 534517838, 414404348, 908511268, 456893249, 428728872, 898523343, 475679013, 204427484, 81104282, 478073801, 354447944, 123137613, 638177091, 169491720, 708992949, 905194707, 990966759, 342395463, 245669038, 863598950, 100180736, 713872336, 767981252, 892657132, 894825963, 411924550, 318553443, 950671381, 468979341, 479178882, 247198005, 849653041, 315640554, 34744104, 714259221, 333482891, 553377415, 884112971, 337904252, 293232602, 744339277, 501599334, 662827172, 818971329, 518464449, 423765060, 987164669, 897329830, 67655249, 148540893, 995094076, 113235355, 628859291, 384527180, 327414052, 574277638, 28594680, 836820066, 689745064, 243695296, 512265434, 582224239, 687971437, 328485529, 375441535, 235441884, 784336109, 469845337, 58623229, 626581982, 334261131, 808435983, 340514423, 379174361, 457007090, 210508262, 782012683, 665538916, 228001136, 596333185, 833707316, 798250577, 567287628, 713686503, 208167258, 717156530, 754127471, 216674800, 104769787, 270623803, 277991236, 702484016, 674518682, 687690477, 47069009, 37700967, 170492248, 416735805, 143321016, 223895772, 566505207, 325457559, 157264779, 317052570, 73555058, 410542354, 385035658, 118598331, 806283812, 524884184, 828194775, 854201696, 285840435, 904903100, 798593583, 314427535, 202681467, 584537486, 365523295, 691178343, 783458235, 14843163, 198180313, 133694499, 210156545, 606632511, 511482713, 354103696, 757610402, 637722934, 272726227, 572900790, 577424048, 280206110, 12667742, 338940814, 952852312, 720219729, 332788617, 756336225, 447831344, 221190641, 677641290, 944481419, 520405083, 795825933, 410999079, 838950675, 959402275, 81423067, 719029437, 633838321, 4521204, 300943182, 17618854, 724417773, 321728094, 984024927, 549965505, 874924742, 730380516, 487740261, 895489037, 652340342, 763627725, 791749494, 807605999, 982457621, 923625209, 338731152, 163598470, 255261741, 981964233, 641446452, 94909572, 954499064, 299765046, 214914337, 542674416, 852513444, 774861600, 285425989, 706220092, 332591414, 839715503, 79697283, 976689450, 667728307, 498686398, 139248714, 785642933, 665052546, 79560628, 562634815, 646971828, 398229790, 822233847, 11929900, 186400922, 977413936, 300020367, 382923752, 988735401, 694893501, 301107569, 783187651, 874905424, 568540401, 760001784, 8785451, 247690337, 318191557, 832311629, 106458031, 938522382, 380296744, 306935624, 950005363, 254457520, 507775044, 329123753, 474489568, 48507364, 76969129, 310096794, 231206787, 282709700, 83248443, 890306236, 152379635, 509694217, 817590825, 568249284, 639754916, 551779849, 951442277, 171415781, 161547905, 53227824, 792386849, 625639347, 757487106, 68501529, 233007063, 173496805, 332316700, 256668051, 456142286, 759686747, 239271298, 675190306, 974213838, 33277217, 646293016, 51864530, 94745922, 164680829, 103691299, 96208557, 595719825, 642168996, 781423156, 629312853, 812223087, 449391773, 299335997, 740367772, 409546146, 363028912, 405152424, 82331860, 636765150, 229979207, 620271031, 18047966, 164224670, 994080285, 41890240, 69086165, 456483257, 331292189, 373352562, 379986524, 826974395, 268034908, 796122517, 520859133, 887555405, 230634955, 443623324, 72530821, 727627208, 289469128, 192992419, 659499429, 624541158, 567719784, 175198602, 501873077, 223098318, 913787484, 662681588, 205985144, 855554851, 32179380, 249011372, 681976873, 354440247, 204862596, 374048620, 490138974, 735991251, 806215965, 970813983, 451408610, 629653976, 505911277, 670980493, 962313273, 983426225, 589965559, 512085283, 179513847, 970789895, 974407036, 871878168, 519407270, 213787136, 435312911, 957130814, 714462968, 367972902, 149862953, 308663127, 751112190, 390748270, 359604398, 363849558, 540688939, 662202220, 321865674, 474169642, 246018538, 123637757, 818303253, 94831753, 909951539, 832017920, 665494128, 518637182, 146436693, 332069927, 764619268, 51886526, 984183835, 213930736, 96984077, 484826595, 950144369, 872228620, 122262411, 382061242, 593413693, 598899431, 793829838, 388105672, 741172425, 127383832, 879865239, 308593665, 601092758, 901350943, 537798849, 316224106, 214628154, 977268237, 56953881, 356325375, 866389599, 416820206, 421884148, 461199847, 474122134, 464732399, 555846098, 26205593, 650281206, 861326745, 905219735, 131306342, 272711562, 461668834, 595131428, 740174807, 149604134, 203582280, 550924548, 617780248, 346973069, 52961673, 363304543, 960584750, 715409895, 377268815, 243432524, 910002725, 478143441, 145064986, 218402664, 160144795, 654899205, 765880285, 563593153, 246764202, 977761044, 412249894, 853998093, 922459685, 603405022, 473836407, 976134853, 575300962, 656718439, 207732642, 278964651, 207172482, 888351815, 92774363, 742391977, 112911605, 442788662, 986755823, 856015925, 328161999, 108748489, 265852700, 52714856, 440570772, 354597167, 567283979, 557799111, 375549545, 678821530, 82422050, 745534640, 758177795, 579039645, 722894917, 88168681, 353492563, 356037330, 875286433, 572494411, 625028197, 24519520, 32527634, 112322867, 24377161, 923539512, 352967150, 319343328, 218630822, 444908343, 24466634, 12872474, 531895132, 142281605, 709484004, 218268872, 88729105, 114835213, 859412747, 723170776, 265596085, 192651435, 662182362, 123220569, 803241393, 162651859, 524022653, 948733864, 439430586, 770455835, 833151389, 488002927, 570939124, 105028205, 937333404, 970239795, 818411408, 980843148, 82076745, 655012473, 124006612, 619341464, 148179593, 733386522, 295941216, 339738243, 616749417, 995095161, 474285884, 599799109, 537285966, 5674616, 315254972, 833300256, 986417228, 821498707, 873106118, 501076512, 254134857, 788570978, 567023142, 812418445, 134254381, 11306201, 884074756, 736647957, 977428484, 260979275, 133574657, 979267192, 961153790, 299940782, 946333588, 360463820, 164103371, 151769583, 855780972, 216995231, 892099773, 615799476, 769764290, 361163841, 396482055, 64155010, 271258829, 291877754, 604401366, 527642014, 966904110, 45135663, 47079232, 66521675, 392294054, 408670114, 955340396, 217764416, 832048501, 315708653, 215601094, 623923404, 72203508, 74424259, 538785543, 8663837, 288694100, 371031602, 271905879, 177311256, 317496554, 602747755, 356192056, 999788827, 513118911, 901673364, 426288494, 626642654, 311795627, 871488221, 307250822, 340508432, 483905311, 307001793, 570868533, 26331559, 777105696, 69909183, 783193663, 4000291, 720282550, 52663335, 849294804, 678107324, 687435018, 763603679, 543100949, 430095749, 531853263, 307852485, 752942231, 875694728, 963506531, 165332675, 600713028, 379539258, 412393491, 406957906, 70939284, 889088099, 752134401, 257817634, 232847111, 436105026, 776847771, 744770924, 769578186, 71887705, 303494083, 992142101, 360344634, 339887545, 429371150, 45515921, 710858848, 962091466, 552142829, 535274495, 914949069, 76326728, 27382066, 992076983, 343851264, 853878887, 167356651, 231402540, 225117688, 875682285, 830417784, 417554547, 749098485, 179828024, 237503278, 595608227, 802931343, 960180196, 955041070, 431707585, 124615021, 526166462, 3341267, 233955711, 533291858, 376385527, 880052435, 607441080, 182966682, 318276024, 450796394, 502364727, 58938279, 675688443, 95535238, 94718393, 635902325, 276742404, 198387753, 160582077, 815072989, 795188138, 127027051, 654435886, 681393657, 389609796, 976420598, 391413211, 596045079, 378748674, 766200807, 664143348, 82654450, 712949680, 331931774, 823969389, 490460618, 857970130, 764204150, 798359448, 550268754, 341089622, 513432899, 238590008, 547465205, 642712352, 273529, 985062952, 934294839, 351238064, 150900952, 244739175, 306328911, 178232013, 744870262, 314938808, 306433119, 157621755, 294349341, 450207990, 803486604, 17903521, 487786152, 357763808, 688313820, 388139770, 216308853, 616750365, 982506404, 222793233, 956283320, 154858886, 231081209, 449800229, 620738046, 118373372, 806262433, 264656499, 239424267, 998118673, 492699830, 48766658, 142141266, 464880063, 533754916, 956447145, 750410809, 61592775, 110237239, 299544244, 871566244, 550376516, 122946793, 837379588, 392224096, 789122814, 436405968, 7143430, 275116115, 360398980, 272814024, 597827958, 952703570, 716780835, 661687126, 581171204, 220754211, 558837649, 433336814, 900453224, 288576977, 954478224, 228278495, 75631727, 77339749, 935587771, 51404384, 918885028, 8108475, 862734306, 176693037, 621628979, 556957848, 852560884, 874412746, 95337731, 496267315, 529123285, 117632351, 970423716, 682018439, 948442434, 629373135, 688394323, 534681603, 947487052, 928097063, 320477208, 135847495, 882651011, 107351286, 233190436, 151531331, 606316850, 559986692, 588637630, 930445900, 534166368, 747650018, 499622913, 662347792, 460071957, 400123062, 962364885, 667399069, 928008246, 90893442, 293304471, 438232580, 10117799, 628768338, 133923333, 934271246, 182546504, 806582111, 232922673, 330062332, 688783102, 448905010, 42538542, 279512099, 432379341, 270251259, 952857288, 154181517, 873674553, 500620960, 467218138, 995042728, 107750979, 515722934, 346174346, 779946430, 833449361, 594470199, 784254466, 595280071, 651535659, 821466995, 77600910, 387885271, 908194951, 100116453, 914654756, 588393299, 131603507, 147337900, 633931297, 473286328, 715821694, 636911893, 413556217, 393208143, 303910982, 195748121, 155069852, 520849828, 551121447, 38393454, 505356437, 182901490, 142353067, 802113852, 459445111, 253961999, 365035644, 277418366, 464723584, 494713494, 676866901, 776909006, 923206193, 899029608, 508402507, 717140547, 292875250, 209600315, 52862936, 41350067, 501618274, 474191713, 655846053, 724994345, 833582004, 155905573, 277189735, 976198278, 377219535, 734863494, 212375756, 860970572, 37055864, 577310743, 492894920, 366296747, 30668241, 449621236, 428440838, 401419206, 481631646, 425840886, 945393505, 850806536, 967941893, 922219013, 37168747, 967095169, 682825279, 33634887, 607641989, 485258787, 179742935, 354821384, 360105444, 455011818, 968739812, 99263363, 73904606, 925979781, 849915628, 103765459, 171099714, 831011792, 108121515, 356607712, 491736069, 855901244, 778508202, 153456390, 140649779, 597343258, 296524403, 545755799, 391244037, 500401561, 244383636, 903192182, 910600366, 527355627, 656610707, 274938347, 641178184, 327495212, 975361050, 156387646, 940989615, 287656975, 144118176, 829558885, 346967708, 677306382, 751630059, 889494249, 343429418, 136331635, 582603196, 758157453, 583229983, 360367433, 758601460, 469573870, 10167408, 422506365, 104757020, 794446268, 544777325, 779624273, 451987742, 753809324, 797907294, 580802485, 848366827, 485502287, 507273975, 319208931, 231742457, 830483190, 455117382, 861888325, 98349212, 50106314, 587815285, 587950685, 485025927, 894158900, 808864345, 279953044, 38047190, 417741773, 262728592, 836760734, 367211265, 838822391, 408064560, 973983252, 900240155, 365485651, 632285314, 602100491, 198472204, 340046646, 730302950, 159920059, 540047837, 236723552, 465029703, 412573032, 527187841, 985246501, 168524348, 195798237, 705544668, 684571212, 792596451, 743910198, 413020186, 418387865, 580255666, 59437982, 82068165, 829979501, 947644459, 203809926, 118772326, 575352833, 118334362, 408188815, 37072805, 253578569, 272912291, 377039962, 880587369, 426442129, 482764823, 524412568, 431509526, 962578701, 905505021, 240279959, 14659523, 904218653, 900877879, 838285584, 435923024, 486296614, 869020704, 316000588, 331908377, 20217469, 98876626, 141466250, 975573779, 105347048, 482264665, 33990321, 723273598, 411491504, 146787578, 868425947, 57482667, 735792496, 948321622, 42620594, 58225935, 488275893, 148233138, 703915410, 482148489, 41510851, 236307056, 469523886, 721717406, 453143751, 795717820, 669826256, 438908863, 81347266, 514107720, 413916730, 459249818, 903244875, 933321714, 439366813, 64654852, 152357132, 347299586, 758383737, 634368986, 572705896, 861386064, 213503949, 787075935, 393554326, 781890798, 580310749, 148796190, 201394643, 233067502, 766153164, 56355506, 518442151, 768972020, 589759038, 923440187, 221820669, 365872712, 542966254, 624404284, 774889110, 601095189, 226301356, 9142249, 583744436, 652302562, 335273088, 634969744, 550458686, 577309446, 297124893, 910017728, 403414254, 308352826, 564110301, 599395876, 306087690, 20258045, 852076074, 570751314, 321625739, 68665361, 653713490, 936361915, 323142693, 51290479, 485160563, 951185255, 434922411, 409629921, 582325749, 530156803, 585906733, 851723745, 536746066, 922612799, 118210625, 957248213, 342452559, 602667871, 284557240, 385133705, 913771796, 551692407, 747708878, 218798798, 52470422, 453474531, 63446709, 63411891, 63685281, 245466989, 992241973, 166089120, 880597866, 408588910, 847676353, 671992541, 511918808, 711813433, 522939506, 191787067, 878163519, 610788407, 166874307, 140259662, 204313941, 28106585, 294509991, 429650063, 76043058, 252960694, 819975738, 697680603, 611722454, 467096332, 751678042, 859642611, 822480776, 430952964, 521732527, 72544686, 201960166, 340054889, 158564617, 505283454, 184214811, 733356253, 686612085, 54292760, 403899871, 941831863, 953288290, 962719879, 631529545, 403768198, 810638560, 361049370, 429128791, 275338804, 273372069, 140809006, 413728739, 177544468, 34951266, 420293984, 659025438, 326848194, 333934333, 347069743, 521967829, 398189093, 280311412, 788234106, 654787289, 444373203, 506032060, 185725937, 385927182, 334015967, 52615733, 583101600, 194972567, 467819286, 253677809, 593003482, 433197103, 786376470, 192860968, 15394493, 501509732, 38375084, 484910089, 724630254, 975556971, 396112407, 470554190, 80202950, 970335563, 202129477, 499417644, 815536070, 100190760, 999742470, 73751243, 37398270, 779683748, 988972673, 143892235, 910054003, 46992249, 180481957, 204073553, 566849535, 206534481, 468778549, 124188126, 897018429, 337822105, 864112480, 827027776, 47597832, 756124654, 702943727, 506896748, 507053319, 486562691, 198534995, 204602446, 846906669, 420901797, 724916454, 799691195, 202181331, 207261422, 329660989, 646997645, 811665255, 320058791, 104619375, 800279638, 268261853, 107071772, 215128380, 361289557, 472243927, 803585948, 660675810, 931541977, 401764522, 565372626, 661383953, 755492234, 897696113, 715217554, 245902933, 188340719, 765048833, 732200806, 739958923, 636193986, 787198757, 95524746, 796852803, 910663558, 760326891, 584221822, 945184772, 93362258, 14005747, 189293526, 692397039, 714674870, 89556867, 263533101, 215481576, 358593109, 354499204, 636457853, 901593886, 27120570, 11142581, 739175479, 191863411, 803562038, 629344959, 166921326, 479969626, 814221235, 327286230, 157144197, 83527609, 110318190, 120253910, 179014128, 213401456, 66327246, 787401906, 65619567, 234655400, 481120798, 732398136, 161882911, 516072273, 832643132, 724787412, 339511614, 410195345, 887006303, 173538822, 832961986, 730085639, 905757342, 21173715, 992312638, 690835792, 882165427, 293677541, 347595247, 299457711, 783195558, 667930662, 679021537, 180527831, 745976359, 824142787, 247970738, 372157247, 773783145, 23422384, 311467738, 588476487, 762098210, 389220929, 665504299, 211771523, 178711248, 913128624, 588741549, 975775552, 688906147, 468518758, 867726005, 12038593, 31562961, 471718631, 779053591, 538071029, 656449666, 898674634, 793842387, 19423262, 890623570, 185398705, 846538636, 40705904, 445334128, 36874394, 657972029, 616611767, 229895069, 655058861, 155090270, 241408806, 641957114, 726645926, 967902040, 983305458, 845026322, 324752474, 885748074, 389895033, 9669376, 428681072, 676138410, 801683954, 898200682, 866388853, 49284203, 990825503, 35741725, 475728051, 952365472, 409593399, 290039292, 656880875, 84505291, 672458895, 790683407, 93080402, 850470889, 617552878, 897397682, 616431017, 919271931, 538894576, 28566956, 639387051, 397480659, 888331808, 312516383, 712129676, 139094357, 925189146, 429828751, 669729148, 657455429, 44143137, 896419502, 373965432, 654395835, 522667826, 393589332, 287876558, 651339364, 828680821, 314498597, 144910474, 361388886, 948141017, 899042070, 604577387, 297048197, 700671202, 243720448, 222587948, 421418856, 427568080, 669262092, 94881694, 350564702, 816069148, 933921780, 787406109, 394279576, 247194716, 659840096, 963491497, 621926141, 942366846, 377839543, 904423135, 106961356, 877196550, 630280496, 328306029, 381912402, 259658267, 256524873, 14405468, 91643580, 692379638, 778066527, 343401228, 265240258, 890313044, 800722146, 764711705, 88369697, 528098498, 768397667, 13367371, 983321651, 305640149, 967903231, 204662940, 756849127, 386404985, 473020925, 13509173, 189775432, 83246022, 122585254, 309783836, 919737386, 251511120, 224937099, 649517015, 42791830, 846714461, 954366529, 328480025, 308171454, 834735999, 832990885, 716279439, 676745862, 834852009, 890280653, 869334953, 655241739, 778403030, 392085988, 728926556, 129185573, 555171776, 475758340, 828180676, 229343747, 545625292, 632710143, 214951555, 887768252, 180476872, 540305624, 488375293, 447961778, 897829630, 150266682, 935871494, 239897628, 36306920, 14787071, 137613306, 19047148, 167181446, 221686307, 926231605, 440085342, 708241065, 321713012, 700623013, 523542251, 269123659, 394643556, 408705072, 430388587, 173026158, 90373298, 742817204, 679707901, 916179928, 827473012, 830180200, 389508837, 726194344, 34322543, 60782569, 810967191, 296956110, 985551922, 802735228, 69099689, 861993337, 882544894, 3086387, 354689796, 637067784, 147299021, 323439936, 749598214, 64963473, 875874873, 260169214, 786704608, 261894718, 832429561, 754318611, 736660374, 115594129, 71586299, 378870353, 263657928, 15351768, 115135473, 763413863, 306155139, 922764812, 918217812, 193842385, 113220505, 283673234, 20446421, 16479967, 685827685, 117524362, 817386440, 717058666, 227736181, 634222817, 962294687, 241449362, 254390688, 412708733, 547966203, 442524448, 926032328, 256891420, 892134103, 479945158, 235592616, 347569648, 954914412, 515973257, 350763691, 638109141, 69620416, 839227397, 51302625, 449501182, 366481472, 832015107, 905697926, 676741743, 37441717, 811644502, 416274325, 789866577, 872878678, 726743340, 572104693, 828643521, 720840242, 947503774, 827075515, 550898106, 867141112, 679405518, 98209130, 957702403, 892647889, 588425572, 227007937, 763830442, 318240083, 58845407, 237942466, 393609077, 548918027, 593320301, 471151375, 782958204, 680266100, 849048920, 365677646, 536392314, 258833786, 522137945, 497522065, 157628999, 138290860, 222570880, 278588036, 754198935, 765300737, 243730127, 364842562, 689214696, 860588574, 23809147, 751837441, 383716938, 107467979, 102524014, 141604079, 22445434, 383708256, 454334769, 766131067, 512348531, 434643671, 635422439, 481936828, 340270682, 479822553, 387097373, 478628106, 136538298, 729873250, 989536834, 485814185, 839194198, 969893055, 4900737, 372276126, 391256330, 586272280, 322400955, 116257783, 201582517, 799154006, 794300225, 236835686, 279983815, 993477477, 369815430, 804647179, 892199865, 979192861, 324767845, 793631281, 994992220, 664601851, 815841973, 802152572, 481526271, 221601743, 503349374, 80012548, 962958858, 84624952, 97545324, 792969558, 869502280, 5952227, 12200442, 275611054, 79173264, 328296047, 894689272, 111856616, 73832169, 961291301, 579954169, 418718740, 247387610, 878376348, 368490908, 714899354, 228963972, 607773140, 245918092, 386527512, 558984436, 136381378, 997533886, 132702955, 467577010, 848031070, 100820775, 491987507, 282871800, 336610001, 620134615, 769068281, 501973455, 139295754, 264083146, 272601696, 430570829, 807093744, 219252454, 832278446, 950552888, 343405088, 545771506, 85628197, 756524483, 489444644, 87426885, 991414415, 718515819, 178071277, 832206183, 782271513, 748136731, 746048966, 977128489, 392663501, 611073025, 961012791, 281531197, 770616258, 131516578, 460010674, 181559960, 184901923, 140130222, 620508282, 280619199, 736895170, 913924541, 539355591, 632174008, 541178774, 632340676, 398202035, 600686647, 818558575, 486505624, 342993818, 847300612, 356669333, 526124381, 60567816, 666820815, 365779667, 123664146, 83567939, 462288019, 838231379, 783678923, 953912780, 874530275, 307029860, 634172780, 744553708, 988942517, 927420850, 521610862, 191596103, 264213125, 779301551, 588329793, 138105331, 712890588, 76568775, 92592673, 709013842, 849662506, 594870278, 156091065, 342054969, 655158962, 65059224, 293813930, 179844671, 795943374, 562903713, 792017900, 332165468, 800009698, 355719822, 141410014, 772197398, 29987170, 496971202, 782096921, 9511903, 973860547, 483125136, 20856925, 489468238, 901683957, 540086535, 218100136, 55992999, 473142471, 137700979, 915020229, 484106322, 762566259, 688489059, 804832718, 501763064, 948104876, 869080139, 257758839, 926620505, 539801937, 636121458, 496520651, 874918960, 534686459, 635437789, 877337546, 343780108, 665644544, 860966196, 352073035, 697749070, 1196294, 960876676, 421307696, 731840674, 27625675, 973116910, 313212096, 128107501, 812220873, 534450936, 994009495, 228306850, 291519315, 417323364, 252461543, 142252, 931128482, 693419140, 601231913, 126368157, 671843300, 722421087, 864681501, 779788315, 325781437, 282912149, 737300065, 285388811, 369858176, 683062870, 931836669, 681026178, 247155506, 326225335, 736894177, 424866420, 58488925, 866913535, 891622170, 816644639, 648093625, 405827352, 911260283, 182424257, 770290395, 174191184, 4150411, 774823618, 4108660, 743975446, 208168787, 490626462, 198138364, 366394351, 870445957, 387643075, 444604691, 331991698, 435191328, 923185048, 177753715, 104798450, 646219911, 905397024, 638164196, 654227840, 883176406, 905225405, 823111004, 956537599, 652464395, 505104612, 769438038, 271049490, 680409691, 510953996, 362219503, 942628136, 686594763, 634394679, 307769389, 761259012, 661809624, 650113291, 630632362, 168359320, 810572495, 643931930, 784647314, 95056044, 951033146, 638136740, 863588614, 853675748, 47578849, 421899416, 331160152, 834725851, 855728453, 607509943, 36937423, 743193693, 936642759, 290411570, 411723191, 990451633, 332825027, 398059801, 640363300, 287945920, 693537698, 282145936, 306438604, 847249586, 131540678, 369443719, 330733776, 781509985, 12753738, 438680734, 285309347, 314556861, 958172992, 219745090, 260961079, 730818986, 719235046, 839848415, 193625212, 243314522, 959630475, 176591567, 758314340, 316260654, 46265904, 295087648, 160330897, 108167996, 884371830, 142154423, 502958324, 565641005, 657529573, 475968605, 757412074, 327458913, 199322076, 966625898, 30609535, 416300726, 938067022, 564112476, 437062694, 512900551, 27007244, 21411781, 239239009, 428130388, 633965992, 603277200, 643979336, 230237357, 211907456, 642880142, 919276860, 414752027, 143108587, 634480737, 120346170, 450902980, 77506502, 274185939, 597194145, 662190081, 897906438, 150517776, 831574552, 449974368, 428361517, 312056912, 773669575, 489389838, 285569902, 79459623, 542069951, 712228583, 107133132, 28761430, 940563832, 553415065, 292817390, 711512976, 258030994, 354450575, 876418054, 336882332, 524380790, 340457841, 108415604, 300285695, 954742499, 327667475, 828543638, 988106149, 506696635, 895943391, 950797161, 553319755, 486769371, 512421505, 698746901, 409456769, 490436629, 275097524, 803398459, 585682747, 949493785, 978811112, 771552726, 845687037, 811847611, 496213004, 141468545, 129098766, 783328915, 440395657, 985895271, 855593251, 260813747, 483653543, 735144407, 122805111, 645551721, 279599743, 373817348, 920627756, 400492120, 270723787, 153974836, 866940480, 937663953, 68447484, 292793089, 988017721, 850209413, 522828609, 476495156, 765260244, 73146616, 250529999, 247408492, 961215420, 354036239, 714267514, 270162488, 315275377, 64284984, 272811048, 524935662, 375512948, 995059382, 223363315, 871038308, 837292827, 372529388, 975813179, 885087224, 763766290, 427781802, 216285222, 883435572, 939301911, 832218136, 699834542, 938060958, 450736661, 189622830, 686595908, 404014021, 145447413, 304864036, 157931319, 781374529, 51334533, 80066663, 474144275, 409862634, 174241401, 62369199, 750698486, 428009152, 201924928, 246472049, 849223496, 14321115, 528092793, 935882597, 267703850, 949060350, 119274948, 952920191, 752989341, 644805712, 632290442, 797867240, 613135422, 267184003, 864580937, 709291509, 930645476, 833849270, 26910290, 132152252, 774331604, 763015350, 687893553, 961045022, 878919182, 655664716, 75110999, 726722434, 392052977, 884378557, 768761661, 530037520, 335780024, 926209323, 553648276, 899025089, 769672356, 920142909, 332516539, 851326071, 474128310, 790250909, 465012543, 854401454, 741220762, 44974397, 266177744, 658219589, 41359588, 932579637, 845079905, 330929584, 719197572, 158556786, 444671906, 236216541, 652255089, 119750372, 78567224, 476084798, 16104567, 769990105, 4385926, 524021409, 965209151, 963443075, 387345629, 160924037, 955094541, 700752062, 170935525, 960810971, 809840496, 3982538, 19994417, 30185983, 236521818, 713127687, 203677366, 47983868, 717727818, 972556160, 232861568, 231662767, 904004862, 755642036, 29457129, 277769254, 585253452, 277981545, 115847117, 677230769, 487431193, 572866114, 316910769, 556676775, 488775236, 505033356, 541400509, 104393324, 356155412, 115222322, 492928764, 273205066, 625762419, 947496921, 65056186, 636060195, 260205126, 570651840, 995034333, 556903501, 761729331, 456869460, 100080824, 62081710, 208851629, 290945946, 514943910, 355417413, 486276010, 514831643, 631767619, 313131595, 849376, 746536661, 434813839, 25464667, 494667124, 194855833, 570764320, 273836659, 550422141, 205177688, 263178313, 391247897, 21951665, 626653896, 302342080, 176401659, 553027694, 72178859, 888660654, 398725672, 658265119, 733193879, 386076982, 912509770, 641719246, 455560541, 889066423, 158587127, 642040622, 728285824, 780839552, 406184814, 362814576, 712296434, 647535550, 163490514, 798221621, 593830090, 724650049, 86603361, 881761606, 53832115, 313828577, 875270519, 939997497, 407375321, 929479910, 872074954, 945068522, 109393944, 938467617, 414812412, 10409960, 25772565, 712551400, 926173003, 199685988, 390319752, 246017328, 428132190, 599545382, 545915202, 6876745, 851674151, 901278445, 668133852, 272606349, 128022117, 698685899, 403823418, 609321976, 717169795, 187808238, 254097371, 362365200, 341106691, 154931165, 771141195, 933732672, 616851683, 396374271, 219403139, 264212049, 399657805, 225757282, 196605253, 817450839, 225629518, 724288677, 859386010, 584885734, 18260864, 577643118, 710565245, 552254248, 436923526, 74859890, 705758579, 602000236, 131074437, 272937640, 592850745, 888013602, 277537830, 752852015, 792681417, 463336138, 983939838, 738028481, 724196602, 801781135, 729496683, 754972245, 747061526, 890067393, 298872469, 539917557, 928681337, 877221080, 815221049, 273229945, 59082971, 906025094, 860794087, 799204428, 954765796, 620688610, 537137738, 266413104, 653833811, 678846494, 107148693, 46164602, 816867248, 297129194, 121615924, 288405236, 601501449, 480103606, 152827946, 343611543, 373427912, 151307732, 341343022, 819318930, 533440995, 789778380, 578630242, 699687809, 980092775, 155496667, 683399245, 183823976, 282644429, 666145530, 436427448, 529534562, 870102806, 907770348, 501085587, 227549161, 459761418, 825139320, 784646555, 92825692, 65716852, 659496592, 232824395, 665691623, 161121878, 80933319, 688223307, 215275170, 404989072, 506895231, 680871717, 253949804, 978409557, 652192262, 644423896, 255706671, 893871805, 538609166, 486678020, 808014636, 624992105, 503405147, 992779407, 465631270, 765242606, 348571657, 207047104, 667282887, 812553048, 311835076, 392216584, 927785205, 828722269, 962107289, 217369794, 48204234, 653114285, 500894596, 346567966, 77436469, 822725552, 752908036, 207071842, 601161420, 279867888, 367588002, 488366613, 638716131, 206945428, 161165215, 327893869, 920716605, 609238686, 510144253, 674500370, 897332081, 964185025, 572973816, 269584410, 738300021, 652093758, 390547580, 644888977, 15760567, 392152302, 90256095, 79135934, 824849257, 317707387, 674326181, 759783729, 966232368, 259733935, 960435791, 528362441, 775640408, 719474797, 127387871, 51962261, 980940310, 316977232, 588277253, 342540573, 526928489, 376054928, 823828884, 558563255, 317350968, 255503538, 887395085, 289082337, 174189809, 646585598, 339256439, 459966266, 442937407, 837074550, 325331295, 409345710, 641930711, 182211392, 684324793, 610533681, 940268406, 410170191, 540887672, 767596889, 903265490, 37421414, 624682016, 565426447, 567388063, 375068042, 287281501, 463007953, 640610845, 364969975, 909198326, 856530971, 71009693, 304230722, 709243669, 560257292, 50929644, 854492979, 815092109, 250742891, 377486035, 223723865, 151521094, 445351469, 322216648, 384545313, 43030515, 477707583, 835058645, 783435222, 568116482, 86281731, 332556669, 285172777, 319304784, 944298492, 747267426, 435972653, 234406837, 850831516, 994458533, 259161356, 917919473, 946323815, 590866870, 858558782, 883315464, 811934570, 99590502, 276038125, 259772089, 402015391, 568414745, 548816403, 616441902, 890543095, 850554065, 132514130, 270183825, 118282956, 713247837, 428263233, 554404790, 451898917, 814738486, 860076982, 998482216, 94299634, 454903883, 205566914, 271846077, 250878922, 711272210, 804519712, 405266401, 713216399, 246101042, 373254260, 607711104, 205323747, 385630409, 973426684, 413705171, 379357265, 487948061, 457914101, 647279841, 63130713, 45769349, 495055788, 577397462, 351521353, 924889771, 577010219, 133267422, 434294021, 189827663, 196341921, 429681985, 933398897, 482198966, 43473109, 712956207, 878175367, 748910972, 750409572, 595710400, 885205199, 100840886, 475592361, 736782579, 251267673, 295152869, 990954632, 911030842, 677566837, 299513962, 956572824, 343725589, 476999838, 120098873, 921660328, 259706027, 155764922, 348491650, 580898952, 54744830, 701158327, 276009207, 599142801, 64003728, 602197008, 701035209, 858970919, 489725061, 670611656, 420049812, 915970181, 327594742, 598336881, 645769244, 124629598, 93258424, 838587170, 945581794, 972568743, 554982540, 260202586, 683222978, 263200192, 337729622, 753690806, 812311178, 994499840, 700721887, 273722148, 706798544, 62840720, 743314081, 574985732, 370004104, 270260137, 890910361, 513165174, 416040337, 993086525, 499898267, 685426513, 217404368, 536985014, 902042262, 627370239, 141241742, 177100540, 623762037, 821122245, 807498404, 700532187, 201537832, 799351125, 233905464, 661925349, 392200030, 652804348, 498793818, 731108883, 854709274, 366609248, 830076707, 47792956, 179488799, 254449067, 920253666, 931931681, 85063150, 408804226, 362184849, 65475380, 470414731, 286204643, 194045790, 840223828, 278060791, 748022798, 687067234, 617291517, 231458253, 815834204, 247187323, 416819409, 139888134, 580423209, 740694299, 441597397, 928330264, 860911551, 198180356, 31207990, 670965392, 918103020, 298005583, 503649707, 390119991, 222904065, 691826545, 794267812, 527356081, 261371633, 53799248, 493569238, 499494306, 811954487, 450671545, 593881102, 861247761, 500349865, 984956760, 348881212, 238898369, 51925851, 140795233, 146812238, 976845190, 926507078, 776401657, 973977046, 319542959, 650371605, 703915384, 595916887, 489247914, 902731663, 675251957, 355385882, 541569982, 416725711, 826311200, 485544719, 728710764, 294826729, 587381335, 71506197, 338861067, 461664600, 750974253, 799043876, 697881863, 386962531, 120073323, 51980544, 597206945, 167100008, 909448462, 285646025, 423071721, 910340263, 591669951, 505009781, 741048131, 172747664, 625745772, 992007875, 420635320, 698439770, 205060455, 476539910, 527088152, 308245179, 515952859, 680263972, 818047545, 109463172, 729141376, 927832725, 107885821, 323103873, 806109936, 724893457, 834749467, 792477316, 33112255, 768545839, 653609548, 50560309, 538964995, 989299606, 911055212, 891886750, 833000883, 953543220, 484841399, 275005795, 748180709, 680692618, 868364378, 756155580, 536639201, 907976035, 928327361, 271929844, 744273497, 488463221, 863939852, 498463600, 407434223, 803529914, 288641798, 848073858, 997476638, 888140717, 136634180, 941959940, 189132057, 406424369, 913391405, 776343648, 643673574, 238609772, 137207148, 528639743, 37228254, 67848085, 943969485, 284615267, 833172452, 13936530, 47154039, 367151477, 597956196, 68907850, 937285129, 840496172, 886452027, 972631079, 210614486, 453232156, 411378388, 916348876, 562780129, 42411267, 362859653, 236876989, 63429436, 518756760, 683078480, 195055935, 997881204, 273469350, 135294073, 895899648, 504569586, 821923230, 622765828, 204761819, 837153718, 843738097, 114578501, 808707756, 413096248, 40301403, 710426501, 816997126, 542766907, 835325038, 415226274, 534819205, 699448574, 446112970, 638703812, 34782637, 197319290, 785914000, 505753199, 337069284, 480009994, 669364264, 174801251, 832625841, 916674854, 457336753, 307663939, 526844759, 82591284, 798644865, 421978467, 635340560, 215624763, 299176563, 289506471, 561243274, 897318856, 358876871, 305196296, 986420735, 82787891, 638399497, 747671921, 360201260, 755415131, 287578032, 822326129, 45259867, 847794028, 498546025, 930707187, 852840083, 36683045, 22633146, 58168256, 614184710, 281716685, 695294646, 126844102, 884314290, 334169409, 233219187, 250429498, 115725024, 14688906, 433700321, 594935993, 297880885, 360232101, 688423466, 699439847, 623388527, 216161199, 234379689, 833486619, 852270426, 745713105, 466456948, 910639312, 146756022, 834840770, 355289007, 372847708, 661211377, 597296877, 539099087, 659257064, 942842740, 98919366, 554433373, 31447235, 678583434, 755288119, 345626868, 619733276, 966933067, 384102165, 217356781, 989761573, 173056867, 640790874, 2763688, 153653850, 249167913, 692820118, 135496, 222074741, 60103080, 155073379, 837032798, 762943992, 136265398, 508182254, 643976666, 402210364, 45870844, 943426375, 4233875, 567129266, 838936497, 968701592, 730283030, 284296722, 57683495, 21265333, 620956154, 757355995, 850364070, 992909733, 650015825, 387841578, 666061114, 480815410, 334821416, 316486978, 178518833, 677891574, 415820695, 908606220, 449431480, 663666055, 71820030, 393140681, 4894284, 400475413, 966414297, 892380430, 924813795, 388017159, 689530464, 112598501, 859747346, 356142632, 406767134, 768779313, 265562156, 641325210, 350430149, 215965983, 226075042, 4078570, 196830379, 946395527, 509737810, 360561181, 874516617, 357030979, 398482668, 635301664, 779851943, 434947363, 99565464, 231558591, 610436046, 158774925, 872813757, 882848273, 110258487, 75659726, 220431860, 699876385, 621039731, 716333097, 460253787, 234174190, 384655273, 90085425, 617402144, 717406241, 721024333, 334170866, 909643953, 82179475, 374364121, 365631848, 510592627, 296990417, 689219808, 226035033, 365210617, 338894027, 69196656, 361252214, 97327534, 557041556, 520542549, 894694523, 682773587, 549232909, 508156394, 100328961, 114503854, 400990861, 8775129, 538671047, 701652494, 213797193, 105456172, 700742296, 716433970, 240850991, 983604861, 683669864, 868902283, 745012844, 953160286, 196149903, 19797501, 121556193, 335069560, 654911562, 28629223, 37078931, 176765500, 119634305, 55194190, 291624122, 882507728, 296692222, 252673094, 553032586, 826782799, 607389521, 520269570, 877368324, 255381589, 464414850, 815446841, 379901126, 778964985, 730538769, 774193657, 936995082, 410631333, 217516935, 767586668, 807546907, 603468839, 469263663, 151934408, 481060594, 130498305, 984509549, 40131792, 198120413, 539661606, 4634204, 115403576, 651339502, 562424455, 105355632, 351841854, 428637068, 445063772, 77647810, 913307529, 213116906, 935262736, 578838510, 648756140, 664678803, 393249287, 336526046, 731906395, 112122331, 744364101, 811327798, 117977037, 878992381, 788380250, 46252097, 871216303, 805476786, 120910819, 76933797, 78279525, 877866916, 366321785, 858513335, 465860558, 549530172, 664660078, 544383310, 717497224, 304272802, 263040487, 633794279, 9882143, 333168730, 350107127, 846094748, 222959279, 444830568, 106721657, 425681136, 121033601, 515281109, 749899391, 876051460, 622981884, 564357240, 441956274, 156714363, 744725273, 981964425, 656093936, 655651932, 218528239, 174751861, 390587341, 477738225, 730205415, 277009613, 275650903, 814582262, 384437177, 691339514, 767457167, 490029856, 644318469, 671685959, 26730300, 196363399, 435088080, 110485903, 672227232, 487202742, 509746765, 478541880, 692392912, 940732485, 829178325, 259034712, 618316003, 669248359, 432426980, 619558927, 659930758, 467990963, 847249811, 607398665, 332400118, 427573769, 147912417, 351478051, 131261000, 688859924, 302665184, 577707013, 842972551, 979653766, 150195102, 334905819, 178413724, 328635598, 614977465, 466062090, 154837206, 470064868, 792463664, 311529973, 298859742, 842321258, 666385831, 780049850, 736544056, 406725512, 705271552, 421074040, 159231871, 237349410, 976500005, 695137659, 836413720, 955968990, 15228263, 195083845, 27911060, 329721009, 904901023, 178046688, 280684151, 164036032, 520821138, 867389640, 331011361, 257532803, 477994721, 710137048, 439878942, 944141385, 452529848, 564767691, 92742400, 55245765, 544093541, 433702430, 625172501, 801640689, 589259290, 933704498, 484432773, 934889363, 322530341, 976985492, 378325950, 386807409, 741085510, 985817668, 214586804, 756365519, 209150745, 533572208, 794844225, 113928437, 921524034, 338069977, 302982574, 864041183, 383769249, 83056502, 283327759, 791888621, 48724982, 483883280, 270517291, 306158502, 166884030, 113740652, 757310079, 157070723, 76897164, 534222037, 730994329, 80661216, 879110609, 603639029, 759649075, 490331938, 349897879, 929805724, 259481009, 207190289, 16563597, 699420776, 874229687, 595541109, 714907032, 784721093, 309187483, 729561427, 492142566, 831007873, 508302431, 33038817, 608348603, 152817656, 405237716, 985682011, 684551333, 927032937, 363716281, 38414066, 640739106, 975555036, 51752881, 131902399, 863725658, 543383394, 819406343, 394085882, 186977748, 379090547, 553001434, 99574491, 643277025, 5735851, 396377709, 405316928, 940572054, 809212344, 16600679, 794265701, 602887552, 84709338, 884731221, 419142874, 211690433, 148865430, 752137121, 640056619, 896097187, 266692157, 606929172, 680590309, 615203049, 897806623, 50418224, 548441633, 3685210, 940130055, 159718684, 964837371, 511275029, 916746829, 943140012, 558107004, 830925002, 427874024, 543845029, 232185792, 200955652, 482291340, 520892074, 854427873, 428281684, 290409805, 472624468, 399068836, 174848496, 459857570, 302828734, 519927154, 543276936, 729077687, 687288019, 490605009, 81009771, 145480452, 403882915, 644231960, 234331507, 290586925, 944876052, 286404972, 756891076, 686833042, 861922003, 329397496, 311347126, 449165068, 645215355, 758114971, 828217262, 953399294, 16589279, 570039527, 974395327, 687997639, 987370663, 165487250, 87453989, 386867036, 690346928, 459934965, 78308132, 66423094, 689926028, 574534329, 300011216, 638765049, 152526746, 918121765, 167405643, 711558113, 171731646, 639746161, 213498637, 458622712, 923537579, 403645326, 514838512, 917662531, 968724472, 138663413, 461449486, 408934839, 847297755, 687592889, 365219226, 19303767, 965497968, 923992532, 460903392, 322013944, 934361824, 75650549, 799046007, 706898352, 453974419, 548247275, 526204439, 389231750, 283704223, 93706973, 99705835, 771999154, 596084134, 827939194, 793718875, 369991083, 911845143, 258518926, 733872243, 345351803, 841920064, 89124813, 906000908, 937565824, 753571666, 5073504, 118904995, 158550672, 290696755, 347065303, 788064957, 735001313, 802366638, 289634, 936587428, 593358220, 344975653, 571837125, 476373717, 15012571, 261682882, 501975824, 714738988, 467203865, 125242158, 433514336, 83776959, 212178554, 162875153, 814220286, 571394877, 714351330, 672325427, 68839099, 834982674, 212495414, 497657983, 954177126, 873088522, 872704438, 960839978, 409288298, 586173681, 535641770, 4446666, 343349013, 104810877, 981493694, 400385005, 295211199, 605696855, 926443425, 839945484, 75925086, 66483862, 39509997, 883439326, 931859236, 310504680, 335286281, 389030615, 944502668, 313653884, 629080141, 788643086, 935470534, 320566538, 987474008, 216513281, 974306672, 732765111, 879734309, 26558825, 210050369, 267930502, 800455626, 359181400, 277669252, 949069984, 543609750, 233232894, 823232293, 461300901, 775132902, 599796388, 161436834, 876155905, 729465038, 797173018, 272425372, 131050927, 118185683, 473137822, 297411751, 504112514, 351139200, 810133927, 729742625, 48567996, 819585300, 705797866, 994249236, 237264968, 584894608, 860847293, 536374241, 451726445, 741694908, 638519272, 292750585, 889427066, 514545607, 29813529, 604297063, 511692233, 854768316, 498884968, 420253942, 616068162, 994543256, 925144297, 830455355, 379970687, 401795333, 39665370, 62699411, 57787904, 714404208, 581818366, 539423601, 457707772, 129102851, 831766586, 210186240, 736646498, 182323764, 465493818, 311463768, 577184491, 22582706, 806613440, 306172788, 641725415, 210967557, 5360114, 803167245, 307724100, 3191382, 295421530, 46191682, 160736494, 298308912, 992950028, 443069863, 1861804, 999978070, 960367494, 104226904, 298641531, 263323251, 25127384, 944535356, 584948530, 730798909, 372046823, 18398708, 675249940, 621293267, 287290813, 750215603, 885020075, 232815657, 67990115, 876334605, 380572865, 935843595, 398713344, 156946674, 713542848, 274200599, 254218626, 341782720, 808494794, 926850890, 216171, 762278065, 827122270, 662284060, 291415141, 930313282, 848385559, 387539985, 367042431, 500108908, 6238546, 55222123, 446947634, 545595838, 787046847, 942458577, 944561046, 431914705, 384158677, 992990204, 474876567, 364820464, 643511118, 600278173, 93056526, 274144218, 166763049, 373583075, 656927410, 177845305, 112176156, 863703418, 133886378, 975405053, 206466510, 219495619, 768349225, 220816902, 132353280, 822874692, 336803861, 220859658, 98832326, 381543485, 885710372, 329818206, 91211382, 923133308, 848753740, 801163608, 952295254, 773435718, 377394041, 717167000, 331179512, 749520701, 392473732, 695296608, 301954407, 913243045, 340430690, 367776826, 744634512, 825747631, 771581576, 946982172, 752568203, 656578791, 954486987, 518776941, 396058077, 806516400, 808482489, 578170380, 765833304, 729415520, 773630297, 728199437, 293473061, 192371643, 689263976, 132106109, 304124003, 749458128, 946129895, 833282698, 938524997, 324662387, 610979214, 119305720, 636872264, 108426849, 711307825, 723026877, 371998056, 523873981, 315808439, 337794035, 216425701, 247263602, 300384420, 995321040, 575534699, 586194523, 904305706, 452677296, 148465985, 47996954, 8696841, 930698144, 780524835, 692449916, 680677899, 674853883, 85621279, 353941257, 234907702, 199050028, 685132749, 904556588, 906210665, 944974047, 473955554, 574289358, 808210082, 486127859, 454296370, 967203940, 243078965, 117980326, 134077763, 146438551, 24577226, 822848552, 229063630, 564650240, 618220910, 900098963, 814476785, 420652255, 842114899, 915344446, 685804195, 650324655, 741309995, 758411057, 826271867, 235532936, 868432870, 349115519, 436033698, 401553293, 242955628, 47324182, 610283492, 747227548, 976199971, 530209708, 800407598, 725923382, 878652336, 464045608, 163091104, 634245446, 376109733, 626943116, 784720804, 305068853, 706728158, 405215668, 578817138, 755457295, 701269499, 879421749, 821725372, 400418474, 749692925, 129235058, 415644434, 542171230, 567048234, 875886554, 867777348, 53372952, 193230606, 706817432, 542619345, 652072343, 534300465, 694358898, 859520971, 123404375, 93927350, 461983173, 327944286, 185468777, 713484499, 174173140, 852398481, 157583882, 757054177, 272422878, 441525677, 937932404, 196355609, 432697636, 898097872, 928889185, 289932873, 450768008, 55738955, 191872666, 628892374, 365457023, 205106958, 734327271, 735508802, 203611158, 68127015, 171847505, 269245163, 363542238, 635965271, 295990957, 429977984, 126121269, 585997776, 310604507, 768311454, 341204071, 14065295, 901226690, 75980080, 733146249, 25867520, 34346053, 120147876, 267555879, 301556282, 833879052, 843944068, 656307408, 61730217, 821190340, 24655288, 874274770, 64447875, 713051176, 830796007, 308878628, 233699602, 970148957, 830490979, 756679690, 483110771, 463538391, 15586322, 594617560, 389792, 906423338, 111429312, 983728932, 685047707, 471892369, 795061526, 631374293, 256798159, 745543546, 587685094, 455029969, 537025944, 89469549, 897062439, 649498216, 979499603, 815329051, 919778649, 947987399, 179234439, 620527023, 268281665, 938102485, 976342193, 549706471, 835388408, 721638017, 455899658, 629493030, 46564404, 411661455, 976409204, 864650181, 837754339, 908201236, 605855973, 112166898, 586692085, 694471783, 775511362, 233053600, 701927921, 409852769, 510296852, 597967854, 203211870, 752457138, 265676367, 83447782, 962838203, 38403167, 687831288, 142708251, 137572041, 592511272, 560169740, 369970975, 82564165, 425972761, 524533142, 451333643, 305864250, 868463055, 707075470, 750479351, 546787523, 959869450, 485773607, 801983769, 351652728, 208723143, 599900391, 453631015, 760911837, 134810667, 428161134, 980669654, 455151357, 763047060, 465431428, 499817764, 397311398, 434432916, 140121039, 535337886, 644458695, 769917599, 141332517, 186722156, 293092668, 978221272, 651930801, 224573006, 488531706, 924007855, 899478699, 730770649, 957950896, 705121578, 979012630, 661522772, 978071303, 941421074, 488688487, 610994226, 547910532, 346837842, 66065227, 566367689, 187894785, 847978414, 447547684, 838780664, 336857899, 204944326, 730051587, 665839627, 258337726, 372422548, 341713939, 560923312, 97300577, 761787653, 356410972, 869200548, 775654017, 143141762, 530325991, 440708338, 80793973, 923741126, 694742166, 133435955, 596708375, 220255416, 897087125, 591452585, 90611240, 906842421, 907587153, 16904446, 46375617, 644907562, 679590337, 309398775, 404742408, 478546794, 326763442, 737796184, 670074792, 589760673, 458178186, 951848316, 291013388, 585581284, 182544259, 732874393, 633765291, 479023395, 664341462, 227866916, 440496824, 715701761, 987106438, 823325427, 869524205, 48559726, 459855222, 930316080, 205502007, 717298911, 200734565, 941114014, 838329859, 686456442, 821972081, 766205384, 462039938, 736227003, 965554341, 983051608, 924766654, 500432947, 90444312, 546015721, 623937343, 294459334, 913605042, 101017094, 446340727, 7836468, 314995833, 300193848, 712965755, 970594207, 91738429, 881981465, 565648082, 336195622, 290700620, 992204096, 409034618, 189002184, 397320147, 588816424, 267969483, 363061523, 768218706, 84714614, 518571798, 586857517, 836432504, 74560523, 948947207, 757983958, 139727978, 84382272, 573047656, 724899354, 508308220, 253875387, 580679782, 643695463, 292354638, 356338950, 478699206, 58448196, 420376028, 657286767, 320007067, 246151559, 878764149, 296711043, 592410667, 10568867, 585471558, 536331077, 993947035, 178583876, 775827396, 501796231, 923239192, 110225978, 767245972, 752767996, 886328642, 758379909, 167603767, 840718557, 484937861, 505133615, 936847885, 194510870, 697417611, 977547419, 126618649, 921186609, 713324254, 576600549, 677225630, 671386100, 788978691, 421681162, 143504641, 185579187, 348248513, 662598415, 60113435, 715228960, 187480280, 722551237, 980334501, 590330030, 848732957, 699634322, 80268823, 208378506, 362833224, 386341785, 810121991, 495690934, 53946695, 382873441, 435481389, 427530752, 611352170, 129288216, 406406086, 990315783, 541065402, 609949369, 430890187, 2947243, 949013254, 416624121, 845953837, 875868003, 274902308, 798795895, 531595981, 965261218, 742113680, 310040597, 808660413, 968403862, 581330058, 973294187, 89006972, 413337831, 940020313, 557211491, 14580100, 105741647, 554279219, 471740475, 150018178, 186039465, 553684874, 538135400, 466431382, 982701750, 823903919, 598640543, 327795616, 387564918, 938627799, 921689244, 534616127, 764646423, 948270555, 513890077, 139490050, 159804936, 53184469, 574419359, 4670339, 138007721, 953020732, 430662493, 371464899, 40936869, 334028520, 222032197, 142808692, 295254046, 260486072, 291398412, 314836737, 134949970, 580427675, 108533554, 255702859, 346178258, 420005350, 10539747, 332897142, 501882224, 511173200, 48279312, 55075005, 990787671, 286910859, 522277278, 37386125, 350624157, 187016110, 138099628, 393042624, 363061945, 349947988, 813782085, 758333929, 668568615, 745638665, 513875030, 120154674, 861436891, 745556244, 777273430, 588467903, 406947471, 446158060, 428652575, 515427286, 611862693, 912620998, 337281932, 616931272, 850126012, 51180426, 369647120, 881472215, 3003687, 189766862, 423012861, 187489227, 545672730, 116479320, 273949032, 819043008, 424542917, 312617791, 4759068, 933445960, 298415764, 868519440, 696295124, 855794752, 23357612, 563160673, 597931176, 281903382, 93083508, 177612095, 128496558, 905732051, 971774804, 783377889, 63130801, 907832739, 648026978, 965527041, 87479593, 52165052, 977130959, 548868669, 166006145, 850266317, 426860290, 86617559, 346695931, 876195761, 479635224, 287669510, 700665509, 394700909, 391737880, 573085877, 62530738, 309729237, 573397110, 445831080, 348329813, 290738351, 472922928, 237249089, 442662541, 403774612, 922490582, 759846254, 597774738, 583228918, 631813345, 668568976, 620278603, 599004911, 833015799, 271460226, 452501270, 228856253, 624487660, 356440264, 908974906, 384891699, 924330567, 328999732, 864645800, 217122286, 444566724, 390088872, 771430184, 831682123, 138682027, 525016624, 142328279, 724502047, 923433668, 608866413, 30254329, 139475559, 709660875, 679813341, 208001394, 372068957, 738001104, 621912998, 558541819, 896705505, 77751679, 733567768, 462165806, 806614597, 271859812, 914307444, 382534983, 997629370, 730199653, 876452211, 257680856, 924247697, 139393682, 775563538, 651038233, 652050081, 868976294, 650325291, 230640109, 163540671, 275882470, 917863931, 300323333, 612860130, 209243909, 855612637, 45753044, 266004767, 993647108, 700837994, 44630317, 967101176, 610354062, 369743647, 228164613, 514544486, 434603945, 895326813, 45362622, 816382667, 548775210, 865648139, 904805948, 625367226, 139448857, 588388793, 369683361, 150138201, 433969899, 521437556, 22960569, 355058588, 176359581, 529320749, 247228849, 685290079, 649107497, 88922435, 704789487, 143859945, 565681078, 397349487, 637764413, 547748749, 947767655, 888210644, 953526207, 685971171, 438519098, 771687513, 393410592, 940619107, 850731896, 602379227, 411850800, 79470447, 420711720, 293754344, 877638846, 107846827, 726215029, 333410080, 830374361, 634000372, 567183573, 472724541, 272895349, 375824215, 526928602, 607412895, 10679176, 591460897, 826623062, 412641625, 494058630, 18124599, 511424779, 884478686, 727206321, 543350741, 450592763, 149757264, 651122466, 518513838, 285732754, 71478075, 80314242, 429267163, 383037866, 736766935, 100536270, 13345576, 904922373, 337981857, 738641569, 858419443, 502733597, 801805202, 870212783, 64166528, 804557197, 674108543, 504388947, 669467646, 689689155, 83889348, 967929885, 97788917, 624998188, 999110192, 595125573, 765326823, 18506023, 607992291, 191283825, 883467869, 640843752, 418344665, 581022957, 824369753, 141663068, 648677026, 276465461, 16882183, 751494246, 28653440, 299619821, 25445241, 368245965, 631070325, 244113571, 543958988, 250499064, 251952754, 876258049, 80391134, 176588194, 854091226, 594097468, 311352364, 425035866, 862682608, 171356131, 641425043, 512141066, 242891722, 151902131, 111952973, 724801250, 743153297, 991200555, 760595067, 813288327, 397287476, 845132365, 20030118, 503778855, 303465534, 624869262, 933971979, 184284126, 184175029, 193680870, 174438509, 909181501, 624085807, 633609567, 293304550, 654582117, 820885139, 435178992, 333436593, 65145734, 99044971, 569910471, 93485083, 934130945, 359732018, 234084823, 153917278, 134662438, 833950943, 4491618, 132744782, 734491884, 133012598, 387170275, 904908884, 402878784, 624178696, 260819547, 811868669, 434563442, 831240811, 718440803, 638971602, 687968303, 104577444, 145692867, 38090690, 191772326, 310695741, 972943207, 432980067, 430365514, 533743887, 180127638, 171924806, 963402013, 193438641, 317140688, 578120132, 147698126, 462774292, 350163983, 329260420, 605284167, 661786948, 21405110, 214704079, 990926018, 744536073, 392214473, 241263486, 370653313, 557423579, 714879005, 987135655, 578653474, 170179641, 972822288, 546235624, 975412793, 919313561, 378826961, 833190593, 591045316, 801884211, 720756616, 117684342, 806023212, 22665961, 520846810, 702018728, 373287289, 725996812, 49653371, 492643278, 964172546, 598900595, 966828544, 823933265, 358172210, 300218029, 482368016, 40231699, 867433770, 387672976, 413671836, 260359276, 244759984, 750438530, 274184363, 62742637, 790237718, 404966332, 78335987, 995152419, 416556790, 506410779, 558278316, 343423548, 117353689, 377850069, 325183448, 524473605, 126097172, 965263264, 565835459, 148530859, 99145339, 73518511, 619314042, 892842342, 669593030, 157219371, 500112251, 16533326, 125015285, 753767759, 444923974, 418738185, 843337907, 39068549, 18398607, 41790962, 778183235, 802842761, 225471446, 56086864, 464471636, 279714264, 523827677, 690000606, 274845746, 577465910, 407139616, 617257032, 827284904, 274261188, 842215877, 794765069, 916361968, 185171889, 860171668, 982468226, 530769472, 430396482, 914905983, 111756846, 296362200, 86295910, 844581627, 829375857, 870776962, 828250508, 882314141, 883661383, 891833480, 744289163, 55395406, 850939255, 203065919, 704121952, 726171955, 479763324, 747256635, 733491837, 883344734, 975866356, 74613810, 739560869, 213661489, 660376761, 941367130, 487078515, 897686333, 928722865, 715522957, 368786754, 461896814, 765584763, 843871047, 458052626, 313906411, 164528854, 195317924, 766910643, 955800036, 134557542, 292035855, 495705452, 138124140, 339422162, 12847197, 322704582, 903704106, 399216881, 592712640, 777010870, 890324006, 619126809, 512153021, 518467845, 845957042, 883523342, 841450419, 644704600, 326573751, 578996451, 186676474, 907783996, 545843120, 196793726, 344981562, 974564956, 690726715, 602996002, 455954386, 966277204, 31805654, 84283022, 242218050, 111560802, 489759674, 761291856, 279878360, 759876982, 489825174, 936607957, 263192874, 814082347, 493584990, 804514692, 882930428, 730637595, 975161462, 984356057, 246837585, 122294835, 534927017, 9150432, 138145749, 473628624, 765238411, 289029466, 296461798, 75333273, 20344581, 856748251, 3253889, 327019966, 775519567, 598025560, 123154931, 222219723, 964985650, 744448401, 883036655, 882700598, 832733881, 619092150, 988453744, 277127432, 616735026, 995541301, 953428866, 951782814, 746337806, 479475002, 610118144, 163847354, 432588895, 379810697, 616924871, 411597718, 775483393, 713984951, 165158360, 51096701, 920820780, 843875635, 82569976, 23316312, 608041671, 808909162, 156828680, 403392120, 613354108, 119993846, 798915557, 268687622, 238501275, 114873907, 746111502, 952437493, 992964014, 255920052, 895767598, 950061730, 834958520, 6260151, 518820984, 521892396, 494720417, 748046539, 395689278, 354896458, 67277447, 595665550, 520211457, 6939113, 971741404, 658068022, 213668462, 515553911, 976021812, 567377416, 733439442, 376360597, 678396046, 409599866, 892422394, 734127012, 327836213, 512772256, 433586811, 507107991, 290126123, 439908188, 775553325, 874924164, 742410603, 228798234, 305794769, 582273251, 760276341, 610850916, 16305915, 810051582, 995447153, 188400810, 529265745, 115453972, 385213159, 512082220, 878084202, 252444888, 993085143, 514462924, 524950542, 421036295, 19562447, 889352566, 75522430, 201958363, 447424413, 699973379, 534875884, 816412501, 839027956, 214241134, 309456700, 500346344, 707542904, 686161471, 384807117, 36133326, 940919650, 255246337, 203626637, 340988865, 598164384, 417340743, 206822797, 622625529, 142565972, 293960790, 510359771, 357528158, 666375621, 230533841, 971476294, 807351569, 747375054, 677396447, 640113521, 494309367, 100850234, 938372089, 816887698, 111055408, 510372777, 997605314, 206373273, 339205673, 460147546, 117710591, 912084635, 888267784, 309813565, 590349704, 807030825, 889987364, 744933409, 752375192, 237424752, 32956202, 106959243, 675474761, 115482323, 307388277, 904507964, 28105232, 508543157, 910285842, 543123034, 975847701, 656762063, 371442473, 386923283, 503445049, 865938456, 306330433, 999340435, 476965574, 401330385, 168601543, 194193112, 973318809, 66621951, 842022892, 460551406, 260643528, 495469432, 567954203, 254175588, 455195458, 344210984, 534972103, 920098096, 970544065, 818121943, 920955771, 121714032, 914729591, 307107938, 464319798, 23994455, 271998668, 594034124, 631801969, 576241071, 609047540, 402506080, 809624398, 179557957, 314826272, 329019081, 394128753, 311528152, 647200111, 351019838, 885897300, 701063455, 978065201, 216946510, 447649941, 275687837, 889760104, 939913980, 754815293, 461283024, 349123819, 225739767, 557756574, 200500331, 867848172, 279755978, 690082284, 941826627, 302469376, 901627996, 482996489, 984258509, 669096568, 805254920, 49761820, 525008937, 848220708, 907109112, 468196344, 762478612, 899869314, 712986839, 812132901, 216584716, 237490074, 792702365, 450253535, 986999671, 385766885, 732438840, 318841488, 569365667, 546584131, 263213064, 653112886, 94107127, 116901870, 404542654, 711493261, 993542671, 734074181, 547236483, 59639057, 158705309, 561337821, 398424979, 780911604, 74903278, 117607480, 450486024, 697634154, 695311575, 81695937, 232377628, 956706647, 613307710, 866555862, 688796364, 586767250, 896482228, 452542431, 726999356, 703263045, 374592560, 748561191, 573714045, 896818573, 231899745, 612033150, 436365650, 22298705, 582673944, 402091484, 765156263, 723277443, 912008371, 111862302, 240438291, 762217732, 682045949, 286654980, 179972077, 416788235, 779538767, 805111206, 808325469, 948138512, 280206076, 144420510, 159672849, 92619793, 182838633, 95956787, 913795001, 623764671, 603708219, 239963837, 641379050, 420473401, 614081745, 221084081, 920009623, 396518146, 571834631, 672378426, 526933373, 354606608, 788035789, 545623302, 961830661, 932223324, 333110692, 163671255, 169804151, 814702831, 789725368, 784650000, 833697166, 821256167, 54059460, 974535415, 257214523, 373847391, 211881760, 202226475, 565791018, 668822067, 788266097, 561416126, 476927883, 718978868, 909903716, 198215687, 884374859, 396617733, 964086201, 795219868, 596033080, 377716678, 113706750, 811987232, 576044147, 221209155, 852475394, 134889783, 699267396, 153315378, 979187154, 935288123, 182149824, 255216589, 881538790, 631679378, 762356647, 115994612, 83728326, 583211339, 397020670, 544744913, 619435410, 334300136, 385726758, 168520286, 540839095, 807273614, 120648622, 285335901, 183997864, 2043740, 593551504, 692448325, 657503847, 579293881, 428626563, 195222528, 607440385, 974444953, 438447595, 559585492, 647707357, 847260648, 340723685, 410208334, 514844129, 705101916, 151820061, 471335460, 200759107, 612441677, 709718945, 449330869, 116174763, 665621024, 475298901, 820599227, 335045349, 656804976, 210298915, 585510452, 783656789, 875371921, 614910503, 871129129, 951329455, 119521283, 175620890, 184122126, 620537014, 610316410, 682946529, 134436837, 691048929, 375196453, 100670951, 823270276, 583373683, 736584562, 609299257, 818277182, 851315716, 680387380, 934452263, 907999285, 764299049, 321365405, 314221627, 613056685, 560444217, 302541666, 606333067, 846003154, 268358026, 364149785, 82069597, 951576492, 182526837, 675079055, 318157063, 463220587, 791287145, 867759910, 62358070, 860477145, 438468177, 177071150, 214470288, 423322928, 556990716, 243095980, 679389379, 529566764, 836824353, 428105600, 839013945, 316700332, 799703262, 566321870, 285196972, 984548763, 554682146, 434555824, 417884292, 185525306, 228830196, 461151248, 634678092, 36451933, 407805218, 47401782, 857174036, 332305672, 514107848, 371684996, 862112404, 25382775, 316320036, 748098178, 396748036, 851732610, 851208989, 489088174, 153337010, 519049902, 610619575, 189647647, 746845941, 182260345, 611648063, 28563007, 767439638, 255261578, 594054679, 959600479, 640675781, 419590643, 402740208, 627505673, 123709908, 335393013, 373020213, 293301473, 181968473, 251192746, 739292081, 488331580, 270899573, 304087602, 250843565, 145105072, 893656715, 340286293, 48108172, 392977087, 879846609, 865618216, 755619014, 779537941, 379927251, 225701632, 170245826, 909800050, 947425042, 456901985, 600677787, 519396074, 799352185, 373564636, 313522, 43543400, 376037315, 69236069, 85268651, 455265717, 692565345, 556732399, 912010652, 976459108, 943038789, 687819347, 93742940, 263343559, 731953030, 594105763, 864625215, 873606701, 780657473, 567691521, 538598469, 296000459, 481351061, 626406399, 573579952, 737942593, 247541014, 623273377, 978228806, 490979452, 688789276, 964442441, 597170672, 431815215, 428128065, 210334627, 896352805, 922238517, 22978901, 56265874, 719041973, 742660897, 823128244, 374075397, 916990823, 275254871, 197704297, 989273446, 370134254, 927028884, 638065367, 448561588, 852987736, 478335231, 330948070, 615118618, 803729160, 703075758, 788175491, 38892123, 480085281, 817449930, 549152010, 939119308, 308490311, 321672869, 697088342, 612720184, 780003628, 920402949, 166008591, 724266051, 194917295, 465904825, 572805048, 277267949, 647461951, 61749989, 900662155, 969794724, 998358022, 429842175, 220559310, 286710859, 14328913, 514928027, 465186078, 327192927, 973201322, 993786557, 919089360, 51243744, 120872027, 665978363, 262881196, 798776210, 979163328, 885729657, 772916126, 229423298, 806534276, 817231642, 952497773, 162383257, 436454722, 726536912, 581918860, 279541219, 589765699, 215996002, 607320667, 162816337, 63288398, 823531493, 911869840, 8694232, 276370109, 182897472, 256975892, 171090956, 667180517, 116691404, 79184375, 133789360, 605609122, 712506406, 135571523, 450966423, 626096677, 874950668, 574558373, 382310154, 471885363, 589971357, 921552835, 9542904, 639668044, 189313346, 317725412, 623972251, 332479201, 504596274, 712451902, 802718358, 536524638, 460684058, 122107320, 922189837, 691218768, 164247671, 969937800, 611281305, 263008695, 367229393, 586048651, 861453782, 167471838, 157104039, 762918603, 712252718, 717807572, 977247606, 442558536, 384197658, 648823123, 717214619, 568906868, 905431622, 904314411, 303856446, 10998048, 377918238, 129610395, 780630835, 968110717, 827305938, 391135789, 972399035, 581346853, 998813454, 132990688, 483869678, 861978831, 53545400, 688869781, 961327384, 948394285, 341725148, 314922955, 278245907, 614761297, 886958384, 81054050, 892031394, 117040139, 385074054, 249827990, 971713053, 770628774, 685919230, 906539561, 256139030, 126047428, 989302180, 642798623, 618277131, 621746003, 607302255, 404913183, 52417652, 35961656, 642389040, 870215670, 235004457, 449195318, 343977502, 168182850, 672705525, 697716834, 825464548, 606935619, 829812039, 899906909, 999659043, 371737782, 686325280, 79250015, 512249278, 731960679, 266084172, 375268530, 845653298, 519424770, 300967692, 161194525, 269079027, 200212333, 399165232, 947340192, 445609420, 524552813, 536915359, 961490620, 449426111, 417561213, 30877431, 803907250, 354826006, 2097029, 545166313, 860369142, 434479940, 308380967, 851363717, 25447691, 183376278, 213515233, 396949452, 994979281, 113767566, 650075662, 441104935, 481649725, 206029197, 657651333, 243173554, 278467842, 669828667, 637674947, 155007935, 415409762, 576937276, 953519569, 559719468, 744512328, 742430759, 165592820, 401770329, 346417343, 144966813, 731406585, 876579418, 224771699, 892681625, 234092337, 251262715, 871583674, 708202001, 924990942, 7209880, 84265826, 331020973, 989095841, 654434562, 969565269, 705629097, 973558073, 19876453, 801569312, 414931590, 100209963, 807174159, 174345286, 966248780, 765800644, 546531854, 655843653, 591810240, 81590486, 59904298, 92458332, 818373329, 17568766, 227213152, 393674472, 194539410, 522949629, 318998465, 262696628, 841408281, 184957444, 302443630, 978293339, 944999768, 826992703, 703904031, 262742485, 461223676, 479976587, 666866460, 178055443, 140058962, 574826055, 43396201, 883157844, 1100430, 822103013, 482805371, 996917793, 342788413, 811373353, 820439793, 63576317, 644317482, 702280562, 720919969, 894880935, 570181239, 406126817, 845204330, 312886303, 303578803, 706573525, 391923267, 545772956, 838806053, 775888052, 584147239, 830059658, 254340680, 604802644, 762873258, 881414936, 860368834, 225765957, 473812272, 71126142, 787129499, 768471033, 452430649, 687682406, 769807236, 593438390, 391516700, 236363302, 140957627, 670257573, 958865346, 990662987, 844028463, 400827712, 826166663, 608590733, 775253823, 365915012, 131137839, 885559886, 681384904, 454368167, 452645885, 266394763, 239878687, 647591272, 967165437, 376655558, 683436930, 435207900, 795816275, 122365797, 808042663, 3825827, 642216831, 439197620, 14406671, 551005946, 979455021, 815453794, 27840161, 690923584, 983076016, 59433425, 960171977, 479493245, 224756780, 245817873, 422743600, 89326238, 596854208, 744252641, 477840792, 705867514, 901677093, 119474256, 285224081, 58741597, 153532838, 92335023, 379216862, 571176548, 932451528, 31400094, 686312309, 462978255, 923216750, 193479985, 872522624, 644375568, 413125043, 828762594, 803649994, 787440779, 741977358, 651332111, 48931113, 407553192, 417881496, 737324344, 798108804, 449116781, 633778960, 922454447, 973463214, 323445422, 788848060, 292575880, 461558723, 705916487, 687096029, 726037533, 667561264, 259681355, 86312869, 397909144, 193421088, 698189499, 617050984, 945640191, 846391861, 308329884, 490385182, 146570530, 27834996, 867179877, 513040224, 223719104, 807476131, 328425298, 773191152, 740315457, 390207220, 835344859, 712740191, 809327344, 593379237, 813879252, 892811552, 863875194, 85087631, 530507225, 481812116, 117877870, 544807119, 988581552, 936011402, 30756631, 847933477, 955829158, 342304866, 857986807, 446423422, 670791848, 596967790, 787560369, 791228088, 688328238, 265375739, 415107519, 2571782, 238040981, 628620592, 704503070, 80228612, 633766433, 393690909, 404720240, 402145370, 929445195, 361706511, 479572929, 187055390, 463636893, 283967160, 378444422, 446084107, 37628444, 918486384, 887878761, 669351880, 496523265, 453860722, 617370930, 248600918, 319176341, 807384744, 787923863, 600256309, 39133972, 278097765, 733438333, 745139819, 627838016, 575761523, 188898676, 843997370, 202600987, 132200795, 405364877, 703355813, 672736471, 402752874, 724454558, 66721677, 728393002, 502746254, 273009679, 943007699, 77480715, 422736081, 805996196, 793589789, 856581890, 561842743, 353465053, 39133127, 85230213, 329079545, 55275548, 677675112, 257025525, 883975814, 704536425, 801303103, 618712365, 395908805, 319044795, 952055233, 910606518, 826565411, 200356867, 608037858, 498455292, 970134255, 338839518, 397178794, 862234794, 97082413, 483604989, 757382205, 666491826, 606948757, 790183583, 902178932, 344908722, 174506800, 873042807, 748384559, 914883879, 556988886, 19707308, 820079746, 992717644, 132689692, 764892644, 621734646, 336626291, 685323659, 904122876, 831427268, 663429281, 556288880, 386481658, 317343377, 490720184, 762243254, 755511594, 934658630, 997732619, 559096976, 506329727, 246861293, 500756815, 454165964, 28052999, 252975746, 555568850, 996224232, 36576431, 641577844, 967709774, 817682973, 789354099, 88071654, 516105950, 911148441, 354644128, 431732829, 64275907, 928787475, 366980244, 204020300, 241937554, 613501692, 736798555, 539599850, 78006767, 309755482, 231388479, 738373856, 223982168, 284090605, 203372172, 197456543, 162067322, 395990965, 750549652, 994801286, 566059177, 297123330, 883381832, 684351869, 153961313, 915312875, 22721509, 337175844, 643329057, 713595604, 291564721, 676303368, 549034608, 81395479, 553929469, 214060126, 1029583, 524206988, 813036369, 769172366, 165194077, 313376366, 502379858, 107844553, 92548988, 65443299, 450581244, 427838475, 102304873, 843569048, 487892343, 920103589, 216166967, 34278329, 299459157, 578814462, 848327647, 108446701, 382738630, 113794782, 123116233, 689424553, 614233790, 501727886, 726348979, 62688403, 264819659, 10136182, 228847810, 772624788, 20472823, 363663608, 814273889, 204446917, 915215338, 974066569, 258749485, 629758716, 542414270, 445752218, 303913029, 438949846, 512517259, 134292603, 847405242, 169063776, 282323951, 885631239, 477835165, 483224783, 939707557, 797066191, 893398664, 859857487, 994832155, 336009334, 831772370, 779205891, 499925574, 473169465, 200126511, 851924593, 269575133, 126301593, 525422348, 40271292, 51895092, 660112941, 391620661, 835955351, 466149902, 50116952, 740155238, 899805505, 253352349, 837231837, 265027343, 199480759, 691120059, 788948306, 607247576, 165538620, 873512678, 623455768, 819444741, 595287256, 947922041, 326462531, 373174830, 812049219, 897382613, 398991397, 482803763, 743892995, 700456812, 568397645, 390697448, 570389764, 258763728, 349104835, 348576360, 517544542, 368656049, 793263549, 132224059, 499335499, 630671522, 381895253, 38013230, 960756510, 718529757, 405472687, 849808641, 454277416, 365816955, 438542796, 726366258, 558400119, 250673195, 26392865, 571592525, 347809294, 844006044, 984377169, 436211774, 609819842, 221006792, 356267406, 759051001, 549404900, 971675571, 583018494, 612373244, 467784740, 197898351, 170571231, 266492929, 818350935, 188961635, 154447928, 980695873, 474888976, 449981565, 540045475, 923372488, 970318479, 937107449, 927444914, 641877117, 586411631, 743208361, 463251508, 738868453, 656639117, 381863005, 750689770, 190232977, 466457833, 880470255, 921193273, 638859999, 79179216, 666235349, 603825134, 645004915, 199053719, 222270308, 195242620, 584773589, 129602716, 999970134, 965958189, 50233019, 204581605, 514177962, 801418967, 349096876, 437007043, 696874279, 454942869, 446278432, 255728452, 317795954, 57244220, 815486881, 758015678, 409496625, 479029996, 737111165, 989260795, 599515069, 423297131, 153674739, 35705330, 628980536, 960480772, 641055015, 719101866, 84222850, 90241041, 499186039, 298154557, 473531982, 487430621, 63280298, 3667743, 303836336, 363120326, 259372254, 730068192, 264629856, 617006795, 372506776, 455434497, 606415223, 172223327, 577118158, 225144301, 911356451, 901416976, 547205404, 495697065, 475332061, 529274056, 958172747, 453679069, 51968705, 753594053, 950398232, 245909563, 619499106, 26856622, 413582687, 303664036, 331925226, 353094350, 873299542, 162029097, 405897126, 108137676, 812406113, 668826721, 261385555, 157356200, 867868674, 33671962, 772597645, 926994122, 768320427, 908356500, 997039290, 140085145, 443553926, 998262743, 191017610, 22967719, 72328040, 693591425, 81504653, 656271910, 654845861, 957828571, 891194798, 823431160, 264225635, 740562467, 306566928, 643757593, 310501191, 310442803, 962321158, 574886071, 423249947, 974109728, 528031610, 47658248, 910884070, 844287025, 270786160, 347519770, 26624165, 511066741, 966172820, 21043815, 337959945, 968224979, 373025435, 218406019, 138167711, 557266252, 312820107, 20752134, 421978623, 859167915, 302080362, 451009568, 679245748, 154312601, 889650242, 71880242, 618973157, 294369986, 3132837, 967757557, 263675359, 847066591, 379583446, 624107835, 78543969, 881633582, 47288676, 853649256, 910268841, 578672830, 413635229, 673403941, 464805031, 828468655, 165198672, 418292597, 679174311, 164366083, 134512055, 145818049, 826059545, 342064142, 111446462, 48122276, 714382604, 441445256, 943750268, 571768581, 136018635, 187644319, 755907251, 65575997, 422536029, 303484571, 744311318, 820818711, 486056402, 924364450, 784907380, 176016273, 43529120, 878737584, 339098936, 704342167, 452633217, 16544268, 54737028, 661604787, 127282809, 959020368, 747437709, 293908004, 981656425, 15480714, 28417854, 792548595, 91612921, 453473613, 259964974, 267026395, 372057541, 573895214, 804326076, 587470228, 269729041, 723908238, 853433588, 976274272, 795066001, 460428912, 874526302, 285260249, 621420986, 682968239, 44989433, 394071893, 53194464, 606182771, 14619781, 310246532, 220168351, 100437291, 314054631, 807375075, 492179756, 997937382, 47823793, 873226831, 919774859, 701049883, 988150835, 466569589, 607683131, 769909548, 508917733, 737024072, 776102385, 273083066, 593327258, 779776598, 3148777, 556641527, 786205334, 104806453, 570513293, 465625414, 358464159, 694613427, 289477265, 574043257, 528896410, 754731626, 440267685, 658186964, 473453267, 645002088, 760168168, 79896964, 486822901, 504673673, 41878941, 71792760, 479403213, 132130855, 274910856, 348773045, 213489497, 544279947, 537350164, 40931800, 674503136, 511639378, 587013116, 261225389, 800766927, 763984733, 671370680, 120833663, 924869237, 107892284, 565988401, 943079096, 158784286, 244297833, 500527267, 524721037, 532677338, 251803295, 335260529, 284844198, 752517155, 124363465, 710552459, 332085986, 79092330, 751263458, 551077211, 73414440, 643730784, 389668684, 340316086, 831210441, 267281839, 622879012, 438515497, 390822591, 320749978, 890562676, 803885122, 910755593, 512062404, 720873969, 894084459, 628884045, 982391617, 278350352, 535939301, 200701051, 795800066, 622940788, 743493482, 98522656, 693357568, 405332838, 377272662, 607869130, 483994213, 459432220, 87985441, 941062596, 866534053, 980379818, 191531664, 562473589, 162655587, 397516031, 611580019, 331477204, 95015624, 465362285, 202721448, 520936623, 731475497, 318086982, 265108273, 990136136, 835194661, 780111882, 121260507, 88857256, 996759562, 776559982, 46526888, 616335369, 519110347, 937557680, 639772917, 942290618, 289797867, 880600726, 445952974, 704760491, 404449045, 275747462, 505402523, 5990106, 302393344, 630314978, 859479603, 236913322, 343791218, 451726654, 195935068, 10236036, 61973998, 968640208, 193712913, 520009635, 795118110, 6173351, 310094144, 344296550, 729377633, 534602065, 761823237, 695295524, 68291470, 41748188, 84897716, 358277357, 939757181, 249391120, 488878174, 861289412, 5196668, 478317741, 565114580, 107510506, 737618625, 471462912, 591103894, 228963424, 283224790, 621236765, 222867756, 489617399, 638329380, 972272505, 398391465, 271170678, 149837526, 678867865, 553424057, 394166688, 371382438, 245822891, 369182065, 635850771, 286409873, 210239318, 79061340, 868431399, 345094203, 197021628, 95345090, 178470248, 350494693, 224568562, 503752723, 443789166, 226410346, 600605603, 674328975, 881252885, 25815293, 703715792, 388104418, 673778929, 878732457, 412131201, 536477784, 534127503, 628545107, 804827436, 899542643, 120606461, 271695886, 603161262, 605982580, 384990338, 384084683, 34183036, 50053457, 242032862, 465621844, 927037988, 787980469, 408634719, 484860233, 30891031, 222640075, 804701580, 739725524, 173141450, 515495560, 166375320, 150455553, 635583748, 192596914, 408647982, 273144891, 356685517, 241334250, 199629196, 522455205, 737241978, 515720430, 178366604, 880254257, 122448141, 795859798, 930216495, 762179922, 906200448, 213157269, 710197716, 20771653, 320065923, 5170704, 818344462, 815145313, 140235481, 306949005, 589840447, 869064934, 348140943, 465030676, 246362399, 799672205, 821615727, 551498413, 277260682, 579970803, 566651583, 42593005, 74777112, 967429344, 195501346, 922716081, 421289206, 739420906, 64363054, 283561643, 275962780, 494774437, 789068205, 405024194, 483862352, 574899559, 401757846, 173197963, 761950362, 586751288, 797332811, 420179009, 214293185, 166939136, 88288917, 246795739, 502624802, 823131100, 691076712, 468242046, 943453946, 800375900, 408857284, 833916359, 190523170, 938467185, 331005919, 207920874, 409950005, 646392553, 981101106, 943435167, 481180073, 686764310, 767123520, 692312353, 774321255, 921967814, 809001619, 161139938, 441764148, 582022521, 101499238, 769939564, 533840386, 531579777, 323668285, 736056274, 840666616, 657510840, 848091829, 460851996, 977898731, 559440571, 672894916, 320328404, 729857010, 428849865, 39082340, 460149621, 838407309, 701979557, 316205536, 335721415, 727435818, 163661839, 483536953, 965923311, 482211940, 924904721, 770958265, 646798995, 616312214, 479728902, 846291599, 643695215, 569078529, 183678424, 956811652, 357281682, 158565183, 389459215, 506802653, 694834972, 569030765, 962594766, 197568975, 696617831, 684798653, 897889752, 159638959, 269150986, 384947930, 941378817, 32089227, 143966079, 609885071, 310665929, 203389004, 880013582, 743770857, 274642086, 698244648, 777801645, 213057204, 971672669, 316603568, 108031716, 706496125, 822259355, 656198548, 78086070, 551809815, 94347256, 571278897, 790215185, 47705922, 71968170, 639287111, 385332839, 647468497, 879013699, 474819, 229566440, 55433383, 49635426, 723430416, 504241394, 950623050, 468188022, 595692967, 100689008, 417117000, 602637805, 712672849, 274830924, 420749934, 794427799, 677488576, 946444288, 395791008, 185020432, 647004676, 73064760, 139983040, 787498235, 688419272, 117376050, 261963995, 45373969, 365604656, 233414722, 229962253, 787056207, 786475799, 143330781, 578170280, 766694378, 628584554, 940570718, 960758338, 863999198, 843329977, 977362283, 330390645, 604002101, 778730111, 700354102, 882215683, 491049815, 695211877, 25273529, 490965043, 587189988, 894285533, 205535004, 421019025, 266038175, 605854002, 349813868, 972233664, 107248036, 885875301, 959306383, 227029453, 126261119, 718053567, 484030383, 442840603, 666959150, 313955655, 26705224, 509065208, 250175896, 528714339, 448519785, 608417163, 774888833, 846182275, 581564098, 380486443, 689777931, 223153498, 914836395, 264017247, 117781674, 871096127, 317419173, 151071419, 363560404, 707465846, 650602218, 798964735, 935485103, 723848140, 234586941, 618372979, 150356020, 178471720, 481654887, 247048784, 737967599, 955165951, 18426398, 453713156, 508573256, 527643180, 35902083, 964802851, 177358694, 926352082, 230659029, 566442862, 596223563, 975248374, 322395264, 711042483, 31877419, 117055455, 81068688, 840898436, 113340682, 16942018, 652701609, 219888807, 542743087, 30097105, 276088300, 378988170, 237630635, 146276538, 988310249, 83514882, 629817785, 214085132, 43354895, 457226665, 667591998, 132693644, 70064664, 866199459, 44502383, 798469421, 598574541, 812210278, 345691839, 231217461, 176064824, 415685599, 125360264, 695401054, 109392523, 118624825, 787709111, 702504265, 966030590, 434722431, 174003413, 21423265, 888668493, 825099902, 747308511, 145109983, 441290905, 635269413, 225709091, 255811932, 630763450, 957003062, 271614243, 238057113, 799838270, 514105866, 339502471, 822050487, 35718792, 121798020, 206005197, 972279936, 859865053, 107969471, 256927075, 280127701, 121255451, 280256675, 334189811, 305041154, 886286835, 399829563, 842272948, 424051348, 655836312, 981162283, 206349521, 717556514, 845106700, 658131468, 635666348, 875715857, 610472065, 152940338, 10769513, 439985599, 793552322, 651106539, 354535216, 49423594, 194181187, 909819031, 136924816, 354824876, 534431338, 933938079, 534886236, 946137316, 526200772, 208675999, 734073212, 572187226, 70071580, 179946096, 699313791, 178447352, 930796746, 575050434, 842149214, 924900139, 576435589, 523898250, 24386557, 140794893, 654282063, 321944122, 769650994, 147540660, 5697624, 899154054, 158321670, 714222303, 691720688, 747091974, 994904044, 732136011, 222129723, 712793727, 176482280, 335966037, 247071565, 443339667, 976089952, 851321071, 183452925, 22259808, 163371403, 266303530, 632365062, 877258175, 477839496, 387700965, 726388647, 423064365, 958702329, 161883994, 29690117, 684258595, 979291243, 726287938, 613282828, 854452428, 975503689, 190855442, 67687636, 961216136, 631337984, 667140838, 21575952, 814611482, 693771581, 339989465, 310008587, 65439909, 790424391, 84458477, 712782284, 224104358, 278389588, 936843264, 489593234, 836398727, 301304376, 461312334, 611636048, 337159007, 623030116, 465615300, 548885173, 177563731, 605279600, 784132904, 654544359, 426207401, 713432644, 888382607, 676834909, 957891676, 694119415, 948702394, 364534663, 701826428, 475185507, 497188134, 943449211, 567925103, 516510185, 71682449, 394336032, 686011513, 342011286, 391274054, 278094928, 565612252, 588356905, 232538879, 246074463, 115803067, 220596762, 841581547, 237490814, 880073478, 740278801, 990336857, 652211824, 207942969, 723614743, 62693851, 20327856, 275464249, 635469666, 572776709, 126546937, 799866398, 448696935, 931213540, 687824346, 365929233, 2053223, 626886257, 908960575, 751307781, 244075911, 439316330, 787851180, 243741001, 181877165, 212687295, 250383702, 540528166, 217813528, 166153717, 175349348, 718000239, 837914422, 805251931, 441416588, 686816919, 656447579, 524584845, 984955876, 33671691, 254188249, 673365282, 244703341, 397145880, 437814423, 593206321, 540310768, 329893552, 240026886, 429401491, 560755555, 328945660, 772674438, 241598062, 712186625, 543770198, 683523392, 936172872, 217388681, 881256393, 16830693, 177459922, 857307961, 133514862, 125024437, 952179717, 81901735, 975807830, 107901631, 380931548, 308714936, 936549133, 373769169, 646779658, 627474307, 927773117, 850430874, 247160966, 32778553, 290958478, 857813439, 20636022, 272995014, 47241802, 452131722, 355217295, 128274565, 475428658, 313523209, 715590046, 703623633, 891588081, 975003476, 451195438, 950365554, 751444459, 223829899, 932568, 24086733, 997041092, 961159186, 468821683, 496100171, 164902682, 259713050, 144698734, 32134691, 985488502, 46053888, 444376259, 718688528, 886025773, 248825898, 248231911, 436210444, 302063961, 36613674, 100142069, 405412960, 16817911, 270939313, 863748780, 782779308, 476863017, 438373876, 738855865, 531345742, 583557995, 765481398, 256012346, 744142518, 507263450, 25378357, 837337127, 346107352, 309853101, 194201382, 654593740, 45413601, 378099023, 798805894, 696003855, 97624017, 839409593, 857756040, 326085586, 570494453, 829143178, 755607350, 418912574, 624261943, 189916293, 559793239, 448378029, 610113729, 701640032, 239506906, 370132670, 216923871, 503275052, 636732594, 289395910, 295581947, 871058864, 392627315, 469501598, 254218363, 782687545, 518696883, 412668276, 141950152, 674310632, 276205980, 904053237, 649759320, 472168606, 771631392, 237898635, 436502365, 512737339, 716812848, 969417993, 991929312, 657605570, 203529344, 232312059, 559653774, 511913864, 661022141, 902995986, 105710572, 582166281, 608880596, 828852217, 251459919, 297705125, 401777684, 366811408, 422175629, 562790119, 148074678, 846368494, 933896857, 904998396, 31627529, 404704403, 934812370, 518281257, 289780699, 366351383, 678352784, 915715604, 173940703, 139205886, 160978464, 159443480, 991666438, 733165363, 680841872, 796572076, 789460669, 556729601, 641797695, 18167140, 90168910, 851224977, 657419727, 114442594, 509532254, 888107870, 34934140, 16229164, 612938374, 328750374, 652761236, 857261256, 187001174, 125483294, 337853717, 201892771, 69378062, 908432279, 240643537, 795447968, 726500815, 352173812, 953996079, 683077433, 920792886, 556034830, 801272578, 148204342, 766693250, 544574657, 773475996, 493978814, 429888870, 252137705, 660702463, 314971045, 927000093, 399759496, 942883349, 945569157, 452203324, 753882962, 39658626, 861448215, 131993800, 316844327, 880360969, 700516282, 834299971, 2390045, 24587586, 242641000, 782666967, 506101596, 921765653, 297791704, 817888245, 978488676, 945060583, 672242654, 954174968, 104277823, 383822861, 105871305, 51120674, 867231035, 167886727, 997497451, 917766482, 994112378, 312995438, 866935977, 478750872, 859864384, 107484218, 463349007, 798293718, 672467112, 85007489, 421658114, 530800955, 410179511, 575990490, 190074907, 968465168, 741619989, 694381130, 25056808, 237888809, 166055166, 634440465, 95448884, 120840486, 187143398, 556101897, 153082477, 697723485, 581132005, 132706122, 597516453, 162324831, 674695841, 969706466, 860797918, 594141913, 194508071, 555005941, 77494402, 129875785, 117470207, 343726690, 261913344, 421145425, 652681408, 898601179, 134947368, 185531862, 922455891, 993647208, 547227817, 640264941, 475087705, 629496561, 226019815, 678020333, 236477962, 791787409, 641197247, 118984411, 160268209, 667393706, 152104060, 677530025, 127179496, 709596345, 71830148, 93188926, 176105288, 746200981, 300681468, 817984475, 404155263, 467789638, 130847810, 503333987, 442143760, 42516390, 997047347, 395296136, 121953134, 345323133, 469682553, 363512043, 759311644, 709359054, 982521659, 851986742, 171496031, 682091849, 508035342, 859286783, 643931777, 157236269, 477647717, 166085004, 722579272, 748027468, 496921621, 425306271, 56460017, 151303918, 755080160, 279256672, 227574876, 16920993, 237875084, 407857424, 63952313, 837039229, 654836389, 433857032, 285422046, 376552965, 882811803, 552255329, 419077537, 470042296, 253731241, 72034593, 429012430, 860816187, 314969002, 339096458, 313203811, 825557332, 77805563, 423545773, 472199798, 950303581, 914701389, 622022737, 942687380, 635283630, 174247379, 453269500, 682371585, 995462949, 384579795, 323560956, 429244367, 249952353, 152914488, 702217307, 198006366, 769376045, 500446061, 831291705, 596830753, 414073223, 289909077, 667922324, 83010679, 500824587, 587018739, 738367386, 172762335, 98592425, 84623223, 264478025, 671149297, 175479375, 696715034, 684972882, 480974093, 855886456, 482943954, 598234149, 172973180, 428123645, 639537402, 286581942, 91256900, 158507754, 870610752, 38257658, 868150238, 146350056, 547824412, 400211160, 376984086, 111790599, 892390107, 436845036, 945418013, 321578301, 522500443, 973840201, 495795310, 172701803, 497025329, 549532880, 585031586, 268462585, 28850932, 306575834, 329531346, 644293431, 910620621, 188297542, 567667286, 134973418, 377218507, 169385488, 959675015, 780033530, 686766625, 771756327, 451873460, 725246748, 948132693, 714235952, 58219198, 182581539, 871339263, 251662230, 390162300, 206753362, 996175136, 78316066, 134614369, 520749387, 894919602, 461380291, 531962253, 647286150, 65340310, 701288768, 2921841, 336309996, 329939561, 761650007, 748996323, 575843864, 842077096, 6993788, 215382838, 489077595, 101446301, 74967471, 741394266, 894600557, 880908037, 354994785, 437953348, 31796653, 480624591, 651487197, 803289400, 909192009, 644685447, 943924986, 463148244, 417164605, 494797876, 26415924, 374491051, 657552247, 494207716, 46757841, 237396748, 569342668, 322575053, 526927666, 800478006, 225456051, 586439460, 330777277, 548699151, 147109473, 691875374, 309265165, 960473003, 82074737, 161198297, 506873213, 22088830, 504604167, 165179104, 40567993, 374757030, 465938377, 360191472, 202175185, 173392799, 114665724, 562688824, 86906781, 449429624, 793793612, 341428026, 911351165, 363735090, 386228142, 379036790, 374858679, 173138815, 846661075, 399896092, 303908836, 558207450, 405212689, 563117315, 574506735, 367277729, 186181511, 304275957, 125253927, 201184901, 172764816, 633071616, 18228695, 191110523, 83822766, 170548392, 106591641, 948081276, 317468612, 841011521, 949512935, 450286781, 518783474, 599543883, 870667826, 468142316, 801950169, 347827379, 390022414, 164330383, 857308635, 568863533, 305017649, 418724381, 37466849, 762060078, 853188133, 81869546, 154868006, 552536051, 601208878, 534306146, 368993056, 794258316, 992556723, 60593559, 582834420, 327556705, 243328030, 148718277, 387569811, 934289187, 73025211, 68156096, 667547910, 906360413, 937245665, 898194774, 772173656, 378648639, 21728081, 212758620, 155014187, 829477567, 90665635, 210270110, 147150037, 74076575, 638144688, 931009703, 688688730, 119254181, 140060885, 257662338, 202162732, 322070921, 559344556, 235898513, 776131614, 718544612, 782366569, 524848084, 281248351, 146041453, 475686813, 350682414, 79458615, 90158529, 328207548, 326297532, 12590192, 185141375, 58642356, 841379988, 615941862, 142561788, 475858309, 363831118, 770489347, 381593028, 134377733, 335933734, 22773633, 385017363, 939631378, 249906010, 806483139, 115564447, 529443122, 61868479, 478196910, 119499794, 728210282, 532169554, 408192404, 945683569, 969372995, 173824942, 162475143, 25483873, 67364572, 43523643, 349786713, 185217021, 839108952, 827544284, 138283401, 449778489, 275226028, 665891234, 696746612, 92061760, 704966768, 561527910, 214262485, 82723536, 147804570, 360482843, 215656052, 675794614, 705531899, 958443571, 826005136, 709603941, 645720308, 639796062, 227728059, 298177492, 623507842, 461719658, 58455899, 887525459, 115768428, 992499276, 522923444, 239330253, 241529911, 240037491, 653168169, 192236885, 353807552, 545874745, 306803682, 33225978, 683026170, 799840669, 225769538, 657201408, 792059566, 636480042, 256174319, 926153066, 196996619, 433259347, 536959537, 555239707, 504681861, 521027554, 572909195, 926632720, 613757564, 799922825, 656160426, 853646302, 304546885, 924700588, 444972969, 982588341, 921014669, 621786721, 764695967, 942509676, 362267422, 486813154, 900610444, 609460336, 861646296, 998665057, 438902376, 391512054, 24365420, 335929992, 375176394, 842737796, 835430423, 566770338, 860301698, 623154136, 435257796, 484249021, 368162132, 336192472, 811936726, 257895890, 402124446, 257386914, 91623178, 50120098, 99225201, 79204999, 50169195, 451772892, 238660591, 390041067, 620024254, 817660275, 927730343, 258573729, 270059533, 148544460, 771031637, 136209646, 941400895, 739762794, 381381441, 328795222, 565593734, 795927437, 398332956, 809484676, 521018756, 862242500, 843078520, 659334479, 900312741, 4546535, 894696467, 138027774, 799927174, 429868598, 973739591, 231987266, 760360819, 483605855, 46062837, 331046640, 137306217, 650665303, 731660714, 930346731, 661626285, 785510359, 520955060, 362258551, 430444, 708797497, 254751385, 985049799, 765805107, 562110834, 598861304, 234167252, 374603604, 271289826, 337107575, 533130098, 390975048, 542060877, 607424388, 320661448, 449551351, 104623404, 630633144, 863374218, 927831650, 46466675, 851355121, 69450494, 507162300, 354110002, 662901268, 331164902, 741035059, 85656378, 387244694, 128087733, 417672297, 622534218, 531867296, 419116948, 680098259, 426719542, 762681129, 33216737, 769071272, 757078138, 370817494, 360853768, 73231408, 466951809, 103465742, 187452234, 373775765, 899510466, 741160667, 302459525, 489570216, 194156998, 413854778, 470876855, 9344347, 311581419, 425305137, 647881409, 863270455, 492248097, 106460509, 926546929, 804812870, 732915392, 450931185, 785666398, 532334683, 65876972, 979656592, 919383540, 831745720, 77745461, 60221636, 690846033, 579534977, 902419931, 630326662, 594168420, 356547642, 554065279, 138618844, 496838004, 740457307, 935112395, 753300567, 481880920, 523094111, 137032378, 747935064, 464768117, 740549173, 705850608, 996794061, 612848867, 728769289, 882454768, 945726178, 338876332, 840641174, 299712055, 538372906, 123306261, 107901338, 561172934, 763994914, 427260042, 832095400, 881402757, 706884759, 277793946, 208301942, 540802443, 138208743, 229741417, 884534816, 997309574, 915830288, 345310362, 481461958, 151410834, 725967056, 228529339, 696073415, 771651291, 760920088, 898706005, 760136536, 248705596, 747138945, 148833661, 181865015, 861704246, 888085101, 250737379, 496002020, 732760453, 832177595, 821079397, 346442896, 923946490, 407545873, 347642559, 508686268, 762084477, 452184697, 523382851, 130668425, 960964395, 165234366, 477433246, 558890579, 951934247, 264687535, 794691581, 747131492, 744113593, 808568492, 603326259, 522838977, 579718225, 150581400, 259180960, 804194318, 508193020, 775721498, 490703202, 998066529, 151293238, 953699382, 140021083, 584214691, 234955870, 759539668, 937804249, 480964392, 402872967, 14297146, 317394305, 376458606, 358192909, 665300754, 203857157, 2537787, 505757957, 464750115, 869053089, 924973041, 465343813, 283956523, 856861331, 873760574, 96618303, 397221152, 189929252, 497548463, 989941701, 848293074, 339944593, 944396836, 312410650, 187977308, 67641374, 56412432, 578521856, 78189752, 769409679, 792868285, 342065721, 859096865, 618841702, 635215588, 365768059, 984295959, 79807804, 171841219, 928335981, 502351801, 55596915, 9329444, 264279575, 543971160, 918784838, 912751667, 302901153, 994304106, 371005700, 185068122, 469793634, 812799295, 693836133, 511599547, 7020636, 522401532, 87255130, 143464402, 743080251, 803022592, 435429013, 752377992, 536466256, 573040946, 348581226, 534637752, 903834368, 632901180, 209629009, 226504595, 683495778, 137635280, 667746476, 102600186, 257971611, 729183647, 606198649, 730745044, 290415263, 999582515, 906861780, 630115984, 830877405, 719005346, 382946381, 345709305, 636798390, 477365459, 792676008, 606619821, 561159895, 536629381, 524500206, 12657640, 148527931, 292234292, 480784360, 532678523, 540134186, 671872508, 555212654, 465234703, 31309666, 529294837, 966306736, 544947567, 114866766, 36918679, 434402941, 826282151, 506492560, 742616890, 66518472, 902213140, 398199551, 619248374, 407311089, 532501229, 911601290, 951342188, 946673948, 3489547, 569420136, 292652731, 334676511, 607154937, 82989062, 785917518, 522642677, 868480025, 606469484, 15163149, 603265611, 921390363, 142993439, 31091322, 352082009, 198131027, 497135237, 924503577, 887749018, 260060250, 474589637, 582920218, 135168810, 307221675, 750053358, 252527291, 57575871, 358456715, 459435296, 199258252, 423598607, 776552944, 596484693, 4659253, 759187480, 346576223, 951240952, 288181201, 999793404, 846754321, 577586476, 281923166, 523806504, 993627722, 261695575, 76751819, 488303642, 918171506, 57307341, 926081655, 819605794, 395259729, 283184801, 847914162, 679638098, 625704556, 794565986, 136807078, 797327596, 244125396, 825632231, 535005068, 148616822, 364307201, 787159611, 120268515, 237496999, 724444323, 471410143, 201900655, 186584042, 209304545, 32893109, 744174619, 86113303, 172078727, 838547720, 173355122, 132050108, 864615849, 622774824, 920521259, 434235822, 576046766, 447401221, 311311058, 27833745, 3315810, 338224143, 74525666, 30456560, 35732148, 138703640, 464126587, 358715191, 327680600, 101855122, 72043779, 776541624, 815561232, 246272235, 747802497, 182560708, 218064557, 657509886, 67363686, 225855540, 542228353, 809655987, 345971543, 161575631, 384860044, 960957067, 859974286, 443046604, 127481904, 292070612, 742822210, 579032061, 148784930, 495001182, 981127115, 192165566, 313826231, 926018367, 926741440, 411976507, 32888672, 264323297, 688953091, 703219983, 910207425, 404302366, 173034259, 392063327, 634545310, 402595138, 883709030, 609922214, 805362501, 600651196, 480054806, 829569679, 356775664, 315424491, 658707429, 128893240, 774978688, 408515427, 533189623, 861218776, 914251327, 951699258, 83042959, 377826609, 512605907, 971484453, 310484571, 386790272, 827112343, 184068727, 387827907, 939616879, 955733570, 689955168, 904481086, 758158714, 167633397, 639937474, 232429141, 81849297, 999611815, 153933765, 473088159, 262695197, 391860051, 713210863, 362912785, 922040160, 308770874, 554329574, 643956647, 470658298, 531761690, 541669159, 464743740, 742834201, 937894411, 165753613, 361459163, 929042673, 851527686, 378776718, 586256033, 368114238, 358578696, 790298912, 704452703, 570548812, 936563430, 898337666, 773881724, 332244691, 491417236, 368429036, 44818062, 506908588, 483563127, 900532285, 935416337, 243734018, 865132997, 271088203, 42350269, 489224031, 147578598, 292656519, 284622587, 928806080, 148540941, 366442025, 349425442, 795216291, 55128573, 101785395, 998467658, 381330123, 849072808, 337407574, 117776242, 864388937, 14426344, 401590769, 763697975, 286554770, 529102332, 564812194, 525614028, 781373615, 709604252, 466627912, 568191606, 948061833, 894313503, 261133659, 266772125, 142330325, 150546359, 733489209, 290605388, 981211945, 952990165, 537078882, 692045038, 782477825, 7384379, 300586464, 20684335, 564298757, 611810844, 902077436, 535689825, 787377882, 987204556, 132196148, 385526839, 392701902, 631983041, 268029246, 943087957, 548096225, 233965031, 852978541, 750119142, 248081047, 423831132, 203804983, 561451936, 622267015, 927885973, 306757580, 619368790, 994451595, 663804613, 545276237, 563175555, 116096580, 972097057, 923009568, 376837530, 300205274, 749285296, 98592441, 785549582, 31170969, 853546481, 668350998, 455289311, 11570424, 743387457, 707511167, 348882754, 172619954, 372708412, 972041870, 712974950, 346400108, 273697351, 753243296, 537736159, 913500283, 726658946, 531871731, 505308041, 545953252, 782904417, 891585084, 433627630, 692819713, 811756247, 594735726, 593179207, 174481984, 439208784, 473838655, 931104947, 819569220, 364687719, 307091330, 152992154, 778965411, 70008022, 858001317, 701273070, 800318140, 686353928, 455236499, 960587319, 837135748, 23033324, 448733118, 988814103, 368637194, 929022977, 983820479, 468624373, 529622554, 54265359, 693686093, 586898227, 525558570, 752614722, 739699857, 900736607, 316633860, 734801657, 408492474, 921326165, 153545320, 100666570, 798440233, 65086200, 337653083, 289486764, 359738895, 152653712, 150038006, 659282004, 748049998, 796398617, 633206511, 368936219, 390622841, 953054045, 324413269, 856715395, 587876650, 463510625, 498168333, 724607967, 105908302, 983322076, 183852331, 240032408, 362025768, 69532121, 312106189, 6976115, 343111377, 191411125, 692079552, 168295145, 60869490, 580471168, 146056223, 806158778, 552740516, 804552812, 295633386, 697567156, 386873012, 587801028, 180313774, 973932128, 679779322, 109642043, 220805832, 324914313, 591026687, 359282024, 502418639, 514090714, 143735026, 278152243, 760941011, 737088487, 465386552, 939429334, 734549724, 593327796, 469949296, 916584529, 669348786, 181105413, 860784898, 177256286, 790373768, 165710614, 160941365, 448566165, 232291363, 97360780, 200355626, 960692337, 333438664, 351214363, 55396128, 859848795, 241957996, 132883384, 157016800, 902918308, 160285814, 39327559, 472002100, 871733043, 678655633, 447188867, 307765163, 380480662, 645653370, 272819082, 48618364, 540404861, 390015919, 929841222, 90637755, 874431330, 549450830, 792920922, 236915471, 988975483, 70642015, 870384664, 441175914, 143321101, 886005383, 143996174, 336918263, 463967985, 440209484, 83814922, 753215934, 381025259, 443702872, 328182348, 365558654, 106173553, 190221224, 838182002, 873571967, 300297228, 969466036, 985200568, 192121969, 373794360, 440545410, 622830561, 963023399, 519275269, 515148896, 549251011, 835005796, 858221835, 208080003, 634896921, 527642309, 430653849, 937502324, 543424954, 288596549, 849912046, 763392655, 426659562, 583854054, 213340960, 339360710, 441625836, 438417070, 608867048, 736407610, 707179452, 585247913, 33618873, 954189456, 581685223, 578856643, 499272296, 277025268, 291365709, 297306872, 137304232, 517574090, 556180295, 334106705, 156208515, 887848946, 22190045, 799627073, 840783171, 259216736, 464022750, 754993013, 802922363, 437544373, 471047180, 783997981, 383678880, 994758943, 432232076, 568516993, 569227698, 56076404, 577736470, 616873659, 62903022, 534094955, 838752546, 18461256, 530085745, 488340541, 467292489, 705969930, 995352663, 170056798, 290188835, 237834301, 888311774, 968347677, 319347422, 318991644, 643920433, 441526449, 179104338, 589373578, 245497220, 161743446, 720970751, 828435313, 696435840, 10910918, 90019267, 874673722, 164281563, 926728909, 37402580, 330174751, 699225650, 411822758, 16422681, 604450824, 406198713, 985832569, 856436104, 321748864, 593992021, 103153241, 593759034, 316477763, 899445920, 797751181, 261364498, 359642242, 853364879, 386834538, 881994851, 859237396, 465231619, 777624279, 637982356, 21975150, 350558218, 360359366, 103435568, 941206151, 718823880, 556739335, 52140885, 641002407, 141156012, 211177431, 490892171, 890395219, 479678772, 496466921, 723343490, 5575014, 151045353, 813393583, 938384101, 741473145, 946358568, 693808562, 558457699, 691246275, 962741524, 459647351, 156173685, 462047687, 149877049, 815818893, 977269899, 187977746, 943658597, 214410271, 332927349, 918391399, 680776036, 290533981, 821447543, 169145596, 708668825, 151855033, 90872537, 880746529, 251862564, 970262298, 435204075, 855612714, 384924750, 475325868, 979103170, 415518196, 368560062, 334413265, 147072057, 199695724, 796087006, 546571039, 871032754, 282098848, 281356002, 57705305, 492437763, 572715515, 531930672, 385118161, 271977065, 227695784, 491063490, 891523751, 711944931, 548493093, 242809237, 463360090, 25609939, 596883499, 122702736, 679328193, 541590417, 897605195, 784034284, 566266217, 838174210, 987127862, 186202747, 611923737, 10786901, 235691190, 578877026, 157935828, 186909870, 265568128, 514133804, 576536566, 844251987, 739226238, 93586766, 195634136, 672324743, 441433748, 178137989, 670678808, 310792565, 531230523, 797698100, 685664974, 836270614, 80825256, 935412140, 30182119, 290100737, 399159858, 250867787, 60499126, 60893079, 895758569, 759630979, 209679371, 147234962, 192983216, 336734179, 641190788, 218803753, 836495529, 697086796, 69709590, 466399811, 463497675, 962431339, 855253778, 205848600, 650856665, 300218028, 620866228, 252678536, 566373393, 664939516, 657825782, 328058215, 756526842, 880336595, 836774095, 981038499, 50863285, 335359838, 213554189, 882872497, 960308938, 255286736, 976561121, 349614818, 982093607, 994741338, 903063645, 49583351, 350151087, 713557257, 68410914, 313456411, 656733632, 619282563, 832167661, 92021600, 336447619, 727461282, 76646117, 334358270, 337198330, 140932798, 166090209, 173527799, 883361171, 119828921, 66134120, 322874673, 986111699, 344602195, 215248502, 449176224, 276149440, 602945691, 64799117, 98869846, 604889311, 854275256, 601148626, 726948686, 906872933, 928314663, 800792606, 704801016, 568639149, 383796961, 848147918, 507993710, 376159438, 289966358, 923881701, 937874538, 166751778, 205267078, 79771387, 982258111, 952875031, 962761435, 141593639, 414479701, 532283024, 283975085, 340645540, 491056088, 474908665, 639518125, 158501447, 419635491, 383098723, 631784845, 501504284, 887212575, 964774395, 615209831, 999233560, 763767416, 149082431, 70763103, 115030657, 599982493, 569779811, 7028724, 132266735, 507000700, 753487373, 453129007, 619311309, 400104940, 934477582, 756852663, 938693160, 297603918, 41428249, 769432013, 770919433, 880220045, 108832111, 856654405, 822460990, 444099539, 765985351, 541704445, 659139227, 419539079, 436609583, 562231037, 70987482, 615827124, 782387992, 833864145, 788118175, 616848003, 583841824, 872602066, 597290616, 28532339, 233888812, 718386275, 488293222, 405414770, 107461697, 616691384, 697164613, 724920976, 326601578, 510583891, 864587038, 738795575, 669715256, 671697049, 454114342, 646115064, 36753808, 764075544, 469908780, 748347267, 999261756, 486078165, 610465882, 595880113, 79448527, 600423849, 892405858, 197007609, 847516391, 270291663, 921157202, 619844161, 487595440, 136042957, 205648567, 683546128, 315910276, 431249888, 959070058, 843829366, 697738403, 326573055, 708112024, 882162891, 552732300, 969477687, 919669977, 577936631, 585966407, 926460156, 857508081, 676403431, 197202501, 652013807, 478614987, 559497731, 341651193, 195191395, 488594979, 703211053, 165341756, 906142481, 292084696, 615463509, 618228990, 552519620, 531491759, 306831921, 722567092, 645303904, 277478012, 450682211, 898367516, 72058684, 500334307, 575384738, 456178382, 327594383, 743592973, 996449644, 345007412, 691174351, 30600114, 875427987, 744228945, 521419564, 407530028, 677625356, 907585339, 31013652, 253778672, 109597141, 664090339, 375949512, 10159257, 368304795, 554114605, 977977756, 674023777, 482917202, 861621751, 481902756, 664785386, 486167657, 405414970, 736476425, 61015990, 831984389, 312371054, 816674110, 222733564, 180566652, 698158443, 378484619, 150013547, 79625341, 802732791, 726720272, 930730374, 248129713, 381072985, 970652006, 904111638, 301635787, 205800724, 251925163, 727932004, 742200255, 662708133, 87259305, 249874101, 742783418, 548777916, 747537650, 537207025, 115391342, 186168306, 129834595, 731541131, 172817269, 210897938, 580929538, 934148815, 326873979, 45880246, 761634460, 759070510, 825136576, 483869540, 445648461, 783171460, 562381775, 736635581, 291095356, 295968974, 590652222, 505338102, 580525909, 323121504, 72910151, 601420103, 396221761, 427838409, 944072551, 981077005, 208850058, 686320627, 423714246, 517565118, 434472814, 146025103, 838733092, 550486522, 322576509, 274060018, 149362446, 532441107, 188193049, 998600213, 212979904, 426070412, 183759625, 734085114, 404667675, 923539566, 78341383, 969985267, 807506811, 615361360, 495263785, 417886699, 735514374, 13987456, 415670857, 473473267, 339930237, 89585419, 723520532, 214647618, 515495219, 844398327, 697466621, 834659741, 515485745, 793474819, 841165598, 783121405, 130059915, 789137472, 186094640, 596738261, 993561331, 512883807, 263554114, 519848933, 434153692, 622008899, 419673224, 454732060, 159708754, 38348117, 479781176, 499284625, 888067780, 267146435, 62513036, 946109138, 249807078, 217107116, 814297851, 761139524, 378497293, 457348187, 727861603, 996832215, 259340172, 488438111, 210586378, 319484377, 690443462, 633822308, 631356551, 852325627, 871113399, 904650441, 971975591, 207926141, 270245251, 172925401, 15181777, 336652880, 885461121, 159228947, 620035981, 936932688, 858191529, 9896751, 168845605, 562801584, 433657591, 182839930, 400130920, 152215166, 426582897, 930016739, 563228661, 741447608, 554463746, 25332863, 667822072, 514548901, 58359018, 494800919, 222998686, 989461484, 105724262, 543499597, 476116921, 598024180, 481182858, 631882311, 222757132, 300831519, 345052233, 641633137, 674552773, 421498643, 189433942, 136466827, 744705535, 118438744, 489246312, 233656048, 756236867, 74779155, 235176059, 906589291, 566506135, 412521115, 600625956, 154083061, 981735981, 136129602, 98387211, 375591548, 635958061, 274790559, 448518396, 313518094, 857800717, 605993596, 15447884, 272621006, 124187483, 325430772, 92826058, 837586159, 998305175, 516668595, 64582348, 998701830, 960989428, 636109612, 785883533, 567133035, 742129337, 566659012, 216529779, 455491595, 171061503, 444807542, 806779366, 162446093, 145109581, 168713434, 100662475, 969680682, 144646927, 275668537, 452993593, 742372181, 985466796, 316852186, 492182759, 148014244, 711391363, 454636125, 47596124, 867461713, 864229826, 314324858, 706106121, 753266844, 376808277, 283730412, 837763349, 394938644, 363313185, 537395046, 459463961, 204779357, 726861414, 380612253, 384029618, 589294402, 399547522, 467411206, 892236031, 171050155, 590028002, 103387382, 629690080, 805395014, 422947072, 705076762, 92644958, 603177096, 141213642, 329794242, 176914774, 931278524, 822499819, 873193415, 443863583, 479609661, 693357233, 38098964, 364877528, 871551457, 726126803, 238463909, 727643975, 426556602, 288959041, 941449184, 518093740, 238104667, 189383576, 786947827, 132075658, 121196326, 767801986, 683337924, 855395332, 361083683, 529157569, 685403735, 39561231, 389329136, 15712411, 454444807, 420958612, 496216943, 599522405, 90466094, 777721992, 38424129, 923838186, 580691169, 425491997, 918152906, 272600622, 116892578, 278311114, 710220426, 823861300, 880849959, 763300524, 628321595, 560531612, 302300511, 378213951, 833084264, 325870331, 850451252, 359430513, 323689001, 190706320, 622852217, 50554328, 595669296, 934847430, 891683275, 5900879, 841015915, 54593795, 559767624, 831819467, 223165046, 576789703, 513262642, 946427613, 863526652, 295707833, 183908360, 480848400, 686383806, 946172830, 215327513, 881662550, 264037886, 918639149, 851649193, 175515540, 752702286, 262372706, 558189581, 963081953, 234577763, 300380744, 644267786, 979814849, 823266768, 795530277, 6728557, 923226163, 383664867, 15601581, 348718733, 184797403, 785997609, 413272067, 242602900, 106837045, 898947432, 473678133, 723977431, 769952878, 386656480, 59588996, 262342840, 482463914, 368070846, 28936275, 637469017, 760199095, 160193144, 990598129, 327732191, 96712132, 545573759, 105628870, 748870511, 886456091, 495694939, 4748788, 917731239, 696703153, 760778742, 464864061, 562250007, 180601434, 690306033, 264292000, 755162565, 751910290, 152330738, 471406964, 520051007, 431262608, 869287489, 558604664, 44601752, 755977033, 482927789, 58617493, 974870791, 36478812, 922213904, 213032063, 444965951, 390117392, 215799152, 85756782, 134140803, 430771310, 163781821, 64209941, 551403399, 569625558, 267617159, 672455767, 591604607, 621182131, 101723902, 922702678, 452821175, 512946800, 424192428, 555152494, 791037774, 516330924, 215523184, 591206380, 146045520, 576381483, 79145897, 64968289, 564056672, 101100546, 950261941, 329297182, 284682611, 923524085, 881334633, 133099915, 632662202, 161030795, 816095861, 98825160, 989055459, 120933761, 236651295, 930696083, 167574638, 813641653, 221158219, 697040754, 438958669, 497364058, 478148310, 200089678, 736866228, 148512300, 603478327, 984587667, 390792129, 74576650, 850380598, 163904710, 549573146, 324397856, 558850560, 926022818, 869008462, 546158153, 149498924, 257923602, 823736354, 589634072, 995104244, 777948221, 782864030, 629522915, 809714646, 628847804, 638048889, 127714928, 612254149, 99388306, 132571236, 645208670, 283193544, 387930477, 803140439, 606071833, 343060020, 678920279, 461089344, 647114388, 192280669, 551612045, 884022047, 557227009, 193917434, 481696344, 669505102, 187957502, 74533246, 668247094, 169166721, 372462179, 50940488, 286735152, 459731413, 611772880, 368788054, 615545022, 859900048, 135848442, 978937468, 519230046, 270532011, 413252664, 474954309, 794047031, 993459706, 348735789, 978203251, 716179165, 362553195, 719153047, 691036575, 698579889, 178832738, 241695475, 552314679, 436133743, 246780809, 406058224, 508731644, 917321466, 569280302, 758529609, 199454167, 556234331, 694362381, 866075091, 379865168, 625016407, 715557594, 129290654, 611128004, 783085567, 426554812, 487340154, 850380197, 253532739, 956266111, 792760196, 606137546, 246424790, 638389017, 848248437, 8397469, 381740671, 728614230, 522688754, 880937028, 226148759, 593137689, 143368296, 77777770, 412056677, 993183684, 841839466, 11825131, 767282522, 123825091, 21385936, 130853826, 36722913, 488187862, 248739575, 241729409, 808621378, 246975624, 873342769, 932893490, 462345502, 746048129, 356562398, 619963851, 936759093, 111829358, 508029294, 818482096, 81367826, 928378690, 125670481, 240336674, 173976984, 745296673, 674005265, 648492491, 99092211, 972465182, 262823109, 791560895, 443284003, 681384203, 629435423, 754546657, 178072640, 119290796, 848166360, 651378992, 283931406, 403783173, 27507743, 260067152, 496618815, 995913203, 166073410, 179225065, 503298655, 756498528, 682901327, 531106497, 4349416, 71627, 198113784, 888248101, 758252159, 770277083, 906755704, 537938951, 820809038, 263676145, 184932210, 274840034, 65286031, 18115013, 62286842, 663137301, 738105553, 473176266, 360693455, 724663637, 882070169, 306597286, 401044896, 590269045, 636720374, 39882710, 104772641, 640752367, 154880716, 470113561, 277481007, 5426612, 259552287, 494570368, 310680251, 109282774, 539641229, 996466203, 518432046, 912919211, 172359426, 895487216, 317870657, 454789381, 493968236, 308090551, 864863101, 503411014, 414727903, 72211299, 299502677, 635970360, 725363961, 364733104, 190695709, 859905896, 318511715, 194680847, 661377515, 311974022, 104211013, 557970519, 138960626, 435243662, 235582851, 825232971, 341490126, 556907031, 358519387, 416160145, 307606193, 343868939, 548120998, 791719098, 884943199, 364238645, 13832787, 510493340, 152015874, 26184973, 651361671, 572844238, 925369899, 97719759, 481792726, 954350343, 962070184, 178587268, 639221883, 478377747, 879313196, 220147119, 818647862, 65855531, 27395569, 94059410, 657771435, 721348465, 426956289, 611820548, 334048530, 28844581, 819673670, 311728486, 601763717, 962067779, 458920797, 303993498, 659045004, 888093834, 870079863, 278698184, 809650429, 671738318, 927727926, 947026591, 879568572, 74943796, 653013322, 376410158, 983385571, 118895072, 432432614, 705446142, 520591570, 684212485, 244691742, 909748538, 391665544, 277161396, 519694827, 874304712, 284620170, 106508836, 839949459, 266579021, 489014321, 621127008, 475660424, 776677565, 386575564, 12471060, 52907084, 81922209, 474827042, 687394029, 984774765, 416911248, 85736670, 66276353, 40855538, 112756094, 439084133, 207718326, 231323355, 519329985, 176742867, 889461107, 453350857, 451768693, 365977305, 446659228, 209053182, 772966030, 344608783, 330476236, 548446049, 151251983, 531447902, 972616941, 979858963, 522680144, 229873574, 937044459, 229209471, 55833958, 39294961, 802972223, 34842370, 983639228, 62061138, 10920891, 128578483, 861056237, 435623049, 301952095, 345144589, 110286233, 867601119, 848126981, 531963348, 859915530, 708489800, 2441070, 229553688, 266838501, 772899334, 192225112, 418778542, 460405584, 662995858, 996213351, 78697609, 613601039, 42084236, 143602569, 217732188, 43160513, 204208269, 12636466, 415757425, 590669165, 361067484, 393888218, 301101895, 937162978, 16461768, 302336242, 745709970, 404853179, 818923795, 584264649, 649739293, 508745541, 938152798, 237585195, 28273127, 218855308, 844763688, 785982935, 18686035, 820386293, 295715742, 582690865, 580984072, 417304743, 299274074, 735146395, 777782413, 587503135, 198392061, 341389903, 712966755, 945329046, 520832312, 597771037, 26306322, 178264160, 598366709, 255835914, 213547238, 219767683, 933552009, 254820196, 409059083, 902557616, 439046740, 110181803, 956151002, 789941512, 996246792, 881151919, 799854181, 261701124, 415194373, 542764107, 967240518, 975764593, 693436116, 958514302, 875347546, 798275782, 884164883, 816435919, 296562533, 155739327, 402326631, 475028781, 914661061, 699502211, 979938348, 46868776, 643063066, 384900640, 756238626, 974862119, 596263850, 720561048, 11035104, 491445872, 30734351, 212009557, 561180503, 293908160, 29416856, 105758322, 254249772, 613763906, 69989888, 636269888, 565018547, 752917217, 146437249, 183394111, 301289214, 798808054, 753484822, 925972670, 806694211, 199202177, 721358645, 947528209, 299986634, 954227347, 302691509, 829745364, 741124913, 626848764, 590124058, 212388416, 938031742, 611602961, 346599556, 548521920, 551123534, 925159104, 504023207, 660152010, 461557675, 598616118, 655403474, 743966843, 416660637, 354901831, 162927565, 776203206, 946998337, 597405961, 295964973, 489155022, 562020940, 163545046, 754122435, 290367499, 53604900, 628731526, 143504592, 358851520, 15746286, 614508528, 386404296, 595239818, 977280737, 435510824, 469573614, 79829570, 177443076, 621907450, 723463949, 515948562, 476660676, 179811557, 750579534, 226358663, 466007645, 372812925, 192865819, 5807040, 95455526, 625624472, 243832458, 988717529, 655605310, 393256781, 673096728, 559971261, 970409101, 603950155, 5974697, 402696520, 473759155, 159808581, 306576946, 677133095, 763955014, 566314526, 130284264, 198394173, 285039505, 187483337, 786891082, 392860422, 57366596, 689699097, 144614152, 756499980, 774302436, 474553625, 839568136, 739738571, 74827121, 366207886, 265727401, 861696091, 543319501, 599984846, 74771381, 685591075, 492515611, 605146162, 873203266, 585117544, 622195462, 93565395, 675293716, 99019461, 94664567, 71245039, 880491949, 506790439, 848189657, 800732093, 537574860, 430527507, 611733415, 775380702, 484537194, 859045635, 446164870, 895083733, 316504, 243946510, 352467441, 269602604, 270126434, 657941733, 505293180, 559029330, 96774500, 960028541, 122800974, 450584684, 957828640, 954287447, 767856198, 762967599, 984514851, 396309809, 398991896, 860594398, 169016830, 912930566, 450212146, 41342043, 610141521, 710909485, 89426554, 174206921, 175225989, 463775426, 958645219, 693747847, 873791316, 900502087, 980548929, 370346229, 360965230, 767379015, 882241157, 562921239, 567350935, 926710531, 592260879, 20354337, 463153485, 235184886, 461878929, 86271418, 700782808, 584817519, 386973833, 541392885, 466114376, 111225663, 823701522, 251028787, 337480052, 962719053, 259807363, 487213258, 638359663, 62214485, 376839032, 91432388, 487382422, 806765258, 613903715, 451754967, 858070970, 924397083, 494544281, 559345079, 382639216, 826813935, 333028226, 209178829, 437433326, 760617107, 443580962, 356128129, 774249164, 356854234, 196350001, 254905565, 478320404, 30227139, 655781299, 554802027, 650637776, 350135639, 752627688, 655066974, 60510811, 441992651, 948946612, 873790570, 331316654, 680900577, 987994584, 460854972, 577606058, 947135165, 609591, 578921917, 246863656, 61318949, 188234796, 788938167, 213402915, 736452916, 114026145, 239602063, 793328841, 150637232, 379049599, 823928229, 282144310, 397815948, 447261548, 294125464, 309570413, 901649723, 83253591, 215227861, 951199698, 94218052, 320620574, 193327276, 719466608, 567096384, 483406887, 942435672, 77244863, 153198825, 450904010, 675854873, 841627525, 596715915, 966741776, 260746125, 378190364, 688016088, 304103903, 783017435, 994627214, 92713210, 495724484, 639699352, 321108002, 390544005, 385536555, 977966908, 780378191, 972238118, 4095571, 538552544, 49204349, 413014129, 581052293, 510632640, 922349005, 695830688, 823448412, 422753559, 880333501, 864818788, 721147922, 627976437, 408940982, 830754688, 754292329, 836862233, 752073723, 102666113, 930925087, 203218849, 758433486, 8701030, 686106338, 825121176, 7664782, 727514817, 998862164, 61372229, 386231474, 314450697, 772522139, 285427078, 239734918, 863711529, 743678890, 151100309, 483521005, 449497567, 106359832, 771877885, 49269974, 942197677, 839356444, 234933732, 755188184, 975044361, 467430581, 681038511, 681037302, 599564793, 603890192, 29855375, 90750930, 298186726, 92900204, 52587263, 871692306, 690955412, 674305383, 143395477, 424576464, 143249329, 814213576, 498318747, 76328771, 468836849, 794905920, 127086620, 282231379, 399109042, 368160600, 651461963, 68455784, 809263947, 353997121, 417239842, 82295251, 560499835, 365113717, 158367206, 791103997, 799848786, 869954935, 602222450, 776616157, 202330794, 752277459, 882714991, 643546835, 11639367, 990664578, 535467506, 57193402, 702033444, 642974707, 246383293, 961495061, 800631368, 92480703, 803458153, 239839021, 522969784, 314952741, 289030202, 290119208, 904243737, 555694826, 392744401, 106284532, 171045252, 133459289, 436192016, 714115847, 485971316, 884809578, 510404328, 758730396, 784383865, 696707844, 284166840, 395893456, 623675905, 434581762, 826639492, 650134360, 934163734, 29258652, 808433574, 218588638, 932393362, 480465354, 584101426, 807961121, 557668490, 902686723, 666130522, 62155534, 860152918, 52499331, 995087542, 671422796, 546244924, 843382516, 387427894, 364509399, 659989588, 317534014, 323898171, 613840248, 72829887, 436547116, 708098493, 672996953, 524074516, 988218951, 148865785, 244294192, 313144469, 73000171, 216305689, 57003781, 608714936, 624067570, 36140707, 434195915, 210618902, 937661998, 350591954, 948053658, 250312268, 545974075, 326607569, 466835596, 427090797, 340943208, 835957807, 593545395, 211138636, 514923598, 952388555, 735593807, 195907149, 629507492, 820987640, 1582058, 52471562, 733567938, 961417675, 38868615, 847211057, 365810754, 48375151, 696008220, 684169958, 567360023, 158792851, 755404677, 475509157, 174425376, 359466365, 311396831, 949596887, 631297849, 205518660, 497606656, 961209049, 168228295, 690482308, 773036610, 714138454, 719870998, 516154261, 697835006, 960394770, 558336361, 964146047, 955086055, 186765891, 412932610, 642110134, 952573300, 133975310, 1775075, 10768028, 782676097, 562855633, 541496398, 506295038, 767943613, 985078136, 438105488, 2804, 598117700, 530471683, 591537231, 895532438, 813402013, 506628931, 847101488, 321093330, 466902988, 891309375, 349999660, 411350052, 51704615, 876947213, 501674726, 122509609, 104266868, 723367728, 529409305, 901192356, 992655915, 170789234, 247304345, 55139395, 162733694, 665014441, 34380165, 719129559, 629199314, 946920712, 855759682, 516493444, 230507954, 9009287, 532725406, 348844323, 397634277, 843157752, 183974678, 860372662, 153691164, 862376838, 355827073, 653905104, 186569608, 97602389, 108984864, 889080249, 834427072, 309036947, 598100311, 592828160, 39247249, 293924931, 149781410, 420445549, 310517702, 797035238, 639849007, 915035996, 671820335, 640159454, 40965612, 661841800, 609887380, 38233293, 402995892, 678123340, 618031959, 718523862, 375072132, 236750786, 648103054, 346585879, 547627910, 169508167, 693365699, 317985533, 518208195, 727314128, 185998084, 631034371, 804322823, 922460495, 535537621, 446288913, 77880923, 366168970, 606027147, 884253458, 99370767, 255587618, 818618415, 126110268, 72596769, 383440002, 949743369, 487531504, 82781950, 970575212, 537053226, 497239178, 422183052, 824211392, 188398300, 958635255, 989264493, 33154684, 204140200, 257141813, 206917714, 543099652, 675058301, 32551936, 64136525, 793995633, 324893473, 246627787, 101433571, 728715593, 121558696, 76840164, 981056315, 747471258, 266165239, 772625047, 12762936, 838550535, 176252514, 500527728, 11418605, 308125351, 741227982, 285757853, 482902335, 330710541, 657367896, 120884354, 295067812, 360982527, 742005052, 727582900, 444914741, 894096659, 245620487, 970613030, 208133301, 132112272, 696385307, 538889824, 270307626, 707518653, 964486771, 982975035, 605636698, 888326219, 183744049, 933413809, 145278820, 1832642, 705753625, 933581143, 478576264, 774443999, 514540695, 953116014, 304035977, 748995052, 412794168, 182068198, 294920457, 812621809, 256750205, 164168674, 234467380, 163578309, 297633839, 705268496, 735471743, 869047982, 395791929, 53568474, 972019821, 632084202, 86876175, 287973391, 698246309, 48884265, 201392833, 91272799, 137582095, 353653373, 144664142, 248954776, 152451402, 286780857, 83892611, 655333943, 178380858, 379492650, 864812345, 156091190, 638029186, 893002497, 409065800, 535447962, 232378785, 464396408, 972995477, 925534142, 436833402, 261063874, 931180609, 693107185, 694927906, 217891515, 795709713, 952040278, 198779851, 560392441, 32434852, 278964395, 515285298, 843307113, 681915761, 399359186, 358527257, 870552927, 244317638, 939208086, 681480213, 58891111, 658021191, 280425191, 905363879, 359931996, 240205942, 415904505, 523271123, 94109247, 499057590, 424792993, 81868495, 275908744, 550143816, 330317449, 549680921, 314789961, 804512875, 547586493, 669386972, 300948906, 292406856, 241275312, 34720202, 579255691, 74568182, 125160383, 321657731, 235487421, 944335540, 254377982, 317643334, 861533235, 548408404, 890411756, 493459895, 174624188, 555620205, 465232771, 186995834, 375163330, 819435900, 361583488, 28989695, 34076824, 126034998, 983917709, 199571029, 562726464, 381407588, 164091963, 855167276, 104019578, 789682254, 25262751, 167818698, 693913780, 403197612, 230053062, 156917626, 866639943, 975702876, 430253239, 682789934, 528425139, 116445910, 160966775, 728223187, 472743014, 245425938, 92889533, 698938693, 80649629, 746314086, 49694076, 165147163, 275466494, 379522454, 887553720, 269180179, 317184320, 616078934, 973736013, 244355743, 344418653, 443089805, 975754013, 272679627, 503968084, 971888262, 550226257, 35935079, 167420269, 37570865, 360980268, 322891981, 516002356, 821108729, 986774210, 182902791, 904199778, 180022194, 131246044, 200870264, 531483171, 812199729, 772559622, 771143732, 276653620, 315174114, 693701322, 140747947, 438931854, 450019356, 860844249, 345816688, 519625853, 436161043, 954143744, 524921785, 724057043, 568525832, 46334975, 492955999, 329856753, 587145043, 955062619, 377219235, 149818119, 289824719, 132399363, 198916424, 462652011, 509884693, 969439294, 856486815, 118479816, 753271941, 456530411, 449830128, 801224331, 456375980, 406335558, 159419557, 561013657, 167115554, 398990117, 244222, 86923001, 744763514, 145522114, 289889212, 106610662, 380351210, 631777516, 91226396, 129333901, 655178046, 252844605, 541101109])," 39818 (continuousSubarrays [986576039, 601518733, 744798894, 581260814, 819551063, 25280437, 912790185, 566200129, 512449764, 813324259, 935779477, 75523677, 110564640, 996917008, 24329099, 81044379, 639852709, 485230276, 868577009, 991579590, 173179412, 153444229, 696412320, 668285025, 665305513, 374760041, 395657366, 431207308, 723415171, 78217974, 231578479, 44787201, 520128365, 190886570, 99544457, 834752183, 839840220, 23156798, 568958840, 828175027, 573601719, 646397626, 359922464, 610592950, 761436656, 991866724, 975548126, 596278074, 51352469, 709760089, 137138347, 35412739, 740326384, 428595150, 561686033, 826522352, 528512395, 166766340, 903971986, 930175620, 291876450, 325746465, 226954604, 342184919, 786100937, 33431144, 559960353, 228435020, 981753250, 477182859, 853319621, 531074058, 293762369, 756977260, 982115626, 109505171, 97662291, 597546699, 25539355, 514871975, 21469506, 866882384, 749542329, 187314233, 668059077, 880111727, 802394008, 684226238, 295590795, 933475698, 603784570, 805706585, 106664159, 706632391, 920925278, 534703454, 809799056, 533469791, 699009564, 574769508, 286021995, 580299338, 927136527, 182061139, 50256606, 963343548, 2079973, 759980720, 239896735, 944973942, 715128164, 958534922, 284255197, 962076026, 543624223, 280308022, 922047898, 608663068, 462272761, 947562676, 27146468, 341833914, 373203844, 406807671, 587150376, 428133803, 347613221, 515250274, 825463982, 900359800, 907386894, 758524660, 920655262, 270154021, 958873500, 110226802, 114234297, 326643960, 5861654, 49217327, 698710492, 81052676, 486338667, 421658147, 698878003, 522872439, 376629510, 608900195, 61788074, 690780333, 11942994, 539935304, 292087332, 12152539, 317686301, 915961372, 150374730, 869266096, 1003629, 142908381, 204197001, 394544263, 969450770, 171841363, 370991241, 650184990, 292091080, 505109506, 592028441, 596806545, 834483109, 673378639, 767537232, 201264498, 585809426, 849412291, 631715774, 259388106, 462631908, 473311307, 585798379, 905873551, 750313742, 391002361, 68500749, 679610590, 82384498, 896993563, 234936883, 75315577, 354955786, 941817712, 104302093, 713662616, 936482013, 43657259, 745642043, 405663793, 895477621, 69916754, 662157906, 108643574, 133515441, 947816601, 42991330, 35801373, 846689945, 783572043, 615345014, 800773933, 436105384, 559804754, 325938750, 603283553, 389448681, 445037108, 787491667, 185306896, 634916738, 477037552, 787317467, 959074084, 555832639, 203512770, 942124651, 552642935, 946815932, 511046362, 791528968, 910331118, 417421115, 171635618, 60882630, 695292693, 979469165, 954647745, 664340639, 608490206, 175615746, 788066583, 210609215, 662081854, 502078228, 552639148, 408995863, 928867883, 788865214, 78446845, 390010046, 956279858, 273414686, 456561571, 177779246, 215293145, 144082790, 620526520, 398982331, 234873517, 527385946, 613566832, 477765282, 278465563, 989951319, 385737853, 481073764, 240056230, 749226389, 667689555, 935319591, 540379075, 897989401, 613685104, 385113713, 338480692, 257208208, 875552232, 739900834, 742532026, 42254847, 502853370, 396247091, 481159225, 557415631, 914083869, 281797106, 292457360, 112959996, 351547590, 265676736, 923147125, 266464434, 687374493, 580794148, 716602199, 338798401, 913791489, 677172734, 738912761, 152982023, 525315575, 430182817, 354623499, 937500825, 376724848, 757581895, 876521213, 551782406, 151721898, 789720210, 342190487, 319203609, 966485054, 958968137, 513122548, 975613889, 866247534, 281738095, 917981986, 531829981, 359842995, 6622721, 904674242, 974976449, 748258437, 567842348, 638743706, 61494949, 303462355, 445161378, 749225931, 787139081, 668259182, 234981552, 462258435, 726625304, 341510016, 577058185, 992554850, 749445478, 582595339, 780481917, 750180751, 262124589, 106535883, 367687558, 971214612, 61319084, 965726400, 657516977, 883701697, 862522904, 64115696, 513783295, 999052937, 486700811, 796573702, 280239976, 234185826, 461204650, 758125925, 126775922, 838175995, 806801831, 700071822, 989267637, 910282003, 878022355, 244255278, 225338144, 881659572, 538074143, 865267119, 764307133, 253726616, 4475863, 87932273, 729809419, 268502433, 65681120, 535102289, 173483085, 798364418, 968369339, 396296576, 73922307, 899252389, 412462346, 964316305, 761282647, 255990326, 949404058, 812590373, 34026036, 97939548, 322224015, 510940653, 506559314, 503977550, 774514848, 36247643, 437658632, 479381, 51878343, 337682815, 597869299, 870247035, 663466909, 420381212, 288653041, 58094622, 9581960, 423701880, 571611425, 593983811, 982942712, 615198986, 370820134, 665231038, 466181876, 543638295, 78012277, 808025712, 110429581, 481671110, 198451122, 555980045, 252794221, 789193201, 299465441, 145553688, 174638070, 110315978, 181179796, 552120081, 995670736, 455857983, 158953526, 789054048, 936324288, 712896109, 176108370, 623745811, 385669462, 386367438, 216076496, 852262157, 392113704, 800367361, 35297933, 382493560, 153843060, 691569272, 206751308, 496810232, 948567947, 909942776, 22548182, 269168821, 784279534, 404708186, 642552253, 157290956, 844643546, 749012594, 319158474, 309157145, 449213107, 253681659, 306003941, 528681663, 947286174, 13134287, 868446224, 362358182, 264069010, 580630077, 322123947, 773675502, 415357338, 756222969, 259106790, 105858528, 30623735, 167775546, 197595956, 450054857, 724671100, 682749838, 558106911, 883549230, 269667837, 756991009, 252082110, 787111586, 56626871, 790643061, 566304803, 587813314, 77961425, 273087539, 830963409, 133834852, 587489818, 989427376, 498572580, 639829475, 751779327, 41302627, 222532052, 697417077, 52806010, 982963393, 149885608, 395105597, 645764472, 191141038, 845031106, 312109458, 729512844, 176127964, 809793848, 664968995, 704916862, 875673216, 141833510, 182051317, 992183445, 297792113, 355574825, 606046037, 194300931, 632720241, 610881837, 186754220, 720832108, 146071000, 243419454, 828709151, 43639123, 666855247, 163869981, 268559201, 361847381, 104957194, 190591744, 634468624, 321594174, 862283064, 205152266, 177397962, 556311619, 863894633, 373831766, 942279545, 653006149, 160951075, 236801325, 493232814, 339583131, 484320386, 21025914, 256711360, 849624193, 401395721, 496381864, 332735864, 217338016, 331625978, 57067206, 524966047, 567366924, 118409006, 770385788, 603521587, 306874647, 230486584, 917544600, 410833394, 488486675, 88688023, 501855718, 308799624, 198553054, 293888196, 109345877, 584831299, 935375323, 319691116, 790173522, 433793231, 350306105, 656922791, 254787836, 648834473, 69769848, 79680095, 577271913, 577615598, 83426119, 167136032, 716304509, 840447832, 554251141, 917904548, 611101123, 78487475, 472387413, 187390057, 831236707, 74874951, 451113402, 934949752, 252310862, 79253725, 903689754, 269740554, 752807142, 982768130, 5205489, 201734494, 538149812, 306360124, 504690456, 216678578, 141422302, 142708240, 334420714, 789870378, 332615884, 644067726, 846846492, 889176620, 421265897, 962675830, 944303527, 217209454, 293583694, 823750001, 492538867, 305676053, 309983666, 902029229, 854985728, 144425088, 642729776, 526520803, 366059436, 172215933, 976733788, 909084484, 124595472, 453968460, 99113563, 173436747, 636604497, 866277760, 505575047, 520608862, 46301245, 868493326, 269333051, 940295888, 595054344, 809152297, 540724164, 154224803, 873893058, 733259375, 536533553, 617692870, 733884839, 460666106, 274602303, 950741840, 468289936, 544801847, 496872794, 188022530, 308361846, 473824480, 644807993, 410054596, 482314084, 372411277, 28145300, 517628091, 494398440, 108336654, 231230366, 455525638, 785967900, 909775888, 663148606, 947641873, 547442634, 327586571, 368743086, 812934032, 242359806, 900501040, 481701585, 625197976, 906163166, 572389826, 749804175, 770180626, 423149784, 690990313, 764392216, 779926189, 145452549, 395972668, 642625619, 450047676, 140155889, 654897705, 340834937, 596247349, 253367486, 772441625, 397178326, 516751524, 656974341, 141116671, 773481839, 180473357, 636719804, 936547609, 336092653, 191634486, 258920566, 953378934, 161483711, 733252003, 212620250, 72639104, 920522471, 376147673, 351072337, 750975083, 474000170, 431964154, 604802291, 936933417, 536723843, 325972811, 81511779, 183576561, 394027356, 865906962, 408834402, 520074229, 245029833, 415970722, 487181359, 525147700, 955420289, 419546405, 35534058, 244737094, 351570728, 393362930, 864420719, 987440502, 914151300, 732024790, 517887877, 940220056, 474807908, 54332016, 450628737, 248165962, 708385943, 277002523, 540665248, 729421264, 372474544, 173854046, 848679620, 591958283, 387139566, 366709532, 490529618, 733230433, 555310779, 212871363, 634593613, 789815897, 344012663, 192291081, 754686060, 693344777, 852397477, 482465668, 402928302, 976386953, 185141768, 215267652, 159292854, 640962388, 156621561, 706192644, 946595396, 641923802, 848690811, 729896504, 199608705, 447301337, 736791970, 878841552, 30301284, 468198364, 332347314, 764408034, 62518773, 893624383, 511404789, 216219825, 459444145, 9837850, 851832373, 396526624, 408886323, 260246028, 272648477, 662543268, 884571944, 504589438, 735466421, 943634437, 987392460, 174198798, 985001154, 628559284, 274251988, 739793275, 768341410, 880418500, 364542649, 393945987, 247599498, 851319424, 345604729, 455254550, 913063364, 598539995, 386146064, 695090808, 156259258, 73962034, 588884334, 800086874, 740188025, 59302474, 181600767, 66082533, 510776571, 36633108, 728512690, 635382302, 393939959, 767127464, 687207892, 323448714, 903413875, 784772324, 769847240, 385363892, 277499606, 552770739, 198009999, 865700508, 6122709, 998815288, 639486594, 737034697, 426771340, 995923120, 843073558, 674510925, 171483616, 950272084, 473017770, 276155357, 946732144, 77878333, 326866906, 284809603, 11916753, 76483263, 491178725, 195357618, 32928657, 360264741, 368002046, 797667558, 479883567, 3806652, 100053441, 49764335, 233827150, 966165851, 299691293, 191059346, 424648450, 937697832, 891631170, 810474530, 141424072, 494037220, 426259722, 105210394, 673567320, 480246657, 395288408, 530636929, 499914791, 304213778, 715201314, 901449164, 381721199, 913862153, 179346872, 148469490, 223565496, 79303151, 994169369, 470918881, 86267931, 501375786, 404137902, 788330108, 296937007, 253346788, 845839600, 728150937, 44676193, 957357770, 152888575, 835705180, 196081889, 90926363, 504445250, 806072267, 53423666, 459045713, 761478620, 748173243, 377592615, 794069247, 46074891, 618733588, 613480327, 807958893, 738744322, 177399515, 489924779, 737922419, 339764223, 784456098, 666610787, 123385633, 200519390, 916326464, 524138634, 459359318, 432076898, 92551987, 126605305, 647923175, 151676410, 748276775, 952524998, 610607034, 535093358, 69335779, 651055828, 968479865, 851695058, 219941076, 587985205, 933745954, 259887416, 56597410, 389914717, 402822378, 904001354, 527432726, 961502247, 470139454, 745115869, 524821435, 720089395, 497674929, 538781692, 126687566, 849812508, 510357606, 700626030, 641862225, 900942001, 700885907, 735519805, 584910579, 994399994, 771534636, 311788676, 305841072, 124840659, 426699010, 925815049, 828691029, 568176087, 358396156, 770402906, 616542608, 502606997, 33565309, 756280776, 490494482, 865071710, 124254311, 505042767, 507835801, 149903760, 541774159, 680101366, 515097761, 910887206, 200928602, 25018206, 137263416, 471738493, 300829837, 772014793, 477042531, 668810692, 449670700, 274442516, 617516315, 216702299, 582885872, 630457303, 455678745, 112646971, 716419192, 820618514, 854269641, 742875822, 682600898, 27486674, 648247165, 325734409, 149726892, 996802993, 860986715, 222003754, 856662976, 18652603, 202240329, 387477952, 270113319, 679287443, 974880243, 49504286, 895388288, 22300516, 13751064, 976411258, 958640931, 221159301, 327380748, 955221902, 9425450, 181415223, 854854441, 989110191, 329839749, 733713179, 6866679, 187093683, 723886631, 294524679, 726149748, 135382460, 935085411, 495085316, 497704213, 99324041, 511778957, 543128576, 996621738, 744290255, 301798288, 527774475, 2283682, 459737942, 731435429, 349076351, 375330492, 381836982, 524367832, 997958386, 606338879, 365247869, 989070681, 423330089, 430331870, 430450084, 674033136, 699278942, 982132569, 673877576, 478823225, 588011223, 572520597, 52590548, 658849578, 109285107, 498488460, 534344859, 484576872, 557655008, 900053888, 922972287, 559122206, 484335605, 419515969, 964121136, 498330080, 183983701, 166898608, 728609354, 683295908, 951496687, 913234493, 228643392, 122451236, 326248725, 381025726, 553549307, 175233471, 787119947, 346584126, 807008210, 564651643, 744271522, 514794366, 924364324, 545214668, 658854025, 880745050, 241643207, 548526374, 998536424, 975604461, 478134892, 829968428, 612135198, 438573255, 687846362, 224800446, 678060653, 957344959, 492412450, 36273190, 113782707, 865842852, 704565173, 406187724, 973340673, 301125429, 478044041, 314361811, 180597293, 744883721, 628700550, 604143322, 451008067, 480834434, 183988201, 859180156, 375001260, 889386689, 451787242, 652102751, 167156824, 413155326, 519672357, 319886201, 300779618, 58124313, 830567026, 250707961, 513720380, 610627934, 112843799, 191436616, 747163762, 115774537, 151884727, 266636220, 657665974, 920606028, 164187109, 862474737, 917705845, 82584871, 511206272, 107922931, 103875332, 542355762, 297863866, 700687804, 412327941, 263152644, 319526495, 387630768, 650176479, 651400390, 522673786, 50844782, 887565269, 395477533, 706752245, 508399207, 413363997, 445076369, 169200104, 130908062, 768044002, 347537954, 697579513, 796408345, 132850467, 597617278, 602475506, 945958255, 23823331, 970944437, 537329692, 103848475, 47006196, 525250853, 323465378, 345220343, 647712376, 620256803, 561723687, 306535944, 147888705, 759909856, 313402006, 525375313, 871856491, 301130834, 137546158, 499821461, 714292167, 580737118, 84985910, 468713941, 728211737, 464327518, 280414810, 846609010, 5789267, 711396078, 721326933, 838225532, 889825409, 296774397, 573675103, 296627806, 694496114, 228034366, 312583229, 413396179, 650706030, 810763132, 656748092, 326338824, 367130339, 963050464, 612700577, 38078765, 369620097, 402721352, 612846892, 719511018, 887400356, 780477034, 405419444, 639851418, 636069705, 807024698, 324792234, 448441139, 556194397, 962751237, 397277287, 250853382, 117616066, 333782066, 56221931, 346456768, 668230224, 205064744, 674434480, 152685602, 333711527, 833552139, 946801018, 134996218, 396930307, 704721069, 586389265, 127493541, 293380144, 315930416, 876779591, 415510520, 595467505, 186618457, 571640009, 210841865, 115248499, 697830266, 785552679, 691774331, 531882328, 320296450, 319948371, 948942538, 781146654, 125631270, 753976436, 933707675, 286978444, 721564824, 110497466, 360327851, 220193725, 969813144, 133861104, 86184704, 645801405, 412238564, 524205942, 669156985, 725418297, 572124885, 235305580, 620443728, 378158887, 992849496, 944447407, 289657433, 972558855, 760792668, 939409858, 113833843, 121870897, 989112181, 968319028, 461233291, 313896944, 166320624, 978652417, 828343576, 285392956, 930176169, 479437221, 909866334, 327089606, 741593535, 695211265, 653341008, 493140645, 943135234, 892369361, 391458871, 372977658, 663522758, 70745703, 296573451, 987563405, 930230329, 818530969, 468783218, 284551398, 785158843, 422830132, 866042448, 539399871, 172742336, 953610433, 735901718, 755671210, 24687842, 918059021, 891693651, 773627646, 262804676, 845835876, 104771818, 330078383, 673195378, 199614261, 715142396, 570957848, 195133203, 659682907, 551511513, 597871569, 389806908, 728219943, 912136988, 922329718, 980340515, 786933442, 555838838, 348248307, 995182610, 553338903, 634432486, 238909929, 505060720, 60007623, 332681811, 229138999, 750056366, 135608661, 867659239, 517673397, 214592814, 329258851, 110379871, 536266069, 831653225, 156869239, 57866175, 372771662, 198587103, 232800264, 582995445, 619477519, 145249641, 994266095, 883176178, 627987925, 673311512, 359530039, 223425877, 668057290, 320699950, 712859313, 576683225, 752391878, 967753571, 992482062, 38524512, 810422231, 190495740, 990497174, 682326920, 783553180, 586085802, 913440283, 245612384, 86481359, 507195397, 692434313, 24230073, 867891023, 985253645, 249976897, 211546544, 132271048, 68067628, 862357524, 158078750, 758267781, 114455258, 712586056, 546994934, 808326761, 838981173, 966368905, 864995256, 934999680, 276125059, 979540976, 399015349, 329343570, 623837261, 904989746, 995350662, 974746624, 20126639, 256669532, 644585916, 906817904, 622607804, 680167615, 64433292, 487201484, 627663049, 356459009, 993489733, 491229920, 295500541, 198780092, 331908340, 842045201, 880406211, 340937757, 325862857, 243407439, 658087317, 956308756, 644062108, 873353301, 183457389, 378005760, 409772395, 581053569, 751042001, 993256723, 324826774, 608797529, 815824680, 242532832, 880535373, 317717750, 672372272, 371416030, 431423441, 103602024, 67109546, 329893263, 988786735, 224973953, 724462393, 427459818, 327145347, 277712776, 394072537, 584870600, 266303282, 836513660, 300418431, 2665482, 215218726, 273713571, 651405723, 571305561, 834307748, 29659598, 137383013, 292524, 901038717, 461619099, 41101029, 971364034, 679805575, 244587278, 384179079, 318209343, 620799662, 118743259, 168203256, 435370432, 317463526, 972645750, 344845525, 280522222, 329343261, 763470329, 253303267, 43401087, 633539460, 904801161, 152589864, 129198178, 698207955, 688597268, 759347235, 216463268, 119184452, 230246787, 483164029, 90684422, 484813684, 995044366, 647524100, 250111736, 31109154, 760403936, 355380622, 220397008, 877296750, 576011695, 526398022, 977541168, 909186901, 358538309, 369908689, 976733050, 395469033, 618950160, 148817624, 96391011, 841554406, 886450972, 628474861, 168667519, 693433495, 976034748, 584654523, 972189615, 696216855, 473742137, 586122783, 334414483, 418400651, 102585734, 198955796, 383351846, 89621709, 186397325, 901228819, 206592579, 442678482, 646847024, 215762963, 705052374, 166308595, 236009260, 308007156, 733144348, 911714719, 576867231, 350502547, 517696144, 10419386, 373477478, 500895193, 682732667, 352496488, 337175771, 732797690, 425202741, 189448651, 861389089, 125820957, 475905145, 390855792, 122541166, 589138727, 703690873, 488638808, 765217488, 245796100, 327336741, 409359149, 940996252, 150631338, 471300375, 986460604, 894064038, 1271202, 434271359, 546018019, 476511333, 16274396, 595108601, 380198879, 559298182, 384680037, 110631233, 189454993, 371278246, 438550068, 408497749, 234126240, 585862047, 71382324, 197836158, 841610406, 358700792, 38659181, 120561653, 237770088, 636994454, 61088040, 437579765, 976439946, 676199075, 319278431, 680302593, 631122874, 899726990, 125230482, 437347682, 503862589, 909489156, 370869300, 572185459, 436662762, 66527855, 575593536, 134605578, 833703074, 927607631, 219336839, 6906079, 490219673, 622744038, 994220801, 327163518, 887086762, 676735112, 347495993, 876531703, 55373820, 819152967, 356113070, 232027931, 189446369, 162238011, 344681371, 394444617, 299084855, 927274627, 925424622, 472383396, 107913977, 555582312, 598634062, 451341034, 832988297, 711016734, 555276702, 892173115, 190973611, 697102582, 840375991, 123038610, 212299011, 491374175, 772594350, 584439670, 277605241, 928636891, 804987172, 445970535, 355038974, 617029532, 589983294, 682217758, 89625762, 803571486, 593180573, 484509209, 947433617, 86872088, 285874384, 960332023, 434347604, 622491942, 350191556, 843130289, 341556911, 507105248, 239449109, 912622725, 581724026, 722136006, 691139400, 703803324, 935445408, 555548639, 914421790, 116080079, 9294548, 848156274, 499314704, 7342392, 814923956, 92860087, 220102440, 634212351, 679221602, 920296890, 388852010, 642053629, 807079836, 922941714, 820219917, 185082979, 235055663, 403019282, 297803197, 930570216, 855126672, 914359065, 287327286, 877444406, 432392221, 398392751, 851638454, 514697828, 218853487, 730052752, 775191292, 725225009, 634512699, 350910894, 890116956, 308432895, 708563535, 804739795, 751841678, 152162816, 677584120, 837057032, 444390754, 589864873, 645654364, 66226096, 73229082, 377199914, 839959549, 952209899, 769216269, 133837249, 674305692, 13606016, 76489727, 625780525, 665901670, 671489906, 547958357, 20365291, 910977788, 416499743, 72598511, 762595046, 616621649, 425171642, 114440826, 640871155, 750138018, 335887902, 210052080, 124424056, 421611272, 547746156, 621604874, 811503057, 972326559, 909589502, 50174297, 142719028, 368497648, 840597435, 87540760, 640825534, 953150151, 197124631, 283419391, 241154464, 563244807, 829610363, 55522671, 746971220, 861129400, 535995036, 4215625, 933231512, 342380750, 520767203, 679638508, 210050792, 558489503, 576267227, 177348452, 580515022, 383894600, 283750129, 766520363, 506062684, 446629186, 279138609, 284978643, 859734483, 305991557, 315187158, 974921157, 117576867, 169089999, 925761418, 764373041, 405651415, 647875816, 53415649, 491300306, 723776343, 221852702, 372818911, 743061445, 429331787, 232384, 128746533, 489187589, 126689009, 184608888, 25045905, 184934206, 955719495, 517276052, 83447309, 367792505, 274706927, 345760393, 920153104, 854530779, 956425369, 986933640, 900088347, 234028316, 189010951, 834443404, 332383957, 720470590, 493349935, 623682564, 771936958, 629287634, 230042467, 120160190, 128074868, 972127117, 428933190, 31688257, 831349278, 717314750, 526708673, 966963183, 157001778, 526208230, 442311495, 50603303, 752250239, 949894597, 603541187, 6269166, 922597839, 755528875, 300932105, 954591827, 810255418, 777227661, 707459169, 100480160, 502639112, 343216866, 939581098, 68653891, 115840262, 122262261, 952432533, 918594966, 699504172, 437275013, 647702839, 736325185, 597375337, 900388168, 218015160, 93655587, 88257692, 162604800, 20672805, 571083319, 328362800, 326033993, 871864315, 704539602, 693795848, 268722689, 575146902, 544684235, 223700567, 789120757, 994333602, 795505390, 763615908, 238029391, 640693473, 184815452, 630113412, 72071330, 295628311, 430088647, 241075639, 278667254, 749705384, 664147718, 125130661, 993682714, 544763375, 903367057, 542017263, 726764966, 220151078, 229955686, 5212841, 440922845, 297316977, 858145969, 92622074, 141001854, 960320811, 764211441, 729251622, 774205031, 522150538, 781133985, 744754267, 362391736, 469529585, 751349436, 953868544, 59811003, 614778948, 894074215, 949287753, 793052735, 236202071, 255051005, 180439030, 383519238, 265909058, 807498554, 509766146, 886416122, 50880873, 458742912, 429742515, 823121209, 409883806, 62630351, 225481646, 525314727, 360855493, 926715425, 558581733, 96074629, 56471696, 604239828, 662595248, 235077164, 250607577, 462515565, 452300935, 628372017, 426346660, 653144897, 521868355, 955790793, 355374280, 618179015, 260855274, 35277335, 377535052, 517302416, 127035430, 586928688, 320411861, 654938124, 629723419, 167412238, 912487835, 510492008, 815020417, 31788417, 33529360, 65186782, 759977513, 960720405, 818056734, 868804836, 766835333, 776352926, 63367556, 735909085, 889872994, 49765661, 174063293, 245237911, 449418849, 682970022, 839172805, 463939462, 100736418, 380402157, 9061407, 548163824, 368840454, 84615631, 257757918, 182127386, 376794701, 65856158, 601753845, 670936689, 317886345, 341748076, 806444113, 3737778, 721181926, 32647468, 4736468, 10918975, 423801524, 560284523, 650483626, 289657048, 698364862, 58927298, 598768927, 804287668, 920878181, 77898939, 72452829, 783763756, 249048354, 573063387, 631533880, 202741975, 643453093, 617659082, 33643917, 483505542, 948412732, 846131071, 743930, 711856856, 296980839, 483010592, 436519969, 11190890, 708922535, 148094106, 579583246, 577829389, 746848688, 632920240, 616367274, 375545667, 793456996, 741810189, 394206866, 434039440, 959454100, 849854952, 319106341, 883123155, 654999752, 132785683, 195809817, 616816108, 592308316, 130639031, 801536267, 448027297, 456391331, 415067985, 320675141, 95346307, 72945622, 64121938, 405322477, 388802816, 389599993, 799007370, 645482210, 326781402, 67604548, 721508019, 549669015, 6934247, 851855876, 603204343, 559726058, 432817983, 516100652, 667962146, 501070070, 42266921, 841233220, 977458990, 318723580, 246398453, 654783477, 825836134, 162559306, 143289014, 323071962, 633247251, 43039917, 268058280, 754633280, 845133748, 191928692, 887548131, 128541, 13948703, 803610402, 806522931, 851623468, 520461919, 929480302, 259414838, 531434782, 60281330, 886313490, 200667907, 787773947, 617771333, 260405048, 817086321, 805698257, 71375144, 756957149, 13486796, 717612617, 686063691, 15213485, 277778354, 490540748, 7007016, 452304510, 91141491, 839657227, 53907887, 475468234, 453265091, 923008830, 570124892, 64231546, 397691429, 188072356, 591490965, 933097387, 817134155, 432785777, 775343623, 302451124, 227795582, 228841479, 98800598, 704272462, 654840714, 640935261, 813973555, 654728203, 448787508, 911383314, 210486298, 655880496, 672453622, 437321762, 729855343, 352752534, 236291785, 341980717, 915027601, 689301897, 278836475, 942793486, 578152146, 472508049, 136121057, 416755895, 493246860, 488641408, 973216434, 459385216, 136088924, 579924464, 388400813, 13195159, 775011893, 17663574, 465973123, 131356934, 569769804, 984198730, 953264250, 252183195, 532346146, 754390766, 626612734, 594561146, 942816846, 116112412, 965321568, 980368854, 418148218, 630254272, 180102482, 778418086, 801146575, 23520247, 597264595, 582591953, 848193494, 242049540, 587081940, 55372911, 163529373, 6597606, 710057761, 265927480, 183631325, 581225743, 362932861, 49004629, 460152851, 529438055, 822430771, 798950224, 495435605, 148360068, 549387665, 86923119, 511997226, 748201368, 911514329, 340058083, 916915838, 989430614, 716587270, 793730435, 603430274, 702680784, 140199876, 289341908, 847530806, 716934163, 635505378, 806661448, 840708180, 383437566, 335990415, 611797694, 762895183, 292734082, 362255094, 467994684, 584189206, 548896020, 395742238, 26365817, 465620147, 368052838, 834434978, 477330746, 624248485, 396403443, 465779826, 740952398, 93001567, 275138027, 564041897, 839787464, 567082944, 477432405, 236387712, 230458838, 371799818, 991120726, 342076033, 954237051, 553643873, 608140350, 278259543, 952913556, 669117032, 162463966, 581386365, 292386153, 312967626, 557488077, 722001828, 123129121, 682186795, 831279410, 448654567, 658821312, 116391311, 541782326, 763980852, 184938202, 318982151, 651407791, 351365424, 520278092, 890359285, 876675294, 182822782, 18748040, 916571707, 750587716, 278555242, 8009990, 126607627, 8323219, 605058452, 969321900, 176712248, 485398843, 227545829, 55758292, 52880424, 497547351, 686894369, 119244350, 637578478, 807175975, 646890547, 621748480, 898435345, 968654831, 918716337, 47190041, 974512999, 270441707, 679237163, 830257507, 652152960, 681011783, 843800897, 735032661, 145424971, 620328333, 139930119, 818019690, 991851758, 446815153, 767831439, 924813682, 510081042, 851256241, 186811769, 891451206, 446773688, 196164199, 214643654, 910341835, 637520024, 172065480, 887573010, 700997131, 531733496, 656672082, 36075340, 664335614, 108372306, 495177697, 841693596, 619225803, 393083816, 48262744, 442105323, 37990760, 923595516, 773580990, 742932707, 874130362, 86535282, 254622390, 46386604, 800219045, 627094331, 570881064, 417315119, 878168401, 471621287, 965360993, 346737256, 772113295, 571678353, 102222720, 356769943, 801308721, 414093192, 7274657, 297140410, 900476622, 26545369, 330836775, 781778198, 189015037, 301927085, 737704355, 755271210, 451584653, 743869747, 952811301, 204992213, 846888761, 389810920, 790341554, 374273343, 649743534, 944740304, 126553505, 448897970, 787676728, 36720535, 685601135, 546688979, 758263620, 766166623, 831630231, 328622466, 914611096, 405631388, 296847439, 389358530, 605879232, 557670692, 27170848, 978622976, 276222900, 556902984, 832945328, 816863085, 523227373, 124927231, 546915054, 938785584, 927487954, 101424099, 399756993, 681275342, 89120137, 992215643, 684064376, 466859536, 935208624, 401920582, 263219327, 280287859, 605028222, 233931078, 244555238, 9454390, 592914144, 904953631, 21541492, 133371738, 798172242, 759785395, 125284326, 173327525, 435343047, 865305356, 605619062, 947865034, 804190994, 749830301, 719047130, 446471442, 431901713, 593538832, 792773282, 108359957, 401824407, 581195461, 371443516, 779789087, 769205262, 824721709, 601456405, 485616383, 185544580, 95385672, 297682149, 442739750, 85022014, 480946068, 232546994, 437720966, 197141447, 452344290, 475346394, 448968866, 556880073, 235260629, 741357253, 969813968, 68715074, 657033311, 836737364, 655196179, 403647660, 916100633, 805881321, 467378822, 816937888, 790551592, 390806718, 314687318, 54278481, 402885488, 862114635, 392390476, 98850108, 162298090, 876541434, 326488770, 204919626, 461286844, 195632246, 868570469, 137157266, 450948928, 526416205, 555660735, 216343143, 35886438, 525808681, 959312986, 679788284, 772376614, 940967231, 474988741, 167486380, 219420893, 944251785, 66285368, 616133153, 997395884, 899104230, 768787298, 385221046, 685913055, 892972249, 932064476, 785378186, 659973230, 848832618, 968344528, 505944211, 507114713, 235289417, 918163896, 692505315, 834927456, 756195638, 37427989, 341549252, 943622643, 194055173, 461959777, 970392575, 99217183, 914418247, 934314709, 948122650, 357117528, 460256407, 57147611, 648063189, 897179811, 733995206, 530782294, 133743367, 103618827, 299293793, 713124880, 179358768, 249518162, 302670054, 290429864, 554726363, 819151452, 730553853, 514463096, 370877976, 255852831, 651401778, 606842639, 60721709, 220761774, 444053767, 884453197, 504646309, 921344230, 529398215, 943939959, 43454959, 795249684, 515658780, 818350977, 314270107, 726271232, 843665591, 67458445, 320394839, 637780031, 169937442, 787160719, 200208585, 204768851, 305296710, 386984798, 105196401, 408298448, 610609537, 22592327, 999077140, 321915257, 346366718, 292441921, 744917334, 605218192, 427501465, 901289145, 869043943, 276640175, 354058877, 352450856, 518532572, 538221075, 567350761, 149051501, 702656305, 141233430, 240610869, 550509442, 520758643, 160914009, 647178859, 76449582, 779024598, 250046377, 378744548, 513531663, 878425057, 617538842, 298370855, 699488348, 228206810, 722830496, 453503962, 436791122, 177593047, 356773497, 548572252, 640434155, 166473740, 971968542, 479297232, 96198247, 380111658, 608803298, 75052686, 759147855, 617721202, 143741817, 661602088, 880098795, 604182246, 125336277, 49877053, 34548867, 570896299, 888150380, 72907235, 459960666, 870237203, 172094126, 141538958, 895282074, 355111110, 848265364, 6704928, 522419913, 968827293, 823328680, 270896549, 706719677, 149619187, 287429763, 754377052, 507202626, 992743343, 990757015, 214437200, 209904640, 642019325, 746459080, 599636726, 488022744, 953893170, 153409683, 657933071, 370525149, 351468672, 194576011, 842767546, 33057, 225090164, 757950439, 368141655, 552226479, 31359432, 743706892, 442623670, 646948925, 838333757, 814760907, 480914407, 862033625, 706789671, 713642893, 46287214, 88831530, 961140999, 445781649, 300458461, 560143054, 784986980, 660938773, 663212491, 482549052, 605333289, 967370204, 218206398, 849976133, 901176090, 743863425, 114642946, 202590218, 651005392, 216645793, 799057299, 364767266, 619375310, 778945782, 848890405, 381488849, 845815373, 520448078, 597026690, 203342712, 103184205, 398891166, 521442381, 372682677, 135134729, 206367196, 332376787, 462103570, 210200967, 768681256, 382192136, 362401990, 374954224, 668284735, 110094511, 52476413, 219511306, 12637816, 177198682, 486433255, 171661952, 730556114, 38820146, 722637309, 557980333, 461208812, 152235679, 816228319, 453300754, 223532473, 520790128, 946809769, 637886279, 84171018, 712702015, 291973126, 993493794, 551298327, 217660394, 610901649, 904379303, 256879979, 980553146, 207079755, 289881296, 461453215, 741148609, 769133734, 244262326, 447055210, 550402450, 274057369, 436419980, 709930607, 487361319, 161597939, 615414142, 940420157, 165156501, 561417111, 229040581, 578885580, 368835808, 760980160, 452734404, 337934681, 3315128, 55233429, 619285614, 442318876, 573260694, 66271070, 703974984, 369485891, 311073703, 508785052, 676163350, 585732715, 815869603, 692430286, 359447110, 950855123, 659053977, 815807927, 860378567, 70223700, 511820699, 196837545, 784728013, 131672076, 42892773, 376068736, 911982463, 80798098, 515712249, 221974133, 148383753, 797663870, 908814999, 581344672, 549012261, 72985707, 372284951, 184119969, 460135231, 615914409, 668543305, 776191559, 119414179, 649559894, 428507884, 514984443, 194695522, 103878983, 250811486, 362369938, 882373766, 443020108, 602484135, 40281377, 772412226, 452973083, 305600188, 938049828, 483542563, 718497324, 187128782, 294634681, 145774537, 999840436, 868096855, 690784224, 451136972, 890490038, 676442403, 219850051, 337947119, 35556822, 217588532, 467499312, 327054616, 206119070, 532785811, 360204811, 451828340, 652759019, 23275788, 256866858, 945300335, 890975666, 601563775, 187551252, 374284843, 437182482, 227680064, 472966274, 790310295, 709547557, 425227694, 693988265, 904046356, 640487227, 594988499, 571741202, 630165059, 557312568, 500463297, 605221758, 647986367, 13100109, 947479680, 365662029, 321825758, 104495209, 257268029, 819419290, 923593954, 679503020, 110391213, 973494463, 321013779, 796313290, 19891823, 112360900, 325156860, 557562806, 133392328, 182512378, 578233468, 513223587, 143464387, 668904644, 508763604, 420416416, 347022086, 464746581, 217997224, 965033078, 840805883, 392585432, 378114188, 502312553, 706204727, 240852805, 554731655, 555855622, 969074772, 878541689, 291079659, 234461704, 265735317, 578628270, 630066211, 617611411, 614756556, 432680618, 506644774, 273705391, 853518284, 944757304, 134688505, 425190142, 786155015, 447927499, 281438999, 265643492, 775608158, 644842792, 176291337, 556294405, 614429562, 653312303, 77264730, 209766134, 545702931, 409037798, 812067719, 703858040, 875190548, 667146978, 713926731, 945888913, 940819321, 386664157, 365583076, 715116161, 43477113, 550741628, 532103657, 665685383, 791505484, 681837388, 946733680, 832599074, 349570595, 15480007, 120784291, 837278084, 779863437, 965608893, 551180002, 41886636, 578383287, 454924643, 999028303, 648966755, 741336997, 593536591, 65740948, 362020726, 518218849, 640495427, 483418543, 622575356, 155418034, 110226931, 216657821, 666656955, 584606375, 491448759, 956087708, 159214277, 910034857, 315946950, 355773330, 588527314, 712570910, 612529133, 662935433, 531876812, 842860336, 409244660, 504363670, 598338775, 448117849, 254479755, 757551275, 240890696, 779738256, 291245509, 731586472, 654721303, 888990568, 98322842, 594921965, 284895538, 648922231, 754067479, 726228569, 342340223, 236259683, 472211605, 186167998, 829894773, 444927358, 782119357, 693600488, 436851297, 103064180, 222115546, 444526840, 605578599, 176587866, 736973798, 473086610, 74101891, 762745807, 854794122, 541897801, 187198378, 632407095, 536862994, 120703424, 604573334, 464315876, 729453392, 781448295, 782320759, 948980113, 357587823, 150233004, 291149587, 731564774, 413682917, 610311931, 683360474, 675247150, 323802092, 496184625, 743022134, 34196944, 259929883, 976034591, 484787059, 940794516, 602842406, 128087058, 204552993, 329963919, 595147756, 373203080, 342962348, 889378250, 129697687, 370872758, 789493700, 782375648, 913505252, 582185331, 847391977, 374901328, 787135007, 722567593, 444681766, 185442461, 940246385, 246532151, 460032693, 320527969, 669436954, 876930300, 214562744, 713522966, 276045913, 520408452, 24480611, 514346684, 400147134, 972418751, 131374302, 415982421, 860286275, 493929934, 334621196, 436875290, 715716170, 592387495, 527723524, 728780028, 506605524, 688973166, 671888141, 905386111, 520383626, 862925921, 830575591, 403104684, 106425503, 331808456, 188089443, 10815219, 565642939, 358094969, 867175074, 29066438, 924721666, 544286766, 949220361, 830356434, 322186438, 797193948, 999088195, 944168751, 17296315, 890667968, 228600007, 689463800, 549461114, 407062945, 992741540, 644421095, 256227231, 449048778, 511541812, 433690742, 471926479, 298416439, 922848226, 463237372, 696399197, 990165276, 126746212, 929465355, 171829000, 688944091, 386745327, 30684224, 583176818, 535162625, 57037215, 902111214, 610620379, 779236177, 721063716, 907064426, 194030915, 275393172, 627252200, 464694205, 543426838, 302281508, 598425543, 154663581, 968630936, 70174958, 772688641, 460094785, 845398822, 923687205, 119662297, 12986991, 329973646, 229840711, 888382852, 929917485, 180103723, 363932208, 965428031, 705458355, 294353381, 532132948, 900202384, 47863497, 43684819, 290522645, 453193026, 389886117, 871853160, 65327774, 592273774, 791906761, 303073314, 825127167, 7861424, 652106810, 707997475, 853473899, 288078750, 296366579, 753958320, 92979083, 880497856, 580041700, 336240302, 943001247, 558273475, 666893107, 232852259, 910943303, 734718839, 992576534, 972667864, 934536176, 122186083, 798138702, 878165482, 987682975, 415555455, 638826798, 973746721, 748252865, 605406427, 395229697, 916495069, 808527122, 764273058, 504442542, 942513426, 53045046, 998103045, 402982620, 610150125, 78643856, 370691006, 606947766, 699127215, 581310088, 520189570, 731093766, 200942881, 410997201, 506764123, 270889434, 3214019, 67917091, 192861192, 118168651, 872261890, 614385714, 253792561, 29201571, 974773766, 191634218, 549402052, 932941723, 453093668, 222666012, 971800714, 90668489, 736496201, 973834698, 323221978, 181780500, 370769177, 601972012, 464746187, 820205139, 5631204, 225121752, 999690739, 218099399, 914055263, 468644838, 27536217, 437735413, 82202453, 336712227, 957416531, 609854370, 91358152, 685143970, 607945368, 323506158, 499834623, 900243029, 17405950, 155272930, 299324309, 501638246, 188885176, 950085620, 957576258, 795527746, 808378867, 974679676, 346445754, 663524805, 410945110, 194188112, 481769462, 719420608, 451804077, 549610158, 349558025, 679008651, 189047350, 613770535, 564426911, 999313000, 379723930, 829627532, 68213419, 406843175, 765938588, 982766631, 109028515, 508739701, 937509627, 241297356, 547559258, 570983840, 996991456, 715856085, 901737485, 935048656, 354467528, 49428885, 578632410, 611433240, 631619443, 751726794, 612270331, 373695102, 545065749, 744959829, 371470059, 739772678, 913550211, 167484129, 66634279, 868468519, 560011929, 570066733, 978652222, 278915183, 497105318, 501406252, 505469007, 44424902, 861468706, 655961020, 967413462, 269595980, 961337940, 61978990, 721043629, 259634431, 836576635, 885521519, 546441422, 190080486, 806491576, 416577696, 911560487, 555314857, 827301887, 65700299, 95583493, 989384574, 932878488, 843009525, 901915327, 175894974, 346037861, 281003195, 883692425, 419706572, 470318984, 70227489, 207090707, 941495333, 918758130, 662850211, 101330114, 583187243, 953062301, 384887919, 108018284, 450598564, 326501138, 930485101, 300867470, 267614698, 447740996, 881038602, 368237118, 413718958, 505675570, 88786161, 892089332, 839845015, 745241488, 285892382, 209713032, 911931071, 676073164, 759319822, 781061092, 190291952, 742717837, 81117746, 904929968, 892834302, 987145938, 529683689, 471349853, 885797666, 743496573, 906527721, 886027926, 905291228, 103945278, 315591141, 91061696, 753720009, 26178002, 217917690, 951492207, 951406264, 369770442, 441621808, 621470889, 667286255, 596259589, 422938507, 939320694, 535141947, 57332918, 877994421, 188347799, 338590617, 13682392, 83040141, 664788894, 776147858, 891525260, 302886385, 903522802, 217885392, 597132833, 920161087, 960156739, 409495545, 998535992, 8917970, 176154406, 38453571, 668158421, 52500275, 274086399, 296723018, 997397688, 16213568, 724741923, 624178400, 705804348, 778000057, 647593158, 314325022, 227594710, 564258072, 368451036, 437069493, 108946197, 118469114, 38843632, 399539341, 294386849, 622196728, 270713816, 753365648, 701083767, 174267094, 554640305, 191358519, 16899022, 140901269, 394250193, 746041002, 637316636, 224800036, 702358732, 723810604, 755404900, 410025473, 393850672, 196035405, 409421379, 573665010, 883218846, 664923003, 662585796, 405014269, 778258328, 758945783, 31098884, 470593804, 835918086, 654029947, 299107080, 630252741, 784651504, 824280924, 531336009, 729832690, 19250974, 832861208, 493183055, 898480941, 459502292, 588482201, 111557187, 993019915, 641188960, 640672998, 189700268, 819705047, 385076358, 104696782, 771313886, 534769807, 156143141, 550616193, 832417358, 244086153, 943943389, 367451730, 828534121, 886694721, 836510198, 67701662, 564481459, 602836040, 410216558, 106992468, 792801219, 549645882, 759241084, 399824233, 209316885, 522901372, 149102861, 762357531, 235701969, 68577912, 901337136, 473930717, 893053762, 750922847, 144041187, 186174561, 887627528, 205426865, 589009819, 87107494, 920196240, 983140536, 102121639, 783686011, 97734112, 425404216, 982190774, 387782503, 869494970, 992593396, 565442077, 469391335, 226832602, 197033040, 911039500, 457228487, 432352132, 77077779, 120261726, 470304300, 322034176, 370805045, 291436924, 332229928, 395352732, 41563722, 845389930, 381878511, 325863614, 397889250, 695119672, 752493429, 92762301, 473841878, 495959726, 727357277, 231784134, 950186296, 961684510, 821247368, 983495697, 345894586, 898191128, 246316098, 580022122, 294050132, 974283293, 169991162, 94307333, 696229949, 715721934, 62870355, 493757314, 69302701, 571791870, 123982466, 548294631, 409693909, 220827204, 421438557, 34618256, 547935185, 965860576, 322835389, 521530010, 955908493, 868139673, 979753097, 513067041, 842606279, 732476154, 111138436, 1657182, 870130807, 423931151, 559675266, 953707177, 553313698, 819382176, 364562663, 303699218, 516464167, 363487640, 307656948, 8760029, 758736431, 129262889, 672525553, 26049884, 278808835, 255337588, 120612924, 818270566, 713988212, 790347750, 19099710, 92695610, 376725301, 404270887, 716722565, 582533559, 889958979, 102641439, 501914051, 926757613, 14633289, 653476358, 736415081, 970267289, 650287860, 670710925, 855085978, 891046183, 655795636, 431892716, 679211064, 248380657, 837610515, 676163700, 153629147, 459229857, 671573062, 830281455, 596057407, 936670166, 287013197, 192164446, 980990740, 390816208, 934542498, 631076711, 970641919, 467451663, 356901889, 920627624, 843378964, 898524355, 761808047, 663799447, 590479885, 430072083, 57564303, 369798365, 696972611, 452525695, 765701606, 226838962, 539619984, 896814690, 397521927, 695447533, 81296124, 787929606, 439955988, 983224675, 161635573, 854381594, 177129388, 185547037, 887624794, 221931249, 600816462, 733073665, 910370145, 114686897, 437485077, 863341806, 501838021, 9053931, 759546133, 312968900, 254634339, 709225937, 300649094, 995732236, 743435725, 888926342, 962819185, 700389830, 853288255, 822977590, 607231344, 603294436, 254202060, 956995867, 785615133, 483367706, 538049782, 833595097, 118652448, 53600746, 565477479, 875515443, 320488266, 555304249, 622984510, 725781097, 740660225, 915004905, 125795075, 231831629, 320973517, 971375215, 416413727, 19369321, 818811537, 638517355, 732642423, 404738070, 883768603, 221945452, 628630828, 447463835, 213374755, 793083226, 535617260, 697307058, 891073176, 49462967, 915659272, 406236695, 4172174, 967581898, 589077504, 463557772, 587011878, 25681370, 667278613, 824751350, 138415654, 818998509, 244348375, 566289087, 505379178, 719960320, 425268390, 833923057, 107288952, 232791640, 903518268, 819430027, 635068909, 204151962, 203995830, 621749655, 120617360, 141692446, 796948433, 859910161, 307679122, 458190182, 301631516, 408047460, 827044205, 945829145, 438580256, 535655861, 654752002, 820438095, 552227983, 65279650, 245565220, 457305011, 539439573, 461009708, 729321239, 954511080, 194765059, 708304314, 446710905, 621024607, 337774371, 800347618, 971344589, 250340891, 971065072, 525152759, 235402812, 259290305, 539441840, 242781598, 246111995, 26879317, 589926868, 436576020, 980390610, 937813048, 634376378, 587584248, 777873570, 836464431, 372479223, 368949362, 293443707, 242779055, 810758409, 610296916, 717914911, 571331642, 75452382, 375425906, 281149284, 423107974, 150049876, 869311390, 902039205, 413717965, 41118469, 461367202, 916379846, 258965117, 700325562, 303092891, 86800329, 49310758, 952473190, 538870766, 49466714, 735035154, 524113292, 164599405, 877290077, 446531628, 654727039, 565450812, 494589836, 357049151, 97030971, 677413473, 69086640, 982706192, 819680197, 953099202, 647453216, 758805489, 690820344, 390630169, 754051408, 155446519, 10603184, 369554723, 350714089, 373607463, 104246760, 678068028, 886424273, 101591392, 854029229, 899238578, 609541379, 943451378, 677655517, 365804023, 517987198, 316097811, 630337763, 118921212, 20608702, 853172095, 529234628, 414138542, 434625299, 410545284, 764998678, 960152790, 580552277, 596193119, 581276702, 665324394, 457100260, 133019534, 873634210, 53255530, 497985717, 669282348, 571546133, 241494652, 489182388, 810737001, 774501013, 680226697, 200465027, 693491541, 113783516, 596327367, 676374254, 120806007, 496607189, 262120651, 278992181, 75721762, 854949310, 462051187, 655531299, 221589171, 687083955, 292734943, 314006533, 946191589, 562736332, 946955199, 570265764, 733648586, 677492119, 444434066, 875130968, 88914647, 553988425, 610849011, 189275568, 512186308, 64714314, 892718001, 928762219, 668824200, 191816319, 994183189, 695340557, 511358681, 956444470, 891323066, 686607568, 990877883, 208053993, 953333254, 101824103, 240541336, 361420109, 902559492, 76109821, 773081586, 408338839, 154495692, 784722256, 189603220, 830282775, 861839574, 216865899, 172486948, 723052708, 796607840, 602166123, 654981828, 646781070, 486580438, 373212519, 874561697, 554070373, 167441550, 750171145, 118223373, 300683884, 981300789, 432653897, 766230010, 106833584, 964693921, 386664714, 626962744, 11473185, 314015696, 2672577, 312071384, 275603243, 694392504, 166444513, 587020837, 86475791, 294231551, 215741055, 699764571, 116139525, 586501687, 177722947, 564474623, 652038712, 511882547, 471977172, 815783462, 531546739, 152910342, 16711971, 425667472, 37533101, 600003268, 914653573, 402056459, 433868203, 229126770, 769215350, 375429561, 807734105, 75324370, 752198179, 601127580, 771601530, 620581496, 373249689, 530186652, 957848364, 853378087, 487710824, 997238512, 867921136, 542672403, 705186705, 54122350, 559808962, 493820787, 142427631, 12509719, 522143765, 110733668, 516362496, 840929793, 771843860, 979094839, 67840472, 885942071, 51138090, 760613808, 226511243, 186517046, 181640884, 565507634, 574424189, 297063504, 323851881, 103760229, 241454390, 658225333, 26368553, 178506139, 637315973, 539727341, 750232099, 143616984, 68083813, 20134678, 499571753, 770007381, 712585131, 744480811, 706305647, 441987970, 619279583, 336872586, 210455073, 75966377, 871530093, 134922569, 166714264, 17639355, 578345769, 145635, 332270560, 283219630, 625282943, 84102072, 269936478, 950431044, 783972134, 525673851, 402641490, 354256278, 265235451, 702634934, 865872523, 739354480, 466181327, 512846015, 27833641, 292351458, 44133307, 899987661, 329438586, 751599880, 588113901, 907508690, 561087799, 95427431, 436519310, 159846905, 139508027, 642572586, 211911196, 784693506, 808923493, 367118805, 660581143, 157778860, 678716255, 735781260, 463543857, 901630623, 929926592, 432638269, 313909667, 334644815, 94732082, 472254851, 41725816, 813657249, 831659891, 862483890, 760375856, 165957802, 138950716, 548867407, 788856493, 190796801, 312834157, 782140171, 120039234, 767506325, 581444432, 995401619, 360786105, 416813730, 49064924, 78119635, 638015791, 855921776, 311067115, 254350764, 499887089, 749059205, 976457171, 31214816, 748181237, 836496917, 250619827, 630893932, 349732314, 899372695, 670644530, 118036884, 749881420, 760297040, 597812342, 888852281, 617446105, 834637373, 404888581, 433887930, 252575530, 962884275, 277900486, 554245737, 319506045, 258954451, 370921394, 782675613, 761624438, 978806362, 51065618, 995089471, 185815913, 937819890, 321820508, 65378678, 776461611, 154775569, 770159843, 869523911, 235135585, 749248182, 370507750, 337676952, 211749682, 324910470, 402202464, 691789883, 978287174, 377541733, 586508972, 921078682, 341660957, 80867431, 664669371, 791577960, 142420963, 40655853, 253334589, 378452395, 261206111, 849667451, 345437009, 763928719, 345129243, 628523175, 86382500, 428696581, 408207142, 49910328, 559786467, 248794057, 6676487, 201370850, 12648471, 267054088, 839719785, 362638702, 975517714, 596639507, 230421708, 362762923, 57787446, 743004975, 633616035, 298801715, 464893346, 415110350, 696591795, 298937150, 765366805, 843120015, 669037895, 13487239, 960168215, 862606920, 968644335, 329802181, 863102717, 839104638, 976203464, 598119310, 843551558, 995177134, 69168761, 649247976, 711017717, 254636619, 136728592, 607723295, 882064751, 511429583, 559246940, 684821565, 255356174, 524354061, 562206129, 823586022, 134995736, 717068194, 545773852, 267980342, 651986664, 915101771, 538431240, 902228229, 542480907, 180960353, 901305213, 808553644, 302801958, 835952470, 887023268, 807365582, 863312452, 891841, 827027403, 788340107, 199522754, 70827764, 841959434, 258994338, 591132244, 279437053, 616385878, 203635184, 128824370, 970082409, 627212132, 901849047, 119777219, 610000608, 295999813, 695061694, 861311570, 486737863, 58456488, 374900942, 319131727, 865393319, 953430586, 919040101, 584692873, 731531993, 998563224, 502694191, 848160792, 194895064, 549824870, 821187886, 676343041, 322966670, 154202671, 842338863, 296181701, 430133676, 439629268, 702652307, 216386072, 389741675, 185817946, 440387328, 894537922, 336722056, 973924095, 478261103, 992907905, 364378103, 352038298, 164151351, 161125679, 779096237, 635760530, 8088846, 960330672, 563516561, 803763353, 623728659, 463829494, 800826562, 48280692, 89564913, 157720853, 75506721, 199288195, 266824590, 22431626, 983518810, 611747341, 702683777, 95454039, 527747369, 146117868, 611998825, 298655910, 994808582, 476774076, 747444674, 402995445, 603051398, 221373106, 454514409, 555724143, 878115456, 842958132, 800243495, 112083217, 526598869, 113934522, 327129830, 421966678, 869831096, 885780597, 674522806, 269282212, 706389509, 705681255, 38702430, 404985527, 249996177, 623868707, 293286923, 438744192, 442519584, 861374360, 477487083, 349748852, 865333113, 440769555, 536533373, 187442392, 784096282, 26932394, 241589254, 55175047, 538862299, 160902027, 737579369, 85103511, 409643639, 483318631, 543183304, 620725431, 468217457, 224757657, 978536901, 791871715, 710605863, 33312080, 753469505, 906728486, 209298248, 399896029, 625752086, 286975498, 693872612, 430959972, 109166424, 800032686, 840371529, 613495193, 822426667, 165521172, 771762221, 612143940, 805452791, 73584331, 820997608, 350094672, 299617181, 781675916, 291073487, 412860254, 510915688, 704899772, 863034099, 315875887, 106086302, 301712802, 791203342, 167196613, 778633799, 174989425, 18286133, 647826669, 513168041, 590231295, 575815779, 949480769, 294281935, 809644322, 625869164, 969686783, 719992388, 633544746, 739388324, 69248318, 896692519, 442685441, 583561100, 789766844, 356052239, 140149248, 412173036, 274380692, 734888340, 375918521, 884867598, 413208837, 495902991, 165572488, 581953179, 963544308, 201208195, 638228065, 730158902, 946020246, 420116986, 97300496, 94579099, 396413086, 919275372, 275620808, 739431286, 330792837, 331811130, 683633297, 983400538, 273919185, 41527513, 639414538, 747065240, 212116645, 881968589, 107885185, 300078257, 886969463, 669995077, 448816021, 899806604, 30000900, 893603686, 486668473, 929726267, 444341559, 80741964, 128118760, 687442595, 258945335, 729366318, 182120644, 389861525, 290115649, 264665261, 386219993, 310644253, 519266580, 400353444, 30983579, 655025070, 910821985, 727158963, 904171034, 840231768, 56347682, 299367596, 974453300, 835834637, 954753125, 654116376, 689251059, 938156675, 427009525, 913353246, 154901290, 673642788, 796176844, 864864014, 893580269, 338726382, 31892362, 43263181, 941985369, 261983580, 261556368, 85995705, 729063824, 398764625, 739091344, 149542575, 182245285, 450378773, 947518607, 679578960, 566394058, 574925612, 15751191, 746112028, 277174192, 309954594, 316786900, 634284768, 21746509, 570478224, 429581392, 585301103, 784214977, 497577212, 394136466, 898482550, 307675926, 9537559, 821626235, 310476691, 806951780, 988109586, 156038206, 73195493, 884297747, 82754242, 822937850, 915908519, 588564381, 434427486, 502479448, 84314377, 760195689, 875107757, 547265520, 971203689, 226020219, 331910469, 966153157, 965730160, 387092392, 311717364, 882214270, 309760050, 150034346, 950966700, 474236987, 637672854, 674590620, 353389932, 789294112, 418842060, 462039398, 346011415, 186883243, 783371307, 321195572, 763131578, 707931162, 761293684, 857275067, 450688967, 365297895, 826722743, 867620367, 751092466, 542966857, 651936638, 520549115, 860538705, 562477681, 180730138, 701323489, 643078766, 996183122, 475096869, 810662781, 17540252, 362995215, 869884826, 404930008, 300005920, 698863623, 208365879, 103827198, 442837073, 8668328, 974687216, 132832980, 655452843, 260181735, 559457259, 787374062, 445289976, 246924038, 620039171, 662954386, 626280296, 697968998, 571940671, 571402991, 170638761, 988154874, 850655062, 653603513, 618953959, 155732817, 217036651, 630602896, 628387385, 722246879, 995233160, 754228094, 598346886, 117608204, 550053513, 131820839, 950285522, 839445244, 646084628, 700314276, 737370241, 255640417, 153189076, 994981342, 286059797, 711656309, 345438216, 35926743, 678771606, 890297202, 281235431, 240784899, 399917064, 509325438, 763077172, 779389632, 799932195, 338383869, 116872261, 689923738, 203550735, 319193010, 441439073, 738704912, 669585777, 730641692, 266021944, 189893970, 774543085, 351706363, 113651295, 734740611, 918495446, 265461548, 659659326, 391900267, 596252484, 365201030, 598274221, 370826911, 244510029, 689141182, 119410676, 10343580, 439287889, 499146090, 331794920, 666567614, 281992529, 502770083, 305091160, 201666550, 728994232, 204202710, 722555787, 22464031, 172876159, 827372965, 429315435, 371820638, 452214155, 39696828, 969206450, 705760693, 812279939, 95307565, 4111065, 617655, 851741487, 107999871, 15354719, 396442631, 735278380, 131876443, 921585112, 741527016, 484966030, 830165491, 372460408, 972897367, 465580542, 853402983, 526251621, 162979560, 88253680, 639921709, 223661240, 233702433, 834760908, 381341548, 534289448, 583711114, 617362645, 414329819, 73021259, 91277810, 149139162, 436606813, 156866303, 109296135, 643616911, 693398491, 346259067, 455421565, 677197809, 893005993, 213208475, 550686918, 676116780, 751275722, 94085680, 357096623, 327463044, 910670295, 786183306, 475353918, 881517271, 973964242, 687919547, 298898408, 224958673, 410052733, 780675438, 752229324, 938636524, 128854994, 985251938, 154589371, 317368160, 175436951, 670763097, 134708138, 92525470, 445876349, 9870277, 823279039, 832025292, 601866834, 657593542, 562114049, 667899343, 259256387, 449730514, 90049481, 232889706, 302857085, 158602748, 379555203, 177568239, 313187993, 158365268, 681219686, 390645789, 19342663, 427583740, 895051127, 725934247, 76089452, 378303528, 382297831, 949516414, 704001063, 226980081, 561009316, 434623712, 215981203, 193900780, 48503257, 867947979, 50525230, 187521487, 160687268, 158211534, 122218198, 41112553, 918600876, 850075240, 798956125, 416523471, 641669096, 570315789, 940699243, 243224063, 468155632, 926801555, 694412756, 126304776, 983508325, 96026416, 680153341, 709498101, 91442717, 992558391, 419997461, 196021007, 645369311, 826927240, 494233052, 193566425, 583102363, 225153408, 322613966, 674582672, 44611739, 640701898, 8581508, 375550018, 652309558, 773872686, 915241885, 591860033, 490857049, 115041257, 920666949, 356913049, 859505755, 16679878, 731155980, 734651919, 194382589, 722172786, 597359734, 907093853, 265924588, 324885586, 259480601, 243852158, 800676484, 648674980, 734824566, 274026659, 569733284, 303489513, 950644676, 625403037, 165031728, 472276861, 412850980, 709723947, 15367513, 538220726, 589380627, 669108141, 513956987, 523361134, 173567461, 268745890, 674414148, 803506583, 519645396, 983132447, 237961585, 218250916, 623856322, 331580081, 499916733, 788439496, 867129642, 556198816, 652043849, 64417408, 372258142, 602375596, 399859994, 248075779, 564989100, 319476826, 19329350, 626952412, 845826669, 719685576, 451805181, 891062739, 666376296, 952883424, 921822635, 469565716, 687551490, 906916656, 960004330, 188624276, 82723782, 275366813, 953368885, 814065722, 162099127, 794357798, 508063434, 551654224, 394171122, 497924298, 963612472, 47335286, 209101940, 876856523, 81206168, 647375608, 867035131, 594211198, 314479061, 532062269, 730503093, 25382420, 632167989, 908275038, 832089108, 859392397, 745438659, 783398541, 594869050, 777814513, 403902555, 749908626, 976879765, 322519990, 487264781, 451080455, 768566840, 963689504, 956909630, 379760871, 214794607, 138260268, 248705930, 865181611, 690514283, 119052845, 308179111, 534857366, 363487890, 456694794, 68423438, 709889323, 490492453, 726347823, 285193503, 726936701, 224472328, 955710675, 994204844, 575981905, 202346463, 318950289, 864103813, 899140796, 857176467, 864910678, 688999432, 668873811, 613386244, 360945398, 838928068, 937954184, 833571945, 961740823, 614495158, 838626033, 547620253, 261583236, 686236176, 195364830, 314636411, 835726227, 74522664, 611565480, 858520189, 720298177, 217538070, 46481923, 493923236, 478135761, 916479343, 607810678, 297391607, 677904747, 773654039, 558357951, 555652643, 617572874, 124694055, 882443707, 906941998, 355394326, 112964691, 100472106, 36881425, 709494465, 693717979, 561017375, 133961901, 971863953, 481571089, 324289225, 843451368, 278959473, 399226812, 285579945, 78482752, 417278379, 428924163, 775015819, 913043980, 388307991, 714962673, 460884407, 265627241, 30023227, 181732789, 937017994, 563602271, 668869547, 743843327, 602918341, 96439516, 334038585, 176299133, 787008171, 937862774, 487375385, 409903689, 29132219, 964945257, 241356155, 649303935, 358294921, 397325414, 220586918, 851883989, 557898870, 747959571, 1156663, 10480960, 271586610, 53620157, 860978931, 652996630, 794127643, 933697420, 674632487, 88067458, 403708304, 35256285, 43914945, 255850543, 234732819, 206817332, 94023423, 222849008, 67875524, 852019111, 488458783, 590622193, 19301788, 378079574, 375463915, 149529648, 787005579, 790633926, 281263642, 686351790, 934450906, 471731947, 295900320, 972080183, 292897916, 620832144, 235275649, 117411466, 622645231, 701293943, 681053313, 581386546, 226124776, 915370984, 383103454, 901736473, 535980730, 424008117, 554220558, 625554190, 841458974, 304356743, 144978538, 792142906, 759017383, 323808241, 139897770, 681340962, 267494673, 561628911, 932328241, 861512346, 184630696, 866136153, 241088282, 58676422, 334864133, 641431435, 453564203, 420333321, 107821497, 469861846, 953120914, 603508891, 783813592, 297462390, 779763938, 905266075, 616096518, 788619104, 707675929, 630130931, 670169489, 892612188, 266190309, 562573589, 684540397, 701936636, 387117407, 417406534, 326834057, 133110960, 526988889, 520532681, 740095320, 133375094, 180346519, 299335942, 243801356, 620944196, 735791181, 408196243, 153998233, 900096231, 820092296, 769411869, 896530768, 147048906, 753000275, 17746593, 768119246, 614921133, 592559349, 899387616, 440376725, 527994247, 68704492, 497622519, 61287001, 621093931, 258088115, 471988152, 774106770, 710689144, 356125804, 902896641, 718302370, 744993559, 330500311, 573449279, 234058350, 21373459, 217780589, 504008949, 697327891, 836937429, 467088609, 537891470, 270280412, 434344271, 803960467, 84444777, 347503651, 599884060, 777709014, 778884240, 181962406, 43030662, 533763747, 708954442, 93029678, 627304698, 940082859, 53459599, 583094296, 537429716, 462352188, 113027941, 521464874, 549910627, 316053539, 53902286, 838853294, 726530849, 379139509, 373985941, 648801534, 423892201, 736178419, 8451307, 776163973, 389451609, 500402603, 550454654, 973473754, 324431379, 878704036, 534455398, 901780046, 350129121, 685953906, 909412156, 713328606, 429443220, 543783702, 521191758, 979198648, 353724462, 879663608, 993799631, 484844452, 24848104, 955427905, 141942568, 590771295, 552453013, 736274028, 116067877, 88925904, 48414268, 191487445, 558316821, 183999024, 573345138, 797299896, 981515883, 493258351, 686263625, 39929343, 890564813, 875874168, 659485263, 852719729, 257534565, 211274719, 945830860, 377340725, 352421164, 184800603, 106936992, 51969625, 644343678, 222517051, 475164643, 295179641, 680088666, 539195866, 221932867, 784881018, 255498536, 264594958, 49927463, 722288873, 221146538, 785135560, 99582529, 128756142, 59352238, 291264479, 811676475, 630926012, 947380867, 214126329, 975880579, 283613796, 126042478, 372870386, 711488531, 272122269, 831466360, 685211001, 125346271, 466799008, 315452855, 364880166, 49007027, 984657751, 9164978, 804217705, 2049449, 263581761, 344230816, 623166199, 242279521, 397344468, 583577504, 936579884, 28380236, 218643714, 95064749, 19977315, 922579290, 371968273, 523121972, 67246632, 769156572, 647150692, 229397126, 530149022, 236543736, 175240155, 364330900, 939420927, 744129181, 139243439, 387086470, 891163341, 968153719, 520565693, 484789336, 723605279, 610639127, 608005870, 490360624, 573757589, 54053021, 63732927, 244172885, 715329966, 44847971, 418999532, 438198856, 657732023, 757688222, 504152852, 914632687, 186725859, 791873050, 234933455, 738160319, 478151913, 786484263, 252377528, 135932468, 478995225, 363202526, 212509401, 320391497, 534839415, 466030517, 759954544, 623134661, 542232528, 667133635, 337593371, 732873748, 788773058, 490014758, 793155137, 800604579, 285728211, 651189402, 284974861, 84334217, 41475237, 256334745, 565545805, 370262567, 756355197, 366819468, 49918500, 163111163, 478601917, 778853449, 106486145, 284149223, 662441035, 110796247, 683839526, 483178694, 551874305, 398796274, 699577285, 118742729, 367599290, 602239483, 630388583, 144621073, 992187706, 746649662, 617926710, 750120746, 153336042, 76037972, 82169988, 879708995, 988146344, 347829385, 699095545, 833610981, 695445138, 308891230, 485223142, 106200028, 803773752, 847263200, 829808875, 148939117, 925174048, 856652746, 769624111, 748778060, 622611248, 439189205, 999562693, 353776032, 986849973, 818696263, 206059914, 592999423, 267166713, 120320461, 879492521, 319451236, 977949469, 467055967, 9325256, 506195155, 113696033, 314428178, 110264589, 918713707, 218702989, 747279103, 63550672, 637886578, 412359030, 194763760, 362527211, 718662614, 455439376, 145586915, 250152678, 449743695, 244685004, 770872414, 317640769, 81013618, 737532282, 515590961, 541374555, 628868034, 421757720, 837653538, 886781920, 891521400, 250498725, 729143583, 36219749, 52471322, 774066491, 759637083, 881255802, 761308218, 566902011, 413489429, 973843296, 270912492, 244159089, 437504135, 406389056, 459326396, 439253318, 515621856, 287381241, 701790927, 924293223, 774479979, 908409961, 96875283, 385572489, 815651137, 284859709, 948122728, 772397431, 417289356, 128887741, 811764897, 65415832, 214814416, 729420550, 244351556, 914997482, 86873257, 17947347, 211607219, 55422350, 869138566, 98839823, 488760678, 629313263, 599145477, 576604485, 749302865, 44447713, 666422499, 913621468, 41286968, 263640051, 8430690, 226742403, 858080467, 413309803, 465617442, 862685254, 269636798, 885344144, 597792513, 279832370, 733396309, 780285949, 364920942, 561388916, 236123094, 57277316, 395967465, 866739189, 923506524, 676921919, 741366127, 983787889, 33316734, 300720930, 349739964, 243982600, 228498962, 371615839, 377044750, 402756128, 366266447, 794831306, 729184717, 317210475, 519724850, 995576522, 862408208, 729612085, 454968405, 77004022, 535249291, 429590455, 810539863, 89488124, 149068650, 352139401, 874487477, 370030145, 577191338, 797907638, 837272794, 386502608, 636777727, 393006584, 462939091, 476730583, 628345902, 463764081, 38829272, 776658229, 201287732, 227713219, 863415766, 325934344, 888290701, 716696955, 416599106, 202094387, 456096032, 103524342, 230451257, 998635276, 342970028, 918080754, 22831863, 221915146, 390624461, 437206479, 394398030, 243000000, 670721054, 912445961, 74864262, 476547875, 801255080, 729739227, 729221810, 624002653, 648269782, 128130116, 843043130, 63665483, 316499054, 231346872, 881481429, 79174268, 51306796, 789268367, 198806327, 636807586, 111801567, 941913818, 485453654, 769935806, 231757606, 477760008, 744305469, 23629295, 203837574, 217151623, 67965759, 8190394, 446948106, 876481005, 313672514, 934273856, 532699571, 848731664, 846624933, 517222488, 841083327, 200760308, 549628088, 460859838, 814780401, 843189296, 846812980, 859058037, 291660257, 201539829, 109029071, 494825648, 880472371, 598258397, 766585137, 873375955, 507762524, 205978125, 633289121, 734034923, 289580785, 363046386, 651070685, 318899903, 145202317, 73908216, 3142068, 846707767, 7113165, 858063193, 644999694, 808856820, 993748726, 221051976, 15598435, 420003338, 902969444, 694745684, 828167871, 810904867, 317734049, 191083092, 808201616, 986075462, 551687290, 715309706, 332578268, 301789762, 381606632, 843232612, 339239828, 984499952, 336255863, 360770146, 496901229, 911604616, 91818915, 768240702, 318069251, 432109927, 419764356, 247799605, 102817127, 791848549, 140468460, 12045087, 302047297, 193839744, 150573720, 705935135, 403407650, 564932267, 740460372, 757688892, 482784982, 913791137, 363485331, 345569238, 950359899, 93062422, 629685502, 847513776, 925100076, 718142463, 986372300, 919229573, 404923887, 471528720, 704229689, 745418910, 283346025, 626718914, 702953297, 676166469, 453608470, 730754799, 902331172, 329668504, 553498284, 90026620, 946094141, 924677701, 115634849, 243796448, 478829336, 552531469, 777486156, 602013014, 199524112, 579007450, 48587912, 8358767, 681495410, 796860332, 114434910, 648172113, 738184908, 317997965, 23349328, 42484611, 644990308, 814706888, 820503307, 718176532, 233861260, 58672922, 98283572, 295881315, 843116494, 243359375, 911674214, 316653367, 563060777, 560165272, 231632551, 967808205, 273204379, 704473631, 627151166, 652375849, 268348197, 673816725, 325816970, 180343180, 966174754, 585075566, 446336585, 547582773, 224067922, 204952166, 338737959, 591493604, 896926445, 125206887, 753547725, 296537993, 269487239, 210098904, 415865744, 566450721, 326377800, 434989884, 29970038, 177151577, 537179916, 837105710, 676897480, 765071744, 337712511, 730605054, 678657310, 162712899, 73558948, 630873262, 941409157, 904956337, 340627376, 335451498, 584489298, 252793995, 811590417, 162560194, 937965402, 463608421, 351697922, 299953999, 77028390, 699881357, 739619696, 523972260, 732276412, 74782845, 877026950, 155305330, 491180858, 471141939, 509000990, 159701444, 444053003, 60028990, 815655870, 948952958, 97932922, 302771436, 488966978, 39943696, 696874510, 239288884, 846085380, 285276767, 246297884, 965050473, 269465290, 501472407, 94469383, 965106662, 974278269, 687454157, 740899227, 760903207, 534875943, 920322773, 726930556, 905597667, 134777919, 423669592, 362289628, 718879036, 684409563, 226265314, 143266892, 121585634, 473663893, 505957348, 617015910, 545810339, 42416038, 841217058, 254594564, 699268568, 543532012, 776506428, 210495869, 879550592, 457153931, 605571461, 185263474, 478420582, 440214267, 764221488, 998464340, 999019585, 348346806, 819345373, 770270118, 328424697, 475579213, 780403117, 102381261, 882208094, 89997765, 807012804, 458750682, 64519435, 728954279, 203218941, 769231203, 500397655, 517554281, 577070807, 402720915, 714218465, 966165376, 974814347, 320917521, 862995438, 938731897, 286185221, 534561390, 603199838, 279734903, 258680720, 372393945, 701287795, 288179654, 74648268, 117163070, 952179512, 346482194, 259050326, 790389825, 578954253, 661943953, 71558136, 706157438, 695220544, 22553693, 952684967, 86500704, 215999817, 65908789, 303018315, 398722670, 397497342, 805904607, 684178989, 432307133, 272727537, 925110602, 70159148, 205435585, 21906141, 871478165, 530943217, 600367208, 883731665, 278231993, 434103141, 845572613, 331282809, 890758999, 483086733, 414585638, 556984683, 438581130, 398892726, 705728767, 277712531, 595503689, 32482125, 82003183, 279535338, 405146322, 905003159, 487248654, 296781320, 226065754, 22795241, 31944465, 228149790, 894909981, 124005246, 514598000, 216688263, 207450543, 723845751, 790105238, 271695677, 72903010, 591802009, 166198351, 966747001, 921850414, 847697476, 639173146, 672985428, 654360672, 38930364, 615929832, 983633030, 8835968, 770034920, 334184725, 163424463, 373994706, 761900776, 306316197, 433002814, 242273226, 311241275, 778784712, 987947715, 638426621, 626496423, 395284020, 533118818, 423574416, 733483485, 730727351, 591641676, 702168136, 530162517, 226803345, 849265858, 348815240, 973507787, 717119120, 931609226, 748068158, 443584370, 504224731, 283973261, 29294275, 955948979, 11258704, 564938254, 339774751, 744071891, 907835982, 92397457, 524038045, 382560811, 172080338, 129515527, 928886176, 327726128, 517668380, 41343112, 945869231, 458576682, 193244051, 475253942, 320259643, 136311721, 776099463, 456006334, 245804384, 675576800, 359978700, 357493669, 913521369, 901534771, 593630558, 744408305, 170260732, 144936252, 506827243, 427410807, 986218071, 172000910, 709127117, 619688646, 889963575, 18840956, 543711174, 808206974, 857169470, 50886794, 87275099, 650881351, 460537741, 879646050, 810488007, 671665385, 707286958, 64200578, 655026126, 553719640, 91233365, 323320711, 856932891, 746826921, 19157953, 95135123, 104014495, 702146261, 472994556, 578185033, 898070864, 699657337, 850016666, 724087635, 72376413, 421168232, 631426931, 296714136, 297479180, 957599232, 497847475, 355432644, 877041442, 805016511, 673194497, 31097010, 237191936, 958691346, 184806223, 707349700, 24622857, 891101226, 850485744, 563985859, 185372338, 348282877, 382013156, 529347546, 768969458, 903769492, 596434605, 609058558, 709613104, 757032974, 875248778, 536290552, 571805823, 774476841, 333359946, 189873424, 533195333, 531257363, 33553140, 96354606, 997826886, 443542786, 580129941, 501283751, 849492301, 29179980, 360739097, 184705719, 550518477, 174498708, 370793071, 435537138, 183035156, 546190171, 727800269, 323669353, 81971452, 715927126, 635042852, 379228559, 162319545, 913154790, 736839744, 690367065, 284561553, 408592547, 386431306, 502076370, 776332442, 935900269, 432106808, 717775049, 716946335, 664418038, 711420724, 195840896, 11585560, 404386916, 513054013, 868824830, 920076748, 175238985, 833208655, 531183662, 698433053, 937329688, 433580610, 895604239, 261140546, 516815089, 569654986, 512663801, 581619329, 431389095, 872988301, 971435274, 862526288, 226627610, 319272207, 205210774, 622117200, 923217463, 150625902, 647398667, 472282282, 419121646, 294631655, 576092446, 586418990, 242408655, 258670650, 831065741, 232982921, 463827966, 536404483, 957114841, 943615484, 345288404, 261464510, 530384155, 101601990, 836944071, 79641783, 704575063, 821510669, 915433760, 864410950, 927505142, 206104110, 222516796, 687944239, 931241837, 9243085, 281234265, 600381204, 16895487, 693140415, 642052399, 64501088, 972541029, 518111532, 266036664, 846392743, 993923893, 716347145, 141146981, 946226726, 477001904, 793987103, 140071203, 33204314, 585478901, 363591863, 998890976, 497501213, 557255484, 970405444, 28227915, 655328291, 885990146, 170531223, 605501230, 334129286, 295496697, 181637058, 939276393, 543684612, 360874346, 647045756, 433906655, 759840919, 380079816, 324936924, 867252024, 699384748, 984998296, 28204191, 29373904, 153769521, 957897651, 274895551, 76556346, 51069235, 968402492, 450484417, 962816948, 935018419, 770040062, 590216630, 560679166, 734426274, 346188120, 612894029, 666496828, 824212602, 387313157, 134981767, 572658141, 770379071, 430267150, 650520413, 349007077, 523284190, 35880412, 500495379, 524147664, 48745947, 15233558, 19489814, 668036224, 216990515, 636656515, 227150935, 833821348, 873782787, 454448846, 155161264, 139859645, 612862153, 873871450, 752479549, 542665885, 594496792, 643937142, 986144816, 957816041, 883772613, 477225144, 558224944, 510631804, 557594918, 943588438, 763159942, 634978373, 883757948, 638236268, 940482311, 616150143, 244927255, 456974788, 714735556, 892428236, 732314555, 886301374, 453015702, 988653086, 914816734, 10519312, 795554260, 146071247, 364327336, 698018543, 938121404, 872106307, 183891481, 160239925, 380273607, 970726066, 671797814, 792214836, 79527292, 158057141, 378849799, 830938767, 453424408, 946481827, 208641561, 29817330, 404701453, 20240999, 240941391, 205506889, 820011060, 13572413, 476682267, 232325224, 245500566, 984881183, 629285054, 76919553, 976633877, 803773721, 699622345, 930462214, 222126497, 473871246, 538145309, 461799840, 708874837, 924860910, 387352601, 755795283, 921577676, 685085156, 890896196, 790499022, 477799837, 52142507, 914931803, 263145336, 827355181, 440261269, 239159666, 589009658, 975581463, 575399382, 423694655, 300925534, 693845629, 505751867, 588254858, 706460411, 956683067, 962324950, 19204232, 170036417, 214514882, 541201696, 498136510, 374826368, 608268625, 885967937, 720542104, 104227274, 827998256, 84554812, 72458141, 791249573, 425097027, 807003161, 982002914, 994732675, 468127261, 671358602, 782369960, 317799042, 145384939, 242133778, 778355345, 477138187, 656981445, 942544258, 981265209, 320189147, 67853561, 951889867, 228964884, 814019672, 705739715, 585127128, 225467595, 769830596, 608704377, 907681319, 315170825, 849866770, 493344217, 958059185, 45919048, 381264700, 55646738, 870686738, 282420712, 495126066, 372819491, 547544083, 138644298, 264562177, 813878855, 406658793, 810944312, 97367274, 483631052, 296983907, 800789954, 191192528, 796689767, 39147558, 97681407, 118982634, 715402925, 669600832, 156384380, 287790075, 773714053, 216878800, 229688724, 91730127, 149996630, 691284980, 400108935, 367324551, 96640800, 504237405, 217678714, 74055471, 66491526, 707653825, 542853192, 428127996, 216704955, 543728001, 354600118, 188393247, 64068703, 899323411, 429272645, 886283685, 728239886, 823235610, 290963866, 771048478, 84556843, 364594694, 404242004, 667466130, 573765757, 12372859, 446331684, 529432113, 265792451, 500603186, 875066766, 176489562, 513698152, 95174117, 802303091, 63690658, 684579233, 184036102, 244479655, 769051503, 351910673, 167611055, 595634616, 108646009, 410616622, 731904193, 543672294, 793146628, 971218977, 435061682, 330468673, 567101916, 339681007, 417309905, 106522137, 662457098, 380584950, 841259532, 417296723, 414640133, 86146840, 691431511, 24958705, 151409647, 544984737, 745016960, 297916835, 884833141, 632257310, 837155737, 285790629, 719791707, 172960546, 318403324, 627769689, 715669799, 958640570, 610713626, 826450499, 809778506, 965677433, 598622562, 343244646, 844195297, 18036010, 668029946, 836398434, 145925486, 854004060, 70763827, 34861353, 143402246, 144524644, 989783120, 769336667, 851201145, 372687590, 78477705, 526419789, 969126988, 357895011, 59387627, 388917625, 864175196, 651520698, 876988379, 968384986, 261834486, 874835013, 74602801, 379609499, 543906942, 61554716, 186356578, 629970048, 846910324, 329468652, 50503345, 326231778, 543850408, 124553398, 38851850, 803625465, 215582731, 624638484, 696489744, 828639507, 84616754, 302638473, 422705117, 916694750, 305055940, 218648246, 992283505, 552722442, 33930849, 70107543, 240240361, 412295933, 336015128, 618647554, 837385498, 861134480, 969488578, 406710011, 268577735, 846138148, 949450669, 859825702, 33858967, 931848339, 900810978, 477557084, 265467053, 82661930, 962523347, 143421667, 950951991, 192221293, 971110430, 859367614, 435098013, 519617528, 476027942, 112468806, 424056327, 42097006, 786810272, 792876291, 826034255, 291637928, 38295626, 926469602, 135976947, 45565748, 861469891, 828314052, 393669869, 170864220, 112908162, 256658066, 63758852, 797088366, 166129785, 776785360, 211080611, 441271392, 259311545, 135637411, 528759008, 402891449, 879143227, 606879316, 661886261, 190417934, 741968692, 151131335, 656281264, 944011088, 301258972, 162526355, 224577933, 233121901, 513644260, 186916431, 826138007, 799999207, 758904719, 974840222, 356750522, 741213101, 28197275, 295032380, 704341215, 47263181, 609800198, 698950786, 317795865, 550177711, 351931304, 94470693, 895827688, 209057933, 835870878, 769973034, 968895808, 966798841, 422840629, 406988244, 979618393, 180104053, 91242857, 779830079, 951849963, 397869634, 845328085, 79297522, 532545797, 246709541, 363080326, 67254292, 77083263, 487909674, 919920000, 207277677, 124092212, 372687464, 913149281, 620545734, 738527769, 195124821, 445517334, 56466180, 476391591, 515823874, 782140203, 632954178, 675954149, 24850130, 240602312, 250631988, 654881467, 877791219, 851193367, 477820710, 660753598, 158719491, 750489604, 680454504, 195149741, 543409457, 825095896, 446263310, 96229602, 245104600, 724872414, 314060623, 897589964, 881596546, 250350783, 396926474, 705314383, 330558523, 980062111, 796149493, 674811586, 791891020, 121387826, 692350987, 462307449, 943848788, 737692950, 123161210, 551508752, 656398699, 901705389, 443181639, 754693639, 604277805, 306125925, 756960630, 813606399, 230666577, 100981563, 351083580, 129208490, 501072656, 74316675, 85472309, 318432614, 189032535, 656028550, 184111103, 254939971, 889999737, 855183396, 93388353, 113155590, 297056668, 732128387, 444800251, 215299851, 505709642, 737512155, 543542831, 236225077, 436272057, 32929106, 371616796, 938394400, 950717276, 623385347, 357129800, 906249759, 616113587, 227465443, 383349018, 898784165, 701377559, 340684249, 106114586, 730912767, 827326728, 871998015, 843269938, 841751999, 463662346, 843803120, 888385884, 438315550, 516443924, 376845132, 154291675, 543792931, 327504933, 479954589, 600075003, 21651795, 159596432, 333872405, 596598213, 812608731, 444225341, 801041848, 343629743, 13896159, 876266495, 70004632, 12571559, 229135159, 643856259, 346634405, 391802517, 942118661, 276158429, 520247069, 358694284, 457303457, 425018064, 556832282, 833308084, 775575864, 514707862, 466315055, 209007311, 330598670, 354367393, 809394048, 736275145, 219521949, 990584169, 99278815, 774556327, 134408240, 230284410, 390862998, 751124590, 899405624, 272934271, 574844632, 678640376, 362199681, 921892032, 750244632, 583756931, 571497070, 443326612, 389084281, 527775626, 43912368, 306501497, 591009230, 569758158, 980328582, 126692175, 43071447, 87013294, 602335496, 346576933, 74807718, 627414249, 9978230, 287416714, 948445893, 242171497, 721724914, 911932075, 284112217, 850601881, 313735895, 358112566, 194971182, 117153032, 605233136, 937046399, 749530021, 878891557, 551703667, 617422420, 980979054, 452827952, 391411758, 899921381, 504975528, 799522321, 884156255, 60618558, 816653900, 368569935, 350184073, 889851978, 790920355, 205692030, 712789485, 590358025, 108793766, 61060083, 174825221, 764475126, 468864015, 157674953, 999681726, 697921083, 834878552, 970171640, 204277399, 92311844, 968513919, 909752366, 676618781, 477056366, 590899132, 46491492, 482236456, 163873115, 713624163, 697250127, 336036136, 161659227, 625538375, 161861964, 539792550, 308481311, 771785108, 181461731, 761112947, 636869415, 462699868, 204277542, 356281836, 12285448, 147677896, 441078147, 187060773, 113907391, 267117339, 337126916, 224005462, 666604566, 306036264, 887672464, 627236084, 850252019, 156045892, 925442707, 508670816, 696350876, 557394507, 331063236, 640002895, 35407870, 234641076, 151790369, 607943472, 292655944, 289601652, 72730343, 418167231, 924729281, 287209651, 380899109, 671595932, 553701793, 141302697, 314902010, 831951339, 832439276, 339974816, 275660018, 614385315, 544359201, 448107167, 486880255, 859366778, 5465148, 370813241, 87633658, 409000395, 690884025, 136116370, 546268230, 96022786, 795950870, 778050868, 54889553, 913805309, 992338269, 267730003, 251714190, 372078835, 760298368, 909611236, 953522692, 813802805, 973118189, 615951557, 485192314, 239609232, 578058948, 982557728, 434841529, 870854141, 269926672, 211103787, 559590877, 132632102, 733784718, 22405694, 63787653, 535200627, 202750729, 651955880, 417649088, 233855484, 867104841, 358253286, 436799116, 800008590, 110155457, 240458095, 334625669, 679318025, 709930986, 619346389, 669840902, 973904384, 779738945, 759561330, 424780055, 967467612, 560268945, 949477666, 338572125, 859656993, 685343587, 937227731, 705140853, 48344109, 18951735, 556771290, 260027411, 722026190, 933987230, 799512919, 120297053, 812503725, 38224828, 89816636, 513285347, 53423485, 170977100, 872130779, 785727821, 744249599, 806779766, 7668171, 270649102, 21750586, 504846251, 358627443, 411029566, 349082514, 241652977, 450269385, 461591700, 931882124, 23265187, 692078122, 802953520, 290184719, 508902087, 658880174, 148803298, 947245377, 203297454, 160961216, 208404700, 201246478, 641906347, 29764624, 671179072, 269891554, 684419768, 483838031, 22539352, 668620852, 86558175, 347902793, 891482597, 246995302, 611116868, 904824780, 107083874, 582098679, 733503064, 580846735, 891352095, 430468568, 768002790, 324650218, 607307530, 393421892, 784929440, 223550593, 503070351, 558872695, 955994170, 954905525, 613151598, 192688303, 510635010, 923542833, 512252745, 997890823, 522204813, 997399672, 816585452, 794941905, 603995751, 927938364, 444395994, 884967614, 602822812, 29059190, 762821261, 988786263, 9099927, 715979502, 34374309, 481536701, 940979333, 747258875, 5673684, 646752137, 962112032, 10136576, 576983697, 376369791, 430300296, 349945589, 473702758, 240642140, 647939317, 527903497, 742740935, 348430629, 297540506, 743219192, 36294792, 879362823, 395366220, 119809385, 909921622, 187472659, 118805683, 266118030, 702795323, 131712592, 841972304, 152492742, 935494351, 808917460, 412002585, 59210531, 87775266, 906877557, 916289822, 122119195, 405081817, 16574665, 207672203, 637238136, 478801407, 820982703, 448900929, 605882035, 464649343, 97647335, 317829887, 647171225, 710270612, 632781032, 110461794, 613525651, 74449948, 403440931, 387585029, 561604231, 622050143, 840804994, 96296864, 246391522, 699538215, 627150052, 779901295, 209279994, 440130458, 312788613, 510369858, 297086189, 390739295, 884708305, 229858971, 578272510, 915835891, 484256672, 955298663, 333008241, 411630624, 508077021, 663885661, 469600236, 376980240, 200673522, 574419448, 292668495, 358192098, 944146252, 891325880, 695543809, 211331729, 163504525, 587295260, 97648747, 276421622, 941863258, 151673871, 578382767, 246576195, 598063131, 746880727, 843117422, 486710546, 185463097, 286520803, 140748354, 296090531, 581473274, 32032301, 963900725, 666739002, 162152382, 115292942, 47792170, 175716485, 578283676, 766277538, 480872606, 278113172, 819305991, 842885678, 346160156, 661157710, 444157048, 29181397, 516238414, 142926449, 715409874, 806094053, 143612014, 694417955, 788174086, 880736416, 143857191, 415549819, 92387957, 120416653, 43174815, 449401706, 127811276, 408075702, 977533795, 580986024, 696636278, 323670792, 566352355, 311507901, 240754479, 513012377, 184827528, 398532777, 894617761, 90082434, 699137063, 130822160, 366426365, 119811345, 529859520, 226894169, 889460584, 166873267, 16333668, 22612992, 95322665, 633358374, 302690951, 715934458, 123651182, 466082148, 657903002, 595802193, 5799723, 395789706, 883902071, 642114024, 428308441, 979701351, 777720115, 876709179, 332538889, 232925409, 544161267, 335583320, 598889867, 896556408, 753727113, 586628175, 988287113, 721151323, 902306399, 460346444, 146973138, 160605781, 257603123, 39790478, 765899337, 169386609, 982556892, 209540248, 578699075, 745551659, 378793816, 108142294, 1799315, 805647775, 833917799, 312720743, 685791641, 452681219, 914293464, 15240643, 523776806, 726085577, 987473956, 971254459, 283831715, 638431362, 225634583, 777112030, 586443550, 316908482, 35971162, 249314171, 742617540, 493427233, 996142536, 41528691, 12171165, 382006435, 813615288, 942850098, 735863001, 717711678, 219776004, 335776818, 535388077, 274196478, 706710747, 380813783, 400863923, 251875489, 96961365, 144273571, 755103290, 621983174, 535303188, 386033466, 600650184, 73296030, 962882627, 404324016, 241293051, 147525610, 255437320, 765439751, 54051675, 282136741, 561381177, 952700846, 426402967, 179311373, 774263254, 361984363, 547994636, 138393261, 331543729, 332770812, 707555296, 987220383, 345930078, 359021247, 311971885, 905755812, 489866397, 428933345, 170994206, 386391723, 145103068, 85662060, 667516336, 197283554, 470113870, 797482288, 330714922, 303272531, 131805153, 582690722, 292265383, 103200303, 567875857, 905241537, 636193136, 609807477, 114093752, 172287790, 933713386, 172175836, 557087258, 709231264, 946313347, 170056426, 713803018, 10641456, 719064472, 653919069, 104000967, 158802678, 986867814, 502986035, 8056914, 994499126, 785354446, 252442040, 969753736, 486338665, 21362896, 321999925, 618323000, 223022683, 389125175, 643570581, 679765310, 873250597, 20472660, 271068353, 417111976, 635861730, 960302840, 320422954, 955543385, 613237997, 314479779, 702301691, 789819905, 563242998, 727709933, 104970003, 352210988, 389340740, 689229277, 505317493, 914590859, 97261561, 156429978, 329256582, 986320092, 955343167, 608418357, 211358446, 390046792, 995166773, 727507, 772905268, 317553089, 131393370, 924021144, 543361104, 692701319, 889461118, 60087007, 794936747, 245274985, 117554833, 974712488, 306110196, 250651028, 462659695, 691227912, 700557242, 543191576, 808307571, 298502357, 877877241, 598887971, 475345532, 428858717, 623613046, 853142602, 5940176, 823049685, 406930559, 39729568, 817569660, 696402804, 491990040, 124353060, 130967204, 938743547, 69706916, 35663534, 570483983, 248998169, 143209424, 793674611, 48378595, 416039885, 514212401, 140645815, 38310434, 718830216, 566671271, 671308358, 40742041, 878579039, 221255041, 896595133, 658870554, 751443022, 648238062, 700122099, 362811096, 841846185, 769707091, 889526992, 735930794, 273344514, 486397214, 108150417, 213170575, 803989989, 975422103, 461003364, 673731947, 982852612, 989183174, 945744090, 931291636, 54927288, 446520509, 208576632, 667880767, 234614270, 825609432, 819343549, 433181697, 304018187, 812894315, 16419547, 821836858, 210746602, 62786045, 77460897, 467742801, 40918231, 837459602, 908678895, 896171482, 614977721, 329667359, 840929756, 599411284, 63521810, 261988607, 740109007, 283732559, 561984544, 773027594, 815563296, 501926230, 797644293, 705873791, 165169491, 66353534, 809018851, 673131136, 391860501, 359634532, 421925888, 749135510, 566972576, 210135147, 65050849, 772896666, 825212811, 601483129, 452806235, 105738409, 295455317, 677189026, 380662220, 769112673, 34444817, 190653494, 820714897, 425807465, 756009917, 224548719, 442160213, 455281408, 667987684, 394740208, 575666021, 799631588, 203320519, 193622798, 853746866, 667901992, 596872864, 621067049, 629124989, 893419701, 821047595, 990571468, 306225910, 716741857, 222173136, 755581271, 128678196, 586552101, 234314461, 796204519, 790789301, 500189527, 819200240, 236524150, 416980345, 552695720, 867632708, 57153096, 818045233, 450722181, 306573263, 444415550, 395552971, 601982849, 800849517, 520857953, 457813291, 248176424, 354445568, 529515278, 123791706, 984965617, 385588410, 283811546, 719693960, 988997421, 859294728, 9141725, 803468339, 279879917, 543445385, 587640023, 302571940, 366879167, 501608887, 468240942, 996247885, 58932320, 18275384, 231121155, 708630370, 578367479, 927676837, 747379621, 646297107, 690093097, 989451226, 404928327, 714181980, 279694755, 820097880, 433444076, 139771498, 582678772, 538714249, 775123331, 831829355, 507222582, 107163489, 994438286, 898672757, 919744423, 637808815, 704595917, 702224731, 455455906, 698796936, 285339550, 872182579, 562716676, 201234731, 862375074, 541435378, 238366036, 746236984, 784249985, 133420147, 239976697, 624929763, 798106185, 199524593, 138882332, 750652375, 928821489, 289671838, 406888460, 626180032, 456528523, 616472734, 817440624, 44941298, 536509370, 68007678, 440206578, 145109004, 947340191, 860939768, 549028357, 631910835, 193738558, 172320586, 20242775, 985414839, 186330740, 670301703, 49515218, 271590540, 887515888, 511508667, 999924627, 928691585, 198025574, 278455234, 575496364, 839949669, 847315041, 291280566, 563862026, 163310631, 157347865, 330392463, 453667138, 790734550, 24860928, 262861120, 696814680, 305792398, 178803813, 131057582, 579216520, 320678795, 90093940, 815997813, 67829503, 863933969, 751119236, 87506135, 792477305, 103356236, 454766194, 872003249, 936036183, 47715692, 421770460, 290278314, 798802021, 699280073, 325064405, 787414279, 943909903, 900421774, 479452237, 221903334, 280934808, 2736175, 342472468, 687536791, 529260484, 174376041, 741418220, 263755756, 626301334, 317760797, 260758519, 713423500, 415308849, 561195454, 217963749, 499109725, 955662922, 429191987, 71531800, 501799089, 188865312, 718305927, 416529161, 728632616, 462779994, 580205595, 889915334, 361097692, 391732092, 462879482, 11364672, 575670546, 99617937, 935126145, 419265807, 841678250, 742645081, 72143468, 243304447, 878295163, 377553258, 89568242, 239166601, 983951484, 231851425, 444598786, 583752810, 175799177, 645828225, 658034160, 114492453, 323378716, 395362181, 685635342, 62242603, 445512116, 179031261, 47354534, 258468962, 75834826, 464096676, 60569516, 1148157, 410765643, 259353187, 529430046, 451655396, 808653204, 917216242, 683007357, 83778593, 10510338, 749528061, 347168377, 956892923, 694940513, 383375539, 928286032, 114063832, 865061420, 203654685, 557863440, 798918046, 765009768, 787347140, 545208566, 680970669, 25503588, 356426285, 927261766, 732017521, 892266263, 488194652, 566953646, 839051699, 670576110, 213878972, 980796052, 280444148, 315564087, 195528852, 102148936, 839991225, 151916071, 954368873, 120979623, 665793011, 64461344, 495475814, 963340978, 380042803, 764784660, 436133482, 831515997, 796739668, 204735844, 173566806, 439421739, 782421097, 551660635, 402612653, 68476461, 885811354, 721572294, 197535973, 184562215, 192924504, 769761267, 958412091, 419701188, 361859137, 876181907, 552603913, 286715402, 318579774, 357111442, 940767138, 617494323, 708712391, 129628486, 212770791, 811488605, 174877559, 399316331, 564281582, 909138907, 508364778, 891567784, 30000961, 497316489, 856141933, 537564185, 43314122, 283648923, 444005104, 894947996, 276975825, 193211468, 580842508, 852394302, 768080764, 210037348, 549881157, 55948298, 217070899, 166819403, 290380122, 908578792, 294146588, 108257057, 138657736, 570163454, 833899572, 592698651, 490708240, 744928205, 464827271, 218198747, 383797216, 673700066, 102349891, 510260196, 850688535, 529607188, 689292466, 636410462, 484969774, 883262169, 208321824, 250463828, 31754939, 942951640, 610437894, 732582410, 772822246, 123112012, 664706812, 82702259, 146700234, 328387320, 355522575, 865808334, 344293037, 381048705, 492268882, 193422256, 140058299, 908733860, 960953598, 726363950, 394154879, 985720116, 443530815, 260505478, 382900745, 703630264, 983890944, 378831388, 847165580, 808103374, 924421768, 304302718, 425533912, 935592011, 402664723, 967453713, 335913276, 727657788, 447573773, 827399158, 227658645, 857199118, 433737299, 426205454, 14961062, 330727284, 632180593, 389169865, 301534664, 144669735, 195818667, 589641655, 605429417, 849624055, 962063010, 705612189, 369680507, 491760566, 130151390, 371799820, 7649828, 926066955, 298864892, 459686713, 75951519, 141838199, 2022073, 360672400, 995271440, 681950314, 213838349, 343135082, 421279119, 151527135, 914982551, 704371665, 981141003, 836481399, 383219543, 964806747, 834862181, 636100822, 373832751, 929524975, 707820065, 826891122, 998710104, 600751741, 43702923, 611758807, 540734737, 32752670, 944724561, 720739690, 879135789, 295470074, 589144283, 719229156, 30548842, 498604947, 563135053, 604009750, 898737668, 966546640, 639590869, 672183606, 280548435, 13116591, 187443183, 807474103, 169415203, 193152060, 959693494, 158277431, 828566722, 41702011, 574313919, 219111828, 112227251, 892461874, 483473527, 264471151, 183102642, 618965012, 533985337, 143569397, 955502465, 53292424, 653969017, 153790661, 877190932, 345791657, 902137131, 135679105, 738745208, 236266754, 604272926, 972420370, 160523008, 262031829, 953343331, 197973309, 65234771, 211834110, 820242087, 654435690, 117876544, 506401914, 750150116, 338898516, 621950475, 16181949, 798702387, 106709232, 13826661, 876658973, 104000590, 202808154, 690299095, 595729816, 643301397, 323877730, 297777216, 13989614, 922377895, 350753160, 694509508, 277991035, 720459748, 683041462, 413539143, 360359316, 813834407, 779101948, 401160568, 685066243, 376869643, 357491228, 158851430, 644682358, 100373933, 859603509, 500747334, 888082707, 282754342, 457757341, 532652380, 2948609, 16254612, 342719626, 420249853, 211636898, 330220770, 36017210, 2339268, 728825485, 112276790, 408147851, 211773355, 426309864, 66082527, 921836670, 931349837, 775731733, 43722937, 657197034, 293178567, 677072967, 552429256, 640143864, 808474358, 685854045, 423951761, 714533840, 213164972, 592565922, 642101617, 350689379, 34913472, 239291636, 473733831, 927055318, 117297053, 144804740, 587701686, 356162278, 649139353, 701320825, 811986856, 824902778, 426697658, 443853039, 659536867, 613765802, 136110943, 206939411, 854362971, 838228240, 584048129, 419497266, 159166509, 987001882, 142020333, 998980575, 939656032, 56190079, 837614335, 90471104, 853695092, 124686073, 810635338, 777250927, 613764389, 418207056, 827824649, 577049578, 54607483, 459155841, 317477662, 559419056, 773195697, 97938056, 581863346, 46297487, 113584296, 898438388, 618322733, 203423728, 559022547, 938766389, 119809374, 276902935, 319493308, 156551190, 901631681, 312317724, 130907035, 108056408, 736234348, 585324415, 197181451, 478687086, 606661636, 380050833, 6459561, 394848214, 12464262, 621070195, 793327019, 252027645, 231793375, 354018755, 5219119, 219707631, 262859774, 282768978, 462561195, 365499126, 773863438, 583983783, 98151134, 28633751, 272515221, 614070035, 586763884, 723738649, 283243923, 920976043, 316664167, 887831195, 440843759, 243689065, 63472663, 741815318, 992463042, 775464448, 947777879, 527274021, 946072478, 100457046, 169509822, 13467830, 584068663, 392235932, 239454510, 403679684, 435641965, 461584752, 909469567, 775582869, 196885681, 629866707, 388550171, 172670362, 318140544, 380268617, 782499826, 696466947, 816213879, 902896323, 20079659, 29342698, 613436978, 20693325, 250735405, 310745242, 3353893, 694337601, 717407246, 880944813, 599799369, 669383452, 304066699, 604577967, 326740607, 404944348, 697721834, 440808658, 581584746, 397365361, 47579241, 309414350, 833812143, 302636640, 172390188, 872112511, 575914710, 831162131, 698051312, 22949753, 785587486, 31643859, 616660562, 582810953, 71821263, 581620677, 270273767, 852455731, 49273196, 724038376, 546665635, 847356882, 854426633, 624709050, 227519058, 606704103, 403561023, 636719235, 397884546, 130117130, 754396729, 899834678, 298242858, 362705477, 51144826, 735112731, 477609910, 907479131, 22467798, 250814610, 836553146, 105528222, 129350994, 245670049, 938445283, 896188584, 684758741, 170672606, 590654267, 852909970, 346782112, 697669411, 695451293, 212187734, 687975078, 277418562, 460452066, 478244391, 883377172, 735570549, 609327750, 721911133, 991518215, 390836158, 96713729, 207163383, 356941033, 901919528, 994154952, 340860253, 780269912, 604155342, 997899915, 806661683, 247368833, 246795439, 784924589, 879727963, 565763387, 448005580, 608691458, 658653970, 297312642, 561583232, 505625346, 484440771, 719883044, 29634863, 707412625, 281275386, 888872051, 624549590, 351800435, 183259790, 688889972, 466942713, 384460091, 452390939, 227110060, 689623803, 473900608, 250131661, 521918815, 616319148, 249419342, 356534311, 564640176, 676779585, 704963942, 418231242, 549553595, 299006552, 923863198, 193852416, 686250583, 221535266, 268430507, 357301115, 665362416, 146473269, 759852153, 172162872, 736018386, 838449085, 66004204, 891192167, 786307698, 769648622, 999588054, 412821103, 968362234, 98515912, 191726332, 223329202, 389410572, 192966055, 205597169, 527358375, 8262336, 669884635, 143098815, 832234999, 1483786, 777225002, 74277934, 1558641, 790373364, 271940266, 781824791, 460438690, 504001533, 910759765, 910660415, 661940815, 747366719, 892351003, 150901558, 149270089, 490770176, 122933572, 372867313, 628761306, 207037212, 3822517, 893890365, 334482285, 443779427, 683644816, 548362365, 222587541, 848754849, 227912924, 916709666, 407619599, 99515491, 990190472, 646046786, 640471507, 273327980, 313578681, 117056870, 582819445, 904218356, 225798770, 788351660, 622056127, 639558709, 13539901, 844858969, 357533386, 292020044, 493980712, 788755128, 197794208, 527738252, 380522422, 224969111, 302977041, 977977822, 332180242, 934432170, 167827132, 500492891, 249366552, 96410552, 746587089, 922414610, 911235137, 448278667, 784348332, 57416331, 593225491, 856399779, 842528640, 156186871, 620749373, 78785451, 774461370, 835217147, 421929220, 853129529, 319045001, 874370765, 344391903, 754294934, 201782612, 711098510, 392989540, 788634882, 707891680, 269800052, 326586889, 882435831, 242132414, 782071493, 157141033, 85776491, 417833560, 622130429, 66317624, 750682056, 854176874, 746567924, 696792547, 622793065, 227247326, 459887907, 936852761, 527729311, 368401290, 449300595, 203917648, 888173730, 555666812, 905370142, 587405853, 380815101, 53750786, 354060332, 487885518, 502120738, 107318466, 966452551, 899120774, 301147836, 158627599, 746668193, 449161010, 479922398, 26275448, 883714027, 188311446, 718268148, 693427355, 632497217, 380360804, 209656722, 610878926, 869291919, 136667829, 944516826, 548406991, 866707717, 687291201, 453965074, 730477913, 45752540, 70875801, 123969685, 529674065, 585797004, 567750099, 680991802, 846544733, 596044458, 825970617, 267836369, 393413684, 593324893, 468606398, 91117135, 972097509, 142542523, 103045253, 547657907, 790643050, 545913651, 30133631, 232411941, 513916303, 45300323, 519493285, 32579373, 237394487, 655995674, 331505993, 77683927, 542430814, 688616639, 936806911, 866477245, 251284127, 907902991, 689741382, 839654389, 537678996, 972862283, 796085401, 809960278, 417979261, 529429803, 383877936, 450792801, 282781426, 436432544, 303352449, 623330065, 299438017, 609738655, 808528303, 623407049, 577826572, 11327463, 458159990, 414771553, 525483863, 617747750, 201491013, 169519321, 248537923, 947381861, 652402786, 67911911, 351620329, 667810578, 10473782, 197214014, 106177589, 117048964, 586628712, 121257459, 182426924, 249930667, 21002122, 364082117, 108199469, 544209976, 174292284, 773121479, 42352401, 697424933, 279410098, 166232318, 656552762, 142353021, 189898692, 949611774, 306848993, 664630216, 168506352, 897855258, 833590386, 87559798, 521149754, 852612556, 909296165, 657375660, 495186784, 254689948, 644209034, 763387436, 355181267, 19320616, 979422779, 300292233, 344068642, 980375218, 105525376, 88253358, 939778701, 838942120, 610612867, 994816045, 105514711, 394207258, 326991288, 335869922, 85998738, 595242027, 303023149, 634528197, 89394285, 779515048, 208949946, 267055870, 938697586, 854614051, 185245003, 699594787, 598775692, 658825337, 679386898, 351877405, 731354577, 146834343, 99128962, 747507300, 318548288, 70151273, 913204432, 47405517, 505080720, 850017889, 681182903, 218124883, 42198316, 725729666, 221391719, 909433719, 514442062, 705164428, 424204630, 719454258, 216298730, 927457804, 376009698, 364690013, 794126718, 803333581, 212028580, 831608656, 553407929, 925766485, 100257577, 472292202, 245251761, 131666035, 603218638, 148273479, 12971044, 92621709, 354362202, 32081930, 62704975, 347653043, 317177199, 513447489, 886430424, 77043977, 119526735, 770366026, 346296225, 290572064, 938141588, 345477243, 45847431, 523057056, 17476776, 791543877, 344922729, 634486369, 304090301, 531291351, 988985927, 782371749, 575011352, 538911930, 799699871, 585997607, 206240830, 533809113, 360676008, 206118078, 560300272, 79479823, 611675573, 270958999, 523627039, 194816654, 916732536, 680149003, 473984670, 400921278, 939229953, 895007407, 935686466, 187452479, 850869117, 335870360, 291764299, 117118395, 478835661, 200575876, 200861258, 286759594, 610723415, 283682825, 410195261, 511572762, 693844702, 274037870, 215279426, 622633969, 939746069, 993145192, 895586520, 525124491, 985982765, 469141388, 389532774, 236671135, 818686599, 85547650, 25068300, 685334392, 133989866, 802813270, 144153439, 877668158, 693764835, 315430606, 482374564, 751180018, 533972397, 636480274, 859495173, 851384603, 671688909, 257677172, 748744846, 589301644, 573849378, 262631040, 593637835, 944376894, 368842327, 682616025, 393233711, 111713127, 254886180, 499556320, 827927588, 731808489, 242897958, 744384361, 113335117, 917552939, 471044691, 522236704, 599627797, 150692741, 456155692, 412722797, 549442671, 347107335, 390292152, 412919466, 438367551, 151425188, 92414080, 181599403, 656433497, 237913972, 56665766, 916704590, 878773471, 906306801, 721847904, 683297165, 528143122, 56348014, 370806584, 395779454, 238276771, 225917520, 443698934, 322257537, 133005297, 733083416, 352030484, 416417987, 31046177, 789610154, 143078289, 972144169, 519585422, 713773983, 743953909, 789468052, 579673103, 793077905, 561509525, 547511691, 593908937, 426791970, 304949014, 92605386, 311836787, 351572040, 416125165, 15472407, 735831411, 737020969, 498659090, 960977342, 285434549, 170962514, 594956944, 309926421, 674016021, 916315119, 29939701, 688865608, 426322789, 905395416, 397284131, 471742146, 296394215, 387697167, 505295992, 345166291, 477731925, 769333391, 96180846, 460853583, 234052321, 798098319, 849346879, 731258574, 429623658, 401958066, 71962849, 935393286, 935306780, 809304567, 507944616, 859484908, 286095697, 662967281, 85859510, 296579683, 993281324, 422814357, 33626861, 611097269, 572518423, 161063952, 160650037, 297723925, 250327663, 471902634, 926101990, 154045072, 780099016, 552910104, 804265347, 673658970, 778480557, 187521644, 870275979, 878530300, 777726947, 453108825, 961072409, 578291182, 36501843, 216442318, 821779412, 12635942, 349467917, 373418970, 925297933, 942637689, 365317250, 367852686, 49791316, 419923008, 811268382, 305959333, 936228679, 317854878, 743876490, 333509752, 935519233, 722300783, 32138366, 236289356, 411396024, 866498365, 25533157, 31403714, 921008884, 249715479, 221580585, 259604756, 785352734, 473300458, 211225496, 245946816, 878165324, 114587802, 894937202, 852051504, 653135057, 864154595, 293382658, 140584367, 214829093, 541484804, 636368738, 275908913, 630990221, 52287870, 135102029, 157684645, 551869617, 256866758, 867163657, 313571664, 230201671, 264659636, 365218866, 838051052, 361977820, 506668830, 958067380, 94215046, 394261684, 290131835, 201232719, 906987965, 490955060, 828745297, 325680669, 792873507, 491884312, 309420133, 368844860, 360275305, 82615682, 169824353, 438015288, 720404055, 22496448, 974401044, 399085001, 548353350, 764889531, 169949759, 573087189, 527679337, 536934990, 184154604, 947085119, 306214358, 835979189, 395101060, 672311951, 638748746, 346214892, 145910820, 419220379, 633452007, 82074997, 569742361, 843233207, 468175601, 836581049, 433826698, 238339172, 962079774, 172080233, 606581687, 452831506, 225247041, 696785545, 132485734, 335275890, 596403077, 235472522, 7311951, 51374839, 488429779, 345241863, 415525054, 80860917, 323782201, 944627672, 731920277, 554379450, 531284688, 835425170, 932370287, 740648950, 733268791, 878758718, 295272248, 430588860, 962686527, 765421094, 336808317, 806559711, 300462122, 169516450, 572985532, 928559132, 704134186, 138111481, 20596399, 2397533, 892867010, 971069636, 971323697, 391576882, 15306792, 866272869, 182721887, 460134764, 619704157, 732255009, 769073573, 172078313, 890065983, 446203991, 963161522, 435109120, 225052066, 56883933, 661502941, 805074765, 250239271, 585018648, 487906196, 881558834, 135670766, 337529928, 433594809, 398879773, 548362613, 285300625, 98432571, 158374060, 537034894, 805816233, 49044300, 124122579, 543925542, 585773748, 980897343, 898348949, 457553989, 922350488, 752938305, 708119865, 172528328, 471951795, 609034098, 989630209, 841727420, 271862097, 351706597, 256718269, 232614165, 670509500, 903185872, 982459788, 363350187, 970600865, 814171627, 357990800, 808504596, 531122928, 572208398, 518022365, 122547055, 124470049, 481557735, 769396486, 3495307, 103349173, 491768391, 104537750, 195536897, 602217169, 734622399, 106565302, 868728965, 341247443, 235533602, 383986358, 684989650, 851734868, 371465755, 672574893, 74163486, 504501605, 784942139, 736621646, 154109523, 508281373, 745708661, 803155514, 211936417, 713077183, 771442077, 685768328, 314937687, 794244951, 323349738, 283603904, 599564081, 525123408, 756461336, 162522900, 642476502, 28277410, 760492107, 380921533, 848381540, 573222682, 155204004, 871905629, 349765603, 229753852, 435579468, 942475017, 537401518, 664892757, 49097599, 979515817, 733596390, 291916738, 924533445, 5237515, 835901177, 198385216, 515236823, 192555486, 112070315, 632609485, 965585751, 28355587, 961248183, 16759605, 590769780, 713999165, 844686638, 560919609, 955981811, 826128466, 31136076, 763754777, 973511878, 314183718, 297409165, 434118760, 974092364, 834781362, 183120393, 733824595, 665460098, 80130820, 616392854, 611382187, 940138038, 826243756, 275228295, 665025095, 84795116, 142488551, 768655555, 619278626, 376307873, 770001805, 258571358, 967199493, 477627567, 604871755, 770956248, 346331922, 991286173, 514976182, 830629451, 956044352, 248850561, 440387509, 482276865, 602783791, 533059261, 221837307, 243283294, 798792589, 220381983, 305796150, 659097514, 857179223, 160169776, 562384655, 524380909, 29593579, 192403950, 458152320, 710712925, 544206001, 2189089, 843515265, 931146764, 468134614, 420807519, 854981143, 37322675, 601121046, 450634292, 621607298, 164396962, 662130050, 918427797, 767222412, 93498564, 286046994, 960351024, 445349969, 472744730, 567226357, 926401017, 130218543, 252744011, 142674459, 441669541, 22203417, 415433244, 807555956, 569271461, 319221987, 954967958, 749377940, 35584261, 31350250, 159355915, 388002186, 199182605, 724492140, 42898601, 377948317, 839718206, 780466903, 551324929, 378592251, 510179683, 141872831, 696800866, 637044321, 138831305, 724838741, 50681291, 641321803, 668999329, 83888322, 730985912, 402647325, 343110130, 187938311, 645739752, 642275207, 551049599, 36141837, 32033551, 131636805, 342801278, 192051462, 204043333, 302454997, 468686439, 421545508, 221590818, 975016376, 700155211, 15183851, 847118995, 673173803, 282824164, 973115914, 443666189, 987340313, 533526077, 125472168, 694143633, 161173970, 426497860, 715045458, 875176998, 218430033, 326657225, 644865309, 23933391, 167071016, 398223623, 449389961, 725517176, 128904936, 241319892, 49696880, 605030102, 32042374, 124249240, 692645923, 853223384, 162263594, 940540236, 909835584, 945664999, 46034178, 446675554, 514360176, 261262499, 165505131, 995566070, 836768339, 203852759, 324415270, 310159539, 694458590, 154373895, 212255971, 336434345, 303908698, 399332118, 135701511, 701081927, 428262038, 416121134, 2218658, 603925156, 122414996, 872572839, 713113718, 187728101, 163765542, 753641172, 885075064, 927388705, 288985921, 848642816, 443951843, 729206188, 882945987, 652814722, 976909454, 923538500, 695773511, 718966519, 954757456, 446476119, 760573933, 970398455, 941429085, 410347056, 364893492, 447306283, 179404217, 864039695, 519300250, 451583160, 760150404, 252545589, 427959888, 903556055, 5060832, 758978429, 13078736, 894393961, 886413421, 624665766, 529331765, 145441798, 423309500, 5701368, 494734368, 381487959, 926821008, 166128837, 157119093, 650945805, 262320858, 720653639, 13919612, 193906056, 141383686, 812764885, 134504427, 153452702, 779744098, 803848399, 371249709, 468612421, 909276166, 764916539, 460693708, 435203406, 969071140, 18112654, 576341769, 611312664, 721846682, 684390252, 993611079, 166118612, 690657594, 622002333, 100754341, 990659253, 25186307, 838338647, 262217242, 874525662, 366571802, 82199410, 268389854, 701461894, 124803758, 619268577, 695615062, 973053757, 984550390, 300512020, 792906532, 725021225, 213221716, 865494131, 164528207, 626659692, 710289451, 412492345, 799777047, 845554355, 383097634, 460923821, 78219324, 816697679, 442330272, 468101124, 719353050, 446670631, 661555455, 17933926, 490089616, 935480244, 92820514, 467853163, 317070516, 562951588, 777125215, 601329505, 466104218, 333510011, 891970822, 175348915, 48044660, 904657631, 830131672, 616396728, 650764363, 652412519, 501147544, 484521989, 619607066, 874257758, 14142788, 258778420, 134421995, 684650543, 995525689, 675726598, 699149849, 562090912, 256886552, 993136461, 209995554, 187900142, 359667358, 469366773, 928610905, 776757799, 880269748, 358732575, 793762438, 672760617, 346914643, 249295820, 698077454, 315429962, 194822823, 270560, 32065196, 193479561, 732149753, 968817337, 761883097, 830753, 946073030, 730397015, 831964041, 354793996, 959087495, 236418845, 568660035, 76201685, 564918274, 386928675, 349150986, 116505627, 457554331, 692203413, 291365098, 22519046, 15472805, 223507623, 100146284, 300694563, 829247071, 672021530, 945078586, 234683603, 26442681, 57268515, 492648311, 267817732, 762499214, 307340057, 266286106, 22789079, 105564697, 628267543, 380802673, 840694527, 383421605, 789351305, 742661675, 63982133, 250232067, 677301124, 963376201, 629571313, 581368651, 540139265, 315352492, 995731916, 652243234, 85860182, 911952530, 617270275, 457447134, 971435619, 375843644, 666288526, 121460229, 600592140, 143952232, 898468791, 923614341, 901705394, 220682387, 25238581, 652077558, 893364186, 721335697, 832488786, 299929164, 7048817, 808122349, 493831213, 770353336, 609455737, 81316157, 47707244, 201351344, 389040217, 317102773, 681938890, 173342253, 34405110, 648830192, 981323980, 515698953, 6372545, 665048853, 617199746, 478730093, 355610841, 298273073, 741419122, 709908993, 571790679, 355661072, 924843415, 586160294, 53228001, 147647409, 494488994, 31549834, 550954735, 264318373, 536313245, 401322785, 508119563, 615122054, 214915475, 531666473, 566996142, 515377467, 916359065, 522304736, 787386686, 909564698, 228765854, 116695588, 478852948, 473005300, 481356062, 348717616, 984063960, 14317413, 286773810, 366615, 19707164, 688542535, 321262801, 591153012, 918875252, 223927970, 59190891, 746177690, 527915232, 96171570, 590439468, 936420473, 520674289, 131791792, 899601970, 395891923, 654404096, 789444026, 604373936, 543551305, 844121449, 921104358, 731741792, 17253410, 999882469, 450934822, 239207533, 674360674, 563015352, 841757334, 189041483, 953373394, 722807309, 652680376, 496732536, 784995206, 137132942, 407272146, 831711854, 310245725, 732028082, 166962027, 125070710, 561094953, 728309579, 907767201, 151323696, 638055342, 129840896, 503873311, 414105261, 84435840, 331336178, 84108599, 304682092, 139621389, 468742216, 450355345, 842946636, 79244312, 94293806, 825039370, 804822231, 621202289, 198367794, 883859363, 572222452, 842336546, 761156656, 652938617, 527694132, 224785750, 970398563, 938226703, 326090918, 741104246, 174270617, 14628012, 163615293, 258692877, 813007055, 236982895, 206444232, 125737839, 145214723, 148140948, 567708674, 559262431, 598938337, 176656210, 346089052, 38517754, 246935917, 996714514, 716373486, 373631941, 109296952, 277380732, 9867536, 573803764, 994084059, 996296344, 444276926, 808475779, 613073958, 650153119, 380426480, 674645832, 641407710, 599796556, 579061117, 618187912, 921512391, 978205515, 765527425, 450412050, 918965883, 683879666, 91092704, 2060337, 973165258, 260370625, 970268658, 607779034, 921604218, 354228084, 255790563, 600977888, 543505576, 162761113, 659621584, 862427805, 48395682, 659608724, 515051598, 321131197, 795616390, 412024338, 182602409, 113725272, 577317006, 806389805, 706419690, 768788117, 716617876, 555245957, 626962554, 609898936, 585042482, 572481961, 662775524, 26152675, 775583272, 284551047, 805608448, 46601761, 435877133, 642608809, 225014936, 947351526, 674191420, 94210197, 661630841, 501895977, 589819651, 56061857, 591920205, 306335498, 235720179, 187996397, 109076676, 212258037, 18806379, 704921619, 29065513, 312245014, 460852442, 113347196, 348777197, 296894075, 954047397, 166816684, 976451957, 786001657, 382433029, 103159197, 999300705, 600062232, 767324743, 852658857, 27955141, 946093509, 571307419, 478419613, 69422873, 32791318, 504900661, 631976273, 458459298, 556288675, 830436046, 409469613, 633680916, 694853189, 234377872, 831941578, 307692878, 93417879, 437991293, 738566875, 29071738, 967752955, 345228424, 799466808, 486908939, 247079283, 332321175, 359442027, 818467117, 782532663, 985861204, 950448050, 942953796, 870979853, 168593535, 873019271, 943022554, 843553954, 450166857, 387015546, 563474530, 753992524, 496994008, 973012857, 330964207, 216826113, 808514236, 160913572, 563985531, 484514245, 181387609, 126392208, 658680021, 220474408, 247048587, 404744375, 125869550, 794243357, 330379701, 789365091, 937270256, 488452043, 178860235, 112572671, 770123010, 689369859, 494579646, 934655351, 654444005, 299942220, 354339838, 864670265, 869616167, 288397811, 879076025, 958726295, 920247464, 438009021, 377635852, 457329646, 180891798, 551936712, 754547525, 38700280, 424439215, 64218147, 773993782, 122170188, 156293912, 112753837, 108442117, 191980910, 124773611, 322228571, 417582531, 148906922, 593528441, 504597850, 442460132, 321169789, 10186217, 498967481, 132185195, 869232253, 55220946, 343517944, 100150656, 874898699, 818718240, 492391063, 937478415, 797735750, 981531107, 360110763, 997496965, 164700734, 437422135, 435714044, 555713332, 423260531, 523466755, 296687039, 901003093, 585359029, 996656965, 963849710, 185492948, 151472620, 858181987, 230733479, 593391210, 686680786, 592667522, 125666884, 530561946, 378864710, 725252877, 557674108, 467491194, 630581906, 685866809, 971681825, 703236088, 38175141, 13354206, 879630360, 500469866, 662703637, 6505129, 160694368, 707358224, 476605899, 274298675, 42032014, 968437477, 427251980, 369246364, 97233556, 509739248, 281690967, 535537297, 137596508, 756828402, 785510168, 489688367, 290147236, 616328296, 261951265, 29550469, 17164306, 294223944, 421680359, 482058167, 248984997, 515860609, 749347651, 863347129, 524198958, 284379674, 270125988, 315262257, 30308059, 335552859, 348041033, 147266523, 370007756, 922331939, 359728108, 829072467, 700259779, 472753930, 647117325, 597886929, 631911847, 751884093, 211146129, 246130219, 280370701, 220406260, 23599735, 688389490, 54601535, 869184516, 123853969, 891353789, 729129868, 455114276, 331417358, 107235494, 616292797, 202567167, 722053683, 17026864, 921951687, 379550553, 652214052, 784716637, 865145873, 555924123, 99729399, 547450891, 141630236, 265366331, 913621332, 740596852, 802453918, 293227861, 777061220, 275644209, 53013662, 659243083, 370686554, 550178825, 674325902, 746585199, 891043801, 229634964, 718833785, 531554473, 562018886, 650003074, 389516143, 723981737, 306577384, 797138857, 843159529, 60495958, 276007533, 274747970, 934860618, 297264474, 148423922, 410503489, 409776418, 288385786, 735392563, 847514490, 561809620, 795834628, 858394720, 540503720, 801566515, 420477314, 58582833, 384586716, 722603957, 990693488, 181655902, 608918611, 628265379, 741717925, 275043332, 915487751, 750538532, 446629638, 311708560, 903285376, 499891289, 376591808, 395533892, 49006501, 600765095, 427077902, 741301863, 332126846, 7895827, 894881512, 614524168, 15353313, 912826176, 568593747, 42297770, 644000572, 391335302, 880313573, 790265985, 533221853, 388419280, 744998837, 376307201, 343379415, 563973690, 235881475, 160385904, 799045291, 583921334, 717081597, 267094819, 996746242, 748753038, 38913665, 904533540, 905791671, 679199170, 543778983, 614208087, 553788239, 905011652, 525286002, 19772510, 441615032, 894373481, 951361320, 897959878, 344113971, 623528071, 469835084, 446104348, 543630107, 884827011, 829092398, 822504001, 782524695, 661238212, 906555986, 695220599, 402525621, 605874754, 833459458, 858710397, 628579473, 62693522, 574975796, 663299575, 900923391, 424744909, 517809985, 972417857, 161187141, 42458426, 168473300, 842844706, 799715602, 70935144, 373215513, 277453353, 846343474, 75503954, 613618491, 34807420, 713323123, 149515617, 26598624, 840877756, 626474967, 125714371, 515929801, 202908734, 314326717, 465234945, 295602001, 431272976, 93391274, 424645419, 455274020, 739989340, 516717877, 787740422, 475999874, 382872511, 464735890, 926129047, 355207206, 369760677, 558002190, 262163298, 430086295, 203554272, 520983080, 306518520, 726329248, 99640741, 285492629, 349943304, 775752325, 992866188, 97207011, 57299242, 998598988, 635711271, 763416184, 44656149, 163390108, 797855174, 695305361, 560243809, 179157315, 900190017, 953845994, 744799255, 649814180, 858592642, 249476167, 960317777, 349253487, 853003288, 243172703, 70458743, 807023161, 275930756, 368443496, 373115789, 407970033, 913083795, 789317019, 286122178, 441322471, 326415897, 405486483, 203995852, 600903593, 77100505, 786147360, 459903034, 474584720, 249084960, 3804547, 647981135, 74503689, 892895756, 749760613, 595012395, 256318116, 499032197, 968098591, 770320295, 760007083, 26849484, 770409054, 788684182, 880440369, 280706893, 461016767, 564237910, 973392124, 385659270, 652583441, 633931532, 189626842, 35337614, 608785619, 860278743, 30178449, 160783387, 603302242, 263556644, 568107144, 376562178, 964303469, 843004581, 77276115, 41244275, 929694283, 768122525, 402469877, 100600554, 951630171, 749427392, 977723268, 961905471, 125181640, 683234812, 876978079, 319051103, 314216376, 765210395, 99409402, 977335358, 228643244, 334470828, 881027766, 973854217, 518503526, 56526401, 376315483, 332477269, 590949227, 953996370, 728062481, 84764756, 336207609, 802005322, 605535537, 209438327, 857802365, 929955439, 478441381, 543475903, 207241610, 175088292, 130028661, 207546687, 241634137, 68260727, 355639175, 638650472, 328898557, 519092642, 37286917, 979764824, 745882537, 587966150, 697758397, 137629763, 212066470, 817832666, 639717282, 6357857, 94212857, 660052466, 171796015, 669714215, 210660829, 2044437, 869069584, 478139369, 321066807, 880154338, 834061329, 759616479, 23548247, 5172068, 599614816, 869266597, 269394785, 173262487, 334417599, 977517366, 630838251, 5192410, 793264665, 195534386, 567101510, 425764506, 728736936, 305960951, 796725237, 113248809, 649262628, 658287778, 135328977, 322625805, 552922573, 615922778, 923744383, 778221586, 725033066, 521285726, 884105989, 161535762, 753093267, 10312256, 426179691, 394872112, 259252858, 132563719, 146785274, 538561016, 135912688, 166948319, 872183439, 377116162, 637038155, 722504267, 421955892, 54261878, 374690273, 721221665, 848806401, 542707589, 27636530, 439232121, 54998719, 762110098, 131228296, 74606423, 722656332, 394330531, 35968402, 756010928, 797987807, 937013339, 732045205, 627435054, 968848943, 262942701, 866797727, 231936715, 115142366, 485794677, 341469061, 926416479, 626966140, 372881042, 108259309, 820940027, 599236400, 518091081, 355753007, 669431518, 71225844, 448389289, 183560522, 112806999, 914329366, 114699008, 848940086, 761392156, 360583348, 303794666, 15735626, 913144113, 847340076, 643982419, 350417398, 614673409, 702316442, 633023007, 264069491, 488132171, 101981640, 614999199, 998504717, 697650534, 32951143, 815591968, 983040712, 487424124, 827379026, 974278602, 347211296, 241092780, 66276998, 635873871, 718247728, 838659880, 117371352, 150349874, 22729099, 999265435, 961592630, 141434750, 959745671, 913412261, 725444217, 725871614, 970988777, 357966697, 413996919, 933504419, 535578924, 702360068, 775608700, 798756577, 932210019, 631181645, 42123917, 580341945, 459090480, 545096447, 500471616, 742301239, 500676739, 918250701, 861937408, 8280869, 639926834, 656185952, 561163726, 736323876, 507277165, 651666706, 281074016, 437181713, 948189449, 629982350, 186579761, 182453591, 772837696, 21585112, 18662620, 85708314, 863213229, 942777407, 289582393, 275613653, 73153973, 199050554, 778575806, 100848257, 299267636, 138664184, 58380279, 156407473, 811008534, 738864498, 565535313, 847979462, 243990363, 462176763, 47470630, 714911269, 518052990, 739199340, 811462171, 892763361, 926994665, 830055654, 749458370, 384326141, 167063871, 486970881, 528990087, 582449234, 720493175, 69040626, 199769815, 376541564, 570737090, 709910928, 781655745, 129254432, 435152478, 879133647, 748862042, 292922549, 754049270, 374622468, 937140144, 641874572, 540582450, 106467705, 464423930, 144197909, 619269359, 272323162, 65440667, 630113736, 877130843, 100224033, 472705006, 574935651, 441585831, 673440368, 720406916, 86182358, 707790620, 973604957, 871929702, 687504409, 277667190, 248413966, 81196684, 20036225, 435832959, 235781349, 319143872, 712403026, 182482729, 178597127, 917657598, 798732108, 930724816, 675858490, 285556424, 16284690, 860555597, 266862304, 855365897, 519634996, 227539515, 79958251, 221064119, 548463771, 162313483, 789262911, 880028850, 829245666, 960773735, 85178354, 749243297, 954810539, 983111419, 885457784, 323032775, 380164502, 546223482, 405159918, 696325217, 922387410, 279357074, 67387491, 126580273, 240803894, 638710421, 59490484, 283585228, 838799954, 241862971, 994659720, 323502749, 699300057, 366918356, 494727339, 1024681, 388277619, 747484210, 83616577, 769593534, 907067909, 62760932, 543825333, 880901277, 563001392, 100460915, 414154226, 282745336, 565682060, 635321750, 118299597, 597759801, 19889596, 43042958, 252100829, 311404069, 372771824, 758661218, 485544760, 663996948, 362440128, 444026297, 136780373, 376442843, 687414262, 664594787, 680420599, 117875129, 392569481, 332488239, 757949615, 681925457, 905492653, 280609200, 344219740, 157434544, 391064327, 418611297, 15755941, 822219247, 549602928, 641015850, 693095160, 257923416, 907260118, 523343607, 658059729, 350444051, 845394114, 69644221, 919554829, 538461120, 784523405, 993460647, 643365807, 619933079, 904180143, 792262657, 763969016, 445235545, 172714017, 203987133, 835494425, 6943654, 418420601, 516283366, 286437902, 775230428, 429955581, 359414909, 604317007, 44971019, 203911818, 463184002, 681839771, 243684114, 927102705, 268090772, 882401972, 477165818, 162004921, 401340496, 937816774, 244556256, 27431235, 752251367, 240273721, 71801001, 622439643, 895958220, 547884921, 692117173, 655351950, 382446893, 713967805, 956142661, 12597096, 726864219, 152098110, 649297589, 477932358, 366418538, 364509162, 454629907, 638384414, 705524845, 265642660, 291184178, 384856795, 398303390, 597833102, 640466525, 231011273, 838529434, 35418702, 844765019, 72763678, 422894784, 903584718, 427507133, 347922855, 656495467, 766618509, 361805703, 475545353, 488531214, 599609589, 305472999, 297064377, 593161933, 733619287, 167749290, 656300912, 527812076, 729427239, 651175038, 856840668, 886077269, 596789076, 602186572, 353774743, 175596176, 32898709, 550250194, 163051871, 548082146, 975803247, 704015217, 763413709, 476166265, 361463272, 935941909, 782410867, 164197608, 415075040, 746644402, 912222943, 884033559, 335395033, 129817968, 883803328, 261814408, 181745608, 173942592, 794380828, 958514213, 472041161, 533027824, 610650000, 80838522, 107805476, 513203870, 197600551, 838247769, 214463082, 330068127, 178707351, 875667251, 676601934, 539638424, 405589312, 579013248, 336277012, 890338651, 334536953, 759052267, 241601832, 133324125, 84521621, 586378603, 245442140, 820529434, 589738323, 666336143, 659548438, 549182076, 702940427, 906532988, 877542615, 336775413, 139824534, 774367420, 743734441, 643112670, 378428506, 911484539, 257865298, 28523855, 90563137, 732487786, 812154152, 885681848, 277288064, 735080496, 819510677, 599552368, 565844761, 197516557, 964974571, 206761206, 254786802, 111656708, 688082166, 127106272, 520682500, 10998749, 922304211, 318772816, 891103200, 7250144, 316276777, 953357416, 731365014, 115373675, 888961496, 269780044, 62009377, 54525210, 423956543, 764845318, 377753156, 709944970, 757549368, 371389093, 112542248, 802309757, 354180689, 910308264, 898861658, 104164436, 332310998, 879768239, 148384358, 869276119, 476857480, 423609118, 323130891, 816150689, 48948387, 586158466, 627028051, 270823037, 64202148, 130775948, 951650694, 860515850, 63724305, 567198025, 952893157, 5652813, 816611892, 772709698, 99850417, 737131893, 482048764, 718108736, 488065568, 763943650, 442413271, 405528809, 903687726, 532356596, 286199778, 359784070, 169860390, 897382605, 703431116, 560576068, 474289376, 66383975, 391618092, 819853316, 962693745, 731148239, 700566784, 113234750, 600906768, 11152377, 151966172, 997445506, 878214815, 943385219, 430025849, 534811567, 640539163, 617098204, 518944618, 574755527, 762810663, 385058712, 901167239, 859972170, 446978605, 935839343, 951326371, 716241883, 763576893, 282408570, 734330358, 852471763, 131141618, 621043402, 775298012, 609688584, 45033053, 774534917, 708269490, 398003900, 856421876, 537959975, 856394681, 512548399, 254383052, 688604107, 848932266, 844529508, 770908770, 221347721, 547104787, 814451709, 424062741, 430361380, 322808354, 629665142, 495331185, 638295734, 473054492, 3759407, 893173367, 604273846, 544750922, 262007758, 678585628, 612576231, 855981471, 904367380, 432074886, 326565578, 146318194, 129786947, 977241798, 352057925, 243776739, 183196659, 87982829, 733597206, 386320971, 995770082, 815630532, 856413075, 479942212, 291367612, 172526851, 359013372, 288363442, 41506582, 208740122, 842104349, 847089179, 312925971, 884773571, 327643864, 232034733, 609119837, 276284523, 164823052, 895983932, 130289088, 727145030, 55119274, 402362369, 61689409, 514512153, 526171655, 236329542, 99150039, 308034637, 32575637, 123102176, 770539916, 780399635, 838864777, 827309366, 238902699, 932737103, 441688292, 275118677, 220889654, 12262326, 518057800, 384044823, 945771671, 504151470, 303785273, 542678951, 161018490, 432971574, 762193646, 562971521, 707460493, 163133188, 517197231, 974382823, 648389296, 726138962, 683280263, 828474126, 537440692, 182201047, 550027420, 398410329, 639210330, 998791579, 790501947, 162938885, 344814228, 248730821, 680270246, 209266398, 978135715, 628616202, 155861357, 63346321, 573211563, 991520229, 719240673, 854074538, 44543058, 19838979, 198338550, 608332081, 617909526, 521968666, 975122232, 405806427, 850595463, 676397369, 201244222, 740138564, 34425404, 251516993, 355289598, 75929233, 395319685, 238423626, 612112850, 968175998, 994268020, 545132249, 880453590, 897492165, 541999679, 863220635, 281629870, 673757460, 248446919, 416769731, 814507328, 576033008, 139385176, 364848634, 509828150, 954731831, 19765277, 814222992, 579854984, 901438171, 691516188, 671461595, 756926586, 906590703, 882675528, 349252897, 563938360, 746242133, 960739993, 951927094, 248613442, 547359002, 951771783, 381561694, 415192127, 637439611, 754588237, 394282302, 496255210, 5698622, 994933195, 907694035, 973594873, 132972243, 484428358, 341754567, 401969810, 389891654, 692401913, 398749165, 642201226, 788787815, 693469651, 213818224, 848703806, 669865526, 817002932, 620790802, 621178361, 79921241, 292246655, 531276409, 63851981, 831544678, 31724463, 769271241, 140019214, 114444306, 270719928, 888284663, 658139657, 84674633, 910290933, 184906694, 621144015, 375356783, 250200207, 903142899, 486742375, 815664840, 924860499, 249473133, 447126146, 402262263, 158494528, 951075723, 402369309, 935739360, 302252169, 264303032, 306264765, 713195216, 909511516, 51542163, 764134472, 658880907, 91794972, 428410328, 616090065, 410124957, 853888549, 434113112, 655926463, 660971813, 61671738, 997962962, 661765829, 406879449, 440719067, 886385138, 928355130, 671344844, 285424056, 802308116, 617030581, 528752009, 55390350, 918529354, 618733972, 326398092, 28284861, 547675417, 214074341, 432170719, 390952069, 351741090, 26296748, 2673052, 694014516, 939907871, 820004542, 377476295, 871721159, 109601510, 662308225, 97020374, 883996416, 32878892, 603636652, 864672861, 543631259, 854845307, 913986810, 467607544, 270468442, 307683874, 631017134, 476188572, 946463352, 36678345, 965360754, 979835110, 257071893, 307998109, 512251967, 7396003, 477526692, 719334699, 258741376, 297284301, 190384272, 442954713, 986939577, 433662670, 637571738, 235354050, 920397333, 940004735, 925164120, 525665397, 540082402, 619069831, 693072720, 269134391, 883068466, 375159674, 235250888, 474537248, 492380181, 64810575, 960200631, 555035412, 639077177, 902359660, 228427736, 861917607, 933816759, 246992974, 117868675, 953526831, 832727574, 176791330, 94166204, 774586698, 863252000, 808846802, 210002673, 447770042, 695469409, 911321593, 160602700, 327364465, 936455648, 159184321, 288475381, 962645859, 266574850, 655494890, 535703975, 144299369, 266023458, 789976809, 503890316, 680203671, 139364015, 191721686, 136303482, 167890963, 385733298, 396973093, 715545432, 283419581, 403820989, 449881610, 508224619, 75042411, 115470705, 453024555, 84064004, 20904844, 529457355, 963783020, 703886942, 124543796, 201389325, 508971003, 89681260, 686259307, 510661876, 55966729, 98563160, 245938590, 359653537, 340866589, 29932285, 425929960, 657145626, 925923682, 202314685, 40196349, 438556220, 329178285, 336514401, 80331344, 112037042, 591593770, 723325844, 150521601, 268748844, 941604590, 685319323, 730969331, 191662397, 747874072, 584712626, 592284998, 811073002, 309901800, 487784316, 495397557, 342549, 517391480, 678012624, 700053136, 633299300, 575102495, 753113048, 490321246, 864922955, 234006069, 206424571, 166370377, 764339191, 963833550, 328197093, 527726385, 297481306, 632912262, 844063002, 489659517, 233332323, 745716264, 120465693, 64599939, 565186717, 49558498, 573250773, 551152778, 974350265, 493266784, 531183327, 706993856, 814713783, 180823112, 535218055, 158783478, 550771994, 863674501, 295922182, 812045430, 707996573, 508054161, 566243350, 191383862, 653252955, 646602194, 949034611, 694323867, 417958632, 504639167, 842839832, 880120414, 97196651, 29172659, 572560814, 362298722, 649535528, 968085477, 490451093, 486885312, 181035975, 976337549, 547139982, 337117495, 503150031, 447207361, 936428878, 451994772, 582801903, 266214091, 635636018, 790944012, 345248270, 12741962, 214919800, 53820100, 41039801, 422758675, 763194779, 438899082, 464178890, 418685789, 692307465, 109754932, 928211947, 842319900, 457713325, 407058802, 650592661, 81577063, 904111687, 107733459, 316226209, 467642459, 700214466, 359875716, 526383549, 885657892, 739879786, 533693685, 225702804, 56684377, 335648978, 834115450, 675173390, 323355127, 213027756, 342213032, 317303413, 599508382, 490635002, 214571991, 343461440, 248270546, 93225317, 840541484, 310288733, 258696141, 282684485, 301374384, 536414270, 379543679, 424287452, 891365780, 693093025, 875567783, 287458839, 808369820, 518837599, 779129224, 43555002, 464957442, 483246176, 176236615, 116493180, 677096772, 645590529, 788249982, 276112575, 591886897, 354554060, 337452726, 594553656, 353544897, 93095187, 643456065, 448008944, 668074971, 16469741, 566566119, 325510620, 887961604, 513855572, 665116931, 183537138, 354347506, 422683566, 475405138, 810563012, 332120407, 113846153, 355063817, 322886194, 89633227, 476510004, 229552630, 37330339, 89840177, 778656572, 397002822, 94849392, 485367025, 694110556, 992617187, 12224487, 238333290, 992811266, 91532536, 483736226, 180596510, 739263100, 27173345, 408703627, 125911928, 861707658, 909933249, 640871073, 718649191, 982093080, 695650104, 364255963, 587972631, 614725630, 659113614, 581891460, 167484911, 292827660, 701153967, 318799084, 655692538, 52505362, 972450197, 298359317, 968899185, 495797557, 461394395, 655070372, 38019002, 186209351, 123226904, 569655959, 839698507, 426793526, 120001674, 848351916, 405821506, 480391566, 56108455, 903297189, 761871428, 620921666, 53086403, 961706806, 697013924, 802968544, 86403102, 872084265, 396286794, 575144149, 273949336, 193530295, 496525995, 874955996, 773897489, 675185385, 721082033, 895630773, 894417600, 220925803, 427868089, 64837301, 485192178, 793988748, 449254835, 358706485, 486580399, 424217172, 635706223, 4477775, 577906432, 555689671, 435079780, 436649269, 253352805, 57146299, 911139477, 256958133, 574888866, 525536903, 530507181, 669548584, 832034351, 451992574, 846941128, 494354805, 617309410, 878072023, 369302250, 673969187, 227944978, 698974770, 564197780, 451460533, 35891183, 357138925, 894039299, 687040721, 739011001, 109340960, 204171232, 24470041, 375461076, 97196682, 689623442, 444955514, 612766067, 795003545, 219236470, 207306131, 608629542, 711786568, 692172424, 450940279, 943399972, 733098474, 108305534, 638927472, 2853788, 629484912, 631183135, 881045895, 264521970, 476875628, 315664685, 927815305, 840244324, 820409515, 220111397, 452781068, 566725857, 9046532, 77053593, 417307747, 60528746, 47980282, 969094810, 734039453, 686588444, 712645152, 579084236, 301852231, 84284376, 992391295, 173936729, 358698817, 559465136, 563989175, 839834779, 249276436, 285357626, 552524333, 55245200, 594761723, 377939522, 853274016, 630083652, 279059869, 511031468, 714894163, 906414892, 203828130, 383852761, 254628245, 606424538, 729864405, 459009821, 394219795, 914954096, 777334307, 292424255, 635270225, 400426787, 912680940, 868550215, 975694236, 225345746, 770787257, 429666221, 414083488, 976120147, 461114148, 518664708, 83378344, 321100666, 752176027, 84185176, 417829537, 616685422, 142298837, 376507489, 231831349, 256389089, 750251114, 497344155, 99737296, 785409928, 445599030, 391378411, 463709831, 943547204, 350424060, 98078702, 648220229, 977739439, 410295980, 21905264, 270807761, 155101687, 486650107, 414508567, 682891156, 491444743, 450438301, 396565874, 469387518, 942364311, 135027469, 297085866, 426610199, 4997814, 387654759, 386297650, 868341221, 97460259, 924991977, 443923791, 475943090, 437277219, 835412428, 180220632, 602503582, 679935369, 737289131, 581301413, 893319970, 990060056, 528583181, 283520577, 227653409, 788528774, 914711846, 534984893, 305561072, 258743325, 208881225, 763111794, 837963897, 795400588, 912682564, 711440561, 579732930, 738611475, 158395684, 188367775, 339899200, 271377262, 292146360, 710453664, 427125480, 24925201, 923055269, 520910261, 297253032, 769302660, 27265467, 357231129, 307238005, 515072349, 458156592, 339329086, 867209461, 507438067, 286882719, 512847335, 584614770, 51757485, 803903573, 153341653, 795780297, 384747884, 366442700, 686951938, 624505316, 936611077, 285544303, 483214906, 600606463, 891373053, 958598456, 305785506, 773577830, 14563262, 111792130, 655999038, 451356757, 491839318, 592122939, 699094223, 333286970, 651477571, 681952502, 435889236, 570648901, 921546237, 430392845, 686303269, 881101750, 977404297, 107414835, 864528906, 775178265, 692808137, 6729171, 916698534, 323378979, 124995529, 47455253, 265320042, 647731329, 782944569, 415726785, 598981059, 952068364, 45645819, 300773919, 445493956, 311457993, 352758057, 648111110, 955593906, 722863280, 360562123, 39504466, 69827274, 628550576, 282895426, 753905090, 566140057, 331269055, 122772696, 756422518, 129123994, 242031048, 793216161, 80180942, 47557061, 879173845, 711187195, 208458674, 998156779, 560146678, 502187485, 636399733, 557657361, 430011865, 844270555, 119557967, 480599326, 754138367, 132542186, 561072095, 583659347, 356367004, 901689683, 235139568, 805532957, 369317902, 315674688, 539263987, 552598102, 727227132, 681758860, 268387118, 740922567, 29655649, 447875151, 523405226, 426879137, 629213569, 225404966, 973957145, 3131649, 424747468, 792110986, 776632439, 158725263, 632443299, 321052689, 172977442, 383928916, 597021478, 605674309, 842521879, 109270910, 237990125, 283103895, 51478354, 516567175, 675950121, 474644165, 110706931, 101161479, 814855041, 328136184, 953984427, 460678248, 821486824, 521578752, 20893078, 842445597, 233110662, 536073882, 6070899, 491169338, 541791987, 953268955, 403568703, 166272985, 995507144, 245669355, 131836584, 143237404, 914783361, 428490420, 359013388, 763076357, 934794404, 851894616, 400615478, 575199947, 252570298, 143840147, 998842679, 129003058, 802300757, 953665068, 490687576, 30981485, 400652107, 320686927, 206088528, 135699127, 535210934, 789090753, 192722360, 123819993, 745904578, 950065808, 216337554, 863177543, 287556830, 179610429, 339373019, 900506148, 575211468, 906496551, 469928213, 912749664, 274044086, 222048557, 933476943, 121795040, 892948567, 306476338, 542454291, 165673214, 292313701, 618990545, 518742811, 780617024, 475490939, 388777352, 29664402, 211933264, 113782837, 86598788, 956608325, 769782407, 742819970, 413804262, 258996019, 655892344, 50889250, 423199319, 885818710, 469473075, 57288920, 464987397, 220016741, 429883616, 895420125, 791719362, 336119839, 953363924, 324661290, 961383344, 29302452, 316003978, 14502851, 691389979, 552753299, 255318302, 742906325, 13188593, 239626465, 500563830, 154979491, 622228645, 88528475, 883732367, 102230432, 371225343, 437314221, 322777771, 310265925, 575705030, 425779276, 37407570, 320350349, 675592983, 120139100, 336073721, 967362227, 479389477, 373576464, 214528105, 684809621, 73117252, 401728246, 628585838, 429562946, 691400077, 239461651, 33079510, 416929522, 307990346, 148355062, 385836862, 21993270, 323707395, 54230867, 412596911, 372979886, 43546425, 436452551, 598217416, 824073001, 771656973, 165006636, 197586302, 667042834, 334057196, 54960185, 985573913, 352255773, 366381544, 828736491, 315964124, 731340225, 597816192, 54173456, 307242489, 981869607, 529477538, 333543779, 678681776, 431986446, 957594935, 274522642, 715105238, 28794427, 65138256, 690066824, 453782254, 136173311, 804749072, 454073130, 118473747, 46643202, 224010865, 500031641, 698378436, 895636803, 715504516, 862777219, 270643697, 592770910, 528177380, 766582830, 701729619, 968109788, 682287803, 853035954, 840258912, 144811203, 150456104, 882087137, 768645428, 514332188, 235985524, 216547968, 866450876, 613073758, 405670890, 642175890, 675622064, 112551797, 764218449, 773474216, 106901256, 688242996, 651886495, 163678301, 202741736, 104273190, 553399159, 239455240, 677757781, 836169968, 899580888, 534633893, 455484195, 984037262, 860915549, 776324347, 314179479, 729847769, 895319746, 388116565, 607396109, 706585658, 210933250, 721296475, 938988935, 675925150, 27411417, 400129426, 175543931, 565538225, 411349380, 729076358, 205395768, 970043045, 216538015, 874914611, 159232198, 637960750, 92343346, 6125275, 339556520, 867185775, 903669597, 240849465, 378518641, 716811641, 137140376, 500286929, 116509627, 102396404, 953789441, 478043492, 349468572, 827078719, 650132045, 548386065, 249657928, 784289350, 883176065, 875473866, 511087971, 992808904, 902602910, 348186688, 489586165, 122216078, 217022904, 146886775, 535364013, 71667259, 936965629, 708139634, 773297905, 633253408, 597442270, 425404862, 737423214, 384278300, 487473963, 899086993, 982531550, 592740256, 737262357, 781015909, 290271428, 828133234, 211626672, 534344250, 306805002, 202048988, 567932300, 516249494, 460312738, 757281124, 588771802, 251938826, 496167204, 618220052, 433565981, 340154910, 75232983, 758184412, 495618854, 369834492, 627827911, 376876642, 593123918, 474041096, 401725121, 275413500, 451563092, 902170997, 240339154, 616834680, 443588292, 799057588, 536191819, 34009148, 613775575, 746886681, 722240601, 37772184, 765972055, 663959844, 696896982, 61379729, 276675257, 88233785, 292402912, 257465946, 239862616, 440377402, 63715394, 52404902, 294408353, 215618341, 183054356, 106784806, 837400649, 419876786, 99286146, 142745404, 382490913, 139390062, 354892006, 70651506, 246121556, 737308093, 239813908, 711253785, 666311777, 560776350, 212928408, 866454660, 696044611, 2386397, 823465128, 406493874, 737551456, 616100517, 27470896, 348397400, 328766985, 184823742, 93775102, 821164234, 942485202, 811473457, 244526795, 385315166, 172633639, 676495075, 688818973, 388784085, 461061939, 938448529, 655258841, 174208457, 436332946, 657400240, 54981356, 404583854, 412748284, 663464818, 732871469, 736298901, 219193599, 46259103, 289557552, 344594570, 404578656, 647824033, 790049869, 463404340, 764765397, 674085352, 105217376, 855703786, 11855461, 923245036, 644644321, 410518287, 621845606, 340544974, 95062463, 52787153, 780594757, 712241366, 427619624, 893032986, 682149446, 503870964, 406004068, 294550100, 934346071, 296310678, 362825530, 802791621, 418533905, 178001762, 913224370, 922326605, 175378482, 262134665, 682530977, 207979752, 996973816, 472767408, 998976339, 16861024, 987024620, 673834692, 399439172, 596692085, 652521442, 949657179, 33973541, 251392289, 188212130, 667242453, 421549362, 382898279, 569733545, 727561473, 397487683, 762806463, 711435264, 753501845, 746076791, 69601812, 510257390, 514519719, 180051536, 317091452, 213608677, 319291496, 181898947, 459640392, 1260826, 570243308, 670106523, 610077765, 361557740, 493450938, 809397559, 207329482, 502743920, 329817438, 211796127, 864415077, 850825798, 575765688, 225054518, 57236854, 444015186, 318381382, 318163333, 22866781, 58976866, 165719121, 371582920, 748308460, 272761519, 399649738, 338158841, 31759462, 514974992, 682757308, 801164990, 31712403, 786330217, 882478234, 343215355, 847390703, 106478433, 696097831, 137781359, 215306131, 536035612, 70301654, 28418496, 98422251, 177477857, 763525829, 724399276, 524161107, 945439952, 718285180, 904590532, 367484346, 178862069, 210981193, 133272729, 782829828, 779975948, 214082941, 905906800, 196735092, 97629186, 401998992, 1309135, 384495691, 87164178, 381524951, 747908229, 258613503, 857775094, 511528684, 529155034, 3892900, 236892050, 442061365, 734521449, 78687372, 354125273, 526388541, 41692542, 984642719, 774581516, 494317064, 547350126, 19123710, 28668667, 919392617, 415768241, 795092014, 221859952, 318476194, 767763050, 383711792, 248053793, 767953111, 678776616, 444295899, 238604791, 426653852, 635305334, 786463072, 969406340, 892890754, 419254193, 142386276, 742571975, 788142112, 144421321, 512684191, 292666379, 301968560, 470532311, 278627357, 807983453, 475754364, 632766953, 647670689, 4491528, 656977701, 47496963, 255040743, 977271273, 111199846, 677455132, 442130607, 139437520, 424242510, 181046351, 728666858, 122133193, 910629415, 183141283, 279640298, 608172145, 841857944, 686973783, 88067233, 519167458, 910920633, 57897382, 140788536, 382010048, 853053477, 929943141, 80619984, 553643205, 383716227, 897167410, 92838210, 89523673, 858121327, 806189957, 581510164, 918692397, 727764920, 141192989, 103057354, 416615187, 181052914, 386754223, 117283255, 116744352, 107876835, 142217033, 841565775, 693752787, 551172192, 338495693, 185057378, 720011062, 693028111, 813814167, 581516104, 838672758, 664026559, 361226798, 836210323, 149544411, 634203948, 903143800, 701236869, 874021604, 652868437, 419964383, 450438185, 306189946, 465132877, 256845149, 185496894, 247655037, 648621801, 785943410, 110058370, 607686725, 302930475, 242951700, 648814829, 466775753, 172626561, 522230370, 823959636, 669065160, 776533785, 610247571, 155600806, 610874345, 874257109, 490741397, 819928806, 294609210, 339870442, 712324637, 305617798, 298968660, 781174243, 478103255, 948648115, 666365048, 179723839, 979665869, 256856553, 162606996, 48696894, 321788711, 432609218, 727176980, 675769685, 764931003, 943587527, 159659281, 6454602, 51230891, 535837892, 762613317, 66616438, 459459743, 147258921, 80120588, 971179724, 990614681, 933426694, 169378120, 940226552, 171662375, 49009516, 667032069, 141368688, 211686499, 32338413, 715784474, 299696283, 164933582, 93188307, 577469153, 103301458, 664955202, 51871111, 933823576, 119570170, 730086066, 157270753, 518089592, 228469577, 677154030, 865893788, 418393504, 879193400, 609921150, 775778897, 70396072, 213992875, 670280246, 932929790, 867339999, 503231391, 723483926, 165778155, 885655461, 356115307, 711207330, 587949339, 107402201, 909424595, 621838503, 997099283, 806773023, 289567862, 773249799, 909858779, 945189338, 559637767, 28583803, 783455910, 939817811, 762386439, 986390722, 733684702, 83043709, 877762503, 767189930, 511853626, 206911864, 443358833, 310138825, 456865381, 358404987, 245365537, 857941315, 572549750, 377633627, 603974410, 179880331, 795842328, 389034700, 470890310, 897879736, 867420234, 179354450, 500695422, 919361384, 99066697, 783558979, 295688465, 50731484, 958099435, 603766474, 142873585, 561093144, 10847208, 24423881, 467551725, 866590130, 697376306, 157560541, 419727876, 599885327, 733899739, 820557908, 260973644, 492330736, 859575691, 153551715, 672540411, 905551537, 616352711, 44419232, 659751428, 386978154, 187257512, 817121937, 781910388, 321646635, 285721287, 524715662, 40607574, 511738450, 212605281, 527291341, 753557294, 417986221, 684551848, 572470467, 629213296, 392737450, 912038352, 78662453, 59768261, 452888036, 71881063, 235813254, 532081040, 303672179, 527081417, 566635268, 746077098, 411337006, 663455731, 234637655, 779011486, 647559656, 736685740, 307997276, 449164027, 876323182, 631850864, 211076751, 153459373, 727685260, 307532588, 127690912, 617386044, 109688540, 537460267, 266102822, 533340937, 171820835, 490430214, 391764478, 415224691, 335340431, 671662228, 346779629, 574377111, 291803367, 453652095, 714827064, 492617163, 500061606, 304313558, 140499516, 577419863, 31043163, 206933980, 828573784, 91846181, 983826216, 584191473, 803202312, 322601827, 167424048, 2096042, 667603483, 142146891, 328858242, 930779362, 304680931, 646749882, 637496618, 311705001, 244842714, 166433418, 894084424, 802708097, 590216807, 529963479, 232937427, 146764839, 860838922, 510905658, 874995555, 777591464, 356987957, 544699671, 403058554, 749148375, 227495545, 637849595, 896792696, 34423927, 227535910, 634224327, 982475882, 936318119, 626781025, 869759675, 303679757, 439774921, 88618577, 657113042, 238500436, 458566512, 172026435, 179615605, 617215193, 817952791, 310221542, 701897958, 386945664, 582446504, 544587236, 865957872, 693523376, 923629577, 749660376, 516430742, 110952710, 644496080, 44033681, 524499247, 228851361, 564774126, 410492701, 227772752, 280532345, 466869511, 701791839, 732060456, 427291437, 907642905, 239593063, 890225918, 65181351, 44790496, 498194442, 350420866, 565654900, 849339592, 115159004, 717812548, 849377671, 252442328, 682376521, 382530524, 62265902, 349581205, 242212392, 240025836, 620622866, 13011704, 673341543, 817784290, 99075486, 642668028, 813621723, 61884683, 613222565, 79836216, 860177088, 146641573, 484890808, 999595687, 907801570, 288948229, 206156742, 617044769, 950855812, 467721976, 764845221, 559345475, 350859832, 110492303, 292925234, 916811388, 970394913, 362409869, 703445858, 682368394, 254501015, 523796438, 326124648, 139073736, 440772350, 819098536, 656758845, 59740017, 59847804, 586103165, 190070548, 202460049, 422646247, 249542629, 689077318, 176916304, 773005945, 503739032, 211756959, 728282725, 903439614, 607993261, 996750646, 772747365, 318535162, 492718728, 821535469, 617315545, 970611660, 703314809, 278777079, 297654956, 405565379, 625892970, 517268242, 689253698, 954378328, 15500598, 534655258, 725198877, 317564931, 879592133, 395446070, 971703996, 145360328, 197639188, 95623455, 837029629, 197663461, 855103374, 850479560, 793249129, 912762378, 364650022, 174891476, 601233451, 262147166, 744097767, 138596866, 464278862, 863368134, 763382991, 926945942, 287059201, 38515433, 156211935, 299091210, 155618237, 961465663, 86877695, 101401229, 684628237, 960689870, 555511931, 224811864, 235119294, 394484931, 424030543, 486238472, 776983866, 487879294, 755999894, 358292525, 651724387, 586863005, 974925485, 328509708, 445730880, 575704914, 458864055, 819880377, 621208158, 770241378, 225739453, 929544022, 856074862, 255756381, 236576569, 347205385, 939852378, 719992411, 750365886, 656326352, 523852223, 739762587, 854833590, 231386604, 190599098, 100946815, 647535549, 783710939, 822113161, 963658082, 686559963, 544274683, 379595556, 331318565, 298261636, 419844821, 632229373, 186353687, 61969555, 35700984, 709192372, 443645976, 212005854, 435666616, 71371467, 597090820, 599043761, 365701165, 76614725, 529624623, 875546428, 633204518, 463785493, 235100547, 913535437, 121157369, 326249435, 457378619, 392009333, 881405508, 512033222, 541573674, 411389172, 111033103, 568033648, 135546543, 753494875, 362346880, 631372537, 383990903, 245792664, 556673021, 922450312, 792117178, 790231865, 493114913, 31718604, 85651179, 268759748, 239648044, 593030616, 830298563, 244754426, 631109101, 397216063, 64896776, 48760959, 239550911, 643525498, 47292571, 930386446, 656640743, 354112885, 99828003, 507327249, 831865333, 635655477, 585960508, 869365432, 15849435, 90255234, 399888327, 568108342, 549770633, 883937874, 478770524, 876586561, 213237848, 334869304, 525773424, 255227041, 375049744, 671586028, 100362885, 185916136, 994476550, 339595626, 700899131, 859804284, 524343004, 822349663, 759213601, 756901794, 111607908, 180801163, 355165655, 750314930, 557828276, 797896272, 369808155, 799170337, 902912131, 507294577, 279242753, 217696097, 439048676, 210351560, 640993739, 108409280, 884751268, 259241787, 497082039, 847427574, 488622848, 799326223, 774746729, 286907382, 839194872, 893523556, 68558333, 268040503, 345398771, 661143812, 481983019, 397598357, 14851905, 355984460, 777245739, 921121591, 577985740, 974383236, 881441670, 152720249, 708083188, 309248100, 313666447, 440322367, 465889527, 775512782, 169075792, 876180540, 820320285, 865008556, 924929810, 772013783, 649715678, 751577405, 155944303, 811114353, 320459190, 859098203, 267342918, 507370346, 419189773, 613287463, 501035965, 505344582, 530308775, 742656727, 287777102, 666375511, 347382105, 23619795, 368373197, 993802733, 826018715, 65570875, 985727416, 179391926, 599350221, 661732144, 674899949, 255738289, 134326644, 28233386, 383140068, 763428948, 523436104, 290337172, 331859719, 242761924, 815327029, 990712420, 288536865, 735168877, 724562935, 643366053, 613424758, 109468700, 205273889, 145547491, 41237257, 856039006, 698145743, 644570717, 162276548, 199244642, 280736094, 967846460, 64058055, 682364453, 950919946, 20757921, 760790909, 113613254, 569449431, 76500970, 675782708, 869827284, 812687712, 732203422, 759129752, 880702106, 877050919, 719465408, 712559585, 962860767, 423196149, 176520506, 810830294, 49355261, 77433615, 410630304, 465037790, 847434130, 147591492, 560644303, 370395701, 16763986, 819517872, 817295352, 953311248, 43939517, 649277166, 702455863, 76761818, 878595367, 716395107, 573124123, 503493125, 550559855, 60181377, 857416448, 573166242, 918201524, 447325883, 442424120, 858040618, 824822617, 736709316, 378247792, 331247023, 249333895, 348961621, 682840569, 34126502, 315700532, 72856849, 652810624, 662695314, 947654119, 892420703, 402734321, 973481297, 262645085, 901670079, 541369833, 781524862, 26287986, 847488235, 198506932, 756542168, 370540646, 90866626, 483428311, 755044935, 108660534, 670581529, 926586535, 253461644, 619838354, 722221975, 809142114, 710226723, 47801838, 48921733, 90289542, 585359222, 320841126, 959678946, 939928422, 415260132, 337139462, 778884017, 224999621, 5828161, 900130472, 747171630, 794726081, 378447249, 294773686, 512867789, 9273730, 450387647, 763864885, 80587959, 667725713, 822014127, 427072318, 863768187, 993261796, 679157876, 558856011, 224816823, 243350180, 412828452, 455492471, 806431699, 462747535, 38591367, 587570040, 825428805, 465856749, 459827856, 727915347, 87354187, 809716835, 25101241, 544602493, 318224914, 185851343, 882216779, 695197120, 388711205, 75664101, 677307818, 717934588, 542040860, 694102242, 825588608, 610350976, 167892085, 534065796, 408024754, 658132654, 369180727, 990904808, 334322104, 393648665, 774536392, 365547423, 662911796, 373977922, 238428683, 547340419, 787522244, 381847907, 148828060, 239365182, 900599044, 577241780, 666355672, 643514845, 104932402, 965227386, 627858291, 635100599, 710388632, 247094330, 144999007, 496165340, 75509098, 393807454, 489425162, 492335193, 373906443, 849679382, 978272287, 82736088, 697330226, 533745636, 624676015, 268060357, 259953855, 438424658, 21794482, 33054202, 861855384, 746464529, 396787019, 277967004, 827301024, 468583961, 817621180, 304518586, 584453155, 337661710, 70782571, 995277741, 844042172, 749043641, 177584711, 275638128, 820097884, 263141088, 963282371, 223003411, 460135221, 530262740, 729843152, 277998800, 441076884, 434746678, 627754166, 31746587, 355810291, 272881078, 238088808, 434244785, 440114008, 474891191, 278651577, 632522426, 90966191, 567574506, 835345810, 634067863, 89013316, 841054204, 300284974, 12610450, 54347857, 335295604, 955177984, 60477382, 738094173, 8511592, 267861202, 568977949, 782555886, 813391362, 622612687, 34989910, 900373451, 930477132, 744325536, 27312717, 110180198, 452631930, 625506622, 884880932, 669532860, 991636922, 864843772, 865989710, 302575388, 819427561, 39471331, 171181881, 963774660, 958808352, 559166975, 809704743, 406297510, 48113105, 10709460, 37010998, 808202679, 372122308, 18479159, 47009610, 414332774, 51326073, 484734100, 416589416, 805591882, 692526210, 813031245, 789646275, 892042591, 938671398, 732169101, 465388741, 543745275, 65133168, 62591848, 887854502, 965040958, 213207638, 659192885, 815769308, 643823515, 889420891, 138071985, 941365128, 176788381, 946379950, 16047902, 646476826, 379397383, 170442602, 771977719, 815374649, 323978153, 486775828, 760120380, 969888376, 771351304, 200034070, 975946002, 414607430, 696603478, 736815330, 631270672, 491285422, 672845324, 690727359, 575962458, 841257354, 938029154, 502302573, 47232312, 849863841, 97838212, 503280957, 836163247, 336434150, 670244886, 231896633, 930160990, 811628524, 455847351, 298023294, 310603334, 396591345, 114964124, 433665735, 191230677, 734323251, 825390858, 842163168, 635309758, 210995664, 171587067, 687015715, 111284748, 145450521, 395142051, 621308774, 934282032, 394444932, 947714979, 566851314, 331922541, 192902103, 35791284, 942480562, 722420988, 189556766, 132076627, 460104497, 774001110, 798699792, 346116223, 500916115, 475288466, 911097845, 406483956, 398658213, 940532410, 369806543, 607122474, 863056409, 776579987, 668633247, 173951958, 746416023, 852179098, 884037426, 41365597, 875984112, 981283089, 394440043, 110774421, 653138996, 915960716, 171668305, 29963977, 778895672, 869732510, 83802934, 457788176, 943793413, 278652132, 22547710, 632846888, 327104047, 61550435, 240639486, 809010043, 515833625, 219418196, 230817224, 661068976, 837693310, 105593796, 682402239, 252588509, 606700140, 450173431, 468254417, 478214465, 161762799, 333110613, 876218307, 640643801, 968597920, 492197706, 735661350, 960366346, 613691437, 228251188, 831508878, 117916025, 93533982, 890022696, 248091678, 488794655, 240425219, 229377606, 787858458, 337893355, 579380439, 135783476, 124602981, 378632906, 554130256, 306768669, 53783203, 248977175, 25765309, 273199936, 769878755, 381228679, 82585866, 13617401, 48870250, 623873106, 172152084, 794071683, 906878694, 596748018, 340145711, 51965141, 748805967, 29156173, 156147080, 466790759, 326076328, 750454984, 628749592, 805109512, 128600432, 87966224, 556839365, 714403006, 476090948, 325629474, 874923740, 754402904, 330451074, 840238478, 230906879, 121475924, 22965396, 318075684, 139188312, 134264620, 962145037, 810889333, 999664717, 495080238, 380901160, 14873888, 844091738, 12862184, 176619219, 358981385, 202898398, 314402497, 280053892, 918573112, 937847769, 146223422, 905932530, 254275309, 465507241, 583122162, 412243882, 535897676, 979382090, 188178283, 546805327, 980214939, 677814102, 805712305, 251127143, 873380065, 425051550, 929577324, 449732242, 414215658, 115044560, 209876386, 983409653, 157379717, 415835435, 182908938, 419398139, 171712634, 639996498, 779694343, 413640533, 719274956, 435572318, 916374460, 592004688, 746016066, 985593665, 183631920, 459183159, 684687028, 865211783, 363600925, 341962094, 437916009, 295570993, 926107576, 702417742, 332416185, 853882631, 696826478, 635460395, 919071685, 288646534, 579354045, 493160563, 703312815, 563978530, 362378436, 455059566, 302123239, 551908220, 581667454, 121575625, 677534337, 369133681, 97595996, 768201903, 400981769, 932529968, 677293794, 992633022, 650370266, 265148569, 859426669, 839354843, 307627803, 383460864, 195024268, 75746305, 788604383, 434760907, 209011696, 154469806, 288755805, 429675873, 590961118, 976458141, 517323041, 992718700, 252229161, 480217481, 22125964, 328789567, 611381297, 511464002, 450070164, 102743149, 84752319, 102244397, 909310761, 70008260, 726386628, 8930065, 809871151, 415585470, 934913727, 191958874, 323248104, 250978464, 828021491, 955543966, 806336125, 782671787, 814955936, 224400113, 740951951, 893960378, 963295724, 478265924, 187061102, 640161733, 516404532, 541058852, 107848943, 88114010, 903817202, 776233101, 99840255, 15608283, 823116246, 727334144, 776890412, 414235309, 284441588, 827200010, 8132541, 1889149, 313667458, 663189209, 731617268, 868620554, 553235324, 278789546, 104092994, 189171485, 992326918, 295901567, 979438423, 575050379, 253063158, 815363083, 123344178, 594457935, 914614830, 628643890, 968033151, 429977686, 575629983, 237016481, 420699111, 90897153, 989112663, 622833562, 497179019, 643348292, 802549704, 453581788, 189754165, 349378299, 571022588, 367795146, 599289419, 686045601, 580445975, 231810700, 67499522, 595151602, 833188096, 849750938, 298555496, 215346700, 761609014, 823593509, 705517136, 323903516, 527240214, 535306500, 580828105, 531704427, 168741436, 850727776, 331341569, 585529251, 170366334, 86885736, 673818317, 168381788, 652711355, 204457981, 520665726, 270132391, 766426995, 971752155, 507965075, 298505121, 690588185, 44893863, 932180021, 653891284, 369714035, 572055565, 345046505, 813294993, 788544867, 620600064, 733164805, 139100851, 966658376, 293486511, 525889037, 935850133, 299837452, 133328064, 38129194, 478473373, 35718017, 948656518, 650546962, 510618201, 440715660, 884081662, 315634878, 460559751, 366779061, 704891858, 794507884, 309268955, 509785984, 839508331, 348283666, 293135542, 604514839, 817973677, 714137296, 960947804, 46896418, 22815135, 614007247, 295215873, 6553938, 517592421, 542961791, 317706935, 845829861, 619555212, 464621881, 402428848, 69976301, 202046623, 564333294, 332875760, 14349164, 908217652, 114482922, 50644432, 218468915, 791072235, 448936181, 584102390, 174907776, 436932146, 194480567, 917050378, 134572969, 367556337, 244807059, 909384604, 368422838, 841274505, 702549276, 761429137, 215890965, 411155465, 721025600, 735862980, 770999425, 754033919, 870893538, 556338620, 278482083, 752619169, 444164650, 854908003, 598160708, 667743708, 729061515, 989516901, 825014768, 921826819, 799516822, 812762698, 214852986, 620461900, 869971667, 662550409, 577601286, 336553383, 839485361, 617432516, 827842993, 633417342, 354043727, 670684396, 63399594, 661221843, 175229187, 83227990, 650533811, 295058707, 796178499, 154628718, 873940848, 889669929, 772156321, 897849045, 31072958, 878202628, 350649092, 27219624, 181442155, 848564823, 489020160, 218236804, 883255437, 800860271, 525491312, 599127262, 902281259, 405505168, 42440692, 340349524, 601324565, 395325789, 68807301, 229902452, 872821805, 341466201, 16782445, 49039866, 960849375, 62863235, 591622128, 795029532, 739343348, 63929144, 276857275, 997366843, 83691421, 88778132, 941994078, 361866967, 423881130, 237844290, 678136033, 957956017, 611920934, 918376654, 904777732, 20643010, 701319938, 242547366, 614777907, 559886872, 381989125, 683007201, 54931969, 993550747, 625221727, 812857531, 83404540, 706248888, 760983237, 974612160, 500892444, 723762396, 393866907, 337348882, 955323514, 999887525, 140610140, 420939709, 801493926, 136797408, 547288414, 734862798, 985868293, 886074080, 86804592, 410548738, 792420786, 114031742, 719713081, 757688703, 475701821, 368000951, 581600583, 76427658, 955542578, 505260987, 572679556, 1880081, 955556056, 625376097, 357894472, 100083258, 361606809, 281049806, 385207071, 473386094, 485047466, 155065676, 458386627, 295315776, 230675754, 949889955, 76786339, 714091557, 851411350, 157778460, 246714929, 190238933, 705872446, 678418043, 875475253, 948466698, 841658047, 993921990, 143555326, 389150691, 332877812, 18852856, 412433860, 967299083, 44750778, 441158818, 682124971, 323863273, 411541626, 597871306, 149789263, 56592961, 457347271, 361838030, 597095221, 911072886, 943395909, 595285032, 15750916, 208770221, 379118132, 137618471, 326374187, 997899394, 247680269, 269959485, 787599564, 562933582, 959437074, 570072262, 716316951, 582905787, 260564454, 356738771, 233006062, 443432538, 555501732, 316270890, 458239566, 703141615, 352860678, 531494454, 694035889, 688264144, 707904865, 971067318, 506658965, 140225879, 563967039, 382010243, 27977662, 42080293, 46642449, 143270409, 494175467, 93526500, 662947735, 912026465, 807241989, 347369665, 642981916, 989785125, 652421633, 775846074, 865164585, 500349694, 104237840, 91353990, 36012196, 147126290, 65277588, 655913818, 350265093, 311685281, 585786496, 414146170, 963762506, 686782687, 870675617, 774684683, 217113329, 668055898, 567630772, 917569731, 93711244, 640135174, 978819037, 408094212, 426149422, 967013731, 740091464, 269010180, 938934236, 800711052, 315738085, 895349402, 575618809, 202123651, 810145307, 312032375, 613818651, 343931181, 399766007, 956253314, 187301877, 784577875, 570297697, 294458739, 188845270, 645898151, 741508067, 994600469, 21782098, 580005946, 980804918, 643865319, 801837394, 564809058, 81157706, 585254458, 459675257, 223000974, 742580424, 765034978, 744955354, 951826943, 749408749, 813941756, 191975918, 488962071, 8575810, 567578883, 678698983, 147537963, 145693312, 71319377, 100585756, 126139422, 150491861, 868090359, 281864217, 746107900, 704423641, 650130288, 721724918, 498108211, 259540353, 528022336, 22497318, 37906951, 778244897, 303663049, 898906997, 249538581, 563920856, 121627774, 476030136, 50148918, 618722700, 574042139, 389349113, 71006430, 116703301, 568998388, 884217382, 278715399, 932335224, 275233138, 852181515, 583431310, 602060669, 166493373, 277012698, 805021754, 721232478, 555316115, 813125580, 402050049, 217839946, 906029111, 415074046, 446585827, 586970903, 573219164, 661332828, 66525060, 687233014, 932110565, 438159, 572057460, 157768071, 715950248, 507845526, 627453463, 883032957, 504393184, 197050393, 891718758, 194165892, 432186948, 733280707, 404068614, 1709172, 860764399, 5148366, 724848856, 734607491, 677215036, 322677671, 143301455, 90068959, 641733304, 807403052, 398857762, 624219676, 796029024, 208134324, 582333135, 590090010, 896222722, 994323405, 275101997, 868055698, 199216492, 152714980, 944940648, 752500951, 176024901, 261127988, 361100049, 176721081, 344531376, 72866967, 59296316, 988325511, 91347430, 433535541, 869624796, 497005482, 62165488, 213090133, 127742951, 527632049, 50538673, 910700888, 649340341, 945618343, 525949178, 919305152, 551879330, 492339898, 368291375, 113453513, 629845817, 258737092, 72015780, 813048674, 384847827, 23396161, 985045371, 846730716, 377279147, 262696200, 290861828, 602716889, 604686755, 736329737, 717607998, 973522918, 281881968, 716734203, 105866459, 839198353, 81672533, 570282821, 805430656, 325037959, 14187227, 636356941, 939909676, 295049569, 438595025, 199027317, 126128725, 510159863, 312386971, 257783723, 33732381, 805850386, 573626254, 203776569, 909440655, 973242220, 870969879, 280282376, 576880465, 376119086, 607126586, 54262542, 785085271, 671710792, 308168229, 699380014, 626675748, 996569460, 893021990, 973709731, 493491601, 159451285, 162121314, 143065036, 464106217, 259770187, 959788837, 679426080, 788593101, 521865319, 462017685, 639349137, 644025213, 10841013, 925722184, 395650458, 107482552, 205016125, 973498906, 781451695, 165640182, 324843967, 924438777, 183684052, 587627572, 246648644, 576881121, 79248821, 192340389, 779505505, 737282734, 960934187, 181418593, 832800321, 391633124, 596178494, 309331068, 246865783, 932125576, 927623955, 667262585, 1935841, 456825319, 192409714, 110998672, 245940518, 443528644, 681480540, 598964852, 370996190, 272786700, 58925569, 688634194, 812216049, 532014023, 942529502, 240922132, 137107567, 173879911, 690740091, 145897827, 987647783, 435726355, 132149188, 804474410, 419656634, 898808858, 320209035, 821279425, 240594847, 444091537, 159295033, 350917217, 723692159, 918636128, 690419236, 353652549, 519620739, 807114831, 757392663, 196080064, 544606576, 126515777, 465990018, 304474011, 388560024, 553316265, 78027007, 459795656, 252604593, 569992563, 465238944, 853333860, 193158107, 212910653, 885692515, 504832220, 106743877, 889581021, 364480740, 3996190, 458682497, 376144421, 807686633, 469566097, 632641717, 590175602, 324135810, 121245160, 918570161, 229411798, 577782715, 983851497, 755405130, 630252776, 12762252, 390752330, 168384363, 812946448, 558129043, 622407966, 148773249, 69918728, 524456702, 146833132, 819322093, 170734357, 311386339, 390524893, 678097498, 859895242, 149416892, 36353569, 398487397, 636028455, 461815336, 784322596, 613049692, 727065957, 62155657, 871366035, 580729855, 221007468, 376468400, 828508807, 30924235, 251558176, 731288469, 694781288, 73575474, 193301905, 598982886, 565993529, 318918372, 486052832, 135326268, 633413403, 814663261, 230272333, 920355688, 460187934, 185961359, 321577692, 21440156, 111500140, 37925321, 781545171, 576631925, 109973668, 536320995, 22991234, 777735744, 503260722, 362489484, 129486993, 438981907, 493588937, 628752524, 243774361, 62233331, 957934411, 178400013, 997910131, 924233089, 6483827, 387132442, 706170500, 296965348, 941686106, 774729626, 505767628, 672896118, 537684855, 512534858, 258578604, 538505609, 906187124, 218675954, 575185832, 756832772, 671679194, 285244713, 416762208, 742588745, 707485219, 410995085, 16294995, 639014325, 709768977, 987952736, 30573038, 691502938, 232605205, 648337369, 128192503, 929754459, 74437226, 316256119, 252282840, 659007314, 752308051, 941171282, 253174528, 464557180, 274505891, 345749670, 290786504, 651057404, 651129293, 84456330, 606604760, 44245741, 83004648, 149714901, 212252324, 23778305, 431830116, 91657540, 946206470, 954467713, 873042990, 715112730, 759646576, 841550970, 809286308, 228681604, 275804629, 478733442, 735192797, 657912376, 319694632, 225719301, 792653703, 638504206, 14297761, 793634122, 999856267, 7295995, 806441945, 752093076, 336579929, 688390144, 418641422, 722039112, 801301997, 971963094, 414506591, 521653166, 184661365, 154274462, 143616134, 116437389, 649754795, 355110959, 2336542, 512729787, 530223661, 536755995, 773648073, 463228243, 626516806, 717320137, 787020568, 389407301, 444480506, 814241993, 987824013, 854698579, 760319849, 831379428, 515023388, 426910952, 277410256, 386639791, 61762587, 861858869, 980406759, 807273305, 694295377, 744678716, 636884098, 684485816, 578253501, 161734734, 237612955, 256495268, 310007263, 762669279, 31158012, 974624785, 20335412, 526839655, 73937357, 177108889, 287756333, 793705499, 597664209, 691673205, 197594617, 462833046, 320413248, 340360621, 230961078, 464616329, 766510947, 769414221, 569201388, 736161203, 900139588, 958139010, 888177993, 525240454, 229181186, 592276588, 363943864, 316162159, 683931078, 346002519, 370905085, 199950519, 944452918, 786885740, 415684506, 145763796, 191112048, 676409251, 337693099, 283690484, 16860168, 608170365, 985843515, 485053591, 148815573, 644965945, 512367112, 620707801, 593330275, 146627513, 134444288, 686678858, 62044510, 666205908, 958236429, 41813797, 492003065, 424357713, 906671434, 746858007, 55437609, 445560292, 709702398, 74662063, 191868486, 889088930, 545752488, 506046187, 669999823, 202678655, 57770031, 730789328, 723877858, 237151232, 537466581, 14890076, 913492945, 526567672, 978781191, 28731026, 256739534, 832077002, 706988456, 654643834, 124196213, 617960730, 783859637, 925202917, 259631387, 866529567, 736091111, 185807404, 485144014, 58240898, 521997172, 96345976, 875687815, 452905811, 692339728, 1771392, 306519447, 273341419, 874438585, 471810764, 537304038, 266473462, 585984650, 613506419, 512757869, 241809614, 421696409, 324906227, 587524199, 141781920, 160374296, 160160619, 308425831, 26382883, 602287959, 235907456, 868698634, 127562550, 168180296, 390659128, 155719244, 225084612, 543438055, 767575402, 604074972, 216167916, 942169591, 174410045, 61258936, 687834747, 303028272, 671719175, 281520829, 535122722, 418069513, 467795411, 836074608, 932508796, 614831178, 638773558, 895154567, 298796357, 622102451, 88026062, 64351753, 571786206, 368723945, 749972366, 804193204, 33913062, 513492667, 653923765, 793019029, 680271540, 84130108, 187814673, 345529235, 486224776, 68731105, 534140844, 93253577, 350076926, 837609825, 594168797, 355100458, 330673214, 568533015, 297150888, 908244979, 285042117, 848918537, 190453671, 350886286, 136752253, 727367905, 848029823, 634862148, 892317080, 464019027, 500164973, 834681333, 732794144, 763293064, 722790909, 59178612, 165797595, 408452116, 130127591, 200712973, 642207046, 872838913, 494083354, 776866346, 181431839, 617175622, 400063647, 968376480, 509540086, 83677139, 458022179, 484906370, 653969303, 914071878, 133779426, 908347670, 157763730, 336848052, 118493809, 769251885, 712149232, 730857150, 390060997, 414844005, 897182622, 509721337, 378800592, 500861772, 438177011, 46143200, 925185854, 649832118, 248885133, 159952500, 737986818, 594191365, 505426825, 898318960, 536327995, 789402176, 581792550, 332124362, 613778045, 266511109, 412227397, 601296740, 589656655, 219824325, 240955817, 991811079, 566556091, 448157401, 254373426, 959457873, 524632311, 325831673, 346989868, 488127763, 976362851, 441426880, 373684292, 517657835, 697642739, 376149252, 664769264, 213623883, 883137710, 552871739, 586310270, 565728301, 805888194, 538524453, 888855094, 788923625, 250342251, 15554433, 465127779, 871284977, 480705394, 842158178, 671177222, 516751731, 373904364, 311402506, 780863322, 458951854, 971987421, 453400163, 146258295, 254512205, 370801995, 755632722, 755268142, 774311182, 566118035, 519831301, 822280599, 75265589, 845306049, 255676800, 556185937, 612223842, 588132955, 690155632, 150153575, 27365200, 315501983, 725494863, 59688761, 600731531, 692738880, 802134567, 391695295, 172204672, 475920284, 827798885, 409626969, 715158804, 149377727, 331701974, 597707005, 5247636, 702756760, 519366914, 668375974, 182611525, 948871606, 976018906, 967624984, 689576711, 457036964, 89951903, 823169773, 132151349, 743808207, 191836130, 532602795, 90224748, 599485015, 124676649, 278875244, 599353127, 870196732, 908953516, 202409704, 312286198, 420904776, 359559687, 205815286, 444560053, 549239063, 147397210, 17841422, 218889978, 842416015, 497001114, 723684238, 95982422, 8354017, 514857908, 636479688, 612469165, 692897717, 365339805, 360766864, 267620755, 734619844, 735559411, 410579136, 249729923, 175592664, 889901648, 472999620, 851916723, 721417037, 389429806, 54701227, 829194423, 742634766, 612228605, 298022503, 634934126, 582026413, 234059157, 49143156, 454945832, 382010785, 429387857, 230909354, 655987640, 327249246, 540871731, 985921911, 253140794, 920993632, 613281847, 576507344, 352689696, 160461992, 889968354, 487757697, 612247143, 390425795, 641629984, 600053079, 673930306, 410703647, 788728718, 524537597, 247649967, 707337496, 174862991, 263042568, 877392734, 921069759, 529346212, 798915350, 905481733, 332237332, 41367280, 734154323, 788562583, 416605508, 589307751, 661464935, 890557166, 4511581, 182285219, 411477560, 464238404, 375885763, 710261732, 438379274, 213379163, 840697802, 298464897, 583244265, 856923728, 607586512, 203371691, 63326311, 314013626, 868707774, 952768120, 381495488, 227485859, 753066815, 877136745, 24527367, 310793455, 156643423, 81496687, 771116326, 492208002, 513928635, 364780306, 798371846, 366701245, 539502986, 324952141, 194318502, 810024194, 394688006, 862002165, 791724752, 488094998, 4829209, 887703245, 134001726, 213105485, 304472952, 365448652, 821397809, 243153278, 890320934, 719790091, 295124973, 348698912, 97616234, 830926388, 870288045, 601695075, 944298204, 2838524, 58908133, 306986918, 996958935, 265965394, 835917535, 87053197, 360689714, 873550770, 98244563, 981073979, 701178289, 775269899, 461170862, 776601819, 836875644, 84501465, 719309232, 332997101, 611187862, 137713876, 206373938, 850807769, 178821812, 264356103, 98756345, 131557329, 433256711, 312645399, 80722125, 279563077, 576283301, 618776306, 648932114, 183614756, 571400002, 322743438, 402602329, 502626556, 86139102, 16161485, 133570512, 855547929, 631143158, 725692022, 212656733, 739997988, 875671298, 961845591, 906236791, 97475956, 519962358, 221492850, 39077844, 119927089, 484980968, 880102060, 526694905, 127415747, 897990930, 501479682, 27108898, 207915205, 282188993, 846864650, 445028351, 377473055, 891656144, 468587632, 817853499, 964649186, 83106895, 610305391, 71153501, 922296616, 631101094, 651190324, 190683674, 995320864, 739628743, 705201714, 379940709, 92103366, 360756610, 417820404, 516340298, 812084621, 450320941, 958094100, 426293261, 989640267, 518635420, 344699896, 217447693, 364745159, 823806256, 514192650, 599952515, 179181541, 839878930, 189673100, 10138778, 464349919, 238118280, 544098974, 161076383, 608530744, 988766717, 787230487, 187568018, 788824346, 592357387, 870697567, 326890649, 203257174, 840256502, 420949778, 65366324, 18726784, 538326910, 127679756, 121538426, 676906267, 152545856, 730434149, 673412366, 229439742, 340784897, 836369040, 444345334, 414677870, 561864495, 750548128, 45609383, 41785322, 937259288, 844234060, 55150590, 334392896, 730783083, 295413139, 102335884, 207855526, 264925758, 649663928, 479669231, 518615215, 176023566, 402360127, 548716438, 419252197, 127926036, 725260335, 860197855, 382857026, 19639238, 875856319, 930779118, 556414216, 294932608, 767699470, 715449833, 947883629, 779601017, 980240690, 655549797, 204653543, 584282038, 100641757, 173763809, 715456322, 397364756, 184826948, 285014919, 193382889, 857400879, 403905887, 652621619, 933204725, 497984193, 375444510, 773673722, 571061782, 639583485, 81699934, 95135494, 535660654, 867799407, 899579264, 277731882, 891329600, 932191948, 78492934, 845151810, 155779450, 196877912, 724512259, 832356582, 738508195, 277214997, 64245370, 183583929, 33876711, 587429397, 821827741, 459688744, 536406323, 281989382, 26579463, 902706730, 767072482, 163220933, 366291606, 77350376, 371376936, 684407032, 92393654, 882910882, 959733119, 964108314, 129151454, 120526849, 864344647, 597559025, 2325089, 528440978, 405090366, 698506819, 508913741, 880615144, 560685357, 447772076, 841567562, 528725059, 865560795, 359553110, 56021873, 225357088, 140291257, 66847947, 582490779, 63002829, 271735944, 514623948, 519994549, 894584907, 231692245, 518207131, 889452865, 148612524, 856397488, 556795537, 973110387, 270452570, 27763201, 918759212, 485407663, 537493362, 920441521, 927490951, 371545223, 840692055, 492771006, 803319982, 161983317, 571360634, 673468603, 736500827, 19252079, 99448104, 855213456, 684564928, 208908833, 169054256, 309713554, 936524882, 936306717, 173402544, 802764769, 684710843, 55940702, 990981232, 14743186, 23804486, 499858268, 57658474, 333827928, 557042438, 957177321, 765709101, 64625784, 847048000, 816237086, 302287655, 885824095, 896512056, 323788104, 36801912, 365999286, 745809261, 295286055, 371469877, 655138859, 181136929, 410408326, 754072177, 892759739, 9258495, 507025679, 729219919, 238162985, 974515700, 636349799, 36516011, 35342115, 500263894, 461161449, 139617791, 998678857, 337309190, 337207014, 8936616, 251149063, 442499058, 441474055, 85232778, 820300485, 729749047, 94376453, 125392103, 425927842, 93901954, 176269209, 415651264, 250430247, 122995152, 327453157, 252353904, 717465821, 627284531, 878329112, 83803592, 94168037, 938606031, 353051810, 543473928, 725664113, 205119137, 461206966, 456061460, 375712170, 670920333, 403768884, 608547114, 467454605, 113911885, 647829358, 69553203, 399929076, 977306098, 879676986, 29663927, 880786007, 713338776, 129252590, 2343793, 138156540, 521683851, 489163101, 894693981, 535880491, 429176001, 864551759, 559788534, 256521528, 972789700, 981526272, 667176545, 499093633, 130483252, 610365345, 666603083, 884360963, 673800212, 653891098, 435858848, 214693735, 249857604, 41880834, 854961773, 425792374, 263744462, 69883056, 864997978, 235915575, 874596987, 549091674, 73304342, 480723689, 934868056, 700955024, 842975461, 656222499, 489448846, 651538463, 610823701, 111129487, 930800426, 690327670, 471745287, 787206015, 171428460, 276035870, 823029622, 309923914, 910562892, 214198661, 194327125, 395743316, 294379922, 520906223, 41032589, 98218936, 183741072, 692202828, 404112154, 361639487, 919320628, 402439405, 440721501, 903573892, 998817898, 931605854, 583214122, 235966550, 703982598, 692249827, 451466118, 19361831, 423975098, 244150373, 898341039, 225080841, 443372008, 5717787, 39866530, 805269137, 445693501, 379876676, 919449617, 992499986, 173441897, 903387139, 839815970, 714931906, 928994965, 72628924, 640827115, 402479941, 260679674, 45393352, 724852247, 373421945, 895245659, 668790237, 476946160, 576595537, 618347943, 51402887, 223027424, 821775490, 618786999, 39343872, 388046565, 587697251, 82791816, 226139118, 710467798, 720339492, 72871237, 256676182, 923763350, 970788003, 593769184, 619722326, 85928439, 986679131, 343631991, 523991643, 282431765, 491777352, 856026124, 689182188, 712075240, 909245841, 407715189, 543192090, 195174081, 358921289, 256344001, 848282376, 704523246, 839970445, 435693776, 131523028, 47099300, 377334804, 13188979, 374952454, 696557433, 660665833, 810875565, 706024573, 125603141, 260320524, 456905514, 649860205, 63730584, 499317530, 579584292, 310610305, 675344924, 29875350, 518513977, 489775140, 343736924, 398112995, 417612318, 670960891, 352924219, 536346597, 723176813, 581803731, 95290714, 443898974, 932443991, 606593824, 589070057, 12883098, 9997912, 969976834, 591834126, 539952778, 635371460, 552595130, 938250591, 157858650, 877926464, 704961236, 600713088, 249359122, 347269494, 357328560, 630070548, 585674060, 93181009, 305052703, 480386090, 312226164, 150983080, 213256738, 663406884, 13250122, 748409109, 223313651, 835224313, 509733495, 533432454, 904453904, 287208613, 652021505, 127689201, 902488867, 796208028, 901661034, 451022754, 640528916, 869093012, 677023367, 376311315, 289612822, 699644561, 587632458, 880794543, 570372608, 842345585, 433269712, 75391473, 154370509, 977954268, 259749715, 329605221, 54975581, 979949685, 962681629, 722931629, 698990709, 659803294, 410876451, 236991610, 286108964, 988015968, 579263550, 600198469, 352233925, 619791351, 809497313, 723268530, 667205986, 505574561, 422395968, 473678343, 2618772, 111496407, 898333899, 938645154, 722728083, 88617753, 358866608, 174356375, 523359374, 682314968, 812736650, 382136656, 835251463, 372185700, 227853714, 193053339, 515934976, 69732367, 301617296, 572385545, 401575989, 2294265, 737486292, 484491830, 521036527, 675304381, 194831501, 789263412, 980776379, 543505264, 45653299, 43221231, 883169955, 257091989, 437069085, 199850079, 299883122, 797538256, 467792138, 784867678, 147675644, 785384443, 464295015, 199682165, 633667362, 343256494, 614996900, 280929975, 15374265, 234180959, 25826286, 931991764, 167762382, 125432545, 11774318, 28678928, 499801697, 696729529, 488378104, 377646822, 920229100, 493676124, 145930727, 59744823, 25680677, 589888452, 941909058, 702354002, 751192963, 333310023, 182429621, 628187958, 859119678, 505230968, 846124106, 353936886, 491249947, 957435506, 588876526, 667459739, 591531018, 267981804, 343333736, 165479920, 407877715, 186522456, 71424610, 91082199, 523475223, 53552718, 987493791, 963597440, 272883182, 596316037, 492564680, 377361455, 414810695, 120499637, 368428653, 274628184, 903046512, 939827633, 480244893, 485553539, 226059972, 856839041, 898484587, 417769184, 403015253, 639510471, 929781597, 279343597, 454239802, 34193364, 656888393, 747013666, 616862193, 437037838, 890894003, 532525378, 664154629, 577923877, 419814478, 460412966, 50482910, 788237267, 623021749, 947030299, 647476819, 631529780, 998457045, 408196886, 268030138, 361271589, 493554433, 614985282, 523526624, 462388192, 129378932, 474571093, 857194926, 491031489, 88463643, 265098533, 398063521, 820656776, 656929649, 934100143, 368835966, 76954013, 33172832, 551620180, 964383603, 37702960, 841047411, 369298375, 540732811, 740530804, 115727540, 12327410, 299629090, 773659246, 565366036, 472233273, 91439131, 398255646, 43896713, 610213457, 408336739, 729630941, 870984049, 225483882, 54879221, 990417587, 418900776, 509723392, 874825167, 255673019, 699923303, 272163674, 137291683, 349913071, 401314692, 918689511, 117584311, 774644802, 52151368, 149929074, 836382182, 773104296, 359290595, 154807351, 853818189, 818155449, 725696057, 806808547, 85945075, 875941350, 158961379, 514890991, 895525926, 370265061, 176998479, 544075736, 111063243, 539296455, 847064143, 88924344, 903309550, 983886064, 195376541, 870208097, 507882215, 316430623, 289903141, 360920837, 99702958, 917989972, 732627418, 45131458, 948231811, 5975589, 173553600, 863841788, 110706355, 738997573, 841172935, 646643952, 592630171, 674650275, 707426910, 85498765, 328506812, 118948212, 302273152, 183490299, 131892184, 709081640, 419045924, 517387527, 378972783, 554795530, 777033878, 754143677, 900681105, 878510993, 914745977, 631747687, 293558810, 643135792, 357053313, 437417920, 841448495, 176404081, 782623794, 435765034, 864437660, 393195282, 777840052, 409701319, 352483832, 191536007, 928607057, 722899634, 967398698, 389661321, 322474973, 572496365, 825155445, 393953075, 443164399, 305530363, 24116117, 531897807, 764128421, 112995744, 406325075, 366697522, 656883410, 222505706, 12746672, 811279362, 107789942, 919028444, 921356861, 820556442, 331299560, 912525664, 397625803, 266038982, 788212719, 615873799, 895263325, 822569978, 358086679, 13411423, 130502809, 27457381, 39097756, 319480702, 369667693, 877074578, 643764663, 382810554, 992698853, 165459882, 539555009, 53617565, 144150991, 132360266, 408902805, 161698726, 452353756, 954747322, 744617304, 415137447, 967001135, 802788613, 585703216, 456015463, 632028539, 723677219, 387568939, 698159824, 532824282, 549871874, 863561420, 975780517, 710295000, 991273443, 263575879, 438662587, 982524373, 489304339, 164614518, 846473896, 828987125, 958767933, 311895492, 947383090, 755311456, 913901135, 537617157, 878926387, 579189548, 638890658, 678458501, 475778263, 819525620, 139408182, 631024563, 743452645, 741731520, 836189391, 970134383, 638896719, 904460586, 483340371, 141999462, 579040050, 380253728, 994590094, 572999102, 968908980, 843589653, 314704300, 338509050, 970247105, 181392165, 178208966, 65969920, 672350878, 819581416, 970697566, 33322247, 987200701, 845302361, 427035892, 850160640, 438216972, 640602603, 469087482, 949489800, 701264781, 627859430, 981034739, 492623530, 267133738, 827046430, 694562924, 512154082, 307020553, 572792806, 815181985, 737203185, 75970187, 76010293, 197304969, 209683904, 229395786, 938843866, 76795716, 332628395, 672580662, 943962119, 307747611, 648862489, 780140679, 546482706, 672114176, 906295356, 438197194, 449173706, 321801242, 874026543, 390491358, 837540119, 342558211, 268449283, 507042684, 202693938, 9066281, 423770205, 630239056, 515651442, 539679236, 74677779, 807455026, 133847856, 883759264, 378729053, 376956352, 232514674, 403657262, 667288456, 695631944, 833839000, 386125524, 851991705, 971733644, 373235409, 824815027, 21059224, 794462101, 763016785, 873863147, 89004160, 212134658, 727190646, 428467583, 537491449, 151071070, 721769905, 912434426, 674706931, 5692172, 890289559, 878762416, 957871034, 772379641, 205635005, 115562386, 283557485, 711504519, 89278997, 839968171, 154147873, 371418567, 663380923, 728219480, 681110338, 166071219, 443162123, 846684542, 719713404, 868930306, 181321494, 87333910, 993023640, 689177814, 164849761, 229447487, 553040685, 565469089, 503250571, 128317815, 767962413, 258010480, 974352974, 154778476, 135951485, 816950094, 678714207, 351835075, 520953896, 624087702, 657801304, 912974940, 251339188, 986631943, 812158992, 13740311, 657019699, 618360959, 867356827, 601661946, 793594330, 178428992, 161998299, 216406065, 694923333, 49438865, 990291935, 509148138, 115844003, 630127421, 532492345, 846714384, 447651101, 496811116, 478033995, 949151567, 250091934, 540915063, 719603462, 606028696, 773167810, 413016499, 131067940, 906662044, 784437211, 165972551, 126498026, 730138771, 8261135, 76089380, 486299236, 354532166, 16037735, 697192029, 816757803, 960099152, 29901659, 575118012, 253060884, 919012580, 594436573, 829251935, 469035056, 161293866, 657450636, 430913806, 314293731, 150289542, 795576845, 758006778, 68003623, 917745020, 256918708, 563424214, 231468468, 469380715, 716292121, 357221791, 646402652, 994121168, 518546581, 221475260, 562775621, 32522520, 291304291, 996021564, 799234554, 268958415, 724125817, 900231164, 419941101, 587466772, 207863204, 4128356, 105052830, 234036726, 857751928, 330046185, 46756661, 497660006, 564196851, 433798804, 111388607, 110001759, 131505138, 241189800, 792076622, 118264502, 474528676, 968444727, 796218661, 442775428, 367799575, 400414636, 738256013, 399032936, 95880832, 58834186, 786452165, 740152682, 620169133, 524667053, 692584535, 981692229, 552088608, 888414738, 581395061, 466449417, 514611425, 687208699, 286283603, 596207508, 916187857, 408926108, 919261489, 315351705, 378855918, 410222324, 830369205, 323173341, 95585561, 855297490, 87701193, 765842198, 442402948, 621082904, 277240910, 711792064, 3947785, 133423134, 891366793, 133213052, 363043444, 93640413, 246125464, 723251303, 779008026, 245419594, 669433851, 917670855, 917469074, 672277988, 657711858, 384787816, 45660429, 17553455, 744956052, 957045787, 466676967, 683205679, 721947801, 683828822, 291840346, 612378543, 933404052, 345402397, 888145868, 714861998, 257118267, 275470006, 587584486, 190470237, 223642626, 900717637, 564767362, 494575592, 131163760, 925601722, 413268683, 292586476, 56394416, 833073186, 305069260, 468404833, 141427710, 275945289, 307696055, 710659153, 997408465, 487050908, 629294772, 795656416, 481782322, 430654987, 141327789, 198114839, 315952264, 376806055, 198364674, 87510827, 844247625, 999893816, 693858280, 266405016, 685056097, 476398661, 8403550, 792612318, 328854920, 50520483, 605401824, 333059196, 331690885, 468653162, 275396323, 353499338, 987339763, 786571483, 804576794, 518915749, 731370244, 92333643, 73645554, 196114684, 190498456, 11152309, 223563610, 964940860, 359892050, 249351704, 540021460, 164120359, 541535035, 202506563, 503025927, 230913366, 161234535, 698676317, 898735814, 128898853, 945146739, 296937014, 136930700, 516316283, 750501850, 739440115, 92385198, 816790890, 37359368, 57357961, 560142102, 682311707, 71767951, 770786303, 131478374, 666312391, 197399420, 508129834, 265021213, 265929477, 158476067, 965848737, 852982880, 24346489, 83835622, 702431000, 140731154, 728583433, 848122024, 42822975, 236412835, 127589923, 986462906, 871669998, 512076163, 420378621, 19318063, 776338151, 42932228, 561058723, 458785974, 892617809, 940989152, 159518319, 55441098, 728881507, 609897929, 601220660, 801604467, 980120705, 187654980, 409735043, 895327450, 362473826, 144610335, 191151840, 542034392, 281475527, 443127209, 25313581, 403591852, 4998600, 814473319, 474361403, 279186513, 246058333, 414366938, 761160369, 296333322, 247678578, 899908528, 68397979, 672693834, 525211449, 972832784, 73369804, 199525754, 192903441, 943880814, 3032743, 467352031, 746959959, 982237962, 163736345, 337743714, 1575345, 401865441, 798692489, 585210627, 981885409, 13703448, 483040832, 380022861, 930648367, 933247249, 811697070, 769366818, 925095141, 850881699, 33998833, 812504313, 434515516, 525952801, 61162688, 441886866, 848854240, 509380772, 918428943, 796673875, 184843378, 96189754, 857034956, 812366312, 702078460, 541579421, 61493883, 768560206, 822813381, 980900947, 115721082, 718863257, 684632622, 713181074, 588602398, 766105878, 700167421, 452809580, 868953833, 169029859, 836457760, 504111812, 95872149, 128434321, 63817115, 545521463, 718927862, 806622202, 277268344, 241415758, 252780424, 48142844, 936865670, 724512127, 291572774, 162145195, 273765227, 841889579, 185560948, 440113137, 230616149, 841264995, 288075310, 578013418, 758441329, 519454302, 436987240, 844836295, 264832209, 812985390, 846292806, 394518142, 348973247, 360104409, 669536055, 876096774, 932465938, 74700793, 134930439, 577139781, 988588106, 241622432, 506697348, 969164017, 28924576, 917701625, 919509033, 174785391, 207975062, 966774708, 49451431, 533874769, 336018906, 63335597, 220692475, 10277779, 137704696, 841398327, 812332744, 2538307, 139396617, 66321398, 432815322, 213707353, 77348425, 368421590, 283531904, 352111639, 647111252, 298558675, 16597579, 624534301, 62344657, 530099869, 308384456, 680761246, 98552510, 394338147, 460740897, 897714941, 225337029, 587035696, 560083095, 850421309, 945666927, 859244528, 94749904, 885934563, 529561981, 819095083, 37138274, 329751971, 970915640, 877093036, 229827899, 29349447, 865461062, 5562048, 870847215, 267797325, 655465315, 163008749, 731796265, 146444274, 89321290, 366922142, 316578891, 252251936, 788410748, 667729832, 200799669, 305178243, 489280635, 223020463, 555711042, 725620931, 630678766, 194952975, 371882761, 325822875, 164835306, 321365624, 4696613, 47055443, 553843452, 322696408, 798886301, 982848001, 230399098, 869603347, 938614479, 766435168, 783909785, 299014480, 147432547, 958890122, 667353842, 520093357, 844795961, 478730112, 881366995, 213029755, 362071249, 940396157, 659528386, 49537646, 750106248, 379073144, 551518420, 838561140, 780696686, 201860695, 498573007, 886171087, 89882792, 669439041, 889852666, 340082834, 561315536, 100307817, 863181298, 707025911, 673846944, 168309030, 771453180, 9133166, 978142315, 683981551, 874483875, 441721334, 479337942, 571889810, 693971431, 491142174, 84523777, 995195076, 893856479, 742879722, 945974800, 335422033, 516359552, 570553441, 934136296, 709754778, 534888962, 981468002, 324695348, 547216780, 87385342, 269323421, 516482251, 247996726, 747341886, 647086344, 756219876, 674793002, 567216641, 488524473, 999455875, 664626322, 481454134, 253835163, 347484149, 980783510, 431595097, 44241714, 159681053, 369801472, 63065345, 547143090, 392152911, 245741074, 464638167, 652936042, 469475983, 153851556, 788437707, 26183251, 738119285, 829186848, 362396552, 807606498, 408332541, 104717376, 10126100, 371423684, 114925605, 737142129, 681808245, 547890635, 748982901, 829944870, 60685221, 766388111, 289945203, 4905966, 912738308, 678008996, 98598288, 82083476, 535092435, 845483854, 439507678, 566148456, 112834742, 430087177, 471268101, 383543732, 290781562, 889258925, 846628335, 547651327, 396046703, 485092737, 634687725, 671497720, 849587886, 121640019, 102890954, 974236192, 27817075, 862694814, 79852123, 385794647, 333432372, 135888585, 879056425, 566937903, 355939601, 784838386, 515733474, 619274434, 248135564, 280614798, 888286016, 409042012, 740765221, 946255696, 831015025, 942790425, 4620438, 129804195, 697878431, 698101266, 415004912, 124512864, 648271875, 290321858, 494280647, 269916465, 186523315, 692153961, 866044259, 456565545, 867703162, 903711912, 693683649, 887798699, 374794141, 961439707, 987572024, 324103, 469579076, 208694146, 699096753, 475012066, 928100761, 440834117, 834654794, 269716503, 639695861, 796648501, 532009533, 278773625, 372722949, 129440253, 856487985, 1904118, 19499975, 50849331, 200602327, 914201026, 843431277, 4422622, 627598265, 885563942, 630305235, 319966781, 311584711, 293493198, 345009835, 928911903, 243394949, 195544504, 536169822, 593715124, 57769865, 970039359, 871459038, 220620954, 844684604, 137858476, 184583026, 71890200, 268671105, 443022747, 786649143, 90751148, 915044461, 520736457, 596810973, 103321764, 777446607, 267764825, 165915815, 972010221, 587145602, 679254225, 687126563, 935117418, 631456730, 592466370, 671178158, 156493515, 826803522, 664970071, 995696784, 645118596, 375029570, 52841348, 277758920, 984226480, 125674742, 732163821, 680701020, 918195239, 33051804, 361506341, 580325942, 557075056, 269628418, 707226206, 616211791, 77735845, 219921236, 247037390, 453772529, 255134613, 104632581, 674872186, 259492533, 674000299, 7063990, 101256548, 435865749, 896524302, 550873563, 50026765, 746590892, 571272371, 134361171, 731122020, 506824308, 160421953, 290547488, 491553619, 446368077, 541515801, 664744807, 959286155, 673516598, 376088256, 656047823, 486260335, 381963470, 830401065, 577180301, 770581081, 21677998, 274390091, 943037993, 433444622, 152644915, 78778498, 263270046, 711652546, 814903530, 815193959, 631145673, 489286607, 758402103, 162194413, 996080405, 44179469, 863623448, 778649769, 947265028, 773903368, 326770950, 648170896, 692720037, 412530596, 889138348, 961340348, 74072619, 78201465, 133734761, 151339974, 799578501, 681139946, 529721677, 845926684, 884311353, 973259070, 357603567, 366256590, 555471590, 684565719, 836737538, 929858618, 537530198, 353542685, 330278017, 79967226, 565347351, 918332528, 988720613, 176507082, 395429302, 287483779, 495252357, 608236651, 727604882, 294500618, 699659325, 855392600, 577649118, 612447287, 476219667, 991373902, 812162823, 453589620, 239419779, 897971518, 483495950, 938617313, 485461633, 205797988, 102827077, 709944140, 97960623, 673633091, 266070189, 547962296, 568435826, 443094678, 184669243, 125913964, 464358971, 352923333, 902505092, 941206942, 869051165, 246348126, 372691047, 802470916, 325585291, 701296239, 352652075, 236245547, 903302297, 31989297, 45749676, 720269239, 637031435, 145373404, 217215200, 723787358, 244199174, 260335747, 740128985, 879242821, 70294168, 821334495, 479230240, 930383370, 70817972, 200546940, 619930199, 489087810, 54349688, 139088378, 563247699, 263066024, 743094435, 370932430, 447504066, 153844238, 638488801, 601985491, 453636076, 499313842, 34760929, 9485195, 243162735, 778652543, 715967737, 714965281, 489122109, 188559721, 637660068, 238628709, 271235655, 942971853, 947652994, 999410192, 540414868, 626107828, 226048171, 182367621, 104517092, 611980698, 709709167, 684769299, 954232006, 653948574, 486955208, 681747572, 496570812, 659043641, 825267398, 83372392, 371922306, 79585534, 861097570, 70930214, 523036654, 14823773, 792703220, 509376247, 453620331, 911252367, 655600430, 893445629, 599287572, 659818844, 204428856, 843758251, 473863005, 735866181, 636465606, 933822225, 811334133, 27901594, 66485855, 977481244, 652946394, 730819628, 935053353, 199370286, 293573328, 459524247, 482492634, 291551448, 402902043, 948297237, 349971513, 782899633, 701584495, 327068310, 786716092, 289467382, 526340015, 914305513, 894130414, 268685684, 135873222, 854887437, 354118229, 990617597, 674850424, 592523892, 158508561, 705495007, 521342146, 673270692, 211190367, 870459775, 440193048, 99972808, 508863118, 206205938, 378875840, 310029102, 986611476, 656467878, 354980920, 889649754, 983443023, 651067233, 619042050, 13242676, 178356902, 661629994, 825710339, 139529742, 959638333, 85354561, 321537511, 767570911, 804976772, 672881542, 889104338, 595656976, 401613620, 390669817, 881343300, 382620817, 699897178, 562805837, 983615912, 879676898, 706659868, 375778604, 324491915, 715017660, 122427005, 625820835, 236527259, 660194331, 38856314, 996199754, 743886795, 407452556, 996510941, 109479318, 785138777, 245336509, 526305054, 523556764, 52747388, 928147564, 36156849, 280019977, 506076456, 876409002, 214872899, 841307054, 389393672, 307670226, 374083815, 483879524, 942380015, 360287770, 411166558, 552532444, 20362631, 763842364, 629270137, 642602782, 628232986, 687042667, 182317496, 500976760, 588810855, 721686709, 941437960, 280577135, 508451954, 409772085, 548620504, 291083189, 740035663, 912091655, 936515601, 162048973, 83015523, 408447938, 576831116, 889297826, 220772000, 675569001, 502102036, 479374478, 202654480, 187374782, 513094434, 203368758, 895059619, 768584939, 628030998, 933676235, 47381206, 487083888, 378386982, 495332950, 640577408, 630137005, 689021145, 325689118, 237560173, 671836236, 265247132, 90181613, 33484661, 574700895, 313854348, 660264463, 209792787, 333717051, 812928064, 934427838, 618482205, 577300073, 522770707, 438756281, 171711171, 351665106, 525416930, 97107745, 47097081, 618515390, 186604942, 109941126, 374819782, 205754748, 613970699, 573023482, 701288562, 86111714, 235752642, 82506274, 46217516, 428263566, 613565717, 192238089, 153619499, 637049695, 127309069, 720976269, 546728774, 62890546, 474843172, 679456166, 240624002, 113682884, 63931679, 133203869, 338525581, 7615614, 958139544, 753357455, 99931652, 605335603, 721440483, 328484290, 664157575, 774127958, 108342084, 422677449, 392124925, 794889428, 158650533, 503446483, 508683553, 963497342, 26558303, 168135536, 29484000, 76939759, 908451157, 238847561, 770599539, 28977670, 528043483, 456786532, 241847401, 629990996, 260246871, 221874582, 497671631, 250025917, 114007840, 370290898, 652842334, 886995709, 624983670, 653614605, 65200106, 5726389, 707626096, 147647527, 568770130, 276441894, 683979691, 753328558, 896269060, 86312901, 533710485, 306798283, 843905846, 525855472, 477404927, 180988372, 168638268, 595099235, 269852184, 825172693, 125045031, 806892293, 685502283, 177114102, 264825941, 484888652, 618335741, 765412424, 842665153, 318094454, 766082442, 127033181, 325845334, 319369632, 187577220, 163831444, 443773665, 24772454, 710353326, 752981125, 808402389, 809661972, 528881574, 945420558, 239635094, 192678854, 435382136, 31206453, 178433992, 50409089, 312497856, 653544561, 370507032, 712664094, 187057659, 373560224, 837692852, 227654693, 925838144, 325824874, 633089236, 214642040, 50773784, 770647372, 765067748, 586793305, 213673073, 510654749, 537130068, 151618294, 536948683, 417625595, 6668351, 231864618, 765570071, 423646274, 260353763, 702258501, 511117411, 637025251, 933900151, 14257946, 428882242, 563610598, 215689215, 525076951, 723939898, 357152512, 67639477, 133322456, 343167214, 306685626, 549873695, 757095556, 774656522, 86054106, 51371040, 878879588, 241943292, 831133542, 265940589, 435898247, 978697468, 149987882, 883988926, 681563322, 896541571, 102707236, 776278973, 717700952, 838445720, 584417945, 806331456, 428231910, 115177245, 462036209, 857219544, 118524332, 857008204, 774548365, 755632978, 666855244, 274715876, 414452278, 43689051, 739316877, 809608195, 637278213, 322399029, 168753214, 785234172, 888313027, 503295764, 289295722, 68192958, 704521501, 489356131, 512859860, 815194307, 963807323, 475839098, 259729792, 200073511, 740678317, 702387174, 957703704, 734975559, 795062619, 747651610, 251198478, 146416112, 792891051, 113907425, 634647452, 638614028, 519305424, 5347193, 269175041, 769396972, 18633872, 328228960, 324249051, 639584650, 194262913, 365580245, 58675816, 777933203, 106195375, 905603572, 74583354, 489229336, 332773212, 41026033, 815540976, 316976500, 995861551, 465452503, 704399048, 860459309, 701295233, 768289746, 702787946, 317107676, 128507029, 845662511, 264594787, 936795572, 105416006, 603821817, 411904995, 680534808, 20844794, 391683293, 902451025, 479221704, 751864121, 32067785, 590846770, 412550280, 686389294, 979586319, 567781757, 125435511, 334589965, 818387069, 274365856, 818335600, 688388211, 995735525, 397678180, 475936837, 930646328, 59314877, 911653594, 303419082, 826485027, 227600587, 489399108, 183170796, 873825702, 338318533, 69772286, 260125053, 409150425, 385980619, 187450750, 883459971, 547869531, 966562583, 105331657, 849724494, 353682615, 830000048, 385904783, 305355730, 153652834, 30975478, 617977000, 920676101, 863552030, 864582615, 550486779, 767263383, 572489480, 647875999, 363383985, 687913224, 944341654, 163537293, 716825758, 629235568, 889898943, 995999775, 324188567, 187194520, 63353177, 574119970, 919220142, 356257980, 280451809, 595949319, 400426142, 641482758, 262031, 521586065, 69543994, 398250529, 342254279, 80679661, 645748250, 854888531, 997296650, 754489902, 707492135, 164100814, 79763541, 784973948, 451324267, 542168073, 238606515, 76917255, 779595350, 708271785, 665050774, 359801426, 997013986, 87465508, 105306260, 237670398, 668148548, 681552733, 42805663, 294205161, 712202382, 151268837, 475041200, 464370666, 740936305, 262047680, 201617776, 197632205, 804121146, 984446865, 681009902, 522144762, 388662524, 86529350, 415205538, 111742467, 51407974, 553573153, 397976056, 657043924, 76668010, 509892480, 864115412, 893568252, 868452415, 945431449, 396820033, 569165452, 813741397, 421953957, 216408679, 225479506, 357777648, 96450575, 478594017, 342907012, 311835031, 520906139, 733385171, 991949201, 936291492, 242647665, 530531462, 62340474, 794373860, 246521862, 199545098, 606433912, 731336344, 737943073, 772098615, 112747362, 259707167, 67197268, 264073453, 776437029, 69315328, 279980333, 935520695, 599409565, 355052057, 976635953, 16870860, 247878215, 183742255, 885231733, 910850248, 381268519, 510287517, 704491140, 895310915, 243018923, 693314473, 808734189, 420582935, 666339221, 466947493, 590471918, 998806089, 396645822, 148402610, 347013090, 372464149, 179564886, 131732198, 998378343, 508776184, 861649268, 571612191, 558061666, 905568948, 559365812, 390762998, 575667928, 451848386, 125591147, 440797383, 193865619, 834437307, 939217988, 826191316, 301045527, 62180104, 845602327, 231443918, 322378828, 500759974, 778720117, 896705337, 660411899, 689998085, 763302598, 929403168, 691488234, 618145269, 74887455, 586898694, 927914231, 19484441, 608688259, 844197614, 356028569, 132898986, 773543499, 328372784, 586903971, 634528859, 682944971, 766528593, 878004588, 843321638, 26949301, 257700974, 966429459, 484949070, 74815500, 155398003, 385874365, 821937046, 357441254, 413444585, 921949471, 89897908, 671958443, 536733515, 952751465, 334240292, 686954004, 440027909, 527745906, 233688192, 175236064, 210060665, 891756295, 135516646, 321653460, 590170812, 45055701, 267949970, 458955011, 430754872, 32128400, 792918191, 594208917, 847267281, 301886299, 343908788, 753734009, 587678547, 986080445, 921758297, 877649659, 447170495, 432734057, 53223820, 276711947, 494185667, 684434482, 886802071, 827086348, 378368415, 43018833, 852497642, 958137291, 972202068, 116851059, 813146452, 53318843, 781560549, 550571684, 373596523, 882485218, 74675785, 957797542, 658508716, 465058349, 431786414, 300420339, 738837764, 893350276, 537117670, 404513286, 63677786, 937789110, 947885788, 492881309, 92719951, 796005878, 392609066, 453664195, 967243268, 612474073, 678241553, 130178835, 609214553, 1305806, 149337632, 508470077, 921204896, 61103850, 514056611, 742660901, 287766351, 687880854, 990805186, 714958436, 416369453, 105932139, 192122533, 44756720, 272582589, 673783678, 278849352, 406312918, 529974894, 993649076, 335104139, 976413146, 74343139, 624660408, 269677090, 840659346, 547893220, 491007719, 972796683, 692362985, 127386173, 439428799, 141862439, 523521601, 262146584, 795139615, 270403405, 255438845, 609877796, 17888765, 165597639, 120489448, 944496425, 479394385, 763287987, 616577993, 518162895, 814809512, 474248913, 599185834, 793460718, 825522328, 249456531, 16870550, 971347951, 53847782, 18260255, 62705940, 729336887, 501011516, 440324012, 710701542, 566583831, 718196163, 480129055, 767731532, 411905637, 911332325, 704023100, 707667681, 930015387, 876976606, 422919440, 636278719, 350988981, 719258582, 178436818, 69923632, 230996323, 706269687, 291386979, 344613475, 390925772, 833913242, 793089953, 56340542, 192806762, 197781666, 702675174, 497172389, 106921258, 181799608, 660326219, 307738063, 803948747, 153099730, 333080704, 976367107, 953011714, 691787785, 359365340, 197036160, 935319918, 369393637, 207874328, 364074460, 302313238, 694742050, 683160629, 850365307, 343914383, 845223416, 893232210, 805639371, 950029311, 462055761, 826002218, 224753888, 227550905, 630768686, 164634439, 354049027, 853769624, 968214308, 692529434, 410469603, 251274117, 498121192, 315075127, 874038098, 642476222, 587909665, 835115101, 997643519, 734258281, 990964437, 616753490, 491924719, 292281717, 693524515, 320317955, 903943386, 247266094, 696177267, 797158741, 854566367, 941294044, 485826406, 515425501, 852027979, 946420811, 128429715, 593206699, 730478595, 196841116, 259066570, 94271953, 673946163, 559061031, 442529961, 806699411, 728873788, 486578960, 704603435, 251037277, 425769312, 208139852, 394715076, 622929056, 618638106, 773425178, 656221297, 539781856, 136472352, 713597070, 576588395, 891296403, 133844083, 809672218, 466771256, 921876309, 158461473, 567350, 332360788, 166187547, 879954080, 626629140, 664316986, 130723156, 372661398, 942900733, 248219023, 854569281, 229007931, 291214564, 305039383, 192257504, 785108566, 803998527, 354833821, 492933753, 197782910, 118579285, 281708278, 208909522, 132687259, 304869656, 476034378, 45941304, 875614275, 447883271, 743262934, 82405230, 435658132, 428264370, 406384717, 797556277, 889866648, 620247745, 964990606, 239491738, 879217103, 287694830, 975908032, 853819746, 876628667, 854271443, 998557940, 187234556, 302226831, 2902488, 219095297, 542239379, 127705548, 959032859, 628345596, 205686923, 994028705, 959368127, 169199021, 648340519, 909345064, 587304783, 189399373, 404859250, 67466457, 216961082, 439532522, 420711641, 11263556, 17509430, 216598977, 89871708, 940625639, 77743552, 391491256, 458920870, 863442257, 437160316, 787237706, 863226851, 397981589, 717239917, 962894518, 549050125, 67105413, 51827120, 788850010, 909220432, 648921583, 374536160, 513884469, 793335416, 933608023, 608828980, 747223556, 762749882, 438335570, 65856652, 289138440, 235336459, 845326940, 969557163, 719972486, 910655501, 481328718, 728053348, 519121420, 813716244, 876639527, 739519862, 660845855, 525983157, 881559087, 115240987, 990966506, 590054870, 800522951, 459745791, 969880680, 787543290, 747656646, 282068057, 557326328, 591157504, 806831914, 225249875, 57419579, 876798190, 352140707, 480262810, 327916441, 760565285, 493079242, 592394839, 186778434, 529621984, 290546429, 917484691, 513860089, 549081078, 41734746, 732435642, 403728253, 208117794, 459109314, 57718925, 992892497, 112643818, 427117139, 484606428, 381372000, 696953083, 386690980, 792058267, 478257086, 210653464, 363981393, 656239726, 463007182, 30962799, 259433288, 618191299, 250669930, 276098218, 156249354, 158409915, 506368306, 752435603, 50869059, 696143338, 433086568, 86113180, 955727652, 646840649, 23442257, 33065215, 40869542, 440168586, 526339973, 794868534, 115160226, 985977591, 514406652, 562971566, 604551408, 183976065, 874109619, 922351428, 254056511, 959037989, 358865248, 37966714, 78598190, 835742455, 7744740, 627028633, 993432281, 480942448, 104552939, 965648615, 414513071, 335256350, 544587719, 371601386, 265117608, 562087191, 189167579, 150680386, 121281830, 438470999, 308406480, 341424613, 948218840, 551827609, 796337299, 159047020, 695475657, 190102914, 341837347, 862894752, 960827247, 181088493, 942564442, 306895916, 292450843, 998919837, 634714320, 76801660, 111538059, 779195007, 298224506, 753874503, 248183040, 943290200, 260924196, 496612522, 105881817, 630176445, 392051922, 65795996, 924871045, 91631944, 16048059, 622213309, 929120551, 875307039, 158848706, 178258000, 720267734, 803150570, 43977412, 607521218, 939186539, 719491271, 55119685, 39746932, 328096722, 898037476, 195705478, 787978661, 898462337, 168342264, 100443278, 185297139, 555016709, 274225048, 494561083, 484073414, 246274620, 409884976, 519272222, 669449352, 950286242, 228650837, 887025485, 819630022, 109450038, 852982313, 157908449, 397843853, 918475513, 432162258, 687588256, 453905806, 641484222, 815809312, 120857234, 607252232, 484575934, 530159635, 21382794, 104168201, 610716825, 578984581, 921729477, 553913482, 438482353, 967290581, 147444329, 195364868, 738662059, 618827435, 622813305, 839258693, 27342041, 76879443, 502349206, 149495581, 45461032, 434870940, 709750128, 284152119, 862171761, 901030955, 92507875, 130812759, 331672837, 862417776, 755560399, 219504742, 951149314, 229138593, 401730412, 493215355, 619140001, 858064982, 884762034, 422120232, 808709288, 330215643, 72524013, 494644279, 750825763, 737327934, 706422304, 547261355, 384776986, 403826170, 798655218, 419514880, 960600763, 196914195, 734583320, 217668605, 134665126, 403865335, 121979869, 195197362, 301739304, 862875222, 182146598, 711957234, 233136951, 958742539, 552412762, 594663695, 430177018, 975002700, 859130431, 690678487, 600049483, 996320679, 312499380, 83480915, 475473144, 988387081, 928926977, 780648876, 300775473, 943269480, 564997101, 349733680, 686929026, 858642198, 605101591, 89270591, 205678734, 178450033, 886301092, 838077867, 991221060, 212973450, 612284585, 975173970, 437294836, 849767679, 773989194, 674340421, 144717426, 163023702, 722399141, 598263875, 314792583, 688568932, 453908602, 152766327, 164730460, 611331558, 467396745, 471606670, 870027816, 483422264, 520243821, 429442583, 849813640, 607618141, 962919378, 827896118, 178331625, 888695600, 265901630, 15922874, 396110082, 649583331, 830937207, 60621105, 791261112, 168079422, 489711756, 748588854, 985385522, 71854332, 512933896, 767950191, 12472926, 599941054, 633018199, 441889182, 375446904, 221801218, 88875514, 826809639, 288746131, 870118992, 66981866, 167272987, 859234189, 252902211, 701727075, 716785485, 317599513, 17668797, 331599353, 661178357, 205624727, 564440045, 708425384, 278657540, 491896240, 233079622, 985807386, 781097074, 344725593, 542798355, 488881882, 267350075, 467876317, 142883074, 418962000, 788276614, 76705362, 999255864, 633931376, 174543134, 78982088, 696706947, 260370293, 209117804, 180704309, 104383854, 513967897, 316656700, 309469336, 573888252, 350956031, 698066393, 410901630, 332169164, 422227012, 489899553, 812646942, 349789835, 389741635, 729513398, 691650590, 260783078, 119002497, 278300817, 803673102, 632625138, 141954481, 916681464, 154749626, 481826196, 892669084, 11328018, 282917752, 555253217, 764747364, 7047083, 499818407, 706139669, 927768961, 989313270, 93416806, 686421545, 772008104, 217397902, 622410727, 271788893, 897977827, 410952489, 345032165, 940699678, 871718162, 305459686, 104060220, 608261895, 719476719, 1580942, 181653723, 717006503, 498192533, 813646946, 548968882, 975870219, 385552187, 452539906, 598141428, 890396898, 976840593, 181777756, 484721904, 750110707, 265496406, 502539170, 168163827, 53600807, 606529708, 366786374, 39817358, 921448385, 801412758, 981917979, 523446702, 191281933, 17468610, 200048198, 235118916, 366897640, 93955655, 604900441, 256845572, 624182164, 460175348, 281753381, 41437322, 3091712, 694634548, 494959177, 21048538, 800735037, 927578002, 297539160, 846641985, 235139177, 487774514, 811225483, 901537277, 797603105, 238190523, 606904417, 428343688, 975774712, 409764451, 582378893, 224769862, 647137391, 502320582, 694681031, 510682148, 708630317, 793459579, 170048160, 109306056, 285540087, 184492501, 268858158, 503054278, 633155670, 682058837, 349442137, 70360344, 947677536, 872229653, 131556495, 145085854, 260610960, 338909152, 228431826, 27423133, 693868374, 426010515, 723807249, 437430295, 403482664, 119263545, 991723177, 519651238, 658726118, 581134376, 828217253, 39641908, 775971897, 788233197, 412311879, 507870045, 609638015, 250311410, 278937276, 320844316, 873647532, 263655498, 222321788, 330443052, 53329843, 525207350, 174348371, 616923785, 863188325, 386439453, 581850155, 608281404, 19282529, 993685590, 986096343, 228455017, 55176102, 623254139, 857462164, 402579076, 54999617, 411301568, 925816859, 68443292, 293931098, 899640030, 426543657, 597451213, 96866387, 695982124, 707254452, 690480319, 808896644, 989067061, 843900016, 103513320, 218978948, 66846784, 912571692, 625802799, 300340752, 56588521, 341255768, 714333365, 544625842, 950124284, 31014761, 77937596, 129528551, 42346485, 696959188, 421274885, 512670630, 572902335, 437311640, 430207549, 239686357, 70011857, 158245009, 829324646, 425196056, 295892674, 768366860, 958699042, 670571366, 332081891, 958771420, 376104656, 434408074, 172514630, 87476998, 934423611, 344444557, 265054586, 741003158, 543575231, 704772756, 420654765, 626084629, 880741702, 372740698, 205737829, 327161919, 672210592, 560183980, 264072993, 411684732, 983473927, 796746688, 905938996, 840942870, 951691109, 666030037, 1974398, 54932731, 661793718, 925695603, 240903629, 874843463, 151530852, 383035114, 565695958, 274670473, 203291624, 287863301, 221421425, 993291508, 753191798, 870520814, 22233997, 434745071, 795625145, 217479910, 974432612, 44338847, 169745036, 238805134, 177018899, 505689108, 53708709, 695304759, 769154442, 675655371, 610124599, 101761809, 143824267, 696490600, 633734497, 250224506, 408848496, 823112795, 229093963, 112150830, 493498714, 260898733, 360062261, 298620752, 685175970, 496144125, 359232227, 527708838, 159034608, 166075364, 794734684, 896279086, 851714082, 703539420, 645927097, 742642621, 494964519, 847934072, 250597160, 354729236, 821215862, 553183991, 935604317, 521908995, 859168974, 63054176, 306659948, 495565416, 745039384, 227455252, 97415741, 451278784, 529339811, 462458825, 99068292, 578964231, 275939435, 670079070, 931737412, 604754229, 802391719, 804796879, 546683742, 830057059, 370476774, 944144879, 818288455, 7196, 874266759, 417727968, 528968353, 235911857, 809237044, 413028434, 208933505, 23920190, 577983127, 788854247, 456961621, 747846754, 599741848, 137286922, 346929368, 130497715, 543596088, 289136723, 519440605, 355642872, 804114103, 208317896, 216013318, 403945583, 526333082, 593224258, 912533254, 139571803, 428510389, 656843177, 356530126, 939795738, 824890527, 437165737, 547345537, 188863319, 685250695, 16245761, 206538377, 634288720, 777404702, 804239641, 728767415, 598568307, 335738634, 425645535, 305376840, 399516873, 286699755, 20848175, 875316404, 595800091, 270815159, 394243920, 637225255, 245835536, 468940523, 275337854, 755995489, 264580468, 65634440, 754207693, 616182640, 85591113, 392838428, 726114283, 417795761, 386120651, 603927949, 747122369, 552413820, 928808280, 685156935, 613220170, 612277255, 613744794, 788707229, 984919085, 45985546, 340063915, 904067092, 362974624, 183963321, 463360543, 621507787, 809566801, 878592420, 847477429, 9312053, 566904911, 246359439, 705889100, 745329604, 216356718, 344324700, 477698712, 46049720, 488163638, 67690668, 833175293, 508766244, 913013917, 67302659, 67503105, 716617961, 398106561, 638516600, 148553382, 509966402, 961424263, 271521527, 536979787, 45797631, 252419760, 829484401, 416467636, 176082825, 647524889, 799073312, 127362270, 639764824, 24206710, 523259473, 351442261, 628065873, 998357563, 349654283, 515184617, 170520173, 137926365, 485039151, 463474319, 423577173, 132358962, 804070230, 378997149, 949338724, 405512305, 425988943, 467186165, 683550150, 984772932, 215427713, 134109790, 656717834, 564967803, 693477258, 483100920, 651047885, 238777496, 912457661, 415143532, 396287110, 160147761, 718929943, 106375850, 65622385, 598097835, 308311596, 891108016, 514778905, 15946287, 480651066, 808253737, 986027556, 388267911, 975779962, 44287553, 974193343, 293394641, 654337403, 918881815, 387335016, 379115267, 242854779, 90384282, 787134346, 119265416, 817483155, 984853017, 851579346, 217573137, 953173807, 499729564, 996433457, 66971678, 153669459, 780993894, 141433204, 470912662, 852651051, 622846245, 89036864, 737043062, 880627555, 619165256, 123258613, 920796837, 533351098, 154349285, 439080158, 839276664, 139779643, 458283270, 655211931, 193847628, 310793748, 310188487, 393678623, 843041345, 651595877, 372785867, 729223920, 4765085, 579323054, 830092628, 713835191, 975629161, 26524044, 264271559, 221461445, 188891559, 98992006, 708493699, 565041516, 501136240, 559183024, 326403294, 485857982, 336542293, 244491964, 578563678, 176401693, 312083906, 560379734, 949455924, 571326283, 191324448, 270072833, 596023184, 361693704, 303766377, 171278565, 9864715, 672024780, 741817466, 742085160, 544560521, 333187334, 687217695, 852443714, 447513700, 489965305, 380979537, 610605157, 691727379, 818691899, 646002588, 530894894, 81589735, 283939528, 471146216, 487541794, 404206278, 971712188, 504578842, 525375418, 163047530, 441588565, 16234968, 51907052, 842199873, 214195050, 85625379, 728100337, 869171499, 376845369, 173509981, 443939752, 447973640, 755229208, 506065651, 184914068, 676382266, 758785995, 420435728, 524661868, 188278911, 933339454, 211515220, 398092380, 833143349, 612067307, 569304021, 635592056, 916053081, 207844324, 388585929, 668131598, 227059319, 854859413, 294983001, 525606372, 896047825, 561300045, 819382210, 749974134, 687777625, 241748260, 764393351, 14793187, 140150895, 318036687, 236113923, 119426377, 571954821, 287720154, 678401350, 752580438, 567180715, 123346652, 225918193, 104113279, 728122516, 4486949, 564627264, 742777576, 470263349, 108983572, 271687232, 318628834, 865482019, 679478084, 622465012, 544095152, 468277887, 82806120, 724568267, 726523946, 352724289, 247678618, 979013452, 874085356, 751556744, 754515765, 673625090, 997139504, 686064025, 430836516, 496886260, 874152899, 998611739, 448836022, 798399781, 696409683, 516398137, 975353670, 654072845, 304963721, 19777615, 730350765, 729067047, 872865711, 80507283, 725832865, 276833634, 884516462, 259299579, 275245845, 608662407, 101596240, 574729702, 677085082, 161742063, 540890369, 29906642, 192535530, 776576289, 602121652, 198079457, 10034163, 872662919, 546031730, 66236638, 816269810, 742456985, 92889924, 791399182, 409289038, 285010621, 342799112, 571139781, 553250887, 486692820, 581256897, 184741886, 847257436, 259186717, 548989947, 856030573, 275785965, 5783073, 690579079, 301298757, 205766067, 991372743, 205702938, 993912149, 478160342, 226148106, 942488839, 281380788, 739574366, 734319006, 228945744, 889023744, 876074559, 482941241, 449715207, 576607053, 416382965, 769020271, 888368040, 962489132, 423180122, 269788131, 589768664, 6464419, 290252173, 817288615, 670029577, 939895919, 518957863, 199379513, 569578959, 483122331, 651991350, 807708770, 934531134, 345037977, 507473429, 261239439, 130045997, 620839083, 211913187, 821461332, 558346195, 244289773, 429096824, 603403955, 608196214, 906057704, 91992812, 914513104, 778536544, 830748556, 974418872, 881313021, 373755243, 890982173, 147254449, 803254551, 561626428, 219578361, 234121168, 966084005, 401546095, 334568025, 728950471, 184140047, 80538845, 719217159, 126024177, 540450816, 762567820, 67873783, 204351991, 132418225, 994575368, 977635252, 146167505, 112114251, 360056644, 797901546, 847273587, 411038862, 271337288, 123065693, 270435828, 506274631, 238010520, 225756681, 97946928, 495501962, 111525375, 722475322, 663363243, 151869791, 685437592, 925456897, 831830913, 50512571, 927526404, 585726813, 377890302, 525720503, 972917563, 302012072, 331179630, 981732085, 198830732, 483646123, 186276329, 592573890, 116680555, 811721884, 442744461, 139843102, 243067975, 935831581, 254185367, 370015195, 407260454, 815719404, 314117126, 441478219, 4358188, 244521162, 151654969, 907982826, 667608335, 533012464, 342510068, 874608661, 689525775, 453013324, 158666512, 100403301, 754523088, 936831733, 237076593, 232789926, 269299400, 221205828, 512791005, 11709004, 275837375, 683476268, 576766308, 103573825, 706574807, 193738172, 702658307, 820938763, 772521311, 714902584, 790222121, 616929377, 771463749, 152495121, 784347014, 165833030, 462108089, 911545890, 118838785, 960234221, 805798154, 987896837, 613623585, 77261426, 120187584, 784543552, 652393259, 815707642, 80771725, 90942185, 194140359, 702357073, 968971822, 678016206, 810228791, 691680709, 335407068, 725804688, 509462002, 327630901, 418504775, 909692446, 874002136, 591224518, 770943390, 396494497, 225840592, 474712679, 568610270, 918606523, 818252144, 557611375, 966540368, 137517604, 915666622, 734597970, 606978393, 376295287, 515279572, 266352319, 858342482, 259638812, 219121278, 84450301, 917500465, 276283695, 484133131, 881074642, 878901645, 770461034, 848947235, 353513303, 324926938, 101109856, 888264873, 642157001, 45078000, 96989775, 210254483, 63196183, 688356023, 894956645, 861220884, 587962395, 668213598, 119665681, 398251433, 675694966, 999086120, 683198212, 273468838, 238095961, 148713097, 394188228, 253242693, 795647009, 136897182, 119844594, 808719709, 50032544, 407808876, 738584225, 95300045, 12503292, 997466558, 806285702, 629346955, 746204626, 645326050, 842746471, 190624676, 187544715, 252949750, 18605000, 631589951, 534486810, 921409422, 162744658, 385358203, 376954784, 297332583, 596576466, 72840012, 596407994, 715724818, 880885655, 350465645, 394812025, 864465702, 952609032, 187669261, 678667463, 937379334, 655349578, 41813829, 473174119, 750600260, 979345131, 406062982, 884754603, 800616963, 598215418, 672358486, 477694185, 86179939, 526961051, 541989700, 223941133, 359250937, 392125427, 181619185, 870503861, 685565454, 431301204, 334514534, 268456038, 98248982, 451875485, 290492944, 499607938, 854674740, 648606263, 598740156, 477211256, 155020682, 302868056, 207140483, 138633125, 658929923, 631884921, 311758821, 460928872, 131791182, 53335310, 559540138, 994819424, 475745322, 393181644, 829606487, 239769124, 662905965, 585113031, 978814053, 641962504, 464405049, 628921583, 101745000, 874207344, 371388886, 453252949, 456029037, 873458325, 892537860, 603411979, 855613838, 502920570, 838346438, 15437696, 753073362, 644365174, 322463141, 141346544, 14527871, 276469594, 666840280, 759650337, 620631333, 287496652, 852123074, 125920564, 557324973, 677418029, 656191506, 798998440, 209455835, 913064304, 465497406, 895911052, 391951881, 860321034, 646783113, 66189039, 555804336, 343227258, 800171546, 849684073, 430996071, 318349993, 483188840, 587509292, 767872198, 341375158, 541950523, 767793476, 274386856, 100254917, 104727740, 395302263, 449899356, 390843379, 863329313, 842638414, 109103335, 441915923, 990730438, 554759896, 268200411, 839125055, 513600857, 945434841, 251388263, 307273628, 295898667, 945817410, 90936555, 373432336, 108214309, 926053611, 564988946, 669829542, 123543438, 756066419, 260631543, 955870155, 190715, 724104638, 585775255, 213300477, 283216266, 419709842, 975664882, 448612339, 71274640, 27598387, 94291987, 689564862, 548846689, 175983219, 240276252, 290199229, 394538687, 256121787, 143009432, 367438287, 394442563, 717471595, 209714222, 360434935, 759874372, 765051980, 573432365, 810746581, 715663005, 710010712, 2763857, 481831936, 661443686, 95870374, 132516411, 880559774, 768503402, 399817133, 540463548, 844118813, 294850596, 782850195, 689819606, 726316030, 929551008, 544916256, 441345499, 337263069, 942843636, 961349906, 810245984, 409859617, 403634314, 197070363, 636858187, 219616804, 364343620, 272326701, 709793631, 555674260, 596338922, 93668999, 678707424, 105172622, 738240378, 184169336, 7871361, 773418172, 144385151, 559938344, 342624945, 903250965, 980799402, 664392122, 9975315, 117967570, 876600930, 518678823, 887314055, 924462563, 740080433, 347010148, 907877187, 990812087, 876308627, 763008000, 736172163, 122521294, 806475115, 831140680, 274879792, 39869967, 779150239, 232861936, 387763827, 630654987, 884427889, 488325117, 427315126, 694880138, 739844175, 452514992, 956608783, 74956031, 619535825, 487361279, 219641237, 499595949, 299466294, 49004948, 290132491, 171375203, 928768348, 68229757, 288890792, 988466136, 583057039, 984146186, 799107945, 928032089, 894103602, 871292270, 328090417, 211144895, 348212316, 693270394, 977787775, 359111950, 546279142, 332189024, 22152623, 322392025, 175957409, 689972732, 916707147, 735297369, 174035272, 638381075, 447329618, 38039822, 362833245, 778764691, 743706250, 934681343, 191923322, 141578303, 259270111, 566616804, 815187344, 241029196, 154055420, 327307145, 174591000, 727167689, 404140967, 792025457, 829077588, 671289435, 312569320, 835069383, 5447096, 256222080, 416942274, 331572399, 918874728, 987799633, 491290092, 992672333, 939429871, 336987329, 599798227, 751748057, 48623364, 660906491, 483298529, 790604907, 931970346, 384818392, 500389663, 682648397, 687212261, 931635093, 63561014, 647646529, 66429847, 111976858, 604910209, 506679375, 555515669, 123847693, 44492632, 178847708, 946204343, 845354283, 427846975, 690556757, 914308617, 189403235, 36675450, 542238247, 794804663, 577442071, 517924905, 795204990, 501340080, 613354260, 854322902, 571260895, 510260438, 414373757, 959194226, 105045310, 477394368, 72800755, 445731641, 103854338, 841523771, 957791852, 191532511, 961580297, 388877143, 102309775, 428357400, 830081461, 563818151, 866259007, 485835690, 30082297, 948589886, 562392830, 499109369, 58433073, 733283579, 36428328, 742298882, 982643403, 593203780, 144755224, 578059814, 254472399, 22301867, 789998879, 735889165, 918792549, 557462809, 552573722, 576530981, 680153828, 916392479, 646974858, 34567001, 994679482, 9460630, 972487263, 300018493, 640747865, 657751837, 627670811, 587663859, 814605409, 776005740, 344540768, 914442808, 323409866, 565987127, 539745133, 675037315, 450123788, 413095721, 54159360, 368457255, 171562353, 621533236, 59200583, 982705473, 142943196, 24181977, 786801377, 843283079, 40385945, 194742271, 75718708, 644665269, 829591822, 640312514, 509973082, 836543579, 306452012, 813042080, 944898820, 550143784, 62021861, 992978935, 196696601, 710776674, 757759648, 788128770, 508886684, 407131667, 523136459, 620527910, 480558764, 915736219, 812216291, 91417414, 520775627, 949658687, 84409460, 816577062, 384304457, 930699848, 511428540, 836975433, 968245972, 453251047, 921779564, 216048536, 494252696, 254735994, 205744844, 981264789, 990061028, 985782286, 822067443, 316563393, 763292217, 708024504, 693075248, 99141092, 956296872, 55694579, 52732834, 308486669, 557081203, 58042609, 935091786, 601181323, 938701215, 779116109, 989803820, 873890548, 589353904, 723945581, 876703675, 211910418, 896307042, 762777210, 278865821, 110798924, 437579393, 628929110, 829831404, 526410075, 619011952, 978008449, 65222966, 849172173, 144839480, 782970345, 398869366, 641298141, 698001818, 170673426, 345647972, 659858130, 112495963, 432970454, 7230343, 585967399, 715821978, 40623996, 971749782, 842350030, 580042921, 989912562, 166642836, 973760291, 161765884, 782228883, 527819807, 138626752, 850353393, 333606921, 648705625, 47313075, 266982238, 201833381, 308526839, 68814931, 927686741, 262022530, 535614874, 863188936, 616955547, 104202132, 171104622, 331238109, 251912037, 286572272, 573456646, 949203657, 53043725, 806243760, 203265019, 876486006, 948937495, 567449238, 415256129, 988070406, 968023790, 17019473, 248737963, 120681248, 583983950, 153993219, 201935152, 136164457, 829871955, 626291047, 394802246, 260007922, 607931843, 24306224, 28575069, 225321218, 908829358, 169220022, 936512506, 665776761, 704549784, 698417525, 255461139, 163951408, 261229082, 220008280, 348623912, 807148420, 371106186, 366690995, 544609152, 213870993, 408196963, 754669215, 399795747, 559323631, 485832609, 350352952, 721747050, 21631935, 355573914, 206023787, 964425951, 691307920, 159549218, 671420169, 951126219, 634927534, 643582950, 274406843, 632962879, 760518512, 229811483, 390881175, 924757771, 38194303, 293272202, 173491328, 486019127, 734258251, 387215108, 437262928, 728554527, 275024192, 248976244, 343245733, 701258706, 170540138, 465617442, 858198203, 574360296, 946008040, 664094170, 517178634, 693040995, 799594735, 255316661, 449678209, 87199479, 511287441, 125791016, 282384294, 785396986, 457604138, 287610759, 723403051, 10837888, 746035325, 640711757, 995757787, 2202152, 917093046, 577936335, 648767243, 785286990, 635011419, 695112654, 374068143, 14921666, 440382233, 660237890, 526475247, 957351727, 252635667, 812396571, 412310376, 326907154, 30634198, 706007029, 970271608, 580512741, 972748916, 201325968, 314261339, 716665373, 962091777, 486226702, 273466370, 840975366, 599150520, 164993432, 484979571, 418559139, 363203519, 162207943, 208330032, 473511398, 794841071, 171891390, 336414769, 600986238, 936969299, 859143400, 350403043, 292803417, 958133236, 937969576, 384765730, 741217260, 719124565, 511975130, 529929688, 872979520, 413094461, 630884202, 651374826, 857264663, 228977297, 822943843, 77199492, 710743715, 932154071, 658944343, 426960928, 905863513, 849222023, 315065974, 933274562, 40403835, 803059944, 407747168, 714968487, 955036691, 961766212, 307500705, 475154160, 623864479, 399106155, 274460576, 874887932, 936834756, 339899692, 94033093, 512791616, 159687579, 734508020, 867806917, 575669353, 479473359, 574347008, 79762627, 134124861, 471750395, 165249715, 875142716, 792987970, 24874855, 280763719, 405529976, 351781845, 254659557, 344786449, 430895550, 933134790, 249828212, 490208485, 678075790, 434169584, 949903024, 747154630, 302454525, 893883097, 226358666, 752566952, 839129014, 742747936, 33190139, 395772530, 458036737, 292028714, 192074274, 74568408, 403968414, 748157558, 257293201, 281945344, 653838435, 6418166, 891108797, 915633643, 346851287, 238668024, 519068579, 990641799, 785190834, 689000043, 617317650, 214079151, 651673204, 509008143, 739303645, 839388246, 925063421, 921156601, 846270348, 23338925, 77029027, 980991821, 827897533, 469982935, 53943776, 846861414, 697151374, 165612553, 633591435, 796789686, 94826135, 191030409, 643245772, 130417543, 247948564, 119420540, 580850845, 676206991, 72685894, 636684603, 927693599, 49440245, 847822314, 682549684, 556752146, 961680458, 169120186, 531127546, 728504491, 155076752, 472477553, 26185430, 314397086, 593668662, 434302073, 803071656, 166722904, 728113321, 419246569, 823603977, 150361255, 524260741, 503555043, 714625615, 899435873, 935657071, 874663104, 400776830, 362487258, 525738000, 760317843, 548463811, 885266979, 839427412, 433041928, 412050312, 612894997, 821381333, 652561053, 229504992, 846168965, 640505243, 931920981, 276540988, 449906316, 911718584, 415403493, 558731555, 210481417, 997112380, 677146064, 356596017, 440393803, 795920226, 536832024, 380483176, 750339439, 586263421, 998945515, 742636966, 19095687, 544759610, 601077107, 910875650, 945314815, 63859444, 662491110, 300032016, 403559725, 419986460, 776754797, 628474677, 467268624, 829082135, 908578842, 585907583, 789607167, 744806186, 183096567, 761609482, 249420887, 836197476, 253923842, 308179723, 450254095, 243805445, 266396839, 346532591, 905313627, 551598215, 702201115, 726758130, 687676614, 236631803, 640582483, 423115271, 686022811, 633283961, 827195312, 15568263, 353725033, 784509879, 492037019, 149962977, 442760370, 802224471, 84215802, 419503084, 192316496, 71993407, 898152326, 526961975, 549858601, 420927066, 647960203, 952264125, 611390294, 881248879, 420701208, 60215625, 141109577, 140160557, 666087815, 899711095, 497256422, 239930430, 321162812, 247695959, 381869073, 479077357, 90739426, 900726892, 976853294, 956843221, 967708363, 216888022, 867880771, 358897449, 13482112, 922833301, 106553674, 364182536, 125102074, 136642006, 688150639, 908680559, 829094436, 783161410, 568528323, 465539993, 312580456, 995303187, 981020101, 163170974, 610314979, 514265265, 891956656, 534089572, 612165061, 474487037, 420431481, 81497077, 710994339, 499216688, 424426240, 487816844, 567122801, 892902782, 26150520, 808970139, 588523652, 958430586, 105232988, 52316094, 34727794, 987544946, 87835266, 680533528, 263981250, 834389173, 899284767, 953714733, 713657205, 540007592, 214744952, 937463253, 217212870, 326849700, 348041291, 65211132, 267468726, 437899834, 547960261, 634687043, 392830359, 329034061, 362074703, 328208783, 422784216, 932991516, 547859838, 705978615, 566715229, 113056206, 595149478, 241510837, 687025596, 152375504, 236767204, 922545066, 426562337, 764458519, 378479846, 490049868, 837941031, 791007688, 249012139, 383285845, 45636102, 911597607, 203463101, 989067196, 692922359, 203195107, 451818278, 508067011, 342071527, 910130955, 137533350, 352096990, 738630796, 869751449, 86932798, 340287770, 188560444, 307565626, 401961661, 224216713, 621863829, 842680673, 571616418, 735386469, 2994442, 554920496, 363702774, 583077970, 171947489, 823150020, 823902366, 111183003, 398388622, 522257152, 566670610, 788013440, 590697365, 640831838, 39024039, 912499884, 8811370, 62327191, 687633831, 304313578, 981335386, 482320016, 206110601, 332061080, 718366693, 329269658, 164039620, 390897235, 57110029, 241165783, 701173195, 435585244, 587926996, 578277565, 506059373, 823881904, 588590690, 840384877, 75079957, 338120657, 579233837, 539072223, 792473388, 668530066, 291709434, 495383836, 823482821, 358797138, 975488661, 758708968, 925414921, 360134510, 741241064, 37619542, 682589918, 48862538, 570095291, 763958119, 621446693, 354067065, 940041555, 342589058, 638973134, 749428019, 399463367, 889464314, 664903991, 720245045, 306576824, 230806347, 880052144, 629948087, 913718898, 476414358, 697858195, 61381550, 61461081, 859594576, 587650728, 998124639, 306126281, 653894853, 307950863, 14633817, 284023905, 590365765, 545910454, 819049149, 573339380, 646451912, 641630250, 724397922, 708891862, 635458180, 129075787, 767080136, 123487615, 882529405, 675313439, 703226753, 739187981, 853046248, 948038338, 643249244, 768863064, 701097138, 75531109, 102341767, 633534452, 24761866, 736101180, 901665193, 778152980, 460992832, 464506199, 203942172, 559441245, 327089644, 46981070, 890113926, 75116040, 972911787, 675457626, 551810784, 861759921, 656744224, 150777945, 234041263, 870554880, 48222598, 274714785, 922810899, 77014428, 475706068, 136451449, 515841741, 932306844, 653963566, 648096103, 127387380, 324983733, 264651335, 553422746, 527078004, 555777622, 760112411, 813247311, 771462213, 877911242, 904042902, 217633781, 173158697, 584727329, 706707, 610046718, 40515473, 571061819, 293189931, 721063574, 684877919, 593336402, 518410949, 673907818, 514645308, 856952067, 317852271, 563922201, 629861151, 336665376, 506707673, 833158059, 918759307, 728126286, 600815654, 746718612, 530026694, 73916388, 113380899, 485324156, 819072449, 60419600, 317004428, 673267345, 115082905, 650069318, 692402405, 370925640, 260504939, 968442637, 690558453, 719518542, 845572865, 44393154, 656342609, 706521349, 675521812, 920522813, 74338647, 506450328, 303648011, 414981551, 990147473, 903752679, 656120861, 373969947, 460605808, 218197943, 343657869, 801041350, 365256237, 186579864, 363974994, 33095639, 248969511, 596486751, 976626114, 175936801, 398791517, 706523353, 305891304, 324467721, 605883243, 102235086, 670445618, 421578110, 937202171, 861036786, 629395370, 902333728, 851475660, 848159169, 604164741, 546868877, 481435383, 819203296, 92821429, 532217465, 782357409, 639142220, 466790988, 516584104, 61030522, 112368078, 37749876, 701033099, 104647262, 858917270, 999384912, 71321166, 476244126, 830106372, 544502078, 420715197, 460469625, 584895085, 148621123, 385574952, 705794784, 476184414, 22499926, 661112901, 689485482, 740713953, 496915368, 773467369, 659268335, 852433556, 733186459, 679050719, 950680433, 463354019, 838588445, 632758605, 380703242, 443091731, 863618103, 856823436, 715628120, 877256093, 615311867, 183404594, 831364448, 670076213, 283444682, 536917618, 946639188, 474329183, 132762094, 377620255, 20938794, 630938362, 728185366, 654971181, 659659924, 474502329, 399361003, 831846199, 866451000, 528151476, 698318225, 21578227, 13484903, 386393512, 932173833, 159886041, 611743992, 481581898, 821427954, 476051379, 229569326, 40498099, 722860691, 580949579, 188563007, 361986406, 164323131, 855539550, 472627050, 196008803, 448757672, 60147938, 380236897, 342414189, 992665181, 854067633, 537199697, 815002180, 949668564, 995420461, 252792146, 506939191, 588591261, 465239896, 923936433, 459213428, 790016887, 953428129, 198562045, 134433120, 390731329, 237861089, 352207466, 198838063, 650966007, 907524701, 973836631, 194280773, 313362887, 841713715, 741555664, 289571749, 182026438, 676853213, 338403868, 971741892, 599536672, 447400313, 453102960, 388256185, 540775774, 135006146, 832590058, 856498157, 513902142, 748409569, 437107926, 150070716, 197283110, 89733469, 981088839, 287384371, 890684329, 503581152, 112951890, 386935, 223185113, 820225465, 180025191, 261169410, 498382002, 882687321, 406839741, 902823003, 224733556, 624419782, 921001849, 924363120, 371344149, 384057924, 107488408, 817392123, 560377711, 150550232, 727251767, 484686273, 795929620, 97335536, 690323329, 399346394, 651586337, 100114919, 189352689, 403674965, 778330339, 955315906, 458162032, 88324999, 914924605, 543829871, 640807812, 422743119, 724498518, 64719281, 858268302, 422233699, 462267402, 988865491, 687690797, 113871494, 423064530, 972072447, 43486560, 278071456, 984831690, 818741308, 82364960, 502040092, 729686853, 617882051, 628893994, 233796161, 558171484, 443469250, 915910912, 872876582, 206772666, 966593565, 306375982, 989755171, 176775937, 225837963, 77474066, 948191818, 117085995, 173420583, 476397306, 912878478, 521710220, 132154911, 577540016, 747417741, 748470411, 103087652, 775127361, 622349710, 851280213, 310066490, 674759422, 166691120, 652824521, 449089140, 468357719, 969748336, 380534571, 807099450, 296158404, 220916255, 823203704, 944496576, 521983178, 956426189, 998398177, 617619846, 156418679, 93712391, 362638936, 753430600, 26038008, 466165272, 328264083, 384970500, 819703612, 373541233, 722749887, 584543402, 411704180, 165278640, 306712970, 481492020, 14792935, 994039037, 778079817, 10797187, 299941497, 135937569, 23554048, 624234941, 44403889, 594511540, 778366993, 341523603, 505308650, 439021223, 403041835, 672153445, 758973978, 449806207, 496684321, 645325154, 351693378, 596645329, 313193861, 664630058, 714591689, 600853143, 815744859, 113013761, 919272573, 801116015, 665991004, 517341576, 985084526, 809821486, 282384491, 58315628, 330791718, 428356156, 814152980, 868066649, 531323996, 23821439, 675287952, 273833187, 389878180, 946274035, 291083151, 333883021, 186152604, 573417850, 808374986, 775059355, 799597656, 819308879, 996826153, 806820696, 54120541, 635740259, 357873666, 545269632, 605499640, 671166872, 461812857, 114856031, 133484564, 206773696, 836706678, 342845268, 414529581, 897124006, 816038766, 646947121, 945231149, 816991153, 892650799, 47249382, 162285210, 95957867, 767761183, 993420812, 635432003, 323889691, 450636372, 388490735, 62915124, 203797467, 614608242, 619663878, 968085565, 995891825, 490866337, 15929608, 122271888, 795415673, 356177681, 784433321, 570130425, 702662225, 122958230, 819513736, 35730060, 894722321, 975275319, 763543796, 850828039, 334775150, 492257525, 959334232, 237013909, 305682828, 156520940, 35991473, 66198886, 281137634, 969016320, 782453162, 343968108, 243713420, 374114407, 516562255, 352288841, 666834571, 85608581, 803140843, 242398302, 31688794, 804221635, 361036875, 249129344, 993671805, 609750962, 446212271, 485951259, 985671232, 577935586, 862199000, 632148540, 279508034, 721746014, 237200564, 652212722, 87685516, 25143314, 398122225, 66972651, 491896791, 220593876, 539336501, 663497910, 526153292, 269715156, 495593716, 42621373, 855786274, 90687105, 780527801, 27806373, 438172694, 301675144, 208317744, 817116931, 752722689, 429310674, 258181958, 768977567, 283628015, 351072331, 544837875, 760515204, 331136661, 938022905, 429787769, 48229663, 438247536, 589444452, 904963613, 822375608, 920165216, 510679307, 129785810, 628752487, 304822709, 647592754, 54721439, 970901985, 654793480, 677833424, 928274087, 187702904, 564833637, 753722930, 537256772, 914386439, 564632792, 806678587, 218615742, 712809008, 18456551, 606560007, 652254524, 362382103, 225610908, 45108532, 149382676, 311793692, 449915414, 460217855, 404116920, 979543882, 158669251, 874690777, 844661936, 365098734, 684341563, 849928485, 221425130, 759669828, 361040617, 762331829, 657807221, 960325681, 988574631, 90801365, 177369198, 847767572, 246623445, 838601621, 930521264, 119407793, 593388444, 489313410, 448574489, 349496338, 476886260, 204618925, 798812712, 948800524, 982903132, 817607822, 122145922, 939011800, 761150305, 768746374, 904255629, 377328698, 861067152, 565840120, 814080805, 846197143, 100070009, 115121747, 4794494, 437869142, 125923431, 909143679, 215445248, 996053455, 714906352, 113136051, 344378635, 897365626, 112980894, 912468444, 512974104, 790273993, 820982727, 149344919, 860445130, 603826364, 17524662, 71617417, 668881656, 691324148, 317772586, 989487738, 761531163, 573906794, 283745905, 843418579, 855624374, 80911880, 579115416, 723709971, 761375577, 227640224, 806909587, 198799948, 429370687, 416547153, 704520613, 522049522, 388032450, 878629882, 405575040, 389638498, 435374108, 95257077, 232218936, 186557331, 384518599, 722751421, 451478752, 987891555, 411215134, 319701476, 626044609, 929851570, 696956615, 593719023, 165631373, 31113609, 277772666, 384098694, 681146999, 60579862, 27969567, 199669819, 945161475, 463130709, 536779528, 9918650, 452184757, 343552320, 328368690, 172775376, 534360189, 518240281, 222148990, 168915281, 22111349, 54850381, 268094778, 721281870, 373897306, 674275086, 231091274, 985059674, 708807550, 465793647, 252820800, 995408259, 144243848, 787001796, 142889231, 920236296, 541023273, 827037954, 725236611, 702586499, 458556832, 214444598, 177376678, 688758570, 889195801, 325250553, 494992, 335245354, 663800100, 553846389, 713664205, 40795768, 713040466, 352133193, 257962983, 435161560, 540558180, 148467171, 824899859, 591623284, 287770878, 844592551, 597840141, 756672696, 125161684, 77625643, 727733629, 677401932, 977002146, 475075822, 547839372, 487390404, 359103874, 820885348, 573672410, 959547848, 964485433, 755110607, 391081756, 414992551, 225702950, 87427772, 754353808, 549197043, 810235068, 994782119, 700626406, 727978273, 728394893, 66314870, 678146814, 864057926, 319734341, 972070207, 114557696, 30985117, 643142626, 697571160, 404360373, 999781036, 451921543, 196494961, 121389722, 583451070, 361961662, 550465955, 499291816, 763327108, 400808047, 242921605, 872574074, 228589764, 438866545, 753842, 226530700, 286017299, 956966107, 569283358, 952846502, 9105751, 368453422, 299372519, 261041244, 878080173, 773411448, 314011997, 852671694, 657067561, 401471727, 704111140, 645487496, 996917309, 851595852, 114532715, 940287214, 5412057, 176538797, 182618370, 354439696, 170946495, 210228363, 789932920, 724540540, 875873137, 991543791, 59365427, 957541799, 595436325, 595178129, 646449991, 999135056, 755600978, 466862105, 521342747, 622443129, 963403392, 332147557, 629948104, 287601044, 472243910, 751373365, 589991470, 770609168, 255927480, 242694466, 705231654, 926559103, 417379338, 745872627, 985551716, 587685809, 309817047, 574440066, 955196538, 684384664, 535745911, 3869235, 65638140, 766068824, 127804175, 998406814, 416767052, 623676990, 802239553, 623707060, 854335206, 755612068, 314706117, 430011066, 80602555, 667295792, 39906305, 654638183, 860533618, 461805653, 570673212, 97563302, 144850872, 712722693, 654225117, 395554701, 110128394, 143624490, 592734389, 985680928, 297547688, 940039435, 140966669, 837116361, 123340973, 905986838, 512456135, 49845206, 938100224, 83103860, 755892854, 683031408, 482697864, 883298326, 223001629, 334618454, 723478739, 226763291, 810665668, 664403323, 61829583, 602190449, 298713246, 927340639, 253523770, 653593048, 18338981, 671532829, 810477206, 51578726, 366403504, 635890108, 586673215, 883907689, 446026920, 82860574, 858344365, 617077824, 281208964, 146278779, 703798050, 436195336, 917055911, 773032465, 40973761, 233941271, 176759421, 977889077, 803613325, 622223644, 729276593, 985427806, 538269071, 854683567, 946551100, 656628143, 686292560, 907040331, 829731296, 437748484, 973992568, 141824555, 794335140, 827409377, 294099587, 386553357, 232856843, 950893595, 882814603, 143094950, 196402292, 195292356, 154475156, 415621172, 337788857, 757532708, 836286159, 327559762, 398027270, 93946094, 592488156, 933427054, 376944623, 214478089, 814816713, 651659755, 540363005, 735017108, 630485858, 743448954, 518071660, 308072573, 384779151, 270179497, 368075025, 777609333, 259367444, 192071033, 852146396, 527426831, 686352, 910339518, 768960781, 458014174, 873725932, 821371367, 961874001, 323862525, 599315539, 976190282, 244224318, 562162857, 390681672, 903476493, 973667245, 747892227, 344239338, 598342065, 181720354, 660719179, 853341242, 721247596, 817576524, 646629034, 369969766, 275490552, 542983348, 391694266, 312587840, 577918652, 483013297, 222577962, 246050625, 550021767, 631983411, 124676445, 403831237, 30431663, 202772267, 383986644, 418308562, 537984796, 639572477, 981804859, 122946880, 661104476, 795495545, 153912772, 531381974, 718905464, 268540152, 562579601, 702517233, 236615789, 593694061, 842220953, 284363147, 445436719, 189572020, 130567489, 134639331, 345543873, 973394064, 165956637, 278797541, 384444102, 217315862, 83807333, 326981675, 484164694, 80165886, 511387076, 750879124, 622351447, 57149934, 572776425, 851344389, 492686069, 764158670, 100337843, 811227648, 367243272, 849258581, 402510371, 4923888, 214958230, 981713433, 833733153, 199881005, 141725982, 930995332, 60004419, 858554703, 787094236, 781794052, 237227928, 225466738, 427926591, 482129408, 443739531, 43355532, 337453283, 804945489, 2491058, 249849165, 398913822, 467791624, 400509065, 459581367, 962990925, 690989829, 364169054, 895165168, 532778156, 662061056, 198905049, 304037144, 462461953, 579239787, 826514406, 298104478, 400743947, 996545477, 389017394, 156585037, 231349437, 894406530, 699143037, 281860178, 240625350, 658017814, 183144767, 37835281, 982306868, 823892625, 538353285, 22085152, 540260334, 122756032, 939637118, 661357847, 152499782, 652415242, 711829352, 160895697, 833299055, 380043790, 61047311, 455280624, 427003562, 127377627, 263371423, 352265402, 555370632, 3342546, 546515490, 915170071, 320970482, 309331195, 866003123, 445329210, 239760193, 270145790, 262699349, 109063579, 293605958, 28028742, 43108044, 714531802, 292831882, 5258158, 960578706, 174313495, 50686647, 38306937, 263794623, 34698030, 545961364, 417771782, 432359561, 595953435, 385752188, 548660554, 285702298, 673161030, 608012755, 205230966, 498956144, 368135075, 216958840, 446938231, 568591358, 331547128, 559376318, 68611527, 665301170, 34844435, 516892973, 845043683, 240248260, 401307982, 567153471, 960405747, 153609039, 857419861, 118309051, 547682379, 648148426, 991952539, 882545773, 184061399, 999070781, 765982521, 267411076, 419502384, 124165446, 224058051, 857998522, 14496073, 264213459, 986820692, 570282129, 211753213, 245597268, 930143204, 774551498, 514652876, 925073693, 921086628, 640773887, 73060225, 529715420, 40958571, 366734118, 683946677, 432313285, 992760200, 784693488, 930677383, 619151604, 805284759, 457772432, 592456091, 485100032, 955898868, 391900453, 219676832, 562759638, 430856434, 967077015, 421103699, 992963917, 110482359, 777569921, 470580703, 460032189, 233271275, 82572015, 650552543, 189372307, 550063160, 647746980, 236384115, 179347295, 402139142, 159629222, 273418934, 139601570, 639676421, 652064016, 84453428, 465043456, 114055612, 584001438, 882590566, 676394963, 483216179, 745966194, 825327985, 985623490, 306947409, 409524159, 138263163, 64619898, 417338433, 406408681, 176380047, 442151325, 151506186, 149746198, 474173500, 102746034, 226566556, 996627825, 966584070, 365471770, 849933266, 413800255, 598244754, 126970922, 185758186, 706461626, 401986302, 678089530, 630918032, 620166883, 400240225, 221398836, 433075871, 195422184, 666716900, 602329513, 751455164, 227663599, 121331035, 46276718, 596554704, 50099848, 554281974, 271420442, 500849468, 661363368, 634675694, 460763583, 913662985, 991783536, 333018579, 731640294, 559230455, 999669244, 758691851, 593952435, 511148631, 493139256, 94739801, 638739681, 281785165, 660608903, 886479304, 978275634, 683136324, 434348291, 724037738, 886238552, 683542926, 3901775, 770688715, 985889474, 744394045, 687499632, 112022925, 709757837, 808444152, 388990657, 414047616, 771749579, 40009897, 498367058, 958240729, 510152993, 969036435, 944212125, 311926042, 395130471, 761896151, 180718861, 980058142, 562067677, 69013272, 789419877, 169030287, 934204461, 315969032, 819974762, 550314188, 144251778, 822839592, 632707453, 420496940, 348080391, 772142856, 290303779, 943238844, 849751516, 485101918, 860570586, 469092857, 46109389, 874054586, 699654764, 761626656, 568016869, 600632192, 355393880, 762871144, 90723412, 421396573, 821959691, 688529170, 1176013, 636078683, 112883067, 320579043, 381618296, 65758063, 25110816, 490864813, 386913272, 267005790, 562375298, 289107207, 762698447, 434785338, 856447011, 259157584, 270443820, 38413935, 900862060, 219634624, 624575829, 287227775, 972836461, 345965740, 122320627, 994577485, 892542517, 410959298, 971836054, 585178827, 117477242, 84885627, 212011083, 294328681, 180829844, 579330251, 12516062, 70827964, 248185109, 531725514, 74432849, 906905354, 514687983, 780610483, 153238624, 849709297, 946298535, 53595615, 745693607, 804622002, 54756627, 43445771, 681610311, 38927291, 250831651, 92816901, 208539633, 621293214, 38923469, 40014046, 94843065, 835306181, 420634293, 34189616, 137708148, 520134747, 933145517, 831535807, 123049281, 651596986, 290989476, 517207984, 479116597, 81926487, 304904974, 813467686, 898725379, 136962177, 297897895, 269825097, 250849752, 841034435, 52275124, 410518997, 430127781, 228071649, 857447845, 538068858, 870164542, 486173353, 408732220, 508445817, 690253051, 460612092, 861451465, 825936684, 792543852, 33860420, 246938348, 74650582, 274397244, 779003226, 47608585, 373548413, 729452187, 450947645, 64419561, 570761831, 893669977, 512129496, 560247894, 157216026, 460511522, 286346537, 125211998, 68607530, 453266903, 322374612, 609662657, 941008795, 447510415, 622127857, 232525273, 271107278, 146650050, 798543450, 199014443, 378559878, 2556259, 485621987, 525607726, 982004596, 891950318, 691909166, 986595406, 477928614, 879722556, 343044273, 843756926, 934192441, 734762611, 451061712, 218968049, 164305574, 360301957, 346527467, 3541627, 831749710, 554744489, 863022260, 469664021, 195610995, 716813815, 468569610, 505213642, 891866880, 497163608, 516967543, 663054584, 17592232, 266839037, 75364631, 640890895, 42432106, 400458258, 50573085, 635496654, 987670980, 54635066, 106795671, 287172203, 407075415, 987319132, 14555118, 364617675, 762036431, 130174471, 746255821, 523371353, 192952137, 917919583, 592421069, 260621830, 727676083, 718418651, 478613439, 341651556, 32387074, 33993304, 670410400, 778137207, 816385576, 779768161, 348218763, 558107106, 377331256, 348076380, 463754910, 968312238, 623691316, 843438135, 192144111, 263062791, 8396254, 188375947, 268693563, 655663148, 980204049, 662748233, 886987069, 500848743, 127991937, 90328199, 655925105, 802214454, 551894196, 338525449, 272553358, 89074570, 403690229, 750680529, 963767653, 348220040, 992991157, 481705836, 368971410, 520848735, 487146815, 200981416, 473334755, 102479729, 150311732, 733699420, 994750700, 701747533, 176834944, 953437533, 290193853, 770726758, 323588193, 875700073, 247099866, 94618591, 244764061, 295905921, 730670025, 438770849, 646314144, 167970305, 672538052, 707512052, 247123584, 608636102, 66828623, 932791585, 697725469, 739802925, 417783928, 530322736, 689774871, 936311568, 241103937, 3521906, 943169413, 818582953, 441718464, 736967953, 32964558, 876680770, 571792946, 877812978, 298006531, 946872519, 818601383, 397880826, 306917487, 974441601, 417490162, 596268138, 550148939, 728347200, 525715189, 252588339, 159300732, 908036027, 485683162, 319262407, 650688839, 444978653, 675148744, 663825138, 595867279, 601918782, 509387871, 387643530, 252143331, 175342659, 369316536, 955448187, 468611249, 827371036, 106674969, 792723706, 921717691, 261315152, 438355800, 536649863, 118600045, 580022577, 837980446, 915027864, 488953072, 166942234, 121702104, 282827493, 33811094, 264601835, 697395753, 758331025, 460562419, 661776659, 603126663, 135508693, 18070721, 816161078, 43800422, 745569448, 297127530, 252617221, 409557014, 504670446, 880394325, 819534188, 449546171, 669337584, 820619341, 184891006, 809311187, 159490172, 934081215, 471144905, 917871470, 383249098, 767639231, 501804806, 867699982, 97482663, 991894058, 502902913, 457924233, 235772728, 120059640, 471404572, 418640164, 796749337, 884715396, 373490539, 315204547, 875694208, 882820176, 571585124, 795112399, 899878622, 950346063, 734371932, 435264627, 823235001, 764596698, 944984736, 724990926, 518324522, 208374588, 143958253, 295957868, 997607882, 622113846, 89409853, 324426646, 526812725, 887937857, 9242879, 868877127, 391738492, 565950121, 291059769, 922024566, 415464520, 551954645, 807666712, 413521823, 228025840, 526452536, 562960385, 906565819, 803103892, 666267790, 929723599, 976953569, 111074976, 429420284, 837161900, 312739976, 12447175, 74041168, 687543860, 633979864, 846578667, 450391738, 107315174, 233237385, 80426975, 311773273, 590603851, 162972060, 912706750, 517798952, 720431751, 591764198, 798839458, 370700607, 636758625, 651751707, 725876751, 831139589, 202094277, 352227371, 743385763, 493988052, 891721329, 313094736, 198719551, 84095382, 208912988, 157142055, 466731154, 963034302, 665968701, 316810614, 199275182, 934727791, 797407116, 257650561, 416314489, 631506157, 614898732, 691145005, 586859638, 836139692, 409334067, 887604882, 531412748, 431268935, 722847932, 870789722, 625150397, 767377140, 784795644, 342128836, 241530187, 112350823, 769080106, 353760448, 53585152, 319520015, 642906548, 3268567, 616176553, 565160808, 238703460, 945973409, 193817389, 652493598, 388666686, 122337561, 530505008, 556664850, 451765895, 612451766, 564998699, 980721121, 670499449, 486266383, 685585232, 983390550, 515573142, 723486808, 429971424, 186489493, 900915107, 446162002, 44195415, 721458526, 419382420, 38472364, 833236265, 742693020, 152289252, 788193186, 158534880, 709857716, 749692283, 838669423, 246931602, 432779306, 452892037, 379150706, 932674412, 834895791, 63823237, 971883606, 19950235, 125686603, 184080153, 771784856, 931889805, 910272493, 91086825, 672174521, 129873723, 120628653, 153232096, 421582024, 134854291, 857585432, 791909848, 886973026, 684807308, 522339755, 27019515, 120986756, 93938277, 394714582, 137916484, 545632001, 416067371, 955901998, 737197454, 276881529, 200880494, 200210786, 201382939, 88603172, 968466280, 946719592, 852109140, 170208850, 618661849, 808755398, 93699019, 472965026, 666049850, 864672953, 202150658, 146219364, 529903725, 694968427, 774710888, 695690527, 975561063, 543791842, 712420773, 339634466, 412937220, 445125911, 816632838, 180353024, 794988472, 272128307, 558280784, 685474672, 794226082, 308420646, 161604439, 664740149, 57270111, 671706433, 403836511, 690809050, 639963225, 257216895, 967186256, 877003452, 33371717, 678943845, 205349068, 204266438, 113014077, 311831096, 271180892, 230863634, 834664394, 189741775, 225454859, 701649003, 28558475, 46024313, 129103814, 927831952, 336871941, 268368470, 534710260, 98266561, 860456173, 58303246, 713763110, 545122597, 304308805, 377925326, 967056249, 24270457, 492144901, 963185690, 575042937, 676016448, 572412148, 127449999, 942812609, 464498389, 686975585, 634310698, 726970388, 223304640, 392076644, 37436532, 999577952, 433596510, 450893746, 41594508, 938064667, 162362543, 180567918, 330826407, 831883855, 872498659, 905374879, 234314456, 1690028, 932882230, 813821405, 897120941, 610312780, 153021946, 394075752, 564315820, 217724865, 645556053, 201955868, 432667550, 625254382, 100396400, 407275555, 159267747, 266617410, 505037638, 187305277, 421879283, 329845624, 845971555, 932712123, 794330869, 280222316, 993534372, 15709157, 410064240, 45223373, 130810233, 181848167, 972495506, 855473340, 184899409, 276596449, 361359373, 197311659, 929170490, 154515025, 612426231, 706645594, 716582270, 212234101, 949264455, 246580819, 472303767, 387761508, 438163293, 373034005, 752732522, 676156721, 770717256, 282166512, 414653065, 239175977, 947929162, 31315205, 632910563, 918021486, 449701935, 732284512, 705089200, 410280868, 567651668, 499123066, 623183068, 648501761, 7725981, 697760836, 680474976, 267185913, 86724888, 595682747, 326720240, 338784224, 643186769, 894638394, 779067952, 518106609, 652334385, 45367437, 306138260, 754313117, 882783693, 856647229, 996142913, 928719098, 582462674, 770351642, 48025526, 268455896, 901856644, 987586738, 311824759, 868528826, 43557545, 243134916, 901640220, 29174898, 495498466, 364574572, 124758335, 7676108, 588380837, 686922015, 732555383, 474906951, 983070077, 559261369, 377986296, 225211041, 525653320, 220795793, 39190849, 938714152, 100850287, 532570449, 184165016, 274486516, 606523033, 39713904, 618708245, 472665290, 62905052, 922767035, 649502393, 125297053, 88722436, 316629164, 16682629, 263267114, 276770014, 295062126, 379134026, 560665854, 690349664, 489001678, 67937508, 314009954, 463869681, 769704707, 312100972, 543248859, 148302438, 686338912, 217231154, 109690457, 357692698, 480765785, 779119801, 613561320, 451754302, 228132163, 221412586, 121589493, 847573833, 866828181, 556242893, 712003522, 474446048, 70029459, 165874727, 774201826, 245574651, 809070706, 13008546, 695215898, 683067125, 763593209, 764710607, 489313451, 796268962, 196597499, 251558476, 51341986, 740910897, 873204250, 249131287, 667507174, 786856346, 604474983, 942253712, 837743906, 713990862, 668204701, 705857922, 899556484, 481658146, 954306340, 462799196, 408862387, 314726495, 429050331, 807263256, 468763545, 204361148, 508259725, 671412127, 615761930, 877899480, 970615258, 227853658, 753566040, 610081705, 645749538, 462300112, 681249544, 275807651, 479644612, 48748794, 24844886, 895940714, 433970387, 687222785, 124592386, 565405950, 456695031, 626509407, 18150260, 284511170, 37810205, 934391563, 423893106, 960097671, 584923487, 188729211, 950909944, 837558087, 327692653, 858304808, 400231520, 475217469, 677530166, 155821128, 942491270, 16444835, 479988130, 558363586, 189198735, 751679344, 858475479, 902405036, 217947462, 465251689, 761568755, 747427843, 460037280, 183235588, 318795864, 362667376, 572179478, 744213751, 978238392, 940658530, 403486194, 109213485, 829453427, 20394071, 901216926, 681821836, 953926582, 13300776, 10681424, 755248434, 242720529, 686708382, 382546355, 636177389, 728025130, 862204907, 846166989, 976762670, 682555094, 815289826, 908553720, 827180134, 582985652, 494652516, 723567369, 630844740, 430517347, 751647587, 440188199, 777122922, 571440430, 838592354, 653873765, 136228969, 203934228, 635274763, 63272117, 969045804, 812242788, 314170822, 861884924, 893357962, 727143427, 336358730, 318791986, 617264357, 386186885, 102880216, 140639030, 897868620, 890232980, 209394415, 230074373, 505083221, 238948881, 208252468, 975355388, 98368664, 95480383, 611957140, 755038565, 112340234, 107372298, 282964981, 59454795, 881044741, 467207094, 409453124, 56606141, 651896222, 718951682, 326917272, 146368147, 482080110, 885369886, 471896742, 925897479, 686605303, 735037199, 559209066, 332676394, 229659200, 400785554, 552179900, 821141865, 448169209, 570112747, 339462652, 188532255, 561273645, 744969872, 380669713, 672318286, 146690548, 91741325, 380885031, 977518244, 825548322, 616080575, 559251848, 586438587, 775199138, 435295099, 319868821, 613649805, 849405103, 114212011, 355672673, 964248912, 620258708, 471262175, 954996483, 960138710, 688094520, 775210168, 696492812, 57686194, 110404064, 442305718, 83428432, 502177232, 935689106, 581167159, 78504597, 624937500, 730342428, 755428666, 100159332, 604288964, 968216276, 385884642, 868759727, 383356248, 345206870, 36814550, 277183278, 583804276, 616420055, 775059128, 847835043, 139488823, 580987814, 652493418, 696486925, 478440735, 360700735, 595793307, 181137332, 563852413, 267774103, 825120992, 214720247, 5318311, 524436263, 461688175, 913288165, 980742124, 147904858, 561681453, 401165469, 355073056, 125008541, 321218820, 15908594, 423015611, 659907261, 740488558, 196570463, 380714533, 22107340, 205233727, 479035013, 278836630, 536593570, 267994686, 368908909, 396765180, 711518235, 857313996, 59356538, 731472739, 519640328, 959942868, 408844447, 254480486, 968014610, 484256446, 545374673, 136703931, 30669465, 5655597, 303716087, 819891267, 319826206, 439503712, 447309052, 433973195, 197247272, 226285280, 178649181, 682763048, 702168261, 592791496, 69055537, 879816207, 422873596, 64957935, 606980159, 720596994, 782342545, 14625896, 607151750, 602873833, 539892258, 950208134, 835865482, 4447765, 423035275, 775139035, 151728578, 315317838, 16898165, 844024823, 372920263, 905799025, 273008680, 874673976, 176402825, 163833626, 544752903, 357546787, 806690655, 478831369, 158403968, 470499899, 762579643, 745619967, 533962789, 987236412, 645546035, 646352823, 289185650, 651287169, 766274199, 643506546, 611287705, 59352029, 944461980, 309643678, 734119328, 347146702, 590550647, 60749610, 158714924, 580457711, 333714420, 856518404, 464755333, 895477869, 663289463, 895396732, 501001558, 85266375, 379875325, 298463576, 755399790, 244318525, 580187875, 7199134, 183290209, 962292727, 992089208, 134538998, 200683816, 645861912, 865923905, 78535994, 281937871, 173574170, 398454248, 860958422, 637437768, 624320127, 20126064, 658493639, 765097934, 57137425, 683783651, 679414790, 297471854, 341076940, 956229375, 629961940, 847381884, 399607287, 599601074, 43833924, 42150779, 208563553, 610307813, 98659168, 933330881, 898833570, 997420634, 389224083, 884233642, 872788184, 238451280, 470201872, 770043293, 371300959, 295112562, 891370563, 728976045, 995191024, 320882776, 194398767, 292269689, 117112992, 678423562, 487333118, 95765960, 190009770, 348993691, 260041689, 699134365, 471678793, 342999415, 122737384, 894844054, 653383246, 337290883, 3065964, 237673342, 157268126, 708047007, 773257874, 562216848, 683285690, 986336100, 535889424, 26985864, 872837416, 272284351, 460016280, 185858984, 429584916, 585603286, 581305222, 133472310, 681119877, 246471283, 403621953, 846844353, 781549352, 187546341, 879255202, 452058691, 569854191, 27063255, 487457855, 641487822, 9225698, 449451784, 307541033, 708160509, 745471212, 861208075, 768232471, 167953326, 233360853, 175217320, 437741600, 99932833, 330317052, 90319782, 20707655, 372037950, 176977836, 585825723, 196646106, 137246156, 112941997, 740407981, 790528804, 522747088, 291174166, 390972587, 615610314, 484877548, 217550936, 897262751, 191692754, 760104027, 257288794, 509702830, 507258890, 132814310, 196376917, 663851522, 852213852, 419901023, 949985895, 22477927, 231685824, 567728211, 214503116, 194357603, 790071354, 792416044, 749560886, 210263952, 660997683, 840210728, 793519616, 354485711, 198716207, 194504322, 454804011, 77875936, 344367387, 225936631, 69006046, 610655039, 878431516, 721522978, 393191837, 873482784, 316248801, 993193659, 712431810, 558637298, 863284362, 355851112, 99164405, 672089354, 838002714, 239147862, 418511889, 329898526, 683759881, 128348574, 531006072, 721437774, 565902759, 111930463, 902260402, 386917368, 197682330, 334218947, 923375749, 638396654, 202030766, 802341545, 260902797, 743865100, 900054634, 537211025, 629316524, 85982149, 436084541, 687383101, 352705514, 593182780, 335298662, 15149435, 892675868, 706853099, 818082592, 834324972, 222456075, 168148103, 249865195, 855199946, 654598886, 304808561, 483756325, 575073647, 424156165, 923837106, 423847277, 333883018, 702480469, 960381536, 832561886, 374187823, 361017231, 790998837, 285740862, 139184071, 860486939, 853034367, 945175819, 62072175, 300620109, 744503867, 89484259, 503897498, 392232511, 232649891, 713272552, 279424593, 531796026, 217130314, 157248173, 712937081, 488342488, 37423682, 343881772, 536638416, 377484952, 858221762, 849246978, 487246932, 660743520, 18719792, 556132483, 801771864, 719160610, 662869582, 97364353, 807212759, 256972176, 26517698, 494417720, 424395535, 128579660, 221917257, 544474030, 282443565, 92252792, 986956661, 337155475, 858532998, 80484372, 528893305, 801294870, 60291982, 952617324, 996827571, 998796880, 944318572, 544525289, 578532461, 534988074, 875565775, 53838220, 140211625, 107183450, 816591767, 603876683, 23032991, 295109360, 301241956, 301107275, 550180524, 154912203, 387673283, 696800161, 131789624, 254069311, 550567955, 276436431, 174419605, 451616086, 950905114, 320452390, 683127737, 502708025, 54655819, 501388054, 62097464, 997857814, 696144975, 601832532, 674328002, 848908953, 530998785, 220440588, 872179573, 223939703, 920777017, 98883482, 199656749, 30792653, 731069901, 30580567, 864687202, 558637068, 710655356, 445225062, 521512996, 272215571, 339211861, 424528489, 295805899, 787292624, 282381961, 31005678, 570001074, 790144579, 306735478, 794192860, 752403826, 318150678, 386197008, 44299858, 529050008, 378611591, 8127356, 314513246, 825567852, 701950378, 959176235, 745827370, 991532702, 703676246, 31449349, 440613326, 569650908, 421253867, 401404122, 677135028, 353940298, 286282797, 385144711, 113314322, 107693898, 663756440, 162887284, 796379634, 505838938, 887422847, 551430538, 654300439, 991944488, 348259568, 395360717, 120445308, 599324553, 714793921, 77976707, 82491505, 144466254, 278543027, 124850295, 424510953, 777841441, 234539617, 341744986, 260977580, 195489659, 548757014, 723300495, 808871041, 643772040, 759943485, 893363058, 676270748, 926949219, 351295457, 766188765, 865150097, 347551611, 592112698, 558051016, 613151238, 95014958, 105832930, 769922352, 563460614, 756803588, 505083261, 925562586, 270967336, 832275163, 232597928, 241968392, 389513882, 81294937, 415376924, 935884559, 755640816, 504224487, 230526568, 200155956, 389380601, 611716464, 44801050, 146401806, 691000590, 887692342, 151711747, 99583145, 151089993, 761019296, 954702920, 702524054, 974558440, 556367325, 909849264, 345500154, 819320046, 266417474, 59530039, 373581039, 191485717, 820612413, 667427691, 224616580, 12840638, 264796352, 696256056, 253655424, 675863721, 103722785, 671047034, 319653155, 768223028, 642636814, 614637776, 106856282, 354474186, 886530582, 308449101, 513516428, 174577269, 740770924, 727773892, 192088924, 827403631, 924325387, 251267394, 627566030, 939882816, 835337507, 173526786, 953499757, 917390368, 950240045, 272723423, 843924938, 51552042, 825388908, 779707273, 352288039, 934433876, 418755913, 967180594, 953770786, 210859924, 349186812, 458179482, 100305747, 101547526, 775531664, 253793745, 564356228, 285230071, 593983199, 983301497, 499052724, 627185405, 986198050, 857412383, 992512664, 393174002, 543514663, 837798460, 248081279, 519176381, 371406007, 328927014, 840728318, 123081289, 274976193, 423840560, 2225477, 668820258, 305842183, 695351429, 112293993, 499483595, 428203836, 186037180, 290944764, 415356981, 94398010, 689781729, 770573549, 287419102, 405682794, 243540918, 472328033, 70035397, 780358734, 718273097, 598779918, 16043589, 973632690, 619250067, 833240826, 552237187, 93137254, 602291945, 787007210, 302663075, 154667191, 537908167, 198757782, 58587313, 735833574, 128224406, 112673785, 478561052, 266070427, 877026739, 542489264, 204227384, 821471097, 207778079, 997498763, 151231557, 927081060, 920473677, 365094269, 159532403, 434861685, 858054751, 323886309, 394434268, 49901571, 86001227, 74483994, 957369807, 188220023, 22459593, 216251751, 6658931, 862942417, 850172338, 291662443, 782326732, 834271756, 967533368, 601019018, 879880125, 637821937, 690373524, 221616164, 877063910, 781008972, 881229426, 917225031, 929404585, 96064546, 488648881, 671720685, 670741475, 462408108, 60817248, 257836222, 262358412, 591677625, 338222755, 161975451, 140110473, 263721016, 750588170, 333791301, 180150838, 586775840, 339779166, 418113408, 955375821, 410677758, 616030933, 967511492, 587070885, 648306063, 339107222, 926805547, 891284989, 799854258, 106780076, 582094959, 713936385, 655903800, 903964777, 51968587, 142320192, 71501772, 25805228, 23056306, 574052113, 143440083, 497745452, 998843550, 79828138, 26412418, 58230957, 690619599, 297032095, 51729757, 661753912, 648827504, 336390232, 230257090, 400036906, 947862198, 876258686, 135133770, 590618895, 119987411, 864626764, 107612666, 978515591, 754766987, 672225591, 94639628, 170910703, 244342265, 414447081, 210003734, 643354269, 582992249, 390505883, 251252369, 620310440, 273701060, 164898093, 714983766, 743954156, 278750153, 855718465, 519085776, 735107401, 471562590, 712753569, 560107498, 707971694, 336113812, 298157748, 301584153, 427069770, 44953005, 652364548, 658951932, 357659605, 721413358, 32108926, 115618048, 574373670, 920897616, 220954639, 31942913, 189336255, 774069051, 252050459, 339989221, 236572258, 663541465, 859364263, 633690439, 381782640, 748898259, 173726746, 412451028, 192222001, 326106306, 722802391, 102167411, 781395059, 550993423, 553777713, 363608429, 281876836, 43467319, 778748756, 725914308, 776129343, 755860080, 678279456, 976874720, 565872094, 141999997, 250519009, 441586558, 500983751, 749803394, 63556107, 22738804, 309858397, 15358229, 358981331, 633657724, 440726909, 28431541, 657422571, 592330081, 572637125, 482291682, 9360301, 872346107, 743341423, 87379793, 322839812, 668409060, 236584975, 907718373, 711291879, 481224321, 958172333, 197220472, 695947102, 52791705, 730262568, 254185580, 386864563, 653577178, 113670251, 295759287, 488828824, 716955596, 243210998, 346501369, 821076608, 132757075, 573747037, 823473820, 927897562, 869547288, 712990389, 448900886, 342956013, 62946866, 470700815, 778713867, 591184071, 874254021, 850048762, 862801087, 906022336, 381745405, 888489701, 72579896, 674193275, 523047089, 57562013, 488742855, 723796291, 502818880, 70231012, 194873222, 248436665, 881011336, 493388234, 986871195, 266001859, 805574107, 324129304, 291286451, 939365850, 614937137, 799592506, 124645474, 591165664, 264480988, 43946154, 365319517, 254900857, 395105462, 661158006, 623284071, 56606772, 438868503, 899964353, 610261048, 592220551, 262264227, 113867784, 193973750, 40568260, 790754049, 266615786, 417989549, 444677017, 728938005, 420210665, 231476103, 651387430, 372132429, 733363133, 643252984, 545154801, 584039189, 315191527, 729476622, 347283407, 706782604, 836868755, 369557298, 722335612, 596740966, 993239046, 705077042, 522757734, 169234038, 722358125, 312995249, 31523089, 947857746, 845743937, 579326153, 442766549, 29389217, 905422346, 409334484, 269631386, 233631683, 225724529, 923951812, 889956534, 203715968, 829383665, 62973801, 386543036, 526031756, 297744561, 345911153, 273523115, 759380623, 248452136, 29734461, 319129446, 730199171, 754935454, 364320935, 659271948, 955157818, 651552939, 70070951, 426377554, 158188832, 737182146, 482712249, 627256339, 423009123, 10595346, 208226972, 725354163, 891720318, 285833075, 742188228, 739170820, 829286826, 500004038, 176466978, 34633101, 491439998, 47563491, 895379997, 72325094, 979727784, 525918634, 597037233, 1253490, 438491495, 383927229, 348915987, 270213822, 659637193, 121572526, 439308598, 956950675, 182997059, 543564241, 416640645, 963245065, 120805278, 602403709, 751118608, 232868269, 967076615, 303760989, 963744205, 483762681, 714566879, 249844387, 967301203, 121533022, 173534810, 924948108, 23115684, 204503280, 689877536, 577238466, 291860468, 364110721, 894053981, 535662030, 687738242, 351387870, 239733208, 919563012, 351181369, 854385366, 527299716, 380170568, 154063459, 16250013, 385313238, 620445227, 347477450, 294600438, 149666332, 934544422, 530343938, 229559987, 320684072, 471431174, 771536056, 467021111, 474014384, 383660108, 117813690, 206262236, 588464004, 834122700, 869784968, 520256984, 797257253, 62929844, 312485086, 60133028, 573082857, 961228181, 281469050, 628843197, 429330412, 162744004, 646175539, 1119615, 459335628, 629751548, 844476576, 212719391, 118526553, 69086729, 7888637, 258349798, 182878265, 97088305, 736633711, 229899339, 657544631, 716401531, 28103941, 822945063, 781537595, 477796317, 751840789, 264327691, 554124683, 693636310, 815951077, 737246147, 486654437, 14564934, 508572660, 427849, 93341145, 109271727, 191201461, 964702303, 596816148, 443996292, 136131341, 487972056, 91204483, 265979813, 502920362, 810652210, 478113065, 810938198, 951164190, 967510479, 788860727, 650928434, 79677902, 545421232, 181472052, 14673997, 914766164, 13900403, 224019226, 67467365, 60795978, 518290825, 717627223, 975622168, 950805529, 800048952, 781975241, 435302116, 920976938, 222344303, 92228384, 357481763, 763469708, 551757242, 529802867, 127801267, 873137987, 57456621, 439295858, 861592037, 584621490, 558554354, 817920676, 681672740, 453879759, 305645955, 891782738, 216672678, 942240725, 705006341, 99312050, 266519177, 186216016, 564809469, 736787018, 509886679, 869468409, 267862731, 365288612, 940687816, 190167702, 803221656, 294247907, 816607721, 360314708, 816463969, 242280715, 103002439, 647240311, 723793354, 708057443, 918857346, 872745297, 737529797, 213492298, 401841981, 197781877, 18314148, 561996337, 596215117, 269788807, 915492200, 629275831, 438737245, 641655389, 129473076, 547024393, 289350393, 284817603, 480810091, 344470024, 967164418, 155882593, 240184933, 463033732, 792336817, 672727114, 741774492, 936871003, 799531606, 577861735, 988296746, 569271364, 107811251, 706334064, 700896456, 856812505, 483560612, 741885122, 842665023, 805590109, 680494655, 190087409, 22835001, 408769441, 785450835, 655472403, 157232143, 424900489, 1428815, 883888354, 232631142, 163571550, 827219382, 805423309, 400736232, 471821397, 678960641, 14946273, 297619210, 753401614, 696104761, 973608492, 618241016, 916517496, 246092140, 986113339, 449436269, 796051684, 523098985, 650155079, 968339192, 397789538, 747677460, 360278724, 232528717, 859384884, 780813321, 284468717, 59629660, 272186618, 47149208, 86189919, 489326197, 142622130, 528676838, 889214301, 124532962, 73805032, 268027056, 564189199, 643179526, 346409773, 704099365, 703682192, 883495791, 638565274, 506041885, 904792883, 950423991, 25595872, 296701822, 160345722, 799298124, 820023780, 64056660, 523187286, 839651709, 635754596, 377451821, 933403465, 124438534, 647769566, 894993535, 255206134, 509238907, 801489120, 502358555, 893148781, 340278576, 253716224, 884287930, 430536841, 56703288, 134109891, 611372364, 606526574, 514880499, 281196454, 39118238, 496620646, 73564383, 2045781, 845082077, 267046152, 366291041, 277249272, 644064829, 648372340, 24754877, 422260005, 72568596, 830676766, 673380800, 448823683, 340912770, 336532722, 35338522, 842824103, 901938081, 509822792, 579791271, 709427380, 868948900, 997416744, 380050961, 789382894, 537263910, 281279593, 519139875, 356376464, 47450668, 802137427, 584325278, 391760856, 631574623, 163631814, 111067538, 395021283, 839469472, 826685366, 875327254, 221831810, 173890589, 569934909, 492428303, 108646901, 776875922, 972082680, 162499885, 307668300, 67677843, 785210953, 13668041, 946792292, 654377006, 232857064, 601398917, 574414818, 48402038, 634501201, 278974905, 811584033, 182486049, 280613626, 474327105, 695373979, 410639160, 71958394, 697710470, 361348190, 65335366, 444062089, 283877944, 458743115, 771705543, 889517223, 730069642, 221797191, 825303326, 391107255, 806963926, 449451927, 56089637, 909463275, 651971216, 353644255, 94916656, 714005232, 364392261, 547519371, 983798782, 483362481, 199700172, 359032329, 550141309, 975703808, 666386277, 737548896, 584729075, 574642655, 860877794, 429374975, 173541631, 214964176, 935835921, 722077452, 718178829, 359127597, 515885040, 296305929, 751014390, 114983681, 896003398, 347907595, 395202565, 624300244, 475798849, 172054989, 405255293, 534357038, 146301815, 817211577, 796278904, 62082228, 532529227, 437232494, 153775651, 531052977, 897452785, 477712354, 240784643, 470012081, 910541507, 567847581, 118037769, 22060264, 699421501, 712455587, 993185775, 402240159, 857590714, 307532047, 853741297, 381254894, 88270740, 407461014, 94254701, 701052201, 123255635, 325947910, 732068367, 126017248, 556424519, 645579305, 377571373, 774828982, 328673431, 355901675, 268234906, 854625516, 304196401, 116349503, 870905463, 473340326, 636759474, 850205857, 787689375, 874006619, 782105927, 758929485, 904557879, 539197176, 80517907, 600289406, 366794950, 516315995, 350075455, 59845417, 325469171, 507518298, 295261308, 186598941, 348053987, 706289713, 808114633, 317197685, 493548718, 644216752, 979690156, 135155851, 290996686, 245488300, 75736133, 196225048, 588907915, 63930052, 294235470, 296867975, 545539171, 839390727, 48633409, 538805545, 454578993, 708262224, 666406987, 581105933, 952684106, 915659543, 837928462, 866632693, 148752556, 877170998, 185555570, 187368999, 691548607, 844878054, 841017640, 63452495, 793588850, 545058075, 302068802, 174602921, 424715309, 722757680, 591693806, 209407808, 740141027, 652418247, 21205979, 195824769, 442702605, 872376274, 77017008, 323605836, 631443149, 623278404, 227262090, 43130591, 913592143, 217789247, 279647811, 938394328, 527793598, 595053355, 724938793, 217326614, 403445015, 25532656, 592239841, 927309624, 570210233, 826108064, 722287683, 324254064, 317202445, 131103538, 896663107, 590619181, 98501759, 435957877, 407867899, 785324371, 826888191, 373490561, 928187274, 65121529, 768450279, 662175583, 972732993, 689754817, 733883467, 572433702, 999865442, 457517042, 408951853, 997820839, 818342470, 198420266, 50481007, 102547840, 81100718, 201101185, 776008358, 827774931, 94774976, 537896954, 361166401, 645808838, 972739634, 529808788, 584756322, 93751597, 337896177, 35927701, 843934946, 534021463, 782345690, 268485641, 312800497, 956899137, 595545090, 378742831, 150299769, 604479316, 6111559, 242140679, 986658238, 857028141, 470103712, 521246039, 1206572, 170978346, 692057147, 450947426, 911033537, 445478876, 394709266, 532247027, 280375281, 820487896, 105207321, 937025196, 927519840, 830234939, 788048149, 875723770, 99053303, 978528135, 850350575, 691196852, 900166361, 360710102, 268331617, 516468232, 238024446, 723010707, 717719779, 800802601, 385452281, 892466786, 796627760, 462173604, 469222129, 596482971, 815980398, 448828491, 374170018, 579274025, 585309314, 529025641, 21484839, 754656326, 598517323, 765241878, 668590316, 150197314, 847436458, 347942147, 474974548, 882735152, 536163114, 869089128, 767671456, 803171036, 421485242, 59612141, 538673456, 964244387, 93996827, 222825415, 665001341, 798897502, 663990172, 650350901, 53664039, 516894341, 257510729, 247765140, 589927162, 503307224, 534305866, 951876540, 315923406, 492888505, 410295720, 561554848, 797688707, 837240079, 168327000, 107309626, 22353151, 786902000, 898255547, 296648999, 560934694, 694211945, 96477912, 3669769, 473702283, 356673289, 957604259, 799464580, 836732947, 835214815, 718137918, 19374895, 635815665, 555800761, 597287525, 899222272, 189391537, 475193476, 616732875, 37621319, 121489398, 867910102, 20855178, 142429321, 745269930, 621897377, 650559613, 463225670, 950836285, 578835712, 535313730, 307526338, 47527675, 3533005, 632764154, 893819029, 66578746, 770487183, 47130177, 120271116, 938492701, 483647907, 956885313, 383716011, 941866472, 192931995, 787960595, 923447369, 382616089, 861500718, 281158144, 661084841, 349218552, 188361441, 75102744, 324498333, 846920045, 28845621, 224005854, 958707590, 912793218, 785835703, 725639442, 184237717, 774244317, 548255498, 693332044, 628808591, 959636655, 958311127, 939146175, 708886525, 513165677, 313436627, 494736671, 526812940, 678015008, 460257599, 836010513, 154357106, 625912439, 421229738, 55951323, 573392089, 57061417, 389255502, 686906384, 498788030, 814180755, 252948531, 939804987, 752303815, 53909635, 775868636, 830440088, 232400900, 338868567, 676319977, 282397759, 521012445, 152163299, 506001548, 607371717, 378989209, 432250053, 36286821, 769296018, 504260135, 543742730, 129934092, 367419982, 789960940, 229222175, 42189780, 456385978, 504365754, 624204216, 714073216, 536217608, 671368979, 547946196, 323745992, 985082505, 912950206, 258641034, 507608191, 646352877, 58521971, 283732034, 212896505, 71680601, 24625836, 809686630, 843588491, 483107929, 775095540, 482836543, 315858264, 164119128, 258079306, 842883635, 52923925, 746395361, 993155668, 907931041, 238917278, 943025427, 681671456, 596418830, 743289852, 809012756, 24571235, 631716840, 764151947, 433462061, 880706492, 357441226, 413850113, 138736616, 500693300, 697393163, 821093756, 626242223, 787819966, 381064479, 509586938, 228579830, 821679743, 730894938, 555761402, 770421453, 716434546, 918122412, 334242765, 401664382, 623323548, 465254441, 162447404, 932815885, 965382344, 891555791, 255082036, 375969108, 950636069, 983189641, 378173311, 52573390, 650142418, 982256994, 443682143, 247643659, 679756860, 410616901, 68319351, 107362669, 523594593, 388593708, 708757452, 373955785, 969164217, 72812237, 249985093, 87168275, 401718756, 475620170, 189564414, 19574942, 56060636, 557088232, 123852003, 101680522, 512327747, 470773045, 804028110, 905074534, 817847144, 78907144, 287001307, 523101522, 596144520, 940176675, 451492945, 729231384, 168334691, 378996733, 697557519, 897990902, 57479189, 980603873, 830969557, 56643110, 653899069, 973536564, 65548762, 687267076, 999555960, 140811332, 96759756, 990085874, 536829929, 530427414, 301363726, 550814368, 211031293, 514040843, 668255735, 464715234, 914374478, 568594562, 547697425, 142381245, 664095624, 542034533, 599260227, 208787039, 430478178, 1901043, 957133817, 619144063, 667293697, 152737069, 558835375, 998240327, 20919229, 278293823, 941888758, 849707178, 547130287, 12315257, 564719416, 5808845, 346715048, 589804000, 831878458, 11837854, 989265559, 356432357, 247832014, 763731429, 617252076, 115836420, 608405494, 647909382, 119666521, 103124803, 374421701, 503951735, 59475368, 972498929, 468596447, 90810908, 55216537, 362317252, 156541955, 373968315, 559509132, 765496655, 903105387, 165225030, 446305479, 448484195, 990066521, 923117455, 153204165, 129088537, 470425245, 434417803, 624855229, 303074898, 511174627, 305991001, 733317651, 234554084, 43796977, 973811833, 26466208, 611419446, 111760345, 893573557, 806935792, 948601341, 47468969, 554075070, 181127368, 470669046, 64051768, 921808246, 263802239, 994506385, 793176606, 18532048, 817381537, 16329382, 448615304, 680720897, 45121596, 318284576, 584030794, 399563773, 291830076, 312555357, 713522538, 408590852, 225124363, 854616821, 981945637, 309600402, 606889734, 5637693, 18304272, 168819764, 66093062, 170405242, 992278358, 687257285, 695591104, 224631768, 741114099, 934834771, 444657592, 265715821, 163809508, 268613978, 232883504, 425960621, 880840291, 414662471, 544746236, 971863892, 468782179, 923624547, 87241799, 859167687, 374387972, 405822268, 482789304, 877175890, 528020272, 95717776, 515066666, 5661940, 728640439, 754690237, 92923743, 539575692, 310493127, 814579501, 124055270, 315368293, 864703032, 629068724, 380745558, 365623199, 5827209, 427110588, 241200957, 540910306, 116043043, 269590632, 749484381, 376140340, 978885863, 417716400, 828586745, 425629647, 464560992, 562002956, 91299940, 805193554, 497298607, 39772937, 552867122, 290224033, 210945804, 550028335, 81171184, 728936463, 754067963, 437610537, 590497958, 223035169, 45404270, 148791411, 394387547, 143604048, 86414520, 815029160, 667768656, 616656901, 208352710, 711498025, 770850644, 54747174, 762624405, 676068853, 341217678, 701455687, 624789989, 811229164, 554900350, 267872379, 553483722, 893703499, 136444788, 732527786, 859762273, 618750479, 841084963, 893545502, 90176780, 973442234, 178366420, 256522328, 893417992, 216331323, 305403837, 932555406, 803103063, 932578986, 541075978, 781680725, 38275944, 803971252, 866787178, 380875875, 32981102, 105014563, 931474280, 417744106, 188954433, 903124332, 455674192, 498990554, 394592099, 66627341, 6180776, 980577504, 278297854, 988303797, 403442988, 806614674, 225413154, 929659053, 595084761, 522213835, 253603207, 120083210, 690667857, 101368480, 968445519, 116441793, 638573728, 413233316, 121160630, 425559558, 732023072, 208854584, 517394750, 727760999, 218542663, 45665071, 641469519, 915925611, 23508259, 897908457, 687378138, 696391798, 628519267, 278306633, 707034941, 598544185, 467482528, 273382676, 213726009, 226608443, 510107210, 491994627, 29441924, 295410470, 305374166, 595180995, 641685156, 644145150, 699091218, 940532453, 766590666, 895365139, 518178338, 23299416, 106405403, 571381207, 582292521, 380052160, 856572264, 322131608, 819296652, 849386644, 904120492, 442231527, 663290319, 783364802, 334971974, 916515126, 880400578, 420519342, 354143891, 825610063, 96228593, 782778425, 36057410, 807755811, 612015380, 168865563, 538670235, 75791290, 34835301, 278086492, 458908914, 780371304, 226840985, 509261940, 747294759, 895321485, 893521884, 199714389, 776500141, 180498837, 575770756, 455149403, 99963456, 305037795, 600945257, 740223827, 362646136, 331932108, 892767685, 944982135, 621489854, 456312081, 938661908, 808181523, 302408532, 53948291, 918699047, 705208452, 118328474, 584609922, 3855995, 659137873, 767971462, 303070052, 170198304, 943754754, 819368007, 988419637, 57256373, 740101435, 145357089, 355409283, 507552156, 932349910, 731760110, 921676800, 137195679, 936303874, 625954583, 968999469, 790034376, 957452455, 313446667, 590817412, 852159993, 699214507, 224273411, 109146919, 801889664, 495244906, 134854579, 268016249, 707928762, 819793825, 475929011, 863787009, 130389973, 209095520, 871139387, 459356463, 994895502, 284440683, 86090192, 814313986, 98739619, 862607429, 409458903, 865901953, 779129574, 829740389, 184898970, 565261835, 522306288, 103760875, 800628288, 448238440, 37138864, 23593016, 190762927, 15701713, 464027619, 455132617, 604907393, 970608805, 61293634, 53928008, 431394516, 310196710, 933826028, 467232135, 667350424, 335035604, 515855097, 697867277, 54984315, 391983482, 328395586, 251145225, 863794634, 97565404, 971729905, 763563013, 354048014, 757198833, 765214887, 885890351, 648595090, 690199291, 107214863, 163217862, 529383258, 811417026, 819210766, 659196905, 369331536, 108977903, 349553862, 790414061, 396697274, 363325450, 327305319, 559471324, 871221532, 477785782, 354161149, 990217719, 348837620, 309611724, 862242079, 397962406, 142961948, 244509781, 624851695, 996861382, 875256683, 545148143, 225646399, 740060257, 353713758, 640618767, 260624143, 754822791, 98652192, 694525354, 121614204, 11612764, 870386523, 86642858, 832780632, 304804871, 357382015, 794524990, 969326746, 516213812, 607155279, 182283448, 318970225, 939755489, 874532114, 999697860, 997309426, 472557058, 443187259, 713469498, 425777103, 95177149, 998924688, 626812254, 397060259, 919898708, 521501046, 129626112, 156186722, 574295788, 250002624, 340666707, 749206106, 495414499, 78020226, 772290034, 787707334, 653473077, 797286807, 251895784, 770264888, 855920456, 710132820, 500385234, 629100460, 265559566, 972580306, 933347892, 606484099, 45443317, 85089213, 892085992, 884950211, 24938107, 993149547, 556390451, 325459652, 801558409, 178116387, 565294918, 454566099, 814792580, 315151493, 783637850, 396020517, 773893710, 239568126, 235693699, 442755467, 240987976, 468477054, 994358940, 235162395, 976184102, 632357929, 519509068, 435334498, 873652813, 728316272, 855715466, 928639210, 427797531, 73789579, 659752264, 49023225, 164149389, 176635802, 154364457, 825568255, 809479909, 149718931, 320071960, 855633415, 210674953, 484127433, 805383942, 233877307, 448852045, 733049424, 187782139, 356271770, 565597010, 876775324, 907545382, 90001322, 667967532, 475011002, 806197273, 338646026, 608724463, 987540658, 42466771, 553000296, 72381452, 737305182, 332861429, 160462848, 847383672, 576302693, 47861800, 162601912, 322811093, 215950220, 65428160, 752861773, 682082974, 710425236, 602859585, 438822725, 393232565, 682956926, 747500370, 994673642, 617979877, 271339811, 247224764, 752096724, 876430953, 11899254, 465454672, 866059624, 968398668, 579665242, 27146612, 749763940, 865545682, 711405086, 450848881, 579977880, 487633244, 106813059, 697545030, 518372418, 911343857, 757714474, 250814709, 950415578, 310473690, 651018128, 673967075, 742411343, 628973523, 898336676, 612025879, 719256045, 656208550, 916494597, 854256865, 372208696, 612403430, 349840234, 881576298, 110930348, 89378906, 38080217, 619104723, 152243846, 824406728, 673649884, 654093757, 883207414, 183072448, 493003196, 122022724, 641997183, 134169783, 734773893, 926013012, 351364105, 731673433, 279192243, 148658601, 545178716, 427747991, 906492413, 977043108, 356972133, 107563071, 261037535, 359183435, 591148574, 345368609, 820043677, 931106836, 872035820, 102484111, 581070439, 643260451, 126106997, 879966982, 811595632, 256410725, 90947920, 750895360, 77322771, 638969439, 841730416, 163294853, 956912894, 587097955, 116166183, 8845222, 440387449, 803739267, 676661658, 237026484, 482237103, 593147314, 721400219, 729100504, 141805034, 91438899, 412904983, 928556719, 504019727, 408586119, 369980598, 679073549, 617381323, 725530303, 424363395, 428562168, 820393061, 739888336, 35670799, 602047458, 319945731, 449257369, 462481716, 497233695, 41456287, 723103253, 135241060, 165572223, 773659773, 934536318, 949499478, 567455091, 927169223, 285706177, 607604309, 369397231, 197192979, 95065252, 427894496, 933402591, 99439073, 622663082, 265423967, 738336812, 713870421, 770580313, 164850171, 227809813, 59684670, 965559985, 62469515, 833373235, 591870749, 460458609, 948232831, 445681207, 364622836, 966319561, 925440557, 592067802, 310096430, 812746709, 533933634, 308459228, 431276641, 170159199, 148512880, 590766228, 903525579, 981163176, 899634160, 583807110, 842685873, 563290202, 444401100, 872117754, 524134995, 204376238, 560771833, 956956078, 534218966, 437867466, 191144989, 736283146, 541608636, 424814238, 460842328, 728795300, 902746668, 360152615, 120264116, 386646222, 64865594, 252625082, 779729158, 887621412, 646379539, 195156464, 570302675, 614773064, 580517378, 120330820, 228415631, 168082007, 403320616, 944311666, 496559196, 810202606, 744561256, 204373272, 237210500, 297606078, 240111274, 274250, 268460726, 546111470, 556372357, 427031701, 764565458, 630182628, 573463013, 839694916, 533925831, 138355152, 97742583, 786035307, 869666321, 90990689, 619823506, 561301354, 716913445, 483539151, 305094395, 645209915, 632477715, 733031609, 725623304, 528253606, 813830704, 16768231, 522858685, 381749510, 97177616, 924251166, 773983254, 429403313, 588027334, 713054238, 503776138, 209445811, 593460990, 248284608, 351372515, 383774208, 244384301, 799863342, 29943714, 74552905, 442262534, 59691909, 487342671, 368484759, 980432440, 306936262, 166047338, 770029420, 244363679, 805007873, 674466862, 727761333, 766449047, 507831964, 274375128, 640245116, 980616243, 465923433, 777151878, 655725993, 655471391, 437059324, 230382405, 61325531, 466983513, 955440324, 661701336, 712604877, 442908169, 940248174, 568802928, 439746442, 791693494, 676169829, 276783621, 715847073, 893666447, 737403414, 313460699, 555075596, 69913114, 616707631, 501219349, 807284493, 355431425, 904562860, 814317461, 639973534, 798508943, 889541065, 95241704, 17294787, 908332215, 235138517, 221730952, 720249237, 122031642, 652243151, 909065723, 208847459, 75316948, 551095230, 326971053, 973445060, 11420993, 664214616, 779976382, 675577048, 900308200, 420837649, 319648840, 125576596, 998699406, 9798110, 244589798, 358273953, 116893548, 673021657, 462822565, 87016896, 342194587, 602890161, 682388546, 769619208, 95230424, 394778262, 111849353, 202211103, 769467527, 310554035, 565768153, 520405489, 185143915, 403350515, 411310737, 38190128, 219194604, 487625023, 247453768, 684373216, 318016633, 610994322, 664290343, 859866901, 351328936, 196507651, 189360664, 953111028, 149776873, 217424809, 775799505, 210286088, 875544883, 469213261, 82973865, 623156242, 841984025, 992049850, 348107512, 306443657, 623812872, 10623407, 779260107, 325434507, 663258218, 284015252, 549239098, 560984020, 654938147, 899382267, 888436538, 19305141, 74940696, 148363523, 807447417, 973558635, 476532136, 865487040, 272407631, 655630501, 52061733, 795625494, 513146800, 374959316, 810153941, 975591313, 480182889, 898378300, 166782095, 148644558, 974607307, 323486395, 854429988, 190236779, 599218310, 893598001, 845383157, 214414484, 445990978, 382139423, 806863152, 495051380, 884115121, 407334821, 766286808, 405103311, 411703362, 370973434, 611024242, 33210016, 496927953, 593192723, 933782305, 893206985, 870062899, 34228923, 335732358, 267334020, 829588831, 366730218, 499012303, 828413860, 389631637, 855865996, 441944288, 694260849, 9180457, 133293314, 530796362, 994451356, 811035272, 87596036, 228239287, 66121526, 76999727, 975853232, 661592784, 7157673, 754303622, 642612073, 857950145, 158426810, 171571850, 66366491, 361225197, 729127412, 194358394, 348624339, 47520307, 394691079, 580799653, 812312702, 175124540, 950829891, 826579517, 359195428, 730778419, 108575628, 427459159, 111268217, 483725758, 265700593, 630927720, 58191940, 364551355, 374740417, 261047376, 516868920, 302031156, 975663522, 528730608, 964206454, 698225241, 53863366, 28561846, 127681440, 321266752, 192787526, 358300595, 904984245, 463892416, 639329024, 174737038, 84936967, 389410408, 580238546, 26479574, 451503345, 315852356, 514982652, 334695497, 470942614, 771942501, 693428024, 577652741, 453932381, 876546717, 223202380, 211300658, 587177273, 26273627, 945425172, 323120808, 49182317, 673038725, 662343241, 58758502, 468497766, 404767326, 975931226, 789879238, 937961440, 433052760, 227779378, 854779405, 945841174, 885989513, 268143286, 254945316, 856766229, 689107275, 433854672, 69822338, 602346551, 230945224, 618184599, 832598984, 451112799, 424790354, 487632330, 582629664, 952196338, 197506451, 131475977, 993122146, 625633681, 68373577, 846339868, 756508912, 297098605, 220073018, 276928389, 107184998, 969172180, 202769283, 170878744, 140103125, 64413140, 719202931, 283927707, 976564097, 559368709, 215549418, 892477546, 240986347, 826672270, 726825377, 526767845, 426055934, 914350974, 33342675, 991080260, 80139223, 212122515, 539480169, 211517330, 649681681, 673933201, 804130678, 538082172, 719925797, 240423191, 659825404, 183897574, 662232042, 504064396, 587381503, 743541302, 981660877, 363267644, 78876861, 369112785, 337625744, 804111731, 561043876, 581497287, 699330723, 595662853, 291864412, 430704250, 775023669, 744870078, 992671369, 813968163, 293509551, 878280305, 880513372, 647872909, 573117395, 395240038, 766261535, 961532976, 941591900, 401203607, 712549829, 249369013, 873792874, 801483222, 329398569, 65174936, 659771060, 692707195, 846411902, 312976913, 224085188, 505354458, 701948221, 742026269, 432627585, 577936443, 463347295, 961595081, 637712385, 595582740, 195291006, 124569602, 626435158, 950685648, 725371946, 502356972, 227215932, 282530161, 613603139, 830382434, 945729511, 856444413, 159320705, 651969654, 962061199, 403645629, 476790246, 348714860, 719965958, 762314695, 498534288, 110256931, 801717234, 255055712, 461639814, 226102296, 179450993, 55316122, 557999971, 933291484, 356779828, 450488582, 180199575, 166409116, 703691314, 787965127, 573472191, 991889950, 710490872, 261889876, 203158524, 723839812, 393684365, 76843307, 877287641, 530174659, 921573337, 771784570, 357938435, 270958405, 832015711, 697545459, 955252552, 657570840, 275434815, 884994725, 609012138, 689543558, 245758129, 702420967, 837070213, 362055582, 14159338, 734897836, 662102462, 33082345, 811971998, 793587768, 984595443, 841202834, 810316703, 100859587, 393351803, 128488539, 635757568, 494933873, 661214914, 634600896, 581836243, 687121779, 281685145, 551289616, 892917001, 973541694, 609710351, 263849791, 663630335, 321850502, 517992051, 755626652, 176453367, 850323963, 145827465, 777307227, 727876468, 856642971, 73181940, 551625965, 827294043, 264471380, 929238631, 404367107, 607926156, 718043112, 290001864, 330278560, 533562017, 154162929, 4110593, 6018653, 383713095, 989679532, 47469540, 862771313, 969167162, 620068356, 830536761, 936047463, 943659483, 954566180, 566788898, 334322320, 227302308, 814518089, 211631757, 892691351, 321579696, 891497258, 986059241, 73004084, 375225753, 665495412, 41523120, 560564313, 61311013, 397725207, 876194170, 192604656, 296519260, 602629913, 460759326, 241280322, 134692821, 575624863, 382686863, 626687363, 65052012, 211056330, 746314798, 672057706, 172250570, 667873757, 190050810, 394971825, 33908734, 228474483, 364899295, 888880283, 603979224, 908489409, 709707775, 361674213, 918789844, 475457209, 458233649, 141163886, 141369088, 50798026, 63900555, 463178127, 476389833, 362003658, 275724540, 327453508, 632456207, 170221614, 287395486, 17817613, 628356326, 394643194, 645648841, 31312362, 127783830, 502361927, 256149444, 62089184, 871693780, 169421995, 207668740, 700306959, 734222937, 797251613, 213076186, 863501582, 350855761, 38421872, 510736669, 817707483, 381277079, 872128627, 65206971, 161189445, 15431851, 498573302, 358857210, 323228059, 669487198, 682032776, 858634776, 392272879, 501685419, 986109947, 374558482, 804011978, 269230248, 962692090, 45842300, 141551052, 871764785, 652398618, 32393840, 634371060, 349374746, 147060487, 453166990, 762703224, 824393718, 776318219, 648417761, 988554891, 939775431, 361529110, 933740706, 289373728, 227234039, 536528355, 41339786, 764442127, 233604481, 257266699, 381149365, 729158449, 522486578, 546019307, 146287852, 930694116, 90008755, 424330431, 487445174, 572648134, 962840614, 494019937, 321825151, 355020886, 138633544, 275109357, 436280664, 592915588, 939632589, 912578005, 442127724, 72526311, 411577835, 395949900, 529004299, 447942720, 885525703, 937358782, 718151020, 9208171, 274479847, 439889477, 538973743, 949210202, 94432148, 156071740, 942306036, 759100257, 591148742, 230735595, 278776122, 725413435, 409225743, 476050567, 658824088, 442298973, 816794040, 743565699, 919839227, 788376774, 103745504, 318415091, 749420093, 275600838, 369300363, 163374543, 643770620, 907192686, 78989546, 41118799, 874561775, 48435351, 213572892, 780166819, 363991396, 144137356, 248528083, 236491112, 356743157, 845660075, 991256474, 318146952, 96593683, 103060001, 942914845, 123067998, 597920777, 769162210, 838221314, 104016786, 835219687, 350548880, 207584677, 964063259, 481716124, 261928649, 622664897, 291628851, 4070510, 126696335, 667869101, 23733622, 298421648, 993439682, 888172374, 806469111, 112276310, 750306965, 763977681, 700701189, 775420167, 568977404, 725713149, 334700146, 294821454, 740134296, 12467748, 527484894, 299892101, 34453278, 922337396, 551417214, 474082976, 894650308, 629637355, 527301238, 51987057, 634869252, 119642258, 538143231, 396625006, 479612167, 284813651, 308045758, 760574246, 321851894, 69874748, 981626676, 241441187, 395157513, 123725985, 456561299, 819607006, 488597475, 963084577, 626599924, 416875721, 920503144, 806638202, 44185495, 694641742, 426040986, 576822688, 587890609, 874085990, 245492986, 990588699, 902324428, 478166465, 630163117, 652322655, 691774702, 726041102, 997210045, 887434515, 925781915, 395284642, 467986985, 653984645, 160684134, 115042867, 984616555, 224037035, 235668566, 604594754, 301123944, 109995806, 803007829, 476109644, 960607613, 641402975, 496486832, 636084305, 234102648, 883875240, 156582557, 757602118, 712936604, 101899289, 898613904, 57455409, 398264593, 194457379, 3075162, 81109220, 89948470, 32539664, 603742698, 677356359, 542612475, 698202203, 319679279, 32178710, 124184170, 556471759, 415989399, 134821426, 654456179, 81524781, 472360352, 641340755, 337575578, 303948539, 227446907, 313849217, 659440278, 712740755, 156592784, 706675632, 652694438, 451049965, 560523017, 656146355, 601360187, 420886154, 411525674, 283151623, 118145294, 325909968, 168681856, 344136304, 777063399, 19395518, 942487837, 222120838, 148330985, 1537594, 990387959, 874543287, 118046944, 603772537, 483090057, 922081316, 130916018, 703568136, 941237073, 720371686, 425033383, 111652452, 768436390, 225904196, 262856765, 270263702, 933939341, 63977023, 678541383, 493201842, 65591572, 622650188, 626153602, 485340516, 768268355, 842940195, 286532127, 847767297, 679552179, 615095193, 108427237, 131794833, 424098449, 102032942, 178461411, 398451121, 250970009, 157981278, 890426906, 530615092, 778917995, 976838595, 32801313, 87015558, 524272063, 468666664, 629438017, 360710690, 484051057, 589142096, 621550759, 746941543, 65226776, 699283267, 845541591, 232467648, 340703355, 485821337, 966641417, 617579938, 911785189, 668269633, 601857977, 587109096, 157208720, 727643271, 376030472, 850263867, 759904130, 781907744, 656734045, 43406179, 543601073, 874228208, 83335087, 857667271, 634595907, 755801743, 991328532, 770772534, 51335257, 67987993, 569243021, 405090906, 811952624, 465160579, 313196346, 40954909, 267349697, 854908705, 84213508, 549029513, 593732381, 887617779, 318010086, 868207622, 546019321, 804252734, 839408917, 764936156, 366013232, 642739538, 206744394, 779517242, 196445227, 935776326, 596600096, 113749095, 449377795, 821590621, 234282385, 155750006, 3210504, 931484805, 265654853, 488383667, 408803783, 183277731, 66120858, 441697997, 716228403, 912055686, 953478742, 770747172, 618371798, 543004634, 216042791, 536738115, 292180719, 181669924, 147336032, 761055082, 708788867, 701926947, 604166552, 605781890, 305262933, 830270420, 840949796, 468953786, 305079982, 211407008, 183837544, 558340987, 244744720, 673333037, 32073969, 253008061, 153676706, 50024921, 868109893, 687985138, 800445637, 235856596, 843153286, 954207371, 372855950, 197660071, 17138960, 378403391, 714168818, 721730386, 860169708, 909692379, 312884099, 699313230, 523406877, 224698123, 522394758, 805721804, 399535228, 79351898, 793558593, 317956623, 469377347, 915767636, 322265569, 113567841, 882165768, 375418991, 375787698, 406264355, 754374381, 65736069, 513294537, 13915602, 311895837, 174364363, 551314634, 230115406, 17509191, 731640718, 184750965, 240936982, 608459212, 759556139, 386427072, 939941306, 1084596, 944622295, 888105818, 683429213, 467941196, 167555162, 800811412, 943520634, 685245164, 365344722, 625947429, 590033489, 288294686, 426303363, 760000717, 686610972, 983654797, 30223327, 172279920, 963468190, 988195975, 930101545, 447318843, 107940831, 279717184, 768256643, 359825952, 124638361, 313620877, 715856057, 918988234, 558561981, 989231476, 21003731, 747581316, 476059631, 513294160, 366960105, 522654444, 92677193, 306088597, 841367108, 139531625, 787389549, 799651660, 550269972, 88698557, 593197782, 232982813, 689678434, 986844354, 761831103, 126982039, 33465291, 460509975, 368177552, 937219458, 235033911, 720237139, 825279117, 190825576, 233886638, 71204959, 332110214, 589417586, 245733294, 898966545, 434155050, 894429496, 585259268, 316509982, 178786252, 624388191, 660786840, 767113303, 764543690, 788631982, 167750499, 742082530, 531415963, 213174695, 616996716, 334574013, 580504278, 199717139, 850009152, 841537564, 196654876, 80266104, 116741407, 667361367, 981984716, 976840858, 460754639, 937996385, 838440728, 214294784, 879479458, 809817791, 445464182, 150596300, 823856223, 448103373, 773219400, 974944955, 502792891, 352686926, 525624070, 619956052, 473238333, 253580407, 687413772, 818788556, 56760352, 209812276, 33792159, 333566025, 39078170, 898679936, 291796560, 888947360, 329867394, 755413328, 47219272, 658943141, 237915059, 615934050, 503022788, 956240610, 80616816, 962431806, 19549209, 460822167, 319645836, 362350400, 710827991, 86264545, 674413469, 295518697, 651762883, 910589985, 605286588, 973310188, 449044243, 519204052, 622339434, 655855127, 568395026, 972546951, 917275994, 740527326, 263374100, 520628329, 184557159, 258614287, 816946929, 447570458, 508861, 275081474, 291974591, 730087353, 851185258, 710364590, 311354896, 631130942, 961147529, 82739541, 961145646, 984697287, 718206659, 21764960, 54510538, 24519650, 721515678, 958759189, 957430601, 746631037, 609729141, 93658442, 360745944, 987356916, 292121280, 497821393, 824333194, 74286612, 313399709, 917396775, 295822238, 607511685, 889658547, 549139919, 708774626, 362549790, 973150238, 292092011, 947383079, 852676077, 160314994, 865491006, 671889161, 489158857, 605942765, 108322917, 18795017, 317117032, 428474051, 339761377, 691469075, 396274082, 309970246, 513596893, 857381369, 901433946, 176869187, 441183761, 209526799, 786822940, 859679505, 651239734, 790121296, 509212792, 438472130, 174189969, 903043816, 270602641, 354054956, 284536458, 429755216, 876290380, 206661418, 866409550, 64084268, 986880876, 953794047, 189532375, 542905201, 646572213, 427516189, 25482982, 883203732, 764534192, 347676473, 562783816, 845541065, 196815944, 588370287, 185936183, 348688018, 34943815, 165931412, 89741939, 76699180, 864208276, 2404070, 332217312, 945088076, 878169220, 524468853, 587817646, 972565213, 426902669, 25971855, 413641425, 560821069, 822281268, 44567671, 153763262, 356458470, 690319201, 415999535, 881209647, 48305157, 975762445, 920708188, 905282401, 577243441, 201592697, 684366277, 904052808, 896596240, 354975142, 131960987, 893244763, 83723961, 342350361, 196034410, 112495163, 948597001, 278089646, 105570022, 649957672, 481107234, 977707439, 895273007, 818563848, 509038466, 359768011, 63504892, 372846840, 527375253, 707243422, 689616871, 102383695, 698207106, 123651426, 948438160, 535497711, 131534098, 16658316, 403169530, 643566501, 161522635, 183850167, 352800487, 947019580, 299185716, 405296286, 867141854, 350771533, 870507931, 27009692, 973925489, 309578891, 494835714, 298561821, 160872588, 6862296, 113446258, 152857019, 956147144, 989695262, 336468124, 892508321, 174059518, 262175966, 662392475, 20747370, 397147732, 178690478, 431528937, 374329264, 963338409, 573516642, 352864060, 483298332, 401691709, 442975669, 461591058, 887727334, 185041345, 661306440, 863201774, 246063444, 329089016, 786956189, 117517976, 961495315, 286759501, 419145665, 913321646, 204035774, 19380998, 565439199, 490761667, 856236244, 13195176, 599609243, 441845076, 611677230, 933405833, 381525746, 822746530, 194403901, 667143271, 793103110, 468159389, 277666996, 997633658, 419910676, 546587783, 340123275, 88942993, 911635474, 306830386, 597275106, 216726959, 639616019, 892079684, 388053367, 729962713, 147117206, 716948108, 589977770, 55940031, 200666733, 748524309, 443198776, 347528534, 407249340, 499066939, 172348639, 457514235, 962178581, 470101229, 198321865, 922990170, 624953146, 552401725, 524837661, 864305256, 282422892, 255562397, 414153710, 721844924, 246288528, 129984255, 588884486, 679412175, 246368085, 653829215, 842883845, 120580762, 178617481, 861788961, 251478023, 449666290, 580073675, 700044777, 938011894, 163991800, 592823833, 71376831, 704025309, 695426386, 391098840, 807107018, 577911888, 50383105, 88784452, 494774456, 520254808, 25103493, 562961574, 69353142, 469096372, 718612190, 512938717, 675473213, 221263375, 800602198, 347838878, 635033361, 310918017, 396346634, 165230804, 310983013, 549187643, 417158682, 202973967, 13352410, 858661706, 651956804, 217227360, 416323479, 942154520, 79712880, 405875331, 456145960, 143486723, 289391373, 381298204, 902258301, 288874258, 148340326, 688795004, 325162635, 640047735, 156613373, 197560165, 737694642, 436223750, 33628984, 734415543, 189299067, 728080996, 391513459, 361945171, 351827650, 222919459, 139184834, 586243457, 986168753, 531487947, 644321099, 432079745, 868371871, 279178176, 39005609, 70001961, 478138480, 342461408, 873352067, 252095936, 231398461, 341674849, 826221847, 22720563, 539680857, 883796549, 115691161, 916712734, 790238066, 460243813, 171187443, 932370625, 183196236, 677091601, 595281894, 647352007, 469898729, 970737815, 574693367, 596676918, 593589709, 490349561, 349443365, 305312163, 548364821, 103120937, 868984703, 125904814, 661716466, 559368625, 40960031, 479119670, 496828400, 597814141, 41281820, 770235948, 742927443, 846757222, 37518979, 339517917, 389103789, 442350892, 645847346, 534448774, 747233460, 177065154, 72186333, 548098688, 854027439, 425984264, 542699688, 602164789, 110406150, 48678539, 991060483, 738079760, 556553247, 124463927, 6024661, 354933786, 168241782, 705693286, 965254357, 864471863, 65635684, 865820111, 102583220, 230197041, 977914964, 694617178, 407424471, 9918295, 773169689, 189595968, 947766535, 574952795, 898693372, 512832757, 130715656, 269481036, 199067150, 86794194, 758819874, 786516855, 434603480, 813137386, 603134710, 184066083, 154548272, 332658552, 781428919, 98298478, 387036520, 124746509, 705276545, 251671563, 93305257, 96479509, 388404506, 508915714, 543479223, 192878197, 618531230, 636837678, 812512015, 708963024, 656659626, 236414500, 883671081, 253852993, 741945285, 905822784, 418918585, 883790402, 794789015, 278860852, 258177663, 111724771, 294270156, 70041412, 979531849, 692908281, 322837068, 659929806, 477939119, 668735400, 893669091, 53667357, 640574557, 114428629, 247205984, 564261738, 325492575, 184244529, 616829362, 799041771, 598895557, 543350205, 7308893, 874277818, 518837647, 539298296, 118357996, 272239214, 75005465, 51690737, 129643894, 479833642, 809478979, 7275918, 648278177, 453347504, 736870103, 818284380, 828669043, 955200610, 847389936, 664743906, 309029792, 483925235, 975891916, 267380949, 775640858, 836256493, 663624264, 305412531, 112949625, 928585716, 339686382, 766743636, 997271816, 424953165, 207370178, 447236056, 479228237, 605803283, 883591327, 994592584, 473559264, 691825390, 59026281, 917978763, 46972958, 425183058, 16064290, 1839961, 303342030, 656684479, 609323398, 433475501, 985528226, 101388875, 136302585, 591960578, 91508745, 184542045, 809719350, 22428967, 902867101, 638182620, 626640464, 793625058, 446718846, 318363922, 420538361, 642814064, 409262984, 383302368, 115376576, 474868455, 705817310, 670369963, 542155010, 430439664, 625850429, 111647532, 313083692, 283134903, 126900746, 467748257, 394877761, 552775839, 915791764, 613204921, 870150479, 214240138, 709655150, 442856918, 170094840, 773014055, 562719901, 509492555, 907295643, 714342542, 767339475, 707888996, 460529712, 474737587, 74092315, 187948792, 195903948, 298823132, 14508169, 516251583, 640486235, 510535706, 341073976, 110725252, 244465724, 720416993, 123562227, 560385561, 984851360, 227622481, 295240153, 7468945, 158115048, 100392990, 161449362, 752302130, 796605070, 463713576, 313737765, 266787460, 55065998, 884326617, 371613208, 790683251, 245621505, 540302462, 493947350, 146045611, 953972417, 850269168, 921316959, 782715586, 51088433, 814291941, 191519440, 766857391, 303594649, 418905653, 117909535, 600535368, 638574670, 860152644, 722121204, 531142523, 624268601, 519013605, 264059325, 182407573, 693056269, 80285468, 1737389, 546519070, 567843451, 780277723, 661325243, 888114650, 901522208, 804051424, 631855074, 781359457, 253006678, 207782284, 864062314, 130778504, 328706482, 914627015, 582085819, 412437047, 31803047, 534517838, 414404348, 908511268, 456893249, 428728872, 898523343, 475679013, 204427484, 81104282, 478073801, 354447944, 123137613, 638177091, 169491720, 708992949, 905194707, 990966759, 342395463, 245669038, 863598950, 100180736, 713872336, 767981252, 892657132, 894825963, 411924550, 318553443, 950671381, 468979341, 479178882, 247198005, 849653041, 315640554, 34744104, 714259221, 333482891, 553377415, 884112971, 337904252, 293232602, 744339277, 501599334, 662827172, 818971329, 518464449, 423765060, 987164669, 897329830, 67655249, 148540893, 995094076, 113235355, 628859291, 384527180, 327414052, 574277638, 28594680, 836820066, 689745064, 243695296, 512265434, 582224239, 687971437, 328485529, 375441535, 235441884, 784336109, 469845337, 58623229, 626581982, 334261131, 808435983, 340514423, 379174361, 457007090, 210508262, 782012683, 665538916, 228001136, 596333185, 833707316, 798250577, 567287628, 713686503, 208167258, 717156530, 754127471, 216674800, 104769787, 270623803, 277991236, 702484016, 674518682, 687690477, 47069009, 37700967, 170492248, 416735805, 143321016, 223895772, 566505207, 325457559, 157264779, 317052570, 73555058, 410542354, 385035658, 118598331, 806283812, 524884184, 828194775, 854201696, 285840435, 904903100, 798593583, 314427535, 202681467, 584537486, 365523295, 691178343, 783458235, 14843163, 198180313, 133694499, 210156545, 606632511, 511482713, 354103696, 757610402, 637722934, 272726227, 572900790, 577424048, 280206110, 12667742, 338940814, 952852312, 720219729, 332788617, 756336225, 447831344, 221190641, 677641290, 944481419, 520405083, 795825933, 410999079, 838950675, 959402275, 81423067, 719029437, 633838321, 4521204, 300943182, 17618854, 724417773, 321728094, 984024927, 549965505, 874924742, 730380516, 487740261, 895489037, 652340342, 763627725, 791749494, 807605999, 982457621, 923625209, 338731152, 163598470, 255261741, 981964233, 641446452, 94909572, 954499064, 299765046, 214914337, 542674416, 852513444, 774861600, 285425989, 706220092, 332591414, 839715503, 79697283, 976689450, 667728307, 498686398, 139248714, 785642933, 665052546, 79560628, 562634815, 646971828, 398229790, 822233847, 11929900, 186400922, 977413936, 300020367, 382923752, 988735401, 694893501, 301107569, 783187651, 874905424, 568540401, 760001784, 8785451, 247690337, 318191557, 832311629, 106458031, 938522382, 380296744, 306935624, 950005363, 254457520, 507775044, 329123753, 474489568, 48507364, 76969129, 310096794, 231206787, 282709700, 83248443, 890306236, 152379635, 509694217, 817590825, 568249284, 639754916, 551779849, 951442277, 171415781, 161547905, 53227824, 792386849, 625639347, 757487106, 68501529, 233007063, 173496805, 332316700, 256668051, 456142286, 759686747, 239271298, 675190306, 974213838, 33277217, 646293016, 51864530, 94745922, 164680829, 103691299, 96208557, 595719825, 642168996, 781423156, 629312853, 812223087, 449391773, 299335997, 740367772, 409546146, 363028912, 405152424, 82331860, 636765150, 229979207, 620271031, 18047966, 164224670, 994080285, 41890240, 69086165, 456483257, 331292189, 373352562, 379986524, 826974395, 268034908, 796122517, 520859133, 887555405, 230634955, 443623324, 72530821, 727627208, 289469128, 192992419, 659499429, 624541158, 567719784, 175198602, 501873077, 223098318, 913787484, 662681588, 205985144, 855554851, 32179380, 249011372, 681976873, 354440247, 204862596, 374048620, 490138974, 735991251, 806215965, 970813983, 451408610, 629653976, 505911277, 670980493, 962313273, 983426225, 589965559, 512085283, 179513847, 970789895, 974407036, 871878168, 519407270, 213787136, 435312911, 957130814, 714462968, 367972902, 149862953, 308663127, 751112190, 390748270, 359604398, 363849558, 540688939, 662202220, 321865674, 474169642, 246018538, 123637757, 818303253, 94831753, 909951539, 832017920, 665494128, 518637182, 146436693, 332069927, 764619268, 51886526, 984183835, 213930736, 96984077, 484826595, 950144369, 872228620, 122262411, 382061242, 593413693, 598899431, 793829838, 388105672, 741172425, 127383832, 879865239, 308593665, 601092758, 901350943, 537798849, 316224106, 214628154, 977268237, 56953881, 356325375, 866389599, 416820206, 421884148, 461199847, 474122134, 464732399, 555846098, 26205593, 650281206, 861326745, 905219735, 131306342, 272711562, 461668834, 595131428, 740174807, 149604134, 203582280, 550924548, 617780248, 346973069, 52961673, 363304543, 960584750, 715409895, 377268815, 243432524, 910002725, 478143441, 145064986, 218402664, 160144795, 654899205, 765880285, 563593153, 246764202, 977761044, 412249894, 853998093, 922459685, 603405022, 473836407, 976134853, 575300962, 656718439, 207732642, 278964651, 207172482, 888351815, 92774363, 742391977, 112911605, 442788662, 986755823, 856015925, 328161999, 108748489, 265852700, 52714856, 440570772, 354597167, 567283979, 557799111, 375549545, 678821530, 82422050, 745534640, 758177795, 579039645, 722894917, 88168681, 353492563, 356037330, 875286433, 572494411, 625028197, 24519520, 32527634, 112322867, 24377161, 923539512, 352967150, 319343328, 218630822, 444908343, 24466634, 12872474, 531895132, 142281605, 709484004, 218268872, 88729105, 114835213, 859412747, 723170776, 265596085, 192651435, 662182362, 123220569, 803241393, 162651859, 524022653, 948733864, 439430586, 770455835, 833151389, 488002927, 570939124, 105028205, 937333404, 970239795, 818411408, 980843148, 82076745, 655012473, 124006612, 619341464, 148179593, 733386522, 295941216, 339738243, 616749417, 995095161, 474285884, 599799109, 537285966, 5674616, 315254972, 833300256, 986417228, 821498707, 873106118, 501076512, 254134857, 788570978, 567023142, 812418445, 134254381, 11306201, 884074756, 736647957, 977428484, 260979275, 133574657, 979267192, 961153790, 299940782, 946333588, 360463820, 164103371, 151769583, 855780972, 216995231, 892099773, 615799476, 769764290, 361163841, 396482055, 64155010, 271258829, 291877754, 604401366, 527642014, 966904110, 45135663, 47079232, 66521675, 392294054, 408670114, 955340396, 217764416, 832048501, 315708653, 215601094, 623923404, 72203508, 74424259, 538785543, 8663837, 288694100, 371031602, 271905879, 177311256, 317496554, 602747755, 356192056, 999788827, 513118911, 901673364, 426288494, 626642654, 311795627, 871488221, 307250822, 340508432, 483905311, 307001793, 570868533, 26331559, 777105696, 69909183, 783193663, 4000291, 720282550, 52663335, 849294804, 678107324, 687435018, 763603679, 543100949, 430095749, 531853263, 307852485, 752942231, 875694728, 963506531, 165332675, 600713028, 379539258, 412393491, 406957906, 70939284, 889088099, 752134401, 257817634, 232847111, 436105026, 776847771, 744770924, 769578186, 71887705, 303494083, 992142101, 360344634, 339887545, 429371150, 45515921, 710858848, 962091466, 552142829, 535274495, 914949069, 76326728, 27382066, 992076983, 343851264, 853878887, 167356651, 231402540, 225117688, 875682285, 830417784, 417554547, 749098485, 179828024, 237503278, 595608227, 802931343, 960180196, 955041070, 431707585, 124615021, 526166462, 3341267, 233955711, 533291858, 376385527, 880052435, 607441080, 182966682, 318276024, 450796394, 502364727, 58938279, 675688443, 95535238, 94718393, 635902325, 276742404, 198387753, 160582077, 815072989, 795188138, 127027051, 654435886, 681393657, 389609796, 976420598, 391413211, 596045079, 378748674, 766200807, 664143348, 82654450, 712949680, 331931774, 823969389, 490460618, 857970130, 764204150, 798359448, 550268754, 341089622, 513432899, 238590008, 547465205, 642712352, 273529, 985062952, 934294839, 351238064, 150900952, 244739175, 306328911, 178232013, 744870262, 314938808, 306433119, 157621755, 294349341, 450207990, 803486604, 17903521, 487786152, 357763808, 688313820, 388139770, 216308853, 616750365, 982506404, 222793233, 956283320, 154858886, 231081209, 449800229, 620738046, 118373372, 806262433, 264656499, 239424267, 998118673, 492699830, 48766658, 142141266, 464880063, 533754916, 956447145, 750410809, 61592775, 110237239, 299544244, 871566244, 550376516, 122946793, 837379588, 392224096, 789122814, 436405968, 7143430, 275116115, 360398980, 272814024, 597827958, 952703570, 716780835, 661687126, 581171204, 220754211, 558837649, 433336814, 900453224, 288576977, 954478224, 228278495, 75631727, 77339749, 935587771, 51404384, 918885028, 8108475, 862734306, 176693037, 621628979, 556957848, 852560884, 874412746, 95337731, 496267315, 529123285, 117632351, 970423716, 682018439, 948442434, 629373135, 688394323, 534681603, 947487052, 928097063, 320477208, 135847495, 882651011, 107351286, 233190436, 151531331, 606316850, 559986692, 588637630, 930445900, 534166368, 747650018, 499622913, 662347792, 460071957, 400123062, 962364885, 667399069, 928008246, 90893442, 293304471, 438232580, 10117799, 628768338, 133923333, 934271246, 182546504, 806582111, 232922673, 330062332, 688783102, 448905010, 42538542, 279512099, 432379341, 270251259, 952857288, 154181517, 873674553, 500620960, 467218138, 995042728, 107750979, 515722934, 346174346, 779946430, 833449361, 594470199, 784254466, 595280071, 651535659, 821466995, 77600910, 387885271, 908194951, 100116453, 914654756, 588393299, 131603507, 147337900, 633931297, 473286328, 715821694, 636911893, 413556217, 393208143, 303910982, 195748121, 155069852, 520849828, 551121447, 38393454, 505356437, 182901490, 142353067, 802113852, 459445111, 253961999, 365035644, 277418366, 464723584, 494713494, 676866901, 776909006, 923206193, 899029608, 508402507, 717140547, 292875250, 209600315, 52862936, 41350067, 501618274, 474191713, 655846053, 724994345, 833582004, 155905573, 277189735, 976198278, 377219535, 734863494, 212375756, 860970572, 37055864, 577310743, 492894920, 366296747, 30668241, 449621236, 428440838, 401419206, 481631646, 425840886, 945393505, 850806536, 967941893, 922219013, 37168747, 967095169, 682825279, 33634887, 607641989, 485258787, 179742935, 354821384, 360105444, 455011818, 968739812, 99263363, 73904606, 925979781, 849915628, 103765459, 171099714, 831011792, 108121515, 356607712, 491736069, 855901244, 778508202, 153456390, 140649779, 597343258, 296524403, 545755799, 391244037, 500401561, 244383636, 903192182, 910600366, 527355627, 656610707, 274938347, 641178184, 327495212, 975361050, 156387646, 940989615, 287656975, 144118176, 829558885, 346967708, 677306382, 751630059, 889494249, 343429418, 136331635, 582603196, 758157453, 583229983, 360367433, 758601460, 469573870, 10167408, 422506365, 104757020, 794446268, 544777325, 779624273, 451987742, 753809324, 797907294, 580802485, 848366827, 485502287, 507273975, 319208931, 231742457, 830483190, 455117382, 861888325, 98349212, 50106314, 587815285, 587950685, 485025927, 894158900, 808864345, 279953044, 38047190, 417741773, 262728592, 836760734, 367211265, 838822391, 408064560, 973983252, 900240155, 365485651, 632285314, 602100491, 198472204, 340046646, 730302950, 159920059, 540047837, 236723552, 465029703, 412573032, 527187841, 985246501, 168524348, 195798237, 705544668, 684571212, 792596451, 743910198, 413020186, 418387865, 580255666, 59437982, 82068165, 829979501, 947644459, 203809926, 118772326, 575352833, 118334362, 408188815, 37072805, 253578569, 272912291, 377039962, 880587369, 426442129, 482764823, 524412568, 431509526, 962578701, 905505021, 240279959, 14659523, 904218653, 900877879, 838285584, 435923024, 486296614, 869020704, 316000588, 331908377, 20217469, 98876626, 141466250, 975573779, 105347048, 482264665, 33990321, 723273598, 411491504, 146787578, 868425947, 57482667, 735792496, 948321622, 42620594, 58225935, 488275893, 148233138, 703915410, 482148489, 41510851, 236307056, 469523886, 721717406, 453143751, 795717820, 669826256, 438908863, 81347266, 514107720, 413916730, 459249818, 903244875, 933321714, 439366813, 64654852, 152357132, 347299586, 758383737, 634368986, 572705896, 861386064, 213503949, 787075935, 393554326, 781890798, 580310749, 148796190, 201394643, 233067502, 766153164, 56355506, 518442151, 768972020, 589759038, 923440187, 221820669, 365872712, 542966254, 624404284, 774889110, 601095189, 226301356, 9142249, 583744436, 652302562, 335273088, 634969744, 550458686, 577309446, 297124893, 910017728, 403414254, 308352826, 564110301, 599395876, 306087690, 20258045, 852076074, 570751314, 321625739, 68665361, 653713490, 936361915, 323142693, 51290479, 485160563, 951185255, 434922411, 409629921, 582325749, 530156803, 585906733, 851723745, 536746066, 922612799, 118210625, 957248213, 342452559, 602667871, 284557240, 385133705, 913771796, 551692407, 747708878, 218798798, 52470422, 453474531, 63446709, 63411891, 63685281, 245466989, 992241973, 166089120, 880597866, 408588910, 847676353, 671992541, 511918808, 711813433, 522939506, 191787067, 878163519, 610788407, 166874307, 140259662, 204313941, 28106585, 294509991, 429650063, 76043058, 252960694, 819975738, 697680603, 611722454, 467096332, 751678042, 859642611, 822480776, 430952964, 521732527, 72544686, 201960166, 340054889, 158564617, 505283454, 184214811, 733356253, 686612085, 54292760, 403899871, 941831863, 953288290, 962719879, 631529545, 403768198, 810638560, 361049370, 429128791, 275338804, 273372069, 140809006, 413728739, 177544468, 34951266, 420293984, 659025438, 326848194, 333934333, 347069743, 521967829, 398189093, 280311412, 788234106, 654787289, 444373203, 506032060, 185725937, 385927182, 334015967, 52615733, 583101600, 194972567, 467819286, 253677809, 593003482, 433197103, 786376470, 192860968, 15394493, 501509732, 38375084, 484910089, 724630254, 975556971, 396112407, 470554190, 80202950, 970335563, 202129477, 499417644, 815536070, 100190760, 999742470, 73751243, 37398270, 779683748, 988972673, 143892235, 910054003, 46992249, 180481957, 204073553, 566849535, 206534481, 468778549, 124188126, 897018429, 337822105, 864112480, 827027776, 47597832, 756124654, 702943727, 506896748, 507053319, 486562691, 198534995, 204602446, 846906669, 420901797, 724916454, 799691195, 202181331, 207261422, 329660989, 646997645, 811665255, 320058791, 104619375, 800279638, 268261853, 107071772, 215128380, 361289557, 472243927, 803585948, 660675810, 931541977, 401764522, 565372626, 661383953, 755492234, 897696113, 715217554, 245902933, 188340719, 765048833, 732200806, 739958923, 636193986, 787198757, 95524746, 796852803, 910663558, 760326891, 584221822, 945184772, 93362258, 14005747, 189293526, 692397039, 714674870, 89556867, 263533101, 215481576, 358593109, 354499204, 636457853, 901593886, 27120570, 11142581, 739175479, 191863411, 803562038, 629344959, 166921326, 479969626, 814221235, 327286230, 157144197, 83527609, 110318190, 120253910, 179014128, 213401456, 66327246, 787401906, 65619567, 234655400, 481120798, 732398136, 161882911, 516072273, 832643132, 724787412, 339511614, 410195345, 887006303, 173538822, 832961986, 730085639, 905757342, 21173715, 992312638, 690835792, 882165427, 293677541, 347595247, 299457711, 783195558, 667930662, 679021537, 180527831, 745976359, 824142787, 247970738, 372157247, 773783145, 23422384, 311467738, 588476487, 762098210, 389220929, 665504299, 211771523, 178711248, 913128624, 588741549, 975775552, 688906147, 468518758, 867726005, 12038593, 31562961, 471718631, 779053591, 538071029, 656449666, 898674634, 793842387, 19423262, 890623570, 185398705, 846538636, 40705904, 445334128, 36874394, 657972029, 616611767, 229895069, 655058861, 155090270, 241408806, 641957114, 726645926, 967902040, 983305458, 845026322, 324752474, 885748074, 389895033, 9669376, 428681072, 676138410, 801683954, 898200682, 866388853, 49284203, 990825503, 35741725, 475728051, 952365472, 409593399, 290039292, 656880875, 84505291, 672458895, 790683407, 93080402, 850470889, 617552878, 897397682, 616431017, 919271931, 538894576, 28566956, 639387051, 397480659, 888331808, 312516383, 712129676, 139094357, 925189146, 429828751, 669729148, 657455429, 44143137, 896419502, 373965432, 654395835, 522667826, 393589332, 287876558, 651339364, 828680821, 314498597, 144910474, 361388886, 948141017, 899042070, 604577387, 297048197, 700671202, 243720448, 222587948, 421418856, 427568080, 669262092, 94881694, 350564702, 816069148, 933921780, 787406109, 394279576, 247194716, 659840096, 963491497, 621926141, 942366846, 377839543, 904423135, 106961356, 877196550, 630280496, 328306029, 381912402, 259658267, 256524873, 14405468, 91643580, 692379638, 778066527, 343401228, 265240258, 890313044, 800722146, 764711705, 88369697, 528098498, 768397667, 13367371, 983321651, 305640149, 967903231, 204662940, 756849127, 386404985, 473020925, 13509173, 189775432, 83246022, 122585254, 309783836, 919737386, 251511120, 224937099, 649517015, 42791830, 846714461, 954366529, 328480025, 308171454, 834735999, 832990885, 716279439, 676745862, 834852009, 890280653, 869334953, 655241739, 778403030, 392085988, 728926556, 129185573, 555171776, 475758340, 828180676, 229343747, 545625292, 632710143, 214951555, 887768252, 180476872, 540305624, 488375293, 447961778, 897829630, 150266682, 935871494, 239897628, 36306920, 14787071, 137613306, 19047148, 167181446, 221686307, 926231605, 440085342, 708241065, 321713012, 700623013, 523542251, 269123659, 394643556, 408705072, 430388587, 173026158, 90373298, 742817204, 679707901, 916179928, 827473012, 830180200, 389508837, 726194344, 34322543, 60782569, 810967191, 296956110, 985551922, 802735228, 69099689, 861993337, 882544894, 3086387, 354689796, 637067784, 147299021, 323439936, 749598214, 64963473, 875874873, 260169214, 786704608, 261894718, 832429561, 754318611, 736660374, 115594129, 71586299, 378870353, 263657928, 15351768, 115135473, 763413863, 306155139, 922764812, 918217812, 193842385, 113220505, 283673234, 20446421, 16479967, 685827685, 117524362, 817386440, 717058666, 227736181, 634222817, 962294687, 241449362, 254390688, 412708733, 547966203, 442524448, 926032328, 256891420, 892134103, 479945158, 235592616, 347569648, 954914412, 515973257, 350763691, 638109141, 69620416, 839227397, 51302625, 449501182, 366481472, 832015107, 905697926, 676741743, 37441717, 811644502, 416274325, 789866577, 872878678, 726743340, 572104693, 828643521, 720840242, 947503774, 827075515, 550898106, 867141112, 679405518, 98209130, 957702403, 892647889, 588425572, 227007937, 763830442, 318240083, 58845407, 237942466, 393609077, 548918027, 593320301, 471151375, 782958204, 680266100, 849048920, 365677646, 536392314, 258833786, 522137945, 497522065, 157628999, 138290860, 222570880, 278588036, 754198935, 765300737, 243730127, 364842562, 689214696, 860588574, 23809147, 751837441, 383716938, 107467979, 102524014, 141604079, 22445434, 383708256, 454334769, 766131067, 512348531, 434643671, 635422439, 481936828, 340270682, 479822553, 387097373, 478628106, 136538298, 729873250, 989536834, 485814185, 839194198, 969893055, 4900737, 372276126, 391256330, 586272280, 322400955, 116257783, 201582517, 799154006, 794300225, 236835686, 279983815, 993477477, 369815430, 804647179, 892199865, 979192861, 324767845, 793631281, 994992220, 664601851, 815841973, 802152572, 481526271, 221601743, 503349374, 80012548, 962958858, 84624952, 97545324, 792969558, 869502280, 5952227, 12200442, 275611054, 79173264, 328296047, 894689272, 111856616, 73832169, 961291301, 579954169, 418718740, 247387610, 878376348, 368490908, 714899354, 228963972, 607773140, 245918092, 386527512, 558984436, 136381378, 997533886, 132702955, 467577010, 848031070, 100820775, 491987507, 282871800, 336610001, 620134615, 769068281, 501973455, 139295754, 264083146, 272601696, 430570829, 807093744, 219252454, 832278446, 950552888, 343405088, 545771506, 85628197, 756524483, 489444644, 87426885, 991414415, 718515819, 178071277, 832206183, 782271513, 748136731, 746048966, 977128489, 392663501, 611073025, 961012791, 281531197, 770616258, 131516578, 460010674, 181559960, 184901923, 140130222, 620508282, 280619199, 736895170, 913924541, 539355591, 632174008, 541178774, 632340676, 398202035, 600686647, 818558575, 486505624, 342993818, 847300612, 356669333, 526124381, 60567816, 666820815, 365779667, 123664146, 83567939, 462288019, 838231379, 783678923, 953912780, 874530275, 307029860, 634172780, 744553708, 988942517, 927420850, 521610862, 191596103, 264213125, 779301551, 588329793, 138105331, 712890588, 76568775, 92592673, 709013842, 849662506, 594870278, 156091065, 342054969, 655158962, 65059224, 293813930, 179844671, 795943374, 562903713, 792017900, 332165468, 800009698, 355719822, 141410014, 772197398, 29987170, 496971202, 782096921, 9511903, 973860547, 483125136, 20856925, 489468238, 901683957, 540086535, 218100136, 55992999, 473142471, 137700979, 915020229, 484106322, 762566259, 688489059, 804832718, 501763064, 948104876, 869080139, 257758839, 926620505, 539801937, 636121458, 496520651, 874918960, 534686459, 635437789, 877337546, 343780108, 665644544, 860966196, 352073035, 697749070, 1196294, 960876676, 421307696, 731840674, 27625675, 973116910, 313212096, 128107501, 812220873, 534450936, 994009495, 228306850, 291519315, 417323364, 252461543, 142252, 931128482, 693419140, 601231913, 126368157, 671843300, 722421087, 864681501, 779788315, 325781437, 282912149, 737300065, 285388811, 369858176, 683062870, 931836669, 681026178, 247155506, 326225335, 736894177, 424866420, 58488925, 866913535, 891622170, 816644639, 648093625, 405827352, 911260283, 182424257, 770290395, 174191184, 4150411, 774823618, 4108660, 743975446, 208168787, 490626462, 198138364, 366394351, 870445957, 387643075, 444604691, 331991698, 435191328, 923185048, 177753715, 104798450, 646219911, 905397024, 638164196, 654227840, 883176406, 905225405, 823111004, 956537599, 652464395, 505104612, 769438038, 271049490, 680409691, 510953996, 362219503, 942628136, 686594763, 634394679, 307769389, 761259012, 661809624, 650113291, 630632362, 168359320, 810572495, 643931930, 784647314, 95056044, 951033146, 638136740, 863588614, 853675748, 47578849, 421899416, 331160152, 834725851, 855728453, 607509943, 36937423, 743193693, 936642759, 290411570, 411723191, 990451633, 332825027, 398059801, 640363300, 287945920, 693537698, 282145936, 306438604, 847249586, 131540678, 369443719, 330733776, 781509985, 12753738, 438680734, 285309347, 314556861, 958172992, 219745090, 260961079, 730818986, 719235046, 839848415, 193625212, 243314522, 959630475, 176591567, 758314340, 316260654, 46265904, 295087648, 160330897, 108167996, 884371830, 142154423, 502958324, 565641005, 657529573, 475968605, 757412074, 327458913, 199322076, 966625898, 30609535, 416300726, 938067022, 564112476, 437062694, 512900551, 27007244, 21411781, 239239009, 428130388, 633965992, 603277200, 643979336, 230237357, 211907456, 642880142, 919276860, 414752027, 143108587, 634480737, 120346170, 450902980, 77506502, 274185939, 597194145, 662190081, 897906438, 150517776, 831574552, 449974368, 428361517, 312056912, 773669575, 489389838, 285569902, 79459623, 542069951, 712228583, 107133132, 28761430, 940563832, 553415065, 292817390, 711512976, 258030994, 354450575, 876418054, 336882332, 524380790, 340457841, 108415604, 300285695, 954742499, 327667475, 828543638, 988106149, 506696635, 895943391, 950797161, 553319755, 486769371, 512421505, 698746901, 409456769, 490436629, 275097524, 803398459, 585682747, 949493785, 978811112, 771552726, 845687037, 811847611, 496213004, 141468545, 129098766, 783328915, 440395657, 985895271, 855593251, 260813747, 483653543, 735144407, 122805111, 645551721, 279599743, 373817348, 920627756, 400492120, 270723787, 153974836, 866940480, 937663953, 68447484, 292793089, 988017721, 850209413, 522828609, 476495156, 765260244, 73146616, 250529999, 247408492, 961215420, 354036239, 714267514, 270162488, 315275377, 64284984, 272811048, 524935662, 375512948, 995059382, 223363315, 871038308, 837292827, 372529388, 975813179, 885087224, 763766290, 427781802, 216285222, 883435572, 939301911, 832218136, 699834542, 938060958, 450736661, 189622830, 686595908, 404014021, 145447413, 304864036, 157931319, 781374529, 51334533, 80066663, 474144275, 409862634, 174241401, 62369199, 750698486, 428009152, 201924928, 246472049, 849223496, 14321115, 528092793, 935882597, 267703850, 949060350, 119274948, 952920191, 752989341, 644805712, 632290442, 797867240, 613135422, 267184003, 864580937, 709291509, 930645476, 833849270, 26910290, 132152252, 774331604, 763015350, 687893553, 961045022, 878919182, 655664716, 75110999, 726722434, 392052977, 884378557, 768761661, 530037520, 335780024, 926209323, 553648276, 899025089, 769672356, 920142909, 332516539, 851326071, 474128310, 790250909, 465012543, 854401454, 741220762, 44974397, 266177744, 658219589, 41359588, 932579637, 845079905, 330929584, 719197572, 158556786, 444671906, 236216541, 652255089, 119750372, 78567224, 476084798, 16104567, 769990105, 4385926, 524021409, 965209151, 963443075, 387345629, 160924037, 955094541, 700752062, 170935525, 960810971, 809840496, 3982538, 19994417, 30185983, 236521818, 713127687, 203677366, 47983868, 717727818, 972556160, 232861568, 231662767, 904004862, 755642036, 29457129, 277769254, 585253452, 277981545, 115847117, 677230769, 487431193, 572866114, 316910769, 556676775, 488775236, 505033356, 541400509, 104393324, 356155412, 115222322, 492928764, 273205066, 625762419, 947496921, 65056186, 636060195, 260205126, 570651840, 995034333, 556903501, 761729331, 456869460, 100080824, 62081710, 208851629, 290945946, 514943910, 355417413, 486276010, 514831643, 631767619, 313131595, 849376, 746536661, 434813839, 25464667, 494667124, 194855833, 570764320, 273836659, 550422141, 205177688, 263178313, 391247897, 21951665, 626653896, 302342080, 176401659, 553027694, 72178859, 888660654, 398725672, 658265119, 733193879, 386076982, 912509770, 641719246, 455560541, 889066423, 158587127, 642040622, 728285824, 780839552, 406184814, 362814576, 712296434, 647535550, 163490514, 798221621, 593830090, 724650049, 86603361, 881761606, 53832115, 313828577, 875270519, 939997497, 407375321, 929479910, 872074954, 945068522, 109393944, 938467617, 414812412, 10409960, 25772565, 712551400, 926173003, 199685988, 390319752, 246017328, 428132190, 599545382, 545915202, 6876745, 851674151, 901278445, 668133852, 272606349, 128022117, 698685899, 403823418, 609321976, 717169795, 187808238, 254097371, 362365200, 341106691, 154931165, 771141195, 933732672, 616851683, 396374271, 219403139, 264212049, 399657805, 225757282, 196605253, 817450839, 225629518, 724288677, 859386010, 584885734, 18260864, 577643118, 710565245, 552254248, 436923526, 74859890, 705758579, 602000236, 131074437, 272937640, 592850745, 888013602, 277537830, 752852015, 792681417, 463336138, 983939838, 738028481, 724196602, 801781135, 729496683, 754972245, 747061526, 890067393, 298872469, 539917557, 928681337, 877221080, 815221049, 273229945, 59082971, 906025094, 860794087, 799204428, 954765796, 620688610, 537137738, 266413104, 653833811, 678846494, 107148693, 46164602, 816867248, 297129194, 121615924, 288405236, 601501449, 480103606, 152827946, 343611543, 373427912, 151307732, 341343022, 819318930, 533440995, 789778380, 578630242, 699687809, 980092775, 155496667, 683399245, 183823976, 282644429, 666145530, 436427448, 529534562, 870102806, 907770348, 501085587, 227549161, 459761418, 825139320, 784646555, 92825692, 65716852, 659496592, 232824395, 665691623, 161121878, 80933319, 688223307, 215275170, 404989072, 506895231, 680871717, 253949804, 978409557, 652192262, 644423896, 255706671, 893871805, 538609166, 486678020, 808014636, 624992105, 503405147, 992779407, 465631270, 765242606, 348571657, 207047104, 667282887, 812553048, 311835076, 392216584, 927785205, 828722269, 962107289, 217369794, 48204234, 653114285, 500894596, 346567966, 77436469, 822725552, 752908036, 207071842, 601161420, 279867888, 367588002, 488366613, 638716131, 206945428, 161165215, 327893869, 920716605, 609238686, 510144253, 674500370, 897332081, 964185025, 572973816, 269584410, 738300021, 652093758, 390547580, 644888977, 15760567, 392152302, 90256095, 79135934, 824849257, 317707387, 674326181, 759783729, 966232368, 259733935, 960435791, 528362441, 775640408, 719474797, 127387871, 51962261, 980940310, 316977232, 588277253, 342540573, 526928489, 376054928, 823828884, 558563255, 317350968, 255503538, 887395085, 289082337, 174189809, 646585598, 339256439, 459966266, 442937407, 837074550, 325331295, 409345710, 641930711, 182211392, 684324793, 610533681, 940268406, 410170191, 540887672, 767596889, 903265490, 37421414, 624682016, 565426447, 567388063, 375068042, 287281501, 463007953, 640610845, 364969975, 909198326, 856530971, 71009693, 304230722, 709243669, 560257292, 50929644, 854492979, 815092109, 250742891, 377486035, 223723865, 151521094, 445351469, 322216648, 384545313, 43030515, 477707583, 835058645, 783435222, 568116482, 86281731, 332556669, 285172777, 319304784, 944298492, 747267426, 435972653, 234406837, 850831516, 994458533, 259161356, 917919473, 946323815, 590866870, 858558782, 883315464, 811934570, 99590502, 276038125, 259772089, 402015391, 568414745, 548816403, 616441902, 890543095, 850554065, 132514130, 270183825, 118282956, 713247837, 428263233, 554404790, 451898917, 814738486, 860076982, 998482216, 94299634, 454903883, 205566914, 271846077, 250878922, 711272210, 804519712, 405266401, 713216399, 246101042, 373254260, 607711104, 205323747, 385630409, 973426684, 413705171, 379357265, 487948061, 457914101, 647279841, 63130713, 45769349, 495055788, 577397462, 351521353, 924889771, 577010219, 133267422, 434294021, 189827663, 196341921, 429681985, 933398897, 482198966, 43473109, 712956207, 878175367, 748910972, 750409572, 595710400, 885205199, 100840886, 475592361, 736782579, 251267673, 295152869, 990954632, 911030842, 677566837, 299513962, 956572824, 343725589, 476999838, 120098873, 921660328, 259706027, 155764922, 348491650, 580898952, 54744830, 701158327, 276009207, 599142801, 64003728, 602197008, 701035209, 858970919, 489725061, 670611656, 420049812, 915970181, 327594742, 598336881, 645769244, 124629598, 93258424, 838587170, 945581794, 972568743, 554982540, 260202586, 683222978, 263200192, 337729622, 753690806, 812311178, 994499840, 700721887, 273722148, 706798544, 62840720, 743314081, 574985732, 370004104, 270260137, 890910361, 513165174, 416040337, 993086525, 499898267, 685426513, 217404368, 536985014, 902042262, 627370239, 141241742, 177100540, 623762037, 821122245, 807498404, 700532187, 201537832, 799351125, 233905464, 661925349, 392200030, 652804348, 498793818, 731108883, 854709274, 366609248, 830076707, 47792956, 179488799, 254449067, 920253666, 931931681, 85063150, 408804226, 362184849, 65475380, 470414731, 286204643, 194045790, 840223828, 278060791, 748022798, 687067234, 617291517, 231458253, 815834204, 247187323, 416819409, 139888134, 580423209, 740694299, 441597397, 928330264, 860911551, 198180356, 31207990, 670965392, 918103020, 298005583, 503649707, 390119991, 222904065, 691826545, 794267812, 527356081, 261371633, 53799248, 493569238, 499494306, 811954487, 450671545, 593881102, 861247761, 500349865, 984956760, 348881212, 238898369, 51925851, 140795233, 146812238, 976845190, 926507078, 776401657, 973977046, 319542959, 650371605, 703915384, 595916887, 489247914, 902731663, 675251957, 355385882, 541569982, 416725711, 826311200, 485544719, 728710764, 294826729, 587381335, 71506197, 338861067, 461664600, 750974253, 799043876, 697881863, 386962531, 120073323, 51980544, 597206945, 167100008, 909448462, 285646025, 423071721, 910340263, 591669951, 505009781, 741048131, 172747664, 625745772, 992007875, 420635320, 698439770, 205060455, 476539910, 527088152, 308245179, 515952859, 680263972, 818047545, 109463172, 729141376, 927832725, 107885821, 323103873, 806109936, 724893457, 834749467, 792477316, 33112255, 768545839, 653609548, 50560309, 538964995, 989299606, 911055212, 891886750, 833000883, 953543220, 484841399, 275005795, 748180709, 680692618, 868364378, 756155580, 536639201, 907976035, 928327361, 271929844, 744273497, 488463221, 863939852, 498463600, 407434223, 803529914, 288641798, 848073858, 997476638, 888140717, 136634180, 941959940, 189132057, 406424369, 913391405, 776343648, 643673574, 238609772, 137207148, 528639743, 37228254, 67848085, 943969485, 284615267, 833172452, 13936530, 47154039, 367151477, 597956196, 68907850, 937285129, 840496172, 886452027, 972631079, 210614486, 453232156, 411378388, 916348876, 562780129, 42411267, 362859653, 236876989, 63429436, 518756760, 683078480, 195055935, 997881204, 273469350, 135294073, 895899648, 504569586, 821923230, 622765828, 204761819, 837153718, 843738097, 114578501, 808707756, 413096248, 40301403, 710426501, 816997126, 542766907, 835325038, 415226274, 534819205, 699448574, 446112970, 638703812, 34782637, 197319290, 785914000, 505753199, 337069284, 480009994, 669364264, 174801251, 832625841, 916674854, 457336753, 307663939, 526844759, 82591284, 798644865, 421978467, 635340560, 215624763, 299176563, 289506471, 561243274, 897318856, 358876871, 305196296, 986420735, 82787891, 638399497, 747671921, 360201260, 755415131, 287578032, 822326129, 45259867, 847794028, 498546025, 930707187, 852840083, 36683045, 22633146, 58168256, 614184710, 281716685, 695294646, 126844102, 884314290, 334169409, 233219187, 250429498, 115725024, 14688906, 433700321, 594935993, 297880885, 360232101, 688423466, 699439847, 623388527, 216161199, 234379689, 833486619, 852270426, 745713105, 466456948, 910639312, 146756022, 834840770, 355289007, 372847708, 661211377, 597296877, 539099087, 659257064, 942842740, 98919366, 554433373, 31447235, 678583434, 755288119, 345626868, 619733276, 966933067, 384102165, 217356781, 989761573, 173056867, 640790874, 2763688, 153653850, 249167913, 692820118, 135496, 222074741, 60103080, 155073379, 837032798, 762943992, 136265398, 508182254, 643976666, 402210364, 45870844, 943426375, 4233875, 567129266, 838936497, 968701592, 730283030, 284296722, 57683495, 21265333, 620956154, 757355995, 850364070, 992909733, 650015825, 387841578, 666061114, 480815410, 334821416, 316486978, 178518833, 677891574, 415820695, 908606220, 449431480, 663666055, 71820030, 393140681, 4894284, 400475413, 966414297, 892380430, 924813795, 388017159, 689530464, 112598501, 859747346, 356142632, 406767134, 768779313, 265562156, 641325210, 350430149, 215965983, 226075042, 4078570, 196830379, 946395527, 509737810, 360561181, 874516617, 357030979, 398482668, 635301664, 779851943, 434947363, 99565464, 231558591, 610436046, 158774925, 872813757, 882848273, 110258487, 75659726, 220431860, 699876385, 621039731, 716333097, 460253787, 234174190, 384655273, 90085425, 617402144, 717406241, 721024333, 334170866, 909643953, 82179475, 374364121, 365631848, 510592627, 296990417, 689219808, 226035033, 365210617, 338894027, 69196656, 361252214, 97327534, 557041556, 520542549, 894694523, 682773587, 549232909, 508156394, 100328961, 114503854, 400990861, 8775129, 538671047, 701652494, 213797193, 105456172, 700742296, 716433970, 240850991, 983604861, 683669864, 868902283, 745012844, 953160286, 196149903, 19797501, 121556193, 335069560, 654911562, 28629223, 37078931, 176765500, 119634305, 55194190, 291624122, 882507728, 296692222, 252673094, 553032586, 826782799, 607389521, 520269570, 877368324, 255381589, 464414850, 815446841, 379901126, 778964985, 730538769, 774193657, 936995082, 410631333, 217516935, 767586668, 807546907, 603468839, 469263663, 151934408, 481060594, 130498305, 984509549, 40131792, 198120413, 539661606, 4634204, 115403576, 651339502, 562424455, 105355632, 351841854, 428637068, 445063772, 77647810, 913307529, 213116906, 935262736, 578838510, 648756140, 664678803, 393249287, 336526046, 731906395, 112122331, 744364101, 811327798, 117977037, 878992381, 788380250, 46252097, 871216303, 805476786, 120910819, 76933797, 78279525, 877866916, 366321785, 858513335, 465860558, 549530172, 664660078, 544383310, 717497224, 304272802, 263040487, 633794279, 9882143, 333168730, 350107127, 846094748, 222959279, 444830568, 106721657, 425681136, 121033601, 515281109, 749899391, 876051460, 622981884, 564357240, 441956274, 156714363, 744725273, 981964425, 656093936, 655651932, 218528239, 174751861, 390587341, 477738225, 730205415, 277009613, 275650903, 814582262, 384437177, 691339514, 767457167, 490029856, 644318469, 671685959, 26730300, 196363399, 435088080, 110485903, 672227232, 487202742, 509746765, 478541880, 692392912, 940732485, 829178325, 259034712, 618316003, 669248359, 432426980, 619558927, 659930758, 467990963, 847249811, 607398665, 332400118, 427573769, 147912417, 351478051, 131261000, 688859924, 302665184, 577707013, 842972551, 979653766, 150195102, 334905819, 178413724, 328635598, 614977465, 466062090, 154837206, 470064868, 792463664, 311529973, 298859742, 842321258, 666385831, 780049850, 736544056, 406725512, 705271552, 421074040, 159231871, 237349410, 976500005, 695137659, 836413720, 955968990, 15228263, 195083845, 27911060, 329721009, 904901023, 178046688, 280684151, 164036032, 520821138, 867389640, 331011361, 257532803, 477994721, 710137048, 439878942, 944141385, 452529848, 564767691, 92742400, 55245765, 544093541, 433702430, 625172501, 801640689, 589259290, 933704498, 484432773, 934889363, 322530341, 976985492, 378325950, 386807409, 741085510, 985817668, 214586804, 756365519, 209150745, 533572208, 794844225, 113928437, 921524034, 338069977, 302982574, 864041183, 383769249, 83056502, 283327759, 791888621, 48724982, 483883280, 270517291, 306158502, 166884030, 113740652, 757310079, 157070723, 76897164, 534222037, 730994329, 80661216, 879110609, 603639029, 759649075, 490331938, 349897879, 929805724, 259481009, 207190289, 16563597, 699420776, 874229687, 595541109, 714907032, 784721093, 309187483, 729561427, 492142566, 831007873, 508302431, 33038817, 608348603, 152817656, 405237716, 985682011, 684551333, 927032937, 363716281, 38414066, 640739106, 975555036, 51752881, 131902399, 863725658, 543383394, 819406343, 394085882, 186977748, 379090547, 553001434, 99574491, 643277025, 5735851, 396377709, 405316928, 940572054, 809212344, 16600679, 794265701, 602887552, 84709338, 884731221, 419142874, 211690433, 148865430, 752137121, 640056619, 896097187, 266692157, 606929172, 680590309, 615203049, 897806623, 50418224, 548441633, 3685210, 940130055, 159718684, 964837371, 511275029, 916746829, 943140012, 558107004, 830925002, 427874024, 543845029, 232185792, 200955652, 482291340, 520892074, 854427873, 428281684, 290409805, 472624468, 399068836, 174848496, 459857570, 302828734, 519927154, 543276936, 729077687, 687288019, 490605009, 81009771, 145480452, 403882915, 644231960, 234331507, 290586925, 944876052, 286404972, 756891076, 686833042, 861922003, 329397496, 311347126, 449165068, 645215355, 758114971, 828217262, 953399294, 16589279, 570039527, 974395327, 687997639, 987370663, 165487250, 87453989, 386867036, 690346928, 459934965, 78308132, 66423094, 689926028, 574534329, 300011216, 638765049, 152526746, 918121765, 167405643, 711558113, 171731646, 639746161, 213498637, 458622712, 923537579, 403645326, 514838512, 917662531, 968724472, 138663413, 461449486, 408934839, 847297755, 687592889, 365219226, 19303767, 965497968, 923992532, 460903392, 322013944, 934361824, 75650549, 799046007, 706898352, 453974419, 548247275, 526204439, 389231750, 283704223, 93706973, 99705835, 771999154, 596084134, 827939194, 793718875, 369991083, 911845143, 258518926, 733872243, 345351803, 841920064, 89124813, 906000908, 937565824, 753571666, 5073504, 118904995, 158550672, 290696755, 347065303, 788064957, 735001313, 802366638, 289634, 936587428, 593358220, 344975653, 571837125, 476373717, 15012571, 261682882, 501975824, 714738988, 467203865, 125242158, 433514336, 83776959, 212178554, 162875153, 814220286, 571394877, 714351330, 672325427, 68839099, 834982674, 212495414, 497657983, 954177126, 873088522, 872704438, 960839978, 409288298, 586173681, 535641770, 4446666, 343349013, 104810877, 981493694, 400385005, 295211199, 605696855, 926443425, 839945484, 75925086, 66483862, 39509997, 883439326, 931859236, 310504680, 335286281, 389030615, 944502668, 313653884, 629080141, 788643086, 935470534, 320566538, 987474008, 216513281, 974306672, 732765111, 879734309, 26558825, 210050369, 267930502, 800455626, 359181400, 277669252, 949069984, 543609750, 233232894, 823232293, 461300901, 775132902, 599796388, 161436834, 876155905, 729465038, 797173018, 272425372, 131050927, 118185683, 473137822, 297411751, 504112514, 351139200, 810133927, 729742625, 48567996, 819585300, 705797866, 994249236, 237264968, 584894608, 860847293, 536374241, 451726445, 741694908, 638519272, 292750585, 889427066, 514545607, 29813529, 604297063, 511692233, 854768316, 498884968, 420253942, 616068162, 994543256, 925144297, 830455355, 379970687, 401795333, 39665370, 62699411, 57787904, 714404208, 581818366, 539423601, 457707772, 129102851, 831766586, 210186240, 736646498, 182323764, 465493818, 311463768, 577184491, 22582706, 806613440, 306172788, 641725415, 210967557, 5360114, 803167245, 307724100, 3191382, 295421530, 46191682, 160736494, 298308912, 992950028, 443069863, 1861804, 999978070, 960367494, 104226904, 298641531, 263323251, 25127384, 944535356, 584948530, 730798909, 372046823, 18398708, 675249940, 621293267, 287290813, 750215603, 885020075, 232815657, 67990115, 876334605, 380572865, 935843595, 398713344, 156946674, 713542848, 274200599, 254218626, 341782720, 808494794, 926850890, 216171, 762278065, 827122270, 662284060, 291415141, 930313282, 848385559, 387539985, 367042431, 500108908, 6238546, 55222123, 446947634, 545595838, 787046847, 942458577, 944561046, 431914705, 384158677, 992990204, 474876567, 364820464, 643511118, 600278173, 93056526, 274144218, 166763049, 373583075, 656927410, 177845305, 112176156, 863703418, 133886378, 975405053, 206466510, 219495619, 768349225, 220816902, 132353280, 822874692, 336803861, 220859658, 98832326, 381543485, 885710372, 329818206, 91211382, 923133308, 848753740, 801163608, 952295254, 773435718, 377394041, 717167000, 331179512, 749520701, 392473732, 695296608, 301954407, 913243045, 340430690, 367776826, 744634512, 825747631, 771581576, 946982172, 752568203, 656578791, 954486987, 518776941, 396058077, 806516400, 808482489, 578170380, 765833304, 729415520, 773630297, 728199437, 293473061, 192371643, 689263976, 132106109, 304124003, 749458128, 946129895, 833282698, 938524997, 324662387, 610979214, 119305720, 636872264, 108426849, 711307825, 723026877, 371998056, 523873981, 315808439, 337794035, 216425701, 247263602, 300384420, 995321040, 575534699, 586194523, 904305706, 452677296, 148465985, 47996954, 8696841, 930698144, 780524835, 692449916, 680677899, 674853883, 85621279, 353941257, 234907702, 199050028, 685132749, 904556588, 906210665, 944974047, 473955554, 574289358, 808210082, 486127859, 454296370, 967203940, 243078965, 117980326, 134077763, 146438551, 24577226, 822848552, 229063630, 564650240, 618220910, 900098963, 814476785, 420652255, 842114899, 915344446, 685804195, 650324655, 741309995, 758411057, 826271867, 235532936, 868432870, 349115519, 436033698, 401553293, 242955628, 47324182, 610283492, 747227548, 976199971, 530209708, 800407598, 725923382, 878652336, 464045608, 163091104, 634245446, 376109733, 626943116, 784720804, 305068853, 706728158, 405215668, 578817138, 755457295, 701269499, 879421749, 821725372, 400418474, 749692925, 129235058, 415644434, 542171230, 567048234, 875886554, 867777348, 53372952, 193230606, 706817432, 542619345, 652072343, 534300465, 694358898, 859520971, 123404375, 93927350, 461983173, 327944286, 185468777, 713484499, 174173140, 852398481, 157583882, 757054177, 272422878, 441525677, 937932404, 196355609, 432697636, 898097872, 928889185, 289932873, 450768008, 55738955, 191872666, 628892374, 365457023, 205106958, 734327271, 735508802, 203611158, 68127015, 171847505, 269245163, 363542238, 635965271, 295990957, 429977984, 126121269, 585997776, 310604507, 768311454, 341204071, 14065295, 901226690, 75980080, 733146249, 25867520, 34346053, 120147876, 267555879, 301556282, 833879052, 843944068, 656307408, 61730217, 821190340, 24655288, 874274770, 64447875, 713051176, 830796007, 308878628, 233699602, 970148957, 830490979, 756679690, 483110771, 463538391, 15586322, 594617560, 389792, 906423338, 111429312, 983728932, 685047707, 471892369, 795061526, 631374293, 256798159, 745543546, 587685094, 455029969, 537025944, 89469549, 897062439, 649498216, 979499603, 815329051, 919778649, 947987399, 179234439, 620527023, 268281665, 938102485, 976342193, 549706471, 835388408, 721638017, 455899658, 629493030, 46564404, 411661455, 976409204, 864650181, 837754339, 908201236, 605855973, 112166898, 586692085, 694471783, 775511362, 233053600, 701927921, 409852769, 510296852, 597967854, 203211870, 752457138, 265676367, 83447782, 962838203, 38403167, 687831288, 142708251, 137572041, 592511272, 560169740, 369970975, 82564165, 425972761, 524533142, 451333643, 305864250, 868463055, 707075470, 750479351, 546787523, 959869450, 485773607, 801983769, 351652728, 208723143, 599900391, 453631015, 760911837, 134810667, 428161134, 980669654, 455151357, 763047060, 465431428, 499817764, 397311398, 434432916, 140121039, 535337886, 644458695, 769917599, 141332517, 186722156, 293092668, 978221272, 651930801, 224573006, 488531706, 924007855, 899478699, 730770649, 957950896, 705121578, 979012630, 661522772, 978071303, 941421074, 488688487, 610994226, 547910532, 346837842, 66065227, 566367689, 187894785, 847978414, 447547684, 838780664, 336857899, 204944326, 730051587, 665839627, 258337726, 372422548, 341713939, 560923312, 97300577, 761787653, 356410972, 869200548, 775654017, 143141762, 530325991, 440708338, 80793973, 923741126, 694742166, 133435955, 596708375, 220255416, 897087125, 591452585, 90611240, 906842421, 907587153, 16904446, 46375617, 644907562, 679590337, 309398775, 404742408, 478546794, 326763442, 737796184, 670074792, 589760673, 458178186, 951848316, 291013388, 585581284, 182544259, 732874393, 633765291, 479023395, 664341462, 227866916, 440496824, 715701761, 987106438, 823325427, 869524205, 48559726, 459855222, 930316080, 205502007, 717298911, 200734565, 941114014, 838329859, 686456442, 821972081, 766205384, 462039938, 736227003, 965554341, 983051608, 924766654, 500432947, 90444312, 546015721, 623937343, 294459334, 913605042, 101017094, 446340727, 7836468, 314995833, 300193848, 712965755, 970594207, 91738429, 881981465, 565648082, 336195622, 290700620, 992204096, 409034618, 189002184, 397320147, 588816424, 267969483, 363061523, 768218706, 84714614, 518571798, 586857517, 836432504, 74560523, 948947207, 757983958, 139727978, 84382272, 573047656, 724899354, 508308220, 253875387, 580679782, 643695463, 292354638, 356338950, 478699206, 58448196, 420376028, 657286767, 320007067, 246151559, 878764149, 296711043, 592410667, 10568867, 585471558, 536331077, 993947035, 178583876, 775827396, 501796231, 923239192, 110225978, 767245972, 752767996, 886328642, 758379909, 167603767, 840718557, 484937861, 505133615, 936847885, 194510870, 697417611, 977547419, 126618649, 921186609, 713324254, 576600549, 677225630, 671386100, 788978691, 421681162, 143504641, 185579187, 348248513, 662598415, 60113435, 715228960, 187480280, 722551237, 980334501, 590330030, 848732957, 699634322, 80268823, 208378506, 362833224, 386341785, 810121991, 495690934, 53946695, 382873441, 435481389, 427530752, 611352170, 129288216, 406406086, 990315783, 541065402, 609949369, 430890187, 2947243, 949013254, 416624121, 845953837, 875868003, 274902308, 798795895, 531595981, 965261218, 742113680, 310040597, 808660413, 968403862, 581330058, 973294187, 89006972, 413337831, 940020313, 557211491, 14580100, 105741647, 554279219, 471740475, 150018178, 186039465, 553684874, 538135400, 466431382, 982701750, 823903919, 598640543, 327795616, 387564918, 938627799, 921689244, 534616127, 764646423, 948270555, 513890077, 139490050, 159804936, 53184469, 574419359, 4670339, 138007721, 953020732, 430662493, 371464899, 40936869, 334028520, 222032197, 142808692, 295254046, 260486072, 291398412, 314836737, 134949970, 580427675, 108533554, 255702859, 346178258, 420005350, 10539747, 332897142, 501882224, 511173200, 48279312, 55075005, 990787671, 286910859, 522277278, 37386125, 350624157, 187016110, 138099628, 393042624, 363061945, 349947988, 813782085, 758333929, 668568615, 745638665, 513875030, 120154674, 861436891, 745556244, 777273430, 588467903, 406947471, 446158060, 428652575, 515427286, 611862693, 912620998, 337281932, 616931272, 850126012, 51180426, 369647120, 881472215, 3003687, 189766862, 423012861, 187489227, 545672730, 116479320, 273949032, 819043008, 424542917, 312617791, 4759068, 933445960, 298415764, 868519440, 696295124, 855794752, 23357612, 563160673, 597931176, 281903382, 93083508, 177612095, 128496558, 905732051, 971774804, 783377889, 63130801, 907832739, 648026978, 965527041, 87479593, 52165052, 977130959, 548868669, 166006145, 850266317, 426860290, 86617559, 346695931, 876195761, 479635224, 287669510, 700665509, 394700909, 391737880, 573085877, 62530738, 309729237, 573397110, 445831080, 348329813, 290738351, 472922928, 237249089, 442662541, 403774612, 922490582, 759846254, 597774738, 583228918, 631813345, 668568976, 620278603, 599004911, 833015799, 271460226, 452501270, 228856253, 624487660, 356440264, 908974906, 384891699, 924330567, 328999732, 864645800, 217122286, 444566724, 390088872, 771430184, 831682123, 138682027, 525016624, 142328279, 724502047, 923433668, 608866413, 30254329, 139475559, 709660875, 679813341, 208001394, 372068957, 738001104, 621912998, 558541819, 896705505, 77751679, 733567768, 462165806, 806614597, 271859812, 914307444, 382534983, 997629370, 730199653, 876452211, 257680856, 924247697, 139393682, 775563538, 651038233, 652050081, 868976294, 650325291, 230640109, 163540671, 275882470, 917863931, 300323333, 612860130, 209243909, 855612637, 45753044, 266004767, 993647108, 700837994, 44630317, 967101176, 610354062, 369743647, 228164613, 514544486, 434603945, 895326813, 45362622, 816382667, 548775210, 865648139, 904805948, 625367226, 139448857, 588388793, 369683361, 150138201, 433969899, 521437556, 22960569, 355058588, 176359581, 529320749, 247228849, 685290079, 649107497, 88922435, 704789487, 143859945, 565681078, 397349487, 637764413, 547748749, 947767655, 888210644, 953526207, 685971171, 438519098, 771687513, 393410592, 940619107, 850731896, 602379227, 411850800, 79470447, 420711720, 293754344, 877638846, 107846827, 726215029, 333410080, 830374361, 634000372, 567183573, 472724541, 272895349, 375824215, 526928602, 607412895, 10679176, 591460897, 826623062, 412641625, 494058630, 18124599, 511424779, 884478686, 727206321, 543350741, 450592763, 149757264, 651122466, 518513838, 285732754, 71478075, 80314242, 429267163, 383037866, 736766935, 100536270, 13345576, 904922373, 337981857, 738641569, 858419443, 502733597, 801805202, 870212783, 64166528, 804557197, 674108543, 504388947, 669467646, 689689155, 83889348, 967929885, 97788917, 624998188, 999110192, 595125573, 765326823, 18506023, 607992291, 191283825, 883467869, 640843752, 418344665, 581022957, 824369753, 141663068, 648677026, 276465461, 16882183, 751494246, 28653440, 299619821, 25445241, 368245965, 631070325, 244113571, 543958988, 250499064, 251952754, 876258049, 80391134, 176588194, 854091226, 594097468, 311352364, 425035866, 862682608, 171356131, 641425043, 512141066, 242891722, 151902131, 111952973, 724801250, 743153297, 991200555, 760595067, 813288327, 397287476, 845132365, 20030118, 503778855, 303465534, 624869262, 933971979, 184284126, 184175029, 193680870, 174438509, 909181501, 624085807, 633609567, 293304550, 654582117, 820885139, 435178992, 333436593, 65145734, 99044971, 569910471, 93485083, 934130945, 359732018, 234084823, 153917278, 134662438, 833950943, 4491618, 132744782, 734491884, 133012598, 387170275, 904908884, 402878784, 624178696, 260819547, 811868669, 434563442, 831240811, 718440803, 638971602, 687968303, 104577444, 145692867, 38090690, 191772326, 310695741, 972943207, 432980067, 430365514, 533743887, 180127638, 171924806, 963402013, 193438641, 317140688, 578120132, 147698126, 462774292, 350163983, 329260420, 605284167, 661786948, 21405110, 214704079, 990926018, 744536073, 392214473, 241263486, 370653313, 557423579, 714879005, 987135655, 578653474, 170179641, 972822288, 546235624, 975412793, 919313561, 378826961, 833190593, 591045316, 801884211, 720756616, 117684342, 806023212, 22665961, 520846810, 702018728, 373287289, 725996812, 49653371, 492643278, 964172546, 598900595, 966828544, 823933265, 358172210, 300218029, 482368016, 40231699, 867433770, 387672976, 413671836, 260359276, 244759984, 750438530, 274184363, 62742637, 790237718, 404966332, 78335987, 995152419, 416556790, 506410779, 558278316, 343423548, 117353689, 377850069, 325183448, 524473605, 126097172, 965263264, 565835459, 148530859, 99145339, 73518511, 619314042, 892842342, 669593030, 157219371, 500112251, 16533326, 125015285, 753767759, 444923974, 418738185, 843337907, 39068549, 18398607, 41790962, 778183235, 802842761, 225471446, 56086864, 464471636, 279714264, 523827677, 690000606, 274845746, 577465910, 407139616, 617257032, 827284904, 274261188, 842215877, 794765069, 916361968, 185171889, 860171668, 982468226, 530769472, 430396482, 914905983, 111756846, 296362200, 86295910, 844581627, 829375857, 870776962, 828250508, 882314141, 883661383, 891833480, 744289163, 55395406, 850939255, 203065919, 704121952, 726171955, 479763324, 747256635, 733491837, 883344734, 975866356, 74613810, 739560869, 213661489, 660376761, 941367130, 487078515, 897686333, 928722865, 715522957, 368786754, 461896814, 765584763, 843871047, 458052626, 313906411, 164528854, 195317924, 766910643, 955800036, 134557542, 292035855, 495705452, 138124140, 339422162, 12847197, 322704582, 903704106, 399216881, 592712640, 777010870, 890324006, 619126809, 512153021, 518467845, 845957042, 883523342, 841450419, 644704600, 326573751, 578996451, 186676474, 907783996, 545843120, 196793726, 344981562, 974564956, 690726715, 602996002, 455954386, 966277204, 31805654, 84283022, 242218050, 111560802, 489759674, 761291856, 279878360, 759876982, 489825174, 936607957, 263192874, 814082347, 493584990, 804514692, 882930428, 730637595, 975161462, 984356057, 246837585, 122294835, 534927017, 9150432, 138145749, 473628624, 765238411, 289029466, 296461798, 75333273, 20344581, 856748251, 3253889, 327019966, 775519567, 598025560, 123154931, 222219723, 964985650, 744448401, 883036655, 882700598, 832733881, 619092150, 988453744, 277127432, 616735026, 995541301, 953428866, 951782814, 746337806, 479475002, 610118144, 163847354, 432588895, 379810697, 616924871, 411597718, 775483393, 713984951, 165158360, 51096701, 920820780, 843875635, 82569976, 23316312, 608041671, 808909162, 156828680, 403392120, 613354108, 119993846, 798915557, 268687622, 238501275, 114873907, 746111502, 952437493, 992964014, 255920052, 895767598, 950061730, 834958520, 6260151, 518820984, 521892396, 494720417, 748046539, 395689278, 354896458, 67277447, 595665550, 520211457, 6939113, 971741404, 658068022, 213668462, 515553911, 976021812, 567377416, 733439442, 376360597, 678396046, 409599866, 892422394, 734127012, 327836213, 512772256, 433586811, 507107991, 290126123, 439908188, 775553325, 874924164, 742410603, 228798234, 305794769, 582273251, 760276341, 610850916, 16305915, 810051582, 995447153, 188400810, 529265745, 115453972, 385213159, 512082220, 878084202, 252444888, 993085143, 514462924, 524950542, 421036295, 19562447, 889352566, 75522430, 201958363, 447424413, 699973379, 534875884, 816412501, 839027956, 214241134, 309456700, 500346344, 707542904, 686161471, 384807117, 36133326, 940919650, 255246337, 203626637, 340988865, 598164384, 417340743, 206822797, 622625529, 142565972, 293960790, 510359771, 357528158, 666375621, 230533841, 971476294, 807351569, 747375054, 677396447, 640113521, 494309367, 100850234, 938372089, 816887698, 111055408, 510372777, 997605314, 206373273, 339205673, 460147546, 117710591, 912084635, 888267784, 309813565, 590349704, 807030825, 889987364, 744933409, 752375192, 237424752, 32956202, 106959243, 675474761, 115482323, 307388277, 904507964, 28105232, 508543157, 910285842, 543123034, 975847701, 656762063, 371442473, 386923283, 503445049, 865938456, 306330433, 999340435, 476965574, 401330385, 168601543, 194193112, 973318809, 66621951, 842022892, 460551406, 260643528, 495469432, 567954203, 254175588, 455195458, 344210984, 534972103, 920098096, 970544065, 818121943, 920955771, 121714032, 914729591, 307107938, 464319798, 23994455, 271998668, 594034124, 631801969, 576241071, 609047540, 402506080, 809624398, 179557957, 314826272, 329019081, 394128753, 311528152, 647200111, 351019838, 885897300, 701063455, 978065201, 216946510, 447649941, 275687837, 889760104, 939913980, 754815293, 461283024, 349123819, 225739767, 557756574, 200500331, 867848172, 279755978, 690082284, 941826627, 302469376, 901627996, 482996489, 984258509, 669096568, 805254920, 49761820, 525008937, 848220708, 907109112, 468196344, 762478612, 899869314, 712986839, 812132901, 216584716, 237490074, 792702365, 450253535, 986999671, 385766885, 732438840, 318841488, 569365667, 546584131, 263213064, 653112886, 94107127, 116901870, 404542654, 711493261, 993542671, 734074181, 547236483, 59639057, 158705309, 561337821, 398424979, 780911604, 74903278, 117607480, 450486024, 697634154, 695311575, 81695937, 232377628, 956706647, 613307710, 866555862, 688796364, 586767250, 896482228, 452542431, 726999356, 703263045, 374592560, 748561191, 573714045, 896818573, 231899745, 612033150, 436365650, 22298705, 582673944, 402091484, 765156263, 723277443, 912008371, 111862302, 240438291, 762217732, 682045949, 286654980, 179972077, 416788235, 779538767, 805111206, 808325469, 948138512, 280206076, 144420510, 159672849, 92619793, 182838633, 95956787, 913795001, 623764671, 603708219, 239963837, 641379050, 420473401, 614081745, 221084081, 920009623, 396518146, 571834631, 672378426, 526933373, 354606608, 788035789, 545623302, 961830661, 932223324, 333110692, 163671255, 169804151, 814702831, 789725368, 784650000, 833697166, 821256167, 54059460, 974535415, 257214523, 373847391, 211881760, 202226475, 565791018, 668822067, 788266097, 561416126, 476927883, 718978868, 909903716, 198215687, 884374859, 396617733, 964086201, 795219868, 596033080, 377716678, 113706750, 811987232, 576044147, 221209155, 852475394, 134889783, 699267396, 153315378, 979187154, 935288123, 182149824, 255216589, 881538790, 631679378, 762356647, 115994612, 83728326, 583211339, 397020670, 544744913, 619435410, 334300136, 385726758, 168520286, 540839095, 807273614, 120648622, 285335901, 183997864, 2043740, 593551504, 692448325, 657503847, 579293881, 428626563, 195222528, 607440385, 974444953, 438447595, 559585492, 647707357, 847260648, 340723685, 410208334, 514844129, 705101916, 151820061, 471335460, 200759107, 612441677, 709718945, 449330869, 116174763, 665621024, 475298901, 820599227, 335045349, 656804976, 210298915, 585510452, 783656789, 875371921, 614910503, 871129129, 951329455, 119521283, 175620890, 184122126, 620537014, 610316410, 682946529, 134436837, 691048929, 375196453, 100670951, 823270276, 583373683, 736584562, 609299257, 818277182, 851315716, 680387380, 934452263, 907999285, 764299049, 321365405, 314221627, 613056685, 560444217, 302541666, 606333067, 846003154, 268358026, 364149785, 82069597, 951576492, 182526837, 675079055, 318157063, 463220587, 791287145, 867759910, 62358070, 860477145, 438468177, 177071150, 214470288, 423322928, 556990716, 243095980, 679389379, 529566764, 836824353, 428105600, 839013945, 316700332, 799703262, 566321870, 285196972, 984548763, 554682146, 434555824, 417884292, 185525306, 228830196, 461151248, 634678092, 36451933, 407805218, 47401782, 857174036, 332305672, 514107848, 371684996, 862112404, 25382775, 316320036, 748098178, 396748036, 851732610, 851208989, 489088174, 153337010, 519049902, 610619575, 189647647, 746845941, 182260345, 611648063, 28563007, 767439638, 255261578, 594054679, 959600479, 640675781, 419590643, 402740208, 627505673, 123709908, 335393013, 373020213, 293301473, 181968473, 251192746, 739292081, 488331580, 270899573, 304087602, 250843565, 145105072, 893656715, 340286293, 48108172, 392977087, 879846609, 865618216, 755619014, 779537941, 379927251, 225701632, 170245826, 909800050, 947425042, 456901985, 600677787, 519396074, 799352185, 373564636, 313522, 43543400, 376037315, 69236069, 85268651, 455265717, 692565345, 556732399, 912010652, 976459108, 943038789, 687819347, 93742940, 263343559, 731953030, 594105763, 864625215, 873606701, 780657473, 567691521, 538598469, 296000459, 481351061, 626406399, 573579952, 737942593, 247541014, 623273377, 978228806, 490979452, 688789276, 964442441, 597170672, 431815215, 428128065, 210334627, 896352805, 922238517, 22978901, 56265874, 719041973, 742660897, 823128244, 374075397, 916990823, 275254871, 197704297, 989273446, 370134254, 927028884, 638065367, 448561588, 852987736, 478335231, 330948070, 615118618, 803729160, 703075758, 788175491, 38892123, 480085281, 817449930, 549152010, 939119308, 308490311, 321672869, 697088342, 612720184, 780003628, 920402949, 166008591, 724266051, 194917295, 465904825, 572805048, 277267949, 647461951, 61749989, 900662155, 969794724, 998358022, 429842175, 220559310, 286710859, 14328913, 514928027, 465186078, 327192927, 973201322, 993786557, 919089360, 51243744, 120872027, 665978363, 262881196, 798776210, 979163328, 885729657, 772916126, 229423298, 806534276, 817231642, 952497773, 162383257, 436454722, 726536912, 581918860, 279541219, 589765699, 215996002, 607320667, 162816337, 63288398, 823531493, 911869840, 8694232, 276370109, 182897472, 256975892, 171090956, 667180517, 116691404, 79184375, 133789360, 605609122, 712506406, 135571523, 450966423, 626096677, 874950668, 574558373, 382310154, 471885363, 589971357, 921552835, 9542904, 639668044, 189313346, 317725412, 623972251, 332479201, 504596274, 712451902, 802718358, 536524638, 460684058, 122107320, 922189837, 691218768, 164247671, 969937800, 611281305, 263008695, 367229393, 586048651, 861453782, 167471838, 157104039, 762918603, 712252718, 717807572, 977247606, 442558536, 384197658, 648823123, 717214619, 568906868, 905431622, 904314411, 303856446, 10998048, 377918238, 129610395, 780630835, 968110717, 827305938, 391135789, 972399035, 581346853, 998813454, 132990688, 483869678, 861978831, 53545400, 688869781, 961327384, 948394285, 341725148, 314922955, 278245907, 614761297, 886958384, 81054050, 892031394, 117040139, 385074054, 249827990, 971713053, 770628774, 685919230, 906539561, 256139030, 126047428, 989302180, 642798623, 618277131, 621746003, 607302255, 404913183, 52417652, 35961656, 642389040, 870215670, 235004457, 449195318, 343977502, 168182850, 672705525, 697716834, 825464548, 606935619, 829812039, 899906909, 999659043, 371737782, 686325280, 79250015, 512249278, 731960679, 266084172, 375268530, 845653298, 519424770, 300967692, 161194525, 269079027, 200212333, 399165232, 947340192, 445609420, 524552813, 536915359, 961490620, 449426111, 417561213, 30877431, 803907250, 354826006, 2097029, 545166313, 860369142, 434479940, 308380967, 851363717, 25447691, 183376278, 213515233, 396949452, 994979281, 113767566, 650075662, 441104935, 481649725, 206029197, 657651333, 243173554, 278467842, 669828667, 637674947, 155007935, 415409762, 576937276, 953519569, 559719468, 744512328, 742430759, 165592820, 401770329, 346417343, 144966813, 731406585, 876579418, 224771699, 892681625, 234092337, 251262715, 871583674, 708202001, 924990942, 7209880, 84265826, 331020973, 989095841, 654434562, 969565269, 705629097, 973558073, 19876453, 801569312, 414931590, 100209963, 807174159, 174345286, 966248780, 765800644, 546531854, 655843653, 591810240, 81590486, 59904298, 92458332, 818373329, 17568766, 227213152, 393674472, 194539410, 522949629, 318998465, 262696628, 841408281, 184957444, 302443630, 978293339, 944999768, 826992703, 703904031, 262742485, 461223676, 479976587, 666866460, 178055443, 140058962, 574826055, 43396201, 883157844, 1100430, 822103013, 482805371, 996917793, 342788413, 811373353, 820439793, 63576317, 644317482, 702280562, 720919969, 894880935, 570181239, 406126817, 845204330, 312886303, 303578803, 706573525, 391923267, 545772956, 838806053, 775888052, 584147239, 830059658, 254340680, 604802644, 762873258, 881414936, 860368834, 225765957, 473812272, 71126142, 787129499, 768471033, 452430649, 687682406, 769807236, 593438390, 391516700, 236363302, 140957627, 670257573, 958865346, 990662987, 844028463, 400827712, 826166663, 608590733, 775253823, 365915012, 131137839, 885559886, 681384904, 454368167, 452645885, 266394763, 239878687, 647591272, 967165437, 376655558, 683436930, 435207900, 795816275, 122365797, 808042663, 3825827, 642216831, 439197620, 14406671, 551005946, 979455021, 815453794, 27840161, 690923584, 983076016, 59433425, 960171977, 479493245, 224756780, 245817873, 422743600, 89326238, 596854208, 744252641, 477840792, 705867514, 901677093, 119474256, 285224081, 58741597, 153532838, 92335023, 379216862, 571176548, 932451528, 31400094, 686312309, 462978255, 923216750, 193479985, 872522624, 644375568, 413125043, 828762594, 803649994, 787440779, 741977358, 651332111, 48931113, 407553192, 417881496, 737324344, 798108804, 449116781, 633778960, 922454447, 973463214, 323445422, 788848060, 292575880, 461558723, 705916487, 687096029, 726037533, 667561264, 259681355, 86312869, 397909144, 193421088, 698189499, 617050984, 945640191, 846391861, 308329884, 490385182, 146570530, 27834996, 867179877, 513040224, 223719104, 807476131, 328425298, 773191152, 740315457, 390207220, 835344859, 712740191, 809327344, 593379237, 813879252, 892811552, 863875194, 85087631, 530507225, 481812116, 117877870, 544807119, 988581552, 936011402, 30756631, 847933477, 955829158, 342304866, 857986807, 446423422, 670791848, 596967790, 787560369, 791228088, 688328238, 265375739, 415107519, 2571782, 238040981, 628620592, 704503070, 80228612, 633766433, 393690909, 404720240, 402145370, 929445195, 361706511, 479572929, 187055390, 463636893, 283967160, 378444422, 446084107, 37628444, 918486384, 887878761, 669351880, 496523265, 453860722, 617370930, 248600918, 319176341, 807384744, 787923863, 600256309, 39133972, 278097765, 733438333, 745139819, 627838016, 575761523, 188898676, 843997370, 202600987, 132200795, 405364877, 703355813, 672736471, 402752874, 724454558, 66721677, 728393002, 502746254, 273009679, 943007699, 77480715, 422736081, 805996196, 793589789, 856581890, 561842743, 353465053, 39133127, 85230213, 329079545, 55275548, 677675112, 257025525, 883975814, 704536425, 801303103, 618712365, 395908805, 319044795, 952055233, 910606518, 826565411, 200356867, 608037858, 498455292, 970134255, 338839518, 397178794, 862234794, 97082413, 483604989, 757382205, 666491826, 606948757, 790183583, 902178932, 344908722, 174506800, 873042807, 748384559, 914883879, 556988886, 19707308, 820079746, 992717644, 132689692, 764892644, 621734646, 336626291, 685323659, 904122876, 831427268, 663429281, 556288880, 386481658, 317343377, 490720184, 762243254, 755511594, 934658630, 997732619, 559096976, 506329727, 246861293, 500756815, 454165964, 28052999, 252975746, 555568850, 996224232, 36576431, 641577844, 967709774, 817682973, 789354099, 88071654, 516105950, 911148441, 354644128, 431732829, 64275907, 928787475, 366980244, 204020300, 241937554, 613501692, 736798555, 539599850, 78006767, 309755482, 231388479, 738373856, 223982168, 284090605, 203372172, 197456543, 162067322, 395990965, 750549652, 994801286, 566059177, 297123330, 883381832, 684351869, 153961313, 915312875, 22721509, 337175844, 643329057, 713595604, 291564721, 676303368, 549034608, 81395479, 553929469, 214060126, 1029583, 524206988, 813036369, 769172366, 165194077, 313376366, 502379858, 107844553, 92548988, 65443299, 450581244, 427838475, 102304873, 843569048, 487892343, 920103589, 216166967, 34278329, 299459157, 578814462, 848327647, 108446701, 382738630, 113794782, 123116233, 689424553, 614233790, 501727886, 726348979, 62688403, 264819659, 10136182, 228847810, 772624788, 20472823, 363663608, 814273889, 204446917, 915215338, 974066569, 258749485, 629758716, 542414270, 445752218, 303913029, 438949846, 512517259, 134292603, 847405242, 169063776, 282323951, 885631239, 477835165, 483224783, 939707557, 797066191, 893398664, 859857487, 994832155, 336009334, 831772370, 779205891, 499925574, 473169465, 200126511, 851924593, 269575133, 126301593, 525422348, 40271292, 51895092, 660112941, 391620661, 835955351, 466149902, 50116952, 740155238, 899805505, 253352349, 837231837, 265027343, 199480759, 691120059, 788948306, 607247576, 165538620, 873512678, 623455768, 819444741, 595287256, 947922041, 326462531, 373174830, 812049219, 897382613, 398991397, 482803763, 743892995, 700456812, 568397645, 390697448, 570389764, 258763728, 349104835, 348576360, 517544542, 368656049, 793263549, 132224059, 499335499, 630671522, 381895253, 38013230, 960756510, 718529757, 405472687, 849808641, 454277416, 365816955, 438542796, 726366258, 558400119, 250673195, 26392865, 571592525, 347809294, 844006044, 984377169, 436211774, 609819842, 221006792, 356267406, 759051001, 549404900, 971675571, 583018494, 612373244, 467784740, 197898351, 170571231, 266492929, 818350935, 188961635, 154447928, 980695873, 474888976, 449981565, 540045475, 923372488, 970318479, 937107449, 927444914, 641877117, 586411631, 743208361, 463251508, 738868453, 656639117, 381863005, 750689770, 190232977, 466457833, 880470255, 921193273, 638859999, 79179216, 666235349, 603825134, 645004915, 199053719, 222270308, 195242620, 584773589, 129602716, 999970134, 965958189, 50233019, 204581605, 514177962, 801418967, 349096876, 437007043, 696874279, 454942869, 446278432, 255728452, 317795954, 57244220, 815486881, 758015678, 409496625, 479029996, 737111165, 989260795, 599515069, 423297131, 153674739, 35705330, 628980536, 960480772, 641055015, 719101866, 84222850, 90241041, 499186039, 298154557, 473531982, 487430621, 63280298, 3667743, 303836336, 363120326, 259372254, 730068192, 264629856, 617006795, 372506776, 455434497, 606415223, 172223327, 577118158, 225144301, 911356451, 901416976, 547205404, 495697065, 475332061, 529274056, 958172747, 453679069, 51968705, 753594053, 950398232, 245909563, 619499106, 26856622, 413582687, 303664036, 331925226, 353094350, 873299542, 162029097, 405897126, 108137676, 812406113, 668826721, 261385555, 157356200, 867868674, 33671962, 772597645, 926994122, 768320427, 908356500, 997039290, 140085145, 443553926, 998262743, 191017610, 22967719, 72328040, 693591425, 81504653, 656271910, 654845861, 957828571, 891194798, 823431160, 264225635, 740562467, 306566928, 643757593, 310501191, 310442803, 962321158, 574886071, 423249947, 974109728, 528031610, 47658248, 910884070, 844287025, 270786160, 347519770, 26624165, 511066741, 966172820, 21043815, 337959945, 968224979, 373025435, 218406019, 138167711, 557266252, 312820107, 20752134, 421978623, 859167915, 302080362, 451009568, 679245748, 154312601, 889650242, 71880242, 618973157, 294369986, 3132837, 967757557, 263675359, 847066591, 379583446, 624107835, 78543969, 881633582, 47288676, 853649256, 910268841, 578672830, 413635229, 673403941, 464805031, 828468655, 165198672, 418292597, 679174311, 164366083, 134512055, 145818049, 826059545, 342064142, 111446462, 48122276, 714382604, 441445256, 943750268, 571768581, 136018635, 187644319, 755907251, 65575997, 422536029, 303484571, 744311318, 820818711, 486056402, 924364450, 784907380, 176016273, 43529120, 878737584, 339098936, 704342167, 452633217, 16544268, 54737028, 661604787, 127282809, 959020368, 747437709, 293908004, 981656425, 15480714, 28417854, 792548595, 91612921, 453473613, 259964974, 267026395, 372057541, 573895214, 804326076, 587470228, 269729041, 723908238, 853433588, 976274272, 795066001, 460428912, 874526302, 285260249, 621420986, 682968239, 44989433, 394071893, 53194464, 606182771, 14619781, 310246532, 220168351, 100437291, 314054631, 807375075, 492179756, 997937382, 47823793, 873226831, 919774859, 701049883, 988150835, 466569589, 607683131, 769909548, 508917733, 737024072, 776102385, 273083066, 593327258, 779776598, 3148777, 556641527, 786205334, 104806453, 570513293, 465625414, 358464159, 694613427, 289477265, 574043257, 528896410, 754731626, 440267685, 658186964, 473453267, 645002088, 760168168, 79896964, 486822901, 504673673, 41878941, 71792760, 479403213, 132130855, 274910856, 348773045, 213489497, 544279947, 537350164, 40931800, 674503136, 511639378, 587013116, 261225389, 800766927, 763984733, 671370680, 120833663, 924869237, 107892284, 565988401, 943079096, 158784286, 244297833, 500527267, 524721037, 532677338, 251803295, 335260529, 284844198, 752517155, 124363465, 710552459, 332085986, 79092330, 751263458, 551077211, 73414440, 643730784, 389668684, 340316086, 831210441, 267281839, 622879012, 438515497, 390822591, 320749978, 890562676, 803885122, 910755593, 512062404, 720873969, 894084459, 628884045, 982391617, 278350352, 535939301, 200701051, 795800066, 622940788, 743493482, 98522656, 693357568, 405332838, 377272662, 607869130, 483994213, 459432220, 87985441, 941062596, 866534053, 980379818, 191531664, 562473589, 162655587, 397516031, 611580019, 331477204, 95015624, 465362285, 202721448, 520936623, 731475497, 318086982, 265108273, 990136136, 835194661, 780111882, 121260507, 88857256, 996759562, 776559982, 46526888, 616335369, 519110347, 937557680, 639772917, 942290618, 289797867, 880600726, 445952974, 704760491, 404449045, 275747462, 505402523, 5990106, 302393344, 630314978, 859479603, 236913322, 343791218, 451726654, 195935068, 10236036, 61973998, 968640208, 193712913, 520009635, 795118110, 6173351, 310094144, 344296550, 729377633, 534602065, 761823237, 695295524, 68291470, 41748188, 84897716, 358277357, 939757181, 249391120, 488878174, 861289412, 5196668, 478317741, 565114580, 107510506, 737618625, 471462912, 591103894, 228963424, 283224790, 621236765, 222867756, 489617399, 638329380, 972272505, 398391465, 271170678, 149837526, 678867865, 553424057, 394166688, 371382438, 245822891, 369182065, 635850771, 286409873, 210239318, 79061340, 868431399, 345094203, 197021628, 95345090, 178470248, 350494693, 224568562, 503752723, 443789166, 226410346, 600605603, 674328975, 881252885, 25815293, 703715792, 388104418, 673778929, 878732457, 412131201, 536477784, 534127503, 628545107, 804827436, 899542643, 120606461, 271695886, 603161262, 605982580, 384990338, 384084683, 34183036, 50053457, 242032862, 465621844, 927037988, 787980469, 408634719, 484860233, 30891031, 222640075, 804701580, 739725524, 173141450, 515495560, 166375320, 150455553, 635583748, 192596914, 408647982, 273144891, 356685517, 241334250, 199629196, 522455205, 737241978, 515720430, 178366604, 880254257, 122448141, 795859798, 930216495, 762179922, 906200448, 213157269, 710197716, 20771653, 320065923, 5170704, 818344462, 815145313, 140235481, 306949005, 589840447, 869064934, 348140943, 465030676, 246362399, 799672205, 821615727, 551498413, 277260682, 579970803, 566651583, 42593005, 74777112, 967429344, 195501346, 922716081, 421289206, 739420906, 64363054, 283561643, 275962780, 494774437, 789068205, 405024194, 483862352, 574899559, 401757846, 173197963, 761950362, 586751288, 797332811, 420179009, 214293185, 166939136, 88288917, 246795739, 502624802, 823131100, 691076712, 468242046, 943453946, 800375900, 408857284, 833916359, 190523170, 938467185, 331005919, 207920874, 409950005, 646392553, 981101106, 943435167, 481180073, 686764310, 767123520, 692312353, 774321255, 921967814, 809001619, 161139938, 441764148, 582022521, 101499238, 769939564, 533840386, 531579777, 323668285, 736056274, 840666616, 657510840, 848091829, 460851996, 977898731, 559440571, 672894916, 320328404, 729857010, 428849865, 39082340, 460149621, 838407309, 701979557, 316205536, 335721415, 727435818, 163661839, 483536953, 965923311, 482211940, 924904721, 770958265, 646798995, 616312214, 479728902, 846291599, 643695215, 569078529, 183678424, 956811652, 357281682, 158565183, 389459215, 506802653, 694834972, 569030765, 962594766, 197568975, 696617831, 684798653, 897889752, 159638959, 269150986, 384947930, 941378817, 32089227, 143966079, 609885071, 310665929, 203389004, 880013582, 743770857, 274642086, 698244648, 777801645, 213057204, 971672669, 316603568, 108031716, 706496125, 822259355, 656198548, 78086070, 551809815, 94347256, 571278897, 790215185, 47705922, 71968170, 639287111, 385332839, 647468497, 879013699, 474819, 229566440, 55433383, 49635426, 723430416, 504241394, 950623050, 468188022, 595692967, 100689008, 417117000, 602637805, 712672849, 274830924, 420749934, 794427799, 677488576, 946444288, 395791008, 185020432, 647004676, 73064760, 139983040, 787498235, 688419272, 117376050, 261963995, 45373969, 365604656, 233414722, 229962253, 787056207, 786475799, 143330781, 578170280, 766694378, 628584554, 940570718, 960758338, 863999198, 843329977, 977362283, 330390645, 604002101, 778730111, 700354102, 882215683, 491049815, 695211877, 25273529, 490965043, 587189988, 894285533, 205535004, 421019025, 266038175, 605854002, 349813868, 972233664, 107248036, 885875301, 959306383, 227029453, 126261119, 718053567, 484030383, 442840603, 666959150, 313955655, 26705224, 509065208, 250175896, 528714339, 448519785, 608417163, 774888833, 846182275, 581564098, 380486443, 689777931, 223153498, 914836395, 264017247, 117781674, 871096127, 317419173, 151071419, 363560404, 707465846, 650602218, 798964735, 935485103, 723848140, 234586941, 618372979, 150356020, 178471720, 481654887, 247048784, 737967599, 955165951, 18426398, 453713156, 508573256, 527643180, 35902083, 964802851, 177358694, 926352082, 230659029, 566442862, 596223563, 975248374, 322395264, 711042483, 31877419, 117055455, 81068688, 840898436, 113340682, 16942018, 652701609, 219888807, 542743087, 30097105, 276088300, 378988170, 237630635, 146276538, 988310249, 83514882, 629817785, 214085132, 43354895, 457226665, 667591998, 132693644, 70064664, 866199459, 44502383, 798469421, 598574541, 812210278, 345691839, 231217461, 176064824, 415685599, 125360264, 695401054, 109392523, 118624825, 787709111, 702504265, 966030590, 434722431, 174003413, 21423265, 888668493, 825099902, 747308511, 145109983, 441290905, 635269413, 225709091, 255811932, 630763450, 957003062, 271614243, 238057113, 799838270, 514105866, 339502471, 822050487, 35718792, 121798020, 206005197, 972279936, 859865053, 107969471, 256927075, 280127701, 121255451, 280256675, 334189811, 305041154, 886286835, 399829563, 842272948, 424051348, 655836312, 981162283, 206349521, 717556514, 845106700, 658131468, 635666348, 875715857, 610472065, 152940338, 10769513, 439985599, 793552322, 651106539, 354535216, 49423594, 194181187, 909819031, 136924816, 354824876, 534431338, 933938079, 534886236, 946137316, 526200772, 208675999, 734073212, 572187226, 70071580, 179946096, 699313791, 178447352, 930796746, 575050434, 842149214, 924900139, 576435589, 523898250, 24386557, 140794893, 654282063, 321944122, 769650994, 147540660, 5697624, 899154054, 158321670, 714222303, 691720688, 747091974, 994904044, 732136011, 222129723, 712793727, 176482280, 335966037, 247071565, 443339667, 976089952, 851321071, 183452925, 22259808, 163371403, 266303530, 632365062, 877258175, 477839496, 387700965, 726388647, 423064365, 958702329, 161883994, 29690117, 684258595, 979291243, 726287938, 613282828, 854452428, 975503689, 190855442, 67687636, 961216136, 631337984, 667140838, 21575952, 814611482, 693771581, 339989465, 310008587, 65439909, 790424391, 84458477, 712782284, 224104358, 278389588, 936843264, 489593234, 836398727, 301304376, 461312334, 611636048, 337159007, 623030116, 465615300, 548885173, 177563731, 605279600, 784132904, 654544359, 426207401, 713432644, 888382607, 676834909, 957891676, 694119415, 948702394, 364534663, 701826428, 475185507, 497188134, 943449211, 567925103, 516510185, 71682449, 394336032, 686011513, 342011286, 391274054, 278094928, 565612252, 588356905, 232538879, 246074463, 115803067, 220596762, 841581547, 237490814, 880073478, 740278801, 990336857, 652211824, 207942969, 723614743, 62693851, 20327856, 275464249, 635469666, 572776709, 126546937, 799866398, 448696935, 931213540, 687824346, 365929233, 2053223, 626886257, 908960575, 751307781, 244075911, 439316330, 787851180, 243741001, 181877165, 212687295, 250383702, 540528166, 217813528, 166153717, 175349348, 718000239, 837914422, 805251931, 441416588, 686816919, 656447579, 524584845, 984955876, 33671691, 254188249, 673365282, 244703341, 397145880, 437814423, 593206321, 540310768, 329893552, 240026886, 429401491, 560755555, 328945660, 772674438, 241598062, 712186625, 543770198, 683523392, 936172872, 217388681, 881256393, 16830693, 177459922, 857307961, 133514862, 125024437, 952179717, 81901735, 975807830, 107901631, 380931548, 308714936, 936549133, 373769169, 646779658, 627474307, 927773117, 850430874, 247160966, 32778553, 290958478, 857813439, 20636022, 272995014, 47241802, 452131722, 355217295, 128274565, 475428658, 313523209, 715590046, 703623633, 891588081, 975003476, 451195438, 950365554, 751444459, 223829899, 932568, 24086733, 997041092, 961159186, 468821683, 496100171, 164902682, 259713050, 144698734, 32134691, 985488502, 46053888, 444376259, 718688528, 886025773, 248825898, 248231911, 436210444, 302063961, 36613674, 100142069, 405412960, 16817911, 270939313, 863748780, 782779308, 476863017, 438373876, 738855865, 531345742, 583557995, 765481398, 256012346, 744142518, 507263450, 25378357, 837337127, 346107352, 309853101, 194201382, 654593740, 45413601, 378099023, 798805894, 696003855, 97624017, 839409593, 857756040, 326085586, 570494453, 829143178, 755607350, 418912574, 624261943, 189916293, 559793239, 448378029, 610113729, 701640032, 239506906, 370132670, 216923871, 503275052, 636732594, 289395910, 295581947, 871058864, 392627315, 469501598, 254218363, 782687545, 518696883, 412668276, 141950152, 674310632, 276205980, 904053237, 649759320, 472168606, 771631392, 237898635, 436502365, 512737339, 716812848, 969417993, 991929312, 657605570, 203529344, 232312059, 559653774, 511913864, 661022141, 902995986, 105710572, 582166281, 608880596, 828852217, 251459919, 297705125, 401777684, 366811408, 422175629, 562790119, 148074678, 846368494, 933896857, 904998396, 31627529, 404704403, 934812370, 518281257, 289780699, 366351383, 678352784, 915715604, 173940703, 139205886, 160978464, 159443480, 991666438, 733165363, 680841872, 796572076, 789460669, 556729601, 641797695, 18167140, 90168910, 851224977, 657419727, 114442594, 509532254, 888107870, 34934140, 16229164, 612938374, 328750374, 652761236, 857261256, 187001174, 125483294, 337853717, 201892771, 69378062, 908432279, 240643537, 795447968, 726500815, 352173812, 953996079, 683077433, 920792886, 556034830, 801272578, 148204342, 766693250, 544574657, 773475996, 493978814, 429888870, 252137705, 660702463, 314971045, 927000093, 399759496, 942883349, 945569157, 452203324, 753882962, 39658626, 861448215, 131993800, 316844327, 880360969, 700516282, 834299971, 2390045, 24587586, 242641000, 782666967, 506101596, 921765653, 297791704, 817888245, 978488676, 945060583, 672242654, 954174968, 104277823, 383822861, 105871305, 51120674, 867231035, 167886727, 997497451, 917766482, 994112378, 312995438, 866935977, 478750872, 859864384, 107484218, 463349007, 798293718, 672467112, 85007489, 421658114, 530800955, 410179511, 575990490, 190074907, 968465168, 741619989, 694381130, 25056808, 237888809, 166055166, 634440465, 95448884, 120840486, 187143398, 556101897, 153082477, 697723485, 581132005, 132706122, 597516453, 162324831, 674695841, 969706466, 860797918, 594141913, 194508071, 555005941, 77494402, 129875785, 117470207, 343726690, 261913344, 421145425, 652681408, 898601179, 134947368, 185531862, 922455891, 993647208, 547227817, 640264941, 475087705, 629496561, 226019815, 678020333, 236477962, 791787409, 641197247, 118984411, 160268209, 667393706, 152104060, 677530025, 127179496, 709596345, 71830148, 93188926, 176105288, 746200981, 300681468, 817984475, 404155263, 467789638, 130847810, 503333987, 442143760, 42516390, 997047347, 395296136, 121953134, 345323133, 469682553, 363512043, 759311644, 709359054, 982521659, 851986742, 171496031, 682091849, 508035342, 859286783, 643931777, 157236269, 477647717, 166085004, 722579272, 748027468, 496921621, 425306271, 56460017, 151303918, 755080160, 279256672, 227574876, 16920993, 237875084, 407857424, 63952313, 837039229, 654836389, 433857032, 285422046, 376552965, 882811803, 552255329, 419077537, 470042296, 253731241, 72034593, 429012430, 860816187, 314969002, 339096458, 313203811, 825557332, 77805563, 423545773, 472199798, 950303581, 914701389, 622022737, 942687380, 635283630, 174247379, 453269500, 682371585, 995462949, 384579795, 323560956, 429244367, 249952353, 152914488, 702217307, 198006366, 769376045, 500446061, 831291705, 596830753, 414073223, 289909077, 667922324, 83010679, 500824587, 587018739, 738367386, 172762335, 98592425, 84623223, 264478025, 671149297, 175479375, 696715034, 684972882, 480974093, 855886456, 482943954, 598234149, 172973180, 428123645, 639537402, 286581942, 91256900, 158507754, 870610752, 38257658, 868150238, 146350056, 547824412, 400211160, 376984086, 111790599, 892390107, 436845036, 945418013, 321578301, 522500443, 973840201, 495795310, 172701803, 497025329, 549532880, 585031586, 268462585, 28850932, 306575834, 329531346, 644293431, 910620621, 188297542, 567667286, 134973418, 377218507, 169385488, 959675015, 780033530, 686766625, 771756327, 451873460, 725246748, 948132693, 714235952, 58219198, 182581539, 871339263, 251662230, 390162300, 206753362, 996175136, 78316066, 134614369, 520749387, 894919602, 461380291, 531962253, 647286150, 65340310, 701288768, 2921841, 336309996, 329939561, 761650007, 748996323, 575843864, 842077096, 6993788, 215382838, 489077595, 101446301, 74967471, 741394266, 894600557, 880908037, 354994785, 437953348, 31796653, 480624591, 651487197, 803289400, 909192009, 644685447, 943924986, 463148244, 417164605, 494797876, 26415924, 374491051, 657552247, 494207716, 46757841, 237396748, 569342668, 322575053, 526927666, 800478006, 225456051, 586439460, 330777277, 548699151, 147109473, 691875374, 309265165, 960473003, 82074737, 161198297, 506873213, 22088830, 504604167, 165179104, 40567993, 374757030, 465938377, 360191472, 202175185, 173392799, 114665724, 562688824, 86906781, 449429624, 793793612, 341428026, 911351165, 363735090, 386228142, 379036790, 374858679, 173138815, 846661075, 399896092, 303908836, 558207450, 405212689, 563117315, 574506735, 367277729, 186181511, 304275957, 125253927, 201184901, 172764816, 633071616, 18228695, 191110523, 83822766, 170548392, 106591641, 948081276, 317468612, 841011521, 949512935, 450286781, 518783474, 599543883, 870667826, 468142316, 801950169, 347827379, 390022414, 164330383, 857308635, 568863533, 305017649, 418724381, 37466849, 762060078, 853188133, 81869546, 154868006, 552536051, 601208878, 534306146, 368993056, 794258316, 992556723, 60593559, 582834420, 327556705, 243328030, 148718277, 387569811, 934289187, 73025211, 68156096, 667547910, 906360413, 937245665, 898194774, 772173656, 378648639, 21728081, 212758620, 155014187, 829477567, 90665635, 210270110, 147150037, 74076575, 638144688, 931009703, 688688730, 119254181, 140060885, 257662338, 202162732, 322070921, 559344556, 235898513, 776131614, 718544612, 782366569, 524848084, 281248351, 146041453, 475686813, 350682414, 79458615, 90158529, 328207548, 326297532, 12590192, 185141375, 58642356, 841379988, 615941862, 142561788, 475858309, 363831118, 770489347, 381593028, 134377733, 335933734, 22773633, 385017363, 939631378, 249906010, 806483139, 115564447, 529443122, 61868479, 478196910, 119499794, 728210282, 532169554, 408192404, 945683569, 969372995, 173824942, 162475143, 25483873, 67364572, 43523643, 349786713, 185217021, 839108952, 827544284, 138283401, 449778489, 275226028, 665891234, 696746612, 92061760, 704966768, 561527910, 214262485, 82723536, 147804570, 360482843, 215656052, 675794614, 705531899, 958443571, 826005136, 709603941, 645720308, 639796062, 227728059, 298177492, 623507842, 461719658, 58455899, 887525459, 115768428, 992499276, 522923444, 239330253, 241529911, 240037491, 653168169, 192236885, 353807552, 545874745, 306803682, 33225978, 683026170, 799840669, 225769538, 657201408, 792059566, 636480042, 256174319, 926153066, 196996619, 433259347, 536959537, 555239707, 504681861, 521027554, 572909195, 926632720, 613757564, 799922825, 656160426, 853646302, 304546885, 924700588, 444972969, 982588341, 921014669, 621786721, 764695967, 942509676, 362267422, 486813154, 900610444, 609460336, 861646296, 998665057, 438902376, 391512054, 24365420, 335929992, 375176394, 842737796, 835430423, 566770338, 860301698, 623154136, 435257796, 484249021, 368162132, 336192472, 811936726, 257895890, 402124446, 257386914, 91623178, 50120098, 99225201, 79204999, 50169195, 451772892, 238660591, 390041067, 620024254, 817660275, 927730343, 258573729, 270059533, 148544460, 771031637, 136209646, 941400895, 739762794, 381381441, 328795222, 565593734, 795927437, 398332956, 809484676, 521018756, 862242500, 843078520, 659334479, 900312741, 4546535, 894696467, 138027774, 799927174, 429868598, 973739591, 231987266, 760360819, 483605855, 46062837, 331046640, 137306217, 650665303, 731660714, 930346731, 661626285, 785510359, 520955060, 362258551, 430444, 708797497, 254751385, 985049799, 765805107, 562110834, 598861304, 234167252, 374603604, 271289826, 337107575, 533130098, 390975048, 542060877, 607424388, 320661448, 449551351, 104623404, 630633144, 863374218, 927831650, 46466675, 851355121, 69450494, 507162300, 354110002, 662901268, 331164902, 741035059, 85656378, 387244694, 128087733, 417672297, 622534218, 531867296, 419116948, 680098259, 426719542, 762681129, 33216737, 769071272, 757078138, 370817494, 360853768, 73231408, 466951809, 103465742, 187452234, 373775765, 899510466, 741160667, 302459525, 489570216, 194156998, 413854778, 470876855, 9344347, 311581419, 425305137, 647881409, 863270455, 492248097, 106460509, 926546929, 804812870, 732915392, 450931185, 785666398, 532334683, 65876972, 979656592, 919383540, 831745720, 77745461, 60221636, 690846033, 579534977, 902419931, 630326662, 594168420, 356547642, 554065279, 138618844, 496838004, 740457307, 935112395, 753300567, 481880920, 523094111, 137032378, 747935064, 464768117, 740549173, 705850608, 996794061, 612848867, 728769289, 882454768, 945726178, 338876332, 840641174, 299712055, 538372906, 123306261, 107901338, 561172934, 763994914, 427260042, 832095400, 881402757, 706884759, 277793946, 208301942, 540802443, 138208743, 229741417, 884534816, 997309574, 915830288, 345310362, 481461958, 151410834, 725967056, 228529339, 696073415, 771651291, 760920088, 898706005, 760136536, 248705596, 747138945, 148833661, 181865015, 861704246, 888085101, 250737379, 496002020, 732760453, 832177595, 821079397, 346442896, 923946490, 407545873, 347642559, 508686268, 762084477, 452184697, 523382851, 130668425, 960964395, 165234366, 477433246, 558890579, 951934247, 264687535, 794691581, 747131492, 744113593, 808568492, 603326259, 522838977, 579718225, 150581400, 259180960, 804194318, 508193020, 775721498, 490703202, 998066529, 151293238, 953699382, 140021083, 584214691, 234955870, 759539668, 937804249, 480964392, 402872967, 14297146, 317394305, 376458606, 358192909, 665300754, 203857157, 2537787, 505757957, 464750115, 869053089, 924973041, 465343813, 283956523, 856861331, 873760574, 96618303, 397221152, 189929252, 497548463, 989941701, 848293074, 339944593, 944396836, 312410650, 187977308, 67641374, 56412432, 578521856, 78189752, 769409679, 792868285, 342065721, 859096865, 618841702, 635215588, 365768059, 984295959, 79807804, 171841219, 928335981, 502351801, 55596915, 9329444, 264279575, 543971160, 918784838, 912751667, 302901153, 994304106, 371005700, 185068122, 469793634, 812799295, 693836133, 511599547, 7020636, 522401532, 87255130, 143464402, 743080251, 803022592, 435429013, 752377992, 536466256, 573040946, 348581226, 534637752, 903834368, 632901180, 209629009, 226504595, 683495778, 137635280, 667746476, 102600186, 257971611, 729183647, 606198649, 730745044, 290415263, 999582515, 906861780, 630115984, 830877405, 719005346, 382946381, 345709305, 636798390, 477365459, 792676008, 606619821, 561159895, 536629381, 524500206, 12657640, 148527931, 292234292, 480784360, 532678523, 540134186, 671872508, 555212654, 465234703, 31309666, 529294837, 966306736, 544947567, 114866766, 36918679, 434402941, 826282151, 506492560, 742616890, 66518472, 902213140, 398199551, 619248374, 407311089, 532501229, 911601290, 951342188, 946673948, 3489547, 569420136, 292652731, 334676511, 607154937, 82989062, 785917518, 522642677, 868480025, 606469484, 15163149, 603265611, 921390363, 142993439, 31091322, 352082009, 198131027, 497135237, 924503577, 887749018, 260060250, 474589637, 582920218, 135168810, 307221675, 750053358, 252527291, 57575871, 358456715, 459435296, 199258252, 423598607, 776552944, 596484693, 4659253, 759187480, 346576223, 951240952, 288181201, 999793404, 846754321, 577586476, 281923166, 523806504, 993627722, 261695575, 76751819, 488303642, 918171506, 57307341, 926081655, 819605794, 395259729, 283184801, 847914162, 679638098, 625704556, 794565986, 136807078, 797327596, 244125396, 825632231, 535005068, 148616822, 364307201, 787159611, 120268515, 237496999, 724444323, 471410143, 201900655, 186584042, 209304545, 32893109, 744174619, 86113303, 172078727, 838547720, 173355122, 132050108, 864615849, 622774824, 920521259, 434235822, 576046766, 447401221, 311311058, 27833745, 3315810, 338224143, 74525666, 30456560, 35732148, 138703640, 464126587, 358715191, 327680600, 101855122, 72043779, 776541624, 815561232, 246272235, 747802497, 182560708, 218064557, 657509886, 67363686, 225855540, 542228353, 809655987, 345971543, 161575631, 384860044, 960957067, 859974286, 443046604, 127481904, 292070612, 742822210, 579032061, 148784930, 495001182, 981127115, 192165566, 313826231, 926018367, 926741440, 411976507, 32888672, 264323297, 688953091, 703219983, 910207425, 404302366, 173034259, 392063327, 634545310, 402595138, 883709030, 609922214, 805362501, 600651196, 480054806, 829569679, 356775664, 315424491, 658707429, 128893240, 774978688, 408515427, 533189623, 861218776, 914251327, 951699258, 83042959, 377826609, 512605907, 971484453, 310484571, 386790272, 827112343, 184068727, 387827907, 939616879, 955733570, 689955168, 904481086, 758158714, 167633397, 639937474, 232429141, 81849297, 999611815, 153933765, 473088159, 262695197, 391860051, 713210863, 362912785, 922040160, 308770874, 554329574, 643956647, 470658298, 531761690, 541669159, 464743740, 742834201, 937894411, 165753613, 361459163, 929042673, 851527686, 378776718, 586256033, 368114238, 358578696, 790298912, 704452703, 570548812, 936563430, 898337666, 773881724, 332244691, 491417236, 368429036, 44818062, 506908588, 483563127, 900532285, 935416337, 243734018, 865132997, 271088203, 42350269, 489224031, 147578598, 292656519, 284622587, 928806080, 148540941, 366442025, 349425442, 795216291, 55128573, 101785395, 998467658, 381330123, 849072808, 337407574, 117776242, 864388937, 14426344, 401590769, 763697975, 286554770, 529102332, 564812194, 525614028, 781373615, 709604252, 466627912, 568191606, 948061833, 894313503, 261133659, 266772125, 142330325, 150546359, 733489209, 290605388, 981211945, 952990165, 537078882, 692045038, 782477825, 7384379, 300586464, 20684335, 564298757, 611810844, 902077436, 535689825, 787377882, 987204556, 132196148, 385526839, 392701902, 631983041, 268029246, 943087957, 548096225, 233965031, 852978541, 750119142, 248081047, 423831132, 203804983, 561451936, 622267015, 927885973, 306757580, 619368790, 994451595, 663804613, 545276237, 563175555, 116096580, 972097057, 923009568, 376837530, 300205274, 749285296, 98592441, 785549582, 31170969, 853546481, 668350998, 455289311, 11570424, 743387457, 707511167, 348882754, 172619954, 372708412, 972041870, 712974950, 346400108, 273697351, 753243296, 537736159, 913500283, 726658946, 531871731, 505308041, 545953252, 782904417, 891585084, 433627630, 692819713, 811756247, 594735726, 593179207, 174481984, 439208784, 473838655, 931104947, 819569220, 364687719, 307091330, 152992154, 778965411, 70008022, 858001317, 701273070, 800318140, 686353928, 455236499, 960587319, 837135748, 23033324, 448733118, 988814103, 368637194, 929022977, 983820479, 468624373, 529622554, 54265359, 693686093, 586898227, 525558570, 752614722, 739699857, 900736607, 316633860, 734801657, 408492474, 921326165, 153545320, 100666570, 798440233, 65086200, 337653083, 289486764, 359738895, 152653712, 150038006, 659282004, 748049998, 796398617, 633206511, 368936219, 390622841, 953054045, 324413269, 856715395, 587876650, 463510625, 498168333, 724607967, 105908302, 983322076, 183852331, 240032408, 362025768, 69532121, 312106189, 6976115, 343111377, 191411125, 692079552, 168295145, 60869490, 580471168, 146056223, 806158778, 552740516, 804552812, 295633386, 697567156, 386873012, 587801028, 180313774, 973932128, 679779322, 109642043, 220805832, 324914313, 591026687, 359282024, 502418639, 514090714, 143735026, 278152243, 760941011, 737088487, 465386552, 939429334, 734549724, 593327796, 469949296, 916584529, 669348786, 181105413, 860784898, 177256286, 790373768, 165710614, 160941365, 448566165, 232291363, 97360780, 200355626, 960692337, 333438664, 351214363, 55396128, 859848795, 241957996, 132883384, 157016800, 902918308, 160285814, 39327559, 472002100, 871733043, 678655633, 447188867, 307765163, 380480662, 645653370, 272819082, 48618364, 540404861, 390015919, 929841222, 90637755, 874431330, 549450830, 792920922, 236915471, 988975483, 70642015, 870384664, 441175914, 143321101, 886005383, 143996174, 336918263, 463967985, 440209484, 83814922, 753215934, 381025259, 443702872, 328182348, 365558654, 106173553, 190221224, 838182002, 873571967, 300297228, 969466036, 985200568, 192121969, 373794360, 440545410, 622830561, 963023399, 519275269, 515148896, 549251011, 835005796, 858221835, 208080003, 634896921, 527642309, 430653849, 937502324, 543424954, 288596549, 849912046, 763392655, 426659562, 583854054, 213340960, 339360710, 441625836, 438417070, 608867048, 736407610, 707179452, 585247913, 33618873, 954189456, 581685223, 578856643, 499272296, 277025268, 291365709, 297306872, 137304232, 517574090, 556180295, 334106705, 156208515, 887848946, 22190045, 799627073, 840783171, 259216736, 464022750, 754993013, 802922363, 437544373, 471047180, 783997981, 383678880, 994758943, 432232076, 568516993, 569227698, 56076404, 577736470, 616873659, 62903022, 534094955, 838752546, 18461256, 530085745, 488340541, 467292489, 705969930, 995352663, 170056798, 290188835, 237834301, 888311774, 968347677, 319347422, 318991644, 643920433, 441526449, 179104338, 589373578, 245497220, 161743446, 720970751, 828435313, 696435840, 10910918, 90019267, 874673722, 164281563, 926728909, 37402580, 330174751, 699225650, 411822758, 16422681, 604450824, 406198713, 985832569, 856436104, 321748864, 593992021, 103153241, 593759034, 316477763, 899445920, 797751181, 261364498, 359642242, 853364879, 386834538, 881994851, 859237396, 465231619, 777624279, 637982356, 21975150, 350558218, 360359366, 103435568, 941206151, 718823880, 556739335, 52140885, 641002407, 141156012, 211177431, 490892171, 890395219, 479678772, 496466921, 723343490, 5575014, 151045353, 813393583, 938384101, 741473145, 946358568, 693808562, 558457699, 691246275, 962741524, 459647351, 156173685, 462047687, 149877049, 815818893, 977269899, 187977746, 943658597, 214410271, 332927349, 918391399, 680776036, 290533981, 821447543, 169145596, 708668825, 151855033, 90872537, 880746529, 251862564, 970262298, 435204075, 855612714, 384924750, 475325868, 979103170, 415518196, 368560062, 334413265, 147072057, 199695724, 796087006, 546571039, 871032754, 282098848, 281356002, 57705305, 492437763, 572715515, 531930672, 385118161, 271977065, 227695784, 491063490, 891523751, 711944931, 548493093, 242809237, 463360090, 25609939, 596883499, 122702736, 679328193, 541590417, 897605195, 784034284, 566266217, 838174210, 987127862, 186202747, 611923737, 10786901, 235691190, 578877026, 157935828, 186909870, 265568128, 514133804, 576536566, 844251987, 739226238, 93586766, 195634136, 672324743, 441433748, 178137989, 670678808, 310792565, 531230523, 797698100, 685664974, 836270614, 80825256, 935412140, 30182119, 290100737, 399159858, 250867787, 60499126, 60893079, 895758569, 759630979, 209679371, 147234962, 192983216, 336734179, 641190788, 218803753, 836495529, 697086796, 69709590, 466399811, 463497675, 962431339, 855253778, 205848600, 650856665, 300218028, 620866228, 252678536, 566373393, 664939516, 657825782, 328058215, 756526842, 880336595, 836774095, 981038499, 50863285, 335359838, 213554189, 882872497, 960308938, 255286736, 976561121, 349614818, 982093607, 994741338, 903063645, 49583351, 350151087, 713557257, 68410914, 313456411, 656733632, 619282563, 832167661, 92021600, 336447619, 727461282, 76646117, 334358270, 337198330, 140932798, 166090209, 173527799, 883361171, 119828921, 66134120, 322874673, 986111699, 344602195, 215248502, 449176224, 276149440, 602945691, 64799117, 98869846, 604889311, 854275256, 601148626, 726948686, 906872933, 928314663, 800792606, 704801016, 568639149, 383796961, 848147918, 507993710, 376159438, 289966358, 923881701, 937874538, 166751778, 205267078, 79771387, 982258111, 952875031, 962761435, 141593639, 414479701, 532283024, 283975085, 340645540, 491056088, 474908665, 639518125, 158501447, 419635491, 383098723, 631784845, 501504284, 887212575, 964774395, 615209831, 999233560, 763767416, 149082431, 70763103, 115030657, 599982493, 569779811, 7028724, 132266735, 507000700, 753487373, 453129007, 619311309, 400104940, 934477582, 756852663, 938693160, 297603918, 41428249, 769432013, 770919433, 880220045, 108832111, 856654405, 822460990, 444099539, 765985351, 541704445, 659139227, 419539079, 436609583, 562231037, 70987482, 615827124, 782387992, 833864145, 788118175, 616848003, 583841824, 872602066, 597290616, 28532339, 233888812, 718386275, 488293222, 405414770, 107461697, 616691384, 697164613, 724920976, 326601578, 510583891, 864587038, 738795575, 669715256, 671697049, 454114342, 646115064, 36753808, 764075544, 469908780, 748347267, 999261756, 486078165, 610465882, 595880113, 79448527, 600423849, 892405858, 197007609, 847516391, 270291663, 921157202, 619844161, 487595440, 136042957, 205648567, 683546128, 315910276, 431249888, 959070058, 843829366, 697738403, 326573055, 708112024, 882162891, 552732300, 969477687, 919669977, 577936631, 585966407, 926460156, 857508081, 676403431, 197202501, 652013807, 478614987, 559497731, 341651193, 195191395, 488594979, 703211053, 165341756, 906142481, 292084696, 615463509, 618228990, 552519620, 531491759, 306831921, 722567092, 645303904, 277478012, 450682211, 898367516, 72058684, 500334307, 575384738, 456178382, 327594383, 743592973, 996449644, 345007412, 691174351, 30600114, 875427987, 744228945, 521419564, 407530028, 677625356, 907585339, 31013652, 253778672, 109597141, 664090339, 375949512, 10159257, 368304795, 554114605, 977977756, 674023777, 482917202, 861621751, 481902756, 664785386, 486167657, 405414970, 736476425, 61015990, 831984389, 312371054, 816674110, 222733564, 180566652, 698158443, 378484619, 150013547, 79625341, 802732791, 726720272, 930730374, 248129713, 381072985, 970652006, 904111638, 301635787, 205800724, 251925163, 727932004, 742200255, 662708133, 87259305, 249874101, 742783418, 548777916, 747537650, 537207025, 115391342, 186168306, 129834595, 731541131, 172817269, 210897938, 580929538, 934148815, 326873979, 45880246, 761634460, 759070510, 825136576, 483869540, 445648461, 783171460, 562381775, 736635581, 291095356, 295968974, 590652222, 505338102, 580525909, 323121504, 72910151, 601420103, 396221761, 427838409, 944072551, 981077005, 208850058, 686320627, 423714246, 517565118, 434472814, 146025103, 838733092, 550486522, 322576509, 274060018, 149362446, 532441107, 188193049, 998600213, 212979904, 426070412, 183759625, 734085114, 404667675, 923539566, 78341383, 969985267, 807506811, 615361360, 495263785, 417886699, 735514374, 13987456, 415670857, 473473267, 339930237, 89585419, 723520532, 214647618, 515495219, 844398327, 697466621, 834659741, 515485745, 793474819, 841165598, 783121405, 130059915, 789137472, 186094640, 596738261, 993561331, 512883807, 263554114, 519848933, 434153692, 622008899, 419673224, 454732060, 159708754, 38348117, 479781176, 499284625, 888067780, 267146435, 62513036, 946109138, 249807078, 217107116, 814297851, 761139524, 378497293, 457348187, 727861603, 996832215, 259340172, 488438111, 210586378, 319484377, 690443462, 633822308, 631356551, 852325627, 871113399, 904650441, 971975591, 207926141, 270245251, 172925401, 15181777, 336652880, 885461121, 159228947, 620035981, 936932688, 858191529, 9896751, 168845605, 562801584, 433657591, 182839930, 400130920, 152215166, 426582897, 930016739, 563228661, 741447608, 554463746, 25332863, 667822072, 514548901, 58359018, 494800919, 222998686, 989461484, 105724262, 543499597, 476116921, 598024180, 481182858, 631882311, 222757132, 300831519, 345052233, 641633137, 674552773, 421498643, 189433942, 136466827, 744705535, 118438744, 489246312, 233656048, 756236867, 74779155, 235176059, 906589291, 566506135, 412521115, 600625956, 154083061, 981735981, 136129602, 98387211, 375591548, 635958061, 274790559, 448518396, 313518094, 857800717, 605993596, 15447884, 272621006, 124187483, 325430772, 92826058, 837586159, 998305175, 516668595, 64582348, 998701830, 960989428, 636109612, 785883533, 567133035, 742129337, 566659012, 216529779, 455491595, 171061503, 444807542, 806779366, 162446093, 145109581, 168713434, 100662475, 969680682, 144646927, 275668537, 452993593, 742372181, 985466796, 316852186, 492182759, 148014244, 711391363, 454636125, 47596124, 867461713, 864229826, 314324858, 706106121, 753266844, 376808277, 283730412, 837763349, 394938644, 363313185, 537395046, 459463961, 204779357, 726861414, 380612253, 384029618, 589294402, 399547522, 467411206, 892236031, 171050155, 590028002, 103387382, 629690080, 805395014, 422947072, 705076762, 92644958, 603177096, 141213642, 329794242, 176914774, 931278524, 822499819, 873193415, 443863583, 479609661, 693357233, 38098964, 364877528, 871551457, 726126803, 238463909, 727643975, 426556602, 288959041, 941449184, 518093740, 238104667, 189383576, 786947827, 132075658, 121196326, 767801986, 683337924, 855395332, 361083683, 529157569, 685403735, 39561231, 389329136, 15712411, 454444807, 420958612, 496216943, 599522405, 90466094, 777721992, 38424129, 923838186, 580691169, 425491997, 918152906, 272600622, 116892578, 278311114, 710220426, 823861300, 880849959, 763300524, 628321595, 560531612, 302300511, 378213951, 833084264, 325870331, 850451252, 359430513, 323689001, 190706320, 622852217, 50554328, 595669296, 934847430, 891683275, 5900879, 841015915, 54593795, 559767624, 831819467, 223165046, 576789703, 513262642, 946427613, 863526652, 295707833, 183908360, 480848400, 686383806, 946172830, 215327513, 881662550, 264037886, 918639149, 851649193, 175515540, 752702286, 262372706, 558189581, 963081953, 234577763, 300380744, 644267786, 979814849, 823266768, 795530277, 6728557, 923226163, 383664867, 15601581, 348718733, 184797403, 785997609, 413272067, 242602900, 106837045, 898947432, 473678133, 723977431, 769952878, 386656480, 59588996, 262342840, 482463914, 368070846, 28936275, 637469017, 760199095, 160193144, 990598129, 327732191, 96712132, 545573759, 105628870, 748870511, 886456091, 495694939, 4748788, 917731239, 696703153, 760778742, 464864061, 562250007, 180601434, 690306033, 264292000, 755162565, 751910290, 152330738, 471406964, 520051007, 431262608, 869287489, 558604664, 44601752, 755977033, 482927789, 58617493, 974870791, 36478812, 922213904, 213032063, 444965951, 390117392, 215799152, 85756782, 134140803, 430771310, 163781821, 64209941, 551403399, 569625558, 267617159, 672455767, 591604607, 621182131, 101723902, 922702678, 452821175, 512946800, 424192428, 555152494, 791037774, 516330924, 215523184, 591206380, 146045520, 576381483, 79145897, 64968289, 564056672, 101100546, 950261941, 329297182, 284682611, 923524085, 881334633, 133099915, 632662202, 161030795, 816095861, 98825160, 989055459, 120933761, 236651295, 930696083, 167574638, 813641653, 221158219, 697040754, 438958669, 497364058, 478148310, 200089678, 736866228, 148512300, 603478327, 984587667, 390792129, 74576650, 850380598, 163904710, 549573146, 324397856, 558850560, 926022818, 869008462, 546158153, 149498924, 257923602, 823736354, 589634072, 995104244, 777948221, 782864030, 629522915, 809714646, 628847804, 638048889, 127714928, 612254149, 99388306, 132571236, 645208670, 283193544, 387930477, 803140439, 606071833, 343060020, 678920279, 461089344, 647114388, 192280669, 551612045, 884022047, 557227009, 193917434, 481696344, 669505102, 187957502, 74533246, 668247094, 169166721, 372462179, 50940488, 286735152, 459731413, 611772880, 368788054, 615545022, 859900048, 135848442, 978937468, 519230046, 270532011, 413252664, 474954309, 794047031, 993459706, 348735789, 978203251, 716179165, 362553195, 719153047, 691036575, 698579889, 178832738, 241695475, 552314679, 436133743, 246780809, 406058224, 508731644, 917321466, 569280302, 758529609, 199454167, 556234331, 694362381, 866075091, 379865168, 625016407, 715557594, 129290654, 611128004, 783085567, 426554812, 487340154, 850380197, 253532739, 956266111, 792760196, 606137546, 246424790, 638389017, 848248437, 8397469, 381740671, 728614230, 522688754, 880937028, 226148759, 593137689, 143368296, 77777770, 412056677, 993183684, 841839466, 11825131, 767282522, 123825091, 21385936, 130853826, 36722913, 488187862, 248739575, 241729409, 808621378, 246975624, 873342769, 932893490, 462345502, 746048129, 356562398, 619963851, 936759093, 111829358, 508029294, 818482096, 81367826, 928378690, 125670481, 240336674, 173976984, 745296673, 674005265, 648492491, 99092211, 972465182, 262823109, 791560895, 443284003, 681384203, 629435423, 754546657, 178072640, 119290796, 848166360, 651378992, 283931406, 403783173, 27507743, 260067152, 496618815, 995913203, 166073410, 179225065, 503298655, 756498528, 682901327, 531106497, 4349416, 71627, 198113784, 888248101, 758252159, 770277083, 906755704, 537938951, 820809038, 263676145, 184932210, 274840034, 65286031, 18115013, 62286842, 663137301, 738105553, 473176266, 360693455, 724663637, 882070169, 306597286, 401044896, 590269045, 636720374, 39882710, 104772641, 640752367, 154880716, 470113561, 277481007, 5426612, 259552287, 494570368, 310680251, 109282774, 539641229, 996466203, 518432046, 912919211, 172359426, 895487216, 317870657, 454789381, 493968236, 308090551, 864863101, 503411014, 414727903, 72211299, 299502677, 635970360, 725363961, 364733104, 190695709, 859905896, 318511715, 194680847, 661377515, 311974022, 104211013, 557970519, 138960626, 435243662, 235582851, 825232971, 341490126, 556907031, 358519387, 416160145, 307606193, 343868939, 548120998, 791719098, 884943199, 364238645, 13832787, 510493340, 152015874, 26184973, 651361671, 572844238, 925369899, 97719759, 481792726, 954350343, 962070184, 178587268, 639221883, 478377747, 879313196, 220147119, 818647862, 65855531, 27395569, 94059410, 657771435, 721348465, 426956289, 611820548, 334048530, 28844581, 819673670, 311728486, 601763717, 962067779, 458920797, 303993498, 659045004, 888093834, 870079863, 278698184, 809650429, 671738318, 927727926, 947026591, 879568572, 74943796, 653013322, 376410158, 983385571, 118895072, 432432614, 705446142, 520591570, 684212485, 244691742, 909748538, 391665544, 277161396, 519694827, 874304712, 284620170, 106508836, 839949459, 266579021, 489014321, 621127008, 475660424, 776677565, 386575564, 12471060, 52907084, 81922209, 474827042, 687394029, 984774765, 416911248, 85736670, 66276353, 40855538, 112756094, 439084133, 207718326, 231323355, 519329985, 176742867, 889461107, 453350857, 451768693, 365977305, 446659228, 209053182, 772966030, 344608783, 330476236, 548446049, 151251983, 531447902, 972616941, 979858963, 522680144, 229873574, 937044459, 229209471, 55833958, 39294961, 802972223, 34842370, 983639228, 62061138, 10920891, 128578483, 861056237, 435623049, 301952095, 345144589, 110286233, 867601119, 848126981, 531963348, 859915530, 708489800, 2441070, 229553688, 266838501, 772899334, 192225112, 418778542, 460405584, 662995858, 996213351, 78697609, 613601039, 42084236, 143602569, 217732188, 43160513, 204208269, 12636466, 415757425, 590669165, 361067484, 393888218, 301101895, 937162978, 16461768, 302336242, 745709970, 404853179, 818923795, 584264649, 649739293, 508745541, 938152798, 237585195, 28273127, 218855308, 844763688, 785982935, 18686035, 820386293, 295715742, 582690865, 580984072, 417304743, 299274074, 735146395, 777782413, 587503135, 198392061, 341389903, 712966755, 945329046, 520832312, 597771037, 26306322, 178264160, 598366709, 255835914, 213547238, 219767683, 933552009, 254820196, 409059083, 902557616, 439046740, 110181803, 956151002, 789941512, 996246792, 881151919, 799854181, 261701124, 415194373, 542764107, 967240518, 975764593, 693436116, 958514302, 875347546, 798275782, 884164883, 816435919, 296562533, 155739327, 402326631, 475028781, 914661061, 699502211, 979938348, 46868776, 643063066, 384900640, 756238626, 974862119, 596263850, 720561048, 11035104, 491445872, 30734351, 212009557, 561180503, 293908160, 29416856, 105758322, 254249772, 613763906, 69989888, 636269888, 565018547, 752917217, 146437249, 183394111, 301289214, 798808054, 753484822, 925972670, 806694211, 199202177, 721358645, 947528209, 299986634, 954227347, 302691509, 829745364, 741124913, 626848764, 590124058, 212388416, 938031742, 611602961, 346599556, 548521920, 551123534, 925159104, 504023207, 660152010, 461557675, 598616118, 655403474, 743966843, 416660637, 354901831, 162927565, 776203206, 946998337, 597405961, 295964973, 489155022, 562020940, 163545046, 754122435, 290367499, 53604900, 628731526, 143504592, 358851520, 15746286, 614508528, 386404296, 595239818, 977280737, 435510824, 469573614, 79829570, 177443076, 621907450, 723463949, 515948562, 476660676, 179811557, 750579534, 226358663, 466007645, 372812925, 192865819, 5807040, 95455526, 625624472, 243832458, 988717529, 655605310, 393256781, 673096728, 559971261, 970409101, 603950155, 5974697, 402696520, 473759155, 159808581, 306576946, 677133095, 763955014, 566314526, 130284264, 198394173, 285039505, 187483337, 786891082, 392860422, 57366596, 689699097, 144614152, 756499980, 774302436, 474553625, 839568136, 739738571, 74827121, 366207886, 265727401, 861696091, 543319501, 599984846, 74771381, 685591075, 492515611, 605146162, 873203266, 585117544, 622195462, 93565395, 675293716, 99019461, 94664567, 71245039, 880491949, 506790439, 848189657, 800732093, 537574860, 430527507, 611733415, 775380702, 484537194, 859045635, 446164870, 895083733, 316504, 243946510, 352467441, 269602604, 270126434, 657941733, 505293180, 559029330, 96774500, 960028541, 122800974, 450584684, 957828640, 954287447, 767856198, 762967599, 984514851, 396309809, 398991896, 860594398, 169016830, 912930566, 450212146, 41342043, 610141521, 710909485, 89426554, 174206921, 175225989, 463775426, 958645219, 693747847, 873791316, 900502087, 980548929, 370346229, 360965230, 767379015, 882241157, 562921239, 567350935, 926710531, 592260879, 20354337, 463153485, 235184886, 461878929, 86271418, 700782808, 584817519, 386973833, 541392885, 466114376, 111225663, 823701522, 251028787, 337480052, 962719053, 259807363, 487213258, 638359663, 62214485, 376839032, 91432388, 487382422, 806765258, 613903715, 451754967, 858070970, 924397083, 494544281, 559345079, 382639216, 826813935, 333028226, 209178829, 437433326, 760617107, 443580962, 356128129, 774249164, 356854234, 196350001, 254905565, 478320404, 30227139, 655781299, 554802027, 650637776, 350135639, 752627688, 655066974, 60510811, 441992651, 948946612, 873790570, 331316654, 680900577, 987994584, 460854972, 577606058, 947135165, 609591, 578921917, 246863656, 61318949, 188234796, 788938167, 213402915, 736452916, 114026145, 239602063, 793328841, 150637232, 379049599, 823928229, 282144310, 397815948, 447261548, 294125464, 309570413, 901649723, 83253591, 215227861, 951199698, 94218052, 320620574, 193327276, 719466608, 567096384, 483406887, 942435672, 77244863, 153198825, 450904010, 675854873, 841627525, 596715915, 966741776, 260746125, 378190364, 688016088, 304103903, 783017435, 994627214, 92713210, 495724484, 639699352, 321108002, 390544005, 385536555, 977966908, 780378191, 972238118, 4095571, 538552544, 49204349, 413014129, 581052293, 510632640, 922349005, 695830688, 823448412, 422753559, 880333501, 864818788, 721147922, 627976437, 408940982, 830754688, 754292329, 836862233, 752073723, 102666113, 930925087, 203218849, 758433486, 8701030, 686106338, 825121176, 7664782, 727514817, 998862164, 61372229, 386231474, 314450697, 772522139, 285427078, 239734918, 863711529, 743678890, 151100309, 483521005, 449497567, 106359832, 771877885, 49269974, 942197677, 839356444, 234933732, 755188184, 975044361, 467430581, 681038511, 681037302, 599564793, 603890192, 29855375, 90750930, 298186726, 92900204, 52587263, 871692306, 690955412, 674305383, 143395477, 424576464, 143249329, 814213576, 498318747, 76328771, 468836849, 794905920, 127086620, 282231379, 399109042, 368160600, 651461963, 68455784, 809263947, 353997121, 417239842, 82295251, 560499835, 365113717, 158367206, 791103997, 799848786, 869954935, 602222450, 776616157, 202330794, 752277459, 882714991, 643546835, 11639367, 990664578, 535467506, 57193402, 702033444, 642974707, 246383293, 961495061, 800631368, 92480703, 803458153, 239839021, 522969784, 314952741, 289030202, 290119208, 904243737, 555694826, 392744401, 106284532, 171045252, 133459289, 436192016, 714115847, 485971316, 884809578, 510404328, 758730396, 784383865, 696707844, 284166840, 395893456, 623675905, 434581762, 826639492, 650134360, 934163734, 29258652, 808433574, 218588638, 932393362, 480465354, 584101426, 807961121, 557668490, 902686723, 666130522, 62155534, 860152918, 52499331, 995087542, 671422796, 546244924, 843382516, 387427894, 364509399, 659989588, 317534014, 323898171, 613840248, 72829887, 436547116, 708098493, 672996953, 524074516, 988218951, 148865785, 244294192, 313144469, 73000171, 216305689, 57003781, 608714936, 624067570, 36140707, 434195915, 210618902, 937661998, 350591954, 948053658, 250312268, 545974075, 326607569, 466835596, 427090797, 340943208, 835957807, 593545395, 211138636, 514923598, 952388555, 735593807, 195907149, 629507492, 820987640, 1582058, 52471562, 733567938, 961417675, 38868615, 847211057, 365810754, 48375151, 696008220, 684169958, 567360023, 158792851, 755404677, 475509157, 174425376, 359466365, 311396831, 949596887, 631297849, 205518660, 497606656, 961209049, 168228295, 690482308, 773036610, 714138454, 719870998, 516154261, 697835006, 960394770, 558336361, 964146047, 955086055, 186765891, 412932610, 642110134, 952573300, 133975310, 1775075, 10768028, 782676097, 562855633, 541496398, 506295038, 767943613, 985078136, 438105488, 2804, 598117700, 530471683, 591537231, 895532438, 813402013, 506628931, 847101488, 321093330, 466902988, 891309375, 349999660, 411350052, 51704615, 876947213, 501674726, 122509609, 104266868, 723367728, 529409305, 901192356, 992655915, 170789234, 247304345, 55139395, 162733694, 665014441, 34380165, 719129559, 629199314, 946920712, 855759682, 516493444, 230507954, 9009287, 532725406, 348844323, 397634277, 843157752, 183974678, 860372662, 153691164, 862376838, 355827073, 653905104, 186569608, 97602389, 108984864, 889080249, 834427072, 309036947, 598100311, 592828160, 39247249, 293924931, 149781410, 420445549, 310517702, 797035238, 639849007, 915035996, 671820335, 640159454, 40965612, 661841800, 609887380, 38233293, 402995892, 678123340, 618031959, 718523862, 375072132, 236750786, 648103054, 346585879, 547627910, 169508167, 693365699, 317985533, 518208195, 727314128, 185998084, 631034371, 804322823, 922460495, 535537621, 446288913, 77880923, 366168970, 606027147, 884253458, 99370767, 255587618, 818618415, 126110268, 72596769, 383440002, 949743369, 487531504, 82781950, 970575212, 537053226, 497239178, 422183052, 824211392, 188398300, 958635255, 989264493, 33154684, 204140200, 257141813, 206917714, 543099652, 675058301, 32551936, 64136525, 793995633, 324893473, 246627787, 101433571, 728715593, 121558696, 76840164, 981056315, 747471258, 266165239, 772625047, 12762936, 838550535, 176252514, 500527728, 11418605, 308125351, 741227982, 285757853, 482902335, 330710541, 657367896, 120884354, 295067812, 360982527, 742005052, 727582900, 444914741, 894096659, 245620487, 970613030, 208133301, 132112272, 696385307, 538889824, 270307626, 707518653, 964486771, 982975035, 605636698, 888326219, 183744049, 933413809, 145278820, 1832642, 705753625, 933581143, 478576264, 774443999, 514540695, 953116014, 304035977, 748995052, 412794168, 182068198, 294920457, 812621809, 256750205, 164168674, 234467380, 163578309, 297633839, 705268496, 735471743, 869047982, 395791929, 53568474, 972019821, 632084202, 86876175, 287973391, 698246309, 48884265, 201392833, 91272799, 137582095, 353653373, 144664142, 248954776, 152451402, 286780857, 83892611, 655333943, 178380858, 379492650, 864812345, 156091190, 638029186, 893002497, 409065800, 535447962, 232378785, 464396408, 972995477, 925534142, 436833402, 261063874, 931180609, 693107185, 694927906, 217891515, 795709713, 952040278, 198779851, 560392441, 32434852, 278964395, 515285298, 843307113, 681915761, 399359186, 358527257, 870552927, 244317638, 939208086, 681480213, 58891111, 658021191, 280425191, 905363879, 359931996, 240205942, 415904505, 523271123, 94109247, 499057590, 424792993, 81868495, 275908744, 550143816, 330317449, 549680921, 314789961, 804512875, 547586493, 669386972, 300948906, 292406856, 241275312, 34720202, 579255691, 74568182, 125160383, 321657731, 235487421, 944335540, 254377982, 317643334, 861533235, 548408404, 890411756, 493459895, 174624188, 555620205, 465232771, 186995834, 375163330, 819435900, 361583488, 28989695, 34076824, 126034998, 983917709, 199571029, 562726464, 381407588, 164091963, 855167276, 104019578, 789682254, 25262751, 167818698, 693913780, 403197612, 230053062, 156917626, 866639943, 975702876, 430253239, 682789934, 528425139, 116445910, 160966775, 728223187, 472743014, 245425938, 92889533, 698938693, 80649629, 746314086, 49694076, 165147163, 275466494, 379522454, 887553720, 269180179, 317184320, 616078934, 973736013, 244355743, 344418653, 443089805, 975754013, 272679627, 503968084, 971888262, 550226257, 35935079, 167420269, 37570865, 360980268, 322891981, 516002356, 821108729, 986774210, 182902791, 904199778, 180022194, 131246044, 200870264, 531483171, 812199729, 772559622, 771143732, 276653620, 315174114, 693701322, 140747947, 438931854, 450019356, 860844249, 345816688, 519625853, 436161043, 954143744, 524921785, 724057043, 568525832, 46334975, 492955999, 329856753, 587145043, 955062619, 377219235, 149818119, 289824719, 132399363, 198916424, 462652011, 509884693, 969439294, 856486815, 118479816, 753271941, 456530411, 449830128, 801224331, 456375980, 406335558, 159419557, 561013657, 167115554, 398990117, 244222, 86923001, 744763514, 145522114, 289889212, 106610662, 380351210, 631777516, 91226396, 129333901, 655178046, 252844605, 541101109]))
+
+test7 :: Test
+test7 = TestCase (assertEqual "for (continuousSubarrays [748485140, 818457444, 506065671, 457502910, 80372915, 643314518, 575934438, 977493309, 303861502, 451292516, 562893213, 16654857, 164224969, 879121749, 598354394, 701732173, 855419816, 850202985, 284556313, 786617533, 174731254, 284227629, 730932068, 546999279, 263147370, 592212889, 844828648, 140569546, 654375423, 290560037, 443563630, 556480490, 248418885, 427128412, 128528319, 262290964, 560252607, 205632148, 687252519, 201341706, 542114760, 751315222, 28054952, 146060555, 286324553, 723395795, 699205139, 180609404, 92395765, 573013363, 142337050, 933004554, 663088753, 924545618, 755655796, 256864418, 960884095, 289990794, 397781173, 489499719, 497985443, 730080985, 684649399, 330016731, 161441770, 354948023, 781487770, 720656125, 197428971, 917922707, 789355336, 389182177, 762560462, 247402397, 651424144, 770212175, 842449487, 727531591, 237869863, 128497350, 666827756, 839086166, 397376566, 651932279, 804371459, 270030139, 833803204, 25908662, 642012770, 851688874, 165974817, 784039105, 890083015, 256982738, 886128275, 795837824, 187760541, 129855962, 91277951, 853077955, 590688246, 848102515, 152750841, 184457533, 648973262, 841734895, 964190308, 70362282, 79703103, 493825689, 349646103, 211451060, 268377359, 837673454, 342044293, 265176922, 834512107, 518893195, 804270417, 333365103, 193576017, 759059662, 19268886, 74023257, 196874840, 174457978, 514350726, 817238427, 20126176, 265050606, 661973434, 548579457, 834944212, 606004756, 353779028, 88387346, 925072092, 765879579, 537170780, 327187423, 230021199, 441746236, 723031939, 187730389, 39545903, 871045935, 957851449, 839848047, 757035608, 574359194, 876186364, 268495605, 191211461, 32495289, 855754793, 528305120, 794377215, 637750799, 369230176, 56038536, 314861731, 165635742, 337338682, 884353685, 153900907, 359675668, 309822853, 847625751, 154542801, 614677625, 604354591, 873534143, 485555082, 632628782, 520496101, 337219759, 959490696, 221350910, 571855248, 209423887, 944995065, 140319420, 729049916, 76623696, 295987652, 554821245, 489737977, 366881335, 700360668, 730101700, 711530731, 131392855, 157351040, 873990335, 682339223, 645336330, 237732964, 510195169, 565306639, 933645929, 789180248, 967125671, 191162213, 484789721, 124612606, 813932065, 95871726, 808880817, 766277347, 37518466, 130461075, 129676869, 984370812, 850862559, 788718100, 734665378, 427922548, 199620735, 789264713, 852751376, 300958415, 498227492, 308360560, 281244809, 458753439, 143138232, 621076864, 619828741, 926524721, 481741485, 139704752, 601799065, 290015865, 300032004, 273244397, 966656352, 794886180, 429986394, 950572328, 213800006, 57897882, 680570699, 141523367, 535867642, 972056488, 31738710, 58465003, 903077976, 414092516, 816593501, 546738417, 886829547, 245219729, 655614316, 521360774, 18844803, 761536269, 373783572, 216014949, 124610564, 339267818, 878683618, 843926900, 765554304, 959196167, 425257971, 102124907, 118061052, 208312151, 442183411, 693410321, 789954619, 286181441, 513284181, 952560656, 606559166, 149155130, 808094720, 787096110, 17020039, 531598700, 451274187, 223888101, 841504491, 819611390, 988076016, 268266187, 935083015, 351017155, 266521776, 322550169, 995246669, 369790663, 852602567, 585142557, 589249516, 443183573, 564213629, 99476363, 804329589, 431350062, 311519511, 987506029, 746744174, 965140064, 448156137, 203477361, 842743007, 770043015, 325008565, 758454426, 217299200, 782899590, 61032634, 480484445, 838480881, 799208231, 630331102, 155766141, 295672090, 983294487, 8943328, 342071707, 111989203, 608376793, 147032987, 762741989, 668406659, 428744627, 866024213, 969858466, 724437042, 177505980, 286615873, 368577390, 283714618, 551748673, 293410211, 305864488, 101095935, 792433685, 696841184, 405599547, 984100687, 222822032, 616749292, 226515016, 797023376, 761307335, 443700130, 937163513, 402143219, 104905182, 566823965, 132335584, 911094355, 198224795, 17659941, 958383853, 91657534, 662797460, 747858577, 114704298, 206750671, 157395969, 133428743, 730270035, 448699666, 349642221, 226147470, 248282400, 560485188, 153113708, 806626346, 499590439, 439418289, 236546438, 392209482, 147371422, 217819547, 779781158, 432902043, 533877275, 907617117, 447335227, 991411950, 266260239, 231239254, 545489560, 225857942, 629498751, 37749914, 981869524, 615897331, 81260211, 276723944, 640356819, 300363283, 480490524, 298711824, 52573678, 688374440, 481549509, 106170017, 733532305, 101812206, 760019185, 375331128, 820923186, 743939829, 651113393, 15236452, 45849677, 437180219, 960988373, 435301213, 144759072, 113625062, 55604366, 267956332, 49508301, 736939200, 519820366, 296927810, 418541696, 934626969, 353402892, 906028813, 360976852, 575137012, 746850155, 360167674, 379261638, 139320675, 76565334, 3958497, 16677925, 911126688, 996645048, 617146209, 13611945, 323387463, 339114251, 236019074, 406031823, 186339762, 987109806, 703927908, 637081125, 817273321, 600844307, 334961346, 403171917, 131056190, 344139884, 477830262, 973028331, 707764706, 396800997, 135436098, 39886909, 894613079, 468853585, 800713085, 725047370, 95526485, 529322301, 520105482, 527054180, 298791947, 515483373, 35974647, 836684990, 924761399, 128197804, 948015992, 126059517, 1204693, 795519267, 984868861, 398755515, 92254080, 873398082, 533756541, 432264926, 747642049, 365600030, 47549680, 756911109, 115499757, 600591458, 361043758, 479239578, 924900542, 382403558, 134820506, 885214733, 214375743, 729698841, 696156237, 262989446, 780660574, 566669387, 317090746, 245284682, 434338790, 166008824, 131609705, 971996773, 290952561, 506708065, 563585090, 525030275, 156568851, 960798951, 770310051, 325083595, 53621322, 724524764, 815068099, 202061012, 114639222, 825213335, 325895361, 363861402, 529220602, 5871426, 491116460, 222305677, 550496304, 485641377, 477758422, 81593837, 344691973, 352430242, 729932390, 653710630, 328675557, 262513481, 876009158, 531011911, 39981886, 222782594, 233028668, 536368887, 963754227, 373743898, 743528700, 816690336, 299551861, 785650862, 854972615, 290937784, 6935446, 400544202, 697015437, 986928456, 121169140, 890059455, 279327971, 158345031, 916595063, 508156449, 886377770, 583743834, 324637544, 73344229, 744345267, 79409073, 183549600, 668195795, 46731435, 282318666, 907972584, 128741603, 559245966, 814019823, 253202135, 157109433, 893074590, 899185076, 295894858, 699630740, 180160054, 155987237, 74612369, 493167821, 802023606, 750708744, 639346175, 166183841, 775993581, 131164218, 869650150, 54062311, 59319656, 688898310, 17731652, 812709503, 909032031, 581268400, 813108790, 77435105, 695878098, 957148297, 584422565, 973645802, 975974139, 850720564, 820097046, 513759074, 147217339, 59668526, 618472170, 402324114, 458398076, 769230171, 884540460, 146420103, 113470389, 508772974, 175144632, 318451539, 723084496, 273592098, 354912599, 294811814, 513207569, 919538668, 785561695, 265446139, 922822398, 758370844, 605517393, 876419736, 724331638, 204363819, 785615117, 189664515, 653842070, 551928009, 574810047, 294709894, 534569739, 785732600, 296195080, 690648420, 951329410, 519301102, 574044808, 672140478, 164227393, 608787170, 379002322, 982894579, 262637329, 678744123, 506104266, 92596723, 923572788, 565205389, 18544142, 697578576, 419246213, 194189146, 455881540, 744578594, 618487355, 509745610, 679847120, 714963785, 508121049, 468160690, 20034558, 962748748, 273950013, 896186132, 277044656, 214706135, 61101217, 177497959, 612025683, 972015962, 323883593, 281554906, 185556441, 9437573, 449694178, 609116723, 165208634, 485241528, 243884028, 710662400, 484589402, 110413377, 504778061, 839316221, 25108129, 677008538, 780669038, 289112691, 478070485, 989378825, 242605313, 849929893, 590080723, 228429644, 269250038, 505039195, 176006772, 693936837, 11621482, 600484241, 742349506, 241501964, 825662057, 54027229, 170989431, 554251656, 357045885, 788847240, 915523261, 678283956, 870083479, 319686275, 529398311, 797273390, 530036547, 231840157, 244957971, 724525878, 974304895, 336531669, 647283782, 280526396, 279306465, 408240023, 301447422, 308385615, 376188075, 497022756, 2476683, 663043006, 798607523, 885431623, 366221448, 514043499, 782115954, 486305031, 452952388, 594734152, 89072615, 56724351, 793783249, 149364752, 474011963, 154864220, 152729874, 518445700, 595185814, 180723164, 133607298, 595049994, 322079639, 569788882, 317190776, 521722284, 473686804, 347151485, 545674690, 556021319, 775584598, 466197954, 564024569, 496352869, 392994387, 146818321, 790232392, 882714968, 524149546, 142057685, 479013444, 625382323, 44027004, 483957105, 890696120, 838363015, 249919050, 238967804, 635511617, 648625626, 500722480, 873390348, 744548888, 423532071, 894139061, 553605705, 59488144, 488667129, 880712296, 742384651, 67742024, 715093808, 873088969, 443731234, 181555488, 109151584, 102957371, 848824546, 711259588, 320432594, 321060858, 882851471, 615235205, 196782725, 707888042, 955456874, 558134221, 31047364, 213203402, 99491659, 22300404, 306628809, 756516451, 945905633, 30787674, 871298532, 392034147, 121009584, 208559778, 485626124, 152759455, 438609683, 570314263, 252248306, 667983479, 324068526, 507953416, 459522995, 248011008, 808109072, 467946276, 24759494, 122618311, 961238575, 6970299, 866304396, 130783401, 836752729, 591418916, 863713465, 456618583, 262653, 400283984, 518807113, 406688506, 527710785, 880641150, 788966442, 489884576, 557655723, 89044643, 893092400, 976137909, 138970760, 422784003, 288939331, 302788989, 222911820, 334030734, 376238572, 131012521, 388864015, 409140160, 687641522, 68157161, 850627294, 78345, 295282276, 431695930, 376911732, 263743826, 958635536, 316555613, 179222826, 693012216, 544315240, 329360515, 302181972, 192006037, 978434133, 437282340, 58706327, 12667183, 676543489, 594029511, 794415885, 941759408, 541026225, 945068012, 141590355, 195039273, 719862257, 948680422, 724029677, 40719482, 834814309, 526348938, 920832238, 801734449, 136088836, 152292571, 311799060, 286158897, 832133166, 467114919, 749104718, 12218709, 538141538, 577758040, 117897077, 277395076, 469137083, 287398468, 485521712, 846119383, 723723819, 378055727, 6574944, 50626160, 669686362, 625563880, 302437703, 807466162, 1797813, 211078507, 25658168, 248981061, 745633359, 33095442, 610474509, 426866823, 568052535, 243075577, 321221767, 763122989, 943285449, 339699252, 321092959, 3148582, 615551049, 159411817, 815798051, 485192419, 159925357, 590868091, 670798960, 91856800, 295562268, 934130273, 426376652, 107359677, 167226099, 765147931, 621130061, 633124528, 97666752, 823770258, 812852883, 573424940, 752701805, 970288168, 603072798, 828112431, 634855343, 651489699, 344326216, 290579838, 244991220, 320918147, 746911462, 120161938, 293812777, 43397250, 961075027, 550134742, 447134612, 211048103, 307372615, 108292934, 288699938, 562692578, 875758787, 973536709, 688154227, 287497318, 990586497, 589933507, 690572114, 668432653, 329260404, 822006493, 662101669, 531013448, 442109063, 675258646, 330147502, 181659752, 253335540, 431849848, 392141110, 633212150, 220498682, 911387881, 289624303, 842615521, 247554864, 707863038, 642863191, 160227693, 724174624, 397668291, 285827723, 17479921, 636886110, 256328214, 904495917, 527144643, 776195621, 150111687, 975220878, 30553798, 719032322, 795733152, 497054940, 112269952, 404011861, 624415674, 287644939, 661048140, 695875251, 315367952, 394112390, 257567971, 449342215, 499789730, 937414369, 21846598, 994122613, 440793919, 586079413, 180397629, 243521067, 850914261, 558451216, 452286953, 76625603, 622862908, 783053901, 393860178, 294294339, 818921228, 569663180, 237955193, 265783037, 43782175, 239924839, 678208704, 604182178, 824054526, 177538594, 897599347, 800247491, 743575745, 739208502, 981655045, 712286007, 17961836, 83814550, 379802853, 425817532, 667628659, 409773093, 673930867, 360431114, 318356109, 202065529, 928514529, 202383698, 274644200, 786667259, 91780979, 221736354, 461097882, 65592912, 530274680, 8589, 219460841, 393467602, 663152524, 53027156, 527931992, 168536945, 846558454, 29443212, 598711907, 592378252, 606917117, 579563590, 875863837, 739403787, 9189937, 473885926, 727512343, 734684195, 316201751, 132691566, 136515646, 715407233, 827268982, 907009986, 384433581, 573038794, 794893534, 600445267, 140735225, 619266996, 66939388, 689068511, 721963080, 99302522, 92339517, 980688736, 91213504, 918317674, 128334533, 320290206, 936668224, 967135982, 408171147, 186972979, 566436512, 590171036, 310006223, 871880060, 941538926, 514796130, 270265109, 310712432, 458555262, 780633984, 944707642, 187749389, 115257016, 962262610, 541516715, 632924307, 656274538, 304816816, 629081045, 234850083, 236340837, 647028802, 333968395, 627570472, 312597841, 202377250, 798653042, 754101296, 477797216, 910362065, 860119445, 913720805, 206861443, 132664552, 439872567, 54907521, 288152482, 92152121, 683095196, 609197435, 788252635, 982569832, 154394254, 301838301, 359717596, 874307197, 845486183, 552449526, 375291865, 930221696, 592817589, 156123788, 118929292, 467290722, 195892856, 272296004, 212939240, 904730458, 519306913, 246179513, 770198319, 430550467, 97570725, 317880683, 410973270, 860129732, 521013249, 863420915, 855699511, 817603876, 256457641, 951190112, 948280967, 972938274, 584773059, 373323094, 515756985, 31219854, 271033056, 817757775, 888742662, 357456340, 749520719, 146061248, 672284022, 12571614, 51088545, 466792238, 732763676, 367351143, 429685217, 829089764, 621696397, 692520505, 643410547, 507067336, 304847218, 143620469, 555420956, 851181710, 166984203, 751198951, 482549692, 925466245, 29286695, 863072426, 603601709, 587239364, 959176087, 891540262, 787438966, 498976128, 358346970, 261845220, 68489456, 601716845, 999410640, 817401677, 802563518, 76733511, 975440361, 2276998, 792373158, 358566582, 655734495, 515874241, 432156573, 902862653, 215090726, 516372150, 373284049, 195760946, 893141896, 667191635, 96858981, 711232159, 463416635, 465158012, 218030684, 720969562, 265109590, 645354775, 837460424, 641457638, 336971879, 397092851, 433712232, 798932454, 691850253, 825550483, 196858365, 205569510, 35396813, 171053310, 308242663, 955990656, 600948148, 537660889, 441530135, 221081516, 996134157, 473361744, 586992443, 144049495, 974254372, 133472446, 727568552, 291224373, 752508672, 928988475, 131544784, 58887900, 540720627, 836842650, 723725797, 74492062, 195770285, 746865991, 236845498, 461308137, 612018663, 186672335, 669574120, 177838546, 320617405, 243062637, 61523876, 860847866, 291394259, 440875414, 124596941, 439510313, 950156356, 796400724, 946724825, 614833352, 46470976, 471829714, 95314021, 917698400, 110012279, 651110540, 680137580, 890185882, 150938897, 915603342, 229150227, 740124651, 50158650, 585657756, 979950978, 755241152, 235744246, 504822783, 925314767, 51112405, 941171378, 830341452, 230145568, 888480142, 456078129, 654415446, 571180422, 952203526, 125846481, 356241593, 373795685, 913628423, 713218055, 171583376, 441087964, 994435808, 209242523, 622762990, 270100603, 108178505, 430304908, 96857099, 164808955, 89117285, 992190799, 424141064, 18894847, 676609576, 981080645, 951451750, 315879162, 543169380, 710735252, 460975386, 536428905, 209313474, 804813040, 389232815, 608617014, 618152153, 249512599, 822445162, 366742904, 47168485, 295580307, 137976362, 801112837, 676657595, 256951595, 765860629, 239396244, 636747580, 450872701, 791657845, 610054487, 550583303, 339415725, 883363572, 881833184, 397036789, 251347555, 397792695, 346925269, 961098425, 185806472, 843783052, 121611461, 807568618, 184337678, 714716254, 207678348, 30833445, 708314810, 736077699, 363662209, 267986416, 459584245, 698842305, 334982813, 264654222, 645359267, 911514932, 371513377, 389352093, 54137949, 980028816, 723077961, 870261826, 67785917, 307989780, 13133900, 450547943, 232187540, 407715969, 204436595, 769169965, 906760181, 240121045, 307010420, 297065848, 779580011, 830133228, 825131819, 300273684, 951607101, 231128018, 814048585, 862390852, 858632208, 915808740, 111089961, 245314282, 335093588, 873500593, 345285648, 577400433, 323310179, 550224431, 990074151, 603649836, 883226821, 333828514, 982843284, 164094856, 665481454, 77220631, 182217347, 801093664, 557364360, 377291798, 589924418, 325268712, 974126658, 310235865, 225297504, 744291843, 29155592, 472699270, 9682851, 213026345, 127745316, 917800106, 726224307, 80428037, 40022138, 766001052, 237006454, 479680711, 880448853, 450352179, 128875732, 618823197, 839542521, 625905079, 961559891, 357037921, 588136650, 937522512, 300291536, 396606177, 474939644, 109640613, 797166558, 994886174, 777678880, 332761198, 956731980, 475449816, 393650828, 692935415, 839760001, 113668831, 820989662, 237646024, 14718815, 404895739, 139608203, 648703639, 918634021, 781265120, 358291861, 313890587, 344753318, 13693303, 145039552, 744628808, 694497075, 378434451, 19792793, 612086964, 612940437, 212537851, 681148301, 968104162, 231048289, 126608855, 944956033, 118621456, 423025622, 718205921, 284513733, 124196680, 10109288, 999649708, 68164117, 460625207, 829018903, 717784045, 424464059, 962459417, 309147279, 429491153, 953693041, 231429868, 344729507, 584491885, 996959535, 205351935, 18794978, 206433266, 677628803, 609319953, 655742298, 295455023, 596457070, 692084840, 104965940, 879693478, 245139886, 941675494, 417655662, 698616179, 640504889, 743884648, 422923162, 395729315, 818547061, 277568028, 861397507, 701133279, 836154849, 963719188, 958131783, 762993102, 325472013, 261116661, 988511278, 7179887, 650120359, 957015863, 70619713, 574309329, 873794746, 262016615, 473376861, 203408812, 302340125, 300816930, 753088528, 963500456, 459335464, 284243852, 480149675, 865476479, 543054492, 295422644, 476815097, 905571550, 608105429, 280559553, 882890216, 834309966, 681040244, 560141996, 43183443, 886510901, 242487238, 514104179, 370925641, 337683599, 505778526, 936224432, 127014958, 935435038, 168361596, 193263960, 877357471, 390664425, 197622326, 477662658, 316679566, 196295589, 879225597, 450567200, 506539125, 707131531, 466037425, 36918159, 644449219, 184862782, 403408782, 203276909, 740966903, 571864285, 70986410, 661904320, 945174100, 605567132, 394987596, 218391221, 357330028, 225873759, 528442058, 230126162, 770871265, 162609537, 883240731, 785015721, 962328239, 913524503, 891073500, 782603052, 977100889, 162743708, 490861146, 124722122, 3896961, 11302583, 767559066, 438694342, 323486819, 896823402, 127794951, 362701637, 135196241, 819204129, 12283025, 86559435, 29662009, 91282915, 999316178, 259657912, 34858522, 703587346, 653533102, 197692406, 257666001, 982767729, 69814910, 473364082, 367328628, 808215862, 742999351, 970891462, 254200350, 307178583, 843357803, 427860946, 921836239, 787411499, 123646888, 152503773, 495894665, 360119407, 914223676, 224764875, 908867026, 369330287, 396452818, 126886971, 740822328, 869446842, 583741341, 761876898, 741494514, 55016979, 585546510, 591045638, 195337337, 556311181, 814316750, 27783452, 218187979, 59964278, 863047704, 143900307, 367382823, 67110084, 648193980, 809901190, 299702296, 346298077, 701633876, 850436678, 546057463, 26794087, 548852587, 262867638, 840549667, 284574716, 458250692, 44664849, 844852876, 688948421, 78346919, 564400687, 751880848, 423103146, 967830621, 632876843, 565986688, 296367665, 382692892, 542303431, 694744353, 476468009, 500798075, 802526325, 825795433, 504841257, 760126100, 979392126, 879683379, 490805336, 100448667, 217807375, 339023451, 276053099, 234510396, 263301863, 536898482, 304586545, 772742301, 384826143, 209746290, 259216428, 594674934, 571367800, 210515729, 264160396, 153721824, 95412832, 778776181, 263679946, 959573349, 869191643, 441994231, 704286019, 663556532, 319363164, 612795973, 430257262, 909706607, 111926776, 375760917, 387304565, 335773545, 831500736, 35014834, 485494995, 963327447, 750778462, 856301811, 595960184, 561078086, 757147130, 487286310, 4640847, 916794602, 996463629, 144298586, 187437932, 631043184, 445823195, 767166259, 236034948, 837053060, 157657477, 654123499, 748318470, 891263020, 316541253, 964263500, 851821599, 434177168, 962275260, 68195477, 795769386, 484737203, 527057106, 802326351, 140226534, 86619100, 909117955, 184708746, 901108691, 988527573, 30801946, 678499884, 131610512, 666590653, 965699409, 60343534, 289331153, 521673741, 29660230, 637561402, 170703387, 978619909, 200367382, 337434285, 97358163, 62550481, 830574717, 708878867, 450087846, 753242449, 35871901, 644447052, 434884281, 780779475, 739208537, 602369758, 219643987, 926302798, 154087764, 193252757, 114470464, 545461823, 32788279, 290608129, 930546363, 953429340, 463125615, 103913033, 150358728, 976263423, 895878172, 474984807, 909167523, 852366518, 248870616, 214014785, 728079494, 537112349, 699541647, 296187355, 485415759, 500286242, 111944956, 171072966, 554227006, 261947382, 516121960, 455539221, 130770917, 637455848, 441957245, 627066084, 105493028, 198358664, 353437280, 60377016, 454261355, 577030023, 539632514, 477526946, 973886645, 435211684, 327724799, 597914696, 2839768, 621274802, 12319405, 762035363, 764748119, 379259907, 202745841, 6478619, 688843486, 862313085, 6324729, 285755942, 682407538, 670817617, 875261293, 739743535, 59518439, 541848422, 177775535, 153468441, 716506693, 733687833, 345930288, 938050532, 83136435, 70872586, 906537941, 21555049, 515048173, 839242802, 396906130, 310844657, 578603052, 821791122, 872165888, 837396195, 267304170, 64252641, 92024826, 182063818, 638303727, 88513975, 30603118, 829512185, 236040182, 670559513, 556011540, 814032526, 697410735, 69716649, 977743132, 811443499, 830138007, 572299923, 261253051, 225993063, 427923983, 746630623, 121078088, 635180664, 142548090, 799979233, 861949709, 734661067, 217336233, 30476061, 408959552, 346240279, 552774360, 806711370, 599717665, 662719669, 419845059, 153401332, 617877386, 660614953, 417711170, 52089229, 68964516, 917775244, 305402871, 22077740, 912043225, 285478562, 264097633, 533731202, 388966654, 356120859, 391669852, 922609595, 839616185, 608268608, 694720341, 803080401, 765661076, 936703485, 882564282, 142026427, 502112227, 356191972, 372356019, 810261805, 873717309, 211403108, 529743845, 816203589, 245680434, 885981464, 225116394, 101446118, 732342305, 755156935, 645706422, 32901056, 707620143, 390899886, 371230218, 730030440, 202489953, 143790117, 502078862, 625946620, 361640377, 46606866, 489332711, 389593984, 718820968, 144983849, 392882268, 43407580, 293382243, 360436177, 289975915, 696633121, 267213181, 58783815, 616820779, 570924631, 381895775, 406727995, 738869277, 226677353, 926450165, 443701265, 241699512, 815355105, 165731339, 398388471, 305704214, 958583772, 999310443, 482541030, 225861310, 394364634, 155947867, 525867350, 337614651, 862717659, 886483590, 604701743, 328793927, 380581264, 754679321, 961635353, 715473285, 288378121, 317869910, 757254394, 654152543, 198855116, 897378163, 243078873, 638921911, 762826746, 302261514, 951550396, 472055446, 170484666, 265630047, 691426587, 339452964, 663555665, 451518992, 984237181, 898254722, 856910644, 598411706, 748721493, 587042997, 517300560, 585082834, 252604371, 858796853, 394773734, 802638187, 741853816, 813654068, 192632646, 352555281, 570731809, 118817410, 937374179, 272959731, 128954769, 580325202, 489394273, 60864222, 710845313, 588077355, 581122667, 720487650, 904387127, 55824796, 213073178, 491030842, 226307843, 981618726, 999183561, 252285236, 669480205, 397652265, 572910774, 106399719, 529029196, 487038794, 358199063, 184252193, 39810213, 921497584, 479936708, 350615481, 913251663, 410360918, 236527262, 3273410, 491282665, 197093618, 836546833, 302059528, 838742905, 364568697, 870392842, 617864889, 837035589, 823070392, 552719864, 256552804, 436932076, 271321255, 223383624, 541002390, 211062393, 152323162, 648108415, 708332503, 655431100, 905851294, 899201527, 287905870, 706895298, 8010099, 210999447, 340591980, 788681467, 555735451, 682888758, 566068058, 753141323, 654378632, 118307181, 157531640, 187810340, 906919065, 344150301, 265294027, 615332938, 576197907, 528060274, 986777427, 684680667, 497086902, 786943757, 926426311, 818801297, 600414424, 46783191, 826197257, 36485369, 317621789, 544071040, 240034613, 121129800, 716588695, 472131014, 884536476, 165372877, 119828403, 118015176, 946758315, 992760610, 277991022, 534944059, 74280538, 678940507, 584964240, 855069419, 476523737, 174217435, 234806386, 433561952, 576387509, 960053037, 200046595, 315555736, 150028048, 816910592, 867762899, 768500478, 486329187, 946146638, 60169656, 151193975, 146435633, 592686894, 487609037, 154316845, 619204765, 583334615, 587674471, 137468870, 649742795, 260152717, 335098173, 43323971, 703307711, 4262961, 808817355, 980628188, 950645282, 67584687, 989908066, 669540264, 202607953, 849569311, 822091528, 754541026, 154445211, 371049246, 424909193, 8511421, 875016145, 846454022, 102848760, 705643615, 394891893, 374475832, 198720485, 768049468, 484338783, 416937591, 647462094, 558141410, 662742458, 927825694, 239627899, 386289290, 623074731, 840163120, 682959071, 538426258, 892233569, 939556303, 100691498, 785698047, 108157984, 630529622, 402898321, 508198859, 815808664, 380838889, 411168765, 130824049, 891583800, 762301127, 398971318, 222643438, 395187579, 123050023, 944474421, 695524406, 453959289, 763358690, 285551739, 728794601, 762006757, 797442229, 415750047, 336445417, 981860869, 763569132, 811966949, 299178363, 707384889, 511848885, 358798731, 770457958, 207892432, 698597689, 562570228, 629384962, 902770311, 494627955, 780031068, 333744202, 311503230, 784176620, 720845318, 403199100, 667755680, 88599589, 516132434, 101302989, 272124185, 529423178, 351144657, 236463660, 659551070, 322132096, 105240346, 936635430, 577705060, 591699763, 976150035, 734000082, 602451982, 868010952, 573615048, 761351654, 304042848, 539898935, 349540345, 271056900, 238737353, 394503006, 226594667, 358242776, 181421141, 445334993, 773131211, 301920154, 626772149, 923641463, 591082243, 779651228, 392358732, 244291968, 22066113, 317635297, 906211588, 457806316, 790412805, 456791221, 150377730, 35980422, 603121273, 917535343, 529567571, 431279691, 654945736, 774160043, 488889970, 857735083, 457932881, 270940642, 399238250, 258316495, 588732825, 390483122, 247077668, 125942765, 757789104, 511539742, 603032884, 420311492, 820762092, 581434594, 482607891, 534179499, 914476831, 754704353, 650184237, 327426516, 150746960, 225901977, 789550388, 873953303, 649404569, 483404972, 227496115, 772614930, 713557967, 22345002, 699974385, 877741546, 118634217, 347942257, 571671112, 809436319, 231662033, 971549852, 557401431, 32426230, 595046748, 286586657, 171485793, 204460740, 789079647, 676190045, 107094235, 649254718, 600148150, 374024915, 199420522, 98725757, 983652010, 540447672, 781838014, 194696644, 466897999, 556047888, 713791342, 291243555, 78409475, 653274845, 960613549, 374929162, 111209672, 540669270, 272415610, 295505150, 825868366, 441534497, 220988650, 548210359, 139709727, 225590494, 662018976, 18077117, 458050591, 540020878, 168847228, 795028187, 959070721, 29924543, 552233003, 702972941, 413344001, 546127372, 491361621, 673014068, 290416045, 645951585, 559888950, 408805156, 357148430, 186182321, 286600964, 303029461, 648126502, 15770432, 824353861, 504105342, 171313482, 393092450, 202141747, 62733809, 913255273, 768068841, 7223375, 69047771, 147730430, 145667731, 868773367, 263130725, 476230858, 192714203, 134670198, 705750319, 225606794, 763728292, 74200498, 661154162, 695061738, 815396115, 707415765, 541442274, 61720027, 85515471, 794854366, 234274997, 608390732, 279068739, 924462359, 807030823, 732558088, 709236999, 909600081, 789672143, 924005184, 106947426, 680107032, 352306653, 104814480, 356696088, 906707209, 947080414, 816133898, 615913584, 562918295, 407362190, 940331825, 824177808, 878252740, 309217436, 427517190, 506147383, 562093565, 390848307, 561431244, 793474723, 535203655, 523386307, 751957643, 674954383, 646454174, 815068363, 140399880, 209048542, 64741185, 902259347, 513006960, 895967480, 838340772, 72950412, 233307687, 19082098, 119972751, 111666656, 722117522, 214539098, 876989464, 982201945, 796722292, 75328712, 598165741, 167603416, 662666295, 142859666, 793048514, 691393683, 739010980, 105813984, 636238392, 132659186, 261418489, 787437244, 991485718, 37787212, 953941275, 765545037, 131563952, 583154641, 295203646, 886769611, 365924432, 760083224, 925724428, 618472533, 872622259, 344959941, 470268009, 772794657, 63695359, 958064019, 235358244, 24395152, 648596117, 786365491, 853217412, 577508448, 476505883, 213282295, 206709562, 387046887, 540456019, 280751971, 136187670, 917411286, 146898889, 100238509, 23566725, 182582276, 141975492, 363149584, 484802117, 355605404, 536657891, 422394911, 685619243, 782217027, 415979514, 399911791, 125966291, 968478048, 670832832, 53881125, 649226000, 695549367, 463444057, 859202110, 571112817, 337829989, 907721085, 158466530, 582287366, 417306949, 277010179, 241770028, 753044437, 26531710, 606182519, 898179708, 401743060, 546729919, 18741453, 556353181, 670615521, 303065718, 48851391, 793259118, 291276996, 389733542, 244807981, 664581388, 829876599, 22479523, 18680367, 179268379, 987949667, 195322851, 521022077, 50858558, 559094427, 325905444, 353315759, 741150396, 319934614, 511847079, 10934580, 904405024, 104595248, 285771287, 85725780, 937971357, 589056836, 102538932, 707284285, 489817280, 75429788, 346742114, 749697136, 199967610, 880349854, 759411723, 896540000, 467058438, 582863535, 945926993, 609297962, 830941171, 817497563, 231127614, 238691685, 308866404, 947827940, 721001207, 947193382, 104505798, 179573970, 809458132, 430189145, 236026437, 152042887, 372231389, 794146987, 508651490, 913715325, 609318769, 499637986, 198884809, 629130884, 637779756, 460909575, 234587020, 644994413, 335376957, 995035956, 953810799, 863592394, 863689945, 977798568, 814519468, 940979168, 360238477, 508334867, 13390434, 508586629, 543740352, 231362530, 825992271, 411544144, 806384225, 612023271, 779162588, 797607832, 65751085, 969781516, 59610828, 655139907, 337604242, 274376688, 774998849, 291462339, 497783766, 620721974, 959638332, 345075750, 498459288, 429085627, 882063156, 207582851, 169535911, 961021390, 81382898, 668606094, 690039278, 564264230, 463599585, 673515134, 355294910, 197759316, 798193274, 907635449, 255077638, 994172123, 892962125, 765605942, 68444434, 903541229, 467922366, 787722391, 476730095, 294385258, 374501198, 241818891, 4678379, 700728385, 63920313, 993890710, 608616696, 765202731, 620591396, 895401710, 371961404, 170358924, 585802360, 460648986, 628908951, 722736283, 78521892, 91878694, 365677902, 334930491, 908499049, 411515350, 368642022, 760261495, 801433106, 967641913, 302199450, 842378998, 516377313, 110947724, 486027524, 632247955, 84074992, 506338430, 392997720, 302430120, 699887251, 656777199, 857502523, 196100287, 254611843, 661657820, 379187726, 156554470, 773116798, 985788970, 982421412, 864395121, 142487525, 270958922, 716366925, 647242852, 533812907, 157831746, 120069248, 682898340, 421637217, 138228744, 716057727, 417099336, 857868839, 414531802, 939290145, 517323713, 137322910, 469776365, 800699041, 242138298, 881736301, 871740118, 293726353, 202391575, 859855125, 557584508, 524815440, 931406078, 835815911, 640135760, 858499564, 118165448, 461249745, 775769661, 960340494, 116747435, 598769028, 17593050, 238825925, 409714594, 651731446, 720761435, 427136927, 517795150, 851828181, 41586004, 443835906, 43539190, 882075653, 588305350, 900510609, 275727336, 84016644, 888556532, 897056576, 766297851, 847574641, 555917019, 110301545, 659882724, 39976293, 323605296, 434538725, 144102434, 506990377, 674851144, 369792761, 416468692, 309924813, 346067202, 678543542, 991708095, 4880461, 170880149, 650479424, 48925066, 270729866, 503526245, 657705595, 253482515, 298691209, 881108057, 204784173, 756249349, 89617940, 801177968, 777739540, 799208635, 289284005, 842991500, 678842802, 968006939, 853301148, 852504947, 887229972, 698190440, 693130679, 706764382, 267396245, 142895429, 206483700, 303864900, 216773225, 757864030, 868887329, 681158082, 435725884, 41922072, 280939852, 836548438, 67115418, 528173216, 645901363, 612500030, 30078978, 611206859, 812360380, 617911133, 319136166, 649564252, 260055159, 910875000, 802672823, 757744903, 196258810, 163954117, 830010254, 849516850, 472616274, 263982756, 128210931, 181608257, 297373858, 561894395, 48083242, 541073115, 957172672, 824385926, 196932457, 762730332, 438510115, 190937391, 954668190, 699473187, 16962679, 653336583, 489830012, 260824471, 731796959, 970905082, 388258413, 797834012, 964655733, 992488484, 147014956, 967036622, 134981747, 50603502, 594774265, 66219327, 723456176, 818991649, 519400849, 698408110, 697790313, 224274081, 96599985, 29867394, 897728617, 71712792, 306492511, 470388903, 75676302, 500124082, 819041783, 671247845, 763412280, 325025617, 131165109, 725737030, 464509343, 818516446, 286295658, 604992195, 46095997, 920375713, 849830005, 328730535, 742258922, 184508231, 985958485, 449343580, 160959225, 396781940, 976084524, 662607621, 855448787, 424554177, 952660654, 314353703, 414240211, 110163286, 469841550, 279244078, 226910344, 211546961, 202536666, 838881611, 266156438, 316252751, 236829485, 705886351, 93051321, 53890011, 869465381, 275839124, 824577738, 589583629, 42356413, 598732679, 579457922, 972098933, 616090548, 621758047, 928060065, 878158811, 220833600, 435050901, 678774104, 273619419, 182337109, 189204025, 509157117, 747864079, 842095868, 975218997, 241435456, 928452309, 947689012, 907735582, 720187015, 396860548, 939440231, 552810821, 518778975, 414848115, 737353945, 64929815, 58509229, 539747643, 977594570, 711380958, 864861635, 943622898, 557138674, 864243166, 223698344, 975719122, 602242482, 53772608, 199584009, 22388947, 784646891, 612291628, 322637417, 354505839, 352710790, 413615433, 7153838, 99781033, 708635610, 672347198, 734430887, 669589234, 479712324, 77707819, 528475178, 579972092, 861943078, 870301944, 882953158, 977338499, 231253302, 873220825, 445997189, 414084861, 824712174, 331065494, 927730953, 607707545, 743042310, 138938541, 731656189, 375705897, 137992094, 739253497, 378922581, 545412633, 856506705, 305683477, 168509290, 528062038, 339133264, 533068138, 122346592, 453095236, 758543649, 451361311, 660099519, 354559011, 930635143, 96757989, 180668576, 850480527, 405696983, 970767223, 839213346, 609754293, 50397047, 724068419, 908907857, 544031760, 609214669, 57856097, 114364609, 302383450, 638920020, 8851462, 909290543, 164049788, 832779231, 297199053, 564671390, 400725359, 123446938, 706441311, 977719466, 569517206, 483303453, 21530429, 104943945, 791268552, 109178525, 577687899, 640260229, 346364982, 994562742, 617075880, 374485426, 482599587, 870955651, 12515210, 992555253, 253486222, 540127219, 974303167, 523130594, 225303810, 979670384, 841152181, 949721832, 96125158, 113219080, 298042893, 47298842, 975531110, 275167750, 483620277, 460837271, 452825069, 970946168, 592938730, 567467983, 819131134, 313972354, 125412402, 501420645, 913007370, 939578505, 659851272, 828484132, 891974584, 115766166, 615467399, 38250425, 484688264, 238127809, 743507067, 439363741, 729676230, 137975, 809850551, 273715752, 932438242, 663757524, 995699631, 975832550, 770989012, 505383382, 559495973, 606137319, 41053329, 332805605, 548609665, 448143659, 60062481, 886530373, 614499661, 862625497, 716356011, 343096447, 59793366, 340221101, 880271367, 253499086, 811407273, 15929565, 357267023, 300315670, 434543574, 711555417, 154183608, 349524893, 788661419, 127109223, 450239207, 374469821, 297561392, 735180767, 943606275, 599833261, 73811277, 930477209, 342421648, 23249947, 464304221, 151034134, 982355319, 646788866, 966088286, 657697802, 572392365, 488463020, 508876502, 748415023, 654524878, 964525755, 256197837, 109989541, 955403294, 662179812, 385880124, 67946664, 809639283, 236115557, 243145549, 551835108, 466440433, 607323352, 855901775, 250746588, 602609794, 789114937, 154251351, 38553254, 313072763, 751307059, 734206374, 554037860, 299090136, 89682698, 359588717, 559252909, 979554890, 991295037, 229996806, 963883790, 626204669, 876073815, 97706658, 596992975, 857470575, 214674563, 115830047, 591350883, 128493032, 400894721, 845926338, 352185546, 218533766, 935855625, 966400076, 754345735, 598438558, 914263876, 577322492, 905423559, 495043989, 684045569, 554386577, 152358701, 886482104, 477624235, 163431801, 930107946, 511086167, 16423662, 925160254, 133984317, 908873611, 427118425, 215059201, 359648444, 932969373, 834737618, 973302847, 661683603, 43178810, 694772346, 526689590, 601376757, 731289381, 40658231, 777847917, 277795352, 555635893, 222351373, 690238888, 539957983, 820049970, 15193645, 785377403, 504432799, 563113701, 650360634, 343366662, 527755709, 601419994, 345850351, 757656219, 505588854, 960726911, 75666303, 790626917, 517454592, 495242413, 567375637, 718702459, 47390287, 612106489, 276258944, 476223334, 475687297, 159997012, 186689834, 52349310, 226998296, 514267176, 860404765, 293854319, 218812309, 33445329, 111295150, 461164734, 762485090, 109133076, 176553424, 484946207, 56617623, 96692897, 14756158, 64282391, 343173464, 297335857, 179217537, 496085843, 433257419, 594110398, 146486976, 161252030, 269303745, 239107017, 538060954, 328210101, 798060726, 458481296, 225500603, 449856650, 68373634, 410054598, 318534265, 933383247, 273398934, 395435400, 436942136, 597086418, 690602918, 84397063, 683306269, 529452245, 201388304, 127438681, 542108652, 212231292, 72785610, 216827967, 588076084, 354593269, 48848820, 721083403, 892466522, 120001854, 904105303, 417205138, 488489245, 592162008, 380840968, 962673516, 132646587, 818791712, 581633789, 334943913, 262534680, 348773522, 923408682, 821508308, 572052747, 94625948, 602978947, 451639763, 219945196, 425549853, 239703804, 587451226, 862543083, 655206363, 290023983, 173884946, 991384952, 147361692, 876773642, 14032771, 229886590, 305715678, 646756362, 478919109, 717543129, 815894250, 931954197, 300249755, 685161122, 416521540, 406322998, 37850623, 166982452, 39705475, 519710746, 208685057, 563743928, 243778537, 156069832, 899009479, 145071607, 367765236, 703578338, 807844244, 218180733, 487197040, 739553413, 17812660, 808147319, 631456228, 41971746, 385792127, 281438319, 287212164, 338851446, 504758999, 938945233, 399724503, 151786142, 219020322, 451813772, 636945813, 993010113, 436323940, 176802220, 45323516, 772843147, 931690402, 782260032, 883499658, 672768845, 417625519, 532274216, 55142270, 680916264, 656823882, 375904110, 588691699, 29765796, 160427298, 592785958, 760118665, 246179657, 706749056, 556092080, 338908195, 924573315, 102261207, 367059629, 702952111, 442958889, 216305694, 677454541, 116856852, 97189728, 887361109, 966032341, 724652139, 95083015, 815588269, 229089139, 824029928, 109583925, 513405153, 868911359, 368140829, 138125594, 952221954, 190901465, 746857147, 179865168, 589367049, 846903937, 886840809, 310895194, 957462718, 797594523, 322650655, 864650594, 382854188, 646893295, 744695202, 444503675, 687797829, 348637856, 73674092, 276834527, 760997230, 361098203, 728834241, 13877519, 939672036, 106249442, 994981286, 219947947, 90654931, 853408370, 934153577, 879027665, 710541847, 110754105, 106286891, 66455836, 856575621, 732539477, 672527315, 535023072, 226363860, 943925204, 734516626, 308244979, 77706482, 4175063, 600949023, 932642240, 429830815, 272847758, 76239423, 525174797, 595943381, 115923165, 775515204, 996739560, 171768983, 988590016, 420170432, 337666349, 683298911, 776948497, 101075550, 778367234, 788527721, 12466095, 425231330, 795637135, 53499920, 512901567, 599846080, 25652947, 170385704, 679889220, 534931385, 201319017, 857567192, 152006784, 184486576, 640592788, 244806662, 562587498, 987423774, 518649047, 162647315, 619401399, 361674428, 489471781, 943897025, 860224495, 346790548, 586598132, 628213884, 219202003, 402631907, 536293435, 230423649, 977348056, 569558102, 833788259, 107553973, 516237652, 684670733, 899853137, 52125085, 237864690, 250511049, 189878892, 42883715, 880943997, 466037336, 271548161, 413157702, 538147056, 798287741, 666262336, 195559694, 91349461, 340120954, 444163391, 334809394, 603090921, 389702701, 385137702, 370036613, 849282222, 184339877, 182785938, 334786632, 669388096, 777289130, 179125278, 231602480, 211417976, 696626468, 481307906, 633121538, 196154129, 475645526, 369880036, 223500570, 645811851, 465697064, 256562820, 687382010, 213349080, 440356368, 611731924, 303188518, 271802658, 43719109, 718091830, 918262287, 485514616, 667782547, 985511561, 46958857, 454636223, 529917303, 457241233, 803740427, 463301238, 748877939, 982766452, 568889008, 868745397, 47593417, 994049325, 25697632, 498217764, 965462128, 162520377, 34462886, 286567373, 907530170, 964324314, 25669721, 833166189, 173240889, 475167374, 150606074, 250204420, 245291084, 427868654, 994906022, 956589209, 165014840, 271122329, 820974806, 712102377, 801634434, 260845687, 804514998, 353080327, 531088631, 134002242, 964888197, 142850324, 494831630, 929449825, 85520024, 626539131, 703541230, 299047180, 116443630, 894274345, 418426762, 329280725, 824396019, 529698375, 506626426, 489592694, 464365693, 527161381, 842825364, 774954965, 315456147, 388237057, 549186875, 650144130, 479050823, 809262524, 639759583, 511142829, 844385668, 109299790, 396413397, 278595651, 414242047, 861345848, 210854031, 91549955, 263260642, 40699545, 414980228, 995272947, 807821112, 756830141, 798893664, 477720518, 22590465, 350606706, 312238323, 684776548, 891999876, 463169075, 338929220, 89238628, 680649959, 912525259, 639457236, 581358671, 34934119, 775984768, 126770755, 206889167, 813169029, 60214736, 409773251, 196067065, 96278509, 275308734, 340349619, 194613552, 971293337, 995810250, 338880975, 247763936, 987653679, 426756174, 122870979, 231373118, 996072727, 235927246, 674223981, 545851807, 950423807, 131154558, 131991753, 577893774, 678235296, 910375340, 506819034, 123142911, 845483728, 151148148, 652397541, 614162980, 247028282, 944425433, 484933562, 88854735, 292841978, 33001029, 21789509, 25878688, 710188776, 56324568, 154095860, 66748830, 372052917, 425421258, 625249866, 655729018, 582642620, 384172338, 713381381, 141587357, 977408258, 625306982, 972149374, 181679982, 655260716, 667642849, 704903845, 251286243, 194413984, 170869414, 671916447, 986511833, 405639261, 298448901, 391375633, 709412880, 882317650, 179145778, 113420542, 314586184, 640970787, 763092619, 204395261, 556246410, 522919443, 464553774, 427901011, 790024685, 715882525, 831115497, 463852932, 897274722, 177123203, 346526934, 264068232, 226777000, 309844436, 13867468, 607736895, 729225295, 424406524, 806361360, 855906873, 405534870, 314155114, 518447154, 996036884, 972311518, 824116382, 630835747, 362262571, 543659872, 179028938, 579170997, 336015235, 419070725, 503730703, 535746427, 699304043, 200628624, 927713478, 727817425, 547564489, 468145421, 4133464, 636265708, 439391674, 714428971, 182913298, 417981940, 878774525, 992062123, 827139039, 513029032, 535293648, 843850857, 532885882, 939014205, 858293446, 46479285, 400000526, 73140703, 26932494, 865609078, 307075340, 603423853, 122207213, 353026459, 12658734, 369026917, 203782707, 462476625, 481922339, 479619, 198244407, 205189706, 628181064, 180376190, 84372409, 368770760, 554142694, 542983709, 207110326, 589869267, 135412727, 504198280, 22079371, 150854793, 26579829, 983032256, 877466270, 929084991, 498551314, 710830070, 741037931, 7616842, 424196730, 707450777, 82824092, 792195659, 448005487, 834909916, 728326018, 598714654, 653764889, 64993161, 252152643, 380242721, 723425244, 548605430, 936246969, 883719482, 277269277, 805903179, 600819922, 762366049, 838345241, 85269274, 780852527, 584347352, 743219695, 625277902, 616839958, 111407861, 328597203, 392192684, 109298049, 125833704, 210569387, 561410819, 398888164, 634083082, 295709686, 867755764, 371309061, 17854404, 440159220, 701982665, 172593180, 823677615, 664642808, 587801367, 540634838, 336465454, 855761506, 437362804, 757925876, 853824597, 378356367, 259019047, 211701426, 123096159, 139676256, 17522212, 102612022, 648328699, 864218700, 642386094, 977709750, 981977755, 614998185, 680525736, 781476326, 360843516, 703788834, 841629128, 199058263, 8042962, 904221880, 668028402, 166565743, 34694694, 367884111, 5193822, 400120912, 622123518, 73386049, 648965074, 258758758, 471654376, 771438145, 182435344, 268852930, 351733834, 864038618, 941533821, 258385857, 130057268, 181141433, 980772740, 758851052, 797052695, 68038475, 681476722, 158100693, 864360180, 932965124, 264197156, 605885009, 14839607, 49330576, 87053757, 584568357, 105457064, 495122156, 657370344, 18314956, 311055917, 304268322, 760968931, 242591909, 673232358, 863534557, 172668770, 579831571, 908121049, 368913390, 636005736, 329405762, 280690146, 713479131, 771650235, 254913936, 210552087, 928445753, 374178868, 269403729, 70076725, 657990415, 793243576, 625108762, 45204702, 757730860, 277328822, 53989575, 625583075, 215456836, 196885320, 459044025, 336556594, 867853176, 188738354, 659495314, 890797224, 901803829, 713885653, 824968837, 145313905, 262007654, 875686844, 310927421, 432571451, 653898364, 944516994, 746523208, 40826290, 535344571, 825377623, 84538257, 486695317, 173534289, 179977543, 432105520, 152633613, 336685204, 279604749, 350456648, 737057640, 841913751, 100395845, 73929560, 197003312, 874117379, 960471730, 579855696, 318671658, 771855599, 72697019, 996231611, 197547798, 979740565, 572877398, 601864058, 572200364, 606943061, 28218527, 46030173, 907475291, 827990109, 6726068, 978363915, 676547297, 961238129, 908746528, 512766604, 894596885, 484558993, 384075327, 355381270, 99284579, 346546529, 139377338, 855284628, 167931921, 728592844, 470247228, 720658303, 656867092, 95428784, 199449355, 768739012, 777678793, 958436683, 251202328, 721733443, 669251354, 578633896, 936962973, 715154642, 805652515, 55782893, 370302316, 632206006, 242354655, 204476990, 835056945, 775602408, 163754038, 879169823, 703967833, 824072407, 214475008, 641860191, 268754809, 216087289, 718032366, 142332701, 632853481, 702446963, 891709951, 731998817, 422552101, 81378710, 764833875, 42893122, 556507053, 172960947, 381948299, 651870048, 228997248, 94655805, 141953309, 526752259, 966780751, 54382969, 441818321, 708726472, 434822243, 196849113, 457855871, 716677932, 189649829, 785616454, 271650559, 608968629, 534823594, 277631945, 348892618, 368982089, 81278327, 578171494, 171163307, 605858308, 7658123, 252035000, 338412282, 352958728, 592577704, 543881897, 475567987, 951988853, 823947663, 605589186, 696664882, 733536734, 575029327, 144361527, 145962741, 948706629, 83278360, 998071795, 388423775, 268551908, 261269646, 456304881, 518717759, 511797652, 508760463, 270695064, 461753344, 939374715, 802428202, 329151151, 896919535, 497655896, 99197650, 390701739, 719739813, 941724868, 162937455, 627212545, 200955675, 467669991, 762222960, 20092694, 367033599, 852235456, 568585291, 672081508, 790601977, 538659500, 4910189, 304964195, 449232854, 692438695, 356535554, 400062149, 679154931, 101610113, 50419812, 989983486, 890225574, 448983223, 446086620, 140984043, 798152241, 223002946, 466758863, 571436833, 414195847, 756466135, 26271420, 31858256, 623823185, 535167443, 634117383, 858872597, 829534080, 609991327, 988180541, 694982124, 826890053, 438208015, 309668820, 573049916, 629584600, 127538866, 279336908, 406198592, 923366307, 907266738, 413203799, 634201689, 764939975, 770806209, 97311300, 139892086, 172488527, 827192064, 910239084, 496093112, 441201993, 497735624, 981966175, 370546844, 405062807, 349178179, 127040073, 693626548, 112380224, 571666418, 125497826, 916204312, 456032504, 7761186, 79519658, 642133932, 742781731, 415796825, 320269282, 505257783, 221395408, 553419679, 485970390, 499072715, 992206979, 116157302, 777525034, 161863411, 719984750, 896431964, 276648333, 930065072, 851036374, 944638175, 742438202, 332957063, 764847456, 213035382, 880749427, 224052088, 336367312, 725285002, 267142809, 108466341, 76046913, 884170691, 746085260, 251650795, 14678928, 231276287, 891621747, 564977203, 135436711, 842736871, 432553014, 127532906, 824822432, 294929893, 585498793, 301225972, 232147337, 873620669, 512151905, 251253832, 707766032, 784214477, 896418975, 941254593, 295805925, 18172893, 973721530, 247894268, 247581952, 94701548, 854148113, 95695244, 626042576, 621246352, 157336174, 205077955, 997585113, 350854897, 770935971, 619821000, 24196814, 407524014, 39099211, 439654442, 99665796, 376315825, 892998546, 606717552, 911685320, 313114622, 950381865, 746476861, 310808069, 981757307, 289368292, 124918720, 293515050, 379873180, 979865553, 198406277, 447224294, 986994929, 144244665, 831577981, 881605803, 812557879, 776702926, 336577920, 429324137, 519450189, 579590286, 577603943, 544339022, 410770934, 850270313, 175562519, 571394754, 121079984, 798163701, 375661735, 392955211, 289993703, 479720925, 730262546, 924086800, 151928756, 507624958, 625751897, 687729792, 289223515, 182044357, 115027825, 37371627, 671070782, 410012270, 413967926, 811183598, 256740992, 584507147, 682153269, 657065316, 587983135, 264805251, 894579924, 790612711, 251839421, 425532724, 908418620, 449954661, 245405846, 739928171, 479727355, 535125764, 605338935, 336500950, 74744004, 413905083, 478683636, 408636008, 485734405, 753096786, 156689850, 813343000, 640402878, 3535181, 787472952, 699818323, 765162949, 531747374, 540854872, 994123221, 411780778, 840237126, 242259109, 178711743, 572635599, 233754785, 151435636, 397352333, 478079435, 450452143, 704263824, 99386287, 9298028, 363657268, 746957255, 919091990, 235076884, 746770991, 106936348, 534380820, 837021316, 473570052, 591611174, 697377279, 239343647, 934476997, 559690249, 526806015, 855171805, 386238491, 195571360, 626362064, 683966693, 96304749, 321359528, 456730236, 755197914, 491055641, 676726606, 833071212, 53024307, 771392003, 240101495, 824260265, 788118047, 45317600, 888138347, 265989754, 768381614, 686487678, 880643651, 276579806, 728865620, 829573025, 452354428, 532913863, 589796442, 576223610, 894287703, 382021422, 268135238, 695681677, 487256214, 633111640, 210520699, 617939043, 121765745, 653112440, 403317800, 437029127, 147363346, 32609452, 805976762, 368133348, 675341664, 770254911, 986885018, 483825078, 558510489, 489662433, 576459432, 862083822, 460186208, 574862669, 584440296, 555660488, 218239757, 978902721, 416018519, 981019233, 354329165, 582792143, 261693965, 769805587, 632579098, 738986184, 370291507, 782253323, 980763129, 18533537, 983755178, 500526387, 797147422, 81631120, 622313918, 803295232, 451237892, 964971536, 526287144, 757584009, 765707906, 928395101, 928223383, 841059232, 121000150, 592851393, 845546070, 906830568, 16705267, 540546212, 982757919, 50973281, 246538160, 807601820, 580923135, 612214016, 454998415, 264485217, 359761171, 856294564, 734379740, 978143555, 599667248, 639015199, 340910893, 229865339, 427580556, 252651300, 655112807, 514852923, 142057283, 350552396, 276886127, 71063149, 565746213, 312419984, 136765522, 340376232, 114149069, 600547594, 445364207, 562235387, 581117370, 72279753, 378031850, 865804464, 340832190, 263423759, 704484490, 727839027, 189872265, 154727068, 767449037, 554258323, 229615350, 121830625, 591655559, 55827857, 446339301, 361638968, 201840486, 430271214, 151381882, 301866342, 804265686, 842593820, 213272929, 274177725, 892342313, 973921652, 95492985, 43746362, 728006905, 219015440, 227286134, 612826689, 656151473, 635984146, 864874211, 828308681, 195052258, 461018227, 492300035, 664588194, 902152648, 282711396, 379896977, 966453954, 575991070, 655214723, 100903574, 583389662, 88078801, 722253646, 476611436, 413507733, 952452614, 360416936, 305529697, 315712376, 399621278, 941955210, 363063775, 363390103, 817616595, 674113191, 985917391, 503521206, 29315461, 946415278, 584831861, 693242548, 982837617, 300538316, 201478377, 705038472, 777909086, 79184164, 767255931, 51913775, 558409763, 895494228, 13846218, 490954785, 241520683, 997148516, 841597144, 612613929, 351146621, 2113828, 335681201, 881045117, 573332255, 118276468, 677348934, 853283362, 544276066, 964807467, 678716356, 309444766, 834055080, 565989280, 379011552, 96619258, 856143607, 730392256, 387102201, 269618656, 572843020, 356263168, 239991725, 149150716, 756207502, 230864260, 582947557, 71702718, 738183866, 124131287, 719531331, 611848744, 662118805, 990829274, 917563586, 723065527, 241282159, 750383785, 244492157, 870728585, 519666209, 789039616, 597245339, 761701, 882838381, 749343000, 292844684, 396240977, 298575076, 273148390, 326938701, 682193720, 895846362, 844140837, 900079749, 924515657, 72577193, 342126201, 238450563, 288932750, 493612165, 684428621, 838967318, 777643414, 200242642, 202199385, 922200067, 775868420, 918740118, 286681112, 667747834, 437362908, 158809633, 318356843, 972332997, 659639947, 849187188, 9853468, 239144260, 29235218, 657281722, 256411554, 369308329, 457750881, 386384884, 713251972, 142214747, 179394754, 832431112, 479092275, 359627024, 498349067, 374443364, 306573058, 854199547, 885416869, 79570428, 735582879, 115600024, 632304816, 552462408, 374941812, 203533966, 768811530, 143218768, 486571515, 544752193, 683739561, 600373448, 586781894, 639589462, 432985275, 749578316, 709262918, 28996285, 552881648, 385916384, 882020959, 846861920, 958476042, 512665730, 997043273, 511288398, 432773377, 625365372, 671569741, 323440456, 382424785, 478417642, 432372440, 263120268, 92874068, 604233178, 276920602, 414863446, 558186636, 863317768, 569141703, 130051356, 553383751, 796668200, 87568554, 429638625, 254074032, 652796773, 4529389, 643978891, 36253820, 778820791, 905877978, 775937462, 489001381, 722140675, 937978843, 265737250, 335856338, 248161169, 28509057, 40030492, 597770835, 828167433, 934115102, 178341441, 610009790, 230999177, 723449242, 518813938, 170927597, 53979119, 492441006, 139995225, 932089640, 784480563, 932201868, 948670754, 930977515, 298588856, 981552231, 212421858, 232941731, 547764671, 688886622, 324855664, 772870138, 230590245, 912964601, 843717703, 875459796, 370079545, 193743447, 824708359, 368678518, 795927626, 259316174, 699299888, 732892408, 416933826, 718452142, 394944293, 230880106, 199810763, 773752036, 316316729, 267554020, 447727561, 469940587, 30071011, 752277509, 746587134, 402210033, 812375918, 590966952, 357431593, 669425987, 30603888, 494454789, 811404176, 526969192, 231344651, 8293417, 288755051, 485708142, 837909647, 134143943, 330432340, 877662376, 536578660, 716308157, 359504197, 645472644, 151109351, 297022231, 930673008, 465823437, 84902109, 886106653, 966374790, 858633247, 80297291, 396610961, 590718178, 48276233, 590139152, 77926215, 886959084, 257198597, 489921147, 843229570, 397933895, 535482356, 350857993, 402280224, 179767896, 310255426, 886760008, 867362962, 382972413, 708948534, 129527805, 751994024, 461940510, 607167165, 326349927, 695510689, 726228091, 231945985, 467185332, 637980536, 883925953, 908876669, 625830894, 526541373, 42253277, 553348855, 394576715, 488355560, 852995700, 798077461, 496452164, 184405549, 27631213, 833260060, 323367436, 613388453, 430145768, 831275335, 100528257, 669829537, 829381147, 26036492, 433656331, 244664221, 105731409, 159494024, 439293440, 691177001, 927886881, 558880688, 768949098, 720733226, 875077986, 115826347, 744024849, 24253618, 606111634, 830513436, 69478854, 357947434, 725832651, 490196295, 851122228, 498633594, 8064961, 711186675, 669108715, 200416743, 177395529, 792035220, 838908846, 529870220, 637696496, 787788548, 205180344, 720474998, 687110157, 15909865, 954191507, 379893107, 338164460, 437675712, 235690857, 454361593, 649258283, 785160398, 903721213, 24506485, 635747426, 48789177, 358083769, 620892721, 959403089, 37666789, 298611461, 522759234, 543209880, 138029511, 858907323, 353558179, 618549566, 126858341, 996009399, 351332761, 458187136, 927843521, 437818257, 632928001, 749915521, 924560962, 834679355, 606480031, 640830287, 525966148, 452722646, 834655482, 464428461, 751165466, 527257244, 384827448, 129596971, 772990696, 222837597, 927785858, 761027641, 57584477, 732831219, 752349686, 847660775, 535995742, 901607571, 103013784, 197789131, 198027455, 392418982, 398199114, 293629309, 86104703, 178500342, 607566749, 899123660, 346072892, 343773781, 904389346, 106856930, 711982752, 573042531, 211660564, 214152083, 757893636, 26644069, 345149901, 64099700, 583419772, 938871244, 885471394, 210805774, 252794491, 972052642, 196047784, 199349164, 391785697, 938272653, 163092495, 261593225, 81258106, 414632129, 790811962, 839934427, 69947310, 12593935, 329217006, 26225524, 929123565, 121863496, 747754577, 840290803, 796375643, 296153578, 72482784, 465889261, 352600643, 630942925, 163668371, 207513289, 240386659, 259948558, 138350602, 93300586, 690834593, 546214070, 43159143, 929762280, 778075546, 423764416, 928661929, 846047748, 710249953, 573502245, 203554904, 943042256, 337467417, 585996627, 453806983, 843282735, 401859555, 599552627, 966107919, 62382518, 715434079, 648639233, 977635795, 807743770, 96854359, 975520210, 118561201, 855887780, 228659867, 845172092, 378694948, 756034278, 366177518, 724243129, 484336806, 520536274, 380088158, 597371844, 563270615, 750338252, 785329953, 253354614, 907771131, 893459253, 804530142, 882194288, 359070463, 338234278, 107961042, 519838258, 183852379, 65156270, 416331369, 856328686, 273859488, 98892591, 296784789, 788570652, 342778687, 542675977, 580672885, 275322258, 187877474, 448630918, 82458126, 987029974, 822844787, 156004415, 171344911, 219184907, 615850785, 155618397, 863663881, 539342044, 221257849, 321638357, 133842966, 889252620, 716463185, 620227463, 864180442, 768818664, 112961522, 880859051, 607541536, 748216033, 917348826, 100449066, 534012763, 41131063, 387426391, 41131549, 457325764, 296397796, 691943940, 384268490, 880064598, 255900122, 281144472, 762759814, 607679373, 348798876, 582684885, 726010886, 755187214, 109675553, 196106436, 136427051, 444091038, 238723644, 734790106, 836955134, 632712404, 928520278, 804166017, 53732783, 643801288, 668717396, 713947865, 42926925, 27284041, 433527222, 559409653, 319222639, 507978331, 96997509, 383628607, 485114135, 179645336, 217628509, 153979979, 684661420, 358110671, 88969439, 945436681, 620994494, 713695100, 367996619, 617985051, 485671926, 411311734, 263662072, 309402046, 365571681, 518825031, 725025794, 106274994, 257243039, 339073066, 856880752, 241099788, 77647896, 284891500, 70426411, 423992114, 693698071, 97237482, 540030537, 986784637, 305682110, 401356189, 577247208, 749325541, 838990545, 554174551, 174090104, 329051919, 553404479, 511247142, 175428601, 813198975, 724778302, 255629980, 408677893, 599555191, 265674183, 428219256, 361954225, 39583609, 345209898, 323956872, 286053476, 482343428, 580113904, 870245049, 792769699, 760248826, 488537239, 849814242, 173373971, 261223058, 387894663, 689267879, 3396297, 525922710, 934089958, 84255851, 415513480, 99927995, 271660144, 215888196, 74074580, 403671020, 146791905, 23383816, 709346609, 750926671, 752349985, 864713893, 698465048, 891345893, 570738870, 701322581, 432049711, 453129299, 526230029, 52916332, 145495373, 835339448, 294236847, 364975605, 933306148, 875658776, 122801809, 155651500, 61118143, 957744542, 936305349, 112135580, 80563010, 167340139, 194845717, 71809109, 943409895, 606140720, 562806049, 74640241, 988195753, 634718868, 424117256, 2347901, 588631659, 363504482, 552696463, 474042911, 788154299, 162864101, 164047742, 266892662, 742015651, 102924081, 235324453, 507077598, 238115929, 878317149, 829777437, 197706637, 629141982, 563645090, 573814216, 630532458, 579242232, 597286121, 679919573, 395694932, 11397510, 822212276, 133514141, 303980944, 371882828, 247275763, 395068995, 359645849, 864823228, 514426458, 851010121, 389795733, 109633470, 775716368, 768735834, 652195701, 37488111, 328516579, 653173753, 25941478, 140649306, 649443206, 424955046, 753432972, 63193556, 913402064, 924587434, 986727538, 213696106, 999443457, 825106759, 869832372, 782495847, 284477591, 552880683, 666288077, 812093552, 820130978, 977162096, 392270060, 435941714, 812082044, 620262747, 680040496, 706046172, 819096205, 890037557, 872879652, 584827786, 498992363, 403866714, 75094288, 787208234, 276038463, 336438088, 366937752, 686196365, 287398310, 87590654, 215764361, 273805552, 140045439, 819137444, 300623786, 714817780, 73474220, 913830231, 873451617, 683894181, 707168056, 418994292, 945012416, 398811908, 92776778, 547431996, 816770512, 740297546, 281545844, 228360459, 480245523, 867622341, 116918754, 545976060, 506342895, 136307285, 217816559, 583819045, 328116516, 534254772, 605831121, 984788393, 649529062, 671306911, 164108016, 586017063, 215764167, 589548507, 261052570, 688887947, 9818077, 750244626, 850913858, 354137735, 988052783, 18722694, 901970747, 570265941, 24565998, 575376838, 120226663, 693236349, 504024854, 187002771, 688662615, 319639972, 496033462, 794790116, 534764117, 224629244, 776648010, 448653974, 541323117, 30517724, 376634134, 784732472, 649877103, 942500074, 296523965, 668861307, 721931306, 536326567, 569708049, 1566966, 319101118, 504067937, 699096980, 850510000, 299585846, 837954805, 768190302, 843841566, 443953946, 98121215, 4908962, 112872374, 684113028, 101831955, 344062399, 861331562, 863256995, 780593114, 764978981, 417720048, 384988742, 260270190, 729886894, 334729786, 134608672, 144146049, 403783027, 251203262, 746703317, 613211162, 271614460, 433097652, 586255066, 602399977, 40295187, 765826993, 362691995, 197502442, 870453789, 62362106, 855081159, 844436002, 435730044, 312403215, 223427065, 49873143, 896904327, 2342153, 521806040, 943880807, 847779253, 370566870, 31938760, 323204774, 952357305, 474187391, 989706548, 407479590, 59005963, 904685512, 779517599, 856379682, 406453270, 512366196, 274732853, 999149410, 637470284, 579598700, 470571016, 21758437, 928369826, 460786326, 495594648, 126857862, 635719301, 325601236, 820009842, 153357873, 746610568, 307349224, 392468222, 703012968, 222813311, 709073629, 668132804, 277196569, 636009502, 553780343, 721510160, 174663883, 41853991, 264705115, 695666580, 507298996, 236247944, 632302062, 449429224, 526292323, 363761000, 386884378, 982318253, 835017606, 608095545, 904901300, 200743132, 701600001, 389944478, 339761422, 946264079, 15356580, 831210727, 592914280, 644013205, 187268727, 858299727, 828985921, 1372943, 310211569, 341850149, 639052181, 895901079, 999123407, 209874292, 626137427, 529888343, 492441905, 878974555, 353183936, 904475733, 802271544, 839064190, 763541577, 987268828, 350895703, 545931256, 243793436, 402536458, 416376065, 370175733, 882646692, 563808192, 169621561, 424355774, 208960658, 761043268, 636782377, 281968537, 871268845, 149499454, 510708406, 835673382, 896410393, 899023027, 155135281, 950289484, 652653874, 476055598, 164062438, 74425368, 379974883, 530452831, 517636586, 940347489, 559699047, 310063153, 958660236, 714812053, 675987472, 399191827, 804130950, 400229209, 10220646, 326508746, 770419741, 75329810, 539180346, 712369291, 5663874, 856258011, 316568476, 605288650, 986154435, 642718347, 603696769, 737431647, 938189478, 153477720, 72650991, 58961813, 355546877, 195758483, 515639216, 912696512, 765823299, 775316716, 433820389, 550026806, 720489347, 994769848, 660364685, 522759006, 5395350, 792560882, 223072425, 906535256, 628657753, 900816908, 206992543, 339900342, 782671071, 136416944, 202909920, 986606497, 503539440, 925292794, 952065065, 17410347, 647828592, 353115253, 740403719, 296756580, 123405859, 11985581, 905074295, 232199059, 323910773, 713010752, 415405310, 647483927, 808341987, 816876421, 47996940, 556114397, 600872578, 429800149, 147992232, 969853116, 31181429, 659446935, 278026256, 914043974, 822737684, 491685049, 832656042, 479348855, 215601276, 439410574, 359030064, 864027025, 439188979, 541458695, 142719501, 584684884, 826623249, 419766591, 186805577, 961025725, 129716907, 445344886, 232184892, 329191603, 94231161, 156844334, 700940076, 308454700, 557771707, 60331659, 961503083, 699645548, 460535046, 785568491, 464806674, 904396830, 493436186, 186814067, 302015248, 59511333, 770068384, 965578614, 169109416, 207112189, 361964701, 22985890, 778182105, 656447422, 585142139, 970288682, 507476774, 495338254, 321073107, 125451049, 884569493, 502101160, 768903283, 837524695, 578426669, 261893209, 185432458, 154682311, 345671068, 93759586, 2087734, 943389717, 360824346, 3756632, 298170633, 428148185, 680407721, 814171095, 568399900, 462556909, 579943388, 289369542, 414022249, 123243805, 902685896, 722359004, 121430, 748761491, 385789976, 10209741, 890773032, 99020772, 788506484, 29768911, 372370195, 573118353, 71349775, 57559716, 135387307, 968528251, 875735342, 732054059, 828465058, 997006187, 559840258, 740194092, 509125705, 668974094, 741254146, 754120893, 52546360, 208858186, 773274610, 792685640, 778475828, 350830055, 288491264, 553022410, 857223777, 579666927, 932474985, 401159647, 846319379, 225932562, 319425366, 15378021, 15542200, 222569523, 217897611, 942050136, 472802045, 805557994, 502138031, 780267022, 707434009, 36588592, 610858310, 960359910, 961597620, 236337302, 350532792, 9479909, 659072616, 558608329, 610256223, 272084305, 476200070, 950105698, 995318981, 746880676, 458574429, 918395518, 231991487, 576277395, 515731897, 634179366, 10082505, 875563409, 864355021, 62156857, 872336917, 273993146, 10745216, 609172670, 967905110, 523936040, 92961766, 263961488, 455834944, 794033406, 677448165, 560476864, 689750926, 417025257, 924725894, 231241896, 504426207, 422710107, 16396416, 932706884, 812702000, 806404015, 951825931, 701466177, 701066624, 120142545, 851167461, 69932288, 434507277, 46451684, 925211081, 579420560, 234873694, 480716265, 959647894, 396014448, 998573121, 194458321, 908322783, 494890180, 359701303, 271039195, 119422054, 271297939, 846128755, 383523997, 380778256, 972080419, 150069145, 389424885, 627810778, 420464325, 665615768, 460336056, 626652508, 737667039, 448282346, 562709106, 31492570, 483483590, 189550460, 165183778, 343767875, 567919591, 112306373, 790069562, 518116586, 514850351, 245880502, 312488441, 884193058, 133932880, 332135446, 372387772, 162168865, 969692717, 233922695, 63071794, 628533781, 672416228, 580198259, 483386985, 517536892, 330587148, 131683088, 702105790, 503558956, 840033705, 864989288, 541113786, 426211952, 8458208, 42884423, 77502239, 106822208, 813380287, 445828010, 589881010, 345608675, 188448958, 960711908, 632534373, 511628734, 693037183, 62539512, 23446774, 17854434, 796943653, 511973624, 1660243, 347241489, 266314353, 717768371, 614484938, 850261922, 27357113, 29029923, 570166216, 225131066, 703886138, 929840747, 122257127, 18209399, 143727134, 326820926, 692639481, 135938737, 991443419, 90906615, 844171608, 580544868, 743773058, 242940773, 122147367, 509035863, 816118670, 649188265, 460280776, 415811256, 188273632, 64199211, 833736244, 37513865, 616653811, 985081368, 892839815, 108321157, 201486455, 669137292, 671180886, 701496573, 539368506, 295619818, 454077668, 119017120, 81179241, 336039191, 811489071, 386180248, 364633360, 492683576, 810109618, 854490845, 850585611, 561688654, 741400592, 933001164, 350836133, 551515276, 477410853, 309534319, 282432534, 647950272, 237788439, 635359669, 284618688, 132922920, 313113265, 463529770, 352768742, 992780315, 9174440, 46625884, 325177683, 206088815, 104079020, 957318072, 215634933, 870526397, 615591366, 886461425, 469285530, 228717852, 945467210, 412478884, 457170464, 874931156, 738365034, 258764616, 350180264, 960651502, 625974248, 480231615, 89003849, 55408119, 374487090, 1960728, 964199304, 668779031, 312663138, 321455760, 708037356, 670710645, 946219497, 169077229, 923243718, 959648870, 660292897, 431209152, 466527259, 301036491, 514621476, 990185820, 254190832, 33518017, 501482036, 274412437, 21311095, 277249510, 169769927, 569909625, 370473533, 920949017, 624474338, 867031091, 924073158, 970669853, 512375537, 804813824, 899950831, 469158459, 921412879, 123969024, 839160895, 299996467, 661993522, 994337389, 568958425, 316497412, 549100635, 938132567, 398107189, 106494703, 123453903, 753255416, 32383529, 71053937, 830483691, 752035653, 1936945, 499464628, 904791512, 323374430, 813507358, 7726640, 507498108, 215948565, 43282894, 581396375, 374363815, 833994669, 742223240, 208176321, 770820597, 356036635, 933182413, 625821654, 333061118, 75386225, 718772920, 86520334, 545972220, 605834149, 685436991, 835009645, 345413347, 417629925, 486755298, 423548985, 945904657, 273880921, 762967379, 374162100, 418323179, 395379971, 908086425, 293524081, 173018994, 908234135, 493429651, 147073841, 609638513, 302209453, 922057062, 359456043, 879922463, 79035287, 149373233, 891742621, 537543771, 11092256, 503523287, 685089262, 474555764, 215228684, 541902057, 442016444, 4019283, 158700661, 923528206, 558994633, 424354725, 737664763, 293375026, 465801472, 3318609, 22412915, 115750586, 987697007, 391772360, 883236460, 709075523, 547128862, 139546388, 326059763, 798967910, 583960558, 260416370, 304380166, 40209142, 868612310, 679884906, 632137294, 999006732, 219910078, 416704959, 577878292, 310105899, 562780104, 293093956, 555485800, 320353362, 88359680, 383148655, 930582706, 582713554, 561042800, 119760680, 147032946, 697703766, 924301452, 889944832, 875288538, 748462973, 817430984, 346786393, 82633572, 687820032, 470648186, 574470218, 996205877, 377896267, 76864730, 454248568, 835513032, 794710329, 603923878, 581744523, 729587908, 899205155, 838214886, 66129912, 526015524, 139415075, 939761951, 745021137, 6552936, 232239071, 487923490, 282582754, 140887890, 744828461, 636406289, 39452632, 32585266, 350601966, 898598725, 644432587, 711275470, 401193589, 587040222, 147724482, 899149277, 217649986, 7881790, 561374951, 921219042, 788329782, 262995523, 668264422, 884804435, 411357735, 842459171, 74734481, 143702830, 944626164, 584006151, 723274350, 845856314, 212493627, 396753522, 779609006, 610027570, 474061641, 288812381, 116219676, 950717842, 614825205, 576347056, 508085928, 791855348, 377696391, 27988049, 954727748, 851581484, 656590760, 615312965, 612612931, 607052525, 362550457, 667061303, 855044802, 363712574, 964748589, 776410804, 619843163, 661967159, 45868539, 513827848, 89610023, 463433732, 854749878, 425975124, 288142771, 398052019, 532426391, 611975516, 21705804, 655471979, 465805330, 52126396, 735533395, 948633596, 965138982, 94716937, 490230855, 638341912, 464137950, 79594343, 153641834, 129919091, 505092817, 108095829, 768491705, 882068120, 314141661, 589604649, 919395718, 974015679, 998293613, 108767746, 45958469, 17015055, 89255688, 702416247, 844854338, 515807416, 954811889, 867612873, 443170227, 696670935, 107287508, 256502092, 214362168, 458743609, 900791395, 687518594, 482092050, 961462722, 920747184, 589402920, 459968631, 634415911, 426965808, 44346994, 365608533, 873665995, 528599665, 915805595, 522968925, 174367691, 582573072, 391209460, 339580723, 697485317, 791387213, 40604497, 980411052, 871918875, 39697104, 880723177, 727589003, 997090745, 47724679, 486481655, 316510105, 736022871, 447640199, 229766441, 522976336, 161072455, 573205780, 270560906, 189815650, 369931695, 142246802, 558293791, 831702206, 947116247, 349675379, 891200963, 814668224, 869123986, 469841455, 894306024, 543517499, 244277026, 892705971, 84874982, 32168210, 508838558, 75923562, 790903426, 294456825, 45530817, 773332621, 81099327, 938988242, 529282332, 714835223, 347483435, 64452069, 934924650, 861360937, 264474420, 235091635, 473870955, 189303961, 305618105, 475995560, 752714221, 678157459, 62428451, 958007217, 324656477, 854152119, 327678229, 626472724, 466456034, 446212762, 207345475, 784261101, 91628654, 777539356, 5908986, 590266889, 708333041, 596762356, 893388921, 412807023, 430674113, 766606145, 72960166, 715832622, 131360945, 394073901, 762307877, 924081548, 12192880, 753486333, 128716190, 839223028, 201002265, 683166992, 420240289, 397542073, 664411492, 733765908, 232353993, 958386008, 870002439, 296895476, 691351168, 961619833, 854560590, 777758272, 526631646, 481810008, 769128351, 903883856, 743663387, 118717893, 979494369, 491606873, 194080085, 900703562, 981684348, 831786058, 224483471, 648603684, 899182506, 904256255, 132139831, 370912774, 208337422, 598966416, 961486465, 728652034, 884283185, 32193326, 86465783, 396099661, 387096559, 567232172, 48561037, 552519901, 870910130, 736973556, 693088726, 780585526, 92447474, 234126125, 642280503, 632997328, 424217859, 186746443, 658938044, 110704560, 39604829, 452838366, 273087717, 288618540, 260647455, 577226034, 120338516, 311424339, 814783006, 370516400, 692382426, 780415300, 286074983, 864718134, 756981992, 178018439, 390495024, 302192140, 429391105, 880437085, 233239042, 675171045, 456855548, 702009774, 321718293, 205347987, 407074151, 821908861, 619874843, 402401308, 13596934, 905996484, 275634244, 706257532, 867550399, 232616329, 334919801, 513872488, 236232438, 705058435, 407812824, 184968182, 648528692, 672974917, 822083975, 462670069, 119346145, 501550199, 512009335, 236102315, 869529336, 198610960, 534594135, 607296974, 989781088, 962044943, 692821728, 403948549, 644578728, 343740146, 587002124, 308903028, 984023112, 837443123, 470391871, 772610545, 126522670, 686277750, 250267334, 618201702, 451126038, 880011797, 947088248, 261036184, 484551532, 321113294, 189466420, 256746588, 946760889, 845759000, 79541145, 797949892, 829685687, 27871240, 910024992, 186075914, 959397314, 132761847, 578724021, 232875247, 474833064, 65958179, 301205556, 466237286, 162842224, 673848515, 920364999, 267343835, 78245226, 137577656, 984680998, 87860886, 794688742, 696533307, 83028599, 472844167, 812894716, 760457114, 558044161, 70696653, 67938471, 164216664, 52731757, 69655294, 526876510, 45121267, 167886388, 960711502, 148186371, 373272605, 443690307, 78029979, 255511044, 440907506, 473811877, 61350531, 284357057, 688946012, 97462154, 324745797, 754948357, 970647251, 223579094, 579364243, 647346161, 510740952, 970257450, 409825670, 934767069, 778221004, 617132070, 381328017, 102017509, 634298269, 80247832, 977354757, 245373831, 736097326, 836156089, 643783558, 984965546, 406417065, 115304155, 209268929, 398865683, 521731308, 489666427, 325015189, 723057274, 813590763, 93900132, 882904650, 768604618, 297716884, 268161410, 470152329, 770061657, 28454420, 927119836, 308077135, 287625417, 364351011, 422883215, 417042843, 554299493, 855164678, 103061724, 876560452, 836960026, 230013227, 723329863, 836832832, 317236576, 181855355, 532169448, 168018599, 194626148, 785032330, 491368709, 31086564, 585801173, 955845904, 877862538, 323824068, 485220785, 109002597, 120144860, 136036714, 783940990, 196379089, 981895364, 891620800, 307576176, 468260365, 172709910, 965030130, 187661845, 540743103, 270104205, 476261786, 427407206, 43099955, 385519187, 579355310, 931703169, 452334862, 292890241, 828910589, 109061134, 595523061, 790786166, 359888074, 693712366, 137877462, 302533005, 806711258, 474337016, 196121186, 22596802, 685616802, 624416393, 789189998, 927958211, 33424249, 958090756, 229527197, 549636481, 28722855, 236040527, 629233696, 611746656, 901808916, 254232292, 337962914, 461669513, 417067485, 629554184, 304984283, 338249709, 658076372, 979113545, 932999739, 587728607, 867664171, 630193875, 383384507, 744242553, 571118451, 657267577, 15480770, 921448383, 532178110, 531498418, 709102513, 478079892, 712905102, 967107567, 887048171, 342108648, 669371768, 417858336, 709733922, 404002423, 990542159, 654989328, 617929516, 553066013, 193558655, 458947544, 904839348, 302226479, 648606920, 979390301, 586936597, 49054229, 218535926, 811736080, 192002852, 102087691, 774093919, 622383934, 573980173, 269746643, 29991811, 252665563, 706415447, 293388706, 480286700, 671167998, 630478240, 975520894, 287295947, 446318360, 359470573, 569640314, 322522167, 622265103, 739319095, 745701199, 102510055, 887475444, 653525088, 715651175, 440186634, 750603908, 762237398, 987799332, 358669001, 857541490, 753847489, 642775326, 778227475, 357191066, 2407189, 902878687, 57199604, 689043255, 955535146, 108574322, 409681345, 627465531, 869235679, 421335134, 155633150, 813770746, 185159007, 359470954, 406469836, 461431503, 622390959, 880274209, 814553050, 787639416, 273895743, 19884772, 967816742, 536773417, 692731340, 207626197, 249340210, 327446501, 995242291, 965828267, 57620022, 50287427, 851008086, 277234616, 261616682, 773457611, 413141091, 214836151, 185693232, 767513205, 193833357, 81136524, 460191867, 171457078, 858339248, 762476926, 948617816, 561763884, 153850043, 709467743, 24086144, 299996937, 973860038, 881356291, 326352553, 443620794, 772273541, 370987241, 205469758, 680962261, 82724141, 298608385, 937033670, 310076899, 489297858, 345590444, 447879203, 423810194, 935553213, 552773341, 892167819, 538131808, 169008269, 556174282, 989318981, 495041915, 738567955, 11051833, 477395738, 814061508, 198488098, 303212811, 715372176, 769502230, 655117530, 604740028, 567396579, 990068245, 257102951, 124193773, 25787815, 466758572, 281961845, 205057337, 896964619, 211731888, 906610892, 101211009, 508285921, 672868106, 392359849, 35195822, 914895285, 883391557, 778111240, 926131450, 353729397, 525236003, 467554805, 33404374, 821638195, 420634775, 532499639, 990679527, 275282799, 99180736, 275608512, 896023728, 353640894, 743455518, 342040096, 849154546, 479273416, 212405061, 414566780, 254083479, 927681605, 41049914, 609939861, 79237546, 777896549, 941128832, 97791358, 924592181, 299873212, 529429681, 817354240, 503840368, 99448296, 493134631, 6885185, 937476333, 462726403, 983263402, 86930555, 202217113, 603779233, 524973265, 405383974, 911102210, 22452567, 303420818, 90432373, 591168781, 632709307, 407452552, 73960574, 76615808, 880514188, 734230164, 778713946, 515020281, 72377740, 83496866, 992753020, 525913557, 2093640, 610939829, 38344002, 447372354, 638195162, 16660958, 121403183, 949776221, 551176826, 892819572, 428826742, 387479432, 797392705, 189206693, 834683583, 906113991, 536397382, 712951348, 21458099, 286505608, 144861903, 177637613, 395388951, 943159326, 372864832, 362630968, 111948849, 122344374, 670147933, 768362532, 18587688, 620466631, 802655608, 428879680, 232523594, 926744339, 369930068, 983906680, 167796080, 454554358, 134382008, 452483109, 189057923, 109831637, 715568116, 649306011, 348891761, 681966771, 856221780, 22060550, 706899, 269863653, 963177190, 309924100, 101310241, 516100583, 34822825, 186971465, 176169728, 891757332, 195017813, 723811898, 235300878, 182123291, 351894705, 975289636, 555746340, 518074107, 949450240, 307967536, 949375002, 352166447, 82998965, 422142107, 935925977, 899002335, 304439943, 105909155, 936514426, 53929951, 932416519, 81517091, 503779714, 34123452, 195444947, 61850243, 168533451, 616370423, 623981088, 771792635, 902466331, 425156494, 145991807, 15441962, 230119667, 595729082, 555485843, 792397514, 36206209, 510349624, 890449064, 739438341, 4757924, 752248106, 926216804, 111060372, 794172031, 689524697, 301907753, 855003751, 325962497, 643730347, 676705149, 126983754, 393884257, 895861942, 290380463, 473759791, 901875069, 859832944, 141437648, 872224071, 245725313, 860888251, 689392876, 786466075, 235834589, 184489494, 675694603, 102349506, 826302814, 100225002, 34398985, 174577697, 22767812, 56178237, 827226525, 385383460, 648902953, 632478463, 188427667, 119979958, 501732383, 799723639, 910291867, 722567280, 309188479, 175682078, 939607097, 837522517, 735424083, 961901704, 705355349, 496961041, 297883443, 44779246, 975533211, 404868117, 438260458, 423780221, 382952267, 265547020, 205090589, 669348972, 618319271, 710375903, 385452414, 64898165, 66202067, 629445427, 354472116, 202148204, 705326601, 563864185, 851039856, 278120412, 160495780, 763543378, 962577368, 723857424, 855810033, 326496982, 477279337, 524437371, 533689243, 895129137, 142153064, 198798511, 238008706, 366359797, 544343729, 879607889, 588615328, 306126683, 596773421, 708404102, 495400268, 528629936, 514915680, 422971170, 169417639, 433529269, 232197246, 302341245, 465452518, 690708649, 98840167, 82780958, 481692443, 866100781, 936710178, 257200011, 769156970, 930368958, 354434993, 165891451, 856449825, 735453482, 212595512, 52490667, 237996394, 251610577, 131883269, 658606444, 284203299, 990788003, 990443448, 662611395, 496263920, 843100770, 173074355, 682673766, 992169557, 723560930, 997505653, 221945393, 720172440, 750203316, 532056869, 261409517, 674894055, 8281486, 950083598, 561567742, 705542104, 603104293, 36625302, 282028353, 111836018, 402096645, 256376816, 724178197, 534408803, 197161675, 417140877, 66021011, 13871079, 142006862, 382397126, 372678129, 900622761, 979488712, 883538954, 146141136, 992037399, 940085732, 81450919, 34738385, 617690481, 611872320, 342616799, 499417603, 940771935, 823548276, 624852964, 770731074, 864730537, 920291644, 206892658, 283618714, 984324735, 696569932, 281921452, 682822724, 2795194, 34810474, 222490679, 961546016, 991819821, 855125163, 880339363, 517488829, 791528584, 749027990, 792566233, 769911885, 723789195, 404376358, 212689279, 610199926, 364574782, 291635406, 26163603, 682867016, 875413436, 382178577, 953956264, 958721727, 676858449, 345502209, 976529581, 200218275, 175581840, 874812727, 251398992, 403252093, 875169315, 129779719, 330388847, 446643431, 665113210, 152941233, 317146098, 813243727, 582157270, 107477229, 823832434, 536992229, 250734729, 952250109, 611959332, 917921866, 844658586, 522874907, 735358626, 392565517, 128246887, 671219261, 231324543, 816176624, 822431600, 439409188, 812122073, 225550610, 99320405, 811877578, 159536767, 31818105, 176597298, 481713269, 107329749, 665108604, 601030234, 375907162, 741775157, 914292733, 730797841, 516785669, 639790066, 249120862, 497501951, 970137697, 442079827, 486569637, 247646436, 922699253, 132219861, 985956821, 347174828, 117894314, 12686666, 584546283, 489802973, 85456780, 365969648, 421462787, 945980925, 454099501, 270905241, 578628530, 116718721, 237250634, 251503819, 186670007, 558534433, 158041951, 127942755, 574817521, 92149688, 378373628, 678877240, 417008095, 2526207, 15029807, 810502152, 885501486, 646165360, 180092205, 907311749, 808499453, 637890286, 583238084, 222752945, 337030627, 5304346, 212634516, 178057209, 137449738, 941812020, 278729643, 377995705, 638582856, 199157688, 328677867, 811334644, 621891679, 506939960, 714684272, 271463928, 792478894, 377252730, 839991211, 747202265, 354044508, 680281853, 911402325, 995188298, 452885271, 861605340, 534865357, 293795026, 415085564, 830575817, 269568158, 929045668, 551739070, 587253212, 138494099, 432439069, 518199773, 499244291, 342489911, 513497367, 945724216, 490095681, 862629541, 268390083, 244037632, 654571641, 971210629, 828816383, 371676373, 854374569, 2869277, 388777822, 315626881, 187614999, 635646108, 885887990, 626717155, 165786258, 20599600, 674058504, 302410008, 993938880, 980213513, 57790096, 396592703, 333278168, 872593392, 55488766, 732878777, 542014469, 11468969, 648818554, 862291123, 879916599, 711022849, 329675767, 35901718, 911321791, 137412405, 906347224, 80634320, 256432804, 51522444, 243527183, 308460088, 483166184, 617060655, 205814466, 685840867, 399014135, 154822264, 233014577, 814869690, 299458436, 435568159, 467161225, 429544245, 216424621, 363644283, 531746539, 705512708, 37928949, 853653392, 954345158, 172994014, 901746159, 536854191, 379049000, 337733685, 117906935, 228936283, 362518951, 517748704, 984834065, 68277825, 310009757, 748634140, 621018932, 490686775, 787240081, 253217229, 146211032, 235998382, 600594953, 368357038, 628390342, 426250316, 373115086, 471593720, 915905440, 159497932, 383469235, 6468337, 300793392, 669302956, 724834517, 276521188, 353860599, 862887760, 558926611, 860112753, 729148275, 573618883, 612107229, 574889468, 271446905, 62524775, 283652102, 33338281, 260452490, 358370265, 596857509, 52979516, 359689314, 195835867, 6619121, 202910036, 304426560, 786469291, 842697200, 935629786, 917978183, 819751326, 52882003, 573084174, 521561474, 655884102, 127963562, 509193377, 538383740, 743729651, 372262289, 894297929, 767148921, 100802334, 741186734, 286686576, 686263711, 42014138, 55050538, 362866173, 672397011, 104489291, 483090117, 535789899, 106774516, 753322394, 141066064, 171569897, 764202277, 957267156, 53004148, 300080104, 483361232, 110074521, 337782114, 208327892, 706680373, 846581444, 870631560, 766141469, 327934593, 781629719, 923444372, 539522788, 693843671, 688045937, 558416481, 760394345, 556117394, 24624384, 933632268, 486466837, 493444902, 615358410, 54936404, 977664610, 603170610, 371422861, 273726529, 388590030, 354123509, 852994581, 641381817, 36537772, 221862024, 971962572, 224856563, 616189961, 772434268, 372924159, 200009835, 906134615, 49420985, 284641378, 878461777, 712231071, 703866115, 769873013, 656126363, 456894889, 638971732, 165274267, 144925967, 155470202, 800340758, 399262268, 640714023, 219669411, 874273032, 564891859, 640826567, 388464019, 773042360, 177646473, 747448653, 864527343, 915284205, 760598877, 841672427, 385694550, 794524321, 372153736, 225950158, 10701377, 787679039, 205928828, 254882384, 842287878, 734159049, 365291092, 701401208, 948825540, 795037996, 560710245, 447140723, 768422441, 842075531, 434471668, 522530934, 108648300, 83896146, 324766437, 491917879, 663038118, 475644313, 215039367, 962916939, 461580376, 40379745, 495218671, 682745319, 284069834, 792819469, 149115036, 949223458, 739249098, 435596598, 338477860, 476243182, 801609340, 424628122, 262457868, 15934341, 254096529, 978402953, 423935479, 689644008, 639974467, 270084537, 976374796, 580417004, 195856071, 286254387, 638027332, 944671904, 23403372, 43615334, 31296647, 122821281, 821800358, 933743955, 33029713, 696921644, 157258897, 548523983, 921245975, 381037536, 590522620, 638732044, 404589832, 245292619, 317092398, 442336393, 451696173, 608917625, 273937344, 155228634, 744171917, 368896844, 710323045, 19127964, 561417302, 112630192, 591000058, 295934237, 211855288, 550415625, 523708585, 288615266, 940615312, 564922165, 947632132, 789955743, 466643611, 23280546, 407972314, 382458346, 719296642, 705010024, 303797864, 49024495, 117099454, 966991442, 715688799, 364912007, 849445654, 46242070, 212571519, 17852092, 97098161, 366639947, 532780218, 836671222, 954990327, 410192345, 984184240, 232119842, 948368911, 851453197, 505855443, 138905267, 937745585, 61619128, 722981163, 380851000, 393603395, 567610653, 590979738, 195980178, 926384477, 982788821, 623972193, 433183152, 416758874, 59440471, 644095890, 826905916, 773734007, 317570183, 384107287, 269730941, 59580786, 156958716, 857326074, 674066720, 227076936, 446446917, 451530867, 60414125, 309835870, 84768491, 885465319, 107317810, 998059621, 553150046, 534414351, 314473380, 106407765, 340935174, 250396294, 272018724, 628784043, 942183150, 59484174, 158731507, 159867528, 977558259, 258661424, 284417508, 384872119, 973602246, 572048636, 683095150, 147214583, 70005093, 986039017, 374792464, 970910853, 858271677, 111162411, 182714050, 440331783, 302236798, 103806354, 275234449, 830175676, 113125319, 509594188, 640391253, 143356463, 561842589, 588875767, 496178274, 356916799, 389437263, 742656768, 967991926, 567823143, 189235863, 291227893, 661708015, 986312762, 602418279, 355058743, 111662131, 271939823, 425547858, 678012078, 502853605, 963117209, 47872358, 170283034, 707915402, 94092180, 150340294, 101809703, 587779651, 718980732, 924281151, 145345923, 649360238, 471636622, 732802533, 561443503, 255762077, 310208874, 26675667, 315316371, 692846619, 663196980, 706761706, 760239090, 462497832, 461463235, 685094083, 848688834, 453537354, 208765702, 842978652, 425802336, 419525713, 641333403, 606263425, 309188327, 932729601, 394982417, 558398467, 688930700, 323966397, 800636683, 534780685, 73609921, 25424632, 635777570, 830202001, 745951135, 521234131, 328828021, 288037277, 923115308, 229311398, 11706556, 431219124, 888795225, 451732703, 904506959, 238489949, 58625107, 14266884, 847481585, 281787457, 51506424, 188648674, 643834131, 665072711, 776981408, 598610086, 306634814, 845921377, 561067049, 227754108, 918617670, 394191717, 792935146, 853330001, 877291060, 488049098, 686646812, 756281901, 956416453, 797979234, 958384397, 799694888, 275754440, 819365265, 861760012, 544184076, 481224145, 171546998, 848755816, 509116060, 146984606, 538497366, 667920810, 687001732, 921631087, 955363037, 463225506, 848202417, 749746887, 397250619, 607839247, 916129362, 565748590, 982276772, 202645499, 354435405, 584944154, 19782531, 352893674, 493188668, 5697558, 780126303, 907728490, 979923954, 747687192, 780758173, 582210240, 545432774, 25068245, 100880723, 577050836, 765771517, 467716249, 667647737, 542208791, 235014903, 187049310, 474053278, 254599581, 148298967, 114598714, 338593013, 223523790, 481551496, 789431180, 882850529, 923440130, 430548143, 691519979, 463358910, 157964398, 414602593, 986297993, 12816364, 978511269, 891917067, 50470828, 733672589, 824992740, 486269480, 470240495, 900585518, 722239526, 996614283, 459093322, 165844410, 765235429, 391658125, 781742215, 45856623, 773874153, 804710366, 113324183, 740304899, 599843232, 701408084, 191750911, 841232048, 349001373, 468717157, 335998325, 786475315, 917700002, 470234063, 350402095, 398526196, 514664312, 37004936, 115896903, 172309654, 950396232, 981303078, 135086078, 395993337, 909604398, 936952338, 463751089, 242581460, 783840975, 497988886, 607874299, 761194661, 866472974, 986519694, 803257195, 713713148, 410193292, 308525673, 594731310, 474021236, 959853062, 962922785, 39594272, 54385165, 193317839, 599516771, 476517425, 638032124, 415177512, 427825443, 869493855, 14578512, 378560997, 636873316, 26493504, 154570418, 344791121, 112109658, 959516590, 438361717, 310686124, 581837481, 198753779, 216890896, 700611758, 922977764, 311134203, 20308982, 201656177, 771317938, 169898324, 362911544, 119840309, 789289905, 989786118, 226528978, 831574997, 764307895, 462665964, 260101334, 580749785, 948911500, 356587899, 89647430, 527828260, 626676957, 410393184, 996424829, 19267490, 946298683, 329630343, 679610121, 516974884, 197164269, 348602528, 205917177, 680038116, 22253275, 663162864, 644434597, 597149073, 938059938, 96771311, 404408092, 734917191, 762408285, 947707484, 888620072, 276040982, 176553345, 565485343, 734675295, 995110196, 158556740, 622155832, 800275645, 650062653, 262252396, 791168285, 986942902, 833469806, 118893738, 776787597, 859882149, 39757659, 58415360, 546574672, 11737664, 637661015, 190955110, 393437450, 474259696, 843672680, 81260898, 930188990, 503095958, 518370425, 719170188, 43571477, 640246812, 211166442, 945472953, 769079613, 612760126, 155411524, 35454536, 97874301, 721943741, 688427166, 642594017, 311096169, 948894694, 389550709, 110541446, 846199486, 134607612, 406085254, 574278314, 156169343, 190869291, 388855766, 497980521, 363713391, 268082469, 229370348, 782375734, 955349973, 132748708, 899543888, 619254487, 549321102, 718340635, 247933009, 772653783, 884464779, 148781054, 714133122, 192256467, 889683756, 172740959, 263308912, 964642982, 316373887, 57018463, 897392175, 209607107, 533062583, 88517822, 102213546, 418145984, 987296368, 757221485, 752009338, 897931079, 981809619, 641583511, 347262049, 878485321, 316513158, 70868431, 391170428, 54749347, 264608408, 192386638, 709065930, 502054911, 409518219, 504899727, 464679050, 974462207, 311435715, 434352913, 698221686, 587094183, 15566057, 734679500, 481451196, 6265739, 981495785, 365846878, 54577138, 759917571, 823261541, 20546776, 368931502, 199839501, 95952209, 428762441, 750209556, 48560259, 725129062, 780598800, 613395246, 901794021, 318640119, 42337317, 130324245, 284636646, 971476124, 415160554, 778950188, 666393682, 690335077, 589593341, 365255238, 904430553, 726475096, 257735697, 727336783, 402718151, 98852681, 229275990, 618377982, 128492888, 557091995, 832238376, 134612862, 832798295, 507787868, 53559650, 685541235, 695569728, 295806261, 644912833, 920351560, 201029361, 803430816, 941839950, 201126249, 517359766, 400914932, 988412115, 275094075, 462224447, 949662390, 875067186, 753937356, 275739024, 548473403, 145652518, 649287905, 837272741, 413297558, 700676613, 730699235, 210057998, 481461600, 566399941, 524940182, 856863611, 744688296, 617459822, 827431035, 763632730, 831787650, 94090438, 240680867, 453280563, 75544045, 111159857, 164638788, 916317593, 435623829, 793649563, 881600237, 398143727, 859301724, 111534455, 81050918, 154900304, 435766338, 892779665, 573285926, 108561330, 616432907, 637404458, 747105472, 118835413, 652288492, 826175611, 668183033, 26040151, 669686400, 872586840, 227881125, 648325404, 659843825, 218509900, 629548075, 260785028, 535338649, 893904532, 522821741, 877628126, 282827503, 570254615, 568303866, 919817294, 988498328, 614425557, 43459060, 623503500, 664627032, 636303328, 846601150, 197334938, 526310684, 619049058, 789060025, 686637563, 867850112, 154139784, 261720116, 35831544, 721463940, 161369224, 780775980, 697414629, 145547088, 221230954, 153687793, 469588504, 978148441, 50048980, 117019186, 274831128, 255191748, 604300245, 524045461, 880688992, 541303925, 235393700, 868264109, 750989643, 393801159, 838425660, 627770641, 765059226, 183285887, 828393977, 587358077, 407005805, 755346208, 344145447, 330245966, 653277952, 791037848, 480469963, 990525261, 165129978, 129342904, 435802014, 908584743, 31229286, 33333853, 659522029, 948967107, 926033323, 356766237, 681467201, 672673775, 194542944, 9624188, 554499206, 683909176, 658915424, 330252267, 672478137, 945779009, 993872159, 721577635, 676148650, 552185018, 918372895, 140628262, 727753714, 46780573, 663134934, 601998410, 741297441, 79385187, 257136217, 247488653, 14425974, 986149050, 932169123, 976451676, 215650991, 280702372, 778357313, 973218874, 70145232, 591122301, 106638860, 82259984, 630943819, 308341727, 658687739, 67419299, 340396609, 326371351, 894640391, 904804662, 944888383, 407138456, 224174219, 782447273, 975533514, 808076619, 333414274, 621647827, 960023131, 806741528, 198514958, 482309024, 831122759, 779010018, 214320713, 502431488, 393805221, 862240704, 802495452, 231605508, 652450847, 69475894, 66104521, 374395856, 378890881, 592964851, 148855116, 214377296, 93311165, 710487487, 958673078, 164315687, 873975138, 162089425, 466077831, 894907222, 244817896, 453436180, 785586484, 808555297, 368831538, 46404247, 966605528, 198230080, 87039385, 919810160, 199566146, 583003047, 505762735, 940318827, 387384971, 531240650, 163464159, 673613533, 206305521, 116821597, 425084142, 636437447, 325260380, 92478291, 466428575, 331684460, 511303054, 83371744, 945411808, 451863638, 998399487, 549042416, 195588184, 41048384, 324678709, 218925207, 578132615, 474512881, 888131715, 609629634, 315967544, 524785860, 405721454, 361433872, 453017770, 892259124, 567026430, 713985013, 819121313, 422010737, 765491505, 504281676, 702381649, 283027779, 577050682, 372692946, 185180195, 517515333, 130614056, 225476154, 544197050, 700962027, 387277058, 382713705, 897324537, 503164822, 444887701, 182420609, 873744283, 142151601, 284062282, 961518134, 316391925, 664035305, 611570173, 24232991, 471119, 323356678, 43330530, 13872733, 604098192, 588688422, 477815164, 28066396, 551944250, 460373571, 96655403, 519957638, 815269331, 416066431, 430559538, 315149778, 548579026, 144990926, 469697664, 276807062, 830591963, 951764295, 181848880, 936068345, 572837639, 922297302, 609309316, 330946439, 508778308, 138257464, 421918210, 465536165, 371395717, 879111175, 570454301, 830387367, 926260287, 24090362, 960884016, 260751119, 996609075, 111744778, 128011844, 523180531, 192744573, 804516130, 647879744, 223890485, 359009507, 567955455, 574421554, 518996687, 326162726, 871568286, 418548285, 112048199, 890909087, 311404778, 568729494, 421224695, 350162901, 530242863, 747467203, 381611934, 211446083, 883811171, 341527122, 412057865, 811642307, 185679076, 693170600, 788624238, 324099109, 714729921, 31356006, 72118479, 491162410, 901593054, 803110250, 729605150, 855521063, 268775178, 419314366, 753323676, 310695325, 14882242, 584744584, 760135015, 46726244, 913262988, 892162333, 215206709, 809773945, 250669583, 777730266, 19450704, 702498879, 964618982, 267313963, 609535043, 558209734, 495170008, 68248695, 177889478, 146557513, 247721302, 701384298, 961420809, 734219767, 207894810, 293042802, 293754022, 161043132, 33836350, 112703232, 308818022, 917612884, 904664444, 764605481, 721832183, 343251085, 535612219, 879224758, 691905948, 773951553, 133690810, 593984604, 683971398, 689706459, 811968322, 418017082, 912737146, 205916616, 620772420, 973120125, 165572580, 874491045, 377610832, 987486511, 137290989, 390283999, 826562467, 502995563, 783002407, 570344785, 943064667, 970189318, 846452798, 910267561, 606471603, 680750341, 13209701, 468553463, 278295269, 586389010, 215888907, 515018790, 290759640, 393043623, 904615213, 399187537, 483720295, 155353426, 480587699, 251176122, 878655491, 945782190, 196430423, 997750136, 737070689, 654911200, 900154099, 653028623, 519477937, 744073449, 48870015, 200239316, 862792603, 852827755, 764608931, 631529838, 68492396, 820545240, 15322234, 923996892, 710514931, 454075106, 307582112, 5596337, 213142075, 783881400, 503204458, 863642973, 622375992, 778393993, 967651055, 472266469, 12492125, 895669047, 576735023, 822130813, 135054580, 986196429, 167304411, 572081855, 312889093, 133434946, 484136785, 27619672, 824559119, 569931161, 364774245, 144501670, 462692314, 852202576, 879708780, 178015665, 165811852, 257595208, 384360173, 583044569, 328069145, 127484629, 36017441, 166951728, 201443580, 374458905, 214316611, 837862950, 330948504, 928369647, 639204931, 960058276, 292730470, 345248316, 650427571, 163294601, 641836373, 743064912, 794775263, 324321877, 293118790, 485852066, 647219404, 290640014, 339336921, 128921383, 172558961, 251488718, 26134814, 518135827, 817519804, 965718961, 998183557, 14356515, 309847210, 800796571, 698024049, 433423728, 624395971, 706256749, 216670216, 531234307, 906399856, 499959003, 327123064, 605677605, 365936149, 23417693, 799846383, 269136168, 281086763, 978885725, 545643835, 744612804, 461852542, 270463078, 646302576, 522422656, 154464799, 767445782, 792690212, 68531666, 727570090, 72525894, 996396683, 531010544, 42382280, 748769835, 624205808, 917361334, 236588044, 683084372, 889299825, 739741424, 386436941, 161695028, 337328517, 732263393, 555123611, 13607752, 721847151, 688945925, 216078132, 787473780, 216773720, 389278179, 210405803, 115155670, 575011183, 142497196, 934190229, 873078055, 893489232, 841062861, 372625759, 524356234, 705734718, 456517066, 113604423, 682896572, 382894982, 292023447, 150781316, 653322739, 377341932, 736185517, 593162607, 982179695, 18344146, 215489687, 720125294, 292238403, 637434014, 826539540, 34389162, 867023883, 340526526, 182197168, 652306162, 754353476, 783716047, 706451325, 565701736, 918716329, 55128814, 606803527, 281611323, 699214000, 544949215, 398639786, 268919645, 146984344, 985558486, 651820584, 40965084, 211572085, 405641597, 886035512, 379642306, 987968472, 571318584, 388854058, 679511123, 178404902, 619666669, 37325691, 126439140, 718961704, 105767623, 132055858, 451792081, 839424105, 922053245, 337398532, 337602664, 821637002, 590990074, 439307823, 274112008, 822812816, 537355043, 853428308, 212266193, 677332430, 715807269, 543367766, 753088099, 626618211, 88080978, 274815962, 728566522, 452748624, 814108626, 572062352, 387846671, 587890075, 21902248, 324882097, 385259863, 642963956, 115903935, 811531629, 791276173, 491769116, 86655851, 978170677, 727392696, 976548235, 233236675, 470161347, 756371738, 964215940, 289517144, 903187947, 132052521, 926446996, 471022374, 524184036, 939485998, 19313477, 272591455, 152879235, 284778297, 155648411, 926752440, 937497612, 598055938, 436823197, 140856734, 826702154, 695789314, 211755308, 772041401, 815275856, 898885101, 939092236, 332085738, 414887140, 165913449, 90159444, 387258040, 362208994, 593838498, 496214776, 285234523, 456871368, 573753097, 332272601, 80952038, 188700799, 814309681, 315361587, 631246765, 906865090, 69234278, 56872263, 786848192, 180121065, 353959013, 76342305, 482159028, 516729698, 768235688, 644318208, 528299940, 381880859, 979832443, 204472572, 573131302, 527913439, 847382839, 228761510, 904580691, 109070876, 248715477, 490821722, 247750636, 692003504, 955294532, 733363377, 906421302, 38216708, 498213846, 99737571, 659819621, 971345624, 196392115, 399381532, 405223146, 570308177, 109505366, 157974544, 143941350, 975962499, 733358050, 36353563, 806084118, 902134268, 71425854, 693379929, 757086353, 190549254, 370389201, 107304604, 330192799, 638892369, 409005196, 744363224, 144260281, 258534409, 390744484, 424573251, 671394479, 376480140, 92042280, 299414306, 996034076, 802706701, 42715847, 215367075, 152272317, 976000108, 821481350, 185817634, 749930474, 270696197, 893600017, 702639588, 189856356, 474844682, 32178996, 174950456, 388112219, 97745755, 237879854, 591557837, 540827254, 957274883, 469264349, 886899378, 74115552, 598446033, 109167706, 281288734, 910191665, 415021408, 474028449, 826192411, 509799476, 573127606, 629050467, 434243062, 948834658, 260496179, 93422098, 124933035, 380999408, 814003347, 369674530, 379570541, 70533413, 622860057, 91399722, 708878091, 63259494, 306118696, 626124869, 903483281, 243370302, 994326739, 251195719, 716840980, 616400017, 560936446, 711091045, 569272026, 169433628, 422681260, 263619108, 630679479, 129059004, 697412708, 527092326, 852194680, 391348102, 245425768, 471988384, 395853239, 109281366, 334785503, 521080953, 479227667, 962776910, 996886447, 421385359, 284619225, 592796161, 745179158, 682783888, 794444690, 405677095, 339542147, 519373187, 251376371, 784433220, 295839397, 204806433, 326771075, 464110799, 422944048, 283239975, 133916479, 705063525, 512000782, 801158220, 816118285, 176581266, 122711343, 18130617, 287891526, 217359446, 283972099, 389752158, 117874017, 539329450, 778361467, 869321699, 146584112, 546542016, 305073073, 414187408, 302664058, 441836153, 536586834, 132806967, 820063234, 309521382, 245241901, 233962008, 349444664, 926858280, 674414320, 104286806, 899291098, 404954414, 19417076, 558968023, 168396078, 388843788, 725817073, 914761260, 473797995, 259439033, 710617135, 7084936, 178227413, 738188531, 238820096, 663307924, 925433927, 917312186, 39255082, 538164176, 746778665, 14316368, 534052356, 397086481, 888821955, 425303363, 901384613, 607028982, 645968304, 402958865, 80572801, 599903073, 841514658, 136866129, 594463733, 85075122, 416863014, 772599426, 62923435, 906002409, 201984976, 864338241, 454813084, 329492663, 951638941, 673229563, 153318228, 174861084, 298896244, 960886050, 639735168, 191284060, 491443708, 622333898, 850398306, 671712832, 856908547, 445179879, 991510500, 248066076, 698256833, 62659631, 636809808, 764247046, 938491880, 367135949, 940835581, 23487449, 600406769, 989542858, 438930091, 564234871, 138769209, 303013160, 150244534, 624820812, 425468411, 332440299, 771320989, 167777080, 670434366, 249064387, 950732628, 23839470, 12997652, 613734055, 750054601, 433425470, 987390811, 436147491, 391261859, 557911767, 414728463, 307268554, 546634716, 284628887, 515118129, 953847703, 752229596, 246319253, 906938658, 745135572, 936312292, 628634676, 665921289, 470508413, 364075993, 601399541, 570681563, 155779289, 253912219, 474162457, 149885586, 720679008, 232892856, 414481343, 423534185, 543753500, 426480489, 35246575, 809666912, 618672381, 798450695, 709187178, 615508162, 451099096, 659377516, 79248, 357633383, 505025016, 349900850, 15050757, 632610527, 488339714, 942263030, 884711838, 518116521, 116397517, 741026266, 416080162, 635917488, 555425648, 939975010, 567525376, 135872304, 995228884, 311730060, 660459726, 631117779, 720635282, 735076865, 628303013, 57821815, 281044590, 257062522, 328138316, 406968033, 177955781, 620646295, 411472475, 454647271, 61035658, 5764322, 506736101, 14921371, 738388271, 259702369, 771727834, 357032607, 296974274, 63556331, 276675891, 754891663, 36048852, 315827234, 49993405, 83894124, 208523947, 364516740, 793602084, 842626151, 7598586, 487329444, 32320528, 645361525, 588540401, 666522557, 307519701, 843041595, 310550237, 491741720, 693358882, 516294829, 961665733, 660674910, 730413262, 712822257, 623310143, 43927952, 94109738, 302714480, 642367456, 193460661, 846245654, 405174208, 233328175, 311344327, 966694206, 249784046, 48449034, 650156331, 715554637, 216784608, 539419156, 783107307, 797295186, 739932289, 581497356, 764422806, 140736626, 78161229, 772617845, 506100042, 993938987, 16367065, 69882797, 771747432, 243833454, 288170026, 355857926, 176656157, 330647978, 40613111, 268623801, 61783000, 35623974, 928971418, 492220319, 476730235, 306825090, 144436171, 125553758, 24846881, 798006269, 570582373, 305161973, 493571515, 6815311, 919835645, 392154460, 83127345, 452154469, 118326288, 355036093, 778480914, 712439676, 666022133, 574258207, 934261615, 654581884, 996685295, 439938167, 972137886, 261311048, 856880013, 136375422, 18564928, 707079416, 408607465, 245511502, 414777908, 63803665, 526836738, 768912071, 151544407, 453757663, 970690088, 164449918, 567006218, 467935317, 777290758, 989656919, 6859546, 870105898, 702894545, 911528517, 653012009, 428165313, 468895676, 339637487, 21174704, 451752439, 453213689, 607018573, 541340975, 635875033, 104248001, 88385613, 409142001, 819232821, 219602573, 70109749, 164259132, 164713803, 980755094, 909672094, 957519393, 726931126, 229171174, 90708937, 903123305, 757187051, 919868359, 43279400, 720906524, 744637698, 818656578, 859315224, 633687375, 109228342, 105700069, 516322475, 840278932, 106272498, 384202827, 499634737, 193903156, 264682628, 829500713, 704120328, 889534734, 31633744, 147001, 3613636, 757555952, 125610124, 446253588, 405591068, 877984385, 376389163, 356828715, 790843312, 98335705, 919276204, 316050088, 422947613, 25635871, 984962279, 873022511, 668642329, 141453264, 6427320, 130475015, 98895971, 473660619, 405686161, 308262218, 173580532, 183121236, 678389237, 104858247, 583346471, 235860839, 686554092, 996439834, 525513925, 125120308, 745034697, 766095867, 770111731, 612706082, 120912206, 794654493, 490777884, 189782375, 66897223, 753365462, 198873575, 441018870, 387534247, 74261217, 614464818, 216973462, 478892645, 994393053, 944660058, 869496825, 825839658, 756357267, 548636811, 683490031, 436104422, 532800641, 298776979, 124837160, 623671420, 43929620, 844267273, 731416451, 359240453, 46117276, 724272180, 430765440, 214085573, 944825456, 383739673, 28821023, 810412219, 244137103, 574316374, 350128243, 29819005, 1247382, 480100773, 585116290, 346525623, 827013555, 360392949, 519512743, 330887732, 810898473, 523572150, 547928, 588582976, 888924043, 764065696, 267181970, 526153729, 742645527, 634671306, 57484132, 309239056, 643410636, 968755390, 373800891, 139760158, 639211474, 134568256, 609020178, 53806559, 489921080, 385717334, 11888830, 571233149, 34421204, 650092640, 188959285, 769618321, 990504664, 239825576, 537407436, 386564863, 676356745, 382202690, 912242078, 917535431, 106130333, 98931852, 269267361, 908076481, 820230442, 974041080, 73765229, 290268938, 160685959, 829762445, 239779924, 179218227, 421902006, 967773668, 672588862, 651168274, 221282374, 191845020, 74463284, 364847720, 11165345, 488895678, 403061986, 114570990, 164172591, 279512070, 951120940, 45030147, 147891004, 772106675, 104435975, 925698914, 89316600, 463003002, 201123470, 327497383, 871382888, 416327261, 116346868, 775086676, 748588738, 739153286, 717994008, 382064649, 598363976, 953798233, 927577353, 428482038, 64025497, 509169964, 60992949, 741366738, 11378006, 214844771, 957866360, 892435834, 742909330, 615970603, 852261118, 617821276, 886888993, 471216066, 405929988, 336322714, 329922405, 800469233, 761235371, 833049314, 115262210, 123644589, 915395421, 541643682, 605207285, 298101848, 440957879, 396586454, 402887104, 627031051, 388332881, 423286131, 259449613, 990409043, 75115104, 483868661, 655781090, 270078343, 451589071, 462549279, 340138595, 453779779, 824944115, 596890183, 243096088, 317857852, 466258276, 16282839, 277496751, 695283119, 589664125, 311711332, 101906354, 890193861, 163383380, 512793151, 643426797, 990668911, 604057265, 629125267, 8580700, 704620611, 696964885, 94180246, 425668004, 138920216, 852094782, 293374185, 378586328, 127469487, 831811545, 169217472, 735544343, 532482335, 498764771, 276211799, 213007705, 496968977, 689818517, 778803907, 178431274, 738295583, 464340094, 718663323, 422492698, 389310969, 918929642, 722009647, 59182085, 418017568, 109340327, 856841760, 850587639, 949571415, 244300495, 245178093, 38289473, 228262803, 937240885, 473098785, 96071831, 376858066, 821559427, 869634256, 553242521, 519814707, 824502550, 721067062, 632446168, 558268745, 521512122, 83398317, 728405015, 608589457, 365577397, 224671332, 413765572, 784452033, 410078097, 841983806, 921970714, 42491125, 962122806, 537711565, 906419655, 269097230, 229317919, 11538729, 439973640, 401921723, 108711208, 371142119, 2950040, 872711588, 881211198, 166168321, 596705875, 108403477, 777876158, 537922528, 185724930, 169930979, 899204935, 210558880, 853695579, 422274098, 19502218, 626764987, 283031632, 402480908, 5945353, 697148970, 626382453, 995860583, 253422437, 693646497, 56924554, 155815891, 648153744, 432522145, 285778297, 996243823, 468033302, 956871303, 505626543, 683894106, 659210468, 112182275, 199112104, 541724077, 394915390, 414590931, 723611053, 499746697, 87014069, 824516968, 422188341, 607680381, 718257322, 576880232, 893027349, 845147616, 802854849, 342293678, 216211899, 287224389, 551498934, 694379854, 422363200, 827900652, 277045077, 388433168, 588472285, 35412051, 244942820, 232908024, 64584580, 521934630, 161884804, 165636607, 935511943, 263523285, 954899866, 438024795, 258145217, 561217657, 9828643, 917964613, 370395035, 92799513, 327589282, 224763719, 765420940, 847323269, 631741480, 665925631, 676787554, 47756535, 121492640, 733499604, 837360405, 335908410, 425127499, 235223767, 307068766, 732269678, 241983531, 37409213, 636886401, 84868446, 491977033, 747353147, 851030172, 31197388, 794614089, 200340826, 170217959, 419491768, 317276899, 435292911, 866479811, 966005642, 724790804, 797426833, 173486727, 864520498, 83963930, 111936333, 822162998, 868082553, 137684647, 236953631, 422300877, 910184632, 830066395, 484330084, 17019027, 729135048, 367810545, 554732222, 847936155, 181545846, 723940824, 298734643, 652615663, 857262625, 179926747, 875295157, 626431222, 787753340, 198403317, 262603508, 175412269, 670974983, 802843748, 688775850, 986184252, 278469555, 215126598, 820879922, 631985141, 96726712, 648145206, 387856461, 992672997, 210522201, 483157765, 854507005, 244423782, 801257671, 131532142, 363275089, 671413346, 830937328, 298261486, 87076064, 436117649, 129154018, 988028285, 343877808, 212101321, 547147503, 677728016, 319132211, 963561280, 429239018, 303935822, 696479051, 677736921, 842066161, 885567238, 412058871, 457880824, 582588751, 35933892, 949681221, 236945432, 943828250, 232444214, 547308253, 413934646, 216911206, 558075217, 543134619, 87028197, 539327735, 27338235, 449216211, 682824069, 854522260, 717380673, 280847898, 177888575, 114874327, 277421803, 643594566, 798751711, 963834246, 326979114, 603670382, 531378152, 981683582, 204984763, 13970901, 628811380, 164796945, 54554069, 65073262, 136520837, 428052725, 511459814, 356136618, 745053213, 709173298, 264039741, 510766781, 606215677, 520533550, 76743238, 166579966, 487725766, 928552155, 87529586, 311859760, 558917895, 230711254, 36550719, 640999896, 285558569, 840326500, 517270150, 396066180, 322465547, 252905598, 355849815, 851702703, 50976361, 564838014, 942207272, 160875813, 998703101, 281997827, 577577387, 503148725, 657508089, 385454933, 208364306, 60373569, 444345040, 376801009, 585018797, 838499672, 946754821, 848061731, 862272402, 970976423, 805890237, 432892233, 398899534, 907524212, 605172923, 696937463, 41788588, 569359768, 215127958, 533737466, 41540744, 622828173, 787255368, 265126446, 627450741, 384706228, 701598137, 329574379, 329151069, 576457410, 640527768, 830515456, 171092532, 756695825, 329828566, 23330086, 96741552, 782215636, 843716037, 32641110, 479858768, 877488614, 48150069, 955749282, 883124289, 55233878, 432452327, 759484333, 273701839, 543734510, 233350965, 542549000, 424923966, 243176247, 826369938, 800792698, 618942576, 591465454, 112536449, 38557628, 285545314, 613043048, 768248588, 519903289, 714149440, 901390312, 143990411, 549738230, 571012180, 728537998, 818121334, 778021790, 929293067, 325497046, 183071648, 774868843, 806024324, 380139097, 662982241, 925559900, 93887167, 497506449, 928301316, 324935544, 934475728, 635717243, 267358801, 772916716, 912099582, 626664081, 293514463, 142394504, 239955020, 73876330, 268318244, 742536399, 343627203, 625562045, 520136605, 675500647, 699014133, 614554433, 543247733, 368257502, 40773663, 765466051, 143238693, 327947127, 895933866, 433567756, 502503525, 985065836, 717506007, 337084464, 36076345, 573552261, 511498855, 415192237, 629748233, 652988202, 457527023, 112122047, 611780034, 295921976, 464607458, 281460681, 647364220, 734589224, 571238698, 684208564, 483563203, 851730560, 353364490, 940497658, 438942336, 365068187, 454406352, 882350856, 256389563, 889043471, 31779796, 317591692, 320385083, 533420612, 890180282, 828776415, 386337541, 574170123, 52547847, 605282184, 764525176, 3630144, 362136598, 99521170, 424968696, 355891747, 986314010, 776123362, 304024196, 889476703, 692710673, 247263792, 142774345, 931230718, 794778245, 639066407, 536981755, 958692076, 881313105, 926996960, 957054294, 269856518, 53577170, 92173210, 831791542, 367249742, 702317587, 8792379, 678240730, 778915393, 250862351, 67397385, 52065119, 575918572, 31505292, 686498791, 431053355, 159746074, 54402796, 377498506, 468756710, 941291373, 433173284, 875882057, 641197579, 16532868, 782732012, 420584626, 517509015, 364255107, 814471347, 316816485, 342953836, 304759290, 443566531, 934134786, 607674469, 548805002, 706162376, 278975853, 505940218, 19264182, 188620742, 348041282, 110451455, 579488211, 634652404, 441609621, 477117410, 12736796, 332897245, 116186313, 296480505, 134649064, 279167017, 922271527, 297871875, 237941574, 724770081, 535896969, 610040044, 785294497, 907978587, 883662490, 379714479, 41334267, 371326988, 282806880, 472850964, 234929073, 817761359, 505554347, 295630288, 519742665, 54418313, 482735909, 955744555, 385903085, 460772580, 440968937, 476077716, 115016417, 618260042, 203229340, 435901032, 713286623, 352334210, 626303116, 418038318, 983942275, 695435805, 167124811, 578776395, 540625019, 494524924, 720313280, 533887797, 105677935, 182362905, 100623744, 550053421, 427605100, 740269460, 437096232, 704560404, 775642308, 463038713, 666291618, 296070278, 1998823, 205330442, 912393155, 700574385, 485830848, 754983092, 382363159, 758090400, 594782906, 2400, 734396168, 106561398, 81735870, 707322883, 240481096, 704943783, 967209806, 871379207, 508763415, 68087488, 349422153, 98643097, 862538376, 312168966, 256791805, 963837355, 17037396, 171459683, 783635248, 855373252, 638965653, 946091300, 313973786, 637338870, 177405772, 852821754, 907254182, 586412178, 987141284, 67768549, 601906070, 62930873, 138454949, 838538302, 926639582, 173446360, 740972611, 907287040, 381423274, 339668858, 647764921, 306100972, 780132831, 108093818, 981761565, 478074047, 360519309, 361416114, 722219204, 374997416, 79665698, 587717734, 732391191, 245615818, 668018755, 514524258, 739690989, 342931827, 452144628, 159927635, 75728531, 299973023, 851968370, 942808525, 868441139, 112658005, 696722083, 723118459, 536276052, 62709575, 188126390, 762321328, 689670336, 510313914, 337906022, 993886920, 715281316, 485744830, 434674406, 373091905, 576771310, 549561633, 718888695, 333632198, 354860968, 313483883, 51039555, 936591776, 221358034, 581074656, 560475355, 78464943, 605233853, 952973879, 590349733, 304797067, 635244884, 714614303, 819591991, 634900773, 730314240, 570864691, 156049065, 787614114, 985513191, 490065807, 570231908, 170712750, 960987805, 874947941, 325346436, 96013401, 838393705, 734030921, 873466204, 368089626, 725146983, 770851292, 892496805, 311531581, 772137092, 408205350, 516525615, 682071490, 476207080, 373611228, 56873579, 590740289, 305557645, 38096685, 894523011, 366354894, 955532963, 746302482, 162421028, 184679217, 905635963, 435298253, 353972262, 768130079, 828354015, 182309654, 781760719, 815887529, 503732439, 301084181, 856580199, 818546494, 48288079, 869117463, 899540368, 698183377, 159564613, 981837679, 249425151, 352870487, 259413306, 932504656, 321200320, 895206842, 344759681, 747668406, 840099286, 874748104, 24845897, 453452469, 452878396, 611262290, 377155372, 763821111, 893602406, 74505220, 536280576, 910208373, 831102525, 753808264, 490264059, 692415496, 297973104, 600542591, 737519575, 499459297, 845928912, 290571871, 364950389, 999258546, 678958160, 213874001, 536475497, 516337662, 916622187, 193611046, 536555861, 189567238, 356137830, 477801936, 325730482, 831732431, 504124819, 434469606, 819270302, 82792672, 986095289, 31179231, 719708638, 639259941, 484743372, 782550562, 257846996, 620010177, 963544743, 958178199, 854131531, 740300523, 680639410, 202587736, 857331742, 250502354, 666693604, 962581248, 365808962, 470250354, 295209374, 58172439, 83080368, 87419188, 918757592, 379702314, 521079865, 560419727, 123571638, 691791570, 544517212, 335545328, 984805079, 860619459, 511915035, 343745683, 106901876, 28235080, 77736456, 38549619, 794615865, 630279760, 941977268, 399156559, 852340710, 663082038, 282274562, 897522009, 996408528, 486744544, 782421529, 452337056, 376100059, 957296259, 254593990, 561507941, 929396192, 332493579, 37259616, 301834014, 912928942, 938017399, 730241559, 548385029, 159110245, 365303197, 368919374, 110640567, 945154918, 470756698, 264331902, 62402622, 602911464, 426094172, 74517531, 429858243, 106009494, 417719734, 396864756, 750133641, 227392752, 809615351, 139964303, 573553087, 254639332, 479442429, 191814594, 496786601, 51342363, 822727429, 541218951, 258812113, 79128776, 553349917, 289590040, 12134915, 892068134, 482705207, 713597568, 446098888, 813159363, 593610974, 654822188, 675278887, 922213531, 194279345, 346941059, 431269477, 356706824, 708378429, 755758254, 257024443, 182566019, 223768824, 505073625, 98347382, 231339780, 451355588, 448905354, 294487207, 685618238, 66879130, 642466043, 133029468, 138574402, 736404368, 91659212, 609082023, 166987445, 751396219, 83747562, 726893953, 163299920, 664279075, 188564449, 220117644, 660684605, 705970855, 880317924, 570615653, 203953362, 196697011, 414028396, 108835889, 463285401, 158642406, 594380349, 408097794, 445940066, 266604838, 310508879, 414164911, 182505603, 879790776, 592490523, 280762853, 25307171, 11001480, 996061048, 135432241, 504743734, 510070432, 11143284, 163069966, 749287096, 901333153, 406267644, 791040263, 188065359, 325571828, 18088581, 868045035, 994298635, 317565969, 438082862, 722820370, 848977568, 351045004, 370248629, 953284317, 485590176, 692303493, 427588136, 744784234, 332666262, 278260618, 632515269, 72076721, 496421078, 485353494, 421662942, 211776754, 264712080, 907155112, 302746221, 853449186, 858566292, 821429113, 803608354, 660820423, 516803806, 276442489, 640468839, 459601393, 856696110, 455554035, 33119006, 726284324, 168213512, 519652230, 534850227, 389335441, 446608162, 391490323, 159317945, 60782794, 438039220, 553854984, 883591721, 656135897, 609483306, 935026941, 86746090, 678015254, 668805524, 621182102, 473012268, 502347463, 836320461, 936593136, 318404369, 840436426, 949592876, 908677687, 789645841, 933504882, 891668291, 914257896, 419836839, 403660560, 908515367, 677807119, 300044940, 45674675, 481004223, 740093695, 724850796, 419551386, 988369414, 769274579, 783666462, 467738968, 661464707, 861228843, 225945057, 549723815, 554144721, 700234174, 906587244, 19555392, 4091284, 808843070, 625192648, 405980304, 645708980, 950300865, 274658847, 277242785, 549330566, 823055685, 168126397, 546277034, 820591112, 745350055, 800765793, 994411156, 854382110, 969141348, 522805235, 661862664, 762305574, 100096985, 780429579, 106787438, 75672397, 4922656, 488533499, 669074579, 950669063, 97474279, 962985696, 216554541, 240482684, 628178300, 16384888, 153916785, 832409450, 645773689, 949552734, 410243892, 505114248, 200527771, 550352760, 358786881, 445830793, 624316549, 4102484, 177647438, 300361074, 231497652, 518791284, 1059777, 100401186, 680627689, 955715215, 106285706, 486510259, 12313282, 771336194, 665410402, 742755876, 525346292, 503311794, 145915120, 773639198, 27327732, 377623055, 238688707, 942579326, 732694492, 106720504, 430681223, 288291772, 901024778, 123175420, 535053947, 559726198, 206414933, 194668042, 772137016, 410732194, 826821450, 685843970, 114942212, 69962990, 205674373, 235231960, 139388791, 117352135, 168335781, 934452054, 865934194, 456527126, 713588198, 375433765, 364461240, 606610583, 335367086, 548848776, 807061050, 10302700, 354144889, 973684715, 689319525, 492181507, 86966933, 172130427, 810943293, 877210100, 650397778, 672622227, 707854024, 289912198, 603793423, 287458890, 619210569, 634345013, 367856269, 647554481, 652329613, 622666810, 488939986, 460433625, 195298772, 686055182, 511699556, 208560208, 904188770, 799727412, 651031902, 899880252, 697676842, 199027563, 21930259, 468751952, 677066768, 565335049, 460238949, 556648478, 960763130, 261595819, 9408120, 863726557, 941007143, 700330008, 131098054, 186697235, 270771256, 157596131, 654051695, 543068508, 181661699, 212999220, 14167148, 439423841, 529578556, 166839019, 132690019, 869644190, 722597467, 324897074, 394028197, 891210048, 919749542, 518973184, 130020002, 676971481, 22146411, 957946270, 646028030, 335596710, 124204454, 589489945, 802576696, 737659112, 527099713, 967613708, 780060223, 20063471, 217684253, 83263071, 892651926, 251517939, 383097403, 234624532, 519703983, 541773256, 263889627, 159202964, 527379814, 845407348, 986407067, 398085103, 302941472, 272857088, 735753314, 676345405, 801040575, 435957093, 322264901, 905310981, 651225061, 698025496, 687086033, 105946191, 807727501, 195579478, 461091366, 841003811, 849463882, 721746446, 824935868, 737137468, 67138342, 910670851, 211617308, 630312644, 892671426, 18464686, 524501938, 493290030, 256712016, 38388004, 337552356, 16135259, 610559453, 174538124, 351494227, 447340423, 370419722, 678644862, 614839286, 694690771, 787841178, 830795979, 78747111, 628145648, 366446835, 924023464, 281506365, 739008953, 947583061, 425974538, 158340465, 562979652, 398444334, 975572169, 442027230, 744951339, 783495652, 853018042, 96866257, 391809454, 411839547, 444665939, 733183907, 301338715, 5029412, 334266496, 785746950, 312127081, 93398445, 316789837, 496591133, 9086123, 150259716, 832818610, 391842061, 851504145, 601825447, 581542987, 736787591, 395938862, 588774663, 108995832, 897943190, 266501624, 936822326, 566287709, 196108121, 426700437, 379147563, 507378396, 104889000, 12551617, 389744695, 636360398, 70045406, 548142234, 359005953, 890152810, 262989352, 265022744, 274319387, 234496278, 943658006, 2587636, 679243412, 657940092, 486116036, 922557628, 833799770, 286914012, 896881636, 753909027, 2254299, 244480533, 993412922, 59196745, 190630391, 340634992, 913204583, 890480690, 388242314, 164689025, 468002245, 420851326, 466579486, 271029505, 494940426, 716449541, 548402829, 117632462, 985902010, 965613430, 518228321, 167535795, 151054354, 868707389, 46511877, 324993432, 786665482, 604039934, 714266563, 934808399, 408644269, 351233519, 642344362, 136642676, 677525207, 569720540, 553168968, 500186347, 79021263, 710470592, 327179434, 457938337, 513883621, 399299355, 111337486, 308537759, 443479964, 474689095, 463536323, 742862710, 88251128, 323884749, 474309049, 454529429, 931492544, 271528801, 814603601, 244937907, 19966316, 203838551, 233959837, 864241217, 370632105, 120683822, 297071752, 773269445, 932339420, 760709552, 387091632, 336727735, 363172498, 198312630, 492980219, 66825899, 131117604, 588619912, 164665876, 128657716, 336161256, 4099010, 599260226, 111805634, 843940110, 882420536, 684513140, 458788778, 621791869, 317476546, 601123373, 361414164, 510551376, 796075541, 62962582, 270077516, 674878218, 597759612, 312095666, 1798450, 890564183, 676590467, 343898546, 183824824, 922215761, 98785592, 907039888, 125082584, 72796322, 106213319, 73115388, 604249635, 680621824, 508283677, 131616563, 249837753, 292671378, 448527865, 323992237, 109180664, 709686516, 603300943, 574437254, 182938907, 919180455, 234397702, 421744475, 928683912, 419340127, 603003913, 502431677, 837814895, 308815549, 291117792, 817771292, 240007556, 287161097, 322527208, 200056716, 696263764, 376095653, 640335140, 397850999, 198263966, 674886770, 176181272, 711318925, 842375981, 954327838, 831482095, 887230910, 669939979, 108042495, 291625032, 405051284, 527388577, 265332754, 748901666, 159586651, 853169860, 926083764, 32661925, 421172194, 692606544, 530126998, 63530847, 706320908, 798220839, 217520675, 115410594, 822714819, 625583370, 216648311, 36204645, 234736451, 394172261, 785887908, 524533068, 141261069, 792323480, 4810741, 5260454, 610353862, 284881864, 100790927, 187966162, 918356240, 737457825, 372059118, 355681836, 620876731, 485513108, 759626188, 346561701, 196179597, 459687547, 804192470, 700283288, 386896427, 852493382, 971247760, 93712327, 326371914, 181943962, 848151987, 735631029, 292883450, 465610209, 962816203, 148871769, 819490217, 223719093, 571620827, 468787516, 987794372, 152932960, 910401675, 2128721, 654511336, 6590456, 520449156, 522170508, 147351440, 800440838, 675153284, 838179460, 814662818, 201593052, 577928685, 958191817, 698708245, 251171124, 46587663, 557682161, 883162189, 235765990, 962930541, 651855759, 458034939, 901315154, 265378920, 169166438, 906390384, 104492235, 889438008, 622798221, 573298519, 15931116, 608200480, 41332652, 257668058, 742231946, 733318468, 588153740, 359536256, 657575116, 696263877, 868131117, 347954756, 934434339, 430863112, 777779281, 195028280, 270709338, 319783769, 414820149, 984200675, 815483880, 212063502, 516051807, 965279460, 796256100, 238031420, 168864638, 873243556, 780757481, 760614889, 852727598, 276995100, 298826244, 582882016, 929243153, 496579164, 323453621, 983512777, 240151539, 919042994, 955402911, 745873226, 476810409, 460692629, 678589281, 561259236, 409331699, 753418370, 7027069, 2521447, 663746358, 556304074, 186052160, 535411158, 888243793, 4796231, 697108387, 909806718, 404583696, 152640611, 295941568, 272558634, 383732769, 615432369, 768445776, 569529696, 775678423, 969910309, 762084380, 149737190, 904215290, 35631600, 883559439, 973951692, 473914567, 325335913, 522398499, 49990956, 86052225, 579173450, 756822646, 346991125, 105166241, 366408821, 7977517, 94441721, 598430316, 892187303, 952942551, 758306675, 77870063, 68531674, 39402636, 154589070, 987808262, 34652284, 832132374, 265687873, 203461439, 5859146, 135877875, 58631580, 607983736, 971018014, 395659302, 138667846, 589384747, 87898452, 175397189, 398195647, 953111305, 114206554, 435771449, 468690304, 151763901, 153616649, 905014534, 324793865, 362425786, 445613971, 70410014, 533298662, 943109753, 99138205, 969078676, 613807945, 277557133, 346881415, 574211405, 812665031, 922992149, 906115989, 323216288, 193753664, 21384932, 849289388, 699755921, 735532201, 388896843, 605613584, 312308535, 270343312, 276794372, 687643035, 282534390, 387204739, 610883960, 80478173, 952747027, 899712031, 779890597, 940416079, 212535364, 465993297, 903680919, 576559490, 638147975, 790504349, 282452462, 219330066, 921103998, 436618144, 114296442, 456956811, 939406174, 754842594, 199237860, 910179265, 139744129, 781058913, 242418094, 417040249, 85508845, 297222575, 297437000, 497358029, 902245823, 397571381, 249949442, 86576388, 319900308, 774288723, 215536319, 649942813, 147284848, 141973128, 70347551, 184610680, 879107166, 841509306, 379245195, 618988757, 786519206, 764524300, 557642989, 646329794, 162797993, 153970635, 351600767, 39151982, 959166309, 544997669, 525343157, 182832633, 791349426, 726935992, 500404979, 301575127, 133181533, 475324256, 468232788, 456613914, 724204716, 33078438, 65591547, 579336587, 472094108, 874268368, 851934712, 33240127, 317442702, 765782121, 177948233, 261486538, 17243785, 685311672, 939633051, 534693634, 653186798, 120692524, 828420921, 262199739, 873340154, 287538596, 608103264, 261199967, 68517277, 937809881, 964679506, 259547020, 647555171, 928179910, 860749598, 573358021, 19165987, 441877755, 471335590, 747043443, 583633086, 171373058, 177876824, 65176876, 470893928, 954755789, 373797503, 424547386, 825704496, 410473902, 526582920, 407697522, 313057827, 48347387, 263645164, 256371113, 498594085, 770834335, 851903661, 12478099, 34621115, 472068429, 811393747, 186188077, 684187001, 123458061, 753011463, 845880727, 243384848, 339893253, 135359570, 898261917, 606757967, 534312032, 655421703, 588121559, 252376669, 135702799, 616055349, 214209433, 386005360, 538316596, 711867737, 851969843, 349015218, 167913513, 402660772, 230529217, 64162697, 655668777, 230439025, 100666049, 117290718, 466381215, 502209634, 229316848, 159600772, 58689895, 38338912, 190672548, 25922211, 62149800, 103534088, 815504856, 756521567, 493170839, 116426480, 714649447, 310038768, 318233713, 740794430, 787335387, 967297275, 227455115, 569908549, 923328931, 965296675, 628250823, 604408897, 745605140, 772453297, 887709382, 995635157, 620066279, 6383577, 245084692, 740425194, 143630662, 82756495, 916150692, 401428665, 615943405, 898236333, 942831472, 952632898, 985543191, 377349815, 424683091, 52285380, 245405143, 387426423, 351886766, 546919369, 929561215, 750172521, 488855888, 266124591, 838382624, 446361468, 532704737, 300166008, 172673305, 933657307, 544069251, 913634158, 686747477, 836779972, 297714776, 460081981, 675709973, 343826625, 258995138, 658227604, 847822177, 551704214, 303005176, 232605682, 733324191, 815720146, 843664435, 810828951, 888913038, 434055248, 29580491, 626007723, 69144178, 744787989, 107298062, 569453107, 887998946, 675226463, 848515632, 284107131, 784261922, 151274111, 718440452, 877480239, 702665010, 278388597, 17309173, 239706976, 248769157, 731538403, 440455564, 918547691, 825607306, 854335978, 774116674, 788073273, 182336989, 710596200, 280423224, 606609550, 146913188, 28078818, 61875958, 663368652, 498535041, 194470828, 813559028, 12952251, 312097215, 657785688, 479925992, 755815940, 186799440, 442857583, 151830564, 144269796, 461577678, 351357144, 744335392, 110644308, 936642666, 289575684, 81572677, 562433223, 745079003, 404272999, 809419919, 382541601, 196123560, 812596841, 372083132, 657302321, 445738182, 153734021, 746772455, 659587727, 749557084, 777161862, 105653640, 559518307, 319802792, 992640264, 416040878, 276828213, 509882869, 96328018, 410195495, 499598670, 326556304, 618620226, 136907283, 527549521, 58151195, 98684956, 240333860, 983665222, 17480482, 280503589, 868221253, 256345009, 969202761, 312178542, 944089903, 964396389, 12299489, 469796288, 964297044, 157566903, 364015997, 319103717, 817892418, 579021930, 13677696, 81862186, 552268366, 145225733, 388095503, 835391628, 899739479, 319232009, 741650706, 259035996, 472983593, 651203832, 645633811, 193106569, 23591317, 148115254, 310279506, 513486516, 847450668, 45400720, 489956078, 527481763, 765286711, 464628520, 43814676, 245624788, 456723528, 709087979, 374794217, 933408756, 660895036, 927503873, 148415378, 194248852, 890876037, 695777143, 158301504, 755698743, 602362757, 677017704, 657889469, 534924368, 906157099, 382047775, 68279386, 76621292, 604910747, 283898328, 453566602, 443115388, 31641528, 725517746, 591864580, 90808422, 969026338, 190882515, 416617419, 157758160, 881928648, 629865722, 800165209, 511282808, 898696760, 578525058, 371514080, 49131097, 126668129, 186068404, 427736328, 785459346, 23767989, 669984880, 890020822, 402534919, 69056634, 848663083, 974292456, 622632991, 84774312, 330073660, 705731053, 659224886, 564812260, 649993895, 385054430, 639330675, 494642764, 763088190, 86778686, 840781219, 895158191, 412067119, 450850376, 47635117, 172333627, 91271992, 788572284, 302401653, 800347516, 794689606, 700740291, 852590826, 49249717, 818709665, 647090186, 75581632, 316979279, 836540000, 207412402, 341122333, 904925442, 17970509, 804488249, 181088845, 457398613, 641738096, 521076958, 399535905, 927038206, 531581514, 89755185, 568210035, 264083792, 438147707, 461067118, 155435223, 398745882, 428485169, 841376145, 888486503, 433938380, 479839583, 236777894, 889109990, 767959216, 276015167, 923418640, 951730010, 534519502, 699641113, 380516833, 199557862, 174042508, 492490188, 857719861, 652378172, 825825681, 177262010, 773390060, 859803241, 685291053, 94900922, 280171837, 697390878, 904267490, 405140498, 631378470, 735534598, 949785971, 120002797, 309548330, 392018343, 432632349, 803442113, 319940288, 171938115, 750132408, 395291572, 274433260, 950621238, 953601888, 316724827, 732615007, 709398114, 357961232, 226435930, 463719669, 119004500, 926046566, 375367143, 456280577, 897363230, 321707875, 362916142, 546932742, 800455892, 354747381, 507935717, 103050101, 506884744, 55819037, 572143961, 514826014, 735798258, 355822775, 621152637, 744207156, 325624090, 461341348, 449653283, 572669991, 67842315, 908180319, 640268618, 214377936, 345061032, 394355323, 363272056, 583544296, 628143121, 464769054, 922713954, 15093013, 221899731, 759359213, 661226419, 394837828, 462854204, 102577214, 952013726, 29268988, 559480792, 163067244, 799746170, 143043352, 456394057, 613172581, 390756588, 603039635, 516751536, 537510974, 694536720, 324874892, 947905364, 143363324, 517069727, 179807105, 172570294, 510718023, 743288959, 791826781, 841717186, 885627222, 423890772, 577575354, 544384027, 820901164, 740283059, 858971381, 792995135, 936553376, 851461564, 782293872, 693233446, 461509240, 187624377, 791137831, 784374961, 203830873, 492588654, 308808656, 381023831, 875252069, 66785800, 928896491, 946135909, 295777704, 303528680, 59465674, 499892963, 736343621, 720898217, 136177980, 191790815, 963639605, 612089790, 553735257, 652603572, 279565238, 284811676, 802051791, 331824789, 420300691, 385533274, 128219793, 475295901, 297534144, 535879851, 573286487, 742646615, 714183684, 146112243, 139400012, 746368583, 566102987, 553941001, 264149160, 125034729, 515789662, 542392160, 56327781, 305689939, 737888971, 58360682, 35891408, 891629542, 171201773, 956858784, 481267569, 141956424, 18176841, 62093440, 291526336, 389045064, 104831872, 386939601, 992118669, 411185546, 899820633, 505699349, 396925773, 227287069, 567729032, 994329549, 928702396, 819829153, 349309642, 890228519, 672642785, 872605296, 368046973, 154831670, 633639130, 217667319, 165428127, 741162097, 678142049, 27491680, 453055494, 170509226, 923958955, 319488734, 623224269, 92762864, 248798156, 967761957, 998710547, 777616116, 196065571, 145225836, 134357071, 461790303, 576095229, 358107149, 61235146, 716113754, 992352141, 313190476, 511924580, 937347609, 41375478, 51775066, 530073957, 955109316, 916994986, 260081676, 709431976, 697558728, 962020390, 996588840, 141125234, 60590577, 966654833, 155357884, 102697907, 112898930, 8750637, 614723779, 24143598, 47435647, 117695370, 765745083, 467003640, 557086033, 931497785, 547286816, 599040751, 543317106, 204924491, 851852724, 550990846, 177871652, 549411262, 674929463, 693983684, 55598775, 933420143, 904858686, 771046057, 251906115, 479599854, 244319877, 271827370, 457121060, 804648012, 898996298, 787583321, 350011602, 769830665, 507106790, 328268200, 9504213, 246428039, 579847696, 483007996, 772344185, 388853114, 746161209, 937911085, 215218066, 881279093, 68265430, 694006849, 40111062, 709556927, 500066158, 107015854, 569466694, 604127736, 390527271, 855376375, 355085380, 31751835, 782308835, 314041218, 907981606, 103624655, 987998306, 35968255, 930621935, 675955959, 859345023, 927278408, 953540104, 992801210, 182504195, 383725050, 276520873, 246966463, 391205972, 212005696, 690702135, 186650932, 630398988, 481863705, 820015855, 442326399, 785545883, 841273753, 92426057, 449643783, 189886063, 138153159, 396886018, 739599060, 641413452, 24476340, 922971701, 893629356, 985437278, 586641179, 509379420, 555732712, 505009851, 671905716, 556584290, 289599284, 139764999, 695277572, 503815554, 909325787, 621298816, 293512420, 248179018, 383133127, 968070236, 872969345, 817987845, 652179350, 378207171, 34177948, 70241621, 113916537, 478378153, 908929536, 10166896, 699797025, 147754948, 656537505, 579940131, 664465798, 996233037, 593335905, 918064827, 2065452, 646937142, 394751358, 119065882, 485852922, 242470264, 347962003, 17657596, 716927956, 81373929, 835611828, 630184962, 482982242, 973654650, 976377416, 326248504, 664195339, 44276393, 501270155, 187746381, 427395652, 366401777, 588381632, 56236201, 405081809, 78399728, 496785917, 284161896, 490287294, 502107933, 996130009, 947183803, 136146833, 723951808, 181920328, 360592448, 439901487, 742041754, 557296007, 847825951, 511586277, 823812031, 191815237, 727731252, 925854096, 413775230, 476750720, 366711887, 792758532, 816942176, 997322568, 145404730, 602647887, 182558738, 36807904, 872052864, 315192563, 392354005, 260542904, 580706386, 141973022, 511510520, 107304785, 400632580, 243670953, 326191509, 411945471, 675713528, 526957650, 149389086, 179364331, 647778848, 138600071, 249117340, 546864927, 979349945, 67808872, 547041736, 512150929, 147077767, 576105543, 645945672, 127974098, 681299234, 312340595, 697427740, 700601900, 657776191, 267335493, 918940571, 806243777, 703088867, 742171183, 8951367, 809116931, 667411335, 917100968, 378292853, 743198626, 83595656, 673674792, 416694515, 170769902, 741094564, 200654720, 968594408, 38946492, 383169515, 803482351, 548200916, 287857019, 371909539, 410762153, 668456788, 257618086, 83225437, 222298408, 643990538, 219077737, 303315224, 840702335, 85003284, 129613337, 378185304, 769344296, 506312307, 296624102, 343197132, 318442114, 571254354, 800861788, 109491652, 730343462, 123117716, 520521008, 621304375, 352658350, 659152786, 651140117, 510695816, 847572924, 506365788, 462408197, 458119812, 745994505, 468807045, 896804386, 141332484, 923660756, 808135126, 195159726, 668797625, 520779149, 129325566, 27095726, 939400343, 206158841, 535088594, 139027203, 863703791, 498885699, 976596021, 714896696, 819469678, 1279997, 90365482, 903798754, 700268470, 870267946, 855640216, 39457079, 795480236, 707019362, 108365705, 612370460, 439961296, 618625803, 785704098, 629524918, 358669986, 353321846, 527198276, 265881583, 386829745, 91537597, 426036189, 794311266, 452522100, 893410293, 646958029, 978910282, 875048570, 816664033, 547776577, 148831325, 545281705, 181893272, 588376625, 62593072, 888920566, 313325803, 78359331, 381464578, 224730194, 404361952, 975407616, 464857567, 915028074, 716394403, 409223194, 669537840, 518372565, 916535279, 170618544, 364985000, 180346444, 534089468, 188250689, 110435801, 76054691, 325076645, 224336409, 338296942, 952959759, 298918395, 112708497, 28485961, 392773777, 106271402, 484200090, 139616303, 868349938, 124123113, 413287692, 961573763, 911750608, 182365930, 611526846, 188589527, 477527507, 540301926, 133540213, 749299777, 894949049, 971258674, 761492664, 249214242, 885086884, 429147401, 737787165, 982556888, 863846614, 115721024, 938927586, 612661859, 17091504, 267060844, 778239705, 458136520, 883421189, 721172740, 615793083, 754098139, 383566737, 688881149, 259641751, 456252274, 413316161, 562039340, 562192441, 657022339, 825491338, 364605250, 248927821, 204332727, 21115867, 510692262, 547664591, 27368304, 626054110, 453477733, 965426413, 585572958, 894198098, 845202972, 57197158, 582307377, 829596124, 77481595, 214923002, 488494530, 31254777, 716749955, 663408918, 639832850, 45551037, 88577302, 960775348, 675777393, 257870671, 430844645, 86126314, 325639211, 595215303, 66682611, 323588591, 898159938, 729765373, 11361702, 857244969, 630428198, 344005864, 481615157, 658026623, 97544919, 40361661, 893515481, 766527939, 424658384, 932286115, 269103540, 333073589, 784319589, 398354827, 197302528, 494412144, 583078520, 480617409, 518234867, 177659258, 214449957, 20963735, 900367187, 600820470, 320312511, 495578462, 283645598, 508062608, 628218230, 37482362, 239572250, 512315321, 725284373, 329358694, 511101447, 17083723, 181215734, 430570474, 156212125, 567079692, 566874172, 123539018, 103484222, 828681010, 167409191, 121506138, 267206966, 856688470, 56361382, 722745969, 847272439, 437591959, 319565600, 392298627, 481204969, 666056962, 782720838, 537508427, 625053504, 820013911, 505950233, 402501589, 441291047, 156588594, 646148518, 597632784, 38704452, 882438880, 182831039, 201861877, 214871672, 347776958, 498966166, 13991764, 186628637, 439574240, 838784693, 483188207, 755924290, 596112254, 802433472, 228400846, 664005281, 650094825, 506397465, 439217975, 305561355, 54217457, 600511626, 490785232, 1649907, 748198621, 645582163, 777058810, 201541310, 57009871, 579221951, 541039822, 471485806, 748598385, 615889740, 546860529, 330406932, 322731805, 982367741, 818703031, 273296534, 43035933, 657442515, 982472703, 481021724, 688884116, 607818969, 308607606, 703894795, 160710333, 448703867, 470892206, 675198664, 325443419, 329269404, 292558494, 923915177, 656166591, 216923439, 660414179, 753500699, 289755539, 620404950, 601398870, 757483412, 178843327, 983829953, 112013701, 866733650, 369873708, 169291068, 946381508, 723657354, 501733586, 765991423, 660672633, 462432433, 534678965, 960114105, 478030057, 576741383, 927244947, 568691151, 337841329, 800298708, 663841121, 123101591, 31311010, 68366341, 65165974, 600361210, 974624309, 838005743, 577896194, 766078471, 129390525, 818814813, 686624171, 551035884, 46879852, 317890314, 635665688, 487841437, 300655302, 78056140, 727070939, 419063024, 35461523, 869303525, 290644421, 158898529, 36591900, 35932549, 491065967, 449285323, 829778130, 761092654, 953459382, 141711666, 87519509, 881631857, 485437614, 300335821, 950731292, 580969588, 940335515, 874367637, 681873953, 110323914, 512987426, 793764117, 164114441, 584875946, 599719008, 343366864, 317639726, 286574686, 223429676, 109626798, 271232912, 805229066, 636524151, 399512727, 728031157, 183389042, 240731497, 832918711, 863223866, 701214502, 785514330, 757145035, 638327644, 486896902, 210683227, 709159461, 893785527, 714707413, 291065956, 999180266, 122549883, 830609307, 846498912, 16263862, 128743972, 316450436, 654045884, 2667771, 639740716, 595030690, 814156724, 30060942, 463033516, 425135015, 511412426, 399096923, 112030017, 385210716, 713407011, 974495556, 228396928, 803477439, 428612817, 340684355, 72070760, 661050305, 145548457, 41848067, 741469985, 596122892, 827433175, 420735745, 963880730, 738094746, 263156429, 449136427, 399451173, 342636970, 581766334, 96331502, 30635618, 114056719, 240169419, 751723815, 599882908, 910300988, 49418037, 967270681, 101121314, 143258377, 145181715, 158797876, 585227295, 23144662, 324317639, 685286511, 520305496, 509810754, 921733454, 50741067, 878047818, 736089818, 15273616, 323040697, 30108054, 15068584, 58471634, 578082785, 20642577, 286970666, 730836577, 607705242, 555594036, 504706512, 582579350, 83851870, 692968480, 594253565, 69355371, 652810495, 572877221, 12675090, 278374149, 532340997, 149499197, 715393047, 845510390, 928969371, 575979034, 680217443, 500814202, 119577756, 506931006, 101649554, 198617091, 518917334, 499063175, 492713623, 858866802, 797638168, 295227410, 882469394, 971018232, 551105351, 739936130, 503618350, 559698672, 618570125, 960008051, 863481674, 972823379, 160466945, 30720638, 445961060, 286895704, 458040928, 302542247, 325039416, 479504528, 931417282, 683967532, 666139637, 9991762, 187602289, 458596573, 818086442, 242830795, 122597351, 727616093, 123368857, 282625062, 567700247, 68607397, 914037843, 147696028, 687194905, 866005643, 978248889, 555420622, 727126270, 640616225, 548698971, 263975710, 329730182, 436205256, 568625402, 289566410, 645796652, 278832022, 139591237, 65490675, 665248265, 687048204, 351603338, 584771907, 502139850, 705085022, 194555831, 114214203, 729387849, 413271856, 982113843, 731114040, 611240364, 894952804, 432362002, 579196880, 788832870, 442757143, 787490007, 729317446, 961282976, 331606650, 388259442, 162412649, 693372406, 163655305, 737570121, 386030526, 265107968, 304725384, 812938031, 443370736, 434792423, 500793616, 592545986, 745377341, 719552500, 867609304, 601099036, 607883599, 998057841, 789056402, 365658873, 149088710, 308289341, 430274004, 345414421, 340356641, 426565857, 172990618, 732893980, 489388715, 37016057, 117067653, 809157265, 730000686, 576105973, 429487411, 318150681, 625812265, 913332975, 669343980, 205587230, 184749504, 393830158, 154991424, 576042862, 477673738, 833760365, 354231984, 814955152, 416337635, 281175219, 315628929, 67409441, 366689386, 940485182, 920961387, 788517102, 808207830, 274637504, 899500216, 552941030, 839681726, 550615209, 834768476, 175688311, 767414138, 891283798, 487869796, 779908830, 262397563, 97957945, 518098706, 153345380, 338971039, 994229640, 490068585, 946447166, 678583938, 75123218, 235576054, 513454964, 639419480, 77347963, 795890683, 159723456, 569050398, 623873583, 125638143, 253964077, 613120119, 307009781, 854050535, 523573170, 714981420, 735043974, 117609445, 873078861, 821395210, 416884431, 551841717, 920180672, 445619884, 661170098, 465506917, 364926006, 125389213, 170173885, 100910327, 977123424, 146573031, 970984521, 904275789, 489280726, 509545633, 596709755, 950887506, 493717384, 522869309, 706685638, 49693980, 599015929, 726781311, 880241855, 443163728, 571153042, 647921132, 793190240, 512532854, 282023390, 809801873, 111727026, 973177567, 613751497, 769784802, 507304665, 571643155, 304539836, 679568797, 161684763, 286298293, 447731745, 492590686, 400021136, 611999579, 768517328, 33340443, 197160426, 851347989, 382782348, 437827909, 49122159, 14858325, 107808501, 642702771, 820265079, 908044217, 975192565, 42740071, 301569486, 261609215, 483783697, 270845855, 953525411, 433334045, 733915151, 804122035, 837514072, 354035885, 42231432, 804131838, 533637918, 765414540, 585782503, 254571584, 284420630, 717248775, 823482331, 67706263, 420823869, 594456106, 854322358, 513724108, 796436270, 167121631, 277730292, 572520115, 387455970, 134510209, 530854230, 770485945, 137770742, 653489764, 911450672, 169076299, 973178465, 33325229, 583884415, 298279630, 482710605, 979898824, 578986265, 967704297, 927480704, 673929354, 17265624, 412209691, 483584233, 465444235, 91759926, 523183038, 671884341, 772191809, 241990322, 451363386, 23746642, 328530889, 100439015, 138197742, 454265287, 234010943, 235321965, 286354839, 11399980, 442681280, 395354176, 196387261, 526979845, 979069696, 384445778, 63922004, 448449347, 467370161, 12501931, 525437941, 844347868, 363993639, 123390245, 372779450, 438871378, 928702535, 922774227, 275955025, 909268037, 608648648, 851511781, 79820971, 477676219, 82909042, 61552992, 272303691, 453058165, 993740161, 566756540, 671139562, 700984913, 247814663, 988630482, 272647691, 617940939, 682088710, 929502509, 72528955, 228647483, 924385736, 784288807, 687504084, 493172243, 7410409, 859693916, 217420272, 972954735, 660448464, 532104048, 975942124, 229732924, 706527599, 571326966, 193850527, 237189012, 401193577, 127124624, 269099324, 68791900, 451538840, 158570712, 750202343, 316017115, 165738112, 557182428, 768177748, 856448411, 323678236, 640304369, 474279161, 29826084, 762921065, 87921973, 407928921, 436529019, 501224008, 486249084, 943991388, 946188406, 384685847, 231434383, 141741953, 680389033, 822665682, 444399901, 799183797, 663502868, 525755303, 487019121, 678607004, 413471252, 975144104, 600232661, 410453636, 125643759, 995333824, 625072704, 656856267, 29165491, 995396459, 698351985, 179153523, 264982931, 962247732, 216429303, 930388221, 797840513, 901444140, 632566162, 443659361, 147257622, 281229688, 785370406, 577252509, 731936559, 273753812, 76779878, 380368629, 644275718, 573230520, 493659766, 266905553, 243566667, 380853726, 114931170, 430751495, 802318964, 919127446, 673178934, 970375091, 907607115, 319313506, 587301254, 250999742, 258792256, 447081012, 468733794, 970626616, 897978065, 463664449, 51397328, 539144356, 728740584, 837285070, 851810376, 629764446, 787280916, 443292918, 298992759, 369282910, 864984646, 753903636, 795916933, 688922010, 838829218, 94284665, 15509263, 479376501, 561458676, 429169887, 901950913, 687756508, 687355375, 434569662, 253369819, 224996566, 841357494, 114495548, 886494687, 812746448, 187540856, 392036841, 127095745, 327286411, 315200890, 84297428, 157246599, 763142283, 637770490, 832677583, 483569130, 970479427, 450326407, 934091187, 381667328, 290242337, 745057995, 533205288, 596242510, 777546839, 412524307, 847153910, 72760249, 378715840, 597103228, 612559387, 931986257, 855861072, 820309088, 605509719, 528765490, 750796560, 311999270, 359922248, 382974881, 350854819, 992673088, 733944253, 437015554, 440981394, 417248658, 131439216, 921810301, 501725205, 620447276, 223802491, 281081526, 988528589, 478355744, 959214946, 696577650, 880824010, 404671473, 327341940, 32317431, 20632093, 91096564, 22818900, 508487342, 202034724, 57999344, 233609823, 985933648, 612612331, 447616295, 891828679, 353172084, 539546840, 161740521, 389477744, 976353332, 377773136, 633080644, 471328234, 747249619, 569689149, 549460196, 14799733, 898787794, 379352341, 877998726, 570107923, 194509816, 320007186, 463390388, 308607781, 654123396, 711851182, 304809894, 617155242, 724319137, 367406963, 739244270, 87910673, 746819934, 1178927, 223818234, 554632586, 170983226, 498414774, 197951135, 757131737, 980448822, 125626797, 487202159, 810996759, 310736614, 444506831, 140418853, 532051654, 446905400, 278577398, 527950683, 891820968, 92906649, 329905152, 473144030, 43814803, 461257283, 634758102, 405923927, 29220667, 680335797, 542156697, 477131634, 314185414, 71910901, 785906496, 252926479, 112854736, 678531333, 556628929, 741722780, 177925912, 175365762, 553537913, 453923993, 977490551, 397779306, 801129699, 191616718, 229632237, 442420621, 52927797, 79284149, 386709118, 113048869, 536654831, 421800798, 541397772, 595264521, 472694126, 640955324, 165745531, 154866111, 743678172, 46045478, 781287616, 216750854, 476770061, 706449057, 306686175, 234358938, 229869080, 172751777, 42956039, 241195090, 304152759, 834631911, 757190040, 920247127, 309562775, 369773444, 230361404, 305073218, 567408047, 840825590, 958762400, 107669202, 515797060, 476521963, 442557479, 249570164, 675065553, 483014817, 941495359, 116372705, 882279888, 758708275, 153093552, 391149479, 484238397, 718314970, 963258005, 691794246, 99793208, 6338400, 961825228, 947006026, 752473202, 161659130, 182496786, 3122622, 996353371, 150446498, 980812371, 754700903, 780407038, 802268842, 947780711, 530444064, 74369919, 902045066, 712443016, 672046971, 720031995, 922881144, 215081315, 2250549, 998252364, 831236137, 741383722, 149891404, 86913957, 721854944, 843451921, 218572964, 37230118, 758772720, 661958072, 554509729, 786751819, 881667279, 505374590, 823682180, 623172397, 243120469, 6539839, 557379213, 949475248, 551823191, 808601773, 315679851, 223597941, 870088954, 443794246, 393456967, 512552598, 57799144, 13360621, 669560115, 623026901, 834837175, 444927581, 876725919, 911501941, 134128261, 886925545, 930224105, 965896857, 292879457, 928914934, 141727616, 935680434, 51851171, 150396873, 24847966, 500915562, 486757577, 540019214, 55853489, 108621927, 737156343, 151923591, 973143029, 512270629, 327127090, 536883356, 185914975, 703842406, 728797651, 540188878, 42160700, 642880945, 216563644, 311624814, 151782577, 848252666, 189560895, 489896391, 606673706, 477062676, 446644148, 778873783, 814837387, 692753915, 298254874, 474282593, 590440383, 373937995, 28664783, 290759282, 478670892, 374793239, 152668103, 256529599, 361741209, 734661330, 629656470, 101372930, 398054724, 9636274, 700938601, 394375124, 447839531, 923825587, 883887936, 109190820, 73982244, 829186778, 16513258, 733663097, 709063354, 156942950, 708088710, 142442430, 623079224, 905067813, 921787352, 194898122, 756352724, 376358456, 427240693, 23008617, 121954673, 80670576, 730172577, 398047139, 880342786, 209505917, 803036246, 986832779, 516548337, 348678032, 697340655, 80870953, 336297845, 590579043, 343049269, 941476688, 479867074, 748968334, 548677738, 233667877, 867548695, 813565310, 133826010, 863315175, 65369616, 539960852, 127648788, 768336751, 879231011, 72685788, 681114404, 341483393, 618641504, 788543415, 360947072, 262332306, 332846017, 413342482, 492065521, 102755137, 791322677, 711313182, 890734267, 492150585, 125125008, 158457087, 97204061, 255896443, 21662273, 683490888, 302721519, 989989035, 355583540, 237787066, 561453197, 828929839, 164861810, 192138276, 690983548, 949279993, 484955415, 839515591, 681853964, 21380012, 295171078, 314087392, 40374860, 767869541, 545272218, 212003252, 694448309, 44344931, 294686192, 440648271, 20916910, 304839557, 442586723, 849649902, 504233930, 919804906, 243756418, 667790619, 94325456, 197539560, 839452643, 224087231, 627657281, 837977546, 62922730, 331375971, 656602411, 267306152, 646542233, 487011467, 420200739, 970374781, 193136116, 259551460, 56982938, 728288841, 877085417, 398787597, 645414471, 716729114, 522970862, 289335820, 849274957, 985782289, 330336549, 147831414, 466994242, 590239740, 321187523, 794232676, 275379993, 255595671, 414539271, 761754840, 226070463, 279749557, 732716955, 811049178, 267851811, 827283297, 286282041, 425923377, 557700597, 462224865, 110283250, 79349055, 755741525, 502338110, 381407165, 190857386, 818974661, 599482603, 786949806, 385480110, 59045835, 157508595, 182230741, 109034878, 663875278, 414664510, 834570591, 162208199, 201896677, 73169007, 775056072, 330562395, 815702053, 732871952, 386497876, 727735957, 297512344, 81102614, 64476290, 763774422, 917856597, 642712557, 805370903, 704418524, 661864000, 844613262, 821173623, 842084599, 945420882, 520178812, 773063105, 794559769, 799900264, 328083492, 257583309, 641450022, 959167493, 240352054, 746212096, 269576727, 954496482, 329632531, 968567750, 581413162, 219409399, 72863109, 860214367, 299985002, 63422574, 809876326, 780785206, 380595378, 25228291, 24290698, 671549493, 803549511, 862783237, 540871561, 973377335, 131801959, 11176116, 914264846, 324107268, 918567020, 789962631, 121197919, 618432354, 154456435, 739408644, 51975043, 757920761, 714140418, 873931170, 452598584, 292123373, 374357692, 113426574, 552896353, 121348198, 276598753, 814778153, 289076078, 917730154, 581892186, 288423807, 812924586, 436475971, 440860691, 915416455, 45972390, 781929164, 108115081, 67895699, 461145967, 400782986, 343751241, 982140232, 729460550, 607555884, 892556185, 481211205, 199154478, 941194400, 994988401, 21201877, 64975225, 331511033, 89723152, 533112592, 654513138, 382203987, 25875181, 848441524, 924504106, 550904921, 247212425, 400103200, 778578014, 946038035, 729967462, 792567330, 953244200, 527344015, 352484943, 669514388, 534144817, 424467032, 9675580, 352381485, 666843361, 44034870, 541153935, 816210145, 953213442, 407931221, 704341148, 48330616, 514704450, 144695788, 184403991, 62960299, 191076319, 644998535, 442223021, 618251637, 755340441, 356681774, 218131464, 2978461, 450513234, 56953981, 480386266, 918847154, 805051221, 979852035, 118357490, 602408901, 553500929, 402905028, 903200700, 608983836, 405465625, 884447450, 871320490, 574492645, 712721281, 545141199, 643122217, 455215864, 369286023, 829432298, 776340057, 746110064, 68400584, 694929667, 995903084, 849605148, 576780248, 297871623, 303644935, 959665945, 452916334, 504177808, 820330346, 672231643, 913320081, 153716995, 764632276, 778920425, 691358472, 484676167, 95821096, 273930055, 520933369, 204880888, 424771231, 200001599, 87544369, 812055738, 538360875, 389588008, 636287768, 84756670, 254316911, 135791788, 16698340, 595254671, 129897621, 756266851, 27945539, 246861100, 722185540, 970046209, 39132860, 420284908, 109249154, 621775209, 793429254, 477823184, 349975049, 467697256, 283134610, 7435339, 473904132, 703210014, 5884256, 493905062, 383020607, 422180150, 645579239, 284678640, 278157633, 843814632, 343164063, 614280810, 207149706, 630108890, 302060276, 142419270, 411896770, 454642609, 934066465, 896529156, 146798296, 504507378, 958966589, 304013059, 948429585, 392481251, 254044560, 282406870, 887025082, 902797934, 539316751, 942190980, 5252342, 999409064, 50427638, 104863710, 141514226, 197878183, 617105815, 108470700, 160936855, 571960966, 353857459, 970714138, 792518450, 588528770, 323896906, 677665602, 223925331, 645076183, 993628448, 730498993, 402415856, 446794188, 945405635, 448390446, 214111759, 74497214, 184142502, 813117555, 668871099, 783119305, 996142076, 226135507, 577796324, 329545370, 988992000, 73044736, 411465544, 200504287, 924848901, 177046628, 989795947, 130728192, 997915863, 865837634, 661184773, 703324798, 262713345, 28593644, 996184056, 142245015, 19508658, 37681962, 661981888, 492487715, 667415848, 305802038, 173225528, 685210486, 864388607, 225597345, 798535436, 449389286, 136315069, 32345122, 929895305, 147323848, 677431408, 435047674, 710520022, 917237286, 802170166, 596301180, 330141808, 966573354, 486292390, 343187508, 27664074, 619814055, 215127628, 714645534, 916021956, 760532089, 238737276, 472084060, 512188992, 27980516, 126239791, 703842483, 719181325, 872476177, 280828447, 998014522, 810156848, 9095615, 133505117, 964341752, 500824092, 699278322, 417738879, 821867151, 761302150, 273113640, 529451739, 7504309, 408075009, 10481411, 74292520, 747006173, 155794391, 612619410, 242364339, 795031449, 271265863, 827379559, 759365341, 794503485, 308729031, 924636219, 831682905, 132824252, 179956176, 292387844, 945907836, 211902044, 506896220, 192162599, 288497260, 908500796, 607926588, 963885398, 315597984, 494049563, 454462008, 437321629, 873175947, 200142483, 437404520, 925119378, 92051283, 561832924, 782446142, 461384531, 558199564, 594402860, 402201002, 156307356, 638004907, 731912411, 532324848, 186539354, 162472138, 865653607, 613957306, 734426270, 242605294, 708775200, 779255108, 780575404, 874213601, 886138578, 715656599, 418436674, 375892373, 576968504, 18837905, 14295565, 207589159, 437850017, 376276578, 166671335, 826636670, 487924644, 226221935, 906397620, 174988783, 792880388, 206995952, 816055216, 428250773, 817658744, 684993800, 82264763, 831309350, 458138684, 49574207, 270808604, 825151109, 148770538, 648239351, 633278693, 197076205, 518606898, 31609875, 962334258, 824591239, 997100439, 489774508, 951961539, 55532917, 659325538, 176288451, 918122177, 723005631, 253014882, 582037725, 263157487, 3226987, 796837840, 600602947, 440564985, 323683983, 370872857, 385407079, 522181762, 920803915, 964023237, 256516454, 584141566, 740520415, 433128581, 509928724, 308512547, 643674726, 549080964, 280856286, 393373043, 948578721, 698656914, 20219761, 576665457, 875751145, 409713218, 792417128, 269686833, 448714061, 144745134, 648564912, 584178303, 290170274, 144220609, 306987168, 40841974, 430455506, 566729298, 421638541, 778783083, 17289484, 665864060, 536448907, 126696701, 167350399, 266735986, 409472452, 976393432, 805632957, 504865996, 623642531, 742001966, 326660963, 855964451, 561728230, 988533789, 369677775, 761348118, 206908048, 285112917, 121948112, 10216001, 326844419, 371012682, 799016679, 499123420, 44877962, 598595131, 55759500, 51703762, 738088616, 98209656, 724348010, 801684435, 312997755, 192933405, 563251252, 77398632, 799269973, 115590821, 170009480, 2228651, 777714936, 382386619, 405782582, 777244192, 595426642, 916499213, 385705294, 349128092, 928141415, 827376584, 716968143, 603054543, 220710078, 143824763, 254336918, 21548149, 303017596, 532072341, 456543303, 13156810, 693132247, 164645665, 311352402, 438434511, 919757848, 804380068, 831343576, 281023015, 76366074, 881646710, 88084156, 227155845, 113409937, 627831359, 104898819, 103785588, 208051426, 210291855, 858669765, 68193698, 781562175, 194933864, 715413339, 537864664, 426704775, 884411200, 506387794, 538414723, 166925336, 22617916, 899135438, 295979381, 660818380, 259192009, 568165232, 887937943, 889030957, 659348010, 68200141, 638267214, 907878763, 449360680, 619530036, 486146957, 157855016, 113905829, 607392571, 356861554, 388402264, 467556083, 776034722, 528301974, 130837829, 917795250, 412425595, 298454172, 713167038, 844658626, 931759593, 596015297, 820499906, 934172298, 923506507, 935338128, 63807269, 551927209, 299286058, 131227394, 8229835, 940560522, 3897516, 160616183, 524416544, 857250389, 696924628, 190758067, 328678523, 693607113, 564963428, 50942004, 676453069, 344114809, 694022431, 283065256, 319127404, 197135463, 670145776, 884206417, 134301145, 850926874, 440868563, 88579426, 84462250, 364416619, 456465163, 591586491, 19282466, 491689503, 305745803, 227096210, 911057582, 752703061, 608129018, 94112366, 768584995, 924799472, 713539276, 423324057, 460020059, 328595831, 834830060, 482597770, 633175311, 258061666, 331582110, 275220987, 698049269, 937872083, 808084221, 673665839, 48404513, 270077924, 239756875, 795473322, 588518689, 116699213, 406211939, 897031828, 147768788, 268451755, 639755930, 677931542, 441388367, 695919727, 896599985, 79313427, 66418172, 556643467, 564347745, 208554987, 636279106, 826963082, 26550350, 9696371, 901847850, 17434915, 881515122, 500383346, 390089535, 984749798, 396253174, 415759380, 928819511, 972088554, 973904278, 939157909, 463790313, 949992584, 817227006, 453310501, 708966035, 126911614, 142165630, 617832995, 87855895, 157636860, 778557483, 345371634, 683055791, 557601417, 283904673, 16356069, 48070577, 131148008, 456728330, 303395276, 452301947, 334037985, 111029123, 799277775, 485555613, 911878258, 984390555, 925335914, 171133589, 788657196, 405548598, 674442220, 678980086, 517055793, 323572451, 624014070, 18426152, 909431046, 501316087, 448171002, 356807897, 385581497, 452925860, 373569161, 170959943, 739464883, 424322386, 184090522, 518569448, 50247597, 903418550, 631257682, 355273159, 785861341, 655523202, 677360557, 60538226, 71942065, 666553961, 632047299, 296725915, 170136817, 362924295, 900045729, 79227015, 959514907, 625586377, 204409131, 41504955, 920070681, 293610462, 868053309, 587403592, 123251967, 909823035, 722562099, 814085834, 260913298, 315275309, 635325652, 887606574, 591824050, 10866176, 906955383, 980401033, 407159229, 645749207, 287087587, 793280590, 738329457, 951690403, 723874569, 13066007, 191254454, 741302592, 141418861, 309603703, 32593739, 348501916, 446688882, 33767511, 61101429, 875336453, 188295012, 144988141, 259053529, 492472002, 515699210, 214493883, 825974050, 326253045, 649238666, 480881708, 191150855, 762075073, 102431005, 251903274, 143063249, 302665735, 130854181, 321900914, 191588228, 285659786, 927817815, 220041203, 338476609, 821745517, 425303663, 371361971, 698185721, 272180033, 808690858, 948477836, 395978805, 914443234, 411794600, 850922114, 925875669, 495965331, 561805058, 347943614, 926614209, 102974157, 256834507, 216762634, 821215423, 983424837, 22765516, 408606307, 503958400, 245838152, 39206076, 912296663, 373674169, 727157350, 154889862, 826965028, 850552234, 318042387, 76539733, 179953164, 766460899, 600536710, 402671630, 391187694, 446276575, 56226589, 689888919, 674349593, 633491202, 789352215, 787915845, 876168832, 686601409, 837876577, 268798001, 194426204, 540786824, 135135828, 668919576, 76883619, 741633843, 258900908, 563099011, 277110121, 670752324, 467625163, 95054092, 405971679, 308091542, 590842035, 228898769, 811342064, 277242563, 603558661, 190005449, 933646818, 45433685, 176901578, 567104685, 944899241, 549685286, 436015026, 689002326, 23537771, 499029634, 772409148, 151507492, 151831195, 706167332, 657400398, 851557021, 956966565, 674757458, 891160818, 736178081, 475097147, 760027493, 311706286, 232261023, 639073021, 987578543, 984777698, 492143358, 660014671, 637076535, 94909101, 868845893, 307224693, 67978032, 41056226, 159530478, 471890763, 829449685, 697338268, 748560735, 594457962, 697133831, 589748050, 682037935, 946108593, 957332888, 754300983, 358640289, 805186407, 122487671, 294074346, 506861481, 51235197, 703022942, 493306204, 544108656, 20932086, 458066090, 355948060, 860238604, 243390419, 906323866, 800076150, 178303158, 875728275, 509046953, 202730020, 930257467, 497925152, 58373887, 272328322, 523723531, 742075079, 921653268, 370322066, 351159480, 701164570, 185395549, 630859390, 127462678, 29158539, 523984968, 937956737, 358545181, 864582734, 697340465, 459421425, 329438551, 282515394, 642531695, 974865253, 945839808, 164945210, 272220680, 775888674, 521449537, 165054140, 237645948, 332836401, 662464085, 269596546, 991650543, 44392692, 820354118, 916960689, 688669540, 393110117, 941451385, 825025408, 518251613, 138426653, 531194683, 626059836, 118032964, 250684845, 698795988, 308653849, 70340524, 279576665, 587910351, 602087783, 856501595, 916601573, 815623514, 303315105, 256352482, 675645946, 22037997, 578954422, 249247807, 923330071, 791726806, 966052627, 705556781, 983110977, 928759761, 734691552, 132262368, 688188430, 664914958, 235271185, 84337379, 373664096, 601794293, 836096273, 370594369, 936981576, 177766011, 733684281, 189210313, 761804815, 218996981, 844736724, 410150254, 424302996, 288585305, 841056971, 384455570, 787260947, 254687351, 250075244, 317220471, 246365067, 132677641, 531083388, 675669942, 215494017, 578482797, 420714273, 263359972, 683669756, 542127070, 505061250, 289802339, 867018999, 592498814, 334100480, 165891460, 963288539, 281914265, 408655893, 275222917, 729631404, 415893908, 164779455, 584715018, 900483581, 207066285, 831282935, 171395342, 969355168, 972515278, 250691675, 45536958, 11009743, 67537048, 821719062, 21904973, 523395998, 605628861, 261855759, 799438646, 449983643, 771449356, 325407749, 358367578, 309998816, 512460490, 930037931, 495688263, 318284168, 510783652, 142620512, 2867094, 593363550, 925668105, 393009024, 941025756, 301656439, 163852254, 28912643, 158553237, 133201461, 46954060, 689945516, 911523147, 701178538, 270580236, 355407987, 318630677, 337564681, 205086901, 577977055, 540415965, 612178635, 101364512, 891430598, 37699311, 803594803, 554433225, 382760931, 792107028, 742350144, 646413636, 757969103, 262713542, 778523547, 300155584, 607976468, 452203859, 700998071, 76575658, 321148144, 659250130, 847525741, 911188245, 968515642, 345031058, 930559669, 713725423, 304805834, 151362076, 794772152, 927306101, 973483068, 836348661, 554015342, 336743932, 558982094, 743876959, 876121073, 879962923, 835723801, 105652703, 709542582, 284365195, 709446046, 256587421, 723975227, 457760420, 812363053, 932426145, 599981523, 191330384, 998420366, 165460994, 400424269, 540484158, 872483576, 436331635, 356362959, 866098452, 229379060, 51451725, 133945514, 447677920, 770499142, 678192075, 548478470, 526702050, 636267288, 483150326, 790587892, 773590396, 191166688, 858118688, 979223018, 497625795, 855001392, 125748804, 568063716, 854334623, 428730513, 897030034, 971478914, 809497246, 507930181, 221556357, 604926130, 213160079, 7911590, 614295538, 50770494, 371684224, 861306492, 861549264, 696718950, 678889581, 522900739, 812952163, 243625384, 575566153, 896174564, 221601374, 208325253, 116101981, 982602467, 196531346, 113409245, 528046868, 184299619, 975638877, 659795945, 633916421, 325663955, 518255513, 760304175, 914556900, 354467660, 909423416, 512743817, 330770917, 231859342, 226659880, 968620404, 439670840, 57705089, 280621796, 718586638, 874814543, 202059070, 903950529, 766471613, 304881685, 919190292, 163980363, 738272581, 511078708, 813038036, 130100323, 140116400, 34500025, 177004975, 205280710, 848336001, 6474910, 578879877, 676665586, 474422896, 693311722, 726587245, 407466403, 372820996, 646489613, 430931662, 610717070, 69019138, 897420002, 155438116, 688892794, 43855050, 267070466, 88719168, 46434770, 904940428, 806481289, 301617425, 814373108, 978102137, 657721071, 648890928, 902059810, 374682927, 500001187, 583004571, 680660479, 83476396, 952050749, 147142124, 667868984, 657981113, 102671734, 358784078, 406697934, 707360486, 79134085, 604272737, 802224196, 359174134, 905288041, 791473640, 705865359, 590596904, 482590074, 925952674, 249054790, 180335802, 805655799, 746382056, 323052014, 899967149, 32984016, 537312948, 132667091, 834672206, 67723077, 436776631, 720157959, 445584565, 172829630, 342353780, 210551357, 970813894, 476334706, 180353311, 628928452, 602225966, 630556805, 717321883, 392963294, 99908994, 608294323, 444400321, 606894858, 388718499, 645952890, 960802119, 815989760, 611081929, 515344465, 513745265, 478997037, 841229177, 81699563, 759153050, 290183996, 553585503, 258645917, 395561574, 838949038, 699144010, 400097453, 571410236, 742353342, 284590289, 724337428, 639213966, 188625724, 667340156, 905643341, 113801389, 129651186, 466292399, 49327126, 726348983, 580551664, 522575405, 485001534, 32732886, 492505603, 776219900, 413569230, 937198155, 581047538, 862338393, 735628726, 42344845, 650356065, 740921998, 476714290, 280044829, 390324929, 639307692, 277601448, 130490230, 981471572, 445515616, 55039966, 139395400, 992187062, 176428499, 84483977, 373695028, 866137141, 887707339, 972632444, 135577939, 144522927, 45395272, 932859467, 3304288, 596864250, 98607035, 330198971, 589425880, 205294887, 817961346, 898055339, 50025294, 237907481, 754693395, 886319703, 343529901, 358161878, 57883200, 481423241, 744249684, 479802159, 901964104, 26400013, 808880608, 382363714, 753484364, 646117930, 381035115, 562411862, 450448173, 376350285, 734567770, 158001496, 828150606, 191238366, 641198638, 311865738, 623345660, 588807770, 19064924, 860408002, 7215291, 160532920, 404924763, 25558595, 85980775, 641483392, 695974581, 443713208, 711205642, 891325696, 888101740, 652300377, 103451107, 132337129, 27502070, 948014283, 17432707, 631532195, 663291589, 616281819, 919043717, 757543774, 45245528, 302654374, 328556942, 936274297, 176231505, 151888113, 351931047, 364991243, 868237703, 747414509, 954295354, 662728395, 407927180, 701763401, 12120358, 233229959, 966364394, 378388142, 595958622, 855750799, 860593286, 48893470, 359440557, 37816729, 832386225, 659673076, 776627678, 442541449, 363031215, 801506551, 769684159, 375244167, 275585422, 956835861, 720893326, 156903009, 396059299, 445843775, 389052259, 340385495, 34824334, 561486049, 30009939, 372130312, 411525921, 36921145, 53955169, 711368141, 220391230, 782784952, 749903946, 834534156, 364576311, 480528678, 322418017, 645506118, 472648710, 260737466, 872832886, 324645168, 766133278, 925335001, 261580448, 487355484, 395538348, 117930219, 419601748, 475634067, 671184525, 276454446, 78836157, 638263388, 14933760, 533073125, 231288575, 948878832, 521165023, 219182772, 7816096, 58434354, 738294610, 601400928, 502409390, 139330536, 104265080, 760578555, 289141574, 666481811, 477865324, 765546483, 167353989, 281862569, 164836432, 326949968, 992394590, 484755863, 261339860, 884945072, 991226987, 849299889, 103312384, 676566652, 611663090, 500238707, 405924087, 434854045, 375728396, 443188028, 247909028, 681248163, 520568537, 746173706, 871012858, 123196665, 80291871, 231424919, 245773292, 120326785, 483431738, 206735911, 705494418, 258101346, 589081226, 238546689, 724522547, 455866600, 36884090, 208620713, 646876678, 636863122, 919820500, 962138799, 65024136, 938163587, 740764418, 771308598, 804687401, 371488709, 82211194, 996131667, 123631037, 179351493, 157282064, 975598215, 717449574, 814700806, 539394511, 365985310, 756708917, 888967856, 373365499, 305980342, 225348052, 929194678, 610705307, 211098695, 771819106, 263123564, 711998233, 52320014, 595787038, 273241116, 466831716, 385016640, 556643335, 726987307, 746062282, 736406683, 921367943, 785642029, 31326659, 145228692, 415137177, 737999878, 100571572, 178792177, 499739869, 186880494, 596467385, 970655117, 521656287, 462513197, 132620834, 387744314, 238651287, 694175528, 70184414, 519167856, 522521537, 2005858, 218767832, 680742007, 438257374, 76817528, 688452568, 895354733, 918866191, 7318798, 609268671, 186245199, 603551033, 489650150, 840125047, 296496959, 297448780, 242646618, 510733932, 590619730, 667547869, 358480680, 889204903, 623045270, 217094185, 235555929, 742665461, 408497822, 337635002, 965559064, 685412141, 459111378, 885024629, 460239279, 5275609, 167669090, 81206502, 111807514, 506352447, 141729644, 79543454, 417294650, 894618098, 132839841, 767973196, 233992958, 712019970, 100635612, 357774572, 117741945, 864258788, 314356190, 537802534, 686656167, 722712393, 81405732, 518593552, 722854357, 408540965, 254507342, 788627036, 158334603, 443525180, 620505678, 517229011, 809220119, 231034807, 134266248, 313223891, 328809813, 79067639, 300355335, 202040856, 371687074, 581700088, 849877180, 57248930, 791248509, 185817881, 671496747, 203529097, 10908228, 632668273, 434867216, 857392007, 107665785, 591137820, 3457647, 640008124, 656690000, 680937823, 679996340, 856842106, 131105789, 905995003, 73252569, 290244745, 844528600, 473319890, 602018894, 98436196, 264942163, 272478100, 946681686, 54353880, 822008960, 825171091, 137304229, 520827470, 470341839, 742372521, 562173570, 589302737, 22596466, 145674450, 444869534, 130331603, 965804630, 462788376, 593796803, 629873139, 113830036, 138624301, 562385004, 330492632, 274627018, 340715208, 53375996, 616817622, 420492159, 166972126, 980686687, 11864210, 678297785, 811962436, 175046252, 227458614, 667382936, 541147984, 514755933, 130355527, 392069061, 496693252, 733930050, 337945022, 509805981, 848100440, 18761095, 111160059, 737318808, 221722521, 482226709, 181496172, 793850136, 172127868, 751755810, 457577469, 763562719, 540089068, 225930282, 164908279, 39937272, 992340001, 917459431, 237904607, 66472213, 95176975, 562097284, 667616317, 172420928, 184147575, 505315245, 696228224, 647580524, 619570466, 912909519, 331284995, 548924687, 246699567, 564260391, 431793115, 537509031, 5092482, 970987775, 424366246, 560858810, 946022098, 520062930, 749339692, 540877886, 746572627, 114133095, 749392516, 16860316, 810445549, 301546279, 210908134, 972602750, 544317778, 922234798, 763715953, 51793920, 231693922, 699194813, 328712687, 675769966, 770860114, 21887398, 308181865, 113473133, 384811424, 944859136, 597676756, 941259184, 354562037, 962741347, 180379369, 758900544, 806343119, 146666667, 426910382, 532647178, 273309101, 829716007, 882377450, 432108257, 389619105, 234685509, 596005058, 109103774, 45512734, 763657892, 628550407, 377680891, 159883702, 145768788, 473122713, 762276165, 791794601, 496248877, 998262218, 58723405, 441605100, 972663438, 816136569, 961695276, 660726364, 149536649, 974695146, 46248201, 798781321, 982115087, 978781286, 603643482, 502812608, 919781707, 60725272, 387210601, 618470497, 508235175, 573015316, 63599787, 592138958, 500608861, 818917981, 991164358, 830669907, 403706840, 985518779, 626947546, 308275356, 929851297, 328485766, 986034355, 709529008, 545511116, 675471861, 185170364, 68369936, 313645790, 455534672, 537874596, 836721303, 768564597, 971112960, 431213377, 86979324, 69877533, 67043743, 615570859, 162488353, 915923213, 24833089, 737741332, 580491192, 128691197, 380957538, 862869118, 807503123, 355051218, 36031037, 508249730, 4497248, 990922003, 489594474, 327302059, 468795969, 12613873, 183490612, 776918793, 814735371, 888471277, 318111325, 856392012, 703498871, 585142103, 392008124, 643649758, 731378783, 601952208, 314300299, 463033312, 574278617, 123099244, 509136559, 22539099, 13413800, 745656969, 928771153, 394531939, 783924753, 271982955, 834261322, 945961670, 398133718, 291377161, 731914184, 355139025, 441598564, 175150545, 509435909, 906650728, 925837964, 277877668, 816521268, 113311795, 161729781, 792107286, 525434849, 225182811, 986834893, 508659945, 762347912, 890287352, 584048637, 907244699, 118205212, 268103601, 171416042, 79742277, 552115615, 482979511, 593772893, 5068208, 836135129, 422920176, 20050101, 383807519, 419879565, 455943056, 651636323, 758753484, 411395313, 292445010, 704600300, 420861918, 799379751, 449538926, 81295305, 928690853, 722011020, 446697166, 47538366, 858989284, 198063068, 462564550, 183519410, 779940492, 205671995, 895155875, 529054893, 446239514, 199157217, 518257111, 396114126, 68563814, 874921879, 736323592, 441584109, 65732508, 348190076, 326245510, 226414391, 225689536, 148128704, 940827687, 294773386, 379081324, 871315023, 356943149, 133004656, 737776189, 240591746, 11156653, 240973618, 955292202, 294499230, 359599684, 496133300, 833820808, 783928834, 294607360, 736858450, 431169489, 401522594, 463403692, 476888642, 471793753, 606662505, 423636130, 433149478, 136686782, 390296992, 564776675, 418098783, 146889284, 537883423, 305493804, 785934757, 187660481, 930545770, 983250812, 925917079, 513152098, 532050797, 805380179, 908309857, 345686684, 125425291, 266242629, 62889205, 806457212, 945499116, 35879420, 434120915, 682346695, 526255071, 539963819, 596174073, 631654580, 167180270, 730795208, 714868912, 364768101, 309628853, 827484660, 506982923, 791570877, 159532933, 475634968, 172958200, 526137436, 414835473, 593935992, 232124616, 354405078, 730163246, 38665014, 147711594, 356481243, 935325489, 192349232, 130024821, 488412762, 989165625, 977898574, 284523049, 89357299, 237356403, 1527762, 373057482, 345785965, 673141922, 664997469, 9845404, 239495077, 68845102, 357835869, 721149139, 927753384, 172578787, 245734052, 743209878, 417669399, 826515189, 875916799, 824755926, 90763637, 950111811, 415328260, 414756725, 800640977, 680127208, 102774729, 357160509, 338445309, 322849954, 350631204, 157135219, 982150301, 642257214, 214308629, 726715764, 436555339, 561180237, 253118780, 186774497, 631240209, 861612728, 962405460, 310351171, 474040803, 199609960, 57756402, 482733128, 940916274, 127583600, 266065977, 160253772, 966547415, 664172956, 508345748, 997741474, 604685218, 443873540, 318438316, 919802939, 592839954, 831450338, 452756860, 74430138, 764054924, 108425985, 688645583, 736918715, 521394149, 325645175, 374035690, 827944461, 430475951, 179184865, 481158399, 970058432, 93520511, 97257965, 137602799, 748667640, 338327387, 69368916, 151879537, 532321217, 995156585, 605886895, 173454269, 894405403, 275909606, 696258561, 551794779, 134088996, 921268720, 755899823, 670951680, 660248940, 571176837, 318654231, 729244383, 89591999, 76668422, 557667945, 517952584, 693197222, 142054279, 824583944, 339182415, 902197269, 578170545, 517071793, 107756137, 910319728, 108186706, 652517552, 943389504, 679664199, 351134214, 866141506, 695090336, 381582395, 241302379, 512158508, 498921022, 467515942, 516966699, 97958864, 584039673, 92911284, 421915439, 932381060, 227247835, 630256980, 755597990, 300662031, 834880969, 502878425, 878772216, 382464202, 410564427, 882937539, 774035424, 213214061, 955445835, 606560688, 165827270, 118841858, 427876392, 426707812, 285566898, 17592272, 832166691, 848426341, 10485695, 948850914, 669931590, 776991342, 743580684, 125091775, 211311874, 906249638, 67900676, 55538096, 251908071, 592576792, 442510483, 418665084, 59821538, 352956732, 706234830, 402660839, 744793216, 905542122, 182797697, 369020518, 787948633, 720842438, 405663671, 543045805, 252867354, 773087928, 410072448, 888168454, 361539234, 796373583, 460281799, 948544634, 89122264, 171737134, 790003949, 405745833, 646528811, 535999454, 728563231, 47172722, 934568870, 505574159, 499248629, 730208718, 777213835, 160939827, 437210596, 296600448, 475054581, 461567173, 908728238, 706154383, 690270470, 923797952, 654168770, 824801377, 590454439, 324316702, 746059699, 629890079, 148859080, 289153751, 542504294, 853884878, 614867754, 396440219, 47330225, 193068917, 732115039, 85581227, 655192194, 627934413, 620243179, 245329978, 289676684, 127839270, 714073460, 382362263, 742014382, 297125342, 889770224, 920630135, 894601449, 487107235, 354687789, 715960342, 370469297, 732283027, 125082576, 953829476, 997853643, 454594146, 470999420, 378181663, 519186829, 167145679, 988218119, 406512976, 570465032, 141144173, 8314213, 979870996, 173186069, 322376416, 238544927, 460199310, 286894443, 517468391, 117630339, 315988658, 349101085, 364918043, 990873650, 12654796, 488556705, 627482707, 603343210, 460697828, 497388155, 439226955, 814342221, 250171005, 892520764, 855103887, 454432090, 657234319, 207140674, 528561702, 319680754, 130833035, 593665384, 883477392, 968904449, 646557904, 186957500, 684109809, 592870837, 777771883, 776795938, 789660442, 236073132, 349863627, 532213347, 927142953, 643496788, 332154261, 907340648, 782908281, 470654992, 920993589, 847847271, 121873692, 332850311, 338862278, 578878832, 106135192, 571310506, 798057182, 335420646, 619715819, 34820268, 465354077, 223517842, 113369403, 38206018, 815773300, 353944934, 821714651, 535479512, 138563145, 997699381, 143316945, 787507188, 758688684, 493805656, 729220263, 39906807, 970813322, 733748031, 341646503, 471093151, 292451775, 188349683, 736618190, 464505831, 389625868, 625361156, 991443089, 878151510, 55888442, 594152939, 12494394, 339373325, 958238469, 357084495, 541280896, 556350947, 865290887, 660898378, 890066179, 637263677, 862889353, 890820908, 599086340, 394909081, 273747662, 446477613, 889416404, 653482764, 874938425, 115291359, 58732885, 533469315, 845346093, 310247608, 151972838, 355275116, 583381789, 201815586, 693824831, 220353018, 25968025, 157346556, 568993587, 745767988, 232416049, 664894252, 423906825, 751886640, 658681857, 579195005, 170490400, 838846573, 205966259, 278316866, 939319474, 773795755, 117211327, 446302078, 719363665, 111195129, 108951313, 975780548, 997663798, 596688878, 186611091, 527306372, 950529752, 275895953, 53409520, 890970779, 618243460, 200925466, 536279771, 997873588, 187702893, 861936503, 997488926, 246271163, 599166785, 786380875, 802187158, 470812596, 470567163, 430011078, 808624719, 940715203, 95160261, 774261935, 494215562, 665245754, 289552077, 128092541, 938645517, 749823126, 309402520, 227027475, 894768091, 120245482, 839935764, 721698797, 165846899, 96538926, 897092232, 58377861, 854437709, 734047029, 54134707, 241154724, 739668748, 672913792, 478958172, 229884339, 706416642, 219066762, 987781653, 166133913, 209825807, 697715994, 330779143, 547627419, 704444116, 152044971, 754197169, 214086460, 871917310, 274437444, 410004769, 214828452, 895936299, 649942205, 778398893, 411566421, 654401003, 887756481, 952211613, 272426064, 739438646, 864260045, 395060153, 651949643, 975774067, 648771106, 395611592, 609966369, 871801698, 778167750, 916317463, 512011068, 666109481, 907972724, 11768846, 553132196, 550624824, 198957339, 425252375, 35595768, 577997037, 725911448, 693563862, 4937500, 217323776, 783574472, 581035139, 697595682, 541928388, 207331809, 10528246, 816036631, 258632450, 36189794, 205269194, 604048001, 284862093, 121100828, 739846682, 883391181, 642894820, 669783298, 227374927, 918462784, 696525062, 409548938, 27397397, 524570189, 330278584, 69438076, 774720248, 190321577, 744040611, 739490484, 903941854, 854955435, 582335013, 214135089, 104040531, 5259239, 770918722, 478552077, 611592488, 210109870, 127206871, 655958553, 585914036, 634870727, 740693186, 459438391, 615806311, 317352958, 906714971, 472600376, 214328363, 901165102, 246550359, 495070362, 491992279, 846202946, 266907329, 828421802, 818737528, 952886501, 189269502, 896928831, 78344931, 551986206, 453316774, 346665261, 797451291, 395231582, 260670970, 883055220, 774812666, 627056990, 686018843, 173843287, 142297782, 603805165, 923471312, 527338922, 986850229, 645773593, 462806468, 366711049, 858404732, 666246775, 19728500, 294911667, 149831492, 351382310, 669751995, 186997274, 766824519, 72249024, 44430075, 541375988, 949432299, 421180942, 872378599, 852716712, 477806186, 303201264, 450189522, 180176349, 617860906, 269029013, 807272582, 109078354, 549804112, 504483761, 570220036, 961246351, 95140550, 521457389, 936128962, 678132915, 432014259, 840953601, 304212276, 28316936, 983680213, 715789277, 991105077, 785147537, 419999752, 250345589, 722605857, 628411635, 627622318, 37703820, 196082842, 818863697, 120001885, 172838216, 180400384, 195249769, 658073595, 189541805, 973996132, 465349113, 966926666, 681566038, 562364524, 279661709, 993903829, 502226901, 525158704, 180172612, 731044762, 491604204, 9733311, 160829924, 382645562, 673690856, 256056606, 865875092, 704435027, 316220615, 437576362, 178235074, 876840393, 474872524, 230140121, 180873059, 14121867, 11044191, 125982327, 111080628, 830931203, 346654760, 381636351, 182088576, 939211120, 383740565, 955571578, 952435280, 536286369, 139192642, 541100978, 902873727, 866002586, 359274987, 914634977, 151081015, 407103355, 261833189, 629620720, 665719100, 998463848, 181325618, 872779980, 867829061, 422441638, 495725118, 592032780, 417970460, 579928173, 877817931, 106290997, 717269259, 58900671, 817418104, 640380163, 567698976, 437298919, 859490629, 197598389, 523660651, 222472653, 612611145, 271865376, 693853853, 208104193, 156108307, 893739819, 67998836, 431898785, 963230558, 550080832, 457933133, 471825027, 563964247, 967407438, 658896042, 488310086, 983488917, 683191107, 190417544, 87324813, 57241675, 226741342, 12523918, 756559064, 395024800, 429208749, 52913037, 503797309, 17879225, 354032587, 359914191, 598191715, 583338074, 85104603, 836253297, 555151306, 178505156, 27405871, 473720620, 475452424, 535930132, 613348063, 812280582, 436480941, 564624032, 35462251, 928753687, 682999495, 502946546, 300705276, 91933735, 194048327, 43741771, 465567751, 297755975, 729761980, 782762318, 634039038, 233419873, 858630959, 461863856, 354375560, 224080945, 681538862, 141580372, 951561499, 807826395, 395103570, 582544384, 354794434, 784275095, 938822298, 890183321, 847073222, 852285850, 760197151, 994335122, 307821300, 867574159, 25033177, 330790694, 252964, 229801110, 653647795, 665888536, 726104709, 528544429, 979057446, 228588398, 120373773, 935331104, 520646510, 949894265, 176545213, 501395480, 588029964, 45041616, 969672256, 986313592, 96621476, 807171205, 599046826, 492871089, 475801315, 867010667, 301250337, 158944538, 939039233, 866027003, 323942634, 95505376, 867207722, 589580336, 424295263, 419535757, 169073176, 558294184, 256464261, 820852558, 48074509, 941350327, 719175369, 958584502, 79571628, 573363434, 673003058, 896671424, 341127484, 500237726, 550658291, 724734946, 778747581, 324791692, 914014994, 19034269, 516628774, 464399592, 101548733, 678702314, 796487595, 480099257, 817185108, 544518124, 539625709, 179953146, 768581955, 921985621, 565873045, 145973515, 551707100, 440641639, 67102758, 376529953, 994072568, 672757942, 165144321, 247230159, 319740056, 901370681, 549904836, 512221415, 234924409, 960394843, 231057882, 257924299, 760585219, 874538056, 318818325, 484671725, 188430217, 16383767, 374829728, 13994853, 714106481, 852568786, 549043724, 462491242, 218596678, 216563368, 754994128, 288992621, 335176735, 603469568, 900906633, 859908452, 726452161, 690766078, 690623844, 3948411, 262217984, 211791453, 230830478, 328037297, 371781464, 298281271, 526469479, 464900742, 898678115, 525921895, 875706489, 571867960, 809757355, 640392801, 314182298, 408264483, 709739868, 272625843, 804220068, 997829449, 820667808, 984975374, 434094896, 472843342, 988246858, 391824861, 942211323, 962949687, 609588325, 464205437, 159089412, 497778439, 150595707, 801298767, 379488945, 433605679, 181123815, 401563763, 664164585, 124955801, 919193945, 986232291, 961626928, 152728533, 102282651, 507765658, 94169795, 929683763, 659437654, 405719841, 931028985, 19690189, 350954787, 599495668, 523495309, 211663620, 376290070, 967172594, 938885688, 625692791, 551453640, 95458749, 331237285, 779413563, 102917623, 471574875, 2990259, 994346371, 950877142, 684969702, 590754569, 809556027, 944601190, 723121467, 732327085, 261683588, 298568299, 733176961, 180637927, 388881275, 652410463, 196052455, 394881676, 12409119, 546500116, 429695008, 84930751, 398810167, 672366618, 109294807, 758703386, 291691830, 779401424, 534995317, 861826117, 235394545, 115705260, 935581145, 692060362, 471005276, 833513897, 92224663, 942919201, 846986509, 858722058, 853214023, 20288554, 896909347, 705814227, 644941594, 501149299, 139942743, 918974085, 941879232, 907738629, 381885920, 936949593, 789623534, 831859236, 844461341, 244128135, 777521232, 392369366, 519717987, 196334833, 654043504, 800316207, 381708954, 408502590, 364760741, 295798822, 471704797, 157224673, 395988323, 52785729, 947755677, 207435779, 721988696, 517858146, 981443381, 967816489, 771388873, 168961272, 813931488, 798892198, 145383069, 549099626, 368304867, 685290692, 548812448, 346431389, 327340608, 195470042, 501823481, 720978970, 53003467, 188990822, 67661121, 995352031, 871792734, 558813346, 292858488, 897358336, 388871295, 715908016, 955842869, 42133877, 848011477, 598437631, 472523095, 935212530, 835856962, 761930488, 425755983, 9681735, 945728646, 624857960, 876623440, 297924908, 141609281, 305202769, 783074460, 592483743, 483650675, 937134075, 929529045, 453049415, 332716547, 25891933, 43298149, 620189402, 740182449, 804203390, 961154528, 485205369, 543414088, 911961502, 384008312, 636079646, 860103778, 268879414, 196047970, 532726830, 172773709, 709103162, 383189862, 130184298, 608583098, 941799322, 55139063, 37863988, 542154321, 825326096, 491983144, 692907788, 993944855, 871788197, 519285221, 934486987, 549449865, 4136852, 662737433, 494628227, 336108695, 681379274, 215548536, 971637643, 653171883, 500888915, 156376863, 833319174, 901418676, 124658927, 890058062, 681677509, 49856722, 109878491, 146473580, 988813651, 502367556, 710549523, 173844269, 565962839, 508734931, 656755234, 61285755, 449760921, 58444106, 834322306, 940832309, 674443005, 506473316, 148902852, 219085746, 101005201, 851116813, 76998774, 159569609, 172637413, 346744429, 288354669, 737034367, 795616791, 660786867, 946349502, 469048460, 924167714, 633339066, 672676287, 583537173, 46853181, 436623825, 381270508, 981342049, 552166197, 216744960, 49924696, 821442705, 91565010, 818880137, 749544345, 6383306, 805383169, 36380130, 552742605, 665308867, 889021708, 320737691, 984907707, 989295754, 712399271, 966922214, 651618501, 760600576, 237790158, 541480644, 352873768, 212185443, 856638777, 731997101, 87243773, 363863470, 317091219, 868823383, 22041901, 776412125, 866381354, 954261885, 925067148, 76869787, 145671420, 871346165, 44628787, 184775451, 209128476, 970342343, 505298592, 891518382, 437767620, 425395266, 573576230, 445213238, 338394821, 493976750, 840066155, 191063403, 424038545, 823052804, 715153154, 60456180, 688565747, 109490869, 997141523, 100854523, 722908753, 545031224, 780775759, 801197772, 890615662, 489644866, 949703683, 888629689, 592122628, 613528642, 308896844, 531845230, 452357088, 836630425, 118629843, 427925568, 745084968, 852691336, 555071334, 978013444, 483774537, 487160899, 868906818, 142050346, 341462793, 351128587, 323290699, 306523382, 208828127, 185375249, 862042214, 125334925, 877453024, 310587611, 583690444, 43994531, 30838351, 973710608, 93936280, 65494224, 3059885, 549639664, 947295929, 927061134, 482091306, 337345301, 386979688, 417058477, 250988759, 683397464, 873979134, 140318905, 33763854, 465597417, 717122705, 185107928, 50901857, 639268474, 637173356, 937258188, 16477705, 455804326, 380687028, 36424122, 331699849, 926817318, 25695671, 744359055, 680960917, 608377789, 319923038, 194026819, 715230264, 103545495, 36101888, 173932070, 376050809, 780598189, 656912696, 242981346, 614656577, 473697773, 523181652, 112677835, 702589236, 162765979, 159950981, 700608055, 811710652, 741812727, 562652964, 155836630, 711650664, 726208376, 307306791, 381398893, 469695914, 453779125, 782779644, 779947304, 561386081, 563659010, 467524582, 349788050, 170778200, 4798427, 70060982, 827058942, 549783419, 843405480, 597589910, 758510542, 729927733, 983758977, 608240097, 368453686, 398547407, 652349651, 138514395, 280901268, 998194101, 306671114, 237518443, 80603323, 64722467, 189117823, 74056010, 866272455, 57054978, 174427826, 376469395, 366106917, 414626613, 936557367, 779780365, 72767552, 215732257, 356031807, 431284292, 430455360, 231451542, 832888694, 650609490, 609818692, 549688365, 19463480, 847723999, 525224611, 247519092, 862926659, 105574295, 889755444, 540676380, 617771682, 211357184, 205732607, 457504712, 260717587, 889434271, 205709759, 344441039, 129472903, 133437551, 847553136, 147089818, 704646622, 718128711, 588113305, 470295204, 378923226, 837622064, 160341370, 883110304, 956199565, 863899603, 386961488, 364735922, 856703585, 699280985, 340839047, 287812156, 50068143, 25493241, 953450383, 526351344, 617855218, 677721453, 56794912, 131088625, 917961701, 528390797, 688848881, 555199129, 707701594, 13455631, 963468477, 97831921, 99289752, 677352202, 650025640, 491151110, 278048345, 851649542, 3107482, 295348994, 125928009, 678213983, 180328979, 293999008, 377506103, 941109334, 927003839, 151861142, 628873225, 304412041, 815208724, 767090152, 2474284, 243670433, 336216048, 861487777, 414176903, 419940991, 378185616, 657160804, 562336874, 420523131, 316932479, 276796562, 993692444, 894531252, 145796408, 897773896, 208681567, 129196062, 632092606, 284308825, 917716509, 480071796, 418240530, 859573468, 524332371, 143112615, 980193191, 654005800, 444761733, 427093389, 492974617, 348294626, 859616637, 817169978, 617817979, 811887444, 428027005, 849967980, 884838188, 42929348, 582820864, 506079404, 143304826, 49296127, 844058675, 260262069, 843482654, 767629508, 819763012, 201542778, 363644238, 141997309, 774549031, 72990924, 116492822, 10320265, 366920074, 344871228, 130564507, 329504388, 458310793, 642742244, 726827596, 682059533, 841348957, 780434704, 687388347, 360585267, 773623453, 430355228, 187438488, 264499845, 624065369, 848474908, 371850479, 696815207, 182411318, 317182729, 284470722, 379249476, 630959884, 32012846, 500462613, 584258606, 264462129, 422237347, 655691211, 421785122, 136121803, 720820779, 782006883, 99888898, 260525395, 719634253, 390044503, 430222316, 363457715, 370375745, 110098847, 671030135, 342300088, 18528258, 942360912, 884526208, 190492382, 836003864, 302244646, 865833473, 145228817, 910899179, 22744425, 269519121, 664379403, 904804063, 249620618, 75687839, 843520966, 897303851, 264141553, 142510450, 917225300, 233402874, 329995862, 963004055, 204520942, 578037147, 815739174, 433493933, 911900922, 654327418, 275027410, 254258158, 724002985, 737528494, 811491196, 797984038, 126132856, 96234813, 473972539, 316901348, 337120643, 520582520, 41603988, 774078059, 331587006, 348582689, 699473440, 752141438, 712906850, 237644881, 142750714, 527777006, 671723505, 765530950, 953169370, 773189990, 825256070, 527368982, 122951971, 941756132, 509167698, 160485394, 936979955, 771645485, 391931163, 63299770, 556585023, 229996205, 52988186, 839997818, 512390062, 341261872, 863979062, 538434329, 497622200, 914496046, 614670183, 777499037, 85139886, 799488085, 52079430, 578890090, 324125936, 739187816, 254937749, 986143171, 844910916, 83315336, 712712020, 221127749, 51366867, 373281186, 964189859, 231016679, 778424169, 384316069, 424359574, 936045006, 848616460, 439421270, 763090471, 604842303, 363431762, 593796959, 402591654, 396762957, 213878019, 799351813, 509303809, 584983380, 331924603, 169401937, 222619905, 559630831, 428165382, 299957767, 34645508, 20128900, 68282382, 353416168, 837548468, 181498752, 476282713, 116959082, 902249785, 8631364, 992111516, 82785477, 957530330, 823898854, 520318089, 278185450, 98295329, 80023269, 26609638, 202668990, 55603010, 858851965, 260801570, 550334361, 936257933, 248344387, 714497033, 353396804, 385117010, 817156054, 770763601, 603701401, 549164984, 954218086, 229764223, 493760926, 593185711, 232587355, 182759259, 727195346, 214543738, 250597143, 506022558, 440880148, 374212279, 356418379, 609598688, 815045745, 900495814, 132359135, 68320377, 36710695, 799619518, 494630134, 5738574, 162387505, 49157946, 545896461, 74357794, 257705681, 513501848, 565034013, 584084359, 748979883, 62330496, 101222542, 424976340, 884783876, 76361503, 259929118, 677008362, 926837112, 580999288, 859217496, 229137028, 652600882, 122319421, 268563734, 469597034, 590418710, 151882749, 308664931, 99731046, 505788486, 556986742, 714325422, 190502551, 608150650, 634601220, 589167605, 189202151, 994649860, 380999955, 954431847, 403276848, 413842015, 972021025, 832419937, 575204643, 26067307, 888102767, 139456010, 525678981, 121571568, 144193895, 906225997, 260385839, 844198581, 745844384, 826564854, 919329275, 582131740, 224250162, 745932159, 84219221, 42846950, 486651629, 426018424, 124464468, 432805501, 79924687, 501804460, 586591774, 344808066, 147151415, 572498893, 108863255, 147357739, 14366754, 601802277, 796895212, 914905525, 841506017, 293747645, 35373934, 376123163, 95217170, 308437615, 783503681, 998162965, 190980836, 641266167, 852280182, 966931394, 309258747, 695453846, 287652140, 223858212, 992209630, 94147104, 361441952, 22605574, 438323800, 400281101, 802606360, 376793343, 958379093, 927558480, 535868973, 329557549, 801872412, 38150049, 195003594, 916630083, 286466150, 737390892, 606641354, 426585630, 565985347, 973108567, 781356356, 962670911, 827600663, 67331812, 861836194, 228739495, 468172255, 311896983, 597461665, 488068311, 809403629, 988410607, 720096800, 442082264, 656228184, 99358845, 832025788, 376492407, 422228584, 396643070, 871679345, 697614674, 645517781, 787225508, 126111790, 653809576, 250475332, 127473135, 859116742, 948540187, 135012986, 833323750, 397988628, 161893085, 281491662, 804642097, 598457249, 822335046, 605933812, 633197134, 341502307, 956716904, 796842750, 565770801, 826128462, 95802285, 309096821, 972342455, 129161982, 101161909, 672986238, 691812761, 200725169, 411954294, 863514649, 28880886, 114645038, 703796868, 549348441, 365672409, 471706037, 228006082, 486667973, 550654979, 735987513, 395420032, 789205378, 161588703, 619884215, 738419330, 207368072, 157505286, 425590061, 957343174, 788938, 81456874, 419409209, 139954056, 97447982, 499537342, 261101738, 723250597, 17696619, 12680933, 326469800, 388396407, 446876457, 916192588, 821200177, 458448645, 840617926, 50455332, 354589093, 493979499, 144694805, 861876947, 520300929, 340875484, 381047745, 596528919, 485306352, 139275449, 423724393, 861508975, 833733028, 889676073, 879561657, 846196580, 722047162, 805016700, 839980764, 257075054, 775394094, 618343924, 188470059, 844108754, 649570433, 674593535, 586700846, 258535941, 325435871, 423533607, 399142853, 874790175, 948835757, 399442623, 434093995, 926431647, 564065432, 70254189, 370557007, 948726596, 703544544, 725446729, 340351407, 734053213, 476640420, 904274215, 480952631, 595979028, 615412581, 711144110, 187467392, 700723780, 153707502, 895233753, 653328063, 849338549, 138808446, 689824497, 455995867, 110694636, 468355011, 427544718, 947242223, 447366106, 130029087, 183620828, 435276061, 342612835, 556060591, 548123850, 227942832, 261492794, 231526572, 382854050, 852389611, 726153043, 184686820, 869838656, 162577538, 802855948, 738745671, 550407781, 511825640, 840193591, 503626172, 789066659, 994023357, 937883637, 433463109, 645936087, 291366906, 783520790, 74270484, 872590262, 813937277, 517592880, 692567856, 536926783, 721029924, 27483453, 196955855, 452524233, 431853363, 592280476, 265460841, 721300733, 700931361, 914001146, 404598740, 861410849, 186515822, 153627537, 38107317, 420148217, 827778972, 35326955, 448851653, 571974484, 727137578, 190896949, 364974602, 689262244, 777971518, 801973584, 17447993, 23684652, 271612881, 418083423, 726280579, 842912709, 565422649, 255804624, 187928002, 917595447, 865306980, 983108208, 704760819, 909968513, 476819294, 67774625, 448482247, 406396398, 806953688, 603544857, 388456644, 308737065, 581572923, 517441962, 445764545, 423264982, 323027899, 319134817, 339235596, 180226258, 159888800, 743480173, 542243203, 527574816, 769906810, 623750967, 389691637, 702127127, 517334467, 571722997, 723164669, 367778949, 820809271, 443964397, 522681718, 283609211, 972805771, 661626676, 555369976, 769151358, 146916022, 653959841, 12015911, 803910786, 653777218, 736444695, 146685274, 66263252, 577224202, 662245917, 786425611, 97939941, 278258589, 182954927, 18715589, 162725601, 155042315, 82310641, 151374829, 863401897, 981634624, 553317149, 519299408, 667284536, 98212715, 631135724, 298127538, 477714296, 521442947, 199753889, 356712791, 671669564, 859887468, 670507452, 721153508, 902488555, 281847599, 938831552, 876253231, 250253351, 387291702, 722559024, 876937601, 420741590, 955651913, 372644066, 532134521, 788351027, 720982454, 130677215, 109410504, 508826207, 353260498, 768011614, 213014952, 903377297, 447432676, 251523640, 958564178, 307430205, 824279056, 714737156, 496845458, 954002795, 770108817, 540905437, 784952696, 529652935, 881489397, 887133983, 123074812, 863516928, 110735561, 29989082, 191361343, 47783934, 412487538, 261055180, 388773056, 831107117, 376121253, 147287402, 760042206, 375219033, 216089443, 224946496, 315405637, 616760797, 964243871, 622690833, 605885570, 739258270, 3930110, 334837781, 802932159, 842989391, 833622698, 293594133, 20287036, 391639640, 665600725, 359923715, 604204048, 168393254, 123861860, 535219963, 841746944, 824935565, 369317863, 662866662, 110136628, 532413379, 166737499, 509307705, 963317816, 470058354, 227197367, 759725090, 646207068, 64904471, 187636757, 671496799, 327041288, 221345116, 574182298, 992331287, 749797790, 52442070, 195573730, 176004801, 404654772, 484934916, 752177285, 687539380, 536449354, 99964167, 538042143, 600593653, 624206249, 843251481, 667125250, 456858280, 858647288, 543837960, 941373583, 504012598, 939245967, 845227356, 620577375, 470174870, 642485268, 260431968, 75697703, 265392296, 137634893, 200386975, 981992598, 673936139, 84448399, 296639284, 325065381, 91526006, 759633842, 350866379, 175727528, 511927278, 949695302, 523872457, 675612590, 950747029, 287536676, 317031973, 242401952, 142082045, 470213641, 658133990, 411420987, 597566633, 116157837, 400075732, 869804688, 282920082, 86779910, 345256875, 294931689, 230041975, 489296457, 507276130, 209263102, 546005937, 384231392, 490042551, 393191006, 770263007, 855322551, 944684031, 992651471, 958002714, 545058638, 631453321, 749608603, 530857658, 510359078, 104988700, 616364300, 421457600, 177569433, 231439643, 925839259, 674552087, 346749470, 163689591, 28255657, 924685811, 520927990, 249026079, 854322762, 113194213, 390314545, 582924153, 138614392, 159687754, 478913799, 633543241, 198839467, 795615262, 831290843, 61355001, 863709214, 382434826, 755954744, 32098311, 600525031, 518538621, 872820188, 573257189, 708383150, 648444315, 167648458, 428416290, 590500629, 857710063, 671088856, 845575655, 579032221, 509874410, 237818213, 971497660, 106069459, 491136313, 162112187, 773150942, 633878989, 72861605, 260439158, 644478135, 348164382, 472355008, 440044106, 536599941, 918639187, 137275782, 197295365, 181818045, 49974107, 324194603, 890462736, 375509986, 359963750, 327678415, 310572219, 721213250, 541130480, 781862989, 873319827, 204385268, 753811477, 368057894, 155654069, 152204768, 776118664, 605027847, 97684496, 478753959, 886807790, 506010449, 718653618, 510379861, 245033329, 619441329, 558213597, 288276221, 184073514, 673066840, 25003614, 546121331, 821555119, 913528783, 655214908, 999119221, 452741779, 74286160, 437258386, 812724685, 672301546, 429163287, 558216042, 320245987, 567006544, 349939067, 140622042, 798631477, 94093233, 355985362, 479009390, 913958702, 424386897, 514171340, 740175870, 679049514, 738354630, 700965574, 328225497, 872369797, 124920074, 659699380, 19741898, 176524296, 810970903, 589356117, 482661217, 105305244, 746566901, 789469440, 677706042, 194890281, 253528370, 397859137, 770080761, 236334065, 87948780, 99206944, 722161690, 897947100, 240769076, 598835286, 600921808, 238244315, 872557392, 483424546, 596154945, 675606989, 628370739, 529572462, 23699032, 652857066, 336137559, 359768599, 499057424, 934946367, 960779913, 528437328, 897308609, 734105908, 366963058, 433849598, 422068143, 973174747, 807166647, 311646721, 131692434, 126981280, 117469648, 702585623, 312063105, 950598783, 436053434, 553680247, 991777645, 781768666, 357847954, 861331217, 765639204, 769123620, 72584091, 268948840, 147658171, 439073692, 41103978, 64227160, 403969730, 46089518, 181999348, 388227680, 745583308, 933660977, 755735818, 4934025, 936389697, 234270892, 38682384, 645849153, 104101994, 274682751, 241354347, 763819314, 395351573, 591458719, 963607725, 655774111, 868801530, 349477037, 674217147, 882427429, 812742007, 91411120, 56043224, 464914548, 1217781, 391567808, 399848482, 996798040, 32019349, 625182146, 350440573, 459952144, 688897311, 348287771, 904348592, 921105239, 434965027, 148993771, 977813688, 613236453, 455752469, 932400122, 939358943, 694058769, 846062183, 33002098, 796353925, 703485451, 520003614, 82660090, 600657664, 320283740, 843184092, 458604141, 340574707, 63070898, 269261813, 272535906, 107613807, 778371093, 97827903, 311892346, 580174851, 45805994, 472021231, 709361944, 189442939, 491232893, 205639899, 386693013, 576740612, 655916612, 237590830, 196887617, 853949232, 785206377, 669571297, 233943219, 448392670, 222818691, 243953454, 52688383, 693709636, 776288967, 395486042, 533916635, 175065613, 47289139, 785826033, 746838142, 816505585, 227376558, 106508825, 86981736, 814988754, 722453464, 666497236, 8616033, 463514351, 287803623, 427908485, 208754762, 356147891, 377209810, 442206377, 565961933, 692427023, 395522831, 223996557, 41841748, 893250781, 748689284, 360609640, 187154855, 221657012, 36202516, 156562165, 429607806, 934696684, 956335906, 331578738, 581678078, 837907858, 747688550, 687032364, 498408054, 366099882, 777559421, 36577525, 464181836, 258039807, 337526388, 357227151, 138911815, 639834153, 972331785, 951319795, 147282623, 631873378, 199399763, 693399772, 216268970, 123725999, 397039078, 713815395, 813468150, 128537007, 67004187, 592812887, 956169828, 418820158, 840274031, 315199380, 15409495, 161428486, 995586748, 140654002, 890010959, 321572424, 518185008, 991271088, 900698211, 84164148, 553509310, 985762974, 711862704, 553138546, 805625916, 268740984, 78338468, 912716700, 486627123, 839703200, 454630664, 915141867, 361582583, 351099484, 322112376, 207395083, 103882974, 47321378, 781780617, 450713808, 983538285, 430886614, 17573966, 302051260, 450329092, 413205741, 824158352, 443254903, 155710340, 402979476, 817411605, 766802637, 3615041, 416499992, 598212441, 970011273, 233771460, 159084754, 151790844, 222270775, 400925162, 169208563, 545824114, 696850537, 152430797, 198526869, 144024571, 654635592, 982179450, 555576709, 42081818, 542937451, 909268422, 413317282, 677889967, 461464035, 566607698, 734068264, 186216802, 87930066, 916286730, 798180568, 30687978, 419017240, 824184796, 558886031, 714010688, 544323989, 75921, 264321272, 224769730, 107516097, 403374198, 964087924, 565274970, 313674231, 209532809, 918911287, 11445835, 23497918, 582725718, 574917712, 425085520, 965246209, 893871358, 591235575, 545443491, 914922636, 825202818, 427644876, 923776310, 601619990, 90556112, 647865051, 738104114, 729020864, 750133899, 126654449, 658829179, 753586045, 511030065, 726974439, 293328315, 25532456, 392648458, 499944451, 176497898, 544559414, 209855279, 282481319, 120944895, 263471012, 780300258, 363956265, 339025476, 99930725, 591066286, 790053093, 725428817, 401202144, 481723305, 254668562, 454386553, 604517657, 797101384, 428664915, 145954969, 360052720, 624880596, 609091624, 756877828, 70659939, 390864773, 483097318, 492669960, 53553364, 951404996, 37903909, 184143179, 933767806, 735644415, 99139295, 258845402, 351063895, 322464119, 326347579, 66574353, 588891707, 295424150, 209869761, 288600076, 174718425, 360744371, 72787955, 822612263, 771774099, 589109822, 267458153, 370285106, 842358212, 84621455, 527670450, 690625586, 343761171, 640996344, 79927790, 39866247, 863014698, 269214881, 278344691, 475025301, 137643283, 251653003, 740022409, 679818796, 134373413, 714503249, 478220456, 982257749, 688013831, 307420480, 32220480, 676725343, 204137465, 17791316, 201252906, 450152503, 265924519, 930466191, 678144207, 821950395, 230037509, 249217604, 314243789, 724276252, 922733191, 34065719, 466171322, 990571552, 459590307, 507855700, 81785234, 748192332, 861669612, 88486170, 796656296, 819085914, 728824036, 382069167, 613357411, 297358967, 544407691, 149158740, 291161742, 427760134, 517664856, 973333287, 956389269, 836238650, 824134076, 672994535, 492718643, 832839074, 32311145, 529751691, 814623194, 560352474, 356476393, 187721119, 458664436, 132689958, 118782274, 151222498, 551131605, 154817210, 432037914, 336333494, 688348507, 628533305, 373002926, 108114153, 295987957, 816504251, 964029366, 396316526, 427848532, 343756867, 875931463, 368614870, 425407799, 798541614, 448175878, 808622055, 6261405, 463936176, 715212044, 741668416, 662524720, 867534735, 392914339, 237627203, 870357035, 64539771, 558634677, 609564009, 350228661, 885103561, 825348228, 467557135, 273685866, 905078010, 387131968, 129883344, 154429411, 990802367, 499244034, 170780505, 29414727, 621689603, 277739329, 75534186, 624527703, 95916895, 515419177, 354064108, 805069009, 220195063, 67735268, 112523415, 922407073, 592361810, 374737716, 501167281, 697513369, 648299447, 180070958, 377412146, 962150069, 593107727, 116873117, 210157670, 804552617, 506047513, 578565229, 935630550, 912995536, 382797115, 183992634, 328359363, 685854195, 825252117, 850800045, 811468792, 812790678, 908910868, 506843680, 356065096, 239427724, 711571395, 583582385, 715453746, 904073257, 225496985, 767367741, 228803714, 499805592, 378580287, 345934695, 876096795, 204353121, 430907784, 783193701, 272289680, 631276965, 437085087, 410026256, 237748274, 842246934, 105255443, 152472313, 299100931, 363125357, 116935302, 6736630, 265080445, 6505868, 355054357, 713687872, 519153898, 57499428, 125704193, 707855665, 376449618, 66552371, 256199280, 287728803, 617904417, 85505749, 220164699, 542097359, 111679398, 278607329, 546644586, 134907096, 739172351, 604823266, 312562383, 910426043, 245324188, 332699775, 907252473, 296082014, 884002653, 915961653, 395359228, 745945522, 439259935, 632654648, 137902452, 350906026, 627102832, 66649423, 999298178, 453030555, 573887402, 715005957, 25982503, 591598335, 594612139, 557483521, 547730269, 485666592, 920843799, 358774395, 330263123, 769731487, 316446525, 481409930, 763013270, 925371204, 981028867, 164841236, 642528237, 425772449, 500332086, 597729612, 714430737, 883277778, 612213198, 314943190, 282209849, 12388557, 515250598, 139702693, 39059054, 762287529, 164696574, 554882576, 896192996, 99334758, 781556853, 91297158, 823443818, 668876709, 965895794, 611828703, 618247683, 117722137, 932383541, 942272978, 479960950, 882203269, 770173842, 873675823, 295969305, 400110068, 466210161, 568107042, 839524169, 228336, 100621009, 214801639, 612538659, 90078913, 929644239, 64315854, 710593123, 709370185, 532124911, 907943139, 458696722, 140112296, 229030223, 400699683, 24752364, 403013480, 364488938, 972951774, 295936097, 741791737, 181560610, 226729072, 27753805, 720311269, 117705850, 63768219, 380541073, 538276187, 533825662, 477238854, 460913851, 373852699, 291777784, 274910063, 793843200, 69765839, 880338808, 835453180, 891474859, 890652668, 929034213, 162580621, 947834921, 507135076, 154946964, 170811912, 706203180, 538421717, 843925244, 294192447, 768253911, 241972689, 497436004, 29200409, 980725397, 124277108, 157858142, 729182395, 515961809, 323678170, 532244903, 684374103, 135249258, 13649967, 935133118, 322801801, 811400550, 651258807, 502170439, 562602754, 439189458, 70975474, 513109917, 882728293, 490755878, 397773986, 849924468, 234796071, 628914932, 986012934, 418911290, 216210511, 460710630, 249516190, 35673358, 79010543, 151841084, 611259786, 169276481, 13333292, 809762781, 419966533, 694106731, 814417970, 603611899, 150468244, 78696099, 163822650, 845574316, 720412345, 353302483, 217634688, 630702260, 199250109, 364050889, 268529835, 654844258, 318989699, 48154229, 84843538, 298623644, 78503435, 735713568, 344569278, 919420997, 597778066, 133346338, 95974336, 807822601, 739348622, 249968053, 879057969, 981370738, 750605252, 621112330, 695745958, 603712474, 355611867, 899165510, 298961875, 772413497, 893020872, 338184728, 398971757, 827687159, 818788663, 865756594, 573749550, 194819840, 301966842, 766127204, 385844795, 42108248, 547080955, 614218136, 147305042, 543294153, 280615684, 600107625, 955334847, 81887934, 2747919, 654795877, 470778732, 913200005, 539071892, 57055490, 183013872, 696329593, 785034737, 707225615, 653932001, 998865087, 605374612, 295956085, 602348077, 402473829, 403365839, 500122178, 369769249, 658308812, 281992771, 801891169, 988865828, 11468210, 193245920, 95531170, 436102380, 50552070, 906222874, 351919074, 253309753, 839652276, 19438360, 201520021, 116078909, 972580276, 861195504, 711909346, 290490768, 536212560, 704722015, 690379215, 772084156, 671697096, 358355211, 743652179, 963731952, 320025863, 877233792, 260325575, 677943338, 75707957, 618053835, 552011365, 367753784, 720701009, 235004683, 730668142, 38684111, 775629035, 169444981, 521409860, 724377935, 448121513, 341679313, 53332428, 892896881, 513567684, 221301861, 751537657, 353763928, 27342636, 680745957, 632287441, 669232951, 475322774, 319285454, 885857379, 907345762, 338929319, 140759684, 962576389, 69600715, 492402494, 691217266, 358218315, 17241357, 731433315, 100169348, 254757126, 618469876, 549451202, 713544652, 220352458, 8443836, 556905295, 941909739, 539177260, 503135216, 694405441, 802441413, 566731459, 383988326, 36142944, 272739724, 540066416, 223245884, 255046865, 656250480, 401723232, 921687556, 118794424, 870482409, 881272218, 714103337, 704258482, 83153729, 382328447, 507759523, 992883496, 549743073, 838520433, 372842799, 365179952, 174144994, 335959257, 229984671, 146921221, 886831430, 878125842, 102804460, 938494183, 67796111, 446627792, 399169445, 876387298, 276624240, 62695644, 526651118, 890475611, 686009225, 549165215, 727969799, 817924712, 704735855, 137989947, 198412117, 239770193, 676685915, 333413070, 63421847, 343354510, 126073994, 196345710, 352882828, 82081414, 22893589, 410466461, 286179103, 449757442, 867827259, 151731009, 606735194, 980296773, 268259126, 150677143, 134881451, 879598730, 788568059, 728868910, 837385478, 570124080, 371312344, 889419846, 64068901, 102794964, 175456699, 367881664, 737731905, 755248306, 315003251, 866507713, 294993808, 798684984, 833801639, 75814469, 290597933, 43588121, 420750050, 606303656, 884888547, 552839635, 402987856, 831816940, 186448138, 554750212, 317066944, 656070957, 666514306, 580021958, 770345275, 565025434, 91236743, 478391685, 32073921, 894561025, 676488951, 13141959, 725173092, 437793855, 730753226, 220115550, 493308468, 765610104, 244258992, 674614338, 796056104, 695471400, 583516256, 281706944, 911261299, 859176611, 793939201, 925628364, 979529575, 638496391, 221426561, 612959602, 837148585, 953165810, 26455312, 109782014, 578437832, 424990170, 710936478, 793303533, 951183326, 703216647, 894396100, 852692643, 389988604, 441031505, 333911823, 387166072, 766755505, 344422502, 19103269, 790783721, 314578930, 469938744, 338226305, 94389966, 702357910, 397926786, 699394126, 851519487, 468453092, 334432556, 449597806, 134291730, 849456614, 520470783, 848358651, 244680543, 263550758, 888744222, 278588170, 744305928, 622692435, 784745983, 200196582, 908761904, 315984042, 82438423, 694733729, 692476486, 424637268, 264312579, 599433903, 571752224, 492813892, 469771634, 38516569, 743276106, 224710251, 411839419, 61694956, 479579803, 954934975, 94160672, 106235790, 731140031, 471591348, 31561419, 798527742, 169196452, 457888065, 494006551, 129538819, 578454227, 663844379, 106499078, 929904847, 18889698, 271980561, 598215212, 765472626, 69761408, 118503273, 922112780, 545913460, 557029302, 234522951, 75158031, 22799753, 474913430, 245625241, 565990999, 385203343, 196414830, 782604311, 442093657, 360199547, 522874059, 572494054, 850476855, 740555387, 85577323, 643580382, 420428708, 535087884, 394600088, 15045991, 253535858, 5734639, 701735051, 294930533, 945826916, 936417064, 788919336, 287308850, 187892313, 18813511, 466218126, 278661172, 491532670, 307114122, 659121972, 200859996, 413259513, 494398650, 243511295, 318071623, 867403214, 234217076, 688000251, 114715569, 948816241, 84008235, 46702211, 802500048, 604642853, 143172408, 447798614, 459334684, 223414599, 489368667, 465951815, 805741640, 190922190, 813360549, 364968873, 101600692, 880031173, 528035556, 727088214, 691987138, 359733254, 219731825, 415293566, 444525132, 752943444, 950686530, 62175404, 138133238, 490730010, 560119393, 764880025, 857140952, 100979172, 996129333, 520245293, 916390396, 167835338, 750160451, 455758377, 63790636, 386772227, 366130659, 362802958, 305702022, 356407472, 850467040, 973918362, 328090878, 33032251, 710153647, 540131182, 960838508, 267410315, 675854303, 511459280, 237287405, 45905539, 377750244, 441017123, 338746933, 203357928, 825867543, 849137773, 869110662, 678483108, 147053275, 717061925, 577821803, 57789959, 23245378, 256298231, 466613996, 262109814, 249459137, 809347037, 960653773, 716533059, 953166476, 668417152, 583307737, 107118571, 606322527, 79945305, 517922997, 995333290, 334816364, 929237782, 788192632, 890562069, 351748675, 72025065, 180788946, 284201268, 876937308, 248229030, 680170755, 652122322, 748093510, 140751265, 241206430, 695808540, 573986474, 98789534, 83120084, 2089375, 464014173, 870286683, 558441494, 655171238, 977375158, 489223637, 68239737, 838047143, 474360549, 145750561, 532057440, 836856358, 912052064, 517464772, 300858628, 747199756, 764121124, 485368657, 687037938, 590712650, 67364637, 282177200, 413983446, 893558135, 111816992, 641690308, 522321460, 478634200, 157524944, 598453252, 883961284, 707926493, 998620230, 701600498, 567012788, 307076720, 689271474, 489791025, 812173495, 595042386, 825300387, 914867479, 88320098, 508603012, 849981242, 529625895, 617303049, 410778154, 919039292, 528777389, 147107838, 451476478, 329430265, 179152187, 991537916, 259721921, 30725579, 156638568, 221065823, 123258382, 466809330, 675721186, 654458281, 917935848, 2501350, 487824988, 137608525, 180583273, 841081243, 353195777, 990478280, 363086965, 362025650, 646560007, 835057279, 365741411, 425361179, 483118497, 7297084, 328617414, 726190501, 363843180, 453736826, 914164413, 133286676, 51055289, 440174340, 391113226, 252742893, 187586623, 730633335, 278887981, 509273140, 761013086, 122206702, 820403876, 170852800, 905519835, 14814800, 552890772, 564476511, 949517229, 498819128, 224137622, 55191011, 622331414, 860206242, 848970515, 215587345, 514865100, 19873687, 247993841, 397312881, 810671406, 104648203, 500568155, 129785649, 702773058, 730019453, 514793763, 791882056, 831294089, 328840364, 882532858, 757335659, 561655368, 96667185, 488464417, 74351228, 148803846, 447567628, 817874486, 49635711, 496694043, 510020364, 735031401, 165904811, 141825609, 159863657, 638689983, 156380597, 143386032, 295924266, 870087431, 804447504, 364237224, 134495481, 436843912, 887449277, 138889158, 748694274, 981080723, 61694980, 866979335, 303997963, 869885278, 443952662, 456479092, 20892427, 577972441, 158853840, 805130207, 323797792, 202115262, 490529690, 381121965, 305945295, 929504194, 717062217, 988449296, 372506125, 741243777, 721686599, 889890304, 711709004, 231026847, 441893187, 268120378, 55922620, 711167874, 353475877, 453193027, 601442182, 854960559, 261451592, 496569580, 478554734, 156338588, 659608498, 923386208, 375940194, 307712871, 950152921, 936073298, 874387945, 335685360, 271856565, 423952067, 541057496, 703421423, 901406470, 336609097, 107736742, 623280355, 848030477, 990398051, 212396201, 184262891, 764497749, 871975504, 982292964, 544678100, 969717526, 425596513, 601815154, 154765169, 308614979, 388755423, 515351435, 976891529, 284028071, 174932130, 312297934, 523524250, 878131143, 586975156, 928370051, 148169160, 736702034, 491539511, 571048316, 423708532, 112567454, 612816237, 582291067, 41134564, 711035860, 709530716, 153643540, 736237554, 934205359, 975200079, 865996160, 534254348, 198340914, 324833574, 809649940, 218973778, 869958542, 750146648, 135308274, 110280718, 83742756, 670996563, 271086450, 406238904, 857790192, 725379204, 716576109, 673502050, 587633654, 796736617, 174190186, 493699056, 251581732, 469175084, 25342022, 623866797, 569038630, 207485730, 375652169, 752697540, 234715117, 323437176, 410796617, 361356226, 736363402, 299518676, 197874614, 503787765, 61455137, 390349056, 145002462, 215720366, 672382857, 322310446, 691775928, 674057657, 758564736, 113538604, 353447164, 548566, 898786055, 255429398, 49729780, 467742071, 595819500, 118042979, 337513913, 799415981, 93481136, 613185864, 47577155, 43213085, 603660434, 374358414, 646671790, 700093662, 995520039, 240378661, 875346997, 878857823, 394199585, 777019337, 447972869, 581666745, 400704068, 489564199, 762206331, 370621313, 116325443, 693826907, 775219851, 916982045, 477372139, 773954759, 46766475, 7688727, 663217052, 498439308, 977613980, 637951759, 960620325, 564127332, 205734939, 752641647, 716820303, 692286126, 199511703, 544489476, 915319053, 361230820, 456059264, 366121263, 136556931, 189317911, 52493483, 547372615, 7982484, 621407868, 340311774, 528553563, 751682285, 570866391, 339458038, 591758922, 919637246, 679804265, 23241301, 346693728, 516570840, 477091419, 411303774, 452666387, 739632321, 126866175, 22757971, 345302826, 434406224, 319505581, 540228587, 511587216, 415733425, 57784073, 482057849, 829989174, 34987267, 520633606, 322509909, 110893328, 101885715, 409293218, 543860315, 488196498, 252859888, 314036360, 353744305, 812218121, 30904105, 509471035, 431292614, 689547841, 295411759, 825936503, 674348338, 942975259, 101062333, 343242008, 14889005, 656808801, 183107748, 445055887, 460838593, 634682472, 11100052, 776076142, 622323090, 974548709, 367115090, 91334971, 216923168, 511953120, 832545599, 980323357, 686525259, 491909056, 755528788, 758535861, 36506318, 731669526, 826563897, 665763894, 923052300, 867885211, 356159220, 969756173, 550209870, 387791950, 685497574, 463907196, 598627613, 384177423, 817120199, 914254848, 86933540, 172537262, 462217938, 24239915, 696596836, 585731285, 124539339, 737022556, 438374133, 673256211, 526874289, 932950713, 478877452, 882109015, 390788387, 113949563, 293140258, 948539816, 314724867, 707783293, 838489810, 60609262, 953654584, 298396433, 940304024, 413274269, 681889808, 376109379, 522210845, 31852759, 330949064, 580580861, 822356527, 286785418, 634312638, 884821161, 378728195, 898966056, 409888696, 921582608, 982207136, 926951242, 634927867, 624471111, 492759889, 748771210, 56197026, 737340636, 592098827, 50156383, 853828019, 793537903, 721816470, 337807698, 203197929, 391293454, 499414079, 320113871, 222454629, 44302023, 74780413, 813728518, 417780879, 420103863, 414961294, 545329351, 891044083, 164302490, 830578095, 637938186, 253196159, 64594004, 192094522, 166660434, 126137201, 207963699, 146574965, 840937579, 77305848, 101630742, 230052449, 828498041, 639896228, 625642933, 812820350, 159593642, 58657240, 222601483, 271273317, 891730255, 504857464, 692506984, 431809916, 653596507, 796969120, 416018570, 40958645, 50955590, 348279520, 944562442, 89882194, 66497614, 838312273, 240778853, 414431516, 235129152, 408233954, 344562972, 417694244, 743301835, 537061523, 243385647, 918810022, 393975841, 327984360, 353520852, 158472718, 381512905, 723666210, 380829988, 334342550, 802853962, 275333922, 667465579, 898469454, 621802517, 189777000, 42251344, 771065541, 726131757, 957662419, 179845593, 966643983, 538967706, 875368079, 945507236, 473307275, 258971216, 807624652, 767468338, 767810694, 744971635, 177496321, 724678333, 460327150, 480868443, 77018779, 710922686, 27361279, 902651034, 789866667, 223009410, 368144779, 242199308, 790106729, 190262615, 393561607, 765950455, 784967487, 274137914, 742758242, 861502071, 482915836, 961278815, 280788900, 118254935, 950507472, 623137360, 755287687, 92934145, 107640430, 918016184, 156846643, 286804270, 341092369, 763318889, 925233961, 139007559, 938446133, 913545173, 367861093, 871629079, 286743766, 553271460, 174877034, 940773927, 293462204, 865772012, 788618003, 205048891, 91078265, 606464953, 620231314, 58645034, 549315663, 940629030, 475057097, 967192666, 782455165, 751644815, 487487490, 601675265, 360220716, 316222070, 394226646, 3210534, 946592750, 218179781, 65160559, 65628412, 746903756, 550290164, 171499823, 960511466, 945803222, 169460176, 676420844, 482714546, 449046701, 964546437, 277505057, 462409143, 178172474, 799760171, 253447786, 571777957, 470993173, 107746870, 327363162, 936501679, 896114752, 105208199, 421345091, 952551939, 363586302, 250613880, 491650565, 635766737, 13097555, 640489492, 320121715, 107549380, 727438304, 97213428, 561215854, 694489047, 273228591, 629644982, 395765621, 334457056, 727488271, 533047942, 808390709, 371070084, 741383509, 859564457, 421727850, 710964673, 699375472, 886599174, 875128915, 451531736, 275653812, 598359591, 46140876, 68608050, 218768792, 460705982, 556917088, 927850518, 401573802, 963799643, 979897233, 378721919, 437133244, 534515302, 946147321, 212433199, 160002603, 414545798, 761101363, 477489175, 999727331, 710033229, 351680479, 604719358, 211698211, 829984421, 874103657, 582021546, 975094811, 4740157, 144570955, 510312735, 99634150, 296768382, 608215342, 689543377, 98200433, 383836935, 118740394, 925499078, 543914190, 475730089, 508796972, 194253472, 919177964, 334643470, 455716078, 945779528, 989514669, 552182155, 271048121, 509864599, 976802849, 81710821, 207380400, 885007432, 675301491, 321073390, 674531875, 800863340, 112494342, 475016545, 335218136, 942060993, 866070331, 633279033, 573493407, 586871834, 131004653, 236311251, 903014542, 997411283, 604584532, 527108135, 964305591, 202342221, 267093537, 570668787, 531078620, 710034979, 460702384, 712318325, 430571533, 489959379, 456072413, 223180614, 492839719, 160724045, 248633353, 704095579, 199523772, 876167844, 759720698, 295614113, 95502646, 165897438, 594614139, 324908488, 790836192, 714566109, 430425813, 373396709, 951323510, 441290302, 180106632, 394368575, 746899524, 649455162, 568971727, 49405270, 393088868, 795246665, 312414381, 214563476, 346816129, 971039961, 907250036, 183293785, 638750158, 935364085, 441342776, 391913030, 534857485, 409729413, 643851925, 329034015, 407931714, 890551706, 440468596, 726631687, 766450846, 464320765, 207573782, 282464062, 787888479, 549762614, 772465857, 517053909, 594568524, 787088836, 350775335, 437133515, 363447050, 509535512, 4846866, 455431013, 628262804, 842629535, 837893049, 70705782, 17726256, 246744894, 890510357, 380445426, 831768892, 389531756, 78725180, 376122210, 329814230, 515370187, 574732507, 407184038, 15452071, 86689135, 724747350, 514415724, 475127827, 250755582, 586017799, 280243887, 412146834, 279336786, 396352788, 264394113, 52404501, 125077957, 888500881, 554266952, 86967590, 437422430, 202372390, 966231439, 213705124, 319654912, 327706227, 604516154, 838729579, 244443587, 691974396, 670229964, 419206891, 5257885, 716775423, 278654957, 492538897, 11616702, 646950986, 306026643, 833796337, 78834178, 275922590, 685293512, 101203566, 623763509, 656078816, 945604774, 324717775, 192790388, 606547432, 816500784, 414238241, 58806450, 745968573, 310554062, 972523071, 438568065, 189445485, 960001260, 460803121, 51605253, 687345870, 404736964, 670252702, 370607189, 996543775, 692270390, 483658090, 512498805, 152887874, 900798326, 321902214, 232558689, 812792038, 89627325, 385482292, 85511775, 114980633, 906256203, 132176164, 113938045, 860499716, 610603742, 627199142, 77262047, 251651528, 736521679, 167738946, 281319374, 226793959, 873959147, 950424104, 287498818, 699383203, 678933526, 452903220, 805152685, 860641963, 79880703, 620991139, 222909835, 85240261, 664591172, 153476076, 656403564, 171552097, 531498953, 709326521, 556667839, 956693548, 309369435, 273469420, 363742884, 697635661, 750181230, 600174547, 790602406, 83903616, 271661984, 794607831, 419228654, 87801484, 367167886, 88560573, 765286104, 951006428, 750250006, 896580675, 160985003, 996341938, 686112700, 496608652, 8826906, 970375031, 283690876, 588602869, 551235124, 124407441, 122553690, 380714466, 903534647, 250454724, 331601977, 397264783, 894642660, 697242661, 325271889, 176018730, 524552932, 209331090, 17930224, 696956093, 581641945, 71616876, 655056447, 326755790, 904206703, 333932104, 810098296, 51872570, 691086075, 786154701, 500477300, 774379189, 932139088, 808276112, 46281558, 882020616, 642937407, 78626763, 744976438, 745900487, 840621754, 293141714, 406778811, 512339028, 982985545, 200090743, 96379688, 731892731, 194786370, 587797329, 215409805, 448536756, 574049504, 994450246, 130062120, 452197417, 853728347, 478142793, 245992732, 990418743, 89912813, 530916549, 444842591, 10607588, 692738728, 617786191, 262912104, 966519363, 683722786, 857540414, 116745736, 873227363, 77067215, 176555643, 68957746, 43363488, 533182106, 910732883, 152380108, 993295616, 340926397, 970676595, 308785303, 62200157, 273981489, 832809292, 729118812, 699676301, 818970131, 628088803, 235687281, 220074142, 998712515, 979946995, 3490108, 15691038, 220726452, 936613564, 604889399, 600492828, 83126672, 131431487, 723542994, 333587942, 250747279, 317759186, 699894415, 741249907, 7101324, 110266899, 198449991, 26216686, 353232706, 802104277, 408746362, 665417824, 888368646, 565370168, 430576891, 957735373, 589780883, 799338300, 10920922, 900024492, 338080518, 70219947, 609907255, 841878633, 414994208, 236555139, 352814288, 178796140, 602748240, 80664841, 737010978, 286608976, 147147970, 18477242, 868938670, 12924669, 134576177, 644507763, 447517763, 208712927, 802536461, 719573433, 129481234, 298151133, 302976809, 17764986, 872842257, 192362484, 88605057, 611210823, 868691884, 862020191, 445825009, 749126389, 826650661, 623427745, 144373772, 96987882, 328114637, 455886080, 118534529, 224522919, 1826663, 720845079, 96064957, 796380633, 159885838, 742949386, 504235461, 883292996, 991983004, 729246603, 807137342, 128814960, 733948180, 481492365, 899445598, 255846118, 190089810, 327434115, 912920518, 988080331, 498448004, 553641460, 640688024, 252451323, 342240180, 135018369, 979439393, 727039561, 174193302, 66274203, 457837276, 716730170, 261296156, 144719489, 573831035, 434965159, 765425199, 114748479, 297912773, 797611702, 918896316, 884540955, 444936329, 706027557, 528667314, 753222655, 384721590, 431614072, 758575995, 303344420, 577720745, 382372457, 264857816, 964538069, 942767103, 61569185, 785097010, 521691169, 489780864, 27067643, 275636751, 846000150, 599164211, 33967024, 274318063, 53917069, 454942982, 928280442, 892727017, 583311796, 951639658, 970330026, 242301121, 350184455, 689276298, 551191919, 286150645, 248465465, 73584682, 693620621, 914895403, 571499980, 860297805, 60282498, 919630150, 490457567, 561589717, 579460503, 679088169, 152190912, 979184344, 182649412, 20770295, 48782943, 25201019, 442057952, 31044094, 114676915, 747894309, 946704711, 310304449, 601324803, 152276689, 81019229, 373384289, 420645317, 758387642, 95166071, 590866597, 477548481, 901198885, 128453774, 74144784, 278235862, 263372211, 217763683, 633538336, 647670257, 284268114, 880933233, 837201417, 385173529, 41347500, 450044983, 621644040, 14441178, 702517056, 498978326, 817540745, 503613053, 14021254, 829559619, 174636142, 605466876, 213804699, 550740383, 772428266, 386703427, 659200105, 919826246, 854732201, 871762476, 141204776, 171895765, 136625246, 480685906, 202583237, 883935275, 692888472, 369179280, 749021910, 686247880, 54499796, 215419337, 652954969, 820599356, 857397439, 940555642, 938980318, 198806725, 947205582, 234537643, 201980654, 22174187, 182489994, 401980344, 879057254, 974027179, 615545365, 979436321, 387729601, 11969829, 460377333, 662590116, 992785026, 791742096, 927817366, 6327010, 562716420, 568834003, 676326927, 739534038, 503739630, 829851770, 508235597, 642629603, 937514799, 710207569, 812799516, 637873812, 866020060, 373265106, 139223466, 621652546, 677221261, 95689412, 242545922, 334053200, 872322489, 493210994, 89945409, 28060643, 768300917, 719548519, 747111158, 249961649, 257818060, 625722808, 135659885, 931171511, 361150126, 5563793, 512217956, 547780113, 257468888, 424163016, 365800372, 908277773, 753044111, 813146384, 559377887, 512579304, 989702247, 785076417, 515022706, 589090973, 171359496, 667814595, 334432268, 688173536, 858095229, 372273614, 587373130, 90861762, 458009342, 253190700, 94037520, 996229644, 723908746, 461234802, 230100913, 444083252, 962184442, 231841712, 320239636, 457564113, 527113402, 118414292, 328252525, 389066051, 277832689, 466288003, 690910597, 673658704, 123684924, 776259973, 573511155, 658427104, 813136143, 939539837, 206945640, 894659705, 64084700, 186565026, 123773533, 42194133, 859847116, 120090172, 892486754, 429268798, 618247805, 420722218, 998943769, 416689395, 806586082, 232197893, 200003513, 438346326, 170382569, 459671528, 540467873, 595480241, 907598149, 967127074, 895834117, 893329952, 741563567, 490928162, 947659008, 490034792, 713815386, 926922099, 57181714, 142199882, 897840179, 776051490, 612466997, 436561879, 542987473, 765874581, 551321275, 258428046, 656593313, 62175677, 160664063, 290961152, 661063175, 486908487, 729879131, 407468266, 448901953, 383788019, 528651108, 635168523, 162589619, 795175358, 920847486, 894021833, 840642003, 28089638, 132424694, 580531444, 587383053, 806448356, 321869756, 105519650, 623603208, 601056231, 409303935, 942466086, 118505096, 756871084, 21972320, 514268708, 74609495, 431099325, 773043852, 770479134, 779244966, 685227747, 708253984, 120537723, 783985651, 205040376, 731229226, 541984320, 793670003, 562720839, 702001124, 748616488, 245323642, 515204547, 564160806, 326778203, 595361646, 416163812, 330638170, 134894272, 989638968, 637503943, 327144227, 829009601, 735845097, 338830524, 873074509, 783254491, 17184112, 625948964, 392497500, 552916, 992889233, 782431309, 142488919, 985030505, 819834659, 538610339, 847486583, 734334921, 667225420, 475892643, 50645425, 110862471, 563485708, 309911318, 869610514, 553262445, 336772126, 585160625, 818985898, 124107016, 568214004, 664239993, 400916289, 993275698, 457194639, 685678108, 842283352, 308692554, 485128153, 735747250, 12352104, 150792695, 942063233, 622828732, 517373604, 215478236, 907742333, 573271340, 836591734, 672421477, 638182020, 420266803, 228283280, 850492062, 763003834, 818561254, 988007863, 90772248, 632535366, 759250788, 221969688, 608830114, 735673136, 547861170, 908972157, 665387572, 353620077, 909838188, 615033367, 979541354, 648510681, 696870704, 602249994, 826617657, 323010723, 701015038, 557837186, 5958245, 463567488, 684893206, 148854794, 976853814, 395563000, 81091298, 838431121, 730477998, 187423796, 577528840, 210082301, 521577004, 767016397, 825505242, 44561195, 34972184, 760482563, 805331970, 413748777, 255754969, 13424725, 70677732, 217636024, 602186127, 68604795, 543123306, 160448209, 34812457, 999084309, 212026390, 219257631, 424351852, 758024195, 312120147, 677003322, 578474208, 247338979, 550211971, 84432810, 203677930, 860600738, 567303627, 451781699, 706680208, 857369988, 932869413, 155909843, 305466478, 509927770, 376269316, 891610453, 302290875, 159325679, 609381920, 433908436, 703787323, 80652248, 461303672, 382350539, 198532756, 340779313, 613266691, 652320148, 566342044, 466749003, 427224375, 816378628, 404914876, 134747644, 1195043, 254040569, 506720491, 411777647, 112169828, 657248069, 720437222, 716949443, 578388558, 733946110, 231637763, 432933337, 158634991, 776923951, 665068553, 417020433, 327806294, 74569036, 813093763, 522108277, 263440200, 854456461, 408331474, 468929862, 781946183, 344566907, 943249447, 382463585, 7508656, 989784308, 690671871, 361007644, 26503230, 567742526, 522728803, 746410191, 575905060, 598124512, 199451237, 515769403, 714375902, 446009916, 321965390, 58301803, 880793239, 821285251, 199698273, 194845190, 161252160, 816478737, 79170840, 9787340, 618781362, 236626673, 218119709, 953034152, 575512017, 988641404, 628532128, 321823349, 838693197, 476363826, 388910715, 883486156, 378350474, 803551173, 182438749, 875245938, 282180177, 942753946, 635288468, 584522905, 137996785, 620609370, 362003347, 83483065, 455398863, 284359821, 963934881, 831110359, 820366887, 782299294, 978147958, 951104408, 316807300, 164508676, 299594126, 554390339, 442284353, 994913468, 505022743, 788510391, 825305081, 679894914, 193079875, 165535837, 452144215, 432037650, 360379353, 829435548, 144771429, 36241074, 65127927, 290250554, 719302089, 369226062, 370077669, 918694442, 713292299, 89560871, 430788487, 483954625, 747727825, 192940588, 322755190, 763540863, 113609289, 824759770, 130160680, 79102378, 159966509, 786105129, 754575887, 461190313, 403816879, 525426061, 823025203, 535915724, 392078547, 462693556, 347318545, 175312774, 170701780, 485307946, 780315636, 972989398, 244211118, 828320985, 569897480, 503212283, 143450910, 271486393, 273205956, 335256190, 74904289, 539447684, 710812217, 988962791, 424839011, 816015234, 690468240, 538362184, 881222, 976602359, 540778546, 105493488, 833275471, 527988660, 759542395, 316140533, 836819713, 629271360, 897338862, 656380836, 500715733, 716170082, 99899699, 724874175, 691670599, 24112102, 280194474, 302781152, 918322274, 651000118, 868764976, 761020043, 562518786, 553814794, 880054413, 481757401, 371079139, 77656159, 537790066, 460007765, 89536263, 401322694, 969487399, 18457128, 657979782, 126827796, 986721927, 425651283, 349259507, 945824777, 760094238, 870000491, 576392845, 958774217, 112132705, 921828782, 791297740, 625997400, 541833680, 939700277, 756885209, 815523198, 506106250, 419852744, 713355596, 115496383, 460961793, 591268061, 599074306, 684010359, 935833175, 188159853, 862104222, 679935343, 64880697, 168213929, 890158503, 828873259, 450541962, 370708712, 352480658, 876191254, 449182939, 985588741, 798393941, 829490351, 324510479, 981169144, 737264075, 345635011, 811006440, 195923428, 48376185, 985303652, 138396208, 335927965, 956061067, 792647985, 161015997, 765750898, 847721856, 73626005, 513276106, 250181343, 528945174, 727531954, 712140924, 390069872, 411044648, 966103977, 499852931, 971007026, 436459433, 998234202, 476754591, 114566706, 57010266, 770658010, 340732667, 176462073, 611588798, 346561449, 630818369, 303687536, 518546296, 474000922, 932714083, 546930667, 850529175, 910353142, 52572666, 624205161, 980007995, 9761075, 80605263, 26910544, 409156881, 182193731, 698116968, 759543734, 789799629, 776567557, 693482369, 90712193, 893630038, 719040269, 691810755, 820435502, 794587458, 470211536, 13324548, 894912673, 446097096, 683864252, 656502542, 398758351, 591959939, 527755342, 715494994, 803643537, 612477901, 454439190, 258189423, 595945734, 252150095, 409930192, 821339678, 340973019, 683821424, 632879990, 161752397, 322824838, 529136272, 84227620, 954213581, 309051264, 868056712, 576185414, 814035301, 895097837, 274734646, 909603204, 951213846, 99745973, 685968232, 326857618, 261551513, 275421353, 353715955, 379019012, 56222117, 973522155, 581924708, 67195162, 799981940, 403459263, 935195606, 257897278, 50469948, 21016063, 189018368, 522123657, 335461431, 33769908, 541149454, 781742771, 261805545, 928969380, 282417377, 222763139, 332806977, 105759304, 530978426, 648871779, 609398129, 232335442, 414678167, 20111297, 927850811, 37035487, 318771550, 550638639, 219458922, 946115662, 158663371, 750045243, 498790691, 149133215, 702265613, 594340071, 558966539, 195549741, 863031081, 5007310, 64154074, 107131672, 920493435, 567339417, 941647010, 444635666, 442823492, 454544830, 532768252, 849906184, 186171153, 566881898, 122590559, 584914347, 772636719, 121638692, 189121256, 815473832, 534279914, 557020095, 237531843, 765644225, 752287640, 693633247, 599927388, 959562466, 708335321, 369601862, 188121978, 799576681, 558308849, 113788713, 907580402, 773993752, 272549632, 842690798, 267959223, 755472497, 789820620, 26361818, 43860648, 160481998, 209012762, 829219237, 315437588, 914233071, 877318124, 54420481, 694579096, 696149548, 733300822, 451662301, 571227951, 97067078, 35424107, 868321812, 134708083, 451790745, 810347592, 850656055, 395850573, 407380795, 303365359, 449823115, 369070052, 313946831, 866017326, 912157599, 929233112, 626668676, 695889064, 431225309, 509769357, 19930167, 719013341, 712215110, 933343372, 57981427, 887596285, 590807009, 874182380, 120507255, 198543410, 369743752, 793799077, 680857854, 515581560, 319201048, 452483529, 692744351, 521835990, 477275380, 683024723, 692314022, 696934813, 534050163, 10391463, 394129242, 534482876, 237642900, 65598493, 407686512, 336217822, 820314054, 917810023, 928732418, 901312913, 757845187, 221084558, 40296587, 860864457, 105346502, 92159415, 756191461, 801453106, 577137553, 168803970, 681665839, 583282880, 381321747, 942465428, 654726895, 852572876, 320333453, 186370985, 720771289, 518552735, 866537027, 949924042, 106665417, 213436261, 95615208, 942713181, 766428630, 850920970, 105109854, 99022906, 301501451, 714567423, 400326758, 614744733, 980671531, 48368283, 298672952, 493589886, 632120875, 532329520, 840700238, 414783676, 917358182, 13849266, 263339269, 291998584, 587956421, 922004876, 279886412, 380013437, 579059391, 154422599, 581712079, 455895913, 384364458, 214214516, 526080888, 836105044, 741228629, 486387969, 964304991, 793132515, 516331387, 650660843, 582200669, 866885503, 488093538, 875492075, 404850934, 268927179, 864990673, 254635178, 718145272, 684996444, 5570375, 711144327, 367193702, 326705053, 265697343, 110996427, 364004741, 982521479, 574983515, 292950817, 200599756, 850309423, 120247264, 272031696, 378958075, 444616971, 375238118, 592889182, 522545701, 384792339, 829135181, 652570564, 542500371, 21490391, 518994475, 769803130, 667929838, 831026070, 565356333, 814778043, 980514928, 534810970, 235683970, 770711496, 456959338, 130580535, 429913060, 693146237, 893596359, 150237832, 623901780, 24955420, 758677244, 683826033, 32751933, 687246890, 920376141, 44059763, 206189172, 779755072, 228125848, 284545518, 36130352, 79834813, 134926384, 574476397, 376040, 803880556, 517389210, 417325092, 930129493, 716372089, 296779740, 149961999, 440722102, 414551794, 171358789, 602693270, 790390075, 415172446, 972649159, 507123138, 260330617, 955697677, 688498836, 850768931, 557613802, 25046253, 851182505, 621029551, 296243037, 677427431, 556619846, 876023627, 772622608, 450392159, 681370067, 772211310, 348639884, 714744090, 550373688, 602190662, 676201832, 738276061, 387901645, 863939457, 722451716, 710114627, 31969674, 920513079, 435301114, 217673533, 418524233, 810701192, 587687584, 980744715, 511567964, 616381604, 364715966, 680216488, 303798206, 532614425, 172092012, 682040294, 237201707, 881673581, 857871287, 603015009, 61255080, 239244457, 990293944, 100161687, 553362148, 230402228, 467361363, 772524061, 926680815, 483883214, 288761756, 716483088, 209609777, 765826347, 613482686, 214801193, 714647210, 566757887, 646227272, 842767620, 255749895, 277754928, 36853066, 91855199, 453776434, 62838713, 27191314, 279230930, 198844828, 17278153, 295090422, 190912569, 138227180, 222506206, 631978198, 117158330, 527118820, 817119896, 128970895, 524671221, 405557394, 246431438, 68704571, 157679935, 294523339, 790981188, 918651776, 368322397, 318010189, 410575622, 494304015, 179940090, 962044655, 45997876, 626779330, 190966194, 787888528, 492513935, 161787803, 783034882, 672583634, 545035874, 49430096, 944663250, 446660749, 457088655, 778540426, 252473221, 965149368, 343922219, 649287125, 527240620, 678181820, 11187082, 98777536, 1853308, 66250875, 787817634, 272576328, 89948356, 484008708, 582583500, 410266943, 712476335, 647629680, 221551989, 886942561, 1908450, 47511267, 477427936, 465791489, 17483474, 927474836, 48084365, 774095145, 990902171, 120638760, 964482180, 379090601, 537122549, 752402597, 491966041, 23687209, 854507954, 457473794, 839894733, 530652497, 453358242, 576077582, 981971866, 711674169, 709430531, 647943727, 876611044, 728285217, 769163815, 400278290, 672312379, 674840669, 7769616, 560755884, 750556615, 38142945, 183556208, 299735398, 338327322, 697786936, 120928551, 891003589, 397271951, 681917588, 692196926, 25877270, 273656862, 116960535, 458749063, 878868851, 430203760, 662683356, 454806847, 55101326, 496828187, 123297613, 932639343, 423439826, 633306286, 398223617, 396180473, 507505188, 197958818, 243389366, 213396199, 787293909, 147716951, 361558144, 875950600, 354906796, 477636859, 942837670, 997398633, 95492024, 991148588, 431342359, 881836049, 71826532, 162990613, 657452404, 431709824, 242912233, 252904222, 364381958, 121973730, 83404069, 109387824, 754196893, 191707321, 168411420, 773641118, 70798162, 951321748, 684821727, 960172075, 818796622, 88533058, 282885094, 965336393, 176141487, 538615162, 467144579, 73086666, 750017352, 211936837, 896021806, 707836500, 506590047, 194455955, 899906043, 159793296, 997725941, 129574686, 465632353, 697758541, 917637653, 387399335, 492050452, 51229230, 756731134, 750169813, 879832987, 573913645, 161808320, 741320087, 357152118, 157022401, 794940243, 608153429, 256945643, 260971152, 795580573, 910631662, 712387323, 185674301, 30121646, 435139389, 415688177, 420141667, 464634167, 19260635, 466547109, 835771343, 141465533, 975700784, 202588411, 72638826, 164466351, 289459109, 36182903, 239704823, 268832240, 513590080, 178862716, 346206457, 586663822, 925131742, 922031809, 749573404, 468022716, 340437215, 613034473, 393853485, 513881430, 124189816, 131889078, 776918727, 20664858, 583314185, 621842208, 910576063, 670711456, 2425344, 558424037, 524071743, 836858853, 550095029, 959510419, 963998613, 478407602, 375298539, 141396226, 611854734, 963346213, 23637685, 653168416, 546975078, 454441760, 50526581, 11428745, 147046226, 819971836, 900331567, 76561069, 290606880, 546556240, 262098571, 218773575, 114612974, 238097497, 880247328, 222576960, 28469507, 961938469, 963840243, 180693394, 666680659, 920797884, 320104563, 773556184, 159590040, 94814384, 161473392, 363258482, 197517919, 509151349, 50874660, 663783919, 389081299, 669702026, 925911412, 561245876, 429387045, 269185631, 651559625, 799174400, 109253474, 151968315, 336423044, 386077688, 750802971, 321479651, 771928877, 619659976, 964687903, 378728122, 821210743, 832171502, 227465199, 956208380, 889280186, 925375711, 637628731, 811604675, 739216468, 592638189, 82784139, 72423201, 982402109, 950684214, 576605466, 920291954, 250067481, 522137782, 954283141, 378282026, 448699971, 293712929, 297152112, 215495054, 967862844, 100749604, 903656717, 897703369, 227835547, 124823164, 57165720, 767921770, 583391086, 501694421, 405280872, 745979612, 923961563, 599545999, 351012334, 431900066, 250761463, 713826088, 666832423, 710653107, 88057938, 501332861, 965970810, 669021345, 487829654, 671122194, 682597637, 871773594, 287848249, 562071499, 243531239, 152705970, 151083337, 489414456, 193474326, 360231907, 603825675, 303065727, 41292205, 358000022, 451632717, 83805122, 385690458, 699783620, 69932015, 855092591, 20254903, 742564359, 338812379, 172158740, 759664004, 672626956, 50142697, 646254061, 35228171, 221773893, 781911810, 315018347, 886535474, 388040960, 853349158, 683127546, 981100150, 407021009, 215143467, 535800583, 612520821, 391949832, 457780795, 175988719, 315110011, 990783967, 431382494, 984695635, 525377962, 200421864, 434952292, 786539298, 214783351, 24874876, 133307338, 951434448, 693124599, 903258294, 782523497, 505797524, 861039022, 355172498, 953289880, 986157939, 989724246, 239367964, 530717691, 513400187, 12035253, 38216372, 223460404, 336324263, 503072370, 541553706, 941371157, 475589941, 367352522, 385823355, 805385408, 375096645, 135453609, 958226597, 387881677, 297222332, 762577877, 762770115, 118226204, 373872526, 543209616, 159643874, 666727030, 686282412, 591249697, 910669556, 16963229, 341426900, 861407152, 578201471, 423169514, 72169917, 39626743, 435326638, 423199487, 868213901, 973877706, 679035267, 219246534, 304668370, 58083992, 37677382, 756457231, 329300322, 842023599, 580183047, 485047813, 762818917, 137593555, 222921479, 635974814, 268734612, 235944276, 352126652, 360242133, 593407356, 853867255, 469076413, 815976645, 96646356, 418143840, 134095206, 265380985, 936173095, 944455058, 557789200, 277805037, 677819802, 576669692, 268538534, 828908530, 820735870, 951345774, 711794447, 924076096, 657342834, 425890710, 798682365, 689248851, 168459894, 823675503, 816866314, 474869241, 188643250, 960771615, 862606025, 961085006, 221609891, 732423791, 948028385, 435989822, 205319360, 316459031, 753597891, 529056227, 892759962, 274250633, 547499987, 445147485, 506216019, 736772584, 405508332, 889663256, 572848579, 204831516, 547465007, 818171649, 506552791, 877181749, 338670786, 241179195, 940416745, 406903895, 478685898, 893994740, 62090731, 359866286, 479271962, 995542471, 524526743, 330553397, 88160527, 864435074, 531384718, 904272563, 272099224, 232428325, 771496781, 611752309, 482829362, 626532252, 469547488, 406151417, 673991492, 982230677, 110608144, 305472707, 202102722, 911354329, 566510721, 978366584, 91536627, 421495913, 917759132, 19213889, 90189152, 798543597, 634182145, 139064302, 437464008, 721618959, 17823511, 847061648, 550786224, 606080999, 275890052, 585065939, 227637404, 740433782, 313011158, 328908951, 231901691, 225019884, 452726941, 954848383, 652630139, 819300286, 7058772, 516399762, 922568409, 287528309, 697258359, 106122212, 365031094, 762031022, 97889283, 415494804, 183334472, 891144412, 970585419, 401652716, 544445400, 522072845, 470375412, 829602586, 620215909, 316415776, 393208198, 451001485, 990746608, 645083613, 376611177, 667407726, 55746839, 362437643, 471089962, 43989236, 732120110, 778905674, 677648772, 41627677, 323274092, 387118039, 379081206, 970998182, 131889231, 248507290, 285301826, 755715978, 197416720, 404595113, 173096886, 399637131, 263236646, 467806592, 285387327, 298170886, 617944894, 512707466, 754372474, 117692189, 223989691, 62903061, 479605065, 163368677, 346895642, 133812726, 845714434, 495932465, 658035517, 207747278, 599301397, 912863798, 92202870, 285404463, 592803951, 781361083, 962093247, 583853499, 218237798, 386949128, 343895607, 971697754, 866484826, 640802299, 80197980, 313726857, 773149992, 605161329, 455638442, 428265953, 892777295, 982527498, 40791588, 560570515, 436600933, 478219144, 438144611, 422825526, 259795103, 857629820, 212850592, 594068238, 843254073, 973752375, 560681021, 239828553, 900366410, 885318507, 483605019, 215637614, 324569995, 332406731, 767896754, 922009278, 296986916, 681109404, 800656703, 728333631, 52585276, 551728994, 627789000, 784744640, 544897026, 383860120, 759196839, 828596683, 377137115, 360170936, 768115968, 174490284, 395300266, 485846210, 578501760, 909874985, 678280865, 618472277, 676364952, 933757206, 399741200, 243305405, 64278304, 366454816, 664749865, 293952296, 968895913, 813469551, 60181934, 666293359, 823010485, 937025608, 264627387, 580768287, 377638609, 880875020, 172389997, 817456019, 546280000, 72670078, 263214339, 188906769, 312017742, 18775803, 174065663, 460119932, 120839350, 674939293, 767743814, 26923210, 967748308, 112760854, 355835935, 447716699, 595213499, 545196428, 389926502, 236496079, 613053500, 875552527, 645546339, 949719764, 465665286, 354090667, 173640591, 216017586, 235896169, 590336193, 525064112, 136490918, 265430775, 989989389, 973747529, 346285065, 852969387, 689503931, 670635492, 629906259, 938176303, 96110328, 486024168, 2206499, 700928398, 885045157, 833889824, 133978281, 7923685, 128263291, 701498533, 9354286, 50491603, 523571295, 555424423, 970335891, 90614422, 287003499, 335702805, 311852763, 551623285, 43720590, 25487458, 463866267, 966848903, 553844800, 10055852, 697504952, 740841029, 943253704, 784217052, 575784958, 322338761, 516406855, 173550061, 816450501, 236192205, 489894677, 871324998, 349414932, 760343463, 143091013, 691633639, 718959354, 488874422, 9453637, 929013282, 687983658, 838469932, 362222469, 42629464, 23023075, 160157568, 759385699, 869335896, 925772315, 561355367, 525955097, 872723029, 91560619, 158351306, 924804652, 195013569, 425642617, 854202408, 459801242, 23645352, 721328094, 552182552, 3351707, 846122874, 875441719, 942452367, 662027549, 131395764, 840741328, 873252774, 995898964, 160013325, 959282292, 805739719, 766997606, 427106559, 523130204, 480690469, 897671965, 556031283, 965354800, 730050931, 602008730, 473153208, 244673957, 25112095, 59035890, 522563790, 199678615, 685499551, 289838972, 230061461, 132305402, 483663425, 960746561, 488677482, 178038459, 421901761, 939955394, 721357881, 66652909, 781025115, 467816808, 831092720, 350300031, 292178517, 702002781, 986894001, 393409643, 761581637, 816326850, 401403349, 927965492, 902274360, 245962260, 143531290, 398984105, 417453273, 986993044, 936744368, 376078970, 525251249, 270971582, 461410882, 72981590, 220997600, 587683378, 591648179, 331287372, 968833923, 822596760, 778998702, 941521294, 858640569, 808479357, 110497576, 57396930, 256955004, 585608823, 236065997, 703205691, 746919789, 474985313, 240309315, 17526834, 713916040, 826234210, 103346086, 185769110, 410415522, 551943577, 687871662, 361495253, 161579828, 43969667, 531915733, 699045808, 312692851, 117510341, 60873779, 657795195, 496107297, 247052816, 409350349, 654254733, 418569138, 329822442, 794579782, 191478659, 906933594, 481488950, 840039898, 151063715, 877423139, 489138466, 419975351, 708366073, 179201076, 15403111, 102002181, 726941971, 682429311, 170746037, 522023826, 340714209, 947221573, 744966558, 61700876, 969844367, 81724583, 177105666, 476786394, 126092909, 473243552, 857823341, 561342062, 1950164, 650468558, 364317885, 37497996, 426588110, 766325248, 165727498, 377652088, 870561804, 948127809, 366634230, 981134891, 324337709, 675688756, 884334884, 773279952, 408674853, 937844205, 812544291, 32305020, 991828200, 660984350, 503177235, 927124578, 846638656, 486551167, 865653268, 487626128, 668409434, 29004665, 591231153, 443999401, 648371255, 643825439, 910709894, 255057559, 648630325, 579183732, 652993616, 257823539, 714161094, 136541350, 574495905, 76720960, 190632072, 417444530, 304149634, 170836742, 45188149, 117391230, 100829775, 361072328, 443051171, 318014558, 169593804, 214436098, 103598884, 231202136, 507258096, 693185119, 202155992, 961652439, 976349743, 559917668, 872056234, 888513965, 273311120, 960795928, 347166919, 731078491, 652737576, 971007319, 228899402, 645226791, 948062121, 932307718, 50639227, 400195416, 369136560, 455196994, 555612996, 808164238, 819068161, 741489630, 977403371, 658969736, 296785969, 664643147, 859521999, 785693464, 681644119, 434337414, 741397672, 83270381, 697067266, 989574075, 485810378, 362120026, 85821266, 186209716, 821342284, 336655257, 812225390, 201596621, 726499291, 491702122, 262363716, 155687642, 282282511, 262769968, 756205548, 971962, 921732270, 118046884, 386358617, 308791122, 215818302, 489586853, 32448832, 722330571, 571685286, 549699721, 737454722, 112741631, 390000399, 569929907, 824653881, 113167534, 224034182, 603869789, 343335208, 114809976, 79566661, 667699981, 89767431, 32686383, 312227049, 167177142, 961088792, 178873944, 608690720, 482320428, 48160885, 355600796, 232684351, 454138451, 817074340, 266237176, 653346727, 670429387, 927101151, 306129136, 198399880, 600108027, 730955009, 890157613, 860758407, 666283938, 79338775, 20301367, 577613071, 894462129, 174876144, 759910428, 585605680, 373111785, 373217299, 754871146, 567189864, 87796790, 622312334, 533262721, 545802946, 890012591, 473599724, 925727195, 357973571, 479054151, 85090483, 506355684, 728267653, 624213187, 419829336, 907914081, 637242239, 903662735, 147127600, 265847146, 934400884, 118851207, 235064096, 37892961, 370941544, 425163828, 219004765, 644607772, 320818169, 682084551, 260697159, 758040417, 828535267, 675823186, 472377233, 154399448, 632309253, 220067652, 937672009, 471135531, 898054677, 57535850, 16838276, 24137792, 999322825, 176203333, 257320767, 128629863, 964896015, 969869916, 239031605, 288234834, 948347961, 732508726, 409779988, 582448837, 725365187, 700758549, 974029665, 987685733, 208157229, 705223782, 643642186, 421148068, 43784342, 38836383, 504153539, 545319461, 47297170, 856264868, 948072254, 894518778, 562473688, 659509714, 548253669, 91044579, 704120130, 674908751, 349480934, 123372199, 166371877, 939701438, 237401965, 792308572, 546013809, 131537488, 415949979, 867877439, 174149298, 57569861, 664998431, 678165458, 358916066, 51623567, 353717503, 461599611, 40499155, 369593471, 36676759, 264812475, 123715641, 470688370, 593472824, 888327082, 959345626, 525813245, 803211641, 33680413, 7152350, 9533475, 67154487, 230149005, 705440769, 564287215, 839554901, 439693, 58630236, 632621303, 193915581, 860547841, 42642979, 371122612, 133215996, 179278438, 946692336, 130456065, 528801948, 630991102, 567783980, 586657279, 832806122, 345190553, 374305766, 439913458, 758950359, 569035316, 25405455, 334777719, 78969806, 469171060, 288873447, 572426436, 282256600, 775289958, 141901153, 469542832, 423519670, 399428638, 470406167, 614954380, 863059093, 816921958, 430706384, 61206815, 672397939, 466256017, 207553294, 479373210, 560183259, 271960753, 608420930, 220789815, 224659139, 375078449, 877030288, 898878905, 401678290, 660371704, 326951799, 949890650, 810691450, 733410621, 580874766, 633436165, 66966220, 389326689, 313396849, 139309842, 433084417, 229927478, 431277552, 194484188, 70923261, 733141318, 585005130, 838304891, 130553005, 889943815, 820460585, 363133071, 338016718, 363880448, 795406273, 741595375, 864885523, 422268059, 158762460, 654719400, 610747512, 388933379, 552288255, 841268100, 649400929, 561263206, 835514764, 920671985, 320832044, 765676994, 122589299, 79283088, 765759620, 873565544, 81605367, 888507061, 713469328, 341204338, 889329646, 530895806, 767226163, 541246571, 139209837, 765376270, 767833885, 316375726, 882259350, 529830601, 793495591, 771521026, 187599318, 790057604, 779209879, 364817410, 504708141, 560766401, 476329153, 238532911, 493558338, 948635418, 675549130, 958231709, 577844914, 929863319, 224493682, 275112393, 624487428, 141846201, 324623267, 287024816, 506520244, 506977776, 322908743, 976445103, 63693151, 721463596, 712066519, 353758458, 573328372, 307954379, 411253196, 966558107, 30622353, 248747469, 569264185, 94026131, 405736092, 775457203, 413495482, 47827349, 514301740, 209128485, 129513115, 791538074, 450786746, 855533020, 957750087, 698485616, 492581427, 204527145, 81357909, 970255042, 452557132, 258691013, 49775000, 339849587, 164142201, 873412158, 703236150, 719328439, 246770862, 146074393, 448828285, 123131600, 480165499, 318144199, 485481918, 924427704, 784137743, 114205664, 582652572, 785524683, 741501256, 661776278, 133438654, 4006172, 386432524, 725888498, 755756547, 3680007, 316027353, 448160006, 398810294, 515445604, 620572806, 512121573, 466445888, 931093571, 580919835, 314419761, 617687804, 842032613, 846770922, 907206263, 347278080, 286460903, 652945512, 554115165, 260646233, 815877527, 430449681, 691984032, 89028337, 588521566, 780085387, 566355042, 429913487, 42789379, 99829926, 936705619, 679335571, 998726690, 85328008, 501063127, 740141131, 46162349, 330414828, 402696027, 732745281, 262969170, 910343505, 586070865, 163887961, 66025593, 972354619, 293850591, 576135593, 265996767, 607334905, 749207587, 569041329, 855150047, 503777289, 6173687, 178315177, 750762154, 51424231, 33796580, 121052392, 908308829, 581431255, 258924928, 973320903, 93366171, 6503797, 597217665, 314985936, 904172156, 911450384, 521553619, 749588040, 265243981, 654167351, 287452972, 356166895, 8220813, 732956100, 550477169, 175423306, 99093909, 414975847, 757970733, 103969369, 66421878, 712006509, 989216382, 576890915, 795643276, 78577570, 360529040, 361812012, 433535405, 192629086, 925124614, 437961832, 49246140, 689999553, 565822180, 22971266, 50266551, 758288487, 744425768, 796441458, 967387998, 33430524, 188466216, 732917336, 312556134, 423963113, 168550387, 350690114, 145310337, 364558808, 347593395, 709636014, 945108455, 671566789, 828181309, 220065977, 150351674, 100734715, 261336962, 886771332, 943535182, 446786616, 758388721, 689367384, 284512716, 486842493, 81021949, 448822193, 43135728, 150155604, 740667260, 854317117, 8326871, 371001426, 363448344, 933716475, 360341510, 318322509, 539834538, 345588807, 557888330, 809321779, 998910262, 639440773, 165269137, 524935848, 640240621, 243339118, 726981224, 35761187, 494300067, 992653190, 92210298, 302996144, 846826660, 720653338, 875143355, 181138170, 671299202, 991940965, 196195445, 78536551, 448296750, 535525141, 373413194, 833686775, 114915586, 990515304, 728587357, 152884375, 379621636, 222320007, 492198611, 4272683, 57930557, 436384161, 827997364, 905778380, 273742775, 508179215, 717769547, 608948993, 196291324, 10164407, 97813745, 35222133, 930891959, 874410288, 124259331, 15608370, 256325131, 244234687, 556379437, 586206779, 952021692, 4652030, 915043394, 279008014, 857429902, 890220512, 302201939, 305407260, 632865272, 614380002, 281205725, 363506537, 604314400, 381833535, 843581038, 78161400, 951559833, 13260176, 67211565, 923355954, 471116546, 800607159, 392937123, 355406020, 429844235, 134255046, 571160861, 903721209, 517550733, 489520853, 449706526, 768047558, 320910658, 674021521, 748448968, 182146580, 103076942, 789593777, 718666274, 640505281, 645430243, 947556837, 787598027, 2447642, 687442132, 752080623, 377867102, 26438417, 285016861, 150625668, 213166511, 580501556, 895288605, 21849366, 76661503, 278969455, 336497719, 728774076, 572103279, 101179756, 395689447, 195837654, 367345598, 212884006, 380505628, 399251664, 621160694, 51374556, 483240249, 487430698, 607534604, 1265225, 3814582, 277091546, 86498077, 843280645, 652299465, 665046698, 777145470, 949576078, 919101823, 102172560, 445094612, 725426868, 608555580, 702831769, 948159218, 305239540, 238834963, 984564673, 875005929, 596713859, 323332952, 689390217, 768867673, 645201655, 764042, 693748458, 839052260, 533225787, 134814176, 112977608, 451705762, 353507570, 635959353, 236190195, 684703195, 950210278, 522455419, 874025269, 539316458, 70618246, 263142310, 402388511, 250550480, 415389268, 82120625, 919423747, 130436340, 612149658, 857098793, 635436421, 298044755, 274240289, 791704955, 188248531, 527079831, 106711311, 142292579, 995950961, 538302240, 446367795, 345896290, 593940199, 729119924, 588586887, 318247821, 581677648, 119619323, 281906093, 32473029, 115250540, 112412175, 200440251, 32892598, 547188426, 630902521, 896831693, 652447848, 367094549, 659014251, 319671390, 234757003, 119199673, 412676452, 746410992, 948009543, 83549541, 374479575, 153730521, 580637702, 702148014, 718540177, 290767823, 728891921, 522252076, 617334404, 112229197, 541078048, 159257113, 7867766, 842253071, 698509123, 662102712, 157891057, 605074508, 166898048, 299369023, 705514247, 61129316, 609592887, 54622497, 742051540, 961673077, 479640496, 501242301, 492355489, 33192801, 58929878, 590529846, 994315046, 672700733, 745347663, 138111583, 149966276, 143359000, 907138084, 740297667, 356753525, 810983284, 275490430, 335309217, 402040636, 113183122, 121827608, 235136141, 136944699, 794596195, 101620600, 101356116, 529328847, 543773557, 329274294, 822747538, 157113429, 130781412, 762096006, 117788692, 463288359, 84406183, 694950174, 439182551, 640180188, 45896175, 711520608, 28335541, 194745171, 256513199, 588647587, 72260706, 579066223, 76622789, 988431476, 681768231, 571557349, 206108426, 308365347, 351927434, 347234294, 867194970, 211950876, 83352767, 347538436, 486738764, 385008380, 206944845, 167218288, 441656553, 729442141, 31218597, 165022450, 462981471, 966786625, 17312526, 886160073, 63605608, 352032781, 724254796, 458418470, 300258250, 797537678, 103091768, 508639908, 582601742, 69160514, 524344508, 921469160, 684290004, 960835534, 790792909, 605677796, 652058070, 705722105, 715635774, 817248874, 814798346, 837351320, 92156489, 517583077, 593686690, 491952271, 20182918, 416203831, 644639432, 751787226, 694486520, 599372209, 807482998, 702800189, 332947502, 767515368, 720786374, 443407723, 851541235, 267059886, 13120877, 265507666, 339745463, 527016810, 255476210, 383833261, 362817658, 462343570, 359888882, 854639004, 180088620, 126054595, 781159544, 415054174, 836322486, 214834785, 814291788, 884083440, 933117201, 300331476, 215612967, 619499992, 838368891, 744192967, 514277829, 277484205, 924588935, 948741289, 529606919, 205840555, 859671123, 714555037, 418752497, 740745094, 373202385, 475986548, 426404826, 598371597, 881872059, 725466107, 838033092, 251065961, 518572785, 973614068, 358671356, 523079572, 581886104, 190373165, 710655515, 148435561, 514556787, 265975399, 158694963, 592201651, 393982414, 116907114, 18774476, 267727985, 565861600, 977345221, 35694974, 564332016, 563486065, 846820962, 17295085, 335825297, 482399932, 592161546, 820847705, 915928866, 86202501, 471533606, 601397679, 844104879, 776807282, 233250642, 627783162, 96993327, 950345122, 163764005, 314101301, 571875420, 746320579, 642132945, 137155361, 481530459, 174853581, 918875362, 1975755, 605177242, 226225923, 177742603, 844323421, 810884044, 555677759, 79497713, 377826339, 610642968, 578006664, 139568262, 165854549, 46384806, 514124993, 40308798, 925812329, 139829529, 994305424, 708539986, 976091953, 41557546, 628616343, 658586918, 506436036, 623734761, 216291003, 923720287, 369847886, 752427129, 499311111, 810064011, 814082952, 69323074, 666344028, 954212056, 19988714, 606530788, 189967179, 995784003, 16047173, 420825300, 170173386, 133436116, 625221852, 436193291, 789814167, 440076340, 366889481, 190965736, 908369814, 514714179, 230110170, 206436257, 939506575, 871916997, 383649762, 678053254, 817683914, 958637682, 500964256, 903768898, 460325249, 87109913, 939904830, 236353841, 714548688, 796494020, 918150481, 369418962, 170957760, 712939054, 334417753, 268423866, 73462369, 424452041, 663721720, 975462799, 396085637, 973280899, 510757734, 398573614, 766458548, 742412326, 562025113, 886673004, 829838767, 228596774, 546913595, 319267377, 618116543, 572381609, 247803977, 683222864, 574238157, 963202487, 236320086, 687400735, 297793516, 997245608, 996675339, 635389552, 669333082, 512592751, 875932750, 587799853, 400301033, 183615861, 798816918, 408519968, 68351386, 518277156, 531732896, 257180482, 170457528, 872466126, 917011781, 797414255, 808892818, 591081809, 814149636, 51956910, 591285933, 912284219, 40211521, 484229477, 652082280, 32607334, 143137295, 31508098, 693890111, 983841694, 362188389, 975709695, 136798120, 470861519, 726454632, 777775897, 74554038, 600007123, 975277766, 378266830, 926726922, 277383886, 464475513, 214186599, 946026087, 990651332, 838152604, 190806448, 574979778, 377618150, 549120191, 548735400, 836621467, 289366065, 301678843, 736623427, 778024077, 648990288, 363167715, 343578453, 172820553, 60469571, 514153788, 885828331, 184109709, 704502930, 375243179, 783831224, 956089071, 524611639, 664039469, 657044376, 45821405, 403901760, 309865518, 162516413, 485079541, 863497440, 909298281, 138352555, 287667575, 772465015, 154139049, 966595683, 707605772, 261623709, 967412181, 746381320, 444297756, 822642392, 417734384, 583335234, 20938289, 48565750, 165112854, 195112866, 574145244, 837642490, 393557688, 575234190, 505366293, 608459422, 630833743, 535003335, 297717540, 664507419, 546406516, 306866781, 406383694, 616300997, 751355597, 342804699, 910165382, 964927398, 441237469, 967548193, 965224995, 517407605, 548964671, 257203515, 951896096, 813607533, 212172964, 844621016, 833880666, 116778311, 715395590, 739440330, 855738413, 105265552, 335691010, 206747046, 690726422, 797075350, 352003689, 835851624, 400325479, 308260958, 346035373, 442656918, 230079243, 63303473, 877454663, 229626540, 204580209, 960532969, 395730592, 350735387, 576696996, 803012971, 809656807, 3618355, 967627547, 622134835, 526616133, 140525826, 268571333, 828897111, 276965627, 112774079, 117379394, 740770889, 965999849, 408260028, 229816352, 86820168, 738520095, 713573005, 936718587, 954798030, 343553637, 930143139, 669853668, 916847824, 491469648, 910005358, 439304997, 525730225, 167187626, 462231352, 622874111, 713309510, 875690786, 478500732, 78288328, 507677229, 790494831, 811364957, 184010585, 799805178, 730724044, 868051588, 377989506, 29537517, 754779310, 232895193, 114094357, 364202175, 997595654, 148406441, 581177473, 140622653, 377278303, 755372156, 802106099, 109903959, 357257187, 52944000, 106332245, 204056210, 178777762, 516148652, 309427725, 268026408, 969916428, 470534448, 246331814, 387812310, 345033609, 754098486, 414293223, 453065975, 101261953, 848156122, 696644732, 72209275, 44605820, 58132560, 829477489, 541643812, 626315204, 863179246, 344220950, 350262847, 295564615, 893181089, 127954018, 794621593, 809889944, 66315717, 918374213, 415739652, 314200715, 561461893, 591222778, 255456333, 657932189, 41387322, 958871154, 394492291, 62409540, 66845475, 617426176, 38427431, 689922529, 225019980, 79881242, 282018028, 231723183, 212854585, 541772964, 156226852, 214136510, 145182052, 738664183, 545629520, 243607098, 168561793, 482831232, 224564069, 859918554, 298393624, 723108177, 263764184, 606885679, 405260039, 782853984, 942773706, 858010793, 317040396, 372623895, 360119900, 448879090, 979312313, 974444185, 797731091, 716805321, 742897805, 618589214, 98763294, 756726084, 581269868, 954129205, 958963189, 310176652, 834512723, 670775430, 174788124, 850579096, 585431497, 722812427, 759213863, 490287745, 831689039, 922467142, 696922554, 785682700, 175926624, 620552534, 736950255, 533713670, 425658853, 942699412, 229529841, 374935957, 54580543, 105072495, 474234464, 961263354, 241128930, 903246729, 592029225, 421555294, 681196577, 548010014, 103316, 110604608, 752802736, 392290456, 299288989, 55279192, 260505154, 447368382, 548687811, 187475241, 526814002, 393126442, 964601207, 732492074, 776031440, 18824339, 157272679, 552894273, 299178330, 622570469, 540305334, 267480888, 104480997, 451748388, 544848403, 529126230, 28433533, 889776765, 298107582, 49055241, 553490657, 603577810, 199292271, 570808346, 115259339, 874001441, 534897623, 260309741, 669864151, 274002666, 434378341, 59093172, 241490240, 889351732, 546051358, 776028130, 975218997, 513662934, 51350118, 418526118, 368124381, 193661075, 260676459, 679778823, 508333692, 798758724, 330941489, 496912187, 752928666, 650746327, 777846048, 887359390, 202860897, 741661107, 512808464, 150378939, 651102978, 616653925, 561971174, 416022321, 766329169, 572247629, 923113215, 64290191, 143539847, 936112167, 646540992, 113423996, 190256883, 643894838, 146101704, 787301183, 670244118, 690513637, 613288907, 285001559, 731086073, 745125216, 473397184, 156355772, 797820038, 644883565, 378048450, 938548768, 805419473, 79336369, 497534273, 89824224, 46524778, 528241297, 52930953, 921415150, 298446278, 715703330, 93047225, 193361757, 837871629, 541375564, 261740842, 694746933, 931304646, 463720414, 968656529, 673302817, 637062984, 294902472, 767777728, 643308096, 405908621, 203699692, 703291394, 888569860, 997458205, 322949296, 487472528, 884812371, 955657810, 848222499, 754087402, 678646662, 924056413, 350935853, 622287912, 231650902, 365136259, 127545277, 527616156, 532021199, 153368739, 844769644, 742013261, 643028109, 957098590, 636584375, 279938118, 437649491, 344028619, 395575744, 153715216, 747313672, 974451996, 183963644, 673854265, 876986776, 569696459, 494424661, 797935409, 228020199, 949092065, 372368128, 667572933, 420327981, 1370335, 583841631, 697777781, 486099808, 785253809, 656856245, 244920094, 276729760, 636611249, 810298230, 336688525, 107588674, 883899196, 852569404, 922936432, 376998422, 129391477, 309405037, 86084464, 165458144, 120249913, 777756242, 693966639, 308115720, 507793432, 318181301, 45509756, 368088879, 27270357, 544804237, 385501086, 90311234, 538802495, 277587147, 352853136, 416758375, 132824258, 310959610, 979154124, 426980530, 259941145, 107852094, 494516905, 46266440, 388812432, 543394319, 75513376, 820288092, 961358905, 834709709, 534404831, 273670225, 114088298, 888023312, 563029788, 831754580, 640137162, 848968006, 500333685, 262734260, 730921203, 510137731, 75085459, 31524303, 360124208, 817394038, 700694434, 504215125, 422750041, 117525523, 645625810, 685883801, 538280266, 618751352, 844051982, 824694400, 122700181, 554842785, 202819432, 84963850, 33122832, 710884652, 543924158, 393669286, 293148500, 618325522, 451748303, 93364102, 651656324, 810837588, 842724532, 624100345, 202576090, 278839967, 619233854, 138245890, 531993201, 955415378, 968933407, 231652559, 239989792, 625300805, 326412969, 304691922, 726001551, 454028242, 540692052, 318552549, 229046176, 263958105, 938619911, 820922390, 241280811, 199994497, 852390652, 496387300, 324549679, 525886114, 801341270, 961848584, 973263389, 875200369, 20830378, 104489555, 336584511, 434771737, 318015650, 608547183, 478510296, 453704922, 812850446, 558796171, 402541731, 298144835, 880218326, 375789452, 318049429, 516220155, 983356741, 554155888, 624579266, 326474276, 73030277, 271334365, 376360340, 841575065, 531123959, 966203342, 124384881, 325298762, 805462972, 903819891, 211737550, 295491188, 945831876, 84956690, 101494884, 271001641, 483498391, 654500109, 679057882, 182503314, 8271912, 998633409, 394831691, 521708181, 1733360, 981073300, 815586090, 23307717, 367279229, 913024195, 563223367, 522341497, 353604960, 261125289, 695608402, 659718554, 389350797, 744022407, 959985168, 946822462, 734090527, 673247896, 326684372, 201903352, 877575705, 428992706, 23097332, 668053307, 261863569, 497025921, 301281076, 628203416, 637426684, 971619874, 914024705, 173042595, 574541671, 141718678, 76155353, 330917248, 837135062, 865772937, 977707271, 526053051, 463987019, 704765315, 907581884, 704683974, 163747574, 131418646, 922167641, 808143644, 908329057, 303032182, 612043648, 423055338, 897818238, 929999257, 867327269, 813737015, 41055413, 64312266, 943548738, 670789200, 208823035, 666075126, 486507924, 977897216, 14083940, 463257894, 193836813, 121049423, 884681659, 647149181, 286624458, 837287465, 851039543, 266229318, 138013656, 407873925, 146351768, 6461417, 19790310, 145337811, 459796400, 205770054, 610896410, 216382426, 497877457, 220982427, 533338440, 35235941, 228828120, 540433982, 937868595, 457529904, 775382022, 170636831, 738587474, 896698823, 731452782, 174735832, 768963931, 959201248, 892534846, 796155143, 993599708, 325812466, 727949402, 936582172, 435464621, 129491508, 574739847, 805699668, 969529719, 983159066, 920090744, 279231607, 420941210, 628466093, 476189556, 361221019, 896718588, 838297276, 189675788, 801836161, 885155347, 919495226, 554381996, 864331629, 229688629, 393033443, 66629243, 825891248, 954463244, 932652174, 915577304, 12570300, 245585503, 761742809, 433436171, 314215816, 992792055, 739448856, 73408006, 380659340, 557352292, 594351226, 869898295, 700987861, 760080859, 747512073, 167841934, 67684137, 465720746, 697935998, 587014785, 169388310, 48807224, 347743558, 17088195, 264885854, 23567704, 118589031, 336665382, 583116593, 47190533, 842054386, 361208602, 97590652, 697747696, 650830564, 424799343, 925806356, 615333311, 582652316, 624785716, 414369717, 577624611, 317390730, 605320126, 505479316, 368912816, 290628717, 304203636, 620396991, 868991186, 432544075, 86910624, 535913876, 772885102, 706254863, 651857165, 187870985, 831402038, 924587296, 924664917, 367243432, 286382187, 253488200, 620685168, 71462529, 51652042, 884763792, 878543922, 969793504, 778235867, 690915499, 75242353, 462398210, 181011938, 975835078, 717009334, 649422791, 642534333, 556367840, 773427096, 869479473, 492393490, 406156169, 663308230, 699624795, 502565425, 947613072, 282862777, 533960178, 399795559, 2897454, 648019625, 607114054, 862256458, 765700750, 627843332, 906470411, 855896066, 711876680, 503463710, 53435759, 653304614, 618735109, 2520048, 791095687, 210518110, 278536522, 715432822, 413748074, 13825926, 570414886, 43330261, 508286807, 370513167, 963127493, 617426133, 698024031, 585147351, 528251733, 95747763, 889793728, 368695373, 365409780, 897444625, 180038609, 852221481, 506333721, 446194484, 707776564, 670636962, 239242608, 663159594, 261470371, 266072023, 63621171, 226576323, 572530145, 521459548, 220305602, 868747307, 533469765, 948499024, 983084453, 351267715, 267174394, 129163979, 911938522, 821218787, 673888726, 281553664, 141905811, 345693441, 3061218, 403301258, 373606973, 955542405, 474477831, 304152305, 559630926, 655843896, 111429743, 728649639, 747637555, 672528639, 911153022, 55536710, 990659043, 585192843, 182212583, 745691071, 270185474, 669134167, 923040067, 208752837, 612966100, 15761230, 76441109, 112132922, 278790166, 190036272, 985101917, 470645049, 54110323, 137007610, 379547925, 848153406, 213615407, 349419123, 354257302, 46443141, 693748681, 35650369, 285209127, 70458428, 917103937, 379559938, 657219180, 684443474, 258121732, 114563761, 688607795, 46825595, 369563350, 312896632, 883719848, 835386317, 392121970, 773443188, 352794456, 389876434, 907422259, 913047329, 958242946, 172819754, 943027992, 990116219, 409700441, 476429512, 787438359, 835866423, 640795449, 782417639, 188839133, 389440421, 231910453, 391423604, 577397638, 271951130, 256892007, 504544994, 72475303, 750058158, 957550601, 603202204, 119921061, 929877118, 866291830, 78607519, 54856254, 761607881, 564490323, 443778600, 276060, 904949601, 512119573, 863851348, 882560479, 46747771, 619953152, 798826966, 618100748, 961303696, 699784382, 414698315, 832616899, 206473507, 378238932, 314948390, 229257613, 597805436, 838045122, 703226114, 961950848, 772637058, 844993324, 289781949, 339892130, 954599865, 353379600, 489753665, 593581183, 641192051, 924391467, 748675884, 771783268, 814840638, 346307077, 363027924, 196193152, 696890534, 1898295, 195867604, 281935631, 349469309, 62392226, 518752655, 668869286, 513459529, 825537663, 207438347, 200886105, 95927475, 898231708, 311857667, 303103955, 756348020, 817469020, 984435664, 303951566, 494857662, 72059534, 843232879, 490799439, 606537732, 125501174, 24138707, 877100041, 210278819, 488901650, 868829846, 402277466, 561975466, 593648660, 803853049, 279263031, 758211196, 978735008, 687464078, 414942997, 352944044, 291803839, 464016197, 74501185, 705684118, 202939956, 337435526, 57406528, 76173907, 280988603, 615436383, 896316987, 780307796, 805789434, 192367414, 727350854, 220133602, 981066016, 736990970, 434947406, 19473967, 133764983, 20372012, 414948469, 716916654, 153579710, 470082689, 370480552, 856231050, 494752289, 386715594, 327916578, 94407789, 411095555, 873175264, 320965070, 652683875, 593710782, 419560103, 413489491, 918367228, 981964973, 825510625, 872371687, 153374157, 99528025, 469180715, 41374940, 10661702, 127432873, 176499171, 247632838, 28855725, 724609526, 753367677, 629498586, 188224904, 281666628, 48255296, 227688489, 366307144, 478476068, 675526919, 449066592, 407053240, 623264708, 794871032, 739087283, 453890992, 449307919, 284457874, 146279027, 818402649, 679932333, 432824782, 187149426, 984466640, 881197194, 62498977, 871638480, 152189637, 793361722, 876514128, 72578044, 60299321, 744553331, 376322423, 802772736, 903881822, 270139825, 728148750, 496642480, 235702683, 829846084, 362504806, 819122937, 136605321, 408911094, 679292971, 817110185, 279659665, 655644079, 983303651, 22571127, 232499558, 723286524, 594819293, 706753, 669012845, 563116331, 306625666, 777347982, 32653856, 943521027, 123128225, 755510749, 761196725, 327977990, 898041841, 278262408, 489718575, 265482004, 888405032, 38749287, 42953476, 525901400, 8319378, 463846092, 926140629, 472358581, 712784375, 461241792, 637042695, 392668547, 774435992, 904985831, 809379149, 906772679, 356921994, 869609733, 307633214, 546285988, 751173825, 316739098, 872224946, 883574556, 154141589, 746560056, 934826845, 981943199, 332897410, 2192, 652659492, 626223938, 387238229, 437990088, 131867652, 562809824, 314248031, 367268403, 182497570, 196619479, 169065008, 99532006, 393674437, 156596841, 12237272, 810432365, 496782445, 219450011, 907385917, 440651774, 854629510, 649893485, 847961502, 335849109, 863972479, 366563946, 990043228, 452212651, 758677191, 179492606, 257029103, 680387388, 747003452, 551649481, 752968972, 500702012, 64827185, 317750181, 597669587, 793871948, 258572069, 611468028, 835687165, 795287851, 680499159, 642156482, 483113001, 751817252, 785782371, 779387785, 588656163, 195969465, 553523677, 191915494, 381944650, 992395720, 763166702, 330684827, 319080506, 356591004, 358963387, 417076669, 989562486, 666780197, 166517154, 68239187, 620755772, 797364933, 746193157, 753436659, 619116506, 262096085, 374604715, 235032778, 316526106, 675211281, 942030934, 580470502, 848328200, 801309946, 691686581, 468829606, 968653378, 821231476, 283512738, 910427233, 414916605, 673897637, 221420052, 174227146, 263469889, 828944097, 133276303, 145172368, 155652747, 604895642, 13398295, 52866090, 800533100, 66202985, 366176115, 239960524, 784184848, 727224596, 215864718, 464586614, 400637718, 278707855, 231274670, 493024974, 384959339, 327182263, 681836722, 1425502, 170848405, 852952063, 512215945, 524087766, 22386812, 241321806, 733305400, 85168158, 911982138, 938762810, 807243527, 960412269, 611915491, 580206772, 479169536, 773921779, 850340623, 863853171, 703856303, 104817945, 414138279, 356272630, 809828861, 225313893, 328924744, 138916155, 774761638, 20477613, 775339590, 2095187, 494071825, 681301176, 334616950, 861299875, 84666172, 255968476, 435038569, 963270119, 749326859, 803471911, 380934107, 518705272, 526366651, 612940506, 434537501, 869967534, 793070789, 628403497, 735211557, 801430813, 753339326, 634215190, 266088866, 627964573, 913513334, 353879708, 928825037, 48924605, 511356261, 38896469, 946152284, 589227196, 217769624, 524339629, 880557584, 973126164, 576262072, 621373243, 897920455, 801029673, 23473871, 885288683, 206989449, 953633798, 214411392, 65399981, 215220662, 674027851, 228118843, 675384815, 903463287, 315499297, 865546196, 771618671, 864693478, 903231528, 818197229, 524529171, 544374741, 759656066, 568272127, 938331296, 112098492, 2932350, 331032221, 834356094, 385721137, 346919086, 265108169, 89006657, 321412806, 780716939, 602672244, 141595305, 309770166, 316737199, 18823443, 580506550, 766325813, 372558996, 546683400, 701595816, 937668533, 134496796, 372555898, 500867674, 483144886, 173767011, 875040205, 933243915, 463752814, 990019613, 868571030, 821143544, 365914968, 513232273, 138097226, 931489576, 509974540, 42746507, 670176996, 159930854, 520693754, 177316886, 378952239, 835134520, 160826833, 33246251, 412463466, 616079976, 238365215, 806334674, 910755643, 638145689, 151489829, 575796417, 687338838, 545700703, 102399534, 789753507, 58350680, 442301973, 30380040, 187973969, 276860293, 10529067, 831442762, 630077967, 279979080, 317145227, 402757723, 448376710, 283665824, 250503898, 562160239, 699418723, 724642398, 830887049, 686912263, 821293871, 304827466, 858702880, 673553952, 263619072, 807263426, 435919415, 368372407, 59488916, 894694580, 322481730, 114673702, 697100440, 710855958, 970701722, 583336373, 220582845, 597506983, 982082689, 685538597, 575305607, 907832241, 402461991, 273790957, 854985014, 572506407, 125583006, 950846781, 914035741, 244386812, 639370920, 882301012, 70403363, 240678140, 116984746, 926738015, 499810131, 307116070, 581717037, 523561535, 533818737, 591788665, 123261521, 821122230, 204218381, 314369989, 749931467, 876618459, 852048349, 6787268, 112383575, 951515500, 828254046, 255907460, 701949546, 292335717, 738305791, 171871042, 344046938, 483761272, 899921774, 531439472, 512192278, 744121463, 273221131, 663835209, 283349758, 810905617, 668774437, 742630923, 951669268, 20262547, 954062870, 85094508, 304289258, 744382570, 237733984, 369651623, 631869267, 812046294, 841468127, 610262965, 169619291, 219031916, 749070486, 500573983, 509939606, 948227668, 418079994, 11345757, 55409260, 428443074, 825950974, 959448611, 285932813, 979603257, 231016137, 253935485, 202239244, 44862852, 621198066, 112343872, 340251770, 642119138, 317838637, 670666472, 243905799, 43647893, 296603849, 53734137, 790739904, 271564605, 153463579, 869031470, 386763986, 363268245, 182311775, 178550421, 562876989, 953731866, 174749993, 964766427, 351253755, 61898172, 232105211, 765995997, 82723579, 599246905, 813897906, 534174540, 238843023, 587948238, 55893034, 789444599, 691753337, 871938673, 8492792, 996494073, 331645288, 410844443, 842939353, 627009904, 434701566, 835611615, 208435348, 440497456, 227263632, 456340127, 620600643, 555256227, 935559527, 151326051, 513686259, 633111404, 952202545, 977264058, 601176787, 550454344, 165360116, 503040520, 966177170, 512706441, 838117112, 777503711, 41769242, 941287258, 887075868, 537603585, 841954290, 133614728, 639392446, 160051215, 324125447, 216552251, 206892861, 870764285, 439658762, 565788743, 277979466, 10672797, 710944034, 937184274, 504950057, 514111568, 560043214, 383053697, 611601853, 395311310, 915211197, 153517563, 414260872, 247966997, 743366467, 69049348, 693593578, 759566784, 625345326, 272326369, 890987210, 382926800, 929615019, 457952276, 797747600, 652953311, 818560872, 390836666, 725431654, 618648367, 279471663, 586959178, 294910482, 945650237, 420662031, 491649396, 752279352, 369776382, 854263467, 76197636, 339083422, 467960341, 959032798, 77114530, 659033178, 124382220, 542412067, 654100584, 463524931, 702265410, 453709769, 286992157, 947547399, 552268277, 77053605, 93655879, 934568947, 782259001, 550413858, 612339465, 102301715, 379092377, 751581432, 889067106, 351621155, 718616573, 173863364, 77456891, 112578538, 234736818, 817054906, 814273416, 589371334, 397942708, 671385688, 347777130, 862811763, 103776448, 214558890, 818315771, 705245078, 902724873, 768969227, 422505972, 585029973, 939561420, 549166931, 543967578, 901910321, 869958186, 525201714, 249684770, 254188801, 171196413, 515233844, 402295930, 364261582, 931537296, 613030428, 359513031, 214497759, 499339645, 419728029, 86707024, 152069141, 199106446, 839584218, 685998841, 494685727, 962252604, 843093542, 619971564, 558751181, 593634291, 32350899, 354419374, 384307361, 200086528, 874380977, 813951655, 835051669, 192515333, 322407463, 410128619, 621928849, 111367893, 759580082, 569442893, 414021718, 477216891, 705437820, 220428195, 637723943, 960600264, 660062620, 879263824, 785525176, 499075495, 991708110, 70212211, 543366829, 998892058, 658238906, 335226321, 255411589, 171095638, 35336097, 88045685, 516674392, 604824830, 282614942, 467363071, 937726992, 293574475, 740468107, 921395707, 102048009, 781775711, 817436562, 662861176, 680822381, 913286867, 868115140, 856559913, 936252239, 544047844, 807258620, 348007488, 630232400, 577548559, 918871453, 162069086, 462953792, 140346420, 760974628, 187027244, 143693210, 548272498, 998859621, 507380742, 264068531, 246695758, 700749574, 259632007, 911157169, 526405378, 753207981, 992651451, 162251620, 763742336, 453140470, 765051969, 95027403, 115246976, 554700724, 240773467, 666447217, 920450966, 339452127, 435307216, 684789239, 696899235, 406211176, 474321440, 686168095, 261363031, 140157882, 686167015, 401692372, 33843209, 854881691, 643023522, 461285456, 40306365, 538707044, 355186258, 141415379, 873736472, 552864944, 561575598, 582663527, 861505696, 483692851, 617786289, 33622286, 59305863, 185445432, 132057046, 83325193, 700279367, 248949535, 794270548, 633292845, 392246441, 627081523, 309418022, 440714786, 271564458, 139402603, 867248507, 51941491, 514688719, 369906224, 706623176, 252719754, 461989536, 668429032, 172217529, 414713756, 577129402, 144164339, 350826227, 188476444, 603148629, 595696074, 491950060, 176904094, 86446972, 380922238, 282530120, 762684183, 901464170, 314901133, 982751785, 645243466, 607373047, 130625862, 373695176, 985437769, 674297946, 454581226, 190386942, 166141975, 772535195, 740268300, 564560496, 777677913, 183871958, 868604077, 686092057, 396801196, 446703630, 495536090, 763121335, 889019709, 292783739, 673508260, 26784746, 531850867, 296677124, 750936994, 287475424, 34844611, 454725016, 992648457, 717188185, 996038577, 490056308, 119204302, 213522976, 647999798, 489638342, 170075585, 256164762, 426094260, 751528684, 927998702, 396215993, 718894230, 200303980, 738997223, 233041063, 869928386, 962123845, 202328896, 769435799, 172638025, 861810940, 84211097, 626622989, 190170802, 266205836, 810016256, 265995887, 849350948, 663581160, 353099647, 678426999, 664962987, 643085040, 25887832, 129251781, 355235736, 726899051, 944520516, 329622253, 358289405, 395719534, 656712509, 930908775, 878791776, 918347047, 941546078, 795373863, 179994037, 202069273, 273982607, 413251591, 402149349, 407039272, 997800486, 645823083, 609409490, 74000274, 501908033, 718480230, 789439895, 462663407, 985294033, 562302668, 859085962, 104692311, 810663630, 646417821, 325953929, 127025698, 355768988, 905947346, 143277169, 209953702, 177468524, 467175525, 377856453, 800332147, 281981444, 904946709, 921687584, 282246627, 281142151, 424066820, 683315601, 998740707, 98447040, 745844050, 19111410, 885818644, 593360181, 450529245, 523843454, 554810586, 916020529, 795628593, 655833327, 498538488, 205334456, 306836339, 232600986, 205430942, 272839032, 729618383, 109394413, 644666313, 750743815, 878411744, 27686645, 581847396, 238038122, 102028393, 835920451, 15269968, 505855777, 602560490, 641483593, 26827159, 108427466, 956039161, 508072119, 71997470, 440033082, 26404842, 957766654, 313490725, 846287944, 770188802, 730840959, 54720803, 919212602, 250388658, 106328127, 139035218, 992422758, 327038616, 401339945, 529578197, 294302563, 346836174, 644651888, 94816095, 849779382, 951717157, 967478393, 388407598, 454986195, 995850207, 448423420, 263375322, 332884750, 434846221, 552938789, 407863623, 286125942, 574892709, 347713260, 910426646, 173874133, 764835097, 776069398, 609154922, 991855903, 107618076, 629136123, 307847007, 710076398, 166180463, 132295215, 511807681, 925259475, 15144988, 595827180, 956118659, 457421448, 166203219, 172453806, 309993096, 648706719, 875470141, 123393178, 606367504, 301411557, 21232050, 471170024, 911759285, 538311690, 913477377, 276536945, 584653063, 431504256, 589948931, 929968121, 914272500, 674461041, 625871554, 985355345, 220512656, 656127555, 926799244, 351042012, 697774226, 455568888, 873323637, 22107964, 796360945, 383160754, 7965890, 4636079, 97766141, 199182741, 625620074, 959437964, 747976098, 968186125, 909303072, 922451235, 292676973, 489358525, 475244730, 276223295, 175500938, 986401594, 785461472, 702302204, 177521210, 738080648, 156839724, 323694006, 454667, 82688268, 665777686, 583646325, 450911548, 942038157, 885784486, 529519020, 143759998, 237787826, 723142937, 399932541, 381598105, 68932071, 409067718, 367972030, 843652452, 630818834, 208538886, 548742370, 625665752, 141164744, 216918345, 328715435, 647325440, 187471841, 922012491, 841947045, 797498633, 481945845, 507729020, 636881455, 310536307, 188347137, 995412217, 920616152, 267241042, 924676700, 356682078, 787542506, 421654194, 598596768, 585418037, 835714984, 515669951, 311327507, 766524617, 798783660, 999857825, 495995025, 604693206, 179066278, 94805248, 758649557, 453806947, 260316354, 476343544, 593943328, 959648862, 332920281, 873954041, 236776059, 839993753, 663967576, 454079509, 132631797, 383783558, 21474045, 703489551, 988816896, 245887697, 101112590, 795143314, 466929806, 850272713, 717600851, 752962425, 414648026, 192933053, 385061867, 995833406, 639520374, 20404463, 371949057, 834744590, 858149917, 18724796, 518922769, 689570604, 95738871, 827760861, 392519225, 804277944, 62006701, 751363400, 839853665, 28821129, 695163928, 65758410, 897498003, 137192909, 706062514, 396336913, 175332144, 326725514, 421460783, 410709110, 933654864, 346968131, 729740363, 112342416, 209813611, 831488109, 881117074, 106353373, 975587577, 249848856, 714344519, 46434118, 732584381, 617872645, 294267140, 950113638, 552897151, 393794069, 123953149, 622835242, 943734817, 882159653, 111782873, 510722136, 862207302, 837919105, 271729829, 206197516, 90227504, 695174798, 680799556, 393831093, 516037735, 539915772, 284516789, 899235577, 208359898, 419112869, 459972800, 787051369, 61234902, 821522863, 266996711, 20286035, 526426786, 114015659, 905902746, 178018333, 84719735, 692149934, 138193549, 1807567, 95759683, 285196713, 156237164, 816796678, 491360690, 872060141, 183696997, 354837137, 324939033, 70524281, 64893916, 61196968, 217390066, 309803538, 327981913, 829204157, 222229748, 153316764, 785717225, 7285302, 335434214, 224435104, 395044035, 869620696, 983474094, 561990986, 7138215, 724165029, 537359771, 442392295, 214472757, 388115494, 999724473, 116134487, 925708176, 746427493, 66439494, 388110990, 695779202, 787660736, 190107323, 811559999, 745417727, 443310769, 275424987, 133133837, 820291374, 958741339, 246153527, 86591325, 939988951, 617124214, 898061442, 790179316, 739813209, 230639713, 557133055, 69014343, 36224542, 362472253, 656301172, 233606164, 107307741, 672115472, 137033497, 438401678, 937910960, 718467982, 866662565, 853247635, 819192886, 385931114, 456696865, 343695363, 925106189, 556664530, 842187059, 289014425, 979935624, 943427265, 108276470, 37109300, 996374235, 723841051, 713359382, 636128082, 700513246, 9762195, 679089480, 972432725, 59538558, 60141790, 197446722, 475606973, 207152394, 949822816, 667573484, 554375829, 805701045, 52118162, 573417072, 38618014, 379452772, 734815007, 279448974, 165855178, 837684185, 303266367, 42775691, 170054897, 152941720, 376346090, 80027775, 196385699, 666741353, 279200277, 598319876, 565951881, 223948077, 829086261, 404416220, 765857935, 32132946, 773944329, 323122800, 11380158, 700999829, 843122284, 284109052, 500783639, 986258308, 935535923, 125641497, 843022069, 438289011, 231629648, 520124168, 131854516, 889483637, 547741461, 321354783, 590548256, 408219947, 374068408, 833897018, 905627122, 322048739, 980087652, 964141892, 249046734, 355599006, 84387793, 582727503, 239545611, 676180110, 74197874, 568227380, 944415316, 395492152, 496507001, 384407231, 903594842, 93861193, 863718595, 245393920, 390032449, 220461144, 237393608, 498814221, 415326199, 870627747, 348157175, 452381582, 275898195, 245829230, 395004048, 238412407, 756000476, 799618515, 294766621, 653924366, 772578689, 217194004, 13383335, 323679355, 504209077, 924360425, 135691753, 86745224, 426518058, 469233839, 510890765, 747589077, 282204965, 929404088, 636660454, 388671559, 780383597, 410164735, 561408191, 338050992, 738720900, 839907255, 670353704, 971951235, 994241537, 388133760, 413989946, 323116881, 580993974, 25522031, 619596265, 318094310, 194066677, 510414573, 723471813, 92026411, 364369465, 998196257, 286942023, 417151157, 565231353, 709548719, 85073614, 113466139, 843769458, 654957516, 826079091, 226407387, 915118241, 808155449, 103804189, 212188916, 488368294, 348073490, 586046913, 833754902, 130789335, 159722771, 537679333, 347911397, 941887342, 886559423, 462310055, 218746555, 317818072, 162731075, 585011230, 212891590, 89999079, 627688822, 99201727, 533174107, 236405564, 941961201, 526654575, 232547817, 733145787, 960574151, 212417309, 41626117, 442141825, 106251091, 471526052, 290923897, 843313749, 30797354, 4809073, 565104219, 16440097, 701508143, 295751425, 679202763, 868158005, 564537667, 948841054, 881260394, 766290540, 11877525, 626151846, 599497681, 604976512, 16158726, 932435433, 563793216, 166588512, 220711642, 182313362, 932806038, 948741966, 514240338, 56127881, 483537474, 920437154, 457815376, 33219577, 831050238, 451738277, 486789041, 28341652, 548599215, 256184762, 688898843, 766956195, 603771139, 781991718, 632924959, 900128067, 155680449, 860135633, 491145985, 757838692, 130353361, 911118752, 446989264, 604834023, 405048958, 521529631, 83745171, 197353357, 756209742, 130616944, 989172992, 636866871, 241333350, 633921845, 54039164, 702823451, 304801770, 704209457, 392353135, 456796204, 920665001, 54635940, 475877781, 574356206, 887152622, 497741448, 172846328, 996337564, 496784157, 992776146, 774773305, 245802426, 424931427, 681676830, 556994026, 167411230, 470797333, 758489785, 750526101, 786197582, 597309187, 504526964, 8671467, 23352691, 259810451, 781155488, 558397011, 862411692, 761103380, 877706060, 762078887, 868157366, 949932214, 58952586, 375625154, 316169613, 766310089, 873718677, 63574937, 723738531, 766010913, 255660332, 668893637, 958316218, 422557891, 988679660, 454334828, 267919892, 200520728, 885078132, 275448207, 148544634, 140121798, 341414418, 832664314, 233224135, 333976464, 698067226, 855006806, 840885633, 343344781, 493507943, 909182849, 373882003, 132689307, 889316637, 394966380, 87683304, 639006233, 636737581, 381648955, 434811206, 341341450, 517227108, 332592976, 621581375, 147467541, 375198408, 265382654, 881133095, 55958149, 55528482, 240782512, 195961042, 508744491, 670326622, 349887885, 699892222, 76115330, 716658120, 931988425, 203111270, 957621881, 850792822, 690363446, 727887423, 788372688, 551675848, 7490140, 378795091, 207716683, 777135204, 214787207, 390293836, 539447117, 472749299, 495565626, 122014613, 377679720, 61316255, 971106655, 442328801, 134855299, 59144822, 11591070, 458031404, 679628737, 881979320, 948203981, 109821190, 133386303, 162204191, 886207836, 428164456, 582889994, 369724994, 959418687, 756309747, 874394586, 409049194, 744385532, 278195774, 166177573, 841648920, 965120577, 444912549, 709017102, 239078967, 912449961, 295180561, 335254010, 776554113, 124120981, 530049611, 26643368, 32945773, 166066492, 123378855, 454477025, 420725788, 525057445, 310175161, 493093700, 382996171, 122385563, 226927649, 831373620, 156248560, 462675930, 262829716, 5935627, 888163668, 713507206, 8986278, 118927471, 773147951, 306885039, 734202050, 709867921, 797477260, 696278355, 749019792, 633303419, 42997885, 303982469, 442995272, 893197299, 909642011, 576478351, 645157265, 984475116, 980047663, 738136709, 193569505, 953490128, 496633540, 966373333, 570469921, 528698806, 40725479, 772576359, 846855922, 755465888, 128372565, 927340119, 671731828, 211143696, 948582214, 60207593, 478378139, 964879962, 832429964, 67225441, 433276051, 611895020, 309039068, 297082442, 73835777, 329334192, 542586901, 265468861, 887258291, 191832647, 643018676, 859547521, 505247833, 61414050, 894904361, 305444113, 746228761, 364225994, 448600595, 17912070, 446492818, 88940650, 438043331, 600358245, 198912011, 824114323, 380919646, 111909036, 980712431, 143763923, 66540388, 91597656, 873215480, 187074040, 215883299, 874264350, 39685043, 815838587, 356722824, 66647109, 986271674, 114254662, 736392323, 195293704, 931358832, 643049545, 442727268, 322942283, 622183858, 611536694, 141575338, 650782768, 146605631, 107644958, 153116874, 75857484, 183518406, 434150301, 963273499, 604962360, 864625186, 940417183, 291733588, 813849297, 592422106, 127538183, 535298159, 767861471, 253074349, 79965695, 740884808, 1534787, 473541126, 922277117, 323773930, 375366967, 269001456, 505461412, 633464987, 994684633, 235940757, 83258183, 380609367, 581641814, 407437963, 955085238, 529082049, 464190844, 600031502, 922478591, 542476006, 934990743, 604687854, 724576189, 907111560, 328876963, 157288400, 579060805, 997166061, 836747364, 973163095, 848862673, 77351233, 991701225, 864764207, 636146409, 674944220, 108342325, 727576231, 119647541, 20496844, 694512349, 109142555, 610271699, 22973529, 663023945, 682846684, 83501717, 674960792, 875467258, 318087805, 818576359, 256625992, 559206721, 287224148, 175269848, 132872895, 318884026, 207310888, 640310423, 280321437, 943574242, 142031719, 90953374, 360438406, 41948168, 476667208, 424692316, 662574215, 27586630, 680858420, 165601698, 916291672, 773987947, 144382763, 1814363, 226572045, 981695768, 268798143, 469638341, 414251809, 564695733, 261405281, 455787290, 414489201, 999832789, 232617751, 861562109, 49464690, 975169353, 150979571, 332954308, 804879221, 912102871, 527994444, 14450550, 763885657, 276570292, 760359790, 976893891, 368053884, 651327583, 32902893, 550667476, 245929523, 661512280, 804622309, 387411803, 614965002, 163346087, 965305930, 99833236, 287755895, 513469571, 289752386, 185748142, 112001107, 203321793, 78710807, 83957557, 581153965, 197551229, 933929550, 288710366, 761855704, 331692240, 473228512, 31055618, 184407192, 454582832, 661493019, 966524315, 571026418, 191097431, 426905012, 591198668, 23137431, 186610065, 775801462, 483966563, 955206559, 72602673, 31734347, 784674414, 400215839, 219237124, 320193951, 98727393, 224802913, 996394984, 205714840, 811674906, 590599948, 790447070, 434630805, 832198624, 894326911, 568068253, 282374654, 322266700, 816916734, 329349495, 712051012, 808215169, 979693290, 922551960, 70485566, 292882480, 578087326, 200858330, 986934769, 410636874, 691302600, 47749011, 444535028, 116662367, 187922641, 828435865, 526308705, 149794426, 442336805, 92965073, 932783805, 608168555, 111866713, 903701308, 521518008, 976577753, 934809850, 27718368, 67399575, 918984147, 804921926, 405018451, 266079656, 831346722, 804215915, 885642590, 439383863, 601959350, 717673691, 818138764, 124127420, 864137427, 665564234, 455814392, 114849361, 46680929, 712366270, 721588150, 794861795, 3110019, 871035123, 103242621, 390273494, 962899677, 966635571, 477860706, 274391779, 904083140, 521461063, 835471615, 84205978, 243031241, 552085600, 275824953, 909612714, 583979588, 536026716, 401162418, 543956390, 368491600, 536161719, 532609341, 23003177, 310552126, 644957379, 612775394, 445649883, 101258233, 414565589, 870353690, 364170210, 739121881, 102351382, 646464715, 26491965, 551682967, 387689260, 251043322, 494013141, 600887365, 392790596, 811436965, 927707095, 825586838, 121597225, 762285302, 159161105, 368813546, 830098034, 840822205, 801314624, 442966993, 360721591, 222273493, 475571825, 187921539, 281795729, 379829955, 66262756, 464916183, 807838543, 272683609, 228037003, 292883618, 847110673, 901758822, 343658570, 212062564, 332717421, 750171688, 869999775, 910869767, 114708012, 182342441, 439727226, 87532016, 938871142, 17529474, 641978364, 950543063, 219632234, 366091495, 968356273, 167196627, 954856955, 44353608, 276535612, 447931109, 732256676, 322071904, 289652247, 709260606, 352775662, 417870200, 277859878, 160973028, 72984242, 915756583, 313687691, 565942062, 698050295, 788917654, 886894, 305755423, 773010406, 711843854, 213564740, 152945457, 791411500, 144888169, 717223627, 996221599, 914615146, 394247068, 588334525, 727514232, 335638671, 718762664, 687437263, 505434324, 589826817, 512126774, 294388123, 275361302, 177738350, 244448070, 974029754, 497233585, 365655350, 325557834, 392427350, 617532977, 876153834, 7693362, 804195076, 812803882, 381207856, 780815611, 218630886, 389205300, 992378205, 586061580, 783767908, 800894364, 280524780, 764660560, 914608629, 642755538, 437623905, 469644366, 382121265, 251731731, 780833262, 594798329, 726599515, 53598904, 479655090, 832345153, 322299657, 295458538, 894164289, 586536163, 732464109, 426276702, 803795343, 318870512, 60576151, 942717610, 59216417, 745474258, 184788379, 626289032, 453321622, 279130706, 458533018, 114337202, 286385260, 703655774, 915502170, 399081800, 402312130, 77020477, 682075194, 278319045, 156383047, 533506942, 190579167, 87695098, 972341161, 680241870, 143737869, 912235734, 891501675, 449034161, 7785703, 33434248, 366256842, 761113035, 935162892, 684258246, 988025223, 465073303, 430923676, 4361860, 982098602, 348349652, 878149152, 860932969, 698064495, 929972070, 319991446, 412639903, 739199620, 360259009, 650628168, 472558559, 15217078, 741855792, 24034456, 638612244, 361964367, 724091572, 264035740, 100952375, 878034009, 775946372, 231748957, 270775771, 344907948, 638427792, 402065596, 263055727, 185652292, 941174875, 945510249, 798762608, 520910427, 980017213, 154892626, 177602516, 796814040, 394177847, 678481320, 991974266, 650712705, 187801337, 820952483, 986711563, 804125675, 944704410, 565772990, 45216334, 466192275, 254724170, 745304066, 317075074, 132045017, 632896197, 761020612, 257893050, 782173625, 819605033, 229854253, 371860097, 847093980, 634603542, 665427130, 452772827, 637865551, 454164540, 199418230, 607524158, 778674829, 258401320, 117647831, 847516299, 206297633, 527316, 518886740, 428318114, 496762990, 654243480, 547767790, 752157424, 596640024, 61739824, 402472639, 434888543, 803044433, 511225578, 648403797, 736299009, 164551166, 781751985, 524519078, 538199930, 908383891, 417018186, 82183898, 439950352, 465528022, 565614119, 947377413, 868395879, 352417487, 708709166, 268829646, 543953486, 737735438, 616917266, 777550458, 7891068, 410788506, 245518316, 777171815, 671771661, 54396752, 827342737, 359892730, 278529136, 139657064, 745069332, 824875969, 903579425, 991015663, 816145484, 667095761, 788492800, 132846254, 969788393, 366213225, 565773039, 490382150, 643977148, 452671389, 957160043, 67914762, 697061532, 439180079, 1093016, 704337507, 230840616, 444667249, 655071365, 69148956, 826279507, 206710919, 83432490, 656870957, 49202723, 489365879, 81269722, 141516809, 740317230, 812932598, 558015072, 634628979, 639214261, 470994722, 915826969, 798821458, 648633715, 918431034, 954522104, 516241238, 313086531, 478628204, 51839316, 492538785, 529683302, 470147891, 391116515, 463380486, 765265856, 723238424, 198656608, 621218197, 656297582, 462592483, 676587632, 107108345, 774011924, 112314398, 8012842, 896820212, 796336824, 855674853, 86125417, 494770094, 450197020, 258910753, 356135520, 35578131, 14376996, 637432305, 702312875, 215210383, 706237293, 529675477, 206472324, 916200417, 977602457, 774149110, 636244885, 20572841, 292492553, 423421707, 921105438, 427873793, 219452344, 94927427, 570885189, 147634874, 592455156, 808197973, 506350095, 787396941, 674985129, 452826257, 75036949, 926608674, 935953347, 608385588, 975175535, 244862213, 867668438, 822001274, 774022828, 796360442, 716273198, 748077008, 611096698, 454204652, 837179445, 907651202, 673639363, 116631291, 386829604, 254279125, 570870542, 4224398, 59835991, 387085221, 543728229, 746335467, 452560185, 299053886, 656605830, 912106432, 926744567, 898991241, 601221363, 459112304, 681432953, 612703462, 777077656, 3025329, 292123731, 629528756, 257889372, 448214476, 789925417, 769996829, 536958327, 769838285, 42283370, 883636488, 739985453, 693655513, 489583078, 268171979, 457615698, 736130539, 404295568, 55209742, 786631540, 934902981, 750531383, 873249701, 371530919, 438258864, 897337729, 131491615, 718595987, 549615318, 588289048, 593107851, 38826345, 881363435, 477060384, 321332439, 570258069, 694353561, 286165434, 438492801, 709076661, 622509237, 564633377, 991702621, 253154502, 381965881, 679356886, 343598834, 19719083, 89210198, 161050193, 111056881, 412249174, 650289921, 555955879, 329562104, 951625977, 670371235, 570657081, 415729291, 696582178, 345276912, 764414712, 412828278, 983619025, 45799396, 500024509, 751880393, 664882192, 855774950, 980574954, 47403979, 68234020, 657824458, 131306824, 177355960, 483079993, 264515771, 513053474, 81935744, 247690484, 857395693, 692282775, 132259121, 275257634, 66022173, 181068379, 733444945, 762166399, 934262831, 379098734, 658659318, 566587875, 76819664, 922526411, 166945768, 713959006, 640673010, 787436587, 425689505, 41350709, 40809980, 143007079, 795909367, 159291253, 387572907, 54407739, 551761083, 766783761, 576930027, 180043345, 387761643, 713366539, 772160373, 77077576, 519727922, 427492805, 528034230, 21279411, 145127917, 628410377, 546309572, 546790147, 744428253, 903104601, 169458864, 236141611, 847513525, 729165146, 394754308, 685673703, 964666006, 300289735, 907730804, 944535392, 592767041, 503787752, 361616056, 514488249, 440700483, 936304405, 901875157, 860973341, 338594326, 397489613, 457092813, 125861098, 53762492, 361799567, 36611708, 926598867, 249341000, 644707234, 165591954, 78111101, 494716750, 248484253, 32635973, 229064045, 362544105, 392447507, 410694230, 636076547, 848352306, 776951753, 4423650, 550349799, 572219665, 423011144, 882503798, 598551932, 627299490, 609869987, 631643391, 799939393, 481998230, 940786620, 643040240, 901440264, 576071348, 956596515, 855187569, 175344891, 816746713, 410175782, 105388097, 849433004, 978728952, 419341271, 988554511, 923608802, 62972803, 78981882, 224793511, 41173183, 132715077, 545946646, 992302772, 312111314, 96647931, 879285335, 470866068, 472227839, 634208006, 364216086, 845969337, 85774940, 612455959, 651322367, 82398401, 318825898, 689819754, 202712002, 812855671, 531340927, 500283006, 524288160, 619881087, 245922835, 860893569, 440234490, 700456595, 778126889, 227217215, 289054995, 631683847, 461627534, 834095483, 191088531, 900098811, 64374128, 79017279, 567492717, 667333874, 75927726, 882703130, 653608433, 203245054, 248569914, 860565551, 449226165, 402964569, 506085069, 34662553, 325988739, 8074480, 708216356, 910954960, 371900417, 918607079, 276546114, 936244195, 596763749, 384511805, 992951978, 412963820, 723001015, 780583209, 383408740, 815079569, 951280831, 631656358, 74302029, 970120280, 244187901, 269198107, 570090435, 814022594, 955772265, 898839077, 412439783, 659272495, 891863297, 810105771, 231919786, 792089459, 524138679, 784219523, 666130284, 303310442, 878017574, 552283481, 537304401, 395718219, 648110750, 474172996, 216558093, 551212054, 906989464, 681696048, 496583395, 13014889, 460577570, 517703201, 21793957, 61403556, 722885363, 642995281, 889700493, 181210985, 634085056, 18171155, 679004411, 115795981, 597542580, 617667594, 209993656, 672003746, 393606560, 609515466, 204529604, 795260339, 440162325, 725269933, 29206980, 818786002, 804852299, 347150475, 26875881, 668410949, 842328308, 265026531, 765158372, 101705145, 716111015, 468176773, 727440806, 220401855, 593237273, 229490791, 448967071, 268212830, 953499890, 430900749, 569085284, 198872094, 567921270, 828051365, 88189574, 241850884, 352219989, 526565988, 492105785, 289925728, 909340542, 450463698, 687450878, 81473198, 973553328, 485448871, 753662175, 476071443, 73550588, 577654007, 163321700, 85315822, 745429451, 765206800, 939827772, 875963481, 743263350, 293817491, 630182081, 496827089, 817321585, 145171851, 697521600, 239509419, 155231912, 280580260, 697567793, 136609723, 120695596, 432981589, 750490258, 334026853, 484256240, 855800664, 849656113, 680835466, 530102635, 334336154, 519976095, 487584884, 500414262, 773525893, 263516442, 219474183, 907111604, 332537952, 433959397, 525813637, 645865700, 966845350, 889170495, 330797924, 835371408, 404626641, 334938854, 301780476, 314704877, 5927504, 828120981, 625871976, 612724185, 465268710, 139857856, 423949188, 250263767, 269162447, 133973142, 436353933, 945531027, 420548688, 481668853, 233084409, 419844797, 324686364, 823700817, 28684202, 826674160, 237148702, 327044276, 413174733, 514506882, 22544627, 293574881, 199812281, 244627027, 108618091, 508367116, 533877532, 698929438, 872658180, 309226868, 858572015, 455833626, 311822059, 778007344, 615373837, 657285052, 422671164, 102165814, 672993253, 296552528, 984561714, 396570635, 259412694, 262958464, 557750676, 743756848, 385070208, 357139391, 812415756, 776235466, 524368647, 276404479, 537683230, 729322750, 102160572, 586819620, 411324656, 884262427, 332909809, 600814843, 948990041, 399818652, 542112665, 187197822, 597252619, 600125853, 637647506, 544526832, 830127995, 617658269, 786681117, 565577862, 396826486, 153470554, 751416426, 508343683, 666794332, 608513467, 218849866, 496278583, 793184317, 644492316, 448446237, 64541586, 280767354, 393587597, 900358101, 576199471, 392539489, 168128812, 802159795, 545613990, 822456303, 431787134, 415304249, 792678869, 65677500, 274923574, 730533137, 139541209, 94516175, 762927462, 36897881, 799724385, 417610070, 779674174, 638302105, 939603468, 506277941, 546412843, 225684, 42997503, 369092994, 463914790, 378041206, 986977370, 435220144, 937748452, 147381396, 527275705, 963863390, 838770262, 809699519, 146215117, 296210905, 916398315, 381406954, 385221087, 459317093, 170230458, 986238765, 699049128, 292431221, 141530404, 117797892, 455525345, 256555399, 666467778, 939499067, 420691638, 115690183, 857397295, 369201016, 280257691, 707679067, 694182194, 815489247, 630024650, 62491526, 610661671, 468625537, 332972997, 33361760, 720944887, 685630975, 499966768, 165062098, 9563415, 114981388, 596289114, 564174217, 414592399, 732164890, 330546863, 792598267, 449352001, 480865981, 596376355, 639951600, 209817480, 283395779, 822266252, 54748003, 45690187, 122109637, 505823800, 326151015, 358400737, 73837174, 13972919, 766876242, 230631016, 867984102, 437242560, 221817281, 775566548, 221746374, 392979889, 455297600, 23626541, 271776741, 34500403, 282087630, 360462656, 706737466, 945863947, 841967608, 564662504, 516315910, 335102676, 252632236, 988450464, 919398147, 85119231, 606268843, 100268214, 620747724, 178919376, 726707942, 496613764, 745024029, 261992530, 253570057, 858132387, 472472174, 593728303, 327914959, 216421901, 446648858, 534878636, 665058392, 880813853, 299486483, 189203199, 858295416, 528657051, 629022081, 163486619, 622365914, 350852143, 751009730, 249753455, 748433547, 218120833, 507180868, 911115211, 59841376, 238744901, 249649260, 780568740, 707527508, 781476183, 110377533, 748826752, 716492568, 56528514, 902289048, 861299606, 883470205, 488340975, 151569517, 265660145, 679638041, 231951854, 995181716, 874497547, 191189755, 300166038, 552245348, 751360289, 457106583, 848878418, 798734896, 210231026, 932806680, 275253516, 132707267, 650354000, 545375181, 111842069, 514933207, 506736283, 763012410, 166500160, 467255815, 835728024, 886337719, 7423584, 401404087, 348995925, 906530252, 27329724, 195431881, 602829403, 708200851, 756557429, 836582872, 463807339, 848898327, 708674549, 344406822, 726560471, 201707459, 424898550, 243058951, 347398986, 990640001, 43278402, 304626730, 125029228, 761461403, 296500759, 556557819, 234854864, 738380400, 615538704, 55973811, 909351836, 108913710, 129457895, 69389340, 239606469, 470665490, 89105499, 589333495, 585279497, 553119914, 577779882, 412885735, 337363130, 344684352, 500356824, 761192668, 227675827, 548908931, 339834126, 191689423, 23255804, 25899994, 305323570, 80355921, 346507605, 125949268, 483219314, 533612708, 538098365, 374500291, 55074958, 504839840, 104891452, 194243473, 358666429, 661037675, 300094280, 49545714, 54786773, 32279794, 543919390, 818805324, 311068533, 886108551, 66793683, 927911011, 198981426, 643826860, 556078974, 540408232, 715531942, 152341837, 936043466, 816991944, 892278862, 435558112, 352193230, 155808563, 223923779, 183466745, 46962780, 378469678, 563368937, 981012759, 758061531, 316354699, 876198285, 363050383, 410625862, 749888536, 63226210, 196556368, 90784624, 481776393, 707634356, 733861093, 378216077, 747026400, 360437925, 370998997, 937363520, 512403871, 764800668, 31295508, 415414821, 499087662, 667897864, 837728252, 898924818, 492976663, 41623519, 699884705, 946894626, 378252855, 32850173, 427961728, 801113015, 29142557, 875833946, 916800261, 826524401, 507335150, 30272771, 250348252, 231974665, 50347644, 43200134, 909235590, 959656527, 734310847, 395571189, 251705795, 45163187, 666680456, 635392353, 190943831, 659985807, 597256047, 89384145, 526899415, 961156890, 853963877, 437021427, 843492168, 906872321, 684812699, 84793550, 876585623, 309615500, 181578226, 202684043, 608297473, 977007229, 766896331, 280330534, 863059731, 38329256, 465286939, 872683566, 213855020, 256429573, 640624282, 820067827, 847017955, 276034649, 7201311, 500648246, 438603590, 258331170, 372678923, 25133011, 903168859, 597308779, 158230717, 865964699, 981453012, 286857750, 443247972, 11790168, 188720686, 547172030, 376363023, 609683144, 428614632, 915373570, 509018488, 191937709, 123045756, 861212877, 16877136, 97699742, 502840819, 879212773, 382957991, 289983146, 719564206, 46779625, 891853354, 237707400, 801278201, 92257839, 250923060, 297390723, 279796271, 247244642, 371503988, 872486430, 964203989, 409092985, 226029674, 487283298, 914850196, 96008465, 319668324, 4695367, 775160292, 791521060, 955942438, 692409700, 485512970, 657696622, 661281474, 401892499, 842317887, 216456950, 792752416, 79451270, 922131916, 294839334, 234141295, 852951179, 926568728, 579911190, 28620941, 182976160, 158976315, 866936130, 848260973, 341740042, 788480180, 332009487, 738572978, 651410322, 442842075, 670243602, 447884846, 390114538, 21452290, 232503372, 351034677, 353038149, 932544268, 569157823, 397415061, 609426261, 138432648, 202767729, 661814990, 956335343, 126843779, 384440535, 505571778, 980226854, 205448200, 866311079, 785063764, 487443575, 775721175, 658150361, 958999301, 581709113, 508925001, 867836012, 250251595, 303403046, 558275857, 540537670, 519339405, 888782612, 849827258, 374396963, 44165798, 591719875, 402343329, 24350016, 190836097, 380364073, 498561891, 274091866, 800216719, 987961989, 497901878, 43461330, 700290446, 440892929, 546356396, 651446615, 160899048, 829343559, 116293616, 309843921, 102442901, 439391982, 237783462, 503943874, 898365646, 125014035, 606192718, 434723858, 375290967, 125876818, 507276353, 5830030, 114251510, 447579051, 475349555, 277690344, 913194321, 781810767, 459054424, 327542948, 780086815, 205600525, 810446607, 173832714, 558593781, 527565107, 606743237, 323302728, 979134514, 499936823, 663322998, 974851249, 107490351, 439936812, 586355137, 329663100, 401748901, 524960854, 245283367, 504492821, 162422113, 331099537, 689126379, 937382179, 102392915, 177825665, 763423223, 409488099, 315306249, 906615556, 282474948, 677353915, 415943106, 557791799, 305745405, 421455224, 454508527, 940299741, 183998628, 727705724, 925110103, 894307173, 363647427, 713012420, 22532035, 660284583, 11828639, 530583137, 955063017, 781430665, 944008165, 276296892, 458495592, 888227965, 931519294, 696994189, 413990725, 383339020, 768207525, 352984195, 537296036, 383944913, 858381101, 699690328, 905103450, 439535625, 658405217, 720202498, 601398566, 704596860, 369863420, 663730969, 278214691, 55641729, 698693068, 486794840, 130481722, 634621766, 379166910, 332971774, 159388572, 251167744, 561464420, 991181935, 178262956, 825929209, 462210031, 864755480, 712185089, 153997407, 786524845, 35889050, 259124198, 119710533, 904017084, 100425467, 155269054, 867768801, 579753659, 842290148, 186742776, 418921551, 211185016, 213742917, 155781881, 501537961, 222663062, 148661954, 890698166, 356966631, 614378593, 471968853, 843996490, 572924322, 24613238, 124081443, 142313821, 979119853, 688899150, 564091061, 545766764, 213765954, 612614550, 867898770, 992944106, 373847244, 459726042, 907544974, 149815555, 19133910, 691260535, 244327437, 170322599, 166687243, 884283747, 882934687, 428267603, 524775519, 190312233, 19892236, 976144914, 24096898, 606679946, 343277347, 522368157, 181783325, 545237035, 937638705, 338068696, 42304124, 900164247, 180492934, 63039260, 907008506, 362179153, 177662829, 245446151, 344263710, 918698183, 795666921, 789205924, 486910270, 501544911, 558021472, 646484670, 357458234, 255909001, 170520381, 556054427, 471524195, 17214972, 69367764, 848063147, 327541364, 595392862, 875714342, 903113896, 382921395, 716097696, 711586273, 267967551, 452344407, 880009039, 28783344, 779242954, 77060562, 481086139, 360343136, 108177268, 8598763, 40848594, 809123497, 797113363, 13979441, 483339819, 896058347, 598988857, 919954268, 296635520, 107557249, 119505943, 812365724, 835542344, 678522088, 2743322, 626232930, 936205306, 246546919, 553078520, 334172963, 545105537, 484990099, 473636279, 996426651, 606617284, 113556733, 498837594, 826832860, 953247659, 657337620, 741533252, 739149436, 811481603, 495831105, 805543385, 246516753, 387285761, 792205130, 188466744, 925734281, 97103027, 990239510, 68588072, 926506843, 293751142, 20877978, 248092379, 818957877, 752459570, 894149980, 697924344, 518227142, 182171690, 123134231, 897644960, 780350760, 911436156, 541502543, 503251539, 331489145, 746339985, 302925112, 384782831, 929827443, 710478850, 174099936, 628776506, 754185193, 644809381, 344637037, 365139008, 918250829, 890138354, 347251138, 659973668, 906714914, 87830316, 806369729, 579738007, 828415710, 905860092, 337866453, 949482296, 946507105, 124298559, 357098308, 851734768, 562645173, 527817579, 957662326, 710678666, 35029286, 141192566, 379756881, 315311457, 734890957, 620019330, 420995922, 363281371, 553313209, 582770718, 123173546, 776433211, 248627708, 935908452, 889157617, 767195579, 212855103, 982150151, 424306659, 148567917, 706111525, 613721683, 831533695, 811482223, 365507720, 737834911, 840967903, 588731867, 864415759, 720731220, 189144708, 258581450, 726794634, 845556913, 946594141, 225275837, 145432171, 302436733, 555236481, 21427587, 587896816, 183172551, 348751876, 980253513, 640104576, 445012454, 617926677, 769443484, 207457127, 459391019, 587884413, 987216028, 116096532, 352920058, 927875340, 763865983, 228297117, 196880980, 503959725, 976331708, 936634556, 234997151, 658918949, 241118641, 752349768, 321775034, 475928318, 625386233, 626447830, 270016662, 878030359, 696947796, 38522765, 300421187, 838257225, 431346489, 348004130, 797291521, 420351692, 912378372, 531937948, 2904073, 548202614, 198769456, 844684035, 633245563, 160486554, 165546420, 786075947, 173909195, 896905728, 695171859, 657216987, 281645645, 754702588, 472281440, 3997669, 867303133, 838833991, 772972692, 212257253, 557166224, 40567206, 99879901, 849909818, 902676048, 181480704, 956024786, 773838228, 935013661, 426119407, 825423274, 892951399, 357137028, 64037843, 570189418, 295046251, 425017233, 51247859, 973959001, 946244520, 614061128, 781455514, 972614609, 696146631, 521032686, 133860682, 959875993, 82183382, 139161703, 279322483, 768631545, 710474713, 651300672, 542071466, 951676897, 495986378, 880285913, 773083424, 308423475, 277126591, 449383133, 7726186, 169978299, 422293608, 536207064, 550260657, 878274543, 498235037, 965978073, 225097053, 759164300, 719657282, 513146806, 682914779, 260201109, 694984536, 205975863, 12383496, 518877660, 748121550, 408196007, 108709300, 963427875, 734031080, 849023573, 201429092, 609315666, 621806624, 132174241, 595967507, 258768390, 822288896, 935995708, 66030739, 970974589, 728425857, 88193748, 957615321, 720758678, 594586857, 482803770, 574061466, 221581926, 902122152, 129251632, 172464764, 111645284, 649544137, 376011398, 981373832, 99510149, 322062494, 549042905, 32239745, 632782304, 475954, 727380918, 5146060, 697172694, 52704761, 907286709, 10105196, 443638487, 180435053, 775585849, 322179685, 531607693, 466890608, 853833121, 579833264, 642627175, 785604292, 922808630, 197425785, 218776142, 641056039, 452543051, 397383922, 903166312, 677463527, 354489745, 761351967, 985080563, 219778406, 581106113, 272432793, 291405435, 645643057, 155139137, 576605355, 548037512, 673265462, 980259800, 206983569, 9277482, 349144951, 428308395, 916379262, 214184430, 96256386, 200468746, 794862337, 214479529, 297767260, 395999407, 427501082, 819584564, 244769277, 351072414, 687600704, 743294089, 912675110, 594716870, 66584939, 966250320, 932427325, 547766184, 388102572, 835772940, 7974684, 705962708, 664799181, 352765685, 49475840, 847713140, 830434093, 536887699, 603000036, 135407433, 618920050, 585927386, 817330490, 891185141, 221711434, 253875591, 911074386, 160743379, 153432301, 178149838, 862638119, 636596557, 756630288, 200391227, 574466044, 596736109, 598616143, 14879197, 335762070, 996826887, 908271429, 388621970, 487538025, 163104572, 996108040, 536123935, 584453867, 882283697, 117560809, 259541975, 182772280, 819948279, 89264416, 449036357, 676988152, 598860070, 720906951, 556689277, 450807449, 507426058, 858758621, 140926833, 281547304, 521255171, 138533966, 214258572, 530390608, 467581644, 45221833, 669207039, 434305708, 748714357, 728770708, 405203926, 960537961, 717320121, 339643766, 14908435, 485544927, 550818862, 506939994, 696859470, 925359216, 988355999, 135588002, 538287948, 607755575, 24062955, 357866392, 677641500, 839651492, 469980255, 249399681, 337211831, 54969732, 340609260, 963221663, 880478117, 732781577, 280371762, 418468848, 744629258, 125380202, 356713790, 79693156, 405213903, 197592840, 174494699, 324213536, 235448412, 146214242, 790579918, 910727713, 471421598, 529270537, 656538006, 368984664, 834044197, 412394767, 496941147, 334487799, 672077241, 592956255, 896296175, 894401845, 649841356, 180212586, 858042869, 642482850, 441725102, 942682254, 732279346, 582580336, 273903172, 372307407, 332234231, 66333947, 526117717, 749664151, 459857426, 248160828, 225717648, 790062680, 77236154, 419653995, 821166783, 397544390, 280128042, 943600161, 264702671, 114352431, 11599334, 622532225, 802214998, 922346, 172559713, 683685941, 250557921, 607595193, 725846330, 341571312, 493773439, 1994619, 164808640, 437532097, 668472869, 434993375, 161095196, 788893648, 706139106, 750295655, 897268456, 615022653, 818800405, 434790152, 652085260, 107182067, 534960655, 30941999, 399581804, 484659829, 400491966, 240865672, 610631292, 747690168, 598709032, 650793969, 214403426, 169620570, 290760950, 393871644, 549403283, 407333390, 747690225, 163215833, 664477184, 350809985, 74078985, 689727500, 701103044, 742303141, 700667100, 772322457, 577985468, 33707910, 123352122, 592484673, 995333186, 708371729, 766944846, 574970692, 254781940, 541708397, 192190717, 732566421, 970594654, 190304906, 343122170, 184017886, 789780971, 235670826, 227529193, 470480840, 37648794, 689387113, 202966054, 574566232, 804770098, 759653013, 798214662, 327599851, 109494921, 245053572, 312138325, 747072711, 884563601, 679956528, 747217584, 633992640, 736780402, 373895678, 977582016, 768862443, 231121174, 218786911, 172846506, 534857325, 640442804, 50286004, 223507040, 63358199, 47640394, 777395478, 151842594, 186438425, 967784508, 929436148, 40690597, 490496427, 690053428, 598271283, 362014543, 416237935, 5141164, 940325817, 390137499, 826883440, 956963276, 794776354, 528230307, 985452332, 448218148, 45701621, 859444276, 41293330, 288343550, 766589685, 975593080, 41427159, 733961567, 178011131, 911222165, 973610163, 676799941, 44550913, 453886101, 691129800, 832556347, 967085573, 612817598, 988174766, 426871786, 905658570, 481070334, 470479757, 635208009, 877677907, 529168890, 100216632, 167416604, 728490267, 48554472, 933249436, 62680778, 75974806, 420704481, 960541669, 136180257, 840809100, 805988582, 543840577, 893217221, 296243460, 10161384, 870645084, 78310377, 891549330, 329503648, 636745435, 116889865, 123588229, 758874443, 937101217, 409878830, 996019463, 199209522, 191553278, 283010534, 861441024, 407528222, 209295046, 524861539, 63199021, 2279819, 218141595, 461324892, 996046776, 827022941, 958321836, 391046866, 505055038, 326486330, 870009919, 181847635, 232365710, 459173621, 586236628, 879717612, 249203751, 153392615, 523023101, 857306172, 925699895, 118956408, 508393091, 432790089, 237500699, 356281584, 742554552, 946310947, 978542671, 535522123, 625998780, 103429283, 610007369, 639431643, 134016987, 66119474, 61112638, 506563181, 570471983, 895132727, 498949435, 459971124, 249881230, 138978320, 423112666, 315921994, 88997362, 585681619, 880712045, 138221813, 571206056, 432845137, 830911181, 73220146, 439876119, 227119702, 564744171, 984943360, 514625649, 993409496, 34456918, 335484318, 175085375, 12009487, 224819623, 458700869, 233059406, 737913424, 241742672, 120421402, 829212830, 160515605, 141747960, 872283025, 206923978, 948413863, 882340115, 884403857, 438714362, 138734905, 924791619, 30474198, 392457538, 971554813, 208861957, 463782274, 258734454, 522928168, 554105121, 834831562, 707465442, 147385827, 469401887, 407934237, 956557509, 586732404, 286273033, 9439438, 427336457, 405453540, 734578789, 75777251, 743536553, 312952551, 807201019, 719229141, 18704873, 955396200, 925274735, 256535340, 75976725, 293996987, 96464497, 662532954, 629244412, 228373197, 2251376, 188220214, 124752392, 927956699, 556292031, 945164321, 612397678, 936173797, 565616637, 55344386, 831949901, 188703119, 566541683, 437174895, 513794248, 88308412, 74704734, 222696142, 810565375, 808023794, 667631724, 671823562, 15585503, 394588763, 12632164, 225788257, 985416553, 789039465, 269777200, 388455753, 241991996, 161298600, 542797998, 29055703, 630250597, 389807074, 560417903, 789087885, 876092352, 707403584, 875354069, 63512764, 23798842, 535478904, 839354711, 156817066, 816591472, 847966224, 405485816, 992502048, 303670794, 792266559, 606611261, 357945754, 325927609, 298144288, 364755983, 16354151, 182077745, 483541796, 505830070, 90800549, 776837831, 438657269, 510240377, 81878039, 909318643, 882767291, 744582804, 210307312, 287515798, 653485572, 731724493, 301225037, 143181092, 847897170, 401389487, 852645156, 326111491, 856111092, 366963114, 663142914, 891204192, 218974434, 578682162, 815578315, 374001676, 144821451, 472824044, 384103551, 987417480, 640394281, 178846731, 419824749, 127060054, 244545798, 602385471, 547927694, 954786848, 953538526, 934731307, 238895497, 42668070, 997905616, 357284621, 816901224, 235553760, 637635019, 104691758, 279223423, 530640007, 538909175, 93179652, 137708189, 565686463, 109059019, 505041412, 679026520, 807935414, 953371576, 991631087, 752290960, 849584241, 179728441, 52288403, 471210852, 493818908, 561381371, 79231197, 823631973, 677242455, 235216897, 56303160, 74994289, 289729481, 480884679, 242776241, 597217227, 57046665, 723392081, 87995894, 568402591, 633085087, 553242884, 76967736, 973473687, 977269943, 939060479, 236346759, 307574471, 548827408, 238511270, 607830769, 579318842, 90554404, 589652761, 536117902, 358169860, 839391444, 243362868, 762139888, 548925830, 930639844, 928600632, 167161105, 856187412, 397456574, 855502146, 54378365, 489799824, 21921949, 971765922, 168564168, 474979166, 499886006, 993764123, 991552839, 395273030, 323375742, 609140840, 444139243, 851140661, 831903750, 549711905, 439852353, 677306112, 28062859, 233786291, 90022157, 148797798, 151033868, 338426910, 118778440, 64185437, 311852612, 382264739, 199334700, 874797393, 837449793, 137045101, 741141912, 764398166, 645854725, 52899497, 518483978, 899224637, 937631544, 278301410, 686325646, 983625782, 75834074, 656845285, 325485715, 15231346, 208228923, 748981614, 94611302, 80092524, 461452957, 309936111, 179154731, 678894565, 361674154, 77414080, 955280064, 279946708, 818061092, 151410450, 979660792, 28747351, 232710251, 234525915, 82412799, 420696669, 216650111, 201390630, 195452140, 402148651, 360033369, 339941384, 110368570, 558865647, 854774039, 458397599, 47689154, 879538328, 147187060, 148597962, 201965620, 178378363, 901138785, 556536551, 362461088, 97279837, 283678855, 638634652, 305056112, 66673850, 375058007, 213504874, 590865712, 289373194, 348600478, 468046815, 920164515, 550581595, 368021395, 761821403, 704402017, 222699276, 183071783, 984627181, 625478677, 312646600, 802477541, 316721457, 594940898, 993356568, 564822351, 881152123, 425399099, 909206342, 900007277, 854954341, 123066083, 613351794, 721946950, 1614907, 56470973, 830938456, 857834771, 388971484, 590500533, 33820835, 887986442, 679675220, 116734194, 968297751, 824830031, 781459631, 863211121, 965965448, 213237771, 542742863, 663779145, 303746323, 164792166, 601554881, 492588745, 887839589, 284563794, 127449792, 541569747, 341386844, 712719355, 551845840, 330865970, 965243966, 510022626, 92277597, 519100917, 556995751, 131196484, 799101001, 604386500, 32607587, 955857209, 737124038, 298748379, 771802076, 478723150, 521737127, 103447350, 45624085, 954944717, 497867921, 878218662, 655076141, 650093540, 355113226, 766430760, 976935339, 312914296, 134686624, 309919478, 250460497, 595990014, 580010718, 165452616, 635106454, 163266029, 386308218, 297213713, 684144629, 413032858, 35015691, 796279677, 149719926, 50248479, 492866972, 518841732, 936558986, 497326626, 746329640, 923857349, 937104309, 925339167, 204160254, 86334603, 749061765, 943666102, 433414758, 972347360, 389897807, 900779609, 157513719, 786321316, 78351510, 186214580, 672925056, 642392393, 229968294, 630448905, 688664936, 979724689, 660936740, 249588028, 451154857, 327364503, 747544041, 457640616, 708619755, 346129863, 423635682, 923567495, 209309993, 629377211, 723222266, 810213457, 332713404, 821821352, 319824599, 516480654, 936720964, 65729115, 919991597, 541260414, 343197303, 429371507, 345713013, 250448528, 14189279, 979037470, 226076680, 131347918, 603209236, 515102331, 249516437, 83202974, 933271132, 564260202, 506823408, 625139590, 671506930, 146427613, 162715498, 506956471, 308059018, 808066128, 700875276, 164086265, 240193129, 131309642, 230153350, 874207135, 981856827, 226658793, 933991643, 384576778, 381616436, 68612374, 929392133, 727019245, 813617889, 181342357, 867408156, 17402533, 9591570, 391533585, 973239968, 372747648, 387285947, 174723808, 872219108, 573589946, 488290672, 718763643, 840682925, 346788784, 191104474, 356592058, 186900455, 435608532, 652980281, 844359774, 499313230, 923372729, 848981597, 360604722, 931579095, 530077117, 344789266, 128030394, 538059672, 201058822, 354269657, 795170300, 46988854, 833467330, 622491787, 774412964, 488881226, 685721684, 592777622, 732934099, 740487815, 541622835, 759161960, 365496649, 900743943, 20767609, 754448033, 453983632, 547605318, 718800767, 262507072, 276126485, 58207078, 635929515, 519985672, 291447907, 599357574, 753342337, 159225410, 73403929, 97714166, 84004622, 368013065, 873199974, 44183454, 276257900, 537407976, 790960789, 151008974, 268728124, 6796065, 822851275, 340714887, 332501227, 105839661, 932850091, 2225462, 118072807, 786577643, 375226513, 999436956, 169015842, 554925874, 517932133, 876967023, 257269480, 325045611, 64671623, 992053957, 77192470, 506165744, 826510809, 551119331, 490457682, 967009652, 446038635, 354493285, 8445503, 185116199, 424131892, 928587129, 158402364, 831486768, 902256724, 366359298, 780523608, 515703628, 836341583, 875254471, 936555612, 916442121, 401718199, 534970233, 259888876, 580589855, 590956014, 369043898, 97512651, 702012316, 787426333, 87064035, 259518787, 853564148, 140169442, 933363159, 775947294, 723436712, 115433032, 249822938, 947282828, 250229432, 192809473, 675197211, 412681507, 731035895, 438220093, 1299443, 522730924, 235874069, 654094422, 638636915, 491318617, 716816090, 915140727, 586459939, 315658276, 956173662, 447340291, 268348200, 950086773, 525720528, 411285115, 244706014, 149562713, 987062280, 972317332, 705359684, 408633249, 470426935, 812363308, 53513791, 524219111, 735838143, 194592478, 314542104, 436731456, 734218937, 239187061, 114150649, 123796881, 104961538, 428491002, 723209136, 157612994, 798566442, 114038679, 303028738, 288546280, 14896023, 914307270, 421370068, 64544821, 972582169, 648904716, 319493793, 738954079, 612142999, 871028833, 625017976, 506871367, 736798862, 823546375, 980718244, 224031002, 245903696, 771864904, 179992740, 200983897, 168104064, 438734809, 357181240, 388298543, 803587121, 366801074, 920302786, 474253808, 384525192, 660798387, 80236646, 75350931, 206860908, 494671008, 983708477, 432080890, 938625968, 531851862, 882405039, 936151401, 27017252, 215151461, 739241405, 155645928, 153854661, 536924100, 19296916, 20517633, 858377345, 286953545, 377543790, 720002733, 449355212, 929385922, 248261024, 364250284, 931107403, 447658613, 729185209, 925075654, 645525108, 718254056, 485692488, 776276476, 606231095, 439787477, 850171576, 42313496, 165109681, 33889129, 611545233, 714906586, 975967508, 65912905, 598225615, 161151426, 78374580, 322003433, 169450095, 11266540, 339670728, 121862230, 218639402, 266315327, 910959403, 51333918, 712163529, 258794097, 887427871, 328571876, 721848299, 22525706, 920614624, 129695699, 447635955, 158638122, 550656073, 56174381, 933017812, 1455855, 143217309, 725917452, 892851494, 427122829, 66135344, 982572134, 146650732, 450252915, 627993606, 919838189, 549582479, 427262842, 857357072, 855573109, 892536218, 336435013, 933508302, 756956001, 813903024, 239705144, 406983873, 393046170, 39756835, 161411330, 551427950, 451332493, 528831502, 2300168, 317718575, 374984575, 236680049, 436422393, 168590014, 810197305, 846734445, 118661735, 134041372, 344772948, 121460070, 73649065, 80581720, 482553392, 528202712, 738142731, 739598252, 90693690, 838904109, 643042677, 836476324, 341173829, 262415735, 453303577, 886871059, 753156140, 270879570, 791626521, 526944027, 822684191, 650282197, 61177496, 612803681, 415361080, 681932251, 625237658, 738503519, 430479888, 81061638, 86354775, 305710426, 287898419, 76861785, 827335455, 64025053, 786111349, 61932477, 191372161, 708891423, 457484777, 160332219, 513613254, 506229347, 369519698, 489134484, 213850746, 806359717, 492000889, 914010637, 9567627, 543143922, 525877243, 301345315, 794555753, 235695934, 27351800, 498339247, 545727518, 663460590, 671033785, 14313321, 220803145, 924804508, 170765935, 328347698, 422057464, 421206954, 910321426, 603437112, 77703273, 628939494, 999775690, 909210824, 739476996, 805286765, 567211764, 599987815, 250793383, 843277832, 913534903, 352990966, 821846600, 736155261, 152540269, 642012003, 947945796, 128971873, 82126173, 635985788, 175454933, 702325326, 696017189, 369266773, 58274128, 589091440, 650144482, 183871569, 578602362, 936387616, 120609948, 348055661, 66760305, 728389869, 32579773, 553826853, 917071766, 475842075, 463263018, 85375969, 673184088, 124363371, 842320319, 21954077, 897249950, 77929946, 811506583, 460540329, 503432924, 556496230, 174696610, 877220919, 624338502, 741574657, 72209927, 212904338, 20050059, 431766006, 244746640, 118842916, 859312022, 35319922, 759179399, 409276170, 794989185, 81618193, 83362611, 976472520, 890003444, 957277438, 267622178, 668624864, 977777814, 98424722, 975991716, 198139011, 272419893, 424963616, 404758665, 35914173, 492677297, 282978751, 101119169, 83412184, 954459679, 273989444, 77063583, 962018903, 180021932, 574871343, 136860883, 963074951, 769669373, 615905925, 977346629, 265827251, 931022358, 160162034, 407507737, 867056647, 851732056, 400680143, 388023040, 835135807, 796126934, 255605978, 1660846, 711364005, 388335915, 773306241, 74545850, 849583848, 902917633, 817121187, 91496444, 573835785, 539240646, 924547397, 292096976, 421992516, 200183044, 77201579, 404857073, 258415258, 183536097, 378242635, 399160116, 918143152, 956711964, 333432485, 442309143, 629679988, 930346753, 427853136, 457735177, 697713128, 658254593, 316472137, 436230680, 658417023, 860022276, 690086330, 276508447, 173405422, 520728774, 985785315, 926017311, 754635885, 980677511, 703047392, 121169632, 65779674, 98826736, 93368467, 885556704, 752957167, 973110172, 219918650, 354106478, 329107546, 496209367, 360930654, 785588446, 937729323, 964595155, 430895026, 871161639, 513018267, 620914649, 352309748, 26834511, 77090502, 914793038, 929704669, 111651143, 387238338, 542366151, 90491071, 167632219, 674170315, 848527643, 968918982, 388398354, 678124690, 440864721, 799480543, 951713715, 470521203, 613360481, 997491797, 15919614, 158328032, 750798785, 412890396, 327117530, 949301928, 432587178, 387399183, 426743655, 757620192, 891858449, 177593377, 210701993, 803634174, 954625979, 489147436, 984366598, 27237179, 616070344, 272001179, 38788503, 82875118, 697456363, 52695656, 988504358, 420135592, 447702830, 483733739, 935223874, 913607512, 377809160, 872222311, 449852874, 130878518, 552022179, 632758788, 625199318, 665840055, 635448203, 800183013, 561332091, 22093161, 766014672, 187139214, 132340889, 407830840, 509332010, 939687413, 160780133, 392097084, 102594301, 392028281, 627197165, 573505524, 438369872, 513357251, 238522528, 635055588, 266973249, 201081694, 399723218, 297754961, 464243801, 115032340, 877133348, 312042471, 334942955, 598278786, 236196272, 937554985, 98867044, 351959561, 962811729, 543102763, 579894639, 868823259, 769288704, 190791414, 539633889, 517852007, 962297053, 133742956, 56716334, 478914107, 941045890, 56494253, 204965552, 618499946, 9753811, 435281555, 777506798, 263997819, 981392378, 255907227, 510747790, 878421435, 519850142, 401220730, 956429893, 619932320, 717196086, 585717282, 183726207, 657196934, 201614840, 456041452, 632920166, 473293420, 831267110, 348537694, 656623710, 617066125, 704875443, 111354529, 969658245, 572880405, 594422054, 638523070, 117258404, 116737896, 375860759, 547744627, 646977602, 607314166, 294917709, 456438791, 581897379, 310556775, 903731795, 953947248, 262151622, 350055065, 850703057, 463327974, 884052516, 676540548, 346616558, 461845655, 292490984, 623896661, 813892740, 572711631, 549569830, 897323813, 834071539, 378705355, 295994016, 746097732, 213062767, 675241259, 10620023, 904133478, 753643195, 611859914, 784180728, 662131080, 280682104, 281888645, 344016080, 236747904, 141547581, 70650473, 296222485, 742901880, 487503434, 700557381, 395399303, 140635401, 784811398, 826280881, 934562935, 199827264, 299189032, 397244016, 179301656, 319660654, 52415336, 100896644, 504077933, 115502502, 682919782, 548377847, 20825942, 632402932, 672035575, 658972112, 197610108, 247652724, 661660274, 236995906, 759891375, 638038345, 703458672, 223259536, 716621023, 898379706, 50278929, 249545765, 564143590, 621067617, 437313742, 954771477, 893746920, 88889814, 601318813, 321525348, 565766102, 595591302, 749493120, 639138184, 11664739, 476562253, 331575081, 923894403, 558812038, 441132467, 775759616, 892642659, 508086398, 199975166, 230793759, 369239599, 702626960, 165558732, 724775449, 330350826, 83535302, 369778529, 990448844, 899451693, 190902910, 942413328, 895653515, 771970038, 269473747, 243384291, 278057968, 943244080, 655115227, 678815515, 279985845, 200854823, 131098517, 278824384, 722502102, 228111525, 848646346, 426605403, 768824612, 871903529, 62289564, 762165727, 914943309, 204088658, 55538664, 17137814, 206529388, 400316115, 279717402, 472431285, 785068846, 34192951, 444958501, 857850597, 721561631, 252769720, 443425570, 492224218, 223622315, 754802576, 378568958, 368089325, 167076408, 351629824, 621777175, 442577910, 647069213, 390789550, 758414960, 774220609, 316490856, 432231289, 799503263, 267859903, 480444384, 781057082, 747216944, 591502486, 132577290, 413868689, 892825, 806235223, 816656782, 736134566, 264360889, 988196198, 845324867, 807169022, 597072731, 147282123, 50873762, 142250463, 651594901, 55306034, 837735497, 786898925, 759629479, 839256302, 738913485, 427251647, 899245725, 948199003, 437153371, 600057637, 772968913, 639612148, 192252241, 686559077, 588088531, 623137512, 70511678, 566364352, 697114348, 598937133, 36036611, 218683946, 786460920, 874022242, 951768559, 286997634, 971028620, 820082680, 203231489, 24895502, 150649958, 104124154, 55424217, 229783831, 296953426, 170878075, 883232831, 133758452, 89496051, 541830193, 331681803, 452363629, 99951716, 107625570, 311840278, 607482118, 628327761, 300475412, 887292082, 489117914, 229147886, 664465544, 422671938, 112521216, 376459612, 775437349, 680149068, 224437018, 527050981, 201640537, 717140281, 365758622, 332757509, 642983451, 252120726, 918856571, 41286249, 196667815, 280456568, 937730772, 881542078, 159552582, 642123071, 354158213, 120986022, 76971174, 636882909, 999631101, 690532393, 243053167, 597107706, 951257025, 442075807, 758045533, 918359136, 384823599, 495355987, 577009002, 401754048, 275345603, 649387936, 461784419, 392802505, 934401895, 559292081, 492494275, 595537030, 360926844, 673476995, 599680584, 94136601, 647504921, 807956795, 700261049, 657274109, 190689489, 4430251, 913643621, 781061071, 802062567, 179324641, 725041470, 598708835, 191941292, 202167403, 201414904, 184154198, 732947936, 762666947, 972211519, 575951977, 23304892, 360281246, 94615153, 853463643, 98107762, 81717576, 382791510, 361814798, 110285133, 557162100, 14749739, 492641163, 776717776, 256670865, 808699105, 748229919, 527264049, 939760139, 729647240, 317013599, 215986763, 830435634, 223396573, 224456587, 615938345, 98749033, 872869819, 115833446, 834225202, 949145316, 415342997, 676226134, 368768832, 522189885, 353415922, 293060840, 950809283, 61214491, 176196585, 831509771, 110295024, 89590617, 305700450, 331456615, 172341970, 118461593, 391749209, 558077568, 245928712, 229181064, 943022351, 450881486, 964130062, 967233849, 489251308, 572648405, 555197975, 920178034, 930681838, 123107581, 268358889, 62357993, 75447502, 613452334, 7789527, 723059507, 534734586, 814281767, 792773748, 71626146, 224530020, 880562720, 155348470, 724599253, 916081055, 589871142, 699209021, 471772671, 460694535, 672606519, 361461720, 861128980, 361943098, 335380192, 436952781, 36317709, 876674894, 836666403, 449897794, 274131368, 996943147, 948307743, 611019285, 643421641, 61459214, 555669332, 521046596, 25746295, 615891371, 986577674, 613000189, 958892583, 892515569, 922753454, 224418864, 704309220, 680742773, 641952273, 285130009, 868319401, 137665786, 677845083, 8457024, 964583677, 762824532, 975203794, 184012831, 597636608, 85785384, 735505376, 233190880, 5839378, 838129429, 477950590, 381473948, 559033, 234593520, 576034390, 46149290, 272211202, 791370544, 659260984, 825167986, 784122326, 648187855, 566106007, 142674188, 796455567, 249533639, 241937152, 388521562, 558346660, 519039044, 777947231, 362103064, 920574858, 606241004, 983886973, 210813154, 815800294, 205931407, 658378073, 389413778, 705658278, 205430669, 191372789, 487705491, 628651080, 108385659, 412820498, 639887624, 449038274, 675641871, 417282152, 577840478, 585356406, 164346803, 922519294, 352977060, 18638223, 982143718, 118794971, 484134079, 91583371, 623002840, 3482795, 108296032, 742779108, 481868576, 890045314, 191743983, 338004860, 533765826, 731031342, 355158930, 793733032, 615312530, 650185556, 191799837, 335715973, 351713738, 594500849, 45665036, 415765318, 149824770, 534583453, 748141168, 796906552, 753986443, 931681697, 739640217, 680219355, 146051506, 344490110, 286006037, 383990478, 824028601, 399677204, 648616159, 732967544, 812591622, 644484933, 488725186, 303921016, 61467287, 839403249, 77609203, 972484059, 339162784, 145771993, 534801331, 232453905, 668072420, 883295932, 196978970, 653862720, 294135999, 130380761, 997089842, 181396474, 798468076, 518868995, 780540021, 698170649, 151122454, 6148023, 706122356, 496409015, 978334527, 89504916, 746376942, 328379185, 93355177, 773331262, 173340783, 83657411, 952083087, 508187551, 795365719, 378135472, 814868331, 505122960, 834807888, 5514779, 988593237, 115605187, 129842970, 84694543, 350754223, 575930176, 989360718, 529162374, 861434560, 433325270, 202216636, 186918105, 990255228, 517761992, 712355253, 280518323, 838569445, 375041019, 145405007, 412779355, 564473441, 301691736, 188855329, 764295204, 997608028, 710990607, 896381506, 337415560, 39389566, 775505121, 563398041, 110573861, 442500765, 346268439, 295699419, 31161493, 319500813, 795460676, 453875988, 472168713, 825604145, 37325283, 207664123, 128660004, 313637812, 153808311, 905643187, 509201096, 13763280, 370215025, 929810242, 200055012, 12552184, 469125164, 187745450, 625734626, 769309744, 400763993, 559691882, 999520308, 681231718, 477022107, 319537286, 186696036, 212526663, 194722464, 889036273, 316186754, 746473341, 89666255, 83625947, 450799743, 998614173, 928841454, 382622439, 105936957, 573754394, 82035961, 489508911, 637706327, 999048954, 723782302, 470706133, 496873089, 820381362, 970412034, 668612285, 16185802, 151234114, 835195935, 178728400, 74249244, 392520891, 423539561, 812049603, 52120288, 798299114, 198439319, 697731870, 303884532, 862454817, 294640557, 205823861, 538843041, 249584219, 774568170, 609028547, 536697086, 767484913, 542952649, 623085413, 15635083, 819766320, 245935055, 217900054, 238081397, 501559110, 513524036, 643473124, 53403342, 148819648, 494354815, 414378059, 225789288, 375978562, 140898040, 415793802, 37925706, 163630651, 222625161, 695546847, 634799769, 528911903, 592744056, 83218037, 586436071, 451816073, 38812950, 370712532, 729530476, 56304673, 592936222, 661762572, 596515772, 115445391, 50741909, 735459524, 100166590, 906738944, 523613294, 38725665, 819565617, 466272334, 275259664, 11096482, 668787258, 664830170, 845414052, 335620688, 66327113, 837100856, 575305977, 181424456, 380286353, 139850227, 460053099, 334938246, 935616735, 971894923, 101082057, 864983858, 193605650, 202623772, 14956299, 376531601, 391139379, 444393177, 928028288, 654734125, 575637450, 596750500, 690714746, 60425109, 943704518, 404344363, 932659456, 854176794, 89155746, 737064964, 366181962, 64228448, 860980768, 542576385, 294716010, 558288896, 853114799, 529598433, 567383338, 83239015, 655948406, 535316183, 161487742, 153497186, 323244584, 514361636, 628159467, 619950453, 558021164, 111810359, 489435787, 429256450, 712946159, 884551010, 37976262, 373088190, 937430487, 406104709, 978144201, 723554541, 731706461, 780546643, 32920059, 764351648, 424463937, 733785681, 487958675, 51134750, 788050196, 702778177, 192779459, 803748488, 1056430, 684693820, 559492709, 405914836, 670943254, 21963251, 790408255, 8786968, 11410130, 510557604, 630538636, 595649089, 144629295, 104477209, 365272957, 455619206, 69823439, 945984094, 656901235, 951624891, 233891381, 832655357, 407623379, 511260369, 723680466, 804453701, 13749542, 96560727, 966865233, 480815193, 244386940, 711072523, 895637688, 919497194, 886960640, 902375339, 802478016, 89598090, 833098079, 649746581, 646147824, 793283967, 170145349, 119156652, 616345393, 276521738, 649859201, 48806606, 710592867, 868263554, 567829659, 53833455, 689152966, 478257680, 131761791, 761551146, 753871157, 37249661, 49155309, 459721283, 409682165, 571479808, 635275691, 4566365, 747645171, 935936442, 5925126, 824199412, 675673575, 192482814, 706808556, 988646688, 26235811, 386344774, 326750773, 550846551, 10434489, 926489944, 9442567, 421809841, 358724860, 158389061, 401985449, 157037423, 671765013, 257437521, 563183630, 736687214, 365249928, 297588430, 337818898, 799349091, 203577773, 112999587, 866047954, 35766882, 606890796, 245827155, 111947665, 967329037, 393348033, 665352456, 27352556, 177118471, 947062603, 152223734, 800066116, 882163945, 69477330, 909331543, 344192536, 257178663, 583712104, 89711003, 913476651, 787325325, 401801379, 943437258, 518862744, 779141450, 697930608, 435426073, 427576633, 994252376, 450848753, 424294580, 994273603, 853156253, 684057277, 67937717, 202784923, 193687484, 395938712, 749803810, 596293420, 692658711, 972572514, 55974944, 711359306, 707589263, 404011632, 424817673, 549587856, 624690110, 61942297, 703143845, 329769830, 609630872, 500748336, 128307321, 925703276, 28793889, 284348235, 644810652, 760497840, 316153199, 319356912, 317023094, 223341673, 221510489, 125466703, 155333264, 532686446, 369497692, 576438547, 584466240, 473388717, 824067208, 460492318, 243130662, 831343187, 86682420, 321886768, 897202145, 49796122, 86319448, 791018765, 171647183, 964787536, 899657946, 236784822, 473123125, 202488872, 225115927, 315813502, 919737681, 15688696, 549349353, 505386661, 892695260, 99236414, 171486479, 848165542, 392323177, 936843357, 250875890, 446843587, 583589468, 709668506, 127754166, 982348359, 244111998, 404865348, 246164107, 27596021, 949061098, 402291281, 602948375, 203007667, 145488012, 527716424, 721073539, 6053013, 307956318, 475066026, 948586242, 90927781, 239763679, 58803153, 66699966, 264537658, 691347465, 904013857, 436890195, 146763609, 150461045, 362009859, 862839738, 711798940, 628507881, 313173132, 871296139, 171544327, 118493574, 257444841, 387412955, 356204849, 891596676, 885340244, 581046848, 741003963, 214775118, 230388119, 950760399, 365990119, 832286638, 498152820, 376570416, 930961372, 241471907, 458980162, 856728312, 607251679, 364682576, 170626831, 727780808, 112029603, 263547155, 445008214, 824395752, 511235454, 701019846, 74660227, 421225492, 923594823, 985777855, 54494130, 584046873, 624047846, 681756446, 193703606, 683237760, 614264382, 271415407, 455124786, 87862608, 139407128, 229305863, 978643237, 208767015, 939195356, 468440037, 206459383, 616829478, 721576467, 33333370, 321427416, 285231891, 40994820, 389541300, 95653657, 274966757, 751387007, 309196002, 176427434, 575905407, 673034691, 709747180, 804480148, 592222348, 137937099, 141658261, 78235141, 757045558, 374816735, 410073073, 755955005, 952113710, 547621883, 626731023, 690253930, 868752529, 701162060, 942595623, 214511170, 767371440, 827344355, 792940485, 381197024, 869603856, 885981035, 848805185, 565025276, 128253667, 405120971, 757217666, 92445735, 860167399, 794312423, 790201739, 587618132, 599971717, 962616788, 993768341, 258188961, 338227381, 884392328, 764708856, 50841270, 808315287, 42503360, 396301443, 499841907, 688907531, 951921332, 854910633, 707133451, 689380899, 770959720, 976646728, 806263311, 403512938, 278597154, 224704058, 441893014, 755357293, 366775262, 845005873, 622869129, 922937098, 737068890, 490200042, 316458440, 896355260, 25399364, 817727909, 366776876, 492538283, 124275331, 341540805, 601435614, 991898362, 861381184, 976066064, 686789830, 888755975, 636086261, 838149306, 403798534, 248022989, 616860961, 317491874, 303009954, 255418117, 728379121, 174602440, 682153139, 544077864, 792400905, 429151937, 9559327, 889898111, 134183845, 882179731, 676082208, 808983815, 964639270, 908382736, 221825815, 948780640, 941380776, 51756748, 435649327, 801722616, 848915505, 766752858, 792250102, 551732029, 286915993, 420835918, 55414752, 832156527, 66448055, 234065806, 615900565, 417944236, 560649120, 376085942, 737178151, 230353039, 883705100, 854938354, 459016101, 122364890, 778603173, 660866310, 167313542, 788524018, 30773400, 853196443, 799821777, 828791608, 98544368, 780080656, 185484851, 785102071, 791086800, 568933610, 855522219, 353912199, 891487113, 460368218, 204377445, 359806775, 737786461, 53651396, 641602731, 804692109, 203647032, 969548915, 194194323, 515186623, 500919740, 444357902, 630414082, 670213970, 15950731, 128877217, 496638017, 839506540, 420914059, 825031294, 547901953, 175439595, 35435121, 516962158, 750056847, 108393962, 902488984, 321394837, 754892154, 951698765, 806725271, 631159720, 261139450, 149501931, 24614401, 548282656, 120024540, 391652118, 82699131, 315561562, 131856090, 379368560, 935350, 978386352, 364037588, 800351117, 401548329, 828745004, 465255763, 164490792, 430603761, 792107189, 632803474, 317150751, 74394861, 160129167, 31114396, 627180503, 407601897, 362515730, 583477969, 734868755, 954569646, 26423502, 884943379, 524489780, 728810012, 12751735, 110362774, 50851537, 835589295, 843218025, 60052536, 22532462, 200951670, 933302265, 182294533, 519974426, 800210538, 849659551, 739894512, 999360036, 623575645, 240940902, 136009573, 871459910, 387266827, 427792462, 861862734, 495689024, 874310955, 325836993, 201133935, 859334430, 689148346, 95022384, 278769422, 468203449, 909417663, 873269778, 972193159, 232861713, 423185514, 690154161, 58710631, 227660419, 501551519, 545407000, 493990315, 595701606, 285529618, 490056138, 830530895, 81345283, 204314238, 572151079, 509434433, 599397054, 715269061, 971728569, 507279500, 311502653, 304808149, 130278074, 138490184, 54522305, 687922683, 284249396, 213761938, 437295313, 592839815, 343330950, 962773618, 593897662, 183980314, 783159684, 997604994, 908982760, 936857843, 283689478, 956527480, 831736278, 3975774, 505784111, 640737276, 454572914, 274101666, 406443695, 866063595, 593304362, 951844861, 689040047, 213417061, 345884754, 460694710, 773351475, 129341447, 374195130, 742502881, 554501810, 420838668, 367882762, 744524326, 519298981, 764198027, 437744865, 187232628, 767596965, 422367411, 169794052, 997713825, 152070130, 444217900, 136334467, 828856363, 258374898, 204241548, 516538332, 487801609, 807907762, 415298661, 469915030, 133307238, 46299087, 348871454, 463385395, 787713577, 700241272, 342726954, 18802002, 614761786, 959343860, 310101176, 658343864, 396725914, 623687633, 192284770, 918990858, 731820804, 568503703, 457227958, 141672886, 797546948, 785676282, 868450226, 692469464, 364289308, 763115048, 27047461, 986086255, 814916089, 247404034, 309199771, 472635788, 850127870, 735232283, 543154030, 832190660, 653766530, 982364780, 111701192, 637574509, 912369879, 262426461, 146766977, 69314286, 653523377, 901871167, 638695547, 359007738, 660813993, 391271132, 21676697, 87669486, 842840493, 635500321, 336744904, 273523470, 751828381, 988170507, 287300093, 847788859, 802182748, 515229832, 215703057, 954251113, 607667942, 915398223, 969253435, 550407383, 182810374, 452128605, 519693521, 861246668, 215864718, 166976288, 665979948, 129902100, 877347734, 596596015, 1020870, 494089763, 8778567, 489068177, 928588369, 710566649, 383019948, 862530958, 377186966, 433148478, 190375156, 408700934, 215442599, 861897811, 325508539, 100931688, 548879316, 207344246, 468978601, 460083014, 564405246, 317620801, 694457396, 932605259, 495845660, 905441809, 293402728, 667387758, 646026442, 15067393, 950999672, 725649955, 540067176, 740949069, 830265228, 804781000, 843764826, 676179535, 645121477, 333053691, 848745200, 177325116, 189005151, 943916087, 273667375, 909768476, 104655848, 606294632, 429918008, 665164447, 721720683, 309860692, 898514351, 874546785, 732741586, 442736886, 747485219, 321650587, 985723648, 229383327, 805257810, 934530073, 847497721, 178799401, 959454270, 899287643, 725248941, 595008482, 914498518, 91044506, 869129293, 120581184, 838542598, 25612977, 871131109, 589967216, 378566752, 931720650, 794046274, 235279279, 651131407, 958607680, 862078049, 643547469, 670398406, 116688285, 265726446, 547447226, 270354930, 548902707, 45805120, 361828369, 927724476, 269141291, 885856420, 712140164, 271191049, 328998194, 658937822, 602563522, 384991863, 850107725, 910259810, 538669556, 284519952, 937632951, 421642576, 528875493, 940815553, 5303440, 469243430, 671100709, 138660835, 318732140, 837857760, 982841626, 964303293, 424533757, 96488749, 515033208, 346486876, 241264320, 515013425, 165935773, 259534973, 711585959, 170405135, 583401306, 324452137, 246013349, 829214250, 78057933, 10973390, 335530903, 766166152, 676422462, 909652990, 62043054, 284714244, 772098704, 900050595, 338081174, 330044988, 450154005, 830008262, 691171247, 881984196, 750627451, 797335993, 731839233, 525229811, 461813564, 143411210, 366780810, 154644, 137291893, 801337233, 531332269, 161465356, 960998395, 131068443, 421110178, 379945830, 169204066, 154493430, 424437052, 146923156, 763618940, 257431939, 919381715, 222900362, 857958444, 409668835, 991938650, 654204512, 308473143, 207028569, 343424777, 136128946, 213705119, 73224039, 997584129, 384000298, 73473850, 467665761, 181725743, 74903678, 4368287, 341429149, 776640373, 767836337, 28766763, 64025693, 809034838, 839353531, 451091511, 469276172, 930028185, 322164704, 924930020, 632953915, 425240328, 351107261, 975697411, 322136655, 363429134, 220439150, 243289451, 937986111, 726692582, 375621949, 500916136, 182544, 7458363, 670526023, 472551501, 391241422, 51532131, 430483387, 124205288, 41237718, 576177491, 459396406, 239701773, 216307662, 50930252, 73403103, 302614988, 302811921, 48978594, 786678891, 718211587, 748586289, 894920992, 170374244, 449491003, 275007745, 950314122, 459220187, 680621344, 741449756, 250408513, 370375855, 519809765, 666588947, 750294463, 524471161, 938977824, 860595088, 192659736, 450209503, 590589110, 100792236, 567005204, 235088011, 815499923, 169810656, 358463180, 966296640, 652812913, 920358086, 491341436, 365807187, 728396835, 120233355, 352244494, 242634256, 191764795, 893123186, 496582447, 168996828, 604041007, 872018375, 220318585, 630578354, 576976196, 142028431, 452723098, 463382074, 264111718, 735836935, 751529277, 821784708, 48926059, 878924423, 98332396, 390471958, 619849302, 353528974, 326841877, 984393319, 709628897, 695894172, 620046530, 326698509, 254886795, 258233328, 908288736, 560128657, 868674601, 477516089, 339247235, 887504824, 756470497, 241660839, 238481445, 495062985, 346327421, 474553634, 634005509, 758591366, 639812987, 641509333, 963356644, 581915422, 291511697, 146417392, 107644590, 164024983, 113935874, 70277103, 276499010, 704147142, 290811389, 687370468, 327993392, 965649515, 291073645, 14354010, 491973935, 360009466, 828878475, 787912674, 809666438, 542353117, 716139461, 95658771, 288538349, 225707327, 667446279, 461554152, 173820694, 519002555, 572733046, 217385159, 524717282, 149290079, 46268110, 474792266, 285847827, 177065120, 795940597, 219888685, 68691464, 826806080, 660582501, 243785806, 676265103, 353634280, 686777668, 877689344, 146406, 525909470, 446635861, 553838026, 645170666, 265462693, 184941251, 492412364, 726302610, 671216395, 962286290, 49071180, 697555623, 556431209, 65057183, 826246296, 175892515, 996807064, 497394809, 18250212, 16064546, 514847961, 941906627, 545833422, 484063826, 705236563, 399363201, 753670834, 12420303, 715184689, 492931907, 669378467, 302560911, 15566484, 923400098, 84124942, 709460988, 751517942, 759120289, 574267846, 395827573, 82244812, 93928397, 85801020, 361395474, 491415086, 659493331, 33915316, 678096934, 461421017, 280891355, 667487746, 670548379, 338383235, 454761420, 494544079, 77013077, 529891743, 59873685, 501809116, 323518874, 422865923, 223917189, 650421614, 244055384, 946045179, 693624542, 509264752, 405224329, 115986947, 517690526, 976839968, 202849498, 218278597, 527519520, 612062159, 647326851, 704874329, 78992284, 224490505, 208092506, 195580044, 340328249, 991919764, 736067748, 443912321, 382550801, 311519741, 972487889, 327248674, 655142861, 577152448, 59997163, 727922212, 853651524, 575376677, 864002884, 335735938, 379578541, 363037512, 556739349, 621314048, 681017905, 914789426, 771568299, 960138836, 447869350, 236850791, 975086234, 404388591, 971964166, 971035965, 587045399, 913332020, 955976759, 258478404, 186458349, 488735426, 25074223, 431183565, 802236962, 628825549, 98508965, 143636588, 132232978, 278528678, 378172373, 291136841, 641551370, 636243718, 399949395, 963192152, 358493821, 230843025, 272852980, 475925332, 987546666, 202974821, 552994274, 856462999, 480114431, 144074356, 334646934, 795749452, 13102793, 510068321, 81856937, 739383126, 488614364, 706949822, 558778159, 64592931, 435684031, 433423918, 375067103, 423686756, 755813394, 537816571, 944202586, 899323309, 411801663, 938907210, 282107857, 859377372, 528873409, 196097286, 715222093, 578778259, 322255723, 182808284, 14650055, 503418789, 885936883, 841151650, 272201445, 33150715, 377697459, 776853434, 500497827, 168603761, 817208035, 219448082, 383876378, 816024601, 781375682, 407947532, 709362081, 51017255, 750619175, 650860184, 182475658, 25155949, 411745539, 197704833, 494774857, 916067789, 498825180, 746454471, 160626879, 323687027, 368311575, 101001017, 754429117, 68496902, 597400254, 399664642, 856562678, 187035166, 885647743, 427791734, 127376289, 941213390, 717081487, 134663266, 855996703, 743806596, 215940541, 527616773, 381564014, 61564717, 443654749, 351002743, 233026530, 686092368, 443696771, 823751585, 260498037, 285543207, 47762170, 896332249, 542293479, 267146571, 280455549, 589415219, 885206047, 444711546, 404064545, 219437567, 407848364, 572953618, 967122173, 642521225, 901684407, 114826305, 680331487, 553702707, 184474388, 732810015, 339289465, 614671025, 377957024, 563232977, 55177382, 748212269, 389068865, 212182344, 997448126, 656256438, 284286277, 429762224, 283790151, 109116952, 231965258, 526485860, 838742654, 647611552, 267004277, 434562674, 374165526, 368807703, 944453773, 122274138, 983985383, 32251076, 90709030, 6178163, 958493993, 75441930, 179706305, 945694876, 331332899, 626509477, 161760448, 205067019, 651424422, 784711305, 677992709, 489865161, 870118782, 148009097, 977666062, 539762395, 616927903, 177280733, 745522698, 400781406, 783668149, 67335416, 656836024, 18810902, 399749288, 223386648, 53896346, 497905880, 766917739, 145373190, 213456471, 430689672, 372764602, 217989471, 318320050, 916170808, 657230869, 959893829, 768817743, 582928089, 562140594, 521875284, 160444861, 705365441, 124779785, 938499475, 465606215, 72564109, 698130843, 327263635, 522245158, 933147447, 801936003, 960931114, 433705298, 764935426, 205957858, 871981392, 846754730, 778835502, 547036456, 547517430, 54152475, 532186996, 227588653, 408883896, 319299298, 128293744, 213893976, 609889995, 799127372, 726698101, 357892563, 887069979, 322390736, 628669999, 448857441, 952191372, 203568950, 474592021, 532123855, 357505717, 86284799, 481774523, 613729477, 618149478, 627571567, 879481357, 818908420, 906286499, 60453434, 499206233, 142981579, 310963409, 698843724, 501870719, 761222212, 448494649, 267652977, 987617510, 949261219, 886749350, 205257178, 905975074, 140979188, 510024357, 892337698, 669116593, 407921105, 427914316, 605863520, 73739201, 614928951, 90883732, 846370333, 905712739, 832660718, 110279005, 31611181, 146533570, 666985809, 827729453, 491718029, 643907707, 66275463, 40245149, 947524249, 742212008, 585539281, 413017131, 126376842, 68298608, 302393430, 435165490, 26503293, 815130279, 675087932, 107881595, 840086088, 701234019, 536094191, 663501145, 628963517, 674939349, 490033401, 480056560, 357135496, 534761106, 343551173, 126017165, 181289491, 436525873, 987046783, 842060927, 772013738, 489829483, 94951556, 924378715, 328252560, 57945729, 707601773, 688590445, 38068465, 964651183, 689954423, 312671805, 570087222, 4196461, 783708100, 577469181, 547380694, 377396979, 976275546, 50225063, 231305932, 703428506, 491037325, 757920136, 176553368, 213119299, 654831186, 861242704, 511429760, 580217063, 549329141, 923004767, 662464674, 106632071, 815057066, 532364958, 811617179, 11415899, 924602251, 673184293, 580930053, 469075104, 744826072, 991461777, 165783116, 660852531, 222398158, 681091170, 580310921, 897468129, 573196333, 377011076, 866933702, 94957456, 654443792, 516010221, 436067520, 462676445, 271067994, 622348445, 929746934, 82795144, 186849365, 636331910, 810786423, 891215067, 235074652, 818281839, 600809112, 494809589, 312679942, 495111688, 457232182, 100237761, 980059424, 101457023, 25434915, 918915723, 466475446, 851747177, 850186393, 406409027, 604995180, 423222026, 644984426, 13344909, 594926983, 281135623, 575613213, 143434178, 570874040, 844693516, 304963158, 71384940, 777924505, 553768787, 555998765, 810429914, 740219772, 358643796, 937987367, 238534992, 450672347, 231136336, 567142847, 924525168, 203363500, 368753888, 688525299, 728077826, 472448062, 819092077, 669581611, 275204072, 237889087, 230810420, 431084982, 370064776, 373005663, 347771227, 234327802, 332983457, 652105844, 360514010, 556542337, 10147344, 300854960, 579673019, 967773822, 5061648, 640950783, 160225112, 981163323, 440299434, 198895116, 962695923, 887167356, 401125764, 913222003, 722829407, 443017177, 904678506, 484697212, 824306126, 768316575, 557596878, 847460751, 902474580, 984162744, 744786179, 530084082, 650226794, 207719868, 425547564, 661845087, 4202024, 998474523, 700223810, 677454576, 688623029, 973524347, 273813171, 77049366, 386674742, 321718848, 73126696, 159045761, 975041048, 287943488, 331863, 564894412, 462465371, 86757553, 886476080, 733549533, 150858886, 151253206, 985998664, 779129542, 858114908, 464304222, 689722461, 236188111, 381126197, 213900298, 773876363, 682288412, 47755546, 424620579, 376237295, 117447917, 471973733, 775410769, 91189318, 908560458, 927041561, 689920918, 178431799, 735294980, 343870465, 50622121, 994204988, 656578217, 384720935, 353373236, 290282050, 883463752, 691866859, 781417317, 103461182, 790352454, 156774538, 891412624, 782563109, 636679896, 657163827, 970509203, 355676476, 107867198, 181748163, 603035328, 387066665, 191913258, 337674059, 654576829, 659434937, 882076997, 172882733, 144058809, 432209540, 920321977, 880734291, 663049804, 280640122, 223307983, 477189228, 57743957, 184148008, 550592555, 655332321, 459514678, 447750874, 835825826, 195713025, 327924150, 806954875, 983552781, 955585627, 75462159, 291452025, 290376332, 137069054, 495191391, 292913784, 133618992, 673366011, 867897718, 14458914, 73544545, 174117416, 474654290, 822132777, 219237344, 56395630, 572974578, 871179828, 435778036, 833641906, 938768188, 408050350, 670048894, 190147219, 516573021, 75955534, 876212394, 451993310, 288853045, 971754122, 409299900, 316436432, 31281853, 80854520, 968680807, 391411434, 472437088, 320679758, 97711674, 907321343, 326732154, 981552670, 853563899, 85923257, 517251147, 123159103, 905735440, 197484120, 706303914, 831029485, 292621305, 930117004, 170322072, 1451031, 751647768, 827842293, 779303957, 883355738, 863950698, 270877430, 678004121, 568426440, 182022039, 66096857, 222584827, 910570598, 253920297, 592605502, 170920579, 45814838, 124226994, 140398329, 42882377, 256927901, 674316016, 719676070, 226549176, 11413944, 107540639, 290947814, 154681172, 423066585, 96694517, 475559748, 597858790, 39523571, 753315665, 432960009, 324412630, 39941460, 230910863, 625644984, 159514532, 711582166, 372861225, 243025423, 756247067, 947600046, 600495254, 510616868, 540605049, 586998267, 178145421, 556165169, 835514976, 357998798, 921659492, 595194740, 284526486, 498230054, 81887986, 734638769, 415490919, 370768014, 160930014, 551054869, 118738689, 977282961, 635958283, 139081463, 618968018, 178288673, 419344581, 175872018, 553313499, 673768710, 502102987, 743831052, 351425820, 721841848, 355656116, 877967229, 67586381, 872478608, 734120876, 213556123, 626422480, 806426276, 8533743, 65624911, 323007104, 295083069, 777262720, 561130735, 308571208, 859555744, 580233179, 224206956, 935131746, 856462359, 324836846, 489028860, 563133917, 690292593, 805508480, 48644829, 154553615, 638010934, 334023946, 310775952, 643884000, 903596127, 276398816, 415785319, 772946477, 889207549, 847574860, 912821164, 687214721, 892911747, 971530236, 458006319, 999285012, 734345478, 966931708, 32196913, 924093083, 40032900, 584028513, 512259044, 269882359, 852076481, 44159930, 241493807, 53534923, 900197608, 116736536, 229730240, 355010463, 153302907, 828080925, 344681876, 973570927, 135014198, 450232366, 994370714, 830517604, 730779447, 72758679, 977686320, 755868190, 400719737, 531829834, 835231642, 914306996, 364252675, 650669536, 226398179, 193801001, 594746679, 659612404, 78599344, 601840387, 959042846, 3593329, 164763455, 465652679, 586344829, 327547980, 168033214, 683695410, 644717243, 460290537, 412174056, 776394047, 676593592, 721088692, 352088361, 277176946, 59035524, 647973077, 127043513, 748166083, 829104130, 124556120, 117487496, 898184159, 162733398, 670755398, 952928597, 992506320, 185933914, 622468397, 726768975, 792923651, 407354109, 748366826, 800644806, 13259317, 832988454, 332683215, 67486443, 611890433, 895992806, 42756341, 287398524, 812907700, 783511747, 976194021, 270490897, 448563858, 16384316, 150083744, 88229732, 331283155, 58272910, 395169049, 661168113, 427455244, 443870314, 145795886, 241637839, 915088316, 778888339, 381375911, 821276925, 889107782, 69429915, 921664259, 21584389, 233733788, 704612078, 672369191, 302167687, 903548069, 241680092, 732217842, 847501183, 175800560, 405097782, 473402447, 268748298, 947225478, 11485582, 407885025, 155378487, 490478649, 484480737, 423734127, 645177310, 5614874, 59463219, 271107793, 437826279, 758097756, 746215433, 25182883, 679955516, 726533363, 418057249, 947260191, 936827032, 104643285, 564947833, 944820637, 673026729, 219734433, 603601681, 77859228, 694549492, 644984885, 288437332, 2630825, 161857492, 280522076, 962397920, 282710295, 810616234, 238022161, 311801009, 839549629, 916465202, 935837143, 491427845, 721997496, 114910220, 227044834, 905026533, 856223337, 662998693, 239338832, 376604275, 48928132, 409999942, 79037396, 648270923, 740942328, 197757434, 517099279, 66937382, 165722643, 340981600, 644988498, 757964940, 31182121, 166160746, 318413933, 126790419, 73517148, 947675065, 330392616, 486677776, 552707738, 369178353, 325559411, 227255557, 426598780, 79598008, 658421447, 719989849, 832898372, 991998232, 228697576, 320091020, 298070722, 309736670, 982674958, 643747743, 199700721, 426028930, 873823380, 616841419, 839525840, 252240671, 239218570, 612967749, 33086165, 186633748, 792935216, 114191137, 855715709, 54073383, 479010860, 847887282, 167394413, 760566387, 659029831, 678836208, 522807816, 413653999, 846515069, 20731046, 744854876, 887079695, 669920084, 541162093, 729661147, 543987797, 707093381, 562515484, 530241580, 940280173, 924398603, 592178729, 498747025, 77434759, 247287280, 407225108, 125977137, 226375793, 375692428, 355238728, 116875334, 138125031, 770337811, 592872960, 229668288, 207143249, 328067047, 93483923, 145703746, 194892898, 770042758, 589633516, 344032296, 651916448, 520051419, 643368480, 162620108, 229220017, 725622271, 423294919, 607072860, 389973348, 624765890, 287219607, 968113313, 275549649, 638752601, 83833629, 498945677, 929150992, 88918062, 796274246, 637146520, 656363185, 62002492, 409769165, 789503215, 610269558, 373023663, 171912114, 295789406, 585720101, 188608993, 743722589, 349157368, 251608950, 110503759, 566395441, 749243458, 24468040, 796337956, 424551392, 819773960, 51906614, 794992948, 693737022, 430599374, 960947138, 958160333, 195284029, 592252826, 404025209, 28978628, 532353705, 92051673, 17589498, 406022430, 295331916, 101545855, 746627514, 483860413, 696192671, 892677910, 644971288, 943348529, 268030503, 215791961, 702664315, 696329767, 636442178, 693780603, 811358108, 145702639, 628804316, 887904474, 28018554, 474064015, 469423011, 495654095, 595102715, 337689682, 885999955, 324912193, 490848807, 338402429, 612603894, 295959891, 321629190, 414224610, 484124926, 122026768, 470011174, 643504441, 571739250, 638083871, 93385071, 74363955, 839211711, 349201206, 324891197, 473950778, 672197561, 869943020, 165209594, 944135966, 894506104, 577748886, 962629671, 469724352, 532721182, 525334372, 639015202, 310740986, 756080540, 703390087, 205255663, 229079749, 104470601, 547485253, 47092430, 210297865, 810317993, 851470973, 281052350, 51790877, 57288198, 542258594, 145007480, 412635563, 739348492, 480984922, 24993312, 352368606, 207272281, 265226849, 349885097, 916680719, 346433846, 271365567, 627740781, 480155433, 200892994, 555121210, 379628605, 500308860, 459101155, 801364750, 806817172, 928046396, 963668979, 837469462, 171580551, 359178515, 841493430, 174146620, 307255480, 696000907, 933890120, 353864035, 554375827, 336576450, 992055115, 557539596, 596911209, 750241259, 877071220, 108272835, 615695197, 761056628, 778622376, 395949167, 864082239, 313657380, 953595264, 505846582, 13432831, 379843509, 113183095, 26274154, 90056193, 885490865, 816094269, 649225544, 621445084, 129340007, 513264101, 26060418, 448153470, 436790701, 791402053, 436831108, 638304686, 360063654, 293130869, 626846666, 809271853, 177242942, 589169206, 57802368, 770326836, 232324722, 78006417, 546066793, 538656419, 179156844, 725003957, 210716559, 707489757, 550685148, 625065163, 798789356, 808385706, 784756305, 188565571, 892042656, 565092306, 53136525, 881686314, 30427062, 811735117, 108738575, 188278110, 738501707, 463946400, 850822605, 423195889, 261744295, 86729515, 251776316, 1476700, 57593647, 636696605, 546524875, 27047499, 720356409, 212087146, 923676985, 835518567, 446592452, 287885011, 847428139, 545974766, 342262176, 557119689, 720604557, 359559450, 491212785, 181925919, 431545865, 217250169, 227058321, 107582155, 292975769, 115081730, 675266800, 771992595, 340695168, 4571430, 628150709, 358317095, 829515425, 170052032, 939727438, 722403037, 769623847, 204464121, 544555392, 669854412, 994835790, 434218090, 810848954, 847343525, 994345975, 627718764, 976263102, 665542642, 882363533, 257631331, 83810873, 952009911, 264682472, 346300476, 239173095, 655900044, 95025082, 489721917, 327987912, 272752433, 969336669, 198814581, 280957965, 612010436, 382696924, 612953474, 55769811, 489587760, 49890806, 63175779, 497051549, 362479590, 49500275, 639783825, 322234134, 964491970, 838981261, 335918080, 3049553, 90439112, 369800296, 350540106, 53042905, 252465284, 215550432, 410267679, 26804611, 304243864, 212804762, 31491545, 884518773, 206424418, 116351655, 414447643, 26784291, 779267608, 546929528, 890717919, 949590142, 601585143, 335157813, 572328552, 710654198, 783192292, 677879400, 181293267, 408197390, 214268964, 915120990, 24437114, 994148373, 648423533, 651088501, 200851469, 246332794, 688318717, 732592513, 347025967, 795603875, 396831528, 413514542, 789562055, 367867572, 764231259, 843564887, 149314158, 424723477, 103946826, 609697033, 970277978, 651523993, 584122484, 746759651, 140585654, 610389669, 385761215, 6816276, 990874898, 317968933, 4300163, 993660975, 420220970, 339996748, 680936970, 976462920, 318245685, 863611434, 346394132, 868325616, 876951122, 700509864, 729802347, 256442269, 445867223, 330909457, 774495126, 809545999, 196739552, 58636696, 347831760, 449609426, 642752726, 182870380, 503196977, 366086209, 612263548, 636585107, 104478681, 406703421, 265892892, 545955391, 773405840, 344114510, 249223533, 652869507, 714568227, 29548069, 374599324, 907401917, 872390550, 636035012, 639521042, 309292200, 965735296, 297648331, 935902293, 812860617, 400828478, 857969447, 200187156, 362818649, 804370575, 379686695, 24325680, 422843978, 106230185, 702456353, 786507593, 127375121, 786796965, 582864695, 414896579, 387085119, 212789607, 985957380, 21811430, 536685967, 186326108, 87599311, 744919198, 664327528, 364516699, 947549106, 725874350, 340543415, 310038303, 350268706, 647328031, 590026275, 734978871, 616625415, 282451690, 87242078, 820695614, 66249954, 251188338, 899511248, 439506457, 809002333, 675676403, 98773780, 221955881, 821644928, 869704863, 199764320, 59090726, 354073375, 251073441, 324727590, 747798506, 446019795, 96366819, 580892467, 72283387, 809536546, 142792452, 23063445, 205308577, 361745710, 124583837, 838826915, 373965923, 833283341, 103174692, 685341827, 643235569, 183934113, 858340764, 263006362, 690667906, 93318394, 504727090, 479247616, 745960932, 322066757, 201900100, 656211252, 618132798, 26984289, 101130706, 845257592, 817423157, 22642397, 233911651, 493337831, 514954956, 423176889, 234112003, 978597216, 648106405, 613894491, 213521853, 357625992, 213407606, 326015936, 578176873, 822360723, 29101865, 508238509, 199795038, 374071251, 104880182, 220221565, 645537045, 19338948, 654863953, 649055226, 859526981, 59752839, 944419755, 826540483, 859959596, 175067963, 555349538, 93397922, 365111928, 139138283, 221288289, 19509823, 591255377, 150285675, 459268987, 53618970, 189319722, 238074825, 401920241, 411059330, 248301442, 851720795, 605229376, 892624985, 320253725, 958272538, 108478551, 894424464, 938096034, 991799076, 284599132, 665386127, 552082748, 362600338, 976339152, 791297660, 725624404, 700087112, 603878181, 271581949, 512095655, 220470568, 253787676, 796269055, 755028543, 338140418, 747596480, 863880296, 943201355, 918061271, 79053128, 338881953, 9081365, 11288933, 213135352, 697147634, 134808322, 783965535, 359345895, 668077426, 803443816, 450340836, 161247429, 825742210, 506798694, 127936740, 365843319, 520758918, 111231319, 387271471, 523767808, 630935701, 584065657, 336774332, 711839397, 425899687, 465335455, 809618613, 856710290, 262620597, 107370020, 919899960, 451111013, 561001351, 32318571, 115846721, 636422643, 771585669, 91614779, 53189063, 990390442, 325352811, 472546845, 451670257, 239352956, 899108669, 299915465, 841165349, 250692287, 456668930, 612483531, 117447918, 355553164, 752999524, 246822276, 943353160, 47883680, 29550445, 761110392, 767017225, 914023061, 497307864, 631915439, 378182874, 989392710, 826951470, 302813039, 416635059, 486737377, 176462286, 775208669, 347224390, 885521652, 894369452, 826953821, 204829552, 414302159, 350741366, 318675315, 879093110, 329158064, 828839817, 825000262, 157648617, 731061109, 283159342, 74515075, 159201577, 399645390, 859472894, 362233241, 357255939, 208011746, 992326065, 389319851, 74455506, 143157336, 847866410, 464039829, 590305087, 769077384, 566004365, 197817404, 49667255, 363483343, 883090186, 836703876, 875644927, 788724457, 325214736, 594693127, 958596513, 195357870, 321453787, 730176888, 382555283, 506876378, 458945136, 526744585, 398311317, 441195891, 613804006, 419083439, 736327674, 658463933, 5633086, 97118524, 446769171, 445586549, 749607371, 46491280, 815018369, 602032616, 780432502, 889328059, 365181401, 333819662, 97887074, 588502803, 882799226, 994805247, 623139999, 18887330, 654823028, 265933125, 855193598, 15529935, 857278321, 890238930, 2211453, 627997816, 400293473, 568016872, 274704439, 68259449, 653209318, 426292959, 604046609, 541701664, 76649200, 122529380, 610818132, 576431272, 842052783, 210587903, 39615934, 195133333, 579085203, 113464331, 287995784, 865650145, 384464326, 613972442, 374532436, 272227285, 199013954, 344109365, 288150074, 492777376, 665766287, 312029956, 329880495, 402464948, 232834912, 488477323, 726379989, 424518919, 582775104, 689515607, 621387736, 546586505, 51449919, 487121293, 524931594, 116978778, 376668309, 86093936, 178621492, 100899089, 86888327, 382364018, 348792781, 202202168, 193059820, 330811292, 899214312, 187418097, 261142950, 933235950, 830926532, 526476853, 607071966, 834430659, 774096530, 833643020, 908847992, 506477803, 530479497, 551860801, 933646262, 919731471, 277726924, 423506136, 949354009, 302337558, 941144680, 526088782, 736571885, 163882493, 608456314, 623724135, 262489509, 46537034, 751123661, 714699609, 480313820, 480165022, 656834560, 972208853, 93977586, 140078264, 982184042, 136362190, 279210853, 66380676, 43599452, 906836065, 864645313, 561467839, 298228927, 451695698, 796878249, 533277586, 283679018, 198293550, 579937395, 832247153, 314436145, 745965929, 926979422, 828604683, 745110878, 595126806, 395345738, 760784274, 535752614, 227754074, 624854533, 998043424, 214348214, 575537348, 742409631, 929983220, 645594268, 168945797, 733310260, 999875050, 573879437, 524325796, 495049013, 389185392, 266943510, 531430334, 806159228, 270891412, 528881370, 252888708, 557167706, 854765721, 741916282, 853940592, 944229020, 655939417, 988348132, 516283167, 536476930, 398372919, 668683561, 453125958, 594047740, 340770898, 843865097, 865147722, 551607995, 119944440, 928420640, 876788069, 435683758, 576878743, 10462514, 783182946, 921927987, 257402070, 688573402, 300786675, 866764579, 990863808, 760873133, 476312504, 557423240, 437398113, 536064652, 631668914, 173998625, 169017583, 192582323, 701443609, 188417260, 472086368, 306801146, 186577692, 689787528, 773083813, 264427360, 598786886, 884536244, 288544343, 158744152, 145559446, 821120847, 340032588, 177474826, 896841866, 707478261, 956324675, 453953335, 860971386, 161150820, 22911003, 603431639, 840870628, 285462255, 695397145, 519356478, 745148402, 316374780, 34500997, 580164695, 792532503, 310838113, 254944989, 618074788, 570457721, 844704717, 759102768, 942142823, 562386241, 474830030, 960364846, 154692015, 569276462, 664103654, 443304004, 897685732, 682258696, 668387643, 713256899, 763204567, 71115229, 7213068, 654370875, 733166965, 347400182, 968136389, 566121767, 654016069, 663592356, 317119817, 197197978, 735392655, 890560168, 145524099, 931403758, 945848294, 356582002, 812911737, 242741590, 221002186, 406259175, 301572002, 109757381, 689807517, 255527424, 312912606, 281699109, 751182063, 377284844, 134515739, 18666806, 541261426, 945266428, 258816166, 270882952, 529638692, 462675800, 474557723, 692996398, 995542515, 388623380, 654047332, 201812463, 305225261, 517561675, 849260915, 376990725, 916939753, 942904646, 620807047, 502572473, 543738333, 600301356, 518610968, 677796078, 674994425, 709406320, 414878354, 242518799, 638214957, 629995597, 967806692, 751072064, 862141043, 62535368, 496802197, 654691817, 514360716, 987057274, 529733831, 857728253, 624501902, 512646422, 762655724, 126530142, 405594466, 24608412, 686532447, 999637558, 535136506, 993932355, 359863206, 401562335, 97354001, 70127689, 925344515, 375449756, 562958155, 809119620, 523652620, 10601431, 511037241, 98279126, 382927356, 455525071, 521840141, 129699738, 712794374, 324162837, 344209813, 18426786, 37272926, 466814875, 412962603, 62989020, 67339265, 153653277, 833448077, 599661078, 695243029, 399875064, 216277408, 469054495, 230969145, 721162904, 1632023, 302055744, 127735354, 830739298, 323052937, 767936878, 828396673, 606731519, 156032932, 76729851, 529794149, 775862821, 496585677, 108762847, 430433844, 928825752, 119897268, 196459274, 729353908, 948014486, 912632056, 891045239, 417340153, 375219130, 364654577, 834522376, 907579761, 842191780, 237192210, 769837047, 748044303, 766608343, 433715069, 996314049, 251544301, 988673609, 202076849, 837304172, 408329160, 224665171, 86370235, 687246211, 562362123, 284717347, 658176759, 435712690, 548271244, 723236726, 844916274, 397040420, 736281957, 882649858, 69838106, 257853912, 26449098, 875521300, 78911375, 212888899, 860058849, 684994309, 912519492, 698141324, 699511065, 663688739, 638699032, 644088894, 561144309, 538883126, 444637533, 573678613, 780745947, 561714860, 386280551, 654718379, 848767583, 658585617, 909966016, 570635179, 674765762, 922629753, 653746470, 768942574, 588097820, 620924827, 756988819, 316604572, 448318074, 329043964, 967887450, 901264944, 964092753, 478918993, 572251209, 841787440, 518649722, 466232644, 577900293, 53287648, 327789205, 712512244, 866694218, 34906200, 127173555, 650256332, 628850204, 711503396, 159349969, 211399306, 984577743, 960206552, 542659546, 714748279, 612596517, 810006895, 212746894, 259052267, 40123914, 242185201, 339001309, 222369090, 834656066, 583003782, 585006072, 136588829, 46750646, 127640092, 215998045, 154363517, 862652611, 717993634, 358042110, 658545108, 705763907, 96293871, 303464049, 74077771, 706438795, 842172990, 467188500, 255279388, 230027553, 166330715, 874737558, 934948426, 600382171, 329320114, 783823181, 809446958, 213856580, 46425793, 630285539, 979916109, 158248514, 977329075, 937703705, 695222667, 916842092, 278288211, 106921477, 337161531, 211114768, 690118794, 422319317, 481001106, 790498656, 116198171, 226095580, 718998131, 344260487, 505281505, 711404659, 192081921, 875992270, 163162754, 853402514, 895954564, 267026867, 680028050, 283566021, 862055172, 267708724, 944188127, 153847435, 428940182, 226849216, 164519634, 657038017, 295906429, 675006941, 797319203, 585728514, 249265901, 981698857, 682959936, 157553022, 33448524, 233862289, 555417076, 248255717, 409689794, 640730346, 563725998, 509490886, 634342765, 715622188, 295793632, 507569267, 878718442, 915106893, 777646124, 259927599, 214175861, 108409662, 534996264, 934230592, 321512747, 264541297, 143601708, 427620548, 849091917, 654014744, 883879304, 125879069, 531816815, 199888696, 621927786, 534419185, 769659899, 506219293, 681892880, 508429200, 444921379, 27655085, 355821095, 18443445, 664336474, 269653739, 998576801, 706100131, 317406953, 993081647, 98186393, 301136272, 330229587, 690805002, 373484147, 709585198, 25071891, 611274099, 401039619, 731155963, 501833731, 881241491, 569113281, 644964605, 914500991, 660176555, 868513974, 533480233, 928178084, 469908490, 760695401, 996692376, 875316291, 137806082, 394487762, 238350401, 303875954, 392351625, 664332381, 223470415, 212683354, 94207701, 311732941, 898328600, 217607037, 275711302, 540430686, 541215032, 428258966, 931571524, 169143644, 260980594, 943158186, 36436097, 120522238, 576571200, 230244450, 977600690, 245945106, 408987293, 50849287, 628882463, 561710948, 128119738, 764016086, 295988697, 923683925, 723441488, 810206014, 243099984, 294925377, 260394529, 256007138, 429523957, 45164716, 831581603, 811116764, 767905686, 272842009, 583770718, 376688831, 176847554, 921567955, 992850863, 607157447, 301527057, 843740211, 459574927, 451719134, 477465206, 584258544, 223671821, 164569055, 394574241, 953715739, 40840227, 510136511, 351822209, 650709998, 567513660, 881630854, 66958846, 580568440, 351643460, 2099925, 648438021, 48322692, 788162427, 310043681, 334245154, 219534041, 734981263, 523700396, 76075684, 429370726, 404808006, 954816440, 15731953, 839329545, 941469543, 112732353, 960092836, 44191065, 489039790, 489986909, 673696658, 361112995, 83847255, 364733466, 894151709, 597770862, 222124532, 281981457, 802159731, 906958894, 433381510, 711308859, 845243298, 39953120, 763736837, 318989595, 676867411, 815311150, 716495258, 606506464, 950103600, 171050626, 145110590, 456709425, 441232135, 904219448, 68752491, 213781355, 471956578, 607797669, 776335771, 957152920, 590817187, 167986493, 513498403, 41728980, 213389439, 726850715, 410522034, 443920041, 920936789, 129744258, 948288781, 261396922, 635887681, 348907669, 336285731, 409907623, 345474550, 3328200, 647466856, 3405175, 774581220, 534281775, 228316053, 4277200, 548194845, 257996715, 633301746, 317558208, 937726815, 967125705, 371533327, 793322228, 660127797, 395676001, 115139502, 34121656, 125196206, 963593604, 899521848, 121349475, 627798519, 828233481, 922783698, 253614824, 1399298, 211589680, 672379005, 389427320, 546329663, 325368348, 71930994, 689837699, 78081434, 697573654, 98687642, 613299491, 80765, 898989444, 785096225, 481496534, 77023232, 732831625, 759755941, 477196835, 877380048, 635608718, 862857266, 941568303, 808149499, 647295484, 402059303, 812582093, 625739890, 188503984, 938150679, 872550892, 676283364, 759479791, 926559881, 339858017, 684651326, 159207433, 275938050, 480643844, 247774189, 668777575, 975223347, 635884255, 105273987, 835898508, 93187971, 655379640, 558513782, 886270197, 539758705, 852007039, 260911558, 230352600, 565961989, 446564535, 7084830, 654888808, 300162985, 690374724, 3280115, 572680241, 277300791, 573874920, 738328538, 602700555, 568152660, 316479593, 502250378, 192109818, 443693427, 350247134, 886552074, 376574603, 173126423, 394505777, 826584361, 153144424, 264776787, 621476235, 512454377, 3738976, 796436970, 118206086, 645377536, 999918455, 459693886, 528716796, 604645404, 203296476, 993094576, 133124985, 726783690, 415528556, 595507650, 966559974, 389304098, 819316573, 362451410, 818716739, 681326665, 462236656, 911893248, 160490517, 292987790, 623216348, 691524985, 21282196, 235700793, 728332948, 35574266, 618965399, 361770139, 232263810, 875044449, 37239105, 130338016, 742368068, 679587176, 930161847, 523959443, 768337693, 708865905, 249054073, 921472587, 272700100, 871895963, 762862963, 110941213, 298250714, 341775298, 651521343, 210532584, 588576505, 314370522, 970077230, 500793136, 792331347, 248382699, 550666258, 923304774, 716874477, 334882335, 505598672, 771838256, 76710630, 359140795, 238443165, 997277970, 495625016, 558969856, 780675354, 914326854, 837936789, 304522113, 459364168, 698059202, 379209966, 565189139, 125977475, 137881655, 252726569, 458614942, 378076602, 538776931, 735037545, 342830234, 123312590, 777895380, 118497027, 195743061, 831039823, 702993485, 455540683, 401151396, 313721505, 433112671, 304928121, 718632749, 848310209, 965677393, 900456869, 369774775, 60678706, 538326045, 271443035, 226437671, 795103013, 233632074, 972448850, 633088865, 889329193, 82316274, 445336957, 563612400, 6125396, 703265543, 281175531, 349980359, 189096690, 844968034, 856910016, 794241778, 29484886, 143158321, 501075354, 7593763, 637741162, 127639540, 33479831, 924942728, 575132802, 457321009, 997531224, 818682401, 364469911, 242777803, 529874430, 196858582, 510807603, 902833081, 952209372, 693003218, 675577097, 906770537, 287775036, 100080705, 409976650, 436012202, 262427339, 330448916, 908381761, 371841564, 2993233, 904530352, 631976794, 648679439, 113099499, 134989150, 499182890, 518418177, 617313033, 684211293, 243540669, 31061982, 453998280, 146309182, 335487050, 2435793, 74808891, 459797696, 575280952, 8431804, 238028934, 689970467, 332412037, 126413059, 246384521, 465021681, 238149443, 63334026, 412946045, 774184314, 706034535, 506044032, 71510490, 414319573, 57686554, 149576807, 985627493, 994231763, 246527305, 470812988, 421850623, 372112556, 196514504, 998276032, 689628312, 85107620, 959040471, 707317447, 36066606, 962470937, 96108377, 280797382, 989074134, 481814049, 38881716, 866572730, 246604663, 683112771, 94794718, 912630219, 622981719, 64030758, 755678918, 626759532, 984531147, 148484154, 607461880, 582093347, 915258144, 463617203, 620033451, 144763228, 517164274, 597997610, 286002728, 131194508, 806020914, 134977511, 331594722, 234530879, 685140102, 599581550, 13921044, 786099302, 939115889, 713845223, 615439314, 3056149, 524743327, 308006006, 79585517, 756251991, 488681577, 520432809, 742501695, 840603525, 607457126, 9032869, 736181676, 576372310, 430834993, 511055207, 890082076, 538322835, 641968612, 157906813, 59785723, 618597577, 314499223, 276903565, 960190646, 187770211, 28830928, 296188716, 870328814, 699189064, 18529220, 77135781, 539387204, 293293081, 2875092, 776142305, 973250512, 404912103, 323232984, 912343031, 824860048, 898073763, 53422853, 162973704, 604976211, 98516591, 466546908, 279903736, 796349595, 21298746, 800488063, 667929277, 180840061, 64362928, 239592858, 805329116, 283860344, 261185299, 903495407, 992625764, 845922289, 277733255, 365162077, 493042932, 625476587, 401777150, 519159229, 951960319, 315089823, 781842776, 835292561, 159572455, 539149920, 639245933, 630777700, 463612003, 63938110, 878786456, 428806237, 86905547, 451933259, 429984010, 702450340, 206838074, 799273837, 866397174, 718791201, 4915113, 766460382, 909762215, 517302875, 330628979, 270416584, 478453085, 921684272, 818532182, 479583298, 549919042, 699672828, 232205802, 408378424, 67831850, 881224621, 777306304, 927162801, 149829690, 145503039, 407025343, 878488463, 855403693, 765747957, 46150642, 197488955, 288739236, 731409886, 692096972, 89204612, 769719261, 991719914, 25749662, 217857567, 416524186, 175795123, 242853201, 506897447, 600329853, 366103718, 17014783, 186816695, 472198647, 425157877, 519261838, 215527010, 764403876, 685628150, 338518515, 706276134, 735569729, 325749341, 623606790, 970033856, 382555381, 848831845, 184326136, 690021367, 885321738, 364886568, 284670940, 800698591, 640430016, 566938260, 764390867, 816248013, 40968170, 246072912, 619745477, 223854093, 290632013, 809211290, 411699931, 263295209, 488329079, 917850834, 485923725, 945872920, 591837066, 22547031, 691463762, 256441290, 44656969, 566962176, 337721091, 693439058, 588412704, 287860921, 776057357, 240827689, 685597643, 457719875, 476093981, 815397454, 295233221, 941408753, 240009493, 450604370, 796671468, 794808899, 158026604, 334191051, 513834291, 424271963, 146311528, 545741302, 579162521, 376536502, 585551551, 678935125, 490608095, 466077767, 927550697, 997431098, 615221715, 807344459, 58361137, 593373778, 154032980, 601241283, 120972216, 189661983, 63858069, 656570511, 917651634, 109291252, 543855481, 357884059, 536396091, 243687589, 747029967, 492063370, 280079132, 538429140, 365892863, 14403812, 226316938, 846408075, 487067058, 105598577, 543216064, 845163479, 514352744, 137448745, 560262548, 382979051, 645103558, 104245062, 525821603, 743374528, 792542945, 447852133, 966836286, 406391512, 882877381, 989219603, 299895144, 787063983, 850905583, 654137485, 760733999, 560554464, 615637094, 412491017, 179063782, 544590607, 915660732, 763524090, 999511179, 664697336, 477086527, 402446789, 177786045, 787940835, 389223953, 132206251, 871396326, 377037303, 618218881, 668234500, 439475724, 438332976, 415447526, 981069919, 24402087, 269909356, 215680609, 894901367, 633243881, 407204689, 364008807, 430491776, 346962438, 75124771, 811001002, 265377858, 20940786, 763066637, 423198392, 887426825, 211589123, 426048370, 979151899, 419113581, 69206632, 26173175, 745923897, 546978520, 427885185, 833800397, 332392546, 79881653, 963306976, 938370157, 899455254, 666681265, 315916808, 717239328, 795670567, 784581478, 251627912, 149485371, 31910059, 252154834, 61676837, 296634727, 511375217, 85558601, 335849395, 441885368, 453651735, 561888434, 625187030, 86168157, 843627210, 102541378, 740367093, 828862430, 932250448, 239495599, 278312818, 893435643, 362363171, 353308789, 465565002, 408404815, 508116653, 506344231, 284097463, 500777521, 523045343, 895428988, 216749801, 634097340, 728013421, 351822484, 375488245, 788791444, 94911838, 19902915, 242703957, 644819820, 566185958, 61047058, 822992889, 9136737, 534436174, 987325993, 988916051, 313549544, 830558297, 508304174, 868124120, 213487446, 222226422, 667952758, 95883881, 351753730, 94835942, 838458382, 659310101, 137219962, 955250478, 9576734, 299388096, 812943497, 692054546, 78165867, 626122957, 20688893, 537174623, 899935250, 349463895, 145504564, 395743026, 865947393, 709806632, 618940221, 819348618, 356330626, 122915690, 749159412, 320945124, 702387107, 762060274, 219797378, 407377716, 295281312, 984470369, 307238025, 277690646, 144224830, 186113345, 675771532, 835698419, 894508084, 789177391, 485280408, 752623614, 446750101, 42860691, 635911469, 115547760, 796986032, 516459729, 327599453, 641144935, 75492418, 273964807, 698339921, 733487540, 912635855, 727972703, 462358715, 161547640, 520896244, 8418238, 378686640, 356752525, 442147857, 968105711, 246264628, 212321836, 40891109, 403411945, 457884666, 592782564, 268199217, 861347332, 223498206, 284397032, 514685424, 246007011, 436464434, 972781063, 252140190, 425642602, 956583234, 376387467, 724827368, 865111695, 115384420, 167913621, 364600870, 346361317, 712931738, 216285265, 511613, 268553346, 964878058, 722478395, 120683360, 821399004, 244943549, 352161526, 766263121, 148169791, 773880182, 410956167, 773944690, 918279606, 963164468, 439351651, 684455348, 460140208, 582049229, 74760309, 852674465, 573105431, 245886563, 934524039, 613694327, 733890786, 36787384, 408613227, 408349855, 157011727, 58721458, 774747498, 751474232, 64646363, 634052576, 635686915, 36483430, 888049810, 157879795, 218327633, 658331081, 166632761, 716064956, 904434217, 621227225, 900974141, 367396236, 530553486, 447818712, 866808420, 166869100, 695022309, 512145020, 52352069, 581129903, 299432397, 65363292, 504599574, 331842634, 997387629, 420895985, 621333871, 661022172, 240947838, 583595693, 656842493, 672790934, 989893484, 832444634, 86038748, 412277577, 929755265, 330468340, 276765025, 835010400, 87334612, 225918093, 591371137, 941442634, 457386019, 413025727, 984554457, 480521965, 576126120, 863101757, 270117858, 293320930, 218204946, 319425860, 973113332, 930024697, 18565143, 468725365, 102742868, 236576857, 907911596, 923496842, 200724543, 18630475, 158751099, 436347374, 131375975, 665812896, 751540660, 452542433, 629511012, 899320906, 559986185, 930813292, 992182, 342758609, 952885314, 494407464, 434186396, 46859264, 399569829, 31319588, 970662516, 162038533, 566788228, 143956926, 686269392, 507526985, 649926691, 794230107, 905590608, 79314254, 478847844, 147374876, 594044089, 313420940, 490375907, 122625810, 687586557, 217483090, 191989653, 97872295, 993387293, 303538947, 497629708, 758366284, 246255223, 689114182, 808533983, 543798758, 533995896, 546496962, 804674711, 936742701, 319804962, 956743692, 708620183, 399561292, 390994660, 268280849, 614396211, 765387437, 410192669, 376602510, 100606307, 752372472, 619328085, 153601265, 417606157, 469480691, 530031075, 673636403, 998765304, 715189483, 519167963, 3959054, 241703719, 15289739, 827428805, 545530883, 586310643, 880883353, 917076185, 514729777, 271448640, 491875933, 907160251, 524230719, 24631461, 59744862, 927446042, 351475903, 57012369, 191962211, 630174134, 440514130, 10942444, 28573082, 974508531, 448555948, 781459024, 786850159, 974295193, 89281692, 804327188, 106169885, 2697786, 60489891, 476297934, 344960206, 783200836, 970093073, 347171713, 583800522, 369670550, 730792331, 35730712, 843893941, 363162406, 70036414, 413064180, 617484722, 689677497, 418542287, 324158230, 262750494, 203765504, 62407311, 285407525, 70653120, 153084069, 240920515, 305254279, 361516058, 308431672, 84960603, 503022600, 874828308, 686073915, 716067632, 103529715, 321966232, 203181187, 541851541, 38136604, 916292602, 996240183, 660950382, 851658258, 173059937, 453659384, 565339848, 502369250, 489999513, 125907048, 961823567, 741525394, 629442362, 545794190, 928158202, 332478674, 290595052, 135585210, 324432901, 418975250, 163834915, 604191012, 268515786, 120361356, 46361996, 382878605, 394530649, 286153823, 225686185, 6974515, 411631386, 710190757, 234634553, 3578674, 113568739, 328502827, 362688750, 900530138, 265503995, 947157843, 617491137, 411319299, 365158191, 720536020, 157328043, 762946233, 71168746, 251917234, 112753155, 885442518, 857209561, 159290153, 645987770, 119205545, 834746252, 454781612, 541976282, 45198622, 278640465, 532790019, 286536169, 715626008, 956160150, 133082629, 342350966, 328424009, 724660319, 540738107, 75511546, 426434919, 4616282, 726216691, 623508685, 284641868, 582866436, 104807735, 276026323, 307271523, 553573411, 916523250, 399400399, 523383765, 120920849, 204765808, 302865388, 412321297, 808022098, 69912337, 970179132, 368545782, 98298089, 417497207, 89943269, 460948487, 335980559, 395470028, 857443593, 829828413, 522656466, 768757787, 296678285, 228236779, 441407772, 840414215, 769788583, 85295889, 214091876, 806186517, 241792405, 666443908, 881804590, 558974847, 51576902, 486985445, 86815410, 244821965, 599593373, 896629548, 204175843, 684326175, 609269841, 547626372, 602328326, 298492867, 400308438, 968740924, 457264357, 597461301, 450217442, 494156373, 615903533, 860141396, 432952491, 823561012, 17599375, 529927993, 719407207, 157038180, 105510245, 596122492, 715828559, 7155489, 649290198, 659446127, 945905639, 59341927, 659441768, 990820565, 273214932, 893562181, 476361487, 432880931, 732201014, 828738194, 190046645, 941418874, 731374869, 730775339, 484332142, 832595926, 224570913, 34461462, 160579035, 165490529, 425419801, 614096317, 993943129, 960238103, 39180413, 293244647, 54701670, 565405201, 319081755, 614401163, 110777614, 904907761, 155926133, 317261056, 614553702, 905937360, 18066981, 129708316, 178817062, 442933505, 37702290, 178828850, 479718548, 978836256, 420690651, 286595784, 178239280, 493958858, 223246166, 956710315, 998725887, 760713897, 762106772, 638321828, 787899946, 715059928, 338102667, 885658541, 172186755, 88281667, 397900362, 785107603, 888656691, 178971269, 797647901, 598169661, 422353018, 892452616, 588650956, 489052678, 192819298, 128049616, 166079681, 648913553, 735067695, 590489744, 265229143, 120986062, 654753653, 267222090, 93893913, 118043496, 806898245, 138594108, 231705537, 147104406, 878613595, 279991448, 15979722, 951042955, 763587463, 223458716, 416861665, 385296255, 325966280, 501115401, 243663354, 571383941, 141333035, 517209393, 246902567, 272142243, 416737282, 677859396, 385276061, 502026414, 947230934, 330392617, 994440493, 657589375, 682039898, 777384549, 39762860, 569574787, 915354445, 976584116, 230537066, 739937349, 376880344, 21447352, 84474037, 244815420, 997087581, 24285447, 23972313, 192873259, 471689639, 400378974, 237825169, 422295993, 773075416, 868598673, 980497521, 83446735, 339446729, 629669427, 763795838, 95934695, 524236496, 459539461, 132701079, 617329596, 170203435, 16888373, 773868327, 534536971, 940603742, 566832679, 33608082, 191907427, 568665844, 824980160, 948317253, 805910654, 501043017, 246567532, 111799366, 38166064, 677260144, 124753040, 50769208, 80496696, 988688820, 453749408, 894205422, 911849078, 62631672, 30881226, 387707192, 865405843, 959003492, 172203112, 896554582, 434576101, 625391923, 999789625, 987312988, 487590823, 932994406, 90942628, 512781876, 161482764, 998729653, 112908747, 452596413, 75573698, 725728221, 721284511, 918884487, 656876982, 615991073, 517237676, 623149952, 516357984, 36272997, 735854847, 914746886, 830612906, 290453609, 447026937, 710790226, 508205804, 48219345, 416252909, 86392509, 716339862, 756795048, 505420821, 236642549, 995130094, 788372590, 848470982, 155348778, 173049609, 227723827, 369943676, 998327363, 335222965, 425469664, 24187927, 170760157, 237731854, 430619698, 411550512, 893537295, 910757465, 681811097, 470583597, 818796598, 476676857, 746650750, 127962665, 522733085, 918392927, 13223697, 758943091, 455007899, 894064171, 912629115, 890326090, 996444450, 898065198, 954452038, 552119164, 385538891, 848896559, 32204645, 890934203, 296621719, 62051334, 47849556, 13015273, 534085731, 205784668, 974425181, 555846393, 214321694, 542609013, 226020090, 846463591, 456964047, 142821187, 34046320, 299032502, 480915508, 319772286, 136017242, 599913936, 244246766, 218023623, 342554719, 619573177, 50629433, 159422855, 572606792, 834864001, 320282295, 330425044, 558271653, 143389245, 490790982, 657175307, 42340789, 595111260, 884326903, 431961111, 19759239, 865119527, 953111854, 281197412, 913505433, 613022313, 781473028, 194357795, 420554249, 965268528, 773229342, 875777265, 239362664, 647479736, 853245748, 483733026, 792139242, 478893574, 376956541, 897449982, 679457144, 391272527, 226697435, 376121763, 930214275, 649082365, 214172003, 467730412, 79398863, 419092837, 320159444, 754810913, 990581983, 223885586, 981201128, 785047301, 355565713, 224031241, 93532366, 326458394, 934506470, 780303719, 511083359, 149810365, 42393183, 876086208, 162417542, 540595415, 843269405, 915218166, 672115267, 160731759, 26967764, 386991125, 206582928, 619033238, 540316174, 16747135, 13623373, 217702516, 578956351, 756885180, 389131199, 989434552, 522600153, 355999307, 862294008, 153260306, 631497478, 742815811, 173541087, 964339680, 328517325, 853151521, 117215556, 885421427, 613077597, 861471447, 658422941, 952888205, 465017217, 13031238, 315831081, 478998302, 39591923, 447701607, 456992155, 978772828, 71245935, 950109473, 28351825, 414825364, 794172799, 942923654, 893858705, 544520126, 563836610, 207479418, 647470605, 583463263, 176252467, 829362319, 885646465, 813037643, 183652643, 486138089, 451921474, 697077284, 469176264, 818516753, 304406351, 853601723, 40334749, 664544155, 867547880, 534947431, 51740331, 558401418, 998681903, 596195423, 914418182, 181265358, 758250826, 830947286, 390870438, 814947039, 449572495, 699426888, 955648142, 125380365, 235355681, 330469903, 121480563, 614567717, 150373441, 305037767, 483915721, 851111036, 721810470, 84768170, 918229376, 477735260, 56193570, 444594157, 179198006, 220499731, 729670555, 446814377, 15496699, 160571597, 847091443, 621686844, 926166898, 636903850, 342341192, 869890839, 844722621, 372371039, 780779393, 323801186, 693675185, 790740153, 424742899, 667322117, 954324, 680136069, 851334410, 864192615, 261419536, 92597505, 779537253, 77040446, 192986738, 329720605, 47874727, 846786014, 205909535, 78777682, 190891366, 126650896, 675568969, 222281421, 115428089, 70094546, 81812805, 134758506, 33522266, 830067143, 617381609, 531428042, 456666876, 475950794, 482613776, 574805824, 592719726, 41538801, 50814492, 967950162, 968365358, 666119903, 892559617, 770033452, 979365960, 101316864, 877457777, 421711513, 789826045, 42828020, 251263919, 598206500, 71518387, 86193294, 414984397, 803031, 430365452, 682172307, 881851972, 312385470, 786866851, 239179832, 131354236, 277928169, 555173781, 699663109, 760178674, 789865948, 415597716, 822220954, 293950139, 768079498, 591922973, 383991762, 191165733, 542203387, 781478175, 895378810, 739645640, 863094922, 678684222, 735934099, 783070175, 892556750, 806052217, 345480190, 17260939, 140698505, 367349427, 707570644, 854903429, 205443267, 3800546, 683833089, 755039609, 581986694, 697016415, 117333626, 140952062, 906753170, 839656234, 628716135, 820528426, 625897942, 958616928, 563491627, 525091167, 331485149, 767914534, 728237044, 501787216, 179007234, 953897356, 848175321, 315972744, 698383331, 409235940, 467617229, 486880384, 488372836, 107519838, 820259743, 980991655, 921858541, 3355930, 256453518, 331282408, 663235232, 447734667, 257288078, 814525306, 608728185, 257439617, 213167057, 722827567, 914304286, 51870360, 611559863, 757387463, 198469085, 286372171, 669597175, 51808749, 553557117, 268378746, 353264257, 544455330, 463031182, 222897279, 420459894, 331588766, 713367050, 211377521, 524354690, 150339011, 484705649, 520126105, 87700232, 553770513, 98339831, 226786543, 611737015, 765737867, 659307432, 496054385, 614272064, 737079603, 41997072, 578138159, 554254859, 700070286, 944841125, 480484611, 508862640, 411480599, 894449870, 499518892, 592894032, 475310646, 485441524, 222277166, 481847176, 182363071, 718213929, 282050970, 460475408, 76896508, 685903685, 294396921, 288195784, 168869636, 896537932, 443927812, 595563800, 729077505, 545159501, 89447973, 273004471, 82223820, 466191495, 756254584, 106114025, 165009169, 816216704, 396879782, 518323930, 752647759, 430964911, 861306877, 717733267, 260979827, 887208241, 965418211, 273341289, 91940406, 880142021, 580326054, 399105772, 856717173, 78476775, 639096339, 253847213, 564547787, 606482627, 554978998, 806927270, 78012564, 628192802, 995050154, 352740278, 232910319, 450039834, 258833797, 238812131, 756676114, 120896019, 375091824, 227569594, 435715958, 73305994, 178417433, 711577306, 256768938, 45881077, 896445924, 757014885, 189917480, 173517422, 534836580, 722143138, 213932602, 917377514, 452988714, 425066907, 54925471, 610107482, 160620157, 309769992, 6007174, 901850002, 522539751, 898584768, 109668331, 962717265, 59749884, 895278769, 392214872, 166943758, 904147121, 40831663, 177414658, 711621384, 334197402, 195284460, 901593138, 58146163, 28391912, 699682805, 821709029, 635421360, 927795092, 280475275, 712837568, 244542667, 183048282, 666072032, 335751366, 793109545, 120895967, 192036212, 264664952, 134555234, 51274419, 961102349, 710247695, 602828549, 259112858, 286949172, 888529162, 852840545, 627008798, 45485364, 770582573, 292000940, 32377715, 233041037, 833396416, 437765362, 105158076, 657687372, 882221006, 474552806, 938445095, 926459550, 935541830, 14063994, 235852777, 354180162, 511941292, 8264341, 902337101, 782643553, 422878674, 343665052, 36881942, 423170827, 887659796, 43377451, 495102736, 911365290, 586302321, 504815255, 716812933, 638230789, 216247245, 562246178, 124100932, 84536200, 16090442, 192651060, 526228843, 898966274, 912511610, 225554667, 92784977, 104448762, 500391502, 689105849, 811367599, 525027401, 334788993, 431694710, 578379324, 743068473, 960327678, 399343350, 269582615, 695819457, 456156857, 808565249, 381304486, 999491855, 913822013, 618751148, 355199682, 804012223, 446439148, 427999808, 557519523, 732673464, 31002668, 377494499, 803143870, 752274943, 835553376, 133796857, 501490563, 367788472, 549626383, 698292526, 616671020, 57331371, 866522775, 252688664, 73079821, 598010598, 935039559, 973635626, 167334978, 205390148, 416893582, 381448901, 909477861, 514781976, 926213018, 793030261, 471849287, 829274734, 6830426, 670718671, 369155178, 519021448, 15181537, 968602958, 520593986, 791350973, 653767936, 389458775, 896075347, 949701433, 408501057, 188688550, 208391063, 998943231, 370363469, 654088759, 186473784, 731593873, 957150765, 62249602, 205478239, 643762449, 287400187, 75225367, 694661878, 769926121, 7931011, 496161682, 536275344, 766515420, 985302108, 925308582, 297991551, 986945914, 580689860, 764330714, 805441069, 485877674, 170393735, 524319680, 906018676, 318661376, 946838366, 752224903, 989435563, 289371532, 398898489, 870838356, 87599701, 163844294, 758756318, 771892077, 39184761, 930507079, 836250308, 781412781, 414155517, 879479718, 52963062, 188592211, 841390817, 261433561, 612250197, 449607289, 378593611, 503704137, 714773805, 856742951, 38076769, 549568523, 24433136, 549513333, 841764937, 657960238, 135708313, 60137125, 450270140, 788012071, 560930972, 787004400, 880670414, 811020794, 274819659, 235177316, 257557555, 710160367, 386607253, 372805402, 497050060, 59798280, 808019769, 617749308, 829203192, 959210582, 776701271, 551561858, 183914007, 79861006, 716134964, 299728215, 949515576, 736442578, 567955620, 355718206, 324276721, 509862630, 414907090, 667693536, 750492336, 605139641, 930738673, 225066005, 832061703, 68670658, 483072647, 274656799, 110861781, 483483931, 423520352, 525306175, 3617466, 323515564, 14898873, 901815199, 965461156, 790216007, 301406644, 293138495, 759445817, 842555899, 256301951, 135629952, 540861235, 9901891, 638382103, 31319034, 456244327, 814282659, 649904568, 174248138, 445330339, 6606823, 424421073, 943529020, 986785176, 880094610, 266075594, 8685663, 38632818, 963156620, 112390969, 196520930, 705024554, 137654076, 122707870, 815128681, 950241017, 23617798, 801366869, 187019213, 924339888, 106562069, 301364014, 691695039, 292145803, 467870822, 550842201, 646532946, 560186847, 888514575, 215736251, 227563114, 747639433, 592782235, 610882913, 632598727, 283225389, 86351023, 437344032, 558977185, 935972160, 283235629, 793173456, 605138365, 878880702, 537664145, 770341481, 47733832, 682513920, 949021620, 66191829, 214713533, 893991132, 978241244, 701798995, 83987517, 961280541, 868186841, 177920193, 555929191, 779330927, 450062780, 232686049, 596959742, 79208002, 14757535, 462751744, 960906784, 438755040, 240781538, 655699225, 176469005, 941665601, 222757718, 587695592, 430393768, 62848155, 215192495, 174214894, 207129154, 495795751, 432116904, 842949006, 360701245, 130637653, 300484745, 382951966, 800862996, 252452096, 146433287, 163414401, 326210832, 545509255, 716446486, 645468215, 57889849, 444784573, 361621120, 684974344, 945413745, 177031223, 776695156, 924972214, 409158561, 24596275, 684862967, 895156343, 362401327, 706524705, 548806544, 427263869, 458834863, 871612741, 583683405, 177495027, 945029074, 94913250, 51895268, 607216377, 959821807, 985765135, 382848887, 522980366, 655355040, 771717856, 627965810, 256700099, 16537888, 530374178, 470735867, 623020084, 53902856, 568950030, 398878341, 283682962, 891149041, 836479770, 390664394, 714133670, 487606900, 172226739, 349215055, 875165812, 512439406, 608784943, 970522459, 554892661, 45166492, 314307751, 439942392, 423791580, 940666800, 126516949, 888694196, 741991969, 466762370, 393584109, 225734211, 81527881, 884951817, 979328692, 676159225, 786518724, 260352957, 476180116, 575444356, 514335255, 959222258, 312011651, 847670416, 422024528, 711175261, 411112581, 159915105, 580916138, 744781020, 630226595, 139402129, 122828063, 798060094, 90781603, 991260760, 408082714, 619716260, 626513240, 374912004, 639943932, 610164857, 864491768, 477734490, 227029163, 131114935, 691150575, 535142511, 992121613, 609293729, 201673921, 524436968, 907309183, 268353439, 177228182, 21794512, 190731973, 810894784, 992769272, 739036579, 389534337, 967511704, 763372910, 935012352, 64128538, 48190377, 867018058, 996380042, 420780598, 929753161, 68986622, 845206981, 394444638, 211765547, 79131930, 932777596, 478675414, 759426025, 884733619, 747276503, 426912120, 516069620, 78830699, 646480874, 24672688, 184643608, 481124433, 269694463, 32077626, 907644484, 390252575, 262091312, 73937905, 46525203, 95454906, 535705793, 662143412, 881377268, 982662398, 675891294, 710102324, 421115228, 337611961, 666348812, 658782370, 989757007, 661061898, 963598978, 992380849, 483437648, 499147303, 513117342, 264064067, 100528606, 12222382, 132403761, 439280442, 742802954, 61777822, 622855461, 372584426, 147727116, 45830519, 980801443, 526910810, 674897126, 855862864, 202744168, 10493031, 117682876, 686249241, 7079169, 853496237, 912038580, 447630545, 103524112, 692267867, 152968562, 543830855, 181050977, 211757142, 774311994, 113817448, 315902384, 940443387, 783835584, 645350335, 125547747, 747052773, 142993010, 673033657, 844437958, 787409594, 48378546, 910808092, 630134744, 113218300, 667710251, 996509871, 198532695, 445856547, 875973782, 42306348, 791012231, 404889352, 356668561, 49851057, 592958454, 676537236, 178756817, 312622085, 829348988, 603168866, 654877090, 18425729, 826747737, 754265353, 951185364, 706318471, 102788002, 343502696, 398938350, 413394823, 750310469, 45343657, 401449639, 618729621, 62351445, 844313505, 395397964, 963648077, 651995323, 838212355, 850847780, 999071869, 871989294, 572992765, 261470632, 632797985, 716621396, 744901322, 535930132, 201620911, 101951774, 702903213, 522918587, 702823119, 973911205, 634509294, 798231993, 133293751, 809566081, 157704814, 544498301, 333373231, 92723622, 779596356, 937707353, 880866598, 233728921, 562694570, 810057287, 113083873, 164088099, 143264421, 339290781, 589770107, 861136339, 758030776, 409520632, 871102261, 247847069, 573305941, 321883511, 315100525, 876785258, 740717397, 62002586, 178261364, 361744169, 167072334, 108847058, 358148752, 270768595, 808184931, 938512609, 843759802, 449236291, 919289971, 795370337, 417679458, 197715162, 138241360, 101933235, 984052744, 719363270, 792909809, 165780290, 886077458, 486436465, 876546243, 924956403, 394761858, 851249682, 807090575, 973521072, 11174078, 328566182, 403828733, 432932288, 431710249, 884496443, 546693001, 542358792, 224275405, 588680978, 90464244, 85287478, 71991940, 80222350, 561055237, 506543667, 375246969, 101343817, 183578744, 621734530, 288335469, 716668481, 38057259, 129784541, 951631837, 997143879, 959061123, 796051847, 349673827, 519850893, 487255013, 812018827, 250027359, 748273919, 145868348, 311430422, 37965045, 319918407, 183170340, 646916464, 459226382, 656807501, 915620393, 225465700, 630787960, 440004231, 786806684, 705030301, 197806032, 70788076, 457579912, 799280078, 330846114, 638035010, 924660472, 541776518, 257961657, 750123548, 129833402, 469180741, 750339922, 758653678, 257063404, 558443537, 496983318, 767625441, 432991580, 474236944, 150240799, 198718103, 197817385, 849529177, 397143458, 16882738, 197880370, 823543591, 89403997, 953685112, 601388905, 601182098, 659537392, 535396075, 751685999, 335583693, 197315686, 472399654, 571059657, 206323517, 206374223, 24002176, 753774507, 443822538, 882418544, 258135869, 328173194, 571707488, 685650102, 251646705, 652822036, 576206939, 661922189, 904725256, 292043343, 204291128, 976670096, 842340157, 291200222, 425677498, 517660168, 165986789, 587451396, 245600941, 635857758, 752784930, 744893399, 351273336, 296056002, 904292182, 462569412, 987074589, 73683088, 767818219, 893690658, 606969296, 503490423, 842389148, 426933629, 67110827, 85649744, 199203408, 304017697, 10237790, 976233517, 42315581, 776902407, 770922679, 173572947, 585320719, 72444716, 505389556, 488264740, 926372382, 407754262, 388065142, 157527537, 558833258, 212612289, 691424655, 9685933, 52158997, 633535740, 938767558, 667478627, 184645243, 879040778, 630151381, 928552979, 932056479, 420309219, 859747306, 318244352, 186259527, 296881442, 851718548, 647936877, 193348484, 459219850, 228153444, 966312639, 497165300, 896644231, 311823762, 963546765, 143186218, 992846370, 378428503, 421881945, 174172642, 628890499, 793055267, 312849373, 708865812, 391435264, 917729439, 749970452, 481945070, 591073126, 775686251, 418763299, 765436259, 136951135, 547038812, 746455081, 542311913, 520571978, 269289429, 859118737, 140981392, 869786499, 191918239, 255591316, 706147053, 482824952, 124422990, 783745646, 875740214, 953379459, 340585243, 220658798, 102646316, 436587005, 247681674, 48484193, 949686010, 131497075, 332111544, 185253036, 339425941, 728434345, 571827032, 664209333, 884529072, 812848625, 413866365, 586092408, 724535855, 695053701, 32947595, 427492187, 726639656, 239195781, 382674583, 397170187, 317037048, 285394649, 28582444, 154393927, 845943157, 667189694, 505186376, 152001205, 69890279, 700534095, 464122047, 132970103, 464467796, 200686423, 356022417, 687608388, 732185599, 192113935, 640469456, 46307778, 71434413, 456508991, 476217272, 262199818, 258100938, 24606521, 552281656, 667779321, 504120700, 608468467, 197773949, 535176362, 479608772, 882267847, 31488415, 543141118, 173019967, 364683757, 570823918, 225113597, 353992855, 803060273, 963166573, 703190115, 499484075, 268366685, 359268854, 753396714, 52876584, 927348410, 548917903, 392543513, 934116997, 370072870, 870300660, 422155840, 683695309, 424388172, 178019500, 289206458, 76455177, 953413903, 151115141, 348706154, 637376528, 475236070, 515932608, 218807011, 479339192, 253955050, 105195330, 603154913, 183713770, 588944977, 731527770, 670286984, 923559625, 77492802, 785020458, 509231478, 120485872, 182401120, 272232947, 871378281, 217005366, 542808669, 427741951, 360401189, 874219007, 241901547, 23859185, 310819405, 61331253, 656177843, 682584499, 142682598, 895534961, 843970673, 212037472, 693555255, 509046092, 839250486, 654124990, 630406427, 870528465, 806739311, 738511194, 477092368, 647782711, 621360480, 604768237, 274910334, 552344723, 5072231, 499865159, 984109026, 444172667, 676206831, 604301647, 527350123, 430214573, 610482340, 220636515, 550505443, 618958227, 713192165, 510024904, 344994657, 194098951, 700401204, 630887290, 914590490, 591741284, 952721192, 238813291, 314387534, 254911996, 79214472, 650204897, 847889864, 547806038, 456115762, 223821335, 202406119, 560949839, 803053119, 95571707, 399911447, 43842239, 565317566, 622096491, 695089438, 815601030, 595672301, 392268544, 716146722, 470803653, 883834020, 970847560, 701765548, 286157300, 62924619, 748525139, 103577624, 943337595, 73155459, 760843757, 513708679, 705977475, 366623856, 579043914, 200616919, 784209559, 429366696, 320469284, 192143620, 311619636, 799020161, 220053335, 196995147, 717079613, 427586579, 388575636, 208859669, 415268595, 590869920, 328211133, 29818295, 379537630, 427982953, 721932372, 451089583, 944258357, 449670675, 8802472, 462535856, 374221990, 544518804, 614939751, 664155080, 220791023, 646747963, 141730058, 600567676, 548746593, 42006939, 506928919, 388337441, 805528704, 433753194, 394583450, 26629244, 587712934, 563865967, 649227328, 563795660, 286992375, 550530692, 28451011, 901274004, 539503532, 849292216, 808264190, 138679221, 66181290, 671917361, 486995805, 752205886, 392618571, 692021192, 837119478, 860851165, 378477125, 938792542, 862795395, 801355905, 499947997, 224446091, 66286805, 756665739, 126387897, 212884619, 595415220, 576785178, 781865583, 149149915, 496972965, 457513292, 153414755, 858918106, 771554527, 419538573, 308555511, 641992757, 229520170, 619989260, 801167848, 923537064, 62456999, 805429262, 166156920, 2996241, 238660490, 402147108, 817778157, 754301442, 527076474, 830831377, 734932704, 423902497, 896820147, 99592025, 198462893, 846713152, 812178420, 139241356, 604331222, 338794956, 994147529, 617404366, 884982071, 105606778, 318049457, 674176627, 402907225, 472915616, 666916973, 115696169, 121522052, 346201588, 265420476, 241426472, 413971409, 375509601, 734351173, 698251107, 168990865, 530779350, 987373229, 846153091, 181246339, 435735688, 811139917, 954497675, 533565947, 306560157, 883675041, 403591046, 594079703, 447723377, 160233497, 699890327, 481446190, 340177737, 90051617, 104042955, 903427388, 399734068, 950080702, 397002681, 482815551, 735449742, 442518669, 804685851, 222025961, 176726922, 756802312, 53240321, 996490375, 278888697, 461820122, 941150509, 535695007, 184199036, 119026832, 617381930, 195032511, 629269426, 153911428, 810652848, 669186940, 449059710, 565078906, 63503115, 607333641, 65519100, 62520163, 891814964, 685913413, 690853830, 843473121, 227903954, 72685350, 861825444, 614094701, 279767975, 843394998, 649833079, 228462507, 121017706, 119912336, 235917690, 618164566, 67439665, 282252586, 258698732, 802348389, 33030743, 451131762, 257667573, 796526681, 82324688, 821493618, 910025481, 274484513, 783760658, 821157014, 879946706, 427556643, 306153549, 47759392, 129436233, 615242295, 388269609, 510647271, 415237161, 339943817, 714607725, 5403790, 473921077, 334491268, 889077548, 344974702, 659147233, 858948144, 220988141, 249775464, 777565725, 337626174, 574899167, 276312473, 93806878, 91766178, 888726234, 429774383, 884927249, 958938121, 841309991, 139074064, 761865438, 320014750, 289049382, 667619706, 49926729, 375921454, 673654388, 826913537, 559433004, 806631585, 207537306, 941870265, 668193961, 113905888, 511181923, 365504016, 29332193, 179733032, 689968524, 33818359, 732032382, 366769639, 440841737, 590597302, 711029776, 641907359, 400842032, 119609123, 877410219, 366472486, 830246618, 126457080, 102061641, 938917340, 577298030, 990630671, 235857330, 607068700, 523329816, 773185738, 912346756, 852868708, 626880520, 258242438, 339641582, 677501985, 616492245, 975155276, 750076618, 507379511, 727882452, 634604422, 160799383, 553760785, 187170102, 153389875, 172765314, 242365684, 103080367, 960917262, 725618540, 136782716, 306935868, 332251414, 302827560, 4534558, 599731380, 512070813, 498370165, 628168342, 780047487, 857655236, 932633002, 236247944, 375334199, 156553997, 427961739, 948384369, 690781519, 876343048, 740570290, 261355178, 279373818, 726386489, 150264219, 103475017, 605507994, 725013850, 160330044, 990045725, 285002667, 885231440, 273234191, 41226453, 798600253, 176854507, 829642569, 113344172, 828579146, 129645139, 935947574, 389423159, 613816075, 725641575, 646889249, 356863614, 379165206, 964162487, 772991295, 102696809, 83348596, 241606638, 210388072, 829761545, 436132480, 216201543, 388347211, 297034652, 386171361, 70350523, 777688829, 607571964, 693073127, 85965889, 999706772, 175782562, 359112370, 229532332, 735872523, 784025234, 967205006, 844390165, 426559001, 671283170, 12556703, 971898846, 261302708, 662132944, 465308733, 970721821, 880284676, 177954132, 955699292, 397936773, 692351474, 844663115, 662969474, 485324703, 708373230, 152037471, 417568351, 311562436, 418736167, 646330711, 624931158, 174508782, 751386573, 992294204, 32952294, 476510762, 631071515, 301909226, 162293674, 447679893, 89187280, 286486730, 743712692, 492707928, 673605204, 631966861, 531999259, 229362730, 129274509, 967869309, 109336746, 426951290, 308759016, 918220516, 886049562, 642630626, 606432014, 981716920, 475748692, 812953939, 440652169, 846148060, 479598670, 137167102, 862420932, 228343608, 905810535, 33945182, 29445612, 988773226, 124888137, 944000876, 908020561, 475646924, 919103029, 153527250, 712325776, 514620425, 56512204, 169752547, 515000856, 337176629, 917358580, 782430354, 506382267, 985688172, 266225068, 135274447, 474138818, 318635774, 527702092, 753878886, 497118316, 790981254, 856316321, 715127204, 243401468, 439797950, 774130813, 58807987, 445075727, 253345427, 962833228, 788947732, 859866028, 659618817, 973963885, 941852995, 253924284, 111356119, 506584661, 133781686, 977883746, 609409996, 217337620, 15851274, 838212745, 935170426, 539815132, 571883823, 48322423, 231490064, 402695197, 336135665, 365023505, 893483072, 320104217, 35182744, 37458171, 65053925, 218779454, 607804935, 93952143, 219582073, 873502930, 784989166, 328744560, 6205386, 668962822, 870244124, 908379624, 424809034, 706968776, 711820257, 954809493, 637057553, 879389526, 467574501, 843444928, 575788170, 698363325, 538204942, 938436212, 11976087, 907584229, 905416357, 526113975, 341147043, 469172221, 195494350, 922522072, 515773557, 930190105, 934808202, 927113914, 772530198, 465422090, 279076776, 665643551, 384601289, 434862352, 357607828, 793915336, 574493776, 922723623, 198214099, 246041536, 710748361, 79015603, 49485032, 825069684, 504870388, 567309366, 687355213, 914537538, 142564239, 44249321, 718758238, 892605190, 478721229, 434772407, 379838174, 302902597, 913462671, 433537235, 792380351, 371467913, 857463587, 847013545, 730519600, 409906301, 694948870, 456102678, 370654650, 682494653, 789667529, 837137505, 47739666, 552751410, 569634310, 560626162, 149605477, 973234220, 147296732, 459483329, 735640021, 288530144, 752954645, 364664456, 880109840, 658787517, 159947055, 841126934, 795135335, 24939459, 374747370, 53132679, 919320475, 145105089, 730188285, 281851290, 133658085, 158239624, 395277620, 304814744, 753250845, 184935586, 153256123, 724572479, 290022686, 23078244, 946851486, 469742398, 499880909, 981339354, 327805000, 652554592, 356193727, 859016057, 61840734, 768407729, 561904805, 788865026, 226989488, 388635589, 353446729, 78290734, 73959268, 827087172, 679400782, 697421671, 206161038, 530950509, 111878419, 780343086, 9401845, 876798512, 298197704, 751574568, 312827502, 605792728, 728544474, 452972411, 735067677, 27809658, 908703755, 957416164, 456250770, 870056156, 221394430, 169537189, 138164745, 382800667, 98731449, 863423187, 331122026, 911360499, 378888971, 112087501, 931297153, 73858829, 591682848, 936703850, 571153770, 307632926, 866931411, 675253548, 785654430, 105570264, 601897938, 295342893, 277254187, 253861857, 825936179, 955263670, 863444231, 12571252, 517584217, 922762502, 171163720, 519208521, 934298448, 392893482, 859792948, 791314479, 2324107, 425485280, 573027761, 793180981, 699339825, 197704285, 114064034, 882761520, 525188987, 352258399, 158591921, 228223744, 577727842, 497444636, 799917260, 441665280, 384163823, 616538328, 714985455, 606302457, 257523249, 207376543, 728981296, 866240522, 985477881, 429098309, 350421686, 24010149, 723930411, 320259348, 406539069, 472932965, 382231923, 116812682, 284521223, 291869729, 134697644, 276439368, 898610094, 194470465, 522279580, 388612777, 833342687, 461123050, 713766610, 356357286, 666853884, 146054534, 690711667, 726069790, 163566060, 359279748, 521333801, 987127921, 163516327, 816443479, 611069314, 835224770, 202559099, 13802093, 845225036, 761416117, 519420361, 768359526, 456400279, 871116785, 701482091, 61038050, 440033230, 644995589, 152672101, 527104927, 453373572, 868641804, 159175001, 478346239, 928308397, 726577447, 595954195, 488684548, 499735113, 257036062, 696849821, 841399275, 796094269, 371078262, 200339798, 39035855, 991218947, 286915617, 270073602, 265738012, 944318782, 593490283, 27962583, 138443278, 447633219, 571308086, 983897444, 947307235, 185124736, 694727686, 808734406, 764577151, 171514099, 297681165, 601010684, 374185819, 243756247, 532895680, 628338818, 288692972, 335581945, 547315962, 427685919, 733713837, 79372441, 747567966, 537249669, 819332669, 463162192, 85348741, 133032751, 973678012, 152544867, 896016500, 893948763, 933343979, 725291732, 516201750, 323711994, 4955764, 715569801, 742067799, 905556224, 45075824, 282584140, 65258721, 10821258, 441093980, 92338026, 611171698, 684934465, 471407231, 656313587, 990167632, 748876024, 353382160, 440277781, 964869659, 384660957, 261846480, 763852824, 271197915, 300104924, 644736159, 506999404, 292838219, 961780596, 654345329, 704309011, 520850047, 661086541, 892443638, 515797075, 621833933, 588550793, 54434134, 235229589, 20452239, 843698190, 382595353, 68803072, 302331110, 482059101, 856602208, 912449090, 782836868, 717915070, 876163, 546737205, 969161625, 941089739, 978052532, 788410283, 21637417, 238832062, 799665806, 789692577, 261882831, 808041826, 595679052, 783778842, 452690765, 302590529, 772683109, 272994777, 324617638, 584442710, 178322849, 916503917, 436462436, 880331045, 222286886, 854165314, 902841519, 542848999, 712588454, 687723278, 542254198, 411562833, 241493298, 954062139, 608770946, 506542822, 645763541, 729455441, 627476190, 385977377, 985329603, 128767485, 190689089, 343800938, 963013049, 398551470, 526633738, 993384415, 641341434, 757778102, 25424711, 263562699, 109914044, 547734031, 312181506, 632714500, 244077900, 224954441, 549086300, 42803437, 276505836, 919073149, 427077491, 637392197, 623330204, 82491643, 568625578, 215993018, 93161856, 163660074, 178832488, 124087955, 642078082, 997408906, 384000579, 631662498, 333599272, 23186278, 9146450, 510692715, 568326071, 610055998, 776362615, 438844177, 914729695, 5579212, 155140044, 674993697, 296196648, 162296212, 135585782, 771136084, 905039604, 27250355, 10902330, 57501528, 689240616, 580448567, 183798520, 584155994, 763830496, 918063969, 415436914, 860123327, 4037531, 438019975, 620710857, 517393953, 935310691, 936350458, 652933810, 108166201, 254717021, 838766651, 578110211, 297122264, 161513933, 142068016, 813118274, 175328604, 236880202, 177838176, 838473253, 867641450, 434988297, 178194957, 711345205, 849864501, 376796250, 334502636, 65760746, 192154802, 364665139, 18281603, 440637375, 522543044, 28333790, 119203428, 694252338, 941092310, 598319854, 10745261, 281789358, 603329421, 261353889, 385147876, 660182898, 532904332, 708844732, 331937461, 734907547, 155614260, 26965500, 81416529, 702286142, 53097958, 434314221, 309996497, 403730290, 33611546, 262870855, 739870499, 578971574, 379966093, 929443081, 999303963, 602668536, 787234850, 75306367, 936064135, 977197769, 688496845, 195256983, 477542351, 417079871, 377274369, 577742029, 177404513, 980327634, 583677071, 517056576, 640631518, 708879489, 805535680, 62894695, 595664511, 332571737, 812388404, 779658741, 942064486, 335893628, 167197329, 358479894, 491007543, 612890661, 779679952, 689904636, 253336999, 278620343, 371248251, 789888057, 149049342, 912304668, 631848248, 751602437, 273356057, 563164676, 711330911, 968382210, 201161873, 823282905, 877999884, 355340529, 272037407, 705670101, 753401301, 619249959, 169713387, 354500180, 502261125, 828818069, 127957696, 356290682, 598682980, 289808365, 86836967, 737227251, 489364928, 402516509, 482667885, 27247025, 299364406, 232686476, 353990562, 560169800, 661198913, 485710145, 343717403, 746713295, 908408637, 576013552, 246980795, 558385699, 96650865, 470613989, 848850021, 529660384, 652740924, 882066171, 227805158, 784099461, 725325670, 579542137, 663899280, 19989021, 516443020, 533274478, 679360672, 612206249, 938321270, 779779223, 202830049, 890713030, 466780607, 59045285, 174181504, 417579350, 306813352, 332892802, 996020366, 997409112, 97136920, 919173956, 107404537, 244154386, 878150105, 279007526, 236061846, 906587212, 789798941, 642466144, 149849458, 643110359, 79453605, 32484311, 840717495, 171946073, 913153448, 615861679, 541677868, 955147237, 695453787, 247788629, 654621383, 684095846, 666908694, 863771718, 730329282, 396811286, 732726019, 724198053, 929353732, 850798639, 582666304, 998456410, 841578171, 695631877, 520195833, 490898042, 472610759, 808377280, 375998947, 884012641, 99754886, 451617520, 118229153, 145697836, 397620199, 351293222, 383430910, 848033608, 42648166, 105573834, 986671983, 447479418, 501872849, 545090887, 744467435, 616184657, 558987255, 882315864, 319858016, 705622429, 541828974, 175441691, 424211646, 517736727, 301637700, 103063174, 847424044, 273788175, 905504751, 545919758, 578212973, 549941108, 826902534, 797082592, 99461489, 855480423, 878817983, 306095917, 819900440, 584827789, 724406483, 202536633, 868182991, 299426620, 479363599, 267451955, 513026284, 732436566, 41702584, 397384173, 794933583, 746860671, 772837952, 258059398, 500306772, 972570470, 629604993, 578820131, 849870064, 281734709, 634880960, 807145677, 667604919, 79466003, 188577198, 888052060, 349561531, 382827997, 196624888, 535816530, 638357181, 554926955, 106556471, 222277358, 747327164, 405325440, 22201634, 421677514, 391400292, 619558344, 330555734, 577023864, 64194471, 703650259, 677716371, 131765253, 281669338, 124867831, 414344706, 369038508, 603210693, 165471764, 357685849, 991888913, 511522954, 382258712, 643530117, 27113254, 640665893, 295801566, 382467765, 766234858, 530400395, 165709546, 89532349, 564924291, 6244531, 790752453, 883923231, 496870526, 316651458, 612924929, 788248302, 966351751, 323400513, 911478210, 569092655, 943879308, 422203714, 965523746, 562984424, 64022586, 806190705, 167496758, 641805918, 191764120, 295850998, 375417589, 809207166, 975411321, 375831846, 158385880, 987281039, 550957028, 593983760, 805398028, 39828354, 132308789, 818953620, 246552239, 365293586, 304977690, 844723195, 24991068, 123169971, 512153742, 469442084, 625537010, 243830985, 579082318, 353164745, 305293231, 627043652, 730121496, 442351250, 52870137, 238325162, 762372626, 598122954, 314344798, 159357364, 610825037, 455649989, 199640835, 580817601, 613661415, 754476177, 936752510, 109748067, 653115716, 712255458, 401863929, 640516390, 664852079, 401302699, 254879859, 315908518, 279849270, 112849837, 953629181, 995921890, 220350355, 549745687, 427174515, 907809848, 20919751, 111232368, 276049483, 481628247, 357664604, 586618352, 232879139, 237347783, 567933790, 213482734, 555080147, 473242178, 657828545, 370108160, 269452828, 860964504, 510731579, 643413980, 625358220, 574859101, 363078768, 103512628, 816503444, 599387487, 774433068, 767168299, 920746951, 415520927, 340801084, 820009054, 743778893, 288321944, 741104433, 203429562, 690390373, 357767917, 382025003, 832632768, 832466060, 550533818, 794618693, 607152667, 130682746, 944415824, 473084480, 580884539, 153551990, 566800058, 190993674, 480529763, 619221763, 109524653, 723282101, 22936687, 20462711, 595445807, 883342438, 284958572, 401924811, 414775488, 588064839, 557690363, 65322563, 848430476, 172272590, 615519974, 524496378, 768499263, 345888790, 155648476, 202614185, 566449064, 73984069, 21337723, 225372443, 828662486, 82036917, 715953250, 902452421, 99003514, 207539752, 29686005, 586158854, 398755500, 551822239, 246818291, 413785141, 92594693, 94815105, 703404793, 770710501, 108204816, 321819180, 915025673, 549339806, 447557876, 691203951, 298179857, 267334611, 280167880, 442528720, 734913948, 611020569, 200461785, 57147134, 138272981, 192983449, 61724384, 131418270, 721246983, 166256437, 602942736, 789661974, 856055504, 993889285, 32943987, 38870262, 889783590, 675882966, 186126058, 147392348, 267077975, 162847064, 451272139, 347767396, 674363424, 6561597, 487788186, 863080357, 776253077, 320940847, 406959622, 977166986, 962793811, 761803083, 558621740, 390311319, 665108584, 839874035, 395475552, 982250578, 449222169, 245474248, 888772349, 317351668, 712597707, 391040573, 532191613, 542430254, 108020254, 236575508, 352573974, 412429020, 761860104, 765472973, 31680253, 656728313, 728796173, 431308889, 393938417, 481593201, 87613488, 938855903, 968748621, 919118133, 450291598, 666874298, 305595859, 403915275, 414246186, 407731775, 858108781, 87948805, 724866802, 486734095, 439327007, 480352316, 234598758, 538357265, 602781913, 438408161, 649404278, 693105091, 230529754, 233390615, 954418926, 60657938, 99032537, 380244989, 786706427, 276414103, 641838071, 449884631, 173088613, 822506735, 853710559, 428092076, 347803147, 823991279, 765585931, 323141307, 989116973, 543175492, 34269431, 527565142, 362203788, 775863907, 815000041, 752575968, 150027644, 521604403, 664575867, 153380163, 697285986, 453674017, 230576213, 1181919, 380124291, 175003433, 658105446, 839760262, 303754046, 328263577, 208327180, 968613495, 3519562, 129139485, 629147239, 88805630, 157913059, 293098095, 92022106, 760846725, 668078469, 319045230, 6669585, 743015403, 154683625, 674288556, 348453602, 986828487, 961732412, 367219468, 996543718, 103758602, 304513366, 136051729, 186177115, 163413509, 586537839, 225994947, 599064389, 89439754, 793296950, 692184861, 235611153, 266496256, 224762201, 556601693, 482947678, 947915775, 555939991, 157633548, 765118763, 82831052, 865267165, 546073611, 825221959, 303947129, 733751585, 859320546, 310021265, 49036059, 697259756, 889918958, 386530732, 419010310, 405377320, 921083875, 724093996, 664122095, 440211938, 496103772, 160272802, 383005149, 545216551, 656152483, 341765248, 456592703, 803534566, 558626205, 247698093, 139054892, 222491365, 59943983, 310424314, 892943384, 446931163, 216894848, 408033008, 694313587, 60829767, 452291139, 644544335, 123964878, 29123779, 668630747, 702083790, 595684217, 804488833, 195320448, 643271785, 370416330, 56613113, 73544884, 715752792, 318118026, 718162549, 449997356, 636794699, 931221080, 812527150, 339549486, 931155348, 429196402, 213435547, 267552028, 856183034, 675091611, 303823105, 12310835, 500614708, 573374278, 531426335, 386541988, 152968393, 827257032, 216032747, 869439813, 140966325, 243224305, 939310904, 45251479, 785252086, 882372071, 883417183, 381177940, 688392972, 543638110, 132979153, 786585900, 708763701, 550948086, 624516180, 424267958, 305036542, 817893120, 629894705, 152578382, 982451184, 19082850, 604653613, 357978737, 837021256, 694995689, 480638298, 695433963, 96717917, 749491387, 397508095, 790904007, 969217436, 964081954, 276903491, 459828375, 875153999, 465360195, 841117767, 682834924, 80167580, 791010863, 439412786, 53207135, 584557075, 320961177, 199570703, 417365984, 268137477, 955591191, 843585161, 28755312, 364078606, 341342576, 333972191, 330757611, 495371071, 917804256, 813833033, 571319981, 709023241, 903020404, 815931441, 133898134, 481814853, 286964017, 259281113, 15371922, 17655491, 544707247, 625212523, 343134107, 445448816, 202042404, 953365011, 829658741, 487289511, 454231530, 757080686, 803954153, 240051944, 600189350, 631455473, 545993733, 497602211, 723605378, 306687726, 811251489, 48476437, 972922801, 457106779, 710628144, 709155984, 576162853, 344024790, 816376890, 196429546, 650450533, 790567063, 609123122, 140479732, 487008302, 369417524, 410474233, 11813284, 338146957, 203188630, 88102837, 170677347, 775550018, 464573727, 90153625, 541346175, 396924120, 299508089, 527710787, 791032897, 268564730, 42565954, 426977014, 336755137, 403212182, 685513930, 860705604, 850541170, 346493308, 449478059, 110951442, 136671989, 743900574, 344735236, 732703913, 136341356, 260215485, 998541286, 66049556, 76863135, 621931343, 985266622, 310981433, 252356189, 87419649, 412550387, 827098746, 344850697, 496390241, 369977236, 451804701, 800828418, 146286550, 787903606, 425723941, 574942637, 276837778, 342477284, 54756520, 664519710, 976015346, 482419563, 303072745, 550977753, 904426405, 85264193, 612955089, 407665082, 37748982, 61475960, 920998609, 672794839, 968810138, 792910737, 50548557, 301565461, 906655161, 128234837, 223760348, 230026089, 565798302, 754632310, 537260842, 751777667, 506880979, 600136789, 494985158, 677530979, 721576499, 35405317, 882354364, 422438968, 889433442, 347294828, 271092958, 512493351, 775370194, 78737810, 913395194, 897901175, 304137313, 660334285, 445626175, 809645137, 776420503, 736085824, 912571887, 699437957, 171929029, 671923949, 509305513, 378349236, 651277485, 122346307, 49591519, 674514626, 481954838, 666347680, 504895686, 752117684, 278636413, 769505779, 567601552, 680010508, 631200296, 973446048, 883371933, 885899834, 634569103, 176560710, 221166564, 549093171, 153813284, 364504722, 98760078, 665602446, 194151028, 525242702, 92538385, 381755011, 130991245, 778507278, 124865678, 14272788, 297724620, 304489867, 930758239, 481089049, 154931032, 733649495, 388095642, 239453848, 823842734, 10444581, 349741361, 63335399, 721524986, 838739037, 489711692, 253298657, 257176411, 641917782, 161128040, 344875658, 585148129, 670319011, 893520022, 76081745, 395731149, 339944870, 141815783, 358925659, 602137232, 507679952, 717039033, 117698351, 176692785, 605620911, 214618123, 871594292, 29550497, 436923319, 895643206, 967674489, 286252059, 948972642, 78451656, 162734352, 657456496, 381774145, 228053671, 274601057, 677924121, 339345251, 622719822, 945162065, 334975364, 693638534, 901314321, 297672549, 200281431, 723205570, 50355776, 356163487, 839915477, 490168671, 301725111, 562800612, 905966369, 704232448, 132044849, 865196055, 643432579, 702922075, 896763731, 186411651, 189733557, 616494184, 588079910, 835637604, 49607359, 867079690, 399563719, 926730595, 409191642, 62016944, 199166737, 51726493, 437552208, 561678237, 553396151, 326755083, 214644391, 241145677, 859679638, 395101672, 840272035, 5395829, 302547336, 527213488, 402371398, 947772447, 40460387, 631014116, 47273829, 376527015, 205088412, 999591195, 612492796, 96886772, 656900360, 450759419, 64659009, 745138929, 721779261, 186265385, 7844576, 158488755, 635839269, 499216146, 970953970, 180478362, 302603671, 634629607, 736887111, 165986394, 245649947, 160545025, 217631601, 953310807, 8684568, 572232893, 273648126, 989391590, 365358013, 181862891, 376076035, 266483727, 134241586, 123990104, 30983681, 179596556, 903950726, 678607216, 218442403, 704261288, 448391995, 86255317, 342155702, 738094846, 433821052, 187167301, 755669208, 76747788, 175173991, 916407634, 83540991, 490093700, 561315184, 372637720, 571337702, 795213203, 942734536, 658218630, 866202070, 419477828, 815139043, 358815032, 701061429, 344239562, 658886250, 905394596, 256692567, 523754643, 426772438, 820004502, 290500056, 301444506, 887680978, 768335275, 52468787, 697010351, 679253824, 688908625, 440122348, 319889522, 810420547, 113823091, 378128385, 596393259, 520104589, 57322075, 248931053, 284520835, 121037934, 785244534, 694617743, 911694088, 570282400, 474362624, 22709166, 230096113, 524087429, 420452243, 411633800, 334702851, 270203555, 534168447, 938004410, 907880246, 574229832, 553690840, 397582945, 531081371, 142455337, 350359642, 463641365, 70522874, 455850683, 160317199, 160954644, 691602670, 21680611, 745122717, 985110278, 471362921, 180404964, 163499070, 552221301, 544873473, 77047805, 100813730, 729635337, 530399110, 416201065, 91901151, 251742917, 84948823, 70360328, 619934206, 754484773, 125006984, 52456028, 209935159, 532292505, 956160482, 319215667, 773037368, 653017635, 487766112, 327234175, 672767315, 463331495, 888171378, 749618900, 156233392, 10537697, 366419216, 44104553, 69336931, 165236844, 352871762, 46299973, 531477339, 41417364, 775044365, 320600462, 125980965, 395192846, 850377669, 224083642, 348676404, 416603672, 372531946, 112600302, 962920248, 159467673, 834649100, 816132811, 230736193, 805050062, 27564539, 83243956, 194762129, 863932750, 450436943, 526335516, 641386226, 385057115, 236867949, 701593856, 837310229, 913838064, 441748334, 518067402, 369993532, 713134894, 455384439, 506514016, 227561447, 928439499, 747660066, 80936653, 857910292, 536118965, 372855979, 477553629, 158859614, 717036020, 612910221, 177371875, 920614988, 267855119, 904937494, 817679231, 244709354, 168288296, 388272226, 354465469, 448813267, 477006816, 274207732, 704675430, 549310363, 527084485, 989736419, 402272791, 785457031, 663755886, 727428753, 997462612, 428652370, 752489691, 749790283, 668794814, 626392404, 468315365, 477735580, 79469587, 8457964, 183635575, 191476519, 729948415, 87362202, 250262505, 236313093, 31527590, 755414697, 823387100, 409436960, 542845763, 587272099, 608270713, 526772735, 343601689, 155136791, 169618479, 116916779, 426422, 115813795, 609828936, 65047314, 681646366, 679204049, 396017727, 83920520, 639617970, 126699525, 302059639, 236274394, 393520908, 569169869, 402334979, 735408329, 174636318, 365258609, 12134705, 598436276, 254099894, 224887800, 820146868, 911966314, 89176212, 22568506, 44322479, 854077800, 418553421, 200565557, 47887077, 38167258, 993707106, 599260284, 772176880, 875475806, 784372658, 125789906, 926015584, 263241596, 662814547, 927543603, 521655845, 811487023, 221117204, 180427532, 659903398, 354777245, 753162304, 913435497, 113210286, 290747230, 273404460, 380278124, 500177934, 807648982, 436431573, 450626776, 708871174, 987763825, 110751987, 937794440, 878045771, 113722498, 899272204, 808941047, 280746994, 727777315, 112355986, 938779698, 607279688, 647531776, 292546703, 999439469, 747531740, 816751666, 501482229, 269017391, 333044675, 34562390, 478907946, 378881140, 603090272, 423964905, 96756416, 103413711, 463501695, 878746807, 972077031, 878121455, 70097295, 771555163, 778515751, 714265021, 709181122, 68932333, 372787435, 999488673, 815926121, 173613637, 325590456, 529982576, 844716595, 188643255, 729160602, 408965474, 203355813, 808010222, 125687696, 721530689, 803243417, 888503393, 760548223, 569136273, 20328868, 982368399, 682418271, 424299068, 646818202, 699893522, 526681114, 769602723, 486617880, 992631097, 313072497, 931738011, 211135186, 5746355, 334007899, 336459593, 928838298, 506138360, 186941476, 264032572, 436245078, 87901755, 938428222, 425600912, 505894359, 432286816, 899291953, 127275090, 528488766, 749136397, 398685024, 371444122, 691263398, 731718923, 319232361, 151885042, 822189268, 533107845, 570043448, 452688062, 874884006, 671046844, 869349848, 111413012, 953377055, 594145079, 782669788, 987070770, 87658612, 812401213, 612678411, 44813677, 624621652, 473825015, 280525464, 440493655, 359736933, 34254641, 602103293, 963384938, 450477231, 22173927, 731978510, 206379448, 656241647, 518134940, 609599363, 739238590, 123258423, 93171933, 394618864, 186397051, 168046789, 106955776, 810590060, 179640257, 687150097, 392957799, 945213335, 358515734, 543366776, 727244010, 96020968, 357373675, 243813900, 90829957, 490805934, 98604323, 344396328, 648898255, 241392633, 1113720, 905283694, 559844998, 272094024, 734328486, 188910214, 563835739, 337776564, 446607577, 493873526, 227864556, 871081261, 654347423, 446513361, 611383372, 459240535, 160431001, 231124459, 941308378, 67690495, 328193053, 281672013, 22206639, 957646372, 752437488, 617674345, 188070410, 940710351, 639551016, 984915811, 180188020, 313171538, 488180930, 887839533, 882228438, 562540406, 532304800, 526631259, 199396620, 888925226, 74489323, 453351465, 947411300, 788564203, 840687243, 51253137, 944182383, 323664159, 175399870, 125549825, 276196386, 544373155, 705403798, 322167113, 73082, 109252886, 719006514, 541315191, 516518781, 155873634, 443035733, 867524142, 183344163, 718253009, 240127773, 667416016, 950891200, 698492329, 666445631, 653196047, 506845481, 705054333, 465723740, 770146624, 152049796, 940243019, 110322032, 952172457, 987628161, 337310716, 2122874, 672925316, 736991198, 611116165, 745810664, 953394515, 238095528, 671319513, 129742674, 159326003, 293819073, 257185290, 684470299, 313732565, 420077798, 455520364, 483580307, 920787938, 45498430, 720216354, 143934963, 965257030, 854515136, 201754485, 319215167, 882710377, 952067054, 735997232, 51121482, 522966021, 385394847, 842815890, 516638894, 277628157, 785970042, 579547568, 800399524, 360043058, 221773747, 132955765, 164743300, 290596823, 734001533, 39487451, 597318901, 41322123, 32770386, 998173637, 828741308, 233082254, 271609464, 566269358, 290222267, 229714795, 637918410, 697028384, 976809100, 625082790, 185417212, 560443453, 338637098, 848013038, 303892301, 999044609, 335534195, 700741370, 948263319, 558955995, 815310390, 720641834, 720199038, 35192372, 553844147, 571871329, 740106835, 56279522, 155130106, 28355311, 667766615, 302110574, 607531371, 348202759, 28153049, 258040098, 597236980, 892348000, 73127641, 604235512, 36439253, 686069722, 37673850, 776902894, 228897428, 523215026, 435493636, 370958227, 678470443, 534592547, 419300099, 614230853, 145812527, 752910039, 345687844, 33945602, 845994740, 718317511, 395537594, 513277302, 131824308, 181223449, 225660100, 862532956, 779694590, 124676145, 657555548, 514377047, 740287209, 516501672, 341946560, 537495966, 78259785, 371536142, 359274132, 151062832, 768494887, 67443270, 472199249, 148937622, 543409903, 483079474, 722594099, 877237931, 220789635, 644224022, 923337533, 845377124, 287126024, 564135750, 622864905, 86901598, 518806202, 39568124, 835578564, 386263819, 863208844, 479577616, 267345079, 456977289, 373548102, 9349275, 700128232, 64867943, 840363993, 773106100, 486368129, 790973117, 166056743, 712053907, 60617201, 650720066, 80735909, 183486488, 511277826, 186743662, 500557022, 577208194, 272661751, 778560138, 253806232, 102478312, 332953516, 194226963, 366841568, 380456344, 812294104, 765258082, 119968256, 779454367, 28916191, 265876041, 684815589, 66081806, 721340536, 924815994, 155313968, 650221673, 619694263, 159848594, 328300755, 934197039, 792458056, 290622615, 58831436, 717608066, 130188335, 603710009, 731776980, 204451494, 606842610, 280810714, 567802217, 844169825, 597836602, 83004783, 950793744, 876823889, 324563832, 551375853, 779470571, 909969171, 707591803, 898997241, 33452772, 499626838, 8844973, 869890759, 779803414, 648691559, 765973682, 315643128, 221328971, 311823643, 790270835, 176204155, 553094134, 458230773, 481716477, 341419295, 933415311, 828985444, 732945258, 567677708, 877688254, 243113686, 961534503, 601017727, 250577348, 803946132, 620318594, 984107353, 979413122, 261743691, 117567182, 331338037, 977214155, 328372228, 162344702, 455285117, 6860340, 553136275, 896843127, 585823598, 670984387, 821267475, 652726919, 647888977, 633776261, 37160358, 321204169, 720173067, 537167637, 414491555, 141906925, 741113291, 780287347, 954339076, 42364810, 968897074, 345383775, 196296909, 488043309, 880366669, 651576777, 435315435, 975494115, 639521813, 647459257, 412537298, 13505783, 74802694, 514631987, 957529938, 166483659, 171457274, 982516182, 619841584, 961984203, 253058234, 55147038, 967290933, 598653393, 49249287, 714691832, 633659711, 175441846, 668740102, 391531889, 872260053, 143540086, 437242799, 759336832, 835185940, 492424387, 58838124, 34169997, 38650138, 335497990, 686027410, 340082218, 729259404, 85167036, 704677792, 715863273, 5379784, 736539120, 21837290, 500947688, 568680404, 18649062, 353165769, 743281846, 329790609, 803022825, 106323560, 939790055, 855118932, 395247380, 710215084, 671835621, 707495924, 954616224, 145382418, 309782559, 380021233, 570022296, 740358204, 832340771, 579888834, 142792920, 589092762, 689187508, 504758140, 300552837, 133555385, 842785059, 639107222, 837323793, 263810491, 195810803, 821647624, 426378577, 699223550, 689003199, 656249640, 929574682, 87549840, 696460103, 889202159, 775939967, 896540159, 116563655, 216835057, 162099264, 675770938, 77234716, 451158789, 563555059, 639340466, 936996486, 160390920, 198452932, 11038333, 279077222, 366041130, 93308031, 561604254, 813866084, 939061355, 673503323, 169067299, 125707721, 28174435, 399197699, 678389024, 441997489, 419945054, 882171674, 354712320, 152304180, 732244574, 200146818, 218794429, 241978804, 410513720, 228877864, 167640672, 187451390, 399603526, 70020303, 176513943, 367739406, 163114736, 298677807, 609378713, 22487780, 354514935, 547428836, 35613962, 454339127, 494023427, 524108015, 565770256, 15939085, 28990761, 675966, 108936604, 958223018, 851997590, 682696332, 156189253, 281446565, 201939306, 302523879, 368600640, 794114046, 10011188, 245407482, 552736200, 519434087, 320195289, 783119685, 873325425, 247461467, 289913835, 954404293, 745804436, 350678315, 463521194, 576768293, 577275038, 969797140, 385197568, 4453837, 337394214, 764253889, 495945328, 362826645, 908362492, 710787106, 654436238, 12228836, 950450515, 656446180, 122144614, 667684938, 968354333, 680755237, 509080470, 196181123, 276902870, 594732571, 984547746, 453341453, 962600924, 718494878, 109028389, 843373674, 709694653, 364692641, 336546855, 342293435, 581272676, 781212038, 77385414, 844730252, 949300304, 696328887, 794183512, 59302651, 136851735, 331528308, 480288297, 668491931, 441318910, 264391635, 375415256, 659972923, 256529279, 561805913, 682905248, 969226309, 392237220, 378596482, 601302704, 179872567, 261197532, 688886620, 196342349, 63579702, 906141476, 900401622, 132665497, 267899516, 96039340, 472080731, 749859703, 860109195, 384106975, 831311528, 307315446, 95858417, 798244728, 226045537, 943911566, 769617560, 977665238, 135579293, 828948207, 510681499, 625275971, 68127783, 940618113, 876263403, 456468793, 939988553, 593944374, 761203847, 791926862, 241901930, 271111793, 641809141, 560035831, 406965522, 682281115, 409427272, 550790902, 849628222, 959503013, 131164739, 253912116, 820154388, 145116559, 704236450, 94652228, 892822914, 734825559, 255292494, 731935773, 84624086, 363901594, 916807666, 896295469, 796983581, 188133361, 325126133, 306834182, 737051508, 349490488, 907463069, 792309590, 862097218, 547824147, 50527423, 552469419, 129186640, 432893930, 704277729, 139564637, 927343431, 775883947, 60661774, 906931062, 441855316, 546876848, 742733234, 882463833, 999218664, 390767066, 879062833, 347196037, 904571972, 202518812, 924792524, 913103774, 433216228, 231516884, 110931814, 204767186, 892020301, 758498003, 55632240, 852626194, 853208641, 39201337, 796591584, 788632600, 815499432, 981290889, 43954371, 587594948, 770181213, 235788939, 843711087, 237226942, 666737944, 94412029, 603393417, 652172729, 559300265, 207410178, 58695385, 407605841, 858452849, 798941281, 757273232, 863487460, 787288378, 659887735, 742526642, 202003257, 378793867, 85464143, 772799246, 422553219, 573341602, 479946375, 695467144, 592803960, 204900362, 357149545, 411780601, 460015373, 46177022, 810443724, 4998103, 849888747, 168690068, 807520421, 171341175, 390408419, 837402058, 96470358, 644921218, 616492482, 396748270, 460562573, 84686751, 516775039, 359195286, 437074236, 385430819, 199471215, 565683707, 890472090, 239676516, 348591199, 251220598, 59754611, 106711362, 433166386, 139950191, 685355789, 965423068, 753063559, 352431649, 357175377, 778150449, 608294897, 143969024, 870055442, 504505470, 247977459, 285118569, 639750206, 657535213, 129015953, 67320789, 748963577, 931759266, 579707749, 735872711, 256093077, 575383146, 727208984, 97087993, 266117315, 672173920, 721198879, 680053140, 784775260, 394836836, 51237261, 869519151, 534873320, 505798032, 70184179, 920885931, 138718091, 935138104, 64225916, 73657433, 17554304, 791798442, 14707325, 572153957, 441576886, 95420858, 601842546, 485861636, 843971544, 849396962, 729506776, 138700555, 831196616, 788578208, 947957916, 346652400, 993829964, 953057948, 493175676, 256190744, 688454369, 849398004, 71861147, 900422978, 849333005, 831503155, 454906122, 994345876, 992758758, 45374321, 564416840, 442153328, 745751603, 300979271, 57774193, 887695041, 766121248, 178679156, 501292817, 333625589, 658978505, 370603314, 255397765, 274270154, 368842703, 515681402, 498556003, 257347027, 668949872, 879921221, 208621658, 654651245, 649848072, 472732771, 201061534, 436739422, 301068100, 782765014, 686269160, 635093404, 857519413, 401924617, 550387690, 334378784, 525295474, 25948021, 552728773, 521777225, 934866256, 153451934, 211065657, 168820683, 394652294, 512638707, 68905478, 536143599, 877958269, 935582786, 504060141, 340358382, 555478512, 221375451, 864211794, 345730522, 385228539, 73838715, 794136318, 479570483, 160133441, 750198643, 37063576, 135719724, 513636614, 476173229, 599783681, 45660220, 974156231, 508910135, 815742270, 529643223, 332651916, 853220478, 448484874, 552250318, 334941100, 712397461, 309729375, 523068161, 850764689, 794087837, 651854732, 485082547, 214224545, 661273051, 580813188, 574042496, 993241373, 591440418, 456533555, 385100150, 874318066, 643792474, 242075776, 102660884, 797703766, 839523159, 294682614, 652844107, 232709449, 321268731, 496894840, 21991314, 318705898, 141375591, 124309995, 957825245, 424932418, 193977154, 20732419, 800736195, 128943605, 649469039, 366411072, 193727350, 408963945, 570034592, 281456521, 471974484, 224620510, 355638671, 73273236, 802723431, 925788702, 826774875, 533853327, 227555857, 961275778, 951832413, 901421971, 544099966, 540983783, 391620533, 257475744, 994543572, 61582749, 981044414, 117314833, 222362142, 75598939, 502511852, 770805727, 931285479, 724055455, 308403531, 164221563, 57855964, 437725114, 141064199, 786152392, 461216043, 728451253, 971910866, 729824082, 305917575, 767807271, 182712996, 362581653, 758162553, 650031362, 993650256, 269349581, 642299280, 380152479, 273112546, 620883381, 180406508, 394336999, 173960662, 990874306, 417589107, 932088011, 585627299, 723213559, 103335868, 522320198, 439026761, 159841539, 971261321, 427604108, 713981145, 700113156, 655705799, 402643841, 458898955, 115863006, 258098856, 387046647, 292526576, 292025798, 219485186, 502146940, 413593091, 248743336, 63381455, 57746196, 916614017, 328447741, 373035506, 503531631, 46902466, 18488179, 255826181, 630007726, 371712011, 670915511, 483391191, 16098305, 439262622, 65883633, 195950252, 389960392, 744939546, 521697715, 993543313, 618896876, 217579697, 794416823, 795043445, 576780954, 340439630, 259732044, 689064235, 613528794, 323885169, 536188469, 607648997, 752127874, 724872515, 653630031, 670933602, 30038067, 603781647, 231999045, 982139237, 827262455, 399202390, 249451210, 768358106, 252142702, 187910318, 856458271, 586308429, 501559943, 862727520, 105868172, 475099564, 413414332, 76559668, 348707716, 534257277, 932272110, 927209874, 240442031, 844689251, 588897811, 607854439, 565482524, 970439685, 14774155, 962874912, 568767320, 198285363, 830844131, 435629888, 711547957, 809562685, 33902507, 311162592, 111235200, 27029480, 50101687, 171692189, 759367125, 859710193, 269912015, 241500588, 295267549, 737764433, 598659092, 373101780, 993054350, 667068800, 288211915, 939779167, 825257091, 200140191, 710827886, 126002153, 48299132, 667572331, 771312046, 487849659, 763639019, 989099084, 192419063, 331175045, 399479298, 347860457, 780027420, 883108357, 722251242, 854085129, 926352119, 858226544, 945784468, 93640950, 21582141, 271672477, 130639094, 845434739, 896636845, 226192907, 509995429, 517116109, 30534644, 452612264, 491872459, 481750868, 154005272, 174810002, 78343286, 836965177, 717878295, 209914299, 771376396, 587363625, 19629475, 834194252, 775877013, 84703971, 757745999, 656653263, 830147872, 786385888, 742037812, 632870462, 429539192, 19721526, 792936592, 124913830, 366304124, 303652978, 39479117, 708999396, 540486612, 677023529, 139414087, 687370347, 439051260, 322198716, 795155349, 495140016, 545679751, 715844493, 898967914, 953812843, 964374146, 796754548, 223533222, 836900317, 177890438, 470904957, 22812032, 685406949, 298995309, 584235407, 662690924, 377134769, 821220798, 709110485, 861414494, 253098874, 407322935, 913995520, 945081793, 128913923, 515911708, 110929745, 85567669, 905706543, 969884808, 55650951, 406248797, 872994309, 335672315, 389289726, 548800171, 100265421, 897085779, 423942871, 17033924, 801821408, 231137169, 814621133, 606411059, 389003024, 266843536, 590861206, 645028699, 883908064, 68254637, 174725051, 549066205, 184870169, 794928408, 332263122, 835437140, 584326212, 126150821, 786069224, 18054001, 946143754, 583359531, 309909369, 148241648, 672771710, 984978423, 183139644, 220648948, 711860564, 639507861, 988168375, 655328654, 723192081, 856234001, 225657874, 416932069, 408856552, 323186070, 148611545, 190440093, 22822661, 499565480, 823445580, 20432976, 879388250, 648225967, 179300955, 115180248, 341648981, 230389453, 383723097, 584726049, 298168678, 182197077, 320184470, 399510789, 514820618, 886640983, 445934109, 721423184, 769225495, 439972079, 445793201, 938367920, 484590540, 910326390, 150788460, 529913185, 927776235, 138576642, 471264914, 501101146, 474411004, 897407936, 437252502, 377612464, 451470763, 416482801, 510185721, 428906062, 201192675, 889892421, 218565480, 509083180, 251008259, 595465945, 240348143, 492772579, 902429440, 368533515, 436082982, 10772773, 297155571, 214966812, 122506792, 945566685, 855862239, 890434028, 259219731, 3121148, 997383103, 189117447, 712572901, 757718296, 12636393, 918963182, 8991490, 520702503, 938559462, 741942020, 548695132, 740709088, 214890626, 204171199, 571831745, 445774103, 431013474, 791557538, 918672570, 538272442, 710695519, 590912697, 823036267, 939479895, 397237871, 61321892, 19273675, 584404641, 300505567, 461846287, 128898737, 227333678, 751868761, 834113785, 563607231, 607878072, 612493536, 924884692, 937603456, 293070111, 435612004, 312615589, 772083543, 893318033, 79560794, 247178381, 756710277, 814685082, 764949834, 680544175, 851179595, 308209256, 758027394, 880870878, 974184459, 866560176, 930144485, 508422105, 173435669, 947985048, 469092307, 881763363, 39938678, 494941081, 395221711, 816340373, 951157388, 912218757, 348537262, 505843153, 435818353, 652817791, 733033378, 956140759, 985451786, 667411621, 895208710, 465169766, 454400079, 978586020, 68752661, 601134189, 115979080, 499203155, 287956828, 949970329, 612155370, 440467938, 916528907, 75693095, 878078798, 368129265, 636648356, 655755239, 122393776, 715642934, 477649616, 667073150, 435904554, 795806862, 548786062, 57081765, 692663819, 187205878, 32291245, 154042234, 70745720, 277786182, 129193854, 451128157, 206958992, 333316630, 372848943, 275575500, 341699386, 120751631, 704502060, 778929770, 363482856, 867070234, 103558099, 465185707, 702565980, 25323306, 851494448, 525906472, 416009705, 298848131, 588452532, 663738440, 297677459, 162757732, 89729989, 479356327, 924785, 398304201, 787625182, 842548036, 598227226, 993281678, 695789684, 710790865, 376809755, 641895152, 87585884, 487676489, 259129684, 45901412, 381051003, 235875814, 54082278, 106191202, 345207702, 823284450, 128073997, 609153669, 855169689, 26957210, 381104156, 391395786, 742083711, 551325829, 503886461, 877898800, 329225464, 582476815, 908240110, 724394706, 650067972, 193936806, 168468738, 126914850, 327283981, 694756582, 656766795, 718055685, 99163215, 853644871, 567625250, 610927461, 174038540, 4284302, 65319, 530805149, 401663605, 432355937, 71780558, 750694303, 137647437, 472577239, 58346470, 217350257, 437661780, 590472677, 319838450, 305641879, 436611477, 80111207, 486655307, 328413353, 675028849, 463213405, 389821695, 285479991, 150451804, 878222479, 133681518, 392478983, 480486156, 121858385, 495207158, 664182078, 939519108, 308067041, 13250886, 902646495, 269267823, 566665409, 628875001, 724915906, 209349110, 240257554, 984220446, 201478021, 597560921, 495654541, 577983012, 517426380, 722604550, 468856779, 574864522, 593805433, 581997475, 944918407, 851783026, 806849726, 870647730, 844626496, 532729254, 509795690, 908872837, 628915297, 947981255, 715189592, 25024446, 947271100, 147592944, 750871572, 792070665, 642664333, 461918765, 275265522, 496660941, 870170620, 830056888, 957045141, 199406422, 439810, 661449997, 946385970, 697180259, 579412060, 432265979, 157200988, 217658740, 920116793, 800963342, 544976828, 211297501, 930459883, 103855624, 903616798, 22078694, 20340421, 911670400, 818293035, 550815446, 636705791, 431370700, 185367277, 943729250, 161518389, 10772915, 445300177, 278435807, 827037228, 852177914, 675400928, 631934363, 180305796, 355172345, 740342098, 722583253, 84278726, 140351160, 291827515, 934221305, 62121420, 839099627, 57241306, 679437605, 989882225, 586487879, 863769484, 377447155, 270805843, 432530129, 286875949, 539854661, 903850367, 964154446, 132140398, 724587744, 900545538, 699244153, 389827555, 603213113, 561883833, 771620912, 959713188, 293455975, 942132154, 36209312, 759689209, 90292570, 5369608, 608787776, 402389053, 804671494, 261774931, 777244648, 161671645, 682005787, 218922866, 145595999, 632822722, 615076111, 60400606, 911602783, 635937728, 200268167, 599948160, 557236153, 636346631, 212054887, 850428787, 209859369, 285152629, 326972526, 776096752, 762318504, 543239774, 797644565, 31931619, 780171322, 314190531, 649913886, 158003871, 119289108, 57743499, 567747755, 177021052, 964664454, 15337497, 38335945, 290274962, 408221971, 401159767, 42356248, 576839203, 695251614, 283466976, 21918427, 517665424, 191087239, 262442568, 686310757, 84821890, 704278945, 206994502, 474855578, 603556078, 137422463, 439711342, 171935307, 367785377, 180118194, 615875182, 622246939, 855842587, 455100332, 548318194, 532225442, 356797278, 834057765, 295707356, 550228800, 498181386, 646336409, 305430721, 675651217, 721449310, 41832220, 237258260, 939231333, 764568827, 423837891, 909415557, 850553884, 435511584, 332879618, 738842919, 89390230, 780301793, 960497416, 82382273, 833966810, 572387150, 937779769, 148054255, 745661192, 536268224, 872681147, 911240413, 261928940, 168104360, 95545580, 277589796, 608026861, 459541118, 65499425, 932149248, 142452129, 287248164, 797279738, 264022503, 892300745, 775167820, 398179949, 862392042, 812950043, 997322129, 571576688, 238503647, 296930185, 557000198, 156390660, 48064481, 67498011, 854695491, 254333474, 223113449, 507104026, 578748604, 291433868, 248644793, 846318317, 416992242, 293259346, 931964890, 587768104, 968452454, 890431358, 244500783, 857480349, 636473480, 857487651, 240436211, 817540386, 226294936, 839009922, 387608153, 913141918, 284272695, 959573613, 701903432, 968263196, 765172834, 481013306, 18596511, 267211980, 253658514, 91770029, 306763949, 874789850, 588175056, 744980046, 947098563, 274203804, 721782303, 755168674, 847155342, 118083735, 998878592, 17845493, 842821869, 262485037, 3657268, 667005487, 190949753, 130914712, 79401350, 626630350, 987047200, 814336045, 364844008, 101713611, 211623574, 555120974, 682625425, 904095890, 814251438, 591227555, 52517350, 134973753, 949023865, 230297159, 997072075, 872605135, 168771176, 167263325, 21982170, 688778198, 498981905, 641642436, 805547581, 217994858, 564477198, 88713771, 309482707, 386631739, 720010748, 505756282, 587500386, 988549425, 366363542, 831471546, 582202991, 652710605, 182800603, 352097976, 631427435, 915687347, 779368105, 26209886, 45274527, 615977557, 158224408, 438503606, 342988222, 524649749, 752687841, 109561910, 380593793, 536911176, 504335824, 90114726, 901528492, 796006591, 992460360, 680171937, 8642927, 277686363, 941526576, 718808719, 794699082, 64104580, 127184947, 435809784, 521280119, 101978205, 165922814, 888778997, 867578948, 529543072, 730497338, 129790029, 25957923, 437972614, 594221529, 10944832, 362323070, 571978362, 347787857, 771581340, 786664295, 850667343, 597329689, 355554290, 741603187, 796593227, 334353690, 391949062, 478255934, 261182841, 238652137, 552096208, 175373804, 692125305, 849229358, 509588252, 757033312, 644027411, 253654659, 45066607, 506235806, 831303395, 720839041, 190785570, 778043328, 433579540, 996180198, 356501579, 939713884, 318771557, 252582353, 176507676, 38790592, 263518135, 797483898, 132914812, 874915547, 991778086, 686346732, 839252507, 79431229, 299513911, 958919041, 922542202, 844830532, 817556712, 94340424, 940217018, 581907938, 771757665, 771759809, 717759565, 462159149, 949197779, 484091814, 706157092, 390183738, 633076378, 183638551, 236272850, 696002465, 252781297, 498824874, 442612254, 582836756, 678863848, 723200825, 197666694, 639204822, 685775809, 645410302, 374438384, 439577407, 164093305, 531214485, 585336486, 815064550, 931466452, 6303388, 199037835, 462906037, 521473211, 756060285, 29136342, 634559377, 699369959, 60813892, 406824645, 216742186, 611547407, 890820082, 714078741, 168648991, 538167279, 529353376, 112000705, 867290946, 669604151, 862358600, 685439392, 790821035, 543169541, 921339819, 916238069, 712135248, 244840014, 997444331, 722073300, 426358056, 296912170, 163693130, 748983299, 747888429, 923248622, 357161877, 146954839, 2764540, 880829910, 937594915, 513421923, 314754196, 184695180, 705415822, 145786376, 584274722, 760437914, 914348281, 282025625, 284861532, 160559352, 154909831, 71642307, 36851642, 930960391, 468072531, 708236180, 523682292, 612834533, 397702410, 240277097, 156684868, 640072772, 289027168, 639057227, 873097294, 624990159, 854145512, 435589492, 872588194, 534252487, 828679833, 780481647, 70637590, 402613358, 929324463, 49856650, 66578754, 733548133, 812641041, 282652924, 306119943, 337693988, 967431260, 574586795, 708883222, 613270197, 154118607, 416464848, 462305853, 14455328, 64299396, 854297929, 722307974, 741382207, 557030286, 972264717, 346447029, 822797021, 335292761, 359239206, 476836151, 199307137, 802552699, 529389802, 40705378, 279909599, 637992772, 939602696, 766789648, 413518763, 305052414, 898913355, 176703396, 67986608, 757167538, 975859929, 496172257, 87069582, 692892574, 90077206, 175333088, 287035373, 914335128, 187795724, 638335285, 797479256, 278588495, 187430124, 675728537, 634055760, 768279964, 286007065, 793199096, 712218870, 315395332, 127653478, 197723401, 729233007, 908741410, 827391220, 517760150, 497837169, 522181433, 196468998, 58820522, 675527092, 642487545, 880391688, 298431012, 603061648, 395910974, 891719282, 813936204, 297246437, 663533740, 724986921, 274601706, 802085817, 145004196, 640530688, 741144904, 87395571, 636437574, 971505958, 908368542, 668592554, 852804503, 776686583, 841021708, 987291399, 187339405, 10477533, 997728565, 197281302, 390942001, 15357400, 524396887, 223847134, 763550155, 216884853, 791310388, 572841234, 195223265, 970333876, 953555200, 23661116, 548992695, 11420769, 499207930, 959785370, 701909607, 896506799, 888435592, 272073812, 337621080, 373834359, 213280551, 952036878, 259716567, 178658863, 218553987, 288578098, 529682630, 801937700, 957420350, 624220675, 284719882, 848116046, 129314313, 978095507, 992914664, 861744483, 571760665, 98501359, 864590394, 378462076, 703217121, 931584924, 969529365, 461582946, 547990610, 802057707, 435923215, 430013472, 696117132, 421398304, 386358332, 594558483, 557976187, 388999821, 36588433, 716579440, 850467310, 751006761, 857974993, 462148049, 640304510, 14806628, 511149350, 134095703, 91098208, 245729141, 571061761, 357915926, 772389283, 836004959, 886079217, 895467423, 816481391, 733914572, 737201584, 303019881, 171206635, 239531484, 277628307, 864908442, 970018667, 394712424, 487521180, 587739206, 538246304, 975026208, 971793410, 385330169, 105465470, 432680102, 665757368, 329509654, 244310653, 756378309, 423568488, 793648151, 647472026, 549693935, 239652687, 355367952, 620024835, 128834307, 327926998, 123259435, 22677623, 328799045, 174640706, 485026527, 390884909, 877592372, 492863467, 547857513, 540588022, 581591735, 834387376, 657937816, 458520168, 360537616, 391283416, 778531388, 581446206, 536338246, 977181206, 436803484, 214943570, 145652381, 766289855, 656652966, 3613295, 468108480, 419741547, 883224441, 612829924, 972081104, 347931761, 39148008, 856814869, 891561034, 869539619, 309155072, 859423504, 990231125, 621844969, 841800137, 786762325, 883479353, 813065999, 92726630, 257226324, 902615578, 348261780, 794272293, 150986987, 307064294, 10643687, 75104208, 60948843, 188394381, 859108793, 796554273, 491183521, 315962546, 896190199, 698900148, 293664036, 385428892, 462868967, 900065902, 204075442, 698550611, 173475737, 683897762, 147900133, 585781922, 469355064, 943447783, 567384662, 813627785, 78879951, 742334771, 899984358, 588155940, 920456021, 778498864, 363186127, 190272684, 703670819, 628457422, 822245606, 732431291, 315036459, 221062336, 397221611, 225287120, 66523752, 108836931, 677208159, 134256630, 881239899, 890611974, 205418486, 843493213, 491299204, 463460621, 516621405, 109499996, 88647917, 742975401, 479968985, 157918752, 755746626, 322806058, 925938266, 950492858, 138866001, 594132446, 330264088, 154014079, 139875080, 722952756, 240909420, 751837772, 512562406, 194386053, 864232815, 948407570, 818419175, 2206255, 492841276, 747703923, 41417212, 696538591, 233744548, 313378063, 348170117, 526035301, 19546255, 641301114, 447694180, 748620684, 303825886, 337182923, 220021200, 553103182, 606666420, 966991734, 871485851, 959166114, 47175392, 60813862, 394179811, 924538083, 809829539, 946472271, 800409805, 390228801, 190355306, 650490817, 640253617, 829628831, 118684483, 392589620, 916329535, 761761304, 751432509, 876414685, 900990432, 650994812, 552409789, 837758882, 281566026, 376237118, 737360456, 571852725, 653756555, 892289651, 863022151, 292696126, 509716658, 491571681, 812779464, 535811188, 449539393, 185841894, 353939136, 426396645, 64350744, 324676552, 948753710, 44454015, 179610892, 908814548, 897913796, 284242296, 317149607, 360127567, 572741500, 635260558, 10689358, 606281229, 980952456, 382101194, 10974366, 99436639, 694327764, 830097302, 921007707, 148889839, 768170911, 464195444, 409533053, 214613262, 414651219, 668372833, 948576074, 336639452, 948841293, 253533551, 744398774, 661625774, 263128538, 445732475, 699051449, 999065265, 863737064, 708285580, 727910263, 693434863, 324403711, 314960258, 874904816, 464655656, 42728788, 944554178, 935760521, 32682942, 226524216, 321534052, 219969575, 63871806, 423692101, 814392677, 832777748, 393386520, 331897039, 247381899, 911275566, 604450913, 933332327, 460048858, 415883190, 38216994, 182653754, 967368374, 382694521, 952046023, 578243781, 260989550, 59824283, 520852935, 596329913, 516516819, 458014931, 614663587, 122147473, 581912905, 953338545, 542975098, 50144972, 613098606, 11099411, 102321457, 954516357, 901440493, 386955984, 896856103, 897144933, 72367860, 233788363, 691106393, 583514274, 369587732, 360878776, 172839038, 264347251, 604888371, 923415436, 838472103, 237705395, 777880386, 316428279, 99392509, 908353262, 245224607, 539801735, 596842274, 83408729, 459643218, 7518940, 944950129, 175926323, 74152010, 81306648, 275173038, 800512710, 973241498, 265703490, 690495786, 135079119, 758281994, 249951250, 284185889, 241835586, 56401782, 109706133, 730562988, 867729337, 373759362, 607928385, 343580231, 427549760, 123308699, 35921612, 689132609, 771774015, 906968430, 32892923, 713281698, 412682059, 646782876, 841064387, 605295209, 543783500, 625369761, 205519227, 822380188, 206632568, 251012971, 745695747, 196300166, 892841365, 78773177, 985566260, 969318175, 683316655, 837068473, 791072210, 243678148, 140865842, 72660718, 881380838, 538063396, 37493481, 509851565, 20418379, 526479005, 732037785, 477430234, 527605318, 73146344, 625319593, 160562077, 741527942, 905030870, 41470686, 754526713, 559130300, 753095530, 631801599, 369037368, 520298555, 711950448, 954644154, 707617184, 358505846, 219872100, 524866216, 998245296, 718108439, 324623640, 406072672, 272238275, 842032162, 892682221, 967762635, 915257425, 718891842, 137337068, 981028853, 24852099, 518644157, 416154501, 975145192, 882970034, 762967064, 452960453, 714077274, 368515991, 92093515, 883582495, 350022345, 972127967, 897691824, 862484418, 50453860, 765972770, 776675487, 220297344, 719230475, 734906146, 466730578, 109036935, 488160229, 275997032, 510766425, 986955570, 629087520, 994511487, 465628615, 227215044, 384890636, 532943426, 887125852, 305364822, 923931376, 478140246, 642843524, 120444978, 16297668, 476969862, 699673778, 245863129, 24104075, 88520521, 604658106, 388678943, 202922461, 399924948, 557217325, 676758005, 579574710, 523624253, 681361313, 510323340, 149758874, 769648490, 826092815, 350926880, 653845897, 797882992, 86289504, 773885190, 628166051, 427387195, 922773884, 880031469, 845125135, 504637386, 935210436, 545431825, 885413394, 830118372, 707295076, 343590766, 892308268, 432359632, 307563805, 846043970, 676220080, 721974176, 922163550, 377672348, 74153659, 487575882, 208818326, 808095633, 617221221, 96566640, 662946818, 113513815, 322351567, 784207463, 26105831, 285536221, 768212505, 469063978, 965662275, 271136411, 349917103, 922504437, 446740386, 870766859, 956130225, 456780899, 243731664, 938994497, 676045953, 411520052, 829672919, 395089552, 856226046, 826369624, 574373992, 629891191, 387571669, 646489575, 715345105, 449696863, 483240107, 920528911, 611976389, 385374334, 208293094, 938905158, 891445399, 492129556, 233007161, 311429379, 909581302, 672164598, 859378737, 30992520, 546715355, 859716820, 581253696, 119594751, 383655730, 806115305, 749163130, 11762412, 900573967, 546536418, 365537555, 716526815, 687736965, 552330389, 419599286, 549545254, 813944411, 179530342, 919337293, 326991489, 470628052, 360418541, 46906385, 623808890, 26896809, 741082390, 898124611, 874694677, 655784677, 673632844, 616355535, 722182536, 396036108, 558147763, 869719621, 31478883, 302740186, 559593546, 182027168, 170526069, 321092190, 229894078, 276473519, 802462107, 457206092, 130227100, 416031942, 526334357, 254960808, 485313316, 335695413, 829228682, 624448852, 799618631, 925032177, 60571346, 691736941, 392920134, 786072370, 507077065, 55461533, 650312599, 425948203, 94203395, 458632235, 506126349, 595844681, 147750469, 883983746, 192417321, 936183015, 11332920, 28937026, 693371680, 601090828, 402763235, 898777848, 684218087, 690945025, 388328106, 304745881, 397624675, 708178649, 605686869, 347476267, 484342668, 978417341, 528680368, 704858603, 522803587, 136861028, 730925771, 716977407, 76859242, 568984343, 627528035, 779719917, 552287963, 316881380, 484533248, 695388307, 15555302, 75815421, 574623617, 551325561, 972589086, 977844304, 25512381, 147963675, 923101860, 747928698, 705434625, 370967243, 898776319, 804662616, 700012273, 321113482, 852435323, 42187589, 587657442, 98826793, 187060080, 269988812, 757757403, 580311009, 807746399, 832861236, 261299811, 792987561, 42523733, 442610343, 718900971, 205956243, 780676092, 592626476, 901578338, 81027554, 229121281, 709418994, 294482880, 891996880, 934482797, 253326983, 742269569, 935594561, 449788631, 619243419, 386424343, 905028144, 663230087, 411489300, 235136044, 175447041, 167352602, 402406855, 641401496, 110266506, 868237777, 374380092, 609676764, 16283023, 478016800, 921309087, 437653234, 102385095, 646522994, 807326463, 175007533, 400573507, 765957392, 304191435, 994055551, 843678837, 863148167, 595238244, 678189361, 442405521, 309937718, 733779000, 998566826, 325443154, 290546274, 351800101, 774087390, 56701840, 766005310, 502122825, 684003871, 167925794, 997462584, 862319921, 643190097, 184650864, 348852682, 722358725, 508969533, 371306782, 251176314, 199747211, 275778056, 995751734, 469096559, 550476241, 772986259, 437769121, 812866103, 987221926, 341575321, 200961005, 604948205, 991841651, 410016107, 522037193, 622921020, 82691733, 448218973, 568154646, 535655485, 201477910, 747352525, 779012135, 374544306, 563601984, 434265525, 61735689, 789458835, 523423607, 781895212, 222630957, 256890085, 693710608, 746943260, 458450606, 7104475, 223817220, 107805963, 663199247, 525689509, 524976494, 147877708, 92465077, 958207131, 393249732, 1416629, 496214417, 181177504, 96556729, 290552216, 842370233, 863478147, 681904269, 601108165, 431562171, 5519117, 592419675, 989890395, 736617772, 867877959, 151241851, 986289192, 266826784, 36148395, 814250670, 394756585, 53449818, 995138249, 618338735, 331304244, 637390763, 936952671, 552271467, 640116009, 578693986, 227923536, 142161513, 689612688, 738676446, 696024487, 447792995, 713990924, 13806438, 60601670, 131680549, 223164240, 25713940, 323676213, 300541350, 444171989, 494685123, 190483332, 819539286, 238252572, 168689891, 880459830, 689372635, 404625365, 812368825, 979117506, 811758124, 859398688, 164365070, 389861928, 853784875, 796898239, 854579830, 533509371, 456362017, 800713813, 331839411, 717719030, 56558840, 285863843, 553731565, 979004904, 714457462, 930877526, 833378744, 495505889, 865653138, 13272610, 678854548, 347364705, 877424009, 931050427, 275661990, 690047182, 88106953, 526194343, 488936811, 797805947, 591411026, 597965948, 648950541, 556979462, 308919992, 888412384, 127708888, 637125954, 911822154, 539639875, 760589400, 458357677, 109462271, 844068139, 86866776, 54297612, 254075278, 792078178, 187023532, 958403505, 351265885, 960887716, 961815383, 827337247, 141684456, 753876605, 873585888, 166388053, 259077160, 512185560, 11938638, 736254029, 166133128, 629868718, 530102940, 689153635, 477002487, 42891996, 302446143, 982272744, 911772595, 154075448, 750827690, 212396365, 159775328, 2454068, 763020428, 932007298, 78372699, 728232895, 279123736, 576813421, 901226220, 11602560, 512406807, 147213231, 618859702, 365823558, 477212684, 732737821, 80762275, 906569449, 344181378, 573390529, 132904059, 279450880, 384399566, 718554319, 827078868, 227304824, 177132710, 463588734, 979713829, 340157849, 535558255, 150486664, 164984455, 3395298, 475568885, 248306231, 59663944, 409138700, 565697696, 769965577, 178065708, 955870692, 27894942, 366476731, 225976070, 398774301, 193838285, 791528162, 148150573, 446256430, 984457232, 932654496, 533957739, 38137750, 978182351, 307734322, 531510193, 250746182, 412707717, 608671965, 124638047, 322631625, 954539539, 934262650, 49399905, 911185361, 262920749, 433948174, 593038688, 878188370, 819385227, 496279929, 359820546, 956546224, 494126741, 447190903, 599079182, 412883483, 891914623, 401769107, 411010004, 927006123, 995286956, 41378645, 885476137, 371163054, 428991785, 412057863, 416892742, 350767077, 322638787, 528087127, 581143976, 126877073, 609473480, 774999714, 895623269, 480397105, 990217787, 497563909, 72813886, 595902425, 99262034, 229456039, 589384461, 359464137, 548842164, 610136547, 485848908, 495762370, 783721993, 353923822, 853329517, 637203351, 757279653, 515175643, 39500963, 252765689, 247350251, 774243607, 453635659, 173558481, 906611118, 189779266, 244170175, 903438997, 665468415, 309708433, 299764295, 230902444, 646284372, 489346961, 617541621, 32218204, 253759425, 831664282, 944727796, 644135637, 508241705, 881108255, 784520693, 829934582, 461295661, 719486209, 207580084, 941352409, 40192920, 197720789, 530166516, 494339006, 640347142, 990099578, 140045112, 523119355, 882074266, 506004997, 530755404, 637303647, 431269197, 16598680, 927604905, 682114665, 684548890, 926455738, 940778855, 239174570, 518140533, 110526819, 608095728, 926108359, 892804989, 301022839, 393718292, 504625674, 394841498, 725708767, 39236550, 662165057, 574098391, 55533945, 819736167, 90749025, 126787050, 850189677, 637793204, 709608182, 514868605, 562571109, 25876680, 607987635, 76489297, 457297535, 65507381, 588688177, 927502450, 763370785, 378627173, 347453029, 322506925, 441033073, 548601236, 526159561, 329875814, 938441351, 321443306, 233384475, 680473255, 282117650, 648589980, 377834744, 116910022, 736926184, 310767695, 344876368, 692028004, 344807812, 144090870, 68316903, 439710770, 222486070, 683772093, 956263338, 205514668, 611553088, 815443796, 69769466, 95334349, 826946166, 402123977, 433392333, 826788194, 208666973, 302093695, 119456512, 585697877, 762095028, 958474411, 299167241, 440572058, 441693526, 544396024, 736891231, 405601517, 768857615, 906804296, 561898145, 968569469, 71735971, 871192656, 900316907, 129354411, 290044413, 919114788, 409569160, 832488277, 16243068, 870135071, 945656804, 443763010, 622090129, 885133162, 930184758, 466711, 742178924, 355155311, 981792982, 203993215, 807962310, 982185226, 472029684, 177130366, 17828862, 686898275, 22466159, 580023089, 705824912, 604649964, 496165221, 864735406, 373851675, 696419278, 766993306, 66346755, 294675703, 939295418, 111054455, 870326716, 196252823, 591255213, 911884301, 209579714, 758549827, 410116458, 578643507, 631413008, 752897696, 525041382, 311783514, 78719976, 29350015, 247413324, 157105505, 121616058, 464340979, 770574921, 591538945, 779853362, 140552962, 647114194, 10421307, 771830956, 734580848, 869955683, 718577726, 970920367, 908017909, 749244531, 254787565, 785516483, 869782000, 217876858, 342768248, 514884430, 793006076, 349806180, 336142619, 100809288, 169429397, 941934662, 772810071, 278016435, 48508429, 987073751, 217875297, 879511970, 422462708, 617043315, 287179242, 395521836, 151002220, 509117733, 595360406, 891204632, 41332295, 143704431, 318650746, 670619632, 512410046, 23094248, 255890922, 746638491, 126033062, 123476126, 470641294, 886013843, 567137330, 955507903, 834985735, 716191832, 258902626, 262626217, 832010979, 2243511, 425695040, 531378565, 619782389, 499607317, 712012246, 6083263, 456339794, 376891969, 458783146, 952470455, 637477413, 173703427, 846812698, 983142625, 298677959, 326967322, 560559166, 910326899, 269783537, 385704149, 514451987, 445657780, 804842105, 287336949, 557184562, 117202039, 219885529, 876671859, 927638357, 500194095, 953219677, 311369633, 574091713, 424756849, 60015699, 354602625, 157943821, 835463238, 845915027, 589796262, 885248359, 484772018, 648467139, 911607773, 985624496, 973197112, 202428315, 47191163, 446307586, 103648117, 244225272, 327188093, 940213128, 207856177, 439088688, 359491807, 349788261, 404188362, 63136545, 725989994, 179774270, 509771938, 40134806, 494219249, 310076701, 79312892, 65472975, 394785235, 263099987, 380753797, 949353994, 226640830, 353834267, 578730885, 537234713, 311719879, 766100114, 934917255, 801422628, 434959512, 510140040, 406378751, 212315157, 799560904, 158878528, 834230824, 230160649, 241769388, 73316638, 766603725, 786418430, 353704448, 769490225, 630468773, 633982785, 80462235, 786080045, 148061142, 469151977, 528065927, 919048103, 993220721, 705409904, 25424922, 484307474, 492176822, 654525856, 789200723, 962965634, 130178825, 800327576, 149925717, 699186976, 892097540, 439412832, 797746613, 879489285, 585470132, 918919896, 738735928, 923944408, 434784039, 683120483, 93223567, 341919486, 908513717, 539087832, 432531058, 203463530, 696928876, 872457813, 252267263, 226741558, 792938348, 782079425, 930681637, 569590536, 766718512, 408696446, 728896059, 760291611, 751033792, 653554795, 937503895, 943682897, 548615151, 8161960, 299476511, 385534485, 168535803, 647506572, 511596008, 348491599, 821892188, 726886062, 383588626, 94104561, 379204550, 117715106, 139105367, 139815299, 165417065, 203487044, 427050382, 551214159, 934504095, 477663389, 137088323, 808507148, 201789123, 922282096, 955132108, 131387865, 911228877, 987295584, 970795525, 321315947, 185839181, 570665485, 579391667, 880808035, 30772090, 565511630, 71097709, 937361049, 380889508, 948726556, 378113336, 203372853, 606196502, 87766627, 64136744, 196188220, 485219513, 700721100, 303916775, 696140630, 967877745, 217885803, 385590897, 513324838, 611595940, 130580879, 126141384, 499038665, 458887552, 105498389, 441273910, 134046216, 512450893, 80369351, 792783164, 715879914, 75521062, 326721187, 499063091, 124693215, 851711996, 963516869, 940833866, 491500035, 115114267, 230355297, 937708978, 860098413, 181922021, 329624157, 632145055, 405574781, 797822689, 752356710, 676540973, 583070551, 471639363, 443628730, 108228476, 819138652, 541983001, 276561980, 975646534, 869281045, 647898888, 118315254, 434633540, 956678955, 411373781, 316361169, 721490592, 322543870, 281046231, 238758013, 669165787, 386312352, 72560714, 384631017, 893959998, 579854331, 391944918, 161713961, 491574239, 696922674, 990379479, 149588845, 986174012, 939732259, 771834147, 867839118, 92351103, 228590315, 382761487, 825840454, 39352643, 550989740, 990378550, 377911617, 752798451, 772227676, 451378239, 297164816, 67622849, 609524845, 415189570, 208241046, 784407103, 824264036, 13567336, 725632326, 54096151, 77454895, 562116074, 987609844, 769772137, 593206631, 677261571, 285000032, 289113020, 213168630, 926697366, 478963405, 554278309, 972438228, 909545874, 749730988, 834953916, 772076699, 725239817, 155001124, 913515988, 666212821, 438541015, 408742736, 510973239, 119066774, 281834944, 463685691, 450937321, 912950319, 123280972, 152821959, 143131780, 595876603, 219394490, 505525527, 869529552, 370429676, 417010059, 181223564, 454097834, 1181749, 967831348, 299064078, 38439121, 534561185, 865786626, 905674030, 705801195, 260743792, 994046133, 388358173, 639900453, 302810817, 309338067, 38988431, 674812505, 624474421, 922386360, 750052311, 15562223, 811706703, 624150078, 6115738, 391143290, 357787557, 101226270, 838025427, 923931389, 92540601, 774770168, 110825807, 488008137, 165271745, 906730972, 9238196, 214978712, 829021670, 306669454, 149167712, 669643844, 648623177, 854517409, 421717093, 781070531, 197009935, 549914256, 11987666, 486044954, 901495355, 251055863, 478287395, 495995906, 463305126, 436519556, 662093244, 356916088, 708797580, 821620351, 309954370, 531420873, 189861386, 319664354, 796101118, 483340852, 817270347, 825615275, 115429373, 871717873, 855487446, 749806563, 98347125, 210058968, 329545457, 670584145, 650318783, 518786085, 464411460, 534342896, 301506788, 993386215, 895219634, 84381763, 208451709, 515987326, 951793858, 11335603, 94159693, 98254455, 84905815, 368425864, 146356705, 961492254, 747722821, 932227101, 663571805, 450105334, 438076064, 735959965, 117615025, 24489988, 571262081, 519336046, 59361850, 390613000, 1882910, 531036792, 910728780, 377376450, 298670006, 497794573, 620983738, 850715160, 904396158, 755570221, 393623193, 868995967, 529858885, 852812428, 386871762, 97703564, 760193160, 205238011, 115360648, 563739870, 238072139, 956372970, 988591018, 632658759, 113544152, 547499427, 729533811, 567636600, 849957232, 937776494, 95767261, 235447577, 235029629, 704702000, 386484507, 428473261, 662775624, 29834023, 268937877, 801618494, 69172468, 450968574, 323470116, 620162726, 59844916, 327052908, 764103716, 553941549, 958484253, 641627640, 771587749, 836160167, 289347122, 168572211, 662518555, 413495957, 780421041, 69764052, 915578129, 102823551, 854438510, 169788843, 772591873, 870666093, 244608096, 855293798, 585981856, 551280641, 559699405, 284735532, 71348811, 938890047, 59610354, 995283704, 213064249, 789846436, 667879716, 322579280, 148477665, 791286309, 328376461, 244108001, 577550604, 71214374, 671116710, 851399771, 705750601, 800687485, 668855105, 702645315, 138316801, 337231539, 421765087, 2646965, 466127102, 865766472, 413132512, 467514450, 980391176, 32951064, 999690893, 351170161, 900857721, 310629013, 369769597, 811476399, 474488413, 190045893, 165994452, 394221448, 734846438, 606223571, 965171840, 243003599, 744401306, 743309790, 36021116, 12376056, 789073097, 440579836, 292925184, 616124534, 482362576, 895383694, 163727754, 475407563, 167443215, 921867217, 344656468, 792203553, 645296896, 576087708, 258869879, 381305555, 174753973, 861298413, 487219948, 525196678, 319099227, 459745584, 925563481, 729275968, 301549343, 42119433, 262266842, 978288127, 604755331, 44824632, 844347615, 245995816, 734213416, 295634549, 12317067, 168752699, 571210850, 929657084, 195630989, 158367730, 209109355, 791508975, 51235395, 893950232, 41403402, 516294371, 203219039, 207812843, 824677895, 588477071, 203873569, 92265080, 623564722, 325934241, 96204788, 846632356, 501045910, 866849521, 984006070, 210429927, 637032033, 897755540, 638545880, 120479326, 910282864, 757220955, 534625523, 82641645, 467341011, 15953981, 485647513, 288885392, 175412920, 118831417, 794981793, 81937699, 200862613, 607095656, 879536634, 449834129, 196910421, 759714087, 692602850, 120293748, 998796535, 765092879, 806127028, 124172324, 643891881, 766010945, 954796874, 880542032, 968816307, 837175636, 480060400, 749823254, 370337457, 795188430, 296426896, 929407547, 502992878, 437575596, 850757535, 899880190, 955755502, 424555596, 397724397, 928279214, 603840476, 844244327, 297637745, 401684784, 796258063, 851678668, 347395064, 91991574, 304908571, 294739154, 461067860, 135740600, 934493969, 341665493, 899843762, 296580617, 824063128, 50782262, 859738396, 473042784, 666916276, 100245787, 950414982, 4092375, 174727576, 226392212, 544121758, 44354562, 137031002, 518339167, 864063091, 664252964, 318517040, 524110696, 8787475, 232454851, 262039474, 803053371, 653792635, 108751301, 974759855, 905176849, 529953256, 26185480, 392195875, 914356270, 570892803, 499674755, 45773589, 429664955, 822121439, 319180634, 814454434, 852709549, 554979276, 724364565, 682684317, 206510099, 418666622, 139782935, 350168529, 237394471, 603520948, 124282610, 954285566, 716714831, 341893687, 281511538, 12528208, 31926458, 480664414, 793832377, 29554841, 508959902, 877751144, 115195923, 824580311, 684744586, 519928947, 356064126, 484051551, 526657871, 27499180, 656726752, 253869247, 681392072, 459581044, 78738415, 395149943, 438036986, 630066787, 13134695, 746779719, 916562541, 320200905, 676532176, 467701427, 801481432, 378352200, 125429972, 190782146, 45635975, 223317835, 598339365, 291280067, 912641901, 126299475, 777672938, 204888762, 634906639, 549850831, 731441209, 553241933, 576897442, 987044998, 718961844, 530579231, 183461319, 83610601, 137506922, 88532257, 481184701, 283821935, 915754583, 190244087, 894264950, 748945263, 475021282, 790461523, 913113197, 654124903, 340593951, 402539229, 313040498, 535192699, 390685668, 27799661, 935318347, 933281378, 374072993, 379253978, 974143790, 741014146, 72163582, 229669448, 491059726, 352412470, 389600213, 477460057, 916656810, 493084728, 924702382, 175982552, 52367001, 167667492, 618364111, 420749467, 988024247, 802619293, 275172221, 783309874, 55318712, 323717712, 271365470, 719253837, 772781559, 121676494, 100473970, 880864722, 221641192, 598618497, 93070061, 33904378, 177136413, 744364125, 914045872, 407847825, 651368825, 497748379, 183677015, 788634188, 784812891, 292271179, 922010028, 810681286, 70078394, 909947089, 672266344, 39780096, 866201642, 191872071, 204829346, 740155838, 535930014, 958829419, 316446390, 130987448, 956066885, 542295779, 434318264, 633945380, 258570927, 871891127, 842409765, 254828335, 94208419, 143724127, 829416949, 634725165, 208721346, 618603362, 420499068, 499282937, 731289124, 716903206, 689187129, 976908526, 862069307, 154110741, 195576477, 982338926, 813901982, 35031278, 967325884, 421083267, 832412096, 916169084, 516776429, 831598131, 506607552, 920820602, 759890431, 240492130, 709221415, 286713113, 992765900, 57149169, 741392988, 532151844, 739533404, 285416044, 81191760, 358147503, 326815707, 596426085, 934597597, 298511004, 882115345, 331069788, 116497791, 700101820, 126112762, 21948647, 234419168, 563602777, 575544149, 795346528, 716860266, 208500031, 426250219, 547249506, 395761876, 890354947, 427805237, 616758761, 212696523, 834249622, 791387973, 767421384, 33681131, 298249851, 98350460, 954739937, 348736210, 80558600, 830015574, 141566338, 252660872, 937189240, 11972519, 214515822, 409096220, 954469167, 382519659, 189423731, 703031976, 673019079, 497667946, 282504480, 756198246, 81533378, 200430547, 35093750, 949358692, 794644479, 581871045, 349947208, 784345353, 233015891, 620509882, 654290489, 438383717, 478927941, 91672018, 873084850, 991058414, 88513012, 728726526, 395424153, 925772615, 264460985, 894018905, 485779829, 356332947, 464679936, 677167413, 779523679, 552356164, 774324890, 491145847, 28419849, 967343731, 661187189, 130822180, 14645912, 235832443, 926042841, 871146159, 64539097, 121070718, 307437128, 208854038, 866186858, 775828942, 893993800, 394478828, 469840309, 372445458, 767819887, 452865714, 680802885, 400285326, 76024698, 608956887, 587469953, 13247872, 982282517, 983734957, 959937356, 254298331, 466956040, 656719220, 370657337, 256910500, 621508263, 261565545, 148487563, 671413117, 492784137, 780559249, 384897808, 980642223, 517318877, 859879223, 513656151, 84484185, 922555262, 38415864, 488064893, 369431357, 918375036, 906046057, 9623338, 70787840, 441804268, 474814718, 564203404, 481536431, 802008691, 817296096, 77312750, 776312237, 156914598, 860996657, 350283304, 776316228, 7655797, 421666164, 100458098, 382193582, 379257817, 916944601, 939469887, 1456959, 119123651, 296189398, 786375803, 124278456, 301272588, 284300563, 947044541, 909214766, 710653000, 876929944, 968437527, 458133016, 482556048, 695317157, 757716019, 403294629, 961274438, 742062222, 790127838, 620844609, 614866891, 238126020, 587621429, 174144108, 329949078, 358775485, 541210370, 85799900, 852338545, 688247797, 528885461, 51880910, 617169584, 401802161, 679174488, 919579318, 327408394, 294351542, 935953278, 554517614, 3813015, 220109298, 579319674, 924250750, 428175801, 469953502, 125896854, 377203211, 959541160, 248660627, 559664518, 354945015, 667780890, 860783144, 925979438, 32481023, 798663899, 475734421, 898680391, 721184810, 264528225, 153634558, 614986965, 254999663, 172316691, 211186893, 73611667, 62267308, 820204129, 254333912, 880100249, 448387919, 434117050, 81258799, 711611279, 459349219, 954628587, 160490335, 817234550, 467485646, 581825213, 551025178, 540974055, 682032438, 899158827, 755793616, 56947907, 490977998, 589352142, 299663254, 933928423, 519398543, 838064025, 615036894, 451161817, 121718389, 356481805, 453614193, 954490169, 845525137, 81616210, 58124660, 513054042, 297972839, 299779068, 643857739, 282552838, 776361796, 262089286, 712556832, 488584687, 298047869, 676764184, 401662106, 329616553, 916303764, 976502236, 701256985, 717338088, 249129581, 696611448, 490725341, 311128419, 249205775, 421180069, 239697444, 802122072, 170438607, 437608300, 648887091, 675608063, 87109158, 583422149, 826314663, 50990538, 704081742, 714074289, 544490936, 466984224, 964059456, 421784996, 801767291, 930252818, 904618401, 533444808, 946778842, 561824464, 288633719, 222152600, 77625470, 472609652, 703507670, 220379304, 751955985, 856253845, 278290546, 329189524, 738359131, 574769868, 711170443, 851031980, 622968494, 107060124, 428321183, 383008988, 108046963, 155702247, 346796923, 425477307, 289183252, 83858516, 693108327, 338049480, 291354759, 926840637, 264331806, 247638840, 709693510, 61528290, 540471482, 600411176, 496214446, 471631529, 150618031, 26146757, 395433089, 30488383, 538040980, 188490583, 172917232, 492363139, 969414849, 877376098, 805622788, 857786302, 693553811, 454721266, 380823919, 936864664, 521417436, 817099431, 83994308, 794037729, 410387509, 415538000, 547169065, 174922433, 308760987, 800584536, 715484788, 92396494, 510453197, 466914542, 380202382, 232627891, 904021216, 392914645, 459194483, 221619536, 738861080, 465484182, 112619407, 932177943, 322219343, 996493891, 149029047, 168094788, 498564786, 387572621, 348032105, 716689041, 891765006, 785176825, 401745993, 467791237, 389426836, 669393483, 228682381, 869831738, 383777623, 516564436, 836264603, 490911319, 231280676, 532242812, 842891114, 485420862, 131845466, 752412750, 787614024, 428879296, 36724281, 650798023, 565148490, 430779543, 879868241, 705929309, 91315619, 849945863, 751934185, 887813480, 716265258, 369891931, 628224108, 731981161, 833257395, 668049480, 225286335, 229852277, 504159134, 872686830, 179997452, 512157155, 571303088, 336312895, 85488452, 62761163, 224651052, 993663680, 333462247, 134513630, 420070810, 155252560, 795545157, 657606076, 13213511, 587164424, 33672720, 42869946, 844791388, 38393002, 758911534, 445172099, 598565563, 2912290, 130478161, 765412407, 414574653, 919217810, 282853719, 400330435, 173444888, 871645025, 412502995, 153207118, 820402527, 115405257, 516951070, 40576533, 935044768, 992924440, 955570919, 659635194, 11849008, 644524476, 840479909, 6038268, 284219341, 365659998, 723999039, 623435260, 934051275, 754260566, 458048291, 872221568, 182691824, 31215432, 360710029, 413634254, 438969385, 304214637, 715802403, 882881991, 820453463, 913410412, 25350690, 290064757, 132713376, 665986753, 191175479, 990421936, 231946319, 690709282, 929079010, 238473147, 750528983, 491678603, 704267208, 996904975, 624685370, 773727037, 633674410, 127670947, 865994857, 935354569, 704544619, 748902320, 725017617, 469305965, 464871577, 245007341, 456000749, 243921110, 832487779, 731858314, 157581905, 806086790, 838756906, 792625209, 77400904, 619123997, 813340287, 95319352, 423960519, 375501275, 443182424, 561434924, 34228522, 257918834, 892553726, 817853411, 96708423, 838041044, 11698767, 934554488, 845650563, 477869568, 89180757, 838104911, 244158958, 378168357, 235354327, 975840491, 678283851, 206827798, 988189475, 913256752, 950552157, 520446674, 989827337, 941804601, 501162187, 68123887, 237274303, 792495263, 986644018, 137296193, 528772966, 901320430, 533795718, 590523934, 989135365, 184630240, 437351466, 717270996, 174770060, 387816217, 349942231, 398305247, 532968406, 610687026, 988686182, 413560228, 71210722, 561118314, 662974704, 307321905, 127311873, 140973770, 566134130, 101371515, 416511692, 972201311, 760524353, 648808917, 693308196, 942424426, 72478408, 21123753, 782686820, 775560363, 248722352, 698222891, 531064041, 833843459, 202432608, 686646068, 313352558, 631312360, 574710914, 882969952, 994842893, 282199936, 106172520, 827980900, 327820874, 19967781, 36264527, 623691481, 102581101, 453289507, 531463907, 722169713, 154937370, 505638202, 525560503, 533273062, 499216283, 143071770, 217654972, 789947860, 682664276, 792103564, 156381789, 287876115, 128017152, 595747923, 959554130, 640312418, 22652120, 976513617, 202121655, 601614498, 523061688, 165711862, 817224478, 638062292, 572229812, 71015846, 423876174, 457143249, 69109302, 483064632, 595054183, 697776098, 119447587, 104386391, 748328572, 817124090, 728328891, 946005106, 137125041, 689700710, 96364325, 839161084, 926896205, 822147869, 651577009, 161074377, 802827379, 319706037, 677389112, 155934601, 667593075, 714446594, 974735563, 713450743, 33303116, 241794912, 448556485, 784530550, 897586863, 821151668, 272129833, 447172912, 191216054, 126651671, 542743614, 211815963, 501183846, 738017866, 19604937, 502514391, 746671154, 846293207, 539573967, 786709481, 98031283, 775710818, 532147472, 189007013, 386004597, 674890311, 786576701, 429484566, 618747493, 360440275, 788818393, 909359296, 469307787, 949418679, 523870989, 656431972, 193267204, 433055332, 125313434, 802587301, 105013075, 589864472, 472322030, 432673156, 156259501, 634376262, 660464319, 109407525, 832055637, 255585342, 469849644, 781099796, 528831612, 457794331, 839365918, 501586252, 561739809, 79268546, 855962619, 352092882, 63647910, 476122092, 649642751, 228185366, 556211326, 219461134, 443882777, 293768986, 148695762, 282404945, 309226261, 265109181, 695232709, 365950269, 338719101, 84039131, 755988250, 335007221, 210668458, 411433759, 213092967, 538455438, 450814803, 341712855, 980587780, 907889067, 796923249, 485558346, 35227835, 615755893, 118302509, 226354367, 186213897, 394030218, 945229255, 797256189, 654550956, 913907289, 375358587, 825723506, 704092284, 474967210, 768909475, 326029759, 446157367, 871240791, 864489768, 34315278, 180211163, 918567848, 929989364, 456240139, 56316971, 811948329, 369246725, 121365874, 85278137, 634778135, 760374233, 968129975, 544781188, 768215872, 429796919, 927263012, 55203057, 417783040, 509828398, 293092707, 342517288, 500929136, 226332345, 170784419, 643826980, 654571103, 187786923, 275543438, 169791197, 636884170, 289063239, 492547118, 899220922, 304368987, 675622977, 58799988, 188126619, 819367499, 59734258, 115014796, 82858165, 826332855, 85751819, 724009120, 420881320, 564321918, 808140645, 556952431, 239171047, 259770322, 833465155, 633253778, 336030241, 662320109, 3221065, 475042185, 78047300, 870487772, 261710372, 639332353, 919745737, 35408777, 248590095, 549833040, 74786908, 290009215, 598063670, 877208762, 967065226, 575992209, 920274723, 879041701, 952030226, 460772433, 337498185, 457083644, 411888885, 382780817, 961889391, 987974374, 315631010, 489353618, 226883540, 366820470, 846699493, 642847099, 873902104, 471123748, 632159616, 183152407, 909924598, 544166251, 451529708, 194192174, 286731241, 854787588, 539141794, 300938201, 31963038, 700969263, 273356705, 293498539, 273914358, 722435061, 160677926, 481355490, 141771775, 768025700, 954559339, 953271571, 545713471, 828589433, 6224530, 795811226, 107174785, 897200947, 972007356, 208212359, 595229114, 34492761, 363504929, 610150362, 451152663, 409452973, 776079673, 372473959, 463090321, 398836389, 470996050, 832524921, 65450700, 168283684, 996195462, 452298840, 688156795, 32709952, 24748517, 21167942, 204081425, 679429093, 26442891, 287214782, 217680231, 873016386, 279283408, 322390232, 217045560, 722924468, 293345836, 18754427, 635567199, 789908590, 782755273, 704373123, 267156844, 131929445, 165768890, 435870174, 258738243, 570830007, 257339383, 690383364, 735971309, 668440972, 115816649, 681397934, 366206109, 106801578, 623445333, 925702482, 293328393, 506745495, 491209677, 661396433, 805858221, 729411752, 18102240, 935667426, 930089544, 100030624, 848038920, 214269147, 856730420, 860330251, 822816903, 774399033, 357633447, 63030740, 336198404, 360077845, 770230567, 13039615, 584108228, 62528494, 806993130, 535125131, 201864745, 38437338, 618320769, 628108504, 993652285, 935228346, 526559135, 99911100, 25379427, 787792215, 485008731, 536503010, 928083612, 913027844, 450946625, 562601385, 139859049, 421654676, 664766461, 671932705, 749479525, 375369202, 247437255, 101119732, 684784913, 69723127, 251759726, 819661666, 25611483, 6425277, 146668902, 169987185, 879309793, 766220456, 403014922, 437003965, 122281100, 383775935, 989356566, 386255518, 276418438, 240985552, 381363670, 188596075, 163327758, 215243089, 85191265, 555625466, 91586927, 208523340, 367563964, 331606848, 472530939, 255008366, 105595008, 240642142, 601947775, 344202156, 488390593, 97868832, 88884102, 708409400, 68344890, 206635038, 466156389, 290142786, 507351260, 162567873, 233905652, 949181437, 292311991, 92887598, 565145825, 12328234, 471378983, 84903853, 990035095, 636671971, 147700491, 863951859, 44683069, 291797555, 735061603, 682305062, 198529138, 437791035, 879637384, 100275225, 835116828, 610521686, 337051893, 389319237, 216905148, 331348139, 593625243, 919748745, 153423372, 578473788, 969188920, 886294877, 679575806, 770288304, 922166788, 676176483, 605366466, 141650162, 890687550, 643980768, 249934161, 909458790, 848329724, 302426453, 716733627, 770910080, 790052318, 281435357, 110130871, 512922063, 418277726, 420074603, 885280993, 385211309, 880250525, 973086495, 529635586, 997478945, 985474178, 50937041, 441522811, 741858179, 900589521, 163984401, 520926539, 224450969, 184923152, 383431046, 144351781, 175424179, 824025172, 873700944, 943923068, 164413477, 595684285, 411361477, 409371678, 731516776, 325409897, 173863195, 889011852, 106974074, 588575108, 306246991, 525876069, 100854231, 865998021, 421694468, 589486682, 387925890, 176933632, 381882656, 333800495, 99150795, 754470068, 521862367, 853583017, 629335097, 837262794, 493695246, 168826152, 552747557, 842333923, 10955555, 621977875, 709090405, 812325633, 509950986, 539596555, 689518276, 272658047, 116421634, 629130018, 814621969, 359751612, 962766136, 508103972, 166715451, 165304653, 680508795, 341284460, 664059955, 247574615, 519948762, 42610492, 171646825, 318794210, 795663572, 830139986, 634507675, 30772993, 513979756, 362477108, 44486925, 362339998, 975333700, 946101820, 450727207, 55890732, 28136320, 793818162, 455903476, 832442513, 411216333, 907624076, 977247839, 429522831, 877326859, 900520428, 992814663, 901045807, 733442889, 388514927, 599951793, 99558161, 629085561, 334285094, 41746752, 714099738, 361175720, 729138963, 342056075, 340260008, 853589513, 673133949, 448927161, 286331285, 791175573, 475120250, 586255968, 46459802, 187327216, 855747942, 548527795, 914317231, 136901869, 574108659, 307230967, 668948977, 317611480, 478763334, 466576070, 140358558, 678890764, 124005773, 339978604, 698457441, 981535144, 538903071, 439511035, 321941716, 207975530, 974780566, 949014583, 420904868, 360699473, 203865863, 181619968, 741724082, 151397980, 589495564, 420196724, 896655233, 37788940, 853423696, 400139342, 662358314, 344501703, 19313051, 908146088, 986763147, 907157195, 794508093, 987440237, 510750177, 227968038, 54451587, 383318704, 613424395, 356868083, 798312418, 217649715, 779214564, 180715888, 459948563, 98537255, 764559883, 244937243, 796207990, 877694465, 187680411, 86185946, 170708209, 106400297, 101758267, 780558654, 913987233, 623074015, 414695701, 274205155, 197937537, 478892300, 423593465, 741023439, 35376771, 595887615, 143377168, 627031506, 184663262, 344750727, 804285417, 973688333, 938187000, 143472812, 681075681, 176513811, 788821931, 430369487, 624488808, 449340649, 133442947, 120026367, 307409569, 15110808, 688104549, 620418540, 761310263, 324298562, 686010141, 587893031, 502399959, 827160100, 307539677, 344293292, 201063374, 86265720, 447278288, 667219218, 506586523, 581006289, 830610785, 363199539, 715011865, 355172051, 452901719, 845500332, 572349524, 233227249, 682981442, 101141797, 945585859, 759142260, 655460380, 646237978, 62014568, 542381864, 816885872, 82784420, 466213137, 407664543, 443173258, 963829475, 446854388, 944188137, 106711900, 781834988, 918145673, 842727398, 274422539, 152236406, 636243817, 124069009, 778908769, 851862522, 89514304, 504283870, 874401198, 249398585, 257973735, 881269862, 275009826, 235365588, 473670551, 30258159, 900004235, 690219360, 78287025, 916797612, 949398119, 986664378, 728627648, 188340392, 871103667, 540433963, 135888178, 968959608, 878793292, 697413502, 540662034, 120289793, 540027563, 310974804, 397773155, 758656092, 217452232, 359468994, 348696161, 242091041, 905123879, 545672593, 172430543, 398292631, 164015806, 328592482, 268815388, 469593578, 535993821, 18522775, 344783021, 722899591, 435025296, 164428945, 111029304, 611953709, 94222603, 928623888, 502628146, 541866638, 286471401, 112402837, 785896075, 180622259, 62911176, 459059139, 835737105, 630844898, 51865029, 167251013, 44729274, 637725417, 968448954, 490538625, 377479662, 781038494, 25660107, 283004427, 623705473, 44680414, 19777321, 890788622, 193709645, 272351792, 733545626, 629116475, 451374011, 599165764, 352664940, 62494127, 930521695, 434708175, 954662089, 713479269, 849848140, 413673108, 997639905, 38770391, 514070377, 559166306, 476575434, 129562129, 58433978, 747688928, 85247345, 516878220, 518268079, 454947910, 585023987, 185304275, 871149539, 994207687, 403923540, 137079792, 895505113, 531882398, 9154681, 371804183, 156694144, 762712051, 790784483, 200047014, 562603146, 39402117, 553598117, 853287858, 614680911, 929000063, 912196946, 659326934, 872596300, 108750028, 418661395, 791426798, 665665313, 38313888, 180332208, 878741756, 8118643, 530861006, 209450104, 621078342, 759178890, 294005767, 957703505, 381343304, 749198901, 535831500, 96513052, 865495569, 478889577, 826231665, 190883805, 81186632, 247807638, 468427089, 540840517, 861421380, 330943646, 957391092, 187501714, 639382606, 234906284, 978408659, 425394184, 8071744, 562127602, 592592867, 787485766, 714933642, 356568226, 7506140, 42403547, 549272538, 383149908, 327074780, 386141803, 144996770, 803134588, 766997687, 945777880, 42674510, 926367014, 373504334, 915599544, 38460597, 446445462, 792467873, 569617903, 38546781, 843922964, 635457246, 742550217, 731018534, 92117555, 673674202, 139653548, 66810205, 282113724, 315774958, 297766918, 858607934, 8504760, 206842332, 526450397, 752276360, 645974487, 99183736, 416974832, 810449471, 616582437, 669812473, 24552842, 98108049, 569386652, 246806476, 374751321, 611979279, 670461003, 703761855, 333650518, 421155558, 829199441, 614530607, 985247950, 241285062, 400761415, 934223657, 839306225, 759161635, 978247007, 770735143, 670969738, 653699922, 16664194, 442566609, 667536906, 476536969, 351853371, 185982584, 839689475, 939927980, 270006536, 132924170, 516273975, 335284117, 214627787, 97662169, 313546430, 314665095, 197551793, 680540718, 573897521, 70344387, 525706098, 827902601, 624036471, 383907933, 364991988, 630890904, 954592846, 453729640, 339496826, 538862767, 944908617, 202139603, 440539376, 467662899, 213082828, 356150121, 695309905, 88091267, 693004209, 641630206, 315622923, 651941461, 638168548, 663022326, 835338642, 699654436, 805325609, 322453894, 864187717, 717884130, 903810129, 523936908, 764116872, 904572820, 739365368, 98670736, 479056072, 568605872, 159933152, 628092432, 964121435, 971690800, 436749224, 26428634, 50718733, 617714589, 77779308, 173058146, 187694340, 904493570, 262091440, 104246361, 32415915, 362890376, 95100880, 563052197, 930563670, 220230810, 383454239, 95494752, 553042284, 883739285, 952981538, 520223399, 252374125, 528567522, 466435947, 514359509, 950061486, 446626983, 7089685, 532575016, 809167840, 75318249, 919363086, 813739209, 896314756, 36823111, 114254456, 915853945, 407758907, 143782043, 793426357, 535363257, 337797094, 454876306, 214434596, 789065420, 670971464, 213638622, 874292602, 702292668, 671688023, 690672453, 840361284, 736295080, 864147838, 501265971, 18956078, 479263395, 208228205, 370710365, 575375738, 162914563, 698072055, 512977843, 16976227, 390690955, 785716542, 1140312, 976035546, 941144837, 168644833, 901269567, 991997187, 210672986, 633230536, 553018208, 510682767, 760250034, 952132588, 377776054, 615384332, 192461022, 412503446, 257333794, 293162977, 541897873, 665777401, 665111888, 671790569, 364144796, 967421168, 512118546, 483785832, 683623789, 843443030, 948189737, 639776275, 63985105, 691713312, 805200323, 386134395, 912739240, 673166364, 110541520, 242270560, 955202082, 436227462, 277625266, 959148158, 586149252, 958576913, 235164190, 224157792, 440243691, 76621364, 12479290, 664815559, 813266023, 694483564, 722444986, 689911403, 708481260, 96192064, 892432256, 196852793, 759960740, 497734439, 122902177, 361185801, 612879452, 237985314, 257119292, 857924927, 116144304, 468818202, 618560287, 406066790, 324294636, 818173397, 408144715, 551973393, 418631114, 282270075, 944706957, 692688623, 177335195, 967050179, 13683178, 289139002, 757153818, 6191609, 316980614, 134070139, 281514265, 463841842, 461764110, 162336797, 160424569, 892466450, 937025911, 271552615, 153192150, 709055503, 992166486, 53676242, 475922941, 334821416, 408172256, 482326707, 510543603, 215409406, 136113689, 276686878, 747258617, 63128999, 513201025, 611357914, 44650280, 546177989, 900930584, 111141125, 241706621, 24069621, 2033949, 670333178, 339387875, 276895464, 219557013, 377886559, 35636058, 138684085, 977759263, 276055927, 83146771, 181466577, 586615151, 508757819, 838960644, 848897799, 987429562, 814816063, 434775108, 486805627, 901642078, 837434682, 568834165, 564085526, 441904833, 574163056, 42795809, 295861173, 65315763, 836939794, 574619030, 836081181, 883614369, 452107193, 216452633, 368084015, 65655811, 77580935, 460980448, 238808856, 125873097, 118861280, 5374756, 420768156, 975306034, 658076922, 698581433, 20305148, 921202839, 417255187, 712371769, 475753926, 607016659, 208957309, 461972270, 890146165, 310669128, 476203270, 848134778, 875165059, 269551972, 527872355, 16944336, 497556689, 338989073, 632217660, 850476997, 617793137, 145872261, 167497040, 507605611, 823572637, 951023632, 93089555, 132862169, 862981744, 433094440, 940735622, 129493824, 208324422, 136659048, 203543412, 466418025, 691690535, 405250325, 298304940, 527772023, 37125900, 149231270, 60986733, 171685200, 180023381, 907899765, 835975113, 223677287, 726731769, 964098419, 609912187, 392356318, 87427754, 101071322, 629025163, 117885245, 590708906, 328847949, 520128908, 404442726, 580388479, 911463296, 922856533, 533179046, 501365064, 353875685, 492155311, 912724262, 548039836, 842602983, 737568717, 318130294, 303274840, 992725316, 843051108, 54034634, 923979487, 705765036, 811910350, 840600724, 384252941, 166685811, 909197781, 99112191, 127799424, 742592856, 968024089, 736939479, 543322669, 48855888, 788295398, 427431347, 677555701, 923504210, 537060550, 523211122, 23985247, 586458655, 457254066, 893372943, 700152132, 739531166, 45904730, 54123127, 916042722, 851586820, 465659068, 651146116, 534482593, 260926820, 61781956, 490872389, 577487034, 690717759, 229966902, 398884109, 195886757, 255929502, 156589692, 554653070, 304979878, 299143461, 351696910, 767854318, 552596379, 184467030, 492612881, 278815150, 305206799, 105331684, 653418189, 425444827, 340857074, 281243931, 17082301, 158856171, 780445885, 211160686, 595998461, 881942570, 475933886, 241079928, 20886539, 719278216, 614395983, 648341394, 105345861, 794616121, 994205952, 627897545, 50714456, 11965472, 635051662, 905677612, 616061332, 685429660, 543742574, 84319467, 843021551, 562636008, 478239558, 680931897, 457088943, 462254530, 515157094, 863729039, 495653364, 571039049, 82166414, 531458589, 574053918, 545711741, 30922289, 584448998, 659040254, 849334987, 65042771, 782094846, 342440402, 884464429, 342285886, 579646744, 573548, 840240468, 483498672, 653327427, 909488454, 281871374, 726238845, 553011301, 40041876, 747339987, 623895369, 839263852, 739124955, 728871220, 162114481, 808463245, 603308853, 953174982, 932393623, 933011718, 733573949, 336238011, 392324076, 42984483, 205887927, 243788112, 920585637, 472842536, 399308536, 193325325, 795694951, 577035047, 31185985, 32271103, 478018371, 46235443, 161188091, 252710958, 471606155, 852988790, 856164213, 261632795, 177719305, 38338399, 402509637, 969367904, 834152735, 66694088, 546490370, 344340916, 229996729, 703345365, 271238189, 277604501, 169508644, 18697593, 589639073, 842795914, 375838048, 488071695, 356906642, 797068447, 872696346, 19640488, 39656132, 524499898, 286562376, 530138833, 529519019, 256246978, 224171753, 982741754, 454414383, 325929538, 673361040, 266768340, 708998031, 144669929, 412628731, 925184897, 145692923, 441679527, 491457425, 821293285, 682553585, 102687487, 746211770, 911746071, 446314495, 457154232, 37660008, 142541984, 745214008, 479041666, 559696863, 649801948, 263553218, 42953594, 737391787, 569498224, 964599086, 197502025, 747794014, 175506564, 903799602, 240075777, 924005182, 617410682, 365958374, 277437243, 618184396, 34732255, 271938477, 423939921, 387219346, 621680439, 580886712, 863603961, 511837627, 215987410, 175649319, 200132118, 161594754, 170496207, 171771615, 348042998, 537227810, 496357969, 488138289, 499987947, 711519082, 464232646, 334479001, 424989750, 839975949, 154638457, 151000242, 213847755, 711292058, 567393877, 965126624, 702781156, 611197870, 567112308, 216116951, 687876461, 186847750, 608520166, 700112587, 112003489, 975948010, 357297650, 747573730, 917270048, 577302003, 597468686, 463023648, 407317915, 581654034, 295641574, 670352699, 673551745, 644542313, 97137504, 105715704, 7693737, 196685331, 503375863, 678269729, 92594379, 188110722, 358741325, 562616795, 469312313, 170455130, 502918511, 895156619, 387657986, 216233607, 133908502, 59238313, 629517666, 513620799, 147090546, 578827177, 526231196, 538818330, 115071375, 857558531, 742149129, 208987557, 238588524, 775588797, 561048920, 334022514, 231341338, 964361740, 932787923, 763845565, 532658257, 809376300, 495047226, 394564424, 849976505, 32697161, 55549731, 958606132, 689295682, 942001834, 671187135, 754144122, 529984238, 924818941, 141537498, 60962682, 828858889, 920549848, 830772301, 804445022, 339107343, 627845244, 317197895, 911362864, 772952749, 543326850, 520732558, 504690170, 492071011, 500099313, 949506150, 716084397, 571456853, 407985680, 899431821, 166646875, 693431229, 53106786, 894538489, 159077133, 293224366, 204198544, 694637751, 1782490, 798981851, 904317996, 877305846, 170337790, 376369792, 300833231, 139668557, 543989833, 644479249, 622258788, 450692951, 201791495, 425666955, 964809189, 526014855, 333061178, 702838638, 627192765, 181541954, 964147496, 893024696, 282837237, 602216867, 453529401, 416565624, 899943478, 974728421, 55784462, 516269, 92364448, 981639016, 373044212, 540319200, 952305647, 523850372, 419411939, 615938190, 200855434, 192274936, 133846781, 669240518, 287422916, 255991470, 675878484, 938831191, 777594139, 332841653, 321480413, 387053759, 169525154, 275165268, 879573694, 758431066, 923311498, 907602165, 97130602, 288693361, 362125318, 927889343, 855880360, 606420109, 421292364, 393121946, 615802713, 187475516, 107457080, 713183189, 865111159, 49985581, 486816259, 628477652, 280906954, 781860409, 364200085, 465442321, 545075984, 543886619, 803333491, 794656290, 641553340, 163638674, 15844931, 582695550, 57792730, 124325857, 180896528, 289595703, 378937261, 526247606, 323766544, 827784888, 885482976, 596474681, 619235220, 206389786, 217080550, 841124191, 392138867, 719742449, 729242435, 558621658, 152686207, 536975793, 277647347, 738104266, 912966635, 225058960, 721867639, 944739152, 54371179, 109774262, 544427514, 748665679, 16676391, 876439945, 238200118, 38086185, 578168449, 887047362, 909454392, 857278239, 171298684, 882094671, 249178401, 727106370, 42281941, 700811582, 70804240, 892137899, 262409521, 314250149, 164516856, 231707145, 403322444, 26578977, 137281825, 710481198, 909342558, 843242938, 241916189, 941928915, 515459071, 296660300, 274893369, 215652305, 517864806, 248196426, 73051430, 387513344, 192709819, 999038705, 444988370, 315056214, 779020211, 574234783, 801549459, 571614345, 203810805, 22067865, 357176261, 51624199, 475314386, 492934588, 312387109, 956069660, 167191543, 814221837, 428181676, 813813641, 692700998, 885146730, 497477584, 771209185, 769672053, 943640467, 422049880, 8166387, 144071157, 712122089, 428134652, 996682950, 610295392, 11449564, 229463642, 298071971, 794035438, 325145849, 934274942, 429581097, 765500374, 447460691, 652062385, 862651925, 66587892, 51366049, 996194151, 829909227, 397870340, 508703487, 383967602, 705202767, 51719691, 849443271, 256734599, 593418845, 358167646, 710844184, 633935131, 821295524, 660473185, 191154226, 705583180, 649952674, 643409099, 547203014, 38597166, 544488564, 504138314, 416271498, 252795865, 312901648, 575774107, 3828794, 424850128, 72997672, 8532913, 435995251, 863730491, 883224721, 95296476, 877631371, 350355084, 994140496, 642757524, 755526044, 973436934, 825138204, 532493786, 854111739, 770310875, 329004771, 131352650, 28032416, 24482178, 697723310, 535289716, 798465988, 967346905, 388813747, 770880011, 490224355, 281919516, 982981851, 244024512, 872097397, 519448605, 128916359, 339114384, 487550442, 638124281, 854674609, 76041989, 781279832, 519218702, 232662812, 388837678, 135439941, 87092666, 767282990, 97651678, 766136790, 987342206, 165716370, 574048967, 173267713, 137638958, 169862899, 598415538, 953703835, 55201691, 437912217, 811661738, 290159340, 71243031, 19811541, 422869858, 158739031, 699551385, 674563661, 872473268, 578339553, 774058843, 822267218, 135691519, 863981553, 570123713, 754411196, 979632395, 658378112, 302960373, 540511194, 23743763, 853054676, 23316229, 85494958, 337371784, 3303379, 380211156, 879633311, 252240431, 198324599, 804349313, 579772152, 933920955, 701666603, 896146672, 742193299, 721317928, 980950804, 942190731, 619435573, 951464379, 683002249, 66397949, 964800454, 255491445, 251481889, 72926474, 401990749, 16147204, 128664366, 968448338, 892994461, 685120593, 888586694, 828615719, 771986912, 699931807, 130223076, 205345656, 486492247, 793068177, 744887115, 23373833, 521609900, 630283475, 239381219, 148945759, 652553768, 384695381, 76410096, 439613585, 116293204, 893097062, 671797526, 559692730, 106118216, 253208749, 840787382, 584324576, 109882531, 744772066, 965821295, 958125497, 639765378, 854252127, 353767454, 71154219, 261001628, 445668931, 471849882, 947075382, 161131719, 911457694, 373776233, 527385614, 890618779, 998729426, 388088769, 616213365, 91827479, 573292220, 320891800, 57214091, 693135527, 642022667, 682907114, 444462650, 271748110, 703625472, 986512877, 141574511, 310019269, 404500548, 491405546, 830657411, 192762859, 473380276, 334468282, 176477825, 616041326, 251692895, 897327486, 475849746, 286184737, 358869759, 916311503, 372214435, 241067600, 420974256, 992024710, 669125802, 887301199, 386324526, 207312838, 689587193, 219795312, 644637052, 442063803, 487298461, 803385223, 942058159, 264462202, 983546900, 811673194, 830995380, 273268101, 182185290, 586669378, 425076991, 556480783, 787907006, 884882496, 577674966, 992467307, 620558966, 797232951, 980439686, 117525297, 657604150, 642535044, 412360169, 126747265, 879047479, 402619496, 336117928, 581552705, 497351069, 911702844, 2057658, 811829527, 93137978, 67749751, 220579101, 289819696, 73414553, 616104959, 707151512, 297486800, 711676927, 108720652, 824695548, 112213701, 208346433, 172914732, 287709512, 705616061, 228055102, 115850219, 13017878, 413622925, 740842844, 858234122, 25535891, 393419522, 904678570, 859820259, 673762245, 643463919, 699414796, 294540779, 374113268, 194912514, 533740615, 996836580, 204595742, 104878149, 550127469, 201312643, 653615212, 748673664, 612185639, 262811721, 872364838, 499119915, 338827429, 42528237, 51082089, 642407015, 898466798, 799628134, 44828523, 304267310, 195325482, 558471436, 735475066, 271280981, 393052951, 131948653, 932597088, 923122865, 183950556, 312460212, 415438966, 710646663, 615462543, 852232865, 596950847, 531925377, 967926728, 612521585, 410498078, 198622289, 732196545, 960479074, 70825295, 278701530, 15118102, 336209173, 672949353, 225636065, 933061244, 185006178, 470786479, 651861298, 453237366, 535894388, 190609735, 618151090, 941483477, 802408310, 666293154, 986697604, 167555482, 756175351, 783016410, 334619546, 298303083, 389034042, 510813425, 102372837, 372050496, 268346617, 888684233, 511466864, 330723533, 801940023, 852913957, 927784526, 922572004, 897457993, 101886103, 781331239, 435734887, 191261161, 781282816, 126213642, 795692605, 782173337, 479625132, 367749463, 291398424, 725330704, 324911728, 467392326, 652057351, 912142883, 388637314, 184344520, 325234170, 212443695, 225289743, 211261276, 835598193, 194576367, 431073784, 266996321, 119113863, 680028321, 17442043, 450484345, 467278657, 875772739, 930217166, 810984637, 697545879, 333373148, 104037288, 147396570, 61311230, 594174106, 45928872, 562078999, 435621310, 683594762, 254564888, 187688010, 197855843, 20285429, 906985481, 373368102, 759471660, 558168297, 622805208, 454430905, 469509557, 285887140, 408723396, 726628940, 103133008, 102539582, 697333038, 102151737, 125118053, 992363783, 846367604, 143105301, 430129285, 997708497, 114319657, 492057562, 611935769, 59847535, 456535574, 930408220, 974310721, 501125541, 964000378, 512448382, 626981387, 260128946, 797629713, 361622266, 5909026, 999422221, 576215674, 671149426, 724280309, 340075159, 932902623, 901092639, 897853181, 760468043, 875553241, 736281344, 946174836, 65130418, 300636388, 478019324, 589556362, 168001393, 899983754, 243924386, 946117138, 246899459, 389813433, 145502041, 97252856, 271190419, 42453092, 793702207, 688388228, 461877404, 793153865, 480702996, 262150883, 286061157, 44546660, 232057617, 146494907, 412034503, 292867368, 427469926, 762515305, 932982320, 259014176, 19980860, 973583021, 842042647, 471403714, 483438583, 920460190, 142721205, 944425681, 991391971, 791171386, 310874482, 533414448, 703941988, 634262878, 305748229, 970753216, 45447909, 33064018, 550923388, 590054924, 222036896, 292568785, 985020589, 470678552, 299062560, 111887459, 941437539, 950992385, 42412256, 168488631, 386549325, 743043916, 31635899, 963461494, 242111356, 871667535, 40049816, 478206881, 239556250, 797117073, 659780339, 568611719, 828498817, 857696017, 305049086, 409797324, 361929037, 153920519, 877877485, 759933952, 672972217, 505841239, 47294425, 89185316, 566634188, 812434890, 653246171, 712292314, 690815767, 808225669, 170977580, 868025440, 304461191, 648881388, 792483224, 606430274, 199946391, 317309123, 519327574, 585272936, 187354928, 337691462, 551010841, 940320937, 208673977, 126939957, 135138938, 567096644, 633221472, 721605616, 93906439, 875348163, 562306156, 774306611, 405609305, 216433975, 584333463, 237597000, 103716686, 207111498, 797964130, 606803935, 561925061, 736154123, 43072834, 635777801, 261911303, 563553923, 2743470, 708475215, 418113744, 266429444, 265724394, 152695767, 708774127, 638030237, 679561514, 405432359, 293833668, 138977136, 398893572, 985549285, 194245117, 700946080, 723926972, 46284155, 598679148, 2476156, 754462969, 30549998, 187116440, 174159601, 620008630, 240015176, 16044992, 710672239, 683615516, 283391334, 928225611, 896353220, 583963438, 302766567, 612320608, 470834019, 699990358, 141066015, 717993424, 939098960, 529261407, 795615926, 510263051, 820930451, 810634249, 739913747, 673556647, 502064056, 690603371, 156936260, 922879980, 432958771, 433141733, 105360318, 22337468, 692644007, 555819134, 47139922, 98422979, 414329170, 282302501, 123449688, 641172423, 101323749, 542821350, 64922671, 904065950, 442703928, 790223573, 115124191, 459027780, 52023842, 432861497, 347267220, 871748824, 26345040, 588357627, 27942653, 683870853, 855766141, 580297318, 373175417, 750028534, 603873982, 976672331, 938914081, 45632328, 528987096, 309572911, 733902097, 25594077, 347844683, 834127886, 640125677, 749385982, 296511792, 284349641, 472062449, 856180710, 98249532, 914702275, 174400365, 277590703, 469579240, 178875769, 795962270, 975584957, 430226765, 40507460, 29143593, 60730283, 1299511, 628474795, 447288855, 465329193, 122615316, 386072876, 923298507, 190658909, 13119769, 888490648, 257556540, 561341958, 339394710, 295753954, 118485507, 202387935, 690807430, 969804689, 558138098, 176688191, 767937348, 918612975, 921183393, 913051011, 786791575, 990585885, 603824399, 132073529, 339658124, 564826620, 984122679, 470971076, 649293664, 864579736, 5093252, 720418591, 265465508, 120628545, 774313336, 396087171, 318857761, 813188721, 45179827, 687577319, 89998955, 58574170, 774875214, 739263246, 29384005, 37702632, 58537191, 107620223, 639264915, 281312964, 909458555, 947241030, 748937888, 175857638, 176427891, 110304581, 180301058, 3661706, 33639313, 84524157, 396614043, 91970406, 432746632, 617107160, 882939726, 622212814, 970011713, 782416966, 597698336, 567423121, 405914026, 862770284, 390125804, 973966271, 309845983, 254203688, 441590872, 963165537, 748116026, 507366211, 99656805, 427548474, 290329375, 576179823, 378502933, 612246305, 397197886, 127842377, 177988780, 177507337, 185825839, 121744503, 832622252, 904950004, 565038994, 41467535, 283225272, 160553908, 384274043, 933122299, 810965893, 606910257, 489262321, 729258533, 123754693, 538230679, 134769669, 545270361, 455715563, 896887510, 192683218, 767688662, 636466895, 891390597, 63379606, 493509559, 36140688, 336546093, 401483149, 106730693, 440030626, 701725941, 890903593, 344852305, 991021987, 420316086, 513578355, 424637310, 982385452, 140035148, 632786899, 179327061, 864825647, 186672638, 773575214, 930524785, 252908514, 516572888, 649008976, 235188047, 177859665, 67103358, 389556595, 975020481, 410671543, 119903504, 455270180, 59672004, 799464605, 281870832, 28302160, 855967333, 342796966, 170854259, 261109786, 685818346, 732898664, 690516263, 868175314, 596310147, 913242241, 854232764, 134069343, 727604274, 202908183, 446392695, 19606332, 846306897, 465972730, 892902621, 161656885, 527664776, 395935107, 182115395, 871903073, 231094142, 486318713, 821001808, 838195046, 834823059, 217004377, 924106551, 989063820, 768968652, 606096321, 146175990, 614461446, 792471439, 870600162, 756806650, 384666549, 512794389, 418691417, 306837201, 76286206, 701789843, 767408172, 411864588, 730582386, 412787719, 497469416, 697515168, 595095072, 416537109, 469458676, 385469531, 695487626, 377557857, 891705906, 970962357, 341929442, 642202624, 567891479, 431108097, 593678314, 917889312, 705953653, 382129331, 547039650, 35017396, 814175751, 295723452, 613616995, 20099072, 574186044, 170487707, 984972517, 488343722, 940824309, 492591919, 209445780, 413737042, 597107403, 34752340, 877976842, 730171682, 184852249, 820098056, 337951794, 131254735, 802740879, 439948946, 523005955, 288401562, 428691835, 200954461, 25827851, 526115199, 391665759, 197785840, 424821590, 546009823, 724127312, 113823477, 788940310, 330958005, 283516308, 102242832, 636516458, 463602609, 345554800, 109281356, 277204845, 461322007, 787979587, 679689355, 952493533, 882292877, 955139649, 29529529, 567783705, 717792082, 300802428, 919410685, 366629501, 331111067, 509399791, 815963447, 599467467, 878893565, 419423586, 471358511, 237504256, 819450587, 153136994, 916585026, 453448725, 780363409, 902060263, 753605562, 882142201, 180183209, 233212869, 755392259, 754405153, 787496825, 75789668, 86828644, 925711873, 198304261, 631189285, 202737017, 581323839, 314289139, 8190635, 362488030, 981011289, 561221671, 146569183, 749517803, 300398388, 649406309, 870736762, 139809449, 725368630, 41218295, 168306679, 217806732, 733359658, 38321435, 219408894, 773653719, 343162300, 138846111, 523979643, 771173464, 288562185, 463108743, 776060174, 731563636, 968532695, 303541014, 996176357, 511658734, 12388040, 497463648, 673837929, 270458666, 987639300, 3189899, 601567436, 506409190, 484397217, 59262287, 576643563, 595162455, 249889979, 185105863, 312026612, 675098123, 53914180, 77017127, 649144729, 564024223, 975088830, 670669143, 284913492, 680514905, 470411125, 121706766, 248666714, 416157673, 719805490, 266640447, 9142116, 471879490, 433225354, 768203371, 106906336, 95002365, 915692307, 182623884, 122999673, 850067910, 588975298, 562663716, 381679088, 318782017, 980636706, 344852410, 294544256, 749992337, 47947646, 567838636, 159758838, 325507522, 13727067, 84847987, 802830161, 980431195, 389263239, 228414775, 106026058, 979527013, 741236442, 242089696, 293280297, 111329394, 957440228, 431939072, 688756619, 338330305, 358807818, 739951106, 920145848, 800071443, 446797790, 856931945, 930703346, 651895374, 691955141, 15353968, 568131368, 82116936, 568034940, 449591222, 790583271, 868405479, 447946956, 637593212, 4013086, 380484775, 858868169, 656647641, 550119671, 489856533, 802014694, 600495273, 813058922, 843527285, 288142472, 750286132, 810334536, 145025198, 796644276, 132330164, 621451686, 55041365, 121840625, 942700715, 324853889, 759068246, 500930641, 579526824, 526176032, 976256307, 911675065, 680466653, 698406177, 107313220, 460714315, 482544776, 563034282, 625815097, 355570502, 13418757, 240018175, 627251813, 871476826, 531020103, 839340558, 369871222, 970316765, 2236561, 721965137, 589809684, 778062565, 443280537, 475583499, 509039217, 43985312, 114956511, 596656795, 331526489, 2366185, 283163991, 897992156, 78210158, 625085925, 768980660, 567786546, 792170691, 709386877, 698003959, 567176221, 668051681, 900821921, 383802451, 470576833, 392244288, 265876872, 10841287, 671261813, 48743517, 799882228, 204731129, 885433590, 490002786, 156047812, 311460050, 309670284, 928783811, 206122353, 170302832, 659466240, 957262431, 961188298, 402878680, 632465474, 715240529, 364562883, 84310006, 903919629, 464845867, 369877798, 151434961, 483594500, 545947299, 629165037, 544185109, 246318437, 661583067, 438334121, 38558059, 761458875, 710009127, 739121255, 357455242, 882979048, 642198287, 410674759, 815635675, 495148606, 745945399, 605386386, 724496245, 924778150, 336825138, 364141636, 817823474, 39482370, 59276128, 935253335, 980117934, 659324746, 56393104, 234622397, 826091158, 757363322, 796753552, 726709478, 936960829, 955100955, 684136815, 135144330, 352822050, 28763099, 179585272, 407092721, 351416276, 478117318, 66250121, 259570192, 768019885, 796875393, 974014516, 876424606, 986015940, 847062398, 958197005, 755523137, 211105823, 671074569, 276942736, 566496471, 693004857, 946339808, 153413776, 246413837, 362829435, 15041915, 136912476, 385168602, 48259886, 944356214, 753616685, 903438269, 219865223, 337133761, 644404767, 514856961, 379089831, 349820651, 286310283, 539325945, 328532268, 23584006, 283676605, 156674674, 18452770, 366167387, 628369239, 331644284, 813881022, 164060800, 249257716, 694580592, 89785337, 117350824, 486395368, 398161964, 822630353, 797168393, 797913789, 344421667, 182004253, 507167506, 442667278, 992312313, 112139967, 620625210, 698427418, 720770876, 760800951, 419296669, 502479415, 659959438, 517332183, 627717357, 857331941, 774574070, 276690402, 568068206, 643371068, 984177122, 743945614, 789281903, 69683635, 579208539, 862603053, 881819135, 762424201, 133161271, 560261428, 744537248, 637067597, 641268417, 646781334, 543275334, 193559960, 779872263, 477597649, 224878155, 339153109, 114979427, 31341505, 705028754, 906476107, 158822327, 980285697, 132563926, 136985099, 315426872, 381862479, 194791527, 956782923, 888128329, 679110085, 282542795, 633208856, 341316673, 382715105, 794250114, 429568544, 164496257, 258232919, 195789832, 867640229, 917772949, 243596237, 861442884, 223432920, 754117646, 233704458, 358774681, 432659212, 663138747, 770072067, 93392192, 905577846, 889053919, 517024047, 287468451, 471198888, 259203476, 159380811, 788718226, 289323682, 120228767, 423891804, 5642756, 922182092, 96796750, 664861962, 313204607, 600185832, 85141697, 886365782, 619314977, 712370399, 531402261, 657510674, 451988200, 909710802, 24408463, 628996106, 776658265, 116173753, 652168710, 763221739, 16369198, 660952623, 606465063, 272738169, 920042100, 691876796, 967947104, 375388792, 612724912, 252822037, 400165568, 335508669, 241429745, 517623771, 132138225, 60014406, 370722653, 33279050, 539978266, 72263316, 213857752, 244549587, 506392811, 977376664, 553879949, 257570238, 130152211, 872765227, 148783439, 740072107, 839018867, 221329179, 169196146, 568973677, 256589502, 220651505, 939608334, 490133986, 208674268, 687055310, 101461074, 494015970, 478374743, 173889792, 443162338, 624587032, 558398316, 430105946, 119898962, 716937587, 198902422, 641657050, 738596308, 123257045, 108574887, 990769445, 588655333, 884604777, 393026293, 561932388, 924032586, 38038165, 397185332, 974349070, 937804937, 674357147, 760654994, 272726656, 911981376, 645210756, 904117268, 149188059, 305767238, 477815004, 530821867, 248209800, 683207566, 202277902, 461605704, 201734322, 855836681, 86940338, 747128455, 133750794, 729313337, 692560018, 399395014, 601323983, 805422151, 825647617, 986077074, 724721228, 886983003, 854647188, 137088128, 236190729, 895368532, 297310414, 386012943, 987053550, 395793650, 353844264, 373967426, 368374563, 40320203, 1304478, 576583576, 389531050, 399157187, 562093966, 139346053, 148720983, 897408406, 105539702, 302518414, 832069887, 277105501, 198393604, 399867682, 424770034, 609161390, 960161291, 953893576, 369878778, 116481174, 114046612, 702221785, 13385542, 704047417, 314961564, 980653684, 596066018, 246020963, 887958120, 568540022, 405565996, 859348351, 435337214, 346737490, 809013045, 811179794, 2617195, 72586131, 499834418, 321449248, 141509095, 537779268, 463581592, 910656117, 998462647, 996351965, 592594978, 160664796, 544533809, 276446784, 462802892, 433054989, 724898840, 85692447, 729260681, 409961628, 746895365, 450446789, 881040567, 722613851, 630386019, 94039585, 944891207, 398130030, 682995567, 367817146, 792781949, 102273830, 539312204, 331371368, 172835541, 883077955, 763020047, 784385023, 412193453, 297501645, 66282355, 358942021, 659153754, 921888506, 522455872, 548405040, 541662524, 836511894, 893644161, 142310550, 813118791, 456081713, 577134183, 467631175, 102154198, 124586569, 193726182, 924330731, 143138720, 446505563, 265306237, 131294605, 424474886, 589379471, 948645380, 469169534, 784306614, 156813266, 763730026, 857065413, 159485511, 433576361, 381750993, 398522565, 448390460, 543278364, 611869209, 227905191, 794125499, 359938849, 164661786, 716607737, 655446089, 713273694, 130143360, 488653297, 38558440, 616876776, 486240021, 506973866, 143376539, 476507647, 577934922, 544776470, 364712218, 714421114, 252529012, 948550585, 413634152, 985626729, 909929633, 814558983, 287151392, 124706403, 782858808, 66785087, 630675230, 217565655, 365073851, 263536845, 941372026, 196945967, 335312844, 561238101, 10207063, 301416583, 639644426, 709203664, 677388652, 118826182, 469784456, 953511360, 812637751, 403262451, 284887214, 324508775, 476667689, 417698125, 289272662, 937532146, 119397016, 171505574, 79945350, 937430742, 158299929, 252702951, 282839320, 32513954, 271329808, 618673645, 826648750, 560798105, 82865562, 629396901, 789109241, 690062332, 507366224, 417375135, 238346833, 552338806, 612464454, 834871501, 947409330, 450478343, 453619157, 255511334, 872962656, 649020174, 216851134, 902575043, 151898934, 962647908, 281274393, 94049845, 990359823, 548348429, 967816935, 204398871, 425481996, 162202705, 405722122, 953376929, 806652644, 913697044, 752590217, 802476744, 668091182, 341815893, 646651686, 76489449, 559977031, 752409332, 988194224, 771846726, 290027817, 3782019, 697895763, 306289108, 713005926, 415750382, 811540103, 1171407, 682739375, 458361602, 114666538, 454027964, 380401073, 727479619, 355551937, 865299354, 661395338, 413675003, 261301252, 537080286, 617168246, 282139395, 828024664, 794002470, 550946954, 995994251, 360206226, 209947941, 542394122, 328651734, 865261275, 630487368, 539068343, 508372767, 598901797, 40341750, 133931993, 754526374, 781145615, 381562603, 76559505, 85655586, 59058562, 646792669, 175931740, 210458636, 600754749, 704250034, 131062778, 972073767, 869888901, 957436749, 484864151, 577429563, 533728949, 169626743, 753793696, 532601608, 356187773, 810938869, 465707150, 150205581, 485820466, 780802277, 212492666, 956883304, 170512998, 867751977, 54339086, 293186518, 204416850, 953119079, 478278168, 687287622, 714948996, 928832814, 10438071, 647913500, 172177082, 156829242, 627650401, 39560196, 473345998, 496565862, 957310889, 733170016, 251044400, 623399045, 215767644, 761253428, 69193187, 456318677, 562776235, 175716916, 572481624, 104479390, 499699595, 188588151, 451702022, 806443970, 921385339, 328803284, 934677442, 364213209, 638239725, 669351828, 281122124, 526646052, 866488167, 604666657, 488802036, 630292935, 214927688, 837071940, 141538293, 843556781, 92078948, 654786466, 630701352, 224122555, 647063046, 312941802, 174748163, 540404840, 988584405, 618493780, 236447486, 319638949, 376789905, 683695868, 107598582, 690992557, 384663682, 750658989, 355604451, 611953574, 979598008, 441611218, 549236603, 591668355, 576280797, 475665659, 592672758, 822081013, 852153879, 851267606, 810810894, 286985531, 457437970, 751654650, 735968375, 856134031, 185864122, 62601430, 907281458, 593516140, 167388163, 89107395, 640699799, 535847812, 13452641, 154372161, 146226393, 369492725, 710231427, 235635757, 441060837, 704044591, 951301822, 267689437, 695941550, 81858075, 825406743, 737687142, 875980513, 816835828, 72143987, 273058407, 47697397, 291384580, 124238055, 948872597, 312833850, 725456692, 290012009, 682647339, 264699913, 562895877, 124241422, 59071704, 928558413, 691477889, 118448918, 43867023, 414816189, 442303356, 358842866, 411528257, 50053583, 288412163, 234320422, 237941954, 397234704, 732138091, 472236888, 976425300, 831639818, 162906638, 843496770, 45372721, 773128196, 270885460, 602417894, 47648092, 293225047, 481059680, 285875474, 597541793, 494291542, 764755697, 83064005, 112054153, 987193011, 132082062, 240976881, 898685079, 745500620, 840604468, 171502537, 652232130, 536733612, 484798212, 2715582, 180648307, 264845704, 550546249, 966566812, 418838020, 330703437, 610637438, 924603572, 108400776, 996184690, 525246776, 106211954, 431705163, 60011429, 471146335, 629933227, 654629850, 609687984, 176221788, 511820880, 240815206, 216383711, 857705798, 285959480, 526789216, 579165555, 524358478, 912079186, 627467217, 186255826, 721580186, 612012797, 568460333, 446756535, 714277801, 988735675, 953327170, 618170835, 915666464, 235858580, 944371284, 812337510, 567323261, 977353318, 871551360, 777781355, 608865313, 733520311, 645613730, 609983317, 946938827, 414731933, 17823345, 488424910, 683493248, 283082785, 960498397, 510929887, 972964020, 337555639, 404620024, 817179438, 634675511, 275727714, 932340313, 945490322, 125724568, 153394497, 131530124, 282253801, 279907232, 630419208, 471999492, 490319653, 883118084, 587204008, 738936336, 809110708, 471057793, 797211607, 27334724, 859438375, 659194646, 206268531, 972739248, 408427831, 105299391, 825568904, 981689735, 708942213, 643042291, 161127138, 723734070, 420655779, 204707105, 211167521, 22362841, 808841947, 174559469, 470303403, 758953780, 66731869, 56843740, 706495151, 351395588, 956046747, 522012386, 235160745, 658338213, 648688243, 354135936, 218332179, 508016882, 680024136, 824701592, 302452759, 846806099, 764899527, 47894634, 6652627, 375369046, 830121902, 314328655, 296438943, 350375862, 483294235, 19670014, 1932520, 400144924, 908847310, 614828809, 786555944, 152726567, 516215738, 650525874, 657770761, 568147771, 408214058, 992205475, 611478042, 615277446, 312514355, 454142882, 61998975, 841007365, 960025665, 729777119, 997477786, 224962812, 145390433, 179282525, 965882122, 547050963, 222477178, 780596772, 151704332, 47174180, 363388766, 746968708, 790735471, 815499557, 805233417, 166291342, 589618657, 794133062, 62874767, 175562360, 689418453, 284609182, 936930642, 39864117, 909595029, 382180606, 696204721, 106656182, 295662002, 342199783, 313710589, 204752962, 5366544, 796558303, 126043997, 879801520, 485064954, 41764357, 250666020, 364938853, 500565883, 266830299, 614364924, 776142049, 347407809, 613819933, 598225197, 29557152, 26968956, 648484294, 849911709, 286585365, 175305016, 118946806, 384300176, 385803072, 688802096, 479256751, 522571595, 974859336, 605428655, 307459914, 752459606, 425883071, 571959311, 920621491, 938731042, 520243818, 472478919, 341157227, 315832783, 329138198, 714873979, 150914046, 760746048, 33177627, 358516264, 545630295, 532905077, 453855334, 95090984, 768489628, 401361831, 656212862, 404696317, 820847917, 201317505, 439095185, 101906154, 10430277, 901568666, 118141686, 804141776, 942461657, 658104125, 408614134, 735159862, 920810848, 859651755, 378362314, 753337261, 691449628, 631665807, 152178879, 915888654, 398489323, 825759641, 824100236, 85406807, 911260352, 535156227, 752232849, 830580958, 414043117, 605810090, 641158516, 631076944, 967031125, 826347746, 502792603, 722439669, 954936619, 540119043, 555407481, 478802317, 188025815, 343153308, 577608018, 665951667, 193358826, 816203737, 534525164, 824897715, 854850199, 819412685, 454824895, 246387198, 853368365, 857570825, 948255969, 902350306, 677913280, 979587656, 709892622, 134401000, 21246010, 517597097, 781732870, 152760461, 344966202, 335207820, 611760852, 432599037, 691413141, 772396525, 893752510, 518760225, 648388078, 527397843, 694467369, 691016291, 466205792, 513940944, 622244088, 949144805, 403987195, 841391731, 894358038, 452988480, 802220966, 367066918, 834334876, 672489115, 816157970, 863807236, 80901863, 477838050, 119583078, 843604311, 683574849, 8444180, 518153589, 803958816, 669390761, 444513118, 185326762, 58213733, 539853816, 980238166, 119950347, 931035007, 536696188, 790295072, 415486311, 57116893, 215930371, 673761692, 767622921, 756797789, 349916104, 282559987, 411180949, 539444599, 374058015, 454076129, 750182128, 223244038, 518935415, 663651512, 612382773, 900620670, 583397168, 285952738, 769338355, 953638545, 924833584, 324942928, 229831647, 884338522, 184486719, 22244226, 784614482, 778215065, 663472900, 18464169, 962110590, 423243212, 358881200, 359801041, 618093057, 912164809, 31572509, 148749239, 954458053, 196669505, 147397014, 379317571, 877936018, 477489791, 33694633, 493784788, 226095220, 302146394, 185577159, 538609659, 203445465, 335265502, 640665393, 978997696, 477092658, 203554989, 673621648, 677107419, 816858691, 197850853, 991439207, 582285334, 962787356, 367910793, 156929699, 930151981, 349204878, 336473842, 717318277, 965288662, 765245767, 190553265, 978557221, 903976697, 941157815, 38058258, 529199890, 956002618, 448455536, 678142354, 287270849, 275272482, 115004451, 962700057, 856393714, 991739431, 741740215, 879047593, 892067178, 720740209, 245978196, 773081990, 352560897, 858457161, 144301417, 903403348, 637045501, 560927975, 121389115, 390295380, 26312819, 853019954, 207111242, 985091797, 99930239, 529186589, 712046418, 42826895, 72445921, 415094526, 940753674, 655562399, 504844599, 485787398, 583563864, 655285001, 440959043, 429856024, 988819802, 88795516, 183762429, 886595502, 640795995, 569973802, 433086672, 859560589, 959336337, 389301788, 628447723, 551625392, 928328769, 366059163, 381989753, 168521420, 382091957, 890009586, 213096978, 333438591, 205140414, 269872734, 61050751, 21253928, 379853025, 628864167, 142031623, 451998839, 943379750, 591023622, 951390229, 737777400, 264872557, 223032396, 439968999, 325421404, 163541760, 739332363, 66909486, 460577370, 454293130, 392007755, 579460658, 429682346, 595402519, 171165134, 446676127, 873858638, 114196777, 329210619, 215425923, 297349581, 477347859, 467284279, 180613671, 77025143, 530802926, 309337923, 605183638, 381561720, 350857378, 260625055, 414658472, 656783628, 839198853, 945803590, 820174032, 444359558, 293755855, 786914460, 532930786, 77287096, 170893652, 921844764, 896284956, 108578970, 176542882, 344657216, 139806401, 911669275, 414550047, 719344367, 833269958, 634970677, 58246087, 73763132, 748804179, 850727225, 240639217, 419608633, 78591804, 829024329, 40790353, 574628703, 485067387, 292386771, 595921638, 280772584, 382329516, 266028363, 133394040, 944227656, 869304418, 548184118, 744480437, 421615174, 803795718, 538330959, 93898877, 88264803, 711254470, 508349999, 219725405, 468241873, 881497116, 544377925, 493844656, 338392337, 522640931, 927684478, 454442435, 25068134, 579680349, 19185956, 169871194, 104877696, 782870077, 740027971, 868917423, 437609332, 249337389, 52937545, 902448492, 273968821, 838372145, 303971026, 370271741, 933499980, 950471102, 96217327, 752094240, 465189797, 988884973, 734411149, 281850473, 176748130, 447843380, 914992627, 566718444, 21238955, 876942878, 989808825, 395126695, 432505138, 419262843, 452320810, 210488884, 772334592, 142345486, 512320831, 317486343, 687672403, 956669636, 428044591, 860387608, 219183019, 843390750, 381338429, 209621043, 61590845, 875789191, 155144869, 542397984, 788438747, 821100021, 230002830, 125320118, 313192652, 53215268, 700280758, 6475673, 791832219, 452155877, 936679807, 32433298, 497611533, 127879262, 445246747, 737819475, 131025606, 316092859, 89542725, 560199245, 915749697, 499187697, 760376301, 207977009, 878494163, 854813853, 552179383, 428042878, 459060183, 763827591, 304123919, 650875773, 697925802, 589473231, 365637287, 452996377, 262819224, 665229785, 272611222, 870950811, 67517789, 523045399, 294362250, 448259243, 522824567, 483109534, 499272907, 976494751, 316977261, 557979886, 890373813, 180648743, 753238763, 142734557, 597809831, 417113221, 530888231, 39517168, 74835540, 470314516, 360845164, 40570143, 16398937, 370530878, 732623351, 98026004, 557439294, 741971862, 18107327, 476019058, 823120842, 742670730, 503754677, 872441558, 758953903, 599731755, 45424343, 729442456, 725335493, 703805825, 657855139, 103716972, 134040675, 735815327, 858331416, 978564940, 759951254, 685406067, 51463272, 161586469, 232878003, 653658655, 66436685, 736156555, 305341934, 657827092, 584702159, 488590458, 709904649, 907763203, 5282953, 695713384, 158573427, 896721835, 761686101, 811239947, 833432837, 702913278, 649557639, 5706430, 802244302, 886173041, 934678111, 105979083, 265408286, 461691739, 193564368, 276620931, 499449974, 784681712, 733696258, 663052848, 783049718, 873280545, 452616226, 850561393, 505096914, 144913651, 153243869, 453879176, 38365037, 958902104, 195487295, 650270582, 228840938, 917839613, 863603968, 298682808, 621054446, 167543409, 358789870, 868276354, 280804326, 374596204, 322753300, 57308801, 615711755, 511448558, 317023369, 854960621, 193494528, 440305110, 433952841, 221882373, 672491618, 570018661, 707464243, 524643636, 871556065, 874358759, 976654810, 438924571, 430336233, 941246759, 829484027, 400312044, 390820787, 534622585, 666897166, 444524334, 4334617, 138556249, 687306145, 870837449, 639574271, 410249555, 625388502, 374748117, 276057746, 217031982, 675590891, 996142155, 807026201, 117091271, 300968076, 619325061, 769575419, 932466127, 187627430, 192836459, 933056231, 277838880, 801363274, 653868977, 214049132, 506913315, 969925852, 63397372, 9329009, 917591030, 619124865, 881598223, 787257911, 565605831, 259377370, 649593079, 895734874, 720598147, 448548786, 981549471, 971817598, 672927664, 908464128, 528977172, 85476263, 352278148, 137985178, 767324733, 674395146, 471310141, 416878622, 263626213, 985526375, 551133376, 325294337, 688236939, 21856759, 708650268, 810605732, 315318543, 133755794, 579063940, 216014308, 913890770, 259615637, 254822442, 587490633, 785394181, 334740369, 722906568, 573251844, 40318339, 213408597, 811763687, 99189531, 946827197, 998851961, 140456357, 46469424, 174604124, 308706889, 587342760, 664951844, 501726538, 123000244, 758229424, 622513545, 595284984, 886995107, 597101932, 605656454, 135584667, 941096858, 415459014, 460497594, 823773203, 981566127, 59718919, 958348400, 428708813, 982183400, 790050503, 529824712, 92858154, 99216118, 449149907, 863913085, 205107600, 99315620, 631884992, 900830810, 335542185, 830282810, 774711418, 39903375, 4538865, 863371065, 178860404, 21647106, 528781892, 951773446, 357460194, 512858593, 339840818, 818413277, 20397423, 910670880, 404349021, 929530296, 924827091, 542317885, 262493194, 26075313, 423171762, 742177165, 188056875, 679601948, 774883188, 109899404, 18818503, 289712343, 869542107, 658583165, 440539147, 509828253, 738713920, 909719017, 115024881, 527956249, 374849852, 202085776, 960322202, 120276597, 257525308, 447111761, 888830242, 666103532, 842497306, 922529404, 963270322, 480190395, 424928838, 579668099, 667677054, 355487380, 626035288, 893912027, 948597222, 946950758, 399836558, 460187944, 701369001, 515931121, 412791986, 502566181, 163088501, 95177809, 869800535, 160213457, 273914353, 615474514, 629407518, 5648033, 942228222, 172958853, 280911475, 246693365, 736274995, 861507335, 825607676, 563496698, 110875838, 269990826, 219130276, 629771302, 727370566, 703036516, 176946719, 189770554, 589926260, 314718667, 4741966, 810064771, 143023331, 745419089, 25480238, 338688541, 340146062, 863814506, 888342289, 224326007, 533147836, 449947692, 303159702, 565896553, 273893607, 9044623, 882384941, 448030280, 14424983, 484484771, 365827044, 973671866, 786916484, 567258722, 214721761, 43051811, 914217937, 41253490, 397795741, 805750609, 595520186, 265366743, 401260201, 746088412, 960167547, 419322906, 277195708, 216797953, 214957596, 86690845, 806032087, 226608082, 849107395, 812985968, 812917962, 373208323, 427971815, 326130096, 737189664, 771849871, 813089453, 478668986, 20641802, 674350829, 37217200, 641084495, 59138492, 968226359, 235467161, 375700467, 388780808, 411421856, 459611286, 960701528, 595758912, 85360132, 53116232, 442319348, 221812899, 621803476, 377289625, 430986034, 424837220, 168584325, 771378244, 127538056, 613329449, 672845241, 685151276, 509556530, 322841452, 447699967, 164923157, 329244811, 245490032, 326964219, 685096133, 814239922, 232677793, 926306015, 233315879, 744595771, 938457017, 980432321, 582594856, 641879955, 691851156, 190889773, 467587132, 266410417, 974711315, 41274813, 223052967, 846012000, 588744607, 697734333, 532125795, 821051369, 716261507, 290775111, 1714045, 912618388, 198931295, 914989605, 959284532, 223796303, 12279611, 334177055, 594842213, 388294018, 719770702, 461732735, 104392020, 252984152, 613866898, 884545116, 222180069, 140516383, 23423854, 945878720, 965591379, 191948532, 752300669, 207461879, 430474527, 656468691, 306492169, 912306463, 92958364, 403423377, 850873292, 313267380, 109018448, 483515441, 36843849, 692617773, 990793202, 386848323, 416054660, 404592204, 390833510, 718961662, 700313291, 201267927, 730318442, 440381605, 439571376, 558275589, 96038706, 175646570, 695673332, 280775892, 909736072, 946501901, 490520715, 425072267, 230585352, 388436859, 589148860, 731285277, 426402488, 841646984, 19695196, 994434577, 955631804, 328373000, 24390280, 939094962, 594131914, 446148963, 793778915, 811262307, 457255494, 880022463, 629591830, 779087970, 831529102, 850810937, 885194122, 606355222, 414573319, 359456203, 324299903, 224419166, 882683700, 734881081, 336277422, 584822066, 861833018, 546304246, 922610726, 589039183, 140707576, 626039565, 825079159, 662448837, 314348137, 580984723, 475418159, 999961996, 197374916, 681174677, 356432918, 352315235, 669165156, 634236391, 428039156, 186611321, 806016509, 601519025, 96661717, 814974459, 184205621, 964082610, 817410011, 731583202, 643459677, 315643767, 126081007, 66366148, 551058710, 512277048, 900427045, 249769732, 61542367, 862752810, 505745528, 355228920, 477250609, 866423079, 486167974, 272113561, 605697490, 775317665, 683184779, 653899289, 997631626, 678556837, 928383373, 680186015, 889385700, 805339806, 806573340, 589352104, 659680801, 787224319, 489644599, 237407015, 524679431, 258120315, 921655578, 840169841, 565121553, 332936256, 294123912, 54997852, 992050943, 324019534, 538623976, 950602255, 554778764, 886106854, 347629143, 933993584, 925065077, 984968724, 693876453, 405733605, 108086293, 88530444, 602639802, 78622713, 405123737, 623720592, 311821837, 276706600, 520056864, 290912456, 987628000, 774755682, 963368315, 208388326, 268759446, 398441247, 983490898, 679638016, 923520827, 847651952, 307521481, 130592976, 70654175, 941004832, 400097931, 438769481, 466955635, 265293456, 56100280, 742064674, 142473369, 854441840, 139035740, 643305527, 705728578, 10652322, 138913110, 904548980, 308536992, 655319873, 862678448, 508532456, 389254199, 129550314, 496621128, 600140692, 349828315, 799307731, 608833398, 956326135, 989620149, 842625735, 135771202, 862416212, 521037480, 440938809, 320266946, 248763769, 616564646, 443476635, 708752233, 442783579, 94181367, 94283924, 792352497, 600814622, 253897205, 343770488, 710275664, 12946099, 602291279, 334396099, 66502283, 131852772, 206587492, 663606089, 837354577, 396597273, 342258212, 43871562, 867973666, 461717253, 381630778, 134372080, 516647814, 5616833, 247852765, 922278177, 269713069, 174468676, 824710622, 927270186, 234885195, 767884675, 674099711, 629228763, 826475622, 912907552, 381730052, 326952553, 925431836, 606337421, 97529742, 521112416, 577841385, 224388469, 399277485, 799334212, 877518602, 551915127, 578830729, 701057974, 472803381, 495952723, 870040802, 585350734, 110887956, 937282914, 804823633, 814372503, 213883392, 778032856, 320551659, 389786347, 832032943, 249621779, 77769345, 730869829, 169678330, 985041364, 409495128, 999982627, 104593700, 630750176, 220418243, 715666992, 366699731, 621761838, 784446040, 321161475, 950014826, 832217626, 485895092, 60937561, 190432955, 16015023, 293401277, 960143062, 944112978, 218178211, 950068353, 555544132, 84590396, 421254799, 773605340, 895103051, 963434624, 45745258, 853630996, 843249346, 27892004, 373892039, 909187431, 892125291, 880234128, 226406735, 583611563, 652638377, 412728405, 763624842, 656076756, 472528738, 155229805, 960750227, 570482309, 621087012, 383683489, 985801476, 640722445, 908496770, 146875600, 183141487, 762488823, 167050075, 444476182, 472889400, 304660674, 247403607, 772249519, 647011050, 615479567, 298273242, 200593131, 944402935, 730126277, 909725833, 608093574, 734137353, 980376073, 46927247, 483760579, 942752677, 909812560, 151945919, 555662282, 910214827, 277870185, 559442281, 100148938, 937270762, 602235308, 853757388, 533772678, 996842306, 994611913, 855317360, 958608093, 844508171, 400941585, 23309344, 573739316, 524606879, 936068675, 841591421, 746587726, 357280174, 194745931, 52267859, 781747256, 390279553, 844612420, 112645336, 690376423, 218211711, 850047309, 938936941, 978729383, 241730972, 481611581, 691231701, 442470144, 63830228, 113364147, 949883678, 173799432, 879888820, 305288025, 934834363, 108003864, 142933464, 527929947, 807082904, 457693527, 300290304, 306469817, 764198844, 205752179, 184557903, 341829525, 674385389, 658831551, 126279990, 935554649, 610861904, 859445849, 939594508, 871251514, 599001103, 739703054, 882312385, 899189648, 586241329, 597661747, 444820719, 213661949, 83433685, 510394756, 762263957, 611611364, 830889783, 70640537, 514512857, 618315089, 937342825, 122281658, 815672440, 319020581, 499705316, 274422834, 940975572, 980878798, 740332277, 826425550, 950477091, 136179165, 543708016, 102249918, 215639954, 572055369, 753949057, 669426332, 171361151, 113488869, 665129711, 553874755, 926247117, 848701050, 594782252, 199096025, 931204646, 355225953, 235898822, 436669441, 81494902, 349844549, 216886432, 200265903, 178299285, 428241342, 816418925, 212383244, 257655290, 548864440, 512521854, 763357075, 96534639, 803624832, 85673861, 711173183, 453980323, 651577819, 909175353, 269591856, 978748624, 511949007, 721167265, 137988773, 558271612, 419411620, 72592186, 874567866, 340195470, 762314888, 760717792, 18022114, 23622279, 666158573, 63288432, 751557252, 209572908, 541987270, 977244540, 887365879, 522521086, 638476200, 682049631, 994836371, 744149126, 44257358, 868058520, 665390554, 669018151, 338329318, 957981752, 692472399, 28722247, 230726534, 757282262, 408840656, 66539194, 544039005, 904100930, 38934295, 374015377, 899703130, 475805904, 862675440, 452687044, 213637027, 809076628, 686019609, 926308950, 571700800, 733110574, 942873865, 716809818, 139968565, 997262732, 503640619, 422127631, 248326994, 39265692, 881859001, 281871650, 164573111, 417999405, 91337650, 535220790, 184440822, 128599994, 47858942, 350644437, 20525244, 162237578, 73424099, 137110164, 74835958, 429599367, 614258924, 714384727, 533930764, 607740901, 692159169, 120390614, 816841085, 422894861, 699592046, 784228641, 572705121, 712543900, 40895399, 426955698, 529559158, 777408506, 194031277, 438361988, 572012726, 130606746, 679335991, 408287937, 707658221, 759194084, 68254426, 63896421, 938981841, 852542141, 31412826, 352042272, 442171426, 59619798, 5931436, 848652240, 557405785, 469452, 794353973, 413790416, 231546630, 717339866, 814224710, 761259328, 569293531, 715637927, 803616900, 801884389, 793894897, 264567501, 892355933, 762572035, 473190324, 386852283, 934984893, 6100069, 352067353, 240818121, 230316041, 876348730, 653184143, 136634904, 187382996, 403215073, 663424704, 640143886, 204766901, 905192114, 146154696, 47289825, 427718187, 607360875, 477930745, 991617266, 627643338, 261291489, 100368909, 846936745, 818393741, 656780455, 773927684, 890079767, 839105519, 666328121, 488719003, 184432821, 922397341, 798691039, 266654772, 839071081, 152684094, 644219104, 814070951, 274890154, 421166949, 782680750, 95617312, 638577561, 452745832, 937127183, 239962821, 380246877, 285459767, 336606339, 61804210, 285220169, 715638013, 572414365, 147947867, 497446450, 520774501, 860678253, 128644034, 636499052, 32331188, 881098628, 314594965, 922361976, 719541506, 83432761, 88195814, 486799846, 31544917, 579003109, 881135097, 166251592, 311163203, 632889659, 808689999, 336297578, 351629130, 813743753, 102813884, 361965546, 496914589, 170871507, 271684707, 361957701, 580640291, 69096200, 530738840, 966272935, 976567612, 868551600, 179459822, 758308102, 971098025, 847183567, 815545321, 770130293, 860782814, 614476701, 640412051, 220084966, 435360363, 517313655, 194855852, 330223063, 487833151, 504751127, 106381593, 504011759, 894216455, 239554318, 513532911, 93081430, 238958592, 928665287, 749223770, 681529513, 623517303, 632344049, 800579581, 130793179, 713495617, 587188901, 865188860, 462766004, 906091784, 231432718, 42850671, 854726594, 244093281, 512450699, 956519123, 204662748, 318289352, 579259058, 995278506, 19966998, 237124823, 567213824, 900531003, 218342001, 491823276, 319347051, 892524386, 154755369, 890354872, 485366193, 837368211, 566084130, 641565019, 287823302, 298923274, 923388396, 138409658, 284368657, 536049584, 118413458, 955873473, 53825828, 937720311, 974677108, 827741536, 381794571, 435262179, 639287549, 208235001, 288071879, 208433498, 739991069, 241393320, 973382434, 344127473, 807204275, 109702691, 590081556, 586102470, 376669458, 886114464, 226876849, 977358703, 211476682, 387252239, 547312772, 641035235, 307576804, 633586398, 177390274, 393552819, 379013803, 981493329, 940576108, 925462496, 667544857, 814462982, 645974885, 128930788, 164123115, 98469962, 307282582, 723306474, 748041705, 727559233, 992416160, 893761116, 927075915, 210242437, 976663697, 449165652, 143148826, 330276275, 398638630, 871274235, 277540341, 433223545, 651770020, 876795154, 502620262, 478040576, 450215153, 915149601, 543408502, 616575590, 390433334, 411279091, 803835966, 765330182, 438212596, 332838317, 466967006, 394341182, 768988676, 225677251, 137270347, 127670475, 610130485, 639472031, 635674871, 390212380, 12485352, 622187778, 617482464, 652298865, 465384255, 460162739, 584114392, 97285133, 883845596, 693332518, 76153751, 29249933, 407775489, 97661218, 273927432, 523576585, 92372540, 728901884, 53442047, 302098902, 873516552, 62054711, 583199284, 704158105, 152548846, 429564522, 645024331, 794800908, 78913986, 50009324, 657223707, 736821736, 606003002, 726927743, 712736290, 194261012, 494447223, 535190135, 247273706, 546682767, 374207489, 903585543, 915737374, 939201144, 234556060, 533951387, 771962919, 338718846, 986423039, 914370398, 95226875, 382336949, 662584847, 340269160, 248483354, 470967788, 728725968, 466934241, 534471796, 881692013, 230479545, 379904230, 338215243, 318656702, 104883052, 151730952, 976975231, 232155713, 951198518, 918100682, 214630368, 428286483, 414528801, 245616516, 908239634, 521226205, 782086579, 427397355, 392020524, 581010240, 927524606, 349401164, 285354569, 448537013, 823975806, 382465002, 250506950, 798808150, 382346939, 195562197, 695408241, 802782773, 729343268, 293596838, 70500571, 668781903, 545348230, 144905689, 804091690, 150655098, 886698831, 75267747, 893576917, 559431529, 191975545, 554859536, 18096756, 746567288, 125928704, 891605013, 576033663, 925356268, 663638119, 232189500, 818532107, 250516720, 2315464, 31102504, 707670272, 310341594, 468510832, 551110480, 574870655, 925544507, 681616496, 788333896, 650917473, 560758297, 111569264, 842255575, 913646817, 578908689, 292256582, 171018668, 975170407, 312508217, 411612946, 331241059, 683106522, 398612112, 625199426, 896041541, 539673152, 635713515, 475876707, 334446047, 359693198, 755502825, 41100554, 786137207, 958587167, 563951019, 716000312, 812839636, 278627633, 840763795, 882821823, 972791859, 307224842, 901776573, 624051381, 827757436, 699068299, 854683094, 371241394, 951529260, 496597412, 652637482, 837431147, 21089965, 464838134, 779282536, 671006485, 192804425, 206055930, 23760205, 866740682, 49268483, 95962094, 864054022, 378323558, 734400464, 526969275, 584986917, 271694321, 580534194, 999651458, 488350207, 499296925, 56805446, 804747564, 363322075, 924916630, 902066118, 806215172, 664353061, 518292421, 888068686, 417505305, 86879959, 823666649, 411448204, 705993118, 488981154, 281487532, 966416878, 493397004, 300826413, 125804414, 97381819, 127495781, 980710675, 909045092, 594072642, 26255185, 796553574, 229658923, 980835834, 55385113, 552352244, 77544969, 542268243, 527611920, 505971000, 913689003, 315615021, 508409711, 337638480, 467784613, 44917229, 414206139, 487301763, 914329243, 217899058, 104418525, 868450522, 362319724, 414706512, 691137477, 307146782, 571190616, 773203648, 652019585, 450483992, 519301802, 871180480, 988781748, 547079931, 990430342, 249640515, 525596923, 34467639, 240381025, 338572984, 419378822, 223803808, 325548960, 358936855, 535870289, 575861770, 403478760, 628770254, 357892256, 244624903, 972787366, 831875134, 902587738, 823944715, 202021529, 151956272, 190332948, 887414206, 583591361, 296985527, 545315767, 90659690, 277159930, 406159755, 835727440, 251527557, 872063594, 67911442, 673584969, 530013805, 5692192, 985643158, 717333278, 411004349, 186228878, 98796417, 250053442, 48520036, 87557258, 580152607, 423358617, 726471847, 751040013, 148127202, 283150641, 951782185, 881035141, 918658721, 9912402, 967779847, 674270613, 679091521, 868877312, 184081622, 85487207, 168163906, 43742570, 175603454, 22855325, 208993781, 697011379, 608820271, 4054153, 638860081, 273672570, 318556825, 7747608, 460275562, 20794958, 230991488, 849585073, 413749000, 571484199, 971503507, 717070807, 526306621, 530781114, 620042413, 767408866, 453791715, 980701857, 792551934, 964148491, 499395853, 54938896, 269260165, 609427695, 460154009, 353229187, 933838952, 664384635, 200517290, 377617089, 144024476, 519946588, 613897340, 954950376, 508670024, 885319998, 903814716, 845574007, 767394457, 53131253, 342219644, 364942629, 221536513, 919395927, 31803873, 794980982, 946404374, 583408458, 81178689, 118668427, 931395896, 378845780, 973901046, 632923313, 997644144, 772294835, 332242413, 90101407, 706782441, 539285425, 949776958, 497701956, 187777411, 676270998, 325571627, 8326525, 945082073, 909756032, 304066075, 713957548, 321399845, 847307861, 331772435, 963028581, 484807615, 984999567, 202765612, 452177476, 332204325, 884732606, 611112184, 9850400, 551548985, 685251216, 555285594, 883457801, 153418136, 234993980, 435263449, 975418989, 131540712, 385508001, 378711013, 727673122, 768714569, 322502371, 792857983, 248037118, 697011317, 547403462, 522913563, 120480094, 405109714, 590791712, 133358552, 685587018, 798066848, 425520757, 638827472, 607013511, 142175604, 388205612, 767346163, 451761201, 801702887, 478728656, 819179457, 292195712, 679610881, 493541232, 644331909, 441597279, 337219090, 900097079, 481153362, 630860432, 778453696, 869440448, 391946963, 593701412, 543396509, 358964674, 173370410, 543704719, 38355573, 301530953, 866667815, 63157013, 340935639, 505001734, 181053759, 163238927, 446868792, 954887345, 920286183, 746739353, 18940541, 713138023, 458201345, 11166433, 116204699, 664340479, 632396386, 177838138, 237644222, 578261215, 223816276, 157440659, 771911423, 713061115, 358919920, 776685360, 487960649, 20317843, 106890020, 333513885, 447246279, 422561916, 622091557, 225005129, 45404173, 284174910, 947941571, 530041397, 604580418, 398913041, 728114544, 522742294, 115220267, 765779093, 133446011, 756417943, 933282946, 140635326, 81567016, 238395439, 917990043, 703851877, 104862581, 11098374, 722513684, 571239269, 957598268, 972362108, 291102674, 738343250, 921522583, 843651269, 20189671, 790878125, 231311449, 740981445, 669295367, 572105219, 291246871, 44530129, 562831038, 14262637, 943472897, 584458912, 861427010, 919213068, 881487425, 62973032, 297064923, 633602006, 478631759, 550813290, 928770358, 662131849, 248287420, 433549757, 393587837, 234998678, 752143347, 979282197, 368654312, 400019443, 626652166, 288943967, 689834202, 666695315, 134216473, 610498122, 833801593, 229089647, 223659368, 484876607, 737308125, 167331058, 2689655, 93837365, 820236228, 783976727, 662711567, 801221856, 687170806, 407682837, 762801549, 157711360, 603871847, 339062317, 888125032, 906029490, 96197535, 205413627, 592545252, 268473841, 937762336, 750949359, 352280553, 806689058, 254844734, 88994820, 854849203, 872971180, 594090493, 490010431, 55917788, 473216152, 465756527, 163349034, 644799571, 416519307, 375156043, 741838556, 379745065, 690953888, 977580942, 606609922, 388704608, 322126696, 28911393, 562662762, 500143428, 809198787, 850098402, 148724182, 992368927, 299830765, 897424341, 228370891, 452279774, 855816199, 485105739, 625184121, 379039627, 575058232, 109892165, 888409911, 773238494, 381458138, 383746535, 763613211, 520180524, 759567013, 634690389, 310172663, 935801492, 718550637, 553653134, 679350549, 852495699, 41625283, 641814388, 926957733, 881838740, 456547302, 13397495, 520292443, 65317694, 771970046, 854120390, 901903908, 117623581, 278439108, 113587513, 270953501, 993171619, 938482350, 522051783, 268924967, 881206070, 212788268, 623853297, 798079608, 728905124, 966867770, 653712715, 615806065, 795651943, 118287697, 920052531, 261273994, 62091991, 547548347, 489998096, 171901713, 772342113, 959901414, 901273571, 349719849, 219990792, 700707398, 996236165, 278344350, 491780541, 728016075, 427521596, 324362233, 917926331, 258085224, 159942096, 802550481, 825716105, 84910421, 122441817, 436090365, 83166638, 749019528, 573553918, 104419005, 75025930, 694761218, 966965884, 387883452, 167311476, 811897347, 319129981, 984641182, 907021698, 776076407, 197537342, 978090576, 761447549, 425576184, 474092657, 655468963, 896711906, 31572034, 684794344, 632421372, 463116386, 878904101, 635188937, 341867016, 856540560, 610488376, 983768268, 16263096, 259694215, 177833665, 284935782, 829415587, 319451168, 569073678, 653188276, 351101504, 853253948, 173822252, 528072849, 889902390, 448101099, 489777915, 840481977, 630598964, 710639273, 195123964, 463275876, 491155533, 803125050, 220326319, 653309921, 368398013, 68486994, 827128292, 637608161, 717465097, 528303845, 268174628, 444799650, 931161428, 263008556, 825347740, 551567512, 121983096, 671589573, 661147931, 812070403, 391623281, 736832370, 424696971, 781827588, 566216038, 381402339, 662993172, 929685843, 192627161, 701703925, 287745536, 945450170, 102258012, 255829065, 7084213, 746777427, 549739978, 180187950, 816845704, 687294428, 888707155, 142588470, 762783366, 533326098, 478013756, 60939317, 662187761, 862426588, 466826249, 307450041, 621348185, 666156624, 711982210, 803667115, 667661955, 407380441, 319134879, 262803522, 779292048, 691414739, 453795529, 185183224, 954267798, 50548190, 584015291, 980969230, 400542442, 325597488, 935642100, 675168157, 404704446, 288388001, 631686508, 938695631, 389010170, 391489883, 726728299, 592216716, 537965094, 58586436, 388157076, 634544736, 181304873, 866828587, 249847758, 322858583, 133386536, 252633891, 848677142, 521699944, 588341256, 543261652, 979056079, 455508066, 361097841, 216635854, 320874688, 564222478, 552897293, 419515191, 125672440, 872206381, 759851135, 354306216, 597501212, 895767051, 529930455, 743338121, 673362889, 375021403, 48536164, 141462549, 85045283, 884590894, 834559591, 338082654, 891070452, 916638082, 951407365, 797181877, 225226424, 439434542, 591932327, 325814969, 906667475, 923862233, 573714027, 731389616, 573886343, 594446920, 224856828, 400736358, 791856085, 278035343, 459227454, 792371041, 471789939, 110992585, 154047603, 508003729, 250813748, 964103054, 863137741, 33324003, 571348238, 467501696, 202586164, 758804365, 82508570, 417390468, 842610768, 623781048, 360302682, 842161036, 597570129, 40027034, 860727515, 76857568, 754751043, 219115752, 901365375, 947402163, 737369877, 401992442, 229228894, 597137333, 931688386, 49622922, 731847144, 207783437, 243080504, 439566037, 784821628, 109312345, 558772056, 670651134, 589921723, 22254415, 741268607, 825859882, 772662894, 596909991, 458658915, 818481332, 830802216, 792698265, 591132472, 599734235, 399880373, 895355031, 656516135, 446936339, 169353727, 221224938, 869146455, 902468500, 870981528, 110409262, 236476847, 262526291, 425101717, 991118799, 913362798, 815818651, 236952133, 988782751, 812824170, 134394647, 745971341, 819239796, 916874668, 854451534, 906936027, 610941815, 517493644, 120798904, 95089714, 78799980, 698210024, 574110888, 242834266, 225748191, 254466190, 599460372, 824037415, 129714838, 847462667, 502040870, 72019134, 210079352, 165059810, 876762586, 162042041, 793366073, 966247512, 692893842, 451893178, 122182544, 287677080, 580883055, 196477145, 439112237, 173659486, 415086380, 205220987, 112647149, 565031370, 223629393, 841097069, 432554640, 183807016, 268259717, 571117268, 812545508, 437380639, 903547263, 783985768, 942794899, 160694689, 897207651, 876265941, 301848581, 255264567, 335584090, 655852543, 688162120, 18306602, 568075118, 616930726, 485550977, 425585628, 275470197, 913879936, 435972471, 159983293, 533340679, 729496771, 458057177, 576671402, 247562747, 824210776, 408473047, 658948385, 707039292, 367979994, 952177254, 757249518, 420237467, 445927227, 325705065, 733934771, 835100696, 827273144, 303668891, 392461534, 505284772, 242700137, 226138503, 767463947, 949457019, 920563077, 883719131, 362525556, 375621650, 933735471, 149734053, 665079249, 882328189, 71246179, 164006904, 270767265, 535370908, 550191323, 729885278, 557141923, 792593163, 805290206, 403226271, 23108664, 785677141, 844280792, 363960080, 75847140, 612557903, 815290982, 262430372, 287784928, 888532659, 287191639, 790988975, 709363160, 283304652, 307957217, 453694100, 184872300, 49855762, 908429056, 447514682, 611037119, 827737832, 114528571, 706407670, 710655675, 802588033, 142673907, 379498106, 729083146, 790093890, 728623439, 363730713, 423684512, 171763897, 656840705, 600729280, 901426624, 359698296, 150726857, 726685229, 475205746, 38484880, 179917831, 543975251, 688207973, 36313145, 652600748, 51819706, 995820544, 368844646, 350843564, 576253806, 633899454, 586668023, 412665036, 808026104, 919635248, 894843830, 85152845, 821558769, 876755084, 790674639, 430171016, 790037234, 743229417, 575340275, 312358401, 893655508, 671335731, 939662597, 348539828, 387611530, 88454237, 936164136, 879515170, 63965561, 741415701, 44280574, 545580662, 203641733, 394928252, 49421583, 763411654, 521799677, 171393491, 686139749, 208953092, 158083865, 104221217, 868004691, 192154689, 222063632, 697879610, 576095039, 191550054, 909872831, 873255000, 683790670, 167536497, 545085508, 984763988, 121030243, 301674566, 223115685, 328452844, 527723331, 774593755, 311253153, 674289385, 720231876, 63321085, 612595161, 130286667, 806989113, 556443607, 817211446, 72220580, 520755524, 378319988, 372159221, 235378434, 478738937, 397284608, 845432315, 470635937, 489273239, 453012727, 401907922, 921690863, 839158900, 943065254, 781063736, 563563585, 224945383, 322268329, 242504650, 275517228, 270547948, 421911587, 767684920, 471525355, 837752351, 666262379, 832700365, 376200079, 679571707, 753931353, 346912442, 385949162, 534056337, 712333120, 933092909, 835758701, 932508884, 112983277, 88794717, 964026498, 328655242, 285410454, 294776892, 202003380, 176088957, 766926270, 711474037, 244916578, 533225397, 842931038, 649309118, 693142946, 471745433, 379887345, 531102516, 919623947, 879631971, 997438016, 157906821, 625439833, 448718219, 13683975, 414344707, 23589681, 475146074, 199217227, 788627261, 600784885, 177430038, 595320824, 975553306, 124989643, 867691499, 650140017, 629582961, 738130161, 825121572, 590689557, 121458764, 258219544, 354890347, 290241887, 3138117, 337130538, 19451890, 576299177, 368399207, 738615294, 471384283, 956444558, 380686898, 11977038, 262543578, 418318124, 781964223, 629933779, 543544763, 38975439, 746014229, 724057664, 832235415, 895853974, 76565648, 718049671, 433898898, 645706164, 532431891, 28274948, 876549332, 36252375, 584045688, 510345333, 175810628, 256726802, 796815549, 121822906, 11274347, 781838977, 55621720, 824912596, 786604426, 797891516, 222245143, 720203127, 831337905, 509653659, 565854320, 185788683, 386906924, 282826983, 851027280, 218727515, 197675225, 594819179, 851649835, 16495202, 785025364, 131598987, 301333809, 102017050, 64051170, 144890800, 890727031, 682127258, 184742615, 56982910, 616827047, 853119399, 345538431, 291347702, 894283924, 652034538, 747208012, 15624009, 125752169, 739953843, 345231844, 344520022, 874773586, 459676952, 662851448, 873339592, 852381733, 444891814, 680682145, 406318085, 395495536, 606325604, 524303837, 560503643, 484215281, 882742965, 666637562, 919962134, 80793925, 82334712, 320954554, 527440876, 728987451, 279804612, 885541843, 271724015, 436504359, 497927961, 831838451, 547512111, 599063249, 487312450, 861051116, 463268542, 996461453, 325124005, 501773635, 76722283, 340444839, 606528514, 931197942, 711521557, 630653238, 126539963, 469650694, 945445627, 320035575, 425925332, 974369893, 646309468, 780207211, 888904107, 454218914, 437377026, 493158433, 36092513, 203429830, 599620780, 720818713, 377414251, 649305598, 841605345, 838353421, 359036333, 821959276, 12955601, 536792759, 951245309, 531945672, 729802359, 794472730, 25335565, 384893628, 262310254, 178458304, 978420882, 27489735, 191721741, 696201622, 194688465, 901057268, 274766244, 39851636, 255066715, 317286431, 412001350, 563575169, 594006816, 864622826, 777891598, 355937196, 768261056, 956465993, 573578026, 134954098, 407033878, 367544548, 323785844, 966383661, 456492882, 926040870, 266950291, 935865430, 568612772, 813707782, 640256330, 440051143, 521721007, 781954796, 819425596, 835874200, 51940350, 623809231, 121347887, 111813647, 76001019, 536716255, 444323693, 646610971, 836568729, 631301826, 23998532, 16440822, 903832297, 414869840, 991768258, 285966840, 996757943, 951218600, 613032314, 353050737, 85462660, 412787115, 908033047, 710316452, 330655209, 683873045, 722753185, 326646564, 468403006, 906602549, 457856828, 668508206, 26014085, 546050243, 233423601, 923924298, 805829845, 546670894, 231989978, 8711537, 147251693, 674683999, 389608510, 220715603, 837648626, 760386690, 660625349, 411410566, 450984772, 64514444, 468939755, 66577800, 944977182, 183875028, 699157303, 828678253, 727027552, 565007934, 969628529, 476115626, 989814368, 991051404, 731849295, 993944394, 878381490, 183984090, 410385222, 450223598, 411822393, 216965858, 137791210, 571991481, 708502855, 29089559, 403730235, 11986006, 501898830, 375785879, 841669744, 448083530, 131989282, 461238264, 516415421, 519460779, 887938980, 3495493, 598508651, 514407038, 701451757, 516835110, 105458796, 373705855, 162684286, 651715059, 934966223, 672370680, 764556048, 690185688, 67257161, 194541885, 610581021, 200051979, 921454650, 851787851, 181910320, 957010903, 188845968, 833531053, 268583857, 405455784, 908688542, 177273218, 546526975, 845638271, 591756491, 633815217, 178214016, 14265891, 645675617, 493404115, 625964556, 819798271, 147305242, 995041124, 418637714, 691123702, 311039906, 275129064, 298199244, 713832761, 455934675, 484423812, 217738686, 521348172, 865461581, 452931521, 694958785, 44748928, 216759046, 481993820, 856768390, 815443337, 68536034, 203817794, 736264225, 791839257, 63590536, 206857488, 544764877, 172743072, 319182166, 441052157, 462435620, 726817194, 489357249, 418502421, 839377398, 32587524, 702668383, 137877931, 64221325, 833038651, 662887587, 499835202, 428679150, 246794417, 84964988, 911083466, 572269010, 573118639, 412448643, 674435910, 267547738, 436841942, 609716018, 824615141, 543321984, 926191543, 370140913, 916060299, 110197790, 365926104, 211350324, 677109124, 776937691, 744476864, 774889902, 417047081, 256813403, 70398587, 904833308, 616581288, 303024991, 50178569, 788164336, 364188977, 688594852, 566925941, 29353042, 590958534, 841036030, 389522266, 252285036, 592069387, 762178817, 258416024, 199887122, 438043387, 123777593, 246668894, 248245465, 689113350, 86744162, 85589464, 823986334, 59408935, 105699441, 87800880, 72308138, 393846139, 420624912, 681292058, 438096673, 561906248, 565976040, 421431768, 994837910, 453728236, 101196084, 958882570, 52820605, 182668073, 638430450, 618828566, 399559015, 688191431, 390178168, 340003950, 476573910, 522574851, 836089563, 333074378, 324108492, 927235391, 500491144, 26744424, 612843701, 121319743, 45772115, 127290836, 818301469, 120010291, 217040351, 663734849, 400686147, 268249326, 569654444, 857825258, 598286490, 181022445, 553504842, 694120462, 292441257, 667967145, 726030183, 627684362, 696231028, 182838129, 239464817, 421077508, 497383119, 331610908, 549202390, 373211188, 62567231, 404926127, 487463714, 620440535, 82901602, 67256074, 596598392, 728218619, 26843579, 240656053, 572867631, 454273257, 216793540, 444326906, 212138938, 57504998, 811413926, 92661697, 457952632, 197075365, 273338380, 981537845, 916392440, 269095157, 623787382, 582957835, 922589129, 61928253, 41695983, 1114867, 250679260, 511779644, 730026107, 378077782, 172305200, 797307182, 523280129, 237726864, 387353154, 553585371, 492929990, 731747894, 863945582, 210451014, 787308760, 60781888, 367380687, 984946566, 171547266, 661907950, 671983401, 939820637, 156539808, 386740173, 957444264, 325857058, 375348966, 671100344, 421549191, 764640387, 875660594, 633106432, 865383519, 69362146, 719437548, 59701427, 822580802, 865717551, 925305673, 167146175, 256867287, 445669235, 145356981, 339576785, 934448516, 335618299, 91905052, 848074471, 697804651, 93273269, 790564224, 645372726, 802645298, 108382971, 155201146, 62607326, 602632386, 595402591, 135110497, 661706533, 230084566, 68450496, 961603770, 645923521, 968071887, 168494170, 556377909, 35768659, 214395511, 111483472, 527013130, 720750565, 619754423, 186741927, 832469848, 500835367, 387099367, 160572033, 830972679, 917589286, 485132922, 525669363, 146108926, 501200552, 848856070, 944911877, 41320991, 740802817, 34263051, 683537959, 758721221, 175349198, 896338757, 29542943, 698534678, 900489480, 867408787, 669852482, 981863278, 412765195, 809669110, 903236530, 311136801, 222469979, 435484726, 266583447, 599427229, 464835329, 529964144, 346530450, 714531073, 180766293, 272507684, 12326671, 628465850, 617929109, 323504512, 25151034, 877664480, 702805651, 798898175, 535037559, 24018663, 830235064, 538354595, 361428759, 901306445, 186889656, 4225109, 205807030, 167470521, 80476365, 828323175, 692448681, 642142864, 307814215, 588515187, 914011589, 738424462, 873661535, 627404931, 929041157, 290513802, 761568193, 10068165, 589697962, 645327983, 357162583, 838765122, 462917779, 755819420, 882971405, 438833273, 215252406, 947754772, 125007745, 51097910, 581049060, 174432706, 60075501, 617803332, 464634162, 53099501, 920456699, 154635616, 465764304, 160576355, 544991070, 186582452, 872094083, 324841651, 616155786, 629112067, 877637680, 94023552, 356049186, 451245670, 190790189, 605092789, 679701044, 974830731, 237255795, 338489080, 453242826, 594967835, 298531523, 912993547, 704987945, 830014409, 959237820, 459085732, 908445843, 807377552, 112789383, 163974574, 539558358, 645869, 750998792, 795475868, 981891869, 365954921, 880369623, 239145581, 243106408, 937791534, 46110232, 260625061, 361794224, 930746, 245122342, 441199986, 243894044, 678757670, 68586219, 750416153, 751141691, 329052903, 821860449, 829444684, 29693029, 688832897, 691139994, 347223014, 321793030, 514653202, 453022866, 210198295, 262685712, 324841065, 706988967, 129807372, 163422061, 393923969, 818896122, 624517716, 59543476, 739211050, 118838014, 162120268, 622846579, 125867963, 946202497, 183496950, 31822624, 86349448, 620634409, 772342210, 413854534, 153614782, 389676165, 782796790, 197730536, 937255679, 838792560, 67287703, 257415278, 756979081, 627457375, 505270324, 431700759, 830128922, 183669594, 445702379, 894305854, 366063645, 195167758, 70277643, 913662365, 134682345, 831620747, 580932227, 741465076, 229994073, 850804745, 723717532, 642975915, 120661234, 945710673, 108632737, 488793874, 643120305, 861092972, 765759497, 124103582, 920128940, 705375243, 920685752, 753535693, 932287984, 999102595, 954687811, 495407980, 792562047, 824515692, 526241887, 265163648, 612663937, 444786994, 554325704, 393591852, 821127317, 269053297, 365833617, 217320469, 567081368, 748909615, 412709665, 367092944, 998873345, 569835350, 591873895, 320539428, 12454483, 768030958, 272479635, 814672512, 667440675, 60545536, 917626764, 578864459, 432131283, 722760715, 908911502, 386289416, 230321430, 685723160, 455675853, 437956393, 263440707, 633473766, 840675659, 194529518, 355199194, 404396595, 3603788, 800809369, 508391764, 454563511, 508110572, 843014338, 811609364, 934810003, 177725969, 134707752, 344283825, 706085827, 449749696, 467644988, 716082576, 752597010, 7193781, 218523565, 164841658, 655831076, 769262783, 133194128, 795771984, 914223292, 617395297, 753186711, 488123938, 618343519, 528164610, 321548360, 720484468, 925709297, 874274609, 589732866, 25397614, 986913681, 625137847, 608564551, 893673748, 347484413, 379555863, 177553010, 911553260, 980874415, 113265970, 903262038, 149600616, 690992760, 152326329, 374428129, 850800373, 144085669, 917176218, 374902943, 62186563, 563968478, 4330611, 783591821, 931629303, 436163114, 364705501, 383699549, 602684152, 228294784, 997947927, 687390735, 86403932, 98334099, 177185374, 889652031, 217362800, 649662572, 641553204, 598660200, 404650098, 303319951, 251936194, 962426474, 396845082, 162343561, 180327436, 882460209, 252212540, 33829521, 639687879, 96724652, 922410073, 13628354, 667765117, 315921120, 890564693, 702631041, 319629722, 646512983, 224748565, 549115954, 99692988, 86630230, 289171046, 463986635, 723784171, 11259204, 358271790, 24407235, 879636298, 641248512, 688766517, 371100743, 751872178, 73944537, 928046837, 608167410, 710884031, 652016251, 987595300, 840420618, 658405832, 350381980, 369989755, 496368091, 318703417, 617461100, 678634988, 199360577, 960013572, 673454490, 875357169, 798494933, 295433961, 426809540, 676724444, 335746689, 669019441, 322346126, 414864531, 799753725, 278939891, 508133097, 423788982, 302314442, 722693003, 621964029, 675908443, 247956675, 245998457, 536814741, 913610629, 785983095, 410716879, 101798046, 291596284, 456638102, 513378448, 410535089, 795320033, 680786764, 664084541, 804285919, 569022641, 855669673, 399181849, 807078001, 227291187, 544922341, 3527604, 208852589, 397372278, 566624113, 216115979, 528444227, 536927586, 539594583, 678498118, 214991011, 819622142, 94131597, 257703788, 129180513, 162947759, 156607852, 631432639, 22634598, 279475231, 218668421, 646254675, 275687956, 536640694, 564137330, 263110389, 495342344, 737627840, 537865287, 352125309, 985867673, 419037676, 522886675, 621832378, 25593453, 752597712, 566402029, 925438872, 825690200, 817733707, 984717621, 166670242, 891719795, 232853254, 217693992, 75758252, 613727926, 990465848, 721473483, 56327740, 950678343, 977675639, 434207424, 691506444, 255850776, 508396534, 672311043, 705875280, 117690340, 756716768, 5316521, 433033595, 776976447, 809203818, 276176411, 886380803, 341583557, 388069919, 933581002, 852868788, 200257573, 801663182, 806063295, 225891685, 218688829, 503489218, 748806965, 22761385, 916319932, 612792397, 570189069, 919870057, 537691610, 261238715, 171963578, 235147452, 622094326, 833343137, 918544191, 300757201, 224132407, 657216833, 979346839, 729024682, 815608944, 250962493, 243796542, 398027520, 61940752, 650478887, 965018879, 254572269, 32721121, 326707981, 282632928, 413832830, 492469841, 966602313, 409503860, 872764787, 514267941, 841826792, 159939592, 171262920, 401251692, 2927120, 48966683, 129526315, 623142147, 738666031, 174804882, 64899612, 108936370, 597661636, 589851418, 127858515, 194069959, 304694501, 216939833, 139854844, 926971059, 276353220, 173945902, 771115242, 180066803, 535374189, 185969706, 50889914, 879123992, 365568257, 14674608, 3473797, 610478456, 333482726, 432014471, 1273434, 853082332, 322836879, 434896407, 611251700, 263092424, 502357838, 405224787, 437790842, 190499856, 145616760, 693454353, 732699847, 467828643, 47606982, 428044718, 411102847, 402602090, 982228787, 851909341, 242479192, 171590810, 303983445, 555338218, 447444989, 934103858, 97646685, 71888437, 130004725, 288092227, 967611541, 143011683, 645117147, 143218506, 978431691, 528229826, 342712351, 178109168, 429381945, 753284384, 92863914, 261886235, 623419893, 240237511, 900334790, 793758285, 457978620, 932142801, 762680086, 11987587, 512608877, 918950076, 259229468, 4269494, 18636948, 981401179, 610478119, 587584239, 521018094, 219918277, 16689753, 721388050, 71759491, 320593534, 741021241, 904612988, 671318205, 543258285, 391331653, 815172969, 472921113, 6346250, 678906254, 290864507, 407088931, 176655634, 914380929, 989063993, 625326351, 999322534, 196634858, 768110196, 512516311, 424034367, 168477118, 256112883, 14884490, 586866098, 687791858, 405865236, 375672305, 645886450, 648964249, 644570314, 570432063, 59969527, 751215459, 149942451, 900143297, 267946075, 79003680, 78954313, 851697499, 137511671, 621142115, 956995256, 219649249, 274497951, 111876437, 493186739, 739045751, 639994381, 795984602, 128249865, 386710230, 657936151, 424416886, 312772318, 389014079, 110640604, 525124576, 700984094, 358561022, 245819481, 573866636, 257871186, 960956923, 57505209, 577992488, 277420464, 308154006, 295640489, 510538676, 920942945, 199991785, 624153999, 676951952, 234694175, 340870474, 941035516, 12773744, 48633577, 923790333, 752525124, 805272461, 160782206, 394886702, 917887087, 63068328, 437845662, 236321443, 165195041, 387761917, 35198204, 168214652, 393934417, 546512767, 692332211, 97362754, 775684454, 659713849, 788558770, 163402131, 90240482, 432864080, 264632347, 991211129, 279488562, 358062039, 218893220, 779467430, 180284379, 902311527, 665882660, 620432408, 18369784, 760100541, 299054059, 432021504, 736340526, 871394383, 788191197, 880234839, 82036064, 705365916, 394490858, 862915693, 745709807, 701934306, 802081418, 889452076, 963389145, 754964647, 927895661, 165444774, 695416374, 946563794, 748314161, 662511605, 68350130, 897492627, 484873890, 572547657, 433591110, 537404517, 8930307, 343976210, 345027127, 239344496, 975080239, 909615971, 629921575, 869964224, 337428328, 823093952, 470413175, 527974137, 718395215, 662563287, 533656378, 542646973, 802527755, 512437800, 7370941, 261042907, 653417425, 977352864, 863707948, 328621446, 142179202, 740483938, 510524022, 797405983, 363586804, 431824906, 685147701, 205538480, 452504197, 809152966, 646251349, 727154603, 519547909, 715081597, 276967386, 50967279, 978373903, 219779023, 729561001, 85869024, 794952971, 269026989, 523998565, 519637660, 663291263, 521052753, 973690533, 925467424, 156130575, 155729748, 501194945, 761710471, 490306437, 482375260, 341733568, 693700167, 725031766, 676978737, 269850694, 816961906, 934893082, 122337432, 469953132, 775097950, 561440860, 58846075, 706282037, 90850140, 917133798, 109777365, 901974525, 490546893, 653213923, 901851481, 867767630, 272368428, 126231383, 465644620, 913062305, 941917230, 813578086, 273255769, 582694848, 192332629, 344819683, 250525282, 579009455, 430937118, 517163278, 190041094, 461307340, 787521347, 585137159, 102974346, 143318033, 894969852, 61658639, 818092790, 876268755, 44451576, 559789603, 630559381, 37617890, 356177275, 841647678, 904450401, 931163947, 831620571, 885112093, 92193298, 500969105, 487642887, 427538956, 540751137, 294075643, 771338686, 311351767, 870485136, 641027057, 532279596, 695908849, 778194104, 667095749, 77535491, 207104965, 209443874, 30031781, 717760350, 609373516, 353286757, 723191694, 146260469, 489347857, 899936, 213638022, 985606489, 329189595, 820837652, 432651145, 939872314, 759419820, 88287126, 956966224, 394486643, 241428064, 725317802, 486194627, 835910089, 8680988, 182249958, 358961540, 708956045, 790215528, 879554115, 578400923, 44210669, 582796462, 165248660, 713817131, 220960570, 553315157, 757658885, 982213327, 393312568, 242310564, 795132158, 748349050, 697538798, 239949498, 160232751, 734781060, 556810288, 829257072, 687299714, 683957020, 989129975, 398165312, 389734499, 19745136, 658684268, 98406648, 392316027, 751727186, 539789671, 867754015, 136338178, 45098410, 493919460, 880412635, 908839631, 68541610, 850829588, 161979687, 559607904, 903921977, 345088433, 282248290, 471747905, 259658888, 520220622, 981066934, 209079755, 112504652, 16093788, 979256450, 356885980, 426828204, 802465207, 870847467, 934419962, 29420639, 290873438, 146456116, 887464171, 357931820, 566193341, 617575147, 393824865, 21751288, 227814911, 858772843, 621356981, 684219472, 713786108, 901731410, 452251047, 174504418, 541341339, 886326836, 200861074, 506473117, 162100235, 308738157, 88491141, 330288708, 206700698, 303912371, 405859863, 110695475, 220420623, 295253393, 44617701, 658202902, 332688958, 158248932, 643817926, 514380239, 17642907, 226569319, 248808722, 4124113, 606501387, 151576188, 110968338, 794130320, 705786921, 560128040, 696165693, 432481241, 492208462, 751204449, 283988997, 434542204, 824897372, 250578730, 527863486, 915661097, 71820798, 790170193, 111157730, 985009033, 668875383, 816009052, 734711662, 894920468, 280606616, 662480191, 108971381, 477136419, 551371481, 22980783, 806162148, 291496873, 431101647, 731808966, 507910995, 717343915, 915495267, 347590091, 753239236, 852607987, 930382917, 556861755, 270278658, 640230343, 744474751, 362002120, 46813151, 489175389, 156539550, 814085263, 31289123, 53845746, 553318934, 487255480, 635412403, 834325433, 958515807, 797397503, 102484201, 709357917, 691127437, 481405393, 660874147, 181971204, 720766279, 547917393, 924722500, 338545716, 890200052, 745798892, 145183727, 692383843, 893069267, 698884197, 995864521, 595393825, 602740342, 799091808, 814885145, 719603689, 284750790, 284560647, 798144898, 998847655, 919751540, 428391078, 187937562, 476646851, 377478797, 797943658, 483199957, 815000823, 97680774, 84777375, 924293932, 735115891, 29944539, 235831710, 690854673, 70883147, 844039430, 693849277, 369194790, 98222089, 542812568, 443981270, 576327902, 987103331, 79889479, 817090697, 74869731, 771210110, 600299850, 158237037, 566783777, 782121298, 633219692, 535423546, 781142942, 603777085, 378237354, 236084850, 655674055, 477570880, 187522789, 481505989, 389338535, 960280140, 142704753, 960928171, 804437123, 710201614, 612319618, 948766922, 959482242, 410649151, 62677912, 916145054, 131107891, 550989602, 751847784, 980476045, 588406680, 771975257, 51516379, 110374575, 29796756, 752719837, 620818363, 149645833, 712385518, 734374589, 154228, 691766016, 407967856, 989534103, 112015936, 317787084, 213668328, 528304764, 912369352, 450416891, 73237672, 497999433, 285869714, 897823087, 365293092, 618151015, 915128625, 951268164, 729977529, 610300570, 61817493, 610449571, 341210808, 29026066, 133893314, 212617928, 499188278, 255034836, 784790342, 338056706, 831471416, 936766645, 732606666, 20561275, 462335191, 816521638, 934357535, 154494685, 109014898, 992035603, 379844626, 684996526, 162190368, 814986370, 974285818, 804869099, 300770244, 137036807, 36592889, 857838530, 132889382, 926950932, 746175844, 217200532, 316892416, 49782444, 302282227, 613042195, 28496260, 214762473, 885230168, 816807074, 405808959, 157414329, 341488105, 548884258, 285483144, 736155324, 684481648, 319929474, 409387402, 737590923, 985830449, 848501316, 446096411, 552966811, 678840044, 669050279, 551901504, 205786073, 196618259, 176636942, 64283667, 291979430, 527758619, 332414897, 560470591, 123906693, 130361720, 953515452, 267628549, 113489800, 919535088, 586980595, 111045194, 179781887, 340790953, 127872355, 653858543, 485846402, 917483202, 723961850, 981452188, 466423071, 350498850, 39024715, 692570938, 6421070, 380511146, 250526615, 543577881, 138340191, 861355661, 355836973, 987461650, 556377086, 622740481, 648134713, 69921183, 739905578, 514977629, 871104676, 338943882, 891717901, 61681643, 553853336, 243078959, 978254674, 524720642, 308278551, 678520102, 679267389, 883891132, 994615313, 806124273, 458704280, 904074633, 699538884, 112053654, 93284301, 494983522, 665090215, 407705760, 220297722, 463165083, 706740681, 305964200, 506922142, 473986433, 435940295, 562540029, 497304976, 199614342, 601097331, 711766882, 193354742, 286556941, 380065048, 116809947, 946877957, 922925297, 161995026, 979490645, 408025462, 443907526, 124791822, 555842940, 694444830, 165974034, 254329926, 694157796, 321072914, 303257810, 607850625, 293479650, 207159196, 8844942, 473243276, 200212675, 553433213, 467995270, 406551106, 591413581, 188758696, 292974147, 976609005, 899474705, 563415042, 743412878, 48042526, 283939402, 372881731, 30005193, 938980886, 710844446, 105911973, 557997745, 877037539, 221599604, 468920766, 413082035, 664540390, 219039214, 497598926, 551886739, 139162884, 175001223, 580159459, 993804215, 693907540, 525284365, 614242397, 927787322, 766684546, 693465654, 402909214, 722308345, 416161814, 927929439, 234847340, 343289645, 908447085, 929694207, 748061288, 313072740, 761612202, 962348712, 684075467, 693893100, 189205540, 280479043, 316020210, 329353986, 890910405, 848165342, 929406598, 463478918, 236453784, 358843861, 599491348, 255188989, 853179461, 341528402, 117021475, 773947, 843733239, 495899666, 149009053, 582112091, 755255812, 65757627, 344054015, 131515808, 294763359, 208406902, 189078186, 149022417, 33401137, 895558564, 768231214, 382313749, 201492614, 951380466, 455759976, 264987901, 142690027, 442263076, 486671884, 444509090, 532975145, 44624264, 464693039, 31047841, 122089415, 459368458, 836762436, 819875814, 790302793, 891237782, 368140488, 165292350, 641222235, 466855335, 459495729, 651965948, 452004212, 593568153, 900335213, 215116167, 687740103, 906600359, 131906032, 743592410, 264488455, 895823837, 549112711, 56013899, 557661217, 452711924, 410608149, 505445269, 114160595, 358114158, 866665195, 65794416, 868760061, 965513848, 176012509, 114934047, 89304557, 830240927, 384742355, 309685530, 669270407, 910197771, 403556928, 208994172, 377930073, 647215512, 452729770, 543143182, 36803039, 789024889, 435906055, 29897488, 341595483, 624864792, 113207937, 352519706, 40574513, 872111443, 480677815, 65605089, 803635431, 298368573, 8343622, 725978615, 848226008, 934361278, 838751453, 695832720, 921134643, 431654234, 365161861, 885275213, 595056554, 954961288, 79085120, 344958830, 238963093, 334950351, 746306386, 307177173, 4525885, 856184585, 120471873, 941156496, 780328777, 869031764, 749324491, 858349244, 264320346, 322310240, 480817522, 578673988, 409187713, 942842940, 898543933, 245509458, 735700160, 716627428, 50824273, 131202497, 583148640, 630688290, 150450022, 823484729, 865867060, 247329511, 338175880, 736824598, 545222005, 163453148, 227443968, 333225881, 10310701, 61841256, 251614574, 395837721, 881522653, 476682710, 602494623, 975260190, 539932691, 730647053, 799135513, 781785282, 590756360, 194554281, 86434605, 641996355, 153578299, 789872657, 62176256, 368843314, 858407102, 536025310, 228071265, 282028783, 934609893, 228304583, 309851224, 471102166, 174284324, 68698420, 191358955, 385351717, 887632298, 497501717, 140748849, 565643238, 507398760, 470246012, 202282303, 71043943, 385520149, 835508118, 867266438, 949364292, 378290368, 794079736, 878824091, 494143768, 542509940, 55566299, 385422282, 996666740, 927234935, 990292582, 356591064, 366914656, 589672311, 835938191, 746829320, 816003570, 78683348, 249622411, 754148756, 732053972, 115755970, 196205155, 949219818, 965250954, 760501045, 167268579, 281921423, 693285590, 223561476, 205169032, 602764607, 399301363, 84269072, 861558881, 275676003, 352666739, 717050253, 888573667, 600442012, 313216662, 542722452, 289561282, 819282488, 815487819, 532719937, 480526859, 422053238, 732108210, 88405093, 422242743, 825873406, 838299645, 300555273, 86822582, 256591185, 419876159, 121959856, 426838771, 947848861, 172386262, 355559811, 854881314, 91640570, 586567231, 897084998, 723159500, 692237737, 109126179, 149178613, 180290885, 860816149, 138598876, 285972095, 957320714, 555036267, 260268207, 996207092, 438829457, 943469715, 225580091, 96523748, 162029198, 830617734, 640494464, 5706511, 16206384, 23280246, 108795954, 483238413, 45159600, 918476740, 782143001, 514873613, 782806265, 461666479, 958342177, 118681107, 855573603, 581781639, 174326156, 211285154, 570481437, 549801734, 651872294, 837243181, 361033419, 820712414, 803099515, 836715691, 230721231, 308528289, 978854535, 807434316, 66734947, 415207902, 82369553, 853054472, 591543910, 168295747, 320671660, 889878421, 855613296, 797116719, 726287729, 674142662, 53145704, 863716812, 997826995, 243547734, 827564013, 103628398, 317559969, 26025272, 856562893, 958779856, 345759705, 387359493, 725909164, 518974626, 308400085, 169691165, 840322433, 605404289, 121046524, 779414092, 368708983, 99769095, 287951829, 712313285, 628771854, 954344494, 199189490, 882758878, 282881422, 252875967, 311262976, 191118247, 800154145, 143111007, 818861319, 917369068, 266183317, 180820631, 760985262, 993756274, 760661057, 467293171, 542387065, 183257760, 971411539, 805203055, 808927747, 442949441, 950362157, 93296917, 949924395, 427525949, 685367332, 22399081, 521689100, 275625204, 478907402, 7606173, 157799554, 271008731, 804029538, 574826379, 280765977, 52566813, 102735920, 163342223, 668309017, 54433149, 900712398, 572778022, 473590410, 688463632, 433212947, 410411794, 609215475, 108349721, 707977132, 476680152, 836217046, 79428900, 161827619, 825941008, 833026936, 511948086, 498708358, 976644509, 968337522, 673415556, 558012830, 552011674, 744163321, 196899909, 598762724, 475932421, 495708404, 52631053, 654414775, 755024116, 985591367, 603176313, 789636669, 948000408, 193545235, 932073542, 98652849, 397680524, 553285259, 511995680, 921174587, 32907144, 994448014, 925783852, 434098669, 178338428, 80441921, 236119127, 678141159, 980761279, 338481519, 970300193, 183232381, 752524693, 47858268, 363205951, 41659802, 230687703, 282857444, 335729628, 427501640, 653305194, 505574468, 147577837, 32062532, 986391603, 326110471, 450649471, 282615194, 174492105, 229786153, 227345651, 974142529, 634630325, 730106725, 690489483, 29105196, 630958759, 39711772, 357284800, 535726471, 738205494, 623214106, 399998268, 638391304, 578076359, 324714283, 749838562, 759579721, 674929218, 437970607, 564795138, 230363780, 906940654, 423254862, 624511868, 870013876, 993968881, 967711320, 901392007, 957714744, 166260833, 913972088, 321728888, 545902993, 638674772, 924039574, 468469620, 936865751, 586413457, 994414840, 108567782, 95883563, 615478462, 873779928, 310766067, 754970061, 738633888, 220934679, 175021908, 398771086, 102209725, 634526549, 810051284, 507869345, 16858275, 382853483, 613566058, 92090652, 399708602, 784045261, 870549240, 90923564, 156750032, 603356992, 132984417, 565748942, 542338527, 288343661, 980936041, 844619705, 758723556, 339247193, 667345025, 507426094, 869101398, 404868131, 677526796, 725416468, 539125982, 188759187, 388046890, 350981878, 293509962, 797028375, 964454717, 867475818, 372988816, 508318785, 292682818, 268669537, 67108171, 852723467, 406759916, 767846179, 81919582, 601391241, 627329724, 980061401, 825673593, 706113417, 66264735, 723975422, 843390317, 668568376, 182779702, 541448239, 833786823, 347739122, 688638821, 880645407, 917574760, 906346305, 868138, 478754136, 42406185, 590186248, 730573708, 280942181, 208903918, 658236979, 998136625, 739597657, 788028501, 156241864, 792161429, 127708520, 271572389, 166084609, 382588377, 796552571, 727101065, 650373757, 422239303, 96761991, 153707037, 261125093, 906169327, 167743659, 340061944, 849673655, 147741599, 434281233, 261745985, 796220828, 206283607, 652510040, 535620442, 332739751, 444188510, 436851724, 496095046, 314180501, 120843378, 454921126, 123902417, 88890785, 319231762, 518958171, 631399543, 953623556, 655266470, 5448729, 649532546, 992884196, 998977721, 821259063, 905161708, 600938960, 366782075, 279229090, 933593835, 787261932, 891546901, 51482243, 835234209, 434764920, 674879843, 884017755, 687149907, 637366144, 301608849, 368748501, 112439951, 878924957, 830811186, 524261965, 905878986, 863044436, 91510487, 784139595, 850238906, 575186122, 392245613, 234155669, 113915905, 340851284, 144509912, 893064706, 51515140, 753866714, 247446570, 81234483, 964115931, 749074871, 657354216, 239226087, 262706918, 155039260, 227689698, 372426355, 797947039, 692707184, 279969831, 337910323, 21663850, 597587869, 555768279, 363340467, 396809600, 562676737, 442905554, 549987570, 956422887, 113542963, 922456248, 177455939, 345340143, 933105720, 210323177, 61441534, 706227319, 288427178, 562190330, 114088060, 866889622, 326801254, 144263634, 825325731, 879378382, 784319952, 362943412, 594476147, 790867177, 481931750, 31691194, 564931147, 1508258, 959131112, 756846096, 586889065, 273244603, 993826396, 926509266, 845094966, 276701431, 492474939, 926031586, 924842374, 285320568, 40331645, 206638165, 906828359, 471471790, 432966233, 562072808, 127551705, 219645077, 714288733, 942536415, 824127986, 907649246, 768815283, 283917909, 41221942, 861794227, 644561919, 537890237, 937134856, 971974566, 803066150, 369071167, 490461198, 265071386, 904163508, 814675247, 435107427, 803697387, 599487352, 880170510, 94803834, 159642681, 434198248, 3401228, 238663796, 447884074, 805262191, 65392435, 189295756, 692791808, 526055458, 962433690, 952196849, 1675302, 483120183, 452451483, 46164348, 750551604, 427524609, 783152072, 754455385, 858845175, 385726403, 191965142, 152123518, 990636071, 538328968, 47494598, 867502707, 496226511, 513023584, 743349545, 190024334, 520604629, 52117516, 949761968, 57681039, 54760992, 221357085, 68582734, 714694109, 286983687, 920279371, 667969047, 564677047, 952449845, 174213211, 14846302, 212111706, 655056758, 406829841, 739007944, 215758154, 162776217, 51297932, 564512516, 152357581, 46526581, 2306931, 537926235, 510826353, 947948449, 581757813, 80281424, 285068739, 726077597, 898075151, 75967339, 353669347, 821957271, 267532488, 777148657, 300424507, 120075797, 526365204, 224804874, 292931374, 429710185, 403571069, 355817402, 673695938, 886915227, 740318853, 203674484, 697233329, 914507921, 762846838, 483732671, 655752867, 343397312, 158883669, 399996953, 375143506, 685084644, 185027350, 853434550, 493596582, 736924964, 525355119, 868659443, 55914753, 145609268, 405164251, 337952696, 535615087, 717645666, 559904985, 669575872, 348949315, 419536870, 540874802, 638369402, 921986548, 561017311, 539392464, 585749131, 23616794, 571120155, 825905961, 846402600, 732910926, 788523590, 880175704, 901689774, 301433574, 14785792, 21839190, 895978755, 389018525, 775520521, 479684720, 412066529, 515224745, 919090512, 774518890, 947706318, 280967086, 897476239, 22756859, 59639791, 311308044, 790724392, 194915554, 131713616, 897747748, 172238490, 115601461, 935709744, 652714569, 860277715, 772561136, 731173612, 415333673, 792237954, 490429753, 379024778, 944705984, 300987292, 734404783, 679327553, 800469200, 596427174, 275596343, 931167700, 254589990, 554991586, 964940592, 190461758, 252034606, 266721894, 435635966, 868070939, 567075788, 474761885, 143395409, 114792214, 644688620, 707677943, 181694865, 788536600, 95369055, 939474991, 653613656, 450713008, 735389019, 428775457, 737826517, 977161649, 120193551, 124473814, 496197017, 316476312, 55317515, 763465291, 746271880, 989002864, 504160950, 656673795, 523902983, 163283641, 914573300, 279606846, 412345523, 749450610, 501354181, 562080993, 772080524, 861783747, 627999843, 999341575, 811163238, 856112445, 505787615, 69437479, 864850036, 269883948, 650915490, 178531760, 937501219, 784771570, 786304796, 306040005, 277614909, 162659272, 179290339, 387711436, 887618981, 804611884, 930750221, 763024974, 739767687, 880171462, 361412073, 99264565, 458232747, 582602362, 912750982, 567516444, 82078757, 780059042, 646839977, 977461642, 651155274, 934164143, 123145697, 125010521, 106097306, 5803436, 579826281, 36000236, 64076061, 20625908, 86017058, 441525824, 333092927, 135556128, 283116378, 488002015, 313621061, 399686117, 495479462, 769233686, 807619580, 955449456, 329377846, 574523104, 447543881, 74234038, 711305411, 15844523, 324079597, 783214925, 788133501, 443601857, 403755704, 924397740, 602431031, 790174109, 7043080, 112583026, 967269030, 938003268, 974578773, 165684293, 668856220, 244050278, 780626326, 59914606, 515576350, 234609617, 958618530, 273335615, 701571291, 708027798, 777170804, 184204076, 761514232, 543495510, 307475293, 595557569, 385002705, 14895380, 54784530, 435487374, 213772115, 490940622, 77557279, 561549751, 180585793, 420749726, 571457192, 494072454, 837710340, 716136464, 168706977, 413366246, 845887765, 411660277, 400562906, 432516047, 402339325, 445785363, 160938921, 714059335, 404940900, 908979881, 541672358, 876760536, 169993925, 572214784, 778877928, 77779566, 74050616, 799625413, 710457488, 758485191, 905988748, 17638419, 308101692, 99738246, 848100917, 589127479, 707165202, 341120450, 17551556, 769480003, 114931698, 875344010, 319176392, 790225158, 317843559, 353149070, 717243402, 807188246, 167516670, 769160180, 610507581, 112892413, 673053471, 491268887, 172091785, 389577002, 657428820, 518818174, 780990383, 977514522, 348583532, 503351856, 619669037, 677089159, 341387962, 508516288, 27165435, 299078861, 213723549, 667188790, 628443262, 959652828, 506933459, 52347692, 437031417, 656202604, 175693573, 311881057, 617632023, 634127924, 834748292, 660471901, 471786792, 284258050, 773806564, 513611234, 565975063, 139515243, 449558474, 213375673, 893563392, 86264932, 642828816, 713448297, 940348394, 845707020, 57929344, 632513704, 207179914, 99795608, 637997990, 467380123, 305253348, 733514931, 783283452, 402191561, 736881270, 37585624, 759373286, 487448494, 450251289, 841059365, 762176431, 804447567, 200408873, 369833570, 39646408, 753847606, 111897863, 342461601, 857288833, 814828202, 391082561, 916939452, 119791666, 306458035, 67762415, 674181422, 48648245, 810767517, 541757133, 537550584, 136630746, 513210788, 889423235, 136671179, 439481334, 548184015, 302057588, 322775071, 47625018, 609906767, 485853760, 475266518, 912023262, 607388616, 349103216, 829335055, 495128455, 915403487, 869184519, 826237033, 925910115, 435211711, 77077300, 109182301, 232952259, 356809569, 535082041, 572320928, 55670656, 63414766, 560343986, 878543345, 549485766, 60881599, 424632309, 698468420, 549091633, 928813281, 26500094, 847746861, 753241385, 133468635, 701130501, 316283538, 82810679, 496540964, 417786221, 910104475, 635058301, 721831621, 944675596, 145067363, 431521462, 685193979, 602963035, 438647391, 109591753, 40047468, 17209805, 736391535, 737159606, 97937783, 644328110, 289647387, 337558637, 170552556, 476779108, 670597770, 817264256, 985353776, 411540904, 316373900, 736271874, 771501127, 546495615, 493876034, 913203497, 985834074, 354536155, 515241670, 789539917, 945845829, 721094171, 457634040, 899723858, 900190043, 752109367, 344635047, 570546316, 873645155, 797314644, 755769652, 665950869, 500157456, 811237286, 765356810, 738270361, 329389284, 602469432, 646550924, 546034652, 148706720, 825559690, 811746500, 655972356, 948826525, 800664670, 202290568, 527892887, 128650998, 740983728, 470387561, 927206458, 839816862, 64769991, 59662812, 583375164, 118391793, 137094089, 751221012, 94355399, 784013981, 733816674, 278291099, 396611264, 233882905, 319508050, 462150424, 70613295, 735004024, 591228366, 404070486, 148562952, 931487529, 680593895, 162662371, 177338255, 974634915, 915978223, 188665460, 706389032, 395481659, 657001109, 269975361, 183276976, 877926391, 899125169, 425664136, 502233650, 536931313, 790414953, 346230723, 274060232, 899628521, 352615783, 839924848, 700482312, 247887825, 549952663, 755600974, 81188258, 481038542, 632028794, 198942311, 635807794, 259770733, 962495078, 88614682, 318880759, 623447584, 171772843, 852777898, 939937078, 321970458, 867351624, 167482500, 759083847, 193253172, 318366299, 604053306, 521879926, 352523891, 597478576, 220248421, 660291843, 888274232, 755733440, 992848583, 773545491, 847413005, 279202736, 803255349, 204243250, 660944089, 952543146, 824647228, 203222185, 313362920, 921152630, 221019294, 549745221, 955888947, 574922025, 678689488, 74457185, 519751581, 601783982, 956226137, 615948638, 488401425, 287844093, 616759291, 563656246, 515512172, 627825504, 83038576, 277959017, 706840469, 155174544, 818153946, 327080906, 625379013, 556875469, 373842649, 164447665, 504406332, 789528619, 942725113, 252321503, 824767563, 144652678, 645699473, 666347855, 863384190, 228124495, 330723015, 727798509, 679790075, 567772550, 805858102, 343170601, 64421191, 542689502, 26063965, 576754242, 816906564, 594313988, 456792518, 444275520, 278824495, 65325183, 923585796, 861530044, 72613209, 544448645, 234832191, 824846013, 967029159, 500497417, 942105312, 949255552, 908968639, 806901981, 904108895, 819290174, 689264075, 891390605, 433290835, 443119529, 295111558, 438264238, 72830132, 766105406, 263631974, 377354203, 991714390, 451013641, 158491845, 206034535, 111587260, 883972774, 458289308, 308609697, 823738431, 869727012, 272340488, 198357554, 5980570, 850344160, 795086207, 258707600, 301455313, 973557234, 861692037, 894405674, 954049658, 929429474, 38731687, 336023314, 141534674, 853155698, 925153299, 275276108, 966307032, 181301902, 341553668, 316427922, 670182931, 787849699, 627877032, 19844131, 733839435, 608112335, 240206095, 989855028, 74494524, 341822488, 831759251, 955146985, 261047742, 612071964, 637861469, 706390395, 206559492, 284032844, 579310975, 631717079, 193616295, 112002695, 387329814, 470724520, 861854410, 519753971, 774123835, 837847338, 268474108, 975529413, 175914920, 803896265, 913372284, 807771863, 834146326, 687514968, 334010017, 865837585, 223936057, 147346909, 564168230, 923442320, 9943682, 744274627, 384801239, 661363456, 595708954, 852934907, 727444648, 168786588, 225174111, 626189596, 376631067, 370510654, 344047432, 765237059, 927988587, 168653747, 166042090, 999955779, 816732904, 179522029, 534731375, 582014919, 768120898, 176604090, 939840222, 109497437, 616278183, 281101494, 948277687, 640498307, 296208367, 692701198, 200271976, 500626088, 850649320, 436829465, 195955426, 937516498, 403746228, 892260446, 377214393, 447765755, 352609601, 689894489, 80799801, 115599757, 820880670, 803168542, 685734800, 98373084, 762368233, 790760758, 331077229, 270161154, 655648867, 800320488, 743537426, 824761905, 300330606, 280451122, 485618624, 176527537, 425700643, 691815298, 410106909, 485608768, 168975336, 128872253, 609490585, 636916040, 215061353, 859691966, 198920880, 805028777, 528989160, 545134228, 966808437, 148732638, 267187306, 261608455, 409826799, 657083106, 623077627, 584610383, 121294691, 369795233, 247769240, 400501626, 712620035, 426158934, 891942319, 127893442, 226580031, 388064981, 77852364, 385879766, 422143795, 480494196, 549685723, 907058722, 819268580, 619362730, 6265090, 630548550, 387353449, 336720689, 450272236, 930047818, 989489644, 396097936, 787518221, 809607405, 205246867, 297439418, 34855232, 462790083, 846346767, 797531515, 102172165, 167027672, 317352864, 216677442, 474071437, 487789477, 919127557, 278896005, 574688391, 724758992, 472663080, 185339381, 747675897, 31016656, 238673033, 165072932, 363781528, 969439782, 585508890, 63899064, 407238401, 508623956, 294012921, 917687781, 97119880, 631027699, 41037659, 345870048, 612118646, 874852988, 461828236, 421399639, 922893975, 340493676, 353700962, 655757317, 284648573, 755410743, 23554422, 496388759, 261028957, 507871006, 703558642, 42157316, 286799796, 268017876, 287771316, 358995862, 666834507, 182096684, 866412521, 647188766, 306199698, 142399827, 4331307, 329903024, 531740795, 304752599, 827366243, 226317808, 746724366, 61267950, 617891259, 444892293, 510493353, 537564157, 343226957, 538597449, 411870742, 192408718, 490499625, 928377676, 301172480, 479615720, 792812421, 633667699, 578819504, 41014939, 614064893, 181609451, 724395413, 599437690, 761210559, 173732850, 588553288, 839249326, 65353966, 162407706, 131286979, 63067452, 785836239, 443634840, 878832597, 390060538, 355129495, 503312963, 633415103, 963742264, 443998020, 429455726, 118253432, 651983639, 355644421, 427154469, 216028858, 466128453, 218784672, 784802199, 357077901, 210277323, 553315907, 729978338, 290963278, 330632808, 861759787, 45699845, 495847831, 476577215, 598053906, 808284766, 689931348, 755022328, 993426180, 848078116, 429237173, 439706732, 546115968, 652128178, 559416166, 103897264, 230271721, 501872028, 900933772, 800474520, 549486618, 342584511, 131978478, 361818954, 180724904, 691572023, 46184790, 451318317, 532821322, 823348611, 217456746, 556678744, 6601410, 519951935, 507993404, 127272797, 747933800, 293178497, 937200251, 377073342, 513733663, 319283007, 670106853, 333773730, 391305477, 313144176, 544137022, 856360836, 707692031, 833773046, 223098769, 732190113, 951309898, 956599568, 521832202, 515368749, 937307062, 742869120, 502674023, 760824069, 188577030, 589908974, 622718865, 417790531, 861332779, 139559455, 107192017, 950032028, 864926228, 816540343, 166587497, 210331363, 383101752, 527110539, 314220067, 953580500, 911848053, 693907025, 25562592, 976989531, 79534411, 887767191, 680574803, 851112371, 730730534, 118684517, 622991585, 221769758, 547527701, 329911045, 981831803, 5538209, 13663115, 411988101, 936435120, 741392318, 391962758, 713027991, 438449633, 297652748, 922245819, 587518830, 849459173, 344007537, 448446359, 29278692, 251782971, 543824420, 353161495, 320673717, 768591391, 218326353, 880756716, 676401718, 109041298, 723338833, 345030330, 788842226, 801454985, 381590682, 943112048, 27279444, 518109849, 602039331, 361432466, 970791522, 953155458, 36846487, 959851201, 642948170, 2909983, 562334585, 892134336, 722714052, 358259701, 67927883, 108662402, 111900159, 625946148, 666181530, 557559361, 632734050, 164778599, 393302799, 439432220, 277087254, 33693778, 605446798, 40810694, 596235935, 522957335, 626111326, 454057887, 226598971, 2350661, 894429053, 835529591, 366821004, 291979648, 389040830, 371848423, 69074410, 767676588, 270824796, 545978971, 699514981, 539948422, 408070370, 916267922, 45284456, 294145699, 856815675, 133576392, 220037642, 862755293, 409310550, 571161382, 470452350, 55617965, 225959181, 624494833, 43050189, 49727488, 252447920, 86693838, 411472843, 197388483, 448712265, 615234073, 357872691, 270461655, 30685815, 582026156, 701927024, 115876868, 449443934, 424330966, 665315647, 115476481, 507781331, 252811528, 734497587, 447926018, 355432116, 74832786, 861780645, 167092810, 163874424, 64250696, 604524831, 919801763, 596294147, 336393222, 637997303, 311915669, 876869359, 913169000, 965290818, 523285388, 869502737, 696077004, 845222977, 692861982, 631612467, 185392771, 225926647, 771536900, 662691677, 616886933, 257726329, 441665180, 564341955, 389415525, 312874630, 960730219, 100142257, 323947796, 503286694, 768243519, 784656415, 415319855, 900008342, 502134224, 591137581, 727184987, 883269818, 910684506, 290349, 713139992, 400166559, 14943106, 980851625, 473935995, 331356737, 636162195, 301309400, 723850348, 79770584, 960999674, 869645760, 596535433, 902916765, 836037743, 207624546, 57216585, 250938562, 147827947, 897208047, 243846151, 503223188, 308687799, 692052707, 576652924, 50301161, 640742897, 608036367, 421627936, 199548436, 241653655, 140312064, 542983552, 636140615, 53073266, 767687163, 758300088, 781723149, 897132514, 282893794, 183108476, 46146864, 819062558, 722299850, 624783502, 998621855, 675430811, 905232417, 669088660, 26647762, 819999010, 518998114, 787052864, 260489816, 615734996, 447556314, 606404010, 441827192, 566142061, 902439605, 559712808, 334267420, 907299566, 989779488, 392524417, 232414038, 802501249, 773595667, 147108560, 909342842, 38622639, 708529344, 687134270, 974753841, 80036131, 754985250, 453857409, 898892063, 186390286, 298683259, 990914105, 134794183, 132421344, 517863645, 353169773, 409384478, 48924891, 827202374, 735589832, 538699777, 974181106, 703332228, 203925401, 3616343, 438917393, 773435352, 181709616, 309247837, 411874775, 814949780, 711651783, 707267247, 430541584, 78127369, 286382703, 913921881, 577753318, 957489071, 266591689, 774211945, 620675562, 759024419, 617833084, 671206086, 644645004, 944430403, 725955797, 90728847, 707947337, 637537593, 971779046, 323185913, 163672038, 166949747, 325291979, 815699505, 613909450, 391887420, 967706485, 205315618, 842439915, 372424915, 640170990, 484483134, 661474620, 973091841, 419477396, 890790693, 869816348, 560088953, 887870953, 256861255, 953211578, 902311946, 69844649, 165119771, 264544399, 196528576, 587594559, 547110099, 447914958, 719110921, 19248018, 20739006, 279661242, 969806130, 114524929, 204312681, 309726464, 962845388, 254459077, 147270979, 316596250, 245159229, 849173217, 954548279, 780718423, 90161730, 825866614, 314751623, 460826138, 770973601, 467522816, 608287664, 83803494, 698768095, 324889221, 119085542, 264783144, 360207973, 101595966, 936390987, 259876402, 136082877, 478769679, 780421304, 192550227, 250079086, 149352928, 579002026, 826592282, 273540000, 568565807, 148765353, 401627187, 973698818, 153074871, 869487896, 656876388, 912058004, 919956800, 17779196, 126726454, 425727099, 486077355, 38870646, 400189452, 65545830, 789053926, 434439236, 387236877, 336174139, 792715405, 612571301, 236729338, 620210765, 823214713, 7099211, 799484648, 103241315, 741137153, 739853928, 529855880, 288388037, 391351088, 658288479, 880620104, 728932612, 486128410, 213305292, 4973837, 301791196, 182172152, 262343602, 540694905, 978521140, 519959754, 813581089, 30254433, 456836238, 246058163, 675681258, 518825878, 424267907, 873641291, 621033570, 383739329, 738631385, 764858645, 640435262, 154810419, 405527788, 326339155, 264347150, 486848873, 866251907, 574276174, 585005647, 110591758, 534668943, 504826876, 206763053, 869015254, 107731164, 355133364, 463937636, 334397614, 692043197, 697339177, 851859048, 163579594, 904110630, 437516135, 590537564, 483403079, 609956414, 715021826, 324884750, 175001095, 574245771, 630922260, 450593863, 693025235, 590292697, 857799943, 781947635, 813842127, 559497929, 171594185, 623907981, 970205770, 387995249, 617193214, 75185021, 224981013, 985498400, 463284642, 467809052, 538106604, 571705750, 938780633, 237830295, 440753667, 990569200, 401560486, 824063723, 986831163, 337908087, 756542417, 854522967, 648796478, 107627793, 362791790, 352067481, 855937259, 61621390, 660410179, 393873920, 408531163, 726584752, 711755598, 150777980, 901420688, 21116262, 118212195, 463904518, 40437102, 384572615, 664512612, 849261872, 592391793, 482364952, 41700473, 647184508, 219989873, 611585002, 398110368, 53279761, 213265591, 10317258, 381235227, 932039007, 769964944, 508894874, 343211210, 452628742, 138344387, 633311729, 275336912, 740362259, 321096281, 749159996, 140114257, 491224283, 215902315, 76049174, 319217479, 130684632, 520420563, 301270425, 403321156, 913180086, 842814575, 918551424, 753211578, 872583184, 956426045, 633102793, 523498681, 574621209, 293736132, 810273865, 348685773, 905022277, 608916156, 353863100, 669530489, 298695950, 433567607, 585700336, 977363720, 275697596, 302580940, 393568637, 404602357, 121744670, 59485354, 515739528, 125703227, 233545639, 323122209, 217145903, 352229062, 624193993, 404949986, 995321855, 326306076, 903463160, 364811621, 272108687, 876578819, 710361788, 401094147, 859295229, 668943022, 570354661, 708206467, 491126306, 996534976, 941563829, 342990348, 434771971, 569552395, 210402422, 45653349, 864047037, 464182197, 896320329, 244759072, 976777723, 805562433, 894266645, 394631602, 831013215, 224177115, 898499321, 268147284, 957293777, 915350631, 779183343, 451890408, 9758605, 393874805, 548426854, 964395151, 968071877, 408206793, 79276067, 833028716, 927729703, 65720099, 743524296, 257885678, 274623891, 544110869, 275249614, 33656122, 248964681, 138466353, 165927826, 328581873, 549447073, 847804982, 503755847, 415748610, 743141538, 588376779, 183982509, 957902280, 556618925, 36949752, 84353667, 841062877, 784825945, 541319883, 293526935, 714788965, 185513796, 7982536, 923113901, 216247495, 251372930, 170837837, 786175298, 568666345, 77041016, 212500796, 357606480, 663579792, 726057389, 320396715, 950831938, 808349354, 403491028, 351664578, 256641476, 590127060, 929557351, 11247051, 411976991, 850620016, 481322710, 63218652, 796390821, 647842705, 267015707, 421852780, 795494390, 564357667, 397095304, 811244253, 391126054, 877182423, 887597263, 243350102, 887580952, 514346032, 90642624, 269788107, 695394248, 107775977, 445545300, 464806846, 765180981, 908536353, 787016452, 788647640, 74787604, 412491589, 954395863, 285553644, 411788255, 355690507, 881077702, 307995107, 32690489, 52291398, 392896178, 214343704, 823778385, 988897034, 36393620, 837624910, 725377091, 4390217, 60172313, 529905486, 230010432, 839899606, 636068666, 736313825, 872296181, 406883402, 550610649, 881944983, 668757112, 238616385, 74278611, 195776287, 86705198, 731738513, 587695930, 587660545, 510020318, 137489, 888213512, 533270927, 364137387, 3454114, 968796036, 522062385, 800228181, 284483886, 457798248, 205942063, 67877983, 299867943, 416827875, 548507603, 896568663, 818673249, 652537561, 283208810, 869119230, 714136913, 471047381, 4967476, 190173467, 84885478, 150395080, 433173990, 358950675, 698435743, 608233185, 412634047, 230589094, 881989784, 442447865, 61542345, 868992713, 247875912, 821902949, 512647326, 193311895, 83995171, 104123773, 430589457, 382191911, 962426642, 621583928, 565132040, 474459902, 115070797, 213037519, 6205883, 554864985, 261854859, 748371253, 716988859, 199581255, 499270608, 84521876, 274473139, 391639496, 19043509, 775439394, 783309274, 486131919, 460136711, 114085893, 498987138, 798967953, 160234466, 766080633, 90862888, 13501891, 334514017, 904841144, 464434514, 753534370, 954317802, 665069191, 169272617, 986800806, 416908883, 247194318, 879995431, 645975114, 287613381, 845492632, 753321568, 559598219, 855632286, 416001705, 855605631, 186913472, 661751198, 404514599, 1407592, 978467862, 598532716, 45616281, 667036447, 2200989, 495431100, 401256995, 949082885, 401316299, 975954469, 127852396, 347959638, 461493212, 889201134, 112679327, 175604522, 998239877, 413435523, 364899983, 66235337, 962647346, 207289448, 157731003, 817507121, 498790304, 557306558, 228677637, 242689947, 446400311, 749704080, 64945097, 821926716, 17502397, 888658716, 916812334, 65152930, 777196609, 233392492, 580097240, 861725668, 990539513, 547646217, 891693444, 96582405, 578852059, 458908957, 23995630, 437212151, 918011186, 603569957, 526030869, 365737375, 176471564, 831153806, 665415494, 387719751, 864347278, 467405573, 207359958, 113057239, 811496543, 915019756, 339438531, 85887912, 566229779, 746716897, 244790173, 549687511, 861674534, 16616363, 789568, 49789684, 75218938, 937733040, 61102375, 523424622, 475890319, 841682036, 118502735, 201196641, 207137635, 144814578, 5347211, 278468450, 949218469, 594168730, 529691320, 523563477, 584062815, 14254586, 438078013, 992837460, 859117252, 241549951, 129478924, 317686482, 348749424, 354502161, 964016349, 608019944, 737089407, 572334837, 51987590, 977687721, 27185815, 206747107, 1402812, 687356819, 981729286, 528084240, 558617285, 488974231, 251435220, 505133217, 296386784, 269808285, 591850041, 181014263, 240337246, 689914960, 156975331, 412936976, 610948373, 887877639, 852489100, 414871339, 122041337, 938377308, 836756739, 21182323, 383303170, 271922969, 821085082, 324919894, 425354512, 348015025, 706884820, 149216302, 586492217, 899048361, 103685904, 924077873, 94481609, 930472301, 465483850, 831447796, 370080760, 714482151, 989515904, 219528355, 279445483, 343790239, 902778508, 110709840, 127388469, 459646444, 59020953, 443897864, 802138568, 325137720, 338158588, 456948796, 972948486, 233841748, 629348713, 77121266, 164898752, 483345009, 135403928, 936644587, 496809829, 369190521, 654093763, 973146570, 197705156, 248509819, 940691342, 742580208, 554751523, 422005170, 537177179, 441487401, 265217723, 545318147, 187428857, 999850045, 872074170, 653157703, 28633288, 725964226, 266039411, 307259816, 884115866, 776899411, 937270174, 716868080, 924972206, 288328585, 684180023, 773680316, 325693392, 102907195, 488323751, 724220670, 6854166, 564112584, 848033383, 541286855, 646034336, 842756613, 243552069, 895862625, 950565000, 802793089, 753597253, 102652813, 918586512, 219710224, 564641455, 42657736, 852286022, 845972604, 740130979, 782057374, 903187754, 150239883, 883886507, 469897670, 552535770, 85728438, 862952352, 287756184, 53954411, 371430805, 492358739, 505548511, 341190078, 390876482, 997426043, 123185684, 436242290, 607558916, 439765131, 91858451, 2995454, 666392632, 305519863, 794908904, 33402300, 714476232, 545158863, 1738261, 130968744, 516152232, 806803288, 916905403, 296052934, 235488585, 802538597, 677928113, 88979558, 405474486, 538760012, 724967316, 785694399, 419827745, 220472946, 626837519, 324548937, 783632880, 703332703, 854319660, 238887208, 347053444, 343972018, 750148458, 358338195, 809710154, 917564917, 227562776, 238372453, 474828255, 592507337, 965579549, 483489110, 233126992, 521948128, 255979263, 709102774, 14923803, 347535138, 144564241, 12700866, 878620444, 796156284, 73343497, 120035009, 270291050, 851895732, 261592438, 840507566, 591626514, 516362791, 601582128, 784604055, 650769728, 466700064, 3206192, 882638430, 61400900, 882782980, 368449941, 448030697, 534751512, 726634743, 420443734, 542871550, 128447283, 148657896, 239418545, 764702712, 358439496, 561997385, 235948621, 284921568, 761975518, 111671353, 944129733, 579823248, 796774066, 876946534, 39163759, 6250493, 181816583, 651979184, 605546910, 492157655, 394585242, 454087453, 844062393, 875429913, 908926514, 676443194, 145465745, 336286680, 46722407, 944908524, 801167925, 416818222, 596992856, 506472270, 813364335, 479839916, 147552067, 413281082, 153982979, 329715720, 915075808, 103696273, 358917310, 313723776, 798610137, 651887484, 996921134, 418876678, 298824886, 273059694, 878911260, 439707357, 484085124, 615488356, 172953638, 192387826, 508753609, 457373516, 544236641, 58394006, 653034589, 496037521, 8765614, 498280364, 371352490, 496993246, 920759060, 215489825, 715293516, 561516902, 72810625, 513092165, 13664585, 498915562, 389587999, 653515871, 17832382, 361919656, 385344638, 236186840, 499664264, 386299478, 506087872, 742805026, 587752947, 889836312, 302398685, 436466927, 772619648, 321445518, 561165658, 651833340, 365288029, 302946534, 308547153, 131981423, 562812208, 185688147, 142002113, 488699280, 612254638, 99775179, 392174457, 328155082, 969334917, 350447723, 429246573, 860601968, 36982736, 566404176, 871979766, 192328493, 818662091, 229550609, 731469154, 446591661, 35826953, 234511793, 283607939, 783589561, 798819865, 105428820, 947463126, 852161032, 268766818, 84436809, 963719442, 930284269, 775341323, 508911542, 135859449, 568046905, 270760382, 308802116, 446012992, 161305476, 693028268, 991800795, 238213067, 575428147, 181651068, 385989071, 628274439, 482435321, 758503498, 915114286, 574786671, 295340716, 530182867, 429183097, 23249881, 842230499, 863075492, 402482306, 589531819, 354943525, 752996688, 477468879, 737499015, 19132676, 924595401, 239600311, 729137519, 415246006, 105692861, 895304704, 390456105, 982205707, 802147640, 977202929, 230093559, 481770100, 312167844, 798675461, 973934928, 13372156, 790080775, 140531577, 89959616, 360444353, 793674014, 624363544, 594802945, 345527009, 197676891, 432551555, 265557370, 856134484, 879598632, 800259730, 202255344, 872728147, 722747520, 550401444, 251004007, 672380761, 428703487, 72015405, 580819730, 55887145, 287385111, 180174293, 397984729, 957807302, 86513676, 83035174, 549103604, 123390579, 677144616, 655260887, 51110882, 871299219, 207238119, 500718614, 599074176, 996861793, 4470381, 599814082, 86030253, 752868554, 349412695, 473742470, 192394246, 312165875, 261567131, 717792468, 335182342, 822367078, 35344063, 886777503, 623762971, 151180567, 26236730, 15747982, 296715016, 701526980, 580230466, 509873608, 932789420, 547797583, 899462369, 326722604, 791320218, 609529852, 230348868, 660871762, 856425929, 595249900, 380816693, 427069752, 421037651, 966149171, 471555608, 753880636, 707659140, 394001376, 13693522, 72368928, 151598263, 94060959, 95100354, 843840989, 978449429, 253158863, 399217209, 997703082, 65226948, 891291149, 668281830, 949688716, 130877163, 127437730, 123788318, 129824492, 290935819, 111402318, 403309091, 34852076, 605476007, 681403732, 955545392, 952694297, 928556028, 234381232, 289898382, 83924720, 723714069, 49510464, 856959739, 370278484, 694977034, 435367138, 853558003, 367823559, 17526084, 562648254, 550973104, 115634214, 738739077, 365606478, 470886521, 297020905, 251718369, 413900543, 227451617, 926833798, 272398984, 353845228, 706365770, 871662830, 431565673, 688830134, 977252593, 237959416, 73354011, 50334389, 319057172, 715236965, 220372087, 478113710, 442794129, 424577405, 481468160, 268439925, 923946624, 354513394, 996624995, 664054468, 360350668, 461446801, 484899240, 958696402, 694003034, 131604498, 962562188, 502680090, 335599483, 630047325, 72351733, 369651237, 347036344, 610645579, 829426239, 673760805, 152208897, 407333745, 491311027, 343533975, 144289114, 417842162, 152272517, 611869621, 948002471, 392838167, 730526237, 742069112, 749611246, 40150416, 824427597, 809679242, 801226223, 952549814, 579930082, 441241265, 14713811, 465415915, 314202932, 461876787, 593271140, 792167122, 118620943, 528260524, 690103686, 895394744, 918671096, 191743252, 311406260, 777866513, 411552965, 762824567, 642802233, 14926476, 350302725, 271457787, 180518870, 133628178, 560632364, 39296920, 730315992, 260892665, 835596828, 65341812, 240978142, 396132219, 35164359, 362713153, 625722546, 975848981, 207149025, 184717855, 323383146, 274678764, 189772021, 125237107, 320653743, 658594867, 186628759, 972928677, 356307020, 805810621, 316931608, 419872376, 129891311, 394274377, 616957763, 478059665, 330065208, 408303130, 714125030, 806316154, 626747223, 951095425, 229241464, 7841232, 439194351, 18923465, 978177013, 353128868, 909699478, 914563670, 4316031, 390352157, 307905103, 393901719, 281481132, 155346317, 580588779, 560236865, 807584629, 181900585, 639864445, 197235099, 223767946, 57368020, 440000021, 149816321, 80536718, 244590875, 310640058, 928099002, 628466812, 394949990, 836685635, 775137772, 589228134, 895811855, 256848707, 128432311, 737834129, 148056955, 127089730, 886188730, 978592039, 699079633, 732060854, 859632111, 690854509, 634833237, 349561343, 918482331, 571029125, 909669772, 889035019, 93243298, 350450458, 915964769, 38936256, 878376026, 999231487, 410313434, 11320940, 53370832, 56632939, 432506338, 306371768, 103021269, 872019733, 213464587, 580225737, 372849497, 435154401, 682912147, 58741213, 658761280, 549618663, 246704949, 174903624, 606991178, 334272506, 496318587, 160005160, 653967160, 964399295, 58734367, 780208173, 870345051, 924525908, 76032538, 287923164, 598716744, 807792182, 783770957, 474386022, 376375662, 712149075, 555673005, 197086001, 9257612, 746548876, 466061650, 984689684, 386328261, 661372919, 849308779, 823708888, 214396088, 861288331, 59454412, 177550779, 416644489, 350800181, 345538481, 848981551, 47617316, 210151396, 251326838, 669451093, 652680935, 402080657, 823265004, 290578083, 557075321, 968170715, 220203396, 701440436, 959938163, 109173215, 984485392, 491292363, 709587870, 948596337, 442179472, 744475421, 848057036, 251752679, 468415546, 308705982, 481927806, 229050347, 305060587, 970799975, 257462142, 321599599, 270308377, 728589357, 323031794, 108956464, 486553287, 904692256, 427641591, 877200904, 17030754, 815388989, 631306036, 339923243, 715758807, 103909596, 804508005, 465742225, 232824645, 822487008, 198299021, 645060099, 598846314, 766338304, 393462383, 765218086, 58214914, 834418510, 770056726, 657852089, 754147135, 522365723, 329541301, 115508831, 792268000, 477985541, 923212105, 96169518, 639805769, 618513587, 873103243, 852188161, 758339464, 406398588, 299149743, 514988487, 559690438, 554798683, 288654312, 220925176, 752488823, 6797141, 413427116, 722813403, 384035824, 174133225, 130837050, 131243251, 618229270, 720376268, 669511871, 440987050, 965127620, 733042604, 454072593, 837593746, 432548811, 448945224, 753159176, 354788391, 209236304, 65208358, 371913917, 920448927, 284572421, 557828778, 928162512, 319698263, 990393729, 913289996, 480209150, 371206958, 258463933, 410022682, 398574631, 637451399, 535364076, 913574655, 112700844, 184500025, 640517832, 736984120, 204454983, 415762976, 874256717, 961376677, 971114066, 764094920, 681150508, 205315253, 519477921, 882059124, 230618441, 189877358, 425103165, 925781591, 48052242, 96829909, 709478267, 566493813, 250213558, 203703987, 936786388, 681218288, 787481099, 148310924, 908389500, 445230470, 371969945, 489634730, 448310993, 749134765, 308001912, 759667087, 895172983, 310969893, 445873521, 370029131, 354347434, 890224291, 628443461, 736962658, 487414723, 648266427, 28177872, 841438696, 207331251, 98194814, 917982939, 997862521, 411420661, 900989669, 418638805, 245941305, 819231460, 813740656, 358073167, 77029968, 282216957, 935401941, 916397735, 176354899, 909926626, 355608756, 782788047, 495675778, 321666835, 579912971, 256767860, 133261953, 709887907, 547423888, 350843595, 834304878, 349046332, 653782718, 869828044, 558950595, 980321859, 470576802, 290951952, 608386568, 889981480, 789277655, 738736082, 395716853, 773241871, 899822156, 585199258, 422963608, 706498825, 375555601, 525427966, 455597113, 615186795, 811510546, 426612564, 329768322, 902921027, 383107976, 604292490, 783247674, 380339988, 692499613, 805314727, 225186400, 744792043, 124601648, 206228184, 135746595, 439716260, 86495551, 21251852, 426056990, 611651521, 250268848, 332385476, 965242058, 360165259, 42253276, 635487881, 234454761, 422214432, 90205016, 366151004, 541738891, 196231259, 585283363, 911591678, 205169733, 674277560, 525132376, 405728700, 944060220, 26526590, 857729998, 149610957, 343349107, 731049433, 7087776, 770746459, 105515454, 245806807, 684488046, 878491665, 620498190, 710386293, 222700920, 808762203, 66460084, 405411683, 340745716, 726475025, 709973590, 233332302, 414683822, 439559678, 529243707, 579774928, 726588317, 284306947, 760338208, 800160152, 236763630, 574842526, 140730692, 946544956, 308834239, 934461975, 230612962, 612369899, 901986267, 449567412, 107427404, 250370835, 950771238, 721718555, 780632593, 761799236, 85658279, 582634479, 975465030, 427761386, 412346266, 731521727, 616967815, 784858571, 479267549, 766481260, 926064819, 202727977, 189970041, 31016101, 838366078, 463696003, 953429886, 234240933, 749126611, 542106985, 454243698, 529366165, 761609320, 983432197, 122664443, 618592347, 306573134, 384831165, 530469464, 121905370, 355680240, 735260220, 989623306, 464761013, 421318642, 865577605, 88122116, 965400038, 357427249, 984530836, 363226367, 338915674, 452987525, 881575817, 323437649, 150730951, 129108527, 35269248, 362921746, 471631265, 885155746, 345807340, 806575929, 514978014, 512047713, 431368353, 401276955, 313120225, 777649016, 330715707, 977871443, 143453650, 928066187, 415172575, 970067257, 294007875, 903324224, 323413401, 353462397, 991700702, 591656235, 245425474, 248759108, 998498750, 697069118, 825106766, 309979423, 820991342, 429192285, 786443346, 462274242, 38454974, 253604528, 561120662, 930273484, 928386481, 583234678, 896738694, 255650022, 331599913, 878861316, 301785908, 505180809, 251777997, 404445305, 51037689, 756178223, 703371134, 879501069, 166379400, 686801158, 993880344, 684601431, 387094916, 817865212, 164044196, 991678292, 295758941, 522982881, 81797848, 524197407, 713514828, 520508682, 460553017, 57041071, 381948281, 955458047, 428738441, 237178300, 509338480, 653989244, 543720852, 656739866, 795939850, 900507419, 99316162, 918787952, 319360585, 49012999, 214596824, 150391710, 316821361, 826547284, 512381161, 479682773, 614638262, 457047073, 345489520, 643813367, 944511068, 719926076, 542615571, 775887944, 253783217, 215156260, 284325447, 51511585, 99799989, 832772807, 935692162, 830470332, 738668042, 402795664, 651309300, 776841170, 518856227, 22126863, 378970564, 364305424, 53385579, 896449527, 519407418, 456215076, 649651835, 514541624, 307361757, 629341053, 850809930, 692902463, 2001195, 306825533, 812751196, 290021495, 630964311, 399705940, 596050185, 369084255, 856931739, 906359687, 829155986, 106524845, 361492389, 3383379, 724438740, 407014988, 687536137, 682297906, 561352060, 153894438, 851682648, 387567942, 756484134, 847143216, 569059766, 294606026, 684048631, 682267761, 666084351, 241845944, 891269487, 393067661, 117578050, 374888112, 277405563, 451144853, 683866363, 718232327, 745203321, 35906727, 156478976, 444798819, 117421397, 345294670, 321750844, 538849664, 509896039, 320761602, 234632354, 472900151, 733214671, 299054562, 547775552, 856359635, 121476836, 725732720, 584441379, 780927626, 67481124, 985196345, 265047391, 518630642, 979773767, 213719422, 691797765, 970228622, 324815719, 714838553, 210250389, 497416856, 508681833, 94091294, 374735814, 96763218, 243327495, 942678385, 355233504, 824846934, 832755591, 785242851, 142466494, 342781242, 578073336, 406131169, 378612581, 604848342, 549311181, 986204173, 96099079, 973556306, 42505695, 433476902, 590046343, 810859406, 880719295, 843618990, 12717804, 540903764, 343466892, 203192777, 21294849, 656003514, 941983714, 991444583, 569813693, 972637428, 316879800, 119973258, 671536222, 143027649, 239252287, 402064146, 290216059, 991806245, 208511770, 695935450, 626956187, 502911217, 610722473, 190223478, 405314688, 221366452, 463912349, 363728624, 506254303, 82950872, 517634519, 54733063, 268263591, 432668799, 853696225, 676286384, 254718679, 66734910, 342912022, 561578941, 637775048, 937191155, 358674490, 582966484, 519150202, 271406198, 277423704, 107910907, 302768285, 225657638, 624508873, 835646061, 255944934, 572803947, 323184365, 410568122, 77342942, 751432351, 175563504, 561036796, 350373663, 205685198, 603257258, 847773926, 134367282, 274176335, 356493756, 916629653, 171044791, 783390422, 153485183, 181491566, 872591094, 508925455, 641211134, 901952768, 811097053, 548187933, 831229053, 492918224, 914767040, 831960779, 774741042, 128027072, 314031757, 401786953, 127691963, 795144498, 251169140, 824379196, 984108947, 423671280, 385398549, 534795706, 896432832, 88079610, 238725186, 429193393, 262951280, 742482249, 698643417, 620494298, 394998150, 754279792, 505583246, 613858743, 762751549, 327835066, 628247449, 747800478, 925321275, 465544873, 440293549, 766877458, 939779789, 169889299, 816089920, 522770384, 755611905, 486549492, 104750945, 425612160, 132636378, 968833063, 315983772, 379991396, 90307314, 923334526, 851291553, 60521503, 720340208, 812873243, 50137872, 451138124, 342673760, 341072862, 703625889, 682151350, 591038320, 199544023, 233125555, 360777258, 410918759, 429998140, 444680911, 649307690, 943286368, 831044234, 464145988, 465511359, 206064724, 446429209, 634288143, 284809174, 728469250, 387708762, 506867175, 250479395, 649137885, 887672446, 930651743, 24143094, 443558875, 458556379, 154763134, 749152889, 255455604, 872963974, 650909351, 860352674, 193488038, 664247929, 178014256, 2745995, 475339812, 558720949, 385545007, 854598747, 153940845, 328870865, 498914411, 64014139, 583879801, 613008563, 199922922, 572140709, 514704420, 511671953, 771653226, 391862896, 579140798, 767887893, 740336285, 415971195, 206544989, 543232753, 724053366, 24573738, 956694881, 51907071, 731259173, 678928800, 728839260, 343511859, 716152734, 629599773, 863238735, 6835245, 446262105, 609251642, 108852068, 588912848, 83557353, 719325864, 837688744, 997907132, 680316723, 43385441, 960197449, 955510917, 530792498, 536101520, 373242887, 953392463, 369582721, 373798720, 268171436, 317842274, 215681532, 59235511, 972777051, 630697276, 991059825, 907233592, 614360776, 353636620, 121194588, 84081463, 589229623, 543303789, 747801399, 156778673, 296623164, 72970537, 291185259, 867786056, 189068410, 39460839, 622527854, 543082985, 159323927, 721266135, 404855783, 107900699, 10036381, 748845503, 40846328, 456136142, 348822089, 101604344, 730509355, 812824428, 889028784, 99218540, 133673369, 493868922, 768512281, 160589616, 387159092, 171072497, 212198923, 849176450, 365156757, 39841924, 599811335, 845282738, 233289111, 354556714, 534768637, 454255041, 864380845, 283723349, 806345883, 133162642, 724106997, 246456919, 967196664, 320060361, 469373314, 87550624, 493944406, 684481325, 32171841, 524093852, 542070665, 871986979, 791024572, 721444420, 341440701, 437265387, 855356458, 600906880, 190723522, 852464241, 724807119, 678174431, 675606623, 628306422, 56167450, 166536923, 743702931, 289800474, 910195168, 297231047, 79959107, 544921549, 874135592, 852103790, 979066322, 791112437, 999561889, 431321821, 653270311, 851465256, 205506086, 377180940, 558938896, 974542309, 278266513, 298554988, 102793672, 814058624, 587331528, 777731654, 634240162, 737977587, 581588241, 398024699, 921210610, 295024623, 572215238, 909849250, 93997019, 378714285, 439760076, 214487204, 588700811, 230580786, 855122162, 845985568, 741857725, 302125292, 89487226, 549629540, 719991007, 23373061, 318419242, 337628558, 782314116, 480714015, 621795668, 177316212, 534177789, 752229391, 475722319, 406405444, 208328539, 648114708, 240250654, 26986415, 300632899, 4781630, 325415423, 301316502, 387032914, 376151128, 685252565, 843794386, 816885766, 113625259, 187088100, 862482823, 153592021, 174314036, 768357464, 62064970, 864528596, 418835392, 998960888, 293280200, 344382162, 46047683, 373898174, 873452910, 711627572, 496697062, 437210975, 224735785, 354131405, 926227805, 994603066, 256481701, 469916407, 509437727, 176302158, 489474594, 845451684, 224645957, 479237601, 21444862, 686267503, 477049565, 11303881, 302351494, 389953606, 84132445, 836349708, 154378763, 984848027, 405385905, 385362777, 243218242, 525727977, 550191535, 542056858, 670061399, 639735786, 527506943, 692416064, 242638447, 590501255, 236133560, 146008741, 352060767, 40377928, 183717754, 359608266, 946053736, 392435899, 142794454, 778501812, 129535775, 365978343, 224197879, 957078516, 805748034, 806989303, 854534765, 479544910, 74552741, 356415406, 703806073, 930354348, 210964345, 422667210, 757202292, 580373003, 649939575, 777920710, 941385047, 118536671, 477727472, 429678166, 237362495, 478991493, 907036303, 335926051, 796020543, 602800382, 376679026, 496911002, 759888542, 212504672, 267541020, 940085627, 27662303, 449210472, 757403359, 154561932, 249554554, 131191140, 861525562, 648191528, 386063391, 634273884, 584862416, 608566755, 295817579, 806022855, 300476221, 30022500, 843820066, 21105378, 311848987, 973662617, 687844454, 947696579, 376448317, 166736622, 428143552, 685312106, 853390875, 425734774, 740495011, 953577276, 953958992, 977519279, 398744923, 381476214, 377186498, 256255880, 513019256, 134876452, 900569672, 186588614, 774925128, 909903032, 57559153, 209051252, 355444310, 890593549, 863856178, 975985914, 633328452, 288652261, 819154953, 775848678, 675587940, 899998084, 755422394, 12577421, 339974365, 784185886, 513646289, 9954006, 445475757, 168214332, 648743940, 705193969, 261927669, 518679536, 294481640, 54383157, 568050755, 84822737, 993639777, 809617923, 235868377, 79140041, 243010849, 296542568, 502428638, 51607474, 157543442, 802212916, 249731307, 674333010, 702182005, 104272537, 397545624, 322073071, 880773395, 675295402, 188011312, 369930821, 509106860, 432055056, 607373067, 36907595, 91156509, 561721882, 810426643, 283532272, 918859676, 318279412, 412751112, 325981351, 126888468, 76484904, 54570144, 64903371, 739642303, 957027324, 919871140, 658293654, 219805443, 375299177, 869623595, 586651816, 169017832, 85468028, 234295650, 633174432, 456612714, 290473715, 225164537, 207302020, 976574623, 497601231, 711223219, 729900198, 28207938, 188802568, 277275526, 772177080, 536489772, 261734074, 255160713, 311331082, 154864773, 642591873, 534156848, 642929633, 361198616, 548507029, 503938584, 322285408, 456653808, 206438638, 313241138, 530604089, 359912600, 395623001, 985016769, 260745615, 756014306, 956319619, 486114486, 226011484, 952776968, 721068776, 211857863, 89574523, 943068655, 568491868, 154854201, 254374516, 290677111, 943874943, 650297832, 407442313, 800355608, 316940100, 699819551, 898982233, 336527861, 136362101, 542792021, 888027732, 212749315, 567782986, 292630376, 657083511, 739850591, 84403546, 119488151, 255065793, 99892073, 156822246, 73677094, 545372195, 385394796, 649903146, 884620112, 638412744, 967834387, 659616502, 209131242, 25106386, 229796720, 775148654, 255938828, 843116805, 586210749, 58127714, 516169527, 726503867, 634936155, 435818614, 84280534, 333823794, 449832003, 493111507, 616047196, 293762087, 130617118, 492622282, 7565482, 234580707, 553081409, 977100975, 99654939, 665343212, 156505653, 549987480, 954997912, 489788971, 158024217, 917545661, 948545969, 830665431, 912611868, 143429623, 930602878, 3685636, 725455542, 115330233, 194131999, 687543451, 333859549, 464262694, 441250279, 1136646, 88698245, 69746098, 246098266, 364756776, 540856779, 96174566, 647653714, 191342970, 917273118, 130934459, 751136977, 659872735, 670607742, 19565883, 475570147, 27593596, 834838171, 359859135, 531524179, 869658984, 722233028, 596697937, 278272865, 979559620, 735966250, 34947704, 67504636, 835364258, 398468681, 58157021, 637064931, 668583229, 254183325, 710976264, 515091051, 249302257, 899208421, 813908203, 753606324, 877122157, 951469994, 215743796, 58228767, 762842914, 872302707, 165179625, 328544019, 885335569, 468634353, 263911133, 690194999, 325726519, 456489180, 850066793, 783896509, 31013309, 636729936, 77082217, 929916854, 126108154, 41231044, 210415896, 707867854, 761834645, 627413121, 458101437, 962082784, 811863097, 423212166, 156095949, 673054830, 584458437, 377406435, 277593201, 299030061, 598950299, 178935371, 922140411, 893488690, 320643141, 686867573, 464452974, 236819277, 31128315, 835958427, 845611617, 486436686, 111790678, 718004673, 254459062, 253743542, 515283955, 868486655, 58461504, 995174007, 351608901, 482893203, 296102233, 137781910, 32338029, 254028278, 980655116, 967074372, 846112760, 356346778, 660252990, 988756762, 421839365, 721812384, 814658188, 494368916, 50446137, 595589211, 332873866, 210228294, 764797653, 224926680, 282378685, 580744647, 860261723, 9282143, 879434181, 321656407, 841006706, 587447810, 739605120, 755093506, 388436506, 505465991, 703656934, 10728785, 635916863, 454793874, 652325767, 636830852, 719718254, 128896683, 78785022, 891925518, 852840446, 532196474, 108231884, 824475804, 857937504, 244760542, 93670767, 147077631, 760446552, 692324472, 379755342, 222352151, 430685529, 743925772, 86764158, 570520386, 160787157, 455942121, 396799919, 429843355, 342778347, 123909598, 723149903, 428952088, 159896201, 137974448, 763884626, 757453290, 2438481, 24205579, 700586023, 144797368, 356800045, 483817101, 913362395, 164505989, 900941379, 381677951, 103793779, 51423071, 939450418, 213753788, 15228284, 922158526, 159419087, 571421929, 212551961, 864443501, 827024224, 713409601, 341380004, 917304118, 409185339, 576837402, 428486192, 428571264, 379287037, 905069045, 685446996, 996109385, 292020122, 101334429, 791899699, 762986805, 809893547, 445073724, 114523734, 140185899, 27355873, 434373907, 235715905, 200925552, 780599386, 107981954, 250793089, 908266233, 493448344, 269836035, 725479801, 753226967, 185259470, 599420151, 697830677, 924952670, 903235939, 495981854, 78311135, 601701090, 726130453, 255280740, 803488449, 826549743, 801136428, 396546473, 404831747, 767907385, 175300177, 54177736, 305456880, 535242656, 410004349, 450514991, 247312985, 376764733, 950919961, 451167392, 246294441, 502799991, 802126638, 366797574, 720576081, 437069361, 979272060, 114914896, 406061079, 993935186, 473763641, 361873740, 206640990, 214853992, 796068050, 247489878, 190394935, 692955095, 640597111, 759098643, 280777241, 682923641, 587902208, 12334950, 27420994, 69624293, 352177277, 954989669, 95788719, 473731556, 124644329, 13615098, 8287880, 578646125, 657254478, 730495541, 55327443, 777600694, 998122262, 702175866, 873014768, 931848261, 162511393, 98295121, 601232886, 115101145, 301258357, 276999495, 611253110, 824036967, 837277555, 272463205, 529213677, 931325597, 305294151, 752521114, 685074283, 605885821, 273659312, 848506670, 405432792, 531101086, 636100175, 368642467, 662256840, 344230717, 879218285, 975159826, 319469424, 556894877, 605068310, 438278190, 820895285, 861558766, 321568578, 690124046, 405265676, 541730263, 176446741, 391823514, 791860699, 463180887, 906934122, 669373428, 987710750, 70299882, 352135590, 877674363, 198587066, 356934023, 97062584, 697935040, 455380708, 725874594, 301587041, 655025579, 170363756, 728810931, 282438713, 686540060, 734902961, 859016434, 848984969, 825697539, 789031671, 176613556, 586145506, 259887404, 252985365, 313443669, 489779409, 302381617, 828924026, 85781984, 190987074, 996167556, 522188209, 393224476, 155895938, 870851806, 552137419, 561884602, 486241685, 345792672, 723057732, 831512132, 205022548, 16454387, 404731997, 292655534, 391085990, 779670218, 94016446, 737586401, 247310174, 81834609, 365049723, 387915321, 353646166, 852666552, 689319213, 951029063, 760930084, 148958843, 301412893, 739738532, 789664039, 140035664, 662148121, 505621762, 865562097, 888361534, 670072765, 307598968, 732206707, 576228899, 787231305, 498225983, 583754872, 486618012, 975603446, 244459595, 540899403, 792639454, 280676309, 141987025, 467776594, 180251629, 768206582, 118126291, 887918115, 518669482, 781586627, 723142551, 698510657, 468861451, 109232275, 37221369, 489959703, 296800020, 435890414, 681518672, 954584695, 113281501, 277101090, 457759507, 625687994, 131896152, 942835310, 450713478, 338436019, 552523589, 513639196, 998413756, 809638850, 404269581, 504405117, 599624059, 369647093, 21570657, 945109320, 194650036, 396593382, 222726005, 418060053, 215513707, 343107059, 21204308, 235733707, 553124419, 616736700, 462018288, 641813106, 512387696, 246669411, 302865765, 223152610, 106295212, 119487092, 430764110, 412259648, 361984064, 375396555, 71242730, 125550121, 58145652, 475515109, 140887458, 774979493, 168690606, 440837973, 807787082, 721620558, 631167718, 169150540, 143828252, 591263086, 499387337, 995227704, 490322491, 26025295, 264142419, 67103855, 453691272, 174686654, 570794586, 689498507, 133598800, 918550657, 47735251, 238790543, 870692177, 670359306, 407154767, 684453453, 217146683, 287476385, 495044032, 471448050, 7223013, 317006333, 37530063, 804959056, 404599138, 251360640, 146578301, 781081617, 706655216, 817297359, 843294231, 209906299, 814007061, 755757415, 89941950, 59721151, 315561143, 758934294, 409466167, 660660657, 978021895, 901321464, 929635608, 438839981, 254264201, 497491634, 790716556, 552980336, 881917005, 237165173, 767811125, 365793954, 725826928, 804355551, 834573482, 148271769, 408541240, 34551960, 353740286, 402239974, 661510509, 633009669, 919775223, 437799739, 562776889, 206626261, 955039298, 816286844, 424409939, 479286450, 489697212, 945280258, 793015382, 943721195, 740383091, 674358901, 592130739, 160657131, 962043680, 887943659, 524683841, 886475274, 33257275, 490009721, 154838886, 77746197, 444696361, 485029311, 545963479, 878796815, 347275506, 479596455, 689938739, 953707214, 944880896, 666993429, 449585211, 460891005, 72601608, 633219525, 229340387, 447182634, 302183131, 165027110, 589461617, 396040097, 349037943, 261245413, 769696224, 301954540, 725936261, 108716149, 846849054, 397007732, 480364744, 35189175, 379418446, 831380226, 285214700, 869339760, 217119711, 251626738, 781349222, 226349189, 955992516, 765351188, 880602888, 311344227, 488934278, 884613409, 181076585, 620552099, 422647001, 662670947, 876736117, 320682418, 289471147, 905292709, 108794144, 112542401, 369019507, 362634417, 429077491, 573066637, 423452858, 324887032, 627554738, 502674440, 452547380, 755426586, 422794575, 251083667, 298823852, 791950296, 677042167, 143310839, 882624153, 566512560, 276394136, 202652316, 786602983, 320157612, 119356137, 945561814, 26091245, 219796233, 247868133, 744959302, 814842606, 62656827, 930964748, 648246895, 466850249, 955220569, 570813789, 309784565, 376675125, 106808020, 353476724, 374417394, 88631301, 81064138, 177123124, 545508267, 118718517, 654485994, 675237145, 66164288, 913911677, 61944757, 74421542, 604519451, 267087275, 972364891, 406722391, 286056419, 11104619, 923648315, 20206942, 854001414, 613339781, 870535698, 284258446, 365035512, 570837376, 986037007, 681155033, 497792285, 109057244, 244656174, 856746709, 448198132, 981535584, 648729844, 33105424, 855575389, 838278815, 992083314, 545022780, 140790648, 196451814, 842532313, 181625778, 602787657, 678406100, 597284918, 159045103, 619023827, 304286473, 606731967, 988883497, 501326358, 874188302, 426506018, 953146638, 197973976, 488934664, 889452014, 593669770, 456215545, 816749260, 782357513, 178662900, 452166781, 836045353, 314648104, 700907774, 481453531, 796092525, 599161908, 494954101, 986071926, 512933740, 323455666, 65308238, 938387207, 227284118, 848852708, 754053877, 652774876, 893058592, 782827541, 353255788, 509633260, 452669006, 740829361, 34938026, 591379202, 101957406, 102711973, 105917028, 454529323, 990781017, 546817355, 179844021, 558898106, 442140477, 175973614, 430116020, 185241086, 6818434, 901305907, 996904133, 347866314, 598067930, 420997785, 762195634, 310411942, 415653382, 29212306, 312641324, 521727923, 303864059, 442481456, 317932037, 556498903, 669289723, 221077531, 278085653, 156522314, 364874138, 108839522, 942899499, 546682044, 673462477, 933582168, 810413905, 565849347, 505367645, 846498493, 389240450, 231414339, 880994386, 788938691, 876143799, 134698526, 739983631, 95563098, 893503287, 959544312, 467263941, 872713599, 728418482, 511793689, 533836153, 682213437, 499272915, 196312233, 3753537, 3798486, 732185706, 82807340, 487844748, 47314476, 968290563, 845847094, 713516936, 538112868, 641406946, 74588438, 702750124, 879875828, 971299442, 886025782, 975029374, 344190849, 4885099, 500335638, 606475193, 635068903, 553749411, 584754753, 991561865, 136940739, 112461045, 773120673, 442919196, 756658834, 954178863, 342335309, 874153781, 398350266, 281141911, 186846473, 567449078, 459785552, 51376417, 860163299, 878202191, 670226912, 910085553, 418859204, 695945723, 846328060, 655860837, 686446182, 580428906, 465831479, 284592704, 707908027, 975262090, 991182082, 72808778, 584091244, 209254587, 564649891, 883941526, 669638442, 458824130, 855310432, 243757999, 364212989, 981094036, 249701842, 752429670, 840332721, 146933633, 29658099, 139390809, 35371723, 951293186, 553746568, 267733516, 949642255, 153176934, 171471849, 117168761, 607435408, 393285553, 129120886, 489186096, 464592118, 672370752, 313039692, 162896893, 238923014, 152323229, 658115965, 821416207, 676113728, 244788938, 52794614, 651470095, 980518206, 252510674, 350643162, 763811687, 531927943, 454416798, 151117452, 902987953, 590799963, 442077733, 160249814, 253867721, 527311765, 535798886, 812339920, 224757523, 36428221, 662520122, 648979121, 358252502, 285114776, 933990874, 452291624, 347837423, 496242472, 327899043, 72982800, 177482180, 160818166, 850379658, 510106919, 472599344, 61188782, 905783378, 916946202, 36245111, 563328154, 789589322, 809777891, 731946831, 382370178, 128202124, 193717575, 522799482, 611583118, 83707396, 729357122, 405124020, 215183177, 580413973, 418679917, 837331614, 873510627, 997881836, 358775199, 238725650, 888770306, 960932551, 837152151, 362673290, 786649188, 973140959, 58592421, 727328072, 228714547, 147949105, 656932553, 499522285, 979283757, 16679427, 897350159, 939117139, 210078105, 747426248, 425802195, 571359916, 947782918, 207960865, 979725385, 704622643, 402163294, 109819574, 924328507, 225142771, 477490928, 435344015, 924556680, 135514569, 900183469, 770267984, 690371836, 379815502, 803896312, 859744226, 880071720, 242338870, 339537199, 542968898, 358755635, 682284404, 389632732, 701216806, 411790361, 479684223, 714836463, 319108229, 318616121, 59201325, 698697545, 713775925, 911440631, 900851702, 994909994, 120660464, 495645885, 317750234, 856191855, 322117928, 212499154, 921090541, 288119885, 252453927, 90828626, 373200522, 496768974, 778556257, 187976376, 920759121, 143932017, 870692987, 423186292, 513852559, 605972342, 463803510, 930278523, 403577940, 160538352, 761988598, 34806325, 494934469, 97287561, 913865289, 525666830, 217735145, 405021370, 804290824, 214390161, 362953443, 742031615, 989790937, 80256306, 785890068, 127254769, 680550144, 936704702, 331755468, 824978201, 568088207, 625804262, 771614419, 386240510, 560293677, 394016189, 487611956, 895957316, 544760666, 244804967, 896322319, 56315573, 361141307, 286966090, 292200229, 317144568, 975961900, 21856705, 13438971, 581763482, 536057155, 908483139, 159674950, 371983349, 651029438, 249466348, 870632791, 239908497, 661579841, 535253232, 685300665, 281221814, 64575962, 231050977, 52170623, 500685715, 51804691, 1404911, 941168479, 493126726, 202152416, 151875211, 378787584, 249580285, 281760871, 900199133, 787541311, 476968205, 282712963, 178544109, 513583522, 482459054, 228825644, 56180844, 750643387, 467735755, 574102746, 5333045, 142772703, 139903714, 378150074, 604798426, 13774957, 793815377, 433032845, 859260452, 541829594, 254286818, 480654242, 899520187, 777595747, 737831863, 235570668, 79402550, 389058645, 469533840, 824341802, 962130181, 626141511, 543156603, 525427626, 941966893, 788584693, 977490552, 908464159, 101469303, 204619689, 445150028, 923169729, 987240505, 760665958, 595626940, 922392152, 359153306, 4381277, 294903915, 888383012, 568737050, 705314315, 212043954, 249906736, 943284205, 163945594, 159429741, 512653994, 447539493, 245128752, 991417496, 301766226, 66502865, 914720780, 165700431, 670946428, 26407354, 991948170, 206696220, 18591922, 517381263, 837938103, 995569622, 761317079, 64464575, 992726774, 106695521, 76071157, 359158219, 575982976, 356592265, 977156958, 81647354, 819837220, 877223483, 230849427, 543770717, 21245359, 834548196, 841850681, 499968089, 972828454, 110330487, 323097839, 226542005, 815592661, 764298037, 70604950, 153704308, 769389121, 751088136, 188687853, 587494454, 762197903, 729943324, 414117866, 759585217, 876297823, 707678255, 84230063, 385304279, 976709658, 802521844, 511877623, 180843000, 546110908, 357335999, 76746037, 918288533, 88234988, 811052938, 839844379, 60718371, 813348929, 704224454, 776344264, 574031941, 855635783, 599903221, 505228915, 734029360, 572003372, 972816961, 741734234, 17719173, 198376178, 433344052, 222067795, 649137331, 115288736, 825994177, 273477875, 485987050, 474635913, 650328805, 713749096, 315673329, 819068887, 449870384, 831491018, 788857904, 652534248, 54210088, 567699491, 412179179, 375406596, 339532731, 413467150, 87985504, 560802858, 170648584, 513959401, 156120872, 743842935, 120948221, 885234250, 746549993, 282249770, 424827599, 739310707, 998083861, 376466078, 153123319, 247314385, 899419580, 901313295, 192913455, 288730775, 486568012, 59176822, 249664482, 552315300, 745197916, 547751098, 454359106, 541950164, 808333559, 684934034, 580585551, 12928426, 42888921, 288646884, 431620237, 516219862, 469880754, 624166350, 935507209, 787331643, 249632282, 120433639, 941759323, 840389204, 739687963, 742882317, 690872363, 811628383, 582842443, 735893773, 464008507, 818734688, 943597945, 110384116, 221034400, 449503300, 934514217, 897276446, 54042732, 400347214, 712864439, 867678433, 394676046, 488588580, 826495002, 862816217, 859365820, 783737544, 978174440, 476678375, 737756762, 258081128, 838008823, 71106873, 427355688, 174846538, 531021291, 589090326, 116394984, 652197602, 48087579, 776243343, 366109923, 91064273, 888216042, 287028337, 655385682, 382804818, 920546135, 159247205, 713285454, 25130336, 646970842, 316100822, 397862946, 566088723, 733333640, 205353559, 482820043, 506561510, 562285384, 968092480, 684611344, 31439074, 413002757, 11318070, 183555330, 314784779, 906577685, 573012915, 696979517, 996032951, 721974607, 943600346, 675761461, 735248240, 485046379, 10560545, 856115556, 368972881, 86247104, 149438652, 243366157, 944475931, 185602460, 410923664, 144437286, 589988818, 281386883, 826255389, 877180475, 150111753, 918941174, 830519674, 292651458, 617059982, 805626835, 355243266, 175819045, 969383459, 601301297, 523733223, 952612061, 68196406, 388920097, 675878929, 558494114, 948258885, 102683784, 710705116, 340282324, 802743606, 505728733, 882118662, 569553911, 261763830, 194957459, 203313621, 824005795, 545942601, 146216328, 317619223, 596622874, 864863993, 88197288, 130677807, 619401097, 363435772, 423743219, 620379969, 944736530, 3057090, 929389005, 684949120, 21282331, 983246527, 54862192, 879534012, 272135482, 737238353, 880213923, 484227833, 231193014, 524166777, 500829056, 632448443, 655660913, 238315612, 497665487, 37492976, 94805082, 521940084, 873942002, 280484652, 744575707, 848726793, 954006855, 456650725, 330642918, 269229745, 58862551, 53998277, 562228552, 596080031, 851610753, 829225593, 911256498, 783696277, 885900941, 575957242, 679205122, 250386215, 482657082, 871413067, 932428399, 440690149, 419972824, 368658967, 341410380, 852737911, 512975282, 802438385, 204947000, 53795990, 907421541, 833476422, 17897168, 73191484, 258816420, 919628577, 695361790, 501248480, 965218670, 722196544, 387640308, 532929678, 176362623, 300035958, 409555775, 445099460, 461332800, 85506479, 209397837, 754496766, 854861793, 767634140, 583454317, 44592486, 605955918, 308280773, 254412108, 161764284, 407615881, 227818633, 453515321, 242331149, 622317623, 317534411, 445846642, 216302006, 682265996, 769480607, 733441398, 345609594, 333022359, 723336628, 124065258, 324627270, 949147849, 868588258, 460190091, 891590663, 371329022, 233634427, 388830095, 935829914, 109925990, 403657738, 84656024, 393438207, 605254046, 66446398, 318287411, 202786639, 486038302, 173366410, 387579212, 16219452, 130970295, 457123653, 207974392, 697370709, 247091419, 693851011, 154122021, 968790234, 537729643, 785063539, 712924506, 224873313, 564570193, 793814400, 725032053, 671104592, 228132194, 981593256, 249252507, 24756327, 679947608, 262304832, 892568385, 506165821, 536860101, 544295896, 908105577, 206976793, 422367480, 345205613, 353383787, 902053476, 310550244, 724871644, 339782356, 264678584, 559743019, 598197265, 613295328, 565817125, 263716362, 148842316, 791935059, 340560800, 647609895, 640333074, 670917529, 741816263, 387732698, 654057624, 471224144, 400983004, 248303715, 895193060, 741654552, 702773481, 455773903, 989383658, 794666324, 615697762, 76008713, 902322780, 833909842, 568366969, 194664830, 230008047, 840767544, 354370256, 63027273, 888066917, 175656521, 11445824, 321601794, 97246519, 182402122, 295803320, 164325535, 460764790, 172241145, 925334383, 452098023, 951831796, 816458358, 254028331, 838055453, 842820593, 958246646, 232675906, 931644530, 966843696, 190726319, 337876763, 308428602, 152246316, 793572725, 331600747, 238342747, 978472520, 445977650, 771590032, 429402641, 356265099, 813114156, 435668554, 328775177, 826162490, 15214292, 980982005, 448801119, 770810601, 194213856, 519180718, 763444478, 38277670, 855482284, 126075838, 90472074, 109847947, 355676621, 299051294, 413079091, 748984016, 160364924, 537732304, 55246645, 339828442, 91460745, 681765440, 938499409, 600785349, 489774063, 422142535, 416909283, 395093071, 966776880, 351764812, 244338638, 410476495, 365196757, 413709526, 81989617, 977315678, 329596400, 978057906, 14044134, 218619731, 921812069, 199543754, 158763032, 151830804, 557448191, 920228698, 748473248, 254004579, 954640679, 689740041, 259223311, 131677030, 714287030, 708480969, 933011715, 62179299, 126917010, 389522027, 538917365, 557491392, 708306661, 423883500, 749101504, 712563592, 472870219, 985292464, 910805360, 640098480, 528287005, 917048301, 23737464, 942989119, 535490966, 352028148, 147796860, 493999454, 992837122, 259524200, 675629121, 912346197, 392764617, 169064049, 950208454, 258894607, 506178071, 105973942, 415171238, 101994024, 511335945, 71611851, 448722378, 973131989, 606642598, 192731803, 487788928, 408577674, 680996656, 377786811, 418261155, 272516239, 82659286, 335625756, 968276064, 318741763, 380979081, 856612603, 319696172, 877427358, 10022181, 440682877, 14256092, 442746377, 305625023, 414657842, 428546312, 257372516, 907178853, 774226775, 450269520, 318707109, 528706776, 314782409, 272917130, 182749173, 103771718, 771392224, 889362750, 322038033, 642056045, 769863562, 413570108, 824974461, 995118222, 268027428, 843790934, 208013332, 437910018, 684206342, 411926993, 811598108, 117752427, 275112328, 945694436, 920446810, 705246118, 303657750, 689000691, 107613705, 545621231, 774349584, 619455526, 239661803, 858991489, 675518171, 823249428, 973500902, 400504207, 854189613, 34632725, 568977308, 174283618, 229662878, 747442705, 684076390, 381359947, 477478599, 61349772, 209620104, 838633941, 598683227, 262652577, 282310021, 248452768, 988284317, 90393353, 704682389, 555652558, 855520663, 747301159, 677639742, 344100361, 965513939, 352501075, 445290248, 448308832, 965344280, 631729169, 335295721, 341560803, 514256132, 318430082, 698443260, 942878596, 392659042, 739956794, 306052988, 807077540, 967363701, 900572000, 684069416, 159136849, 247879675, 256296969, 451820528, 507233518, 495305849, 649312214, 950482152, 947697307, 757442036, 850341810, 731064131, 750231994, 259284933, 196597955, 83522720, 528272710, 905042751, 486525609, 485117201, 700555441, 193224048, 366945903, 637120070, 783027950, 26463423, 901660662, 523485361, 28697014, 431341136, 79670929, 500232861, 142203695, 115251379, 713618100, 363102328, 715379616, 769176714, 166465372, 511700037, 410395875, 793831882, 951682630, 981188162, 25207034, 145162367, 694604000, 572227300, 517241614, 763444789, 581340979, 951576200, 470194693, 918743494, 295985518, 929157380, 930847133, 724629772, 139982499, 62984224, 805866811, 306254984, 83217978, 113738620, 345338308, 668447623, 572662225, 35189229, 871016735, 364888927, 157081238, 945826079, 785195784, 384223971, 942005942, 96764265, 131242563, 109899630, 311996657, 882660605, 732076008, 47875581, 664703669, 823724610, 900119135, 271622520, 496872456, 365668015, 949067023, 408777403, 538363785, 925362418, 29791186, 706656108, 477683040, 944506024, 339953711, 719761163, 381296863, 936025500, 940131332, 352688994, 109673784, 633151318, 423673261, 405928200, 739859920, 616623775, 134826231, 946523066, 440173070, 201273999, 851102543, 187256004, 312423371, 38875908, 887463000, 3503832, 387199670, 244824157, 311946288, 981309406, 127246463, 35799916, 191353155, 130469630, 985033755, 574896099, 572521539, 281538238, 832869826, 867315361, 254648462, 973774234, 123825784, 569653829, 39035537, 104962316, 876438037, 377217212, 808328613, 845998404, 64535468, 102282502, 122900356, 214608267, 678454755, 932471769, 894645798, 873399727, 464805901, 563015566, 660110145, 893765478, 727138892, 462153990, 297726136, 697681310, 753683625, 463981476, 771643849, 127355052, 322863606, 2262938, 191714188, 185036580, 69425801, 2820816, 726010154, 633977627, 286799342, 329675561, 258101316, 674906355, 697881515, 936106667, 71262158, 72093230, 585375963, 223517490, 380065365, 125733941, 185175926, 352110624, 997708859, 902421103, 381277720, 387208173, 999886767, 433663407, 229614454, 508868076, 616807437, 997917214, 420481549, 314486592, 641761300, 39364810, 348125280, 93848129, 500985068, 265348944, 404504872, 178828217, 802160216, 614256718, 846122876, 679647044, 864688911, 638476433, 663537890, 429792826, 537794680, 111136156, 629250557, 275315198, 294685531, 650249552, 915921636, 590255399, 80646240, 627704077, 144347005, 824349797, 812984585, 994414631, 209882779, 833710718, 611404349, 963009823, 63541503, 77233503, 860330713, 308352582, 544554588, 783316880, 163382272, 668889060, 128985667, 925877052, 598257156, 529778657, 128430789, 955232877, 128700, 80349701, 251612752, 999763861, 835482422, 264543223, 798564130, 345165800, 638446335, 164999739, 749225798, 880709428, 432375294, 197583760, 927520111, 391232979, 304510800, 814207782, 766728882, 769353452, 95615545, 862830753, 921838285, 438341795, 912688204, 850470367, 794142568, 774453024, 890312836, 111788379, 810157, 385269309, 806664647, 738798769, 321720812, 397429559, 285323916, 16861129, 502082117, 500584115, 174549172, 370304120, 718830285, 344649166, 697348032, 932602849, 586506483, 275116303, 293669235, 884937310, 746603521, 506523972, 384060315, 182590934, 301774905, 133133022, 184594956, 879430538, 2038938, 590681068, 267117226, 955482146, 881527870, 751787332, 639238909, 106360909, 762164345, 160475819, 218960008, 281707110, 653642878, 291528929, 53579768, 175276056, 822006956, 37926288, 881841337, 694515423, 544110593, 44597251, 918862845, 531750628, 494668365, 440201415, 695085339, 224893935, 876107861, 882827194, 35335009, 218068667, 171364598, 515274083, 705054170, 591867945, 197725680, 32259623, 523470334, 870143260, 771300523, 575784771, 805397802, 456522344, 347239952, 449229168, 882409565, 226270736, 22602079, 787595245, 749466240, 348939768, 337334755, 39638608, 854090748, 930304340, 652114342, 437581760, 686528533, 258771193, 381223123, 855932759, 338204580, 890715163, 929021218, 423042889, 524534325, 622418076, 653845432, 923733807, 430453486, 608496317, 822992802, 851391791, 687669279, 861917975, 981663410, 403939953, 114642665, 407861596, 703360894, 281573612, 874745742, 332300994, 920660729, 673296896, 473299407, 871182245, 742453285, 32303082, 637698115, 309922329, 512596718, 174245852, 14592485, 430674126, 81931891, 336037481, 522276783, 532727431, 879294942, 543926451, 542306614, 262118888, 91759457, 741720351, 705491375, 703307775, 630986275, 476803671, 58356822, 973536119, 384916859, 830043503, 475955053, 445156617, 685369644, 972171710, 381357790, 594955442, 641301166, 669583732, 151110314, 122513467, 825536648, 61798897, 619607828, 139681312, 40017872, 42526746, 762686940, 623216423, 321602560, 847723293, 642172594, 131104479, 608907738, 438120754, 635065113, 356221645, 283980573, 517035742, 265742780, 831068701, 451169548, 554768749, 797506972, 958875767, 163739725, 740987184, 836383930, 504505026, 869214651, 285917730, 539539603, 12040476, 741770405, 245066216, 750127583, 270600152, 152717269, 543149391, 324316214, 560656728, 569888085, 709226977, 722532162, 806237210, 568948756, 727569017, 665430942, 673913372, 965985082, 411152767, 105080178, 797630901, 98835914, 949543399, 987140151, 239715237, 977926399, 917238705, 644629853, 315261824, 185175100, 581810049, 291736736, 788305306, 626134982, 247481272, 266973130, 330732457, 439259257, 989610386, 416587897, 36851835, 335961673, 758855607, 961515146, 448486767, 457670344, 216771555, 651355235, 864484555, 625886304, 678167696, 98198178, 617614858, 122180256, 243660051, 172441807, 654085811, 867125175, 810152371, 100921472, 419735394, 625189788, 424950610, 735863858, 157795894, 685320849, 30717151, 517710009, 156743164, 857428017, 222361332, 605247789, 812913695, 873720664, 57059210, 132314601, 616479199, 433691497, 427897623, 190246301, 727680809, 126656621, 530348708, 399542028, 744188470, 261174226, 239511018, 37315222, 558259197, 712667221, 390123681, 68436236, 77094373, 955540657, 479513281, 921313234, 402966769, 668975742, 928066976, 48174814, 325109749, 880495439, 357113227, 116916359, 243616187, 422016270, 922207251, 212874699, 124786887, 395768726, 293876385, 369594896, 81260699, 546646590, 975278228, 800427611, 449811022, 459410450, 402125056, 831283513, 37495652, 488015043, 742742790, 840808700, 693960677, 557791072, 681033200, 200847345, 19838786, 593451935, 122622020, 106655500, 373033515, 688540551, 104378388, 581426371, 584463368, 718568544, 127646390, 717583279, 645626251, 591146316, 775460503, 92412034, 170100961, 825764520, 869012208, 464577533, 375135727, 743533286, 40492962, 94461370, 273929227, 663917843, 758773074, 664172494, 893832411, 427326827, 670097112, 190887713, 173807789, 982743582, 215947260, 760608162, 730674440, 46674450, 903164787, 361479928, 88879931, 820165303, 663750787, 400231364, 185959629, 963791906, 590232477, 315354128, 33331520, 176829264, 923576202, 196156334, 697581350, 626375012, 404787605, 640763847, 930927503, 328512526, 811996542, 653470381, 794246178, 211569224, 40478865, 227869437, 488832447, 320712038, 577163685, 286929019, 855914972, 394641497, 266222326, 688396814, 237951474, 474647182, 747598166, 647104170, 567216984, 828889397, 427247119, 28659705, 459443657, 587167564, 264951327, 320890717, 368234864, 47777410, 452453038, 921286540, 560547196, 958411597, 820361374, 371549303, 220074465, 486445902, 995537423, 615477603, 999817851, 585858374, 505847325, 602435131, 991353075, 90224972, 388724876, 530205587, 208705459, 978920991, 714222546, 378704705, 867211259, 131135897, 34919529, 552616246, 760447980, 475958905, 347189443, 338679637, 614837889, 622273224, 152479006, 95256598, 155838430, 290560300, 188239608, 265842987, 352830847, 807295011, 918909254, 644520085, 819799815, 807294323, 48741207, 387624044, 791954730, 961052720, 813822603, 600668452, 447819241, 518358906, 37564246, 923326816, 544867615, 307807045, 445858007, 248232427, 454738699, 39968256, 889315128, 79043969, 442767786, 73433426, 628011229, 785470146, 642193942, 881556907, 572690886, 653910656, 927090798, 559262750, 168725739, 323619038, 349233080, 920377628, 893116861, 331359102, 741675202, 85892562, 878833251, 978240009, 437581441, 956968588, 195127647, 987073822, 673920036, 180080352, 825111958, 185500967, 186134329, 94873339, 407693504, 698935924, 684831342, 782444163, 17742704, 123630431, 275958888, 571828338, 361899968, 349618415, 128343390, 610410179, 706210951, 232202646, 107643413, 133362785, 368633009, 414950126, 459331484, 764217865, 968854625, 33576192, 87977043, 119603327, 818420617, 208147329, 412849925, 966439421, 19261629, 837812073, 211503748, 318617576, 366458523, 279978993, 238148943, 458787494, 844460344, 819529433, 716116339, 766346722, 612079361, 466883122, 38768749, 668596478, 321689783, 875859319, 732243382, 690443533, 737518094, 618741195, 540577597, 17067091, 629026951, 306211025, 115873160, 998011411, 853745809, 616127598, 734669703, 658766328, 182166568, 776341604, 623278328, 597293638, 544183780, 922294873, 374265284, 570470761, 419754042, 759350557, 175999503, 116358094, 671865539, 377817509, 933703054, 291359294, 988847998, 810434930, 619014530, 94086979, 150766695, 581908493, 729661839, 867221695, 479105681, 8841617, 921614194, 713057443, 842290960, 586311329, 29176592, 587017613, 874544882, 280643074, 906791035, 785750528, 283148162, 12187136, 194655973, 43309834, 477330976, 133251619, 98469121, 752759514, 794303233, 19094212, 831406988, 66186066, 204352028, 987420632, 91366895, 90552169, 248685431, 627916193, 717092819, 999244467, 837258056, 975452249, 918408080, 372155467, 550737082, 877496210, 396804016, 5468682, 820722114, 559965445, 417600280, 280048792, 767380121, 853167699, 116734490, 419225678, 159662091, 688883249, 251684835, 778412921, 636217921, 774208309, 271219763, 36792462, 98654136, 208518775, 528445879, 57723910, 628952593, 467423542, 605815403, 197659164, 813305420, 21986121, 953049163, 442187677, 260713906, 863133348, 474441761, 587590062, 922051441, 250498541, 665676883, 953186200, 659188410, 756531726, 866396295, 726376117, 645436762, 264030924, 415783292, 976046457, 377975358, 746114090, 777838489, 346914008, 182974702, 531492362, 59867346, 839500544, 665630650, 396608053, 378032483, 929256120, 985530235, 316937351, 274357663, 737974303, 709028358, 97825036, 608162639, 910678507, 286634391, 306816368, 453174146, 288246539, 727770263, 180442525, 596076757, 640003318, 537775396, 974491915, 246294504, 741267978, 721832951, 118106386, 319220458, 813232871, 255882537, 406915683, 917944079, 578604217, 541810101, 681666858, 22483301, 244260246, 468851005, 529602079, 819865439, 552431281, 347912230, 591541617, 254501166, 869031648, 586929810, 763414540, 623329786, 15562637, 19383800, 573515579, 405695436, 677831419, 77125076, 597516288, 114973785, 365159060, 85253869, 181872957, 846539000, 869944897, 426463230, 596071074, 789936387, 483566722, 734888840, 244436691, 597733845, 115881726, 879935515, 888034669, 675448506, 164140971, 771018330, 968541769, 157136987, 785205516, 219479274, 24423877, 435751612, 546097856, 733407154, 227161648, 367955487, 684885180, 550122989, 960434773, 787978019, 28096113, 159615158, 556525625, 935208301, 850825835, 758043798, 558723117, 260357670, 832376701, 551844912, 9037664, 70126641, 972974109, 443826219, 989096137, 721400349, 311307122, 676385871, 724430806, 792623434, 608104757, 266738125, 539629022, 884226369, 843292947, 606497020, 238996751, 151091091, 65802764, 586306478, 755457071, 325481320, 682620539, 461271456, 785189439, 985889856, 287018156, 224168359, 568325280, 92320195, 406228944, 476828602, 58690505, 463186163, 49392113, 492110736, 28891896, 54557198, 56684131, 15350761, 884056248, 489247276, 242464540, 871240281, 188424735, 586959990, 492756594, 580649279, 734223054, 986824993, 466077268, 213235395, 594503681, 192444036, 519385543, 863633155, 632958168, 805228021, 597726784, 445117631, 945306305, 652218659, 702207465, 928911805, 984482742, 584429906, 702928876, 962292494, 952069223, 435485092, 977705066, 358987145, 965879954, 846014219, 583044688, 221506755, 376581195, 901195607, 136417385, 471448395, 988727094, 720939150, 167683559, 289287305, 237062080, 227625425, 95765024, 523019585, 911131599, 916657507, 235744473, 264586789, 650375957, 21278225, 322877419, 534956862, 65142945, 207164080, 412577293, 236698399, 415466325, 35044311, 607500564, 323521473, 104546821, 493836617, 627732955, 244929518, 194116809, 823735298, 75412787, 286333094, 575738484, 406552821, 949876463, 454033455, 127615716, 63599387, 248902419, 543283401, 827040942, 597088274, 464663718, 70801270, 503694485, 739436130, 793351815, 86187037, 745793826, 67757025, 815178335, 804185060, 396509277, 352558005, 584686909, 426204879, 662205226, 30645961, 574226735, 898725912, 417490804, 627656384, 989039546, 529838682, 148253772, 57695215, 83485749, 920635026, 806247634, 496755410, 739373926, 493671140, 476056085, 975397154, 673924673, 110949088, 24956187, 275458074, 191202126, 875503129, 624102564, 993448207, 135230123, 444620806, 978740284, 251544104, 606062024, 218217864, 470875597, 152047928, 83756252, 992479154, 663075320, 799485823, 938344264, 537932167, 945959906, 371193914, 432098964, 351774996, 522865845, 558241995, 800205675, 574721633, 792016903, 625733095, 683430121, 805172678, 750865396, 923208764, 635499644, 453445541, 277420911, 76921109, 836046427, 760571086, 751629600, 663474170, 322241151, 576611210, 231320655, 289673826, 656395732, 265844534, 298931073, 69939028, 447549195, 259878972, 211513085, 552119613, 338657612, 896992981, 271108571, 644853908, 608210120, 667562036, 605439405, 175174104, 714074195, 296878134, 364310949, 349462631, 244966883, 131813135, 258534074, 640223262, 393015697, 959432959, 504637734, 29582834, 607207112, 886849226, 984945956, 427864287, 372464490, 995938842, 205040759, 587438732, 364189507, 634487581, 910802534, 20723340, 992832600, 74383618, 540255983, 178643940, 515304333, 697002019, 891276032, 457279798, 880330865, 156196674, 671464386, 353694316, 616245022, 452584318, 865890288, 692213815, 192854694, 784024323, 526380404, 275020369, 236611918, 167049483, 470125573, 886696210, 128346577, 123509498, 501322194, 747992671, 589325131, 20557281, 267752541, 544445034, 478619007, 358665615, 642544898, 310575894, 729250131, 218718383, 685840054, 755182505, 161335747, 104779653, 497274556, 112539584, 140604702, 722724249, 114978663, 882951608, 73774842, 27515275, 949613311, 822293288, 480843927, 398687573, 557313357, 747278567, 478299696, 730036901, 482774309, 315100133, 326398075, 754929374, 22124239, 308812122, 185080306, 477269220, 934807130, 462450862, 461216332, 555045415, 838890931, 182626124, 798241483, 635710947, 3955116, 635089401, 203974469, 403642, 441094613, 549271549, 678094364, 225244265, 502058387, 827555373, 408597422, 774374424, 78564984, 986873249, 805971185, 488113118, 296890697, 188678363, 650534508, 939023656, 712335322, 1592039, 524604504, 827735120, 98905262, 765178526, 321356743, 805457688, 615850837, 344213225, 473866428, 789428627, 327163611, 814095241, 203768296, 307074401, 988585802, 103231948, 932858164, 963300965, 739997984, 803461939, 698695066, 822233733, 547119767, 770356325, 69073489, 713214265, 95410730, 99055474, 2506809, 265734513, 902491601, 597558802, 713499292, 26574927, 419279433, 885266562, 42856806, 811468396, 259578171, 65762810, 934752106, 934317321, 750743497, 800617882, 27784585, 365585274, 630330414, 322082518, 508054707, 499706678, 441666197, 291394971, 214552982, 417449979, 264242186, 507283058, 974467940, 962032555, 100050859, 326994714, 653190982, 763058455, 112788398, 534012987, 881285456, 706659382, 680299958, 14270206, 536762174, 8670249, 645726452, 231751588, 72834745, 671214185, 158038351, 485580632, 814400712, 160539216, 638678275, 116343253, 432145349, 733755915, 375566454, 574020674, 945942401, 994671464, 726138910, 90268414, 572758825, 598776869, 664942258, 417223974, 528151091, 52039924, 519505567, 715151781, 577293308, 569467608, 923947416, 741666250, 886163163, 908765625, 584305937, 886605588, 197920972, 429716492, 600676760, 89791971, 144690243, 177067030, 838705323, 567169154, 853754432, 818506794, 978524416, 244814710, 295072036, 300511460, 661177167, 465430791, 387806586, 35178273, 966404691, 322969652, 317319303, 271441355, 249613386, 774996725, 770230632, 705096114, 875514064, 514480519, 41870930, 386588785, 631355561, 809381170, 559659682, 987435199, 727449648, 27885941, 286982534, 376452376, 806312998, 763820150, 714149379, 590347896, 275028487, 301792224, 875431535, 154842297, 499239850, 996979165, 442051087, 660032634, 855066738, 817504431, 594899863, 839170061, 574808810, 910058025, 202445624, 819424614, 604506266, 187593671, 795458782, 982408627, 190388222, 66539501, 819894552, 109449551, 551815730, 138427707, 718686425, 325424027, 853298335, 350635873, 254271870, 286420730, 378063951, 757812959, 179863611, 512278302, 604208473, 546119390, 408476561, 975885089, 775155433, 912560899, 361528907, 224213317, 785818728, 382330574, 593435055, 3049416, 342341873, 223660904, 958324914, 498445820, 438784467, 23609675, 670801514, 224128342, 915855771, 568204873, 112674180, 494010177, 679930327, 276321998, 95748372, 651481466, 293729616, 622287685, 531897402, 234970010, 167623426, 976591775, 48464207, 793046571, 879302867, 939252967, 900673271, 764722449, 400670317, 390298060, 741661107, 97291975, 615860962, 374917427, 51141771, 90366775, 549996110, 56738575, 804432113, 897318687, 872741699, 513817778, 646317692, 378340935, 586502881, 939111789, 671310899, 773042077, 316117506, 119832425, 126550698, 322357177, 677955060, 139594989, 66660934, 98604438, 286056356, 413506561, 967271786, 925185029, 547057289, 241234799, 20973757, 303756585, 570469771, 358458676, 642875309, 202033346, 395514480, 127340927, 130155927, 622914628, 263168819, 607135260, 772431455, 805329271, 405730914, 284552024, 978725660, 750564148, 887972248, 521369553, 213319637, 725733271, 196138345, 77276052, 16120543, 183087899, 851836881, 978857989, 646627237, 390044860, 532365562, 68956352, 92151982, 382082281, 279428743, 568550334, 541196261, 891383701, 595643416, 816782801, 564628579, 808504904, 332864535, 43646124, 712669536, 692657966, 702252816, 728252287, 921385943, 291011040, 861432503, 844316702, 703608330, 433124203, 137728672, 912260831, 10788755, 361717181, 603583979, 976196390, 912135729, 164205435, 126515274, 595706121, 206651770, 842457460, 415475079, 505558851, 529389237, 75974270, 81907469, 685289488, 996170527, 10743788, 404101784, 612324872, 46948140, 431320315, 199891061, 531360566, 534978572, 783379028, 404588829, 526882790, 501269090, 29360185, 934559905, 600049059, 930491802, 721052593, 121506896, 117318322, 336574422, 703071355, 867802218, 524004494, 403294329, 529328624, 199766438, 387856338, 201066863, 826312427, 230860127, 401664811, 138054467, 466178485, 786425869, 846981328, 828918982, 26813705, 350297955, 750808002, 847279810, 654458467, 318989954, 279850322, 582724686, 530716661, 207769267, 765562612, 786026920, 197858616, 71466300, 726650354, 984652523, 999935642, 305613574, 542801023, 427502343, 407956760, 14391474, 380735536, 670480931, 641693718, 401942290, 407714521, 671653383, 114869144, 987907964, 160427615, 915329440, 869418214, 770155037, 664844463, 43180135, 168545711, 239479629, 805201598, 955651589, 20687245, 178806002, 868880027, 672610356, 806033607, 304027735, 101465749, 18050953, 177236804, 990059411, 751947054, 83572651, 492263594, 579755793, 88337688, 327142754, 655282189, 156560313, 594778269, 246350684, 425614646, 384353146, 45621067, 430017065, 763352562, 195360968, 707744967, 330244762, 980734244, 11350546, 925023040, 494604491, 109645983, 733456857, 781526638, 774778620, 623166809, 846352856, 40533802, 384053882, 533957030, 506049220, 27411621, 752969920, 770606010, 871882787, 326287859, 532643030, 327689101, 732731186, 686732398, 234214658, 362065542, 591108121, 633268709, 726187757, 771534415, 773373102, 692962841, 460139793, 932444051, 196186309, 634109831, 423471814, 590422037, 404710419, 925958441, 426086976, 36206926, 427247757, 197321079, 857393206, 637432807, 645529433, 281499134, 449063048, 66914723, 823482207, 13663360, 750421351, 917018520, 445194179, 267146737, 349953696, 971035691, 47318453, 204714347, 982129211, 705516410, 134109671, 314368396, 153579740, 769754189, 341012188, 644273372, 184168526, 664680987, 382175847, 897595710, 953188846, 157901401, 6623272, 324411895, 39500340, 861917557, 699505808, 595628060, 399336621, 406266724, 446215823, 185777039, 963546155, 303213193, 772338872, 274203224, 646103995, 722638769, 795290923, 534473675, 440917965, 585977529, 380555784, 205969671, 503722980, 621859330, 978524402, 915245617, 279753588, 173549910, 35132363, 776907769, 235326925, 643765214, 182887085, 960869071, 817410933, 681461437, 733015801, 275977318, 843773276, 784228299, 75959967, 635809403, 716330315, 349903503, 231086842, 916403627, 828459117, 680279965, 924519048, 236194083, 822721129, 538071040, 718010321, 874929884, 491330478, 477822112, 763086454, 124882195, 948797441, 697783226, 951621665, 576773247, 511834351, 780984364, 513457886, 355931958, 459988953, 415418116, 199070362, 853824951, 126995199, 476348276, 733020297, 104903497, 408492762, 285148489, 738054843, 42511272, 523864560, 269236745, 720603332, 41183000, 374270323, 77722088, 942713050, 654839700, 623268294, 478995796, 551904652, 237271718, 931503986, 645209865, 446385239, 420671794, 239276607, 303945172, 561625181, 667012511, 648014184, 219099845, 494080490, 474458068, 312001033, 150563969, 674205499, 351454429, 370890573, 296302475, 809946356, 691238254, 434811867, 289132865, 839403619, 870621080, 233612159, 280249248, 540742236, 538593058, 537403092, 325171612, 636434509, 892866055, 592264551, 249235249, 276316574, 163894902, 611021312, 561570938, 345544652, 833046772, 462162414, 369194321, 563984211, 276954621, 329769128, 182275916, 467556857, 100016303, 595128772, 51445408, 38302155, 528407933, 590298651, 43180779, 811518179, 153773300, 171519648, 803376791, 415949282, 817114465, 702926121, 961888586, 563047977, 554871028, 892424034, 600197113, 102023217, 967685433, 710354346, 297007060, 572495976, 914653866, 420543136, 320375609, 732060881, 181900514, 414104246, 844367071, 61985727, 471935821, 736133721, 224224100, 820188859, 774364484, 658685584, 783567300, 894719885, 902437169, 450293422, 537614304, 603003673, 695527677, 33477364, 373317106, 843541334, 305154916, 452356929, 834788983, 943890885, 445899667, 79851031, 108186146, 452070576, 92387170, 331156868, 275245877, 296416839, 936640360, 685831130, 868812989, 915596066, 678972807, 754249988, 406167568, 160681810, 660958811, 801603577, 947578752, 502651831, 912770141, 437664415, 627559790, 315623856, 263278599, 56070131, 926167700, 147350937, 601383020, 621413940, 343087776, 251881850, 525406698, 265803238, 471572691, 637436028, 587102849, 363901548, 590504900, 891306181, 366371033, 325488875, 667100227, 516704324, 16879300, 362378545, 190040034, 540504494, 975343646, 234430331, 815218222, 461693743, 820876620, 144793822, 142995887, 456319093, 132922305, 752114655, 767188848, 95934703, 613972664, 834423381, 918805792, 235493147, 72559876, 209897844, 992815670, 138900484, 292876180, 315567952, 947986497, 950650058, 380468913, 419365845, 717698624, 130401724, 615955603, 295089303, 139727018, 859088438, 495165904, 641635218, 646776510, 25275977, 568932960, 915466186, 177263414, 123119015, 222808544, 601531433, 320686271, 38657674, 33341563, 540484864, 176427122, 478048767, 711210909, 96693174, 555230597, 218650209, 999282939, 826849027, 720295236, 211238214, 52698506, 613914477, 194109098, 876710066, 740138593, 609597647, 829699314, 193911959, 600063819, 914668029, 402069880, 504001455, 831306027, 495271578, 642362942, 545055197, 322599862, 921843493, 104401477, 244222994, 865026305, 482608882, 279862423, 164476967, 736868035, 188542687, 760615120, 14413673, 847067883, 913467119, 673951911, 492066128, 907837021, 836633958, 312762616, 929953324, 860290954, 174302586, 306718652, 556027318, 691973675, 907135332, 198313673, 884292464, 829716890, 447890050, 341940186, 560612745, 541737591, 726742527, 335317368, 822330113, 875628287, 17438720, 828233949, 416362631, 214929144, 3655356, 164785001, 267643460, 654887575, 894986394, 102336681, 507531493, 447079009, 722100891, 20397053, 17640550, 565513073, 555350345, 592767495, 428176895, 242137443, 476998216, 623941632, 297492083, 579885130, 748672385, 936813735, 146638073, 476767361, 834389850, 658253321, 50349432, 659061798, 67496531, 470026459, 193340410, 514301136, 298893713, 578774448, 138473231, 703492494, 60103250, 898739995, 926685585, 423813353, 175530585, 680684771, 39364359, 283130905, 940338496, 113125389, 157570241, 47994871, 832795239, 5287096, 684437057, 615554685, 96208823, 761568288, 923726072, 995358813, 452670317, 371753118, 511939459, 965163604, 226371662, 20183866, 577406537, 115436603, 615331239, 632008506, 949151680, 460183828, 833132391, 318461745, 839343205, 269025128, 968404852, 821455476, 211957250, 158729405, 659098138, 425183001, 161100921, 286700588, 950509483, 178645800, 748229213, 890509064, 57207506, 623516070, 708365332, 88099293, 518176507, 700815364, 332104718, 697974528, 899117691, 403656851, 238124293, 177788700, 654046185, 210279692, 53715410, 478439060, 145821513, 897727942, 854418278, 413765749, 132758185, 476540988, 315307553, 848485705, 315803239, 10390200, 308922453, 815043257, 712833573, 283271309, 525858563, 427009938, 46003245, 915641768, 225010458, 191377149, 444792935, 664680927, 737914454, 477515571, 635590664, 835569692, 7152073, 501997554, 13932364, 471668042, 86511176, 756563600, 837976086, 755841568, 813963085, 553473580, 715181114, 953336989, 273765479, 675197462, 520153248, 641267624, 463850910, 586355695, 434218453, 613107372, 794543421, 1020046, 645121407, 384033994, 855521433, 838143419, 319343479, 577747873, 839795879, 393362941, 516893158, 82301763, 290362167, 856685045, 247905434, 324047179, 680227096, 397059343, 278976432, 661203055, 206890045, 747767444, 263966943, 524255474, 422212147, 816669601, 237991583, 26848067, 242694713, 154316093, 945187521, 724032888, 148203675, 795503055, 45531841, 240922095, 400387137, 593490876, 410802113, 605077910, 467869353, 114769798, 643420920, 768644737, 604600101, 198026422, 901107088, 966098664, 497700068, 984510086, 616658039, 394513213, 246638263, 663153727, 617467370, 562945366, 265218043, 847516105, 279492707, 836617384, 425971442, 367691207, 887841400, 503666251, 829708904, 616201951, 185966599, 292534372, 460296313, 246522171, 649891094, 888886999, 528523662, 517663184, 785897101, 988035429, 486120222, 158370017, 247343432, 99206430, 892283992, 569724163, 377857525, 647734522, 409790203, 322352773, 846730733, 176163705, 993413861, 155232264, 654867959, 723801216, 259419176, 905445859, 672697451, 40399767, 43603995, 220183154, 294954692, 849566077, 792790812, 303040515, 517692657, 22080115, 53469171, 860233062, 611713004, 740257910, 21628858, 672580967, 7593955, 638089828, 778416092, 457271664, 713404687, 901144298, 900535664, 40531342, 475392485, 198767070, 124663139, 717919240, 934132322, 536521176, 680046757, 592662421, 997223762, 119524533, 664899813, 760523929, 201051606, 311331045, 415806946, 753830269, 412496812, 147548382, 608368035, 194579471, 116084263, 986062917, 999940801, 437534855, 38449069, 54384647, 612885065, 733918673, 169794969, 374219835, 348546857, 723290481, 180481761, 22538372, 549259245, 736514491, 833803556, 359241938, 514046896, 307173066, 538026579, 544430343, 272220015, 617060573, 966698457, 105510039, 659930004, 506529112, 832853879, 220941040, 926095080, 499825836, 296781069, 140097163, 918958313, 92814395, 892839224, 115154020, 1669334, 645032602, 668333186, 494717080, 501577952, 89370274, 648260252, 147084787, 23125469, 371742017, 488512437, 196656685, 609167227, 37884310, 768020659, 36765915, 428090371, 299611919, 966056617, 595916781, 27992170, 110187565, 347338454, 296106245, 499376143, 190262380, 976364813, 388733277, 20458164, 836844912, 675424168, 440540651, 260987632, 197538201, 65570069, 938318065, 208066606, 72169826, 898198784, 739976140, 67660710, 552462689, 211721968, 319356794, 823296503, 348843836, 317729328, 591876466, 351571143, 33153205, 206665763, 21316827, 722227926, 128141207, 554926784, 94943272, 440968713, 560071080, 501315404, 901560510, 661041883, 284158196, 163010720, 796978096, 484608235, 185460979, 582897248, 6416710, 143436971, 226260741, 196744862, 607171540, 703420602, 4245468, 606075394, 402308263, 719825292, 671348888, 758684337, 745097348, 497264234, 697604287, 918632439, 530980022, 436519731, 308544879, 824361791, 994845113, 381649894, 540073170, 676718674, 337866028, 70966995, 306918437, 901227815, 597622729, 523582088, 784340209, 182599319, 608561047, 167502578, 808823195, 508056705, 630383054, 684401167, 744330752, 923247274, 435031887, 832934442, 845125429, 29788829, 243960280, 2564289, 20366529, 631014583, 419398325, 30371791, 166766004, 133463985, 363355516, 782464838, 424939430, 126855619, 22290180, 389086101, 420461061, 556955553, 347296987, 715918163, 367337305, 193271334, 360722279, 560316853, 526316198, 963878882, 373568006, 588778073, 878633476, 184177768, 437611984, 151562606, 662198590, 400701275, 376594002, 104522546, 204970609, 268843498, 748551872, 138635369, 428116776, 299090758, 153409908, 332571776, 127147422, 347901476, 14256459, 37963537, 479191517, 655348984, 500056576, 330696011, 918953611, 803887228, 234725879, 926686411, 723567914, 629879454, 955939381, 185983973, 476720855, 377389831, 991736325, 247774440, 924339126, 328944639, 372139135, 30746903, 865619518, 787362034, 480309016, 935344352, 478254609, 949604089, 681367044, 674086284, 576288736, 104558710, 904907013, 34398891, 911766899, 83583147, 416672108, 529401400, 73099522, 636709918, 900779777, 51034873, 303489032, 312083484, 678253112, 245506416, 203461683, 608974611, 489270666, 880036793, 664203533, 891661301, 2804095, 154192147, 860905245, 715044268, 339761117, 871997873, 60780173, 555715589, 135230786, 306651561, 275955609, 406290494, 682069929, 709184634, 719736247, 796253432, 574436903, 445152394, 707521650, 372432375, 414457367, 433570691, 723731401, 348107849, 571509039, 243727678, 835106433, 753936018, 411762019, 116215490, 15286026, 147017079, 231273084, 266864420, 197777750, 427271733, 115058887, 401850615, 575254191, 336069694, 174508222, 51115836, 720492340, 535245458, 735194248, 575313530, 827544079, 250287243, 789442265, 968220057, 886013656, 718398043, 829456253, 253086529, 480935146, 864334124, 370801299, 500981434, 89885000, 674332296, 91766048, 237234052, 114787108, 628054285, 616895300, 308803462, 141604843, 510611067, 211800585, 258383305, 538507370, 612943068, 127418360, 980299367, 571271532, 817651130, 635872327, 660018072, 680017800, 270785276, 588694653, 993937037, 91729047, 138614043, 64300901, 436153885, 856311564, 307281716, 786197757, 492466916, 55150247, 637799827, 291737391, 306197395, 334367952, 675096250, 535171341, 35105564, 326509034, 702092213, 611975464, 503028040, 188087380, 79929325, 407336906, 671889287, 593162842, 416030260, 615719523, 807960229, 661744918, 838316273, 859436071, 871569305, 765501855, 154840577, 755001489, 666144786, 348068997, 488998370, 779700427, 38345468, 643262701, 509498174, 905227375, 491183951, 492630548, 153139353, 343069959, 801976972, 214053804, 248791388, 866214699, 56565399, 837241217, 240691769, 459146758, 980099187, 62886175, 568700650, 173815688, 96921164, 708626879, 31965500, 512687679, 65574023, 742231721, 915559680, 48437455, 933204085, 763225172, 912261891, 948090827, 798084292, 916916547, 966707075, 700065856, 210963937, 379571648, 846978766, 584864532, 609231764, 440655051, 304524379, 633927846, 46738658, 995320932, 249110868, 187847220, 953313517, 687579615, 81877344, 583342271, 158410804, 703290615, 639023995, 633534132, 181582285, 151382978, 503011822, 292627432, 684530370, 933886687, 733544460, 628909297, 347942319, 263637585, 119755559, 593479292, 398855628, 105944223, 89829342, 214384316, 547082276, 996952400, 889476017, 986820801, 234525462, 714726030, 94573995, 194287341, 551523039, 293993938, 17407829, 998186221, 970015319, 26562866, 732571879, 83384526, 336824733, 880008609, 6622283, 907851385, 368392612, 641240987, 559465269, 245794340, 872751952, 254004691, 899144520, 413399243, 398787510, 702464228, 205930289, 971317457, 995311038, 896068555, 94604044, 506439332, 4525421, 890487787, 239714593, 890155884, 222936380, 809794957, 297886483, 835627849, 794298185, 99599752, 497008734, 40062579, 423568794, 454486976, 726158391, 372636689, 893360805, 549443150, 349026482, 172818696, 134885415, 119273865, 909085311, 606264296, 902540145, 982598355, 318240682, 620338598, 346495516, 961879071, 89684885, 879138238, 611780731, 477956795, 333558486, 419188555, 119388611, 719705490, 694641619, 952629301, 500380852, 484546615, 658112594, 174919436, 573291294, 341425267, 692242050, 728369704, 758897235, 952828418, 47038124, 911226302, 82407010, 398127652, 79199623, 848207030, 44380156, 131701140, 823792444, 99469898, 936544572, 440532809, 366109597, 997718003, 857979138, 356885468, 777226787, 482696700, 572259390, 965415114, 543433947, 119446161, 45117111, 653442769, 38738629, 548170071, 501933239, 989020890, 953294315, 537852787, 288745347, 570444267, 971852376, 289254684, 243671291, 618595801, 588800025, 511757513, 991094535, 951827228, 205056252, 655644882, 844425358, 740018699, 741723617, 740002077, 710375996, 352206755, 956311673, 596690368, 234503169, 678998720, 109002451, 167801007, 773253513, 814689089, 674771042, 584694066, 952677528, 130863541, 946278786, 677130471, 740412761, 194400645, 650638869, 400921381, 63069315, 959653202, 484328420, 241037160, 366140585, 934482926, 721207660, 723063889, 215537287, 587615651, 918480568, 452333009, 739135417, 390158764, 838528392, 553033667, 547211375, 540822338, 940535392, 46220202, 285031622, 72870692, 599207803, 14585891, 553246034, 558183089, 268556482, 737129481, 764631959, 330139990, 67377040, 735108123, 750782183, 759727687, 924062618, 849391813, 572756593, 557649511, 455922732, 165157339, 843974048, 160778373, 169566099, 697068715, 31647665, 824052043, 287114112, 46339934, 550050885, 382928114, 108420237, 674746580, 252223926, 123376108, 567829532, 327638670, 790945042, 308170094, 445359262, 235548571, 243118513, 148520842, 659086789, 668026880, 379705513, 932170970, 307716568, 855175467, 395296817, 639190883, 653049225, 97595854, 791793633, 544709389, 193103137, 219425975, 735281959, 243703471, 763306041, 374483666, 838369298, 992498978, 639253473, 547803011, 383639031, 245043948, 844625039, 316841306, 320509026, 754159067, 400823942, 973800626, 429805070, 122863771, 850691829, 865749942, 115080483, 275585674, 228440964, 137638545, 465947545, 975058262, 264397549, 713118066, 941935905, 7593033, 494206785, 575556865, 281494797, 992266180, 596692491, 347542292, 798232030, 305703874, 474844267, 209109326, 498423357, 330877418, 723179561, 337868996, 7452623, 831131930, 202967560, 335142427, 809752833, 859484418, 632073917, 996965058, 741388417, 652402396, 287151310, 31409926, 875119226, 9319459, 296527219, 868966899, 195642491, 689040885, 299528237, 324724001, 306848304, 139417170, 843523579, 240097071, 993376313, 456123381, 15020355, 925721671, 29088463, 64445687, 585354243, 633012089, 940581352, 511083292, 18657706, 196808956, 595429931, 883385386, 634260849, 261144832, 26356571, 336735998, 337647088, 865752521, 849825310, 382497617, 453776525, 72407340, 507099110, 446874228, 758225897, 684068506, 591438794, 249431821, 729983964, 305490198, 271178924, 245641532, 264983633, 374335978, 370677796, 670035326, 132836486, 291274670, 362778590, 62781286, 563991464, 49998203, 128594057, 414695656, 234876667, 351287459, 954446844, 635466718, 654372788, 61324826, 668988704, 378260576, 93829519, 770211287, 964598146, 977534326, 936017378, 540114112, 587751274, 486934700, 961627845, 304504072, 753996992, 112363365, 364301282, 980794915, 36930460, 636529782, 758986689, 836519912, 21742302, 117727023, 331393166, 183904635, 928243868, 401250250, 678955563, 594345092, 908009695, 261793282, 887020965, 401664969, 791403188, 83576262, 102538832, 298658588, 882017163, 609462730, 912228499, 90889578, 680638849, 705817768, 977596314, 87056142, 869370708, 435535481, 23848002, 264344942, 862681715, 212396864, 925052164, 170524036, 3645807, 189267013, 74596197, 418544773, 628845578, 877730725, 39815300, 151130790, 337863074, 916178421, 552938533, 289215807, 621689275, 775609286, 312392128, 779997964, 739778818, 756016200, 289064309, 128222212, 391722406, 498593025, 819706441, 75885901, 497954257, 777133448, 351412775, 161810140, 226766222, 41810522, 979702354, 888925399, 851147738, 503595926, 675389332, 399814273, 804326985, 266357228, 71241623, 161342573, 271683228, 623009996, 607989034, 64734153, 297862084, 515958467, 423902678, 843213037, 84695643, 48509604, 138072235, 495758895, 524797466, 567255076, 934241597, 34827542, 297850098, 73952001, 383326568, 129158754, 21640925, 144498584, 98480378, 410237571, 626839123, 117557783, 39545461, 720844289, 805063465, 270447093, 913731074, 715238001, 588822135, 201956343, 180662181, 964856668, 317033667, 768209155, 949143379, 668248565, 641033297, 356495854, 580365767, 288875043, 391789824, 258976123, 886103524, 482337620, 473086104, 816334415, 949737667, 768727236, 977207608, 189287698, 190603024, 514142475, 633973954, 977077483, 418768023, 307928665, 659870404, 212307058, 755779302, 161847536, 924725543, 813681466, 750422338, 487929323, 929630104, 483752278, 33049920, 398334893, 26510537, 765781294, 569238289, 520203927, 846247476, 334137773, 203398137, 345801643, 807522726, 766675351, 703884431, 123873030, 541713672, 634185667, 969083505, 723861133, 443875298, 576881629, 554610568, 815609257, 138261723, 923210809, 535907730, 636715143, 916857974, 315843936, 154315421, 353531911, 303980333, 165665766, 163117359, 425984064, 583264162, 462889545, 905945735, 460259903, 792109269, 246864269, 399696160, 670467552, 854048077, 794575679, 976189174, 554584260, 237391658, 435791467, 759577329, 121232721, 439697792, 654175144, 100121694, 781478076, 172713757, 913699543, 17749901, 546062547, 182479739, 917053535, 891613160, 348009709, 378407148, 948299090, 465355362, 548564148, 239068902, 213045242, 123278644, 676705310, 583021430, 445663841, 968459098, 138037680, 852333026, 569115566, 23369747, 475631191, 346387693, 92243116, 52686098, 220225424, 355338546, 538382909, 230078507, 431703849, 360649226, 877600660, 502582596, 744810400, 544680460, 222101509, 820807599, 106703200, 956122749, 153981991, 576784618, 44777979, 3288094, 575610203, 353087029, 479790647, 984123426, 345744741, 837557881, 966564975, 286608254, 970480634, 309795204, 771091986, 697487348, 749486992, 851603872, 587868672, 694634692, 189246182, 350915293, 550999163, 141184329, 517918298, 469829117, 12680272, 629720303, 199756372, 837379094, 322722637, 700555176, 943294563, 187275840, 272702244, 694606634, 229449324, 719152162, 527827402, 385830250, 81040086, 669988275, 756289420, 113468980, 29560874, 331240777, 767866754, 375661873, 346032423, 893772581, 327538816, 272730742, 180560508, 39063572, 907197783, 793169391, 653432866, 478904006, 181037367, 899760775, 801153391, 390936959, 793905204, 717898632, 855439175, 835291830, 701181615, 213083997, 762796196, 831381123, 60260588, 416062411, 977601748, 48708968, 923696777, 51008002, 869853341, 297251993, 592001279, 696404820, 748398586, 757458696, 664293888, 692711084, 594753332, 925696339, 841892500, 149667549, 375416295, 868321652, 11958256, 101836524, 107004414, 747332757, 490589501, 356604511, 230840611, 779565557, 711023894, 374292417, 6888410, 10514769, 874923659, 303479804, 583204698, 421474231, 35461899, 733696213, 514277466, 321026889, 796038404, 699710401, 662435100, 45985020, 40121939, 161982429, 183904178, 533086005, 216477093, 38423014, 615288841, 73828842, 378208598, 406069857, 64178655, 460002841, 274421965, 835814694, 296867364, 185992749, 176780637, 492536082, 585826605, 152731180, 299550027, 334869202, 172492536, 931207928, 400712754, 731716179, 84594932, 270027634, 124138919, 101399511, 278925415, 564169655, 100624546, 764055386, 775449079, 746944776, 856115239, 127656587, 550324711, 116976197, 921933056, 82058154, 374548515, 623426022, 197643794, 654948717, 177667753, 294562379, 413206787, 195312372, 17990018, 771785827, 715197471, 303110093, 390477336, 70280597, 362354153, 936883994, 88926799, 88271662, 210017593, 186273692, 473678617, 8917116, 295039044, 655329686, 943736253, 538866775, 779378472, 208022165, 46411408, 626143454, 161206589, 333948047, 610214655, 432623858, 865448034, 584783817, 735537679, 170744553, 814844570, 97099798, 109057876, 482097351, 666592015, 606430886, 451411733, 18656267, 803207798, 456575295, 155762867, 842221391, 340066485, 390859269, 877383132, 501194417, 630751942, 311578334, 549694738, 241015043, 360819906, 981099651, 122329593, 728620134, 620111007, 674338897, 584352950, 371152544, 45739191, 235973054, 163047210, 350296370, 938907915, 103558668, 281063488, 719525035, 186289364, 304671628, 77846650, 619529922, 445312994, 370513136, 627853863, 915863339, 388136827, 148178928, 118675349, 589559146, 709374322, 29046359, 207184442, 421614262, 571173393, 996999216, 201548028, 34977803, 338975242, 422018112, 923490047, 429092178, 280316830, 921449849, 329563533, 893080485, 729979187, 148010000, 28072732, 278397406, 914987775, 161635896, 592093844, 828455108, 634049660, 275960547, 604588867, 539169729, 162512590, 735439079, 767162671, 454331093, 941842608, 691250441, 874844862, 236488201, 295588767, 776202478, 147640403, 832183408, 150364629, 656498863, 786882467, 106018038, 44014229, 324107588, 711122323, 582844570, 841300476, 323180341, 46981865, 802384313, 294049674, 607464493, 82548850, 414376626, 765350423, 222150314, 770451120, 322320766, 432231114, 310449255, 908654734, 198007268, 639868488, 437560953, 731759748, 588203707, 688352256, 266739643, 414511254, 248858682, 381464397, 192418237, 269026368, 194448311, 924212743, 507413382, 422370217, 831145461, 576328181, 112747847, 7865546, 920968819, 294622308, 309057742, 540353875, 728611328, 443204132, 45848007, 38489785, 196535267, 443068511, 526990794, 663953718, 77513005, 645475018, 755048298, 675197796, 366369044, 598640143, 619043494, 488733124, 688426316, 111193688, 231425791, 183341843, 716716540, 502992386, 152795518, 781344756, 436658406, 321260580, 892357972, 714965045, 536527256, 661208371, 659720095, 591157269, 810419991, 317909271, 33531219, 759818806, 670719810, 461801784, 443719651, 823957255, 868673953, 675459829, 412548998, 339161234, 46805176, 587687150, 983512154, 840547438, 285783998, 241104924, 59686202, 546441718, 626116793, 812294585, 797389015, 917879336, 44503950, 308556441, 636731104, 220790106, 323285683, 383694865, 166324805, 690725662, 315346127, 358411002, 322549766, 880369824, 129889095, 366765895, 504147994, 606764823, 914721706, 7398589, 998846607, 612329302, 18091262, 921318624, 741972518, 502281651, 194196286, 327765225, 185800077, 237051549, 111393562, 745059228, 833130819, 211095503, 634277700, 244002354, 560696185, 848935838, 382843033, 357278003, 649331897, 219893898, 728063519, 120271831, 295472083, 25079353, 268926476, 344021173, 169678146, 975538923, 9032007, 137496496, 356045166, 544757287, 330822484, 950308613, 84953750, 703842091, 781762770, 854238852, 613311760, 322172867, 468062724, 693331404, 350646734, 803224052, 704397952, 512141909, 419016142, 38692978, 659025690, 38830520, 836158070, 995498534, 164019865, 229851653, 77333295, 482051567, 200554771, 422152368, 748694059, 868085754, 164037222, 656309841, 890660765, 260551617, 852599137, 773489216, 336262588, 292944997, 76626902, 570610493, 881226487, 417660601, 502500087, 165706491, 560328029, 26363355, 596369154, 171691966, 314673153, 897360718, 922064751, 440384156, 993345165, 421741134, 261212731, 569787882, 40518085, 345517012, 927591966, 863974782, 856100760, 324445435, 501709412, 733855591, 595165462, 851549665, 833485632, 608897633, 39334093, 641452582, 135813115, 717426384, 973481355, 696759493, 602957670, 687502545, 266714610, 573584016, 78678407, 396593827, 589368010, 326570276, 182339910, 405796502, 620392282, 906042067, 992982272, 979005061, 709193702, 281092031, 473430072, 591445429, 878619911, 666336907, 221578948, 254519201, 422051275, 466401908, 815091455, 544758592, 346978033, 310182341, 658859074, 410138301, 914606511, 527137172, 504838568, 361676942, 737666945, 158120835, 405066896, 639207709, 420334803, 476543625, 538302495, 744609572, 565845387, 868655433, 564997925, 941188460, 281360055, 417874935, 510230137, 812478435, 619936385, 208803220, 466184000, 370581880, 962929043, 10098295, 237710701, 452536679, 641503329, 363854061, 458954230, 505190210, 159453231, 341666089, 997485490, 675177824, 9654666, 762010718, 213302796, 579766030, 788740823, 295273855, 725883142, 104724655, 621797573, 330246116, 74380411, 103379362, 915454016, 137927424, 862058143, 9217396, 522555888, 798652790, 367873928, 200170735, 565650568, 865722312, 267238412, 25000728, 856364469, 813972861, 694363077, 139121707, 211579708, 601395610, 503557733, 769496101, 693179641, 48047359, 466998202, 18549990, 900944339, 87186498, 901898147, 874663700, 581726955, 57381273, 384326840, 118792183, 267422300, 737513091, 1673791, 712741603, 778866979, 830087227, 168341695, 22451972, 422464357, 816521070, 785606429, 70101470, 668499892, 286402479, 773283615, 200566839, 330032557, 252848342, 770200903, 703202841, 477598901, 876344525, 782747962, 121593342, 423075188, 174753167, 336541407, 979341468, 116192292, 51813357, 255941034, 798219333, 737548673, 674982490, 851184496, 64169224, 130821456, 995642022, 549269646, 740033922, 341608247, 125957279, 233646173, 237063735, 949551915, 433355380, 514872954, 830677573, 693679763, 700648574, 72261095, 9612242, 484790378, 70035443, 470257148, 194274107, 40611221, 778652187, 99176294, 21348349, 198913019, 876912404, 700907330, 577488375, 168046264, 639349239, 56415561, 114470778, 275415578, 162984811, 793508285, 330741348, 450025522, 193407300, 962554720, 896445440, 934075192, 351457674, 147786517, 659318098, 321504728, 770948002, 705786938, 597113890, 676562851, 820158972, 768003710, 223006262, 26267736, 331790174, 264555158, 278473456, 654645457, 321828187, 213362161, 234603615, 137339665, 748326446, 782826454, 721400140, 293563326, 227948240, 333921407, 656178134, 957736994, 965788998, 975115241, 380832798, 377829801, 8529762, 237324959, 2491038, 982305035, 26838784, 285903646, 973566180, 150875297, 136201332, 657952633, 68463910, 350537860, 247056371, 763887639, 461867105, 913483919, 691771237, 767994698, 193173470, 903317726, 729410896, 228257154, 169828878, 226391126, 320027954, 547672121, 472753065, 959231222, 310891319, 624278109, 75844588, 238287172, 583523232, 537567468, 708083578, 560331808, 685474188, 166788148, 823873335, 869147558, 952914294, 528995915, 649072740, 634851779, 980004540, 511154182, 252867703, 221314097, 347653273, 91246712, 301627535, 591521456, 577844972, 773613478, 81404825, 275344645, 246264040, 473042974, 685092659, 677062329, 969388423, 754119136, 47798720, 924245858, 447118416, 581152063, 652134340, 125386500, 988932588, 96773876, 457424102, 894543525, 381015787, 268371255, 539213654, 165739841, 107362182, 655586385, 487408855, 837636509, 93797859, 597409802, 62443767, 53854118, 889523522, 813380317, 41999690, 428404381, 78850539, 587905971, 188491176, 733212436, 420673705, 280815020, 240706289, 486139591, 679542839, 760174466, 962237249, 611893687, 889967068, 638835881, 893396210, 129740952, 75436709, 680615210, 293351780, 57444098, 304127551, 106389804, 374499615, 216348081, 690839620, 439949845, 338726038, 864638532, 320996580, 420720273, 301225863, 50924307, 918750369, 527985804, 413900299, 72980712, 250446955, 456425406, 311928624, 611264145, 64653101, 53141676, 390277773, 253867013, 843248491, 564596423, 338597031, 589929655, 730856601, 777642183, 686570097, 984187843, 559475472, 947212965, 792636361, 428604843, 562038006, 207099603, 608663954, 788440291, 203046907, 866750296, 841929807, 128465925, 706431626, 786608379, 610905143, 197775914, 264178956, 679926802, 627902295, 878031322, 975280916, 299558479, 336876619, 844495477, 691717459, 543571157, 509386487, 24217262, 627638381, 127289052, 492643143, 2141566, 734525065, 675471864, 253203213, 191583088, 248121575, 571410940, 510654243, 198911528, 520403733, 34470506, 481195397, 283978720, 304284951, 818501300, 755491402, 616167685, 960985571, 167844067, 69489618, 115517223, 318086233, 232340057, 883095378, 410209177, 404723381, 200825899, 365790913, 842173353, 168514405, 379878447, 535470158, 601436505, 782775711, 222728212, 93003591, 290680615, 577777854, 461443927, 997661957, 827059267, 222424238, 970741470, 140221610, 206884084, 510989527, 801571951, 668501487, 218104412, 523963227, 349513369, 324573817, 32499887, 610058419, 28541809, 193810162, 706393275, 447742303, 927474462, 56310162, 223217715, 605244261, 78902666, 310865992, 683257517, 340835538, 848131976, 435739421, 671438384, 372312368, 763822488, 263435126, 273420085, 674733217, 421748835, 218884179, 790339646, 896681999, 423591434, 799107370, 788912572, 50792677, 73828673, 976816517, 324312260, 28806446, 26448685, 579616971, 77979712, 206182438, 556368551, 313629938, 587892506, 637467992, 196064211, 507488517, 728672498, 571001913, 318897325, 118415189, 697824005, 142382857, 688458389, 342765785, 222936456, 823454981, 912392653, 893149161, 245221430, 791284311, 496037899, 953909771, 877770043, 772466319, 371547921, 696126197, 106317898, 457294656, 748415498, 522892518, 577174075, 200292696, 580395742, 390278813, 906411897, 711652594, 402067075, 522649966, 821757693, 907459880, 91251625, 353645650, 261555659, 402733514, 262814470, 442981268, 823736374, 39155952, 203362003, 263638177, 197787991, 625968150, 414867546, 650078641, 932761629, 541985224, 918541648, 471847793, 184809963, 308499121, 413285059, 315538622, 855225203, 523224772, 341295582, 540928023, 26158701, 779890975, 979095355, 86072097, 100447974, 650159067, 642214508, 663631945, 943157801, 972372101, 766972831, 221148846, 861250446, 477981749, 767618087, 869366637, 693511845, 278437772, 541661620, 603397742, 7558861, 717156300, 436238781, 974677566, 317794876, 708315481, 777418716, 369568081, 843678669, 229405123, 757934114, 514544346, 921500798, 989444082, 270974501, 280641071, 212377751, 845538993, 566866336, 237246672, 464611523, 899050419, 479403466, 276108263, 977284813, 752372591, 610881631, 364596077, 685228662, 594537672, 128435893, 916208917, 879577076, 56548626, 669395403, 364441374, 420287662, 181070845, 955928713, 884049410, 798174712, 687288182, 337844648, 73504197, 521419448, 358361564, 599541635, 39583603, 936489373, 873481845, 358426664, 465852698, 760393265, 997846540, 502965772, 786102692, 768481823, 159205080, 169332222, 506022761, 977619585, 384142171, 418314004, 224072450, 2583192, 235219992, 560002824, 158070061, 318113108, 876734750, 450168680, 221006594, 792333743, 58228918, 814963828, 430949668, 823264536, 417350813, 164784888, 978826994, 197683647, 892368149, 73219681, 383530616, 159618498, 45702277, 206821692, 828132622, 923966555, 951662371, 67423613, 445012954, 818326614, 22882712, 95880755, 656318470, 113358876, 568977145, 233333078, 905650167, 356876213, 265887495, 693459227, 680168100, 814683704, 722640893, 482726557, 716094685, 784348493, 271339206, 691309172, 629515513, 747445815, 243920063, 820425165, 688345894, 77627900, 276166473, 738032293, 652673130, 25794318, 525513535, 25390286, 269097131, 714086524, 967385267, 865761104, 489078914, 207020084, 964721365, 727243753, 216034184, 155539400, 436464710, 425989023, 527091048, 404385710, 912148101, 189938433, 49559422, 620363861, 888365503, 259075044, 704087273, 614542101, 812979997, 109776375, 872927405, 143212089, 52877135, 710517719, 246301141, 755827165, 712471190, 894041596, 346440258, 326283250, 937670985, 637825875, 833297189, 725755383, 463801901, 154634133, 887980225, 126896256, 8356055, 41445869, 267293347, 166897664, 803130721, 882771272, 94095371, 595498686, 145562619, 763011176, 204316838, 642964248, 43025905, 27564571, 574573954, 491014345, 457058920, 784945035, 430644207, 997628978, 372523541, 321844904, 222732328, 607432880, 350286161, 692797463, 34771348, 280468417, 318960747, 441920192, 418096875, 786033218, 352392063, 783937023, 411780277, 116546542, 152069736, 900947673, 94739282, 992348776, 482574657, 594345635, 461194232, 817007189, 217921374, 559060992, 769743281, 767399213, 145755354, 783943296, 190438278, 786401027, 580490158, 386271572, 898282104, 244357270, 374532240, 108651191, 722598934, 583485816, 484822492, 553800948, 761046908, 469661844, 513986865, 388154041, 26953634, 708047879, 911043341, 477248857, 676929285, 350360228, 1147943, 745541103, 580606833, 944461511, 762917369, 89099707, 973185815, 831965917, 147140762, 189401564, 798150129, 81603696, 953272764, 415872692, 739137665, 96766098, 896060594, 966486248, 338292840, 748366569, 348009531, 281248812, 502309536, 374539160, 784978215, 406575734, 42261256, 642341950, 447914001, 630305320, 908123821, 477758118, 144401278, 901533125, 714592090, 311043831, 728722177, 234302332, 543618579, 743683292, 115845881, 945845431, 289122549, 290364939, 742992073, 309769268, 586360882, 116875857, 966180569, 681730571, 677677541, 74517024, 334283359, 376492878, 446115460, 340797265, 185313847, 425511116, 197429403, 977089547, 867748503, 249784285, 527794307, 182212983, 840725739, 251491121, 28204417, 162373009, 814960156, 480667456, 917238619, 885365909, 601724532, 460982040, 944715107, 354012563, 562580301, 627281358, 493882922, 146205800, 720768777, 358354103, 748178905, 66766518, 958922899, 63302523, 560848975, 283844532, 413847699, 13510360, 894415164, 570375351, 270871610, 143288243, 204007157, 983739022, 118628985, 664574790, 215266720, 568380631, 750912899, 993006184, 782343079, 239644487, 513118193, 676294376, 452362659, 722992633, 273750868, 623588101, 933698416, 465311637, 265360501, 702936784, 802695075, 925424372, 947282294, 826238565, 880730363, 169933401, 742304736, 193896226, 426081214, 985316118, 648798321, 585004242, 801444525, 730422905, 94179851, 609519021, 31418846, 354185126, 559818288, 73271117, 521518879, 753830664, 560309551, 33190199, 734095831, 707736656, 912557723, 953411522, 548206249, 515539812, 520370562, 557311449, 580044600, 345485879, 263197735, 971322729, 639854263, 663425595, 871361883, 686463593, 216861866, 48908105, 454905422, 802408682, 645669233, 366221972, 858795455, 213437335, 678890900, 820038443, 89636186, 391581430, 550541485, 73531233, 242504987, 690762442, 344059698, 318627989, 542808544, 963814554, 863089201, 97571340, 889029365, 211284334, 75132742, 21223487, 411066284, 31113544, 294610365, 758808752, 891576713, 265533304, 111279579, 705482653, 621541466, 739256579, 826669809, 76743837, 149412573, 480597551, 937197024, 82103462, 647770201, 739185201, 415112520, 285530639, 926979842, 497534341, 732101922, 115633796, 364581963, 200446602, 869907871, 88205684, 730973548, 559952528, 38857217, 830644927, 236407670, 828985431, 715299764, 738421124, 872255993, 446766237, 609140255, 205963657, 197592069, 811864306, 837817332, 318767867, 134185222, 381457407, 759949340, 771500490, 202662200, 81953023, 311296320, 986118258, 656420949, 651553697, 765157923, 565976071, 522791031, 562809604, 175716133, 534128490, 932109233, 565436859, 827728835, 993564668, 429853684, 629626719, 971432997, 736379548, 319356040, 440857621, 442845761, 770307713, 79508375, 4470205, 238457189, 203265012, 910542151, 598310294, 998084415, 938403016, 975164596, 641794677, 859793144, 482520126, 946006900, 307156824, 806275165, 482814829, 704301824, 669065153, 907047496, 493010019, 451220141, 248279844, 867634218, 787144314, 641648710, 457781895, 473838354, 304109249, 667118133, 389048804, 569560448, 53724592, 829362208, 384157396, 375417869, 585567992, 541317987, 391914995, 258019496, 313252152, 610342360, 255241665, 123714709, 654291484, 698097023, 441973734, 438392624, 151859827, 952586979, 297534805, 951137250, 523155871, 105596295, 990982975, 865886278, 495736295, 532350311, 18456226, 507956234, 296092520, 454946850, 325278574, 294138234, 976912219, 558193586, 345350806, 970434581, 573842878, 139335585, 339101999, 247797979, 580693866, 581313543, 8914838, 851089948, 170649446, 485524397, 781900688, 788295104, 68253555, 362916012, 452219872, 999849035, 255227005, 800312622, 802431840, 192123196, 323933173, 865311084, 782710459, 418328642, 371149591, 197698298, 980337061, 643355867, 430405789, 677196738, 381678385, 528486387, 11314128, 505259594, 374557826, 592473736, 405761052, 504515117, 636824693, 552713104, 619092744, 322409136, 398413861, 150722187, 715616633, 179063477, 330636904, 823042256, 300113908, 105937171, 5324654, 737320329, 483098270, 223251367, 779056835, 944836892, 750395096, 568284577, 750198091, 545781894, 810798022, 846694164, 662344319, 100394131, 426382257, 86416706, 63467792, 4724602, 398277517, 273449346, 47373084, 553543298, 628228272, 187572765, 769730078, 887015843, 809852168, 508364146, 116582117, 547407150, 272718995, 217784517, 720291871, 286866203, 834600344, 104458880, 502746258, 144301389, 157636463, 895711148, 222489371, 680854485, 99080642, 243744773, 145313646, 44775274, 330645754, 929438944, 774013617, 894023302, 119673146, 279480661, 23225101, 880386161, 400561248, 236752047, 483043477, 880486499, 323744514, 353906237, 522351916, 774433100, 825669369, 260477946, 493374523, 241256788, 372972530, 95742030, 287039515, 698670810, 603502356, 657652103, 649859053, 912984071, 743827797, 702920742, 968728150, 365180886, 522163153, 490378886, 969768816, 164734787, 544598594, 187393029, 727175937, 253552409, 101872466, 123195884, 528261612, 225320260, 154211301, 922507862, 531675716, 466566939, 802863731, 800188732, 329237837, 579043098, 313098750, 837031367, 728437447, 629564699, 310210767, 452886945, 104219144, 631736786, 768162725, 777492046, 9608241, 553979147, 271027186, 960753097, 191326137, 587966273, 589795612, 332879269, 414387126, 764650545, 519607759, 119639797, 88240680, 77355526, 122760679, 458449498, 628668069, 631812541, 266075580, 264768759, 698104336, 374704106, 932613033, 310630430, 832776034, 65563254, 542081269, 719674847, 908164446, 3873669, 912157460, 21782389, 778809401, 361949088, 177125034, 952424076, 194921116, 595176932, 757449166, 809080845, 676109381, 186486107, 83435077, 476595420, 235237333, 529073335, 840152386, 61623270, 173062769, 38149479, 68230606, 847622306, 392307168, 284599849, 617625918, 400328040, 738656642, 588764161, 797630380, 410136425, 906628267, 722686186, 817735111, 436184444, 474887103, 165296275, 272142047, 790020157, 17793683, 140787485, 61150645, 126766523, 708098114, 539240980, 226050501, 864755609, 764929193, 562399660, 872294579, 79792192, 261915425, 848033336, 460171127, 495409616, 196156281, 288777934, 763731884, 257699960, 338296126, 144520210, 196347491, 988375478, 784151668, 34450913, 686494283, 60726186, 384554068, 671755671, 305590282, 939504672, 950051204, 746567810, 778037578, 449231426, 958507022, 309522501, 445864758, 569018906, 320854731, 616666768, 910041839, 328895507, 51915519, 156299669, 632807612, 888316197, 366755383, 795753061, 764561616, 239268373, 144307349, 261131472, 602820768, 285440807, 759468641, 266229776, 89054182, 465011002, 489802595, 536524130, 448460904, 497606315, 532495788, 643080597, 951267367, 924812288, 994762580, 715952455, 941561865, 680906369, 965854785, 224080307, 263527011, 827852920, 197553215, 264677755, 404578494, 209640709, 14861637, 796859581, 584106661, 349761193, 562190828, 899754425, 989142398, 733729082, 927070191, 173430587, 265302998, 489015487, 204036919, 337563357, 743817250, 880599210, 773343240, 204714488, 624179832, 535449044, 512066507, 47258276, 722506270, 196688546, 679007165, 881407266, 459841188, 20926735, 677307136, 755554977, 203306428, 939898604, 508368015, 168807091, 573349011, 295048108, 749736367, 220876916, 826805891, 132651737, 820028656, 962935577, 928761303, 493737600, 311176158, 783624020, 832078687, 547449131, 954608444, 987748971, 730310087, 127501410, 376041906, 12654847, 663363389, 549848640, 187064132, 128790419, 193670644, 526587794, 635279021, 772273428, 439059629, 668522382, 857321532, 331953752, 659332694, 126380697, 357917227, 609614343, 79063964, 650912720, 311332959, 358396615, 303027597, 615122419, 727980017, 497133939, 443811340, 988181783, 611850025, 298340495, 21120222, 971965787, 569816863, 129503834, 635049509, 483389763, 204583678, 671260458, 522716347, 630761221, 363944909, 534550195, 18567462, 632077363, 264851141, 813391116, 988135772, 522582766, 339064638, 27316734, 210090067, 551833945, 267719775, 568446732, 644044664, 749156338, 366845484, 393062727, 647728174, 700172306, 258621578, 880523333, 802104638, 345221126, 484992340, 987171469, 246752683, 545790285, 67091513, 50673214, 565705219, 125065995, 906656760, 310188114, 170582570, 568314068, 351725581, 244019138, 565503636, 106963670, 127984744, 578787652, 575685464, 765110670, 931124855, 992377631, 75539581, 92874379, 24215012, 137876791, 42052658, 692471577, 690905019, 90978287, 406738704, 570825033, 90172233, 72746215, 563099042, 654305196, 605133470, 585128547, 348748595, 901604971, 144737305, 117823255, 978783048, 310505589, 228804406, 297178064, 974900529, 748541366, 540653153, 685748783, 484957694, 968875043, 980616849, 354673352, 408223642, 145919730, 912726603, 230678678, 855387434, 900669461, 935358630, 139230379, 206823635, 487981741, 181008120, 106532957, 614282824, 757785606, 980847116, 394401705, 335868236, 924070556, 540580120, 342050451, 634536569, 460705597, 34081551, 300825458, 695027998, 11314587, 138236557, 794641000, 520080071, 741088935, 241281604, 548126171, 188092905, 508984427, 18132874, 138907285, 259820075, 592629183, 865851088, 461193341, 240952179, 296874376, 160596216, 194827639, 926760476, 176267791, 451060867, 383127452, 709634343, 312340026, 164131335, 902499075, 857015850, 421553833, 927531520, 763161785, 325100699, 975820691, 476570355, 566332124, 952051079, 26539165, 576335309, 487703144, 47288769, 681729610, 509561599, 206027596, 579696436, 866907860, 174781714, 713321003, 293270690, 936487312, 656762376, 888988459, 41925133, 404352595, 584845545, 112225746, 899424034, 187356581, 584074328, 244005259, 815095548, 158872322, 492536236, 358608008, 14710447, 285346726, 622504824, 223361831, 157500976, 291153974, 427466235, 422451645, 916873363, 684920272, 19751975, 690452734, 321844035, 728403332, 207990035, 116238562, 955725757, 628292393, 983454292, 200589999, 365712301, 319699308, 722923098, 559513296, 457235542, 161114850, 549153314, 390519393, 78604226, 487693296, 602911244, 993626858, 807459933, 636765173, 103129286, 381666842, 619036744, 868391306, 127688466, 688161222, 97893105, 112584430, 607979283, 34549114, 859666652, 536524708, 482909910, 953551361, 973560825, 597302570, 554737604, 411427400, 921192819, 506451512, 733441022, 71085910, 277881573, 738521574, 842300194, 767618698, 192407979, 628827892, 145745607, 157238231, 696650942, 69809672, 97519029, 219035922, 975890162, 349715732, 976463521, 390243942, 481647877, 259600062, 441921512, 238947130, 354277475, 904294732, 83274657, 668531261, 725830362, 643435797, 149756796, 235441103, 457753451, 827722995, 350457048, 994405427, 393298660, 637530463, 992893684, 346928471, 101519573, 73285314, 740341377, 651237669, 184373821, 783384103, 547243893, 153328407, 22609554, 570461263, 359800600, 719239782, 971124337, 800057362, 299380175, 474678593, 357445895, 555082836, 373011509, 561868118, 519230795, 239028462, 202091383, 932884975, 224025863, 953772041, 363476907, 225659652, 999486858, 229995555, 198061702, 91650129, 707719157, 163132156, 766203165, 507609103, 304633283, 666363032, 325965478, 693281038, 572746562, 278389415, 156156763, 44557302, 71445366, 834041017, 266459271, 544795332, 562395637, 922820704, 494339832, 148014461, 731733123, 257906147, 821309928, 866718860, 952669950, 213975390, 977572434, 40403999, 111604379, 272893517, 176259950, 984793395, 928283675, 123507413, 415653739, 234903675, 41778588, 100419384, 165950749, 697574664, 622976287, 148203639, 907752714, 700856552, 741802741, 761484176, 934068556, 399236902, 505579215, 901921484, 213611441, 82261048, 785702093, 467476707, 427929464, 140973057, 832665284, 2366916, 509321049, 271554775, 194834535, 853972138, 986363264, 362570607, 938170947, 653629774, 519061135, 954786603, 894743456, 810380469, 76563650, 381240983, 90476865, 797757105, 568506537, 792447623, 808173311, 870019719, 581058644, 51651027, 10712147, 604680179, 324882177, 730125509, 553361623, 454164915, 656503426, 570505534, 761265282, 238232361, 166462767, 504330852, 74237884, 701458160, 377482893, 135790798, 538441180, 46600668, 655151919, 360698986, 300288975, 807890728, 342833901, 280323106, 829784272, 18879719, 993251176, 260185156, 749103637, 555193741, 182537742, 370535900, 853167077, 881334835, 354015336, 193486549, 107474492, 627261649, 93363505, 200283757, 932813448, 514283671, 732116546, 69754994, 203791371, 6736095, 818891609, 753753157, 933731757, 221609545, 448590221, 717159602, 56277206, 942572136, 404909920, 742469080, 309409984, 68213805, 976198431, 415136053, 69461574, 741954874, 584448704, 752632325, 557718186, 957073503, 920625415, 756041586, 943692675, 50453952, 333816201, 791984168, 638764263, 639137988, 393224740, 124268680, 861503048, 328746373, 860580954, 825918742, 632835667, 759895911, 736706085, 76732489, 183867523, 471553570, 479372425, 894857238, 619090547, 608827866, 504562269, 750112892, 483162967, 524755869, 889170524, 959733221, 1305610, 393138125, 498067281, 140284643, 264031610, 378886432, 139726753, 836378106, 103014658, 523049398, 230949958, 101325638, 629103755, 327585920, 829022994, 832996975, 281046633, 542181370, 890616809, 8066514, 989247851, 305353791, 506105968, 728216203, 578083538, 173232183, 475777282, 580504100, 992032903, 418837253, 614143766, 498945968, 455348525, 790929671, 948530126, 574743267, 51794624, 560347785, 944348091, 518077400, 431578654, 551957818, 421959462, 534052272, 231684498, 205969493, 586299416, 877388765, 978930344, 32374062, 806925909, 400304464, 118606830, 669942829, 190123796, 649980739, 374440510, 264493269, 623068644, 857123944, 501639148, 138648533, 589184265, 700221406, 579901665, 680540363, 400196345, 972213646, 628671825, 154673716, 91917455, 255840552, 983765110, 314252176, 691591290, 355550045, 611383258, 356672793, 100459445, 485347651, 837651386, 985195305, 652181785, 44456769, 702817904, 592969118, 743058772, 84607726, 614531568, 227435602, 905748821, 988396164, 825722365, 202494537, 988873499, 641999066, 260163073, 784337193, 850763625, 770390685, 407281685, 390673261, 228515432, 481104248, 840137246, 18061815, 422044279, 245150661, 432154035, 218780795, 746265680, 665823434, 496880541, 57820039, 243737401, 124735897, 246376449, 809643976, 764355122, 484208912, 584892380, 531349221, 445108906, 110604337, 829529337, 256576653, 413057015, 825711736, 74363058, 99192814, 158977575, 36470963, 368641892, 359097779, 256013876, 621485504, 779466231, 28589126, 152603147, 791240144, 451349873, 470503020, 792906797, 532839653, 494658522, 282402971, 716382806, 80553065, 905021953, 132088116, 9209409, 70047955, 128281608, 352393908, 737563898, 145263867, 762643030, 289231650, 954648871, 888366559, 813175924, 92060628, 790480593, 439464868, 541888867, 443305113, 521880856, 600860662, 916027555, 629670053, 224711855, 877854586, 78709954, 340673649, 1405525, 986188671, 178169065, 548411633, 811380430, 54342286, 151822299, 200821575, 458720628, 86034773, 221166951, 912796568, 249534530, 207748931, 58777094, 385642814, 657386417, 348929041, 704216210, 793299311, 866283492, 223087146, 101723232, 610439741, 956984109, 235867732, 991423229, 424495952, 381352101, 161230539, 481422195, 650495857, 143705145, 681770397, 928987968, 936711082, 973291065, 37230060, 944824467, 401994731, 895886165, 697268116, 991481364, 313873237, 337889980, 357002828, 384171837, 861939455, 82621595, 516763579, 153453914, 688772181, 595053473, 532489153, 977074636, 804072482, 220054150, 903855227, 879893590, 261800906, 213969431, 553293367, 168317081, 702530706, 983329619, 477457294, 1754767, 166479690, 667384605, 936909877, 104306727, 445744239, 451507264, 517660616, 230169834, 703398962, 930830949, 89349991, 73245564, 117853156, 10836443, 842309398, 581781568, 771652922, 261569962, 125779591, 543351246, 994562433, 463878752, 479764742, 181523752, 933427601, 436343804, 325944806, 835948704, 330734210, 261263278, 155686133, 108552719, 398644945, 683447201, 762347760, 890770125, 2543570, 822248764, 681803183, 99572627, 39358405, 741905043, 885093805, 26179277, 832781630, 783161033, 605507652, 745788955, 727857475, 397510222, 367860562, 799917998, 757621927, 674918615, 399990754, 902661792, 745644621, 274957336, 732788189, 655507371, 170084296, 473936667, 652060907, 30100180, 647228331, 912931306, 110898876, 32904974, 263329744, 295428969, 955196031, 235663084, 867563600, 160801103, 781801691, 147128877, 949007028, 154582256, 28829082, 190729756, 584037585, 220395121, 28373797, 612989846, 367657805, 671599743, 770536264, 652629998, 322458056, 553916948, 602717700, 327774228, 807026705, 907412648, 341893022, 760724440, 436557497, 350301637, 468835378, 326318388, 812231542, 686026357, 618572303, 863248578, 561890861, 331334429, 593838580, 381506608, 379047607, 28043423, 341267375, 563371843, 662101273, 180421536, 780622656, 391845386, 370694974, 854956739, 897347397, 79661773, 575545232, 834490734, 328018116, 419702480, 315310910, 907942379, 13619022, 502756790, 752608247, 241646720, 881841366, 652960863, 970657804, 67567859, 940143265, 515961903, 308268846, 356031566, 384668244, 616153365, 475908529, 939524671, 507843365, 779487085, 588270173, 390926006, 853109561, 177659608, 93488429, 277261799, 571753786, 999183197, 6719325, 834315694, 299775482, 930491826, 696995669, 350619788, 981413341, 865530263, 494070121, 77118824, 586798734, 840473812, 145961642, 300413643, 975049151, 432212248, 87851635, 617875381, 781029541, 255818186, 802305857, 552168799, 387266455, 942790871, 213394771, 368986175, 801276651, 283354151, 199634821, 260313502, 44990612, 999502978, 437761265, 698873925, 184457511, 454775288, 547089273, 340990362, 13489745, 634211620, 849231367, 5159699, 404062697, 69533213, 97681198, 638148037, 268068711, 632896647, 272313363, 940284948, 960597152, 652355929, 545292276, 326112022, 344772759, 105348267, 911745684, 601609571, 750325621, 111592251, 886275505, 39422328, 17871803, 839435705, 980790154, 811567034, 312785561, 992747864, 817460044, 815261033, 248114432, 276355004, 922883230, 683790275, 785832651, 838648328, 345328733, 691612115, 352074686, 294043517, 805181623, 669951421, 959843154, 568238196, 633174204, 144477427, 503252189, 393388927, 74215147, 36066650, 544781886, 293230732, 519391142, 83144638, 640099821, 228816297, 350857066, 631901410, 717104485, 944555745, 923879235, 98568061, 967533616, 437528785, 902770138, 164342655, 977645533, 430929579, 121678247, 222431533, 396075493, 579271798, 432873038, 800504364, 36809919, 56549150, 729019838, 387971506, 854351588, 625925253, 621804230, 90860798, 754034555, 851235574, 779425975, 737898861, 91477703, 56984502, 871250757, 1264913, 21042737, 788463746, 364002391, 309377787, 292855513, 925450187, 668368479, 267561747, 281139456, 595593391, 298067117, 508721287, 317289536, 148587493, 613126556, 229981093, 279090281, 296954172, 900662825, 121231665, 920892563, 652178542, 805980775, 46107186, 544375905, 40926503, 254553977, 823403767, 619844316, 240997198, 491833370, 547172735, 631547740, 12089767, 994888060, 851456370, 575218530, 509307581, 517475075, 104082106, 297117476, 457512495, 174224765, 192604679, 102865821, 794743399, 942942276, 887904178, 739406563, 672463527, 235603789, 710299870, 846176603, 25873690, 387521477, 880336594, 234774068, 583613345, 764763701, 347507613, 949289568, 684167590, 116179716, 207503073, 466958582, 378805696, 998933869, 537642009, 966438421, 852063011, 910567393, 213815448, 43432548, 433761335, 62800761, 625826805, 383811653, 249409547, 744218045, 573369390, 928687180, 712126217, 45671983, 809305399, 821587488, 959113382, 20912077, 300615908, 633626105, 479311606, 339250551, 624762238, 342855740, 383342410, 684111888, 259446107, 544321873, 901001729, 554685553, 496103191, 758489987, 14493469, 399314907, 151235287, 601826193, 327374626, 340732622, 688307249, 157341463, 936684380, 118784566, 855040211, 718283724, 667701294, 657903532, 531069263, 170619616, 70126781, 290290256, 68225028, 517947972, 105273219, 608654902, 265888009, 672121216, 612496891, 486815888, 763947168, 387002479, 217365683, 772418588, 202042619, 142175617, 443132385, 593016966, 26104785, 699718187, 152789668, 525962092, 833826591, 810720744, 416000497, 244112640, 301459909, 702876510, 444069977, 191690407, 215469938, 781463248, 882359462, 391866182, 535569895, 656560465, 431554761, 935439157, 273407382, 640201257, 201111601, 660383161, 760623988, 337490329, 195168259, 671887240, 441017535, 453517851, 713177431, 75130069, 388906883, 912814870, 753963014, 517790986, 941251464, 463785050, 444859019, 46931780, 847344290, 298291242, 857394604, 792953550, 607783335, 568373546, 965799189, 144881457, 546833135, 679068829, 738209844, 52910751, 925700434, 640399418, 286349524, 681517498, 85062648, 24313210, 726357741, 177933693, 250225993, 298779403, 809752408, 721124259, 529872344, 883106502, 856300278, 293155925, 322670254, 451149465, 588604671, 643372363, 700346119, 932890587, 138759934, 478621058, 745858545, 39463858, 850305651, 401108826, 469756922, 863350851, 703876012, 327633902, 10748953, 245206620, 974431488, 530842641, 541899532, 922477404, 88118400, 49453427, 571591814, 787201417, 4183623, 95562823, 757804434, 377455279, 254333216, 281324559, 575021458, 478779005, 919549683, 704026558, 945141831, 873694462, 798896121, 181927353, 958420301, 754727116, 655732669, 886509913, 553976795, 336030183, 300250596, 141823374, 274300379, 912997458, 115565868, 425475712, 963139266, 540609149, 355875381, 171060967, 653767215, 18434848, 927569889, 160037223, 721746673, 283923693, 575477761, 740528915, 567689627, 143377634, 798089665, 117950977, 62637039, 785279860, 127312632, 58871129, 802825913, 468175560, 979635290, 706235134, 883431604, 762915034, 955272419, 26193161, 995668997, 30692548, 247700284, 222933650, 104296648, 125924088, 963402285, 972509480, 603687058, 517255290, 167688770, 532040958, 293242517, 893427750, 781376835, 219697185, 527666858, 450472782, 872866013, 47190211, 254649036, 531166278, 349684561, 814076815, 454132899, 411555878, 297734845, 212206882, 914792389, 554338412, 890272839, 902634921, 464891875, 823393444, 783255204, 363527720, 998099339, 754839267, 780616460, 336610554, 917784974, 555348486, 412697210, 347569528, 554741901, 479018550, 342897458, 511929128, 303107749, 348355202, 848528395, 434516779, 844688798, 51469151, 92523538, 388366597, 332362368, 791354096, 733326031, 960266412, 600914479, 157886252, 872568652, 484675382, 108250234, 118050132, 941774991, 468770043, 535377580, 766235130, 459083184, 708458698, 741249300, 683518839, 197353681, 147355252, 393546464, 943427692, 13910928, 123647216, 478427589, 641344853, 936002084, 389431232, 899265780, 459788443, 401939225, 395317586, 367112682, 828856370, 366217056, 127884066, 381562183, 70247739, 582226048, 531306214, 832350578, 329702556, 351212747, 99960942, 61194076, 441656964, 829187296, 831797521, 338975397, 17875220, 795805506, 905315098, 598625003, 467520268, 595600848, 321639444, 956300866, 270585629, 687129522, 23262768, 178471648, 822662776, 78248397, 330592244, 530942707, 252531105, 544745905, 669889680, 437996822, 212645271, 604693689, 979101412, 891503346, 299918440, 618362965, 93164921, 37755039, 42507951, 316087737, 914804443, 618536901, 531139169, 15617722, 767040594, 303792626, 804245343, 988247458, 468550089, 719876710, 551187336, 656269843, 876800805, 326570912, 906220176, 749055775, 629415291, 156109368, 940170968, 504753554, 695714047, 252524220, 508744939, 488598037, 642065334, 124526234, 750619279, 20258865, 977387767, 494116741, 81176431, 576610832, 951086458, 74408987, 661744404, 428467765, 972770802, 576128588, 262649465, 784479091, 893979777, 90170002, 508670125, 279726646, 287079062, 831522181, 617175992, 634793445, 743457752, 493679913, 520776664, 885109896, 825956967, 434193499, 81360461, 69437537, 973974344, 448969705, 378462879, 998415997, 731693211, 184206072, 804749779, 276933757, 410569920, 776475599, 291374510, 754199066, 781579726, 238604672, 169767314, 733090112, 786270043, 119203816, 651389543, 146292235, 80835708, 724568534, 521332755, 498375991, 147722278, 142893352, 46464361, 319170580, 174281632, 287996835, 445271151, 281933364, 73498069, 318379380, 33840919, 73839195, 223244948, 495208269, 75794125, 611267756, 800377808, 494083297, 807528630, 368206199, 850468275, 886983662, 570385161, 261210902, 930228543, 584663972, 533636472, 965855613, 294159653, 641599519, 520490296, 328031480, 509906425, 653199067, 716935320, 126263131, 473452177, 469644893, 552266774, 588326919, 71919202, 546704399, 654631863, 607332860, 562321967, 724198122, 619513233, 898422420, 600119169, 244983280, 107578419, 455621537, 462602223, 779674098, 367972828, 358246431, 628466683, 292863158, 263408368, 844281735, 276658450, 481681416, 812588633, 592627588, 690730189, 631345766, 361082383, 234618527, 705729493, 934124290, 299308355, 387966286, 980268675, 632672933, 600770423, 45527305, 424369074, 820645439, 834932032, 818171929, 598487194, 509866714, 905006565, 909143369, 745918804, 963414626, 652155603, 607155386, 180435916, 234623590, 797486826, 421870654, 590357215, 687447759, 780465885, 401824112, 262706384, 211374739, 274660524, 175893836, 240898236, 741197693, 859757372, 72627208, 439831437, 947812150, 783191999, 507155059, 399958818, 574129575, 12070646, 611753879, 97432940, 486990699, 358805393, 812553130, 761768871, 35217120, 236510950, 5096621, 647600410, 638382901, 875267723, 64201396, 99681284, 695774846, 960604115, 636596478, 228069042, 872562997, 678247635, 342919725, 462955955, 258066224, 906448638, 932790563, 653304294, 8683187, 203257886, 601346021, 481445162, 936920612, 61180124, 836952749, 145076771, 407344476, 437590953, 993839252, 495234460, 490261088, 659287647, 626130734, 225834055, 393812989, 33389480, 760410263, 117761702, 759081457, 757198096, 90954553, 634425661, 593119417, 825846405, 865826803, 907395740, 966453984, 672239502, 937129774, 493120405, 22751965, 510019605, 222583035, 568265510, 424018942, 507653341, 330010377, 901825427, 588127426, 984288036, 359152505, 257544735, 588708428, 329843979, 59052836, 151438456, 653619177, 562213922, 816733043, 206369274, 479461755, 613548104, 689636649, 842283740, 730572195, 721441336, 829180661, 868449540, 84624980, 648215073, 879331396, 295312176, 586662101, 762397018, 485941429, 721746889, 862843781, 466863118, 214053806, 155112641, 350337381, 45635958, 396485181, 963542364, 865760578, 293471205, 162335995, 699569777, 385246753, 941855633, 26261696, 818758453, 197788068, 453636284, 144533009, 7293949, 455556245, 837059955, 351579340, 849331356, 265866969, 933983573, 871066503, 420884889, 626179411, 345904714, 717243648, 459062641, 395843590, 53091942, 709135395, 199697497, 262668269, 527431071, 768884774, 773694035, 436046314, 687796445, 325405151, 695265345, 596731315, 980732690, 220885874, 477115348, 502402924, 255155849, 204075831, 169975378, 865373599, 758268773, 658378473, 910799821, 46875477, 412333403, 487004293, 501599028, 419875528, 609798552, 582539048, 942577179, 200381814, 303887505, 305490891, 779057204, 628807761, 102518957, 828222068, 472803029, 669163638, 848266303, 812640491, 152941519, 536751813, 58257948, 580399909, 127615702, 950565365, 996973225, 952933891, 469823054, 300964120, 76309789, 655088877, 61308738, 406688870, 683463391, 817495898, 390734084, 911089002, 744333132, 563271954, 996553951, 425907162, 257555292, 631884237, 204829449, 651371932, 858424481, 432840522, 810560309, 856082923, 780664495, 242402829, 907374821, 562163515, 835013696, 16934307, 845272154, 785509001, 369017104, 768176779, 840120032, 67454982, 163656735, 973466698, 466677143, 907378130, 821874419, 992187122, 133891672, 939565772, 418891727, 202947470, 927513849, 790272520, 213720966, 196770108, 454886675, 779774138, 187281409, 941090949, 688411563, 777409161, 873231173, 648990261, 594212862, 725995494, 826710113, 371656210, 345919351, 422954686, 451638911, 399309252, 644097984, 403261547, 30750100, 907379546, 72239815, 939500797, 909797662, 664817248, 504537149, 604021070, 259420260, 611302283, 452188710, 166762112, 129379316, 696366065, 517035120, 748294504, 929395739, 141295528, 336508626, 639341992, 471908220, 496783788, 5929256, 109090575, 978885824, 393979169, 729860242, 882345675, 350084184, 507692198, 819832473, 495969380, 324558594, 916980203, 710083210, 375891733, 669684555, 780223651, 80607029, 359887434, 905018575, 175994506, 957914682, 916412298, 288737675, 43406432, 162774071, 134519692, 595721610, 3662024, 852886233, 862263605, 869738544, 781951935, 280260186, 868917066, 667199533, 819946646, 478158874, 118174745, 382873610, 860727781, 547653217, 822418292, 25379677, 922599815, 650627162, 665732, 321113672, 348401438, 630402462, 327587761, 227583538, 898030789, 169914437, 223333171, 531579499, 945756743, 255668785, 819301179, 672272705, 980511066, 687238025, 301600639, 986296355, 679327444, 362870071, 612252004, 937469853, 684540915, 7137163, 553421033, 424350669, 237640672, 30455664, 566573672, 461941414, 823590928, 908183417, 31923929, 957726824, 600320913, 788625413, 177315749, 284836116, 600925089, 798298905, 65677576, 143390720, 755607688, 555043304, 468583492, 458387922, 801269520, 311063992, 78001167, 205520141, 143528215, 323634035, 460975518, 835976261, 653211129, 831183478, 32580705, 370649843, 369852723, 482842410, 329134901, 303182512, 628586012, 523445002, 119054118, 643769620, 824321664, 476276000, 82908491, 98070938, 266912415, 195461769, 225810469, 941834950, 919016274, 527472991, 808315256, 889642329, 709529616, 686721196, 150976778, 195924769, 818207977, 678319295, 883799876, 830531152, 759436371, 753236704, 950776945, 534627417, 910686395, 368223451, 652003946, 752378035, 873658559, 771418398, 223925762, 838300765, 70550569, 405005978, 449312605, 289170851, 571606280, 878727493, 758446367, 625039650, 933476236, 185641281, 265338051, 23263761, 977460277, 131853501, 177239684, 249260940, 929255633, 660309409, 703950399, 28287170, 675503915, 16060922, 677957255, 839796259, 920491985, 216686814, 999240701, 234107109, 370552584, 332441659, 887450552, 380407691, 815865797, 507878696, 789783112, 186105252, 828109836, 97446341, 880967583, 62905455, 798346658, 374337244, 452208758, 495386413, 256600543, 488645050, 664958798, 32056452, 295763797, 485262441, 657506774, 859451763, 684498252, 119355183, 856914225, 352118990, 386805816, 267296130, 202063633, 998647475, 98021615, 141475641, 486823634, 7867973, 919128790, 612176836, 934752899, 664271502, 780217163, 900594232, 725243872, 805204536, 726647896, 402276851, 73675026, 580767992, 50802461, 101961959, 410840953, 963200102, 210698348, 638349889, 781197177, 137475940, 583453298, 553686021, 386735522, 631165445, 622148070, 226268677, 50283240, 44369289, 640678861, 419889931, 659020449, 203612462, 775485421, 148903667, 273365418, 171906512, 181978428, 170180152, 657680639, 302545716, 426721938, 453411994, 548472050, 285722925, 800814555, 523004676, 520963984, 788659952, 456076941, 768426744, 44234183, 546770815, 230967288, 99346665, 720654662, 230845990, 629130005, 611483877, 791415614, 927677072, 352045213, 772457850, 90719648, 834087630, 846151172, 699238888, 864597813, 282414648, 677143957, 518941098, 648550903, 564482130, 56485107, 928126641, 140913948, 466308790, 243877803, 313535875, 687290822, 920334063, 338696836, 783728056, 833527243, 943359844, 674795522, 327125209, 851317050, 790898193, 427910505, 130929872, 117534392, 214669821, 251254858, 910214407, 46786992, 242945720, 205538039, 39922242, 768482410, 37935149, 957830011, 860083320, 633209344, 314966427, 160080554, 5068132, 510751574, 71674938, 787661232, 996269166, 113305800, 196139482, 87840208, 861208159, 61478813, 198261304, 649220263, 897274337, 161655706, 852566275, 852708857, 879335054, 621685380, 263087812, 863408478, 923549847, 940370373, 118301612, 324690441, 139928075, 512661402, 137145026, 257566368, 254467241, 281240552, 546044592, 532496807, 5360490, 695331635, 533302414, 412967114, 356290083, 734556371, 61537262, 209458763, 231105814, 62952415, 272358328, 772525527, 170678460, 735801812, 784013968, 915247034, 346442198, 231904726, 668629021, 397695460, 839789134, 173308527, 364506076, 34222942, 244025768, 787154637, 61116923, 874002237, 157983012, 536959498, 177945470, 823278467, 6099843, 115374268, 679940436, 817985012, 275448981, 129981417, 301871400, 665961924, 805521040, 119565591, 924477998, 527157905, 296177816, 877516455, 588542959, 200788276, 256929291, 366665471, 759998572, 412739730, 6071302, 408169794, 521075639, 889700099, 759069348, 653283728, 617426966, 979408602, 238379066, 802959942, 576739654, 140211485, 30250077, 113556455, 9139694, 607541889, 350918866, 643362412, 870003543, 822004748, 827366690, 569070596, 721830530, 618987133, 145036996, 158410266, 201135777, 17659305, 42611987, 657877751, 878530529, 501273811, 755648132, 46875143, 468158706, 833781088, 939207982, 262973558, 180197267, 963411252, 468914979, 240481784, 270441009, 545856676, 455633438, 635429835, 443735293, 787894210, 674192408, 870385513, 647909747, 611122456, 615578829, 402826308, 956051225, 943629033, 549302422, 152191712, 125586750, 472904342, 598131985, 831507292, 198162107, 111679497, 134711267, 897338516, 393017618, 979516601, 874959375, 870110898, 102352012, 614857708, 217226102, 566027801, 14150152, 251508685, 45902598, 175005429, 985862281, 374699638, 541042551, 654906054, 559355773, 110974445, 968331493, 359051760, 630522955, 304730401, 874651776, 284625312, 195088667, 388467853, 867136693, 987254115, 774244778, 47921142, 413465930, 600834718, 50645133, 712051601, 918650227, 251231138, 385204136, 613602087, 538419805, 947735845, 441169950, 364079544, 801332261, 333155666, 964516084, 200690166, 397639294, 790282267, 356166417, 96931493, 572574261, 205620006, 228155186, 219084443, 37556513, 669956660, 266320746, 204702708, 279035551, 537557000, 372593913, 907360408, 296992626, 184774453, 988754429, 646341796, 272449974, 431852017, 765547114, 455653173, 445326037, 461045180, 105963459, 553390742, 912389525, 879219684, 14153611, 21457101, 866835861, 932209863, 66026085, 421808333, 872196606, 953944985, 392105806, 211201548, 533481920, 817421245, 105023958, 903632181, 41632558, 305389569, 890837959, 331603700, 168791944, 349100887, 100286509, 342913393, 802160403, 881876610, 836236443, 254879116, 660802927, 680842704, 377312105, 738176597, 964673635, 29882095, 168655971, 661398051, 432774238, 582131731, 635534895, 542861035, 91319100, 322031513, 745410799, 523050174, 217818130, 271964484, 175464637, 708758035, 549249832, 951908089, 651860364, 884686263, 1134896, 228036796, 38327130, 822274549, 282916945, 339049838, 491060826, 529843200, 881753600, 223025791, 322458407, 261382033, 912302527, 24785097, 432267393, 850406857, 675698488, 988515613, 456235477, 59051024, 650229008, 177839846, 257799726, 712136175, 217117556, 897006590, 166579771, 737327678, 65775487, 81551797, 893302591, 117309513, 831538348, 460806833, 491624105, 212282019, 416088911, 94693522, 766466013, 684547322, 744511399, 72013297, 633707703, 292196425, 391029783, 320947184, 784907024, 389504851, 857832983, 478303596, 634929764, 10195287, 741385909, 131609584, 240527798, 904691944, 462309024, 120865579, 756193563, 13767180, 195379307, 655349585, 839893172, 298234900, 855849308, 555959406, 308619413, 856866643, 473210522, 666818969, 341381285, 107633383, 739841331, 386594279, 534084774, 952500532, 756102475, 689417195, 604701541, 618434285, 355737406, 454617527, 418903054, 876746330, 627722994, 883899977, 401469087, 602080319, 898148909, 827679206, 249020102, 285895522, 848048108, 867367220, 261149548, 45747959, 65181111, 107961285, 123866544, 475649887, 951002988, 146905291, 467694764, 973728531, 730563197, 428314983, 761587336, 551118690, 593049534, 780904160, 12827720, 252950439, 429637180, 697531085, 283991269, 624914945, 256692015, 185388069, 611094331, 231251697, 716908007, 137730151, 245046585, 105849779, 955659016, 480838292, 269764251, 488610961, 309832682, 319013678, 562143702, 301432804, 209120435, 281282735, 874295065, 811940535, 606769098, 57142154, 616128371, 849020857, 745764175, 798697551, 869903294, 140345894, 900486291, 477928786, 987263771, 11375420, 619964357, 961191189, 803628475, 172040302, 317574757, 925427473, 622684805, 778165717, 362319266, 684103149, 157758824, 450539585, 378142643, 69866750, 689298790, 221991267, 864662329, 496879102, 323957402, 14088386, 708403352, 751322066, 479537062, 571019743, 377700987, 221488149, 319679932, 90437572, 979502799, 573233981, 870608772, 803144176, 627611622, 764253377, 672085772, 212646210, 283895536, 823885630, 111037932, 644465283, 879932904, 172092056, 588209182, 766965245, 224777000, 544087478, 589186070, 925350937, 623094895, 770240938, 567622166, 173522847, 420031253, 744152268, 170840006, 375767907, 22516478, 697926128, 699916101, 325697006, 608049927, 627891875, 245872960, 289694776, 937768219, 462319548, 216608416, 467878185, 700699069, 194656072, 586515013, 874806524, 551185547, 808291563, 177617797, 553094583, 115513759, 179191062, 164866712, 679343996, 308112205, 174720774, 589592038, 293547279, 311396294, 733346983, 13593045, 731898664, 602657183, 105204137, 533806595, 884465697, 485674901, 224868878, 78116516, 998308725, 582068219, 315046893, 620783824, 912591868, 219529933, 544987400, 126518852, 861333840, 120047791, 967987412, 666614096, 963889943, 375155270, 893623847, 322789951, 196703420, 839334288, 710135879, 905186098, 493036672, 898432495, 119858870, 799574080, 379792238, 885975853, 400409283, 688689376, 683444878, 690161195, 80234343, 982812904, 255107232, 887122588, 518283071, 473081079, 635912076, 623122894, 851859557, 506596631, 271174566, 252700020, 779182435, 973607466, 105122196, 89801492, 192768051, 152374809, 669903149, 367275421, 619276038, 25322307, 833941329, 820624764, 311749271, 566357205, 948207336, 194472722, 265516015, 521227518, 314506095, 488319010, 538217763, 468986007, 220450701, 160614915, 526544326, 784359843, 655983066, 28351039, 42985772, 18129666, 941856149, 910334509, 698127148, 204317083, 970094576, 61678399, 620240859, 592973363, 655680651, 724528618, 249403415, 66177577, 296937365, 790509693, 344076948, 380845307, 694230913, 932821451, 257367692, 873890073, 451669430, 932716951, 610483693, 80665493, 941894616, 836884482, 732636174, 361307846, 531352328, 691365811, 21523313, 333818794, 258305839, 708401740, 385145697, 334557828, 748208857, 876599090, 966602362, 328716365, 718908562, 773056303, 683849416, 961003614, 49585164, 759138096, 612066044, 876669842, 80601278, 266528601, 167275562, 141707585, 732033420, 920082623, 67167621, 107751958, 907199053, 219195152, 75766421, 289400094, 880319028, 135761394, 456571825, 154553171, 673846720, 340959714, 70262880, 322531028, 834150118, 997897466, 146880515, 900889629, 90630481, 778952407, 584795812, 821195559, 195486474, 570064361, 26978173, 846587676, 398899331, 568613813, 764870261, 254906737, 32642525, 388050003, 333513800, 975479324, 218510483, 768443550, 488671908, 626553749, 117020755, 34779238, 493839034, 182208594, 972969763, 34616493, 380223045, 538960519, 503371837, 691210367, 171023399, 422079712, 286814220, 424487195, 922122158, 738924737, 868229932, 510757485, 202161093, 375783253, 271610870, 670283891, 844577774, 799627859, 125334950, 339914146, 68815094, 829025627, 200778482, 852480068, 979720045, 973509420, 824518378, 666821550, 604277451, 667733781, 800329655, 327443814, 347706800, 687780742, 408637444, 767500535, 395009134, 8824902, 940007289, 685310882, 721154429, 502225272, 921208612, 530228208, 590300458, 430264586, 204250103, 986629833, 808420919, 504805097, 757500657, 801821831, 28220971, 66164332, 346993060, 72304628, 344728971, 36857048, 3175924, 472394935, 92169265, 769653287, 65965678, 314897175, 288463883, 601181932, 570239707, 496875518, 497831374, 408715748, 201658487, 769752678, 346226040, 447508812, 64314175, 316063907, 800663852, 372934160, 317185926, 111486382, 950063543, 183197921, 181156529, 148220101, 513416377, 75613712, 989948469, 809381119, 603597759, 997975504, 470697762, 473365265, 397691882, 99862880, 314722661, 446818965, 800395473, 334723047, 154152191, 755253092, 430471315, 673943459, 555796641, 867602444, 289846013, 100243609, 628070766, 422634268, 220652514, 324836578, 266692207, 102407758, 461897659, 120219001, 622269125, 78749453, 308277874, 932107074, 614337716, 570141034, 605311136, 442736566, 357711393, 427003389, 351007818, 415227317, 713929764, 989310721, 336062896, 746828909, 267765425, 854607652, 302453454, 950364490, 133952754, 326631245, 128421400, 258228003, 484675305, 176376103, 876288008, 151898213, 247938896, 829351610, 756448724, 179917040, 890785035, 425595032, 36318999, 980939718, 487272466, 552506531, 3058245, 964435746, 484615841, 420469931, 577074108, 922427017, 820354264, 64594533, 599502482, 726126443, 516302836, 25224341, 776854079, 189916267, 882074377, 264303184, 485069185, 155056620, 810301641, 467965264, 124310969, 308596684, 450291148, 796594486, 725375723, 494793934, 723724295, 982703271, 95903539, 189720051, 216674255, 954965437, 307318733, 762732073, 536137384, 670427182, 209863533, 427554460, 115355595, 887506503, 291227187, 765939889, 429813212, 711478948, 502020696, 692273415, 131711583, 718748512, 769363628, 928989254, 497675878, 491928053, 113670898, 612697949, 658613792, 726956420, 604485631, 925780283, 265402980, 303438168, 825047463, 626704009, 752203180, 244854201, 511939692, 448221046, 693980440, 846772101, 245540804, 494181830, 821529149, 367503263, 305124963, 446082456, 132713709, 266404348, 37174059, 390309740, 783842144, 647872816, 975428728, 915066198, 240763349, 928943215, 745255960, 745994031, 265915903, 366361042, 333254321, 594127680, 675902845, 819272927, 36475816, 534952569, 51874255, 179169208, 366445028, 767963146, 57670216, 656525280, 630451601, 501305178, 805016351, 34426867, 663496822, 961930989, 338052002, 373382376, 588916255, 568380267, 323933730, 420752166, 138443603, 360453961, 914691863, 129475189, 443732190, 122070758, 420508009, 676007351, 574075962, 433588527, 704804429, 597656138, 667775167, 711480868, 431110530, 596543867, 737577520, 407748451, 564704069, 476511114, 494202646, 934293822, 249088176, 863858010, 173943943, 806646130, 245903820, 731686497, 888310090, 60153136, 407891529, 249421455, 992226626, 478585977, 354849088, 979070170, 436045412, 619649327, 699830308, 263922803, 758710116, 553630215, 728182959, 834801410, 355362230, 358500102, 673777190, 185006843, 356645991, 220354792, 74320232, 727920357, 624698317, 718061189, 372344714, 230053191, 758632923, 265653725, 781382385, 18815310, 76191897, 61241013, 860063344, 971153859, 333947781, 258880559, 414550228, 293347822, 601729421, 851278713, 638608624, 643347398, 453626671, 853137707, 295734741, 795988573, 241367817, 986906792, 392294713, 323988429, 742003273, 796055262, 88528144, 310092912, 213211622, 925842225, 376279601, 692158144, 727251591, 520657412, 151933265, 579281464, 287826946, 217076577, 865204716, 114207293, 456027966, 676984068, 744568237, 758623630, 876817368, 16596897, 641468719, 173026368, 977738789, 58101825, 229453612, 497930335, 155608146, 560036838, 777151770, 266699600, 697399132, 470031817, 848256930, 135971092, 604120287, 487415289, 299105304, 956965477, 934872782, 816245098, 134642098, 67576862, 521148489, 951898128, 531710900, 973571147, 166135469, 145914124, 994009347, 115554051, 981380591, 542854298, 546010093, 194800541, 609049202, 697398439, 157159314, 844164236, 640741566, 933470549, 586221052, 246100695, 423506346, 209681550, 255970112, 846261931, 231945881, 145931689, 73402566, 469793077, 958286891, 707105894, 69330479, 273135265, 895108389, 924907288, 153991670, 270843564, 868750071, 889867049, 26797919, 521792235, 823686813, 787238941, 138816617, 17483670, 118506143, 343395846, 609123310, 463032443, 179655945, 58931218, 12107735, 446553379, 941797092, 550341910, 30796484, 144983746, 866458050, 967978298, 121751131, 306763009, 177230881, 308961773, 118060619, 216064686, 534725961, 737392274, 430418760, 594228686, 219566756, 982416931, 842310249, 945285664, 658193690, 364957206, 623905965, 973537944, 535452536, 550487850, 702462448, 70563259, 598750618, 985480827, 292545921, 615242422, 471804827, 883786558, 61363155, 609305680, 735532102, 189862924, 479212373, 485140732, 433663019, 277821755, 298465935, 440118930, 100734788, 518316660, 4895681, 306177065, 761467333, 808796007, 471906729, 981472621, 98297081, 891004063, 605721453, 418526290, 516911690, 781488275, 997020069, 555640464, 586822188, 154247027, 38484461, 404401001, 777335953, 54829763, 397925511, 391187113, 289763170, 491105850, 969788201, 412587517, 519263767, 428355896, 161551391, 41620798, 781679865, 126259869, 366198821, 690230939, 827933158, 385576589, 231608703, 242887563, 987499762, 950691328, 74043965, 328971985, 920988563, 427817779, 733989025, 805388847, 406639061, 394265637, 977339288, 341029237, 98527599, 276279270, 356076811, 392301297, 842294982, 167835792, 686585025, 118914670, 136850681, 618306421, 980793372, 521029011, 336976146, 834938942, 847365637, 929151126, 874834874, 427118199, 704542249, 552424108, 434783460, 905529502, 726852478, 2742244, 961098133, 389017169, 997957022, 704940740, 137796580, 740671384, 313578321, 260271860, 286811921, 639440814, 985952440, 117113721, 626548526, 699078424, 432526166, 94277281, 352096930, 762853759, 77006242, 45592259, 22062007, 858315706, 456585263, 653723087, 492058875, 887309463, 106197182, 364028827, 655944326, 906284184, 518083769, 797612162, 129144587, 732329862, 877051946, 559803013, 757711997, 262311210, 514167648, 651838173, 826097042, 94735162, 830332325, 677372501, 202333862, 55298115, 333657570, 503567405, 180086814, 385608457, 702014411, 40968963, 602118070, 960765600, 711283617, 436684519, 30919197, 336228650, 166463267, 620008191, 207317032, 228284747, 783199976, 788043489, 165646081, 18194087, 647254026, 1823099, 588459917, 738241589, 892156714, 116034248, 89167915, 887510844, 759119709, 787968104, 984506189, 337478663, 462266627, 111811898, 691045312, 227324864, 7347663, 722515809, 834434580, 757367515, 254612781, 835021991, 691243860, 8279800, 645583386, 790911504, 800329957, 675218730, 469080868, 896629341, 220370114, 50790954, 384698417, 302688956, 966543523, 267489759, 796805677, 640428627, 837673151, 696092032, 253613989, 306557951, 854574708, 857566419, 726486707, 768006861, 766618301, 995179295, 205525275, 238947881, 323572960, 956725034, 869692799, 614174485, 69713676, 363888036, 911653395, 488977250, 258593424, 795581292, 223767118, 926609254, 349471337, 704759548, 409500674, 879439407, 564349087, 139244156, 207120996, 411896070, 453998111, 132984112, 225657553, 833582714, 384966538, 232516823, 534057372, 305956363, 274835151, 799572109, 504973442, 993818135, 747723586, 103065976, 726445754, 98392231, 32237871, 131173106, 627433912, 297616363, 793197584, 643071336, 602943845, 64313501, 464557016, 976450405, 321706306, 702891295, 953155982, 93700079, 385067591, 585890062, 696941175, 772032689, 100307061, 381992000, 885845945, 752820440, 285228433, 533689908, 954209323, 583016594, 129369053, 449814115, 426872220, 765527641, 322401117, 874002637, 77773302, 853185070, 517167846, 265116473, 622822627, 532729226, 433975690, 328383236, 425921253, 782738023, 939632197, 425242621, 870398735, 231052844, 513198904, 231808501, 556495662, 887074364, 528990818, 904935131, 168906933, 755181646, 338458455, 877016386, 715182664, 641133844, 340470042, 846481483, 381800844, 462420544, 749820876, 939827908, 567056822, 838492264, 330250344, 264348480, 228002208, 76095284, 28530699, 47257901, 887503995, 787407829, 15983818, 888405627, 740850289, 133502987, 462913493, 364170704, 383340425, 935000501, 604092918, 488611454, 330169664, 572318145, 718619303, 959357051, 690642536, 873020987, 466936785, 472282687, 539875542, 542866127, 703472855, 292223971, 262314351, 923292239, 2608769, 918560146, 930468721, 541216832, 733219610, 389042305, 448229245, 885798768, 834669473, 123565446, 248112067, 596745013, 800068310, 146118865, 772162807, 620953539, 455950702, 927694028, 783166843, 257519589, 251318171, 115685423, 463969143, 447164810, 891868078, 539194444, 178654407, 44936566, 579775108, 526057627, 933515873, 363648942, 558653501, 731823898, 222758673, 380089997, 752533103, 188100605, 920822291, 656810967, 716399397, 963702468, 651444529, 70028402, 796444429, 218435145, 665762901, 658239423, 879994500, 85935264, 95836082, 623279667, 316523435, 983137175, 506815629, 218247181, 833609939, 500685610, 173739749, 14591764, 547824806, 287118380, 477601753, 523737105, 806969289, 219584492, 610342035, 326168981, 11159360, 828597597, 832514244, 899245870, 645793531, 599222382, 165816450, 747898454, 174393002, 687277376, 722654033, 530113946, 90801132, 191748222, 671163011, 380567230, 904457224, 823476948, 857836637, 890625689, 204367449, 961707799, 301227773, 261028571, 899479705, 734232576, 638494682, 311095824, 565470054, 670092101, 512873223, 510102461, 941594173, 652930704, 513540451, 932892386, 653037147, 326062674, 322383902, 404173842, 840677566, 192454688, 153264054, 965613228, 568085467, 325246899, 253752817, 609631536, 869225059, 162178052, 254554840, 693680098, 659152680, 788239015, 546858231, 614754985, 873616706, 286921505, 970696047, 650747935, 375575264, 57553585, 126309070, 931262836, 261153019, 794375252, 63713418, 911076743, 404182185, 316172916, 491957325, 17370979, 757095598, 141156322, 311226020, 283113778, 700199609, 375121801, 408176820, 774458930, 181302606, 217805162, 201055723, 328451893, 591373725, 7127093, 129041963, 634375453, 873441499, 403473741, 21316931, 361194382, 626334121, 293965290, 200953792, 191589027, 519816374, 14409316, 195077225, 434177354, 123927718, 25479523, 528042380, 534458077, 709332739, 17083251, 566724576, 922556599, 467543962, 664494457, 224512911, 193588339, 862743355, 509252835, 757284486, 614715254, 762242728, 798887523, 212068363, 592047105, 105429681, 470234896, 729511132, 389940435, 968130120, 41745200, 563614542, 879980076, 882784328, 740348697, 59863785, 106920246, 577894037, 710898819, 810444706, 974618264, 879450069, 130892177, 687273038, 709679692, 660944408, 44212594, 435615182, 775495933, 966624627, 624082300, 811819362, 627726253, 429746873, 864451226, 634390303, 499078261, 616173946, 317117873, 302026673, 489799326, 97486109, 41749155, 466727621, 739763990, 825014142, 247920673, 349357924, 390855892, 712376595, 796384612, 948457471, 892966168, 91611643, 183427654, 992399948, 475838680, 796718928, 203254070, 138285398, 712964673, 710900438, 683245971, 217544523, 494204029, 523491646, 365936435, 390678729, 175659471, 598028999, 946804520, 167407918, 828212457, 889379779, 763684710, 44853734, 209917686, 773541949, 983267772, 205394091, 151754236, 421011463, 48050534, 392679555, 402448240, 542527478, 557490328, 440992980, 519248858, 554591511, 490277180, 321447571, 753975946, 940098233, 702304214, 469224538, 571584890, 830001345, 340597497, 833660983, 145944146, 98649480, 581693045, 489117661, 78261234, 88303801, 88076833, 658227111, 243810461, 589368679, 422463915, 407048880, 990078158, 1646385, 253273316, 80974863, 514338923, 70643149, 643013849, 198891153, 126421904, 267759077, 429547306, 126751279, 700146498, 595945573, 79173284, 969485957, 702008961, 512279452, 139737947, 995651721, 788582655, 350590670, 188647053, 295101987, 659640538, 97207258, 724453757, 688599603, 778370217, 67675145, 707993786, 894194755, 35279586, 580741419, 122275162, 495543500, 117789606, 496522580, 676243912, 988881512, 478328282, 196868932, 572749147, 458238947, 443168126, 519002909, 466675952, 998341141, 27807170, 702468369, 360746645, 568104502, 760960293, 893708519, 644392678, 926039664, 817828210, 433483952, 659211466, 165815258, 451241196, 551671955, 663583853, 775688888, 306124507, 91477673, 932069128, 92557221, 844425285, 542397909, 476321511, 793066397, 974558804, 833754985, 316402601, 356056253, 889383946, 864279698, 874457965, 85741837, 442977616, 22126986, 610723398, 798958191, 212712326, 554951671, 257351201, 529289970, 629422022, 459108872, 95780072, 986045896, 335558232, 389606020, 266574428, 983302608, 417804034, 492659581, 399077530, 314147085, 438022693, 477378573, 162579894, 326893321, 763922397, 67822164, 885168603, 566293141, 961841049, 970225136, 372621033, 781904016, 677600894, 590906467, 909602624, 227026146, 163129135, 548368385, 839867899, 959878516, 56812694, 138753574, 734134752, 37323853, 501757647, 842737560, 748492885, 389505751, 354847280, 849755280, 19451867, 123916754, 525166027, 654188105, 978183096, 351093150, 972970582, 621338780, 798794178, 572905848, 803209951, 845301812, 766737732, 389226624, 846689398, 413625069, 490586639, 631586826, 378589688, 836557811, 298154316, 31550638, 575857436, 884666977, 338329041, 666289992, 845821941, 672345682, 498434266, 485997262, 316901288, 362517089, 858639832, 568635741, 9090826, 828720586, 464542139, 819450928, 845756338, 139284947, 822868503, 927587461, 768173705, 686644380, 553145604, 987085641, 712869100, 437206790, 554208782, 216837812, 550494128, 218573020, 994172585, 197382209, 846614905, 844381101, 495973807, 923473273, 770064470, 474553276, 582607329, 928170141, 198273723, 267529348, 162448742, 602663051, 887820245, 894542273, 143165078, 222754070, 270134085, 369397216, 383752744, 923638922, 833746924, 464643367, 939053018, 625039551, 138250407, 684754564, 653888083, 77584811, 153381605, 267764306, 55548030, 670665762, 713113377, 250746560, 796781822, 574872096, 137396558, 97992218, 643567908, 769303843, 238318228, 885306077, 344078609, 455908651, 481375148, 390467196, 756403596, 250543363, 254106239, 305312370, 697823345, 185632939, 303466665, 520706244, 305341095, 724350281, 330350566, 694065866, 566795840, 348183995, 973341959, 16460408, 946195946, 726690204, 233492455, 624485263, 190103870, 898798914, 198358000, 115599517, 397641714, 828132695, 411507287, 63544983, 742148282, 30747595, 416763103, 17061113, 257557708, 186461406, 4381305, 644934287, 510791642, 797186850, 812005925, 696888993, 414092524, 180144570, 775829679, 472129826, 164432295, 124786350, 821282266, 136591359, 759397016, 797603163, 538060212, 152939272, 798360892, 457545364, 371090318, 877856063, 650137909, 267614336, 910958341, 137198102, 127223669, 865663889, 463612153, 722878747, 416860024, 740218237, 328572624, 471695065, 809298608, 234445342, 494969084, 937480286, 109402336, 508398900, 550558476, 514396704, 63571165, 310028486, 608824330, 101996740, 239543383, 561300118, 760193553, 952610873, 769173707, 921348646, 685616635, 559924838, 367054628, 213039820, 239553880, 155826009, 405177463, 892816871, 165333212, 861353313, 193064920, 513180677, 856568067, 745043189, 258049110, 381746855, 511605606, 900978508, 834569510, 421154462, 161473798, 929148617, 90201051, 551338129, 27633110, 732930346, 567842006, 298074047, 1061767, 630751244, 202262528, 694784735, 337164707, 886779822, 102165902, 247984353, 683751371, 17868734, 66707208, 911196892, 974790711, 467095017, 463151314, 735745658, 123272806, 66558913, 954851456, 350711835, 689025441, 728753691, 917114605, 907930175, 794367978, 696555265, 653040327, 906160420, 671969, 360875573, 920652157, 211872763, 567621380, 103294387, 295031015, 674135555, 853107515, 791207260, 841335217, 433337896, 493999494, 917674277, 102757610, 984274533, 285666066, 730585897, 868368289, 743806716, 412141593, 80202822, 2894317, 212704744, 649931404, 255365633, 313685806, 57933498, 751608290, 478281542, 654923284, 950451286, 692620740, 596616388, 160419153, 46210776, 188926596, 964312106, 143496799, 220148206, 620414542, 636565605, 198643734, 241261660, 21423809, 955518731, 982878300, 256641267, 277847645, 781043200, 188913749, 963564460, 72169654, 288319234, 453077058, 294041022, 486306069, 862077662, 582894124, 469603475, 372667901, 795305584, 883613340, 888285083, 744274749, 230977391, 394997360, 584484381, 111381748, 326008895, 934960997, 410164758, 387971230, 379021857, 89999435, 932886172, 850820290, 98082169, 482434330, 731406663, 80051257, 235153814, 551501099, 332408719, 460504015, 757752949, 315714874, 514811747, 770188234, 337533536, 918171607, 849308811, 962738467, 79384221, 525260160, 152481736, 449726429, 197314406, 729327155, 912930763, 964585211, 959032990, 388299826, 837934198, 73094022, 86580961, 712637327, 337805083, 74470135, 282166411, 500303093, 202276840, 422866592, 462574912, 895787247, 172947364, 266965779, 133405502, 452639847, 530245110, 495993423, 711736866, 430833794, 344794436, 778557454, 236165920, 296516385, 928083184, 721813371, 626895607, 334164694, 757739740, 76926176, 991331464, 450533354, 601875907, 587611810, 578297095, 282886288, 992919626, 17055335, 435660600, 841076708, 900875499, 615910406, 905587496, 20607533, 744540748, 396195846, 198834249, 339249619, 924658827, 397500918, 972423757, 703444685, 382701100, 859700130, 487786229, 872686668, 416271639, 151574597, 717666364, 607258443, 192804477, 111339181, 709842838, 59855303, 119634771, 221165364, 741157331, 553124437, 769473048, 36283976, 754532711, 316554063, 612759022, 364676254, 952562009, 659775602, 594203749, 216948367, 895494634, 49958794, 880355483, 655447460, 33189964, 531341583, 47018871, 808704953, 332814977, 64930670, 268305305, 104414182, 394472951, 369342489, 508366358, 91994217, 736286325, 413432634, 56421862, 924155515, 871671908, 610408886, 809497240, 151925139, 156884821, 69211297, 717002155, 264498705, 811653080, 295444967, 872828141, 772742151, 2910625, 888805674, 940999907, 139491555, 805927478, 919907330, 574867984, 723666476, 259617368, 211003894, 814240874, 390931485, 225288853, 382652870, 902921942, 180436558, 775491531, 836499188, 794889727, 148307509, 743133254, 943530540, 673922848, 296438452, 921465662, 690898376, 941480058, 178485806, 24988052, 41105869, 566754804, 263921946, 117178904, 268360622, 998806275, 56929072, 17814973, 800348333, 390747312, 158210081, 169622296, 839333568, 391427233, 568298410, 512771163, 6333082, 662796781, 688238601, 152014612, 577838084, 32606580, 65628863, 594178982, 489494432, 777780790, 794114241, 637476519, 463183641, 980617724, 590345065, 96063030, 972079773, 299720498, 5947571, 882637955, 480118213, 454519875, 781375564, 450705388, 394333747, 914562362, 158195536, 53375101, 154000616, 705878779, 961408382, 15632383, 886323930, 102313130, 460533131, 84552090, 727327845, 296900214, 547541480, 441032744, 668576080, 182563663, 885540950, 813397672, 706980309, 932364125, 481102131, 805772216, 785175579, 233764608, 83790441, 741292334, 135692340, 463074050, 444629406, 418755944, 974950203, 482567032, 280357469, 343538375, 761359174, 226518203, 231881262, 499679633, 108103116, 468336777, 486045075, 397679194, 269300791, 817146553, 720667336, 673511261, 583468462, 371033467, 896974405, 445142947, 665599231, 547893885, 379383735, 50065911, 736135676, 955318528, 445399543, 96709177, 315582246, 707721876, 413582734, 276204150, 168041196, 317484854, 688147993, 426522346, 685888134, 326492050, 355362028, 140993932, 229407599, 828694266, 815370575, 198776499, 33615986, 443816851, 390899006, 341787982, 8619930, 188170422, 788267709, 771804672, 994544201, 128082287, 286070813, 34746808, 997596079, 910233063, 338130218, 54153119, 484192666, 531752610, 529787106, 281815334, 19622006, 983208319, 390728415, 949600968, 565254116, 947056289, 192627962, 679798517, 892485443, 359712490, 973679665, 85091031, 856757172, 961031659, 546766553, 686316518, 439984944, 218706028, 911397368, 260540520, 330397271, 890384500, 66171949, 558784781, 956412660, 674835188, 319607901, 965521925, 998987708, 586013621, 883377831, 286909577, 213260217, 486323908, 188960244, 63815362, 542384865, 474142085, 856411791, 397136228, 24630246, 66583431, 321205559, 276337667, 926031342, 67256766, 162607461, 975309678, 337990656, 971663879, 963880255, 527931718, 107448285, 862164120, 485420821, 498184932, 329430212, 506005578, 226605309, 990684303, 197156963, 600110734, 139011527, 882391905, 932559910, 681284484, 964627503, 786920815, 332881913, 653270238, 760650532, 451306042, 272187923, 21941107, 631982892, 648867886, 812644549, 441579689, 547202413, 801881283, 910528597, 489667908, 271762765, 150412289, 352857974, 69728686, 754271998, 33012629, 638060805, 881490999, 564982984, 784912553, 467860359, 851650436, 756894983, 145355806, 445821172, 559871909, 207055706, 909071422, 483304288, 712896515, 737886345, 310878070, 519491242, 622683601, 36072199, 966379128, 909956258, 193312624, 947985441, 598636237, 378499003, 612612633, 364262151, 568070387, 348109005, 763433617, 617876187, 804931332, 93795279, 422138047, 864439232, 617060142, 168934003, 839528052, 689295804, 619629266, 71533724, 221128224, 55517596, 152521769, 651069803, 72130098, 484446624, 523105504, 922383299, 784839316, 616070091, 188683647, 508264634, 553522608, 331571129, 428219380, 517121904, 450123087, 778073195, 978229342, 60746178, 847353292, 335736934, 858032328, 490854259, 823395619, 39470445, 237959695, 911597306, 343791770, 624599490, 304869348, 886099067, 989967748, 907556134, 243094930, 396906672, 93376627, 987734109, 651490166, 662316069, 914084805, 562757970, 942284017, 950512074, 888011331, 470368951, 150312256, 232758642, 254627966, 967857221, 706896740, 459409863, 332347746, 512287938, 760035301, 364776562, 694333266, 507137931, 742656128, 612430431, 352795536, 622907655, 695419941, 565110511, 663636147, 723143820, 717213617, 218478822, 720022337, 937529862, 780770012, 473435823, 154749909, 431310644, 501085449, 203969105, 427353285, 844437744, 743299363, 201509207, 322504359, 813086507, 222867930, 930882769, 70735391, 533865755, 668408365, 361384871, 828176481, 8591962, 206749836, 555037000, 680646693, 721042082, 443522281, 216478942, 242086189, 160837557, 14178399, 803102443, 730102881, 445089362])," 72504 (continuousSubarrays [748485140, 818457444, 506065671, 457502910, 80372915, 643314518, 575934438, 977493309, 303861502, 451292516, 562893213, 16654857, 164224969, 879121749, 598354394, 701732173, 855419816, 850202985, 284556313, 786617533, 174731254, 284227629, 730932068, 546999279, 263147370, 592212889, 844828648, 140569546, 654375423, 290560037, 443563630, 556480490, 248418885, 427128412, 128528319, 262290964, 560252607, 205632148, 687252519, 201341706, 542114760, 751315222, 28054952, 146060555, 286324553, 723395795, 699205139, 180609404, 92395765, 573013363, 142337050, 933004554, 663088753, 924545618, 755655796, 256864418, 960884095, 289990794, 397781173, 489499719, 497985443, 730080985, 684649399, 330016731, 161441770, 354948023, 781487770, 720656125, 197428971, 917922707, 789355336, 389182177, 762560462, 247402397, 651424144, 770212175, 842449487, 727531591, 237869863, 128497350, 666827756, 839086166, 397376566, 651932279, 804371459, 270030139, 833803204, 25908662, 642012770, 851688874, 165974817, 784039105, 890083015, 256982738, 886128275, 795837824, 187760541, 129855962, 91277951, 853077955, 590688246, 848102515, 152750841, 184457533, 648973262, 841734895, 964190308, 70362282, 79703103, 493825689, 349646103, 211451060, 268377359, 837673454, 342044293, 265176922, 834512107, 518893195, 804270417, 333365103, 193576017, 759059662, 19268886, 74023257, 196874840, 174457978, 514350726, 817238427, 20126176, 265050606, 661973434, 548579457, 834944212, 606004756, 353779028, 88387346, 925072092, 765879579, 537170780, 327187423, 230021199, 441746236, 723031939, 187730389, 39545903, 871045935, 957851449, 839848047, 757035608, 574359194, 876186364, 268495605, 191211461, 32495289, 855754793, 528305120, 794377215, 637750799, 369230176, 56038536, 314861731, 165635742, 337338682, 884353685, 153900907, 359675668, 309822853, 847625751, 154542801, 614677625, 604354591, 873534143, 485555082, 632628782, 520496101, 337219759, 959490696, 221350910, 571855248, 209423887, 944995065, 140319420, 729049916, 76623696, 295987652, 554821245, 489737977, 366881335, 700360668, 730101700, 711530731, 131392855, 157351040, 873990335, 682339223, 645336330, 237732964, 510195169, 565306639, 933645929, 789180248, 967125671, 191162213, 484789721, 124612606, 813932065, 95871726, 808880817, 766277347, 37518466, 130461075, 129676869, 984370812, 850862559, 788718100, 734665378, 427922548, 199620735, 789264713, 852751376, 300958415, 498227492, 308360560, 281244809, 458753439, 143138232, 621076864, 619828741, 926524721, 481741485, 139704752, 601799065, 290015865, 300032004, 273244397, 966656352, 794886180, 429986394, 950572328, 213800006, 57897882, 680570699, 141523367, 535867642, 972056488, 31738710, 58465003, 903077976, 414092516, 816593501, 546738417, 886829547, 245219729, 655614316, 521360774, 18844803, 761536269, 373783572, 216014949, 124610564, 339267818, 878683618, 843926900, 765554304, 959196167, 425257971, 102124907, 118061052, 208312151, 442183411, 693410321, 789954619, 286181441, 513284181, 952560656, 606559166, 149155130, 808094720, 787096110, 17020039, 531598700, 451274187, 223888101, 841504491, 819611390, 988076016, 268266187, 935083015, 351017155, 266521776, 322550169, 995246669, 369790663, 852602567, 585142557, 589249516, 443183573, 564213629, 99476363, 804329589, 431350062, 311519511, 987506029, 746744174, 965140064, 448156137, 203477361, 842743007, 770043015, 325008565, 758454426, 217299200, 782899590, 61032634, 480484445, 838480881, 799208231, 630331102, 155766141, 295672090, 983294487, 8943328, 342071707, 111989203, 608376793, 147032987, 762741989, 668406659, 428744627, 866024213, 969858466, 724437042, 177505980, 286615873, 368577390, 283714618, 551748673, 293410211, 305864488, 101095935, 792433685, 696841184, 405599547, 984100687, 222822032, 616749292, 226515016, 797023376, 761307335, 443700130, 937163513, 402143219, 104905182, 566823965, 132335584, 911094355, 198224795, 17659941, 958383853, 91657534, 662797460, 747858577, 114704298, 206750671, 157395969, 133428743, 730270035, 448699666, 349642221, 226147470, 248282400, 560485188, 153113708, 806626346, 499590439, 439418289, 236546438, 392209482, 147371422, 217819547, 779781158, 432902043, 533877275, 907617117, 447335227, 991411950, 266260239, 231239254, 545489560, 225857942, 629498751, 37749914, 981869524, 615897331, 81260211, 276723944, 640356819, 300363283, 480490524, 298711824, 52573678, 688374440, 481549509, 106170017, 733532305, 101812206, 760019185, 375331128, 820923186, 743939829, 651113393, 15236452, 45849677, 437180219, 960988373, 435301213, 144759072, 113625062, 55604366, 267956332, 49508301, 736939200, 519820366, 296927810, 418541696, 934626969, 353402892, 906028813, 360976852, 575137012, 746850155, 360167674, 379261638, 139320675, 76565334, 3958497, 16677925, 911126688, 996645048, 617146209, 13611945, 323387463, 339114251, 236019074, 406031823, 186339762, 987109806, 703927908, 637081125, 817273321, 600844307, 334961346, 403171917, 131056190, 344139884, 477830262, 973028331, 707764706, 396800997, 135436098, 39886909, 894613079, 468853585, 800713085, 725047370, 95526485, 529322301, 520105482, 527054180, 298791947, 515483373, 35974647, 836684990, 924761399, 128197804, 948015992, 126059517, 1204693, 795519267, 984868861, 398755515, 92254080, 873398082, 533756541, 432264926, 747642049, 365600030, 47549680, 756911109, 115499757, 600591458, 361043758, 479239578, 924900542, 382403558, 134820506, 885214733, 214375743, 729698841, 696156237, 262989446, 780660574, 566669387, 317090746, 245284682, 434338790, 166008824, 131609705, 971996773, 290952561, 506708065, 563585090, 525030275, 156568851, 960798951, 770310051, 325083595, 53621322, 724524764, 815068099, 202061012, 114639222, 825213335, 325895361, 363861402, 529220602, 5871426, 491116460, 222305677, 550496304, 485641377, 477758422, 81593837, 344691973, 352430242, 729932390, 653710630, 328675557, 262513481, 876009158, 531011911, 39981886, 222782594, 233028668, 536368887, 963754227, 373743898, 743528700, 816690336, 299551861, 785650862, 854972615, 290937784, 6935446, 400544202, 697015437, 986928456, 121169140, 890059455, 279327971, 158345031, 916595063, 508156449, 886377770, 583743834, 324637544, 73344229, 744345267, 79409073, 183549600, 668195795, 46731435, 282318666, 907972584, 128741603, 559245966, 814019823, 253202135, 157109433, 893074590, 899185076, 295894858, 699630740, 180160054, 155987237, 74612369, 493167821, 802023606, 750708744, 639346175, 166183841, 775993581, 131164218, 869650150, 54062311, 59319656, 688898310, 17731652, 812709503, 909032031, 581268400, 813108790, 77435105, 695878098, 957148297, 584422565, 973645802, 975974139, 850720564, 820097046, 513759074, 147217339, 59668526, 618472170, 402324114, 458398076, 769230171, 884540460, 146420103, 113470389, 508772974, 175144632, 318451539, 723084496, 273592098, 354912599, 294811814, 513207569, 919538668, 785561695, 265446139, 922822398, 758370844, 605517393, 876419736, 724331638, 204363819, 785615117, 189664515, 653842070, 551928009, 574810047, 294709894, 534569739, 785732600, 296195080, 690648420, 951329410, 519301102, 574044808, 672140478, 164227393, 608787170, 379002322, 982894579, 262637329, 678744123, 506104266, 92596723, 923572788, 565205389, 18544142, 697578576, 419246213, 194189146, 455881540, 744578594, 618487355, 509745610, 679847120, 714963785, 508121049, 468160690, 20034558, 962748748, 273950013, 896186132, 277044656, 214706135, 61101217, 177497959, 612025683, 972015962, 323883593, 281554906, 185556441, 9437573, 449694178, 609116723, 165208634, 485241528, 243884028, 710662400, 484589402, 110413377, 504778061, 839316221, 25108129, 677008538, 780669038, 289112691, 478070485, 989378825, 242605313, 849929893, 590080723, 228429644, 269250038, 505039195, 176006772, 693936837, 11621482, 600484241, 742349506, 241501964, 825662057, 54027229, 170989431, 554251656, 357045885, 788847240, 915523261, 678283956, 870083479, 319686275, 529398311, 797273390, 530036547, 231840157, 244957971, 724525878, 974304895, 336531669, 647283782, 280526396, 279306465, 408240023, 301447422, 308385615, 376188075, 497022756, 2476683, 663043006, 798607523, 885431623, 366221448, 514043499, 782115954, 486305031, 452952388, 594734152, 89072615, 56724351, 793783249, 149364752, 474011963, 154864220, 152729874, 518445700, 595185814, 180723164, 133607298, 595049994, 322079639, 569788882, 317190776, 521722284, 473686804, 347151485, 545674690, 556021319, 775584598, 466197954, 564024569, 496352869, 392994387, 146818321, 790232392, 882714968, 524149546, 142057685, 479013444, 625382323, 44027004, 483957105, 890696120, 838363015, 249919050, 238967804, 635511617, 648625626, 500722480, 873390348, 744548888, 423532071, 894139061, 553605705, 59488144, 488667129, 880712296, 742384651, 67742024, 715093808, 873088969, 443731234, 181555488, 109151584, 102957371, 848824546, 711259588, 320432594, 321060858, 882851471, 615235205, 196782725, 707888042, 955456874, 558134221, 31047364, 213203402, 99491659, 22300404, 306628809, 756516451, 945905633, 30787674, 871298532, 392034147, 121009584, 208559778, 485626124, 152759455, 438609683, 570314263, 252248306, 667983479, 324068526, 507953416, 459522995, 248011008, 808109072, 467946276, 24759494, 122618311, 961238575, 6970299, 866304396, 130783401, 836752729, 591418916, 863713465, 456618583, 262653, 400283984, 518807113, 406688506, 527710785, 880641150, 788966442, 489884576, 557655723, 89044643, 893092400, 976137909, 138970760, 422784003, 288939331, 302788989, 222911820, 334030734, 376238572, 131012521, 388864015, 409140160, 687641522, 68157161, 850627294, 78345, 295282276, 431695930, 376911732, 263743826, 958635536, 316555613, 179222826, 693012216, 544315240, 329360515, 302181972, 192006037, 978434133, 437282340, 58706327, 12667183, 676543489, 594029511, 794415885, 941759408, 541026225, 945068012, 141590355, 195039273, 719862257, 948680422, 724029677, 40719482, 834814309, 526348938, 920832238, 801734449, 136088836, 152292571, 311799060, 286158897, 832133166, 467114919, 749104718, 12218709, 538141538, 577758040, 117897077, 277395076, 469137083, 287398468, 485521712, 846119383, 723723819, 378055727, 6574944, 50626160, 669686362, 625563880, 302437703, 807466162, 1797813, 211078507, 25658168, 248981061, 745633359, 33095442, 610474509, 426866823, 568052535, 243075577, 321221767, 763122989, 943285449, 339699252, 321092959, 3148582, 615551049, 159411817, 815798051, 485192419, 159925357, 590868091, 670798960, 91856800, 295562268, 934130273, 426376652, 107359677, 167226099, 765147931, 621130061, 633124528, 97666752, 823770258, 812852883, 573424940, 752701805, 970288168, 603072798, 828112431, 634855343, 651489699, 344326216, 290579838, 244991220, 320918147, 746911462, 120161938, 293812777, 43397250, 961075027, 550134742, 447134612, 211048103, 307372615, 108292934, 288699938, 562692578, 875758787, 973536709, 688154227, 287497318, 990586497, 589933507, 690572114, 668432653, 329260404, 822006493, 662101669, 531013448, 442109063, 675258646, 330147502, 181659752, 253335540, 431849848, 392141110, 633212150, 220498682, 911387881, 289624303, 842615521, 247554864, 707863038, 642863191, 160227693, 724174624, 397668291, 285827723, 17479921, 636886110, 256328214, 904495917, 527144643, 776195621, 150111687, 975220878, 30553798, 719032322, 795733152, 497054940, 112269952, 404011861, 624415674, 287644939, 661048140, 695875251, 315367952, 394112390, 257567971, 449342215, 499789730, 937414369, 21846598, 994122613, 440793919, 586079413, 180397629, 243521067, 850914261, 558451216, 452286953, 76625603, 622862908, 783053901, 393860178, 294294339, 818921228, 569663180, 237955193, 265783037, 43782175, 239924839, 678208704, 604182178, 824054526, 177538594, 897599347, 800247491, 743575745, 739208502, 981655045, 712286007, 17961836, 83814550, 379802853, 425817532, 667628659, 409773093, 673930867, 360431114, 318356109, 202065529, 928514529, 202383698, 274644200, 786667259, 91780979, 221736354, 461097882, 65592912, 530274680, 8589, 219460841, 393467602, 663152524, 53027156, 527931992, 168536945, 846558454, 29443212, 598711907, 592378252, 606917117, 579563590, 875863837, 739403787, 9189937, 473885926, 727512343, 734684195, 316201751, 132691566, 136515646, 715407233, 827268982, 907009986, 384433581, 573038794, 794893534, 600445267, 140735225, 619266996, 66939388, 689068511, 721963080, 99302522, 92339517, 980688736, 91213504, 918317674, 128334533, 320290206, 936668224, 967135982, 408171147, 186972979, 566436512, 590171036, 310006223, 871880060, 941538926, 514796130, 270265109, 310712432, 458555262, 780633984, 944707642, 187749389, 115257016, 962262610, 541516715, 632924307, 656274538, 304816816, 629081045, 234850083, 236340837, 647028802, 333968395, 627570472, 312597841, 202377250, 798653042, 754101296, 477797216, 910362065, 860119445, 913720805, 206861443, 132664552, 439872567, 54907521, 288152482, 92152121, 683095196, 609197435, 788252635, 982569832, 154394254, 301838301, 359717596, 874307197, 845486183, 552449526, 375291865, 930221696, 592817589, 156123788, 118929292, 467290722, 195892856, 272296004, 212939240, 904730458, 519306913, 246179513, 770198319, 430550467, 97570725, 317880683, 410973270, 860129732, 521013249, 863420915, 855699511, 817603876, 256457641, 951190112, 948280967, 972938274, 584773059, 373323094, 515756985, 31219854, 271033056, 817757775, 888742662, 357456340, 749520719, 146061248, 672284022, 12571614, 51088545, 466792238, 732763676, 367351143, 429685217, 829089764, 621696397, 692520505, 643410547, 507067336, 304847218, 143620469, 555420956, 851181710, 166984203, 751198951, 482549692, 925466245, 29286695, 863072426, 603601709, 587239364, 959176087, 891540262, 787438966, 498976128, 358346970, 261845220, 68489456, 601716845, 999410640, 817401677, 802563518, 76733511, 975440361, 2276998, 792373158, 358566582, 655734495, 515874241, 432156573, 902862653, 215090726, 516372150, 373284049, 195760946, 893141896, 667191635, 96858981, 711232159, 463416635, 465158012, 218030684, 720969562, 265109590, 645354775, 837460424, 641457638, 336971879, 397092851, 433712232, 798932454, 691850253, 825550483, 196858365, 205569510, 35396813, 171053310, 308242663, 955990656, 600948148, 537660889, 441530135, 221081516, 996134157, 473361744, 586992443, 144049495, 974254372, 133472446, 727568552, 291224373, 752508672, 928988475, 131544784, 58887900, 540720627, 836842650, 723725797, 74492062, 195770285, 746865991, 236845498, 461308137, 612018663, 186672335, 669574120, 177838546, 320617405, 243062637, 61523876, 860847866, 291394259, 440875414, 124596941, 439510313, 950156356, 796400724, 946724825, 614833352, 46470976, 471829714, 95314021, 917698400, 110012279, 651110540, 680137580, 890185882, 150938897, 915603342, 229150227, 740124651, 50158650, 585657756, 979950978, 755241152, 235744246, 504822783, 925314767, 51112405, 941171378, 830341452, 230145568, 888480142, 456078129, 654415446, 571180422, 952203526, 125846481, 356241593, 373795685, 913628423, 713218055, 171583376, 441087964, 994435808, 209242523, 622762990, 270100603, 108178505, 430304908, 96857099, 164808955, 89117285, 992190799, 424141064, 18894847, 676609576, 981080645, 951451750, 315879162, 543169380, 710735252, 460975386, 536428905, 209313474, 804813040, 389232815, 608617014, 618152153, 249512599, 822445162, 366742904, 47168485, 295580307, 137976362, 801112837, 676657595, 256951595, 765860629, 239396244, 636747580, 450872701, 791657845, 610054487, 550583303, 339415725, 883363572, 881833184, 397036789, 251347555, 397792695, 346925269, 961098425, 185806472, 843783052, 121611461, 807568618, 184337678, 714716254, 207678348, 30833445, 708314810, 736077699, 363662209, 267986416, 459584245, 698842305, 334982813, 264654222, 645359267, 911514932, 371513377, 389352093, 54137949, 980028816, 723077961, 870261826, 67785917, 307989780, 13133900, 450547943, 232187540, 407715969, 204436595, 769169965, 906760181, 240121045, 307010420, 297065848, 779580011, 830133228, 825131819, 300273684, 951607101, 231128018, 814048585, 862390852, 858632208, 915808740, 111089961, 245314282, 335093588, 873500593, 345285648, 577400433, 323310179, 550224431, 990074151, 603649836, 883226821, 333828514, 982843284, 164094856, 665481454, 77220631, 182217347, 801093664, 557364360, 377291798, 589924418, 325268712, 974126658, 310235865, 225297504, 744291843, 29155592, 472699270, 9682851, 213026345, 127745316, 917800106, 726224307, 80428037, 40022138, 766001052, 237006454, 479680711, 880448853, 450352179, 128875732, 618823197, 839542521, 625905079, 961559891, 357037921, 588136650, 937522512, 300291536, 396606177, 474939644, 109640613, 797166558, 994886174, 777678880, 332761198, 956731980, 475449816, 393650828, 692935415, 839760001, 113668831, 820989662, 237646024, 14718815, 404895739, 139608203, 648703639, 918634021, 781265120, 358291861, 313890587, 344753318, 13693303, 145039552, 744628808, 694497075, 378434451, 19792793, 612086964, 612940437, 212537851, 681148301, 968104162, 231048289, 126608855, 944956033, 118621456, 423025622, 718205921, 284513733, 124196680, 10109288, 999649708, 68164117, 460625207, 829018903, 717784045, 424464059, 962459417, 309147279, 429491153, 953693041, 231429868, 344729507, 584491885, 996959535, 205351935, 18794978, 206433266, 677628803, 609319953, 655742298, 295455023, 596457070, 692084840, 104965940, 879693478, 245139886, 941675494, 417655662, 698616179, 640504889, 743884648, 422923162, 395729315, 818547061, 277568028, 861397507, 701133279, 836154849, 963719188, 958131783, 762993102, 325472013, 261116661, 988511278, 7179887, 650120359, 957015863, 70619713, 574309329, 873794746, 262016615, 473376861, 203408812, 302340125, 300816930, 753088528, 963500456, 459335464, 284243852, 480149675, 865476479, 543054492, 295422644, 476815097, 905571550, 608105429, 280559553, 882890216, 834309966, 681040244, 560141996, 43183443, 886510901, 242487238, 514104179, 370925641, 337683599, 505778526, 936224432, 127014958, 935435038, 168361596, 193263960, 877357471, 390664425, 197622326, 477662658, 316679566, 196295589, 879225597, 450567200, 506539125, 707131531, 466037425, 36918159, 644449219, 184862782, 403408782, 203276909, 740966903, 571864285, 70986410, 661904320, 945174100, 605567132, 394987596, 218391221, 357330028, 225873759, 528442058, 230126162, 770871265, 162609537, 883240731, 785015721, 962328239, 913524503, 891073500, 782603052, 977100889, 162743708, 490861146, 124722122, 3896961, 11302583, 767559066, 438694342, 323486819, 896823402, 127794951, 362701637, 135196241, 819204129, 12283025, 86559435, 29662009, 91282915, 999316178, 259657912, 34858522, 703587346, 653533102, 197692406, 257666001, 982767729, 69814910, 473364082, 367328628, 808215862, 742999351, 970891462, 254200350, 307178583, 843357803, 427860946, 921836239, 787411499, 123646888, 152503773, 495894665, 360119407, 914223676, 224764875, 908867026, 369330287, 396452818, 126886971, 740822328, 869446842, 583741341, 761876898, 741494514, 55016979, 585546510, 591045638, 195337337, 556311181, 814316750, 27783452, 218187979, 59964278, 863047704, 143900307, 367382823, 67110084, 648193980, 809901190, 299702296, 346298077, 701633876, 850436678, 546057463, 26794087, 548852587, 262867638, 840549667, 284574716, 458250692, 44664849, 844852876, 688948421, 78346919, 564400687, 751880848, 423103146, 967830621, 632876843, 565986688, 296367665, 382692892, 542303431, 694744353, 476468009, 500798075, 802526325, 825795433, 504841257, 760126100, 979392126, 879683379, 490805336, 100448667, 217807375, 339023451, 276053099, 234510396, 263301863, 536898482, 304586545, 772742301, 384826143, 209746290, 259216428, 594674934, 571367800, 210515729, 264160396, 153721824, 95412832, 778776181, 263679946, 959573349, 869191643, 441994231, 704286019, 663556532, 319363164, 612795973, 430257262, 909706607, 111926776, 375760917, 387304565, 335773545, 831500736, 35014834, 485494995, 963327447, 750778462, 856301811, 595960184, 561078086, 757147130, 487286310, 4640847, 916794602, 996463629, 144298586, 187437932, 631043184, 445823195, 767166259, 236034948, 837053060, 157657477, 654123499, 748318470, 891263020, 316541253, 964263500, 851821599, 434177168, 962275260, 68195477, 795769386, 484737203, 527057106, 802326351, 140226534, 86619100, 909117955, 184708746, 901108691, 988527573, 30801946, 678499884, 131610512, 666590653, 965699409, 60343534, 289331153, 521673741, 29660230, 637561402, 170703387, 978619909, 200367382, 337434285, 97358163, 62550481, 830574717, 708878867, 450087846, 753242449, 35871901, 644447052, 434884281, 780779475, 739208537, 602369758, 219643987, 926302798, 154087764, 193252757, 114470464, 545461823, 32788279, 290608129, 930546363, 953429340, 463125615, 103913033, 150358728, 976263423, 895878172, 474984807, 909167523, 852366518, 248870616, 214014785, 728079494, 537112349, 699541647, 296187355, 485415759, 500286242, 111944956, 171072966, 554227006, 261947382, 516121960, 455539221, 130770917, 637455848, 441957245, 627066084, 105493028, 198358664, 353437280, 60377016, 454261355, 577030023, 539632514, 477526946, 973886645, 435211684, 327724799, 597914696, 2839768, 621274802, 12319405, 762035363, 764748119, 379259907, 202745841, 6478619, 688843486, 862313085, 6324729, 285755942, 682407538, 670817617, 875261293, 739743535, 59518439, 541848422, 177775535, 153468441, 716506693, 733687833, 345930288, 938050532, 83136435, 70872586, 906537941, 21555049, 515048173, 839242802, 396906130, 310844657, 578603052, 821791122, 872165888, 837396195, 267304170, 64252641, 92024826, 182063818, 638303727, 88513975, 30603118, 829512185, 236040182, 670559513, 556011540, 814032526, 697410735, 69716649, 977743132, 811443499, 830138007, 572299923, 261253051, 225993063, 427923983, 746630623, 121078088, 635180664, 142548090, 799979233, 861949709, 734661067, 217336233, 30476061, 408959552, 346240279, 552774360, 806711370, 599717665, 662719669, 419845059, 153401332, 617877386, 660614953, 417711170, 52089229, 68964516, 917775244, 305402871, 22077740, 912043225, 285478562, 264097633, 533731202, 388966654, 356120859, 391669852, 922609595, 839616185, 608268608, 694720341, 803080401, 765661076, 936703485, 882564282, 142026427, 502112227, 356191972, 372356019, 810261805, 873717309, 211403108, 529743845, 816203589, 245680434, 885981464, 225116394, 101446118, 732342305, 755156935, 645706422, 32901056, 707620143, 390899886, 371230218, 730030440, 202489953, 143790117, 502078862, 625946620, 361640377, 46606866, 489332711, 389593984, 718820968, 144983849, 392882268, 43407580, 293382243, 360436177, 289975915, 696633121, 267213181, 58783815, 616820779, 570924631, 381895775, 406727995, 738869277, 226677353, 926450165, 443701265, 241699512, 815355105, 165731339, 398388471, 305704214, 958583772, 999310443, 482541030, 225861310, 394364634, 155947867, 525867350, 337614651, 862717659, 886483590, 604701743, 328793927, 380581264, 754679321, 961635353, 715473285, 288378121, 317869910, 757254394, 654152543, 198855116, 897378163, 243078873, 638921911, 762826746, 302261514, 951550396, 472055446, 170484666, 265630047, 691426587, 339452964, 663555665, 451518992, 984237181, 898254722, 856910644, 598411706, 748721493, 587042997, 517300560, 585082834, 252604371, 858796853, 394773734, 802638187, 741853816, 813654068, 192632646, 352555281, 570731809, 118817410, 937374179, 272959731, 128954769, 580325202, 489394273, 60864222, 710845313, 588077355, 581122667, 720487650, 904387127, 55824796, 213073178, 491030842, 226307843, 981618726, 999183561, 252285236, 669480205, 397652265, 572910774, 106399719, 529029196, 487038794, 358199063, 184252193, 39810213, 921497584, 479936708, 350615481, 913251663, 410360918, 236527262, 3273410, 491282665, 197093618, 836546833, 302059528, 838742905, 364568697, 870392842, 617864889, 837035589, 823070392, 552719864, 256552804, 436932076, 271321255, 223383624, 541002390, 211062393, 152323162, 648108415, 708332503, 655431100, 905851294, 899201527, 287905870, 706895298, 8010099, 210999447, 340591980, 788681467, 555735451, 682888758, 566068058, 753141323, 654378632, 118307181, 157531640, 187810340, 906919065, 344150301, 265294027, 615332938, 576197907, 528060274, 986777427, 684680667, 497086902, 786943757, 926426311, 818801297, 600414424, 46783191, 826197257, 36485369, 317621789, 544071040, 240034613, 121129800, 716588695, 472131014, 884536476, 165372877, 119828403, 118015176, 946758315, 992760610, 277991022, 534944059, 74280538, 678940507, 584964240, 855069419, 476523737, 174217435, 234806386, 433561952, 576387509, 960053037, 200046595, 315555736, 150028048, 816910592, 867762899, 768500478, 486329187, 946146638, 60169656, 151193975, 146435633, 592686894, 487609037, 154316845, 619204765, 583334615, 587674471, 137468870, 649742795, 260152717, 335098173, 43323971, 703307711, 4262961, 808817355, 980628188, 950645282, 67584687, 989908066, 669540264, 202607953, 849569311, 822091528, 754541026, 154445211, 371049246, 424909193, 8511421, 875016145, 846454022, 102848760, 705643615, 394891893, 374475832, 198720485, 768049468, 484338783, 416937591, 647462094, 558141410, 662742458, 927825694, 239627899, 386289290, 623074731, 840163120, 682959071, 538426258, 892233569, 939556303, 100691498, 785698047, 108157984, 630529622, 402898321, 508198859, 815808664, 380838889, 411168765, 130824049, 891583800, 762301127, 398971318, 222643438, 395187579, 123050023, 944474421, 695524406, 453959289, 763358690, 285551739, 728794601, 762006757, 797442229, 415750047, 336445417, 981860869, 763569132, 811966949, 299178363, 707384889, 511848885, 358798731, 770457958, 207892432, 698597689, 562570228, 629384962, 902770311, 494627955, 780031068, 333744202, 311503230, 784176620, 720845318, 403199100, 667755680, 88599589, 516132434, 101302989, 272124185, 529423178, 351144657, 236463660, 659551070, 322132096, 105240346, 936635430, 577705060, 591699763, 976150035, 734000082, 602451982, 868010952, 573615048, 761351654, 304042848, 539898935, 349540345, 271056900, 238737353, 394503006, 226594667, 358242776, 181421141, 445334993, 773131211, 301920154, 626772149, 923641463, 591082243, 779651228, 392358732, 244291968, 22066113, 317635297, 906211588, 457806316, 790412805, 456791221, 150377730, 35980422, 603121273, 917535343, 529567571, 431279691, 654945736, 774160043, 488889970, 857735083, 457932881, 270940642, 399238250, 258316495, 588732825, 390483122, 247077668, 125942765, 757789104, 511539742, 603032884, 420311492, 820762092, 581434594, 482607891, 534179499, 914476831, 754704353, 650184237, 327426516, 150746960, 225901977, 789550388, 873953303, 649404569, 483404972, 227496115, 772614930, 713557967, 22345002, 699974385, 877741546, 118634217, 347942257, 571671112, 809436319, 231662033, 971549852, 557401431, 32426230, 595046748, 286586657, 171485793, 204460740, 789079647, 676190045, 107094235, 649254718, 600148150, 374024915, 199420522, 98725757, 983652010, 540447672, 781838014, 194696644, 466897999, 556047888, 713791342, 291243555, 78409475, 653274845, 960613549, 374929162, 111209672, 540669270, 272415610, 295505150, 825868366, 441534497, 220988650, 548210359, 139709727, 225590494, 662018976, 18077117, 458050591, 540020878, 168847228, 795028187, 959070721, 29924543, 552233003, 702972941, 413344001, 546127372, 491361621, 673014068, 290416045, 645951585, 559888950, 408805156, 357148430, 186182321, 286600964, 303029461, 648126502, 15770432, 824353861, 504105342, 171313482, 393092450, 202141747, 62733809, 913255273, 768068841, 7223375, 69047771, 147730430, 145667731, 868773367, 263130725, 476230858, 192714203, 134670198, 705750319, 225606794, 763728292, 74200498, 661154162, 695061738, 815396115, 707415765, 541442274, 61720027, 85515471, 794854366, 234274997, 608390732, 279068739, 924462359, 807030823, 732558088, 709236999, 909600081, 789672143, 924005184, 106947426, 680107032, 352306653, 104814480, 356696088, 906707209, 947080414, 816133898, 615913584, 562918295, 407362190, 940331825, 824177808, 878252740, 309217436, 427517190, 506147383, 562093565, 390848307, 561431244, 793474723, 535203655, 523386307, 751957643, 674954383, 646454174, 815068363, 140399880, 209048542, 64741185, 902259347, 513006960, 895967480, 838340772, 72950412, 233307687, 19082098, 119972751, 111666656, 722117522, 214539098, 876989464, 982201945, 796722292, 75328712, 598165741, 167603416, 662666295, 142859666, 793048514, 691393683, 739010980, 105813984, 636238392, 132659186, 261418489, 787437244, 991485718, 37787212, 953941275, 765545037, 131563952, 583154641, 295203646, 886769611, 365924432, 760083224, 925724428, 618472533, 872622259, 344959941, 470268009, 772794657, 63695359, 958064019, 235358244, 24395152, 648596117, 786365491, 853217412, 577508448, 476505883, 213282295, 206709562, 387046887, 540456019, 280751971, 136187670, 917411286, 146898889, 100238509, 23566725, 182582276, 141975492, 363149584, 484802117, 355605404, 536657891, 422394911, 685619243, 782217027, 415979514, 399911791, 125966291, 968478048, 670832832, 53881125, 649226000, 695549367, 463444057, 859202110, 571112817, 337829989, 907721085, 158466530, 582287366, 417306949, 277010179, 241770028, 753044437, 26531710, 606182519, 898179708, 401743060, 546729919, 18741453, 556353181, 670615521, 303065718, 48851391, 793259118, 291276996, 389733542, 244807981, 664581388, 829876599, 22479523, 18680367, 179268379, 987949667, 195322851, 521022077, 50858558, 559094427, 325905444, 353315759, 741150396, 319934614, 511847079, 10934580, 904405024, 104595248, 285771287, 85725780, 937971357, 589056836, 102538932, 707284285, 489817280, 75429788, 346742114, 749697136, 199967610, 880349854, 759411723, 896540000, 467058438, 582863535, 945926993, 609297962, 830941171, 817497563, 231127614, 238691685, 308866404, 947827940, 721001207, 947193382, 104505798, 179573970, 809458132, 430189145, 236026437, 152042887, 372231389, 794146987, 508651490, 913715325, 609318769, 499637986, 198884809, 629130884, 637779756, 460909575, 234587020, 644994413, 335376957, 995035956, 953810799, 863592394, 863689945, 977798568, 814519468, 940979168, 360238477, 508334867, 13390434, 508586629, 543740352, 231362530, 825992271, 411544144, 806384225, 612023271, 779162588, 797607832, 65751085, 969781516, 59610828, 655139907, 337604242, 274376688, 774998849, 291462339, 497783766, 620721974, 959638332, 345075750, 498459288, 429085627, 882063156, 207582851, 169535911, 961021390, 81382898, 668606094, 690039278, 564264230, 463599585, 673515134, 355294910, 197759316, 798193274, 907635449, 255077638, 994172123, 892962125, 765605942, 68444434, 903541229, 467922366, 787722391, 476730095, 294385258, 374501198, 241818891, 4678379, 700728385, 63920313, 993890710, 608616696, 765202731, 620591396, 895401710, 371961404, 170358924, 585802360, 460648986, 628908951, 722736283, 78521892, 91878694, 365677902, 334930491, 908499049, 411515350, 368642022, 760261495, 801433106, 967641913, 302199450, 842378998, 516377313, 110947724, 486027524, 632247955, 84074992, 506338430, 392997720, 302430120, 699887251, 656777199, 857502523, 196100287, 254611843, 661657820, 379187726, 156554470, 773116798, 985788970, 982421412, 864395121, 142487525, 270958922, 716366925, 647242852, 533812907, 157831746, 120069248, 682898340, 421637217, 138228744, 716057727, 417099336, 857868839, 414531802, 939290145, 517323713, 137322910, 469776365, 800699041, 242138298, 881736301, 871740118, 293726353, 202391575, 859855125, 557584508, 524815440, 931406078, 835815911, 640135760, 858499564, 118165448, 461249745, 775769661, 960340494, 116747435, 598769028, 17593050, 238825925, 409714594, 651731446, 720761435, 427136927, 517795150, 851828181, 41586004, 443835906, 43539190, 882075653, 588305350, 900510609, 275727336, 84016644, 888556532, 897056576, 766297851, 847574641, 555917019, 110301545, 659882724, 39976293, 323605296, 434538725, 144102434, 506990377, 674851144, 369792761, 416468692, 309924813, 346067202, 678543542, 991708095, 4880461, 170880149, 650479424, 48925066, 270729866, 503526245, 657705595, 253482515, 298691209, 881108057, 204784173, 756249349, 89617940, 801177968, 777739540, 799208635, 289284005, 842991500, 678842802, 968006939, 853301148, 852504947, 887229972, 698190440, 693130679, 706764382, 267396245, 142895429, 206483700, 303864900, 216773225, 757864030, 868887329, 681158082, 435725884, 41922072, 280939852, 836548438, 67115418, 528173216, 645901363, 612500030, 30078978, 611206859, 812360380, 617911133, 319136166, 649564252, 260055159, 910875000, 802672823, 757744903, 196258810, 163954117, 830010254, 849516850, 472616274, 263982756, 128210931, 181608257, 297373858, 561894395, 48083242, 541073115, 957172672, 824385926, 196932457, 762730332, 438510115, 190937391, 954668190, 699473187, 16962679, 653336583, 489830012, 260824471, 731796959, 970905082, 388258413, 797834012, 964655733, 992488484, 147014956, 967036622, 134981747, 50603502, 594774265, 66219327, 723456176, 818991649, 519400849, 698408110, 697790313, 224274081, 96599985, 29867394, 897728617, 71712792, 306492511, 470388903, 75676302, 500124082, 819041783, 671247845, 763412280, 325025617, 131165109, 725737030, 464509343, 818516446, 286295658, 604992195, 46095997, 920375713, 849830005, 328730535, 742258922, 184508231, 985958485, 449343580, 160959225, 396781940, 976084524, 662607621, 855448787, 424554177, 952660654, 314353703, 414240211, 110163286, 469841550, 279244078, 226910344, 211546961, 202536666, 838881611, 266156438, 316252751, 236829485, 705886351, 93051321, 53890011, 869465381, 275839124, 824577738, 589583629, 42356413, 598732679, 579457922, 972098933, 616090548, 621758047, 928060065, 878158811, 220833600, 435050901, 678774104, 273619419, 182337109, 189204025, 509157117, 747864079, 842095868, 975218997, 241435456, 928452309, 947689012, 907735582, 720187015, 396860548, 939440231, 552810821, 518778975, 414848115, 737353945, 64929815, 58509229, 539747643, 977594570, 711380958, 864861635, 943622898, 557138674, 864243166, 223698344, 975719122, 602242482, 53772608, 199584009, 22388947, 784646891, 612291628, 322637417, 354505839, 352710790, 413615433, 7153838, 99781033, 708635610, 672347198, 734430887, 669589234, 479712324, 77707819, 528475178, 579972092, 861943078, 870301944, 882953158, 977338499, 231253302, 873220825, 445997189, 414084861, 824712174, 331065494, 927730953, 607707545, 743042310, 138938541, 731656189, 375705897, 137992094, 739253497, 378922581, 545412633, 856506705, 305683477, 168509290, 528062038, 339133264, 533068138, 122346592, 453095236, 758543649, 451361311, 660099519, 354559011, 930635143, 96757989, 180668576, 850480527, 405696983, 970767223, 839213346, 609754293, 50397047, 724068419, 908907857, 544031760, 609214669, 57856097, 114364609, 302383450, 638920020, 8851462, 909290543, 164049788, 832779231, 297199053, 564671390, 400725359, 123446938, 706441311, 977719466, 569517206, 483303453, 21530429, 104943945, 791268552, 109178525, 577687899, 640260229, 346364982, 994562742, 617075880, 374485426, 482599587, 870955651, 12515210, 992555253, 253486222, 540127219, 974303167, 523130594, 225303810, 979670384, 841152181, 949721832, 96125158, 113219080, 298042893, 47298842, 975531110, 275167750, 483620277, 460837271, 452825069, 970946168, 592938730, 567467983, 819131134, 313972354, 125412402, 501420645, 913007370, 939578505, 659851272, 828484132, 891974584, 115766166, 615467399, 38250425, 484688264, 238127809, 743507067, 439363741, 729676230, 137975, 809850551, 273715752, 932438242, 663757524, 995699631, 975832550, 770989012, 505383382, 559495973, 606137319, 41053329, 332805605, 548609665, 448143659, 60062481, 886530373, 614499661, 862625497, 716356011, 343096447, 59793366, 340221101, 880271367, 253499086, 811407273, 15929565, 357267023, 300315670, 434543574, 711555417, 154183608, 349524893, 788661419, 127109223, 450239207, 374469821, 297561392, 735180767, 943606275, 599833261, 73811277, 930477209, 342421648, 23249947, 464304221, 151034134, 982355319, 646788866, 966088286, 657697802, 572392365, 488463020, 508876502, 748415023, 654524878, 964525755, 256197837, 109989541, 955403294, 662179812, 385880124, 67946664, 809639283, 236115557, 243145549, 551835108, 466440433, 607323352, 855901775, 250746588, 602609794, 789114937, 154251351, 38553254, 313072763, 751307059, 734206374, 554037860, 299090136, 89682698, 359588717, 559252909, 979554890, 991295037, 229996806, 963883790, 626204669, 876073815, 97706658, 596992975, 857470575, 214674563, 115830047, 591350883, 128493032, 400894721, 845926338, 352185546, 218533766, 935855625, 966400076, 754345735, 598438558, 914263876, 577322492, 905423559, 495043989, 684045569, 554386577, 152358701, 886482104, 477624235, 163431801, 930107946, 511086167, 16423662, 925160254, 133984317, 908873611, 427118425, 215059201, 359648444, 932969373, 834737618, 973302847, 661683603, 43178810, 694772346, 526689590, 601376757, 731289381, 40658231, 777847917, 277795352, 555635893, 222351373, 690238888, 539957983, 820049970, 15193645, 785377403, 504432799, 563113701, 650360634, 343366662, 527755709, 601419994, 345850351, 757656219, 505588854, 960726911, 75666303, 790626917, 517454592, 495242413, 567375637, 718702459, 47390287, 612106489, 276258944, 476223334, 475687297, 159997012, 186689834, 52349310, 226998296, 514267176, 860404765, 293854319, 218812309, 33445329, 111295150, 461164734, 762485090, 109133076, 176553424, 484946207, 56617623, 96692897, 14756158, 64282391, 343173464, 297335857, 179217537, 496085843, 433257419, 594110398, 146486976, 161252030, 269303745, 239107017, 538060954, 328210101, 798060726, 458481296, 225500603, 449856650, 68373634, 410054598, 318534265, 933383247, 273398934, 395435400, 436942136, 597086418, 690602918, 84397063, 683306269, 529452245, 201388304, 127438681, 542108652, 212231292, 72785610, 216827967, 588076084, 354593269, 48848820, 721083403, 892466522, 120001854, 904105303, 417205138, 488489245, 592162008, 380840968, 962673516, 132646587, 818791712, 581633789, 334943913, 262534680, 348773522, 923408682, 821508308, 572052747, 94625948, 602978947, 451639763, 219945196, 425549853, 239703804, 587451226, 862543083, 655206363, 290023983, 173884946, 991384952, 147361692, 876773642, 14032771, 229886590, 305715678, 646756362, 478919109, 717543129, 815894250, 931954197, 300249755, 685161122, 416521540, 406322998, 37850623, 166982452, 39705475, 519710746, 208685057, 563743928, 243778537, 156069832, 899009479, 145071607, 367765236, 703578338, 807844244, 218180733, 487197040, 739553413, 17812660, 808147319, 631456228, 41971746, 385792127, 281438319, 287212164, 338851446, 504758999, 938945233, 399724503, 151786142, 219020322, 451813772, 636945813, 993010113, 436323940, 176802220, 45323516, 772843147, 931690402, 782260032, 883499658, 672768845, 417625519, 532274216, 55142270, 680916264, 656823882, 375904110, 588691699, 29765796, 160427298, 592785958, 760118665, 246179657, 706749056, 556092080, 338908195, 924573315, 102261207, 367059629, 702952111, 442958889, 216305694, 677454541, 116856852, 97189728, 887361109, 966032341, 724652139, 95083015, 815588269, 229089139, 824029928, 109583925, 513405153, 868911359, 368140829, 138125594, 952221954, 190901465, 746857147, 179865168, 589367049, 846903937, 886840809, 310895194, 957462718, 797594523, 322650655, 864650594, 382854188, 646893295, 744695202, 444503675, 687797829, 348637856, 73674092, 276834527, 760997230, 361098203, 728834241, 13877519, 939672036, 106249442, 994981286, 219947947, 90654931, 853408370, 934153577, 879027665, 710541847, 110754105, 106286891, 66455836, 856575621, 732539477, 672527315, 535023072, 226363860, 943925204, 734516626, 308244979, 77706482, 4175063, 600949023, 932642240, 429830815, 272847758, 76239423, 525174797, 595943381, 115923165, 775515204, 996739560, 171768983, 988590016, 420170432, 337666349, 683298911, 776948497, 101075550, 778367234, 788527721, 12466095, 425231330, 795637135, 53499920, 512901567, 599846080, 25652947, 170385704, 679889220, 534931385, 201319017, 857567192, 152006784, 184486576, 640592788, 244806662, 562587498, 987423774, 518649047, 162647315, 619401399, 361674428, 489471781, 943897025, 860224495, 346790548, 586598132, 628213884, 219202003, 402631907, 536293435, 230423649, 977348056, 569558102, 833788259, 107553973, 516237652, 684670733, 899853137, 52125085, 237864690, 250511049, 189878892, 42883715, 880943997, 466037336, 271548161, 413157702, 538147056, 798287741, 666262336, 195559694, 91349461, 340120954, 444163391, 334809394, 603090921, 389702701, 385137702, 370036613, 849282222, 184339877, 182785938, 334786632, 669388096, 777289130, 179125278, 231602480, 211417976, 696626468, 481307906, 633121538, 196154129, 475645526, 369880036, 223500570, 645811851, 465697064, 256562820, 687382010, 213349080, 440356368, 611731924, 303188518, 271802658, 43719109, 718091830, 918262287, 485514616, 667782547, 985511561, 46958857, 454636223, 529917303, 457241233, 803740427, 463301238, 748877939, 982766452, 568889008, 868745397, 47593417, 994049325, 25697632, 498217764, 965462128, 162520377, 34462886, 286567373, 907530170, 964324314, 25669721, 833166189, 173240889, 475167374, 150606074, 250204420, 245291084, 427868654, 994906022, 956589209, 165014840, 271122329, 820974806, 712102377, 801634434, 260845687, 804514998, 353080327, 531088631, 134002242, 964888197, 142850324, 494831630, 929449825, 85520024, 626539131, 703541230, 299047180, 116443630, 894274345, 418426762, 329280725, 824396019, 529698375, 506626426, 489592694, 464365693, 527161381, 842825364, 774954965, 315456147, 388237057, 549186875, 650144130, 479050823, 809262524, 639759583, 511142829, 844385668, 109299790, 396413397, 278595651, 414242047, 861345848, 210854031, 91549955, 263260642, 40699545, 414980228, 995272947, 807821112, 756830141, 798893664, 477720518, 22590465, 350606706, 312238323, 684776548, 891999876, 463169075, 338929220, 89238628, 680649959, 912525259, 639457236, 581358671, 34934119, 775984768, 126770755, 206889167, 813169029, 60214736, 409773251, 196067065, 96278509, 275308734, 340349619, 194613552, 971293337, 995810250, 338880975, 247763936, 987653679, 426756174, 122870979, 231373118, 996072727, 235927246, 674223981, 545851807, 950423807, 131154558, 131991753, 577893774, 678235296, 910375340, 506819034, 123142911, 845483728, 151148148, 652397541, 614162980, 247028282, 944425433, 484933562, 88854735, 292841978, 33001029, 21789509, 25878688, 710188776, 56324568, 154095860, 66748830, 372052917, 425421258, 625249866, 655729018, 582642620, 384172338, 713381381, 141587357, 977408258, 625306982, 972149374, 181679982, 655260716, 667642849, 704903845, 251286243, 194413984, 170869414, 671916447, 986511833, 405639261, 298448901, 391375633, 709412880, 882317650, 179145778, 113420542, 314586184, 640970787, 763092619, 204395261, 556246410, 522919443, 464553774, 427901011, 790024685, 715882525, 831115497, 463852932, 897274722, 177123203, 346526934, 264068232, 226777000, 309844436, 13867468, 607736895, 729225295, 424406524, 806361360, 855906873, 405534870, 314155114, 518447154, 996036884, 972311518, 824116382, 630835747, 362262571, 543659872, 179028938, 579170997, 336015235, 419070725, 503730703, 535746427, 699304043, 200628624, 927713478, 727817425, 547564489, 468145421, 4133464, 636265708, 439391674, 714428971, 182913298, 417981940, 878774525, 992062123, 827139039, 513029032, 535293648, 843850857, 532885882, 939014205, 858293446, 46479285, 400000526, 73140703, 26932494, 865609078, 307075340, 603423853, 122207213, 353026459, 12658734, 369026917, 203782707, 462476625, 481922339, 479619, 198244407, 205189706, 628181064, 180376190, 84372409, 368770760, 554142694, 542983709, 207110326, 589869267, 135412727, 504198280, 22079371, 150854793, 26579829, 983032256, 877466270, 929084991, 498551314, 710830070, 741037931, 7616842, 424196730, 707450777, 82824092, 792195659, 448005487, 834909916, 728326018, 598714654, 653764889, 64993161, 252152643, 380242721, 723425244, 548605430, 936246969, 883719482, 277269277, 805903179, 600819922, 762366049, 838345241, 85269274, 780852527, 584347352, 743219695, 625277902, 616839958, 111407861, 328597203, 392192684, 109298049, 125833704, 210569387, 561410819, 398888164, 634083082, 295709686, 867755764, 371309061, 17854404, 440159220, 701982665, 172593180, 823677615, 664642808, 587801367, 540634838, 336465454, 855761506, 437362804, 757925876, 853824597, 378356367, 259019047, 211701426, 123096159, 139676256, 17522212, 102612022, 648328699, 864218700, 642386094, 977709750, 981977755, 614998185, 680525736, 781476326, 360843516, 703788834, 841629128, 199058263, 8042962, 904221880, 668028402, 166565743, 34694694, 367884111, 5193822, 400120912, 622123518, 73386049, 648965074, 258758758, 471654376, 771438145, 182435344, 268852930, 351733834, 864038618, 941533821, 258385857, 130057268, 181141433, 980772740, 758851052, 797052695, 68038475, 681476722, 158100693, 864360180, 932965124, 264197156, 605885009, 14839607, 49330576, 87053757, 584568357, 105457064, 495122156, 657370344, 18314956, 311055917, 304268322, 760968931, 242591909, 673232358, 863534557, 172668770, 579831571, 908121049, 368913390, 636005736, 329405762, 280690146, 713479131, 771650235, 254913936, 210552087, 928445753, 374178868, 269403729, 70076725, 657990415, 793243576, 625108762, 45204702, 757730860, 277328822, 53989575, 625583075, 215456836, 196885320, 459044025, 336556594, 867853176, 188738354, 659495314, 890797224, 901803829, 713885653, 824968837, 145313905, 262007654, 875686844, 310927421, 432571451, 653898364, 944516994, 746523208, 40826290, 535344571, 825377623, 84538257, 486695317, 173534289, 179977543, 432105520, 152633613, 336685204, 279604749, 350456648, 737057640, 841913751, 100395845, 73929560, 197003312, 874117379, 960471730, 579855696, 318671658, 771855599, 72697019, 996231611, 197547798, 979740565, 572877398, 601864058, 572200364, 606943061, 28218527, 46030173, 907475291, 827990109, 6726068, 978363915, 676547297, 961238129, 908746528, 512766604, 894596885, 484558993, 384075327, 355381270, 99284579, 346546529, 139377338, 855284628, 167931921, 728592844, 470247228, 720658303, 656867092, 95428784, 199449355, 768739012, 777678793, 958436683, 251202328, 721733443, 669251354, 578633896, 936962973, 715154642, 805652515, 55782893, 370302316, 632206006, 242354655, 204476990, 835056945, 775602408, 163754038, 879169823, 703967833, 824072407, 214475008, 641860191, 268754809, 216087289, 718032366, 142332701, 632853481, 702446963, 891709951, 731998817, 422552101, 81378710, 764833875, 42893122, 556507053, 172960947, 381948299, 651870048, 228997248, 94655805, 141953309, 526752259, 966780751, 54382969, 441818321, 708726472, 434822243, 196849113, 457855871, 716677932, 189649829, 785616454, 271650559, 608968629, 534823594, 277631945, 348892618, 368982089, 81278327, 578171494, 171163307, 605858308, 7658123, 252035000, 338412282, 352958728, 592577704, 543881897, 475567987, 951988853, 823947663, 605589186, 696664882, 733536734, 575029327, 144361527, 145962741, 948706629, 83278360, 998071795, 388423775, 268551908, 261269646, 456304881, 518717759, 511797652, 508760463, 270695064, 461753344, 939374715, 802428202, 329151151, 896919535, 497655896, 99197650, 390701739, 719739813, 941724868, 162937455, 627212545, 200955675, 467669991, 762222960, 20092694, 367033599, 852235456, 568585291, 672081508, 790601977, 538659500, 4910189, 304964195, 449232854, 692438695, 356535554, 400062149, 679154931, 101610113, 50419812, 989983486, 890225574, 448983223, 446086620, 140984043, 798152241, 223002946, 466758863, 571436833, 414195847, 756466135, 26271420, 31858256, 623823185, 535167443, 634117383, 858872597, 829534080, 609991327, 988180541, 694982124, 826890053, 438208015, 309668820, 573049916, 629584600, 127538866, 279336908, 406198592, 923366307, 907266738, 413203799, 634201689, 764939975, 770806209, 97311300, 139892086, 172488527, 827192064, 910239084, 496093112, 441201993, 497735624, 981966175, 370546844, 405062807, 349178179, 127040073, 693626548, 112380224, 571666418, 125497826, 916204312, 456032504, 7761186, 79519658, 642133932, 742781731, 415796825, 320269282, 505257783, 221395408, 553419679, 485970390, 499072715, 992206979, 116157302, 777525034, 161863411, 719984750, 896431964, 276648333, 930065072, 851036374, 944638175, 742438202, 332957063, 764847456, 213035382, 880749427, 224052088, 336367312, 725285002, 267142809, 108466341, 76046913, 884170691, 746085260, 251650795, 14678928, 231276287, 891621747, 564977203, 135436711, 842736871, 432553014, 127532906, 824822432, 294929893, 585498793, 301225972, 232147337, 873620669, 512151905, 251253832, 707766032, 784214477, 896418975, 941254593, 295805925, 18172893, 973721530, 247894268, 247581952, 94701548, 854148113, 95695244, 626042576, 621246352, 157336174, 205077955, 997585113, 350854897, 770935971, 619821000, 24196814, 407524014, 39099211, 439654442, 99665796, 376315825, 892998546, 606717552, 911685320, 313114622, 950381865, 746476861, 310808069, 981757307, 289368292, 124918720, 293515050, 379873180, 979865553, 198406277, 447224294, 986994929, 144244665, 831577981, 881605803, 812557879, 776702926, 336577920, 429324137, 519450189, 579590286, 577603943, 544339022, 410770934, 850270313, 175562519, 571394754, 121079984, 798163701, 375661735, 392955211, 289993703, 479720925, 730262546, 924086800, 151928756, 507624958, 625751897, 687729792, 289223515, 182044357, 115027825, 37371627, 671070782, 410012270, 413967926, 811183598, 256740992, 584507147, 682153269, 657065316, 587983135, 264805251, 894579924, 790612711, 251839421, 425532724, 908418620, 449954661, 245405846, 739928171, 479727355, 535125764, 605338935, 336500950, 74744004, 413905083, 478683636, 408636008, 485734405, 753096786, 156689850, 813343000, 640402878, 3535181, 787472952, 699818323, 765162949, 531747374, 540854872, 994123221, 411780778, 840237126, 242259109, 178711743, 572635599, 233754785, 151435636, 397352333, 478079435, 450452143, 704263824, 99386287, 9298028, 363657268, 746957255, 919091990, 235076884, 746770991, 106936348, 534380820, 837021316, 473570052, 591611174, 697377279, 239343647, 934476997, 559690249, 526806015, 855171805, 386238491, 195571360, 626362064, 683966693, 96304749, 321359528, 456730236, 755197914, 491055641, 676726606, 833071212, 53024307, 771392003, 240101495, 824260265, 788118047, 45317600, 888138347, 265989754, 768381614, 686487678, 880643651, 276579806, 728865620, 829573025, 452354428, 532913863, 589796442, 576223610, 894287703, 382021422, 268135238, 695681677, 487256214, 633111640, 210520699, 617939043, 121765745, 653112440, 403317800, 437029127, 147363346, 32609452, 805976762, 368133348, 675341664, 770254911, 986885018, 483825078, 558510489, 489662433, 576459432, 862083822, 460186208, 574862669, 584440296, 555660488, 218239757, 978902721, 416018519, 981019233, 354329165, 582792143, 261693965, 769805587, 632579098, 738986184, 370291507, 782253323, 980763129, 18533537, 983755178, 500526387, 797147422, 81631120, 622313918, 803295232, 451237892, 964971536, 526287144, 757584009, 765707906, 928395101, 928223383, 841059232, 121000150, 592851393, 845546070, 906830568, 16705267, 540546212, 982757919, 50973281, 246538160, 807601820, 580923135, 612214016, 454998415, 264485217, 359761171, 856294564, 734379740, 978143555, 599667248, 639015199, 340910893, 229865339, 427580556, 252651300, 655112807, 514852923, 142057283, 350552396, 276886127, 71063149, 565746213, 312419984, 136765522, 340376232, 114149069, 600547594, 445364207, 562235387, 581117370, 72279753, 378031850, 865804464, 340832190, 263423759, 704484490, 727839027, 189872265, 154727068, 767449037, 554258323, 229615350, 121830625, 591655559, 55827857, 446339301, 361638968, 201840486, 430271214, 151381882, 301866342, 804265686, 842593820, 213272929, 274177725, 892342313, 973921652, 95492985, 43746362, 728006905, 219015440, 227286134, 612826689, 656151473, 635984146, 864874211, 828308681, 195052258, 461018227, 492300035, 664588194, 902152648, 282711396, 379896977, 966453954, 575991070, 655214723, 100903574, 583389662, 88078801, 722253646, 476611436, 413507733, 952452614, 360416936, 305529697, 315712376, 399621278, 941955210, 363063775, 363390103, 817616595, 674113191, 985917391, 503521206, 29315461, 946415278, 584831861, 693242548, 982837617, 300538316, 201478377, 705038472, 777909086, 79184164, 767255931, 51913775, 558409763, 895494228, 13846218, 490954785, 241520683, 997148516, 841597144, 612613929, 351146621, 2113828, 335681201, 881045117, 573332255, 118276468, 677348934, 853283362, 544276066, 964807467, 678716356, 309444766, 834055080, 565989280, 379011552, 96619258, 856143607, 730392256, 387102201, 269618656, 572843020, 356263168, 239991725, 149150716, 756207502, 230864260, 582947557, 71702718, 738183866, 124131287, 719531331, 611848744, 662118805, 990829274, 917563586, 723065527, 241282159, 750383785, 244492157, 870728585, 519666209, 789039616, 597245339, 761701, 882838381, 749343000, 292844684, 396240977, 298575076, 273148390, 326938701, 682193720, 895846362, 844140837, 900079749, 924515657, 72577193, 342126201, 238450563, 288932750, 493612165, 684428621, 838967318, 777643414, 200242642, 202199385, 922200067, 775868420, 918740118, 286681112, 667747834, 437362908, 158809633, 318356843, 972332997, 659639947, 849187188, 9853468, 239144260, 29235218, 657281722, 256411554, 369308329, 457750881, 386384884, 713251972, 142214747, 179394754, 832431112, 479092275, 359627024, 498349067, 374443364, 306573058, 854199547, 885416869, 79570428, 735582879, 115600024, 632304816, 552462408, 374941812, 203533966, 768811530, 143218768, 486571515, 544752193, 683739561, 600373448, 586781894, 639589462, 432985275, 749578316, 709262918, 28996285, 552881648, 385916384, 882020959, 846861920, 958476042, 512665730, 997043273, 511288398, 432773377, 625365372, 671569741, 323440456, 382424785, 478417642, 432372440, 263120268, 92874068, 604233178, 276920602, 414863446, 558186636, 863317768, 569141703, 130051356, 553383751, 796668200, 87568554, 429638625, 254074032, 652796773, 4529389, 643978891, 36253820, 778820791, 905877978, 775937462, 489001381, 722140675, 937978843, 265737250, 335856338, 248161169, 28509057, 40030492, 597770835, 828167433, 934115102, 178341441, 610009790, 230999177, 723449242, 518813938, 170927597, 53979119, 492441006, 139995225, 932089640, 784480563, 932201868, 948670754, 930977515, 298588856, 981552231, 212421858, 232941731, 547764671, 688886622, 324855664, 772870138, 230590245, 912964601, 843717703, 875459796, 370079545, 193743447, 824708359, 368678518, 795927626, 259316174, 699299888, 732892408, 416933826, 718452142, 394944293, 230880106, 199810763, 773752036, 316316729, 267554020, 447727561, 469940587, 30071011, 752277509, 746587134, 402210033, 812375918, 590966952, 357431593, 669425987, 30603888, 494454789, 811404176, 526969192, 231344651, 8293417, 288755051, 485708142, 837909647, 134143943, 330432340, 877662376, 536578660, 716308157, 359504197, 645472644, 151109351, 297022231, 930673008, 465823437, 84902109, 886106653, 966374790, 858633247, 80297291, 396610961, 590718178, 48276233, 590139152, 77926215, 886959084, 257198597, 489921147, 843229570, 397933895, 535482356, 350857993, 402280224, 179767896, 310255426, 886760008, 867362962, 382972413, 708948534, 129527805, 751994024, 461940510, 607167165, 326349927, 695510689, 726228091, 231945985, 467185332, 637980536, 883925953, 908876669, 625830894, 526541373, 42253277, 553348855, 394576715, 488355560, 852995700, 798077461, 496452164, 184405549, 27631213, 833260060, 323367436, 613388453, 430145768, 831275335, 100528257, 669829537, 829381147, 26036492, 433656331, 244664221, 105731409, 159494024, 439293440, 691177001, 927886881, 558880688, 768949098, 720733226, 875077986, 115826347, 744024849, 24253618, 606111634, 830513436, 69478854, 357947434, 725832651, 490196295, 851122228, 498633594, 8064961, 711186675, 669108715, 200416743, 177395529, 792035220, 838908846, 529870220, 637696496, 787788548, 205180344, 720474998, 687110157, 15909865, 954191507, 379893107, 338164460, 437675712, 235690857, 454361593, 649258283, 785160398, 903721213, 24506485, 635747426, 48789177, 358083769, 620892721, 959403089, 37666789, 298611461, 522759234, 543209880, 138029511, 858907323, 353558179, 618549566, 126858341, 996009399, 351332761, 458187136, 927843521, 437818257, 632928001, 749915521, 924560962, 834679355, 606480031, 640830287, 525966148, 452722646, 834655482, 464428461, 751165466, 527257244, 384827448, 129596971, 772990696, 222837597, 927785858, 761027641, 57584477, 732831219, 752349686, 847660775, 535995742, 901607571, 103013784, 197789131, 198027455, 392418982, 398199114, 293629309, 86104703, 178500342, 607566749, 899123660, 346072892, 343773781, 904389346, 106856930, 711982752, 573042531, 211660564, 214152083, 757893636, 26644069, 345149901, 64099700, 583419772, 938871244, 885471394, 210805774, 252794491, 972052642, 196047784, 199349164, 391785697, 938272653, 163092495, 261593225, 81258106, 414632129, 790811962, 839934427, 69947310, 12593935, 329217006, 26225524, 929123565, 121863496, 747754577, 840290803, 796375643, 296153578, 72482784, 465889261, 352600643, 630942925, 163668371, 207513289, 240386659, 259948558, 138350602, 93300586, 690834593, 546214070, 43159143, 929762280, 778075546, 423764416, 928661929, 846047748, 710249953, 573502245, 203554904, 943042256, 337467417, 585996627, 453806983, 843282735, 401859555, 599552627, 966107919, 62382518, 715434079, 648639233, 977635795, 807743770, 96854359, 975520210, 118561201, 855887780, 228659867, 845172092, 378694948, 756034278, 366177518, 724243129, 484336806, 520536274, 380088158, 597371844, 563270615, 750338252, 785329953, 253354614, 907771131, 893459253, 804530142, 882194288, 359070463, 338234278, 107961042, 519838258, 183852379, 65156270, 416331369, 856328686, 273859488, 98892591, 296784789, 788570652, 342778687, 542675977, 580672885, 275322258, 187877474, 448630918, 82458126, 987029974, 822844787, 156004415, 171344911, 219184907, 615850785, 155618397, 863663881, 539342044, 221257849, 321638357, 133842966, 889252620, 716463185, 620227463, 864180442, 768818664, 112961522, 880859051, 607541536, 748216033, 917348826, 100449066, 534012763, 41131063, 387426391, 41131549, 457325764, 296397796, 691943940, 384268490, 880064598, 255900122, 281144472, 762759814, 607679373, 348798876, 582684885, 726010886, 755187214, 109675553, 196106436, 136427051, 444091038, 238723644, 734790106, 836955134, 632712404, 928520278, 804166017, 53732783, 643801288, 668717396, 713947865, 42926925, 27284041, 433527222, 559409653, 319222639, 507978331, 96997509, 383628607, 485114135, 179645336, 217628509, 153979979, 684661420, 358110671, 88969439, 945436681, 620994494, 713695100, 367996619, 617985051, 485671926, 411311734, 263662072, 309402046, 365571681, 518825031, 725025794, 106274994, 257243039, 339073066, 856880752, 241099788, 77647896, 284891500, 70426411, 423992114, 693698071, 97237482, 540030537, 986784637, 305682110, 401356189, 577247208, 749325541, 838990545, 554174551, 174090104, 329051919, 553404479, 511247142, 175428601, 813198975, 724778302, 255629980, 408677893, 599555191, 265674183, 428219256, 361954225, 39583609, 345209898, 323956872, 286053476, 482343428, 580113904, 870245049, 792769699, 760248826, 488537239, 849814242, 173373971, 261223058, 387894663, 689267879, 3396297, 525922710, 934089958, 84255851, 415513480, 99927995, 271660144, 215888196, 74074580, 403671020, 146791905, 23383816, 709346609, 750926671, 752349985, 864713893, 698465048, 891345893, 570738870, 701322581, 432049711, 453129299, 526230029, 52916332, 145495373, 835339448, 294236847, 364975605, 933306148, 875658776, 122801809, 155651500, 61118143, 957744542, 936305349, 112135580, 80563010, 167340139, 194845717, 71809109, 943409895, 606140720, 562806049, 74640241, 988195753, 634718868, 424117256, 2347901, 588631659, 363504482, 552696463, 474042911, 788154299, 162864101, 164047742, 266892662, 742015651, 102924081, 235324453, 507077598, 238115929, 878317149, 829777437, 197706637, 629141982, 563645090, 573814216, 630532458, 579242232, 597286121, 679919573, 395694932, 11397510, 822212276, 133514141, 303980944, 371882828, 247275763, 395068995, 359645849, 864823228, 514426458, 851010121, 389795733, 109633470, 775716368, 768735834, 652195701, 37488111, 328516579, 653173753, 25941478, 140649306, 649443206, 424955046, 753432972, 63193556, 913402064, 924587434, 986727538, 213696106, 999443457, 825106759, 869832372, 782495847, 284477591, 552880683, 666288077, 812093552, 820130978, 977162096, 392270060, 435941714, 812082044, 620262747, 680040496, 706046172, 819096205, 890037557, 872879652, 584827786, 498992363, 403866714, 75094288, 787208234, 276038463, 336438088, 366937752, 686196365, 287398310, 87590654, 215764361, 273805552, 140045439, 819137444, 300623786, 714817780, 73474220, 913830231, 873451617, 683894181, 707168056, 418994292, 945012416, 398811908, 92776778, 547431996, 816770512, 740297546, 281545844, 228360459, 480245523, 867622341, 116918754, 545976060, 506342895, 136307285, 217816559, 583819045, 328116516, 534254772, 605831121, 984788393, 649529062, 671306911, 164108016, 586017063, 215764167, 589548507, 261052570, 688887947, 9818077, 750244626, 850913858, 354137735, 988052783, 18722694, 901970747, 570265941, 24565998, 575376838, 120226663, 693236349, 504024854, 187002771, 688662615, 319639972, 496033462, 794790116, 534764117, 224629244, 776648010, 448653974, 541323117, 30517724, 376634134, 784732472, 649877103, 942500074, 296523965, 668861307, 721931306, 536326567, 569708049, 1566966, 319101118, 504067937, 699096980, 850510000, 299585846, 837954805, 768190302, 843841566, 443953946, 98121215, 4908962, 112872374, 684113028, 101831955, 344062399, 861331562, 863256995, 780593114, 764978981, 417720048, 384988742, 260270190, 729886894, 334729786, 134608672, 144146049, 403783027, 251203262, 746703317, 613211162, 271614460, 433097652, 586255066, 602399977, 40295187, 765826993, 362691995, 197502442, 870453789, 62362106, 855081159, 844436002, 435730044, 312403215, 223427065, 49873143, 896904327, 2342153, 521806040, 943880807, 847779253, 370566870, 31938760, 323204774, 952357305, 474187391, 989706548, 407479590, 59005963, 904685512, 779517599, 856379682, 406453270, 512366196, 274732853, 999149410, 637470284, 579598700, 470571016, 21758437, 928369826, 460786326, 495594648, 126857862, 635719301, 325601236, 820009842, 153357873, 746610568, 307349224, 392468222, 703012968, 222813311, 709073629, 668132804, 277196569, 636009502, 553780343, 721510160, 174663883, 41853991, 264705115, 695666580, 507298996, 236247944, 632302062, 449429224, 526292323, 363761000, 386884378, 982318253, 835017606, 608095545, 904901300, 200743132, 701600001, 389944478, 339761422, 946264079, 15356580, 831210727, 592914280, 644013205, 187268727, 858299727, 828985921, 1372943, 310211569, 341850149, 639052181, 895901079, 999123407, 209874292, 626137427, 529888343, 492441905, 878974555, 353183936, 904475733, 802271544, 839064190, 763541577, 987268828, 350895703, 545931256, 243793436, 402536458, 416376065, 370175733, 882646692, 563808192, 169621561, 424355774, 208960658, 761043268, 636782377, 281968537, 871268845, 149499454, 510708406, 835673382, 896410393, 899023027, 155135281, 950289484, 652653874, 476055598, 164062438, 74425368, 379974883, 530452831, 517636586, 940347489, 559699047, 310063153, 958660236, 714812053, 675987472, 399191827, 804130950, 400229209, 10220646, 326508746, 770419741, 75329810, 539180346, 712369291, 5663874, 856258011, 316568476, 605288650, 986154435, 642718347, 603696769, 737431647, 938189478, 153477720, 72650991, 58961813, 355546877, 195758483, 515639216, 912696512, 765823299, 775316716, 433820389, 550026806, 720489347, 994769848, 660364685, 522759006, 5395350, 792560882, 223072425, 906535256, 628657753, 900816908, 206992543, 339900342, 782671071, 136416944, 202909920, 986606497, 503539440, 925292794, 952065065, 17410347, 647828592, 353115253, 740403719, 296756580, 123405859, 11985581, 905074295, 232199059, 323910773, 713010752, 415405310, 647483927, 808341987, 816876421, 47996940, 556114397, 600872578, 429800149, 147992232, 969853116, 31181429, 659446935, 278026256, 914043974, 822737684, 491685049, 832656042, 479348855, 215601276, 439410574, 359030064, 864027025, 439188979, 541458695, 142719501, 584684884, 826623249, 419766591, 186805577, 961025725, 129716907, 445344886, 232184892, 329191603, 94231161, 156844334, 700940076, 308454700, 557771707, 60331659, 961503083, 699645548, 460535046, 785568491, 464806674, 904396830, 493436186, 186814067, 302015248, 59511333, 770068384, 965578614, 169109416, 207112189, 361964701, 22985890, 778182105, 656447422, 585142139, 970288682, 507476774, 495338254, 321073107, 125451049, 884569493, 502101160, 768903283, 837524695, 578426669, 261893209, 185432458, 154682311, 345671068, 93759586, 2087734, 943389717, 360824346, 3756632, 298170633, 428148185, 680407721, 814171095, 568399900, 462556909, 579943388, 289369542, 414022249, 123243805, 902685896, 722359004, 121430, 748761491, 385789976, 10209741, 890773032, 99020772, 788506484, 29768911, 372370195, 573118353, 71349775, 57559716, 135387307, 968528251, 875735342, 732054059, 828465058, 997006187, 559840258, 740194092, 509125705, 668974094, 741254146, 754120893, 52546360, 208858186, 773274610, 792685640, 778475828, 350830055, 288491264, 553022410, 857223777, 579666927, 932474985, 401159647, 846319379, 225932562, 319425366, 15378021, 15542200, 222569523, 217897611, 942050136, 472802045, 805557994, 502138031, 780267022, 707434009, 36588592, 610858310, 960359910, 961597620, 236337302, 350532792, 9479909, 659072616, 558608329, 610256223, 272084305, 476200070, 950105698, 995318981, 746880676, 458574429, 918395518, 231991487, 576277395, 515731897, 634179366, 10082505, 875563409, 864355021, 62156857, 872336917, 273993146, 10745216, 609172670, 967905110, 523936040, 92961766, 263961488, 455834944, 794033406, 677448165, 560476864, 689750926, 417025257, 924725894, 231241896, 504426207, 422710107, 16396416, 932706884, 812702000, 806404015, 951825931, 701466177, 701066624, 120142545, 851167461, 69932288, 434507277, 46451684, 925211081, 579420560, 234873694, 480716265, 959647894, 396014448, 998573121, 194458321, 908322783, 494890180, 359701303, 271039195, 119422054, 271297939, 846128755, 383523997, 380778256, 972080419, 150069145, 389424885, 627810778, 420464325, 665615768, 460336056, 626652508, 737667039, 448282346, 562709106, 31492570, 483483590, 189550460, 165183778, 343767875, 567919591, 112306373, 790069562, 518116586, 514850351, 245880502, 312488441, 884193058, 133932880, 332135446, 372387772, 162168865, 969692717, 233922695, 63071794, 628533781, 672416228, 580198259, 483386985, 517536892, 330587148, 131683088, 702105790, 503558956, 840033705, 864989288, 541113786, 426211952, 8458208, 42884423, 77502239, 106822208, 813380287, 445828010, 589881010, 345608675, 188448958, 960711908, 632534373, 511628734, 693037183, 62539512, 23446774, 17854434, 796943653, 511973624, 1660243, 347241489, 266314353, 717768371, 614484938, 850261922, 27357113, 29029923, 570166216, 225131066, 703886138, 929840747, 122257127, 18209399, 143727134, 326820926, 692639481, 135938737, 991443419, 90906615, 844171608, 580544868, 743773058, 242940773, 122147367, 509035863, 816118670, 649188265, 460280776, 415811256, 188273632, 64199211, 833736244, 37513865, 616653811, 985081368, 892839815, 108321157, 201486455, 669137292, 671180886, 701496573, 539368506, 295619818, 454077668, 119017120, 81179241, 336039191, 811489071, 386180248, 364633360, 492683576, 810109618, 854490845, 850585611, 561688654, 741400592, 933001164, 350836133, 551515276, 477410853, 309534319, 282432534, 647950272, 237788439, 635359669, 284618688, 132922920, 313113265, 463529770, 352768742, 992780315, 9174440, 46625884, 325177683, 206088815, 104079020, 957318072, 215634933, 870526397, 615591366, 886461425, 469285530, 228717852, 945467210, 412478884, 457170464, 874931156, 738365034, 258764616, 350180264, 960651502, 625974248, 480231615, 89003849, 55408119, 374487090, 1960728, 964199304, 668779031, 312663138, 321455760, 708037356, 670710645, 946219497, 169077229, 923243718, 959648870, 660292897, 431209152, 466527259, 301036491, 514621476, 990185820, 254190832, 33518017, 501482036, 274412437, 21311095, 277249510, 169769927, 569909625, 370473533, 920949017, 624474338, 867031091, 924073158, 970669853, 512375537, 804813824, 899950831, 469158459, 921412879, 123969024, 839160895, 299996467, 661993522, 994337389, 568958425, 316497412, 549100635, 938132567, 398107189, 106494703, 123453903, 753255416, 32383529, 71053937, 830483691, 752035653, 1936945, 499464628, 904791512, 323374430, 813507358, 7726640, 507498108, 215948565, 43282894, 581396375, 374363815, 833994669, 742223240, 208176321, 770820597, 356036635, 933182413, 625821654, 333061118, 75386225, 718772920, 86520334, 545972220, 605834149, 685436991, 835009645, 345413347, 417629925, 486755298, 423548985, 945904657, 273880921, 762967379, 374162100, 418323179, 395379971, 908086425, 293524081, 173018994, 908234135, 493429651, 147073841, 609638513, 302209453, 922057062, 359456043, 879922463, 79035287, 149373233, 891742621, 537543771, 11092256, 503523287, 685089262, 474555764, 215228684, 541902057, 442016444, 4019283, 158700661, 923528206, 558994633, 424354725, 737664763, 293375026, 465801472, 3318609, 22412915, 115750586, 987697007, 391772360, 883236460, 709075523, 547128862, 139546388, 326059763, 798967910, 583960558, 260416370, 304380166, 40209142, 868612310, 679884906, 632137294, 999006732, 219910078, 416704959, 577878292, 310105899, 562780104, 293093956, 555485800, 320353362, 88359680, 383148655, 930582706, 582713554, 561042800, 119760680, 147032946, 697703766, 924301452, 889944832, 875288538, 748462973, 817430984, 346786393, 82633572, 687820032, 470648186, 574470218, 996205877, 377896267, 76864730, 454248568, 835513032, 794710329, 603923878, 581744523, 729587908, 899205155, 838214886, 66129912, 526015524, 139415075, 939761951, 745021137, 6552936, 232239071, 487923490, 282582754, 140887890, 744828461, 636406289, 39452632, 32585266, 350601966, 898598725, 644432587, 711275470, 401193589, 587040222, 147724482, 899149277, 217649986, 7881790, 561374951, 921219042, 788329782, 262995523, 668264422, 884804435, 411357735, 842459171, 74734481, 143702830, 944626164, 584006151, 723274350, 845856314, 212493627, 396753522, 779609006, 610027570, 474061641, 288812381, 116219676, 950717842, 614825205, 576347056, 508085928, 791855348, 377696391, 27988049, 954727748, 851581484, 656590760, 615312965, 612612931, 607052525, 362550457, 667061303, 855044802, 363712574, 964748589, 776410804, 619843163, 661967159, 45868539, 513827848, 89610023, 463433732, 854749878, 425975124, 288142771, 398052019, 532426391, 611975516, 21705804, 655471979, 465805330, 52126396, 735533395, 948633596, 965138982, 94716937, 490230855, 638341912, 464137950, 79594343, 153641834, 129919091, 505092817, 108095829, 768491705, 882068120, 314141661, 589604649, 919395718, 974015679, 998293613, 108767746, 45958469, 17015055, 89255688, 702416247, 844854338, 515807416, 954811889, 867612873, 443170227, 696670935, 107287508, 256502092, 214362168, 458743609, 900791395, 687518594, 482092050, 961462722, 920747184, 589402920, 459968631, 634415911, 426965808, 44346994, 365608533, 873665995, 528599665, 915805595, 522968925, 174367691, 582573072, 391209460, 339580723, 697485317, 791387213, 40604497, 980411052, 871918875, 39697104, 880723177, 727589003, 997090745, 47724679, 486481655, 316510105, 736022871, 447640199, 229766441, 522976336, 161072455, 573205780, 270560906, 189815650, 369931695, 142246802, 558293791, 831702206, 947116247, 349675379, 891200963, 814668224, 869123986, 469841455, 894306024, 543517499, 244277026, 892705971, 84874982, 32168210, 508838558, 75923562, 790903426, 294456825, 45530817, 773332621, 81099327, 938988242, 529282332, 714835223, 347483435, 64452069, 934924650, 861360937, 264474420, 235091635, 473870955, 189303961, 305618105, 475995560, 752714221, 678157459, 62428451, 958007217, 324656477, 854152119, 327678229, 626472724, 466456034, 446212762, 207345475, 784261101, 91628654, 777539356, 5908986, 590266889, 708333041, 596762356, 893388921, 412807023, 430674113, 766606145, 72960166, 715832622, 131360945, 394073901, 762307877, 924081548, 12192880, 753486333, 128716190, 839223028, 201002265, 683166992, 420240289, 397542073, 664411492, 733765908, 232353993, 958386008, 870002439, 296895476, 691351168, 961619833, 854560590, 777758272, 526631646, 481810008, 769128351, 903883856, 743663387, 118717893, 979494369, 491606873, 194080085, 900703562, 981684348, 831786058, 224483471, 648603684, 899182506, 904256255, 132139831, 370912774, 208337422, 598966416, 961486465, 728652034, 884283185, 32193326, 86465783, 396099661, 387096559, 567232172, 48561037, 552519901, 870910130, 736973556, 693088726, 780585526, 92447474, 234126125, 642280503, 632997328, 424217859, 186746443, 658938044, 110704560, 39604829, 452838366, 273087717, 288618540, 260647455, 577226034, 120338516, 311424339, 814783006, 370516400, 692382426, 780415300, 286074983, 864718134, 756981992, 178018439, 390495024, 302192140, 429391105, 880437085, 233239042, 675171045, 456855548, 702009774, 321718293, 205347987, 407074151, 821908861, 619874843, 402401308, 13596934, 905996484, 275634244, 706257532, 867550399, 232616329, 334919801, 513872488, 236232438, 705058435, 407812824, 184968182, 648528692, 672974917, 822083975, 462670069, 119346145, 501550199, 512009335, 236102315, 869529336, 198610960, 534594135, 607296974, 989781088, 962044943, 692821728, 403948549, 644578728, 343740146, 587002124, 308903028, 984023112, 837443123, 470391871, 772610545, 126522670, 686277750, 250267334, 618201702, 451126038, 880011797, 947088248, 261036184, 484551532, 321113294, 189466420, 256746588, 946760889, 845759000, 79541145, 797949892, 829685687, 27871240, 910024992, 186075914, 959397314, 132761847, 578724021, 232875247, 474833064, 65958179, 301205556, 466237286, 162842224, 673848515, 920364999, 267343835, 78245226, 137577656, 984680998, 87860886, 794688742, 696533307, 83028599, 472844167, 812894716, 760457114, 558044161, 70696653, 67938471, 164216664, 52731757, 69655294, 526876510, 45121267, 167886388, 960711502, 148186371, 373272605, 443690307, 78029979, 255511044, 440907506, 473811877, 61350531, 284357057, 688946012, 97462154, 324745797, 754948357, 970647251, 223579094, 579364243, 647346161, 510740952, 970257450, 409825670, 934767069, 778221004, 617132070, 381328017, 102017509, 634298269, 80247832, 977354757, 245373831, 736097326, 836156089, 643783558, 984965546, 406417065, 115304155, 209268929, 398865683, 521731308, 489666427, 325015189, 723057274, 813590763, 93900132, 882904650, 768604618, 297716884, 268161410, 470152329, 770061657, 28454420, 927119836, 308077135, 287625417, 364351011, 422883215, 417042843, 554299493, 855164678, 103061724, 876560452, 836960026, 230013227, 723329863, 836832832, 317236576, 181855355, 532169448, 168018599, 194626148, 785032330, 491368709, 31086564, 585801173, 955845904, 877862538, 323824068, 485220785, 109002597, 120144860, 136036714, 783940990, 196379089, 981895364, 891620800, 307576176, 468260365, 172709910, 965030130, 187661845, 540743103, 270104205, 476261786, 427407206, 43099955, 385519187, 579355310, 931703169, 452334862, 292890241, 828910589, 109061134, 595523061, 790786166, 359888074, 693712366, 137877462, 302533005, 806711258, 474337016, 196121186, 22596802, 685616802, 624416393, 789189998, 927958211, 33424249, 958090756, 229527197, 549636481, 28722855, 236040527, 629233696, 611746656, 901808916, 254232292, 337962914, 461669513, 417067485, 629554184, 304984283, 338249709, 658076372, 979113545, 932999739, 587728607, 867664171, 630193875, 383384507, 744242553, 571118451, 657267577, 15480770, 921448383, 532178110, 531498418, 709102513, 478079892, 712905102, 967107567, 887048171, 342108648, 669371768, 417858336, 709733922, 404002423, 990542159, 654989328, 617929516, 553066013, 193558655, 458947544, 904839348, 302226479, 648606920, 979390301, 586936597, 49054229, 218535926, 811736080, 192002852, 102087691, 774093919, 622383934, 573980173, 269746643, 29991811, 252665563, 706415447, 293388706, 480286700, 671167998, 630478240, 975520894, 287295947, 446318360, 359470573, 569640314, 322522167, 622265103, 739319095, 745701199, 102510055, 887475444, 653525088, 715651175, 440186634, 750603908, 762237398, 987799332, 358669001, 857541490, 753847489, 642775326, 778227475, 357191066, 2407189, 902878687, 57199604, 689043255, 955535146, 108574322, 409681345, 627465531, 869235679, 421335134, 155633150, 813770746, 185159007, 359470954, 406469836, 461431503, 622390959, 880274209, 814553050, 787639416, 273895743, 19884772, 967816742, 536773417, 692731340, 207626197, 249340210, 327446501, 995242291, 965828267, 57620022, 50287427, 851008086, 277234616, 261616682, 773457611, 413141091, 214836151, 185693232, 767513205, 193833357, 81136524, 460191867, 171457078, 858339248, 762476926, 948617816, 561763884, 153850043, 709467743, 24086144, 299996937, 973860038, 881356291, 326352553, 443620794, 772273541, 370987241, 205469758, 680962261, 82724141, 298608385, 937033670, 310076899, 489297858, 345590444, 447879203, 423810194, 935553213, 552773341, 892167819, 538131808, 169008269, 556174282, 989318981, 495041915, 738567955, 11051833, 477395738, 814061508, 198488098, 303212811, 715372176, 769502230, 655117530, 604740028, 567396579, 990068245, 257102951, 124193773, 25787815, 466758572, 281961845, 205057337, 896964619, 211731888, 906610892, 101211009, 508285921, 672868106, 392359849, 35195822, 914895285, 883391557, 778111240, 926131450, 353729397, 525236003, 467554805, 33404374, 821638195, 420634775, 532499639, 990679527, 275282799, 99180736, 275608512, 896023728, 353640894, 743455518, 342040096, 849154546, 479273416, 212405061, 414566780, 254083479, 927681605, 41049914, 609939861, 79237546, 777896549, 941128832, 97791358, 924592181, 299873212, 529429681, 817354240, 503840368, 99448296, 493134631, 6885185, 937476333, 462726403, 983263402, 86930555, 202217113, 603779233, 524973265, 405383974, 911102210, 22452567, 303420818, 90432373, 591168781, 632709307, 407452552, 73960574, 76615808, 880514188, 734230164, 778713946, 515020281, 72377740, 83496866, 992753020, 525913557, 2093640, 610939829, 38344002, 447372354, 638195162, 16660958, 121403183, 949776221, 551176826, 892819572, 428826742, 387479432, 797392705, 189206693, 834683583, 906113991, 536397382, 712951348, 21458099, 286505608, 144861903, 177637613, 395388951, 943159326, 372864832, 362630968, 111948849, 122344374, 670147933, 768362532, 18587688, 620466631, 802655608, 428879680, 232523594, 926744339, 369930068, 983906680, 167796080, 454554358, 134382008, 452483109, 189057923, 109831637, 715568116, 649306011, 348891761, 681966771, 856221780, 22060550, 706899, 269863653, 963177190, 309924100, 101310241, 516100583, 34822825, 186971465, 176169728, 891757332, 195017813, 723811898, 235300878, 182123291, 351894705, 975289636, 555746340, 518074107, 949450240, 307967536, 949375002, 352166447, 82998965, 422142107, 935925977, 899002335, 304439943, 105909155, 936514426, 53929951, 932416519, 81517091, 503779714, 34123452, 195444947, 61850243, 168533451, 616370423, 623981088, 771792635, 902466331, 425156494, 145991807, 15441962, 230119667, 595729082, 555485843, 792397514, 36206209, 510349624, 890449064, 739438341, 4757924, 752248106, 926216804, 111060372, 794172031, 689524697, 301907753, 855003751, 325962497, 643730347, 676705149, 126983754, 393884257, 895861942, 290380463, 473759791, 901875069, 859832944, 141437648, 872224071, 245725313, 860888251, 689392876, 786466075, 235834589, 184489494, 675694603, 102349506, 826302814, 100225002, 34398985, 174577697, 22767812, 56178237, 827226525, 385383460, 648902953, 632478463, 188427667, 119979958, 501732383, 799723639, 910291867, 722567280, 309188479, 175682078, 939607097, 837522517, 735424083, 961901704, 705355349, 496961041, 297883443, 44779246, 975533211, 404868117, 438260458, 423780221, 382952267, 265547020, 205090589, 669348972, 618319271, 710375903, 385452414, 64898165, 66202067, 629445427, 354472116, 202148204, 705326601, 563864185, 851039856, 278120412, 160495780, 763543378, 962577368, 723857424, 855810033, 326496982, 477279337, 524437371, 533689243, 895129137, 142153064, 198798511, 238008706, 366359797, 544343729, 879607889, 588615328, 306126683, 596773421, 708404102, 495400268, 528629936, 514915680, 422971170, 169417639, 433529269, 232197246, 302341245, 465452518, 690708649, 98840167, 82780958, 481692443, 866100781, 936710178, 257200011, 769156970, 930368958, 354434993, 165891451, 856449825, 735453482, 212595512, 52490667, 237996394, 251610577, 131883269, 658606444, 284203299, 990788003, 990443448, 662611395, 496263920, 843100770, 173074355, 682673766, 992169557, 723560930, 997505653, 221945393, 720172440, 750203316, 532056869, 261409517, 674894055, 8281486, 950083598, 561567742, 705542104, 603104293, 36625302, 282028353, 111836018, 402096645, 256376816, 724178197, 534408803, 197161675, 417140877, 66021011, 13871079, 142006862, 382397126, 372678129, 900622761, 979488712, 883538954, 146141136, 992037399, 940085732, 81450919, 34738385, 617690481, 611872320, 342616799, 499417603, 940771935, 823548276, 624852964, 770731074, 864730537, 920291644, 206892658, 283618714, 984324735, 696569932, 281921452, 682822724, 2795194, 34810474, 222490679, 961546016, 991819821, 855125163, 880339363, 517488829, 791528584, 749027990, 792566233, 769911885, 723789195, 404376358, 212689279, 610199926, 364574782, 291635406, 26163603, 682867016, 875413436, 382178577, 953956264, 958721727, 676858449, 345502209, 976529581, 200218275, 175581840, 874812727, 251398992, 403252093, 875169315, 129779719, 330388847, 446643431, 665113210, 152941233, 317146098, 813243727, 582157270, 107477229, 823832434, 536992229, 250734729, 952250109, 611959332, 917921866, 844658586, 522874907, 735358626, 392565517, 128246887, 671219261, 231324543, 816176624, 822431600, 439409188, 812122073, 225550610, 99320405, 811877578, 159536767, 31818105, 176597298, 481713269, 107329749, 665108604, 601030234, 375907162, 741775157, 914292733, 730797841, 516785669, 639790066, 249120862, 497501951, 970137697, 442079827, 486569637, 247646436, 922699253, 132219861, 985956821, 347174828, 117894314, 12686666, 584546283, 489802973, 85456780, 365969648, 421462787, 945980925, 454099501, 270905241, 578628530, 116718721, 237250634, 251503819, 186670007, 558534433, 158041951, 127942755, 574817521, 92149688, 378373628, 678877240, 417008095, 2526207, 15029807, 810502152, 885501486, 646165360, 180092205, 907311749, 808499453, 637890286, 583238084, 222752945, 337030627, 5304346, 212634516, 178057209, 137449738, 941812020, 278729643, 377995705, 638582856, 199157688, 328677867, 811334644, 621891679, 506939960, 714684272, 271463928, 792478894, 377252730, 839991211, 747202265, 354044508, 680281853, 911402325, 995188298, 452885271, 861605340, 534865357, 293795026, 415085564, 830575817, 269568158, 929045668, 551739070, 587253212, 138494099, 432439069, 518199773, 499244291, 342489911, 513497367, 945724216, 490095681, 862629541, 268390083, 244037632, 654571641, 971210629, 828816383, 371676373, 854374569, 2869277, 388777822, 315626881, 187614999, 635646108, 885887990, 626717155, 165786258, 20599600, 674058504, 302410008, 993938880, 980213513, 57790096, 396592703, 333278168, 872593392, 55488766, 732878777, 542014469, 11468969, 648818554, 862291123, 879916599, 711022849, 329675767, 35901718, 911321791, 137412405, 906347224, 80634320, 256432804, 51522444, 243527183, 308460088, 483166184, 617060655, 205814466, 685840867, 399014135, 154822264, 233014577, 814869690, 299458436, 435568159, 467161225, 429544245, 216424621, 363644283, 531746539, 705512708, 37928949, 853653392, 954345158, 172994014, 901746159, 536854191, 379049000, 337733685, 117906935, 228936283, 362518951, 517748704, 984834065, 68277825, 310009757, 748634140, 621018932, 490686775, 787240081, 253217229, 146211032, 235998382, 600594953, 368357038, 628390342, 426250316, 373115086, 471593720, 915905440, 159497932, 383469235, 6468337, 300793392, 669302956, 724834517, 276521188, 353860599, 862887760, 558926611, 860112753, 729148275, 573618883, 612107229, 574889468, 271446905, 62524775, 283652102, 33338281, 260452490, 358370265, 596857509, 52979516, 359689314, 195835867, 6619121, 202910036, 304426560, 786469291, 842697200, 935629786, 917978183, 819751326, 52882003, 573084174, 521561474, 655884102, 127963562, 509193377, 538383740, 743729651, 372262289, 894297929, 767148921, 100802334, 741186734, 286686576, 686263711, 42014138, 55050538, 362866173, 672397011, 104489291, 483090117, 535789899, 106774516, 753322394, 141066064, 171569897, 764202277, 957267156, 53004148, 300080104, 483361232, 110074521, 337782114, 208327892, 706680373, 846581444, 870631560, 766141469, 327934593, 781629719, 923444372, 539522788, 693843671, 688045937, 558416481, 760394345, 556117394, 24624384, 933632268, 486466837, 493444902, 615358410, 54936404, 977664610, 603170610, 371422861, 273726529, 388590030, 354123509, 852994581, 641381817, 36537772, 221862024, 971962572, 224856563, 616189961, 772434268, 372924159, 200009835, 906134615, 49420985, 284641378, 878461777, 712231071, 703866115, 769873013, 656126363, 456894889, 638971732, 165274267, 144925967, 155470202, 800340758, 399262268, 640714023, 219669411, 874273032, 564891859, 640826567, 388464019, 773042360, 177646473, 747448653, 864527343, 915284205, 760598877, 841672427, 385694550, 794524321, 372153736, 225950158, 10701377, 787679039, 205928828, 254882384, 842287878, 734159049, 365291092, 701401208, 948825540, 795037996, 560710245, 447140723, 768422441, 842075531, 434471668, 522530934, 108648300, 83896146, 324766437, 491917879, 663038118, 475644313, 215039367, 962916939, 461580376, 40379745, 495218671, 682745319, 284069834, 792819469, 149115036, 949223458, 739249098, 435596598, 338477860, 476243182, 801609340, 424628122, 262457868, 15934341, 254096529, 978402953, 423935479, 689644008, 639974467, 270084537, 976374796, 580417004, 195856071, 286254387, 638027332, 944671904, 23403372, 43615334, 31296647, 122821281, 821800358, 933743955, 33029713, 696921644, 157258897, 548523983, 921245975, 381037536, 590522620, 638732044, 404589832, 245292619, 317092398, 442336393, 451696173, 608917625, 273937344, 155228634, 744171917, 368896844, 710323045, 19127964, 561417302, 112630192, 591000058, 295934237, 211855288, 550415625, 523708585, 288615266, 940615312, 564922165, 947632132, 789955743, 466643611, 23280546, 407972314, 382458346, 719296642, 705010024, 303797864, 49024495, 117099454, 966991442, 715688799, 364912007, 849445654, 46242070, 212571519, 17852092, 97098161, 366639947, 532780218, 836671222, 954990327, 410192345, 984184240, 232119842, 948368911, 851453197, 505855443, 138905267, 937745585, 61619128, 722981163, 380851000, 393603395, 567610653, 590979738, 195980178, 926384477, 982788821, 623972193, 433183152, 416758874, 59440471, 644095890, 826905916, 773734007, 317570183, 384107287, 269730941, 59580786, 156958716, 857326074, 674066720, 227076936, 446446917, 451530867, 60414125, 309835870, 84768491, 885465319, 107317810, 998059621, 553150046, 534414351, 314473380, 106407765, 340935174, 250396294, 272018724, 628784043, 942183150, 59484174, 158731507, 159867528, 977558259, 258661424, 284417508, 384872119, 973602246, 572048636, 683095150, 147214583, 70005093, 986039017, 374792464, 970910853, 858271677, 111162411, 182714050, 440331783, 302236798, 103806354, 275234449, 830175676, 113125319, 509594188, 640391253, 143356463, 561842589, 588875767, 496178274, 356916799, 389437263, 742656768, 967991926, 567823143, 189235863, 291227893, 661708015, 986312762, 602418279, 355058743, 111662131, 271939823, 425547858, 678012078, 502853605, 963117209, 47872358, 170283034, 707915402, 94092180, 150340294, 101809703, 587779651, 718980732, 924281151, 145345923, 649360238, 471636622, 732802533, 561443503, 255762077, 310208874, 26675667, 315316371, 692846619, 663196980, 706761706, 760239090, 462497832, 461463235, 685094083, 848688834, 453537354, 208765702, 842978652, 425802336, 419525713, 641333403, 606263425, 309188327, 932729601, 394982417, 558398467, 688930700, 323966397, 800636683, 534780685, 73609921, 25424632, 635777570, 830202001, 745951135, 521234131, 328828021, 288037277, 923115308, 229311398, 11706556, 431219124, 888795225, 451732703, 904506959, 238489949, 58625107, 14266884, 847481585, 281787457, 51506424, 188648674, 643834131, 665072711, 776981408, 598610086, 306634814, 845921377, 561067049, 227754108, 918617670, 394191717, 792935146, 853330001, 877291060, 488049098, 686646812, 756281901, 956416453, 797979234, 958384397, 799694888, 275754440, 819365265, 861760012, 544184076, 481224145, 171546998, 848755816, 509116060, 146984606, 538497366, 667920810, 687001732, 921631087, 955363037, 463225506, 848202417, 749746887, 397250619, 607839247, 916129362, 565748590, 982276772, 202645499, 354435405, 584944154, 19782531, 352893674, 493188668, 5697558, 780126303, 907728490, 979923954, 747687192, 780758173, 582210240, 545432774, 25068245, 100880723, 577050836, 765771517, 467716249, 667647737, 542208791, 235014903, 187049310, 474053278, 254599581, 148298967, 114598714, 338593013, 223523790, 481551496, 789431180, 882850529, 923440130, 430548143, 691519979, 463358910, 157964398, 414602593, 986297993, 12816364, 978511269, 891917067, 50470828, 733672589, 824992740, 486269480, 470240495, 900585518, 722239526, 996614283, 459093322, 165844410, 765235429, 391658125, 781742215, 45856623, 773874153, 804710366, 113324183, 740304899, 599843232, 701408084, 191750911, 841232048, 349001373, 468717157, 335998325, 786475315, 917700002, 470234063, 350402095, 398526196, 514664312, 37004936, 115896903, 172309654, 950396232, 981303078, 135086078, 395993337, 909604398, 936952338, 463751089, 242581460, 783840975, 497988886, 607874299, 761194661, 866472974, 986519694, 803257195, 713713148, 410193292, 308525673, 594731310, 474021236, 959853062, 962922785, 39594272, 54385165, 193317839, 599516771, 476517425, 638032124, 415177512, 427825443, 869493855, 14578512, 378560997, 636873316, 26493504, 154570418, 344791121, 112109658, 959516590, 438361717, 310686124, 581837481, 198753779, 216890896, 700611758, 922977764, 311134203, 20308982, 201656177, 771317938, 169898324, 362911544, 119840309, 789289905, 989786118, 226528978, 831574997, 764307895, 462665964, 260101334, 580749785, 948911500, 356587899, 89647430, 527828260, 626676957, 410393184, 996424829, 19267490, 946298683, 329630343, 679610121, 516974884, 197164269, 348602528, 205917177, 680038116, 22253275, 663162864, 644434597, 597149073, 938059938, 96771311, 404408092, 734917191, 762408285, 947707484, 888620072, 276040982, 176553345, 565485343, 734675295, 995110196, 158556740, 622155832, 800275645, 650062653, 262252396, 791168285, 986942902, 833469806, 118893738, 776787597, 859882149, 39757659, 58415360, 546574672, 11737664, 637661015, 190955110, 393437450, 474259696, 843672680, 81260898, 930188990, 503095958, 518370425, 719170188, 43571477, 640246812, 211166442, 945472953, 769079613, 612760126, 155411524, 35454536, 97874301, 721943741, 688427166, 642594017, 311096169, 948894694, 389550709, 110541446, 846199486, 134607612, 406085254, 574278314, 156169343, 190869291, 388855766, 497980521, 363713391, 268082469, 229370348, 782375734, 955349973, 132748708, 899543888, 619254487, 549321102, 718340635, 247933009, 772653783, 884464779, 148781054, 714133122, 192256467, 889683756, 172740959, 263308912, 964642982, 316373887, 57018463, 897392175, 209607107, 533062583, 88517822, 102213546, 418145984, 987296368, 757221485, 752009338, 897931079, 981809619, 641583511, 347262049, 878485321, 316513158, 70868431, 391170428, 54749347, 264608408, 192386638, 709065930, 502054911, 409518219, 504899727, 464679050, 974462207, 311435715, 434352913, 698221686, 587094183, 15566057, 734679500, 481451196, 6265739, 981495785, 365846878, 54577138, 759917571, 823261541, 20546776, 368931502, 199839501, 95952209, 428762441, 750209556, 48560259, 725129062, 780598800, 613395246, 901794021, 318640119, 42337317, 130324245, 284636646, 971476124, 415160554, 778950188, 666393682, 690335077, 589593341, 365255238, 904430553, 726475096, 257735697, 727336783, 402718151, 98852681, 229275990, 618377982, 128492888, 557091995, 832238376, 134612862, 832798295, 507787868, 53559650, 685541235, 695569728, 295806261, 644912833, 920351560, 201029361, 803430816, 941839950, 201126249, 517359766, 400914932, 988412115, 275094075, 462224447, 949662390, 875067186, 753937356, 275739024, 548473403, 145652518, 649287905, 837272741, 413297558, 700676613, 730699235, 210057998, 481461600, 566399941, 524940182, 856863611, 744688296, 617459822, 827431035, 763632730, 831787650, 94090438, 240680867, 453280563, 75544045, 111159857, 164638788, 916317593, 435623829, 793649563, 881600237, 398143727, 859301724, 111534455, 81050918, 154900304, 435766338, 892779665, 573285926, 108561330, 616432907, 637404458, 747105472, 118835413, 652288492, 826175611, 668183033, 26040151, 669686400, 872586840, 227881125, 648325404, 659843825, 218509900, 629548075, 260785028, 535338649, 893904532, 522821741, 877628126, 282827503, 570254615, 568303866, 919817294, 988498328, 614425557, 43459060, 623503500, 664627032, 636303328, 846601150, 197334938, 526310684, 619049058, 789060025, 686637563, 867850112, 154139784, 261720116, 35831544, 721463940, 161369224, 780775980, 697414629, 145547088, 221230954, 153687793, 469588504, 978148441, 50048980, 117019186, 274831128, 255191748, 604300245, 524045461, 880688992, 541303925, 235393700, 868264109, 750989643, 393801159, 838425660, 627770641, 765059226, 183285887, 828393977, 587358077, 407005805, 755346208, 344145447, 330245966, 653277952, 791037848, 480469963, 990525261, 165129978, 129342904, 435802014, 908584743, 31229286, 33333853, 659522029, 948967107, 926033323, 356766237, 681467201, 672673775, 194542944, 9624188, 554499206, 683909176, 658915424, 330252267, 672478137, 945779009, 993872159, 721577635, 676148650, 552185018, 918372895, 140628262, 727753714, 46780573, 663134934, 601998410, 741297441, 79385187, 257136217, 247488653, 14425974, 986149050, 932169123, 976451676, 215650991, 280702372, 778357313, 973218874, 70145232, 591122301, 106638860, 82259984, 630943819, 308341727, 658687739, 67419299, 340396609, 326371351, 894640391, 904804662, 944888383, 407138456, 224174219, 782447273, 975533514, 808076619, 333414274, 621647827, 960023131, 806741528, 198514958, 482309024, 831122759, 779010018, 214320713, 502431488, 393805221, 862240704, 802495452, 231605508, 652450847, 69475894, 66104521, 374395856, 378890881, 592964851, 148855116, 214377296, 93311165, 710487487, 958673078, 164315687, 873975138, 162089425, 466077831, 894907222, 244817896, 453436180, 785586484, 808555297, 368831538, 46404247, 966605528, 198230080, 87039385, 919810160, 199566146, 583003047, 505762735, 940318827, 387384971, 531240650, 163464159, 673613533, 206305521, 116821597, 425084142, 636437447, 325260380, 92478291, 466428575, 331684460, 511303054, 83371744, 945411808, 451863638, 998399487, 549042416, 195588184, 41048384, 324678709, 218925207, 578132615, 474512881, 888131715, 609629634, 315967544, 524785860, 405721454, 361433872, 453017770, 892259124, 567026430, 713985013, 819121313, 422010737, 765491505, 504281676, 702381649, 283027779, 577050682, 372692946, 185180195, 517515333, 130614056, 225476154, 544197050, 700962027, 387277058, 382713705, 897324537, 503164822, 444887701, 182420609, 873744283, 142151601, 284062282, 961518134, 316391925, 664035305, 611570173, 24232991, 471119, 323356678, 43330530, 13872733, 604098192, 588688422, 477815164, 28066396, 551944250, 460373571, 96655403, 519957638, 815269331, 416066431, 430559538, 315149778, 548579026, 144990926, 469697664, 276807062, 830591963, 951764295, 181848880, 936068345, 572837639, 922297302, 609309316, 330946439, 508778308, 138257464, 421918210, 465536165, 371395717, 879111175, 570454301, 830387367, 926260287, 24090362, 960884016, 260751119, 996609075, 111744778, 128011844, 523180531, 192744573, 804516130, 647879744, 223890485, 359009507, 567955455, 574421554, 518996687, 326162726, 871568286, 418548285, 112048199, 890909087, 311404778, 568729494, 421224695, 350162901, 530242863, 747467203, 381611934, 211446083, 883811171, 341527122, 412057865, 811642307, 185679076, 693170600, 788624238, 324099109, 714729921, 31356006, 72118479, 491162410, 901593054, 803110250, 729605150, 855521063, 268775178, 419314366, 753323676, 310695325, 14882242, 584744584, 760135015, 46726244, 913262988, 892162333, 215206709, 809773945, 250669583, 777730266, 19450704, 702498879, 964618982, 267313963, 609535043, 558209734, 495170008, 68248695, 177889478, 146557513, 247721302, 701384298, 961420809, 734219767, 207894810, 293042802, 293754022, 161043132, 33836350, 112703232, 308818022, 917612884, 904664444, 764605481, 721832183, 343251085, 535612219, 879224758, 691905948, 773951553, 133690810, 593984604, 683971398, 689706459, 811968322, 418017082, 912737146, 205916616, 620772420, 973120125, 165572580, 874491045, 377610832, 987486511, 137290989, 390283999, 826562467, 502995563, 783002407, 570344785, 943064667, 970189318, 846452798, 910267561, 606471603, 680750341, 13209701, 468553463, 278295269, 586389010, 215888907, 515018790, 290759640, 393043623, 904615213, 399187537, 483720295, 155353426, 480587699, 251176122, 878655491, 945782190, 196430423, 997750136, 737070689, 654911200, 900154099, 653028623, 519477937, 744073449, 48870015, 200239316, 862792603, 852827755, 764608931, 631529838, 68492396, 820545240, 15322234, 923996892, 710514931, 454075106, 307582112, 5596337, 213142075, 783881400, 503204458, 863642973, 622375992, 778393993, 967651055, 472266469, 12492125, 895669047, 576735023, 822130813, 135054580, 986196429, 167304411, 572081855, 312889093, 133434946, 484136785, 27619672, 824559119, 569931161, 364774245, 144501670, 462692314, 852202576, 879708780, 178015665, 165811852, 257595208, 384360173, 583044569, 328069145, 127484629, 36017441, 166951728, 201443580, 374458905, 214316611, 837862950, 330948504, 928369647, 639204931, 960058276, 292730470, 345248316, 650427571, 163294601, 641836373, 743064912, 794775263, 324321877, 293118790, 485852066, 647219404, 290640014, 339336921, 128921383, 172558961, 251488718, 26134814, 518135827, 817519804, 965718961, 998183557, 14356515, 309847210, 800796571, 698024049, 433423728, 624395971, 706256749, 216670216, 531234307, 906399856, 499959003, 327123064, 605677605, 365936149, 23417693, 799846383, 269136168, 281086763, 978885725, 545643835, 744612804, 461852542, 270463078, 646302576, 522422656, 154464799, 767445782, 792690212, 68531666, 727570090, 72525894, 996396683, 531010544, 42382280, 748769835, 624205808, 917361334, 236588044, 683084372, 889299825, 739741424, 386436941, 161695028, 337328517, 732263393, 555123611, 13607752, 721847151, 688945925, 216078132, 787473780, 216773720, 389278179, 210405803, 115155670, 575011183, 142497196, 934190229, 873078055, 893489232, 841062861, 372625759, 524356234, 705734718, 456517066, 113604423, 682896572, 382894982, 292023447, 150781316, 653322739, 377341932, 736185517, 593162607, 982179695, 18344146, 215489687, 720125294, 292238403, 637434014, 826539540, 34389162, 867023883, 340526526, 182197168, 652306162, 754353476, 783716047, 706451325, 565701736, 918716329, 55128814, 606803527, 281611323, 699214000, 544949215, 398639786, 268919645, 146984344, 985558486, 651820584, 40965084, 211572085, 405641597, 886035512, 379642306, 987968472, 571318584, 388854058, 679511123, 178404902, 619666669, 37325691, 126439140, 718961704, 105767623, 132055858, 451792081, 839424105, 922053245, 337398532, 337602664, 821637002, 590990074, 439307823, 274112008, 822812816, 537355043, 853428308, 212266193, 677332430, 715807269, 543367766, 753088099, 626618211, 88080978, 274815962, 728566522, 452748624, 814108626, 572062352, 387846671, 587890075, 21902248, 324882097, 385259863, 642963956, 115903935, 811531629, 791276173, 491769116, 86655851, 978170677, 727392696, 976548235, 233236675, 470161347, 756371738, 964215940, 289517144, 903187947, 132052521, 926446996, 471022374, 524184036, 939485998, 19313477, 272591455, 152879235, 284778297, 155648411, 926752440, 937497612, 598055938, 436823197, 140856734, 826702154, 695789314, 211755308, 772041401, 815275856, 898885101, 939092236, 332085738, 414887140, 165913449, 90159444, 387258040, 362208994, 593838498, 496214776, 285234523, 456871368, 573753097, 332272601, 80952038, 188700799, 814309681, 315361587, 631246765, 906865090, 69234278, 56872263, 786848192, 180121065, 353959013, 76342305, 482159028, 516729698, 768235688, 644318208, 528299940, 381880859, 979832443, 204472572, 573131302, 527913439, 847382839, 228761510, 904580691, 109070876, 248715477, 490821722, 247750636, 692003504, 955294532, 733363377, 906421302, 38216708, 498213846, 99737571, 659819621, 971345624, 196392115, 399381532, 405223146, 570308177, 109505366, 157974544, 143941350, 975962499, 733358050, 36353563, 806084118, 902134268, 71425854, 693379929, 757086353, 190549254, 370389201, 107304604, 330192799, 638892369, 409005196, 744363224, 144260281, 258534409, 390744484, 424573251, 671394479, 376480140, 92042280, 299414306, 996034076, 802706701, 42715847, 215367075, 152272317, 976000108, 821481350, 185817634, 749930474, 270696197, 893600017, 702639588, 189856356, 474844682, 32178996, 174950456, 388112219, 97745755, 237879854, 591557837, 540827254, 957274883, 469264349, 886899378, 74115552, 598446033, 109167706, 281288734, 910191665, 415021408, 474028449, 826192411, 509799476, 573127606, 629050467, 434243062, 948834658, 260496179, 93422098, 124933035, 380999408, 814003347, 369674530, 379570541, 70533413, 622860057, 91399722, 708878091, 63259494, 306118696, 626124869, 903483281, 243370302, 994326739, 251195719, 716840980, 616400017, 560936446, 711091045, 569272026, 169433628, 422681260, 263619108, 630679479, 129059004, 697412708, 527092326, 852194680, 391348102, 245425768, 471988384, 395853239, 109281366, 334785503, 521080953, 479227667, 962776910, 996886447, 421385359, 284619225, 592796161, 745179158, 682783888, 794444690, 405677095, 339542147, 519373187, 251376371, 784433220, 295839397, 204806433, 326771075, 464110799, 422944048, 283239975, 133916479, 705063525, 512000782, 801158220, 816118285, 176581266, 122711343, 18130617, 287891526, 217359446, 283972099, 389752158, 117874017, 539329450, 778361467, 869321699, 146584112, 546542016, 305073073, 414187408, 302664058, 441836153, 536586834, 132806967, 820063234, 309521382, 245241901, 233962008, 349444664, 926858280, 674414320, 104286806, 899291098, 404954414, 19417076, 558968023, 168396078, 388843788, 725817073, 914761260, 473797995, 259439033, 710617135, 7084936, 178227413, 738188531, 238820096, 663307924, 925433927, 917312186, 39255082, 538164176, 746778665, 14316368, 534052356, 397086481, 888821955, 425303363, 901384613, 607028982, 645968304, 402958865, 80572801, 599903073, 841514658, 136866129, 594463733, 85075122, 416863014, 772599426, 62923435, 906002409, 201984976, 864338241, 454813084, 329492663, 951638941, 673229563, 153318228, 174861084, 298896244, 960886050, 639735168, 191284060, 491443708, 622333898, 850398306, 671712832, 856908547, 445179879, 991510500, 248066076, 698256833, 62659631, 636809808, 764247046, 938491880, 367135949, 940835581, 23487449, 600406769, 989542858, 438930091, 564234871, 138769209, 303013160, 150244534, 624820812, 425468411, 332440299, 771320989, 167777080, 670434366, 249064387, 950732628, 23839470, 12997652, 613734055, 750054601, 433425470, 987390811, 436147491, 391261859, 557911767, 414728463, 307268554, 546634716, 284628887, 515118129, 953847703, 752229596, 246319253, 906938658, 745135572, 936312292, 628634676, 665921289, 470508413, 364075993, 601399541, 570681563, 155779289, 253912219, 474162457, 149885586, 720679008, 232892856, 414481343, 423534185, 543753500, 426480489, 35246575, 809666912, 618672381, 798450695, 709187178, 615508162, 451099096, 659377516, 79248, 357633383, 505025016, 349900850, 15050757, 632610527, 488339714, 942263030, 884711838, 518116521, 116397517, 741026266, 416080162, 635917488, 555425648, 939975010, 567525376, 135872304, 995228884, 311730060, 660459726, 631117779, 720635282, 735076865, 628303013, 57821815, 281044590, 257062522, 328138316, 406968033, 177955781, 620646295, 411472475, 454647271, 61035658, 5764322, 506736101, 14921371, 738388271, 259702369, 771727834, 357032607, 296974274, 63556331, 276675891, 754891663, 36048852, 315827234, 49993405, 83894124, 208523947, 364516740, 793602084, 842626151, 7598586, 487329444, 32320528, 645361525, 588540401, 666522557, 307519701, 843041595, 310550237, 491741720, 693358882, 516294829, 961665733, 660674910, 730413262, 712822257, 623310143, 43927952, 94109738, 302714480, 642367456, 193460661, 846245654, 405174208, 233328175, 311344327, 966694206, 249784046, 48449034, 650156331, 715554637, 216784608, 539419156, 783107307, 797295186, 739932289, 581497356, 764422806, 140736626, 78161229, 772617845, 506100042, 993938987, 16367065, 69882797, 771747432, 243833454, 288170026, 355857926, 176656157, 330647978, 40613111, 268623801, 61783000, 35623974, 928971418, 492220319, 476730235, 306825090, 144436171, 125553758, 24846881, 798006269, 570582373, 305161973, 493571515, 6815311, 919835645, 392154460, 83127345, 452154469, 118326288, 355036093, 778480914, 712439676, 666022133, 574258207, 934261615, 654581884, 996685295, 439938167, 972137886, 261311048, 856880013, 136375422, 18564928, 707079416, 408607465, 245511502, 414777908, 63803665, 526836738, 768912071, 151544407, 453757663, 970690088, 164449918, 567006218, 467935317, 777290758, 989656919, 6859546, 870105898, 702894545, 911528517, 653012009, 428165313, 468895676, 339637487, 21174704, 451752439, 453213689, 607018573, 541340975, 635875033, 104248001, 88385613, 409142001, 819232821, 219602573, 70109749, 164259132, 164713803, 980755094, 909672094, 957519393, 726931126, 229171174, 90708937, 903123305, 757187051, 919868359, 43279400, 720906524, 744637698, 818656578, 859315224, 633687375, 109228342, 105700069, 516322475, 840278932, 106272498, 384202827, 499634737, 193903156, 264682628, 829500713, 704120328, 889534734, 31633744, 147001, 3613636, 757555952, 125610124, 446253588, 405591068, 877984385, 376389163, 356828715, 790843312, 98335705, 919276204, 316050088, 422947613, 25635871, 984962279, 873022511, 668642329, 141453264, 6427320, 130475015, 98895971, 473660619, 405686161, 308262218, 173580532, 183121236, 678389237, 104858247, 583346471, 235860839, 686554092, 996439834, 525513925, 125120308, 745034697, 766095867, 770111731, 612706082, 120912206, 794654493, 490777884, 189782375, 66897223, 753365462, 198873575, 441018870, 387534247, 74261217, 614464818, 216973462, 478892645, 994393053, 944660058, 869496825, 825839658, 756357267, 548636811, 683490031, 436104422, 532800641, 298776979, 124837160, 623671420, 43929620, 844267273, 731416451, 359240453, 46117276, 724272180, 430765440, 214085573, 944825456, 383739673, 28821023, 810412219, 244137103, 574316374, 350128243, 29819005, 1247382, 480100773, 585116290, 346525623, 827013555, 360392949, 519512743, 330887732, 810898473, 523572150, 547928, 588582976, 888924043, 764065696, 267181970, 526153729, 742645527, 634671306, 57484132, 309239056, 643410636, 968755390, 373800891, 139760158, 639211474, 134568256, 609020178, 53806559, 489921080, 385717334, 11888830, 571233149, 34421204, 650092640, 188959285, 769618321, 990504664, 239825576, 537407436, 386564863, 676356745, 382202690, 912242078, 917535431, 106130333, 98931852, 269267361, 908076481, 820230442, 974041080, 73765229, 290268938, 160685959, 829762445, 239779924, 179218227, 421902006, 967773668, 672588862, 651168274, 221282374, 191845020, 74463284, 364847720, 11165345, 488895678, 403061986, 114570990, 164172591, 279512070, 951120940, 45030147, 147891004, 772106675, 104435975, 925698914, 89316600, 463003002, 201123470, 327497383, 871382888, 416327261, 116346868, 775086676, 748588738, 739153286, 717994008, 382064649, 598363976, 953798233, 927577353, 428482038, 64025497, 509169964, 60992949, 741366738, 11378006, 214844771, 957866360, 892435834, 742909330, 615970603, 852261118, 617821276, 886888993, 471216066, 405929988, 336322714, 329922405, 800469233, 761235371, 833049314, 115262210, 123644589, 915395421, 541643682, 605207285, 298101848, 440957879, 396586454, 402887104, 627031051, 388332881, 423286131, 259449613, 990409043, 75115104, 483868661, 655781090, 270078343, 451589071, 462549279, 340138595, 453779779, 824944115, 596890183, 243096088, 317857852, 466258276, 16282839, 277496751, 695283119, 589664125, 311711332, 101906354, 890193861, 163383380, 512793151, 643426797, 990668911, 604057265, 629125267, 8580700, 704620611, 696964885, 94180246, 425668004, 138920216, 852094782, 293374185, 378586328, 127469487, 831811545, 169217472, 735544343, 532482335, 498764771, 276211799, 213007705, 496968977, 689818517, 778803907, 178431274, 738295583, 464340094, 718663323, 422492698, 389310969, 918929642, 722009647, 59182085, 418017568, 109340327, 856841760, 850587639, 949571415, 244300495, 245178093, 38289473, 228262803, 937240885, 473098785, 96071831, 376858066, 821559427, 869634256, 553242521, 519814707, 824502550, 721067062, 632446168, 558268745, 521512122, 83398317, 728405015, 608589457, 365577397, 224671332, 413765572, 784452033, 410078097, 841983806, 921970714, 42491125, 962122806, 537711565, 906419655, 269097230, 229317919, 11538729, 439973640, 401921723, 108711208, 371142119, 2950040, 872711588, 881211198, 166168321, 596705875, 108403477, 777876158, 537922528, 185724930, 169930979, 899204935, 210558880, 853695579, 422274098, 19502218, 626764987, 283031632, 402480908, 5945353, 697148970, 626382453, 995860583, 253422437, 693646497, 56924554, 155815891, 648153744, 432522145, 285778297, 996243823, 468033302, 956871303, 505626543, 683894106, 659210468, 112182275, 199112104, 541724077, 394915390, 414590931, 723611053, 499746697, 87014069, 824516968, 422188341, 607680381, 718257322, 576880232, 893027349, 845147616, 802854849, 342293678, 216211899, 287224389, 551498934, 694379854, 422363200, 827900652, 277045077, 388433168, 588472285, 35412051, 244942820, 232908024, 64584580, 521934630, 161884804, 165636607, 935511943, 263523285, 954899866, 438024795, 258145217, 561217657, 9828643, 917964613, 370395035, 92799513, 327589282, 224763719, 765420940, 847323269, 631741480, 665925631, 676787554, 47756535, 121492640, 733499604, 837360405, 335908410, 425127499, 235223767, 307068766, 732269678, 241983531, 37409213, 636886401, 84868446, 491977033, 747353147, 851030172, 31197388, 794614089, 200340826, 170217959, 419491768, 317276899, 435292911, 866479811, 966005642, 724790804, 797426833, 173486727, 864520498, 83963930, 111936333, 822162998, 868082553, 137684647, 236953631, 422300877, 910184632, 830066395, 484330084, 17019027, 729135048, 367810545, 554732222, 847936155, 181545846, 723940824, 298734643, 652615663, 857262625, 179926747, 875295157, 626431222, 787753340, 198403317, 262603508, 175412269, 670974983, 802843748, 688775850, 986184252, 278469555, 215126598, 820879922, 631985141, 96726712, 648145206, 387856461, 992672997, 210522201, 483157765, 854507005, 244423782, 801257671, 131532142, 363275089, 671413346, 830937328, 298261486, 87076064, 436117649, 129154018, 988028285, 343877808, 212101321, 547147503, 677728016, 319132211, 963561280, 429239018, 303935822, 696479051, 677736921, 842066161, 885567238, 412058871, 457880824, 582588751, 35933892, 949681221, 236945432, 943828250, 232444214, 547308253, 413934646, 216911206, 558075217, 543134619, 87028197, 539327735, 27338235, 449216211, 682824069, 854522260, 717380673, 280847898, 177888575, 114874327, 277421803, 643594566, 798751711, 963834246, 326979114, 603670382, 531378152, 981683582, 204984763, 13970901, 628811380, 164796945, 54554069, 65073262, 136520837, 428052725, 511459814, 356136618, 745053213, 709173298, 264039741, 510766781, 606215677, 520533550, 76743238, 166579966, 487725766, 928552155, 87529586, 311859760, 558917895, 230711254, 36550719, 640999896, 285558569, 840326500, 517270150, 396066180, 322465547, 252905598, 355849815, 851702703, 50976361, 564838014, 942207272, 160875813, 998703101, 281997827, 577577387, 503148725, 657508089, 385454933, 208364306, 60373569, 444345040, 376801009, 585018797, 838499672, 946754821, 848061731, 862272402, 970976423, 805890237, 432892233, 398899534, 907524212, 605172923, 696937463, 41788588, 569359768, 215127958, 533737466, 41540744, 622828173, 787255368, 265126446, 627450741, 384706228, 701598137, 329574379, 329151069, 576457410, 640527768, 830515456, 171092532, 756695825, 329828566, 23330086, 96741552, 782215636, 843716037, 32641110, 479858768, 877488614, 48150069, 955749282, 883124289, 55233878, 432452327, 759484333, 273701839, 543734510, 233350965, 542549000, 424923966, 243176247, 826369938, 800792698, 618942576, 591465454, 112536449, 38557628, 285545314, 613043048, 768248588, 519903289, 714149440, 901390312, 143990411, 549738230, 571012180, 728537998, 818121334, 778021790, 929293067, 325497046, 183071648, 774868843, 806024324, 380139097, 662982241, 925559900, 93887167, 497506449, 928301316, 324935544, 934475728, 635717243, 267358801, 772916716, 912099582, 626664081, 293514463, 142394504, 239955020, 73876330, 268318244, 742536399, 343627203, 625562045, 520136605, 675500647, 699014133, 614554433, 543247733, 368257502, 40773663, 765466051, 143238693, 327947127, 895933866, 433567756, 502503525, 985065836, 717506007, 337084464, 36076345, 573552261, 511498855, 415192237, 629748233, 652988202, 457527023, 112122047, 611780034, 295921976, 464607458, 281460681, 647364220, 734589224, 571238698, 684208564, 483563203, 851730560, 353364490, 940497658, 438942336, 365068187, 454406352, 882350856, 256389563, 889043471, 31779796, 317591692, 320385083, 533420612, 890180282, 828776415, 386337541, 574170123, 52547847, 605282184, 764525176, 3630144, 362136598, 99521170, 424968696, 355891747, 986314010, 776123362, 304024196, 889476703, 692710673, 247263792, 142774345, 931230718, 794778245, 639066407, 536981755, 958692076, 881313105, 926996960, 957054294, 269856518, 53577170, 92173210, 831791542, 367249742, 702317587, 8792379, 678240730, 778915393, 250862351, 67397385, 52065119, 575918572, 31505292, 686498791, 431053355, 159746074, 54402796, 377498506, 468756710, 941291373, 433173284, 875882057, 641197579, 16532868, 782732012, 420584626, 517509015, 364255107, 814471347, 316816485, 342953836, 304759290, 443566531, 934134786, 607674469, 548805002, 706162376, 278975853, 505940218, 19264182, 188620742, 348041282, 110451455, 579488211, 634652404, 441609621, 477117410, 12736796, 332897245, 116186313, 296480505, 134649064, 279167017, 922271527, 297871875, 237941574, 724770081, 535896969, 610040044, 785294497, 907978587, 883662490, 379714479, 41334267, 371326988, 282806880, 472850964, 234929073, 817761359, 505554347, 295630288, 519742665, 54418313, 482735909, 955744555, 385903085, 460772580, 440968937, 476077716, 115016417, 618260042, 203229340, 435901032, 713286623, 352334210, 626303116, 418038318, 983942275, 695435805, 167124811, 578776395, 540625019, 494524924, 720313280, 533887797, 105677935, 182362905, 100623744, 550053421, 427605100, 740269460, 437096232, 704560404, 775642308, 463038713, 666291618, 296070278, 1998823, 205330442, 912393155, 700574385, 485830848, 754983092, 382363159, 758090400, 594782906, 2400, 734396168, 106561398, 81735870, 707322883, 240481096, 704943783, 967209806, 871379207, 508763415, 68087488, 349422153, 98643097, 862538376, 312168966, 256791805, 963837355, 17037396, 171459683, 783635248, 855373252, 638965653, 946091300, 313973786, 637338870, 177405772, 852821754, 907254182, 586412178, 987141284, 67768549, 601906070, 62930873, 138454949, 838538302, 926639582, 173446360, 740972611, 907287040, 381423274, 339668858, 647764921, 306100972, 780132831, 108093818, 981761565, 478074047, 360519309, 361416114, 722219204, 374997416, 79665698, 587717734, 732391191, 245615818, 668018755, 514524258, 739690989, 342931827, 452144628, 159927635, 75728531, 299973023, 851968370, 942808525, 868441139, 112658005, 696722083, 723118459, 536276052, 62709575, 188126390, 762321328, 689670336, 510313914, 337906022, 993886920, 715281316, 485744830, 434674406, 373091905, 576771310, 549561633, 718888695, 333632198, 354860968, 313483883, 51039555, 936591776, 221358034, 581074656, 560475355, 78464943, 605233853, 952973879, 590349733, 304797067, 635244884, 714614303, 819591991, 634900773, 730314240, 570864691, 156049065, 787614114, 985513191, 490065807, 570231908, 170712750, 960987805, 874947941, 325346436, 96013401, 838393705, 734030921, 873466204, 368089626, 725146983, 770851292, 892496805, 311531581, 772137092, 408205350, 516525615, 682071490, 476207080, 373611228, 56873579, 590740289, 305557645, 38096685, 894523011, 366354894, 955532963, 746302482, 162421028, 184679217, 905635963, 435298253, 353972262, 768130079, 828354015, 182309654, 781760719, 815887529, 503732439, 301084181, 856580199, 818546494, 48288079, 869117463, 899540368, 698183377, 159564613, 981837679, 249425151, 352870487, 259413306, 932504656, 321200320, 895206842, 344759681, 747668406, 840099286, 874748104, 24845897, 453452469, 452878396, 611262290, 377155372, 763821111, 893602406, 74505220, 536280576, 910208373, 831102525, 753808264, 490264059, 692415496, 297973104, 600542591, 737519575, 499459297, 845928912, 290571871, 364950389, 999258546, 678958160, 213874001, 536475497, 516337662, 916622187, 193611046, 536555861, 189567238, 356137830, 477801936, 325730482, 831732431, 504124819, 434469606, 819270302, 82792672, 986095289, 31179231, 719708638, 639259941, 484743372, 782550562, 257846996, 620010177, 963544743, 958178199, 854131531, 740300523, 680639410, 202587736, 857331742, 250502354, 666693604, 962581248, 365808962, 470250354, 295209374, 58172439, 83080368, 87419188, 918757592, 379702314, 521079865, 560419727, 123571638, 691791570, 544517212, 335545328, 984805079, 860619459, 511915035, 343745683, 106901876, 28235080, 77736456, 38549619, 794615865, 630279760, 941977268, 399156559, 852340710, 663082038, 282274562, 897522009, 996408528, 486744544, 782421529, 452337056, 376100059, 957296259, 254593990, 561507941, 929396192, 332493579, 37259616, 301834014, 912928942, 938017399, 730241559, 548385029, 159110245, 365303197, 368919374, 110640567, 945154918, 470756698, 264331902, 62402622, 602911464, 426094172, 74517531, 429858243, 106009494, 417719734, 396864756, 750133641, 227392752, 809615351, 139964303, 573553087, 254639332, 479442429, 191814594, 496786601, 51342363, 822727429, 541218951, 258812113, 79128776, 553349917, 289590040, 12134915, 892068134, 482705207, 713597568, 446098888, 813159363, 593610974, 654822188, 675278887, 922213531, 194279345, 346941059, 431269477, 356706824, 708378429, 755758254, 257024443, 182566019, 223768824, 505073625, 98347382, 231339780, 451355588, 448905354, 294487207, 685618238, 66879130, 642466043, 133029468, 138574402, 736404368, 91659212, 609082023, 166987445, 751396219, 83747562, 726893953, 163299920, 664279075, 188564449, 220117644, 660684605, 705970855, 880317924, 570615653, 203953362, 196697011, 414028396, 108835889, 463285401, 158642406, 594380349, 408097794, 445940066, 266604838, 310508879, 414164911, 182505603, 879790776, 592490523, 280762853, 25307171, 11001480, 996061048, 135432241, 504743734, 510070432, 11143284, 163069966, 749287096, 901333153, 406267644, 791040263, 188065359, 325571828, 18088581, 868045035, 994298635, 317565969, 438082862, 722820370, 848977568, 351045004, 370248629, 953284317, 485590176, 692303493, 427588136, 744784234, 332666262, 278260618, 632515269, 72076721, 496421078, 485353494, 421662942, 211776754, 264712080, 907155112, 302746221, 853449186, 858566292, 821429113, 803608354, 660820423, 516803806, 276442489, 640468839, 459601393, 856696110, 455554035, 33119006, 726284324, 168213512, 519652230, 534850227, 389335441, 446608162, 391490323, 159317945, 60782794, 438039220, 553854984, 883591721, 656135897, 609483306, 935026941, 86746090, 678015254, 668805524, 621182102, 473012268, 502347463, 836320461, 936593136, 318404369, 840436426, 949592876, 908677687, 789645841, 933504882, 891668291, 914257896, 419836839, 403660560, 908515367, 677807119, 300044940, 45674675, 481004223, 740093695, 724850796, 419551386, 988369414, 769274579, 783666462, 467738968, 661464707, 861228843, 225945057, 549723815, 554144721, 700234174, 906587244, 19555392, 4091284, 808843070, 625192648, 405980304, 645708980, 950300865, 274658847, 277242785, 549330566, 823055685, 168126397, 546277034, 820591112, 745350055, 800765793, 994411156, 854382110, 969141348, 522805235, 661862664, 762305574, 100096985, 780429579, 106787438, 75672397, 4922656, 488533499, 669074579, 950669063, 97474279, 962985696, 216554541, 240482684, 628178300, 16384888, 153916785, 832409450, 645773689, 949552734, 410243892, 505114248, 200527771, 550352760, 358786881, 445830793, 624316549, 4102484, 177647438, 300361074, 231497652, 518791284, 1059777, 100401186, 680627689, 955715215, 106285706, 486510259, 12313282, 771336194, 665410402, 742755876, 525346292, 503311794, 145915120, 773639198, 27327732, 377623055, 238688707, 942579326, 732694492, 106720504, 430681223, 288291772, 901024778, 123175420, 535053947, 559726198, 206414933, 194668042, 772137016, 410732194, 826821450, 685843970, 114942212, 69962990, 205674373, 235231960, 139388791, 117352135, 168335781, 934452054, 865934194, 456527126, 713588198, 375433765, 364461240, 606610583, 335367086, 548848776, 807061050, 10302700, 354144889, 973684715, 689319525, 492181507, 86966933, 172130427, 810943293, 877210100, 650397778, 672622227, 707854024, 289912198, 603793423, 287458890, 619210569, 634345013, 367856269, 647554481, 652329613, 622666810, 488939986, 460433625, 195298772, 686055182, 511699556, 208560208, 904188770, 799727412, 651031902, 899880252, 697676842, 199027563, 21930259, 468751952, 677066768, 565335049, 460238949, 556648478, 960763130, 261595819, 9408120, 863726557, 941007143, 700330008, 131098054, 186697235, 270771256, 157596131, 654051695, 543068508, 181661699, 212999220, 14167148, 439423841, 529578556, 166839019, 132690019, 869644190, 722597467, 324897074, 394028197, 891210048, 919749542, 518973184, 130020002, 676971481, 22146411, 957946270, 646028030, 335596710, 124204454, 589489945, 802576696, 737659112, 527099713, 967613708, 780060223, 20063471, 217684253, 83263071, 892651926, 251517939, 383097403, 234624532, 519703983, 541773256, 263889627, 159202964, 527379814, 845407348, 986407067, 398085103, 302941472, 272857088, 735753314, 676345405, 801040575, 435957093, 322264901, 905310981, 651225061, 698025496, 687086033, 105946191, 807727501, 195579478, 461091366, 841003811, 849463882, 721746446, 824935868, 737137468, 67138342, 910670851, 211617308, 630312644, 892671426, 18464686, 524501938, 493290030, 256712016, 38388004, 337552356, 16135259, 610559453, 174538124, 351494227, 447340423, 370419722, 678644862, 614839286, 694690771, 787841178, 830795979, 78747111, 628145648, 366446835, 924023464, 281506365, 739008953, 947583061, 425974538, 158340465, 562979652, 398444334, 975572169, 442027230, 744951339, 783495652, 853018042, 96866257, 391809454, 411839547, 444665939, 733183907, 301338715, 5029412, 334266496, 785746950, 312127081, 93398445, 316789837, 496591133, 9086123, 150259716, 832818610, 391842061, 851504145, 601825447, 581542987, 736787591, 395938862, 588774663, 108995832, 897943190, 266501624, 936822326, 566287709, 196108121, 426700437, 379147563, 507378396, 104889000, 12551617, 389744695, 636360398, 70045406, 548142234, 359005953, 890152810, 262989352, 265022744, 274319387, 234496278, 943658006, 2587636, 679243412, 657940092, 486116036, 922557628, 833799770, 286914012, 896881636, 753909027, 2254299, 244480533, 993412922, 59196745, 190630391, 340634992, 913204583, 890480690, 388242314, 164689025, 468002245, 420851326, 466579486, 271029505, 494940426, 716449541, 548402829, 117632462, 985902010, 965613430, 518228321, 167535795, 151054354, 868707389, 46511877, 324993432, 786665482, 604039934, 714266563, 934808399, 408644269, 351233519, 642344362, 136642676, 677525207, 569720540, 553168968, 500186347, 79021263, 710470592, 327179434, 457938337, 513883621, 399299355, 111337486, 308537759, 443479964, 474689095, 463536323, 742862710, 88251128, 323884749, 474309049, 454529429, 931492544, 271528801, 814603601, 244937907, 19966316, 203838551, 233959837, 864241217, 370632105, 120683822, 297071752, 773269445, 932339420, 760709552, 387091632, 336727735, 363172498, 198312630, 492980219, 66825899, 131117604, 588619912, 164665876, 128657716, 336161256, 4099010, 599260226, 111805634, 843940110, 882420536, 684513140, 458788778, 621791869, 317476546, 601123373, 361414164, 510551376, 796075541, 62962582, 270077516, 674878218, 597759612, 312095666, 1798450, 890564183, 676590467, 343898546, 183824824, 922215761, 98785592, 907039888, 125082584, 72796322, 106213319, 73115388, 604249635, 680621824, 508283677, 131616563, 249837753, 292671378, 448527865, 323992237, 109180664, 709686516, 603300943, 574437254, 182938907, 919180455, 234397702, 421744475, 928683912, 419340127, 603003913, 502431677, 837814895, 308815549, 291117792, 817771292, 240007556, 287161097, 322527208, 200056716, 696263764, 376095653, 640335140, 397850999, 198263966, 674886770, 176181272, 711318925, 842375981, 954327838, 831482095, 887230910, 669939979, 108042495, 291625032, 405051284, 527388577, 265332754, 748901666, 159586651, 853169860, 926083764, 32661925, 421172194, 692606544, 530126998, 63530847, 706320908, 798220839, 217520675, 115410594, 822714819, 625583370, 216648311, 36204645, 234736451, 394172261, 785887908, 524533068, 141261069, 792323480, 4810741, 5260454, 610353862, 284881864, 100790927, 187966162, 918356240, 737457825, 372059118, 355681836, 620876731, 485513108, 759626188, 346561701, 196179597, 459687547, 804192470, 700283288, 386896427, 852493382, 971247760, 93712327, 326371914, 181943962, 848151987, 735631029, 292883450, 465610209, 962816203, 148871769, 819490217, 223719093, 571620827, 468787516, 987794372, 152932960, 910401675, 2128721, 654511336, 6590456, 520449156, 522170508, 147351440, 800440838, 675153284, 838179460, 814662818, 201593052, 577928685, 958191817, 698708245, 251171124, 46587663, 557682161, 883162189, 235765990, 962930541, 651855759, 458034939, 901315154, 265378920, 169166438, 906390384, 104492235, 889438008, 622798221, 573298519, 15931116, 608200480, 41332652, 257668058, 742231946, 733318468, 588153740, 359536256, 657575116, 696263877, 868131117, 347954756, 934434339, 430863112, 777779281, 195028280, 270709338, 319783769, 414820149, 984200675, 815483880, 212063502, 516051807, 965279460, 796256100, 238031420, 168864638, 873243556, 780757481, 760614889, 852727598, 276995100, 298826244, 582882016, 929243153, 496579164, 323453621, 983512777, 240151539, 919042994, 955402911, 745873226, 476810409, 460692629, 678589281, 561259236, 409331699, 753418370, 7027069, 2521447, 663746358, 556304074, 186052160, 535411158, 888243793, 4796231, 697108387, 909806718, 404583696, 152640611, 295941568, 272558634, 383732769, 615432369, 768445776, 569529696, 775678423, 969910309, 762084380, 149737190, 904215290, 35631600, 883559439, 973951692, 473914567, 325335913, 522398499, 49990956, 86052225, 579173450, 756822646, 346991125, 105166241, 366408821, 7977517, 94441721, 598430316, 892187303, 952942551, 758306675, 77870063, 68531674, 39402636, 154589070, 987808262, 34652284, 832132374, 265687873, 203461439, 5859146, 135877875, 58631580, 607983736, 971018014, 395659302, 138667846, 589384747, 87898452, 175397189, 398195647, 953111305, 114206554, 435771449, 468690304, 151763901, 153616649, 905014534, 324793865, 362425786, 445613971, 70410014, 533298662, 943109753, 99138205, 969078676, 613807945, 277557133, 346881415, 574211405, 812665031, 922992149, 906115989, 323216288, 193753664, 21384932, 849289388, 699755921, 735532201, 388896843, 605613584, 312308535, 270343312, 276794372, 687643035, 282534390, 387204739, 610883960, 80478173, 952747027, 899712031, 779890597, 940416079, 212535364, 465993297, 903680919, 576559490, 638147975, 790504349, 282452462, 219330066, 921103998, 436618144, 114296442, 456956811, 939406174, 754842594, 199237860, 910179265, 139744129, 781058913, 242418094, 417040249, 85508845, 297222575, 297437000, 497358029, 902245823, 397571381, 249949442, 86576388, 319900308, 774288723, 215536319, 649942813, 147284848, 141973128, 70347551, 184610680, 879107166, 841509306, 379245195, 618988757, 786519206, 764524300, 557642989, 646329794, 162797993, 153970635, 351600767, 39151982, 959166309, 544997669, 525343157, 182832633, 791349426, 726935992, 500404979, 301575127, 133181533, 475324256, 468232788, 456613914, 724204716, 33078438, 65591547, 579336587, 472094108, 874268368, 851934712, 33240127, 317442702, 765782121, 177948233, 261486538, 17243785, 685311672, 939633051, 534693634, 653186798, 120692524, 828420921, 262199739, 873340154, 287538596, 608103264, 261199967, 68517277, 937809881, 964679506, 259547020, 647555171, 928179910, 860749598, 573358021, 19165987, 441877755, 471335590, 747043443, 583633086, 171373058, 177876824, 65176876, 470893928, 954755789, 373797503, 424547386, 825704496, 410473902, 526582920, 407697522, 313057827, 48347387, 263645164, 256371113, 498594085, 770834335, 851903661, 12478099, 34621115, 472068429, 811393747, 186188077, 684187001, 123458061, 753011463, 845880727, 243384848, 339893253, 135359570, 898261917, 606757967, 534312032, 655421703, 588121559, 252376669, 135702799, 616055349, 214209433, 386005360, 538316596, 711867737, 851969843, 349015218, 167913513, 402660772, 230529217, 64162697, 655668777, 230439025, 100666049, 117290718, 466381215, 502209634, 229316848, 159600772, 58689895, 38338912, 190672548, 25922211, 62149800, 103534088, 815504856, 756521567, 493170839, 116426480, 714649447, 310038768, 318233713, 740794430, 787335387, 967297275, 227455115, 569908549, 923328931, 965296675, 628250823, 604408897, 745605140, 772453297, 887709382, 995635157, 620066279, 6383577, 245084692, 740425194, 143630662, 82756495, 916150692, 401428665, 615943405, 898236333, 942831472, 952632898, 985543191, 377349815, 424683091, 52285380, 245405143, 387426423, 351886766, 546919369, 929561215, 750172521, 488855888, 266124591, 838382624, 446361468, 532704737, 300166008, 172673305, 933657307, 544069251, 913634158, 686747477, 836779972, 297714776, 460081981, 675709973, 343826625, 258995138, 658227604, 847822177, 551704214, 303005176, 232605682, 733324191, 815720146, 843664435, 810828951, 888913038, 434055248, 29580491, 626007723, 69144178, 744787989, 107298062, 569453107, 887998946, 675226463, 848515632, 284107131, 784261922, 151274111, 718440452, 877480239, 702665010, 278388597, 17309173, 239706976, 248769157, 731538403, 440455564, 918547691, 825607306, 854335978, 774116674, 788073273, 182336989, 710596200, 280423224, 606609550, 146913188, 28078818, 61875958, 663368652, 498535041, 194470828, 813559028, 12952251, 312097215, 657785688, 479925992, 755815940, 186799440, 442857583, 151830564, 144269796, 461577678, 351357144, 744335392, 110644308, 936642666, 289575684, 81572677, 562433223, 745079003, 404272999, 809419919, 382541601, 196123560, 812596841, 372083132, 657302321, 445738182, 153734021, 746772455, 659587727, 749557084, 777161862, 105653640, 559518307, 319802792, 992640264, 416040878, 276828213, 509882869, 96328018, 410195495, 499598670, 326556304, 618620226, 136907283, 527549521, 58151195, 98684956, 240333860, 983665222, 17480482, 280503589, 868221253, 256345009, 969202761, 312178542, 944089903, 964396389, 12299489, 469796288, 964297044, 157566903, 364015997, 319103717, 817892418, 579021930, 13677696, 81862186, 552268366, 145225733, 388095503, 835391628, 899739479, 319232009, 741650706, 259035996, 472983593, 651203832, 645633811, 193106569, 23591317, 148115254, 310279506, 513486516, 847450668, 45400720, 489956078, 527481763, 765286711, 464628520, 43814676, 245624788, 456723528, 709087979, 374794217, 933408756, 660895036, 927503873, 148415378, 194248852, 890876037, 695777143, 158301504, 755698743, 602362757, 677017704, 657889469, 534924368, 906157099, 382047775, 68279386, 76621292, 604910747, 283898328, 453566602, 443115388, 31641528, 725517746, 591864580, 90808422, 969026338, 190882515, 416617419, 157758160, 881928648, 629865722, 800165209, 511282808, 898696760, 578525058, 371514080, 49131097, 126668129, 186068404, 427736328, 785459346, 23767989, 669984880, 890020822, 402534919, 69056634, 848663083, 974292456, 622632991, 84774312, 330073660, 705731053, 659224886, 564812260, 649993895, 385054430, 639330675, 494642764, 763088190, 86778686, 840781219, 895158191, 412067119, 450850376, 47635117, 172333627, 91271992, 788572284, 302401653, 800347516, 794689606, 700740291, 852590826, 49249717, 818709665, 647090186, 75581632, 316979279, 836540000, 207412402, 341122333, 904925442, 17970509, 804488249, 181088845, 457398613, 641738096, 521076958, 399535905, 927038206, 531581514, 89755185, 568210035, 264083792, 438147707, 461067118, 155435223, 398745882, 428485169, 841376145, 888486503, 433938380, 479839583, 236777894, 889109990, 767959216, 276015167, 923418640, 951730010, 534519502, 699641113, 380516833, 199557862, 174042508, 492490188, 857719861, 652378172, 825825681, 177262010, 773390060, 859803241, 685291053, 94900922, 280171837, 697390878, 904267490, 405140498, 631378470, 735534598, 949785971, 120002797, 309548330, 392018343, 432632349, 803442113, 319940288, 171938115, 750132408, 395291572, 274433260, 950621238, 953601888, 316724827, 732615007, 709398114, 357961232, 226435930, 463719669, 119004500, 926046566, 375367143, 456280577, 897363230, 321707875, 362916142, 546932742, 800455892, 354747381, 507935717, 103050101, 506884744, 55819037, 572143961, 514826014, 735798258, 355822775, 621152637, 744207156, 325624090, 461341348, 449653283, 572669991, 67842315, 908180319, 640268618, 214377936, 345061032, 394355323, 363272056, 583544296, 628143121, 464769054, 922713954, 15093013, 221899731, 759359213, 661226419, 394837828, 462854204, 102577214, 952013726, 29268988, 559480792, 163067244, 799746170, 143043352, 456394057, 613172581, 390756588, 603039635, 516751536, 537510974, 694536720, 324874892, 947905364, 143363324, 517069727, 179807105, 172570294, 510718023, 743288959, 791826781, 841717186, 885627222, 423890772, 577575354, 544384027, 820901164, 740283059, 858971381, 792995135, 936553376, 851461564, 782293872, 693233446, 461509240, 187624377, 791137831, 784374961, 203830873, 492588654, 308808656, 381023831, 875252069, 66785800, 928896491, 946135909, 295777704, 303528680, 59465674, 499892963, 736343621, 720898217, 136177980, 191790815, 963639605, 612089790, 553735257, 652603572, 279565238, 284811676, 802051791, 331824789, 420300691, 385533274, 128219793, 475295901, 297534144, 535879851, 573286487, 742646615, 714183684, 146112243, 139400012, 746368583, 566102987, 553941001, 264149160, 125034729, 515789662, 542392160, 56327781, 305689939, 737888971, 58360682, 35891408, 891629542, 171201773, 956858784, 481267569, 141956424, 18176841, 62093440, 291526336, 389045064, 104831872, 386939601, 992118669, 411185546, 899820633, 505699349, 396925773, 227287069, 567729032, 994329549, 928702396, 819829153, 349309642, 890228519, 672642785, 872605296, 368046973, 154831670, 633639130, 217667319, 165428127, 741162097, 678142049, 27491680, 453055494, 170509226, 923958955, 319488734, 623224269, 92762864, 248798156, 967761957, 998710547, 777616116, 196065571, 145225836, 134357071, 461790303, 576095229, 358107149, 61235146, 716113754, 992352141, 313190476, 511924580, 937347609, 41375478, 51775066, 530073957, 955109316, 916994986, 260081676, 709431976, 697558728, 962020390, 996588840, 141125234, 60590577, 966654833, 155357884, 102697907, 112898930, 8750637, 614723779, 24143598, 47435647, 117695370, 765745083, 467003640, 557086033, 931497785, 547286816, 599040751, 543317106, 204924491, 851852724, 550990846, 177871652, 549411262, 674929463, 693983684, 55598775, 933420143, 904858686, 771046057, 251906115, 479599854, 244319877, 271827370, 457121060, 804648012, 898996298, 787583321, 350011602, 769830665, 507106790, 328268200, 9504213, 246428039, 579847696, 483007996, 772344185, 388853114, 746161209, 937911085, 215218066, 881279093, 68265430, 694006849, 40111062, 709556927, 500066158, 107015854, 569466694, 604127736, 390527271, 855376375, 355085380, 31751835, 782308835, 314041218, 907981606, 103624655, 987998306, 35968255, 930621935, 675955959, 859345023, 927278408, 953540104, 992801210, 182504195, 383725050, 276520873, 246966463, 391205972, 212005696, 690702135, 186650932, 630398988, 481863705, 820015855, 442326399, 785545883, 841273753, 92426057, 449643783, 189886063, 138153159, 396886018, 739599060, 641413452, 24476340, 922971701, 893629356, 985437278, 586641179, 509379420, 555732712, 505009851, 671905716, 556584290, 289599284, 139764999, 695277572, 503815554, 909325787, 621298816, 293512420, 248179018, 383133127, 968070236, 872969345, 817987845, 652179350, 378207171, 34177948, 70241621, 113916537, 478378153, 908929536, 10166896, 699797025, 147754948, 656537505, 579940131, 664465798, 996233037, 593335905, 918064827, 2065452, 646937142, 394751358, 119065882, 485852922, 242470264, 347962003, 17657596, 716927956, 81373929, 835611828, 630184962, 482982242, 973654650, 976377416, 326248504, 664195339, 44276393, 501270155, 187746381, 427395652, 366401777, 588381632, 56236201, 405081809, 78399728, 496785917, 284161896, 490287294, 502107933, 996130009, 947183803, 136146833, 723951808, 181920328, 360592448, 439901487, 742041754, 557296007, 847825951, 511586277, 823812031, 191815237, 727731252, 925854096, 413775230, 476750720, 366711887, 792758532, 816942176, 997322568, 145404730, 602647887, 182558738, 36807904, 872052864, 315192563, 392354005, 260542904, 580706386, 141973022, 511510520, 107304785, 400632580, 243670953, 326191509, 411945471, 675713528, 526957650, 149389086, 179364331, 647778848, 138600071, 249117340, 546864927, 979349945, 67808872, 547041736, 512150929, 147077767, 576105543, 645945672, 127974098, 681299234, 312340595, 697427740, 700601900, 657776191, 267335493, 918940571, 806243777, 703088867, 742171183, 8951367, 809116931, 667411335, 917100968, 378292853, 743198626, 83595656, 673674792, 416694515, 170769902, 741094564, 200654720, 968594408, 38946492, 383169515, 803482351, 548200916, 287857019, 371909539, 410762153, 668456788, 257618086, 83225437, 222298408, 643990538, 219077737, 303315224, 840702335, 85003284, 129613337, 378185304, 769344296, 506312307, 296624102, 343197132, 318442114, 571254354, 800861788, 109491652, 730343462, 123117716, 520521008, 621304375, 352658350, 659152786, 651140117, 510695816, 847572924, 506365788, 462408197, 458119812, 745994505, 468807045, 896804386, 141332484, 923660756, 808135126, 195159726, 668797625, 520779149, 129325566, 27095726, 939400343, 206158841, 535088594, 139027203, 863703791, 498885699, 976596021, 714896696, 819469678, 1279997, 90365482, 903798754, 700268470, 870267946, 855640216, 39457079, 795480236, 707019362, 108365705, 612370460, 439961296, 618625803, 785704098, 629524918, 358669986, 353321846, 527198276, 265881583, 386829745, 91537597, 426036189, 794311266, 452522100, 893410293, 646958029, 978910282, 875048570, 816664033, 547776577, 148831325, 545281705, 181893272, 588376625, 62593072, 888920566, 313325803, 78359331, 381464578, 224730194, 404361952, 975407616, 464857567, 915028074, 716394403, 409223194, 669537840, 518372565, 916535279, 170618544, 364985000, 180346444, 534089468, 188250689, 110435801, 76054691, 325076645, 224336409, 338296942, 952959759, 298918395, 112708497, 28485961, 392773777, 106271402, 484200090, 139616303, 868349938, 124123113, 413287692, 961573763, 911750608, 182365930, 611526846, 188589527, 477527507, 540301926, 133540213, 749299777, 894949049, 971258674, 761492664, 249214242, 885086884, 429147401, 737787165, 982556888, 863846614, 115721024, 938927586, 612661859, 17091504, 267060844, 778239705, 458136520, 883421189, 721172740, 615793083, 754098139, 383566737, 688881149, 259641751, 456252274, 413316161, 562039340, 562192441, 657022339, 825491338, 364605250, 248927821, 204332727, 21115867, 510692262, 547664591, 27368304, 626054110, 453477733, 965426413, 585572958, 894198098, 845202972, 57197158, 582307377, 829596124, 77481595, 214923002, 488494530, 31254777, 716749955, 663408918, 639832850, 45551037, 88577302, 960775348, 675777393, 257870671, 430844645, 86126314, 325639211, 595215303, 66682611, 323588591, 898159938, 729765373, 11361702, 857244969, 630428198, 344005864, 481615157, 658026623, 97544919, 40361661, 893515481, 766527939, 424658384, 932286115, 269103540, 333073589, 784319589, 398354827, 197302528, 494412144, 583078520, 480617409, 518234867, 177659258, 214449957, 20963735, 900367187, 600820470, 320312511, 495578462, 283645598, 508062608, 628218230, 37482362, 239572250, 512315321, 725284373, 329358694, 511101447, 17083723, 181215734, 430570474, 156212125, 567079692, 566874172, 123539018, 103484222, 828681010, 167409191, 121506138, 267206966, 856688470, 56361382, 722745969, 847272439, 437591959, 319565600, 392298627, 481204969, 666056962, 782720838, 537508427, 625053504, 820013911, 505950233, 402501589, 441291047, 156588594, 646148518, 597632784, 38704452, 882438880, 182831039, 201861877, 214871672, 347776958, 498966166, 13991764, 186628637, 439574240, 838784693, 483188207, 755924290, 596112254, 802433472, 228400846, 664005281, 650094825, 506397465, 439217975, 305561355, 54217457, 600511626, 490785232, 1649907, 748198621, 645582163, 777058810, 201541310, 57009871, 579221951, 541039822, 471485806, 748598385, 615889740, 546860529, 330406932, 322731805, 982367741, 818703031, 273296534, 43035933, 657442515, 982472703, 481021724, 688884116, 607818969, 308607606, 703894795, 160710333, 448703867, 470892206, 675198664, 325443419, 329269404, 292558494, 923915177, 656166591, 216923439, 660414179, 753500699, 289755539, 620404950, 601398870, 757483412, 178843327, 983829953, 112013701, 866733650, 369873708, 169291068, 946381508, 723657354, 501733586, 765991423, 660672633, 462432433, 534678965, 960114105, 478030057, 576741383, 927244947, 568691151, 337841329, 800298708, 663841121, 123101591, 31311010, 68366341, 65165974, 600361210, 974624309, 838005743, 577896194, 766078471, 129390525, 818814813, 686624171, 551035884, 46879852, 317890314, 635665688, 487841437, 300655302, 78056140, 727070939, 419063024, 35461523, 869303525, 290644421, 158898529, 36591900, 35932549, 491065967, 449285323, 829778130, 761092654, 953459382, 141711666, 87519509, 881631857, 485437614, 300335821, 950731292, 580969588, 940335515, 874367637, 681873953, 110323914, 512987426, 793764117, 164114441, 584875946, 599719008, 343366864, 317639726, 286574686, 223429676, 109626798, 271232912, 805229066, 636524151, 399512727, 728031157, 183389042, 240731497, 832918711, 863223866, 701214502, 785514330, 757145035, 638327644, 486896902, 210683227, 709159461, 893785527, 714707413, 291065956, 999180266, 122549883, 830609307, 846498912, 16263862, 128743972, 316450436, 654045884, 2667771, 639740716, 595030690, 814156724, 30060942, 463033516, 425135015, 511412426, 399096923, 112030017, 385210716, 713407011, 974495556, 228396928, 803477439, 428612817, 340684355, 72070760, 661050305, 145548457, 41848067, 741469985, 596122892, 827433175, 420735745, 963880730, 738094746, 263156429, 449136427, 399451173, 342636970, 581766334, 96331502, 30635618, 114056719, 240169419, 751723815, 599882908, 910300988, 49418037, 967270681, 101121314, 143258377, 145181715, 158797876, 585227295, 23144662, 324317639, 685286511, 520305496, 509810754, 921733454, 50741067, 878047818, 736089818, 15273616, 323040697, 30108054, 15068584, 58471634, 578082785, 20642577, 286970666, 730836577, 607705242, 555594036, 504706512, 582579350, 83851870, 692968480, 594253565, 69355371, 652810495, 572877221, 12675090, 278374149, 532340997, 149499197, 715393047, 845510390, 928969371, 575979034, 680217443, 500814202, 119577756, 506931006, 101649554, 198617091, 518917334, 499063175, 492713623, 858866802, 797638168, 295227410, 882469394, 971018232, 551105351, 739936130, 503618350, 559698672, 618570125, 960008051, 863481674, 972823379, 160466945, 30720638, 445961060, 286895704, 458040928, 302542247, 325039416, 479504528, 931417282, 683967532, 666139637, 9991762, 187602289, 458596573, 818086442, 242830795, 122597351, 727616093, 123368857, 282625062, 567700247, 68607397, 914037843, 147696028, 687194905, 866005643, 978248889, 555420622, 727126270, 640616225, 548698971, 263975710, 329730182, 436205256, 568625402, 289566410, 645796652, 278832022, 139591237, 65490675, 665248265, 687048204, 351603338, 584771907, 502139850, 705085022, 194555831, 114214203, 729387849, 413271856, 982113843, 731114040, 611240364, 894952804, 432362002, 579196880, 788832870, 442757143, 787490007, 729317446, 961282976, 331606650, 388259442, 162412649, 693372406, 163655305, 737570121, 386030526, 265107968, 304725384, 812938031, 443370736, 434792423, 500793616, 592545986, 745377341, 719552500, 867609304, 601099036, 607883599, 998057841, 789056402, 365658873, 149088710, 308289341, 430274004, 345414421, 340356641, 426565857, 172990618, 732893980, 489388715, 37016057, 117067653, 809157265, 730000686, 576105973, 429487411, 318150681, 625812265, 913332975, 669343980, 205587230, 184749504, 393830158, 154991424, 576042862, 477673738, 833760365, 354231984, 814955152, 416337635, 281175219, 315628929, 67409441, 366689386, 940485182, 920961387, 788517102, 808207830, 274637504, 899500216, 552941030, 839681726, 550615209, 834768476, 175688311, 767414138, 891283798, 487869796, 779908830, 262397563, 97957945, 518098706, 153345380, 338971039, 994229640, 490068585, 946447166, 678583938, 75123218, 235576054, 513454964, 639419480, 77347963, 795890683, 159723456, 569050398, 623873583, 125638143, 253964077, 613120119, 307009781, 854050535, 523573170, 714981420, 735043974, 117609445, 873078861, 821395210, 416884431, 551841717, 920180672, 445619884, 661170098, 465506917, 364926006, 125389213, 170173885, 100910327, 977123424, 146573031, 970984521, 904275789, 489280726, 509545633, 596709755, 950887506, 493717384, 522869309, 706685638, 49693980, 599015929, 726781311, 880241855, 443163728, 571153042, 647921132, 793190240, 512532854, 282023390, 809801873, 111727026, 973177567, 613751497, 769784802, 507304665, 571643155, 304539836, 679568797, 161684763, 286298293, 447731745, 492590686, 400021136, 611999579, 768517328, 33340443, 197160426, 851347989, 382782348, 437827909, 49122159, 14858325, 107808501, 642702771, 820265079, 908044217, 975192565, 42740071, 301569486, 261609215, 483783697, 270845855, 953525411, 433334045, 733915151, 804122035, 837514072, 354035885, 42231432, 804131838, 533637918, 765414540, 585782503, 254571584, 284420630, 717248775, 823482331, 67706263, 420823869, 594456106, 854322358, 513724108, 796436270, 167121631, 277730292, 572520115, 387455970, 134510209, 530854230, 770485945, 137770742, 653489764, 911450672, 169076299, 973178465, 33325229, 583884415, 298279630, 482710605, 979898824, 578986265, 967704297, 927480704, 673929354, 17265624, 412209691, 483584233, 465444235, 91759926, 523183038, 671884341, 772191809, 241990322, 451363386, 23746642, 328530889, 100439015, 138197742, 454265287, 234010943, 235321965, 286354839, 11399980, 442681280, 395354176, 196387261, 526979845, 979069696, 384445778, 63922004, 448449347, 467370161, 12501931, 525437941, 844347868, 363993639, 123390245, 372779450, 438871378, 928702535, 922774227, 275955025, 909268037, 608648648, 851511781, 79820971, 477676219, 82909042, 61552992, 272303691, 453058165, 993740161, 566756540, 671139562, 700984913, 247814663, 988630482, 272647691, 617940939, 682088710, 929502509, 72528955, 228647483, 924385736, 784288807, 687504084, 493172243, 7410409, 859693916, 217420272, 972954735, 660448464, 532104048, 975942124, 229732924, 706527599, 571326966, 193850527, 237189012, 401193577, 127124624, 269099324, 68791900, 451538840, 158570712, 750202343, 316017115, 165738112, 557182428, 768177748, 856448411, 323678236, 640304369, 474279161, 29826084, 762921065, 87921973, 407928921, 436529019, 501224008, 486249084, 943991388, 946188406, 384685847, 231434383, 141741953, 680389033, 822665682, 444399901, 799183797, 663502868, 525755303, 487019121, 678607004, 413471252, 975144104, 600232661, 410453636, 125643759, 995333824, 625072704, 656856267, 29165491, 995396459, 698351985, 179153523, 264982931, 962247732, 216429303, 930388221, 797840513, 901444140, 632566162, 443659361, 147257622, 281229688, 785370406, 577252509, 731936559, 273753812, 76779878, 380368629, 644275718, 573230520, 493659766, 266905553, 243566667, 380853726, 114931170, 430751495, 802318964, 919127446, 673178934, 970375091, 907607115, 319313506, 587301254, 250999742, 258792256, 447081012, 468733794, 970626616, 897978065, 463664449, 51397328, 539144356, 728740584, 837285070, 851810376, 629764446, 787280916, 443292918, 298992759, 369282910, 864984646, 753903636, 795916933, 688922010, 838829218, 94284665, 15509263, 479376501, 561458676, 429169887, 901950913, 687756508, 687355375, 434569662, 253369819, 224996566, 841357494, 114495548, 886494687, 812746448, 187540856, 392036841, 127095745, 327286411, 315200890, 84297428, 157246599, 763142283, 637770490, 832677583, 483569130, 970479427, 450326407, 934091187, 381667328, 290242337, 745057995, 533205288, 596242510, 777546839, 412524307, 847153910, 72760249, 378715840, 597103228, 612559387, 931986257, 855861072, 820309088, 605509719, 528765490, 750796560, 311999270, 359922248, 382974881, 350854819, 992673088, 733944253, 437015554, 440981394, 417248658, 131439216, 921810301, 501725205, 620447276, 223802491, 281081526, 988528589, 478355744, 959214946, 696577650, 880824010, 404671473, 327341940, 32317431, 20632093, 91096564, 22818900, 508487342, 202034724, 57999344, 233609823, 985933648, 612612331, 447616295, 891828679, 353172084, 539546840, 161740521, 389477744, 976353332, 377773136, 633080644, 471328234, 747249619, 569689149, 549460196, 14799733, 898787794, 379352341, 877998726, 570107923, 194509816, 320007186, 463390388, 308607781, 654123396, 711851182, 304809894, 617155242, 724319137, 367406963, 739244270, 87910673, 746819934, 1178927, 223818234, 554632586, 170983226, 498414774, 197951135, 757131737, 980448822, 125626797, 487202159, 810996759, 310736614, 444506831, 140418853, 532051654, 446905400, 278577398, 527950683, 891820968, 92906649, 329905152, 473144030, 43814803, 461257283, 634758102, 405923927, 29220667, 680335797, 542156697, 477131634, 314185414, 71910901, 785906496, 252926479, 112854736, 678531333, 556628929, 741722780, 177925912, 175365762, 553537913, 453923993, 977490551, 397779306, 801129699, 191616718, 229632237, 442420621, 52927797, 79284149, 386709118, 113048869, 536654831, 421800798, 541397772, 595264521, 472694126, 640955324, 165745531, 154866111, 743678172, 46045478, 781287616, 216750854, 476770061, 706449057, 306686175, 234358938, 229869080, 172751777, 42956039, 241195090, 304152759, 834631911, 757190040, 920247127, 309562775, 369773444, 230361404, 305073218, 567408047, 840825590, 958762400, 107669202, 515797060, 476521963, 442557479, 249570164, 675065553, 483014817, 941495359, 116372705, 882279888, 758708275, 153093552, 391149479, 484238397, 718314970, 963258005, 691794246, 99793208, 6338400, 961825228, 947006026, 752473202, 161659130, 182496786, 3122622, 996353371, 150446498, 980812371, 754700903, 780407038, 802268842, 947780711, 530444064, 74369919, 902045066, 712443016, 672046971, 720031995, 922881144, 215081315, 2250549, 998252364, 831236137, 741383722, 149891404, 86913957, 721854944, 843451921, 218572964, 37230118, 758772720, 661958072, 554509729, 786751819, 881667279, 505374590, 823682180, 623172397, 243120469, 6539839, 557379213, 949475248, 551823191, 808601773, 315679851, 223597941, 870088954, 443794246, 393456967, 512552598, 57799144, 13360621, 669560115, 623026901, 834837175, 444927581, 876725919, 911501941, 134128261, 886925545, 930224105, 965896857, 292879457, 928914934, 141727616, 935680434, 51851171, 150396873, 24847966, 500915562, 486757577, 540019214, 55853489, 108621927, 737156343, 151923591, 973143029, 512270629, 327127090, 536883356, 185914975, 703842406, 728797651, 540188878, 42160700, 642880945, 216563644, 311624814, 151782577, 848252666, 189560895, 489896391, 606673706, 477062676, 446644148, 778873783, 814837387, 692753915, 298254874, 474282593, 590440383, 373937995, 28664783, 290759282, 478670892, 374793239, 152668103, 256529599, 361741209, 734661330, 629656470, 101372930, 398054724, 9636274, 700938601, 394375124, 447839531, 923825587, 883887936, 109190820, 73982244, 829186778, 16513258, 733663097, 709063354, 156942950, 708088710, 142442430, 623079224, 905067813, 921787352, 194898122, 756352724, 376358456, 427240693, 23008617, 121954673, 80670576, 730172577, 398047139, 880342786, 209505917, 803036246, 986832779, 516548337, 348678032, 697340655, 80870953, 336297845, 590579043, 343049269, 941476688, 479867074, 748968334, 548677738, 233667877, 867548695, 813565310, 133826010, 863315175, 65369616, 539960852, 127648788, 768336751, 879231011, 72685788, 681114404, 341483393, 618641504, 788543415, 360947072, 262332306, 332846017, 413342482, 492065521, 102755137, 791322677, 711313182, 890734267, 492150585, 125125008, 158457087, 97204061, 255896443, 21662273, 683490888, 302721519, 989989035, 355583540, 237787066, 561453197, 828929839, 164861810, 192138276, 690983548, 949279993, 484955415, 839515591, 681853964, 21380012, 295171078, 314087392, 40374860, 767869541, 545272218, 212003252, 694448309, 44344931, 294686192, 440648271, 20916910, 304839557, 442586723, 849649902, 504233930, 919804906, 243756418, 667790619, 94325456, 197539560, 839452643, 224087231, 627657281, 837977546, 62922730, 331375971, 656602411, 267306152, 646542233, 487011467, 420200739, 970374781, 193136116, 259551460, 56982938, 728288841, 877085417, 398787597, 645414471, 716729114, 522970862, 289335820, 849274957, 985782289, 330336549, 147831414, 466994242, 590239740, 321187523, 794232676, 275379993, 255595671, 414539271, 761754840, 226070463, 279749557, 732716955, 811049178, 267851811, 827283297, 286282041, 425923377, 557700597, 462224865, 110283250, 79349055, 755741525, 502338110, 381407165, 190857386, 818974661, 599482603, 786949806, 385480110, 59045835, 157508595, 182230741, 109034878, 663875278, 414664510, 834570591, 162208199, 201896677, 73169007, 775056072, 330562395, 815702053, 732871952, 386497876, 727735957, 297512344, 81102614, 64476290, 763774422, 917856597, 642712557, 805370903, 704418524, 661864000, 844613262, 821173623, 842084599, 945420882, 520178812, 773063105, 794559769, 799900264, 328083492, 257583309, 641450022, 959167493, 240352054, 746212096, 269576727, 954496482, 329632531, 968567750, 581413162, 219409399, 72863109, 860214367, 299985002, 63422574, 809876326, 780785206, 380595378, 25228291, 24290698, 671549493, 803549511, 862783237, 540871561, 973377335, 131801959, 11176116, 914264846, 324107268, 918567020, 789962631, 121197919, 618432354, 154456435, 739408644, 51975043, 757920761, 714140418, 873931170, 452598584, 292123373, 374357692, 113426574, 552896353, 121348198, 276598753, 814778153, 289076078, 917730154, 581892186, 288423807, 812924586, 436475971, 440860691, 915416455, 45972390, 781929164, 108115081, 67895699, 461145967, 400782986, 343751241, 982140232, 729460550, 607555884, 892556185, 481211205, 199154478, 941194400, 994988401, 21201877, 64975225, 331511033, 89723152, 533112592, 654513138, 382203987, 25875181, 848441524, 924504106, 550904921, 247212425, 400103200, 778578014, 946038035, 729967462, 792567330, 953244200, 527344015, 352484943, 669514388, 534144817, 424467032, 9675580, 352381485, 666843361, 44034870, 541153935, 816210145, 953213442, 407931221, 704341148, 48330616, 514704450, 144695788, 184403991, 62960299, 191076319, 644998535, 442223021, 618251637, 755340441, 356681774, 218131464, 2978461, 450513234, 56953981, 480386266, 918847154, 805051221, 979852035, 118357490, 602408901, 553500929, 402905028, 903200700, 608983836, 405465625, 884447450, 871320490, 574492645, 712721281, 545141199, 643122217, 455215864, 369286023, 829432298, 776340057, 746110064, 68400584, 694929667, 995903084, 849605148, 576780248, 297871623, 303644935, 959665945, 452916334, 504177808, 820330346, 672231643, 913320081, 153716995, 764632276, 778920425, 691358472, 484676167, 95821096, 273930055, 520933369, 204880888, 424771231, 200001599, 87544369, 812055738, 538360875, 389588008, 636287768, 84756670, 254316911, 135791788, 16698340, 595254671, 129897621, 756266851, 27945539, 246861100, 722185540, 970046209, 39132860, 420284908, 109249154, 621775209, 793429254, 477823184, 349975049, 467697256, 283134610, 7435339, 473904132, 703210014, 5884256, 493905062, 383020607, 422180150, 645579239, 284678640, 278157633, 843814632, 343164063, 614280810, 207149706, 630108890, 302060276, 142419270, 411896770, 454642609, 934066465, 896529156, 146798296, 504507378, 958966589, 304013059, 948429585, 392481251, 254044560, 282406870, 887025082, 902797934, 539316751, 942190980, 5252342, 999409064, 50427638, 104863710, 141514226, 197878183, 617105815, 108470700, 160936855, 571960966, 353857459, 970714138, 792518450, 588528770, 323896906, 677665602, 223925331, 645076183, 993628448, 730498993, 402415856, 446794188, 945405635, 448390446, 214111759, 74497214, 184142502, 813117555, 668871099, 783119305, 996142076, 226135507, 577796324, 329545370, 988992000, 73044736, 411465544, 200504287, 924848901, 177046628, 989795947, 130728192, 997915863, 865837634, 661184773, 703324798, 262713345, 28593644, 996184056, 142245015, 19508658, 37681962, 661981888, 492487715, 667415848, 305802038, 173225528, 685210486, 864388607, 225597345, 798535436, 449389286, 136315069, 32345122, 929895305, 147323848, 677431408, 435047674, 710520022, 917237286, 802170166, 596301180, 330141808, 966573354, 486292390, 343187508, 27664074, 619814055, 215127628, 714645534, 916021956, 760532089, 238737276, 472084060, 512188992, 27980516, 126239791, 703842483, 719181325, 872476177, 280828447, 998014522, 810156848, 9095615, 133505117, 964341752, 500824092, 699278322, 417738879, 821867151, 761302150, 273113640, 529451739, 7504309, 408075009, 10481411, 74292520, 747006173, 155794391, 612619410, 242364339, 795031449, 271265863, 827379559, 759365341, 794503485, 308729031, 924636219, 831682905, 132824252, 179956176, 292387844, 945907836, 211902044, 506896220, 192162599, 288497260, 908500796, 607926588, 963885398, 315597984, 494049563, 454462008, 437321629, 873175947, 200142483, 437404520, 925119378, 92051283, 561832924, 782446142, 461384531, 558199564, 594402860, 402201002, 156307356, 638004907, 731912411, 532324848, 186539354, 162472138, 865653607, 613957306, 734426270, 242605294, 708775200, 779255108, 780575404, 874213601, 886138578, 715656599, 418436674, 375892373, 576968504, 18837905, 14295565, 207589159, 437850017, 376276578, 166671335, 826636670, 487924644, 226221935, 906397620, 174988783, 792880388, 206995952, 816055216, 428250773, 817658744, 684993800, 82264763, 831309350, 458138684, 49574207, 270808604, 825151109, 148770538, 648239351, 633278693, 197076205, 518606898, 31609875, 962334258, 824591239, 997100439, 489774508, 951961539, 55532917, 659325538, 176288451, 918122177, 723005631, 253014882, 582037725, 263157487, 3226987, 796837840, 600602947, 440564985, 323683983, 370872857, 385407079, 522181762, 920803915, 964023237, 256516454, 584141566, 740520415, 433128581, 509928724, 308512547, 643674726, 549080964, 280856286, 393373043, 948578721, 698656914, 20219761, 576665457, 875751145, 409713218, 792417128, 269686833, 448714061, 144745134, 648564912, 584178303, 290170274, 144220609, 306987168, 40841974, 430455506, 566729298, 421638541, 778783083, 17289484, 665864060, 536448907, 126696701, 167350399, 266735986, 409472452, 976393432, 805632957, 504865996, 623642531, 742001966, 326660963, 855964451, 561728230, 988533789, 369677775, 761348118, 206908048, 285112917, 121948112, 10216001, 326844419, 371012682, 799016679, 499123420, 44877962, 598595131, 55759500, 51703762, 738088616, 98209656, 724348010, 801684435, 312997755, 192933405, 563251252, 77398632, 799269973, 115590821, 170009480, 2228651, 777714936, 382386619, 405782582, 777244192, 595426642, 916499213, 385705294, 349128092, 928141415, 827376584, 716968143, 603054543, 220710078, 143824763, 254336918, 21548149, 303017596, 532072341, 456543303, 13156810, 693132247, 164645665, 311352402, 438434511, 919757848, 804380068, 831343576, 281023015, 76366074, 881646710, 88084156, 227155845, 113409937, 627831359, 104898819, 103785588, 208051426, 210291855, 858669765, 68193698, 781562175, 194933864, 715413339, 537864664, 426704775, 884411200, 506387794, 538414723, 166925336, 22617916, 899135438, 295979381, 660818380, 259192009, 568165232, 887937943, 889030957, 659348010, 68200141, 638267214, 907878763, 449360680, 619530036, 486146957, 157855016, 113905829, 607392571, 356861554, 388402264, 467556083, 776034722, 528301974, 130837829, 917795250, 412425595, 298454172, 713167038, 844658626, 931759593, 596015297, 820499906, 934172298, 923506507, 935338128, 63807269, 551927209, 299286058, 131227394, 8229835, 940560522, 3897516, 160616183, 524416544, 857250389, 696924628, 190758067, 328678523, 693607113, 564963428, 50942004, 676453069, 344114809, 694022431, 283065256, 319127404, 197135463, 670145776, 884206417, 134301145, 850926874, 440868563, 88579426, 84462250, 364416619, 456465163, 591586491, 19282466, 491689503, 305745803, 227096210, 911057582, 752703061, 608129018, 94112366, 768584995, 924799472, 713539276, 423324057, 460020059, 328595831, 834830060, 482597770, 633175311, 258061666, 331582110, 275220987, 698049269, 937872083, 808084221, 673665839, 48404513, 270077924, 239756875, 795473322, 588518689, 116699213, 406211939, 897031828, 147768788, 268451755, 639755930, 677931542, 441388367, 695919727, 896599985, 79313427, 66418172, 556643467, 564347745, 208554987, 636279106, 826963082, 26550350, 9696371, 901847850, 17434915, 881515122, 500383346, 390089535, 984749798, 396253174, 415759380, 928819511, 972088554, 973904278, 939157909, 463790313, 949992584, 817227006, 453310501, 708966035, 126911614, 142165630, 617832995, 87855895, 157636860, 778557483, 345371634, 683055791, 557601417, 283904673, 16356069, 48070577, 131148008, 456728330, 303395276, 452301947, 334037985, 111029123, 799277775, 485555613, 911878258, 984390555, 925335914, 171133589, 788657196, 405548598, 674442220, 678980086, 517055793, 323572451, 624014070, 18426152, 909431046, 501316087, 448171002, 356807897, 385581497, 452925860, 373569161, 170959943, 739464883, 424322386, 184090522, 518569448, 50247597, 903418550, 631257682, 355273159, 785861341, 655523202, 677360557, 60538226, 71942065, 666553961, 632047299, 296725915, 170136817, 362924295, 900045729, 79227015, 959514907, 625586377, 204409131, 41504955, 920070681, 293610462, 868053309, 587403592, 123251967, 909823035, 722562099, 814085834, 260913298, 315275309, 635325652, 887606574, 591824050, 10866176, 906955383, 980401033, 407159229, 645749207, 287087587, 793280590, 738329457, 951690403, 723874569, 13066007, 191254454, 741302592, 141418861, 309603703, 32593739, 348501916, 446688882, 33767511, 61101429, 875336453, 188295012, 144988141, 259053529, 492472002, 515699210, 214493883, 825974050, 326253045, 649238666, 480881708, 191150855, 762075073, 102431005, 251903274, 143063249, 302665735, 130854181, 321900914, 191588228, 285659786, 927817815, 220041203, 338476609, 821745517, 425303663, 371361971, 698185721, 272180033, 808690858, 948477836, 395978805, 914443234, 411794600, 850922114, 925875669, 495965331, 561805058, 347943614, 926614209, 102974157, 256834507, 216762634, 821215423, 983424837, 22765516, 408606307, 503958400, 245838152, 39206076, 912296663, 373674169, 727157350, 154889862, 826965028, 850552234, 318042387, 76539733, 179953164, 766460899, 600536710, 402671630, 391187694, 446276575, 56226589, 689888919, 674349593, 633491202, 789352215, 787915845, 876168832, 686601409, 837876577, 268798001, 194426204, 540786824, 135135828, 668919576, 76883619, 741633843, 258900908, 563099011, 277110121, 670752324, 467625163, 95054092, 405971679, 308091542, 590842035, 228898769, 811342064, 277242563, 603558661, 190005449, 933646818, 45433685, 176901578, 567104685, 944899241, 549685286, 436015026, 689002326, 23537771, 499029634, 772409148, 151507492, 151831195, 706167332, 657400398, 851557021, 956966565, 674757458, 891160818, 736178081, 475097147, 760027493, 311706286, 232261023, 639073021, 987578543, 984777698, 492143358, 660014671, 637076535, 94909101, 868845893, 307224693, 67978032, 41056226, 159530478, 471890763, 829449685, 697338268, 748560735, 594457962, 697133831, 589748050, 682037935, 946108593, 957332888, 754300983, 358640289, 805186407, 122487671, 294074346, 506861481, 51235197, 703022942, 493306204, 544108656, 20932086, 458066090, 355948060, 860238604, 243390419, 906323866, 800076150, 178303158, 875728275, 509046953, 202730020, 930257467, 497925152, 58373887, 272328322, 523723531, 742075079, 921653268, 370322066, 351159480, 701164570, 185395549, 630859390, 127462678, 29158539, 523984968, 937956737, 358545181, 864582734, 697340465, 459421425, 329438551, 282515394, 642531695, 974865253, 945839808, 164945210, 272220680, 775888674, 521449537, 165054140, 237645948, 332836401, 662464085, 269596546, 991650543, 44392692, 820354118, 916960689, 688669540, 393110117, 941451385, 825025408, 518251613, 138426653, 531194683, 626059836, 118032964, 250684845, 698795988, 308653849, 70340524, 279576665, 587910351, 602087783, 856501595, 916601573, 815623514, 303315105, 256352482, 675645946, 22037997, 578954422, 249247807, 923330071, 791726806, 966052627, 705556781, 983110977, 928759761, 734691552, 132262368, 688188430, 664914958, 235271185, 84337379, 373664096, 601794293, 836096273, 370594369, 936981576, 177766011, 733684281, 189210313, 761804815, 218996981, 844736724, 410150254, 424302996, 288585305, 841056971, 384455570, 787260947, 254687351, 250075244, 317220471, 246365067, 132677641, 531083388, 675669942, 215494017, 578482797, 420714273, 263359972, 683669756, 542127070, 505061250, 289802339, 867018999, 592498814, 334100480, 165891460, 963288539, 281914265, 408655893, 275222917, 729631404, 415893908, 164779455, 584715018, 900483581, 207066285, 831282935, 171395342, 969355168, 972515278, 250691675, 45536958, 11009743, 67537048, 821719062, 21904973, 523395998, 605628861, 261855759, 799438646, 449983643, 771449356, 325407749, 358367578, 309998816, 512460490, 930037931, 495688263, 318284168, 510783652, 142620512, 2867094, 593363550, 925668105, 393009024, 941025756, 301656439, 163852254, 28912643, 158553237, 133201461, 46954060, 689945516, 911523147, 701178538, 270580236, 355407987, 318630677, 337564681, 205086901, 577977055, 540415965, 612178635, 101364512, 891430598, 37699311, 803594803, 554433225, 382760931, 792107028, 742350144, 646413636, 757969103, 262713542, 778523547, 300155584, 607976468, 452203859, 700998071, 76575658, 321148144, 659250130, 847525741, 911188245, 968515642, 345031058, 930559669, 713725423, 304805834, 151362076, 794772152, 927306101, 973483068, 836348661, 554015342, 336743932, 558982094, 743876959, 876121073, 879962923, 835723801, 105652703, 709542582, 284365195, 709446046, 256587421, 723975227, 457760420, 812363053, 932426145, 599981523, 191330384, 998420366, 165460994, 400424269, 540484158, 872483576, 436331635, 356362959, 866098452, 229379060, 51451725, 133945514, 447677920, 770499142, 678192075, 548478470, 526702050, 636267288, 483150326, 790587892, 773590396, 191166688, 858118688, 979223018, 497625795, 855001392, 125748804, 568063716, 854334623, 428730513, 897030034, 971478914, 809497246, 507930181, 221556357, 604926130, 213160079, 7911590, 614295538, 50770494, 371684224, 861306492, 861549264, 696718950, 678889581, 522900739, 812952163, 243625384, 575566153, 896174564, 221601374, 208325253, 116101981, 982602467, 196531346, 113409245, 528046868, 184299619, 975638877, 659795945, 633916421, 325663955, 518255513, 760304175, 914556900, 354467660, 909423416, 512743817, 330770917, 231859342, 226659880, 968620404, 439670840, 57705089, 280621796, 718586638, 874814543, 202059070, 903950529, 766471613, 304881685, 919190292, 163980363, 738272581, 511078708, 813038036, 130100323, 140116400, 34500025, 177004975, 205280710, 848336001, 6474910, 578879877, 676665586, 474422896, 693311722, 726587245, 407466403, 372820996, 646489613, 430931662, 610717070, 69019138, 897420002, 155438116, 688892794, 43855050, 267070466, 88719168, 46434770, 904940428, 806481289, 301617425, 814373108, 978102137, 657721071, 648890928, 902059810, 374682927, 500001187, 583004571, 680660479, 83476396, 952050749, 147142124, 667868984, 657981113, 102671734, 358784078, 406697934, 707360486, 79134085, 604272737, 802224196, 359174134, 905288041, 791473640, 705865359, 590596904, 482590074, 925952674, 249054790, 180335802, 805655799, 746382056, 323052014, 899967149, 32984016, 537312948, 132667091, 834672206, 67723077, 436776631, 720157959, 445584565, 172829630, 342353780, 210551357, 970813894, 476334706, 180353311, 628928452, 602225966, 630556805, 717321883, 392963294, 99908994, 608294323, 444400321, 606894858, 388718499, 645952890, 960802119, 815989760, 611081929, 515344465, 513745265, 478997037, 841229177, 81699563, 759153050, 290183996, 553585503, 258645917, 395561574, 838949038, 699144010, 400097453, 571410236, 742353342, 284590289, 724337428, 639213966, 188625724, 667340156, 905643341, 113801389, 129651186, 466292399, 49327126, 726348983, 580551664, 522575405, 485001534, 32732886, 492505603, 776219900, 413569230, 937198155, 581047538, 862338393, 735628726, 42344845, 650356065, 740921998, 476714290, 280044829, 390324929, 639307692, 277601448, 130490230, 981471572, 445515616, 55039966, 139395400, 992187062, 176428499, 84483977, 373695028, 866137141, 887707339, 972632444, 135577939, 144522927, 45395272, 932859467, 3304288, 596864250, 98607035, 330198971, 589425880, 205294887, 817961346, 898055339, 50025294, 237907481, 754693395, 886319703, 343529901, 358161878, 57883200, 481423241, 744249684, 479802159, 901964104, 26400013, 808880608, 382363714, 753484364, 646117930, 381035115, 562411862, 450448173, 376350285, 734567770, 158001496, 828150606, 191238366, 641198638, 311865738, 623345660, 588807770, 19064924, 860408002, 7215291, 160532920, 404924763, 25558595, 85980775, 641483392, 695974581, 443713208, 711205642, 891325696, 888101740, 652300377, 103451107, 132337129, 27502070, 948014283, 17432707, 631532195, 663291589, 616281819, 919043717, 757543774, 45245528, 302654374, 328556942, 936274297, 176231505, 151888113, 351931047, 364991243, 868237703, 747414509, 954295354, 662728395, 407927180, 701763401, 12120358, 233229959, 966364394, 378388142, 595958622, 855750799, 860593286, 48893470, 359440557, 37816729, 832386225, 659673076, 776627678, 442541449, 363031215, 801506551, 769684159, 375244167, 275585422, 956835861, 720893326, 156903009, 396059299, 445843775, 389052259, 340385495, 34824334, 561486049, 30009939, 372130312, 411525921, 36921145, 53955169, 711368141, 220391230, 782784952, 749903946, 834534156, 364576311, 480528678, 322418017, 645506118, 472648710, 260737466, 872832886, 324645168, 766133278, 925335001, 261580448, 487355484, 395538348, 117930219, 419601748, 475634067, 671184525, 276454446, 78836157, 638263388, 14933760, 533073125, 231288575, 948878832, 521165023, 219182772, 7816096, 58434354, 738294610, 601400928, 502409390, 139330536, 104265080, 760578555, 289141574, 666481811, 477865324, 765546483, 167353989, 281862569, 164836432, 326949968, 992394590, 484755863, 261339860, 884945072, 991226987, 849299889, 103312384, 676566652, 611663090, 500238707, 405924087, 434854045, 375728396, 443188028, 247909028, 681248163, 520568537, 746173706, 871012858, 123196665, 80291871, 231424919, 245773292, 120326785, 483431738, 206735911, 705494418, 258101346, 589081226, 238546689, 724522547, 455866600, 36884090, 208620713, 646876678, 636863122, 919820500, 962138799, 65024136, 938163587, 740764418, 771308598, 804687401, 371488709, 82211194, 996131667, 123631037, 179351493, 157282064, 975598215, 717449574, 814700806, 539394511, 365985310, 756708917, 888967856, 373365499, 305980342, 225348052, 929194678, 610705307, 211098695, 771819106, 263123564, 711998233, 52320014, 595787038, 273241116, 466831716, 385016640, 556643335, 726987307, 746062282, 736406683, 921367943, 785642029, 31326659, 145228692, 415137177, 737999878, 100571572, 178792177, 499739869, 186880494, 596467385, 970655117, 521656287, 462513197, 132620834, 387744314, 238651287, 694175528, 70184414, 519167856, 522521537, 2005858, 218767832, 680742007, 438257374, 76817528, 688452568, 895354733, 918866191, 7318798, 609268671, 186245199, 603551033, 489650150, 840125047, 296496959, 297448780, 242646618, 510733932, 590619730, 667547869, 358480680, 889204903, 623045270, 217094185, 235555929, 742665461, 408497822, 337635002, 965559064, 685412141, 459111378, 885024629, 460239279, 5275609, 167669090, 81206502, 111807514, 506352447, 141729644, 79543454, 417294650, 894618098, 132839841, 767973196, 233992958, 712019970, 100635612, 357774572, 117741945, 864258788, 314356190, 537802534, 686656167, 722712393, 81405732, 518593552, 722854357, 408540965, 254507342, 788627036, 158334603, 443525180, 620505678, 517229011, 809220119, 231034807, 134266248, 313223891, 328809813, 79067639, 300355335, 202040856, 371687074, 581700088, 849877180, 57248930, 791248509, 185817881, 671496747, 203529097, 10908228, 632668273, 434867216, 857392007, 107665785, 591137820, 3457647, 640008124, 656690000, 680937823, 679996340, 856842106, 131105789, 905995003, 73252569, 290244745, 844528600, 473319890, 602018894, 98436196, 264942163, 272478100, 946681686, 54353880, 822008960, 825171091, 137304229, 520827470, 470341839, 742372521, 562173570, 589302737, 22596466, 145674450, 444869534, 130331603, 965804630, 462788376, 593796803, 629873139, 113830036, 138624301, 562385004, 330492632, 274627018, 340715208, 53375996, 616817622, 420492159, 166972126, 980686687, 11864210, 678297785, 811962436, 175046252, 227458614, 667382936, 541147984, 514755933, 130355527, 392069061, 496693252, 733930050, 337945022, 509805981, 848100440, 18761095, 111160059, 737318808, 221722521, 482226709, 181496172, 793850136, 172127868, 751755810, 457577469, 763562719, 540089068, 225930282, 164908279, 39937272, 992340001, 917459431, 237904607, 66472213, 95176975, 562097284, 667616317, 172420928, 184147575, 505315245, 696228224, 647580524, 619570466, 912909519, 331284995, 548924687, 246699567, 564260391, 431793115, 537509031, 5092482, 970987775, 424366246, 560858810, 946022098, 520062930, 749339692, 540877886, 746572627, 114133095, 749392516, 16860316, 810445549, 301546279, 210908134, 972602750, 544317778, 922234798, 763715953, 51793920, 231693922, 699194813, 328712687, 675769966, 770860114, 21887398, 308181865, 113473133, 384811424, 944859136, 597676756, 941259184, 354562037, 962741347, 180379369, 758900544, 806343119, 146666667, 426910382, 532647178, 273309101, 829716007, 882377450, 432108257, 389619105, 234685509, 596005058, 109103774, 45512734, 763657892, 628550407, 377680891, 159883702, 145768788, 473122713, 762276165, 791794601, 496248877, 998262218, 58723405, 441605100, 972663438, 816136569, 961695276, 660726364, 149536649, 974695146, 46248201, 798781321, 982115087, 978781286, 603643482, 502812608, 919781707, 60725272, 387210601, 618470497, 508235175, 573015316, 63599787, 592138958, 500608861, 818917981, 991164358, 830669907, 403706840, 985518779, 626947546, 308275356, 929851297, 328485766, 986034355, 709529008, 545511116, 675471861, 185170364, 68369936, 313645790, 455534672, 537874596, 836721303, 768564597, 971112960, 431213377, 86979324, 69877533, 67043743, 615570859, 162488353, 915923213, 24833089, 737741332, 580491192, 128691197, 380957538, 862869118, 807503123, 355051218, 36031037, 508249730, 4497248, 990922003, 489594474, 327302059, 468795969, 12613873, 183490612, 776918793, 814735371, 888471277, 318111325, 856392012, 703498871, 585142103, 392008124, 643649758, 731378783, 601952208, 314300299, 463033312, 574278617, 123099244, 509136559, 22539099, 13413800, 745656969, 928771153, 394531939, 783924753, 271982955, 834261322, 945961670, 398133718, 291377161, 731914184, 355139025, 441598564, 175150545, 509435909, 906650728, 925837964, 277877668, 816521268, 113311795, 161729781, 792107286, 525434849, 225182811, 986834893, 508659945, 762347912, 890287352, 584048637, 907244699, 118205212, 268103601, 171416042, 79742277, 552115615, 482979511, 593772893, 5068208, 836135129, 422920176, 20050101, 383807519, 419879565, 455943056, 651636323, 758753484, 411395313, 292445010, 704600300, 420861918, 799379751, 449538926, 81295305, 928690853, 722011020, 446697166, 47538366, 858989284, 198063068, 462564550, 183519410, 779940492, 205671995, 895155875, 529054893, 446239514, 199157217, 518257111, 396114126, 68563814, 874921879, 736323592, 441584109, 65732508, 348190076, 326245510, 226414391, 225689536, 148128704, 940827687, 294773386, 379081324, 871315023, 356943149, 133004656, 737776189, 240591746, 11156653, 240973618, 955292202, 294499230, 359599684, 496133300, 833820808, 783928834, 294607360, 736858450, 431169489, 401522594, 463403692, 476888642, 471793753, 606662505, 423636130, 433149478, 136686782, 390296992, 564776675, 418098783, 146889284, 537883423, 305493804, 785934757, 187660481, 930545770, 983250812, 925917079, 513152098, 532050797, 805380179, 908309857, 345686684, 125425291, 266242629, 62889205, 806457212, 945499116, 35879420, 434120915, 682346695, 526255071, 539963819, 596174073, 631654580, 167180270, 730795208, 714868912, 364768101, 309628853, 827484660, 506982923, 791570877, 159532933, 475634968, 172958200, 526137436, 414835473, 593935992, 232124616, 354405078, 730163246, 38665014, 147711594, 356481243, 935325489, 192349232, 130024821, 488412762, 989165625, 977898574, 284523049, 89357299, 237356403, 1527762, 373057482, 345785965, 673141922, 664997469, 9845404, 239495077, 68845102, 357835869, 721149139, 927753384, 172578787, 245734052, 743209878, 417669399, 826515189, 875916799, 824755926, 90763637, 950111811, 415328260, 414756725, 800640977, 680127208, 102774729, 357160509, 338445309, 322849954, 350631204, 157135219, 982150301, 642257214, 214308629, 726715764, 436555339, 561180237, 253118780, 186774497, 631240209, 861612728, 962405460, 310351171, 474040803, 199609960, 57756402, 482733128, 940916274, 127583600, 266065977, 160253772, 966547415, 664172956, 508345748, 997741474, 604685218, 443873540, 318438316, 919802939, 592839954, 831450338, 452756860, 74430138, 764054924, 108425985, 688645583, 736918715, 521394149, 325645175, 374035690, 827944461, 430475951, 179184865, 481158399, 970058432, 93520511, 97257965, 137602799, 748667640, 338327387, 69368916, 151879537, 532321217, 995156585, 605886895, 173454269, 894405403, 275909606, 696258561, 551794779, 134088996, 921268720, 755899823, 670951680, 660248940, 571176837, 318654231, 729244383, 89591999, 76668422, 557667945, 517952584, 693197222, 142054279, 824583944, 339182415, 902197269, 578170545, 517071793, 107756137, 910319728, 108186706, 652517552, 943389504, 679664199, 351134214, 866141506, 695090336, 381582395, 241302379, 512158508, 498921022, 467515942, 516966699, 97958864, 584039673, 92911284, 421915439, 932381060, 227247835, 630256980, 755597990, 300662031, 834880969, 502878425, 878772216, 382464202, 410564427, 882937539, 774035424, 213214061, 955445835, 606560688, 165827270, 118841858, 427876392, 426707812, 285566898, 17592272, 832166691, 848426341, 10485695, 948850914, 669931590, 776991342, 743580684, 125091775, 211311874, 906249638, 67900676, 55538096, 251908071, 592576792, 442510483, 418665084, 59821538, 352956732, 706234830, 402660839, 744793216, 905542122, 182797697, 369020518, 787948633, 720842438, 405663671, 543045805, 252867354, 773087928, 410072448, 888168454, 361539234, 796373583, 460281799, 948544634, 89122264, 171737134, 790003949, 405745833, 646528811, 535999454, 728563231, 47172722, 934568870, 505574159, 499248629, 730208718, 777213835, 160939827, 437210596, 296600448, 475054581, 461567173, 908728238, 706154383, 690270470, 923797952, 654168770, 824801377, 590454439, 324316702, 746059699, 629890079, 148859080, 289153751, 542504294, 853884878, 614867754, 396440219, 47330225, 193068917, 732115039, 85581227, 655192194, 627934413, 620243179, 245329978, 289676684, 127839270, 714073460, 382362263, 742014382, 297125342, 889770224, 920630135, 894601449, 487107235, 354687789, 715960342, 370469297, 732283027, 125082576, 953829476, 997853643, 454594146, 470999420, 378181663, 519186829, 167145679, 988218119, 406512976, 570465032, 141144173, 8314213, 979870996, 173186069, 322376416, 238544927, 460199310, 286894443, 517468391, 117630339, 315988658, 349101085, 364918043, 990873650, 12654796, 488556705, 627482707, 603343210, 460697828, 497388155, 439226955, 814342221, 250171005, 892520764, 855103887, 454432090, 657234319, 207140674, 528561702, 319680754, 130833035, 593665384, 883477392, 968904449, 646557904, 186957500, 684109809, 592870837, 777771883, 776795938, 789660442, 236073132, 349863627, 532213347, 927142953, 643496788, 332154261, 907340648, 782908281, 470654992, 920993589, 847847271, 121873692, 332850311, 338862278, 578878832, 106135192, 571310506, 798057182, 335420646, 619715819, 34820268, 465354077, 223517842, 113369403, 38206018, 815773300, 353944934, 821714651, 535479512, 138563145, 997699381, 143316945, 787507188, 758688684, 493805656, 729220263, 39906807, 970813322, 733748031, 341646503, 471093151, 292451775, 188349683, 736618190, 464505831, 389625868, 625361156, 991443089, 878151510, 55888442, 594152939, 12494394, 339373325, 958238469, 357084495, 541280896, 556350947, 865290887, 660898378, 890066179, 637263677, 862889353, 890820908, 599086340, 394909081, 273747662, 446477613, 889416404, 653482764, 874938425, 115291359, 58732885, 533469315, 845346093, 310247608, 151972838, 355275116, 583381789, 201815586, 693824831, 220353018, 25968025, 157346556, 568993587, 745767988, 232416049, 664894252, 423906825, 751886640, 658681857, 579195005, 170490400, 838846573, 205966259, 278316866, 939319474, 773795755, 117211327, 446302078, 719363665, 111195129, 108951313, 975780548, 997663798, 596688878, 186611091, 527306372, 950529752, 275895953, 53409520, 890970779, 618243460, 200925466, 536279771, 997873588, 187702893, 861936503, 997488926, 246271163, 599166785, 786380875, 802187158, 470812596, 470567163, 430011078, 808624719, 940715203, 95160261, 774261935, 494215562, 665245754, 289552077, 128092541, 938645517, 749823126, 309402520, 227027475, 894768091, 120245482, 839935764, 721698797, 165846899, 96538926, 897092232, 58377861, 854437709, 734047029, 54134707, 241154724, 739668748, 672913792, 478958172, 229884339, 706416642, 219066762, 987781653, 166133913, 209825807, 697715994, 330779143, 547627419, 704444116, 152044971, 754197169, 214086460, 871917310, 274437444, 410004769, 214828452, 895936299, 649942205, 778398893, 411566421, 654401003, 887756481, 952211613, 272426064, 739438646, 864260045, 395060153, 651949643, 975774067, 648771106, 395611592, 609966369, 871801698, 778167750, 916317463, 512011068, 666109481, 907972724, 11768846, 553132196, 550624824, 198957339, 425252375, 35595768, 577997037, 725911448, 693563862, 4937500, 217323776, 783574472, 581035139, 697595682, 541928388, 207331809, 10528246, 816036631, 258632450, 36189794, 205269194, 604048001, 284862093, 121100828, 739846682, 883391181, 642894820, 669783298, 227374927, 918462784, 696525062, 409548938, 27397397, 524570189, 330278584, 69438076, 774720248, 190321577, 744040611, 739490484, 903941854, 854955435, 582335013, 214135089, 104040531, 5259239, 770918722, 478552077, 611592488, 210109870, 127206871, 655958553, 585914036, 634870727, 740693186, 459438391, 615806311, 317352958, 906714971, 472600376, 214328363, 901165102, 246550359, 495070362, 491992279, 846202946, 266907329, 828421802, 818737528, 952886501, 189269502, 896928831, 78344931, 551986206, 453316774, 346665261, 797451291, 395231582, 260670970, 883055220, 774812666, 627056990, 686018843, 173843287, 142297782, 603805165, 923471312, 527338922, 986850229, 645773593, 462806468, 366711049, 858404732, 666246775, 19728500, 294911667, 149831492, 351382310, 669751995, 186997274, 766824519, 72249024, 44430075, 541375988, 949432299, 421180942, 872378599, 852716712, 477806186, 303201264, 450189522, 180176349, 617860906, 269029013, 807272582, 109078354, 549804112, 504483761, 570220036, 961246351, 95140550, 521457389, 936128962, 678132915, 432014259, 840953601, 304212276, 28316936, 983680213, 715789277, 991105077, 785147537, 419999752, 250345589, 722605857, 628411635, 627622318, 37703820, 196082842, 818863697, 120001885, 172838216, 180400384, 195249769, 658073595, 189541805, 973996132, 465349113, 966926666, 681566038, 562364524, 279661709, 993903829, 502226901, 525158704, 180172612, 731044762, 491604204, 9733311, 160829924, 382645562, 673690856, 256056606, 865875092, 704435027, 316220615, 437576362, 178235074, 876840393, 474872524, 230140121, 180873059, 14121867, 11044191, 125982327, 111080628, 830931203, 346654760, 381636351, 182088576, 939211120, 383740565, 955571578, 952435280, 536286369, 139192642, 541100978, 902873727, 866002586, 359274987, 914634977, 151081015, 407103355, 261833189, 629620720, 665719100, 998463848, 181325618, 872779980, 867829061, 422441638, 495725118, 592032780, 417970460, 579928173, 877817931, 106290997, 717269259, 58900671, 817418104, 640380163, 567698976, 437298919, 859490629, 197598389, 523660651, 222472653, 612611145, 271865376, 693853853, 208104193, 156108307, 893739819, 67998836, 431898785, 963230558, 550080832, 457933133, 471825027, 563964247, 967407438, 658896042, 488310086, 983488917, 683191107, 190417544, 87324813, 57241675, 226741342, 12523918, 756559064, 395024800, 429208749, 52913037, 503797309, 17879225, 354032587, 359914191, 598191715, 583338074, 85104603, 836253297, 555151306, 178505156, 27405871, 473720620, 475452424, 535930132, 613348063, 812280582, 436480941, 564624032, 35462251, 928753687, 682999495, 502946546, 300705276, 91933735, 194048327, 43741771, 465567751, 297755975, 729761980, 782762318, 634039038, 233419873, 858630959, 461863856, 354375560, 224080945, 681538862, 141580372, 951561499, 807826395, 395103570, 582544384, 354794434, 784275095, 938822298, 890183321, 847073222, 852285850, 760197151, 994335122, 307821300, 867574159, 25033177, 330790694, 252964, 229801110, 653647795, 665888536, 726104709, 528544429, 979057446, 228588398, 120373773, 935331104, 520646510, 949894265, 176545213, 501395480, 588029964, 45041616, 969672256, 986313592, 96621476, 807171205, 599046826, 492871089, 475801315, 867010667, 301250337, 158944538, 939039233, 866027003, 323942634, 95505376, 867207722, 589580336, 424295263, 419535757, 169073176, 558294184, 256464261, 820852558, 48074509, 941350327, 719175369, 958584502, 79571628, 573363434, 673003058, 896671424, 341127484, 500237726, 550658291, 724734946, 778747581, 324791692, 914014994, 19034269, 516628774, 464399592, 101548733, 678702314, 796487595, 480099257, 817185108, 544518124, 539625709, 179953146, 768581955, 921985621, 565873045, 145973515, 551707100, 440641639, 67102758, 376529953, 994072568, 672757942, 165144321, 247230159, 319740056, 901370681, 549904836, 512221415, 234924409, 960394843, 231057882, 257924299, 760585219, 874538056, 318818325, 484671725, 188430217, 16383767, 374829728, 13994853, 714106481, 852568786, 549043724, 462491242, 218596678, 216563368, 754994128, 288992621, 335176735, 603469568, 900906633, 859908452, 726452161, 690766078, 690623844, 3948411, 262217984, 211791453, 230830478, 328037297, 371781464, 298281271, 526469479, 464900742, 898678115, 525921895, 875706489, 571867960, 809757355, 640392801, 314182298, 408264483, 709739868, 272625843, 804220068, 997829449, 820667808, 984975374, 434094896, 472843342, 988246858, 391824861, 942211323, 962949687, 609588325, 464205437, 159089412, 497778439, 150595707, 801298767, 379488945, 433605679, 181123815, 401563763, 664164585, 124955801, 919193945, 986232291, 961626928, 152728533, 102282651, 507765658, 94169795, 929683763, 659437654, 405719841, 931028985, 19690189, 350954787, 599495668, 523495309, 211663620, 376290070, 967172594, 938885688, 625692791, 551453640, 95458749, 331237285, 779413563, 102917623, 471574875, 2990259, 994346371, 950877142, 684969702, 590754569, 809556027, 944601190, 723121467, 732327085, 261683588, 298568299, 733176961, 180637927, 388881275, 652410463, 196052455, 394881676, 12409119, 546500116, 429695008, 84930751, 398810167, 672366618, 109294807, 758703386, 291691830, 779401424, 534995317, 861826117, 235394545, 115705260, 935581145, 692060362, 471005276, 833513897, 92224663, 942919201, 846986509, 858722058, 853214023, 20288554, 896909347, 705814227, 644941594, 501149299, 139942743, 918974085, 941879232, 907738629, 381885920, 936949593, 789623534, 831859236, 844461341, 244128135, 777521232, 392369366, 519717987, 196334833, 654043504, 800316207, 381708954, 408502590, 364760741, 295798822, 471704797, 157224673, 395988323, 52785729, 947755677, 207435779, 721988696, 517858146, 981443381, 967816489, 771388873, 168961272, 813931488, 798892198, 145383069, 549099626, 368304867, 685290692, 548812448, 346431389, 327340608, 195470042, 501823481, 720978970, 53003467, 188990822, 67661121, 995352031, 871792734, 558813346, 292858488, 897358336, 388871295, 715908016, 955842869, 42133877, 848011477, 598437631, 472523095, 935212530, 835856962, 761930488, 425755983, 9681735, 945728646, 624857960, 876623440, 297924908, 141609281, 305202769, 783074460, 592483743, 483650675, 937134075, 929529045, 453049415, 332716547, 25891933, 43298149, 620189402, 740182449, 804203390, 961154528, 485205369, 543414088, 911961502, 384008312, 636079646, 860103778, 268879414, 196047970, 532726830, 172773709, 709103162, 383189862, 130184298, 608583098, 941799322, 55139063, 37863988, 542154321, 825326096, 491983144, 692907788, 993944855, 871788197, 519285221, 934486987, 549449865, 4136852, 662737433, 494628227, 336108695, 681379274, 215548536, 971637643, 653171883, 500888915, 156376863, 833319174, 901418676, 124658927, 890058062, 681677509, 49856722, 109878491, 146473580, 988813651, 502367556, 710549523, 173844269, 565962839, 508734931, 656755234, 61285755, 449760921, 58444106, 834322306, 940832309, 674443005, 506473316, 148902852, 219085746, 101005201, 851116813, 76998774, 159569609, 172637413, 346744429, 288354669, 737034367, 795616791, 660786867, 946349502, 469048460, 924167714, 633339066, 672676287, 583537173, 46853181, 436623825, 381270508, 981342049, 552166197, 216744960, 49924696, 821442705, 91565010, 818880137, 749544345, 6383306, 805383169, 36380130, 552742605, 665308867, 889021708, 320737691, 984907707, 989295754, 712399271, 966922214, 651618501, 760600576, 237790158, 541480644, 352873768, 212185443, 856638777, 731997101, 87243773, 363863470, 317091219, 868823383, 22041901, 776412125, 866381354, 954261885, 925067148, 76869787, 145671420, 871346165, 44628787, 184775451, 209128476, 970342343, 505298592, 891518382, 437767620, 425395266, 573576230, 445213238, 338394821, 493976750, 840066155, 191063403, 424038545, 823052804, 715153154, 60456180, 688565747, 109490869, 997141523, 100854523, 722908753, 545031224, 780775759, 801197772, 890615662, 489644866, 949703683, 888629689, 592122628, 613528642, 308896844, 531845230, 452357088, 836630425, 118629843, 427925568, 745084968, 852691336, 555071334, 978013444, 483774537, 487160899, 868906818, 142050346, 341462793, 351128587, 323290699, 306523382, 208828127, 185375249, 862042214, 125334925, 877453024, 310587611, 583690444, 43994531, 30838351, 973710608, 93936280, 65494224, 3059885, 549639664, 947295929, 927061134, 482091306, 337345301, 386979688, 417058477, 250988759, 683397464, 873979134, 140318905, 33763854, 465597417, 717122705, 185107928, 50901857, 639268474, 637173356, 937258188, 16477705, 455804326, 380687028, 36424122, 331699849, 926817318, 25695671, 744359055, 680960917, 608377789, 319923038, 194026819, 715230264, 103545495, 36101888, 173932070, 376050809, 780598189, 656912696, 242981346, 614656577, 473697773, 523181652, 112677835, 702589236, 162765979, 159950981, 700608055, 811710652, 741812727, 562652964, 155836630, 711650664, 726208376, 307306791, 381398893, 469695914, 453779125, 782779644, 779947304, 561386081, 563659010, 467524582, 349788050, 170778200, 4798427, 70060982, 827058942, 549783419, 843405480, 597589910, 758510542, 729927733, 983758977, 608240097, 368453686, 398547407, 652349651, 138514395, 280901268, 998194101, 306671114, 237518443, 80603323, 64722467, 189117823, 74056010, 866272455, 57054978, 174427826, 376469395, 366106917, 414626613, 936557367, 779780365, 72767552, 215732257, 356031807, 431284292, 430455360, 231451542, 832888694, 650609490, 609818692, 549688365, 19463480, 847723999, 525224611, 247519092, 862926659, 105574295, 889755444, 540676380, 617771682, 211357184, 205732607, 457504712, 260717587, 889434271, 205709759, 344441039, 129472903, 133437551, 847553136, 147089818, 704646622, 718128711, 588113305, 470295204, 378923226, 837622064, 160341370, 883110304, 956199565, 863899603, 386961488, 364735922, 856703585, 699280985, 340839047, 287812156, 50068143, 25493241, 953450383, 526351344, 617855218, 677721453, 56794912, 131088625, 917961701, 528390797, 688848881, 555199129, 707701594, 13455631, 963468477, 97831921, 99289752, 677352202, 650025640, 491151110, 278048345, 851649542, 3107482, 295348994, 125928009, 678213983, 180328979, 293999008, 377506103, 941109334, 927003839, 151861142, 628873225, 304412041, 815208724, 767090152, 2474284, 243670433, 336216048, 861487777, 414176903, 419940991, 378185616, 657160804, 562336874, 420523131, 316932479, 276796562, 993692444, 894531252, 145796408, 897773896, 208681567, 129196062, 632092606, 284308825, 917716509, 480071796, 418240530, 859573468, 524332371, 143112615, 980193191, 654005800, 444761733, 427093389, 492974617, 348294626, 859616637, 817169978, 617817979, 811887444, 428027005, 849967980, 884838188, 42929348, 582820864, 506079404, 143304826, 49296127, 844058675, 260262069, 843482654, 767629508, 819763012, 201542778, 363644238, 141997309, 774549031, 72990924, 116492822, 10320265, 366920074, 344871228, 130564507, 329504388, 458310793, 642742244, 726827596, 682059533, 841348957, 780434704, 687388347, 360585267, 773623453, 430355228, 187438488, 264499845, 624065369, 848474908, 371850479, 696815207, 182411318, 317182729, 284470722, 379249476, 630959884, 32012846, 500462613, 584258606, 264462129, 422237347, 655691211, 421785122, 136121803, 720820779, 782006883, 99888898, 260525395, 719634253, 390044503, 430222316, 363457715, 370375745, 110098847, 671030135, 342300088, 18528258, 942360912, 884526208, 190492382, 836003864, 302244646, 865833473, 145228817, 910899179, 22744425, 269519121, 664379403, 904804063, 249620618, 75687839, 843520966, 897303851, 264141553, 142510450, 917225300, 233402874, 329995862, 963004055, 204520942, 578037147, 815739174, 433493933, 911900922, 654327418, 275027410, 254258158, 724002985, 737528494, 811491196, 797984038, 126132856, 96234813, 473972539, 316901348, 337120643, 520582520, 41603988, 774078059, 331587006, 348582689, 699473440, 752141438, 712906850, 237644881, 142750714, 527777006, 671723505, 765530950, 953169370, 773189990, 825256070, 527368982, 122951971, 941756132, 509167698, 160485394, 936979955, 771645485, 391931163, 63299770, 556585023, 229996205, 52988186, 839997818, 512390062, 341261872, 863979062, 538434329, 497622200, 914496046, 614670183, 777499037, 85139886, 799488085, 52079430, 578890090, 324125936, 739187816, 254937749, 986143171, 844910916, 83315336, 712712020, 221127749, 51366867, 373281186, 964189859, 231016679, 778424169, 384316069, 424359574, 936045006, 848616460, 439421270, 763090471, 604842303, 363431762, 593796959, 402591654, 396762957, 213878019, 799351813, 509303809, 584983380, 331924603, 169401937, 222619905, 559630831, 428165382, 299957767, 34645508, 20128900, 68282382, 353416168, 837548468, 181498752, 476282713, 116959082, 902249785, 8631364, 992111516, 82785477, 957530330, 823898854, 520318089, 278185450, 98295329, 80023269, 26609638, 202668990, 55603010, 858851965, 260801570, 550334361, 936257933, 248344387, 714497033, 353396804, 385117010, 817156054, 770763601, 603701401, 549164984, 954218086, 229764223, 493760926, 593185711, 232587355, 182759259, 727195346, 214543738, 250597143, 506022558, 440880148, 374212279, 356418379, 609598688, 815045745, 900495814, 132359135, 68320377, 36710695, 799619518, 494630134, 5738574, 162387505, 49157946, 545896461, 74357794, 257705681, 513501848, 565034013, 584084359, 748979883, 62330496, 101222542, 424976340, 884783876, 76361503, 259929118, 677008362, 926837112, 580999288, 859217496, 229137028, 652600882, 122319421, 268563734, 469597034, 590418710, 151882749, 308664931, 99731046, 505788486, 556986742, 714325422, 190502551, 608150650, 634601220, 589167605, 189202151, 994649860, 380999955, 954431847, 403276848, 413842015, 972021025, 832419937, 575204643, 26067307, 888102767, 139456010, 525678981, 121571568, 144193895, 906225997, 260385839, 844198581, 745844384, 826564854, 919329275, 582131740, 224250162, 745932159, 84219221, 42846950, 486651629, 426018424, 124464468, 432805501, 79924687, 501804460, 586591774, 344808066, 147151415, 572498893, 108863255, 147357739, 14366754, 601802277, 796895212, 914905525, 841506017, 293747645, 35373934, 376123163, 95217170, 308437615, 783503681, 998162965, 190980836, 641266167, 852280182, 966931394, 309258747, 695453846, 287652140, 223858212, 992209630, 94147104, 361441952, 22605574, 438323800, 400281101, 802606360, 376793343, 958379093, 927558480, 535868973, 329557549, 801872412, 38150049, 195003594, 916630083, 286466150, 737390892, 606641354, 426585630, 565985347, 973108567, 781356356, 962670911, 827600663, 67331812, 861836194, 228739495, 468172255, 311896983, 597461665, 488068311, 809403629, 988410607, 720096800, 442082264, 656228184, 99358845, 832025788, 376492407, 422228584, 396643070, 871679345, 697614674, 645517781, 787225508, 126111790, 653809576, 250475332, 127473135, 859116742, 948540187, 135012986, 833323750, 397988628, 161893085, 281491662, 804642097, 598457249, 822335046, 605933812, 633197134, 341502307, 956716904, 796842750, 565770801, 826128462, 95802285, 309096821, 972342455, 129161982, 101161909, 672986238, 691812761, 200725169, 411954294, 863514649, 28880886, 114645038, 703796868, 549348441, 365672409, 471706037, 228006082, 486667973, 550654979, 735987513, 395420032, 789205378, 161588703, 619884215, 738419330, 207368072, 157505286, 425590061, 957343174, 788938, 81456874, 419409209, 139954056, 97447982, 499537342, 261101738, 723250597, 17696619, 12680933, 326469800, 388396407, 446876457, 916192588, 821200177, 458448645, 840617926, 50455332, 354589093, 493979499, 144694805, 861876947, 520300929, 340875484, 381047745, 596528919, 485306352, 139275449, 423724393, 861508975, 833733028, 889676073, 879561657, 846196580, 722047162, 805016700, 839980764, 257075054, 775394094, 618343924, 188470059, 844108754, 649570433, 674593535, 586700846, 258535941, 325435871, 423533607, 399142853, 874790175, 948835757, 399442623, 434093995, 926431647, 564065432, 70254189, 370557007, 948726596, 703544544, 725446729, 340351407, 734053213, 476640420, 904274215, 480952631, 595979028, 615412581, 711144110, 187467392, 700723780, 153707502, 895233753, 653328063, 849338549, 138808446, 689824497, 455995867, 110694636, 468355011, 427544718, 947242223, 447366106, 130029087, 183620828, 435276061, 342612835, 556060591, 548123850, 227942832, 261492794, 231526572, 382854050, 852389611, 726153043, 184686820, 869838656, 162577538, 802855948, 738745671, 550407781, 511825640, 840193591, 503626172, 789066659, 994023357, 937883637, 433463109, 645936087, 291366906, 783520790, 74270484, 872590262, 813937277, 517592880, 692567856, 536926783, 721029924, 27483453, 196955855, 452524233, 431853363, 592280476, 265460841, 721300733, 700931361, 914001146, 404598740, 861410849, 186515822, 153627537, 38107317, 420148217, 827778972, 35326955, 448851653, 571974484, 727137578, 190896949, 364974602, 689262244, 777971518, 801973584, 17447993, 23684652, 271612881, 418083423, 726280579, 842912709, 565422649, 255804624, 187928002, 917595447, 865306980, 983108208, 704760819, 909968513, 476819294, 67774625, 448482247, 406396398, 806953688, 603544857, 388456644, 308737065, 581572923, 517441962, 445764545, 423264982, 323027899, 319134817, 339235596, 180226258, 159888800, 743480173, 542243203, 527574816, 769906810, 623750967, 389691637, 702127127, 517334467, 571722997, 723164669, 367778949, 820809271, 443964397, 522681718, 283609211, 972805771, 661626676, 555369976, 769151358, 146916022, 653959841, 12015911, 803910786, 653777218, 736444695, 146685274, 66263252, 577224202, 662245917, 786425611, 97939941, 278258589, 182954927, 18715589, 162725601, 155042315, 82310641, 151374829, 863401897, 981634624, 553317149, 519299408, 667284536, 98212715, 631135724, 298127538, 477714296, 521442947, 199753889, 356712791, 671669564, 859887468, 670507452, 721153508, 902488555, 281847599, 938831552, 876253231, 250253351, 387291702, 722559024, 876937601, 420741590, 955651913, 372644066, 532134521, 788351027, 720982454, 130677215, 109410504, 508826207, 353260498, 768011614, 213014952, 903377297, 447432676, 251523640, 958564178, 307430205, 824279056, 714737156, 496845458, 954002795, 770108817, 540905437, 784952696, 529652935, 881489397, 887133983, 123074812, 863516928, 110735561, 29989082, 191361343, 47783934, 412487538, 261055180, 388773056, 831107117, 376121253, 147287402, 760042206, 375219033, 216089443, 224946496, 315405637, 616760797, 964243871, 622690833, 605885570, 739258270, 3930110, 334837781, 802932159, 842989391, 833622698, 293594133, 20287036, 391639640, 665600725, 359923715, 604204048, 168393254, 123861860, 535219963, 841746944, 824935565, 369317863, 662866662, 110136628, 532413379, 166737499, 509307705, 963317816, 470058354, 227197367, 759725090, 646207068, 64904471, 187636757, 671496799, 327041288, 221345116, 574182298, 992331287, 749797790, 52442070, 195573730, 176004801, 404654772, 484934916, 752177285, 687539380, 536449354, 99964167, 538042143, 600593653, 624206249, 843251481, 667125250, 456858280, 858647288, 543837960, 941373583, 504012598, 939245967, 845227356, 620577375, 470174870, 642485268, 260431968, 75697703, 265392296, 137634893, 200386975, 981992598, 673936139, 84448399, 296639284, 325065381, 91526006, 759633842, 350866379, 175727528, 511927278, 949695302, 523872457, 675612590, 950747029, 287536676, 317031973, 242401952, 142082045, 470213641, 658133990, 411420987, 597566633, 116157837, 400075732, 869804688, 282920082, 86779910, 345256875, 294931689, 230041975, 489296457, 507276130, 209263102, 546005937, 384231392, 490042551, 393191006, 770263007, 855322551, 944684031, 992651471, 958002714, 545058638, 631453321, 749608603, 530857658, 510359078, 104988700, 616364300, 421457600, 177569433, 231439643, 925839259, 674552087, 346749470, 163689591, 28255657, 924685811, 520927990, 249026079, 854322762, 113194213, 390314545, 582924153, 138614392, 159687754, 478913799, 633543241, 198839467, 795615262, 831290843, 61355001, 863709214, 382434826, 755954744, 32098311, 600525031, 518538621, 872820188, 573257189, 708383150, 648444315, 167648458, 428416290, 590500629, 857710063, 671088856, 845575655, 579032221, 509874410, 237818213, 971497660, 106069459, 491136313, 162112187, 773150942, 633878989, 72861605, 260439158, 644478135, 348164382, 472355008, 440044106, 536599941, 918639187, 137275782, 197295365, 181818045, 49974107, 324194603, 890462736, 375509986, 359963750, 327678415, 310572219, 721213250, 541130480, 781862989, 873319827, 204385268, 753811477, 368057894, 155654069, 152204768, 776118664, 605027847, 97684496, 478753959, 886807790, 506010449, 718653618, 510379861, 245033329, 619441329, 558213597, 288276221, 184073514, 673066840, 25003614, 546121331, 821555119, 913528783, 655214908, 999119221, 452741779, 74286160, 437258386, 812724685, 672301546, 429163287, 558216042, 320245987, 567006544, 349939067, 140622042, 798631477, 94093233, 355985362, 479009390, 913958702, 424386897, 514171340, 740175870, 679049514, 738354630, 700965574, 328225497, 872369797, 124920074, 659699380, 19741898, 176524296, 810970903, 589356117, 482661217, 105305244, 746566901, 789469440, 677706042, 194890281, 253528370, 397859137, 770080761, 236334065, 87948780, 99206944, 722161690, 897947100, 240769076, 598835286, 600921808, 238244315, 872557392, 483424546, 596154945, 675606989, 628370739, 529572462, 23699032, 652857066, 336137559, 359768599, 499057424, 934946367, 960779913, 528437328, 897308609, 734105908, 366963058, 433849598, 422068143, 973174747, 807166647, 311646721, 131692434, 126981280, 117469648, 702585623, 312063105, 950598783, 436053434, 553680247, 991777645, 781768666, 357847954, 861331217, 765639204, 769123620, 72584091, 268948840, 147658171, 439073692, 41103978, 64227160, 403969730, 46089518, 181999348, 388227680, 745583308, 933660977, 755735818, 4934025, 936389697, 234270892, 38682384, 645849153, 104101994, 274682751, 241354347, 763819314, 395351573, 591458719, 963607725, 655774111, 868801530, 349477037, 674217147, 882427429, 812742007, 91411120, 56043224, 464914548, 1217781, 391567808, 399848482, 996798040, 32019349, 625182146, 350440573, 459952144, 688897311, 348287771, 904348592, 921105239, 434965027, 148993771, 977813688, 613236453, 455752469, 932400122, 939358943, 694058769, 846062183, 33002098, 796353925, 703485451, 520003614, 82660090, 600657664, 320283740, 843184092, 458604141, 340574707, 63070898, 269261813, 272535906, 107613807, 778371093, 97827903, 311892346, 580174851, 45805994, 472021231, 709361944, 189442939, 491232893, 205639899, 386693013, 576740612, 655916612, 237590830, 196887617, 853949232, 785206377, 669571297, 233943219, 448392670, 222818691, 243953454, 52688383, 693709636, 776288967, 395486042, 533916635, 175065613, 47289139, 785826033, 746838142, 816505585, 227376558, 106508825, 86981736, 814988754, 722453464, 666497236, 8616033, 463514351, 287803623, 427908485, 208754762, 356147891, 377209810, 442206377, 565961933, 692427023, 395522831, 223996557, 41841748, 893250781, 748689284, 360609640, 187154855, 221657012, 36202516, 156562165, 429607806, 934696684, 956335906, 331578738, 581678078, 837907858, 747688550, 687032364, 498408054, 366099882, 777559421, 36577525, 464181836, 258039807, 337526388, 357227151, 138911815, 639834153, 972331785, 951319795, 147282623, 631873378, 199399763, 693399772, 216268970, 123725999, 397039078, 713815395, 813468150, 128537007, 67004187, 592812887, 956169828, 418820158, 840274031, 315199380, 15409495, 161428486, 995586748, 140654002, 890010959, 321572424, 518185008, 991271088, 900698211, 84164148, 553509310, 985762974, 711862704, 553138546, 805625916, 268740984, 78338468, 912716700, 486627123, 839703200, 454630664, 915141867, 361582583, 351099484, 322112376, 207395083, 103882974, 47321378, 781780617, 450713808, 983538285, 430886614, 17573966, 302051260, 450329092, 413205741, 824158352, 443254903, 155710340, 402979476, 817411605, 766802637, 3615041, 416499992, 598212441, 970011273, 233771460, 159084754, 151790844, 222270775, 400925162, 169208563, 545824114, 696850537, 152430797, 198526869, 144024571, 654635592, 982179450, 555576709, 42081818, 542937451, 909268422, 413317282, 677889967, 461464035, 566607698, 734068264, 186216802, 87930066, 916286730, 798180568, 30687978, 419017240, 824184796, 558886031, 714010688, 544323989, 75921, 264321272, 224769730, 107516097, 403374198, 964087924, 565274970, 313674231, 209532809, 918911287, 11445835, 23497918, 582725718, 574917712, 425085520, 965246209, 893871358, 591235575, 545443491, 914922636, 825202818, 427644876, 923776310, 601619990, 90556112, 647865051, 738104114, 729020864, 750133899, 126654449, 658829179, 753586045, 511030065, 726974439, 293328315, 25532456, 392648458, 499944451, 176497898, 544559414, 209855279, 282481319, 120944895, 263471012, 780300258, 363956265, 339025476, 99930725, 591066286, 790053093, 725428817, 401202144, 481723305, 254668562, 454386553, 604517657, 797101384, 428664915, 145954969, 360052720, 624880596, 609091624, 756877828, 70659939, 390864773, 483097318, 492669960, 53553364, 951404996, 37903909, 184143179, 933767806, 735644415, 99139295, 258845402, 351063895, 322464119, 326347579, 66574353, 588891707, 295424150, 209869761, 288600076, 174718425, 360744371, 72787955, 822612263, 771774099, 589109822, 267458153, 370285106, 842358212, 84621455, 527670450, 690625586, 343761171, 640996344, 79927790, 39866247, 863014698, 269214881, 278344691, 475025301, 137643283, 251653003, 740022409, 679818796, 134373413, 714503249, 478220456, 982257749, 688013831, 307420480, 32220480, 676725343, 204137465, 17791316, 201252906, 450152503, 265924519, 930466191, 678144207, 821950395, 230037509, 249217604, 314243789, 724276252, 922733191, 34065719, 466171322, 990571552, 459590307, 507855700, 81785234, 748192332, 861669612, 88486170, 796656296, 819085914, 728824036, 382069167, 613357411, 297358967, 544407691, 149158740, 291161742, 427760134, 517664856, 973333287, 956389269, 836238650, 824134076, 672994535, 492718643, 832839074, 32311145, 529751691, 814623194, 560352474, 356476393, 187721119, 458664436, 132689958, 118782274, 151222498, 551131605, 154817210, 432037914, 336333494, 688348507, 628533305, 373002926, 108114153, 295987957, 816504251, 964029366, 396316526, 427848532, 343756867, 875931463, 368614870, 425407799, 798541614, 448175878, 808622055, 6261405, 463936176, 715212044, 741668416, 662524720, 867534735, 392914339, 237627203, 870357035, 64539771, 558634677, 609564009, 350228661, 885103561, 825348228, 467557135, 273685866, 905078010, 387131968, 129883344, 154429411, 990802367, 499244034, 170780505, 29414727, 621689603, 277739329, 75534186, 624527703, 95916895, 515419177, 354064108, 805069009, 220195063, 67735268, 112523415, 922407073, 592361810, 374737716, 501167281, 697513369, 648299447, 180070958, 377412146, 962150069, 593107727, 116873117, 210157670, 804552617, 506047513, 578565229, 935630550, 912995536, 382797115, 183992634, 328359363, 685854195, 825252117, 850800045, 811468792, 812790678, 908910868, 506843680, 356065096, 239427724, 711571395, 583582385, 715453746, 904073257, 225496985, 767367741, 228803714, 499805592, 378580287, 345934695, 876096795, 204353121, 430907784, 783193701, 272289680, 631276965, 437085087, 410026256, 237748274, 842246934, 105255443, 152472313, 299100931, 363125357, 116935302, 6736630, 265080445, 6505868, 355054357, 713687872, 519153898, 57499428, 125704193, 707855665, 376449618, 66552371, 256199280, 287728803, 617904417, 85505749, 220164699, 542097359, 111679398, 278607329, 546644586, 134907096, 739172351, 604823266, 312562383, 910426043, 245324188, 332699775, 907252473, 296082014, 884002653, 915961653, 395359228, 745945522, 439259935, 632654648, 137902452, 350906026, 627102832, 66649423, 999298178, 453030555, 573887402, 715005957, 25982503, 591598335, 594612139, 557483521, 547730269, 485666592, 920843799, 358774395, 330263123, 769731487, 316446525, 481409930, 763013270, 925371204, 981028867, 164841236, 642528237, 425772449, 500332086, 597729612, 714430737, 883277778, 612213198, 314943190, 282209849, 12388557, 515250598, 139702693, 39059054, 762287529, 164696574, 554882576, 896192996, 99334758, 781556853, 91297158, 823443818, 668876709, 965895794, 611828703, 618247683, 117722137, 932383541, 942272978, 479960950, 882203269, 770173842, 873675823, 295969305, 400110068, 466210161, 568107042, 839524169, 228336, 100621009, 214801639, 612538659, 90078913, 929644239, 64315854, 710593123, 709370185, 532124911, 907943139, 458696722, 140112296, 229030223, 400699683, 24752364, 403013480, 364488938, 972951774, 295936097, 741791737, 181560610, 226729072, 27753805, 720311269, 117705850, 63768219, 380541073, 538276187, 533825662, 477238854, 460913851, 373852699, 291777784, 274910063, 793843200, 69765839, 880338808, 835453180, 891474859, 890652668, 929034213, 162580621, 947834921, 507135076, 154946964, 170811912, 706203180, 538421717, 843925244, 294192447, 768253911, 241972689, 497436004, 29200409, 980725397, 124277108, 157858142, 729182395, 515961809, 323678170, 532244903, 684374103, 135249258, 13649967, 935133118, 322801801, 811400550, 651258807, 502170439, 562602754, 439189458, 70975474, 513109917, 882728293, 490755878, 397773986, 849924468, 234796071, 628914932, 986012934, 418911290, 216210511, 460710630, 249516190, 35673358, 79010543, 151841084, 611259786, 169276481, 13333292, 809762781, 419966533, 694106731, 814417970, 603611899, 150468244, 78696099, 163822650, 845574316, 720412345, 353302483, 217634688, 630702260, 199250109, 364050889, 268529835, 654844258, 318989699, 48154229, 84843538, 298623644, 78503435, 735713568, 344569278, 919420997, 597778066, 133346338, 95974336, 807822601, 739348622, 249968053, 879057969, 981370738, 750605252, 621112330, 695745958, 603712474, 355611867, 899165510, 298961875, 772413497, 893020872, 338184728, 398971757, 827687159, 818788663, 865756594, 573749550, 194819840, 301966842, 766127204, 385844795, 42108248, 547080955, 614218136, 147305042, 543294153, 280615684, 600107625, 955334847, 81887934, 2747919, 654795877, 470778732, 913200005, 539071892, 57055490, 183013872, 696329593, 785034737, 707225615, 653932001, 998865087, 605374612, 295956085, 602348077, 402473829, 403365839, 500122178, 369769249, 658308812, 281992771, 801891169, 988865828, 11468210, 193245920, 95531170, 436102380, 50552070, 906222874, 351919074, 253309753, 839652276, 19438360, 201520021, 116078909, 972580276, 861195504, 711909346, 290490768, 536212560, 704722015, 690379215, 772084156, 671697096, 358355211, 743652179, 963731952, 320025863, 877233792, 260325575, 677943338, 75707957, 618053835, 552011365, 367753784, 720701009, 235004683, 730668142, 38684111, 775629035, 169444981, 521409860, 724377935, 448121513, 341679313, 53332428, 892896881, 513567684, 221301861, 751537657, 353763928, 27342636, 680745957, 632287441, 669232951, 475322774, 319285454, 885857379, 907345762, 338929319, 140759684, 962576389, 69600715, 492402494, 691217266, 358218315, 17241357, 731433315, 100169348, 254757126, 618469876, 549451202, 713544652, 220352458, 8443836, 556905295, 941909739, 539177260, 503135216, 694405441, 802441413, 566731459, 383988326, 36142944, 272739724, 540066416, 223245884, 255046865, 656250480, 401723232, 921687556, 118794424, 870482409, 881272218, 714103337, 704258482, 83153729, 382328447, 507759523, 992883496, 549743073, 838520433, 372842799, 365179952, 174144994, 335959257, 229984671, 146921221, 886831430, 878125842, 102804460, 938494183, 67796111, 446627792, 399169445, 876387298, 276624240, 62695644, 526651118, 890475611, 686009225, 549165215, 727969799, 817924712, 704735855, 137989947, 198412117, 239770193, 676685915, 333413070, 63421847, 343354510, 126073994, 196345710, 352882828, 82081414, 22893589, 410466461, 286179103, 449757442, 867827259, 151731009, 606735194, 980296773, 268259126, 150677143, 134881451, 879598730, 788568059, 728868910, 837385478, 570124080, 371312344, 889419846, 64068901, 102794964, 175456699, 367881664, 737731905, 755248306, 315003251, 866507713, 294993808, 798684984, 833801639, 75814469, 290597933, 43588121, 420750050, 606303656, 884888547, 552839635, 402987856, 831816940, 186448138, 554750212, 317066944, 656070957, 666514306, 580021958, 770345275, 565025434, 91236743, 478391685, 32073921, 894561025, 676488951, 13141959, 725173092, 437793855, 730753226, 220115550, 493308468, 765610104, 244258992, 674614338, 796056104, 695471400, 583516256, 281706944, 911261299, 859176611, 793939201, 925628364, 979529575, 638496391, 221426561, 612959602, 837148585, 953165810, 26455312, 109782014, 578437832, 424990170, 710936478, 793303533, 951183326, 703216647, 894396100, 852692643, 389988604, 441031505, 333911823, 387166072, 766755505, 344422502, 19103269, 790783721, 314578930, 469938744, 338226305, 94389966, 702357910, 397926786, 699394126, 851519487, 468453092, 334432556, 449597806, 134291730, 849456614, 520470783, 848358651, 244680543, 263550758, 888744222, 278588170, 744305928, 622692435, 784745983, 200196582, 908761904, 315984042, 82438423, 694733729, 692476486, 424637268, 264312579, 599433903, 571752224, 492813892, 469771634, 38516569, 743276106, 224710251, 411839419, 61694956, 479579803, 954934975, 94160672, 106235790, 731140031, 471591348, 31561419, 798527742, 169196452, 457888065, 494006551, 129538819, 578454227, 663844379, 106499078, 929904847, 18889698, 271980561, 598215212, 765472626, 69761408, 118503273, 922112780, 545913460, 557029302, 234522951, 75158031, 22799753, 474913430, 245625241, 565990999, 385203343, 196414830, 782604311, 442093657, 360199547, 522874059, 572494054, 850476855, 740555387, 85577323, 643580382, 420428708, 535087884, 394600088, 15045991, 253535858, 5734639, 701735051, 294930533, 945826916, 936417064, 788919336, 287308850, 187892313, 18813511, 466218126, 278661172, 491532670, 307114122, 659121972, 200859996, 413259513, 494398650, 243511295, 318071623, 867403214, 234217076, 688000251, 114715569, 948816241, 84008235, 46702211, 802500048, 604642853, 143172408, 447798614, 459334684, 223414599, 489368667, 465951815, 805741640, 190922190, 813360549, 364968873, 101600692, 880031173, 528035556, 727088214, 691987138, 359733254, 219731825, 415293566, 444525132, 752943444, 950686530, 62175404, 138133238, 490730010, 560119393, 764880025, 857140952, 100979172, 996129333, 520245293, 916390396, 167835338, 750160451, 455758377, 63790636, 386772227, 366130659, 362802958, 305702022, 356407472, 850467040, 973918362, 328090878, 33032251, 710153647, 540131182, 960838508, 267410315, 675854303, 511459280, 237287405, 45905539, 377750244, 441017123, 338746933, 203357928, 825867543, 849137773, 869110662, 678483108, 147053275, 717061925, 577821803, 57789959, 23245378, 256298231, 466613996, 262109814, 249459137, 809347037, 960653773, 716533059, 953166476, 668417152, 583307737, 107118571, 606322527, 79945305, 517922997, 995333290, 334816364, 929237782, 788192632, 890562069, 351748675, 72025065, 180788946, 284201268, 876937308, 248229030, 680170755, 652122322, 748093510, 140751265, 241206430, 695808540, 573986474, 98789534, 83120084, 2089375, 464014173, 870286683, 558441494, 655171238, 977375158, 489223637, 68239737, 838047143, 474360549, 145750561, 532057440, 836856358, 912052064, 517464772, 300858628, 747199756, 764121124, 485368657, 687037938, 590712650, 67364637, 282177200, 413983446, 893558135, 111816992, 641690308, 522321460, 478634200, 157524944, 598453252, 883961284, 707926493, 998620230, 701600498, 567012788, 307076720, 689271474, 489791025, 812173495, 595042386, 825300387, 914867479, 88320098, 508603012, 849981242, 529625895, 617303049, 410778154, 919039292, 528777389, 147107838, 451476478, 329430265, 179152187, 991537916, 259721921, 30725579, 156638568, 221065823, 123258382, 466809330, 675721186, 654458281, 917935848, 2501350, 487824988, 137608525, 180583273, 841081243, 353195777, 990478280, 363086965, 362025650, 646560007, 835057279, 365741411, 425361179, 483118497, 7297084, 328617414, 726190501, 363843180, 453736826, 914164413, 133286676, 51055289, 440174340, 391113226, 252742893, 187586623, 730633335, 278887981, 509273140, 761013086, 122206702, 820403876, 170852800, 905519835, 14814800, 552890772, 564476511, 949517229, 498819128, 224137622, 55191011, 622331414, 860206242, 848970515, 215587345, 514865100, 19873687, 247993841, 397312881, 810671406, 104648203, 500568155, 129785649, 702773058, 730019453, 514793763, 791882056, 831294089, 328840364, 882532858, 757335659, 561655368, 96667185, 488464417, 74351228, 148803846, 447567628, 817874486, 49635711, 496694043, 510020364, 735031401, 165904811, 141825609, 159863657, 638689983, 156380597, 143386032, 295924266, 870087431, 804447504, 364237224, 134495481, 436843912, 887449277, 138889158, 748694274, 981080723, 61694980, 866979335, 303997963, 869885278, 443952662, 456479092, 20892427, 577972441, 158853840, 805130207, 323797792, 202115262, 490529690, 381121965, 305945295, 929504194, 717062217, 988449296, 372506125, 741243777, 721686599, 889890304, 711709004, 231026847, 441893187, 268120378, 55922620, 711167874, 353475877, 453193027, 601442182, 854960559, 261451592, 496569580, 478554734, 156338588, 659608498, 923386208, 375940194, 307712871, 950152921, 936073298, 874387945, 335685360, 271856565, 423952067, 541057496, 703421423, 901406470, 336609097, 107736742, 623280355, 848030477, 990398051, 212396201, 184262891, 764497749, 871975504, 982292964, 544678100, 969717526, 425596513, 601815154, 154765169, 308614979, 388755423, 515351435, 976891529, 284028071, 174932130, 312297934, 523524250, 878131143, 586975156, 928370051, 148169160, 736702034, 491539511, 571048316, 423708532, 112567454, 612816237, 582291067, 41134564, 711035860, 709530716, 153643540, 736237554, 934205359, 975200079, 865996160, 534254348, 198340914, 324833574, 809649940, 218973778, 869958542, 750146648, 135308274, 110280718, 83742756, 670996563, 271086450, 406238904, 857790192, 725379204, 716576109, 673502050, 587633654, 796736617, 174190186, 493699056, 251581732, 469175084, 25342022, 623866797, 569038630, 207485730, 375652169, 752697540, 234715117, 323437176, 410796617, 361356226, 736363402, 299518676, 197874614, 503787765, 61455137, 390349056, 145002462, 215720366, 672382857, 322310446, 691775928, 674057657, 758564736, 113538604, 353447164, 548566, 898786055, 255429398, 49729780, 467742071, 595819500, 118042979, 337513913, 799415981, 93481136, 613185864, 47577155, 43213085, 603660434, 374358414, 646671790, 700093662, 995520039, 240378661, 875346997, 878857823, 394199585, 777019337, 447972869, 581666745, 400704068, 489564199, 762206331, 370621313, 116325443, 693826907, 775219851, 916982045, 477372139, 773954759, 46766475, 7688727, 663217052, 498439308, 977613980, 637951759, 960620325, 564127332, 205734939, 752641647, 716820303, 692286126, 199511703, 544489476, 915319053, 361230820, 456059264, 366121263, 136556931, 189317911, 52493483, 547372615, 7982484, 621407868, 340311774, 528553563, 751682285, 570866391, 339458038, 591758922, 919637246, 679804265, 23241301, 346693728, 516570840, 477091419, 411303774, 452666387, 739632321, 126866175, 22757971, 345302826, 434406224, 319505581, 540228587, 511587216, 415733425, 57784073, 482057849, 829989174, 34987267, 520633606, 322509909, 110893328, 101885715, 409293218, 543860315, 488196498, 252859888, 314036360, 353744305, 812218121, 30904105, 509471035, 431292614, 689547841, 295411759, 825936503, 674348338, 942975259, 101062333, 343242008, 14889005, 656808801, 183107748, 445055887, 460838593, 634682472, 11100052, 776076142, 622323090, 974548709, 367115090, 91334971, 216923168, 511953120, 832545599, 980323357, 686525259, 491909056, 755528788, 758535861, 36506318, 731669526, 826563897, 665763894, 923052300, 867885211, 356159220, 969756173, 550209870, 387791950, 685497574, 463907196, 598627613, 384177423, 817120199, 914254848, 86933540, 172537262, 462217938, 24239915, 696596836, 585731285, 124539339, 737022556, 438374133, 673256211, 526874289, 932950713, 478877452, 882109015, 390788387, 113949563, 293140258, 948539816, 314724867, 707783293, 838489810, 60609262, 953654584, 298396433, 940304024, 413274269, 681889808, 376109379, 522210845, 31852759, 330949064, 580580861, 822356527, 286785418, 634312638, 884821161, 378728195, 898966056, 409888696, 921582608, 982207136, 926951242, 634927867, 624471111, 492759889, 748771210, 56197026, 737340636, 592098827, 50156383, 853828019, 793537903, 721816470, 337807698, 203197929, 391293454, 499414079, 320113871, 222454629, 44302023, 74780413, 813728518, 417780879, 420103863, 414961294, 545329351, 891044083, 164302490, 830578095, 637938186, 253196159, 64594004, 192094522, 166660434, 126137201, 207963699, 146574965, 840937579, 77305848, 101630742, 230052449, 828498041, 639896228, 625642933, 812820350, 159593642, 58657240, 222601483, 271273317, 891730255, 504857464, 692506984, 431809916, 653596507, 796969120, 416018570, 40958645, 50955590, 348279520, 944562442, 89882194, 66497614, 838312273, 240778853, 414431516, 235129152, 408233954, 344562972, 417694244, 743301835, 537061523, 243385647, 918810022, 393975841, 327984360, 353520852, 158472718, 381512905, 723666210, 380829988, 334342550, 802853962, 275333922, 667465579, 898469454, 621802517, 189777000, 42251344, 771065541, 726131757, 957662419, 179845593, 966643983, 538967706, 875368079, 945507236, 473307275, 258971216, 807624652, 767468338, 767810694, 744971635, 177496321, 724678333, 460327150, 480868443, 77018779, 710922686, 27361279, 902651034, 789866667, 223009410, 368144779, 242199308, 790106729, 190262615, 393561607, 765950455, 784967487, 274137914, 742758242, 861502071, 482915836, 961278815, 280788900, 118254935, 950507472, 623137360, 755287687, 92934145, 107640430, 918016184, 156846643, 286804270, 341092369, 763318889, 925233961, 139007559, 938446133, 913545173, 367861093, 871629079, 286743766, 553271460, 174877034, 940773927, 293462204, 865772012, 788618003, 205048891, 91078265, 606464953, 620231314, 58645034, 549315663, 940629030, 475057097, 967192666, 782455165, 751644815, 487487490, 601675265, 360220716, 316222070, 394226646, 3210534, 946592750, 218179781, 65160559, 65628412, 746903756, 550290164, 171499823, 960511466, 945803222, 169460176, 676420844, 482714546, 449046701, 964546437, 277505057, 462409143, 178172474, 799760171, 253447786, 571777957, 470993173, 107746870, 327363162, 936501679, 896114752, 105208199, 421345091, 952551939, 363586302, 250613880, 491650565, 635766737, 13097555, 640489492, 320121715, 107549380, 727438304, 97213428, 561215854, 694489047, 273228591, 629644982, 395765621, 334457056, 727488271, 533047942, 808390709, 371070084, 741383509, 859564457, 421727850, 710964673, 699375472, 886599174, 875128915, 451531736, 275653812, 598359591, 46140876, 68608050, 218768792, 460705982, 556917088, 927850518, 401573802, 963799643, 979897233, 378721919, 437133244, 534515302, 946147321, 212433199, 160002603, 414545798, 761101363, 477489175, 999727331, 710033229, 351680479, 604719358, 211698211, 829984421, 874103657, 582021546, 975094811, 4740157, 144570955, 510312735, 99634150, 296768382, 608215342, 689543377, 98200433, 383836935, 118740394, 925499078, 543914190, 475730089, 508796972, 194253472, 919177964, 334643470, 455716078, 945779528, 989514669, 552182155, 271048121, 509864599, 976802849, 81710821, 207380400, 885007432, 675301491, 321073390, 674531875, 800863340, 112494342, 475016545, 335218136, 942060993, 866070331, 633279033, 573493407, 586871834, 131004653, 236311251, 903014542, 997411283, 604584532, 527108135, 964305591, 202342221, 267093537, 570668787, 531078620, 710034979, 460702384, 712318325, 430571533, 489959379, 456072413, 223180614, 492839719, 160724045, 248633353, 704095579, 199523772, 876167844, 759720698, 295614113, 95502646, 165897438, 594614139, 324908488, 790836192, 714566109, 430425813, 373396709, 951323510, 441290302, 180106632, 394368575, 746899524, 649455162, 568971727, 49405270, 393088868, 795246665, 312414381, 214563476, 346816129, 971039961, 907250036, 183293785, 638750158, 935364085, 441342776, 391913030, 534857485, 409729413, 643851925, 329034015, 407931714, 890551706, 440468596, 726631687, 766450846, 464320765, 207573782, 282464062, 787888479, 549762614, 772465857, 517053909, 594568524, 787088836, 350775335, 437133515, 363447050, 509535512, 4846866, 455431013, 628262804, 842629535, 837893049, 70705782, 17726256, 246744894, 890510357, 380445426, 831768892, 389531756, 78725180, 376122210, 329814230, 515370187, 574732507, 407184038, 15452071, 86689135, 724747350, 514415724, 475127827, 250755582, 586017799, 280243887, 412146834, 279336786, 396352788, 264394113, 52404501, 125077957, 888500881, 554266952, 86967590, 437422430, 202372390, 966231439, 213705124, 319654912, 327706227, 604516154, 838729579, 244443587, 691974396, 670229964, 419206891, 5257885, 716775423, 278654957, 492538897, 11616702, 646950986, 306026643, 833796337, 78834178, 275922590, 685293512, 101203566, 623763509, 656078816, 945604774, 324717775, 192790388, 606547432, 816500784, 414238241, 58806450, 745968573, 310554062, 972523071, 438568065, 189445485, 960001260, 460803121, 51605253, 687345870, 404736964, 670252702, 370607189, 996543775, 692270390, 483658090, 512498805, 152887874, 900798326, 321902214, 232558689, 812792038, 89627325, 385482292, 85511775, 114980633, 906256203, 132176164, 113938045, 860499716, 610603742, 627199142, 77262047, 251651528, 736521679, 167738946, 281319374, 226793959, 873959147, 950424104, 287498818, 699383203, 678933526, 452903220, 805152685, 860641963, 79880703, 620991139, 222909835, 85240261, 664591172, 153476076, 656403564, 171552097, 531498953, 709326521, 556667839, 956693548, 309369435, 273469420, 363742884, 697635661, 750181230, 600174547, 790602406, 83903616, 271661984, 794607831, 419228654, 87801484, 367167886, 88560573, 765286104, 951006428, 750250006, 896580675, 160985003, 996341938, 686112700, 496608652, 8826906, 970375031, 283690876, 588602869, 551235124, 124407441, 122553690, 380714466, 903534647, 250454724, 331601977, 397264783, 894642660, 697242661, 325271889, 176018730, 524552932, 209331090, 17930224, 696956093, 581641945, 71616876, 655056447, 326755790, 904206703, 333932104, 810098296, 51872570, 691086075, 786154701, 500477300, 774379189, 932139088, 808276112, 46281558, 882020616, 642937407, 78626763, 744976438, 745900487, 840621754, 293141714, 406778811, 512339028, 982985545, 200090743, 96379688, 731892731, 194786370, 587797329, 215409805, 448536756, 574049504, 994450246, 130062120, 452197417, 853728347, 478142793, 245992732, 990418743, 89912813, 530916549, 444842591, 10607588, 692738728, 617786191, 262912104, 966519363, 683722786, 857540414, 116745736, 873227363, 77067215, 176555643, 68957746, 43363488, 533182106, 910732883, 152380108, 993295616, 340926397, 970676595, 308785303, 62200157, 273981489, 832809292, 729118812, 699676301, 818970131, 628088803, 235687281, 220074142, 998712515, 979946995, 3490108, 15691038, 220726452, 936613564, 604889399, 600492828, 83126672, 131431487, 723542994, 333587942, 250747279, 317759186, 699894415, 741249907, 7101324, 110266899, 198449991, 26216686, 353232706, 802104277, 408746362, 665417824, 888368646, 565370168, 430576891, 957735373, 589780883, 799338300, 10920922, 900024492, 338080518, 70219947, 609907255, 841878633, 414994208, 236555139, 352814288, 178796140, 602748240, 80664841, 737010978, 286608976, 147147970, 18477242, 868938670, 12924669, 134576177, 644507763, 447517763, 208712927, 802536461, 719573433, 129481234, 298151133, 302976809, 17764986, 872842257, 192362484, 88605057, 611210823, 868691884, 862020191, 445825009, 749126389, 826650661, 623427745, 144373772, 96987882, 328114637, 455886080, 118534529, 224522919, 1826663, 720845079, 96064957, 796380633, 159885838, 742949386, 504235461, 883292996, 991983004, 729246603, 807137342, 128814960, 733948180, 481492365, 899445598, 255846118, 190089810, 327434115, 912920518, 988080331, 498448004, 553641460, 640688024, 252451323, 342240180, 135018369, 979439393, 727039561, 174193302, 66274203, 457837276, 716730170, 261296156, 144719489, 573831035, 434965159, 765425199, 114748479, 297912773, 797611702, 918896316, 884540955, 444936329, 706027557, 528667314, 753222655, 384721590, 431614072, 758575995, 303344420, 577720745, 382372457, 264857816, 964538069, 942767103, 61569185, 785097010, 521691169, 489780864, 27067643, 275636751, 846000150, 599164211, 33967024, 274318063, 53917069, 454942982, 928280442, 892727017, 583311796, 951639658, 970330026, 242301121, 350184455, 689276298, 551191919, 286150645, 248465465, 73584682, 693620621, 914895403, 571499980, 860297805, 60282498, 919630150, 490457567, 561589717, 579460503, 679088169, 152190912, 979184344, 182649412, 20770295, 48782943, 25201019, 442057952, 31044094, 114676915, 747894309, 946704711, 310304449, 601324803, 152276689, 81019229, 373384289, 420645317, 758387642, 95166071, 590866597, 477548481, 901198885, 128453774, 74144784, 278235862, 263372211, 217763683, 633538336, 647670257, 284268114, 880933233, 837201417, 385173529, 41347500, 450044983, 621644040, 14441178, 702517056, 498978326, 817540745, 503613053, 14021254, 829559619, 174636142, 605466876, 213804699, 550740383, 772428266, 386703427, 659200105, 919826246, 854732201, 871762476, 141204776, 171895765, 136625246, 480685906, 202583237, 883935275, 692888472, 369179280, 749021910, 686247880, 54499796, 215419337, 652954969, 820599356, 857397439, 940555642, 938980318, 198806725, 947205582, 234537643, 201980654, 22174187, 182489994, 401980344, 879057254, 974027179, 615545365, 979436321, 387729601, 11969829, 460377333, 662590116, 992785026, 791742096, 927817366, 6327010, 562716420, 568834003, 676326927, 739534038, 503739630, 829851770, 508235597, 642629603, 937514799, 710207569, 812799516, 637873812, 866020060, 373265106, 139223466, 621652546, 677221261, 95689412, 242545922, 334053200, 872322489, 493210994, 89945409, 28060643, 768300917, 719548519, 747111158, 249961649, 257818060, 625722808, 135659885, 931171511, 361150126, 5563793, 512217956, 547780113, 257468888, 424163016, 365800372, 908277773, 753044111, 813146384, 559377887, 512579304, 989702247, 785076417, 515022706, 589090973, 171359496, 667814595, 334432268, 688173536, 858095229, 372273614, 587373130, 90861762, 458009342, 253190700, 94037520, 996229644, 723908746, 461234802, 230100913, 444083252, 962184442, 231841712, 320239636, 457564113, 527113402, 118414292, 328252525, 389066051, 277832689, 466288003, 690910597, 673658704, 123684924, 776259973, 573511155, 658427104, 813136143, 939539837, 206945640, 894659705, 64084700, 186565026, 123773533, 42194133, 859847116, 120090172, 892486754, 429268798, 618247805, 420722218, 998943769, 416689395, 806586082, 232197893, 200003513, 438346326, 170382569, 459671528, 540467873, 595480241, 907598149, 967127074, 895834117, 893329952, 741563567, 490928162, 947659008, 490034792, 713815386, 926922099, 57181714, 142199882, 897840179, 776051490, 612466997, 436561879, 542987473, 765874581, 551321275, 258428046, 656593313, 62175677, 160664063, 290961152, 661063175, 486908487, 729879131, 407468266, 448901953, 383788019, 528651108, 635168523, 162589619, 795175358, 920847486, 894021833, 840642003, 28089638, 132424694, 580531444, 587383053, 806448356, 321869756, 105519650, 623603208, 601056231, 409303935, 942466086, 118505096, 756871084, 21972320, 514268708, 74609495, 431099325, 773043852, 770479134, 779244966, 685227747, 708253984, 120537723, 783985651, 205040376, 731229226, 541984320, 793670003, 562720839, 702001124, 748616488, 245323642, 515204547, 564160806, 326778203, 595361646, 416163812, 330638170, 134894272, 989638968, 637503943, 327144227, 829009601, 735845097, 338830524, 873074509, 783254491, 17184112, 625948964, 392497500, 552916, 992889233, 782431309, 142488919, 985030505, 819834659, 538610339, 847486583, 734334921, 667225420, 475892643, 50645425, 110862471, 563485708, 309911318, 869610514, 553262445, 336772126, 585160625, 818985898, 124107016, 568214004, 664239993, 400916289, 993275698, 457194639, 685678108, 842283352, 308692554, 485128153, 735747250, 12352104, 150792695, 942063233, 622828732, 517373604, 215478236, 907742333, 573271340, 836591734, 672421477, 638182020, 420266803, 228283280, 850492062, 763003834, 818561254, 988007863, 90772248, 632535366, 759250788, 221969688, 608830114, 735673136, 547861170, 908972157, 665387572, 353620077, 909838188, 615033367, 979541354, 648510681, 696870704, 602249994, 826617657, 323010723, 701015038, 557837186, 5958245, 463567488, 684893206, 148854794, 976853814, 395563000, 81091298, 838431121, 730477998, 187423796, 577528840, 210082301, 521577004, 767016397, 825505242, 44561195, 34972184, 760482563, 805331970, 413748777, 255754969, 13424725, 70677732, 217636024, 602186127, 68604795, 543123306, 160448209, 34812457, 999084309, 212026390, 219257631, 424351852, 758024195, 312120147, 677003322, 578474208, 247338979, 550211971, 84432810, 203677930, 860600738, 567303627, 451781699, 706680208, 857369988, 932869413, 155909843, 305466478, 509927770, 376269316, 891610453, 302290875, 159325679, 609381920, 433908436, 703787323, 80652248, 461303672, 382350539, 198532756, 340779313, 613266691, 652320148, 566342044, 466749003, 427224375, 816378628, 404914876, 134747644, 1195043, 254040569, 506720491, 411777647, 112169828, 657248069, 720437222, 716949443, 578388558, 733946110, 231637763, 432933337, 158634991, 776923951, 665068553, 417020433, 327806294, 74569036, 813093763, 522108277, 263440200, 854456461, 408331474, 468929862, 781946183, 344566907, 943249447, 382463585, 7508656, 989784308, 690671871, 361007644, 26503230, 567742526, 522728803, 746410191, 575905060, 598124512, 199451237, 515769403, 714375902, 446009916, 321965390, 58301803, 880793239, 821285251, 199698273, 194845190, 161252160, 816478737, 79170840, 9787340, 618781362, 236626673, 218119709, 953034152, 575512017, 988641404, 628532128, 321823349, 838693197, 476363826, 388910715, 883486156, 378350474, 803551173, 182438749, 875245938, 282180177, 942753946, 635288468, 584522905, 137996785, 620609370, 362003347, 83483065, 455398863, 284359821, 963934881, 831110359, 820366887, 782299294, 978147958, 951104408, 316807300, 164508676, 299594126, 554390339, 442284353, 994913468, 505022743, 788510391, 825305081, 679894914, 193079875, 165535837, 452144215, 432037650, 360379353, 829435548, 144771429, 36241074, 65127927, 290250554, 719302089, 369226062, 370077669, 918694442, 713292299, 89560871, 430788487, 483954625, 747727825, 192940588, 322755190, 763540863, 113609289, 824759770, 130160680, 79102378, 159966509, 786105129, 754575887, 461190313, 403816879, 525426061, 823025203, 535915724, 392078547, 462693556, 347318545, 175312774, 170701780, 485307946, 780315636, 972989398, 244211118, 828320985, 569897480, 503212283, 143450910, 271486393, 273205956, 335256190, 74904289, 539447684, 710812217, 988962791, 424839011, 816015234, 690468240, 538362184, 881222, 976602359, 540778546, 105493488, 833275471, 527988660, 759542395, 316140533, 836819713, 629271360, 897338862, 656380836, 500715733, 716170082, 99899699, 724874175, 691670599, 24112102, 280194474, 302781152, 918322274, 651000118, 868764976, 761020043, 562518786, 553814794, 880054413, 481757401, 371079139, 77656159, 537790066, 460007765, 89536263, 401322694, 969487399, 18457128, 657979782, 126827796, 986721927, 425651283, 349259507, 945824777, 760094238, 870000491, 576392845, 958774217, 112132705, 921828782, 791297740, 625997400, 541833680, 939700277, 756885209, 815523198, 506106250, 419852744, 713355596, 115496383, 460961793, 591268061, 599074306, 684010359, 935833175, 188159853, 862104222, 679935343, 64880697, 168213929, 890158503, 828873259, 450541962, 370708712, 352480658, 876191254, 449182939, 985588741, 798393941, 829490351, 324510479, 981169144, 737264075, 345635011, 811006440, 195923428, 48376185, 985303652, 138396208, 335927965, 956061067, 792647985, 161015997, 765750898, 847721856, 73626005, 513276106, 250181343, 528945174, 727531954, 712140924, 390069872, 411044648, 966103977, 499852931, 971007026, 436459433, 998234202, 476754591, 114566706, 57010266, 770658010, 340732667, 176462073, 611588798, 346561449, 630818369, 303687536, 518546296, 474000922, 932714083, 546930667, 850529175, 910353142, 52572666, 624205161, 980007995, 9761075, 80605263, 26910544, 409156881, 182193731, 698116968, 759543734, 789799629, 776567557, 693482369, 90712193, 893630038, 719040269, 691810755, 820435502, 794587458, 470211536, 13324548, 894912673, 446097096, 683864252, 656502542, 398758351, 591959939, 527755342, 715494994, 803643537, 612477901, 454439190, 258189423, 595945734, 252150095, 409930192, 821339678, 340973019, 683821424, 632879990, 161752397, 322824838, 529136272, 84227620, 954213581, 309051264, 868056712, 576185414, 814035301, 895097837, 274734646, 909603204, 951213846, 99745973, 685968232, 326857618, 261551513, 275421353, 353715955, 379019012, 56222117, 973522155, 581924708, 67195162, 799981940, 403459263, 935195606, 257897278, 50469948, 21016063, 189018368, 522123657, 335461431, 33769908, 541149454, 781742771, 261805545, 928969380, 282417377, 222763139, 332806977, 105759304, 530978426, 648871779, 609398129, 232335442, 414678167, 20111297, 927850811, 37035487, 318771550, 550638639, 219458922, 946115662, 158663371, 750045243, 498790691, 149133215, 702265613, 594340071, 558966539, 195549741, 863031081, 5007310, 64154074, 107131672, 920493435, 567339417, 941647010, 444635666, 442823492, 454544830, 532768252, 849906184, 186171153, 566881898, 122590559, 584914347, 772636719, 121638692, 189121256, 815473832, 534279914, 557020095, 237531843, 765644225, 752287640, 693633247, 599927388, 959562466, 708335321, 369601862, 188121978, 799576681, 558308849, 113788713, 907580402, 773993752, 272549632, 842690798, 267959223, 755472497, 789820620, 26361818, 43860648, 160481998, 209012762, 829219237, 315437588, 914233071, 877318124, 54420481, 694579096, 696149548, 733300822, 451662301, 571227951, 97067078, 35424107, 868321812, 134708083, 451790745, 810347592, 850656055, 395850573, 407380795, 303365359, 449823115, 369070052, 313946831, 866017326, 912157599, 929233112, 626668676, 695889064, 431225309, 509769357, 19930167, 719013341, 712215110, 933343372, 57981427, 887596285, 590807009, 874182380, 120507255, 198543410, 369743752, 793799077, 680857854, 515581560, 319201048, 452483529, 692744351, 521835990, 477275380, 683024723, 692314022, 696934813, 534050163, 10391463, 394129242, 534482876, 237642900, 65598493, 407686512, 336217822, 820314054, 917810023, 928732418, 901312913, 757845187, 221084558, 40296587, 860864457, 105346502, 92159415, 756191461, 801453106, 577137553, 168803970, 681665839, 583282880, 381321747, 942465428, 654726895, 852572876, 320333453, 186370985, 720771289, 518552735, 866537027, 949924042, 106665417, 213436261, 95615208, 942713181, 766428630, 850920970, 105109854, 99022906, 301501451, 714567423, 400326758, 614744733, 980671531, 48368283, 298672952, 493589886, 632120875, 532329520, 840700238, 414783676, 917358182, 13849266, 263339269, 291998584, 587956421, 922004876, 279886412, 380013437, 579059391, 154422599, 581712079, 455895913, 384364458, 214214516, 526080888, 836105044, 741228629, 486387969, 964304991, 793132515, 516331387, 650660843, 582200669, 866885503, 488093538, 875492075, 404850934, 268927179, 864990673, 254635178, 718145272, 684996444, 5570375, 711144327, 367193702, 326705053, 265697343, 110996427, 364004741, 982521479, 574983515, 292950817, 200599756, 850309423, 120247264, 272031696, 378958075, 444616971, 375238118, 592889182, 522545701, 384792339, 829135181, 652570564, 542500371, 21490391, 518994475, 769803130, 667929838, 831026070, 565356333, 814778043, 980514928, 534810970, 235683970, 770711496, 456959338, 130580535, 429913060, 693146237, 893596359, 150237832, 623901780, 24955420, 758677244, 683826033, 32751933, 687246890, 920376141, 44059763, 206189172, 779755072, 228125848, 284545518, 36130352, 79834813, 134926384, 574476397, 376040, 803880556, 517389210, 417325092, 930129493, 716372089, 296779740, 149961999, 440722102, 414551794, 171358789, 602693270, 790390075, 415172446, 972649159, 507123138, 260330617, 955697677, 688498836, 850768931, 557613802, 25046253, 851182505, 621029551, 296243037, 677427431, 556619846, 876023627, 772622608, 450392159, 681370067, 772211310, 348639884, 714744090, 550373688, 602190662, 676201832, 738276061, 387901645, 863939457, 722451716, 710114627, 31969674, 920513079, 435301114, 217673533, 418524233, 810701192, 587687584, 980744715, 511567964, 616381604, 364715966, 680216488, 303798206, 532614425, 172092012, 682040294, 237201707, 881673581, 857871287, 603015009, 61255080, 239244457, 990293944, 100161687, 553362148, 230402228, 467361363, 772524061, 926680815, 483883214, 288761756, 716483088, 209609777, 765826347, 613482686, 214801193, 714647210, 566757887, 646227272, 842767620, 255749895, 277754928, 36853066, 91855199, 453776434, 62838713, 27191314, 279230930, 198844828, 17278153, 295090422, 190912569, 138227180, 222506206, 631978198, 117158330, 527118820, 817119896, 128970895, 524671221, 405557394, 246431438, 68704571, 157679935, 294523339, 790981188, 918651776, 368322397, 318010189, 410575622, 494304015, 179940090, 962044655, 45997876, 626779330, 190966194, 787888528, 492513935, 161787803, 783034882, 672583634, 545035874, 49430096, 944663250, 446660749, 457088655, 778540426, 252473221, 965149368, 343922219, 649287125, 527240620, 678181820, 11187082, 98777536, 1853308, 66250875, 787817634, 272576328, 89948356, 484008708, 582583500, 410266943, 712476335, 647629680, 221551989, 886942561, 1908450, 47511267, 477427936, 465791489, 17483474, 927474836, 48084365, 774095145, 990902171, 120638760, 964482180, 379090601, 537122549, 752402597, 491966041, 23687209, 854507954, 457473794, 839894733, 530652497, 453358242, 576077582, 981971866, 711674169, 709430531, 647943727, 876611044, 728285217, 769163815, 400278290, 672312379, 674840669, 7769616, 560755884, 750556615, 38142945, 183556208, 299735398, 338327322, 697786936, 120928551, 891003589, 397271951, 681917588, 692196926, 25877270, 273656862, 116960535, 458749063, 878868851, 430203760, 662683356, 454806847, 55101326, 496828187, 123297613, 932639343, 423439826, 633306286, 398223617, 396180473, 507505188, 197958818, 243389366, 213396199, 787293909, 147716951, 361558144, 875950600, 354906796, 477636859, 942837670, 997398633, 95492024, 991148588, 431342359, 881836049, 71826532, 162990613, 657452404, 431709824, 242912233, 252904222, 364381958, 121973730, 83404069, 109387824, 754196893, 191707321, 168411420, 773641118, 70798162, 951321748, 684821727, 960172075, 818796622, 88533058, 282885094, 965336393, 176141487, 538615162, 467144579, 73086666, 750017352, 211936837, 896021806, 707836500, 506590047, 194455955, 899906043, 159793296, 997725941, 129574686, 465632353, 697758541, 917637653, 387399335, 492050452, 51229230, 756731134, 750169813, 879832987, 573913645, 161808320, 741320087, 357152118, 157022401, 794940243, 608153429, 256945643, 260971152, 795580573, 910631662, 712387323, 185674301, 30121646, 435139389, 415688177, 420141667, 464634167, 19260635, 466547109, 835771343, 141465533, 975700784, 202588411, 72638826, 164466351, 289459109, 36182903, 239704823, 268832240, 513590080, 178862716, 346206457, 586663822, 925131742, 922031809, 749573404, 468022716, 340437215, 613034473, 393853485, 513881430, 124189816, 131889078, 776918727, 20664858, 583314185, 621842208, 910576063, 670711456, 2425344, 558424037, 524071743, 836858853, 550095029, 959510419, 963998613, 478407602, 375298539, 141396226, 611854734, 963346213, 23637685, 653168416, 546975078, 454441760, 50526581, 11428745, 147046226, 819971836, 900331567, 76561069, 290606880, 546556240, 262098571, 218773575, 114612974, 238097497, 880247328, 222576960, 28469507, 961938469, 963840243, 180693394, 666680659, 920797884, 320104563, 773556184, 159590040, 94814384, 161473392, 363258482, 197517919, 509151349, 50874660, 663783919, 389081299, 669702026, 925911412, 561245876, 429387045, 269185631, 651559625, 799174400, 109253474, 151968315, 336423044, 386077688, 750802971, 321479651, 771928877, 619659976, 964687903, 378728122, 821210743, 832171502, 227465199, 956208380, 889280186, 925375711, 637628731, 811604675, 739216468, 592638189, 82784139, 72423201, 982402109, 950684214, 576605466, 920291954, 250067481, 522137782, 954283141, 378282026, 448699971, 293712929, 297152112, 215495054, 967862844, 100749604, 903656717, 897703369, 227835547, 124823164, 57165720, 767921770, 583391086, 501694421, 405280872, 745979612, 923961563, 599545999, 351012334, 431900066, 250761463, 713826088, 666832423, 710653107, 88057938, 501332861, 965970810, 669021345, 487829654, 671122194, 682597637, 871773594, 287848249, 562071499, 243531239, 152705970, 151083337, 489414456, 193474326, 360231907, 603825675, 303065727, 41292205, 358000022, 451632717, 83805122, 385690458, 699783620, 69932015, 855092591, 20254903, 742564359, 338812379, 172158740, 759664004, 672626956, 50142697, 646254061, 35228171, 221773893, 781911810, 315018347, 886535474, 388040960, 853349158, 683127546, 981100150, 407021009, 215143467, 535800583, 612520821, 391949832, 457780795, 175988719, 315110011, 990783967, 431382494, 984695635, 525377962, 200421864, 434952292, 786539298, 214783351, 24874876, 133307338, 951434448, 693124599, 903258294, 782523497, 505797524, 861039022, 355172498, 953289880, 986157939, 989724246, 239367964, 530717691, 513400187, 12035253, 38216372, 223460404, 336324263, 503072370, 541553706, 941371157, 475589941, 367352522, 385823355, 805385408, 375096645, 135453609, 958226597, 387881677, 297222332, 762577877, 762770115, 118226204, 373872526, 543209616, 159643874, 666727030, 686282412, 591249697, 910669556, 16963229, 341426900, 861407152, 578201471, 423169514, 72169917, 39626743, 435326638, 423199487, 868213901, 973877706, 679035267, 219246534, 304668370, 58083992, 37677382, 756457231, 329300322, 842023599, 580183047, 485047813, 762818917, 137593555, 222921479, 635974814, 268734612, 235944276, 352126652, 360242133, 593407356, 853867255, 469076413, 815976645, 96646356, 418143840, 134095206, 265380985, 936173095, 944455058, 557789200, 277805037, 677819802, 576669692, 268538534, 828908530, 820735870, 951345774, 711794447, 924076096, 657342834, 425890710, 798682365, 689248851, 168459894, 823675503, 816866314, 474869241, 188643250, 960771615, 862606025, 961085006, 221609891, 732423791, 948028385, 435989822, 205319360, 316459031, 753597891, 529056227, 892759962, 274250633, 547499987, 445147485, 506216019, 736772584, 405508332, 889663256, 572848579, 204831516, 547465007, 818171649, 506552791, 877181749, 338670786, 241179195, 940416745, 406903895, 478685898, 893994740, 62090731, 359866286, 479271962, 995542471, 524526743, 330553397, 88160527, 864435074, 531384718, 904272563, 272099224, 232428325, 771496781, 611752309, 482829362, 626532252, 469547488, 406151417, 673991492, 982230677, 110608144, 305472707, 202102722, 911354329, 566510721, 978366584, 91536627, 421495913, 917759132, 19213889, 90189152, 798543597, 634182145, 139064302, 437464008, 721618959, 17823511, 847061648, 550786224, 606080999, 275890052, 585065939, 227637404, 740433782, 313011158, 328908951, 231901691, 225019884, 452726941, 954848383, 652630139, 819300286, 7058772, 516399762, 922568409, 287528309, 697258359, 106122212, 365031094, 762031022, 97889283, 415494804, 183334472, 891144412, 970585419, 401652716, 544445400, 522072845, 470375412, 829602586, 620215909, 316415776, 393208198, 451001485, 990746608, 645083613, 376611177, 667407726, 55746839, 362437643, 471089962, 43989236, 732120110, 778905674, 677648772, 41627677, 323274092, 387118039, 379081206, 970998182, 131889231, 248507290, 285301826, 755715978, 197416720, 404595113, 173096886, 399637131, 263236646, 467806592, 285387327, 298170886, 617944894, 512707466, 754372474, 117692189, 223989691, 62903061, 479605065, 163368677, 346895642, 133812726, 845714434, 495932465, 658035517, 207747278, 599301397, 912863798, 92202870, 285404463, 592803951, 781361083, 962093247, 583853499, 218237798, 386949128, 343895607, 971697754, 866484826, 640802299, 80197980, 313726857, 773149992, 605161329, 455638442, 428265953, 892777295, 982527498, 40791588, 560570515, 436600933, 478219144, 438144611, 422825526, 259795103, 857629820, 212850592, 594068238, 843254073, 973752375, 560681021, 239828553, 900366410, 885318507, 483605019, 215637614, 324569995, 332406731, 767896754, 922009278, 296986916, 681109404, 800656703, 728333631, 52585276, 551728994, 627789000, 784744640, 544897026, 383860120, 759196839, 828596683, 377137115, 360170936, 768115968, 174490284, 395300266, 485846210, 578501760, 909874985, 678280865, 618472277, 676364952, 933757206, 399741200, 243305405, 64278304, 366454816, 664749865, 293952296, 968895913, 813469551, 60181934, 666293359, 823010485, 937025608, 264627387, 580768287, 377638609, 880875020, 172389997, 817456019, 546280000, 72670078, 263214339, 188906769, 312017742, 18775803, 174065663, 460119932, 120839350, 674939293, 767743814, 26923210, 967748308, 112760854, 355835935, 447716699, 595213499, 545196428, 389926502, 236496079, 613053500, 875552527, 645546339, 949719764, 465665286, 354090667, 173640591, 216017586, 235896169, 590336193, 525064112, 136490918, 265430775, 989989389, 973747529, 346285065, 852969387, 689503931, 670635492, 629906259, 938176303, 96110328, 486024168, 2206499, 700928398, 885045157, 833889824, 133978281, 7923685, 128263291, 701498533, 9354286, 50491603, 523571295, 555424423, 970335891, 90614422, 287003499, 335702805, 311852763, 551623285, 43720590, 25487458, 463866267, 966848903, 553844800, 10055852, 697504952, 740841029, 943253704, 784217052, 575784958, 322338761, 516406855, 173550061, 816450501, 236192205, 489894677, 871324998, 349414932, 760343463, 143091013, 691633639, 718959354, 488874422, 9453637, 929013282, 687983658, 838469932, 362222469, 42629464, 23023075, 160157568, 759385699, 869335896, 925772315, 561355367, 525955097, 872723029, 91560619, 158351306, 924804652, 195013569, 425642617, 854202408, 459801242, 23645352, 721328094, 552182552, 3351707, 846122874, 875441719, 942452367, 662027549, 131395764, 840741328, 873252774, 995898964, 160013325, 959282292, 805739719, 766997606, 427106559, 523130204, 480690469, 897671965, 556031283, 965354800, 730050931, 602008730, 473153208, 244673957, 25112095, 59035890, 522563790, 199678615, 685499551, 289838972, 230061461, 132305402, 483663425, 960746561, 488677482, 178038459, 421901761, 939955394, 721357881, 66652909, 781025115, 467816808, 831092720, 350300031, 292178517, 702002781, 986894001, 393409643, 761581637, 816326850, 401403349, 927965492, 902274360, 245962260, 143531290, 398984105, 417453273, 986993044, 936744368, 376078970, 525251249, 270971582, 461410882, 72981590, 220997600, 587683378, 591648179, 331287372, 968833923, 822596760, 778998702, 941521294, 858640569, 808479357, 110497576, 57396930, 256955004, 585608823, 236065997, 703205691, 746919789, 474985313, 240309315, 17526834, 713916040, 826234210, 103346086, 185769110, 410415522, 551943577, 687871662, 361495253, 161579828, 43969667, 531915733, 699045808, 312692851, 117510341, 60873779, 657795195, 496107297, 247052816, 409350349, 654254733, 418569138, 329822442, 794579782, 191478659, 906933594, 481488950, 840039898, 151063715, 877423139, 489138466, 419975351, 708366073, 179201076, 15403111, 102002181, 726941971, 682429311, 170746037, 522023826, 340714209, 947221573, 744966558, 61700876, 969844367, 81724583, 177105666, 476786394, 126092909, 473243552, 857823341, 561342062, 1950164, 650468558, 364317885, 37497996, 426588110, 766325248, 165727498, 377652088, 870561804, 948127809, 366634230, 981134891, 324337709, 675688756, 884334884, 773279952, 408674853, 937844205, 812544291, 32305020, 991828200, 660984350, 503177235, 927124578, 846638656, 486551167, 865653268, 487626128, 668409434, 29004665, 591231153, 443999401, 648371255, 643825439, 910709894, 255057559, 648630325, 579183732, 652993616, 257823539, 714161094, 136541350, 574495905, 76720960, 190632072, 417444530, 304149634, 170836742, 45188149, 117391230, 100829775, 361072328, 443051171, 318014558, 169593804, 214436098, 103598884, 231202136, 507258096, 693185119, 202155992, 961652439, 976349743, 559917668, 872056234, 888513965, 273311120, 960795928, 347166919, 731078491, 652737576, 971007319, 228899402, 645226791, 948062121, 932307718, 50639227, 400195416, 369136560, 455196994, 555612996, 808164238, 819068161, 741489630, 977403371, 658969736, 296785969, 664643147, 859521999, 785693464, 681644119, 434337414, 741397672, 83270381, 697067266, 989574075, 485810378, 362120026, 85821266, 186209716, 821342284, 336655257, 812225390, 201596621, 726499291, 491702122, 262363716, 155687642, 282282511, 262769968, 756205548, 971962, 921732270, 118046884, 386358617, 308791122, 215818302, 489586853, 32448832, 722330571, 571685286, 549699721, 737454722, 112741631, 390000399, 569929907, 824653881, 113167534, 224034182, 603869789, 343335208, 114809976, 79566661, 667699981, 89767431, 32686383, 312227049, 167177142, 961088792, 178873944, 608690720, 482320428, 48160885, 355600796, 232684351, 454138451, 817074340, 266237176, 653346727, 670429387, 927101151, 306129136, 198399880, 600108027, 730955009, 890157613, 860758407, 666283938, 79338775, 20301367, 577613071, 894462129, 174876144, 759910428, 585605680, 373111785, 373217299, 754871146, 567189864, 87796790, 622312334, 533262721, 545802946, 890012591, 473599724, 925727195, 357973571, 479054151, 85090483, 506355684, 728267653, 624213187, 419829336, 907914081, 637242239, 903662735, 147127600, 265847146, 934400884, 118851207, 235064096, 37892961, 370941544, 425163828, 219004765, 644607772, 320818169, 682084551, 260697159, 758040417, 828535267, 675823186, 472377233, 154399448, 632309253, 220067652, 937672009, 471135531, 898054677, 57535850, 16838276, 24137792, 999322825, 176203333, 257320767, 128629863, 964896015, 969869916, 239031605, 288234834, 948347961, 732508726, 409779988, 582448837, 725365187, 700758549, 974029665, 987685733, 208157229, 705223782, 643642186, 421148068, 43784342, 38836383, 504153539, 545319461, 47297170, 856264868, 948072254, 894518778, 562473688, 659509714, 548253669, 91044579, 704120130, 674908751, 349480934, 123372199, 166371877, 939701438, 237401965, 792308572, 546013809, 131537488, 415949979, 867877439, 174149298, 57569861, 664998431, 678165458, 358916066, 51623567, 353717503, 461599611, 40499155, 369593471, 36676759, 264812475, 123715641, 470688370, 593472824, 888327082, 959345626, 525813245, 803211641, 33680413, 7152350, 9533475, 67154487, 230149005, 705440769, 564287215, 839554901, 439693, 58630236, 632621303, 193915581, 860547841, 42642979, 371122612, 133215996, 179278438, 946692336, 130456065, 528801948, 630991102, 567783980, 586657279, 832806122, 345190553, 374305766, 439913458, 758950359, 569035316, 25405455, 334777719, 78969806, 469171060, 288873447, 572426436, 282256600, 775289958, 141901153, 469542832, 423519670, 399428638, 470406167, 614954380, 863059093, 816921958, 430706384, 61206815, 672397939, 466256017, 207553294, 479373210, 560183259, 271960753, 608420930, 220789815, 224659139, 375078449, 877030288, 898878905, 401678290, 660371704, 326951799, 949890650, 810691450, 733410621, 580874766, 633436165, 66966220, 389326689, 313396849, 139309842, 433084417, 229927478, 431277552, 194484188, 70923261, 733141318, 585005130, 838304891, 130553005, 889943815, 820460585, 363133071, 338016718, 363880448, 795406273, 741595375, 864885523, 422268059, 158762460, 654719400, 610747512, 388933379, 552288255, 841268100, 649400929, 561263206, 835514764, 920671985, 320832044, 765676994, 122589299, 79283088, 765759620, 873565544, 81605367, 888507061, 713469328, 341204338, 889329646, 530895806, 767226163, 541246571, 139209837, 765376270, 767833885, 316375726, 882259350, 529830601, 793495591, 771521026, 187599318, 790057604, 779209879, 364817410, 504708141, 560766401, 476329153, 238532911, 493558338, 948635418, 675549130, 958231709, 577844914, 929863319, 224493682, 275112393, 624487428, 141846201, 324623267, 287024816, 506520244, 506977776, 322908743, 976445103, 63693151, 721463596, 712066519, 353758458, 573328372, 307954379, 411253196, 966558107, 30622353, 248747469, 569264185, 94026131, 405736092, 775457203, 413495482, 47827349, 514301740, 209128485, 129513115, 791538074, 450786746, 855533020, 957750087, 698485616, 492581427, 204527145, 81357909, 970255042, 452557132, 258691013, 49775000, 339849587, 164142201, 873412158, 703236150, 719328439, 246770862, 146074393, 448828285, 123131600, 480165499, 318144199, 485481918, 924427704, 784137743, 114205664, 582652572, 785524683, 741501256, 661776278, 133438654, 4006172, 386432524, 725888498, 755756547, 3680007, 316027353, 448160006, 398810294, 515445604, 620572806, 512121573, 466445888, 931093571, 580919835, 314419761, 617687804, 842032613, 846770922, 907206263, 347278080, 286460903, 652945512, 554115165, 260646233, 815877527, 430449681, 691984032, 89028337, 588521566, 780085387, 566355042, 429913487, 42789379, 99829926, 936705619, 679335571, 998726690, 85328008, 501063127, 740141131, 46162349, 330414828, 402696027, 732745281, 262969170, 910343505, 586070865, 163887961, 66025593, 972354619, 293850591, 576135593, 265996767, 607334905, 749207587, 569041329, 855150047, 503777289, 6173687, 178315177, 750762154, 51424231, 33796580, 121052392, 908308829, 581431255, 258924928, 973320903, 93366171, 6503797, 597217665, 314985936, 904172156, 911450384, 521553619, 749588040, 265243981, 654167351, 287452972, 356166895, 8220813, 732956100, 550477169, 175423306, 99093909, 414975847, 757970733, 103969369, 66421878, 712006509, 989216382, 576890915, 795643276, 78577570, 360529040, 361812012, 433535405, 192629086, 925124614, 437961832, 49246140, 689999553, 565822180, 22971266, 50266551, 758288487, 744425768, 796441458, 967387998, 33430524, 188466216, 732917336, 312556134, 423963113, 168550387, 350690114, 145310337, 364558808, 347593395, 709636014, 945108455, 671566789, 828181309, 220065977, 150351674, 100734715, 261336962, 886771332, 943535182, 446786616, 758388721, 689367384, 284512716, 486842493, 81021949, 448822193, 43135728, 150155604, 740667260, 854317117, 8326871, 371001426, 363448344, 933716475, 360341510, 318322509, 539834538, 345588807, 557888330, 809321779, 998910262, 639440773, 165269137, 524935848, 640240621, 243339118, 726981224, 35761187, 494300067, 992653190, 92210298, 302996144, 846826660, 720653338, 875143355, 181138170, 671299202, 991940965, 196195445, 78536551, 448296750, 535525141, 373413194, 833686775, 114915586, 990515304, 728587357, 152884375, 379621636, 222320007, 492198611, 4272683, 57930557, 436384161, 827997364, 905778380, 273742775, 508179215, 717769547, 608948993, 196291324, 10164407, 97813745, 35222133, 930891959, 874410288, 124259331, 15608370, 256325131, 244234687, 556379437, 586206779, 952021692, 4652030, 915043394, 279008014, 857429902, 890220512, 302201939, 305407260, 632865272, 614380002, 281205725, 363506537, 604314400, 381833535, 843581038, 78161400, 951559833, 13260176, 67211565, 923355954, 471116546, 800607159, 392937123, 355406020, 429844235, 134255046, 571160861, 903721209, 517550733, 489520853, 449706526, 768047558, 320910658, 674021521, 748448968, 182146580, 103076942, 789593777, 718666274, 640505281, 645430243, 947556837, 787598027, 2447642, 687442132, 752080623, 377867102, 26438417, 285016861, 150625668, 213166511, 580501556, 895288605, 21849366, 76661503, 278969455, 336497719, 728774076, 572103279, 101179756, 395689447, 195837654, 367345598, 212884006, 380505628, 399251664, 621160694, 51374556, 483240249, 487430698, 607534604, 1265225, 3814582, 277091546, 86498077, 843280645, 652299465, 665046698, 777145470, 949576078, 919101823, 102172560, 445094612, 725426868, 608555580, 702831769, 948159218, 305239540, 238834963, 984564673, 875005929, 596713859, 323332952, 689390217, 768867673, 645201655, 764042, 693748458, 839052260, 533225787, 134814176, 112977608, 451705762, 353507570, 635959353, 236190195, 684703195, 950210278, 522455419, 874025269, 539316458, 70618246, 263142310, 402388511, 250550480, 415389268, 82120625, 919423747, 130436340, 612149658, 857098793, 635436421, 298044755, 274240289, 791704955, 188248531, 527079831, 106711311, 142292579, 995950961, 538302240, 446367795, 345896290, 593940199, 729119924, 588586887, 318247821, 581677648, 119619323, 281906093, 32473029, 115250540, 112412175, 200440251, 32892598, 547188426, 630902521, 896831693, 652447848, 367094549, 659014251, 319671390, 234757003, 119199673, 412676452, 746410992, 948009543, 83549541, 374479575, 153730521, 580637702, 702148014, 718540177, 290767823, 728891921, 522252076, 617334404, 112229197, 541078048, 159257113, 7867766, 842253071, 698509123, 662102712, 157891057, 605074508, 166898048, 299369023, 705514247, 61129316, 609592887, 54622497, 742051540, 961673077, 479640496, 501242301, 492355489, 33192801, 58929878, 590529846, 994315046, 672700733, 745347663, 138111583, 149966276, 143359000, 907138084, 740297667, 356753525, 810983284, 275490430, 335309217, 402040636, 113183122, 121827608, 235136141, 136944699, 794596195, 101620600, 101356116, 529328847, 543773557, 329274294, 822747538, 157113429, 130781412, 762096006, 117788692, 463288359, 84406183, 694950174, 439182551, 640180188, 45896175, 711520608, 28335541, 194745171, 256513199, 588647587, 72260706, 579066223, 76622789, 988431476, 681768231, 571557349, 206108426, 308365347, 351927434, 347234294, 867194970, 211950876, 83352767, 347538436, 486738764, 385008380, 206944845, 167218288, 441656553, 729442141, 31218597, 165022450, 462981471, 966786625, 17312526, 886160073, 63605608, 352032781, 724254796, 458418470, 300258250, 797537678, 103091768, 508639908, 582601742, 69160514, 524344508, 921469160, 684290004, 960835534, 790792909, 605677796, 652058070, 705722105, 715635774, 817248874, 814798346, 837351320, 92156489, 517583077, 593686690, 491952271, 20182918, 416203831, 644639432, 751787226, 694486520, 599372209, 807482998, 702800189, 332947502, 767515368, 720786374, 443407723, 851541235, 267059886, 13120877, 265507666, 339745463, 527016810, 255476210, 383833261, 362817658, 462343570, 359888882, 854639004, 180088620, 126054595, 781159544, 415054174, 836322486, 214834785, 814291788, 884083440, 933117201, 300331476, 215612967, 619499992, 838368891, 744192967, 514277829, 277484205, 924588935, 948741289, 529606919, 205840555, 859671123, 714555037, 418752497, 740745094, 373202385, 475986548, 426404826, 598371597, 881872059, 725466107, 838033092, 251065961, 518572785, 973614068, 358671356, 523079572, 581886104, 190373165, 710655515, 148435561, 514556787, 265975399, 158694963, 592201651, 393982414, 116907114, 18774476, 267727985, 565861600, 977345221, 35694974, 564332016, 563486065, 846820962, 17295085, 335825297, 482399932, 592161546, 820847705, 915928866, 86202501, 471533606, 601397679, 844104879, 776807282, 233250642, 627783162, 96993327, 950345122, 163764005, 314101301, 571875420, 746320579, 642132945, 137155361, 481530459, 174853581, 918875362, 1975755, 605177242, 226225923, 177742603, 844323421, 810884044, 555677759, 79497713, 377826339, 610642968, 578006664, 139568262, 165854549, 46384806, 514124993, 40308798, 925812329, 139829529, 994305424, 708539986, 976091953, 41557546, 628616343, 658586918, 506436036, 623734761, 216291003, 923720287, 369847886, 752427129, 499311111, 810064011, 814082952, 69323074, 666344028, 954212056, 19988714, 606530788, 189967179, 995784003, 16047173, 420825300, 170173386, 133436116, 625221852, 436193291, 789814167, 440076340, 366889481, 190965736, 908369814, 514714179, 230110170, 206436257, 939506575, 871916997, 383649762, 678053254, 817683914, 958637682, 500964256, 903768898, 460325249, 87109913, 939904830, 236353841, 714548688, 796494020, 918150481, 369418962, 170957760, 712939054, 334417753, 268423866, 73462369, 424452041, 663721720, 975462799, 396085637, 973280899, 510757734, 398573614, 766458548, 742412326, 562025113, 886673004, 829838767, 228596774, 546913595, 319267377, 618116543, 572381609, 247803977, 683222864, 574238157, 963202487, 236320086, 687400735, 297793516, 997245608, 996675339, 635389552, 669333082, 512592751, 875932750, 587799853, 400301033, 183615861, 798816918, 408519968, 68351386, 518277156, 531732896, 257180482, 170457528, 872466126, 917011781, 797414255, 808892818, 591081809, 814149636, 51956910, 591285933, 912284219, 40211521, 484229477, 652082280, 32607334, 143137295, 31508098, 693890111, 983841694, 362188389, 975709695, 136798120, 470861519, 726454632, 777775897, 74554038, 600007123, 975277766, 378266830, 926726922, 277383886, 464475513, 214186599, 946026087, 990651332, 838152604, 190806448, 574979778, 377618150, 549120191, 548735400, 836621467, 289366065, 301678843, 736623427, 778024077, 648990288, 363167715, 343578453, 172820553, 60469571, 514153788, 885828331, 184109709, 704502930, 375243179, 783831224, 956089071, 524611639, 664039469, 657044376, 45821405, 403901760, 309865518, 162516413, 485079541, 863497440, 909298281, 138352555, 287667575, 772465015, 154139049, 966595683, 707605772, 261623709, 967412181, 746381320, 444297756, 822642392, 417734384, 583335234, 20938289, 48565750, 165112854, 195112866, 574145244, 837642490, 393557688, 575234190, 505366293, 608459422, 630833743, 535003335, 297717540, 664507419, 546406516, 306866781, 406383694, 616300997, 751355597, 342804699, 910165382, 964927398, 441237469, 967548193, 965224995, 517407605, 548964671, 257203515, 951896096, 813607533, 212172964, 844621016, 833880666, 116778311, 715395590, 739440330, 855738413, 105265552, 335691010, 206747046, 690726422, 797075350, 352003689, 835851624, 400325479, 308260958, 346035373, 442656918, 230079243, 63303473, 877454663, 229626540, 204580209, 960532969, 395730592, 350735387, 576696996, 803012971, 809656807, 3618355, 967627547, 622134835, 526616133, 140525826, 268571333, 828897111, 276965627, 112774079, 117379394, 740770889, 965999849, 408260028, 229816352, 86820168, 738520095, 713573005, 936718587, 954798030, 343553637, 930143139, 669853668, 916847824, 491469648, 910005358, 439304997, 525730225, 167187626, 462231352, 622874111, 713309510, 875690786, 478500732, 78288328, 507677229, 790494831, 811364957, 184010585, 799805178, 730724044, 868051588, 377989506, 29537517, 754779310, 232895193, 114094357, 364202175, 997595654, 148406441, 581177473, 140622653, 377278303, 755372156, 802106099, 109903959, 357257187, 52944000, 106332245, 204056210, 178777762, 516148652, 309427725, 268026408, 969916428, 470534448, 246331814, 387812310, 345033609, 754098486, 414293223, 453065975, 101261953, 848156122, 696644732, 72209275, 44605820, 58132560, 829477489, 541643812, 626315204, 863179246, 344220950, 350262847, 295564615, 893181089, 127954018, 794621593, 809889944, 66315717, 918374213, 415739652, 314200715, 561461893, 591222778, 255456333, 657932189, 41387322, 958871154, 394492291, 62409540, 66845475, 617426176, 38427431, 689922529, 225019980, 79881242, 282018028, 231723183, 212854585, 541772964, 156226852, 214136510, 145182052, 738664183, 545629520, 243607098, 168561793, 482831232, 224564069, 859918554, 298393624, 723108177, 263764184, 606885679, 405260039, 782853984, 942773706, 858010793, 317040396, 372623895, 360119900, 448879090, 979312313, 974444185, 797731091, 716805321, 742897805, 618589214, 98763294, 756726084, 581269868, 954129205, 958963189, 310176652, 834512723, 670775430, 174788124, 850579096, 585431497, 722812427, 759213863, 490287745, 831689039, 922467142, 696922554, 785682700, 175926624, 620552534, 736950255, 533713670, 425658853, 942699412, 229529841, 374935957, 54580543, 105072495, 474234464, 961263354, 241128930, 903246729, 592029225, 421555294, 681196577, 548010014, 103316, 110604608, 752802736, 392290456, 299288989, 55279192, 260505154, 447368382, 548687811, 187475241, 526814002, 393126442, 964601207, 732492074, 776031440, 18824339, 157272679, 552894273, 299178330, 622570469, 540305334, 267480888, 104480997, 451748388, 544848403, 529126230, 28433533, 889776765, 298107582, 49055241, 553490657, 603577810, 199292271, 570808346, 115259339, 874001441, 534897623, 260309741, 669864151, 274002666, 434378341, 59093172, 241490240, 889351732, 546051358, 776028130, 975218997, 513662934, 51350118, 418526118, 368124381, 193661075, 260676459, 679778823, 508333692, 798758724, 330941489, 496912187, 752928666, 650746327, 777846048, 887359390, 202860897, 741661107, 512808464, 150378939, 651102978, 616653925, 561971174, 416022321, 766329169, 572247629, 923113215, 64290191, 143539847, 936112167, 646540992, 113423996, 190256883, 643894838, 146101704, 787301183, 670244118, 690513637, 613288907, 285001559, 731086073, 745125216, 473397184, 156355772, 797820038, 644883565, 378048450, 938548768, 805419473, 79336369, 497534273, 89824224, 46524778, 528241297, 52930953, 921415150, 298446278, 715703330, 93047225, 193361757, 837871629, 541375564, 261740842, 694746933, 931304646, 463720414, 968656529, 673302817, 637062984, 294902472, 767777728, 643308096, 405908621, 203699692, 703291394, 888569860, 997458205, 322949296, 487472528, 884812371, 955657810, 848222499, 754087402, 678646662, 924056413, 350935853, 622287912, 231650902, 365136259, 127545277, 527616156, 532021199, 153368739, 844769644, 742013261, 643028109, 957098590, 636584375, 279938118, 437649491, 344028619, 395575744, 153715216, 747313672, 974451996, 183963644, 673854265, 876986776, 569696459, 494424661, 797935409, 228020199, 949092065, 372368128, 667572933, 420327981, 1370335, 583841631, 697777781, 486099808, 785253809, 656856245, 244920094, 276729760, 636611249, 810298230, 336688525, 107588674, 883899196, 852569404, 922936432, 376998422, 129391477, 309405037, 86084464, 165458144, 120249913, 777756242, 693966639, 308115720, 507793432, 318181301, 45509756, 368088879, 27270357, 544804237, 385501086, 90311234, 538802495, 277587147, 352853136, 416758375, 132824258, 310959610, 979154124, 426980530, 259941145, 107852094, 494516905, 46266440, 388812432, 543394319, 75513376, 820288092, 961358905, 834709709, 534404831, 273670225, 114088298, 888023312, 563029788, 831754580, 640137162, 848968006, 500333685, 262734260, 730921203, 510137731, 75085459, 31524303, 360124208, 817394038, 700694434, 504215125, 422750041, 117525523, 645625810, 685883801, 538280266, 618751352, 844051982, 824694400, 122700181, 554842785, 202819432, 84963850, 33122832, 710884652, 543924158, 393669286, 293148500, 618325522, 451748303, 93364102, 651656324, 810837588, 842724532, 624100345, 202576090, 278839967, 619233854, 138245890, 531993201, 955415378, 968933407, 231652559, 239989792, 625300805, 326412969, 304691922, 726001551, 454028242, 540692052, 318552549, 229046176, 263958105, 938619911, 820922390, 241280811, 199994497, 852390652, 496387300, 324549679, 525886114, 801341270, 961848584, 973263389, 875200369, 20830378, 104489555, 336584511, 434771737, 318015650, 608547183, 478510296, 453704922, 812850446, 558796171, 402541731, 298144835, 880218326, 375789452, 318049429, 516220155, 983356741, 554155888, 624579266, 326474276, 73030277, 271334365, 376360340, 841575065, 531123959, 966203342, 124384881, 325298762, 805462972, 903819891, 211737550, 295491188, 945831876, 84956690, 101494884, 271001641, 483498391, 654500109, 679057882, 182503314, 8271912, 998633409, 394831691, 521708181, 1733360, 981073300, 815586090, 23307717, 367279229, 913024195, 563223367, 522341497, 353604960, 261125289, 695608402, 659718554, 389350797, 744022407, 959985168, 946822462, 734090527, 673247896, 326684372, 201903352, 877575705, 428992706, 23097332, 668053307, 261863569, 497025921, 301281076, 628203416, 637426684, 971619874, 914024705, 173042595, 574541671, 141718678, 76155353, 330917248, 837135062, 865772937, 977707271, 526053051, 463987019, 704765315, 907581884, 704683974, 163747574, 131418646, 922167641, 808143644, 908329057, 303032182, 612043648, 423055338, 897818238, 929999257, 867327269, 813737015, 41055413, 64312266, 943548738, 670789200, 208823035, 666075126, 486507924, 977897216, 14083940, 463257894, 193836813, 121049423, 884681659, 647149181, 286624458, 837287465, 851039543, 266229318, 138013656, 407873925, 146351768, 6461417, 19790310, 145337811, 459796400, 205770054, 610896410, 216382426, 497877457, 220982427, 533338440, 35235941, 228828120, 540433982, 937868595, 457529904, 775382022, 170636831, 738587474, 896698823, 731452782, 174735832, 768963931, 959201248, 892534846, 796155143, 993599708, 325812466, 727949402, 936582172, 435464621, 129491508, 574739847, 805699668, 969529719, 983159066, 920090744, 279231607, 420941210, 628466093, 476189556, 361221019, 896718588, 838297276, 189675788, 801836161, 885155347, 919495226, 554381996, 864331629, 229688629, 393033443, 66629243, 825891248, 954463244, 932652174, 915577304, 12570300, 245585503, 761742809, 433436171, 314215816, 992792055, 739448856, 73408006, 380659340, 557352292, 594351226, 869898295, 700987861, 760080859, 747512073, 167841934, 67684137, 465720746, 697935998, 587014785, 169388310, 48807224, 347743558, 17088195, 264885854, 23567704, 118589031, 336665382, 583116593, 47190533, 842054386, 361208602, 97590652, 697747696, 650830564, 424799343, 925806356, 615333311, 582652316, 624785716, 414369717, 577624611, 317390730, 605320126, 505479316, 368912816, 290628717, 304203636, 620396991, 868991186, 432544075, 86910624, 535913876, 772885102, 706254863, 651857165, 187870985, 831402038, 924587296, 924664917, 367243432, 286382187, 253488200, 620685168, 71462529, 51652042, 884763792, 878543922, 969793504, 778235867, 690915499, 75242353, 462398210, 181011938, 975835078, 717009334, 649422791, 642534333, 556367840, 773427096, 869479473, 492393490, 406156169, 663308230, 699624795, 502565425, 947613072, 282862777, 533960178, 399795559, 2897454, 648019625, 607114054, 862256458, 765700750, 627843332, 906470411, 855896066, 711876680, 503463710, 53435759, 653304614, 618735109, 2520048, 791095687, 210518110, 278536522, 715432822, 413748074, 13825926, 570414886, 43330261, 508286807, 370513167, 963127493, 617426133, 698024031, 585147351, 528251733, 95747763, 889793728, 368695373, 365409780, 897444625, 180038609, 852221481, 506333721, 446194484, 707776564, 670636962, 239242608, 663159594, 261470371, 266072023, 63621171, 226576323, 572530145, 521459548, 220305602, 868747307, 533469765, 948499024, 983084453, 351267715, 267174394, 129163979, 911938522, 821218787, 673888726, 281553664, 141905811, 345693441, 3061218, 403301258, 373606973, 955542405, 474477831, 304152305, 559630926, 655843896, 111429743, 728649639, 747637555, 672528639, 911153022, 55536710, 990659043, 585192843, 182212583, 745691071, 270185474, 669134167, 923040067, 208752837, 612966100, 15761230, 76441109, 112132922, 278790166, 190036272, 985101917, 470645049, 54110323, 137007610, 379547925, 848153406, 213615407, 349419123, 354257302, 46443141, 693748681, 35650369, 285209127, 70458428, 917103937, 379559938, 657219180, 684443474, 258121732, 114563761, 688607795, 46825595, 369563350, 312896632, 883719848, 835386317, 392121970, 773443188, 352794456, 389876434, 907422259, 913047329, 958242946, 172819754, 943027992, 990116219, 409700441, 476429512, 787438359, 835866423, 640795449, 782417639, 188839133, 389440421, 231910453, 391423604, 577397638, 271951130, 256892007, 504544994, 72475303, 750058158, 957550601, 603202204, 119921061, 929877118, 866291830, 78607519, 54856254, 761607881, 564490323, 443778600, 276060, 904949601, 512119573, 863851348, 882560479, 46747771, 619953152, 798826966, 618100748, 961303696, 699784382, 414698315, 832616899, 206473507, 378238932, 314948390, 229257613, 597805436, 838045122, 703226114, 961950848, 772637058, 844993324, 289781949, 339892130, 954599865, 353379600, 489753665, 593581183, 641192051, 924391467, 748675884, 771783268, 814840638, 346307077, 363027924, 196193152, 696890534, 1898295, 195867604, 281935631, 349469309, 62392226, 518752655, 668869286, 513459529, 825537663, 207438347, 200886105, 95927475, 898231708, 311857667, 303103955, 756348020, 817469020, 984435664, 303951566, 494857662, 72059534, 843232879, 490799439, 606537732, 125501174, 24138707, 877100041, 210278819, 488901650, 868829846, 402277466, 561975466, 593648660, 803853049, 279263031, 758211196, 978735008, 687464078, 414942997, 352944044, 291803839, 464016197, 74501185, 705684118, 202939956, 337435526, 57406528, 76173907, 280988603, 615436383, 896316987, 780307796, 805789434, 192367414, 727350854, 220133602, 981066016, 736990970, 434947406, 19473967, 133764983, 20372012, 414948469, 716916654, 153579710, 470082689, 370480552, 856231050, 494752289, 386715594, 327916578, 94407789, 411095555, 873175264, 320965070, 652683875, 593710782, 419560103, 413489491, 918367228, 981964973, 825510625, 872371687, 153374157, 99528025, 469180715, 41374940, 10661702, 127432873, 176499171, 247632838, 28855725, 724609526, 753367677, 629498586, 188224904, 281666628, 48255296, 227688489, 366307144, 478476068, 675526919, 449066592, 407053240, 623264708, 794871032, 739087283, 453890992, 449307919, 284457874, 146279027, 818402649, 679932333, 432824782, 187149426, 984466640, 881197194, 62498977, 871638480, 152189637, 793361722, 876514128, 72578044, 60299321, 744553331, 376322423, 802772736, 903881822, 270139825, 728148750, 496642480, 235702683, 829846084, 362504806, 819122937, 136605321, 408911094, 679292971, 817110185, 279659665, 655644079, 983303651, 22571127, 232499558, 723286524, 594819293, 706753, 669012845, 563116331, 306625666, 777347982, 32653856, 943521027, 123128225, 755510749, 761196725, 327977990, 898041841, 278262408, 489718575, 265482004, 888405032, 38749287, 42953476, 525901400, 8319378, 463846092, 926140629, 472358581, 712784375, 461241792, 637042695, 392668547, 774435992, 904985831, 809379149, 906772679, 356921994, 869609733, 307633214, 546285988, 751173825, 316739098, 872224946, 883574556, 154141589, 746560056, 934826845, 981943199, 332897410, 2192, 652659492, 626223938, 387238229, 437990088, 131867652, 562809824, 314248031, 367268403, 182497570, 196619479, 169065008, 99532006, 393674437, 156596841, 12237272, 810432365, 496782445, 219450011, 907385917, 440651774, 854629510, 649893485, 847961502, 335849109, 863972479, 366563946, 990043228, 452212651, 758677191, 179492606, 257029103, 680387388, 747003452, 551649481, 752968972, 500702012, 64827185, 317750181, 597669587, 793871948, 258572069, 611468028, 835687165, 795287851, 680499159, 642156482, 483113001, 751817252, 785782371, 779387785, 588656163, 195969465, 553523677, 191915494, 381944650, 992395720, 763166702, 330684827, 319080506, 356591004, 358963387, 417076669, 989562486, 666780197, 166517154, 68239187, 620755772, 797364933, 746193157, 753436659, 619116506, 262096085, 374604715, 235032778, 316526106, 675211281, 942030934, 580470502, 848328200, 801309946, 691686581, 468829606, 968653378, 821231476, 283512738, 910427233, 414916605, 673897637, 221420052, 174227146, 263469889, 828944097, 133276303, 145172368, 155652747, 604895642, 13398295, 52866090, 800533100, 66202985, 366176115, 239960524, 784184848, 727224596, 215864718, 464586614, 400637718, 278707855, 231274670, 493024974, 384959339, 327182263, 681836722, 1425502, 170848405, 852952063, 512215945, 524087766, 22386812, 241321806, 733305400, 85168158, 911982138, 938762810, 807243527, 960412269, 611915491, 580206772, 479169536, 773921779, 850340623, 863853171, 703856303, 104817945, 414138279, 356272630, 809828861, 225313893, 328924744, 138916155, 774761638, 20477613, 775339590, 2095187, 494071825, 681301176, 334616950, 861299875, 84666172, 255968476, 435038569, 963270119, 749326859, 803471911, 380934107, 518705272, 526366651, 612940506, 434537501, 869967534, 793070789, 628403497, 735211557, 801430813, 753339326, 634215190, 266088866, 627964573, 913513334, 353879708, 928825037, 48924605, 511356261, 38896469, 946152284, 589227196, 217769624, 524339629, 880557584, 973126164, 576262072, 621373243, 897920455, 801029673, 23473871, 885288683, 206989449, 953633798, 214411392, 65399981, 215220662, 674027851, 228118843, 675384815, 903463287, 315499297, 865546196, 771618671, 864693478, 903231528, 818197229, 524529171, 544374741, 759656066, 568272127, 938331296, 112098492, 2932350, 331032221, 834356094, 385721137, 346919086, 265108169, 89006657, 321412806, 780716939, 602672244, 141595305, 309770166, 316737199, 18823443, 580506550, 766325813, 372558996, 546683400, 701595816, 937668533, 134496796, 372555898, 500867674, 483144886, 173767011, 875040205, 933243915, 463752814, 990019613, 868571030, 821143544, 365914968, 513232273, 138097226, 931489576, 509974540, 42746507, 670176996, 159930854, 520693754, 177316886, 378952239, 835134520, 160826833, 33246251, 412463466, 616079976, 238365215, 806334674, 910755643, 638145689, 151489829, 575796417, 687338838, 545700703, 102399534, 789753507, 58350680, 442301973, 30380040, 187973969, 276860293, 10529067, 831442762, 630077967, 279979080, 317145227, 402757723, 448376710, 283665824, 250503898, 562160239, 699418723, 724642398, 830887049, 686912263, 821293871, 304827466, 858702880, 673553952, 263619072, 807263426, 435919415, 368372407, 59488916, 894694580, 322481730, 114673702, 697100440, 710855958, 970701722, 583336373, 220582845, 597506983, 982082689, 685538597, 575305607, 907832241, 402461991, 273790957, 854985014, 572506407, 125583006, 950846781, 914035741, 244386812, 639370920, 882301012, 70403363, 240678140, 116984746, 926738015, 499810131, 307116070, 581717037, 523561535, 533818737, 591788665, 123261521, 821122230, 204218381, 314369989, 749931467, 876618459, 852048349, 6787268, 112383575, 951515500, 828254046, 255907460, 701949546, 292335717, 738305791, 171871042, 344046938, 483761272, 899921774, 531439472, 512192278, 744121463, 273221131, 663835209, 283349758, 810905617, 668774437, 742630923, 951669268, 20262547, 954062870, 85094508, 304289258, 744382570, 237733984, 369651623, 631869267, 812046294, 841468127, 610262965, 169619291, 219031916, 749070486, 500573983, 509939606, 948227668, 418079994, 11345757, 55409260, 428443074, 825950974, 959448611, 285932813, 979603257, 231016137, 253935485, 202239244, 44862852, 621198066, 112343872, 340251770, 642119138, 317838637, 670666472, 243905799, 43647893, 296603849, 53734137, 790739904, 271564605, 153463579, 869031470, 386763986, 363268245, 182311775, 178550421, 562876989, 953731866, 174749993, 964766427, 351253755, 61898172, 232105211, 765995997, 82723579, 599246905, 813897906, 534174540, 238843023, 587948238, 55893034, 789444599, 691753337, 871938673, 8492792, 996494073, 331645288, 410844443, 842939353, 627009904, 434701566, 835611615, 208435348, 440497456, 227263632, 456340127, 620600643, 555256227, 935559527, 151326051, 513686259, 633111404, 952202545, 977264058, 601176787, 550454344, 165360116, 503040520, 966177170, 512706441, 838117112, 777503711, 41769242, 941287258, 887075868, 537603585, 841954290, 133614728, 639392446, 160051215, 324125447, 216552251, 206892861, 870764285, 439658762, 565788743, 277979466, 10672797, 710944034, 937184274, 504950057, 514111568, 560043214, 383053697, 611601853, 395311310, 915211197, 153517563, 414260872, 247966997, 743366467, 69049348, 693593578, 759566784, 625345326, 272326369, 890987210, 382926800, 929615019, 457952276, 797747600, 652953311, 818560872, 390836666, 725431654, 618648367, 279471663, 586959178, 294910482, 945650237, 420662031, 491649396, 752279352, 369776382, 854263467, 76197636, 339083422, 467960341, 959032798, 77114530, 659033178, 124382220, 542412067, 654100584, 463524931, 702265410, 453709769, 286992157, 947547399, 552268277, 77053605, 93655879, 934568947, 782259001, 550413858, 612339465, 102301715, 379092377, 751581432, 889067106, 351621155, 718616573, 173863364, 77456891, 112578538, 234736818, 817054906, 814273416, 589371334, 397942708, 671385688, 347777130, 862811763, 103776448, 214558890, 818315771, 705245078, 902724873, 768969227, 422505972, 585029973, 939561420, 549166931, 543967578, 901910321, 869958186, 525201714, 249684770, 254188801, 171196413, 515233844, 402295930, 364261582, 931537296, 613030428, 359513031, 214497759, 499339645, 419728029, 86707024, 152069141, 199106446, 839584218, 685998841, 494685727, 962252604, 843093542, 619971564, 558751181, 593634291, 32350899, 354419374, 384307361, 200086528, 874380977, 813951655, 835051669, 192515333, 322407463, 410128619, 621928849, 111367893, 759580082, 569442893, 414021718, 477216891, 705437820, 220428195, 637723943, 960600264, 660062620, 879263824, 785525176, 499075495, 991708110, 70212211, 543366829, 998892058, 658238906, 335226321, 255411589, 171095638, 35336097, 88045685, 516674392, 604824830, 282614942, 467363071, 937726992, 293574475, 740468107, 921395707, 102048009, 781775711, 817436562, 662861176, 680822381, 913286867, 868115140, 856559913, 936252239, 544047844, 807258620, 348007488, 630232400, 577548559, 918871453, 162069086, 462953792, 140346420, 760974628, 187027244, 143693210, 548272498, 998859621, 507380742, 264068531, 246695758, 700749574, 259632007, 911157169, 526405378, 753207981, 992651451, 162251620, 763742336, 453140470, 765051969, 95027403, 115246976, 554700724, 240773467, 666447217, 920450966, 339452127, 435307216, 684789239, 696899235, 406211176, 474321440, 686168095, 261363031, 140157882, 686167015, 401692372, 33843209, 854881691, 643023522, 461285456, 40306365, 538707044, 355186258, 141415379, 873736472, 552864944, 561575598, 582663527, 861505696, 483692851, 617786289, 33622286, 59305863, 185445432, 132057046, 83325193, 700279367, 248949535, 794270548, 633292845, 392246441, 627081523, 309418022, 440714786, 271564458, 139402603, 867248507, 51941491, 514688719, 369906224, 706623176, 252719754, 461989536, 668429032, 172217529, 414713756, 577129402, 144164339, 350826227, 188476444, 603148629, 595696074, 491950060, 176904094, 86446972, 380922238, 282530120, 762684183, 901464170, 314901133, 982751785, 645243466, 607373047, 130625862, 373695176, 985437769, 674297946, 454581226, 190386942, 166141975, 772535195, 740268300, 564560496, 777677913, 183871958, 868604077, 686092057, 396801196, 446703630, 495536090, 763121335, 889019709, 292783739, 673508260, 26784746, 531850867, 296677124, 750936994, 287475424, 34844611, 454725016, 992648457, 717188185, 996038577, 490056308, 119204302, 213522976, 647999798, 489638342, 170075585, 256164762, 426094260, 751528684, 927998702, 396215993, 718894230, 200303980, 738997223, 233041063, 869928386, 962123845, 202328896, 769435799, 172638025, 861810940, 84211097, 626622989, 190170802, 266205836, 810016256, 265995887, 849350948, 663581160, 353099647, 678426999, 664962987, 643085040, 25887832, 129251781, 355235736, 726899051, 944520516, 329622253, 358289405, 395719534, 656712509, 930908775, 878791776, 918347047, 941546078, 795373863, 179994037, 202069273, 273982607, 413251591, 402149349, 407039272, 997800486, 645823083, 609409490, 74000274, 501908033, 718480230, 789439895, 462663407, 985294033, 562302668, 859085962, 104692311, 810663630, 646417821, 325953929, 127025698, 355768988, 905947346, 143277169, 209953702, 177468524, 467175525, 377856453, 800332147, 281981444, 904946709, 921687584, 282246627, 281142151, 424066820, 683315601, 998740707, 98447040, 745844050, 19111410, 885818644, 593360181, 450529245, 523843454, 554810586, 916020529, 795628593, 655833327, 498538488, 205334456, 306836339, 232600986, 205430942, 272839032, 729618383, 109394413, 644666313, 750743815, 878411744, 27686645, 581847396, 238038122, 102028393, 835920451, 15269968, 505855777, 602560490, 641483593, 26827159, 108427466, 956039161, 508072119, 71997470, 440033082, 26404842, 957766654, 313490725, 846287944, 770188802, 730840959, 54720803, 919212602, 250388658, 106328127, 139035218, 992422758, 327038616, 401339945, 529578197, 294302563, 346836174, 644651888, 94816095, 849779382, 951717157, 967478393, 388407598, 454986195, 995850207, 448423420, 263375322, 332884750, 434846221, 552938789, 407863623, 286125942, 574892709, 347713260, 910426646, 173874133, 764835097, 776069398, 609154922, 991855903, 107618076, 629136123, 307847007, 710076398, 166180463, 132295215, 511807681, 925259475, 15144988, 595827180, 956118659, 457421448, 166203219, 172453806, 309993096, 648706719, 875470141, 123393178, 606367504, 301411557, 21232050, 471170024, 911759285, 538311690, 913477377, 276536945, 584653063, 431504256, 589948931, 929968121, 914272500, 674461041, 625871554, 985355345, 220512656, 656127555, 926799244, 351042012, 697774226, 455568888, 873323637, 22107964, 796360945, 383160754, 7965890, 4636079, 97766141, 199182741, 625620074, 959437964, 747976098, 968186125, 909303072, 922451235, 292676973, 489358525, 475244730, 276223295, 175500938, 986401594, 785461472, 702302204, 177521210, 738080648, 156839724, 323694006, 454667, 82688268, 665777686, 583646325, 450911548, 942038157, 885784486, 529519020, 143759998, 237787826, 723142937, 399932541, 381598105, 68932071, 409067718, 367972030, 843652452, 630818834, 208538886, 548742370, 625665752, 141164744, 216918345, 328715435, 647325440, 187471841, 922012491, 841947045, 797498633, 481945845, 507729020, 636881455, 310536307, 188347137, 995412217, 920616152, 267241042, 924676700, 356682078, 787542506, 421654194, 598596768, 585418037, 835714984, 515669951, 311327507, 766524617, 798783660, 999857825, 495995025, 604693206, 179066278, 94805248, 758649557, 453806947, 260316354, 476343544, 593943328, 959648862, 332920281, 873954041, 236776059, 839993753, 663967576, 454079509, 132631797, 383783558, 21474045, 703489551, 988816896, 245887697, 101112590, 795143314, 466929806, 850272713, 717600851, 752962425, 414648026, 192933053, 385061867, 995833406, 639520374, 20404463, 371949057, 834744590, 858149917, 18724796, 518922769, 689570604, 95738871, 827760861, 392519225, 804277944, 62006701, 751363400, 839853665, 28821129, 695163928, 65758410, 897498003, 137192909, 706062514, 396336913, 175332144, 326725514, 421460783, 410709110, 933654864, 346968131, 729740363, 112342416, 209813611, 831488109, 881117074, 106353373, 975587577, 249848856, 714344519, 46434118, 732584381, 617872645, 294267140, 950113638, 552897151, 393794069, 123953149, 622835242, 943734817, 882159653, 111782873, 510722136, 862207302, 837919105, 271729829, 206197516, 90227504, 695174798, 680799556, 393831093, 516037735, 539915772, 284516789, 899235577, 208359898, 419112869, 459972800, 787051369, 61234902, 821522863, 266996711, 20286035, 526426786, 114015659, 905902746, 178018333, 84719735, 692149934, 138193549, 1807567, 95759683, 285196713, 156237164, 816796678, 491360690, 872060141, 183696997, 354837137, 324939033, 70524281, 64893916, 61196968, 217390066, 309803538, 327981913, 829204157, 222229748, 153316764, 785717225, 7285302, 335434214, 224435104, 395044035, 869620696, 983474094, 561990986, 7138215, 724165029, 537359771, 442392295, 214472757, 388115494, 999724473, 116134487, 925708176, 746427493, 66439494, 388110990, 695779202, 787660736, 190107323, 811559999, 745417727, 443310769, 275424987, 133133837, 820291374, 958741339, 246153527, 86591325, 939988951, 617124214, 898061442, 790179316, 739813209, 230639713, 557133055, 69014343, 36224542, 362472253, 656301172, 233606164, 107307741, 672115472, 137033497, 438401678, 937910960, 718467982, 866662565, 853247635, 819192886, 385931114, 456696865, 343695363, 925106189, 556664530, 842187059, 289014425, 979935624, 943427265, 108276470, 37109300, 996374235, 723841051, 713359382, 636128082, 700513246, 9762195, 679089480, 972432725, 59538558, 60141790, 197446722, 475606973, 207152394, 949822816, 667573484, 554375829, 805701045, 52118162, 573417072, 38618014, 379452772, 734815007, 279448974, 165855178, 837684185, 303266367, 42775691, 170054897, 152941720, 376346090, 80027775, 196385699, 666741353, 279200277, 598319876, 565951881, 223948077, 829086261, 404416220, 765857935, 32132946, 773944329, 323122800, 11380158, 700999829, 843122284, 284109052, 500783639, 986258308, 935535923, 125641497, 843022069, 438289011, 231629648, 520124168, 131854516, 889483637, 547741461, 321354783, 590548256, 408219947, 374068408, 833897018, 905627122, 322048739, 980087652, 964141892, 249046734, 355599006, 84387793, 582727503, 239545611, 676180110, 74197874, 568227380, 944415316, 395492152, 496507001, 384407231, 903594842, 93861193, 863718595, 245393920, 390032449, 220461144, 237393608, 498814221, 415326199, 870627747, 348157175, 452381582, 275898195, 245829230, 395004048, 238412407, 756000476, 799618515, 294766621, 653924366, 772578689, 217194004, 13383335, 323679355, 504209077, 924360425, 135691753, 86745224, 426518058, 469233839, 510890765, 747589077, 282204965, 929404088, 636660454, 388671559, 780383597, 410164735, 561408191, 338050992, 738720900, 839907255, 670353704, 971951235, 994241537, 388133760, 413989946, 323116881, 580993974, 25522031, 619596265, 318094310, 194066677, 510414573, 723471813, 92026411, 364369465, 998196257, 286942023, 417151157, 565231353, 709548719, 85073614, 113466139, 843769458, 654957516, 826079091, 226407387, 915118241, 808155449, 103804189, 212188916, 488368294, 348073490, 586046913, 833754902, 130789335, 159722771, 537679333, 347911397, 941887342, 886559423, 462310055, 218746555, 317818072, 162731075, 585011230, 212891590, 89999079, 627688822, 99201727, 533174107, 236405564, 941961201, 526654575, 232547817, 733145787, 960574151, 212417309, 41626117, 442141825, 106251091, 471526052, 290923897, 843313749, 30797354, 4809073, 565104219, 16440097, 701508143, 295751425, 679202763, 868158005, 564537667, 948841054, 881260394, 766290540, 11877525, 626151846, 599497681, 604976512, 16158726, 932435433, 563793216, 166588512, 220711642, 182313362, 932806038, 948741966, 514240338, 56127881, 483537474, 920437154, 457815376, 33219577, 831050238, 451738277, 486789041, 28341652, 548599215, 256184762, 688898843, 766956195, 603771139, 781991718, 632924959, 900128067, 155680449, 860135633, 491145985, 757838692, 130353361, 911118752, 446989264, 604834023, 405048958, 521529631, 83745171, 197353357, 756209742, 130616944, 989172992, 636866871, 241333350, 633921845, 54039164, 702823451, 304801770, 704209457, 392353135, 456796204, 920665001, 54635940, 475877781, 574356206, 887152622, 497741448, 172846328, 996337564, 496784157, 992776146, 774773305, 245802426, 424931427, 681676830, 556994026, 167411230, 470797333, 758489785, 750526101, 786197582, 597309187, 504526964, 8671467, 23352691, 259810451, 781155488, 558397011, 862411692, 761103380, 877706060, 762078887, 868157366, 949932214, 58952586, 375625154, 316169613, 766310089, 873718677, 63574937, 723738531, 766010913, 255660332, 668893637, 958316218, 422557891, 988679660, 454334828, 267919892, 200520728, 885078132, 275448207, 148544634, 140121798, 341414418, 832664314, 233224135, 333976464, 698067226, 855006806, 840885633, 343344781, 493507943, 909182849, 373882003, 132689307, 889316637, 394966380, 87683304, 639006233, 636737581, 381648955, 434811206, 341341450, 517227108, 332592976, 621581375, 147467541, 375198408, 265382654, 881133095, 55958149, 55528482, 240782512, 195961042, 508744491, 670326622, 349887885, 699892222, 76115330, 716658120, 931988425, 203111270, 957621881, 850792822, 690363446, 727887423, 788372688, 551675848, 7490140, 378795091, 207716683, 777135204, 214787207, 390293836, 539447117, 472749299, 495565626, 122014613, 377679720, 61316255, 971106655, 442328801, 134855299, 59144822, 11591070, 458031404, 679628737, 881979320, 948203981, 109821190, 133386303, 162204191, 886207836, 428164456, 582889994, 369724994, 959418687, 756309747, 874394586, 409049194, 744385532, 278195774, 166177573, 841648920, 965120577, 444912549, 709017102, 239078967, 912449961, 295180561, 335254010, 776554113, 124120981, 530049611, 26643368, 32945773, 166066492, 123378855, 454477025, 420725788, 525057445, 310175161, 493093700, 382996171, 122385563, 226927649, 831373620, 156248560, 462675930, 262829716, 5935627, 888163668, 713507206, 8986278, 118927471, 773147951, 306885039, 734202050, 709867921, 797477260, 696278355, 749019792, 633303419, 42997885, 303982469, 442995272, 893197299, 909642011, 576478351, 645157265, 984475116, 980047663, 738136709, 193569505, 953490128, 496633540, 966373333, 570469921, 528698806, 40725479, 772576359, 846855922, 755465888, 128372565, 927340119, 671731828, 211143696, 948582214, 60207593, 478378139, 964879962, 832429964, 67225441, 433276051, 611895020, 309039068, 297082442, 73835777, 329334192, 542586901, 265468861, 887258291, 191832647, 643018676, 859547521, 505247833, 61414050, 894904361, 305444113, 746228761, 364225994, 448600595, 17912070, 446492818, 88940650, 438043331, 600358245, 198912011, 824114323, 380919646, 111909036, 980712431, 143763923, 66540388, 91597656, 873215480, 187074040, 215883299, 874264350, 39685043, 815838587, 356722824, 66647109, 986271674, 114254662, 736392323, 195293704, 931358832, 643049545, 442727268, 322942283, 622183858, 611536694, 141575338, 650782768, 146605631, 107644958, 153116874, 75857484, 183518406, 434150301, 963273499, 604962360, 864625186, 940417183, 291733588, 813849297, 592422106, 127538183, 535298159, 767861471, 253074349, 79965695, 740884808, 1534787, 473541126, 922277117, 323773930, 375366967, 269001456, 505461412, 633464987, 994684633, 235940757, 83258183, 380609367, 581641814, 407437963, 955085238, 529082049, 464190844, 600031502, 922478591, 542476006, 934990743, 604687854, 724576189, 907111560, 328876963, 157288400, 579060805, 997166061, 836747364, 973163095, 848862673, 77351233, 991701225, 864764207, 636146409, 674944220, 108342325, 727576231, 119647541, 20496844, 694512349, 109142555, 610271699, 22973529, 663023945, 682846684, 83501717, 674960792, 875467258, 318087805, 818576359, 256625992, 559206721, 287224148, 175269848, 132872895, 318884026, 207310888, 640310423, 280321437, 943574242, 142031719, 90953374, 360438406, 41948168, 476667208, 424692316, 662574215, 27586630, 680858420, 165601698, 916291672, 773987947, 144382763, 1814363, 226572045, 981695768, 268798143, 469638341, 414251809, 564695733, 261405281, 455787290, 414489201, 999832789, 232617751, 861562109, 49464690, 975169353, 150979571, 332954308, 804879221, 912102871, 527994444, 14450550, 763885657, 276570292, 760359790, 976893891, 368053884, 651327583, 32902893, 550667476, 245929523, 661512280, 804622309, 387411803, 614965002, 163346087, 965305930, 99833236, 287755895, 513469571, 289752386, 185748142, 112001107, 203321793, 78710807, 83957557, 581153965, 197551229, 933929550, 288710366, 761855704, 331692240, 473228512, 31055618, 184407192, 454582832, 661493019, 966524315, 571026418, 191097431, 426905012, 591198668, 23137431, 186610065, 775801462, 483966563, 955206559, 72602673, 31734347, 784674414, 400215839, 219237124, 320193951, 98727393, 224802913, 996394984, 205714840, 811674906, 590599948, 790447070, 434630805, 832198624, 894326911, 568068253, 282374654, 322266700, 816916734, 329349495, 712051012, 808215169, 979693290, 922551960, 70485566, 292882480, 578087326, 200858330, 986934769, 410636874, 691302600, 47749011, 444535028, 116662367, 187922641, 828435865, 526308705, 149794426, 442336805, 92965073, 932783805, 608168555, 111866713, 903701308, 521518008, 976577753, 934809850, 27718368, 67399575, 918984147, 804921926, 405018451, 266079656, 831346722, 804215915, 885642590, 439383863, 601959350, 717673691, 818138764, 124127420, 864137427, 665564234, 455814392, 114849361, 46680929, 712366270, 721588150, 794861795, 3110019, 871035123, 103242621, 390273494, 962899677, 966635571, 477860706, 274391779, 904083140, 521461063, 835471615, 84205978, 243031241, 552085600, 275824953, 909612714, 583979588, 536026716, 401162418, 543956390, 368491600, 536161719, 532609341, 23003177, 310552126, 644957379, 612775394, 445649883, 101258233, 414565589, 870353690, 364170210, 739121881, 102351382, 646464715, 26491965, 551682967, 387689260, 251043322, 494013141, 600887365, 392790596, 811436965, 927707095, 825586838, 121597225, 762285302, 159161105, 368813546, 830098034, 840822205, 801314624, 442966993, 360721591, 222273493, 475571825, 187921539, 281795729, 379829955, 66262756, 464916183, 807838543, 272683609, 228037003, 292883618, 847110673, 901758822, 343658570, 212062564, 332717421, 750171688, 869999775, 910869767, 114708012, 182342441, 439727226, 87532016, 938871142, 17529474, 641978364, 950543063, 219632234, 366091495, 968356273, 167196627, 954856955, 44353608, 276535612, 447931109, 732256676, 322071904, 289652247, 709260606, 352775662, 417870200, 277859878, 160973028, 72984242, 915756583, 313687691, 565942062, 698050295, 788917654, 886894, 305755423, 773010406, 711843854, 213564740, 152945457, 791411500, 144888169, 717223627, 996221599, 914615146, 394247068, 588334525, 727514232, 335638671, 718762664, 687437263, 505434324, 589826817, 512126774, 294388123, 275361302, 177738350, 244448070, 974029754, 497233585, 365655350, 325557834, 392427350, 617532977, 876153834, 7693362, 804195076, 812803882, 381207856, 780815611, 218630886, 389205300, 992378205, 586061580, 783767908, 800894364, 280524780, 764660560, 914608629, 642755538, 437623905, 469644366, 382121265, 251731731, 780833262, 594798329, 726599515, 53598904, 479655090, 832345153, 322299657, 295458538, 894164289, 586536163, 732464109, 426276702, 803795343, 318870512, 60576151, 942717610, 59216417, 745474258, 184788379, 626289032, 453321622, 279130706, 458533018, 114337202, 286385260, 703655774, 915502170, 399081800, 402312130, 77020477, 682075194, 278319045, 156383047, 533506942, 190579167, 87695098, 972341161, 680241870, 143737869, 912235734, 891501675, 449034161, 7785703, 33434248, 366256842, 761113035, 935162892, 684258246, 988025223, 465073303, 430923676, 4361860, 982098602, 348349652, 878149152, 860932969, 698064495, 929972070, 319991446, 412639903, 739199620, 360259009, 650628168, 472558559, 15217078, 741855792, 24034456, 638612244, 361964367, 724091572, 264035740, 100952375, 878034009, 775946372, 231748957, 270775771, 344907948, 638427792, 402065596, 263055727, 185652292, 941174875, 945510249, 798762608, 520910427, 980017213, 154892626, 177602516, 796814040, 394177847, 678481320, 991974266, 650712705, 187801337, 820952483, 986711563, 804125675, 944704410, 565772990, 45216334, 466192275, 254724170, 745304066, 317075074, 132045017, 632896197, 761020612, 257893050, 782173625, 819605033, 229854253, 371860097, 847093980, 634603542, 665427130, 452772827, 637865551, 454164540, 199418230, 607524158, 778674829, 258401320, 117647831, 847516299, 206297633, 527316, 518886740, 428318114, 496762990, 654243480, 547767790, 752157424, 596640024, 61739824, 402472639, 434888543, 803044433, 511225578, 648403797, 736299009, 164551166, 781751985, 524519078, 538199930, 908383891, 417018186, 82183898, 439950352, 465528022, 565614119, 947377413, 868395879, 352417487, 708709166, 268829646, 543953486, 737735438, 616917266, 777550458, 7891068, 410788506, 245518316, 777171815, 671771661, 54396752, 827342737, 359892730, 278529136, 139657064, 745069332, 824875969, 903579425, 991015663, 816145484, 667095761, 788492800, 132846254, 969788393, 366213225, 565773039, 490382150, 643977148, 452671389, 957160043, 67914762, 697061532, 439180079, 1093016, 704337507, 230840616, 444667249, 655071365, 69148956, 826279507, 206710919, 83432490, 656870957, 49202723, 489365879, 81269722, 141516809, 740317230, 812932598, 558015072, 634628979, 639214261, 470994722, 915826969, 798821458, 648633715, 918431034, 954522104, 516241238, 313086531, 478628204, 51839316, 492538785, 529683302, 470147891, 391116515, 463380486, 765265856, 723238424, 198656608, 621218197, 656297582, 462592483, 676587632, 107108345, 774011924, 112314398, 8012842, 896820212, 796336824, 855674853, 86125417, 494770094, 450197020, 258910753, 356135520, 35578131, 14376996, 637432305, 702312875, 215210383, 706237293, 529675477, 206472324, 916200417, 977602457, 774149110, 636244885, 20572841, 292492553, 423421707, 921105438, 427873793, 219452344, 94927427, 570885189, 147634874, 592455156, 808197973, 506350095, 787396941, 674985129, 452826257, 75036949, 926608674, 935953347, 608385588, 975175535, 244862213, 867668438, 822001274, 774022828, 796360442, 716273198, 748077008, 611096698, 454204652, 837179445, 907651202, 673639363, 116631291, 386829604, 254279125, 570870542, 4224398, 59835991, 387085221, 543728229, 746335467, 452560185, 299053886, 656605830, 912106432, 926744567, 898991241, 601221363, 459112304, 681432953, 612703462, 777077656, 3025329, 292123731, 629528756, 257889372, 448214476, 789925417, 769996829, 536958327, 769838285, 42283370, 883636488, 739985453, 693655513, 489583078, 268171979, 457615698, 736130539, 404295568, 55209742, 786631540, 934902981, 750531383, 873249701, 371530919, 438258864, 897337729, 131491615, 718595987, 549615318, 588289048, 593107851, 38826345, 881363435, 477060384, 321332439, 570258069, 694353561, 286165434, 438492801, 709076661, 622509237, 564633377, 991702621, 253154502, 381965881, 679356886, 343598834, 19719083, 89210198, 161050193, 111056881, 412249174, 650289921, 555955879, 329562104, 951625977, 670371235, 570657081, 415729291, 696582178, 345276912, 764414712, 412828278, 983619025, 45799396, 500024509, 751880393, 664882192, 855774950, 980574954, 47403979, 68234020, 657824458, 131306824, 177355960, 483079993, 264515771, 513053474, 81935744, 247690484, 857395693, 692282775, 132259121, 275257634, 66022173, 181068379, 733444945, 762166399, 934262831, 379098734, 658659318, 566587875, 76819664, 922526411, 166945768, 713959006, 640673010, 787436587, 425689505, 41350709, 40809980, 143007079, 795909367, 159291253, 387572907, 54407739, 551761083, 766783761, 576930027, 180043345, 387761643, 713366539, 772160373, 77077576, 519727922, 427492805, 528034230, 21279411, 145127917, 628410377, 546309572, 546790147, 744428253, 903104601, 169458864, 236141611, 847513525, 729165146, 394754308, 685673703, 964666006, 300289735, 907730804, 944535392, 592767041, 503787752, 361616056, 514488249, 440700483, 936304405, 901875157, 860973341, 338594326, 397489613, 457092813, 125861098, 53762492, 361799567, 36611708, 926598867, 249341000, 644707234, 165591954, 78111101, 494716750, 248484253, 32635973, 229064045, 362544105, 392447507, 410694230, 636076547, 848352306, 776951753, 4423650, 550349799, 572219665, 423011144, 882503798, 598551932, 627299490, 609869987, 631643391, 799939393, 481998230, 940786620, 643040240, 901440264, 576071348, 956596515, 855187569, 175344891, 816746713, 410175782, 105388097, 849433004, 978728952, 419341271, 988554511, 923608802, 62972803, 78981882, 224793511, 41173183, 132715077, 545946646, 992302772, 312111314, 96647931, 879285335, 470866068, 472227839, 634208006, 364216086, 845969337, 85774940, 612455959, 651322367, 82398401, 318825898, 689819754, 202712002, 812855671, 531340927, 500283006, 524288160, 619881087, 245922835, 860893569, 440234490, 700456595, 778126889, 227217215, 289054995, 631683847, 461627534, 834095483, 191088531, 900098811, 64374128, 79017279, 567492717, 667333874, 75927726, 882703130, 653608433, 203245054, 248569914, 860565551, 449226165, 402964569, 506085069, 34662553, 325988739, 8074480, 708216356, 910954960, 371900417, 918607079, 276546114, 936244195, 596763749, 384511805, 992951978, 412963820, 723001015, 780583209, 383408740, 815079569, 951280831, 631656358, 74302029, 970120280, 244187901, 269198107, 570090435, 814022594, 955772265, 898839077, 412439783, 659272495, 891863297, 810105771, 231919786, 792089459, 524138679, 784219523, 666130284, 303310442, 878017574, 552283481, 537304401, 395718219, 648110750, 474172996, 216558093, 551212054, 906989464, 681696048, 496583395, 13014889, 460577570, 517703201, 21793957, 61403556, 722885363, 642995281, 889700493, 181210985, 634085056, 18171155, 679004411, 115795981, 597542580, 617667594, 209993656, 672003746, 393606560, 609515466, 204529604, 795260339, 440162325, 725269933, 29206980, 818786002, 804852299, 347150475, 26875881, 668410949, 842328308, 265026531, 765158372, 101705145, 716111015, 468176773, 727440806, 220401855, 593237273, 229490791, 448967071, 268212830, 953499890, 430900749, 569085284, 198872094, 567921270, 828051365, 88189574, 241850884, 352219989, 526565988, 492105785, 289925728, 909340542, 450463698, 687450878, 81473198, 973553328, 485448871, 753662175, 476071443, 73550588, 577654007, 163321700, 85315822, 745429451, 765206800, 939827772, 875963481, 743263350, 293817491, 630182081, 496827089, 817321585, 145171851, 697521600, 239509419, 155231912, 280580260, 697567793, 136609723, 120695596, 432981589, 750490258, 334026853, 484256240, 855800664, 849656113, 680835466, 530102635, 334336154, 519976095, 487584884, 500414262, 773525893, 263516442, 219474183, 907111604, 332537952, 433959397, 525813637, 645865700, 966845350, 889170495, 330797924, 835371408, 404626641, 334938854, 301780476, 314704877, 5927504, 828120981, 625871976, 612724185, 465268710, 139857856, 423949188, 250263767, 269162447, 133973142, 436353933, 945531027, 420548688, 481668853, 233084409, 419844797, 324686364, 823700817, 28684202, 826674160, 237148702, 327044276, 413174733, 514506882, 22544627, 293574881, 199812281, 244627027, 108618091, 508367116, 533877532, 698929438, 872658180, 309226868, 858572015, 455833626, 311822059, 778007344, 615373837, 657285052, 422671164, 102165814, 672993253, 296552528, 984561714, 396570635, 259412694, 262958464, 557750676, 743756848, 385070208, 357139391, 812415756, 776235466, 524368647, 276404479, 537683230, 729322750, 102160572, 586819620, 411324656, 884262427, 332909809, 600814843, 948990041, 399818652, 542112665, 187197822, 597252619, 600125853, 637647506, 544526832, 830127995, 617658269, 786681117, 565577862, 396826486, 153470554, 751416426, 508343683, 666794332, 608513467, 218849866, 496278583, 793184317, 644492316, 448446237, 64541586, 280767354, 393587597, 900358101, 576199471, 392539489, 168128812, 802159795, 545613990, 822456303, 431787134, 415304249, 792678869, 65677500, 274923574, 730533137, 139541209, 94516175, 762927462, 36897881, 799724385, 417610070, 779674174, 638302105, 939603468, 506277941, 546412843, 225684, 42997503, 369092994, 463914790, 378041206, 986977370, 435220144, 937748452, 147381396, 527275705, 963863390, 838770262, 809699519, 146215117, 296210905, 916398315, 381406954, 385221087, 459317093, 170230458, 986238765, 699049128, 292431221, 141530404, 117797892, 455525345, 256555399, 666467778, 939499067, 420691638, 115690183, 857397295, 369201016, 280257691, 707679067, 694182194, 815489247, 630024650, 62491526, 610661671, 468625537, 332972997, 33361760, 720944887, 685630975, 499966768, 165062098, 9563415, 114981388, 596289114, 564174217, 414592399, 732164890, 330546863, 792598267, 449352001, 480865981, 596376355, 639951600, 209817480, 283395779, 822266252, 54748003, 45690187, 122109637, 505823800, 326151015, 358400737, 73837174, 13972919, 766876242, 230631016, 867984102, 437242560, 221817281, 775566548, 221746374, 392979889, 455297600, 23626541, 271776741, 34500403, 282087630, 360462656, 706737466, 945863947, 841967608, 564662504, 516315910, 335102676, 252632236, 988450464, 919398147, 85119231, 606268843, 100268214, 620747724, 178919376, 726707942, 496613764, 745024029, 261992530, 253570057, 858132387, 472472174, 593728303, 327914959, 216421901, 446648858, 534878636, 665058392, 880813853, 299486483, 189203199, 858295416, 528657051, 629022081, 163486619, 622365914, 350852143, 751009730, 249753455, 748433547, 218120833, 507180868, 911115211, 59841376, 238744901, 249649260, 780568740, 707527508, 781476183, 110377533, 748826752, 716492568, 56528514, 902289048, 861299606, 883470205, 488340975, 151569517, 265660145, 679638041, 231951854, 995181716, 874497547, 191189755, 300166038, 552245348, 751360289, 457106583, 848878418, 798734896, 210231026, 932806680, 275253516, 132707267, 650354000, 545375181, 111842069, 514933207, 506736283, 763012410, 166500160, 467255815, 835728024, 886337719, 7423584, 401404087, 348995925, 906530252, 27329724, 195431881, 602829403, 708200851, 756557429, 836582872, 463807339, 848898327, 708674549, 344406822, 726560471, 201707459, 424898550, 243058951, 347398986, 990640001, 43278402, 304626730, 125029228, 761461403, 296500759, 556557819, 234854864, 738380400, 615538704, 55973811, 909351836, 108913710, 129457895, 69389340, 239606469, 470665490, 89105499, 589333495, 585279497, 553119914, 577779882, 412885735, 337363130, 344684352, 500356824, 761192668, 227675827, 548908931, 339834126, 191689423, 23255804, 25899994, 305323570, 80355921, 346507605, 125949268, 483219314, 533612708, 538098365, 374500291, 55074958, 504839840, 104891452, 194243473, 358666429, 661037675, 300094280, 49545714, 54786773, 32279794, 543919390, 818805324, 311068533, 886108551, 66793683, 927911011, 198981426, 643826860, 556078974, 540408232, 715531942, 152341837, 936043466, 816991944, 892278862, 435558112, 352193230, 155808563, 223923779, 183466745, 46962780, 378469678, 563368937, 981012759, 758061531, 316354699, 876198285, 363050383, 410625862, 749888536, 63226210, 196556368, 90784624, 481776393, 707634356, 733861093, 378216077, 747026400, 360437925, 370998997, 937363520, 512403871, 764800668, 31295508, 415414821, 499087662, 667897864, 837728252, 898924818, 492976663, 41623519, 699884705, 946894626, 378252855, 32850173, 427961728, 801113015, 29142557, 875833946, 916800261, 826524401, 507335150, 30272771, 250348252, 231974665, 50347644, 43200134, 909235590, 959656527, 734310847, 395571189, 251705795, 45163187, 666680456, 635392353, 190943831, 659985807, 597256047, 89384145, 526899415, 961156890, 853963877, 437021427, 843492168, 906872321, 684812699, 84793550, 876585623, 309615500, 181578226, 202684043, 608297473, 977007229, 766896331, 280330534, 863059731, 38329256, 465286939, 872683566, 213855020, 256429573, 640624282, 820067827, 847017955, 276034649, 7201311, 500648246, 438603590, 258331170, 372678923, 25133011, 903168859, 597308779, 158230717, 865964699, 981453012, 286857750, 443247972, 11790168, 188720686, 547172030, 376363023, 609683144, 428614632, 915373570, 509018488, 191937709, 123045756, 861212877, 16877136, 97699742, 502840819, 879212773, 382957991, 289983146, 719564206, 46779625, 891853354, 237707400, 801278201, 92257839, 250923060, 297390723, 279796271, 247244642, 371503988, 872486430, 964203989, 409092985, 226029674, 487283298, 914850196, 96008465, 319668324, 4695367, 775160292, 791521060, 955942438, 692409700, 485512970, 657696622, 661281474, 401892499, 842317887, 216456950, 792752416, 79451270, 922131916, 294839334, 234141295, 852951179, 926568728, 579911190, 28620941, 182976160, 158976315, 866936130, 848260973, 341740042, 788480180, 332009487, 738572978, 651410322, 442842075, 670243602, 447884846, 390114538, 21452290, 232503372, 351034677, 353038149, 932544268, 569157823, 397415061, 609426261, 138432648, 202767729, 661814990, 956335343, 126843779, 384440535, 505571778, 980226854, 205448200, 866311079, 785063764, 487443575, 775721175, 658150361, 958999301, 581709113, 508925001, 867836012, 250251595, 303403046, 558275857, 540537670, 519339405, 888782612, 849827258, 374396963, 44165798, 591719875, 402343329, 24350016, 190836097, 380364073, 498561891, 274091866, 800216719, 987961989, 497901878, 43461330, 700290446, 440892929, 546356396, 651446615, 160899048, 829343559, 116293616, 309843921, 102442901, 439391982, 237783462, 503943874, 898365646, 125014035, 606192718, 434723858, 375290967, 125876818, 507276353, 5830030, 114251510, 447579051, 475349555, 277690344, 913194321, 781810767, 459054424, 327542948, 780086815, 205600525, 810446607, 173832714, 558593781, 527565107, 606743237, 323302728, 979134514, 499936823, 663322998, 974851249, 107490351, 439936812, 586355137, 329663100, 401748901, 524960854, 245283367, 504492821, 162422113, 331099537, 689126379, 937382179, 102392915, 177825665, 763423223, 409488099, 315306249, 906615556, 282474948, 677353915, 415943106, 557791799, 305745405, 421455224, 454508527, 940299741, 183998628, 727705724, 925110103, 894307173, 363647427, 713012420, 22532035, 660284583, 11828639, 530583137, 955063017, 781430665, 944008165, 276296892, 458495592, 888227965, 931519294, 696994189, 413990725, 383339020, 768207525, 352984195, 537296036, 383944913, 858381101, 699690328, 905103450, 439535625, 658405217, 720202498, 601398566, 704596860, 369863420, 663730969, 278214691, 55641729, 698693068, 486794840, 130481722, 634621766, 379166910, 332971774, 159388572, 251167744, 561464420, 991181935, 178262956, 825929209, 462210031, 864755480, 712185089, 153997407, 786524845, 35889050, 259124198, 119710533, 904017084, 100425467, 155269054, 867768801, 579753659, 842290148, 186742776, 418921551, 211185016, 213742917, 155781881, 501537961, 222663062, 148661954, 890698166, 356966631, 614378593, 471968853, 843996490, 572924322, 24613238, 124081443, 142313821, 979119853, 688899150, 564091061, 545766764, 213765954, 612614550, 867898770, 992944106, 373847244, 459726042, 907544974, 149815555, 19133910, 691260535, 244327437, 170322599, 166687243, 884283747, 882934687, 428267603, 524775519, 190312233, 19892236, 976144914, 24096898, 606679946, 343277347, 522368157, 181783325, 545237035, 937638705, 338068696, 42304124, 900164247, 180492934, 63039260, 907008506, 362179153, 177662829, 245446151, 344263710, 918698183, 795666921, 789205924, 486910270, 501544911, 558021472, 646484670, 357458234, 255909001, 170520381, 556054427, 471524195, 17214972, 69367764, 848063147, 327541364, 595392862, 875714342, 903113896, 382921395, 716097696, 711586273, 267967551, 452344407, 880009039, 28783344, 779242954, 77060562, 481086139, 360343136, 108177268, 8598763, 40848594, 809123497, 797113363, 13979441, 483339819, 896058347, 598988857, 919954268, 296635520, 107557249, 119505943, 812365724, 835542344, 678522088, 2743322, 626232930, 936205306, 246546919, 553078520, 334172963, 545105537, 484990099, 473636279, 996426651, 606617284, 113556733, 498837594, 826832860, 953247659, 657337620, 741533252, 739149436, 811481603, 495831105, 805543385, 246516753, 387285761, 792205130, 188466744, 925734281, 97103027, 990239510, 68588072, 926506843, 293751142, 20877978, 248092379, 818957877, 752459570, 894149980, 697924344, 518227142, 182171690, 123134231, 897644960, 780350760, 911436156, 541502543, 503251539, 331489145, 746339985, 302925112, 384782831, 929827443, 710478850, 174099936, 628776506, 754185193, 644809381, 344637037, 365139008, 918250829, 890138354, 347251138, 659973668, 906714914, 87830316, 806369729, 579738007, 828415710, 905860092, 337866453, 949482296, 946507105, 124298559, 357098308, 851734768, 562645173, 527817579, 957662326, 710678666, 35029286, 141192566, 379756881, 315311457, 734890957, 620019330, 420995922, 363281371, 553313209, 582770718, 123173546, 776433211, 248627708, 935908452, 889157617, 767195579, 212855103, 982150151, 424306659, 148567917, 706111525, 613721683, 831533695, 811482223, 365507720, 737834911, 840967903, 588731867, 864415759, 720731220, 189144708, 258581450, 726794634, 845556913, 946594141, 225275837, 145432171, 302436733, 555236481, 21427587, 587896816, 183172551, 348751876, 980253513, 640104576, 445012454, 617926677, 769443484, 207457127, 459391019, 587884413, 987216028, 116096532, 352920058, 927875340, 763865983, 228297117, 196880980, 503959725, 976331708, 936634556, 234997151, 658918949, 241118641, 752349768, 321775034, 475928318, 625386233, 626447830, 270016662, 878030359, 696947796, 38522765, 300421187, 838257225, 431346489, 348004130, 797291521, 420351692, 912378372, 531937948, 2904073, 548202614, 198769456, 844684035, 633245563, 160486554, 165546420, 786075947, 173909195, 896905728, 695171859, 657216987, 281645645, 754702588, 472281440, 3997669, 867303133, 838833991, 772972692, 212257253, 557166224, 40567206, 99879901, 849909818, 902676048, 181480704, 956024786, 773838228, 935013661, 426119407, 825423274, 892951399, 357137028, 64037843, 570189418, 295046251, 425017233, 51247859, 973959001, 946244520, 614061128, 781455514, 972614609, 696146631, 521032686, 133860682, 959875993, 82183382, 139161703, 279322483, 768631545, 710474713, 651300672, 542071466, 951676897, 495986378, 880285913, 773083424, 308423475, 277126591, 449383133, 7726186, 169978299, 422293608, 536207064, 550260657, 878274543, 498235037, 965978073, 225097053, 759164300, 719657282, 513146806, 682914779, 260201109, 694984536, 205975863, 12383496, 518877660, 748121550, 408196007, 108709300, 963427875, 734031080, 849023573, 201429092, 609315666, 621806624, 132174241, 595967507, 258768390, 822288896, 935995708, 66030739, 970974589, 728425857, 88193748, 957615321, 720758678, 594586857, 482803770, 574061466, 221581926, 902122152, 129251632, 172464764, 111645284, 649544137, 376011398, 981373832, 99510149, 322062494, 549042905, 32239745, 632782304, 475954, 727380918, 5146060, 697172694, 52704761, 907286709, 10105196, 443638487, 180435053, 775585849, 322179685, 531607693, 466890608, 853833121, 579833264, 642627175, 785604292, 922808630, 197425785, 218776142, 641056039, 452543051, 397383922, 903166312, 677463527, 354489745, 761351967, 985080563, 219778406, 581106113, 272432793, 291405435, 645643057, 155139137, 576605355, 548037512, 673265462, 980259800, 206983569, 9277482, 349144951, 428308395, 916379262, 214184430, 96256386, 200468746, 794862337, 214479529, 297767260, 395999407, 427501082, 819584564, 244769277, 351072414, 687600704, 743294089, 912675110, 594716870, 66584939, 966250320, 932427325, 547766184, 388102572, 835772940, 7974684, 705962708, 664799181, 352765685, 49475840, 847713140, 830434093, 536887699, 603000036, 135407433, 618920050, 585927386, 817330490, 891185141, 221711434, 253875591, 911074386, 160743379, 153432301, 178149838, 862638119, 636596557, 756630288, 200391227, 574466044, 596736109, 598616143, 14879197, 335762070, 996826887, 908271429, 388621970, 487538025, 163104572, 996108040, 536123935, 584453867, 882283697, 117560809, 259541975, 182772280, 819948279, 89264416, 449036357, 676988152, 598860070, 720906951, 556689277, 450807449, 507426058, 858758621, 140926833, 281547304, 521255171, 138533966, 214258572, 530390608, 467581644, 45221833, 669207039, 434305708, 748714357, 728770708, 405203926, 960537961, 717320121, 339643766, 14908435, 485544927, 550818862, 506939994, 696859470, 925359216, 988355999, 135588002, 538287948, 607755575, 24062955, 357866392, 677641500, 839651492, 469980255, 249399681, 337211831, 54969732, 340609260, 963221663, 880478117, 732781577, 280371762, 418468848, 744629258, 125380202, 356713790, 79693156, 405213903, 197592840, 174494699, 324213536, 235448412, 146214242, 790579918, 910727713, 471421598, 529270537, 656538006, 368984664, 834044197, 412394767, 496941147, 334487799, 672077241, 592956255, 896296175, 894401845, 649841356, 180212586, 858042869, 642482850, 441725102, 942682254, 732279346, 582580336, 273903172, 372307407, 332234231, 66333947, 526117717, 749664151, 459857426, 248160828, 225717648, 790062680, 77236154, 419653995, 821166783, 397544390, 280128042, 943600161, 264702671, 114352431, 11599334, 622532225, 802214998, 922346, 172559713, 683685941, 250557921, 607595193, 725846330, 341571312, 493773439, 1994619, 164808640, 437532097, 668472869, 434993375, 161095196, 788893648, 706139106, 750295655, 897268456, 615022653, 818800405, 434790152, 652085260, 107182067, 534960655, 30941999, 399581804, 484659829, 400491966, 240865672, 610631292, 747690168, 598709032, 650793969, 214403426, 169620570, 290760950, 393871644, 549403283, 407333390, 747690225, 163215833, 664477184, 350809985, 74078985, 689727500, 701103044, 742303141, 700667100, 772322457, 577985468, 33707910, 123352122, 592484673, 995333186, 708371729, 766944846, 574970692, 254781940, 541708397, 192190717, 732566421, 970594654, 190304906, 343122170, 184017886, 789780971, 235670826, 227529193, 470480840, 37648794, 689387113, 202966054, 574566232, 804770098, 759653013, 798214662, 327599851, 109494921, 245053572, 312138325, 747072711, 884563601, 679956528, 747217584, 633992640, 736780402, 373895678, 977582016, 768862443, 231121174, 218786911, 172846506, 534857325, 640442804, 50286004, 223507040, 63358199, 47640394, 777395478, 151842594, 186438425, 967784508, 929436148, 40690597, 490496427, 690053428, 598271283, 362014543, 416237935, 5141164, 940325817, 390137499, 826883440, 956963276, 794776354, 528230307, 985452332, 448218148, 45701621, 859444276, 41293330, 288343550, 766589685, 975593080, 41427159, 733961567, 178011131, 911222165, 973610163, 676799941, 44550913, 453886101, 691129800, 832556347, 967085573, 612817598, 988174766, 426871786, 905658570, 481070334, 470479757, 635208009, 877677907, 529168890, 100216632, 167416604, 728490267, 48554472, 933249436, 62680778, 75974806, 420704481, 960541669, 136180257, 840809100, 805988582, 543840577, 893217221, 296243460, 10161384, 870645084, 78310377, 891549330, 329503648, 636745435, 116889865, 123588229, 758874443, 937101217, 409878830, 996019463, 199209522, 191553278, 283010534, 861441024, 407528222, 209295046, 524861539, 63199021, 2279819, 218141595, 461324892, 996046776, 827022941, 958321836, 391046866, 505055038, 326486330, 870009919, 181847635, 232365710, 459173621, 586236628, 879717612, 249203751, 153392615, 523023101, 857306172, 925699895, 118956408, 508393091, 432790089, 237500699, 356281584, 742554552, 946310947, 978542671, 535522123, 625998780, 103429283, 610007369, 639431643, 134016987, 66119474, 61112638, 506563181, 570471983, 895132727, 498949435, 459971124, 249881230, 138978320, 423112666, 315921994, 88997362, 585681619, 880712045, 138221813, 571206056, 432845137, 830911181, 73220146, 439876119, 227119702, 564744171, 984943360, 514625649, 993409496, 34456918, 335484318, 175085375, 12009487, 224819623, 458700869, 233059406, 737913424, 241742672, 120421402, 829212830, 160515605, 141747960, 872283025, 206923978, 948413863, 882340115, 884403857, 438714362, 138734905, 924791619, 30474198, 392457538, 971554813, 208861957, 463782274, 258734454, 522928168, 554105121, 834831562, 707465442, 147385827, 469401887, 407934237, 956557509, 586732404, 286273033, 9439438, 427336457, 405453540, 734578789, 75777251, 743536553, 312952551, 807201019, 719229141, 18704873, 955396200, 925274735, 256535340, 75976725, 293996987, 96464497, 662532954, 629244412, 228373197, 2251376, 188220214, 124752392, 927956699, 556292031, 945164321, 612397678, 936173797, 565616637, 55344386, 831949901, 188703119, 566541683, 437174895, 513794248, 88308412, 74704734, 222696142, 810565375, 808023794, 667631724, 671823562, 15585503, 394588763, 12632164, 225788257, 985416553, 789039465, 269777200, 388455753, 241991996, 161298600, 542797998, 29055703, 630250597, 389807074, 560417903, 789087885, 876092352, 707403584, 875354069, 63512764, 23798842, 535478904, 839354711, 156817066, 816591472, 847966224, 405485816, 992502048, 303670794, 792266559, 606611261, 357945754, 325927609, 298144288, 364755983, 16354151, 182077745, 483541796, 505830070, 90800549, 776837831, 438657269, 510240377, 81878039, 909318643, 882767291, 744582804, 210307312, 287515798, 653485572, 731724493, 301225037, 143181092, 847897170, 401389487, 852645156, 326111491, 856111092, 366963114, 663142914, 891204192, 218974434, 578682162, 815578315, 374001676, 144821451, 472824044, 384103551, 987417480, 640394281, 178846731, 419824749, 127060054, 244545798, 602385471, 547927694, 954786848, 953538526, 934731307, 238895497, 42668070, 997905616, 357284621, 816901224, 235553760, 637635019, 104691758, 279223423, 530640007, 538909175, 93179652, 137708189, 565686463, 109059019, 505041412, 679026520, 807935414, 953371576, 991631087, 752290960, 849584241, 179728441, 52288403, 471210852, 493818908, 561381371, 79231197, 823631973, 677242455, 235216897, 56303160, 74994289, 289729481, 480884679, 242776241, 597217227, 57046665, 723392081, 87995894, 568402591, 633085087, 553242884, 76967736, 973473687, 977269943, 939060479, 236346759, 307574471, 548827408, 238511270, 607830769, 579318842, 90554404, 589652761, 536117902, 358169860, 839391444, 243362868, 762139888, 548925830, 930639844, 928600632, 167161105, 856187412, 397456574, 855502146, 54378365, 489799824, 21921949, 971765922, 168564168, 474979166, 499886006, 993764123, 991552839, 395273030, 323375742, 609140840, 444139243, 851140661, 831903750, 549711905, 439852353, 677306112, 28062859, 233786291, 90022157, 148797798, 151033868, 338426910, 118778440, 64185437, 311852612, 382264739, 199334700, 874797393, 837449793, 137045101, 741141912, 764398166, 645854725, 52899497, 518483978, 899224637, 937631544, 278301410, 686325646, 983625782, 75834074, 656845285, 325485715, 15231346, 208228923, 748981614, 94611302, 80092524, 461452957, 309936111, 179154731, 678894565, 361674154, 77414080, 955280064, 279946708, 818061092, 151410450, 979660792, 28747351, 232710251, 234525915, 82412799, 420696669, 216650111, 201390630, 195452140, 402148651, 360033369, 339941384, 110368570, 558865647, 854774039, 458397599, 47689154, 879538328, 147187060, 148597962, 201965620, 178378363, 901138785, 556536551, 362461088, 97279837, 283678855, 638634652, 305056112, 66673850, 375058007, 213504874, 590865712, 289373194, 348600478, 468046815, 920164515, 550581595, 368021395, 761821403, 704402017, 222699276, 183071783, 984627181, 625478677, 312646600, 802477541, 316721457, 594940898, 993356568, 564822351, 881152123, 425399099, 909206342, 900007277, 854954341, 123066083, 613351794, 721946950, 1614907, 56470973, 830938456, 857834771, 388971484, 590500533, 33820835, 887986442, 679675220, 116734194, 968297751, 824830031, 781459631, 863211121, 965965448, 213237771, 542742863, 663779145, 303746323, 164792166, 601554881, 492588745, 887839589, 284563794, 127449792, 541569747, 341386844, 712719355, 551845840, 330865970, 965243966, 510022626, 92277597, 519100917, 556995751, 131196484, 799101001, 604386500, 32607587, 955857209, 737124038, 298748379, 771802076, 478723150, 521737127, 103447350, 45624085, 954944717, 497867921, 878218662, 655076141, 650093540, 355113226, 766430760, 976935339, 312914296, 134686624, 309919478, 250460497, 595990014, 580010718, 165452616, 635106454, 163266029, 386308218, 297213713, 684144629, 413032858, 35015691, 796279677, 149719926, 50248479, 492866972, 518841732, 936558986, 497326626, 746329640, 923857349, 937104309, 925339167, 204160254, 86334603, 749061765, 943666102, 433414758, 972347360, 389897807, 900779609, 157513719, 786321316, 78351510, 186214580, 672925056, 642392393, 229968294, 630448905, 688664936, 979724689, 660936740, 249588028, 451154857, 327364503, 747544041, 457640616, 708619755, 346129863, 423635682, 923567495, 209309993, 629377211, 723222266, 810213457, 332713404, 821821352, 319824599, 516480654, 936720964, 65729115, 919991597, 541260414, 343197303, 429371507, 345713013, 250448528, 14189279, 979037470, 226076680, 131347918, 603209236, 515102331, 249516437, 83202974, 933271132, 564260202, 506823408, 625139590, 671506930, 146427613, 162715498, 506956471, 308059018, 808066128, 700875276, 164086265, 240193129, 131309642, 230153350, 874207135, 981856827, 226658793, 933991643, 384576778, 381616436, 68612374, 929392133, 727019245, 813617889, 181342357, 867408156, 17402533, 9591570, 391533585, 973239968, 372747648, 387285947, 174723808, 872219108, 573589946, 488290672, 718763643, 840682925, 346788784, 191104474, 356592058, 186900455, 435608532, 652980281, 844359774, 499313230, 923372729, 848981597, 360604722, 931579095, 530077117, 344789266, 128030394, 538059672, 201058822, 354269657, 795170300, 46988854, 833467330, 622491787, 774412964, 488881226, 685721684, 592777622, 732934099, 740487815, 541622835, 759161960, 365496649, 900743943, 20767609, 754448033, 453983632, 547605318, 718800767, 262507072, 276126485, 58207078, 635929515, 519985672, 291447907, 599357574, 753342337, 159225410, 73403929, 97714166, 84004622, 368013065, 873199974, 44183454, 276257900, 537407976, 790960789, 151008974, 268728124, 6796065, 822851275, 340714887, 332501227, 105839661, 932850091, 2225462, 118072807, 786577643, 375226513, 999436956, 169015842, 554925874, 517932133, 876967023, 257269480, 325045611, 64671623, 992053957, 77192470, 506165744, 826510809, 551119331, 490457682, 967009652, 446038635, 354493285, 8445503, 185116199, 424131892, 928587129, 158402364, 831486768, 902256724, 366359298, 780523608, 515703628, 836341583, 875254471, 936555612, 916442121, 401718199, 534970233, 259888876, 580589855, 590956014, 369043898, 97512651, 702012316, 787426333, 87064035, 259518787, 853564148, 140169442, 933363159, 775947294, 723436712, 115433032, 249822938, 947282828, 250229432, 192809473, 675197211, 412681507, 731035895, 438220093, 1299443, 522730924, 235874069, 654094422, 638636915, 491318617, 716816090, 915140727, 586459939, 315658276, 956173662, 447340291, 268348200, 950086773, 525720528, 411285115, 244706014, 149562713, 987062280, 972317332, 705359684, 408633249, 470426935, 812363308, 53513791, 524219111, 735838143, 194592478, 314542104, 436731456, 734218937, 239187061, 114150649, 123796881, 104961538, 428491002, 723209136, 157612994, 798566442, 114038679, 303028738, 288546280, 14896023, 914307270, 421370068, 64544821, 972582169, 648904716, 319493793, 738954079, 612142999, 871028833, 625017976, 506871367, 736798862, 823546375, 980718244, 224031002, 245903696, 771864904, 179992740, 200983897, 168104064, 438734809, 357181240, 388298543, 803587121, 366801074, 920302786, 474253808, 384525192, 660798387, 80236646, 75350931, 206860908, 494671008, 983708477, 432080890, 938625968, 531851862, 882405039, 936151401, 27017252, 215151461, 739241405, 155645928, 153854661, 536924100, 19296916, 20517633, 858377345, 286953545, 377543790, 720002733, 449355212, 929385922, 248261024, 364250284, 931107403, 447658613, 729185209, 925075654, 645525108, 718254056, 485692488, 776276476, 606231095, 439787477, 850171576, 42313496, 165109681, 33889129, 611545233, 714906586, 975967508, 65912905, 598225615, 161151426, 78374580, 322003433, 169450095, 11266540, 339670728, 121862230, 218639402, 266315327, 910959403, 51333918, 712163529, 258794097, 887427871, 328571876, 721848299, 22525706, 920614624, 129695699, 447635955, 158638122, 550656073, 56174381, 933017812, 1455855, 143217309, 725917452, 892851494, 427122829, 66135344, 982572134, 146650732, 450252915, 627993606, 919838189, 549582479, 427262842, 857357072, 855573109, 892536218, 336435013, 933508302, 756956001, 813903024, 239705144, 406983873, 393046170, 39756835, 161411330, 551427950, 451332493, 528831502, 2300168, 317718575, 374984575, 236680049, 436422393, 168590014, 810197305, 846734445, 118661735, 134041372, 344772948, 121460070, 73649065, 80581720, 482553392, 528202712, 738142731, 739598252, 90693690, 838904109, 643042677, 836476324, 341173829, 262415735, 453303577, 886871059, 753156140, 270879570, 791626521, 526944027, 822684191, 650282197, 61177496, 612803681, 415361080, 681932251, 625237658, 738503519, 430479888, 81061638, 86354775, 305710426, 287898419, 76861785, 827335455, 64025053, 786111349, 61932477, 191372161, 708891423, 457484777, 160332219, 513613254, 506229347, 369519698, 489134484, 213850746, 806359717, 492000889, 914010637, 9567627, 543143922, 525877243, 301345315, 794555753, 235695934, 27351800, 498339247, 545727518, 663460590, 671033785, 14313321, 220803145, 924804508, 170765935, 328347698, 422057464, 421206954, 910321426, 603437112, 77703273, 628939494, 999775690, 909210824, 739476996, 805286765, 567211764, 599987815, 250793383, 843277832, 913534903, 352990966, 821846600, 736155261, 152540269, 642012003, 947945796, 128971873, 82126173, 635985788, 175454933, 702325326, 696017189, 369266773, 58274128, 589091440, 650144482, 183871569, 578602362, 936387616, 120609948, 348055661, 66760305, 728389869, 32579773, 553826853, 917071766, 475842075, 463263018, 85375969, 673184088, 124363371, 842320319, 21954077, 897249950, 77929946, 811506583, 460540329, 503432924, 556496230, 174696610, 877220919, 624338502, 741574657, 72209927, 212904338, 20050059, 431766006, 244746640, 118842916, 859312022, 35319922, 759179399, 409276170, 794989185, 81618193, 83362611, 976472520, 890003444, 957277438, 267622178, 668624864, 977777814, 98424722, 975991716, 198139011, 272419893, 424963616, 404758665, 35914173, 492677297, 282978751, 101119169, 83412184, 954459679, 273989444, 77063583, 962018903, 180021932, 574871343, 136860883, 963074951, 769669373, 615905925, 977346629, 265827251, 931022358, 160162034, 407507737, 867056647, 851732056, 400680143, 388023040, 835135807, 796126934, 255605978, 1660846, 711364005, 388335915, 773306241, 74545850, 849583848, 902917633, 817121187, 91496444, 573835785, 539240646, 924547397, 292096976, 421992516, 200183044, 77201579, 404857073, 258415258, 183536097, 378242635, 399160116, 918143152, 956711964, 333432485, 442309143, 629679988, 930346753, 427853136, 457735177, 697713128, 658254593, 316472137, 436230680, 658417023, 860022276, 690086330, 276508447, 173405422, 520728774, 985785315, 926017311, 754635885, 980677511, 703047392, 121169632, 65779674, 98826736, 93368467, 885556704, 752957167, 973110172, 219918650, 354106478, 329107546, 496209367, 360930654, 785588446, 937729323, 964595155, 430895026, 871161639, 513018267, 620914649, 352309748, 26834511, 77090502, 914793038, 929704669, 111651143, 387238338, 542366151, 90491071, 167632219, 674170315, 848527643, 968918982, 388398354, 678124690, 440864721, 799480543, 951713715, 470521203, 613360481, 997491797, 15919614, 158328032, 750798785, 412890396, 327117530, 949301928, 432587178, 387399183, 426743655, 757620192, 891858449, 177593377, 210701993, 803634174, 954625979, 489147436, 984366598, 27237179, 616070344, 272001179, 38788503, 82875118, 697456363, 52695656, 988504358, 420135592, 447702830, 483733739, 935223874, 913607512, 377809160, 872222311, 449852874, 130878518, 552022179, 632758788, 625199318, 665840055, 635448203, 800183013, 561332091, 22093161, 766014672, 187139214, 132340889, 407830840, 509332010, 939687413, 160780133, 392097084, 102594301, 392028281, 627197165, 573505524, 438369872, 513357251, 238522528, 635055588, 266973249, 201081694, 399723218, 297754961, 464243801, 115032340, 877133348, 312042471, 334942955, 598278786, 236196272, 937554985, 98867044, 351959561, 962811729, 543102763, 579894639, 868823259, 769288704, 190791414, 539633889, 517852007, 962297053, 133742956, 56716334, 478914107, 941045890, 56494253, 204965552, 618499946, 9753811, 435281555, 777506798, 263997819, 981392378, 255907227, 510747790, 878421435, 519850142, 401220730, 956429893, 619932320, 717196086, 585717282, 183726207, 657196934, 201614840, 456041452, 632920166, 473293420, 831267110, 348537694, 656623710, 617066125, 704875443, 111354529, 969658245, 572880405, 594422054, 638523070, 117258404, 116737896, 375860759, 547744627, 646977602, 607314166, 294917709, 456438791, 581897379, 310556775, 903731795, 953947248, 262151622, 350055065, 850703057, 463327974, 884052516, 676540548, 346616558, 461845655, 292490984, 623896661, 813892740, 572711631, 549569830, 897323813, 834071539, 378705355, 295994016, 746097732, 213062767, 675241259, 10620023, 904133478, 753643195, 611859914, 784180728, 662131080, 280682104, 281888645, 344016080, 236747904, 141547581, 70650473, 296222485, 742901880, 487503434, 700557381, 395399303, 140635401, 784811398, 826280881, 934562935, 199827264, 299189032, 397244016, 179301656, 319660654, 52415336, 100896644, 504077933, 115502502, 682919782, 548377847, 20825942, 632402932, 672035575, 658972112, 197610108, 247652724, 661660274, 236995906, 759891375, 638038345, 703458672, 223259536, 716621023, 898379706, 50278929, 249545765, 564143590, 621067617, 437313742, 954771477, 893746920, 88889814, 601318813, 321525348, 565766102, 595591302, 749493120, 639138184, 11664739, 476562253, 331575081, 923894403, 558812038, 441132467, 775759616, 892642659, 508086398, 199975166, 230793759, 369239599, 702626960, 165558732, 724775449, 330350826, 83535302, 369778529, 990448844, 899451693, 190902910, 942413328, 895653515, 771970038, 269473747, 243384291, 278057968, 943244080, 655115227, 678815515, 279985845, 200854823, 131098517, 278824384, 722502102, 228111525, 848646346, 426605403, 768824612, 871903529, 62289564, 762165727, 914943309, 204088658, 55538664, 17137814, 206529388, 400316115, 279717402, 472431285, 785068846, 34192951, 444958501, 857850597, 721561631, 252769720, 443425570, 492224218, 223622315, 754802576, 378568958, 368089325, 167076408, 351629824, 621777175, 442577910, 647069213, 390789550, 758414960, 774220609, 316490856, 432231289, 799503263, 267859903, 480444384, 781057082, 747216944, 591502486, 132577290, 413868689, 892825, 806235223, 816656782, 736134566, 264360889, 988196198, 845324867, 807169022, 597072731, 147282123, 50873762, 142250463, 651594901, 55306034, 837735497, 786898925, 759629479, 839256302, 738913485, 427251647, 899245725, 948199003, 437153371, 600057637, 772968913, 639612148, 192252241, 686559077, 588088531, 623137512, 70511678, 566364352, 697114348, 598937133, 36036611, 218683946, 786460920, 874022242, 951768559, 286997634, 971028620, 820082680, 203231489, 24895502, 150649958, 104124154, 55424217, 229783831, 296953426, 170878075, 883232831, 133758452, 89496051, 541830193, 331681803, 452363629, 99951716, 107625570, 311840278, 607482118, 628327761, 300475412, 887292082, 489117914, 229147886, 664465544, 422671938, 112521216, 376459612, 775437349, 680149068, 224437018, 527050981, 201640537, 717140281, 365758622, 332757509, 642983451, 252120726, 918856571, 41286249, 196667815, 280456568, 937730772, 881542078, 159552582, 642123071, 354158213, 120986022, 76971174, 636882909, 999631101, 690532393, 243053167, 597107706, 951257025, 442075807, 758045533, 918359136, 384823599, 495355987, 577009002, 401754048, 275345603, 649387936, 461784419, 392802505, 934401895, 559292081, 492494275, 595537030, 360926844, 673476995, 599680584, 94136601, 647504921, 807956795, 700261049, 657274109, 190689489, 4430251, 913643621, 781061071, 802062567, 179324641, 725041470, 598708835, 191941292, 202167403, 201414904, 184154198, 732947936, 762666947, 972211519, 575951977, 23304892, 360281246, 94615153, 853463643, 98107762, 81717576, 382791510, 361814798, 110285133, 557162100, 14749739, 492641163, 776717776, 256670865, 808699105, 748229919, 527264049, 939760139, 729647240, 317013599, 215986763, 830435634, 223396573, 224456587, 615938345, 98749033, 872869819, 115833446, 834225202, 949145316, 415342997, 676226134, 368768832, 522189885, 353415922, 293060840, 950809283, 61214491, 176196585, 831509771, 110295024, 89590617, 305700450, 331456615, 172341970, 118461593, 391749209, 558077568, 245928712, 229181064, 943022351, 450881486, 964130062, 967233849, 489251308, 572648405, 555197975, 920178034, 930681838, 123107581, 268358889, 62357993, 75447502, 613452334, 7789527, 723059507, 534734586, 814281767, 792773748, 71626146, 224530020, 880562720, 155348470, 724599253, 916081055, 589871142, 699209021, 471772671, 460694535, 672606519, 361461720, 861128980, 361943098, 335380192, 436952781, 36317709, 876674894, 836666403, 449897794, 274131368, 996943147, 948307743, 611019285, 643421641, 61459214, 555669332, 521046596, 25746295, 615891371, 986577674, 613000189, 958892583, 892515569, 922753454, 224418864, 704309220, 680742773, 641952273, 285130009, 868319401, 137665786, 677845083, 8457024, 964583677, 762824532, 975203794, 184012831, 597636608, 85785384, 735505376, 233190880, 5839378, 838129429, 477950590, 381473948, 559033, 234593520, 576034390, 46149290, 272211202, 791370544, 659260984, 825167986, 784122326, 648187855, 566106007, 142674188, 796455567, 249533639, 241937152, 388521562, 558346660, 519039044, 777947231, 362103064, 920574858, 606241004, 983886973, 210813154, 815800294, 205931407, 658378073, 389413778, 705658278, 205430669, 191372789, 487705491, 628651080, 108385659, 412820498, 639887624, 449038274, 675641871, 417282152, 577840478, 585356406, 164346803, 922519294, 352977060, 18638223, 982143718, 118794971, 484134079, 91583371, 623002840, 3482795, 108296032, 742779108, 481868576, 890045314, 191743983, 338004860, 533765826, 731031342, 355158930, 793733032, 615312530, 650185556, 191799837, 335715973, 351713738, 594500849, 45665036, 415765318, 149824770, 534583453, 748141168, 796906552, 753986443, 931681697, 739640217, 680219355, 146051506, 344490110, 286006037, 383990478, 824028601, 399677204, 648616159, 732967544, 812591622, 644484933, 488725186, 303921016, 61467287, 839403249, 77609203, 972484059, 339162784, 145771993, 534801331, 232453905, 668072420, 883295932, 196978970, 653862720, 294135999, 130380761, 997089842, 181396474, 798468076, 518868995, 780540021, 698170649, 151122454, 6148023, 706122356, 496409015, 978334527, 89504916, 746376942, 328379185, 93355177, 773331262, 173340783, 83657411, 952083087, 508187551, 795365719, 378135472, 814868331, 505122960, 834807888, 5514779, 988593237, 115605187, 129842970, 84694543, 350754223, 575930176, 989360718, 529162374, 861434560, 433325270, 202216636, 186918105, 990255228, 517761992, 712355253, 280518323, 838569445, 375041019, 145405007, 412779355, 564473441, 301691736, 188855329, 764295204, 997608028, 710990607, 896381506, 337415560, 39389566, 775505121, 563398041, 110573861, 442500765, 346268439, 295699419, 31161493, 319500813, 795460676, 453875988, 472168713, 825604145, 37325283, 207664123, 128660004, 313637812, 153808311, 905643187, 509201096, 13763280, 370215025, 929810242, 200055012, 12552184, 469125164, 187745450, 625734626, 769309744, 400763993, 559691882, 999520308, 681231718, 477022107, 319537286, 186696036, 212526663, 194722464, 889036273, 316186754, 746473341, 89666255, 83625947, 450799743, 998614173, 928841454, 382622439, 105936957, 573754394, 82035961, 489508911, 637706327, 999048954, 723782302, 470706133, 496873089, 820381362, 970412034, 668612285, 16185802, 151234114, 835195935, 178728400, 74249244, 392520891, 423539561, 812049603, 52120288, 798299114, 198439319, 697731870, 303884532, 862454817, 294640557, 205823861, 538843041, 249584219, 774568170, 609028547, 536697086, 767484913, 542952649, 623085413, 15635083, 819766320, 245935055, 217900054, 238081397, 501559110, 513524036, 643473124, 53403342, 148819648, 494354815, 414378059, 225789288, 375978562, 140898040, 415793802, 37925706, 163630651, 222625161, 695546847, 634799769, 528911903, 592744056, 83218037, 586436071, 451816073, 38812950, 370712532, 729530476, 56304673, 592936222, 661762572, 596515772, 115445391, 50741909, 735459524, 100166590, 906738944, 523613294, 38725665, 819565617, 466272334, 275259664, 11096482, 668787258, 664830170, 845414052, 335620688, 66327113, 837100856, 575305977, 181424456, 380286353, 139850227, 460053099, 334938246, 935616735, 971894923, 101082057, 864983858, 193605650, 202623772, 14956299, 376531601, 391139379, 444393177, 928028288, 654734125, 575637450, 596750500, 690714746, 60425109, 943704518, 404344363, 932659456, 854176794, 89155746, 737064964, 366181962, 64228448, 860980768, 542576385, 294716010, 558288896, 853114799, 529598433, 567383338, 83239015, 655948406, 535316183, 161487742, 153497186, 323244584, 514361636, 628159467, 619950453, 558021164, 111810359, 489435787, 429256450, 712946159, 884551010, 37976262, 373088190, 937430487, 406104709, 978144201, 723554541, 731706461, 780546643, 32920059, 764351648, 424463937, 733785681, 487958675, 51134750, 788050196, 702778177, 192779459, 803748488, 1056430, 684693820, 559492709, 405914836, 670943254, 21963251, 790408255, 8786968, 11410130, 510557604, 630538636, 595649089, 144629295, 104477209, 365272957, 455619206, 69823439, 945984094, 656901235, 951624891, 233891381, 832655357, 407623379, 511260369, 723680466, 804453701, 13749542, 96560727, 966865233, 480815193, 244386940, 711072523, 895637688, 919497194, 886960640, 902375339, 802478016, 89598090, 833098079, 649746581, 646147824, 793283967, 170145349, 119156652, 616345393, 276521738, 649859201, 48806606, 710592867, 868263554, 567829659, 53833455, 689152966, 478257680, 131761791, 761551146, 753871157, 37249661, 49155309, 459721283, 409682165, 571479808, 635275691, 4566365, 747645171, 935936442, 5925126, 824199412, 675673575, 192482814, 706808556, 988646688, 26235811, 386344774, 326750773, 550846551, 10434489, 926489944, 9442567, 421809841, 358724860, 158389061, 401985449, 157037423, 671765013, 257437521, 563183630, 736687214, 365249928, 297588430, 337818898, 799349091, 203577773, 112999587, 866047954, 35766882, 606890796, 245827155, 111947665, 967329037, 393348033, 665352456, 27352556, 177118471, 947062603, 152223734, 800066116, 882163945, 69477330, 909331543, 344192536, 257178663, 583712104, 89711003, 913476651, 787325325, 401801379, 943437258, 518862744, 779141450, 697930608, 435426073, 427576633, 994252376, 450848753, 424294580, 994273603, 853156253, 684057277, 67937717, 202784923, 193687484, 395938712, 749803810, 596293420, 692658711, 972572514, 55974944, 711359306, 707589263, 404011632, 424817673, 549587856, 624690110, 61942297, 703143845, 329769830, 609630872, 500748336, 128307321, 925703276, 28793889, 284348235, 644810652, 760497840, 316153199, 319356912, 317023094, 223341673, 221510489, 125466703, 155333264, 532686446, 369497692, 576438547, 584466240, 473388717, 824067208, 460492318, 243130662, 831343187, 86682420, 321886768, 897202145, 49796122, 86319448, 791018765, 171647183, 964787536, 899657946, 236784822, 473123125, 202488872, 225115927, 315813502, 919737681, 15688696, 549349353, 505386661, 892695260, 99236414, 171486479, 848165542, 392323177, 936843357, 250875890, 446843587, 583589468, 709668506, 127754166, 982348359, 244111998, 404865348, 246164107, 27596021, 949061098, 402291281, 602948375, 203007667, 145488012, 527716424, 721073539, 6053013, 307956318, 475066026, 948586242, 90927781, 239763679, 58803153, 66699966, 264537658, 691347465, 904013857, 436890195, 146763609, 150461045, 362009859, 862839738, 711798940, 628507881, 313173132, 871296139, 171544327, 118493574, 257444841, 387412955, 356204849, 891596676, 885340244, 581046848, 741003963, 214775118, 230388119, 950760399, 365990119, 832286638, 498152820, 376570416, 930961372, 241471907, 458980162, 856728312, 607251679, 364682576, 170626831, 727780808, 112029603, 263547155, 445008214, 824395752, 511235454, 701019846, 74660227, 421225492, 923594823, 985777855, 54494130, 584046873, 624047846, 681756446, 193703606, 683237760, 614264382, 271415407, 455124786, 87862608, 139407128, 229305863, 978643237, 208767015, 939195356, 468440037, 206459383, 616829478, 721576467, 33333370, 321427416, 285231891, 40994820, 389541300, 95653657, 274966757, 751387007, 309196002, 176427434, 575905407, 673034691, 709747180, 804480148, 592222348, 137937099, 141658261, 78235141, 757045558, 374816735, 410073073, 755955005, 952113710, 547621883, 626731023, 690253930, 868752529, 701162060, 942595623, 214511170, 767371440, 827344355, 792940485, 381197024, 869603856, 885981035, 848805185, 565025276, 128253667, 405120971, 757217666, 92445735, 860167399, 794312423, 790201739, 587618132, 599971717, 962616788, 993768341, 258188961, 338227381, 884392328, 764708856, 50841270, 808315287, 42503360, 396301443, 499841907, 688907531, 951921332, 854910633, 707133451, 689380899, 770959720, 976646728, 806263311, 403512938, 278597154, 224704058, 441893014, 755357293, 366775262, 845005873, 622869129, 922937098, 737068890, 490200042, 316458440, 896355260, 25399364, 817727909, 366776876, 492538283, 124275331, 341540805, 601435614, 991898362, 861381184, 976066064, 686789830, 888755975, 636086261, 838149306, 403798534, 248022989, 616860961, 317491874, 303009954, 255418117, 728379121, 174602440, 682153139, 544077864, 792400905, 429151937, 9559327, 889898111, 134183845, 882179731, 676082208, 808983815, 964639270, 908382736, 221825815, 948780640, 941380776, 51756748, 435649327, 801722616, 848915505, 766752858, 792250102, 551732029, 286915993, 420835918, 55414752, 832156527, 66448055, 234065806, 615900565, 417944236, 560649120, 376085942, 737178151, 230353039, 883705100, 854938354, 459016101, 122364890, 778603173, 660866310, 167313542, 788524018, 30773400, 853196443, 799821777, 828791608, 98544368, 780080656, 185484851, 785102071, 791086800, 568933610, 855522219, 353912199, 891487113, 460368218, 204377445, 359806775, 737786461, 53651396, 641602731, 804692109, 203647032, 969548915, 194194323, 515186623, 500919740, 444357902, 630414082, 670213970, 15950731, 128877217, 496638017, 839506540, 420914059, 825031294, 547901953, 175439595, 35435121, 516962158, 750056847, 108393962, 902488984, 321394837, 754892154, 951698765, 806725271, 631159720, 261139450, 149501931, 24614401, 548282656, 120024540, 391652118, 82699131, 315561562, 131856090, 379368560, 935350, 978386352, 364037588, 800351117, 401548329, 828745004, 465255763, 164490792, 430603761, 792107189, 632803474, 317150751, 74394861, 160129167, 31114396, 627180503, 407601897, 362515730, 583477969, 734868755, 954569646, 26423502, 884943379, 524489780, 728810012, 12751735, 110362774, 50851537, 835589295, 843218025, 60052536, 22532462, 200951670, 933302265, 182294533, 519974426, 800210538, 849659551, 739894512, 999360036, 623575645, 240940902, 136009573, 871459910, 387266827, 427792462, 861862734, 495689024, 874310955, 325836993, 201133935, 859334430, 689148346, 95022384, 278769422, 468203449, 909417663, 873269778, 972193159, 232861713, 423185514, 690154161, 58710631, 227660419, 501551519, 545407000, 493990315, 595701606, 285529618, 490056138, 830530895, 81345283, 204314238, 572151079, 509434433, 599397054, 715269061, 971728569, 507279500, 311502653, 304808149, 130278074, 138490184, 54522305, 687922683, 284249396, 213761938, 437295313, 592839815, 343330950, 962773618, 593897662, 183980314, 783159684, 997604994, 908982760, 936857843, 283689478, 956527480, 831736278, 3975774, 505784111, 640737276, 454572914, 274101666, 406443695, 866063595, 593304362, 951844861, 689040047, 213417061, 345884754, 460694710, 773351475, 129341447, 374195130, 742502881, 554501810, 420838668, 367882762, 744524326, 519298981, 764198027, 437744865, 187232628, 767596965, 422367411, 169794052, 997713825, 152070130, 444217900, 136334467, 828856363, 258374898, 204241548, 516538332, 487801609, 807907762, 415298661, 469915030, 133307238, 46299087, 348871454, 463385395, 787713577, 700241272, 342726954, 18802002, 614761786, 959343860, 310101176, 658343864, 396725914, 623687633, 192284770, 918990858, 731820804, 568503703, 457227958, 141672886, 797546948, 785676282, 868450226, 692469464, 364289308, 763115048, 27047461, 986086255, 814916089, 247404034, 309199771, 472635788, 850127870, 735232283, 543154030, 832190660, 653766530, 982364780, 111701192, 637574509, 912369879, 262426461, 146766977, 69314286, 653523377, 901871167, 638695547, 359007738, 660813993, 391271132, 21676697, 87669486, 842840493, 635500321, 336744904, 273523470, 751828381, 988170507, 287300093, 847788859, 802182748, 515229832, 215703057, 954251113, 607667942, 915398223, 969253435, 550407383, 182810374, 452128605, 519693521, 861246668, 215864718, 166976288, 665979948, 129902100, 877347734, 596596015, 1020870, 494089763, 8778567, 489068177, 928588369, 710566649, 383019948, 862530958, 377186966, 433148478, 190375156, 408700934, 215442599, 861897811, 325508539, 100931688, 548879316, 207344246, 468978601, 460083014, 564405246, 317620801, 694457396, 932605259, 495845660, 905441809, 293402728, 667387758, 646026442, 15067393, 950999672, 725649955, 540067176, 740949069, 830265228, 804781000, 843764826, 676179535, 645121477, 333053691, 848745200, 177325116, 189005151, 943916087, 273667375, 909768476, 104655848, 606294632, 429918008, 665164447, 721720683, 309860692, 898514351, 874546785, 732741586, 442736886, 747485219, 321650587, 985723648, 229383327, 805257810, 934530073, 847497721, 178799401, 959454270, 899287643, 725248941, 595008482, 914498518, 91044506, 869129293, 120581184, 838542598, 25612977, 871131109, 589967216, 378566752, 931720650, 794046274, 235279279, 651131407, 958607680, 862078049, 643547469, 670398406, 116688285, 265726446, 547447226, 270354930, 548902707, 45805120, 361828369, 927724476, 269141291, 885856420, 712140164, 271191049, 328998194, 658937822, 602563522, 384991863, 850107725, 910259810, 538669556, 284519952, 937632951, 421642576, 528875493, 940815553, 5303440, 469243430, 671100709, 138660835, 318732140, 837857760, 982841626, 964303293, 424533757, 96488749, 515033208, 346486876, 241264320, 515013425, 165935773, 259534973, 711585959, 170405135, 583401306, 324452137, 246013349, 829214250, 78057933, 10973390, 335530903, 766166152, 676422462, 909652990, 62043054, 284714244, 772098704, 900050595, 338081174, 330044988, 450154005, 830008262, 691171247, 881984196, 750627451, 797335993, 731839233, 525229811, 461813564, 143411210, 366780810, 154644, 137291893, 801337233, 531332269, 161465356, 960998395, 131068443, 421110178, 379945830, 169204066, 154493430, 424437052, 146923156, 763618940, 257431939, 919381715, 222900362, 857958444, 409668835, 991938650, 654204512, 308473143, 207028569, 343424777, 136128946, 213705119, 73224039, 997584129, 384000298, 73473850, 467665761, 181725743, 74903678, 4368287, 341429149, 776640373, 767836337, 28766763, 64025693, 809034838, 839353531, 451091511, 469276172, 930028185, 322164704, 924930020, 632953915, 425240328, 351107261, 975697411, 322136655, 363429134, 220439150, 243289451, 937986111, 726692582, 375621949, 500916136, 182544, 7458363, 670526023, 472551501, 391241422, 51532131, 430483387, 124205288, 41237718, 576177491, 459396406, 239701773, 216307662, 50930252, 73403103, 302614988, 302811921, 48978594, 786678891, 718211587, 748586289, 894920992, 170374244, 449491003, 275007745, 950314122, 459220187, 680621344, 741449756, 250408513, 370375855, 519809765, 666588947, 750294463, 524471161, 938977824, 860595088, 192659736, 450209503, 590589110, 100792236, 567005204, 235088011, 815499923, 169810656, 358463180, 966296640, 652812913, 920358086, 491341436, 365807187, 728396835, 120233355, 352244494, 242634256, 191764795, 893123186, 496582447, 168996828, 604041007, 872018375, 220318585, 630578354, 576976196, 142028431, 452723098, 463382074, 264111718, 735836935, 751529277, 821784708, 48926059, 878924423, 98332396, 390471958, 619849302, 353528974, 326841877, 984393319, 709628897, 695894172, 620046530, 326698509, 254886795, 258233328, 908288736, 560128657, 868674601, 477516089, 339247235, 887504824, 756470497, 241660839, 238481445, 495062985, 346327421, 474553634, 634005509, 758591366, 639812987, 641509333, 963356644, 581915422, 291511697, 146417392, 107644590, 164024983, 113935874, 70277103, 276499010, 704147142, 290811389, 687370468, 327993392, 965649515, 291073645, 14354010, 491973935, 360009466, 828878475, 787912674, 809666438, 542353117, 716139461, 95658771, 288538349, 225707327, 667446279, 461554152, 173820694, 519002555, 572733046, 217385159, 524717282, 149290079, 46268110, 474792266, 285847827, 177065120, 795940597, 219888685, 68691464, 826806080, 660582501, 243785806, 676265103, 353634280, 686777668, 877689344, 146406, 525909470, 446635861, 553838026, 645170666, 265462693, 184941251, 492412364, 726302610, 671216395, 962286290, 49071180, 697555623, 556431209, 65057183, 826246296, 175892515, 996807064, 497394809, 18250212, 16064546, 514847961, 941906627, 545833422, 484063826, 705236563, 399363201, 753670834, 12420303, 715184689, 492931907, 669378467, 302560911, 15566484, 923400098, 84124942, 709460988, 751517942, 759120289, 574267846, 395827573, 82244812, 93928397, 85801020, 361395474, 491415086, 659493331, 33915316, 678096934, 461421017, 280891355, 667487746, 670548379, 338383235, 454761420, 494544079, 77013077, 529891743, 59873685, 501809116, 323518874, 422865923, 223917189, 650421614, 244055384, 946045179, 693624542, 509264752, 405224329, 115986947, 517690526, 976839968, 202849498, 218278597, 527519520, 612062159, 647326851, 704874329, 78992284, 224490505, 208092506, 195580044, 340328249, 991919764, 736067748, 443912321, 382550801, 311519741, 972487889, 327248674, 655142861, 577152448, 59997163, 727922212, 853651524, 575376677, 864002884, 335735938, 379578541, 363037512, 556739349, 621314048, 681017905, 914789426, 771568299, 960138836, 447869350, 236850791, 975086234, 404388591, 971964166, 971035965, 587045399, 913332020, 955976759, 258478404, 186458349, 488735426, 25074223, 431183565, 802236962, 628825549, 98508965, 143636588, 132232978, 278528678, 378172373, 291136841, 641551370, 636243718, 399949395, 963192152, 358493821, 230843025, 272852980, 475925332, 987546666, 202974821, 552994274, 856462999, 480114431, 144074356, 334646934, 795749452, 13102793, 510068321, 81856937, 739383126, 488614364, 706949822, 558778159, 64592931, 435684031, 433423918, 375067103, 423686756, 755813394, 537816571, 944202586, 899323309, 411801663, 938907210, 282107857, 859377372, 528873409, 196097286, 715222093, 578778259, 322255723, 182808284, 14650055, 503418789, 885936883, 841151650, 272201445, 33150715, 377697459, 776853434, 500497827, 168603761, 817208035, 219448082, 383876378, 816024601, 781375682, 407947532, 709362081, 51017255, 750619175, 650860184, 182475658, 25155949, 411745539, 197704833, 494774857, 916067789, 498825180, 746454471, 160626879, 323687027, 368311575, 101001017, 754429117, 68496902, 597400254, 399664642, 856562678, 187035166, 885647743, 427791734, 127376289, 941213390, 717081487, 134663266, 855996703, 743806596, 215940541, 527616773, 381564014, 61564717, 443654749, 351002743, 233026530, 686092368, 443696771, 823751585, 260498037, 285543207, 47762170, 896332249, 542293479, 267146571, 280455549, 589415219, 885206047, 444711546, 404064545, 219437567, 407848364, 572953618, 967122173, 642521225, 901684407, 114826305, 680331487, 553702707, 184474388, 732810015, 339289465, 614671025, 377957024, 563232977, 55177382, 748212269, 389068865, 212182344, 997448126, 656256438, 284286277, 429762224, 283790151, 109116952, 231965258, 526485860, 838742654, 647611552, 267004277, 434562674, 374165526, 368807703, 944453773, 122274138, 983985383, 32251076, 90709030, 6178163, 958493993, 75441930, 179706305, 945694876, 331332899, 626509477, 161760448, 205067019, 651424422, 784711305, 677992709, 489865161, 870118782, 148009097, 977666062, 539762395, 616927903, 177280733, 745522698, 400781406, 783668149, 67335416, 656836024, 18810902, 399749288, 223386648, 53896346, 497905880, 766917739, 145373190, 213456471, 430689672, 372764602, 217989471, 318320050, 916170808, 657230869, 959893829, 768817743, 582928089, 562140594, 521875284, 160444861, 705365441, 124779785, 938499475, 465606215, 72564109, 698130843, 327263635, 522245158, 933147447, 801936003, 960931114, 433705298, 764935426, 205957858, 871981392, 846754730, 778835502, 547036456, 547517430, 54152475, 532186996, 227588653, 408883896, 319299298, 128293744, 213893976, 609889995, 799127372, 726698101, 357892563, 887069979, 322390736, 628669999, 448857441, 952191372, 203568950, 474592021, 532123855, 357505717, 86284799, 481774523, 613729477, 618149478, 627571567, 879481357, 818908420, 906286499, 60453434, 499206233, 142981579, 310963409, 698843724, 501870719, 761222212, 448494649, 267652977, 987617510, 949261219, 886749350, 205257178, 905975074, 140979188, 510024357, 892337698, 669116593, 407921105, 427914316, 605863520, 73739201, 614928951, 90883732, 846370333, 905712739, 832660718, 110279005, 31611181, 146533570, 666985809, 827729453, 491718029, 643907707, 66275463, 40245149, 947524249, 742212008, 585539281, 413017131, 126376842, 68298608, 302393430, 435165490, 26503293, 815130279, 675087932, 107881595, 840086088, 701234019, 536094191, 663501145, 628963517, 674939349, 490033401, 480056560, 357135496, 534761106, 343551173, 126017165, 181289491, 436525873, 987046783, 842060927, 772013738, 489829483, 94951556, 924378715, 328252560, 57945729, 707601773, 688590445, 38068465, 964651183, 689954423, 312671805, 570087222, 4196461, 783708100, 577469181, 547380694, 377396979, 976275546, 50225063, 231305932, 703428506, 491037325, 757920136, 176553368, 213119299, 654831186, 861242704, 511429760, 580217063, 549329141, 923004767, 662464674, 106632071, 815057066, 532364958, 811617179, 11415899, 924602251, 673184293, 580930053, 469075104, 744826072, 991461777, 165783116, 660852531, 222398158, 681091170, 580310921, 897468129, 573196333, 377011076, 866933702, 94957456, 654443792, 516010221, 436067520, 462676445, 271067994, 622348445, 929746934, 82795144, 186849365, 636331910, 810786423, 891215067, 235074652, 818281839, 600809112, 494809589, 312679942, 495111688, 457232182, 100237761, 980059424, 101457023, 25434915, 918915723, 466475446, 851747177, 850186393, 406409027, 604995180, 423222026, 644984426, 13344909, 594926983, 281135623, 575613213, 143434178, 570874040, 844693516, 304963158, 71384940, 777924505, 553768787, 555998765, 810429914, 740219772, 358643796, 937987367, 238534992, 450672347, 231136336, 567142847, 924525168, 203363500, 368753888, 688525299, 728077826, 472448062, 819092077, 669581611, 275204072, 237889087, 230810420, 431084982, 370064776, 373005663, 347771227, 234327802, 332983457, 652105844, 360514010, 556542337, 10147344, 300854960, 579673019, 967773822, 5061648, 640950783, 160225112, 981163323, 440299434, 198895116, 962695923, 887167356, 401125764, 913222003, 722829407, 443017177, 904678506, 484697212, 824306126, 768316575, 557596878, 847460751, 902474580, 984162744, 744786179, 530084082, 650226794, 207719868, 425547564, 661845087, 4202024, 998474523, 700223810, 677454576, 688623029, 973524347, 273813171, 77049366, 386674742, 321718848, 73126696, 159045761, 975041048, 287943488, 331863, 564894412, 462465371, 86757553, 886476080, 733549533, 150858886, 151253206, 985998664, 779129542, 858114908, 464304222, 689722461, 236188111, 381126197, 213900298, 773876363, 682288412, 47755546, 424620579, 376237295, 117447917, 471973733, 775410769, 91189318, 908560458, 927041561, 689920918, 178431799, 735294980, 343870465, 50622121, 994204988, 656578217, 384720935, 353373236, 290282050, 883463752, 691866859, 781417317, 103461182, 790352454, 156774538, 891412624, 782563109, 636679896, 657163827, 970509203, 355676476, 107867198, 181748163, 603035328, 387066665, 191913258, 337674059, 654576829, 659434937, 882076997, 172882733, 144058809, 432209540, 920321977, 880734291, 663049804, 280640122, 223307983, 477189228, 57743957, 184148008, 550592555, 655332321, 459514678, 447750874, 835825826, 195713025, 327924150, 806954875, 983552781, 955585627, 75462159, 291452025, 290376332, 137069054, 495191391, 292913784, 133618992, 673366011, 867897718, 14458914, 73544545, 174117416, 474654290, 822132777, 219237344, 56395630, 572974578, 871179828, 435778036, 833641906, 938768188, 408050350, 670048894, 190147219, 516573021, 75955534, 876212394, 451993310, 288853045, 971754122, 409299900, 316436432, 31281853, 80854520, 968680807, 391411434, 472437088, 320679758, 97711674, 907321343, 326732154, 981552670, 853563899, 85923257, 517251147, 123159103, 905735440, 197484120, 706303914, 831029485, 292621305, 930117004, 170322072, 1451031, 751647768, 827842293, 779303957, 883355738, 863950698, 270877430, 678004121, 568426440, 182022039, 66096857, 222584827, 910570598, 253920297, 592605502, 170920579, 45814838, 124226994, 140398329, 42882377, 256927901, 674316016, 719676070, 226549176, 11413944, 107540639, 290947814, 154681172, 423066585, 96694517, 475559748, 597858790, 39523571, 753315665, 432960009, 324412630, 39941460, 230910863, 625644984, 159514532, 711582166, 372861225, 243025423, 756247067, 947600046, 600495254, 510616868, 540605049, 586998267, 178145421, 556165169, 835514976, 357998798, 921659492, 595194740, 284526486, 498230054, 81887986, 734638769, 415490919, 370768014, 160930014, 551054869, 118738689, 977282961, 635958283, 139081463, 618968018, 178288673, 419344581, 175872018, 553313499, 673768710, 502102987, 743831052, 351425820, 721841848, 355656116, 877967229, 67586381, 872478608, 734120876, 213556123, 626422480, 806426276, 8533743, 65624911, 323007104, 295083069, 777262720, 561130735, 308571208, 859555744, 580233179, 224206956, 935131746, 856462359, 324836846, 489028860, 563133917, 690292593, 805508480, 48644829, 154553615, 638010934, 334023946, 310775952, 643884000, 903596127, 276398816, 415785319, 772946477, 889207549, 847574860, 912821164, 687214721, 892911747, 971530236, 458006319, 999285012, 734345478, 966931708, 32196913, 924093083, 40032900, 584028513, 512259044, 269882359, 852076481, 44159930, 241493807, 53534923, 900197608, 116736536, 229730240, 355010463, 153302907, 828080925, 344681876, 973570927, 135014198, 450232366, 994370714, 830517604, 730779447, 72758679, 977686320, 755868190, 400719737, 531829834, 835231642, 914306996, 364252675, 650669536, 226398179, 193801001, 594746679, 659612404, 78599344, 601840387, 959042846, 3593329, 164763455, 465652679, 586344829, 327547980, 168033214, 683695410, 644717243, 460290537, 412174056, 776394047, 676593592, 721088692, 352088361, 277176946, 59035524, 647973077, 127043513, 748166083, 829104130, 124556120, 117487496, 898184159, 162733398, 670755398, 952928597, 992506320, 185933914, 622468397, 726768975, 792923651, 407354109, 748366826, 800644806, 13259317, 832988454, 332683215, 67486443, 611890433, 895992806, 42756341, 287398524, 812907700, 783511747, 976194021, 270490897, 448563858, 16384316, 150083744, 88229732, 331283155, 58272910, 395169049, 661168113, 427455244, 443870314, 145795886, 241637839, 915088316, 778888339, 381375911, 821276925, 889107782, 69429915, 921664259, 21584389, 233733788, 704612078, 672369191, 302167687, 903548069, 241680092, 732217842, 847501183, 175800560, 405097782, 473402447, 268748298, 947225478, 11485582, 407885025, 155378487, 490478649, 484480737, 423734127, 645177310, 5614874, 59463219, 271107793, 437826279, 758097756, 746215433, 25182883, 679955516, 726533363, 418057249, 947260191, 936827032, 104643285, 564947833, 944820637, 673026729, 219734433, 603601681, 77859228, 694549492, 644984885, 288437332, 2630825, 161857492, 280522076, 962397920, 282710295, 810616234, 238022161, 311801009, 839549629, 916465202, 935837143, 491427845, 721997496, 114910220, 227044834, 905026533, 856223337, 662998693, 239338832, 376604275, 48928132, 409999942, 79037396, 648270923, 740942328, 197757434, 517099279, 66937382, 165722643, 340981600, 644988498, 757964940, 31182121, 166160746, 318413933, 126790419, 73517148, 947675065, 330392616, 486677776, 552707738, 369178353, 325559411, 227255557, 426598780, 79598008, 658421447, 719989849, 832898372, 991998232, 228697576, 320091020, 298070722, 309736670, 982674958, 643747743, 199700721, 426028930, 873823380, 616841419, 839525840, 252240671, 239218570, 612967749, 33086165, 186633748, 792935216, 114191137, 855715709, 54073383, 479010860, 847887282, 167394413, 760566387, 659029831, 678836208, 522807816, 413653999, 846515069, 20731046, 744854876, 887079695, 669920084, 541162093, 729661147, 543987797, 707093381, 562515484, 530241580, 940280173, 924398603, 592178729, 498747025, 77434759, 247287280, 407225108, 125977137, 226375793, 375692428, 355238728, 116875334, 138125031, 770337811, 592872960, 229668288, 207143249, 328067047, 93483923, 145703746, 194892898, 770042758, 589633516, 344032296, 651916448, 520051419, 643368480, 162620108, 229220017, 725622271, 423294919, 607072860, 389973348, 624765890, 287219607, 968113313, 275549649, 638752601, 83833629, 498945677, 929150992, 88918062, 796274246, 637146520, 656363185, 62002492, 409769165, 789503215, 610269558, 373023663, 171912114, 295789406, 585720101, 188608993, 743722589, 349157368, 251608950, 110503759, 566395441, 749243458, 24468040, 796337956, 424551392, 819773960, 51906614, 794992948, 693737022, 430599374, 960947138, 958160333, 195284029, 592252826, 404025209, 28978628, 532353705, 92051673, 17589498, 406022430, 295331916, 101545855, 746627514, 483860413, 696192671, 892677910, 644971288, 943348529, 268030503, 215791961, 702664315, 696329767, 636442178, 693780603, 811358108, 145702639, 628804316, 887904474, 28018554, 474064015, 469423011, 495654095, 595102715, 337689682, 885999955, 324912193, 490848807, 338402429, 612603894, 295959891, 321629190, 414224610, 484124926, 122026768, 470011174, 643504441, 571739250, 638083871, 93385071, 74363955, 839211711, 349201206, 324891197, 473950778, 672197561, 869943020, 165209594, 944135966, 894506104, 577748886, 962629671, 469724352, 532721182, 525334372, 639015202, 310740986, 756080540, 703390087, 205255663, 229079749, 104470601, 547485253, 47092430, 210297865, 810317993, 851470973, 281052350, 51790877, 57288198, 542258594, 145007480, 412635563, 739348492, 480984922, 24993312, 352368606, 207272281, 265226849, 349885097, 916680719, 346433846, 271365567, 627740781, 480155433, 200892994, 555121210, 379628605, 500308860, 459101155, 801364750, 806817172, 928046396, 963668979, 837469462, 171580551, 359178515, 841493430, 174146620, 307255480, 696000907, 933890120, 353864035, 554375827, 336576450, 992055115, 557539596, 596911209, 750241259, 877071220, 108272835, 615695197, 761056628, 778622376, 395949167, 864082239, 313657380, 953595264, 505846582, 13432831, 379843509, 113183095, 26274154, 90056193, 885490865, 816094269, 649225544, 621445084, 129340007, 513264101, 26060418, 448153470, 436790701, 791402053, 436831108, 638304686, 360063654, 293130869, 626846666, 809271853, 177242942, 589169206, 57802368, 770326836, 232324722, 78006417, 546066793, 538656419, 179156844, 725003957, 210716559, 707489757, 550685148, 625065163, 798789356, 808385706, 784756305, 188565571, 892042656, 565092306, 53136525, 881686314, 30427062, 811735117, 108738575, 188278110, 738501707, 463946400, 850822605, 423195889, 261744295, 86729515, 251776316, 1476700, 57593647, 636696605, 546524875, 27047499, 720356409, 212087146, 923676985, 835518567, 446592452, 287885011, 847428139, 545974766, 342262176, 557119689, 720604557, 359559450, 491212785, 181925919, 431545865, 217250169, 227058321, 107582155, 292975769, 115081730, 675266800, 771992595, 340695168, 4571430, 628150709, 358317095, 829515425, 170052032, 939727438, 722403037, 769623847, 204464121, 544555392, 669854412, 994835790, 434218090, 810848954, 847343525, 994345975, 627718764, 976263102, 665542642, 882363533, 257631331, 83810873, 952009911, 264682472, 346300476, 239173095, 655900044, 95025082, 489721917, 327987912, 272752433, 969336669, 198814581, 280957965, 612010436, 382696924, 612953474, 55769811, 489587760, 49890806, 63175779, 497051549, 362479590, 49500275, 639783825, 322234134, 964491970, 838981261, 335918080, 3049553, 90439112, 369800296, 350540106, 53042905, 252465284, 215550432, 410267679, 26804611, 304243864, 212804762, 31491545, 884518773, 206424418, 116351655, 414447643, 26784291, 779267608, 546929528, 890717919, 949590142, 601585143, 335157813, 572328552, 710654198, 783192292, 677879400, 181293267, 408197390, 214268964, 915120990, 24437114, 994148373, 648423533, 651088501, 200851469, 246332794, 688318717, 732592513, 347025967, 795603875, 396831528, 413514542, 789562055, 367867572, 764231259, 843564887, 149314158, 424723477, 103946826, 609697033, 970277978, 651523993, 584122484, 746759651, 140585654, 610389669, 385761215, 6816276, 990874898, 317968933, 4300163, 993660975, 420220970, 339996748, 680936970, 976462920, 318245685, 863611434, 346394132, 868325616, 876951122, 700509864, 729802347, 256442269, 445867223, 330909457, 774495126, 809545999, 196739552, 58636696, 347831760, 449609426, 642752726, 182870380, 503196977, 366086209, 612263548, 636585107, 104478681, 406703421, 265892892, 545955391, 773405840, 344114510, 249223533, 652869507, 714568227, 29548069, 374599324, 907401917, 872390550, 636035012, 639521042, 309292200, 965735296, 297648331, 935902293, 812860617, 400828478, 857969447, 200187156, 362818649, 804370575, 379686695, 24325680, 422843978, 106230185, 702456353, 786507593, 127375121, 786796965, 582864695, 414896579, 387085119, 212789607, 985957380, 21811430, 536685967, 186326108, 87599311, 744919198, 664327528, 364516699, 947549106, 725874350, 340543415, 310038303, 350268706, 647328031, 590026275, 734978871, 616625415, 282451690, 87242078, 820695614, 66249954, 251188338, 899511248, 439506457, 809002333, 675676403, 98773780, 221955881, 821644928, 869704863, 199764320, 59090726, 354073375, 251073441, 324727590, 747798506, 446019795, 96366819, 580892467, 72283387, 809536546, 142792452, 23063445, 205308577, 361745710, 124583837, 838826915, 373965923, 833283341, 103174692, 685341827, 643235569, 183934113, 858340764, 263006362, 690667906, 93318394, 504727090, 479247616, 745960932, 322066757, 201900100, 656211252, 618132798, 26984289, 101130706, 845257592, 817423157, 22642397, 233911651, 493337831, 514954956, 423176889, 234112003, 978597216, 648106405, 613894491, 213521853, 357625992, 213407606, 326015936, 578176873, 822360723, 29101865, 508238509, 199795038, 374071251, 104880182, 220221565, 645537045, 19338948, 654863953, 649055226, 859526981, 59752839, 944419755, 826540483, 859959596, 175067963, 555349538, 93397922, 365111928, 139138283, 221288289, 19509823, 591255377, 150285675, 459268987, 53618970, 189319722, 238074825, 401920241, 411059330, 248301442, 851720795, 605229376, 892624985, 320253725, 958272538, 108478551, 894424464, 938096034, 991799076, 284599132, 665386127, 552082748, 362600338, 976339152, 791297660, 725624404, 700087112, 603878181, 271581949, 512095655, 220470568, 253787676, 796269055, 755028543, 338140418, 747596480, 863880296, 943201355, 918061271, 79053128, 338881953, 9081365, 11288933, 213135352, 697147634, 134808322, 783965535, 359345895, 668077426, 803443816, 450340836, 161247429, 825742210, 506798694, 127936740, 365843319, 520758918, 111231319, 387271471, 523767808, 630935701, 584065657, 336774332, 711839397, 425899687, 465335455, 809618613, 856710290, 262620597, 107370020, 919899960, 451111013, 561001351, 32318571, 115846721, 636422643, 771585669, 91614779, 53189063, 990390442, 325352811, 472546845, 451670257, 239352956, 899108669, 299915465, 841165349, 250692287, 456668930, 612483531, 117447918, 355553164, 752999524, 246822276, 943353160, 47883680, 29550445, 761110392, 767017225, 914023061, 497307864, 631915439, 378182874, 989392710, 826951470, 302813039, 416635059, 486737377, 176462286, 775208669, 347224390, 885521652, 894369452, 826953821, 204829552, 414302159, 350741366, 318675315, 879093110, 329158064, 828839817, 825000262, 157648617, 731061109, 283159342, 74515075, 159201577, 399645390, 859472894, 362233241, 357255939, 208011746, 992326065, 389319851, 74455506, 143157336, 847866410, 464039829, 590305087, 769077384, 566004365, 197817404, 49667255, 363483343, 883090186, 836703876, 875644927, 788724457, 325214736, 594693127, 958596513, 195357870, 321453787, 730176888, 382555283, 506876378, 458945136, 526744585, 398311317, 441195891, 613804006, 419083439, 736327674, 658463933, 5633086, 97118524, 446769171, 445586549, 749607371, 46491280, 815018369, 602032616, 780432502, 889328059, 365181401, 333819662, 97887074, 588502803, 882799226, 994805247, 623139999, 18887330, 654823028, 265933125, 855193598, 15529935, 857278321, 890238930, 2211453, 627997816, 400293473, 568016872, 274704439, 68259449, 653209318, 426292959, 604046609, 541701664, 76649200, 122529380, 610818132, 576431272, 842052783, 210587903, 39615934, 195133333, 579085203, 113464331, 287995784, 865650145, 384464326, 613972442, 374532436, 272227285, 199013954, 344109365, 288150074, 492777376, 665766287, 312029956, 329880495, 402464948, 232834912, 488477323, 726379989, 424518919, 582775104, 689515607, 621387736, 546586505, 51449919, 487121293, 524931594, 116978778, 376668309, 86093936, 178621492, 100899089, 86888327, 382364018, 348792781, 202202168, 193059820, 330811292, 899214312, 187418097, 261142950, 933235950, 830926532, 526476853, 607071966, 834430659, 774096530, 833643020, 908847992, 506477803, 530479497, 551860801, 933646262, 919731471, 277726924, 423506136, 949354009, 302337558, 941144680, 526088782, 736571885, 163882493, 608456314, 623724135, 262489509, 46537034, 751123661, 714699609, 480313820, 480165022, 656834560, 972208853, 93977586, 140078264, 982184042, 136362190, 279210853, 66380676, 43599452, 906836065, 864645313, 561467839, 298228927, 451695698, 796878249, 533277586, 283679018, 198293550, 579937395, 832247153, 314436145, 745965929, 926979422, 828604683, 745110878, 595126806, 395345738, 760784274, 535752614, 227754074, 624854533, 998043424, 214348214, 575537348, 742409631, 929983220, 645594268, 168945797, 733310260, 999875050, 573879437, 524325796, 495049013, 389185392, 266943510, 531430334, 806159228, 270891412, 528881370, 252888708, 557167706, 854765721, 741916282, 853940592, 944229020, 655939417, 988348132, 516283167, 536476930, 398372919, 668683561, 453125958, 594047740, 340770898, 843865097, 865147722, 551607995, 119944440, 928420640, 876788069, 435683758, 576878743, 10462514, 783182946, 921927987, 257402070, 688573402, 300786675, 866764579, 990863808, 760873133, 476312504, 557423240, 437398113, 536064652, 631668914, 173998625, 169017583, 192582323, 701443609, 188417260, 472086368, 306801146, 186577692, 689787528, 773083813, 264427360, 598786886, 884536244, 288544343, 158744152, 145559446, 821120847, 340032588, 177474826, 896841866, 707478261, 956324675, 453953335, 860971386, 161150820, 22911003, 603431639, 840870628, 285462255, 695397145, 519356478, 745148402, 316374780, 34500997, 580164695, 792532503, 310838113, 254944989, 618074788, 570457721, 844704717, 759102768, 942142823, 562386241, 474830030, 960364846, 154692015, 569276462, 664103654, 443304004, 897685732, 682258696, 668387643, 713256899, 763204567, 71115229, 7213068, 654370875, 733166965, 347400182, 968136389, 566121767, 654016069, 663592356, 317119817, 197197978, 735392655, 890560168, 145524099, 931403758, 945848294, 356582002, 812911737, 242741590, 221002186, 406259175, 301572002, 109757381, 689807517, 255527424, 312912606, 281699109, 751182063, 377284844, 134515739, 18666806, 541261426, 945266428, 258816166, 270882952, 529638692, 462675800, 474557723, 692996398, 995542515, 388623380, 654047332, 201812463, 305225261, 517561675, 849260915, 376990725, 916939753, 942904646, 620807047, 502572473, 543738333, 600301356, 518610968, 677796078, 674994425, 709406320, 414878354, 242518799, 638214957, 629995597, 967806692, 751072064, 862141043, 62535368, 496802197, 654691817, 514360716, 987057274, 529733831, 857728253, 624501902, 512646422, 762655724, 126530142, 405594466, 24608412, 686532447, 999637558, 535136506, 993932355, 359863206, 401562335, 97354001, 70127689, 925344515, 375449756, 562958155, 809119620, 523652620, 10601431, 511037241, 98279126, 382927356, 455525071, 521840141, 129699738, 712794374, 324162837, 344209813, 18426786, 37272926, 466814875, 412962603, 62989020, 67339265, 153653277, 833448077, 599661078, 695243029, 399875064, 216277408, 469054495, 230969145, 721162904, 1632023, 302055744, 127735354, 830739298, 323052937, 767936878, 828396673, 606731519, 156032932, 76729851, 529794149, 775862821, 496585677, 108762847, 430433844, 928825752, 119897268, 196459274, 729353908, 948014486, 912632056, 891045239, 417340153, 375219130, 364654577, 834522376, 907579761, 842191780, 237192210, 769837047, 748044303, 766608343, 433715069, 996314049, 251544301, 988673609, 202076849, 837304172, 408329160, 224665171, 86370235, 687246211, 562362123, 284717347, 658176759, 435712690, 548271244, 723236726, 844916274, 397040420, 736281957, 882649858, 69838106, 257853912, 26449098, 875521300, 78911375, 212888899, 860058849, 684994309, 912519492, 698141324, 699511065, 663688739, 638699032, 644088894, 561144309, 538883126, 444637533, 573678613, 780745947, 561714860, 386280551, 654718379, 848767583, 658585617, 909966016, 570635179, 674765762, 922629753, 653746470, 768942574, 588097820, 620924827, 756988819, 316604572, 448318074, 329043964, 967887450, 901264944, 964092753, 478918993, 572251209, 841787440, 518649722, 466232644, 577900293, 53287648, 327789205, 712512244, 866694218, 34906200, 127173555, 650256332, 628850204, 711503396, 159349969, 211399306, 984577743, 960206552, 542659546, 714748279, 612596517, 810006895, 212746894, 259052267, 40123914, 242185201, 339001309, 222369090, 834656066, 583003782, 585006072, 136588829, 46750646, 127640092, 215998045, 154363517, 862652611, 717993634, 358042110, 658545108, 705763907, 96293871, 303464049, 74077771, 706438795, 842172990, 467188500, 255279388, 230027553, 166330715, 874737558, 934948426, 600382171, 329320114, 783823181, 809446958, 213856580, 46425793, 630285539, 979916109, 158248514, 977329075, 937703705, 695222667, 916842092, 278288211, 106921477, 337161531, 211114768, 690118794, 422319317, 481001106, 790498656, 116198171, 226095580, 718998131, 344260487, 505281505, 711404659, 192081921, 875992270, 163162754, 853402514, 895954564, 267026867, 680028050, 283566021, 862055172, 267708724, 944188127, 153847435, 428940182, 226849216, 164519634, 657038017, 295906429, 675006941, 797319203, 585728514, 249265901, 981698857, 682959936, 157553022, 33448524, 233862289, 555417076, 248255717, 409689794, 640730346, 563725998, 509490886, 634342765, 715622188, 295793632, 507569267, 878718442, 915106893, 777646124, 259927599, 214175861, 108409662, 534996264, 934230592, 321512747, 264541297, 143601708, 427620548, 849091917, 654014744, 883879304, 125879069, 531816815, 199888696, 621927786, 534419185, 769659899, 506219293, 681892880, 508429200, 444921379, 27655085, 355821095, 18443445, 664336474, 269653739, 998576801, 706100131, 317406953, 993081647, 98186393, 301136272, 330229587, 690805002, 373484147, 709585198, 25071891, 611274099, 401039619, 731155963, 501833731, 881241491, 569113281, 644964605, 914500991, 660176555, 868513974, 533480233, 928178084, 469908490, 760695401, 996692376, 875316291, 137806082, 394487762, 238350401, 303875954, 392351625, 664332381, 223470415, 212683354, 94207701, 311732941, 898328600, 217607037, 275711302, 540430686, 541215032, 428258966, 931571524, 169143644, 260980594, 943158186, 36436097, 120522238, 576571200, 230244450, 977600690, 245945106, 408987293, 50849287, 628882463, 561710948, 128119738, 764016086, 295988697, 923683925, 723441488, 810206014, 243099984, 294925377, 260394529, 256007138, 429523957, 45164716, 831581603, 811116764, 767905686, 272842009, 583770718, 376688831, 176847554, 921567955, 992850863, 607157447, 301527057, 843740211, 459574927, 451719134, 477465206, 584258544, 223671821, 164569055, 394574241, 953715739, 40840227, 510136511, 351822209, 650709998, 567513660, 881630854, 66958846, 580568440, 351643460, 2099925, 648438021, 48322692, 788162427, 310043681, 334245154, 219534041, 734981263, 523700396, 76075684, 429370726, 404808006, 954816440, 15731953, 839329545, 941469543, 112732353, 960092836, 44191065, 489039790, 489986909, 673696658, 361112995, 83847255, 364733466, 894151709, 597770862, 222124532, 281981457, 802159731, 906958894, 433381510, 711308859, 845243298, 39953120, 763736837, 318989595, 676867411, 815311150, 716495258, 606506464, 950103600, 171050626, 145110590, 456709425, 441232135, 904219448, 68752491, 213781355, 471956578, 607797669, 776335771, 957152920, 590817187, 167986493, 513498403, 41728980, 213389439, 726850715, 410522034, 443920041, 920936789, 129744258, 948288781, 261396922, 635887681, 348907669, 336285731, 409907623, 345474550, 3328200, 647466856, 3405175, 774581220, 534281775, 228316053, 4277200, 548194845, 257996715, 633301746, 317558208, 937726815, 967125705, 371533327, 793322228, 660127797, 395676001, 115139502, 34121656, 125196206, 963593604, 899521848, 121349475, 627798519, 828233481, 922783698, 253614824, 1399298, 211589680, 672379005, 389427320, 546329663, 325368348, 71930994, 689837699, 78081434, 697573654, 98687642, 613299491, 80765, 898989444, 785096225, 481496534, 77023232, 732831625, 759755941, 477196835, 877380048, 635608718, 862857266, 941568303, 808149499, 647295484, 402059303, 812582093, 625739890, 188503984, 938150679, 872550892, 676283364, 759479791, 926559881, 339858017, 684651326, 159207433, 275938050, 480643844, 247774189, 668777575, 975223347, 635884255, 105273987, 835898508, 93187971, 655379640, 558513782, 886270197, 539758705, 852007039, 260911558, 230352600, 565961989, 446564535, 7084830, 654888808, 300162985, 690374724, 3280115, 572680241, 277300791, 573874920, 738328538, 602700555, 568152660, 316479593, 502250378, 192109818, 443693427, 350247134, 886552074, 376574603, 173126423, 394505777, 826584361, 153144424, 264776787, 621476235, 512454377, 3738976, 796436970, 118206086, 645377536, 999918455, 459693886, 528716796, 604645404, 203296476, 993094576, 133124985, 726783690, 415528556, 595507650, 966559974, 389304098, 819316573, 362451410, 818716739, 681326665, 462236656, 911893248, 160490517, 292987790, 623216348, 691524985, 21282196, 235700793, 728332948, 35574266, 618965399, 361770139, 232263810, 875044449, 37239105, 130338016, 742368068, 679587176, 930161847, 523959443, 768337693, 708865905, 249054073, 921472587, 272700100, 871895963, 762862963, 110941213, 298250714, 341775298, 651521343, 210532584, 588576505, 314370522, 970077230, 500793136, 792331347, 248382699, 550666258, 923304774, 716874477, 334882335, 505598672, 771838256, 76710630, 359140795, 238443165, 997277970, 495625016, 558969856, 780675354, 914326854, 837936789, 304522113, 459364168, 698059202, 379209966, 565189139, 125977475, 137881655, 252726569, 458614942, 378076602, 538776931, 735037545, 342830234, 123312590, 777895380, 118497027, 195743061, 831039823, 702993485, 455540683, 401151396, 313721505, 433112671, 304928121, 718632749, 848310209, 965677393, 900456869, 369774775, 60678706, 538326045, 271443035, 226437671, 795103013, 233632074, 972448850, 633088865, 889329193, 82316274, 445336957, 563612400, 6125396, 703265543, 281175531, 349980359, 189096690, 844968034, 856910016, 794241778, 29484886, 143158321, 501075354, 7593763, 637741162, 127639540, 33479831, 924942728, 575132802, 457321009, 997531224, 818682401, 364469911, 242777803, 529874430, 196858582, 510807603, 902833081, 952209372, 693003218, 675577097, 906770537, 287775036, 100080705, 409976650, 436012202, 262427339, 330448916, 908381761, 371841564, 2993233, 904530352, 631976794, 648679439, 113099499, 134989150, 499182890, 518418177, 617313033, 684211293, 243540669, 31061982, 453998280, 146309182, 335487050, 2435793, 74808891, 459797696, 575280952, 8431804, 238028934, 689970467, 332412037, 126413059, 246384521, 465021681, 238149443, 63334026, 412946045, 774184314, 706034535, 506044032, 71510490, 414319573, 57686554, 149576807, 985627493, 994231763, 246527305, 470812988, 421850623, 372112556, 196514504, 998276032, 689628312, 85107620, 959040471, 707317447, 36066606, 962470937, 96108377, 280797382, 989074134, 481814049, 38881716, 866572730, 246604663, 683112771, 94794718, 912630219, 622981719, 64030758, 755678918, 626759532, 984531147, 148484154, 607461880, 582093347, 915258144, 463617203, 620033451, 144763228, 517164274, 597997610, 286002728, 131194508, 806020914, 134977511, 331594722, 234530879, 685140102, 599581550, 13921044, 786099302, 939115889, 713845223, 615439314, 3056149, 524743327, 308006006, 79585517, 756251991, 488681577, 520432809, 742501695, 840603525, 607457126, 9032869, 736181676, 576372310, 430834993, 511055207, 890082076, 538322835, 641968612, 157906813, 59785723, 618597577, 314499223, 276903565, 960190646, 187770211, 28830928, 296188716, 870328814, 699189064, 18529220, 77135781, 539387204, 293293081, 2875092, 776142305, 973250512, 404912103, 323232984, 912343031, 824860048, 898073763, 53422853, 162973704, 604976211, 98516591, 466546908, 279903736, 796349595, 21298746, 800488063, 667929277, 180840061, 64362928, 239592858, 805329116, 283860344, 261185299, 903495407, 992625764, 845922289, 277733255, 365162077, 493042932, 625476587, 401777150, 519159229, 951960319, 315089823, 781842776, 835292561, 159572455, 539149920, 639245933, 630777700, 463612003, 63938110, 878786456, 428806237, 86905547, 451933259, 429984010, 702450340, 206838074, 799273837, 866397174, 718791201, 4915113, 766460382, 909762215, 517302875, 330628979, 270416584, 478453085, 921684272, 818532182, 479583298, 549919042, 699672828, 232205802, 408378424, 67831850, 881224621, 777306304, 927162801, 149829690, 145503039, 407025343, 878488463, 855403693, 765747957, 46150642, 197488955, 288739236, 731409886, 692096972, 89204612, 769719261, 991719914, 25749662, 217857567, 416524186, 175795123, 242853201, 506897447, 600329853, 366103718, 17014783, 186816695, 472198647, 425157877, 519261838, 215527010, 764403876, 685628150, 338518515, 706276134, 735569729, 325749341, 623606790, 970033856, 382555381, 848831845, 184326136, 690021367, 885321738, 364886568, 284670940, 800698591, 640430016, 566938260, 764390867, 816248013, 40968170, 246072912, 619745477, 223854093, 290632013, 809211290, 411699931, 263295209, 488329079, 917850834, 485923725, 945872920, 591837066, 22547031, 691463762, 256441290, 44656969, 566962176, 337721091, 693439058, 588412704, 287860921, 776057357, 240827689, 685597643, 457719875, 476093981, 815397454, 295233221, 941408753, 240009493, 450604370, 796671468, 794808899, 158026604, 334191051, 513834291, 424271963, 146311528, 545741302, 579162521, 376536502, 585551551, 678935125, 490608095, 466077767, 927550697, 997431098, 615221715, 807344459, 58361137, 593373778, 154032980, 601241283, 120972216, 189661983, 63858069, 656570511, 917651634, 109291252, 543855481, 357884059, 536396091, 243687589, 747029967, 492063370, 280079132, 538429140, 365892863, 14403812, 226316938, 846408075, 487067058, 105598577, 543216064, 845163479, 514352744, 137448745, 560262548, 382979051, 645103558, 104245062, 525821603, 743374528, 792542945, 447852133, 966836286, 406391512, 882877381, 989219603, 299895144, 787063983, 850905583, 654137485, 760733999, 560554464, 615637094, 412491017, 179063782, 544590607, 915660732, 763524090, 999511179, 664697336, 477086527, 402446789, 177786045, 787940835, 389223953, 132206251, 871396326, 377037303, 618218881, 668234500, 439475724, 438332976, 415447526, 981069919, 24402087, 269909356, 215680609, 894901367, 633243881, 407204689, 364008807, 430491776, 346962438, 75124771, 811001002, 265377858, 20940786, 763066637, 423198392, 887426825, 211589123, 426048370, 979151899, 419113581, 69206632, 26173175, 745923897, 546978520, 427885185, 833800397, 332392546, 79881653, 963306976, 938370157, 899455254, 666681265, 315916808, 717239328, 795670567, 784581478, 251627912, 149485371, 31910059, 252154834, 61676837, 296634727, 511375217, 85558601, 335849395, 441885368, 453651735, 561888434, 625187030, 86168157, 843627210, 102541378, 740367093, 828862430, 932250448, 239495599, 278312818, 893435643, 362363171, 353308789, 465565002, 408404815, 508116653, 506344231, 284097463, 500777521, 523045343, 895428988, 216749801, 634097340, 728013421, 351822484, 375488245, 788791444, 94911838, 19902915, 242703957, 644819820, 566185958, 61047058, 822992889, 9136737, 534436174, 987325993, 988916051, 313549544, 830558297, 508304174, 868124120, 213487446, 222226422, 667952758, 95883881, 351753730, 94835942, 838458382, 659310101, 137219962, 955250478, 9576734, 299388096, 812943497, 692054546, 78165867, 626122957, 20688893, 537174623, 899935250, 349463895, 145504564, 395743026, 865947393, 709806632, 618940221, 819348618, 356330626, 122915690, 749159412, 320945124, 702387107, 762060274, 219797378, 407377716, 295281312, 984470369, 307238025, 277690646, 144224830, 186113345, 675771532, 835698419, 894508084, 789177391, 485280408, 752623614, 446750101, 42860691, 635911469, 115547760, 796986032, 516459729, 327599453, 641144935, 75492418, 273964807, 698339921, 733487540, 912635855, 727972703, 462358715, 161547640, 520896244, 8418238, 378686640, 356752525, 442147857, 968105711, 246264628, 212321836, 40891109, 403411945, 457884666, 592782564, 268199217, 861347332, 223498206, 284397032, 514685424, 246007011, 436464434, 972781063, 252140190, 425642602, 956583234, 376387467, 724827368, 865111695, 115384420, 167913621, 364600870, 346361317, 712931738, 216285265, 511613, 268553346, 964878058, 722478395, 120683360, 821399004, 244943549, 352161526, 766263121, 148169791, 773880182, 410956167, 773944690, 918279606, 963164468, 439351651, 684455348, 460140208, 582049229, 74760309, 852674465, 573105431, 245886563, 934524039, 613694327, 733890786, 36787384, 408613227, 408349855, 157011727, 58721458, 774747498, 751474232, 64646363, 634052576, 635686915, 36483430, 888049810, 157879795, 218327633, 658331081, 166632761, 716064956, 904434217, 621227225, 900974141, 367396236, 530553486, 447818712, 866808420, 166869100, 695022309, 512145020, 52352069, 581129903, 299432397, 65363292, 504599574, 331842634, 997387629, 420895985, 621333871, 661022172, 240947838, 583595693, 656842493, 672790934, 989893484, 832444634, 86038748, 412277577, 929755265, 330468340, 276765025, 835010400, 87334612, 225918093, 591371137, 941442634, 457386019, 413025727, 984554457, 480521965, 576126120, 863101757, 270117858, 293320930, 218204946, 319425860, 973113332, 930024697, 18565143, 468725365, 102742868, 236576857, 907911596, 923496842, 200724543, 18630475, 158751099, 436347374, 131375975, 665812896, 751540660, 452542433, 629511012, 899320906, 559986185, 930813292, 992182, 342758609, 952885314, 494407464, 434186396, 46859264, 399569829, 31319588, 970662516, 162038533, 566788228, 143956926, 686269392, 507526985, 649926691, 794230107, 905590608, 79314254, 478847844, 147374876, 594044089, 313420940, 490375907, 122625810, 687586557, 217483090, 191989653, 97872295, 993387293, 303538947, 497629708, 758366284, 246255223, 689114182, 808533983, 543798758, 533995896, 546496962, 804674711, 936742701, 319804962, 956743692, 708620183, 399561292, 390994660, 268280849, 614396211, 765387437, 410192669, 376602510, 100606307, 752372472, 619328085, 153601265, 417606157, 469480691, 530031075, 673636403, 998765304, 715189483, 519167963, 3959054, 241703719, 15289739, 827428805, 545530883, 586310643, 880883353, 917076185, 514729777, 271448640, 491875933, 907160251, 524230719, 24631461, 59744862, 927446042, 351475903, 57012369, 191962211, 630174134, 440514130, 10942444, 28573082, 974508531, 448555948, 781459024, 786850159, 974295193, 89281692, 804327188, 106169885, 2697786, 60489891, 476297934, 344960206, 783200836, 970093073, 347171713, 583800522, 369670550, 730792331, 35730712, 843893941, 363162406, 70036414, 413064180, 617484722, 689677497, 418542287, 324158230, 262750494, 203765504, 62407311, 285407525, 70653120, 153084069, 240920515, 305254279, 361516058, 308431672, 84960603, 503022600, 874828308, 686073915, 716067632, 103529715, 321966232, 203181187, 541851541, 38136604, 916292602, 996240183, 660950382, 851658258, 173059937, 453659384, 565339848, 502369250, 489999513, 125907048, 961823567, 741525394, 629442362, 545794190, 928158202, 332478674, 290595052, 135585210, 324432901, 418975250, 163834915, 604191012, 268515786, 120361356, 46361996, 382878605, 394530649, 286153823, 225686185, 6974515, 411631386, 710190757, 234634553, 3578674, 113568739, 328502827, 362688750, 900530138, 265503995, 947157843, 617491137, 411319299, 365158191, 720536020, 157328043, 762946233, 71168746, 251917234, 112753155, 885442518, 857209561, 159290153, 645987770, 119205545, 834746252, 454781612, 541976282, 45198622, 278640465, 532790019, 286536169, 715626008, 956160150, 133082629, 342350966, 328424009, 724660319, 540738107, 75511546, 426434919, 4616282, 726216691, 623508685, 284641868, 582866436, 104807735, 276026323, 307271523, 553573411, 916523250, 399400399, 523383765, 120920849, 204765808, 302865388, 412321297, 808022098, 69912337, 970179132, 368545782, 98298089, 417497207, 89943269, 460948487, 335980559, 395470028, 857443593, 829828413, 522656466, 768757787, 296678285, 228236779, 441407772, 840414215, 769788583, 85295889, 214091876, 806186517, 241792405, 666443908, 881804590, 558974847, 51576902, 486985445, 86815410, 244821965, 599593373, 896629548, 204175843, 684326175, 609269841, 547626372, 602328326, 298492867, 400308438, 968740924, 457264357, 597461301, 450217442, 494156373, 615903533, 860141396, 432952491, 823561012, 17599375, 529927993, 719407207, 157038180, 105510245, 596122492, 715828559, 7155489, 649290198, 659446127, 945905639, 59341927, 659441768, 990820565, 273214932, 893562181, 476361487, 432880931, 732201014, 828738194, 190046645, 941418874, 731374869, 730775339, 484332142, 832595926, 224570913, 34461462, 160579035, 165490529, 425419801, 614096317, 993943129, 960238103, 39180413, 293244647, 54701670, 565405201, 319081755, 614401163, 110777614, 904907761, 155926133, 317261056, 614553702, 905937360, 18066981, 129708316, 178817062, 442933505, 37702290, 178828850, 479718548, 978836256, 420690651, 286595784, 178239280, 493958858, 223246166, 956710315, 998725887, 760713897, 762106772, 638321828, 787899946, 715059928, 338102667, 885658541, 172186755, 88281667, 397900362, 785107603, 888656691, 178971269, 797647901, 598169661, 422353018, 892452616, 588650956, 489052678, 192819298, 128049616, 166079681, 648913553, 735067695, 590489744, 265229143, 120986062, 654753653, 267222090, 93893913, 118043496, 806898245, 138594108, 231705537, 147104406, 878613595, 279991448, 15979722, 951042955, 763587463, 223458716, 416861665, 385296255, 325966280, 501115401, 243663354, 571383941, 141333035, 517209393, 246902567, 272142243, 416737282, 677859396, 385276061, 502026414, 947230934, 330392617, 994440493, 657589375, 682039898, 777384549, 39762860, 569574787, 915354445, 976584116, 230537066, 739937349, 376880344, 21447352, 84474037, 244815420, 997087581, 24285447, 23972313, 192873259, 471689639, 400378974, 237825169, 422295993, 773075416, 868598673, 980497521, 83446735, 339446729, 629669427, 763795838, 95934695, 524236496, 459539461, 132701079, 617329596, 170203435, 16888373, 773868327, 534536971, 940603742, 566832679, 33608082, 191907427, 568665844, 824980160, 948317253, 805910654, 501043017, 246567532, 111799366, 38166064, 677260144, 124753040, 50769208, 80496696, 988688820, 453749408, 894205422, 911849078, 62631672, 30881226, 387707192, 865405843, 959003492, 172203112, 896554582, 434576101, 625391923, 999789625, 987312988, 487590823, 932994406, 90942628, 512781876, 161482764, 998729653, 112908747, 452596413, 75573698, 725728221, 721284511, 918884487, 656876982, 615991073, 517237676, 623149952, 516357984, 36272997, 735854847, 914746886, 830612906, 290453609, 447026937, 710790226, 508205804, 48219345, 416252909, 86392509, 716339862, 756795048, 505420821, 236642549, 995130094, 788372590, 848470982, 155348778, 173049609, 227723827, 369943676, 998327363, 335222965, 425469664, 24187927, 170760157, 237731854, 430619698, 411550512, 893537295, 910757465, 681811097, 470583597, 818796598, 476676857, 746650750, 127962665, 522733085, 918392927, 13223697, 758943091, 455007899, 894064171, 912629115, 890326090, 996444450, 898065198, 954452038, 552119164, 385538891, 848896559, 32204645, 890934203, 296621719, 62051334, 47849556, 13015273, 534085731, 205784668, 974425181, 555846393, 214321694, 542609013, 226020090, 846463591, 456964047, 142821187, 34046320, 299032502, 480915508, 319772286, 136017242, 599913936, 244246766, 218023623, 342554719, 619573177, 50629433, 159422855, 572606792, 834864001, 320282295, 330425044, 558271653, 143389245, 490790982, 657175307, 42340789, 595111260, 884326903, 431961111, 19759239, 865119527, 953111854, 281197412, 913505433, 613022313, 781473028, 194357795, 420554249, 965268528, 773229342, 875777265, 239362664, 647479736, 853245748, 483733026, 792139242, 478893574, 376956541, 897449982, 679457144, 391272527, 226697435, 376121763, 930214275, 649082365, 214172003, 467730412, 79398863, 419092837, 320159444, 754810913, 990581983, 223885586, 981201128, 785047301, 355565713, 224031241, 93532366, 326458394, 934506470, 780303719, 511083359, 149810365, 42393183, 876086208, 162417542, 540595415, 843269405, 915218166, 672115267, 160731759, 26967764, 386991125, 206582928, 619033238, 540316174, 16747135, 13623373, 217702516, 578956351, 756885180, 389131199, 989434552, 522600153, 355999307, 862294008, 153260306, 631497478, 742815811, 173541087, 964339680, 328517325, 853151521, 117215556, 885421427, 613077597, 861471447, 658422941, 952888205, 465017217, 13031238, 315831081, 478998302, 39591923, 447701607, 456992155, 978772828, 71245935, 950109473, 28351825, 414825364, 794172799, 942923654, 893858705, 544520126, 563836610, 207479418, 647470605, 583463263, 176252467, 829362319, 885646465, 813037643, 183652643, 486138089, 451921474, 697077284, 469176264, 818516753, 304406351, 853601723, 40334749, 664544155, 867547880, 534947431, 51740331, 558401418, 998681903, 596195423, 914418182, 181265358, 758250826, 830947286, 390870438, 814947039, 449572495, 699426888, 955648142, 125380365, 235355681, 330469903, 121480563, 614567717, 150373441, 305037767, 483915721, 851111036, 721810470, 84768170, 918229376, 477735260, 56193570, 444594157, 179198006, 220499731, 729670555, 446814377, 15496699, 160571597, 847091443, 621686844, 926166898, 636903850, 342341192, 869890839, 844722621, 372371039, 780779393, 323801186, 693675185, 790740153, 424742899, 667322117, 954324, 680136069, 851334410, 864192615, 261419536, 92597505, 779537253, 77040446, 192986738, 329720605, 47874727, 846786014, 205909535, 78777682, 190891366, 126650896, 675568969, 222281421, 115428089, 70094546, 81812805, 134758506, 33522266, 830067143, 617381609, 531428042, 456666876, 475950794, 482613776, 574805824, 592719726, 41538801, 50814492, 967950162, 968365358, 666119903, 892559617, 770033452, 979365960, 101316864, 877457777, 421711513, 789826045, 42828020, 251263919, 598206500, 71518387, 86193294, 414984397, 803031, 430365452, 682172307, 881851972, 312385470, 786866851, 239179832, 131354236, 277928169, 555173781, 699663109, 760178674, 789865948, 415597716, 822220954, 293950139, 768079498, 591922973, 383991762, 191165733, 542203387, 781478175, 895378810, 739645640, 863094922, 678684222, 735934099, 783070175, 892556750, 806052217, 345480190, 17260939, 140698505, 367349427, 707570644, 854903429, 205443267, 3800546, 683833089, 755039609, 581986694, 697016415, 117333626, 140952062, 906753170, 839656234, 628716135, 820528426, 625897942, 958616928, 563491627, 525091167, 331485149, 767914534, 728237044, 501787216, 179007234, 953897356, 848175321, 315972744, 698383331, 409235940, 467617229, 486880384, 488372836, 107519838, 820259743, 980991655, 921858541, 3355930, 256453518, 331282408, 663235232, 447734667, 257288078, 814525306, 608728185, 257439617, 213167057, 722827567, 914304286, 51870360, 611559863, 757387463, 198469085, 286372171, 669597175, 51808749, 553557117, 268378746, 353264257, 544455330, 463031182, 222897279, 420459894, 331588766, 713367050, 211377521, 524354690, 150339011, 484705649, 520126105, 87700232, 553770513, 98339831, 226786543, 611737015, 765737867, 659307432, 496054385, 614272064, 737079603, 41997072, 578138159, 554254859, 700070286, 944841125, 480484611, 508862640, 411480599, 894449870, 499518892, 592894032, 475310646, 485441524, 222277166, 481847176, 182363071, 718213929, 282050970, 460475408, 76896508, 685903685, 294396921, 288195784, 168869636, 896537932, 443927812, 595563800, 729077505, 545159501, 89447973, 273004471, 82223820, 466191495, 756254584, 106114025, 165009169, 816216704, 396879782, 518323930, 752647759, 430964911, 861306877, 717733267, 260979827, 887208241, 965418211, 273341289, 91940406, 880142021, 580326054, 399105772, 856717173, 78476775, 639096339, 253847213, 564547787, 606482627, 554978998, 806927270, 78012564, 628192802, 995050154, 352740278, 232910319, 450039834, 258833797, 238812131, 756676114, 120896019, 375091824, 227569594, 435715958, 73305994, 178417433, 711577306, 256768938, 45881077, 896445924, 757014885, 189917480, 173517422, 534836580, 722143138, 213932602, 917377514, 452988714, 425066907, 54925471, 610107482, 160620157, 309769992, 6007174, 901850002, 522539751, 898584768, 109668331, 962717265, 59749884, 895278769, 392214872, 166943758, 904147121, 40831663, 177414658, 711621384, 334197402, 195284460, 901593138, 58146163, 28391912, 699682805, 821709029, 635421360, 927795092, 280475275, 712837568, 244542667, 183048282, 666072032, 335751366, 793109545, 120895967, 192036212, 264664952, 134555234, 51274419, 961102349, 710247695, 602828549, 259112858, 286949172, 888529162, 852840545, 627008798, 45485364, 770582573, 292000940, 32377715, 233041037, 833396416, 437765362, 105158076, 657687372, 882221006, 474552806, 938445095, 926459550, 935541830, 14063994, 235852777, 354180162, 511941292, 8264341, 902337101, 782643553, 422878674, 343665052, 36881942, 423170827, 887659796, 43377451, 495102736, 911365290, 586302321, 504815255, 716812933, 638230789, 216247245, 562246178, 124100932, 84536200, 16090442, 192651060, 526228843, 898966274, 912511610, 225554667, 92784977, 104448762, 500391502, 689105849, 811367599, 525027401, 334788993, 431694710, 578379324, 743068473, 960327678, 399343350, 269582615, 695819457, 456156857, 808565249, 381304486, 999491855, 913822013, 618751148, 355199682, 804012223, 446439148, 427999808, 557519523, 732673464, 31002668, 377494499, 803143870, 752274943, 835553376, 133796857, 501490563, 367788472, 549626383, 698292526, 616671020, 57331371, 866522775, 252688664, 73079821, 598010598, 935039559, 973635626, 167334978, 205390148, 416893582, 381448901, 909477861, 514781976, 926213018, 793030261, 471849287, 829274734, 6830426, 670718671, 369155178, 519021448, 15181537, 968602958, 520593986, 791350973, 653767936, 389458775, 896075347, 949701433, 408501057, 188688550, 208391063, 998943231, 370363469, 654088759, 186473784, 731593873, 957150765, 62249602, 205478239, 643762449, 287400187, 75225367, 694661878, 769926121, 7931011, 496161682, 536275344, 766515420, 985302108, 925308582, 297991551, 986945914, 580689860, 764330714, 805441069, 485877674, 170393735, 524319680, 906018676, 318661376, 946838366, 752224903, 989435563, 289371532, 398898489, 870838356, 87599701, 163844294, 758756318, 771892077, 39184761, 930507079, 836250308, 781412781, 414155517, 879479718, 52963062, 188592211, 841390817, 261433561, 612250197, 449607289, 378593611, 503704137, 714773805, 856742951, 38076769, 549568523, 24433136, 549513333, 841764937, 657960238, 135708313, 60137125, 450270140, 788012071, 560930972, 787004400, 880670414, 811020794, 274819659, 235177316, 257557555, 710160367, 386607253, 372805402, 497050060, 59798280, 808019769, 617749308, 829203192, 959210582, 776701271, 551561858, 183914007, 79861006, 716134964, 299728215, 949515576, 736442578, 567955620, 355718206, 324276721, 509862630, 414907090, 667693536, 750492336, 605139641, 930738673, 225066005, 832061703, 68670658, 483072647, 274656799, 110861781, 483483931, 423520352, 525306175, 3617466, 323515564, 14898873, 901815199, 965461156, 790216007, 301406644, 293138495, 759445817, 842555899, 256301951, 135629952, 540861235, 9901891, 638382103, 31319034, 456244327, 814282659, 649904568, 174248138, 445330339, 6606823, 424421073, 943529020, 986785176, 880094610, 266075594, 8685663, 38632818, 963156620, 112390969, 196520930, 705024554, 137654076, 122707870, 815128681, 950241017, 23617798, 801366869, 187019213, 924339888, 106562069, 301364014, 691695039, 292145803, 467870822, 550842201, 646532946, 560186847, 888514575, 215736251, 227563114, 747639433, 592782235, 610882913, 632598727, 283225389, 86351023, 437344032, 558977185, 935972160, 283235629, 793173456, 605138365, 878880702, 537664145, 770341481, 47733832, 682513920, 949021620, 66191829, 214713533, 893991132, 978241244, 701798995, 83987517, 961280541, 868186841, 177920193, 555929191, 779330927, 450062780, 232686049, 596959742, 79208002, 14757535, 462751744, 960906784, 438755040, 240781538, 655699225, 176469005, 941665601, 222757718, 587695592, 430393768, 62848155, 215192495, 174214894, 207129154, 495795751, 432116904, 842949006, 360701245, 130637653, 300484745, 382951966, 800862996, 252452096, 146433287, 163414401, 326210832, 545509255, 716446486, 645468215, 57889849, 444784573, 361621120, 684974344, 945413745, 177031223, 776695156, 924972214, 409158561, 24596275, 684862967, 895156343, 362401327, 706524705, 548806544, 427263869, 458834863, 871612741, 583683405, 177495027, 945029074, 94913250, 51895268, 607216377, 959821807, 985765135, 382848887, 522980366, 655355040, 771717856, 627965810, 256700099, 16537888, 530374178, 470735867, 623020084, 53902856, 568950030, 398878341, 283682962, 891149041, 836479770, 390664394, 714133670, 487606900, 172226739, 349215055, 875165812, 512439406, 608784943, 970522459, 554892661, 45166492, 314307751, 439942392, 423791580, 940666800, 126516949, 888694196, 741991969, 466762370, 393584109, 225734211, 81527881, 884951817, 979328692, 676159225, 786518724, 260352957, 476180116, 575444356, 514335255, 959222258, 312011651, 847670416, 422024528, 711175261, 411112581, 159915105, 580916138, 744781020, 630226595, 139402129, 122828063, 798060094, 90781603, 991260760, 408082714, 619716260, 626513240, 374912004, 639943932, 610164857, 864491768, 477734490, 227029163, 131114935, 691150575, 535142511, 992121613, 609293729, 201673921, 524436968, 907309183, 268353439, 177228182, 21794512, 190731973, 810894784, 992769272, 739036579, 389534337, 967511704, 763372910, 935012352, 64128538, 48190377, 867018058, 996380042, 420780598, 929753161, 68986622, 845206981, 394444638, 211765547, 79131930, 932777596, 478675414, 759426025, 884733619, 747276503, 426912120, 516069620, 78830699, 646480874, 24672688, 184643608, 481124433, 269694463, 32077626, 907644484, 390252575, 262091312, 73937905, 46525203, 95454906, 535705793, 662143412, 881377268, 982662398, 675891294, 710102324, 421115228, 337611961, 666348812, 658782370, 989757007, 661061898, 963598978, 992380849, 483437648, 499147303, 513117342, 264064067, 100528606, 12222382, 132403761, 439280442, 742802954, 61777822, 622855461, 372584426, 147727116, 45830519, 980801443, 526910810, 674897126, 855862864, 202744168, 10493031, 117682876, 686249241, 7079169, 853496237, 912038580, 447630545, 103524112, 692267867, 152968562, 543830855, 181050977, 211757142, 774311994, 113817448, 315902384, 940443387, 783835584, 645350335, 125547747, 747052773, 142993010, 673033657, 844437958, 787409594, 48378546, 910808092, 630134744, 113218300, 667710251, 996509871, 198532695, 445856547, 875973782, 42306348, 791012231, 404889352, 356668561, 49851057, 592958454, 676537236, 178756817, 312622085, 829348988, 603168866, 654877090, 18425729, 826747737, 754265353, 951185364, 706318471, 102788002, 343502696, 398938350, 413394823, 750310469, 45343657, 401449639, 618729621, 62351445, 844313505, 395397964, 963648077, 651995323, 838212355, 850847780, 999071869, 871989294, 572992765, 261470632, 632797985, 716621396, 744901322, 535930132, 201620911, 101951774, 702903213, 522918587, 702823119, 973911205, 634509294, 798231993, 133293751, 809566081, 157704814, 544498301, 333373231, 92723622, 779596356, 937707353, 880866598, 233728921, 562694570, 810057287, 113083873, 164088099, 143264421, 339290781, 589770107, 861136339, 758030776, 409520632, 871102261, 247847069, 573305941, 321883511, 315100525, 876785258, 740717397, 62002586, 178261364, 361744169, 167072334, 108847058, 358148752, 270768595, 808184931, 938512609, 843759802, 449236291, 919289971, 795370337, 417679458, 197715162, 138241360, 101933235, 984052744, 719363270, 792909809, 165780290, 886077458, 486436465, 876546243, 924956403, 394761858, 851249682, 807090575, 973521072, 11174078, 328566182, 403828733, 432932288, 431710249, 884496443, 546693001, 542358792, 224275405, 588680978, 90464244, 85287478, 71991940, 80222350, 561055237, 506543667, 375246969, 101343817, 183578744, 621734530, 288335469, 716668481, 38057259, 129784541, 951631837, 997143879, 959061123, 796051847, 349673827, 519850893, 487255013, 812018827, 250027359, 748273919, 145868348, 311430422, 37965045, 319918407, 183170340, 646916464, 459226382, 656807501, 915620393, 225465700, 630787960, 440004231, 786806684, 705030301, 197806032, 70788076, 457579912, 799280078, 330846114, 638035010, 924660472, 541776518, 257961657, 750123548, 129833402, 469180741, 750339922, 758653678, 257063404, 558443537, 496983318, 767625441, 432991580, 474236944, 150240799, 198718103, 197817385, 849529177, 397143458, 16882738, 197880370, 823543591, 89403997, 953685112, 601388905, 601182098, 659537392, 535396075, 751685999, 335583693, 197315686, 472399654, 571059657, 206323517, 206374223, 24002176, 753774507, 443822538, 882418544, 258135869, 328173194, 571707488, 685650102, 251646705, 652822036, 576206939, 661922189, 904725256, 292043343, 204291128, 976670096, 842340157, 291200222, 425677498, 517660168, 165986789, 587451396, 245600941, 635857758, 752784930, 744893399, 351273336, 296056002, 904292182, 462569412, 987074589, 73683088, 767818219, 893690658, 606969296, 503490423, 842389148, 426933629, 67110827, 85649744, 199203408, 304017697, 10237790, 976233517, 42315581, 776902407, 770922679, 173572947, 585320719, 72444716, 505389556, 488264740, 926372382, 407754262, 388065142, 157527537, 558833258, 212612289, 691424655, 9685933, 52158997, 633535740, 938767558, 667478627, 184645243, 879040778, 630151381, 928552979, 932056479, 420309219, 859747306, 318244352, 186259527, 296881442, 851718548, 647936877, 193348484, 459219850, 228153444, 966312639, 497165300, 896644231, 311823762, 963546765, 143186218, 992846370, 378428503, 421881945, 174172642, 628890499, 793055267, 312849373, 708865812, 391435264, 917729439, 749970452, 481945070, 591073126, 775686251, 418763299, 765436259, 136951135, 547038812, 746455081, 542311913, 520571978, 269289429, 859118737, 140981392, 869786499, 191918239, 255591316, 706147053, 482824952, 124422990, 783745646, 875740214, 953379459, 340585243, 220658798, 102646316, 436587005, 247681674, 48484193, 949686010, 131497075, 332111544, 185253036, 339425941, 728434345, 571827032, 664209333, 884529072, 812848625, 413866365, 586092408, 724535855, 695053701, 32947595, 427492187, 726639656, 239195781, 382674583, 397170187, 317037048, 285394649, 28582444, 154393927, 845943157, 667189694, 505186376, 152001205, 69890279, 700534095, 464122047, 132970103, 464467796, 200686423, 356022417, 687608388, 732185599, 192113935, 640469456, 46307778, 71434413, 456508991, 476217272, 262199818, 258100938, 24606521, 552281656, 667779321, 504120700, 608468467, 197773949, 535176362, 479608772, 882267847, 31488415, 543141118, 173019967, 364683757, 570823918, 225113597, 353992855, 803060273, 963166573, 703190115, 499484075, 268366685, 359268854, 753396714, 52876584, 927348410, 548917903, 392543513, 934116997, 370072870, 870300660, 422155840, 683695309, 424388172, 178019500, 289206458, 76455177, 953413903, 151115141, 348706154, 637376528, 475236070, 515932608, 218807011, 479339192, 253955050, 105195330, 603154913, 183713770, 588944977, 731527770, 670286984, 923559625, 77492802, 785020458, 509231478, 120485872, 182401120, 272232947, 871378281, 217005366, 542808669, 427741951, 360401189, 874219007, 241901547, 23859185, 310819405, 61331253, 656177843, 682584499, 142682598, 895534961, 843970673, 212037472, 693555255, 509046092, 839250486, 654124990, 630406427, 870528465, 806739311, 738511194, 477092368, 647782711, 621360480, 604768237, 274910334, 552344723, 5072231, 499865159, 984109026, 444172667, 676206831, 604301647, 527350123, 430214573, 610482340, 220636515, 550505443, 618958227, 713192165, 510024904, 344994657, 194098951, 700401204, 630887290, 914590490, 591741284, 952721192, 238813291, 314387534, 254911996, 79214472, 650204897, 847889864, 547806038, 456115762, 223821335, 202406119, 560949839, 803053119, 95571707, 399911447, 43842239, 565317566, 622096491, 695089438, 815601030, 595672301, 392268544, 716146722, 470803653, 883834020, 970847560, 701765548, 286157300, 62924619, 748525139, 103577624, 943337595, 73155459, 760843757, 513708679, 705977475, 366623856, 579043914, 200616919, 784209559, 429366696, 320469284, 192143620, 311619636, 799020161, 220053335, 196995147, 717079613, 427586579, 388575636, 208859669, 415268595, 590869920, 328211133, 29818295, 379537630, 427982953, 721932372, 451089583, 944258357, 449670675, 8802472, 462535856, 374221990, 544518804, 614939751, 664155080, 220791023, 646747963, 141730058, 600567676, 548746593, 42006939, 506928919, 388337441, 805528704, 433753194, 394583450, 26629244, 587712934, 563865967, 649227328, 563795660, 286992375, 550530692, 28451011, 901274004, 539503532, 849292216, 808264190, 138679221, 66181290, 671917361, 486995805, 752205886, 392618571, 692021192, 837119478, 860851165, 378477125, 938792542, 862795395, 801355905, 499947997, 224446091, 66286805, 756665739, 126387897, 212884619, 595415220, 576785178, 781865583, 149149915, 496972965, 457513292, 153414755, 858918106, 771554527, 419538573, 308555511, 641992757, 229520170, 619989260, 801167848, 923537064, 62456999, 805429262, 166156920, 2996241, 238660490, 402147108, 817778157, 754301442, 527076474, 830831377, 734932704, 423902497, 896820147, 99592025, 198462893, 846713152, 812178420, 139241356, 604331222, 338794956, 994147529, 617404366, 884982071, 105606778, 318049457, 674176627, 402907225, 472915616, 666916973, 115696169, 121522052, 346201588, 265420476, 241426472, 413971409, 375509601, 734351173, 698251107, 168990865, 530779350, 987373229, 846153091, 181246339, 435735688, 811139917, 954497675, 533565947, 306560157, 883675041, 403591046, 594079703, 447723377, 160233497, 699890327, 481446190, 340177737, 90051617, 104042955, 903427388, 399734068, 950080702, 397002681, 482815551, 735449742, 442518669, 804685851, 222025961, 176726922, 756802312, 53240321, 996490375, 278888697, 461820122, 941150509, 535695007, 184199036, 119026832, 617381930, 195032511, 629269426, 153911428, 810652848, 669186940, 449059710, 565078906, 63503115, 607333641, 65519100, 62520163, 891814964, 685913413, 690853830, 843473121, 227903954, 72685350, 861825444, 614094701, 279767975, 843394998, 649833079, 228462507, 121017706, 119912336, 235917690, 618164566, 67439665, 282252586, 258698732, 802348389, 33030743, 451131762, 257667573, 796526681, 82324688, 821493618, 910025481, 274484513, 783760658, 821157014, 879946706, 427556643, 306153549, 47759392, 129436233, 615242295, 388269609, 510647271, 415237161, 339943817, 714607725, 5403790, 473921077, 334491268, 889077548, 344974702, 659147233, 858948144, 220988141, 249775464, 777565725, 337626174, 574899167, 276312473, 93806878, 91766178, 888726234, 429774383, 884927249, 958938121, 841309991, 139074064, 761865438, 320014750, 289049382, 667619706, 49926729, 375921454, 673654388, 826913537, 559433004, 806631585, 207537306, 941870265, 668193961, 113905888, 511181923, 365504016, 29332193, 179733032, 689968524, 33818359, 732032382, 366769639, 440841737, 590597302, 711029776, 641907359, 400842032, 119609123, 877410219, 366472486, 830246618, 126457080, 102061641, 938917340, 577298030, 990630671, 235857330, 607068700, 523329816, 773185738, 912346756, 852868708, 626880520, 258242438, 339641582, 677501985, 616492245, 975155276, 750076618, 507379511, 727882452, 634604422, 160799383, 553760785, 187170102, 153389875, 172765314, 242365684, 103080367, 960917262, 725618540, 136782716, 306935868, 332251414, 302827560, 4534558, 599731380, 512070813, 498370165, 628168342, 780047487, 857655236, 932633002, 236247944, 375334199, 156553997, 427961739, 948384369, 690781519, 876343048, 740570290, 261355178, 279373818, 726386489, 150264219, 103475017, 605507994, 725013850, 160330044, 990045725, 285002667, 885231440, 273234191, 41226453, 798600253, 176854507, 829642569, 113344172, 828579146, 129645139, 935947574, 389423159, 613816075, 725641575, 646889249, 356863614, 379165206, 964162487, 772991295, 102696809, 83348596, 241606638, 210388072, 829761545, 436132480, 216201543, 388347211, 297034652, 386171361, 70350523, 777688829, 607571964, 693073127, 85965889, 999706772, 175782562, 359112370, 229532332, 735872523, 784025234, 967205006, 844390165, 426559001, 671283170, 12556703, 971898846, 261302708, 662132944, 465308733, 970721821, 880284676, 177954132, 955699292, 397936773, 692351474, 844663115, 662969474, 485324703, 708373230, 152037471, 417568351, 311562436, 418736167, 646330711, 624931158, 174508782, 751386573, 992294204, 32952294, 476510762, 631071515, 301909226, 162293674, 447679893, 89187280, 286486730, 743712692, 492707928, 673605204, 631966861, 531999259, 229362730, 129274509, 967869309, 109336746, 426951290, 308759016, 918220516, 886049562, 642630626, 606432014, 981716920, 475748692, 812953939, 440652169, 846148060, 479598670, 137167102, 862420932, 228343608, 905810535, 33945182, 29445612, 988773226, 124888137, 944000876, 908020561, 475646924, 919103029, 153527250, 712325776, 514620425, 56512204, 169752547, 515000856, 337176629, 917358580, 782430354, 506382267, 985688172, 266225068, 135274447, 474138818, 318635774, 527702092, 753878886, 497118316, 790981254, 856316321, 715127204, 243401468, 439797950, 774130813, 58807987, 445075727, 253345427, 962833228, 788947732, 859866028, 659618817, 973963885, 941852995, 253924284, 111356119, 506584661, 133781686, 977883746, 609409996, 217337620, 15851274, 838212745, 935170426, 539815132, 571883823, 48322423, 231490064, 402695197, 336135665, 365023505, 893483072, 320104217, 35182744, 37458171, 65053925, 218779454, 607804935, 93952143, 219582073, 873502930, 784989166, 328744560, 6205386, 668962822, 870244124, 908379624, 424809034, 706968776, 711820257, 954809493, 637057553, 879389526, 467574501, 843444928, 575788170, 698363325, 538204942, 938436212, 11976087, 907584229, 905416357, 526113975, 341147043, 469172221, 195494350, 922522072, 515773557, 930190105, 934808202, 927113914, 772530198, 465422090, 279076776, 665643551, 384601289, 434862352, 357607828, 793915336, 574493776, 922723623, 198214099, 246041536, 710748361, 79015603, 49485032, 825069684, 504870388, 567309366, 687355213, 914537538, 142564239, 44249321, 718758238, 892605190, 478721229, 434772407, 379838174, 302902597, 913462671, 433537235, 792380351, 371467913, 857463587, 847013545, 730519600, 409906301, 694948870, 456102678, 370654650, 682494653, 789667529, 837137505, 47739666, 552751410, 569634310, 560626162, 149605477, 973234220, 147296732, 459483329, 735640021, 288530144, 752954645, 364664456, 880109840, 658787517, 159947055, 841126934, 795135335, 24939459, 374747370, 53132679, 919320475, 145105089, 730188285, 281851290, 133658085, 158239624, 395277620, 304814744, 753250845, 184935586, 153256123, 724572479, 290022686, 23078244, 946851486, 469742398, 499880909, 981339354, 327805000, 652554592, 356193727, 859016057, 61840734, 768407729, 561904805, 788865026, 226989488, 388635589, 353446729, 78290734, 73959268, 827087172, 679400782, 697421671, 206161038, 530950509, 111878419, 780343086, 9401845, 876798512, 298197704, 751574568, 312827502, 605792728, 728544474, 452972411, 735067677, 27809658, 908703755, 957416164, 456250770, 870056156, 221394430, 169537189, 138164745, 382800667, 98731449, 863423187, 331122026, 911360499, 378888971, 112087501, 931297153, 73858829, 591682848, 936703850, 571153770, 307632926, 866931411, 675253548, 785654430, 105570264, 601897938, 295342893, 277254187, 253861857, 825936179, 955263670, 863444231, 12571252, 517584217, 922762502, 171163720, 519208521, 934298448, 392893482, 859792948, 791314479, 2324107, 425485280, 573027761, 793180981, 699339825, 197704285, 114064034, 882761520, 525188987, 352258399, 158591921, 228223744, 577727842, 497444636, 799917260, 441665280, 384163823, 616538328, 714985455, 606302457, 257523249, 207376543, 728981296, 866240522, 985477881, 429098309, 350421686, 24010149, 723930411, 320259348, 406539069, 472932965, 382231923, 116812682, 284521223, 291869729, 134697644, 276439368, 898610094, 194470465, 522279580, 388612777, 833342687, 461123050, 713766610, 356357286, 666853884, 146054534, 690711667, 726069790, 163566060, 359279748, 521333801, 987127921, 163516327, 816443479, 611069314, 835224770, 202559099, 13802093, 845225036, 761416117, 519420361, 768359526, 456400279, 871116785, 701482091, 61038050, 440033230, 644995589, 152672101, 527104927, 453373572, 868641804, 159175001, 478346239, 928308397, 726577447, 595954195, 488684548, 499735113, 257036062, 696849821, 841399275, 796094269, 371078262, 200339798, 39035855, 991218947, 286915617, 270073602, 265738012, 944318782, 593490283, 27962583, 138443278, 447633219, 571308086, 983897444, 947307235, 185124736, 694727686, 808734406, 764577151, 171514099, 297681165, 601010684, 374185819, 243756247, 532895680, 628338818, 288692972, 335581945, 547315962, 427685919, 733713837, 79372441, 747567966, 537249669, 819332669, 463162192, 85348741, 133032751, 973678012, 152544867, 896016500, 893948763, 933343979, 725291732, 516201750, 323711994, 4955764, 715569801, 742067799, 905556224, 45075824, 282584140, 65258721, 10821258, 441093980, 92338026, 611171698, 684934465, 471407231, 656313587, 990167632, 748876024, 353382160, 440277781, 964869659, 384660957, 261846480, 763852824, 271197915, 300104924, 644736159, 506999404, 292838219, 961780596, 654345329, 704309011, 520850047, 661086541, 892443638, 515797075, 621833933, 588550793, 54434134, 235229589, 20452239, 843698190, 382595353, 68803072, 302331110, 482059101, 856602208, 912449090, 782836868, 717915070, 876163, 546737205, 969161625, 941089739, 978052532, 788410283, 21637417, 238832062, 799665806, 789692577, 261882831, 808041826, 595679052, 783778842, 452690765, 302590529, 772683109, 272994777, 324617638, 584442710, 178322849, 916503917, 436462436, 880331045, 222286886, 854165314, 902841519, 542848999, 712588454, 687723278, 542254198, 411562833, 241493298, 954062139, 608770946, 506542822, 645763541, 729455441, 627476190, 385977377, 985329603, 128767485, 190689089, 343800938, 963013049, 398551470, 526633738, 993384415, 641341434, 757778102, 25424711, 263562699, 109914044, 547734031, 312181506, 632714500, 244077900, 224954441, 549086300, 42803437, 276505836, 919073149, 427077491, 637392197, 623330204, 82491643, 568625578, 215993018, 93161856, 163660074, 178832488, 124087955, 642078082, 997408906, 384000579, 631662498, 333599272, 23186278, 9146450, 510692715, 568326071, 610055998, 776362615, 438844177, 914729695, 5579212, 155140044, 674993697, 296196648, 162296212, 135585782, 771136084, 905039604, 27250355, 10902330, 57501528, 689240616, 580448567, 183798520, 584155994, 763830496, 918063969, 415436914, 860123327, 4037531, 438019975, 620710857, 517393953, 935310691, 936350458, 652933810, 108166201, 254717021, 838766651, 578110211, 297122264, 161513933, 142068016, 813118274, 175328604, 236880202, 177838176, 838473253, 867641450, 434988297, 178194957, 711345205, 849864501, 376796250, 334502636, 65760746, 192154802, 364665139, 18281603, 440637375, 522543044, 28333790, 119203428, 694252338, 941092310, 598319854, 10745261, 281789358, 603329421, 261353889, 385147876, 660182898, 532904332, 708844732, 331937461, 734907547, 155614260, 26965500, 81416529, 702286142, 53097958, 434314221, 309996497, 403730290, 33611546, 262870855, 739870499, 578971574, 379966093, 929443081, 999303963, 602668536, 787234850, 75306367, 936064135, 977197769, 688496845, 195256983, 477542351, 417079871, 377274369, 577742029, 177404513, 980327634, 583677071, 517056576, 640631518, 708879489, 805535680, 62894695, 595664511, 332571737, 812388404, 779658741, 942064486, 335893628, 167197329, 358479894, 491007543, 612890661, 779679952, 689904636, 253336999, 278620343, 371248251, 789888057, 149049342, 912304668, 631848248, 751602437, 273356057, 563164676, 711330911, 968382210, 201161873, 823282905, 877999884, 355340529, 272037407, 705670101, 753401301, 619249959, 169713387, 354500180, 502261125, 828818069, 127957696, 356290682, 598682980, 289808365, 86836967, 737227251, 489364928, 402516509, 482667885, 27247025, 299364406, 232686476, 353990562, 560169800, 661198913, 485710145, 343717403, 746713295, 908408637, 576013552, 246980795, 558385699, 96650865, 470613989, 848850021, 529660384, 652740924, 882066171, 227805158, 784099461, 725325670, 579542137, 663899280, 19989021, 516443020, 533274478, 679360672, 612206249, 938321270, 779779223, 202830049, 890713030, 466780607, 59045285, 174181504, 417579350, 306813352, 332892802, 996020366, 997409112, 97136920, 919173956, 107404537, 244154386, 878150105, 279007526, 236061846, 906587212, 789798941, 642466144, 149849458, 643110359, 79453605, 32484311, 840717495, 171946073, 913153448, 615861679, 541677868, 955147237, 695453787, 247788629, 654621383, 684095846, 666908694, 863771718, 730329282, 396811286, 732726019, 724198053, 929353732, 850798639, 582666304, 998456410, 841578171, 695631877, 520195833, 490898042, 472610759, 808377280, 375998947, 884012641, 99754886, 451617520, 118229153, 145697836, 397620199, 351293222, 383430910, 848033608, 42648166, 105573834, 986671983, 447479418, 501872849, 545090887, 744467435, 616184657, 558987255, 882315864, 319858016, 705622429, 541828974, 175441691, 424211646, 517736727, 301637700, 103063174, 847424044, 273788175, 905504751, 545919758, 578212973, 549941108, 826902534, 797082592, 99461489, 855480423, 878817983, 306095917, 819900440, 584827789, 724406483, 202536633, 868182991, 299426620, 479363599, 267451955, 513026284, 732436566, 41702584, 397384173, 794933583, 746860671, 772837952, 258059398, 500306772, 972570470, 629604993, 578820131, 849870064, 281734709, 634880960, 807145677, 667604919, 79466003, 188577198, 888052060, 349561531, 382827997, 196624888, 535816530, 638357181, 554926955, 106556471, 222277358, 747327164, 405325440, 22201634, 421677514, 391400292, 619558344, 330555734, 577023864, 64194471, 703650259, 677716371, 131765253, 281669338, 124867831, 414344706, 369038508, 603210693, 165471764, 357685849, 991888913, 511522954, 382258712, 643530117, 27113254, 640665893, 295801566, 382467765, 766234858, 530400395, 165709546, 89532349, 564924291, 6244531, 790752453, 883923231, 496870526, 316651458, 612924929, 788248302, 966351751, 323400513, 911478210, 569092655, 943879308, 422203714, 965523746, 562984424, 64022586, 806190705, 167496758, 641805918, 191764120, 295850998, 375417589, 809207166, 975411321, 375831846, 158385880, 987281039, 550957028, 593983760, 805398028, 39828354, 132308789, 818953620, 246552239, 365293586, 304977690, 844723195, 24991068, 123169971, 512153742, 469442084, 625537010, 243830985, 579082318, 353164745, 305293231, 627043652, 730121496, 442351250, 52870137, 238325162, 762372626, 598122954, 314344798, 159357364, 610825037, 455649989, 199640835, 580817601, 613661415, 754476177, 936752510, 109748067, 653115716, 712255458, 401863929, 640516390, 664852079, 401302699, 254879859, 315908518, 279849270, 112849837, 953629181, 995921890, 220350355, 549745687, 427174515, 907809848, 20919751, 111232368, 276049483, 481628247, 357664604, 586618352, 232879139, 237347783, 567933790, 213482734, 555080147, 473242178, 657828545, 370108160, 269452828, 860964504, 510731579, 643413980, 625358220, 574859101, 363078768, 103512628, 816503444, 599387487, 774433068, 767168299, 920746951, 415520927, 340801084, 820009054, 743778893, 288321944, 741104433, 203429562, 690390373, 357767917, 382025003, 832632768, 832466060, 550533818, 794618693, 607152667, 130682746, 944415824, 473084480, 580884539, 153551990, 566800058, 190993674, 480529763, 619221763, 109524653, 723282101, 22936687, 20462711, 595445807, 883342438, 284958572, 401924811, 414775488, 588064839, 557690363, 65322563, 848430476, 172272590, 615519974, 524496378, 768499263, 345888790, 155648476, 202614185, 566449064, 73984069, 21337723, 225372443, 828662486, 82036917, 715953250, 902452421, 99003514, 207539752, 29686005, 586158854, 398755500, 551822239, 246818291, 413785141, 92594693, 94815105, 703404793, 770710501, 108204816, 321819180, 915025673, 549339806, 447557876, 691203951, 298179857, 267334611, 280167880, 442528720, 734913948, 611020569, 200461785, 57147134, 138272981, 192983449, 61724384, 131418270, 721246983, 166256437, 602942736, 789661974, 856055504, 993889285, 32943987, 38870262, 889783590, 675882966, 186126058, 147392348, 267077975, 162847064, 451272139, 347767396, 674363424, 6561597, 487788186, 863080357, 776253077, 320940847, 406959622, 977166986, 962793811, 761803083, 558621740, 390311319, 665108584, 839874035, 395475552, 982250578, 449222169, 245474248, 888772349, 317351668, 712597707, 391040573, 532191613, 542430254, 108020254, 236575508, 352573974, 412429020, 761860104, 765472973, 31680253, 656728313, 728796173, 431308889, 393938417, 481593201, 87613488, 938855903, 968748621, 919118133, 450291598, 666874298, 305595859, 403915275, 414246186, 407731775, 858108781, 87948805, 724866802, 486734095, 439327007, 480352316, 234598758, 538357265, 602781913, 438408161, 649404278, 693105091, 230529754, 233390615, 954418926, 60657938, 99032537, 380244989, 786706427, 276414103, 641838071, 449884631, 173088613, 822506735, 853710559, 428092076, 347803147, 823991279, 765585931, 323141307, 989116973, 543175492, 34269431, 527565142, 362203788, 775863907, 815000041, 752575968, 150027644, 521604403, 664575867, 153380163, 697285986, 453674017, 230576213, 1181919, 380124291, 175003433, 658105446, 839760262, 303754046, 328263577, 208327180, 968613495, 3519562, 129139485, 629147239, 88805630, 157913059, 293098095, 92022106, 760846725, 668078469, 319045230, 6669585, 743015403, 154683625, 674288556, 348453602, 986828487, 961732412, 367219468, 996543718, 103758602, 304513366, 136051729, 186177115, 163413509, 586537839, 225994947, 599064389, 89439754, 793296950, 692184861, 235611153, 266496256, 224762201, 556601693, 482947678, 947915775, 555939991, 157633548, 765118763, 82831052, 865267165, 546073611, 825221959, 303947129, 733751585, 859320546, 310021265, 49036059, 697259756, 889918958, 386530732, 419010310, 405377320, 921083875, 724093996, 664122095, 440211938, 496103772, 160272802, 383005149, 545216551, 656152483, 341765248, 456592703, 803534566, 558626205, 247698093, 139054892, 222491365, 59943983, 310424314, 892943384, 446931163, 216894848, 408033008, 694313587, 60829767, 452291139, 644544335, 123964878, 29123779, 668630747, 702083790, 595684217, 804488833, 195320448, 643271785, 370416330, 56613113, 73544884, 715752792, 318118026, 718162549, 449997356, 636794699, 931221080, 812527150, 339549486, 931155348, 429196402, 213435547, 267552028, 856183034, 675091611, 303823105, 12310835, 500614708, 573374278, 531426335, 386541988, 152968393, 827257032, 216032747, 869439813, 140966325, 243224305, 939310904, 45251479, 785252086, 882372071, 883417183, 381177940, 688392972, 543638110, 132979153, 786585900, 708763701, 550948086, 624516180, 424267958, 305036542, 817893120, 629894705, 152578382, 982451184, 19082850, 604653613, 357978737, 837021256, 694995689, 480638298, 695433963, 96717917, 749491387, 397508095, 790904007, 969217436, 964081954, 276903491, 459828375, 875153999, 465360195, 841117767, 682834924, 80167580, 791010863, 439412786, 53207135, 584557075, 320961177, 199570703, 417365984, 268137477, 955591191, 843585161, 28755312, 364078606, 341342576, 333972191, 330757611, 495371071, 917804256, 813833033, 571319981, 709023241, 903020404, 815931441, 133898134, 481814853, 286964017, 259281113, 15371922, 17655491, 544707247, 625212523, 343134107, 445448816, 202042404, 953365011, 829658741, 487289511, 454231530, 757080686, 803954153, 240051944, 600189350, 631455473, 545993733, 497602211, 723605378, 306687726, 811251489, 48476437, 972922801, 457106779, 710628144, 709155984, 576162853, 344024790, 816376890, 196429546, 650450533, 790567063, 609123122, 140479732, 487008302, 369417524, 410474233, 11813284, 338146957, 203188630, 88102837, 170677347, 775550018, 464573727, 90153625, 541346175, 396924120, 299508089, 527710787, 791032897, 268564730, 42565954, 426977014, 336755137, 403212182, 685513930, 860705604, 850541170, 346493308, 449478059, 110951442, 136671989, 743900574, 344735236, 732703913, 136341356, 260215485, 998541286, 66049556, 76863135, 621931343, 985266622, 310981433, 252356189, 87419649, 412550387, 827098746, 344850697, 496390241, 369977236, 451804701, 800828418, 146286550, 787903606, 425723941, 574942637, 276837778, 342477284, 54756520, 664519710, 976015346, 482419563, 303072745, 550977753, 904426405, 85264193, 612955089, 407665082, 37748982, 61475960, 920998609, 672794839, 968810138, 792910737, 50548557, 301565461, 906655161, 128234837, 223760348, 230026089, 565798302, 754632310, 537260842, 751777667, 506880979, 600136789, 494985158, 677530979, 721576499, 35405317, 882354364, 422438968, 889433442, 347294828, 271092958, 512493351, 775370194, 78737810, 913395194, 897901175, 304137313, 660334285, 445626175, 809645137, 776420503, 736085824, 912571887, 699437957, 171929029, 671923949, 509305513, 378349236, 651277485, 122346307, 49591519, 674514626, 481954838, 666347680, 504895686, 752117684, 278636413, 769505779, 567601552, 680010508, 631200296, 973446048, 883371933, 885899834, 634569103, 176560710, 221166564, 549093171, 153813284, 364504722, 98760078, 665602446, 194151028, 525242702, 92538385, 381755011, 130991245, 778507278, 124865678, 14272788, 297724620, 304489867, 930758239, 481089049, 154931032, 733649495, 388095642, 239453848, 823842734, 10444581, 349741361, 63335399, 721524986, 838739037, 489711692, 253298657, 257176411, 641917782, 161128040, 344875658, 585148129, 670319011, 893520022, 76081745, 395731149, 339944870, 141815783, 358925659, 602137232, 507679952, 717039033, 117698351, 176692785, 605620911, 214618123, 871594292, 29550497, 436923319, 895643206, 967674489, 286252059, 948972642, 78451656, 162734352, 657456496, 381774145, 228053671, 274601057, 677924121, 339345251, 622719822, 945162065, 334975364, 693638534, 901314321, 297672549, 200281431, 723205570, 50355776, 356163487, 839915477, 490168671, 301725111, 562800612, 905966369, 704232448, 132044849, 865196055, 643432579, 702922075, 896763731, 186411651, 189733557, 616494184, 588079910, 835637604, 49607359, 867079690, 399563719, 926730595, 409191642, 62016944, 199166737, 51726493, 437552208, 561678237, 553396151, 326755083, 214644391, 241145677, 859679638, 395101672, 840272035, 5395829, 302547336, 527213488, 402371398, 947772447, 40460387, 631014116, 47273829, 376527015, 205088412, 999591195, 612492796, 96886772, 656900360, 450759419, 64659009, 745138929, 721779261, 186265385, 7844576, 158488755, 635839269, 499216146, 970953970, 180478362, 302603671, 634629607, 736887111, 165986394, 245649947, 160545025, 217631601, 953310807, 8684568, 572232893, 273648126, 989391590, 365358013, 181862891, 376076035, 266483727, 134241586, 123990104, 30983681, 179596556, 903950726, 678607216, 218442403, 704261288, 448391995, 86255317, 342155702, 738094846, 433821052, 187167301, 755669208, 76747788, 175173991, 916407634, 83540991, 490093700, 561315184, 372637720, 571337702, 795213203, 942734536, 658218630, 866202070, 419477828, 815139043, 358815032, 701061429, 344239562, 658886250, 905394596, 256692567, 523754643, 426772438, 820004502, 290500056, 301444506, 887680978, 768335275, 52468787, 697010351, 679253824, 688908625, 440122348, 319889522, 810420547, 113823091, 378128385, 596393259, 520104589, 57322075, 248931053, 284520835, 121037934, 785244534, 694617743, 911694088, 570282400, 474362624, 22709166, 230096113, 524087429, 420452243, 411633800, 334702851, 270203555, 534168447, 938004410, 907880246, 574229832, 553690840, 397582945, 531081371, 142455337, 350359642, 463641365, 70522874, 455850683, 160317199, 160954644, 691602670, 21680611, 745122717, 985110278, 471362921, 180404964, 163499070, 552221301, 544873473, 77047805, 100813730, 729635337, 530399110, 416201065, 91901151, 251742917, 84948823, 70360328, 619934206, 754484773, 125006984, 52456028, 209935159, 532292505, 956160482, 319215667, 773037368, 653017635, 487766112, 327234175, 672767315, 463331495, 888171378, 749618900, 156233392, 10537697, 366419216, 44104553, 69336931, 165236844, 352871762, 46299973, 531477339, 41417364, 775044365, 320600462, 125980965, 395192846, 850377669, 224083642, 348676404, 416603672, 372531946, 112600302, 962920248, 159467673, 834649100, 816132811, 230736193, 805050062, 27564539, 83243956, 194762129, 863932750, 450436943, 526335516, 641386226, 385057115, 236867949, 701593856, 837310229, 913838064, 441748334, 518067402, 369993532, 713134894, 455384439, 506514016, 227561447, 928439499, 747660066, 80936653, 857910292, 536118965, 372855979, 477553629, 158859614, 717036020, 612910221, 177371875, 920614988, 267855119, 904937494, 817679231, 244709354, 168288296, 388272226, 354465469, 448813267, 477006816, 274207732, 704675430, 549310363, 527084485, 989736419, 402272791, 785457031, 663755886, 727428753, 997462612, 428652370, 752489691, 749790283, 668794814, 626392404, 468315365, 477735580, 79469587, 8457964, 183635575, 191476519, 729948415, 87362202, 250262505, 236313093, 31527590, 755414697, 823387100, 409436960, 542845763, 587272099, 608270713, 526772735, 343601689, 155136791, 169618479, 116916779, 426422, 115813795, 609828936, 65047314, 681646366, 679204049, 396017727, 83920520, 639617970, 126699525, 302059639, 236274394, 393520908, 569169869, 402334979, 735408329, 174636318, 365258609, 12134705, 598436276, 254099894, 224887800, 820146868, 911966314, 89176212, 22568506, 44322479, 854077800, 418553421, 200565557, 47887077, 38167258, 993707106, 599260284, 772176880, 875475806, 784372658, 125789906, 926015584, 263241596, 662814547, 927543603, 521655845, 811487023, 221117204, 180427532, 659903398, 354777245, 753162304, 913435497, 113210286, 290747230, 273404460, 380278124, 500177934, 807648982, 436431573, 450626776, 708871174, 987763825, 110751987, 937794440, 878045771, 113722498, 899272204, 808941047, 280746994, 727777315, 112355986, 938779698, 607279688, 647531776, 292546703, 999439469, 747531740, 816751666, 501482229, 269017391, 333044675, 34562390, 478907946, 378881140, 603090272, 423964905, 96756416, 103413711, 463501695, 878746807, 972077031, 878121455, 70097295, 771555163, 778515751, 714265021, 709181122, 68932333, 372787435, 999488673, 815926121, 173613637, 325590456, 529982576, 844716595, 188643255, 729160602, 408965474, 203355813, 808010222, 125687696, 721530689, 803243417, 888503393, 760548223, 569136273, 20328868, 982368399, 682418271, 424299068, 646818202, 699893522, 526681114, 769602723, 486617880, 992631097, 313072497, 931738011, 211135186, 5746355, 334007899, 336459593, 928838298, 506138360, 186941476, 264032572, 436245078, 87901755, 938428222, 425600912, 505894359, 432286816, 899291953, 127275090, 528488766, 749136397, 398685024, 371444122, 691263398, 731718923, 319232361, 151885042, 822189268, 533107845, 570043448, 452688062, 874884006, 671046844, 869349848, 111413012, 953377055, 594145079, 782669788, 987070770, 87658612, 812401213, 612678411, 44813677, 624621652, 473825015, 280525464, 440493655, 359736933, 34254641, 602103293, 963384938, 450477231, 22173927, 731978510, 206379448, 656241647, 518134940, 609599363, 739238590, 123258423, 93171933, 394618864, 186397051, 168046789, 106955776, 810590060, 179640257, 687150097, 392957799, 945213335, 358515734, 543366776, 727244010, 96020968, 357373675, 243813900, 90829957, 490805934, 98604323, 344396328, 648898255, 241392633, 1113720, 905283694, 559844998, 272094024, 734328486, 188910214, 563835739, 337776564, 446607577, 493873526, 227864556, 871081261, 654347423, 446513361, 611383372, 459240535, 160431001, 231124459, 941308378, 67690495, 328193053, 281672013, 22206639, 957646372, 752437488, 617674345, 188070410, 940710351, 639551016, 984915811, 180188020, 313171538, 488180930, 887839533, 882228438, 562540406, 532304800, 526631259, 199396620, 888925226, 74489323, 453351465, 947411300, 788564203, 840687243, 51253137, 944182383, 323664159, 175399870, 125549825, 276196386, 544373155, 705403798, 322167113, 73082, 109252886, 719006514, 541315191, 516518781, 155873634, 443035733, 867524142, 183344163, 718253009, 240127773, 667416016, 950891200, 698492329, 666445631, 653196047, 506845481, 705054333, 465723740, 770146624, 152049796, 940243019, 110322032, 952172457, 987628161, 337310716, 2122874, 672925316, 736991198, 611116165, 745810664, 953394515, 238095528, 671319513, 129742674, 159326003, 293819073, 257185290, 684470299, 313732565, 420077798, 455520364, 483580307, 920787938, 45498430, 720216354, 143934963, 965257030, 854515136, 201754485, 319215167, 882710377, 952067054, 735997232, 51121482, 522966021, 385394847, 842815890, 516638894, 277628157, 785970042, 579547568, 800399524, 360043058, 221773747, 132955765, 164743300, 290596823, 734001533, 39487451, 597318901, 41322123, 32770386, 998173637, 828741308, 233082254, 271609464, 566269358, 290222267, 229714795, 637918410, 697028384, 976809100, 625082790, 185417212, 560443453, 338637098, 848013038, 303892301, 999044609, 335534195, 700741370, 948263319, 558955995, 815310390, 720641834, 720199038, 35192372, 553844147, 571871329, 740106835, 56279522, 155130106, 28355311, 667766615, 302110574, 607531371, 348202759, 28153049, 258040098, 597236980, 892348000, 73127641, 604235512, 36439253, 686069722, 37673850, 776902894, 228897428, 523215026, 435493636, 370958227, 678470443, 534592547, 419300099, 614230853, 145812527, 752910039, 345687844, 33945602, 845994740, 718317511, 395537594, 513277302, 131824308, 181223449, 225660100, 862532956, 779694590, 124676145, 657555548, 514377047, 740287209, 516501672, 341946560, 537495966, 78259785, 371536142, 359274132, 151062832, 768494887, 67443270, 472199249, 148937622, 543409903, 483079474, 722594099, 877237931, 220789635, 644224022, 923337533, 845377124, 287126024, 564135750, 622864905, 86901598, 518806202, 39568124, 835578564, 386263819, 863208844, 479577616, 267345079, 456977289, 373548102, 9349275, 700128232, 64867943, 840363993, 773106100, 486368129, 790973117, 166056743, 712053907, 60617201, 650720066, 80735909, 183486488, 511277826, 186743662, 500557022, 577208194, 272661751, 778560138, 253806232, 102478312, 332953516, 194226963, 366841568, 380456344, 812294104, 765258082, 119968256, 779454367, 28916191, 265876041, 684815589, 66081806, 721340536, 924815994, 155313968, 650221673, 619694263, 159848594, 328300755, 934197039, 792458056, 290622615, 58831436, 717608066, 130188335, 603710009, 731776980, 204451494, 606842610, 280810714, 567802217, 844169825, 597836602, 83004783, 950793744, 876823889, 324563832, 551375853, 779470571, 909969171, 707591803, 898997241, 33452772, 499626838, 8844973, 869890759, 779803414, 648691559, 765973682, 315643128, 221328971, 311823643, 790270835, 176204155, 553094134, 458230773, 481716477, 341419295, 933415311, 828985444, 732945258, 567677708, 877688254, 243113686, 961534503, 601017727, 250577348, 803946132, 620318594, 984107353, 979413122, 261743691, 117567182, 331338037, 977214155, 328372228, 162344702, 455285117, 6860340, 553136275, 896843127, 585823598, 670984387, 821267475, 652726919, 647888977, 633776261, 37160358, 321204169, 720173067, 537167637, 414491555, 141906925, 741113291, 780287347, 954339076, 42364810, 968897074, 345383775, 196296909, 488043309, 880366669, 651576777, 435315435, 975494115, 639521813, 647459257, 412537298, 13505783, 74802694, 514631987, 957529938, 166483659, 171457274, 982516182, 619841584, 961984203, 253058234, 55147038, 967290933, 598653393, 49249287, 714691832, 633659711, 175441846, 668740102, 391531889, 872260053, 143540086, 437242799, 759336832, 835185940, 492424387, 58838124, 34169997, 38650138, 335497990, 686027410, 340082218, 729259404, 85167036, 704677792, 715863273, 5379784, 736539120, 21837290, 500947688, 568680404, 18649062, 353165769, 743281846, 329790609, 803022825, 106323560, 939790055, 855118932, 395247380, 710215084, 671835621, 707495924, 954616224, 145382418, 309782559, 380021233, 570022296, 740358204, 832340771, 579888834, 142792920, 589092762, 689187508, 504758140, 300552837, 133555385, 842785059, 639107222, 837323793, 263810491, 195810803, 821647624, 426378577, 699223550, 689003199, 656249640, 929574682, 87549840, 696460103, 889202159, 775939967, 896540159, 116563655, 216835057, 162099264, 675770938, 77234716, 451158789, 563555059, 639340466, 936996486, 160390920, 198452932, 11038333, 279077222, 366041130, 93308031, 561604254, 813866084, 939061355, 673503323, 169067299, 125707721, 28174435, 399197699, 678389024, 441997489, 419945054, 882171674, 354712320, 152304180, 732244574, 200146818, 218794429, 241978804, 410513720, 228877864, 167640672, 187451390, 399603526, 70020303, 176513943, 367739406, 163114736, 298677807, 609378713, 22487780, 354514935, 547428836, 35613962, 454339127, 494023427, 524108015, 565770256, 15939085, 28990761, 675966, 108936604, 958223018, 851997590, 682696332, 156189253, 281446565, 201939306, 302523879, 368600640, 794114046, 10011188, 245407482, 552736200, 519434087, 320195289, 783119685, 873325425, 247461467, 289913835, 954404293, 745804436, 350678315, 463521194, 576768293, 577275038, 969797140, 385197568, 4453837, 337394214, 764253889, 495945328, 362826645, 908362492, 710787106, 654436238, 12228836, 950450515, 656446180, 122144614, 667684938, 968354333, 680755237, 509080470, 196181123, 276902870, 594732571, 984547746, 453341453, 962600924, 718494878, 109028389, 843373674, 709694653, 364692641, 336546855, 342293435, 581272676, 781212038, 77385414, 844730252, 949300304, 696328887, 794183512, 59302651, 136851735, 331528308, 480288297, 668491931, 441318910, 264391635, 375415256, 659972923, 256529279, 561805913, 682905248, 969226309, 392237220, 378596482, 601302704, 179872567, 261197532, 688886620, 196342349, 63579702, 906141476, 900401622, 132665497, 267899516, 96039340, 472080731, 749859703, 860109195, 384106975, 831311528, 307315446, 95858417, 798244728, 226045537, 943911566, 769617560, 977665238, 135579293, 828948207, 510681499, 625275971, 68127783, 940618113, 876263403, 456468793, 939988553, 593944374, 761203847, 791926862, 241901930, 271111793, 641809141, 560035831, 406965522, 682281115, 409427272, 550790902, 849628222, 959503013, 131164739, 253912116, 820154388, 145116559, 704236450, 94652228, 892822914, 734825559, 255292494, 731935773, 84624086, 363901594, 916807666, 896295469, 796983581, 188133361, 325126133, 306834182, 737051508, 349490488, 907463069, 792309590, 862097218, 547824147, 50527423, 552469419, 129186640, 432893930, 704277729, 139564637, 927343431, 775883947, 60661774, 906931062, 441855316, 546876848, 742733234, 882463833, 999218664, 390767066, 879062833, 347196037, 904571972, 202518812, 924792524, 913103774, 433216228, 231516884, 110931814, 204767186, 892020301, 758498003, 55632240, 852626194, 853208641, 39201337, 796591584, 788632600, 815499432, 981290889, 43954371, 587594948, 770181213, 235788939, 843711087, 237226942, 666737944, 94412029, 603393417, 652172729, 559300265, 207410178, 58695385, 407605841, 858452849, 798941281, 757273232, 863487460, 787288378, 659887735, 742526642, 202003257, 378793867, 85464143, 772799246, 422553219, 573341602, 479946375, 695467144, 592803960, 204900362, 357149545, 411780601, 460015373, 46177022, 810443724, 4998103, 849888747, 168690068, 807520421, 171341175, 390408419, 837402058, 96470358, 644921218, 616492482, 396748270, 460562573, 84686751, 516775039, 359195286, 437074236, 385430819, 199471215, 565683707, 890472090, 239676516, 348591199, 251220598, 59754611, 106711362, 433166386, 139950191, 685355789, 965423068, 753063559, 352431649, 357175377, 778150449, 608294897, 143969024, 870055442, 504505470, 247977459, 285118569, 639750206, 657535213, 129015953, 67320789, 748963577, 931759266, 579707749, 735872711, 256093077, 575383146, 727208984, 97087993, 266117315, 672173920, 721198879, 680053140, 784775260, 394836836, 51237261, 869519151, 534873320, 505798032, 70184179, 920885931, 138718091, 935138104, 64225916, 73657433, 17554304, 791798442, 14707325, 572153957, 441576886, 95420858, 601842546, 485861636, 843971544, 849396962, 729506776, 138700555, 831196616, 788578208, 947957916, 346652400, 993829964, 953057948, 493175676, 256190744, 688454369, 849398004, 71861147, 900422978, 849333005, 831503155, 454906122, 994345876, 992758758, 45374321, 564416840, 442153328, 745751603, 300979271, 57774193, 887695041, 766121248, 178679156, 501292817, 333625589, 658978505, 370603314, 255397765, 274270154, 368842703, 515681402, 498556003, 257347027, 668949872, 879921221, 208621658, 654651245, 649848072, 472732771, 201061534, 436739422, 301068100, 782765014, 686269160, 635093404, 857519413, 401924617, 550387690, 334378784, 525295474, 25948021, 552728773, 521777225, 934866256, 153451934, 211065657, 168820683, 394652294, 512638707, 68905478, 536143599, 877958269, 935582786, 504060141, 340358382, 555478512, 221375451, 864211794, 345730522, 385228539, 73838715, 794136318, 479570483, 160133441, 750198643, 37063576, 135719724, 513636614, 476173229, 599783681, 45660220, 974156231, 508910135, 815742270, 529643223, 332651916, 853220478, 448484874, 552250318, 334941100, 712397461, 309729375, 523068161, 850764689, 794087837, 651854732, 485082547, 214224545, 661273051, 580813188, 574042496, 993241373, 591440418, 456533555, 385100150, 874318066, 643792474, 242075776, 102660884, 797703766, 839523159, 294682614, 652844107, 232709449, 321268731, 496894840, 21991314, 318705898, 141375591, 124309995, 957825245, 424932418, 193977154, 20732419, 800736195, 128943605, 649469039, 366411072, 193727350, 408963945, 570034592, 281456521, 471974484, 224620510, 355638671, 73273236, 802723431, 925788702, 826774875, 533853327, 227555857, 961275778, 951832413, 901421971, 544099966, 540983783, 391620533, 257475744, 994543572, 61582749, 981044414, 117314833, 222362142, 75598939, 502511852, 770805727, 931285479, 724055455, 308403531, 164221563, 57855964, 437725114, 141064199, 786152392, 461216043, 728451253, 971910866, 729824082, 305917575, 767807271, 182712996, 362581653, 758162553, 650031362, 993650256, 269349581, 642299280, 380152479, 273112546, 620883381, 180406508, 394336999, 173960662, 990874306, 417589107, 932088011, 585627299, 723213559, 103335868, 522320198, 439026761, 159841539, 971261321, 427604108, 713981145, 700113156, 655705799, 402643841, 458898955, 115863006, 258098856, 387046647, 292526576, 292025798, 219485186, 502146940, 413593091, 248743336, 63381455, 57746196, 916614017, 328447741, 373035506, 503531631, 46902466, 18488179, 255826181, 630007726, 371712011, 670915511, 483391191, 16098305, 439262622, 65883633, 195950252, 389960392, 744939546, 521697715, 993543313, 618896876, 217579697, 794416823, 795043445, 576780954, 340439630, 259732044, 689064235, 613528794, 323885169, 536188469, 607648997, 752127874, 724872515, 653630031, 670933602, 30038067, 603781647, 231999045, 982139237, 827262455, 399202390, 249451210, 768358106, 252142702, 187910318, 856458271, 586308429, 501559943, 862727520, 105868172, 475099564, 413414332, 76559668, 348707716, 534257277, 932272110, 927209874, 240442031, 844689251, 588897811, 607854439, 565482524, 970439685, 14774155, 962874912, 568767320, 198285363, 830844131, 435629888, 711547957, 809562685, 33902507, 311162592, 111235200, 27029480, 50101687, 171692189, 759367125, 859710193, 269912015, 241500588, 295267549, 737764433, 598659092, 373101780, 993054350, 667068800, 288211915, 939779167, 825257091, 200140191, 710827886, 126002153, 48299132, 667572331, 771312046, 487849659, 763639019, 989099084, 192419063, 331175045, 399479298, 347860457, 780027420, 883108357, 722251242, 854085129, 926352119, 858226544, 945784468, 93640950, 21582141, 271672477, 130639094, 845434739, 896636845, 226192907, 509995429, 517116109, 30534644, 452612264, 491872459, 481750868, 154005272, 174810002, 78343286, 836965177, 717878295, 209914299, 771376396, 587363625, 19629475, 834194252, 775877013, 84703971, 757745999, 656653263, 830147872, 786385888, 742037812, 632870462, 429539192, 19721526, 792936592, 124913830, 366304124, 303652978, 39479117, 708999396, 540486612, 677023529, 139414087, 687370347, 439051260, 322198716, 795155349, 495140016, 545679751, 715844493, 898967914, 953812843, 964374146, 796754548, 223533222, 836900317, 177890438, 470904957, 22812032, 685406949, 298995309, 584235407, 662690924, 377134769, 821220798, 709110485, 861414494, 253098874, 407322935, 913995520, 945081793, 128913923, 515911708, 110929745, 85567669, 905706543, 969884808, 55650951, 406248797, 872994309, 335672315, 389289726, 548800171, 100265421, 897085779, 423942871, 17033924, 801821408, 231137169, 814621133, 606411059, 389003024, 266843536, 590861206, 645028699, 883908064, 68254637, 174725051, 549066205, 184870169, 794928408, 332263122, 835437140, 584326212, 126150821, 786069224, 18054001, 946143754, 583359531, 309909369, 148241648, 672771710, 984978423, 183139644, 220648948, 711860564, 639507861, 988168375, 655328654, 723192081, 856234001, 225657874, 416932069, 408856552, 323186070, 148611545, 190440093, 22822661, 499565480, 823445580, 20432976, 879388250, 648225967, 179300955, 115180248, 341648981, 230389453, 383723097, 584726049, 298168678, 182197077, 320184470, 399510789, 514820618, 886640983, 445934109, 721423184, 769225495, 439972079, 445793201, 938367920, 484590540, 910326390, 150788460, 529913185, 927776235, 138576642, 471264914, 501101146, 474411004, 897407936, 437252502, 377612464, 451470763, 416482801, 510185721, 428906062, 201192675, 889892421, 218565480, 509083180, 251008259, 595465945, 240348143, 492772579, 902429440, 368533515, 436082982, 10772773, 297155571, 214966812, 122506792, 945566685, 855862239, 890434028, 259219731, 3121148, 997383103, 189117447, 712572901, 757718296, 12636393, 918963182, 8991490, 520702503, 938559462, 741942020, 548695132, 740709088, 214890626, 204171199, 571831745, 445774103, 431013474, 791557538, 918672570, 538272442, 710695519, 590912697, 823036267, 939479895, 397237871, 61321892, 19273675, 584404641, 300505567, 461846287, 128898737, 227333678, 751868761, 834113785, 563607231, 607878072, 612493536, 924884692, 937603456, 293070111, 435612004, 312615589, 772083543, 893318033, 79560794, 247178381, 756710277, 814685082, 764949834, 680544175, 851179595, 308209256, 758027394, 880870878, 974184459, 866560176, 930144485, 508422105, 173435669, 947985048, 469092307, 881763363, 39938678, 494941081, 395221711, 816340373, 951157388, 912218757, 348537262, 505843153, 435818353, 652817791, 733033378, 956140759, 985451786, 667411621, 895208710, 465169766, 454400079, 978586020, 68752661, 601134189, 115979080, 499203155, 287956828, 949970329, 612155370, 440467938, 916528907, 75693095, 878078798, 368129265, 636648356, 655755239, 122393776, 715642934, 477649616, 667073150, 435904554, 795806862, 548786062, 57081765, 692663819, 187205878, 32291245, 154042234, 70745720, 277786182, 129193854, 451128157, 206958992, 333316630, 372848943, 275575500, 341699386, 120751631, 704502060, 778929770, 363482856, 867070234, 103558099, 465185707, 702565980, 25323306, 851494448, 525906472, 416009705, 298848131, 588452532, 663738440, 297677459, 162757732, 89729989, 479356327, 924785, 398304201, 787625182, 842548036, 598227226, 993281678, 695789684, 710790865, 376809755, 641895152, 87585884, 487676489, 259129684, 45901412, 381051003, 235875814, 54082278, 106191202, 345207702, 823284450, 128073997, 609153669, 855169689, 26957210, 381104156, 391395786, 742083711, 551325829, 503886461, 877898800, 329225464, 582476815, 908240110, 724394706, 650067972, 193936806, 168468738, 126914850, 327283981, 694756582, 656766795, 718055685, 99163215, 853644871, 567625250, 610927461, 174038540, 4284302, 65319, 530805149, 401663605, 432355937, 71780558, 750694303, 137647437, 472577239, 58346470, 217350257, 437661780, 590472677, 319838450, 305641879, 436611477, 80111207, 486655307, 328413353, 675028849, 463213405, 389821695, 285479991, 150451804, 878222479, 133681518, 392478983, 480486156, 121858385, 495207158, 664182078, 939519108, 308067041, 13250886, 902646495, 269267823, 566665409, 628875001, 724915906, 209349110, 240257554, 984220446, 201478021, 597560921, 495654541, 577983012, 517426380, 722604550, 468856779, 574864522, 593805433, 581997475, 944918407, 851783026, 806849726, 870647730, 844626496, 532729254, 509795690, 908872837, 628915297, 947981255, 715189592, 25024446, 947271100, 147592944, 750871572, 792070665, 642664333, 461918765, 275265522, 496660941, 870170620, 830056888, 957045141, 199406422, 439810, 661449997, 946385970, 697180259, 579412060, 432265979, 157200988, 217658740, 920116793, 800963342, 544976828, 211297501, 930459883, 103855624, 903616798, 22078694, 20340421, 911670400, 818293035, 550815446, 636705791, 431370700, 185367277, 943729250, 161518389, 10772915, 445300177, 278435807, 827037228, 852177914, 675400928, 631934363, 180305796, 355172345, 740342098, 722583253, 84278726, 140351160, 291827515, 934221305, 62121420, 839099627, 57241306, 679437605, 989882225, 586487879, 863769484, 377447155, 270805843, 432530129, 286875949, 539854661, 903850367, 964154446, 132140398, 724587744, 900545538, 699244153, 389827555, 603213113, 561883833, 771620912, 959713188, 293455975, 942132154, 36209312, 759689209, 90292570, 5369608, 608787776, 402389053, 804671494, 261774931, 777244648, 161671645, 682005787, 218922866, 145595999, 632822722, 615076111, 60400606, 911602783, 635937728, 200268167, 599948160, 557236153, 636346631, 212054887, 850428787, 209859369, 285152629, 326972526, 776096752, 762318504, 543239774, 797644565, 31931619, 780171322, 314190531, 649913886, 158003871, 119289108, 57743499, 567747755, 177021052, 964664454, 15337497, 38335945, 290274962, 408221971, 401159767, 42356248, 576839203, 695251614, 283466976, 21918427, 517665424, 191087239, 262442568, 686310757, 84821890, 704278945, 206994502, 474855578, 603556078, 137422463, 439711342, 171935307, 367785377, 180118194, 615875182, 622246939, 855842587, 455100332, 548318194, 532225442, 356797278, 834057765, 295707356, 550228800, 498181386, 646336409, 305430721, 675651217, 721449310, 41832220, 237258260, 939231333, 764568827, 423837891, 909415557, 850553884, 435511584, 332879618, 738842919, 89390230, 780301793, 960497416, 82382273, 833966810, 572387150, 937779769, 148054255, 745661192, 536268224, 872681147, 911240413, 261928940, 168104360, 95545580, 277589796, 608026861, 459541118, 65499425, 932149248, 142452129, 287248164, 797279738, 264022503, 892300745, 775167820, 398179949, 862392042, 812950043, 997322129, 571576688, 238503647, 296930185, 557000198, 156390660, 48064481, 67498011, 854695491, 254333474, 223113449, 507104026, 578748604, 291433868, 248644793, 846318317, 416992242, 293259346, 931964890, 587768104, 968452454, 890431358, 244500783, 857480349, 636473480, 857487651, 240436211, 817540386, 226294936, 839009922, 387608153, 913141918, 284272695, 959573613, 701903432, 968263196, 765172834, 481013306, 18596511, 267211980, 253658514, 91770029, 306763949, 874789850, 588175056, 744980046, 947098563, 274203804, 721782303, 755168674, 847155342, 118083735, 998878592, 17845493, 842821869, 262485037, 3657268, 667005487, 190949753, 130914712, 79401350, 626630350, 987047200, 814336045, 364844008, 101713611, 211623574, 555120974, 682625425, 904095890, 814251438, 591227555, 52517350, 134973753, 949023865, 230297159, 997072075, 872605135, 168771176, 167263325, 21982170, 688778198, 498981905, 641642436, 805547581, 217994858, 564477198, 88713771, 309482707, 386631739, 720010748, 505756282, 587500386, 988549425, 366363542, 831471546, 582202991, 652710605, 182800603, 352097976, 631427435, 915687347, 779368105, 26209886, 45274527, 615977557, 158224408, 438503606, 342988222, 524649749, 752687841, 109561910, 380593793, 536911176, 504335824, 90114726, 901528492, 796006591, 992460360, 680171937, 8642927, 277686363, 941526576, 718808719, 794699082, 64104580, 127184947, 435809784, 521280119, 101978205, 165922814, 888778997, 867578948, 529543072, 730497338, 129790029, 25957923, 437972614, 594221529, 10944832, 362323070, 571978362, 347787857, 771581340, 786664295, 850667343, 597329689, 355554290, 741603187, 796593227, 334353690, 391949062, 478255934, 261182841, 238652137, 552096208, 175373804, 692125305, 849229358, 509588252, 757033312, 644027411, 253654659, 45066607, 506235806, 831303395, 720839041, 190785570, 778043328, 433579540, 996180198, 356501579, 939713884, 318771557, 252582353, 176507676, 38790592, 263518135, 797483898, 132914812, 874915547, 991778086, 686346732, 839252507, 79431229, 299513911, 958919041, 922542202, 844830532, 817556712, 94340424, 940217018, 581907938, 771757665, 771759809, 717759565, 462159149, 949197779, 484091814, 706157092, 390183738, 633076378, 183638551, 236272850, 696002465, 252781297, 498824874, 442612254, 582836756, 678863848, 723200825, 197666694, 639204822, 685775809, 645410302, 374438384, 439577407, 164093305, 531214485, 585336486, 815064550, 931466452, 6303388, 199037835, 462906037, 521473211, 756060285, 29136342, 634559377, 699369959, 60813892, 406824645, 216742186, 611547407, 890820082, 714078741, 168648991, 538167279, 529353376, 112000705, 867290946, 669604151, 862358600, 685439392, 790821035, 543169541, 921339819, 916238069, 712135248, 244840014, 997444331, 722073300, 426358056, 296912170, 163693130, 748983299, 747888429, 923248622, 357161877, 146954839, 2764540, 880829910, 937594915, 513421923, 314754196, 184695180, 705415822, 145786376, 584274722, 760437914, 914348281, 282025625, 284861532, 160559352, 154909831, 71642307, 36851642, 930960391, 468072531, 708236180, 523682292, 612834533, 397702410, 240277097, 156684868, 640072772, 289027168, 639057227, 873097294, 624990159, 854145512, 435589492, 872588194, 534252487, 828679833, 780481647, 70637590, 402613358, 929324463, 49856650, 66578754, 733548133, 812641041, 282652924, 306119943, 337693988, 967431260, 574586795, 708883222, 613270197, 154118607, 416464848, 462305853, 14455328, 64299396, 854297929, 722307974, 741382207, 557030286, 972264717, 346447029, 822797021, 335292761, 359239206, 476836151, 199307137, 802552699, 529389802, 40705378, 279909599, 637992772, 939602696, 766789648, 413518763, 305052414, 898913355, 176703396, 67986608, 757167538, 975859929, 496172257, 87069582, 692892574, 90077206, 175333088, 287035373, 914335128, 187795724, 638335285, 797479256, 278588495, 187430124, 675728537, 634055760, 768279964, 286007065, 793199096, 712218870, 315395332, 127653478, 197723401, 729233007, 908741410, 827391220, 517760150, 497837169, 522181433, 196468998, 58820522, 675527092, 642487545, 880391688, 298431012, 603061648, 395910974, 891719282, 813936204, 297246437, 663533740, 724986921, 274601706, 802085817, 145004196, 640530688, 741144904, 87395571, 636437574, 971505958, 908368542, 668592554, 852804503, 776686583, 841021708, 987291399, 187339405, 10477533, 997728565, 197281302, 390942001, 15357400, 524396887, 223847134, 763550155, 216884853, 791310388, 572841234, 195223265, 970333876, 953555200, 23661116, 548992695, 11420769, 499207930, 959785370, 701909607, 896506799, 888435592, 272073812, 337621080, 373834359, 213280551, 952036878, 259716567, 178658863, 218553987, 288578098, 529682630, 801937700, 957420350, 624220675, 284719882, 848116046, 129314313, 978095507, 992914664, 861744483, 571760665, 98501359, 864590394, 378462076, 703217121, 931584924, 969529365, 461582946, 547990610, 802057707, 435923215, 430013472, 696117132, 421398304, 386358332, 594558483, 557976187, 388999821, 36588433, 716579440, 850467310, 751006761, 857974993, 462148049, 640304510, 14806628, 511149350, 134095703, 91098208, 245729141, 571061761, 357915926, 772389283, 836004959, 886079217, 895467423, 816481391, 733914572, 737201584, 303019881, 171206635, 239531484, 277628307, 864908442, 970018667, 394712424, 487521180, 587739206, 538246304, 975026208, 971793410, 385330169, 105465470, 432680102, 665757368, 329509654, 244310653, 756378309, 423568488, 793648151, 647472026, 549693935, 239652687, 355367952, 620024835, 128834307, 327926998, 123259435, 22677623, 328799045, 174640706, 485026527, 390884909, 877592372, 492863467, 547857513, 540588022, 581591735, 834387376, 657937816, 458520168, 360537616, 391283416, 778531388, 581446206, 536338246, 977181206, 436803484, 214943570, 145652381, 766289855, 656652966, 3613295, 468108480, 419741547, 883224441, 612829924, 972081104, 347931761, 39148008, 856814869, 891561034, 869539619, 309155072, 859423504, 990231125, 621844969, 841800137, 786762325, 883479353, 813065999, 92726630, 257226324, 902615578, 348261780, 794272293, 150986987, 307064294, 10643687, 75104208, 60948843, 188394381, 859108793, 796554273, 491183521, 315962546, 896190199, 698900148, 293664036, 385428892, 462868967, 900065902, 204075442, 698550611, 173475737, 683897762, 147900133, 585781922, 469355064, 943447783, 567384662, 813627785, 78879951, 742334771, 899984358, 588155940, 920456021, 778498864, 363186127, 190272684, 703670819, 628457422, 822245606, 732431291, 315036459, 221062336, 397221611, 225287120, 66523752, 108836931, 677208159, 134256630, 881239899, 890611974, 205418486, 843493213, 491299204, 463460621, 516621405, 109499996, 88647917, 742975401, 479968985, 157918752, 755746626, 322806058, 925938266, 950492858, 138866001, 594132446, 330264088, 154014079, 139875080, 722952756, 240909420, 751837772, 512562406, 194386053, 864232815, 948407570, 818419175, 2206255, 492841276, 747703923, 41417212, 696538591, 233744548, 313378063, 348170117, 526035301, 19546255, 641301114, 447694180, 748620684, 303825886, 337182923, 220021200, 553103182, 606666420, 966991734, 871485851, 959166114, 47175392, 60813862, 394179811, 924538083, 809829539, 946472271, 800409805, 390228801, 190355306, 650490817, 640253617, 829628831, 118684483, 392589620, 916329535, 761761304, 751432509, 876414685, 900990432, 650994812, 552409789, 837758882, 281566026, 376237118, 737360456, 571852725, 653756555, 892289651, 863022151, 292696126, 509716658, 491571681, 812779464, 535811188, 449539393, 185841894, 353939136, 426396645, 64350744, 324676552, 948753710, 44454015, 179610892, 908814548, 897913796, 284242296, 317149607, 360127567, 572741500, 635260558, 10689358, 606281229, 980952456, 382101194, 10974366, 99436639, 694327764, 830097302, 921007707, 148889839, 768170911, 464195444, 409533053, 214613262, 414651219, 668372833, 948576074, 336639452, 948841293, 253533551, 744398774, 661625774, 263128538, 445732475, 699051449, 999065265, 863737064, 708285580, 727910263, 693434863, 324403711, 314960258, 874904816, 464655656, 42728788, 944554178, 935760521, 32682942, 226524216, 321534052, 219969575, 63871806, 423692101, 814392677, 832777748, 393386520, 331897039, 247381899, 911275566, 604450913, 933332327, 460048858, 415883190, 38216994, 182653754, 967368374, 382694521, 952046023, 578243781, 260989550, 59824283, 520852935, 596329913, 516516819, 458014931, 614663587, 122147473, 581912905, 953338545, 542975098, 50144972, 613098606, 11099411, 102321457, 954516357, 901440493, 386955984, 896856103, 897144933, 72367860, 233788363, 691106393, 583514274, 369587732, 360878776, 172839038, 264347251, 604888371, 923415436, 838472103, 237705395, 777880386, 316428279, 99392509, 908353262, 245224607, 539801735, 596842274, 83408729, 459643218, 7518940, 944950129, 175926323, 74152010, 81306648, 275173038, 800512710, 973241498, 265703490, 690495786, 135079119, 758281994, 249951250, 284185889, 241835586, 56401782, 109706133, 730562988, 867729337, 373759362, 607928385, 343580231, 427549760, 123308699, 35921612, 689132609, 771774015, 906968430, 32892923, 713281698, 412682059, 646782876, 841064387, 605295209, 543783500, 625369761, 205519227, 822380188, 206632568, 251012971, 745695747, 196300166, 892841365, 78773177, 985566260, 969318175, 683316655, 837068473, 791072210, 243678148, 140865842, 72660718, 881380838, 538063396, 37493481, 509851565, 20418379, 526479005, 732037785, 477430234, 527605318, 73146344, 625319593, 160562077, 741527942, 905030870, 41470686, 754526713, 559130300, 753095530, 631801599, 369037368, 520298555, 711950448, 954644154, 707617184, 358505846, 219872100, 524866216, 998245296, 718108439, 324623640, 406072672, 272238275, 842032162, 892682221, 967762635, 915257425, 718891842, 137337068, 981028853, 24852099, 518644157, 416154501, 975145192, 882970034, 762967064, 452960453, 714077274, 368515991, 92093515, 883582495, 350022345, 972127967, 897691824, 862484418, 50453860, 765972770, 776675487, 220297344, 719230475, 734906146, 466730578, 109036935, 488160229, 275997032, 510766425, 986955570, 629087520, 994511487, 465628615, 227215044, 384890636, 532943426, 887125852, 305364822, 923931376, 478140246, 642843524, 120444978, 16297668, 476969862, 699673778, 245863129, 24104075, 88520521, 604658106, 388678943, 202922461, 399924948, 557217325, 676758005, 579574710, 523624253, 681361313, 510323340, 149758874, 769648490, 826092815, 350926880, 653845897, 797882992, 86289504, 773885190, 628166051, 427387195, 922773884, 880031469, 845125135, 504637386, 935210436, 545431825, 885413394, 830118372, 707295076, 343590766, 892308268, 432359632, 307563805, 846043970, 676220080, 721974176, 922163550, 377672348, 74153659, 487575882, 208818326, 808095633, 617221221, 96566640, 662946818, 113513815, 322351567, 784207463, 26105831, 285536221, 768212505, 469063978, 965662275, 271136411, 349917103, 922504437, 446740386, 870766859, 956130225, 456780899, 243731664, 938994497, 676045953, 411520052, 829672919, 395089552, 856226046, 826369624, 574373992, 629891191, 387571669, 646489575, 715345105, 449696863, 483240107, 920528911, 611976389, 385374334, 208293094, 938905158, 891445399, 492129556, 233007161, 311429379, 909581302, 672164598, 859378737, 30992520, 546715355, 859716820, 581253696, 119594751, 383655730, 806115305, 749163130, 11762412, 900573967, 546536418, 365537555, 716526815, 687736965, 552330389, 419599286, 549545254, 813944411, 179530342, 919337293, 326991489, 470628052, 360418541, 46906385, 623808890, 26896809, 741082390, 898124611, 874694677, 655784677, 673632844, 616355535, 722182536, 396036108, 558147763, 869719621, 31478883, 302740186, 559593546, 182027168, 170526069, 321092190, 229894078, 276473519, 802462107, 457206092, 130227100, 416031942, 526334357, 254960808, 485313316, 335695413, 829228682, 624448852, 799618631, 925032177, 60571346, 691736941, 392920134, 786072370, 507077065, 55461533, 650312599, 425948203, 94203395, 458632235, 506126349, 595844681, 147750469, 883983746, 192417321, 936183015, 11332920, 28937026, 693371680, 601090828, 402763235, 898777848, 684218087, 690945025, 388328106, 304745881, 397624675, 708178649, 605686869, 347476267, 484342668, 978417341, 528680368, 704858603, 522803587, 136861028, 730925771, 716977407, 76859242, 568984343, 627528035, 779719917, 552287963, 316881380, 484533248, 695388307, 15555302, 75815421, 574623617, 551325561, 972589086, 977844304, 25512381, 147963675, 923101860, 747928698, 705434625, 370967243, 898776319, 804662616, 700012273, 321113482, 852435323, 42187589, 587657442, 98826793, 187060080, 269988812, 757757403, 580311009, 807746399, 832861236, 261299811, 792987561, 42523733, 442610343, 718900971, 205956243, 780676092, 592626476, 901578338, 81027554, 229121281, 709418994, 294482880, 891996880, 934482797, 253326983, 742269569, 935594561, 449788631, 619243419, 386424343, 905028144, 663230087, 411489300, 235136044, 175447041, 167352602, 402406855, 641401496, 110266506, 868237777, 374380092, 609676764, 16283023, 478016800, 921309087, 437653234, 102385095, 646522994, 807326463, 175007533, 400573507, 765957392, 304191435, 994055551, 843678837, 863148167, 595238244, 678189361, 442405521, 309937718, 733779000, 998566826, 325443154, 290546274, 351800101, 774087390, 56701840, 766005310, 502122825, 684003871, 167925794, 997462584, 862319921, 643190097, 184650864, 348852682, 722358725, 508969533, 371306782, 251176314, 199747211, 275778056, 995751734, 469096559, 550476241, 772986259, 437769121, 812866103, 987221926, 341575321, 200961005, 604948205, 991841651, 410016107, 522037193, 622921020, 82691733, 448218973, 568154646, 535655485, 201477910, 747352525, 779012135, 374544306, 563601984, 434265525, 61735689, 789458835, 523423607, 781895212, 222630957, 256890085, 693710608, 746943260, 458450606, 7104475, 223817220, 107805963, 663199247, 525689509, 524976494, 147877708, 92465077, 958207131, 393249732, 1416629, 496214417, 181177504, 96556729, 290552216, 842370233, 863478147, 681904269, 601108165, 431562171, 5519117, 592419675, 989890395, 736617772, 867877959, 151241851, 986289192, 266826784, 36148395, 814250670, 394756585, 53449818, 995138249, 618338735, 331304244, 637390763, 936952671, 552271467, 640116009, 578693986, 227923536, 142161513, 689612688, 738676446, 696024487, 447792995, 713990924, 13806438, 60601670, 131680549, 223164240, 25713940, 323676213, 300541350, 444171989, 494685123, 190483332, 819539286, 238252572, 168689891, 880459830, 689372635, 404625365, 812368825, 979117506, 811758124, 859398688, 164365070, 389861928, 853784875, 796898239, 854579830, 533509371, 456362017, 800713813, 331839411, 717719030, 56558840, 285863843, 553731565, 979004904, 714457462, 930877526, 833378744, 495505889, 865653138, 13272610, 678854548, 347364705, 877424009, 931050427, 275661990, 690047182, 88106953, 526194343, 488936811, 797805947, 591411026, 597965948, 648950541, 556979462, 308919992, 888412384, 127708888, 637125954, 911822154, 539639875, 760589400, 458357677, 109462271, 844068139, 86866776, 54297612, 254075278, 792078178, 187023532, 958403505, 351265885, 960887716, 961815383, 827337247, 141684456, 753876605, 873585888, 166388053, 259077160, 512185560, 11938638, 736254029, 166133128, 629868718, 530102940, 689153635, 477002487, 42891996, 302446143, 982272744, 911772595, 154075448, 750827690, 212396365, 159775328, 2454068, 763020428, 932007298, 78372699, 728232895, 279123736, 576813421, 901226220, 11602560, 512406807, 147213231, 618859702, 365823558, 477212684, 732737821, 80762275, 906569449, 344181378, 573390529, 132904059, 279450880, 384399566, 718554319, 827078868, 227304824, 177132710, 463588734, 979713829, 340157849, 535558255, 150486664, 164984455, 3395298, 475568885, 248306231, 59663944, 409138700, 565697696, 769965577, 178065708, 955870692, 27894942, 366476731, 225976070, 398774301, 193838285, 791528162, 148150573, 446256430, 984457232, 932654496, 533957739, 38137750, 978182351, 307734322, 531510193, 250746182, 412707717, 608671965, 124638047, 322631625, 954539539, 934262650, 49399905, 911185361, 262920749, 433948174, 593038688, 878188370, 819385227, 496279929, 359820546, 956546224, 494126741, 447190903, 599079182, 412883483, 891914623, 401769107, 411010004, 927006123, 995286956, 41378645, 885476137, 371163054, 428991785, 412057863, 416892742, 350767077, 322638787, 528087127, 581143976, 126877073, 609473480, 774999714, 895623269, 480397105, 990217787, 497563909, 72813886, 595902425, 99262034, 229456039, 589384461, 359464137, 548842164, 610136547, 485848908, 495762370, 783721993, 353923822, 853329517, 637203351, 757279653, 515175643, 39500963, 252765689, 247350251, 774243607, 453635659, 173558481, 906611118, 189779266, 244170175, 903438997, 665468415, 309708433, 299764295, 230902444, 646284372, 489346961, 617541621, 32218204, 253759425, 831664282, 944727796, 644135637, 508241705, 881108255, 784520693, 829934582, 461295661, 719486209, 207580084, 941352409, 40192920, 197720789, 530166516, 494339006, 640347142, 990099578, 140045112, 523119355, 882074266, 506004997, 530755404, 637303647, 431269197, 16598680, 927604905, 682114665, 684548890, 926455738, 940778855, 239174570, 518140533, 110526819, 608095728, 926108359, 892804989, 301022839, 393718292, 504625674, 394841498, 725708767, 39236550, 662165057, 574098391, 55533945, 819736167, 90749025, 126787050, 850189677, 637793204, 709608182, 514868605, 562571109, 25876680, 607987635, 76489297, 457297535, 65507381, 588688177, 927502450, 763370785, 378627173, 347453029, 322506925, 441033073, 548601236, 526159561, 329875814, 938441351, 321443306, 233384475, 680473255, 282117650, 648589980, 377834744, 116910022, 736926184, 310767695, 344876368, 692028004, 344807812, 144090870, 68316903, 439710770, 222486070, 683772093, 956263338, 205514668, 611553088, 815443796, 69769466, 95334349, 826946166, 402123977, 433392333, 826788194, 208666973, 302093695, 119456512, 585697877, 762095028, 958474411, 299167241, 440572058, 441693526, 544396024, 736891231, 405601517, 768857615, 906804296, 561898145, 968569469, 71735971, 871192656, 900316907, 129354411, 290044413, 919114788, 409569160, 832488277, 16243068, 870135071, 945656804, 443763010, 622090129, 885133162, 930184758, 466711, 742178924, 355155311, 981792982, 203993215, 807962310, 982185226, 472029684, 177130366, 17828862, 686898275, 22466159, 580023089, 705824912, 604649964, 496165221, 864735406, 373851675, 696419278, 766993306, 66346755, 294675703, 939295418, 111054455, 870326716, 196252823, 591255213, 911884301, 209579714, 758549827, 410116458, 578643507, 631413008, 752897696, 525041382, 311783514, 78719976, 29350015, 247413324, 157105505, 121616058, 464340979, 770574921, 591538945, 779853362, 140552962, 647114194, 10421307, 771830956, 734580848, 869955683, 718577726, 970920367, 908017909, 749244531, 254787565, 785516483, 869782000, 217876858, 342768248, 514884430, 793006076, 349806180, 336142619, 100809288, 169429397, 941934662, 772810071, 278016435, 48508429, 987073751, 217875297, 879511970, 422462708, 617043315, 287179242, 395521836, 151002220, 509117733, 595360406, 891204632, 41332295, 143704431, 318650746, 670619632, 512410046, 23094248, 255890922, 746638491, 126033062, 123476126, 470641294, 886013843, 567137330, 955507903, 834985735, 716191832, 258902626, 262626217, 832010979, 2243511, 425695040, 531378565, 619782389, 499607317, 712012246, 6083263, 456339794, 376891969, 458783146, 952470455, 637477413, 173703427, 846812698, 983142625, 298677959, 326967322, 560559166, 910326899, 269783537, 385704149, 514451987, 445657780, 804842105, 287336949, 557184562, 117202039, 219885529, 876671859, 927638357, 500194095, 953219677, 311369633, 574091713, 424756849, 60015699, 354602625, 157943821, 835463238, 845915027, 589796262, 885248359, 484772018, 648467139, 911607773, 985624496, 973197112, 202428315, 47191163, 446307586, 103648117, 244225272, 327188093, 940213128, 207856177, 439088688, 359491807, 349788261, 404188362, 63136545, 725989994, 179774270, 509771938, 40134806, 494219249, 310076701, 79312892, 65472975, 394785235, 263099987, 380753797, 949353994, 226640830, 353834267, 578730885, 537234713, 311719879, 766100114, 934917255, 801422628, 434959512, 510140040, 406378751, 212315157, 799560904, 158878528, 834230824, 230160649, 241769388, 73316638, 766603725, 786418430, 353704448, 769490225, 630468773, 633982785, 80462235, 786080045, 148061142, 469151977, 528065927, 919048103, 993220721, 705409904, 25424922, 484307474, 492176822, 654525856, 789200723, 962965634, 130178825, 800327576, 149925717, 699186976, 892097540, 439412832, 797746613, 879489285, 585470132, 918919896, 738735928, 923944408, 434784039, 683120483, 93223567, 341919486, 908513717, 539087832, 432531058, 203463530, 696928876, 872457813, 252267263, 226741558, 792938348, 782079425, 930681637, 569590536, 766718512, 408696446, 728896059, 760291611, 751033792, 653554795, 937503895, 943682897, 548615151, 8161960, 299476511, 385534485, 168535803, 647506572, 511596008, 348491599, 821892188, 726886062, 383588626, 94104561, 379204550, 117715106, 139105367, 139815299, 165417065, 203487044, 427050382, 551214159, 934504095, 477663389, 137088323, 808507148, 201789123, 922282096, 955132108, 131387865, 911228877, 987295584, 970795525, 321315947, 185839181, 570665485, 579391667, 880808035, 30772090, 565511630, 71097709, 937361049, 380889508, 948726556, 378113336, 203372853, 606196502, 87766627, 64136744, 196188220, 485219513, 700721100, 303916775, 696140630, 967877745, 217885803, 385590897, 513324838, 611595940, 130580879, 126141384, 499038665, 458887552, 105498389, 441273910, 134046216, 512450893, 80369351, 792783164, 715879914, 75521062, 326721187, 499063091, 124693215, 851711996, 963516869, 940833866, 491500035, 115114267, 230355297, 937708978, 860098413, 181922021, 329624157, 632145055, 405574781, 797822689, 752356710, 676540973, 583070551, 471639363, 443628730, 108228476, 819138652, 541983001, 276561980, 975646534, 869281045, 647898888, 118315254, 434633540, 956678955, 411373781, 316361169, 721490592, 322543870, 281046231, 238758013, 669165787, 386312352, 72560714, 384631017, 893959998, 579854331, 391944918, 161713961, 491574239, 696922674, 990379479, 149588845, 986174012, 939732259, 771834147, 867839118, 92351103, 228590315, 382761487, 825840454, 39352643, 550989740, 990378550, 377911617, 752798451, 772227676, 451378239, 297164816, 67622849, 609524845, 415189570, 208241046, 784407103, 824264036, 13567336, 725632326, 54096151, 77454895, 562116074, 987609844, 769772137, 593206631, 677261571, 285000032, 289113020, 213168630, 926697366, 478963405, 554278309, 972438228, 909545874, 749730988, 834953916, 772076699, 725239817, 155001124, 913515988, 666212821, 438541015, 408742736, 510973239, 119066774, 281834944, 463685691, 450937321, 912950319, 123280972, 152821959, 143131780, 595876603, 219394490, 505525527, 869529552, 370429676, 417010059, 181223564, 454097834, 1181749, 967831348, 299064078, 38439121, 534561185, 865786626, 905674030, 705801195, 260743792, 994046133, 388358173, 639900453, 302810817, 309338067, 38988431, 674812505, 624474421, 922386360, 750052311, 15562223, 811706703, 624150078, 6115738, 391143290, 357787557, 101226270, 838025427, 923931389, 92540601, 774770168, 110825807, 488008137, 165271745, 906730972, 9238196, 214978712, 829021670, 306669454, 149167712, 669643844, 648623177, 854517409, 421717093, 781070531, 197009935, 549914256, 11987666, 486044954, 901495355, 251055863, 478287395, 495995906, 463305126, 436519556, 662093244, 356916088, 708797580, 821620351, 309954370, 531420873, 189861386, 319664354, 796101118, 483340852, 817270347, 825615275, 115429373, 871717873, 855487446, 749806563, 98347125, 210058968, 329545457, 670584145, 650318783, 518786085, 464411460, 534342896, 301506788, 993386215, 895219634, 84381763, 208451709, 515987326, 951793858, 11335603, 94159693, 98254455, 84905815, 368425864, 146356705, 961492254, 747722821, 932227101, 663571805, 450105334, 438076064, 735959965, 117615025, 24489988, 571262081, 519336046, 59361850, 390613000, 1882910, 531036792, 910728780, 377376450, 298670006, 497794573, 620983738, 850715160, 904396158, 755570221, 393623193, 868995967, 529858885, 852812428, 386871762, 97703564, 760193160, 205238011, 115360648, 563739870, 238072139, 956372970, 988591018, 632658759, 113544152, 547499427, 729533811, 567636600, 849957232, 937776494, 95767261, 235447577, 235029629, 704702000, 386484507, 428473261, 662775624, 29834023, 268937877, 801618494, 69172468, 450968574, 323470116, 620162726, 59844916, 327052908, 764103716, 553941549, 958484253, 641627640, 771587749, 836160167, 289347122, 168572211, 662518555, 413495957, 780421041, 69764052, 915578129, 102823551, 854438510, 169788843, 772591873, 870666093, 244608096, 855293798, 585981856, 551280641, 559699405, 284735532, 71348811, 938890047, 59610354, 995283704, 213064249, 789846436, 667879716, 322579280, 148477665, 791286309, 328376461, 244108001, 577550604, 71214374, 671116710, 851399771, 705750601, 800687485, 668855105, 702645315, 138316801, 337231539, 421765087, 2646965, 466127102, 865766472, 413132512, 467514450, 980391176, 32951064, 999690893, 351170161, 900857721, 310629013, 369769597, 811476399, 474488413, 190045893, 165994452, 394221448, 734846438, 606223571, 965171840, 243003599, 744401306, 743309790, 36021116, 12376056, 789073097, 440579836, 292925184, 616124534, 482362576, 895383694, 163727754, 475407563, 167443215, 921867217, 344656468, 792203553, 645296896, 576087708, 258869879, 381305555, 174753973, 861298413, 487219948, 525196678, 319099227, 459745584, 925563481, 729275968, 301549343, 42119433, 262266842, 978288127, 604755331, 44824632, 844347615, 245995816, 734213416, 295634549, 12317067, 168752699, 571210850, 929657084, 195630989, 158367730, 209109355, 791508975, 51235395, 893950232, 41403402, 516294371, 203219039, 207812843, 824677895, 588477071, 203873569, 92265080, 623564722, 325934241, 96204788, 846632356, 501045910, 866849521, 984006070, 210429927, 637032033, 897755540, 638545880, 120479326, 910282864, 757220955, 534625523, 82641645, 467341011, 15953981, 485647513, 288885392, 175412920, 118831417, 794981793, 81937699, 200862613, 607095656, 879536634, 449834129, 196910421, 759714087, 692602850, 120293748, 998796535, 765092879, 806127028, 124172324, 643891881, 766010945, 954796874, 880542032, 968816307, 837175636, 480060400, 749823254, 370337457, 795188430, 296426896, 929407547, 502992878, 437575596, 850757535, 899880190, 955755502, 424555596, 397724397, 928279214, 603840476, 844244327, 297637745, 401684784, 796258063, 851678668, 347395064, 91991574, 304908571, 294739154, 461067860, 135740600, 934493969, 341665493, 899843762, 296580617, 824063128, 50782262, 859738396, 473042784, 666916276, 100245787, 950414982, 4092375, 174727576, 226392212, 544121758, 44354562, 137031002, 518339167, 864063091, 664252964, 318517040, 524110696, 8787475, 232454851, 262039474, 803053371, 653792635, 108751301, 974759855, 905176849, 529953256, 26185480, 392195875, 914356270, 570892803, 499674755, 45773589, 429664955, 822121439, 319180634, 814454434, 852709549, 554979276, 724364565, 682684317, 206510099, 418666622, 139782935, 350168529, 237394471, 603520948, 124282610, 954285566, 716714831, 341893687, 281511538, 12528208, 31926458, 480664414, 793832377, 29554841, 508959902, 877751144, 115195923, 824580311, 684744586, 519928947, 356064126, 484051551, 526657871, 27499180, 656726752, 253869247, 681392072, 459581044, 78738415, 395149943, 438036986, 630066787, 13134695, 746779719, 916562541, 320200905, 676532176, 467701427, 801481432, 378352200, 125429972, 190782146, 45635975, 223317835, 598339365, 291280067, 912641901, 126299475, 777672938, 204888762, 634906639, 549850831, 731441209, 553241933, 576897442, 987044998, 718961844, 530579231, 183461319, 83610601, 137506922, 88532257, 481184701, 283821935, 915754583, 190244087, 894264950, 748945263, 475021282, 790461523, 913113197, 654124903, 340593951, 402539229, 313040498, 535192699, 390685668, 27799661, 935318347, 933281378, 374072993, 379253978, 974143790, 741014146, 72163582, 229669448, 491059726, 352412470, 389600213, 477460057, 916656810, 493084728, 924702382, 175982552, 52367001, 167667492, 618364111, 420749467, 988024247, 802619293, 275172221, 783309874, 55318712, 323717712, 271365470, 719253837, 772781559, 121676494, 100473970, 880864722, 221641192, 598618497, 93070061, 33904378, 177136413, 744364125, 914045872, 407847825, 651368825, 497748379, 183677015, 788634188, 784812891, 292271179, 922010028, 810681286, 70078394, 909947089, 672266344, 39780096, 866201642, 191872071, 204829346, 740155838, 535930014, 958829419, 316446390, 130987448, 956066885, 542295779, 434318264, 633945380, 258570927, 871891127, 842409765, 254828335, 94208419, 143724127, 829416949, 634725165, 208721346, 618603362, 420499068, 499282937, 731289124, 716903206, 689187129, 976908526, 862069307, 154110741, 195576477, 982338926, 813901982, 35031278, 967325884, 421083267, 832412096, 916169084, 516776429, 831598131, 506607552, 920820602, 759890431, 240492130, 709221415, 286713113, 992765900, 57149169, 741392988, 532151844, 739533404, 285416044, 81191760, 358147503, 326815707, 596426085, 934597597, 298511004, 882115345, 331069788, 116497791, 700101820, 126112762, 21948647, 234419168, 563602777, 575544149, 795346528, 716860266, 208500031, 426250219, 547249506, 395761876, 890354947, 427805237, 616758761, 212696523, 834249622, 791387973, 767421384, 33681131, 298249851, 98350460, 954739937, 348736210, 80558600, 830015574, 141566338, 252660872, 937189240, 11972519, 214515822, 409096220, 954469167, 382519659, 189423731, 703031976, 673019079, 497667946, 282504480, 756198246, 81533378, 200430547, 35093750, 949358692, 794644479, 581871045, 349947208, 784345353, 233015891, 620509882, 654290489, 438383717, 478927941, 91672018, 873084850, 991058414, 88513012, 728726526, 395424153, 925772615, 264460985, 894018905, 485779829, 356332947, 464679936, 677167413, 779523679, 552356164, 774324890, 491145847, 28419849, 967343731, 661187189, 130822180, 14645912, 235832443, 926042841, 871146159, 64539097, 121070718, 307437128, 208854038, 866186858, 775828942, 893993800, 394478828, 469840309, 372445458, 767819887, 452865714, 680802885, 400285326, 76024698, 608956887, 587469953, 13247872, 982282517, 983734957, 959937356, 254298331, 466956040, 656719220, 370657337, 256910500, 621508263, 261565545, 148487563, 671413117, 492784137, 780559249, 384897808, 980642223, 517318877, 859879223, 513656151, 84484185, 922555262, 38415864, 488064893, 369431357, 918375036, 906046057, 9623338, 70787840, 441804268, 474814718, 564203404, 481536431, 802008691, 817296096, 77312750, 776312237, 156914598, 860996657, 350283304, 776316228, 7655797, 421666164, 100458098, 382193582, 379257817, 916944601, 939469887, 1456959, 119123651, 296189398, 786375803, 124278456, 301272588, 284300563, 947044541, 909214766, 710653000, 876929944, 968437527, 458133016, 482556048, 695317157, 757716019, 403294629, 961274438, 742062222, 790127838, 620844609, 614866891, 238126020, 587621429, 174144108, 329949078, 358775485, 541210370, 85799900, 852338545, 688247797, 528885461, 51880910, 617169584, 401802161, 679174488, 919579318, 327408394, 294351542, 935953278, 554517614, 3813015, 220109298, 579319674, 924250750, 428175801, 469953502, 125896854, 377203211, 959541160, 248660627, 559664518, 354945015, 667780890, 860783144, 925979438, 32481023, 798663899, 475734421, 898680391, 721184810, 264528225, 153634558, 614986965, 254999663, 172316691, 211186893, 73611667, 62267308, 820204129, 254333912, 880100249, 448387919, 434117050, 81258799, 711611279, 459349219, 954628587, 160490335, 817234550, 467485646, 581825213, 551025178, 540974055, 682032438, 899158827, 755793616, 56947907, 490977998, 589352142, 299663254, 933928423, 519398543, 838064025, 615036894, 451161817, 121718389, 356481805, 453614193, 954490169, 845525137, 81616210, 58124660, 513054042, 297972839, 299779068, 643857739, 282552838, 776361796, 262089286, 712556832, 488584687, 298047869, 676764184, 401662106, 329616553, 916303764, 976502236, 701256985, 717338088, 249129581, 696611448, 490725341, 311128419, 249205775, 421180069, 239697444, 802122072, 170438607, 437608300, 648887091, 675608063, 87109158, 583422149, 826314663, 50990538, 704081742, 714074289, 544490936, 466984224, 964059456, 421784996, 801767291, 930252818, 904618401, 533444808, 946778842, 561824464, 288633719, 222152600, 77625470, 472609652, 703507670, 220379304, 751955985, 856253845, 278290546, 329189524, 738359131, 574769868, 711170443, 851031980, 622968494, 107060124, 428321183, 383008988, 108046963, 155702247, 346796923, 425477307, 289183252, 83858516, 693108327, 338049480, 291354759, 926840637, 264331806, 247638840, 709693510, 61528290, 540471482, 600411176, 496214446, 471631529, 150618031, 26146757, 395433089, 30488383, 538040980, 188490583, 172917232, 492363139, 969414849, 877376098, 805622788, 857786302, 693553811, 454721266, 380823919, 936864664, 521417436, 817099431, 83994308, 794037729, 410387509, 415538000, 547169065, 174922433, 308760987, 800584536, 715484788, 92396494, 510453197, 466914542, 380202382, 232627891, 904021216, 392914645, 459194483, 221619536, 738861080, 465484182, 112619407, 932177943, 322219343, 996493891, 149029047, 168094788, 498564786, 387572621, 348032105, 716689041, 891765006, 785176825, 401745993, 467791237, 389426836, 669393483, 228682381, 869831738, 383777623, 516564436, 836264603, 490911319, 231280676, 532242812, 842891114, 485420862, 131845466, 752412750, 787614024, 428879296, 36724281, 650798023, 565148490, 430779543, 879868241, 705929309, 91315619, 849945863, 751934185, 887813480, 716265258, 369891931, 628224108, 731981161, 833257395, 668049480, 225286335, 229852277, 504159134, 872686830, 179997452, 512157155, 571303088, 336312895, 85488452, 62761163, 224651052, 993663680, 333462247, 134513630, 420070810, 155252560, 795545157, 657606076, 13213511, 587164424, 33672720, 42869946, 844791388, 38393002, 758911534, 445172099, 598565563, 2912290, 130478161, 765412407, 414574653, 919217810, 282853719, 400330435, 173444888, 871645025, 412502995, 153207118, 820402527, 115405257, 516951070, 40576533, 935044768, 992924440, 955570919, 659635194, 11849008, 644524476, 840479909, 6038268, 284219341, 365659998, 723999039, 623435260, 934051275, 754260566, 458048291, 872221568, 182691824, 31215432, 360710029, 413634254, 438969385, 304214637, 715802403, 882881991, 820453463, 913410412, 25350690, 290064757, 132713376, 665986753, 191175479, 990421936, 231946319, 690709282, 929079010, 238473147, 750528983, 491678603, 704267208, 996904975, 624685370, 773727037, 633674410, 127670947, 865994857, 935354569, 704544619, 748902320, 725017617, 469305965, 464871577, 245007341, 456000749, 243921110, 832487779, 731858314, 157581905, 806086790, 838756906, 792625209, 77400904, 619123997, 813340287, 95319352, 423960519, 375501275, 443182424, 561434924, 34228522, 257918834, 892553726, 817853411, 96708423, 838041044, 11698767, 934554488, 845650563, 477869568, 89180757, 838104911, 244158958, 378168357, 235354327, 975840491, 678283851, 206827798, 988189475, 913256752, 950552157, 520446674, 989827337, 941804601, 501162187, 68123887, 237274303, 792495263, 986644018, 137296193, 528772966, 901320430, 533795718, 590523934, 989135365, 184630240, 437351466, 717270996, 174770060, 387816217, 349942231, 398305247, 532968406, 610687026, 988686182, 413560228, 71210722, 561118314, 662974704, 307321905, 127311873, 140973770, 566134130, 101371515, 416511692, 972201311, 760524353, 648808917, 693308196, 942424426, 72478408, 21123753, 782686820, 775560363, 248722352, 698222891, 531064041, 833843459, 202432608, 686646068, 313352558, 631312360, 574710914, 882969952, 994842893, 282199936, 106172520, 827980900, 327820874, 19967781, 36264527, 623691481, 102581101, 453289507, 531463907, 722169713, 154937370, 505638202, 525560503, 533273062, 499216283, 143071770, 217654972, 789947860, 682664276, 792103564, 156381789, 287876115, 128017152, 595747923, 959554130, 640312418, 22652120, 976513617, 202121655, 601614498, 523061688, 165711862, 817224478, 638062292, 572229812, 71015846, 423876174, 457143249, 69109302, 483064632, 595054183, 697776098, 119447587, 104386391, 748328572, 817124090, 728328891, 946005106, 137125041, 689700710, 96364325, 839161084, 926896205, 822147869, 651577009, 161074377, 802827379, 319706037, 677389112, 155934601, 667593075, 714446594, 974735563, 713450743, 33303116, 241794912, 448556485, 784530550, 897586863, 821151668, 272129833, 447172912, 191216054, 126651671, 542743614, 211815963, 501183846, 738017866, 19604937, 502514391, 746671154, 846293207, 539573967, 786709481, 98031283, 775710818, 532147472, 189007013, 386004597, 674890311, 786576701, 429484566, 618747493, 360440275, 788818393, 909359296, 469307787, 949418679, 523870989, 656431972, 193267204, 433055332, 125313434, 802587301, 105013075, 589864472, 472322030, 432673156, 156259501, 634376262, 660464319, 109407525, 832055637, 255585342, 469849644, 781099796, 528831612, 457794331, 839365918, 501586252, 561739809, 79268546, 855962619, 352092882, 63647910, 476122092, 649642751, 228185366, 556211326, 219461134, 443882777, 293768986, 148695762, 282404945, 309226261, 265109181, 695232709, 365950269, 338719101, 84039131, 755988250, 335007221, 210668458, 411433759, 213092967, 538455438, 450814803, 341712855, 980587780, 907889067, 796923249, 485558346, 35227835, 615755893, 118302509, 226354367, 186213897, 394030218, 945229255, 797256189, 654550956, 913907289, 375358587, 825723506, 704092284, 474967210, 768909475, 326029759, 446157367, 871240791, 864489768, 34315278, 180211163, 918567848, 929989364, 456240139, 56316971, 811948329, 369246725, 121365874, 85278137, 634778135, 760374233, 968129975, 544781188, 768215872, 429796919, 927263012, 55203057, 417783040, 509828398, 293092707, 342517288, 500929136, 226332345, 170784419, 643826980, 654571103, 187786923, 275543438, 169791197, 636884170, 289063239, 492547118, 899220922, 304368987, 675622977, 58799988, 188126619, 819367499, 59734258, 115014796, 82858165, 826332855, 85751819, 724009120, 420881320, 564321918, 808140645, 556952431, 239171047, 259770322, 833465155, 633253778, 336030241, 662320109, 3221065, 475042185, 78047300, 870487772, 261710372, 639332353, 919745737, 35408777, 248590095, 549833040, 74786908, 290009215, 598063670, 877208762, 967065226, 575992209, 920274723, 879041701, 952030226, 460772433, 337498185, 457083644, 411888885, 382780817, 961889391, 987974374, 315631010, 489353618, 226883540, 366820470, 846699493, 642847099, 873902104, 471123748, 632159616, 183152407, 909924598, 544166251, 451529708, 194192174, 286731241, 854787588, 539141794, 300938201, 31963038, 700969263, 273356705, 293498539, 273914358, 722435061, 160677926, 481355490, 141771775, 768025700, 954559339, 953271571, 545713471, 828589433, 6224530, 795811226, 107174785, 897200947, 972007356, 208212359, 595229114, 34492761, 363504929, 610150362, 451152663, 409452973, 776079673, 372473959, 463090321, 398836389, 470996050, 832524921, 65450700, 168283684, 996195462, 452298840, 688156795, 32709952, 24748517, 21167942, 204081425, 679429093, 26442891, 287214782, 217680231, 873016386, 279283408, 322390232, 217045560, 722924468, 293345836, 18754427, 635567199, 789908590, 782755273, 704373123, 267156844, 131929445, 165768890, 435870174, 258738243, 570830007, 257339383, 690383364, 735971309, 668440972, 115816649, 681397934, 366206109, 106801578, 623445333, 925702482, 293328393, 506745495, 491209677, 661396433, 805858221, 729411752, 18102240, 935667426, 930089544, 100030624, 848038920, 214269147, 856730420, 860330251, 822816903, 774399033, 357633447, 63030740, 336198404, 360077845, 770230567, 13039615, 584108228, 62528494, 806993130, 535125131, 201864745, 38437338, 618320769, 628108504, 993652285, 935228346, 526559135, 99911100, 25379427, 787792215, 485008731, 536503010, 928083612, 913027844, 450946625, 562601385, 139859049, 421654676, 664766461, 671932705, 749479525, 375369202, 247437255, 101119732, 684784913, 69723127, 251759726, 819661666, 25611483, 6425277, 146668902, 169987185, 879309793, 766220456, 403014922, 437003965, 122281100, 383775935, 989356566, 386255518, 276418438, 240985552, 381363670, 188596075, 163327758, 215243089, 85191265, 555625466, 91586927, 208523340, 367563964, 331606848, 472530939, 255008366, 105595008, 240642142, 601947775, 344202156, 488390593, 97868832, 88884102, 708409400, 68344890, 206635038, 466156389, 290142786, 507351260, 162567873, 233905652, 949181437, 292311991, 92887598, 565145825, 12328234, 471378983, 84903853, 990035095, 636671971, 147700491, 863951859, 44683069, 291797555, 735061603, 682305062, 198529138, 437791035, 879637384, 100275225, 835116828, 610521686, 337051893, 389319237, 216905148, 331348139, 593625243, 919748745, 153423372, 578473788, 969188920, 886294877, 679575806, 770288304, 922166788, 676176483, 605366466, 141650162, 890687550, 643980768, 249934161, 909458790, 848329724, 302426453, 716733627, 770910080, 790052318, 281435357, 110130871, 512922063, 418277726, 420074603, 885280993, 385211309, 880250525, 973086495, 529635586, 997478945, 985474178, 50937041, 441522811, 741858179, 900589521, 163984401, 520926539, 224450969, 184923152, 383431046, 144351781, 175424179, 824025172, 873700944, 943923068, 164413477, 595684285, 411361477, 409371678, 731516776, 325409897, 173863195, 889011852, 106974074, 588575108, 306246991, 525876069, 100854231, 865998021, 421694468, 589486682, 387925890, 176933632, 381882656, 333800495, 99150795, 754470068, 521862367, 853583017, 629335097, 837262794, 493695246, 168826152, 552747557, 842333923, 10955555, 621977875, 709090405, 812325633, 509950986, 539596555, 689518276, 272658047, 116421634, 629130018, 814621969, 359751612, 962766136, 508103972, 166715451, 165304653, 680508795, 341284460, 664059955, 247574615, 519948762, 42610492, 171646825, 318794210, 795663572, 830139986, 634507675, 30772993, 513979756, 362477108, 44486925, 362339998, 975333700, 946101820, 450727207, 55890732, 28136320, 793818162, 455903476, 832442513, 411216333, 907624076, 977247839, 429522831, 877326859, 900520428, 992814663, 901045807, 733442889, 388514927, 599951793, 99558161, 629085561, 334285094, 41746752, 714099738, 361175720, 729138963, 342056075, 340260008, 853589513, 673133949, 448927161, 286331285, 791175573, 475120250, 586255968, 46459802, 187327216, 855747942, 548527795, 914317231, 136901869, 574108659, 307230967, 668948977, 317611480, 478763334, 466576070, 140358558, 678890764, 124005773, 339978604, 698457441, 981535144, 538903071, 439511035, 321941716, 207975530, 974780566, 949014583, 420904868, 360699473, 203865863, 181619968, 741724082, 151397980, 589495564, 420196724, 896655233, 37788940, 853423696, 400139342, 662358314, 344501703, 19313051, 908146088, 986763147, 907157195, 794508093, 987440237, 510750177, 227968038, 54451587, 383318704, 613424395, 356868083, 798312418, 217649715, 779214564, 180715888, 459948563, 98537255, 764559883, 244937243, 796207990, 877694465, 187680411, 86185946, 170708209, 106400297, 101758267, 780558654, 913987233, 623074015, 414695701, 274205155, 197937537, 478892300, 423593465, 741023439, 35376771, 595887615, 143377168, 627031506, 184663262, 344750727, 804285417, 973688333, 938187000, 143472812, 681075681, 176513811, 788821931, 430369487, 624488808, 449340649, 133442947, 120026367, 307409569, 15110808, 688104549, 620418540, 761310263, 324298562, 686010141, 587893031, 502399959, 827160100, 307539677, 344293292, 201063374, 86265720, 447278288, 667219218, 506586523, 581006289, 830610785, 363199539, 715011865, 355172051, 452901719, 845500332, 572349524, 233227249, 682981442, 101141797, 945585859, 759142260, 655460380, 646237978, 62014568, 542381864, 816885872, 82784420, 466213137, 407664543, 443173258, 963829475, 446854388, 944188137, 106711900, 781834988, 918145673, 842727398, 274422539, 152236406, 636243817, 124069009, 778908769, 851862522, 89514304, 504283870, 874401198, 249398585, 257973735, 881269862, 275009826, 235365588, 473670551, 30258159, 900004235, 690219360, 78287025, 916797612, 949398119, 986664378, 728627648, 188340392, 871103667, 540433963, 135888178, 968959608, 878793292, 697413502, 540662034, 120289793, 540027563, 310974804, 397773155, 758656092, 217452232, 359468994, 348696161, 242091041, 905123879, 545672593, 172430543, 398292631, 164015806, 328592482, 268815388, 469593578, 535993821, 18522775, 344783021, 722899591, 435025296, 164428945, 111029304, 611953709, 94222603, 928623888, 502628146, 541866638, 286471401, 112402837, 785896075, 180622259, 62911176, 459059139, 835737105, 630844898, 51865029, 167251013, 44729274, 637725417, 968448954, 490538625, 377479662, 781038494, 25660107, 283004427, 623705473, 44680414, 19777321, 890788622, 193709645, 272351792, 733545626, 629116475, 451374011, 599165764, 352664940, 62494127, 930521695, 434708175, 954662089, 713479269, 849848140, 413673108, 997639905, 38770391, 514070377, 559166306, 476575434, 129562129, 58433978, 747688928, 85247345, 516878220, 518268079, 454947910, 585023987, 185304275, 871149539, 994207687, 403923540, 137079792, 895505113, 531882398, 9154681, 371804183, 156694144, 762712051, 790784483, 200047014, 562603146, 39402117, 553598117, 853287858, 614680911, 929000063, 912196946, 659326934, 872596300, 108750028, 418661395, 791426798, 665665313, 38313888, 180332208, 878741756, 8118643, 530861006, 209450104, 621078342, 759178890, 294005767, 957703505, 381343304, 749198901, 535831500, 96513052, 865495569, 478889577, 826231665, 190883805, 81186632, 247807638, 468427089, 540840517, 861421380, 330943646, 957391092, 187501714, 639382606, 234906284, 978408659, 425394184, 8071744, 562127602, 592592867, 787485766, 714933642, 356568226, 7506140, 42403547, 549272538, 383149908, 327074780, 386141803, 144996770, 803134588, 766997687, 945777880, 42674510, 926367014, 373504334, 915599544, 38460597, 446445462, 792467873, 569617903, 38546781, 843922964, 635457246, 742550217, 731018534, 92117555, 673674202, 139653548, 66810205, 282113724, 315774958, 297766918, 858607934, 8504760, 206842332, 526450397, 752276360, 645974487, 99183736, 416974832, 810449471, 616582437, 669812473, 24552842, 98108049, 569386652, 246806476, 374751321, 611979279, 670461003, 703761855, 333650518, 421155558, 829199441, 614530607, 985247950, 241285062, 400761415, 934223657, 839306225, 759161635, 978247007, 770735143, 670969738, 653699922, 16664194, 442566609, 667536906, 476536969, 351853371, 185982584, 839689475, 939927980, 270006536, 132924170, 516273975, 335284117, 214627787, 97662169, 313546430, 314665095, 197551793, 680540718, 573897521, 70344387, 525706098, 827902601, 624036471, 383907933, 364991988, 630890904, 954592846, 453729640, 339496826, 538862767, 944908617, 202139603, 440539376, 467662899, 213082828, 356150121, 695309905, 88091267, 693004209, 641630206, 315622923, 651941461, 638168548, 663022326, 835338642, 699654436, 805325609, 322453894, 864187717, 717884130, 903810129, 523936908, 764116872, 904572820, 739365368, 98670736, 479056072, 568605872, 159933152, 628092432, 964121435, 971690800, 436749224, 26428634, 50718733, 617714589, 77779308, 173058146, 187694340, 904493570, 262091440, 104246361, 32415915, 362890376, 95100880, 563052197, 930563670, 220230810, 383454239, 95494752, 553042284, 883739285, 952981538, 520223399, 252374125, 528567522, 466435947, 514359509, 950061486, 446626983, 7089685, 532575016, 809167840, 75318249, 919363086, 813739209, 896314756, 36823111, 114254456, 915853945, 407758907, 143782043, 793426357, 535363257, 337797094, 454876306, 214434596, 789065420, 670971464, 213638622, 874292602, 702292668, 671688023, 690672453, 840361284, 736295080, 864147838, 501265971, 18956078, 479263395, 208228205, 370710365, 575375738, 162914563, 698072055, 512977843, 16976227, 390690955, 785716542, 1140312, 976035546, 941144837, 168644833, 901269567, 991997187, 210672986, 633230536, 553018208, 510682767, 760250034, 952132588, 377776054, 615384332, 192461022, 412503446, 257333794, 293162977, 541897873, 665777401, 665111888, 671790569, 364144796, 967421168, 512118546, 483785832, 683623789, 843443030, 948189737, 639776275, 63985105, 691713312, 805200323, 386134395, 912739240, 673166364, 110541520, 242270560, 955202082, 436227462, 277625266, 959148158, 586149252, 958576913, 235164190, 224157792, 440243691, 76621364, 12479290, 664815559, 813266023, 694483564, 722444986, 689911403, 708481260, 96192064, 892432256, 196852793, 759960740, 497734439, 122902177, 361185801, 612879452, 237985314, 257119292, 857924927, 116144304, 468818202, 618560287, 406066790, 324294636, 818173397, 408144715, 551973393, 418631114, 282270075, 944706957, 692688623, 177335195, 967050179, 13683178, 289139002, 757153818, 6191609, 316980614, 134070139, 281514265, 463841842, 461764110, 162336797, 160424569, 892466450, 937025911, 271552615, 153192150, 709055503, 992166486, 53676242, 475922941, 334821416, 408172256, 482326707, 510543603, 215409406, 136113689, 276686878, 747258617, 63128999, 513201025, 611357914, 44650280, 546177989, 900930584, 111141125, 241706621, 24069621, 2033949, 670333178, 339387875, 276895464, 219557013, 377886559, 35636058, 138684085, 977759263, 276055927, 83146771, 181466577, 586615151, 508757819, 838960644, 848897799, 987429562, 814816063, 434775108, 486805627, 901642078, 837434682, 568834165, 564085526, 441904833, 574163056, 42795809, 295861173, 65315763, 836939794, 574619030, 836081181, 883614369, 452107193, 216452633, 368084015, 65655811, 77580935, 460980448, 238808856, 125873097, 118861280, 5374756, 420768156, 975306034, 658076922, 698581433, 20305148, 921202839, 417255187, 712371769, 475753926, 607016659, 208957309, 461972270, 890146165, 310669128, 476203270, 848134778, 875165059, 269551972, 527872355, 16944336, 497556689, 338989073, 632217660, 850476997, 617793137, 145872261, 167497040, 507605611, 823572637, 951023632, 93089555, 132862169, 862981744, 433094440, 940735622, 129493824, 208324422, 136659048, 203543412, 466418025, 691690535, 405250325, 298304940, 527772023, 37125900, 149231270, 60986733, 171685200, 180023381, 907899765, 835975113, 223677287, 726731769, 964098419, 609912187, 392356318, 87427754, 101071322, 629025163, 117885245, 590708906, 328847949, 520128908, 404442726, 580388479, 911463296, 922856533, 533179046, 501365064, 353875685, 492155311, 912724262, 548039836, 842602983, 737568717, 318130294, 303274840, 992725316, 843051108, 54034634, 923979487, 705765036, 811910350, 840600724, 384252941, 166685811, 909197781, 99112191, 127799424, 742592856, 968024089, 736939479, 543322669, 48855888, 788295398, 427431347, 677555701, 923504210, 537060550, 523211122, 23985247, 586458655, 457254066, 893372943, 700152132, 739531166, 45904730, 54123127, 916042722, 851586820, 465659068, 651146116, 534482593, 260926820, 61781956, 490872389, 577487034, 690717759, 229966902, 398884109, 195886757, 255929502, 156589692, 554653070, 304979878, 299143461, 351696910, 767854318, 552596379, 184467030, 492612881, 278815150, 305206799, 105331684, 653418189, 425444827, 340857074, 281243931, 17082301, 158856171, 780445885, 211160686, 595998461, 881942570, 475933886, 241079928, 20886539, 719278216, 614395983, 648341394, 105345861, 794616121, 994205952, 627897545, 50714456, 11965472, 635051662, 905677612, 616061332, 685429660, 543742574, 84319467, 843021551, 562636008, 478239558, 680931897, 457088943, 462254530, 515157094, 863729039, 495653364, 571039049, 82166414, 531458589, 574053918, 545711741, 30922289, 584448998, 659040254, 849334987, 65042771, 782094846, 342440402, 884464429, 342285886, 579646744, 573548, 840240468, 483498672, 653327427, 909488454, 281871374, 726238845, 553011301, 40041876, 747339987, 623895369, 839263852, 739124955, 728871220, 162114481, 808463245, 603308853, 953174982, 932393623, 933011718, 733573949, 336238011, 392324076, 42984483, 205887927, 243788112, 920585637, 472842536, 399308536, 193325325, 795694951, 577035047, 31185985, 32271103, 478018371, 46235443, 161188091, 252710958, 471606155, 852988790, 856164213, 261632795, 177719305, 38338399, 402509637, 969367904, 834152735, 66694088, 546490370, 344340916, 229996729, 703345365, 271238189, 277604501, 169508644, 18697593, 589639073, 842795914, 375838048, 488071695, 356906642, 797068447, 872696346, 19640488, 39656132, 524499898, 286562376, 530138833, 529519019, 256246978, 224171753, 982741754, 454414383, 325929538, 673361040, 266768340, 708998031, 144669929, 412628731, 925184897, 145692923, 441679527, 491457425, 821293285, 682553585, 102687487, 746211770, 911746071, 446314495, 457154232, 37660008, 142541984, 745214008, 479041666, 559696863, 649801948, 263553218, 42953594, 737391787, 569498224, 964599086, 197502025, 747794014, 175506564, 903799602, 240075777, 924005182, 617410682, 365958374, 277437243, 618184396, 34732255, 271938477, 423939921, 387219346, 621680439, 580886712, 863603961, 511837627, 215987410, 175649319, 200132118, 161594754, 170496207, 171771615, 348042998, 537227810, 496357969, 488138289, 499987947, 711519082, 464232646, 334479001, 424989750, 839975949, 154638457, 151000242, 213847755, 711292058, 567393877, 965126624, 702781156, 611197870, 567112308, 216116951, 687876461, 186847750, 608520166, 700112587, 112003489, 975948010, 357297650, 747573730, 917270048, 577302003, 597468686, 463023648, 407317915, 581654034, 295641574, 670352699, 673551745, 644542313, 97137504, 105715704, 7693737, 196685331, 503375863, 678269729, 92594379, 188110722, 358741325, 562616795, 469312313, 170455130, 502918511, 895156619, 387657986, 216233607, 133908502, 59238313, 629517666, 513620799, 147090546, 578827177, 526231196, 538818330, 115071375, 857558531, 742149129, 208987557, 238588524, 775588797, 561048920, 334022514, 231341338, 964361740, 932787923, 763845565, 532658257, 809376300, 495047226, 394564424, 849976505, 32697161, 55549731, 958606132, 689295682, 942001834, 671187135, 754144122, 529984238, 924818941, 141537498, 60962682, 828858889, 920549848, 830772301, 804445022, 339107343, 627845244, 317197895, 911362864, 772952749, 543326850, 520732558, 504690170, 492071011, 500099313, 949506150, 716084397, 571456853, 407985680, 899431821, 166646875, 693431229, 53106786, 894538489, 159077133, 293224366, 204198544, 694637751, 1782490, 798981851, 904317996, 877305846, 170337790, 376369792, 300833231, 139668557, 543989833, 644479249, 622258788, 450692951, 201791495, 425666955, 964809189, 526014855, 333061178, 702838638, 627192765, 181541954, 964147496, 893024696, 282837237, 602216867, 453529401, 416565624, 899943478, 974728421, 55784462, 516269, 92364448, 981639016, 373044212, 540319200, 952305647, 523850372, 419411939, 615938190, 200855434, 192274936, 133846781, 669240518, 287422916, 255991470, 675878484, 938831191, 777594139, 332841653, 321480413, 387053759, 169525154, 275165268, 879573694, 758431066, 923311498, 907602165, 97130602, 288693361, 362125318, 927889343, 855880360, 606420109, 421292364, 393121946, 615802713, 187475516, 107457080, 713183189, 865111159, 49985581, 486816259, 628477652, 280906954, 781860409, 364200085, 465442321, 545075984, 543886619, 803333491, 794656290, 641553340, 163638674, 15844931, 582695550, 57792730, 124325857, 180896528, 289595703, 378937261, 526247606, 323766544, 827784888, 885482976, 596474681, 619235220, 206389786, 217080550, 841124191, 392138867, 719742449, 729242435, 558621658, 152686207, 536975793, 277647347, 738104266, 912966635, 225058960, 721867639, 944739152, 54371179, 109774262, 544427514, 748665679, 16676391, 876439945, 238200118, 38086185, 578168449, 887047362, 909454392, 857278239, 171298684, 882094671, 249178401, 727106370, 42281941, 700811582, 70804240, 892137899, 262409521, 314250149, 164516856, 231707145, 403322444, 26578977, 137281825, 710481198, 909342558, 843242938, 241916189, 941928915, 515459071, 296660300, 274893369, 215652305, 517864806, 248196426, 73051430, 387513344, 192709819, 999038705, 444988370, 315056214, 779020211, 574234783, 801549459, 571614345, 203810805, 22067865, 357176261, 51624199, 475314386, 492934588, 312387109, 956069660, 167191543, 814221837, 428181676, 813813641, 692700998, 885146730, 497477584, 771209185, 769672053, 943640467, 422049880, 8166387, 144071157, 712122089, 428134652, 996682950, 610295392, 11449564, 229463642, 298071971, 794035438, 325145849, 934274942, 429581097, 765500374, 447460691, 652062385, 862651925, 66587892, 51366049, 996194151, 829909227, 397870340, 508703487, 383967602, 705202767, 51719691, 849443271, 256734599, 593418845, 358167646, 710844184, 633935131, 821295524, 660473185, 191154226, 705583180, 649952674, 643409099, 547203014, 38597166, 544488564, 504138314, 416271498, 252795865, 312901648, 575774107, 3828794, 424850128, 72997672, 8532913, 435995251, 863730491, 883224721, 95296476, 877631371, 350355084, 994140496, 642757524, 755526044, 973436934, 825138204, 532493786, 854111739, 770310875, 329004771, 131352650, 28032416, 24482178, 697723310, 535289716, 798465988, 967346905, 388813747, 770880011, 490224355, 281919516, 982981851, 244024512, 872097397, 519448605, 128916359, 339114384, 487550442, 638124281, 854674609, 76041989, 781279832, 519218702, 232662812, 388837678, 135439941, 87092666, 767282990, 97651678, 766136790, 987342206, 165716370, 574048967, 173267713, 137638958, 169862899, 598415538, 953703835, 55201691, 437912217, 811661738, 290159340, 71243031, 19811541, 422869858, 158739031, 699551385, 674563661, 872473268, 578339553, 774058843, 822267218, 135691519, 863981553, 570123713, 754411196, 979632395, 658378112, 302960373, 540511194, 23743763, 853054676, 23316229, 85494958, 337371784, 3303379, 380211156, 879633311, 252240431, 198324599, 804349313, 579772152, 933920955, 701666603, 896146672, 742193299, 721317928, 980950804, 942190731, 619435573, 951464379, 683002249, 66397949, 964800454, 255491445, 251481889, 72926474, 401990749, 16147204, 128664366, 968448338, 892994461, 685120593, 888586694, 828615719, 771986912, 699931807, 130223076, 205345656, 486492247, 793068177, 744887115, 23373833, 521609900, 630283475, 239381219, 148945759, 652553768, 384695381, 76410096, 439613585, 116293204, 893097062, 671797526, 559692730, 106118216, 253208749, 840787382, 584324576, 109882531, 744772066, 965821295, 958125497, 639765378, 854252127, 353767454, 71154219, 261001628, 445668931, 471849882, 947075382, 161131719, 911457694, 373776233, 527385614, 890618779, 998729426, 388088769, 616213365, 91827479, 573292220, 320891800, 57214091, 693135527, 642022667, 682907114, 444462650, 271748110, 703625472, 986512877, 141574511, 310019269, 404500548, 491405546, 830657411, 192762859, 473380276, 334468282, 176477825, 616041326, 251692895, 897327486, 475849746, 286184737, 358869759, 916311503, 372214435, 241067600, 420974256, 992024710, 669125802, 887301199, 386324526, 207312838, 689587193, 219795312, 644637052, 442063803, 487298461, 803385223, 942058159, 264462202, 983546900, 811673194, 830995380, 273268101, 182185290, 586669378, 425076991, 556480783, 787907006, 884882496, 577674966, 992467307, 620558966, 797232951, 980439686, 117525297, 657604150, 642535044, 412360169, 126747265, 879047479, 402619496, 336117928, 581552705, 497351069, 911702844, 2057658, 811829527, 93137978, 67749751, 220579101, 289819696, 73414553, 616104959, 707151512, 297486800, 711676927, 108720652, 824695548, 112213701, 208346433, 172914732, 287709512, 705616061, 228055102, 115850219, 13017878, 413622925, 740842844, 858234122, 25535891, 393419522, 904678570, 859820259, 673762245, 643463919, 699414796, 294540779, 374113268, 194912514, 533740615, 996836580, 204595742, 104878149, 550127469, 201312643, 653615212, 748673664, 612185639, 262811721, 872364838, 499119915, 338827429, 42528237, 51082089, 642407015, 898466798, 799628134, 44828523, 304267310, 195325482, 558471436, 735475066, 271280981, 393052951, 131948653, 932597088, 923122865, 183950556, 312460212, 415438966, 710646663, 615462543, 852232865, 596950847, 531925377, 967926728, 612521585, 410498078, 198622289, 732196545, 960479074, 70825295, 278701530, 15118102, 336209173, 672949353, 225636065, 933061244, 185006178, 470786479, 651861298, 453237366, 535894388, 190609735, 618151090, 941483477, 802408310, 666293154, 986697604, 167555482, 756175351, 783016410, 334619546, 298303083, 389034042, 510813425, 102372837, 372050496, 268346617, 888684233, 511466864, 330723533, 801940023, 852913957, 927784526, 922572004, 897457993, 101886103, 781331239, 435734887, 191261161, 781282816, 126213642, 795692605, 782173337, 479625132, 367749463, 291398424, 725330704, 324911728, 467392326, 652057351, 912142883, 388637314, 184344520, 325234170, 212443695, 225289743, 211261276, 835598193, 194576367, 431073784, 266996321, 119113863, 680028321, 17442043, 450484345, 467278657, 875772739, 930217166, 810984637, 697545879, 333373148, 104037288, 147396570, 61311230, 594174106, 45928872, 562078999, 435621310, 683594762, 254564888, 187688010, 197855843, 20285429, 906985481, 373368102, 759471660, 558168297, 622805208, 454430905, 469509557, 285887140, 408723396, 726628940, 103133008, 102539582, 697333038, 102151737, 125118053, 992363783, 846367604, 143105301, 430129285, 997708497, 114319657, 492057562, 611935769, 59847535, 456535574, 930408220, 974310721, 501125541, 964000378, 512448382, 626981387, 260128946, 797629713, 361622266, 5909026, 999422221, 576215674, 671149426, 724280309, 340075159, 932902623, 901092639, 897853181, 760468043, 875553241, 736281344, 946174836, 65130418, 300636388, 478019324, 589556362, 168001393, 899983754, 243924386, 946117138, 246899459, 389813433, 145502041, 97252856, 271190419, 42453092, 793702207, 688388228, 461877404, 793153865, 480702996, 262150883, 286061157, 44546660, 232057617, 146494907, 412034503, 292867368, 427469926, 762515305, 932982320, 259014176, 19980860, 973583021, 842042647, 471403714, 483438583, 920460190, 142721205, 944425681, 991391971, 791171386, 310874482, 533414448, 703941988, 634262878, 305748229, 970753216, 45447909, 33064018, 550923388, 590054924, 222036896, 292568785, 985020589, 470678552, 299062560, 111887459, 941437539, 950992385, 42412256, 168488631, 386549325, 743043916, 31635899, 963461494, 242111356, 871667535, 40049816, 478206881, 239556250, 797117073, 659780339, 568611719, 828498817, 857696017, 305049086, 409797324, 361929037, 153920519, 877877485, 759933952, 672972217, 505841239, 47294425, 89185316, 566634188, 812434890, 653246171, 712292314, 690815767, 808225669, 170977580, 868025440, 304461191, 648881388, 792483224, 606430274, 199946391, 317309123, 519327574, 585272936, 187354928, 337691462, 551010841, 940320937, 208673977, 126939957, 135138938, 567096644, 633221472, 721605616, 93906439, 875348163, 562306156, 774306611, 405609305, 216433975, 584333463, 237597000, 103716686, 207111498, 797964130, 606803935, 561925061, 736154123, 43072834, 635777801, 261911303, 563553923, 2743470, 708475215, 418113744, 266429444, 265724394, 152695767, 708774127, 638030237, 679561514, 405432359, 293833668, 138977136, 398893572, 985549285, 194245117, 700946080, 723926972, 46284155, 598679148, 2476156, 754462969, 30549998, 187116440, 174159601, 620008630, 240015176, 16044992, 710672239, 683615516, 283391334, 928225611, 896353220, 583963438, 302766567, 612320608, 470834019, 699990358, 141066015, 717993424, 939098960, 529261407, 795615926, 510263051, 820930451, 810634249, 739913747, 673556647, 502064056, 690603371, 156936260, 922879980, 432958771, 433141733, 105360318, 22337468, 692644007, 555819134, 47139922, 98422979, 414329170, 282302501, 123449688, 641172423, 101323749, 542821350, 64922671, 904065950, 442703928, 790223573, 115124191, 459027780, 52023842, 432861497, 347267220, 871748824, 26345040, 588357627, 27942653, 683870853, 855766141, 580297318, 373175417, 750028534, 603873982, 976672331, 938914081, 45632328, 528987096, 309572911, 733902097, 25594077, 347844683, 834127886, 640125677, 749385982, 296511792, 284349641, 472062449, 856180710, 98249532, 914702275, 174400365, 277590703, 469579240, 178875769, 795962270, 975584957, 430226765, 40507460, 29143593, 60730283, 1299511, 628474795, 447288855, 465329193, 122615316, 386072876, 923298507, 190658909, 13119769, 888490648, 257556540, 561341958, 339394710, 295753954, 118485507, 202387935, 690807430, 969804689, 558138098, 176688191, 767937348, 918612975, 921183393, 913051011, 786791575, 990585885, 603824399, 132073529, 339658124, 564826620, 984122679, 470971076, 649293664, 864579736, 5093252, 720418591, 265465508, 120628545, 774313336, 396087171, 318857761, 813188721, 45179827, 687577319, 89998955, 58574170, 774875214, 739263246, 29384005, 37702632, 58537191, 107620223, 639264915, 281312964, 909458555, 947241030, 748937888, 175857638, 176427891, 110304581, 180301058, 3661706, 33639313, 84524157, 396614043, 91970406, 432746632, 617107160, 882939726, 622212814, 970011713, 782416966, 597698336, 567423121, 405914026, 862770284, 390125804, 973966271, 309845983, 254203688, 441590872, 963165537, 748116026, 507366211, 99656805, 427548474, 290329375, 576179823, 378502933, 612246305, 397197886, 127842377, 177988780, 177507337, 185825839, 121744503, 832622252, 904950004, 565038994, 41467535, 283225272, 160553908, 384274043, 933122299, 810965893, 606910257, 489262321, 729258533, 123754693, 538230679, 134769669, 545270361, 455715563, 896887510, 192683218, 767688662, 636466895, 891390597, 63379606, 493509559, 36140688, 336546093, 401483149, 106730693, 440030626, 701725941, 890903593, 344852305, 991021987, 420316086, 513578355, 424637310, 982385452, 140035148, 632786899, 179327061, 864825647, 186672638, 773575214, 930524785, 252908514, 516572888, 649008976, 235188047, 177859665, 67103358, 389556595, 975020481, 410671543, 119903504, 455270180, 59672004, 799464605, 281870832, 28302160, 855967333, 342796966, 170854259, 261109786, 685818346, 732898664, 690516263, 868175314, 596310147, 913242241, 854232764, 134069343, 727604274, 202908183, 446392695, 19606332, 846306897, 465972730, 892902621, 161656885, 527664776, 395935107, 182115395, 871903073, 231094142, 486318713, 821001808, 838195046, 834823059, 217004377, 924106551, 989063820, 768968652, 606096321, 146175990, 614461446, 792471439, 870600162, 756806650, 384666549, 512794389, 418691417, 306837201, 76286206, 701789843, 767408172, 411864588, 730582386, 412787719, 497469416, 697515168, 595095072, 416537109, 469458676, 385469531, 695487626, 377557857, 891705906, 970962357, 341929442, 642202624, 567891479, 431108097, 593678314, 917889312, 705953653, 382129331, 547039650, 35017396, 814175751, 295723452, 613616995, 20099072, 574186044, 170487707, 984972517, 488343722, 940824309, 492591919, 209445780, 413737042, 597107403, 34752340, 877976842, 730171682, 184852249, 820098056, 337951794, 131254735, 802740879, 439948946, 523005955, 288401562, 428691835, 200954461, 25827851, 526115199, 391665759, 197785840, 424821590, 546009823, 724127312, 113823477, 788940310, 330958005, 283516308, 102242832, 636516458, 463602609, 345554800, 109281356, 277204845, 461322007, 787979587, 679689355, 952493533, 882292877, 955139649, 29529529, 567783705, 717792082, 300802428, 919410685, 366629501, 331111067, 509399791, 815963447, 599467467, 878893565, 419423586, 471358511, 237504256, 819450587, 153136994, 916585026, 453448725, 780363409, 902060263, 753605562, 882142201, 180183209, 233212869, 755392259, 754405153, 787496825, 75789668, 86828644, 925711873, 198304261, 631189285, 202737017, 581323839, 314289139, 8190635, 362488030, 981011289, 561221671, 146569183, 749517803, 300398388, 649406309, 870736762, 139809449, 725368630, 41218295, 168306679, 217806732, 733359658, 38321435, 219408894, 773653719, 343162300, 138846111, 523979643, 771173464, 288562185, 463108743, 776060174, 731563636, 968532695, 303541014, 996176357, 511658734, 12388040, 497463648, 673837929, 270458666, 987639300, 3189899, 601567436, 506409190, 484397217, 59262287, 576643563, 595162455, 249889979, 185105863, 312026612, 675098123, 53914180, 77017127, 649144729, 564024223, 975088830, 670669143, 284913492, 680514905, 470411125, 121706766, 248666714, 416157673, 719805490, 266640447, 9142116, 471879490, 433225354, 768203371, 106906336, 95002365, 915692307, 182623884, 122999673, 850067910, 588975298, 562663716, 381679088, 318782017, 980636706, 344852410, 294544256, 749992337, 47947646, 567838636, 159758838, 325507522, 13727067, 84847987, 802830161, 980431195, 389263239, 228414775, 106026058, 979527013, 741236442, 242089696, 293280297, 111329394, 957440228, 431939072, 688756619, 338330305, 358807818, 739951106, 920145848, 800071443, 446797790, 856931945, 930703346, 651895374, 691955141, 15353968, 568131368, 82116936, 568034940, 449591222, 790583271, 868405479, 447946956, 637593212, 4013086, 380484775, 858868169, 656647641, 550119671, 489856533, 802014694, 600495273, 813058922, 843527285, 288142472, 750286132, 810334536, 145025198, 796644276, 132330164, 621451686, 55041365, 121840625, 942700715, 324853889, 759068246, 500930641, 579526824, 526176032, 976256307, 911675065, 680466653, 698406177, 107313220, 460714315, 482544776, 563034282, 625815097, 355570502, 13418757, 240018175, 627251813, 871476826, 531020103, 839340558, 369871222, 970316765, 2236561, 721965137, 589809684, 778062565, 443280537, 475583499, 509039217, 43985312, 114956511, 596656795, 331526489, 2366185, 283163991, 897992156, 78210158, 625085925, 768980660, 567786546, 792170691, 709386877, 698003959, 567176221, 668051681, 900821921, 383802451, 470576833, 392244288, 265876872, 10841287, 671261813, 48743517, 799882228, 204731129, 885433590, 490002786, 156047812, 311460050, 309670284, 928783811, 206122353, 170302832, 659466240, 957262431, 961188298, 402878680, 632465474, 715240529, 364562883, 84310006, 903919629, 464845867, 369877798, 151434961, 483594500, 545947299, 629165037, 544185109, 246318437, 661583067, 438334121, 38558059, 761458875, 710009127, 739121255, 357455242, 882979048, 642198287, 410674759, 815635675, 495148606, 745945399, 605386386, 724496245, 924778150, 336825138, 364141636, 817823474, 39482370, 59276128, 935253335, 980117934, 659324746, 56393104, 234622397, 826091158, 757363322, 796753552, 726709478, 936960829, 955100955, 684136815, 135144330, 352822050, 28763099, 179585272, 407092721, 351416276, 478117318, 66250121, 259570192, 768019885, 796875393, 974014516, 876424606, 986015940, 847062398, 958197005, 755523137, 211105823, 671074569, 276942736, 566496471, 693004857, 946339808, 153413776, 246413837, 362829435, 15041915, 136912476, 385168602, 48259886, 944356214, 753616685, 903438269, 219865223, 337133761, 644404767, 514856961, 379089831, 349820651, 286310283, 539325945, 328532268, 23584006, 283676605, 156674674, 18452770, 366167387, 628369239, 331644284, 813881022, 164060800, 249257716, 694580592, 89785337, 117350824, 486395368, 398161964, 822630353, 797168393, 797913789, 344421667, 182004253, 507167506, 442667278, 992312313, 112139967, 620625210, 698427418, 720770876, 760800951, 419296669, 502479415, 659959438, 517332183, 627717357, 857331941, 774574070, 276690402, 568068206, 643371068, 984177122, 743945614, 789281903, 69683635, 579208539, 862603053, 881819135, 762424201, 133161271, 560261428, 744537248, 637067597, 641268417, 646781334, 543275334, 193559960, 779872263, 477597649, 224878155, 339153109, 114979427, 31341505, 705028754, 906476107, 158822327, 980285697, 132563926, 136985099, 315426872, 381862479, 194791527, 956782923, 888128329, 679110085, 282542795, 633208856, 341316673, 382715105, 794250114, 429568544, 164496257, 258232919, 195789832, 867640229, 917772949, 243596237, 861442884, 223432920, 754117646, 233704458, 358774681, 432659212, 663138747, 770072067, 93392192, 905577846, 889053919, 517024047, 287468451, 471198888, 259203476, 159380811, 788718226, 289323682, 120228767, 423891804, 5642756, 922182092, 96796750, 664861962, 313204607, 600185832, 85141697, 886365782, 619314977, 712370399, 531402261, 657510674, 451988200, 909710802, 24408463, 628996106, 776658265, 116173753, 652168710, 763221739, 16369198, 660952623, 606465063, 272738169, 920042100, 691876796, 967947104, 375388792, 612724912, 252822037, 400165568, 335508669, 241429745, 517623771, 132138225, 60014406, 370722653, 33279050, 539978266, 72263316, 213857752, 244549587, 506392811, 977376664, 553879949, 257570238, 130152211, 872765227, 148783439, 740072107, 839018867, 221329179, 169196146, 568973677, 256589502, 220651505, 939608334, 490133986, 208674268, 687055310, 101461074, 494015970, 478374743, 173889792, 443162338, 624587032, 558398316, 430105946, 119898962, 716937587, 198902422, 641657050, 738596308, 123257045, 108574887, 990769445, 588655333, 884604777, 393026293, 561932388, 924032586, 38038165, 397185332, 974349070, 937804937, 674357147, 760654994, 272726656, 911981376, 645210756, 904117268, 149188059, 305767238, 477815004, 530821867, 248209800, 683207566, 202277902, 461605704, 201734322, 855836681, 86940338, 747128455, 133750794, 729313337, 692560018, 399395014, 601323983, 805422151, 825647617, 986077074, 724721228, 886983003, 854647188, 137088128, 236190729, 895368532, 297310414, 386012943, 987053550, 395793650, 353844264, 373967426, 368374563, 40320203, 1304478, 576583576, 389531050, 399157187, 562093966, 139346053, 148720983, 897408406, 105539702, 302518414, 832069887, 277105501, 198393604, 399867682, 424770034, 609161390, 960161291, 953893576, 369878778, 116481174, 114046612, 702221785, 13385542, 704047417, 314961564, 980653684, 596066018, 246020963, 887958120, 568540022, 405565996, 859348351, 435337214, 346737490, 809013045, 811179794, 2617195, 72586131, 499834418, 321449248, 141509095, 537779268, 463581592, 910656117, 998462647, 996351965, 592594978, 160664796, 544533809, 276446784, 462802892, 433054989, 724898840, 85692447, 729260681, 409961628, 746895365, 450446789, 881040567, 722613851, 630386019, 94039585, 944891207, 398130030, 682995567, 367817146, 792781949, 102273830, 539312204, 331371368, 172835541, 883077955, 763020047, 784385023, 412193453, 297501645, 66282355, 358942021, 659153754, 921888506, 522455872, 548405040, 541662524, 836511894, 893644161, 142310550, 813118791, 456081713, 577134183, 467631175, 102154198, 124586569, 193726182, 924330731, 143138720, 446505563, 265306237, 131294605, 424474886, 589379471, 948645380, 469169534, 784306614, 156813266, 763730026, 857065413, 159485511, 433576361, 381750993, 398522565, 448390460, 543278364, 611869209, 227905191, 794125499, 359938849, 164661786, 716607737, 655446089, 713273694, 130143360, 488653297, 38558440, 616876776, 486240021, 506973866, 143376539, 476507647, 577934922, 544776470, 364712218, 714421114, 252529012, 948550585, 413634152, 985626729, 909929633, 814558983, 287151392, 124706403, 782858808, 66785087, 630675230, 217565655, 365073851, 263536845, 941372026, 196945967, 335312844, 561238101, 10207063, 301416583, 639644426, 709203664, 677388652, 118826182, 469784456, 953511360, 812637751, 403262451, 284887214, 324508775, 476667689, 417698125, 289272662, 937532146, 119397016, 171505574, 79945350, 937430742, 158299929, 252702951, 282839320, 32513954, 271329808, 618673645, 826648750, 560798105, 82865562, 629396901, 789109241, 690062332, 507366224, 417375135, 238346833, 552338806, 612464454, 834871501, 947409330, 450478343, 453619157, 255511334, 872962656, 649020174, 216851134, 902575043, 151898934, 962647908, 281274393, 94049845, 990359823, 548348429, 967816935, 204398871, 425481996, 162202705, 405722122, 953376929, 806652644, 913697044, 752590217, 802476744, 668091182, 341815893, 646651686, 76489449, 559977031, 752409332, 988194224, 771846726, 290027817, 3782019, 697895763, 306289108, 713005926, 415750382, 811540103, 1171407, 682739375, 458361602, 114666538, 454027964, 380401073, 727479619, 355551937, 865299354, 661395338, 413675003, 261301252, 537080286, 617168246, 282139395, 828024664, 794002470, 550946954, 995994251, 360206226, 209947941, 542394122, 328651734, 865261275, 630487368, 539068343, 508372767, 598901797, 40341750, 133931993, 754526374, 781145615, 381562603, 76559505, 85655586, 59058562, 646792669, 175931740, 210458636, 600754749, 704250034, 131062778, 972073767, 869888901, 957436749, 484864151, 577429563, 533728949, 169626743, 753793696, 532601608, 356187773, 810938869, 465707150, 150205581, 485820466, 780802277, 212492666, 956883304, 170512998, 867751977, 54339086, 293186518, 204416850, 953119079, 478278168, 687287622, 714948996, 928832814, 10438071, 647913500, 172177082, 156829242, 627650401, 39560196, 473345998, 496565862, 957310889, 733170016, 251044400, 623399045, 215767644, 761253428, 69193187, 456318677, 562776235, 175716916, 572481624, 104479390, 499699595, 188588151, 451702022, 806443970, 921385339, 328803284, 934677442, 364213209, 638239725, 669351828, 281122124, 526646052, 866488167, 604666657, 488802036, 630292935, 214927688, 837071940, 141538293, 843556781, 92078948, 654786466, 630701352, 224122555, 647063046, 312941802, 174748163, 540404840, 988584405, 618493780, 236447486, 319638949, 376789905, 683695868, 107598582, 690992557, 384663682, 750658989, 355604451, 611953574, 979598008, 441611218, 549236603, 591668355, 576280797, 475665659, 592672758, 822081013, 852153879, 851267606, 810810894, 286985531, 457437970, 751654650, 735968375, 856134031, 185864122, 62601430, 907281458, 593516140, 167388163, 89107395, 640699799, 535847812, 13452641, 154372161, 146226393, 369492725, 710231427, 235635757, 441060837, 704044591, 951301822, 267689437, 695941550, 81858075, 825406743, 737687142, 875980513, 816835828, 72143987, 273058407, 47697397, 291384580, 124238055, 948872597, 312833850, 725456692, 290012009, 682647339, 264699913, 562895877, 124241422, 59071704, 928558413, 691477889, 118448918, 43867023, 414816189, 442303356, 358842866, 411528257, 50053583, 288412163, 234320422, 237941954, 397234704, 732138091, 472236888, 976425300, 831639818, 162906638, 843496770, 45372721, 773128196, 270885460, 602417894, 47648092, 293225047, 481059680, 285875474, 597541793, 494291542, 764755697, 83064005, 112054153, 987193011, 132082062, 240976881, 898685079, 745500620, 840604468, 171502537, 652232130, 536733612, 484798212, 2715582, 180648307, 264845704, 550546249, 966566812, 418838020, 330703437, 610637438, 924603572, 108400776, 996184690, 525246776, 106211954, 431705163, 60011429, 471146335, 629933227, 654629850, 609687984, 176221788, 511820880, 240815206, 216383711, 857705798, 285959480, 526789216, 579165555, 524358478, 912079186, 627467217, 186255826, 721580186, 612012797, 568460333, 446756535, 714277801, 988735675, 953327170, 618170835, 915666464, 235858580, 944371284, 812337510, 567323261, 977353318, 871551360, 777781355, 608865313, 733520311, 645613730, 609983317, 946938827, 414731933, 17823345, 488424910, 683493248, 283082785, 960498397, 510929887, 972964020, 337555639, 404620024, 817179438, 634675511, 275727714, 932340313, 945490322, 125724568, 153394497, 131530124, 282253801, 279907232, 630419208, 471999492, 490319653, 883118084, 587204008, 738936336, 809110708, 471057793, 797211607, 27334724, 859438375, 659194646, 206268531, 972739248, 408427831, 105299391, 825568904, 981689735, 708942213, 643042291, 161127138, 723734070, 420655779, 204707105, 211167521, 22362841, 808841947, 174559469, 470303403, 758953780, 66731869, 56843740, 706495151, 351395588, 956046747, 522012386, 235160745, 658338213, 648688243, 354135936, 218332179, 508016882, 680024136, 824701592, 302452759, 846806099, 764899527, 47894634, 6652627, 375369046, 830121902, 314328655, 296438943, 350375862, 483294235, 19670014, 1932520, 400144924, 908847310, 614828809, 786555944, 152726567, 516215738, 650525874, 657770761, 568147771, 408214058, 992205475, 611478042, 615277446, 312514355, 454142882, 61998975, 841007365, 960025665, 729777119, 997477786, 224962812, 145390433, 179282525, 965882122, 547050963, 222477178, 780596772, 151704332, 47174180, 363388766, 746968708, 790735471, 815499557, 805233417, 166291342, 589618657, 794133062, 62874767, 175562360, 689418453, 284609182, 936930642, 39864117, 909595029, 382180606, 696204721, 106656182, 295662002, 342199783, 313710589, 204752962, 5366544, 796558303, 126043997, 879801520, 485064954, 41764357, 250666020, 364938853, 500565883, 266830299, 614364924, 776142049, 347407809, 613819933, 598225197, 29557152, 26968956, 648484294, 849911709, 286585365, 175305016, 118946806, 384300176, 385803072, 688802096, 479256751, 522571595, 974859336, 605428655, 307459914, 752459606, 425883071, 571959311, 920621491, 938731042, 520243818, 472478919, 341157227, 315832783, 329138198, 714873979, 150914046, 760746048, 33177627, 358516264, 545630295, 532905077, 453855334, 95090984, 768489628, 401361831, 656212862, 404696317, 820847917, 201317505, 439095185, 101906154, 10430277, 901568666, 118141686, 804141776, 942461657, 658104125, 408614134, 735159862, 920810848, 859651755, 378362314, 753337261, 691449628, 631665807, 152178879, 915888654, 398489323, 825759641, 824100236, 85406807, 911260352, 535156227, 752232849, 830580958, 414043117, 605810090, 641158516, 631076944, 967031125, 826347746, 502792603, 722439669, 954936619, 540119043, 555407481, 478802317, 188025815, 343153308, 577608018, 665951667, 193358826, 816203737, 534525164, 824897715, 854850199, 819412685, 454824895, 246387198, 853368365, 857570825, 948255969, 902350306, 677913280, 979587656, 709892622, 134401000, 21246010, 517597097, 781732870, 152760461, 344966202, 335207820, 611760852, 432599037, 691413141, 772396525, 893752510, 518760225, 648388078, 527397843, 694467369, 691016291, 466205792, 513940944, 622244088, 949144805, 403987195, 841391731, 894358038, 452988480, 802220966, 367066918, 834334876, 672489115, 816157970, 863807236, 80901863, 477838050, 119583078, 843604311, 683574849, 8444180, 518153589, 803958816, 669390761, 444513118, 185326762, 58213733, 539853816, 980238166, 119950347, 931035007, 536696188, 790295072, 415486311, 57116893, 215930371, 673761692, 767622921, 756797789, 349916104, 282559987, 411180949, 539444599, 374058015, 454076129, 750182128, 223244038, 518935415, 663651512, 612382773, 900620670, 583397168, 285952738, 769338355, 953638545, 924833584, 324942928, 229831647, 884338522, 184486719, 22244226, 784614482, 778215065, 663472900, 18464169, 962110590, 423243212, 358881200, 359801041, 618093057, 912164809, 31572509, 148749239, 954458053, 196669505, 147397014, 379317571, 877936018, 477489791, 33694633, 493784788, 226095220, 302146394, 185577159, 538609659, 203445465, 335265502, 640665393, 978997696, 477092658, 203554989, 673621648, 677107419, 816858691, 197850853, 991439207, 582285334, 962787356, 367910793, 156929699, 930151981, 349204878, 336473842, 717318277, 965288662, 765245767, 190553265, 978557221, 903976697, 941157815, 38058258, 529199890, 956002618, 448455536, 678142354, 287270849, 275272482, 115004451, 962700057, 856393714, 991739431, 741740215, 879047593, 892067178, 720740209, 245978196, 773081990, 352560897, 858457161, 144301417, 903403348, 637045501, 560927975, 121389115, 390295380, 26312819, 853019954, 207111242, 985091797, 99930239, 529186589, 712046418, 42826895, 72445921, 415094526, 940753674, 655562399, 504844599, 485787398, 583563864, 655285001, 440959043, 429856024, 988819802, 88795516, 183762429, 886595502, 640795995, 569973802, 433086672, 859560589, 959336337, 389301788, 628447723, 551625392, 928328769, 366059163, 381989753, 168521420, 382091957, 890009586, 213096978, 333438591, 205140414, 269872734, 61050751, 21253928, 379853025, 628864167, 142031623, 451998839, 943379750, 591023622, 951390229, 737777400, 264872557, 223032396, 439968999, 325421404, 163541760, 739332363, 66909486, 460577370, 454293130, 392007755, 579460658, 429682346, 595402519, 171165134, 446676127, 873858638, 114196777, 329210619, 215425923, 297349581, 477347859, 467284279, 180613671, 77025143, 530802926, 309337923, 605183638, 381561720, 350857378, 260625055, 414658472, 656783628, 839198853, 945803590, 820174032, 444359558, 293755855, 786914460, 532930786, 77287096, 170893652, 921844764, 896284956, 108578970, 176542882, 344657216, 139806401, 911669275, 414550047, 719344367, 833269958, 634970677, 58246087, 73763132, 748804179, 850727225, 240639217, 419608633, 78591804, 829024329, 40790353, 574628703, 485067387, 292386771, 595921638, 280772584, 382329516, 266028363, 133394040, 944227656, 869304418, 548184118, 744480437, 421615174, 803795718, 538330959, 93898877, 88264803, 711254470, 508349999, 219725405, 468241873, 881497116, 544377925, 493844656, 338392337, 522640931, 927684478, 454442435, 25068134, 579680349, 19185956, 169871194, 104877696, 782870077, 740027971, 868917423, 437609332, 249337389, 52937545, 902448492, 273968821, 838372145, 303971026, 370271741, 933499980, 950471102, 96217327, 752094240, 465189797, 988884973, 734411149, 281850473, 176748130, 447843380, 914992627, 566718444, 21238955, 876942878, 989808825, 395126695, 432505138, 419262843, 452320810, 210488884, 772334592, 142345486, 512320831, 317486343, 687672403, 956669636, 428044591, 860387608, 219183019, 843390750, 381338429, 209621043, 61590845, 875789191, 155144869, 542397984, 788438747, 821100021, 230002830, 125320118, 313192652, 53215268, 700280758, 6475673, 791832219, 452155877, 936679807, 32433298, 497611533, 127879262, 445246747, 737819475, 131025606, 316092859, 89542725, 560199245, 915749697, 499187697, 760376301, 207977009, 878494163, 854813853, 552179383, 428042878, 459060183, 763827591, 304123919, 650875773, 697925802, 589473231, 365637287, 452996377, 262819224, 665229785, 272611222, 870950811, 67517789, 523045399, 294362250, 448259243, 522824567, 483109534, 499272907, 976494751, 316977261, 557979886, 890373813, 180648743, 753238763, 142734557, 597809831, 417113221, 530888231, 39517168, 74835540, 470314516, 360845164, 40570143, 16398937, 370530878, 732623351, 98026004, 557439294, 741971862, 18107327, 476019058, 823120842, 742670730, 503754677, 872441558, 758953903, 599731755, 45424343, 729442456, 725335493, 703805825, 657855139, 103716972, 134040675, 735815327, 858331416, 978564940, 759951254, 685406067, 51463272, 161586469, 232878003, 653658655, 66436685, 736156555, 305341934, 657827092, 584702159, 488590458, 709904649, 907763203, 5282953, 695713384, 158573427, 896721835, 761686101, 811239947, 833432837, 702913278, 649557639, 5706430, 802244302, 886173041, 934678111, 105979083, 265408286, 461691739, 193564368, 276620931, 499449974, 784681712, 733696258, 663052848, 783049718, 873280545, 452616226, 850561393, 505096914, 144913651, 153243869, 453879176, 38365037, 958902104, 195487295, 650270582, 228840938, 917839613, 863603968, 298682808, 621054446, 167543409, 358789870, 868276354, 280804326, 374596204, 322753300, 57308801, 615711755, 511448558, 317023369, 854960621, 193494528, 440305110, 433952841, 221882373, 672491618, 570018661, 707464243, 524643636, 871556065, 874358759, 976654810, 438924571, 430336233, 941246759, 829484027, 400312044, 390820787, 534622585, 666897166, 444524334, 4334617, 138556249, 687306145, 870837449, 639574271, 410249555, 625388502, 374748117, 276057746, 217031982, 675590891, 996142155, 807026201, 117091271, 300968076, 619325061, 769575419, 932466127, 187627430, 192836459, 933056231, 277838880, 801363274, 653868977, 214049132, 506913315, 969925852, 63397372, 9329009, 917591030, 619124865, 881598223, 787257911, 565605831, 259377370, 649593079, 895734874, 720598147, 448548786, 981549471, 971817598, 672927664, 908464128, 528977172, 85476263, 352278148, 137985178, 767324733, 674395146, 471310141, 416878622, 263626213, 985526375, 551133376, 325294337, 688236939, 21856759, 708650268, 810605732, 315318543, 133755794, 579063940, 216014308, 913890770, 259615637, 254822442, 587490633, 785394181, 334740369, 722906568, 573251844, 40318339, 213408597, 811763687, 99189531, 946827197, 998851961, 140456357, 46469424, 174604124, 308706889, 587342760, 664951844, 501726538, 123000244, 758229424, 622513545, 595284984, 886995107, 597101932, 605656454, 135584667, 941096858, 415459014, 460497594, 823773203, 981566127, 59718919, 958348400, 428708813, 982183400, 790050503, 529824712, 92858154, 99216118, 449149907, 863913085, 205107600, 99315620, 631884992, 900830810, 335542185, 830282810, 774711418, 39903375, 4538865, 863371065, 178860404, 21647106, 528781892, 951773446, 357460194, 512858593, 339840818, 818413277, 20397423, 910670880, 404349021, 929530296, 924827091, 542317885, 262493194, 26075313, 423171762, 742177165, 188056875, 679601948, 774883188, 109899404, 18818503, 289712343, 869542107, 658583165, 440539147, 509828253, 738713920, 909719017, 115024881, 527956249, 374849852, 202085776, 960322202, 120276597, 257525308, 447111761, 888830242, 666103532, 842497306, 922529404, 963270322, 480190395, 424928838, 579668099, 667677054, 355487380, 626035288, 893912027, 948597222, 946950758, 399836558, 460187944, 701369001, 515931121, 412791986, 502566181, 163088501, 95177809, 869800535, 160213457, 273914353, 615474514, 629407518, 5648033, 942228222, 172958853, 280911475, 246693365, 736274995, 861507335, 825607676, 563496698, 110875838, 269990826, 219130276, 629771302, 727370566, 703036516, 176946719, 189770554, 589926260, 314718667, 4741966, 810064771, 143023331, 745419089, 25480238, 338688541, 340146062, 863814506, 888342289, 224326007, 533147836, 449947692, 303159702, 565896553, 273893607, 9044623, 882384941, 448030280, 14424983, 484484771, 365827044, 973671866, 786916484, 567258722, 214721761, 43051811, 914217937, 41253490, 397795741, 805750609, 595520186, 265366743, 401260201, 746088412, 960167547, 419322906, 277195708, 216797953, 214957596, 86690845, 806032087, 226608082, 849107395, 812985968, 812917962, 373208323, 427971815, 326130096, 737189664, 771849871, 813089453, 478668986, 20641802, 674350829, 37217200, 641084495, 59138492, 968226359, 235467161, 375700467, 388780808, 411421856, 459611286, 960701528, 595758912, 85360132, 53116232, 442319348, 221812899, 621803476, 377289625, 430986034, 424837220, 168584325, 771378244, 127538056, 613329449, 672845241, 685151276, 509556530, 322841452, 447699967, 164923157, 329244811, 245490032, 326964219, 685096133, 814239922, 232677793, 926306015, 233315879, 744595771, 938457017, 980432321, 582594856, 641879955, 691851156, 190889773, 467587132, 266410417, 974711315, 41274813, 223052967, 846012000, 588744607, 697734333, 532125795, 821051369, 716261507, 290775111, 1714045, 912618388, 198931295, 914989605, 959284532, 223796303, 12279611, 334177055, 594842213, 388294018, 719770702, 461732735, 104392020, 252984152, 613866898, 884545116, 222180069, 140516383, 23423854, 945878720, 965591379, 191948532, 752300669, 207461879, 430474527, 656468691, 306492169, 912306463, 92958364, 403423377, 850873292, 313267380, 109018448, 483515441, 36843849, 692617773, 990793202, 386848323, 416054660, 404592204, 390833510, 718961662, 700313291, 201267927, 730318442, 440381605, 439571376, 558275589, 96038706, 175646570, 695673332, 280775892, 909736072, 946501901, 490520715, 425072267, 230585352, 388436859, 589148860, 731285277, 426402488, 841646984, 19695196, 994434577, 955631804, 328373000, 24390280, 939094962, 594131914, 446148963, 793778915, 811262307, 457255494, 880022463, 629591830, 779087970, 831529102, 850810937, 885194122, 606355222, 414573319, 359456203, 324299903, 224419166, 882683700, 734881081, 336277422, 584822066, 861833018, 546304246, 922610726, 589039183, 140707576, 626039565, 825079159, 662448837, 314348137, 580984723, 475418159, 999961996, 197374916, 681174677, 356432918, 352315235, 669165156, 634236391, 428039156, 186611321, 806016509, 601519025, 96661717, 814974459, 184205621, 964082610, 817410011, 731583202, 643459677, 315643767, 126081007, 66366148, 551058710, 512277048, 900427045, 249769732, 61542367, 862752810, 505745528, 355228920, 477250609, 866423079, 486167974, 272113561, 605697490, 775317665, 683184779, 653899289, 997631626, 678556837, 928383373, 680186015, 889385700, 805339806, 806573340, 589352104, 659680801, 787224319, 489644599, 237407015, 524679431, 258120315, 921655578, 840169841, 565121553, 332936256, 294123912, 54997852, 992050943, 324019534, 538623976, 950602255, 554778764, 886106854, 347629143, 933993584, 925065077, 984968724, 693876453, 405733605, 108086293, 88530444, 602639802, 78622713, 405123737, 623720592, 311821837, 276706600, 520056864, 290912456, 987628000, 774755682, 963368315, 208388326, 268759446, 398441247, 983490898, 679638016, 923520827, 847651952, 307521481, 130592976, 70654175, 941004832, 400097931, 438769481, 466955635, 265293456, 56100280, 742064674, 142473369, 854441840, 139035740, 643305527, 705728578, 10652322, 138913110, 904548980, 308536992, 655319873, 862678448, 508532456, 389254199, 129550314, 496621128, 600140692, 349828315, 799307731, 608833398, 956326135, 989620149, 842625735, 135771202, 862416212, 521037480, 440938809, 320266946, 248763769, 616564646, 443476635, 708752233, 442783579, 94181367, 94283924, 792352497, 600814622, 253897205, 343770488, 710275664, 12946099, 602291279, 334396099, 66502283, 131852772, 206587492, 663606089, 837354577, 396597273, 342258212, 43871562, 867973666, 461717253, 381630778, 134372080, 516647814, 5616833, 247852765, 922278177, 269713069, 174468676, 824710622, 927270186, 234885195, 767884675, 674099711, 629228763, 826475622, 912907552, 381730052, 326952553, 925431836, 606337421, 97529742, 521112416, 577841385, 224388469, 399277485, 799334212, 877518602, 551915127, 578830729, 701057974, 472803381, 495952723, 870040802, 585350734, 110887956, 937282914, 804823633, 814372503, 213883392, 778032856, 320551659, 389786347, 832032943, 249621779, 77769345, 730869829, 169678330, 985041364, 409495128, 999982627, 104593700, 630750176, 220418243, 715666992, 366699731, 621761838, 784446040, 321161475, 950014826, 832217626, 485895092, 60937561, 190432955, 16015023, 293401277, 960143062, 944112978, 218178211, 950068353, 555544132, 84590396, 421254799, 773605340, 895103051, 963434624, 45745258, 853630996, 843249346, 27892004, 373892039, 909187431, 892125291, 880234128, 226406735, 583611563, 652638377, 412728405, 763624842, 656076756, 472528738, 155229805, 960750227, 570482309, 621087012, 383683489, 985801476, 640722445, 908496770, 146875600, 183141487, 762488823, 167050075, 444476182, 472889400, 304660674, 247403607, 772249519, 647011050, 615479567, 298273242, 200593131, 944402935, 730126277, 909725833, 608093574, 734137353, 980376073, 46927247, 483760579, 942752677, 909812560, 151945919, 555662282, 910214827, 277870185, 559442281, 100148938, 937270762, 602235308, 853757388, 533772678, 996842306, 994611913, 855317360, 958608093, 844508171, 400941585, 23309344, 573739316, 524606879, 936068675, 841591421, 746587726, 357280174, 194745931, 52267859, 781747256, 390279553, 844612420, 112645336, 690376423, 218211711, 850047309, 938936941, 978729383, 241730972, 481611581, 691231701, 442470144, 63830228, 113364147, 949883678, 173799432, 879888820, 305288025, 934834363, 108003864, 142933464, 527929947, 807082904, 457693527, 300290304, 306469817, 764198844, 205752179, 184557903, 341829525, 674385389, 658831551, 126279990, 935554649, 610861904, 859445849, 939594508, 871251514, 599001103, 739703054, 882312385, 899189648, 586241329, 597661747, 444820719, 213661949, 83433685, 510394756, 762263957, 611611364, 830889783, 70640537, 514512857, 618315089, 937342825, 122281658, 815672440, 319020581, 499705316, 274422834, 940975572, 980878798, 740332277, 826425550, 950477091, 136179165, 543708016, 102249918, 215639954, 572055369, 753949057, 669426332, 171361151, 113488869, 665129711, 553874755, 926247117, 848701050, 594782252, 199096025, 931204646, 355225953, 235898822, 436669441, 81494902, 349844549, 216886432, 200265903, 178299285, 428241342, 816418925, 212383244, 257655290, 548864440, 512521854, 763357075, 96534639, 803624832, 85673861, 711173183, 453980323, 651577819, 909175353, 269591856, 978748624, 511949007, 721167265, 137988773, 558271612, 419411620, 72592186, 874567866, 340195470, 762314888, 760717792, 18022114, 23622279, 666158573, 63288432, 751557252, 209572908, 541987270, 977244540, 887365879, 522521086, 638476200, 682049631, 994836371, 744149126, 44257358, 868058520, 665390554, 669018151, 338329318, 957981752, 692472399, 28722247, 230726534, 757282262, 408840656, 66539194, 544039005, 904100930, 38934295, 374015377, 899703130, 475805904, 862675440, 452687044, 213637027, 809076628, 686019609, 926308950, 571700800, 733110574, 942873865, 716809818, 139968565, 997262732, 503640619, 422127631, 248326994, 39265692, 881859001, 281871650, 164573111, 417999405, 91337650, 535220790, 184440822, 128599994, 47858942, 350644437, 20525244, 162237578, 73424099, 137110164, 74835958, 429599367, 614258924, 714384727, 533930764, 607740901, 692159169, 120390614, 816841085, 422894861, 699592046, 784228641, 572705121, 712543900, 40895399, 426955698, 529559158, 777408506, 194031277, 438361988, 572012726, 130606746, 679335991, 408287937, 707658221, 759194084, 68254426, 63896421, 938981841, 852542141, 31412826, 352042272, 442171426, 59619798, 5931436, 848652240, 557405785, 469452, 794353973, 413790416, 231546630, 717339866, 814224710, 761259328, 569293531, 715637927, 803616900, 801884389, 793894897, 264567501, 892355933, 762572035, 473190324, 386852283, 934984893, 6100069, 352067353, 240818121, 230316041, 876348730, 653184143, 136634904, 187382996, 403215073, 663424704, 640143886, 204766901, 905192114, 146154696, 47289825, 427718187, 607360875, 477930745, 991617266, 627643338, 261291489, 100368909, 846936745, 818393741, 656780455, 773927684, 890079767, 839105519, 666328121, 488719003, 184432821, 922397341, 798691039, 266654772, 839071081, 152684094, 644219104, 814070951, 274890154, 421166949, 782680750, 95617312, 638577561, 452745832, 937127183, 239962821, 380246877, 285459767, 336606339, 61804210, 285220169, 715638013, 572414365, 147947867, 497446450, 520774501, 860678253, 128644034, 636499052, 32331188, 881098628, 314594965, 922361976, 719541506, 83432761, 88195814, 486799846, 31544917, 579003109, 881135097, 166251592, 311163203, 632889659, 808689999, 336297578, 351629130, 813743753, 102813884, 361965546, 496914589, 170871507, 271684707, 361957701, 580640291, 69096200, 530738840, 966272935, 976567612, 868551600, 179459822, 758308102, 971098025, 847183567, 815545321, 770130293, 860782814, 614476701, 640412051, 220084966, 435360363, 517313655, 194855852, 330223063, 487833151, 504751127, 106381593, 504011759, 894216455, 239554318, 513532911, 93081430, 238958592, 928665287, 749223770, 681529513, 623517303, 632344049, 800579581, 130793179, 713495617, 587188901, 865188860, 462766004, 906091784, 231432718, 42850671, 854726594, 244093281, 512450699, 956519123, 204662748, 318289352, 579259058, 995278506, 19966998, 237124823, 567213824, 900531003, 218342001, 491823276, 319347051, 892524386, 154755369, 890354872, 485366193, 837368211, 566084130, 641565019, 287823302, 298923274, 923388396, 138409658, 284368657, 536049584, 118413458, 955873473, 53825828, 937720311, 974677108, 827741536, 381794571, 435262179, 639287549, 208235001, 288071879, 208433498, 739991069, 241393320, 973382434, 344127473, 807204275, 109702691, 590081556, 586102470, 376669458, 886114464, 226876849, 977358703, 211476682, 387252239, 547312772, 641035235, 307576804, 633586398, 177390274, 393552819, 379013803, 981493329, 940576108, 925462496, 667544857, 814462982, 645974885, 128930788, 164123115, 98469962, 307282582, 723306474, 748041705, 727559233, 992416160, 893761116, 927075915, 210242437, 976663697, 449165652, 143148826, 330276275, 398638630, 871274235, 277540341, 433223545, 651770020, 876795154, 502620262, 478040576, 450215153, 915149601, 543408502, 616575590, 390433334, 411279091, 803835966, 765330182, 438212596, 332838317, 466967006, 394341182, 768988676, 225677251, 137270347, 127670475, 610130485, 639472031, 635674871, 390212380, 12485352, 622187778, 617482464, 652298865, 465384255, 460162739, 584114392, 97285133, 883845596, 693332518, 76153751, 29249933, 407775489, 97661218, 273927432, 523576585, 92372540, 728901884, 53442047, 302098902, 873516552, 62054711, 583199284, 704158105, 152548846, 429564522, 645024331, 794800908, 78913986, 50009324, 657223707, 736821736, 606003002, 726927743, 712736290, 194261012, 494447223, 535190135, 247273706, 546682767, 374207489, 903585543, 915737374, 939201144, 234556060, 533951387, 771962919, 338718846, 986423039, 914370398, 95226875, 382336949, 662584847, 340269160, 248483354, 470967788, 728725968, 466934241, 534471796, 881692013, 230479545, 379904230, 338215243, 318656702, 104883052, 151730952, 976975231, 232155713, 951198518, 918100682, 214630368, 428286483, 414528801, 245616516, 908239634, 521226205, 782086579, 427397355, 392020524, 581010240, 927524606, 349401164, 285354569, 448537013, 823975806, 382465002, 250506950, 798808150, 382346939, 195562197, 695408241, 802782773, 729343268, 293596838, 70500571, 668781903, 545348230, 144905689, 804091690, 150655098, 886698831, 75267747, 893576917, 559431529, 191975545, 554859536, 18096756, 746567288, 125928704, 891605013, 576033663, 925356268, 663638119, 232189500, 818532107, 250516720, 2315464, 31102504, 707670272, 310341594, 468510832, 551110480, 574870655, 925544507, 681616496, 788333896, 650917473, 560758297, 111569264, 842255575, 913646817, 578908689, 292256582, 171018668, 975170407, 312508217, 411612946, 331241059, 683106522, 398612112, 625199426, 896041541, 539673152, 635713515, 475876707, 334446047, 359693198, 755502825, 41100554, 786137207, 958587167, 563951019, 716000312, 812839636, 278627633, 840763795, 882821823, 972791859, 307224842, 901776573, 624051381, 827757436, 699068299, 854683094, 371241394, 951529260, 496597412, 652637482, 837431147, 21089965, 464838134, 779282536, 671006485, 192804425, 206055930, 23760205, 866740682, 49268483, 95962094, 864054022, 378323558, 734400464, 526969275, 584986917, 271694321, 580534194, 999651458, 488350207, 499296925, 56805446, 804747564, 363322075, 924916630, 902066118, 806215172, 664353061, 518292421, 888068686, 417505305, 86879959, 823666649, 411448204, 705993118, 488981154, 281487532, 966416878, 493397004, 300826413, 125804414, 97381819, 127495781, 980710675, 909045092, 594072642, 26255185, 796553574, 229658923, 980835834, 55385113, 552352244, 77544969, 542268243, 527611920, 505971000, 913689003, 315615021, 508409711, 337638480, 467784613, 44917229, 414206139, 487301763, 914329243, 217899058, 104418525, 868450522, 362319724, 414706512, 691137477, 307146782, 571190616, 773203648, 652019585, 450483992, 519301802, 871180480, 988781748, 547079931, 990430342, 249640515, 525596923, 34467639, 240381025, 338572984, 419378822, 223803808, 325548960, 358936855, 535870289, 575861770, 403478760, 628770254, 357892256, 244624903, 972787366, 831875134, 902587738, 823944715, 202021529, 151956272, 190332948, 887414206, 583591361, 296985527, 545315767, 90659690, 277159930, 406159755, 835727440, 251527557, 872063594, 67911442, 673584969, 530013805, 5692192, 985643158, 717333278, 411004349, 186228878, 98796417, 250053442, 48520036, 87557258, 580152607, 423358617, 726471847, 751040013, 148127202, 283150641, 951782185, 881035141, 918658721, 9912402, 967779847, 674270613, 679091521, 868877312, 184081622, 85487207, 168163906, 43742570, 175603454, 22855325, 208993781, 697011379, 608820271, 4054153, 638860081, 273672570, 318556825, 7747608, 460275562, 20794958, 230991488, 849585073, 413749000, 571484199, 971503507, 717070807, 526306621, 530781114, 620042413, 767408866, 453791715, 980701857, 792551934, 964148491, 499395853, 54938896, 269260165, 609427695, 460154009, 353229187, 933838952, 664384635, 200517290, 377617089, 144024476, 519946588, 613897340, 954950376, 508670024, 885319998, 903814716, 845574007, 767394457, 53131253, 342219644, 364942629, 221536513, 919395927, 31803873, 794980982, 946404374, 583408458, 81178689, 118668427, 931395896, 378845780, 973901046, 632923313, 997644144, 772294835, 332242413, 90101407, 706782441, 539285425, 949776958, 497701956, 187777411, 676270998, 325571627, 8326525, 945082073, 909756032, 304066075, 713957548, 321399845, 847307861, 331772435, 963028581, 484807615, 984999567, 202765612, 452177476, 332204325, 884732606, 611112184, 9850400, 551548985, 685251216, 555285594, 883457801, 153418136, 234993980, 435263449, 975418989, 131540712, 385508001, 378711013, 727673122, 768714569, 322502371, 792857983, 248037118, 697011317, 547403462, 522913563, 120480094, 405109714, 590791712, 133358552, 685587018, 798066848, 425520757, 638827472, 607013511, 142175604, 388205612, 767346163, 451761201, 801702887, 478728656, 819179457, 292195712, 679610881, 493541232, 644331909, 441597279, 337219090, 900097079, 481153362, 630860432, 778453696, 869440448, 391946963, 593701412, 543396509, 358964674, 173370410, 543704719, 38355573, 301530953, 866667815, 63157013, 340935639, 505001734, 181053759, 163238927, 446868792, 954887345, 920286183, 746739353, 18940541, 713138023, 458201345, 11166433, 116204699, 664340479, 632396386, 177838138, 237644222, 578261215, 223816276, 157440659, 771911423, 713061115, 358919920, 776685360, 487960649, 20317843, 106890020, 333513885, 447246279, 422561916, 622091557, 225005129, 45404173, 284174910, 947941571, 530041397, 604580418, 398913041, 728114544, 522742294, 115220267, 765779093, 133446011, 756417943, 933282946, 140635326, 81567016, 238395439, 917990043, 703851877, 104862581, 11098374, 722513684, 571239269, 957598268, 972362108, 291102674, 738343250, 921522583, 843651269, 20189671, 790878125, 231311449, 740981445, 669295367, 572105219, 291246871, 44530129, 562831038, 14262637, 943472897, 584458912, 861427010, 919213068, 881487425, 62973032, 297064923, 633602006, 478631759, 550813290, 928770358, 662131849, 248287420, 433549757, 393587837, 234998678, 752143347, 979282197, 368654312, 400019443, 626652166, 288943967, 689834202, 666695315, 134216473, 610498122, 833801593, 229089647, 223659368, 484876607, 737308125, 167331058, 2689655, 93837365, 820236228, 783976727, 662711567, 801221856, 687170806, 407682837, 762801549, 157711360, 603871847, 339062317, 888125032, 906029490, 96197535, 205413627, 592545252, 268473841, 937762336, 750949359, 352280553, 806689058, 254844734, 88994820, 854849203, 872971180, 594090493, 490010431, 55917788, 473216152, 465756527, 163349034, 644799571, 416519307, 375156043, 741838556, 379745065, 690953888, 977580942, 606609922, 388704608, 322126696, 28911393, 562662762, 500143428, 809198787, 850098402, 148724182, 992368927, 299830765, 897424341, 228370891, 452279774, 855816199, 485105739, 625184121, 379039627, 575058232, 109892165, 888409911, 773238494, 381458138, 383746535, 763613211, 520180524, 759567013, 634690389, 310172663, 935801492, 718550637, 553653134, 679350549, 852495699, 41625283, 641814388, 926957733, 881838740, 456547302, 13397495, 520292443, 65317694, 771970046, 854120390, 901903908, 117623581, 278439108, 113587513, 270953501, 993171619, 938482350, 522051783, 268924967, 881206070, 212788268, 623853297, 798079608, 728905124, 966867770, 653712715, 615806065, 795651943, 118287697, 920052531, 261273994, 62091991, 547548347, 489998096, 171901713, 772342113, 959901414, 901273571, 349719849, 219990792, 700707398, 996236165, 278344350, 491780541, 728016075, 427521596, 324362233, 917926331, 258085224, 159942096, 802550481, 825716105, 84910421, 122441817, 436090365, 83166638, 749019528, 573553918, 104419005, 75025930, 694761218, 966965884, 387883452, 167311476, 811897347, 319129981, 984641182, 907021698, 776076407, 197537342, 978090576, 761447549, 425576184, 474092657, 655468963, 896711906, 31572034, 684794344, 632421372, 463116386, 878904101, 635188937, 341867016, 856540560, 610488376, 983768268, 16263096, 259694215, 177833665, 284935782, 829415587, 319451168, 569073678, 653188276, 351101504, 853253948, 173822252, 528072849, 889902390, 448101099, 489777915, 840481977, 630598964, 710639273, 195123964, 463275876, 491155533, 803125050, 220326319, 653309921, 368398013, 68486994, 827128292, 637608161, 717465097, 528303845, 268174628, 444799650, 931161428, 263008556, 825347740, 551567512, 121983096, 671589573, 661147931, 812070403, 391623281, 736832370, 424696971, 781827588, 566216038, 381402339, 662993172, 929685843, 192627161, 701703925, 287745536, 945450170, 102258012, 255829065, 7084213, 746777427, 549739978, 180187950, 816845704, 687294428, 888707155, 142588470, 762783366, 533326098, 478013756, 60939317, 662187761, 862426588, 466826249, 307450041, 621348185, 666156624, 711982210, 803667115, 667661955, 407380441, 319134879, 262803522, 779292048, 691414739, 453795529, 185183224, 954267798, 50548190, 584015291, 980969230, 400542442, 325597488, 935642100, 675168157, 404704446, 288388001, 631686508, 938695631, 389010170, 391489883, 726728299, 592216716, 537965094, 58586436, 388157076, 634544736, 181304873, 866828587, 249847758, 322858583, 133386536, 252633891, 848677142, 521699944, 588341256, 543261652, 979056079, 455508066, 361097841, 216635854, 320874688, 564222478, 552897293, 419515191, 125672440, 872206381, 759851135, 354306216, 597501212, 895767051, 529930455, 743338121, 673362889, 375021403, 48536164, 141462549, 85045283, 884590894, 834559591, 338082654, 891070452, 916638082, 951407365, 797181877, 225226424, 439434542, 591932327, 325814969, 906667475, 923862233, 573714027, 731389616, 573886343, 594446920, 224856828, 400736358, 791856085, 278035343, 459227454, 792371041, 471789939, 110992585, 154047603, 508003729, 250813748, 964103054, 863137741, 33324003, 571348238, 467501696, 202586164, 758804365, 82508570, 417390468, 842610768, 623781048, 360302682, 842161036, 597570129, 40027034, 860727515, 76857568, 754751043, 219115752, 901365375, 947402163, 737369877, 401992442, 229228894, 597137333, 931688386, 49622922, 731847144, 207783437, 243080504, 439566037, 784821628, 109312345, 558772056, 670651134, 589921723, 22254415, 741268607, 825859882, 772662894, 596909991, 458658915, 818481332, 830802216, 792698265, 591132472, 599734235, 399880373, 895355031, 656516135, 446936339, 169353727, 221224938, 869146455, 902468500, 870981528, 110409262, 236476847, 262526291, 425101717, 991118799, 913362798, 815818651, 236952133, 988782751, 812824170, 134394647, 745971341, 819239796, 916874668, 854451534, 906936027, 610941815, 517493644, 120798904, 95089714, 78799980, 698210024, 574110888, 242834266, 225748191, 254466190, 599460372, 824037415, 129714838, 847462667, 502040870, 72019134, 210079352, 165059810, 876762586, 162042041, 793366073, 966247512, 692893842, 451893178, 122182544, 287677080, 580883055, 196477145, 439112237, 173659486, 415086380, 205220987, 112647149, 565031370, 223629393, 841097069, 432554640, 183807016, 268259717, 571117268, 812545508, 437380639, 903547263, 783985768, 942794899, 160694689, 897207651, 876265941, 301848581, 255264567, 335584090, 655852543, 688162120, 18306602, 568075118, 616930726, 485550977, 425585628, 275470197, 913879936, 435972471, 159983293, 533340679, 729496771, 458057177, 576671402, 247562747, 824210776, 408473047, 658948385, 707039292, 367979994, 952177254, 757249518, 420237467, 445927227, 325705065, 733934771, 835100696, 827273144, 303668891, 392461534, 505284772, 242700137, 226138503, 767463947, 949457019, 920563077, 883719131, 362525556, 375621650, 933735471, 149734053, 665079249, 882328189, 71246179, 164006904, 270767265, 535370908, 550191323, 729885278, 557141923, 792593163, 805290206, 403226271, 23108664, 785677141, 844280792, 363960080, 75847140, 612557903, 815290982, 262430372, 287784928, 888532659, 287191639, 790988975, 709363160, 283304652, 307957217, 453694100, 184872300, 49855762, 908429056, 447514682, 611037119, 827737832, 114528571, 706407670, 710655675, 802588033, 142673907, 379498106, 729083146, 790093890, 728623439, 363730713, 423684512, 171763897, 656840705, 600729280, 901426624, 359698296, 150726857, 726685229, 475205746, 38484880, 179917831, 543975251, 688207973, 36313145, 652600748, 51819706, 995820544, 368844646, 350843564, 576253806, 633899454, 586668023, 412665036, 808026104, 919635248, 894843830, 85152845, 821558769, 876755084, 790674639, 430171016, 790037234, 743229417, 575340275, 312358401, 893655508, 671335731, 939662597, 348539828, 387611530, 88454237, 936164136, 879515170, 63965561, 741415701, 44280574, 545580662, 203641733, 394928252, 49421583, 763411654, 521799677, 171393491, 686139749, 208953092, 158083865, 104221217, 868004691, 192154689, 222063632, 697879610, 576095039, 191550054, 909872831, 873255000, 683790670, 167536497, 545085508, 984763988, 121030243, 301674566, 223115685, 328452844, 527723331, 774593755, 311253153, 674289385, 720231876, 63321085, 612595161, 130286667, 806989113, 556443607, 817211446, 72220580, 520755524, 378319988, 372159221, 235378434, 478738937, 397284608, 845432315, 470635937, 489273239, 453012727, 401907922, 921690863, 839158900, 943065254, 781063736, 563563585, 224945383, 322268329, 242504650, 275517228, 270547948, 421911587, 767684920, 471525355, 837752351, 666262379, 832700365, 376200079, 679571707, 753931353, 346912442, 385949162, 534056337, 712333120, 933092909, 835758701, 932508884, 112983277, 88794717, 964026498, 328655242, 285410454, 294776892, 202003380, 176088957, 766926270, 711474037, 244916578, 533225397, 842931038, 649309118, 693142946, 471745433, 379887345, 531102516, 919623947, 879631971, 997438016, 157906821, 625439833, 448718219, 13683975, 414344707, 23589681, 475146074, 199217227, 788627261, 600784885, 177430038, 595320824, 975553306, 124989643, 867691499, 650140017, 629582961, 738130161, 825121572, 590689557, 121458764, 258219544, 354890347, 290241887, 3138117, 337130538, 19451890, 576299177, 368399207, 738615294, 471384283, 956444558, 380686898, 11977038, 262543578, 418318124, 781964223, 629933779, 543544763, 38975439, 746014229, 724057664, 832235415, 895853974, 76565648, 718049671, 433898898, 645706164, 532431891, 28274948, 876549332, 36252375, 584045688, 510345333, 175810628, 256726802, 796815549, 121822906, 11274347, 781838977, 55621720, 824912596, 786604426, 797891516, 222245143, 720203127, 831337905, 509653659, 565854320, 185788683, 386906924, 282826983, 851027280, 218727515, 197675225, 594819179, 851649835, 16495202, 785025364, 131598987, 301333809, 102017050, 64051170, 144890800, 890727031, 682127258, 184742615, 56982910, 616827047, 853119399, 345538431, 291347702, 894283924, 652034538, 747208012, 15624009, 125752169, 739953843, 345231844, 344520022, 874773586, 459676952, 662851448, 873339592, 852381733, 444891814, 680682145, 406318085, 395495536, 606325604, 524303837, 560503643, 484215281, 882742965, 666637562, 919962134, 80793925, 82334712, 320954554, 527440876, 728987451, 279804612, 885541843, 271724015, 436504359, 497927961, 831838451, 547512111, 599063249, 487312450, 861051116, 463268542, 996461453, 325124005, 501773635, 76722283, 340444839, 606528514, 931197942, 711521557, 630653238, 126539963, 469650694, 945445627, 320035575, 425925332, 974369893, 646309468, 780207211, 888904107, 454218914, 437377026, 493158433, 36092513, 203429830, 599620780, 720818713, 377414251, 649305598, 841605345, 838353421, 359036333, 821959276, 12955601, 536792759, 951245309, 531945672, 729802359, 794472730, 25335565, 384893628, 262310254, 178458304, 978420882, 27489735, 191721741, 696201622, 194688465, 901057268, 274766244, 39851636, 255066715, 317286431, 412001350, 563575169, 594006816, 864622826, 777891598, 355937196, 768261056, 956465993, 573578026, 134954098, 407033878, 367544548, 323785844, 966383661, 456492882, 926040870, 266950291, 935865430, 568612772, 813707782, 640256330, 440051143, 521721007, 781954796, 819425596, 835874200, 51940350, 623809231, 121347887, 111813647, 76001019, 536716255, 444323693, 646610971, 836568729, 631301826, 23998532, 16440822, 903832297, 414869840, 991768258, 285966840, 996757943, 951218600, 613032314, 353050737, 85462660, 412787115, 908033047, 710316452, 330655209, 683873045, 722753185, 326646564, 468403006, 906602549, 457856828, 668508206, 26014085, 546050243, 233423601, 923924298, 805829845, 546670894, 231989978, 8711537, 147251693, 674683999, 389608510, 220715603, 837648626, 760386690, 660625349, 411410566, 450984772, 64514444, 468939755, 66577800, 944977182, 183875028, 699157303, 828678253, 727027552, 565007934, 969628529, 476115626, 989814368, 991051404, 731849295, 993944394, 878381490, 183984090, 410385222, 450223598, 411822393, 216965858, 137791210, 571991481, 708502855, 29089559, 403730235, 11986006, 501898830, 375785879, 841669744, 448083530, 131989282, 461238264, 516415421, 519460779, 887938980, 3495493, 598508651, 514407038, 701451757, 516835110, 105458796, 373705855, 162684286, 651715059, 934966223, 672370680, 764556048, 690185688, 67257161, 194541885, 610581021, 200051979, 921454650, 851787851, 181910320, 957010903, 188845968, 833531053, 268583857, 405455784, 908688542, 177273218, 546526975, 845638271, 591756491, 633815217, 178214016, 14265891, 645675617, 493404115, 625964556, 819798271, 147305242, 995041124, 418637714, 691123702, 311039906, 275129064, 298199244, 713832761, 455934675, 484423812, 217738686, 521348172, 865461581, 452931521, 694958785, 44748928, 216759046, 481993820, 856768390, 815443337, 68536034, 203817794, 736264225, 791839257, 63590536, 206857488, 544764877, 172743072, 319182166, 441052157, 462435620, 726817194, 489357249, 418502421, 839377398, 32587524, 702668383, 137877931, 64221325, 833038651, 662887587, 499835202, 428679150, 246794417, 84964988, 911083466, 572269010, 573118639, 412448643, 674435910, 267547738, 436841942, 609716018, 824615141, 543321984, 926191543, 370140913, 916060299, 110197790, 365926104, 211350324, 677109124, 776937691, 744476864, 774889902, 417047081, 256813403, 70398587, 904833308, 616581288, 303024991, 50178569, 788164336, 364188977, 688594852, 566925941, 29353042, 590958534, 841036030, 389522266, 252285036, 592069387, 762178817, 258416024, 199887122, 438043387, 123777593, 246668894, 248245465, 689113350, 86744162, 85589464, 823986334, 59408935, 105699441, 87800880, 72308138, 393846139, 420624912, 681292058, 438096673, 561906248, 565976040, 421431768, 994837910, 453728236, 101196084, 958882570, 52820605, 182668073, 638430450, 618828566, 399559015, 688191431, 390178168, 340003950, 476573910, 522574851, 836089563, 333074378, 324108492, 927235391, 500491144, 26744424, 612843701, 121319743, 45772115, 127290836, 818301469, 120010291, 217040351, 663734849, 400686147, 268249326, 569654444, 857825258, 598286490, 181022445, 553504842, 694120462, 292441257, 667967145, 726030183, 627684362, 696231028, 182838129, 239464817, 421077508, 497383119, 331610908, 549202390, 373211188, 62567231, 404926127, 487463714, 620440535, 82901602, 67256074, 596598392, 728218619, 26843579, 240656053, 572867631, 454273257, 216793540, 444326906, 212138938, 57504998, 811413926, 92661697, 457952632, 197075365, 273338380, 981537845, 916392440, 269095157, 623787382, 582957835, 922589129, 61928253, 41695983, 1114867, 250679260, 511779644, 730026107, 378077782, 172305200, 797307182, 523280129, 237726864, 387353154, 553585371, 492929990, 731747894, 863945582, 210451014, 787308760, 60781888, 367380687, 984946566, 171547266, 661907950, 671983401, 939820637, 156539808, 386740173, 957444264, 325857058, 375348966, 671100344, 421549191, 764640387, 875660594, 633106432, 865383519, 69362146, 719437548, 59701427, 822580802, 865717551, 925305673, 167146175, 256867287, 445669235, 145356981, 339576785, 934448516, 335618299, 91905052, 848074471, 697804651, 93273269, 790564224, 645372726, 802645298, 108382971, 155201146, 62607326, 602632386, 595402591, 135110497, 661706533, 230084566, 68450496, 961603770, 645923521, 968071887, 168494170, 556377909, 35768659, 214395511, 111483472, 527013130, 720750565, 619754423, 186741927, 832469848, 500835367, 387099367, 160572033, 830972679, 917589286, 485132922, 525669363, 146108926, 501200552, 848856070, 944911877, 41320991, 740802817, 34263051, 683537959, 758721221, 175349198, 896338757, 29542943, 698534678, 900489480, 867408787, 669852482, 981863278, 412765195, 809669110, 903236530, 311136801, 222469979, 435484726, 266583447, 599427229, 464835329, 529964144, 346530450, 714531073, 180766293, 272507684, 12326671, 628465850, 617929109, 323504512, 25151034, 877664480, 702805651, 798898175, 535037559, 24018663, 830235064, 538354595, 361428759, 901306445, 186889656, 4225109, 205807030, 167470521, 80476365, 828323175, 692448681, 642142864, 307814215, 588515187, 914011589, 738424462, 873661535, 627404931, 929041157, 290513802, 761568193, 10068165, 589697962, 645327983, 357162583, 838765122, 462917779, 755819420, 882971405, 438833273, 215252406, 947754772, 125007745, 51097910, 581049060, 174432706, 60075501, 617803332, 464634162, 53099501, 920456699, 154635616, 465764304, 160576355, 544991070, 186582452, 872094083, 324841651, 616155786, 629112067, 877637680, 94023552, 356049186, 451245670, 190790189, 605092789, 679701044, 974830731, 237255795, 338489080, 453242826, 594967835, 298531523, 912993547, 704987945, 830014409, 959237820, 459085732, 908445843, 807377552, 112789383, 163974574, 539558358, 645869, 750998792, 795475868, 981891869, 365954921, 880369623, 239145581, 243106408, 937791534, 46110232, 260625061, 361794224, 930746, 245122342, 441199986, 243894044, 678757670, 68586219, 750416153, 751141691, 329052903, 821860449, 829444684, 29693029, 688832897, 691139994, 347223014, 321793030, 514653202, 453022866, 210198295, 262685712, 324841065, 706988967, 129807372, 163422061, 393923969, 818896122, 624517716, 59543476, 739211050, 118838014, 162120268, 622846579, 125867963, 946202497, 183496950, 31822624, 86349448, 620634409, 772342210, 413854534, 153614782, 389676165, 782796790, 197730536, 937255679, 838792560, 67287703, 257415278, 756979081, 627457375, 505270324, 431700759, 830128922, 183669594, 445702379, 894305854, 366063645, 195167758, 70277643, 913662365, 134682345, 831620747, 580932227, 741465076, 229994073, 850804745, 723717532, 642975915, 120661234, 945710673, 108632737, 488793874, 643120305, 861092972, 765759497, 124103582, 920128940, 705375243, 920685752, 753535693, 932287984, 999102595, 954687811, 495407980, 792562047, 824515692, 526241887, 265163648, 612663937, 444786994, 554325704, 393591852, 821127317, 269053297, 365833617, 217320469, 567081368, 748909615, 412709665, 367092944, 998873345, 569835350, 591873895, 320539428, 12454483, 768030958, 272479635, 814672512, 667440675, 60545536, 917626764, 578864459, 432131283, 722760715, 908911502, 386289416, 230321430, 685723160, 455675853, 437956393, 263440707, 633473766, 840675659, 194529518, 355199194, 404396595, 3603788, 800809369, 508391764, 454563511, 508110572, 843014338, 811609364, 934810003, 177725969, 134707752, 344283825, 706085827, 449749696, 467644988, 716082576, 752597010, 7193781, 218523565, 164841658, 655831076, 769262783, 133194128, 795771984, 914223292, 617395297, 753186711, 488123938, 618343519, 528164610, 321548360, 720484468, 925709297, 874274609, 589732866, 25397614, 986913681, 625137847, 608564551, 893673748, 347484413, 379555863, 177553010, 911553260, 980874415, 113265970, 903262038, 149600616, 690992760, 152326329, 374428129, 850800373, 144085669, 917176218, 374902943, 62186563, 563968478, 4330611, 783591821, 931629303, 436163114, 364705501, 383699549, 602684152, 228294784, 997947927, 687390735, 86403932, 98334099, 177185374, 889652031, 217362800, 649662572, 641553204, 598660200, 404650098, 303319951, 251936194, 962426474, 396845082, 162343561, 180327436, 882460209, 252212540, 33829521, 639687879, 96724652, 922410073, 13628354, 667765117, 315921120, 890564693, 702631041, 319629722, 646512983, 224748565, 549115954, 99692988, 86630230, 289171046, 463986635, 723784171, 11259204, 358271790, 24407235, 879636298, 641248512, 688766517, 371100743, 751872178, 73944537, 928046837, 608167410, 710884031, 652016251, 987595300, 840420618, 658405832, 350381980, 369989755, 496368091, 318703417, 617461100, 678634988, 199360577, 960013572, 673454490, 875357169, 798494933, 295433961, 426809540, 676724444, 335746689, 669019441, 322346126, 414864531, 799753725, 278939891, 508133097, 423788982, 302314442, 722693003, 621964029, 675908443, 247956675, 245998457, 536814741, 913610629, 785983095, 410716879, 101798046, 291596284, 456638102, 513378448, 410535089, 795320033, 680786764, 664084541, 804285919, 569022641, 855669673, 399181849, 807078001, 227291187, 544922341, 3527604, 208852589, 397372278, 566624113, 216115979, 528444227, 536927586, 539594583, 678498118, 214991011, 819622142, 94131597, 257703788, 129180513, 162947759, 156607852, 631432639, 22634598, 279475231, 218668421, 646254675, 275687956, 536640694, 564137330, 263110389, 495342344, 737627840, 537865287, 352125309, 985867673, 419037676, 522886675, 621832378, 25593453, 752597712, 566402029, 925438872, 825690200, 817733707, 984717621, 166670242, 891719795, 232853254, 217693992, 75758252, 613727926, 990465848, 721473483, 56327740, 950678343, 977675639, 434207424, 691506444, 255850776, 508396534, 672311043, 705875280, 117690340, 756716768, 5316521, 433033595, 776976447, 809203818, 276176411, 886380803, 341583557, 388069919, 933581002, 852868788, 200257573, 801663182, 806063295, 225891685, 218688829, 503489218, 748806965, 22761385, 916319932, 612792397, 570189069, 919870057, 537691610, 261238715, 171963578, 235147452, 622094326, 833343137, 918544191, 300757201, 224132407, 657216833, 979346839, 729024682, 815608944, 250962493, 243796542, 398027520, 61940752, 650478887, 965018879, 254572269, 32721121, 326707981, 282632928, 413832830, 492469841, 966602313, 409503860, 872764787, 514267941, 841826792, 159939592, 171262920, 401251692, 2927120, 48966683, 129526315, 623142147, 738666031, 174804882, 64899612, 108936370, 597661636, 589851418, 127858515, 194069959, 304694501, 216939833, 139854844, 926971059, 276353220, 173945902, 771115242, 180066803, 535374189, 185969706, 50889914, 879123992, 365568257, 14674608, 3473797, 610478456, 333482726, 432014471, 1273434, 853082332, 322836879, 434896407, 611251700, 263092424, 502357838, 405224787, 437790842, 190499856, 145616760, 693454353, 732699847, 467828643, 47606982, 428044718, 411102847, 402602090, 982228787, 851909341, 242479192, 171590810, 303983445, 555338218, 447444989, 934103858, 97646685, 71888437, 130004725, 288092227, 967611541, 143011683, 645117147, 143218506, 978431691, 528229826, 342712351, 178109168, 429381945, 753284384, 92863914, 261886235, 623419893, 240237511, 900334790, 793758285, 457978620, 932142801, 762680086, 11987587, 512608877, 918950076, 259229468, 4269494, 18636948, 981401179, 610478119, 587584239, 521018094, 219918277, 16689753, 721388050, 71759491, 320593534, 741021241, 904612988, 671318205, 543258285, 391331653, 815172969, 472921113, 6346250, 678906254, 290864507, 407088931, 176655634, 914380929, 989063993, 625326351, 999322534, 196634858, 768110196, 512516311, 424034367, 168477118, 256112883, 14884490, 586866098, 687791858, 405865236, 375672305, 645886450, 648964249, 644570314, 570432063, 59969527, 751215459, 149942451, 900143297, 267946075, 79003680, 78954313, 851697499, 137511671, 621142115, 956995256, 219649249, 274497951, 111876437, 493186739, 739045751, 639994381, 795984602, 128249865, 386710230, 657936151, 424416886, 312772318, 389014079, 110640604, 525124576, 700984094, 358561022, 245819481, 573866636, 257871186, 960956923, 57505209, 577992488, 277420464, 308154006, 295640489, 510538676, 920942945, 199991785, 624153999, 676951952, 234694175, 340870474, 941035516, 12773744, 48633577, 923790333, 752525124, 805272461, 160782206, 394886702, 917887087, 63068328, 437845662, 236321443, 165195041, 387761917, 35198204, 168214652, 393934417, 546512767, 692332211, 97362754, 775684454, 659713849, 788558770, 163402131, 90240482, 432864080, 264632347, 991211129, 279488562, 358062039, 218893220, 779467430, 180284379, 902311527, 665882660, 620432408, 18369784, 760100541, 299054059, 432021504, 736340526, 871394383, 788191197, 880234839, 82036064, 705365916, 394490858, 862915693, 745709807, 701934306, 802081418, 889452076, 963389145, 754964647, 927895661, 165444774, 695416374, 946563794, 748314161, 662511605, 68350130, 897492627, 484873890, 572547657, 433591110, 537404517, 8930307, 343976210, 345027127, 239344496, 975080239, 909615971, 629921575, 869964224, 337428328, 823093952, 470413175, 527974137, 718395215, 662563287, 533656378, 542646973, 802527755, 512437800, 7370941, 261042907, 653417425, 977352864, 863707948, 328621446, 142179202, 740483938, 510524022, 797405983, 363586804, 431824906, 685147701, 205538480, 452504197, 809152966, 646251349, 727154603, 519547909, 715081597, 276967386, 50967279, 978373903, 219779023, 729561001, 85869024, 794952971, 269026989, 523998565, 519637660, 663291263, 521052753, 973690533, 925467424, 156130575, 155729748, 501194945, 761710471, 490306437, 482375260, 341733568, 693700167, 725031766, 676978737, 269850694, 816961906, 934893082, 122337432, 469953132, 775097950, 561440860, 58846075, 706282037, 90850140, 917133798, 109777365, 901974525, 490546893, 653213923, 901851481, 867767630, 272368428, 126231383, 465644620, 913062305, 941917230, 813578086, 273255769, 582694848, 192332629, 344819683, 250525282, 579009455, 430937118, 517163278, 190041094, 461307340, 787521347, 585137159, 102974346, 143318033, 894969852, 61658639, 818092790, 876268755, 44451576, 559789603, 630559381, 37617890, 356177275, 841647678, 904450401, 931163947, 831620571, 885112093, 92193298, 500969105, 487642887, 427538956, 540751137, 294075643, 771338686, 311351767, 870485136, 641027057, 532279596, 695908849, 778194104, 667095749, 77535491, 207104965, 209443874, 30031781, 717760350, 609373516, 353286757, 723191694, 146260469, 489347857, 899936, 213638022, 985606489, 329189595, 820837652, 432651145, 939872314, 759419820, 88287126, 956966224, 394486643, 241428064, 725317802, 486194627, 835910089, 8680988, 182249958, 358961540, 708956045, 790215528, 879554115, 578400923, 44210669, 582796462, 165248660, 713817131, 220960570, 553315157, 757658885, 982213327, 393312568, 242310564, 795132158, 748349050, 697538798, 239949498, 160232751, 734781060, 556810288, 829257072, 687299714, 683957020, 989129975, 398165312, 389734499, 19745136, 658684268, 98406648, 392316027, 751727186, 539789671, 867754015, 136338178, 45098410, 493919460, 880412635, 908839631, 68541610, 850829588, 161979687, 559607904, 903921977, 345088433, 282248290, 471747905, 259658888, 520220622, 981066934, 209079755, 112504652, 16093788, 979256450, 356885980, 426828204, 802465207, 870847467, 934419962, 29420639, 290873438, 146456116, 887464171, 357931820, 566193341, 617575147, 393824865, 21751288, 227814911, 858772843, 621356981, 684219472, 713786108, 901731410, 452251047, 174504418, 541341339, 886326836, 200861074, 506473117, 162100235, 308738157, 88491141, 330288708, 206700698, 303912371, 405859863, 110695475, 220420623, 295253393, 44617701, 658202902, 332688958, 158248932, 643817926, 514380239, 17642907, 226569319, 248808722, 4124113, 606501387, 151576188, 110968338, 794130320, 705786921, 560128040, 696165693, 432481241, 492208462, 751204449, 283988997, 434542204, 824897372, 250578730, 527863486, 915661097, 71820798, 790170193, 111157730, 985009033, 668875383, 816009052, 734711662, 894920468, 280606616, 662480191, 108971381, 477136419, 551371481, 22980783, 806162148, 291496873, 431101647, 731808966, 507910995, 717343915, 915495267, 347590091, 753239236, 852607987, 930382917, 556861755, 270278658, 640230343, 744474751, 362002120, 46813151, 489175389, 156539550, 814085263, 31289123, 53845746, 553318934, 487255480, 635412403, 834325433, 958515807, 797397503, 102484201, 709357917, 691127437, 481405393, 660874147, 181971204, 720766279, 547917393, 924722500, 338545716, 890200052, 745798892, 145183727, 692383843, 893069267, 698884197, 995864521, 595393825, 602740342, 799091808, 814885145, 719603689, 284750790, 284560647, 798144898, 998847655, 919751540, 428391078, 187937562, 476646851, 377478797, 797943658, 483199957, 815000823, 97680774, 84777375, 924293932, 735115891, 29944539, 235831710, 690854673, 70883147, 844039430, 693849277, 369194790, 98222089, 542812568, 443981270, 576327902, 987103331, 79889479, 817090697, 74869731, 771210110, 600299850, 158237037, 566783777, 782121298, 633219692, 535423546, 781142942, 603777085, 378237354, 236084850, 655674055, 477570880, 187522789, 481505989, 389338535, 960280140, 142704753, 960928171, 804437123, 710201614, 612319618, 948766922, 959482242, 410649151, 62677912, 916145054, 131107891, 550989602, 751847784, 980476045, 588406680, 771975257, 51516379, 110374575, 29796756, 752719837, 620818363, 149645833, 712385518, 734374589, 154228, 691766016, 407967856, 989534103, 112015936, 317787084, 213668328, 528304764, 912369352, 450416891, 73237672, 497999433, 285869714, 897823087, 365293092, 618151015, 915128625, 951268164, 729977529, 610300570, 61817493, 610449571, 341210808, 29026066, 133893314, 212617928, 499188278, 255034836, 784790342, 338056706, 831471416, 936766645, 732606666, 20561275, 462335191, 816521638, 934357535, 154494685, 109014898, 992035603, 379844626, 684996526, 162190368, 814986370, 974285818, 804869099, 300770244, 137036807, 36592889, 857838530, 132889382, 926950932, 746175844, 217200532, 316892416, 49782444, 302282227, 613042195, 28496260, 214762473, 885230168, 816807074, 405808959, 157414329, 341488105, 548884258, 285483144, 736155324, 684481648, 319929474, 409387402, 737590923, 985830449, 848501316, 446096411, 552966811, 678840044, 669050279, 551901504, 205786073, 196618259, 176636942, 64283667, 291979430, 527758619, 332414897, 560470591, 123906693, 130361720, 953515452, 267628549, 113489800, 919535088, 586980595, 111045194, 179781887, 340790953, 127872355, 653858543, 485846402, 917483202, 723961850, 981452188, 466423071, 350498850, 39024715, 692570938, 6421070, 380511146, 250526615, 543577881, 138340191, 861355661, 355836973, 987461650, 556377086, 622740481, 648134713, 69921183, 739905578, 514977629, 871104676, 338943882, 891717901, 61681643, 553853336, 243078959, 978254674, 524720642, 308278551, 678520102, 679267389, 883891132, 994615313, 806124273, 458704280, 904074633, 699538884, 112053654, 93284301, 494983522, 665090215, 407705760, 220297722, 463165083, 706740681, 305964200, 506922142, 473986433, 435940295, 562540029, 497304976, 199614342, 601097331, 711766882, 193354742, 286556941, 380065048, 116809947, 946877957, 922925297, 161995026, 979490645, 408025462, 443907526, 124791822, 555842940, 694444830, 165974034, 254329926, 694157796, 321072914, 303257810, 607850625, 293479650, 207159196, 8844942, 473243276, 200212675, 553433213, 467995270, 406551106, 591413581, 188758696, 292974147, 976609005, 899474705, 563415042, 743412878, 48042526, 283939402, 372881731, 30005193, 938980886, 710844446, 105911973, 557997745, 877037539, 221599604, 468920766, 413082035, 664540390, 219039214, 497598926, 551886739, 139162884, 175001223, 580159459, 993804215, 693907540, 525284365, 614242397, 927787322, 766684546, 693465654, 402909214, 722308345, 416161814, 927929439, 234847340, 343289645, 908447085, 929694207, 748061288, 313072740, 761612202, 962348712, 684075467, 693893100, 189205540, 280479043, 316020210, 329353986, 890910405, 848165342, 929406598, 463478918, 236453784, 358843861, 599491348, 255188989, 853179461, 341528402, 117021475, 773947, 843733239, 495899666, 149009053, 582112091, 755255812, 65757627, 344054015, 131515808, 294763359, 208406902, 189078186, 149022417, 33401137, 895558564, 768231214, 382313749, 201492614, 951380466, 455759976, 264987901, 142690027, 442263076, 486671884, 444509090, 532975145, 44624264, 464693039, 31047841, 122089415, 459368458, 836762436, 819875814, 790302793, 891237782, 368140488, 165292350, 641222235, 466855335, 459495729, 651965948, 452004212, 593568153, 900335213, 215116167, 687740103, 906600359, 131906032, 743592410, 264488455, 895823837, 549112711, 56013899, 557661217, 452711924, 410608149, 505445269, 114160595, 358114158, 866665195, 65794416, 868760061, 965513848, 176012509, 114934047, 89304557, 830240927, 384742355, 309685530, 669270407, 910197771, 403556928, 208994172, 377930073, 647215512, 452729770, 543143182, 36803039, 789024889, 435906055, 29897488, 341595483, 624864792, 113207937, 352519706, 40574513, 872111443, 480677815, 65605089, 803635431, 298368573, 8343622, 725978615, 848226008, 934361278, 838751453, 695832720, 921134643, 431654234, 365161861, 885275213, 595056554, 954961288, 79085120, 344958830, 238963093, 334950351, 746306386, 307177173, 4525885, 856184585, 120471873, 941156496, 780328777, 869031764, 749324491, 858349244, 264320346, 322310240, 480817522, 578673988, 409187713, 942842940, 898543933, 245509458, 735700160, 716627428, 50824273, 131202497, 583148640, 630688290, 150450022, 823484729, 865867060, 247329511, 338175880, 736824598, 545222005, 163453148, 227443968, 333225881, 10310701, 61841256, 251614574, 395837721, 881522653, 476682710, 602494623, 975260190, 539932691, 730647053, 799135513, 781785282, 590756360, 194554281, 86434605, 641996355, 153578299, 789872657, 62176256, 368843314, 858407102, 536025310, 228071265, 282028783, 934609893, 228304583, 309851224, 471102166, 174284324, 68698420, 191358955, 385351717, 887632298, 497501717, 140748849, 565643238, 507398760, 470246012, 202282303, 71043943, 385520149, 835508118, 867266438, 949364292, 378290368, 794079736, 878824091, 494143768, 542509940, 55566299, 385422282, 996666740, 927234935, 990292582, 356591064, 366914656, 589672311, 835938191, 746829320, 816003570, 78683348, 249622411, 754148756, 732053972, 115755970, 196205155, 949219818, 965250954, 760501045, 167268579, 281921423, 693285590, 223561476, 205169032, 602764607, 399301363, 84269072, 861558881, 275676003, 352666739, 717050253, 888573667, 600442012, 313216662, 542722452, 289561282, 819282488, 815487819, 532719937, 480526859, 422053238, 732108210, 88405093, 422242743, 825873406, 838299645, 300555273, 86822582, 256591185, 419876159, 121959856, 426838771, 947848861, 172386262, 355559811, 854881314, 91640570, 586567231, 897084998, 723159500, 692237737, 109126179, 149178613, 180290885, 860816149, 138598876, 285972095, 957320714, 555036267, 260268207, 996207092, 438829457, 943469715, 225580091, 96523748, 162029198, 830617734, 640494464, 5706511, 16206384, 23280246, 108795954, 483238413, 45159600, 918476740, 782143001, 514873613, 782806265, 461666479, 958342177, 118681107, 855573603, 581781639, 174326156, 211285154, 570481437, 549801734, 651872294, 837243181, 361033419, 820712414, 803099515, 836715691, 230721231, 308528289, 978854535, 807434316, 66734947, 415207902, 82369553, 853054472, 591543910, 168295747, 320671660, 889878421, 855613296, 797116719, 726287729, 674142662, 53145704, 863716812, 997826995, 243547734, 827564013, 103628398, 317559969, 26025272, 856562893, 958779856, 345759705, 387359493, 725909164, 518974626, 308400085, 169691165, 840322433, 605404289, 121046524, 779414092, 368708983, 99769095, 287951829, 712313285, 628771854, 954344494, 199189490, 882758878, 282881422, 252875967, 311262976, 191118247, 800154145, 143111007, 818861319, 917369068, 266183317, 180820631, 760985262, 993756274, 760661057, 467293171, 542387065, 183257760, 971411539, 805203055, 808927747, 442949441, 950362157, 93296917, 949924395, 427525949, 685367332, 22399081, 521689100, 275625204, 478907402, 7606173, 157799554, 271008731, 804029538, 574826379, 280765977, 52566813, 102735920, 163342223, 668309017, 54433149, 900712398, 572778022, 473590410, 688463632, 433212947, 410411794, 609215475, 108349721, 707977132, 476680152, 836217046, 79428900, 161827619, 825941008, 833026936, 511948086, 498708358, 976644509, 968337522, 673415556, 558012830, 552011674, 744163321, 196899909, 598762724, 475932421, 495708404, 52631053, 654414775, 755024116, 985591367, 603176313, 789636669, 948000408, 193545235, 932073542, 98652849, 397680524, 553285259, 511995680, 921174587, 32907144, 994448014, 925783852, 434098669, 178338428, 80441921, 236119127, 678141159, 980761279, 338481519, 970300193, 183232381, 752524693, 47858268, 363205951, 41659802, 230687703, 282857444, 335729628, 427501640, 653305194, 505574468, 147577837, 32062532, 986391603, 326110471, 450649471, 282615194, 174492105, 229786153, 227345651, 974142529, 634630325, 730106725, 690489483, 29105196, 630958759, 39711772, 357284800, 535726471, 738205494, 623214106, 399998268, 638391304, 578076359, 324714283, 749838562, 759579721, 674929218, 437970607, 564795138, 230363780, 906940654, 423254862, 624511868, 870013876, 993968881, 967711320, 901392007, 957714744, 166260833, 913972088, 321728888, 545902993, 638674772, 924039574, 468469620, 936865751, 586413457, 994414840, 108567782, 95883563, 615478462, 873779928, 310766067, 754970061, 738633888, 220934679, 175021908, 398771086, 102209725, 634526549, 810051284, 507869345, 16858275, 382853483, 613566058, 92090652, 399708602, 784045261, 870549240, 90923564, 156750032, 603356992, 132984417, 565748942, 542338527, 288343661, 980936041, 844619705, 758723556, 339247193, 667345025, 507426094, 869101398, 404868131, 677526796, 725416468, 539125982, 188759187, 388046890, 350981878, 293509962, 797028375, 964454717, 867475818, 372988816, 508318785, 292682818, 268669537, 67108171, 852723467, 406759916, 767846179, 81919582, 601391241, 627329724, 980061401, 825673593, 706113417, 66264735, 723975422, 843390317, 668568376, 182779702, 541448239, 833786823, 347739122, 688638821, 880645407, 917574760, 906346305, 868138, 478754136, 42406185, 590186248, 730573708, 280942181, 208903918, 658236979, 998136625, 739597657, 788028501, 156241864, 792161429, 127708520, 271572389, 166084609, 382588377, 796552571, 727101065, 650373757, 422239303, 96761991, 153707037, 261125093, 906169327, 167743659, 340061944, 849673655, 147741599, 434281233, 261745985, 796220828, 206283607, 652510040, 535620442, 332739751, 444188510, 436851724, 496095046, 314180501, 120843378, 454921126, 123902417, 88890785, 319231762, 518958171, 631399543, 953623556, 655266470, 5448729, 649532546, 992884196, 998977721, 821259063, 905161708, 600938960, 366782075, 279229090, 933593835, 787261932, 891546901, 51482243, 835234209, 434764920, 674879843, 884017755, 687149907, 637366144, 301608849, 368748501, 112439951, 878924957, 830811186, 524261965, 905878986, 863044436, 91510487, 784139595, 850238906, 575186122, 392245613, 234155669, 113915905, 340851284, 144509912, 893064706, 51515140, 753866714, 247446570, 81234483, 964115931, 749074871, 657354216, 239226087, 262706918, 155039260, 227689698, 372426355, 797947039, 692707184, 279969831, 337910323, 21663850, 597587869, 555768279, 363340467, 396809600, 562676737, 442905554, 549987570, 956422887, 113542963, 922456248, 177455939, 345340143, 933105720, 210323177, 61441534, 706227319, 288427178, 562190330, 114088060, 866889622, 326801254, 144263634, 825325731, 879378382, 784319952, 362943412, 594476147, 790867177, 481931750, 31691194, 564931147, 1508258, 959131112, 756846096, 586889065, 273244603, 993826396, 926509266, 845094966, 276701431, 492474939, 926031586, 924842374, 285320568, 40331645, 206638165, 906828359, 471471790, 432966233, 562072808, 127551705, 219645077, 714288733, 942536415, 824127986, 907649246, 768815283, 283917909, 41221942, 861794227, 644561919, 537890237, 937134856, 971974566, 803066150, 369071167, 490461198, 265071386, 904163508, 814675247, 435107427, 803697387, 599487352, 880170510, 94803834, 159642681, 434198248, 3401228, 238663796, 447884074, 805262191, 65392435, 189295756, 692791808, 526055458, 962433690, 952196849, 1675302, 483120183, 452451483, 46164348, 750551604, 427524609, 783152072, 754455385, 858845175, 385726403, 191965142, 152123518, 990636071, 538328968, 47494598, 867502707, 496226511, 513023584, 743349545, 190024334, 520604629, 52117516, 949761968, 57681039, 54760992, 221357085, 68582734, 714694109, 286983687, 920279371, 667969047, 564677047, 952449845, 174213211, 14846302, 212111706, 655056758, 406829841, 739007944, 215758154, 162776217, 51297932, 564512516, 152357581, 46526581, 2306931, 537926235, 510826353, 947948449, 581757813, 80281424, 285068739, 726077597, 898075151, 75967339, 353669347, 821957271, 267532488, 777148657, 300424507, 120075797, 526365204, 224804874, 292931374, 429710185, 403571069, 355817402, 673695938, 886915227, 740318853, 203674484, 697233329, 914507921, 762846838, 483732671, 655752867, 343397312, 158883669, 399996953, 375143506, 685084644, 185027350, 853434550, 493596582, 736924964, 525355119, 868659443, 55914753, 145609268, 405164251, 337952696, 535615087, 717645666, 559904985, 669575872, 348949315, 419536870, 540874802, 638369402, 921986548, 561017311, 539392464, 585749131, 23616794, 571120155, 825905961, 846402600, 732910926, 788523590, 880175704, 901689774, 301433574, 14785792, 21839190, 895978755, 389018525, 775520521, 479684720, 412066529, 515224745, 919090512, 774518890, 947706318, 280967086, 897476239, 22756859, 59639791, 311308044, 790724392, 194915554, 131713616, 897747748, 172238490, 115601461, 935709744, 652714569, 860277715, 772561136, 731173612, 415333673, 792237954, 490429753, 379024778, 944705984, 300987292, 734404783, 679327553, 800469200, 596427174, 275596343, 931167700, 254589990, 554991586, 964940592, 190461758, 252034606, 266721894, 435635966, 868070939, 567075788, 474761885, 143395409, 114792214, 644688620, 707677943, 181694865, 788536600, 95369055, 939474991, 653613656, 450713008, 735389019, 428775457, 737826517, 977161649, 120193551, 124473814, 496197017, 316476312, 55317515, 763465291, 746271880, 989002864, 504160950, 656673795, 523902983, 163283641, 914573300, 279606846, 412345523, 749450610, 501354181, 562080993, 772080524, 861783747, 627999843, 999341575, 811163238, 856112445, 505787615, 69437479, 864850036, 269883948, 650915490, 178531760, 937501219, 784771570, 786304796, 306040005, 277614909, 162659272, 179290339, 387711436, 887618981, 804611884, 930750221, 763024974, 739767687, 880171462, 361412073, 99264565, 458232747, 582602362, 912750982, 567516444, 82078757, 780059042, 646839977, 977461642, 651155274, 934164143, 123145697, 125010521, 106097306, 5803436, 579826281, 36000236, 64076061, 20625908, 86017058, 441525824, 333092927, 135556128, 283116378, 488002015, 313621061, 399686117, 495479462, 769233686, 807619580, 955449456, 329377846, 574523104, 447543881, 74234038, 711305411, 15844523, 324079597, 783214925, 788133501, 443601857, 403755704, 924397740, 602431031, 790174109, 7043080, 112583026, 967269030, 938003268, 974578773, 165684293, 668856220, 244050278, 780626326, 59914606, 515576350, 234609617, 958618530, 273335615, 701571291, 708027798, 777170804, 184204076, 761514232, 543495510, 307475293, 595557569, 385002705, 14895380, 54784530, 435487374, 213772115, 490940622, 77557279, 561549751, 180585793, 420749726, 571457192, 494072454, 837710340, 716136464, 168706977, 413366246, 845887765, 411660277, 400562906, 432516047, 402339325, 445785363, 160938921, 714059335, 404940900, 908979881, 541672358, 876760536, 169993925, 572214784, 778877928, 77779566, 74050616, 799625413, 710457488, 758485191, 905988748, 17638419, 308101692, 99738246, 848100917, 589127479, 707165202, 341120450, 17551556, 769480003, 114931698, 875344010, 319176392, 790225158, 317843559, 353149070, 717243402, 807188246, 167516670, 769160180, 610507581, 112892413, 673053471, 491268887, 172091785, 389577002, 657428820, 518818174, 780990383, 977514522, 348583532, 503351856, 619669037, 677089159, 341387962, 508516288, 27165435, 299078861, 213723549, 667188790, 628443262, 959652828, 506933459, 52347692, 437031417, 656202604, 175693573, 311881057, 617632023, 634127924, 834748292, 660471901, 471786792, 284258050, 773806564, 513611234, 565975063, 139515243, 449558474, 213375673, 893563392, 86264932, 642828816, 713448297, 940348394, 845707020, 57929344, 632513704, 207179914, 99795608, 637997990, 467380123, 305253348, 733514931, 783283452, 402191561, 736881270, 37585624, 759373286, 487448494, 450251289, 841059365, 762176431, 804447567, 200408873, 369833570, 39646408, 753847606, 111897863, 342461601, 857288833, 814828202, 391082561, 916939452, 119791666, 306458035, 67762415, 674181422, 48648245, 810767517, 541757133, 537550584, 136630746, 513210788, 889423235, 136671179, 439481334, 548184015, 302057588, 322775071, 47625018, 609906767, 485853760, 475266518, 912023262, 607388616, 349103216, 829335055, 495128455, 915403487, 869184519, 826237033, 925910115, 435211711, 77077300, 109182301, 232952259, 356809569, 535082041, 572320928, 55670656, 63414766, 560343986, 878543345, 549485766, 60881599, 424632309, 698468420, 549091633, 928813281, 26500094, 847746861, 753241385, 133468635, 701130501, 316283538, 82810679, 496540964, 417786221, 910104475, 635058301, 721831621, 944675596, 145067363, 431521462, 685193979, 602963035, 438647391, 109591753, 40047468, 17209805, 736391535, 737159606, 97937783, 644328110, 289647387, 337558637, 170552556, 476779108, 670597770, 817264256, 985353776, 411540904, 316373900, 736271874, 771501127, 546495615, 493876034, 913203497, 985834074, 354536155, 515241670, 789539917, 945845829, 721094171, 457634040, 899723858, 900190043, 752109367, 344635047, 570546316, 873645155, 797314644, 755769652, 665950869, 500157456, 811237286, 765356810, 738270361, 329389284, 602469432, 646550924, 546034652, 148706720, 825559690, 811746500, 655972356, 948826525, 800664670, 202290568, 527892887, 128650998, 740983728, 470387561, 927206458, 839816862, 64769991, 59662812, 583375164, 118391793, 137094089, 751221012, 94355399, 784013981, 733816674, 278291099, 396611264, 233882905, 319508050, 462150424, 70613295, 735004024, 591228366, 404070486, 148562952, 931487529, 680593895, 162662371, 177338255, 974634915, 915978223, 188665460, 706389032, 395481659, 657001109, 269975361, 183276976, 877926391, 899125169, 425664136, 502233650, 536931313, 790414953, 346230723, 274060232, 899628521, 352615783, 839924848, 700482312, 247887825, 549952663, 755600974, 81188258, 481038542, 632028794, 198942311, 635807794, 259770733, 962495078, 88614682, 318880759, 623447584, 171772843, 852777898, 939937078, 321970458, 867351624, 167482500, 759083847, 193253172, 318366299, 604053306, 521879926, 352523891, 597478576, 220248421, 660291843, 888274232, 755733440, 992848583, 773545491, 847413005, 279202736, 803255349, 204243250, 660944089, 952543146, 824647228, 203222185, 313362920, 921152630, 221019294, 549745221, 955888947, 574922025, 678689488, 74457185, 519751581, 601783982, 956226137, 615948638, 488401425, 287844093, 616759291, 563656246, 515512172, 627825504, 83038576, 277959017, 706840469, 155174544, 818153946, 327080906, 625379013, 556875469, 373842649, 164447665, 504406332, 789528619, 942725113, 252321503, 824767563, 144652678, 645699473, 666347855, 863384190, 228124495, 330723015, 727798509, 679790075, 567772550, 805858102, 343170601, 64421191, 542689502, 26063965, 576754242, 816906564, 594313988, 456792518, 444275520, 278824495, 65325183, 923585796, 861530044, 72613209, 544448645, 234832191, 824846013, 967029159, 500497417, 942105312, 949255552, 908968639, 806901981, 904108895, 819290174, 689264075, 891390605, 433290835, 443119529, 295111558, 438264238, 72830132, 766105406, 263631974, 377354203, 991714390, 451013641, 158491845, 206034535, 111587260, 883972774, 458289308, 308609697, 823738431, 869727012, 272340488, 198357554, 5980570, 850344160, 795086207, 258707600, 301455313, 973557234, 861692037, 894405674, 954049658, 929429474, 38731687, 336023314, 141534674, 853155698, 925153299, 275276108, 966307032, 181301902, 341553668, 316427922, 670182931, 787849699, 627877032, 19844131, 733839435, 608112335, 240206095, 989855028, 74494524, 341822488, 831759251, 955146985, 261047742, 612071964, 637861469, 706390395, 206559492, 284032844, 579310975, 631717079, 193616295, 112002695, 387329814, 470724520, 861854410, 519753971, 774123835, 837847338, 268474108, 975529413, 175914920, 803896265, 913372284, 807771863, 834146326, 687514968, 334010017, 865837585, 223936057, 147346909, 564168230, 923442320, 9943682, 744274627, 384801239, 661363456, 595708954, 852934907, 727444648, 168786588, 225174111, 626189596, 376631067, 370510654, 344047432, 765237059, 927988587, 168653747, 166042090, 999955779, 816732904, 179522029, 534731375, 582014919, 768120898, 176604090, 939840222, 109497437, 616278183, 281101494, 948277687, 640498307, 296208367, 692701198, 200271976, 500626088, 850649320, 436829465, 195955426, 937516498, 403746228, 892260446, 377214393, 447765755, 352609601, 689894489, 80799801, 115599757, 820880670, 803168542, 685734800, 98373084, 762368233, 790760758, 331077229, 270161154, 655648867, 800320488, 743537426, 824761905, 300330606, 280451122, 485618624, 176527537, 425700643, 691815298, 410106909, 485608768, 168975336, 128872253, 609490585, 636916040, 215061353, 859691966, 198920880, 805028777, 528989160, 545134228, 966808437, 148732638, 267187306, 261608455, 409826799, 657083106, 623077627, 584610383, 121294691, 369795233, 247769240, 400501626, 712620035, 426158934, 891942319, 127893442, 226580031, 388064981, 77852364, 385879766, 422143795, 480494196, 549685723, 907058722, 819268580, 619362730, 6265090, 630548550, 387353449, 336720689, 450272236, 930047818, 989489644, 396097936, 787518221, 809607405, 205246867, 297439418, 34855232, 462790083, 846346767, 797531515, 102172165, 167027672, 317352864, 216677442, 474071437, 487789477, 919127557, 278896005, 574688391, 724758992, 472663080, 185339381, 747675897, 31016656, 238673033, 165072932, 363781528, 969439782, 585508890, 63899064, 407238401, 508623956, 294012921, 917687781, 97119880, 631027699, 41037659, 345870048, 612118646, 874852988, 461828236, 421399639, 922893975, 340493676, 353700962, 655757317, 284648573, 755410743, 23554422, 496388759, 261028957, 507871006, 703558642, 42157316, 286799796, 268017876, 287771316, 358995862, 666834507, 182096684, 866412521, 647188766, 306199698, 142399827, 4331307, 329903024, 531740795, 304752599, 827366243, 226317808, 746724366, 61267950, 617891259, 444892293, 510493353, 537564157, 343226957, 538597449, 411870742, 192408718, 490499625, 928377676, 301172480, 479615720, 792812421, 633667699, 578819504, 41014939, 614064893, 181609451, 724395413, 599437690, 761210559, 173732850, 588553288, 839249326, 65353966, 162407706, 131286979, 63067452, 785836239, 443634840, 878832597, 390060538, 355129495, 503312963, 633415103, 963742264, 443998020, 429455726, 118253432, 651983639, 355644421, 427154469, 216028858, 466128453, 218784672, 784802199, 357077901, 210277323, 553315907, 729978338, 290963278, 330632808, 861759787, 45699845, 495847831, 476577215, 598053906, 808284766, 689931348, 755022328, 993426180, 848078116, 429237173, 439706732, 546115968, 652128178, 559416166, 103897264, 230271721, 501872028, 900933772, 800474520, 549486618, 342584511, 131978478, 361818954, 180724904, 691572023, 46184790, 451318317, 532821322, 823348611, 217456746, 556678744, 6601410, 519951935, 507993404, 127272797, 747933800, 293178497, 937200251, 377073342, 513733663, 319283007, 670106853, 333773730, 391305477, 313144176, 544137022, 856360836, 707692031, 833773046, 223098769, 732190113, 951309898, 956599568, 521832202, 515368749, 937307062, 742869120, 502674023, 760824069, 188577030, 589908974, 622718865, 417790531, 861332779, 139559455, 107192017, 950032028, 864926228, 816540343, 166587497, 210331363, 383101752, 527110539, 314220067, 953580500, 911848053, 693907025, 25562592, 976989531, 79534411, 887767191, 680574803, 851112371, 730730534, 118684517, 622991585, 221769758, 547527701, 329911045, 981831803, 5538209, 13663115, 411988101, 936435120, 741392318, 391962758, 713027991, 438449633, 297652748, 922245819, 587518830, 849459173, 344007537, 448446359, 29278692, 251782971, 543824420, 353161495, 320673717, 768591391, 218326353, 880756716, 676401718, 109041298, 723338833, 345030330, 788842226, 801454985, 381590682, 943112048, 27279444, 518109849, 602039331, 361432466, 970791522, 953155458, 36846487, 959851201, 642948170, 2909983, 562334585, 892134336, 722714052, 358259701, 67927883, 108662402, 111900159, 625946148, 666181530, 557559361, 632734050, 164778599, 393302799, 439432220, 277087254, 33693778, 605446798, 40810694, 596235935, 522957335, 626111326, 454057887, 226598971, 2350661, 894429053, 835529591, 366821004, 291979648, 389040830, 371848423, 69074410, 767676588, 270824796, 545978971, 699514981, 539948422, 408070370, 916267922, 45284456, 294145699, 856815675, 133576392, 220037642, 862755293, 409310550, 571161382, 470452350, 55617965, 225959181, 624494833, 43050189, 49727488, 252447920, 86693838, 411472843, 197388483, 448712265, 615234073, 357872691, 270461655, 30685815, 582026156, 701927024, 115876868, 449443934, 424330966, 665315647, 115476481, 507781331, 252811528, 734497587, 447926018, 355432116, 74832786, 861780645, 167092810, 163874424, 64250696, 604524831, 919801763, 596294147, 336393222, 637997303, 311915669, 876869359, 913169000, 965290818, 523285388, 869502737, 696077004, 845222977, 692861982, 631612467, 185392771, 225926647, 771536900, 662691677, 616886933, 257726329, 441665180, 564341955, 389415525, 312874630, 960730219, 100142257, 323947796, 503286694, 768243519, 784656415, 415319855, 900008342, 502134224, 591137581, 727184987, 883269818, 910684506, 290349, 713139992, 400166559, 14943106, 980851625, 473935995, 331356737, 636162195, 301309400, 723850348, 79770584, 960999674, 869645760, 596535433, 902916765, 836037743, 207624546, 57216585, 250938562, 147827947, 897208047, 243846151, 503223188, 308687799, 692052707, 576652924, 50301161, 640742897, 608036367, 421627936, 199548436, 241653655, 140312064, 542983552, 636140615, 53073266, 767687163, 758300088, 781723149, 897132514, 282893794, 183108476, 46146864, 819062558, 722299850, 624783502, 998621855, 675430811, 905232417, 669088660, 26647762, 819999010, 518998114, 787052864, 260489816, 615734996, 447556314, 606404010, 441827192, 566142061, 902439605, 559712808, 334267420, 907299566, 989779488, 392524417, 232414038, 802501249, 773595667, 147108560, 909342842, 38622639, 708529344, 687134270, 974753841, 80036131, 754985250, 453857409, 898892063, 186390286, 298683259, 990914105, 134794183, 132421344, 517863645, 353169773, 409384478, 48924891, 827202374, 735589832, 538699777, 974181106, 703332228, 203925401, 3616343, 438917393, 773435352, 181709616, 309247837, 411874775, 814949780, 711651783, 707267247, 430541584, 78127369, 286382703, 913921881, 577753318, 957489071, 266591689, 774211945, 620675562, 759024419, 617833084, 671206086, 644645004, 944430403, 725955797, 90728847, 707947337, 637537593, 971779046, 323185913, 163672038, 166949747, 325291979, 815699505, 613909450, 391887420, 967706485, 205315618, 842439915, 372424915, 640170990, 484483134, 661474620, 973091841, 419477396, 890790693, 869816348, 560088953, 887870953, 256861255, 953211578, 902311946, 69844649, 165119771, 264544399, 196528576, 587594559, 547110099, 447914958, 719110921, 19248018, 20739006, 279661242, 969806130, 114524929, 204312681, 309726464, 962845388, 254459077, 147270979, 316596250, 245159229, 849173217, 954548279, 780718423, 90161730, 825866614, 314751623, 460826138, 770973601, 467522816, 608287664, 83803494, 698768095, 324889221, 119085542, 264783144, 360207973, 101595966, 936390987, 259876402, 136082877, 478769679, 780421304, 192550227, 250079086, 149352928, 579002026, 826592282, 273540000, 568565807, 148765353, 401627187, 973698818, 153074871, 869487896, 656876388, 912058004, 919956800, 17779196, 126726454, 425727099, 486077355, 38870646, 400189452, 65545830, 789053926, 434439236, 387236877, 336174139, 792715405, 612571301, 236729338, 620210765, 823214713, 7099211, 799484648, 103241315, 741137153, 739853928, 529855880, 288388037, 391351088, 658288479, 880620104, 728932612, 486128410, 213305292, 4973837, 301791196, 182172152, 262343602, 540694905, 978521140, 519959754, 813581089, 30254433, 456836238, 246058163, 675681258, 518825878, 424267907, 873641291, 621033570, 383739329, 738631385, 764858645, 640435262, 154810419, 405527788, 326339155, 264347150, 486848873, 866251907, 574276174, 585005647, 110591758, 534668943, 504826876, 206763053, 869015254, 107731164, 355133364, 463937636, 334397614, 692043197, 697339177, 851859048, 163579594, 904110630, 437516135, 590537564, 483403079, 609956414, 715021826, 324884750, 175001095, 574245771, 630922260, 450593863, 693025235, 590292697, 857799943, 781947635, 813842127, 559497929, 171594185, 623907981, 970205770, 387995249, 617193214, 75185021, 224981013, 985498400, 463284642, 467809052, 538106604, 571705750, 938780633, 237830295, 440753667, 990569200, 401560486, 824063723, 986831163, 337908087, 756542417, 854522967, 648796478, 107627793, 362791790, 352067481, 855937259, 61621390, 660410179, 393873920, 408531163, 726584752, 711755598, 150777980, 901420688, 21116262, 118212195, 463904518, 40437102, 384572615, 664512612, 849261872, 592391793, 482364952, 41700473, 647184508, 219989873, 611585002, 398110368, 53279761, 213265591, 10317258, 381235227, 932039007, 769964944, 508894874, 343211210, 452628742, 138344387, 633311729, 275336912, 740362259, 321096281, 749159996, 140114257, 491224283, 215902315, 76049174, 319217479, 130684632, 520420563, 301270425, 403321156, 913180086, 842814575, 918551424, 753211578, 872583184, 956426045, 633102793, 523498681, 574621209, 293736132, 810273865, 348685773, 905022277, 608916156, 353863100, 669530489, 298695950, 433567607, 585700336, 977363720, 275697596, 302580940, 393568637, 404602357, 121744670, 59485354, 515739528, 125703227, 233545639, 323122209, 217145903, 352229062, 624193993, 404949986, 995321855, 326306076, 903463160, 364811621, 272108687, 876578819, 710361788, 401094147, 859295229, 668943022, 570354661, 708206467, 491126306, 996534976, 941563829, 342990348, 434771971, 569552395, 210402422, 45653349, 864047037, 464182197, 896320329, 244759072, 976777723, 805562433, 894266645, 394631602, 831013215, 224177115, 898499321, 268147284, 957293777, 915350631, 779183343, 451890408, 9758605, 393874805, 548426854, 964395151, 968071877, 408206793, 79276067, 833028716, 927729703, 65720099, 743524296, 257885678, 274623891, 544110869, 275249614, 33656122, 248964681, 138466353, 165927826, 328581873, 549447073, 847804982, 503755847, 415748610, 743141538, 588376779, 183982509, 957902280, 556618925, 36949752, 84353667, 841062877, 784825945, 541319883, 293526935, 714788965, 185513796, 7982536, 923113901, 216247495, 251372930, 170837837, 786175298, 568666345, 77041016, 212500796, 357606480, 663579792, 726057389, 320396715, 950831938, 808349354, 403491028, 351664578, 256641476, 590127060, 929557351, 11247051, 411976991, 850620016, 481322710, 63218652, 796390821, 647842705, 267015707, 421852780, 795494390, 564357667, 397095304, 811244253, 391126054, 877182423, 887597263, 243350102, 887580952, 514346032, 90642624, 269788107, 695394248, 107775977, 445545300, 464806846, 765180981, 908536353, 787016452, 788647640, 74787604, 412491589, 954395863, 285553644, 411788255, 355690507, 881077702, 307995107, 32690489, 52291398, 392896178, 214343704, 823778385, 988897034, 36393620, 837624910, 725377091, 4390217, 60172313, 529905486, 230010432, 839899606, 636068666, 736313825, 872296181, 406883402, 550610649, 881944983, 668757112, 238616385, 74278611, 195776287, 86705198, 731738513, 587695930, 587660545, 510020318, 137489, 888213512, 533270927, 364137387, 3454114, 968796036, 522062385, 800228181, 284483886, 457798248, 205942063, 67877983, 299867943, 416827875, 548507603, 896568663, 818673249, 652537561, 283208810, 869119230, 714136913, 471047381, 4967476, 190173467, 84885478, 150395080, 433173990, 358950675, 698435743, 608233185, 412634047, 230589094, 881989784, 442447865, 61542345, 868992713, 247875912, 821902949, 512647326, 193311895, 83995171, 104123773, 430589457, 382191911, 962426642, 621583928, 565132040, 474459902, 115070797, 213037519, 6205883, 554864985, 261854859, 748371253, 716988859, 199581255, 499270608, 84521876, 274473139, 391639496, 19043509, 775439394, 783309274, 486131919, 460136711, 114085893, 498987138, 798967953, 160234466, 766080633, 90862888, 13501891, 334514017, 904841144, 464434514, 753534370, 954317802, 665069191, 169272617, 986800806, 416908883, 247194318, 879995431, 645975114, 287613381, 845492632, 753321568, 559598219, 855632286, 416001705, 855605631, 186913472, 661751198, 404514599, 1407592, 978467862, 598532716, 45616281, 667036447, 2200989, 495431100, 401256995, 949082885, 401316299, 975954469, 127852396, 347959638, 461493212, 889201134, 112679327, 175604522, 998239877, 413435523, 364899983, 66235337, 962647346, 207289448, 157731003, 817507121, 498790304, 557306558, 228677637, 242689947, 446400311, 749704080, 64945097, 821926716, 17502397, 888658716, 916812334, 65152930, 777196609, 233392492, 580097240, 861725668, 990539513, 547646217, 891693444, 96582405, 578852059, 458908957, 23995630, 437212151, 918011186, 603569957, 526030869, 365737375, 176471564, 831153806, 665415494, 387719751, 864347278, 467405573, 207359958, 113057239, 811496543, 915019756, 339438531, 85887912, 566229779, 746716897, 244790173, 549687511, 861674534, 16616363, 789568, 49789684, 75218938, 937733040, 61102375, 523424622, 475890319, 841682036, 118502735, 201196641, 207137635, 144814578, 5347211, 278468450, 949218469, 594168730, 529691320, 523563477, 584062815, 14254586, 438078013, 992837460, 859117252, 241549951, 129478924, 317686482, 348749424, 354502161, 964016349, 608019944, 737089407, 572334837, 51987590, 977687721, 27185815, 206747107, 1402812, 687356819, 981729286, 528084240, 558617285, 488974231, 251435220, 505133217, 296386784, 269808285, 591850041, 181014263, 240337246, 689914960, 156975331, 412936976, 610948373, 887877639, 852489100, 414871339, 122041337, 938377308, 836756739, 21182323, 383303170, 271922969, 821085082, 324919894, 425354512, 348015025, 706884820, 149216302, 586492217, 899048361, 103685904, 924077873, 94481609, 930472301, 465483850, 831447796, 370080760, 714482151, 989515904, 219528355, 279445483, 343790239, 902778508, 110709840, 127388469, 459646444, 59020953, 443897864, 802138568, 325137720, 338158588, 456948796, 972948486, 233841748, 629348713, 77121266, 164898752, 483345009, 135403928, 936644587, 496809829, 369190521, 654093763, 973146570, 197705156, 248509819, 940691342, 742580208, 554751523, 422005170, 537177179, 441487401, 265217723, 545318147, 187428857, 999850045, 872074170, 653157703, 28633288, 725964226, 266039411, 307259816, 884115866, 776899411, 937270174, 716868080, 924972206, 288328585, 684180023, 773680316, 325693392, 102907195, 488323751, 724220670, 6854166, 564112584, 848033383, 541286855, 646034336, 842756613, 243552069, 895862625, 950565000, 802793089, 753597253, 102652813, 918586512, 219710224, 564641455, 42657736, 852286022, 845972604, 740130979, 782057374, 903187754, 150239883, 883886507, 469897670, 552535770, 85728438, 862952352, 287756184, 53954411, 371430805, 492358739, 505548511, 341190078, 390876482, 997426043, 123185684, 436242290, 607558916, 439765131, 91858451, 2995454, 666392632, 305519863, 794908904, 33402300, 714476232, 545158863, 1738261, 130968744, 516152232, 806803288, 916905403, 296052934, 235488585, 802538597, 677928113, 88979558, 405474486, 538760012, 724967316, 785694399, 419827745, 220472946, 626837519, 324548937, 783632880, 703332703, 854319660, 238887208, 347053444, 343972018, 750148458, 358338195, 809710154, 917564917, 227562776, 238372453, 474828255, 592507337, 965579549, 483489110, 233126992, 521948128, 255979263, 709102774, 14923803, 347535138, 144564241, 12700866, 878620444, 796156284, 73343497, 120035009, 270291050, 851895732, 261592438, 840507566, 591626514, 516362791, 601582128, 784604055, 650769728, 466700064, 3206192, 882638430, 61400900, 882782980, 368449941, 448030697, 534751512, 726634743, 420443734, 542871550, 128447283, 148657896, 239418545, 764702712, 358439496, 561997385, 235948621, 284921568, 761975518, 111671353, 944129733, 579823248, 796774066, 876946534, 39163759, 6250493, 181816583, 651979184, 605546910, 492157655, 394585242, 454087453, 844062393, 875429913, 908926514, 676443194, 145465745, 336286680, 46722407, 944908524, 801167925, 416818222, 596992856, 506472270, 813364335, 479839916, 147552067, 413281082, 153982979, 329715720, 915075808, 103696273, 358917310, 313723776, 798610137, 651887484, 996921134, 418876678, 298824886, 273059694, 878911260, 439707357, 484085124, 615488356, 172953638, 192387826, 508753609, 457373516, 544236641, 58394006, 653034589, 496037521, 8765614, 498280364, 371352490, 496993246, 920759060, 215489825, 715293516, 561516902, 72810625, 513092165, 13664585, 498915562, 389587999, 653515871, 17832382, 361919656, 385344638, 236186840, 499664264, 386299478, 506087872, 742805026, 587752947, 889836312, 302398685, 436466927, 772619648, 321445518, 561165658, 651833340, 365288029, 302946534, 308547153, 131981423, 562812208, 185688147, 142002113, 488699280, 612254638, 99775179, 392174457, 328155082, 969334917, 350447723, 429246573, 860601968, 36982736, 566404176, 871979766, 192328493, 818662091, 229550609, 731469154, 446591661, 35826953, 234511793, 283607939, 783589561, 798819865, 105428820, 947463126, 852161032, 268766818, 84436809, 963719442, 930284269, 775341323, 508911542, 135859449, 568046905, 270760382, 308802116, 446012992, 161305476, 693028268, 991800795, 238213067, 575428147, 181651068, 385989071, 628274439, 482435321, 758503498, 915114286, 574786671, 295340716, 530182867, 429183097, 23249881, 842230499, 863075492, 402482306, 589531819, 354943525, 752996688, 477468879, 737499015, 19132676, 924595401, 239600311, 729137519, 415246006, 105692861, 895304704, 390456105, 982205707, 802147640, 977202929, 230093559, 481770100, 312167844, 798675461, 973934928, 13372156, 790080775, 140531577, 89959616, 360444353, 793674014, 624363544, 594802945, 345527009, 197676891, 432551555, 265557370, 856134484, 879598632, 800259730, 202255344, 872728147, 722747520, 550401444, 251004007, 672380761, 428703487, 72015405, 580819730, 55887145, 287385111, 180174293, 397984729, 957807302, 86513676, 83035174, 549103604, 123390579, 677144616, 655260887, 51110882, 871299219, 207238119, 500718614, 599074176, 996861793, 4470381, 599814082, 86030253, 752868554, 349412695, 473742470, 192394246, 312165875, 261567131, 717792468, 335182342, 822367078, 35344063, 886777503, 623762971, 151180567, 26236730, 15747982, 296715016, 701526980, 580230466, 509873608, 932789420, 547797583, 899462369, 326722604, 791320218, 609529852, 230348868, 660871762, 856425929, 595249900, 380816693, 427069752, 421037651, 966149171, 471555608, 753880636, 707659140, 394001376, 13693522, 72368928, 151598263, 94060959, 95100354, 843840989, 978449429, 253158863, 399217209, 997703082, 65226948, 891291149, 668281830, 949688716, 130877163, 127437730, 123788318, 129824492, 290935819, 111402318, 403309091, 34852076, 605476007, 681403732, 955545392, 952694297, 928556028, 234381232, 289898382, 83924720, 723714069, 49510464, 856959739, 370278484, 694977034, 435367138, 853558003, 367823559, 17526084, 562648254, 550973104, 115634214, 738739077, 365606478, 470886521, 297020905, 251718369, 413900543, 227451617, 926833798, 272398984, 353845228, 706365770, 871662830, 431565673, 688830134, 977252593, 237959416, 73354011, 50334389, 319057172, 715236965, 220372087, 478113710, 442794129, 424577405, 481468160, 268439925, 923946624, 354513394, 996624995, 664054468, 360350668, 461446801, 484899240, 958696402, 694003034, 131604498, 962562188, 502680090, 335599483, 630047325, 72351733, 369651237, 347036344, 610645579, 829426239, 673760805, 152208897, 407333745, 491311027, 343533975, 144289114, 417842162, 152272517, 611869621, 948002471, 392838167, 730526237, 742069112, 749611246, 40150416, 824427597, 809679242, 801226223, 952549814, 579930082, 441241265, 14713811, 465415915, 314202932, 461876787, 593271140, 792167122, 118620943, 528260524, 690103686, 895394744, 918671096, 191743252, 311406260, 777866513, 411552965, 762824567, 642802233, 14926476, 350302725, 271457787, 180518870, 133628178, 560632364, 39296920, 730315992, 260892665, 835596828, 65341812, 240978142, 396132219, 35164359, 362713153, 625722546, 975848981, 207149025, 184717855, 323383146, 274678764, 189772021, 125237107, 320653743, 658594867, 186628759, 972928677, 356307020, 805810621, 316931608, 419872376, 129891311, 394274377, 616957763, 478059665, 330065208, 408303130, 714125030, 806316154, 626747223, 951095425, 229241464, 7841232, 439194351, 18923465, 978177013, 353128868, 909699478, 914563670, 4316031, 390352157, 307905103, 393901719, 281481132, 155346317, 580588779, 560236865, 807584629, 181900585, 639864445, 197235099, 223767946, 57368020, 440000021, 149816321, 80536718, 244590875, 310640058, 928099002, 628466812, 394949990, 836685635, 775137772, 589228134, 895811855, 256848707, 128432311, 737834129, 148056955, 127089730, 886188730, 978592039, 699079633, 732060854, 859632111, 690854509, 634833237, 349561343, 918482331, 571029125, 909669772, 889035019, 93243298, 350450458, 915964769, 38936256, 878376026, 999231487, 410313434, 11320940, 53370832, 56632939, 432506338, 306371768, 103021269, 872019733, 213464587, 580225737, 372849497, 435154401, 682912147, 58741213, 658761280, 549618663, 246704949, 174903624, 606991178, 334272506, 496318587, 160005160, 653967160, 964399295, 58734367, 780208173, 870345051, 924525908, 76032538, 287923164, 598716744, 807792182, 783770957, 474386022, 376375662, 712149075, 555673005, 197086001, 9257612, 746548876, 466061650, 984689684, 386328261, 661372919, 849308779, 823708888, 214396088, 861288331, 59454412, 177550779, 416644489, 350800181, 345538481, 848981551, 47617316, 210151396, 251326838, 669451093, 652680935, 402080657, 823265004, 290578083, 557075321, 968170715, 220203396, 701440436, 959938163, 109173215, 984485392, 491292363, 709587870, 948596337, 442179472, 744475421, 848057036, 251752679, 468415546, 308705982, 481927806, 229050347, 305060587, 970799975, 257462142, 321599599, 270308377, 728589357, 323031794, 108956464, 486553287, 904692256, 427641591, 877200904, 17030754, 815388989, 631306036, 339923243, 715758807, 103909596, 804508005, 465742225, 232824645, 822487008, 198299021, 645060099, 598846314, 766338304, 393462383, 765218086, 58214914, 834418510, 770056726, 657852089, 754147135, 522365723, 329541301, 115508831, 792268000, 477985541, 923212105, 96169518, 639805769, 618513587, 873103243, 852188161, 758339464, 406398588, 299149743, 514988487, 559690438, 554798683, 288654312, 220925176, 752488823, 6797141, 413427116, 722813403, 384035824, 174133225, 130837050, 131243251, 618229270, 720376268, 669511871, 440987050, 965127620, 733042604, 454072593, 837593746, 432548811, 448945224, 753159176, 354788391, 209236304, 65208358, 371913917, 920448927, 284572421, 557828778, 928162512, 319698263, 990393729, 913289996, 480209150, 371206958, 258463933, 410022682, 398574631, 637451399, 535364076, 913574655, 112700844, 184500025, 640517832, 736984120, 204454983, 415762976, 874256717, 961376677, 971114066, 764094920, 681150508, 205315253, 519477921, 882059124, 230618441, 189877358, 425103165, 925781591, 48052242, 96829909, 709478267, 566493813, 250213558, 203703987, 936786388, 681218288, 787481099, 148310924, 908389500, 445230470, 371969945, 489634730, 448310993, 749134765, 308001912, 759667087, 895172983, 310969893, 445873521, 370029131, 354347434, 890224291, 628443461, 736962658, 487414723, 648266427, 28177872, 841438696, 207331251, 98194814, 917982939, 997862521, 411420661, 900989669, 418638805, 245941305, 819231460, 813740656, 358073167, 77029968, 282216957, 935401941, 916397735, 176354899, 909926626, 355608756, 782788047, 495675778, 321666835, 579912971, 256767860, 133261953, 709887907, 547423888, 350843595, 834304878, 349046332, 653782718, 869828044, 558950595, 980321859, 470576802, 290951952, 608386568, 889981480, 789277655, 738736082, 395716853, 773241871, 899822156, 585199258, 422963608, 706498825, 375555601, 525427966, 455597113, 615186795, 811510546, 426612564, 329768322, 902921027, 383107976, 604292490, 783247674, 380339988, 692499613, 805314727, 225186400, 744792043, 124601648, 206228184, 135746595, 439716260, 86495551, 21251852, 426056990, 611651521, 250268848, 332385476, 965242058, 360165259, 42253276, 635487881, 234454761, 422214432, 90205016, 366151004, 541738891, 196231259, 585283363, 911591678, 205169733, 674277560, 525132376, 405728700, 944060220, 26526590, 857729998, 149610957, 343349107, 731049433, 7087776, 770746459, 105515454, 245806807, 684488046, 878491665, 620498190, 710386293, 222700920, 808762203, 66460084, 405411683, 340745716, 726475025, 709973590, 233332302, 414683822, 439559678, 529243707, 579774928, 726588317, 284306947, 760338208, 800160152, 236763630, 574842526, 140730692, 946544956, 308834239, 934461975, 230612962, 612369899, 901986267, 449567412, 107427404, 250370835, 950771238, 721718555, 780632593, 761799236, 85658279, 582634479, 975465030, 427761386, 412346266, 731521727, 616967815, 784858571, 479267549, 766481260, 926064819, 202727977, 189970041, 31016101, 838366078, 463696003, 953429886, 234240933, 749126611, 542106985, 454243698, 529366165, 761609320, 983432197, 122664443, 618592347, 306573134, 384831165, 530469464, 121905370, 355680240, 735260220, 989623306, 464761013, 421318642, 865577605, 88122116, 965400038, 357427249, 984530836, 363226367, 338915674, 452987525, 881575817, 323437649, 150730951, 129108527, 35269248, 362921746, 471631265, 885155746, 345807340, 806575929, 514978014, 512047713, 431368353, 401276955, 313120225, 777649016, 330715707, 977871443, 143453650, 928066187, 415172575, 970067257, 294007875, 903324224, 323413401, 353462397, 991700702, 591656235, 245425474, 248759108, 998498750, 697069118, 825106766, 309979423, 820991342, 429192285, 786443346, 462274242, 38454974, 253604528, 561120662, 930273484, 928386481, 583234678, 896738694, 255650022, 331599913, 878861316, 301785908, 505180809, 251777997, 404445305, 51037689, 756178223, 703371134, 879501069, 166379400, 686801158, 993880344, 684601431, 387094916, 817865212, 164044196, 991678292, 295758941, 522982881, 81797848, 524197407, 713514828, 520508682, 460553017, 57041071, 381948281, 955458047, 428738441, 237178300, 509338480, 653989244, 543720852, 656739866, 795939850, 900507419, 99316162, 918787952, 319360585, 49012999, 214596824, 150391710, 316821361, 826547284, 512381161, 479682773, 614638262, 457047073, 345489520, 643813367, 944511068, 719926076, 542615571, 775887944, 253783217, 215156260, 284325447, 51511585, 99799989, 832772807, 935692162, 830470332, 738668042, 402795664, 651309300, 776841170, 518856227, 22126863, 378970564, 364305424, 53385579, 896449527, 519407418, 456215076, 649651835, 514541624, 307361757, 629341053, 850809930, 692902463, 2001195, 306825533, 812751196, 290021495, 630964311, 399705940, 596050185, 369084255, 856931739, 906359687, 829155986, 106524845, 361492389, 3383379, 724438740, 407014988, 687536137, 682297906, 561352060, 153894438, 851682648, 387567942, 756484134, 847143216, 569059766, 294606026, 684048631, 682267761, 666084351, 241845944, 891269487, 393067661, 117578050, 374888112, 277405563, 451144853, 683866363, 718232327, 745203321, 35906727, 156478976, 444798819, 117421397, 345294670, 321750844, 538849664, 509896039, 320761602, 234632354, 472900151, 733214671, 299054562, 547775552, 856359635, 121476836, 725732720, 584441379, 780927626, 67481124, 985196345, 265047391, 518630642, 979773767, 213719422, 691797765, 970228622, 324815719, 714838553, 210250389, 497416856, 508681833, 94091294, 374735814, 96763218, 243327495, 942678385, 355233504, 824846934, 832755591, 785242851, 142466494, 342781242, 578073336, 406131169, 378612581, 604848342, 549311181, 986204173, 96099079, 973556306, 42505695, 433476902, 590046343, 810859406, 880719295, 843618990, 12717804, 540903764, 343466892, 203192777, 21294849, 656003514, 941983714, 991444583, 569813693, 972637428, 316879800, 119973258, 671536222, 143027649, 239252287, 402064146, 290216059, 991806245, 208511770, 695935450, 626956187, 502911217, 610722473, 190223478, 405314688, 221366452, 463912349, 363728624, 506254303, 82950872, 517634519, 54733063, 268263591, 432668799, 853696225, 676286384, 254718679, 66734910, 342912022, 561578941, 637775048, 937191155, 358674490, 582966484, 519150202, 271406198, 277423704, 107910907, 302768285, 225657638, 624508873, 835646061, 255944934, 572803947, 323184365, 410568122, 77342942, 751432351, 175563504, 561036796, 350373663, 205685198, 603257258, 847773926, 134367282, 274176335, 356493756, 916629653, 171044791, 783390422, 153485183, 181491566, 872591094, 508925455, 641211134, 901952768, 811097053, 548187933, 831229053, 492918224, 914767040, 831960779, 774741042, 128027072, 314031757, 401786953, 127691963, 795144498, 251169140, 824379196, 984108947, 423671280, 385398549, 534795706, 896432832, 88079610, 238725186, 429193393, 262951280, 742482249, 698643417, 620494298, 394998150, 754279792, 505583246, 613858743, 762751549, 327835066, 628247449, 747800478, 925321275, 465544873, 440293549, 766877458, 939779789, 169889299, 816089920, 522770384, 755611905, 486549492, 104750945, 425612160, 132636378, 968833063, 315983772, 379991396, 90307314, 923334526, 851291553, 60521503, 720340208, 812873243, 50137872, 451138124, 342673760, 341072862, 703625889, 682151350, 591038320, 199544023, 233125555, 360777258, 410918759, 429998140, 444680911, 649307690, 943286368, 831044234, 464145988, 465511359, 206064724, 446429209, 634288143, 284809174, 728469250, 387708762, 506867175, 250479395, 649137885, 887672446, 930651743, 24143094, 443558875, 458556379, 154763134, 749152889, 255455604, 872963974, 650909351, 860352674, 193488038, 664247929, 178014256, 2745995, 475339812, 558720949, 385545007, 854598747, 153940845, 328870865, 498914411, 64014139, 583879801, 613008563, 199922922, 572140709, 514704420, 511671953, 771653226, 391862896, 579140798, 767887893, 740336285, 415971195, 206544989, 543232753, 724053366, 24573738, 956694881, 51907071, 731259173, 678928800, 728839260, 343511859, 716152734, 629599773, 863238735, 6835245, 446262105, 609251642, 108852068, 588912848, 83557353, 719325864, 837688744, 997907132, 680316723, 43385441, 960197449, 955510917, 530792498, 536101520, 373242887, 953392463, 369582721, 373798720, 268171436, 317842274, 215681532, 59235511, 972777051, 630697276, 991059825, 907233592, 614360776, 353636620, 121194588, 84081463, 589229623, 543303789, 747801399, 156778673, 296623164, 72970537, 291185259, 867786056, 189068410, 39460839, 622527854, 543082985, 159323927, 721266135, 404855783, 107900699, 10036381, 748845503, 40846328, 456136142, 348822089, 101604344, 730509355, 812824428, 889028784, 99218540, 133673369, 493868922, 768512281, 160589616, 387159092, 171072497, 212198923, 849176450, 365156757, 39841924, 599811335, 845282738, 233289111, 354556714, 534768637, 454255041, 864380845, 283723349, 806345883, 133162642, 724106997, 246456919, 967196664, 320060361, 469373314, 87550624, 493944406, 684481325, 32171841, 524093852, 542070665, 871986979, 791024572, 721444420, 341440701, 437265387, 855356458, 600906880, 190723522, 852464241, 724807119, 678174431, 675606623, 628306422, 56167450, 166536923, 743702931, 289800474, 910195168, 297231047, 79959107, 544921549, 874135592, 852103790, 979066322, 791112437, 999561889, 431321821, 653270311, 851465256, 205506086, 377180940, 558938896, 974542309, 278266513, 298554988, 102793672, 814058624, 587331528, 777731654, 634240162, 737977587, 581588241, 398024699, 921210610, 295024623, 572215238, 909849250, 93997019, 378714285, 439760076, 214487204, 588700811, 230580786, 855122162, 845985568, 741857725, 302125292, 89487226, 549629540, 719991007, 23373061, 318419242, 337628558, 782314116, 480714015, 621795668, 177316212, 534177789, 752229391, 475722319, 406405444, 208328539, 648114708, 240250654, 26986415, 300632899, 4781630, 325415423, 301316502, 387032914, 376151128, 685252565, 843794386, 816885766, 113625259, 187088100, 862482823, 153592021, 174314036, 768357464, 62064970, 864528596, 418835392, 998960888, 293280200, 344382162, 46047683, 373898174, 873452910, 711627572, 496697062, 437210975, 224735785, 354131405, 926227805, 994603066, 256481701, 469916407, 509437727, 176302158, 489474594, 845451684, 224645957, 479237601, 21444862, 686267503, 477049565, 11303881, 302351494, 389953606, 84132445, 836349708, 154378763, 984848027, 405385905, 385362777, 243218242, 525727977, 550191535, 542056858, 670061399, 639735786, 527506943, 692416064, 242638447, 590501255, 236133560, 146008741, 352060767, 40377928, 183717754, 359608266, 946053736, 392435899, 142794454, 778501812, 129535775, 365978343, 224197879, 957078516, 805748034, 806989303, 854534765, 479544910, 74552741, 356415406, 703806073, 930354348, 210964345, 422667210, 757202292, 580373003, 649939575, 777920710, 941385047, 118536671, 477727472, 429678166, 237362495, 478991493, 907036303, 335926051, 796020543, 602800382, 376679026, 496911002, 759888542, 212504672, 267541020, 940085627, 27662303, 449210472, 757403359, 154561932, 249554554, 131191140, 861525562, 648191528, 386063391, 634273884, 584862416, 608566755, 295817579, 806022855, 300476221, 30022500, 843820066, 21105378, 311848987, 973662617, 687844454, 947696579, 376448317, 166736622, 428143552, 685312106, 853390875, 425734774, 740495011, 953577276, 953958992, 977519279, 398744923, 381476214, 377186498, 256255880, 513019256, 134876452, 900569672, 186588614, 774925128, 909903032, 57559153, 209051252, 355444310, 890593549, 863856178, 975985914, 633328452, 288652261, 819154953, 775848678, 675587940, 899998084, 755422394, 12577421, 339974365, 784185886, 513646289, 9954006, 445475757, 168214332, 648743940, 705193969, 261927669, 518679536, 294481640, 54383157, 568050755, 84822737, 993639777, 809617923, 235868377, 79140041, 243010849, 296542568, 502428638, 51607474, 157543442, 802212916, 249731307, 674333010, 702182005, 104272537, 397545624, 322073071, 880773395, 675295402, 188011312, 369930821, 509106860, 432055056, 607373067, 36907595, 91156509, 561721882, 810426643, 283532272, 918859676, 318279412, 412751112, 325981351, 126888468, 76484904, 54570144, 64903371, 739642303, 957027324, 919871140, 658293654, 219805443, 375299177, 869623595, 586651816, 169017832, 85468028, 234295650, 633174432, 456612714, 290473715, 225164537, 207302020, 976574623, 497601231, 711223219, 729900198, 28207938, 188802568, 277275526, 772177080, 536489772, 261734074, 255160713, 311331082, 154864773, 642591873, 534156848, 642929633, 361198616, 548507029, 503938584, 322285408, 456653808, 206438638, 313241138, 530604089, 359912600, 395623001, 985016769, 260745615, 756014306, 956319619, 486114486, 226011484, 952776968, 721068776, 211857863, 89574523, 943068655, 568491868, 154854201, 254374516, 290677111, 943874943, 650297832, 407442313, 800355608, 316940100, 699819551, 898982233, 336527861, 136362101, 542792021, 888027732, 212749315, 567782986, 292630376, 657083511, 739850591, 84403546, 119488151, 255065793, 99892073, 156822246, 73677094, 545372195, 385394796, 649903146, 884620112, 638412744, 967834387, 659616502, 209131242, 25106386, 229796720, 775148654, 255938828, 843116805, 586210749, 58127714, 516169527, 726503867, 634936155, 435818614, 84280534, 333823794, 449832003, 493111507, 616047196, 293762087, 130617118, 492622282, 7565482, 234580707, 553081409, 977100975, 99654939, 665343212, 156505653, 549987480, 954997912, 489788971, 158024217, 917545661, 948545969, 830665431, 912611868, 143429623, 930602878, 3685636, 725455542, 115330233, 194131999, 687543451, 333859549, 464262694, 441250279, 1136646, 88698245, 69746098, 246098266, 364756776, 540856779, 96174566, 647653714, 191342970, 917273118, 130934459, 751136977, 659872735, 670607742, 19565883, 475570147, 27593596, 834838171, 359859135, 531524179, 869658984, 722233028, 596697937, 278272865, 979559620, 735966250, 34947704, 67504636, 835364258, 398468681, 58157021, 637064931, 668583229, 254183325, 710976264, 515091051, 249302257, 899208421, 813908203, 753606324, 877122157, 951469994, 215743796, 58228767, 762842914, 872302707, 165179625, 328544019, 885335569, 468634353, 263911133, 690194999, 325726519, 456489180, 850066793, 783896509, 31013309, 636729936, 77082217, 929916854, 126108154, 41231044, 210415896, 707867854, 761834645, 627413121, 458101437, 962082784, 811863097, 423212166, 156095949, 673054830, 584458437, 377406435, 277593201, 299030061, 598950299, 178935371, 922140411, 893488690, 320643141, 686867573, 464452974, 236819277, 31128315, 835958427, 845611617, 486436686, 111790678, 718004673, 254459062, 253743542, 515283955, 868486655, 58461504, 995174007, 351608901, 482893203, 296102233, 137781910, 32338029, 254028278, 980655116, 967074372, 846112760, 356346778, 660252990, 988756762, 421839365, 721812384, 814658188, 494368916, 50446137, 595589211, 332873866, 210228294, 764797653, 224926680, 282378685, 580744647, 860261723, 9282143, 879434181, 321656407, 841006706, 587447810, 739605120, 755093506, 388436506, 505465991, 703656934, 10728785, 635916863, 454793874, 652325767, 636830852, 719718254, 128896683, 78785022, 891925518, 852840446, 532196474, 108231884, 824475804, 857937504, 244760542, 93670767, 147077631, 760446552, 692324472, 379755342, 222352151, 430685529, 743925772, 86764158, 570520386, 160787157, 455942121, 396799919, 429843355, 342778347, 123909598, 723149903, 428952088, 159896201, 137974448, 763884626, 757453290, 2438481, 24205579, 700586023, 144797368, 356800045, 483817101, 913362395, 164505989, 900941379, 381677951, 103793779, 51423071, 939450418, 213753788, 15228284, 922158526, 159419087, 571421929, 212551961, 864443501, 827024224, 713409601, 341380004, 917304118, 409185339, 576837402, 428486192, 428571264, 379287037, 905069045, 685446996, 996109385, 292020122, 101334429, 791899699, 762986805, 809893547, 445073724, 114523734, 140185899, 27355873, 434373907, 235715905, 200925552, 780599386, 107981954, 250793089, 908266233, 493448344, 269836035, 725479801, 753226967, 185259470, 599420151, 697830677, 924952670, 903235939, 495981854, 78311135, 601701090, 726130453, 255280740, 803488449, 826549743, 801136428, 396546473, 404831747, 767907385, 175300177, 54177736, 305456880, 535242656, 410004349, 450514991, 247312985, 376764733, 950919961, 451167392, 246294441, 502799991, 802126638, 366797574, 720576081, 437069361, 979272060, 114914896, 406061079, 993935186, 473763641, 361873740, 206640990, 214853992, 796068050, 247489878, 190394935, 692955095, 640597111, 759098643, 280777241, 682923641, 587902208, 12334950, 27420994, 69624293, 352177277, 954989669, 95788719, 473731556, 124644329, 13615098, 8287880, 578646125, 657254478, 730495541, 55327443, 777600694, 998122262, 702175866, 873014768, 931848261, 162511393, 98295121, 601232886, 115101145, 301258357, 276999495, 611253110, 824036967, 837277555, 272463205, 529213677, 931325597, 305294151, 752521114, 685074283, 605885821, 273659312, 848506670, 405432792, 531101086, 636100175, 368642467, 662256840, 344230717, 879218285, 975159826, 319469424, 556894877, 605068310, 438278190, 820895285, 861558766, 321568578, 690124046, 405265676, 541730263, 176446741, 391823514, 791860699, 463180887, 906934122, 669373428, 987710750, 70299882, 352135590, 877674363, 198587066, 356934023, 97062584, 697935040, 455380708, 725874594, 301587041, 655025579, 170363756, 728810931, 282438713, 686540060, 734902961, 859016434, 848984969, 825697539, 789031671, 176613556, 586145506, 259887404, 252985365, 313443669, 489779409, 302381617, 828924026, 85781984, 190987074, 996167556, 522188209, 393224476, 155895938, 870851806, 552137419, 561884602, 486241685, 345792672, 723057732, 831512132, 205022548, 16454387, 404731997, 292655534, 391085990, 779670218, 94016446, 737586401, 247310174, 81834609, 365049723, 387915321, 353646166, 852666552, 689319213, 951029063, 760930084, 148958843, 301412893, 739738532, 789664039, 140035664, 662148121, 505621762, 865562097, 888361534, 670072765, 307598968, 732206707, 576228899, 787231305, 498225983, 583754872, 486618012, 975603446, 244459595, 540899403, 792639454, 280676309, 141987025, 467776594, 180251629, 768206582, 118126291, 887918115, 518669482, 781586627, 723142551, 698510657, 468861451, 109232275, 37221369, 489959703, 296800020, 435890414, 681518672, 954584695, 113281501, 277101090, 457759507, 625687994, 131896152, 942835310, 450713478, 338436019, 552523589, 513639196, 998413756, 809638850, 404269581, 504405117, 599624059, 369647093, 21570657, 945109320, 194650036, 396593382, 222726005, 418060053, 215513707, 343107059, 21204308, 235733707, 553124419, 616736700, 462018288, 641813106, 512387696, 246669411, 302865765, 223152610, 106295212, 119487092, 430764110, 412259648, 361984064, 375396555, 71242730, 125550121, 58145652, 475515109, 140887458, 774979493, 168690606, 440837973, 807787082, 721620558, 631167718, 169150540, 143828252, 591263086, 499387337, 995227704, 490322491, 26025295, 264142419, 67103855, 453691272, 174686654, 570794586, 689498507, 133598800, 918550657, 47735251, 238790543, 870692177, 670359306, 407154767, 684453453, 217146683, 287476385, 495044032, 471448050, 7223013, 317006333, 37530063, 804959056, 404599138, 251360640, 146578301, 781081617, 706655216, 817297359, 843294231, 209906299, 814007061, 755757415, 89941950, 59721151, 315561143, 758934294, 409466167, 660660657, 978021895, 901321464, 929635608, 438839981, 254264201, 497491634, 790716556, 552980336, 881917005, 237165173, 767811125, 365793954, 725826928, 804355551, 834573482, 148271769, 408541240, 34551960, 353740286, 402239974, 661510509, 633009669, 919775223, 437799739, 562776889, 206626261, 955039298, 816286844, 424409939, 479286450, 489697212, 945280258, 793015382, 943721195, 740383091, 674358901, 592130739, 160657131, 962043680, 887943659, 524683841, 886475274, 33257275, 490009721, 154838886, 77746197, 444696361, 485029311, 545963479, 878796815, 347275506, 479596455, 689938739, 953707214, 944880896, 666993429, 449585211, 460891005, 72601608, 633219525, 229340387, 447182634, 302183131, 165027110, 589461617, 396040097, 349037943, 261245413, 769696224, 301954540, 725936261, 108716149, 846849054, 397007732, 480364744, 35189175, 379418446, 831380226, 285214700, 869339760, 217119711, 251626738, 781349222, 226349189, 955992516, 765351188, 880602888, 311344227, 488934278, 884613409, 181076585, 620552099, 422647001, 662670947, 876736117, 320682418, 289471147, 905292709, 108794144, 112542401, 369019507, 362634417, 429077491, 573066637, 423452858, 324887032, 627554738, 502674440, 452547380, 755426586, 422794575, 251083667, 298823852, 791950296, 677042167, 143310839, 882624153, 566512560, 276394136, 202652316, 786602983, 320157612, 119356137, 945561814, 26091245, 219796233, 247868133, 744959302, 814842606, 62656827, 930964748, 648246895, 466850249, 955220569, 570813789, 309784565, 376675125, 106808020, 353476724, 374417394, 88631301, 81064138, 177123124, 545508267, 118718517, 654485994, 675237145, 66164288, 913911677, 61944757, 74421542, 604519451, 267087275, 972364891, 406722391, 286056419, 11104619, 923648315, 20206942, 854001414, 613339781, 870535698, 284258446, 365035512, 570837376, 986037007, 681155033, 497792285, 109057244, 244656174, 856746709, 448198132, 981535584, 648729844, 33105424, 855575389, 838278815, 992083314, 545022780, 140790648, 196451814, 842532313, 181625778, 602787657, 678406100, 597284918, 159045103, 619023827, 304286473, 606731967, 988883497, 501326358, 874188302, 426506018, 953146638, 197973976, 488934664, 889452014, 593669770, 456215545, 816749260, 782357513, 178662900, 452166781, 836045353, 314648104, 700907774, 481453531, 796092525, 599161908, 494954101, 986071926, 512933740, 323455666, 65308238, 938387207, 227284118, 848852708, 754053877, 652774876, 893058592, 782827541, 353255788, 509633260, 452669006, 740829361, 34938026, 591379202, 101957406, 102711973, 105917028, 454529323, 990781017, 546817355, 179844021, 558898106, 442140477, 175973614, 430116020, 185241086, 6818434, 901305907, 996904133, 347866314, 598067930, 420997785, 762195634, 310411942, 415653382, 29212306, 312641324, 521727923, 303864059, 442481456, 317932037, 556498903, 669289723, 221077531, 278085653, 156522314, 364874138, 108839522, 942899499, 546682044, 673462477, 933582168, 810413905, 565849347, 505367645, 846498493, 389240450, 231414339, 880994386, 788938691, 876143799, 134698526, 739983631, 95563098, 893503287, 959544312, 467263941, 872713599, 728418482, 511793689, 533836153, 682213437, 499272915, 196312233, 3753537, 3798486, 732185706, 82807340, 487844748, 47314476, 968290563, 845847094, 713516936, 538112868, 641406946, 74588438, 702750124, 879875828, 971299442, 886025782, 975029374, 344190849, 4885099, 500335638, 606475193, 635068903, 553749411, 584754753, 991561865, 136940739, 112461045, 773120673, 442919196, 756658834, 954178863, 342335309, 874153781, 398350266, 281141911, 186846473, 567449078, 459785552, 51376417, 860163299, 878202191, 670226912, 910085553, 418859204, 695945723, 846328060, 655860837, 686446182, 580428906, 465831479, 284592704, 707908027, 975262090, 991182082, 72808778, 584091244, 209254587, 564649891, 883941526, 669638442, 458824130, 855310432, 243757999, 364212989, 981094036, 249701842, 752429670, 840332721, 146933633, 29658099, 139390809, 35371723, 951293186, 553746568, 267733516, 949642255, 153176934, 171471849, 117168761, 607435408, 393285553, 129120886, 489186096, 464592118, 672370752, 313039692, 162896893, 238923014, 152323229, 658115965, 821416207, 676113728, 244788938, 52794614, 651470095, 980518206, 252510674, 350643162, 763811687, 531927943, 454416798, 151117452, 902987953, 590799963, 442077733, 160249814, 253867721, 527311765, 535798886, 812339920, 224757523, 36428221, 662520122, 648979121, 358252502, 285114776, 933990874, 452291624, 347837423, 496242472, 327899043, 72982800, 177482180, 160818166, 850379658, 510106919, 472599344, 61188782, 905783378, 916946202, 36245111, 563328154, 789589322, 809777891, 731946831, 382370178, 128202124, 193717575, 522799482, 611583118, 83707396, 729357122, 405124020, 215183177, 580413973, 418679917, 837331614, 873510627, 997881836, 358775199, 238725650, 888770306, 960932551, 837152151, 362673290, 786649188, 973140959, 58592421, 727328072, 228714547, 147949105, 656932553, 499522285, 979283757, 16679427, 897350159, 939117139, 210078105, 747426248, 425802195, 571359916, 947782918, 207960865, 979725385, 704622643, 402163294, 109819574, 924328507, 225142771, 477490928, 435344015, 924556680, 135514569, 900183469, 770267984, 690371836, 379815502, 803896312, 859744226, 880071720, 242338870, 339537199, 542968898, 358755635, 682284404, 389632732, 701216806, 411790361, 479684223, 714836463, 319108229, 318616121, 59201325, 698697545, 713775925, 911440631, 900851702, 994909994, 120660464, 495645885, 317750234, 856191855, 322117928, 212499154, 921090541, 288119885, 252453927, 90828626, 373200522, 496768974, 778556257, 187976376, 920759121, 143932017, 870692987, 423186292, 513852559, 605972342, 463803510, 930278523, 403577940, 160538352, 761988598, 34806325, 494934469, 97287561, 913865289, 525666830, 217735145, 405021370, 804290824, 214390161, 362953443, 742031615, 989790937, 80256306, 785890068, 127254769, 680550144, 936704702, 331755468, 824978201, 568088207, 625804262, 771614419, 386240510, 560293677, 394016189, 487611956, 895957316, 544760666, 244804967, 896322319, 56315573, 361141307, 286966090, 292200229, 317144568, 975961900, 21856705, 13438971, 581763482, 536057155, 908483139, 159674950, 371983349, 651029438, 249466348, 870632791, 239908497, 661579841, 535253232, 685300665, 281221814, 64575962, 231050977, 52170623, 500685715, 51804691, 1404911, 941168479, 493126726, 202152416, 151875211, 378787584, 249580285, 281760871, 900199133, 787541311, 476968205, 282712963, 178544109, 513583522, 482459054, 228825644, 56180844, 750643387, 467735755, 574102746, 5333045, 142772703, 139903714, 378150074, 604798426, 13774957, 793815377, 433032845, 859260452, 541829594, 254286818, 480654242, 899520187, 777595747, 737831863, 235570668, 79402550, 389058645, 469533840, 824341802, 962130181, 626141511, 543156603, 525427626, 941966893, 788584693, 977490552, 908464159, 101469303, 204619689, 445150028, 923169729, 987240505, 760665958, 595626940, 922392152, 359153306, 4381277, 294903915, 888383012, 568737050, 705314315, 212043954, 249906736, 943284205, 163945594, 159429741, 512653994, 447539493, 245128752, 991417496, 301766226, 66502865, 914720780, 165700431, 670946428, 26407354, 991948170, 206696220, 18591922, 517381263, 837938103, 995569622, 761317079, 64464575, 992726774, 106695521, 76071157, 359158219, 575982976, 356592265, 977156958, 81647354, 819837220, 877223483, 230849427, 543770717, 21245359, 834548196, 841850681, 499968089, 972828454, 110330487, 323097839, 226542005, 815592661, 764298037, 70604950, 153704308, 769389121, 751088136, 188687853, 587494454, 762197903, 729943324, 414117866, 759585217, 876297823, 707678255, 84230063, 385304279, 976709658, 802521844, 511877623, 180843000, 546110908, 357335999, 76746037, 918288533, 88234988, 811052938, 839844379, 60718371, 813348929, 704224454, 776344264, 574031941, 855635783, 599903221, 505228915, 734029360, 572003372, 972816961, 741734234, 17719173, 198376178, 433344052, 222067795, 649137331, 115288736, 825994177, 273477875, 485987050, 474635913, 650328805, 713749096, 315673329, 819068887, 449870384, 831491018, 788857904, 652534248, 54210088, 567699491, 412179179, 375406596, 339532731, 413467150, 87985504, 560802858, 170648584, 513959401, 156120872, 743842935, 120948221, 885234250, 746549993, 282249770, 424827599, 739310707, 998083861, 376466078, 153123319, 247314385, 899419580, 901313295, 192913455, 288730775, 486568012, 59176822, 249664482, 552315300, 745197916, 547751098, 454359106, 541950164, 808333559, 684934034, 580585551, 12928426, 42888921, 288646884, 431620237, 516219862, 469880754, 624166350, 935507209, 787331643, 249632282, 120433639, 941759323, 840389204, 739687963, 742882317, 690872363, 811628383, 582842443, 735893773, 464008507, 818734688, 943597945, 110384116, 221034400, 449503300, 934514217, 897276446, 54042732, 400347214, 712864439, 867678433, 394676046, 488588580, 826495002, 862816217, 859365820, 783737544, 978174440, 476678375, 737756762, 258081128, 838008823, 71106873, 427355688, 174846538, 531021291, 589090326, 116394984, 652197602, 48087579, 776243343, 366109923, 91064273, 888216042, 287028337, 655385682, 382804818, 920546135, 159247205, 713285454, 25130336, 646970842, 316100822, 397862946, 566088723, 733333640, 205353559, 482820043, 506561510, 562285384, 968092480, 684611344, 31439074, 413002757, 11318070, 183555330, 314784779, 906577685, 573012915, 696979517, 996032951, 721974607, 943600346, 675761461, 735248240, 485046379, 10560545, 856115556, 368972881, 86247104, 149438652, 243366157, 944475931, 185602460, 410923664, 144437286, 589988818, 281386883, 826255389, 877180475, 150111753, 918941174, 830519674, 292651458, 617059982, 805626835, 355243266, 175819045, 969383459, 601301297, 523733223, 952612061, 68196406, 388920097, 675878929, 558494114, 948258885, 102683784, 710705116, 340282324, 802743606, 505728733, 882118662, 569553911, 261763830, 194957459, 203313621, 824005795, 545942601, 146216328, 317619223, 596622874, 864863993, 88197288, 130677807, 619401097, 363435772, 423743219, 620379969, 944736530, 3057090, 929389005, 684949120, 21282331, 983246527, 54862192, 879534012, 272135482, 737238353, 880213923, 484227833, 231193014, 524166777, 500829056, 632448443, 655660913, 238315612, 497665487, 37492976, 94805082, 521940084, 873942002, 280484652, 744575707, 848726793, 954006855, 456650725, 330642918, 269229745, 58862551, 53998277, 562228552, 596080031, 851610753, 829225593, 911256498, 783696277, 885900941, 575957242, 679205122, 250386215, 482657082, 871413067, 932428399, 440690149, 419972824, 368658967, 341410380, 852737911, 512975282, 802438385, 204947000, 53795990, 907421541, 833476422, 17897168, 73191484, 258816420, 919628577, 695361790, 501248480, 965218670, 722196544, 387640308, 532929678, 176362623, 300035958, 409555775, 445099460, 461332800, 85506479, 209397837, 754496766, 854861793, 767634140, 583454317, 44592486, 605955918, 308280773, 254412108, 161764284, 407615881, 227818633, 453515321, 242331149, 622317623, 317534411, 445846642, 216302006, 682265996, 769480607, 733441398, 345609594, 333022359, 723336628, 124065258, 324627270, 949147849, 868588258, 460190091, 891590663, 371329022, 233634427, 388830095, 935829914, 109925990, 403657738, 84656024, 393438207, 605254046, 66446398, 318287411, 202786639, 486038302, 173366410, 387579212, 16219452, 130970295, 457123653, 207974392, 697370709, 247091419, 693851011, 154122021, 968790234, 537729643, 785063539, 712924506, 224873313, 564570193, 793814400, 725032053, 671104592, 228132194, 981593256, 249252507, 24756327, 679947608, 262304832, 892568385, 506165821, 536860101, 544295896, 908105577, 206976793, 422367480, 345205613, 353383787, 902053476, 310550244, 724871644, 339782356, 264678584, 559743019, 598197265, 613295328, 565817125, 263716362, 148842316, 791935059, 340560800, 647609895, 640333074, 670917529, 741816263, 387732698, 654057624, 471224144, 400983004, 248303715, 895193060, 741654552, 702773481, 455773903, 989383658, 794666324, 615697762, 76008713, 902322780, 833909842, 568366969, 194664830, 230008047, 840767544, 354370256, 63027273, 888066917, 175656521, 11445824, 321601794, 97246519, 182402122, 295803320, 164325535, 460764790, 172241145, 925334383, 452098023, 951831796, 816458358, 254028331, 838055453, 842820593, 958246646, 232675906, 931644530, 966843696, 190726319, 337876763, 308428602, 152246316, 793572725, 331600747, 238342747, 978472520, 445977650, 771590032, 429402641, 356265099, 813114156, 435668554, 328775177, 826162490, 15214292, 980982005, 448801119, 770810601, 194213856, 519180718, 763444478, 38277670, 855482284, 126075838, 90472074, 109847947, 355676621, 299051294, 413079091, 748984016, 160364924, 537732304, 55246645, 339828442, 91460745, 681765440, 938499409, 600785349, 489774063, 422142535, 416909283, 395093071, 966776880, 351764812, 244338638, 410476495, 365196757, 413709526, 81989617, 977315678, 329596400, 978057906, 14044134, 218619731, 921812069, 199543754, 158763032, 151830804, 557448191, 920228698, 748473248, 254004579, 954640679, 689740041, 259223311, 131677030, 714287030, 708480969, 933011715, 62179299, 126917010, 389522027, 538917365, 557491392, 708306661, 423883500, 749101504, 712563592, 472870219, 985292464, 910805360, 640098480, 528287005, 917048301, 23737464, 942989119, 535490966, 352028148, 147796860, 493999454, 992837122, 259524200, 675629121, 912346197, 392764617, 169064049, 950208454, 258894607, 506178071, 105973942, 415171238, 101994024, 511335945, 71611851, 448722378, 973131989, 606642598, 192731803, 487788928, 408577674, 680996656, 377786811, 418261155, 272516239, 82659286, 335625756, 968276064, 318741763, 380979081, 856612603, 319696172, 877427358, 10022181, 440682877, 14256092, 442746377, 305625023, 414657842, 428546312, 257372516, 907178853, 774226775, 450269520, 318707109, 528706776, 314782409, 272917130, 182749173, 103771718, 771392224, 889362750, 322038033, 642056045, 769863562, 413570108, 824974461, 995118222, 268027428, 843790934, 208013332, 437910018, 684206342, 411926993, 811598108, 117752427, 275112328, 945694436, 920446810, 705246118, 303657750, 689000691, 107613705, 545621231, 774349584, 619455526, 239661803, 858991489, 675518171, 823249428, 973500902, 400504207, 854189613, 34632725, 568977308, 174283618, 229662878, 747442705, 684076390, 381359947, 477478599, 61349772, 209620104, 838633941, 598683227, 262652577, 282310021, 248452768, 988284317, 90393353, 704682389, 555652558, 855520663, 747301159, 677639742, 344100361, 965513939, 352501075, 445290248, 448308832, 965344280, 631729169, 335295721, 341560803, 514256132, 318430082, 698443260, 942878596, 392659042, 739956794, 306052988, 807077540, 967363701, 900572000, 684069416, 159136849, 247879675, 256296969, 451820528, 507233518, 495305849, 649312214, 950482152, 947697307, 757442036, 850341810, 731064131, 750231994, 259284933, 196597955, 83522720, 528272710, 905042751, 486525609, 485117201, 700555441, 193224048, 366945903, 637120070, 783027950, 26463423, 901660662, 523485361, 28697014, 431341136, 79670929, 500232861, 142203695, 115251379, 713618100, 363102328, 715379616, 769176714, 166465372, 511700037, 410395875, 793831882, 951682630, 981188162, 25207034, 145162367, 694604000, 572227300, 517241614, 763444789, 581340979, 951576200, 470194693, 918743494, 295985518, 929157380, 930847133, 724629772, 139982499, 62984224, 805866811, 306254984, 83217978, 113738620, 345338308, 668447623, 572662225, 35189229, 871016735, 364888927, 157081238, 945826079, 785195784, 384223971, 942005942, 96764265, 131242563, 109899630, 311996657, 882660605, 732076008, 47875581, 664703669, 823724610, 900119135, 271622520, 496872456, 365668015, 949067023, 408777403, 538363785, 925362418, 29791186, 706656108, 477683040, 944506024, 339953711, 719761163, 381296863, 936025500, 940131332, 352688994, 109673784, 633151318, 423673261, 405928200, 739859920, 616623775, 134826231, 946523066, 440173070, 201273999, 851102543, 187256004, 312423371, 38875908, 887463000, 3503832, 387199670, 244824157, 311946288, 981309406, 127246463, 35799916, 191353155, 130469630, 985033755, 574896099, 572521539, 281538238, 832869826, 867315361, 254648462, 973774234, 123825784, 569653829, 39035537, 104962316, 876438037, 377217212, 808328613, 845998404, 64535468, 102282502, 122900356, 214608267, 678454755, 932471769, 894645798, 873399727, 464805901, 563015566, 660110145, 893765478, 727138892, 462153990, 297726136, 697681310, 753683625, 463981476, 771643849, 127355052, 322863606, 2262938, 191714188, 185036580, 69425801, 2820816, 726010154, 633977627, 286799342, 329675561, 258101316, 674906355, 697881515, 936106667, 71262158, 72093230, 585375963, 223517490, 380065365, 125733941, 185175926, 352110624, 997708859, 902421103, 381277720, 387208173, 999886767, 433663407, 229614454, 508868076, 616807437, 997917214, 420481549, 314486592, 641761300, 39364810, 348125280, 93848129, 500985068, 265348944, 404504872, 178828217, 802160216, 614256718, 846122876, 679647044, 864688911, 638476433, 663537890, 429792826, 537794680, 111136156, 629250557, 275315198, 294685531, 650249552, 915921636, 590255399, 80646240, 627704077, 144347005, 824349797, 812984585, 994414631, 209882779, 833710718, 611404349, 963009823, 63541503, 77233503, 860330713, 308352582, 544554588, 783316880, 163382272, 668889060, 128985667, 925877052, 598257156, 529778657, 128430789, 955232877, 128700, 80349701, 251612752, 999763861, 835482422, 264543223, 798564130, 345165800, 638446335, 164999739, 749225798, 880709428, 432375294, 197583760, 927520111, 391232979, 304510800, 814207782, 766728882, 769353452, 95615545, 862830753, 921838285, 438341795, 912688204, 850470367, 794142568, 774453024, 890312836, 111788379, 810157, 385269309, 806664647, 738798769, 321720812, 397429559, 285323916, 16861129, 502082117, 500584115, 174549172, 370304120, 718830285, 344649166, 697348032, 932602849, 586506483, 275116303, 293669235, 884937310, 746603521, 506523972, 384060315, 182590934, 301774905, 133133022, 184594956, 879430538, 2038938, 590681068, 267117226, 955482146, 881527870, 751787332, 639238909, 106360909, 762164345, 160475819, 218960008, 281707110, 653642878, 291528929, 53579768, 175276056, 822006956, 37926288, 881841337, 694515423, 544110593, 44597251, 918862845, 531750628, 494668365, 440201415, 695085339, 224893935, 876107861, 882827194, 35335009, 218068667, 171364598, 515274083, 705054170, 591867945, 197725680, 32259623, 523470334, 870143260, 771300523, 575784771, 805397802, 456522344, 347239952, 449229168, 882409565, 226270736, 22602079, 787595245, 749466240, 348939768, 337334755, 39638608, 854090748, 930304340, 652114342, 437581760, 686528533, 258771193, 381223123, 855932759, 338204580, 890715163, 929021218, 423042889, 524534325, 622418076, 653845432, 923733807, 430453486, 608496317, 822992802, 851391791, 687669279, 861917975, 981663410, 403939953, 114642665, 407861596, 703360894, 281573612, 874745742, 332300994, 920660729, 673296896, 473299407, 871182245, 742453285, 32303082, 637698115, 309922329, 512596718, 174245852, 14592485, 430674126, 81931891, 336037481, 522276783, 532727431, 879294942, 543926451, 542306614, 262118888, 91759457, 741720351, 705491375, 703307775, 630986275, 476803671, 58356822, 973536119, 384916859, 830043503, 475955053, 445156617, 685369644, 972171710, 381357790, 594955442, 641301166, 669583732, 151110314, 122513467, 825536648, 61798897, 619607828, 139681312, 40017872, 42526746, 762686940, 623216423, 321602560, 847723293, 642172594, 131104479, 608907738, 438120754, 635065113, 356221645, 283980573, 517035742, 265742780, 831068701, 451169548, 554768749, 797506972, 958875767, 163739725, 740987184, 836383930, 504505026, 869214651, 285917730, 539539603, 12040476, 741770405, 245066216, 750127583, 270600152, 152717269, 543149391, 324316214, 560656728, 569888085, 709226977, 722532162, 806237210, 568948756, 727569017, 665430942, 673913372, 965985082, 411152767, 105080178, 797630901, 98835914, 949543399, 987140151, 239715237, 977926399, 917238705, 644629853, 315261824, 185175100, 581810049, 291736736, 788305306, 626134982, 247481272, 266973130, 330732457, 439259257, 989610386, 416587897, 36851835, 335961673, 758855607, 961515146, 448486767, 457670344, 216771555, 651355235, 864484555, 625886304, 678167696, 98198178, 617614858, 122180256, 243660051, 172441807, 654085811, 867125175, 810152371, 100921472, 419735394, 625189788, 424950610, 735863858, 157795894, 685320849, 30717151, 517710009, 156743164, 857428017, 222361332, 605247789, 812913695, 873720664, 57059210, 132314601, 616479199, 433691497, 427897623, 190246301, 727680809, 126656621, 530348708, 399542028, 744188470, 261174226, 239511018, 37315222, 558259197, 712667221, 390123681, 68436236, 77094373, 955540657, 479513281, 921313234, 402966769, 668975742, 928066976, 48174814, 325109749, 880495439, 357113227, 116916359, 243616187, 422016270, 922207251, 212874699, 124786887, 395768726, 293876385, 369594896, 81260699, 546646590, 975278228, 800427611, 449811022, 459410450, 402125056, 831283513, 37495652, 488015043, 742742790, 840808700, 693960677, 557791072, 681033200, 200847345, 19838786, 593451935, 122622020, 106655500, 373033515, 688540551, 104378388, 581426371, 584463368, 718568544, 127646390, 717583279, 645626251, 591146316, 775460503, 92412034, 170100961, 825764520, 869012208, 464577533, 375135727, 743533286, 40492962, 94461370, 273929227, 663917843, 758773074, 664172494, 893832411, 427326827, 670097112, 190887713, 173807789, 982743582, 215947260, 760608162, 730674440, 46674450, 903164787, 361479928, 88879931, 820165303, 663750787, 400231364, 185959629, 963791906, 590232477, 315354128, 33331520, 176829264, 923576202, 196156334, 697581350, 626375012, 404787605, 640763847, 930927503, 328512526, 811996542, 653470381, 794246178, 211569224, 40478865, 227869437, 488832447, 320712038, 577163685, 286929019, 855914972, 394641497, 266222326, 688396814, 237951474, 474647182, 747598166, 647104170, 567216984, 828889397, 427247119, 28659705, 459443657, 587167564, 264951327, 320890717, 368234864, 47777410, 452453038, 921286540, 560547196, 958411597, 820361374, 371549303, 220074465, 486445902, 995537423, 615477603, 999817851, 585858374, 505847325, 602435131, 991353075, 90224972, 388724876, 530205587, 208705459, 978920991, 714222546, 378704705, 867211259, 131135897, 34919529, 552616246, 760447980, 475958905, 347189443, 338679637, 614837889, 622273224, 152479006, 95256598, 155838430, 290560300, 188239608, 265842987, 352830847, 807295011, 918909254, 644520085, 819799815, 807294323, 48741207, 387624044, 791954730, 961052720, 813822603, 600668452, 447819241, 518358906, 37564246, 923326816, 544867615, 307807045, 445858007, 248232427, 454738699, 39968256, 889315128, 79043969, 442767786, 73433426, 628011229, 785470146, 642193942, 881556907, 572690886, 653910656, 927090798, 559262750, 168725739, 323619038, 349233080, 920377628, 893116861, 331359102, 741675202, 85892562, 878833251, 978240009, 437581441, 956968588, 195127647, 987073822, 673920036, 180080352, 825111958, 185500967, 186134329, 94873339, 407693504, 698935924, 684831342, 782444163, 17742704, 123630431, 275958888, 571828338, 361899968, 349618415, 128343390, 610410179, 706210951, 232202646, 107643413, 133362785, 368633009, 414950126, 459331484, 764217865, 968854625, 33576192, 87977043, 119603327, 818420617, 208147329, 412849925, 966439421, 19261629, 837812073, 211503748, 318617576, 366458523, 279978993, 238148943, 458787494, 844460344, 819529433, 716116339, 766346722, 612079361, 466883122, 38768749, 668596478, 321689783, 875859319, 732243382, 690443533, 737518094, 618741195, 540577597, 17067091, 629026951, 306211025, 115873160, 998011411, 853745809, 616127598, 734669703, 658766328, 182166568, 776341604, 623278328, 597293638, 544183780, 922294873, 374265284, 570470761, 419754042, 759350557, 175999503, 116358094, 671865539, 377817509, 933703054, 291359294, 988847998, 810434930, 619014530, 94086979, 150766695, 581908493, 729661839, 867221695, 479105681, 8841617, 921614194, 713057443, 842290960, 586311329, 29176592, 587017613, 874544882, 280643074, 906791035, 785750528, 283148162, 12187136, 194655973, 43309834, 477330976, 133251619, 98469121, 752759514, 794303233, 19094212, 831406988, 66186066, 204352028, 987420632, 91366895, 90552169, 248685431, 627916193, 717092819, 999244467, 837258056, 975452249, 918408080, 372155467, 550737082, 877496210, 396804016, 5468682, 820722114, 559965445, 417600280, 280048792, 767380121, 853167699, 116734490, 419225678, 159662091, 688883249, 251684835, 778412921, 636217921, 774208309, 271219763, 36792462, 98654136, 208518775, 528445879, 57723910, 628952593, 467423542, 605815403, 197659164, 813305420, 21986121, 953049163, 442187677, 260713906, 863133348, 474441761, 587590062, 922051441, 250498541, 665676883, 953186200, 659188410, 756531726, 866396295, 726376117, 645436762, 264030924, 415783292, 976046457, 377975358, 746114090, 777838489, 346914008, 182974702, 531492362, 59867346, 839500544, 665630650, 396608053, 378032483, 929256120, 985530235, 316937351, 274357663, 737974303, 709028358, 97825036, 608162639, 910678507, 286634391, 306816368, 453174146, 288246539, 727770263, 180442525, 596076757, 640003318, 537775396, 974491915, 246294504, 741267978, 721832951, 118106386, 319220458, 813232871, 255882537, 406915683, 917944079, 578604217, 541810101, 681666858, 22483301, 244260246, 468851005, 529602079, 819865439, 552431281, 347912230, 591541617, 254501166, 869031648, 586929810, 763414540, 623329786, 15562637, 19383800, 573515579, 405695436, 677831419, 77125076, 597516288, 114973785, 365159060, 85253869, 181872957, 846539000, 869944897, 426463230, 596071074, 789936387, 483566722, 734888840, 244436691, 597733845, 115881726, 879935515, 888034669, 675448506, 164140971, 771018330, 968541769, 157136987, 785205516, 219479274, 24423877, 435751612, 546097856, 733407154, 227161648, 367955487, 684885180, 550122989, 960434773, 787978019, 28096113, 159615158, 556525625, 935208301, 850825835, 758043798, 558723117, 260357670, 832376701, 551844912, 9037664, 70126641, 972974109, 443826219, 989096137, 721400349, 311307122, 676385871, 724430806, 792623434, 608104757, 266738125, 539629022, 884226369, 843292947, 606497020, 238996751, 151091091, 65802764, 586306478, 755457071, 325481320, 682620539, 461271456, 785189439, 985889856, 287018156, 224168359, 568325280, 92320195, 406228944, 476828602, 58690505, 463186163, 49392113, 492110736, 28891896, 54557198, 56684131, 15350761, 884056248, 489247276, 242464540, 871240281, 188424735, 586959990, 492756594, 580649279, 734223054, 986824993, 466077268, 213235395, 594503681, 192444036, 519385543, 863633155, 632958168, 805228021, 597726784, 445117631, 945306305, 652218659, 702207465, 928911805, 984482742, 584429906, 702928876, 962292494, 952069223, 435485092, 977705066, 358987145, 965879954, 846014219, 583044688, 221506755, 376581195, 901195607, 136417385, 471448395, 988727094, 720939150, 167683559, 289287305, 237062080, 227625425, 95765024, 523019585, 911131599, 916657507, 235744473, 264586789, 650375957, 21278225, 322877419, 534956862, 65142945, 207164080, 412577293, 236698399, 415466325, 35044311, 607500564, 323521473, 104546821, 493836617, 627732955, 244929518, 194116809, 823735298, 75412787, 286333094, 575738484, 406552821, 949876463, 454033455, 127615716, 63599387, 248902419, 543283401, 827040942, 597088274, 464663718, 70801270, 503694485, 739436130, 793351815, 86187037, 745793826, 67757025, 815178335, 804185060, 396509277, 352558005, 584686909, 426204879, 662205226, 30645961, 574226735, 898725912, 417490804, 627656384, 989039546, 529838682, 148253772, 57695215, 83485749, 920635026, 806247634, 496755410, 739373926, 493671140, 476056085, 975397154, 673924673, 110949088, 24956187, 275458074, 191202126, 875503129, 624102564, 993448207, 135230123, 444620806, 978740284, 251544104, 606062024, 218217864, 470875597, 152047928, 83756252, 992479154, 663075320, 799485823, 938344264, 537932167, 945959906, 371193914, 432098964, 351774996, 522865845, 558241995, 800205675, 574721633, 792016903, 625733095, 683430121, 805172678, 750865396, 923208764, 635499644, 453445541, 277420911, 76921109, 836046427, 760571086, 751629600, 663474170, 322241151, 576611210, 231320655, 289673826, 656395732, 265844534, 298931073, 69939028, 447549195, 259878972, 211513085, 552119613, 338657612, 896992981, 271108571, 644853908, 608210120, 667562036, 605439405, 175174104, 714074195, 296878134, 364310949, 349462631, 244966883, 131813135, 258534074, 640223262, 393015697, 959432959, 504637734, 29582834, 607207112, 886849226, 984945956, 427864287, 372464490, 995938842, 205040759, 587438732, 364189507, 634487581, 910802534, 20723340, 992832600, 74383618, 540255983, 178643940, 515304333, 697002019, 891276032, 457279798, 880330865, 156196674, 671464386, 353694316, 616245022, 452584318, 865890288, 692213815, 192854694, 784024323, 526380404, 275020369, 236611918, 167049483, 470125573, 886696210, 128346577, 123509498, 501322194, 747992671, 589325131, 20557281, 267752541, 544445034, 478619007, 358665615, 642544898, 310575894, 729250131, 218718383, 685840054, 755182505, 161335747, 104779653, 497274556, 112539584, 140604702, 722724249, 114978663, 882951608, 73774842, 27515275, 949613311, 822293288, 480843927, 398687573, 557313357, 747278567, 478299696, 730036901, 482774309, 315100133, 326398075, 754929374, 22124239, 308812122, 185080306, 477269220, 934807130, 462450862, 461216332, 555045415, 838890931, 182626124, 798241483, 635710947, 3955116, 635089401, 203974469, 403642, 441094613, 549271549, 678094364, 225244265, 502058387, 827555373, 408597422, 774374424, 78564984, 986873249, 805971185, 488113118, 296890697, 188678363, 650534508, 939023656, 712335322, 1592039, 524604504, 827735120, 98905262, 765178526, 321356743, 805457688, 615850837, 344213225, 473866428, 789428627, 327163611, 814095241, 203768296, 307074401, 988585802, 103231948, 932858164, 963300965, 739997984, 803461939, 698695066, 822233733, 547119767, 770356325, 69073489, 713214265, 95410730, 99055474, 2506809, 265734513, 902491601, 597558802, 713499292, 26574927, 419279433, 885266562, 42856806, 811468396, 259578171, 65762810, 934752106, 934317321, 750743497, 800617882, 27784585, 365585274, 630330414, 322082518, 508054707, 499706678, 441666197, 291394971, 214552982, 417449979, 264242186, 507283058, 974467940, 962032555, 100050859, 326994714, 653190982, 763058455, 112788398, 534012987, 881285456, 706659382, 680299958, 14270206, 536762174, 8670249, 645726452, 231751588, 72834745, 671214185, 158038351, 485580632, 814400712, 160539216, 638678275, 116343253, 432145349, 733755915, 375566454, 574020674, 945942401, 994671464, 726138910, 90268414, 572758825, 598776869, 664942258, 417223974, 528151091, 52039924, 519505567, 715151781, 577293308, 569467608, 923947416, 741666250, 886163163, 908765625, 584305937, 886605588, 197920972, 429716492, 600676760, 89791971, 144690243, 177067030, 838705323, 567169154, 853754432, 818506794, 978524416, 244814710, 295072036, 300511460, 661177167, 465430791, 387806586, 35178273, 966404691, 322969652, 317319303, 271441355, 249613386, 774996725, 770230632, 705096114, 875514064, 514480519, 41870930, 386588785, 631355561, 809381170, 559659682, 987435199, 727449648, 27885941, 286982534, 376452376, 806312998, 763820150, 714149379, 590347896, 275028487, 301792224, 875431535, 154842297, 499239850, 996979165, 442051087, 660032634, 855066738, 817504431, 594899863, 839170061, 574808810, 910058025, 202445624, 819424614, 604506266, 187593671, 795458782, 982408627, 190388222, 66539501, 819894552, 109449551, 551815730, 138427707, 718686425, 325424027, 853298335, 350635873, 254271870, 286420730, 378063951, 757812959, 179863611, 512278302, 604208473, 546119390, 408476561, 975885089, 775155433, 912560899, 361528907, 224213317, 785818728, 382330574, 593435055, 3049416, 342341873, 223660904, 958324914, 498445820, 438784467, 23609675, 670801514, 224128342, 915855771, 568204873, 112674180, 494010177, 679930327, 276321998, 95748372, 651481466, 293729616, 622287685, 531897402, 234970010, 167623426, 976591775, 48464207, 793046571, 879302867, 939252967, 900673271, 764722449, 400670317, 390298060, 741661107, 97291975, 615860962, 374917427, 51141771, 90366775, 549996110, 56738575, 804432113, 897318687, 872741699, 513817778, 646317692, 378340935, 586502881, 939111789, 671310899, 773042077, 316117506, 119832425, 126550698, 322357177, 677955060, 139594989, 66660934, 98604438, 286056356, 413506561, 967271786, 925185029, 547057289, 241234799, 20973757, 303756585, 570469771, 358458676, 642875309, 202033346, 395514480, 127340927, 130155927, 622914628, 263168819, 607135260, 772431455, 805329271, 405730914, 284552024, 978725660, 750564148, 887972248, 521369553, 213319637, 725733271, 196138345, 77276052, 16120543, 183087899, 851836881, 978857989, 646627237, 390044860, 532365562, 68956352, 92151982, 382082281, 279428743, 568550334, 541196261, 891383701, 595643416, 816782801, 564628579, 808504904, 332864535, 43646124, 712669536, 692657966, 702252816, 728252287, 921385943, 291011040, 861432503, 844316702, 703608330, 433124203, 137728672, 912260831, 10788755, 361717181, 603583979, 976196390, 912135729, 164205435, 126515274, 595706121, 206651770, 842457460, 415475079, 505558851, 529389237, 75974270, 81907469, 685289488, 996170527, 10743788, 404101784, 612324872, 46948140, 431320315, 199891061, 531360566, 534978572, 783379028, 404588829, 526882790, 501269090, 29360185, 934559905, 600049059, 930491802, 721052593, 121506896, 117318322, 336574422, 703071355, 867802218, 524004494, 403294329, 529328624, 199766438, 387856338, 201066863, 826312427, 230860127, 401664811, 138054467, 466178485, 786425869, 846981328, 828918982, 26813705, 350297955, 750808002, 847279810, 654458467, 318989954, 279850322, 582724686, 530716661, 207769267, 765562612, 786026920, 197858616, 71466300, 726650354, 984652523, 999935642, 305613574, 542801023, 427502343, 407956760, 14391474, 380735536, 670480931, 641693718, 401942290, 407714521, 671653383, 114869144, 987907964, 160427615, 915329440, 869418214, 770155037, 664844463, 43180135, 168545711, 239479629, 805201598, 955651589, 20687245, 178806002, 868880027, 672610356, 806033607, 304027735, 101465749, 18050953, 177236804, 990059411, 751947054, 83572651, 492263594, 579755793, 88337688, 327142754, 655282189, 156560313, 594778269, 246350684, 425614646, 384353146, 45621067, 430017065, 763352562, 195360968, 707744967, 330244762, 980734244, 11350546, 925023040, 494604491, 109645983, 733456857, 781526638, 774778620, 623166809, 846352856, 40533802, 384053882, 533957030, 506049220, 27411621, 752969920, 770606010, 871882787, 326287859, 532643030, 327689101, 732731186, 686732398, 234214658, 362065542, 591108121, 633268709, 726187757, 771534415, 773373102, 692962841, 460139793, 932444051, 196186309, 634109831, 423471814, 590422037, 404710419, 925958441, 426086976, 36206926, 427247757, 197321079, 857393206, 637432807, 645529433, 281499134, 449063048, 66914723, 823482207, 13663360, 750421351, 917018520, 445194179, 267146737, 349953696, 971035691, 47318453, 204714347, 982129211, 705516410, 134109671, 314368396, 153579740, 769754189, 341012188, 644273372, 184168526, 664680987, 382175847, 897595710, 953188846, 157901401, 6623272, 324411895, 39500340, 861917557, 699505808, 595628060, 399336621, 406266724, 446215823, 185777039, 963546155, 303213193, 772338872, 274203224, 646103995, 722638769, 795290923, 534473675, 440917965, 585977529, 380555784, 205969671, 503722980, 621859330, 978524402, 915245617, 279753588, 173549910, 35132363, 776907769, 235326925, 643765214, 182887085, 960869071, 817410933, 681461437, 733015801, 275977318, 843773276, 784228299, 75959967, 635809403, 716330315, 349903503, 231086842, 916403627, 828459117, 680279965, 924519048, 236194083, 822721129, 538071040, 718010321, 874929884, 491330478, 477822112, 763086454, 124882195, 948797441, 697783226, 951621665, 576773247, 511834351, 780984364, 513457886, 355931958, 459988953, 415418116, 199070362, 853824951, 126995199, 476348276, 733020297, 104903497, 408492762, 285148489, 738054843, 42511272, 523864560, 269236745, 720603332, 41183000, 374270323, 77722088, 942713050, 654839700, 623268294, 478995796, 551904652, 237271718, 931503986, 645209865, 446385239, 420671794, 239276607, 303945172, 561625181, 667012511, 648014184, 219099845, 494080490, 474458068, 312001033, 150563969, 674205499, 351454429, 370890573, 296302475, 809946356, 691238254, 434811867, 289132865, 839403619, 870621080, 233612159, 280249248, 540742236, 538593058, 537403092, 325171612, 636434509, 892866055, 592264551, 249235249, 276316574, 163894902, 611021312, 561570938, 345544652, 833046772, 462162414, 369194321, 563984211, 276954621, 329769128, 182275916, 467556857, 100016303, 595128772, 51445408, 38302155, 528407933, 590298651, 43180779, 811518179, 153773300, 171519648, 803376791, 415949282, 817114465, 702926121, 961888586, 563047977, 554871028, 892424034, 600197113, 102023217, 967685433, 710354346, 297007060, 572495976, 914653866, 420543136, 320375609, 732060881, 181900514, 414104246, 844367071, 61985727, 471935821, 736133721, 224224100, 820188859, 774364484, 658685584, 783567300, 894719885, 902437169, 450293422, 537614304, 603003673, 695527677, 33477364, 373317106, 843541334, 305154916, 452356929, 834788983, 943890885, 445899667, 79851031, 108186146, 452070576, 92387170, 331156868, 275245877, 296416839, 936640360, 685831130, 868812989, 915596066, 678972807, 754249988, 406167568, 160681810, 660958811, 801603577, 947578752, 502651831, 912770141, 437664415, 627559790, 315623856, 263278599, 56070131, 926167700, 147350937, 601383020, 621413940, 343087776, 251881850, 525406698, 265803238, 471572691, 637436028, 587102849, 363901548, 590504900, 891306181, 366371033, 325488875, 667100227, 516704324, 16879300, 362378545, 190040034, 540504494, 975343646, 234430331, 815218222, 461693743, 820876620, 144793822, 142995887, 456319093, 132922305, 752114655, 767188848, 95934703, 613972664, 834423381, 918805792, 235493147, 72559876, 209897844, 992815670, 138900484, 292876180, 315567952, 947986497, 950650058, 380468913, 419365845, 717698624, 130401724, 615955603, 295089303, 139727018, 859088438, 495165904, 641635218, 646776510, 25275977, 568932960, 915466186, 177263414, 123119015, 222808544, 601531433, 320686271, 38657674, 33341563, 540484864, 176427122, 478048767, 711210909, 96693174, 555230597, 218650209, 999282939, 826849027, 720295236, 211238214, 52698506, 613914477, 194109098, 876710066, 740138593, 609597647, 829699314, 193911959, 600063819, 914668029, 402069880, 504001455, 831306027, 495271578, 642362942, 545055197, 322599862, 921843493, 104401477, 244222994, 865026305, 482608882, 279862423, 164476967, 736868035, 188542687, 760615120, 14413673, 847067883, 913467119, 673951911, 492066128, 907837021, 836633958, 312762616, 929953324, 860290954, 174302586, 306718652, 556027318, 691973675, 907135332, 198313673, 884292464, 829716890, 447890050, 341940186, 560612745, 541737591, 726742527, 335317368, 822330113, 875628287, 17438720, 828233949, 416362631, 214929144, 3655356, 164785001, 267643460, 654887575, 894986394, 102336681, 507531493, 447079009, 722100891, 20397053, 17640550, 565513073, 555350345, 592767495, 428176895, 242137443, 476998216, 623941632, 297492083, 579885130, 748672385, 936813735, 146638073, 476767361, 834389850, 658253321, 50349432, 659061798, 67496531, 470026459, 193340410, 514301136, 298893713, 578774448, 138473231, 703492494, 60103250, 898739995, 926685585, 423813353, 175530585, 680684771, 39364359, 283130905, 940338496, 113125389, 157570241, 47994871, 832795239, 5287096, 684437057, 615554685, 96208823, 761568288, 923726072, 995358813, 452670317, 371753118, 511939459, 965163604, 226371662, 20183866, 577406537, 115436603, 615331239, 632008506, 949151680, 460183828, 833132391, 318461745, 839343205, 269025128, 968404852, 821455476, 211957250, 158729405, 659098138, 425183001, 161100921, 286700588, 950509483, 178645800, 748229213, 890509064, 57207506, 623516070, 708365332, 88099293, 518176507, 700815364, 332104718, 697974528, 899117691, 403656851, 238124293, 177788700, 654046185, 210279692, 53715410, 478439060, 145821513, 897727942, 854418278, 413765749, 132758185, 476540988, 315307553, 848485705, 315803239, 10390200, 308922453, 815043257, 712833573, 283271309, 525858563, 427009938, 46003245, 915641768, 225010458, 191377149, 444792935, 664680927, 737914454, 477515571, 635590664, 835569692, 7152073, 501997554, 13932364, 471668042, 86511176, 756563600, 837976086, 755841568, 813963085, 553473580, 715181114, 953336989, 273765479, 675197462, 520153248, 641267624, 463850910, 586355695, 434218453, 613107372, 794543421, 1020046, 645121407, 384033994, 855521433, 838143419, 319343479, 577747873, 839795879, 393362941, 516893158, 82301763, 290362167, 856685045, 247905434, 324047179, 680227096, 397059343, 278976432, 661203055, 206890045, 747767444, 263966943, 524255474, 422212147, 816669601, 237991583, 26848067, 242694713, 154316093, 945187521, 724032888, 148203675, 795503055, 45531841, 240922095, 400387137, 593490876, 410802113, 605077910, 467869353, 114769798, 643420920, 768644737, 604600101, 198026422, 901107088, 966098664, 497700068, 984510086, 616658039, 394513213, 246638263, 663153727, 617467370, 562945366, 265218043, 847516105, 279492707, 836617384, 425971442, 367691207, 887841400, 503666251, 829708904, 616201951, 185966599, 292534372, 460296313, 246522171, 649891094, 888886999, 528523662, 517663184, 785897101, 988035429, 486120222, 158370017, 247343432, 99206430, 892283992, 569724163, 377857525, 647734522, 409790203, 322352773, 846730733, 176163705, 993413861, 155232264, 654867959, 723801216, 259419176, 905445859, 672697451, 40399767, 43603995, 220183154, 294954692, 849566077, 792790812, 303040515, 517692657, 22080115, 53469171, 860233062, 611713004, 740257910, 21628858, 672580967, 7593955, 638089828, 778416092, 457271664, 713404687, 901144298, 900535664, 40531342, 475392485, 198767070, 124663139, 717919240, 934132322, 536521176, 680046757, 592662421, 997223762, 119524533, 664899813, 760523929, 201051606, 311331045, 415806946, 753830269, 412496812, 147548382, 608368035, 194579471, 116084263, 986062917, 999940801, 437534855, 38449069, 54384647, 612885065, 733918673, 169794969, 374219835, 348546857, 723290481, 180481761, 22538372, 549259245, 736514491, 833803556, 359241938, 514046896, 307173066, 538026579, 544430343, 272220015, 617060573, 966698457, 105510039, 659930004, 506529112, 832853879, 220941040, 926095080, 499825836, 296781069, 140097163, 918958313, 92814395, 892839224, 115154020, 1669334, 645032602, 668333186, 494717080, 501577952, 89370274, 648260252, 147084787, 23125469, 371742017, 488512437, 196656685, 609167227, 37884310, 768020659, 36765915, 428090371, 299611919, 966056617, 595916781, 27992170, 110187565, 347338454, 296106245, 499376143, 190262380, 976364813, 388733277, 20458164, 836844912, 675424168, 440540651, 260987632, 197538201, 65570069, 938318065, 208066606, 72169826, 898198784, 739976140, 67660710, 552462689, 211721968, 319356794, 823296503, 348843836, 317729328, 591876466, 351571143, 33153205, 206665763, 21316827, 722227926, 128141207, 554926784, 94943272, 440968713, 560071080, 501315404, 901560510, 661041883, 284158196, 163010720, 796978096, 484608235, 185460979, 582897248, 6416710, 143436971, 226260741, 196744862, 607171540, 703420602, 4245468, 606075394, 402308263, 719825292, 671348888, 758684337, 745097348, 497264234, 697604287, 918632439, 530980022, 436519731, 308544879, 824361791, 994845113, 381649894, 540073170, 676718674, 337866028, 70966995, 306918437, 901227815, 597622729, 523582088, 784340209, 182599319, 608561047, 167502578, 808823195, 508056705, 630383054, 684401167, 744330752, 923247274, 435031887, 832934442, 845125429, 29788829, 243960280, 2564289, 20366529, 631014583, 419398325, 30371791, 166766004, 133463985, 363355516, 782464838, 424939430, 126855619, 22290180, 389086101, 420461061, 556955553, 347296987, 715918163, 367337305, 193271334, 360722279, 560316853, 526316198, 963878882, 373568006, 588778073, 878633476, 184177768, 437611984, 151562606, 662198590, 400701275, 376594002, 104522546, 204970609, 268843498, 748551872, 138635369, 428116776, 299090758, 153409908, 332571776, 127147422, 347901476, 14256459, 37963537, 479191517, 655348984, 500056576, 330696011, 918953611, 803887228, 234725879, 926686411, 723567914, 629879454, 955939381, 185983973, 476720855, 377389831, 991736325, 247774440, 924339126, 328944639, 372139135, 30746903, 865619518, 787362034, 480309016, 935344352, 478254609, 949604089, 681367044, 674086284, 576288736, 104558710, 904907013, 34398891, 911766899, 83583147, 416672108, 529401400, 73099522, 636709918, 900779777, 51034873, 303489032, 312083484, 678253112, 245506416, 203461683, 608974611, 489270666, 880036793, 664203533, 891661301, 2804095, 154192147, 860905245, 715044268, 339761117, 871997873, 60780173, 555715589, 135230786, 306651561, 275955609, 406290494, 682069929, 709184634, 719736247, 796253432, 574436903, 445152394, 707521650, 372432375, 414457367, 433570691, 723731401, 348107849, 571509039, 243727678, 835106433, 753936018, 411762019, 116215490, 15286026, 147017079, 231273084, 266864420, 197777750, 427271733, 115058887, 401850615, 575254191, 336069694, 174508222, 51115836, 720492340, 535245458, 735194248, 575313530, 827544079, 250287243, 789442265, 968220057, 886013656, 718398043, 829456253, 253086529, 480935146, 864334124, 370801299, 500981434, 89885000, 674332296, 91766048, 237234052, 114787108, 628054285, 616895300, 308803462, 141604843, 510611067, 211800585, 258383305, 538507370, 612943068, 127418360, 980299367, 571271532, 817651130, 635872327, 660018072, 680017800, 270785276, 588694653, 993937037, 91729047, 138614043, 64300901, 436153885, 856311564, 307281716, 786197757, 492466916, 55150247, 637799827, 291737391, 306197395, 334367952, 675096250, 535171341, 35105564, 326509034, 702092213, 611975464, 503028040, 188087380, 79929325, 407336906, 671889287, 593162842, 416030260, 615719523, 807960229, 661744918, 838316273, 859436071, 871569305, 765501855, 154840577, 755001489, 666144786, 348068997, 488998370, 779700427, 38345468, 643262701, 509498174, 905227375, 491183951, 492630548, 153139353, 343069959, 801976972, 214053804, 248791388, 866214699, 56565399, 837241217, 240691769, 459146758, 980099187, 62886175, 568700650, 173815688, 96921164, 708626879, 31965500, 512687679, 65574023, 742231721, 915559680, 48437455, 933204085, 763225172, 912261891, 948090827, 798084292, 916916547, 966707075, 700065856, 210963937, 379571648, 846978766, 584864532, 609231764, 440655051, 304524379, 633927846, 46738658, 995320932, 249110868, 187847220, 953313517, 687579615, 81877344, 583342271, 158410804, 703290615, 639023995, 633534132, 181582285, 151382978, 503011822, 292627432, 684530370, 933886687, 733544460, 628909297, 347942319, 263637585, 119755559, 593479292, 398855628, 105944223, 89829342, 214384316, 547082276, 996952400, 889476017, 986820801, 234525462, 714726030, 94573995, 194287341, 551523039, 293993938, 17407829, 998186221, 970015319, 26562866, 732571879, 83384526, 336824733, 880008609, 6622283, 907851385, 368392612, 641240987, 559465269, 245794340, 872751952, 254004691, 899144520, 413399243, 398787510, 702464228, 205930289, 971317457, 995311038, 896068555, 94604044, 506439332, 4525421, 890487787, 239714593, 890155884, 222936380, 809794957, 297886483, 835627849, 794298185, 99599752, 497008734, 40062579, 423568794, 454486976, 726158391, 372636689, 893360805, 549443150, 349026482, 172818696, 134885415, 119273865, 909085311, 606264296, 902540145, 982598355, 318240682, 620338598, 346495516, 961879071, 89684885, 879138238, 611780731, 477956795, 333558486, 419188555, 119388611, 719705490, 694641619, 952629301, 500380852, 484546615, 658112594, 174919436, 573291294, 341425267, 692242050, 728369704, 758897235, 952828418, 47038124, 911226302, 82407010, 398127652, 79199623, 848207030, 44380156, 131701140, 823792444, 99469898, 936544572, 440532809, 366109597, 997718003, 857979138, 356885468, 777226787, 482696700, 572259390, 965415114, 543433947, 119446161, 45117111, 653442769, 38738629, 548170071, 501933239, 989020890, 953294315, 537852787, 288745347, 570444267, 971852376, 289254684, 243671291, 618595801, 588800025, 511757513, 991094535, 951827228, 205056252, 655644882, 844425358, 740018699, 741723617, 740002077, 710375996, 352206755, 956311673, 596690368, 234503169, 678998720, 109002451, 167801007, 773253513, 814689089, 674771042, 584694066, 952677528, 130863541, 946278786, 677130471, 740412761, 194400645, 650638869, 400921381, 63069315, 959653202, 484328420, 241037160, 366140585, 934482926, 721207660, 723063889, 215537287, 587615651, 918480568, 452333009, 739135417, 390158764, 838528392, 553033667, 547211375, 540822338, 940535392, 46220202, 285031622, 72870692, 599207803, 14585891, 553246034, 558183089, 268556482, 737129481, 764631959, 330139990, 67377040, 735108123, 750782183, 759727687, 924062618, 849391813, 572756593, 557649511, 455922732, 165157339, 843974048, 160778373, 169566099, 697068715, 31647665, 824052043, 287114112, 46339934, 550050885, 382928114, 108420237, 674746580, 252223926, 123376108, 567829532, 327638670, 790945042, 308170094, 445359262, 235548571, 243118513, 148520842, 659086789, 668026880, 379705513, 932170970, 307716568, 855175467, 395296817, 639190883, 653049225, 97595854, 791793633, 544709389, 193103137, 219425975, 735281959, 243703471, 763306041, 374483666, 838369298, 992498978, 639253473, 547803011, 383639031, 245043948, 844625039, 316841306, 320509026, 754159067, 400823942, 973800626, 429805070, 122863771, 850691829, 865749942, 115080483, 275585674, 228440964, 137638545, 465947545, 975058262, 264397549, 713118066, 941935905, 7593033, 494206785, 575556865, 281494797, 992266180, 596692491, 347542292, 798232030, 305703874, 474844267, 209109326, 498423357, 330877418, 723179561, 337868996, 7452623, 831131930, 202967560, 335142427, 809752833, 859484418, 632073917, 996965058, 741388417, 652402396, 287151310, 31409926, 875119226, 9319459, 296527219, 868966899, 195642491, 689040885, 299528237, 324724001, 306848304, 139417170, 843523579, 240097071, 993376313, 456123381, 15020355, 925721671, 29088463, 64445687, 585354243, 633012089, 940581352, 511083292, 18657706, 196808956, 595429931, 883385386, 634260849, 261144832, 26356571, 336735998, 337647088, 865752521, 849825310, 382497617, 453776525, 72407340, 507099110, 446874228, 758225897, 684068506, 591438794, 249431821, 729983964, 305490198, 271178924, 245641532, 264983633, 374335978, 370677796, 670035326, 132836486, 291274670, 362778590, 62781286, 563991464, 49998203, 128594057, 414695656, 234876667, 351287459, 954446844, 635466718, 654372788, 61324826, 668988704, 378260576, 93829519, 770211287, 964598146, 977534326, 936017378, 540114112, 587751274, 486934700, 961627845, 304504072, 753996992, 112363365, 364301282, 980794915, 36930460, 636529782, 758986689, 836519912, 21742302, 117727023, 331393166, 183904635, 928243868, 401250250, 678955563, 594345092, 908009695, 261793282, 887020965, 401664969, 791403188, 83576262, 102538832, 298658588, 882017163, 609462730, 912228499, 90889578, 680638849, 705817768, 977596314, 87056142, 869370708, 435535481, 23848002, 264344942, 862681715, 212396864, 925052164, 170524036, 3645807, 189267013, 74596197, 418544773, 628845578, 877730725, 39815300, 151130790, 337863074, 916178421, 552938533, 289215807, 621689275, 775609286, 312392128, 779997964, 739778818, 756016200, 289064309, 128222212, 391722406, 498593025, 819706441, 75885901, 497954257, 777133448, 351412775, 161810140, 226766222, 41810522, 979702354, 888925399, 851147738, 503595926, 675389332, 399814273, 804326985, 266357228, 71241623, 161342573, 271683228, 623009996, 607989034, 64734153, 297862084, 515958467, 423902678, 843213037, 84695643, 48509604, 138072235, 495758895, 524797466, 567255076, 934241597, 34827542, 297850098, 73952001, 383326568, 129158754, 21640925, 144498584, 98480378, 410237571, 626839123, 117557783, 39545461, 720844289, 805063465, 270447093, 913731074, 715238001, 588822135, 201956343, 180662181, 964856668, 317033667, 768209155, 949143379, 668248565, 641033297, 356495854, 580365767, 288875043, 391789824, 258976123, 886103524, 482337620, 473086104, 816334415, 949737667, 768727236, 977207608, 189287698, 190603024, 514142475, 633973954, 977077483, 418768023, 307928665, 659870404, 212307058, 755779302, 161847536, 924725543, 813681466, 750422338, 487929323, 929630104, 483752278, 33049920, 398334893, 26510537, 765781294, 569238289, 520203927, 846247476, 334137773, 203398137, 345801643, 807522726, 766675351, 703884431, 123873030, 541713672, 634185667, 969083505, 723861133, 443875298, 576881629, 554610568, 815609257, 138261723, 923210809, 535907730, 636715143, 916857974, 315843936, 154315421, 353531911, 303980333, 165665766, 163117359, 425984064, 583264162, 462889545, 905945735, 460259903, 792109269, 246864269, 399696160, 670467552, 854048077, 794575679, 976189174, 554584260, 237391658, 435791467, 759577329, 121232721, 439697792, 654175144, 100121694, 781478076, 172713757, 913699543, 17749901, 546062547, 182479739, 917053535, 891613160, 348009709, 378407148, 948299090, 465355362, 548564148, 239068902, 213045242, 123278644, 676705310, 583021430, 445663841, 968459098, 138037680, 852333026, 569115566, 23369747, 475631191, 346387693, 92243116, 52686098, 220225424, 355338546, 538382909, 230078507, 431703849, 360649226, 877600660, 502582596, 744810400, 544680460, 222101509, 820807599, 106703200, 956122749, 153981991, 576784618, 44777979, 3288094, 575610203, 353087029, 479790647, 984123426, 345744741, 837557881, 966564975, 286608254, 970480634, 309795204, 771091986, 697487348, 749486992, 851603872, 587868672, 694634692, 189246182, 350915293, 550999163, 141184329, 517918298, 469829117, 12680272, 629720303, 199756372, 837379094, 322722637, 700555176, 943294563, 187275840, 272702244, 694606634, 229449324, 719152162, 527827402, 385830250, 81040086, 669988275, 756289420, 113468980, 29560874, 331240777, 767866754, 375661873, 346032423, 893772581, 327538816, 272730742, 180560508, 39063572, 907197783, 793169391, 653432866, 478904006, 181037367, 899760775, 801153391, 390936959, 793905204, 717898632, 855439175, 835291830, 701181615, 213083997, 762796196, 831381123, 60260588, 416062411, 977601748, 48708968, 923696777, 51008002, 869853341, 297251993, 592001279, 696404820, 748398586, 757458696, 664293888, 692711084, 594753332, 925696339, 841892500, 149667549, 375416295, 868321652, 11958256, 101836524, 107004414, 747332757, 490589501, 356604511, 230840611, 779565557, 711023894, 374292417, 6888410, 10514769, 874923659, 303479804, 583204698, 421474231, 35461899, 733696213, 514277466, 321026889, 796038404, 699710401, 662435100, 45985020, 40121939, 161982429, 183904178, 533086005, 216477093, 38423014, 615288841, 73828842, 378208598, 406069857, 64178655, 460002841, 274421965, 835814694, 296867364, 185992749, 176780637, 492536082, 585826605, 152731180, 299550027, 334869202, 172492536, 931207928, 400712754, 731716179, 84594932, 270027634, 124138919, 101399511, 278925415, 564169655, 100624546, 764055386, 775449079, 746944776, 856115239, 127656587, 550324711, 116976197, 921933056, 82058154, 374548515, 623426022, 197643794, 654948717, 177667753, 294562379, 413206787, 195312372, 17990018, 771785827, 715197471, 303110093, 390477336, 70280597, 362354153, 936883994, 88926799, 88271662, 210017593, 186273692, 473678617, 8917116, 295039044, 655329686, 943736253, 538866775, 779378472, 208022165, 46411408, 626143454, 161206589, 333948047, 610214655, 432623858, 865448034, 584783817, 735537679, 170744553, 814844570, 97099798, 109057876, 482097351, 666592015, 606430886, 451411733, 18656267, 803207798, 456575295, 155762867, 842221391, 340066485, 390859269, 877383132, 501194417, 630751942, 311578334, 549694738, 241015043, 360819906, 981099651, 122329593, 728620134, 620111007, 674338897, 584352950, 371152544, 45739191, 235973054, 163047210, 350296370, 938907915, 103558668, 281063488, 719525035, 186289364, 304671628, 77846650, 619529922, 445312994, 370513136, 627853863, 915863339, 388136827, 148178928, 118675349, 589559146, 709374322, 29046359, 207184442, 421614262, 571173393, 996999216, 201548028, 34977803, 338975242, 422018112, 923490047, 429092178, 280316830, 921449849, 329563533, 893080485, 729979187, 148010000, 28072732, 278397406, 914987775, 161635896, 592093844, 828455108, 634049660, 275960547, 604588867, 539169729, 162512590, 735439079, 767162671, 454331093, 941842608, 691250441, 874844862, 236488201, 295588767, 776202478, 147640403, 832183408, 150364629, 656498863, 786882467, 106018038, 44014229, 324107588, 711122323, 582844570, 841300476, 323180341, 46981865, 802384313, 294049674, 607464493, 82548850, 414376626, 765350423, 222150314, 770451120, 322320766, 432231114, 310449255, 908654734, 198007268, 639868488, 437560953, 731759748, 588203707, 688352256, 266739643, 414511254, 248858682, 381464397, 192418237, 269026368, 194448311, 924212743, 507413382, 422370217, 831145461, 576328181, 112747847, 7865546, 920968819, 294622308, 309057742, 540353875, 728611328, 443204132, 45848007, 38489785, 196535267, 443068511, 526990794, 663953718, 77513005, 645475018, 755048298, 675197796, 366369044, 598640143, 619043494, 488733124, 688426316, 111193688, 231425791, 183341843, 716716540, 502992386, 152795518, 781344756, 436658406, 321260580, 892357972, 714965045, 536527256, 661208371, 659720095, 591157269, 810419991, 317909271, 33531219, 759818806, 670719810, 461801784, 443719651, 823957255, 868673953, 675459829, 412548998, 339161234, 46805176, 587687150, 983512154, 840547438, 285783998, 241104924, 59686202, 546441718, 626116793, 812294585, 797389015, 917879336, 44503950, 308556441, 636731104, 220790106, 323285683, 383694865, 166324805, 690725662, 315346127, 358411002, 322549766, 880369824, 129889095, 366765895, 504147994, 606764823, 914721706, 7398589, 998846607, 612329302, 18091262, 921318624, 741972518, 502281651, 194196286, 327765225, 185800077, 237051549, 111393562, 745059228, 833130819, 211095503, 634277700, 244002354, 560696185, 848935838, 382843033, 357278003, 649331897, 219893898, 728063519, 120271831, 295472083, 25079353, 268926476, 344021173, 169678146, 975538923, 9032007, 137496496, 356045166, 544757287, 330822484, 950308613, 84953750, 703842091, 781762770, 854238852, 613311760, 322172867, 468062724, 693331404, 350646734, 803224052, 704397952, 512141909, 419016142, 38692978, 659025690, 38830520, 836158070, 995498534, 164019865, 229851653, 77333295, 482051567, 200554771, 422152368, 748694059, 868085754, 164037222, 656309841, 890660765, 260551617, 852599137, 773489216, 336262588, 292944997, 76626902, 570610493, 881226487, 417660601, 502500087, 165706491, 560328029, 26363355, 596369154, 171691966, 314673153, 897360718, 922064751, 440384156, 993345165, 421741134, 261212731, 569787882, 40518085, 345517012, 927591966, 863974782, 856100760, 324445435, 501709412, 733855591, 595165462, 851549665, 833485632, 608897633, 39334093, 641452582, 135813115, 717426384, 973481355, 696759493, 602957670, 687502545, 266714610, 573584016, 78678407, 396593827, 589368010, 326570276, 182339910, 405796502, 620392282, 906042067, 992982272, 979005061, 709193702, 281092031, 473430072, 591445429, 878619911, 666336907, 221578948, 254519201, 422051275, 466401908, 815091455, 544758592, 346978033, 310182341, 658859074, 410138301, 914606511, 527137172, 504838568, 361676942, 737666945, 158120835, 405066896, 639207709, 420334803, 476543625, 538302495, 744609572, 565845387, 868655433, 564997925, 941188460, 281360055, 417874935, 510230137, 812478435, 619936385, 208803220, 466184000, 370581880, 962929043, 10098295, 237710701, 452536679, 641503329, 363854061, 458954230, 505190210, 159453231, 341666089, 997485490, 675177824, 9654666, 762010718, 213302796, 579766030, 788740823, 295273855, 725883142, 104724655, 621797573, 330246116, 74380411, 103379362, 915454016, 137927424, 862058143, 9217396, 522555888, 798652790, 367873928, 200170735, 565650568, 865722312, 267238412, 25000728, 856364469, 813972861, 694363077, 139121707, 211579708, 601395610, 503557733, 769496101, 693179641, 48047359, 466998202, 18549990, 900944339, 87186498, 901898147, 874663700, 581726955, 57381273, 384326840, 118792183, 267422300, 737513091, 1673791, 712741603, 778866979, 830087227, 168341695, 22451972, 422464357, 816521070, 785606429, 70101470, 668499892, 286402479, 773283615, 200566839, 330032557, 252848342, 770200903, 703202841, 477598901, 876344525, 782747962, 121593342, 423075188, 174753167, 336541407, 979341468, 116192292, 51813357, 255941034, 798219333, 737548673, 674982490, 851184496, 64169224, 130821456, 995642022, 549269646, 740033922, 341608247, 125957279, 233646173, 237063735, 949551915, 433355380, 514872954, 830677573, 693679763, 700648574, 72261095, 9612242, 484790378, 70035443, 470257148, 194274107, 40611221, 778652187, 99176294, 21348349, 198913019, 876912404, 700907330, 577488375, 168046264, 639349239, 56415561, 114470778, 275415578, 162984811, 793508285, 330741348, 450025522, 193407300, 962554720, 896445440, 934075192, 351457674, 147786517, 659318098, 321504728, 770948002, 705786938, 597113890, 676562851, 820158972, 768003710, 223006262, 26267736, 331790174, 264555158, 278473456, 654645457, 321828187, 213362161, 234603615, 137339665, 748326446, 782826454, 721400140, 293563326, 227948240, 333921407, 656178134, 957736994, 965788998, 975115241, 380832798, 377829801, 8529762, 237324959, 2491038, 982305035, 26838784, 285903646, 973566180, 150875297, 136201332, 657952633, 68463910, 350537860, 247056371, 763887639, 461867105, 913483919, 691771237, 767994698, 193173470, 903317726, 729410896, 228257154, 169828878, 226391126, 320027954, 547672121, 472753065, 959231222, 310891319, 624278109, 75844588, 238287172, 583523232, 537567468, 708083578, 560331808, 685474188, 166788148, 823873335, 869147558, 952914294, 528995915, 649072740, 634851779, 980004540, 511154182, 252867703, 221314097, 347653273, 91246712, 301627535, 591521456, 577844972, 773613478, 81404825, 275344645, 246264040, 473042974, 685092659, 677062329, 969388423, 754119136, 47798720, 924245858, 447118416, 581152063, 652134340, 125386500, 988932588, 96773876, 457424102, 894543525, 381015787, 268371255, 539213654, 165739841, 107362182, 655586385, 487408855, 837636509, 93797859, 597409802, 62443767, 53854118, 889523522, 813380317, 41999690, 428404381, 78850539, 587905971, 188491176, 733212436, 420673705, 280815020, 240706289, 486139591, 679542839, 760174466, 962237249, 611893687, 889967068, 638835881, 893396210, 129740952, 75436709, 680615210, 293351780, 57444098, 304127551, 106389804, 374499615, 216348081, 690839620, 439949845, 338726038, 864638532, 320996580, 420720273, 301225863, 50924307, 918750369, 527985804, 413900299, 72980712, 250446955, 456425406, 311928624, 611264145, 64653101, 53141676, 390277773, 253867013, 843248491, 564596423, 338597031, 589929655, 730856601, 777642183, 686570097, 984187843, 559475472, 947212965, 792636361, 428604843, 562038006, 207099603, 608663954, 788440291, 203046907, 866750296, 841929807, 128465925, 706431626, 786608379, 610905143, 197775914, 264178956, 679926802, 627902295, 878031322, 975280916, 299558479, 336876619, 844495477, 691717459, 543571157, 509386487, 24217262, 627638381, 127289052, 492643143, 2141566, 734525065, 675471864, 253203213, 191583088, 248121575, 571410940, 510654243, 198911528, 520403733, 34470506, 481195397, 283978720, 304284951, 818501300, 755491402, 616167685, 960985571, 167844067, 69489618, 115517223, 318086233, 232340057, 883095378, 410209177, 404723381, 200825899, 365790913, 842173353, 168514405, 379878447, 535470158, 601436505, 782775711, 222728212, 93003591, 290680615, 577777854, 461443927, 997661957, 827059267, 222424238, 970741470, 140221610, 206884084, 510989527, 801571951, 668501487, 218104412, 523963227, 349513369, 324573817, 32499887, 610058419, 28541809, 193810162, 706393275, 447742303, 927474462, 56310162, 223217715, 605244261, 78902666, 310865992, 683257517, 340835538, 848131976, 435739421, 671438384, 372312368, 763822488, 263435126, 273420085, 674733217, 421748835, 218884179, 790339646, 896681999, 423591434, 799107370, 788912572, 50792677, 73828673, 976816517, 324312260, 28806446, 26448685, 579616971, 77979712, 206182438, 556368551, 313629938, 587892506, 637467992, 196064211, 507488517, 728672498, 571001913, 318897325, 118415189, 697824005, 142382857, 688458389, 342765785, 222936456, 823454981, 912392653, 893149161, 245221430, 791284311, 496037899, 953909771, 877770043, 772466319, 371547921, 696126197, 106317898, 457294656, 748415498, 522892518, 577174075, 200292696, 580395742, 390278813, 906411897, 711652594, 402067075, 522649966, 821757693, 907459880, 91251625, 353645650, 261555659, 402733514, 262814470, 442981268, 823736374, 39155952, 203362003, 263638177, 197787991, 625968150, 414867546, 650078641, 932761629, 541985224, 918541648, 471847793, 184809963, 308499121, 413285059, 315538622, 855225203, 523224772, 341295582, 540928023, 26158701, 779890975, 979095355, 86072097, 100447974, 650159067, 642214508, 663631945, 943157801, 972372101, 766972831, 221148846, 861250446, 477981749, 767618087, 869366637, 693511845, 278437772, 541661620, 603397742, 7558861, 717156300, 436238781, 974677566, 317794876, 708315481, 777418716, 369568081, 843678669, 229405123, 757934114, 514544346, 921500798, 989444082, 270974501, 280641071, 212377751, 845538993, 566866336, 237246672, 464611523, 899050419, 479403466, 276108263, 977284813, 752372591, 610881631, 364596077, 685228662, 594537672, 128435893, 916208917, 879577076, 56548626, 669395403, 364441374, 420287662, 181070845, 955928713, 884049410, 798174712, 687288182, 337844648, 73504197, 521419448, 358361564, 599541635, 39583603, 936489373, 873481845, 358426664, 465852698, 760393265, 997846540, 502965772, 786102692, 768481823, 159205080, 169332222, 506022761, 977619585, 384142171, 418314004, 224072450, 2583192, 235219992, 560002824, 158070061, 318113108, 876734750, 450168680, 221006594, 792333743, 58228918, 814963828, 430949668, 823264536, 417350813, 164784888, 978826994, 197683647, 892368149, 73219681, 383530616, 159618498, 45702277, 206821692, 828132622, 923966555, 951662371, 67423613, 445012954, 818326614, 22882712, 95880755, 656318470, 113358876, 568977145, 233333078, 905650167, 356876213, 265887495, 693459227, 680168100, 814683704, 722640893, 482726557, 716094685, 784348493, 271339206, 691309172, 629515513, 747445815, 243920063, 820425165, 688345894, 77627900, 276166473, 738032293, 652673130, 25794318, 525513535, 25390286, 269097131, 714086524, 967385267, 865761104, 489078914, 207020084, 964721365, 727243753, 216034184, 155539400, 436464710, 425989023, 527091048, 404385710, 912148101, 189938433, 49559422, 620363861, 888365503, 259075044, 704087273, 614542101, 812979997, 109776375, 872927405, 143212089, 52877135, 710517719, 246301141, 755827165, 712471190, 894041596, 346440258, 326283250, 937670985, 637825875, 833297189, 725755383, 463801901, 154634133, 887980225, 126896256, 8356055, 41445869, 267293347, 166897664, 803130721, 882771272, 94095371, 595498686, 145562619, 763011176, 204316838, 642964248, 43025905, 27564571, 574573954, 491014345, 457058920, 784945035, 430644207, 997628978, 372523541, 321844904, 222732328, 607432880, 350286161, 692797463, 34771348, 280468417, 318960747, 441920192, 418096875, 786033218, 352392063, 783937023, 411780277, 116546542, 152069736, 900947673, 94739282, 992348776, 482574657, 594345635, 461194232, 817007189, 217921374, 559060992, 769743281, 767399213, 145755354, 783943296, 190438278, 786401027, 580490158, 386271572, 898282104, 244357270, 374532240, 108651191, 722598934, 583485816, 484822492, 553800948, 761046908, 469661844, 513986865, 388154041, 26953634, 708047879, 911043341, 477248857, 676929285, 350360228, 1147943, 745541103, 580606833, 944461511, 762917369, 89099707, 973185815, 831965917, 147140762, 189401564, 798150129, 81603696, 953272764, 415872692, 739137665, 96766098, 896060594, 966486248, 338292840, 748366569, 348009531, 281248812, 502309536, 374539160, 784978215, 406575734, 42261256, 642341950, 447914001, 630305320, 908123821, 477758118, 144401278, 901533125, 714592090, 311043831, 728722177, 234302332, 543618579, 743683292, 115845881, 945845431, 289122549, 290364939, 742992073, 309769268, 586360882, 116875857, 966180569, 681730571, 677677541, 74517024, 334283359, 376492878, 446115460, 340797265, 185313847, 425511116, 197429403, 977089547, 867748503, 249784285, 527794307, 182212983, 840725739, 251491121, 28204417, 162373009, 814960156, 480667456, 917238619, 885365909, 601724532, 460982040, 944715107, 354012563, 562580301, 627281358, 493882922, 146205800, 720768777, 358354103, 748178905, 66766518, 958922899, 63302523, 560848975, 283844532, 413847699, 13510360, 894415164, 570375351, 270871610, 143288243, 204007157, 983739022, 118628985, 664574790, 215266720, 568380631, 750912899, 993006184, 782343079, 239644487, 513118193, 676294376, 452362659, 722992633, 273750868, 623588101, 933698416, 465311637, 265360501, 702936784, 802695075, 925424372, 947282294, 826238565, 880730363, 169933401, 742304736, 193896226, 426081214, 985316118, 648798321, 585004242, 801444525, 730422905, 94179851, 609519021, 31418846, 354185126, 559818288, 73271117, 521518879, 753830664, 560309551, 33190199, 734095831, 707736656, 912557723, 953411522, 548206249, 515539812, 520370562, 557311449, 580044600, 345485879, 263197735, 971322729, 639854263, 663425595, 871361883, 686463593, 216861866, 48908105, 454905422, 802408682, 645669233, 366221972, 858795455, 213437335, 678890900, 820038443, 89636186, 391581430, 550541485, 73531233, 242504987, 690762442, 344059698, 318627989, 542808544, 963814554, 863089201, 97571340, 889029365, 211284334, 75132742, 21223487, 411066284, 31113544, 294610365, 758808752, 891576713, 265533304, 111279579, 705482653, 621541466, 739256579, 826669809, 76743837, 149412573, 480597551, 937197024, 82103462, 647770201, 739185201, 415112520, 285530639, 926979842, 497534341, 732101922, 115633796, 364581963, 200446602, 869907871, 88205684, 730973548, 559952528, 38857217, 830644927, 236407670, 828985431, 715299764, 738421124, 872255993, 446766237, 609140255, 205963657, 197592069, 811864306, 837817332, 318767867, 134185222, 381457407, 759949340, 771500490, 202662200, 81953023, 311296320, 986118258, 656420949, 651553697, 765157923, 565976071, 522791031, 562809604, 175716133, 534128490, 932109233, 565436859, 827728835, 993564668, 429853684, 629626719, 971432997, 736379548, 319356040, 440857621, 442845761, 770307713, 79508375, 4470205, 238457189, 203265012, 910542151, 598310294, 998084415, 938403016, 975164596, 641794677, 859793144, 482520126, 946006900, 307156824, 806275165, 482814829, 704301824, 669065153, 907047496, 493010019, 451220141, 248279844, 867634218, 787144314, 641648710, 457781895, 473838354, 304109249, 667118133, 389048804, 569560448, 53724592, 829362208, 384157396, 375417869, 585567992, 541317987, 391914995, 258019496, 313252152, 610342360, 255241665, 123714709, 654291484, 698097023, 441973734, 438392624, 151859827, 952586979, 297534805, 951137250, 523155871, 105596295, 990982975, 865886278, 495736295, 532350311, 18456226, 507956234, 296092520, 454946850, 325278574, 294138234, 976912219, 558193586, 345350806, 970434581, 573842878, 139335585, 339101999, 247797979, 580693866, 581313543, 8914838, 851089948, 170649446, 485524397, 781900688, 788295104, 68253555, 362916012, 452219872, 999849035, 255227005, 800312622, 802431840, 192123196, 323933173, 865311084, 782710459, 418328642, 371149591, 197698298, 980337061, 643355867, 430405789, 677196738, 381678385, 528486387, 11314128, 505259594, 374557826, 592473736, 405761052, 504515117, 636824693, 552713104, 619092744, 322409136, 398413861, 150722187, 715616633, 179063477, 330636904, 823042256, 300113908, 105937171, 5324654, 737320329, 483098270, 223251367, 779056835, 944836892, 750395096, 568284577, 750198091, 545781894, 810798022, 846694164, 662344319, 100394131, 426382257, 86416706, 63467792, 4724602, 398277517, 273449346, 47373084, 553543298, 628228272, 187572765, 769730078, 887015843, 809852168, 508364146, 116582117, 547407150, 272718995, 217784517, 720291871, 286866203, 834600344, 104458880, 502746258, 144301389, 157636463, 895711148, 222489371, 680854485, 99080642, 243744773, 145313646, 44775274, 330645754, 929438944, 774013617, 894023302, 119673146, 279480661, 23225101, 880386161, 400561248, 236752047, 483043477, 880486499, 323744514, 353906237, 522351916, 774433100, 825669369, 260477946, 493374523, 241256788, 372972530, 95742030, 287039515, 698670810, 603502356, 657652103, 649859053, 912984071, 743827797, 702920742, 968728150, 365180886, 522163153, 490378886, 969768816, 164734787, 544598594, 187393029, 727175937, 253552409, 101872466, 123195884, 528261612, 225320260, 154211301, 922507862, 531675716, 466566939, 802863731, 800188732, 329237837, 579043098, 313098750, 837031367, 728437447, 629564699, 310210767, 452886945, 104219144, 631736786, 768162725, 777492046, 9608241, 553979147, 271027186, 960753097, 191326137, 587966273, 589795612, 332879269, 414387126, 764650545, 519607759, 119639797, 88240680, 77355526, 122760679, 458449498, 628668069, 631812541, 266075580, 264768759, 698104336, 374704106, 932613033, 310630430, 832776034, 65563254, 542081269, 719674847, 908164446, 3873669, 912157460, 21782389, 778809401, 361949088, 177125034, 952424076, 194921116, 595176932, 757449166, 809080845, 676109381, 186486107, 83435077, 476595420, 235237333, 529073335, 840152386, 61623270, 173062769, 38149479, 68230606, 847622306, 392307168, 284599849, 617625918, 400328040, 738656642, 588764161, 797630380, 410136425, 906628267, 722686186, 817735111, 436184444, 474887103, 165296275, 272142047, 790020157, 17793683, 140787485, 61150645, 126766523, 708098114, 539240980, 226050501, 864755609, 764929193, 562399660, 872294579, 79792192, 261915425, 848033336, 460171127, 495409616, 196156281, 288777934, 763731884, 257699960, 338296126, 144520210, 196347491, 988375478, 784151668, 34450913, 686494283, 60726186, 384554068, 671755671, 305590282, 939504672, 950051204, 746567810, 778037578, 449231426, 958507022, 309522501, 445864758, 569018906, 320854731, 616666768, 910041839, 328895507, 51915519, 156299669, 632807612, 888316197, 366755383, 795753061, 764561616, 239268373, 144307349, 261131472, 602820768, 285440807, 759468641, 266229776, 89054182, 465011002, 489802595, 536524130, 448460904, 497606315, 532495788, 643080597, 951267367, 924812288, 994762580, 715952455, 941561865, 680906369, 965854785, 224080307, 263527011, 827852920, 197553215, 264677755, 404578494, 209640709, 14861637, 796859581, 584106661, 349761193, 562190828, 899754425, 989142398, 733729082, 927070191, 173430587, 265302998, 489015487, 204036919, 337563357, 743817250, 880599210, 773343240, 204714488, 624179832, 535449044, 512066507, 47258276, 722506270, 196688546, 679007165, 881407266, 459841188, 20926735, 677307136, 755554977, 203306428, 939898604, 508368015, 168807091, 573349011, 295048108, 749736367, 220876916, 826805891, 132651737, 820028656, 962935577, 928761303, 493737600, 311176158, 783624020, 832078687, 547449131, 954608444, 987748971, 730310087, 127501410, 376041906, 12654847, 663363389, 549848640, 187064132, 128790419, 193670644, 526587794, 635279021, 772273428, 439059629, 668522382, 857321532, 331953752, 659332694, 126380697, 357917227, 609614343, 79063964, 650912720, 311332959, 358396615, 303027597, 615122419, 727980017, 497133939, 443811340, 988181783, 611850025, 298340495, 21120222, 971965787, 569816863, 129503834, 635049509, 483389763, 204583678, 671260458, 522716347, 630761221, 363944909, 534550195, 18567462, 632077363, 264851141, 813391116, 988135772, 522582766, 339064638, 27316734, 210090067, 551833945, 267719775, 568446732, 644044664, 749156338, 366845484, 393062727, 647728174, 700172306, 258621578, 880523333, 802104638, 345221126, 484992340, 987171469, 246752683, 545790285, 67091513, 50673214, 565705219, 125065995, 906656760, 310188114, 170582570, 568314068, 351725581, 244019138, 565503636, 106963670, 127984744, 578787652, 575685464, 765110670, 931124855, 992377631, 75539581, 92874379, 24215012, 137876791, 42052658, 692471577, 690905019, 90978287, 406738704, 570825033, 90172233, 72746215, 563099042, 654305196, 605133470, 585128547, 348748595, 901604971, 144737305, 117823255, 978783048, 310505589, 228804406, 297178064, 974900529, 748541366, 540653153, 685748783, 484957694, 968875043, 980616849, 354673352, 408223642, 145919730, 912726603, 230678678, 855387434, 900669461, 935358630, 139230379, 206823635, 487981741, 181008120, 106532957, 614282824, 757785606, 980847116, 394401705, 335868236, 924070556, 540580120, 342050451, 634536569, 460705597, 34081551, 300825458, 695027998, 11314587, 138236557, 794641000, 520080071, 741088935, 241281604, 548126171, 188092905, 508984427, 18132874, 138907285, 259820075, 592629183, 865851088, 461193341, 240952179, 296874376, 160596216, 194827639, 926760476, 176267791, 451060867, 383127452, 709634343, 312340026, 164131335, 902499075, 857015850, 421553833, 927531520, 763161785, 325100699, 975820691, 476570355, 566332124, 952051079, 26539165, 576335309, 487703144, 47288769, 681729610, 509561599, 206027596, 579696436, 866907860, 174781714, 713321003, 293270690, 936487312, 656762376, 888988459, 41925133, 404352595, 584845545, 112225746, 899424034, 187356581, 584074328, 244005259, 815095548, 158872322, 492536236, 358608008, 14710447, 285346726, 622504824, 223361831, 157500976, 291153974, 427466235, 422451645, 916873363, 684920272, 19751975, 690452734, 321844035, 728403332, 207990035, 116238562, 955725757, 628292393, 983454292, 200589999, 365712301, 319699308, 722923098, 559513296, 457235542, 161114850, 549153314, 390519393, 78604226, 487693296, 602911244, 993626858, 807459933, 636765173, 103129286, 381666842, 619036744, 868391306, 127688466, 688161222, 97893105, 112584430, 607979283, 34549114, 859666652, 536524708, 482909910, 953551361, 973560825, 597302570, 554737604, 411427400, 921192819, 506451512, 733441022, 71085910, 277881573, 738521574, 842300194, 767618698, 192407979, 628827892, 145745607, 157238231, 696650942, 69809672, 97519029, 219035922, 975890162, 349715732, 976463521, 390243942, 481647877, 259600062, 441921512, 238947130, 354277475, 904294732, 83274657, 668531261, 725830362, 643435797, 149756796, 235441103, 457753451, 827722995, 350457048, 994405427, 393298660, 637530463, 992893684, 346928471, 101519573, 73285314, 740341377, 651237669, 184373821, 783384103, 547243893, 153328407, 22609554, 570461263, 359800600, 719239782, 971124337, 800057362, 299380175, 474678593, 357445895, 555082836, 373011509, 561868118, 519230795, 239028462, 202091383, 932884975, 224025863, 953772041, 363476907, 225659652, 999486858, 229995555, 198061702, 91650129, 707719157, 163132156, 766203165, 507609103, 304633283, 666363032, 325965478, 693281038, 572746562, 278389415, 156156763, 44557302, 71445366, 834041017, 266459271, 544795332, 562395637, 922820704, 494339832, 148014461, 731733123, 257906147, 821309928, 866718860, 952669950, 213975390, 977572434, 40403999, 111604379, 272893517, 176259950, 984793395, 928283675, 123507413, 415653739, 234903675, 41778588, 100419384, 165950749, 697574664, 622976287, 148203639, 907752714, 700856552, 741802741, 761484176, 934068556, 399236902, 505579215, 901921484, 213611441, 82261048, 785702093, 467476707, 427929464, 140973057, 832665284, 2366916, 509321049, 271554775, 194834535, 853972138, 986363264, 362570607, 938170947, 653629774, 519061135, 954786603, 894743456, 810380469, 76563650, 381240983, 90476865, 797757105, 568506537, 792447623, 808173311, 870019719, 581058644, 51651027, 10712147, 604680179, 324882177, 730125509, 553361623, 454164915, 656503426, 570505534, 761265282, 238232361, 166462767, 504330852, 74237884, 701458160, 377482893, 135790798, 538441180, 46600668, 655151919, 360698986, 300288975, 807890728, 342833901, 280323106, 829784272, 18879719, 993251176, 260185156, 749103637, 555193741, 182537742, 370535900, 853167077, 881334835, 354015336, 193486549, 107474492, 627261649, 93363505, 200283757, 932813448, 514283671, 732116546, 69754994, 203791371, 6736095, 818891609, 753753157, 933731757, 221609545, 448590221, 717159602, 56277206, 942572136, 404909920, 742469080, 309409984, 68213805, 976198431, 415136053, 69461574, 741954874, 584448704, 752632325, 557718186, 957073503, 920625415, 756041586, 943692675, 50453952, 333816201, 791984168, 638764263, 639137988, 393224740, 124268680, 861503048, 328746373, 860580954, 825918742, 632835667, 759895911, 736706085, 76732489, 183867523, 471553570, 479372425, 894857238, 619090547, 608827866, 504562269, 750112892, 483162967, 524755869, 889170524, 959733221, 1305610, 393138125, 498067281, 140284643, 264031610, 378886432, 139726753, 836378106, 103014658, 523049398, 230949958, 101325638, 629103755, 327585920, 829022994, 832996975, 281046633, 542181370, 890616809, 8066514, 989247851, 305353791, 506105968, 728216203, 578083538, 173232183, 475777282, 580504100, 992032903, 418837253, 614143766, 498945968, 455348525, 790929671, 948530126, 574743267, 51794624, 560347785, 944348091, 518077400, 431578654, 551957818, 421959462, 534052272, 231684498, 205969493, 586299416, 877388765, 978930344, 32374062, 806925909, 400304464, 118606830, 669942829, 190123796, 649980739, 374440510, 264493269, 623068644, 857123944, 501639148, 138648533, 589184265, 700221406, 579901665, 680540363, 400196345, 972213646, 628671825, 154673716, 91917455, 255840552, 983765110, 314252176, 691591290, 355550045, 611383258, 356672793, 100459445, 485347651, 837651386, 985195305, 652181785, 44456769, 702817904, 592969118, 743058772, 84607726, 614531568, 227435602, 905748821, 988396164, 825722365, 202494537, 988873499, 641999066, 260163073, 784337193, 850763625, 770390685, 407281685, 390673261, 228515432, 481104248, 840137246, 18061815, 422044279, 245150661, 432154035, 218780795, 746265680, 665823434, 496880541, 57820039, 243737401, 124735897, 246376449, 809643976, 764355122, 484208912, 584892380, 531349221, 445108906, 110604337, 829529337, 256576653, 413057015, 825711736, 74363058, 99192814, 158977575, 36470963, 368641892, 359097779, 256013876, 621485504, 779466231, 28589126, 152603147, 791240144, 451349873, 470503020, 792906797, 532839653, 494658522, 282402971, 716382806, 80553065, 905021953, 132088116, 9209409, 70047955, 128281608, 352393908, 737563898, 145263867, 762643030, 289231650, 954648871, 888366559, 813175924, 92060628, 790480593, 439464868, 541888867, 443305113, 521880856, 600860662, 916027555, 629670053, 224711855, 877854586, 78709954, 340673649, 1405525, 986188671, 178169065, 548411633, 811380430, 54342286, 151822299, 200821575, 458720628, 86034773, 221166951, 912796568, 249534530, 207748931, 58777094, 385642814, 657386417, 348929041, 704216210, 793299311, 866283492, 223087146, 101723232, 610439741, 956984109, 235867732, 991423229, 424495952, 381352101, 161230539, 481422195, 650495857, 143705145, 681770397, 928987968, 936711082, 973291065, 37230060, 944824467, 401994731, 895886165, 697268116, 991481364, 313873237, 337889980, 357002828, 384171837, 861939455, 82621595, 516763579, 153453914, 688772181, 595053473, 532489153, 977074636, 804072482, 220054150, 903855227, 879893590, 261800906, 213969431, 553293367, 168317081, 702530706, 983329619, 477457294, 1754767, 166479690, 667384605, 936909877, 104306727, 445744239, 451507264, 517660616, 230169834, 703398962, 930830949, 89349991, 73245564, 117853156, 10836443, 842309398, 581781568, 771652922, 261569962, 125779591, 543351246, 994562433, 463878752, 479764742, 181523752, 933427601, 436343804, 325944806, 835948704, 330734210, 261263278, 155686133, 108552719, 398644945, 683447201, 762347760, 890770125, 2543570, 822248764, 681803183, 99572627, 39358405, 741905043, 885093805, 26179277, 832781630, 783161033, 605507652, 745788955, 727857475, 397510222, 367860562, 799917998, 757621927, 674918615, 399990754, 902661792, 745644621, 274957336, 732788189, 655507371, 170084296, 473936667, 652060907, 30100180, 647228331, 912931306, 110898876, 32904974, 263329744, 295428969, 955196031, 235663084, 867563600, 160801103, 781801691, 147128877, 949007028, 154582256, 28829082, 190729756, 584037585, 220395121, 28373797, 612989846, 367657805, 671599743, 770536264, 652629998, 322458056, 553916948, 602717700, 327774228, 807026705, 907412648, 341893022, 760724440, 436557497, 350301637, 468835378, 326318388, 812231542, 686026357, 618572303, 863248578, 561890861, 331334429, 593838580, 381506608, 379047607, 28043423, 341267375, 563371843, 662101273, 180421536, 780622656, 391845386, 370694974, 854956739, 897347397, 79661773, 575545232, 834490734, 328018116, 419702480, 315310910, 907942379, 13619022, 502756790, 752608247, 241646720, 881841366, 652960863, 970657804, 67567859, 940143265, 515961903, 308268846, 356031566, 384668244, 616153365, 475908529, 939524671, 507843365, 779487085, 588270173, 390926006, 853109561, 177659608, 93488429, 277261799, 571753786, 999183197, 6719325, 834315694, 299775482, 930491826, 696995669, 350619788, 981413341, 865530263, 494070121, 77118824, 586798734, 840473812, 145961642, 300413643, 975049151, 432212248, 87851635, 617875381, 781029541, 255818186, 802305857, 552168799, 387266455, 942790871, 213394771, 368986175, 801276651, 283354151, 199634821, 260313502, 44990612, 999502978, 437761265, 698873925, 184457511, 454775288, 547089273, 340990362, 13489745, 634211620, 849231367, 5159699, 404062697, 69533213, 97681198, 638148037, 268068711, 632896647, 272313363, 940284948, 960597152, 652355929, 545292276, 326112022, 344772759, 105348267, 911745684, 601609571, 750325621, 111592251, 886275505, 39422328, 17871803, 839435705, 980790154, 811567034, 312785561, 992747864, 817460044, 815261033, 248114432, 276355004, 922883230, 683790275, 785832651, 838648328, 345328733, 691612115, 352074686, 294043517, 805181623, 669951421, 959843154, 568238196, 633174204, 144477427, 503252189, 393388927, 74215147, 36066650, 544781886, 293230732, 519391142, 83144638, 640099821, 228816297, 350857066, 631901410, 717104485, 944555745, 923879235, 98568061, 967533616, 437528785, 902770138, 164342655, 977645533, 430929579, 121678247, 222431533, 396075493, 579271798, 432873038, 800504364, 36809919, 56549150, 729019838, 387971506, 854351588, 625925253, 621804230, 90860798, 754034555, 851235574, 779425975, 737898861, 91477703, 56984502, 871250757, 1264913, 21042737, 788463746, 364002391, 309377787, 292855513, 925450187, 668368479, 267561747, 281139456, 595593391, 298067117, 508721287, 317289536, 148587493, 613126556, 229981093, 279090281, 296954172, 900662825, 121231665, 920892563, 652178542, 805980775, 46107186, 544375905, 40926503, 254553977, 823403767, 619844316, 240997198, 491833370, 547172735, 631547740, 12089767, 994888060, 851456370, 575218530, 509307581, 517475075, 104082106, 297117476, 457512495, 174224765, 192604679, 102865821, 794743399, 942942276, 887904178, 739406563, 672463527, 235603789, 710299870, 846176603, 25873690, 387521477, 880336594, 234774068, 583613345, 764763701, 347507613, 949289568, 684167590, 116179716, 207503073, 466958582, 378805696, 998933869, 537642009, 966438421, 852063011, 910567393, 213815448, 43432548, 433761335, 62800761, 625826805, 383811653, 249409547, 744218045, 573369390, 928687180, 712126217, 45671983, 809305399, 821587488, 959113382, 20912077, 300615908, 633626105, 479311606, 339250551, 624762238, 342855740, 383342410, 684111888, 259446107, 544321873, 901001729, 554685553, 496103191, 758489987, 14493469, 399314907, 151235287, 601826193, 327374626, 340732622, 688307249, 157341463, 936684380, 118784566, 855040211, 718283724, 667701294, 657903532, 531069263, 170619616, 70126781, 290290256, 68225028, 517947972, 105273219, 608654902, 265888009, 672121216, 612496891, 486815888, 763947168, 387002479, 217365683, 772418588, 202042619, 142175617, 443132385, 593016966, 26104785, 699718187, 152789668, 525962092, 833826591, 810720744, 416000497, 244112640, 301459909, 702876510, 444069977, 191690407, 215469938, 781463248, 882359462, 391866182, 535569895, 656560465, 431554761, 935439157, 273407382, 640201257, 201111601, 660383161, 760623988, 337490329, 195168259, 671887240, 441017535, 453517851, 713177431, 75130069, 388906883, 912814870, 753963014, 517790986, 941251464, 463785050, 444859019, 46931780, 847344290, 298291242, 857394604, 792953550, 607783335, 568373546, 965799189, 144881457, 546833135, 679068829, 738209844, 52910751, 925700434, 640399418, 286349524, 681517498, 85062648, 24313210, 726357741, 177933693, 250225993, 298779403, 809752408, 721124259, 529872344, 883106502, 856300278, 293155925, 322670254, 451149465, 588604671, 643372363, 700346119, 932890587, 138759934, 478621058, 745858545, 39463858, 850305651, 401108826, 469756922, 863350851, 703876012, 327633902, 10748953, 245206620, 974431488, 530842641, 541899532, 922477404, 88118400, 49453427, 571591814, 787201417, 4183623, 95562823, 757804434, 377455279, 254333216, 281324559, 575021458, 478779005, 919549683, 704026558, 945141831, 873694462, 798896121, 181927353, 958420301, 754727116, 655732669, 886509913, 553976795, 336030183, 300250596, 141823374, 274300379, 912997458, 115565868, 425475712, 963139266, 540609149, 355875381, 171060967, 653767215, 18434848, 927569889, 160037223, 721746673, 283923693, 575477761, 740528915, 567689627, 143377634, 798089665, 117950977, 62637039, 785279860, 127312632, 58871129, 802825913, 468175560, 979635290, 706235134, 883431604, 762915034, 955272419, 26193161, 995668997, 30692548, 247700284, 222933650, 104296648, 125924088, 963402285, 972509480, 603687058, 517255290, 167688770, 532040958, 293242517, 893427750, 781376835, 219697185, 527666858, 450472782, 872866013, 47190211, 254649036, 531166278, 349684561, 814076815, 454132899, 411555878, 297734845, 212206882, 914792389, 554338412, 890272839, 902634921, 464891875, 823393444, 783255204, 363527720, 998099339, 754839267, 780616460, 336610554, 917784974, 555348486, 412697210, 347569528, 554741901, 479018550, 342897458, 511929128, 303107749, 348355202, 848528395, 434516779, 844688798, 51469151, 92523538, 388366597, 332362368, 791354096, 733326031, 960266412, 600914479, 157886252, 872568652, 484675382, 108250234, 118050132, 941774991, 468770043, 535377580, 766235130, 459083184, 708458698, 741249300, 683518839, 197353681, 147355252, 393546464, 943427692, 13910928, 123647216, 478427589, 641344853, 936002084, 389431232, 899265780, 459788443, 401939225, 395317586, 367112682, 828856370, 366217056, 127884066, 381562183, 70247739, 582226048, 531306214, 832350578, 329702556, 351212747, 99960942, 61194076, 441656964, 829187296, 831797521, 338975397, 17875220, 795805506, 905315098, 598625003, 467520268, 595600848, 321639444, 956300866, 270585629, 687129522, 23262768, 178471648, 822662776, 78248397, 330592244, 530942707, 252531105, 544745905, 669889680, 437996822, 212645271, 604693689, 979101412, 891503346, 299918440, 618362965, 93164921, 37755039, 42507951, 316087737, 914804443, 618536901, 531139169, 15617722, 767040594, 303792626, 804245343, 988247458, 468550089, 719876710, 551187336, 656269843, 876800805, 326570912, 906220176, 749055775, 629415291, 156109368, 940170968, 504753554, 695714047, 252524220, 508744939, 488598037, 642065334, 124526234, 750619279, 20258865, 977387767, 494116741, 81176431, 576610832, 951086458, 74408987, 661744404, 428467765, 972770802, 576128588, 262649465, 784479091, 893979777, 90170002, 508670125, 279726646, 287079062, 831522181, 617175992, 634793445, 743457752, 493679913, 520776664, 885109896, 825956967, 434193499, 81360461, 69437537, 973974344, 448969705, 378462879, 998415997, 731693211, 184206072, 804749779, 276933757, 410569920, 776475599, 291374510, 754199066, 781579726, 238604672, 169767314, 733090112, 786270043, 119203816, 651389543, 146292235, 80835708, 724568534, 521332755, 498375991, 147722278, 142893352, 46464361, 319170580, 174281632, 287996835, 445271151, 281933364, 73498069, 318379380, 33840919, 73839195, 223244948, 495208269, 75794125, 611267756, 800377808, 494083297, 807528630, 368206199, 850468275, 886983662, 570385161, 261210902, 930228543, 584663972, 533636472, 965855613, 294159653, 641599519, 520490296, 328031480, 509906425, 653199067, 716935320, 126263131, 473452177, 469644893, 552266774, 588326919, 71919202, 546704399, 654631863, 607332860, 562321967, 724198122, 619513233, 898422420, 600119169, 244983280, 107578419, 455621537, 462602223, 779674098, 367972828, 358246431, 628466683, 292863158, 263408368, 844281735, 276658450, 481681416, 812588633, 592627588, 690730189, 631345766, 361082383, 234618527, 705729493, 934124290, 299308355, 387966286, 980268675, 632672933, 600770423, 45527305, 424369074, 820645439, 834932032, 818171929, 598487194, 509866714, 905006565, 909143369, 745918804, 963414626, 652155603, 607155386, 180435916, 234623590, 797486826, 421870654, 590357215, 687447759, 780465885, 401824112, 262706384, 211374739, 274660524, 175893836, 240898236, 741197693, 859757372, 72627208, 439831437, 947812150, 783191999, 507155059, 399958818, 574129575, 12070646, 611753879, 97432940, 486990699, 358805393, 812553130, 761768871, 35217120, 236510950, 5096621, 647600410, 638382901, 875267723, 64201396, 99681284, 695774846, 960604115, 636596478, 228069042, 872562997, 678247635, 342919725, 462955955, 258066224, 906448638, 932790563, 653304294, 8683187, 203257886, 601346021, 481445162, 936920612, 61180124, 836952749, 145076771, 407344476, 437590953, 993839252, 495234460, 490261088, 659287647, 626130734, 225834055, 393812989, 33389480, 760410263, 117761702, 759081457, 757198096, 90954553, 634425661, 593119417, 825846405, 865826803, 907395740, 966453984, 672239502, 937129774, 493120405, 22751965, 510019605, 222583035, 568265510, 424018942, 507653341, 330010377, 901825427, 588127426, 984288036, 359152505, 257544735, 588708428, 329843979, 59052836, 151438456, 653619177, 562213922, 816733043, 206369274, 479461755, 613548104, 689636649, 842283740, 730572195, 721441336, 829180661, 868449540, 84624980, 648215073, 879331396, 295312176, 586662101, 762397018, 485941429, 721746889, 862843781, 466863118, 214053806, 155112641, 350337381, 45635958, 396485181, 963542364, 865760578, 293471205, 162335995, 699569777, 385246753, 941855633, 26261696, 818758453, 197788068, 453636284, 144533009, 7293949, 455556245, 837059955, 351579340, 849331356, 265866969, 933983573, 871066503, 420884889, 626179411, 345904714, 717243648, 459062641, 395843590, 53091942, 709135395, 199697497, 262668269, 527431071, 768884774, 773694035, 436046314, 687796445, 325405151, 695265345, 596731315, 980732690, 220885874, 477115348, 502402924, 255155849, 204075831, 169975378, 865373599, 758268773, 658378473, 910799821, 46875477, 412333403, 487004293, 501599028, 419875528, 609798552, 582539048, 942577179, 200381814, 303887505, 305490891, 779057204, 628807761, 102518957, 828222068, 472803029, 669163638, 848266303, 812640491, 152941519, 536751813, 58257948, 580399909, 127615702, 950565365, 996973225, 952933891, 469823054, 300964120, 76309789, 655088877, 61308738, 406688870, 683463391, 817495898, 390734084, 911089002, 744333132, 563271954, 996553951, 425907162, 257555292, 631884237, 204829449, 651371932, 858424481, 432840522, 810560309, 856082923, 780664495, 242402829, 907374821, 562163515, 835013696, 16934307, 845272154, 785509001, 369017104, 768176779, 840120032, 67454982, 163656735, 973466698, 466677143, 907378130, 821874419, 992187122, 133891672, 939565772, 418891727, 202947470, 927513849, 790272520, 213720966, 196770108, 454886675, 779774138, 187281409, 941090949, 688411563, 777409161, 873231173, 648990261, 594212862, 725995494, 826710113, 371656210, 345919351, 422954686, 451638911, 399309252, 644097984, 403261547, 30750100, 907379546, 72239815, 939500797, 909797662, 664817248, 504537149, 604021070, 259420260, 611302283, 452188710, 166762112, 129379316, 696366065, 517035120, 748294504, 929395739, 141295528, 336508626, 639341992, 471908220, 496783788, 5929256, 109090575, 978885824, 393979169, 729860242, 882345675, 350084184, 507692198, 819832473, 495969380, 324558594, 916980203, 710083210, 375891733, 669684555, 780223651, 80607029, 359887434, 905018575, 175994506, 957914682, 916412298, 288737675, 43406432, 162774071, 134519692, 595721610, 3662024, 852886233, 862263605, 869738544, 781951935, 280260186, 868917066, 667199533, 819946646, 478158874, 118174745, 382873610, 860727781, 547653217, 822418292, 25379677, 922599815, 650627162, 665732, 321113672, 348401438, 630402462, 327587761, 227583538, 898030789, 169914437, 223333171, 531579499, 945756743, 255668785, 819301179, 672272705, 980511066, 687238025, 301600639, 986296355, 679327444, 362870071, 612252004, 937469853, 684540915, 7137163, 553421033, 424350669, 237640672, 30455664, 566573672, 461941414, 823590928, 908183417, 31923929, 957726824, 600320913, 788625413, 177315749, 284836116, 600925089, 798298905, 65677576, 143390720, 755607688, 555043304, 468583492, 458387922, 801269520, 311063992, 78001167, 205520141, 143528215, 323634035, 460975518, 835976261, 653211129, 831183478, 32580705, 370649843, 369852723, 482842410, 329134901, 303182512, 628586012, 523445002, 119054118, 643769620, 824321664, 476276000, 82908491, 98070938, 266912415, 195461769, 225810469, 941834950, 919016274, 527472991, 808315256, 889642329, 709529616, 686721196, 150976778, 195924769, 818207977, 678319295, 883799876, 830531152, 759436371, 753236704, 950776945, 534627417, 910686395, 368223451, 652003946, 752378035, 873658559, 771418398, 223925762, 838300765, 70550569, 405005978, 449312605, 289170851, 571606280, 878727493, 758446367, 625039650, 933476236, 185641281, 265338051, 23263761, 977460277, 131853501, 177239684, 249260940, 929255633, 660309409, 703950399, 28287170, 675503915, 16060922, 677957255, 839796259, 920491985, 216686814, 999240701, 234107109, 370552584, 332441659, 887450552, 380407691, 815865797, 507878696, 789783112, 186105252, 828109836, 97446341, 880967583, 62905455, 798346658, 374337244, 452208758, 495386413, 256600543, 488645050, 664958798, 32056452, 295763797, 485262441, 657506774, 859451763, 684498252, 119355183, 856914225, 352118990, 386805816, 267296130, 202063633, 998647475, 98021615, 141475641, 486823634, 7867973, 919128790, 612176836, 934752899, 664271502, 780217163, 900594232, 725243872, 805204536, 726647896, 402276851, 73675026, 580767992, 50802461, 101961959, 410840953, 963200102, 210698348, 638349889, 781197177, 137475940, 583453298, 553686021, 386735522, 631165445, 622148070, 226268677, 50283240, 44369289, 640678861, 419889931, 659020449, 203612462, 775485421, 148903667, 273365418, 171906512, 181978428, 170180152, 657680639, 302545716, 426721938, 453411994, 548472050, 285722925, 800814555, 523004676, 520963984, 788659952, 456076941, 768426744, 44234183, 546770815, 230967288, 99346665, 720654662, 230845990, 629130005, 611483877, 791415614, 927677072, 352045213, 772457850, 90719648, 834087630, 846151172, 699238888, 864597813, 282414648, 677143957, 518941098, 648550903, 564482130, 56485107, 928126641, 140913948, 466308790, 243877803, 313535875, 687290822, 920334063, 338696836, 783728056, 833527243, 943359844, 674795522, 327125209, 851317050, 790898193, 427910505, 130929872, 117534392, 214669821, 251254858, 910214407, 46786992, 242945720, 205538039, 39922242, 768482410, 37935149, 957830011, 860083320, 633209344, 314966427, 160080554, 5068132, 510751574, 71674938, 787661232, 996269166, 113305800, 196139482, 87840208, 861208159, 61478813, 198261304, 649220263, 897274337, 161655706, 852566275, 852708857, 879335054, 621685380, 263087812, 863408478, 923549847, 940370373, 118301612, 324690441, 139928075, 512661402, 137145026, 257566368, 254467241, 281240552, 546044592, 532496807, 5360490, 695331635, 533302414, 412967114, 356290083, 734556371, 61537262, 209458763, 231105814, 62952415, 272358328, 772525527, 170678460, 735801812, 784013968, 915247034, 346442198, 231904726, 668629021, 397695460, 839789134, 173308527, 364506076, 34222942, 244025768, 787154637, 61116923, 874002237, 157983012, 536959498, 177945470, 823278467, 6099843, 115374268, 679940436, 817985012, 275448981, 129981417, 301871400, 665961924, 805521040, 119565591, 924477998, 527157905, 296177816, 877516455, 588542959, 200788276, 256929291, 366665471, 759998572, 412739730, 6071302, 408169794, 521075639, 889700099, 759069348, 653283728, 617426966, 979408602, 238379066, 802959942, 576739654, 140211485, 30250077, 113556455, 9139694, 607541889, 350918866, 643362412, 870003543, 822004748, 827366690, 569070596, 721830530, 618987133, 145036996, 158410266, 201135777, 17659305, 42611987, 657877751, 878530529, 501273811, 755648132, 46875143, 468158706, 833781088, 939207982, 262973558, 180197267, 963411252, 468914979, 240481784, 270441009, 545856676, 455633438, 635429835, 443735293, 787894210, 674192408, 870385513, 647909747, 611122456, 615578829, 402826308, 956051225, 943629033, 549302422, 152191712, 125586750, 472904342, 598131985, 831507292, 198162107, 111679497, 134711267, 897338516, 393017618, 979516601, 874959375, 870110898, 102352012, 614857708, 217226102, 566027801, 14150152, 251508685, 45902598, 175005429, 985862281, 374699638, 541042551, 654906054, 559355773, 110974445, 968331493, 359051760, 630522955, 304730401, 874651776, 284625312, 195088667, 388467853, 867136693, 987254115, 774244778, 47921142, 413465930, 600834718, 50645133, 712051601, 918650227, 251231138, 385204136, 613602087, 538419805, 947735845, 441169950, 364079544, 801332261, 333155666, 964516084, 200690166, 397639294, 790282267, 356166417, 96931493, 572574261, 205620006, 228155186, 219084443, 37556513, 669956660, 266320746, 204702708, 279035551, 537557000, 372593913, 907360408, 296992626, 184774453, 988754429, 646341796, 272449974, 431852017, 765547114, 455653173, 445326037, 461045180, 105963459, 553390742, 912389525, 879219684, 14153611, 21457101, 866835861, 932209863, 66026085, 421808333, 872196606, 953944985, 392105806, 211201548, 533481920, 817421245, 105023958, 903632181, 41632558, 305389569, 890837959, 331603700, 168791944, 349100887, 100286509, 342913393, 802160403, 881876610, 836236443, 254879116, 660802927, 680842704, 377312105, 738176597, 964673635, 29882095, 168655971, 661398051, 432774238, 582131731, 635534895, 542861035, 91319100, 322031513, 745410799, 523050174, 217818130, 271964484, 175464637, 708758035, 549249832, 951908089, 651860364, 884686263, 1134896, 228036796, 38327130, 822274549, 282916945, 339049838, 491060826, 529843200, 881753600, 223025791, 322458407, 261382033, 912302527, 24785097, 432267393, 850406857, 675698488, 988515613, 456235477, 59051024, 650229008, 177839846, 257799726, 712136175, 217117556, 897006590, 166579771, 737327678, 65775487, 81551797, 893302591, 117309513, 831538348, 460806833, 491624105, 212282019, 416088911, 94693522, 766466013, 684547322, 744511399, 72013297, 633707703, 292196425, 391029783, 320947184, 784907024, 389504851, 857832983, 478303596, 634929764, 10195287, 741385909, 131609584, 240527798, 904691944, 462309024, 120865579, 756193563, 13767180, 195379307, 655349585, 839893172, 298234900, 855849308, 555959406, 308619413, 856866643, 473210522, 666818969, 341381285, 107633383, 739841331, 386594279, 534084774, 952500532, 756102475, 689417195, 604701541, 618434285, 355737406, 454617527, 418903054, 876746330, 627722994, 883899977, 401469087, 602080319, 898148909, 827679206, 249020102, 285895522, 848048108, 867367220, 261149548, 45747959, 65181111, 107961285, 123866544, 475649887, 951002988, 146905291, 467694764, 973728531, 730563197, 428314983, 761587336, 551118690, 593049534, 780904160, 12827720, 252950439, 429637180, 697531085, 283991269, 624914945, 256692015, 185388069, 611094331, 231251697, 716908007, 137730151, 245046585, 105849779, 955659016, 480838292, 269764251, 488610961, 309832682, 319013678, 562143702, 301432804, 209120435, 281282735, 874295065, 811940535, 606769098, 57142154, 616128371, 849020857, 745764175, 798697551, 869903294, 140345894, 900486291, 477928786, 987263771, 11375420, 619964357, 961191189, 803628475, 172040302, 317574757, 925427473, 622684805, 778165717, 362319266, 684103149, 157758824, 450539585, 378142643, 69866750, 689298790, 221991267, 864662329, 496879102, 323957402, 14088386, 708403352, 751322066, 479537062, 571019743, 377700987, 221488149, 319679932, 90437572, 979502799, 573233981, 870608772, 803144176, 627611622, 764253377, 672085772, 212646210, 283895536, 823885630, 111037932, 644465283, 879932904, 172092056, 588209182, 766965245, 224777000, 544087478, 589186070, 925350937, 623094895, 770240938, 567622166, 173522847, 420031253, 744152268, 170840006, 375767907, 22516478, 697926128, 699916101, 325697006, 608049927, 627891875, 245872960, 289694776, 937768219, 462319548, 216608416, 467878185, 700699069, 194656072, 586515013, 874806524, 551185547, 808291563, 177617797, 553094583, 115513759, 179191062, 164866712, 679343996, 308112205, 174720774, 589592038, 293547279, 311396294, 733346983, 13593045, 731898664, 602657183, 105204137, 533806595, 884465697, 485674901, 224868878, 78116516, 998308725, 582068219, 315046893, 620783824, 912591868, 219529933, 544987400, 126518852, 861333840, 120047791, 967987412, 666614096, 963889943, 375155270, 893623847, 322789951, 196703420, 839334288, 710135879, 905186098, 493036672, 898432495, 119858870, 799574080, 379792238, 885975853, 400409283, 688689376, 683444878, 690161195, 80234343, 982812904, 255107232, 887122588, 518283071, 473081079, 635912076, 623122894, 851859557, 506596631, 271174566, 252700020, 779182435, 973607466, 105122196, 89801492, 192768051, 152374809, 669903149, 367275421, 619276038, 25322307, 833941329, 820624764, 311749271, 566357205, 948207336, 194472722, 265516015, 521227518, 314506095, 488319010, 538217763, 468986007, 220450701, 160614915, 526544326, 784359843, 655983066, 28351039, 42985772, 18129666, 941856149, 910334509, 698127148, 204317083, 970094576, 61678399, 620240859, 592973363, 655680651, 724528618, 249403415, 66177577, 296937365, 790509693, 344076948, 380845307, 694230913, 932821451, 257367692, 873890073, 451669430, 932716951, 610483693, 80665493, 941894616, 836884482, 732636174, 361307846, 531352328, 691365811, 21523313, 333818794, 258305839, 708401740, 385145697, 334557828, 748208857, 876599090, 966602362, 328716365, 718908562, 773056303, 683849416, 961003614, 49585164, 759138096, 612066044, 876669842, 80601278, 266528601, 167275562, 141707585, 732033420, 920082623, 67167621, 107751958, 907199053, 219195152, 75766421, 289400094, 880319028, 135761394, 456571825, 154553171, 673846720, 340959714, 70262880, 322531028, 834150118, 997897466, 146880515, 900889629, 90630481, 778952407, 584795812, 821195559, 195486474, 570064361, 26978173, 846587676, 398899331, 568613813, 764870261, 254906737, 32642525, 388050003, 333513800, 975479324, 218510483, 768443550, 488671908, 626553749, 117020755, 34779238, 493839034, 182208594, 972969763, 34616493, 380223045, 538960519, 503371837, 691210367, 171023399, 422079712, 286814220, 424487195, 922122158, 738924737, 868229932, 510757485, 202161093, 375783253, 271610870, 670283891, 844577774, 799627859, 125334950, 339914146, 68815094, 829025627, 200778482, 852480068, 979720045, 973509420, 824518378, 666821550, 604277451, 667733781, 800329655, 327443814, 347706800, 687780742, 408637444, 767500535, 395009134, 8824902, 940007289, 685310882, 721154429, 502225272, 921208612, 530228208, 590300458, 430264586, 204250103, 986629833, 808420919, 504805097, 757500657, 801821831, 28220971, 66164332, 346993060, 72304628, 344728971, 36857048, 3175924, 472394935, 92169265, 769653287, 65965678, 314897175, 288463883, 601181932, 570239707, 496875518, 497831374, 408715748, 201658487, 769752678, 346226040, 447508812, 64314175, 316063907, 800663852, 372934160, 317185926, 111486382, 950063543, 183197921, 181156529, 148220101, 513416377, 75613712, 989948469, 809381119, 603597759, 997975504, 470697762, 473365265, 397691882, 99862880, 314722661, 446818965, 800395473, 334723047, 154152191, 755253092, 430471315, 673943459, 555796641, 867602444, 289846013, 100243609, 628070766, 422634268, 220652514, 324836578, 266692207, 102407758, 461897659, 120219001, 622269125, 78749453, 308277874, 932107074, 614337716, 570141034, 605311136, 442736566, 357711393, 427003389, 351007818, 415227317, 713929764, 989310721, 336062896, 746828909, 267765425, 854607652, 302453454, 950364490, 133952754, 326631245, 128421400, 258228003, 484675305, 176376103, 876288008, 151898213, 247938896, 829351610, 756448724, 179917040, 890785035, 425595032, 36318999, 980939718, 487272466, 552506531, 3058245, 964435746, 484615841, 420469931, 577074108, 922427017, 820354264, 64594533, 599502482, 726126443, 516302836, 25224341, 776854079, 189916267, 882074377, 264303184, 485069185, 155056620, 810301641, 467965264, 124310969, 308596684, 450291148, 796594486, 725375723, 494793934, 723724295, 982703271, 95903539, 189720051, 216674255, 954965437, 307318733, 762732073, 536137384, 670427182, 209863533, 427554460, 115355595, 887506503, 291227187, 765939889, 429813212, 711478948, 502020696, 692273415, 131711583, 718748512, 769363628, 928989254, 497675878, 491928053, 113670898, 612697949, 658613792, 726956420, 604485631, 925780283, 265402980, 303438168, 825047463, 626704009, 752203180, 244854201, 511939692, 448221046, 693980440, 846772101, 245540804, 494181830, 821529149, 367503263, 305124963, 446082456, 132713709, 266404348, 37174059, 390309740, 783842144, 647872816, 975428728, 915066198, 240763349, 928943215, 745255960, 745994031, 265915903, 366361042, 333254321, 594127680, 675902845, 819272927, 36475816, 534952569, 51874255, 179169208, 366445028, 767963146, 57670216, 656525280, 630451601, 501305178, 805016351, 34426867, 663496822, 961930989, 338052002, 373382376, 588916255, 568380267, 323933730, 420752166, 138443603, 360453961, 914691863, 129475189, 443732190, 122070758, 420508009, 676007351, 574075962, 433588527, 704804429, 597656138, 667775167, 711480868, 431110530, 596543867, 737577520, 407748451, 564704069, 476511114, 494202646, 934293822, 249088176, 863858010, 173943943, 806646130, 245903820, 731686497, 888310090, 60153136, 407891529, 249421455, 992226626, 478585977, 354849088, 979070170, 436045412, 619649327, 699830308, 263922803, 758710116, 553630215, 728182959, 834801410, 355362230, 358500102, 673777190, 185006843, 356645991, 220354792, 74320232, 727920357, 624698317, 718061189, 372344714, 230053191, 758632923, 265653725, 781382385, 18815310, 76191897, 61241013, 860063344, 971153859, 333947781, 258880559, 414550228, 293347822, 601729421, 851278713, 638608624, 643347398, 453626671, 853137707, 295734741, 795988573, 241367817, 986906792, 392294713, 323988429, 742003273, 796055262, 88528144, 310092912, 213211622, 925842225, 376279601, 692158144, 727251591, 520657412, 151933265, 579281464, 287826946, 217076577, 865204716, 114207293, 456027966, 676984068, 744568237, 758623630, 876817368, 16596897, 641468719, 173026368, 977738789, 58101825, 229453612, 497930335, 155608146, 560036838, 777151770, 266699600, 697399132, 470031817, 848256930, 135971092, 604120287, 487415289, 299105304, 956965477, 934872782, 816245098, 134642098, 67576862, 521148489, 951898128, 531710900, 973571147, 166135469, 145914124, 994009347, 115554051, 981380591, 542854298, 546010093, 194800541, 609049202, 697398439, 157159314, 844164236, 640741566, 933470549, 586221052, 246100695, 423506346, 209681550, 255970112, 846261931, 231945881, 145931689, 73402566, 469793077, 958286891, 707105894, 69330479, 273135265, 895108389, 924907288, 153991670, 270843564, 868750071, 889867049, 26797919, 521792235, 823686813, 787238941, 138816617, 17483670, 118506143, 343395846, 609123310, 463032443, 179655945, 58931218, 12107735, 446553379, 941797092, 550341910, 30796484, 144983746, 866458050, 967978298, 121751131, 306763009, 177230881, 308961773, 118060619, 216064686, 534725961, 737392274, 430418760, 594228686, 219566756, 982416931, 842310249, 945285664, 658193690, 364957206, 623905965, 973537944, 535452536, 550487850, 702462448, 70563259, 598750618, 985480827, 292545921, 615242422, 471804827, 883786558, 61363155, 609305680, 735532102, 189862924, 479212373, 485140732, 433663019, 277821755, 298465935, 440118930, 100734788, 518316660, 4895681, 306177065, 761467333, 808796007, 471906729, 981472621, 98297081, 891004063, 605721453, 418526290, 516911690, 781488275, 997020069, 555640464, 586822188, 154247027, 38484461, 404401001, 777335953, 54829763, 397925511, 391187113, 289763170, 491105850, 969788201, 412587517, 519263767, 428355896, 161551391, 41620798, 781679865, 126259869, 366198821, 690230939, 827933158, 385576589, 231608703, 242887563, 987499762, 950691328, 74043965, 328971985, 920988563, 427817779, 733989025, 805388847, 406639061, 394265637, 977339288, 341029237, 98527599, 276279270, 356076811, 392301297, 842294982, 167835792, 686585025, 118914670, 136850681, 618306421, 980793372, 521029011, 336976146, 834938942, 847365637, 929151126, 874834874, 427118199, 704542249, 552424108, 434783460, 905529502, 726852478, 2742244, 961098133, 389017169, 997957022, 704940740, 137796580, 740671384, 313578321, 260271860, 286811921, 639440814, 985952440, 117113721, 626548526, 699078424, 432526166, 94277281, 352096930, 762853759, 77006242, 45592259, 22062007, 858315706, 456585263, 653723087, 492058875, 887309463, 106197182, 364028827, 655944326, 906284184, 518083769, 797612162, 129144587, 732329862, 877051946, 559803013, 757711997, 262311210, 514167648, 651838173, 826097042, 94735162, 830332325, 677372501, 202333862, 55298115, 333657570, 503567405, 180086814, 385608457, 702014411, 40968963, 602118070, 960765600, 711283617, 436684519, 30919197, 336228650, 166463267, 620008191, 207317032, 228284747, 783199976, 788043489, 165646081, 18194087, 647254026, 1823099, 588459917, 738241589, 892156714, 116034248, 89167915, 887510844, 759119709, 787968104, 984506189, 337478663, 462266627, 111811898, 691045312, 227324864, 7347663, 722515809, 834434580, 757367515, 254612781, 835021991, 691243860, 8279800, 645583386, 790911504, 800329957, 675218730, 469080868, 896629341, 220370114, 50790954, 384698417, 302688956, 966543523, 267489759, 796805677, 640428627, 837673151, 696092032, 253613989, 306557951, 854574708, 857566419, 726486707, 768006861, 766618301, 995179295, 205525275, 238947881, 323572960, 956725034, 869692799, 614174485, 69713676, 363888036, 911653395, 488977250, 258593424, 795581292, 223767118, 926609254, 349471337, 704759548, 409500674, 879439407, 564349087, 139244156, 207120996, 411896070, 453998111, 132984112, 225657553, 833582714, 384966538, 232516823, 534057372, 305956363, 274835151, 799572109, 504973442, 993818135, 747723586, 103065976, 726445754, 98392231, 32237871, 131173106, 627433912, 297616363, 793197584, 643071336, 602943845, 64313501, 464557016, 976450405, 321706306, 702891295, 953155982, 93700079, 385067591, 585890062, 696941175, 772032689, 100307061, 381992000, 885845945, 752820440, 285228433, 533689908, 954209323, 583016594, 129369053, 449814115, 426872220, 765527641, 322401117, 874002637, 77773302, 853185070, 517167846, 265116473, 622822627, 532729226, 433975690, 328383236, 425921253, 782738023, 939632197, 425242621, 870398735, 231052844, 513198904, 231808501, 556495662, 887074364, 528990818, 904935131, 168906933, 755181646, 338458455, 877016386, 715182664, 641133844, 340470042, 846481483, 381800844, 462420544, 749820876, 939827908, 567056822, 838492264, 330250344, 264348480, 228002208, 76095284, 28530699, 47257901, 887503995, 787407829, 15983818, 888405627, 740850289, 133502987, 462913493, 364170704, 383340425, 935000501, 604092918, 488611454, 330169664, 572318145, 718619303, 959357051, 690642536, 873020987, 466936785, 472282687, 539875542, 542866127, 703472855, 292223971, 262314351, 923292239, 2608769, 918560146, 930468721, 541216832, 733219610, 389042305, 448229245, 885798768, 834669473, 123565446, 248112067, 596745013, 800068310, 146118865, 772162807, 620953539, 455950702, 927694028, 783166843, 257519589, 251318171, 115685423, 463969143, 447164810, 891868078, 539194444, 178654407, 44936566, 579775108, 526057627, 933515873, 363648942, 558653501, 731823898, 222758673, 380089997, 752533103, 188100605, 920822291, 656810967, 716399397, 963702468, 651444529, 70028402, 796444429, 218435145, 665762901, 658239423, 879994500, 85935264, 95836082, 623279667, 316523435, 983137175, 506815629, 218247181, 833609939, 500685610, 173739749, 14591764, 547824806, 287118380, 477601753, 523737105, 806969289, 219584492, 610342035, 326168981, 11159360, 828597597, 832514244, 899245870, 645793531, 599222382, 165816450, 747898454, 174393002, 687277376, 722654033, 530113946, 90801132, 191748222, 671163011, 380567230, 904457224, 823476948, 857836637, 890625689, 204367449, 961707799, 301227773, 261028571, 899479705, 734232576, 638494682, 311095824, 565470054, 670092101, 512873223, 510102461, 941594173, 652930704, 513540451, 932892386, 653037147, 326062674, 322383902, 404173842, 840677566, 192454688, 153264054, 965613228, 568085467, 325246899, 253752817, 609631536, 869225059, 162178052, 254554840, 693680098, 659152680, 788239015, 546858231, 614754985, 873616706, 286921505, 970696047, 650747935, 375575264, 57553585, 126309070, 931262836, 261153019, 794375252, 63713418, 911076743, 404182185, 316172916, 491957325, 17370979, 757095598, 141156322, 311226020, 283113778, 700199609, 375121801, 408176820, 774458930, 181302606, 217805162, 201055723, 328451893, 591373725, 7127093, 129041963, 634375453, 873441499, 403473741, 21316931, 361194382, 626334121, 293965290, 200953792, 191589027, 519816374, 14409316, 195077225, 434177354, 123927718, 25479523, 528042380, 534458077, 709332739, 17083251, 566724576, 922556599, 467543962, 664494457, 224512911, 193588339, 862743355, 509252835, 757284486, 614715254, 762242728, 798887523, 212068363, 592047105, 105429681, 470234896, 729511132, 389940435, 968130120, 41745200, 563614542, 879980076, 882784328, 740348697, 59863785, 106920246, 577894037, 710898819, 810444706, 974618264, 879450069, 130892177, 687273038, 709679692, 660944408, 44212594, 435615182, 775495933, 966624627, 624082300, 811819362, 627726253, 429746873, 864451226, 634390303, 499078261, 616173946, 317117873, 302026673, 489799326, 97486109, 41749155, 466727621, 739763990, 825014142, 247920673, 349357924, 390855892, 712376595, 796384612, 948457471, 892966168, 91611643, 183427654, 992399948, 475838680, 796718928, 203254070, 138285398, 712964673, 710900438, 683245971, 217544523, 494204029, 523491646, 365936435, 390678729, 175659471, 598028999, 946804520, 167407918, 828212457, 889379779, 763684710, 44853734, 209917686, 773541949, 983267772, 205394091, 151754236, 421011463, 48050534, 392679555, 402448240, 542527478, 557490328, 440992980, 519248858, 554591511, 490277180, 321447571, 753975946, 940098233, 702304214, 469224538, 571584890, 830001345, 340597497, 833660983, 145944146, 98649480, 581693045, 489117661, 78261234, 88303801, 88076833, 658227111, 243810461, 589368679, 422463915, 407048880, 990078158, 1646385, 253273316, 80974863, 514338923, 70643149, 643013849, 198891153, 126421904, 267759077, 429547306, 126751279, 700146498, 595945573, 79173284, 969485957, 702008961, 512279452, 139737947, 995651721, 788582655, 350590670, 188647053, 295101987, 659640538, 97207258, 724453757, 688599603, 778370217, 67675145, 707993786, 894194755, 35279586, 580741419, 122275162, 495543500, 117789606, 496522580, 676243912, 988881512, 478328282, 196868932, 572749147, 458238947, 443168126, 519002909, 466675952, 998341141, 27807170, 702468369, 360746645, 568104502, 760960293, 893708519, 644392678, 926039664, 817828210, 433483952, 659211466, 165815258, 451241196, 551671955, 663583853, 775688888, 306124507, 91477673, 932069128, 92557221, 844425285, 542397909, 476321511, 793066397, 974558804, 833754985, 316402601, 356056253, 889383946, 864279698, 874457965, 85741837, 442977616, 22126986, 610723398, 798958191, 212712326, 554951671, 257351201, 529289970, 629422022, 459108872, 95780072, 986045896, 335558232, 389606020, 266574428, 983302608, 417804034, 492659581, 399077530, 314147085, 438022693, 477378573, 162579894, 326893321, 763922397, 67822164, 885168603, 566293141, 961841049, 970225136, 372621033, 781904016, 677600894, 590906467, 909602624, 227026146, 163129135, 548368385, 839867899, 959878516, 56812694, 138753574, 734134752, 37323853, 501757647, 842737560, 748492885, 389505751, 354847280, 849755280, 19451867, 123916754, 525166027, 654188105, 978183096, 351093150, 972970582, 621338780, 798794178, 572905848, 803209951, 845301812, 766737732, 389226624, 846689398, 413625069, 490586639, 631586826, 378589688, 836557811, 298154316, 31550638, 575857436, 884666977, 338329041, 666289992, 845821941, 672345682, 498434266, 485997262, 316901288, 362517089, 858639832, 568635741, 9090826, 828720586, 464542139, 819450928, 845756338, 139284947, 822868503, 927587461, 768173705, 686644380, 553145604, 987085641, 712869100, 437206790, 554208782, 216837812, 550494128, 218573020, 994172585, 197382209, 846614905, 844381101, 495973807, 923473273, 770064470, 474553276, 582607329, 928170141, 198273723, 267529348, 162448742, 602663051, 887820245, 894542273, 143165078, 222754070, 270134085, 369397216, 383752744, 923638922, 833746924, 464643367, 939053018, 625039551, 138250407, 684754564, 653888083, 77584811, 153381605, 267764306, 55548030, 670665762, 713113377, 250746560, 796781822, 574872096, 137396558, 97992218, 643567908, 769303843, 238318228, 885306077, 344078609, 455908651, 481375148, 390467196, 756403596, 250543363, 254106239, 305312370, 697823345, 185632939, 303466665, 520706244, 305341095, 724350281, 330350566, 694065866, 566795840, 348183995, 973341959, 16460408, 946195946, 726690204, 233492455, 624485263, 190103870, 898798914, 198358000, 115599517, 397641714, 828132695, 411507287, 63544983, 742148282, 30747595, 416763103, 17061113, 257557708, 186461406, 4381305, 644934287, 510791642, 797186850, 812005925, 696888993, 414092524, 180144570, 775829679, 472129826, 164432295, 124786350, 821282266, 136591359, 759397016, 797603163, 538060212, 152939272, 798360892, 457545364, 371090318, 877856063, 650137909, 267614336, 910958341, 137198102, 127223669, 865663889, 463612153, 722878747, 416860024, 740218237, 328572624, 471695065, 809298608, 234445342, 494969084, 937480286, 109402336, 508398900, 550558476, 514396704, 63571165, 310028486, 608824330, 101996740, 239543383, 561300118, 760193553, 952610873, 769173707, 921348646, 685616635, 559924838, 367054628, 213039820, 239553880, 155826009, 405177463, 892816871, 165333212, 861353313, 193064920, 513180677, 856568067, 745043189, 258049110, 381746855, 511605606, 900978508, 834569510, 421154462, 161473798, 929148617, 90201051, 551338129, 27633110, 732930346, 567842006, 298074047, 1061767, 630751244, 202262528, 694784735, 337164707, 886779822, 102165902, 247984353, 683751371, 17868734, 66707208, 911196892, 974790711, 467095017, 463151314, 735745658, 123272806, 66558913, 954851456, 350711835, 689025441, 728753691, 917114605, 907930175, 794367978, 696555265, 653040327, 906160420, 671969, 360875573, 920652157, 211872763, 567621380, 103294387, 295031015, 674135555, 853107515, 791207260, 841335217, 433337896, 493999494, 917674277, 102757610, 984274533, 285666066, 730585897, 868368289, 743806716, 412141593, 80202822, 2894317, 212704744, 649931404, 255365633, 313685806, 57933498, 751608290, 478281542, 654923284, 950451286, 692620740, 596616388, 160419153, 46210776, 188926596, 964312106, 143496799, 220148206, 620414542, 636565605, 198643734, 241261660, 21423809, 955518731, 982878300, 256641267, 277847645, 781043200, 188913749, 963564460, 72169654, 288319234, 453077058, 294041022, 486306069, 862077662, 582894124, 469603475, 372667901, 795305584, 883613340, 888285083, 744274749, 230977391, 394997360, 584484381, 111381748, 326008895, 934960997, 410164758, 387971230, 379021857, 89999435, 932886172, 850820290, 98082169, 482434330, 731406663, 80051257, 235153814, 551501099, 332408719, 460504015, 757752949, 315714874, 514811747, 770188234, 337533536, 918171607, 849308811, 962738467, 79384221, 525260160, 152481736, 449726429, 197314406, 729327155, 912930763, 964585211, 959032990, 388299826, 837934198, 73094022, 86580961, 712637327, 337805083, 74470135, 282166411, 500303093, 202276840, 422866592, 462574912, 895787247, 172947364, 266965779, 133405502, 452639847, 530245110, 495993423, 711736866, 430833794, 344794436, 778557454, 236165920, 296516385, 928083184, 721813371, 626895607, 334164694, 757739740, 76926176, 991331464, 450533354, 601875907, 587611810, 578297095, 282886288, 992919626, 17055335, 435660600, 841076708, 900875499, 615910406, 905587496, 20607533, 744540748, 396195846, 198834249, 339249619, 924658827, 397500918, 972423757, 703444685, 382701100, 859700130, 487786229, 872686668, 416271639, 151574597, 717666364, 607258443, 192804477, 111339181, 709842838, 59855303, 119634771, 221165364, 741157331, 553124437, 769473048, 36283976, 754532711, 316554063, 612759022, 364676254, 952562009, 659775602, 594203749, 216948367, 895494634, 49958794, 880355483, 655447460, 33189964, 531341583, 47018871, 808704953, 332814977, 64930670, 268305305, 104414182, 394472951, 369342489, 508366358, 91994217, 736286325, 413432634, 56421862, 924155515, 871671908, 610408886, 809497240, 151925139, 156884821, 69211297, 717002155, 264498705, 811653080, 295444967, 872828141, 772742151, 2910625, 888805674, 940999907, 139491555, 805927478, 919907330, 574867984, 723666476, 259617368, 211003894, 814240874, 390931485, 225288853, 382652870, 902921942, 180436558, 775491531, 836499188, 794889727, 148307509, 743133254, 943530540, 673922848, 296438452, 921465662, 690898376, 941480058, 178485806, 24988052, 41105869, 566754804, 263921946, 117178904, 268360622, 998806275, 56929072, 17814973, 800348333, 390747312, 158210081, 169622296, 839333568, 391427233, 568298410, 512771163, 6333082, 662796781, 688238601, 152014612, 577838084, 32606580, 65628863, 594178982, 489494432, 777780790, 794114241, 637476519, 463183641, 980617724, 590345065, 96063030, 972079773, 299720498, 5947571, 882637955, 480118213, 454519875, 781375564, 450705388, 394333747, 914562362, 158195536, 53375101, 154000616, 705878779, 961408382, 15632383, 886323930, 102313130, 460533131, 84552090, 727327845, 296900214, 547541480, 441032744, 668576080, 182563663, 885540950, 813397672, 706980309, 932364125, 481102131, 805772216, 785175579, 233764608, 83790441, 741292334, 135692340, 463074050, 444629406, 418755944, 974950203, 482567032, 280357469, 343538375, 761359174, 226518203, 231881262, 499679633, 108103116, 468336777, 486045075, 397679194, 269300791, 817146553, 720667336, 673511261, 583468462, 371033467, 896974405, 445142947, 665599231, 547893885, 379383735, 50065911, 736135676, 955318528, 445399543, 96709177, 315582246, 707721876, 413582734, 276204150, 168041196, 317484854, 688147993, 426522346, 685888134, 326492050, 355362028, 140993932, 229407599, 828694266, 815370575, 198776499, 33615986, 443816851, 390899006, 341787982, 8619930, 188170422, 788267709, 771804672, 994544201, 128082287, 286070813, 34746808, 997596079, 910233063, 338130218, 54153119, 484192666, 531752610, 529787106, 281815334, 19622006, 983208319, 390728415, 949600968, 565254116, 947056289, 192627962, 679798517, 892485443, 359712490, 973679665, 85091031, 856757172, 961031659, 546766553, 686316518, 439984944, 218706028, 911397368, 260540520, 330397271, 890384500, 66171949, 558784781, 956412660, 674835188, 319607901, 965521925, 998987708, 586013621, 883377831, 286909577, 213260217, 486323908, 188960244, 63815362, 542384865, 474142085, 856411791, 397136228, 24630246, 66583431, 321205559, 276337667, 926031342, 67256766, 162607461, 975309678, 337990656, 971663879, 963880255, 527931718, 107448285, 862164120, 485420821, 498184932, 329430212, 506005578, 226605309, 990684303, 197156963, 600110734, 139011527, 882391905, 932559910, 681284484, 964627503, 786920815, 332881913, 653270238, 760650532, 451306042, 272187923, 21941107, 631982892, 648867886, 812644549, 441579689, 547202413, 801881283, 910528597, 489667908, 271762765, 150412289, 352857974, 69728686, 754271998, 33012629, 638060805, 881490999, 564982984, 784912553, 467860359, 851650436, 756894983, 145355806, 445821172, 559871909, 207055706, 909071422, 483304288, 712896515, 737886345, 310878070, 519491242, 622683601, 36072199, 966379128, 909956258, 193312624, 947985441, 598636237, 378499003, 612612633, 364262151, 568070387, 348109005, 763433617, 617876187, 804931332, 93795279, 422138047, 864439232, 617060142, 168934003, 839528052, 689295804, 619629266, 71533724, 221128224, 55517596, 152521769, 651069803, 72130098, 484446624, 523105504, 922383299, 784839316, 616070091, 188683647, 508264634, 553522608, 331571129, 428219380, 517121904, 450123087, 778073195, 978229342, 60746178, 847353292, 335736934, 858032328, 490854259, 823395619, 39470445, 237959695, 911597306, 343791770, 624599490, 304869348, 886099067, 989967748, 907556134, 243094930, 396906672, 93376627, 987734109, 651490166, 662316069, 914084805, 562757970, 942284017, 950512074, 888011331, 470368951, 150312256, 232758642, 254627966, 967857221, 706896740, 459409863, 332347746, 512287938, 760035301, 364776562, 694333266, 507137931, 742656128, 612430431, 352795536, 622907655, 695419941, 565110511, 663636147, 723143820, 717213617, 218478822, 720022337, 937529862, 780770012, 473435823, 154749909, 431310644, 501085449, 203969105, 427353285, 844437744, 743299363, 201509207, 322504359, 813086507, 222867930, 930882769, 70735391, 533865755, 668408365, 361384871, 828176481, 8591962, 206749836, 555037000, 680646693, 721042082, 443522281, 216478942, 242086189, 160837557, 14178399, 803102443, 730102881, 445089362]))
+
+
+-- 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]
+
+-- Running the tests
+main :: IO Counts
+main = runTestTT tests